THE UN IVER SITY OF MICHIGAN COLLEGE OF ENGINEERING Department of Chemical Engineering Technical Report TIE MEASUREMENT AND PREDICTION OF THERMAL PROPERTIES OF SELECTED MIXTURES OF METHANE, ETHANE AND PROPANE Andre W. Furtado Project 345330 supported by: NATURAL GAS PROCESSORS ASSOCIATION TULSA, OKLAHOMA administered through: DIVISION OF RESEARCH DEVELOPMENT AND ADMINISTRATION ANN ARBOR January 1974

Um)f 11o\tt r Andre Wilkinson Furtado All Rights Reserved ii

(I baQ^shr > -Ad J-^ - Vlm4 t^ {^uL ^^^^>t -^S^ L ^^^cT~y^^re XCs C, -"Zi ^o-^^ ^xL Ce 4e 4~c4 -Ce e) Pater, dimitte illis; non enim sciunt quid faciunt. St. Luke iii

To Two Important Women in My Life Annette, my mother Carol, my wife. iv

PREFACE It is admittedly a difficult task to coax anyone to even approach a dissertation of this size and weight without some trepidation and it is, therefore, hoped that the following commentary will induce potential readers to seek out areas of specific interest with greater facility. Chapter I summarizes the important thermodynamic relations relevant to the calculation of enthalpies from various types of measurements, with particular emphasis on flow calorimetry. Chapter II essentially involves a review of the existing thermodynamic data on the systems investigated in this work. Chapter III and IV are concerned with methods for correlating and predicting thermodynamic properties. Many theoretical and empirical techniques are examined in an effort to impart a more eclectic flavor to the review, and to broaden the author's perspective of this very fascinating field. But, the reader is warned that the sections devoted to theoretical methods are perhaps more imbued with a neophyte's fervor than with the wisdom that comes with enlightenment. One asks the reader's indulgence if these sections seem, at first, unintelligible. If it is any consolation at all, the literature on the subject is, in thisaauthois experience, considerably more formidable. The material is best digested if the references alluded to in these sections are examined along with the review. Chapter IV highlights some interesting theoretical developments with respect to the Van der Waal mixing rules. Chapter V concentrates on the development of a new approach for representing mixture enthalpies as a function of composition in a corresponding states framework. Much attention has been paid to ancillary work on the development of reduced correlations for the second virial coefficient, a quantity whose accurate estimation is of pivotal importance to the success of the proposed enthalpy prediction technique. Chapters VI and VII describe the equipment, the experimental procedure, and data reduction techniques in considerable depth in order that Chapter VIII may be concisely devoted to the presentation of smoothed experimental calorimetric data. Although perhaps the most "unfun" part of this work, it is a matter of paramount interest to the sponsors of the Enthalpy Project and also to salivating enthalpy v

correlators all over the country. Comparisons with compilations and other data in the literature are also included. Chapter IX focuses on the evaluation of various mixing rules for the pseudo-critical parameters (previously discussed in Chapters IV and V) for their ability to represent the enthalpy data for the various mixtures of this work in the Powers Generalized Correlation. This chapter should perhaps be read more slowly than others as the author admits to an inexplicable lapse of communicability. Chapter X contains suggestions for further research and offers valuable hindsight into how this research should have been really conducted for maximum effectiveness. In a departure from normal practice, aspects of this research that were either unsuccessful, or which were reluctantly, and abruptly terminated (sometimes tantalizingly near fruition) because of the pressing weight of the experimental commitment, are included in the thesis in the hope firstly, that past sins may not be repeated, and secondly, that promising areas will be eagerly attacked by other investigators, particularly should this author's association with the field end. In the interests of economy, the computer programs used in this work will be placed on file at the Thermal Properties of Fluids Laboratory at the University of Michigan. Acknowledgements are in order: To Professor John E. Powers, Chairman of the Doctoral Committee for permitting the author the luxury of an occasional disagreement, and also for having provided an unforgettable and devastating introduction to manual labor. To Professor Gene E. Smith, Donald L. Katz, James 0. Wilkes and James H. Hand for consenting to serve on the Doctoral Committee. To Joseph C. Golba Sr., and to Victor Yesavage for administering the Initiation Rites to the Enthalpy Project which would be the envy of any and all fraternal organizations. To Joseph Boisseneault for valuable assistance in the capacity of laboratory technician during the early stages of this work. To John Dziuba and Vijay Khanna for assistance in operating the calorimetric facility in times of crucial need, and to Takaya Miyazaki and Kwan Kim for stimulating discussions related to this research. vi

To Lillian Toney, for offering very accomodating service with regard to the reproduction of the material in this work. To Harry Willsher and his convivial crew: The Sallys, Marty and Curry and Eugene "Pink Floyd" Leppanen, fot their help with what seemed like an interminable number of illustrations, and for their good fellowship. To Edward Rupke and Herbert "Hot Hands" Senecal for their assistance in fashioning various pieces of equipment. The fabrication of the modified heater capsule to the isobaric calorimeter was, in particular, excellent enough to make fabrication of the data unnecessary. To Judy Arms for doing an outstanding job in preparing many computer programs relating to the Powers Generalized Correlation. To Kathleen Speer, a veritable angel of deliverance, who cheerfully plunged into the awesome task of typing the manuscript, braving the formidable equations with remarkable equanimity. To the entire chemical engineering department, and particularly the faculty, for having improved immensely my perception of human nature, during my thirteen year stay. To all previous graduate students at the Enthalpy Project, whose relentless toil at the "pit" has not been in vain. To the Natural Gas Processors' Associations who supported this research and provided fellowship money for a period of three years, and who, perhaps, have since then justifiably wondered where their money went. It is hoped that they may someday feel that their patience has not gone unrewarded. To the American Petroleum Institute for secondary financial support. To the Southern California Gas Company for the supply of methane used in this work. To the National Bureau of Standards for the calibration of thermocouples, a standard cell, and a platinum resistance thermometer. On a more personal level the author is indebted to: one-time fellow student, Vasant Bhirud for his sustained empathy with my many frusi trations. To my close friend Arun Vasudev Hejmadi for cheerfully lending a vii

very patient and discriminating ear to a constant barrage of sundry ideas involving this research. To my many friends so very anxious to see the end of the studentexistentialist phase of my life, for their concern. To my in-laws, 1lr. and Mrs. Howard M. Kieft, for providing, on many a weekend, a haven "far from the madding crowds' ignoble strife." To my wife Carol for her infinite patience. To my true friend, the late Professor Lars Thomassen, a man of tremendous warmth, whose keen interest in my academic progress, and whose constant encouragement, particularly in the darkest hours during the early stages of this work, will always be gratefully remembered. To my Maker, for the prospect of an imminent rebirth that awaits only an impending primal scream. "The time has come, the walrus said, To think of other things Of ships and sails and sealing wax Of cabbages and kings." - A famous mathematician more renowned for his fantasy trips - viii

TABLE OF CONTENTS Page DEDICATION iv PREFACE v LIST OF TABLES xv LIST OF FIGURES xxiv LIST OF APPENDICES xxxi NOMENCLATURE xxxiii ABSTRACT xli INTRODUCTION 1 I. PRELIMINARY CONSIDERATIONS 5 Thermal Properties from Volumetric and Phase Equilibria 5 Data. Inadequacies of Volumetric Data and Equations of State 8 in Calculating Thermodynamic Properties. Thermal Properties from Direct Calorimetric Measurements. 11 Thermodynamics of a Shielded Flow Calorimeter. 13 Determination of Enthalpy Derivatives by Flow Calorimetry. 15 II. LITERATURE REVIEW OF EXPERIMENTAL AND CORRELATED DATA 18 a) General Reviews 18 b) Methane 18 c) Ethane 19 i) Compilation of Thermodyanmic Properties 19 ii) Direct Thermal Property Measurements 20 iii) Additional Measurements 22 iv) Conclusions 22 d) Propane 22 e) Methane-Ethane 23 i) Bibliographies and Experimental Data 23 ii) Compilation of Thermodynamic Properties 24 iii) Conclusion 24 f) Ethane-Propane 24 g) Methane-Propane 25 h) Methane-Ethane-Propane 26 i) Recent Calorimetric Measurements on Other Systems 27 of Interest III. SELECTION OF A METHOD FOR REPRESENTING AND PREDICTING 29 PURE COMPONENT ENTHALPIES A) Equations of State - Theoretical. 29 i) The Gas Phase 29 isx

ii) Determination of the Pair Potential Function 31 iii) Dense Fluid Theories 34 iv) Determination of the Radial Distribution Function 35 1) Computer Techniques 36 2) Experimental Measurements 36 3) Approximation Techniques 37 v) Perturbation Models 38 Calculation of Thermodynamic Properties from 40 Perturbation Models B) Equations of State - Empirical 41 C)'The Principle of Corresponding States 43 i) Theoretical Basis for the Two Parameter Case 43 ii) Extended Corresponding States Theory 44 iii) Empirical Extensions of The Corresponding 48 States Principle 1) The Pitzer/Riedel Three Parameter 48 Principle 2) The Shape Factor Approach of Leland 50 3) The Powers Generalized Correlation 51 4) The Representation of the Reference 53 Function in Corresponding States Correlations 5) The Reduced Virial Equation of State 54 D) Comparison Studies of Enthalpy Prediction Methods 56 for Pure Non-Polar Fluids. E) Conclusion 57 IV. SELECTION OF A METHOD FOR REPRESENTING AND PREDICTING 58 MIXTURE ENTHALPIES The Application of the Virial Equation of State to 59 Mixtures in the Gas Phase. Dense Fluid Theoretical Results. 60 Perturbation Techniques. 61 Conformal Solutions. 63 Approximate Technique for Estimating Unlike Pair 65 Interaction Parameters for Conformal Substances. Corresponding States Formulations for Mixtures. 67 a) The One Fluid Model 68 The One Fluid Model - Generalized Van der Waal 70 Mixing Rules b) The Two Fluid Model 74 1) Semi-Random Mixing Rules 74 2) Van der Waal Mixing Rules 75 c) The Three Fluid Model 76 Comparison Between Corresponding States Models For 77 Mixtures a) Functional Differences 77 b) Prediction of Excess Properties of Real Systems 78 c) Prediction of Phase Equilibria for Real Conformal 84 Mixtures d) Problems in Verifying The Corresponding States 86 Principle Using Real Data x

e) Performance of Corresponding States Models for 87 Soft Sphere Mixtures f) Performance of Corresponding States Models 89 for Mixtures of Lennard-Jones Molecules g) Inadequacies of Comparison Studies Based 89 Strictly on the Coefficient of the Second Order Size Term h) The Role of the Distribution Function in 92 Evaluating Corresponding States for Mixtures i) Conclusion 97 The Macroscopic One Fluid Three Parameter Correspon- 97 ding States Principle for Mixtures a) The Pseudo-critical Method 97 b) Empirical Justification for Hydrocarbon Mixtures 99 c) Mixing Rules for Calculating the Pseudo- 100 parameters for a Given Mixture The Use of Equations of State in the Calculation of 103 the Thermodynamic Properties of Mixtures. Comparative Studies of Enthalpy Prediction 105 Techniques for Non-Polar Mixtures. Conclusion 106 V. THE DEVELOPMENT OF ADDITIONAL MIXING RULES FOR THE 107 PSEUDO-CRITICAL METHOD The Fundamental Principle in the Calculation of 108 Pseudo-critical Parameters for Mixtures. The Basic Assumptions. 108 Rigorous Procedure for Evaluating Unlike Pair 110 Interaction Parameters. Difficulties in Implementing the Rigorous Procedure. 111 The Calculation of Mixture Pseudo-parameters from 112 the Van der Waal Equation of State a) The Modified Van der Waal Mixing Rules 113 b) The Practical Utilization of Mixing Rules of 115 the Van der Waal Type Difficulties Involved in Using Second Virial 116 Coefficient Data to Obtain Pseudo-critical Parameters. Proposed Scheme for Calculating Mixture Pseudo- 117 parameters from Enthalpy Data. Selection of a Method for the Representation of the 120 Second Virial Coefficient in a Corresponding States Framework a) Representation of the Reference Fluid: Methane 121 b) Representation of Substances with ac Values 121 Different from Methane c) Performance of the Correlation 127 d) Suggestions for Improving the Correlation 128 Development of a Mixing Rule for RTc /Pc 129 a) Need for the Development of a RewuceW 129 High Temperature Second Virial Coefficient Correlation b) Initial Efforts Towards the Development of the 130 High Temperature Correlation xi

c) The Development of a High Temperature Mixing 131 Rule for RTc /Pc m m Summary m m 135 VI. THE EXPERIMENTAL METHOD 136 The Recycle System. 136 Modifications to the Recycle System. 140 The Isobaric Calorimeter of Faulkner. 142 The Throttling Calorimeter of Mather. 147 Measuring Instruments 150 a) Electrical Measurements 150 b) Temperature Measurement 150 c) Temperature Difference Measurement 151 d) Measurement of Energy Input 153 e) Measurement of Flow Rate 153 f) Pressure and Differential Pressure 160 Measurements i) Measurement Scheme for the Isobaric 160 Calorimeter ii) Original Measurement Scheme for the 162 Throttling Calorimeter iii) Modified Measurement Scheme for the 162 Throttling Calorimeter iv) Electrical Circuitry and Calibration 163 Equations for the Pressure Transducers v) Chronological Survey of Pressure and 167 Differential Pressure Measurement in This Work vi) The Differential Pressure Calibration 169 Manometer g) Composition Analysis 172 Procedure 176 a) Single Phase Operation 176 b) Two Phase Isobaric Operation 178 c) Isothermal and Isenthalpic Operation 179 Operating Schedule 180 Chronology of the Experimental Investigation 180 VII. DATA REDUCTION 181 Reduction of Raw Data to Basic Data 181 Determination of Enthalpy Derivatives Cp, ~, and l 182 from the Basic Data a) Thermodynamic Analysis for Isobaric Data 182 b) The Use of the PGC For the Correction of the 184 Basic Data c) Interpretation of Joule-Thomson Coefficient 185 Data Techniques for Constructing Equal Area Curves 187 a) Graphical 187 b) Linear Regression Techniques 188 c) Non-Linear Regression Techniques 189 d) Computer Aided Graphical Techniques 191 xii

Consistency Checks. 192 Preparation of Pressure-Temperature-Enthalpy 194 Diagrams and Tables. VIII. EXPERIMENTAL AND SMOOTHED CALORIMETRIC DATA 197 Special Tests on Calorimeters 197 a) Unsteady State Behaviour of the Isobaric 197 Calorimeter b) Heat Leak Test 198 c) Capillary Coil Test 202 d) Test for Consistency Between the Faulkner 203 and Mather Calorimeters Error Analysis 204 Experimental Measurements on Ethane 204 Consistency Checks 214 Thermal Property Tables 214 Comparisons with Literature Data and Compilations 220 Discussion on the Maxima in Cp and 2 231 Measurements on Ethane-Propane Mixtures 237 a) Nominal 0.76 Mole Fraction Ethane-Propane 238 Mixture b) Nominal 0.50 Mole Fraction Ethane-Propane 247 Mixture c) Nominal 0.27 Mole Fraction Ethane-Propane 256 Mixture d) Generation of Enthalpy Tables in the Single 262 Phase Region Upto Saturation Measurements on the Methane-Ethane System 265 Measurements on the Methane-Ethane-Propane 270 System Consistency Checks for the Ternary Mixture 274 Enthalpy Tables and Diagrams 274 IX. THE EVALUATION OF ENTHALPY CORRELATION AND 288 PREDICTION METHODS Prediction of Pure Component Enthalpies 288 Optimization of Pseudo-parameters 290 a) General Procedure 290 b) Pseudo-parameter Optimization for Ethane 292 c) Pseudo-parameter Optimization for Mixtures 295 Consistency Test for Examining the Validity of the 297 One Fluid Corresponding States Principle. The Selection of Mixing Rules for This Investigation. 305 Calculation of Optimum Binary Interaction Parameters 306 for Several Mixing Rules. The Evaluation of Mixing Rules of Table IX-10 317 a) Methane-Ethane 317 b) Ethane-Propane 320 c) Methane-Propane 324 d) Ternary Methane-Ethane-Propane Mixture 326 Critique of Mixing Rules 334 Illustrative Contour Plots for Some Enthalpy 336 xiii

Prediction and Correlation Schemes 336 X. SUGGESTIONS FOR FURTHER RESEARCH 343 Suggested Improvements for the Operation of the 343 Existing Facility. Suggestions for Improving the Interpretation of the 345 Basic Data Suggestions for Further Experimental and Correlative Research. APPENDICES 353 BIBLIOGRAPHY 493 xiv

LIST OF TABLES Table Page IV-1 Power Series Expansions for the Excess Free Energy 79 in the Liquid State for Various Corresponding States Models IV-2a Excess Property Predictions for Real Binary Mixtures 81 According to Various Models IV-2b The Size and Energy Parameters for the Components 81 of Table IV-2a Relative to Argon IV-3 The Coefficient of the Second Order Size Term c2 in 88 the Expansion of AE for Soft Sphere Mixtures IV-4 The Coefficient of the Second Order Size Term (2 in 88 the Virial Expansion of AE for Soft Sphere Mixtures IV-5 Comparison of the Coefficients for the Second Order 88 Size Term ~2 in the Free Energy Expansion with Computer Simulation Results IV-6 The Contribution of the Coupling Term In as a 91 Function of n/4 to GE/RT in the Liquid Phase as Derived from the Results of Table IV-I V-l Summary of Results for the Reduced Second Virial 122 Coefficient Correlation [Equation (V-30)] of This Work V-2 Comparison of Second Virial Coefficient Correlations 125 with Respect to Methane and Propane VI-1 Summary of Flowmeter Calibration Equations for All 159 Systems of This Work VI-2 Comparison Between Original and Modified Pressure and 168 Differential Measurement Schemes with Ethane as the Test Fluid VI-3 Summary of the Composition Analysis for the Systems 177 of This Investigation VIII-1 Direct Comparison of the Enthalpy Data from the 203 Isobaric and Throttling Calorimeters VIII-2 Summary of Estimates of Measurement and Data Inter- 205 pretation Errors for the Calorimetric Data of this Work xv

LIST OF TABLES (contd.) Table Page VIII-3 Smoothed Enthalpy Values for 0.996 Ethane at Regular 218 Intervals VIII-4 Smoothed Enthalpy Values for Ethane at Saturation 221 VIII-5 Smoothed Values of the Heat Capacity of Ethane as a 222 Function of Temperature and Pressure VIII-6 Supplementary Smoothed Enthalpy and Isobaric Heat 222 Capacity Values for 0.996 Mole Fraction Ethane in the Vicinity of the Heat Capacity Maxima and in the Two Phase Region VIII-7 Smoothed Values of the Isothermal Throttling 225 Coefficient for 0.996 Mole Fraction Ethane VIII-8 Comparison of the Smoothed Heat Capacities of this 230 Work with the Tabulated Results of Michels et al. in the Gaseous and Supercritical Regions VIII-9 Comparison Between the Enthalpy of Vaporization as 233 a Function of Temperature Obtained from the Enthalpy Diagram of this Work with the Results from the Literature VIII-10 Thermal Properties for Ethane at the Heat Capacity 236 Maxima along Isobars VIII-11 Tabulated Values of the Enthalpy and the Heat 244 Capacity for the Nominal 0.76 Mole Fraction Ethane-Propane Mixture VIII-12 Tabulated Values of the Enthalpy and the Isothermal 246 Throttling Coefficient for the Nominal 0.76 Mole Fraction Ethane-Propane Mixture VIII-13 Tabulated Values of the Enthalpy and the Heat Capacity 253 for the Nominal 0.50 Mole Fraction Ethane-Propane Mixture VIII-14 Tabulated Values of the Enthalpy and the Isothermal 255 Throttling Coefficient for the Nominal 0.50 Mole Fraction Ethane-Propane Mixture VIII-15 Tabulated Values of the Enthalpy and the Heat Capacity 263 for the Nominal 0.27 Mole Fraction Ethane-Propane Mixture xvi

LIST OF TABLES (contd.) Table Page VIII-16 Tabulated Values of the Enthalpy and the Isothermal 264 Throttling Coefficient for the Nominal 0.27 Mole Fraction Ethane-Propane Mixture VIII-17 Saturated Liquid and Vapor Enthalpies for the Nominal 266 Mole Fraction Ethane-Propane Mixture VIII-18 Saturated Liquid and Vapor Enthalpies for the Nominal 266 0.50 Mole Fraction Ethane-Propane Mixture VIII-19 Saturated Liquid and Vapor Enthalpies for the Nominal 266 0.27 Mole Fraction Ethane-Propane Mixture VIII-20 Comparison Between the Calorimetric Data of this 276 Work and the Results from CB&I for the Ternary Mixture at 500 psia VIII-21 Tabulated Values of the Enthalpy and the Heat Capacity 279 for the Ternary Mixture VIII-22 Tabulated Values of the Enthalpy and the Isothermal 281 Throttling Coefficient for the Ternary Mixture VIII-23 Smoothed Values of the Enthalpy for the Ternary 285 Mixture as Obtained from the Enthalpy Diagram VIII-24 Saturated Liquid and Vapor Phase Enthalpies for the 286 Ternary Mixture IX-1 The PGC Enthalpy Predictions Compared with Smoothed 289 Data Using the Critical Parameters for Ethane IX-2 Summary of Results in the Final Stages of Pseudo- 293 parameter Optimization for Ethane in the PGC Framework IX-3 The PGC Enthalpy Predictions Compared with Smoothed 294 Data Using the Optimum Pseudo-critical Parameters for Ethane IX-4 The Variation of the Calculated Interaction Virial 299 Coefficient as a Function of Composition as a Measure of the Consistency Between the Pseudoparameters for the Various Methane-Ethane Mixtures xvii

LIST OF TABLES (contd.) Table Page IX-5 The Variation of the Calculated Interaction Virial 299 Coefficient as a Function of Composition as a Measure of the Consistency Between the Pseudoparameters for the Various Ethane-Propane Mixtures IX-6 The Variation of the Calculated Interaction Virial 300 Coefficient as a Function of Composition as a Measure of the Consistency Between the Pseudoparameters for the Various Methane-Propane Mixtures IX-7 The Calculated Interaction Parameters for Rules II, 310 III, IV, V and VII of Table IX-10 as a Function of Composition for the Methane-Ethane System IX-8 The Calculated Interaction Parameters for Rules II, 310 III, IV, V and VII of Table IX-IO as a Function of Composition for the Ethane-Propane System IX-9 The Calculated Interaction Parameters for Rules II, 311 III, IV, V and VII of Table IX-10 as a Function of Composition for the Methane-Propane System IX-10 Summary of Mixing Rules Examined in This Investiga- 313 tion for the Calculation of Pseudoparameters IX-lla The PGC Enthalpy Predictions for the 0.78 Mole 318 Fraction Methane-Ethane System Using the Optimum Pseudoparameters (I) of Table IX-16 IX-llb The Calculated Pseudo-critical parameters for the 0.78 318 Mole Fraction Methane-Ethane System Using the Mixing Rules of Table IX-10 IX-12a The PGC Enthalpy Predictions for the 0.50 Mole 319 Fraction Methane-Ethane System Using the Optimum Pseudoparameters (I) of Table IX-12b IX-12b The Calculated Pseudo-critical Parameters for the 0.50 319 Mole Fraction Methane-Ethane System Using the Mixing Rules of Table IX-10 IX-13 The Calculated Pseudo-critical Parameters and the PGC 321 Enthalpy Predictions for the 0.763 Mole Fraction Ethane-Propane System Using the Mixing Rules of Table IX-10 IX-14 The Calculated Pseudo-critical Parameters and the PGC 322 Enthalpy Predictions for the 0.498 Mole Fraction Ethane-Propane System Using the Mixing Rules of Table IX-lO xviii

LIST OF TABLES (contd.) Table Page IX-15 The Calculated Pseudo-critical Parameters and the PGC 323 Enthalpy Predictions for the 0.276 Mole Fraction Ethane-Propane System Using the Mixing Rules of Table IX-10 IX-16 The Calculated Pseudo-critical Parameters and the 327 PGC Enthalpy Predictions for the 0.95 Mole Fraction Methane-Propane System Using the Mixing Rules of Table IX-10 IX-17 The Calculated Pseudo-critical Parameters and the PGC 328 Enthalpy Predictions for the 0.883 Mole Fraction Methane-Propane System Using the Mixing Rules of Table IX-1O IX-18 The Calculated Pseudo-critical Parameters and the PGC 329 Enthalpy Predictions for the 0.72 Mole Fraction Methane-Propane System Using the Mixing Rules of Table IX-10 IX-19 The Calculated Pseudo-critical Parameters and the 330 PGC Enthalpy Predictions for the 0.494 Mole Fraction Methane-Propane System Using the Mixing Rules of Table IX-10 IX-20 The Calculated Pseudo-critical Parameters and the PGC 331 Enthalpy Predictions for the 0.234 Mole Fraction Methane-Propane System Using the Mixing Rules of Table IX-10 IX-21 The Calculated Pseudo-critical Parameters and the PGC 332 Enthalpy Predictions for the (0.369 CH, 0.305 C2H6, 0.326 CH ) Ternary Mixture Using the Mixing Rules of Table IX-10 IX-22 Summary of the PGC Enthalpy Predictions for the 333 Mixing Rules of Table IX-10 A-1 National Bureau of Standards Calibration for the 354 Reference Cell A-2- Callendar Equation Constants for the New Platinum 355 Thermometer A-3 Sample Regression Results for the Six Junction 356 Copper-Constantan Thermopile 6M A-4 Original National Bureau of Standards Calibration 357 for the Fifteen Junction Thermopile xix

LIST OF TABLES (contd.) Table Page A-5 Repeated National Bureau of Standards Calibration 358 for the Fifteen Junction Thermopile A-6 Calculation of the Fifteen Junction Thermopile EMF 359 at Uncalibrated Temperatures by Comparison with a Calibrated 6 Junction Thermopile 6M A-7 Least Squares Fit of EMF vs Temperature for the Fifteen 361 Junction Thermopile A-8 Sample Flowmeter Calibration Results for the Ternary 362 Mixture A-9 Calibration Results for Mansfield and Green Dead 363 Weight Gage A-10 Calibration Data for Resistors in the Electrical 364 Circuit for the Pressure Transducers A-11 National Bureau of Standards Calibration of 200 Inch 365 Steel Tape A-12 Sample High Pressure Transducer Calibration Results 367 A-13 Sample Low Pressure Transducer Calibration Results 368 A-14 Sample Differential Pressure Transducer Calibration 369 Results A-15 The Variation of the Differential Pressure Transducer 369 Output as a Function of Pressure Level for a Fixed Pressure Drop of 200 psid B-1 Basic Isobaric Data for 0.996 Mole Fraction Ethane 371 B-2 Basic Isothermal Data for 0.996 Mole Fraction Ethane 375 B-3 Basic Isenthalpic Data for 0.996 Mole Fraction Ethane 376 B-4 Basic Isobaric Data for Nominal 0.76 C2H6, 0.24 377 C 3H Mixture B-5 Basic Isothermal Data for Nominal 0.76 C2H6, 0.24 379 C3H8 Mixture B-6 Basic Isenthalpic Data for Nominal 0.76 C2H6, 0.24 379 C3H8 Mixture xx

LIST OF TABLES (contd.) Table Page B-7 Basic Isobaric Data for Nominal 0.50 C2H6, 0.50 380 C3H8 Mixture 3 8 B-8 Basic Isothermal Data for Nominal 0.50 C2H, 0.50 381 J38 C3H8 Mixture B-9 Basic Isenthalpic Data for Nominal 0.50 C2H6, 0.50 381 C3H8 Mixture B-10 Basic Isobaric Data for Nominal 0.27 C2H6, 0.73 382 C3H8 Mixture B-lla Basic Isothermal Data for Nominal 0.27 C H, 0.73 383 C3H8 Mixture Using Absolute Pressure Transducers B-llb Basic Isothermal Data for Nominal 0.27 C H6, 0.73 383 C3H8 Mixture Using Differential Pressure Transducers B-12 Basic Isenthalpic Data for Nominal 0.27 C 2H, 0.73 384 C3H8 Mixture Using Absolute Pressure Transducers 3 8 B-13 Basic Isobaric Data for Nominal 0.78 CH4, 0.22 385 C2H6 Mixture B-14 Basic Isothermal Data for Nominal 0.78 CH4, 0.22 386 C2H6 Mixture 26 B-15 Basic Isenthalpic Data for Nominal 0.78 CH4, 0.22 386 C2H6 Mixture B-16 Basic Isobaric Data for Nominal 0.48 CH4, 0.52 387 C2H6 Mixture B-17 Basic Isothermal Data for Nominal 0.48 CH4, 0.52 388 C2H6 Mixture B-18 Basic Isenthalpic Data for Nominal 0.48 CH4, 0.52 388 C2H6 Mixture 26 B-19 Basic Isobaric Data for Nominal 0.369 CH4, 0.306 389 C2H6, 0.325 C3H8 Mixture B-20 Basic Isothermal Data for Nominal 0.369 CH4, 0.306 393 C2H6, 0.325 C3H8 Mixture B-21 Basic Isenthalpic Data for Nominal 0.369 CH4, 0.306 393 C2H6, 0.325 C3H8 Mixture xx,

LIST OF TABLES (contd.) Table Page C-1 Sample Results for PGC Corrections to the Basic 395 Data as Applied to the Ternary Mixture C-2a The Results Obtained on Constructing an Equal Area 396 (IH/IP)T Curve for the Ternary Mixture at 126.2~F Using a Non-Linear Least Squares Technique C-2b Computer Aided Interpolation and Integration of 396 Equal Area (/H/UP)T Curve for the Ternary Mixture at 126.20F C-3a Computer Aided Consistency Check Results for 397 Graphically Determined Equal Area Cp Curve as Illustrated for Ethane at 819 psia C-3b Computer Aided Interpolation and Integration of 397 Equal Area Cp Curve as Illustrated for Ethane at 819 psia F-1 Virial Coefficient Data for Calculation of Gas 409 Density at the Flowmeter F-2 Sutherland Constants for the Zero Pressure Viscosity 413 F-3 Estimated Change in the Calculated Value of the 441 Interaction Second Virial Coefficient Using the Technique of Figure V-2 Due to a Modification of the Second Virial Coefficient Correlation of This Work F-4 Sample Results Illustrating the Calculation of the 450 Pseudo-Critical Temperature Tc for the 0.498 Ethane-Propane Mixture Using Rule VII of Table IX-110 F-5 The Calculation of the Second Virial Coefficient of 452 the Ternary Mixture as a Function of Temperature Using the Technique of Figure V-2 F-6 Optimization Results on the Pseudoparameters RTc /Pc 454 and Tc for the Ternary Mixture Using Estimated 2nd Virial Coefficients from Table F-5 J-1 Summary of Characteristic Properties of Substances 472 Used in the Development of the Second Virial Coefficient Correlation of this Work J-2 Least Squares Regression Results for the Reduced 473 Second Virial Coefficient Tabulation of Leland et al. [145] at High Temperatures xxii

LIST OF TABLES (contd.) Table Page J-3 Comprehensive Results for the Generalized Second 474 Virial Coefficient Correlation of This Work K-1 Enthalpy of Methane in Btu/lb Using the Powers 479 Generalized Correlation (PGC) K-2 Enthalpy of Ethane in Btu/lb Using the PGC 481 K-3 Enthalpy of Propane in Btu/lb Using the PGC 483 K-4 Enthalpy of 0.76 C H -C3H Mixture in 485 Btu/lb Using the PC6 K-5 Enthalpy of 0.494 C2H6-C3H8 Mixture in Btu/lb Using 487 the PGC K-6 Enthalpy of 0.275 C2H6-C3H8 Mixture in Btu/lb Using 489 the PGC K-7 Enthalpy of Ternary Mixture in Btu/lb Using the PGC 491 xxiii

LIST OF FIGURES Figure Page I-1 Direct Flow Calorimeter - Schematic 13 II-1 Enthalpy Cycle for the Calculation of AHV as a 21 Function of Pressure III-1 Simple Models for Representing Intermolecular 33 Forces Between Real Fluids III-2 The Radial Distribution Function for Real Fluids - 33 Schematic III-3 Effect of Non-Central Forces on the Reduced Vapor 46 Pressure Curve IV-1 The Performance of Various Corresponding States 85 Models in Predicting HE for the Methane-Nitrogen System Using the Lorentz-Berthelot Rules [272] IV-2 The Performance of Some Models in Predicting GE 85 and HE for a Mixture of Lennard-Jones Molecules [102] IV-3 The Radial Distribution Function g. (-) for All 94 Pair Interactions in the Neon-Krypton System at 260K. V-1 The Reduced Second Virial Coefficient as a Function 115 of Reduced Temperature for a Classical Spherically Symmetric Fluid V-2 Schematic of Proposed Method for Defining Pseudo- 119 Critical Parameters for Multi-Component Mixtures V-3 The Reduced Second Virial Coefficient as a Function 126 of the Modified Reduced Temperature TrH for Methane, Ethane and Propane 4 V-4 Dimensionless Second Virial Coefficient for a 134 Classical Fluid in the Vicinity of the Maximum VI-l The Recycle System (Schematic) 141 VI-2 View of Control Valve Manifold Line Following 141 Explosion xxiv

LIST OF FIGURES (contd.) Figure Page VI-3 View of Rebuilt Valve Manifold 141 VI-4 The Isobaric Calorimeter of Faulkner [79] Before 142 Modifications of this Work VI-5a View of the Parts of the Modified Heater Capsule 145 VI-5b View of the Original Heater Capsule 145 VI-6 The Original and Modified Upper Half of the Heater 148 Capsule Housing VI-7 The Throttling Calorimeter of Mather [168] Before 149 Modification VI-8 Flowmeter Calibration Results at Low Flowrates for all 156 Systems of this Investigation Excluding the Ternary Mixture VI-9 Flowmeter Calibration Results at High Flowrates 156 VI-10 Pressure and Differential Pressure Measurement Scheme 158 at the Recycle Flow Facility VI-11 Electrical Circuit Diagram for Pressure and Differential 164 Pressure Transducers VI-12a View of Differential Pressure Calibration Manometer 170 (D.P.C.M.) Sight Glasses VI-12b View of (D.P.C.M.) Base 170 VI-12c View of (D.P.C.M.) Valve Manifold 170 VI-13 Schematic of Differential Pressure Calibration Facility 171 VI-14 Sample Chromatographic Output for the Ternary Mixture 174 VIII-1 Approach to Steady State as a Function of the Heater 199 Capsule Within the Isobaric Calorimeter VIII-2 Heat Leak Test for the Isobaric Calorimeter, Heat 201 Capacity of Ethane as a Function of Reciprocal Flowrate xxv

LIST OF FIGURES (contd.) Figure Page VIII-3 Effect of the Size of the Capillary Coil on the 201 Measured Value of (dH/dP)T for Ethane Along the 202.14"F Isotherm VIII-4 Temperature and Pressure Range of Calorimetric 206 Measurements of Ethane in this Work, as a Function of Run Number VIII-5 Flowmeter Calibration Results for Ethane 206 VIII-6 Isobaric Heat Capacity for Ethane at 1000 psia 208 VIII-7 Isobaric Heat Capacity for Ethane at 713 psia 209 VIII-8 Isobaric Heat Capacity for Ethane at 819 psia 209 VIII-9a Isobaric Enthalpy Traverse for Ethane Across the 211 Two Phase Region VIII-9b Graphical Procedure for Estimating the Enthalpy of 211 Vaporization at Constant Pressure of the Pseudo-pure Fluid from Actual Measurements on an Impure System VIII-10 Isobaric Heat Capacity for Ethane in the Liquid 212 Phase upto the Saturation Boundary at 500 psia VIII-11 Isobaric Heat Capacity for Ethane in the Vapor 212 Phase upto the Saturation Boundary at 500 psia VIII-12 Isothermal Joule-Thomson Coefficient for Ethane 213 at 89.3~F VIII-13 Joule-Thomson Coefficient Measurements on Ethane at 213 -246.60F VIII-14 Thermodynamic Consistency Checks for the Ethane 215 Calorimetric Data on this Work VIII-15 Temperature-Pressure-Enthalpy Diagram for 0.996 216 Ethane VIII-16 Comparison Between the Measured Mean Heat Capacities 228 of Ethane From this Investigation with the Saturated Liquid Heat Capacity Data in the Literature VIII-17 Comparison Between the Smoothed Heat Capacities of this 228 Work and the Smoothed Values of Michels et al. Obtained from PVT Data xxvi

LIST OF FIGURES (contd.) Figure Page VIII-18 Comparison Between the Enthalpies of Vaporization 232 for Ethane as Derived from this Investigation with Some Results from the Literature VIII-19 The Location of the Cp Maxima Along Isobars, and the 234 ~ Maxima Along Isotherms Relative to the Linear Extrapolation of the Vapor Pressure Curve for Ethane on Logarithmic Coordinates VIII-20 Temperature and Pressure Range of the Calorimetric 239 Measurements for the Nominal 0.76 Mole Fraction Ethane-Propane Mixture as a Function of Run Number VIII-21 Variation of Composition for the Nominal 0.76 Mole 239 Fraction Ethane-Propane Mixture as a Function of Run Number VIII-22 Isobaric Heat Capacity for the Nominal 0.76 Mole 240 Fraction Ethane-Propane Mixture at 1000 psia VIII-23 Isothermal Joule-Thomson Coefficient for the Nominal 241 0.76 Mole Fraction Ethane-Propane Mixture at 250.74~F VIII-24 Adiabatic Joule-Thomson Coefficient Data for the 241 Nominal 0.76 Mole Fraction Ethane-Propane Mixture at -50.18~F VIII-25 Isobaric Enthalpy Traverse for the Nominal 0.76 241 Mole Fraction Ethane-Propane Mixture at 716 psia VIII-26 Thermodynamic Consistency Checks for the Calorimetric 243 Data on the 0.76 Mole Fraction Ethane-Propane Mixture VIII-27 Range of Calorimetric Measurements Obtained in This 248 Work for the Nominal 0.50 Mole Fraction Ethane-Propane Mixture VIII-28 Variation of Composition for the Nominal 0.50 Mole 248 Fraction Ethane-Propane Mixture as a Function of Run Number VIII-29 Isobaric Heat Capacity for the Nominal 0.50 Mole 249 Fraction Ethane-Propane Mixture at 2000 Psia VIII-30 Isobaric Enthalpy Traverse Across the Two Phase 250 Region for the Nominal 0.50 Ethane-Propane Mixture at 250 Psia xxvii

LIST OF FIGURES (contd.) Figure Page VIII-30 Isobaric Enthalpy Traverse Across the Two Phase 250 Region for the Nominal 0.50 Ethane-Propane Mixture at 250 Psia VIII-31 Isobaric Heat Capacity for the Nominal 0.50 Mole 250 Fraction Ethane-Propane Mixture in the Vapor Phase upto the Saturation Boundary at 250 Psia VIII-32 Isothermal Joule-Thomson Coefficient for the Nominal 251 0.50 Mole Fraction Ethane-Propane Mixture at 251.1~F VIII-33 Adiabatic Joule-Thomson Coefficient for the Nominal 251 0.50 Mole Fraction Ethane-Propane Mixture at 37.5 F VIII-34 Thermodynamic Consistency Checks for the Calorimetric 252 Data on the Nominal 0.50 Mole Fraction Ethane-Propane Mixture VIII-35 Range of Calorimetric Measurements Obtained in this 257 Work for the Nominal 0.27 Mole Fraction Ethane-Propane Mixture VIII-36 Variation of Composition for the Nominal 0.27 Mole 257 Fraction Ethane-Propane Mixture VIII-37 Isobaric Heat Capacity for the Nominal 0.27 Mole 258 Fraction Ethane-Propane Mixture VIII-38 Isobaric Enthalpy Traverse for the Nominal 0.27 258 Mole Fraction Ethane-Propane Mixture at 500 Psia VIII-39 Isobaric Liquid Phase Heat Capacity for the Nominal 259 0.27 Mole Fraction Ethane-Propane Mixture upto the Saturation Boundary at 500 Psia VIII-40 Isothermal Joule-Thomson Coefficient for the Nominal 259 0.27 Mole Fraction Ethane-Propane Mixture at 269~F VIII-41 Adiabatic Joule-Thomson Coefficient for the Nominal 259 0.27 Mole Fraction Ethane-Propane Mixture at 1.6~F VIII-42 Thermodynamic Consistency Checks for the Calorimetric 260 Data on the Nominal 0.27 Mole Fraction Ethane-Propane Mixture VIII-43 Range of Calorimetric Measurements Obtained in This 268 Work for the Nominal 0.78 Mole Fraction Methane-Ethane Mixture xxviii

LIST OF FIGURES (contd.) Figure Page VIII-44 Flowmeter Calibration Results for the Nominal 0.78 268 Mole Fraction Methane-Ethane Mixture VIII-45 Range of Calorimetric Measurements Obtained in This 269 Work for the Nominal 0.48 Mole Fraction MethaneEthane Mixture VIII-46 Flowmeter Calibration Results for the Nominal 0.48 269 Mole Fraction Methane-Ethane Mixture VIII-47 Range of Calorimetric Measurements Obtained in this 271 Work for the Ternary (0.369 CH4, 0.305 C2H6, 0.325 C3H8) Mixture VIII-48 The Variation of Composition for the Ternary Mixture 271 for the Duration of the Investigation VIII-49 Flowmeter Calibration Results for the Ternary Mixture 272 VIII-50 Isobaric Heat Capacity for the Ternary Mixture at 272 2000 Psia VIII-51 Isobaric Heat Capacity for the Ternary Mixture at 273 1100 Psia VIII-52 Isothermal Joule-Thomson Coefficient for the Ternary 273 Mixture at 126.30F VIII-53 Adiabatic Joule-Thomson Coefficient for the Ternary 275 Mixture at 236.48~F VIII-54 Isobaric Enthalpy Traverse for the Ternary Mixture 275 Across the Two Phase Region at 500 Psia VIII-55 Isobaric Liquid Phase Heat Capacity Data for the 277 Ternary Mixture at 500 Psia upto the Saturation Boundary VIII-56 Thermodynamic Consistency Checks for the Calorimetric 278 Data on the Ternary'Mixture VIII-57 Temperature-Pressure-Enthalpy Diagram for the Ternary 282 Mixture IX-1. The Use of the Interaction Second Virial Coefficient 301 as a Measure of the Ability of the Corresponding States Principle to Correlate the Thermodynamic Properties of the Methane-Ethane System xxix

LIST OF FIGURES (contd.) Figure Fage IX-2 The Use of the Interaction Second Virial Coefficient 302 as a Measure of the Ability of the Corresponding States Principle to Correlate the Thermodynamic Properties of the Ethane-Propane System IX-3 The Use of the Interaction Second Virial Coefficient 303 as a Measure of the Ability of the Corresponding States Principle to Correlate the Thermodynamic Properties of the Methane-Propane System IX-4 The Performance of Some Corresponding States Techniques 338 in Calculating the Enthalpy Departure for 0.996 Ethane IX-5 The Performance of Some Corresponding States Techniques 339 in Calculating the Enthalpy Departure for the 0.76 Mole Fraction Ethane-Propane Mixture IX-6 The Performance of Some Corresponding States Techniques 340 in Calculating the Enthalpy Departure for the 0.50 Mole Fraction Ethane-Propane Mixture IX-7 The Performance of Some Corresponding States Techniques 341 in Calculating the Enthalpy Departure for the 0.27 Mole Fraction Ethane Propane Mixture IX-8 The Performance of Some Enthalpy Prediction Techniques 342 with Respect to the Ternary (0.369 CH4, 0.306 C2H6, 0.325 CH8) Mixture A-l The Interpolation of the Emf Values for the Fifteen 360 Junction Thermopile Using Detached Calibration Data on a Six Junction Thermopile F-1 Calibration Results for the Chromatograph Using 409 Reference Mixtures of Methane, Ethane and Propane xxx

LIST OF APPENDICES Appendix Page A Sample Calibration Results for Various Instruments 353 B The Basic Calorimetric Data 370 C Sample Results Involving the Smoothing of the Basic 394 Data D Equipment Summary 398 E Detailed Drawings of the Heater Capsule for the 404 Isobaric Calorimeter F Sample Calculations: 408 F-1 Calculation of Mass Flowrate 409 F-2 Sample Calculation Involving the Differential Pressure 416 Calibration System I Measurement of Mercury Density 416 II Calculation of Pressure and Differential Pressure 416 at the Transducers for a Sample Set of Measurements Obtained with the High Pressure Differential Manometer III Sample Calculation of Pressure and Differential 423 Pressure from Transducer Outputs F-3 The Preparation of Calibration Standards for the 426 Composition Measurement F-4 Calculation of System Composition 432 F-5 Derivation of the High Temperature Mixing Rule of 436 Equation (V-41) F-6 Estimation of Errors in the Computation of the Second 439 Interaction Virial Coefficients from the Correlation (Equation V-30) of this Work F-7 Outline of Calculation Procedure for Rules VII, IX 442 and X G Derivation of a Modified Van der Waal Mixing Rule 455 H Selected Thermodynamic Property Calculation: 458 H-l Thermodynamic Properties from the Starling Modified 459 Benedict-Webb-Rubin Equation of State H-2 Combining Rules for Constants in the Starling BWR 460 Equation of State xxxi

LIST OF APPENDICES (contd.) Appendix Cage H-3 Thermodynamic Properties from the Reduced Virial 461 Equation Truncated at the Third Virial Coefficient H-4 Sample Output of Thermodynamic Property Calculations 464 on the Ternary Mixture at 126.20F by Several Techniques I Procedures: I-1 Procedure for Flowmeter Calibration 466 I-2 Procedure for System Mixture Preparation 469 J Data and Results Relevant to the Development of 471 the Second Virial Coefficient Correlations [Equations (V-30), and (V-40)] of This Work K Enthalpy Calculations from the Powers Generalized 478 Correlations (PGC) xxxii

NOMENCLATURE a Spherical core parameter for Kihara potential a,b Constants in the Van der Waal Equation of State a,b,c,d Constants for a flowmeter calibration equation a,b,c,d Constants for the Starling Modified BWR Equation a,b,c,d,e,f,g Constants for the least squares regression equation for Cp and (dH/dP)T a',b',c',d' Constants for a flowmeter calibration equation a",b",c" d" Constants for a flowmeter calibration equation ahbhchdh Constants for the low pressure transducer calibration equation al,bl,cl,dl Constants for the low pressure transducer calibration equation a nb,c,d Constants for the null output of the differential pressure transducer as a function of pressure A Constant in the Sutherland equation for zero pressure viscosity A Area A Helmholtz free energy Ao,Bo,C,Do,E Constants for the Starling Modified BWR Equation b,c,d,e Constants for the polynomial regression of Yesavage, expressing Cp as a function of temperature bd'cd'dd Constants for the differential pressure transducer calibration B Second Virial Coefficient B' dB/dT Bi Second virial coefficient for the i-j intermolecular interaction BM Maximum value of the second virial coefficient Br Reduced second virial coefficient c Coefficient of London attractive dispersion forces c(r) Direct correlation function C Third virial coefficient xxxiii

C' dC/dT Cp Isobaric heat capacity Cs (dQ/dT) for the pure saturated fluid along the vapor pressure curve Cv Isochoric heat capacity d Diameter d Chueh-Prausnitz correlating parameter for the third virial coefficient. d.. Hard sphere diameter for the i-j interaction D Fourth virial coefficient E Total energy E Young's modulus E Voltage EMF Electromotive Force f Symbol for a functional relationship f Partial molal fugacity f Friction factor F Mass flowrate F Symbol for a functional relationship g Symbol for a functional relationship g Gravitational acceleration g Radial distribution function G Symbol for a functional relationship G Free energy h Planck's symbol h Symbol for a functional relationship h Heat transfer coefficient h Height H Enthalpy H Specific enthalpy H Partial molal enthalpy iS (Configurational enthalpy Modified reduced enthalpy due to Powers xxxiv

Hc Enthalpy at the critical point I Current I The configurational energy integral expressed as a function of dimensionless distance k BWR equation parameter in Equation (IV-52) k Boltzmann Constant k.. Correction factor to the geometric mean rule for the 1J unlike i-j pair interaction. K Symbol for a functional relationship L Well width for the square well potential m Mass m Mass flowrate m,n Exponents for the Lennard-Jones bireciprocal intermolecular potential M. Molecular weight n Number of carbon atoms in an n-alkane molecule N Number of molecules N Avogadro number 0 NBP Normal boiling point P Pressure PGC Power's generalized correlation Pc Critical pressure Pc Critical pressure of a mixture x Pk Pressure corresponding to the peak or maximum value of any given thermodynamic property Pr Reduced pressure, P/Pc Ps Saturation pressure for the liquid-vapor transition PY Percus-Yevick pq Indices for mixing rules xxxv

q Rate of heat transfer Q Heat input r Coordinate vector r Distance R Gas constant R Resistance Re Reynolds number, (pvd/P) S Constant in the Sutherland equation for zero pressure viscosity SCFM Standard cubic feet per minute T Temperature T Bath temperature b TPFL Thermal Properties of Fluids laboratory Tb Boyle temperature Tc Critical temperature T Reference temperature o Tc Critical temperature for a mixture x T Temperature at which the second virial coefficient M attains its maximum value Tr Reduced temperature (T/Tc) Tr Modified reduced temperature oo Ts Temperature of calorimetric shield Ts Saturation temperature u(r) Intermolecular potential function U Configurational energy U Internal energy Internal energy of calorimeter v Velocity V Volume Vb Boyle volume, -(TdB/dT)TTb Vc Critical volume xxxvi

Vr Reduced volume, V/Vc V Specific Volume w Mass fraction w Weighting factor w Work input w Rate of transfer of work W Molecular weight x Mole fraction [x] Composition array y Mole fraction (usually gas phase) z Mole fraction (usually for two phase mixtures) z Elevation z Compressibility factor zc Critical compressibility factor ox Constant in Leland-lMueller mixing rule cx Inverse steepness parameter for Barker-Henderson perturbation theory ~,B,y, Constants in the differential pressure transducer calibration equation cx,y Constants in the BWR equation cx~',3',Y',5 Constants in the differential pressure transducer calibration equation cO Average polarizability oc The slope d(lnPr)/d(lnTr) of the vapor pressure curve at the critical point -,8 Perturbation parameter for three parameter corresponding 00 states theories ~~6 ~Perturbation parameter of Cook and Rowlinson 6 Third parameter expressing departure from two parameter corresponding states theory xxxvii

A Difference AH Enthalpy of vaporization C Molecular energy parameter n (e(-. ii)/2oo jj 1t 00 8 Shape factor in corresponding states theory e Time,u Joule-Thomson coefficient, (dT/dP)H,u^ ~ Dipole moment V Index on energy parameter for generalized Van der Waal mixing rules 1 5 ~ Volume density................ N c i=l P Density pr Reduced density, pNo3 0C Molecular size parameter T Powers corresponding states parameter'~ Symbol for a functional form Isothermal throttling coefficient, (dH/dP)T (c. 3_ _... 3)/2' 3 _ ] lJj ii 00oo ~b~I Mean value of (dH/dP)T over some pressure internal X Diagmagnetic susceptibility d dH dCp d2V TY *M-*@@@@v@ dT~-),or -P or T(d-) dT 10 dP dT up Shape factor in corresponding T P states theory 1/2'F 1 - (..icj) I/si Subscripts A Pertaining to point A b Calorimeter bath conditions bp Bubble point condition B Pertaining to point B C Critical point property dp Dew point condition f Final state f Outlet condition h Pertaining to the high pressure side xxxviii

HS Hard sphere property i Inlet condition ij Pertaining to the interaction between molecules of species i and species j i,j,k Component in a mixture k Pertaining to a peak in some specified property 1 Pertaining to the low pressure side m Total mixture property M Pertaining to the condition where the second virial coefficient is a maximum p Constant pressure s Property at saturation T Constant temperature v Constant volume x -Mixture property o Reference substance property o Outlet condition oo Reference property (for the o-o interaction) Superscript o Zero pressure property E Excess property 1 Liquid phase property g Vapor phase property HS Hard sphere property L Property of the liquid phase V Property of the vapor phase Conversion Factors for Units Used in this Work 1 atm = 14.696 psia= 101325 Newtons/sq. meter 1 btu = 1055.87 Joules 1 cu ft = 28317 ml xxxix

1 dyne/cm2 = 1.45038x10-5 psi gc = 980.665 gm-cm/gmf-sec2 in = 0.0254005 meters lb = 0.453592 kg ~R = ~F + 459.67 = (.K)-1.8 R = 10.73147 psi ft3/(~R)(lb mole) xl

ABSTRACT THE MEASUREMENT AND PREDICTION OF THERMAL PROPERTIES OF SELECTED MIXTURES OF METHANE, ETHANE, AND PROPANE by Andre' Wilkinson Furtado Chairman: John E. Powers The major goal of this work is to predict the enthalpy behaviour of a ternary methane-ethane-propane mixture from constituent pure component and binary enthalpy data as part of a broad effort to improve the estimation of the thermodynamic properties of multi-component fluid mixtures of hydrocarbons and other non-polar substances of industrial interest. The objectives of this research are: 1) To improve the overall operation of the calorimetric facility at the Thermal Properties of Fluids Laboratory at the University of Michigan. 2) To review the literature to determine the most practical and efficient procedure for estimating multi-component enthalpies from constituent binary data and to develop new procedures if necessary. 3) To obtain wide ranging enthalpy data on one ternary methane-ethane-propane mixture and on those of its constituent pure component and binary systems that are thus far inadequately characterized in the literature. 4) To use the basic measurements on the individual systems to generate smoothed enthalpies as a function of temperature and pressure at regular intervals. 5) To evaluate the selected prediction techniques for their ability to codify the pure component and binary data and to predict the enthalpy behaviour of the ternary mixture. Major modifications include the installation of strain gage transducers for measuring pressure and differential pressure at the calorimeter, the construction of a differential mercury manometer for the calibration of differential pressures upto 200 psid at line pressures upto 2000 psia, and the fabrication of a new heater capsule for the isobaric calorimeter. Measurements involving discrete enthalpy changes along isobars and isotherms were obtained for ethane, three ethane-propane mixtures containing 0.76, 0.50, and 0.27 mole fraction ethane, respectively, and for a ternary mixture (0.369 CH4, 0.305 C2H6, 0.326 C3H8) over the xli

range -2500F to +3000F and from 100 psia to 2000 psia including the liquid, two phase, critical and gaseous regions using both isobaric and throttling direct flow calorimeters. Some isenthalpic data was also obtained. Cp and (dH/dP)T were obtained from the basic data by graphical equal area smoothing.Computer aided integration yielded smoothed enthalpies over the entire measurement range and down to 0 psia using additional data in the literature. The examination of closed enthalpy paths established that the data were internally self consistent to about + 0.3%. Comprehensive enthalpy diagrams were constructed for ethane and for the ternary mixture. The tabulated enthalpies for all systems investigated are believed to be accurate to within 1 Btu/lb. A comprehensive review of prediction techniques from the standpoint of both theory and practice recommended the use of the pseudocritical method in conjunction with the three parameter Powers Generalized Correlation (PGC). The enthalpies for the individual systems examined were adequately (1% or better on the average) encoded in the PGC framework for an optimum choice of pseudo-parameters for each specific case. A test was also developed to examine the consistency between the pseudo-parameters for all mixturesbelonging to a given binary system based on the composition independence of the second interaction virial coefficient B... Next, ten sets of mixing rules for calculating the pseudo-critical parameters as a function of composition were investigated. Four of these were developed in this work and were based on the exact relationship: n n B = Z xx B.. m i=l =l 1J in the dilute gas region. A pair of reduced three parameter second virial coefficient correlations extending over the ranges 0.5 < Tr < 3.26 and 9.0 < Tr < 30, respectively, were also developed as part of the effort. For eight of the ten rules, the binary interaction constants were all empirically adjusted to fit the available binary enthalpy data. All these rules were found to predict the enthalpy behaviour of the ternary mixture within engineering accuracy (2% or better). xlii

INTRODUCTION Some form of energy transfer to or from a fluid is a common occurence in most chemical processes. In such situations, the characterization of process streams and the sizing of equipment such as heat exchangers, heaters, and refrigerators requires the accurate estimation of the thermal properties of the fluids involved over the range of operating conditions. One solution is to obtain laboratory measurements on the desired system at the conditions of interest. This approach has, In fact, been used to characterize the thermodynamic properties of many industrially important pure fluids and some binary mixtures. However, the systematic acquisition of thermal property data for systems of interest with a greater number of components is too time consuming, experimentally difficult, and financially prohibitive to be considered as a feasible approach to the problem. Early workers in the field were aware of the situation, and sought to predict the thermodynamic properties of a multicomponent mixture solely from those of its pure components by assuming oversimplified solution models with limited success. By the early sixties, a sizable body of binary mixture data confined primarily to volumetric measurements was accumulated. The calculation of mixture enthalpies from such information requires the volumetric data to be differentiated, and consequently yields results of limited accuracy. As the enthalpy prediction techniques improved, the American Petroleum Institute (API) [7] found that mixture data of the range and accuracy necessary to discriminate between the various correlations could scarcely be met by existing sources of data, particularly in the critical region, and recommended that extensive high accuracy calorimetric measurements were desirable. Very little work was reported in this area before 1955, primarily because the direct determination of the enthalpies of fluid mixtures turned out to be a surprisingly difficult experimental problem. The experimental difficulty was further compounded for measurements obtained at high pressures. The established need for reliable mixture enthalpy data led the National Science Foundation (NSF) and The Petroleum Research Fund (PRF) 1

2 to sponsor the development of the Thermal Properties of Fluids Laboratory (TPFL). Support for adapting the facility to handle mixtures was generously provided by the Natural Gas Processors Association. Since the early sixties, the facility has been involved in the measurement of the enthalpies of pure and binary mixed fluids involving helium, nitrogen, methane, and propane over a wide range of operating conditions using direct flow calorimetry. These systems are of direct interest to the petroleum industry, where trends towards lower temperatures in gas processing to allow recovery of light hydrocarbons, without absorption in oil, require that the enthalpy be very accurately estimated in order to ensure the reliability of design calculations under such conditions. More importantly, such measurements have long range value because they can serve as standards for the evaluation of continually evolving thermodynamic property prediction methods for some time to come. The research at the TPFL has also contributed significantly to the interpretation of the basic experimental calorimetric measurements to yield useful and readily accessible smoothed wide ranging thermal property charts and tables with little loss in accuracy. In particular, the construction of a temperature-entropy diagram for a methane-propane mixture containing 0.946 mole fraction methane, including both the single and two phase region [22], has been found to be particularly valuable in the design of natural gas turbo-expander processes. Nevertheless, the acquisition and interpretation of the basic data obtained at the TPFL has at best been a difficult and tedious problem with heavy manpower requirements. Even so, it is the commitment to continuous improvement of the facility that has been primarily responsible for the success obtained in the past. For the present, it appears that equipment modifications that permit the reduction of operating personnel, and the increased use of computer techniques in sensing human error at various stages are both highly desirable if the efficiency of the operation is to be further improved. Having accumulated a fair amount of enthalpy measurements, the research at the TPFL has, in the past few years, been increasingly associated with the evaluation of existing correlations and the development of new techniques for the prediction of mixture enthalpies. The application of such techniques to binary systems investigated at

3 the TPFL has confirmed the need for incorporating empirically determined binary interaction parameters into such correlation schemes. A logical, interesting, and industrially valuable extension of this approach would be to determine if the properties of the multicomponent mixture can be predicted if all the pair interactions in the mixture are thus characterized. A systematic experimental investigation that will allow this approach to be more concretely explored is, therefore, desirable. The investigation of the methane-ethane-propane system is highly suited to this end as explained below. The methane-propane system including the pure components has already been investigated in depth at the TPFL. Correlated enthalpy values for the methane-ethane system are available in the literature. It would appear that the investigation of the ethane-propane system and at least one ternary mixture of methane, ethane, and propane could satisfy the minimum requirements of the proposed research. Surprisingly, reliable enthalpy data for ethane in the subcooled liquid and the critical regions are scarce, and therefore, its examination is also desirable. Such a study would not only serve industrial interests, where the increased demand for ethane both as a fuel and as a petrochemical feedstock has led to cryogenic processing techniques, but would also permit pure component enthalpy prediction techniques to be examined in the rarely investigated subcooled liquid and critical regions. Although thermodynamic property prediction techniques in common use are primarily empirical in nature, recent advances in the application of statistical mechanical techniques to the prediction of mixture properties have, in some cases, suggested the equivalent theoretical approximations at the microscopic level, contributing immensely in the process to a much more fundamental understanding of the problem. These results, coupled with the increasingly successful use of the hard sphere equation of state as a starting point for the calculation of the thermodynamic properties of pure components and mixtures, seem to indicate that a new generation of sophisticated prediction techniques is in the offing. A discussion of such techniques would serve the useful purpose of helping the design engineer keep abreast of the more recent developments in the area.

4 Accordingly, the objectives of this research are as follows: (1) To improve as necessary, the overall operation of the calorimetric facility. (2) To undertake calorimetric measurements on ethane, on selected ethane-propane mixtures, and one, preferably, approximately equimolar methane-ethane-propane mixture over the approximate range -2400F < T < 300~F, 100 psia < P < 2000 psia. (3) To interpret the basic calorimetric measurements so as to yield smoothed tables or diagrams that illustrate the effect of temperature and pressure on the enthalpy and its appropriate derivatives for each system over the region of investigation. (4) To review the present state of enthalpy prediction techniques with special emphasis on theoretical developments that throw new light on long used empirical methods. (5) To select the most suitable framework for the codification of the enthalpy data for the pure component and binary systems that constitute the ternary mixture. (6) To evaluate the prediction of the enthalpy behaviour of the ternary mixture from constituent pure component and binary data within the confines of the framework selected in Step 5. (7) To comment on future directions for both theoretical and experimental investigation as suggested by the acquisition, interpretation, and correlation of the measurements obtained in this work, and also from related investigations.

Chapter I PRELIMINARY CONSIDERATIONS In the past, the thermal properties of pure and mixed fluids have been primarily calculated from PVT data using appropriate thermodynamic relationships instead of attempting to measure them directly by calorimetry, because it is experimentally easier to investigate and control a static system than a dynamic one. Although such relationships are rigorously true in theory, practical difficulties in their application can offset the experimental advantages to be obtained. Some of the more useful of these thermodynamic identities are noted in this chapter and the limitations of such approaches are discussed briefly. Next, various calorimetric techniques are outlined, and the thermodynamics of a flow calorimeter with heat shield, typical of those used in this work, is developed to illustrate how thermal properties may be directly specified from such measurements. Thermal Properties from Volumetric and Phase Equilibria Data Miyazaki, Furtado and Powers [179] used the thermodynamic relations ljI ( PH 2v RT a2 z az' [( H - T( - [ (T a ) + 2([) (I-) T T pT T2 P to calculate the isothermal differences in Cp, and the isobaric differences in (9H/8P)T using a two dimensional interpolation of volumetric data on propane. On integration, Equation (I-1) yields the isothermal throttling coefficient J as a= V - T( a -2 [ ( (V) = ( ) = v - T( ) = (v/T) RT2 dz = TapT = (T —T ( ) (1-2) T P aTT~ P dP P On further integration, we obtain the result P (H - H~)Tp = V[ - T ( ) ] dP /TP (1-3) 0 T where (H-H~) is the isothermal enthalpy departure at pressure P from the ideal gas state at temperature T, and is equivalent to the 5

6 configurational enthalpy f. If we wish to calculate the enthalpy at any T and P for any given substance relative to that in the ideal gas state, HTo, for the same substance at some specified temperature To, then it is necessary to invoke the thermodynamic relation -T,y -'To + I + | [ V- T (,] T (I-3a) To T where Cp~ is the heat capacity at zero pressure. In effect, the enthalpy difference between any two points in the P-T plane may be calculated given sufficient volumetric data, and the behaviour of the zero pressure heat capacity as a function of temperature. If the volumetric data are specified along isochores instead of isotherms, then it is practically easier to obtain the enthalpy departure with T and V as the independent variables as given by the thermodynamic identity (4T,-) - H(T,V) - K- V- [ P-T( )] (1-4) V Equations (1-3) and (1-4) are also applicable to total mixture properties in a mixture of fixed overall composition even within the two phase region. For pure components, however, (dV/dT)p is discontinuous across the saturation boundary. In such cases it is necessary to use an expanded version of Equation (I-3a) which yields T Ps P HT - To + JCP(T) dT + V - T() ]dP + AH+ [V-T(l) ] dP (I-5) To o d Ps P where AHV is the enthalpy change for any first order transition occuring at Ps and T. If AHv corresponds to the enthalpy change on vaporization, then it may also be calculated from a knowledge of the saturation properties at the same temperature using the familiar Clapeyron equation dP AHV r a TTs (V-Tn) (I-6) where the left hand side represents the slope of the vapor pressure curve at T=Ts, and V, V are are the saturated vapor and liquid

7 volumes at the same temperature. If such computations are made at a series of temperatures, then the difference between the saturated liquid and vapor heat capacities along the vapor pressure curve may be obtained by the relation CsV - Cs d - V V a CsV -CsL = [AH ] AH dT T (I-7) where the saturated heat capacity Cs for a given phase can be defined in terms of Cp for the same phase by the relation (C3)Ts,Ps (CP) Ts,Ps -T( ) (dT ) (1-8) Ps Ts,Ps Equations (I-1) through (I-4) are useful for calculating thermal properties of a mixture, only if the volumetric data are obtained on a system of fixed composition. If such data are instead available at a series of compositions, then the enthalpy departure for example, at any composition may be obtained from the relation [H -H~ a In f /YiP mim i Y (I-9) =~ ii aT where the fugacity coefficient fi/yiP is defined from the relation 1 _ RT (fi/YiP) 1- RT I dP nfIYT = [( ) T ] dP (I-10) o 1 T,P,nj where the subscript m stands for the total mixture property in any given phase. These relations can also be used within the two phase region, as demonstrated by Edmister [68] with respect to the heliumhydrogen system, to calculate the enthalpy departures of coexisting liquid and vapor phases along isotherms. Unlike a pure fluid, the value of the enthalpy of vaporization at constant pressure for a saturated liquid mixture differs from that obtained at constant temperature. This happens because the location of the saturated vapor phase corresponding to a saturated liquid mixture depends additionally upon the path selected. As most industrial processes are conducted at constant pressure conditions, the estimation of (AlH ) is therefore more important. If the

8 dew and bubble point temperatures Tdp and Tbp respectively are measured at some constant pressure P, for a given mixture, and if the heat capacities at zero pressure, Cp.i are known for each component i over the interval Tbp to Tdp, then, as Tao [262] has recently determined, (AHV)p may be calculated strictly from vapor phase volumetric data as a function of pressure and composition at the two temperatures Tdp, and Tbp using the relation n a In f R n a n f n Tdp (H)- p RT2p zi( RT )Z + Z Zi Cp i dT (I-ll) -1 Tbp i-1 Tdp i=1 Tb where z. is the mole fraction of component i in the mixture. The 1 second term on the right hand side of the above equation may also be obtained from volumetric data in the gaseous phase as a function of pressure alone along the dew point isotherm using Equation (1-3) instead if the composition corresponds to that of the total mixture. Inadequacies of Volumetric Data and Equations of State in Calculating Thermal Properties Although the thermodynamic relations (1-1) through (1-9) are rigorous, errors in specifying the desired volumetric properties in these relations can cause proportionally larger errors in the calculated values of the thermal properties. The right hand side of Equation (1-3) for example, involves a difference of two terms that are usually both positive and of about equal magnitude. Consequently, the calculated enthalpy departure is at least an order of magnitude less precise than the specified values of V and T(9V/9T)p along any isotherm. Volumetric data are usually not abundant enough to provide measured values of the integrands in Equations (I-3a) and (1-4) for calculating the enthalpy departures for all conditions of interest, and in practice, it is necessary to either interpolate the data, or to fit it to a PVT equation of state. Consequently, the errors introcuded in the calculation of the enthalpy departure stem not only from errors in the basic volumetric measurements, but also from inaccuracies that are inherent in approximate representations of the true P-V-T surface.

9 The fact that P-V-T data are, for engineering purposes, satisfactorily represented by such approximations may at first lead to the deceptively simple conclusion that all other thermodynamic properties may then be calculated to the same degree of accuracy. The deficiencies of some of these formulations with respect to the calculation of thermal properties have been amply illustrated in the literature [24, 182]. The Benedict-Webb-Rubin (BWR) equation of state (20) given by P - RTp + (B RT-A- Co ) p2 + (bRT-a) p3 + aap6 + - [(l+yp2)e Y] (I-12) 0 0 T () has been extensively used in representing the P-V-T surface of pure non-polar fluids. Morsy (182) used both the original and a modified BWR equation of state with 8 and 11 constants respectively to fit the volumetric data for CF4 between 0~C and 350~C and upto 1.6 times the critical density. Tables of derived thermodynamic properties were independently computed over the same range by Harrison and Douslin (97) using their own precise, unsmoothed experimental compressibility data by a combination of analytic and graphical methods. The absolute average deviation in the fit to the compressibility data was obtained as 0.55% and 0.13% respectively for the two empirical equations as monitored by the difference between the calculated and tabulated pressures. Although comparable deviations were also obtained for the configurational free energy, and the entropy, the agreement with the tabulated enthalpy departures were significantly poorer at 11.18% and 2.18%, respectively. In another study involving the origianl BWR equation, Bishnoi [24] determined that both the values of the empirical constants and the goodness of fit with respect to experimental measurements were sensitive to the specific optimization technique employed, the best results being obtained by multiple non-linear regression analysis. It was again noted that even though the compressibility of CO2 from 1000F to 4000F, and up to 4000 psia was represented to better than 0.4%, the fit to experimental heat capacity measurements in the same range using volumetrically derived constants was no better than 6.7%. Simultaneous regression on both properties resulted in only a minor improvement in the

10 representation of heat capacities. These studies suggest that the original BWR equation, widely used for the concise codification of thermodynamic properties, is probably unsuitable for the precise representation of thermal data in the critical and dense fluid regions. Attempts to improve the performance of the equation have involved the addition of a few extra terms [251,254], or the specification of separate constants for the liquid, critical and gaseous regions with the added constraint of smoothness in the thermodynamic properties across the interfaces [76,82]. Other recent attempts to improve the representation of thermal prop erties with a PVT equation of state have required a rather drastic increase in the number of empirical constants used. Jacobsen [115], for example, fitted a 31 constant equation of state to critically selected thermodynamic data for nitrogen with generally good (0.5% or better) results over the entire fluid phase. Nevertheless, the behaviour of the PVT surface in the critical region still appears to be unsatisfactory as deviations of over 60% were obtained with respect to the heat capacity data of Jones [119]. Miyazaki, Furtado, and Powers [179] determined Y in the critical and supercritical region by interpolating the smoothed calorimetric data of Yesavage [284] and from the volumetric data of Reamerr Sage and Lacey [210] using Equation (I-1). The discrepancy between the Y values so calculated averaged to about 28%, with some differences as high as 200%. These differences are particularly significant because the analysis did not require the data in either case to be subjected to the additional constraint of an empirical PVT equation of state. In spite of this precaution, the Y values derived from volumetric data were nevertheless found to be sensitive even to the specific interpolation scheme used. An average Y variation of 6% was traced to differences in the interpolated values for (32z/9T2)p in Equation (I-1) for a given set of z vs T data at some fixed pressure. It was concluded that for the techniques of data interpretation employed in the study, the estimation of volumetric properties from calorimetric data yielded better results than vice-versa. An examination of Equations (1-9) and (I-10) suggest that the calculation of the enthalpy departure as a function of composition,

11 given P-V-T-x data for any system, requires the data to be differentiated not only with respect to temperature, but also with respect to composition. Ellington and Eakin [69] indicate that the interpretation of such data to yield thermal properties could involve a ten to hundred-fold reduction in accuracy, and in conclusion, the authors plead for the acquisition of volumetric data of high (better than 0.02% accuracy) over wide ranges of temperatures and pressures to permit a reliable calculation of PVT derived thermodynamic properties. Thermal Properties from Direct Calorimetric Measurements The arguments so far suggest that thermal properties of fluids, particularly in the critical region, may be more fruitfully obtained by considering other techniques that do not involve the interpretation of volumetric data. Partington and Shilling [190] for example, have reviewed early methods of obtaining the heat capacity both directly and indirectly from a wide variety of measurements involving both static and flow systems including 1) Direct flow calorimetry, 2) Constant volume calorimetry, 3) Heat exchange with the same fluid, 4)Heat exchange with a different fluid, 5) Explosion, 6) Isentropic expansion, 7) Velocity of sound, 8) Resonance, 9) Self-sustained oscillations, 10) Flow comparison, and 11) Molecular spectroscopy. Since then, Rowlinson [222] has outlined methods used in the past half century,. and more recently, McCullough and Scott [158] have published an authoritative compilation of experimental techniques involved in the calorimetry of non-reacting systems in all phases, including the pure saturated fluids. Other reviews on the subject are due to Masi [166], Faulkner [79], Barieau [11], Sturtevant [258], and Yesavage, et al. [286]. These works together encompass a significant body of literature on the subject to which the reader is referred for further information. An examination of the literature suggests that steady state flow calorimetry is to be preferred over static closed system calorimetric techniques for measurements on gases and vapors, because inescapable corrections in the latter case involving the thermal properties of the containing vessel are significant when compared with the relatively low heat capacity of the gas phase. Perhaps the most

12 straightforward technique of flow calorimetry for a system of fixed composition involves adding a known amount of energy to a flowing stream, and monitoring the change in some specified intensive property of the stream, be it temperature or pressure. In the case of fluid mixtures, the technique of flow calorimetry may also be utilized to measure the enthalpy change on mixing the constituent pure components at some specified T and P. If the enthalpy H. of each of the constituent pure components is also known at the same T and P, then the mixture enthalpy H may be calculated from the thermodynamic relation n Hm i xiH + H (1-13) i-i=1 where x. is the mole fraction of component i, and H is the heat of mixing. This technique has two notable advantages. Firstly, if the pure component enthalpies can be accurately specified at the given T E and P, then even relatively crude measurements (5-10%) on H can serve to provide fairly accurate estimates of H, because the mixing effect, H, with the notable exception of the critical and the two phase region, is usually a small fraction of the total contribution of the right hand side of Equation (1-13). Secondly, relative adjustment of the flow rates of the constituent pure components is easily accomplished so that the technique provides for the rapid specification of H as a function of composition at any given T and P, unlike flow m calorimetry at fixed composition. There are, however, two important limitations. Firstly, the application of the technique to exothermic mixing situations also requires the heat capacity of the mixture to be known over the interval of the temperature rise [100], unless the heat generated can be removed isothermally. Secondly, such calorimeters are usually operated in the single pass mode, in view of the impracticability of regenerating the pure components on a continuous basis. The rapid consumption of feed materials is a significant drawback, and has served to limit such investigations to relatively inexpensive systems. These considerations suggest that if thermal property measurements on mixtures are to cover a wide range of conditions, they may be more economically

13 acc(omplished using a flow calorineter in a recycle system at fixed conmposition. Thermodynamics of a Shielded Flow Calorimeter We now discuss the thermodynamics of a flow calorimeter with a heat shield typical of that used in this work to illustrate exactly how thermal properties may be specified from such measurements for a system at constant composition. A schematic of the calorimeter is shown in Figure (I-1) below SURROUNDING TEMP. Tb Tsi Tsf 1 r~ —1 Ti. I~Tf. PfP O I L, __. J L I inlet Calorimeter Outlet Shield Shield Figure I-1. Direct Flow Calorimeter - Schematic. If 6m. and 6m are the quantities of mass transferred across the inlet 1 f and the outlet of the calorimeter respectively, in some time period 6(, an energy balance across the calorimeter in the absence of specially impressed force fields yields (U. + Pi + 2 Vi + g6mz - (6 f + PV f + V2 + gzf) 6mf + Q 6W - (I-14) ~ -- ~vi -2 fgz =2/ _ where U is the specific internal energy of the flowing stream V is the specific volume of the flowing stream v is the velocity of the flowing stream z is the elevation 6Q is the net heat transferred to the calorimeter in time 66 6W is the work obtained from the calorimeter in time 60 (2/F-) is the net change in the total energy of the calorimeter in time 66. Converting (1-14) into a rate equation, and substituting (U + PV) by H, we obtain

14 (H i + gzii - (f + vf zf)ff + 2q - ( (I-15) Q11~~~-1i 2+ +z Vg f fq dsystem For steady state mass flow i f (I-16) Furthermore, neglecting changes in velocity and elevation between the measurement points, we obtain the simplification [ - - ( ) ]/ (-17) system The simplification of Equation (1-17) is valid for the calorimeters of Faulkner [79], and of Mather [168] that are used in this work. In each case, the difference in elevation between inlet and outlet conditions is less than 6 inches, and the resultant head effect is -7 less than 10 Btu/lb. Variations in velocity arise from density changes caused by a pressure drop or a change in phase across the calorimeters. The upper limit of this effect is of the order of 0.002 Btu/lb., and occurs in the case of a liquid inlet and vapor outlet. Referring to the model schematically presented in Figure (I-1), the calorimeter is permitted to exchange heat with the surrounding bath at temperature Tb. The calorimeter is divided into two isothermal components at Ti and Tf respectively, each provided with a separate heat shield at temperature Tsi and Tsf respectively. The shield is in each case interposed between the calorimeter and the bath. The net rate of heat transfer to such a shielded calorimeter is given by q = hiAi (Tsi-Ti) + hfAf (Tsf-Tf) (I-18) where h and A represent the average heat transfer coefficient and the interfacial area for heat transfer respectively. If electrical energy is supplied at the rate EI to the outlet section of the calorimeter, where E is the voltage, and I is the current, then w -E (1-19)

15 As the bath temperature Tb for the calorimeters of this work is essentially maintained at the inlet temperature Ti, there is no need for a shield at the inlet section. For non-isothermal operation, the shield at the outlet section is wrapped with heating wire, the power to which is adjusted until a differential thermocouple between the shield at the outlet section, as monitored by a lamp and scale mirror galvanometer, indicates zero temperature difference. In such cases, the energy generated at the "guard heater" is in theory completely transferred to the bath and q is essentially zero. If a sufficient time period is allowed to elapse after the input of power to the outlet section, the calorimeter will reach its final energy state for any steady state process occurring within. Thus, at steady state d (/dO = 0 (1-20) Under the above restrictions, Equation (1-17) reduces to the form H -H E I TfPf [x] Ti,Pi [x] m (1-21) where Ti, Pi, Tf, Pf, [x], El, and m are all experimentally accessible quantities. Determination of Enthalpy Derivatives by Flow Calorimetry It is possible to obtain specific information on the enthalpy derivatives with respect to temperature or pressure by controlling the operating path of the flow process in the calorimeter. As H is a point function of state, Equation (1-17) may be rewritten as [ H - H _ ElI [H -x ] +[H -H ] El (1-22) Pf, [x] Pi,[] T Tf, [x] Ti [x] Pf m In the absence of unnusual force fields, the differential enthalpy change dH may be given by the exact differential equation aH an n DH dH - ( dP +(-) dT+ ( dwF (1-23) T,[x] P,[x] ill i T,P,w where dw. is a change in the mass of component i. For a system 1

1.6 at constant composition Equation (1-23) may be rewritten as dH = dP + Cp dT (-24) By combining Equations (1-22) and (1-24) we obtain P T f f P ()i dP + (Cp)p dT - EI/m (1-25). Ti f Equation (1-23) and hence (1-25) are valid only when all the enthalpy derivatives in the equations are continuous. This condition is not met for measurements across the saturation boundary in a pure component. In such a case it is necessary to use the more general form P T P T L V V ()T dP + (Cp) dT + AH + dT - EI/d (1-26) P i Ti f P i T f i T i S s where AHV is the enthalpy of vaporization at Ts and Ps. In examining Equation (1-25) we observe that the operation of the calorimeter may be specified so as to enhance the contribution of one term with respect to the other. In isobaric operation, for example, the pressure drop across the calorimeter is made as small as possible so that the electrical energy input is used mainly to raise the temperature of the fluid, and provides us with an integral average of Cp over the temperature range Ti through Tf. In the calorimeter developed by Mather [168], a sizable pressure drop is induced by directing the fluid through a capillary coil of fixed length and diameter. An insulated heating wire coaxial with, and inside the capillary supplies an adjustable quantity of heat to maintain the outlet temperature Tf as near as possible to that of the inlet at temperature T.. Thus, no heat shields or guard heaters are necessary. In cases where a pressure drop causes a rise in temperature in the fluid, the removal of energy required for isothermal operation cannot be accomplished by the above technique. It is then necessary to operate the calorimeter in the isenthalpic mode. In this case, no electrical energy is added to the calorimeter, and the guard heater is activated to compensate for the heat leak at the outlet section of

17 the calorimeter. Equation (I-21) simplifies to yield Tf Pf, [] Ti Pi [X] (I-27) For this case, Equation (1-25) also simplifies to Tf P f (Cp)p dT = - ()T dP (-28) P.1 or (Cp)p ( Tf- T) -( i ( Pf - P (I-29) f where Cp and 4 are the equal area mean values of the derivatives Cp, and 4 over the appropriate intervals. Therefore, Tf - T f -P T -() /(Cp) - (1-30) Pf - P Ti f Thus, the measurement of the temperature and pressure at the inlet and the outlet of the calorimeter defines P, the mean adiabatic JouleThomson coefficient for the fluid, for the specific isenthalp generated across the calorimeter.

Chapter II LITERATURE REVIEW OF EXPERIMENTAL AND CORRELATED DATA Chapter I was concerned with illustrating how classical thermodynamics may be utilized in specifying the thermal properties of substances from experimental measurements. This section is devoted to the examination of the literature for information that is relevant to the description of the thermal properties of those systems which are to be experimentally investigated in this work. These include pure ethane, ethane-propane, and the methane-ethane-propane system. As a major goal of this work involves the use of constituent pure component and binary data to predict the enthalpy of the ternary mixture, the experimental measurements for other subsystems of the methane-ethane-propane system are also reviewed. A brief account of recent calorimetric measurements on other systems of interest is also added. a) General Reviews -Masi [166] has reviewed heat capacity measurements upto 1954 for ten industrially important gases. Mage [161], Mather [168], and Yesavage et al. [286] have since then summarized available heat capacity, isothermal and adiabatic Joule-Thomson coefficient, and enthalpy of vaporization data on both pure and mixed systems. Excess enthalpy measurements on binary mixtures have been tabulated by Hejmadi [100]. Katz and Rzasa [124] have prepared a bibliography that provides general information on the experimental and correlated thermodynamic properties of hydrocarbons upto 1945. This work has been extended to cover the literature upto 1960 by Muckleroy [183]. The American Petroleum Institute [5,6] has since then compiled thermodynamic data sources for pure and mixed hydrocarbons. More recently, Clark et al. [48] have reviewed the volumetric, thermal and transport property measurements for systems of industrial interest that liquefy at cryogenic temperatures. b) Methane A compilation of thermodynamic properties including a comprehensive 18

19 literature search is presented by Tester et al. [264]. A bibliography that includes the thermophysical properties of methane in all phases has recently been prepared by the Cryogenics Data Center of the National Bureau of Standards [52]. The comprehensive isobaric enthalpy measurements of Jones [119] extending from -2400F to 50 ~F and from 150 to 2000 psia, and the volumetric data of Vennix [273] and Douslin et al. [67] deserve special mention for their excellence. c) Ethane i) Compilation of Thermodynamic Properties. Compilations on the thermodynamic properties of ethane have appeared since 1935, when Plank and Kambeitz [199] prepared a Mollier diagram in the range -100~C to 32~C, and from 0.5 to 50 kg/cm2. In 1937, Sage, Webster, and Lacey [234] prepared V, f, H, and S tables for ethane ranging from 70~F to 2500F, and upto 3500 psia. These tables were later extended to 4600F and upto 10,000 psia [209,232]. Similar tabulations covering the range from -2200F to 7000F and upto 1500 psia, but excluding the compressed liquid region were later prepared by Barkelew, Valentine and Hurd [12], in which the thermodynamic properties of the superheated gas were calculated by fitting the volumetric data upto 1947 by the BWR equation of state. The compilation of Tester [264] contains, in addition, a comprehensive and critical discussion of the measurements obtained upto 1957. Since then, Canjar et al. [39] have published thermodynamic property tables derived from the BWR equation of state and covering the range 180K to 1500K and upto 500 atm. [38]. Joffe and Delaney [116] have calculated Cp values from volumetric data in the range 313K to 973K and from 33 atm. to 680 atm. also using the same equation of state. A comprehensive bibliography of the thermophysical properties of ethane upto 1968, covering both experimental measurements and compilations has been prepared by the Cryogenics Data Center [51]. The most recent compilation (1971) is due to Eubank [75], in which the configurational properties of ethane including the enthalpy and heat capacity departures are computed principally from volumetric data using separate sets of BWR constants to fit the liquid, critical and gaseous regions. The compilation covers the range 180K to 540K

20 with pressures upto 500 atm. Significantly, the tabulated compressibility factors reproduce the apparently superior data of Michels and co-workers [171,172,174] to within 0.1% except near the critical region [82]. The compressibility factors and the enthalpy departures were also compared with those of Barkelew et al. [12], Canjar [39], and Tester [264], at 300K, 400K, and 500K, and upto 500 atm. The agreement in z between all sources was exceptionally good with rare discrepancies beyond 1%. The agreement in H - H~ was found to be less satisfactory. The span of the tabulated values at any given T and P was rarely below 1%, and rose to about 4% in the critical region with the magnitude of Tester's and Eubanks values lying consistently above and below the mean, respectively. ii) Direct Thermal Property Measurements. Some direct measurements of the thermal properties of ethane are available in the literature. Tsaturyants [269] obtained adiabatic Joule-Thomson data on ethane from 10-400 atm. and from 320K to 450K. Similar measurements have been reported by Sage, Webster and Lacey [254] from 70"F to 2200F with an estimated accuracy of 2%, and by Stockett and Wenzel [255] from -40~F to +45~F, at pressures extending upto 600 psia in each case. The measurements in the first case also include Cv data in the vicinity of the critical isochore from 600F to 140~F, the accuracy of which is estimated at 2%. Other direct measurements of the heat capacity in the fluid phase have been primarily confined to the liquid along the saturation curve, and the gas phase at and below 1 atm. The data of Eucken and Hauk [77] from 80K to 300K, of Wiebe, Hubbard, and Brevoort [277], from 67.4K upto the critical point, and of Witt and Kemp [280] from 90K to the normal boiling point of 184.1K lie in the first category. The results of Eucken and Hauk are suspected to be poor as they are between 9 and 25% higher than the results from the other two investigations which are mutually consistent to 0.8%. Flow calorimetric measurements on the heat capacity in the gas phase at or below 1 atm. have been obtained by Scheele and Heuse [236] from 193K to 298K, by Thayer and Stegeman [265] from 273K to 338K, and by Dailey and Felsing [56] from 340K to 700K. The

21 spectroscopic data of Smith [267], the thermal conductivity apparatus of Kistiakowski and co-workers [129,130], and the velocity of sound measurements of Dixon, Campbell and Parker [64], have all been used in the calculation of zero pressure heat capacities. Nevertheless, Tester [264] has suggested that the statistical calculations of Cp" by Rossini [220] are to be considered superior to the values derived from experimental data. Apart from the relatively imprecise data (4%) of Dana, et al. [57] from 233.5K to 271.7K, and the single but reliable value of Witt and Kemp [280] at the normal boiling point, direct measurements on the enthalpy of vaporization are scarce. Barkelew et al. [12] and Eubank [74] have tabulated enthalpy of vaporization values as a function of temperature by making use of a closed enthalpy cycle involving the single experimental value of AHv at the normal boiling point, the enthalpy change for both the ideal gas and the liquid along the saturation curve between the normal boiling point and the temperature of interest, and the enthalpy departure for the saturated vapor at the two temperatures, as shown in Figure (11-1) below: Vapor Pressure Tc, Pc Curve HP IH X(H2 - H = (H - )+(H -H) - (H2 -H) 2 — H 2 2 1 222 I 2 1 //8z / Z As ST + O AHV (T2,) = AH(T1,P1) + (H - H) + (H2 - H) [ iH1 H + (Ho - H - 1 1 2 H1) 0 0 T Figure II-1. Enthalpy Cycle for the Calculation of AH as a Function of Pressure. An independent calculation of AH at the normal boiling point by Porter [201] using vapor pressure and saturated volume measurements in conjunction with Equation (1-6) yielded a value that was about 5% lower than the measured result of Witt and Kemp [280].

22 iii) Additional Measurements. Recent investigations on ethane not included in the earlier bibliographies consist of the second and third virial coefficient measurements of Pope [200] from 206K to 307K, the vapor pressure measurements of Carruth [42] from 91.3K to 144.1K,.and the saturated liquid density data of Shana'a and Canfield [239] at -165~F, and of Sliwinski [246] between 283.15K and the critical point. iv) Conclusions. An examination of the literature reveals that the thermal properties of ethane in the critical region are not as yet adequately defined from existing measurements. Ultrasonic velocity measurements in the critical region have been obtained by Noury and co-workers [186,187] and by Tannenberger [261]. In the latter case, the results were used to calculate Cv from 31.5~C to 40~C and from 100 to 200 amagats using the relation Cv - ('~- i) < ) pi a' + ( ) ] 1 T where z is the velocity of ultrasound. The accuracy of these calculated results have not yet been established, and await comparison with direct measurements. The absence of thermodynamic property tabulations for the subcooled liquid region is also noted. The measurement of the enthalpy change as a function of temperature and pressure in this area would be very useful in filling the gaps in existing compilations. Accurate enthalpy of vaporization measurements at higher pressures, and particularly in the vicinity of the critical point are also seen to be necessary. d) Propane A compilation of the thermodynamic properties of propane including an extensive bibliography has been presented by Kuloor et al. [135]. A temperature-pressure-enthalpy table has since been prepared by Yesavage [284] making extensive use of his own excellent calorimetric data from -2400F to +3000F and upto 2000 psia. Ernst et al. [72,73] have also reported low pressure Cp measurements upto 14 kg/cm3. The

23 estimated accuracy of the data is better than 0.5% in each case. e) Methane-Ethane i) Bibliographies and Experimental Data. A bibliography of the thermophysical properties of mixtures containing methane, prepared by the Cryogenics Data Center [53], contains a list of the data sources relevant to this system. Clark et al. [48] have defined existing sources of experimental and correlated thermodynamic data on a series of P-T plots. Michels and Nederbragt [173] have obtained excellent volumetric data on four mixtures ranging from 20 to 80 mole percent ethane from O0C to 50~C and upto 60 atm., including some data in the two phase region. Sage and Lacey [231] have also reported volumetric measurements on several mixtures extending from 700F to 460~F and upto 3000 psia. Morlet [181] has measured liquid densities at -183~C and 1 atm. throughout the composition range, and concluded that there was negligible volume change on mixing under these conditions. Interaction second virial coefficient data extending from 298.15 to 373.15K have recently been obtained by Dantzler et al. [59]. In what must be considered as the most extensive investigation of this system, Bloomer and co-workers [25] have obtained P-V-T-x data for mixtures ranging from 15 to 70 mole % ethane between 140K and 300K, and from saturation conditions upto 300 atm. The critical locus, and the dew and bubble point temperatures above 100 psia were also determined for mixtures containing between 2.5 and 95% ethane. Phase equilibria data were also obtained by Price and Kobayashi [207] from -2000F to +50~F at pressures above 100 psia, by Ruhemann [229] from 5 to 20 atm. between 143K and 236K, and by Levitskaya [156] from 30 to 40 atm., and between 177K and 188K. The agreement between the data of Price et al. and Bloomer et al. is good. The data of Ruhemann are, however, seriously inconsistent with the results of Bloomer et al. particularly near the critical region [70]. Wichterle and Kobayashi [276] have recently obtained additional phase equilibria measurements to supplement the earlier work of Price and Kobayashi. Adiabatic Joule-Thomson data accurate to + 3% were obtained by Budenholzer, Sage, and Lacey [34] for mixtures containing between 23 and 76 mole percent ethane over the range 70~F to 300~F, and

24 upto 100 atm. More recently, the variation in the enthalpy of the gaseous phase as a function of pressure was investigated for three well spaced mixtures containing from 26 to 77 mole percent ethane by Alkasab [4], over the temperature range from -59"F to +35"F and for pressures upto 950 psia by isothermal and adiabatic flow calorimetry. The estimated accuracy of the results is better than 1.5%. ii) Compilations of Thermodynamic Properties. Sage and Lacey [232] have derived thermodynamic properties including the enthalpy departures for the methane-ethane system using principally their own volumetric measurements. The tabulated compressibility factors at 70"F were since found by Berry and Sage [21] to be inconsistent with the more accurate results of Bloomer et al. [25] by as much as 10%, in some cases. Houser and Weber [109] have prepared an enthalpy composition diagram for saturated liquid mixtures using the data of Bloomer et al. [25] in conjunction with the BWR equation of state and a graphical procedure for differentiating mixture enthalpies. The authors have indicated some of the deficiencies of their technique which suggest that an appreciable loss of accuracy occurs in the transformation. Alkasab [4] has prepared an enthalpy diagram over the limited range of the measurements obtained for each mixture investigated. iii) Conclusions. The existing data and the correlated enthalpies for this system have been closely examined, as it was originally intended to use these results to define the binary interaction parameters for the methane-ethane system for later use in predicting the enthalpy of the ternary methane-ethane-propane mixture. It was concluded that the existing compilations, with the possible exception of the results of Alkasab, cannot provide enthalpy values that are comparable either in accuracy or extent to those obtained from direct calorimetric measurements at the TPFL at the University of Michigan. f) Ethane-Propane The experimental measurements for this system upto 1963 are

25 summarized in a bibliography by the American Petroleum Institute [5,6]. Considerable effort has been directed towards the determination of the phase equilibria. Price and Kobayashi [207] have reported measurements at 0~F and 50~F respectively. Mlatschke and Thodos [169] have obtained data at higher temperatures along isotherms between 100~F and 200~F and from 200 psia upto the critical pressure. Special emphasis was placed in specifying the vapor-liquid equilibria in the critical region. These measurements are complemented by the low temperature data of Djordjevich [63] extending from -230"F to 0~F, and from 0.1 mm Hg to 218 psia. The reported equilibrium compositions at 0~F and 100 psia are in agreement with the results of Price and Kobayashi to within 2%. Volumetric measurements on this system are scarce, and are limited to the saturated liquid density data of Shana'a and Canfield [239] at -165~F, for mixtures containing 27% to 81% ethane, and to the gas phase second interaction virial coefficient determinations of Dantzler et al. [59] from 298.15K to 373.15K. Direct calorimetric measurements have not as yet been attempted. The absence of experimental or correlated enthalpy data for the system suggests that its investigation at the present facility would be necessary to establish the required binary interaction parameters for the prediction of the enthalpy behaviour of the ternary mixture. g) Methane-Propane The thermodynamic properties of this system have been extensively reviewed by Mather [168] and later by Yesavage [284], with special emphasis on thermal properties and phase behaviour. Of particular interest to this work is the vast body of isobaric, isothermal, and isenthalpic flow calorimetric measurements on five mixtures containing 94.9, 88.3, 72.0, 49.4 and 23.4 mole percent methane respectively, over the temperature range from -240 F upto 3000F and from 100 psia to 2000 psia obtained in a series of investigations [162,168,284] at this facility. In each case, P-T-H diagrams were constructed for the individual mixtures over the range of the data, and including the two phase region. Smoothed values of Cp, and B are also reported at conditions appropriate to the operating mode of the calorimeters

26 at the facility. In addition, a temperature-enthalpy diagram was constructed for the 94.9% mixture [22] as already explained in the Introduction. Recent measurements not covered by previous reviews include the phase equilibria data of Wichterle and Kobayashi [276] from -225~F to 750F and between 500 psia and the cricondenbar, the saturated liquid density data of Shana'a and Canfield [239] at -165~F, and the second interaction virial coefficient measurements of Dantzler et al. [59] from 298.15K to 373.15K. It appears that the interpretation of the existing enthalpy data may be sufficient to define the necessary methane-propane binary interaction parameters. Consequently, no further investigation of this system is planned in this work. h) Methane-Ethane-Propane The phase equilibria for the system have been investigated in depth by Price and Kobayashi [207] to cover the range from -2000F to 50~F and upwards of 100 psia. Recently Wichterle and Kobayashi [276] have obtained additional measurements from -59.5~F to 115~F and upto 725 psia. Rutherford [230] has determined the location of the liquid-vapor phase boundaries for the system as a function of composition and pressure at 1100F. Adler et al. [1] and Chueh and Prausnitz [47] have correlated the data of Price and Kobayashi using the Redlich-Kwong equation, the interaction constants for which were defined from constituent binary vapor-liquid equilibria data. The correlations differ primarily in the algebraic form of the function used to represent the activity coefficients in the liquid phase as a function of composition. Liquid density measurements at -1610C and -1820C have been reported by Morlet [181] for mixtures containing 5 and 10 mole percent propane, and varying amounts of other components. It was noted that while the three components were completely miscible at these temperatures, the further addition of butane could lead to the formation of two liquid phases. Very accurate measurements were also reported for two ternary mixtures at -1650~C by Shana'a and Canfield [239]. Both investigations confirm that the assumption of ideal mixing at the indicated

27 temperature can provide better estimates of ternary mixture densities than the principle of congruence. Direct thermal property measurements are virtually unknown with the exception of some unpublished data obtained at CB & I [138] using a boil off calorimeter. The investigation was concentrated in the range - 240~F to +125~F and upto 50 psia, although some measurements were obtained at higher pressures upto 500 psia. i) Recent Calorimetric Measurements on Other Systems of Interest A wide variety of calorimetric measurements on many classes of substances have been presented at the First International Conference on Calorimetry and Thermodynamics at Warsaw (1969) and suggests that the use of flow calorimetry for the direct determination of thermal properties is becoming increasingly popular. Balaban [9,10] has used the heat exchanger method for the determination of Cp ratios for nitrogen in the range -20"C to +60~C and upto 2000 psia, for trifluoromethane from 220C to 600C upto and slightly beyond the critical density, and also for two mixtures composed of these components. Bishnoi [24] has used a similar technique for nitrogen in the range 60 to 1500C and upto 2250 psia, and for two binary mixtures of methane and carbon dioxide containing 14.5% and 42.5% methane respectively from 40~C to 150~C with an estimated accuracy of better than 1%. Jacobsen and Barieau [114] have developed a double heat exchanger method to determine the heat capacity of a single phase helium-nitrogen mixture at room temperature and upto 300 atm. in terms of the heat capacity of the pure components at the same conditions. A heat exchange flow calorimeter that measures the energy used to cool natural gases by monitoring the rate of vaporization of liquid nitrogen has been designed by Laverman and Selkukoglu [139]. The device operates at temperatures from 100~F to -3100F and upto 2800 psia and measures isobaric enthalpy changes within + 1%. Francis, McGlashan and Wormald [83] have developed a vapor flow calorimeter with adjustable throttle for the measurement of (dH/dP)T. The authors report experimental results for benzene below 1 atm. over the range 330K to 403K. These low pressure measurements were processed to yield values of the temperature derivative of the second virial

28 coefficient using the thermodynamic relation dH d(B/T) (II-1) T. Pro dT (II-1) (1) = dT T, P-+o where B is the second virial coefficient. The recent resurgence'of interest in the heat of mixing can, in part, be ascribed to the need for measurements that are particularly sensitive to mixture theories. A complete review of such data is beyond the scope of this work. An important contribution is due to Monk and Wadso [180] who constructed a flow calorimeter for the measurement of both exothermic and endothermic heats of mixing, which was improved later by Goodwin and Newsham [90] to permit rapid measurements. Hejmadi [100] has recently developed and tested an outstanding flow calorimetric facility for measurements in the gaseous phase upto 1000 psia. The systems investigated include nitrogen-carbon dioxide, nitrogen-ethane, and nitrogen-oxygen with a reported accuracy of better than 2%. The flow calorimeter of McGlashan and Stoeckli [160] and the isothermal displacement calorimeter of Marsh, Stokes and coworkers [78], which directly measures the partial molal enthalpy of mixing of infinite dilution are some of the other noteworthy developments. Other measurements from existing facilities include the Cp data of Ernst and Busser [73] at pressures upto 14 kg/cm3 for propane, i-butane, and a number of fluoro and chloro substituted methanes from 20 C to 80 C. Maurer [170] has added a throttling calorimeter to the facility at Karlsruhe and obtained Cp and p data on propylene to accuracies of 0.1% and 0.5% respectively from 25 to 125~C and upto 120 bars including the critical region. These results are in good agreement with the tabulations of Michels et al. [175] derived from P-V-T data. Subramanian, Kao, and Lee [259] have made a number of thermodynamic and transport property measurements on natural gas mixtures including phase equilibria, isobaric, and isothermal calorimetric determinations over the range -240~F to +200~F.

Chapter III SELECTION OF A METHOD FOR REPRESENTING AND PREDICTING PURE COMPONENT ENTHALPIES The first step in attempting to predict multicomponent enthalpies from constituent pure component and binary data is to select a framework for representing the constituent pure component data which has in large measure the desirable attributes of being concise, accurate, wide ranging, and universal. This section evaluates several schemes of both theoretical and empirical origin with special emphasis on the principle of corresponding states. The theoretical counterparts of empirical corresponding states schemes are stressed to enhance our insight into such techniques. A) Equations of State - Theoretical Although classical thermodynamics is a powerful tool in establishing the connection between different equilibrium properties, it cannot of itself determine why a particular property should have a certain numerical value at some fixed temperature and pressure, or how equilibrium property measurements on one fluid can be used to calculate those of another. If the dynamics of a real system can be accurately described at the microscopic level by molecular physics, then, statistical thermodynamics permits this information to be scaled up to yield a macroscopic description of the same system. In the initial stages, the engineering applications of statistical thermodynamics were primarily restricted to the prediction of intramolecular properties, i.e., the properties of isolated non-interacting molecules. lMore recently, the discipline is being actively applied towards the calculation of configurational properties, i.e., the properties that depend only on the interaction between two or more molecules. Some of these developments are discussed below. i) The Gas Phase. One of the earliest, and perhaps the best known applications of statistical mechanics to the calculation of configurational properties is provided by the virial equation of state which expresses the compressibility z as a power series expansion 29

30 in inverse volume about the ideal gas PV 1 + B(T) + CV(T) D+ (T) +(-i) NkT V (III-1) where k is the Boltzman constant; and the coefficients B,C,D etc. of the expansion terms are only functions of temperature. Thermal properties may be calculated from Equation (III-1) using the equilibrium property interrelationships of classical thermodynamics. The isothermal throttling coefficient, and the heat capacity departure have been expressed to the first and second order terms respectively in inverse volume [158,167] as ( ) = -(B-TB')+[2B2-2TBB'-2C+TC'- o B"(B-TB')] (III-la) dPT Cp V Cp-Cp= ( -RB" ) + R[(B-TB')2-C+TC'- TVC"] + 2 V 2 (V( + 22V) (Ill-lb) where B' = dB/dT, B" = d2B/dT2 C' = dC/dT, C" = d2C/dT2 The statistical mechanical derivation of the virial equation [167] establishes its applicability to any non-ionized gas, polar or nonpolar. Essentially, the interaction between N bodies is expressed as a series of interactions involving a progressively increasing number of molecules. The second and third virial coefficients B and C, for example, represent deviations from ideality for two and three body interactions, respectively. The virial coefficients can be empirically obtained using wide ranging compressibility data on a given substance, or else, they may, in principle, be calculated from statistical mechanics if the intermolecular forces can be specified. Thus, the second virial coefficient for interactions between spherically symmetric molecules can be rigorously obtained [167] as B N [1 - exp( -uij(r)/kT) 4rr2dr J [1 -u ]k (III-2) where u. (r) is the intermolecular pair potential between molecules i and j, separated by a distance r. The calculation of higher order

31 virial coefficients is obtained in similar fashion [167], but requires the intermolecular potential between three and more molecules to be first specified. This is a difficult problem, and mathematically tractable results in such cases are obtained by making the assumption of pairwise additivity, which requires the intermolecular energy of any arbitrary configuration to be further simplified so as to be expressed as a sum of pair potentials u ( r1.... rN ) (1113):>j ii) Determination of the Pair-Potential Function. From a purely phenomenological standpoint, the fact that gases condense to liquids suggests that intermolecular forces must be attractive at large separations, at least in the average sense. On the other hand, the fact that liquids resist compression indicates that forces at small separation must be repulsive and probably steeply so. In spite of considerable advances with respect to the nature of intermolecular forces in real substances [107,111], the stipulation of the pair potential function from a priori quantum mechanical calculations of the interactions between the electron shells of a given molecular pair is again an intractable problem for all but the simplest molecules such as hydrogen. Mason and Spurling [167] discuss efforts to obtain u..(r) from 13 second virial coefficient data by inversion of Equation (III-2), and have also found them to be unsuccessful. The failure of such direct approaches have led to the common procedure of specifying a microscopic model, i.e., a mathematical expression for the potential energy as a function of interaction distance with undetermined constants, then calculating some macroscopic property (usually the second virial coefficient) in terms of these constants, and lastly specifying these constants by optimizing the agreement with experimental measurements on the same macroscopic property. The model thus determined can then be tested for its ability to predict other properties such as: 1) Second virial coefficients in a different temperature range

32 2) Third virial coefficients 3) Transport coefficients of dilute gases (coefficients of viscosity, thermal conductivity, diffusion, and thermal diffusion) 4) Crystal properties (such as lattice spacing, heat of sublimation, mechanical constants). Perhaps the simplest model which attributes both a size and an attractive force to molecules is the square well potential shown in Figure III-la. This consists of ahard core of diameter C surrounded by an attractive potential well of depth ~, which specifies the minimum energy corresponding to the equilibrium separation, and extends from a to g a: u(r) = 0 r < u(r) = - a < r < g (II-4) u(r) = 0 r > g a For this simple case, the second virial coefficient is obtained from Equation (III-2) as 2TN (3_ (e/kT_l) (III-4a) B(T) = -l [1- (g - 1)(e ]( A more generally useful model which includes the effect of repulsive forces is the Mie potential (Figure III-lb) given by u(r) = m ( m )m-n (a )m (a)n] (11-5) m-n n r r where m and n are the exponents on the repulsive and attractive terms, respectively. Here a is the distance parameter corresponding to the intermolecular separation when the potential energy is zero as sketched in Figure (III-lb). Quantum mechanical calculations lead to the value n=6 for the principle attractive Van der Waal potential contribution for non-polar spherical molecules [153]. For the repulsion, it is found empirically that m=12 corresponds reasonably well with the actual molecular repulsion for rare gas atoms [167]. For this special case, Equation (III-5) reduces to the well known Lennard-Jones 6-12 potential function. The second virial coefficient for this potential function is known to reproduce the principal

33 (a) Square Well (b) Lennard-Jones Potential Potential 0" I r-r Z ar F I F c Figure III-1. Simple Models for Representing Intermolecular Forces Between Real Fluids.,(a) Dilute Gas (b) Dense Fluid 2 2 - v o/ I II Q. J~,,1 1 2 3 1 2 3 r/o r/lo Figure III-2. The Radial Distribution Function for Real Fluids - Schematic.

34 features of experimental data for non-polar molecules over a wide temperature range, and accounts for its popularity. Computations on higher order virial coefficients upto the fifth are available, but the calculations even with high speed computing machines become progressively more difficult [167]. iii) Dense Fluid Theories. The poor convergence of the virial equation in the dense fluid region and its inability to account for the liquid-vapor phase transition has led to an alternative approach that uses the precise description of the spatial distribution of molecules for the purpose of constructing a statistical theory of matter. An important quantity in this connection is the pair distribution function which is defined as the deviation from randomness in the probability of finding two molecules simultaneously in two specified volume elements. The deviation from randomness is, of course, caused by the potential field between the molecules themselves. For spherically symmetric systems it is more convenient to use the radial distribution function g(r) which is the factor by which the "local density" pg(r) at r deviates from the bulk density p. Figure III-2 shows the typical behaviour of g(r) as a function of the distance r from a central molecule in the dilute gas and the liquid region for the potential specified. At large separations, the interaction between molecules is feeble, and consequently g(r) approaches unity. approaches unity. For non-interacting molecules, i.e., for an ideal gas g(r) is unity everywhere. If a molecule of diameter c is impenetrable, then no other molecules would be observed at r < c and consequently g(r) approaches zero in this range. We can also expect g(r) to rise as u(r) becomes negative, reaching a maximum at the position of minimum energy, i.e., at the base of the potential well which is the position of maximum stability. For close packed impenetrable molecules in the liquid phase, g(r) can be expected to show damped oscillations about one molecular diameter apart. Unlike the potential function u(r), g(r) varies also with temperature and density. Although the radial distribution function is a measure of fluid

35 structure, it is primarily of interest in statistical mechanics because the thermodynamic functions of the fluid can be expressed in terms of it. In particular, the configurational energy U, the configurational heat capacity at constant volume Cv, and the equation of state for spherically symmetric molecules are respectively given by 1 N 2V u(r) g(r,p,T) 4aTr2dr (III-6) Cv u(r) ) 4 r2dr ( -7) PV 1 N NkT' 6 kTV r A(r g(r,p,T) 4r2dr (-8) dr (111-8) The proofs of Equations (III-6) and (111-8) are lucidly derived by Hill [105], aind Reed and Gubbins [212] and are exact for spherical molecules with pairwise additivity. "lore general expressions including orientation effects are also indicated by Hill, but their complexity has prohibited their use in practical calculations. In addition to Equation (III-8), there is another independent equation which relates the equation of state to the pair distribution function and is given by [212] kT[ ) - - [g(r,p,T) - 1] 47Tr2dr (III-9) This equation is termed the "compressibility" equation. Given the assumption of pariwise additivity, the consistency between the results obtained from the two equations is a measure of the correctness of the estimated value of g(r,p,T) for the specified potential function. If g(r) is characterized by short range order, as in liquids, then we can expect the integrals in the above equations to converge rapidly, in contrast to convergence problems exhibited in the application of the virial equation to dense fluids. iv) Determination of the Radial Distribution Function. Even if the constants E and o for some specified potential function u(r) have been obtained, for example, from second virial coefficient data, the calculation of thermodynamic properties in the dense fluid requires

36 an accurate estimate of the radial distribution function; a quantity that itself varies with distance, density and temperature. Although this is a task of prohibitive difficulty, there are basically three techniques used for estimating g(r). 1) Computer Techniques: If the pair potential is specified precisely, then g(r) can be obtained by a computer simulation of a model assembly. In the molecular dynamics technique prescribed by Alder and co-workers [2,3], the detailed trajectories of an artificial system of a small number of particles, usually from 30 to 500, are calculated by the numerical solution of the equations of motion for each particle. The molecular distribution is followed with time until a state of equilibrium with respect to both position and velocity is achieved. Thermodynamic properties such as U,T and P are found by computing mean values of the potential energy, kinetic energy and the mean momentum carried across a plane per unit time. The Monte Carlo technique is similar but instead involves an ensemble averaging process [222]. Extensive calculations of this kind have been made for hard spheres and for Lennard-Jones 6-12 molecules [2,3]. The reliability of such procedures is established by their excellent agreement (within 2%) with independently calculated virial coefficients for the hard sphere case [215]. The accuracy of the calculations for Lennard-Jones molecules are, at present, not sufficient to permit good estimates of the vapor pressure to be obtained [227]. Nevertheless, such calculations are valuable in assessing the validity of various approximations that must be made in order to compute macroscopic properties from microscopic situations using statistical mechanical techniques without encountering the inevitable uncertainty involved in applying such calculations to real systems for which the potential function is usually only approximately defined. 2) Experimental Measurements: X-rays or neutrons can be scattered in their passage through a fluid specimen creating a diffraction pattern which is the sum of interference effects from molecular pairs. The intensity of the scattering pattern is a function of the difference between the actual spatial ordering and a random distribution. The

37 quantitative relationships between the two have been summarized by Rowlinson [226]. An interesting feature of this approach is that it provides information on g(r,p,T) for real systems, given pairwise additivity, without specifying u(r), and in principle could suggest an alternate route for the evaluation of intermolecular potential parameters if some thermodynamic properties at the scattering conditions are also known. Liikolaj and Pings [176] have applied the technique to calculate g(r) for argon in the liquid region. The extremes of the scattering angle range which contain the most information of fluid structure are difficult to explore quantitatively. Consequently, the accuracy of the scattering measurements is as yet not sufficient to provide reliable estimates of thermodynamic properties using this technique. 3) Approximation Techniques: In these techniques, the deviation from randomness between the positions of a central molecule A and another specified molecule B due to the action of a potential field is further divided into two parts, a direct influence c(r,p,T) of A on B, and an indirect influence whereby molecule A influences the distribution of other molecules which in turn exert their influence on molecule B. The functions c(r,p,T) and g(r,p,T) can be defined in terms of one another by an integral identity whose discussion is beyond the scope of this work. The approximations involve the specification of an additional independent relationship between c(r,p,T) and g(r,p,T) in order that the distribution function may be evaluated. The accuracy of the approximations are judged by the consistency of the results obtained from Equations (III-8) and (111-9), respectively. The subject is examined in more detail by Rowlinson [225]. The most successful of these approximations from the standpoint of internal consistency and agreement with hard sphere machine calculations is the Percus-Yevick (PY) [191] approximation given by IroT. -u(r)/kT c(r,p,T) - [e-u(r) /kT - 1]0) g(r,p,T) e-u(r)/kT

38 Although the PY approximation yields an analytic solution for a system of hard spheres, its application to more realistic potentials cannot be accomplished without recourse to numerical methods. Furthermore, Rowlinson [227] indicates that at temperatures below the critical, there are densities for which no solution is obtained. O'Connell and Prausnitz [188] have reviewed thermodynamic property calculations on argon from several approximation techniques using the L-J 6-12 potential with parameters derived from second virial coefficient data and concluded that the PY results, though consistent, are not accurate. Furthermore, the uncertainty in the calculations themselves are reported to be as high as + 4%. Such techniques are clearly not yet ready to serve as useable frameworks for the representation of the thermodynamic properties of real substances governed by complex intermolecular forces. v) Perturbation Models. Computer simulation results now provide us with a good understanding of the behaviour of a hard sphere fluid. These results, in turn, have stimulated efforts to obtain accurate analytical formulations for the hard sphere equation of state. The best current approximation due to Carnahan and Starling [41] valid only for the fluid branch, is given by HS + 2 (III-11) (1 - )3 where 5 is the volume density given by 6 1 p N 3, and serves as a measure of the reduced density. Recent efforts to overcome the calculation problems associated with more complex potentials have lead to the development of perturbation theories where a complicated potential is written as a sum of a simple potential (e.g. a hard sphere) for which g(r) and z are fairly well known, and a weak perturbing potential. The effects of the latter are approximated by averaging the perturbation over the known distribution function of the unperturbed assembly. For a first order perturbation about the hard sphere case, we can express this concept mathematically as [287] A HS aHS H NkT W k+i ~1J[u(r)- HS(r)] gSr)47r2dr (111-12) HS a

39 where A is the Helmholtz free energy for the given potential function, and the superscript HS applies to hard sphere properties. If for example, the perturbation potential has the form r) - u(r) * * If ert ~ e (IlI-13) then the equation of state and the configurational energy are given by [120] PV PV N a NkT ( AT ) - e (III-14) 2 (III-15) HS where ( ) can be obtained from Equation (III-11). If instead we express the hard sphere equation of state by the less accurate form PV HS 1 NkT 1 (III-16) V then, Equation (111-14) realizes the well known Van der Waal equation of state where the excluded volume b equals 45/Np. In the hard sphere fluid, there is no distinction between liquid and vapor. The power of this technique is seen in the fact that if the hard spheres are placed in an attractive potential field of infinite range and infinitesmal depth as given by Equation (Il-13), the resultant equation of state predicts, at least qualitatively, the behaviour of real fluids, Even more interesting is the fact that g(r) still remains only a function of density [120]. More complex schemes involving both repulsive and attractive perturbations, and including higher order expansion terms have been excellently reviewed by Mansoori and Canfield [163] and will not be pursued here. The most successful of these is due to Barker and Henderson [13,14]. Recognizing that a more accurate representation of the equation of state of real fluids would require a temperature dependence to be imposed on the distribution function, they ingeniously chose a reference system of hard spheres with temperature varying

40 diameters, and were able by this artifice to obtain rapid convergence of the perturbation series in the liquid phase. Calculation of Thermodynamic Properties from Perturbation Models Rogers and Prausnitz [219] investigated the ability of the Barker and Henderson perturbation model to represent the thermodynamic properties of spherically symmetric molecules such as methane, argon and neo-pentane. The three parameter Kihara pair potential 12 8 r-2a a-2a u(r) 4c [( r-a ) - ( r-a ) > 2a (III-17) u(r) = 0 r < 2a (III-17a) was chosen to represent the fluids on a microscopic level. The parameters E, a and a were obtained from the best fit to a broad spectrum of P,p,T data encompassing the saturated vapor, saturated liquid, critical, and supercritical regions. The pressures in all cases were fitted to an accuracy of 2% or better. Interestingly, the pure fluid Kihara parameters that produced the best fit to the thermodynamic data used by Rogers and Prausnitz in the perturbation framework were significantly different from those obtained by fitting wide ranging second virial coefficient data. In particular, the ~/k value used for methane varied accordingly from 204.15K to 227.13K. Consequently, it is highly unlikely that the perturbation model will yield accurate values of the second virial coefficient at reduced temperatures below 0.7, where the computed value of B becomes very sensitive to the precise value of O/k. A modified perturbation approach was used by Orentlicher and Prausnitz [189] to calculate the volumes and enthalpy departures for the cryogenic fluids A, CH4, N2, C2H6, C02, and C3H8. The pair interactions were governed by the L-J 6-12 potential with a hard sphere core of radius R. The distribution function for the potential was approximated as g(r,p,T) = g (r,p) r < R (III-18)

41 g(r,p,T) [e-u(r)kT] [g (r,p)] r > R (III-18a) A separation of the temperature and density dependance of g(r) was achieved in this manner. Furthermore, Equation (III-18a) gives the correct distribution functions for a hard core molecule in the limit of high temperature and in the limit of zero density. The functional form of the equation also provides a better approximation to the distribution functions of real liquids. To simplify computations, an analytic approximation for g (r,p) was made which was found to preclude the application of the technique to liquids at densities larger than those of saturated liquids at reduced temperatures below 0.8. Enthalpy and volumetric data in the liquid phase from 0.86 to 1.3Tr were simultaneously used to specify the potential parameters. The goodness of fit with respect to the enthalpy departure varied from 2 to 6%. vi) Conclusions: The independent specification of the potential function is, and will continue to be, the chief stumbling block in making a priori calculations of thermodynamic properties. Although the application of theoretically based perturbation treatments to real spherically symmetric systems has made recent spectacular gains, it is clear that the best representation is obtained only by sacrificing some or all of the thermodynamic data in defining the potential parameters. From a practical engineering standpoint, these approaches should then be judged by their ability to compete with empirical equations of state with the same number of adjustable parameters. Even if such approaches were to be found superior for some spherically symmetric systems, more empirical methods will continue to be favored until such treatments can be extended to include more complex molecules with orientation dependent or polar intermolecular forces. B) Equations of State - Empirical The restriction of the theoretically attractive virial equation of state to the gas phase has led to many empirical efforts to obtain functional forms that ensure the concise representation of thermodynamic properties over the entire fluid region. The earliest

42 of these contained few adjustable parameters, and like the two parameter Van der Waal equation, are now beginning to find theoretical meaning which speaks well for the remarkable intuition of early workers in the field. More recent formulations involve an increased number of empirical parameters that serve mainly to improve the goodness of fit. If our goal is to choose a general framework for the representation of thermodynamic properties, our choice is confined to those equations that have been extensively used in correlating thermodynamic data. The most popular form used in design calculations involving hydrocarbons is the eight parameter BWR equation of state [Equation (I-12)]. A compilation of the BWR parameters for 58 compounds has been tabulated by Cooper and Goldfranck [50]. The constants for most equations of state including the BWR are usually derived from volumetric data. If our primary concern is the representation of pure component enthalpies, then for reasons already discussed in Chapter I, we must further restrict ourselves to the examination of equations which represent the PVT surface very precisely. Comparisons made by Yesavage [284] on light hydrocarbons, including propane, have established the inadequacy of the original BWR for representing enthalpies in the liquid phase at low reduced temperatures. A recent modification of the BWR equation by Starling [251,254] expressed in the form C D E P = RTp + (B RT-A - 2 + bRT-a- ) p + ( a + ( ) 6 + 2(l+yp ] -9) 0 T2 T3 T TT 1(+peJy2 (111-19) has been successful in overcoming some of the deficiencies of the original version. The terms involving D and E in the coefficient 0 0 of P2 serve to improve the prediction of the second virial coefficient at low temperature. The other extra constant d improves the performance of the equation in the critical region. The expressions for thermal properties as derived from the above equation are presented in Appendix H-1. Simultaneous regression on volumetric and enthalpy data for methane and propane over the liquid, gaseous and dense fluid regions yielded a fit of about 0.9 Btu/lb in the enthalpy departure and 0.44% in the density, upto a reduced density of 2.0. At very low reduced

43 temperatures, the error in the prediction of the enthalpy departure can, however, be as high as 4%. In a recent review of the state of the art, Martin [165] offers the sobering opinion that only limited objectives may be accomplished with complex empirical equations of state. Even the best of these wide ranging equations can rarely if ever be applied beyond 2.3 times the critical density. Even though more extensively applicable formulations can be expected to appear in the near future, the necessity for recalculating the equation of state constants for all substances of interest to obtain the maximum advantage of new developments as they occur would be an unavoidably cumbersome task. C) The Principle of Corresponding States. i) Theoretical Basis - Two Parameter Theory: Difficulties in the a priori calculation of thermodynamic properties and the time consuming effort required to incorporate thermodynamic measurements into equations of state suggest that it might be easier to attempt to deduce the thermodynamic properties of a given species from the experimental results obtained on another similar substance. Pitzer [193] showed from statistical mechanical considerations that if a class of substances were to satisfy the following requirements: 1) The Hamiltonian of the system, i.e., the sum of the potential and kinetic energy of any arbitrary molecular configuration, is separable into a contribution from the internal degrees of freedom of the molecules, (e.g., the vibration in the case of nitrogen,) depending only on their internal coordinates and momenta, and a configurational contribution depending only on the coordinates and momenta of the centres of mass of the molecules. 2) The configurational contribution above can be treated by the methods of classical statistical mechanics. 3) The intermolecular potentials for all substances are conformal, i.e., the potentials for all substances in the class can be expressed in the form (12,r3 - rn) f( r12 r13,......2 4 r23 a - cr2 I a' nn) (1120)

44 where f is a universal function whose exact nature need not be explicitly specified and n is the number of molecules involved. Then, the equation of state for all substances in the class can be expressed as kT V z = h ( F' N3) (III-21) where h is a universal function. If the state of a reference substance in the class is represented by a PVT surface, then the states of all other conformal substances are represented by geometrically similar surfaces in which the axes of volume and temperature are multiplied by the ratios - 3 and respectively, where the subscript oo applies to the properties of the reference substance. It follows that all characteristic points on the surface such as the solid, liquid and gas at the triple point and the fluid at the critical point have values of P,V, and T in the ratio of these scale factors. Consequently, c/k and Na3 may be substituted by the macroscopically determined parameters Tc and Vc to yield [212] z = h ( T ) (III-22) Tcc V" or z = h'( T P (III-22a) Tc' Pc if Pc is instead used as the reducing parameter. The equations are widely used by engineers in predicting thermodynamic properties of a reference fluid. ii) Extended Corresponding States Theory: Experimental verification of the two parameter principle is spectacular for the rare gases argon, xenon and krypton [188,226]. The principle is applicable to a somewhat lesser degree of accuracy if nitrogen, carbon monoxide, oxygen and methane are included in the family [195,198]. In the case of n-alkanes, for example, as one departs from the critical point, the reduced vapor pressure curve shifts away from that for the

45 simple fluids. At a given reduced temperature, the reduced vapor pressure for a chain molecule such as n-heptane is less than that for a spherical molecule like methane. (See Figure 111-3). Such departures from strict two parameter theory have also been observed for other configurational properties [195,226]. Cook and Rowlinson [49] have attempted to explain such departures for both non-spherical and polar molecules from theoretical considerations. In order to define the magnitude of such effects relative to the spherically symmetric case, they were forced to further restrict the development to a specific molecular model chosen, for convenience, to be the Lennard-Jones 6-12 potential. The effect of orientation, for example, was incorporated into the potential function now defined in terms of additional angular coordinates ~ to yield u(r, ) 4e{( ) - ( r ) + af()3 (III-23) where a is a constant for each species with a value of zero for the unperturbed spherically symmetric case, and f(6) represents the orientation dependence of the attractive forces. For simplicity, the repulsive forces were kept unchanged. The potential function was then integrated over all orientations yielding the expression u(r,T) = 4e[ ( ) (1-2a2 ) ( ) (1-24) where f2 is the weighted average value of f(s) over all angles. If a parameter 6 is now defined such that 6 (T) - a2i2e/kT (III-25) then we obtain u(r,T) - 4[ ( ) (1 - 26(T)) ( ) (III-25a) The net effect of orientation forces is such that the resultant potential is still conformal with the original potential for symmetric molecules but is now also a function of temperature-. The maximum

10 n-C7 H16 "CH4 Critical t Point tPoit Tr Troo CH4 0,U |0 y0 Tr < 1.0, Vapor Pressure Curves Compared o~ ^^ Tr > 1.0, Heat Capacity Maxima Compared 0O _ h n-CTH16 a. 0.1 Troo(n-C7H1i6) Tr(n-C7H1i6) 0.Ol I I I 0.01 O.I 1.0 10 Tr (Log Scale) Figure III-3. Effect of Non-Central Forces on the Reduced Vapor Pressure Curve.

47 depth c, and the collison diameter a were found to be given by e/Ec = 1 + 26(T) (111-26) oo = 1 - (T) (III-27) where the subscript oo denotes a molecule whose potential is obtained from Equation (III-23) by putting a=0. The equation of state was then given by $ [P(1+36), V(1-6), T(1+26)] = oo[P,V,T] (III-28) The equation of state of the asymmetric species was later [223] expressed as a first order perturbation about that of the reference symmetric species by the relation z(Tr~pr) 1 - Tr oo oo z(Tr,pr) = zo(Tr,pr) - 6c [ Tr ][2Tr ( -aT ) + pr( ap ) ] (III-28a) pr p Tr where 6c is the value of 6 at the critical point. It may be noted that the perturbation term is required to change Sign at Tr=l regardless of the reduced density pr. The most important consequence of this approach is that the thermodynamic properties of asymmetric molecules can, for some limiting cases, be obtained from those of symmetric molecules by using temperature dependent scale factors. Similar conclusions were reached for dipolar molecules. A significant drawback of this approach is that it still requires the critical compressibility factor zc to remain unchanged, unlike the situation for real fluids. In fact, zc varies from 0.291 for methane to 0.269 for hexane. Brown [32] has suggested that such changes could be predicted by the theory if non-central repulsive forces were also considered. Nevertheless, the theory in its original form has been tested for a variety of substances including the n-alkanes upto n-butane using 6(Tc) as the correlating the parameter [226]. The calculated value of 6(Tc) from a variety of measurements, including the reduced vapor pressure, liquid density, entropy of vaporization, and the configurational heat capacity

48 was fairly constant. The parameter 6(Tc) was found to be related to the slope of the reduced vapor pressure curve, or the Riedel [216] parameter ac by the expression -c d ( d ) = rc + 11.8 6(Tc) (111-29) d 1n Tr Tr1 00oo where ac is the corresponding value for the spherically symmetric 00 system. It would be presumptuous to expect that such simplified perturbation models are applicable to all systems of interest. A more general approach would require the introduction of additional dimensionless groups involving dipolar moments, quadruple moments, non-isotropic polarizabilities which encompass the orientation effects due to dispersion forces, quantum corrections, and molecular association into the equation of state given by Equation (III-21). The specific contribution of each additional term could then, at least in principle, be ascertained from experimental measurements on the thermodynamic properties and the dimensionless perturbation variables for groups of substances where such effects are separately present. As indicated by Leland et al. [144] in an excellent review of the corresponding states principle, the current state of the extent and accuracy of such measurements precludes the semi-empirical formulation of such an universal approach. Even if such measurements were available, it is not clear whether the predictions would be successful for molecules where two or more of these perturbation effects are coupled. iii) Empirical Extensions of the Corresponding States Principle: 1) The Pitzer-Riedel Three Parameter Principle: Empirical efforts to universalize the two parameter principle have centered around the use of macroscopically determined parameters to serve as a measure of the deviation from the principle. From a physical standpoint, such parameters represent the lumped contribution of non-central forces relative to those in symmetric molecules such as argon and krypton. Considerable success has been obtained by both Pitzer and co-workers [195,198] and Riedel [217] in representing a

49 a class of substances called "normal fluids" by this approach. Included in this category are the spherically symmetric molecules Ar, Kr, etc., the n-alkanes, and other hydrocarbons. If 3 and are the values 00 of the third parameter for the actual and reference substance, respectively, then the reduced configurational properties of "normal" fluids are expressed in terms of those for a simple fluid using the perturbation parameter (3 - 3 ) as the expansion variable. For the reduced 00oo enthalpy departure, one obtains H-H H- d[ dIT-(TrPr)] -H (Tr,Pt) - [ c (Tr,Pr)] + (-,) (. III-30) ~RTc RWlc 0oo d.. oq Pitzer relied on the differences in the reduced vapor pressure curve for pure substances at 0.7Tc to define the third parameters given by -= 1- 1- logPr] (1-31) Tr - 0.7 As W is approximately zero for the spherically symmetric inert gases, it was justifiably called the "acentric factor." Riedel worked with the parameter Oc instead, defined from measured values of the slope of the reduced vapor pressure curve at the critical point. The two parameters are related through the reduced empirical three parameter vapor pressure equation of Riedel [216], which yields [226] 0 - 0.203 (ac-7.00) + 0.242 (111-32) The linear relationship between w and ac implies that the two procedures are essentially interchangeable. The excellent intuition behind these empirical approaches is seen from the fact that the value of Rowlinson's perturbation parameter defined from a consideration of orientation effects is, at the critical point, linearly related to the empirical parameter (ac - ac ) as indicated in Equation (III-29). 00 One important difference between the theoretical approach of Cook and Rowlinson and the above empirical efforts is that the reduction or scale factors used in the latter case do not vary with

50 temperature. In the region between the reduced saturation curves for two substances differing significantly in oc values, (e.g. methane and n-heptane as shown schematically in Figure III-3) serious errors occur in the calculated values of the thermodynamic properties of the asymmetric molecule as its phase differs from that of the symmetric reference under the same reduced conditions. Pitzer and co-workers [195] recognized the problem, and extrapolated the reference fluid properties in each phase, so that once the phase of the asymmetric fluid was correctly identified by an independently obtained reduced three parameter vapor pressure equation, major calculation errors could be avoided. In a broader sense, the conformal mapping of two points, i.e. the critical points, in a corresponding states correlation does not ensure that other characteristic locii in the fluid, such as the vapor pressure curve, the Joule-Thomson inversion curve, [(MH/3P)T = 0], the Boyle curve [(az/3P)T = 0], the Amagat curve [(Oz/VV)p = 0], or the heat capacity maxima (Cp - Cp)} = 0, or ( p ) = 0] wiP T will be simultaneously matched. 2) The Shape Factor Approach of Leland: Leland and co-workers [140] formulated an alternate empirical approach that closely follows the theoretical treatment of Rowlinson. There is no deviation term as in Equation (111-29) which incorporates differences in the reduced dependent variable or configurational property at the same Tr and Pr. Instead, the critical parameters are modified by multiplicative temperature and density dependent "shape factor" corrections to generate the desired configurational properties from the unperturbed framework alone. If at least two or more measured configurational properties of a given fluid are compared with that of the reference fluid, and the corresponding reduced temperatures and pressures which yield identical values of the reduced properties so examined, are obtained, then the "shape" modifiers to Tc and Vc for the given fluid may be uniquely determined as functions of temperature and volume relative to the reference fluid case. Such

51 factors were determined for selected fluids by the process just described and then used to develop empirical correlations that defined these factors for other fluids as functions of reduced temperature and pressure in terms of additional parameters such as the acentric factor W. A drawback of this approach is that the physical correspondence between characteristic points in the PVT surface for any two fluids is lost. For example, at the critical point, the reduced enthalpy departure for propane is greater than that for a symmetric molecule such as methane [284]. Consequently, the shape factors for propane relative to methane will be different from unity if a methane reference table is used. 3) The Powers Generalized Correlation (PGC): The Powers Generalized Correlation [204] has the attractive attributes of both of the above approaches. Firstly, it involves a modification to the independent variable Tr somewhat like the route taken by Leland and coworkers, and secondly, the dependent variable i.e. the reduced configurational property of the fluid, is expressed in terms of the corresponding reduced property of the reference fluid and a perturbation term much like the approaches of Pitzer and Riedel. More importantly, the method seeks to maintain conformality at a singular point, i.e. the critical point, and along other selected locii. The technique was originally devised explicity for the calculation of thermal properties. Consequently, the most desirable locus for conformal mapping is one across which thermal property variations are most severe. The vapor pressure curve upto the critical temperature, and the locus of the heat capacity maxima, (3Cp/2P)T=0, in the supercritical region admirably meet this criterion. In practice, the locus of (DCp/9T)p = 0 was used instead, as there are considerably more experimental determinations of the latter obtained principally at the Thermal Properties of Fluids Laboratory at the University of Michigan [49,161,162,168,284]. However, unlike the locus of the maxima at constant temperature, the locus of (9Cp/9T)p = 0 is not a true configurational property characteristic of the fluid if CpO also varies with temperature. It does, however, serve as a good approximation to another true configurational locus, dT'10] =0, for some distance beyond the P

52 critical temperature [245] and may be used as an acceptable replacement until more precise measurements permit the true configurational locii to be defined. The reduced coordinates used in the technique are given by (T, Pr) where T in Pr8(Tracc...) Tr < 1.0 (111-33) T I n PrM(Tr,ac...) Tr > 1.0 (II-33a) where the subscript s stands for the vapor pressure curve, and the subscript M applies to the locus of (DCp/9T)p=0. Defined in another way, the actual reduced temperature Tr of a substance is modified to another value designated as Tr, such that the reduced saturation pressure Pr (Tr < 1), or the reduced pressure at the heat capacity maximum PrM (Tr > 1) for the given fluid at Tr is the same as that for an archetypical reference fluid at Tr (See Figure III-3). 00 The reduced enthalpy departure for any substance is expressed in terms of that for a reference fluid by the relation (rrc (rrc) + (Tr,Prc) (TrPr ) + (Tr,aco)] [ ac - aco ] (II-34) where the subscript oo applies to the properties of the reference fluid, andi is defined as H - H" + 0HV H - O in the vapor phase (1II-35) (ac - H~) Trl1, Prtl where (Hc - H) is the enthalpy departure at the critical point and AHR is the enthalpy of vaporization at T or Tr. The incorporation 00 of the enthalpy of vaporization permits a more accurate correlation of the relatively small effect involved in the isothermal variation of enthalpy with pressure in the liquid phase without having to contend with the large masking effect associated with a phase change. A special feature of the technique lies in the fact that the dependent variable ( is also defined to be unity at the critical point. A potential disadvantage of the procedure is that it requires the vapor pressure, the locus of heat capacity maxima along isobars, and

53 the enthalpy departure at the critical point to be first established for the fluid in question. However, if the value of the Riedel parameter ac is known, then excellent approximations to the desired information may be obtained. The vapor pressure curve may be adequately expressed by the empirical equation of Riedel [175] as log Pr - - (Tr) - (oc-7) Y(Tr) (111-36) where ) (Tr) - 0.118 0(Tr) - 7 log Tr (III-36a) V (Tr) - 0.0364 G(Tr) - log Tr (III-36b) 0 (Tr) - 36/Tr + 42 log Tr-35-Tr6 (III-36c) The locus of the desired heat capacity maxima can be expressed as In PrM - Oc In Tr Tr > 1.0 (111-37) and the value of (Hc - H~) may be described by the relation Rc- - 1.5113 + 0.5081 (ac - 3.750) (III-38) The empirical relations expressed by Equations (III-37) and (III-38) were obtained principally from an examination of the accumulated measurements at the calorimetric facility of the University of Michigan [202]. 4) The Representation of the Reference Functions in Corresponding States Correlations: A major factor that determines the success of such techniques is the accuracy with which the equation of state for the reference substance can be specified, and it is here that the techniques differ in their original implementation. Pitzer and Curl [195] determined enthalpy departures for the reference fluid and the slope term by graphical processing of smoothed compressibilities, wJhereas Leland and coworkers [80,81,144] used as their reference, an empirical equation of state for methane based on precise volumetric

54 data. Powers [204], however, made direct use of smoothed precise calorimetric data to establish the reference function and the slope term in tabular form. The calorimetric measurements on methane and propane obtained by Jones [119] and Yesavage [284], respectively, were weighted heavily in defining these functions. Propane was also particularly attractive as the enthalpy values in the liquid phase were obtained down to a Tr value of about 0.3, which is lower than the reduced triple point temperature for most substances. Recent extensions of the acentric factor approach by Greenkorn and Chao [91], and the shape factor approach by Fisher and Leland [81] to low reduced temperatures have also featured enthalpy tabulations in the liquid phase obtained from the calorimetric measurements at the University of Michigan. Johnson and Colver [118] directly fitted the Starling BWR equation to the methane and propane enthalpy data and used these results to define the two reduced enthalpy functions [Equation (III-30] in the Pitzer framework. The approach follows that of Yesavage [284], but replaces his reference tables with equations of state. 5) The Reduced Virial Equation of State: If we set for ourselves the more limited objective of restricting our predictions to the gas phase alone, then the reduced virial equation represented by B/Vc C/Vc2 - r +.... (111-39) must be considered as an attractive vehicle for the corresponding state principle in view of its theoretical roots. If this equation is to be implemented, then generalized correlations for the reduced virial coefficients B/Vc, C/Vc2, etc., as a function of Tr, and a third parameter to account for asymmetric effects if necessary, must be developed. The most popular reduced second virial coefficient correlations are those of Pitzer and Curl [196] and McGlashan and Potter [159]. In the former case, the correlation uses the acentric factor and is expressed as Br - RT/c Brio + Brl (111-40) RIC/PC 1oo

55 where Br - 0.1445 - 0.330/Tr - o.1385/Tr2 - 0.0121/TrS (I1l-41) oo Brl - 0.073 + 46/Tr - U.5/Tr2 - 0.097/Tr' - 0.073/Tr (111-42) and is restricted to "normal" fluids over the range 0.5 < Tr < 6.0. Although the equation is generally considered to be very reliable, the predictions are about 8% too negative for ethane at 215K when compared with the apparently precise measurements of Hoover et al. [108], and about 5% too negative at 110.83K for methane when compared with the precise measurement of Byrne et al. [35]. The correlation of McGlashan and Potter [159] developed specifically for n-alkanes is given by B 0.430 - 0.886 0.694 0.0375 (n-i) (111-43) Vc Tr Tr2 Tr' where n is the number of carbon atoms in the molecule. The value of n has been related to ac by the empirical expression [202] n - 23.257 - 9.763 ac + 1.0203 ac2 (III-43a) The authors suggest that the equation is valid over the range 0.5 < Tr < 6.0. An analysis of the methane and propane data by Hecht and Donth [99] indicates that the B/Vc curves for the two substances cross each other at a Tr value slightly higher than unity. A similar result can also be seen in Figure (V-l) if the solid curve for methane is compared with the dashed line for propane. This behaviour is also in substantial agreement with Rowlinson's [222,223] theory which requires the differences between the reduced configurational properties of the reference and perturbed system to change sign at a Tr value of 1.0. A glance at Equation (III-43) indicates that B/Vc for propane will always be more negative than that for methane, and suggests that its functional form is not optimally suited to the representation of wide ranging measurements. The apparent deficiences of these equations underscore, at least for the present, the necessity of developing improved correlations for the reduced second virial coefficient.

56 Chueh and Prausnitz [45] have correlated the third virial coefficient for a number of substances including argon, ethane, neopentane, n-octane and benzene over the region 0.8 < Tr < 4.0 using the relation C 0.232 0.468 (1-1 89Tr2)+ de-(249 + 2.30Tr + 2.70Tr2) (II-44) V 0.25 ]5[ d1- (-44) VC Tr0~-25 Trs where C is the third virial coefficient and d is an empirically determined parameter that has a value of zero for argon. It may be expressed in terms of ac by the approximate relation d = 2.2 (tc - 5.78) (III-44a) as empirically noted in this work. Generalized empirical correlations for higher order virial coefficients are unavailable as the accuracy of the volumetric measurements necessary for the precise calculation of such quantities is beyond the range of most previous investigations. However, truncation at the third virial coefficient will permit reliable calculations of the compressibility and the enthalpy departure upto 0.8 and 0.5 times the critical density, respectively. The range of applicability increases somewhat beyond the critical temperature. Gunn et al. [96] have recently added dimensionless coefficients to the cubic and quartic terms in the virial equation but have cautioned that these are not true higher order virial coefficients. D) Comparison Studies of Enthalpy Prediction Methodsfor Pure Non-polar Fluids: Comparison studies of various correlations against accurate smoothed enthalpy measurements can serve as an invaluable aid in assessing their performance relative to one another. Such techniques are constantly being refined as new data become available, and consequently only the latest comparisons present an accurate picture of their abilities. Starling et al. [253] have recently made comprehensive investigation of eight correlations used in the natural gas industry against the accurate wide ranging enthalpy data for the pure components investigated at the TPFL. LThe correlations were also

57 compared with enthalpy measurements for n-pentane, n-hexene and n-octane from other sources [149,150]. All but two of the methods investigated involve the corresponding states principle in some form, and include most of the techniques discussed in this section with the notable exception of the reduced virial equation. The Powers Generalized Correlation (PGC) was unquestionably superior to the rest for the case of light hydrocarbons upto propane and nitrogen, producing a fit of better than 0.5 Btu/lb with respect to the enthalpy departure. This result is not surprising because these data were heavily involved in the development of the correlation itself. For the systems n-pentane through n-octane, the lowest mean deviation of 1.95 Btu/lb was obtained for the Rice Properties III correlation of Fisher and Leland [81], perhaps, because they use n-pentane as their reference for compounds that are heavier than n-butane. The PGC deviations were only slightly worse at 2.13 Btu/lb. The authors of the comparison study suggested that inaccuracies in the measurements could be responsible for the higher deviations obtained for the heavier systems. F) Conclusion The considerations in this chapter lead us to conclude that the PGC is the most accurate practical framework that we could use to represent the enthalpies of the pure substances methane, ethane, and propane that constitute the ternary mixture whose enthalpies we seek to predict in this work.

Chapter IV SELECTION OF A METHOD FOR REPRESENTING AND PREDICTING MIXTURE ENTHALPIES In Chapter III, the PGC was selected as the most desirable framework for representing pure component enthalpies for non-polar compounds that fall under the category of "normal" fluids as specified by Pitzer [195,198]. The next step in predicting multicomponent mixture enthalpies from constitutent pure component and binary data, is to select a framework that permits the concise and accurate representation of the enthalpies of mixtures of "normal" fluids over the entire fluid phase. The discussion in this section parallels the approach of the previous chapter. First, the specific benefits obtained by applying the virial equation of state to mixtures in the gas phase are summarized. The extension of pure component dense fluid theories, discussed in Chapter III, to mixtures is then examined. Because the PGC is eminently suitable and convenient for representing the thermodynamic properties of pure non-polar substances over a wide range of conditions, one is immediately tempted to use it as a starting point for the representation of mixtures of such substances. Before accepting the empirical extension of the framework to mixtures, it is desirable to establish, at least in theory, the precise circumstances that permit the application of the pure component corresponding states principle to mixtures. The theory of conformal solutions is first briefly discussed. Next, procedures for estimating the unlike pair interaction parameters for conformal molecules are briefly described. Various corresponding states models that issue from the basic theory are noted. Several prescriptions or "mixing rules" for calculating the pseudoparameters of any given mixture as a function of the conformal pair interaction parameters and the composition are outlined. in particular, the theoretical restrictions peculiar to the empirically popular Van der Waal mixing rules are examined. The performance of various mixing rules are compared against the results obtained for a variety of thermodynamic data on both real and artificial systems to determine which of the approximations is the most realistic. The entire 58

59 presentation upto this point is primarily restricted to the two parameter theory because the theoretical studies in the literature have been confined mainly to this case alone. The discussion then proceeds to the examination of the three parameter corresponding states principle. Empirical justification for applying the theory to non-polar mixtures is first presented, and the macroscopic equivalents of some theoretical mixing rules discussed earlier in the chapter are noted. Additional empirically successful rules including one for the third parameter are also discussed. Finally, the results of comparison studies on various enthalpy prediction techniques using mixture enthalpy data are used to select the best framework for representing mixture enthalpies. The Application of the Virial Equation of State to Mixtures in the Gas Phase The prediction of the thermodynamic properties of multicomponent systems from pure component and constituent binary data is most rigorously accomplished for the special case of the virial equation of state but is restricted to mixtures in the gaseous phase only. It can be shown from statistical mechanics [167] that the mixture virial coefficients can be expressed as a function of the constituent pure component and unlike multi-body interaction terms. In particular, the second and third mixture virial coefficients B and C are respectively given by m m n n (B) - E x ixj (Bij) (IV-1) m T i=l j=1 T n n (C) = Z Z x (Cijk (IV-2) m T i=l j=1 k=l 1 T where B.. and Ci.. are the second and third virial coefficients for IJ ijk the i-j and the i-j-k interactions, respectively. If B.i and Bj are known at any given temperature for a mixture of two components i and j of known composition, and if B is measured at the same temperature for the same mixture, then Equation (IV-I) permits B.. to be 1J calculated at the same temperature. This result in turn characterizes the value of B for all binary mixtures of i and j at that temperature. If the interaction virial coefficients are so determined for all binary pairs of a multicomponent mixture at temperature T, then Equation (IV-1) permits the rigorous calculation of B for the multicomponent mixture m

60 from binary data alone. Similarly, the characterization of the nth virial coefficient as a function of composition at a fixed temperature for a given binary mixture requires experimental measurements of the nth virial coefficient for the two pure components and for (n-l) mixtures at the same temperature. This technique has been applied by Douslin [65] to characterize the second, third and fourth virial coefficients of methane-tetrafluoromethane mixtures, but such precise comprehensive measurements are rare. If the potential function for all pair interactions in a mixture can somehow be adequately specified, then the interactions parameters for all pair interactions, including the like and unlike pairs, may be obtained by fitting Equation (III-2) to experimental B.. data for all 1J i,j. Once all constituent pair parameters are thus specified, it is possible to calculate higher order virial coefficients with the usual assumption of pairwise additivity [167]. The importance of the interaction second virial coefficient must not be under-estimated, as the dilute gas is the only region in the entire fluid phase where the theoretically rigorous definition of the parameters for any specified unlike pair potential function is possible. Dense Fluid Theoretical Results The unsuitability of the virial equation for the dense fluid makes it desirable to use the mixture analogues of Equations (III-6) and (III-8) instead in such cases. With the usual assumption of pairwise additivity, the configurational energy U, and the equation of state for a mixture of spherically symmetric molecules are respectively expressed as [212] n n 2 co Nm i xixj | uij(r,p,T,[C], [a],[x]) 4rr2dr (IV-3) m i-i j=l o (1-kT 6 m 1Z -xi E ui (r)gj(r,p,T,[e],[a],[x]) 47rr2dr (IV-4) i=1 j=1 where u. (r) and gij (r) are the pair potential and the radial distribution function, respectively, for the i-j interaction, and [E] and [a] are pair energy and volume parameter arrays, respectively, and [x] is the composition array for the mixture.

61 The first requirement in the application of Equations (IV-3) and (IV-4) to real fluid mixtures is the specification of a reasonable model for all possible pair potentials in the given mixture. This may be difficultly accomplished for unlike pair interactions in complex mixtures if the constituent like pair interactions are found to subscribe to different molecular models. Nevertheless, assuming all uij(r) can be specified, all gij(r) must be next determined. The statistical mechanical problem involving the evaluation of gij(r) in mixtures is much more formidable than in the pure component case, because it is now not only a function of r and.. /kT, but also of the number density pi of each component (or equivalently, the overall mixture density and the mole fraction of each species), and the relative magnitudes of the size and energy parameters for the various molecular species in the given mixture. One simplifying approach, parallel to that used for real pure components, is the express real fluid mixture properties as perturbations about simpler artificial mixed systems which can be more tractably treated. Perturbation Techniques Most efforts in correlating the thermodynamic properties of real fluid mixtures using perturbation approaches have centered around the description of the equation of state and the distribution function of a mixture of hard spheres. Many of these attempts have been discussed by Reed and Gubbins [212], and Mansoori and Canfield [163]. The perturbation approach for pure components exemplified by Equation (III-12) may now be extended to the calculation of thermodynamic properties using the hard sphere mixture as the reference fluid. One of the simplest of such models involves the extension of Equation (III-14) to mixtures to yield HS m (IV-5) z = z (IV-5) m kTV m Lebowitz [141] has obtained an analytic solution of the P-Y equation for hard sphere mixtures. The P-Y compressibility equation result is given by

62 HS 1 Yo 3 y1Y2 3 y2 z + (IV' -6) m = o 1- (1) 2 ( )(Iv-6) n 1 i where ~i 6 Z P kk k=l HS An improved analytic form for z obtained by combining the P-Y m pressure and compressibility equation results has been recently developed by Mansoori and Leland [164]. Their results were in good agreement with the molecular dynamics calculation of Alder [2,3] for mixtures of hard spheres with diameters in the ratio 3:1. The mixture perturbation constant a is given by the relation m am i j aij (IV-7) i j Recent work [98] has suggested that any single component that subscribes to the equation of state given by Equation (III-14), will yield Equation (IV-7) for multicomponent systems if the model is generalized in a consistent manner. Equation (IV-7) is, however, an empirical equation of long standing first suggested by Van der Waals. In fact, if in Equation HS (IV-5), we substitute z by the relatively crude approximation HS 1 Zm N (IV-8) 1 - Z Z xix b - Xi bijV where bi. is the covolume encountered before in Equation (III-16), then we obtain the original multicomponent Van der Waal equation of state. Snider and Herrington [248] have used the equation of state expressed by Equations (IV-5), (IV-6) and (IV-7) to correlate the excess properties of mixtures of spherically symmetric non-polar substances in the liquid phase with considerable success. Their results are analyzed in greater detail at a later stage. Rogers and Prausnitz [219] extended their perturbation model representation of the thermodynamic properties of argon, methane and neo-pentane as discussed in Chapter III to the representation of the vapor-liquid equilibria, critical properties and saturated liquid and vapor densities for the system argon-neopentane at 500C from 40 to 253 atm., and for the system methane-neopentane

63 at 25"C from 20 to 156 atm. The calculated results were found to give excellent (within 2%) agreement with experimental data. It must, however, be noted that the energy parameter c.. for the unlike pair 1J interaction was in each case adjusted to provide the best fit to the data. These results are significant, because they establish for the first time that highly non-random mixtures, i.e, with pure component critical temperature and volume ratios as high as 2.8 and 4.0 respectively, can be successfully treated by theoretically based approaches. These methods are all the more attractive because such calculations can be extended to multicomponent mixtures using only constituent binary data to establish the appropriate unlike pair interaction parameters. There are, however, three important disadvantages to such approaches. Firstly, the theories are at present restricted in application to systems consisting of spherically symmetric molecules. Secondly, even in such cases, the applicability of the method to the entire fluid phase has not yet been demonstrated, and thirdly, as Rogers and Prausnitz [219] indicate, the calculations are very demanding of computer time. Conformal Solutions Before the recent breakthrough in describing the hard sphere equation of state, solution theories were developed which concentrated on the properties of pure real fluids as their starting point in an attempt to avoid the direct statistical mechanical calculation of mixture properties. Most of these theories assume as their first premise that the intermolecular pair potentials for all i-j interactions including those for the unlike species can be expressed in the form uij(r) = iF (IV-9) Oij where F is a universal dimensionless function applicable to all constituent pair interactions and e.. and o.. are the energy and size parameter, respectively, for the i-j pair interaction. Such mixtures were given the name "conformal solutions" by Longuet-Higgins [153]. In principle, it is easy to determine if the like pair interactions for real fluids subscribe to Equation (IV-9), by examining the

64 correspondence between their experimentally determined configurational properties using suitable experimentally determined reduction factors such as the critical temperature and the critical volume. The acquisition of similar experimental evidence for the unlike pair interaction is almost impossible as it requires the effect of the i-j interactions to be isolated from the unavoidable simultaneous effects of the i-i and j-j interactions. The equivalent critical parameter Tcij(ijj), for example, cannot be defined from direct experimental critical measurements on mixtures. Fortunately, as indicated earlier in this chapter, the unlike pair interaction effect may be isolated from experimental measurements on mixture second virial coefficients alone, through Equation (IV-I). If Equation (IV-9) is substituted into Equation (III-2), then one can construct the dimensionless relation B kT f ( kT (IV-10) N.3 Eij o ij where f - {1- exp[ - F( ) ] } 4 ) d( (IV-lOa) 0 Consequently, one can examine the correspondence between reduced B E: second virial coefficients Na3 in all cases as a function of T to determine if the theory applies. A difficulty arises from the fact that j.. and i.. for the unlike pair must themselves be obtained from B.. measurements. 13 If two substances are strictly conformal in a two parameter framework, then the ratio of their temperature and pressure coordinates for all uniquely identifiable characteristic conditions in the P-T plane will be invariant. In particular, the reduction factors for the configurational properties may be equivalently defined from any other characteristic condition besides the critical point. The Boyle point located along the zero pressure axis and defined to be the point where the second virial coefficient has a zero value is one alternative where experimentally accessible parameters may be defined for the unlike pair interaction. Douslin [65] used the parameters Tb and Vb, where Tb is the Boyle temperature, and Vb is the Boyle volume defined by Vb (-T-L) ( dT T b ^ (IV-11) to reduce the second virial coefficients of CH, and CF,.

65 In practice, such specifically located measurements are rarely available, even for pure components, and consequently this technique has not found widespread use. Approxiation Techniques for Estimating Unlike Pair Interaction Parameters for Conformal Substances In the absence of Boyle point data, it is necessary to use approximation techniques for the estimation of unlike pair parameters. The most commonly used combination rule for size is the arithmetic mean rule given by aij (ii + j j/2 (IV-12) The justification for the a rule is simply by analogy with rigid spheres. The rules for ~.. have a more complicated origin. The leading term 1j in the London formula [152] for attractive dispersion forces is given by c' /r6 where c'i. can be approximated by the relation ij 13 1 / 2(1 I )/2 Cjj = (C C) 2(ii j (I-13) i i + (IV-13) for spherically symmetric molecules [167]. Iii and Ij. are the first ionization potentials for molecules i and j, and c', c' are the corresponding pure component constants. The attractive part of any (n-6) potential is given by.i ( ~ )6. If we equate this quantity ij r to c'.., we obtain 1/2 i r CT 3 2(1 I ) a(Ei /2 it2 1i: j I(IV-14) ~iJ Iii+ Ij If the arithmetic mean rule [Equation (IV-12)] holds for 0ij' then Equation (IV-14) requires that =ij kij (ii jj) kij < 1 (IV-14a) This results from the fact that a geometric mean is always less than an arithmetic mean and the other factors in Equation (IV-14) are the ratio of geometric to arithmetic means. Leland [213] developed

66 the equation 3)1/2 ij (ii j) ij 3 (IV-15) as a simplification of Equation (IV-14). Mason and Spurling [167] have shown that if one starts with the Kirkwood-lMueller formula for c', one may obtain the rule =j ~ ) (~T^~~ ^ Ii) ~Q~ ^ s c o )67 1 2/x e g 6 2 1 (IV-16) Ei + Ejj ij Eaii6/X] ii2 + jj jj6/Xjj where X is the diagmagnetic susceptibility. Procedures for calculating I and X for pure components for use in Equations (IV-14) and (IV-16), respectively, have been demonstrated by Hirschfelder, Curtiss and Bird [107]. Pitzer [194] has tabulated the values of these constants for selected pure components. For molecules with similar values of a and X, Equation (IV-16) reduces to =2 cii ij = ii + ejj (IV-16a) C = BL:11 (IV-16a) Although theory has suggested the form of these combination rules, the approximations made in obtaining usable recipes are so drastic that the rules may be considered semi-empirical at best. In a two parameter framework, Equations (IV-12) may be expressed in terms of the equivalent macroscopic parameters Vc or RTc/Pc by the relations c /3 - V + 1/3]2 (IV-17) or / 1/3 1/3 RTc RTci RTc / ( Pc Pc ) +( P /2 (IV-18) J Pcii II if one recognizes the proportionality between c3 and Vc or RTc/Pc. Similarly Equations (IV-14a), (IV-15) and (IV-16a) may be expressed in the forms Tcij = kij (Tcii Tcjj) kij (IV-19)

67 1/2 l ( Vc v ) ij ( TCii TCj)1/2 iv Tio = (Tc 1Tc ) 12 (IV-19a) Tc Tc Tcij 2 T Tc (IV-20) respectively. The advantage in using the macroscopic parameters Tc, and Vc instead of e/k and C3 lies in the fact that they can be unequivocally defined for each pure component from experimental measurements without having to assign a specific molecular model for the conformal pair interactions. If we assume that the i-i, the i-j, and the j-j interactions are mutually conformal, then we can, from the like pair second virial coefficient data, establish an empirical reduced function B T Vc fB ( Tc ) (IV-21) to fit the pure component results. If then, some B.. data are available for i $ j, the parameters Tc.. and Vc.. can be obtained by determining the best fit to the pure component function f.B To ensure some degree of specificity in obtaining the parameters in this fashion, it is necessary to have accurate and wide ranging B.. measurements. Nevertheless, this technique allows the extraction of two parameters from experimental measurements without requiring the potential function to be explicitly specified. Corresponding States Formulations for Mixtures Raving investigated various means for specifying the parameters for all conformal pair interactions in a mixture, we are now in a position to examine the macroscopic consequences of these assumptions. First, a model for expressing the thermodynamic properties of a mixture in terms of the appropriate reduced pure component thermodynamic functions must be proposed, and next, a recipe for specifying the potential parameters for a mixture, if at all necessary, must be established in terms of the constituent pure component and interaction parameters so as to yield the best representation of the mixture properties in the specified framework. All the developments described in this section require the same assumptions used in establishing the pure component corresponding states

68 model as described in Chapter III. The treatment of conformal solutions is, however, further restricted to pairwise additive interactions. The dimensionless argument used to derive the corresponding states principle for pure substances cannot be used for mixtures since the energy of an arbitrary molecular configuration will depend not only on the positions of the molecules, but also upon which chemical species is in each position. Therefore, unlike the pure component case, a variety of models can be proposed. each of which makes a specific statement in regard to the distribution of molecules by species in a mixture. The detailed examination in this work of the theoretical results for mixtures conformal in only two parameters requires some justification especially since the pure components for which we seek to apply such techniques require at least three parameters for an acceptable degree of correspondence. The problem lies in the fact that very little theoretical work has been accomplished for the three parameter framework. Furthermore, the current state of the art is such that the mixing rules for the two parameters common to both frameworks are the same. The one, two and three fluid corresponding state models are examined below. These models derive their names from the number of separate reduced conditions at which the dimensionless reference fluid configurational property function must be evaluated in order to specify completely the appropriate configurational property for a binary mixture. a) The One Fluid Model In this case, the mixture is assumed to be equivalent to a hypothetical pure component with temperature and density independent potential parameters ~ and a which yield the mixture configurational m m properties when used in some reference pure fluid configurational property framework. If the reference fluid parameters are ~ and a 00oo oo respectively, then the configurational enthalpy H of the mixture is given in terms of the reference fluid configurational enthalpy f by the relation ~: E: ~ a m(T,P, x]) = o (kT 0 P 0 3) (IV-22) 00 m m oo where i (T,P,[x]) is identical to the enthalpy departure with respect

69 to the ideal gas state. The excess thermodynamic properties of the mixture may also be expressed in terms of the configurational properties of the reference fluid. The excess enthalpy, for instance, is given by HE(TP [ PCaoo m n ~ii oo oo ii E(T,P, [x]) - o R(kT E-, P 3) - x- (kT,P - -3) (IV-23) 00 m m oo i1l oo ii ii oo and is obtained by combining Equations (IV-22) and (1-13) given the knowledge that HE is zero in the ideal gas state. This model represents the direct extension of the one fluid pure component corresponding states principle to mixtures. In independent investigations, Wojtowicz, Salsburg and Kirkwood [281], and Brown [31] determined from statistical mechanical considerations that the model was rigorously true only for solutions of conformal molecules in a condition of random mixing defined to occur when the potential energy of a mixture for each spatial configuration of molecules is the average over all assignments of the different species to all positions in proportion to the mole fraction. Mathematically n n Um(r) = Z xx Uij(r) (IV-24) j i J where u. (r) is the potential function for each i-j pair. It was also 1J shown that if the molecules were of unequal size, the condition of random mixing required the conformal potentials to be further restricted to the Lennard-Jones p-q form with the mixture parameters c and o given by n n mm P i J i ij (IV-25) Malq _ Xixj xij ijq p (IV-26) mm^1^^^ ~ ^P~~~ ij 1~~~~~~~(IV-26) The most commonly used values of p and q are 6 and 12 respectively. If we apply the model to a case where all..'s are approximately equal and q approaches infinity, then on dividing Equation (IV-26) by the size parameter for the largest molecule imetern for the largest molecule in the mixture, we obtain in the limiting case of infinitely hard repulsion (q -+ o), the absurd

70 result that am is equal to the size of the size of the largest molecule in the mixture even for vanishingly small concentrations of the largest species. This occurs because it is in fact unrealistic to assume that all configurations of a reference pure fluid are equally open to a mixture of small and large molecules. In particular, the replacement of a small molecule by a large one in an already closepacked configuration must lead to an overlapping of such molecules. If the repulsion between such molecules is assumed to be infinitely hard, then an infinite value will be obtained for the configurational energy of that assembly [226,227]. One Fluid Model - Generalized Van der Waal Mixing Rules Leland, Rowlinson and Sather [147] proposed an alternate set of rules that were notably free from any explicit dependence on the potential function. The rules are given by the equations I n i J S']em o3' zzXjXj Di a1j (IV-27)!+V3o nn 1= i j+V 3 Em am XiX- xxj s (IV-28) where v is a variable. For V = 0, the rules yield the simple results a3 Z iXj ij -3V (IV-29) m ij CaM' Z XiX i ami3 (Iv-30) and are essentially those empirically deduced by Van der Waal in extending his equation of state to multicomponent systems. Hence, they are called the Van der Waal mixing rules. We will now attempt to examine the specific restrictions imposed by these rules on the distribution of molecules by species. The application of the one fluid corresponding state theory to mixtures involves the additional assumption that the mixture can be replaced by a hypothetical pure component. The molecular interactions between these hypothetical molecules are also assumed to be conformal with potential fields for each i-j pair interaction. Thus

71 (r) em ( )IV-31) m where c and a are the molecular parameters for the hypothetical pure m m components. We may then express the configurational energy for the mixture using the pure component energy equation [Equation (III-6)] expressed in terms of dimensionless distance. Thus N2 r m 2 r U -v a (-) Goo(,, E-m.) 4r(-) d()( 2Vm a 00 (IV-32) o m m m m where Go is the distribution function for the pure reference fluid 00 expressed in terms of dimensionless distance, and m is the pseudo volume density 61 rpmN m3 for the hypothetical fluid. If the right hand side of Equation (IV-4) is also expressed in dimensionless form, and equated to Equation (IV-32), we obtain the result r # r m r 2 * r my e ~ a'T 4( a) E d ) r r E xx.a. OJ F-M(.'' 4i,p,T,[e,[a],~[x]) mm aM 00 aM~kTm a3 i-I j-1 ii Ao i0 47r( ) d( ) (IV-33) ij - If we define the integral on the left hand side by Io( T Em) and each of the integrals on the right hand side by I.. (p, T, [e], [a], [x] ), we obtain e nnu 3mE X( 3 T' F) 0 T x ixjEij ~ i 3 Ii (p:,T [t] [a],[x]) (IV-34) If for convenience we define Kij such that I Kij(pT.(]c [], [x])'- (IV-35) then Equation (IV-34) can be rewritten in the form n n a E Xix K ij ijaij 3 (IV-36) i=l J=l where Kii + 1.0 as xi + 1.0 at all temperatures and pressures because the mixture parameters must approach those of the pure fluid i as the

72 mole fraction of i approaches unity. Equation (IV-36) is seen to result in the Van der Waal mixing rule given by Equation (IV-30) if Kij - 1 (IV-37) at every temperature and pressure for all i,j. This assumption in turn implies that gi( ) gij ( ) - gJJ ( )'' ) (IV-38) i T,p,[x] T,p,[x] T,p,[x] Physically, the above constraint requires the distribution function for all pair interactions in the mixture to be expressed as a single universal function of dimensionless distance at the specified temperature, density, and composition. Furthermore, this dimensionless function is that obtained from the distribution function of the pure reference fluid at the reduced condition c /kT, * m m In contrast, when the conformal molecules i and j are in their respective pure component states, their distribution functions can be expressed in terms of the reference fluid distribution functions by the relations * r G g ( %0 C ( ii ) (IV-39) " T,p,x =1 * r - o00 kT' jj )(IV-40) 9 j)- r kTJ T,p,xjl Therefore, the distribution functions for the i-i and j-j interactions expressed as a function of dimensionless distance in their respective pure fluids are equivalent only at the same reduced temperature and reduced density. The Van der Waal rule for a 3 can be similarly obtained if we m work instead with the multicomponent equivalent of the equation of state given by Equation (III-8), expand each radial distribution function about the hard sphere case, and equate the corresponding temperature independent hard sphere terms. A detailed proof of the rule is provided by Leland and Chappelear. [144]. A proof of Equation

73 (IV-30) is also provided by the same authors but is less rigorous than the approach used in this work. The generalized Van der Waal equations expressed by Equations (IV-27) and (IV-28) can be obtained if we instead assume the distribution functions in the mixture to be described by the relation V gij( a,P,T,[C], [:], [x] ) = ( ) G*( E m 00kT oa kT' V (IV-41) for all i, j. For non zero values of v, the distribution function for the i-j interaction in the mixture is now also a function of the reduced temperature ~../kT as specified in the above equation. As the distribution functions are well defined for the real dilute gas, we can in fact examine the validity of the Van der Waal rule for this particular case. If we express each term in Equation (IV-1) using the reduced form suggested by Equations (IV-10) and (IV-11) we obtain the result 00 00 3 f { - expt F( )] } ( d( x ) -exp[- l F( ( d( ) a30 kT aM aM aM h kT aiC Y ij (IV-42) If the ratio of the integral for the i-j interaction to that for the mixture in the above equation is denoted by Li., then the above equation may be rewritten as n n n xi x Li ( ij /kT,Em/kT) aij3 (I-43 i-1 J-1j 3 3~~i (IV-43) We see from Equation (IV-42) that the Van der Waal rule for a 3 (L.. = 1, all i,j) is exact either if all the ~ values are identical, or if the temperature is high enough so that all exponential terms are significantly less than unity. For other situations, particularly at lower temperatures, it may be possible to define some optimum non-zero value of v in Equation (IV-27) to yield the best approximation to Equation (IV-42) at any given temperature. The optimum value of V will, of course, increase as the temperature decreases, because the distribution function in this case exhibits a stronger dependence on temperature as the temperature is lowered. Furthermore, we see that L.. also varies with composition at a given temperature because 1J

74 ~ varies with the mixture composition. m If we were to differentiate Equation (IV-1) with respect to temperature and repeat the process we would obtain similar results with respect to the Van der Waal rule for ~ a 3. Leland and colleagues m m [147,148] have expressed the opinion that the Van der Waal rules are not necessarily restricted to the Van der Waal equation of state, and may be applied to all mixtures with conformal potentials. The above considerations suggest that their opinion should be accepted with considerable caution for mixtures of substances with large differences in their E parameters in regions where the distribution functions are strongly dependent on temperature. b) Two Fluid Model The "two fluid" model attempts to relax the too rigid specification of a single average set of parameters for all interactions in the mixture. In this case the actual mixture of n components is replaced by an ideal mixture of n equivalent hypothetical components. Each of these n hypothetical fluids are assigned pseudoparameter values.i and a. which characterize the separate average environments of each species in the actual mixture. Thus, the configurational enthalpy and the heat of mixing can be expressed in terms of the pure reference fluid properties by the relations H (T,P,[x]) = xi H(T i o P a ~ (IV-44) 1 00 0 i 0 00 00 CE i 00 ~~i 0~*oo i i oo ) 1) Semi-Random Mixing Rules. The above model was derived from statistical mechanical considerations by Brown [31,33] given the assumption that all molecules were individually located in cells. It was also assumed that the cell size in each case was proportional to the volume of the molecule contained, and the number of nearest neighbours were allowed to approach infinity. Now, given the premise that the local distribution of molecules around each cell is random, the potential energy for the interaction of a molecule of species i with one of its neighbours is given by [31,33]

75 n Ui(r) = xuij (r) (IV-46) -i1 Brown further noted that the pseudopotential u. (r) was conformal with each pair interaction potential u.. (r), only if they were all 13 represented by the Lennard-Jones p-q form. Under these restricted conditions the pseudopotential parameters s. and i., were related to the pair potential parameters by the expressions n ii i X=:ij xj (IV-47) -li n a j= -1jij ij (q p) (IV-48) These prescriptions coupled with the averaging procedure of Equation (IV-44) together define the "average potential" or the "semi-random mixing" model. This model still provides the same absurd results for hard sphere mixtures that were obtained with the random mixing rule defined by Equation (IV-26), but is superior for softer potentials [19,147]. 2) Van der Waal Mixing Rules. Again, Leland and co-workers [148] provided an alternative prescription for the two fluid model that was independent of the potential function. They proposed the two fluid Van der Waal mixing rules given by n Ji=1 ( xji (IV-49) = Z (IV-50) j=l j iJ (IV-50) If as before, we start with Equation (IV-3), substitute Equation (IV-49) into it, and express it in dimensionless form assuming that the hypothetical potentials u. (r) are conformal with the actual like and unlike pair potentials, we may obtain the averaging procedure for the two fluid model expressed by Equation (IV-44) if the distribution functions for the i-j interactions in the mixture satisfy the constraints [101,102]

76 * r 1 * r r 9 ( I. (, ) + ) ] (IV-51) ij 2 ii ( ii ( JT,P,[x] T,,[x] JT,p,[x] This statement implies that the distribution function for any unlike pair interaction in the mixture expressed as a function of dimensionless distance is the average of those for the pertinent like pair interactions in the mixture at a fixed temperature, pressure and composition. This condition is less restrictive than obtained for the corresponding one fluid Van der Waal model, where all three were required to be expressed by the same function of dimensionless distance. The Van der Waal rule given by Equations (IV-46) may then be similarly derived under the additional constraints, ( r * r i gii C. G00 ( ar i (IV-52) T,p,[x] * ~ r 6j JJj kT' ) (IV-53) T,p,[x] The rule given by Equation (IV-47) may be derived from the multicomponent pressure equation of state [Equation (IV-4)] if the distribution functions are expressed as perturbations about the hard sphere case, and the temperature independent hard sphere terms are treated as outlined above [101,102]. c) The Three Fluid Model In this case, unlike the one and two fluid models, there is no correlation between the distribution functions for the different kinds of pairs in the mixture. For this particular model, the configurational properties of an n component system are averaged over n(n+l)/2 equivalent pure fluids, one for each i-j interaction and characterized by the parameters c.. and a... The configurational enthalpy for instance is 13 given by n n R (T,P,[x]) = Z xixj (T P) (IV-54) i=1 j=1 where it.. is the configurational enthalpy in the pure i-j fluid. For conformal molecules we obtain the further restriction

77 n n e a H (T,P,[x]) i Eij - H (kT P i ) (IV-55) i-l1 J-1 ij ij ij 00oo The model differs from the other two, in that it does not require additional hypothetical fluid parameters to be defined, and may be obtained with Equation (IV-3) as the starting point under the constraint [101,102]. gii (r) gi(r) (IV-56) T,P, x] g i i TP8xi~l. 0gr oo kT i (IV-56),PM " T,P,xi-1.oii ii - 00 for all like pair interactions in the mixture, and with the additional restriction ij (r) = g (r oo kT ) (IV-57) T,P,[x] 0 ij ij o00 In essence, the model implies that the like pair distribution functions in the mixture are the same as those in the corresponding pure fluids at the same temperature and pressure, irrespective of the mixture composition. These like pair fluid distribution functions may in turn be obtained from the pure reference fluid at the same reduced state. The unlike pair distribution function in the mixture is obtained from the same pure reference fluid using the parameters c.. and i.. instead. Comparison Between the Corresponding States Models for Mixtures a) Functional Differences. Each of the models examined permits the characterization of the configurational properties of a binary mixture using six interaction parameters c.., i, oii, i.. E.' j... 11 11 1J 111 JJ JJ They differ primarily in the order of averaging. The one fluid model averages the molecular parameters, while the three fluid model averages the thermodynamic properties. The intermediate two fluid model does some of both. An important feature common to all these models is their ability to predict the configurational properties of any multicomponent mixture purely from a knowledge of all the constituent binary interaction parameters and the configurational properties of the pure reference fluid. The examination of such models is therefore very relevant to the main objective of this work: the prediction of the enthalpies of the ternary methane-ethane-propane mixture.

78 Our next objective is to review the literature to determine how these models and their associated mixing rules have performed in representing and predicting the configurational properties of mixtures. Although we are, in this work, mainly concerned with the prediction of mixture enthalpies, comparison studies on other thermodynamic properties can also provide useful information in regard to these rules. b) Prediction of Excess Properties of Real Systems. Excess property measurements for liquid mixtures of six "simple" fluids such as argon, krypton, xenon, methane, nitrogen, oxygen and carbon monoxide have been extensively used as a testing ground for such theories at low temperatures [19,36,37,147,148,177,248]. We note from Equations (IV-23) and (IV-45) that an excess property is calculated as a small difference in large numbers of the same sign, particularly if all the potential parameter ratios.ij./ and c. /oo approach unity. iJ 00 IJ 00 Consequently, any uncertainty in the value of the pure reference fluid properties at each of the reduced conditions required to establish the excess enthalpy may cause serious errors in the estimation of the latter. Most investigators have, therefore, eschewed the use of the forms examplified by Equations (IV-23) and (IV-45) for calculating excess properties in favor of expanding each term on the right hand side of these equations as a power series involving the pure reference fluid parameters. Brown [31] and Leland et al. [147] have, in fact, developed such expansions for the excess configurational free energy of binary mixtures upto the second order for the one fluid random mixing and Van der Waal models respectively, in terms of variables that involve only the pair interaction parameters, by substituting the appropriate mixing rule for expansion terms involving c and a. The coefficients of m m these expansion variables now involve thermodynamic properties of the reference substance at the temperature and pressure of measurement only, in contrast to the exact form of Equation (IV-23), where 1, for oo example, must be evaluated at three separate reduced conditions. These expansions are cumbersome, but we include here, for simplicity, the result for H upto the first order terms as obtained

79 earlier by Longuet-Higgins [153] given by HE = ~ E XiXj { [ U T ] [ 2 _ -ii E + [(3RT-PV) Td( 3RV ] [2 0 iml Jl C - dT'dT [2 — OJ~'~ll jl~o00 00 00 oij ii j (tV-58) where U and V are the configurational energy and the volume for the reference fluid at a given T and P. The first order expansion is seen to be symmetrical in composition and independent of the specific mixing rule utilized. The properties V, GE, H and S are all required to have the same sign for this particular case [153]. In fact, later efforts to include second order terms were motivated by the observation that measurements on certain systems violated the above restrictions [31]. For liquids at low pressure, U is large relative to PV, and is opposite in sign to dU/dT. In such cases Equation (IV-58) may be simplified to include the one term involving the energy parameters only. Table (IV-I) lists similar simplified expansion results, including additional terms upto the second order for the excess free energy of a binary mixture in the liquid phase at low pressure as calculated by Scott and Fenby [238] using argon at 87K as the reference fluid. Table IV-1 Power Series Expansions for the Excess Free Energy in the Liquid Phase for Varions Corresponding States Models [238] E /xx2 RT 16.1Y + 15.2n2 - 2.0no + 58.0 o2 One Fluid Random Mixing, Eq. (IV-25,26) p-6, q=12 16.1Y + 15.2n2 - 16.1nr - 1.3 2 One' Fluid Van der Waal, Eq. (IV-29,30) 16.1W + 13.4rl - 1.0On + 28.9 2 Two Fluid Average Potential, Eq. (IV-47,48) p=6, q=12 16.1V + 13.4n2 - 8.05n1 - 0.6 *2 Two Fluid Van der Waal, Eq. (IV-49,50) 16.1V + 11.6n2 - 0.3 02 Three Fluid, Eq. (IV-54) k/2 Notation: (1 - ) - (E11e22) 2/ 2n' (a22 - e11 )/0oo ^ l- (022' -l 0o The random mixing and average potential model results reported in Table (IV-l) are obtained for the specific case of the Lennard-Jones

80 6-12 potential function. It is immediately obvious that the rules differ primarily in the second order size contribution d2 to the excess free energy. The terms in q2 are considerably higher for the random mixing and average potential models though the size contribution in the two fluid models is about half of that for the corresponding one fluid case. The excess property calculations for these models require the various pair interaction parameters to be first determined. The like parameters were obtained from critical data on the pure fluids [19,147, 148]. Initially, the unlike pair energy parameter was approximated by the geometric mean rule of Equation (IV-19) with kij equal to unity and the corresponding size parameter was approximated by the arithmetic mean rule of Equation (IV-17). These popular assumptions are collectively known as the Lorentz-Berthlot approximations. The values of GE, HE, and V for several equimolar mixtures of simple liquids as obtained from such calculations have been summarized by Rowlinson [226]. These results are reported as part of Table IV-2a. The appropriate parameter ratios ~/c and 3/aC 3 relative to Argon are shown in Table IV-2b. In general, the random mixing (not shown in the table) and semi-random mixing models realize G and H values that are algebraically larger than the experimental data. The Van der Waal one and two fluid models on the other hand yield excess property values that are algebraically smaller in that order. In making such calculations for the one fluid random mixing model, Brown [31] observed that slight departures from two parameter corresponding states theory could complicate the interpretation of the results. For example, the calculated value of H for the equimolar CO-CH4 mixture at 90.7~K varied from 70 to 105 Joules/gm mole as the reference fluid was changed from CH4 to CO. This emphasized the necessity for restricting the analysis to substances that are strictly conformal in two parameters. The sensitivity of such calculations to the precise choice of the potential parameter ratios El/Eoo and 22 /e and to the selected indices for the potential function for the particular case of the two fluid average potential model given by Equations (IV-47) and (IV-48) was examined by Calado and Staveley [36], using the data on the CH4-Kr system. Three independent sets of Lennard-Jones 6-12 potential

81 TABLE IV-2a Excess Property Predictibns for Real Binary Mixtures According to Various Models System rn 4 Excess Value of Average Pot. Three Van der Van der Van der Van der FLHW FLHW Gas Phase Property Ex. Prop. L-J 6-12 Fluid Waal W Waal Waal Waal Adjusted Adjusted k (Equimolar Two Fluid One Fluid Two Fluid Adjusted Adjusted One Fluid One Fluid S Mixture) ____________________One Fluid Two Fluid (Hard (Dilute a ~~~Exotipfl.~~~~~~~ ~Sphere) Gas) et al. Epti..Lorentz-Berthelot Rules [226] 1147] [148)] 248] [117] I II III IV V VI VII VIII IX X Ar-Kr.14.34 GE +84 +110 +68 +38 +53' (+84)* (+84) (+84) +97 116K VE -0.53 -0.44 -0.28 -0.78 -0.54 -0.66 -0.44 -0.79 -0.78 ki 1.00 1.00 1.00 1.00 0.986 0.990 0.990 0.994 0.994 Ar-N.08 -0.30 GE +34 +80 +15 +40 +27 +46 (+34) (+34) +34 84K2 H +51 +105 +13 +42 +27 (+51) +38 +46 +48 V -0.18 -0.07 -0.20 -0.32 -0.26 -0.31 -0.23 -0.21 -0.21 ki 1.00 1.00 1.00 1.00 0.998 0.997 0.999 0.999 Ar-0.01 -0.02 GE +37 +1 0 +1 0 +42 (+37) (+37) +33 84K- H +60 +2 0 +1 0 (+60) +52 +59 +50 VE +0.14 +0.01 0.00 0.00 0.00'+0.06 +0.05 0.08 +0.07 ki 1.00 1.00 1.00 1.00 0.986 0.988 0.988 0.990 Ar-CO.06 -0.42 GE +57 +70 +8 +26 +16 (+57) (+57) (+57) +55 91K V +0.1 +0.1 -0.14 -0.20 0.17 -0.13 -0.07 +0.07 +0.06 "k 1.00 1.00 1.00 1.00 0.989 0.985 0.985 0.986 Ar-CH4.11 +.29 GE +74 +170 +5 -19 +6 +92 (+74) (+74) +61 91K HE +103 +240 -8 -52 -11 (+103) +85 104 +75 V +0.72 -0.15 -0.15 -0.23 -0.23 -0.16 -0.13 +0.07 +0.02, kij 1.00 1.00 1.00 1.00 0.967 0.979 0.976 0.98 0.988 Kr-CH4.07 -0.13 GE +29 +38 +21 +15 (+29) (+29) (+29) 116K H +55 +56 +25 +17 36.3 35.7 36.8 -0.03 +0.01 -0.14 -0.11 0.13 -0.09 -0.02 kij 1.00 1.00 1.00 0.998 0.995 0.998 1.00 0.q94 Kr-Xe.14 +.27 GE +114.5 +265 +5 +44 (+114.5) (+114.5) (+114.5) 161K V -0.70 +0.97 -0.91 -0.62 -0.61 -0.41 -0.23 kiJ 1.00 1.00 1.00 0.974 0.929 0.989 N -0.09 -0.38 GE +43 +65 +19 +19 +35 +45 (+43) (+43) +46 22 H +46 +85 +17 +17 +35 (+46) +45 +46 +60 V -0.2 -0.11 -0.19 -0.32 -0.25 +0.33 -0.24 -0.33 ki -0.2 1.00 1.00 1.00 1.00 1.002 0.997 1.004 1.001 N2- CO.03.03 - +23 +2 +1 +1 +1 (+23) (+23) (+23) +22 2 V K0.1 -0.01 -0.01 -0.02 -0.01 +0.06 +0.10 0.06 0.09 k84K ij 1.00 1.00 1.00 1.00 0.991 0.992 0.990 0.990 N -CH..16 3 G +135 +94 (+135) 2 4 VE -0.21 -0.82 -0.72 kij 1.00 0.986 CO-CH ~ 4.10 GE +115 +105 +74 +75 +74 +131 (+115) (+115) +65 91K 4 H +105 +80 +64 +23 +43 (+105) +106 +125 +41 VE _-0.32 -0.50 -0.35 -0.84 -0.60 -0.72 -0.44 -0.36 -0.54 kij 1.00 1.00 1.00 1.00 0.982 0.987 0.982 0.998 CH -CF.01 3.0 GE +360 +280 +350 4 +280 4 4 V +0.88 +0.90 1.07 kij 0.908 0.908 n and * are defined in Table IV-1. The reference substance for each mixture is taken to be the component with the larger value of e. * Bracketed term is an adjusted property 4+ See References, 36, 147, 148 for sources of data TABE IV-2b Energy and Volume Parameters Relative to Argon for Substances Examined in Table IV-2Z Substances e /cr o3/ Ar A/ir Argon 1.000 1.000 Krypton 1.387 1.225 Xenon 1.916 1.580 Nitrogen 0.836 1.198 Oxygen 1.022 0.988 Carbon Monoxide 0.881 1.225 Methane 1.226 1.327 Carbon Tetrafluoride 1.245 2.540

82 parameters obtained from the literature were used to characterize each of the pure fluids. The calculated value of G in the liquid phase was found to vary from 11.3 to 38.1 Joules/gm mole for the average potential model depending on the choice of potential parameters. If the L-J 18-6 potential was used instead with appropriately defined parameters, the calculated G value rose to 100.7 Joules/gm mole in marked disagreement with the experimental value of 28.7 Joules/gm mole. This result is all the more disconcerting because the 18-6 potential was found to be considerably superior to the 12-6 in representing the second virial coefficient data for each of the pure components of the mixture [35]. We note from Equation (IV-58), and the expansions in Table IV-I, that the HE and GE values are both sensitive to the precise choice of ~12' Therefore, it appears doubtful whether calculations made with real test data using the Lorentz-Berthelot assumptions are really significant in discriminating between these various theories. The next phase in the examination of these models involves the adjustment of ~12, or the correction term kl2 to the geometric mean approximation, by fitting one excess property measurement (usually G ) exactly for each mixture. The models are then evaluated for their ability to predict other excess properties for the same mixture at the same temperature. The agreement in all cases was significantly improved, [19,147,148,226,248], but the comparison between the rules remains obscure because 612 or kl2 is now specific to each mixing rule instead of being a fixed independently defined quantity as it should be. The results for the one and two fluid VDW models [147,148] after such adjustments are indicated in Columns VI and VII of Table IV-2a. The specific excess property adjusted is enclosed in brackets. The adjusted results obtained by Snider and Herrington [248] with the Longuet-HigginsWidom (LHW) perturbation model described by Equations (IV-5), (IV-6) and (IV-7) were also included because of the theoretical superiority of the hard sphere mixing rule for the size parameter. Although the LHW model calculates the excess properties using the exact one fluid model result instead of a series expansion, each of the pure component configurational property terms [in Equation (IV-23) for example] are calculated from the best fit LHW equation of state. Therefore errors

83 incurred in representing the pure components may decrease the precision of the excess property calculations. We note, however, that since E E G and H are relatively insensitive to the mixing rule for the size parameter in the dense fluid, and since the mixing rule for the parameter a in the Snider and Herrington model is equivalent to that m for e a 3 in the one fluid Van der Waal model, the calculated results m m for these two models should be, and are, in general agreement. The two fluid VDW model results are seen to be slightly superior to both of these. The sensitivity of excess properties to the precise value of kl2 is indicated by the fact that the calculated value of HE for the CO-CH4 system changes from 23 to 106 Joules/gm mole, as the value of k12 for the one fluid VDW model varies from 1.000 to 0.982. Miller [117] repeated the calculations of Snider and Herrington [248], but instead used k12 values determined independently from second virial coefficient data. These results are also indicated in Table (IV-2a), column IX, and are seen to be in reasonable agreement with the experimental measurements (except for the system CO-CH4 where the k12 value was obtained from the examination of a single B12 measurement). Even such calculations are not definitive as the temperature range of available B12 data is almost never sufficient to define kl2 values precisely. Furthermore, the k12 values used by Miller were derived primarily from the data of Brewer [28], and are somewhat different from those obtained by Staveley and co-workers [35] from their own second virial coefficient measurements for the systems Kr-CH4, Ar-Kr, and Ar-CH4. Nevertheless, these results, within the limits of accuracy of the k12 determinations, make a case for the one fluid VDW rule for ~ a 3 11 CT m m Leland et al. [147,148] noted that the kl2 values adjusted with respect to the liquid phase excess properties for the one and two fluid VDW models were almost always below unity in keeping with the restriction imposed by the simple London calculation for the unlike pair dispersion energy [See Equation (IV-19)]. In contrast, the k12 values for the one and two fluid potential dependent models were above unity in several cases [19,36,37]. It was also noted that the adjusted k12 values for both VDW models were in better agreement with the values independently derived from second virial coefficient data.

84 Although such arguments are persuasive, it is difficult to make a definitive statement about these rules from comparisons that are restricted to a single condition in the liquid phase for each system examined. The excess enthalpy data of van Eijnsbergen [270,271] on the systems CH4-Ar, CH4-N2, CH4-H2, He-CH4, and He-Ar as a function of pressure upto 160 atmospheres at selected temperatures, and including the gaseous, critical and dense fluid regions should serve as an excellent source for evaluating the various theories for conformal mixtures. Unfortunately, the analysis of the various models with respect to these results have not been as exhaustive or as critical as for the liquid mixtures described above. Although van Eijnsbergen and Beenakker [272] tested the one, two and three fluid models using the exact expressions for the excess enthalpy in each case, their analysis did not include the VDW rules. Furthermore, no attempt was made to empirically define kl2 values using either part of the excess enthalpy data for each mixture, or independent second virial coefficient measurements. Quantum effects in mixtures containing hydrogen and helium also complicate the evaluation of models which assume classical fluid behaviour. They did, however, make the interesting observation that a single set of scale factors could not be found that would match the reduced configurational enthalpies of the three pure components N2, Ar, and CH4 taken two by two over the entire fluid region. It was suspected that deviations from strict two parameter theory and errors in the tabulated enthalpy values in the literature were jointly responsible for this situation. Figure (IV-1) typifies some of their calculation results on a CH4-N2 mixture for the three models considered. The Lorentz-Berthelot approximations were used in each case. The 12-6 indices were assumed for the one and two fluid models. As the figure and the rest of their calculations show, the calculated value of H decreases in going from the one to the three fluid model. c) Prediction of Phase Equilibria for Real Conformal Mixtures. Watson and Rowlinson [275] applied the one and two fluid Van der Waal models to the calculation of the phase equilibria for the

85 CH4 -N2 XN2 = 044 Experiment 1500 T= 201K One Fluid..~ — Two Fluid - Three Fluid Z 1000E 1' 500- I'.... " 50 100 P (otm) Figure IV-1. The Performance of Various Corresponding States Models in Predicting H for the Methane-Nitrogen System Using the Lorentz-Berthelot Rules [272]. _ 1= One Fluid VDW 2 = Two Fluid VDW 3 =Three Fluid 20.80 01 0 E E E I, oC w -I 22 /12 -22 /12 E221 /El,2) s E (2 / E Figure IV-2. The Performance of Some Models in Predicting G and H for a Mixture of Lennard-Jones Molecules [102].

86 constituent binaries of the Ar-N2-0 system upto 26 atmospheres using k., parameters derived in each case from binary liquid phase G data at low temperatures. The arithmetic mean rule was used to define the unlike pair size parameter in each case. The predictions were generally excellent (within 2%) for both models. The technique used by the authors in making these calculations was presented in a companion paper [228]. The prediction of the phase behaviour of the ternary mixture without the use of additional adjustable parameters was comparable to that obtained for the constituent binary systems. Although it is tempting to conclude that these results speak well for the extension of the corresponding states principle to mixtures of conformal substances, it must be remembered that the critical temperatures and volumes for the pure components of the particular ternary system investigated do not differ by more than 20%, and such results cannot therefore serve as the critical test we are looking for. d) Problems in Verifying the Corresponding States Principle Using Real Data. In summarizing the evidence examined so far, it appears that the accurate assessment of a theory of mixtures by virtue of its ability to predict the thermodynamic properties of real systems is probably more difficultly accomplished than the formulation of the theory itself. The calculation of macroscopic properties from conformal solution theories depends on: 1) The judicious selection of the reference fluid and the accurate specification of its thermodynamic properties. 2) The validity of the assumption of conformal pair interactions for all i-j pairs in the mixture. 3) The accurate determination of the reduction parameters for each pure component in the mixture. 4) The assigned values for the unlike pair interaction parameters, and 5) The mixing rule. As uncertainties associated with the first three steps, and particularly the third step, are unavoidable in application of such theories to real systems, it becomes difficult to establish the superiority of one mixing rule over another. Quasi-experimental

87 computer simulation results or thermodynamic property calculations from statistical mechanical considerations on systems that are simple enough to yield accurate results may serve as a desirable alternative to real data. In such cases the microscopic situation is rigidly and unequivocally fixed and under the complete control of the investigator. By fixing the conformal potential functions and the pair parameters for the like and unlike interactions, the macroscopic consequences are more impartially dependent on the mixing rule. e) Performance of Corresponding States Models for Soft Sphere Mixtures. Although the hard sphere is the simplest model suitable for comparison, it has been previously established in this chapter that the random mixing and average potential models lead to absurd results for this particular case. Consequently, Leland et al. [147] chose to test the theories for the next simplest system; a mixture of soft spheres. The PY equation for the free energy of a mixture of hard spheres [141] was extended to the soft sphere case by replacing the hard sphere diameter a by the temperature dependent function 00 co where E 1/n o77 c = ( kT ) [1 + 0577 + O(n2) (IV-59) [l+-~-)j —10(n2) (IV-59) and n is a variable measure of softness. The value of A was obtained as a power series expansion for both one fluid models and the P-Y case upto the second order term %2 in size difference as defined in Table (IV-3) using the arithmetic mean diameter for the unlike pair. The coefficients of the second order term 2, expressed in each expansion as a function of the reference soft sphere volume density o, were then compared. The results are summarized in Table (IV-3). E If n X 12, A is seen to be large and positive for the random mixing model, and becomes positive infinite as n approaches infinity. The coefficient of (2 for the P-Y and VDW models are essentially small and negative. The authors also expressed the 2 coefficients in terms of the virial expansion truncated at the third virial coefficient. These results are shown in Table (IV-4) where B and C are the 00 00 virial coefficients for the soft sphere reference. This particular

88 TABLE (IV-3) The Coefficient of the Second Order Size Term (2 in the Expansion of AE for Soft Sphere Mixtures [147]. Model Coefficient Percus-Yevick (1 + oo+ oo ) 1 (1 + 2 o)2 Percus-YevIck 4[ ~( - 5 - - - i oo oo Random Mixing 1 4( ~ ^ 3 (I - ) Random Mixing 4[ n + 7 (+oo + 2) (n +1) 12 (1 +2'oo)2 12 (1 - ~ o - 12 2 (1 - Foo)0 (One Fluid) a d 5 2 (1 + + 2) 1 1 (1 + 2 oo) 5 00 00 1 1 __+_2_ 0 Van der Waal 4[ ( - ) 3 ( 0 46 (1- - )3- 3 (1 - 4oo)] (One Fluid) TABLE (IV-4) The Coefficient of the Second Order Size Term <2 in the Virial Expansion AE for Soft Sphere Mixtures [147] Model Coefficient B C Percus-Yevick 4 1 O - 37 i 4 -) ( B C n-5 oo -n -11 Random Mixing (One Fluid) 4[ + ) ) + ( 12 V 12 V2 B C Van der Waal (One Fluid) 4[ - ( ) () 0 n -7 oo n-16 00 Average Potential (Two Fluid) 4[ + ( ( ) + ( ) 24 ( 24 V2 B C Van der Waal (Two Fluid) 4[ - ( V) ] B C 1 5 oo Three Fluid Model 4[ - ( ) TABLE (IV-5) Comparison of the Coefficients for the Second Order Size Term V2 in the Free Energy Expansion with Computer Simulation Results [227] J/mole Monte-Carlo Experiment [243] 4(-200 + 100) Random Mixing (One Fluid, 6-12 Model) 4(+ 9900) Van der Waal (One Fluid Model) 4(- 270) Average Potential (Two Fluid 6-12 Model) 4(+ 4900) Van der Waal (Two Fluid Model) 4(- 170) Three Fluid Model 4(- 85)* Simulation Conditions: Lennard-Jones 6-12 Potential T = 97K 11 1 12 = 22 = 133.5K a12 3.596 A = (a11 + 022)/2 022 /11 = 2.0 * Approximate estimate

89 comparison was made because the P-Y result is exact upto the term C 00 [147,148] and provides a simple standard for judging the other theories. The one and two fluid Van der Waal models are seen to be superior to the rest in that order for n > 3. f) Performance of Corresponding States Models for Mixtures of Lennard-Jones Molecules. An additional comparison study for the more complicated case of the Lennard-Jones 6-12 potential has been made by Rowlinson [227] using the Monte Carlo simulation results of Singer [243] on a binary mixture in the liquid phase with E = = 11 12 E22. The arithmetic mean rule was assumed for o12' and the volume ratio for the pure species was set at 2.0. These conditions were chosen to isolate the effect of size, as the leading term in the GE expansion for G (See Table IV-1) is now of the order of (2. The results are tabulated in Table IV-5. These results again establish the superiority of the Van der Waal mixing recipes. The comparison studies of Leland et al. [147] and Rowlinson [227] have both made a pointed attempt to evaluate the effect of size while ignoring the contributions due to differences in the energy parameters, precisely because it is the size effects that maximize the differences between the potential dependent and the VDW mixing rules for both the one and two fluid models, respectively. For molecules of the same size, we see by comparing Equations (IV-26) and (IV-30) that the random mixing and VDW one fluid models yield the same mixing rule for e. Both two fluid models are also seen to be m equivalent for this limiting case. Our next objective then, is to compare the behaviour of the one and two fluid models for the case where the energy parameters are significantly different. g) Inadequacies of Comparison Studies Based Strictly on the Coefficient of the Second Order Size Term. In referring to Table (IV-]), we note that both the one and two fluid VDW models have significantly higher values for the coefficients of the term n( than each of the corresponding potential dependent cases. The term nA which involves the simultaneous coupling of size and energy effects is seen to be absent for the three fluid model, but considerably complicates

90 the analysis of the energy and/or size effects for the VDW models. This point is inadequately treated in the literature, and merits further discussion here. The contribution of the energy-size effect may be illustrated GE with respect to the liquid phase G expansions presented in Table (IV-l) by calculating the variation of G /xlx2RT as a function of n2 or 2 for various values of n/b for each model. WJe observe that the coefficient of Y is the same for all models, and for simplicity assume the geometric mean rule for s.. ('Y=0) in order to enhance the relative contribution of the other terms in the series. The results are shown in Table (IV-6). The bracketed quantities indicate the % contribution of the coupling term rl to the total value of G /xlx2RT. Several observations may be made from the results presented in Table (IV-6). Firstly, we note that irrespective of the value and sign of np, the value of GE/xlx2RT is always positive for the random mixing and average potential models. The differences between these models and the equivalent Van der Waal formulations are seen to increase as n/4 decreases, i.e. as the size differences get larger. In general, we also observe that the percentage contribution of the coefficient of the coupled term rn is very significant for the one and two fluid Van der Waal models particularly in the ranges 2.5 < - < 0.16, and - 0.16 < < -0.5. In the former case, the molecule with the larger c also has the larger size. In the latter case, the sizes of the two species considered are interchanged. Each condition is seen to discriminate between the various models. Furthermore, even though the coefficient of the second order size term (2 is small for both VDW models, we may, by changing the sign of t for a given r, induce drastic changes in GE including that of sign in both cases. For most of the real liquid mixtures of Table (IV-2a), ln/ lies in the ranges 2.5 < < 0.5, - 0.5 < < -2.5, where the coupling term is seen to be of significant importance for the two Van der Waal models. Therefore, we are forced to conclude that theoretical evaluations based on the examination of the coefficient of the second order expansion term d2 alone are not wholly adequate in providing us with an accurate estimate of the behaviour of the Van der Waal models

TABLE (IV-6) The Contribution of the Coupling Term nr as a Function of n/~ to GE/RT in the Liquid Phase as Derived from the Results of Table IV-I Model n/4 = Tn/~ = 5 n/~ = 2.5 n/ = 1.0 n/ = 0.5 n/ = 0.16 / = 0 VDW (One Fluid) 15.2r 2,(0%) 11.9n2,(-32%) 8.6n2,( -74%) -2.2n2,( 800%) -22.2n2,(145%) -135.4n2,(74%) -1.342,(0%) VDW (Two Fluid) 13.42, (0%) 11. 8n2 (-16%) 10. 1n2,(-170%) 4.7n 2,(-170%) -5. 3n2 (300%) -52.4n2,(97%) -0.652,(0%) (Three Fluid) 11.6n2,(0%) 11.6n2,( 0%).5 0) 10.42,( 0%) 10.4n2,( 0%) -0.1n2,( 0%) 0.32,(%) Random Mixi g (One Fluid) 15.2n2,(0%) 17.1n2,( -2%) 23.7n2,( -3%) 71.2n2,( -3%) 243 n2,( -2%) 2268 n2,(0.6%) +58.0$2,(0%) Average Potential (Two Fluid) 13.4n2,(0%) 14.3n2,( -1%) 17.6n2,( -2%) 40.312,( -2%) 127 2,( -2%) 1136 n2,(0.6%) +28.9$2,(0%) Model n/ = -5 n/ = -2.5 n/= -1.0 n/ = -0.5 n/4 = -0.16 VDW (One Fluid) 17.4n2, (18.5%) 21.5n2,(30%) 30.0n2,(54%) 42.2n2,(77%) +65n2,(154%) VDW (Two Fluid) 16.8n2,(10%) 16.5n12,(20%) 20.8n2,(39%) 26.9n2,(60%) +38n2,(132%) (Three Fluid) 11.6r2,( 0%) 11.5r2,( 0%) 1.3n2,( 0%) 1l.3n2,( 0%) 0 ) Random Mixing (One Fluid) 17.9n2,( 2%) 25.3n2,( 3%) 75.2n2,( 3%) 251n2,(-2%) 2293n2,(0.6%) Average Potential (Two Fluid) 14.88n2,( 1%) 18.4n2,( 2%) 42.3n2,( 2%) 131n2,(-2%) 1148n12,(0.6%) *For Definition of and See Table IVFor Definition of n and 4, See Table IV-I.

92 for real or artificial conformal mixtures whose pure components have significantly different values of ~. A more relevant comparison of the first three models of Table (IV-6) was made by Henderson and Leonard [102] using the quasiexperimental GE, H and VE data of Singer et al. [242,243] for a binary Lorentz-Berthelot mixture of Lennard-Jones 6-12 molecules at 97K for ~22/l12 values varying from 0.8 to 1.2, with a22/a12 fixed at 1.06. The results of these comparisons should be significant with respect to the application of such models to real systems because they extend over the range 1.3 < n/ < -1.3. The results for V and HE are indicated in Figure IV-2. It was concluded that the one fluid Van der Waal model was superior to the other two for the particular case examined. h) The Role of the Distribution Function in Evaluating Corresponding States Models for Mixtures. Earlier in this chapter, we examined various corresponding states models from the standpoint of the constraints that they imposed on the dimensionless radial distribution functions for all pair interactions in the mixture. Therefore, if we are independently able to specify gij (-) in a mixture for all i, j, then we may also evaluate such models by determining how realistic such constraints actually are. In effect, this approach evaluates various models by subjecting the microscopic structure of mixtures to close scrutiny in contrast to the more traditional procedure of rating the same models for their ability to predict the macroscopic properties. Such information has not yet been determined from the direct interpretation of experimental data on real mixtures. Some useful results have, however, been obtained as a byproduct of thermodynamic property calculations on simpler artificially specified systems using either computer simulation or statistical mechanical methods. In a definitive study, Throop and Bearman [267] examined the variation of the radial distribution function for both like and unlike interactions in various binary mixtures as a function of density, composition, and the size and energy parameter ratios for the constituent pure components using both the hard sphere and the Lennard-Jones 6-12 models. The study was primarily confined to the dense fluid

9)3 region at supercritical temperatures because of difficulties experienced with obtaining a numerical solution of the multi-component P-Y equation for the Lennard-Jones potential at other conditions. We will now attempt to briefly show how their results could be used to examine the applicability of the two parameter corresponding states principle to mixtures. For illustrative purposes we confine our interpretation to the calculated values of gij (r), for all constituent i-j pairs of the Ne-Kr system at three compositions with the volume density C and temperature fixed at 0.3 and 260K, respectively. (For reference, the critical temperature and density for krypton occur approximately at c/kT = 0.8 and; = 0.167, respectively). The results are plotted in Figure IV-3 b, c, and d as a function of the dimensionless distance r/oi. for all i, j, instead of the distance r/o.. used in the original work, where j.. is the size parameter JJ jJ of the largest species in the mixture. The change in variable makes it easier to visually relate the results to the various corresponding states models. All pair interactions were assumed to be conformal and of the Lennard-Jones 6-12 type as indicated in Figure IV-3a. The unlike pair parameters were arbitrarily chosen to satisfy the Lorentz-Berthelot rules as indicated by Equations (IV-12) and (IV-14a), respectively, with k.. equal to 1.0. As the volume and energy parameter ratios for the pure components of the mixture are significantly different from unity (3 /c.. = 2.2,../.. = 4.7, where the subscript jj stands for the Kr-Kr interaction), we can expect gi (r/ij) for each i-j pair to be influenced by both size and energy effects. In examining each of the Figures IV-3 b, c, and d separately, we observe that although the general shape of gij (r/ij) is the same for all pair interactions in the mixture, particularly with respect to the location of the extrema, there are some differences in the magnitude of the radial distribution function for the various i-j pairs at any fixed value of r/a especially near the first peak. Therefore, the constraint of Equation (IV-38) which requires all gij (r/c) in the mixture to be equivalent at all values of r/c and which is implied by the one fluid Van der Waal model of Equation (IV-30) with V=0 is not optimally suited to this particular case. If we ascribe the differences in the magnitude of g. (r/n) mainly

94 Dimensionless 0.5 ILennard-Jones () 6-12 Potential... ~: XNe=.O, ^^^ ^ -b... ~.. Kr b ^ \ /^ ^ ^\~ ~ ~ ~' -- Ne-Kr r /o r /oN"' * -'=' -' ~OINe 20- A (b) ^ ^^ (e)1.0 -.0 1.0 1.5 2.0 2.5 r/o- r/o2.0- (b) (e) XN: O -2.0......... Kr:: XNe= 0. r/ KN Figure IV-3. The Radial Distribution Function g..(. ) for All Pair Interactions in the Ne-Krypton System at 260K [266 1..O1.0 15 2.0 2.5 1.0 1.5 2.0 2.5 r/o- r/o2.0'' (c) XN= 0.5 Tb 4InI tr -cto — Ne-Kr No-Kyt 1. S 1.5 2.0 2.5 System at 260K [266].

95 to differences in the value of c for the various L-j pairs, t lthe Equation (IV-41) suggests that a non-zero value for the exoponent ial factor v in the generalized one fluid model of Equation (IV-28) may allow us to compensate for the observed differences in gij (r/o). In fact, if we were to substitute Equation (IV-41) into Equation (IV-33) and repeat the derivation of the Van der Waal mixing rule for the generalized case with V 0, we would find, for example, that Iii (cii/kT)V I i' (E I/kT)~ (IV-60a) - ~jj v where I is defined as before. le may use the above equation to calculate the best value of v from the data in Figure IV-4. In Figure IV-3e, we plot the quantity y(r/G) defined as u(r) y ( CT g 47r2 (IV-60b) y(-) - g( —) 4(or2 for each like pair interaction for the case of the 50% mixture. The quantity I.. in Equation (IV-34) is defined in terms of yij (r/) by the relation.In.Tegrae ion the 4cr ti t Fig / a y ) avl1 (IV-61) Integration of the curves in Figure IV-3e yield a value of 1.15 for Ij./I... Therefore, given the fact that ~../e. = 0.7, Equation (IV-60a) yields the optimum value of V as 0.09. In any case, a cursory glance at Figures IV b, c, and d suggests that the assumption * r r * r (IV-61)r g ) [gi( ) + g ( )]/2 (for all (IV-6a) as embodied by the two fluid model with V = 0 would provide a more realistic representation of the microstructure of the mixture particularly at the first maximum in g(r/a) than the assumption of Equation (IV-36) corresponding to the one fluid case. Irrespective of how the various dimensionless pair distribution functions in the mixture relate to each other, the success of the

96 various corresponding states models still depends upon our ability to relate gij (r/a) in the mixture to that in the pure fluid. By following the variation of g(r/a) for each like pair as a function of composition in Figures IV-3 b,c, and d we note that, apart from a slight decrease in height of the first peak and a shortening of the distance between contiguous peaks as the mole fraction of neon increases, the approximation gi(, T, [x] ) gi(, i, T, xi 1.0) (IV-62) appears to be reasonable for the particular case examined. The implication of Equation (IV-62) is twofold. Firstly, it appears that the behaviour of any like pair distribution function in the mixture can be obtained from the corresponding pure component at the same temperature and volume density, and secondly, the optimum value of v for the generalized Van der Waal models is independent of mixture composition at any fixed temperature as long as the volume density is constant. Unfortunately many more such calculations are needed if we are to obtain more than a partial answer to the interesting question of how the exponent v varies with temperature, density, and composition, or for that matter with the energy and size parameter ratios of the constituent pure components. We emphasize again that although such calculations are tedious and perhaps impractical for design purposes, they promise to yield information that is less ambiguous than obtained from the correlation of real data. The selection of the volume density E as a working parameter instead of the reduced density must be considered as a judicious one. Although the two quantities are equivalent for pure components differing only by the constant factor 1/6 T, the volume density in a mixture is defined by = 6 ~ piOi3 (IV-63) where as the reduced density Pr is expressed as pr - pNe3 (.IV-64)

97 The use of ~ is preferred because, unlike pr, it does not commit us to a specific corresponding states model and does not require us to specify the hypothetical size parameter a. This author believes m that the significance of the parameter ~ should also be investigated in developing practically oriented thermodynamic property correlations. Throop and Bearman [268] have since calculated the excess properties H, G and V for various binary inert gas systems, Ne-Kr and Ne-Xe at the conditions corresponding to their earlier distribution function calculations using the same model. These results have unfortunately not as yet been tested against any of the corresponding states theories examined in this chapter but promise to be discriminating in the event of such an examination in the future. i) Conclusion. The entire discussion on mixtures of molecules governed by artificial potential models including the consideration of the radial distribution function is to be considered valuable because the evidence, unlike the results for real conformal molecules, permits us to conclude with some confidence that the generalized one and two fluid VDW corresponding states models are superior to others in characterizing mixtures of substances that are conformal in two parameters. Of these two models, no one is clearly superior to the other although it appears that the two fluid version is to be preferred at higher densities while the one fluid version is more suitable in the gas phase at subcritical pressures. However, since such evidence does not extend to mixtures of pure substances that subscribe to a three parameter theory, (such as the n-alkanes in which we are primarily interested), it is also necessary to examine the literature for more empirically based efforts involved in the correlation of the thermodynamic properties of mixtures in such extended schemes. iThe Macroscopic One Fluid Three Parameter Corresponding States Principle For Mixtures a) The Pseudocritical Method. It has already been noted in Chapter III that the force constants E.. and a..3 for pure substances conforming to a two parameter theory are proportional to the critical temperature Tc.i and the critical volume TVc.., respectively. In

98 examining the applicability of the one fluid model expressed by Equation (IV-22), to mixtures, one is tempted to replace the ratios ~ /~, and c 3/Cr by Tc /Tc, and Vc /Vc, respectively, where m oo m oo x oo x oo Tc and Vc are the measured true critical properties of the mixture, X X in order to determine if the measured configurational enthalpies of the mixture can be represented by the function H over the single 00 phase region in the P-T plane. The thermodynamic criteria defining the critical point in a mixture are discussed at length by Prigogine and Defay [208]. In brief, the conditions X2 T,P' (IV-65) a3G a X T,P (IV-66) must be satisfied by a binary mixture at the critical point in contrast to the conditions expressed by Equations (V-15) and (V-16) that apply to the pure component case. Other distinctions include the fact that the heat capacity for a pure component approaches infinity at the critical point, but remains finite for a mixture as demonstrated by the experimental measurements of Manker [162] on the 0.949 mole fraction methane-propane mixture. The most common procedure is to determine the parameters Tc and m Vc that produce the best fit of the thermodynamic properties of the given mixture in the specified framework. These are called "pseudocritical" parameters because they take the place of the pure component critical properties when used in corresponding states correlations, but unlike the latter, they are not accessible to direct experimental measurement. In fact, the "pseudo-critical point" always lies within the two phase region. For the special care of the Van der Waal equation of state, Rowlinson [226] has indicated that the pseudocritical parameters and the critical parameters for a binary mixture are related by the expressions: Tc - Tc dTc XT-c x(1-x) [ 3 d_ /Tcx dRT/P me 4 dx x dx( 7)

99 Pc - Pc a P Tc - Tc Pcm T ) V T (IV-68) m VVc T m where (OlnP/MlnT)vc has a value of 4.0. V=Vc m Kreglewski [133,134] determined that the empirical equation (TC1 - Tc22)2 Tc - Tc 2.2 x (-l) Tclll + T22(1) (IV-69) was satisfactory for binary n-alkane mixtures with ethane and n-heptane as extreme components. Equation (IV-68) was found to be considerably better in representing real fluid data if the slope of the pseudocritical isochore is instead expressed by the relation a In 808 + 4.93 ( + 22) (IV-70) V=Vc m where w is the acentric factor. b) Empirical Justification for Hydrocarbon Mixtures. The suitability of the three parameter pure component reduced function as a vehicle for the representation of mixture properties of normal fluids, was examined by Pitzer and Hultgren [197] who determined the pseudocritical parameters for a number of mixtures containing at least one light hydrocarbon by fitting the mixture compressibility data near the minima in z along isotherms to the Pitzer pure component corresponding states framework. Comparisons then made outside this region, even for mixtures of components with significantly different values of Tc and Vc, indicated an agreement of better than 1% in most cases. In an extreme comparison of this type, the second virial coefficient for a mixture containing 40% n-butane and 60% methane was fitted to a worse case deviation of 6cc/mole using Equation (IV-21) and pseudocritical constants obtained from dense fluid z values. However, as the Tc and Vc ratios for the constituent components of a mixture departed from unity, a trend towards poorer representation was observed. For example, in the case of a methane-pentane mixture, experimental isotherms fitted near their minima in z were found to lie about 2% below values predicted from the pure fluid reference at pressures

100 corresponding to half or twice the minimum. Yesavage [284] noted that optimized sets of pseudo-parameters could be determined for each of five methane-propane mixtures that would represent the enthalpy departure over the range -240 F to +300~F and upto 2000 psia and including the single phase liquid, gaseous and dense fluid region to within 1 Btu/lb. The direct use of calorimetric data on the pure components methane and propane to define the reference enthalpy departure functions in the three parameter framework must be appreciated as an optimum choice for the binary system in question. Powers [202] later obtained essentially the same results with the PGC correlation. It is, therefore, tempting to conclude that the one fluid corresponding states model is very suitable for the representation of the thermodynamic property of light hydrocarbon mixtures in the single phase region. This assumption, however, carries with it the implication that all thermodynamic properties can be represented with a single unique set of pseudo-parameters whereas, in fact, each investigation in this connection has been confined to the evaluation of the principle for one specific thermodynamic property. This distinction is an important one and is further clarified in Chapter IX. c) Mixing Rules for Calculating the Pseudo-parameters for a Given Mixture. It is now obvious that the accuracy of the predictions for the thermodynamic properties of a given mixture using the corresponding states principle will depend very heavily on our ability to correctly estimate its pseudo-critical parameters. Much attention has been devoted to the calculation of such parameters as a function of the mole fractions, the true critical properties of the individual pure components and from additional empirically obtained terms that are characteristic of all constituent unlike pair binary interactions appropriate to the mixture. The simplest and perhaps the most widely used rules are due to Kay [125,126] which combine the pure component properties in a linear fashion with respect to composition n m i21 ii i ~~~~~~~~~~~~(IV-71)

101 Pc = Z P. x (IV-72) m ciixi In a three parameter framework, Kay's rule may be extended to impose a similar composition dependence on the third parameter. Thus, the acentric factor w is defined as m n um= Z W iii (IV-73) i=l i Garcia-Rangel and Yen [86] have, in a recent comprehensive study, tested these rules for their ability to predict the enthalpy data of a wide variety of mixtures containing both polar and non-polar components. Kay's rule, however, suffers from the disadvantage of not being able to utilize binary mixture data when available. Pitzer and Hultgrei [197] extended Kay's rule by adding an extra empirical parameter for each binary interaction expressed in terms of the pseudo-critical properties of the equimolar binary mixture. n n n Tc 2 I Tciixi + Z XiXj [ 2 Tc0.5i, 0.5 - Tcjj (IV-74) i=1 Jdi i~j' m ii i i sj i C0.5i, 0.5j iL- - P (IV-75) jin i3 11 n n n m i-wiii Xij [ 2.5i, 0.5j - ] (IV-76) Jii i~J i, where the subscript 0.5., 0.5. refers to the equimolar binary mixture of i and j. These rules are sometimes expressed in an alternate form that is completely quadratic in the composition dependence, For a, for example, we obtain n n Dm I^llll'x i i (IV-76a) where w.. (ijj) is to be regarded strictly as an empirical constant. 13 The authors have tabulated the equimolar mixture pseudo-critical properties for twelve systems including the methane-ethane and the

102 methane-propane systems. These forms all reduce to Kay's rule if the pseudo-critical properties of the equimolar mixture are given by the arithmetic average of the constituent pure component critical properties. If it is assumed that e/kTc, and Vc/NO3 are constant for every term in Equation (IV-29) and (IV-30) as required by two parameter corresponding states theory, then we obtain the mixing rules n n m i1 j ij ij (IV-77) T ^ ~ Ji T!i ^^n n Tc Vc = Z Z XiXj Tcij Vj (IV-78) m m jj i=j1 j=i i If we assume a value of 0.5 for v in Equation (IV-27) and (IV-28), and assume zc is constant, again, as required by two parameter theory, then we obtain the rules RTc n n RTc Dm i-l j1 xix; Pcij (IV-79) 2.5 RTcn T 1 i J X 2 Pc' (IV-80) m i-l1 j Pcij Equations (IV-77) and (IV-78) encompass the Van der Waal pseudocritical mixing rules, whereas Equations (IV-79) and (IV-80) describe the Redlich-Kwong mixing rules. These rules obtain their name from the specific reduced equations of state from which they may be derived. This aspect is treated in greater detail in Chapter V. It must be emphasized that the equivalence between these rules and their microscopic counterparts is not assured in a three parameter framework with which they are frequently used. In such cases, as Leland et al. [144] point out, c/kTc is a function of the third parameter whatever it may be, and one would therefore expect to see an ac or X dependence in these rules. Such improvements have not yet found their way into the literature. In practice, an independent rule for the third parameter usually expressed in the form of Equation (IV-76a) is used concurrently with both sets of rules. The Van der Waal rules of Equations, (IV-77) and (IV-78) are used by both TLeland [81] and Powers [204] in applying their respective

103 corresponding states correlations to mixtures perhaps because of the excellent theoretical credentials behind these rules as noted earlier in this chapter. The approximations of Equations (IV-17) and (IV-19A) are applied to Vc.. and TcijVcij, respectively, if and when appropriate mixture data are not available to permit empirical adjustment of thr interaction parameters. A number of such mixing rules have been summarized by Reid and Sherwood [214], many of which can be derived from the Van der Waal form by making simplifying assumptions for the interaction terms Tc.i and Pc.. or Vc.. in terms of the pure component critical properties, 1J 13 or by fixing an empirically derived exponent different from unity on all Tc terms in Equation (IV-78). The Use of Equations of State in the Calculation of the Thermodynamic Properties of Mixtures The advantages of complex empirical equations of state such as the BWR over simpler forms like the Van der Waal and Redlich-Kwong equations in representing pure component properties do not extend to the representation of multi-component systems as a function of composition because of the increased difficulty in specifying the composition dependence of the equation of state constants. The mixing rules for the Starling BWR equation [Equation (111-19)] for example, are presented in Appendix H-l and are of empirical origin. The original BWR terms use the original BWR mixing rules. The additional terms D, E, and d for the mixture involve constants that must be determined from binary data. By determining the interaction constants D and E from the enthalpy data on the 50.6 mole percent "12 "1 methane-prpane mixure, the enthalpy behaviour for all five methane-propane mixtures investigated at this facility were predicted to about 1.1 Btu/lb in the single phase region. In working with the original BWR equation, Tiwari [268] suggested that mixture constants were better defined from the quadratic mixing rule n n km Z Z XX (IV-81)

104 where k is the mixture constant, if some mixture data were available m to permit the empirical specification of the parameter k... The lack of equation of state constants for all systems of interest have lead to the use of simpler analytic forms whose constants are more manageably related to the critical constants of the constituent pure components of the mixture whose properties are desired. The Wilson [279] modified Redlich-Kwong equation is one such popular example and is expressed as RTZEx x. (fb) i RT j (IV-82) V - Z xibii V(V + E xibii) i i where b.. = 0.0865 RTc../Pc.. 11 11 11 and (fb)ij = f(bii Trii, Trj, LWi' Wjj ai) where a.. is an empirical binary interaction coefficient. The phase LJ equilibria and enthalpy predictions are better than one would expect from the simplicity of the equation. Another interesting approach is due to Vera and Prausnitz [274] HS who, in effect, combined Equations (IV-5) and (IV-7). z was m represented by the closed form mixture hard sphere equation of state due to Carnahan and Starling [41], while z was represented by a complex empirical reduced equation of state expressed in pure component form. The Van der Waal coefficient a.. was then obtained as 11 aHS _RTV - ] (IV-83) aij - RTVm[Zij (IVwhere the superscript SG stands for the empirical Strobridge-Gosman equation of state [90]. The terms within the brackets were evaluated from independent estimates of the interaction parameters Tc.. and Vc... This technique, therefore, ascribes a temperature and density LJ dependence to the term a that is constant in the treatment of Snider m and Herrington [248] and ingeniously avoids the need to specify mixing rules for the individual constants in the complex empirical SG equation of state. Equation (IV-5) is now no longer restricted in application to liquids at low presslure. The technique wa.s uset( t:o fit the phase equilibria of the con;:It-uent In;lrics of tdie te(rnary system N2-02-Ar. The agreement was good (within 2%. of the observedl syte 2-2

105 mole fractions in the vapor phase). The predictions for the ternary system using the empirically determined constituent binary parameters were equally good. The method, however, has the disadvantage of being, for the present, restricted to mixtures of substances that are strictly conformal in a two parameter framework. Comparative Studies of Enthalpy Prediction Techniques for Non-Polar Mixtures The American Petroleum Institute [7] conducted a comprehensive survey of analytical and tabular correlations for both pure and mixed hydrocarbons and recommended the corresponding states approach of Pitzer and co-workers [195,197]. It was cautioned, however, that the paucity of directly obtained mixture enthalpy data at the time could subject their conclusions to reassessment in the future. Since then, the wide ranging mixture enthalpy data on the He-N2, CH4-N2 and the CH4-C3H8 systems obtained at this facility have served as standards for more recent comparison studies. The recent comparison study of Starling et al. [253] with respect to eight enthalpy correlations, already discussed in Chapter III with respect to the prediction of pure components, also provided results on the calculation of mixture enthalpies. Fifteen mixed systems were examined including the University of Michigan data referred to above, the n CH12-n C6H12, and the n C5H12-n C8H18 enthalpy data of Lenoir and co-workers [149,150]. The PGC, the 1970 Rice Properties III correlation of Leland and co-workers [81], and the Starling modified BWR equation were measurably superior to the rest in that order, with mean deviations in the enthalpy departure varying from 1.57 Btu/lb to 1.67 Btu/lb, respectively. The performance of the PGC for the light hydrocarbon systems with propane as the heaviest component was spectacular, yielding a mean deviation of 0.7 Btu/lb. The Rice Properties III correlation is slightly superior for the heavier hydrocarbon mixtures again, no doubt because the heavier n-pentane reference that should be more suited to the prediction of these systems than the propane weighted reference tables in the PGC. The authors also concluded that the increased deviations noted for the best methods applied to the heavier systems could be attributed to errors in the

106 data. Conclusion The empirical evidence suggests that the PGC 3 parameter one fluid corresponding states framework appears to be most suited to the representation of the enthalpies of mixtures of light hydrocarbons. Although the examination of a two fluid model is also recommended from more theoretical considerations, the implementation of such a model has been generally avoided in practice, perhaps because it requires us to specify twice as many parameters as for the one fluid case. Also, Powers [202] has already characterized the methane-propane binary in the one fluid PGC framework. Therefore, for our purposes, less additional effort will be involved in adopting his model to predict the enthalpy of the ternary methane-ethane -propane mixture than a two fluid version of the PGC.

Chapter V THE DEVELOPMENT OF ADDITIONAL MIXING RULES FOR THE PSEUDOCRITICAL METHOD In Chapter III, it was concluded that the PGC was perhaps the most suitable three parameter corresponding states framework for the representation of the enthalpies of pure non-polar species including the light n-alkanes. In Chapter IV, it was noted that the PGC framework was also a very effective vehicle for the one fluid model representation of enthalpy data of light hydrocarbon mixtures. It was also shown that the estimation of the pseudoparameters for mixtures of substances which are conformal in a two parameter framework could, at least in theory, be best accomplished by mixing rules of the Van der Waal type [Equations (IV-27) and (IV-28)]. This section is concerned with the development of additional procedures for evaluating the pseudocritical constants of multicomponent mixtures from constituent binary data in a three parameter corresponding states framework. First, the basic assumptions necessary for the prediction of mixture properties in the specified framework are stated. Next, in a different approach from that of the previous chapter, the Van der Waal mixing rules are derived by restricting the theory to apply to a two parameter reduced equation of state. A modified reduced Van der Waal equation of state is also used to develop another set of concise mixing rules that incorporate the effect of the third parameter acc. A more rigorous procedure for estimating the pseudo parameters for a multicomponent mixture that does not yield concise mixing rules is also presented. Additional considerations and practical difficulties involved in the implementation of the proposed procedure are discussed. In this connection, considerable attention has been paid to the development of two new correlations for the reduced second virial coefficient in the low to moderate temperature region and in the vicinity of the maximum in B, respectively. The application of the developments in this Chapter to the systems investigated in this work is illustrated later in Chapter IX. 107

108 The Fundamental Principle in the Calculation of Pseudo-critical Parameters for Mixtures It has already been indicated in the previous chapter that at any specified temperature, the configurational properties in the dilute gas region for all mixtures belonging to a given binary system may be calculated from experimental information on the configurational properties of the constituent pure components and any one binary mixture. In particular, we recall the relation for the second virial coefficient B of the mixture as m n n (B) = Z Y xix (Bij) (V-l) m T il -1j TFurthermore, we also recall that if Bij values are also experimentally 1J obtained for all constituent binaries of a multicomponent system at a specified temperature, then the value of B for the multicomponent mixture is rigorously known at the same temperature irrespective of marked differences in the nature and complexity of the constituent molecules. Unfortunately, such straight forward predictions for multicomponent systems cannot be invoked elsewhere in the fluid phase. However, if the calculated B values from Equation (V-1) can be coupled with a corresponding states framework with the expressed purpose of generating pseudocritical constants for a given mixture, then such information can be valuably utilized in predicting the configurational properties of the same mixture in the single phase region over the entire P-T plane. We next examine the additional restrictions that must be imposed on the intermolecular forces between all molecules in such a mixture if the procedure is to be justified. The Basic Assumptions I) It is assumed that all the constituent components of the mixture are restricted to a class of substances whose potentials are conformal in three parameters ii,.ii. and ec... uii( ) i F( aC1I) (V-2) iii fi i ii It follows that the macroscopic configurational properties and

109 in particular the second virial coefficient, the compressibility factor and the residual enthalpy can all be represented by suitable three parameter corresponding states functions. ii p T P Cc (V-3) RTcii/Pci' B (Tcii' ii ). f - cii) (V-4) zii fz ( Tcii' PC ii ^iiaii (V-5) JAZ ii tq Tc PTcii' P ii where fB' f and f4 are universal functions, and Tcii, Pci and ac.. are the pure component critical parameters that can be ].1 unequivocally defined by direct measurement. II) It is further assumed that the intermolecular forces between all unlike pairs in the mixture are conformal in the same sense. Thus i ( ) - E F(- rj I it (V-6) Consequently, we are able to write B f(T f cxc..(V-7) RTcij/Pcj fB( Tcij i where it must be emphasized again that the unlike pair parameters Tc.., Pc.. and ac.., cannot be uniquely specified by direct experimental measurements in contrast to the pure component case. III) From the standpoint of the macroscopic consequences of the intermolecular forces in a mixture, it is assumed that all the different species in the mixture may be effectively replaced by a hypothetical pure species, the molecules of which interact according to a potential function conformal with that of Equation (V-2) for some optimum choice of the potential parameters 6, aand a. Therefore Im m m Ur = Em' ~Cfcm ) (V-8) m

110 Also, we obtain as before B m T (RTcm/Pcm) fB( Tc I (V-n) T P multicomponent mixtures are calculated from experimental B.. values for all constituent binary pairs over a wide range of temperatures, then it is, at least in theory, possible to extract the parameters Tc, and P for the mixture from Equation (V-9), and apply these values m m ~Smin Equations' c ) (V- ll) to calculate and atany and m m in the single phase region. The suggested procedure is theoretically rigorous within the restrictions imposed by the three previous basic IV) In consequence of the above assumptions, if B values for m ulticomponent mixtures are calculated from experimental B.. values Our only recourse in evaluating the validity of assumption II then it is, at least in theory, possible to extract th parameters unequivocally determinabled P for the mixture from Equation (V-9), and coefficient data. Forvalues in Equations (V-10) and (V-11) to calculate z and.# at any T and P example, the followingle phasroceduregion. may be suggested procedure is theoretically a) Determine Tbrestri/Tc..,tio and Vbimposed/(RTc../Pc..) for each of by the three previous basic assumptions. Our onrmal purecomponentse in evaluating and V the validity of assumperatureion II and Boyle volume, respectively, obtained from direct measurements on determinable from interaction second virial coefficient data. example, the following procedure may be suggested. a) Determine Tb.i/Tcii, and Vb /(RTc /Pc ) for each of the conformal pure components where Tb.. and Vbii are the Boyle temperature and Boyle volume, respectively, obtained from direct measurements on second virial coefficients. b) Determine the value of the reduced second virial coefficient B../(RPTcii/Pc.i) for each of the pure components at some low temperature that is a specified fraction of the Boyle temperature, i.e. at k(Tb), (k<l). c) Correlate all three reduced variables as a function of OCc..

ii G(aci) (V-12) RTc11/P ^it~iiTCI/PCIII H( ii) (V-13) Bii (R /Pi)] K(acii) (V-14) T = k(Tb) d) Measure Tbij, b.ij and B.. at T = k(Tb) for each i-j pair using interaction second virial coefficient data, and solve for Tcij, RTcij/Pcij, and ac.i using the above three equations. e) Substitute these parameters into Equation (V-3), and determine if the calculated reduced second interaction virial coefficients agree with those obtained from measured Bij values over the entire range of the data, and in particular outside the limits k(Tb)<T<Tb. Difficulties in Implementing the Rigorous Procedure Unfortunately, experimental second virial coefficient data for pure n-alkanes heavier than methane do not extend to high enough reduced temperatures (>2.3 Tr) to permit the evaluation of the Boyle parameters. Furthermore, it is highly unlikely that such evidence may ever be obtained for the heavier hydrocarbons before the onset of thermal decomposition. Also, the specification of the Boyle parameters for any unlike pair interaction would require some mixture data to be available in the high temperature range. Therefore, it is apparent that establishing the identity of the function = g(T/Tb) (V-14a) for both like and unlike pair interactions, in mixtures where all pair interactions are suspected to be conformal, is virtually beyond experimental corroboration. Douslin and Harrison {65] have established the validity of the function (V-14a) for the pure components CH4, CF4, Ar, and Kr over the range 0.55 < T/Tb < 1.2. It was determined that the second interaction virial coefficients for the system CH4-CF4 also subscribed to the same

112 function over the same range of T/Tb. To the best of this authors knowledge, this is the only case where enough experimental measurements have been obtained to allow the conformality of all pair interactions in a mixed system to be tested. The result is significant because the ac value of CF4 is considerably different from that of CH4, and approximately equal to that of n-C4H10 in the n-alkane series. The main purpose of the above arguments is to suggest that, in the absence of conclusive experimental evidence for other non-polar mixtures of interest, it is not unreasonable to assume that the function fB in Equations (V-3) and (V-7) are the same, particularly if the span of cc values for the various components in the given mixture are smaller than for the CH4-CF system. The Calculation of Mixture Pseudoparameters from the Van der Waal Equation of State For illustrative purposes, we now apply the suggested procedure governed by assumptions I through IV to the limiting case when the reference generalized equation of state given by Equations (V-4) and (V-13) is replaced by the reduced two parameter Van der Waal equation of state. If the criteria (= 0 (V-15) T=Tc ( 2p (3P) - 0 (V-16) V2 T=Tc are applied to the Van der Waal equation of state we obtain the result [165] RT 9 R Tc Vc (V-Vc/3) 8 V2 (V-17) The second virial coefficient for both like and unlike interactions is then obtained from the above equation as Bj 3 8 T all,J By combining Equations (V-l) and (V-18) we can obtan te Vn dr W (V-18) By combining Equations (V-l) and (V-18) we can obtain the Van der Waal

113 mixing rules expressed by Equations (IV-77) and (IV-78), respectively. a) The Modified Van der Waal Mixing Rules. If, for example, we apply the criteria V Tap C ) = 0(V-19a) TdTc d In P ( d —nT-) ^ = ac d 1 - = -V c c (V-19b) to the Van der Waal equation of state instead of Equations (V-15) and (V-16) we obtain the mixing rules Tc ac -2 n n T Ctc-2 Pcm il -1 xix [ PC ci ( (V-20) Tc2 (c0C-1) n n TC_ ( 1ac P = a d ei in d (V-21) a These rules are derived in Appendix G, and illustrate, typically, the procedure for obtaining mixing rules from two parameter reduced equations of state. By fitting the slope of the real fluid critical isochore at the critical point to the Van der Waal equation of state, we have been able to develop a mixing rule in a two parameter framework that involves the third parameter ac, and which must, at least in theory, be considered more attractive than the original Van der Waal mixing rules for use in a three parameter framework. However, a third independent relationship between the pseudocritical parameters Tc, Pc m m and ac is still necessary to specify each of them uniquely. The empirical rule n n cCm = c xlxjaci (V-22) mi=l J=l is invoked to satisfy this requirement for both sets of rules. This form is equivalent to the Pitzer-Hultgren rule for the third parameter Wm shown as Equation (IV-76), if the linear relationship between the parameters cc and c is recognized from Equation (III-32). Other mixing rules similar to Equations (V-20) and (V-21) may be obtained either by starting with a different two parameter equation of state, or by

114 choosing different criteria for defining the reduction parameters. b) The Practical Utilization of Mixing Rules of the Van der Waal Type. None of the rules discussed so far can be implemented unless the interaction parameters Tc.., Vc.. (or equivalently RTcij/ Pc..), and ac.. are first defined. The most rigorous way to accomplish this, without destroying the consistency with the original model in each case, is to fit B.. data (ifj) to the specific reduced second virial coefficient function fB that is used to generate the rules. B Figure (V-l) compares the reduced second virial coefficient B/Vc of a non-polar spherically symmetric classical fluid as a function of Tr [145] with the calculated results from Equation (V-18), and from a combination of Equations (G-8) and (G-14) in Appendix G. The latter curve originates from the modified Van der Waal equation of state discussed above and is seen to be slightly superior to Equation (V-18) in representing real systems. However, given B.. data for real pure components, it is unlikely that the parameters Tc.. and Vc.. calculated from the best fit to either of the dashed curves in Figure (V-l) will be in strict agreement with the values obtained by direct measurement of pure component critical properties. This point is raised because Tc.. and Vc.. (iij) cannot 1J JJ be measured directly and we need to find an attractive indirect technique to specify them. It may be anticipated that the technique proposed in the previous paragraph would not be very effective because neither of the dashed curves in Figure (V-l) can accurately represent real pure component data. Recognizing the inadequacies of the Van der Waal and other two parameter equations of state, but impressed by the conciseness of the mixing rules that can be derived from them, it is reasonable to ask why attempts have not been made to generate concise mixing rules starting with empirical representations of the function fB in Equation (V-3) that more accurately represent real data. The reason for this is that most of these functions have more than two constants, and do not lend themselves to the manipulations, typified in Appendix G, that will permit the straight forward extraction of mixing rules which directly relate the pseudocritical parameters of the mixture to the

> -2 From The Reduced Van der Waal Equation of State [Eqn.(V-18)] -.,\ |From The Modified Reduced Van der Waal Equation of State [Eqn.(G-8) and (G-13) ] \ Prom The Tabulation of Leland, Kobayashi and Mueller [145] -3 \ -4 O5 I 0 I Il 10O 10 1 0.1 Tr Figure V-1. The Reduced Second Virial Coefficient as a Function of Reduced Temperature for a Classical Spherically Symmetric Fluid.

116 composition and the constituent pair interaction parameters. Another approach, somewhat less defensible in theory, but more successful in practice, is to fit experimental measurements on binary mixtures to the appropriate reduced thermodynamic functions defined by Equations (V-9), (V-10) and (V-ll). The set of pseudoconstants Tc, Pc and acc generated for the best fit case may then be used together m m with the pure component critical properties to calculate the appropriate unlike pair parameters directly from some specified set of concise mixing rules, say for example, the rules expressed by Equations (V-20) through (V-22). Once all such unlike pair interactions have been determined from binary data, the mixing rules provide a concise technique for calculating the pseudoparameters, and hence the thermodynamic properties of multicomponent systems. Such procedures were indeed used by Pitzer and Hultgren [197], and Yesavage [284] to define binary interaction constants for other more empirical mixing rules from wide ranging volumetric and enthalpy data, respectively. Difficulties Involved in Using Second Virial Coefficient Data to Obtain Pseudocritical Parameters It is difficult to specify pseudocritical or interaction parameters solely from second virial coefficient measurements. The second virial coefficient is well known to be relatively insensitive to the form and details of the intermolecular function chosen to characterize the pair interaction [188]. Even if we were to specify an accurate empirical function fB in Equation (V-3), the parameters for the optimum fit to pure component B data, for example, would not necessarily coincide with the true critical parameters unless the experimental measurements were to extend from at least 0.5Tc to 6Tc. B values for a m multi-component mixture are, therefore, to be specified over approximately the same range of reduced temperatures if the "correct" pseudoparameters are to be extracted from the best fit to the specified function f. As the technique requires Equation (V-l) to determine the set of B values to be used, it is apparent that we will need B.. m l] data below 0.5 Tc.. for interactions where Tc.. < Tc, and above 6.0 Tcoj for interactions where Tcij > Tc. Thus, the effective reduced m

117 temperature range over which direct measurements are required to characterize the mixture pseudoparameters can be considerably broader than that required to determine the reduction parameters for the pure component case alone. There are few pure compounds for which such wide ranging measurements are available in the literature. The situation is even worse with respect to measurements on unlike pairs. If, for example, we consider a multicomponent methane-ethane-propane mixture, the limited range of the constituent binary interaction virial coefficient data would probably not permit more than one pseudocritical parameter to be significantly optimized, forcing the other two parameters to be predetermined from mixing rules bases strictly on the constituent pure component parameters. Prausnitz and Gunn [206], for example, obtained Tc.. (ilj) from a best fit to B.. data using the reduced second virial coefficient correlation of Pitzer and Curl [Equations (III-40) through (III-42)], after having previously fixed W.. and Vc.. from simplifying rules involving only pure component parameters. Proposed Scheme for Calculating Mixture Pseudoparameters from Enthalpy Data We now consider another approach for the calculation of B values m for a multi-component mixture based on the indirect calculation of B.. as a function of temperature for each of the constituent unlike'3 pair interactions. From the considerations in Chapter IV, it appears that, given accurate wide ranging enthalpy data on a light hydrocarbon mixture, there exist suitable empirical representations of the function fq in Equation (V-5) or (V-12), such as the PGC, that will define a pseudocritical parameter set for the mixture with reasonable selectivity. If it is further assumed that these pseudoparameters are also applicable to Equation (V-9), then the B values for the m mixture may be calculated from a suitable function fB over some fixed temperature range. The constituent pure component virial coefficients can also be calculated over the same range using the same function fB as defined in Equation (V-5). If the mixture is restricted to two components, then Bij values for the unlike pair interaction may now be computed over the same fixed temperature range using Equation (V-l).

118 The Bi, values as a function of temperature may be similarly computed for all the constituent unlike pair interactions in a multicomponent mixture by obtaining and processing the enthalpy data on at least one binary mixture in each case. Reapplication of Equation (V-l) to the multi-component mixture yields the desired set of B values as a function of temperature. Equation (V-9) may now be used to evaluate the required parameters Tc, Pc and ac. The set of B.. values m m m mj determined for each i-j pair by this technique is now limited only by the range of of applicability of the function fB and should extend considerably beyond the temperature range of direct measurements in almost all cases. A schematic of the proposed technique for the prediction of the enthalpies of a ternary mixture from the minimum amount of constituent binary enthalpy data is shown in Figure (V-2). An important consequence of this technique is that it permits a direct comparison between experimentally determined B.. values (ilj) 1J when available, with results synthesized from wide ranging enthalpy data. Similar procedures could be invoked to obtain synthesized B.. values as a function of temperature from other thermodynamic measurements; for example, using volumetric data in the liquid and dense fluid region. The consistency between such independently obtained values of B.. as a function of temperature can then serve as a measure of the validity of the one fluid corresponding states model for mixtures of conformal substances. From the discussion in Chapter IV it may be anticipated that as the mixture becomes less random (as the size and energy parameter ratios for the various molecular species in the mixture depart from unity), the validity of the assumption should be more questionable and we may anticipate this to be reflected as an increased disparity between the independent B.. sets obtained as above. It is conceivable, however, that even though the assumption of Equation (V-ll) may be valid, any one of the three functions fB, f and fU in Equations (V-9) through (V-ll) may not by itself be sufficiently selective enough to be able to generate from the appropriate configurational property precisely those pseudoparameters Tc, Pc and ocl that can satisfy the conditions expressed by all three equations simultaneously. The desired parameter set will

119 Pure 1 Pure 2 L....CRITICAL... X2 1.0,DATA T22 22 ac 22 XPure0 \ -.............3.3.3 >33 Binary Mixture A (Xl) (X2) I —1 r K [Tc,,Pcm~acm]A > i t I Binary Mixture C * i (X3)C (Xl)C 1-' } 1:1 r^\ ^c h^ L^^^T>J I i i I~ i i Direct B. -* i Ij B l I — +_ + — Measurements j m AB ^ ^^"^^ I *~"" "^ ___" ____' ~~~cj I I l! < l j /~~~~Bi, T) - B (T) - i ii (T) x;- B jj - x ^ "(T)_ ___ I..t i^^> ^^Y ^B3^)>: I (B12CT)> 23(T B31 Ternary Mixture D 3 3 ( )D', 32) 3,(3 )D rBm (T)l'i xitBij( ) B! ZX f (T,Pr,ac) /[ ]>~ PGC /i~^ (T)~P)rLCD /:-......o.O. ~ Ternary Mixture D Predicted Enthalpies Figure V-2. Schematic of Proposed Scheme for Defining Pseudo-Critical Parameters for Multi-Component Mixtures.

120 hitherto be referred to as the "meaningful" set. In general, one can expect a particular configurational property to be most sensitive to the optimization of those pseudoparameters that are used to express it in reduced form. Given B data for example, we see from Equation (V-3) m that the optimization should be uniformly sensitive to the reduction factor RTc /Pc regardless of the functional dependence of fB on Tc and ac. Similarly, an optimization using reduced enthalpies m m can be expected to be more selective of the pseudocritical temperature, Tc, as was verified by Yesavage [284] for several methane-propane m mixtures. These considerations reveal that the success of the proposed procedure will depend very heavily upon our ability to extract meaningful pseudocritical parameters at every optimization step. Furthermore, if our primary objective is to be able to predict the enthalpy of mixtures, then we particularly need to obtain an accurate value of Tc. Unfortunately, it must be acquired from a property m [Equation (V-9)] that is not particularly suited to this end. This suggests, therefore, that a critical factor in the performance of the proposed technique is the accuracy and temperature range of validity of the function f, and our ability to extract the correct value of B Tc from a set of B values using the function. m m Selection of a Method for the Representation of the Second Virial Coefficient in a Corresponding States Framework Although we seek to select a function fB that is universally suitable for the representation of the seconf virial coefficient of non-polar substances, it is more important that it satisfy the specific objective of representing the experimental measurements on methane, ethane and propane as our test multi-component mixture is composed of these components. The deficiencies of the existing three parameter correlations of Pitzer and Curl [196] and McGlashan and Potter [159] in this regard have already been noted in Chapter III from which it may be concluded that the development of a more accurate correlation is desirable. The plan of attack is to develop a reduced correlation for some spherically symmetric non-polar substance, and to express the reduced second virial coefficients, Br, of other substances as a perturbation

121 about the reference fluid values using the third parameter ac as the perturbation variable. a) Representation of the Reference Fluid: Methane. Methane was selected as the reference fluid in view of the availability of direct measurements over the extended reduced temperature range 0.58 < Tr < 3.26. Furthermore, precise independent measurements [28,35,67,108,200] are in excellent agreement down to 190K. Below this temperature there appears to be significant differences between the precise measurements of Pope [200] and Byrne et al. [35] reaching a maximum of 6% at about 125K. The measurements from all sources were fitted by the empirical equation RTc/Pc = 0.14416 - 0.49095(1-e6) (V-23) The functional form of the above equation is dictated by the result obtained for the square well potential [167] of Equation (III-4), the theoretically equivalent parameters for which are given by C3 = (0.14416) ( RTc (2r/3) No ( Pc ) (V-23a) = 0.68511 Tc (V-23b) [ - ( L + ) 0.49095 RTc [1-(1+ (27T/3) N ] ( ~3 c ) (V-23c) where L is the well width. The constants in Equation (V-23) were obtained by a non-linear regression analysis. Although there are many experimental determinations of the second virial coefficient of methane, only those sources that were deemed to be precise were used in this work. With the exception of the data of Pope below 198.15K, the absolute average deviation for all measurements was under 0.6%. (See the bottom entry in Table V-l). b) Representation of Substances with ac Values Different from Methane. Next, several hydrocarbons from ethane to n-octane, the inert gases Ar and Kr, and also CF4 were examined to determine the

122 TABLE V-1 Summary of Results for the Reduced Second Virial Coefficient Correlation [Equation (V-30)] of This Work Abs. Abs. System Investi- Reduced Temp. No. of Mean Value Avg. Avg. ** Reference gator Range Points of B Dev. Dev. % Low High N cc/gm mole cc/gm mole % Bias [200] C2H6 POPE.69 1.00 6. 216.6 7.5 3.4 +3.4 [] MICHELS.98 1.38 7. 141.8 1.1 0.8 +().7 61 )IAZ PENA.65 1.63 13. 174.5 6,6 3.8 -3.2[ GIJNN 1.23 1.67 3. 83.5 1.9 2.2 -0.7 94 [1591 C3H8 MCGLASHAN.80 1.11 12. 278.2 7.4 2.7 +2.7 (1361 KtNZ.74.86 3. 404.2 3.3 0.8 +0.4 [12 3 KAPALLO.52 1.40 15. 464.4 4.4 1.0 -0.1 6123 [ 61] )IAZ PFENA.68 1.48 13. 229.8 2.5 1.1 -0.4 [240] SILRERPFRG.66.94 6 448.3 6.0 1.3 -0.2 6] 1.00 1.48 9. 169.5 2.8 1.6 -1.6 I)SCHNER.82 1.54 6. 223.6 10.3 4.6 -4.6 [ 27] n-C4H 10 OTTOMLEY.64 1.00 7. 644.4 19.5 3.0 -3.0 22 KAPALL().57 1.00 6. 788.7 51.3 6.5 -6.5 [15 MCGLASHAN.69.97 11. 478.3 9.3 1.9 +1.8 n-CSH12 MCGLASHAN.63.88 11. 837.7 15.6 1.8 -1.1 [159 DIAZ PENA.64 1.07 9. 649.7 11.4 1.7 -0.6 61 [2413 i-C5H12 SILRERRERG.59 1.00 7. 888.1 29.3 3.3 -3.3[241 n-C8H 8 MCGLASHAN.65.72 10. 1841.0 88.7 4.8 -4.8 [159] CF4 DOUSLIN 1.20 2.73 9. 48.6 0.9 1.9 -1.4 [ 66]' 371 LANGE.89 1.61 6. 128.h 4.0 3.1 +2.9 A RYRNE.57 1.80 18. 134.9 2.3 1.7 +1.7 35] KR BYRNE.56 1.20 12. 208.1 6.6 3.2 +3.0 [ BREWER.58 1.54 8. 127.3 4.4 3.4 +1.9 28] CH4 RYRNE.58 3.26 42. 104.5 0.6 0.6 0.0) 31 Hn nv E[R [1081 HnOVER R REWER [ 67] DOUSL IN 67 nOPE.66 1.00 6. 175.4 5.2 2.9 +2.9 [2001 * IB - Bcal N N B N

123 effect of the third parameter ac. It was decided to use a modified reduced temperature parameter Tr to correlate these measurements in 00 view of the singular success obtained by Powers [204] using a similar approach in the correlation of pure component enthalpy data of non-polar compounds. The modified reduced temperature Tr for a substance at oo reduced temperature Tr has already been defined on page 52. This approach is identical to that of Powers who suggests the parameter T defined in Chapter III. The change in parameter was motivated by the belief that readers will have a better "feel" for the concept of a modified reduced temperature Tr than for the parameter T. oo Heavy reliance was placed on the propane data in defining the furnction for several reasons. Firstly, its ac value is significantly different from that of methane. Secondly, the data extend to low reduced temperatures, (Tr < 0.5), and thirdly, since heavy reliance was placed on the propane measurements in defining the PGC enthalpy framework, it was felt that maximum consistency between the two correlations would be achieved. As measurements on propane were not available above 1.54 Tr, the precise measurements of Douslin et al. [66] on CF4 extending to 2.73 Tr were emphasized in this range. We now explain the first but somewhat abortive approach to the problem. The data for the substances examined were individually fit to the form c/Tr Br = a + b(l - e ) (V-24) (V-24) the rationale being that the constants a, b, and c could then be redefined as functions of (Occ - ac ) 00 B -{0.68511 + g(c-_cc )/Tro (RTc/P) 0.14416 + h(ac-acoo) + [0.49095 + k(ac-acc)] [l-e 00 0oo (V-25) where h, k and g are the functions to be specified, and ac is the 00oo ac value for methane. The equation reduces to Equation (V-23) if ac + cc. The empirically observed and theoretically predicted restriction Tr (C RTc/ ) P 00, Tr oo (V-26) 00, 00

124 discussed in Chapter IV leads to the constraint h(ac-ac) + k(ac-ac o) [l-e{068511 + g(ac-ac o)}] (-27) Most of the measurements were obtained over restricted temperature ranges. Furthermore, the reduced temperature range of the data varied considerably from one substance to the next. Consequently, values of a, b, and c for the individual compounds obtained in this manner were not specific enough to permit them to be reasonably correlated as functions of (ac - Oc ). OO The next approach was to select a functional relationship of the form Br(Tr) BrTroo) + [ (T) [ c- Coo i (V-28) involving a linear dependence on (ac - ac ) where Br is given by the right hand side of Equation (V-23). The slope function (dBr/dcc) was determined by investigating the quantity [Br(Troo) - BroTroo) ]/(c-coo (V-29) as a function of Tr for various compounds. This technique, unlike 00 the previous one, has the advantage of allowing accurate data for various compounds in different regions of reduced temperature to be investigated on a common basis. The final result given by the expression B 0.68511/Tr 00.0220 -0.00614 0.00281 0.14416+0.49095(1-e ) + (cc-5.82)(0.0175 0- Tr 2 - (0 ~~~~~~~~~'(RTc/Pc) Tr 00 Tr 00 00 (V-30) oo oo oo was obtained, where the last bracketed term in the above equation is a representation of the slope function in analytic form.'igure V-3 shows a plot of Br for methane, ethane and propane as a function of Tr designated as TrH to indicate the use of methane 00 CHA as a reference fluid. The dotted line shows the smoothed location of the propane data using the actual reduced temperature Tr as the independant variable instead. The separation between the Br

Table V-2 Comparison of Second Virial Coefficient Correlations with Respect to Methane and Propane Species T Tr Tr B B(I) B(II) B(III) B(IV) 4(I) P(II) 4(III) c(IV) 00 Exrt cc/gm. mole Btu/lb/psia Methane 116.79 0.612 0.612 -295.5 -284.6 -284.0 -296.5 -311.9 -0.1483 -0.1468 -0.1609 0.1757 191.06 1.002 1.002 -116.3 -114.7 -113.5 -115.3 -116.0 -0.0624 -0.0625 -0.0633 -0.0647 298.15 1.563 1.563 -42.1 -42.6 -41.7 -43.0 -44.3 -0.0291 -0.0285 -0.0290 -0.0282 623.4 3.269 3.269 +9.7 +11.1 +9.3 +10.1 +5.1 -0.0060 -0.0056 -0.0061 -0.0064 r Propane 244.0 0.660 0.627 -610.29 -618.6 -599.6 -610.2 -658.3 -0.1343 -0.1309 -0.1295 -0.1475 369.97 1.000 1.000 -260.0 -250.6 -245.1 -248.8 -252.2 -0.0547 -0.0516 -0.0542 -0.0561 523.16 1.414 1.476 -100.0 -104.8 -111.9 -105.0 -109.9 -0.0278 -0.0262 -0.0275 -0.0263 Key I - McGlashan and Potter [Eqn. (111-43)] II - Pitzer and Curl [Eqn. (111-40, 111-41, III-42)] III - This Work [Eqn. V-30)] IV - Starling BWR [Appendix H-l]

00 — -02 -"04. REDUCED CURVE FOR C3H8 USING Tr CH -0.61!0~/o To% \ |- 08 // REDUCED CURVE FOR C3H8 USING Tr mo" REDUCED CURVE FOR / r r CH4 / / DPROPANE DATA CH4/ & KUNZ [136] /o v BREWER [281 -1.0- / o KAPPALLO ET AL [122] sJz^~~~~~ ~/ 0 ~o McGLASHAN [159], / o DIAZ-PENA (EQUATION) [62],-12/ / ETHANE DOAT] / POPE [200] cJt:~ ___ Mc~~~~/ T MICHELS 1174] Jl~~~~~~ / ~ti~~ HOOVER 1[08] -1.6 04 06 08 1.0 12 14 Tr OR Tr CH4 Figure V-3. The Reduced Second Virial Coefficient as a Function of the Modified Reduced Temperature Tr for Methane, Ethane and Propane. CH

127 curves for the two substances is seen to be much smaller in the first case. A comparison between the equation and the measurements for the systems examined is summarized in Table V-l. The literature data on individual n-alkanes has also been examined and smoothed by Diaz-i'ena [61,62] using a polynomial function in each case. The equation has also been compared with these smoothed values. Relevant critical properties for the substances examined are summarized in Table J-1, most of which were obtained from tabulations by Reid and Sherwood [214]. The results of Table V-1 are further amplified in Table J-3. c) Performance of the Correlation. For the light hydrocarbons upto n-butane, the correlation is better than the scatter of the data around it. The precise measurements on methane and ethane obtained at Rice University [108,200] are consistently less negative at low reduced temperatures (Tr < 1.0) than predicted by the equation which appears to fit the other measurements more satisfactorily. We recall from Chapter III that similar trends with respect to the Rice University data were also observed for the correlation of Pitzer and Curl [196] and this observation was in part used to justify the need for improving upon the correlation. Thus, the two equations are less dissimilar than was originally anticipated. The predictions for propane at various reduced temperatures using Equations (III-40), (III-43) and (V-2) are compared in Table V-2. The values of o and n in the first two of these equations were expressed in terms of ac using Equations (III-32) and (III-43a), respectively, for the sake of uniformity. Values of the isothermal throttling coefficient (9H/DP)T at zero pressure were also calculated in each case using the identity ( a) _ ( B -T )T (V-31) T,P=O T The results indicate that the differences in B are small except at low reduced temperatures. Differences in (DH/UP)T are, percentage-wise somewhat larger and suggest that isothermal throttling coefficient data, if sufficiently precise, could serve to discriminate between the three correlations. Such direct calorimetric measurements at low

128 reduced temperatures are in general rare, extremely difficult, and usually of poor precision. It is this author's belief that a comprehensive evaluation of the relative accuracy of the B measurements at low reduced temperatures for the various substances is needed before the superiority of any one functional form for the representation of Br can be unequivocally established. Nevertheless, two important statements may be made with respect to the correlation developed in this work. Firstly, by design, it fits the existing second virial coefficient data for methane and propane better than any existing reduced correlations available in the literature, and secondly, the use of the modified reduced temperature parameter represents a significant advance in our efforts to improve the correspondence between various substances subscribing to a three parameter framework. d) Suggestions for Improving the Correlation. The results indicate some possibilities for the future improvement of the correlation and consequently a brief analysis merits consideration. The results for Ar, Kr and CF4 at low reduced temperatures (Tr < 0.9) (See Table J-2) yielded a positive bias with respect to the measurements in all cases. The sign and magnitude of the bias may, in part, be explained by the neglect of quantum corrections for the reference substance methane. Leland et al. [145] have estimated the contribution to be 1 to 2% of the value of Br at a Tr value of approximately 0.7. This suggests that the correlation would probably have been better served using an argon reference with an additional term in Equation (V-18) to account for quantum effects in methane. The deviations for krypton (otc = 5.94) were significantly higher than those for argon (ac = 5.76) particularly at low reduced temperatures where the contribution of ac becomes important. It is suspected that the ac value for krypton obtained from the tabulation of Reid and Sherwood [214] is too high. Koeppe [132] has suggested that Ar, Kr and Xe all have ac values of 5.79 + 0.01. This seems more reasonable in view of the spectacular correspondence obtained between the reduced properties of these substances [226]. In any case, if the ac value of krypton were decreased to that for argon, the observed deviations

129 in the Br values for krypton would have been almost the same as for argon at any given reduced temperature. A negative bias was consistently noted with respect to the experimental measurements for hydrocarbons heavier than n-but ne. The extent of the bias was found to increase with increasing ac. Again, if argon, instead of methane, was used as the reference substance with propane retained as the pivot substance for determining the slope function dBr/dac, then this modification would have the effect of decreasing the negative bias for compounds with ac values higher than propane and decreasing the positive bias for substances with lower ac values. The necessity for using higher order terms in (ac - ac ) 00oo in Equation (V-30) should, however, not be discounted as a possible solution to decreasing the negative bias for markedly non-spherical molecules such as n-octane. Development of a Mixing Rule for RTc /Pc m m a) Need for the Development of a High Temperature Reduced Second Virial Coefficient Correlation. In preliminary application of Equation (V-30) to the extraction of mixture pseudoparameters from Equation (V-12) it was found that the range of the correlation was not sufficient to permit the unambiguous selection of the three parameters required. Even if oc were independently fixed, the specificity of the optimization in the remaining two parameters was found to be marginally acceptable for the parameter Tc if enthalpy values for the mixture are to be accurately predicted. This suggests that the range of the correlation should be further extended. Measurements at reduced temperatures below 0.5 are generally unavailable. Measurements at high reduced temperatures extending beyond the maximum in Br are available only for helium [185]. The quantum effect contribution for helium is well known to be sizable at low temperatures, but only marginal in the vicinity of the maximum in Br [106]. Nevertheless the high temperature measurements on helium cannot be directly used in extending the correlation as its critical properties are themselves subject to quantum corrections. Leland, Kabayashi and Mueller [145] were able to develop a procedure to

1 30 calculate the deviations exhibited by quantum spherically symmetric fluids from classical behaviour in a corresponding states framework. An important consequence of this procedure, and the availability of measurements on quantum fluids, was their ability to calculate the reduced second virial coefficient as a function of reduced temperature for a classical fluid for Tr < 30, well beyond actual measurements on such fluids. It was decided to use their tabulated values in extending the high temperature limit of the correlation from 3.26 Tc to 30 Tc. b) Initial Efforts Towards the Development of the High Temperature Correlation. The functional form of Equation (V-30) suffers from the disadvantage of not being able to account for a maximum in Br at high reduced temperatures, contrary to fact. This shortcoming is attributed to the hardness of the repulsive forces for the square well potential. The Lennard-Jones potential function produces the required maximum in Br but the result cannot be expressed in closed form [92,167]. For a soft sphere conforming to the potential u(r) = E( ) 3 (V-32) r (V-32) the result is [167] 3 B(T) 27T e n 3' 3 ( kT ) (n)(V-33) where f(n) is a gamma function in n diverging for n < 3. The macroscopic two parameter equivalent is given by Br B(n) Tr (-34) and expresses the effect obtained by softening the repulsive part of the potential. Consequently, we are tempted to empirically combine Equation (V-30) and (V-31) and write Booo(Tr) T- oo 3/n [a - + (3C/Tr5) Br ( Tr [a + b(1-e oo) ] OO oi (v- 35)

1 31 to incorporate a maximum into the correlation. The tabulation of Leland et al. [145] described above was used to generate B values for methane over the range 3.26 < Tr < 30. These values were blended in with the experimental measurements extending upto 3.26 Tr and a least squares fit was obtained with respect to Equation (V-35) with n equal to 12. Although the fit to the high temperature data was improved, the fit to the data for Tr < 1.0 was not nearly as good as that obtained with Equation (V-30). This suggests that we need a harder repulsion as the temperature is lowered. In fact, Byrne et al. [35] have demonstrated that the low temperature second virial coefficient data for argon are represented better by the 18-6 Lennard-Jones potential than by the softer 12-6 form which was found to be more suitable at higher temperatures. This suggests that Equation (V-35) could be further improved by expressing n as a function of Tr such that n decreases as Tr increases. Further 00 00 efforts in this direction were beyond the original scope of this work and consequently this pursuit, though attractive, was abandoned. c) The Development of a High Temperature Mixing Rule for RTc /Pc Next, a less ambitious, and perhaps more pragmatic approach was tried. An examination of the B/Vc vs T/Tc tabulation of Leland et al. [145] indicates that Br varies only 18% over the range 9.0 < Tr < 30.0 and suggests that the required function fB of Equation (V-12) is insensitive to the value of Tc in this range. Consequently, the difficulty in extracting at least two, if not three, meaningful pseudoparameters could be somewhat circumvented by splitting the function fB into two parts. The high temperature function could be used to define the reduction parameter RTc/Pc using an approximate estimate of Tc, Thile the low temperature function given by Equation (V-30) could then be used to refine the estimate of Tc using the optimized value of RTc/Pc. The ac dependance of the high temperature part of the function fB poses a problem in that it cannot be ascertained from the table of Leland et al. The assumptions involved in the development of an indirect technique to achieve this end are discussed below. 1) It is assumed that the two parameter corresponding states function B/Vb - O(T/Tb) (V-36)

132 involving the Boyle point parameters is valid for all substances that satisfy the three parameter function fB defined by Equation (V-1 2) regardless of the value of ac. 2) It is assumed that the two parameter corresponding states function B/BM = <(T/TM) (V-37) is also applicable to the non-polar substances that satisfy Equation (V-9) regardless of the value of ac, where BM is the value of the second virial coefficient at the maximum, and T is the temperature at which the maximum occurs. At first, these assumptions may seem implausible, but the reduction parameters are, in each case, directly derived from second virial coefficient data, and produce an exact fit at the Boyle and maximum points, respectively, regardless of how dissimilar the substances examined may be. One would further expect that the functions 6A, OA and B, (B specific to two substances A and B would be similar in varying degrees in the vicinity of the Boyle and the maximum point respectively. It has already been noted earlier in this chapter that substances such as CH4 and CF4 with significant differences in ac could be fit within the limits of accuracy of precise experimental measurements to a single universal function of the form of Equation (V-36) over the range 1.20 < Tr < 2.73, where the Boyle point occurs near the upper limit of the range. The more recent measurements of Lange and Stein [137] down to Tr values as low as 0.89 seem to suggest that the Boyle point conditions are less satisfactory as reducing parameters for these substances below a Tr value of 1.20. At the Boyle temperature, the positive and negative branches of the integrand in Equation (IV-lOa) are of equal magnitude, and B is zero. (See Mason and Spurling [167] for a pictorial representation). It is not unreasonable to assume that if the universality of the function 0 is valid for negative

133 excursions down to Br values of -0.22 (at Tr = 1.20), then it is also valid for positive excursions upto a Br value of 0.144, that is, upto and beyond the maximum. We may then confine the validity of assumptions 1 and 2 above to the range Tb < Tr < 30. 3) Assumptions 1 and 2 lead to the result that BM/Vb and TM/Tb are constants for all substances and independant of cc. The tabulation of Leland et al. [145] was re-expressed in terms of the reduced parameters B/BM vs T/TM. These parameters were obtained from the same table with some slight modification to the value of BM as discussed in Appendix F-5. A fit of better than 0.4% was obtained with respect to the modified tabular values using the equation. B T T T = 0.3517 + 1.5068 ( ) - 1.11739 ( + 0.25874 ( ) (V-38) M M. M TM The equation is plotted as Figure (V-4), and the regression details are presented in Table J-2. The equation was again transformed to involve the variables Tc, Pc, and otc by using the Boyle point data on CH4 and CF4 to establish TM/Tc and BM/(RTc/Pc) as functions of xc. Further details are presented in Appendix F-5. The final result applicable over the range Tb < Tr < 30 is given by Br = [h(ac)] [g(Ctc,Tr)] (V-39) where h(Cc) = BrM = 0.7085 [ 0.1590 + 0.0588(ctc-5.82) ] (V-39a) and g(ac,Tr) is given by the right hand side of Equation (V-38) if we replace TM in terms of Tc and ac as expressed by the relation TM 18 TJI~~~~~~~~~~M 18 _________ ^ __(V-40) Tc [1.0 + 0.189(ac-5.82)] By following the procedure similar to that suggested in Appendix C and applying Equation (V-39) to every component in the mixture one can obtain the mixing rule RTc n n RTci h(ac.) g(c, Tr.) Pc XIXJ Pcij h(acC) g(ac' Tr ) nm il1 j1 Ji in Ti

1.00 -t 0.95 x / Reduced second virial coefficient / using parameters at maximum m 0.90 from tabulation of Leland et l [145] d/ TB | Tc 18/[1+.189(ac-CCH) 0.85 0.5 1.0 1.5 T/TB or (T/TM in Text) "max Figure V-4. Dimensionless Second Virial Coeificient for a Classical Fluid in the Vicinity of the Maximum.

135 if Tb.. < Tr < 30 for all i,j. This reduces exactly to the Van der 13 - Waal rule for Vc if the h(ac) and g(ac,Tr) ratios in the above m equation assume unity values, and if all substances are assumed to have the same value for zc. We now have several options for calculating the pseudo-parameters for multi-component mixtures using the basic framework explained in this Chapter. Given BM values, and aij values for all i,j, Equation (V-22) may be used to determine oc. The optimum values of Tc and m RTc /Pc may then be calculated using Equation (V-30). Alternately, RTc /Pc may be independantly established from Equation (V-41) at m m some high temperature such that Tb.. < Tr < 30, assuming predetermined 1J - ~ values of ac.. and ac, and from independently specified approximate estimates of Tc.. and Tc. Equation (V-30) may then be used to optimize ~ O m the parameter Tc alone from a given set of B values. These options m m will be further examined in Chapter IX. Summary In conclusion, the basic logic in the formulation of mixing rules for the evaluation of mixture pseudoparameters within the one fluid three parameter corresponding states framework has been defined and the rationale behind some additional recipes developed in this work and utilized in Chapter IX has been indicated. The general goal of this work is to predict multi-component mixture enthalpies from constituent binary enthalpy data over the single phase fluid region. More specifically, the goal is to test the technique against the enthalpy data for a ternary methane-ethane-propane mixture using enthalpy measurements on the methane-ethane, ethane-propane and methane-propane binaries, respectively. Before the technique can be applied, the enthalpy data relevant to the examination of the problem must be completely defined. Therefore, the next three chapters are concerned with the experimental aspects of this investigation, and in sequence deal with the experimental method, the data reduction techniques and the experimental results.

Chapter VI THE EXPERIMENTAL METHOD Before the experimental results of this investigation are discussed, it is first useful to describe the experimental setup and the operation of the calorimetric facility at the Thermal Properties of Fluids Laboratory (TPFL) at the University of Michigan. This section is devoted to the description of the recycle system, the two calorimeters, and the measuring instruments. Operating procedures and instrument calibration techniques are also briefly discussed. As the evolution of the facility can be comprehensively traced through a number of doctoral theses [119,161,162,168,284], beginning with the pioneering efforts of Faulkner [79], only modifications with respect to both equipment and operating procedure made during the course of this work are emphasized. The Recycle System The modified recirculating system, incorporating both isobaric and throttling calorimeters for the direct measurement of the effect of temperature and pressure on the enthalpy of multicomponent mixtures of light hydrocarbons, is shown in Figure VI-1. The function of the recycle system as a whole is to provide a steady continuous supply of fluid to the appropriate calorimeter under prescribed and carefully maintained conditions of temperature, pressure, and flowrate which extend from -240~F to +300~F, from 80 psig to 2000 psia, and upto 4 standard cubic feet per minute (SCFM), respectively. The flow stream in Figure VI-1 may be traced starting at the compressor inlet buffer. The fluid is compressed from about 80 psig to some high pressure varying from 1000 psia to an upper limit of 2500 psia using a two stage diaphragm compressor (Item 2, Appendix D) operating at a constant volume rate of 4 SCFM. The fluid subsequently passes through a bomb containing copper fittings located in a heated air bath which serves as an effective oxygen scavenger, and then enters an insulated box containing the control valve mainfold. The outlet pressure at the compressor is adjusted with the compressor throttle CT. The flow is then split between the calorimeter feed 136

137 and bypass lines by relative adjustment of the calorimeter throttle (9T), and bypass throttle (BT) valves, respectively. The two lines eventually merge at approximately 80 psig at the compressor inlet buffer enroute to the compressor. The pressure at the calorimeter is principally determined by the adjustment of the calorimeter throttle. gKather [168] and Yesavage [284] introduced heating tapes ahead of such throttling valves to prevent the condensation of the system fluid due to Joule-Thomson cooling at the valve outlets. The fluid in the calorimeter feed line then enters a buffer tank that is located in an insulated controlled temperature heated air bath, and serves to stabilize the flow conditions. Also located in the same bath, are a bank of five storage tanks that act either as a source or sink for the recycling fluid. The air bath is usually maintained at about 50~F higher than the cricondentherm temperature of the mixture to ensure that fractionation does not occur when the fluid is being initially supplied from the storage tanks to the recycle system. The fluid then travels through a series of conditioning baths designed to bring it to the temperature desired at the calorimeter. In order to reduce holdups, particularly under two phase flow conditions, the baths and the fluid line are arranged to ensure a downward flow path at all times, and the inside diameter of the fluid line is reduced to 1/8" just as it enters the first conditioning bath. A micron filter between the high pressure buffer and the baths serves to trap any particulate thermal decomposition products. A "double pipe" water coil, 15 feet in length, is used to cool the fluid if the desired temperature is below ambient conditions. The coil is bypassed at higher operating temperatures. The first bath that the fluid enters contains 175 feet of 3/16" 0.D. copper tubing which serves to bring the fluid temperature to about -100~F, if necessary, when a dry ice-acetone mixture is used as the bath fluid. The system fluid next enters the "heat exchanger" bath containing 325 feet of 3/16" O.D. copper tubing, and maintained to within + 0.5~F of the desired temperature at the calorimeter using an electronic controller (Item 7, Appendix D) driving a 50 watt immersion heater. The fluid leaves within + 10F of the desired temperature and then passes into the bath where the two calorimeters are located.

r ~^\ CORBLIN I _ ['~DIAPHRAGM SUCTION\ 1 COMPRESSOR BOMB 11 _ BOMBX? IVVVV^MW^VWXXXX I SECOND FLOOR I I -~F"{{SCAVENGER I 7'/ FIRST FLOOR 23 I _ B0MB INLET I CT C ID BOX BUFFER FILTER BYPASSI BT B 8 TO CALORIMETER REGULA VALVES 10 H STORAGE TANKS ADSORBENT' BED I ) I^ /////' HEATED LINES d FL 13 F ) IPRESSURE 2, ~1 I 4L 4Hr D 8; ^^~ ~ i~{EXTERNAL OWAOT L2 0 ESSURE COOLI EXCHANER CYLINDERS FLOW- U E RI COOLINGt FiueFFER.TeRc CO I - EXTERNAL BT 19BENTR BATH TREANSDCER CNPRESSURE.O COOLING L BUFFER COIL BATH BA, BATH RESERVOIR SAMPLE HOT Figure VI-1. ~-he Recycle System (Schematic).

139 There are four cryogenic valves (Item in, Appendix D) inside the calorimeter bath which can be manipulated to guide the fluid through the appropriate calorimeter after it has passed through 100 feet of 3/16" 0.D. copper coil for a final temperature conditioning. The choice of bath fluid for the last two baths in the series depends on the operating temperature. Isopentane is used below -50 F. Kerosene is used in the range -250F to 75~F. Above 75~F, 30 wt. lubricating oil was found to be more suitable. At below ambient temperatures, the bath fluid is cooled by liquid nitrogen supplied from externally located 50 litre dewars. The liquid nitrogen flowrate can be adjusted if the pressure at the dewar is varied by regulating the outlet driving pressure of a nitrogen cyclinder connected to it, or by adjusting a valve located in the effluent vaporized nitrogen line outside the bath. The inlet temperature and pressure, the difference between the inlet and outlet temperature, the pressure drop, and the electrical energy input are the key measurements that are next obtained as the fluid passes through the calorimeter. After it leaves the calorimeter, the fluid enters a temperature controlled hot oil bath designed to vaporize it completely before returning to the valve mainfold where it is throttled (9T) to 80 psig, the selected pressure for the measurement of the flowrate. The fluid leaves the valve mainfold to enter a water bath, where the flowmeter is located. The bath temperature is controlled to 27 + 0.1~C by balancing the cooling effect of a water coil against the heating effect of a 100 watt tubular heater operated by an electronic relay, and actuated by a mercury contact switch (Item 8d, Appendix D). The fluid enters a multiple channel flowmeter (Item 8a, Appendix D) after passing through 50 feet of 3/8" ID copper tubing for temperature conditioning. "icron filters are located on either side of the flowmeter to remove entrained solids from the flowing stream. The fluid passes through another 50 feet of copper tubing after the flowrate is measured and returns to the compressor inlet buffer where it joins the bypass stream prior to being recycled.

140 Modifications to the Recycle System Mather [168], and later Yesavage [284] reported that the recycling fluid stream was in some circumstances contaminated with oil that leaked from the compressor heads around the edges of the oil to gas pressure transmitting metal diaphgrams. A bed of activated charcoal and dehydrite located in the heated air bath just after the compressor was found by Yesavage to be quite inefficient in adsorbing the oil in the fluid stream. This oil had a tendency to separate out at the low pressure of the flowmeter causing serious fouling problems and flowmeter calibration changes. A glass wool bomb placed just before the flowmeter by the same investigator to remedy the problem was also found to be ineffective in this work. The phase equilibria for an oil-gas system are such that the desorption or the condensation of oil from the gas stream is facilitated if the process is conducted at the lowest possible pressure and temperature in that order. A twelve foot double pipe water cooling coil with provisions for bypass was placed in the fluid stream before the flowmeter bath to decrease its temperature from a maximum of 175 F to below the flowmeter bath temperature of 27~C as part of the strategy for condensing as much oil as possible prior to the desorption process. A bypassable adsorbent bed of about 800 cc capacity (Item 13, Appendix D) containing molecular sieves 3A and 4A, activated charcoal and drierite was placed in the flow stream after the water coil. A similar bed was also installed in the bypass stream to the compressor buffer. The molecular sieves effect the removal of nitrogen and unsaturated hydrocarbons, and together with the charcoal, serve to remove the oil. As these beds also adsorb significant quantities of the light saturated hydrocarbons that vary with the temperature of the bed, it is imperative that the temperature of the bed in the flowstream be strictly controlled to prevent spurious contributions to the measured flowrate. During the investigation of the 76% ethane-propane mixture, a severe explosion caused serious damage to the valve manifold resulting in the deposition of carbon black in the manifold lines. The damage is typically illustrated in Figure VI-2. The entire valve manifold had to be completely rebuilt, and the valves replaced. The monitoring of leaks within the control manifold required the frequent removal of

141 I T Figure VI-2. View of Control Valve Manifold Line Following Explosion. Figure VI-3. View of Rebuilt Valve Manifold.

142 the insulated front panel during regular operation. Originally a time consuming process, it was speeded up by the replacement of the single piece valve stems by split stem quick-snapout valve extensions. This modification provided instant control of any valve in the manifold for the duration of such tests. The rebuilt manifold is shown in Figure VI-3. The initial introduction of fluid to the system was previously accomplished through valve 20 ahead of the low pressure buffer which required the fluid to be compressed before it could be stored in a tank. The inclusion of valve FH in this work provides for the direct transfer of fluid at high pressure between the recycle system and an external storage tank if necessary. Other modifications include the use of a water coil as a less expensive replacement for gaseous nitrogen to provide the necessary cooling for the control of the calorimeter bath at above ambient temperatures, the installation of a relief valve (Item 8c, Appendix D) just before the flowmeter, venting at 100 psig, to prevent possible deformation of the flowmeter, and the addition of a shut-off valve at the bypass stream before the compressor inlet buffer to prevent it from overpressurizing in the event of a leakage across any shut-off valve on the low pressure side of the valve manifold when the compressor is shut down. The Isobaric Calorimeter of Faulkner [79] The calorimeter is shown in Figure VI-4. The fluid enters the calorimeter through the tubing in the lower section, passes through the inlet thermowell (1) and into the calorimeter heater capsule (3) where the electrical power is delivered. Passage through a series of baffles (5) brings the fluid to a uniform temperature as it leaves the capsule through tubing H via outlet thermowell J. Previous tests indicate that the exposed surface of the capsule is essentially at constant temperature [119]. Heat leakage is compensated by the use of a Nichrome wire wrapped radiation shield or "guard heater" maintained at the exit gas temperature by appropriate adjustment of a variac. Jones [119] introduced a thermocouple gland (Item lg, Appendix D) to improve the pressure seal on the power input leads. Further modifications relating to the inlet thermowell, the lead wires for the main

Uj 1 j G ~i n In!r I MI 3 rn n I If I ENTRANCE T1HERMOCOUPLE WELL 14 2 MECHANICAL PARTITION 1 3. CALORIMETER HEATER CAPSULE, 4. CALORIMETER HEATER BAFFLES 1 31 4'' i' 5. CALORIMETER CONDITIONING BAFFLES i I 1 6. EXIT THEROCOUPLE WELL 7. MAIN RADIATION SHIELD C 7 Cl i, 8 RADIATION SHIELD' } I 9 LINE OF SIGHT RADIATION SHIELD 10. CONAX MIDGET THERMOCOUPLE GLAND ii II. CALORIMETER HEATER LEADS 6 6 12. ENTRANCE PRESSURE TAP I 13. EXIT PRESSURE TAP i 14. VACUUM LINE 2, A^ I'~~~~~~~~~~~~~~~~~~~~~~ I LI Lj Lj Li. ^' t 4E"<i2 2t~ p Figure VI-4. The Isobaric Calorimeter of Faulkner [79] Aftcr Modifications of this Work.

144 heater, and vacuum seals were reported by Yesavage [284]. A major contribution to this calorimeter was the design and construction of a new heater capsule whose parts are shown in Figure VI-5a. In the original design of Faulkner, the baffles consisted of concentric copper cylindrical shells with hemispherical shells soldered at either end. Frequent burnout of the calorimeter heater resulted in permanent breaches at these soldered joints permitting the fluid to bypass the heater wire and reach the outer shells directly. This resulted in fluctuations in the observed value of the outlet temperature which increased the uncertainty in evaluating the approach of steady state conditions and aggravated the likelihood of more burnouts (See Figure VI-5b). The modified capsule consists of six shells varying from approximately 0.46" O.D. to 1.00" O.D. that are screwed onto a capsule mount. The detailed drawings are presented in Appendix E. The shells and mount are each made of tellurium copper alloy because of its superior machining characteristics. The alternate ends of contiguous baffles are perforated with small holes to permit the counter-current flow of the fluid across each baffle surface. Each shell was machined as a single piece unit to include the upper hemispherical portion where protruding tabs serve to keep the annular spaces uniform at all times. In every case, the shell is 0.01" thick except at the wider threaded portions near the bottom. The three innermost shells are wound with Nichrome wire (Item li, Appendix D) while the rest serve to thermally equilibrate the fluid before it leaves the capsule. The heating wire is glued to the shells by a thermally conducting electrically insulating resin (Item lm, Appendix D). The two outermost shells, silver soldered to each other near the base, appear as a single unit in Figure VI-5a. The tabs on the outside shell serve to prevent the heater capsule from being pushed flush against the outlet tube on the capsule housing causing the flow of gas to be arrested. The tabs are also threaded to accomodate a ring which clamps the heater wires in place. A pair of grooves running along the length of the shell permits the capsule to fit easily in the housing by providing a recessed resting place for the insulated heater wires.

145 Figure VT-5a. View of the Parts of the Modified Heater Capsule. ii:ure'VT-Sb. View of the Original Heater Capsule..:~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~::: iiFiei!i-ii —-ii Figure V-5b. Viw of th Origina HeaterCapsule

146 A number of slots appear on the capsule mount and are designed to carry the bifilarly wound heating wire from shell to shell. The shells are screwed on the mount so as to exert firm pressure on the heating wire in the slots to prevent any leakage of fluid along such paths. The third shell from the inside requires both the heater wire and the fluid to be transferred out at the top, hence the larger opening in this case. The threads on the mount are arranged to stack the shells in a staircase configuration. The threaded bases of the three innermost shells are screwed to the mount in ascending order. The remaining shells are arranged in descending order as the shell diameter increases. This particular feature was incorporated in the design to increase the limited scavenging surface available to the fluid at the mount. The main difference between the original design of Faulkner [79], and the modified version lies in the replacement of the hemispherical shells bottoms by the heavier threaded mount. In effect, the better scavenging characteristics and lighter weight of the original mount design are somewhat compromised in favor of a design that emphasizes ruggedness and ease of accessibility to the heater element in case of repair. Finally, before inserting the capsule into the calorimeter, the uniformity of flow through the perforated holes is carefully checked by passing gas under slight pressure through the bottom of the capsule mount and observing the heating wire slots for leakages with the shells in place. The modified capsule weighs 4.75 oz. This is about 1.5 oz. heavier than the original version and is chiefly due to the increased weight of the new mount. This increase in mass is less significant from the standpoint of the increased time required to attain steady state conditions if it is noted that the flanged capsule housing alone weighs 32 oz. The pressure drop across the capsule for average operating conditions varied from 0.1 psid at high pressures to about 1.0 psid at 250 psia. The efficiency of heat transfer was so improved as a result of the precautions taken, both in design and installation, that the power supply with a rating of 325 volts and 2 amps became the limiting factor in the rate of heat input. To obtain the maximum power consistent with the supply restrictions, the amount of heating wire used should correspond to a total resistance of about 162 ohms.

147 Another modification to the calorimeter was the interchange in the positions of the outlet flow tube H and the heater wire gland 1. in the upper half of the flanged capsule housing. In the original configuration, considerable difficulty was experienced in drawing the heater lead wires through the gland, a necessary step for the removal of the capsule. The abrasion of the insulation on the wires at the sharp bend would sometimes result in a short circuit. This problem was eliminated in the modified housing. The conax gland was swaged due to frequent tightening and was also replaced. Both versions are seen in Figure VI-6. The Throttling Calorimeter of Mather [168] This calorimeter is shown in Figure VI-7. The fluid enters the upper section near 9 and passes into a capillary coil in the lower section which causes the pressure drop. A grounded insulated wire running through the coil serves to supply a manually adjustable energy input to maintain isothermal conditions when operating within the Joule-Thomson inversion curve. After passing through a number of baffles to stabilize its temperature, the fluid leaves through exit thermowell 5. Outside the Joule-Thomson curve, the calorimeter is operated in the isenthalpic mode. The heat leak is balanced by adjusting the power to the radiation shield H such that a three junction differential thermopile between the outermost baffle and the shield indicates zero temperature difference. In Figure VI-7, the inlet thermowell is seen to be in mechanical and thermal contact with the outer wall of the calorimeter, insuring that the bath temperature is, in effect, measured at the thermowell. If, for simplicity, it is assumed that the fluid enters the calorimeter bath at the desired bath temperature, the pressure drop caused by its passage through 100 ft. of 3/16" O.D. thick wall copper tubing before the calorimeter serves to cool or heat the fluid to an extent that, in some circumstances, is not quite matched by the heat transferred between the coil and the bath fluid. These conditions occur chiefly when the magnitudes of the flowrate, the viscosity, and the adiabatic Joule-Thomson coefficient for the fluid are all high and can result in temperature differences as high as 0.40F between the inlet thermowell

148 (a) Original Half. /Biii - ii;!i..!!iii (b) Modified Half. Figure VI-6. The Original and Modified Upper Half of the Heater Capsule Housing.

,1I~ ~ ~ ~ ~ ~ ~, I i 9 A 8 1. Entronce Thermocouplo Well C E 1, 2 Mechanical Partition i \\ 3. Calorimeter Heater Capsule,, 4. Calorimeter Baffles 2 i 5. Exit Thermocouple Well:. 6. Radiation Shield 7. Conox Heater Lead Gland ___ 8. Capillary' 9. Entrance Pressure Top i 10. Exit Pressure Top l2 121-_____ I II. Vacuum Line 12. Temperature Compensated Coupling A-H Difference Thermocouple I Locations H 1 I Inch 6 E Figure VI-7. The Throttling Calorimeter of Mather [168] Before Modification. 7igure VI-7. The Throttling Calorimeter of Mather [168] Before Modification.

150 and the bath. The inlet thermowell was moved by interposing a 4 inch piece of coiled stainless steel tubing between its original location and the wall. Although the discrepancy between the bath and the thermowell temperature is still retained, it no longer appears in the measured temperature difference where the contributing error to the measured mean heat capacity is usually far more serious. Serious leakage problems were found to occur at the pressure seal (12) at cryogenic operating temperatures. It was determined that the temperature compensating clamp (Item lc, Appendix D), and one of the grooves on the seal were deformed. The clamp was replaced, and the sealing problems were minimized by using nickel gaskets with a thicker teflon coating. Measuring Instruments a) Electrical Measurements. All electrical and electrically transduced measurements are made on a K3 potentiometer (Item 3a, Appendix D) using standard resistors to scale down the voltages to the range of the potentiometer. The circuitry for the potentiometer, and the calibration data for the standard resistors is given by Jones [119]. The worst case accuracy is 0.01% of reading + 0.2 microvolts (iv) for the range 0 to 0.01611 volts. Manker [162] has discussed techniques for maintaining the precision of the measurements. In this work, the standard cell for the potentiometer was calibrated by adjusting the cell voltage setting on the potentiometer until the measured value of the EMF of another sparingly used standard cell was equal to its NBS calibrated value corrected for ageing according to a previous history pattern that predicted a steady decrease of 75 vlv/year out of a total value of approximately 1.019 volts. The latest calibration for the reference cell is indicated in Table A-1. b) Temperature Measurement. The temperature of the calorimeter bath as measured by a four lead platinum thermometer (Item 5, Appendix D) is assumed to be the inlet temperature of the calorimeter. As discussed earlier, a worst case discrepancy of 0.4~F may occur. The constants for a modified Callendar equation representing resistance as a function of temperature, the circuitry for the thermometer and

1 51 a sample calculation of the temperature from two voltage measurements at the K3 potentiometer are presented by Jones [119]. A second thermometer in a metal housing (Item 5a, Appendix D) was used beginning with the examination of the 0.27 mole fraction ethane-propane system. The Callendar equation constants determined by the NBS are shown in Table A-2. The accuracy of the bath temperature measurement is 0.04~F. The original thermometer was recently recalibrated by Miyazaki [178] against a Hewlett-Packard Model 2841-A quartz crystal thermometer. The resistance at 0~C was computed as 25.519 ohms, as opposed to the original calibrated value of 25.513 ohms. The discrepancy between the two sources did not exceed 0.01~C, the estimated accuracy of the quartz thermometer. c) Temperature Difference. The temperature difference between the calorimeter inlet and outlet is normally measured using duplicate six junction copper/constantan (Cu/Con) thermopiles calibrated by the NBS at 20~C intervals from -100~C to 160~C, and including calibration points at -1830C and -196~C. The estimated accuracy of the calibration tables for the thermopiles is + 0.10C. The calibration data for thermocouples 3M, 4M, 5M, and 6M used in the isothermal and isobaric calorimeters, respectively, are reported by Yesavage [284]. A fourth degree least squares polynomial fit of EMF vs T was considered adequate for the measurement conditions at the isobaric calorimeter. A typical regression analysis is indicated in Table A-3. The first constant or intercept obtained from the regression was adjusted to indicate a value of Olv at 0~C. It was initially felt that a divided difference polynomial would more accurately calculate the small temperature differences involved in the throttling calorimeter. Both techniques were simultaneously used in this work. An average discrepancy of 0.03% in the calculated values of the temperature difference was observed. However, in the case of Joule-Thomson data obtained for ethane at -246~F, the discrepancy between a fifth order Lagrange interpolating polynomial and the fourth degree least square approach increased to 3%, as seen in Figure VIII-13. The discrepancy could not be improved by changing the order of the interpolating polynomial.

152 difference curve was constructed between the calibration table EMF values of thermopile 6M and an archetypical 6 junction thermopile derived from the comprehensive single junction NBS reference tables [184] as a function of temperature. The results indicated that the estimate from the least square technique was more accurate below -240~F. The inferior performance of the interpolating polynomial is thought to have occurred because the interpolation interval was as high as 83~C in this region, as opposed to 20 C at higher temperatures. In order to improve the sensitivity of the measurement over temperature differences of the order of a few degrees, the thermopiles in the isothermal calorimeter were permanently replaced by a single 15 junction unit. A similar replacement was also made for the isobaric calorimeter over the limited period involving the investigation of the heat capacity maxima for ethane and part of the measurements for the 0.76 mole fraction ethane-propane mixture. The four calibration points initially determined by the NBS are listed in Table A-4, and apply to both thermopiles #1 and #2. The isobaric calorimeter was recalibrated at the four points in Table A-5, including two conditions repeated from the previous calibration. In spite of considerable handling, and a time period lapse of eight months, the calibrations agreed to 0.01%. The four original and the two additional calibration points are not sufficient to obtain an accurate fit over the temperature range from -2400F to +3000F. The following indirect procedure was used to generate additional synthetic data points: i) A fifteen junction thermopile was first synthesized from the calibration data for the six junction thermnnopile 6M by multiplying the EMF values for the latter by 2.5. ii) A fifteen junction thermopile was also constructed from the archetypical single junction thermopile data presented in the NBS tables at the 17 temperature conditions corresponding to the calibration data of 6M. iii) Differences in the EMF values between the two tables in i and ii were plotted as a function of temperature and connected with a smooth curve. iv) A difference curve was also constructed between the IUMI' values

153 for the archetypical fifteen junction thermopile and the actual results for the fifteen junction thermopile #1 at the six calibration points for the latter. v) The shape of the difference curve in step iv between -280~F and +3000F, with only six data points, was guided by the shape of the well established curve in step iii. Both curves are seen in Figure A-1. The difference values for thermocouple #1 were then recorded at 200C intervals, and combined with the archetypical values from step i to yield a set of values summarized in Table A-6. The regression analysis for the synthesized calibration table for #1 is presented in Table A-7. A sample calculation of the outlet temperature at the calorimeter from a knowledge of the EMF generated by the differential thermopile and the inlet temperature as measured by the platinum resistance thermometer is presented by Jones [119]. The measured error in the temperature difference was estimated at 0.2% by Manker [162] for differences greater than 10~F. For smaller differences of the order of 1~F, obtained primarily in the critical region and near the Cp maxima, the accuracy degrades to about 0.5% and 1.0% for the fifteen and six junction thermopiles, respectively, and is limited by the accuracy of the measurement at the potentiometer. d) Measurement of Electrical Energy Input. The electrical energy input to the calorimeters is supplied by a Kepco D.C. power supply (Item 4, Appendix D). A wiring diagram for the power measurement circuit for both calorimeters has been made by Yesavage [284]. Human errors in recording the current or the voltage measurement can be detected as an unusual value in the computed resistance of the heating wire which varies less than 0.5% during the course of a run, and less than 3% over the entire range from -250~F to +300~F. Short circuits within the heater capsule are also detected in this manner. e) Measurement of Flowrate. The mass flowrate is calculated from a knowledge of the pressure drop across a multichannel flowmeter (Item 8a, Appendix D), the density, and the viscosity of the fluid at

154 the flowmeter. The pressure drop is measured by the height difference across a precision 10 inch water manometer (Item 8b, Appendix D) corrected for variations in the water temperature. The density at the flowmeter inlet is estimated from the inlet flowmeter pressure as measured by a 180 inch mercury manometer (Item 8c, Appendix D) and from the measured flowmeter bath temperature, using a suitable equation of state. The flowmeter is calibrated by directly weighing the condensed system fluid accumulated over a measured time period in a liquid nitrogen cooled cylinder. The modified procedural details for the optimal operation of the calibration equipment are indicated in Appendix I-1. The flowrate in normal operation for the systems of this work varied from 0.10 lbs/min to 0.35 lbs/min; the upper limit depending chiefly on the density of the system examined at the flowmeter temperature and pressure. The high energy input required for the measurement of the enthalpy of vaporization required the flowrate to be reduced to below 0.1 lbs/min in most cases in view of power supply limitations. Previous investigators at the laboratory [161,162,168,284] used the series pAP F F 2 F P = a + b( ) + c( ) + d(F) (VI-1) to represent the calibration data where p, i, and F are the density, viscosity, and mass flowrate of the system fluid, and AP is the pressure drop across the flowmeter. This form is seen to be an expansion of the Ergun equation [71] for packed beds given by P A + B( (VI-2) where A and B are constants that are characteristic of a given flowmeter. An alternate form for representing the calibration data can be constructed from the Prandtl universal law 1 4.0 In Re vr - 0.4, 2.1x103< Re < 5x106 (VI-3) recommended in the stated range by Bird, Stewart and Lightfoot [23],

155 where f is the friction factor, and Re is the Reynolds number. Tf the proportionality between f and pAP/p2, and also between Re and F/p for a given flowmeter configuration is recognized, Equation (VI-3) may be transformed to yield - = A + B ln(pAP/V2) (VI-4) In this work, the above equation was expanded in the series 10 F, Cp 103 = )a' + b'[ln( 1 + c'[ln( A 103) + d'[ln( l l03 (V1-5) to extend its range of applicability. The precision of the flowmeter calibration data over the entire range of measurements for all substances investigated was better than the fitting ability of either Equation (VI-1) or (VI-5) upto the third degree. At low flowrates Equation (VI-1) was preferable as it was observed that pAP/pF was a linear function of F/V. [Figure VI-8]. Equation (VI-6) was found to be better in the intermediate and high flow region. The calibration data were consequently split into two or three regions, and separately fitted in each region using the most appropriate functional form. In Figure (VI-9) we see that F//pAP approaches a constant value at high flowrates. Equation (VI-5) is still not the most desirable functional representation for this region because it does not extrapolate to the asymptotic high flow limit of F//oAP, and in retrospect an equation of the form PP= al + b( ) + d"( )3 (VI-6) which satisfies this criterion would have been preferred. We also see that if Equation (VI-6) is truncated upto the second term on the right hand side, it may in fact be obtained by a simple rearrangement of the Ergun equation (VI-2). If the density and the viscosity of the fluid are accurately estimated, then all substances should lie on a single generalized curve, assuming no change in the flowmeter configuration with time. Such a curve would then permit the identification of major errors in the

156 FLOW CRLIBRRTION (LRMINRR) BINRRY MIXTURES 11% -, o C2H6 2 0.76 C2 H6 (C2H6-C3 He) _*^ A.50 C2 H6(C2H6-C3H8)' S 0.27 C H6 (C2H6-C3He) 0.o * ).78 CH4 (CH4-C2 H6) E +.48 CH4 (CH4-C2H6), 0 It C'.0.. 1.2 1.6 2.0 2.4 Fxl~3 ( jx10) (Ibm/min). micropoise Figure VI-R. Flowmeter Calibration Results at Low Flowrates for all Systems of this Investigation Excluding the Ternary Mixture. FLOW CRLIBRRTION C2H6-C3H8 (RLL SYSTEMS) N, 1 0 i " 0 U 4I/ 0./ CHC2H6 E- O.76 C2H6 (C2H6-C3H8) ~^l.<. 50 C2 H (CCH6(C C3 H8) _. o.27 C2H6 (C2H6-C3 H8) -.0 -.9 -.8 -.7 -.6 -.5 -.U -.3 -.2 In AP lbm( in. H20) n J ft3 micropoise2 Figure Vl-9. Flowmeter Calibration Results at High Flowrates.

157 calibration process. The densities of the mixtures were estimated using the virial equation truncated at the second virial coefficient. Both the value and the slope with respect to temperature at 270C for the like and unlike pair second virial coefficients B.. relevant 13 to the ternary methane-ethane-propane mixture were obtained by interpolating the data in the literature. This procedure enables the variation of density with respect to the fluid composition, and with respect to the temperature and pressure of the flowmeter to be calculated to a. high degree of accuracy. A calculation of the density at the flowmeter is presented as part of Appendix F-l. The viscosity of the fluid at the flowmeter was estimated from the correlation of Lee et al. [143], given by the relation p(T,p) = 1~ (T,) exp[X(T)pY(T)] (VI-7) where X(T) = K1 + K2/T+ K5 ii (VI-8) Y(T) = K3 + K4 X(T) (VI-9) K1, K2, K3, K4 and K5 are empirically determined constants that have been tabulated by the authors and are applicable to a number of light hydrocarbons including methane, ethane, and propane. Wi is the molecular weight of component i. The temperature dependence of the zero pressure viscosity p0 was determined using the Sutherland [260] equation AT/2 T + S (VI-10) for each of the pure components. The zero pressure viscosity of a mixture p0 was also determined by Equation (VI-10) after applying the m mixing rules n Xi Ai m n (VI-lla) 1Z xi i i~l - "

158 SM C Xi (-11b) m i=l i (VTI-llh) prescribed by Lee et al. [143] to describe the mixture constants A m Although the variation in the viscosity within the normal operating temperature and pressure limits of the floxwmeter is calculated to be less than 0.1% for any given fluid, the actual value of the viscosity itself is not known to within the precision and repeatability of the flowmeter calibration. Consequently, the Sutherland constants A. and Si for the pure components methane, ethane and propane as determined by Lee and Eakin [142] were adjusted within the limits of accuracy of the data from which they were derived so as to force selected flowmeter calibration data for the three systems ethane, propane, and the 0.95 mole fraction methane-propane mixture to lie on a single curve. A calculation of the viscosity is illustrated in Appendix F-l. Figures VI-8 and VI-9 illustrate the flowmeter calibration results for pure ethane and the binary mixtures investigated in this work using the variables in Equations (VI-1) and (VI-5) for the low and high flowrate regions, respectively. Except for the 27 mole percent ethane-propane mixture in the highly turbulent region, the results for which are interpreted in Chapter IX, a single function is seen to fit the data to all the systems examined to better than 0.25% on the average, attesting to the success of the viscosity mixing rules for the binary systems. In the case of the ternary mixture, (not plotted in these figures), the ordinate values for the curve corresponding to Equation (VI-1) were 0.5% higher than the rest. This may be attributed either to the inferior performance of the viscosity mixing rule for the ternary mixture, or due to a shift in the flowmeter characteristics caused possibly by oil that was entrained prior to the installation of the adsorbent beds. A complete summary of all the flowmeter calibration regression results using the functional representations expressed by Equations (VI-1) and (VI-5) are presented in Table (VI-1). The calculated flowrates in either case are within 0.1% of each other. Although the accuracy of the measurement is estimated at 0.2% [11.9,162,284], the

TABLE VI-1 Summary of Flowmeter Calibration Equations for All Systems of This Work Using Equation (VI-1) Using Equation VI-6 + System Points Range % Std.Dev. Least Sq. Regression Constants Range++ Std.Dev. Least Sq. Regression Contants %onstants Range Z Std.Dev. Least Sq. Regression Constants (F/p) (Flowrate) ---- (pAP/p2 ) (Flowrate) Low High a b c d Low High a' b' c d' All except Ternary Mix 65.0026.0040.2h.30250 -144.?3 38393. -.228H F07.39.77.15 1.4300 -.01693.1166.24915 All except Ternary Mix 9n.0002.0022.18.1040i7 15.984.025.30.16 1.h611.34037 -.03125 Ternary Mixture 44.,nnD.0030.12.10454 18.301 -2330.4.6140 E6n.07.46.11 1.5736.1466h -.14081 -.285 -O1 C26(Upto Calibration 5) 26.0007.0032.1H.10368 18.558 -2681.9.71h6 F06.09.51.16 1.5475.08738 -.1751 -.3515 C2H6(Beyond Calibration 5) 18.0007.0031.11.1019q 21.528 -4264.7.9534 F06..08.14 1.5563.09204 -.1771h -.38174 -01 i C2 H(Combined) 44.0007.0032.19.10250 20.645 -3812.0.8933 EOh.08.51.17 1.5498.08570 -.178h8 -.3h177 F-o 0.50 C2H6 - C3H8?2.0007.0025.13.10179 21.4?7 -3851.8. 107 n06.n8. 3.11 1.6237.211r09 -.1115..73 -01 All C2H6- C3H8 Systems 45.0007.0027.18.10257 19.512 -2438.5.5186 806.08.40.15 1.6379.24548 -.08854 -.20155 -01 All C2H6- C3H8 Systems 29.0007.0071.16.10417 15.955..08.29.14 1.75n4.4419.02707 All C2H6- C3H8 Systems 19.0021.0027.18.10351 15.249 417.1.30.40.14 1.6587.31724 -.01793 All C2H6- C3H8 Systems 37.27.0040.13.72228 -70.510 15787..40.77.08 1.42hs -.R027.10344.744h8 0.77 CH- 2H 12.0007.o017.14.10436 15.017 5h7.1.0.2.11 1.39.35i cr -.0384? -.94 7 -- 7 0.48 CH- C2H.0004.0023.15.10462 14.835 572.5.04.3243.?7545 -.r -.13591 F-1I + Units are lbs/min/micropoise -++ Units are lbm/ft 3(in. H20)/micropoise2

160 frequent occurence of an undetermined mass leakage between the calorimeter inlet and the flowmeter outlet does not always ensure that the flow at the calorimeter is accurately measured at the flowmeter. In fact, on infrequent occasions errors as high as 57 have been observed due to this effect. $) Pressure and Differential Pressure Measurement. The arrangement of the pressure and differential pressure measurement devices used in this work is shown in Figure VI-10. The gauge pressure at the inlet to the calorimeter is measured by a dead weight gauge (Item lOa, Appendix D) using a Ruska gas to oil pressure transmitter and an electronic null detector (Item lOb, Appendix D) sensitive to imbalances as low as 0.05 psid. The resolution of the M & G dead weight gauge is 0.2 psig. The instrument was tested against a calibration standard Model 2400 Ruska dead weight gauge whose accuracy is estimated at 10 ppm. The results are reported in Table A-9. The two sources agreed to 0.1% over the entire pressure range from 250 to 2000 psia. In a previous calibration Mather [168] indicated that the error in the pressure measurement at the dead weight gauge was about 0.03%. The precision of the corrected measurement in this work is estimated at 0.05%. A mass leakage from the line connecting the calorimeter to the dead weight gage can, particularly at low pressures, cause significantly higher errors to occur. i) Measurement Scheme for the Isobaric Calorimeter: The pressure drop across the isobaric calorimeter is measured using a 40 inch differential mercury manometer (item lOe, Appendix D) enclosed in an insulated air bath heated above the critical temperature of the system fluid to prevent liquid holdup in the lines in low temperature operation, and to prevent system fluid head corrections to the mercury level in the manometer. In the latter case, the correction can be substantial (upto 2 in. Hg.) for measurements across the two phase region. With the modified heater capsule, the pressure drop rarely exceeds one inch of mercury for the systems investigated. A precision of 0.05 inches mercury is normally obtained except if some surging action common to measurements in the two phase region, occurs.

ISOTHERMAL CALORIMETER MAIN FLOW STREAM 2 4 2 v ISOBARIC~ I CALORIMETER I 16 18 17 5::\ 6 7T,:8 DIFFERENTIAL 1L_ ^ \ V6 7 q8HG. MANOMETER r ~...-..-~ - --- ~- - (UP TO 40" HG)!IN 27~C BATH 9 10 11 12 ~OI I IIIII L ISOURCEI |'HIGH ~ LOW PRESSURE PRESSURE 24 29 TRANSDUCER 13 TRANSDUCER 21 22 25 DIFFERENTIAL 27 ~ 8r~~'~~ PRESSURE. 14FITRNSDCEFJ 201: A I2 BALANCE I i 31 DO FFERENTIDAL 3I2 F TIAL P UR PRESSURE TRANSDUCER I / I IDEAD WI 14 15 I GAS GAGE I ~'I~ -~~ ~~~ ~-"~I~~~~ ~~- - ~ — ~ SIDE AS TO OIL I PRESSURE DNull~TC TRANSMITTER DETECTOR TO DIFFERENTIAL PRESSURE CALIBRATION MANIFOLD Figure VI-10. Pressure and Differential Pressure Measurement Scheme at the Recycle Flow Facility.

162 ii) Original Measurement Scheme for the Throttling Calorimeter: The pressure drop across the throttling calorimeter was originally measured using the differential pressure dead weight balance due to Roebuck [218] as modified by Mather [168], and Yesavage [284]. The high side pressure transmitted to the instrument is that measured at the M & G dead weight gauge. The outlet pressure at the calorimeter is transmitted to the Roebuck balance through a 36 inch mercury U leg between the system fluid and the oil on its low pressure side. The pressure differential across the balance causes the movement of a piston about a null position. The counterweight necessary to restore the piston to the balance point is equivalent to 19.998 psid/lb. mass according to the calibration of Manker [162]. Under optimum conditions, the accuracy of the measurement is estimated at + 1% by Mather for pressure drops equal to and beyond 100 psid. In this work, the U leg was modified to include sight glasses (Item 10g, Appendix D) in each arm to permit a visual observation of the mercury imbalance previously monitored by a set of frequently malfunctioning electrical probes. The Roebuck balance will unfortunately not sense the true inlet pressure at the calorimeter unless the M & G dead weight gauge is correctly balanced at the instant of measurement. If an imbalance exists, then it will, in effect, be incorporated as a more serious error in the differential pressure. The simultaneous adjustment of both instruments usually requires two operators, particularly, in view of pressure drop fluctuations of the order of 1% in normal operation. iii) Modified Measurement Scheme for the Throttling Calorimeter: In this work, two strain gage transducers (Item 10c, Appendix D) each with an operating range from 0 to 2000 psia were added to determine the inlet and outlet pressure, respectively, at the calorimeter. A similar transducer (Item 10d, Appendix D) with an operating range from 0 to 1000 psid upto inlet pressure levels of 2000 psia served to measure the differential pressure across the throttling calorimeter. The three transducers together, are not only a more convenient substitute for the Roebuck balance, but also provide a redundant determination of the pressure drop. The transducers were placed in the fixed temperature flowmeter

163 bath instead of the calorimeter bath to eliminate the effect of temperature on the transducer output. They were connected to the calorimeters through four 1/8" stainless steel lines welded to a stainless steel block in the wall of the flowmeter bath to which values 9,10,11 and 12 located in the bath were also attached as seen in Figure VI-10. The valves serve to connect the appropriate calorimeter to the pressure measurement section. The four lines are lead in a gently downward sloping plane through the styrofoam insulation surrounding the calorimeter bath and into the flowmeter bath through a stainless steel block in the bath wall. By confining the lines to an essentially horizontal plane, fluid head corrections at the pressure measurement system are avoided. Before the lines reach the flowmeter bath, they are tied to another set of four lines connected to the original system through valves 5,6,7 and 8 to allow one to revert to the original measurement scheme as a standby in case of transducer malfunctions. Valves 14 and 15 connect the transducer section to the M & G dead weight gauge and the Roebuck balance, respectively. iv) Electrical Circuitry and Calibration Equations for the Pressure Transducers: The electrical circuitry for the transducers is presented in Figure VI-ll. An adjustable Kepco power supply (Item lOf, Appendix D) constantly delivers an excitation voltage of approximately 10 volts to each transducer via switch S1. Switch S2 inserts a voltage divider into the circuit that permits the excitation voltage to be scaled within the measurement range of the K-3 potentiometer. The calibrations for the scaling resistors are summarized in Table A-10. A rotary switch connects any desired transducer to the K3 potentiometer. The sensitivity of the pressure transducers is 3 millivolts per excitation volt for a full scale pressure of 2400 psia. The output in each case is very linearly dependent upon pressure. For the differential pressure transducer, the sensitivity is 2 millivolts/ volt for a full scale differential pressure of 1000 psid. The pressure transducers were calibrated against the M & G dead weight gauge taking into account the calibration corrections for the latter as described earlier. The calibration equations

164 10 volts DC/ S S2 1000I_ IOOI_ HP rLP DP ET9 ~ ETII ETI (TRANSDUCER OUTPUT VOLTAGES) Figure VI-11. Electrical Circuit Diagram for Pressure and Differential Pressure Transducers.

165 Eh/10 ah + bh P + Ch (VI-12) E/10 a + bP + l p2 (VI-13) for the high and low pressure transducers, respectively, were found to be sufficient to represent individual calibrations over the range 100 to 2000 psia with an average deviation of better than 0.06% of reading, where E is the output voltage in microvolts, and P is the pressure in psia. Sample calibration results for the pressure transducers are shown in Tables A-12 and A-13, respectively. The representation of the calibration data for the differential pressure transducer by a suitable function is a more difficult problem because the output voltage varies not only with the differential pressure, but also with the pressure level. The output voltage is the result of an imbalance in a Wheatstone bridge circuit containing a strain gage in each arm whose resistance varies only with the absolute pressure impressed. The differential voltage is generated by the electrical subtraction of voltages produced by absolute pressure on the strain gages. Consequently the transducer, unlike the Roebuck balance is not a true differential pressure measuring device. If the high and low side are respectively represented by the individual equations EHD/10 - + B Ph + 6 Ph + 3 Y Ph3 (VI-14) ELD/10 - a' +'P1 + 6'P12 + 3 Y'P13 (V-15) then the measured difference (EHD - ELD)/10 is given by EHD- ELD EHD L -. (-at') + BPh -''P1 + 2h - 26 3P 2 (VI-16) 10 n i n i n i If the output voltage is also obtained for zero pressure difference at P = Ph' then the null point voltage E nl/10 is given as a function of pressure by ull10 = (-ca') + (8-3')Ph + (6-6')ph2 + (Y-Y')P 3 (VI-17)

166 By substituting P1 by Ph in Equation (VI-16), the above equation can be rewritten in the form E /10 = a+P + CnP2 + d P3 (VI-18) null n nh nh nh where a, b, cn, d are empirical constants obtained by calibrating the null voltage as a function of pressure. Equation (VI-16) can now be rewritten in the form EDp EHD -ELD AP AP2 1P HO ='AP +'AP(Ph ) +'P(Ph - P hP + E/1 ( I-19) 10o 10 h 2 h h 3 null where E /10 can be determined either from direct measurement at any given time, or from a previous calibration as summarized by Equation (VI-18). In theory therefore, the behaviour of the transducer can be completely characterized from a knowledge of the output voltage as a function of pressure drop at some fixed pressure level, and from the null point voltage as a function of pressure level. In practice, daily shifts equivalent to as much as + 2 psid are noted in the null voltage corresponding to a given pressure level. These shifts could be attributed to hysteresis effects that are more pronounced during the dynamic conditions of actual measurement than from the relatively static calibration conditions. Therefore, it is believed that a better estimate of the true differential pressure may be obtained by measuring En 11 at Ph for each measurement of EDp instead of calculating it from Equation (VI-18). The differential pressure transducer was calibrated using the precalibrated M & G dead weight gauge and the Ruska dead weight calibration standard to measure the pressure at the high and the low side, respectively. The results are shown in Table A-14. The calculated value of [ EDp - E 1]/[ 10 AP] as a function of pressure level for a fixed pressure drop of 200 psid is shown in Table A-15, and is seen to vary upto 0.35%. A sample calculation of the pressure drop, given

L67 the calibration equations fQo the absolute and the differential pressure transducers, is indicated as part of Appendix F-2. v) Chronological Survey of Pressure and Differential Pressure Measurements in This Work: The Roebuck balance and the M & G dead weight gauge were used to investigate the ternary mixture prior to the installation of the transducers. In the case of ethane, the measured pressures using the M & G gauge and the high pressure transducer are compared in Table VI-2. The pressure drop, as measured separately by the Roebuck balance and the differential pressure transducer is also tabulated. In the first case, the discrepancy between the two instruments is, in certain instances, beyond that expected from the goodness of fit to the transducer calibration data and may be attributed to hysteresis effects. Although the average agreement between the pressure drop measurements was within 1%, discrepancies upto 6%, particularly for pressure drops below 80 psid, wtere observed. The measured values from the Roebuck balance were almost always higher, and in retrospect these differences warranted further consideration. Serious electrical problems in the internal circuitry caused chiefly by corrosion due to prolonged immersion in the flowmeter bath required each transducer to be returned at least once to the manufacturer. As a result, the low pressure transducer was not in service until the investigation of the 0.27 mole fraction ethane-propane system. The constants ah and al for the pressure transducers were adjusted in the time span between formal calibration and actual measurement to improve the agreement with the M & G dead weight gauge if deemed necessary. The practice of measuring all three transducer outputs at the inlet pressure corresponding to each data point as determined by the M & G dead weight gauge provides a simultaneous check on the calibrations for all three instruments during the operation of the isothermal calorimeter. As the transducers could not match the accuracy, or significantly improve the convenience of the original measurement system consisting of the M & G dead weight gauge and the 40 inch mercury differential manometer for the small pressure drops (< 2 in. Hg)

168 TABLE VI-2 Comparison Between Original and Modified Pressure and Differential Measurement Schemes with Ethane as the Test Fluid RUN N,. INLFT I!NL ET RO FI K T A NSU C tH+ PR KFSSIJRF PRES SIRE PRE SSURE PFRSSlURk r, F, C; TKRA NSDUCl)tCR A)RP('P 1)R02P T SI A P SI A PSc lT P S l 1.010?0). 2 )01., 3.2 0. 1 1.0)4n0 r48., 4, ] 64.h 2. 2? 2.020 116. 1 164.7 135.6 1 4.7? n0 40 8H53 6 8537 210.6 20. ( 5 2.050 650.6 648.0 236,. 237.0 2.060 426.3 426.0 1 75.4 174.7 3.020 2 I001.0 2001. 270.2 271.2 3.070 1142.7 1143.1 1 1.6 181.0 4.040 217.9 217.9 11 9.0 117.4 5.020 2001.4 2001.1 190.4 189.8 5. 060 119 2.4 1188.9 246. 8 244.2 5. 090 233.62 228.4 151.0 141. 3 6.020 1999.5 1999.6 97.6 98.3 7.0(0 991.7 992.7 222.6 221.8 -7.080 267.2 267.9 113.6 113..n10 2002.4 2003. 321. 321.5 -.0f50 1032.5 1033.3 101 4 99.9 0. (10 370.9 3B66.3 260.0 n 258. l. n 0 201 3. 201 6.0 288.4. 6.9 12.070 11 ) 0.5 1 147.9 315.2 311. 14.025 448. 1 447.8 8.0 85. 15.0!10 1996.6 1997.9 255.8 255.2 1,5.020 997.2 1996.7 113.8 111.6 15.060 11 8.7 1198.3 2R89. 285.8 15.090 620.7 620.7 499.6 496.6 16.010 20114.0 2014.7 35.2 354.4 1!.070 893.5 895.2 410. 4 409.6 1 (. )09}0 398.7 3Q9.1 296.6 293.7 * Original Scheme + Modified Scheme

169 encountered in the operation of the Faulkner calorimeter, they were not utilized for isobaric measurements. vi) The Differential Pressure Calibration Manometer: It was originally intended to use a 200 in. multileg differential mercury manometer specially constructed in this work to serve as a calibration standard for any differential pressure device used at the facility. Although operating difficulties precluded the regular use of this instrument, it is nevertheless believed that a brief description of the manometer and the calculation of the differential pressure from the actual measurements would serve a useful purpose. The manometer and the associated control panel is shown in Figures VI-12a through VI-12c. A schematic of the differential pressure calibration facility is shown in Figure VI-13. The manometer consists of five legs extending to a height of about 250 inches, and supported on a unistrut frame. The pressure to legs I and V constructed of 1/4" stainless steel tubing, and to legs II, III, and IV made from 1/8" stainless steel tubing is supplied by high pressure nitrogen cylinders equipped with relief venting regulators (Item 14b, Appendix D). The mercury reservoirs at the bottom were constructed by welding together hemispherical forged steel caps for 6 inch pipe. A pressure differential between legs I and II can be created by raising a column of mercury in leg I through controlled venting of nitrogen at the top of the leg. If the mercury column is restricted to appear in sightglass A or B, corresponding approximately to 50 or 100 psid, respectively, then the actual difference in the mercury level between leg I and that in sightglass C, directly connected to leg II, can be measured by a freely suspended vertical ruled tape (Item 14e, Appendix D). The NBS calibration for the tape is presented in Table A-1l. In practice, a system of front surface mirrors is used in conjunction with a telescope (Item 14d, Appendix D) to read the tape within the travel span of the telescope that is located, for convenience, at the control panel. The pressure in leg II is recorded at the dead weight gauge by suitable manipulation of the valves on the control panel shown in Figure VI-12c. If legs IV and V are together cautiously brought to the pressure of leg I, then the subsequent venting of nitrogen gas from the top of

11~ ig Figure VI-12a. View of Differen- Figure VI-12b. View of (D.P.C.M.) Figure VI-12c. Viewof(D.P.C.M.) tial Pressure Cal- Valve Manifold. bration Manometer Base. (D.P.C.M.) Sight Glasses.

171 GAS GAS I TANK TANK GAS VENT H.P\ L.P 3() IX 2' ^~ 3a 4 4 L 5 6 8 9 10 LINES TO CALORIMETERS TO 25 2 27X 28 TO DEAD WT 13 GAGE H.A L-r TRANSDUCER 2 TRANSDUCER 15 D.I,,14~~~ ^ _____^ TRANSDUCER 7X 12X 18 16 30 3 17(X) IGAS-ASOIL-I L.BEL I TRANS. iU 00" SOURCE -^-^U BI I ~R~Em' i DEAD WT. 36X 34X X35 -~ALJ DU T TIROEBUCK { loom^ I~^ ~~~~~~~~~~~~ D.P,~^^~~~~ ^^ ^ ^ ^BALANCE i~ ~i (X) REGULATING VALVES AB,C,D,E LIQUID LEVEL GAGES HG VENT Figure VI-13. Schematic of Differential Pressure Calibration Facility.

172 leg V can raise a column of mercury into sightglass D or E permitting pressure differentials of about 200 psid with respect to leg II to be established. Mercury reservoirs constructed from 3" weld caps (not shown in the schematic) are also placed above sightglasses B and E to check surges in the mercury columns and to prevent contamination of the other legs or the control valve manifold. The system is designed to permit the simultaneous calibration of all three transducers and the Roebuck balance, but is restricted to pressure differentials under 200 psid. Various corrections that are involved in the conversion of a measured mercury head into pressure units have been comprehensively reviewed by Brombacher [29]. A sample calculation involving such corrections including the contribution of a gas head to the difference in pressure between the gas in sightglass C and the M & G dead weight gage is illustrated in Appendix F-2. Difficulties in the use of the instrument can be ascribed to the simultaneous effect of poor definition of the mercury-gas interface in the reflected field sightglasses A,B,D and E, and the uncontrolled surging of the mercury column caused by sluggish regulator control in the gas venting operation. g) Composition Analysis. The composition of the major components in each system is determined by gas-solid chromatographic analysis with a thermal conductivity detector (Item 9a, Appendix D) using helium as a carrier gas. The column and the detector are immersed in the flowmeter bath at 27~C to ensure isothermal operation. The output from the detector is traced on a strip chart recorder (Item 9b, Appendix D). Various techniques for effecting the separation of light hydrocarbons and inorganic gases have been discussed by Chang [43]. A variety of column materials were investigated in this work including HMPA on chromasorb P (Item 93, Appendix D) Porapek Q, silica gel and alumina (Item 9d, Appendix D) in an attempt to obtain a sharp separation of methane, ethane, and propane in a reasonable time period at 270C. Although alumina was very satisfactory at 100~C, its use would have required the installation of an additional controlled temperature bath. At room temperature, the propane el ution curve is very diffuse.

173 A 30 foot column of HMPA on Chromasorb P produced satisfactory peaks for the individual components at room temperature, but required 12 minutes per analysis. iTWhen the column length was decreased to 15 feet, with a foot length of alumina added ahead in series, complete separation was effected in 3 minutes. A sample chromatographic output for the ternary mixture is presented in Figure VI-14. The operating conditions for the column are indicated in Figure F-l. The propane peak height for a sample of fixed composition was found to vary from day to day. This behaviour was not observed by previous investigators at the facility who did not use alumina in the column packing. The chromatographic properties of alumina were investigated in depth by Scott [237], who concluded that trace amounts of water vapor had a significant effect on its performance, particularly with reference to the heavier hydrocarbons. Presaturation of the carrier gas was recommended for improving the reproducibility of the measurements, but was not undertaken in this work. The system composition is analysed by comparing the individual component peak heights of a sample obtained from the flow or bypass stream just before being recycled to the compressor against the peak heights obtained for a standard sample of fixed and predetermined composition. The two samples are always analyzed together to ensure that the propane peaks are always consistent. The standard sample for each system is isolated by filling up a heated evacuated full size (size A) gas cylinder to 80 psig through valve FL on the low pressure side of the control manifold, as seen in Figure VI-1, as soon as the fluid in the system is adjudged to be completely mixed. The pressure in the cylinder is kept low, and the temperature kept high to prevent any fractionation during sampling. A sample calculation of the system composition is shown in Appendix F-4. The composition of the standard samples was determined in the following manner. First, samples for each system investigated were obtained from the standard tank in each case and stored. A number of binary reference mixtures were prepared from ultra-pure constituent pure component samples in 180 cc containers by direct weighing using a precision Christian Becker balance sensitive to 0.1 milligram.

174 2 CH4 -C2H6C3H8 MIXTURE STANDARD CHROMATOGRAPHIC ANALYSIS C2 H6 (Att.64) CH4 (Att. 64) C3H8 (Att. 64) E I5 4 3 2 11 TIME, min. 3: LL. a. (Alt. 1) TIME, min. Figure Vl-14. Sample Chromatographic Output for the Ternary Mixture.

175 Recent simplifications in the experimental technique including a sample calculation are described in Appendix F-3. The reference mixture compositions were designed to lie in the vicinity of the individual system samples and are believed to be known to an accuracy of better than 0.2%. The reference and the standard samples were then analyzed in sequence. A plot of peak height vs. mole fraction was made for each component using all the reference sample results as illustrated in Figure F-l. The propane calibration curve shows the greatest degree of non-linearity. The concentration of a given component in each standard sample was calculated from the appropriate calibration curve given the measured peak height. The departure from unity in the sum of the independently determined mole fractions, including trace components, for any given sample served as a consistency check, and was found to vary between 0.997 and 1.004. Trace components in the standard samples were analyzed by mass spectrometry, and are assumed to be essentially invariant for all samples of a given system. Attempts to obtain corroborative evidence of the major component mole fractions by this technique were almost always unsuccessful, as the agreement was almost never better than 2%. A similar problem was reported by Manker [162]. Persistent work on the pure components, and some reference mixtures led to the discovery of an error in the experimental technique relating to the leakage of a variable quantity of air into the given sample as it was being transferred from the 180 cc can to the evacuated bulb of the mass spectrometer. The extent of the air contamination was evaluated by the discrepancy between the chromatographic and mass spectrometric determinations of the mole fraction of the major components, and an attempt was made to evaluate the trace amounts of nitrogen, oxygen, and carbon dioxide in the system by compensating for the air leakage. As the latter accounted for over 90% of the peak valve in each case, the estimated values of these trace impurities are only approximate. Fortunately, the analysis of the major impurity propylene, introduced into every system because of its occurence in the pure ethane feed, was not complicated by the air leakage. The accuracy of the composition analysis of the major components as obtained during calorimetric measurements is a function of the

176 departure of the system composition at the flowmeter from that of the sample in the standard tank (see Appendix F-3) and averages to + 0.25% for the systems investigated in this work. The average value of the composition for the individual systems is indicated in Table VI-3. Procedure An excellent procedure for starting, operating and shutting down the system is presented by Mlanker [162] and is applicable to this work with only minor modifications relating to the equipment changes discussed earlier. The operating procedures specific to the acquisition of a particular type of thermal data are outlined below. As Manker explains, a very complex situation exists even before measurements can be attempted. The period between start-up and measurement is devoted to achieving the desired inlet conditions of temperature, pressure, and flowrate at the calorimeter. This period may vary anywhere from two to six hours. However, as Jones [119] indicates, true steady state conditions are never reached, and constant adjustment of the appropriate control valves are required to maintain quasi-steady state conditions if the accuracy of the measurements is to be ensured. The constant monitoring of leaks from diverse sources such as the valves in the control manifold and on the various storage cylinders, from fittings, particularly on the instrumentation lines leaving the calorimeter and the flowmeter, and at the compressor heads is a critical aspect of normal operation. If a leak is suspected, further measurements are postponed until the source is determined and the leak arrested. Consecutive measurements are usually spaced thirty to forty-five minutes apart. Jones has listed the more crucial observations that are recorded per isobaric measurement. Upto thirty observations noted over a period of five minutes or less, are made per data point. a) Single Phase Isobaric Operation. A single run consists of a series of data points that are obtained by varying the outlet temperature through suitable adjustment of the heat input rate for a fixed set of inlet conditions. Four to five data points are obtained per run at a reasonably constant flowrate involving temperature rises

TABLE VI-3 Summary of the Composition Analysis for the Systems of this Investigation NOMINAL.76 C2H6.50 C2H6.27 C2H6.78 CH4.48 CH4.37 CH4 1.00 CnMPnSITinNS.24 C3H8.50 C3H8.73 C3H8.22 C2H6.52 C2H6.31 C2H6 C2H6.32 C3H8 CnMPnrtlENTS MOLF FRACTION METHANE.0023.0037.0006.7771.4790.3690.0004 ETHANE.7598.4940.2746.2210.5170.3045.9960 PROPANE.2350.5002.7235.0003.0003.3232.0003 PROPYLENE.0019.0015.0003.0005.0029.0025.0026 NITROGFN.0006.0003.0004.0008.0005.0005.0005 CARBON DIOXIDE.0004.0003.0006.0003.0003.0003.0002 MOL. WT. 33.358 37.054 40.218 19.181 23.390 29.460 30.099

178 from 10~F to 125~F. Contiguous runs along a given isobar are usually arranged so that their temperature spans overlap. This permits their consistency with respect to each other to be evaluated. Over the course of a given run, an average inlet temperature variation of about 0.2~F is observed, as opposed to 0.03~F reported by Manker 1162]. Inlet pressure variations upto + 2 psia per run were allowed. Manker [162] restricted such variations to + 0.3 psia. Such stringent regulation of inlet conditions would have considerably increased the time period for this investigation, and were considered only for measurements in the vicinity of the heat capacity maxima, where the techniques used to compensate the data for variations in inlet conditions, as discussed in the next chapter, are less reliable. The precise location of the heat capacity maximum requires successive data points to be spaced as close as a degree apart in some cases. The solid horizontal bars in Figure VIII-1O for example are typical of single phase isobaric measurements. b) Two Phase Isobaric Operation. For a given system, the dew and bubble points for a specified pressure are first approximately located from the data in the literature when available or by a prediction technique such as the NGPA K value charts [156]. The inlet temperature for the run is chosen to be at least 100F below the estimated bubble point. Initially, the power at a fixed flowrate is adjusted to generate data points over small temperature increments. The bubble point is judged to have been exceeded, if the rate of increase of power is disproportionately high for a given temperature increment. At this point, a couple of additional measurements are made, sufficient to locate the bubble point as a discontinuity in a plot of heat input vs. temperature rise. The flowrate is then dropped to a low value commensurate with the limitations on the power supply, and the measurements are continued over larger temperature intervals until another change of slope is apparent on the same plot. The power is decreased if necessary, and closely spaced measurements that clearly serve to define the dew point are made. Although as many as fifteen data points may be involved in such a run [162], as few as nine may be sufficient to characterize an isobaric run across the two phase region. Again, as no provisions are made to compensate for variations in inlet pressure within the two phase region, such variations must be minimized.

1 79 Similar precautions must extend over the course of the entire run for measurements near the critical region in view of the extreme sensitivity of the enthalpy of vaporization to pressure in such cases. A typical enthalpy traverse is shown in Figure VIII-38. c) Isothermal and Isenthalpic Operation. For the throttling measurements, the inlet pressure is initially set at 2000 psia, and a pressure drop usually in the range 50-400 psid is generated depending on the flowrate and the I.D. and length of the capillary element that is used to create the pressure drop. If the outlet temperature drops below the inlet temperature, an adjustable amount of power is supplied to the heating wire located within the capillary to raise the outlet temperature to within 0.020F of the inlet temperature if possible. If the outlet temperature before the addition of power is above that of the inlet, the operation is restricted to the isenthalpic mode. The heating wire in the capillary is inactive, but the guard heater surrounding the outlet section is supplied with a small adjustable amount of power to balance the heat leak. In either case, the inlet pressure is then decreased to a value near the outlet pressure of the previous data point, and the process repeated until an outlet pressure of approximately 100 psia is obtained. Measurements below 100 psia are restricted by the operating pressure (80 psig) of the flowmeter. Typical isothermal and isenthalpic runs are illustrated in Figures VIII-52 and VIII-41, respectively. In rare cases, two consecutive measurements are initiated at the same inlet pressure, and the pressure drop varied by suitable adjustment of the flowrate. Different size capillary coils should be used for the cryogenic liquid and the gaseous regions if comparable pressure drops for normal flow conditions are to be generated. In this work, a twelve foot 18-19 B & S gauge capillary was used ii uEhe liquid region, while a 16-17 B & S gauge capillary was found to be satisfactory for gas phase measurements. It is necessary to place greater emphasis in limiting the fluctuations in the calorimeter bath temperature in order to prevent relatively significant spurious contributions to the small temperature differences characteristic of such measurements. Although previous investigators at the laboratory [168,284] have

180 reported isothermal enthalpy traverses across the two phase region, the measurement, and in particular the location of the dew point, is experimentally difficult, and has generally been avoided in this work. The chief difficulty is due to severe fluctuations in the flowrate and pressure drop that are observed within the two phase region and caused by the changing quality of the two phase mixture as one almost futilely attempts to adjust the outlet temperature to that of the inlet. Operating Schedule As a rule of thumb, a day of maintenance was found to be necessary per day of operation and illustrates to some extent the difficulty of the experiment. Furthermore, the recycle system was found to suffer from a high degree of inertia. Consequently, it was felt that round the clock operation, with twelve hour shifts, terminated only by the occurrence of a major malfunction would be most productive. This schedule was accordingly implemented. Chronology of the Experimental Investigation The chronological order of examination of the systems of this study was in part dictated by the need to minimize the total investment in the gas fed to the system. A 23.4% methane-propane mixture was left in the storage tanks from a previous investigation [284]. Ethane, and make up quantities of methane, and propane (Item 15a, 15c and 15d, respectively) were added until the system was filled to capacity with the ternary mixture of required composition. After its completion, the entire system including the fluid in the storage tanks was evacuated, flushed, and then filled with ethane. The three ethane-propane mixtures, investigated in order of increasing propane concentration, were prepared by adding propane and make up amounts of ethane to each system in sequence. Upon completion of the investigation, the system was re-evacuated, and appropriate quantities of methane, and ethane were mixed to yield a mixture containing 78% methane. Further addition of ethane was required to generate the 48% methane-ethane mixture. The procedure for mixing the pure fluids in the recycle systems to achieve the desired mixture in the shortest possible time was improved from that of previous investigations and is discussed in Appendix 1-2.

Chapter VII DATA REDUCTION This section describes how smoothed tabulated values of the enthalpy function and its appropriate derivatives with respect to teirperature and pressure are generated so as to accurately reflect the basic data of this work within the constraints of thermodynamic consistency. In sequence, the errors in the original observations must be weeded out and corrected where possible, the basic data must then be interpreted to yield smoothed values of Cp or ( which are in turn integrated along isobars and isotherms, respectively, to generate smoothed enthalpy values. After the enthalpies are examined and adjusted for self consistency, it is possible to proceed with the construction of smoothed enthalpy tables or diagrams using auxiliary enthalpy data at zero pressure. Reduction of Raw Data to Basic Data The basic observations are entered on punched cards, and fed to a master data reduction program in Fortran IV on file at the TPFL and processed on an IBM 360-67 digital computer. The program is designed to accomodate any system consisting primarily of the components methane, ethane and propane. The specific mode of calorimeter operation, the calibration data for those instruments whose characteristic tend to change with time, and information that indicates the desired weighting whenever redundant measurements are obtained must be fed as part of the input in addition to the observations specific to each given data point. The computer output is screened for errors in the noted observations using in part diagnostic techniques discussed in the previous chapter. This basic processed data are generated by the computer in punched card form in which the composition of the three major components, the inlet temperature, the temperature difference, the inlet pressure, the pressure drop, the experimentally observed enthalpy change, and the approximate average value of the enthalpy derivative appropriate to the calorimeter operating mode are recorded. The basic format for the ternary mixture for example is seen in Tables B-19 through B-21. The basic technique for the reduction of the raw data has been 181

182 excellently illustrated by Jones [119] and is utilized in this work with the exception of the modifications discussed in the previous chapter. Sample calculations that illustrate data reduction procedures that are modified in this work are presented in Appendix F-l through 1-4. Determination of Enthalpy Derivatives Cp, 6 and p From the Basic Data The determination of the differential thermal properties Cp and e from the basic data requires the operating mode of the calorimeter to be such that the fluid stream is confined to a path where the effect of a single independent variable may be isolated. In general, simultaneous variations in other independent variables, however small, cannot be entirely avoided during the actual measurement and must be compensated for. a) Thermodynamic Analysis for Isobaric Data. If the reference pressure and composition for an isobaric run are represented by P and [x ], respectively, then every data point in the run obtained at slightly different inlet conditions Pi and [x] must be corrected to the reference point. Furthermore, the pressure drop (Pi - Pf) must also be compensated for. The equation H - H -H + -H TfPo,[X ] T.,Po,[x) =( TfPf P [x] TP TPi,[x]] Tf Pf [x H -H H -H H - -H -Tf'Po'[Xo] Tf'Po [x] TiPi,[x] Ti Po, [X] Ti,P,[x] TiPo, [xo (VII-1) expresses the desired enthalpy difference on the left hand side in terms of the actually measured enthalpy difference (the first bracketed quantity on the right hand side) and additional correction terms. Combining Equation (1-21) with (VII-1), and expressing the correction terms on the right hand side in terms of the appropriate enthalpy derivatives, we obtain [x] n a T) jI1 dx (VII-2) [X] j TiPoX]=The mean heat capacity vr the interval between T and Ti ma now e etermine froay nge be determined from the corrected enthalpy change as

183 Cp - (Cp>) dT/(Tf- ) - (T T (VII-3) Ti Po,[o — TiP[Xo]) /Tf- Ti) The solid horizontal bars in Figure (VIII-10) for example, represent the mean heat capacities over the interval of the bar length, and are( derived from the basic data after correction. A smoothed heat capacity curve can now be constructed along the entire isobar under the constraint of Equation (VII-3) which requires the area under the solid horizontal bars to equal the area under the smoothed curve. As an isobaric run consists of a series of measurements where the inlet conditions are held fairly constant, the corrected basic data may be differenced after making additional corrections for small variations in the inlet conditions. Thus, if T is the reference inlet temperature for a given isobaric run containing two data points A and B with inlet temperatures TiA and TiB, and outlet temperatures TfA and TfB, respectively, then the mean heat capacity over the interval TfA to TfB is given by fB o'_ 0IA ~fA fB cp H ) H - - TfA'Po[xo] TiA-'Po'[ Xo ] 01 TWPo01 T W'P~'[xol T T -J(CP)TP dT + (Cp), dT]/(TfA TfB) (V-4) TIAT00 fA fB (VII-4) TiA TiB where the value of the heat capacity at the inlet condition T, P 0 O is necessary to provide the corrections for the variation in the inlet temperature. If the interval (TfA - TfB) is small with respect to the temperature rises (TfA - TiA) and (T - TiB) for the data points A and B, then errors or inconsistencies in the basic data are magnified and consequently more easily spotted if such differenced mean heat capacity values are also plotted as indicated by the dashed lines in Figure VIII-IO. This information is also seen to be more useful than the basic data in guiding the course of the equal area heat capacity curve by manual techniques. The evaluation of the last four terms in Equation (VII-2) by direct measurement could be very time consuming. Therefore, the estimation of these terms from an enthalpy prediction technique of proven reliability is to be preferred. A satisfactory technique for the accurate estimation of thermal property derivatives is yet to

184 be found. Such difficulties forced previous investigators at the laboratory [162,168,284] to ignore the corrections for all but the pressure drop term in isobaric operation, and the temperature difference term for isothermal runs, both of which were calculated by the original BWR equation of state, unless more reasonable estimates could be obtained from other direct measurements b) The Use of the PGC for the Correction of the Basic Data. Although the PGC was found to be excellent for the prediction of pure component and mixture enthalpies, the tabular nature of the correlation does not ensure that accurate values of enthalpy derivatives can also be calculated. To partially circumvent this problem, a modified data correction technique was used in this work which involved the computation of enthalpy difference ratios using the PGC predictions. For the isobaric case we obtain (H -H H - H (VII-5) Tf.P0,[X [ To,P~ [Xo] Tf Pf, [x] -(V I I-5) 0 o 000 f'tf' where f ( TfPf[x H H T H (VII-5a) f fP [x] TPo I[xO P/ x,P,[x ] (VII-5b) = H TfPf,[x ] To,Pi,[Xo] TfPf,[x] T,Pi,[x] (VI-c) o t( Ho (VII-5b) PAPf ( TTf,p, [xo] To,P, [Xo] Tf,Pf, [Xo] T,P[ (o]-5d) x 0 To 0 Tff [o To,0 [ 0 The last four terms on the right hand side represent fractional corrections to the basic data for variations in composition, inlet temperature, inlet pressure, and pressure difference, respectively. The corrections for variations in inlet temperature are only required if the basic isobaric data are to be differenced. For the isothermal case, one obtains ToPf'[xo, To[x ( Expt[(f [xo )(fT )(fAT) ]v-) H -H (AH) [(f [X o ] where D H -H H -H AT( T P P [xl TP i'pri)(VII-ta) To,Pf,[xo] To,P,[Xo ] T fpf,[Xo] 0-To,Pi,[Xo])

185 and corrects for the temperature difference between the calorimeter outlet and the reference temperature T for the isotherm. Special care is required in applying such correction procedures in the vicinity of the heat capacity maxima, as discrepancies between the PGC and the actual data with respect to the location of the maximum can result in substantial errors in the correction terms. The average total correction was about 0.2% for the isobaric measurements, and about 1% for the isothermal data. In all cases, unreasonably large correction terms were either ignored or substituted by experimentally derived values of Cp or ~ where possible. Thus, corrections for the temperature difference in isothermal measurements, and for variations in inlet temperature in the isobaric data were, in some cases, obtained from Cp values that were determined by preliminary processing of the experimental results. As the PGC was not equipped for the prediction of the phase behaviour of mixtures at the time, two phase data remained uncorrected. In all cases, unreasonably large correction terms were either ignored or substituted by experimentally derived values of Cp or ~ where possible. Thus corrections for the temperature difference in isothermal measurements, and for variations in inlet temperature in the isobaric data were, in some cases, obtained from Cp values that were determined by preliminary processing of the experimental results. Special care is required in applying such correction procedures in the vicinity of the heat capacity maxima, as discrepancies between the PGC and the actual data with respect to the location of the maximum can result in substantial errors in the correction terms. The average total correction was about 0.2% for the isobaric measurements, and about 1% for the isothermal data. c) Interpretation of Joule-Thomson Coefficient Data. It is evident that the fractional correction scheme cannot work for situations involving little or no enthalpy change, i.e., for isenthalpic operation. In this case the fractional correction may be computed with respect to the observed temperature difference. Thus [Tf([Xo]Pf) - ([X],Pi) ] = [Tf([],Pf) - Ti([],Pi) ] [ Tf(P) - )] (VII-7) HO i,Exp f ) - Ti(x],Pi) Expt PGC

186 However, the PGC predictions were such that irregular variations were observed with respect to both the sign and magnitude of the enthalpy deviations for the individual data points in a given run. These variations were, in part, also attributed to truncation effects. It was felt that the PGC corrections for such data, as incorporated in Equation (VII-7), were best ignored in view of the demonstrated irregularities. Isenthalpic measurements are typically illustrated in Figure (VIII-13) where the average value of the Joule-Thomson coefficient hi is plotted over the pressure interval for each data point. It is important to note that successive data points do not, strictly speaking, lie on the same isenthalp if the inlet pressure is varied and the inlet temperature is kept constant throughout the run. Furthermore, the point value of u at any point cannot, in rigid accordance with thermodynamics, be obtained by constructing an equal area curve through the data points in Figure VIII-13. From the standpoint of constructing an enthalpy diagram from such measurements, it is best to interpret the isenthalpic data to generate a pressure-enthalpy isotherm corresponding to the inlet temperature of the run. Recalling Equations (1-27) through (1-30), an experimental determination of yI, and an independent estimate of Cp over the interval (Tf - Ti) permits the value of (T) over the interval (Pf - P) to be calculated. Point values of ~ at T. may now be obtained as a function of pressure by the equal area technique. On integration, the desired pressure-enthalpy isotherm is generated. As the temperature rise AT across individual isenthalpic data points is usually less than 1iF, Cp may be approximated by the point value Cp at the arithmetic mean temperature T = (Ti + Tf)/2. The required estimate of Cp at T and Pf was obtained by cross plotting Cp values obtained along isobars as a function of pressure at T = To. The generation of a pressure enthalpy isotherm from isenthalpic data has been illustrated for propane as Figure 18 in the thesis of Yesavage [284]. In this work, the experimental heat capacity data at the temperature of interest T were sometimes restricted to a single isobar at 0o P, and required a different technique to be used for the estimation of Cp at the desired pressure Pf. It was necessary to assume that

I M / dCp/dPr was uniquely determined at a given Tr and Pr. It was further assumed that the variation of Cp with reduced pressure could be determined from the Cp vs P plot of Yesavage [284] for the 23% methanepropane mixtures as a function of temperature in the liquid and dense fluid region. If the pseudocritical properties of the mixture are approximately estimated (the mixing rules expressed by Equations (IV-77), (IV-78) and (V-22) with the approximations of Equations (IV-17), (IV-19a) and the arithmetic mean for cc.. were used), then the variation of Cp with pressure over the interval P to Pf at temperature T for a substance with pseudocritical parameters Tc and Pc is given by m m Tc Pc Tc Pc Pc Cn(TP) - C~TP) = [C (T m rni mr mr (VII-7a) CP(ToP) - CP(T'Po,P[Cf Pc ) - Cp (To T, P (V )-7a) m m m m m where the square bracketed term on the right hand side represents the quantity evaluated from the plot of Yesavage, and Tcmr, Pcr are the pseudocritical parameters for the 23% methane-propane mixtures. Thus, Cp at Pf may be estimated if Cp at P is independently known. Although this appears to be an approximate technique it must be recognized that the variation of Cp with pressure from saturation conditions in the liquid phase upto pressures as high as 2000 psia rarely exceeds 1.5% in the region of isenthalpic measurements. Consequently errors in the estimation of 4 from such data are bounded by this value even if corrections for the variation of Cp with pressure are completely ignored. Techniques for Constructing Equal Area Curves Unless errors in constructing and integrating equal area curves for the properties Cp and ~ from the basic enthalpy data are scrupulously avoided, all the effort that has been expended in preserving the accuracy of the basic measurements will have been essentially wasted. The construction and integration of these curves was one of the most time consuming problems of this work. The merits and deficiencies of techniques attempted in previous investigations are also discussed along with those tried in this work. a) Graphical. Manker [162], Jones [119] and Mather [168] obtained

188 heat capacities from experimental isobaric data by graphical integration involving a visual judgement of the equal area criterion and claimed a precision of 0.5%. The reported enthalpy values of Manker were, however, directly derived from experimental data by plotting the measured enthalpy change vs temperature rise for each data point in a given run, and by connecting the points with a smooth curve using the inlet temperature as a temporary enthalpy reference. The value of the inlet temperature enthalpy for successive runs along a given isobar were related to each other either from overlapping data or through graphical integration of interpolated heat capacity values when no such overlap existed. Such a procedure does not ensure consistency between the enthalpy and heat capacity values. Bhirud and Powers [22] have used Simpson's rule both to plot the Cp curve from the mean heat capacity values and to integrate the plotted curve to yield consistent enthalpy values. In brief, if Cp is assumed to be a cubic function of T in the interval T to Tf for which the mean heat capacity is known, and plotted as a bar over the given interval, then, at the midpoint of the bar, the vertical distance between the bar and the equal area heat capacity curve must be half of the distance between the bar and the straight line joining the point values of Cp at the extremities Ti and Tf of the bar. Mathematically CP - (C) p) = {( + (Cp) }/2 - Cp (VII-8) (Ti+Tf)/2 T. Tf This technique is very arduous and is susceptible to an indeterminate degree of human error. 2) Linear Regression Techniques. Yesavage [284] assumed that the heat capacity could be expressed as a power series Cp = b + 2cT + 3dT2 + 4eT3 (VII-9) On integration, the result Hf- Hi (Tf2 - Ti2) (Tf3 - T.3) (Tf4 - T 4) ~~- T CP = b + c _,~i + d - ~i + e - T) (VII-10) Tf T1 (Tf VTf (-T) (Tf

1 89 was obtained.'lThe constants bc,(,l, and e are determined by a multivariable linear least squares regression analysis using Ti and T as the independent variables, and Cp as the dependent variable, and may now be used to calculate smoothed values of heat capacity and enthalpy relative to some base temperature. The number of data points for a given set of regression constants was fixed at eight. This technique consequently gave rise to discontinuities in the value of the heat capacity at the interface of successive regression sets along a given isobar. Furthermore, in the absence of weighting procedures, the use of marginal data points in the regression was observed to cause ripples in the heat capacity function in some cases. The method also produced a poor fit in the region of the Cp or ~ maxima where supplementary graphical processing was found to be necessary. c) Non-Linear Regression Techniques. In this work, an attempt was made to process a complete isobar or isotherm with observed maxima using a single analytic functional relationship between Cp and T, or between 0 and P. This technique was tested with the 126.2~F isotherm for the ternary mixture seen in Figure (VIII-52), primarily because of the even distribution of data about the maximum point, and their excellent consistency with respect to each other. Provisions were made for performing a multiple, and if necessary, non-linear regression analysis on a flexible combination of a wide variety of functions using the Gauss method of least squares. A discussion of the technique, and an algorithm is provided by Wolberg [282] which also includes provisions for weighting the data used in the regression. Initially, the form = a + bP + cP2 + dP3 + gfe-f(P-Pk) (VII-11) was attempted, where Pk is the pressure corresponding to the maximum value of 4 along the isotherm. The polynomial terms have some theoretical justification in the gas phase and may be regarded as a truncated version of the virial equation for P. The true virial coefficients cannot, however, be expressed solely in terms of the polynomial constants

190 because of the contribution of the gaussian function to each term. The gaussian function was selected for the specific purpose of fitting the data in the vicinity of the maximum because, unlike most other functional forms, its contribution away from the maximum can be made to decay rapidly, if necessary, by suitable adjustment of the parameter f in Equation (VII-ll). The regression constants were determined from the basic data using the equation _Hf-Hi _- (P p2) (Pf3-P.3) (Pf 4Pi3) ) Pf = a + b + c + 4(Pi) + - g [ erfif(Pf-Pk) - erf{f(Pi-Pk)}] (VII-12) P -P -^2(Pf. 3' (P f-P) 4(P f- - obtained by integration of Equation (VII-11). Convergence was obtained for reasonable initial values of the constants. The value of Pk can be fairly well estimated from the basic data. Reasonable estimates of a, b, c, d, and g were obtained by initially fixing f and Pk, and then conducting a regression on the rest of the linear terms, because convergence is always assured for the linear case. The results of the regression are shown in Table C-2. The fit to the basic data is about 0.6%. The smoothed $ curve resulting from the regression and indicated by the dashed line in Figure VIII-52 does not fit the low pressure data very well and suggests that the representation of ( by Equation (VII-ll) is not the final answer. Other possibilities for improving upon Equation (VII-ll) are discussed in Chapter X. Several factors precluded the further pursuit of this technique in this work. Firstly, the range and distribution of the basic data about the peak value influence the type and number of terms to be used in the regression analysis, requiring considerable experimentation to find the best combination. For example, an isolated isobaric run, or a complete isothermal run in the liquid region would be completely insensitive to the gaussian function, as both Cp and d vary only slightly in the cryogenic liquid region. On the other hand, a run that consists, for example, of only four data points around the maximum in Cp, though accessible to graphical analysis, would demand considerable skill in locating just the right combination of functions that could fit the data within experimental accuracy, without involving three or more adjustable constants. Secondly, the weighting procedure is arbitrary and could involve a

1 91 number of trials before the most desirable weighting scheme from the combined standpoint of smoothness and goodness of fit is obtained. d) Computer Aided Graphical Techniques. Although a graphical construction of the equal area curve circumvents the problem of specifying an appropriate analytic functional form for the least squares fitting of the basic data in different regions, and furthermore permits a visual weighting of the data without requiring the assignment of quantitative weighting factors to each data point, it is nevertheless desirable to monitor such a subjective procedure by computer techniques. A more objective assessment of the equal area curve can be made if the area under the curve so constructed is integrated on the computer and compared with the basic data. The Simpson's rule technique was used to manually construct a smoothed plot of ~ vs P, or Cp vs T from large sized graphs of the basic corrected data plotted as horizontal bars. These plots were generated using a Model 763 Digital Calcomp Plotter. To avoid clutter, only the differenced values between contiguous data points, arranged in order of increasing temperature rise, are plotted in addition to the basic data for the isobaric measurements. Point values of Cp or 4 were obtained from such graphs at frequent intervals of temperature or pressure. The interval between the selected data points was such that rapid changes in the value of the slope dCp/dT or dd/dP were avoided. In the isobaric case, the spacing was usually of the order of 10~F, decreasing to 10F in the vicinity of the maxima. The interval for isothermal data was about 200 psid decreasing to 50 psid near the maxima. The functional relationship in the interval between any two such points was represented by successive five point Lagrange interpolating polynomials. The desired interval is arranged to lie between the third and the fourth of five points whenever possible. The integral over each such interval was also calculated to yield enthalpy differences using Gauss-Legendre quadrature. An algorithm and an excellent discussion of the technique is provided by Carnahan et al. [40]. The integral under the curve was also computed over the intervals corresponding to the basic and differenced data and compared with the experimental values. The overall bias and percentage bias for each loop

192 were calculated in terms of the enthalpy difference AH. for each arm as 4 Bias = E [ ( AHi ) - ( AH ) ] (VII-13) i=l Expt Cal 4 4 % Bias = Z [ (AH) - (AHi) ]/ [AH.] x 100 (VII-13a) i=l Expt Cal i=l Expt These computations provide a check on the graphical technique and indicate regions where adjustments are necessary. The actual curve is then replotted, and appropriate adjustments are made in the point values of Cp or ~ until the bias, after ignoring the contribution of data points with percentage deviations greater than four times the average, is less than 0.25%. At this stage, the Cp, ~ and enthalpy values are uniformly adjusted to compensate for the remaining bias if necessary. The effect of the order of the interpolating polynomial on the integration of tabulated values of d vs T was investigated for the 126.2 F isotherm for the ternary mixture. Maximum local variations of 0.2%, and an average variation of 0.(05% was noted on comparing the three and the five point case. The variation in the total enthalpy change from 0 to 2000 psia was less than 0.1%. To ensure that the Lagrange polynomial integration was accurate, values of ( at 100 psi intervals were obtained from the multiple, non-linear regression analysis results for the same isotherm, and integrated using the five point interpolating polynomial. The agreement with the analytically integrated regression equation [Equation (VII-12)] was better than 0.1%. An examination of the data for the systems of this work indicates that on an average, the goodness of fit is better than 0.3% for the isobaric data, and about 1% for the isothermal measurements. Sample results for the equal area determination of heat capacities and enthalpies from the basic isobaric data are indicated in Table C-3. Consistency Checks The acquisition of isobaric and isothermal data over common regions permits them to be compared for self-consistency. Figure VIII-14, for example, summarizes the consistency checks on the ethane data. The

193 enthalpy loop from -246.30F to -1.23.30F and from 250 psia to 1000 psia is regarded to indicate how such checks may be accomplished. The enthalpy change across each arm of the loop is calculated from the integrated equal area Cp or ~ curve discussed in the previous section. As enthalpy is a point function of state, the net enthalpy change across any path forming a closed loop should be zero. In practice, the algebraic sum across such a loop is a finite quantity (+0.55 Btu/lb in this case) that serves as a measure of the thermodynamic consistency of the data. Before enthalpy tables can be constructed, it is necessary that the values ascribed to each arm of every loop be optimally adjusted, preferably within the estimated accuracy of the data, so that each loop is exactly balanced. In the particular case examined, the initial smoothed value of the enthalpy change at 1000 psia between -246.60F and -123.3~F is 0.65 Btu/lb higher than the final adjusted value of 68.91 Btu/lb; an inconsistency of about 1%. The percentage inconsistency for the entire 4 4 loop defined by ( Z AH/ Z IAH.I)(100) is only 0.4%. Thus, the percentage adjustment to he enthalpy difference AHi across an individual arm of a loop may be considerably higher than that required for the loop as a whole. This behaviour is caused by the fact that the value of Z AH. for any given loop is relatively insensitive to i 1 large consistent errors in parallel arms, particularly, when the enthalpy changes along such arms are not significantly different from each other. In order to avoid a concentration of errors in a small end loop, the largest loop (-24.5"F to 200.60F, and from 500 to 2000 psia) is balanced first, and bounds are established on the total acceptable variation for the individual arms. The smaller constituent loops are than adjusted within these constraints. Errors common to both isobaric and isothermal measurements, such as a mass leak before the flowmeter, are not easily spotted unless one arm of a loop occurs at zero pressure where the enthalpy difference is defined by the API tables [220] which serve as a completely independent data source. The loop from 125~F to 200~F, and from 0 to 250 psia is just such an example. The smoothed Cp and b values for the individual arms generated by the techniques of the previous section are now readjusted, usually

194 by uniform scaling, to conform to the final value of the enthalpv change assigned to the given arm. Particular difficulties exist when the corrections to contiguous arms along isobars or isotherms are in opposite directions, and some smoothness is sacrificed in the values of the appropriate enthalpy derivatives near the junction point. Preparation of Pressure-Temperature-Enthalpy Diagrams and Tables Although the interpretation of the data so far has generated useful results, enthalpy changes across any two conditions not restricted to experimental isotherms or isobars cannot be easily determined from such information. The construction of pressure-temperatureenthalpy diagrams or tables which serve to define the enthalpy at any specified point in relation to the enthalpy at some reference pressure and temperature would be very useful in making such calculations. For reference, an enthalpy value of zero was attributed to each pure component in a mixture in the saturated liquid state at -2800F. This choice of reference conditions is consistent with the reported enthalpy values for previous systems investigated at the facility [119, 162,168,284], and conveniently ascribes positive values to the enthalpies over the range of application of the tables. The computation of the enthalpy of a mixture at the reference condition, i.e., at the saturated liquid state at -2800F is troublesome because it requires the heat of mixing of the constituent pure components to be first established. The ideal gas state is a more desirable reference point for mixtures because the value of the zero pressure enthalpy at any temperature can be rigorously determined from the constituent pure component enthalpy values at the same temperature using the relation H = ZW H T H. =wi (VII-14) where H is the specific enthalpy of the mixture, and w. and H. -In 1 — 1 represent the mass fraction and the specific enthalpy for the ith component. Therefore, to circumvent the problem of computing the heat of mixing for the mixture at -280 F, the enthalpy change for each of the constituent pure components in going from the saturated liquid state at -280~F to the ideal gas state at some arbitrary temperature

195 is first calculated, and the mixture enthalpy at this temperature is then rigorously fixed by Equation (VII-14) above. For convenience, the temperature selected for the definition of the mixture enthalpy at zero pressure is usually chosen to coincide with a measured isotherm in the gaseous phase beyond the cricondentherm temperature. A knowledge of the enthalpy behaviour along the given isotherm, previously calculated as a function of pressure, now specifies a reference enthalpy for every experimental isobar at that temperature. This information in conjunction with isobaric measurements across the given isotherm permits an enthalpy value to be assigned to the mixture at other temperatures along the isobars relative to the saturated liquid pure component references at -2800F. In this fashion, a pressure-temperature network of enthalpy values can be generated. The following calculations illustrate the determination of the reference point for the ternary mixture at 192~F. First, the enthalpy of each of the pure components at 192~F and 0 psia is established below. a) Methane AH (Btu/lb) Enthalpy of saturated liquid at -2800F and 5 psia 0.00 Enthalpy of vaporization at -280~F and 5 psia, (Frank and Clusius [84]) 227.72 Enthalpy change from saturated vapor at 5 psia to the ideal gas at 0 psia and -280"F (Virial equation, this work) 1.15 Enthalpy change as an ideal gas from -2800F to 192~F, (Rossini [220]) 243.32 Enthalpy of methane at 0 psia and 192~F 472.19 b) Ethane Enthalpy of saturated liquid at -280~F 0.00 Enthalpy change from saturated liquid at -280 F to saturated liquid at -128.1~F and 14.7 psia (Witt and Kemp [280]) 84.50 Enthalpy of vaporization at -128.1~F and 14.7 psia (Witt and Kemp [280]) 210.90 Enthalpy change from saturated vapor at 14.7 psia to 0 psia and -128.3~F (Virial equation, this work) 2.40

196 Enthalpy change as an ideal gas from -128.1~F to 1920F AH (Btu/lb) (Rossini [220]) 127.70 Enthalpy of ethane at 0 psia and 192~F 425.50 c) Propane Enthalpy of saturated liquid at -280~F 0.00 Enthalpy change from saturated liquid at -280~F to saturated liquid at 43.7~F and 14.7 psia (Kemp and Egan [127]) 183.17 Enthalpy change from saturated vapor at 14.7 psia to 0 psia and -43.7~F (Virial Equation, this work) 2.43 Enthalpy change as an ideal gas from -280~F to 192~F 93.73 Enthalpy of propane at 0 psia and 192~F 394.63 As the contribution of other components are minor, only the final results are given in the following cases d) Enthalpy of nitrogen at 0 psia and 192"F 193.60 e) Enthalpy of carbon dioxide at 0 psia and 192~F 182.00 f) Enthalpy of propylene at 0 psia and 192"F 370.00 g) Enthalpy of ternary methane-ethane-propane mixture at 0 psia and 192~F using the compositions in Table VI-3 converted to mass fraction for use in Equation (VII-14) 418.70 The calculation of the enthalpy departure for the saturated vapor was in each case accomplished by using the reduced second virial coefficient correlation of this work [Equation (V-30)], and the reduced third virial coefficient correlation of Chueh and Prausnitz [Equation (III-44)]. The appropriate thermodynamic relationships for calculations based on Equation (V-30) are summarized in Appendix H-3. The enthalpy differences at zero pressure were calculated by interpolating the heat content function values [H(T~K) - H(0~K))]/T tabulated at regular intervals by Rossini [220].

Chapter VIII IXP I.RIMENTAL AND SMOOTHED CALORIMETRIC DATA This section summarizes the results obtained from the isobaric, isothermal and isenthalpic calorimetric investigation of ethane, three ethane-propane mixtures, two methane-ethane mixtures, and a ternary mixture of methane, ethane and propane over the liquid, gaseous, critical and two phase regions. Only basic data are reported for the methane-ethane mixtures. For the rest of the systems, the basic data, consistency checks on the smoothed data, and tabulated values of the enthalpy and its appropriate derivative Cp or d are presented at the conditions of measurement. Enthalpy diagrams are also prepared both for ethane and the ternary mixture. The techniques employed to achieve these final results have already been discussed in the previous section. Typical results involving various operating modes for the calorimeters are graphically illustrated for each system. Difficulties in the acquisition and interpretation of the data that are specific to a given system are outlined here. Some comparisons are made with limited sources of data available in the literature. The results of special tests on the calorimeters are also discussed prior to the presentation of the data to examine the validity of several assumptions with respect to operating practice. Special Tests on Calorimeters a) Unsteady State Behaviour of the Isobaric Calorimeter. The estimation of the amount of time required to achieve quasi-steady state conditions for a given data point in normal operation after the initial input of power was made difficult because of observed fluctuations in the temperature rise. These fluctuations appear to be related to problems in maintaining the state and the flowrate of the system fluid at the calorimeter inlet at some fixed pre-determined conditions, and complicated the determination of the time period required for the quantity dU/de in Equation (I-17) to vanish, where U is the energy of the calorimeter. The effect of varying flowrate on the final approach to quasi-steady 197

198 state conditions is minimized if the decay in the temperature difference between the inlet and outlet, caused by suddenly removing the power input to a calorimeter at quasi-steady state, is followed with time instead of the temperature rise. In practice, the power to the calorimeter and the guard heater was switched off after maintaining quasisteady state conditions for about four hours. The experiment was conducted on the 0.49 mole fraction ethane-propane system at a flowrate of 0.244 lbs/min., and for an initial quasi-steady state temperature rise of 100~F. As soon as the power was switched off, the evacuated section between the guard heater and the outlet section of the calorimeter was quickly brought to atmospheric pressure to allow rapid equilibration between their respective temperatures, arresting the radiative and conductive heat transfer to the calorimeter from the guard heater. The results for both the original and modified heater capsules are shown in Figure VIII-1, and indicate that the latter has better heat transfer characteristics. The graph establishes that a 99.9% approach to steady state occurs in a period of about 50 minutes for the modified capsule. For very small temperature differences, ( < 0.05~F), the analysis is complicated by the relatively significant contribution of variations in the calorimeter bath temperature to fluctuations in the observed temperature difference. Although such effects have been qualitatively observed in the time period before the initial input of power to the first data point for a given run, no attempt has been made to quantitatively define such observations as the time interval for the unsteady state experiment would have to be greatly extended. b) Heat Leak Test. If Equations (1-17), (1-18) and (1-19) are combined, and if the temperature difference between the calorimeter bath and the calorimeter inlet T. is ignored in Equation (1-18), we obtain the result E I 1 dA -TfPf -P m +hfAf(Tsf-Tf) - de (VIII-1) If the left hand side of the above equation is expressed in terms of

UNSTEADY STATE ANALYSIS OF ISOBARIC CALORIMETER o Original Heater Capsule o New Heater Capsule Flowrate: 0.244 Ib/min 100 10000( Pressure: 2000 psia i 0000~ Inlet Temp.: 150~F IL System: 0.498 C2H6 (C2H6-C3H8) 0^^ z 0 -- w 10 Iu o 1 00 0 1 2 Within the Isobaric Calorimeter. W 100- ~'~ 0.1 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 TIME (Secs) Figure VPII-1. Approach to Steady State as a Function of the Heater Capsule Within the Isobaric Calorimeter.

200 the enthalpy derivatives Cp and $, as in Equation (1-25), then we obtain the result H -H P p Tf -PsTPs hA (Ts - Tf A1 TfPs TiPs E I- f f(-f f _1 dt+ TdP dP ]/(Tf-Ti) (VIII-2) (Tf Ti) dE + r-n m m m i f Ps Ps Pi on dividing by (Tf - T.) and rearranging, where Ps is the reference pressure to which the actual measurements are corrected. If heat leak and unsteady state effects are ignored, then the apparent heat capacity CPA is defined by the relation Pf Ps Ps Pf Therefore, the true mean heat capacity Cp is defined in terms of the apparent mean heat capacity CPA by the relation 1 dU hfAf(Tsf-Tf) PA ffi -' ]/(Tf-) (VIII-4) A plot of apparent mean heat capacity vs reciprocal flowrate l/m has been prepared for ethane over a fixed temperature rise of 15'F for inlet conditions at 146.6 7F and 1000 psia as illustrated in Figure VIII-2. Successive measurements were taken in order of increasing flowrate. A new point is initiated by first increasing the flowrate, and then adding power till the original specified temperature rise is obtained. In such situations dUZ/d is always initially positive. In the absence of heat leak and unsteady state effects, the plot should yield a horizontal line. Except for the point at the lowest flowrate, the data lie within a span of 0.3%, and the trend is in the opposite direction from that anticipated due to heat leak and unsteady state effects. It is conceivable that the location of the heat shield differential thermopile is such that the guard heat at the observed balance point over-compensates for the true heat leak causing CPA to rise with increasing reciprocal flowrate. The estimated precision of the measured flowrate is also indicated in the figure, and suggests that it may be the limiting factor in this analysis. Point 1 at the lowest flowrate merits further discussion as the computed value of Cp is higher than the rest by about 0.5%. Although

201 CALORIMETER HEAT LEAK TEST FOR ETHANE PRESSURE =1000 psia ~1.075- NLET TEMP. = 146.66~F OUTLET TEMP. = 162.15~F.m~ ~ ~ ~ ~TJ _,.' Accuracy:::3 1.070 -._ _ ~ Span for -1.070 - --- OQel/2I / Flowmeter 1/2 %'dIe~~~~~~~~ I 3 2 ~Calibration 1.065 - 0 1 2 3 4 5 6 7 8 9 10 I/F RECIPROCAL FLOW RATE (min/lb) "igure VIII-2. Heat Leak Test for the Isobaric Calorimeter, Heat Capacity of Ethane as a Function of Reciprocal Flowrate. ISOTHERMRL JOULE THOMSON COEFFICIENT C2H6 202111 OF T i% I — Run 16 5 ~-Run 1, 2 PRESSURE PSI Figure VIII-3. Effect of the Size of the Capillary Coil on the Measured VaRun o ( f E A t.146 0, n -Run 1,2 b 300o 600. 9. 120. 15o0. 80oo. 2100. PRESSURE (PSIRi Figure VIII-3. Effect of the Size of the Capillary Coil on the Measured Value of (dH/dP)T for Ethane Along the 202.14~F Isotherm.

202 the accuracy of the flowmeter calibration is lower at these flowrates, the observed discrepancy is beyond this consideration. The first data point for a given run is not usually initiated until it is judged that the calorimeter inlet temperature has been equilibriated with the bath temperature. In order that the desired state may be more quickly attained, it is normal to pass the fluid through the calorimeter for about 50 minutes after the bath temperature is on control before a measurement is initiated. It is conceivable that since the operating flowrate for the first data point in this experiment was much lower than normal, the desired equilibration did not, in fact, take place before the completion of the measurement. In summary, it is believed that the higher discrepancy for this point is predominantly attributable to unsteady state effects. It is believed that the masking effect of the unsteady state term on the evaluation of the heat leak effect as a function of flowrate could be minimized in future experiments if the measurements were initiated at the highest flowrate instead of the lowest, and if the time period between the data points was increased from 40 minute to at least an hour. The operating flowrates for the systems of the study were, however, generally restricted to the range between points 2 and 3 in Figure VIII-2, where it is felt that corrections for heat leak and unsteady state are, in practice, unnecessary, within the limits of precision of the flow measurements. Nevertheless, Equation (VIII-4) implies that we have a better chance of measuring the true mean heat capacity if the flowrate and temperature rise (Tf - T.) are both large. c) Capillary Coil Test. The effect of pressure on the enthalpy of a fluid, at a given temperature, as measured by the isothermal calorimeter, should be independent of the characteristics of the throttling device used. Measurements were initially obtained on pure ethane at 200.60F using a 15 BWG capillary coil [Runs 1, 2 in Figure VIII-3]. The occurence of a leak in the calorimeter bath necessitated a subsequent repetition of the run. The repeated run was conducted at 202.14"F using a 17 BWG capillary coil. The data at 200.6"F were corrected to 202.140F using the PGC as explained in Chapter VII, and

203 plotted as the dashed lines in Figure VIII-3. The measured pressure drops in Run 16 are about double those in Run 2 for comparable flowrates. The integration of the smoothed ~ curve in the figure, over the interval of the basic data points, indicates that the two sets of measurements agree within + 1%, the results for Runs 1 and 2 being generally higher than those for Run 16. This may in part be attributed to the observed leak during the investigation of Runs 1 and 2. d) Test for Consistency Between the Faulkner and the Mather Calorimeters. Although the throttling calorimeter is usually operated either in isothermal or in isenthalpic mode, it is possible to cause a large temperature rise if sufficient power is supplied. Furthermore, the guard heater for the calorimeter can also function to balance the heat leak in non-isothermal operation. Nevertheless, the extraction of the mean heat capacity from such measurements is to be considered less reliable in view of the substantial correction for the pressure drop across the calorimeter. The performance of both calorimeters may be adequately compared with each other if the operating conditions are confined to the liquid region across the Joule-Thomson inversion curve, where the contribution to the measured enthalpy change in the throttling calorimeter due to a pressure drop is considerably minimized. The basic test data in Table (VIII-1) were, in fact, obtained under such conditions. TABLE VIII-1 Direct Comparison of the Enthalpy Data from the Isobaric and Throttling Calorimeters RUN COMPOSITION INLET OUTLET INLET PRESSURE AH AH MOLE PERCENT TEMP. TEMP. PRESSURE DROP CORRECTED CH4 C2H6 C3H8 (~F) (~F) (PSIA) (PSID) bTUJ/LB BTU/LB 3.010.001.279.720 0.82 10.59 1001.1 0.12 5.689 5.689 + 4.110.001.276.723 1.58 11.45 1043.4 75.25 5.777 5.722 * +ISOBARIC CALORIMETER *THROTTLING CALORIMETER (CORRECTED TO CONDITIONS OF ISOBARIC CALORIMETER) In both cases, sufficient power was supplied to cause a temperature rise of about 9.90F. Run 4.110 was obtained with the throttling calorimeter. The last column in the table indicates the enthalpy change as corrected to the operating conditions of the isobaric calorimeter using the PGC correlation and the Joule-Thomson data obtained in this

204 work. The major contribution to the correction term stemmed from the slight difference in the temperature rise for the two cases, and amounted to 0.057 Btu/lb. A comparison between the two measurements after the appropriate adjustments indicates that the throttling calorimeter yields an enthalpy change that is 0.7% higher than for the isobaric case. This discrepancy is higher than anticipated and may possibly be attributed to unsteady state effects in the former case. Error Analysis' comprehensive error analysis of the basic isobaric measurements and the reduced data was initially undertaken by Jones [119] and subsequently extended by Manker [162]. The accuracy of the throttling data was discussed by Mather [168]. Table VIII-2 indicates the major sources of errors and their effect on the accuracy of the basic enthalpy data. In the latter case, only approximate estimates are possible in view of the highly variable dependence of the enthalpy on temperature, pressure, and composition. Furthermore, the precise contribution of unsteady state and mass leakage is almost always uncertain, and underscores the difficulty of evaluating the quality of such measurements. It is felt that the most reliable index of the accuracy of the results is obtained from the observed discrepancy between the original and adjusted values of the enthalpy difference for each arm of every enthalpy loop for any given system. Experimental Measurements on Ethane The range of experimental determinations is indicated on a P-T diagram shown as Figure (VIII-4). The horizontal lines represent distinct isobaric runs, the vertical lines represent isothermal data. The adiabatic Joule-Thomson data in the liquid region are indicated by lines that are slightly inclined to the vertical. The vapor pressure curve is also indicated to permit the identification of the phase corresponding to each run. As the diagram indicates, the critical region was given special consideration in view of the recognized deficiencies of most empirically fitted PVT equations of state in predicting the enthalpy behaviour in this area. The run numbers are assigned to indicate the clhronolog-ical order of the investigation.

TABLE VIIT-2 Summary of Estimates of Measurement and Data Interpretation Errors for the Calorimetric Data of this Work MEASUREMENT TERR0R %CONTRIBUTION TO OPTIMUM AVERAGE WORST AH/AT AH/AP (AV, CASE) POWER INPUT 0.02 0.05 0.1 0.05 0.05 INLET PRESSIURF 0.02 0.03 0.2 <0.02 <0.0? PRESSURE DROP (ISOBARIC) 3.0 5.0 30.0 <0.02 n PRESSURE DROP (ISOTHERMAL) 0.5 2.0 4.0 20 INLET TFMP. <0.01 0.02 0.05 <0.01 0.05 TEMP. RISE (ISOBARIC) 0.02 0.10 0.5 0.10 TEMP. DIFF.(ISOTHERMAL) 1.0 2.0 5.0 0.05 MASS FLOWRATF 0.1 0.2 4a0 0.2 0.2 COMPOSITION 0.1 0.2 1.0 0.02 0.1 ANCILLIARY ERROR SOURCES UNSTEAI)DY STATE 0.1 0.2 2.0 0.25 0.4 HEAT LEAKAGE (ISOBARIC) 0.0 0.05 0.05 MASS LFAKAGE* 0.00 0.25 4.0 0.25 0.25 INTEGRATION nOE BASIC DATA 0.1 0.25 0.5 0.25 0.2 * Systematic error which tends to increase the measured value of AH/AT or AH/AP

206 371 34 1 1 1'25' 4744 4 2000 6R 1R02 H6 1 R 2 49 \5R \ ^ "~43 5R"I~~~~~~~~~~~~~~I I 1500 3 \ \ 9R 12 \3 41 14 \ I \ I I 4 - X ~ \ 35 \ 32 27 39 1000- ~ = 50 0 50 cn 38 ~ ~ ~ ci I 3 R16 16R cn 50 - V 40,51 cr_ 17 2 v -300 -250 -200 -150 -100 -50 0 50 100 150 200 250 TEMPERATURE ~F ETHANE Figure VTTI-4. Temperature and Pressure Range of Calorimetric Measilremnts of Ethane in this Work, in a Functilon of Riun Number. FLOW CRLIBRRTION _. C2H6 ~.E 40 aR L.0 E 0,,/ C NCalibration Figut.r 1. x I igure VTIII-. T ]owdeter Calibration Resbi.lts for tthone. E3 th A I0 "r=~ ~ ~~~~igr oTTS 3:~wee airto rut o tne

207 The composition of the system presented in Table VI-3 was essentially constant throughout the investigation; the major impurity being 0.3% propylene. Consequently, the results reported apply to the mixture and not to pure ethane. The flowmeter calibration results are summarized in Table VI-1. The data for these five calibrations are also plotted in Figure VIII-5. The basic isobaric, isothermal, and isenthalpic data are presented in Tables B-l, B-2, and B-3 respectively. The P-T diagram of Figure VIII-4 indicates that extensive measurements were also made in the single phase liquid and gaseous regions at 250 psia, and in the supercritical region at 1000 psia and 2000 psia. Isobaric determinations across the two phase region were made at 410, 500, 600 and 677 psia, respectively. A limited number of additional measurements, concentrated chiefly in the vicinity of the heat capacity maxima, were also obtained at 713, 750, 819, 2150, 1500 and 1750 psia. A typical isobar in the supercritical region is illustrated in Figure VIII-6, where the data extends from -260~F to beyond 170~F. At low temperatures, the heat capacity increases only slightly with temperature. As the temperature is further increased, the heat capacity rises sharply, reaching a maximum at a temperature somewhat beyond the critical temperature, and then begins to fall just as rapidly. Previous similar investigations on light hydrocarbons [119, 162] suggest that, beyond 170~F, the heat capacity would go through a broad mimimum, and then rise with a gentle slope. Figure VIII-7 represents an isobar at 713 psia which is less than 5 psia beyond the critical pressure for ethane. Mean heat capacities as high as 9 Btu/lb/0F were obtained on differencing the data for this particular run. Successive data points were, however, not closely spaced enough to define the precise shape of the equal area heat capacity curve between 88 and 92~F. The equal area curve in the vicinity of the heat capacity maximum was more clearly defined for the measurements at 819 psia shown in Figure VIII-8. In this particular case, the difference in outlet temperature between successive measurements is of the order of 1iF. Special efforts were made to maintain the inlet pressure within + 0.5 psia for the entire duration of the run which was conducted at a high flowrate of 0.28 lbs/min. The excellent agreement between the basic (solid bars) and differenced (dotted bars) data

208 ISOBfRIC MERN HERT CRPRCITY C2H6 1000 PSIR Ln (rV 10,0 A -260. -200. -UO. -80. -20. 40. 100. 160. 220. TEMPERRTURE (OF) Figure VIII-6. Isobaric Heat Capacity for Ethane at 1000 psia.

ISOBARIC MEAN HEAT CAPACITY C2H6 819 PSIA U, IIo ISOBARIC MERN HERT CRPRCITY C2H6 713 PSIA _ c2Ms..I. X 1% U..-. I0O. 0. -60. 90. 120, SO. TEMPERATURE ( F) ~igure VIII-7. Isobaric Heat Capacity for Ethane at 713 psia. s5. 98. 101. 104. 107. 1 0. TEMPERATURE (OF) Figure VIII-8. Isobaric Heat Capacity for Ethane at 819 psia.

?10 attest to the precision of the measurements. Although the temperature span for the entire run was only 6~F, the time span for its completion was extended to 12 hours from the point of initial input of power in order to ensure attainment of quasi-steady state conditions. Such careful measurements, though desirable, were unfortunately undertaken in very limited cases only due to the breadth of the experimental commitment of this work. With reference to Figure VIII-4, additional runs were obtained at high flowrates, principally in the 40 series, with the specific purpose of defining the heat capacity more clearly in the vicinity of the maxima. An undetected leak at the calorimeter pressure to vacuum seal during the course of these runs resulted in Cp values that were 1 to 3% too high when compared with the earlier measurements. These results were basically disregarded in all further interpretation of the data. The correspondence between Run 50 at 1000 psia from 146.7~F to 162.2~F, (Point A in Figure VIII-6) obtained after the leak was arrested, and the differenced data for Run 16 from 147.4~F to 167.5~F (Point B in Figure VIII-6) was good. Figure VIII-9 illustrates an enthalpy traverse across the two phase region at 500 psia. The heat capacities for the liquid and vapor upto the saturation point as determined from the same run (Run 22) are also shown in Figures VIII-11 and VIII-10, respectively. The bubble point, as determined by the technique described in Chapter VII is 0.6~F below the dew point. This difference can only be ascribed to the presence of impurities in the ethane, and has the effect of increasing the measured enthalpy of vaporization. The equivalent pure component enthalpy of vaporization is extracted from the measurements, as plotted in Figure VIII-9b, if the two phase region is expressed as a flat line at some mean temperature, (61.1~F in this case) between the observed dew and bubble points, and if the curve through the enthalpies in the single phase liquid and gaseous regions are extrapolated to intersect the two phase line Isothermal runs were made at 49.20F, 89.80F, 125 F, 200.6~F and 202.14~F, and include measurement in the liquid, critical, and gaseous regions. The measurements at 89.8~F, near the critical isotherm,:,re. illustrated in Figure VIII-12. Again, <a very sharp maximum is ob)served

ISOBRRIC ENTHRLPY TRRVERSE C2H6 500 PSIR f1o ^61.10F D 1% -- 2 161.40F.0 "0 ou -J -,a aM C + ^ 4~ 61.10F j H6 I/I J 61. IF 60.80F TEMPERATURE (F) igure VIII-9b. 0Jpc;~~~~~~ 1 L FGraphical Procedure for Estimating -~~~~~~~~~- JTm~ __rn-the Enthalpy of Vaporization at Constant Pressure of the Pseudopure Fluid from Actual Measurements on an Impure System.'14. 55. 65. 75. 85. TEMPERATURE (F) Figure VIII-9a. Isobaric Enthalpy Traverse for Ethane Across the Two Phase Region at 500 Psia.

ISOBFRIC MERN HEAT CFPACITT C2H6 (LIQUID) 500 PSIR ISOBRRIC MERN HERT CRPRCITY KC2H6 (VRPOR) 500 PSIR BUBBLE POINT 60.8 OFI i i% 1 U) T0 1% 0 - -DEW POINT 61.4 OF Ln CU 0 UDV, ^ 1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~- ^ ^ ^ \ ~~~~~~~~~~~~~~~~~o I Q 0 I- 0) cr~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~r CI oo ) v,~~~~~~~~~~~~~~~~~~~~~~~~~~~~r ip ^ —^, —~^ /~~~~~~~~~~~~~~~~~~~~~ — 50. 80. 110. l1o0. 170. 200. TEMPERRTURE (0F) _ Figure VIII-10. Isobaric Heat Capacity for Ethane in the Vapor Phase upto the Saturation ~~-~ Boundary at 500 psia. o -40. -10. 20. 50. TEMPERATURE (OF) "'igure VITI-11. Isobaric Heat Capacity for Ethane in the Liquid Phase upto the Saturation Boundary at 500 psia.

ISOTHERMRL JOULE THOMSON COEFFICIENT o __________C2H6 89.8 OF C; N JOULE THOMSON COEFFICIENT C2H6 -2L6.6 ~F O..~]-~ l% o 0 -x -o- - - - -— 4 - a- D I -— 4,,) * 4 I,. -7 t] Thermocouple Calibrtion Fit oC,' I —-Interpolating Polynomial (5trder) 0E) ( <n l _, I/'o 40. 800. 120. 1600. 20. 0 - ~ > <.~~~^~~~*~ ~*~ ~ ~~~*~~~*~1~*~*~~ b 300. 600. 900. 1200. IS00. 1800. 2100. Figure VIII-12. Isothermal Joule-Thomson Coefficient for Ethane at 89. F. at: 89.8~F.

214 to occur near the critical point, and in fact, mean d values as high as 0.5 Btu/lb/psid were actually measured. Nevertheless, it must be emphasized that the precise shape of the equal area ~ curve cannot be uniquely established in the vicinity of the maximum for this particular case unless an additional set of closely spaced measurements with pressure drops as low as or below 5 psid are obtained in the maximum region. Adiabatic Joule-Thomson measurements were made at -246.6~F, -123,3~F, -24.5~F, and in the high pressure region at 49.2~F. The precision of the data as illustrated in Figure VIII-13 was particularly poor. In this case, the data obtained at the lower flowrates were effectively ignored. In any case, the discrepancy between the two sets results in a difference of only 0.5 Btu/lb in the enthalpy change from 2000 psia down to the saturated liquid state. Consistency Checks The consistency checks between the isobaric and throttling measurements for ethane are presented in Figure VIII-14. The reader is referred to Chapter VII for an interpretation of the diagram. The average and maximum inconsistency for the enthalpy loops is 0.64 Btu/lb or 0.4%, and 1.29 Btu/lb or 1.2%, respectively. The accuracy of the isobaric and isothermal data is estimated at 0.7% and 1.5%, respectively. Thermal Property Tables The enthalpy diagram in Figure VIII-15 illustrates the variation in the enthalpy as a function of temperature for ethane containing 0.4% impurities. The diagram was generated primarily from the calorimetric measurements of this work and the zero pressure enthalpies tabulated by Rossini [220]. Table VIII-3 contains numerical values for the enthalpies at regular intervals, including those for the measured isobars and isotherms. The saturated liquid boundary upto the normal boiling point on the enthalpy diagram was obtained by integrating the saturated liquid heat capacities of Witt and Kemp [280] along the vapor pressure curve calculated by the Riedel correlation [Equation (III-36) through

215 CONSISTENCY CHECKS ETHANE 68,69(+.151) 58.57 (+.28) 48.48 (+.14) 29.46 (+.01) 28.02 69.7 (+.1).02 -.1 0.0 + +.63 1<.l -.15% 1.io +.4% c 1750- -51 +.3, o.i 75.76 (-.31) od 170- -.51 +.35, u - ~ - qczr -.35% +.3% -.2 -4 cr -02o 0 ^ "'"'oo 1500- U 49.85 (+.13) 31.63 (+.18) 32.04 (+.07). 84.06 (+.45); 0.0.1 +.1 +14<. 1 O -.15% ~ +.1% +. 15% 1250C S ~33.37 (+.28) 37.3 (+.1) 92.01 (+.4) -.28 C -.06 " oo -.37% -1% "00 Cy, -1.29 to oc { 68.91(+.65) 59.96 (-.06) 52.06 (+.14) ~ 36.7 (+.5) c 57.08 (+.42) -% + a.!OOO a a 6'rlK~~~~~~~~~~~C +c.. uW o +8610870+ 54.46 (+.08),,W, +.866 oo +1.08 +.15% +.7% +.5% c 58.95 (-.05) 81.3 (-1.06),w 713 r 6$ ~ ~ -77 voJ +.3o-.07 3. +.02 -= c'i,' +.711% +' -246.6 -122.3 (+1.2 ) ~ 27.9 (.12) -.-. 00-.., 1% 677- +.03A 1.06 - 89 Daa of.4hi +o91r:i = -,_.~ +. 4% - 1.2% 51m 1223.32(+1.3) 0-6, 2 47.9 (-.12) 600 UI+ 25 cv. -7 18. +0+ -.28 9 -.1 1 T -,.5 +.j. 2% < 69.31 (+.10) 8. 120) 0 250 -.77 +.18 +T +.U04E d~,1.15% -- +.25%, + i,<. I OL 1 62.97 [ 16.84 -4 15.21 ~ 35.18 - 246.6 -123.3 -24.5 49.2 89.8 125.0 200.6 Figure VIII-14. Thermodynamic Consistency Checks for the Ethane Calorimetric Data of this Work.

TABLE VIII-3 Smoothed Enthalpy+Values for 0.996 Ethane at Regular Intervals 0.* 100. 200. 250. 300. 400. 500. 600. 677. 700. 713. 800. 900. TEMP ( ~F) -280. 250.6 0.3 0.7 0.8 1.0 1.3 1.6 1.9 2.1 2.2 2.2 2.5 2.8 -260. 256.4 11.1 11.4 11.6 11.8 12.1 12.4 12.7 12.9 13.0 13.1 13.3 13.7 -246.6 260.3 18.4 18.7 19.0 19.1 19.4 19.7 20.1 20.2 20.4 20.4 20.7?2.} -240. 262.2 22.1 22.4 22.5 22.7 23.0 23.3 23.6 24.0 24.1 24.1 24.3 24.7 -220. 268.2 33.2 33.5 33.6 33.8 34.1 34.4 34.7 34.9 35.0 35.0 35.4 35.7 -200. 274.3 44.3 44.6 44.7 44.9 45.2 45.5 45.8 46.0 46.0 46.1 46.4 46.7 -180. 280.5 55.4 55.7 55.8 56.0 56.3 J6.6 56.9 57.1 57.2 57.3 57.5 57.8 -160. 286.8 66.7 67.0 67.1 67.2 67.5 68.0 68.2 68.3 68.5 68.7 68.9 69.1 -140. 293.2 78.3 78.6 78.7 78.8 79.0 79.3 79.6 79.8 79.9 79.9 80.2 80.4 -123.3 298.6 88.0 88.1 88.2 88.4 88.6 88.9 89.2 89.4 89.4 89.6 89.8 90.0 -120. 299.7 90.0 90.1 90.2 90.4 90.6 90.8 91.1 91.3 91.4 91.4 91.7 92.0 -100. 306.4 101.9 101.9 102.0 102.0 102.1 102.2 102.4 102.6 102.8 102.9 103.1 103.4 -80. 313.2 114.0 114.0 0 1140 114.1 114.3 114.5 114.8 115.0 115.2 115.1 115.4 115.6 -60. 320.2 126.3 126.3 126.4 126.5 126.7 126.8 127.0 127.1 127.3 127.4 127.6 127.8 -40. 327.4 316.4 139.2 139.2 139,3 139.4 139.5 139.6 139.7 139.8 139.8 139.9 140.1 -24.5 333.4 323.1 149.5 149.5 149.6 149.6 149.7 149.8 149.8 149.9 149.9 150.0 150.1 -20. 334.7 325.0 152.6 152.7 152.8 152.8 152.8 152.9 152.9 153.0 153.0 153.0 153.1 0. 342.3 333.7 322.8 167.2 167.0 166.8 166.6 166.4 166.3 166.2 166.3 166.4 166.4 20. 350.0 342.0 332.8 327.0 182.0 182.5 181.2 181.0 181.0 1 81. 1.0 180.8 180.6 40. 357.9 350.5 342.4 337.8 332.3 198.5 197.6 196.9 196.6 196.3 196.2 195.9 195.0 49.2 361.6 354.3 346.8 342.6 337.8 325.5 205,9 204.9 204.2 204.1 204.0 203.4 202.8 60. 366.0 359.2 352.0 348.0 343.7 332.8 217.2 215.1 214.0 213.7 213.6 212.5 211.7 80. 374.3 368.1 361.6 358.0 354.3 345.7 334.^ 316.3 238.3 237.4 237.0 233.9 231.1 89.8 378.5 372.5 366.4 363.0 359.5 351.4 341.2 327.2 309.2 298.0 260.0 245.3 241.6 100. 382.8 377.1 371.1 368.0 364.6 357.1 348.1 336.8 325.1 320.5 317.3 275.1 256.1 120. 391.5 386.2 380.7 377.7 374.6 368.0 360.5 352.0 344.3 341.8 340.1 326.9 305.1 125. 393.7 388.4 383.0 380.2 377.3 370.8 363.5 355.4 348.2 345.9 344.2 333.6 316.8 140. 400,4 395.5 390.4 387.8 385.0 379.0 372.6 365.4 359.3 357.2 356.1 347.7 336.3 160. 409.5 404.9 400.2 398.8 395.1 389.9 384.2 378.0 373.0 371.3 370.3 363.9 355.4 180. 418.9 414.6 410.2 408.0 405.7 400.9 395.6 390.1 384.5 384.3 383.4 378.0 371.2 200. 428.5 424.5 420.5 418.4 416.2 411.6 406.9 402.0 397.8 396.6 396.0 391.1 385.4 200.6 428.8 424.9 420.8 418.7 416.5 412.1 407.3 402.4 398.4 397.2 396.4 391.6 386.0 220. 438.5 434.8 430.9 428.9 426.R 422.6 418.3 413.9 410.2 409.2 408.5 404.4 399.6 240, 448.6 445.0 441.3 439.5 437,6 433.8 429.9 425.7 422.6 421.3 420.9 417.0 412.4 260. 459.0 455.6 452.2 450.4 448.7 445.0 441.2 437.4 435.8 433.5 433.0 429.6 425.5 280. 469.5 466.2 462.9 461.3 459.7 456.3 452.8 449.3 446.8 445.6 445.1 441.9 438.2 300. 480.1 477.1 474.1 472.5 471. 467.8 464.5 461.2 458.8 457.8 457.2 454.4 450.9 * ZERO PRESSURE VALUES OBTAINED BY INTERPOLATICN OF (H(T)-H(O))/T VALUES AS TABULATEC BY THE API [220] ++ REFERENCE ENTHALPY H=0 FGR EACH PURE COMPUNENT AS A SATURATEC LIQUID Al -280F

TABLE VIII-3 (CONTINUED) 1000. 1100. 1200. 1250. 1300. 1400. 1500. 1600. 1700. 1750. 1800. 1900. 2000. TEMP. ( F) -280. 3.2 3.5 3.8 4.0 4.2 4.5 4.8 5.1 5.4 5.6 5.8 6.1 6.5 -260. 14.1 14.4 14.8 15.0 15.1 15.4 15.7 16.0 16.3 16.5 16.8 17.1 17.4 -246.6 21.4 21.7 22.0 22.2 22.4 22.7 23.0 23.4 23.7 23.8 24.0 24.3 24.6 -240. 25.0 25.3 25.7 25.9 26.0 26.3 26.7 27.0 27.3 27.3 27.7 28.0 28.3 -220. 36.0 36.4 36.7 36.9 37.0 37.4 37.7 38.0 38.3 38.5 38.6 39.0 39.3 -200. 47.0 47.3 47.7 47.9 48.1 48.4 48.8 49.1 49.4 49.5 49.7 50.0 50.4 -180. 58.2 58.5 58.8 59.0 59.2 59.5 59.8 60.2 60.5 60.6 60.8 61.1 61.4 -160. 69.4 69.7 70.0 70.1 70.3 70.5 70.9 71.3 71.6 71.7 71.9 72.2 72.5 -140. 80.7 81.0 81.2 81.5 81.8 82.0 82.3 82.6 82.9 83.0 83.2 83.5 83.9 -123.3 90.3 90.6 90.9 91.1 91.2 91.5 91.8 92.1 92.4 92.6 92.8 93.1 93.4 -120. 92.3 92.5 92.8 93.0 93.1 93.4 93.7 94,0 94.3 94.5 94.7 95.0 95.3 -100. 103.7 104.0 104.2 104.3 104.5 104.8 105.1 105.4 105.7 105.9 106.0 106.3 106.6 -80. 115.8 116.0 116.2 116.3 116.4 116.7 116.9 117.2 117.5 117.6 117.7 118.0 118.2 O -60. 128.0 128.2 128.4 128.5 128.6 128.8 129.2 129.4 129.6 129.7 129.8 130.0 130.2 -40. 140.3 140.5 140.7 140.8 140.9 141.0 141.2 141.5 141.7 141.8 141.9 142.1 142.3 -24.5 150.2 150.3 150.5 150.6 150.7 150.9 151.0 151.1 151.2 151.3 151.5 151.7 151.9 -20. 153.1 153.2 153.3 153.4 153.6 153.7 153.8 154,0 154.1 154.2 154.3 154.6 154.8 0. 166.5 166.6 166.6 166.7 166.7 166.8 166.8 166.9 167.0 167.1 167.2 167.4 167.6 20. 180.4 180.2 180.1 180.1 180.1 180.1 180.1 180,1 180.2 180.2 180.3 180.4 180.5 40. 195.2 194.9 194.7 194.6 194.5 194.3 194.1 193.9 193.9 193.9 194.0 194.0 194.0 49.2 202.3 201.9 201.5 201.4 201.3 201.1 200.9 200.9 200.6 200.6 200.5 200.5 200.4 60. 211.0 210.4 209.9 209.8 209.5 209.1 208.8 208.5 208,3 208.2 208.1 208.1 208.1 80. 229.0 227.3 226.3 226.0 225.6 224.9 224.5 223.8 223.4 223.2 223.0 222.7 222.4 89.8 239.9 236.9 235.4 234.8 234.2 233.2 232.4 231.8 231.2 231.0 230.7 230.3 229.9 100. 251.1 248.0 245.4 244.5 243.6 242.2 241.2 240.4 239.7 239.2 238.9 238.2 237.7 120. 285.0 274.3 268.2 266.0 264.2 261.5 259.4 257.9 256.6 256.0 255.5 254.4 253.6 125. 296,0 281.9 274.7 272.2 270.0 266.8 264.5 262.5 260.9 260.2 259.8 258.7 257.8 140. 322.7 308.5 297.0 292.6 289.1 283.9 280.2 277.5 275.3 274.3 273.4 272.0 270.8 160, 346.0 335.2 325.0 320.5 316.3 308.9 303.2 298.8 295.3 294.0 292.7 290.7 289.9 180. 363.9 356.0 348.0 344.1 340.3 333.3 327.0 321.6 317.1 315.3 313.5 310.4 307.9'00. 379.4 373.0 366.6 363.5 360.2 354.0 348.0 342.7 338.0 336.9 333.9 330.3 327.1 200.6 380.0 373.7 367.4 364.1 360.8 354.5 348.7 343.2 338.4 337.4 334.2 330. 327.6 220. 394.2 388.6 383.0 380.2 377.5 372.2 367.0 362.0 357.3 355.1 353.0 349.2 346.3 240. 407.8 403.2 398.5 396.1 393.9 389.2 384.6 380.0 375.6 373.4 371.6 368.1 364.9 260. 421.2 417.0 412.8 410.0 408.6 404.4 400.2 396.3 392.5 390,8 389.0 385.9 382.9 280. 434.4 430.6 426.8 425.0 423.1 419.4 415.8 412.3 408.9 407.2 405.5 402.3 399.6 300, 447.4 443.9 440.4 438.1 437.2 434.n 430.7 427.6 424.5 422.9 421.4 418.4 415.8

220 (III-36c)] using the critical parameters Tc = 305.4K, Pc = 48.2 atm., and ac = 6.275. Beyond the normal boiling point, the saturated liquid enthalpies were obtained by linearly extrapolating the isotherms in the subcooled liquid region upto the estimated saturation pressure. Having specified the location of the saturated liquid boundary on the diagram, the saturated vapor boundary above 410 psia was estimated from the calorimetric measurements of this work made across the two phase region. The gas phase enthalpies below 300 psia and upto the saturation curve were obtained from the reduced virial equation truncated at the third virial coefficient as discussed previously on page 196. The saturated vapor boundary on the enthalpy diagram between 300 and 410 psia was obtained by extending and blending the two curves on either side. Thus, the enthalpy of vaporization below 410 psia can now be specified from the relative locations of the saturated liquid and vapor boundaries on the enthalpy diagram even though direct calorimetric measurements of AH were not obtained in this region. Table VIII-4 lists the smoothed enthalpy values for ethane at saturation. The variation in the heat capacity as a function of temperature and pressure is presented in Table VIII-5. Above 250 psia, the tabulated values are restricted to the results obtained from the isobaric measurements of this work. The accuracy of these values is estimated at 0.7% on the average. Supplementary heat capacity and enthalpy values in the vicinity of the saturation curve and the heat capacity maxima are presented in Table VIII-6. The heat capacity values at saturation, particularly for the vapor phase, are only approximately determined (+ 3%) from the experimental measurements. The smoothed ~ values for the throttling measurements are shown in Table VIII-7. The procedure for calculating ) values from the basic isenthalpic measurements has already been described in Chapter VII. Comparisons with Literature Data and Compilations In order to permit a comparison between the isobaric heat capacity data of this work at 250 psia and the heat capacities in the liquid phase along the saturation curve due to Witt and Kemp [280] and Wiebe et al. [277], we first need to express the enthalpy change across any two temperatures at 250 psia, in terms of the integral of the heat

221 TABLE VIII-4 Smoothed Enthalpy Values for Ethane at Saturation L I QI VA IOF \I P (R 1 Ff TiP. PR FSStJRE f-NTHALPY F NTHAI. PY ( ~F) (PSIA) HTUJ/LB FATIJ/LK -128.0i 14.7 84., 294.6 -47.3 100 134.4 313.4 -6.6 200 162.3 319.3 2.3 250 173.2 320.5 21.2 3(00 183.0 321.0 44,8 410': 20n2.9 320.7 l t500 2184 317.7 76.5 6i 00:: 235.4 310.3 86.5 h77 7: 253.0 298.9 90.1 709.2 277.7 277.7 4- FN1HALPY [iF VAPORIZATIOIN MEASIRKFNEMENTS ( F THIS WllH K

222 TABLE VIII-5 Smoothed Values of the Heat Capacity of Ethane as a Function of Temperature and Pressure HEAT CAPACITY, CP, (BTUl/L8/~F) TEMP (~F) PRESSURE (PSIA) 0 250. 500. 600. 677. 713. 750. 1000. 1250. 1500. 1750. 2000. -280..285.544 -260..290.546.545.54) -246.6.294.547.546.544 -240..296.548.547. 545 -220..302.550.549. 548 -200.. 38.555.554.552 -180..312.562.560.557 -160..318.568.56.561 -140..324.576.571 565 -123.3.329.583.576. 59 -120..331.584.582.57() -100..338.596.588.578 -80..346.610.599.588 -60..354.627.612.599 -40..362.652.650.630.613 -24.5.369.678.671.645.633.h25 -20..371.683.678.655.637.628 0.. 381.748.709.681.658. 645 20..391.552.770.711.683.663 40..401.518.872.761.714.686 49..405.509.948.887.843.786.754.730.697 60..411.503 1.135 1.030.947.834.786.753.713 80..420.496.782 1.509 1.58 1.414.889.860.808.739 89.8.423.494.692.973 2.38 9.0 1.090.911.840.754 100..428.493.654.832 1.183 1.590 1.260.981.877.778 120..439.495.606.709.946.865 1.000 2.265 1.192.971.825 125..442.496.601.691.778.810.929 2.243 1.273 1.005.904.838 140..450.499.586.758.789 1.403 1.435 1.096.953.878 160..462.506.574.706.980 1.286 1.199 1.031.927 180..478.513.568.660.830 1.065 1.120 1.052.956 200..490.519.568.630.751.908 1.008.986.959 200.6.491.520.568.629.749.906 1.005.984.941 220..502.526.610.808.928.932.895 240..513 260..523 280..529 300..539 ZLER) PRESSURE VALUES OBTAINED BY NUMERICAL DIFFERENTIATION OF IH(T)-H(O))/I AS TABULATED BY THE API [220]

223 TABLE VIII-6 Supplementary Smoothed Enthalpy and Isobaric Heat Capacity Values for 0.996 Mole Fraction Ethane in the Vicinity of the Heat Capacity Maxima and in the Two Phase Region 250 PSIA 410 PSIA TEMP. H CP TEMP. H CP F TII/lP RTIL/LR/OF ~F BTt/LB BTUt/Lf'/ ~ -10. 159.6.710 40. 198.4.917 -5. 143.1.726 42. 200.2.9?3 0. 167.7.748 44, 202.1.943 5. 171.5.785 44.8 202.9.973 8.25 173.2.822 - 44.8 320.7 8.25 320.5.606; 47. 32?.3 10. 321.5.591 49.2 324.2 13. 323.3.578 50. 324.8 18. 326.1.558 55. 328.9 500 PSIA 600 PSIA 1FFP. H CP TFMP. H CP ~F BT{I/I R BTtI/L3/~F OF BTU/IR F 8TtIJ/ / ~F 70. 225.9 1.285 55. 211.7 1.024 73. 230.0 1.425 58. 214.8 1.088 75. 233.0 1.850 60. 217.2 1.135 76.5 235.4 1.690 * 61.1 218.4 1.210 * 76.5 310.0 1.905 * 61.1 317.7 1.110 * 78. 312.7 1.755 63. 319.8 1.046 80. 316.0 1.51) 65. 321.8.972 81.5 318.1 1.340 67. 323.7.919 82.5 319.4 1.254 70. 326.4.852 85. 322.3 1.096 75. 330.4.783 677 PSIA 713 PSIA TEMP. H CP TEMP. H CP F HTIJ/LK FiTI/L/OF ~F BTlH/LHA BTI/LH/oF 77.5 234.5 1.39 50. n24.6.848 80. 238.3 1.58 60. 213.6.947 81.5 241.1 1.76 70. 223.6 1.077 82.5 243.0 1.91 75. 229.3 1.185 84. 246.1 2.22 77.2 232.0 1.245 85. 248.4 2.55 80. 237.0 1.414 85.5 249.8 2.80 82. 238.6 1.53 86. 251.2 3.19 84. 241.9 1.728 86.5 253.0 3.77' 85. 243.6 1.838 86.5 298.9 3.86h * 86. 245.5 1.959 87.5 302.6 3.38 87. 247.4 2.181 88. 304.2 2.80 88. 251.0 4.5 90. 309.2 2.33 89. 257.0 5.5 91. 311.4 2.08 89.8 263.0 8.0 92.5 314.3 1.78 90. 264.5 95. 318.3 1.47 91. 287.3 97.5 3?1.7 1.29 92. 297.0 4.4 100. 325.1 1.18 93. 301.3 3.88 10. 330.3 1.04 94. 304.5 2.985 110. 335.3.956 95. 307.5 2.64? 97. 312.2 2.081 100. 317.3 1.5Q0 104'. 324.5 1.257 110. 3:30.4 1.077 130. 334.4.815 8: SA IIJRATH[) LIOl H1'; ATlURATFI) VAPIHR

224 TABLE VIII-6 (CONTINUED) 819 PSIA ln0O PSIA TFM P. H C P TFMP. H C P ~F RTII/Lh BTtH/LB/~F ~F T!J/I.H RTtl/I / ~ 99. 23. 5 3.25 106. 259.0 1.40? 99.5?26.2 3.53 110. 264.9 1.5l41 100.0 267.0 3.84 112. 268.3 1.770 100.5 2f9.0 4.-2 11 5. 274.0 2.021 101. 271.? 4.59 117. 278.2 2.15] 101.5 273.6 4.98 118. 280.3 2.208 102. 276.2 5.30 120. 285.9 2.265 102.2 277.2 5.41 121.2 287.5 2.270 102.4 278.3 5.48 123. 291.6 2.267 102.7 280.0 5.51 125. 296.1 27.40 103.0 281.6 5.52 126. 298.3 2.?03 103.2 282.7 5.51 128. 302.6 2.053 103.4 283.8 5.50 130. 306.6 1.1 5 103.6 284.9 5.40 135. 315.3 1..54 104. 287.0 5.12 145. 329.4 1.263 104.5 289.5 4.73 150. 335.4 1142 n05. 291.8 4.39 105.5 293.O 4.09 106. 2? 5.9 3.86 1250 PSIA 1 5(00 P A TFMP. CIP FMP. H ClP ~F HTI/Lc BTJI/LF/~F 0 0 BTI/IL H Tt/IO H/ ~F 110. 254.7 1.070 110. 250.2.919 120. 266.0 1.192 120. 259.6.971 130. 278.6 1.337 13. 269.6 1.033 135. 285.4 1.400 40. 280.2 1.09w 140. 292.6 1.435 15. 2)91.5 1.151 143. 296.9 1.440 160. 303.2 1. 199 147. 3n2.6 1.433 1(1.2 304.6 1.206 150. 306.9 1.412 163. 307.5 1.204 155. 313.8 1.353 187. 311.7 1.,01 1i6. 3?0.5 1.286 170. 315.3 1. 186 170. 332.7 1.180 175. 321.2 1.151 18n. 37.0 1. 120 190l. 337.2 1.052 1750 PSIA I' F Ml. H C P oF Thl/l. K I l I/l /~ F 1 5r. 284.1.991 (0h. 2?74. 1.n1 1. 72' u.4 1.046 1 /. 304. 1. 0 1 I.0 1 73.5 3 nH.4 1. 0 A5H 174.5 309.4 1.059 180. 315.3 1.052 18 5. 320).5 1.036 190. 325.6 1.020

225 TABLE VIII-7 Smoothed Values of the Isothermal Throttling Coefficient for 0.996 Mole Fraction Ethane (DH/DP)TX 100 (RTUJ/LB/PSID) PRESSIURF TEMPERATURE ( F) (PSIA) -246.6 -123.3 -24.5 49.2 89.8 12. 0 200.6 n.* -48.20 -15.05 -8.70 -6.36 -5.5n -4.90 -3.88 100..312.194 -11.30 -6.78 -5.70 -5.25 -3.98 200..313.215.046 -8.25 -6.67 -5.7? -4.18 250..314.223.053 -9.50 -7.10 -5.92 -4.28 300..315.232.060. -7.45 -6.17 -4.38 400..316.246.074. -8.43 -6.78 -4.60 500..317.258.085 -1.14 -11.30 -7.59 -4.82 600..318.268.096 -0.94 -18.60 -8.67 -5. 9 677..319.273.102 -0.80 -34.70 -10.0 -5. 30 700..320.274.105 -0.76 -10.5 -5.36 713..320.275.106 -0.74. -10.8 -5.39 750..320.280.109 -0.69 -9.83 -12.1 -5.49 800..321.284.114 -0.63 -4.86 -13.7 -5.62 900..322.290.124 -0.52 -3.13 -20.3 -5.87 1000..323.294.133 -0.43 -2.28 -20.2 -6.10 1100..325.298.142 -0.37 -1.74 -10.0 -6.31 1200..326.302.150 -0.31 -1.36 -5.35 -6.40 1250..326.303.154 -0.28 -1.21 -4.36 -6.52 1300..327.304.157 -0.26 -1.08 -3.68 -6.49 1400..328.307.164 -0.22 -0.84 -2.75 -6.10 1500..330.308.170 -0.17 -0.75 -2.13 -5.65 1600..331.310.177 -0.13 -0.64 -1.68 -5.10 1700..332.310.182 -0.10 -(.56 -1.39 -4.51 1750..332.312.185 -0.090 -0.52 -1.24 -4.20 1800..333.312.188 -0.072 -0.47 -1.15 -3.88 1900..334.313.192 -0.053 -0.40 -0.99 -3.29 2000..336.313,197 -0.036 -0.35 -0.87 -2.76 THE VALUE OF (DH/DP)TAT ZEPC PRESSURE IS OBTAINED FROM EQUATIUNS (V-30) AND (V-31) IN CONJUNCTION WITH THE CRITICAL PARAMETERS IN TABLE IX-1

226 capacity at constant pressure along the saturation curve. Thus T Tf T 250 P250 psiadT = (Cp) Ts [ ( dp ) dP I dT (VIII-5) i i T Ps T where Ps is the saturation pressure. If Cp at the saturation pressure is next expressed in terms of the saturated heat capacity Cs as defined by Equation (1-8), we obtain the result T T T f f fff f (C p)7~dT =i ^ dP (C- dT+ p d (250-Ps)] dT (VIII-6) (C250 psia T T P dT T Ti T Ti Ti where WY is the mean value of dCp/dP over the interval (250-Ps) at any given temperature. In order to obtain an estimate of the last term in Equation (VIII-6) from the experimental data of this work, it was necessary to further assume that V was a constant over the interval T. to Tf, and that it could be estimated from the ~ values reported for the two isenthalps at -246.60F and -123.3~F using the approximation = A/AT = -246.6 - 123.3~)/(-246.6 + 123.3) (VIII-7) where T is the mean value of $ over the interval 250 psia to Ps. The above approximation can be derived from the thermodynamic identity in Equation (I-1), which expresses T in terms of (dH/dP)T. The value of P was estimated to be 0.00011 Btu/lb/~F/psi from Equation (VIII-7). The argument for ignoring the contribution of the middle term in Equation (VIII-6) upto the NBP will now be presented. Eubank [70] has indicated that the term, V(dP/dT), along the saturation curve is about 0.4% of the saturated heat capacity Cs at the NBP. If the ratio [ - T(dV/dT) pV ] can be determined at the NBP, then the relative contribution of the middle term in Equation (VIII-6) can be established. The saturated volume V at the NBP is 55.02 cc/gm mole according to the compilation of Eubank [70]. The value of ~ at the NBP was approximately estimated at 42cc/gm mole from the equal area ~ curve for the -123.3~F isotherm of this work extrapolated to its saturation pressure. if the thermodynamic identity expressed as lquation (I-2) is now used, then the estimated values of d) and V yield a value of 0.235 for the ratio

227 [ - T (dV/dT)p/V ]. Therefore, the maximum contribution of the middle term upto the NBP is about 0.1%, confirming the general rule of Ginnings and Stinson [87] in this regard. As the maximum value of Ps upto the NBP is 14.7 psia, the contribution of Ps to the last term in Equation (VIII-6) was also ignored along with the middle term. On rearranging and dividing by AT, we obtain the result CsdT AH (VIII-8) Cs= s T AT 250 psia + 0.00011 (250) Btu/lb/~F (-8) Ti espressed in Btu/lb/~F. The quantity on the right hand side of Equation (VIII-8) was computed from the basic data of Run 38 and plotted as the horizontal bars in Figure VIII-16.'The differenced data plotted as the dashed bars are of lower precision than the basic data of this work, but were plotted in preference to the latter in order to visually highlight the discrepancy between the curve through the point data in the, literature and the bar data of this work. For perfect consistency, a curve through the points must realize an equal area curve with respect to the solid and dashed bars. The results of this work at -260~F appear to be too high, and may be attributed to the melting of previously solidified unsaturated hydrocarbon Impurities trapped in the heater capsule and also possibly to unsteady state effects that appear to be more prevalent for the first data point in a given run. An accuracy of 0.5% is claimed for both literature sources of Cs data. Apart from the first data point, the agreement between all sources is approximately 0.7%. Comparisons were also made against the smoothed heat capacity values of Michels et al. [174] in the gaseous and supercritical regions as derived from accurate volumetric data along isotherms, and the Cp~ values of Smith [247] derived from spectroscopic data. The results are illustrated in Figure VIII-17. In some cases, the agreement, even at low pressure, was no better than 2%. It was later discovered that the enthalpy change at zero pressure from 77~F to 2120F was calculated as 50.1 Btu/lb from the tables of Michels et al., whereas the API results [220] used in this work yielded a higher value of 51.4 Btu/lb. Tl'he discrepancies between the two sources deserves further consideration,

228 060- HEAT CAPACITY ALONG SATURATION CURVE FOR LIQUID ETHANE 0.59- A A 0.58I —-/ —-I -I -I D 0.57 -- I o I( A 0.56- - — ^-^ —1 i____ IA iA O 1-0 0.55o AQ- A WIEBE, HUBBARD & BREVOORT [277] 0 WITT AND KEMP [283] /AA -:THIS WORK Cs=(C )+0.00274 250 psia 0.54 _ -280 -260 -240 -220 - 200 180 -160 -140 -120 TEMPERATURE, OF Figure VIII-16. Comparison Between the Measured Mean Heat Capacities of Ethane From this Investigation with the Saturated Liquid Heat Capacity Data in the Literature.

2 -9 23. 2. / 1% 22 oF` 1.8t 1.6/ SMOOTHC ISOTHERMS " 77~F CADAROrbIR/C a4TA) /122 el t27 / 1 67 F i / 772 0.4 1 3200 F PRESSURE, (psio Figure VIII-Z 7 Cap aiies een t* S Ob" —ine- zron- PVT D" el a. at:~. 1^ ^C/17J

TABLE VIII-8 Comparison of the Smoothed Heat Capacities of this Work with the Tabulated Results of Michels et al. in the Gaseous and Supercritical Regions TFMP. PR ESSiIRF CP (THIS WORPK) CP (MICHFLS) CP (VMICHFLS) > COR.RFCTFD ) F) RP, F C T r (OF) (PSIa) (TU/LH/ OF) (8TI/Lk/OF) kTtI/L /0F 77 0.418.409.Ii 77 500.770.760.769 -. 122 0.440.432.440) () 122 250.524.514.523 122 500.604.56.05 +0 122 600.702.681.688 -. i 122 677.70 770 79 97-1. 122 713.851.62.71 +.3 122 750.966.52.61C) -0.4 167 0.468.458,46 0. 122 1000 2.268 2.247 2.25 167 250.508.497.507 -. 167 750.966.852.862 -6, 1 67 00 92.05.81 -N * i 67 1201^5.0.31 —0 167 1500 1.2 1.18 - 212 0.497.485.497 K. 212 250.524.,14. ~0.4 212 -750.819.619..31 61.0 212 1250.8H43.822. 3L - i >1 12 1~500.96 1.924.- -> 21? 200. 9.99938 -> - P8FS I 1PF HF-AT CAPACITIES II-n. Tn Ti A FF TH V4ALUH K - F i' ~ -:ef[i741

231 l)articularly since Hill [1.05] points out that: a torsional vibration coniponent of (Cpo thlat is approximately 57 of the total vibration effect escapes detection in spectroscopic analysis. Next, the Cp~ values of Michels et al. were corrected to correspond to those used in this work, and the comparisons repeated. The results are presented in Table VIII-8. The agreement is, on the average, better than 1%, and is of the order of the precision of the interpretation of the volumetric measurements. An unusually high discrepancy of 5%, considerably beyond the estimated limits of accuracy for the data of this work, was however obtained at 750 psia and 212~F. The enthalpies of vaporization calculated from the smoothed data and the enthalpy diagram of this work are compared with the values from the compilations of Tester [264] and Eubank [75], the experimental data of Witt and Kemp [280] at the NBP, the measurements of Dana et al. [57] at higher pressures, and the calculated results of Powers [20] using the Riedel three parameter reduced vapor pressure, saturated liquid, and saturated vapor volume correlations in conjunction with Equation (I-6). The comparisons are indicated in Figure VIII-18 and Table VIII-9. The solid line in the figure represent the smoothed values obtained from the enthalpy diagram of this work. The results of Dana et al. are about 1 to 2% above the line, as are the values of Eubank near the critical region. The calculation procedure of Powers is seen to be less satisfactory below the normal boiling point. The value of the enthalpy of vaporization at the NBP was calculated as 210.1 Btu/lb from the enthalpy diagram of this work, and compares favorably with the value of 210.91 Btu/lb obtained by Witt and Kemp from direct calorimetric measurements. Discussion on the Maxima in Cp and ( The saturation data, the Cp maxima along isobars, and the ~ maxima along isotherms are all plotted on In P vs ln T coordinates as seen in Figure VIII-19. The particular choice of coordinates is dictated by the general observation that the vapor pressure curve is approximately linear as one approaches the critical point on such a plot. The Cp maxima appear to lie on, or close to, the linear extrapolation of the vapor pressure curve beyond the critical temperature.

3T | C2H6: ENTHALPY OF VAPORIZATION x RIEDEL-POWERS (CORRELATION) [202] o TESTER (COMPILATION) [264] o EUBANK (COMPILATION) L74 75] 250-' o WITT 8 KEMP (DATA) [2801 Xx^~~~~~ ^^^^^^^vR~~~~ o~7 DANA ET AL (DATA) [57] < x ~ ^^^^^^^~~~~~~~~~~~o THIS WORK 200- -L T1% 50 50 — I 160 200 250 300 350 400 450 500 550 TEMPERATURE, ~R Figure VIII-18. Comparison Between the Enthalpies of Vaporization for Ethane as Derived from this Investigation with Some Results from the Literature.

233 TABLE VIII-9 Comparison Between the Enthalpy of Vaporization as a Function of Temperature as Obtained from The Enthalpy Diagram of This Work with The Results from The Literature TFMP. ENTHALPY OF VAPORIZATT0N (BTUJ/LR) (OR) TESTER EUlBANK WIEBE RI FFFL WITT THIS WORK [264] [ 74] ET AL [216] ET AL [277] [280] 180 245.4 251.0 200 242.2 244.9 240 236.3 235.4 236.0 R80 225.6 226.8 225.5 B3U 220.1 221.5 219.6 324 212.9 212.8 214.3 214.n 212.2 331.4 210.9 210.9 210.0 211.8 210.9 210.0 342 207.0 206.1 197.1 207.8 206.3 360 200.5 199.5 193.1 2n1.0 199.(6 378 193.6 192.8 188.5 193.6 193.0 396 186.3 185.8 183.2 186.0 186.0 414 178.4 178.1 176.8 177.2 177.9 432 169.5 169.4 169.4 168.0 169.0 450 159.4 159.3 160.7 158.0 158.3 468 148.1 147.8 150.1 147.2 147.2 486 134.8 134.9 137.1 134.7 134.7 504 119.6 120.6 120.6 119.5 118.0 52 98.8 1(1.5 98.1 98.2 98.2 540 58.8 71.9 61.4 65.2 66.0 The values of Wiebe et al, Witt and Kemp, and the results of this work are derived from calorimetric measurements.

\ /'500+ /_~ <~~I~ EXTENSION OF, _j' VAPOR PRESSURE CURVE / 253^' -— ~~WI~TH CONSTANT SLOPE ~ 250- ~ —_ z 900- / u 800t V ^~~~~~~700^^t~~~~~~~ ~- VAPOR PRESSURE CURVE FOR C2H6'I d~~~~nP\~H SATURATION DATA 600- / ac(~n\!) d l 3 o MAXIMA OF Cp ISOBARS = ) -0 I ~~~~~500-F.i~~~ 0' a MAXIMA OF O ISOTHERMS =0 500- 400- 300x-;I t i I II I 20 40 60 80 00 120 140 160 180 200 T, OF (LOG SCALE) Figure VIII-19. The Location of the Cp Maxima Along Isobars, and the. M'axima Along Isotherms Relative to the Linear Extrapolation of the Vapor Pressure Curve for Ethane on Logarithmic Coordinates.

235 Qualitatively speaking, the slight trend towards the right of the extrapolated line as the pressure is increased could be reversed by plotting tiei locus of the maxima in (Cp - Cp~) along isobars instead, to compensate for the increase of Cp" with temperature. Such a plot would, in fact, be more proper because the quantity (Cp - Cp~), unlike Cp, is a true configurational property and is recommended for future analyses along such lines. An ac value of 6.34 was computed for the best straight line fit to the saturation data and the Cp maxima along isobars as opposed to the suggested value of 6.275 [214]. Table VIII-10 lists the location, the value of Cp, and the value of H for the heat capacity maxima at several isobars as determined from the measurements of this work. Also listed, are the predicted temperatures for the heat capacity maxima for a fixed ac value of 6.34. These are seen to agree fairly well with the measured temperatures. The 4 maxima are found to lie on the gas side of the extrapolated vapor pressure line, moving further away from the Cp maxima as the pressure is increased. Other thermodynamic and transport properties are known to follow a similar behaviour in the critical region. Bailey and Kellner [8] observed that the thermal conductivity maxima for Argon were near the location of the critical isochore. Noury et al. [186,187] have obtained minima in the ultrasonic velocities for propane in the supercritical region. Sirota and co-workers [245] have established from precise data on water, that the locus for the maxima in Cp along isotherms, (dCp/dP) = 0, would appear to the right of the locus of (dCp/dT)p = O, if plotted with the coordinates of Figure VIII-19, with the critical isochore lying, for the most part, in between the two curves but closer to the former. These considerations indicate that though there is a change from a more liquid-like phase to a more gas-like phase across the supercritical region, there is no unique prescription for locating a phase transition boundary. The explanation for such phenomena is not vet clear. The absence of discontinuities in the second and higher order derivatives of the hleat capacity with respect to temperature along isobars, or with respect to pressure along isotherms, precludes the occurence of a higher order transition in the supercritical region as a possible extension of the

TABLE VIII-10 Thermal Properties for Ethane at the Heat Capacity Maxima along Isobars PR F.SSt F TEMp. PRIFlR. TFi) TFrp.* (;P)mox H T'T'S lrOrRK APHAC=6-.34n THTS WfRK TI-S trlfRK ( PI ) (0~) (OF) -TI /i/< (TI/L h4. 103.n 10n3. 5.5?2 281.h 1000. 121.? 121. 2.27 2g7.5 12no. 143.0 141.7 1.44 29. ^1500. 1h.2!.1!.?0 0 3 04. 175n. 174.5 174. 1.059 39. 4'nn0 ] 190. 0 188.1 n. C)6 17.3 * Predicted results assuming that the heat capacity maxima lie on a linear extrapolation of the vapor pressure curve on a log P vs log T plot.

237 first order transition across the vapor pressure curve. It may be conjectured that the supercritical phase is composed of a variable number of clusters of molecules, with fewer larger clusters occuring at lower temperatures. The addition of energy to such a phase may be assumed to be partly utilized in raising the kinetic energy of such clusters, and thus the temperature of the phase, and partly in breaking down such clusters into smaller ones. The fraction of energy utilized in the latter case has little or no effect on raising the temperature. At the maximum in Cp, the cluster distribution is such that the fraction of added energy utilized in the breakup of clusters is highest relative to that used in increasing their kinetic energy. Beyond this point, the phase is more gas like, consisting of smaller, more stable clusters, and the added energy is principally used in raising the temperature. Measurements on Ethane-Propane Mixtures An attempt was made in this work to characterize the enthalpy be-haviour of the ethane-propane system as a function of composition with the minimum experimental effort necessary to effectively represent the system in some established enthalpy correlation framework. An analysis of the enthalpy data for five methane-propane systems using an equation of state led Starling [249,250] to conclude that the examination of three well spaced mixtures could permit a level of description that was adequate for engineering purposes. A similar conclusion was independently reached by Powers [202]. Consequently, the investigation of the ethane-propane system was restricted to three such ethane-propane mixtures. A further examination of the methane-propane data in the PGC framework suggested that a sufficiently significant set of optimized pseudo-parameters for any given mixture could be obtained from limited experimental data carefully selected to include. 1) A wide ranging isobar at high pressure. 2) Limited range isobaric data at various pressures in the region of the heat capacity maxima, and specifically just above the cri condenbar. 3) An isotherm near, and preferably just beyond, the

238 cricondentherm. 4) An adiabatic Joule-Thomson run in the liquid region outside the inversion dome, and preferably, at the lowest possible temperature. Although the above criteria were used in selecting the location of the runs for the various ethane-propane mixtures, additional data were also obtained to provide the necessary thermodynamic consistency checks. The three mixtures examined contained 0.76, 0.50 and 0.27 mole fraction ethane, respectively. The compositions and the flowmeter calibration results for these mixtures are summarized in Tables VI-3 and VI-1, respectively. These mixtures are individually discussed below. a) Nominal 0.76 Mole Fraction Ethane-Propane Mixture. The measurement conditions are illustrated in Figure VIII-20. All runs are numbered in chronological sequence. Extensive isobaric data were obtained at 1000 psia and 1500 psia. Isothermal measurements were taken at 500F, 151.650F, and 250.74"F from about 100 psia to 2000 psia, and over a limited range at 102.4~F. Adiabatic Joule-Thomson data were obtained at -50.12~F and in the high pressure region at 500F. Isobaric enthalpy data in the two phase region were taken at 250, 500, and 716 psia. The basic isobaric, isothermal, and isenthalpic measurements are reported in Tables B-4, B-5, and B-6, respectively. The variation of the system composition as a function of run number is shown in Figure VIII-21, where the ethane and propane mole fractions are each normalized to include the impurities at their respective ends of the spectrum. The dotted line indicates the selected normalized ethane composition for the system. Most of the values lie within + 0.6% of this line. Isobaric results at 1000 psia illustrating the variation of the mixture heat capacity in the supercritical region are indicated in Figure VIII-22. The behaviour of the heat capacity variation with temperature is similar to that for pure ethane. A typical isothermal run in the gas phase is shown in Figure VIII-23. Adiabatic Joule-Thomson data at -50.180F are plotted in Figure VIII-24. For this particular case the precision of the measurements is about 2%. An isobaric enthalpy traverse at 716 psia through the two phase region (Run 18.1) is illustrated in Figure VIII-25. This particular run was a repeat of an earlier

239 2000 | - ---- 23, C2 6' 3 8 -(0.763 C2H6) 1500 - - x,4 3_ 2 02 Xr 1000 -5 -1 -5 5 150 200 250 u: LJ i 500 -— r 20 for the Nominal 0.76 _ _Mole Fraction Ethane-Propane Mixture as a Function of Run Number..77 ( -30 0 -20 0 -50 -0 -0 0 (NOMINAL.763 C2H-) 0 0 0 LL 00 0 0 0 00Ui o pt r the Nominal 0.76 Mole Fraction 0 a Function of Run Number. ~2. 0 0 0 c 0 0 LL 0 LJ O:.75 5 10 15 20 25 RUN NUMBER "igure VIII-21. Variation of Composition for the Nominal 0.76 Mole Fraction Ethane-Propane Mixture as a Function of Run Number.

240 ISOBFARIC MERN HEAT CAPACITY C2H6-C3H8 (.76 C2H6) 1000 PSIR ~LL~~~~~~U -l 1%O/o.I c, — 4 0M c, a-4 0 i I0o. 110. PoL. 170. 200. TEMPERATURE (OF) Figure VIII-22. Isobaric Heat Capacity for the Nominal O.76 Mole Fraction Ethane-Propane Mixture at 1000 psia. 00-4,, I > ~~ 1 1 ) 1 1 1 1 1 -4 1. U.17. 20 Mixture at 1000 psia.

241 ISOTHERMAL JOULE-THOMSON COEFFICIENT C2H6-C3H8 (0.76C2H6) 250.74~F -5 0 0 0-4in m 3 - I.. I I I I I I I 0 200 400 600 800 1000 1200 1400 1600 1800 2000 PRESSURE (PSIA)'irtgre VITT-23. Isothermal Joule-Thomaon Coefficient for the Nominal 0.76 Mole Fraction Ethane-Propane Mixture at 250.74~F. ISOBRRIC ENTHRLPY TRRVERSE C2H6-C3H8 (.76 C2H6) 716 PSIR i% o JOULE THOMSON COEFFICIENT C2H6-C3H8 (.76 C2H6) -50.180F J_ 1,.. —Dew Point.; H - O. 1~ 0 128.5~ F ~-'J~~~ X I LO O x "10 400. 800. 1200. 1600. 2000. 9i. 105. 115. 125. 135. 145. 155. PRESSURE (PSIR) TEMPERATURE (0F) I'Agtore 11VI -'4. Adiabatic.Ioule-rhomson Coefficient Data Figure \1111-25. Isobaric Enthalpy Traverse for the Nominal 0.76 Mele for the Nominal 0.76 Mole Fraotion Fraction E Bthan-Propane Minture at 716 p t-,no- ropoor117.5 ~Fre at -50. Run 18 A H = O. at 101.4 ~F'o'0 ~ ~ uoo. 8., 2o0. 1600.:;2000. *~**':'o~.''95~'.S. 115. 125. 135. 11*5. 155. PRESSURE (PSIRF) TEMPERRTURE (OF) lin~nrf~ Vlll-.'. Adiahatic. -loule-Thomson Coefficient Data Figure VIlI-25. Isobaric Enthalpy Traverse for the Nominal 0.76 Mole for the Nominal 0.76 Mole Fraction Fraction Ethane-Propane Mixture at 716 psia. Ethnne-Propane Mixture at -50.18"F.

242 attempt (Run 18.0), where a leak occured in the flowmeter section. The use of low flowrates in these runs magnified the errors, and resulted in discrepancies that were as large as 5%, emphasizing again, the importance of eliminating such problems. The consistency checks on the smoothed data are summarized in Figure V7II-26. The discrepancy between the "experimental" and adjusted enthalpy differences for the arms of several loops involving Runs 7 through 10 (see Figure VIII-20) is worse than indicated in Figure VIII-26 The adjustment of the basic data before the consistency checks is justified as follows: A pressure dependent mass leak across the pressure to vacuum seal of the isobaric calorimeter was found to have occured for the runs in question. Run 23 was then attempted to estimate the magnitude of the error, and the results were about 2% below those for Run 10 over the common range extending between 156.5~F and 180~F. The enthalpy values for Runs 7 through 10 were uniformly decreased by about 2% in the initial processing of the basic data for obtaining smoothed Cp and enthalpy values. The loop checks for Runs 7 through 10 were still uncertain, as a pressure dependent leak was also observed for the 250.74~F isotherm. In consequence, the rest of the basic data were used to determine the optimum pseudo-parameters for the mixture in the PGC framework by techniques to be explained in Chapter IX. These parameters were than used to predict the enthalpy values for the leak-plagued measurements using the PGC at high pressures, and the reduced virial equation in the gas phase upto 500 psia. These predictions were also used as a guide in extrapolating the results of Run 8 and 9 to 151.65~F to permit additional consistency checks to be made. The 50~F isotherm could not serve as an arm of a loop from 2000 to 250 psia as severe instability in the flow conditions did not permit the evaluation of the enthalpy change across the entire two phase region. The maximum and average error in the consistency checks were 1.8 Btu/lb or 0.8%, and 0.83 Btu/lb or 0.45%, respectively. Smoothed Cp and H values for the isobaric measurements are presented in Table VIII-ll. The smoothed s and H values for the isothermal and isenthalpic measurements are summarized in Table VIII-12.

243 CONSISTENCY CHECKS (.76C2H6,.24 C3H8) 2000 52.92 (+.17) 49.75 (+.13) 60.94 (+.26) 72.85 (+.25) 89.62 (+.04) -.31 c^ -.14% + oo i Al Hi = 1.77 ^ 1500- I ^^^ 0 1500 10j tH= 1.77 % 3.9 (+.5) liAHi x 100 =.34% o Zi IA Hil +' _< 100 61.45(+.130 -1.05 oo w < 716 108.37 U+ c 250 53.21 (+.14) 51.21 (+.13) 203.21 (+2.6) 29.09(-1) 24.58(-.08) 51.69 (+1.1) o -.57 -.28 +1.0 C 2501 00 l 29.55 __ 1_ 29.58 _ 1_ i 37.34 _ __ 21.537 21.8 48.07 -240 -140 -50.12 49.98 102.4 151.65 250.74 TEMPERATURE, ~F Figure VIII-26. Thermodynamic Consistency Checks for the Calorimetric Data on the 0.76 Mole Fraction Ethane-Propane Mixture.

TABLE VIII-11 ++ Tabulated Values of the Enthalpy and the Heat Capacity for the Nominal 0.76 Mole Fraction Ethane-Propane Mixture 0 PSIA 2- 50 PISI6 500 PSIA 716 PSI1 TF-P. h OP TEFP. H,P TM6P. CP TFmP. H. F, 9TH/ LB 8Ti/LO/ F F P T61T/L HTI J/I- /0F OFa PTU/L HT)I/LR/ P ~f- kTUi/l1 HT,/L /oF -260. 245.2.265 -280. 0.7.517 -50.1? 126.4 -50.1? 127.5 -260. 250.6.272 -260. 11.0.5?0 49.98 192.1 49.9' 191.0 -240. 256.1.279 -240. 21.4.523 68. 207.9.857 100. 234.0 1.03 -220. 261.8.286 -220. 31.9.526 70. 209.6.871 102.4 236.6 1.04 -200. 267.6.293 -200. 42.4.529 72. 211.3.888 108. 243.4 1.30 -180. 273.5.298 -180. 53.2.534 75. 214.1.914 110. 246.1 1.40 -160. 279.5.305 -160. 63.8.539 78. 216.9.946 112. 249.0 1.55 -1'0. 285.7.312 -140. 74.6.547 80. 218.8.968 114. 252.3 1.76 -120. 292.0.319 -120. 85.7.557 82.2 221.0.980 115. 254.1 1.94 -100. 298.4.327 -100. 96.9.566 83. 225.1 116. 256.3 2.40 -80. 305.1.335 -80. 108.3.578 85. 241.3 117. 258.9 2.90 -60. 311.9.343 -60. 120.0.591 90. 276.8 117.5 260.4 3.10 -50.12 315.3.348 -50.12 125.9.598 95. 305.3 120. 274.7 -40. 318.8.353 -40. 132.0.606 100. 329.5 122.5 291.2 -20. 325.9.362 -20. 144.3.623 100.4 330.7.868 * 125. 303.7 0. 333.3.373 0. 157.0.655 102.4 332.3.840 128.5 315.5 2.30 3 20. 340.9.383 10. 163.7.693 105. 334.4.808 130. 318.6 1.75 40. 348.7.393 15. 167.2.732 110. 338.3.756 132.5 322.6 1.50 49.98 352.6.398 20. 171.1.796 115. 342.0.726 135. 326.4 1.30 3 60. 356.6.404 22.5 173.1.832 151.65 365.7 140. 332.5 1.15 80. 364.8.414 24.2 174.5.863 250.74 424.1 151.65 344.9 100. 373.1.424 25. 179.1 250.74 414.3 102.4 374.1.425 30. 218.6 120. 381.7.435 35. 253.6 140. 390.5.446 40. 283.9 151.65 395.9.453 45. 310.3 160. 399.6.458 49.98 329.1 180. 408.9.473 52.2 332.0.622 ** 200. 418.5.485 55. 333.7.602 220. 428.3.497 60. 336.7.568 240. 438.4.508 65. 339.4.538 250.74 444.0.514 70. 342.1.523 260. 448.6.519 80. 347.1.502 280. 459.1.527 100. 357.1.493 300, 469.7.537 102.4 358.2.493 120. 367.0.494 140. 376.9.497 151.65 382.7.499 160. 386.9.501 180. 397.1.511 200. 407.4.521 220. 418.0.533 240. 428.6.544 250.74 434.4.551 260. 439.9.557 280. 451.1.570 ++ REF ERENCt ENTHALPY H=0 FCR EACH PURE CCHPCNENT AS A SATURATED LIQUID AT -280F 1TURA TF 1 L i'1iI:: TISRA4TFi VAPiR oaa ZEPC PRESSUIRt ENTHALPIES ANl FEAT CAPACITIES CALCULATED FRO HEAT CONTENT FUNCTION AS TABULATED BY THE API [220]

TABLE VIII-11 (CONTINUED) 1000 PSIA 1500 PSIA 2000 PS]A TEMP. H CP TEMP. H CP ~F BTII/LR RTII/LB/0~ TEMP. H CP ~F RTU/LP RTI)/L/ ~F oF BTIJ/I R BTI/LB/~F -50.12 12.7 -50.12 126.8 49.98 190.7 -?80. 6.6.516 49.98 191.5 151.65 269.3.963 -260. 16.9.519 100. 228.7.869 160. 277.5 1.000 -240. 27.2.522 102.4 230.8.887 170. 293.0 1.042 -220. 37.7.525 120. 247.7 1.046 180. 298.4 1.091 -200. 48.3.527 125. 253.1 1.130 190. 309.5 1.118 -180. 58.9.530 135. 265.1 1.302 194. 314.0 1.122 + -160. 69.5.534 140. 272.0 1.499 200. 320.7 1.107 -140. 80.2.539 142. 275.1 1.587 210. 331.8 1.097 -120. 91.0.544 144. 278.4 1.670 220. 342.6 1.061 -100. 101.9.551 147. 283.6 1.797 230. 353.0 1.020 -80. 113.1.558 150, 289.1 1.876 240. 363.0.976 -60. 124.4.568 151.65 292.2 1.893 250.74 373.2.928 -50.12 130.0.573 153. 294.8 1.896 + -40. 135.8.580 155. 298.6 1.888 -20. 147.5.593 160. 307.8 1.796 0. 159.4.607 162.5 312.3 1.746 20. 171.8.624 165. 316.6 1.696 40. 184.5.643 170. 324.8 1.612 49.98 190.9.653 250.74 400.1 60. 197.6.663 80. 211.0.683 100. 224.0.709 102.4 226.8.713 120. 239.4.740 140. 254.6.776 151.65 263.8.803 n10. 270.6.830 180. 287.7.881 200. 305.7.917 220. 323.7.937 240. 343.2.948 250.74 353.4,949 + THE hEAT CAPACITY MAXIMUM PeINT ALJNG THE GIVEN ISObAR

246 TABLE VIII-12 ++ Tabulated Values of the Enthalpy and the Isothermal Throttling Coefficient for the Nominal 0.76 Mole Fraction Ethane-Propane Mixture TEMPERATURE (~F) -50.12~F 50.0~F 151.65~F 250.74 F P H (DH/DP)T H (DH/DP)T H (DH/DP)T H (DH/DP)T X100 X100 X100 X100 PSIA BTU/LB BTU/LB T/LB BT/L/ /LB T/LB/ BRT/LB BTIJ/LB/ BTU/LB BTIJ/LH/ PSIO PSID PSID PSIn * 0. 315.3 -10.6 352.6 -6.8 395.9 -4.72 444.0 -3.69 100. 125.53.195 345.2 -8.0 391.0 -5.15 440.3 -3.81 200. 125.73.200 345.0 -10.0 385.6 -5.64 436.4 -3.93 250. 125.85.203 329.1. 382.7 -5.93 434.4 -3.99 300. 125.94.206 264.2 379.7 -6.24 432.4 -4.04 400. 126.15.210 192.42 -.392 373.1 -6,96 428.3 -4.18 500. 126.36.215 192.06 -.328 365.7 -7.91 424.1 -4.35 600. 126.58.219 191.76 -.274 357.2 -9.21 419.7 -4.52 700. 126.80.223 191.51 -.226 346.9 -11.78 415.1 -4.71 716. 126.83 *224 191.48 -.220 344.9 -12.18 414.3 -4.75 750. 126.91.225 191.40 -.204 339.9 -14.24 412.7 -4.82 800, 127.03.227 191.30 -.185 332.4 -18.63 410.3 -4.92 900. 127.26.230 191.14 -.148 309.9 -21.75 405.3 -5.11 1000. 127.50.234 191.01 -.116 292.2 -13.07 400.1 -5.28 1100. 127.73.237 190.90 -.088 282.6 -6.90 394.8 -5.42 1200. 127.97.240 190.83 -.062 277.2 -4.15 389.3 -5.51 1250. 128.09.241 190.80 -.051 278.9 -3.54 386.5 -5.51 1300. 128.21.243 190.78 -.040 273.8 -2.93 383.7 -5.50 1400. 128.45.245 190.75 -.020 271.3 -2.21 378.4 -5.33 1500. 128.70.248 190.74 -.002 269.3 -1.73 373.2 -5.04 1600. 128.95.250 190.75 +.014 267.8 -1.37 368.8 -4.61 1700. 129.20.252 190.77 +.028 266.5 -1.16 363.9 -4.16 1750. 129.32.253 190.79 +.034 266.0 -1.07 361.9 -3.94 1800. 129.45.254 190.80 +.040 265.4 -0.97 359.9 -3.71 1900. 129.70.256 190.85 +.050 264.5 -0.86 356.4 -3.27 2000. 129.96.258 190.90 +.060 263.8 -0.74 435.3 -2.79 102.38R~F 151.65 ~F P H (H / DP)T P H (DH/[)P)T X100 X100 PSIA 8 T/LB RTiJ/L / PSIA RTU/LR BTU/L8/ PSID PSID 0. 374.1 -5.6 810. 330.4 -20.4 250. 358.2 -7.6 825. 327.2 -22.2 500. 332.3 830. 326.1 -22.6 716. 236.6 850. 321.5 -23.2 800. 233.4 860. 319.1 -23.3 1000. 230.8 880. 314.5 -23.2 890. 312.2 -22.9 925. 304.8 -20.0 950. 300.0 -17.7 * SUPPLEMENTARY VALUES ** THE VALUE OF IDH/DP)TAT ZERO PRESSURE IS OBTAINED FROM EQUATICNS (V-30) AND (V-31) IN CCNJUNCT ION WITH THE PSEUDO-PARAMETERS ( I ) FOR THE GIVEN MIXTURE IN TABLE IX-13 ++ KEFERENCE ENTHALPY H=O FOR EACH PURE COMPONENT AS A SATURATED LIQUID AT -280F

247 b) Nominal 0.50 Mole Fraction Ethane-Propane Mixture. The measurement conditions are illustrated in Figure VIII-27. Isobaric data were obtained in an unbroken stretch from -246~F to 293~F at 2000 psia. Additional limited measurements are reported at 760 and 1000 psia. Isobaric runs across the two phase region were made at 250 and 500 psia. Isothermal runs were obtained at 151.1~F and 251.1~F. Isenthalpic data are reported at 37.5~F and -125.5~F. The basic isobaric, isothermal, and isenthalpic measurements are reported in Tables B-7, B-8 and B-9. The variation in composition during the course of the investigation is illustrated in Figure VIII-28, and is seen to be more severe than usual. The dotted line indicates the selected normalized ethane mole fraction used in the thermal property tabulations. The 2000 psia isobar is shown in Figure VIII-29. The heat capacity maximum is located very near the 300~F high temperature operating limit of the system. Consequently, it was not possible to obtain measurements that would characterize the behaviour of Cp with temperature beyond the maximum. An isobaric enthalpy traverse is plotted as Figure VIII-30. The sharpness in the definition of the dew and bubble points in this case is typical of the traverses obtained at lower pressures. The vapor phase heat capacity at 250 psia, including the best differenced data beyond the dew point for Run 9, and the results of Runs 4 and 5 are plotted. in Figure VIII-31, and illustrates the broad minimum observed in this region. The isothermal measurements in the gas phase at 251.1~F and the isenthalpic measurements in the liquid phase at 37.5~F are illustrated in Figures VIII-32 and VIII-33, respectively. The measurements in the latter case are more precise than usual. The consistency checks are summarized in Figure VIII-34. Seven enthalpy loops were examined. The maximum and average inconsistencies in the loops were - 0.5 Btu/lb or - 0.2%, and 0.3 Btu/lb or 0.14%, respectively. It is felt that these data are among the most precise ever obtained at the facility. Table VIII-13 contains the smoothed H and Cp values for the isobaric data. Table VIII-14 summarizes the smoothed H and t values for the isothermal and isenthalpic throttling data.

248 15 12 IIA 17 2000 - 1 5 1, IA. 1 7 C2H6 - C3H (0.498 C2H6) 1500- 14 13 19 18.o 1000 ~ 2 (,I X: 0'-II.... 500 -,,,, iI O -250 -200 -150 -100 -50 0 50 100 150 200 250 300 TEMPERATURE *F Figure VIII-27. Range of Calorimetric Measurements Obtained in This Work for the Nominal 0.50 Mole Fraction Ethane-Propane Mixture. (C2H6 - C3H8) (NOMINAL.498 C2H6) 0 0.50 - 0 0 N 0 00 O O O O O - O o ~ o~O 0 0 - 0 /. Oo o~~~~~~0.48 0 P 0 O~~0 ~~LL O~0 5 10 15 20 RUN NUMBER Figure VIII-28. Variation of Composition for the Nominal 0.50 Mole Fraction Ethane-Propane Mixture as a Function of Run Number.

ISOBAFIRIC MEAN HEAT CFAPACITY C2H6-C3H8 (,50 C2H6) 2000 PSI A M 0r * /i o 01 0) o-200. 20.. 100. 160. 2. 2. TEKP ERfTURE (OF) Figure VIII-29. Isobaric Heat Capacity for the Nominal 0.50 Mole Fraction Ethane-Propane Mixture at 2000 Psia. -JJ N ~-26i0. -200. -1l0l. 8. -20. 110. 100. 160 220. 280. 3110. TEMP-FERATURE (0F) Figure VIII-29. Isobaric Heat Capacity for the Nominal 0.50 Mole Fraction Ethane-Propane Mixture at 2000 Psia.

250 ISOBARIC ENTHRLPY TRAVERSE C2H6-C3H8 (.50 C2H6) 250 PSIR l% Dew Point ~ / 79.80 F,, P:D / cj I C; A 2l rr'.J ~Bubble Point 48.8 ~F'30 UO0. 50. 60. 70. 80. 90. 100. TEMPERRTURE (~Fj Figure VIII-30. Isobaric Enthalpy Traverse Across the Two Phase Region for the Nominal 0.50 Ethane-Propane Mixture at 250 Psia. ISOBRIC MERN HEAT CAPACITY C2H6-C3H8 (0.50 C2H6) (VAPOR) 250 PSIF DEW POINT Lu co 1m &~ T1% O7. 100. 130. 160. 190. 220. 250. TEMPERATURE (~F) Figure VIII-31. Isobaric Heat Capacity for the Nominal 0.50 Mole Fraction Ethane-Propane Mixture in the Vapor Phase upto the Saturation Boundary at 250 Psia.

251 ISOTHERMRL JOULE-THOMSON COEFFICIENT C2H6-C3H8 (.50 C2H6) 251.1 ~F o o 0 10 a _ b 300. 600. 900. 12O. Soo00. 1800. 2100. PRESSURE lPSIRJ Figure VIII-32. Isothermal Joule-Thomson Coefficient for the Nominal 0.50 Mole Fraction Ethane-Propane Mixture at 251.1~F. JOULE THOMSON COEFFICIENT ___ _ C2H6-C3H8 (.50 C2H6) 37.5 ~F 0 /~ o Iigure ViiI-33. Adiabatic Joule-Thomson Coefficient for the cn C3 b 3 00. 600. 900. 1200. 100. 2000. 2100. PRESSURE (PSIR)'igure VIII-33. Adiasothermaic Joule-Thomson Coefficient for the Nominal 0.50 Nominal 0.50 Mole Fraction Ethane-Propane Mixture at 251.1F. CYC2 HMixture at 37.5F.0 C2H) 37.5 OF Mixture at 37.5'F.

252 CONSISTENCY CHECKS (.50 C2H6,.50 C3H8) 58.73 (+.27) 91.21 (-.26) 75.4 (+.1) 80.61 (+.42) 2000 -.4 +.47 + 2 -.23% +.18% 0d Q1000- l 84.78 (+.5) 122.1 (+. 25) jiAHi = +.44 IiAHi -.19 - o <-.1% - 760- -~ x 100: +.12%. < -.1% figure VIII-34. Thermodynamic Consistency Checks for the Calorimetric Data on the Nominal 0.50 Mole Fraction Ethane-Propane Mixture. CL C A <n w ^ 176.28 (+.5) 62.9 (+.1) _CL 500 - +.2 - -.3 <+.1% ". -.2% o 1 2 I C\, 250 198.71 52.8 (+.1) Q0_______ \__ I 47.31 48.07 -240 -125.5 37. 48 151.0 ~ 251.1 TEMPERATURE, OF figure VIII-34. Thermodynamic Consistency Checks for the Calorimetric Data on the Nominal 0.50 Mole Fraction Ethane-Propane Mixture.

253 TABLE VIII-13 ++ Tabulated Values of Enthalpy and Heat Capacity for the Nominal 0.50 Mole Fraction Ethane-Propane Mixture 0 PSIA *** 250 PSIA 500 PSIA TFMP. H CP TEMP. H CP TEMP. H CP OF HT!I/LH BT11/I.R/OF ~F BTU/LB BTtJ/LB/~F ~F BTU/LB RTl/LA/ ~F -280. 240.9.248 37.48 173.4.670 -125.5 80.14 -260. 246.0.256 40. 175.4.675 30. 168.4.657 -240. 251.5.264 44, 177.8.685 37.48 173.4.666 -220. 256.8.272 48.8 181.1.699 * 40. 175.0.669 -200. 262.4.280 50. 184.4 50. 181.8.683 -180. 268.0.285 55. 202.9 60. 188.7.700 -160. 273.8.293 60. 226.4 70. 195.8.722 -140. 279.7.301 65. 250.2 80. 203.2.750 -125.5 284.1.306 70. 274.2 90. 210.8.790 -120. 285.8.309 75. 302.6 95. 214.9.818 -100. 291.7.317 79.8 333.6.598 *' 100. 219.0.851 -80. 298.5.326 80. 333.7.596 105. 223.4.895 -60. 305.1.335 90. 339.5.568 108. 226.1.929 -40. 311.9.344 100. 345.1.550 110. 228.0.957 -20. 318.9.354 110. 350.6.537 111.8 229.8.980 0. 326.1.365 120. 355.9.530 115. 241.3 20. 333.5.375 140. 366.4.520 120. 263.5 37.48 340.1.385 151.1 372.1.518 125. 289.2 40. 341.1.386 160. 376.7.517 130. 316.3 60. 348.9.397 180. 387.1.520 134. 336.5.844: 80. 357.0.408 200. 397.5.524 135. 337.3.836 100. 365.3.419 220. 408.1.532 140. 341.4.786 120. 373.8.431 240. 418.8.542 145. 345.2.747 140. 382.5.443 251.1 424.9.548 150. 348.9.717 151.1 387.5.449 260. 429.8.555 151.1 349.7.711 160. 391.5.455 155. 352.5.693 180. 400.7.468 160. 355.9.673 200. 410.2.481 170. 362.4.645 220. 419.9.493 180. 368.8.630 240. 429.9.504 190. 375.2.620 251.1 435.5.511 200. 381.2.616 60n. 440.1.515 280. 450.5.575 300. 4,1.]. 536 S SA'lliRATH ) l IOLJI U: SATI IRA TFI) VAPOP *:::, 7)F-l PRESSUIRE FN'THALPIFS AND HEAT CAPACITIES CALCULIATED FRfI0, HEAT CFNTiFJT FItnif.TinN AS TAFI1_ATFF) Y THF API [220] ++ KtFFERENCt tNTHALPY H=U FOR EACH PLRE COMPONENT AS A SATURATEC LIQUID AT -280F

254 TABLE VIII-13 (CONTINUED) 760 PSIO 1000 PSIA 2000 PSIA TEMP. H C TMP. H CP TFMP. H CP ~F RTtJ/ H/L T/L/~F F RTlJ/LB RTI/LH/~F 0F BTH/LR BTtI/L R/~F 100. 212.5.782 37.48 173.7.639 -280. 5.3.492 110. 220.5.814 40. 175.3.642 -260. 15.2.495 120. 228.9.873 60. 188.3.649 -240. 25.1.49 130. 238.2.995 80, 201.8.662 -220. 35.1.503 140. 249.1 1.218 100. 216.2.695 -200. 45.3.507 150. 262.9 1.556 120. 231.4.737 -180. 55.5.511 151.1 264.5 1.596 140. 248.2.793 -160. 65.9.515 155. 271.4 1.867 151.1 258.5.893 -140. 76.3.520 160. 281.7 2.289 160. 267.7.980 -125.5 83.9.523 165. 294.3 2.741 165. 273.3 1.164 -120. 86.7.575 170. 308.4 2.849 170. 279.4 1.267 -100. 97.3.531 175. 322.3 2.620 175. 286.1 1.402 -80. 108.0.538 180. 334.6 2.300 177.5 289.7 1.480 -60. 118.9.548 190. 354.9 1.810 180. 293.5 1.537 -40. 129.9.558 200. 371.2 1.480 183. 298.2 1.590 -20. 141.2.569 210. 384.8 1.360 186. 303.0 1.610 0. 152.6.581 190. 309.4 1.620 20. 164.4.596 195. 317.5 1.600 37.48 175.0.609 198. 322.3 1.566 40. 176.6.611 200. 325.4 1.530 60. 188.9.628 205. 332.8 1.422 80. 201.7.647 210. 339.6 1.325 100. 214.8.668 220. 352.0 1.147 120. 228.4.690 230. 362.7.993 140. 242.5.716 251.1 380.6.731 151.1 250.4.731 160. 257.0.744 180. 272.2.774 200. 287.9.804 220. 304.2.835 240. 321.2.866 251.1 331.0.884 260. 338.9.897 280. 357.0.909 300. 375.0.883

TABLE VIII-14 -++ Tabulated Values of the Enthalpv and the Isothermal Throttling Coefficient for the Nominal 0.50 Mole Fraction Ethane-Propane Mixture TEMPERATIURF ( OF) -125.5%F 37.48F 151.10F 251.10F P H (()H/DP)T (DHH/DP)T H -(DH/DP)T H PTH/H) X100 XIO X100 Xln PSI A BTU/Lk RTlI/LR/ TTU/L/ B i U/L8/ 4TI/LH kTH/LK/ HTI/LH HT(I/LH/ PSin PSID PSI D PSII) 0 284.13 -18.94 340.14 -7.88 387.5 5.18 435.5 4.02 100. 79.20.228. -.050 381.9 5.86 431.3 4.24 200. 79.44.230 173.37 -.027 375.6 6.68 426.9 4.42 250. 79.52.231 173.36 -.017 372.1 7.20 424.9 4.60 300. 79.67.232 173.35 -.008 368.4 7.81 422.5 4.70 400. 79.91.234 173.35.009 359.8 9.40 417.7 5.00 500. 80.14.236 173.37.025 349.7 11.42 412.6 5.34 600. 80.37.237 173.40.040 336.8 13.90 407.0 5.70 700. 80.62.239 173.44.055 270.8 401.1 6.13 750. 80.74.240 173.47.061 264.7 7.20 398.0 6.38 800. 80.86.241 173.51.068 262.8 3.00 394.8 6.62 900. 81.10.242 173.58.080 260.0 2.24 387.9 7.13 1000. 81.35.244 173.67.092 258.5 1.72 380.6 7.53 1100. 81.60.246 173.76.103 256.7 1.49 372.9 7.66 1200. 81.84.247 173.88.112 255.4 1.17 365.3 7.42 1250. 81.96.247 173.93.117 254.8 1.05 361.7 7.11 1300. 82.09.248 173.99.121 254.3.951 358.2 6.73 1400. 82.34.250 174.11.128 253.4.787 351.9 5.86 1500. 82.60.251 174.25.135 252.7.660 346.6 4.83 1600. 82.85.253 174.39.142 252.1.560 342.2 3.93 1700. 83.10.254 174.54.148 251.6.480 338.6 3.26 1750. 83.22.254 174.62.151 251.3.450 337.0 2.98 1800. 83.35.255 174.69.154 251.1.417 335.6 2.73 1900. 83.60.256 174.84.160 250.7.363 333.1 2.28 2000. 83.80.258 175.01.165?250.4.304 331.0 1.94 DATA LIES WITHIN THE TWO PHASE REGION *4 THE VALUE OF (DH/UP)TAi ZiRC PRESSURE IS S3TAINED FRUM E(.UATIONS (V-3J) AND (V-31) IN CCNJUNCTICN WITH THE PSEUUL-PARAMETERS (I) FUR THE GIVEN MIXTURE IN TABLE IX-14 ++;(EF'FiNCE ENTHALPY H=0 FCR tACH PL,(E COMPONENT AS A SATURATED Ll.UiL; AT -2dOF

256 c) Nominal 0.27 Mole Fraction Ethane-Propane Mixture. The range of measurement conditions for this mixture is indicated in Figure VIII-35. The high pressure isobar examined for this system was reduced to 1000 psia so that the region around and beyond the maximum in Cp could be experimentally characterized within the 300~F operating limit. The lowaer pressure also served to decrease the cooling effect and attendant composition upsets involved in throttling the fluid from the calorimeter outlet to the compressor inlet conditions. An isobaric enthalpy traverse was made across the two phase region at 500 psia. Isothermal data were obtained at 127.40F, and 2690F, and 269"F. Adiabatic throttling measurements were made at -150.2~F, 1.6~F, and in the high pressure region at 127.40F. Additional isobaric measurements were obtained over a limited range at 2000 psia to provide the necessary consistency checks for the high temperature data. The basic isobaric, isothermal and isenthalpic measurements are summarized in Tables B-10, B-ll, and B-12, respectively. The variation in composition with run number is illustrated in Figure VIII-36. The mole fraction of ethane decreased by over 1% during the course of the first five runs, and is attributed to the cumulative fractionation effects occuring at mass leaks from high pressure sources into the atmosphere. The isobaric run at 1000 psia is illustrated in Figure VIII-37. The enthalpy traverse at 500 psia is illustrated in Figure VIII-38, and the liquid phase heat capacities as obtained from this run are shown in Figure VIII-39. The isothermal data at 2690F are shown in Figure VIII-40 while the isenthalpic throttling measurements at 1.6~F are demonstrated in Figure VIII-41. Difficulties in sustaining the high temperature required to maintain the mixture in the gas phase outside of the calorimeter section, contributed substantially to the premature termination of the investigation. The consistency checks for the three enthalpy loops are summarized in Figure VIII-42. The absolute average deviation is 1.96 Btu/lb or 0.72%. The maximum deviation is 3.25 Btu/lb and occurs in the loop from 500 to 1000 psia and from 127.4~F to 203.1~F. These rather large inconsistencies were traced to the occurence of a leak at the differential pressure transducer that was used to measure the pressure drop for the throttling measurements. The adjustment of the

257 2000 8 C2H6-C3H 8 12 (.276 C2 H6) 4 5 10 - 1500 0w o 0 2 _ o _ 2 3 7 9 > 1000 u) WI L. 500- -300 -250 -200 -150 -100 -50 0 50 100 150 200 250 300 TEMPERATURE OF ligure VIII-35. Range of Calorimetric Measurements Obtained in this Work for the Nominal 0.27 Mole Fraction Ethane-Propane Mixture..29 C2H6 - C3H8 (NOMINAL.276 C2H6) 0 0 0 0 4D 0.28 0I 0 -2: 280 0 0 0 I-. O0 L. 0 0 0 O 0 0 00 0 0 0 0 0 0 0.27 5 10 15 RUN NUMBER "igure VIII-36. Variation of Composition for the Nominal 0.27 Mole Fraction Ethane-Propane Mixture.

258 ISOBARIC MEFAN HEAT CAPACITY C2H6-C3HB (.27 C2H6) 1000 PSIA II% u) -260. -200. -140.. — 20. W0. 100. 160. 220. 200. 0. TEMPERATURE (OF):igure VIII-37. Isobaric Heat Capacity for the Nominal 0.27 Mole Fraction Ethane-Propane Mixture. ISOBARIC ENTHRLPY TRRVERSE C2H6-C3H8 (.27 C2H6) 500 PSIA Dew Pob e t E M <3 A'=' L.~~ — Bubble Point ^'

259 ISOBfPRIC HMRN HlET CfPRCITY C2H6-C3H8 (.27 C2H6) (LIQUID) 500 PSIA I a-^ ~~BUBBLE 1% POINT T 140.6~F K'6:^~~~~~~~ / ~JOULE THOMSON COEFFICIENT C2H6-C3H8 (.27 C2H6) 1.6 ~F I / ~' I I o. ~~C)X~~~~O IE'D 00 1400. 800. 1200. 1600. 2000.';10. 23. 135. 148. ISO. PRESSURE PS I R) TEMfE!RfTURE (~F) Figure VIII-39. Isobaric Liquid Phase Heat Figure VIII-41. Adiabatic Joule-Thomson Capacity for the Nominal 0.27 Coefficient for the Mole Fraction Ethane-Propane Nominal 027 Mole FracMixture upto the Saturation tion Ethane-Propane Boundary at 500 Psia. Mixture at 1.6~F. ISOTHERMRL JOULE-THOMSON COEFFICIENT c;N ___ C2H6-C3H8 (.27 C2H6) 269.0 ~F T I,_ o -Ib 300. 600. 900. 1200. 1500. 1800. 2100. b 300. 600, 900. 1200. 1500. 1800. 2100. PRESSURE (PSIR) Figure VIII-40. Isothermal Joule-Thomson Coefficient for the Nominal 0.27 Mole Fraction Ethane-Propane Mixture at 269~F.

260 CONSISTENCY CHECKS (0.275 C2H6, 0.725 C3H8) 53.56 (-.5) 2000 _ O 0 + I + ~0R 0___,. -- + - -':W - - _ 00 44.39 (+.19) 81.7 (-.15) 81.23 (+.13) 69.9 (+.16) 82.5 (+.28) 0. 1000 UJ" u) - 3.25. J (8 1.1% a: +, 00 ~Q~~~- 7~0 "0 7 -1.92' r F-'g VI-2 Co e142.02 (+1.0) + 250I ___. __ _49.0 i 49.06..34.61 32.89 -240 -150.2 1.6 127.4 203.1 269.0 TEMPERATURE, OF Figure VITT-42. Thermodynamic Consistency Checks for the Calorimetric Data on the Nominal 0.27 Mole Fraction Ethane-Propane Mixture.

261 isothermal measurements posed a problem that was attacked in the following fashion. 1) Cutler and Morrison [55] have calculated the heat of mixing for saturated liquid mixtures of methane and propane at -2800F from experimental data on the enthalpy of vaporization for both pure components and for several binary mixtures. The maximum value of the excess enthalpy was calculated as 52 Btu/lb mole of mixture. 2) As the size and energy parameter ratios for the pure components of the ethane-propane system are closer to unity than the corresponding ratios for the methane-propane system, it is reasonable to expect that the heat of mixing at -280~F is lower in the former case. 3) For this particular mixture, the lowest temperature of investigation was -240~F. The assumption of ideal mixing for ethane and propane at -2800F and 1000 psia establishes the enthalpy of the mixture as 21.82 Btu/lb at -240~F and 1000 psia, if the ethane enthalpy table of this work and the propane enthalpy table of Yesavage [284] are used in the calculation. A reasonable, but arbitrarily chosen heat of mixing of 11 Btu/lb mole of mixture, assumed constant over the interval from -280~F to -2400F, assigned an enthalpy value of 22.1 Btu/lb to the mixture at -2400F and 1000 psia. 4) The results for the 1000 psia isobar were integrated without adjustments from -240~F upto 203.1~F and 269.0~F, respectively, to fix the enthalpy value at 1000 psia for each experimentally obtained isotherm in the gas phase. 5) The enthalpy values for a given mixture at zero pressure are independently established from the constituent pure component enthalpies at any given temperature using Equation (VII-14). If this is done, then the enthalpy departure at 1000 psia can be independently calculated for each of the two experimental isotherms in the gas phase. These values were about 5% lower in magnitude than that obtained from the analysis of the basic data. 6) Based on the assumption that the isobaric data were relatively free from error, the isothermal enthalpy departures obtained from the basic data at 203.1~F and 269~F were adjusted downwards to conform to the values calculated in Step 5. The PGC enthalpy calculations, using a set of pseudocritical parameters obtained from the

262 optimization of the basic isobaric data alone, as explained in the next chapter, were also instrumental in providing reasonable adjustments to the isothermal data particularly in the range from 1000 psia to 2000 psia. 7) The isenthalpic results were not affected by the mass leakage proper, as the flowrate itself is not involved in the measurements. They are, however, susceptible to errors in the measurement of differential pressure itself, as a consequence of the leak. Such errors, though lower in magnitude than the effect of mass leakage, cannot be precisely evaluated and were arbitrarily set at 2%. such a correction has a very minor effect on the enthalpies in the liquid phase and, in fact, decreases the enthalpy change from 2000 psia down to the saturated liquid by only 0.1 Btu/lb. Smoothed values of H and Cp for the isobaric conditions are listed in Table VIII-15, while the smoothed H and ~ values obtained from the isothermal and isenthalpic throttling data are presented in Table VIII-16. d) Generation of Enthalpy Tables in the Single Phase Region upto Saturation. The construction of comprehensive enthalpy tables extending from -280"F to 300~F and upto 2000 psia for each of the ethane-propane mixtures from the interpretation of the limited data obtained from these systems was one of the major goals of this work. The skeleton enthalpy values obtained from the smoothing of the basic data for each system were used to determine a set of pseudo-critical parameters that would, in each case, produce the best fit in the PGC enthalpy departure framework. The detailed enthalpy networks in Tables K-4 through K-6 were then generated using the optimum pseudo-parameters for each mixture. These tabulations are only applicable in the single phase region, and are consistent with the skeleton tables for the individual mixtures to within 2 Btu/lb. The procedure for determining the optimum parameters from the smoothed enthalpy data is discussed in some depth in Chapter IX. Although the enthalpy correlation technique specifically utilized in this work is restricted to the single phase region, the enthalpy

TABLE VIII-15 ++ Tabulated Values of the Enthalpy and the Beat Capacity for the Nominal 0.27 Mole Fraction Ethane-Propane Mixture 1)300 8T14?000 ^^^'l n P0SIA -0 51 - T P. H CP TEMP. H CP TEMP. H CP TETMP. HT OF 8Til/Hii bTII/l.8/5F OF RTII/i F RTII/LR/5F OF TU/JLR RTl)/LH/5F OF T -280. 23A.6.235 -150.? 65.5 -280. 2.9.477?00. 28.6.7 -260. 243.4.244 1.6 147.3 -260. 12.5.480 203.1 2.0,774 -240. 248.3.253 120. 226.2.783 -240. 22.1.484 22). 29r..7 -220. 253.5.262 125. 230.2.828 -220. 31..488 240. 314.8 815 -200. 258.8.271 127.5 232.2.852 -200. 41.7.493 260. 331.4.839 -18n. 264.3.276 130. 234.5.880 -180. 51.6.498 269. 336.6 *853 -160. 269.9.284 132.5 236.7.913 -160. 61.6.503 280. 348.4.866 -15n.2 272.7.288 135. 239.1.950 -150.2 66.5.505 300. 366).0 *8 -140. 275.7.293 137.5 241.5 1.002 -140. 71.7.507 -120. 281.6.301 140.6 244.7 1.050 -120. 81.9.514 -100. 26H7.7.310 145. 266.4'-100 92.3.521 -80. 294.0.319 150. 295.6 -80. 102..531 -60. 300.5.329 155. 335.1 -60. 11.6.543 -40. 307.1.338 155.4 337.6 1.030 -40. 124.6.555 -20. 314.0.348 157.5 339.9.985 -20. 13.8.566 0. 321.1.359 160. 342.2.933 0 147.3.582 1.6 321.7.360 162.5 344.5.873 1.6 148.2.583 0 20. 328.4.370 165. 346.6.853 20. 159.0.595 40. 335.9.381 170. 350.8.799 40. 171.2.613 60. 343.6.392 180. 358.4.731 60. 183.6.633 80. 351.6.404 190. 65.4.9 80. 196.5.655 100. 359.8.416 200. 372.2.662 100. 209.9.685 120. 368.2.427 203.1 374.2.655 120. 224.0.74 127.4 371.3.432 210. 378.7.642 127.4 229.4.738 140. 376.9.440 160. 255.2.850 160. 385.8.452 170. 263.2.905 180. 395.0.465 180. 273.7.980 200. 404.4.477 180. 285.3 1.085 203.1 405.9.479 200. 285.1 1.255 220. 414.1.489 203.1 299.3 1.330 240. 424.C.501 2t0~ 308.9 1.450 260. 434.1.513 212. 311.8 1.485 269. 438.8.517214. 314.8 1.519 280. 444.5.524 216. 317.9 1.529 300. 455.1.535 2?0. 374.0 1.536 223. 328.6 1.537 + 225. 331.7 1.533 230. 338.9 1.465 240. 351.7 1.206 250. 363.) 1.074 260. 373.3.977 269. 381.6.905 280. 391.3.835 300. 407.0.728 S —ATURATE[ IVAPJR) ~ SATl lflTF1) VAPOR C TIiF i — Al (l"iK>'t.~-7F/68 P8660Sl6E 6 FT0A4PI -S ANiH HFiT C 1PECITIF( 11S.ALCULA 1 U( FUPJN(1rnri Ac, TAHI)IATFI) HY THE API 12201 THF HFAT CAPACITY MaXIMI8 Af_(4N1 THE IVFT AT -2bUF + 41 E.RENLF LNTHALPY H=0 E-C FACh PURE C MPUNENE AS A IATURATLO LIQUI Ar -U

TABLE VITI-16 ++ Tabulated Values of the Enthalpy and the Isothermal Throttling Coefficient for the Nominal 0.27 Mole Fraction Ethane-Propane Mixture TEMPERATURE (~F) -150.2~F 1. ~F 127.40F 203.1~F 269.0 F 203.1~F P H (DH/)P)T H (DH/DP)T H ()H/DP)T H -(DH/DP)T H -(DH/D)P)P)T X100 X100 X10 X100 X10O X100 PSIA BTU/Lb RTlJ/I J / BTll/l R RTII/LB/ RTi/LB BTIJ/Lb/ fTU/LR BTUI/LB/ BTUt/l.R B Tt/LB/ PSIA T/L RTiJ//L8/ Psin PSIPSI SII) PSID PSID PSI 0. 272.7 -26.0 321.7 -10.26 371.4 -6.2 405.91 4.96 438.84 4.00 760. 339.15 22.98 100. 65.04.126 146.64.150 364.8 -7.1 400.74 5.35 434.70 4.08 775. 335.50 24.89 200. 65.10.145 146.79.157 357.0 -8.5 395.21 5.78 430.33 4.22 795. 330.26 28.06 250. 65.16.152 146.87.160 352.5 -9.7 392.20 6.07 428.06 4.46 810. 321.11 28.73 300. 65.23.160 146.96.164 347.2 -11.4 389.10 6.40 425.70 4.59 832. 317.52 28.23 400. 65.38.174 147.12.170 233.10 1.195 382.30 7.33 420.75 4.74 840. 315.13 25.77 500. 65.54.186 147.29.176 232.18.915 374.20 8.32 415.50 5.05 850. 313.15 21.97 > 600. 65.72.197 147.46.181 231.37.713 364.30 8.81 409.94 5.42 860. 306.89 17.62 700. 65.91.207 147.65.183 230.72.570 350.80 13.40 403.80 5.85 750. 66.00.211 147.73.186 230.45.513 341.35 19.34 400.48 6.42 800. 66.10.216 147.82.190 230.21.466 328.84 28.06 397.11 6.81 900. 66.30.224 148.10.195 229.79.386 307.40 11.46 389.74 7.06 100. 66.51.232 148.21.198 229.44.319 299.34 8.15 381.84 7.70 1100. 66.73.239 148.40.202 229.14.260 294.65 6.22 373.57 8.19 1200. 66.96.245 148.60.206 228.90.212 291.83 3.51 365.73 8.10 1250. 67.09.247 148.70.208 228.8.187 290.75 2.34 362.10 7.50 1300. 67.19.251 148.80.210 228.71.169 289.80 2.03 358.82 6.93 1400. 67.43.257 149.00.212 228.56.129 288.22 1.78 353.26 6.21 1500. 67.67.262 149.21.215 228.44.096 286.95 1.42 348.82 4.97 1600. 67.90.269 149.42.219 228.36.070 285.88 1.15 345.28 3.95 1700. 68.16.272 149.64.221 228.30.046 285.00.956 342.42 3.15 1750. 68.29.274 149.74.222 228.28.035 284.60.805 341.27 2.54 1800. 68.43.276 149.85.223 228.26.025 284.22.747 340.13 2.30 1900. 68.69.281 150.06.225 228.27.005 283.63.683 3R8.25 2.10 2000. 68.96.284 150.32.228 228.28 -.015 283.04.585 336.60 1.76 * THE VALUE OF (DH/OP)TAT ZERC PRESSURE IS OBTAINED FRCM LQUATICNS (V-30) AND (V-31) IN CCNJUNCTION WITH THE PSEUDL-PARAMETERS (1) FOR THE GIVEN MIXTURE IN AB LE IX-COMPONENT AS ++ RERENCE ENTHALPY H= O FOP EACH PURE COMPONENT AS A SATURAIED LIQUID AT -280F

265 values at the two phase boundary may be determined if the dew and bubble points are also known. The saturated liquid and vapor enthalpies for each of the mixtures were calculated in the following manner. First, the dew and bubble point conditions at a series of selected isobars and isotherms were calculated from the phase equilibria data of Djordjevich [63] below 0~F, of Price and Kobayashi [207] from 0~F to 50~F, and of Matschke and Thodos [169] from 100~F to 200~F. The PGC enthalpies at these conditions, using the optimum pseudo-parameters in each case, served to define the enthalpy values for the saturated phase. Below 300 psia the enthalpy values for the vapor phase were obtained from the reduced virial equation defined by the combination of (III-44) and (V-30). The calculated enthalpies at saturation are presented in Tables VIII-17 through VIII-19. The experimental dew and bubble point determinations of this investigation and their corresponding enthalpy values are also included for comparison purposes. The results indicate that the two phase region as determined in this work is generally wider than predicted from the results of Matschke and Thodos [169]. Measurements on the Methane-Ethane System Enthalpy data on two methane-ethane mixtures containing 0.78 and 0.48 mole fraction methane, respectively, were obtained at the existing facility subsequent to the completion of the ethane-propane system as part of a continuing effort to characterize the enthalpy behaviour of light hydrocarbon mixtures. It was originally intended to use the enthalpy compilations in the literature to generate the appropriate interaction parameters for the system in the PGC framework with the specific objective of using such information to improve the enthalpy predictions for the ternary mixture. However, as explained in Chapter II, it was felt that neither the quality nor the range of the experimental or correlated enthalpy values in the literature could compete with the results normally obtained at this facility. The modified objective, then, was to carry the interpretation of the raw data for the mixtures investigated in this facility only as far as was necessary to specify the methane-ethane binary interaction parameters. Accordingly, the processing of the measurements was preliminarily

266 TABLE VIII-17 Saturated Liquid and Vapor Enthalpies for the Nominal 0.76 Mole Fraction Ethane-Propane Mixture+ LIQUID VAPOR TEMP, PRESSURE ENTHALPY TFMP. PRESSURE ENTHALPY (~F) (PSIA) (BTU/LB) ( F) (PSIA) (BTU/LB) -100. 24. 96.8 -100. 9. 297.1 ISnTHFRMAl - 50. 70. 125.8 -50. 33. 311.6 0. 162* 159.9 0. 106. 323.1 50. 340. 194.4 50.' 242. 331.7 102.4 600 240.2 102.4 510. 331.6 120. 715. 267.3 120. 633. 325.3 26.5 250. 277.7 52.0 250. 331.8 ISnRARIC 24.2 * 250. 175.8 52.2 * 250. 331.9 24.2 ** 250. 174.5 52. ** 250. 332.0 85.0 500. 223.4 101. 500. 331.5 82.2 * 500. 220.6 100.4 * 500. 331.0 82.2 ** 500. 221.0 100.4 ** 500. 330.7 119. 716. 262.5 127. 716. 314.9 117.5 * 716. 258.4 128.5 * 716. 316.9 117.5 ** 716. 260.4 128.5 ** 716. 315.5 127.3 755. 285.5 127.3 755. 285.5 TABLE VIII-18 Saturated Liquid and Vapor Enthalpies for the Nominal 0.50 Mole Fraction Ethane-Propane Mixture+ LIOJI D VAPOR TEMP. PRESSURF ENTHALPY TEMP. PRESSURF ENTHALPY ( F) (PSIA) (BTiJ/LB) (~F) (PSIA) (BTU/LB) -100. 17. 92.7 -100. 5.8 291.1 ISOTHFRMAL -50. 47. 119.6 -50. 17. 305.7 0. 114. 150.6 0. 66. 319.0 50. 246. 182.9 50. 160. 330.0 100. 427. 219.8 100. 320. 337.2 120. 525. 236.4 120. 415. 338.7 151.1 700. 270.2 151.1 595. 333.4 161. 737. 290.7 161. 737. 290.7 51. 250. 183.5 78. 250. 333.4 ISORARIC 48.8 * 250. 182.1 79.8 * 250. 334.4 48.8 ** 250. 181.1 79.8 ** 250. 333.6 115. 500. 232.1 133. 500. 335.2 111.8 * 500. 229.0 134. * 500. 336.1 111.8 ** 500. 229.8 134. ** 500. 336.5 TABLE VI II-19 Saturated Liquid and Vapor Enthalpies for the Nominal 0.?7 Mole Fraction Ethane-Propane Mixture+ L IQU ID VAP]OR TFMP. PRESSUIRE FNTHALPY TEMP. PRFSSUIRF ENTHALPY (~F) (PSIA) (HTUl/lR) (~F) (PSIA) (RTIl/L8) -100. 11, 91.1 -100. 4. 287.0 ISnTHFRMAl -50. 30. 116.R -50. 14. 301.8 0. 82. 145.4 0. 48. 315.7 50. 176. 178.9 50. 125. 327.4 100. 318. 213.2 100. 240. 338.4 120. 390.?Q. 1 120. 319. 339.9 140. 48 5. 745.6 140. 407. 342.2 160. 585. 265.5 160. 515. 340.0 180. 680. 312.7 180. 639. 333.4 184.3 697. 321.7 184.3 697. 321.7 143. 500. 248.2 158.5 500. 341.5 ISnHARIC 140.6 * 500. 245.7 155.4 * 500. 338.5 140.6 ** 500. 244.7 155.4 ** 500. 337.6 + Unless otherwise indicated, phase equilibria are calculated from the date in the literature (see Text). The enthalpy values are generated by the PGC using the optimum pseudo-critical parameters in each case, except for the gas phase below 300 psia, where the combination of Equations (V-30) and (111-44) is used to generate enthalpies instead. * Saturation temperatures obtained from this work, enthalpy values obtained as above. ** Saturation conditions and enthalpies obtained from the measurements of this work.

267 terminated at the basic data stage.'The regions of measurement: for the 0.78 mole fraction mettlaneethane mixture are indicated in Figure VII[-43. ixtended data were obtained from -240~F to +300~F along an isobar at 1000 psia. Additional isobaric data were concentrated in the peak region. Enthalpy traverses across the two phase region were made at 250 and 500 psia. Isothermal data were obtained at 79.1~F, and at 2550F. Adiabatic Joule-Thomson measurements were taken at -58.4~F, -150.5~F and at -253.2~F, respectively. A detailed composition analysis is indicated in Table VI-3. The flowmeter calibration data, summarized earlier in Table VI-1, are plotted in Figure VIII-44. The basic isobaric, isothermal, and isenthalpic measurements are summarized in Tables B-13, B-14, and B-15, respectively. The range of data obtained for the 0.48 mole fraction methaneethane mixture is summarized in Figure VIII-45. Isobaric data extending from -230"F to just over 300~F were obtained at 1500 psia. Additional isobaric measurements were taken in the vicinity of the heat capacity maxima at 975, 1250, 1500 and 2000 psia. Isobaric determinations were also made across the two phase region at 250, 500 and 750 psia. Isothermal measurements were obtained at 1.8~F, 101.40F and 252.40F, respectively. Adiabatic Joule-Thomson data were taken at -228.5~F and -99.10F, respectively. The composition, including impurities, is indicated in Table VI-3. The flowmeter calibration data are shown in Figure VIII-46. The basic isobaric, isothermal, and isenthalpic measurements are summarized in Tables B-16, B-17 and B-18, respectively. Although the data were not evaluated for self-consistency in this work, preliminary predictions with the PGC, using pseudo-parameters obtained from isobaric data alone, suggest that the isothermal data are about 5% too high. It is probable that the mass leakage at the differential pressure transducer, first observed during the examination of the 0.27 mole fraction ethane-propane mixture, also extended through the investigation of these systems. The smoothed thermal properties, including the consistency checks as obtained from the measurements of this work, have recently been reported by Kant, Furtado and Powers [121].

268 CH4-C2H6~ 1500 LU 50- - 00 15n16' II -250 -200 -150 -100 -50 0 50 100 150 200 250 300 TEMPERATURE OF Figure VIII-43. Pange of Calorimetric Measurements Obained in This Work for the Nominal 0.78 Mole Fraction Methane-Ethane Mixture. FLOW CRLIBRRTION _________CH4-C2H6 (.L48 CHL) N 11%._ Eo y^ Ecv c N -,,, Calibration OI cc'Jt ~ 0 1 Q n3.0. 8 1.2 1.6 2.0 2.1 F Ibm x 000 - min micropoise Figure VIII-44. Flowmeter Calibration Results for the Nominal 0.78 Mole Fraction Methane-Ethane Mixture.

269 2000 CH4-C2H6 - (.480 CH4) 1000 8 a. 500 - r L o I,,,,,,,. -250 -200 -150 -100 -50 0 50 100 150 200 250 300 TEMPERATURE, ~F Figure VIII-45. Range of Calorimetric Measurements Obtained in This Work for the Nominal 0.48 Mole Fraction Methane-Ethane Mixture. FLOW CRLIBRRTION CH4-C2H6 (.78 CH4) ON XI 1% I /3 c E Q^ E -| yCCalibration ^ ^<~~~~,,,,*,,,,,,,',. I 0 2'.0'.U.8 1.2 1.6 2.0 F lbm x 100O P- min micropoise Figure VIII-46. Flowmeter Calibration Results for the Nominal 0.48 Mole Fraction MethaneEthane Mixture.

270 measurements on the Methane-Ethane-Propane System The range of the experimental determinations is indicated on Figure VIII-47. The data extend from -236~F to 2670F, and cover the liquid, gaseous and two phase regions. Extensive isobaric measurements have been obtained in the single phase region. Enthalpy traverses were made across the two phase region at 250, 500, 750 and 1000 psia. Isothermal throttling measurements were taken in the liquid region at -16.04~F near the two phase envelope, at 52.04~F, 126.2~F and 192.0~F. Adiabatic throttling data were obtained in the high pressure region at -16.04~F and at -234~F. The variation in composition as a function of hours of compressor operation is shown in Figure VIII-48. While the ethane analysis was fairly constant to within 0.5%, the methane and propane mole fractions varied over a span of 1.5%. The steady increase in the propane fraction can be attributed to the fractionation that often takes place when a mass leak to the atmosphere occurs from a high pressure point. These leaks were fortunately located in non-critical areas, and, apart from increasing the effort necessary to achieve quasi-steady state conditions, had little effect on the accuracy of the measurements themselves. The detailed analysis, including trace components, for the average mixture composition, whose nominal value is indicated by the solid lines in Figure VIII-48, is shown in Table VI-3. The flowmeter calibration results for the system are plotted in Figure VIII-49. All five calibrations were fit to a single curve to better than 0.08%. The basic isobaric, isothermal, and isenthalpic data are summarized in Tables B-16, B-17 and B-18, respectively. The isobar at 2000 psia (Figure VIII-50) illustrates, typically, the variation in the heat capacity of a dense fluid mixture in going from -236~F to 267~F. The sharpest heat capacity maximum occurs closest to the two phase boundary at 1100 psia as shown in Figure VIII51. Although the ternary isotherm of Rutherford [230] at 110~F suggests that the mixture is in the single phase region at 1100 psia, it is not certain whether the measurements at the peak and those below 110~F are also in the supercritical region. Figure VIII-52 illustrates the occurence of a maximum in d for Run IR at 126.2~F; slightly beyond the cricondentherm temperature. Adiabatic Joule-Thomson data in the

271 25 29 33 16 9 - 42 35 39 1500 36.9%CH4,30.7/oC2H6 17 40_ 36 ~ 324 C3H8 <: Ir \12/1 44 13 1^43 5R D Figure VII-47. Range of Calorimetric Measurements Obtained in this Work5 for the Ternary (0.369 CH4,.305 C2H, 0. 325 C3H8) LOy^1 45 4 cL. X 46, L9, 22 1 6 7R 23 Set.30.8. I N 2-1968 -250 -200 -150 -I00 -50 0 +50 +100 +150 +200 +250 +300 TEMPERATURE OF Figure VIII-47. Range of Calorimetric Measurements Obtained in this Work for the Ternary (0.369 CH4, 0.305 C2H6, 0.325 C3H8) Mixture. July 23'd Sept.30 Oct. 18 Nov. I Nov. 20 -1968 33.0 x x x xx XXX X X 32.5 x x x X X-~XX~ xx X xx X X X XX X XX XXmOw X X XX X! — xC(x XX X x z 32.0- x x xx x W X XX X M XX 01 X X L XX XX X Q- x x 31.5 xx w X I-J~~~ 0 o o 0:- o o co am100 0 0 0 0' 00 00 - -- ---- D- ----— 3) oO 0 0 O0 0 o o ETHANE 36.9 % CH, 30.7% C2 H6,32.4% C3H8 x PROPANE 30.0,... ii. 4300 4400 4500 4600 4700 4800 4900 5000 COMPRESSOR HOURS Figure VIII-48. The Variation of Composition for the Ternary Mixture for the Duration of the Investigation.

272 FLON CRLIBRRTION CHq-C2H6-C3H8 E._ V E 0 E./~-.^~ /^Calibration ^^ ^^ ~~~~A 6..0.. 1.2 1.6 2.0 2.4 2.8 3.2 f Ibm x 1000 1~ min micropoise Figure VIII-49. Flowmeter Calibration Results for the Ternary Mixture. 0 ISOBRRIC MERN HERT CRPRCITY Fir V, CHr -C2H6-C3H8 2000 PSIia c Ta C / a.-7E —w rO.50. -190. -130. -70. -10. 50. 110. 170. 230. 290. TEMPERFlTURE (T)F Figure VIII-50. Isobaric Heat Capacity for the Ternary Mixture at 2000 Psia.

o:1 ISOBRRIC MERN h-ERT CRPRCITY 9 ISOTHERMRL JOULE THOMSON COEFFICIENT 03 ~~~TSOB^IRC MERLN H-ERT CRPRCITY o ^ F ^ _________ CHL4C2H6-C3Hi8 1100 PSI CML&-C2H6-C3H8 12623 0F f~ 1% 11% ^\ in L/n C:3 aS ~~J ~ ^ ~~~~~~~~~~~~~~Graphical Smoothing with \ / ~~~~~~~~~~~~~~~~Gaussian Quadrature Integration \ ~' j.. I T~~~~~~~~~~~~~~~~~~~~~~~~~~00 00 0. 20 Its. ~ 60. ~ ~~~~ 75 90. 10' p120~R P13S'' TEWPEBRTUFiE (7)' PRESSURE LPSIR) O ~~~~~~~~~~~~~~~~~~~~~~~~~~~03 IFigure Vl-52. Isothermal Joule-Thomson Coe'Figure VlIl-51. Isobaric Heat Capacity for the Ternary Mixture at 1100 Psia. Mixture at 126.3~F. a-L I- / cul~~~~~~~~~~~~~~~~~~___rpia Smohn wit O~~Gusa udrtr nerto in U,~~~~~~~~~ o __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ E0. i406. 7. 9. 15 a 3 0. 60 0. 20 50 80 10 Q3~~~~~~TMERTR (c)PRSUR PSR FiueVI-2 stemlJueThmo ofiin o h enr Figr VTI-1 Isoari HetCpct o h erayMxuea 10Psa itr t163

274 liquid phase at -236.48~F are shown in Figure VIII-53. Difficulties in maintaining the calorimeter bath temperature at a fixed value contributed to the lower precision of the measurements in the latter case. An enthalpy traverse across the two phase region at 500 psia, composed of Run 32 from -88.2~F to 59.9~F and Run 23 from 52.2'F upto 127.5~F, is shown in Figure VIII-54. The two separate runs were necessary to establish the enthalpy of vaporization because power supply limitations at the time did not permit a single traverse across the entire two phase region. These runs were meshed together at a temperature of 59.90F. The results for these runs are compared in Table VIII-20 with the basic enthalpy data obtained at CB & I [138], and with enthalpy values from the same source normalized to 100~F inlet temperature. All the data sources were corrected for small differences in pressure and composition using the PGC as explained in Chapter VII. The normalized values are also compared with the results of this work in Figure VIII-54 bases on the assumption that the enthalpies match at 100~F. An absolute average discrepancy of 0.7% between the two sources suggests that the agreement is satisfactory within the precision of the CB & I results. The heat capacity in the liquid phase upto the saturation temperature at 500 psia and also derived from Run 22 is shown in Figure VIII-55. Consistency Checks for the Ternary Mixture A total of 26 enthalpy loops as summarized in Figure VIII-56 were examined for consistency. AIn absolute average deviation of 0.35% or 0.6 Btu/lb was noted. The maximum deviation amounted to 1.1% or 2.25 Btu/lb. A maximum adjustment of 1.9 Btu/lb was made in the arm at 500 psia between 52.04 and 126.2~F, and served to significantly improve the consistency for both enthalpy loops involving the given arm. The smoothed H and Cp values for the isobaric data are presented in Table VIII-21. The smoothed H and ~ values for the isothermal and isenthalpic throttling data are indicated in Table VIII-22. Enthalpy Tables and Diagrams The detailed enthalpy diagram shown as Figure VIII-57 a and b

ISOBRRIC ENTHRLPT TRAVERSE CHL-C2H6-C3H8 500 PSIR | o,o, Dew Point 1% 89.F JOULE THOMSON COEFFICIENT o_ _| CH4-C2H6-C3H8 -236.48 OF ~'%'"-' Q.0. sw. 12X. 1600. 20w. 1 zg' -4o Fgo r VII5.AibtcJueTosnCofiin o3h enr'-4 D O)Lavermant CB T) - 4 I - 0 1400. 800. 12000 1600. 20 0 0. PRESSURE (PS IA) (~F) Figure VIII-53. Adiabatic Joule-Thomson Coefficient for the Ternary Mixture at -23648~Fs Work C~~~~~~~~~~o~ ~~ o 0- 00. -60. -20. 260. 60. 100. 4.. TEMPERPTURE ("F) gigure VIII-54. Isobaric Enthalpy Traverse for the Ternary Mixture Across the Two Phase Region at 500 psia.

TABLE VIII-20 Comparison Between the Calorimetric Data of This Work and the Results from CB&I for the Ternary Mixture at 500 psia T1F i T )p iT F fT AH ((..FI ) I A h 1 F lP. T F si P PR FS lIR F CfPRr FCTFi) iHT I C,P. K ( ) (F) (PSIA), TI.I/L',Tt)/L iHT/L. 12C0. 49.3 498.5 9?.7 9?2. 94.0 109.0 14.6 502.0 1 34.3 134.n 135.4 98.4 -4.7 49.5 393.8 193.9 ] 93. 122.8 -111.1 500.4 257.2 257.5 258H. 1 19.8 -142,0 504~.3?27.4 277.2 75. 7 83.2 -208.8 496.5 282.3 283.0 2831 100. 49 3 498.5 81. 4 81 2 83. 100. 14.6 502.0 130.5 13 0.2 10.0 100. -42.7 49)9.5 195.1 19.2 195.n 100. -111.1 500.4 244.3 244.7 245.2 100. -142.0 504. 3 265.4 266.3 263.7 100. -208. 496.5 303.3 303.5 30.1 For a mixture containing 0.359 CH4, 0.314 C2H6 and 0.327 C3H8 [138]. ** Corrected to the composition of the ternarv mixture in this work as indicated in Table VI-3.

277 ISOBARIC MERN HERT CAPACITY o HCH4-C2H6-C3H8 (LIQUID) 500 PSIR Bubble Point n>^~~~~~~~~ -48.5~F o ~CZ~~~~ _ Lr, -J u- U' 0 0. n -26. -230. -200. -170 -10. -110 0. -850TEMPERATURE (~F) Figure VIII-55. Isobaric Liquid Phase Heat Capacity Data for the Ternary Mixture at 500 Psia upto the Saturation Boundary.

278 CONSISTENCY CHECKS (0.369 CH4, 0.305 C2H6, 0.326 C3H8) 128.9 (-.5) 47.1 60.6 (-.2) 59.89 (+21) 2000 AHp 128.4 -.37 +.04 o +.13 -.4% < 1+ 1% +' +.1% C00 00 64.56(-.26) -9 63.45 (+.08) 1750 - -.65 +.36 o^ ^~-; -.4% +.22" 6 49.51 (+.37) 71.3(+.25) r- 66.11(+.49) ~ 1500- 2" ~, _ ~ -.72 -1.3? +.11 -.7 -7%.8% - +.1% + 1250 _83.3(+3) d 64.99(+.54) 1250 < _'- +.79 " +.61 cl,1+.4% - +.4 +4 vI, o-' 93.7 CL 1100- ~ m- ^!100 c L o. o +.46 ctiJ IUUU-1<] ^- ~< ~ _4 L I" +.2% 00 + 00 _,u') ":1 54.5(+1.1) 102.76(-1.1) o,: 55.8 (+.25) -. t. +1.6 0 -1.65 U +.47 D o 1.1% o -.7%, +3% 30 73.12 (-.52) 107.93 (+.37) 44.9 750..- i^^ +.1 +2.25 -+. 13 AHp=-145.7, <.1% 91% + 1 % 146.3 (-.6) 91.12 (-.6) 95.73(-1.9) ~ 37.87(+.22) 500 —.19 +.16 5 -2.06 1 -.28 <-. 10. 1% s -.93% t +.3% 25 182.96 (-.5) 128.38 (-.78) 37.34(+.22) 33.99 (-.1) 250 qcJ -.78 N +.19 -.04 -.3% +.2'% <0. 1% 06 +.2% 0 75.73 27.39 32.48 ~ 31.27 -234.9 -16.04 52.04 126.2 192.0 TEMPERATURE, OF Figure VIII-56. Thermodynamic Consistency Checks for the Calorimetric Data on the Ternary Mixture.

TABLE VIII-21 ++ Tabulated Values of the Enthalpy and the Heat Capacity for the Ternary Mixture 0 PSIA -250 PSIA 500 PSIA 750 PSIA 100l PSIA TEMP. H CP TEMP. H CP TEMP. H CP TEMP. H CP TEmP. H EF BTU/LB BTU/LR/0F OF BTU/LB BTI/LB/OF OF RTI8/LB RTIJ/LB/F OF BTU/LB TU(J/LB/F OF?Ttl/'_ 8Tf/_ —' -280. 238.2.297 -280. 1.3.548 -280. 2.2.551 -100. 106.4.616 -180. 60.0.''< -260. 244.2.303 -260. 12.6.552 -260. 13.5.554 -80. 118.7.625 -160. 71.6.51 -240. 250.3.310 -240. 23.5.556 -240. 24.3.557 -60. 131.3.641 -140. 83.2.57 -234.9 251.9.312 -234.9 26.4.557 -234.9 27.3.558 -40. 144.3.665 -120. 95.0.5cz -220. 256.6.316 -220. 34.8.561 -220. 35.7.561 -20. 158.1.711 -100. 107.0.605 -200. 263.0.323 -200. 46.2.567 -200. 46.9.567 -16.04 160.9.722 -80. 119.2.620 -180. 269.5.327 -180. 57.5.572 -180. 58.3.572 -10. 165.3.756 -60. 131.8.637 -160. 271.6.333 -160. 69.0.580 -160. 69.9.580 -5, 169.2.795 -40. 144.7.660 -140. 282.8.339 -140. 80.7.594 -140. 81.6.590 0. 173.3.848 -20. 158.1.691 -120. 289.6.346 -120. 92.7.615 -120. 93.5.603 0.5 173.7.857 * -16.04 160.9.699 -100. 296.6.353 -117. 94.6.618 -100. 105.7.619 10. 185.0 0. 172.2.730 -80. 303.7.360 -115.3 95.7.620 4 -80. 118.2.638 20. 196.1 20. 187.2.795 -60. 311.0.368 -100. 113.6 -60. 131.3.664 40. 220.0 40. 203.9.900 -40. 318.5.376 -80. 136.4 -50. 138.0.678 52.04 234.0 52.04 215.4.996 -20. 326.1.385 -60. 156.9 -48.5 139.0.681 60. 246.6 53.0 216.4 1.00 -16.04 327.6.387 -40. 179.4 -40. 147.6 80. 276.7 60. 224.8 4 0. 333.9.394 -16.04 209.4 -20. 169.0 100. 312.5 80. 251.2 20. 341.8.403 -20. 203.8 -16.04 173.6 107.9 325.5 1.037 *4 100. 280.1 40. 349.9.413 0. 233.5 0. 193.5 110. 327.6.992 112.3 300.1 1.444 - 52.4 355.0.418 20. 273.3 20. 217.1 115. 332.3.900 117. 306.7 1.315 60. 358.3.422 40. 320.3 40. 245.4 120. 336.7.835 120. 310.8 1.251 80. 366.9.432 47. 335.1.520 4 60. 279.4 126.2 341.7.784 126.2 318.2 1.112 100. 375.6.443 50. 336.7.518 80. 320.2 140. 352.0.714 130. 322.0 1.067 120. 384.6.454 60. 341.8.510 89.6 338.3.643 *4 160. 365.7.665 140. 332.3.946 126.2 387.5.457 70. 346.9.505 90. 338.5.640 180. 378.8.651 160. 349.7.81 140. 393.8.465 80. 351.9.502 95. 341.7.628 192. 386.6.650 180. 365.2.741 160. 402.8.476 100. 361.9.498 100. 344.1.617 200. 391.8.655 192. 374.0.712 180. 412.8.489 120. 372.0.503 120. 356.0.590 220. 404.9.663 200. 379.6.700 192. 418.7.496 140. 382.1.508 126.2 360.5.584 220. 393.3.6 200. 422.7.500 160. 392.3.514 140. 368.5.578 240. 406.9.63 220. 432.8.512 180. 402.7.524 160. 380.0.575 260. 419.9 240. 443.2.523 192. 409.1.529 180. 391.4.573 260. 453.8.533 200. 413.3.534 192. 389.3.573 280. 464.5.542 220. 423.9.540 200. 402.9.573 300. 475.4.553 240. 434.8.549 220. 414.4.575 260. 445.8.557 240. 425.9.578 280. 457.0.564 260. 437.5.582 300. 468.4.574 280. 449.2.587 300. 461.0.594 SATURATnED LIQUID'AI SAURATED VAPIP * Z ZERO PPRESSURE FNTHALPIES AiD HEAT CAPACITIES CALCULATEI FRJM HEAT CONTENT FIJNCTIION AS TABULATED BY THE API [220] 4+ KEF[RENCE UTHALPY H=0 FOR EAC- PURE CCMPONENT AS A SATURATED LIoQUIJ3 AT -2bOF

TABLE VIII-21 (CONTINUED) 1100 PSIA ++ 1?50 PSIA 1500 PSIA 1750 PSI 2000 PSI1 TFMP. H CP TEMP. H CP TEMP. H CP TEMP. H CP TEMP. H,P OF RTH/LUB TU/LH/L F OF Ttl/LR RTtI/L / F OF BTII/LB B T/LR/0F OF BTH/LB RTU/Lft/0F 0F F TU/LH BTU/LI0F 52.04 214.0.941 52.04 212.4.862 -?0. 158.5.667 40. 200.2.768 -280. 8.0.547 60. 221.8 1.016 60. 219.5.916 -16.04 161.1.672 52.04 209.5.784 -260. 19.2.550 70. 232.5 1.144 80. 239.4 1.082 0. 172.0.695 60. 215.8.798 -240. 30.0.553 75. 238.5 1.223 95. 256.7 1.219 20. 186.2.731 80. 232.2.844 -234.9 32.8.554 80. 244.8 1.296 100. 262.8 1.248 40. 201.1.776 100. 249.6.897 -220. 41.1.556 85. 251.4 1.361 105. 269.1 1.266 52.04 210.6.814 120. 268.1.955 -200. 52.3.560 90. 258.3 1.410 107, 271.7 1.270 + 60. 217.2.839 126.2 274.1.970 -180. 63.5.565 95. 265.5 1.441 108. 273.0 1.269 80. 234.8.921 135. 282.7.993 -160. 74.8.570 100. 272.7 1.437 110. 275.5 1.268 90. 244.2.968 140. 287.7 1.000 -140. 86.3.576 105. 279.8 1.406 115. 281.8 1.260 100. 254.1 1.014 145. 292.7 1.003 -120. 97.9.584 100. 286.8 1.370 120. 288.1 1.241 110. 264.5 1.054 146. 293.7 1.004 + -100. 109.7.592 120. 300.2 1.324 126.2 295.7 1.208 120. 275.2 1.089 150. 297.7 1.001 -80. 121.6.604 126.2 308.2 1.295 140. 311.6 1.110 123.2 281.9 1.099 + 155. 302.7.994 -60. 133.8.616 160. 332.4.970 130. 286.1 1.091 160. 307.7.975 -40. 146.3.631 180. 350.7.858 140. 296.9 1.073 170. 317.3.952 -20. 159.1.649 192. 360.6.803 150. 306.4 1.044 180. 326.7.920 -16.4 161.7.653 200. 366.9.771 160. 317.8 1.009 192. 337.5.883 0. 172.3.672 180. 337.2.930 200. 344.5.864 20. 185.9.698 192. 348.0.881 40. 200.1.725 200. 354.9.852 52.4 208.8.742 220. 371.4.801 60. 214.8.754 240. 386.9.762 80. 230.3.790 260. 401.8.733 100. 246.6.825 280. 416.6.719 120. 263.8.865 300. 431.0.708 126.2 269.4.877 140. 281.7.903 160. 299.9.935 162. 303.6.937 + 180. 318.3.917 192. 329.3.900 200. 336.4.887 220. 353.8.855 240. 370.6.825 260. 386.8.800 280. 402.6.779 + THE HEAT CAPACITY MAXIMUM AL0ON(C THE rT\/EN IS1HAR ++ THE TABULATED HEAT CAPACITIFS BETWEEN 95 F AND 105 F MAY APPLY TO THE TWU PHASE MIXTURE

TABLE VIII-22 Tabulated Values of the Enthalpy and the Isothermal Throttling Coefficient for the Ternary Mixture TEMPERATURE (~F) -234.9~F -16.04OF 52.04~F 126.2~F 192.0~F P H (DH/DP)T H (DH/DP)T H (DH/DP)T H (DH/DP)T H (DH/DP)T X100 X100 OOx1 X100 X100 PSI A TU/LB BTU/LB/ BT0/LB BTtU/L/ BTIJ/LB BTU/LB/ BTU/LB BTU/LB/ BTU/LB BTU/LB/ PSID PSID PSID PSIO PSID 0. 251.87 -36.3 327.6 -7.8 355.0 -5.9 387.5 -4.59 418.7 -3.68 100. 25.86.359 295.0. 348.6 -6.7 382.7 -4.87 415.0 -3.82 200. 26.22.359 225.3 * 341.4 -7.4 377.7 -5.18 411.1 -3.98 250. 26.40.360 209.4. 337.7 -8.0 375.1 -5.37 409.1 -4.08 300. 26.58.360 199.0 * 320.0. 372.3 -5.55 407.0 -4.17 400. 26.94.361 184.0 ~ 286.4. 366.6 -5.99 402.7 -4.35 500. 27.30.361 173.5. 264.7. 360.5 -6.56 398.3 -4.52 600. 27.66.362 165.2. 250.2. 353.4 -7.23 393.8 -4.63 700. 28.13.363 160.78. 238.8. 345.8 -8.00 389.0 -4.81 750. 28.20.363 160.85. 234.0. 341.7 -8.43 386.6 -4.90 800. 28.38.363 160.90 -.020 229.7. 337.4 -8.88 384.2 -4.98 900. 28.75.364 160.89 -.004 222.0. 328.1 -9.69 379.1 -5.13 1000. 29.12.364 160.89.010 215.40 1.57 318.2 -10.07 374.0 -5.25 1100. 29.48.365 160.91.025 213.98 1.27 308.3 -9.49 368.6 -5.34 1200. 29.85.366 160.94.040 212.85 1.00 299.5 -8.03 363.3 -5.34 1250. 30.03.366 160.96.046 212.38.89 295.7 -7.19 360.6 -5.28 1300. 30.21.366 160.99.052 211.95.81 292.3 -6.42 358.0 -5.22 1400. 30.57.367 161.04.068 211.23.66 286.5 -5.09 352.9 -4.99 1500. 30.95.368 161.12.082 210.63.54 281.9 -4.06 348.0 -4.70 1600. 31.31.368 161.21.095 210.13.45 278.3 -3.25 343.6 -4.30 1700. 31.68.369 161.32.104 209.71.38 275.3 -2.60 339.5 -3.92 1750. 31.86.369 161.37.114 209.53.35 274.1 -2.34 337.5 -3.74 1800. 32.15.370 161.43.120 209.36.33 273.0 -2.12 335.7 -3.60 1900. 32.41.370 161.55.133 209.06.29 271.0 -1.75 332.3 -3.20 2000. 32.79.371 161.69.144 208.79.25 269.4 -1.51 329.3 -2.80 ++ REFERENCE ENTHALPY H=0 FUR EACH PURL COMPONENT AS A SATURATED LIQUID AT -Z8E-F * THE VALUE CF (DH/DP)TAT ZERE PRESSURE IS CeTAINED FROM EQUATIONS IV-30J AND (V-31) IN CCNJUNCTION WITH THE PSEUDO-PARAMETERS (I) FOR THE TERNARY MIXTURE IN TABLE IX-21

284 was constructed from the smoothed enthalpy values adjusted for thermodynamic consistency. Table VIII-23 contains essentially the same information in tabular form. The reported enthalpy values are believed to be precise to within 1 Btu/lb. The two phase envelope on the enthalpy diagram from 250 to 1000 psia was guided by the smoothed data of this work. The phase equilibria data of Price and Kobayashi [207] upto 50~F were used to determine the dew and bubble points for the mixture below 250 psia. The enthalpies in the liquid phase at saturation were obtained by extrapolating the subcooled liquid enthalpy lines at any given temperature to the calculated saturation pressure. The saturated vapor phase enthalpies below 250 psia were evaluated from the reduced virial equation truncated at the third virial coefficient as suggested on page 196. The shape of the two phase envelope is somewhat uncertain above 1000 psia. About the only information available in this region is the phase equilibria data of Rutherford [230] at 1100F which predicts a dew point pressure of about 1075 psia. The enthalpies for the liquid and vapor phase at saturation, including the experimental results of this work, are presented in Table VIII-24.

285 TABLE VTTT-23 Smoothed Values of the Enthalpy tor the Ternary Mixture as Obtained from the Enthalpy Diagram 4 (TIU/LH) TE P. R PRFRURF (PS 1) (~OF). 250. 500. 750. 1000. 1250. 1500. 1750.?00. -?80. 238.2 1.3 2.2 3.2 4.1 5.1 6.0 7.0 R.c -?60. 244.2 12.6f 1 3.5 14.5 15.4.16.3 17.3 18.2 1.2 -240. 250.3 23.5 24.3 25.3 26.2 27.1 28.1 29.0 30.0 -234.9 251.9 26.4 27.3 28.2 29. 1 30.0 31.0 31.9 32.2 -220. 256.6 34.8 35.7 36.6 37.5 3R.4 39.3 40.7 41. 1 -200. 263.0 47.2 47 47.8 48.7 49.5 50.5 51.4 52.3 -180. 269.5 57.5 58.3 59.1 60.0 60.9 61.8 62.6 63. -160. 276.1 69.0 69.9 70.7 71.6 72.4 73.2 74.0 74.8 -140. 282.8 80.7 81.6 82.4 83.2 84.0 84.7 85.5 86.3 -120. 289.6 92.7 93.5 94.3 95.0 95.7 96,4 97.1 97.9 -100. 296.6 113.6 105.7 106.4 107.0 107.6 108.3 108.9 109.7 -80. 303.7 136.4 118.2 118.7 119.2 119.8 120.3 120.9 121.6 -60. 311.0 156.9 131.3 131.3 131.8 132.2 132.7 133.3 133.8 -40. 318.5 179.4 147.6 144.3 144.7 145.1 145.4 145.8 146.3 -20. 326.1 203.8 169.0 158.0 158.1 158.3 158.5 158.8 159.1 -16.04 327.6 209.4 173.6 160.9 160.9 161.0 161.1 161.4 161.7 0. 333.9 233.5 193.5 173.3 172.2 172.4 172.0 172.3 172.3 20. 341.8 273.3 217.1 196.1 187.2 186.7 186.2 186.0 185.9 40.0 350.0 320.3 245.4 220.0 203.9 202.2 201.1 200.2 200.1 52.04 355.0 337.7 264.7 234.0 215.4 212.4 210.6 209.5 208.8 80. 366.9 351.9 320.2 276.7 251.2 239.4 234.8 232.2 230.3 60. 358.3 341.8 279.4 246.6 224.8 219.5 217.2 215.8 214.8 100. 375.6 361.9 344.1 312.5 280.1 262.8 254.1 249.6 246.6 120. 384.6 372.0 356.0 336.7 310.8 288.1 275.2 268.1 263.8 126.2 387.5 375.1 360.5 341.7 318.2 295.7 281.9 274.1 269.4 140. 393.8 382.1 368.5 352.0 332.3 311.6 296.9 287.7 281.7 160. 402.8 392.3 380.0 365.7 349.7 332.4 317.8 307.7 299.9 180. 41?.8 402.7 391.4 378.8 365.2 350.7 337.2 326.7 318.3 192. 48.7 409.1 398.3 386.6 374.0 360.6 348.1 337.5 329.3 200. 422.7 413.3 402.9 391.8 379.6 366.9 354.9 344.5 336.4 220. 432.8 423.9 414.4 404.8 393.3 382.0 371.4 361.8 353.8 240. 443.2 434.8 425.9 416.5 406.7 397.0 386.9 378.5 370.6 260. 453.8 445.8 437.5 428.9 419.9 410.9 40)1.8 393.5 386.8 280. 464.5 457.0 449.2 441.1 432.9 424.9 416.6 409.1 402.6 300. 475.4 468.4 461.0 453.4 445.8 438.5 431.0 424.4 418. 3 ++ REFERENCE ENTHALPY H-0 FOR EACH PURE COMPONENT AS A SATURATED LIQUID AT -280F * ZERO PRESSURE VALUES C6TAINEL BY INTEKPULATION OF (HIT )-HO) )/T VALUES AS TABULATED BY THE API [220]

TABLE VIII-24 Saturated Liquid and Vapor Phase Enthalpies for the Ternary Mixture 10111D VAPUP TFNMP. PRKESSURE ENTHALPY++ TEVP. PRESSRHFE FNTHALPY++ (O PIa) T/ (OF) (IPSIA)) HTU/LK -198.5 50. 47.0 -39. 50. 313.8 1SIS IAC1l -168.3 100. 63.8 -h6.5 100. 323.0 -130.2 200. 86.2 33. 200. 332.7 -115.3 250. 95.7 47. 250. 4 335.1 -100.2 300. 105.2 58.2 300. 337.6 -72.8 400. 122.8 76.5 400. 339.0 -48.5 500. 139.0 89.6 500. 4 338.3 -27.3 600. 153.1 99. 600. 334.9 -8.5 700. 167.0 104.4 700. 329.1 0.5 750. 173.7 105.9 750. 3 325.5 53. 1000. 4 216.4 112.3 1000. 300.1 -40. 537. 144.5 -40. 47.5 313.1 ISOITHFRMAL -20. 636. 158.2 -20. 77. 319.6 -16.04 655. 160.8 -16.04 83. 320.8 0. 746. 172.4 0. 113. 324.8 2?0. 847. 187.7 20. 162. 329.8 40. 943. 204.3 40. 223. 33'.2 52.04 996. 215.8 52.04 273. 336.7 60. 1025. 223.1 60. 309. 337.8 4 SMnnTHFI FXPERIMFNTAL MFASIJRFMFI\NTS nF THIS WORK ++ REFLERhECE ENTHALPY H=O FCR EACh PURE CUMPUNENT AS A SATURATEU LIQUIJ AT -260F

Chapter IX THE EVALUATION OF ENTHALPY CORRELATION AND PREDICTION METHODS Chapters VI, VII and VIII have focussed on the experimental aspects of this investigation concluding with the interpretation of the basic measurements to yield smoothed enthalpy values for ethane, three ethane-propane mixtures, and for a ternary methane-ethane-propane mixture over a broad range of temperatures and pressures. Additionally, the calorimetric measurements on two methane-ethane mixtures, investigated after the completion of the ethane-propane system, were processed upto the basic data stage. The enthalpies of five methane-propane mixtures have already been adequately characterized in previous investigations at the facility [162, 168, 284]. Therefore, the necessary data has now been accumulated to pursue the objective outlined at the conclusion of Chapter IV, i.e., the prediction of multi-component mixture enthalpies from constituent pure component and binary enthalpy data. Before any technique can be applied to predict multi-component mixture enthalpies, it is first necessary to establish its ability to accurately represent all the constituent pure component and binary enthalpy data. Furthermore, if the technique is to be utilized for characterizing a variety of systems, it is imperative for such data to be concisely encoded, and rapidly decoded when necessary. Tlhe evidence presented in Chapter IV suggested that the thermodynamic properties of a mixture may, for engineering purposes, be adequately encoded in a corresponding states framework given an optimum set of three pseudo-critical parameters. It was further established that the PGC one fluid model was perhaps the most suitable of such frameworks for representing light hydrocarbons and "normal" fluids. In this chapter, the procedure for calculating the pseudoparameters RTc /PCm, Tc and ac that produce the best fit to the m m m m enthalpy data for each individual mixture taken separately is first outlined. This also provides us with a quantitative measure of the ability of the PGC to encode the enthalpy data of individual mixtures. In the particular case of the ethane-propane system, this analysis allows us to generate comprehensive enthalpy tables in the 287

288 single phase region from skeleton calorimetric data. An important test is then performed for each binary system that evaluates the consistency between the prescribed pseudo-parameters for all mixtures belonging to a given binary system if the one fluid corresponding states model is assumed to be rigorously true for every mixture examined. NText, ten mixing rules, including four developed in this work, are examined for their ability to characterize the enthalpy data for the methane-ethane and the methane-propane binaries as a function of composition.'or eight of these rules, the binary unlike pair interaction parameters are empirically adjusted so that the calculated pseudo-parameters are in close agreement with the optimum pseudoparameters for each mixture. Having specified all the constituent binary like and unlike pair interaction parameters, the rules are subsequently evaluated for their ability to predict the enthalpy of the ternary mixture. Topographical plots are prepared which illustrate the performance of the PGC and other prediction techniques in calculating the enthalpies for the systems of this work. Prediction of Pure Component Enthalpies Before proceeding with the optimization of the pseudo-parameters for each of the mixtures examined in this work, it is necessary to ensure that the PGC framework can adequately represent the enthalpies of the pure components methane, ethane, and propane that constitute the ternary mixture. The PGC enthalpy predictions for the three components using the appropriate critical parameters from Table J-1 are presented in Tables K-l, K-2 and K-3, respectively. The enthalpy values in these tables are obtained by combining the PGC enthalpy departure calculations with the zero pressure enthalpy values of Rossini [220]. As the smoothed methane calorimetric data of Jones [19] and the smoothed propane calorimetric data of Yesavage [284] were mainly used to develop the reference reduced enthalpy tables for the PGC, the accurate prediction of these measurements is virtually assured [203]. Table IX-1 compares the PGC enthalpy predictions with the smoothed entha.lpy data of this work for the system containing 0.996 mole fraction ethane. The critical parameters used in the analysis (also indicated

289 TABLE IX-1 The PGC Enthalpy Predictions Compared With Smoothed Data Using the Critical Parameters for Ethane TEMP. (DEG F) PRESS. (PSIA) ENTHALPY CHANGE DIFFERENCE ISLET OUTLET INLET OJTLET EXP'TAL CALC'D BTU/LB 8TU/LB BTU/LB -246.6r -246.60 2^nl. C0 0.' 235.58 236. 12 -0.54 -. 23 -246.C60 -24b.6' 2'n4.0 n 100.. -6.15 -5.75 -C.40 6. 5' -123.30 -123. 3. 2o0.00 30. 2 5.26 205.60 -0.34 -0 16 -123.30 -123.30 2C2r.0. 2500.^ -5.07 -5.51 C.44 -8.59 -24.50 -24.50 20C0.0 0.o0 181.11 181.26 -0.15 -0.q8 -24.53 -24.30 200. 0^^ 250.C0. -2.44 -1.72 -C.72 29. 69 49.20 49. 20 2^l. OC 700. c 3.64 2.73 0.91 24.92 80.~0 83.? 2'3:. OC 1000.00 6.38 6.55 -0.17 -2.63 80. 80.00n 1'0.0? 713.c0 6.72 7.19 -r.47 -6.94 89.80 89.80 25~.0, 0n, 15.55 15. C6 0.49 3.13 89.80 89.80 5... c. 0. 37.20 36.0" 1.20 3.24 89.80 89.80 677.0 0 p.0 69.69 69.61 0.08..12 89. 0 89.8 0 819. 0 0. 133.0 3 132. 4^..63. 47 89.80 89.80 lnOO.0 0. n 139.43 138.69 0.74;.53 89.80 89.80 15n0.0Q 0.0 145.16 145.43 -r.27 -. 18 89.80 d9.80 20CC.00 0.0 148.57 148.29 0. 28 n. 19 125.(00 125. 00 25.n0r 0. r 13.36 12.99 r0.37 2.78 125.W0 125.~ 0 75.00 0.r 53.66 53.69 -( 03 -0.05 125.0,0 125. 30 1o'o.0o.0 97.56 98.88 -1.32 -1.35 125.00 125.OC 1250.00 0.0 121.55 121.18 0.37 ".30 125. 0 125.00 15 n.00n.C 129.12 128.53 0.59 " 46 125.0 125.0 2 2r.00 0. 135 76 135.22 0.54 0,4 20o. 6C 200.60 250. 0.n O 1C.19 9.98 C.21 2.04 200.60 203.60 75. 00 0. 34.3. 344.12 0. 18 0.52 200.6C 200.06 1C0.00n 0.0 48.90 48.78 0. 12'.24 200.60 200.6, 15^.'. 0 9. 80.24 80.90 -C.66 n.82 200.60 20.60 2C0n n 1 24 101.4 67 -0.43 -n.43 3)0.i' C 303.00 50.0. 0. 15.73 15.41. 32 2.03 30.n0 300.00 1Cen0.0n 0.r 32.73 31.82 C.91 2.77 3 0.00 300.0 2 0.02 0.C 64.33 65.88 -1.55 -2.41 60. n0 63.0) 5 5C.0'0 500. 1n2.82 103.48 -.66 -.64 50.q0 8:5 d0.0 713.00 713.r0 31.03 32.62 -1.59 -5.14 82.n0 93. 001 713.00 713.CO 62.73 56. 16 6.57 10.48 99.n0 1C6.0O 819.00 819.00 32.41 28.22 4.19 12.91 170.0? 20Q.6) 2.00 200.00 29.39 29.37 C.02 0. 6 AVFRAGE ENTHAI PY DIFFERENCE 72.0 BTt/LB STI. DEV. (1RTI/LR) 1.49 BTUt/LR TC 305.44 K PC 708.33 PSIA I PHAC 6.270

290 in the same table) differ slightly from the true critical parameters for ethane because the PGC mixing rules were used to adjust the parameters to account for the propylene impurity. The data used for comparison purposes consists of a representative set of smoothed isothermal and isobaric enthalpy differences extending from -246.6~F to 300~F and upto 2000 psia. Although the standard deviation of 1.49 Btu/lb in the enthalpy difference is not as good as might be expected, its magnitude would be considerably lower but for the relatively large enthalpy deviations of 6.57 and 4.19 Btu/lb observed for two isobaric enthalpy differences across the heat capacity maxima at 713 and 819 psia, respectively. Some rather large percentage deviations are also noted at 24.5~F and 49.2~F. The observations correspond to isothermal enthalpy differences in the liquid phase in the vicinity of the Joule-Thomson inversion curve and involve rather small enthalpy changes. A slight error in predicting the exact location of the Joule-Thomson curve can, therefore, result in large percentage deviations in such cases. Although Yesavage [284] and Powers [203] have previously used the methane and propane enthalpy data to predict the enthalpy departures for nitrogen to within I Btu/lb using three parameter corresponding states frameworks, such predictions did not adequately test the techniques with respect to variations in the third parameter ac, because the ac value for methane and nitrogen are not much different (See Table J-l). The successful prediction of the enthalpy of ethane in the PGC framework is considerably more significant in this respect because its ac value lies in between those for methane and propane. Optimization of Pseudo-parameters a) General Procedure. This section is concerned with the determination of the three pseudo-critical parameters Tc, Pc, and ac that will produce the best fit to the enthalpy data for each m of the mixtures investigated in this work using the PGC framework. Although it is possible to use all the data for each mixture in the optimization scheme, expressed as enthalpy departures at regular intervals over the entire measurement range, the number of calculations in such a trial and error operation may be significantly reduced if a

291 restricted set of test data that cover the entire measurement range are carefully chosen so as to be selective of each of the three pseudo-critical parameters desired. By experience obtained from preliminary attempts at optimization, it was determined that isobaric enthalpy differences across the heat capacity maxima were very selective of ac. The same was true of enthalpy of vaporization data for mixtures with narrow two phase regions. The data just above the critical point were relatively sensitive to Pc. As indicated in Chapter V, enthalpy data are always selective of Tc regardless of location. A representative set of 25 to 35 isobaric and isothermal enthalpy differences were selected from the smoothed enthalpy table for a given mixture. The set was further divided into three subgroups each containing about 5 to 10 points. The data were re-arranged such that each subgroup was independently selective of the pseudo-parameters. The optimization was intially restricted to the first subgroup. The starting estimates for the pseudo-parameters were provided by the PGC mixing rules. The pseudo-parameters were always incremented one at a time in the sequence Tc, Pc and Cc. The smoothed enthalpy differences were compared with the PGC predictions for each such pseudo-parameter set. A particular parameter was negatively incremented about a central value only if the positive increment yielded a higher standard deviation in the enthalpy difference. The optimization is terminated after the cycle is repeated for a specified number of times (usually twice). The results were examined at this point to determine if further optimization was necessary. If not, another subgroup was added and the process repeated. When little or no movement of the optimum condition was observed, the step size for each pseudo-parameter was reduced to half its original value and the process repeated. The search was conducted with initial increments of + 0.50F in Tc, + 2 psia in Pc, and + 0.02 in ac, respectively. A histogram showing the distribution of the PGC predictions as a function of the magnitude and sign of the deviation in Btu/lb from -2 to +3 Btu/lb, in increments of 0.25 Btu/lb, was also generated for each trial. The histogram is useful in monitoring the optimization and can serve to

2q2 ferret out persistent and unusually high deviations that decrease the selectivity of the optimization. It can also indicate if further optimization from a different starting point is necessary, as for example, when the enthalpy deviations in the histogram show a marked bias at the termination of an optimization step. b) Pseudo-parameter Optimization for Ethane. In order to ensure that the optimum pseudo-parameters obtained within the PGC framework by the technique described above are truly meaningful, it is desirable to apply the procedure to a substance whose pseudo-critical parameters are otherwise unequivocally defined. If the ethane enthalpies of this work are subjected to a pseudo-parameter optimization, then the optimized pseudo-critical parameters may be compared with the critical parameters in Table IX-1 to establish the reliability of the technique. The results obtained in the final stages of the optimization, including the histogram, are summarized in Table IX-2 illustrating the general procedure discussed in the previous section. The data involving isobaric enthalpy differences across the two phase region were spread over an interval of a few degrees to prevent the predicted location of the vapor pressure curve from completely dominating the optimization of the pseudo-parameters. Nevertheless, some pseudo-parameter combinations did not predict the observed phase change within the selected latitude, thereby resulting in standard deviations of over 20 Btu/lb. The smoothed experimental data are compared with the enthalpy predictions for the optimum pseudo-parameters in Table IX-3. In this case the input data are arranged in the subgroups used to optimize the pseudo-parameters. The standard deviation in the enthalpy difference for the optimum fit was 1.03 Btu/lb. A relatively high deviation of 3.11 Btu/lb was obtained for an isobaric enthalpy difference of 32.41 Btu/lb at 819 psia in the vicinity of the heat capacity maximum. This suggests that either the smoothed reference enthalpy tables involving the methane and propane data, or the ac dependence of the reduced enthalpy function in Equation (111-35) require some improvement in this region. Nevertheless, it is significant that the optimum pseudo-parameters were within 0.22~F in Tc, 1.8 psia in Pc, and 0.01 in cxc with respect to the critical properties in Table

TABLE IX-2 Summary of Results in the Final Stages of Pseudo-parameter Optimization for Ethane in the PGCC Framevork TC PC ALPHAC ZU STD.DFV. NO.OF TRIAL DEVIATION HISTOGRAM (RTOt/Li) (OK) (PSA) BPTU/L8 POINTS NO. -2 -1 n 1 2 3 >4 305.4 710. 6.280.2848 1.43 10 1 2 1 1 1 3 1 305.5 710. 6.280.2848 1.88 2 1 1 1 1 3 1 1 305.3 710. 6.280.2848 1.05 3 2 1 0 2 0 4 1 305.3 712. 6.280.2848 33.4 4 1 1 0 2 0 4 1 1 305.3 708. 6.280.2845 1.70 5 1 2 1 1 2 2 1 305.3 710. 6.300.2845 1.34 6 2 1 0 1 1 1 2 2 1 305.3 710. 6.260.2858 1.04 7 2 0 1 2 3 1 1 305.4 710. 6.260.2858 1.44 82 0 1 2 3 1 1 305.2 710. 6.260.2858 33.4 9 1 0 0 3 2 1 1 1 305.3 712. 6.260.2858 33.4 10 1 0 1 2 2 3 1 1 305.3 708. 6.260.2858 1.73 11 1 1 1 4 1 1 1 1 305.3 710. 6.280.2848 1.05 12 2 1 0 2 0 4 1 305.3 710. 6.240.2858 33.4 13 1 0 0 2 2 1 1 1 1 1 305.3 710. 6.260.2845 0.98 15 14 1 2 1 3 4 2 0 1 1 305.4 710. 6.260.2845 1.21 15 2 1 1 3 5 1 1 1 305.2 710. 6.260.2845 26.8 16 1 1 0 3 4 1 2 0 1 1 1 305.3 712. 6.260.2845 26.8 17 1 1 1 3 3 4 0 1 1 305.3 708. 6.260.2845 1.46 18 1 2 1 5 2 2 1 1 305.3 710. 6.280.2845 0.91 19 2 1 2 2 1 5 1 1 305.4 710. 6.280.2845 1.18 20 2 1 3 1 2 5 1 305.2 710. 6.280.2845 26.8 21 1 1 1 3 0 6 0 0 1 1 1 305.3 712. 6.280.2845 26.8 22 1 1 2 2 1 5 1 1 1 305.3 708. 6,280.2845 1.40 23 1 2 3 1 3 3 1 1 305.3 710. 6.300.2845 1.16 24 2 2 0 2 2 2 4 1 305.3 710. 6.260.2858 0.97 25 1 2 1 3 4 2 1 0 1 305.3 710. 6.280.2848 0.91 15 26 2 1 2 2 5 1 1 305.3 710. 6.280.2845 1.03 27 2 1 3 1 2 4 1 1 305.2 710. 6.280.2845 0.84 28 2 1 1 3 0 6 0 1 1 305.2 711. 6.280.2845 26.8 29 1 1 1 3 0 6 0 1 1 1 305.2 709. 6.280.2845 1.01 30 1 2 1 3 1 5 0 1 1 305.2 710. 6.290.2848 0.93 31 1 2 0 2 2 1 5 0 1 1 305.2 710. 6.270.2848 0.84 32 2 1 4 0 4 2 0 1 0 305.3 710. 6.280.2848 0.91 33 2 1 2 2 1 5 0 1 1 305.2 710. 6.280.2848 26.8 34 1 1 1 3 0 6 0 0 1 1 1 305.25 711. 6.280.2848 26.8 35 1 1 2 2 0 6 0 1 1 1 305.25 709. 6.280.2848 1.01 36 1 2 1 3 1 5 0 1 1 305.25 710. 6.290.2848 0.93 37 1 2 0 2 2 1 5 0 1 1 303.25 710. 6.270.2848 0.84 38 2 1 4 0 4 2 1 1 30'.25 710. 6.280.2848 0.94 23 39 1 2 1 3 4 0 6 1 2 1 1 0 1 305.28 710. 6.280.2848 0.94 40 1 2 1 4 3 1 5 2 1 1 1 1 305.22 710. 6.280.2848 0.92 41 1 2 1 2 4 1 6 1 2 1 1 305.22 711. 6.280.2848 21.3 42 1 1 1 2 4 0 6 3 1 2 1 1 305.22 709. 6.280.2848 1.00 43 1 1 2 3 4 0 6 1 2 1 1 1 305.22 710. 6.285.2849 0.95 44 1 2 2 2 3 1 6 1 2 1 2 305.22 710. 6.275.2852 21.4 45 1 1 0 2 5 1 5 2 1 2 1 1 1 305.25 710. 6.280.2849 0.94 46 2 1 4 3 0 6 1 2 1 1 1 305.19 710. 6.280.2849 21.4 47 1 1 1 2 4 1 6 1 1 3 1 1 305.22 711. 6.280.2849 21.4 48 1 1 1 2 4 0 6 3 1 2 1 1 305.22 709. 6.280.2849 1.00 49 1 1 2 3 4 0 6 1 2 1 1 1 305.22 710. 6.285.2849 0.95 50 1 2 2 2 3 1 6 1 2 1 2 305.22 710. 6.280.209 1.03 35 51 1 1 2 2 3 4 2 9 3 2? 1 1 1 A OPI1MIZATION RFPFATFf) WITH SMAI.LFP INCREMENTS FOP THF PSFUDO-PiRAMETFRS

294 TABLE IX-3 The PGC Enthalpy Predictions Compared with Smoothed Data Using the Optimum Pseudo-critical Parameters for Ethane TEMP. (DFG F) PRESS. (PSIA) ENTHALPY CHANGE UIFFEiENCE T N FT OUTLET IN.ET OUTLET TLET XP'TAL CALC'0L (BTU/LB) BTU/LB -2 46. (, -2 46.60 2 C (.00 C.C 2 3 5.58?36.79 -1.21 -0.51 -]1 7.30 -123.3(0 2G(.00 250.00 -5.07 -5.48 0.41 -8.00 - 4.5 C -24.5U?Ct O. O 250. C -2.44 -1.66 -0. d 31.93 125.UC 125.C; 75(1.0U 0.0 53.66 53.27 0.3' 0.73 125.(0 125. C 2CCC.OO 0.C 135.76 135.14 0.62 0.46 203'.60 200.60 75.00 0.0 34.30 33.96 0.34 0.98 200.60 20G.6C 20 CC. 00 0.0 1C1.24 101.33 -0.0)'-0.09 6)3.(; 63.00 5CO.OL. 500.00 1C2.82 103.64 -0.82 -0.79 82.00 93.CC 713.00 713.00 62.73 61.19 i.54 2.46 170.00?200.6C 2CC0. 0O 200C.(O 29.39 29.45 -6.0o -0.20 -246.6. -246.6, 2(CCO. 10C.GC -6.15 -5.71 -0.44 7.19 -24.5(0 -24.50 2Ctb.C0 0.O 181.11 181.54 -0.4i -0.24 c.80s 89.830 819.0C 0.0 133.03 131.65 1.3d 1.03 89.82 89.80 2CC;.0;J 0.0 148.57 148.Jg 0.57 0.38 12.. 0 125. C 25;.00 3.0 13.36 12.94 J.4. 3.17 1 2?.O 125.0 10C (CO. 0.0 97.56 97.46 0.IJ.10 2,f). 6C 2C0.6_ 15C O.)0 0. 80.24 80.45 -0.2i -u.26 3.... 3 OC. C 1 C.O.C 3. 0. 22. 73 31.67 1.)ob 3.25 59(.(;t t;U.CC 713.CC 713.00 31.03 33.03 -2.uu -b.45 -1 2.30 -123.30 2CCCC, 0. 20 C5.26 206.34 -0.7d -0.38 89.R O 89.80 5CC0. O 0.0 37.20 35.78 1.42 3.81 8^-'.8 89.80 10C(.COC 0.0 139.43 138.16 1.27 0.91 1?5. ( 125.00 125. 10 0.0 121.55 12u.76 O.79 0.65.r c) 3(,t0. C 5C0. o C. C 15.73 15.34 0.39 2.50 I 25. (' 1?5.00 15C..t O. 0 129..1 1 289.1 8.33 0. 063 99..0 J1 C6.C)0 819. )C 819.00 32.41 29.30 3.11 9.59 49.2t 49.2 2C;C,. C 7CC.00 3.64 2.83 0.81 22.33 SJ.,O0 bC.O.( 20CL. C 10(0.0( 6.38 6.72 -').3 -5.35,.(".0 80. C0 1O Cv., 7 1 3.0C 6.72 7.46 -0.74 -11.08 8.0 PC 89.8(t 25(c.00 C.C 15.55 15.01 J.54 3.47 8;. A 0. 89. 6 77. 00 O.C 69.69 67.86 1.83 2.62 8).8 89.80 1 50. 9C U.O 145. 16 145.J5 0.11. 08 3('.' 3CO.OC 2CC.OC 0.0 64.33 65.56 -1. Z -1.90?C0( ) 2(.60 250.0C 0.0 1 C.19 9.94 0.2;5 2.48 2(.., 2 u.6O lCog.CO 0.0 48.90 48.51 0.39) 0.80 AVERAGE ENTHALPY DIFFERENCE 72.0 STD. DEV. (BTU/LB) 1.03 TC (K) 305.22 PC (PSIA) 710.1 ALPHAC 6.28 ZC 0.2849

295 IX-1. Therefore, it is possible to conclude that, given sufficient, accurate and discriminating input data, the PGC optimization should provide selective and meaningful pseudo-critical parameters. c) Pseudo-parameter Optimization for Mixtures. The pseudoparameter optimization results for the mixtures belonging to the methane-ethane, ethane-propane and methane-propane systems are summarized in Column I of each table from Table IX-11 to Table IX-20, respectively. The results for the ternary mixture are indicated in Column I of Table IX-21. The PGC enthalpy predictions for each condition in the data set, the average value of the enthalpy difference, the standard deviation for the predicted enthalpy differences, and the optimum pseudo-parameters are all indicated for each mixture. As the interpretation of the calorimeteric measurements for the methane-ethane mixtures did not extend to the preparation of consistency checks or smoothed enthalpy tables, it was necessary to use the basic processed data for the determination of the optimum parameters in these cases. With the exception of some mixtures belonging to the methanepropane system, the standard deviation in the enthalpy difference is below 1 Btu/lb, and suggests that the PGC is eminently suitable for correlating the enthalpy data on individual light hydrocarbon mixtures. The fact that the standard deviation for ethane is higher than for most mixtures examined may initially lead us to conclude either that the ethane data are of poorer quality, or that the PGC framework is perhaps better suited to represent mixture enthalpies. Such implications are false. The accurate prediction of the enthalpy change experienced by a pure component in the vicinity of the saturation line or the critical point is very taxing of any correlation. In the case of mixtures these areas are progressively removed from consideration as the two phase region excluded from the corresponding states analysis increases in size, resulting in a lower overall standard deviation. The optimum pseudo-parameter for the methane-propane mixtures were not directly determined in this work from the data sets in Tables IX-16 through IX-20. The predictions in Column I for these tables correspond to a set of pseudo-critical parameters that were optimized by Powers [202] with respect to a different set of data selected by

296 Yesavage [284] that were confined only to enthalpy departures along isotherms. The standard deviation of these enthalpy departures as reported by Yesavage, and later confirmed by Powers using the PGC framework, was better than 1 Btu/lb for all mixtures belonging to the methanepropane system. This is generally better than the performance obtained for the same systems in this work. Two reasons may be forwarded to explain such discrepancies. Firstly, although Yesavage and Powers used three times as much enthalpy data in optimizing the pseudo-parameters, the enthalpies of vaporization and the difficulty predictable single phase region in the immediate vicinity of the two phase envelope were not emphasized. Secondly, it is now believed that some of the isobaric enthalpy differences incorporated in the data sets of this work, and ignored by Powers and Yesavage, are in error. In the case of the 0.883 mole fraction methane-propane mixture, for example, (Table IX-17), such data resulted in deviations as high as 8.85 Btu/lb and were indirectly responsible for raising the standard deviation for the entire data set to 2.65 Btu/lb. Preliminary work with the original enthalpy tabulations of Mather [168] for the 0.946 mole fraction methane-propane mixture indicated similar trends which disappeared after the reinterpreted enthalpy values of Bhirud and Powers [22] for the same mixture were used. The predictions with respect to the latter set of enthalpy values are indicated in Table IX-16 and yield a very respectable standard deviation of 0.64 Btu/lb. It must be emphasized, however, that the relatively high errors in the values of the enthalpy of vaporization for the methane-propane mixtures as tabulated by Mather [168] are primarily incurred in the estimation of the phase boundaries from the basic data and should not reflect on the established accuracy of the basic calorimetric measurements themselves. It is strongly recommended that the critically chosen enthalpy differences in Tables IX-3, and IX-12 through IX-21 (except those values otherwise identified to be in error) be used in preference to isothermal enthalpy departures in evaluating enthalpy correlations.

2<) 7 Consistency Test for Examining the Validity of the One Fluid Corresponding States Principle As indicated in Chapter V, if we are to assume that the one fluid model is applicable to mixtures, then Equations (V-12), (V-13) and (V-14) are all simultaneously valid. In this particular work, we have chosen to define the parameters Tc, Pc and ac from enthalpy data m m m using Equation (V-14) where f~ represents the PGC. Therefore, we may now, in particular, calculate B for each mixture over a range of temperatures for a specified function fB. If the pure component second virial coefficients B.. and B.. are also known at each such 3] JJ temperature for a binary mixture, then Equation (V-l) may be utilized to specify the value of the unlike pair interaction virial coefficient B.. at the same temperature. If the functions fB and f;), chosen to represent the reduced second virial coefficient and the reduced enthalpy departure, respectively, are accurate and if the pseudoparameters that best satisfy Equations (V-12) and (V-14) simultaneously can be obtained from Equation (V-14) alone, and if the principle of corresponding states is valid for every mixture belonging to a given binary system, then the B.. values so computed should be independent of composition at any specified temperature and should be identical to those obtained by direct measurement. In this work the function fB defined by Equation (V-30) is used to characterize the reduced second virial coefficients for both pure components and mixtures. As the equation is valid over the range 0.52 < Tr < 3.26, the B values for the 0.484 mole fraction methane- oo m propane mixture can, for example, be computed over the approximate temperature range 151K < T < 945K given the optimum pseudo-critical parameters in column I of Table IX-19. The B values for methane and propane can also be calculated over the ranges 99K to 623K, and 192K to 1205K, respectively, using the same equation. Therefore, if we plan to calculate the methane-propane interaction virial coefficient B..(ifj) from such information in conjunction with Equation (V-l), it is immediately clear that reliable estimates of B.. can only be obtained over the restricted range 0.52 Tc.. < T < 3.26 Tcii, (Tc.. < Tc..) JJ- - ii i - JJ33 This translates to an approximate temperature range from 192K to 623K for the methane-propane system. In effect, the range of validity of

298 the calculations is limited by the critical temperature ratio of the pure components in the mixture. In particular, the method is completely inapplicable if the ratio Tc../Tc.. exceeds 3.26/0.52 unless the range of validity of Equation (V-30) is further expanded. In extending the technique to the calculation of B values for m a multi-component mixture from Equation (V-l), the effective range over which reliable estimates of B may be obtained is still governed m by the extreme pure components. In particular, reliable calculated values of B for the ternary mixture of this work are still confined m to the range 192K to 623K. In practice, however, all calculations involving Equation (V-l) and (V-30) were restricted to the temperature range from 198.15K to 510K, at regular intervals of 25K. Calculations were also made at a few additional temperatures in this range for which independent direct measurements were available. The B.. values calculated in the above fashion for the mixtures belonging to the methane-ethane, ethane-propane, and methane-propane systems are summarized in Tables IX-4, IX-5 and IX-6, respectively, and include comparisons with direct measurements. These results are also illustrated in Figures IX-i, lX-2 and IX-3, respectively. The consistency between the B.. values derived from enthalpy data for the two methane-ethane mixtures are believed to be within the limits of accuracy of the enthalpy data and the optimization procedure in each case. It is less likely that the differences between the enthalpy based and directly measured B values can be similarly CH -C2H6 4 26 reconciled. The two data points of Hoover [108] at 215K and 240K which seem to differ from the enthalpy based B values are suspect because the ethane second virial coefficients used by Hoover in calculating the B.. values for these two cases are believed to be in error as previously noted in Chapter V. The B.. values obtained 1O from direct measurement are distinctly lower in magnitude than those derived from enthalpy data. The agreement between the B.. values calculated from the enthalpy data for the 0.498 mole fraction ethane-propane mixture and the direct measurements of Dantzler et al. [59] is excellent (See Figure IX-2). The calculated B.. values for the other mixtures are slightly more positive. Nevertheless, the agreement between the enthalpy based B..

TABLE IX-4 The Variation of the Calculated Interaction Virial Coefficient as a Function of Composition as a Measure of the Consistency Between the Pseudo-paraneters for the Various Methane-Ethane Mixtures B. Values in cc/gm mole Selected Values Grained by Interpretation Experimental B Values cc/gm mole T(~K) of Enthalpy Data i c/ _ml.778 CH,.479 0CH4 4 4 GONN DANTZLER GUGGENHFIM HOOVEP [941 ET AL[59] FT AL[173] [108] 198.15 -19S.69 -192.42 -198.69 223.15 -157.87 -153.69 -157.87 248.15 -127.69 -124.77 -127.69 273.16 -104.53 -102.42 -111.9 -109.0 -111.9 -104.53 298.15 -86.27 -84.71 -92.0 -93. -90. -66.27 310.90 -78.36 -77.02 -78.36 323.15 -71.50 -70.34 -75.6 -79.~5 -77. -71.50 348.15 -59.32 -58.45 -68.+4 -59.32 373.15 -49.12 -48.47 -56.+4 -49.12 398.15 -40.45 -39.97 -40.45 423.15 -33.00 -32.65 -33.00 444.30 -27.48 -27.22 -27.48 473.15 -20.87 -20.71 -20.87 510.90 -13.53 -13.47 -13.53 TABLE IX-5 The Variation of the Calculated Interaction Virial Coefficient as a Function of Composition as a Measure of the Consistency Between the Pseudo-parameters for the Various Ethane-Propane Mixtures B Values in cc/gm mole * Chained by Interpretation of Experimental B. Values Selected Values T('K) Enthalpy Datacc/gm mole T(~K) _______Enthalpy Data ___________ _ "_____________i_________cg mJe.763 C2H6.498 C2H.276 C DANTZLER C26 3 8 DANTZLER ET AL[59] 198.15 -600.06 -626.74 -602.14 -614.00 223.15 -468.73 -489.74 -470.04 -478.00 248.15 -371.04 -394.01 -377.53 -387.00 273.16 -309.80 -323.79 -309.56 -317.00 298.15 -258.63 -270.34 -257.74 -274.~11 -263.50 310.-0 -236.98 -247.73 -235.79 -242.50 323.15 -218.42 -228.35 -216.97 -230.~11 -223.00 348.15 -186.11 -194.58 -184.15 -193.~11 -189.50 373.15 -159.63 -166.91 -157.26 -165.~11 -163.00 38. 15 -137.57 -143.86 -134.85 -140.U00 42j.15 -118.91 -124.37 -115.91 -120.00 444.30 -iOS.25 -110.10 -102.03 -106.00 413. 1 -89.14 -93.28 -85.67 -90.00 510C.C -71.52 -74.87 -67.77 -70.00 Selected for application in mixing rules VII, IX and X of Table IX-5.

TABLE IX-6 The Variation of the Calculated Interaction Virial Coefficient as a Function of Composition as a Measure of the Consistency Between the Pseudo-parameters for the Various Methane-Propane Mixtures * T(~K) B CH C H Values in cm3/gm mole Obtained by Interpretation of Enthalpy Data Experimental B CHC3H Values Selected 4 3 8_____________________________________ 4______ __4 3 8 Values.948 CH4 cc/gm mole.948 CH.883 CH4.720 CH4.484 CH4 234 CHELS DATZLER 4 ^^ 4- 4 4MICHELS DANTZLER GN ET AL. [173] ET AL.[59] [94 198.15 -289.24 -290.60 -277.41 -264.86 -236.10 -277.41 223.15 -229.42 -231.36 -223.11 -216.02 -196.81 -223.11 248.15 -185.39 -187.57 -182.20 -178.13 -164.33 -12.20 273.16 -151.74 -154.01 -150.44 -148.10 -137.65 -150.44 298. 15 -125.26 -127.57 -125.18 -123.85 -115.54 -136. -139. +12 -125.18 310.90 -1 13.82 -116.14 -114.21 -113.24 -105.70 -122.5 -114. 1 323.15 -103.90 -106.22 -104.66 -103.96 -97.02 -114. -16. +12 -104.66 348. 15 -86.34 -88.65 -87.69 -87.42 -81.44 -93. -93.+12 -87.69 373.15 -71.66 -73.95 -73.44 -73.48 -68.23 -81. -75.+10 -73.44 398.15 -59.21 -61.49 -61.32 -61.56 -56.88 -55. -61.32 423.15 -48.53 -50.80 -50.90 -51.27 -47.01 -34.8 -50.90 444.30 -40.61 -42.87 -43.15 -43.6 1 -39.64 -43.15 473.15 -31. 16 -33.41 -33.88 -34.43 -30.76 -33.88 5i 0. 0 -20.69 -22.92 -23.59 -24.20 -20.84 -23.59 * Selected for application of mixing rules VII, IX and X of Table IX-10

CONSISTENCY TEST FOR OPTIMUM PG.C. PSEUDO PARAMETERS OF METHANE-ETHANE MIXTURES 0 - 10 PSEUDO PARAMETERS 2 -100 MIXTURE TC(OK) PC(ATM) ALPHAC o=: I^~~~ //O~ ~.778CH4 217.5 47.08 5.94.480 CH4 252.3 48.03 6.07 o.778CH4i DERIVED FROM I^~ //~~~~~ Q~eO.480CH4 ENTHALPY DATA * HOOVER [ 108R GUNN[94 SECOND VIR.AL vDANTZLER ET.AL[59OEFFICIENT DATA 50 -200. 200 300 400 500 T OK Figure IX-I. The Use of the Interaction Second Virial Coefficient as a Measure of the Ability of the Corresponding States Principle to Correlate the Thermodynamic Properties of the Methane-Ethane System.

0" ~ CONSISTENCY TEST FOR OPTIMUM P.GC. PSEUDO PARAMETERS OF ETHANE-PROPANE MIXTURE -100 -200 Il 0 -300 PSEUDO PARAMETERS ZJ^~~~~~ /^~ ~MIXTURE TC(OK) PC(ATM.) ALPHAC m - /^.763 C2H6 321.3 47.09 6.31.498 C2H6 339.5 44.8 6.38 -400 /.276 C2H6 350.25 43.0 6.48 0 0o.763 C2H6 _500 2/ / ao.498 C2H6 DERIVED FROM /-.276 C2H6 ENTHALPY DATA o DANTZLER ETAL. SECOND VI RIAL \ /E \TL iCOEFFICIENT DATA / - 600 200 300 400 500 T OK Figure IX-2. The Use of the Interaction Second Virial Coefficient as a Measure of the Ability of the Corresponding States Principle to Correlate the Thermodynamic Properties of the Ethane-Propane System.

CONSISTENCY TEST FOR OPTIMUM PGC PSEUDO PARAMETERS OF METHANE-PROFANE MIXTURES -20 -60 100 -140 // o3~~~~~ /J^1~~~ ~PSEUDO PARAMETERS CD -/MIXTURE TC(~K) PC(ATM.) ALPHAC - eou ~/.234CH4 331 53 42.43 6430 494CH4 289.76 43.95 6.262 5mo i^~~ ~ //^O720CH4 247.76 44.79 6.098 883CH4 215.44 45.27 5961 f / A^~~~~~ 948CH4 201.03 45.16 5.883 -220 o 234% CH4 ( MICHELS ET AL. [174] o 494% CH4 DERIVED FROM / SECOND VIRIAL x DANTZLER ET AL [59] A 720% CH4 ENTHALPY DATA 2'60" ///COEFFICIENT DATA GUNN [94] 88.3% CH4 o 948% CH4j -300 ~^ ~^~ ~'~00 TOK Figure IX-3. The Use of the InteractiOn Second Virial Coefficient as a Measure of the Ability of the Corresponding States Principle to Correlate the Thermodynamic Properties of the Methane-?ropane System.

304 values is, on a percentage basis, considerably better than that obtained for the methane-ethane mixtures at the lower temperatures. The reverse is true at higher temperatures. A similar analysis for the five mixtures belonging to the methanepropane system as seen in Figure IX-3 reveals a significant lack of consistency between the B.. values for the individual mixtures. In general, the calculated B.. values become less negative as the mole'3 fraction of propane increases. Again, the experimental B.. values are more negative than the enthalpy based values. The high temperature results of Gunn [94] appear to be somewhat inconsistent with the values of Michels et al. [174] and Dantzler et al. [59] at lower temperatures and are believed to be less accurate than the latter. The B.. values for the 0.234 mole fraction methane-propane mixture l3 appear to be much more positive than the rest. It is conceivable that the pseudo-parameters for this particular mixture are not truly optimum as they were not obtained from the carefully chosen data sets in Tables IX-16 through IX-20. For example, the low B.. values'J could have resulted if the'optimum" value of RTc /Pc for the mixture m m was underestimated. To ensure that the calculated B.. values were not influenced by 1J any errors introduced by using Equation (V-30) to calculate B, B.. and B.., a further analysis was undertaken. As seen in Table J-3, the methane second virial coefficient data from different reliable sources are in excellent agreement with the predictions from Equation (\T-30) down to about 190K. The propane data of Kapallo [122,123] and Kunz [136] were subjectively emphasized in relation to the measurements of Brewer [28] and McGlashan et al. [159] in defining the ac dependence of the correlation at low temperatures. Considering the possibility that the latter measurements might be more accurate than the former, the ac dependence of the correlation was redefined by focusing instead on the data of Brewer and McGlashan et al. The sample calculation in Appendix F-6 in this regard, and the results of Table F-3 show that even though the discrepancy between the enthalpy based and directly measured B.. values is slightly decreased, the consistency between 1J the enthalpy based B.. values for the individual mixtures shows no impvement. This analysis therefore suggests that the inaccuracies improvement. This analysis therefore suggests that the inaccuracies

305 in the reduced second virial coefficient correlation are not instrumental in causing the observed inconsistencies. The consistency tests for the three binary systems suggest that the application of the corresponding states principle to mixtures is apt to be less successful as the size and energy parameter ratios for the constituent pure components depart from unity. In particular, the results hint that a set of pseudo-parameters that are optimal for the representation of a given configurational property such as the enthalpy departure, may be less suitable when applied to the estimation of other thermodynamic properties for the same system. The Selection of Mixing Rules for This Investigation Although the enthalpies for the individual mixtures of this study appear to be adequately correlated within the PGC framework, we would now like to determine whether the enthalpies for each of the binary systems that constitute the ternary mixtures can be satisfactorily characterized as a function of composition given enthalpy data on a few selected mixtures. The most concise approach to the problem is to examine various mixing rules that compute the pseudo-parameters as a function of composition for each binary system investigated. A knowledge of the enthalpy behaviour and the optimum pseudo-parameters for each of the selected mixtures of this investigation can serve to evaluate the performance of the mixing rule examined. The mixing rules examined in this chapter are summarized in Table IX-10. These include the more popular recipes discussed in Chapter IV and other rules developed in Chapter V. All rules except VI and VIII are set up to allow empirical adjustment of the unlike pair interaction parameters. Originally, the Pitzer-Hultgren rules (II) prescribed a quadratic mixing rule for the acentric factor c but m the linear relationship between w and ac as given by Equation (I-32) suggests that the quadratic mixing rule for ac used in this work is m essentially equivalent. This mixing rule for acc is also used to m supplement rules III, IV, and V which, strictly speaking, apply only to the two parameter case. Rules V, VII, IX and X are all developed in this work. The

306 basis for each of these rules is explained in Chapter V. Rules VII, IX and X each require B values for the given mixture to be provided over a range of temperatures. Rule VII uses these B values in conjunction m with Equation (V-30) to optimize the value of Tc alone. The values m of RTc /Pc and ac are predetermined by application of the high m m m temperature mixing rule of Equation (V-38) and the quadratic mixing rule for acc, respectively. Rule X optimized both Tc and RTc /Pc m m m m from the set of B values but defines acc from the quadratic rule. m m Rule IX also optimizes Tc and RTc /Pc but instead presupposes that m m m the optimum value of Ctc for the mixture is somehow known. Therefore, m in the strictest sense, it is not a true prediction method. Nevertheless, the various approaches permit us to study the influence of the precise choice of occ on the optimized values of Tc and Pc from m m m a given set of B values. By examining Rules VII, IX and X we are, m in effect, evaluating different compromises to circumvent the practical difficulty of unequivocally defining three pseudo-critical parameters from B data over a limited range of temperatures. m Calculation of Optimum Binary Interaction Parameters for Several Mixing Rules The enthalpy data on each of the constituent binaries of the ternary mixture can now be used to specify an optimum set of the appropriate unlike pair interaction parameters for each mixing rule in Table IX-10 except rules VI and VIII for which the parameters are independently defined from approximations involving pure component critical properties. There are two procedures for accomplishing this objective. In the first approach, the enthalpy data for all mixtures belonging to a given binary system are simultaneously utilized in optimizing the interaction parameters for each mixing rule. In the second case, the interaction parameters are adjusted to yield the best fit to the pseudo-parameters obtained by optimizing the enthalpy data for each mixture taken separately. The two procedures are equivalent only if the unlike pair interaction parameters for a binary system are characterized from enthalpy data on a single mixture. When data are available on more than one mixture, then the first

307 procedure is the more reliable. It is, however, unquestionably more demanding of computer time because not only must all the mixture data for a given binary system be collectively used in the optimization of the interaction parameters, but the optimization process must also be separately repeated for all but two of the mixing rules examined in this work. The second procedure allows us to accomplish our objective given only the optimum pseudo-parameters in Column I of Tables IX-11 through IX-21, and was therefore used in this work. For example, using the second technique, the optimum value of RTcij/Pcij, ijj, for the Redlich-Kwong mixing rule (III) can be determined from the optimum pseudo-parameters for each of the three ethanepropane mixtures by minimizing the quantity k=3 RTc 2 RTc 2 RTc RTc [ k( PC ) - (X2) ( 22 ) - (X3) ( 33 ) 2(x2)(x3)( 23 ) ] (IX-1) k k k 33 k k 23 where wk is a subjectively defined weighting factor for the optimum pseudo-parameters (RTcm/Pcm) for the kth mixture which accounts for relative differences in the quality of the enthalpy data and the estimated reliability of the optimum pseudo-parameters, and x2, X 2k 3k are the ethane and propane mole fractions, respectively, for the kth mixture. The value of (RTc /Pc ) for each of the three m m mixtures is obtained from column I of Tables IX-13 through IX-15, respectively. The values of (RTc22/Pc22) and (RTc33/Pc33) for the pure components ethane and propane, respectively, are defined in Table J-1. The interaction parameter RTc23/Pc23 for the Redlich-Kwong rule can also be determined for each mixture separately using the relation RTC 2 RTc22 2 RTc33 () - (x) ) - (X RTc3 Pm k 22 3k C33 ( Pc23 ) k (IX-2) PC23 k2 2k Therefore, by making use of Equation (IX-2) we may instead minimize the quantity k=3 RT c RTc2 3 wk() (X3) [ 23 ) ( k 2Opt. to specify the optimum value of RTc23/Pc23 from the values calculated

308 for each of the k mixtures taken separately. Thus, in the general case, the optimum interaction parameters (RTc../Pc..), (RTc./Pc..) iJ'J Opt.1 13 Opt and (ac..) for the Redlich-Kwong rule are defined by minimizing 1J Opt the quantities p RTc RTc 2 z E x) (x [ (RXA - ( i j (IX-4) k= k( ik k PCij Pcij k Opt. 2 2 p RTc.. RTc.. 2 k )()k [ (X _ ) _ (_ __ ) ] (IX-5) ki kk Pc k=1 k k k PCij Opt. ifj P kZl Wk(Xi) (Xj)[ (cij) ac ] (IX-6) for the p mixtures for a given binary system taken together. Similar criteria may be used to specify the interaction pseudo-parameters for rules II, IV and V in Table IX-10, respectively. Although the final results are entirely equivalent, the forms represented by (IX-4), (IX-5) and (IX-6) were preferred to the form (IX-1) for specifying the optimum interaction parameters for the Redlich-Kwong rule (III) because the variation in the interaction parameters as a function of composition is obtained in the first case and serves as a measure of the ability of the rule to represent the entire binary system. The forms specified by (IX-4) through (IX-6) also illustrate that the interaction parameters calculated for each mixture must be weighted with respect to the composition product xix. to best define its optimum value. Although each mixture of components i and j provides us with a B.. values at each of the fourteen specified temperatures from iJ 198.15K to 510K, rules VII, IX and X require us to specify a single B.. value for the whole system at each temperature. The averaging of the B.. values could have been achieved in a fashion similar to ii that illustrated for the Redlich-Kwong rule by minimizing the quantity P 2 Wk(xi) (Wj) [ (Bij) - (Bij) ] (IX-7) k=1 k k k Opt. instead at each selected temperature. However, such an averaging procedure would have totally ignored the B.. data obtained from volumetric measurements. In actual practice the final set of B.. values were 1J

309 selected by visual examination of the data in each figure from Figure TX-] through TX-3. In general, more weight was given to the mixtutres whose IB valulies were closer to those obtained from direct measurement. Consequently, it is to be anticipated that the use of such values may sacrifice the goodness of fit to the enthalpy data for the binary systems in question to yield some improvement in the fit to low pressure volumetric measurements. The final selected set of B.. values for the methane-ethane, the ethane-propane and the methane-propane systems are also presented in Tables IX-4, IX-5 and IX-6, respectively. The final B.. values for the methane-ethane system were selected to correspond to those for the 0.778 mole fraction methane-ethane mixture. The B.. values for 13 the ethane-propane system were obtained by averaging the results for all three mixtures. In retrospect this was a poor choice, and the results for the 0.498 mole percent mixture should have been weighted more heavily as they agree very well with the second virial coefficient data of Dantzler et al. [59]. The final B.. values for 1J the methane-propane system were selected to correspond to those for the 0.72 mole fraction methane-propane mixture. The results for the 0.234 mole fraction methane-propane mixture were effectively ignored in view of the observed discrepancy with the results for the other mixtures. The calculated values of the interaction pseudo-parameters for mix:ing rules II, III, IV and V as a function of composition for the methane-ethane, the ethane-propane and the methane-propane systems are presented in Tables IX-7 through IX-9. The value of the parameter (RTcij/Pcij) determined for Rule VII using Equation (V-41) is also indicated. The value of ac.. used in the equation is independently obtained from the quadratic mixing rule for ac. Unlike other mixing m rules, the function g in Equation (V-4) also varies with reduced temperature T/Tci.. The temperature of application of the rule must be such that 8.0<Trij<30 for all i,j as explained earlier (See page 131), and should not be confused with the actual temperature at which enthalpy predictions are desired. A sample calculation of RTcij/Pcij and ac.. for Rule VII using the optimum pseudo-parameter for the 0.498 mole fraction ethane-propane

TABLE IX-7 The Calculated Interaction Parameters for Rules II, III, IV, V and VII of Table IX-10 as a Function of Composition for the Methane-Ethane System Rule Code.778 CH4(CH4-C2H6).479 CH4(CH4-C2H6) WFIGHTED AVERAGE (Table IX-lO) TCfj (RkCTC/PC)ij PCij ALPHAC TCKi (R*TC/PC)ij PCii ALPHACii TCj (R*TC/PC)ij PCij ALPHACi (OKI CC/MOL ATM (OK CC/MOL ATC TCj RC/C Pi (~K) CC/MOL ATM PI TZ ER-HUL TGREN II 251.9 420.5 49.16 6.102 251.9 422.1 48.96 6.074 251.9 421.3 49.07 6.080 VAN DER WAAL III 240.9 423.9 46.64 6.102 240.6 423.6 46.62 6.074 240.75 423.7 46.63 6.080 REOLICH-KWONG IV 236.9 424.6 45.78 6.102 236.3 424.0 45.74 6.074 236.6 424.3 45.7h.080 MOD. VAN DER WAAL V 240.7 425.6 46.40 6.102 240.5 425.9 46.35 6.074 240.6 425.8 46.38 6.080 THIS WORK VII 234.6 422.2 45.60 6.102 231.9 422.8 45.00 6.074 233.3 423.5 45.20 6.080 ARITHMETIC MEAN 4246 6. 047 GEOMETRIC MEAN 241.3 HARMCNIC MEAN 234.8 TABLE IX-8 The Calculated Interaction Parameters for Rules II, III, IV, V and VII of Table IX-1O as a Function of Composition for the Ethane-Propane System Rule Code.763 C2H6(C2H6-C3H8).498 C2H6(C2H6-C3H8).276 C2H6(C2H6-C3H8) EIGHTED AVERAE (Table IX-10) TC; (R*TC / PC)ji PCij ALPHACi] TCj (R*TC/PC)ij PCij ALPHACij TCij (R*TC/PC)ij PCij ALPHACij TCij (R*TC/PC}j PCij ALPHACi j OK CC/MOL ATM ( KI CC/MOL ATM (~K) CC/MOL ATM ( K) CC/ML AM PITZER-HULTGREN II 339.3 604.2 46.09 6.331 341.2 628.9 44.52 6.350 330,0 630.9 43.31 6.440 338.0 625.0 44.38 6.380 VAN DER WAAL III 334.9 595.2 46.17 6.331 336.4 622.3 44.36 6.350 328.0 625.5 43.03 6.440 332.0 hl.O 44.09 MOO. VAN DER WAAL V 334.3 602.3 46.17 6.331 336.0 624.5 44.15 6.350 328.0 623.3 43.19 6.440 331.6 620.0 43.19 6.380 THIS WORK VII 332.2 597.0 45.67 6.331 333.3 618.2 44.24 6.350 321.8 634.9 41.59 6.440 331.0 612.0 44.38 ARI IHMETIC MEAN GCEOMETRIC MEAN 336.1 HARMONIC MEAN 334.6 334.6

TABLE IX-9 The Calculated Interaction Parameters for Rules II, III, IV, V and VII of Table IX-10 as a Function of Composition for the Methane-Propane System Rule Code.948 CH4(CH4-C3H8).883 CH4(CH4-C3H) 72 CH4(CH4- ) (Table IX-10) TCij (R*TC/PC)ij PCij ALPHACij TCij (R*TC/PC)ij PCij ALPHACij TCij (R*TC/PC)ij PCij ALPHACi (~K) CC/MOL ATM (~K) CC/MOL ATM (OK) CC/MOL AT# PI TZER-HULTGREN II 290.6 605.0 39.41 6.439 298.6 563,4 43.49 6.455 297.4 554.2 44.03 6.369 VAN DER WAAL III 254.0 574.8 36.27 6.439 262.3 559.1 38.50 6.455 264.6 551.8 39.34 6.369 REDLICH-KWONG IV 247.2 570.6 35.54 6.439 254.2 552.9 37.73 6.455 255.8 546.0 38.45 6.369 MOD. VAN DER WAAL V 252.6 577.9 35.87 6.439 261.3 558.1 38.42 6.455 263.6 552.6 39.15 6.369 THIS WORK VII 248.6 538.5 37.89 6.439 252.4 527.1 39.29 6.455 248.6 530.2 38.48 6.369.50 CH4(CH4-C3H8).234 CH4(CH4-C3H8) WEIGHTED AVENa-E TCij (R*TC/PC)ij PCij ALPHACij TCij (R*TC/PC)ij PCij ALPHACii TCij (R*TC/PC)ij PCi ALPHACij (~K) CC/MOL ATM (OK) CC/MOL ATM (OK) CC/MOL bAT PITZER-HUL TGREN II 297.1 553.5 44.04 6.335 290.2 559.1 42.6 6.310 295.0 560.0 43.22 6.350 VAN DER WAAL III 268.1 550.9 39.94 6.335 265.6 560.3 38.90 6.310 264.0 555.0 39.03 6.350 REDLICH-KWONG IV 258.5 545.4 38.89 6.335 254.3 553.8 37.69 6.310 255.0 549.0 38.11 6.350 MOD. VAN DER WAAL V 267.2 551.9 39.73 6.335 264.5 558.3 38.80 6.310 263.1 558.0 38.69 6.350 THIS WnRK VII 244.9 535.2 37.55 6.335 232.9 550.9 34.70 6.310 244.0 540.0 37.08 6.350 ARITHMETIC MEAN 508.6 6.180 GEOMETRIC MEAN 265.6 HARMNNIC MEAN 251.7

312 mixture is illustrated in Appendix F-7, part 3. It is established there that the rule may be applied at any temperature between 2960K and 5720K for any system with methane and propane as the extreme components. In this work a temperature of 5000K was arbitrarily selected for the calculation. However, the temperature dependence of the function g(cc, Tr) is very weak, and additional calculations at 4000K and 6000K showed negligible changes (< 0.2K) in the computed value of RTc../Pc... The results of Table IX-7 through IX-9 lJ lJ indicate that the variation in the interaction parameters Tc.. and RTc../Pc.. with composition is minimal for the Redlich-Kwong rule 13 13 (III), although the performance of the other rules is only slightly inferior. "lore significantly, we note that the calculated values of the interaction parameters for a given mixture vary from rule to rule. The Redlich-Kwong Tc.. for example is almost always lower 13 than for the Van der Waal (IV) case. The Tc.. value for the modified 1j Van der Waal rule (V) lies in between the two but is closer to the Van der Waal result. The value of RTc../Pc.. for the modified Van der Waal rule (V) is usually higher than for the Redlich-Kwong rule. The Pitzer-Hultgren (II) interaction constant Tc.. is considerably different from values calculated for the rest of the rules in the case of the methane-propane system. This is not surprising as the interaction parameters for the rule have no theoretical value and are merely empirical constants. In summary, the analysis of the results for Rules III, IV and V indicate that considerable caution is to be exercised in applying empirically obtained interaction parameters from the literature to a particular mixing rule if a different rule is used to specify these parameters from experimental measurements. The geometric and harmonic mean assumptions for Tc.. suggested by Equation (IV-19) with k.. equal to 1.0, and by Equation (IV-20), 1J respectively, and the arithmetic mean assumption for oc..i and RTc../Pc.. (the latter being expressed by Equation (IV-18)) are also included in Tables IX-7 through IX-9 for comparison purposes as they are frequently used with various mixing rules in the absence of binary data. The effectiveness of these assumptions depends on the mixing rule with which they are used. The geometric mean rule for

3 I 3 TABLE IX-10 Summary of Mixing Rules Examined in This Investigation for the Calculation of Pseudoparameters Code Rules Designation I PGC optimized pseudo-parameters using Optimum enthalpy data for individual mixtures II Pc = E Z x.x. Pc.. m i j i] Tc = Z Z x.x. Tc.. Pitzer-Hultgren m j ij j Cc = E X.x,. cC.. m j ij 1 III RT RTc RTc.. pm X x.x I Pc 1 Pc.. m ji 13 2*5 2*5 RTc RTc.. pm = Z x.x. - - Redlich-Kwong Pc J P.. Cc = Z xx. ac.. m 13 m j i 1 J IV Vc = x.x. Vc.. m i i J IJ Tc Vc = E E x.x. Tc.. Vc.. Van der Waal m m i j I J i ac = Z Z x.x. ac.. m i J i j,. 1 - i

314 TABLE IX-1O (contd.) T RT c ac - 2 RTc. a.c.. - 2 RTc 2 [ac - RTc. [ac -1] Van der __i ( P C,, ~) m m C XiXj. a ) Waal PC DICxJ Pc.. 4 m m i( 1J 1. (This Work) ac =- Zx.x. acc.. m m VI PC =( x. PC.. m. i cii 1 Tc = E x. Tc. Kay m i i ac = x. ac.. m. 11 VII ac = Z Z x.x. ac.. m i j i J 13 RTc RTc.. Pc = I I x x [- -][h (c )j1g (oc.., Tr..)] P =i c i j[ ] g,(aci, Tr )] m i jJ ij where hr( c. = 0.15903 + 0.0588 (c.ij - 5.82) ij 0.15903 + 0.0588 (acc - 5.82) m g(acij, Tr.j) gr(acij, Tri 1 ) o(c, Tr ) m ~ m Tr.. g(cij, Trij) = 0.3517 + 1.5068 [ 1 f(ac.i)] ij5 13 18 13 Tr.. 2 - 1.11739 [ 18 * f(acij)] + 0.25874 Tr.. 3 [-^!.f(cc,.)], 8.0<Tr..<30 all i,j 18 13 3 —

315 TABLE TX-1O (contd.) F(ac. ) ]. + 0.189 ((c. - 5.82) i1 i.l Tc is obtained by minimizing the function Z [Br - F[(Tr ) ]2 k=l m over a selected set of temperatures, T.. Tk... where 0 68511 F[Tr] = 0.14416 + 0.49095 [1 - exp (T )] + oo Tr oo 0.0220 0.00614 (ac, - 5.82)[0.0175 - 0220 _ 000614 + m 5 Tr Tr 2 + 00 00 0.002811 Tr 3 00 (Tr ) is defined by the relation 0oo m - f (Tr) - [cC - 7.0][V(Tr )] = - (Tr ) m m o m - [5.82 - 7.0][T(Tr )] m where the functions d and Y are defined in Equations III-36 Z x.x. Bij (Tk) Through III-36c Br (T) = i k m k RTc /Pc m m RT c.. For i=j, Bij(T k) = ( ) [F(Tr) ij k Pc.ij 00ij j T=Tk For i+j, Bij (T ) values are independantly obtained from binar mixture data. from binary mixture data.

316 TABLE IX-10 (contd.) 7III Same as IV with 1/2 Tc.. = (Tc Tc..) 1J 1ii JJ Vc. 1/3 + Vc.1/3 Van der Waal with Vc.. = I- ^^ I.1 i 2 Lorentz-Berthelot approximations aci = (C.ii + jc..)/2 IX ac assumed to be independantly known, m i.e., from rule I RT c and Tc are then simultaneously obtained Pc m m by minimization of the function 1 2 z { Br - F[(Tr ) } m oo k=l m using the same procedure as in rule VII X ac = Z x.x. ac.. m i1 3 i tained as in rule IX RTc m P c m n

317 Tc., is best suited to the Van der Waal rule (IV), while the harmonic lJ mean rule for Tc.. is preferable when used in conjunction with the 13 Redlich-Kwong mixing rule. For the methane-propane system, the arithmetic mean rules for (RTci /Pc..ij) and cij. yield values that are considerably lower than those calculated by the rules examined in Table IX-9. The agreement is better for the methane-ethane and the ethane-propane systems. It is therefore safe to conclude that the effectiveness of these two rules decreases as the differences in the size and energy parameters for the constituent pure components of a binary mixture increase. The Evaluation of the Mixing Rules of Table IX-10 Having specified the optimum values of the interaction parameters, the pseudo-critical parameters for each of the mixtures investigated in this work can now be recalculated for every mixing rule in Table IX-10 and compared with the optimum values obtained earlier. The results for the individual systems are summarized in Tables IX-ll through IX-21. However, a better measure of the relative performance of these rules can be obtained by comparing the predicted enthalpy values for the specified pseudo-parameters in the PGC framework with the smoothed experimental enthalpy data in each case. These calculations are also reported in the same tables. No such enthalpy calculations are reported for the methane-ethane mixtures because the basic enthalpy data used in obtaining the optimum pseudo-parameters for these systems have not yet been evaluated for accuracy and selfconsistency. The enthalpy deviations for the mixing rules averaged over all the mixtures for each of the binary systems methane-propane, and ethane-propane are summarized in Table IX-22 along with the results for the ternary mixture. All these results are analyzed below. a) Methane-Ethane. A comparison between the calculated Tc m values for the various rules in Tables llb and 12b indicate that the predictions in every case are within 1.3K and 2.5K of the optimum Tc values for the 0.778 and 0.478 methane-ethane mixtures, respectively. m The agreement between the optimum parameters (I) and the calculated values of Tc and RTc /Pc for rules II through V is particularly m m m

TABLE IX-11 a) The PGC Enthalpy Predictions for the 0.78 Mole Fraction Methane-Ethane System Using the Optimum Pseudo-parameters (I) of Table IX-11 b. RUN TEMP. (DEG H PRESS. (PSIA) ENTHALPY CHASGE OIFFERENCE NUMBER INLET OUTLET INLET OUTLET EXP'TAL CALC'D BTU/LB BTU/LB BTU/LB 8.010 -59.?3 -38. 57 2000.10 2000.03 19.69 19.09 0.60 3.03 8.050 -59.27 37.80 1999.80 1999.73 101.56 100.38 1.18 1.16 4.040 202.31 277.43 2002.60 2002.46 52.85 52.20 0.65 1.23 9.010 -59.44 -40.36 1502.20 1502.15 21.46 21.04 0.42 1.96 9.030 -59.46 -29.25 1503.40 1503.35 35.03 35.77 -0.75 -2.13 9.060 -59.37 25.36 1499.30 1499.25 106.82 106.77 0.04 0.04 14.0?C -240.76 -189.32 1000.40 1000.35 38.00 37.29 0.71 1.87 18.040 -152.10 -60.85 1002.10 1002.04 90.20 91.94 -1.14 -1.93 10.020 -59.45 -49.65 1001.40 1001.34 19.05 16.85 2.20 11.54 10.030 -59.47 -40.21 1000.10 1000.04 41.63 40.01 1.63 3.90 10.0,40 -59.47 -29.23 1001.80 1001.74 64.72 65.81 -1.10 -1.69 10.090 -59.49 75.58 1000.90 1000.84 164.54 163.68 0.86 0.52 3.050 77.92?0?.95 1000.00 999.81 80.21 79.41 0.80 1.00 5.050 202.17 300.70 1001.40 IC01.?2 63.21 61.60 1.61 2.54 17.020 -152.29 -126.03 500.10 500.03 22.95 22.40 0.55 2.40 17.100 -152.20 -42.23 499.00 498.83 206.37 207.39 -1.02 -0.50 15.030 -240.70 -158.85 251.30 251.20 62.59 62.91 -0.32 -0.51 16.130 -165.75 -59.92 249.10 248.76 227.10 227.05 0.05 0.02 11.060 -59.56 75.29 252.10 251.71 71.29 70.46 0.84 1.18 7.050 -58.49 -58.45 1390.50 995.70 10.13 9.92 0.21 2.07 1.026 79.14 79.13 2000.00 1584.02 15.66 15.44 0.21 1.36 b) The Calculated Pseudo-critical parameters for the 0.78 Mole Fraction Methane-Ethane System Using the Mixing Rules of Table IX-O10 THE CALCULATED PSEUDO-PARAMETERS FOR THE VARIOUS MIXING RULES I II III IV V VI VII VIII IX X TV (K) 217.5 217.5 217.4 217.4 217.5 216.2 217.0 217.7 217.5 216.8 PC (PSIA) 692.0 691.6 691.9 692.4 692.5 680.2 689.6 692.5 692.0 685.8 P TC./PC (ICC/MnLF) 379.2 379.4 379.0 378,8 378.9 383.4 379.6 379.1 379.2 381.5 Al PHAC 5.940 5.932 5.932 5.932 5.932 5.921 5.932 5.921 5.940 5.932 7 C,.289.290.290.290.290.290.290.290.288,290

TABLE IX-12 a) The PGC Enthalpy Predictions for the 0.50 Mole Fraction Methane-Ethane System Using the Optimum Pseudo-parameters (I) of Table IX-12b. ^ T F P. I GF H PRESS. (PSIA) ENTHALPY CHA GF OIFFLRFNCE N'I P flw INLOT OUT FrT INLF-T OUTLFT EXP'TAL. CAL:'D t BTU/LB BPU/LB 3.0 r -229.94 -99.68 1490.40 1490.35 85.41 86.17 -0.75 -0.88 4.110 -16.75 -Il.40?51.50 251.53 228.97 230.17 -1.19 -0.52 5.090 -90.33 9.43 500.70 5C0.56 195.93 197.55 -1.62 -0.83 5.010 -99.42 -78.40 499.70 499.56 16.35 15.84 0.51 3.13 6.010 -1(1.1I1 -70.33 749.90 749.55 23.26 22.49 0.77 3.30 6.080 -101.41 39.13 749.70 749.48 194.94 197.30 -2.06 -1.06 7. 04 -100.04 4.68 974.50 974.42 98.22 97.12 1.10 1.12 8.010 -100.1 7 -69.93 1499.50 1499.44 21.83 22.27 -0.44 -2.01 8.030 -100.13 0.53 1501.30 1501.24 80.00 79.99 0.01 0.01 11.030 249.96 302.8^ 1500.90 15(0.80 36.34 35.73 0.60 1.66 14.050 100).20 251.34 1499.90 1499.75 117.74 115.62 2.12 1.80 ) 1S.030 0.31 25.69 1253.90 1253.80 31.43 29.38 2.06 6.54 15.070 0.25 58.62 1251.90 1251.80 80.49 80.16 0.33 0.41 15.080) -0.44 108.37 1249.60 1249.50 133.89 133.38 0.51 0.38 16.020 0.36 45.82 1502.00 1501.90 49.85 49.87 -0.03 -0.06 16.060 0.21 80.47 1499.10 1499.00 93.32 91.98 1.34 1.44 17.045 0.32 81.41?002.80 2002.67 75.99 75.08 0.91 1.20 b) The Calculated Pseudo-critical Parameters for the 0.50 Mole Fraction Methane-Ethane System Using the Mixing Rules of Table IX-1O THE CALCULATED PSEUDO-PARAMETERS FOR THE VARIOUS MIXING RULES I II III IV V VI VII VIII IX X XI XII TO (K) 252.0 252.3 252.4 252.4 252.3 250.4 253.0 252.6 250.5 250.8 251.0 256.4 PC (P IA) 708.0 706.8 706.2 706.0 706.0 691.3 707.7 706.0 683.8 681.6 706.1 713.0 R TC/P, (CC/ WM I'P 429.3 430.6 431.2 431.1 431.1 436.9 431.3 431.6 442.0 443.9 428.8 433.8 A1IHtC 6.073 6.073 6.073 6.073 6.073 6.057 6.073 6.057 6.073 6.073 6.057 6.010 f<~.288.288.288.288.288.289.288.289.288.289.282.279 * Using the mixing rules and the binary interaction constant for the pseudo-critical temperature as tabulated by Barner and Quinlan [15]. ** Using mixing rule (IT) with interaction pseudo-parameters determined by Pitzer and Hultgren [197] from high pressure volumetric data.

320 striking and suggests that these rules are equally capable of codifying the composition dependence of the pseudo-parameters for mixtures belonging to this particular system, in spite of differences in functional form, by suitable adjustment of the interaction parameters. The predicted values of Tc and RTc /Pc using the Van der Waal m m m rule with the Lorentz-Berthelot assumptions (VIII) are comparable with the results obtained using the Van der Waal rule (IV) with empirically specified interaction parameters. Additional sets of pseudo-parameters XI and XII have been specified for the 0.479 methane-ethane mixture in Table 12b. Set XI corresponds to the results obtained with the Barner and Quinlan [15] mixing rules discussed in Chapter IV. Only the rule for Tc m contains an empirically defined interaction constant derived from second virial coefficient data. The entries in Column (XII) correspond to those obtained with the Pitzer-Hultgren rules [Equations (IV-74) through (IV-76)] with the interaction constants obtained from mixture volumetric data in the single phase region above the cricondenbar pressure [197]. The rules for Tc and Pc in this case m m are the same as those for rule (II) in Table IX-10. The differences in the calculated values of Tc and ac for II and XII are significant. m m Interestingly, the results for rule XI based on limited dilute gas volumetric data are closer to the optimum values (I) determined from enthalpy data. b) Ethane-Propane. Table IX-22 indicates that Rules II, III and IV are about equivalent in overall performance. The deviations for the modified Van der Waal rule (V) which takes into account the effect of c~c in specifying the mixing rules for each of the three pseudo-parameters are unexpectedly 0.5 Btu/lb higher than for the simpler and theoretically less appealing Van der Waal rule (IV) More disturbing is the fact that Kay's rule (VI) with the most primitive assumptions in regard to the interaction parameters works better than rule (VIII) with a supposedly more refined estimate for Tc... Furthermore, its performance is superior to almost all the other rules where the interaction parameters are calculated with the additional benefit of enthalpy data.

TABLE IX-13 The Calculated Pseudo-critical Parameters and the PGC Enthalpy Predictions for the 0.763 Mole Fraction Ethane-Propane System Using the Mixing Rules of Table IX-10 TEM!P. (DEG F) PRESS. [PS~IA) AH (EXP T) DEVIATION IN BTU/LB FROMTH EXTAENALYDFRNCFOECHM IG INLET OUTLET INLET OUTLET BTIl/LB I I 1 I II I IV V VI VII VIllI IXX -280. 00 -280. 00 253. 00 0. 0 244q. 5 3 0. 55 0. 39 0.74 0. 74 2. 24 -1. 22 0. 30 -2. 30 3. 27 21 - 280.00 -280. 00 20.00. 00 2 50.00 -5. 90 0.0 1 0. 09 0. 11 0. 13 0. 21 -0. 05 0. 07 -0. 02 0.34.2 -160, 00 -160. 00 2000. 00 O. C 2 1O.C0 -0. 44 -0. 37 -0.01 0. 00 1.55 -1.6,3 -0.47 -2.65 2.55 15 -50. 12 -50. 12 250. 00 0.0 189.4ql -0. 59 -O. 47 -0. 11 -0.11 1.#45 -1. 37 -0. 56 -2.46 2.30 13 -50. 12 -50.'12 2000.0O0 0.0 185. 30 0. 07 0. 23 0.58 0.60 2. 13 -0. 71 0. 13 -1.75 3.01 20 -50. 12 -SO0. 12 2000. 00 100,00 -4.4 3 0. 36 O. 40 0 0 04.2O.3 03.7 04 52. 20 52. 20 250. 00 0. 0 21. 90 1.64 1.35 1.38 1. 32 1.39 1. 44 1.38 1.04 1. 22 12 49. 98 49. 98 500. O0 0. 0 160.54 -0. 09 0. 17 0.61 0.60 2.46 -0. 35 0.07 - 1.79 3.25 23 49, 98 49, ))8 2000, 00 0. 0 161, 70 0. 48 0. 68 1.04 1.04 2.55 0.0C5 0.59 -1.01 3.30 24 102.40 12. 0 25.00 0.0 15. 98 0. 12 -0.05 -0. 01 -0. 05 0.07 0.02 -0. 03 -0. 26 -.. 102.40 102, 40 716. 00 0.0 137.56 -0. 20 0. 29 0.96 0.91 3.73 0. 10 0. 15 -2.17 4.67 34 102 40 102 401000.00 0. 0 143. 34 1.20 1.5.0 1.98 1.95 4. 02 1. 19 1.40 041 47 102. 40l 102.40 2000. 00 0. 0 147 3 3 0. 17 O. 40 0.76 0.76 2.30 -0.09 0.31 -1.2 2 2. 9 7 1 151. 65 151,605 250. 00 0. 0 13, 20 0. 30 0. 17 0, 20 0. 17 0.25 C. 24 0. 19 0.04 0. 16 01 151. 65 151. 65 500. 00 0. 0 30, 24 0.42 0.08 0.1I8 0.08 0.41 0. 27 0.11 -0.38 0. 21 - 151.65 151. 65 10 00. O0 O. C 103. 69 0. 14 -0. 20 0.66 0.38 3.63 0.61 -0. 23 -3. 12 3. 7 3 2 151. 65 151. 65 1200. 00 0. 0 118. 7 1 0.86 1.07 1.69 1. 59 4. 17 1. 24 0. 98 -0. 97 4. 73 37 151. 65 151, 65 1500.00 0.0 125.60 -0.0 4 0. 15 0.62 0.57 2. 55 0.04 0.07 -1.56 3. 12 22 151. 65 151. 65 2000.00 0. 0 132, 18 0.91 1.08 1.48 1.44 3.08 0.87 1.00 -0.50 3.62 28 250, 74 250, 741 250,0 0 0.0 9.60 0.3 1 0. 24 0.26 0.24 0. 30 0. 30 0. 25 0. 16 0. 24 02 250. 74 250, 74 500.00 0.0C 19,90 0. 18 -0. 02 0.03 -0. 02 0. 11 0. 10 0.00 -0.22 -0. 03-02 250, 74 250, 74 1000o00 0. 0 4a3,90 -0. 61 -1.0 2 -0. 87 -0. 99 -0. 50 -0. 69 -0. 98 -1.60 -.7 250. 74 250, 74 1250, 00 0. 0 57. 50 -0.8 5 - 1. 36 -1. 14 - 1.30 -0. 55 -0. 95 -1.31 -2. 2 2 -0 250, 74 250. 74 1500. 00 0.0 70,80 -1. 22 -1.70 -I1.q4l -1. 58 - 0. 53 -1.2 8 -1. 67 -2. 82 07 250,74 250, 74 2000, 00 0, 0 90, 60 -1.31 -1.5 1 -1. 16 -.2.6 -.1 1 2 -.4 00 24, 20 52, 20 250, 00 250,00 157, 46 -0. 59 -0. 11 0. 35 0. 38 2.25 74 -0.24-.79. 82. 20 100, 40 500, 00 500. 00 10 9. 75 -1.69 - 0. 60 -0. 18 -0. 03 1.96 -1. 26 -.8 1 9 3 115. 00 130. 00 716.00 716. 00 64. 04 0. 11 2 -0.80 -1.89 2.58 42 1.0 172 0..1 115,00 130, 00 716,00 716, 00 64,0 4 0. 11 2. 00 2.28 2.58 4.21 1.01 1.72 0.08 6.1 120, 00 1#0Oo00 1000, 00 1000.00 24#,30 0. 27 0.50.3 044 - 1 1 c 0 47 02 0 2 140.00 170.D00 1000.00 1000.00 52, 80 0.81 1. 70 1. 83 1.99 2.83 1. 06 157 14 3.5 160. 00 180,00 1500,090 1500, 00 20.90 -0. 50 -0. 28 -0. 26 -0.20 0.06 -0. 52 -.3 0 8 0 180.00 200. 00 1SOD. 00 1500. 00 2 2. 27 1.06 1.3q4 1. 40 1. 44 1.69 1.t9 13.3 19 200. 00 220. 00 15q0. 00 1500.00 21.98 1.30 1. 34 1. 37.3 1 43 10 133 12 142 220,00 250, 74 2000, 00 2000, 00 29. 66 1.6 2 1. 82 1.88 1. 91 2. 15 1.6R.79 1,6.3 AVERAGE ENTHALPY DIFFERENCE 86.0O.9 10.2 11 22 9 9.9 29 STD. DEV. (BT(J/LB) 321.3 ~320.8 320.4 320.4 318.7 320.7 320.9 321.9 318.1 3 PC (PSIA) 692,1 683,1 681,8 680,3 67 3,3 687 644 647 652 6 R*TC/PC (CC/MOLE) 560,0 566,5 566,8 56B,1 50. 6. 6. 6. 7. ALPHAC 6.31 6.317 6.317 6.317 6.317 6.337 637 637 63 ZC 24 28.284.284.284 ~284.2842 3.284

TABLE IX-14 The Calctlated Pseudo-critical Parameters and the PGC Enthalpy Predictions for the 0.498 Mole Fraction Ethane-Propane System Using the Mixing Rules of Table IX-lO TEMP. (D.G F) PES3S. (PSIA) AH(EXPT) DEVIATinNT IN r\kTIl/C Fpni6 THE EXP'TAI FTHHALPY iTFFENRFCE (JRP, EACH MIXINIG RILE INLET OUTLET INLET OUTLET BTU/LB I II III Iv V VI VI I VIII IX X -240.00 -240.00 2000.00 0.0 226.30 1.16 2.50 2.91 2.99 3.00 0.3C 1.99 -0.99 6.03 603 -125.50 -125.50 130.00 0.0 204.90 0.04 1.36 1.76 1.84 1.86 -.17 0.89 -1.46 4.59 4.59 -125.50 -123.50 2000.00 100.00 -4.40 0.19 0.22 0.22 0.22 0.23 0.10 0.19 0.08 0.50 0.50 37.48 37.48 2000.00 253.00 -1.48 -0.71 -0.89 -0.95 -0.96 -0.97 -1. o -0.85 -0.8 -119 -1.19 37.48 37.48 1000.00 0.0 166.47 -0.70 0. 7 1.10 1.19 1.24 -.23 0.19 -1.62 4.22 4.22 37.48 37.48 2000.00 0.0 165.13 -0.25 1.05 1.46 1.55 1.59 0.06 0.60 -1.24 4. 46 4.46 80.00 80.00 500.00 0.0 153.84 -1.04 0.62 1.14 1.25 1.31 -0. 3 0.09 -1.75 4.60 4.60 80.00 80.00 1000.00 0.0 155.15 -0.56 0.87 1.33 1.42 1.48 0.14 0.38 -1.31 4.62 4.62 80.00 80.00 20C0.00 0.0 155.30 -0.03 1.26 1.66 1.75 1.80 0.43 0.82 -0.87 4.64 4.64 120.00 120.00 250.00 0.0 17.88 0.41 0.76 0.85 0.87 0.86.89 0.71 0.49 0.84 0.84 120.00 120.00 100.00 0.0 142.36 -0.73 0.95 1.51 1.63 1.72 0.46 0.39 -1.27 5.19 5.19 120.00 120.00 2000.00 0.0 145.34 -0.29 1.11 1.55 1.65 1.71 0.41 0.64 -1.01 4.58 4.58 151.10 15110 250.OC 0.0 15.38 0.38 0.61 0.66 0.68 0.67 0.71 0.58 0.44 0.58 0.58 131.10 151.10 500.00 0.0 37.80 0.30 1.10 1.29 1.35 1.31 1.60 1.04 0.61 1.27 1.27 151.10 151.10 750.00 0.0 122.80 1.42 4.85 6.00 6.26 6.41 5.26 3.86 1.43 13.50 13.50 151.10 151.10 1000.00 0.0 129.00 -0.43 1.77 2.41 2.54 2.62 1.56 1.16 -0.72 6.29 6.29 151.10 151.10 1500.00 0.0 134.75 -0.66 1.14 1.64 1.74 1.80 0.71 0.65 -1.11 4.90 4.90 151.10 151.10 2000.00 0.0 137.04 -0.53 1.05 1.49 1.57 1.63 0.55 0.61 -1.03 4.35 4.35 251.10 251.10 250.OC 0.0 10.65 0.24 0.37 0.40 0.41 0.41 0.48 0.36 0.31 0.31 0.31 251.10 251.10 500.00 0.0 22.97 0.02 0.36 0.44 0.47 0.45 0.56 0.32 0.14 0.30 0.30 251.10 251.10 1000.00 0.0 54.97 -0.25 0.88 1.18 1.26 1.24 1.6C 0.74 0.23 1.25 1.25 251.10 251.10 1500.00 0.0 88.95 -1.23 0.68 1.22 1.35 1.38 1.30 0.26 -0.85 3.12 3.12 251.10 251.10 2000.00 0.0 104.50 0.00 1.63 2.12 2.23 2.27 1.93 1.22 0.13 4.25 4.25 48.80 73.80 250.00 250.00 152.53 -1.31 -0.42 -0.08 -0.01 0.06 -1. -0.83 -2.21 3.7C 3.7C 111.90 134.00 500.00 500.00 106.64 -0.65 0.24 0.64 0.70 0.84 -0.69 -0.30 -1.51 5.56 5.56 160.00 180.00 760.00 760.00 52.88 -1.25 3.01 4.44 4.75 4.95 4.01 1.67 -1.07 11.49 11.49 186.00 198.00 1000.00 1000.00 19.30 -0.22 -1.02 -1.07 -1.08 -1.03 -1.61 -1.01 -0.93 0.56 0.56 251.10 300.00 2000.00 2000.00 43.99 1.17 1.32 1.37 1.38 1.40 1.08 1.23 0.96 2.00 2.00 AVERAGE ENTHALPY DIFFERENCE 102.0 STD. DEV. (BTIJ/LR).74 1.53 1.99 2.09 2.15 1.58 1.14 1.10 5,04 4 TC (K) 339.6 338.0 337.5 337.4 337.3 337.8 33k.5 339.4 333.9 333.9 PC (PSIA) 658.5 657.5 656.6 6. 656.6 65.7 662.6 65.7 661.9 631.4 631.4 R*TC/PC (CC/MOLE) 622.1 62n.n 620.1 619.f 620.5 614.9 61H.9 61.6 638.0 63.0 ALPHAC 6.379 6.379 6.37 6.3379 6.3 6.0 6.37 6.4 6.379 6.379 ZC.2?2.282.28?.2.82.22.281.262.261.262.26

TABLE IX-15 The Calculated Pseudo-critical Parameters and the PGC Enthalpy Predictions for the 0.276 Mole Fraction Ethane-Propane System Using the Mixing Rules of Table IX-O10 TEMP. (DEG F) PRESS. (PSIA) LH(EXPT) DEVIATION IN BTU/LB FROM THE EXP'TAL ENTHALPY DIFFERENCE FOR EACH MIXING RULE TNLET OUTLET INLET OUTLET BTU/LB I II III IV V VI VII VIII IX X -200.00 -200.00 1000.00 0.0 217.12 -0.44 0.38 0.61 0.76 -1.60 -I.16 -0.09 -2.07 -2.58 3.28 -150.20 -150.20 2000.00 1000.00 -2.45 1.14 1.21 1.21 1.20 1.13 1.13 1.21 1.15 1.11 1.30 -150.20 -150.20 2000.00 0.0 203.44 0.34 0.93 1.16 1.31 -0.85 -C.4C 0.45 -1.41 -1.84 3.93 1.60 1.60 100.00 0.0 175.06 -0.28 -0.45 -0.20 -0.04 -1.50 -1.28 -0.95 -2.36 -2.51 2.56 1.60 1.60 1000.00 100.00 -1.57 -0.01 0.01 -0.OC -0.01 0.04..2 0.03 0.08 0.08 -0.10 1.60 1.60 2000.00 100.00 -3.68 0.34 0.49 0.48 0.46 0.41 0.42 0.52 0.51 0.46 0.38 127.40 127.40 500.00 0.0 139.13 0.32 -1.05 -0.7C -0.44 -1.33 -1.33 -1.72 -2.89 -2.63 2.88 127.40 127.40 750.00 0.0 140.85 -0.07 -1.08 -0.78 -0.58 -1.41 -1.51 -1.69 -2.83 -2.67 2.11 127.40 127.40 1000.00 0.0 141.86 -0.07 -0.99 -0.71 -0.52 -1.39 -1.4f -1.54 -2.61 -2.49 2.24 127.40 127.40 1500.00 0.0 142.86 -0.37 -0.96 -0.72 -0.55 -1.53 -1.45 -1.45 -2.52 -2.49 1.82 127.40 127.40 2000.00 0.0 143.02 -0.80 -1.39 -1.15 -1.00 -2.00 -1.q4 -1.87 -2.98 -2.98 1.59 203.10 203.10 250.00 0.0 13.71 0.48 0.40 0.43 0.48 0.42 C.53 0.37 0.33 0.40 0.33 203.10 203.10 500.00 0.0 31.71 -0.06 -0.23 -0.15 -0.02 -0.23 0.C? -0.31 -0.41 -0.26 -0.45 203.10 203.10 750.00 0.0 64.56 0.54 -1.62 -1.07 -0.44 -0.84 -0.27 -2.45 -3.06 -1.85 -0.23 203.10 203.10 1000.00 0.0 106.57 0.65 -2.10 -1.60 -1.15 -1.51 -1.60 -2.99 -3.90 -3.13 2.23 203.10 203.10 1500.00 0.0 118.96 -0.30 -1.50 -1.20 -0.97 -1.57 -1.6n -2.10 -3.01 -2.70 1.39 203.10 203.10 2000.00 0.0 122.87 -1.42 -2.40 -2.14 -1.95 -2.63 -2.62 -2.89 -3.77 -3.59 0.30 269.90 269.90 250.00 0.0 10.74 0.29 0.21 0.23 0.26 0.24 0.30 0.18 0.17 0.23 0.14 269.90 269.90 500.00 0.0 23.30 -0.08 -0.24 -0.18 -0.09 -0.21 -0.0V -0.31 -0.37 -0.25 -0.34 269.90 269.90 1000.00 0.0 56.96 0.12 -0.90 -0.66 -0.36 -0.50 -C.19 -1.23 -1.40 -0.87 -0.50 269.90 269.90 1500.00 0.0 89.98 -0.57 -2.20 -1.86 -1.53 -1.82 -1.7C -2.75 -3.30 -2.73 0.01 269.90 269.90 2000.00 0.0 102.20 -0.61 -1.98 -1.70 -1.45 -1.77 -1.77 -2.48 -3.09 -2.68 0.33 140.60 155.35 500.00 500.00 92.90 -0.00 -0.69 -0.62 -0.74 -1.02 -1.7C -1.04 -1.83 -2.06 3.24 210.00 230.00 1000.00 1000.00 30.00 0.25 0.19 0.14 0.01 -0.11 -r.47 0.19 -0.08 -0.44 1.80 240.00 269.90 2COO.00 2000.00 23.94 -1.45 -1.33 -1.34 -1.36 -1.51 -1.53 -1.34 -1.48 -1.57 -1.00 -240.00 -100.00 1000.00 1000.00 70.16 -0.48 0.28 0.29 0.29 -0.50 -2.?2 0.28 -0.21 -0.49 0.32 170.00 210.00 1000.00 1000.00 44.90 0.55 1.90 1.72 1.50 1.12 1.1C 2.16 2.04 1.48 1.44 AVERAGE ENTHALPY DIFFERENCE 86.0 STD. DEV. (BTU/LR) 0.60 1.24 1.05 0.92 1.29 1.26 1.61 2.26 2.07 1.79 TC (K) 350.3 352.3 352.0 351.8 351.7 352.1 352.9 353.4 352.9 348.7 PC (PSIA) 632.0 638.4 638.1 639.0 637.4 642.7 640.3 642.8 643.3 615.9 R*TC/PC (CC/MOLE) 668.4 665.7 665.4 664.2 665.5 660.8 664.9 663.2 662.0 683.0 ALPHAC 6.480 6.444 6.444 6.444 6.444 6.467 6.444 6.467 6.480 6.444 ZC.279.280.280.280.280.279.280.279.279.280

324 The results for rules IX and X are poor when compared with the results for the other mixing rules, particularly for the 0.498 ethane-propane mixture (Table IX-14) where the standard deviation for the enthalpy differences is as high as 5.04 Btu/lb. This tends to confirm our earlier suspicion that the final B.. values for the ethanepropane system as tabulated in Table IX-5 and later used in specifying Tc and RTc /Pc for these rules should have instead been selected to m m m emphasize the values calculated from the 0.498 ethane-propane mixture. On the contrary, however, the standard deviation is lowest for rule VII which uses the very same set of Bij data to specify the parameter Tc m c) Methane-Propane. The summary results in Table IX-22 indicate that, in contrast to our conclusions for the ethane-propane systems, the deviations for rules VII and IX are higher than for all the other rules that permit empirical adjustment of the interaction parameters. The lowest standard deviation on the other hand is observed for rule X which operates on the same set of B data as rule IX. It m is only the differences in the choice of ac that cause the calculated m pseudo-parameters Tc and RTc /Pc, and hence the enthalpy deviations, m m m to differ in the two cases. Differences in the standard deviations for the two rules are particularly significant for the 0.484 and the 0.234 mole fraction methane-propane mixtures as seen in Tables IX-19 and IX-20, respectively. Tn examining the standard deviations for the mixing rules, we observe that, for all but the 0.95 mole fraction methane-propane mixture, there is at least one rule that yields better results than the "optimum" case in column I. When the differences are small, (< 0.1 Btu/lb) they may be rationalized by the fact that the pseudo-parameters in column I were obtained by optimizing on a different set of data. The superiority of the results for rule X in comparison to rule I for the 0.484 and the 0.234 modification methane-propane mixtures is beyond this consideration and leads us to conclude that the pseudo-critical parameters reported for these mixtures in column I are not optimally define d.

325 The predictions for rules II, III and IV are about equally satisfactory, but are again superior to the results for the modified Van der Waal rule (V). Of the methods based on pure component critical properties alone, the predictions for Kay's rule (VI) are considerably poorer than the rest. In the worst case, the standard deviation in the enthalpy differences for the 0.484 methane-propane mixture (Table IX-19) is as high as 7.4 Btu/lb. The performance of the Van der Waal rule with the Lorentz-Berthelot assumptions (VIII) is more encouraging. The standard deviation for this case is only 0.3 Btu/lb higher than for the equivalent case IV where the parameters are calculated using binary data. The results in columns XI and XII in Table IX-19 correspond to the pseudo-critical parameters calculated for the 0.484 mole fraction methane-propane mixture by the Barner and Quinlan [15], and the Pitzer-Hultgren [197] mixing rules using B.. data and high pressure volumetric measurements, respectively. The calculated value of Tc m in XII is in reasonably good agreement with the optimum case (X). Furthermore, as volumetric data are particularly selective of RTc/Pc, one would normally have to conclude that the estimated value of RTc /Pcm using rule XII should be superior to that for rule XI which uses the arithmetic mean rule to calculate Vc and, hence, RTc /Pcm m m m For the same reason, the RTc /Pc value for rule XII should also be m m more reliable than the values obtained for rules that use binary enthalpy data. A comparison between the calculated RTc /Pc values for rule X m m (which provides the best fit to the enthalpy data), rule XI, and rule XII reveals disconcertingly large discrepancies that extend over a span of 20%, with the enthalpy based value of rule X lying in between the volumetrically based values. Such observations do not augur well for the accurate prediction of volumetric data in the supercritical region if the interaction parameters for any given mixing rule are based on second virial coefficient or enthalpy data, and also seem to offer strong evidence that the optimization of pseudo-critical parameters using a single thermodynamic property, no matter how extensive, can be dangerous if e dangerous if we then wish to calculate other thermodynamic properties. The entire picture is somewhat clouded because Joffe and

326 Zudkevitch [117] have disputed the accuracy of the Pitzer-Hultgren parameters [159] for the methane-propane system. Barner and Quinlan [15] have since compared the pseudo-critical parameters Tc and Pc m m obtained from their mixing rules with those of Pitzer and Hultgren for twelve equimolar binary mixtures including mixtures with components as dissimilar as methane- n-butane. In almost all cases, the values of the Barner and Quinlan parameters were close to (within 2%), but generally below, the corresponding Pitzer-Hultgren parameters. However, an unusually high worst case discrepancy of 20% was obtained on comparing the Pc values for the equimolar methane-propane mixture lending further credibility to the arguments of Joffe and Zudkevitch. Furthermore, the standard deviation in the enthalpy difference for the Pitzer-Hultgren parameters (XII) in Table IX-19, is, at 5.15 Btu/lb, considerably worse than the standard deviation of 2.42 Btu/lb obtained for the Barner and Quinlan parameters (XI). This is all the more remarkable because the value of the parameter Tc (to which the enthalpy predictions appears to be most sensitive) for rule XI is as much as 5.5K above that for the best fit case (X), whereas the Tc value for rule (XII) is only 1.5K above that for rule X. d) Ternary Methane-Ethane-Propane Mixture. It must be emphasized that the enthalpy data for this system have been completely ignored in specifying any interaction parameters for the rules investigated. Therefore, except for rules VI and VII, the performance of a mixing rule is, for the first time, more an index of its ability to predict enthalpy data than to fit it. From Table IX-21 or IX-22 it is seen that the best predictions are obtained for rule VII and rule II in that order. The standard deviation in each case is less than 1.1 Btu/lb. With the exception of Kay's rule (VI), whose performance is to be considered poor, the standard deviation over the single phase liquid and gaseous regions does not exceed 2 Btu/lb for any rule. Sample calculation illustrating the application of rules VII, IX and X in calculating the pseudo-parameters for the ternary mixture are presented in Appendix F-7.

TABLE IX-16 The Calculated Pseudo-critical Parameters and the PGC Enthalpy Predictions for the 0.95 Mole Fraction Methane-Propane System Using the Mixing Rules of Table IX-1O TEB~P. (DG F) PRESS. (PSIA) A~H(EXPT) DEVIATION IN BTU/LB FROM THE EXP'TAL ENTHALPY DIFFERENCE FOR EACH MIXING RULE INLET OUTLET INLET OUTLET BTU/LB I I III IV V VI VII ViI -280.00 -280.00 2000.00 0.0 218.70 -0.08 -0.->2 -1.04 -1.31 -1.46 2.32 1.606 -0.12 -1.91 -0.79 -280.00 -280.00 2000.00 250.00 -8.50 -0.90 -Uo97 -1.00 -1.00 -1.01 -0.98 -U.83 -I.Ob -1.14.1.04 -180.00 -180.00 2000.00 0.0 188.10 0.29 -0.10 -0.81 -1.u8 -1.23 2.34 1.77 -0.08 -1.46 -0.55 -180.00 -180.00 2000.00 500.00 -4.10 0.78 0.80 0.85 0.88 0.89 0.62 0.73 0.77 0.78 0.80 -147.00 -147.00 2000.00 500.00 -1.40 0.80.9 1.2 1.08 1.10 0.30 0.54 0.85 0.97 0.93 -147.00 -147.00 500.00 0.9 177.40 -0.64 -1.15 -1.99 -2.32 -2.49 1.83 1.06 -1.12 -2.51 -1.62 -100.00 -100.00 2000.00 800.00 13.00 0.48 1.-2 j*39 2.20 2.34 -1.38 -0.72 1.29 2.00 1.51 -100.00 -100.00 800.00 0.0 144.90 -0.40 -1.43 -2.87 -3.46 -3.72 4.01 2.40 -1.47 -3.28 -2.14 -27.00 -27.90 2000.00 0.0 116.60 -0.12 -0.54 -1.39 -1.78 -1.93 2.52 1.31 -0.29 -1.29 -0.82 -27.00 -27.00 1000.00 0.0 60.30 -0.18 -0.16 -V.07 -0.97 -1.03 2.06 0.67 0.57 0.05 -0.05 -27.00 -27.O90 500.00 0.9 25.90 0.43 0.49 0.35 0.27 0.25 7 0.67 0.76 0.59 0.55 -50.00 -50.90 2000.00 0.0 131.40 0.14 -0.43 -1.33 -1.72 -1.89 2.59 1.69 -0.45 -1.59 -0.98 -50.00 -50.90 1500.00 0.0 118.60 0.87 0.45 -0.55 -1.04 -1.20 4.31 2.61 0.96 -0.24 0.21 -50.00 -50.00 1000.00 0.0 77.10 -0.76 -0.93 -1.91 -2.44 -2.57 3.05 0.87 0.11 -0.87 0.37 -50.00 -50.00 250.90 0.0 12.90 -0.56 -0.52 -0.59 -0.63 -0.63 -0.21 -0.45 -0.39 -0.46 -0.49 91.60 91.M 0 2000.00 0.0 60.90 1.32 1.9 0.76 0.5^ 0.47 2.88 2.01 1.52 1.12 1.1 91.60 91.60 1500.90 0.0 46.60 0.46 0.3 -0.05 -0.21 -0.24 1.44 0.72 0.56 0.29 0.21 91.60 91.60 1000.00 0.0 30.90 -0.16 -0.11 -0.25 -u.35 -0.36 0.66 0.12 0.23 0.09 -0.01 91.60 91.60 500.00 0.0 15.30 0.07 0*o 0.U3 -0.01 -0.02 0.45 0.19 0.24 0.18 0.14 260.00 260.00 2000.00 0.0 32.30 -0.31 -0.37 -0.5tb -0.67 -0.69 0.42 -0.01 -0.20 -0.34 -0.36 260.90 260.00 250.00 0.0 4.20 -0.31 -0.31 -U.34 -0.35 -0.35 -0.21 -0.26 -0.28 -0.30 -0,1 -95.20 -37.50 800.90 800.00 115.10 -0.94 - -3.4b -3.94 -4.17 2.52 1.80 -2.b9 -4.25 -3.05 -166.50 -60.50. 250.00 250.00 221.00 -1.12 -1.63 -2.36 -2.03 -2.79 0.68 U.33 -1.77 -3.06 -2.13 AVERAGE ENTHALPY DIFFERENCE 79.5 STD. DEV. (BTU/LB) 0.64 0.92 1.47 1.73 1.84 2.11 1.28 1.0 TC (K) 201.0 201.5 202.0 202.2 202.3 200.0 200.2 201.7 202.2 201.8 PC (PSIA) 663.7 669.4 671.2 671.2 671.9 670.2 660.8 677.5 679.3 673.8 R*TC/PC (CC/MOLE) 365.3 363.1 363.2 363.5 363.2 360.0 365.3 359.1 359.0 361.0 ALPHAC 5.883 5.877 5.877 5.877 5.877 5.870 5.877 5.870 5.883 5.877 ZC.289.289.289.289.289.289.289.289.289.289

TABLE IX-17 The Calculated Pseudo-critical Parameters and the PGC Enthalpy Predictions for the 0.883 Mole Fraction Methane-Propane System Using the Mixing Rules of Table IX-10 TEMP. (DEG F) PRESS. (PSIA) AH(EXPT) DEVIATION IN BTU/LB FROM THE EXP'TAL ENTHALPY DIFFERENCE FOR EACH MIXING RULE ISLET OUTLET INLET OUTLET RTlJ/ H I II I IV V VI VII VIII IX X -280.00 -283.00 2000.00 0.0 221.20 -1.58 r.66 -0.56 -0. Q6 -1.10 7.97 -.46 3.29 -3.32 -0n. -280.00 -280.00 2000.00 250.00 -8.60 -1.95 -1.91 -1.94 -1.95 -1.96 -1.86 -1.7: -.0n7 -?.l1 -2.?2 -160.00 -160.00 2000.00 0.0 185.50 -0.49 1.22.0 4 -n.36 -0.49 7.05 3.86 2.9? -2.11 -t.' -160.00 -160.00 2000.00 500.CO -5.80 -1.28 -1.32 -1.24 -1.7 -1.20 -1.63 -1.47 -1.31 -1.2 -1.?7 -70.00 -70.00 2000.00 1000.00 11.70 2.44 2.02 2.97 2.76 2.82 -0.15.q 2.32 3.11?.66 -70.00 -70.00 1000.00 0.0 141.30 -1.98 -0. 7 -1.8? -2.41 -2.60 7.68 3.65 n.7 -4.60 -2.04 10.00 10.00 2000.00 0.0 109.20 -1.10 0.7? -1.08 -1.57 -1.72 6.07?.72 1.15 -1.98 -1. 10.00 10.00 1500.00 0.0 89.80 0.06 1.56 0.08 -0.46 -0.62 7.91 3.96 3.02 -0.35 0,39 10.00 10.00 1000.00 0.0 57.60 1.69?.49 1.75 1.47 1.39 5.98 3.48 3.87 2.01 2.11 10.00 10.00 500.00 0.0 27.30 3.26 3.53 3.31 2.22 3.20 4.77 3.79 4.10 3.43 3.49 80.00 80.00 2000.00 0.0 74.70 -0.06 0.87 -0.09 -0.44 -0.54 4.97 2.49 1.78 -n.21 n.14 83.00 80.00 1000.00 0.0 37.10 0.35 0.75 0.39 n.24 0.21 2.57 1.1R 1.48 0.58 0.59 o0 80.00 80.00 250.00 0.0 8.60 -0.02 0.05 -0.02 -0.04. -0.05 0.38.09. 0.21 0.05 0.03 120.00 120.00 2000.00 1500.00 14.40 0.65 0'.7.0 r).51 0.48 1.76 1.39 0.1 0.40 O.'5 120.00 120.00 1500.00 0.0 47.40 0.50 n^.9q n.49 0.30 0.25 3.29 1.70 1.67 C.6,( 0.'9 180.00 180.00 2000.00 0.0 48.40 0.86 1.31 0.85 0.67 0.62 3.46 1.95 1.92 0.38 ].On 180.00 180.00 1500.00 0.0 37.20 0.30 0.65 0.30 n.16 0.12 2.33 1.05 1.23 0.47 n.48 180.00 180.00 500.00 0.0 12.40 -0.32 -0.21 -. 30 -0.34 -0.35 0.32 -0.11 0.04 -0.20 -0.2 -172.00 -34.00 200.00 200.00 248.30+ 3.29 5.10 3.?2 3.40 3.25 10.89 7.92 6.36 1.51.49 -124.00 4.00 500.00 500.00 200.10+ -8.85 -7.31 -8.54 -8.93 -9.06 -1.87 -4.30 -6.85 -10.76 -8.95 -49.40 4.00 1100.00 1100.00 82.CO+ -4.18 -2.3 7 -4.3. -4.79 -4.96 2.41 n. 46 -3.62 -6.51 -.79 AVERAGE ENTHALPY DIFFERENCE 79.5 STO. DEV. (BT(J/LR) 2.65 2.51 2.63 2.74 2.78 5.13 3.12 3.04 3.43 2.76 TC (K) 215.4 214.7 215.6 215.9 216.0 211.7 212.7 215.2 216.6 215.8 PC (PSIA) 665.3 664.6 667.4 668.0 668.4 666.6 652.4 681.9 680.6 672.8 R* TC/PC (CC/MO E) 390.5 389.7 389.8 389.9 389.8 383.1 393.2 380.6 384.0 387.0 ALPC AC 5.961 5.946 5.946 5.946 5.946 5.904 5.946 5.904 5.961 5.946 7C.287.288.288.288.287.288.288.288.287.288 + These values suspected to be in error

TABLE IX-18 The Calculated Pseudo-critical Parameters and the PGC Enthalpy Predictions for the 0.72 Mole Fraction Methane-Propane System Using the Mixing Rules of Table IX-lO ~EMtt. (S!G f) Pi3S. tiSIA) AH(FXPT) DEVIATION IN BTU/LB FROM THE EXP'TAL ENTHALPY DIFFERENCE FOR EACH MIXING RULE INLET ULJLLT iNLiT 0JtT T/L II III IV V VI VII ViII IX X -280.ou -^^ 8 0 2020. 3 0.0 223.80 -0. 0 0.09 -0.60 -0.71 -0.48 12.73 1.73 5. 32 -40 -096 -20.001 -2'0.^ 0' 2 0 250.00 -6.50 -0.08 -0.05 -0.05 -0.05 -0.04 - 32 0. 00 -0.43 -0.07 -0.08 -16o3. 0 -16(j.00 2060 uj 0.0 192.60 0. 92 1.82 1.13 1.01 1.13 12.5r 3.43 5.07 1.22 0.77 -160.00 -lo 00 2000 0 250.00 -5.40 0.37 0.38 0.3 0. 0.40 0.14 0.38 0.19 038 037 -60.00 -60.CO cco. 00 100U.Oo -2.10 -1.33 -1.47 -1.39 -1.38 -1.35 -2.06 -1.6 -1. 13 -1.36 -135 4.0o -o03.C 1009 cO.0 161.70 -1.77 -0.65 -1.43 -1.5 -1. 55 9. 6 1.20 0.98 -1.3 -1.83 4J.Jo 4u.00 2o03. 0 1500.00 12.10 0. 44 0.36 0.44 0.46 0. 55 -1.s 0.31 -0.98 0.0 0.0 40.00 430J 2000 00 250.CO 110.00 -1.84 -0.74 -1.43 -1.61 -1.70 8.38 0.94 -0.11 -1.52 -1.82 -167.00 11 Ou Z00O00 200.00 259.60 -0.63 0.21 -C.44 -0.55 -0.42 10.38 1.77 331 -035 -080 -1.007 55.Oo 5 00.00.00 221. 0 -3.34 + -2.48 -3.08 -3.16 -3. 07 5.58 -0.98 -1.20 -307 -35 n -47.00 79.00 CO.00 1000.00 155.00 -4. 70+ -3.98 -4.42 -4.49 4.33.96 -2.67 -5.01 -4.50 -4.60 -4.00 64.00 1300.00 1300.00 78.00 -6.29 -6.07 -b.1b -6.16 -5.96 -5.11 -5.49 -8.06 -6.25 -6.39 83.00 80.00 2000.00 0.0 103.80 -0.62 0.39 -0.33 -0.45 -0.63 9.88 1.83 2.17 -0.32 -0.55 0. O0 8.00 1500.00 u.0 85.90 0. 59 1.62 0.86b 0.72 0. 48 11.66 3.04 4.34 0.90 0.68 d0.00 80.00 10 0 0.03 0.0 55.80 2.72 3.15 2.79 2.72 2.56. 89 3. 550.86 2.77 10.00 d0.Ov bOo. O 0.0 24.30 1.39 1.50 1.39 1.37 1.32 3.55 1.65 2.51 1.43 1.40 143.00 143.00 1000.00 0.0 39.80 1.86 2.11 1.90 1.8' 1.75 5.53 2.44 3.5b 1.95 1.90 180.00 180.Ou 2003.00 0.0 64.90 0.91 1.54 1.08 1.00 0.83 7.48 2.40 91 1.10 0.98 180.00 ^180. 00.00 0.0 7.90 0. 9 0.21 0. 19 0. 18 0.17 0.68 0.23 0.49 0.20 0.20 300.00 jO0.0 2(00.03. 40.oO -0. 29 -0.02 -0. 23 -0. 7 -0. 38 3.13 0.33 0.& -0.21 -u.24 30J. 0 J00.0 1(CU.0.0 22.cU 0.'59 J. 9 0.60 0.58 0.53 2. 34 0.1 1.38.6 0.60 30J.00 303.0 250.0 0.0 5.50 -0.12 -J.09 -0. 1z -0.12 -0.14 J.3 -0.06 0.05 -011 0.1 AVFRAGE ENTHALPY DIFFERENCE 86.5 STD. DEV. (BTIJ/LB) 2.16 2.05 2.08 2.10 2.02 718 222 341 211 221 TC (K) 247.8 246.8 247.4 247.5 247.6 240.9 245.4 247.6 247.5 247.7 PC (PSIA) 658.3 653.5 655.6 655.9 655.2 657.4 646.1 683.6 657.2 658.3 R#TC/PC (CC/WtLE) 454.1 455.5 455.2 455.2 455.8 442.0 458.1 436.8 454.8 454.0 ALPHAC 6.098 6.102 6.102 6.102 6.102 6.022 6.102 6.022 6.098 6.102 ZC.285.285.285.285.286.286.285.286 + These values might be in error

TABLE IX-19 The Calculated Pseudo-critical Parameters and the PGC Enthalpy Predictions for the 0.494 Mole Fraction Methane-Propane System Using the Mixing Rules of Table IX-1O TEIP. (nEG F) PRESS. (P'SIA) LH(EXPT) DEVIATION IN BTU/LB FROM THE EXP'TAL ENTHALPY DIFFERENCE FOR EACH MIXING RULE * * INLET OUTLFT INLET IJUTLIT BTU/LB I II III IV V VI VII VIII IX X XI X1 -2SO.0C -280.00?OQO.00 0.0 226.20 -0.98 -1.76 -1.11 -3.72 -0.60 13.08 -2.57 5.50 4.78 0.48 3.12 -9.68 -280.rC -2 80.Jc?'Or.OO 250.00 -6.00 0.77 0.75 0.73 0.73 0.75 0.63 0.73 0.61 1.10 0.93 0.62 1.38 -?0.0.0 -20"). 1u0)0Go.0 0.0 211.10 -1.35 -1.70 -1.03 -0.64 -0.53 11.43 -,.53 3.19 4.29 0.46 1.47 -7.86 -149.0 4 -19.0 1(O^.Jo 0.0 198.30 -0.53 -0.72 -0.34 0.35 0.46 11.61 -1.52 3.97 5.10 1.45 1.60 -o.3o -149.00 -149.00 2000.30 250.00 -5.50 0.29 3.29 0.27 0.27 0.28 0.05 0.28 0.14 0.52 0.43 0.17 1.11 -50.00 -50.00?000.00 750.00 -1.93 0.89 0.77 0.72 0.69 0.69 0.28 0.80 1.08 0.64 0.67 1.19 0.73 -50.00 -50.O0 750.03 0.3 173.30 -0.92 -0.70 0.01 0.42 0.53 10.63 -1.52 2.34 4.75 1.48 -0.17 -4.43 50.00 53.00?00.330 1250.CO 2.00 0.16 -0.13 -0.31 -0.41 -0.42 -2.1? 0.03 0.14 -1.18 -0.55 0.75 0.29 100.00 103.00 1500.00 0.0 119.83 -1.57 -0.65 3.40 0.95 1.00 11.87 -1.62 1.29 4.16 1.46 -2.14 -5.45 130.00 150.00 1250.00 1250.CO 21.80 -0.97 -0.36 -0.07 0.10 0.16 2.06 -0.82 -1.10 0.88 0.49 -2.66 0.32 140.00 160.30 1750.00 1750.00 18.90 -0.71 -0.60 -0.55 -0.50 -0.45 0.13 -0.73 -0.92 0.54 -0.35 -1.14 0.82 130.00 130.00 1250.00 750.00 43.10 -3.46 -2.55 -1.85 -1.50 -1.47 4.92 -3.27 -2.04 0.07 -1.28 -5.10 -4.19 110.00 110.00 500.00 0.0 31.40 2.59 2.59 2.87 2.96 2.89 5.79 2.53 4.34 2.15 2.20 3.72 -3.70 -149.00 50.00 200.00 200.00 260.70 -2.05 -2.28 -1.71 -1.36 -1.24 8.82 -3.02 1.94 3.38 -0.13 -0.21 -5.95 152.20 152.20 2000.00 0.0 105.90 -0.68 0.05 0.91 1.34 1.32 10.05 -0.65 1.95 3.08 1.24 -0.96 -5.85 U. 152.20 152.20 1250.00 0.0 76.80 0.19 0.69 1.66 2.10 1.97 11.55 0.21 4.52 2.12 0.91 1.94 -10.69 152.20 152.20 500.00 0.0 25.33 1.25 1.27 1.48 1.55 1.50 3.69 1.22 2.52 1.02 1.02 2.09 -2.96 251.30 251.30 2000.00 0.0 70.80 0.79 1.35 2.01 2.32 2.26 8.49 0.92 3.12 2.74 1.77 1.30 -4.80 251.30 251.30 1750.00 0.0 63.30 0.72 1.11 1.71 1.96 1.88 7.62 0.80 3.22 1.82 1.18 1.69 -5.85 251.30 251.30 1000.00 0.0 36.20 1.68 1.80 2.11 2.23 2.16 5.07 1.71 3.25 1.55 1.53 2.53 -3.41 251.30 251.30 250.00 0.0 8. 60 0.71 0.73 0.78 0.80, 0.78 1.30 0.72 1.03 0.57 0.63 0.92 -0.43 300.00 300.00 23000.00 0.0 59.10 1.96 2.42 2.9b 3.21 3.15 8.00 2.10 3.78 3.19 2.63 2.27 -3.26 -83. 00 104.00 500.00 500.00 226.10 -3.04 -3.01 -2.6J -2.30 -2.11 5.22 -3.73 -1.12 2.99 -0.46 -2.90 -0.77 11.30 137.03 1000.00 1000.00 142.20 -3.65 -3.75 -3.90 -3.82 -3.56 -1.55 -4.18 -4.98 1.47 -1.31 -5.25 6.27 79.30 114.00 1300.00 1330.O0 41.10 2.70 2.34 2.02 1.92 2.01 1.10 2.44 1.67 3.54 2.33 2.99 6.74 AVERAGE ENTHALPY DIFFERENCE 87.3 STP. DEV. (BTU/LB) 1.73 1.72 1.72 1.75 1.69 7.37 2.02 2.91 2.81 1.34 2.42 5.15 TC (K) 289.8 288.7 288.0 287.6 287.5 281.4 289.5 289.5 284.2 286.6 292.1 288.1 PC (PSIA) 645.9 640.0 639.9 638.9 636.9 644.9 644.4 671.5 602.6 619.8 678.5 556.5 R*TC/PC (CC/MOLE) 541.1 544.2 542.9 543.1 544.5 526.3 541.8 519.9 569.0 558.0 519.3 624.4 ALPHAC 6.262 6.284 6.284 6.284 6.284 6.184 6.284 6.184 6.262 6.284 6.184 6.3 ZC.282.281.281.281.282.284.284.282.282.281.24.?? * Using the mixing rules and the binary interaction constant for the pseudo-critical temperature as tabulated by Barner and Quinlan [15]. ** Using mixing rule (III) and the interaction pseudo-parameters determined by Pitzer and Hultgren [197] from high pressure volumetric data

TABLE IX-20 The Calculated Pseudo-critical Parameters and the PGC Enthalpy Predictions for the 0.234 Mole Fraction Methane-Propane System Using the'Mixing Rules of Table IX-1O TF^P. (DEG r) PRFSS. (PSIA) AH(EXPT) DEVIATION IN BTU/LB FROM THE EXP'TAL ENTHALPY DIFFERENCE FOR EACH MIXING RULE INLET OUTLET INLET OUJTLFT BTU/LR I II III IV V VI VII VIII IX X -?i80.00 -280.00 2000.00 0.0 226.90 -1.57 -4.tb -.^ti -~.t7 -2.52 5.97 -s.' 1.,7 2.72 -,.9o -280.00 -280.00?O0O.00 290.00 -6.80 -1.23 -1. 3 -1.3^ -1.^1 -1.53 -1.09 -1.43 -1.2i -0.61 -1.03 -200.00 -200.00 1000.00 0.0 213.10 -1.08 -3.34 -2.46 -1.76 -1.70 5.54 -4.64 0.92 2.30 -0.37 -150.00 -150.00 1000.00 0.0 201.9.0 -0.94 -3.I1 -2.02 -1.52 -1.45 5.19 -4.4C o 2.41 -3.14 -96.80 -96.80 2000.00 250.00 -4.80 0.50 3.50 u.47 0.47 0.30 C.39 J*45..73 0.b5 -96.80 -96.80 2000.00 0.0 187.70 0.25 -1.82 - 1.76 -0.27 -0.28 6.01 -3.IC 1.50 3.66 1.16 -0.00 -0.00 2000.00 500.00 -2.70 0.02 U.08 -0.01 -0.04 -0.16 -0.06 0.13 0.18 -0.00 -0.00 -0.00 -0.00 2000.00 0.0 166.70 0.14 -1.76 -0.72 -0.23 -0.18 5.26 -3.02 o.76 3.44 1.13 100.00 100.00 2000.00 1000.00 1.80 -0.16 -0.03 -0.18 -Q.25 -0.35 -C.44 0.08 0.22 -0.43 -0.32 100.00 100.00 2000.00 250.00 123.20 -1.68 -3.42 -2.40 -1.92 -2.28 2.19 -4.83 -2.22 2.14 -0.14 102.00 178.00 800.00 800.00 104.90 -2.61 -2.u4 -3.11 -3.37 -6.92 -4.44 -L.30 -4.43 1.43 -0.19 12.00 147.00 500.00 500.00 183.50 -1.78 -2.66 -2.58 -2.28 -3.92 0.59 -3.85 -2.42 2.85 0.53 -100.00 83.00 200.00 200.00 242.10 -2.65 -4.78 -3.67 -3.15 -3.28 2.64 -6.18 -1.73 0.96 -1.58 160.00 160.00 2000.00 1000.00 14.60 0.87 1.b7 0.87 0.51 -0.79 -2.10) 2.12 1.34 -0.31 0.48 201.00 201.00 2000.00 0.0 114.30 -0.46 -2.e3 -0.93 -0.35 0.50 4.21 -3.49 -0.90 2.19 0.40 U. 201.00 201.00 1500.00 0.0 106.10 -0.28 -4.15 -0.89 -0.05 1.58 5.23 -3.37 -0.43 1.74 0.16?01.00 201.00 1250.00 0.0 97.10 0.96 -1.54 0.53 1.37 3.21 7.00 -3.21 0.4u 3.02 1.43 201.00 201.00 1000.00 0.0 76.40 0.12 -2.4u -u.08 0.82 4.54 7.41 -3.72 0.75 0.79 -0.45 201.00 201.00 750.00 0.0 49.60 2.01 0.91 1.95 2.j2 4.30 5.44 0.5b 3.06 1.21 1.12 201.00 201.00 500.00 0.0 27.70 0.48 V.10 0.47 0.60 1.63 2.10 0.08 1.27 -0.28 -0.18 251.00 251.00 2000.00 0.0 96.40 -1.02 -2.58 -1.31 -0.77 0.66 3.39 -3.58 -1.18 0.48 -0.73 251.00 251.00 1000.00 0.0 52.40 0.32 -O.o4 U.3o 0.65 2.69 3.74 -0. 9 1.30 -0.'6 -3.58 251.00 251.00 1500.00 0.0 81.70 -1.20 -2.95 -1.45 -0.33 1.29 3.99 -3.97 -1.03 -0.18 -1.L7 251.00 251.00 250.00 0.0 10.10 -0.02 -0.12 -U. 1 u.03 0.34 0.42 -0.11 0.18 -0.^7 -0.22 300.00 300.00 2000.00 0.0 80.30 -0.91 -2.26 -1.j8 —.6u 1.03 3.08 -3.Jb -0.8d 0.33 -u.d9 300.00 300.00 1000.00 0.0 41.90 0.79 6.14 j.7o 1.U4 2.49 3.21 -%.C01 1 0.1. u.ii 300.00 300.00 500.00 0.0 17.70 -1.01 -1.23 -1.u1 -u.93 -0.33 -C.08 -1.26 -;.63 -1.32 -1.^0 300.00 300.00 250.00 0.0 8.60 -0.10 -0.1L -0.J9 -0.o5 0.23 C.29 -U.19 u.uS -0.29 -J.25 AVERAGE ENTHALPY DIFFERENCE 91.1 STD. DEV. (BTU/LB) 1.17 2.25 1.61 1.45 2.48 4.03 3.13 1.52 1.71 0.80 TC (K) 331.5 333.2 331.9 331.3 331.1 328.0 334.7 333.6 327.7 329.8 PC (PSIA) 623.6 627.0 626.1 625.0 642.7 630.4 635.2 646.4 589.9 603.7 R*TC/PC (CC/MOLE) 641.2 641.2 639.5 639.4 621.4 627.6 635.8 622.6 669.0 659.0 ALPHAC 6.430 6.443 6.443 6.443 6.443 6.372 6.443 6.372 6.430 6.443 ZC.279.279.279.279.279.280.280.280.279.279

TABLE IX-21 The Calculated Pseudo-critical Parameters and the PGC Enthalpy Predictions for the (0 369 CH4, 0.305 C~H. 0. 326 CRHR) Ternary Mixture Using the ~ z b' Mixing Rules of Ta51~ IX-10 TEMP. (nFG F) PRESS, (~SI&! DEVIATION IN 8TU/LB FROM THE EXpmTAL ENTHALPY ~H(EXPT) DIFFERENCE FOR EACH MIXING RULE ~11 ~T nJlTt FT INL~:T n~]TLFT OTU/LB I iI IlI IV V VI Vii Viii IX X -~34. c~0 -:~34.q0'00.00 O.O 226.0! -0.82 -0.18 0.41 0.60 0.70 7. 32 -0.76 1.89 4.33 2.00 -P_34.40-234.40 7000.00 tO0.00 -6.Q3 -0.66 -0.81 -0.79 -0.79 -0.77 -C.85 -0.83 -0.90 -0.59 -0.54 -200.00 -?00.OO 250.00 0.0 216.8~) -0.73 -0.12 0.46 0.65 0.74 6.95 -0.70 1.66 3.98 1.97 -700.00-200.00 7000.00?50.00 -6.10 -0.35 -0.52 -0.49 -0.49 -0.46 -0.37 -0.54 -0.61 -0.18 -0.16 -'40.00 -! 6.0. O0 100.00 0.9 202.09 -0.67 -0.18 0.40 0.59 0.60 6.5'~- -0.75 1.14 3.52 1.95 -140.00 -!&O.00 ~000.00 250.00 -5.57 0.14 0.0q 0.04 0.04 -J.q5 0.05 0.05 0.02 0.16 0.18 -60.00 -60.00 500.00 0.0 17Q. 74 -0.65 -0.26 0.36 0.56 0.66 6. 14 -0.88 0.38 2.90 1.99 -~0. O0 -60.00 7000.00 0.0 177.21 0.22 0.54 1.13 1.33 1.43 6.7? -0.05 1.28 3.84 2.80 -!6.04 -]6.04 750.00 0.0!66.v5 -0.26 0.07 0.71 0.93 1.03 6. S6 -0.57 0.21 2.95 2.40 -,6.04 -16.04 ~000. O0 750.00 -0.8~ 0.52 0.48 0.33 0.28 0.98 ~.65 0.64 0.98 1.1! 0.87 52.0& ~2.0'. 250.00 0.0 17.~5 0.82 1.24 1.28 1.31 1.2B 2.3? 1.17 1.54 1.13 0.93 ~.04 57.04 1000.00 0.0 139.59 -0.25 0.22 1.05 1.34 g. 73 1.45 -0.61 -0.12 2.83 2.9~ K2.04 57.04 1250.00 0.0 142.61 0.05 0.54 1.26 1.52 1.61 8.2C -0.20 0.39 2.98 2.98 ~2.04 ~?.04 7000.00 0.0 146.20 0.20 0.59 1. 17 1.37 1.45 6.96 0.01 0.79 2.90 2.52 ~0.00 qO.00 250.00 0.0 14.06 0.51 0.87 0.90 0.93 O. qO 1.55 0.81 1.11 0.74 0.59 90.00 "0.00 1250.00 0.0 127.4c~ -1.13 -0.37 0.52 0.86 0.95 7.-9% -1.32 -0.97 1.90 2.17 RO.00 ~0.00 ~000. O0 0.0 136.61 0.11 0.59 1.21 1.43 1.51 6.72 -0.05 0.61 2.75 2.53 I00.00 tO0.00 250.00 0.0 13.71 0.43 0.74 0.77 0.8C 0.77 1.36 0.69 0.95 0.61 0.49 100.00 100.00 500.00 0.0 ~0.00 0.65 1.54 1.65 1.73 1.67 3.36 1.36 2.06 1.28 0.95 1 00. O0 100. O0 1250.00 0.0 112.40 -1.91 -0.75 0.22 0.60 0.66 8.81 -1.80 -1.38 1.04 1.52 100. O0 I00. O0 1500.00 0.0 121.53 -0.64 0.25 1.06 1.37 1.44 7.89 -0.61 -0.09 2.10 2.28 O0 lO0. O0!00. O0 2000.00 0.0 124.00 -0.14 0.#8 1.11 1.34 1.39 6.44 -0.17 0.39 2.29 2.16 L~ 124.20 126.20 250.00 0.0 12.39 0.44 0.71 0.7~ 0.76 0.74 l. 23 0.67 0.87 0.58 0.49 bO!26.20 126.20 500.00 0.0 27.02 0.54 1.26 1.32 1.37 1.32 2.62 1.15 1.76 0.99 0.69 126o 20 126.~0 750. O0 0.0 45.7K 0.56 1.93 2.13 2.26 2.18 5.7)8 1.66 2.70 1.52 1.18 126.20!26.20 ~00.00 0.0 59.36 0.77 2.69 3.00 3.19 6. g4 3.08 2.23 3.53 2.06 1.73!26.20!26.20!000.00 0.0 6g.3! -0.17 2.14 2.66 2.94 q.2~. 2.~32 1.43 2.82 1.57 1.~8' 2~. 20!_76.20 1t00.00 0.0 79.19 -0.68 1.72 2.40 2.74 2.63 o. 19 0.85 2.15 1.46 1.51 126.20 126.20 1500. O0 0.0 105.54 -1.07 0.51 1.19 1.49 1.46 7.60 -0.29 0.67 1.24 1.15 126.20 126.20 YOO0. O0 0.0 118.06 -0.59 0.16 0.84 1.09 1.14 6.44 -0.57 -0.27 1.68 1.78 160.00 160.00 ~50.00 0.0 10.51 -0.13 0.11 0.13 0.15 0.13 0.53 0.08 0.25 -0.03 -0.09 160.00 160.00 500.00 0.0 22.86 -0.03 0.5/4 0.60 0.65 0.61 1.68 0.44 0.90 0.32 0.11 160. O0 160.00 1000. O0 0.0 53.10 -0.#4 1.09 1.30 1.45 1.35 4.37 0.75 1.81 0.49 0.18!60.00 1~0.00 1250.00 0.0 70.43 -1.09 0.83 1.25 1.49 1.38 6.14 0.25 1.57 0.50 0.26 laO. 00 160.00 1500.00 0.0 85.07 -1.63 0.10 0.67 0.94 0.88 6.42 -0.61 0.45 0.27 0.23!AO. O0 ]60.00 ~000. O0 0.0 tOY. OR -0.95 0.18 0.75 0.99 0.48 5.91 -0.~8 0.03 0.89 0.95 to?.00 192.00 _750. O0 0.0 9.67 O. 14 0.35 0.38 0.~0 0.38 9.78 0.31 0.44 0.23 0.20!QT.00 192.00 500.00 0.0 20.42 0.20 0.69 0.74 0.78 0.74 1.62 0.61 0.99 0.48 0.31 1~2.00!42.00 1000.00 0.0 ~4.79 -0.17 0.98 1.16 1.27 1.70 3.5C 0.72 1.50 0.54 0.29 ~ ~2. O0 ~92.00 t500.00 0.0 70.70 -0.7# 0.86 1.22 1.42 1.33 ~.41 0.38 1.49 0.~3 0.41 lo?.00 1~?. O0 ~000.00 0.0 ~9.44 -1.19 0.12 0.60 0.83 0.7~ 5.~6 -0.~7 0.26 0.35 0.44?&O.00 260.00 2~0.00 0.0?.95 0.22 0.39 0.40 0.41 0.~9 0.64 0.36 0.48 0.27 0.22?mO. O0 260.00 1000.00 0.0 4t.96 0.52 1.30 1.39 1.45 1.40 2.81 1.16 1.67 0.90 0.73 260.00 260.00 [500.00 0.0 51.96 0.39 1.59 1.77 1.9C I. 82 4.32 1.32 2.14 1.08 0.93 2&O.00 260.00?000.00 0.0 66.92 -0.57 0.56 0.90 1.07 1.03 4. ~R O. 13 0.74 0.42 0.54 -I!'~. ~0 z, ~. O0 ~'50.00 ~50. O0 2~0.40 -1.61 -1 57 -1.02 -0.86 -0,73 4.21 -2.09 -0.72 2.15 0.94 0.~0!07.~0 7~0.00 750.00 153.77 -1.86 -3.30 -2.87 -2.81 -'). 5q -?.60 -3.60 -~.24 0.04 0.09 e~.00 110.00 1250.00 1250.00 I~.R! -0.14 -0.81 -0.86 -0.d9 -O. R4 -C.1% -0.63 -0.88 -0.17 -0.18 AVERAGE ENTHALPY DIFFERENCE 83.3 STO. DEV. (BTU/LB! 0.76 1.06 1.24 1.38 1.37 5.41 1.03 1.~7 1.B3 1.44 TC IK) 288.4 288.4 287.8 287.6 287.5 283.9 289.0 289.6 287.1 286.2 PC {PSla) 654.3 668.6 665.8 665.6 663.8 665.0 670.3 684.6 651.7 642.0 R~TC/PC {CC/MOtE! 531.8 520.3 521.5 521.3 522.4 515.0 520.2 510.1 531.5 535.0 ALPHAC 6.245 6.236 6.236 6.236 6.236 6.192 6.23b 6.192 6.2a5 6.236 ZC.284.284.284.28z~.284.285.284.285.285.2 ~z.

TABLE IX-22 Summary of the PGC Enthalpy Predictions for the Mixing Rules of this Investigation FN\THALP_ Y )FVIATIONS IN (BT/L) H SYS TF MIXING R I IHLFS nP-. II III IV V VI VII VIII IX CHL-C-,Hj 1 7 1.89 1,9? 19?I l 23,5 2.20 2.'3 1.^ C2H6-C3H8 0.71 1.26 1.9 1.39 1.90 1.?Q 1.23 1.82 3.35 3 3 TERN2RY 0.76 1.06 1.24 37 5.41 1.03 1.47 1.83 1.44

334 Critique of Mixing Rules;While no mixing rule is consistently superior in performance for every system considered in this investigation, the Pitzer-Hultgren rule (II) appears to work best on an overall basis. However, as the rule has little, if any, theoretical basis, it is difficult to forecast a similar degree of success in applying the rule to other multi-component systems. The fact that rule VII provides the least deviation for the ethane-propane system and the ternary mixture, and rule X provides the best results for the methane-propane system suggests that the basic approach for calculating mixture pseudo-parameters as a function of composition from a set of extensive second virial coefficient values for the same mixture (synthetically generated if necessary) is fundamentally sound. The three separate techniques encompassed by Rules VII, IX and X for the practical implementation of the same basic scheme were developed and tested to determine if any one approach was consistently superior. The inconclusive nature of the results suggest that further work is needed to refine the technique. It is, however, still unclear whether the relative performance of the mixing rules based on binary enthalpy data can be indisputably evaluated from the results of this investigation. The fact that Kay's rule (VI) works better for the ethane-propane system than other rules with empirically determined interaction parameters (see Table IX-22) clearly indicates that our procedure for specifying these interaction parameters is not yet optimally defined. The fact that the enthalpy predictions for rule V in Table IX-15 are, for example, poorer than for rules III and IV, even though the Tc and RTc /Pc values in the m m m former case are closer to the "optimum" values in I appears to confirm this conclusion. Furthermore, the fact that rules IX and X yield relatively poor results for the ethane-propane system, a system for which the fundamental assumptions used in deriving the rules are least questionable, suggests the possibility that the optimal averaging of the B.. values for these rules is yet to be achieved. Tn retrospect, such inconsistencies could have been avoided if the more time consuming but less uncertain approach of specifying the interaction parameters for each mixing rule by optimizing the fit to the enthalpy data for all mixtures of a binary system taken together

335 were utilized instead. In effect, such a scheme optimizes the three separate mixing rules involving various combinations of the pseudoparameters simultaneously. In particular, the scheme has the added flexibility of permitting the optimum value of the parameter ac.. to vary from rule to rule even when the quadratic mixing rule for Oc is common to many different sets of rules in Table IX-1O. m The analysis of mixing rules based strictly on pure component critical properties is more straight-forward. In general, their performance degrades as the size and energy parameter ratios for the constituent pure components of a mixture depart from unity. 7or example, Kay's rule would appear to be inadequate for enthalpy predictions on mixtures whose components are as dissimilar as methane and propane. The Van der Waal mixing rule with the Lorentz-Berthelot assumptions (VIII) appears to be preferable to Kay's rule, particularly for the prediction of the ternary mixture enthalpies. The results in Tables IX-4 through IX-6 suggest, however, that the Redlich-Kwong rule with the harmonic mean assumption for Tc.. and the arithmetic mean assumption for (RTc../Pc..), has the potential to do as well, even iJ ij though it was not included in Table IX-1O. In comparing the pseudo-parameters and the standard deviation in the enthalpy differences for rules VIII and X in Table IX-21 and rules I and X in Table IX-19, it appears that equivalent low deviations can be produced for substantially different pseudo-parameter sets. In particular, large variations (upto 5%) in the value of RTc /Pc are m m permissible. This appears to conflict with the highly specific and accurate definition of the optimum pseudo-parameters obtained from the enthalpy data for ethane. The decrease in the specificity of the optimization in going from pure components to mixtures may be explained by the fact the data in the vicinity of the critical point, and information on the precise location of the vapor pressure curve that are so useful in selecting the parameters for pure components are inaccessible in the case of mixtures because the pseudo-critical point and the pseudo-reduced vapor pressure curve lie deep within the excluded two phase region. The only alternative to improve the optimization in such cases would be to simultaneously use as many thermodynamic properties as are required to unequivocally define the three desired

336 pseudo-parameters. Notwithstanding our reservations about the theoretical validity of the one fluid corresponding states model for mixtures, and the imperfections in the technique used in this work for specifying the binary interaction parameters from enthalpy data, one can conclude that the enthalpy behaviour of complete binary systems in the single phase region can, for engineering purposes, be adequately characterized as a function of composition in the PGC framework using almost any mixing rule where the interaction parameters are empirically adjusted from limited enthalpy data on the same system. Furthermore, the application of these rules to multi-component systems also appears to be adequate and does not require the use of additional empirical parameters. It is important to emphasize that these conclusions are, for the present, restricted to non-polar systems whose extreme components are not more dissimilar than methane and propane in terms of the ratios of their respective size and energy parameters. Illustrative Contour Plots for Some Enthalpy Prediction and Correlation S chemes The performance of selected correlations over the entire P-T range of measurements is succinctly illustrated in the contour plots of Figures IX-4 through IX-8 for ethane, the three ethane-propane mixtures, and for the ternary mixture respectively. The deviation at any P and T is, in each case, expressed by the experimental minus the calculated enthalpy departure. The reduced virial equation, the PGC with optimum pseudoparameters, and the PGC with pseudoparameters defined by rule VII of Table IX-10 were tested in every case. The reduced virial equation uses Equations (V-30) and (III-44) to define the reduced second and third virial coefficients respectively. The enthalpy departure is calculated using relevant thermodynamic identities in Appendix H-3. The optimum pseudoparameters were used in each case to illustrate the limitations of the range of applicability of the method without introducing the additional uncertainties imposed by mixing rules. The application of the technique was restricted to the gas phase and to the dense fluid above the critical temperature. The

337 truncated virial equation appears to be satisfactory at least upto 500 psia. Its reliability at higher pressures increases as one moves towards the right of the heat capacity maxima. A comparison between the performance of the PGC using optimum pseudoparameters and that obtained with rule VII is a measure of the extent to which the representation of individual mixture enthalpies in a corresponding states framework is degraded by further codifying the results as a function of composition through a mixing rule. The Starling BWR was tested for its ability to represent the ethane enthalpy data using a set of constants provided by the author [249] that were determined primarily by interpreting the volumetric data of Sage and coworkers [209]. The calculations were, however, not extended below -70~F because of calculation errors introduced by this author in applying the technique in the cryogenic liquid region. The ternary mixture enthalpies were compared against six methods including the Rice Properties III [81], the Starling BWR [254] and the Johnson-Colver [118] correlations, all of which are discussed in Chapter III. These three additional methods were already evaluated by Starling et al. in a previous comparison study [253]. However, the "experimental" enthalpies used in the study were actually obtained from a preliminary PGC fit to the basic data and the comparisons have therefore been repeated using the correct results. This author is at present not familiar with how much or what type of constituent binary data was utilized by Starling in applying the above three methods to the ternary mixture. Certainly, the enthalpies for the methane-propane binary were available for some time before the study was initiated. In any case, the PGC predictions using mixing rule VII is seen from Figure IX-8 to be superior to all these methods. We may therefore conclude that the prediction of multi-component mixture can be more fruitfully accomplished if constituent pure component and binary enthalpy data are used in the prediction scheme.

338 VIRIAL EQN. (THIS WORK) OPTIMUM PARAMETERS (.001 CH,,996C2H,.003 C3H,) 2000 I I +.110 NOT APPLICABLE / d=O::3<~~~~~~ \\\IZ-Z 0<1 1 5<1d1<8 r""""5 O0ldl<l 500 - 2'Idi5 -250 -150. -50 50 150 250 TEMPERATURE (*F) PGC (OPTIMUM PARAMETERS) BWR (STARLING) (.0 CH4, 996C H,.003 C 3H (.001 CH,.996C2H6,.003 C0H6) 20001~r-1~\~1 ~ ^ ^) ~ ^^ ~ f'xW ^ 20C~1 + - - 500', + / 1F \1I / COMPARISONS 1' I INTHIS + W cn REGION Figure 1X-4. The Performance of Some Corresponding States Techniques -250~in Calculating the Enthalpy Departure for 0.996 Ethane.TEMPERATURE F(F TEMPERATURE (IF) Figure IX-4. The Performance of Some Corresponding States Techniques in Calculating the Enthalpy Departure for 0.996 Ethane.

339 VIRIAL EQN. (THIS WORK) OPTIMUM PARAMETERS.763C2H6(C2H6-C3H8) 2000 ] --''.. NOT APPLICABLE;i IN THIS REGION \ 0c n\ 3\ Deviatlon d ( AH -O Hc ),6T U/lb LLooo - _d:0 I + 1 / - 8< d-<50 Z^ ^ ~- <ldl<2 500 - / 2d) i 50<dPha fl \\\\No Comparison -50 - 50 - 50 50 150 250 TEMPERATURE (~F) PGC (OPTIMUM PARAMETERS) PGC (MIXING RUL VI I OF THIS WORK).763C2H(C2H6- C3H8).763C2 H(C H6- C3H) 200 2000 / e *I \ \ \/ -Z ~~ ~^50 -1~ ~50 5 ~ 150 ~ 250 - 1500 -150 -50 50 150 250 TEMPERATURE (~F) TEMPERATURE (~P) Fraction Ethane-Propane Mixture. \ a 500 o \ 250........ 250 250 _ -150 -50 50 50 250 -50 -150 -50 50 150 250 TEMPERATURE (F) TEMPERATURE(~FI Figure IX-5. The Performance of Some Corresponding States Techniques in Calculating the Enthalpy Departure for the 0.76 Mole Fraction Ethane-Propane Mixture.

340 VIRIAL EQN. (THIS WORK) OPTIMUM PARAMETERS.498 C2H6(C2 H6-C3H8)?00I NOT APPLICABLE 1500- 2<d5 -230 -150 -50 50 150 250 TEMPERATURE (F) PGC (OPTIMUM PARAMETERS) * PGC (MIXING RULE VII OF THIS WORK).498C2(H6C2H6-C^H8).498C2H6(C2H6-C^H8) on=Fraction Ethane-Propane Mixture. / 5.0 -250 -150 -50 50 150 250 TEMPERATURE (TF) 52000 ~ igr IX6 00h P o omn in"~N C a h parisotng t 20I F o a n i W1000 - L, 1000,~oo I + I 0 — I 0 -250 -150 -50 50 150 250 -2 -150 -50 50 150 250 TEMPERATURE (~F) TEMPERATURE (IF) Figure IX-6. The Performance of Some Corresponding States Techniques in Calculating the Enthalpy Departure for the 0.50 Mole Fraction Ethane-Propane Mixture.

341 VIRIAL EON. (THIS WORK) OPTIMUM PARAMETERS.276 C2H6(C2H6 -C3 H) 2000 - - - - ~ ~r1 - i1500 -o NOT APPLICABLE IN THIS REGION In N i000 _'~ * ) DevloItn d:(a H,8AHa~),BTU ib Zn / ~+ " 2o~~tttl 8cl1d1<50 Two Phase I-\Dt~~~~~''Eff~~~~~~~~.... No Comparilon - 50 -150 -50 50 150 250 TEMPERATURE ("F) PGC (OPTIMUM PARAMETERS) PGC (MIXING RULE V II OF THIS WORK).276 CH6(C2H6-C3 H).276 CzH6{C2zH8-C3He) 20001 2000 - ~\ ~~~/ -~~~/ F ~2500 -150 -50 0 15 Z5+ 1500 o o) +000 + 1000, 500 50... 0 t -150 -5o 50 150 250 -250 -150 -50 50 150 250 -150 TEMPERATURE TEMPERATURE ( TEMPERATURE (F) Figure IX-7. The Performance of Some Corresponding States Techniques in Calculating the Enthalpy Departure for the 0.27 Mole Fraction Ethane Propane Mixture.

_) /4 VIRIAL EON. (THIS WORK) R a0) OPTIMUM PARAMETERS ( a) OPTIMUM PARAMETERS (b).P(;C PMI. RUOE Vl THIS MK (.369CH,.307C2gHe,.324C,H,) (.369CH4, 307CH,, 324CSHe)'+1, 2000. g } T - 2000 \ I \/ \ + I / 150oo- 1500 + |IN THIS REGION + |,IoooO -,oo - d -_, \ "', 3C -24Co-) -... \,o -I-5 -50 50 IS0 250 -2 0 -15 -50 50 150 250 TEMPERATURE (F) TEMPERATURE (F) (c) PGC(OPTIMUM PARAMETERS) (d) RICE PROPERTIES m (.369 CH,.307C,H..324C H.) (.369CH,,.307C, H,.324C$H,) 2000 I I2000 - B'(H. I 1500 ^5 ) 0 S 250i!i 150 \ /Z0 I +./. ~100 — ISO0 No - prlioo o OT I -50 -IO5 -50 50 150 2S0 -250 -50 -50 50 150 250 TEMPERATURE (IF) TEMPERATURE (IF) JOHNSON-COLVER REDUCED CORRELATION ~(e) 369tH C6WR (SCARLINGI (f) (.369CHR,.37t(H,R, 324C,R*I,*w {.369 CH,.3057C2H.324CCHI) 2000 0 2000 -250 ~ -ISO~ -50 50 250 -2 150' - ~~-25o -0 o, 5wo R eo t250 -250 -o150 -503690 250, TEMPERATURE (IF) TEMPERATURE (IF) Deayltbn:d=(aHp-&Ha,,), BTU/Ib -- 5-1d1'. e<ldl<e E2 oldl,< Figure IX-8. The Performance of Some Enthalpy Prediction Techniques with Respect to the Ternary (0. 369 CH, 0. 305 C2H6, 0.323 C3H8) Mixture.

Chapter X SUGGESTIONS FOR FURTHER RESEARCH Specific suggestions for further improvements with respect to various aspects of this investigation have been distributed throughout the text where appropriate. The discussion in this chapter is primarily meant to provide the reader with an overall perspective of various courses for further research as suggested by this study. a) Suggested Improvements for the Operating of the Existing Facility. As the experimental investigation of this work was essentially conducted on a production basis, it was difficult to continuously monitor the precision of the measurements. Under optimum operating conditions, it is believed that the accuracy of the measured enthalpy change can be increased to better than 0.2%. The care and effort necessary to achieve these conditions will undoubtedly require a much longer investment in time and energy per investigation as evidenced by the painstaking work of Manker [162]. The high degree of inertia present in the existing facility, coupled with its enormous maintenance requirements, makes its continued operation prohibitively expensive. Accordingly, the establishment of a less complex facility characterized by minimum valving and quick response is recommended. Notwithstanding the severity of the operating problems in the present faciltiy, the fortunate use of high flowrate has, in the ultimate analysis, prevented the quality of the measurements from being severely compromised. If, however, the continued operation of the existing facility is necessary, then the following improvements are recommended. 1) Assuming that all system variables such as temperature, Pressure, flowrate and compositions at the calorimeter inlet are steadily maintained, a minimum wait of at least sixty minutes, after the intial addition of power to the calorimeter, is recommended to achieve quasi-steady state conditions. 2) During the course of a run, at least one data point, and preferably the first, should be repeated at a significantly different flowrate to evaluate the contributions due to unsteady state and heat 343

344 or mass leaks at the calorimeter. Furthermore, a set of chronologically dispersed replicate measurements should be obtained for some arbitrarily chosen data point to monitor undesirable and otherwise undetectable changes in instrument calibrations or calorimeter operation. 3) As indicated in Appendix F-4, the calculation of the system composition will be more accurately accomplished in the face of composition variations of about 1% or more, if the system fluid is chromatographically analyzed along with two pre-calibrated mixtures differing slightly in the mole fractions of the individual components, instead of the one pre-calibrated standard currently used. 4) The control of the calorimeter and the pre-conditioning baths for operating temperatures below -1500F was seriously disrupted by the periodic replacement of 50 litre liquid nitrogen dewars. It is felt that larger dewars with a capacity of 150 litre or more, providing a steady liquid nitrogen flowrate, would provide a smoother operation. 5) A high precision differential pressure transducer with a measurement range from 0 to 500 psid at pressure levels upto 2000 psia, with a repeatability of better than 0.1% full scale and negligible hysteresis would, in conjunction with the transduer calibration facility, serve to increase the accuracy of the isothermal and isenthalpic measurements. A similar transducer with 1% precision in the range 0 to 5 psid could be used to record the small pressure drops obtained for the isobaric measurements. If all the variables involved in the measurement of composition and flowrate can be similarly transduced to provide an electrical output, then all the critical measurements could be obtained on a high precision (0.01% or better) automaticswitching, self-balancing potentiometer with provisions for direct recording of the data. Such measures would reduce both manpower requirements and human error. 6) The contamination of the valve manifold for the differential pressure transducer calibration manometer due to mercury blowback may be controlled by the installation of a differential pressure gauge (for example, Item 14f, Appendix D) between the gas and the mercury legs for each section of the manometer, permitting the mercury level in the latter case to be more accurately estimated. The use of pressure snubbers to check surges in the mercury filled legs is also

345 recommended. b) Suggestions for Improving the Interpretation of the Basic Data. Although the non-linear least squares regression technique was rejected in favor of the Lagrange polynomial representation of the thermal properties Cp and ~, its attractiveness could be enhanced if it were possible to separately fit the measurements on either side of the peak for a given isobar or isotherm while ensuring the continuity of the function Cp or d and the appropriate first derivative at the peak itself. Two separate polynomial expansions on either side of the peak each incorporating a gaussian term appear to be eminently suitable to meet these requirements. For example, the isothermal throttling coefficient Q may be represented along an isotherm by the functional forms a + b(P - Pk) + c(P - Pk)2 + d(P - Pk)3 + fg e < k (X-la) - f(P - Pk)2 a' + b'(P - Pk) + c'(P - k)2 + d'(P- Pk) + f'ge P Pk (X-lb) The requirement of continuity in the value of ~ at the peak, F = Pk leads to the restriction a + fg a a' + f'g' (X-2) The requirement ( ) = 0 (x-3) P=Pk must be satisfied by Equations (X-la) and (X-lb) separately, and leads to the restriction b = b' = (X-4) Additional polynomial terms may be added as necessary. Asymmetry in the peak region may be obtained by adjustment of the ratio f/f' away from unity. This is advantageous, because the presence of peak

346 asymmetry was noted for both the isobaric and isothermal data of this work. Sirota et al. [244] have also confirmed that the Cp maxima along isobars are steeper on the liquid side near the critical temperature, pass through a point of symmetry, and appear at higher temperatures to be sharper on the gas side. c) Suggestions for Further Experimental and Correlative Research. 1) The enthalpy departures for the propane reference table in the PGC were found to be in error at 150K (near 0.4Tr for propane). The error was traced to a misprint in the zero pressure tables for the function [H(T) - H(0)]/T as compiled by the American Petroleum Institute [220], and used in conjunction with the data of Yesavage [284] to establish the reference table. If the value of the function is changed from 8.14 cal/gm mole K to 8.44 cal/gm mole K, so as to be consistent with the [H(T) - H(0)] tables from the same reference, then the performance of the correlation may be improved in the vicinity of 0.4 Tr for all other substances also. 2) It is suggested that the PGC correlation for the enthalpy departure featuring the ac dependent reduced temperature parameter be extended to include the prediction of other thermodynamic properties including the volume and the heat capacity departure, Cp - Cp~. Although separate reference tables may be used to represent each property, the development and use of a precise equation of state to represent the reference fluid properties over the range of the calorimetric investigation of this work affords a more concise alternative and provides a consistent set of smoothed thermodynamic properties, not assured in the tabular approach. It is, however, doubtful whether any PVT equation of state currently used in engineering design calculations can provide a precise fit to the heat capacity departures for light hydrocarbons over the entire fluid phase. The problem may, perhaps, be more fruitfully tackled by concentrating future efforts on the development of a thermal property equation of state expressing Cp - Cp~, or (, or even the property Y in Equation (I-1) as a function of temperature and pressure. Most thermodynamic properties may then be obtained with little loss in precision, by integration rather than differentation of an equation of state.

347 3) Calorimetric measurements involving enthalpy traverses into, and across, the two phase region for a mixture of fixed overall composition rarely, if ever, specify the quantity and composition of the individual phases. As such information is necessary for the prediction of total mixture enthalpies by most techniques, two phase enthalpy data are consequently ignored in most comparative studies. It is urged that each enthalpy prediction method be accompanied by a technique for the estimation of phase equilibria to permit the extension of such comparisons into the two phase region. In particular, as the phase predictions for techniques based on the corresponding states principle depend on the derivatives of the various pseudo-parameters with respect to composition, (See reference [206] for further information), the analysis of two phase data has the potential of being far more selective of mixing rules than single phase data alone 4) The success of the modified reduced temperature parameter Tr 00 in decreasing the contribution of the perturbation term (Br - Br ) in 00 Equation (V-30), when compared with the equivalent term in other reduced second virial coefficient correlations [159,195] that use the unmodified reduced temperature Tr as the correlating parameter suggests that it may also be useful in correlating higher order virial coefficients. The availability of the precise third and fourth virial coefficient data of Douslin [67] on CH4 and CF4 makes this a feasible venture, but additional measurements below 1.5Tr are also desirable. 5) The accurate estimation of the second virial coefficient from the critical properties of a pure substance and vice-versa, is a crucial factor in the performance of the pseudo-critical parameter calculation technique as encompassed by rules VII, IX and X (See Table IX-10) developed in the work. In particular, if the range of the second virial coefficient correlation used in such calculations can be increased, then it may be possible to increase the range of the B data used to optimize the pseudo-parameters for such rules. In turn, one would expect to obtain a more selective set of optimum parameters, particularly for rules IX and X. The form of Equation (V-35) with n expressed as a function of Tr is suggested as a starting point for extending the correlation expressed by Equation (V-30) so as to cover the range 0.5 < Tr < 20. Additional

348 second virial coefficient measurements are necessary if such a correlation is to be used with confidence. Accurate low temperature data on n alkanes (Tr < 0.7) would be especially useful in resolving inconsistences in the current data in the literature. Measurements at high reduced temperature (Tr > 3.0), particularly in the vicinity of the maximum in B for substances whose ac values are significantly different from the simple fluid case, as for example, CF4, would be very useful in defining the slope term dBr/dac in this region. 6) The discrepancy between the optimum pseudo-parameters of Yesavage [284] and those of Pitzer and Hultgren [197] obtained for individual methane-propane mixtures from wide-ranging thermal and volumetric data, respectively, suggests that the methane-propane system should be completely reanalyzed from the standpoint of the pseudocritical method. The pseudo-parameters for the individual methanepropane mixtures should be recalculated using the enthalpy data sets in Tables IX-16 through IX-20, as they are believed to be more selective than the original set of enthalpy data used in the optimization. The consistency test in Figure IX-6 should then be repeated with the new set of parameters to determine if any change in behaviour results from the reinterpretation. It is possible that the discrepancies may have occurred because the reference enthalpy tables of Yesavage [284] or Powers [304] were not consistent with the volume tables of Curl and Pitzer [54]. Ideally, therefore, both volumetric and enthalpy data should be separately interpreted in thermodynamically consistent schemes, if we wish to determine whether the correlation of any one of the two properties in a corresponding states framework is sufficient to accurately predict the other. It is also possible that the Pitzer optimization was not selective enough because the volumetric data were optimized over the restricted range from 40~F to 4600F. For better selectivity it is recommended that additional PVT measurements be obtained in the liquid phase from -2500F to +40~F and used in the optimization. In fact, Huang, Swift and Kurata [110] have already obtained some data in this region. - everal possibilities could be investigated if the PGC were extended t:o include the correlation and prediction of volumetric propert:i..es. I irst lv, tle exItsting volumetric data alone could be used

generate interaction parameters. These parameters could then be tested for their ability to predict the enthalpies of the methanepropane system. The revised pseudo-parameters based on the optimization of enthalpy data alone could also be used to predict the volumetric behaviour of the methane-propane system. It would also be interesting to determine whether the addition of second virial coefficient measurements to enthalpy data is of any significance in influencing the optimization to yield a set of pseudo-parameters that would improve the fit to the rest of the volumetric data over the entire fluid phase. Lastly, a multi-property optimization using enthalpy, volumetric and second virial coefficient measurements should be attempted to determine if a single set of pseudo-critical parameters can be defined without compromising the goodness of fit relative to the situation where each property is optimized separately. In essence, it is hoped that such a study would provide us with a better idea of the type and extent of experimental measurements that are necessary to accurately characterize a system of two or more non-polar substances in the one fluid corresponding states framework when their size and energy parameters are appreciably different. 7) The new set of interaction constants for the methane-propane system could then be used to reexamine the performance of the various rules in predicting the enthalpies for the ternary mixture. S) Instead of using the body of enthalpy data on hydrocarbon mixtures now accumulated under the sponsorship of the NGPA and the API merely for the purpose of testing prediction methods, one can incorporate such information directly into the prediction techniques themselves. The enthalpy departure of an unknown mixture m, can be expressed in terms of the enthalpy departure of a reference mixture s at the same temperature and pressure by the relation H - -H(T,P)m H - H~(T,P) H -[H - H-(T,P) (X-5) A judicious choice of the reference mixture s, i.e., one whose pseudo-critical parameters are close to that for a given mixture, can serve to significantly decrease the contribution of the contribution second term on the right hand side. As any error involved in the first term

350 is only limited by the accuracy of the data on the reference mixture, any uncertainties involving the adequacy of either the specific corresponding states framework selected, or the particular mixing rule utilized, apply only to the prediction of the second term. The success of the method depends, of course, on the extent and reliability of the data on the reference mixtures, and the availability of a reference whose components and pseudo-critical properties are similar to that for the unknown fluid. Even then, any incentive to develop such a method for practical use would depend upon our ability to accurately codify the properties of the reference mixture in concise form. The advantage of this technique, however, is that we are not subjected to the restrictions imposed by the corresponding states approach in representing the reference mixture properties in concise form. One potential application of the technique involves the use of the methane-propane mixtures containing 0.946 and 0.883 mole fraction methane, respectively, as standards for predicting the properties of natural gas mixtures. For example, if we were confronted with determining the enthalpies of a mixture containing 0.92 mole fraction CH,, 0.01 mole fraction C2H6 and 0.07 mole fraction C3H8, we would use the 0.946 methane-propane mixture as our reference. The second term on the right hand side of Equation (X-5) may be evaluated in one of two ways. In the first case, one may evaluate the term using the PGC framework with the pure component reference tables and some specified mixing rule (not necessarily involving empirically determined interaction parameters). In a different approach, both the 0.946 and the 0.883 mole fraction mixtures may be used to define a new set of reference data in the PGC framework replacing the original tables. The calculation may then be repeated as before. 9) In the continuing search for the utopian mixing rule, one is at first tempted to develop and test as many mixing rules as possible. For example, another modification of the Van der Waal mixing rules, similar to rule VIII of Table IX-IO, may be developed using the general procedure outlined in Appendix G if the criterion in Equation (V-19a) is replaced by the condition (92P/9V2)T = 0 at the critical point. The result is given by

351!/2 1/2 Tc 3(atc - 1) 2 n n Tc 3(ac - 1) -) m T _xx [{ 3~ } - i- 1 (X6) Pc Li c eC X j PC e 3 ofC Pcac o c ix j e Pij ij T c2 tcz 1) 2 n n Tct (tci(X)7 M' ij_' - 3 (x-7) P C acI3 PC ZX cij Pc m cm ii= j1 ij ij Similar rules involving the effect of ac could be developed starting with the reduced Redlich-Kwong equation of state. As long as the interaction parameters are empirically adjusted to suit individual rules, one cannot anticipate significant differences in their performance, unless perhaps such rules are applied to systems where the critical properties of the constituent pure components are markedly different, as for example, in the methane-octane system. To complicate the analysis further, an additional degree of freedom is contributed by the specific corresponding states model used. For example, the entire investigation in Chapter IX could be reworked using the two fluid model. It is clearly questionable whether the repetition of the entire process for other systems, as more data becomes available, is of any real fundamental value to our understanding of the problem. Although statistical thermodynamics is not yet competitive with empirical methods in predicting the configurational properties of real substances, it has advanced enough to permit us to evaluate mixing rules and corresponding states models with little ambiguity for simpler systems, such as Lennard-Jones molecules, because the interaction parameters in such cases can be unequivocally specified. The differences between the various mixing rules and the corresponding states models can, as we have seen in Chapter IV, be accentuated by careful choice of the molecular parameters for the pure components; a luxury that one rarely obtains in working with real systems. Although one must be careful in extrapolating such results to real systems of interest, the fact that such models approximately simulate real fluid behaviour permits us, at least, to reject those rules that perform poorly. It is this author's opinion that further research in this area has considerably more potential for improving our fundamental understanding of the application of the corresponding states principle to real systems than our success or failure in representing real data with empirically adjusted mixing rules.

352 10) The use of the pseudo-critical technique for the correlation of the thermodynamic properties of fluid mixtures suffers from one serious drawback in that the mixture parameters, unlike pure component critical properties, are not subject to direct experimental verification. Consequently, values ascribed to such parameters by indirect techniques often depend upon the type and range of the data analyzed, or on the specific corresponding states framework used. The trajectories of characteristic curves in the P-T plane common to both pure components and mixtures have been traced on reduced coordinates by Brown [30]. These include the Joule-Thomson inversion curve, [(dH/dP)T = 0], the Boyle curve, [(dz/dV)T = 0], and the locii of the heat capacity maxima [(dCp/dP)T = 0, or (d(Cp - Cp~)/dT) = 0]. Characteristic points of special interest include the Boyle temperature Tb in the dilute gas, and the maximum in the Joule-Thomson inversion curve in the dense fluid. An experimental program to map such locii for selected pure components and mixtures would provide incontrovertible evidence in regard to the validity of the corresponding states principle particularly for the mixed systems so mapped. Such measurements would also permit the correlation of the thermodynamic properties of mixtures to be anchored to unequivocally defined parameters. By restricting the degrees of freedom in this manner, it may be possible to make more meaningful improvements in existing correlations.

APPENDIX A Sample Calibration Results for Various Instruments Used in Obtaining the Basic Measurements 353

354 TABLE A-1 National Bureau of Standards Calibration for the Reference Cell FORM NBS-70 (3-67) U.S. DEPARTMENT OF COMMERCE NATIONAL BUREAU OF STANDARDS INSTITUTE FOR BASIC STANDARDS WASHINGTON, D.C. 20234 REPORT OF CALIBRATION UNSATURATED STANDARD CELL Manufacturer: Eppley Laboratory Inc. Cell No. 650924 Submitted by The University of Michigan Research Administration Building Ann Arbor, Michigan 48105 The electromotive forceof thiscellat 24 ~C was,at the time of test, 1.01880 volts. This value, correct to 0.005 percent, is the mean of a series of measurements concluded April 23, 1969. The stated uncertainty (0.005%) includes an allowance of ~ 50 microvolts for variability in the emf of the cell during test. This is an unsaturated cell of the cadmium sulfate type, suitable for work requiring no greater accuracy than 0.005 percent. Such cells have a temperature coefficient that is negligible within the ordinary range of room temperature. Rapid changes in temperature may, however, produce temporary alterations of several hundredths of one percent in the electromotive force. Precautions in using standard cells: (1) the cell should not be exposed to temperatures below 4 ~C, (2) abrupt changes in temperature should be avoided, (3) all parts of the cell should be at the same temperature, (4) current in excess of 0.0001 ampere should never pass through the cell, (5) unsaturated standard cells should be recalibrated at intervals of a year or two because the electromotive force of an unsaturated cell usually decreases with time. For the Director, Institute for Basic Standards Walter J. Harer. Date: April 24, 1969 Chief, Electrochemistry Section Test No.: 211.02/198463 Electricity Division Ref. No.: R 101443 USCOMM-DC 37289oP67

355 Table A-2 Callendar Equation Constants for the New Platinum Thermometer. U.S. DEPARTMENT OF COMMERCE NATIONAL BUREAU OF STANDARDS INSTITUTE FOR BASIC STANDARDS WASHINGTON D.C. 20234 REPORT OF CALIBRATION PLATINUM RESISTANCE THERMOMETER SERIAL NO. 586 SUBMITTED BY UNIVERSITY OF MICHIGAN CHEMICAL AND METALLURGICAL ENGINEERING THIS THERMOMETER WAS CALIBRATED FOR USE WITH CONTINUOUS CURRENT OF 1.0 MA. THROUGH THE THERMOMETER. THE FOLLOWING VALUES WERE FOUND FOR THE CONSTANTS IN THE INTERNATIONAL PRACTICAL TEMPERATURE SCALE (1946) FORMULAS: ALPHA - 3.9261045-03 A - 3.9846691-03 DELTA - 1.4916703 B = -5.8564536-07 BETA -.1101008 C - -4.3229875-12 FOR T > 0 DEGREES 0, BETA - C - O, BY DEFINITION. THE PERTINENT INTERNATIONAL PRACTICAL TEMPERATURE FORMULAS ARE GIVEN IN THE DISCUSSION ON THE FOLLOWING PAGE. THE RESISTANCE AT 0 DEGREES 0 WAS FOUND TO BE 25.5548 ABSOLUTE OHMS. DURING CALIBRATION, THIS RESISTANCE CHANGED BY THE EQUIVALENT OF.0008 DEG C. THIS THERMOMETER IS SATISFACTORY AS A DEFINING STANDARD IN ACCORDANCE WITH THE TEXT OF THE INTERNATIONAL PRACTICAL TEMPERATURE SCALE. FOR THE DIRECTOR, INSTITUTE FOR BASIC STANDARDS HARMON H. PLUMB CHIEF, TEMPERATURE SECTION HEAT DIVISION TEST NO.639288 COMPUTED JUNE 1968 JLR/UNIVAC Temperatures on the International Practical Temperature Scale of 1948 (IPTS-L8) between -182.97 ~C and 631.5 ~C are defined by the indications (resistance values) of standard platinum resistance thermometers together with either of the following formulas. Rt R (1 + At + Bt2 + Ct3 (t-100)) t 0 or, t (-R-) + ( 1-1t, -) 100 + a t( -1) (t)3 where t is the temperature, at the outside surface of the tube protecting the platinum resistor, in ~C on International Practical Temperature Scale of 1948 and R and R are the resistances of the platinum resistor at t~ and 0 OC, respectively, measured with a continuous current through the platinum resistor. The value of this current, together with the constants A, B, and C for the first form of the equation, and a, 6, and B for the second form of the equation, is given on the previous page. The formulas are completely equivalent, the choice between them concerns only which form is less difficult to calculate.

356 TABLE A-3 Sample Regression Results for the Six Junction Copper-Constantan Thermopile 6M Temp. Measured Calculated Difference (OK) Emf Emf (Microvolts) (Microvolts) (Microvolts) Error T E -1 83... - -.j 9 3 0. 4..-t2 _ 3 12 _-I 3.t,, - 5i bqf. - 5198z,.-. 3;.7 -9.1 2 -ioO.:'..) -?'J o.'~ -2?b:/.! ~.7 -03,,1 -~S ). 3O -; 5 1L-.' - 14. - 5. -.4 ) 12 -L.JJ. 35'. 0 -2 3; 4. ) -2033. -3 319 -d.}O - f 6 i d 1.')O - L 6 7 7 76, - 4.7 1:, 24 t- _ 0... 2 _- L 2 9536, 7_..___.. ~- 0.- 7 7.' -8875.9 -I,1 2 ~' 2 -20 *0 - -.i.4. 5 - 55 4" J. t 1 2.3 0.4 2.* 8+. 956 2?u 0 4775.0 477.1 - 7....0. 57 ~,. (O 97b1 9757.1 3.9 J.,4 61.. _. _____ 4.0 14942. _2_ _.4 0 94 _...... 80. 00 2 322.' 20317.5.5 3.5 22 00C.j. CO; 2 b 3.68 0 25872. -4,9 ) 19 1 20. 0 31593.0 31599. 0 -6. u - 19 14'0. C0 37484.0 3748, 1 -2. 1 -i. 1 60.0^ 43530.0 43525.3.7.3 1 1 PERCENT STD. DEVIATION = 0.21 14 NBS Calibration ** Calculated using the Equation: E = 1.9179 + 233.271T + 0.27651T2 - 0.22361x10-3T3 + 0.62684x10-7T4

357 TABLE A-4 Original National Bureau of Standards Calibration for the Fifteen Junction Thermopile FORM NBS-497F (7-65) U.S. DEPARTMENT OF COMMERCE NATIONAL BUREAU OF STANDARDS INSTITUTE FOR BASIC STANDARDS WASHINGTON. D.C. 20234 REPORT OF CALIBRATION THERMOCOUPLE COPPER CONSTANTAN (15 junctions) (Tagged #2) Submitted by The University of Michigan Ann Arbor, Michigan Electromotive Force as a Function of Temperature of Measuring Junction (reference junctions at 32~F) Degrees F* Absolute Degrees F* Absolute Degrees F Microvolts Degrees F Microvolts -166 -54995 + 32 0 122 30800 212 64665 *In this table Degrees F is defined as 9/5x"C (Int. 1948) + 32. The uncertainty in the above values is: ~0.2 OF A discussion of uncertainties inherent in thermocouple calibrations is given in National Bureau of Standards Circular 590, Methods of Testing Thermocouples and Thermocouple Mlaterials. A True Copy August 11 1969 For the Director, Institute for Basic Standards NMcB /s/ Harmon H. Plumb Harmon H. Plumb Test No. 197667 Chief, Temperature Section Completed: January 23, 1969 Heat Pivision JAW:dh

358 TABLE A-5 NBS-497F Repeated National Bureau of Standards Calibration for the Fifteen Junction Thermopile U.S. DEPARTMENT OF COMMERCE NATIONAL BUREAU OF STANDARDS INSTITUTE FOR BASIC STANDARDS WASHINGTON. D.C. 20234 REPORT OF CALIBRATION THERMOCOUPLE Copper Constantan (15 Junctions) (Tagged #2) Submitted by University of Michigan Ann Arbor, Michigan Electromotive Force as a Function of Temperature of Measuring Junction (reference junctions at 32~F) Absolute Absolute Degrees F* Absolute Degrees F* Absolute ^DegreMicrovolts * Microvolts -297.13 -79856 -166.00 -54988 32.00 0 300.00 100316 *In this table Degrees F is defined as 9/5 x 0C (IPTS-68) + 32. The uncertainty in the above values is: ~0.2 OF A discussion of uncertainties inherent in thermocouple calibrations is given in National Bureau of Standards Circular 590, Methods of Testing Thermocouples and Thermocouple Materials. All temperatures in this report are based on the International Practical Temperature Scale of 1968, IPTS-68. This temperature scale was adopted by the International Committee of Weights and Measures at its meeting in October, 1968, and is described in "The International Practical Temperature Scale of 1968," Metrologia, Vol. 5, No. 2, 35 (April 1969). For the Director, Institute for Basic Standards Test No. 199778 J Completed: September 26, 1969 Chief, Temperature Section JAW: MJP Heat Division U SCOMM- C 22429-P89

359 TABLE A-6 Calculation of the Fifteen Junction Thermopile EMF at Uncalibrated Temperatures by Comparison with a Calibrated 6 Junction Thermopile 6M 61 E6M1 E M E 15 ES Temp 15 15(td) 15 - td) StdE )6 6 15 15 A B ~C (>v) (iv) (jv) (jv) (yv) -183. -78927 -1095 -1024 -79856 -160, -73215 -960 -900 -73155 -130. -62850 -781 -737 -62807 -11.0. -628 -54988 -100. -50845 -610 -578 -50813 -80. -41952 -492 -455 -4191D -60, -32390 -365 -342 -32367 -40, -2?192 -247 -225 -22170 -20. -11392 -127 -110 -11375 0. 0 0 0 0 20. 11937 132 11 11916 40. 24402 252 223 24373 50. 304.5 30800 60. 37360 356 3 28 37333 80. 50805 450 425 50780 100. 64670 515 510 64670 120. 78982 578 578 78982 140. 93710 650 645 93705 148.88 671 100316 160. 100882 705 710 100887 E6M is the Emf of the 6 junction thermopile 6M, the calibration results for which are indicated in Table A-3. EStd is the Emf for a single Cu/Constanan thermopile as tabulated in [184]. El5 is the Emf of each of the 15 junction thermopiles used in this work. Column A is obtained by considering the calibration data for the 15 junction thermopiles of this work as indicated in Tables A-4 and A-5. Column B is obtained by interpolating the results of Column A plotted in Figure A-l.

200 2O Difference Curve with Respect to N.B.S. Tables for 15 Junction Cu/Constanton Thermopile 100 0 0 - x a. -a H Iv x Using Equivalent 15 Junction Calibration for 6 Junction Thermopile (6M) i^-100 o Using NBS Calibration Data for -IOOC / ^~~~~~~~~~~~~~15 Junction Thermopile (1) -200 -1000 -800 -600 -400 -200 0 200 400 600 ^ 800 DIFFERENCE IN MICROVOLTS Figure A-1. The Interpolation of the Emf Values for the Fifteen Junction Thermopile Using Detailed Calibration Data on a Six Junction Thermopile

361 TABLE A-7 Least Squares Fit of EMF vs Temperature for the Fifteen Junction Thermopile Temp. Emf Calculated Difference % Emf (~K) (Microvolts) (Microvolts) (Microvolts) Error T E l 8 2 *.8 5 7.-9 8 i6.U7. 9, _ s _ _ Sa _.. -160. 0 - 3 55.0 - 7 Oc..8 -0.O 1 l -1 30.C tO - 2 80 7. -52 81 9.6 12 Z -. ) -1.00 - 499. ) -5'4987.7 -7.3 ) 13 -1.J') -318L au.. -580'3. i-1.0.. 0 20 -80. T 0 -41 9 i 5.5 4). -I. L. l e....-b o._h -12157~.jl~__...._- _.^.3.a^..... _...~........3..2.-.____. i3.... -40. C -22171.. -22174.3.3 - -20.0 -1135 -i 1 37. I- 1378.8 3.8 - 33 C. 0 1 5.8 ]..9 3.9 6b. 5 4 2(. 0 1 91 b. 112 3,8 -7, -0.05 4*: 1.00 (b 4 373.; 24 378. 4 -5.4 -. 022 5,'3 j... 0.8.(..._3 C 7..,,. 4 9 +... 60. 0 37333. j 37335.4 -2.4 -3. 80.C0O 50780. 50 770.9 9.1 J.018 I 0. 0 0o4670.0 6662.2.8 12 IC0,00 b46'5,0 6462.2 28 0.0.04 12 J.00 / 898 i 2. i 7i 8 7.:3 -5.3 -.. C. 07 1460.00 t ) " 8 3. 57.2 512.7. j ^l ib,C 1, C) 7t. 2 1 7 PEfkCEN~T STL.,LEVIATION = 3.3192C) * Obtained from Table A-6 ** Calculated using the Equation: E = -3.887 + 582.78T + 0.691T2 - 0.54565x10-3T3 + 0.253876x10l-T4

362 TABLE A-8 Sample Flowmeter Calibration Results for the Ternary Mixture TABLE OF RESIDUALS RKU NO X VALUE Y VALUEj Y ESTIMATE RESIDUAL PLERR (F/0) (pAP/UF) (-Yest) (Y-Yest) (/100) o.o 0.0032340 U.16103 0.16012 0.00u91 0.568 1.0 0.00CsO148 0.11808 0.11824 -0.03016 -0.134 2:(.0 0.00083092 0.11796 0.11815 -0.00019 -0.161 2..0. 00118b5 0.12908 0.1911 -0.00003 -0.023 Z4.0 0.0015112 0.12874 0.12899 -0.00025 -3.197 2-.0 0.0022499 0.14115 C.14091 0.00024 0.168 6.0 C.0022640 0.14121 0 0.14115 30006 0.040 ~7.0 0.00Ob625 0.14806 0.14833 -0.00027 -0.183 2c.0 0.002t057 0.14819 0.14839 -0.00020 -0.135 2i.0 0.0029143 0.15293 0.15328 -0.00035 -0.228 31.0 3.00Z89b7 0.15262 0.15296 -0.00034 -0.?23 3. 0.0006703 0.11586 0.11594 -0.00008 -0.070 3 U.0 0.0028620 0.15197 0.15222 -0.03025 -3.167 3.0 0.0028510 0.15166 0.15200 -0.00034 -0.224 3',.0 0.002~615 0.15412 0.15425 -0.00013 -0.083 35.0 0.0024250 0.14399 0.14398 0.00001 3.006 30.0 0.0024388 0.14445 0.14422 0.00023 0.162 37.0 C 0021296 0. 13930 C.13887 0.00042 0.304 3'.0 0.0021392 0.13912 0.13904 0.00008 3.059 4t.u0 0.0013908 0.12704 0.12714 -0.00010 -0.078 4.0 u. 014052 0.12727 0.12736 -0.00009 -U.068 41.0 0.0010167 0.12143 C.12138 0.00004 0.035 42. o C.CO1 009 0.12104 0.12114 -0.00009 -0.078't3.0 0.0017624 0.13314 0.13291 0.0O 022 0.1 o8 44.0 u.0017648 0.13308 0.132)5 0.00012 0.093 4~5.0 0.002174 0.14234 0.14208 0.00026 0.183 4.0.0 0.002J317 0.14229 0.14215 0.00014 0.097 4'.0 0.0027C92 0.14930 0.14922 0.00007 0.047 4 c. 0 0.002/216 O. 14943 0.14946 -0.30003 -0.021 4'.u 0.0029013 0.15298 0.15301 -0.00004 -0.324 5.0 0.0028925 0.15259 0.15284 -C.00025 -0.163 5%.0 C. 00to240 O0.11543 0.11520 0.03023 0.196 )3.0 0.00254 1 0.14654 0.14649 0.00005 0.034 4.0() C.0025587 0.14648 0.14639 0.00009 0.061 56.0 J.0013748 0.12672 0.12689 -0. O01b -0.133 6(., o.0021150 G. 1.3867 0.13863 0.00004 O.029 L. C C.OC00C410 0.11570 0.11547 0.03023 0.198 t.0 0.0006392 0.11553 0.11545 0.00008 0.371 t.04 0.0 U02. 047 0.15423 0.15431 -0.00006 -0.051 (c. C.0013875 0.12687 0.12708 -0.03022 -0.173 t(.O 0.0017533 0.13273 0.13277 -0.00004 -0.031 cb.O u.001 445 0.13264 0.13263 0.00001 0.006 t(. 0. 022 398 0.14082 C. 14074 0.00008 03.35 l.0) u.u)02^ 254 0.14057 0.14049 0.00008 0.057 PERCtNT AV. DEVIAT IUN = 0.12014 s ae min. micropoise lb ** Units are (-t-)(in. H20)/(micropoiseIlb /min) + From Calibration Equation Y = 0.10454 + 18.30116X - 2330.416X2 + 0.61398x106X3

363 TABLE A-9 Calibration Results for Mansfield and Green Dead Weight Gage PRuska M&G P RIHSKA DEAD M & ( DEAD CALCUL(JATFI)* WT. GA(;E WT. GAGF CALI,. FON. PR ESSJIR E PRFSSIR E PR ESStUR E ( PS I G(P ) ( PSI) (PS G) 264.8 264.6 264.8 537.8 537.4 537.8 961.1 960.6 961.2 960.0 959.4 960.0 1472.1 1471.4 1472.1 1461.5 1460.7 1461.4 2106.? 2105.0 2106.1 Calibration Date Dec. 16, 1969. Calibration Equation P P = P +.49x10 (P &G + 0.1 psi + Calibration Standard Dead Wt. Gage

363 TABLE A-9 Calibration Results for Mansfield and Green Dead Weight Gage PRuska M&G P RIHSKA DEAD M & ( DEAD CALCUL(JATFI)* WT. GA(;E WT. GAGF CALI,. FON. PR ESSJIR E PRFSSIR E PR ESStUR E ( PS I G(P ) ( PSI) (PS G) 264.8 264.6 264.8 537.8 537.4 537.8 961.1 960.6 961.2 960.0 959.4 960.0 1472.1 1471.4 1472.1 1461.5 1460.7 1461.4 2106.? 2105.0 2106.1 Calibration Date Dec. 16, 1969. Calibration Equation P P = P +.49x10 (P &G + 0.1 psi + Calibration Standard Dead Wt. Gage

365 TABLE A-1.l FORMNBS-580 National Bureau of Standards Calibration of 200 Inch Steel Tape (10-14-64) U.S. DEPARTMENT OF COMMERCE NATIONAL BUREAU OF STANDARDS WASHINGTON, D.C. 20234 NATIONAL BUREAU OF STANDARDS REPORT OF CALIBRATION 300-Inch STEEL TAPE Maker: The Lufkin Rule Co. NBS No. 13872 No. Submitted by The University of Michigan Department of Chemical and Metallurgical Engineering Ann Arbor, Michigan 48104 This tape has been compared with the standards of the United States, and the horizontal straightline distance between the terminal points of the indicated intervals have the following lengths at 680 Fahrenheit (20 OCelsius) when subjected to horizontally applied tensions and conditions of support as indicated below: Supported on a horizontal flat surface: tension, 10 pounds Interval Length Interval Length (inches) (inches) (inches) (inches) 0 to 1 0.999 0 to 150 150.002 7 6.997 160 160.001 10 9.995 170 170.007 20 20.006 180 180.007 30 30.003 190 190.001 40 40.004 200 200.013 50 50.001 210 210.006 60 60.007 212 212.004 70 70.006 220 220.006 80 80.005 230 230.006 90 90.008 240 240.010 99 99.005 250 250.007 100 100.005 260 260.007 110 110.007 270 270.008 120 120.010 280 280.008 130 130.006 290 290.005 140 140.004 300 300.004 The length values given above are not in error by more than 0.006 inch. The average weight per inch of this tape ribbon is 0.0008372 pound. Test No. 212.21/G-38740 Date:'March 11, 1968 USCOMM-DC 26106- P64

366 TABLE A-11 (CONTINUED) Report of Calibration continued Page 2 300-Inch Steel Tape NBS No. 13872 The average AE value of this tape is 88,200 pounds, where A is the crosssectional area of the tape ribbon, and E is Young's Modulus of Elasticity. The terminal points of the indicated intervals are defined as the centers of the graduations nearest the observer when the zero graduation is at his left. The length of the indicated intervals when the tape is suspended vertically from a point above the desired interval with a weight attached to the free end can be computed from the length of the interval on a horizontal flat surface and the change in length (AL) due to the effective change in tension. The total effective change in tension is equal to the weight attached to the free end, the weight of the blank ribbon below the zero graduation (0.0042 pound), the weight of the finger ring (0.0078 pound), plus one half the ribbon weight of the interval, minus the tension applied when the tape was supported on a horizontal flat surface (10 pounds). However, if the attached weight is 10 pounds when the tape is suspended vertically, the length of the 300-inch interval will increase by only 0.0005 inch. Therefore, the lengths of the subintervals when suspended vertically are not stated in this report. If the attached weight is not 10 pounds, the effective change in tension should be recomputed and the change in length determined by the following expression: AL = (effective change in tension) x (length of interval)/AE. For the Director, J. J. S. Beers Acting Chief, Length Section Metrology Division, IBS Test No. 212.21/G-38740 Date: March 11, 1968

367 TABLE A-12 Sample High Pressure Transducer Calibration Results a) Least Squares Regression Results HIGH PRESSUPE TRANSOUCER CALtBRAlION S-T APRIL 179) Observation Pressure, Ph at Measured Output Calculated Percent Dead Wt. Gage Eb/10 ("v) Output Error (psig) (i) 70.0,7,1 47F 04 0.13649E 34 0.13654: 04 -0.36633E-01 7?.n J.1 00n F 04 0.119 62F.4. _01954E 04 0.^584, E-0l 74.(, n.P')rqOF 03 0.95654E 03 0.9557E 0 3 0,78586E-C1 76.n J.31686b C3 0.37540F 03 0*37583E 03 -0.11407E 00 78.'! (.?1281F 03 0.25103E 03 0.25111E 03 -0.32806E-nl 80.0 0.21.65r4r 4 0.25903E 04 0.25902E 04 0.16023E-02 82.0 C(. n0'3E C4 0.23930E 4 0.04 0232.18711E-01 P.4. ( n.l1989r 04 0.19121E 04 0.19119E 04. 13585E-C1 8,.6 0,.13778[ 04 10.16468F 04 0~.16470E 04 -0.1485iE-01 88.0 0.11 79E C4 0.13953E 04, 13956E 04 -0.23745E-C1 90^.(' ^.1. 3E C4 O.12006E 04 0.12008E 04 0120-0.17000F-01 92.0 n.( P20E 03 0.72592E 03 0,72499E 03 0.12763E 00 71. r0.? 1 247F 04 0. 13437E 04 0.13438E 04 -0.47420E-02 7~... 1046E C4 0.12004E 04 0.12000E 04 0.39556E-01 75.f'".n ) 1POE 03 0.95728E 03 0.95699E 03 0.30655E-01 77. n.?. 65E 03 0.35125E 03 0.35160E 03. -0.IC092E 00 70.":.21351[E 3 0.25187E 03 0.25195E 03 -0.32320E-01 81.r, r.?lt338E 04 0.25882E 04 0.25,83E 04 -0.55183E-02 9. r'.l.I-Q.77t- 04 0.23897E 04 0.23895E 04 O.10942E-C1 P6.( 0. O 1_Uo[r 04 0.19243E 04 0.19251E 04 -0.3766RE-01 88.~( 0-.1-7q22E ) 4 0.16642E 04 0.16643E- 04 -0.63082E-02 9g.. f.11713E 04 O.13989E 04 0.13997E 04 -0.53351E-01 97."' n).1.'O 4[ 04 0.12038E 04 0.12040E 04 -0.18171E-01 TABLE A-12 b) Interpolated Results from The Calibration Equation Ph E h/lO (Psig) (v) 200. 3') 235.76 "'. ) ) 355.62 400.'3 475.48 5' or-.)) 5.0 33 6,~.'" 715.17 7 C0. ) 83 5. 0) 0nn."' ) ~ c4.4 P ct, I.',3 1074.65 1(QO..\). \ a 1 14.46 o 110.'.t1314. 27 120,. -) 1434.C7 153.A6 14,~0., 1 1673.65 15J.r 17<'>.43 160n., 1 1q13.20 18-').-) 2_152.72 1i-'O)n. 2"2 2 72.4 7? b io!'. ua' 2 2. 21 * Calibration Equation En -3.9897 + 1.1988 Ph - 0.35262x10-6 Ph

368 TABLE A-13 Sample Low Pressure Transducer Calibration Results a) Sample Low Pressure Transducer Calibration Data LIW PRESSURE TRANSDUCER CALIBRATION SET APRIL 1970 Observation Pressure, P at Measured Calculated Percent Dead Wt. Gae Output, E Output, E Error (Psia) (Bv) (iv) 70.0..11',27E 04 0.13814E 04 0.13824E 04 -0,74299E-01 72.n 3.1 0008F 04 0.12131E 04 0.12129E 04 r.21614E-01 74.0 0.SAOOO 03 0.97455E 03 0.97369E 03 0.88407E-01 76.0 0.31686E 03 0.39364E 03 0.3o417E 03 -0.13465E OC 78.0 0.21281i 03 0.26914E-03 0.26943E 03 -0.10831E 00 80.0 0.21654E 04 0.26020E 04 0.26020E 04 -0.28712E-02 82.0 O. 20n3E 04 0.24058E 04 0.24055E 04'0.13121E-01 84.0 0.159OEn 04 0.19273E 04 0,19271E 04 0.12465E-01 86.0 0.1377E9 04 0,16629E 04 0.16632F 04 -0.20672E-01 88.0 0.1167QE C4 0.14122E 04 0.14126E 04 -0.28128E-01 90.0 n0.0nO05E C4 0.12181E 04 0 12183E 04 -0.12928E-01 92. 0.6,?087E 03 0.74432E 03 0.74318E 03 0.15354E CO b) Interpolated Results from The Calibration Equation P1 E1/10 (Psig) (1iV) 1 ln.'! 134.14?,0. C0 254.07 300. 03 373. 6 400.90 493.81 5090.'3) 613.61 600. 10 733.36 700. 0 1 853.07 800.0) 972.73 90r'). 1092.35 1000.(n 1211.92 1100.00 1331.45 12 )0.0 1450. c3 1300.n 1l370.37 1400.'J;) 1689.76 1500r). O 180. 10 16 Co0. 1928.40 17C0. 0?047.66 10 I00.0') 2166. 87 1900.0)0 2286.03?')0. n 2405. 15 * Calibration Equation 1- 14.155 + 1.2P1 - 0.22708x10-5P12

369 TABLE A-14 Sample Differential Pressure Transducer Calibration Results + +4^+ *Measured Calculated A Obs. Inlet Trans. Outlet Trans. Pressure, Ph Pressure, Diff.Trla. Diff.Trans. Ph-P1 (EDp-E ull) (E-Enull) rr No. Output, Eh/0l Output, Eh/10 (Psia) P (Psia) Null,Eull/10 Output,Ep/10 10 10 Microvolts Microvolts (microvolts) (Microvolts) (Psid) (Microvolts) (Micorvolts) 71. 1343.75 1193.21 1138.79 998.56 74.18 354.38 140.23 280.20 279.60 0.21?l 73. 1200.45 975.85 1019.18 816.81 74.05 477.91 202.37 40B.86 403.45 0.101 75. 957.28 740.30 816.23 620.00 74.44 465.96 196.23 391.5? 391.23 0.07= 77. 351.25 148.72 310.81 126.61 75.36 442.73 184.20 367.37 367.7? -0,1)9h 79. 251.87 15.06 227.89 15.20 74.55 499.38 212.69 424.83 424.7Q 0.010 l1. 25RR.17 2387.72 2178.11 1999.87 62.02 419.12 178.24 357.10 357.09 0.0(03 63. 2R389.7 2175.77 7012.37 1821.97 62.84 443.39 190.40 380.85 380.96 -0.030 86. 1924.33 1673,19 1623.74 1400.61 65.29 512.61 223.13 447.32 445,45 0O.41 R8. 1664.20 1408.56 1406.56 1179.01 66.44 516.93 227.55 450.4q 453.92 -0.76? Q0. 1398.93 1168.66 1185.11 978.29 67.46 480.59 206.82 413.13 412.3'9 O. HO 92. 1203.R8 977.41 1022.26 818.38 68.15 474.93 203.88 406.78 406.46 0.0)7 + Determined from the M&G Dead Wt. Gage and the Barometric pressure ++ Determined from the calibration equation of Table A-13 * Differential tranaducer null determined at Ph ** Calculated using the equation EDp- Eull 0P null- 1.9985 AP - 0.56295xlO-AiP(2Ph- AP) + 0.21745xlO-x AP(3Ph -3PhAP+AP2) where AP - h - P1 h 1 TABLE A-15 The Variation of the Differential Pressure Transducer Output as a Function of Pressure Level for a Fixed Pressure Drop of 200 psid. Transducer Output Pressure DP -E nul 200 paid (Microvolts/psid) (psia) 1.9973?00. 1.9945 630. 1.9935 1000. 1.9963 1600. 2,0001 2000.

APPENDIX B The Basic Calorimetric Data 37()

371 TARM F B-1 Basic IsobatLo Data for 0.996 Mole Fraetlon Xtham RUN Nn. COMPnSITinN INLET OUTLFT INLET PKES. HEAT MFAN 6FAT CH4 C2H6 C3H8 TEMP. TEMP. PRES. DROP INPUT CAPACITY (MOLE FRACTInN) (OF) (~F) (PSIA) (PSID) (BTlU/LR)(RT1/iR~F) 37.010 0.001 0.996 0.003 -257.68 -246.43 1999.4 0.14 h.l62 0.54747 34.010 0.001 0.996 0.003 -246.54 -231.81 2003.2 0.11 8.072 0.54802 34.020 0.001 0.996 0.003 -246.55 -206.83 2003.4 0.15 21.800 0.54RR6 34.030 0.001 0.996 0.003 -246.43 -171.55 2002.1 0.11 41.229 0.55062 34.040 0.001 0.996 0.003 -247.61 -140.05 2001.5 0.12 59.572 0.553R5 34.041 0.001 0.996 0.003 -247.61 -139.30 2001.5 0.12 60.112 0.55498P 34.050 0.001 0.996 0.003 -247.59 -119.16 1999.3 0.13 71.734 0.55854 34.051 0.001 0.996 0.003 -247.59 -118.66 1999.9 0.13 71.867 0.55739 31.010 0.001 0.996 0.003 -123.10 -113.16 2001.9 0.11 5.819 0.5R503 31.015 0.001 0.996 0.003 -123.10 -113.16 2001.9 0.11 5.686 0.57175 U1.020 0.001 0.996 0.003 -122.80 -88.81 2001.7 0.17 19.679 0.57895 31.021 0.001 0.996 0.003 -122.84 -87.33 2003.1 0.13 20.523 0.57799 31.030 0.001 0.996 0.003 -122.75 -63.13 1999.9 0.12 34.921 0.58572 31.040 0.001 0.996 0.003 -122.75 -37.74 1999.4 0.11 50.296 0.59166 31.050 0.001 0.996 0.003 -122.76 -21.62?000.6 0.12 59.998 0.59326 25.010 0.001 0.996 0.003 -22.75 -12.72 2000.6 0.05 6.314 0.62913 25.011 0.001 0.996 0.003 -22.65 -12.64 2000.2 0.05 6.302 0.62994 25.020 0.001 0.996 0.003 -22*78 7.77 1999.7 0.09 19.601 0.64160 1.010 0.001 0.996 0.003 50.74 60.73 2001.4 0.06 7.074 0.70762 1.015 0.001 0.996 0.003 51.34 60.73 2001.4 0.06 6.654 0.70862 1.020 0.001 0.996 0.003 51.37 81.30 2002.2 0.06 21.575 0.72087 1.030 0.001 0.996 0-003 S1l42 105.93 1999.3 0.07 40.423 0.74156 1.110 0.001 0.996 0.003 51.65 62.13 2000.3 0.07 7.342 0.70091 1.111 0.001 0.996 0.003 51.39 61.77 2002.4 0.07 7.332 0.70636 1.120 0.001 0.996 0.003 51.42 81.47 2001.9 0.07 21.700 0.72229 1.130 0.001 0.996 0,003 51.36 104.86 2000.6 0.07 40.262 0.75258 1.140 0.001 0.996 0.003 51.47 126.88 2000.1 0.09 58.146 0.77108 1.150 0.001 0.996 0.003 51*48 144.6e?000.1 0.09 73.607 0.78993 9.010 0.001 0.996 0.003 127.01 136.15 2000.9 0.09 7.864 (.86068 9.011 0.n01 0.996 0.003 127.04 136.18 2003.0 0.07 7.845 0.85804 9.020 0.001 0.996 0.003 127.11 154.04 2001.8 0.07 23.643 0.87619 9,030 0.001 0.996 0.003 127.13 180.06 1999.8 0.09 48.232 0.91117 9.040 0.001 0.996 0.003 127.13 202.79 1999.2 0.12 70.014 0.92538 9.050 0.001 0.996 0.003 127.15 219.91 2001.2 0.12 86.253 0.42977 11.010 0.001 0.996 0.003 126.58 135.69 2001.5 0.10 7.807 0.856A6 11.011 0.0 01 0.996 0.003 126.71 135.92 2000.9 0.07 7.893 0.85743 11.012 0.001 0.996 0.003 126.71 136.01 1999.7 0.07 7.979 0.85841 11.020 0.001 0.996 0.003 126.74 155.24 2001.1 0.12 25.147 0.88250 11.030 0.001 0.996 0.003 126.70 179.48 2002.1 0.10 48.038 0.91018 11.031 0.001 0.996 0.003 126.74 180.05 2002.0 0.10 48.507 0.90983 11.040 0.001 0.996 0.003 126.70 200.78 2001.2 0.09 68.514 n.92480 47.010 0.001 0.996 0.003 176.30 177.39 2000.0 0.15 1.082 0.98676 47.020 0.001 0.996 0.003 176.25 179.15 2000.0 0.15?.840 0.98065 47.030 0.001 0.996 0.003 176.25 180.07 2000.2 0.15 3.768 0.98633 47.040 0.001 0.996 0.003 176.33 182.60 2000.4 0.15 6.179 0.98601 47.050 0.001 0.996 0.003 176.32 183.97 1999.7 0.15 7.552 0.98625 47.060 0.001 0.996 0.003 176.32 186.59 1999.6 0.12 10.139 0.98725 44.010 0.001 0.996 0.003 183.99 185.32 1999.4 0.14 1.3 27 0.99983 44.020 0.001 0.996 0.003 183.96 186.80 1999.4 0.14 2.820 0.q9102 44.021 0.001 0.996 0.003 183.96 186.82 1999.6 0.14 2.824 0.98703 44.030 0.001 0.996 0.003 184.05 188.65 2002.2 0.14 4.547 0.98861 44.031 0.001 0.996 0.003 184.05 188.65 2000.6 0.14 4.538 0.98621 44.032 0.001 0.996 0.003 184,05 188.70 1999.4 0.14 4.559 0.9806( 44.040 0.001 0.99.6 0.003 184.04 190.35 2000.2 0.15 6.252 0.9'107 44.041 0.001 0.996 0.003 184.04 190.35 2000.0 0.15 h.251 0.99075 44.050 0.001 0.996 0.003 184.03 192.29 1999.4 0.15 8.132 0.98445 44.060 0.001 n.996 0.003 184.11 194.54 2002.4 0.15 10.276 0.9852, 48.010 0.001 n.996 0.003 201.51 210.?? 2003.3 0.10 8.560 0.983314 48.020 0.001 0.996 0.003 201.54 216.86 2002.9 0.09 14.956 0.Q97630 48.030 0.001 0.996 0.003 201.60 226.18 1999.9 0.09 23.H43 0.6995 48.040 0.001 0.996 0.003 201.60 246.77 2003.4 0.09 42.986 0.951t1 45.010 0.001 0.996 0.003 201.88 210.39 2002.9 0.10 8.31? 0.97704 45.011 0.001 0.996 0.003 201.88 210.41 2002.6 0.10 8.358 0.98(O17 45.020 0.001 0.996 0.003 201.87 226.40 2001.8 0.11 23.619 0.q6294 45.021 0.001 0.996 0.003 201.87 226.47 2000.5 0.10 23.703 0.9636h) 45.030 0.001 0.996 0.003 201.88 247.06 2003.1 0.10 42.546 0.94179 45.040.o001 0.996 0.003 201.87 269.95 2000.1 0.10 63.062 0.92640 12.010 0.001 n.996 0.003 126.72 135.46 1750.7 0.11 8.051 0.92057 12.011 0.001 0.946 0.003 126.71 135.48 1751.9 0.12 8.073 0.92059 12.020 0.001 0.996 0.003 126.78 153.98 1753.4 0.13 2?.90q 0.95259 12.030 0.001 0.996 0.003 126.76 179.52 1750.5 0.12'?.638 0.99774 12.040 0.001 n.9q6 0.00n 126.71 203.03 1752.6 0.13 7*.761 1.005"5 1?7.050 0.001 0.996 0.003 126.69 216.38 1752.2 0.13 90.0OS 1.00452 1?.056 0.001 0.9936 0.0(03 126.70 1?6h.3 1750.1 0.09 89.430 O.q'3721

372 TARIF B-1. (CONTINUED) RIN Nn. COMPnSITInN INLET nI)TLF1 INLFT PRES. HEAT MEAN HFAT CH4 C2HO C3H8 TEMP. TEMP. PRES. DROP INPUT CAPACITY (MOLE FRACTION) (' F) (~F) (PSTSA (PIDO) (RTU/lB)(BTII/LRF-) 43.010 0.001 0.99h 0.003 168.86 169.8? 1749.2 0,15 1.033 1.0(634 43.020 0.001 0.996 0.003 168.87 170.81 1750.3 0.15 2.033 1.04592 43.021 0.001 0.996 0.003 168.87 170.80 1749.7 0.15?.067 1.06684 43.030 0.001 n.99h 0.003 168.85 172.77 1750.8 0.15 4.172 1.06632 43.040 0.001 0.996 0.003 168.86 174.74 1749.6 0.15 6.301 1.07167 43.041 0.001 0.996 0.003 16R.86 174.77 1754.8 0.15 6.261 1.05878 43.050 0.001 0.996 0.003 168.91 176.54 1749.7 0.15 8.169 1.07041 43.051 0.001 0.996 0.003 168.91 176.52 1751.5 0.15 8.14h 1.07014 43.060 0.001 0.nq6 0.003 16R.92 177.85 1750.0 0.15 9.567 1.07136 43.061 0.001 0.996 n.003 168.92 177.84 1750.5 0.15 9.568 1.n7n04 TA8LF 49.010 0.001 0.996 0.003 179.15 186.56 1750,0 0.10 7.752 1.04674 49.030 0.001?0.96 0.003 179.18 223.99 1748.6 (.13 44.937 1.O0028 49.031 0.001 n0.96 0.003 179.18 224.11 1748.0 0.13 44.993 1.00138 26.010 0.001 0.996 0.003 -22.72 -12.84 1500.9 0.10 6.351 0.64289 26.011 0.001 0.996 0.003 -22.68 -12.73 1502.3 o010 6.377 0.64061?6.020 0.001 0.996 0.003 -22.79 7.32 1499,5 0.10 19.628 0.65174 26.030 0.001 0.996 0.003 -22.77 31.91 1500.9 0.12 36.752 0.67218 26.040 0.001 0.996 0.003 -22.73 51.76 1499.6 0.16 51.036 0.68518 26.050 0.001 0.996 0.003 -22.74 71.80 1500.5 0.10 66.328 0.70159 2.010 0.001 0.996 0.003 51.54 61.28 1500.7 0.08 7.301 0.74990 2.011 0.001 0.996 0.003 51.55 61.23 1500.1 0.08 7.260 0.74941 2.020 0.001 0.996 0.003 51.60 81.42 1501.9 0.08 23.097 0.77465 2.030 0.001 0.99h 0.003 51.59 107.32 1501.6 0.10 45.072 O.80880 2.040 0.001 0.996 0.003 51.59 126.77 1502.8 0.12 63.760 0.84808 2.050 0.001 0.996 0.003 51*63 139.84 1504.3 0.12 77.703 0.88086 13.010 0.001 0.996 0.003 126.70 136.50 1502.5 0.12 10.284 1.04921 13.011 0.001 0.996 0.003 126.70 136.57 1500.6 0.17 10.366 1.05020 13.020 0.001 0.996 0.003 126.64 157.13 1501.1 0.15 33.747 1.10682 13.030 0.001 0.996 0.003 126.77 172.14 1501.1 0.16 58.198 1.28274 13.035 0.001 0.996 0.003 126.77 172.14 1501.1 0.16 57.447 1.26619 13.036 0.001 0.996 0.003 126.77 172.14 1501.1 0.16 51.667 1.13879 13.040 0.001 0.9^6 0.003 126.65 201.33 1500.0 0.16 83.551 1.11870 13.050 n0.00 0.996 0.003 126.71 221.47 1503.1 0.13 102.769 1.08457 42.010 0.001 0.996 0.003 157.29 158.28 1500.6 0.14 1.267 1.27069 42.011 0.001 0.996 0.003 157.26 158.28 1500.8 0.14 1.269 1.24175 42.020 0.001 0.996 0.003 157.31 159.27 1500.5 0.15 2.374 1.206R6 42.021 0.001 0.996 0.003 157.32 159.30 1501.4 0.15 2. 48H 1.20844 42.030 0.001 0.996 0.003 157.30 161.09 1501.0 0.15 4,600 1.21348 42.n31 0.001 0.996 0.003 157.30 161.06 1499.4 0.15 4.59() 1.21993 42.040 0.001 0.996 0.003 157.21 163.08 1499.5 0.15 7.168 1.21942 42.041 0.001 0.996 0.003 157.21 163.09 1499.5 0.15 7.152 1.21603 42.050 0.001 0.996 0.003 157.26 165.00 1501.4 0.17 9.398 1.21358 42.060 0.001 0.996 0.003 157.18 166,20 1499.4 0.15 10.995 1.21R48 42,061 0.001 0.996 0.003 157.23 166.21 1500.0 0.15 10.R93 1.21315 46.010 0.001 0.996 0.003 201.88 210.17 1500.1 0.10 8.221 0.99141 46.011 0.001 0.996 0.003 201.87 210.18 1500.4 0.10 8,252 0.99237 46.015 0.001 0.996 0.003 201.88 210.17 1500.1 0.10 8.249 0.99482 46.016 0.001 0.996 0.003 201.87 210.18 1500.4 0.10 8.275 0.99511 46.020 0.001 0.996 0.003 201.91 218.19 1501.5 0.10 15.937 0.97887 3.010 0.001 0.996 0.003 51.72 61.26 1251.3 0.05 7.504 0.78655 3.011 0.001 0.996 0.003 51.77 61.47 1251.2 0.07 7.578 0.78120 3.020 0.001 0.994 0.003 51.49 80.76 1251.2 0.10 23.970 0.81905 3.030 0.001 0.996 0.003 51.54 106.65 1251.8 0.10 47.949 0.87008 3.040 0.001 0.996 0.003 51.56 126.85 1250.1 0.11 71.802 0.95370 3.050 0.001 0.996 0.003 51.58 135.49 1249.0 0.12 83.188 0.99144 3.051 0.001 0.996 0.003 51.57 135.77 1250.4 0.12 83.429 0.99085 14.010 0.001 0.996 0.003 126.46 136.24 1249.2 0.16 13.437 1.37428 14.011 0.001 0.996 0.003 126.51 136.34 1249.2 0.16 13.494 1.37312 14.020 0.001 0.996 0.003 126.66 149.32 1249.6 0.16 32.087 1.41606 14.030 0.001 0.996 0.003 126.65 177.00 1250.5 0.16 67.303 1.33662 14.040 0.001 0.996 0.003 126.69 201.81 1250.8 0.12 92.066 1.22548 14.050 0.001 0.996 0.003 126.71 222.45 1251.4 0.12 108.979 1.13822 41.010 0.001 0.996 0.003 140.07 141.061 1252.1 0.17 1.517 1.52728 41.020 0.001 0.996 0.003 140.04 142.0? 1253.0 0.15 2.996 1.51143 41.030 0.001 0.996 0.003 140.36 143.38 1252.0 0.15 4.560 1.50661 41.040 0.001 0.996 0.003 139.49 143.65 1252.9 0.15 6,201 1.49009 41.050 0.001 0.996 0.003 140.03 145.10 1252.9 0.15 7.613 1.50101 41.060 0.001 0.996 0.003 140.04 146.85 1252.0 0.15 10.241 1.50228 35.010 0.001 0.996 0.003 -247.72 -232.88 1001.7 0.12 8.188 0.55199 35.020 0.001 0.996 0.003 -247.61 -209.51 1001.4 0.12 20.835 0.54693 35.030 0.001 0.996 0.003 -247.59 -171.71 1000.6 0.12 42.212 0.55631 35.040 0.001 0.996 0.003 -247.62 -140.64 1003.6 0,12 59.289 0.55423 A5.050 0.001 0.996 0.003 -247.55 -120,77 1001.3 0,12 71.211 0.56170 32.010 0.001 0.996 0.003 -123.30 -112.74 1002.1 0.07 6.140 0.58122 32.015 0.001 0.996 0.003 -123.30 -112.74 1002.1 0.07 6.156 0.58279 32.020 0.001 0.996 0.003 -123.32 -89.58 999.0 0.07 19.R3 0,58934 32.030.n01l 0.996 0.003 -123.31 -65.35 999.1 0.10 34.459 0.1.9456 32.040 O.n01 0.996 0.003 -123.26 -36.54 1001.9 0.10 52.26 (U. 02 67 32.050 0.001 0.996 0.003 -123.15 -22.15 1001.5 0.12 61.47?,'.^08nR

373 TAhLF B-1. (CONTINI FE1) RIIM N). CnMPnSITION INLET n)ITLET INLET PkES. HFAT MFAN HFAl CH4 C?H6 C3HR TEMP. TMP. PRES. DROP INPIUT CAPACITY (MOLE FRACTION) (~F) ( F) (PSIA) (PSID) (BTUI/LR)(TTU/LR F) 27.010 0.001 0.996 0.003 -22.74 -12.91 1000.8 0.10 6.441 0.655h4 27.011 0.001 0.996 0.003 -22.72 -13.08 1000.3 0.10 6.328 0.65671 27.020 0.001 0.996 0.003 -22.70 6.5q 999.? 0.10 19.801 0.675H7 27.030 0.001 0.996 0.003 -22.73 37.00 1000.9 0.08 37.974 0.6938) 27.040 0.001 0.996 0.003 -22.71 51.61 1002.7 0.10 53.057 0.71388 27.050 0.n01 0.996 0.003 -22.66 65.74 997.2 0.10 64.689 0.73] 77 4.010 0.001 0.996 0.003 51.64 61.54 1001.0 0.08 8.179 (.8?599 4.011 0.001 0.996 0.003 51.64 61.60 1000.5 0.05 8.180 0.8H167 4.020 0.001 0.996 0.003 51.66 81.4R 1001.8 0.05 26.415 O.H8567 4.030 0.001 0.996 0.003 51.66 106.48 1002.4 0.10 55.570 1.01368 4.040 0.001 0.996 0,003 51.66 121.46 1002.4 0.10 84.196 1.20616 4.050 0.001 0.996 0.003 51.71 131.56 1001.0 0.10 105.888 1.3259H 4.060 0.001 0.996 0.003 51.72 146.80 1002.8 0.10 127.899 1.34515 16.010 0.001 0.996 0.003 116.82 l21.64 1001.3 0.16 10.661 2.^2121 16.011 0.001 0.996 0.003 116.84 121.64 1000.0 0.16 10.700 2.22912 16.012 0.001 0.996 0.003 116.77 121.54 999.8 0.16 10.647 2.?2288 16.020 0.001 0.996 0.003 116.78 126.69 998.8 0.16 22.312 2.25317 16.030 0.001 0.996 0.003 116.75 147.36 999.1 0.19 55.577 1.81)54 16.040 o.no0 0.996 0.003 116.72 167.46 1002.5 0.16 76.309 1.50400 39.010 0.001 0.996 0.003 117.80 118.89 1002.1 0.15 2.479 2.28365 39.020 0.001 0.996 0.003 117.86 119.96 1001.2 0.15 4.774 2.27418 39.030 0.001 0.996 0.003 117.77 120.93 1001.2 0.15 7.274 2.29977 39.040 0.001 0.996 0.003 117.76 121.96 1001.7 0.15 9.621 2.29120 39.050 0.001 0.996 0.003 117.88 123.13 1001.8 0.16 12.087 2.30(,63 39.060 0.001 0.996 0.003 117.76 124.06 999.8 0.15 14.509?.30447 50.010 0.001 0.996 0.003 146.67 162.17 999.8 0.10 16.657 1.07473 50.020 0.001 0.996 0.003 146.68 162.22 998.0 0.10 16.576h.()h655 50.030 0.001 0.996 0.003 146.68 162.19 1000.1 0.20 16.554 1.0)(146 50.031 0.001 0.996 0.003 146.68 162.17 1000.1 0.20 16.540 1.06775 50.040 0.001 0.996 0.003 146.68 162.22 1002.6 0.22 16.622 1.0(704 40.010 0.001 0.996 0.003 99.35 100.35 818.4 0.15 3.825 3.82454 40.020 0.001 0.996 0.003 99.37 101.38 819.8 0.15 8.355 4.14593 40.030 0.001 0.996 0.003 99.37 102.33 818.6 0.15 13.412 4.54513 40.031 0.001 0.996 0.003 99.37 102.31 818.6 0.15 13.415 4.56564 40.040 0.001 0.996 0.003 99.39 103.30 819.8 0.15 18.467 4.72778 40.041 0.001 0.996 0.003 99.39 103.30 819.5 0.15 18.471 4.7285( 40.050.0on1 0.996 0.003 99.39 104.37 819.8 0.15 24.250 4.87076 40.051 0.001 0.996 0.003 99.39 104.40 820.0 0.15 24.225 4.83643 40.060 0.001 0.996 0.003 99.39 105.43 818.4 0.15 29.537 4.89497 40.061 0.001 0.996 0.003 99.39 105.45 818.8 0.15 29.517 4.87334 51.010 0.0Ol 0.996 0.003 100.27 101.11 819.8 0.20 3.785 4.48389 51.020 0.001 0.996 0.003 100.77 101.56 819.8 0.20 3.777 4.78433 51.030 0.001 0.996 0.003 101.29 102.04 819.7 0.20 3.856 5.15570 51.040 0.0On 0.996 0.003 101.95 102.74 819.9 U.20 4.273 5.41780 51.050 0.001 0.996 0.003 102.47 103.27 819.6 (.20 4.433 5.48134 51.060 0.001 0.996 0.003 103.06 103.90 819.8 0.20 4.450 5.29244 17.010 0.001 0.996 0.003 126.36 136.26 750.8 0.37 H8.84 0.86728 17.011 0.001 0.996 0.003 126.43 136.39 750.4 0.37 8.591 0.86261 17.012 0.001 0.99h 0.003 126.36 136.37 749.5 0.36 8.601 0.85951 17.020 0.001 0.996 0.003 126.48 157.15 749.3 0.39 24.205 0.78 17.030 0.001 0.96, 0.003 126.63 177.06 751.1 0.42 37.R85 (.75120 17.040 0.001 0.996 0.003 126.37 201.99 749.9 0.47 54.157 0(.71622 17.050 0.001 0.996 0.003 126.42 221.42 750.3 0.34 66.134 (.69615 5.010 0.001 0.996 0.003 51.49 61.54 714.1 0.05 9.21( 0.,9148 5.011 n.o01 0.996 0.003 51.49 61.60 713.8 0.05 9.218 n.91261 5.020 0.001 0.996 0.003 51.46 81.09 712.0 0.06 31.388 1.05926 5.030 0.001 0.996 0.003 51.44 86.12 712.1 0.07 40.000 1.15336 5.040 0.001 0.996 0.003 51.32 91.26 712.3 0.11 88.130 2.20663 5.050 0.001 0.996 0.003 51.51 96.64 713.8 0.12 105.750 2.34317 5.060 0.001 0.996 0.003 51.52 107.28 713.4 U.09 122.128 2.19(19 5.070 0.001 0.996 0.003 51.69 126.39 712.0 0.10 140.232 1.877?9 5.080 n.001 0.996 0.003 51.73 146.66 713.9 0.10 155.812 1.64)]3 8.010 0.001 0.996 0.003 77.18 87.04 712.2 0.07 15.680 1.5914-7 8.021 0.0nl 0.996 0.003 77.20 93.34 711.6 0.17 72.134 4.46H39 8.030 0.001 0.996 0.003 77.28 107.21 713.1 0.15 96.217 3.21445 R.035 o.00n 0.996 0.003 77.?R 107.21 713.1 0.15 95.351 -.18550 R.040 0.001 0.996 0.003 77.18 130.45 711.6 0.15 117.450 2.2(0485

374 TAHI F B-l. (C. lNT INI5FD) RI1N NlO, CU MP IS I T I 1N INLFT OCITLET INLFT PR-S. HFAT MEAN H-AT CH4 C2H6 C3HH TFMP. TFMP. PRFS. 0IRUP INPUT CAPACITY (MULE F-RACTION) (1F) (~ M) (PS II) (Psi)) (HTII/L(XTI/ LHOI- ) 20.010 0.001 0.996 0.003 78.48 80.74 676.2 0.05 3.5?7 1.)b518 20.011 0.001 0.956 0.003 78.53 80.75 676.1 0.05 3.453 1.55447 20.012 0.001 0.996 0.003 78.56 80.75 675.8 0.04 3.410 1.55805 20.020 0.001 0.996 0.003 78.58 83.49 677.7 0.05 8.475 1.72580 21).030 0.001 0.996 0.003 78.56 84.57 676.4 0.04 10.998 1.H3205 20.040 0.001 0.996 0.003 78.40 86.04 676.2 0.04 17.156 2.24356 20.051 0.001 0.996 0.003 78.58 86.39 676.8 0.11 26.777 3.43185 20.060 0.001 0.996 0.003 78.56 85.36 676.1 0.05 13.284 1.95596 20.070 0.001 0.996 0.003 78.63 86.55 677.6 0.06 35.764 4.51615 20.n08 0.001 0.996 0.003 78.56 86.38 675.8 0.07 55.096 1.048H7 20.090 0.001 0.996 n.003 78.58 89.42 676.7 0.11 74.091 6.H3510 20.100 n.001 0.996 n.003 78.54 87.62 677.6 0.11 68.270 7.51963 2(.110 0.001 0.996 0.003 78.52 92.83 677.2 0.12 81.002 5.66332 20.120 0.001 0.956 0.003 78.55 97.39 677.0 0.12 87.65? 4.65363 20.130 0.001 0.996 0.003 78.58 101.37 676.4 0.14 92.534 4.06136 20.140 0.001 0.596 0.003 78.56 132.18 676,5 0.15 119.371 2.22648 23.010 0.001 0.596 0.003 52.04 60.45 602.4 0.11 8.217 0.97740 23.011 0.001 0.996 0.005 52.0? 60.64 600.1 0.11 8.391 0.97350 23.020 0.001 0.996 0.003 52.07 68,.57 601.4 0.08 17.241 1.04463 21.010 0.001 0.596 0.003 67.01 69.33 602.0 0.02 2.823 1.21419 21.011 0.001 0.996 0.003 66.97 69.32 599.8 0.02 2.848 1.21165 21.020 0.001 0.996 0.003 66.95 71.91 601.3 0.05 6.321 1.27451 21.030 0.001 0.996 0.003 66.94 73.10 600.2 0.04 8.031 1.30)242 21.040 0.001 0.996 0.003 66.98 74.62 602.4 0.04 10.191 1.33`326 21.050 0.001 0.996 0.003 67.21 76.13 600.6 0.06 12.508 1.40108 21.060 0.001 0.996 0.003 66.98 75.94 600.0 0.06 15.479 1.72649 21.070 0.001 0.996 0.003 66.95 75.96 600.2 0.06 17.840 1.97829 21.080 0.001 0.996 0.003 67.01 76.28 601.2 0.06 32.222 3.50(49 21.090 0.001 0.996 0.003 67.13 76.33 601.1 0.08 53.390 5.8O587 21.100 0.001 0.996 0.003 67.10 76.47 601.6 0.06 68.234 7.28658 21.110 0.001 0.996 0.003 67.13 76.94 601.2 0.06 88.064 8.97069 21.120 0.001 0.996 0.003 67.11 76.40 601.0 0.13 79.679 H.5800H 21.130 0.001 0.996 0.003 67.10 79.30 601.4 0.14 92.592 7.5847() 21.140 0.001 0.996 0.003 67.07 83.12 600.4 0.13 98.213 6.1179? 21.150 0.001 0.996 0.003 67.09 86.01 600.4 0.13 101.391 5.35994 21.160 0.001 0.996 0.003 67.09 110.52 600.2 0.15 122.662 2.82393 28.010 0.001 0.996 0.003 -22.82 -13.49 501.5 0.07 6.370 (0.68377 28.011 0.001 0.996 0.003 -22.80n -13.47 501.3 0.07 6.352 0.681037 28.020 0.001n 0.99 0.003 -22.80 5.04 500.7 U.01 19.357 0.69Ah9 28.0310 0.001 0.596 0.003 -23.01 27.69 501.7 0.05 36.785 0).7255H 28.040 0.001 0.996 0.0003 -22.91 53.07 501.3 0.12 5q.182 0(.7 ( 22.010 0.001 0.-96 0.003 51.91 54.26 500.1 0.02 2.361 1.01(6/4 22.011 0.001 0.9)6 0.003 51.43 53.79 499.8 0.02 2.353 (0.1 q,5 22.020 0.001 0.556 0.003 51.56 56.30 500.0 0.03 4.859 1.02355 22.030 0.001Onl 0. 0.003 51.58 58H40 500.2 0.03 7.119 1.04338 22.040 0.001 0.596 0.003 51.56 60.40 499.8 0.04 9.381 1.0167 22.050 0.001on 0.99 0.003 51.58 60.79 500.8 0.12 12.335 1.33955 22.060 0.001 0.996 0.003 51.57 61.17 500.6 0.08, O 16.300 1300 03 22.070 0.0101 0.996 0.003 51.56 60.84 500.5 0.09 22.365 2.40571 22.080 0.001 0.996 0.003 51.54 60.92 500.4 0.10 45.911 4.89801 22.090 0.001 0.996 0.003 51.60 61.12 500.5 0.12 72.363 7.60735 22.100 0.001 0.996 0.003 51.57 61.19 500.3 0.15 103.116 10.71716 22.110 0.001 0.996 0.003 51.58 61.34 500.3 0.15 109.471 11.21786 22.120 0.001 0.996 0.003 51.59 64.25 500.5 0.15 113.183 H8.3627 22.130 0.001 0.996 0.003 51.51 63.03 500.3 0.15 111.884 9.71160 22.140 0.001 0.996 0.003 51.58 66.90 500.1 0.15 115.820 7.56025 22.150 0.001 0.996 0.003 51.58 70.53 500.1 0.15 119.333 6.29717 22.160 0.001 0.,96 0.003 51.56 80.58 500.1 0.15 126.843 4.31178 7.010 0.001 0.996 0.003 77.30 87.47 500.4 0.30 7.674 0.7541? 7.011 0.001 0.996 0.003 77.32 87.57 501.0 0.30 7.700 1.7)18H4 7.020 0.001 0.996 0.003 77.23 106.38 502.2 0.27 20.438 (.70)199 7.030 0.001 0.996 0.003 77.23 131.15 499.7 0.37 35.406 0.65665 7.040 0.001 0.996 0.003 77.28 150.66 500.7 0.37 46.852 0.63844 7.050 0.001 0.996 0.003 77.22 169.6h 501.5 0.29 57.684 0().2400 19.010 0.001 0.996 0.003 126.24 156.32 502.3 0.66 17.723 0.5H915 19.027 0.001 0.996 0.003 126.29 177.47 502.3 0.68 29.753.58177 19.030 0.001 0.996 0.003 126.51 201.66 501.8 0.70 43.304 0.57617 24.010 o.001 0.596 0.003 40.57 42.64 410.4 0.05 1.914 (1.971601 24.020 0.001 0.996 0.003 40.62 44.92 411.1 0.13 4.029 0.93/79 24.030 0.001 0.996 0.0(13 40,61 43.60 410.3 0.05 2.772 ().q2n70?4.040 0.001 o.u9t 0.003 40.6? 44.97 411.0 0.15 5.573 1.28778?4.050 n0.001 0.96 0.003 40.61 45,07 411.1 0.18 22.422 5.021236?4.060 0.001 0.995, 0.003 40.55 45.24 411.0 0.18 54.511 11.63423?4.'170 0.001 0.59 0.0-03 40.59 45.66 410.9 0.20 121.843 23.87392,..06 0.001 0.596 0.003 40.51 50.46 410.7 0.20 125.962 12.65245?4.0oq0 0.001 0.596 0.0(3 40.53 57.19 410.7 0.20 131.384 7.H8713?7.100 n.001 o0.5 0.003 40.54 64.57 411.? 0.17 136.319 5.61(,40 H.01lO 0.001 0.556, 00.013 -249.7 -238f.22 249.1 0.22 1.4H6 (). 551'4'A8.01 1 0.001 0.996 0.On3 -249.75 -236.03 248.6 0.22 7.485 01.545(/ 3H.020 0.001 0.59i6 0.0013 -249.73 -211.11 250.5 0. 17 21.2.31 0.5445 8.030 11,.001 0.996 01.0103 -249,63 -173,76 252.4 0.15 41.983 0,.9339 38.0410 0.n01 0,96 0,003 -249.63 -142.14 249.7 1.15 60.091 0I.559o00 H38.015 0.(001 0.956 0.0113 -249,63 -122..02 249.1 0.17 71.673 1.6t, 166 38.1(1 0.,11 0.596 0.003 -259.83 -248,39 248.5 0.17 6.316 0,55195 38H.111 0.001 0.,56 0,003 -259.87 -248.38 249.2 0.17 6.313 (0.4430

375 TARBL B-1 (CONTINIEt) ) RUN NO. COMPOSITInN INLET OITLFT INLET PRtS. HEAT MFAN HFAI CH4 CH6 C3H8 TEMP. TEMP. PRES. DRIJP INPIIT CAPACITY (MOLF FRACTION) 1(F) (~F) (PSIA) (PSID) (8ITI/LR)(bTIJ/LR~F) 33.010 0.001 0.996 0.003 -122.94 -112.63 251.7 0.05 6.088 0.59032 33.020 0.001 0.996 0.003 -122.93 -90.73 249.2 0.15 19.201 0.59618 33.030 0.001 0.996 0.003 -122.93 -64.34 248.9 0.20 35.602 0.60763 33.040 0.001 0.996 0.003 -123.01 -39.46 248.4 0.20 51.638 0.61807 33.050 0.001 0.996 0.003 -123.02 -24.32 248.9 0.15 61.760 0.62578 o0.010 0.001 0.996 0.003 -23.37 -13.67 248.9 0.15 6.723 0.6u309 30.011 0.001 0.996 0.003 -23.39 -13.69 248.9 0.15 6.728 0.64362 30.020 0.001 0.996 0.003 -23.32 6.94 248.8 0.17 21.897 0.72364 30.030 0.001 0.996 0.003 -23.37 8.26 249.1 0.29 30.156 0.95358 30.040 0.001 0.996 0.003 -23.35 1.87 249.2 0.10 17.916 0.71048 29.010 0.001 0.996 0.003 17.00 21.15 251.7 1.06 2.381 0.57520 29.011 0.001 0.996 0.003 17.00 21.15 248.5 1.06 2.405 0.57921 29.012 0.001 0.996 0.003 17.00 21.28 245.1 1.06 2.443 0.57073 29.020 0.001 0.996 0.003 17*00 27.71 250.4 1.08 5.927 0.55366 29.030 0.001 0.996 0.003 17.00 51.81 248.9 13 13 8.36? 0.52752 6.010 0.001 0.996 0.003 51.52 61.54 252.4 0.64 5.105 0.50932 6.011 0.001 0.996 0.003 51.52 61.60 252.4 0.64 5.130 0.50921 6.020 0.001 0.996 0.003 51.62 82.02 251.3 0.69 15.223 0.50078 6.030 0.001 0.996 0.003 51.52 106.58 250.8 0.91 27.346 0.49667 6,040 0.001 0.996 0.003 51.59 126.85 251.2 0.69 37.360 0.49639 18.010 0.001 0.996 0.003 126.38 136.28 251.9 1.42 5.025 0.50732 18.011 0.001 0.996 0.003 126.32 136.26 252.3 1.42 5.029 0.50608 18.012 0.001 0.996 0.003 126.33 136.28 252.5 1.42 5.035 0.50597 18.020 0.001 0.996 0.003 126.33 156.71 252.0 1.43 15.294 0.50346 18.030 0.001 0.996 0.003 126.35 177.03 251.8 1.50 25.632 0.50579 18.031 0.001 0.996 0.003 126.44 177.35 251.0 1.50 25.737 0.50556 18.040 0.001 0.996 0.003 126.35 201.21 252.4 1.57 38.135 0.50937 18.05n 0.001 0.996 0.003 126.42 221.71 250.6 1.65 48.819 0.51232 TABLE B-2 Basic Isothermal Data for 0.996 Mole Fraction Ethane RUN NO. COMPnSIT IN INLET OUTLET INLET PRES. HEAT ISOTHERMAL CH4 C2H6 C3H8 TEMP. TEMP. PRES. DROP INPUT J.T.COEFF. (MOLE FRACTION) (~F) (OF) (PSIA) (PSID) (HTU/LR) (RTU/LR PSIA) 9.010 0.001 0.996 0.003 49.18 49.18 1676.5 96.79 0.118 -0.00122 9.020 0.001 0.996 0.003 49.24 49.24 1585.5 95.39 0.158 -0.00165 9.030 0.001 0.996 0.003 49.26 49.26 1422.4 96.99 0.221 -0.00228 9.040 0.001 0.996 0.003 49.2? 49.23 1216.9 100.99 0.337 -0.00334 9.050 0.001 0.996 0.003 49.22 49.22 1032.5 101.39 0.456 -0.00449 10.010 0.001 0.996 0.003 49.21 492.7 370.9 259.98 24.947 -0.09596 10.020 0.001 0.996 0.003 49.22 49.19 370.0 144.19 15.503 -0.10752 10.030 0.001 0.996 0.003 49.22 49,20 865.4 101.99 0.606 -0.00594 10.040 0.001 0.996 0.003 49 491 49.19 768.3 106.59 0.789 -0.00740 10.050 0.001 0.996 0.003 49.23 49.22 666.9 108.39 0.982 -(1.00906 14.010 0.001 0.996 0.003 49.24 49.48 448.6 76.19 131.217 -1.72217 14.017 0.001 0.996 0.003 49.24 49,48 448.4 86.19 131.380 -1.52427 14.020 0.001 0.996 0.003 49.22 49,43 448.1 79.99 130.912 -1.63656 14.025 0.001 0.996 0.003 49.22 49.43 448.1 87.99 130.912 -1.48778 11.010 0.001 0.996 0.003 89.87 89.86 839.2 119.39 11.230 -0.09406 11.020 0.001 0.996 0.003 89.84 89.88 727.2 134.59 79.921 -0.59382 12.010 0.001 0.996 0.003 89.70 89.73 2013.6 288.37 1.241 -0.00430 12.015 0.001 0.996 0.003 89.70 89.73 2015.7 288.37 1.240 -(i.00430 12.020 0.001 0.996 0.003 89.78 89.76 2011.7 147.79 0.541 -0.00366 12.030 0.001 0.996 0.003 89.79 89.78 1734.3 285.37 1.861 -(.00652 12.040 0.001 0.996 0.003 89.80 89.78 1732.3 133.59 0.752 -0.00563 12.050 0.001 0.996 0.003 89.80 89.79 1450.6 296.97 3.242 -0.01092 12.060 0.001 0.996 0.003 89,79 89.80 1449.9 192.78 1.894 -0.00983 12.070 0.001 0.996 0.003 89.84 89.85 1150.5 315.17 7.815 -0.02479 13.010 0.001 0.996 0.003 89.80 89.80 836.2 115.99 10.396 -0.08963 13.020 0.001 0.996 0.003 89.77 89.86 608.4 484.55 44.764 -0.09239 13.030 0.001 0.996 0.003 89.80 89.95 605.3 290.37 31.831 -0.10962 13.040 0.001 0.996 0.003 89,78 89.76 668.8 249.38 37.583 -0.15071 15.010 0.001 0.996 0.003 124.99 124.97 1996.6 255.78 2.686 -0.01050 15.020 0.001 0.996 0.003 124.96 124.96 1997.2 113.79 1.063 -0.00934 15.030 0.001 0.996 0.003 124.94 124.89 1742.1 262.58 4.429 -0.01687 15.040 0.001 0.996 0.003 124.96 125.02 1478.3 282.37 10.022 -0.03549 15.050 0.001 0.996 0.003 124.95 125.01 1309.2 114.79 5.219 -0.04546 15.060 0.001 0.996 0.003 124.97 125.04 1198.7 289.77 41.441 -0.14301 15.070 0.001 0.996 0.003 125.00 124.97 1197.8 153.19 13.886 -0.09065 15.080 0.001 0.996 0.003 125.00 125.03 914.2 512.35 57.873 -0.11296 15.090 0.001 0.996 0.003 124.96 124.87 620.7 499.55 34.148 -0.06836 15.100 0.001 0.996 0.003 124.98 125.03 760.5 620,.74 48.491 -0.07812 15.110 0.001 0.996 0.003 124.95 124.97 758.2 503.75 41.645 -0.08267

376 TAHLF B-2 ( CNTI IFn ) RIIN NO. COMPnSITInN INLET OUTLET INLET PRES. HEAT ISOTHERMAL CH4 C2H6 C3H8 TEMP. TEMP. PRES. DRUP INPUT J.T.CEIEFF. (MniE- FRACTION) (OF) (OF) (PSIA) (PSIn) (PTUI/LR) (HTlL/LB PSIA) 1h.010 0.001 0.996 0.003 200.64 200.66 2014.0 356.17 13.481 -0.03785 16.020 0.001 0.996 0.003 200.68 200.65 2008.2 132.99 4.173 -0.03138 16.030 0.001 0.996 0.003 200.67 200.71 1672.2 399.96 23.645 -0.05912 16.040 0.001 0.996 0.003 200.59 200.61 1667.8 179.78 9.695 -0.05393 16.050 0.001 0.996 0.003 200.60 200.63 1278.7 394.96 25.155 -0.06369 16.060 0.001 0.996 0.003 200.60 200.56 1279.7 208.18 13.605 -0.06535 16.061 0.001 0.996 0.003 200.57 200.56 1281.5 208.18 13.604 -0.06535 16.070 0.001 0.996 0.003 200.62 200.61 893.5 410.36 22.026 -0.05367 16.080 0.001 0.996 0.003 200.62 200.66 614.1 362.57 17.111 -0.04719 16.090 0.001 0.996 0.003 200.61 200.56 398.6 296.57 12.762 -0.04303 1.010 O.001 0.996 0.003 202.14 202.16 2001.3 53.20 1.558 -0.02929 1.020 0.001 0.996 0.003 202.14 202.16 1857.8 56.79 2.066 -0.03638 1.021 0.001 0.996 0.003 202.14 202.18 1858.5 55.99 2.072 -0.03701 1.030 0.001 0.996 0.003 202.13 202.13 1758.6 58.39 2.626 -0.04497 1.040 0.001 0.996 0.003 202.12 202.14 1648.5 64.59 3.239 -0.05014 1.050 0.001 0.996 0.003 202.12 202.14 1540.0 71.79 4.106 -0.05720 1.060 0.001 0.996 0.003 202.15 202.17 1422.7 77.99 4.819 -0.06179 2.010 0.001 0.996 0.003 202.10 202.13 1318.0 107.39 7.047 -0.06562 2.020 0.001 0.996 0.003 202.08 202.09 1165.3 135.59 8.687 -0.06407 2.030 0.001 0.996 0.003 202.14 202.17 1016.8 175.98 10.543 -0.05991 2.040 0.001 0.996 0.003 202.13 202.14 853.6 210.58 11.519 -0.05470 2.050 0.001 0.996 0.003 202.15 202.16 650.6 236.78 11.602 -0.04900 2.060 0.001 0.996 0.003 202.14 202.18 426.3 175.38 7.780 -0.04436 2.070 0.001 0.996 0.003 202.13 202.15 272.2 162.38 6.870 -0.04231 TABLE B-3 Basic Isenthalpic Data for 0.996 Mole Fraction Ethane RUN NO. COMPOSITION INLET OUTLET INLET PRES. HEAT J.THOMSO3N CH4 C2H6 C3HR TEMP. TEMP. PRES. DRUP INPUT CO)EFF. (MOLF FRACTION) (~F) (~F) (PSIA) (PSnI) (RTU)/I ) (~F/PSIA) 5.010 0.001 0.996 0.003 -246.57 -243.98 2002.8 414.96 0.000 -0.00625 5.020 0.001 0.996 0.003 -246.61 -245.52 2001.4 190.38 0.000 -0.00576 5.030 0.O01 0.996 0.003 -246.54 -244.04 1588.4 398.76 0.000 -0.00628 5.040 0.001 0.996 0.003 -246.61 -245.54 1589.2 191.38 0.000 -0.00561 5.050 0.001 0.996 0.003 -246.61 -243.81 1193.2 449.96 0.000 -0.00621 5.060 0.001 0.996 0.003 -246.57 -245.12 1192.4 246.78 0.000 -0.00591 5.070 0.001 0.996 0.003 -246.59 -243.30 752.6 524.75 0.000 -0.00625 5.080 0.001 0.996 0.003 -246.61 -245.23 751.1 238.78 0.000 -0.00579 5.090 0.001 0.996 0.003 -246.60 -245.80 233.6 150.99 0.000 -0.00527 3.010 0.001 0.996 0.003 -123.30 -120.68 2003.2 484*15 0.000 -0.00541 3.020 0.001 0.996 0.003 -123.29 -121.92 2001.0 270*17 0.000 -0.00508 3.025 0.001 0.996 0.003 -123.29 -121.92 2001.0 270.17 0.000 -0.00508 3.030 0.001 0.996 0.003 -123.33 -123-11 1996.4 52.80 0.000 -0.00401 3.040 0.001 0.996 0.003 -123.35 -121.29 1520.8 388.56 0.000 -0.00529 3.050 0.001 0.996 0.003 -123.29 -122.02 1520.8 246.58 0.000 -0.00517 3.060 0.001 0.996 0.003 -123.31 -121.26 1141.9 394.56 0.000 -0.00519 3.065 0.001 0.996 0.003 -123.31 -121.26 1141.9 394.56 0.000 -0.00519 3.070 0.001 0.996 0.003 -123.14 -122.23 1142.7 181.58 0.000 -0.0050; 4.010 0.001 0.996 0.003 -123.49 -121.81 760.1 392.96 0.000 -0.00429 4.015 0.001 0.996 0.003 -123.49 -121.81 760.1 392.96 0.000 -0.00429 4.020 0.001 0.996 0.003 -123.51 -122.52 761.8 239.38 0.000 -0.00413 4.030 0.001 0.996 0.003 -123.48 -122.50 393.1 248.78 0.000 -0.00394 4.040 0.001 0.996 0.003 -123.07 -122.76 217.9 118.99 0.000 -0.00262 6.010 0.001 0.996 0.003 -23.88 -22.96 2001.7 303.37 0.000 -0.0030r 6.020 0.001 0.996 0.003 -23.80 -23.55 1999.5 97.59 0.000 -0.00263 7.010 0.001 0.996 0.003 -24.57 -23.61 1700.5 354.57 0.000 -0.00273 7.020 0.001 0.996 0.003 -24.58 -24.24 1702.3 137.59 0.000 -0.00253 7.030 0.001 0.996 0.003 -24.54 -23.71 1349.7 362.77 0.000 -0.00231 7.040 0.001 0.996 0.003 -24.56 -24.20 1349.6 166.78 0.000 -0.00215 7.050 0.001 0.996 0.003 -24.55 -23.90 991.6 363.37 0.000 -0.00179 7.060 0.001 0.996 0.003 -24.57 -24.17 991.6 222.58 0.000 -0.00183 7.070 0.001 0.996 0.003 -24.54 -24.10 635.7 377.36 0.000 -0.00118 7.080 0.001 0.996 0.003 -24.48 -24.44 267.2 113.59 0.000 -0.00035 8.010 0.001 0.996 0.003 49.75 49.45 2002.5 321.57 0.000 0.00095 8.020 0.nl1 0.996 0.003 49.75 49.68 2000.9 108.59 0.000 0.00066.0o30 0.001 0.996 0.003 44.46 44.44 1997.8 99.59 0.000 0.00024

377 TAI ~- B-4 Basic Isobaric Data for Nominal 0.76 C2H6, 0.24 C 3H Mixture RIIN Nn. C-nMPns I T I nr\i INLET 0 IITL F INLFT PRS6. HEAT M6AM H-Ar CH4 C2H6 C3H8 TEMP. TEMP. PRFS. )RUP INPiT (.APA r. 1T (MCOLF FRACTIONI (OF) (OF) (PSIA) (PSID) (HTI)/Lh)(OTI I/ WI-.r 16.010 0.003 0.7h0 0.237 -252.01 -241.5H 2000.2 0.07 5.440 0.51"? 16.020 0.003 0.760 0.237 -251.91 -232.09 2002.3 0.07 10.373 0.52324 16.021 0.003 0.760 0.237 -252.19 -232.27 2003.8 0.07 10.3H4 0.52170 16.030 0.003 0.760 0.237 -252.,12 -191.76 2003.q 0.07 31.697 ().52514 16.031 0.003 0.760 0.237 -251.94 -191.16 2004.7 0.07 31.969 0,2?'(, 16.040 0.003 0.760 0.237 -251.89 -150.93 2000.9 0.07 53.425 0.57913 16.041 0.003 0.760 0.237 -251.89 -150.60 2001.5 0.07 53.539 0.-325 44 16.050 0.003 0.760 0.237 -251.88 -131.84 1995.3 0.07 63.529 0.57923 15.010 0.003 0.754 0.243 -151.04 -140.80 2001.9 0.07 5.495 0r.b3-4a 15.020 0.003 0.754 0.243 -151.01 -131.05 2000.2 0.05 10.762 0.53915 15.030 0.003 0.754 0.243 -151.00 -90.57 2000.2 0.01 33.037 0.5467/ 15.040 0.003 0.754 0.243 -151.00 -49.73 2000.5 0.06 55.986 0.55282 15.050 0.003 0.754 0.243 -151.00 -24.35 2003.4 0.07 70.653 0.557H3 14.010 0.003 0.760 0.237 -51.96 -41.72 1999.7 0.05 5.912 0.17754 14.020 0.003 0.760 0.237 -51.91 -32.24 2002.5 0.05 11.674 0.5936t0 14.030 0.003 0.760 0.237 -51.92 8.49 2001.7 0.06 35.912 0.5 44414.031 0.003 0.760 0.237 -51.92 8.64 2001.3 0.06 35.908 0.5'929 14.040 0.003 0.760 0.237 -51.84 48.09 1997.5 0.07 60.871 0.60912 14.041 0.003 0.760 0.237 -51.84 48.37 1996.3 0.07 61.066 0.6o 937 12.010 0.003 0.766 0.231 47.99 58.87 1999.9 0.10 7.275 0.r,6H60o 12.020 0.003 0.766 0.231 47.95 68.58 2000.7 0.05 13.681 0.66-114 12.030 0.003 0.761 0.236 47.99 98.34 2000.8 0.05 34.376 0.682HO 12.040 0.003 0.761 0.236 47.93 128.74 2003.6 (.05 56.512 (.699)33 12.050.n003 0.761 0.236 47.94 148.59 2003.0 0.07 71.941 0.714kH 23.010 0.003 0.751 0.246 125.64 137.99 2001.7 0.05 9.584.776/? 23.011 0.003 0.751 0.246 125.64 138.16 2004.2 0.05 9.556.7632(o 23.020 0.003 0.751 0.246 125.75 143.99 2001.2 0.05 22.342.790()H?2.030 0.003 0.751 0.246 125.71 179.98 2002.8 0.05 44.061.HIIH4 10.010 0.003 0.765 0.232 149.81 156.46 2001.2 0.12 5.536 1.89]1 10.011 0.003 0.765 0.232 149.82 156.37 2001.5 0,.12 5.392 (.H2239 10.020 0.003 0.765 0.232 149.83 164.6? 2001.7 0.12 12.517 (.H4597 10.030 0.003 0.765 0.232 149.92 175.68 2001.7 0.12 21.785 ()1.a446 1 0.040 0.003 0.765 0.232 149.84 201.95 2001.3 0.1? 46.397 ().891(2 7.010 0.003 0.760 0.237 175.31 185.58 2001., 0.12 9.n80 (1.HH834 7.020 0.003 0.760 0.237 175.34 195.61 2000.2 0.12 18.112 n.89376 7.030 0.003 0.760 0.237 175.26 230.04 1999.4 0.12 5C.324 0.91862 7.040 0.003 0.760 0.237 175.39 251.09 2001.1 0.12 70.127 0.12634 H.010 0.003 0.761 0.236 175.23 181.80 1501.8 0.12 7.146 1.8HH74.020 0.003 0.761 0,.236 175.35 190.61 1501.6 0.16 16.901 1.1072 8.030 0.003 0.762 0.235 175.33 198.91 1502.0 0.16 26.253 1.11306 H.040 0.003 0.759 0.238 175.32 230.30 1502.6 0.16 60.247 1.01957.050n 0.003 0.759 0.238 175.31 248.29 1499.5 0.17 77.998 1.n06166 8.051 0.003 0.759 0.238 175.31 248.69 1501.3 0.17 78.152 1.0n6n05 11.010 0.003 0.760 0.237 101.35 104.93 999.1 0.15 3.203 1.H934-1 11.020 0.003 0.760 0.237 101.34 108.42 999.4 0.15 6.455 11.91160 11.021 0.003 0.760 0.237 101.38 108.50 999.9 0.15 6.440 ().o031)7 11.030 0.003 0.760 0.237 101.36 114.15 1000.1 0.15 11.H5? (11.1276 11.040 0.003 0.760 0.237 101.35 120.40 999.7 0.15 18.266 0.q5/75 11.050 0.003 0.760 0.237 101.32 128.41 1000.3 (1.15 27.255 1.01161s 11.060 0.003 0.760 0.237 101.43 136.H7 999.4 0.15 3H.087 1.0746, 11.061 0.003 0.760 0.237 101.43 137.01 999.2 0.15 37.979 1.0674") 11.070 0.003 0.760 0.237 101.38 145.36 999,6 0.15 51.046 1.16117 11.080 0.003 0.760 0.237 101.50 150.95 999.6 U.15 61.262 1. 21H1 11.090 0.003 0.760 0.237 101.38 158.39 999.6 0.15 75.540 1.92491 11.100 0.003 0.760 0.237 101.38 165.70 999q. 0.15 88H.75 1.36,,7 11.110 0.003 0.760 0.237 101.42 169.84 999.2 0.15 94.,61 1.3 7/( 1H.01n 0.003 0.759 0.238 101.40 108.6? 716.1 0.1n.q6/ 1.14**,s 1!.020 0.003 0.759 0.23H 101.40 110.15 715.9 U.10 11.155 1.211/4 18.030 0.003 0.759 0.238 101.39 1112.01 715.9 0.10 14.146' 1..746 18.040 0.003 0.759 0.298 101.48 114.19 715.3 0.10 17.H15 I.44()1?', 18.050 0.003 0.759 0.238 101.45 114.65 716.1 0.10 22.H1 1.o1 1(31 1H.060 0.003 0.759 0.238 101.45 118.49 715.8 0.10 29.594 1.7'64,/ H1.070 0.003 0.759 0.238 101.44 120.1? 715.4 0.10 41.481?2.21(4 18.080 0.003 0.761 0.236 101.401 123.09 715.5 0.10 61.984?2.H?7,>1 1H.090 0.003 0.761 0.236 101.40 125.83 715.8 0.15 75.91 9.1I(p4 18.100 0.003 0.761 0.236 101.40 130.55 715.6 0.15 H7.19A?.91:/ 18.110 0.003 0.761 0.236 101.41 132.92 715.6 0.15 91.41~?.q()(1(1 18.120 0.003 0.761 0.236 101.43 137.73 715.6 0.15 98.644?.7!744 10.130 0.003 0.761 0.236 101.43 151.47 715.5 0.15 115.040?~.-i<,, 18.210 0.003 0.761 0.236 101.41 10H.06 715.9 0.07 7.91(1 1.1 2;-" 1H.220 0.003 0.761 0.236 101.39 110.38 715.5 0.07 11.105 1. 265( 18.230 0.003 0.761 0.236 101.40 112.?20 715.9 0.07 13.,41 1.2 "10 1H.240 0.003 0.761 0.236 101.40 114.13 715.7 0.07 17.087 1.3471 1H.250 0.003 0.760 0.237 101.36 116,46 715.9 0.10 21.891 1.44,1. 18.260 0.003 0.760 0.237 101.41 118.54 715.7 0.10 28.7?22 1... / 18.270 0.003 N.760 0.237 101.41 120.2H 715.8 0.10 40.474 4.1453 16.280 0.003 0.760 0.237 101.44 123.03 715.9 U.(1 58.962?.( 12 18.290 0.003 0.760 0.237 101.44 126.11 716.1 0.15 7'3.171:.'655 18.300 0.003 0.760 0.237 101.44 130.67 716.0 C0.13 I I.79 2.6634 16.310 0.003 0.756 0.241 101.44 133.10n 716.0 0.15 8 7.93 2.771591 1H.320 0.003 0.756 0.241 101.4' 137.11 716.0,.15 9.207;.{l1] 1>7. 0 0.003 0.756 3.241 101,36 14H8. 715.4 0.15 106..'> 2.2556

378 TALt F B-4 ( CONT INIIF ) RUN N1). COMPo)SI TION INLET (lUTL ET INLFT PRtS. HFAT w FA, HFa r CH4 C?H6h C^H TFMP. TEMP. PRFS. ORUP INPUT CA^ACITY (MOLF FRACII )N) (<~: (F! (PSI(o) (pSI l)) (TtlI/Lti(ITTIIu/ L ~' )?1.)10 N0.no 0.760 0.237 68.95 72.87 499.7 0.07 3.474 O.HH,88 21.011 n0.0n 0.7h0 (0.237 68.93 72.94 499.6 0.07 3.528 (.8H18H5?1.0?0 0.003 0.760 0.237 h8.97 76.00 499.4 0.07 6.284 (.H8939? 21.021 0.003 0.760 0.237 68.93 75.75 499.6 0,07 6.084 ().H9134 21.0?? 0.003 0.760 0.237 68.93 75.78 499.2 0.07 6.085 O.8H732 21.030 0.00o 0.760 0.237 68.97 78.19 499.6 0.07 H.320 0.Q0176 21.040 0.003 0.760 0.237 68.97 82.45 499.7 0.07 13.020 2.1730 21.050 0.003 0.760 0.237 68.93 83.52 500.0 0.07 20.968 1.43677 71.060 0.003 0.760 0.,37 68.92 R6.R8 499.6 0.07 45.^46 2?55H87 21.070 0.003 0,760 0.237 68.92 92.91 499.7 0.07 85.553 4,56^3 h 21.08R 0.003 0.760 0.237 68.92 100.41 499.8 0.07 122.540 3.H913] 21.090 0.003 0.760 0.237 68.99 109.91 499.9 0.07 129.681 3.16920 21.100 0.003 0.7m0 0.737 6.,96 115.56 499.5 0.07 134.405 2.88434 17.010 0.003 0.761 0.236 -25;'.H6 -242.55 250.4 0.05 5.384 (.52235 17.020 0.003 0.761 0.236 -252.85 -233.57 252.0 0.07 10.049 0.52102 17.030 0.003 0.761 0.236 -252.84 -194.06 252.3 0.07 30.989 0.52713 17.040 0.003 0.761 0.236 -252.80 -154.27 250.4 0.10 52.379 0.53160 17.050 0.003 0.761 0.236 -252.87 -130.83 251.2 0.10 65.1'97 0.53427 22.010 0.003 0.751 0.246 -119.25 -108.613 251.8 0.07 5.975 0.56172 22.020 0.003 0.751 0.246 -119.2 -94.729 252.1 0.01 13.805,56367 22.030 0.003 0.751 0.246 -119.18 -56.962 252.2 0.07 35.786.57517 22.040 0.003 0.751 0.246 -119.24 -22.46 251.6 0.07 56.H49.58738 22.050 0.003 0.751 0.246 -119.34 -4.23 250.R 0.07 68.R61.59820 22.060 0.003 0.751 0.246 -119.35 8.52 252.4 0.07 77.161.60344 22.070 0.003 0.751 0.?46 -119.35 17.74 250.9 0.07 R3.307.60769 20.010 0.003 0.761 0.236 8.27 11.28 249.7 0.05 2.086 (.69461 20.011 0.003 0.761 0.236 8.27 11.29 249.8 0.05 2.084 o.69026 20.020 0.003 0.761 0.236 8.27 15.16 249.8 0.05 4.780 0.69436 20.030 0.003 0.761 0.236 R.26 21.13 250.1 0.05 8.991 g 0.9861 20.040 0.003 0.761 0.236 8.25 24.24 249.8 0.17 12.160 (.7601c 20.050 0.003 0.761 0.236 8.25 25.94 249.5 0.22 22.223 1.2562 3 20.060 0.003 0.761 0.236 8.26 29.51 249.4 0.20 52.700 2.47913 20.070 0.003 0.761 0.236 8.31 34.70 249.4 0.20 88.309 3.34611 20.071 0.003 0.761 0.236 8.31 34.43 248.8 0.20 RR.238 3.37782 ().080 0.003 0.761 0.236 8.35 38.17 249.4 0.25 111.R91 i.75200( 2().090 0.003 0.761 0.236 8.25 45.18 249.2 0.25 148.214 4.01374 19.010 0.003 0.764 0.233 37.11 40.72 248.8 0.12 20.71h6.736h4 19.020 0.003 0.764 0.233 37.11 43.93 250.4 0.17 37.685'.5?276 19.030 0.o03 0.764 0.233 37.09 48.46 249.2 0.20 59.664 5.?4836 19.040 0.003 0.764 0.233 37.10 52.20 250.1 0.22 65.208 4.31861 19.050 0.003 0.764 0.233 37.08 56.08 250.5 0.20 67.690.5h6292 19.060 0.003 0.764 0.233 37.10 59.58?50.8 0.20 70.04H 1.11675 19.070 0.003 0.764 0.233 37.13 65.09 250.5 0.20 72.627'.59h82 13.010 0.003 0.763 0.234 48.90 58.9R 248.Q 0.32 7.578,.75149 1A.011 0.003 0.763 0.234 49.16 59.77 24R.8 0.32 7.512 0.70823 19.020 0.003 0.763 n.234 49.01 68.53 249.7 0.32 13.228 0.67786 1R.030 0.003 0.763 0.234 49.00 98.37 249.0 0.3? 27.687 (}.56086 1].031 0.003 0.763 0.234 49.00 98.76 248.8 0.32 27.667 (.55h60 13.040 0.003 0.763 0.234 53.33 106.17 249.1 0.49 27.216 (0.51506 13.050 0.003 0.763 0.214 53.34 128.32 249.1 0.49 38.369 0.51173 13.060 n.003 0.763 0.234 53.34 150.40 249.1 0.49 49.)50 o0.10n5 9.010 0.003 0.761 0.236 175.25 185.19 250.8 1.38 5.231 1.5267^ 9.020 0.003 0.761 0.236 175.27 195.50 252.2 1.40 10.672 n.57761) 9.030 0.003 0.761 0.236 175.35 227.82 251.0 1.47 28.10R ().53571 9.040 0.003 0.761 0.236 175,37 252.34 252.0 1.72 41.554 0.54988

379 TAiA.F B-5 Basic Isothermal Data for Nominal 0.76 C2H6, 0.24 C3H8 Mixture RIIN NO. CnMPFtSI TI ON INLET OUTLET INLET PRKS. HtAT I S(11 HFRAL CH4 C2H6 C3H8 TEMP. TFMP. PRES. DRIJP INPIIT J. T.(lh-F-. (MnLE FRACTION) (OF) (oF) (PSIA) (PSID) (TIIL/L!) (ATli/lf 3.050 0.003 0.760 0.237 49.71 49.65 1418.3 202.32 (0.041 -O.O)O!o i 3.060 0.003 0.760 0.237 49.88 49.O0 1214.2 203.26.) 13 -(.000(o65 3.070 0.003 0.760 0.237 49.82 49.77 1015.1 2U2.53 ().2SF -0.001,8 3.ORO 0.001 0.760 0.237 49.96 49.90 816.2 202.24 0.414 -(O.(005 3.090 0.On 0.760 0.237 49.84 49.83 646.9 222.18 (.71( -0.((001I 3.100 0.003 0.7hn 0.237 50.03 50.02 441.4 96.38 0.39? -0.00407 5.010 0.003 0.765 0.232 102.38 102.37 398.1 290.79 23.H23 -0.08193 5.020 0.003 0.761 0.236 102.36 102.24 1003.5 191.41?.449 -0.01 179 2.010 0.003 0.759 0.238 151.65 151.55 2003.3 199.96 1.64) -0).008 3 2.015 0.003 0.759 0.238 151.65 151.55 2003.3 199.96 1.631 -0.0( 816 2.016 0.003 0.759 0.238 151.65 151.55 2003.3 199. 6 l.(1.60 ()-0.008 2.020 0.003 0.759 0.238 151.85 151.80 1803.4 211.b5?.540 -()0.0101 2.030 0.003 0.759 0.238 152.03 151.97 1602.0 214.01 3.839 -0.01794 2.040 0.003 0.759 0.238 152.16 152.08 1401.1 216.37 6.793 -0.03139 2.050 0.003 0.759 0.238 152.16 152.03 1204.8 250.97?3.154 -(.09226 2.060 0.003 0.762 0.235 152.03 152.00 1001.4 269.38 51.069 -0.18958 2.070 0.003 0.762 0.235 152.43 152.43 800.4 215.13 26.656 -().?1391 2.080 0.003 0.762 0.235 152.43 152.50 600.0 221.09 17.804 -0.08053 2.090 0.003 0.766 0.231 152.37 152.31 401.5 302.12 18.360 -0.06077 1.010 0.003 0.764 0.233 250.74 250.75 1998.3 203.24 6.847 -0.03369 1.020 0.003 0.764 0.233 250.83 250.85 1996.7 82.81 2.576 -0.03111 1.030 0.003 0.764 0.233 250.89 250.85 1798.6 258.77 11.428 -0.04416 1.040 0.003 0.764 0.233 250.84 250.76 1630.9 278.75 14-.394 -0.05164 1.050 0.003 0.756 0.241 250.76 250.71 1349.3 279.03 15.833 -0.05674 1.n60 0.003 0.756 0.241 250.75 250.75 1105.0 286.04 15.537 -0.05432 1.070 0.003 0.756 0.241 250.77 250.79 845.3 306.98 15.079 -0.04912 1.080 0.00 0.756 0.241 250.74 250.65 596.3 381.90 16.509 -0.04323 1.090 0.003 0.760 0.237 250.79 250.87 352.4 255.70 n0.382 -0.04060 TAPLE B-6 Basic Isenthalpic Data for Nominal 0.76 C2H6, 0.24 C3H8 Mixture RIJN N(l. C(1MP()SITION INLET OUFTLET INLFT PkES. (F-AT..IH3IMSii CH4 C2H6 C3H8 TEMP. TFMP. PRFC. I)K()P IN NPT C(1FF-. (M()lF F-RACTII)N) (OF) (OF) (PSIA) (PSI)) (DITu/LL) (~F/PSIA) 4.01n 0.00 0.765 0.232 -50.12 -49.64 7002.1 107.38.000o -n.nn454 4.020 0.00' 0.765 0.232 -50.12 -49.27 2004.9 185.74 0.000 -0.00n45 4.030 0.003 0.765 0.232 -50.18 -49.26 1798.4 209.18 0.000 -0.00442 4.040 0.003 0.765 0.232 -50.22 -49.23 1587.9 226.20 0.00( -0(.(04 -i 4.050 n.n00 0.765 0.232 -50.21 -49.23 1371.2 235.12 o.000 -0.0)0418 4.060 0.003 0.765 0.232 -50.23 -49.27 1135.5 234.58 H o).o0 -n.nO(409 4.070 0.003 0.765 0.232 -50.21 -49.35 901.7 22.40 0.00( -0.F03) / 4.080 0.003 0.765 0.232 -50.19 -49.27 676.0 244.19 ).00( -().003^1 4.090 0.003 0.765 0.232 -50.20 -495.42 425.7 220.76 0.00( -0.0()355 4.100 0.003 0.765 0.232 -50.23 -49.94 221.1 5.79 (.000 -0.(00336 3.010 0.003 0.766 0.231 49.96 49.99 2001.4 93.54 (.0OOF -().OOnOv 3.020 0.003 0.766 0.231 49.97 50.13 2002.6 174.94 n0.0n -O.FnOFR9 3.030 0.003 0.766 0.231 49.70 49.79 1825.3 201.27 0.000( -0.00043 3.040 0.003 0.766 0.?31 49.96 49.99 1621.? 201.60 n.OOo -n0.o(lo15

380 FALE B-7 Basic Isobaric Data for Nominal 0.50 C2H6, 0.50 C3H8 Mixture RUN NO. COMPlISITiON INLFT OITLET INLFT PRES. HEAT M6^A HEAT CH4 C2?H CHR TEMP. TEMP. PRES. )RUP INPUT CAPACITY (Mll.8 F RAcTION) (~F) (OF) (PSIA) (PSID) (HTt)/L8)(HTll/LR~-) 16.010 0.004 0.495 0.501 -246.28 -236.61 2000.1 0.49 4.670 0.48276 16.020 0.004 0.495 0.501 -246.41 -214.98 1999.3 0.49 15.723 0.50031 16.030 0.004 0.495 0.501 -246.19 -187.72 2015.3 0.49 29.439 0.50343 16.040 0.004 0.495 0.501 -246.3n -153.99 2004.7 0.49 47.178 0.51108 16.050 0.004 0.495 0.501 -246.30 -126.90 2003;. 0.49 61.42H 0.51448 16.051 n.004 0.495 0.501 -246.30 -125.63 2003.9 0.49 61.486 0.50955 16.052 0.004 0.495 0.501 -246.30 -125.89 1996.3 0.49 62.011 0.51504 15.010 0.004 0.491 0.505 -125.95 -117.48 2000.7 0.17 4.471 0.52802 15.020 0.004 0.491 0.505 -125.93 -48.19 1999.8 0.17 41.761 (0.53717 1.030n 0.004 0.905 0.491 -125.92 27.5? 2003.2 0.15 85.451 0.55690 12.010 0.004 0.495 0.501 37.15 46.25 2002.2 0.12 5.664 0.62223 12.020 0.004 0.495 0.501 37.18 60.53 2000.0 0.12 14.686 0.62908 12.030 0.004 0.495 0.501 37.13 91.31 2000.4 0.12 35.849 0.66161 12.040 0.004 0.495 0.501 37.09 122.40 2001.2 0.12 55.506 0.65068 12.050 nona4 0.495 0.501 37.09 149.01 2002.0 0.12 74.377 0.66459 1.nl0 0.004 0.481 0.515 150.80 158.22 2000.6 0.06 5.498 0.74132 1.011 0.004 0.481 0.515 150.81 158.31 2001.2 0.06 5.506 0.73453 1.020 0.004 0.485 0.511 150.50 175.26 2000.1 0.06 18.726 0.75801 1.030 0.004 0.491 0.505 150.50 201.76 1999.7 0.06 39.990 0.78016 1.040 0.004 0.489 0.507 150.57 225.81 1999.7 0.06 59.195 0.78672 1.110 0.004 0.494 0.502 149.91 157.51 2001.2 0.08 5.599 0.73707 1.120 0.004 0.494 0.502 150.06 174.71 2003.3 0.08 18.470 0.74942 1.121 0.004 0.494 0.502 150.01 175.30 2000.4 0.07 18.969 0.75010 1.130 0.004 0.494 0.502 150.23 202.63 2001.0 0.12 40.469 0.77231 1.140 0.004 0.494 0.502 149.95 224.85 2000.5 0.08 59.269 0.79129 1.150 0.004 0.494 0.502 149.97 249.96 2000.9 0.05 80.778 0.80786 17.010 0.004 0.497 0.500 250.27 258.13 2003.4 0.12 7.030 0.89472 17.011 0.004 0.497 0.500 250.27 258.00 2003.4 0.12 6.899 0.89279 17.020 0.004 0.497 0.500 250.13 272.20 2001.4 0.12 19.804 0.89728 17.030 0.004 0.497 0.500 250.27 293.73 2000.1 0.12 39.239 0.90293 11.010 0.004 0.502 0.494 37.11 45.86 1000.0 0.11 5.648 0.64542 11.020 n.004 0.502 0.494 37.10 59.62 999.7 0.11 14.717 0.65342 11.030 0.004 0.496 0.500 37.12 90.40 1001.1 0.11 35.999 0.67571 11.040 0.004 0.496 0.500 37.12 119.02 1000.0 0.11 57.752 0.70512 11.050 0.004 0.496 0.500 37.17 131.38 1002.4 0.11 67.804 0.71971 11.060 0.004 0.496 0.500 37.21 149.01 1002.1 0.12 83.704 0.74866 2.010 0.004 0.498 0.498 150.13 157.45 1001.1 0.07 7.431 1.01489 2.011 0.004 0.498 0.498 150.13 157.48 1001.3 0.07 7.426 1.01063 2.020 0.004 0.495 0.501 150.26 174.q4 999.6 0.07 28.327 1.14796 2.030 0.004 0.495 0.501 150.30 198.60 1000.1 0.13 65.686 1.35983 2.040 0.004 0.496 0.500 150.20 223.01 1001.0 0.07 97.860 1.34388 2.050 0.004 0.4Q6 0.500 150.28 251.37 999.6 0.07 123.413 1.22142 6.010 0.004 0.492 0.504 101.78 111.73 762.6 0.05 8.014 0.80473 6.020 0.004 0.492 0.504 101.66 130.72 762.2 0.02 24.890 0.85665 6.030 0.004 0.492 0.504 101.64 158.72 761.3 0.19 65.068 1.13993 6.040 0.004 0.495 0.501 101.72 179.24 759.1 0.07 119.098 1.53629 6.050 0.004 0.495 0.501 101.72 192.11 758.8 0.06 144.928 1.60335 0.o010 0.004 0,4Q5 0.501 37.03 44.69 500.9 0.15 5.153 0.67186 10.015 0.004 0.495 0.501 37.03 44.69 500.9 0.15 5.166 0.67359 10.016 0.004 0.495 0.501 37.03 44.69 500.9 0.15 5.139 10.67015 10.020 0.004 0.495 0.501 37.05 52.37 499,5 0.15 10.372 0.6768] 10.025 0.004 0.495 0.501 37.05 52.37 499.5 0.15 10.398 0.67852 10.026 0.004 0.495 0.501 37.05 52.37 499.5 0.15 10.346 0.67511 10.030 0.004 0.495 0.501 37.10 81.89 499.4 0.15 31.509 0.70345 1(0.040 0.004 0.498 0.498 37.10 103.51 499.9 0.15 49.131 0.73983 10.05n 0.004 0.498 0.498 37,08 115.13 501.8 0.22 68.688 ().8800,.010 0.004 0.486 0.510 150.31 157.50 498.8 1.03 5.196 0.72330 3.020 0.004 0.486 0.510 150.35 175.13 498.9 0.58 17.582 0(70948 3.030 0.004 0.490 0.506 150.35 199.91 501.9 0.69 33.875 0.68347 3.040 0.004 0.490 0.506 150.38 226.33 498.5 0.75 50.340 0.66276 3.050 0.004 0.490 0.506 150.45 248.60 500.3 0.81 62.040 0.63209 7.010 0.004 0.488 0.508 101.71 104.95 501.4 0.05 2.855 0.88085 1.020 0.004 0.488 0.508 101.72 10H.97 501.3 0.10 6.448 0.88969 7.030 0.004 0.488 0.508 101.67 112.28 501.3 0.13 10.262 0.96752 7.040 0.004 0.488 0.508 101.78 115.80 501.4 0.27 23.780 1.69626 7.050 0.004 0.498 0,498 101.56 114.28 501.4 0.14 17.698 1.39081 7.060 0.004 0.498 0.498 101.63 118.R4 501.6 0.17 37.270 2.16497 7.070 0.004 0.498 0,498 101.66 123.14 500.R 0.22 59.176 2.75561 7.080 n.004 0.498 0.498 101.60 127.57 501.1 0.27 81.095 3.12308 7.090 0.004 0.494 0.502 101.61 130.84 501.1 0.27 98.628 3.37378 i.100 0.004 0.494 0.502 101.62 137.02 501.1 0.27 118.143 3.3674 7.110 0.004 0.494 0.502 101.O6 141.25 501.1 0.28 121.573 3.h6636 7.120 o0.04 0.494 0.502 101.70 146.27 501.1 0.28 125.552 2.81667 7.130 n.004 0.494.5n0? 101.7;? 157.?6 501.1 0.28 133.671 2.4n0(6

381 TARLF B-7 (CONTI NIE) ) kIIN NFO. CNMPNSITfinN INLET OIUTLE1 INLFT PkES. HFAT MEAN HFAT CH4 C2H6 C3H8 TEMP. TEMP. PRES. DROP INPUIT CAPACITY (MOLE FRArTInN) (oF) (~F) (PSIS) (PSIO) (0 TIl/LR)(HTIJ/LR~F) 9.010 0.004 0.4H-, 0.510 37.21 39.40 250.0 0.10 1.747 0n.6745 q.020 0.004 0.4R4 0.510 37.22 42.466 250.2 0.10 3.10 0.6744q 4.030 0.004 0.4H6 0.510 37.11 44.50 250,0 0.10 5.038 0.6H205 9.040 0.004 0.489 0.507 37.20 47.60 250.3 0.12 7.136 0.6H6?3 9.050 0.004 0.489 0.507 37.21 50.13 250.1 0.22 11.847 0.416,1 9.060 0.004 0.494 0.502 37.10 51.46 249.9 0.32 16.239 1.13041 9.070 0.004 0.494 0.502 37.19 53.50 250.1 0.37 23.144 1.42036 9.080 0.004 0.495 0.501 37.OP 57.4q 250.2 0.39 43.291 2.0763. 9.090 0.004 0.495 0.501 37.14 62.93 250.0 0.47 hh.546 2.5H077 9.100 0.004 0.495 0.501 37.20 68.45 250.3 0.54 q2.4,4 2.94548 9.110 0.004 0.495 0.501 37.20 73.7R 250.1 0.59 121.075 3.30945 9.120 0.004 0.487 0.509 37.11 97.90 250.3 0.59 171.254 2.84149 9.121 0.00'4 0.487 0.509 37.11 98.23 250. 3 0.34 171.294 2.A0263 9.130 0.004 0.487 0.509 37.06 94.95 250.1 0.37 169.760 2.932.47 9.140 0.004 0.487 0.509 37.06 87.52 250.3 0.37 1]5.401 3.27774 9.150 0.004 0.487 0.509 37.04 85.03 250.2 0.38 164.096 3.42074 9.160 0.004 0.497 0.509 37.07 R2.57 250.4 0.34 162.658 3.57461 Q.170 0.004 0.487 0.509 37.07 79.53 249.6 0.37 156,.26 3.4HN47 4.010 0.004 0.495 0.501 150.15 157.48 248.9 1.47 3.88H 0.430465 4.020 0.004 0.495 0.501 150.13 174.56 250.7 1.47 12.747 (05214 4 4.030 0.004 0.495 0.501 150.21 199.51 248.6 1.47 25.713 0.52154 4.040 0.004 0.495 0.501 150.24 225.65 252.1 1.57 39.,53 0.52545 4.050 0.004 0.495 0.501 150.33 253.52 249.3 1.72 54.428 0.5294( 5.010 0.004 0.466 0.530 101.72 112.46 250.5 1.42 5.844 0,44440 5.020 0.004 0.466 0.530 101.46 122.14 252.1 1.33 11.026 0.53H75 5.030 0.004 0.466 0.530 101.70 130.40 251.2 1.40 15.26() 0.53182 5.040 0.004 0.469 0.527 101.72 158,.72 251.1 1.50 30.037 0.52694 5,.050 0.004 0.469 0.527 101.65 178.R 9 250.1 1.55 40.434 0.52488 TAHLF B-8 Basic Isothermal Data for Nominal 0.50 C2H6, 0.50 C3H8 Mixture RION NO. CnMPnSITINN INLET OUTLET INLET PKES. HEAT IS(ITHFRMAL CH4 C2H6 C03H8 TEMP. TEMP. PRES. O4P INPI.1.COEFF. (MDi.F FRACTION) (oF) (OF) (PSIAI ) (PS1D) (4TII/LH) (RTII/L PS I A) 19.010 0.004 0.506 0.490 151.03 151.00 2000.4 94.61 0.300 -0.00317 19.020 0.004 0.5n6 0.490 150.96 150.46 1795.3 101.11 0.452 -0.00447 19.035 0.004 0.506 0.490 150.98 150.98 1605.0 101.31 0.76R -0.00759 19.034 0.004 0.506 0.490 150.98 150.98 1605.0 101.31 0.621 -0.00613 19.040 0.004 0.506 0.490 150.99 150.96 1401.5 108.42 0.929 -(,.00R57 19.050 0.004 0.504 0.490 151.01 151.00 1204.3 111.04 1.459 -0.01314 19.060 0.004 0.506 0.490 151.00 150.99 968.9 115.13 3.076 -0.01(272 19.080 0.004 0.506 0.490 151.00 151.05 650.6 226.79 55.628 -0.74524 19.090 0.004 0.506 0.490 150.94 150.9R 819.7 137.,2 20.22R -01.1.467 19.100 0.004 0.504 0.490 150.94 150.96 395.9 287.14 21.730 -0.0756H 19.110 0.004 0.506 0.490 150.98 151.04 397.3 287.73 21.481 -0.0746A 1H8.010 0.004 0.492 0.504 250.92 250,92 2015.3 124.29 2.604 -01.02095 18.020 0.004 0.492 0.504 251.30 251.31 1817.6 109.83 3.233 -0.02944 18.030 0.004 0.492 0.504 251.07 251.07 1603.3 103.33 4.514 -0.043fR 18.040 0.004 0.491 0.505 251.17 251.18 1521.3 104,55 5.464f -0.0527H 18.050 0.004 0.491 0.505 250.93 250.97 1221.5 20H.67 15.997 -~0.07666 18.060 0.004 0.491 0.505 251.11 251.14 1021.6 220.h0 15.950 -().07230 18.070 0.nn004 0.493 0.503 251.11 251.11 822.5 251.32 15.462 -10.01525 18.080 0.004 0.493 0.503 251.10 251.07 620.4 225.20 12.174 -10.05401 1R.090 0.004 0.497 0.499 251.13 251.11 617.4 425.34 21.528 -0.01501l 18.100 0.004 0.497 0.499 251.19 251.19 358.7 255.14 11.10 -0.0455] TARLF B-9 Basic Isenthalpic Data for Nominal 0.50 C2H6, 0.50 C3H8 Mixture RIPN Mn. CIMPOSITION INLET OUTLET INLET PRES. HEAT I.THOMS))N CH4 C2H4 C,3HR TEMP. TEMP. PRES. L)R )P 1NP41 COEFFF. (MOlI)E FRACTION) (AF) (OF/L) (4FPSIA) (PS10 (IT1/LB (E/PSIA) 14.010 0.104 0.49s 0.501 -125.53 -124.,49 2009.1 165.54 0(.000 -0.00507 14.020 0.0,04 0.495 0.501 -125.48 -124.69 1619.4 167.36 0.000 -0.0)477 14.030 0.004 0.445 0.501 -125.48 -124.70 1237.4 167.492 0.000 -0.004t65 14.040 0.004 0.497 0.499 -125.49 -124.74 816.8 172.1 0.000 -0.00441 14.050 0.004 0.497 0.499 -125.51 -124.,9 415.8 183.42 0.00)0 -0.00447 14.0hO 0.004 0.497 0.499 -125.51 -125.01 319.5 125.468 0.000 -0.00398 13.010 0.004 0.4(5 0.501 37,48 37.73 2014.0 93.11 0.00O -0.OOta 13.015 0.00,n4 0.495 0.501 37.48 37.74 2014.0 93.11 0.000 -0.(102 1t 13.020 0.004 0.49* 0.501 37.44 37.87 2011.5 15H.04 0.000 -01.00272 13.030 0.004 0.494 0.501 37.51 37.92 1814,4 170.64 1.00)0 -0.0)f,44 13.040 0.004 0.494 0.501 37.48 37.R5 1414.9 16H.08 0.1000 -0.00,24 1.050 0n.004 0.495 0.501 37.52 37.84 1415.4 166.t2,0000 -0.00194 13.060 0.004 0.495 0.501 37.49 37.79 1217.4 180.74 0.000 -O.001b5 13.070 0.004 0.4u% 0,501 37.52 37.72 915.3 141.55 0.00)) -11.00D111 1(.040 0.1104 0,444 0.501 37,39 37,47 41H4. 14,.05 0.00() -0.00-43 13.090 0.004 0.4U% 0.501 37.52 37.51 402,.3 16.7 0.000 0.00007

382 TABLE BI10 Basic Isobaric Data for Nominal 0.27 C226, 0.73 CHp Mixture RUN NO. COMPOSITION INLET OUTLET INLET PRES. HEAT MEAN HE^T CH4 C2H6 C3H8 TEMP. TEMP. PRES. DROP INPUT CAPACITY (MnLE FRACTI)N) (OF) (~F) (PSIA) (PSID) (HTIU/LH)(RTU/LR~-) 8.010 0.001 0.274 0.725 200.82 211.37 2002.1 0.15 8.280 0.7H484 8.020 0.001 0.274 0.725 200.92 225.48 1999.7 0.15 19.254 0.78392.8021 0.001 0.274 0.725 200.92 225.51 1999.6 0.15 19.237 0.78235 8.030 0.001 0.274 0.725 200.81 251.54 2000.2 0.15 40.592 0.80020 8.031 0.001 0.274 0.725 200.81 251.49 1999.2 0.15 40.561 0.n0047 8.040 0.001 0.274 0.725 200.81 274.88 2000.0 0.15 60.442 (.81602 8.050 0.001 0.274 0.725 200.81 294.97 1999.6 0.1b 77.912 (1.R2748 8.051 0.001 0.274 0.725 200.82 294.77 1999.6 0.15 77.730 0.82736 1.010 0.001 0.282 0.717 -238.26 -228.18 1001.1 0.72 4.881 ().48416 1.020 0.001 0.282 0.717 -238.22 -214.40 1000.0 0.72 11.621 0.48793 1.030 0.001 0.281 0.718 -238.24 -186.34 1002.7 0.70 25.665 0.49450 1.040 0.001 0.281 0.718 -238.43 -159.84 999.9 0.72 38.774 0.49335 1.050 0.001 0.282 0.717 -237.96 -139.70 1001.2 0.70 48.743 0.49604 1.060 0.001 0.282 0.717 -238.03 -113.78 1002.5 0.70 62.507 0.50310 1.065 0.001 0.282 0.717 -238.03 -113.78 1002.5 0.70 61.H21 0.49758 1.066 0.001 0.282 0.717 -238.03 -113.78 1002.5 0.70 63.225 0.508RH 2.010 0.001 0.283 0.716 -153.70 -144.59 1000.5 0.55 4.605 0.50569 2.020 0.001 0.283 0.716 -153.70 -131.14 999.0 0.55 11.450 0.5079)4 2.030 0.001 0.283 0.716 -153.67 -101.90 1000.0 0.55 26.546 0.51219 2.040 0.001 0.283 0.716 -153.66 -78.54 1000.2 0.55 38.827 (.51689 2.050 0.001 0.282 0.717 -153.64 -55.91 1003.0 0.50 50.887 0.52069 2.060 0.001 0.282 0.717 -153.64 -36.88 1000.4 0.50 61.395 0.52582 2.070 0.001 0.290 0.709 -153.64 -11.56 1001.0 0.30 75.969 0.53469 2.071 0.001 0.290 0.709 -153.64 -11.47 1001.0 0.30 75.969 0.53433 2.072 0.001 0.290 0.709 -153.64 -11.37 1001.2 0.30 76.073 0).53472 3.010 0.001 0.279 0.720 0.82 10.59 1000.1 0.25 5.722 (058573 3.020 0.001 0.279 0.720 0.85 30-81 1001.9 0.25 17.762 n.59287 3.030 0.001 0.282 0.717 0.88 64.88 1000.3 0.25 39.013 0.60953 3.040 0.001 0.282 0.717 0.89 102-01 1002.9 0.25 63.547 0.62842 3.040 0.001 0.277 0.722 0.82 129.42 999.7 0.25 83.191 (.64691 9.010 0.001 0.274 0.725 200.78 207.65 1000.3 0.35 9.214 1.34252 9.020 0.001 0.274 0.725 200.75 221.56 1000.3 0.35 30.228 1.45273 9.030 0.001 0.274 0.725 200.77 235.23 1000.3 0.35 49.773 1.44404 9.031 0.001 0.274 0.725 200.77 235.27 1000.5 0.35 49.814 1.44369 9.040 0.001 0.274 0.725 200.77 250.73 1001.1 0.35 67.872 1.35845 9.050 0.001 0.275 0.724 200.68 274.10 1001.3 0.35 90.492 1.23252 9.060 0.001 0.275 0.724 200.77 291.48 999.5 0.35 104.567 1.15274 9.061 0.001 0.275 0.724 200.77 291.67 1000.3 0.35 104.756 1.15241 7.010 0.001 0.271 0.728 124.64 134.84 1000.3 0.20 7.633 0.74891 7.011 0.001 0.271 0.728 124.64 134.87 1000.9 0.20 7.658 (.74863 7.020 0.001 0.271 0.728 124.67 159.28 1001.0 0.20 27.178 0.78525 7.030 0.001 0.274 0.725 124.75 175.05 1001.5 0.20 41.178 0.81864 7.040 0.001 0.274 0.725 124.71 194.63 998.7 0.20 61.583 (.88(069 7.050 0.001 0.274 0.725 124.71 205.48 999.9 0.20 75.231 0,93141 6.010 0.001 0.277 0.722 125.21 134.87 498.9 0.45 8.560 0.88602 6.020 0.001 0.277 0.722 125.30 140.12 501.5 0.45 13.'27 0.92599 6.030 0.001 0.277 0.722 125.09 141.75 501.1 0.70 19.816 1.18954 6.040 0.001 0.277 0.722 125.05 144.06 501.1 0.80 31.104 1.63581 6.050 0.001 0.277 0.722 125.09 130.76 501.3 0.40 4.881 O.86195 6.06h 0.001 0.277 0.722 124.97 148.64 501.1 0.80 56.931 2.40513 6.065 0.001 0.277 0.722 124.97 148.64 501.1 0.80 56.409 2.38308 6.066 0.001 0.277 0.722 124.97 148.64 501.1 0.80 57.535 2.43066 6.067 0.001 0.277 0.722 124.97 148.64 501.1 0.80 56.352 2.38068 6.070 0.001 0.277 0.722 124.97 153.59 501.2 0.90 91.403 3.19370 6.080 0.001 0.277 0.722 124.88 155.33 501.0 0.90 106.542 3.49849 6.090 0.001 0.279 0.720 124.95 159.21 501.0 1.00 111.174 3.24552 6.100 0.001 0.279 0.720 124.95 165.80 501.1 1.00 117.432 2.87504 6.110 0.001 0.279 0.720 124.81 175.01 501.0 1.00 124.821 2.48658 6.120 0.001 0.274 0.725 124.73 199.12 501.0 1.00 141.680 1.90460 6.130 0.001 0.279 0.720 124.81 206.01 501.1 1.00 146.337 1.80236

383 TAPI F B-lla Basic Isothermal Data for Nominal 0.27 C2H6, 0.73 C3H8 Mixture Using Abe lute Pressure Transducers RUN NO. COMPnSITION INLET IOUTLET INLET PRES. HEAT IS()THFMAL CH4 C2H6 C3H8 TEMP. TEMP. PRES. DROPP INPUT J.T.COnFF. (MOLE FRACTInN) (~F) (OF) (PSIA) (PSID) (IHTI/LB) (RTI/LB PS I A I PIAI 5.030 0.001 0.277 0.722 127.40 127.37 16i1.l 93.04 0.06? -0.00(106 S.040 0.001 0.277 0.722 127.51 127.50 1412.4 94.,0 n.13P -0.00145 5.050 0.001 0.277 0.722 127.40 127.39 1221.7 91.QQ 0.71? -0.00230 5.055 0.001 0.277 0.722 127.40 127.39 1221.7 91.9w 0.21? -0.00o 30 5.060 0.001 0.272 0.727 127,45 127.45 1015.7 94.H4 0.335 -0.00353 5.070 0.001 0.272 0.727 127.55 127.57 825.2 101.02 0.529 -0.005 3 5.080 0.001 0.272 0.727 127.20 127.19 606.9 105. 86 0.H72 -0.00H24 5.090 0.001 0.275 0.724 127.41 127.39 519.9 79.13 0.783 -0.00990 10.010 0.001 0.275 0.724 202.99 203.00 1996.7 85.97 0.485 -0.00564 10.020 0.001 0.275 0.724 203.11 203.10 1810.9 91.36 0.669 -0.0073A 10.030 0.001 0.275 0.724 203.06 203.04 1613.6 105.85 1.103 -0.01042 10.040 0.001 0.274 0.725 203.31 203.28 1404.8 115.22 1.870 -0.016/3 10.050 0.001 0.274 0.725 203.23 203.22 1218.4 119.99 3.388 -0.02824 10.060 0.001 0.274 0.725 203.07 203.09 1006.8 138.87 13.821 -O.Oq95 10.070 0.001 0.273 0.726 203.17 203.19 R84.0 208.09 47.806 -0.22975 10.075 0.001 0.273 0.726 203.17 203.19 884.0 208.09 47.730 -0.22937 10.076 0.001 0.273 0.726 203.17 203.19 884.0 208.09 47.899 -0.23018 10.080 0.001 0.273 0.726 202.99 203.03 686.0 133.93 17.445 -0.13025 10.090 0.001 0.278 0.721 203.08 203.10 565.0 179.61 16.012 -0.08915 10.100 0.001 0.278 0.721 202.96 202.99 387.5 277.36 17.754 -0.06401 11.010 0.001 0.274 0.725 268.99 268.98 2002.1 122.03 2.065 -0.01692 11.011 0.001 0.274 0.725 268.99 269.01 2010.1 120.40 2.086 -0.01733 11.016 0.001 0.274 0.725 268.99 269.01 2012.1 120.40 2.083 -0.01730 11.020 0.001 0.274 0.725 268.93 268.93 1799.0 125.38 3.134 -0.02499 11.030 0.001 0.274 0.725 268.82 268.80 1600.9 140.56 5.445 -0.03873 11.040 0.001 0.274 0.725 268.84 268.83 1398.0 161.53 10.235 -0.06336 11.050 0.001 0.274 0.725 269.31 269.36 1210.7 202.61 17.071 -0.08425 11.060 0.001 0.275 0.724 268.89 268.92 1003.8 321.70 24.820 -0.07715 11.070 0.001 0.275 0.724 268.86 268.87 800.9 476.33 28.953 -0.06078 11.080 0.001 0.275 0.724 268.86 268.84 599.2 302.06 16.637 -0.05508 11.090 0.001 0.275 0.724 268.71 268.73 465.3 345.41 17.270 -0.05000 - AH VALIES ARE SUISPECTED TO BE FROM 3 TO 10 PERCENT TUO HIH DUE TO MASS LEAK TABLE B-llb Basic Isothermal Data for Nominal 0.27 C2H6, 0.73 C3H8 Mixture Using Differential Pressure Transducer RtN NO. COMPOSITION INLET OUTLET INLET PRES. HEAT ISOTHERMAL CH4 C2H6 C3HR TEMP. TEMP. PRES. DROP TNPUT J.T.COEFF. (MOLE FRACTION) (oF) (oF) (PSIA) (PSID) 1BTU/LR) (RTU/LR PSI ) 5.030 0.001 0.277 0.722 127.40 127.37 1616.1 92.70 0.062 -0.00067 5.040 0.001 0.277 0.722 127.51 127.50 1412.4 94.54 n0.13 -0.00146 5.050 0.001 0.277 0.722 127.40 127.39 1221.7 95.00 0.212 -0.00223 5.055 0.001 0.277 0.722 127.40 127.39 1221.7 93.44 0.212 -0.00227 5.060 0.001 0.272 0.727 127.45 127.45 1015.7 95.35 0.335 -0.00351 5.070 0.001 0.272 0.727 127.55 127.57 825.2 101.17 0.529 -0.00523 5.080 0.001 0.272 0.727 127.20 127.19 606.9 106.70 0.872 -0.00817 5.090 0.001 0.275 0.724 127.41 127.39 519.9 79.79 0.783 -0.00982 10.010 0.001 0.275 0.724 202.99 203.00 1996.7 85.49 0.485 -0.00567 10.020 0.001 0.275 0.724 203.11 203.10 1810.9 90.56 0.669 -0.00799 10.030 0.001 0.275 0.724 203.06 203.04 1613.6 106.18 1.103 -0.01039 10.040 0.001 0.274 0.725 203.31 203.28 1404.8 115.38 1.870 -0.01621 10.050 0.001 0.274 0.725 203.23 203.22 1218.4 120.39 3.388 -0.02814 10.060 0.001 0.274 0.725 203.07 203.09 1006.8 139.62 13.821 -0.09898 10.070 0.001 0.273 0.726 203.17 203.19 884.0 208.78 47.806 -0.22898 10.075 0.001 0.273 0.726 203.17 203.19 884.0 208.78 47.730 -0.2286? 10.076 0.001 0.273 0.726 203.17 203.19 884.0 208.78 47.899 -0.22943 1(.080 0.001 0.273 0.726 202.99 203.03 686.0 134.51 17.445 -0.12969 10.090 0.001 0.278 0.721 203.08 203.10 565.0 181.00 16.012 -0.08846 10.100 0.001 0.278 0.721 202.96 202.99 387.5 279.69 17.754 -0.06348 11.010 0.001 0.274 0.725 268.99 268.98 2002.1 121.37 2.065 -0.01701 11.011 0.001 0.274 0.725 268.99 269.01 2010.1 118.97 2.086 -0.01754 11.016 0.001 0.274 0.725 268.99 269.01 2012.1 118.97 2.083 -0.01751 11.020 0.001 0.274 0.725 268.93 268.93 1799.0 125.88 3.134 -0.02490 11.030 0.001 0.274 0.725 268.82 268.80 1600.9 140.58 5.445 -0.03873 11.040 0.001 0.274 0.725 268.84 268.83 1398.0 162.20 10.235 -0.06310 11.050 0.001 0.274 0.725 269.31 269.36 1210.7 203.49 17.071 -0.O0R89 11.060 0.001 n.275 0.724 268.89 268.92 1003.8 322.89 24.820 -0.07687 1.1.070 0.001 0.275 0.724 268.86 268.87 800.9 477.48 28.953 -0.06()64 11.080 0.001 0.275 0.724 268.86 268.84 599.2 303.62 16.637 -(.05470 11.090 0.001 0.275 0.724 268.71 268.73 465.3 348.4? 17.270 -0.04957 A' ~H VAI.IIES ARF.SUSPFCT ED TO RE FR8(M 3 TI1 10 PERCENT TlI(l HIG.H 1)lUF Til MAS l.t=4K

384 TAHI.F B-12 Basic Isenthalpic Data for Nominal 0.27 C2H6, 0.73 C3H8 Mixture Using Absolute Pressure Transducers RIoN NO. COnMpnOSITinN INLET TLT INLET PRES. HFAT I. H(IMIN CH4 C2H6 C3H8 TEMP. TEMP. PRES. )DROP INPUT Ct-FF-. (MOFE FRACTION) (OF) (OF) (PSIA) (PSID) (O;T1I/LH) (~-/EPSIA) 12.010 0.001 0.272 0.727 -150.23 -149.66 1992.3 100.96 0.000 -(.0OO56H 12.020 0.001 0.272 0.727 -150.23 -149.80 1194.3 118.94 0.000 -0.00967 12.030 0.001 0.272 0.727 -150.22 -149.75 805.7 115.45 0.000 -0.00410 12.040 0.001 0.272 0.727 -150.20 -149q.8 317.9 125.71 0.00() -(0.002 4.010 0.001 0.275 0.724 1.61 2.03 2003.h 104.90 0.000 -0.001)6 4.015 0.001 0.275 0.724 1.61 2.03 2003.5 104.00 0.000 -0).0396 4.030 0.001 0.275 0.724 1.68 2.03 1604.9 109.05 0.0)00 -0.0()137 4.040 0.001 0.273 0.726 1.6t 2.06 1431.0 103.52 0.000 -0.01(16?1 4.050 0.001 0.273 0.726 1.68 2.07 1203.7 109.44 0.000 -0.(0O4sq 4.060 0.001 0.276 0.723 1.68 2.07 1006.6 117.67 0.00( -0.00336 4.070 0.001 0.276 0.723 1.61 1. 711. 116.39 0.)0)) -0.0031 4.080 0.001 0.276 0.723 1.58 1.90 416.1 111.19 0.000 -0.00231 4.090 0.001 0.776 0.723 1.58 1.83 248.3 93.19 0.000 -0.00213 4.100 0.001 0.276 0.723 1.58 1.85 1041.6 81.95 0.000 -0.001334 5.010 0.001 0.277 0.722 127.25 127.27 2018.7 102.91 0.000 -0.00012 5.020 0.001 0.277 0.722 127.35 127.30 1821.a 98.09 0.000 o.on0045 TABLE B-13 Basic Isobaric Data for Nominal 0.78 CH4, 0.22 C2H6 Mixture WINUM,1 NMil. I.iMPSI r )1)N INLFT IITLFT INIFT -St?. HF/ AT i-A8N HFIA C.H4 1 H, C -.H TFMP. TEMP. PRF'. i)k()P INPlT CAPAC. ITY (~111-F NRA(IIN (o "F) ( oF ) (P1^ (.)' ll (KTII/LtIi 1l1/{'n~H.01f)i1 0.71I8H ('. rI (1.0 -. 9.23I -311.5) -, 20)(0. 1.I.0. 19.,h6 1). 9) 4',.0u 0.77) 0.221 I.00) -59., 0 -1.720 149. lQ. )1/ 49.543 (1 I.(i H. n1,n o.vI2 0.271 n.o00 -59.13 1.(? 2001.' 1 0.07 61.04 1.(174H H;.04n O. 7H 0.221 0).001 -59.21 26.011 2002. 0.0 I H. HI, 1.042H 4 M.,)5''./' 11.2'1 ) 1 0.001 -5Q.27 1.10H 199. 0.07 1011.557 I. 4 t,' 4 A.06n 0./I' 0.'21 0.00) -59.2H 42.3 72001.8 (.)f 106.H36 l.r)44311 H.n7r1 0. If 0.21.1).001I -59.7) 52.04 7000.6 0.. 11l4.174 1.031)49 H.OR 1. M 0I.2?) (0.001 -539.23 71.73 2 000. H 0.07 )13.65' I117-,:'.01 0.777 1.222 1o.001 71.06 RR.7 20011.H 0.0,. 1.40 O1. HHH, 2.020 0.777 0.222 0.n001 7R 12 1110.64 2002.5 0.05'. 10) 1.HA58H 1 2.030 0.77Z 0.722 1.001 78.02 13/.3H 2001.) I."6 4 0,>.1.H826H4 2.n40 0.775 0.224 0.001 78.02 16H.6H 20(12.2 1.1), l //.52 (1. /315 2.1050 0./15 0.27124 0.001 78.02 202.04 1999.6 0.)(O 96. -.1.77884 4.010 0.77H 0.2?1 0.001 202.09 212.68 1 99 9. 7 0,.11 /.55 0.713 4.020 0.778 0.2?1 0.001 202.14 226.74 2003.4 0.11 17.320 01.70)433 4.030 0.777 0.22? 0.001 202.16 252.35 2003.3 0.12 3".474,1.7069q 4.040 0.777 0.222 0.001 202.31 277.43 2002.6'i.14 527.846,.7'/ 49 4.0'-0 0.777 0.2?2 0.001 202.24 301.15 2001.? U.14 64.45''.7(,. )0 9.010 0,71t 0..23 0.001 -59.44 -40.36 1502.? 0.5 21.4601 1.1249) 9.020 0.776 0. 23 0.001 -59.47 -1Q.66 1501.0 ).O) 4".344 1.21457 9.030 0.776 0.223 0.001 -59.46 -29.25 1503.4'1.05'9.028 ].154 9_.040 0.776 0.223 0.001 -59.46 -24.h67 1502.4 0.05 41./63 9.050 0.777 0.222 0.001 -59.44 1.41 1500.27 0.05 77.44"9 ).17T277 9.060 0.777 0.?2? 0.001 -59,.37 25.36 1499,. ('.05 106.916 i.26(173 9.070 0.777 0.222 0.001 -59.28 57.35 14c7.', 0.05 11/./60 1.18924 9.080 0,77? 0. 2?? 0.001 -59.37 77.28 1499.4 0.05 155. 6,h.1 31 / 18.010 0.770 0.?22 0.001 -152.14 -127.1? 1001.1 0.01- 0,.24 0.?C7(6 18.016 0.770 0.223 0.001 -152.14 -127.12 1001.1..) 2?'. Hl',). 822' 18.020 0.770 0.229 0.001 -152.14 -102.44 999.7 (1.'h 42.-)r.855.' 18.030 0.771 0.29q 0.001 -152.13 -82.18 999.1 0.126 "3. 5b 1.9)1,:.4 18.040 0.771.228P 0.001 -152.10 -6,0.5 1002.1 o.06 30.703 0n.903 10.010 0.771 0.221 0.001 -59.47 -54.92 998.7,1.06 6.12..."'A 10.015 0.778 0.?l1 0.001 -59.47 -54.92 998.7 0.06 9.10' 1.701)W)'4 10.016 0.778 0.221 0.001 -59.47 -54.92 998.7 0.06 H.15; 1.741'1U.020 0.77H 0.221 0.00) -59.45 -49.65 1001.4 0.O16 1]., 4 ]. 944"' 1..030 0.778 0.1 001 -59.47 -40.21 1000.1 0.06O 41.31. 10.040 0.77H 0.221 0.001 -59.47 -29.23 1001.8 0.()6 h /4. 17,'.111)2 11.0o50 0. 7 0. 0.0)1) -59.43 -14-.64 111))3. 1 01)6 f'l.11i''.F)]l / 1().060 0.777 0.22)? 0.01) -59.42 0.2?4 J:,1 (Q~.16 1104,1. (,44/, I 1110.070 01,77''../ 1.011 -59,46?1,3 1(100(1,0 0.0 I I,. I' i/I''',' I l r.(-7I 1? 1iH! 1 c. -. -'. (.51..58 1~1~ (;, i/.11 * ) {.' 1, /')'' }(~().11'~ (~.( 4 l;~ {,,)I~~(J -q&l I hH t)l{ (J.1, l,,,,,,{ {',

385 TABLE B-13 (CONTINUED) TSIRARIC OATA FOR NOMINAL 0.777 CH4, 0.223 (2H6 MIXTUJRE RIIN Nn. CnMPnsITIni INLET (1LJTLET INLET PRES. HEAT MEAN HFAT CH4 C2H6 C3H8 TEMP. TEMP. PRFS. )ROP INPtT CAPACITY (MOLE FRACTION) (~F) ("F) (PSIA) (PSID) (1Tl/I 9) (8Tll/L8R~F 14.010 0.777 0.22? 0.001 -240.69 -221.28 q99.1 OoB 14.1749 o.773n0 14.020 0.777 0.222 0.001 -240,76 -189.3? 1000.4 0.05 37.4)8 0.73h65 14.030 0.777 0.222 0.001 -240.73 -169,16 1002.2 0,05 53.421 0.74632 14.040 0.777 0,222 0.001 -240.76 -148.43 1002.8 0.05 69.7134 0.7553f, 3.010 0.779 0.220 0.001 78.23 87.84 1001.9 0.14 6.4h0 (.h6175H 3.020 0.779 0.220 0.001 78.00 10P.37 99.3 0.16 20.144 0.66325 3.030 0.779 0.220 0.001 78.00 138.47 999.8 0.19 39.768 0.65765 3.035 0.779 0.220 0.001 78.00 138.47 999.8 0.19 39.701 0,65654 3.040 0.778 0.221 0.001 78.01 167.57 1001.7 0.19 57.916 0.64667 3.050 0.778 0.221 0.001 77.92 202.95 1000.0 0.19 80.211 0.64152 5.010 0.778 0.221 0.001 202.28 212.81 998.4 0.18 5.862 0.55682 5.015 0.778 0.221 0.001 202.28 212.H1 998.4 0.18 5.957 0.96581 5.020 0.778 0.221 0.001 202.21 227.11 1002.6 0.18 15.756 0.63258 5.030 0.778 0.221 0.001 202.25 251.74 1000.5 0.18 31.443 0.63535 5.040 0.778 0.221 0.001 202.20 276.66 1001.9 0.18 47.491 0.63777 5.050 0.778 0.221 0.001 202.17 300.70 1001,4 0.18 63.208 0.64150 17.010 0.771 0.228 0.001 -152.30 -130.83 498.8 0.07 18.797 0.87550 17.020 0.771 0.228 0.001 -152.29 -126.03 500.1 0.07 22.954 0.87423 17.030 0.771 0.228 0.001 -152.31 -116.34 499.4 0.07 32.267 0.89716 17.040 0.771 0.228 0.001 -152.30 -113.10 499.5 0.07 35.137 0.89647 17.050 0.771 0.228 0.001 -152.29 -102.79 501.9 0.17 78.641 1.58857 17.060 0.780 0.219 0.001 -152.28 -90.48 498.9 0.17 111.371 1.80200 17.070 0.780 0.219 0.001 -152.22 -66.00 501.8 0.17 163.664 1.89804 17.080 0.780 0.219 0.001 -152.16 -56.78 500.3 0.17 183.233 1.92109 17.090 0.769 0.230 0,001 -152.17 -51.26 499.5 0.17 193.828 1.92089 17.100 0.769 0.230 0.001 -152.20 -42.23 499.0 0.17 206.370 1.87650 15.010 0.778 0.221 0.001 -240.72 -214.98 249.7 0.10 18.990 0.73771 15.020 0.778 0.221 0.001 -240.71 -185.18 250.1 0.10 41.758 0.75199 15.025 0.778 0.221 0.001 -240.71 -185.18 250.1 0.10 41.853 0.75370 15.030 0.778 0.221 0.001 -240.70 -158.85 251.3 0.10 62.592 0.76470 16.010 0.771 0.228 0.001 -165.84 -161.30 250.1 0.10 3.156 (.H82H/ 16.020 0.771 0.228 0.001 -165.81 -155.50 248.4 0.10 8.551 (,82965 16.030 0.771 0.228 0.001 -165.80 -153.97 250.4 0.34 14.197 1.199h 16.040 0.771 0.228 0.001 -165.81 -153.47 248.9 0.34 21.158 1.714 14 16.045 0.771 0.228 0.001 -165.81 -153.47 248.9 0.34 21.214 1.71,4 16.050 0.771 0.228 0.001 -165.81 -150.23 248.5 0.34 43.735 2.HO8h)( 16.060 0.771 0.228 0.001 -165.78 -131.35 249.7 0.34 92.025 3.23178 16.070 0.769 0.230 0.001 -165.78 -116.63 249 5 0.34 134.149 2.7419^ 16.080 0,769 0.230 0.001 -165.77 -92.31 249.3 0.34 182.35/ 2.48231 16.090 0.76i9 0.230 0.001 -165.77 -90.25 249.1 0.34 186.023 2.463(1h 16.100 0.769 0.230 0.001 -165.77 -86.45 249.7 0.34 194.764?.45534 16.110 0.769 0.230 0.001 -165.76 -78.89 248.9 0.34 212.h51 2.44794 16.120 0.769 0.230 0.001 -165.69 -75.14 249.5 0.34 218.05 2?.40)80) 16.130 0.769 0.230 0.001 -165.75 -59.92 249.1 0.34 227.104 2.14542 11.010 0.777 0.222 0.001 -59.55 -36.41 251.5 0.38 12.736 0. b5n4 11.020 0.777 0.222 0.001 -59.56 -18.86 251.2 0.39 22.246 (,44h5() 11.030 0.777 0.222 0.001 -59.57 1.40 250.3 0.39 32.737 O.5b3h3 11.040 0.778 0.221 0.001 -59.58 25.85 249.7 0.39 45.377 0.53118 11.050 0.778 0.221 0.001 -59.55 50.47 250.0 0.39 58.203 (.529nQ 11.060 0,778 0.221 0.001 -59,56 75.29 252.1 0.39 71.295 (.5,186,

386 TABLE B-14 Basic Isothermal Data for Nominal 0.78 CH4, 0.22 C2H6 Mixture RtUN NO. COMPOSITION INLET OUTLET INLET PHES. HEAT I STHERMAL CH4 C2H6 C3HR TEMP. TEMP. PRES. DRUP INPUT J.T.CEFFFF. (MOLE FRACTION) (1F) (OF) (PSIA) (PSID) (BTI)/LR) (RTWt/LR PSIA) 7.010 0.778 0.221 0.001 -58.37 -58.31 1999.4 178.65 1.033 -0.00578 7.020 0.778 0.221 0.001 -58.46 -58.39 1799.6 70.62 1.595 -0.02258 7.030 0.778 0.221 0.001 -58.45 -58.37 1603.2 263.46 3.138 -0.01191 7.040 0.778 0.221 0.001 -58.44 -58.40 1600.8 432.04 6.312 -0.01461 7.050 0.778 0.221 0,001 -58.49 -58.45 1390.5 394.80 10.130 -0.02566 7.060 0.778 0.221 0.001 -58.60 -58.71 1405.1 517.47 14.667 -0.02834 7.065 0.778 0.221 0.001 -58.60 -58.71 1405.1 504.50 14.667 -0.02907 7.070 0.778 0.221 0.001 -58.47 -58.60 1202.1 243.42 9.285 -0,03814 7.080 0.778 0.221 0.001 -58.32 -58.17 998.8 155.75 20.113 -0.12913 7.090 0.778 0.221 0.001 -58.37 -58.30 984.7 288.02 45.239 -0.15707 7.095 0.778 0.221 0.001 -98.37 -58.30 984.7 275.99 45.232 -0.16389 1.010 0.777 0.222 0.001 79.28 79.31 1996.3 203.70 7.269 -().03568 1.020 0.777 0.222 0.001 79.14 79.13 2000.0 415.98 15.711 -0.03777 1.025 0.777 0.227 0.001 79.14 79.13 2000.0 415.98 15.772 -0.03792 1.026 0.777 0.222 0.001 79*14 79.13 2000.0 415.98 15.656 -0.03764 1.030 0.777 0.222 0.001 79,16 79.12 1602.6 105.93 4.433 -0.04185 1.040 0.778 0.221 0.001 79.07 79.09 1601.2 339.09 14.464 -0.04266 1.050 0.778 0.221 0.001 79.12 79.06 1600.9 541.47 23.433 -0.04328 1.060 0.778 0.221 0.001 79.06 79.04 1045.8 220.67 9.421 -0.04;69 1.070 0.777 0.222 0.001 78.97 7R.90 1045.8 439.20 18.576 -0.04230 1.075 0.777 0.222 0.001 78.97 78.90 1045.8 439.20 18.643 -0.n4?45 1.076 0.777 0.222 0.001 78.97 78.90 1045.8 439.20 18.510 -0.04215 1.RO 80.777 0.222 0.001 79.08 79.02 1048.4 636.18 26.555 -0.04174 1.090 0.777 0.222 0.001 79.07 79.09 1045.6 842.79 34.322 -0.04072 1.095 0.777 0.222 0.001 79.07 79.09 1045.6 842.79 34.415 -0.04083 1.096 0.777 0.222 0.001 79.07 79.09 1045.6 842.79 34.231 -0.0406? 1.100 0.777 0.222 0.001 79.07 79.09 1045.2 918.97 37.292 -0.0405R 6.010 0.778 0.221 0.001 254.86 254.88 1999.9 208.48 3.769 -0.01808 6.020 0.778 0.221 0.001 254.92 254.87 2001.5 424.86 7.876 -0.01854 6.030 0.778 0.221 0.001 254.93 254.93 2000.5 646.95 12.189 -0.01H84 6.040 0.778 0.221 0.001 255.00 254.94 2004.1 857.01 16.394 -0.01913 6.050 0.778 0.221 0.001 255.04 255.04 1153.0 228.69 4.647 -0.02032 6.060 0.778 0.221 0.001 256.22 256.24 1148.2 455.62 9.398 -0.02063 6.070 0.778 0.221 0.001 255.81 255.81 1148.9 635.89 13.144 -0.02067 6.080 0.778 0.221 0.001 256.08 256.05 1148.5 846.91 17.570 -0.02075 6.090 0.778 0.221 0.001 256.13.256.11 1145.1 1038.00 21.489 -0.02073 * H VAIIIFS ARE SIISPECTFO TO RE FROM 3 TO 10 PERCENT TOO HIGH Dl)F TO) MASS LEAK TAHLF B-15 Basic Isanthalpic Data for Nominal 0.78 CH4, 0.22 C2H6 Mixture RIIN NO. COMPnsITin T NTET INLET ITT NT PRES. HFAT JI. THflMSON CH4 C2H6 C3HR TEMP. TEMP. PRFS. [R)LP INPIJT COFl-P. (MnIF FRACTION) (OF) (F) (PSIA) (PSID) (RTI/LP) (eF/PSIA) 13.010 n.777 0.222 0.001 -253.21 -252.39 2008.2 142.38 0.000 -0.0058R 13.020 0.777 0.222 0.001 -253.22 -252.29 1703.3 135.72 0.000 -0.006H6 13.030 0.777 0.222 0.001 -253.23 -252.22 1393.9 132.89 0.000 -0.00757 13.040 0.777 0.222 0.001 -253.18 -252.09 1035.1 119.97 0.000 -0.00906 13.050 0.777 0.222 0.001 -253.23 -252.17 804.0 129.04 0.000 -10.0)0823 13.055 0.777 0.222 0.001 -253.23 -252.17 804.0 124.02 0.000 -0.o0856 12.010 0.778 0.221 0.001 -150.55 -150.57 2000.6 161.29 0.000 0.n0014 12.020 0.778 0.22? 0.001 -150.64 -150.56 1701.1 154.23 0.000 -0.00051 12.030 0.778 0.221 0.001 -150.58 -150.47 1401.7 161.12 0.000 -0.00070 12.n40 0.778 0.221 0.001 -150.57 -150.38 1099.8 161.50 0.000 -0.00114 12.050 0.778 0.221 0.001 -150.53 -150.27 804.0 171.13 0.000 -(.00151 12.060 n.778 0.221 0.001 -150.51 -150.22 603.9 180.39 0.000 -0.00156 17.070 0.778 0.221 0.001 -150.51 -150.14 499.5 160.69 0.000 -0.00230

387 TAHLF B-16 Basic Isobaric Data for Nominal 0.48 CH4, 0.52 C2H6 Mixture RUN NO. CnMPnSITinN INLET nOlTLET INLET PRES. HEAT MEAN HEAT CH4 C?H6 C3H8 TEMP. TEMP. PRES. DRKUP INPUT CAPACITY (MOLE FRACTION) (~F) (OF) (PSIA) (PSID) (BTUI/LR)(BTI)/LRF) 17.010 0.480 0.517 0.003 0.40 28.69 1999.4 0.13 25.032 0.88469 17.020 0.480 0.517 0.003 0.25 51.97 1999.8 0.13 46.758 0.90408 17.030 0.480 0.517 0.003 0.28 75.92 1999.4 0.13 71.930 0.95090 17.040 0.477 0.520 0.003 0.32 81.41 2002.8 0.13 76.394 0.94198 17.045 0.477 0.520 0.003 0.32 81.41 2002.R 0.13 75.991 0.q3701 17.046 0.477 0.520 0.003 0.32 81.41 2002.R 0.13 76.696 0.94570 17.050 0.477 0.520 0.003 0.28 87.18 2001.4 0.13 83.036 0.95562 3.010 0.479 0.518 0.003 -230.03 -204.41 1490.6 0.05 16.624 0.64877 3.020 0.479 0.518 0.003 -230.01 -176.32 1490.5 0.05 34.522 0.64300 3.030 0.480 0.517 0.003 -229.99 -151.58 1489.3 0.05 50.507 0.64412 3.040 0.480 0.517 0.003 -229.99 -127.44 1490.3 0.05 66.492 0.64839 3.050 0.480 0.517 0.003 -229.94 -99.68 1490.4 0.05 85.413 0.65570 8.010 0.479 0.518 0.003 -100.17 -69.83 1499.5 0.06 21.834 0.71972 8.020 0.479 0.518 0.003 -100.13 -30.16 1499.6 0.06 53.577 0.76564 R.030 0.479 0.518 0.003 -100.13 0.53 1501.3 0.06 80.001 0.79410 16.010 0.475 0.522 0.003 0.32 30.04 1499.8 0.10 31.314 1.0539q 16.020 0.475 0.522 0.003 0.36 45.82 1502.0 0.10 49.846 1.0q964 16.030 0.475 0.522 0*003 0.29 49.53 1503.1 0.10 54.226 1.10130 16.040 0.475 0.522 0.003 0.14 53.57 1501.0 0.10 59.847 1.12010 16.050 0.475 0.522 0.003 0.16 57.76 1499.7 0.10 65.432 1.13588 16.060 0.475 0.522 0.003 0.21 80.47 1499.1 0.10 93.322 1.16263 16.070 0.475 0.522 0*003 0.25 102.86 1500.0 0.10 117.013 1.14035 14.010 0.477 0.520 0.003 99.95 133.98 1499.0 0.15 31.293 0.91q57 14.020 0.477 0.520 0.003 99.72 161.32 1499.8 0.15 53.159 0.86290 14.030 0.477 0.520 0.003 99.41 194.38 1499.3 0.15 77.120 0.81204 14.035 0.477 0.520 0.003 99.41 194.38 1499.3 0.15 75.099 0.79076 14.036 0.477 0.520 0.003 99.41 194.38 1499.3 0.15 76.726 0.80790 14.040 0.478 0.519 0.003 99.81 220.49 1502.1 0.15 96.753 0.80172 14.050 0.478 0.519 0.003 100.20 251.34 1499.9 0.15 117.742 0.77904 11.010 0.482 0.514 0.003 249.88 271.97 1500.2 0.10 15.013 0.67971 11.020 0.482 0.514 0.003 249.90 291.23 1500.8 0.10 28.198 0.68227 11.030 0.482 0.514 0.003 249.96 302.80 1500.9 0.10 36.337 0.68772 15.010 0.479 0.518 0.003 0.31 15.62 1253.6 0.10 17.901 1.16871 15.020 0.479 0.518 0.003 0.23 20.10 1253.7 0.10 23.715 1.19314 15.030 0.479 0.518 0.003 0.31 25.69 1253.9 0.10 31.432 1.23812 15.040 0.477 0.520 0.003 0.23 30.38 1251.0 0.10 38.224 1.26791 15.050 0.477 0.520 0.003 0.20 35.91 1249.6 0.10 46.906 1.31361 15.060 0.477 0.520 0.003 0.31 44.70 1248.6 0.10 60.039 1.35234 15.070 0.478 0.519 0.003 0.25 58.62 1251.9 0.10 80.495 1.37893 15.080 0.478 0.519 0.003 -0.44 108.37 1249.6 0.10 133.888 1.23051 7.010 0.479 0.518 0.003 -100.04 -65.41 975.3 0.08 25.935 0.74883 7.020 0.479 0.518 0.003 -100.04 -32.48 975.4 0.08 53.901 0.79787 7.030 0.479 0.518 0.003 -99.96 0.42 975.2 0.08 91.054 0.90714 7.040 0.479 0.518 0.003 -100.04 4.68 974.5 0.08 98.225 0.93796 7.050 0.479 0.518 0.003 -100.03 8.85 976.3 0.08 105.569 O.96956 10.010 0.480 0.517 0.003 0.90 5.87 979.3 0.07 8.041 1.200h 10.020 0.480 0.517 0.003 1.08 8.66 979.6 0.07 13.121 1.73031 10.030 0.480 0.517 0.003 0.95 11.17 978.8 0.07 18.381 1.79725 10.050 0.480 0.517 0.003 1.12 15.83 980.7 0.07 27.496 1.860Rh 10.060 0.479 0.518 0.003 0.98 20.76 979.8 0.07 38.661 1.95505 10.070 0.479 0.518 0.003 1.16 25.69 982.1 0.07 48.736 1.98622 10.080 0.479 0.518 0.003 0.94 32.55 982.7 0.07 62.617 1.9R)50 10.090 0.479 0.518 0.003 0.69 70.80 980.8 U.07 110.389 1.57443 10.100 0.479 0.518 0.003 1.38 103.07 980.1 0.07 135.513 1.33259 4.010 0.475 0.522 0.003 -101.11 -70.33 749.9 0.35 23.257 0.75561 6.020 0.475 0.522 0.003 -100.86 -35.97 751.4 0.22 53.394 O.82290 6.030 0.476 0.521 0.003 -101.49 -31.64 749.5 0.22 58.893 0.84311 6.040 0.476 0.521 0.003 -101.48 -26.18 74q.1 0.22 69.119 0.9179h 6.050 0.476 0.521 0.003 -101.45 -6.30 749.1 0.22 106.737 1.12178 6.060 0.474 0.523 0.003 -101.43 5.83 748.7 0.22 133.614 1.24579 6.070 0.474 0.523 0.003 -101.43 19.99 750.0 0.22 169.160 1.39322 6.080 0.474 0.523 0.003 -101.41 39.13 749.7 0.22 194.937 1.38704 5.010 0.477 0.520 0.003 -99.42 -78.40 499.7 0.14 16.353 0.77818 5.020 0.477 0.520 0.003 -99.35 -75.05 499.6 0.14 19.104 0.78612 5.030 0.477 0.520 0.003 -99.33 -69.80 500.7 0.14 28.84? 0.97678 5.040 0.477 0.520 0.003 -99.33 -64.05 501.5 0.14 39.286 1.11329 5.050 0.483 0.514 0.003 -99.35 -59.64 501.6 0.14 47.317 1.1"14T 5.060 0.481 0.514 0.003 -99.26 -10.74 500.6 0.14 148.787 1.68077 5.070 0.483 0.514 0.003 -99.30 -3.95 499.7 0.14 169.551 1.77817 5.080 0.483 0.514 0.003 -99.33 1.13 500.0 0.14 186.991 1.86118 5.090 0.480 0.517 0.003 -99.33 9.43 500.7 0.14 195.934 1.80148 5.100 0.480 0.517 0.003 -99.20 19.70 500.4 0.14 202.454 1.70444 5.110 0.480 0.517 0.003 -99.35 50.14 501.2 0.14 222.354 1.48749 4.010 0.485 0.51.2 0.003 -136.77 -132.08 250.7 0.07 3.405 0.72732 4.020 0.485 0.512 n.003 -136.71 -128.23 250.9 0.07 7.054 0.83244 4.030 0.485 0.512 0.003 -136.75 -123.88 249.8 0.07 17.310 1.34503 4.040 0.485 0.512 0.003 -136.77 -125.33 248.8 0.07 14.661 1.28094 4.050 0.485 0.512 0.003 -136.75 -120.92 749.6 U.07 23.426 1.47529 4.060 0.485 0.51? 0.003 -136.75 -115.20 249.? 0.07 34.406. 74 4.070 0.485 0.512 0.003 -136.81 -81.69 249.o (1).0?.3 (. 4.75.40 4.080 0.485 0.512 0.003 -136.71 -4h.55 250.7 0.07 17h.q17R l.QtU^T 4.090 0.480 0.517 0.003 -136.71 -41.94 250.2 (.07 l'..?5?./)4H,. 4.100 0.480 0.517 0.003 -136.70 -37.41?51.3 (.n07 V-.0,ns'.14^l 4.110 0.480 0.517 0.003 -136.75 -18.4n0 5] 0.'7;.2.f 1.. 4.120 0.480 0.517 0.003 -136.71 C.27 290.4 0.,1/ >40.N0? I,>:~ 73(

388 TA8LF B-17 Basic Isothermal Data for Nominal 0.48 CH4, 0.52 C2H6 Mixtura RIIN MN. COMPOSITION INLET OUTLET IN.LET PKES. HFAT IsiTlHtEM\,, C.H4 CH6 C3HF TEMP. TEMP. PRFS. I)RUP INPUT J.I.r.f1FFF. (MUlLF FRACTION) (OF) (OF) (PSIa) (PSID)) (RTII/Li) (RItl/.H P IA) 9.045 0,486 0.511 0.003 -99.00 -9R.91 395.5 272.23 83.494 -0. O3071 18.010 0.479 0.18l 0.003 1.71 1.65 2020.7 144.34 0.23 -0.00417 18.020 0.479 0.51A 0.003 1.h4 1.56 1803.8 152.24 0.940 -'O.0,18 18.030 0.479 0.518 0.003 1.53 1.47 1602.7 154.55 1.561 -0.01010 18.035 0.479 0.518 0.003 1.53 1.47 1602.7 154.55 1.399 -0.)00,90) 18.040 0.479 0.518 0.003 1.77 1.65 1397.0 157.35 2.191 -0.0139, 18.050 0.479 0.518 0.003 1.95 1.90 1202.1 163.50 4.060 -0.0?493 18.055 0.479 O.518 0.003 1.95 1.90 1202.1 163.50 4.050 -0.02477 18.056 0.479 0.518 0.003 1.95 1.90 1202.1 163.50 4.06 -(i.0?4HH 1R.060 0.479 O.18A 0.003 1,66 1.86 977.3 134,63 15.876 -0.1179? 18.070 0.479 0.518 0.003 2.00 2.04 978.3 270.76 38.601 -0.14257 P8.080 0.479 0.518 0.003 1.37 1.34 691.5 293.53 71.912 -0.24499 18.090 0.479 0.518 0.003 n.69 0.55 447.9 341.34 27.609 -0.080R7 13.010 0.480 0.517 0.003 101.43 101.31 1959.0 223.91 H.714 -0.03894 13.020 0.480 0.517 0.003 101.45 101.41 1604.R 258.55 15.119 -0.05848 13.030 0.480 0.517 0.003 101.32 101.33 1224.2 301.46 19.197 -0.n63hR 13.040 0.480 0.517 0.007 101.8? 101.63 9H9.1 358.64 20.807 -(0.0502 13.050 0.480 0.517 0.003 101.52 101.50 793.6 344.16 18.330 -0.05368, 13.060 0.480 0.517 0.003 101.59 101.67 598.1 281.95 13.995 -0.04984 13.070 0.4q8 0.517 0.003 101.64 101.55 397.2 294.81 13.333 -0.04527 12.010 0.479 0.51h o0.00 252.57 252.55 1996.8 189.09 4.592 -0.02428 12.020 0.479 0.518 0.003 252.23 252.23 1679.5 234.31 a.500 -0.02774 12.030 0.479 0.51H 0.003 252.22 252.23 1511.7 282.75 7.721 -n.02731 12.035 0.479 O.!1a 0.003 252.22 252.23 1511.7 281.08 7.721 -0.02747 12.040 0.478 0.519.n003 252.38 252.47 1133.9 377.75 lr,.521 -0.027A5 12.050 0.478 0.519 0.003 252.36 252.27 829.7 300.20 H.287 -0.027h6 12.055 0.478 0.519 0.003 252.36 252.27 829.7 300.20 8.3?7 -0.02774 12.056 0.47H 0.519 0.003 252.36 252.27 827.7 300.20 8.74K -0.02747 12.060 0.478 0.519 0.003 252.67 252.77 535.9 296.55 8.131 -0.02742 12.070 0.478 0n.b19 0.003 252.78 252.76 335.4 242.22 3.?200 -0.n1321 * H VAtlUFS IREF SISPFCTED TO RF FRIM 3 TO 10 PERCENT TOO HIGH nD)F Tl) MAS I FAK TAHLE B-18 Basic Isenthalpic Data for Nominal 0.48 CH4, 0.52 C2H6 Mixture RUN Ni. COMPOSI TION INLET OIITLET INLET PKES. HEAT.I.THIMSON CH4 C2H6 C3HR TEMP. TEMP. PRES. DROP INPIT COFFF. (MILLE FRACTION) {(F) (~F) (PSIA) (PSI)) (HTtI/LTH) (~F/PSIA) 1.010 0.481 0.516 0.003 -228.45 -228.40 1961.0 191.09 0.000 -0.00024 1.020 0.4H] 0.516 0.003 -228.41 -228.32 164R.6 204.90 0.n00 -(0.0044 1.030 0.481 0.516 0.003 -228.46 -228.40 1331.1 197.28 0.00( -0.(00031 1.040 O.481 0.516 0.003 -228.47 -227.91 1005.6 212.41 0.000 -0).00266 1.05 0n.468 0.529 0.009 -228.45 -228.18 795.0 205.15 0.000 -0.0o135 1.060 0,468 0.59R 0.003 -228.42 -228.18 588.5 204.37 0.000 -0.00119 2.010 0.479 0.518 0.003 -99.14 -98.69 1980.7 208.76 0.000 -0.00211?2.02 0.477 0.520 0.003 -99.09 -98.17 1668.5 140.48 0.00on -0.005nh 2.030 0.476 0.521 0.003 -99.12 -98.50 1354.5 353.17 0.)000 -0.00)176 q.010 0.479 0.518 0.003 -99.04 -98.63 1272.5 231.76 0.000 -0.00177 9.020 0.479 0.518 0.003 -99.09 -98.93 883.0 184.57 0.000 -0n.(0H6 q.O30 0.486 0.511 0.003 -99.01 -98.92 602.6 218.44 0.)00 -0.0n041

389 1AL1E B-19 Basic Isobaric Data for Nominal 0.369 CH4, 0.306 C2H6, 0.325 C3Hg Mixture RItI NO). rOMPUSI TION INLET OUTLET INLET PRES. HEAT MEAN HEAl CH4 C2H6 C3H8 TEMP, TEMP. PRES. DROP INPUT CAPACITY (MOLE (RACTION) (IF) IoF) (PSIA) (PSID) (BT1l/LA)(RTI)/L0~F) 25.010 0.370 0.303 0.327 -236.16 -226.23 2001.3 0.21 5.50B 0.55424 25.011 0.370 0.303 0.327 -236.16 -226.21 2004.0 0.21 5.515 0.55425 25.020 0.370 0.303 0.327 -236.16 -200.94 2001.3 0.16 19.649 0.557f48 25.030 0.370 0.305 0.325 -236.32 -181.82 2001.6 0.15 30.445 0.55856 25.040 0.370 0.305 0.325 -236.14 -161.80 2001.5 0.13 41.621 0.55991 29.010 0.372 0.305 0.323 -161.91 -145.60 2003.0 0.12 9.343 0.57274 29.011 0.372 0.305 0.323 -161.90 -145.70 2000.6 0.12 9.280 0.57299 29.020 0.372 0.305 0.323 -161.87 -115.22 2002.7 0.12 27.658 0.59285 29.030 0.372 0.303 0.325 -161.89 -93.01 1999.4 0.10 40.183 0.58332 29.040 0.372 0.303 0.325 -161.91 -84.14 1999.9 0.10 45.574 0.58606 29.045 0.372 0.303 0.325 -161.91 -84.14 1999.9 0.10 45.467 0.58468 33.010 0.366 0.303 0.331 -88.09 -78.51 1999.8 0.05 5.792 0.60442 33.011 0.366 0.303 0.331 -88.12 -78.28 1999.5 0.05 5.952 0.60485 33.020 0.366 0.305 0.329 -88.14 -58.95 2000.1 0.05 17.790 0.60954 33.030 0.366 0.305 0.329 -88.14 -38.12 2001.3 0.05 30.849 0.61681 33.040 0.366 0.305 0.329 -88.14 -21.59 1999.7 0.05 41.27H 0.62029 16.010 0.376 0.305 0.319 -22.57 -12.65 1999.7 0.07 6.609 0.66633 16.011 0.376 0.305 0.319 -23.02 -13.05 1999.7 0.07 6.657 0.66776 16.020 0.376 0.305 0.319 -22.69 2.61 2003.3 0.05 16.735 0.661',7 16.021 0.376 0.305 0.319 -22.30 3.05 2002.3 0.06 16.816 0.66342 16.030 0.376 0.305 0.319 -22.44 19.46 2002.8 0.06 28.115 0.67101 16.031 0.376 0.305 0.319 -22.45 19.87 1999,9 0.06 28.488 0.67309 16.040 0.376 0.305 0.319 -22.62 52.69 1999.3 0.08 52.084 0.69167 9,.010 0.369 0.306 0.326 51.75 61.70 2002.5 0.00 7.616 0.76534 9.020 0.369 0.306 0.326 51.69 76.50 1999.9 0.0 19.060 0.76809 9.030 0.369 0.306 0.326 51.69 91.78 2000.2 0.01 31.106 (0.77583 9.040 0.369 0.306 0.326 51.76 110.18 2000.6 0.04 46.328 0.79298 9.050 0.369 0.306 0.326 51.77 126.46 2002.2 0.07 61.106 0.81406 42.010 0.367 0.305 0.328 146.42 149.54 1999.4 0.09 2.867 ().1932 42.011 0.367 0.305 0.328 146,42 149.56 2000.8 0.09 2.870 0.91408 42.021 0.367 0.305 0.328 145.37 151.31 2003.1 0.12 5.395 0.90802 42.030 0.367 0.305 0.328 145.41 155.83 2000.1 0.12 9.527 0.q1505 42.040 0.370 0.304 0.327 145.50 159.12 1999.8 0.12 12.503 0.91793 42.050 0.370 0.304 0.327 141.30 170.57 1999.4 0.12 24.386 0,83303 42.055 0.370 0.304 0.327 141.30 170.57 1999.4 0.12 26.963 0.92105 42.060 0.370 0.304 0.327 140.52 185.57 1998.5 0.15 41.471 0.92065 35.010 0.367 0.303 0.330 193.61 198.97 2000.5 0.24 4.778 0.89064 35.020 0.367 0.303 0.330 193.69 203.18 1999.8 0.24 8.468 ()0.89242 35.030 0.367 0.303 0.330 193.64 208.85 1999.7 0.32 13.419 0.88266 35.040 0.367 0.304 0.330 193.67 213.72 1999.9 0.31 17.689 0.88245 35.050 0.367 0.304 0.330 193.7? 234.26 2002.3 0.34 35.066 0.86509 39.010 0.369 0.303 0.328 227.92 237.63 2001.8 0.07 8.085 0.83221 39.011 0.369 0.303 0.328 227.90 237.55 2002.6 0.07 9.099 0.83924 39.020 0.369 0.303 0.328 227.90 248.07 2000.2 0.07 16.743 (0.83028 39.030 0.369 0.303 0.328 227.93 258.21 1999.6 0.10 24.958 0.82424 39.040 0.369 0.303 0.328 227.59 267.61 2000.4 0.10 32.703 O.H4717 10.010 0.370 0.306 0.325 51.78 62.36 1751.1 0.08 7.967 0.75275 10.012 0.370 0.306 0.325 51.78 62.36 1751.1 0.08 4.318 0.78596 10.015 0.370 0.306 0.325 51.78 62.36 1751.1 0.08 H.342 0.74819 10.020 0.370 0.306 0.325 51.80 76,.76 1781.1 0.09 21.64H 0.8671) 10.026 0.370 0.306 0.325 51.80 76.76 1751.1 0.09 20.050 0.80314 10.025 0.370 0.306 0.325 51.80 76.76 1751.1 0.09 20.121 0.8(0596 10.030 0.370 0.306 0.325 51.77 91.92 1751.0 0.10 33.006 0.82214 10.040 0.370 0.307 0.324 51.79 109.91 1751.? 0.11 49.264 0.84756 10.050 0.370 0.306 0.324 51.79 126.62 1750.6 0.13 65.123 0.87023 41.010 0.371 0.303 0.326 138.44 141.43 1751.8 0.12 2.942 ((.94392 41.020 0.371 0.303 0.326 138.39 144.37 1750.3 0U.1 5.917 0,.98983 41.025 0.371 0.303 0.326 138.39 144.37 1750.3 0.11 5.908 0.98843 41.030 0.371 0.303 0.326 138.41 148.76 1751.3 0.11 10.28( 0.99255 41.040 0.371 0.303 0.326 138.39 151.67 1753.9 0.11 13.159 0.99128 2.010 0.369 0.306 0.325 127.21 137.22 1751.3 U.06 9.8248 O.4l/( 2.020 0.369 0.306 0.325 127.21 147.33 1751.8 0.10 19.630 0.,975c6 2.030 0.f69 0.306 0.325 127.17 152.06 1749.1 0.10 24.H82 0.(99q8 2.035 0.369 0.306 0.325 127.17 152.06 1749.1 0.10 25.29( 1.0161( 2.036 0.369 0.306 0.325 127.17 152.06 1749.1 0.10 28.015 1.12556 2.04n 0.370 0.307 0.323 127.28 167.26 1749.9 0.10 -9.720 0.c)99 38 2.050 0.%70 0.307 0.323 127.19 202.18 1751.0 0.12 71.393 (.952(6 17.010 0.975 0.306 0.319 -22.54 -12.40 1501.7 0.10.H832 (O.,7416 17.011 n.375 0.306 0.319 -22.52 -12.29 1501.2 0.110 6.897 o.67341 17.020 0.375 0.306 0.319 -22.50 2.41 1499.9 1.10 16.9H6 0.6814u 17.021 0.375 0.306 0.319 -22.52 2.42 1500.1 U.10 17.125 ((.6860 17.030 0.374 0.30- 0.320 -22.48 17.69 150-0. 0.10 2H.O66 (.694877 17.031 0.374 0.3n5 0.320 -22.49 17.80 1500.4 0.1(1 21.106 i.69757 17.040 0.374 0.3n5 0.320 -22.49 52.37 1500.8 0.10 54.71 (.730194

390 TABLE B-19 (CONTINUED) RIIN NO. COMPOSITION INLET OUTLET INLET PRES. HEAT MEAN HEAT CH4 C2H6 C3H8 TEMP. TEMP. PRES, DROP INPUT CAPACITY (MOLE FRACTION) (~F) (eF) (PSI1A (PSID) (BTll/LB)(bTU/LReF) 11.010 0.370 0.305 0.325 51.88 61.74 1501.5 0.09 R.186 0.82999 11.020 0.370 0.305 0.325 51,87 76,76 1500.5 0.10 21.347 0.85751 11.030 0.369 0.306 0.326 51.99 91.93 1500.5 0.10 35.514 0.88908 11.040 f.369 0.306 0.326 51.85 110.04 1502.2 0,10 53.344 0.91666 11.050 0.369 0.306 0.326 51.89 126.64 1501.6 0.10 72.117 0.96479 40.010 0.70 0.304 0.325 121.97 124.97 1499.6 0.10 3.271 1.08876 40.020 0.370 0.304 0.325 122.13 128.15 1500.3 0.11 6.604 1.09599 40.040 0.370 0.304 0.325 122.18 134.18 1499.3 0.14 13.131 1.09416 40.045 0.370 0.304 0.325 122.18 134.18 1499.3 0.14 13.145 1.09536 3.010 0.370 0.305 0.325 127.12 132.09 1499.6 0.10 5.484 1.10366 3.015 0.370 0.305 0.325 127.12 132.09 1499.6 0.10 5.498 1.10664 3.020 0.370 0.305 0.325 127.09 137.22 1499.4 0.10 11.116 1.09708 3.030 0.370 0.305 0.325 127.27 152.22 1499.4 0.12 27.084 1.08526 3.040 0.370 0.306 0.324 127.34 167.32 1499.5 0.13 42.473 1.06221 3.050 0.370 0.306 0.324 127.26 202.05 1499.2 0.15 74.395 0.99461 36.010 0.372 0.300 0.328 191.70 201.57 1500.8 0.12 8.634 0.87469 36.011 0.372 0.300 0.328 191.78 201.74 1501.7 0.12 8.684 0.87127 36.020 0.372 0.300 0.328 191.75 218.00 1502.9 0.12 22.184 0.84518 36.030 0.368 0.303 0.328 191.79 237.11 1501.7 0.15 37.305 0.82304 36.040 0.368 0.303 0.328 191.28 264.10 1501.5 0.15 57.994 0.79630 12.010 0.370 0.306 0.325 51.83 61.93 1250.3 0.10 9.102 0.90141 12.020 0.370 0.306 0.325 51.84 76.77 1249.3 0.10 23.770 0.95338 12.030 0.368 0.307 0.326 51.84 91.88 1249.1 0.11 40.659 1.01545 12.040 0.368 0.307 0.326 51.85 111.61 1249.3 0.12 65.310 1.09274 12.050 0.370 0.307 0.324 51.85 122.41 1249.5 0.14 78.991 1.11946 12.060 0.370 0.307 0.324 51.87 126.76 1249.3 0.15 84.311 1.12575 12.065 0.370 0.307 0.324 51.87 126.76 1249.3 0.15 84.387 1.12676 44.010 0.369 0.305 0.326 107.50 110.63 1252.7 0.11 3.987 1.27384 44.020 0.369 0.305 0.326 107.47 114.06 1251.9 0.12 8.390 1.27327 44.030 0.369 0.305 0.326 107.38 117.13 1252.4 0.12 12.398 1.27143 44.040 0.369 0.305 0.326 107.46 120.66 1252.2 0.12 16.691 1.26434 4.010 0.369 0.305 0.326 127.35 137.25 1251.5 0.11 11.700 1.18120 4.020 0.369 0.305 0.326 127.30 152.19 1251.2 0.12 28.107 1.12920 4.030 0.369 0.306 0.324 127.29 167.30 1249.9 0.12 42.861 1.07121 4.040 0.369 0.306 0.324 127.37 202.16 1252.2 0.13 72.332 0.96715 13.010 0.370 0.306 0.324 51.90 61.79 1100.7 0.09 9.688 0.98002 13.020 0.370 0.306 0.324 51.92 76.78 1100.6 0.10 26.617 1.07093 13.030 0.370 0.306 0.324 51.89 91.77 1100.2 0.12 46.774 1.17286 13.040 0.370 0.306 0.325 51.87 101.71 1099.9 0.13 60.881 1.22139 13.050 0.370 0.306 0.325 51.89 106.76 1099.6 0.15 68.116 1.24142 13.060 0.370 0.306 0.324 51.93 127.06 1099.8 0.18 95.161 1.26663 43.010 0.369 0.304 0.327 94.52 96.91 1102.9 0.07 3.422 1.43303 43.011 0.369 0.304 0.327 94.90 97.31 1102.9 0.07 3.427 1.42368 43.020 0.369 0.304 0.327 94.48 99.28 1100.6 0.10 6.R52 1.42657 43.030 0.369 0.304 0.327 94.60 102.18 1101.4 0.10 10.534 1.38827 43.035 0.369 0.304 0.327 94.60 102.18 1101.4 0.10 10.334 1.361R2 43.036 0.369 0.304 0.327 94.60 102.18 1101.4 0.10 10.813 1.42501 43.040 0.369 0.304 0.327 94.48 104.64 1099.1 0.11 14.479 1.42407 30.010 0.373 0.305 0.323 -161.93 -146.51 1002.5 0.05 9.043 0.58661 30.011 0.373 0.305 0.323 -161.81 -146.29 1002.2 0.07 9.021 0.58125 3U.020 0.373 0.305 0.323 -161.97 -116-01 1002.6 0.10 27.068 0.58894 30.030 0.374 0.305 0.321 -161.97 -93.26 1000.8 0.10 40.870 0.59481 30.040 0.374 0.305 0.321 -161.96 -82.65 1000.8 0.10 47.436 0.59814 30.041 0.374 0.305 0.321 -161.68 -82.32 1001.1 0.10 47.437 0.59778 34.010 0.365 0.304 0.331 -88.14 -78.55 999.4 0.0 5.946 0.62023 34.011 0.365 0.304 0.331 -88.14 -78.54 1000.0 0.0 5.946 0.61968 34.020 0.365 0.304 0.331 -88.13 -58.34 1002.1 0.10 18,718 0.62835 34.030 0.364 0.305 0.331 -88.08 -38.62 1000.5 0.11 31.592 0.63868 34.040 0.364 0.305 0.331 -88.07 -13.69 1002.1 0.25 48.537 0.65255 18.010 0.374 0.306 0.321 -22.51 -12.91 1002.2 0.10 6.740 0.70169 18.011 0.374 0.306 0.321 -22.70 -13.06 1002.2 0.10 6.745 0.69950 18.020 0.374 0.306 0.321 -22.66 1.85 1002.3 0.11 17.556 0.71611 18.021 0.374 0.306 0.321 -22.67 1.87 1001.5 0.11 17.578 0.71621 18.030 0.374 0.306 0.321 -22.52 17.49 1001.4 0.11 29.457 0.73624 18.031 0.374 0.306 0.321 -22.64 17.51 1001.6 0.11 29.510 0.73494 18.040 0.374 0.306 0.321 -22.62 52.63 999.H 0.13 61.160 0.81275 18.041 n.374 0.306 0.321 -22.67 52.68 1000.5 0.13 61.283 0.81328 14.010 0.370 0.306 0.324 51.88 61.H4 1000.9 0.06 12.081 1.2130H 14.0?0 0.370 0.306 0.324 51.84 64.00 1001.0 0.09 14.766 1.21399 14.030 0.370 0,306 0.324 51.86 65.91 1000.6 0.11 17.170 1.22248 14.040 0.368 0.309 0.324 51.85 69.62 1000.4 0.14 71.949 1.23476 14.050 0.368 0.309 0.324 51.85 74.45 1000.5 0.11 28.300 1.25173 14.070 0.369 0.307 0.323 51.82 67.03 999.8 0.09 18.685 1.2291l 14.080 0.36H 0.307 0.324 51.86 91.60 1000.1 0.13 57.194 1.31342 14.090 0.368 0.307 0.324 51.81 109.82 999.4 0.16 81.518 1.4f1518 14.100 0.36H 0.307 0.324 51.83 111.86 1000.2 0.17 H4.454 1.40685 14.110 0.368 0.307 0.324 51.84 113.98 999.9 0.ln 87.671 1.41)84 14.120 0.368 0.307 0.324 51.87 103.29 1000.8 0.16 70.737 1.36599 14.130 0.3h6 0.307 0.324 51.84 106.14 1000.6 0.17 75.269 1.3861?

391 TABLE B-19 (CONTINUED) RUN NO. COMPOSITION INLET OUTLET INLET PRES. HEAT MEAN HEAT CH4 C2H6 C3H8 TEMP. TEMP. PRES. DROP INPUT CAPACITY (MOLE FRACTION) (OF) (OF) (PSIA) (PSID) (RT[I/LR)(BTIl/LR~F) 20.010 0.367 0.306 0.327 52.11 65.05 1001.0 0.10 15.630 1.20O02 20.011 0.367 0.306 0.327 52.11 64.95 1000,5 0.10 15.675 1.22085 20.020 0.367 0.306 0.327 52*10 67.55 1001.4 0.06 18.885 1.22239 20.030 0.367 0.306 0.327 52.07 70.22 999.5 0.02 22.363 1.23380 20.040 0.367 0.306 0.327 52.09 74.21 998.9 0.03 27.591 1.24734 20.050 0.367 0.306 0.327 52.19 103.54 1000.8 0.10 70.094 1.6515 20.060 0.367 0.305 0.327 52.30 107.36 1001.5 0.11 75.947 1.37932 20.070 0.367 0.305 0.327 52,14 109.32 1001.5 0.13 79.311 1.38715 20.080 0.367 0.305 0.327 52.13 112.62 1000.9 0.11 H5.119 1.40697 20.090 0.367 0.305 0.327 52.12 99.72 1000.4 0.13 63.778 1.33974 20.100 0.367 0.305 0.327 52.36 93.18 1000.0 0.12 53.549 1.311R3 20.110 0.367 0.305 0.327 52.12 119.15 1001.4 0.14 93.703 1.39786 20.120 0.367 0.305 0.327 52.09 115.87 1001.9 0.13 89.366 1.40125 45.010 0.366 0.304 0.331 52.03 110.06 1001.f 0.15 80.904 1.39412 45.011 0.366 0.304 0.331 52.07 109.70 998.8 0.15 80.169 1.39111 45.020 0.367 0.304 0.329 52.29 120.64 999.8 0.17 95.206 1.39280 45.030 0.367 0.304 0.329 52.20 131,51 1000.8 0.17 107.987 1.36153 37.010 0.369 0.304 0.327 191.74 202.01 1002.7 0.02 7.314 0.71258 37.011 0.369 0.304 0.327 191.71 202.04 1002.0 0.07 7.338 0.71037 37.020 0.369 0.304 0.327 191.75 217.77 1001.5 0.12 18.390 0.70668 37.030 0.369 0.304 0.327 191.78 236.97 1002.0 0.20 31.290 0.69248 37.040 0.369 0.304 0.327 191.74 264.48 1001.8 0.20 49.597 0.68181 5.010 0.369 0.306 0.325 127.28 137.05 1001.8 0.14 10.337 1.05820 5.020 0.369 0.306 0.325 127.31 152.29 1001.4 0.15 24.236 0.97009 5.030 0.369 0.306 0.326 127.32 167.38 1002.2 0.18 36.617 0.91394 5.040 0.369 0.306 0.326 127.35 202.00 1002.9 0.18 62.153 0.83252 46.010 0.364 0.305 0.331 -83.07 -72.76 748.9 0.18 6.495 0.62951 46.011 0.364 0.304 0.331 -83.08 -72.75 749.6 0.18 6.502 0.62947 46.020 0.364 0.304 0.331 -83.00 -63.51 751.0 0.25 12.332 0.63295 46.030 0,364 0.306 0.330 -83.01 -43.24 751.2 0.29 25.721 0.64679 46.040 0.364 0.306 0.330 -82.92 -34.60 751.1 0.30 31.459 0.65103 46.050 0,364 0.306 0.330 -82.94 -23.25 751.5 0.32 39.317 0..5877 19.010 0.374 0.307 0.319 -22.79 -12.76 751.7 0.07 7.255 0.72381 19.011 0.374 0.307 0.319 -22.69 -12.69 752.7 0.06 7.21? 0.72109 19.020 0.374 0.307 0.319 -22.75 0.48 751.1 0.11 17.65? 0.75994 19.021 0.374 0.307 0.319 -22.74 0.42 750.8 0.13 17.583 n.75899 19.030 0.374 0.307 0.319 -22.73 -18.50 751.1 0.07 3,014 0.71O50 19.031 0.374 0.307 0.319 -22.77 -18.53 751.2 0.05 3.006 0.70862 19.040 0.374 0.307 0.319 -22.72 3.57 751.7 0.10 21.229 0.80768 19.050 0.374 0.307 0.319 -22.76 17.39 751.5 0.15 36.677 0.91358 19.051 0.374 0.307 0.319 -22.76 17.33 751.4 0.15 36.754 0.QR187 19.060 0.374 0.307 0.319 -22.72 52.67 750.7 0.21 78.545 1.()4192 19.061 0.374 0.307 0.319 -22.73 52.94 750.7 0.21 80.148 1.05926 19.065 0.374 0.307 0.319 -22.72 52.67 750.7 0.21 79.584 1.05571 22.010 0.373 0.304 0.324 52.03 61.97 748.0 0.07 13.662 1.37186 22.011 0.373 0.304 0,324 52.04 62.02 749,5 0.07 13.634 1.36622 22.020 0.373 0.304 0.324 52.10 77.02 750.4 0.1? 36.040 1.44631 22.030 0.375 0.304 0.321 52.02 91.94 752.4 0.12 61.331 1.53628 22.040 0.375 0.304 0.321 52.09 106.84 752.4 0.15 90.258 1.64854 22.050 0.373 0.303 0.324 52.00 112.00 749.3 0.15 95.668 1.59434 22.060 0.373 0.303 0.324 51.98 118.81 751.8 0.15 101.862 1.52418 22.070 0.369 0.305 0.326 52.05 127.58 750.4 0.17 108.163 1.43208 22.080 0.372 0.305 0.323 52.03 99.95 750.3 0.13 76.547 1.59758 6.010 0.370 0.305 0*324 127.31 137.33 749.1 0.24 7.522 0.75072 6.020 0.370 0.305 0.324 127.39 152.22 750.0 0.24 17.910 0(.72114 6.030 0.370 0.306 0.324 127.21 167.21 750.7 0.24 27.931 0.69820 6.040 0.370 0.306 0.324 127.27 202.05 750.8 0.27 50.542 0.67595 6.045 0.370 0.306 0.324 127.27 202.05 750.8 0.27 50.542 0.67595 26.010 0.371 0.305 0.324 -236.18 -226.87 501.2 0.13 5.193 0.55767 26.020 0.371 0.305 0.324 -236.17 -201.20 501.6 0.13 19.648 0.56183 26.030 0.371 0.305 0.324 -236.16 -181.50 499.9 0.10 30.878 0.56497 26.040 0.371 0.305 0.324 -236.14 -161.61 501.5 0.12 42.323 0.56788 31.010 0.375 0.305 0.321 -161.90 -147.41 501.3 0.12 8.487 0.58559 31.020 0.375 0.305 0.321 -161.92 -113.96 500.5 0.10 28.537 0.59503 31.030 0.373 0.304 0,323 -161.93 -90.84 499.3 0.08 42.761,tu0151 31.040 0.373 0.304 0.323 -161.94 -80.34 499.9 0.08 49.394 0.60530 32.010 0.358 0.305 0.338 -88.20 -78.73 500.0 0.06 5.971 0.63017 32.011 0.358 0.305 0.338 -88.14 -78.62 499.6 0.06 5.970 0.62684 32.020 0.359 0.307 0.333 -88.15 -58.43 499.0 0.08 19.118 0.64330 32.030 0.359 0.306 0.335 -88.14 -48.77 499.5 0.20 25.565 0.64932 32.040 0.363 0.305 0.332 -88.12 -38.65 500.1 0.24 36,466 0.73710 32.050 0.362 0.305 0.333 -88.11 -26.63 499.9 0.25 49.274 0.80142 32.060 0.363 0.308 0.330 -88.11 1.18 500.9 0.31 80.108 0.R9714 32.070 0.361 0.306 0.332 -88.08 27.96 500.1 0.26 113.428H.977SI 32.080 0.361 0.306 0.332 -88.09 59.90 502.4 0.?7 163.350 1.10378

392 TABLE B-19 (CONT I NUED) RUN NO. COMPOSITION INLET OUTLET INLET PRES. HEAT MEAN HEAT CH4 C2H6 C3HR TEMP. TEMP. PRES. DROP INPUT CAPACITY (MOLE FRACTION) (OF) (OF) (PSIA) (PSID) (BTU/L8)(RTII/LR~F) 23.010 0.374 0.303 0.323 52.03 61.80 501.6 0.04 17.606 1.80153 23.011 0.374 0.303 0.323 52.01 61.84 502.0 0.04 17.576 1.78795 23.020 0.374 0.303 0.323 51.99 76.66 500.9 0.10 48.005 1.94634 23.030 0.374 0.303 0.323 51.95 82.68 501.2 0.17 62.130 2.02176 23.031 0.374 0.303 0.323 51.98 82-80 501.3 0.17 62.338 2.02260 23.040 0.374 0.303 0.323 52.03 91.64 502.5 0.09 73.242 1.84942 23.050 0.374 0.303 0.323 52.03 100.72 502.3 0.05 78.761 1.61739 23.060 0.374 0.303 0.323 52.02 114.06 499.0 0.04 86.758 1.39857 23.070 0.374 0.303 0.323 52.02 89.16 499.1 0.02 71.068 1.91358 23.080 0.374 0.303 0.323 52.05 127.50 498.8 0.15 95.670 1.26799 7.010 0.370 0.305 0.325 127.42 137.22 499.4 0.38 5.648 0.57649 7.015 0.370 0.305 0.325 127.42 137.22 499.4 0.38 5.655 0.57725 7.020 0.370 0.305 0.325 127.3h 152.32 500.0 0.40 14.662 0.58740 7.030 0.369 0.305 0.325 127.48 167.45 499.9 0.42 23.097 0.57784 7.040 0.369 0.305 0.325 127.40 202.29 499.9 0.43 43.324 0.57858 38.010 0.369 0.304 0.327 191.69 201.03 500.0 0.33 5.341 0.57175 38.011 0.369 0.304 0.327 191.69 201.05 500.0 0.33 5.347 0.57158 3R.020 0.369 0.304 0.327 191.79 218.14 502.6 0.34 15.111 0.57350 38.030 0.369 0.304 0.327 191.71 236.59 502.1 0.34 25.784 0.57442 38.040 0.369 0.304 0.327 191.68 265.67 501,9 0.39 42.849 0.57910 38.041 0.369 0.304 0.327 191.68 265.54 503.7 0.39 42.720 0.57841 27.010 0.369 0.305 0.326 -213.16 -204-25 251.2 0.15 5.081 0,56994 27.011 0.369 0.305 0.326 -213.16 -204,18 251.3 0.15 5.078 0.56575 27.020 0.369 0.305 0.326 -213.17 -180.80 250.0 0.15 18.406 0.56864 27.030 0.369 0.305 0.326 -213.14 -161.75 250.0 0.15 29.380 0.57168 27.040 0.369 0.305 0.326 -213.21 -135.07 249.6 0.15 44.977 0.57561 28.010 0.369 0.305 0.326 -133.87 -126.53 251.6 0.10 4.415 0.60135 28.020 0.369 0.305 0.326 -133.85 -109.69 251.7 0.27 18.209 0.75375 28.030 0.374 0.305 0.322 -133.84 -104.24 252.2 0.25 24.839 0.83921 28.040 0.374 0.305 0.322 -133.84 -98.26 251.8 0.29 31.921 0.89712 28.050 0.374 0.305 0.322 -133.89 -88.97 251.1 0.27 42.050 0.93611 28.060 0.371 0.302 0.326 -133.80 -53.95 249.9 0.29 78.784 0.98673 28.070 0.371 0.302 0.326 -133.84 -19.86 250.4 0.29 119.575 1.04910 24.010 0.378 0.302 0.320 -22-63 -12.82 252.5 0.29 13.882 1.41497 24.011 0.378 0.302 0.320 -22.69 -12.77 251.3 0.27 14.045 1.41492 24.020 0.381 0.301 0.318 -22.56 2.25 251.0 0.50 37.843 1.52531 24.030 0.379 0.303 0.318 -22.55 17.80 250.6 0.52 67.232 1.66600 24.040 0.379 0.303 0.318 -22.59 38.12 249.4 0.59 116.229 1.91447 24.041 0.379 0.303 0.318 -22.57 38.18 249.4 0.59 116.276 1.91411 24.050 0.379 0.303 0.318 -22.60 53.47 252.2 0.34 138.300 1.81822 21.010 0.368 0.307 0.325 51.97 61.94 252.2 1.23 5.185 0.52018 21.011 0.368 0.307 0.325 52-00 61.94 252.1 1.18 5.187 0.52154 71.020 0.368 0.307 0.325 52.03 77.05 250.1 1.18 12.794 0.51149 21.030 0.368 0.307 0.325 52.03 91.91 251.4 1.19 20.317 0.50939 21.040 0.369 0.307 0.325 52.05 110.77 251.3 1.23 29.741 0.50650 21.050 0.369 0.307 0.325 52.02 126.07 250.9 1.23 37.622 0.50802 21.060 0.369 0.307 0.325 52-05 55.29 250.2 0.98 1.735 0.53451.R010 0.369 0.306 0.326 127.24 137.22 248.R 0.83 5.086 0.50964 8.020 0.368 0.305 0.327 127.46 152.33 249.4 0.83 12.725 0.51169 8.030 0.369 0.306 0.326 127.46 167.26 249.3 0.83 20.477 0.51446 8.040 0.369 0.306 0.326 127.48 202.35 249.3 0.89 38.871 0.5191R

39 3 TARLF B-20 Basic Isothermal Data for Nominal 0.369 CH4, 0.306 C2H,, 0.325 C3H1 Mixture RUMN NO..nMP1S I T ION INLET OIITLET INLET PKES. HEAT I (iTHERMAL CH4 C?H4 C3H8 TEMP. TFMP. PRS,. r)k(.)P INPUT J.T.CU)FFF. (MnLF FRRC.TinN) (OF) (OF) (PSIA) (PSID) (BIT/LR) (RTu/LB PSI A) 4.060 0.36H 0.304 0.327 -16.04 -16.03 935.7 265.38 0.135 -0.00051 4.070 0.370 0.304 0.326 -14.14 -16.14 686.4 205.18 15.34? -0.07477 4.080 0.370 0.304 0.326 -14.13 -16.13 494.1 221.3P 28.094 -7).12690 4.090 0.368 0.302 0.330 -16.04 -16.05 307.0 201.78 88.923 -0.42796 2.010 0.373 0.306 0.320 52.04 52.07 2020.5 122.59 0.341 -0.00278 2.011 0.373 0.30n6 0.320 52.01 52.03 2023.0 122.79 0.341 -0.00278 2.020 0.373 0.306 0.320' 52.00 52.00 1913.6 123.39 0.383 -0.00310 2.021 0.373 0.306 0.320 51.96 51.96 1910.8 123.19 0.383 -0.00311 2.030 0.373 0.306 0.320 51.96 51.97 1794.0 118.89 0.439 -0.00369 2.031 0.373 0.306 0.320 52.11 52.11 1793.6 118.59 0.475 -0.00400 2.040 0.373 0.306 0.320 51.86 51.86 1679.1 117.99 0.517 -0.00438 2.041 0.374 0.305 0.321 52.09 52.09 1683.7 117.99 0.53H -0.00456 2.050 0.374 0.305 0.321 52.04 52.04 1569.1 118.39 0.679 -0.00574 2.051 0.374 0.305 0.321 51.87 51.89 1569.3 118.39 0.668 -o.n0564 2.060 0.374 0.305 0.321 51.93 51.94 1457.6 116.59 0.780 -0.00669 2.061 0.372 0.306 0.321 51.85 51.86 1461.5 114.39 0.781 -0.00688 2.070 0.372 0.306 0.321 51.99 52.00 1348.7 118.59 1.001 -0.00844 2.071 0.372 0.306 0.321 51.99 52.00 1349.7 117.99 1.006 -N.00R53 2.080 0.372 0.306 0.321 52.03 52.03 1232.8 137.19 1.534 -0.01118 2.081 0.372 0.306 0.321 52.02 52.03 1234.1 137.99 1.536 -0.01111 2.082 0.372 0.306 0.321 52.03 52.03 1232.8 137.19 1.543 -0.0112? 2.090 0.371 0.306 0.322 52.00 52.00 1100.9 137.39 4.101 -0.02985 2.091 0.371 0.306 0.322 51.98 51.99 1101.2 135.79 3.889 -0.02864 2.110 0.371 0.306 0.322 52.04 52.07 987.0 131.39 8.8H66 -0.06748 2.111 0.371 0.306 0.322 52.08 52.10 986.7 131.39 8.88? -0.06760 2.120 0.373 0.306 0.321 52.05 52.06 997.8 58.59 3.643 -0.062 17 2.121 0.373 0.306 0.321 52.12 52.13 997.8 58.19 3.657 -0.06284 7.010 0.366 0.304 0.330 52.33 52.34 1077.9 71.69 1.036 -0.01446 7.020 0.366 0.304 0.330 52.32 52.32 1077.0 104.79 2.669 -0.02547 7.030 0.366 0.304 0.330 52.30 52.31 1079.2 150.99 5.698 -0.03774 7.040 0.366 0.304 0.330 52.34 52.35 928.3 258.18 21.103 -0.08174 7.050 0.380 0.305 0.315 52.28 52.30 680.2 403.56 95.166 -0.23581 7.055 0.380 0.305 0.315 52.28 52.30 680.2 403.56 96.023 -0.23794 7.056 0.380 0.305 0.315 52.28 52.30 680.2 403.56 96.581 -0.23932 7.057 0.380 0.305 0.315 52.28 52.30 680.2 403.56 93.797 -0.23242 7.060 0.380 0.305 0.315 52.39 52.40 535.4 427.76 88.506 -0,.20691 1.010 0.371 0.308 0.321 126.30 126.31 2000.0 158.99 2.73? -0.01719 1.011 0.371 0.308 0.321 126.27 126.28 2004.5 156.99 2.668 -0.01699 1.020 0.371 0.308 0.321 126.27 126.28 1837.3 160.69 3.746 -0.02331 1.030 0.371 0.308 0.321 126.26 126.28 1676.0 152.79 5.026 -0.03230 1.031 0.371 0.308 0.321 126.25 126.27 1675.9 152.39 5.008 -0.03286 1.040 0.371 0.308 0.321 126.24 126.26 1531.2 163.98 7.573 -0.04618 1.041 0.371 0.3018 0.321 126.26 126.28 1531.1 166.58 7.727 -0.04638 1.050 0.37? 0.306 0.323 126.25 126.28 1372.9 157.59 10.380 -0.06587 1,051 0.37P 0.306 0.321 126.29 126,.31 1371.4 158.39 10.563 -0.04469 1.060 0.372 0.306 0.323 126.27 126.31 1233,6 161.24 14.153 -0.08777 1.061 0.372 0.306 0.321 126.30 126.33 1232.6 164.38 14.323 -0.08713 1.070 0.372 0.306 0.323 126.23 176.?6 1084.1 170.58 16.944 -0.09933 1.071 0.372 0.307 0.321 126.24 126.27 1085.2 171.78 17.148 -0.09982 1.080 0.372 0.307 0.321 126.21 126.24 922.3 158.49 14.683 -0.09245 1.081 0.37? 0.307 0.321 126.24 126.27 921.7 158.59 14.683 -0.09259 1.090 0.372 0.307 0.321 126.24 126.26 771.1 178.18 14.057 -0.07889 1.091 0.372 0.307 0.321 126.23 126.25 771.1 177.88 13.949 -10.07H42 1.100 0.374 0.303 0.323 126.22 124.24 605.7 167.68 11.245 -0.(06706 1.110 0.374 0.303 0.323 126.26 126.27 448.2 172.38 10.018 -0.05811 1.120 0.374 0.303 0.323 126.50 126.50 278.7 165.78 8.585 -0.0)5178 6.010 N.368 0.305 0.327 191.67 191.72 2002.3 105.19 2,956 -O.02810 6.020 0.368 0.305 0.327 191.99 192.04 2005.0 196.58 6.256 -0.03183 6.030 0.368 0.305 0.327 191.96 191.97 1818.1 228.18 9.080 -0.03979 6.040 0.3O 8 0.303 0.329 192.01 192.01 1593.2 270.77 13.232 -0.04887 6.050 0.368 0.303 0.329 192.01 192.02 1332.6 354.37 19.15( -0.05404 6.060 0.368 0.303 0.329 192.02 192.03 1008.7 255.78 13.268 -0.05187 6.070 0.367 0.304 0.329 192.01 192.03 765.4 256.3H 12.325 -0.04817 6.080 0.367 0.304 0.329 192.05 192.06 521.2 277.77 12.067 -0.04344 6.090 0,367 0.304 0.329 192.05 132.06 339.7 239,.98.711 -.040(147 TABLF B-21 Basic Isenthalpic Data for Nominal 0.369 CH4, 0.306 C2H 6 0.325 C3H8 Mixture RIIN NO. CDMPlIT ION INLFT OUTLFT INLFT PRKS. HFAT J.I.THOMPSnN CH4 C2?H6 C3H8 TEMP. TEMP. PRES. DROP INPUT CU!FFF. (MII. F FRACTION) (OF) (OF) (PS~F) (FPSI) (PSI) (I/LB) (~F/PSIA) 3.010 0.372 0.305 0.323 -236.48 -233.57 1999.4 436.96 0.000 -0.00666 3.011 0.37? 0.305 0.323 -236.47 -233.55 1997.6 437.76 (.00( -0.00667 3.020 0.37? 0.305 0.323 -236.57 -233.52 1586.4 455.36 0.000 -0.00469 3.030 0.345 0.303 0.332 -236.46 -233.88 1139.2 391.16 0.000 -0.00661 3.040 0.465 0.303 0.332 -236.40 -234.67 769.6 267.38 0.000 -0.00640 3.041 0.N36 0.'03 0.332 -236.46 -234.69 773.1 271.97 0.000 -0.00648 3.051 0.370 0.306 0.324 -236.51 -234.8? 512.6 260.q8 {0.000 -0.00647 3.060 0.370 0.306 0.324 -236.40 -235,12 314.5 193.38 0,000 -(.00660 4.010 0.367 0.305 0.328 -16.03 -15.47 1981.5 230,.9H 0.000 -(0.(00199 4.020 0.347 0.305 0.328 -16.07 -15.68 1775.6 252.98 0.000 -O.110144 4.030 0,67 0.304 0.329 -16.09 -15.H1 1529?. 271.37 0.00() -0.00104 4.040 0.367 0.304 0.329 -16.08 -15.3R 1269.8 262.78 0.000 -((.0 003H 4.050 0.348 0.304 0.327 -16.11 -16.10 1022.1 107.59 0.(100( -0.0 1(1

APPENDIX C Sample Results Involving the Smoothing of the Basic Data 394

TABLE C-l Sample Results for PGC Corrections to the Basic Data as Applied to the Ternary Mixture Correction Factors Isobaric p to AP AR PGC Prediction Pi to0 Cor Run Mole Fraction T, T P. AP Q/F For Tto 00 to rreted Devi at on T~~to 500 ~Btu/lb Btu/lb % 4 C2 6 3H 8 F OF psia psid Btu/lb Comp. 127.40F psia 7.010 0.370 0.305 0.325 127.42 137.22 499,4 0.38 5.648 1.000 1.000 -1.007 0.990 5.9626 0.018 0._ 3 7.015 0.370 0.305 0.325 127.42 137.22 499.4 0.38 5.655 1.000 1.000 1.007 0.990 5.633 0.011 0.2 7.020 0.370 0.3C5 0.325 127. 36 152. 32 500 0 0.40 14.662 1.000 0.998 1.000 -.998 14.600 -0321 -2.2 7.030 0.369 0.305 0.325 127.48 167.45 499.9 0.42 23.097 1.000 1.002 1.000 0.999 23.104 -0.184 -08 7.040 0.369 0.305 0.325 127.40 202.29 499.9 0.43 43.324 1.000 1.000 1.000 0.999 43.282 -0.511 -1.2 Isothermal Correction Factors Isothermal ~~~~~~~ ~P ~ ^- H PG P^ rediction Run Mole Fraction T. T P. AP Q/F Fr T t AT ARCedi cion 1 R 1 unr T. to h unchan- to Corre D OH4 C2H C3H 0 1 1 4 C2 6 C318 OF OF psia psid Btu/lb Comp. 192.OOF ged 0F Btu/ 6.010 0.368 0.305 0.327 191.67 191.72 2002.3 105.19 2.956 1.004 0.912 1.000 1.082 2.931 0.332 11.2 6.020 0.368 0.305 0.327 191.99 192.04 2005.0 196.58 6.256 1.004 1.000 -.000 0.993 6.234 0 - 9.68:0 1.:0 0.99 1.^) 1.0 9. - -I - 101 6.030 C.368 0.305 0.327 191.96 191.97 1818.1 228.18 9.80 1.00 0.997 00 1002 9072 0118 6.040 0.368 0.303 0.329 192.01 192.01 1593.2 270.77 13.232 0.996 1.OC1 1.000 0.999 13.181 0402 3, 6.050 0.3168 O.303 0.329 192.01 192.02 1332.6 354.37 19.150 0.993 1.031 1.100 f.999 19.011 0.101 0.5 6.060 0.368 0.303 0.329 192.02 192.03 1008.7 255.78 13.268 0.994 1.002 1.00 (.998 13.183 0.008 0.1 6.C70 0.367 0.304 0.329 192.01 192.03 765.4 25b.38 12.325 0.99? 1.301 1.000 (.998 12.213 -3.141 -1.1 6.080 0.367 0.304 0.329 192.05 192.06 521.2 277.71 12.67 0.995 1.003 1I.0 0.997 12.08 -0.128 - 6.090 0.367 0.304 0.329 192.05 192.06 339.7 239.98 9.711 0.997 1.t3 1.000 ".996 9'.5 -219 -23 Corrected to the ternary conposition of Table VI-3

396 TABLE C-2 a) The Results Obtained on Constructing an Equal Area (aH/aP) Curve for the Ternary Mixture at 126.2~F Using a Non-Linear Least Squares Technique Run No. Inlet Outlet AH/AP AH/AP* Pressure Pressure Expt. Calc. Error Ph (Psia) P (Psia) Btu/lb/~F Btu/lb/psia'.10100t 01 0.20000E 04 0.18410E 04 -0.17190E-01 -0.17207E-01 -0.9e279E-01 3.10110E 01 U.20045E C4 0.18475E 04 -0.16990O-01 -0.16899E-01 0.53781E OU J.1020Et 01 0.18373F 04 0.167661 04 -0.23310E-01 -0.24012E-01 -0.30134E 01 0.10300F'1 0.16760L C4 0.15232F 04 -0.32900-01 -0.31519E-01 0.41979E 01. 103101 01 0. lOCuE 01 O.10000E 01 -0.46500E-01 -0.46121E-01 0.81605 00 0. 10400F 01 0.15312F 04 0.13672F 04 -0.46180E-01 -0.46078E-01 0.22176E 00 0.10413E 01 0.15311E 04 0.13645E 04 -0.46380E-01 -0.46264E-01 0.24970E 00 U.10500E 01 0.13729E 04 0.12153E 04 -0.65870E-01 -0.67876E-01 -0.30450E C1 0.10510E 01 0.13714E 04 0.12130E 04 -0.66690E-01 -0.68149E-01 -0.21877E 01 G.10600E 01 0.1233bE 04 0.10724E 04 -0.87770E-01 -0.85215E-01 0.29110E 01'.10610E 01 0.1232uE C4 0.10682E 04 -0.87130E-01 -0.85419E-01 0.19639E 01 0.10700E 01 0.10841E- 04 0.91352E 03 -0.99330E-01 -0.99743E-01 -0.41567E 00 2.10710E 01 0.10852b 04 0.91342E 03 -0.9982CE-01 -0.99671E-01 0.14922E 00 0.10800F Ul 0.9223CE 03 0.76381E 03 -0.92650E-01 -0.94061E-01 -0.15230E 01..1U81OE 01 0.92170E 03 0.76311E 03 -0.92590E-01 -0.94012E-01 -0.15355E 01 u.10900E 01 0.7711CE 03 0.59292E 03 -0.78890F-01 -0.78468E-01 0.53455E 00 0.10910E 01 0.77110E C3 0.59322E 03 -0.78420E-01 -0.78483E-01 -0.80339E-01 J.1100E J1 0.60570E C3 0.43802E 03 -0.67060E-01 -0.64885E-01 0.32435E 01 O.11100E 01 0.44620F 03 0.27582E 03 -0.58110E-01 -0.57745E-01 0.62896E 00 2.11200E 01 0.27870F U3 0.11292E 03 -0.51780E-01 -0.53329E-01 -0.29914E 01 b) Computer Aided Interpolation and Integration of Equal Area (3H/P)T Curve for the Ternary Mixture at 126.2~F. Pressure dH/dP (H~) dP/P H - H o dP P, (Psia) Btu/lb/psia Btu/lb psia Btu/lb 0. -0. 46070E-01 -0.46070E-01 0.0 0.5000UE 02 -0.48424E-01 -0.47278E-01 -0.23639E 01 O. 1000(.E 03 -0.50418E-01 -0.48364E- -0 -.48364E 01 0.15000E 03 -0.52096E-01 -0.49336E-01 -0.74005E 01 0.2000tE 03 -0.53520E-01 -0.50209E-01 -0.10042E 02 0.25000E 03 -0.54777E-01 -0.50999E-01 -0.12750E 02 0.3000JE 03 -0.55980E-01 -0.51728t-01 -0.15519E 02 0.35000E 03 -0.57266E-01 -0.52426E-01 -0.18349E 02 0.400UE 03 -0.58794E-01 -0.53123E-01 -0.21249E 02 0.45000E 03 -0.60733E-01 -0.53856E-01 -0. 24235t 02 0.50000E 03 -0.63240E-01 -0.54664E-01 -0.27332E 02 0.55000E 03 -0.66437E-01 -0.55583E-01 -0.30571E 02 0.60000t 03 -0.70380E-Cl -0.56647E-01 -0.33988E 02 C.6500CE 03 -0.75023E-01 -0.57878E-01 -0.37621E 02 0.700oOE 03 -0.80196E-01 -0.59285E-01 -0.41499E 02 0.750(00 03 -0.85589E-01 -0.60858E-01 -0.45644E 02 0.80000E 03 -0.90758E-01 -0.62568E-01 -0.50054E 02 0.85000F 03 -0.95148E-01 -0.64361E-01 -0.54707E 02 C.90000CE 03 -0.98148E-01 -0.66162E-01 -0.59546E 02 0.95,)LC 03 -0.99150E-01 -0.67882E-01 -0.64488E 02 O.1000OE 04 -0.97631E-01 -0.69419E-01 -0.69419E 02 0.10500E 04 -0.93214E-01 -0.70669E-01 -0.74203E 02 O.11(O(E 04 -0.89861E-01 -0.71602E-01 -0.78762E 02.110SCuE 04 -0.86154E-01 -0.72321E-01 -0.83169E 02 0. 12000E 04 -0.80886E-C1 -0.72793E-01 -0.87351E 02 J.125G0E 04 -0.74392E-01 -3.72990E-01 -0.91238E 02 0.13000E 04 -0.67130E-01 -0.72906E-01 -0.94778E 02 0.13500E 04 -0.596b4E-01 -0.72553F-01 -0.97946E 02 0.14C0OE 04 -0.52292E-01 -0.71958E-01 -0.10074E 03 0.14500E 04 -0.45588F-01 -0.71163E-01 -0.10319E 03 0.15000E 04 -0.39765E-01 -0.70210E-01 -0.10532E 03. 155U00 04 -0.34952E-01 -0.69148E-01 -0.10718E 03 O.160lbOC 04 -0.31147E-C1 -0.68017E-01 -0.10883E 03 o. lbq^uE )4 -0.28231E-01 -0.66854E- -01 11031E 03 C. 17:JUOE 04 -.OOE- -0.2 05684-0 1 - 0.684- - 11166E 03 0.175cuE 04 -0.24198E-01 -0.64523E-01 -0.11292E 03 O.1PuO(OE 04 -0.22544E-01 -0.63380F-01 -0.11408E 03 0.18500E 04 -0.20760E-01 -0.62253E-01 -0.11517E 03 J. 19GUC0 04 -0.18579E-01 -0.61134F-01 -0.11615t 03 0.1950)E 04 -0.15761E-01 -0.60008E-01 -0.11702E 03 0.2COUOE 04 -0.12091E-01 -0.58858E-01 -0.11772E 03 * Calculated using the equation (dp); -0.0457 - 0.1742x10-'P - 0.8661x10-P + 0.1163x10-9P3 - 0.3250x10-3P' -(0.1018x102)(0.3397x10-2)e-0'003397(P - 1012.1)2 The equation is plotted as the dashed curve in Figure VIII-52

TABLE C-3a Computer Aided Consistency Check Results for Graphically Determined Equal Area Cp Curve as Illustrated for Ethane at 819 psia. * ** (C) (C ) T. (~F) TARF) xpt ( a Percent T T Btu/lb/F Btu/lb/'F Error Btu/lb/lF Btu/lb/~F ^..c 0 J2 o. iuo JJ o. o451b CGl 0.44772F C01 0.9t7E 30 J. 345t JL Q.5.5 3 01 0.99s7D 02 U.iJ44D u3 0.4d570 01 3.48391 01 0.368E 00 J.34561 31 l0.4h17E jl U.537U 0 U.IJ.30 03 j.4 oou Ul 0.4735E 01 -.617E 00 0.3456t 01 o.5>311 01 0.49370 02 0.1u2D 03 0.37474 01 0.3760E 01 -.329E 30 0.3456E 01 0.4107 01 U.9937U 02 0.1u14I 03 0.41361) 01 0.4137E 01 -.234E-01 0.3456 01 0.64893E 01 0.9O 370 0o 0.10230 u3 0.4485U 01 0.4479E 01 0.134E 30 3.3456E 01 0.5460t 01 O.04370 02 u.10330 03 0.47120 01 0.4735E 01 -.487E 00 0.3456E 01 0.5531E 01 0.9'370 02 0.10440 u3 U.d864D 01 0.4839E 31 0.507E 00 0.3456E 01 0.4631E 01 0. 9370 02 U.1054U u3 0.l7o6l 01 0.4773E 31 0.18ia 00 0.3456E J1 J.4130E 31 0U.4370 02.IU54U 03 0.479~0 01 0.4771E 01 0.430E 30 0.3456E 01 0.-4111 01 0.IUUOu 03 0.1~30 u3 U 0.48490 01 0.43351 01 0.305E 00 3.4107E 01 0.5460t 01 0.1230U 03 03 0.10440 03 0.54150 01 0.5363E 01 0.961E 00 0.54b0E 01 ou.4831t 01 U.1 23D 03 0.10440 03 0.5337D 01 0.5356E 01 -.354E 00 0.5453E 01 0.4807E 01 0.10210 03 0.1054D 03 0.50670 01 0.5055E 01 0.237E 00 0.54601 01 0.41301 31 0.10230 03 0.10540 03 0.50840 01 3.5049E 01 0.685E 00 0.5450E 01 0.41191 01 0.1003U 03 0.10330 03 0.50320 Oi 0.5059E 01 -.533E 00 0.4107TE 01 0.55311 01 0.o1003U 03 0.IJ1540 03 0.49930 01 0.4966E 01 0.542E 00 -0.4107E 01 0.4119E 01 0.10330 03 0.10440 03 0.5 440 31 0.5224E 01 0.370E 01 0.5531E 31 0.4831E 01 0.10330 03 0.10540 03 0.49130 01 0.4845E 01 0.139E 01 0.5531E 01 0.4130E 01 0.10330 03 0.10540D 03 0.49390 01 0.4838E 01 0.204E 01 0.5531E 01 0.4119E 31 0.10440 03 0.10540 03 0.44580 01 0.4456E 01 0.523E-01 0.4631E 01 0.4119E 01 * These values differ from those for runs 40 and 51 in Table B-2 as they have been corrected for pressure level, pressure drop and variable inlet temperature as explained in section VII. Calculated from the results in Table C-3b. TABLE C-3b Computer Aided Interpolation and Integration of Equal Area Cp Curve as Illustrated for Ethane at 819 Psia. + T f Ti (F) T (IP) (C) (C )d JCpdT f P T P T IT CpdT]TCal 99'F i. f Btu/lb/fP Btu/lb/'F Btu/lb/~F Btu/lb/'F 0.93000 02 0.Y950D 02 U.32500 01 0.35300 01 0.16950 01 0.1695t 31 0.935U0 u4 u.1iGU0 03 0.35300 01 0.3s400 01 0.18400 01 J.3535E 01.IUlUOO u3 u.lu050 u3 0.3J8400 01 0.42250 01 0.20150 01 0.5550t 01 u.10050 03 0.10100 J3 0.4~250 01 0.45900 01 0.22040 01 0.7754E 01 0.10100 03 0.101I0 03 0.459UD 01 0.49800 01 0.23940 01 0.1015E 02 C0.1010 03 0.10200 03 0.49800 01 0.53000 01 0.25710 01 0.1272E 02 U.IO D u3 o.1I02O 03 0.53000 01 0.54100 01 0.10720 01 0.1379E U2 0.10220 03 0.10240 03 0.54100 01 0.54800 01 0.10930 01 J.1468E 02 0.10240 03 0.10250 03 0.54800 01 0.55000 01 0.54910 00 0.1543E 02 0.J10250 03 0.10300 03 0.55000 01 0.55200 VI 0.27590 01 0.1819E 02 U.1030D 03 0.10340 33 0.55200 01 J.55000 01 0.22110) 01 0.2C40t 02 0.10340 03 0.103Ov 03 U.5500UU 01 0.34t0OD 01. 10910 01 0.2149E 02 U.0IJ6b 03 O.140u G3 0.-4000 l 0.51200UU ul 0.21b0 01 0.2360E 02 u.1O400 03 0.10450 U3 0.51200 01 0.4730J 01 0.24620 01 0.2601b 02 0.10450 03 U0.cu5O 03 0.47300 01 0.43900 01 J.22780 U1 J.2634E 02 0.10500 03 0.1U550 03 0.43900 01 U.40920 U1 0.21183'l1 U.3046E 02 O.IJ550 03 0.10600 33 U.40920 01 0.3osO) 01 0.19811 31 0.32441 02 Cp values are obtained from graphical smoothing of the basic data as shown in Figure VIII-8. The integral is estimated using the Gauss-Legendre Quadrature [40]. The Lagrange interpolating polynomial for the integration is generated using five contiguous points with T, and Tf as the central points.

APPENDIX D Equipment Summary Item Equipment or Material Speci- Function No. fication 1 Calorimeters and Accessories la Isobaric Calorimeter: Construction Basic apparatus for isodetails in reference [79]. Modified baric calorimetric heater capsule drawings in Appendix measurements from -240~F E of this work. to + 300~F and up to 2000 psi. lb Throttling Calorimeter: Construc- Basic apparatus for isotion details in reference [168]. thermal and isenthalpic Modifications described on page 147 measurements over the of this work. above range of conditions. lc AP 10-16 temperature compensated Pressure sealing device coupling using C1344A-TEF, hollow for throttling caloristainless steel double teflon coated meter. gaskets. The D.S.D. Co., Hamden, Conn. Id 16-19 B&S gage hypodermic tubing, Element causing pressure (0.008" wall), C.A. Roberts, drop in throttling caloriDetroit, Michigan. meter. le GTC 100, thermocouple vacuum Original vacuum indicator gauge, 0-1000 microns, Consoli- for either calorimeter. dated Vacuum Corp., Rochester, N.Y. if Televac, thermocouple vacuum gauge Replacement vacuum indi0-1000 microns, Huntingdon Valley, cator for either caloriPenn. meter. lg RPS-MTG-24-L, and MTG-24-A2L Pressure to vacuum sealing Sealing glands, Conax Corp., device for the throttling Buffalo, N.Y. and isobaric calorimeter respectively. lh 26 B &S gage, nichrome heater wire Original heater wire with double glass insulation and supplying energy input to silicone binder 2.594 ohms/ft. calorimeters. Driver-Harris Co., Harrison, N.J. li 26 B &S gage, "Moleculoy" wire Improved substitute for with 0.026 double glass insulation original heater wire. and Hi-Mol binder, 2.557 ohms/ft. Molecu-wire Co., Farmingdale, N.J. 398

399 lj 30 B &S gage, Constantan wire. Leeds and Northrup, Philadelphia, Used in preparation of Penn. multijunction Cu/Constantan thermocouple wires lk 36 B &S gage, (.005") Copper wire for both calorimeters. Consolidated Wire Co., Chicago, Illinois. 11 Apiezon N grease Improvement of thermal contact between thermocouple and thermowell surface. lm CN-967, Beryllia epoxy thermally Materials for binding conductive resin, and CN-773 heater wire to the isothermally conductive resin. baric calorimeter heater Mereco Inc., Cranston, R.I. capsule. In SS-4UK-SW-TEF Bellows stainless Shut off valves in calorivalve operating range from -300~F meter bath to permit to +600~F, Nupro Inc., Cleveland, switching of the flow Ohio. stream from one calorimeter to the other. 2 A2CCV50/250, 2 stage Diaphragm Compression and recirCompressor with remote heads, culation of the system Corblin, Paris, France. fluid in the gaseous state up to 2700 psia. 3 Electrical Measurement Equipment & Accessories 3a No. 7553, Type K-3 Universal Measurement of voltages: Potentiometer Leeds and Northrup, Power input, thermocouple Philadelphia, Penn. output, pressure and differential pressure transducer input and output, Pt. resistance thermometer output. 3b Unsaturated Cadmium Sulfate Reference voltage for standard cell, Eppley potentiometer Laboratories, Inc. 3c No. 9834, D.C. Null Detector Null point indicator for (Maximum sensitivity of 0.1pv/ K-3 potentiometer. scale div.), Leeds and Northrup, Philadelphia, Penn. 3d Model 2500 A. Type R Reflecting Indication of Emf of Mirror Galvanometer. With a differential thermocouple sensitivity of 0.47pv/mm at 1 between guard heater, and meter, Leeds and Northrup, heater capsule. Philadelphia, Penn.

400 4 SM 325-2A(M)X, D.C. Power Supply, Power supply to either 0.01% line and 0.05% load regu- calorimeter, limited to lation respectively, Kepco Inc., 325 volts or 2 amps. Flushing, N.Y. 5 8163-B, Platinum Resistance Thermometer, Leeds and Northrup, Philadelphia, Penn. Measurement of calorimeter bath temperature 5a 162C, Platinum Resistance Thermometer, -2000C to 500~C, Rosemount Engineering, Minneapolis, Minn. 6 SY 152 113(W)-93-11(v) Tempera- Control of calorimeter ture Controller, Honeywell Inc., bath temperature from Minneapolis, Minn. with Model -250~F to +3000F in 73N12 Pneumatic Controller, conjunction with a variConoflo Corp. Philidelphia, able Ni resistor. Penn. 7 Model 243, Electronic Tempera- Control of preture Controller, Bailey Instru- conditioning bath temperaments, Danville, Conn. ture. 8 Flow Measurement and Calibration 8a 50MJ10-1/4, Laminar Flow Element, Measurement of mass flow 0.4SCFM at 4" water differential, through calorimeter. Meriam Instrument Co., Cleveland, Ohio. 8b Model M12, Water Manometer, Measurement of pressure 0-10" water. National Instru- drop at the flowmeter with ment Co., New York, N.Y. an accuracy of 0.001". 8c 180 inch Mercury Manometer. King Measurement of pressure Eng. Co., Ann Arbor, Mich. at the flowmeter. 8d Model 15-180-15 Mercury Thermo- Control of flowmeter bath regulator, and Model 130 Transi- temperature to 27 + 0.2"C. tor Relay, Fisher Scientific, Detroit, Mich. 8e Model 6R-6M-50-SS, Relief venting Relief of flowmeter presvalve, Nupro Inc., Cleveland, sure above 100 psig. Ohio. 8f Model 1014, 30" vacuum to 150 Measurement of pressure psig gages. Ashcroft Inc., in collection cylinders Stratford, Conn. during flowmeter calibration.

401 8g No. 83027 H.R., 3 way Solenoid Switch to transfer flow Switch, American Switch Co., from reservoir cylinder Florham Park, N.J. to collection cylinder and vice versa 8h Model 26-1521-24-067, 0-150 psig, Control of flowmeter preshand loaded non-relieving stain- sure during calibration. less steel regulator. Tescom Inc., Minneapolis, Minn. 9 Composition Measurement 9a Custom portable chromatograph Measurement of system with thermal conductivity detec- composition. tor. Phillips Petroleum, Bartlesville, Oklahoma 9b No. 64101 Speedomax G, adjustable Recording of chromatochart speed chromatographic graphic output. recorder. Leeds and Northrup, Philadelphia, Penn. 9c 30% Hexa-methyl-phosphor amide ] (H.M.P.A.) on 60-80 mesh Columpak. Fisher Chemicals, Materials for chromatoDetroit, Michigan. graphic column for separation of methane, ethane, 9d No. A-540, Adsorption Alumina, and propane. Fisher Chemicals, Detroit, Michigan. 10 Calorimeter Pressure and Differential Pressure Measurement 10a Model 260-W.G., Dead Weight Gauge.) Mansfield and Green, Cleveland, Ohio. Measurement of pressure at calorimeter inlet. 10b Model 2416-2 Differential Pressure Null Indicator and Model 2413-5 Gas to Oil Pressure Transmitter. Ruska Instruments, Houston, Texas. lOc PT 119 HDC-2500 Temperature com- Pressure measurement at pensated (750F-250~F) Strain calorimeter inlet and Gage Pressure Transducers (3 outlet upto a maximum of millivolts/volt full scale). 2500 psia. Dynisco, Cambridge, Mass. d PT-98D-2M +1000 Temperature Measurem ent of differencompensated Differential Pres- tial pressure across the sure Transducer (2 millivolts/ throttling calorimeter volt full scale). Dynisco, with a maximum range of Cambridge, Mass. 1000 psid.

402 10e Model 30-FA-200, high pressure Measurement of differenwell type 40" differential pres- tial pressure across sure manometer. Meriam isobaric calorimeter. Instrument Co., Cleveland, Ohio. 10f KG 25-0 2-0.2(c) D.C. Power Supply, Exitation voltage source 0.005% load regulation, 0 to for all transducers. 25 volts, and upto 0.2 amps, Kepco Inc., Flushing, N.Y. 10g Model X500, 3" length, flat Sightglasses for visual glass reflex liquid level gages, examination of mercury Penberthy Inc., Prophetstown, level in gas to oil Illinois. U leg connected to the calorimeter exit. 11 Model 156x62-P12, Brown Poten- Multipoint temperature tiometer Pyrometer. Honeywell Inc., indicator over the range Minneapolis, Minn. -250 F to +150~F 12 Model 10-11-AF6 shut-off valves Shut off and throttling with Teflon 0 rings, and Model valves used in the control 30-11 HF4-cc- 316 calibrated valve mainfold. control valves with viton O rings. High Pressure Equipment Co., Erie, Penn. 13 Model 6AVD-B Filter Dryers, with Adsorption of oil and ACl, Activated charcoal dessicant. unsaturated hydrocarbon King Engineering, Ann Arbor, Mi. impurities at the flowand Molecular Sieves 3a meter and bypass streams. and 4a, Linde, Cleveland, Ohio. 14 Calibration Manometer 14a OKS2 shutoff, and ORS2 regulating Used to construct the stainless steel valves. Whitey calibration valve maniResearch Tool Co., Emeryville, fold which controls the California. calibration manometer. 14b LC-621, 200-2300 psia outlet Regulation of pressure Relief venting regulator. at each leg of the Standard Pneumatic, Hemet, differential manometer. California. 14c SVR-3, 11 7/8" length, flat Sight glasses for visual glass reflex liquid level gages. examination of mercury Strahman, Inc. Illinois. level at the manometer. 14d Model M-911, Cathetometer. Measurement of mercury Gaertner Inc., Chicago, Illinois. column levels with respect to a reference scale at the 200" Diff. Press. Manometer

403 14e 300 inch steel tape. Lufkin Rule Reference scale for measurCo., Saginaw, Michigan. ing the height of any mercury co lumn. 14f Model 1502-DGS-1. Filter-Fink Indicates the approximate Differential Pressure Indicator height of any given mer0-1000 psid, upto 2000 psia with cury column. (For the 200" variable differential pressure Diff. Press. Manometer) setpoint for the activation of an electric contact. Orange Research, East Orange, N.J. 14g No. 8267C79, stainless steel Used in conjunction with normally closed 2,3,4 way the above device to pregolenoid valve. American vent any mercury column Switch Co., Florham Park, N.J. height from exceeding 210". 15 Materials 15a Methane, 99.8%, Southern Cali- Used in preparation of fornia Gas Co., Bowerbank Well, system mixtures containing Taft, California. methane. 15b Methane, Ultra-High Purity, Used in preparation of (less than 50 ppm impurity reference mixtures concontent). Matheson Co., Joliet, taining methane. Ill. 15c Ethane, 99.5% min., Pure Grade, Used in preparation of and Ethane, 99.99% min., Research system and reference mixGrade, Phillips Petroleum, tures respectively, that Bartlesville, Oklahoma. contain ethane. 15d Propane, 28 gallons, Instrument Used in preparation of Grade 99.9%, and Propane, 99.99% system and reference mixmin., Research Grade, Phillips tures respectively, that Petroleum, Bartlesville, contain propane. Oklahoma. 15e Isopentane, Technical Grade. Calorimeter bath fluid Phillips Petroleum, Bartlesville, in the range -240~F to Oklahoma. -600F. 15f #200 Silicone Fluid. Dow- Calorimeter bath fluid in Corning Corp., Midland, Michigan. the range -60~F to +300"F. 15g Coating No. 756, Front surface To permit the observation mirrors. Libby Owens Ford, of the calibration manoDetroit, Michigan. meter sight glasses at the cathetometer by reflection.

APPENDIX E Detailed Drawings for the Modified Heater Capsule of the Isobaric Calorimeter.625 -.50 0C ALL THREADS ARE TRUNCATED # 56 DRILL (.0465) / V GROOVES HAVE A DEPTH OF.016 HOLES AT 450 AND ARE PLACED AT 450 (TO BE PUT ON ALL PIECES) 0 G I.R. =.2185 0R \. II.R.=.2815 3.312 3.040 3.391 3.094 3.17 3.02 3.15 3.15 SCALE: # 56 DRILL (.0465) AT 450.200 8 thds..156 6thds. t T ^,t t T-. 1 j437.563 -459.585.605 -480 4.585" HEATER CAPSULE SHELLS

L..775 J.- %?r 13/i604 DiA.'n'HOLE FOR W U- IRE PASSAGE (NOT SHOWN IN OTHER VIEW) xx 4C- + ~ # 56 DRILL(.0465) 8 HOLES I.R.= 42 ~ /LR.:.3435 _ _ _________ SCALE: 3.230 2.906 3.45 1 ~~~~~~~~3.04 3,0 2.875 302 2 ROWS,8 HOLES.043 DIA., NO. 57 DRILL EQUALLY SPACED APPROX. THDS.ON I.D..125 5THDS APPROX. 3 THDS.ONO.D.3.37 -.687.04.17.840-.709 4 r-.862 —.730~.~~880 HEATER CAPSULE SHELLS. 908

THREAD TABS FOR 9/16 -40 RING 4 V.063 0 9/16 -40 f / WIRE RETAINER RING APPROX. 1/32 DIA. FOR WIRE Wt RAER 2 PLACES,APPROX. 5/32 SPACING 1/16 DIA. HOLES ____..605-u 8 PLACES I\~. i 1 \EQUALLY SPACED +++ 6) F 3.58 3.54 3.52 3.45 2 SETS, 12 HOLES EACH 1/16 DIA. EQUALLY SPACED:~~, / \ ^~.075APPROX. 3 THREADS ++. ~ ~075.30.37 1 k.91-. -.932-.98 1.0 HEATER CAPSULE SHELLS

1.00 C.825 THREAD DIMENSIONS These threads must match those on shell one 45t two " " "three 8............)" " " on inside of shell five S/LOTS^ ^^i^^^RE~~~~~~~ I(All threads shallow 40 threads/inch, NF) SLOTS ARE 1/16 WIDE SCALE: I I I 1.0 -.796.639 1 /32 R.483.296 45 ^.593 - 1/16 ROUNDS.437 -1/16 ROUNDS.484 CAPSULE MOUNT

APPENDIX F Sample Calculations 408

409 Appendix F-I Calculation of Mass Flowrate System: - 0.276 C2H6 - C3H8 Run: - 4.020 Relevant Data Mercury manometer reading for flowmeter pressure, P = 157.56 in. Hg Temperature of scale on manometer, T = 78.00F ps Temperature of mercury in manometer, T = 78.00F pm Barometric pressure, Pb = 29.20 in. Hg. bar Barometric temperature, T 78.44~F bar Flowmeter bath temperature, Tf = 27.080C Reading on left hand side of water manometer, P = 9.180 in. H20 Reading on right hand side of water manometer, R1 3.005 in. 20 Zero error correction for water manometer, Po = + 0.006 in. H20 Molecular weight of mixture, W = 40.21 m a) Calculation of gas density The density of the fluid stream at the flowmeter is computed from the virial equation truncated at the second virial coefficient. The individual pure component and interaction second virial coefficients and their variation with temperature in the vicinity of 27~C are summarized in Table F-l below Table F-1 Virial Coefficient Data for Calculation of Gas Density at the Flowmeter -5 System Reference B298.15K [dB/d(l/T) ]xlO B27.08C - cm3/mole 298.15K 3 cm3/mole cm /mole cc ~K/mole CH4 [ 67 ] -42.82 0.331 -42.05 C2H6 [174 ] -185.6 1.12 -182.99 C2H6

410 Table F-1. Continued C3H8 [122,123] -388.0 3.08 -380.84 CH4-C 2H [ 59 ] -93.1 0.539 -91.84 CH4-C3H [ 59 ] -139.0 0.539 -136.94 C H -C H [ 59] -274.0 0.885 -270.07 The B values at the flowmeter bath temperature Tf are in each case calculated from the equation dB (Tf - 298.15) (B) 3B + [ I(Fi-1) (Tf 298.15 d() (Tf)(298.15) ( 298.15 These results are also reported in Table F-l. The mixture virial coefficient is then calculated using the relation: n n (B.) = Z Z x.x. B.. (F1-2) x 27.080C i=l j=l' J Thus B ix = (0.001)2(-42.05) + (0.2747)2(-182.99) + (0.7248)2(-380.84) mix + (2)(0.001)(0.2747)(-93.1) + (2) (0.2747)(.7248) (-270.07) + (2) (0. 7248) (0.001) (-136.94) =-321.5 cm3/mole The pressure Pf at the flowmeter outlet in psia is given by P = P F G + P G (Fl-3) fo fg s fg bar bar where F = 1. + 13.34x106 (T -68"F) (F1-4) s ps fg = 0.4894 [1 - 99x10-5(T -680F)] (Fl-5) 0.00275 Gbar = 0.4912 [1- (Tbar-32~] (Fl-6) bar F is the temperature correction factor for the scale of the 180 inch s mercury manometer. Gf involves a conversion of the mercury column

411 height as a function of temperature into psi units. Gb involves the bar conversion of the barometer reading in inches of mercury to psi and was developed by Jones [119] from the manufacturer's calibration included in his thesis. Thus: p = (157.56)(0.4894)[1 - 9.9x10-5(78.-68.)][1. + 13.34x10-6(78. 0 00275 -68. )] + (29.2)(0.49115)[1 - ( 7)(78.44 - 32.)] 29'20 91.32 psia The approximate pressure drop at the flowmeter is given by lAPlap = Eh - R -R = 9.180 - 3.005 - 0.006 approx - 1 o = 6.169 in. H20 (F1-7) AP 0.03612 psia Average pressure at flowmeter, P = P + ( in. H)( 0 i P f Pfo + ( in. H20)( in. H 6.169 91.32 + (' )(0.03612) 91.43 psia (F1-8) The compressibility factor z at the flowmeter conditions is approximated by: z = + BPf/R(Tf + 273.150K) (Fl-9) 321.5 cm3 1 gm mole K 91.43 psia gm-mole (14.696)(82.06) cm3 psia (300.23"K) = 0.91884 The mean density pf at the flowmeter is given by: (Pf) (W ) Pf R(Tf + 273.15)z (Fl-10) 91.43 psia 1 lb. mole K 40.21 lbs 300.23 K 19.314 psia ft3 lb mole 1 lbs0 9 = 0.6900 ft3

412 b) Calculation of pressure drop across flowmeter The true pressure drop, AP, across the flowmeter in inches of water is given by: AP = (Rh - R)(F' ) g ( -- ) (Fl-ll) 1 o0 HO gc g0 H2 where,1.91 4 5.3x10-6 F = 0.99823 -1. x 10- (T - 68.) - H2O 1.8 bar (T ar-68 )2 (Fl-12) PH20 = 62.427(F' ) lb /ft3 (Fl-13) -~,980.314 g = 980.314 0.99964 gc 980.665 and pH 0, pg are the densities of the water, and the system fluid above the water in the water manometer respectively. F'H 0 corrects the height of water in inches to 68~F. The temperature at the water manometer is assumed to be the same as that of the barometer which is located nearby. The compressibility factor z for the gas at the water g manometer is calculated from Equation (Fl-9) as: 1 + (-324.9) cm 1 gm mole 91.43 psia 0.9176 g gm.mole 14.696 cm3 atm. 298.95K where the B value of -324.9 cm3/gm-mole was calculated using Equations m (Fl-l) and (F1-2) at a temperature of 78.44~F. Thus: ( 91.43 psia 1 lb. mole K 40.21 lbs. g 298.95~K 19.314 psia fts. lb.mole 1 0.6939 09176 = 6939ft3 F' (78.44~F) = 0.99752 H2O PH 0 (68~F) = 62.232 lbs./ft3 H2O

413 Therefore: 0 6939 AP = (6.169 in. H20)(0.9975)(0.99964)(1 - 62232 ) 6.083 in. water at 68~F or 20~C c) Calculation of the mixture viscosity at the flowmeter conditions The relations used to calculate the viscosity at the flowmeter conditions are discussed in Section VI. The values of A and S in Equation (VI-10) for the individual pure components are presented in Table F-2. Table F-2 Sutherland Constants for the Zero Pressure Viscosity 1/2 System A.(u poise/~R ) S.(~R) CH4 7.39 295.2 C H6 7.461 466.2 2 6 C3H8 6.700 502.4 The A. and S. values in the above table were obtained from Lee and Eakin [143]. The A. value for propane was, however, adjusted from 6.805 to 6.700. The adjustement was dictated by the desire to match the dimensionless flowmeter calibration curves for ethane and propane [284] as described by Equation (VI-1) by a suitable adjustment of their viscosities relative to each other. This adjustment is believed to be within the accuracy of the data used to generate the original A. set by Lee and Eakin [142]. The mixture constants are calculated as: A Z= x. A.i v / Z x. v. (Fl-14) m. 1 i i i=l i=l 1 1/2 1/2 = (0.001) (7.39) (16.042) + (0.2746)(7.461)(30.070) 1/2 1/2 + (0. 7244) (0.670) (44.094) /[ (0.00t) (16.042)

414 1/2 1/2 + 6.2746 (30.070) + (0.7244)(44.094) ] 6.860 S = Z x.S. m l i i=l (0.001)(295.2) + (0.2746) (466.2) + (0.7244)(502.4) 492.22 (F1-15) 1.5 A [(Tf + 273.15)1.8]1 [(Tf + 273.15)(1.8) + S ] i m 6.86(540.4) - 6~650) = 83.47 micropoises (Fl-16) (540.4 + 492.2) The mixture viscosity pi at the flowmeter pressure is calculated from Equation (VI-7) = p m exp [X(T) p ] (F1-17) where: X(T) = 2.57 + 1T + 73 )(8 0.0095 W (F1-18) (Tf + 273.15)(1.8) m and: Y(T) = 1.11 + 0.04X = 1.3697 (Fl-19) and if p is in gms/cm3. 1. 369 7 m g ft m = 83.47 exp [ 6.435{(0.6900 ft3)(0.01602 gm3 L)} m fmt: 3 cm3 lb m = 85.73 micropoises d) Calculation of mass flowrate Th'le flowmeter calibr;ation data for the systGem was fitted to the calibration equations:

415 10 F 1000 Pf AP - = 1.6587 + 0.3172[ln( )]-0.01793 (p1ap/2 2 (Pf AP) P' 1000 p AP 2 [ln( ( ) ] (F1-20) m P AP 2 f + F F = 0.10351 + 15.2494 ( - ) + 417.06187 ( -- )(F-21) m m m where pf is in lbs./ft3, AP is in inches of water at 680F, i is in micropoises and the mass flowrate F is expressed in lbs/min. If Equation (F1-20) is solved for F we obtain the mass flowrate as 0.29382 lbs./min. A trial and error solution of Equation (F1-21) yields a value of F as 0.2936 lbs/min. In this particular case, the results of Equation (F1-20) were given priority over the results from Equation (F1-21) as the former equation was superior in the representation of the calibration data in the approximate range of the calculated flowrate.

416 Appendix F-2 Sample Calculations involving the Differential Pressure Calibration System. The calculations in this section illustrate how the calibration data for the differential pressure transducer are obtained from measurements using the high pressure differential mercury manometer. The procedure for calculating the differential pressure from the transducer calibration equation is also discussed. I Measurement of Mercury Density The density of mercury used in the manometer is determined by weight using a cylindrical Lucite box of known volume I.D. of Lucite box = 1.4997 in. @ 75~F Depth of Lucite box = 1.4988 in. @ 75~F Volume of box = (14997) 1.4988 = 7.06173 in.3 = 115.721 cm3 4 Wt. of box with mercury = 1873.651 gms. Wt. of mercury = 1565.583 gms. Net calibration correction for weights = 0.006 gms. ieasured temperature = 75 ~F Coefficient of cubical expansion of Lucite = 0.66x10-4 cm3/ C cm3 Corrected volume of Lucite box = (0.66x10-4)(75.-75.)(115.721) + 115.721 = 115.721 cc. Density of mercury 156559 gs = 13.528 115.721 cm cir @ 75~F II Calculation of Pressure and Differential Pressure at the Transducers for a Sample Set of Measurements Obtained with the High Pressure Differential Manometer The sample set is confined to a measured pressure drop of about 100 psid, and consequently uses only legs I and II in Figure VI-13.

417 a) Elevation measurements with respect to Lufkin 300 in scale Elevation of transducers, h = 34.16 in. 0 Elevation of mercury in leg I, h2 212.07 in. Elevation of mercury in reservoir of leg I, hi 6.74 in. b) Electrical measurements Transducer excitation voltage (potentiometer scaled reading), E = 0.90854 volts X Differential pressure transducer output (scaled reading), EDP = 2468 Wv High pressure transducer output (scaled reading), E = 11788 iv Reference transducer excitation voltage (scaled reading), E = 0.90650 lv XO c) Additional data Temperature at top of manometer T = 67~F Temperature at bottom of manometer T = 69~F Mean temperature of manometer T = 68~F m Density of mercury at 1 atm., and 32~F ps = 13.595 gm/cm3 Measured pressure at dead wt. gage at elevation h Pg = 985.6 psig o Barometric pressure P 28.16 bar Barometric temperature Tb = 75 F bar Standard gravity gc = 980.665 cm/sec2 Latitude L = 42 deg. 16.6 min. N. Elevation z = 876 ft. above sea level Local gravity g = 980.314 cm/sec2 Vertical tension on 300 in scale W = 10 lbs. v Coefficient of thermal expansion of tape a = 6.45x10-6 in./in.OF Product of tape cross section A, and the Young's modulus of elasticity E, (Table A-ll), AE = 88200 lbs

418 d) Corrections for scale marking errors NBS Calibration correction at h (Table A-ll) = -0.004 in. 1 NBS Calibration correction at h (Table A-ll) = +0.003 in. Measured height difference, h2 -h1 = 205.33 in. Height difference corrected for scale marking errors = 205.32 in. e) Correction for tension on scale The change in length 6h for a horizontal tension of WH lbs.,is given by: (w - 10)(h2 - h1) 6h = (F2-1) A E where the calibration tension is 10 lbs. horizontally applied. The effect of applying a tension vertically instead of horizontally is to increase the length by 0.0005 in. over a span of 300 in. For a weight of 10 lbs. applied in this work, no correction was necessary. f) Correction for temperature variation of scale length The change in length 61 corresponding to some fixed interval of length AL is given by: 61 = (T - T )AL (F2-2) where O = Coefficient of linear thermal expansion T = Temperature of calibration of the scale, ~F s 61 = o45x10-6 in 61 =.45x106 in ~ (75. - 68.) (205.32) + 0.01 in. in O F Corrected Height = 205.32 in - 0.01 in. = 205.31 in. g) Absolute pressure at the high pressure transducer From Table A-9, the corrected gage pressure P using the M & G dead wt. gage is given by P = (985.6) + 0.1 + 0.49x10-3 (985.6) = 986.1 psia gc The barometric pressure is corrected to psia using the empirical calibration equation of Jones [119]

419 (P ) =[ P - 0.00275(T-32) ] in Hg (0.49116 i ) (F2-3) bar bar in Hg. c =[ 28.16 - 0.00275(75-32) ]0.49116 = 13.98 psia Pressure at high pressure transducer, Pho = 986.1 + 13.98 X 1000.1 psia h) Pressure at bottom of mercury column The pressure at the bottom of the mercury column at the reservoir, Phl, is higher than the corresponding pressure at the transducers by an amount equivalent to the head of nitrogen gas corresponding to the elevation difference hi hl =Pho g PN2 dh (F2-4) ho where PN2 is the density of nitrogen. The minus sign indicates that the elevation convention increases negatively in going from ho to hi. If PN2 is independent of elevation we obtain: P hl = ho (F2-5) hi = Pho + g zRT (hl - ho) (F2-5) where z = compressibility factor for N at 1000.1 psia and 75~F 0.9994 (Reference [232]) 2cm R = 2.9673x106 C2, (Reference [29]) sec K Therefore: Ph = 1000.1 psia - (980.314 m 2)( 10 94 P ) (6.74 - 34.16) in. hl sec 0 9994 cm 1 sec20K 1 2.54.) ( 2.9673x106 m )( 297.03 = 1000.176 psia

420 i) Conversion of mercury column height to psid The relation h2 Ph2 hP gc PHg (h) dh (F2-6) h2 - hl - c rg hi is used to connect the actual mercury column height in inches to the desired units taking into account the variation of mercury density due to temperature and pressure. The density variation of mercury can be expressed as P P P(PT) = P(PsTs) + ( ) dP + ( ) dP h' dp T P Ps P hi T + X ( ) dT (F2-7) Ts where Ps, Ts are the conditions of the actual density measurement using the Lucite box. The pressure dependence of the density of mercury is given by the relation [29] p = p(T, Ps) [ 1 + 137xlO-P] (F2-8) where P is in inches of mercury. The temperature dependence relative to 32~F is expressed as [29]. p = p(32~F,P ) [ 1 - 0.000101 (T-32)] (F2-9) Therefore, expressing P in psia units, Equation (F2-7) yields the result H (Ph, T) = P(T P )[ 1 + 049916 (Phl- P) 1 37x - 10 ( (0.49916 (Ph + Phl) - 0.000101 (T - T)] (F2-10) Expressing the term (Ph - Phl) in terms of inches of mercury, and setting Ps = 14.0 psia, T = 680F, T = 750F, and p(T,PI ) 13.528 gms/cm3 we obtain

421 PH (Ph, T) = 13.528[l.0008 + 137x10- (h - hi) (F2-11) Substituting this result into Equation (F2-7) we obtain h2 P = PP - g I 13.528 [1.0008 + 137x10-9(h - hi)] dh h2 hi gc (F2-12) hi where the height h must now be expressed in terms of inches of mercury with hi as the reference. Therefore: P = Phl - 13.528 [(1.0008)(h2 - hi) + 137x10-9( h22- )] h2 hi 2 gc 1000.176 psia - {13.528 g3 [(1.0008) (205.31) + cm 205.31m 1 gmf sec 37x0 9( 205. 3) ] in. 980.314 2 980.665 gm.cm. 2 sec 3 lbf (2 54)3 cm } (2 ) in 453.59 gms = 1000.076 - 100.313 = 899.863 psia. j.) Pressure at the low pressure transducer The pressure at the low pressure transducer Ph3 is expressed in terms of the pressure at the top of the mercury column in leg I by the relation h3 Ph3 = Ph2 g (PN2 dh (2-14) h2 Ph2 g zRT (h3 - h2) (F2-15) ZN2 = 0.9996 at 900 psia and 75~F [232] Therefore: 899.86 3 h3 = 899.863 - 980.314 ( 9996 )(34.16 - 212.07) 254 1 8297.03 2.9673x106 = 899.863 + 0.452 = 900.32 psia. = 899 + 863 + 0.452 = 900.32 psia

422 True differential pressure at transducers = P - 1 = AP ho h3 true = 1000.18 - 900.32 =99.76 psid k) Adjustment of electrical output Normalization factor for variation of supply voltage to transducers xo 0.90650 0.9977 E 0.90854 x Normalized value of high pressure transducer output = (11802,v)(0.9977) = 11775 Iv Normalized value of Diff. pressure transducer output = (2468)(0.9977) = 2462 pv Normalized value of Diff. pressure tranducer null = (471) (0.9977) 470 pv Normalized value of Ep - (E (2462-470)v DP PNull = 1992 iv Having defined APtrue DP - (ED, and Pho we can from a series true EDp - (Ep)1' and h' w h of such measurements obtain the ca~irlation constant 3', 6' and y' in Equation VI-19.

423 1) Sample Calculation of Pressure and Differential Pressure from Transducer Outputs System: - 28% C2H6 - C3H Run No. 4.020 Relevant Data High pressure transducer reading Eh = 2135.6x10-5 volts at null, Low pressure transducer reading E = 2148.9x10 5 volts ln at null, Differential pressure transducer E = 44.2x10 5 volts null reading at null, High pressure transducer reading, E = 2128.6x10-5 volts Low pressure transducer reading, E1 = 2019.2x10-5 volts Differential pressure transducer E 249x10 5 volts reading, Calibration reference scaled E = 0.90650 volts xo transducer excitation voltage, Actual scaled transducer E = 0.90751 volts x excitation voltage, Inlet pressure to calorimeter Phgr= 1776.7 psig (M & G dead wt. gage), Barometric pressure, P = 29.07 in Hg. bar Barometric temperature, Tb = 75.80F Transducer Calibration Equations High Pressure: Eh/10 = -3.989 + 1.1988 P - 0.3526x10-6 P 2 (F2-16) h hg hg Low Pressure: E /10 = 12.001 + 1.1999 Pi - 0.227x10-5 Plg2 (F2-17) Diff. Pressure: (EDp-E nl)/10 = AP[1.9985 - 0.563xl-5 (2P -AP) + 0.217x10-8 (3Ph2-3PhAP + AP2) (F2-18) where all voltages are expressed in microvolts. The subscript g implies

424 that gage rather than absolute pressure is utilized. Corrected barometer pressure using Equation (F2-3) = [29.2 - 0.00275 (75.8 - 32.0)] [0.49116] = 14.26 psia Corrected M & G pressure using results of Table A-9 = (1776.7) + 0.1 + 0.49x10-3(1776.7) = 1777.6 psid Absolute pressure at calorimeter, Ph = 1777.6 + 14.26 = 1791.9 psia E Corrected value of Ehn = 2135,6x105(E-) = 2133.2x10- volts x The solution of Equation (F2-16) using the corrected value of Ehn yields Phgn = 1783.8 psig where Phgn is the calculated gage pressure at null using the high pressure transducer. Similarly, the solution of Equation (F2-17) using the corrected value of Eln yields Plg = 1784.8 psig where Plgn is the calculated gage pressure at null using the low pressure transducer. Now, as the true pressure is the same in both cases at null, the difference APll defined by P =Pgn - P = 1783.8 - 1784.8 = -1.0 psia null hgn lgn serves as a check for relative calibration changes between the two transducers. For convenience, we adjust a1 in Eqn. (VI-13) so that the low pressure transducer also yields 1784.8 psig. As a result al is changed from 12.001 in Equation (F2-17) to 13.201. Similarly, the values of ~ and E1 corrected for reference voltage changes and used in conjunction with Equations (F2-16) and (F2-17), respectively, yield Phg = 1777.5 psig

425 P1 = 1675.4 psig where al in Equation (F2-17) now has a value of 13.201. Therefore, the pressure drop AP is calculated as AP = Ph -P = 1777.5 - 1675.4 = 102.1 psid. hg lg The values of EDp and Enull corrected for reference voltage changes when used in conjunction with Equation (F2-17) yields the pressure drop AP as 103.1 psid. The discrepancy between the redundant measurements is 1 psi or approximately 1%. The absolute pressure transducers were found to be less susceptible to hysteresis than the differential pressure transducer, and consequently were preferred for specifying the differential pressure on the rare occasions when both of them were in service simultaneously.

426 Appendix F-3 The Preparation of Calibration Standard Mixtures for the Composition Measurement Reference mixtures necessary for the calibration of the chromatograph are prepared by weight using 374. cc capacity steel cans. As the weight of the gas is only between 0.2% and 1.5% of the total weight of a can, calibration changes in the balance must be carefully monitored. Changes in the buoyancy contribution of the ambient air caused by variations in air density or in the can volume as a function of pressure must also be taken into account. To simplify the technique a dummy can, with dimensions similar to the sample can, is maintained at the balance location and weighed along with the sample can at all times. The contribution of such additional measurements is derived below: a) Nomenclature Vd = Volume of dummy can at atmospheric pressure V. = Initial evacuated volume of sample can at pressure Pi V2 = Volume of sample can at filling pressure P2 W = Observed initial weight of sample can at pressure P1 W2 = Observed weight of sample can at pressure P2 D. = Observed weight of dummy can at initial weighing of sample can D2 = Observed weight of dummy can at final weighing of sample can WiT DiT= True weight of can with observed weight Wi or Di vd = Volume of weights used to measure dummy can v1 = Volume of weights used to measure sample can initially V2 = Volume of weights used to measure sample can finally = Density of air at initial conditions 2 = Density of air at final conditions P = Density of weights b) Derivation of the Technique The difference between the true and the observed weight of a can is ascribed to the combined effects of air buoyancy and calibration changes in the weights. Thus:

427 l - 1)1 = IlVd - Vd -+ ('-1) D2T 2 = P2[Vd - vd] + d2 (3-2) W1T -W1 = p[V1 -v] + d + e (F3-3) W2T-W = 2[V -v2] + d2 + e2 (F3-4) where d. is the calibration correction for the true weight DiT, and e. is the calibration correction involved in the true weight difference (WiT- DiT). The development assumes that the true weight and volume of the dummy can is unchanged over the time period covering both sample measurements, and that the change in vd involved in the weight difference (D2 - D1) is negligible. From equations (F3-1) and (F3-2) we obtain: D 2 -D1 = P[Vd - d] - P2[Vd - vd] + d2 - d (F3-5) Similarly, W2T - WT = (W2 - W1) + P2[V2 - v2] - P[V1 - 1] + (d2 - d) + (e2 - e1) (F3-6) The effect of pressure on the displacement volume of a can may be represented by the relation: V. = V. + b(P - P) (F3-7) J 1 j 1 where V. is the can volume at pressure Pj. Equation (F3-6) may now J be represented in the form: W2T - WT = (W2 - 1) + (2 - P1)(Vd - vd) + P2[(V2 - Vd) - (v2 - d)] - [(V - Vd) - (v1 - Vd)] + (d2 - dl) + (e2 - e 1) (F3-8) Using Equation (F3-5) in conjunction with Equation (F3-6) we obtain:

428 2T 1T (W2 - W1 - (D2 - D1) + P2[AV2 - 6v2] - p[AV1 - 6v1] + (e2 - el) (F3-9) Now AV2 = AV1 + b(P2 -P1) (F3-10) W2 - W and 6v = 6v + W- (F3-11) 2 = 6"1 I Thus, on substitution into Equation (F3-8) the result W2 - WT = (W2 - W1) - (D2 - D1) + (2 - P1) (AV1 - 6vl) W - W1 + pb(P2 P^ -1 p ( PW ) + (e2 - e1) (F3-12) is obtained. c) Sample calculation for an ethane-propane mixture Set I Relevant Data Wt. of empty can 8, W1 = 189.0208 gms. Can 8 pressure, P1 = < 10 microns Hg. Observed wt. of reference can 12, D = 187.2046 gms. Evacuated displacement of can 8, V = 374.22 cm Evacuated displacement of can 12 Vd = 372.3 cm Wet bulb temperature, Twb = 67.0~F Dry bulb temperature, Tdbl 76.90F Air temperature at balance, T1 = 26.1~C Corrected Barometric pressure, Pal = 732.9 mm.Hg. Molecular wt. of dry air (MW) = 29.00 r Set II Wt. of can 8 + ethane, W2 = 190.3735 gms. Can 8 pressure, P2 = 30.3 psig P2

429 Observed wt. of reference can, ) = 187.2076 gms. Wet bulb temperature, Tb = 59.0~F wb2 Dry bulb temperature, Tdb2 76.3~F Air temperature at balance, T = 25.2~C Corrected barometric pressure,Pa2 = 745.14 mm. Hg. Set III Observed wt. of can 8 + ethane + propane W3 = 192.0214 gms. Can 8 pressure, P3 68.0 psig Observed wt. of reference can, D = 187.2044 Wet bulb temperature, Twb3 = 75.2"F Dry bulb temperature, Tdb3 = 62.20F Air temperature at balance, T3 = 24.4~C Corrected barometric pressure,Pa3 = 737.65 mm. Hg. Iliscellaneous Data: Volume expansion coefficient for cans, 1 d = 0.156x10-4 psia V dP Specific gravity of weights, pw = 8.7 gms/cm3 Calibration correction to 2 gm. pan weight difference for (W - D1), el = + 0.0012 gms. Calibration correction to 3 gm. pan weight difference for (W - D) e2 = + 0.0014 gms. Calibration correction to 5 gm. pan weight difference for (W3 D3), e3 = + 0.0013 gms. Calculations of air density for Set I Density of dry air at 26.10C and 760 mm. Hg., 1 1 l bs = 575 ft3 = 0.001179 gins3 [192] Sn p13.575 ft cm Saturation pressure of HO20 at 67.00F wet bulb temperature,

430 = 17.04 mm Hg. [192] 17.04 Mole fraction of water in air at saturation = 7 = 0.02325 mole % 732.9 The relative humidity was calculated as 60% from a chart of Tdb vs. (Tb - Twb ) for the conditions of Set I. Actual mole fraction of water in air = (0.02325)(0.6) = 0.01395 mole %. If the compressibility factor of air is assumed to be unchanged by a variation in moisture content, then the change in moist air density may be ascribed entirely due to a change in molecular weight. Molecular wt. of moist air, (MW), = (0.01395)(18.0) + (1.- 0.01395)(29.0) = 28.844. Density of moist = (On) Pal (MW)r 760 (MW)1 air for set I, 1 0.001179 gm 732.9 29.00 =[ 0.001179 1 [ I[ I - ^ ~ 3cmI 760 28.844 0.0011431 gms F3-13) cm Similarly, density of moist air for Set II, p2 = 0.0011757 gms/cm3 Application of Equation (F3-12) for Calculations W2T - WIT AV = 374.22 - 372.30 = 1.92 cm3 6v = 187 1 = 189.021 - 1]87.20463 (F3-14) 6v - - 0.208 cm (F3-14) 1 8.7 8.7 1 dV X-4] cm b = ( V ) (V [0.156xl10 ][374.22] = 0.0058 P V dP 1 Psia (F3-15) W2 - W = 190.3735 - 189.0208 = 1.3527 gms D - D 1872076 - 187.2046 = + 0.0030 gms Substituting into Equation (F3-12) the true weight difference W2T - WiT i.e., the weight of ethane added is calculated as: W - W = 1.3527 - 0.0030 + (0.0011757 - 0.0011489)(1.92 - 0.208) 2T iT 3cm _____ + 0.0011757[0.0058 cm- (30.3 + 14.2) psia - 35 + (e2_ el) psia 8.7 2 1

431 - 1.3525/8.7] + (e2 - el) = 1.3527 - 0.0030 + 0.00006 - 0.000125 + (0.0014 - 0.0012) = 1.3494 gms Moles of ethane added = (1.3494 gms) 30 ) = 0.04489 gm.moles 30.060 gms The above results indicate that the major part of the correction to the weight difference between successive measurements on a given can is represented by the change in weight of the reference can. Furthermore, the contribution of the term (p2 - Pl)(AV1 - 6V1) is not very significant, and its omission may make the determination of the wet and dry bulb temperature, and the barometric pressure unnecessary. Similarly, Wt. of Ethane + Propane = W3 - WT = 3.006 gms. Wt. of Ethane = W2T - WT = 1.3494 gms. Wt. of Propane = W - W2 = 1.6512 gms. Moles of propane added = 1.6512/44.094 = 0.037447 moles. Mole fraction of ethane = 0.04489/(0.04489 + 0.037447) = 0.5452 Mole fraction of propane = 1. - 0.5452 = 0.4547

432 Appendix F-4 Calculation of System Composition From the peak height vs. composition curve of Figure F-l it is reasonable to assume a linear dependence in the relationship between the two quantities in the immediate vicinity (+ 5%) of any given composition. The constants a and b for the functional form x. = a + bh. (F4-1) where the peak height h. corresponding to the mole fraction x. of the ith component can be determined from peak height measurements on two standard mixtures with compositons close to xi, assuming that the measurement conditions are substantially unchanged in all three cases. Thus, a = (x.) - [(x.) -(x.) ](h.) (F4-2) S1 Si S2 Si (x) - (x) Ax. S1 S2 1 b = () ( = ( ) (F4-3) (h.) - (h.) Ah'Si'S2 where S1 and S2 are the two reference mixtures. In practice, only one reference SI is used, and consequently a simpler assumption x. = b'h. (F4-4) is necessary, where (x.)' 51 b' - S (F4-5) (hi) SI The error in the computed value of x. with respect to Equation (F4-1) is given by: (x.) - x. = (b' - b) [(h.) - h.] (F4-6) (F4-1) (F4-4) S1

433 15,000 14 000 ~CHROMATOGRAPH CALIBRATION CURVES FOR SYNTHESIZED MIXTURES 13,000 THERMAL CONDUCTIVITY CELL TEMP. 270C PRESSURE IATM!2,000 CURRENT 9 MILLIAMPS GAS FLOW RATE 0.06 S.C.F.H. CARRIER GAS: He,000- COLUMN' 15 FT OF30%H.M.PA. \ \, O OO — ON CHROMASORB P +I FT. ALUMINA 10,000 /) 9000 H 8000 I 7000, 6000 5000 40000 METHANE 0 ETHANE 3000! - - ^a PROPANE 2000- / 100 PEAK HEIGHT UNITS= 2 M.V. 1000 0 10 20 30 40 50 60 70 80 90 100 MOLE PERCENT COMPONENT Figure F-1. Calibration Results for the Chromatograph Using Reference Mixtures of Methane, Ethane and Propane.

434 and is seen to be proportional to the difference in peak heights between the system and the standard mixture. From Figure F-l, the difference (b' - b) is seen to be a function of composition approaching zero at infinite dilution, and reaching a maximum in the pure component case. For the mixtures of this work, the maximum value of (b' - b) occurs for the propane concentration of the 0.27 C2H6 - C3H8 mixture, and corresponds to an error of 10% in the value of the composition difference between the system and the standard. As the standard tank composition differed by as much as 2% from the system composition for this particular system, the error introduced in the calculated composition by assuming (F4-4) was as high as 0.2%. Relevant Data System: - 0.27 C2H6 - C3H8 Run: - 4.020 Standard Mixture Properties (x ) = 0.001 CH S1 (x ) = 0.271, (h ) = 35.70 units C2 C 6 S1 S1 (x ) = 0.728, (h H ) = 69.9 units C 3H' C 8 1 S1 System Mixture Properties (h H ) = 36.20 units 2 6 (h ) = 70.20 units 3H 8 The methane mole fraction is assumed to be the same for both the system and the standard. Analysis of some methane peaks indicated differences of less than 10% in the peak heights between the system and the standard which were ignored. The ethane and propane mole fractions are calculated using the assumption of Equations (F4-4) and (F4-5) respectively. 36.2 CI = (357 )(0.271) = 0.2747 26Z

435 69.9 xI38 = - ( 702 )(0.7248) = 0.7248 Z x. = 0.001 + 0.2747 + 0.7248 = 1.0005 i=1 The mole fractions are then normalized to yield a unity sum.

436 Appendix F-5 Derivation of High Temperature Mixing Rule of Equation (V-41) Described below are the calculations that were necessary to derive the high temperature mixing rule described by Equation (V-41) using the assumptions described on pages 131 and 132 in Chapter IV. I. Calculations Illustrating the Modification of the Reduced Second Virial Coefficient Tabulation of Leland et al., [145]. The ratio of BM/Vc to B/Vc at Tr values of 1.0 and 2.0 are respectively given by Leland et al. [145] as (B /Vc) T=TM 0.420 = = -0.3296 (F5-l) (B/Vc) -1.275 T=Tc (BM/Vc) T=TM 0.420 420 2.0 (F5-2) (B/Vc) -0.210 T=2Tc If the above results are valid for methane, then the insertion of the appropriate B/Vc values obtained from precise experimental data into the denominators of Equations (F5-1) and (F5-2) should yield identical BM/Vc values that are also in agreement with the results. of Leland et al. Using Equation (F5-1), the precise data of Douslin [67] for methane at T = Tc, at T = 2Tc, and a Vc value of 99.0 cm3/gm mole, we obtain BM - 115.8 [ V -0.3296 [ -. = 0.389 (F5-3) T=191.07K From Equation (F5-2) BM - 19.3 [ e ] = - 2. [ 990 ]= 0.387 (F5-4) Vl c 99so,0T=382.14K Also,

437 B M[ ] = 0.420 (F5-5) Leland et al. Although there is close correspondence between the BM/Vc values calculated in (F5-3) and (F5-4), their agreement with Leland's suggested value is somewhat poorer. The value of BM for methane was adjusted from -41.5 cc/mole as given by the tabulation to -38.5 cc/mole to conform to (F5-3). The function B/Vc vs T/Tc of Leland et al. was then redefined in terms of the variables B/BM and T/TM using the modified value of BM. The function is plotted as Figure V-2. II. Determination of the Ratios TM/Tc and BM/(RTc/Pc) as Functions of ac The experimental data on CF4 and CH4 were used exclusively to derive these relaticnships. From the results of Leland et al. [145], T = 18.0 Tc for methane. From the data of Douslin et al. [67] M Tb = 509.3K for methane. Therefore, TM (18)(191.07) (-)C 593= 6.753 (F5-6) Tb 509.3 CH4 From the data of Douslin et al., Vb = 54.34 for methane Therefore, B ( ) = 0.7085 (F5-7) C4 The experimental second virial coefficient data for CF4 [65] yields: (Vb) = 104.13 cm3/gm.mole CF4 (Tb) = 518.14~K CF4 These results were used in combination with the critical properties for CF4 in Table J-1 to specify the empirical linear relationships

438 Vb RTc/Pc= 0.15903 + 0.05883 (oc - ac ) (F5-8) RTc/Pc oo Tc 1 + 0.189(ac - ac ) Te^~~~~~~ =o ________________(F5-9) Tb 2.6656 ( where ac = ac = 5.82 (F5-10) 00oo CH 4 Therefore: T. T TM TM Th 18. = (M ) ( _ L _ (F5-11) Tc Tb Tc 1.0 + 0.189(ac - 5.82) and BM B Vb c R(c/Pc = [0.7085][0.15903 + 0.05883 RTc/Pc Vb )RTc/Pc (ac - ac )] (F5-12) oo if it is assumed that T /Tb and B /Vb are universal and independent of the ac value of a substance. If TM and BM in Equation (V-38) are expressed in terms of Equations (F5-11) and (F5-12) respectively, then we in fact obtain the generalized reduced correlation of Equation (V-39) valid at high reduced temperatures beyond the Boyle point. The mixing rule of Equation (V-41) may be derived by combining Equation (V-39) with Equation (V-l).

4 3() Apppendix F-6 Estimation of Errors in the Compiutation of the Second Interaction Virial Coefficients from the Correlation of This Work Assumptions. 1) The second virial coefficient of methane is accurately known to as low as 198.15K. 2) The discrepancy 6 between the BC data of Brewer. C3H183 C83H (-579 cm3/gm mole, [28]), and that of Kapallo, (-588.5 cm3/mole, [123]) at 248.15K is taken to be a measure of the uncertainty of the data. 3) For temperatures other than 248.15K, the uncertainty C3H8 is assumed to be proportional to the value of the reduced second virial coefficient Br C3H8 6r = k[BrC ](F6-l) C3H8 3H8 4) As a consequence of the first two assumptions, the uncertainty in the propane data is concentrated in the slope function term of Equation (V-30). The uncertainty, 6, introduced by the correlation in the calculation of the B values for other substances at a given reduced temperature TrCH4, can be expressed as 4 k[ac - OlcH ] 6r= = TBr/8 (F6-2) R.Tc/Pc [ctcC H- OcCH C3H 8 38 4 5) The uncertainty,.ij involved in the calculation of the inter1j action virial coefficient Bi.. from Equation (V-1) due to uncertainties in the B value for the pure components and for the mixture is given by 6 - x.26..- x.26.. 6 -m 1i' j JJ (F6-3) ij 2x.x. 1 j Sample Calculation for 0.498 C2H6 - C3H Mixture n) Determination of the value of k. At 248.15K Br -5885 cm3m mole -0 8143 (Using the data of Kapallo BrC3H8 722.57 cm/gm moleal. et al.)

440 6r - BKapallO Brewer -588.5 + 579.0 (By definition) C3H 8 RTc/Pc 722.57 k[-0.8143] (From Equation F6-1) Therefore, k = 1.617x10-2 gm moles/cm3 b) Calculation of error in 6. at 223.15K. For the given mixture, - 1 Equation (F6-3) reduces to 6. = (6 - 0.248C - 0.252 6 )/0.5 (F6-4) 13 m CR CR 2H6 38 Tc = 339.6K m RTc /Pc = 622.1 cc/mole m m ac = 6.379 m Tr = 223.15K/339.6K = 0.6572 m (Troo) = 0.6410 [Using Equations (111-36) through (III-36c)] m Br = -0.814 @ Tr = 0.6410 C3H8 CH4 From Equation (F6-3), we obtain: 6 = (622.1) (1. 617x10-) 2(6379- 5 82) (-0.814) m 223.15K (6.54 - 5.82) = -6.4 cm3/mole CR~~ H ~2(6.54 - 5.82) Similarly, 6 = (519.98) (1.617xlO) (6254 - 582) (-0.662) 26 = -3.5 cm3/mole and 6 = (722.57) (1.617x10-2) (1)(-1.028) = -12.0 cm3/mole 3 8 Therefore from Equation (F6-4): 6.. = [-6.4 - 0.248(-3.7) - 0.52(-12.0)]/0.5 = -5 cm3/mole 11

441 Table F-3 below contains a list of the calculated values of 6.. for ij several methane-propane and ethane-propane mixtures at 223.15K and 398.15K. The results show that although there are some changes in the calculated values of B.. for each system, the spread in the Bi. values as a function of composition remains relatively unchanged. iJ TABLE F-3 Estimated Change in the Calculated Value of the Interaction Second Virial Coefficient Using the Technique of Figure V-2 Due to a Modification of the Second Virial Coefficient Correlation of this Work TEMPE ATIkRF?23.15 K 39H.I K SYSTEM15 K 6. (CC/ML F) (CC/.l F).7? CH4,.28 C3H8 +1. +l~.q.49 CH4,.51 C3H8 -1.4 +1..23 CH4,.77 C3HR -2.0 +0.?.76 C2H6,.24 C3H8 -4.7 -1..50 CH6,.50 C3HR -5.0 -.28 CH6,.72 C3H8 -6.2 -1.2

442 Appendix F-7 Outline of Calculation Procedure for Rules VII, IX and X 1) Calculation of Mixture Virial Coefficients as a Function of Temperature. This calculation is illustrated for the approximately equimolal ethane-propane mixture which, for the sake of simplicity, is treated as a two component system with the light impurities added to the methane mole fraction and the heavy impurities added to the propane content. a) Relevant Data: i) Composition Mole fraction methane, xl = 0.00 Mole fraction ethane, x2 = 0.498 Mole fraction propane, x3 = 0.502 ii) Critical Parameters for pure components and mixtures Methane Ethane Propane Equimolal Mixture Tcll = 190.7K Tc2 = 305.4K Tc3 = 369.9K Tc = 339.55K ii 22 33 m Pc1l = 45.8 atm Pc22 = 48.2 atm Pc33 = 42.01 atm Pc = 44.8 atm ac = 5.82 ac22 = 6.275 ac3 = 6.540 oc = 6.379 11 22 33 m RT c RT c RT c RT c c1= 341.69 2= 519.96 = 722.57 = 621.97 Pc 341.69 Pc Pc 11 22 33 m cm3/mole cm3ol cm/mole cm3/mole The equimolar mixture pseudo-parameters were specified from Column I of Table IX-14 and were obtained by optimization of the enthalpy data for the given mixture within the framework of the PGC. b) Calculation of B at T = 198.15K. ~m Tr T 198.15K Tr___ =...0.5836 m Tc 339.55K m The modified reduced temperature (Tr ) for the mixture must be caloo culated from Tr and acc before Equation (V-30) can be used to calcuin m late Br. The criterion: m

443 log Pr [Tr, ac ] = log Pr [(Tr), acCH ] (F7-1) m 4 is used to specify (Tro), where Pr is the reduced vapor pressure. If the Riedel vapor pressure equation is used to express Pr as a function of the reduced temperature, then we obtain - q(0.5830) - [6.379 - 7.00]Y(0.5836) = - q((Tr ) ) OO m - [5.82 - 7.00]Y((Tr ) ) OO m where ~ and T are defined by Equations (IV-36 a and b). A trial and error calculation yields (Tr ) = 0.5544 00 m The value of the reduced second virial coefficient Br at 198.15K m is then computed using Equation (V-30). Thus Br = 0.14416 + 0.49095(1 - e68511/0.5544) + (6.379 - 5.82) m [0175 0.220 0.00614 0.0281 [ 0.5544) (0.5544) (05544 = -1.0546 + (6.379 - 5.82) (-0.0256) = -1.069 RTc B (198.15K) = (Br )( m) = (-1.069)(621.97) = -664.86 cc/mole m m Pc m 2) Calculation of the Interaction Second Virial Coefficient B23 at 198.15K. Using Equation (V-30) and the appropriate critical parameters, the second virial coefficients for ethane and propane at 198.15K are respectively calculated as: B22 = -435.75 cc/gm mole B33 = -965.96 cc/gm mole

444 Therefore, given Bll, B22, B33 and B for a binary mixture, Equation (V-l) may be rearranged to permit the extraction of B23. Thus: B - x2B - x3B 2 22 B m x2 B22 3 B33 B23 = (F7-2) 23 2 x2x3 2 3 =-66486 - (0.498)2(-435.75) - (0.502)2(-965.96) (2) (0.498) (0.502) = -626.74 cc/gm mole Using the optimum pseudo-parameters for the 0.498 C2H6 mixture, B23 values were calculated at fourteen selected temperatures. The results appear as part of Table IX-5 in the column appropriate to the equimolal mixture. 3) Calculation of pseudo-parameters ac and RTc /Pc for 23 23-23 Rule VII of Table IX-10. The value of c23 is obtained from the 2ac - ~ 2 23 33 (F7-3) 23 2 x2x3 6.379 - (0.498)2(6.275)- (0.502)2(6.540) 2(0.498)(0.502) = 6.351 The mixing rule for RTc23/Pc23 is independantly obtained from Equation (V-41). a) Calculation of h ratios, h(acii.)/h(oc ):....ii ~ m h(ac ) = 0.7085[0.15903 + 0.0588(6.379 - 5.82)] = 0.13596 m and h(ac22) = 0.7085[0.15903 + 0.0588(6.275 - 5.82)] =0.131625 h(ca2) Therefore, h (c22 = = 0.9675 r 22 hI(=C) m Similarly, h (33) = = 1.049 r ) 3 9914 h.(o,2a) = = 0.9914

445 b) Calculation of g ratios, g(Tr ac. )g(Tr ac) The first step in the evaluation of the terms g(cxc, Tr) is the initial selection of some high temperature where Equation (V-41) is simultaneously applicable to all components, i.e., the reduced temperature for each component must lie in the range 8.0 < Tr < 30. The ultimate application of the rule to the ternary methane-ethanepropane mixture requires the temperature limits to be set by Tcll and Tc33, respectively. Upper temperature limit = (30)(190.7K) = 5721K Lower temperature limit = (8)(369.9K) = 2959K. A value of 5000K was arbitrarily selected for the calculation. Referring to Equation (V-40), we obtain TM/Tc = 18/[1.0 + 0.189(6.379 - 5.82)] = (18)/(1.10565) Also, Tr = 5000K/339.55K = 14.725 m TTherefo Tc (14.725)(1.10565) Therefore, = Tr (-) = = 0.9046 TM m TM (18) g(Trm, cc ) = 0.3517 + 1.5068(0.9046) - 1.11379(0.9046)2 + 0.25874(0.9046) - 0.99189 Similarly, g(Tr22, oc22) = 0.9991 and g(Tr33, oc33) = 1.0072 g(Tr23, ac23) cannot be evaluated until Tc23 is known. An initial estimate is obtained from the Redlich-Kwong rule (III) in Table (IX-8) Assume Tc23 = 335.2K 23 then g(Tr23, c23) = 0.9927 g(Tr22, c2 c gr(Tr22 c22) = (Tr, ) = 0072 gr(Tr33, c33) = 0.9918 gr(Tr23, c'23) = 1.0008

446 The value of RTc23/Pc23 is obtained from the solution of Equation (V-41) rewritten below in the form RTc RTc 2 RTc23 m = x2 22 hr(ac22) gr(Tr22, cc22) + 2x2x3 Pc 2 Pc 22 22 22 3 Pc m 22 23 RTc3 hr(cGc23) gr(Tr23, ac23) + x32 hr(ac33) gr(Tr33,ac33) 33 (F7-4) m621.7 le (0.498)2(519.96)(0.9675)(1.0072) + 2(0.498)(0.502) RTc23 (-PC) (0.991)(1.0008) + (0.502)2(722.57)(1.049) (0.9911) P23 2Th 23 621.97 - 125.7 - 189.61 Therefore, Pc23- 04 = 618.2 cm3/gm mole PC 23 0.496 As a matter of academic interest, the calculation was repeated for selected temperatures of 4000K and 6000K for application of Equation (V-41). The calculated values of RTc23/Pc23 were 617.0 and 617.7 cm3/mole respectively. These results confirm the relative insensitivity of the mixing recipe RTc23/Pc23 in Rule VII to the precise temperature at which it is applied. 4) Calculation of Tc for Rule VII of Table IX-10. The cal23 culated values of RTc23/Pc23 and ac23 are then used in conjunction with Equation (V-30) to determine the best value of Tc23 that will yield a set of B23 values from the equation that are in closest agreement with the results in step 2 over the temperature range from 198.15K to 510K. At each stage in the trial, the value of Tc23 is revised using Newton's method. Thus, n d(Br23) i [Br23 (Br23) dTc cal i~l 23 ^ dTcal i=l cal 23 (Tc23) (Tc23 + New 3 Old n d(Br23) 2 d2(Br3) i d23 cal] - [Br23 - (Br23) dT c]l iLl 2 cal d c —23 Old

447 n if the function Z [Br23 (Br23) ]2 is to be minimized. The i=l cal d(Br23) d2(Br3) calculation of the derivatives c- al and - 2- cal from c23 23 Equation (V-30) is tedious. At any given temperature T. d(Br d(Br23) dTr (Br23 T 23 23 ___al - 2 d(F7-c T c al = T al dTc dTr al(F7-6) dT d Tr 23 23 dBr The quantity dTr is calculated analytically from Equation (V-30). dBr 00 dTr can then be related to this derivative through the expressions developed in Appendix H-2. Similar considerations apply to the evaluation of d2Br23 dTc23 23 The initial estimate for Tc23 was set at 331.5K. The trials are all listed in Table F-6 along with the calculated increments for Tc23 at the end of each stage. The final value of Tc23 is 333.25K. This value of Tc23 is then used to recompute gr(Tr23, ac23). Its value was calculated as 1.0004 as opposed to the original estimate of 1.0008 obtained from the Redlich-Kwong rule. The change in the recomputed value of Tc 23 PC23 lies in the fifth significant figure and can be ignored. The final values of the interaction parameters calculated from the given mixture are: RTc23 = 618.2 cm3/gm mole 23 Tc2 = 333.25K ac 23= 6.351 5) Calculation of Smoothed Mixture Second Virial Coefficients as a Function of Temperature. The B23 values computed from the individual ethane-propane mixtures as a function of temperature are

448 listed in Table IX-5. The final selected values also indicated in the same table were obtained by averaging over all three mixtures in this particular case. The virial coefficients B for the 0.498 m C2H6, 0.502 C3H8 mixture are now recalculated using the averaged B23 values. At T = 198.15K, (B23) =-614.0 cm3/gm mole averaged Using Equation (V-l), B = (0.498)2(-435.75) + 2(0.498)(0.502) (-614.0) + (0.502) (965.96) m = -658.49 cc/mole The calculated results covering the range from 198.15K to 510K are summarized in Table F-5. 6) Recalculation of Pseudo-Parameters for the 0.498 C2H6, 0.502 C H Mixture Using Optimum Interaction Parameters for Rule VII of -5Table IX-10. The values of RTc23 PC23 Tc23 and cc23 as obtained from an analysis of the individual ethanepropane mixtures are indicated in Table IX-8. An RTc23 PC23 value of 612.2 cm3/gm mole was finally selected for rule VII. Similarly, the final value sof oc23 was defined to be 6.380. Therefore, in order to determine how well the mixing rule encodes the enthalpy data for the entire binary system, it is first necessary to recalculate the pseudo-parameters for each mixture using the averaged interaction parameters. The calculations for the 0.498 C2H6 mixture are indicated below. a) Calculation of oc. (See rule for Oac for VII in Table IX-10) -- - - - m m ac = (0.498)2(6.275) + 2 (0.498)(0.502)(6.380)+(6.502)2(6.540) m

449 = 6.394 b) Calculation of RTc /Pc The value of RTc /Pc is computed from m -m m m Equation (V-41) at T = 5000K in a fashion similar to that indicated for RTc23/Pc23 in Step 3. The initial estimate of Tc necessary for the evaluation of g(Tr, ac ) is again calculated from the Redlich-Kwong rule (IV) of Table IX-10 as 337.5K. The value of RTc /Pc is computed to be 618.9 cc/gm mole, as opposed to the optimum value of 621.97 cc/gm mole. This change is mainly attributed to a difference between the value of RTc23/Pc23 used here and that calculated at the end of step 3. c) Calculation of Tc: The calculated values of RTC /Pc and ac m m m m are used together with Equation (V-39) to determine the optimum value of Tc that will realize B values that are in best agreement with m m the results obtained in step 5. The calculation procedure is analogous to that indicated for Tc23 in step 4. The optimum value for Tc is'J m calculated as 338.5K. The trials are indicated in Table F-4 using Newton's method to estimate the increment ATc. These parameters m are then used to calculate the enthalpies for Rule VII in Table IX-14 using the PGC. 7) Calculation of Pseudo-parameters for the Ternary Mixture from Rule IX and X. a) Calculation of Second Virial Coefficients for 0.369 CH4, 0.308 C2H6 and 0.325 C3H8 Mixtures: At 198.15K, Bl = -107.35 cc/mole B22 = -435.75 cc/mole B33 = -965.96 cc/mole B12 = -198.69 cc/mole B23 = -614.0 cc/mole Obtained from Table F-5 B = -277.41 cc/mole The pure component values are obtained from Equation (V-30) using the true critical parameters, and the interaction values are obtained by

TABLE F-4 Sample Results Illustrating The Calculation of The Pseudo-Critical Temperature Tc for the 0.498 Ethane-Propane Mixture Using Rule VII of Table IX-10 Estimation of Tc for Rule VII First Guess Tc =334.5K Second Guess Tc =338.5K ** **+ ++ 44+ m * m T B ~ B C B C H ^ B Br Tr Br -(Br ) Tr Br -(Br) CRH CRHo CH-C m m m m m m m mfl 26 38 26 38 calcal cc/mole cc/mole cc/mole cc/mole l6.i5 -4i5.15 -5 65.96 -6.t00O -658.49 -1.665 4 u. 595 -u.0308 (.5b53 -0.0U35 Z23.15 -441.14 -41.C4 -47d.UG -510.34 -0.B25b L.t672 -0.0217..,92 -0.0010 248.1) -214.47 -)db.53 -3o7.00 -409.68 -C.660 1 C.42u -0.0162 u.?330 0.0003 273.16 -425. lb -479.27 -317.GO -335.12 -0.5399 0.1 8I7 -0.0125 0. 8069 0.0010 298.15 -1'37.42 -397.73 -203.5, -278.46 -C.4490 u.c3'1) -0.0100 C.t807 0.0013 310.-0 -.11.39 -363.t6d -242.50 -255.40 -C..tC8 <..G 6 -0.C091 C.91i4 0.001 ui 323.15 -1.37.6 -334.72 -223.00 -234.94 -0.3(01 6.662 -0.0083 0.9546 0.0015 Z 346,t: -i.bf -284.10 -109.50 -199.62 -C.3213 1.C4U9 -0.0070 1.0284 0.0016 313.15 -1. -144.15 -103.Ju -171.23 -0.27i 1.157 -O.C059 I.1C23 0.0016 3j9h.15 -97.19 -21C.C3 -1'0.u0 -147.18 -0U.2 5 1.1 i0t -0.0051 1.17tl 0.0016 423.15 -_.15 -182.37 -12u.OU -126.63 -C.2040 1.2652 -0.0045 1.2500 0.0016 444.3C -72.84 -1i62.i7 -IJ6.00 -111.93 -0.1d3 1.3284 -.00CU41 1.3124 0.0015 473.15 -60.65 -138.27 -90.o0 -94.89 -C. 15 4 1.4147 -0.0030 1.3976.C01 510.90 -47.28 -1L2.34 -70.00 -75.04 -J.12I0. 1.5%7, -u.0031 1.5092 u.0014 ATc = 4.07K ATc = 0.026K m m + Weighted average values obtained from Table IX-5 -+ Calculated values of the second virial coefficient for the 0.50 mole fraction ethane-propane mixture using Equation (V-l) +-4+ Br = B /(RTc /Pc ), vthere RTc /Pc is obtained as 618.9 cm3/gm mole by application of Equation (V-41) i i m m i m * (Br ) is obtained from Equation (V-30) from specified values of the mixture pseudo-parameter cal ** Obtained from Equation (V-30) using appropriate critical parameters

451 averaging the individual mixture results for each constituent binary system. The ternary mixture virial coefficient, B at 1.98.15K is now m calculated from the rigorous relationship: mix = x 11+ X2 222 +3 B33 + 2 X1X212 + 2 323 + 2X3XlB31 = (0.369)2(-107.35) + (0.308)2(-435.75) + (0.325)2(-965.96) + (2)(0.369)(0.308)(-198.69) + (2)(0.308)(0.325)(-614.0) + (2) (0.325) (0.369) (-277.41) = -392.61 cc/gm mole The results for the temperature range from 198.15K to 510.9K are indicated in Table F-5. b) Determination of (c: The optimum averaged values of ac.. for each m Ij binary system as obtained from Tables IX-4 through IX-6 are: -ac1 = 6.08 ac = 6.38 ac31 = 6.35 Therefore, using the quadratic mixing rule for ac as indicated in Table IX-10, we obtain ac = (0.369)2(5.82) + (0.308)2(6.275) + (0.325)2(6.54) + (2)(0.369)(0.308)(6.08) + (2)(0.308)(0.325)(6.38) + (2) (0.325) (0.369) (6.35) = 6.236 Rule IX only involves the prediction of Tc and RTc /Pc and m m m

TABLE F-5 ++ The Calculation of the Second Virial Coefficient of the Ternary Mixture as a Function of Temperature Using the Technique of Figure V-2 + + + *~C B B B B B B BMiH-C CH C H C,H CH -C H C H-C H C 4I-CH () 4 26 4 26 2 6 3 8 \ s 4r 19.15 -IC7. 5 -435.75 -965.96 - 1%98,69 -614.00 -277.41 -392,61 p 3 I5r -34.25 -341.14 -741, 04 -157.87 -478,00 -223.,11 -307,20 2 4.P 1 50 -6". 9 -2714.47 -5R9. 3 -127.69 -387,00 -182.20 -247,52 73 1AC - 53. 3 -? 2,IB 8 -479.27 -104.53 -317.00 -150,.44 -202.59 2CW.1 p' -4 2.19 -137.42 -397.73 -36.27 -263,50 -125,18 -168,03 zl-~)~~ -3.36? -171.3A -363,68 -78. 36 -242,50 -114.21 -153,65 v Is- ~7 -34.3 -157.6? -334. 72 -71. 50 -223.,00 -104,66 -140.98 343.15 -27.13 -133.56 -284.70 -59,.32 -189.,50 -87,69 -118,89 373 i1S -21,07 -113.75 -244.12 -49.,12 -163.00 -73,44 -100.86 -o is -15.09 -97.19 -210.53 -40.45 -140.00 -61,32 -85.45 423. An -11.,42 -83,15 -182.57 -33.00 -120,00 -50.90 -72,46 4t4'7 -i'^.09 -7,?84 -162.17 -27,48 -106,.00 -43.15 -62.96 47a15' -4.'n -Q.65 -138.27 -20.87 -0,.00 -33.88 -51.33 5ifln.9>n *'.^ -47.238 -112,34 -13. 53 - 7,00 -23,59 -39.05 *Calculated from the Equation B x.x.B... m ij I j +Values Obtained from the Interpretation of the Enthalpy Data of this Work. ++Values Obtained from Eqn.(V-30) Using Appropriate Critical Properties from Table J-l.

453 consequently an ac value of 6.245 obtained from the direct optimization of the ternary enthalpy data in the PGC framework (Rule I, Table (X-10)) is used. c) Determination of RTc /Pc and Tc for Rules IX and X: mm - m m Given the value of ac, the two parameters RTc /Pc and Tc are m m m m adjusted by trial and error to yield the best agreement with the B values from 198.15K to 510.9K. The optimum value of Tc for each estimate of RTc /Pc is again obtained as indicated in Step 2. The m m direction and size of the increment for RTc /Pc is at each stage m m dictated by the goodness of fit. The trials for rules IX and X are summarized in Table F-6. The close agreement between the calculated B values in each case, inspite of the differences in oc, confirms m m the difficulty of extracting three unique parameters from second virial coefficient data. For rule VII, the value of acc is the same as calculated in m Step 7b, the value of RTc /Pc is obtained by repeating the procedure mn m in Step 6b using all constituent binary parameters. Step 7c is repeated using the same set of B values, but only Tc is optimized. m m

454 TABLE F-6 Optimization Results on the Pseudoparameters RTCm/Pcm and Tcm for the Ternary Mixture Using Estimated 2nd Virial Coefficients from Table F-5 ESTIMATED OPTIMI ZED (RTC/PC)m TCm PCm ITERATIONS % STD. DEV. ALPHAC (CC/GM MOL) (~K) (ATM) 541. 285.3 43.28 3.17 6.245 * 545. 284.3 42.81 3.23 537. 286.3 43.75 3 541. 285.3 43.28 3,17 533. 287.3 44.23 3.14 529. 288,3 44.72 3.16 531. 287.8 44.48 3.14 530. 288.0 44.60 2.15 532. 287.5 44.35 3.14 533. 287,3 44.23 2.14 535. 286.8 43.99 2.13 + 541. 285,35 43.29 3.17 6.236 ** 549. 283.41 42.37 3.24 533. 287.34 44.23 3.19 541. 285.35 43.28 3.17 545. 284.38 42.82 3.20 537. 286.34 43.76 3.163 541. 285.35 43.29 2,17 533. 287.34 44.24 2.19 535. 286.84 44*00 2.17 534. 287.09 44.12 2.18 536. 286.59 43.88 3.17 537. 286.34 43.76 3.163 538. 286.09 43.64 3.162 539. 285.84 43.52 3.162 ++ ++ OPTIMUM PSEUDO-PARAMETERS * ALPHAC VALUE USED IN THE OPTIMIZATION FOR RULE IX ** ALPHAC VALUE USED IN THE OPTIMIZATION FOR RULE X

Appendix G Derivation of a Modified Van der Waal Mixing Rule The original Van der Waal Equation has the form ( P+ 2 ) ( V-b) = RT (G-l) where a and b are constants which can be chosen to satisfy certain characteristics of the PVT surface. If we apply the criterion ( ) = 0 (G-la) T=Tc at the critical point, then Equation (G-l) yields (Vc - b)2 R (G-2) 2a As our second criterion, we set the slope of the critical isochore at the critical point to be equivalent to the slope of the vapor pressure curve at the critical point on a log P vs log T plot. The continuity of these two slopes at the critical point has already been established [202]. The condition is mathematically expressed as d in P ( d n ) = ac (G-3) d n T^ V=Vc Substituting Equation (G-3) into Equation (G-l) we obtain RTc 1 ac R Tc 1 (G-4) Pc (Vc - b) Combining Equations (G-2) and (G-4) we obtain ac2 PC2 Vc3 a2 R Tc (G-5) At the critical point Equation (G-1) becomes (Pc + c2) (Vc - b) = R Tc (G-6) 455

456 Substituting Equation (G-4) into Equation (G-6) we obtain ac = (Pc + V2)/Pc (G-7) Vc Resubstituting for a in Equation (G-7) using Equation (G-5), we obtain Pc Vc 2(ac - 1) R Tc zc = c2 (G-8) R Tc ac2 Rearranging Equation (G-4) we obtain R Tc 1 R Tc 1 ( b = Vc [ z (G-9) Pc ec Pc [ tc If we substitute for zc in Equation (G-9) using the right hand side of Equation (G-8) we obtain b =R T[ ((G-10) -c Cc2 Combining Equations (G-5) and (G-8) we obtain ac2 zC3 R2 Tc2 (Oc- 1) 3 R2 Tc2 a =2Pc c4 (G-l 1) 2 Pc OtC4 PC The modified reduced Van der Waal Equation now has the form 4(ac - 1)3 R2 Tc21 R Tc c - 2 ( ) [P+ tc1 Pc z2][v- (-c~ ) ec2 (G-12) Xc4 Pc V Pc ~c2 = RT The second virial coefficient for the above equation can be written as d(z - 1) a B Lim d(1/V) T (G-13) V+ o ( -/V) RT R Tc (ac - 2) _ (ac - 1) 3 R Tc2 ( P c ac2 ac T Pc

457 It is now assumed that Equation (G-14) can be applied to all the constituent pure components of a mixture, to all mixtures of such components, and to the interaction virial coefficients defined by appropriate pseudoconstants Tcij and Pcij. We also recall that the mixture second virial coefficients can be rigorously expressed in terms of like and unlike pair interaction second virials by the relation n n B = Z Z x.x. B.. (G-15) i=l j=l 1 lJ Therefore, it is permissible to substitute Equation (G-14) with appropriate pseudoconstants for each of the B terms in Equation (G-15). Now since Equations (G-14) and (G-15) are presumed to be valid at all temperatures, they are presumed to hold for the special case as T approaches infinity. Therefore, we may substitute Equation (G-14) into Equation (G-15) as T -+, which yields the result R Tc (oc - 2) n n R Tc.. c.. - 2 m m j___ mPc m z z xx - ( ij 2 ) (G-16) PC Otc P m m i=l j=l Pc cij Now, if we substitute Equation (G-14) into Equation (G-15) at any finite temperature and take cognizance of the equality in Equation (G-16), we obtain the result 3 R T (c (c - 1) n n R Tc. (Oc. - 1) m m - Z Z1 ijx/x —-\ Pcuact= E: x x PC.. c. (G-17)a m m i=j=l j= Pcij i J Equations (G-16) and (G-17) now comprise the modified Van der Waal mixing rules. A host of other mixing rules may be similarly derived by either choosing a different two parameter equation of state or by selecting different characterizing conditions for the PVT surface.

APPENDIX H Thermodynamic Property Calculations Using Selected Methods 458

459 Appendix H-1 Thermodynamic Properties from the Starling Modified Benedict-Webb-Rubin Equation of State a) Volume [254] B RT-A -C + D d p3 2 YeP2 P = RTp + ( T3 E /T4 ) p2 + (bRT-a- ) P + (a + ) ap6 + [(1 + yp) e-Y b) Second Virial Coefficient B RT-A -C + D -E RT ( T2 T3 T4 ) c) Third Virial Coefficient 1 d C T bRT - a - 4) Enthalpy Departure - RT-2A -4C + 5Do- 6Eo bRT-3a-2d p2 (1-e- ) e- +P 2 T-"Ho T2 -f ) p +, T' ) p2+ (6a+7d) [ 3' -+ YP2e-~YP 5) Isothermal Throttling Coefficient B RT-A -4C0 +5D -6E YP ( BoT-o 6 ) + T- ) p + (6a+7d) ap4 + ce [ 5p + 5 -2y2p5] B RT-A -C -2D +2E d d d-YP RT + 2p ( 0 0 0 0 ) + 3p2(bRT-a- d ) + 6(a + ) + 6(a + ) ap5 + T [32( + p2) - 2y2 T2 T3 T4 T T T 6) Heat Capacity -R+6C p 12 Dop 20 EP 2 2 e CP - Cp~ -3 + a - 2 p P- + ( 6C3 ) e-YP + C-Cp = T3 yT3 + 2yT 0 - 6c - _ + T5 (X 2 + ( 23 + 2C 3D 4E 2 [R + (Bo + d 2cp2 p )e p2 2A 2C 2D 2E0 d (3c -- 3 2c 6 -YP2 T T3(2B R + 0 O 3 3d P+(b 3T ) p2 + 6adp4 + aap + (3cp + 3c2 2 6a _)e~

460 Appendix H-2 COMBINING RULES FOR CONSTANTS IN THE STARLING B-W-R EQUATION OF STATE 2 1/2 A. = ( x A ) o mix. 1 o. 1 1 B = ( x. B ) o mix i. o. i 1 1/2 C = ( x. ) o mix.i o. 1 1 1/2 1/2 D = [Z xD 1+ Z x.x. h.. [(D + D )/2 - (D D ) o mix i i ~i i=l j=l 1 1J j 1 j 1/2 2 1/2 Eo mix x E ]+ ~ x. x. kij [(Eo + E )/2 - (E E ) ] b. o. ( x. b. ) mix 1 i 1 3 C~mix = i 1/3. = ( xb. ) mix. 1 1 mix.1 1 3 1/2 mix = ( Xi i ) mix

461 Appendix H-3 Thermodynamic Properties from the Reduced Virial Equation Truncated at the Third Virial Coefficient 1) Definitions Br = B/(RTc/Pc) Cr = C/(RTc/Pc)2 Tr = T/Tc V = z Tr/Pr = ZcVr 2) Thermodynamic Relations Pr 1 Pr2 z(z - 1) = Br +-Cr (H2-1) Tr z Trr (dH/dP) = ( dBr 1 dCr 1 Tr (/d BrTr + [(2Cr -Tr ) RTc/Pc dT r V dTr V [ 1+ 2Br- C ] (H2-2) RTc dTr + 0.5 (H2-3) F.T= - d- r dTr ) H - H~O _'U U~ H RTc + Tr(l - z) (H2-4) RTc RTc f/P = exp {[ Br + 0.5 ] + (z- 1)}/z (H2-5) Cv- Cv -Tr dBr dCr 1 d2Br R 2 dr + dTr Tr [ d Tr2 I d Cr 1 z d Tr2 (H2-6) Cp - Cp~ d2Br 1 = ( Br - Tr 2 - Tr2 R dTr ) 2 (HdTr V dCr (27 + ( Cr - Tr d-r 2) (H2-7) )( ~2

462 3) Determination of dBr/dTr and d2Br/dTr2 from the Second Virial Coefficient Correlation of this Work (Equation V-30) If Equation (V-30) is used to represent the reduced second virial coefficient, then the derivatives dBr/dTr and d2Br/dTr 00 00 may be straight forwardly obtained in analytic form by differentiation. The extraction of the derivatives dBr/dTr and d2Br/dTr2 necessary for the calculation of thermodynamic properties is, however, more complicated. We recall from Chapter III that the Riedel reduced vapor pressure equation (111-36) may be used to obtain Tr from 00 Tr by requiring the reduced saturated vapor pressure Pr to be the s same in both cases. Therefore, for methane as the reference fluid we obtain: - ~ (Tr) - (ac - 7) Y(Tr) = - ( Tr ) - (acCH - 7.0) Y(Trc ) CH CH CH (H2-8) where 4 and Y are defined by Equations (III-36a) and (III-36b) respectively. On substituting the ac value for methane and differentiating the above equation, we obtain on rearrangement: dTrCH dTr = - ( [c- 7.00) ] - (5.82-7.00) Y Tr] CHT CH (H2-9) On further differentiation, the result d2Tr d Tr CH CH dT2 = dTr [ T - (5.82-7.0) Tr / rCH4 CH [ (T - (c -7.0) T]r (H2-10) is obtained. The derivatives dBr/dTr, and d2Br/dTr2 required for the evaluation of the thermodynamic properties in 2) can now be

463 expressed in terms of the corresponding derivatives with Trc as variable using the transformations: dTr CH dBr _ dBr 4 (H2-11) Tr d Tr dTr d2Tr dTr 2 d~r CHd d2Br dBr CH C d2Br = dr)) +( d ( (H2-12) dTr dTr dTr dTr dTrdTr CH4 CH4 The value of dCr/dTr and d2Cr/dTr2 can also be directly obtained from Equation III.

Appendix H-4 Sample Output of ThermodynaiBc Property Calculations on the Ternary Mixture at 126.2~F by Several Techniques 8 C PHI CP 0* 1DEP CPDEP Z T P (K) (psio) (cc/gm mole) (cc/gm mole)2 Btu/lb/psia Btu/lb/~F Btu/lb Btu/lb Btu/lb/~F 126.30 0.01 1 -0.1397E 03 -0.4558S-01 0.45703 00 0.3875E 03 -0.0 0.0 0.1000E 01 2 -0.1397E 03 0.9045B 04 -0.45581-01 0.45701 00 0.3875E 03 -0.0 0.0 0.1000E 01 3 -0.14002 03 0.9045B 04 -0.45581-01 0.45701 00 0.38751 03 -0.0 0.0 0.10001 01 4 -0.1389E 03 0.9045E 04 -0.43968-01 0.4570E 00 0.3875E 03 -0.0 0.0 0.1000E 01 5 -0.1432E 03 -0.1113E 04 -0.4709E-01 0.4570E 00 0.3875E 03 -0. 0.0 0.1000E 01 6 0.3875E 03 -0. 126.30 250.00 1 -0.1397E 03 -0.5680E-01 0.50581 00 0.37483 03 -0.1264E 02 0.4876E-01 0.9013E 00 2 -0.1397E 03 0.9045E 04 -0.5305B-01 0.5034E 00 0.3752E 03 -0.1227E 02 0.4637E-01 0.9063E 00 3 -0.1400E 03 0.9045E 04 -0.53081-01 0.5029E 00 0.3752E 03 -0.1227E 02 0.45861-01 0.90613 00 4 -0.1389E 03 0.90458 04 -0.50991-01 0.5015E 00 0.3757E 03 -0.1181E 02 0.4445E-01 0.9070E 00 5 -0.1432E 03 -0.11133 04 -0.54391-01 0.5101E 00 0.3749E 03 -0.1262E 02 0.5302E-01 0.9041E 00 6 0.3756E 03 -0.1189E 02 126.30 500.00 1 -0.1397E 03 -0.84913-01 0.6220E 00 0.3578E 03 -0.2966E 02 0.16501 00 0.7684E 00 2 -0.1397E 03 0.9045E 04 -0.64923-01 0.58603 00 0.3606E 03 -0.2689E 02 0.1290E 00 C.8006E 00 3 -0.14001 03 0.90451 04 -0.6503E-01 0.58503 00 0.36063 03 -0.2690E 02 0.12801 00 0.8001E 00 4 -0.1389E 03 0.9045E 04 -0.6201B-01 0.5790E 00 0.3617E 03 -0.2582E 02 0.1220E 00 0.8024E 00 5 -0.14321 03 -0.1113B 04 -0.6558E-01 0.5966E 00 0.3600E 03 -0.2750E 02 0.13961E 0.7967E 00 6 0.36113 03 -0.26353 02 126.30 750.00~ 1 -0.1397B 03 0.1000B-01 2 -0.13971 03 0.90451 04 -0.85523-01 0.76461 00 0.3420E 03 -0.45451 02 0.30761 00 0.67821 00 3 -0.14008 03 0.90458 04 -0.85932-01 0.76401 00 0.34191 03 -0.4553E 02 0.30703 00 0.67691 00 4 -0.13891 03 0.90458 04 -0.80581-01 0.74088 00 0.34408 03 -0.43443 02 0.28371 00 0.68193 00 5 -0.14321 03 -0. 113E 04 -0.82682-01 0.76131 00 0.34161 03 -0.45911 02 0.3043E 00 0.67513 00 6 0.34251 03 -0.44962 02 126.30 1000.00 1 -0.13978 03 0.10003-01 2 -0.13971 03 0.90453 04 -0.10712 00 0.11531 01 0.31743 03 -0.7008E 02 0.69591 00 0.54411 00 3 -0.14001 03 0.90451 04 -0.10801 00 0.1158B 01 0.3171Z 03 -0.7034E 02 0.7007B 00 0.54161 00 4 -0.13891 03 0*90451 04 -0.98843-01 0.10731 01 0.32111 03 -0.66381 02 0.61621 00 0.55161 00 5 -0.14321 03 -0.1113B 04 -0.91941-01 0.10281 01 0.3191E 03 -0.6837B 02 0.57053 00 0.55221 00 6 0.31841 03 -0.69091 02 126.30 1500.00 1 -0.13972 03 0.10001-01 2 -0.13971 03 0.90451 04 -0.35632-01 0.10843 01 0.2823E 03 -0.1'5'E 03 0.6274B 00 0.46291 00 3 -0.1400E 03 0.90451 04 -0.35348-01 0.10773 01 0.2821E 03 -0.10 ig 03 0.6201E 00 0.46101 00 4 -0.13891 C3 0.90451 04 -0.33491-01 0.10223 01 0.28833 03 -0.991 i C2 0.56471 00 0.46902 00 5 -0.1432E 03 -0.11133 04 -0.40451-01 0.1048E 01 0.2862E 03 -0.1013E OJ 0.5910E 00 0.46758 00 6 - 0.28148 03 -0.1061E (C 126.30 2000.00 1 -0.13971 03 0.10001-01 2 -0.13972 03 0.90451 04 -0.14782-01 0.93541 00 0.27098 03 -0.11663 03 0.4783E 00 0.50823 00 3 -0.14001 03 0.90451 04 -0.14641-01 0.92672 00 0.27078 03 -0.1168E 03 0.46971 00 0.50671 00 4 -0.1389E 03 0.9045- 04 -0.13451-01 0.88941 00 0.27771 03 -0.10983 03 0.43241 00 0.51293 00 5 -0.1432B 03 -0.1113B 04 -0.17183-01 0.9067E 00 0.27261 03 -0.11491 03 0.44971 00 0.50443 00 6 0.2694E 03 -0.11811 03 * Assuming H=0 for the pure components methane, ethane and propane at -280~F. ** Method 1 diverges beyond 750 psia. Code 1. Results obtained with the reduced virial equation using the B correlation of this work [Eqn.(V-30)]. 2. Results obtained with the reduced virial equation using the B correlation of this work [Eqn.(V-30)] and the Chueh-Prausaitz C correlation [En. (III-44)]. 3. Results obtained with the B correlation of Pitzer et al. [Eqn. (III-40)] and the C correlation of [Eqn. (III-44)]. 4. Results obtained with the B correlation of McGlashan and Potter [Eqn. (III-43)] and the C correlation of (Eqn. (III-44)]. 5. Results obtained with the Starling modified BWR Equation [Eqn.(III-19)] 6. Enthalpy values generated by the Powers Generalized correlation Methods 1 through 5 use the optimum pseudo-parameters in Table (IX-19).

APPENDIX I Procedures 465

466 Appendix I-1 Procedure for Flowmeter Calibration The procedure for calibrating the flowmeter has been described in detail by Jones [119]. The basic technique is outlined in Section VI. Further improvements in the procedure are discussed here using Figure VI-1 as a guide. a) Initial preparation Storage tanks 1, 2, 3 and 4 are equalized through valves 11, 12 and 13 in between tanks. By initially increasing the volume of gas involved in the calibration operation, the variation in the measured fluid properties at the flowmeter (including the flowrate) due to a fixed rate of decrease in the supply is kept to a minimum. The pressure in the equalized tanks should not exceed 1000 psia for the heavier hydrocarbons if the Joule-Thomson cooling effect is to be prevented from causing fractionation and subsequent composition upsets at throttle TR. The compressor is started up, and the total gas flow is initially directed through the bypass stream. The water manometer is levelled and pressurized to flowmeter conditions with both legs equalized. The manometer is then isolated at the pressure taps leading to the flowmeter, and the null height difference correction observed. The center tap is shut, isolating the individual legs, and the manometer null reading is observed as a function of time for at least ten minutes. A mass leak is indicated in a given leg if the water level continues to rise with time. b) Leak test of solenoid valves The solenoid valve S (Appendix D, Item 8g) switches the flow instantaneously from the reservoir to the sample cylinder and is normally open at the reservoir. A leaky valve seat can cause the system fluid to simultaneously condense in both cylinders causing serious measurement errors. As a precautionary measure, the line to the reservoir is pressurized to about 80 psig in the open position through valves 16 and 17. The solenoid valve is now electrically activated into the closed position, and the sample line evacuated. A change in pressure

467 at the reservoir line as Tlonitored by an Ashcroft gage (Item 8f, Appendix D), during this operation indicates a leak across the valve in the closed position which must be rectified. Leakage tests in the open position may be similarly conducted. As a further precaution, valve 19 on the reservoir is shut just after the sample cylinder begins to fill. Similarly, valve 18 on the sample cylinder is closed during the reservoir filling period, until just before the solenoid is activated. c) Simulation of calibration conditions. To ensure that the calibration operation is smooth, the conditions are first simulated in recycle mode. The compressed gas is fed directly into tank 1 via valve 10 bypassing the high pressure side of the manifold. The gas to the flowmeter and bypass section is supplied by tank 4 through valve 4H. Valves 6 and 7 opened, and the Tescom regulator (Item 8h Appendix D) TR is adjusted until the desired flowmeter pressure is attained. The desired flow through the flowmeter section is obtained by suitable adjustment of the bypass throttle BT. Variacs supplying electrical energy to heating tapes located at throttling valves are adjusted until steady state temperature conditions are achieved. d) Calibration The compressor is shut down, the bypass valve closed, and the bypass throttle heat removed. The metering valve 17 is adjusted until the desired flowrate is noted at the water manometer. The regulator TR is also adjusted to provide the desired pressure at the flowmeter. The solenoid valve S is activated along with a timer that records the duration of flow into the sample cylinder B. The flowmeter pressure, and the water monometer readings are recorded approximately every 30 seconds. The time of calibration is a function of the flowrate and is chosen to condense equivalent amounts of gas in each sample cylinder. The maximum amount permitted in any sample cylinder is subject to a pressure limitation of 1200 psia at room temperature. Approximately 9 gram moles of gas may be safely condensed per cylinder. Any trend in the flowmeter pressure during calibration may be reversed by

468 adjusting the calibration line heat between valve 6 and TR. The pressure is decreased if the line temperature is increased and vice-versa. e) Post calibration procedure After the solenoid valve S is deactivated, and the calibration time noted, valve 4H is shut, cutting off the gas supply to the flowmeter section. iext, all variacs supplying heat at throttling points are turned off. Chromatographic analyses of the system fluid at the flowmeter and the standard mixture are then made. It is important to ensure that the chromatograph sampling valves located after the flowmeter are shut subsequent to each analysis to prevent the occurence of a leakage path parallel to the sampling cylinder B. The next set of calibration conditions are simulated as in step c. f) Precautions for heavy hydrocarbons In the case of the ethane-propane system, the valve mainfold temperature could not be raised significantly above the critical temperatures of the mixtures investigated. As a result, substantial cooling effects were obtained at all throttling locations. Condensation and subsequent composition upsets were known to occur for the 0.27 C2H6 - C3H8 mixture after the regulator TR. This was in part caused by the accumulation of carbon deposits that decreased the effective orifice size of the regulator around which an additional heating tape were wrapped. The use of such extra tapes before throttling processes are not without their disadvantages. Consequently, for this particular mixture, additional heating tapes were added to the lines after the throttling valves. In some cases, however, this technique overheated the gas entering the flowmeter bath to the extent that the heat transfer area in the bath was insufficient to bring the gas to the bath temperature, which it normally is assumed to have attained, and led to errors in the estimation of the viscosity and density of the fluid used in the calculation of the mass flowrate. To avoid such occurences, the cooling coil before the flowmeter bath should be placed in the path of the gas as it leaves the valve manifold.

Appendix I-2 Procedure for System Mixture Preparation In every case, the mixture investigated at the recycle facility is prepared in situ. The general procedure is explained here using Figure VI-1 as a guide. The pressure is equalized in all the storage tanks prior to the introduction of the external feed gas. An approximate estimate of the total quantity of gas within the tanks can be made from a knowledge of the pressure, temperature, and volume of the tanks, and from the composition of the existing gas mixture. The optimum capacity of the system lies between 2.5 and 3 lb. moles. The amount of each component required to be fed to the system to achieve the desired capacity is then computed for the case where all components in the existing mixture are present in the desired case. The required quantities of the individual pure components are successively fed to the system at between 40 and 120 psig via valve FL on the low side of the valve manifold from external tanks set on a weighing platform. The gas is compressed and distributed to all the storage tanks if valves 1 through 4, and 1H through 5H are kept open. The external pure component tanks are wrapped with heating tapes, either to prevent condensation during the throttling process in the case of a high pressure source, or to generate a steady vapor flowrate from a liquid source such as propane. Valves 1 through 4, and 1H through 5H are shut, and the fluid is circulated successively through the tanks starting with tank 1, if valves 10, 11, 12, 13 and 14 in between succesive tanks are open. Extra heating tapes are utilized to heat the storage tanks during this operation. The fluid is recycled to the compressor from tanks through valve 5L on the low side of the manifold, and the operation continued for about 24 hours. Each tank from 1 to 5 is then emptied in sequence into the rest of the tanks, after which all five tanks are equilibrated. Thus, if tank 3 is to be emptied, all valves on the low side of the manifold are shut except 3L, which supplies the compressor feed. Valves 1H, 2H, 4H and 5H are opened together with valves 1, 2, 4 and 5, while valves 11 through 14 are shut. Ihen tank 3 is empty, valve 3L is shut, and all the tanks are equilibrated by opening valve

470 3H. This technique was found to hasten the mixing process. The composition in each tank is chromatographically monitored through the bypass stream about every 2 hours by temporarily switching to the appropriate tank to feed the compressor. Thus, in order to analyse tank 1, it is necessary to shut valve 5L and open 4L. The analysis is compared with those from independently and accurately prepared standards using 400 cc containers. If the composition upon complete mixing is not quite at the desired value, additional amounts of the appropriate components are then fed to the system and the mixing process continued. It was determined that complete homogeneity could be easily achieved within 64 hours using this technique.

APPENDIX J Data and Results Relevant to the Development of the Second Virial Coefficient Coefficients Correlations [Equations (V-30) and (V-41)] of This Work 471

TABLE J-l Summary of Characteristic Properties of Substances Used in the Development of the Second Virial Coefficient Correlation of This Work Tc Pc ec w Vc Mol. Wt. RTc/Pc l/zc ('K) (Atm) (cc/gm mole) (cc/gm mole) METHANE 19Cs.7 4O 5. Wl 5 i.P2C 0.0130 100.33) 16.042 341.69 3.4067 ARGON 15C.70 48.00 r.76C -0.0020 75.30 39.944 257.64 3.4216 KRYPTON?09.40 54.30 5.940 -0.0020 92.10 83.700 316.46 3.4361 ETHANE 305.40 4.2*0 6.275 0.1050 148.00 30.06P 519.96 3.5132 PROPANE 369.90 42.01 6.540 0.1520 200.00 44.094 722.57 3.6128 BUTANE 425.20 37.50 6.77? 0.2020 255.10 58.120 930.48 3.6475 CF4 227.70 37.00 6.725 0.2100 153.00 88.010 505.02 3.3008 PENTANE 469.50 33.30 7.000 0.2520 311.00 72.250 1157.01 3.7203 OCTANE 568.60 24.60 7.760 0.4080 486.00 114.220 1896.79 3.9029 NITROGEN 126.2? 33. 0 C.C G.040D ". 28.016 309.14 3.4311 C02 3'n4.? 72.90 6.916 0.2250 ^.009 44.010 342.44 3.6429 OXYGEN 154.8' 50.10 5.92C 0.'?10 74-40 32.050 253.56 3.4081 NEOPENTANE 433.80 31.60 6.780C) 0.1950 303.i0 72.150 1126.55 3.7180 ISOPENTANE 46C.40G 32.90 6.870 0.2060 398.01 72.150 1148.38 3.7285

TABLE J-2 Least Squares Regression Results for the Reduced Second Virial Coefficient Tabulation of Leland et al. [145] at High Temperatures++ T/T B/B (B/B ())-( (100) (Y-Y )/Y 14 14 1 "B'B Est Cal 1M M Cal X VAL Lt Y VtLUt L tfT L5JATCI L LLLAL i; CLRLk C.s44qOCL C.i28LcC CJ,2336 O.CC444 0.560 C.5G00J6J L. 2 c.aZaic, 0.00132 0.13 L.5b419^ 0.Ci6iC C.68803 -0.011-3 -l.3b2 C.644'00U CL.cCUC C.4l7 0,.CC413 0.434 C.83330CC C.'t`1C C.9d14 U.CC456 0.462 I.OOOCCCC I.CCOCC C.99967 G.OCC13 O.ClI 1. 1 109 1 C.Il76C 1.0013 7 -.C-C377 -0.378 1.38799S5 C.0330 C.9d2J4 O.UCCS6 0.097 1,66599'4 G.S5710 C.5711L -0.COCI -C.OO1 Absolute Average % Error = 0.38464 B T 2 T3 Using the equation = 0.3517 + 1.5068(j ) -.11739 + 0.25874 ) "m TM MM + Obtained by modification of a tabulation by Leland et al. [145] as explained in Appendix F-5 ++ The reduction parameters TM and BM were substituted for Tc and Vc as used in the original correlation

474 TABLE J-3 Comprehensive Results for The Generalized Second Virial Coefficient Correlation of Equation V-30 + * SysemB Reference System T Tr Bw Br Tr Br B a (~OK) 00 cal cc/mole cc/mole CH4 110.83 0 5812 -0.9661 -0.9608 0.5812 -0.96C8 -'330.1 -378.2R [ 35] 112.43 C. 5896 -0.9362 -0.9342 0.5896 -0.9342 -319.00 -31c.71 114.45 C.6002 -0.9008 -0.9024 0.6002 -0,9024 -G307.80 -303.33 116.70 C,6124 -0.8648 -0,8676 0.6124 -0.8676 -295.50 -296. 45 121.25 9.6358 -0.8034 -0.8070 0.6358 -0,8070 -274.50 -2795.7' 128.84 C0.6756 -0.7150 -0.7183 0.6756 -0.7183 -244.33) -249.44 136.75 0.7171 -0.6406 -0.6412 0.7171 -C.6412 -218.9C -210.1148.28 0.7776 -0.5493 -0,5498 0.7776 -0.5498 -187.70 -187.R7 162.20'. 8510 -0.4636 -0.4630 0.8510 -0.4630 -158.40 -158.22 178.41 0.9356 -0.3869 -0.3860 0.9356 -0.3860 -132.20 -131.P9 202.49 1.0618 -0.3026 -0.3008 1.0618 -0.3008 -103.40 -102.79 221.10 1.1594 -0.2511 -0.2514 1.1594 -0.2514 -85.80 -85.89 243.80 1.2784 -0.2057 -0.2039 1.2784 -0.2039 -70.30 -69.67 273,17 1.4325 -0.1572 -0.1569 1.4325 -0.1569 -53.70 -53.62 191.06 1.0019 -0.34C4 -0.3377 1.0019 -0.3377 -116.30 -11'.38 [108] 200.06 1.0491 -0.3123 -0.3082 1.0491 -0.3082 -106.70 -105.31?15.06 1.1277 -0.2710 -0.2662 1.1277 -0.2662 -92.959 -930.6 240.00 1.2585 -0.2128 -0.2111 1.2585 -0.2111 -72.72 -72.1? 273.15 1.4324 -0.1559 -0.1570 1.4324 -0,1570 -53.28 -53.63 123.15 0.6458 -0.7735 -0.7832 0.6458 -0.7833 -264.30 -267.63 [ 28] 148.15 r.7769 -0.5441 -0.5507 0.7769 -0.5507 -185,.90 -1PP.Iq 173.16 0.9080 -0.4059 -0.4090 0.9080 -0,4090 -119.69 -139.74 198.15 1.0391 -0.3117 -0.3142 1.0391 -0.3142 -I'(.50 -107.39 223.15 1.1702 -0.2446 -0.2466 1.1702 -0.2466 -. 3.58 -84.25 273.1, 1.4324 -0.1561 -0.1570 1.4324 -0,157f -53.35 -53.63 [ 67] 298.19 1.5634 -0.1231 -0.1258 1.5634 -0.125L -42.06 -42.09 273.16 1.4324 -0.1561 -0.1569 1.4324 -0.1569 -53.35 -53.63 298.19 1.5634 -0.1253 -0,1258 1.5634 -0.1258 -42.R? -47.c9 303.15 1.58;7 -0.1197 -0.1203 1.5897 -0.1203 -40.91 -41.12 123.1r 1.6945 -0,1002 -0.1005 1.6945 -0.1005 -34.23 -34.33 348P. 1.8256 -0.0792 -0.0794 1.8256 -0.0794 -27.06 -27.13 373.14 1.9568 -0.0616 -0.0617 1.9568 -0,0617 -21.06 -21.c7 398.17 2.0P79 -0.0464 -0.0465 2.0879 -0.0465 -15.n7 -1'.I 423.1B 2.2191 -0.0336 -0.0334 2.2191 -0.0334 -11.47 -11.4? 448.28 2.35C7 -0.0221 -0.0220 2.3507 -0.0220 -7.57 -7.50 473.71 2.4814 -0.0122 -0.0119 2.4814 -0.0119 -4.16 -4.C,9 498.23?.6126 0.0034 -0.0030 2.6126 -0.0030 1.16 -1.04 523.25?.7438 0.0044 0.0049 2.7438 0.0049 1.40 1.68 54L8.?6 2.8750 0.0114 0.0120 2.8750 0.0120 3.89 4.1' 57?.27 3.C061 0.0175 0.0185 3.0061 0.0185 5.98 6.37 598.29 3.1373 0.0231 0,0243 3.1373 0.0243 7.88 P.-' 623.39 3.2690 0.0283 0.029' 3.2690 0.0297 9.66 10.14 126.6? C.6639 -0.6971 -0.7428 0.6639 -0.7428 -238.20 -253.1. [200] 136.e' C.7132 -0.6304 -0.6480 0.7132 -0.6480 -215.49 -721.43 147.59 P.7739 -0.5414 -0.5547 0.7739 -0.5547 -185.00 -1R9.54 158.90 C.8332 -0.4727 -0.4821 0.8332 -0.4821 -161.50 -164.72 173.46 C. 9096 -0.4027 -0.4076 0.9096 -0.4076 -137.67. -13S.76 191.C7 1.0019 -0.3369 -0.3376 1.0019 -0.3376 -115.10 -115.'7 C2r9.53 0.6860 -0.6991 -0.6977 0.6662 -0.7379 -363.50 -388.36 [200] 2 6 238.75 0.7818 -0.5520 -0.5442 0.7670 -0.5643 -287.00 -297. If 254.8rn'. 8343 -0.4873 -0.4809 0.8227 -0.4940 -253.40 -25q9.4?73.16 0.8944 -0.4218 -0.4210 0.8867 -0.4281 -21o.30 -?>5.2^ 306.07 1.)022 -0,3385 -0.3375 1.0024 -0.3374 -176,:0 -177.74'73.15 C.8944 -C.4258 -0.4210 0.8867 -0.4281 -2?21.40 -22?.2 [174]?98.14 0.9762 -0.3570 -0.3553 0.9744 -0.3566 -185. 4 -187.44 322.75 1.0568 -0.3018 -0.3037 1.0614 -0.3011 -156.00 -150. )4 "47.65 1.1383 -0.2564 -0.2611 1.1499 -0.2557 -133.30 -133.99 1732,'5 1.2199 -0.2194 -0.2258 1.2390 -0.2184 -114.06 -114.19 307.t4 1.3027 -0.1879 -0.1956 1.3299 -0.1867 -97.7? -97.'9 422.74 1.3842 -0.1614 -0.1702 1.4199 -0.1603 -83.91 -A3.-6 273.1 C. 9944 -0.4297 -0.4210 0.8867 -0,4281 -223.41 - 25.:0 [108] 245.0):. 7859 -0.5318 -0.5389 0.7713 -0.5583 -276.51 -293. 3 215.00 C.7040 -0.6551 -0.6641 0.6851 -0.6995 -340.63 -368.'J 200.0C0 0.6540 -0.8757 -0.7625 0.6337 -0.8123 -455.31 -427.4t [ 61] 22 5.1' 03.7367 -0.6733 -0.6091 0.7195 -0.6372 -350.10C -335.4? 250.C C. 8186 -0.5317 -0.4986 0,8060 -0.5136 -276.44 -270.32 275.30".9005 -0.4291 -0.4156 0.8931 -0.4221 -223.14 -22?.n6 ro.0rc C.9823 -0.3529 -0.3510 0.9809 -0.3520 -1 C3.50 -184.o0 325.0:. 1.0642 -0.2949 -0.2995 1.0694 -0.2966 -153.36 -155.66 950.03 1.1460 -0.2500 -0.2575 1.1583 -0.2519 -1O.CO -131.96 "75.00 1.2279 -0.2146 -0.2226 1.2478 -0.2150 -111.60 -11?. 4C.0C'3 1.5098 -0.1864 -0.1932 1.3377 -0.1842 -06.91 -96." 7 4?.O,3 1.3916 -0.1636 -0.1681 1.4280 -0.1581 -85.C4 -82.19 4:}.00 1.4735 -0.1449 -0.1465 1.5188 -0.1357 -75.'5 -7:.77 47 5,~ 1.5553 -0.1296 -0.1276 1.6100 -0.1162 -67.37 -59.03 4'0.3)G 1.6372 -0.1168 -0.1110 1.7015 -0.0992 -60.74 -SC.Pq 377.60 1.2364 -0.2104 -0.2193 1.2571 -0.2116 -1'-.40 -1l1C.I [ 94] 410.9- 1.3454 -0.1724 -0.1818 1.3770 -0.1723 -89.64 -89.75 51-3.^ 1.6729 -0.0990 -0,1043 1.7416 -0,0925 -51.46 -47.'H + Using Equation (V-30) * Indicated reference holds for all data until the next listed reference appears.

475 TABLE J-3 (CONTINUED) T Tr Br Br Tr Br B al eference (K) 00 00 caal cc/mole cc/mole C3H8 24P.15 0.67C9 -0.8013 -0.7281 0.6390 -0.7993 -579.00 -598.53 [ 28] 273.1 n.7384 -0.6477 -0.6064 0.7116 -0.6506 -46P.^0 -470.31 29. 15 0. C60 -0.5370 -0.5135 0.7850 -0.5399 -38P.00 -397.73 295.4C 0.7986 -0.5522 -0.5226 0.7769 -0.5507 -399.0C -405.67 [159] 306.5;.89296 -0.5107 -0.4872 0.8097 -0.5091 -369.00 -374.95 317.60 0.8596 -0.4692 -0.4553 0.8427 -0.4718 -339.0n -347.43 327.63 0.8R56 -0.4484 -0.4290 0.8725 -0.4415 -324.00 -324.09 337. PC 0.9132 -0.4138 -0.4045 0.9031 -0.4133 -299.00 -334.99 347.90 C.94C5 -0.3792 -0.3821 0.9334 -0.3877 -274.00 -285.15 357.93 0.9676 -0.3667 -0.3616 0.9636 -0.3645 -265.00 -267.90 368.2 0 0.9954 -0.3377 -0.3420 0.9948 -0.3424 -244.00 -251.53 377.70 1.0211 -0.3169 -0.3252 1.0237 -0.3236 -229.OC -237.56 388.50 1.050" -0.2948 -0.3075 1.0567 -0.3C38 -213.0C -?2,.P4 400.10 1.0816 -0. 2782 -0.2898 1.0922 -0.2842 -201.00 -208.27 412.9( 1.1162 -0.2519 -0.2719 1.1315 -0.2644 -187.00 -193.50 274.45 0.7420 -0.6606 -0.6010 0.7154 -0.6441 -477,30 -474.49 [1361 297..0 r.C8035 -0.5465 -0.5166 0.7822 -0.5436 -394.00 -400.45 31 q.95 R.865G -0.4710 -0.4489 0.8497 -0.4644 -34.30 -341.96 13q.OO 0.5218 -1.4047 -1.1900 0.4820 -1.3986 -1015.00 -1C25.83 [122,123] 199.Cr C.5353 -1.3314 -1.1305 0.4961 -1.3185 -962.CO -967.63 2C3.r:) 0.549R -1.2622 -1.C757 0.5101 -1.2455 -c12.00 -914.52 21 8.3'.5893 -1.0767 -0.9349 0.5526 -1.0612 -77R.00 -780.11 244.,' 0.6556 -0.8442 -0.7520 0.6270 -0.8290 -610.C0 -610.29 273.Cf ^,731RO -0.6601 -0.6071 0.7112 -0.6514 -477.00 -479.R7?97.C6 C.8C31 -0.5453 -0.5171 0.7818 -0.5441 -394.00 -4C00.85 333.16'.8196 -0.5314 -0.4975 0.7998 -0.5211 -384.00 -383.83 321.06 C. R6Rr, -0.4705 -0.4459 0.8530 -0.4610 -340.CC -3 9.43 348.16 0.9412 -0.4055 -C.3815 0.9342 -0.3871 -293.00 -284.68 369.97 1.000? -0.3598 -0.3388 1.0002 -0.3388 -26n.0O -248.85 423.16 1. 1440 -0.2533 -0.2585 1.1632 -0.2497 -183.3M -182.56 448.16 1.2116 -0.2214 -0.2291 1.2407 -0.2177 -16P.00 -158.73 5?3.16 1.4143 -0.15C9 -0.1618 1.4763 -0.1458 -109.00 -104.98 57C.46 1.5422 -0.1232 -0.1304 1.6271 -0.1129 -89.CO -89.36 246.. 0 C.6569 -0.8681 -0.7579 0.6241 -0.8364 -627.27 -615.71 [240] 258.OC 0.6' 7 -0.7591 -0.6760 0.6675 -0.7351 - 48.5. -541.39 273.CO C.7138 -0.6664 -0.6071 0.7112 -0.6514 -491.52 -479.97 88.00 77 -5918 -0.54774 07551 -0.5812 -427 0-439.2 32".0n -.8732 -0.4603 -0.4408 0.8588 -0.4551 - 32.60 -335.05 348.0- 0.94C8 -0.3775 -0.3818 0.9337 -0.3875 -272.80 -284.97!69.16 r.q0Ro -0.3598 -0.3403 0.9977 -0.3404 -260.CO -250.07 [ 16] 373.16 1.00 -0.3418 -0.3331 1.0099 -0.3324 -247.0 -244.11 39P.16 1.^764 -0.2920 -0.2927 1.0862 -0.2874 -211.00 -210.62 423.16 1.144C -0.2533 -0.2585 1.1632 -0.2497 - 183.00 -182.56 448.16 1..116 -0.2214 -0.,291 1.2407 -0.2177 -160.OC -15.73 473.16 1.7792 -0.1924 -0.2037 1.3187 -0.1903 -139.00 -138.?6 49P.1h 1.0467 -0.1675 -0.1814 1.3973 -0.1665 -121.0C -170.51 523.16 1.4141 -0.1509 -0.1618 1.4763 -0.1458 -109.o0 -104.98 54P.16 1.4910 -0.1329 -0.1444 1.5558 -0.1275 -96.03 -q1.29 303.1. R. 1l -0.5314 -C.4975 0.7998 -0.5211 - 34.00 -393.P3 [ 60] 34 9.1, 1.9412 -C.4055 -0.3815 0.9342 -0.3871 -293.03 -284.68 390.16 1.-74 -0.3100 -0.2927 1.0862 -0.2874 -224.00 -21C.62 423.16 1.1440 -0.2726 -0.2585 1.1632 -0.2497 -197.00 -18?.56 473.16 1.77?2 -^.2145 -0.2037 1.3187 -0.1903 -155.r0 -133.26 57C.46 1.54?? -). 1232 -0.1304 1.6271 -0.1129 -RQ9.0 -9^.6 250.r" 0C.679 -n.8047 -0.7178 0.6443 -0.7866 -581.46 -77.22? [ 61] 275.? f. 7434 -0.6522 -0.5087 0.7170 -0.6413 -471.?3 -47?.47 3CC,.Cr O. 0A11 -0.5395 -0.5075 0.7905 -0.5329 -1R9. 5 - 9?.52 3??.'.'.R794 -0.4537 -0.4356 0.8647 -0.4491 -327.81 -330.6? 35C.r. C.946? -0.3865 -0.3776 0.9398 -0.3827 -279.24 -281.41 375.nr 1.139 -0.3326 -0.3299 1.0155 -0.3288 -?40.33 -241.43 +403." 1.0814 -0.2887 -0.2900 1.0919 -0.2844 -2r8.57 -P20.39 425.:. 1.14c' -0.2521 -0.2561 1.1689 -0.2471 -18?.19 -190.67 450.0) 1.216q -0).214 -0.2271 1.2464 -0.2155 -159.98 -157.12 475.-r 1.2R41 -0.1952 -0.2019 1.3245 -0.1884 -141.03 -136.P7 50C.On 1.3517 -0.1726 -0.1799 1.4031 -0.1649 -124.6Q -t1I.30 5745.n 1.41c- -0.1529 -0.1605 1.4821 -0.1443 -110.45 -1)3.01 550.00 1.46Qs -0.1355 -0.1432 1.5617 -0.1262 -97.94 -90.33

476 TABLE J-3 (CONTINUED) T Tr Br Br Tr Br B Bcal Reference (OK) 00 00 cal cc/mole cc/mole n-C4H1 27?.0 0.64 2 2 -0.9640 -0.7917 0.5983 -0.9077 -897.00 -865.16 [ 27] 797. 1 0.69P88 -0.7899 -0.6735 0.6599 -0.7514 - 735.''O -716.92 321.15 C.76-0 -0.6513 -0.5742 0.7272 -0.6243 -606,.0 -595.97 346.45 G.8148 -0.5613 -0.5031 0.7883 -0.5357 -522.00 -511.26 330.67 0.7777 -0.6395 -0.5497 0.7469 -0,5935 - S5.00 - 56. 6 370.85 C0.722 -0.4825 -0.4418 0.8531 -0.4609 -449.00 -49q.67 397.33 C.9345 -0.4181 -0.3869 0.9242 -0.3952 -389.00 -376. 5 426.21 1.0024 -0.3557 -0.3374 1.0028 -0.3371 -331.00 -320. n 244.00 C.5738 -1.3219 -0.9853 0.5253 -1.1740 -1230.00 -1116.44 [122]?73.4n 0.643C -0.9920 -0.7898 0.5992 -0.,9051 -923.00 -862.6? 282.30 0.6639 -0.9264 -0.7427 0.6219 -0.8423 -86?.00 -C 3.20 297.30 C.6992 -0.8146 -0.6728 0.6603 -0,7505 -758.00 -716.12 321.30 C.7556 -0.6824 -0.5805 0.7224 -0.6323 -635.00 -603.54 423.16 0.9952 -0.3482 -0.3422 0.9944 -0.3427 -324.00 -325.89q 296.40 0.6971 -0.7738 -0.6767 0.6580 -0.7556 -720.00 -770.94 [159] 3C7. 5 0.7232 -0.7168 -0.6310 0.6866 -0.6965 -667.00 -664,77 318.2n 0.7484 -0.6652 -C.5913 0.7144 -0.6459 -619.00 -616.95 32R.90 C.7735 -0.6104 -0.5553 0.7422 -0.6006 -568.00 -573.23 337.83 0. 7944 -0.5728 -0.5278 0.7656 -0.5663 -533.00 -540.57 348.4 5 0.8194 -0. 5384 -0.4977 0.7935 -0.5291 -501.00 -504.96 35P.4" 0.8429 -0.50C8 -0.4716 0.81'99 -0.4971 -466.00 -474.33 368.4'0 0.8664 -C.4729 -0.4474 0.8465 -0.4678 -440.00 -44. 21 377.9~ 0.8888 -0.4406 -0.4261 0.8719 -0.4421 -410.00 -471.56 387.60 0.9116 -0,4116 -0.4059 0.8979 -0.4178 - 33.00 -39P.24 400.4'0 0.9417 -0.3794 -0.3812 0,9325 -0.3885 -353.00 -370.q1 41B3.40 0.9722 -0.3461 -0.3582 0.9678 -0.36' -?72.0C -A'43. 4 i-C5 12 298.2C 3.6351 -1.0320 -0.8087 0.5811 -0.9610 -1194.00 -1144.85 [159] 306.10 J.6520 -0.9654 -0.7690 0.5995 -0.9043 -1117.00 -1077.88 31R8.1'".6775 -0.8738 -0.7144 0.6276 -0.8274 -IQ11.00 -9P6.96 329.10 3.7010 -0.7977 -0.6696 0.6536 -0.7653 -923.00 -013.?4 339.1i 7.7223 -0.7459 -0.6325 0.6774 -0.7148 -F63.00 -853.77 34.I 1' 0.7436 -0.6914 -0.5985 0. 7013 -0.6690 -800.01 -798.84 358.1) 0.7627 -0.6551 -0.5703 0.7229 -0.6315 - 75P.Cc -754.05 36P.60 0.7851 -0. 6059 -0,5399 0.7483 -0.5914 -701.00 -7>-6.21 378.90 0.8070 -0.5635 -0.5123 0.7733 -0.5555 -652.00 -6 t.36 38P.40 0. 8273 -0.5289 -0,4887 0.7966 -0.5252 -812.00 -627.00 4C1.40 C.8550 -0,4906 -0.4590 0.8286 -0.4873 -578.00 -581.54 41 3.60 0.8809 -0.4468 -0.4334 0,8588 -0.4551 -517.00 -54. P85 30(.00 0.639C -1.0181 -0.7993 0.5853 -0.9476 -1177.90 -1129.04 [ 61] 325.00 0.6922 -0.8229 -0.6858 0.6439 -0.7876 -952.07 -939.80 350.00 3.7455 -0.6825 -0.5956 0.7034 -0.6651 -789.65 -794.18 37.0CI 0. 7987 -0. 5779 -0. 5225 0.7638 -0.5687 -668.66 -679.15 400.C0 0.8520 -0.4975 -0.4621 0. 8251 -0.4912 -575.97 -586.2? 42.(0C 0.9052 -0.4337 -0.4114 0.8872 -0.4275 -501.78 - 509). 7? 450.OC C.95E5 -0.3817 -0.3683 0.9503 -0.3745 -441.69 -445.76 475.00 1.0117 -0.3384 -0.3312 1.0141 -0.3297 -391.55 -391.61 5CfC.O0 1.0650 -0.3015 -0.2991 1.0786 -0.2915 -348.81 -345.30 n-C5H12 273.15 0.5933 -1.19C04 -0.9228 0.5415 -1.1047 -1367.00 -13G.CC26 [159] 298.15 0.6476 -1.0014 -0.7790 0.6001 -0.9026 -1150.00 -1064.41 32".15 0.7019 -0.8238 -0.6679 0.6595 -0.7522 -946.0) -88P.'9 348.15 0.7562 -0.6722 -0.5797 0.7198 -0.6367 -772.00 -75?.%2 373.15 0.8105 -0.5643 -0.5082 0.7808 -0.5455 -648.00 -644.24 423.15 f.9191 -0.4319 -0.3995 0.9053 -0.4113 -496.00 -484.97 448.15 C.9734 -0.3738 -0.3573 0.9687 -0.3608 -435.C00 -4?4. 60 46 1.65 1.0027 -0.3509 -0.3371 1.0032 -0.3368 -403.03 -396.07 C 8 R 18 372.00 0.6560 -1.1187 -0.7600 0.5748 -0.9819 -2122.00 -1952.8I [241] 18 378.?C C.6651 -1.0797 -0.7401 0.5852 -0.9479 -2048.0' -188 8.o 383.20 a.6739 -1.0223 -0.7217 0.5953 -0.9169 -1939.00 -1825.08 "84.30 0.6759 -1.0043 -0.7178 0.5975 -0.9102 -1905.00 -1812.07 8 R.l0 0.6826 -0.9853 -0.7044 0.6052 -0.8879 -1869.00 -1768.16 389.21 r..6845 -0.9637 -0,7006 0.6074 -0.8816 -1828.0C -1759.74 l.5C'.6921 -0.9374 -0.6861 0.6162 -0.8575 -1778.00 -1700a.8 394-.? C.6933 -0.9300 -0.6838 0.6176 -0.8536 -1764.00 -17(C'.84 40.503 C.7C096 -0.8651 -0.6541 0.6366 -0.8051 -1641.00 -1605.15 413.;)'.272 -0.8003 -0.6243 0.6573 -0.7572 -1518. -1510.61 378.00 0.6595 -1.0982 -0.7522 0.5788 -0,9686 -2C8?.96 -19q?,51 40, r.7335 -0.8904 -0.6650 0.6294 -0.8229 -1688.81 -164C.23 42".0 ) ".7475 -0.7431 -0.5926 0.6812 -0.7071 -1409q.9 -1411.38 45-. 5 n n.7914 -0.6352 -0.5317 0.7340 -0.6134 -1204.91 -1224.n7 47.00, F.8354 -0.5531 -0.4797 0.7880 -0.5361 -1040.10 -1070.2? r'C.: C. 8794 -0.4880 -0.4349 0.8430 -0.414 -925.59 -94 C. 21?"5.0 O. 9233 -0.4342 -0.3960 0.8993 -0.4166 -823.58 -829.43 55'.n C.q673 -0.3880 -0.3618 0.9566 -0.3697 -73.95 -71 4.11

477 TABLE J-3 (CONTINUED) T Tr Br Br Tr Br B B Reference ^ ^ ^ ^oo B Bcal Reference (OK) o0 00 cal cc/mole K cc/mole cc/mole CF4 273.15 1.19q6 -0.2198 -0.2340 1.2340 -0.2202 -111.00 -112.53 66] 29 8. 1 1.3094 -0.1748 -0, 1933 1.3654 -0.1757 -89830 - 9.11 323.15 1.4192 -0 1394 -0.1605 1.4986 -0.1404 -70.40 -70.47 34P.15 1.5290 -0.1103 -0.1334 1.6333 -0.1117 -55.70 -55.31 37.15 1. 63RP -0.0861 -0.1106 1.7696 -0.0880 -43.50 -47.76 423.15 1.8584 -0.0483 -0.0747 2.0464 -0.0511 -24.40 -23.72 448.1s 1.9682 -0.0333 -0.0603 2.1867 -0.0365 -16.8n -15.49 473.15 2. 070R -0.0200 -0,0476 2.3282 -0.0238 -10.10 -P.76 623.15 2.7367 0.0338 0.C045 3.2005 0.0270 17.05 18.24 203.15 0.89?2 -0.4292 -0,4230 0.8766 -0.4376 -216.75 -2?6.17 [137] 223.15 0.98fC -0.3519 -0.3526 0.9769 -0,3548 -177.71 -183.02 243.15 1.0679 -0.2839 -0,2974 1.0788 -0.2914 -143.36 -149.85 273.15 1.1996 -0.2195 -0.2340 1.2340 -0.2202 -110.87 -112.53 313.15 1.3753 -0.1530 -0.1728 1.4451 -0.1536 -77.26 -77.45 368.15 1.6168 -0.0906 -0.1149 1.7422 -0.0924 -45.75 -45.09 Ar 85.96 0.5704 -0.9711 -0.9967 0.5738 -0.9851 -250.20 -253.43 ( 35] 88.94 0.5902 -0.9063 -0.9323 0.5935 -0.9222 -233.50 -237.25 89.57 0.5944 -0.8857 -0.9196 0.5976 -0.9098 -228.20 -234.C4 93.59 0.6210 -0, 8139 -0 8445 0.6242 -0.8363 -209.70 -215.14 97.69 0.6487 -0.7514 -0.7775 0.6512 -0.77C8 -193.60 -198.27 1C2.79 0.6821 -0.6823 -0.7054 0.6848 -0.7000 -175.80 - 10.C0 107.93 0.7162 -0.6253 -0. 6428 0.7187 -0.6385 -161.10 -164.?4 113.97 0.7563 -0.5667 -0.5796 0.7585 -0.5764 -146.00 -148.27 122.7 r. 8147 -0.4941 -0.5031 0.8165 -0.5011 -127.30 -1 8.90 124.7r 0.8275 -0.4793 -0.4885 0.8291 -0.4867 -123.50 -125.19 130.96 C. 690 -0.4374 -0.4449 0.8703 -0.4437 -112.70 -114.13 140.44 0.9319 -0.3846 -0.889 0.9326 -0.3884 -99.10 -99.91 159.7? 1.0599 -0.2993 -0 3020 1.0592 -0.3023 -77.10 -77.79 179. 5 1.1934 -0.2356 -0.2366 1.1913 -0.2375 -60.7" -41.13 209.94 1.3931 -0.1696 -0.1677 1.3883 -0.1691 -43.70 -43.55 241.04 1.5995 -0.1199 -0.1184 1.5917 -0.1199 -3C.93 -33.93 271.39 1. 800 -0.0850 -0.0831 1.7900 -0.0848 -21.90 -21.90 Kr 117.41 n.5607 -1.0330 -1.0310 0.5539 -1.0560 -326.90 -335.17 1 35] 123.19 0.5740 -0.9729 -0.9845 0.5673 -1.0073 -307.90 -319.73 124.01 0.5922 -0.9085 -0.9261 0.5858 -0.9461 -287.50 -300.32 129.15 G.616l -0.8386 -0.8558 0.6106 -0.8727 -265.40 -277.04 134.60 0.6432 -0.7805 -0.7892 0.6373 -0,8033 -247.00 -255.0? 142.4q 0.6803 -0.6961 -0.7089 0,6749 -0.7199 -220.30 -228.54 150.98 0.7210 -0.6260 -0.6346 0.7161 -0.6428 -198.13 -204.C9 161.12 0. 7694 -0,5536 -0.5609 0.7653 -0.5667 -175.20 -179.92 172.29 C.8228 -0.4882 -0.4938 0.8195 -0.4976 -154.50 -157.98 1 6.84) 0.8924 -0.4193 -0.4228 0.8903 -0.4248 - 132.7 -134.83 2C9.16 0.9989 -0.3378 -0.3397 0.9988 -0.3397 -106.90 -1C7.80 251.94 1.2032 -0,2364 -0.2325 1.2077 -0,2306 -74.80 -73.12 123.15 0.5581 -0.9126 -0.9387 0.5816 -0.9594 -298.80 -304.5Z [ 28] 148.15 C.7C75 -0.6453 -0.6579 0.7024 -0.6669 -204.20 -211.74 173.15 0.8269 -0.4847 -0.4892 0.8237 -0.4928 -153.40 -154.46 198.1 0.9463 -0.3766 -0.3776 0.9452 -0.3784 -119.17 -120.10 223.15 1.657 -C.3000 -0.2987 1.0671 -0.2979 -94.95 -94.50 273.15 1.3044 -0.1989 -0.1953 1.3116 -0.1926 -62.96 -61.02 298.15 1.427P -0.1656 -C.1592 1.4342 -0.1565 -5?.40 -4S.51 323.15 1.5432 -0.1352 -0.1302 1.5571 -0.1272 -42.80 -40.19

APPENDIX K Enthalpy Calculations From the Powers Generalized Correlation (PGC) -H- Reference Enthalpy H=O for Each Pure Component as a Saturated Liquid at -280F ~ 478

479 TABLE K-1 ENTHALPY IF ETHANE IN B.T.U..'ER POUND USING P3WERS GENERALIZED CORRELATION TF'PE PATURE PRESSURE (I/SQ.IN. ~F 0.~ 1"*.l n 250.0 3on. 0 00.n 5no.n0 600.0 750.0 80n0.n 9no. -23.(' 228.75 3.39 2.19 1.78.t00 2.64 2.59 3.21 3.67 4.23 -760'.. 48.67 1 2.1? 18.27 18.24 17.96 17.68 18.16 19.16 19. 45 19.87 -24.r, 7'48.58 34.44 95.08 35.03 34.33 34.14 34.n0 34.35 34.64 35.41 -'~2^'.' 58..43.n 4 2. 7 52.1 1.4 51.44 515.34 51.70 51.?99 52.4m -?., "'69F.4?2S7.35 0o.91 69.79 69.80 69.47 69.24 9.9.2 69.39 69.75 -1 3,.fr?78.3) 267.oq 98.67 88.68 88.32 88.22 87.67 87.77 87.7n 87.69 -16r". 2a8.2n0 274.98?63.72 1 )9.64 108.91 108.32 107.37 106.83 106.64 16.74 -1'"{4). 298.1 2"".74?76.30 272.01 258.19 132.58 130.47 129.57 12P.23 127.48 -1 ".n 3i08.o1 3',. 86 2_.05 285.71 275. 79 262.73 24n.11 158.Ro 156.83 153.91 -1I?'." 317.96 3.68 3 1.93 298.37 290.37 280.85 269.99 244.29 23n.91 198.59 -V.n Z27.06 32??.32 313.59 31'.47 303.80 296.71 288.17 273.14 267.19 252.54 -<'~.'" 338.0?2?'V. 87 324.99 322.23 316.49 310.46 303.95 292.62 288.38 279.09 -4,+l.O 348.12 34. 3r 336.18 333.77 328.80 323.51 317.94 308.64 3n0.32 798.38 - 2,". 0n?58.2Q 3,. 93 47.47 345.28 340.78 336.09 331.41 323.48 320.69 315.01 -'. 3368.51 364.63 358.67 356.64 352.52 348.27 344.23 337.55 335.18 339.37 7.' " 378.79 379.21 369.70 367.84 364.07 360.22 356.50 350.7n 348.65 344.52 4'1.^ 389.15 385.84 380.62 378.91 375.56 372.05 368.57 363.45 361.72 358.06 h'.0 4999.61':A. 53 391. 3 389.97 387.01 383.81 380.55 375.95 374.50 371.20 -."' 410.18 4n7.29 4n2.55 401.12 398.45 395.49 392.45 388.27 386.99 334.07 1.""^' * 420.9n'18.13 413.76 412.44 409.94 407.14 4n4.36 400.52 399.33 396.81 12-.P^ 431.77 4'.1 n 425.10 423.P7 421.51 418.84 416.33 412.73 411.59 4n9.41 1,.3n 442.7 4,1".25 436.57 435.43 433.22 430.68 -428.49 424.97 423.9' 421.91. 453.95 41. 55 +43.17 447.11 445.03 442.6n 440.75 437.28 436.?8 434.40 P"." 4fe5.3^ z(,.. n24 459.91 458.Q4 456.97 454.65 453.12 449.68 448.75 446.94 >r 476.84 474.67!+l.R81 470. 9 469. n 466.83 465.59 462.18 461.32 459.56 72".' 488.55 486, 49 483. 8 483.00 481.26 479.13 478.13 474.78 473.Q8 472.25 4"'4.' 500.43 4'8.47 496.00 495. 2 493.55 491.54 490.59 487.44 486.70 4 5.06 2 5:''". 512.49 ] 1 0. 61 5 e.28 5 7. 53 505.95 5n4.07 503.00 500.1 499. 1 497. 9 2_!." 5924.66 52'?.R7' n.e6 5 19.94 518.44 516.69 515.64 513.00 512.33 51. 96 " *o0 537. 3 ~r:".?3 5 33.19 532.51 531.08 529.45 528.31?5.93 529. 36 524.0n

480 TABLE K-1 (CO1TINUED) ENTHALPY OF METHANE IN B.T.U. PER POUND USING POWERS GFNERAL1tFO CORRELATION PRESSURE (#/SQ.IN.) TFMPERATURE OF 1non.r 11"0.0 1250,n 1300.n 1400.0 1500.0 1600.0 1750.0 1900.0 2000.n 3.86 4.47 5.76 6.22 7.,7 7.82 8.52 9.37 10.01 10,38 -280.0?n. r7 2n. 78 22.05 22.48 23.28 23.97 24.58 25.23 25.5R 25.75 -260.0 36.19 36.92 38.17 38.59 39.34 39.96 40.51 41.16 41.61 41.86 -?40n.'2.72 53.44 54.64 55.04 55.72 56.29 56.80 57.51 58.16 58.55 -220.0'6.94 70. 58 71. 64 71.98 72.59 73.12 73.59 74.23 7479 75'.12 - n00.0 8P.14 8R.60 89.22 89.41 89.82 90.27 90.70 91.24 91.66 91*89 -180.0 1 7.21 107.71 108.12 108.2) 108.57 169.10 109.36 109.54 It^. 1 109.81 -160.0 127.20 127.37 127.55 127.61 127.77 127.94 128.05 128.14 128.21 128.26 -140.0 152.2-1 15.89e 149.01 148.52 147.93 147.84 148.05 147.84 146.83 146.05 -120.0 135.27 178.92 175.15 174.22 172.70 171.52 170.47 168.81 167.42 166.61 -100.0 236.76 221.87 209.90 207.12 202.51 198.44 195.15 191.17 188.66 187.50 -80.0?^o.28 25Q.60 246.12 242.1n 234.75 228.24 222.65 216.51 212.52 210.66 -6n0.?91.11 2a4.17 273.65 270.24 263.49 257.05 251.18 243.67 237.77 234.52 -40.0 35.23 3n3.58 293.31 292.60 287.02 281.38 276.08 268.70 262.05 258.08 -20.0 325.51 372.56 313.57 311.36 306.63 301.65 297.00 290.34 283.99 280.06 -0.0 34'1. 32 336.04 33n.05 328.15 323.99 319.48 315.27 309.32 303.75 300.3n 20.0 354.13 35n.4p 34. 11 343.30 339.60 335.85 332.22 327.05 322.27 319.31 40.n?67.41 376.28 30.2? 357.5n 354.19 351.24 348.18 343.73 339.66 337.11 6n0. 3i".^ 3 377.92 373.3? 371.6n 368.58 366.02 363.27 359.30 355.77 353.55 80n. 7 -4. 8 391.51 387.n30 85.79 382.99 380.43 377.76 374.02 370.85 368.87 0nn0. 4,7.29 4+'4. 5 4n0P,8 3q9, 6 397.08 394.46 391.82 388.26 385.35 383.55 120.f L~r.,2 417.73 414.15 412.98 410.58 468.13 405.70 402.44 399.76 398.09 149.) 432.(1 43r.47 427.15 426.07 423.85 421.60 419.39 416.43 413.94 412.38 160.0 4-5.15 44.15 440.06 439.5 437.00 434.96 432.97 430.29 427.97 426.50 180.0 457. 7 45".q5 452.96 452.'" 45n.11 448.27 446.50 444,07 441.9n 440.51 700n. 47^.35 46HS.9 465.9 464.98 463.21 461.57 459.99 457.79 455.76 454.44 20.0 483.22 8,1.57 479.04 478.18 476,52 474.98 473.50 471.47 469.62 468.43 24.0n 4^56.24 49,. 69 432.33 401.51 48,.95 488.48 487.06 485.14 483.47 482.,42 260.0 - y9.2 57!7.86 5 5.65 5(14.88 503.40 50n.98 500.60 498.77 497.28 496.36 280.0 522.51 521.14 519."6 518.34 516.92 515.56 514.23 512.44 511.11 513.31 300n.

481 TABLE 1-2 ENTHALPY ETHANE IN B.T.U. PE6 PQWiN USI4NG POWERS GENERA ZIZED CORRELATION TEMPtRATURL PRESSURt ( /SQ. INtl "F 0.o Lt.0.U 250.0 300.v 400.0 500.0 600.0 677.0 713.0 750.0 -26u.t:, o. 43 -.1 -0.37 0.20 0.33 0.44 0.66 0.82 1.05 -26J.L 25b.26 10.52 10.47 10. 5 10.92 11.06 11.26 11.50 11.64 11.79 -z40. o 2 0t.19 i. <. 17.87 17.8d 18.01 18.15 18.43 18.70 18.84 18.97 -24,.O,>: ~,..14 21.39 21.49 21.48 21.58 21.71 21.95 22.17 22.29 22.46 -2,L.~ 20 too.12 3c.08 32.53 32.58 32.60 32.71 32.75 32.76 32.84 33.10 -d0.;7.-l e 43.37 43.37 433 4.37 43.91 44.04 43.99 43.91 43.95 44.19 -180I.v 280.41 55.22 55.04 54.88 54.94 55.38 55.31 55.10 55.09 55.32 -160.L 2db.u t(b.99 66.26 65.94 65.96 66.58 66.68 66.58 66.62 66.86 -140.0J 293.12 77.83 77.60 77.49 77.3'' 77.46 77.94 78.50 78.77 79.00 -z. 3. 24;8.7? 7.03 87.16 87.21 87.22 87.10 87.42 87.88 88.08 88.22 -IL..J 299..oo 93.8d U89.Co 89.14 89.18 89.06 89.32 89.69 89.86 89.98 -luO.( Jbc.6.35 1i).65 1O. e7 100.98 101.04 100.97 101.03 101.10 101.15 101.22 -80.0 313.18 112.95 112.90 112.98 113.06 112.97 113.13 113.25 113.35 113.52 -tUo.C 320. 18 125.17 125.20 125.49 125.83 125.73 125.83 125.92 125.99 126.09 -40.U 327.34 316.47 138.72 138.59 138.86 138.76 138.76 138.82 138.86 138.90 -28.5 333.01 32-.94 149.82 149.50 148.49 148.96 148.93 148.95 148.98 149.01 -20.0 334.b7 325.26 152.80 152.78 151.89 151.93 151.92 151.9q 152.04 152.22 r... 342.20 333.22 167.9C 166.81 165.97 165.47 165.54 165.47 165.48 165.20 L2.~L 43.3.3 34.45 328.52 182.97 181.12 180.47 179.70 179.98 180.00 179.20 J.u 3.2.2J 33.22 167.90 166.81 165.97 165.47 165.54 165.47 165.48 165.20 M.J, 361.57 36.20 342.58 338.93 326.66 205.98 203.75 203.28 207.92 202.52 60b.. 355. )8 35' ).65 i48.35 344.32 333.12 217.18 214.80 212.61 211.86 211.40 6... J74. 3'J b5. 16 358.56 354.85 346.40 335.22 316.71 237.79 236.27 234.71 lt..u 302./ 3 11.13 _4Ci8.37 365.10 357.61 349.06 337.31 324.81 316.43 306.69 39.o 31d6.'2 372.45 3t3.35 359.93 351.96 342.41 327.70 308.85 259.63 251.37 100.L 731.77371.13 3d8.37 365.iu 357.61 349.06 337.31 324.81 316.43 306.69 ~L,.0 33'.5 L.4.36 378.20 375.2.' 368.57 360.95 352.28 344.54 340.09 334.97 [1... 3^s j3.h5 ) J 6.04 380.65 377.74 371.13 364.06 355.46 348.51 344.53 339.94 146., 40L.34: 5.55 H88.06 385. 37 379.55 373.14 365.63 356.92 355.72 352.52 loo~.L 4.3.40 4L'. 00 398.08 395.61 390.30 384.50 378.14 372.79 37n.14 367.34 1 0.b. 410..)6 414.72 4V+8.23 405.93 401.02 395.80 390.29 385.84 383.b8 381.39 2LL.J 42.. 4. 4.6J 418.55 416.42 411.93 407.20 402.27 398.29 396.36 394.33 2oC0.t 4268. 4 4 4.S 418.86 416.74 412.26 407.54 402.62 398.65 396.73 394.71.L.L 435.47 434.76 42'9. 9 427. 1i 422.99 418.64 414.17 410.54 408.76 406.92 4u.0 44 8. 6 4,. 3 4 -4.2) 439.89 438.32 434.16 430.09 426.08 422.89 421.30 419.70 36. 0 45')..,U 4',.87 450. 79 449. 3 445.42 441.61 437.93 435.09 433.68 432.24..i. 43t:..i 87.29 472.78 471.23 468.08 464.75 461.49 459.18 458.08 456.83

482 TABLE K-2 (CONTINED) LNTHfALPY,F ETHANE IN B.T.U. rEt POUND USING POWERS GENERALIZED CORRELATION PRESSURc (#/SQ.IN.) TEMPERATURE OV 819., ICCO.O 125u.0 1300.0 1400.0 1500.0 1600.0 T750.0 1900.0 2000.0 1.lb5 11.92 /. 74 3.04 3.62 4.07 4.45 4.99 5.57 5.97 -280.0 1..1,' 12. 51 13.42 13.70 14.25 14.69 15.07 15.61 16.20 16.59 -260.0 l".ct 19.5'7 20.46 2v.72 21.Z2 21.66 22.07 22.65 23.24 23.64 -246.6 z,.7,, 23.03 23.93 24.17 24.65 25.09 25.51 26.12 26.72 27.11 -240.0 J. j, 33.bl 34.71 34.93 35.37 35.82 36.27 36.93 37.53 37.92 -220.0 44. /L 4b.18 45.78 45.99 46.43 46.89 47.35 48.03 48.63 49.01 -200.0 55. iH 56.55 57.04 57.28 57.t6 58.22 58.68 59.35 59.93 60.30 -180.0 o. 4 67.97 6..61 68.85 69.36 69.82 70.27 70.90 71.45 71.79 -160.0 7., 79. 4 80. 5 8').49 80.97 81.42 81.85 82.43 82.91 83.20 -140.0 ob. 4 8b.97 89.39 CJ.12 90.59 91.02 91.42 91 -, 92.41 92.66 -123.3 u.1'; 90.45 91.81 32.04 92.50 92.93 93.33 93.87 94.30 94.54 -120.0 o101.s 102.49 1C3.50 103. 73 104.17 104.57 104.94 105.45 105.89 106.15 -100.0 11i.31 114.42 115.37 115.58 116.00 116.37 116.71 117.20 117.65 117.93 -80.0 126. i' 126.o8 127.45 127.65 128.04 128.38 128.69 129.14 129.58 129.87 -60.0 139.02 139.24 139.81 13).98 140.32 140.62 140.91 141.32 141.71 141.96 -40.0 149.11 149.20 149.64 149.79 150.08 150.35 150.60 150.97 151.30 151.51 -24.5 152.i 152.l1 152.51 152.65 152.92 153.17 153.42 153.77 154.09 154.29 -0.0 ltS. 6'. lbb.'! 15.71 It.t8 165.93 166.11 166.30 166.59 166.84 166.99 0.0 179., 17'9. 5 179.96 179.97 180.00 180.27 180.55 180.55 180.58 180.63 20.0 165.t<+ 165.34 165 71 1(5.78 165.93 166.11 166.30 166.59 166.84 166.99 0.0 u22. JJ O01.73 01.26 221.19 201.02 200.93 200.86 200.62 200.41 200.30 49.2 211i.,, 210.o3 2t 9'.51 2 09).46 209.21 208.95 208.69 208.31 208.10 208.05 60.0 2.~.:2.(' C, 2b. 35 2295.67 224.9? 224.28 223.78 223.25 222.74 222.47 80.0 2,h. i< 252. 1 244.75 244.09 242.96 241.65 240.76 239.65 238.63 238.06 100.0 49.5 23 9.5 2235.42 2,.F7 233.91 232.88 231.91 231.21 230.48 230.01 89.8 206. < 252.. 1o 244. 75 244. 09 242.96 241.65 240.76 239.65 238.63 238.06 100.0 J2't.Z,, 28r4.C5 260.35 205.01 262.31 260.01 258.56 256.81 255.17 254.20 120.0 ooU.l'.2)4. b2 272.42 27U.61 267.74 265,04 263.11 261.04 259.34 258.33 125.0 35. tj 322.44 293.18 29u.10 285'2 281.49 278.50 274.90 272.17 270.81 140.0 3ci..' 45.bt 320.1 316.40 309*62 304.36 299.68 293.81 289.98 288.30 160.0,J ~6 o: 3.Sb 344.2b 340.23 332.73 326.21 320.85 314.41 309.75 307.41 180.0.4<. -, i379.61 363.21 359.34 353.30 347.31 341.95 335.01 329.54 326.57 200.0 3.. —. 3 J I0..5 363.76 36J.40 353.90 347.93 342.56 335.62 330.13 327.14 200.6 ~;. 3q4. 394.u0 380.38 377.58 372.04 366.65 361.55 354.64 348.78 345.41 220.0 41i. 4 40t).._ 395.93 393.54 388,83 384.00 379.32 373.00 367.28 363.81 240.0 42V9.t7 421.97 411.05 409.01 0404.93 400.53 396.12 390.18 384.68 381.28 260.0 454.47 44,.34 439.60 438.04 434*76 431.08 427.28 422.06 417.25 414.29 300.0

483 TABLE K-3 EITdALYX OF PBOPAkI IN U.T.U. PER POUND USING POMERS GENER&LIZED CORRBLATION TEK ^ATUAB PRESSUIa (S/SQ. 3E.) ~F 0.0 100.0 250.0 J0.0 400.0 500.0 600.0 750.0 800.0 900.0 -2eu.O 234.45 0.26 0.25 0.73 0.61 0.68 1.22 1.46 1.48 0.88 -2ou.0 239.16 9.76 8.8S 9.02 9.13 9.48 10.06 10.89 11.12 10.09 -2v.o0 244.15 18.26 17.80 18.03 18.25 18.59 19.04 19.81 20.05 19.34 -2.0.0 249.40 27.17 27.13 27.44 27.70 27.99 28.36 28.92 29.12 28.76 -2i,.0 254.36 37.00 36.87 37.07 37.30 37.61 38.C1 38.50 38.67 38.44 -~la.O0 260.38 46.71 46.69 46.86 47.07 47.29 47.53 48.23 48.41 48.09 -lu4.O 265.87 56.17 56.42 66.60 56.82 56.88 56.86 57.90 58.12 57.69 1-,w.O 271.48 65.98 66.34 66.50 66.70 66.69 66.55 67.64 67.97 67.56 -1.u.O 277.21 76.12 76.25 76.29 76.59 76.63 76.39 77.45 77.88 77.51 -1iv.0 283.09 86.49 86.03 u5.87 86.37 86.62 86.30 87.35 87.78 87.48 -<4.o 289.24 96.48 95.98 95.82 96.15 96.52 96.71 97.66 97.94 97.65 -ou.O 295.58 106.44 106. 2 1u6.31 106.28 106.66 107.52 108.26 108.37 108.05 -~4.0 302.12 116.78 116.87 117.03 117.03 117.25 117.79 118.18 118.32 118.60 -^.0O 308.67 127.55 127.62 1l7.89 128.01 128.11 128.29 128.58 128.78 129.40 —.0 315.43 138.78 138.60 138.91 139.07 139.22 139.44 14C.62 140.19 140.42.V.3 323.01 150.13 150.02 1j0.51 150.69 150.41 151.05 151.63 151.77 151.74 44.0 330.41 162.81 162.03 162.62 162.76 162.82 163.01 163.36 163.48 163.39 ov.0 338.05 327.59 174.82 174.96 174.94 175.06 175.19 175.45 175.56 175.32 44.0 345.32 336.99 188.46 1d7.68 187.25 187.54 187.66 187.95 187.69 187.52!Ij.0 354.05 345.13 201.83 2J1.12 200.08 200.34 200.51 200.53 200.34 200.15 1..0 362.43 354.58 216.90 ^15.42 214.24 213.59 214.03 213.75 213.64 213.55 1-i.0 371.06 364.32 350.53 344.27 229.65 228.46 228.60 227.74 227.72 227.42 lou.O 379.43 373.53 361.98 366.41 247.20 244.39 243.35 242.86 242.72 241.98 lj@.0 389.05 382.87 372.19 368.23 356.56 263.72 260.72 258.51 258.33 257.53 2,. 0 398.40 392.52 383.00 379.29 370.54 356.48 286.25 278.46 276.93 275.06 2a. 0 4C8.00 402.65 393.81 J90.39 382.39 372.62 357.54 306.31 301.31 295.61 240.0 417.85 412.94 404.70 401.53 394.40 386.03 376.02 352.37 340.15 321.23 20..0 427.94 423.25 415.71 412.90 406.69 399.36 390.61 375.06 368.55 354.C5 o0,.o 438.27 433.88 426.87 424.28 416.58 412.06 404.68 392.87 388.21 377.53 344.0 448.83 444.75 438.16 445.71 430.41 424.60 418.39 408.27 404.58 396.85

484 TABLE K-3 (CONTINUED) EI2HALEY OF PBOPAl. IN B.T.U. PEE POUND USING POWSS GENMERLI.ED CORBiL&TION PRBSSUEi (t/SQ.IN.) TE PBERATUBE "F 1C00.0 1100.0 1250.0 13 )0.0 1400.0 1500.0 1600.0 1750.0 1900.C 2000.0 1.06 1.44 1.99 2.18 2.55 2.92 3.29 3.85 4.40 4.77 -280.0 10.1C 10.47 11.32 11.20 11.57 11.94 12.31 12.86 13.42 13.78 -26C.C 19.42 19.78 20.33 20.51 20.88 21.25 21.61 22.16 22.71 23.08 -24c.C 28.92 29.28 29.82 0.00 30.36 30.73 31.09 31.63 32.18 32.54 -220.0 38.63 38.99 39.52 s9.70 40.06 40.42 40.78 41.32 41.85 42.21 -20Ci.( 48.35 48.7C 49.23 49.41 49.76 50.12 50.47 51.00 51.53 51.89 -180.0 58.03 58.38 58.90 59.07 59.42 59.77 60.12 60.64 61.17 61.52 -160.C 67.77 68.11 68.62 b8.79 69.13 69.47 69.82 70. 3 70.84 71.19 -14C.C 77.02 77.95 78.45 78.62 78.95 79.29 79.62 V^ 13 80.63 80.97 -120.0 87.o0 87.93 88.41 d8.58 88.90 89.23 89.56 90.05 9C.54 90.87 -10C. 97.84 98.15 98.62 98.78 99.09 99.41 99.73 10C.20 100.68 101.0C -80.0 108.27 108.57 109.02 109.17 109.48 109.78 110.09 110.55 111.01 111.32 -6P.C 118.d3 119.11 119.54 11,.69 119.98 120.27 120.56 121.C0 121.45 121.74 -40.0 129.64 129.91 130.32 1J0.45 130.73 131.00 131.28 131.70 132.12 132.4C -2C.0 140.67 140.92 141.33 141.43 141.68 141.94 142.20 142.59 142.99 143.25 -0.0 151.94 152.16 152.51 152.62 152.86 153.09 153.33 153.69 154.06 154.3f 20.0 163.50 163.69 163.95 104.09 164.30 164.51 164.72 165.05 165,38 165.60 40.C 175.34 175.50 175.75 175.83 176.01 176.19 176.37 176.65 176.94 177.14 6C.C 187.51 187.(2 187.81 1d7.87 188.01 188.15 188.30 188.53 188.77 188.94 80.0 200.11 200.17 C20.28 400.32 200.40 200.50 200.60 200.78 200.96 201.09 10C.0 213.b4 213.66 213.67 213.79 213.99 213.92 213.84 213.89 213.97 213.99 120.0 227.29 227.26 227.05 227.06 227.05 226.88 226.71 226.60 226.61 226.71 140.C 241.76 241.51 241.01 240.88 240.61 240.30 240.C3 239.78 239.73 239.83 160.0 257.13 256.42 255.6C 4,5.29 254.67 254.14 253.76 253.52 253.47 253.43 180.0 273.76 272.60 271.06,70.44 269.41 268.70 268.21 267.85 267.65 267.42 2C0.0 291.98.89.53 287.38.d6.65 285.53 284.59 283.73 282.88 282.21 281.80 220.0 313.79 309.65 305.23 334.13 302.71 301.60 300.43 298.83 297.48 296.74 240.0 339.62 332.34 325.29.13.61 32C.89 318.78 317.03 314.96 313.37 312.28 260.0 366.55 356.29 346.91 J44.51 340.27 336.72 334.11 331.44 329.69 328.51 280.0 368.10 379.28 367.61 3t4.68 359.47 355.40 352.34 349.11 346.80 345.25 30C.O

485 TABLS K-4 (DWT1NOED) ENTHALPY OF.76 C2H6-C3H8 IN B.T.U. PE, POUND USING POWERS GENFRPALIZ'E C"*l.t. ll TEMPERATURE PRESSURE I(/SQ.IN. ~F0 3000 400.0 500 u.O ICO.0 250.0 300.0 400.0 500.C 600.0 716.' 750. e^OC.C -26u.ou 44.97 2.44 1.77 1.76 2.09 2.24 2.50 3.05 3.2c 4. 3. -260.0 250.40 11.87 11.77 11.93 12.45 12.56 12.72 13.11 13.29 14.14 -240.0 255.99 22.31 22.23 22.27 22.51 22.67 22.95 23. 3 2.49 24.11 -220.0 261.74 32.52 32.69 32.73 32.80 32.96 33.12 33.44 33.63 44. )4 -200.0 267.64 42.91 43.36 43.43 43.46 43.59 43.55 43.73 43.98' 44.4 -180.0 7 73.62 53.81 54.17 S4.20 54.26 54.43 54.31 54.39 54.61 55.77 -160.0..279.67 65.11 64.76 64.57 64.70 65.21 65.05 64.96 65.20 66.47 -140.0 2d5.83 76.11 75.46 75.19 75.26 75.79 75.89 76.09 76.33 77.19 -120.0 292.13 86.47 86.31 86.24 86.r[ 86.19 F6.77 87.65 87. l^ 88.41 -100.0 e28.5b 97.14 97.31 97.41 97.44 97.35 97.65 98.13 q3.22 Ca.71 -80.0 3u5.19 108.49 108.65 108.78 108.84 108.81 108.88 109.04 n19.l11 1. 6 -66.0 311.98 120.31 120.21 120.32 120.35 120.38 120.54 120.82 120.98 121.,4 -50.1 315.40 125.99 126.01 126.22 126.57 126.37 126.52 126.73 126.92 127.' -40.0.18.95 132.07 132.09 132.40 132.67 132.63 132.74 132.c6 133.06t 134.L' -io.O 326.10 144.83 144.99 145.25 145.18 145.21 145.34 145.39 145. 7 0.0 333.45 324.66 158.78 158.42 157.91 157.92 157.90 157.97 158.01!53.?.~ 20.0 341.01 332.02 172.28 172.04 171.08 170.94 170.99 170.92 171.01 17,.3 40.0. 48.77 341.C4 185.49 184.78 1R4.65 184.37 184.24 184..A 56.0 352.72 345.71 332.24 193.db 192.61 191.70 191.46 191.24 11.4. 60.u 356.74 350.31 337.27 201.78 200.45 199.53 19R.63 198.52 1^,'' 80.0 jb4.c1 358.68 346.69 343.22 218.40 216.01 214.82 214.51'13. 5 100.. 373.28 367.20 357.28 353.37 344.'9 237.41 234.09 233.20 731.1 1(2.4 374.29 368.24 358.48 354.65 345.79 333.16 240.28 236.99 236.01 233.53 120.0 381.86 376.08 367.22 363.87 356.06 346.61 331.q1 261.47 252. 7. 140.0 390.66 385.50 377.21 374.11 367.13 358.92 349.51 333.16 327.04.P4.87 151.o 335.90 390.97 383.04 380.11 373.63 366.17 357.70 345.16 340.54 313.6q 160.C 399.70 394.89 387.23 384.44 378.31 371.39 363.1 352.46 348.57 2?7.11 180.0 4u9.01 4U4.49 397.43 394.89 389.40 383.35 376.40 367.18 364.42'?.1 2CC.O 418.59 414.38 407.80 405.44 400.38 394.88 388.95 381.49 379.00n h7. n 22u.0 428.41 424.48 418.29 416.08 411.39 406.43 401.24 394.87 392.9qn 43., 24U. 438.47 434.68 428.90 426.17 42. 418. 418.05 413.34 407.48 405.70 i 7. 5F 250.7 4.3.96 440.30 434.70 432.75 428.64 424.30 419.82 414.22 41?.53.4;.9C 260.0 44d.75 445.23 439.77 437.86 433.89 4Z9.69 425.44 43).11 418.52 411.?2 80.O0 459.18 455.99 450.78 448.97 445.24 441.30 437.48 432.75 431.34 424.P1 300.0 469.82 466.81 461.90 460.19 4S6.70 453.00 44Q.48 44. 26 443.97.P,. 7

486 TABLE K-4 (OOHTIMKD) ENTHALPY OF.76 C2H6-C3H8 IN B.T.U. Pt PtJNOD USING POWERS GENERALIZED CORRELATION PRESSURt ( #/SO.IN. TEMPFQATIIRF ~F 1000.0 1100.0 1250.0 1300.0 1400.0 1500.0 1600.0 1750.0 100).0 2?00.C 3.71 3.77 4.54 4.80 5.28 5.70 6.11 6.69 7.27 7.66 -P 2C. 13.85 14.06 14.89 15.16 15.67 16.06 16.42 16.94 17.51 17.19 -260.^ 23.96 2#.19 24.95 25.19 25.67 26.07 26.44 26.99 27.57 27.95 -240.0 34.04 34.36 35.02 35.24 35.68 ~4.09 36.50 37.10 37.67 38.05 -220.0 44.54 44.87 45.47 45.68 46.09 46.52 46.95 47.58 49.15 48.57, -200.0 55.42 55.52 56.13 56.34 56.t7 t.21 57.65 5 8.27 58.83 5..3 20 -1 Rn. 66.15. 66.22 66.86 6fr.69 T6.w kTt.97 68.40 69".bl 69.55 69.90 -10O.0 77.08 77.24 77.90 78.13 78.59 79.01 79.4.2 80.00 8K0.50 80.82 -14".( 88.10 88.34 88.98 89.21 89.65 90.06 90.45 90.98 91.42 91.70 -120.^ 99.10 99.41 100.04 100.25 100.67 101.06 101.43 101.92 102.31 102.55 -lOP." 110.33 110.68 111.29 111.49 111.89 112.26 112.60 113.07 1.48 113.73 -v3. 121.79 122.14 122.72 122.91 123.30 123.63 123.95 124.40 124.83 125.10 -..n 127.57 127.88 128.43 128.62 128.99 129.31 129.62 130.06 130.49 13(.7t -Sr.1 133.58 133.83 134.37 134.55 134.90 135.21 135.50 135.93 137.35 136.62 -4C.? 145.68 145.83 146.30 146.46 146.78. 147.05 147.32 147.70 14A.1R 148.32 -^. 158.08 158.16 158.56 158.69 158.94 159.19 159.42 159.75 160.05 16C.25 C." 170.90 170.98 171.22 171.29 171.45 171.64 171.82 172.09 17?.34 172.4 2". 184.51 184,7a 184.90 184.91 185.01 185.36 185.57 185.56 185.65 139.74 40. 191.40 191.53 191.67 191.66 191.70 191.94 192.07 191.99 191.99 192.1 S.'" 198.58 198.55 198.64 198.61 198.58- 198.70 198.74 198.59 199.50 19R.4" 6". 213.36 213.36 213.13 213.02 212.82 212.66 212.48 212.18 211.99 2119? ~"." 230.4u 229.60 228.55 228.21 227.72 227.24 226.81 226.32 226.04 225.95 l00.O 232.o1 231.74 230.52 230.14 229.53 229.02 228.57 228.07 227.74 227.-1 1C2.250.09 248.06 246.00 245.52 244.54 243.40 242.48 241.77 241.04 240.61 170.0 274.U6 238.41 264.04 263.03 261.41 260.26 259.27 257.93 2r^h.4 255.6^ 14r". 292.66 283.46 276.83 275.48 272.80 270.66 269.27 267.55 26.397 2t5.C5 151.6 309.28 e95.53 286.56 284.62 281.46 278.82 276.77 274.53?r.R1l?71.7. 1-. " 33b.63 326.65 311.87 308.97 304.'6 300.18 296.44 292.34 628.47 RAP.12 1-.) 359.80 350.73 337.69 333.66 326.95 321.34 316.58 311.08 307.53 305.87 3fi'.r 376.71 369.43 358.42 354.69 347.78 341.98 337.03 331.04 326.63 324.34 220.' 391.83 385.87 376.67 373.56 367.r6' 362.06 357.06 350.57 345.42 342.69 74C. 0 i99.59 394.14 385.79 382.96 377.42 372.16 367.26 360.73 355.37 352.33 75n.7 406.27 401.13 393.27 390.64 385*45 380.39 375.65 369. 27 363.84 36(C. -6 2?60.420.35 s5,.68 408.64 406.39 401.*9 397.25 392.87 386.96 381.59 37HP.5 /^o. 434.09 423.91 423.67 421.73 417.76 413.45 409.31 403.70 398.51 39S.34 nO.^

487 TABLE K-S tNTHALPY UF.494 C2H1-C3H8 IN B.T.U. tr'c,.UNO LSING POWERS GENERALIZED CORRELATION TEMPE ATURE P-ESSURc ( l/SQ.IN.) ~F.0 100.u 250.0 300.0 400. C 500.0 600.0 750.0 800.0 900.0 -280.0 240.50 2.lb 1..4 1.25 1.3* 1.57 2.02 2.97 3.31 3.25 -260.0 245.64 11.09 10.62 10.81 11.19 11.35 11.64 12.45 12.78 12.8a -240.t, 250.98 20.52 Zu.41 20.64 21.0~O 21.16 21.44 22.05 22.29 22.44 -220.0 t5b6.53 30.72 30.58 30,66 30.83 31.06 31.40 31.94 32.13 32.77 -200.0 262.25 40.59 40.76 40.35 40.96 41.14 41.24 41.92 4?.20 42.?2 -180.0 258.04 50.71 51.11 51.21 51.29 51.42 51.31 52.03 5'.40 5.52 -160.0 273.87 61.20 61.50 61. 5 61.67 61.83 61.63 62.25 62.67 6.rl -140.v 719.80 72.0? 71.69 71.54 71.81 2Z.Z7 71.95 72.50 77.95 7.36 -125.5 284.19 79.77 79.06 78.31 79.10 79.68 79.48 80.08 80.50 80.8c -1U.u A285.87 82.59 81.94 81.71 81.94 82.45 82.45 83.14 R8.52 3. 70 -100.L 292.08 92.69 92.48 92.42 92.37 92.54 93.24 94.21 C4.47 Q4.4' -80.J0.8.51 103.13 103.25 103.35 103.34 103.34 103.82 104.40 104.54 14. 8R -6bO.O 305.12 114.11 114.25 114.43 114.49 114.51 114.62 114.88 115.04 115.64 -40.0 311.91 125.60 125.48 125.65 125.73 125*80 125.96 126.48 126.70 1?7.03 -20.L 318.90 131.C6 137.06 137.41 137.57 137.63 137.79 138.26 139.45 1?P.6 )0. 326.09 149.29 14..67 149.88 149.87 149.97 150.23 15. % 1,.4? 20.L 333.49 162.85 162.34 162.20 162.31 162.34 162.52 16?. a1 162.? 37.5 34u.14 i31.06 174.36 174.17 173.11 173.40 173.41 173.32 17.68 17?.ir 40.U 341.11 331.~5 176.C9 175.94 174.65 175.02 175.03 175.49 17s.?6 174.q4 6U.L 346.94 340.47 189.41 1 88.55 188.17 18R.14 188.20 IH 3.1) 187.' 8u.0 3s7.0C 349.85 203.34 202.45 201.96 201.82 201.74 201., 1C0.0 365.Z7 J58.d2 346.60 218.06 217.27 216.30 215.51 21(.4r 1CG.0 373.77 567.51 356.34 352.49 340.77 234.30 232.15 231.1q 21.1? 140.0 362.50 376.47 3t6.81 363.02 354.2d 341.01 252.15 25).45 2').?7 151.1 387.45 381.61 372.49 368.99 360.88 350.03 266.35 276.63?6'.o 160.0 391.47 385.89 377.06 373. 7 365.79 356.38 342.30 283.76 276.77 27C.9' 180.0 4G,.70 395.6o 387.39 384.27 377.26 369.01 359.64 337.63 326.74 3C1.0' 200.0 41U.19 415.42 397.82 395.03 388.92 381.96 373.54 358.88 352.51 336.14 22U.O 419.93 415.45 408.42 405.86 400.32 394.12 387.05 375.23 371.1" 36(. R 240.0 429.90C 445.71 419.14 416.74 411.60 406.01 400.02 390.13 38).57 37e.97 251.1 435.53 431.51 425.14 422.82 417.89 412.63 407.08 398.09 394.87 387.0Q 260.0 440.10 436.17 429.98 427.73 422.96 417.93 412.68 404.21 401.19 394.73 280.0 450.49 44o.72 440.91 438.34 434.47 429.86 425.05 417.26 417.29 4'.-l3 4 0 300.u 401.10 45?.t1 452.C9 450.15 446.09 441.80 437.48 430.42 42.'1 423. "7

488 TABLX K-S (aX00T8O1 D) ENTHALPY OF.494 C2H6-C3H8 IN 8.T.U. E<I PIOUND USING POWERS GENERALIZED CORRFLATION PRESSURe (I/SQ.IN.) Tr oFpRATURf"F 100.0 11U0.O 1250.0 1300.0 1400.0 o500.C 1600.0 1750.0 190).0 2000.n 2.49 2.94 3.58 3.78 4.22 4.65 5.08 5.68 b. 2 -? r. 12.41 12.91 13.65 13.89 14*31 14.68 15.05 15.61 16.18 16.56 -? (. 22.25 22.73 23.47 23.*0 24.11 24.47 24.83 25.38 25.95 26.33 -?4,C. 32.19 32.63 33.31 33.53 33,93 34.31 34.68 35.25 35.81 36.20 -??0.^ 42.17 42.58 43.19 43o.0 43.b 4'.20 W4.60 45/17 45.73 46.11' -?hO.O 52.39 52.78 53.36 53.45 53.96. 34.37 54.78 55,35 55.90 56.27 -10O." 62.64 63.02 63.62 63.82 &4.23 14.64 65.04 65*61 66.15 66.51 -160.0 72.99 p73.37 73.99 74.20 746l1 15.01 75.41 75.96 75.47 76.82 -140.n dC.59 80.97 -81.60 81.81 82.f2 62.61 82.99 83.52 84.03 94.36 -12?;. 83.55 83.93 84.56 84.77 85.17 85.56 85.93 86.46 84.94 a7.?2 -1?".C 94.28 94.66 95.26 95.47 95.86 96.23 96.58 97.06 97.51 07.79 - 105.09 105.46 106.04 106.24 106.60 106.96 107.29 107.73 109.13 10P.39 -3q." 11i.10 116.46 117.02 117.21 117. 117.89 118.20 118.63 113.03 119.79 -U.0 127.30 127.64 128.17 128.35 128*67 128.98 129.28 129.70 13).11 130.3r -4:.0 13b.12 139.04 139.53 139.69 139.99 140.27 140.55 140.95 141.39 1*1.61 -?2.0 15U.44 150.72 151.16 151.31 151.ft 151.83 152.08 152.45 15?.92 153.r6 n.0 162.49 l1o. 13 163.10 163.23 L63.46 163.68 163.90 164.22 164.53 164.72?2.') 173.33 173.52 173.79 173.88 174.07 114.26 174.44 174.71 174.96 175.12'7.5 174.93 17>.11 175.36 175.45 1753.9 175.81 175.99 176.25 176.4u 176.65 4r." 1Bb.2S 108..37 188.45 188.49 188.80 189.09 189.13 189.23 189.41 18o.52.) 201.o6 201.75 201.76 201.75 201.92 202.08 202.02 201.95 201.' 7?"2.0r0,. 2i15.l 215.77 215.60 215.51 215,45 213.39 215.22 214.98 214.9P6 214.83 1 n)." 230.99 230.b66 230.13 229.96 229.60 2.9,23 228.90 228.57 228.46 228.46 12r.0 247.99 247.06 245.57 245.12 244.35 243.74 243,27 242.73 242.41 242.26 140.0 25d.31 256.73 255.05 254.56 253.42 252.34 251.76 251.06 25".50 250.10 ll.l 267.34 264.82 262.75 262.09 260.74 259.72 258.91 257.99 257.26 756.81 160.") 29LC.2 285.3U 281.06 279.83 277.97 274.84 275.78 274.15 272.72 271.89 1PO.O.122.11 310.97 302.49 300.65 297.43 294.89 292.88 290.57 268.79 2R7.79?On.O 349.67 338.50 325.82 323.44 318.83 314.68 311.17 307.52 305.23 304.16 2?0." 370.70 361.91 349.34 345.70 339.62 334.42 330.30 325.87 322.96 321.47 240.0 380.42 372.70 360.78 357.10 350.11 34.955 341.30 336.46 333.06 331~26 251.l 387.74 38U.44 369.31 365.77 359.65 354.45 350.06 344.92 341.14 339.09 260'." 4+3.19 397.15 387.81 384.76 379.07 373.93 369.32 363.57 35.3.06 356.53 29P",.0 417.97 412.70 404.70 402.07 396.90 392.03 387.58 381.74 371.85 374.03 30f.'

489 TABLE K-6 ENTHALPY QT,275 C2H6-C3H8 IN 9.T.U. Ptt< POUND JSING POWERS GENERALIZED CORRELATION TEMPERATURE PRESSURL (/SO.1IN.1 OF 0.0 100.0 50.0) 30!.U 400.0 500.0 600.0 750.0 803.0 900.0 -28v.U 237.61 1.84 1.22 1 1.44 1.4 1.7 2.20 2.92.1 1 2.49 -26(j.U 242.54 11.03 1C.33 13.49 10.69 10.99 11.45 12.34 12.63 12.09 -240.0 Z47.71 19.83 19.73 2U3. 20.3d 20.60 20.92 21.58 21.81 21.59 -2 0.3 253.10 29.75 29.62 29.84 30.09 30.35 30.73 31.26'31.45 31.35 -200.0 258*70 39.81 39.76 39.89 4U.08 40.32 40.59 41.23 41.42 41.26 -18i.0 264.35 49.60 49.84 49. 99 50.18 5C.29 50.28 51.20 51.47 51.15 -160.0 270.01 59.67 6b.05 60.18 60.35 60.39 60.24 61.19 61.56 61.34 -150.2 272.82 64. 7 65.,)7 65.17 65.36 65.40 65.22 66.13 66.55 66.41 -140.0 275.78 70.12 70.23 7 J.25 70.52 It.64 70.38 71.28 71.72 71.63 -12u.0 281l.68 80.78 80.25 R^.07 80.51 8C.88 80.55 81.43, 81.87 81.83 -100.0 287 12 90.87'9.;.36 9fJ. 2 90.44 90.84 91.39 91.99 92.28 92.13 -83.0 294*01 100.99 ICO.91 ICJ.92 100.85 1U1.12 101.95 102.74 102.87 102.69 -6u.0 300.49 111.51 111.l4 111.8u0 11.83 111.94 112.35 112.73 112.8q 113.39 -4U.O 307.16 122.53 122.57 122.80 122.91 123.00 123.15 123.50 123.69 124.25 -20.0 314.0e 133.99 133.75 134.02 134.15 134.31 134.52 135.16 135.36 135.40 O.0 321*10 145.57 145.42 145.91 146.10 146.18 146.37 146.86 147.01 147.02 1.6 321.67 146*55 146.38 146.88 147.07 147.14 147.33 147.80 147.95 147.96 20.0 J28.39 157.78 15d.19 158.32 158.37 158.50 158.79 158.91 158.87 40.0 335.90 326.13 171.32 170.83 170.64 170.77 170.85 171.07 171.17 171.C0 60.0 3436,3 334.55 1d4.59 184.22 183.03 183.43 183.53 183.80 183.54 183.36 80.0 351.59 343.18 197.80 196.82 196.53 196.67 196.61 196.49 196.1I 10.0O 359.79 352.66 211.76 210.72 210.48 210.26 210.22 21C.05 12C.u 368*23 361.72 349.54 343.64 228.72 226.25 225.56 224.96 225.16 224.63 127.4 371.1A 365.00 353.2e 348.27 32. 77 231.46 230.67 230.57 229.84 14,. 376.91 370.63 359.44 355.54 343.22.45.06 241.97 243.28 240.22 239.42 16.u i385.83 379.81 370.0C 366.21 357.21 342.84 2654 26.4 259.82 258.66 257.1C 18;.0.J95.00 3d9.46 380.51 7/1.07 369.03 359.12 343.27 286.6^ 282.61 277.47 2LJ0.u 404.4, 399.40 391.J5 3.2.85 380.62 372.24 361.97 337.64 324.06 303.86 213.0 405.85 400.88 392.63 389.49 382.42 374.10 364.46 341.82 731.02 308.84 221.0 414.C8 409.32 401.7 j9H.83 392.57 385.28 376.66 360.83 354.10 339.10 24,.O 423.99 419.53 412.45 419.85 404.17,97.70 390.32 378.37 j73.76 362.94 2t,..., 434.13 429.98 423.36 42'.91 415.63 +09.8o 403.66 393. 51 JP9.84 382.OC 28u. 44. 44.5 4.44. 3 6 43?.. 5 4 7.16. ~ 01 4 16.62 407.96 404.8 D 398. 1 t.'.0 455.U7 451.33 445.49 443. j7 4 38.88 4j4.16 429.22 421.31 41d.59 412.89

490 TABLE K-6 (CONTINUED) ctilliALPY OF.275 C2H6-C3HM IN B.T.U. PLt POUND JSING POWERS GENERALIZED CORRELATION PRESSUI, ( /bO.IN.) TFMPERArUR, 1L~tWJ.U IlOuX.. L~5.0 1300.0 ~).0 l.O 1600.0 1 ~750.~ 0 19(00.0 2C0C.0(~F l~.U I10u.L. 125U.0 1300.0 l't.O.O 0 luO.O 1600.0 1 750.0 1900.0 200(.~''.33 ~.73 3.3Z 3.51 3.91 4.31 4.70 5.27 5.83 6.21 -280.0 Il.~; 12.3C 12.90 13.10 13.4d 13.86 14.24 14.81 15.37 15.74 -260.0 l. o 22.02 22.64 22.84 23.21 23.57 23.93 24.49 25.05 25.42 -240.0 1.4c 31.82 32.43 32.62 32.99 33.35 33.71 34.27 34.82 35.19 -220.0 t1.41 41.79 42.37 42.56 42.93 43.30 43.66 44.21 44.76 45.13 -200.0.1.39 51.76 52.32 52.50 52.88 53.25 53.61 54.16 54.69 55.C6 -180.0 61.41 bl.77 62.31 62.50 02.87 63.24 63.60 64.14 64.66 65.02 -1&0.r 06.38 66.7P 67.28 67.46 07.83 68.20 68.56 69.09 69.61 t9.97 -150.? 71.55 71.90 72.45 72.63 73.00 73.36 73.72 74.24 74.75 75.10 -140.0 U1.79 82.14 82.68 82.86 83.22 83.57 83.92 84.42 84.92 95.26 -120.r 92.19 92.54 93.07 93.24 93.59 93.93 94.26 94.74 9'5.21 95.54 -100.0 132.63 103.1b 103.67 103.84 1)4.17 104.49 104.81 105.26 lr1..71 106.02 -80.0 113.58 113.'0 114.38 114.54 114.85 115.16 115.46 115.89 116.31 116.60 -6r.3 124.55 124.85 125.31 125.46 125.75 126.04 126.33 126.74 127.15 127.43 -40.0 135.74 136.02 136.45 136.59 136.86 137.13 137.40 137.79 138.19 138.45 -20.0 1i7.17 147.42 147.81 147.94 148.18 148.43 148.67 149.04 149.41 149.65 0.0 148.10 148.35 148.74 148.86 149.lu 149.35 149.59 149.96 150.32 150.56 1.6 i3.,O' 159.il 159.44 159.55 159.17 159.99 160.21 160.53 160.86 161.08 20.0 17..) 171.11 171.38 171.41 171.65 171.84 172.02 172.30 172.57 172.76 40.0 1..33 183.45 183.63 183.69 183.83 183.97 184.11 184.33 184.55 184.70 60.0 t.i.42 19b.46 196.52 196.60 196.81 196.89 196.91 197.04 197.19 197.25 80.0, i.01 210.06 209.95 209.99 210.1s 210.09 209.95 209.89 209.91 209.98 100.0 ~. 1. l'.24.-9 223.74 223.36 223.54 223.34 223.11 222.88 222.78 222.86 120.0.i:. 6O ~29.46 229.01 228.38 228.64 228.37 228.09 227.83 227.71 227.77 127.4 2->-.32 338.33 238.20 237.97?37.50 237.05 236.69 236.41 236.36 236.34 140.0 253.3)4 04.30 253.41 252.92 /52.11 251.45 250.95 250.52 250.35 250.15 160.0.7"4.31 e72.03 270.10 269.35 0h8.06 267.09 266.27 265.51 264.90 264.49 180.0.1.l.).~t.L2 tb7.78 286.68 235.24 284.24 283.07 281.47 280.10 279.38 200.0.,.9H c 95.,21 290.76 289.51 I87.83 286.70 285.53 283.90 282.50 281.68 203.0 3i s^,3 3'J.45 308.26 306.53 303.69 301.49 299.78 297.67 296.06 295.02 220.0'1i.74 340.88.30.63 328.27 323.84 320.05 317.21 314.18 312.41 311.17 240.0 -1.4k 344.53 352.34 349.13 i43.64 339.08 335.67 332.05 329.70 328.06 260.0 3i ).8( 33.42 372.08 368.87.163.29 358.64 354.83 350.46 347.29 345.21 20.0 4.0. f64 430.55 39U.94 37. 99 182.58 377.78 373.60 368.59 364.69 362.27 300.0

491 TABLE K-7 ENTHALEY OF TEENBABY B1ail0h IN B.T.0. PER POUND USING POWERS GENEBALIZ~D CORBELTXOI ~EPBlaATUJRE PRESSURE (#/SQ.IN.).F 0.0 100.0 250.0 300.0 400.0 500.0 O00.0 750.0 8C0.0 900.0 -2d0.0 237.84 0.98 0.83 1.11 1.54 1.60 1.79 2.54 2.87 3.06 -20o.0 243.92 12.22 12.11 12.17 12.29 12.48 12.81 13.41 13.63 13.8C -24,+.0 250.16 23.13 23.45 23.49 23.46 23.64 23.71 24.46 24.76 24.76 -2J4.i 251.78 25.97 26.37 46.41 26.38 26.54 26.53 27.32 27.65 27.64 -2,u.0 256.57 34.58 35.0S 35.10 35.04 35.19 35.07 35.80 36.18 36.34 -2vu.0 263.13 46.67 46.57 46.47 46.65 46.98 46.70 47.34 47.79 48.13 -lou.0 269.73 58.89 58.0i 57.73 58.08 58.67 58.44 59.10 59.54 59.86 -loo.0 276.36 69.67 69.56 69.52 69.73 70.36 71.36 71.62 71.60 -1,. 0 283.08 81.40 dl.49 81.41 81.36 81.81 82.41 82.59 82.99 -1^v.0 289.90 93.39 i3.52 93.41 93.40 93.47 93.80 94.01 94.65 -lu,.0 296.85 105.52 105.62 105.77 106.36 106.61 106.88 -ou.0 303.98 118.55 118.54 118.64 118.98 119.15 119.34 -u.0O 311.27 131.69 131.70 131.88 131.99 132.12'-x.O 318.72 145.C3 145.52 145.27 145.03 -L^.0 326.33 158.83 158.77 158.64 -io.0 327.86 161.61 161.56 161.26 v.0 334.12 326.79 173.11 4.0 342.09 335.36,~.0 350.25 343.73 z.O0 355.25 348.90 338.89 o.0O 358.59 352.40 342.85 339.17 ou.0 367.14 361.t5 352.76 349.41 341.81'uJ.O 375.90 370.79 362.67 339.69 353.18 345.78 336.89 14..0 384.66 380.11 372.67 309.97 364.17 357.76 350.44 338.03 333.66 322.78 lto.2 387.68 383.04 375.76 373.16 367.52 361.32 354.45 342.69 338.44 -329.36 1,j.0 394.04 389.64 382.7 J4d0.23 374.93 369.25 363.17 353.06 349.39 341.42 lou.C 403.45 399.29 392.86 390.57 385.75 380.66 375.33 366.65 363.58 357.07 lov.0 413.09 409.16 403.18 411.08 396.69 392.05 387.25 379.37 376.68 371.13 1~..0 419.00 415.30 409.51 407.49 403.30 398.87 394.45 387.15 384.64 379.51 ^..0 422.49 419.45 413.77 411.80 407.72 403.43 399.24 392.32 389.92 385.03 2.3. #433,10 429.82 424.48 4,2.63 418.83 414.85 411.09 404.94 402.78 398.45 x~.;) a443.45 440.33 435.33 4.3.60 430.05 426.34 422.80 417.35 415.42 411.55 Z:,,..0 45,4.01 451.G2 446.31 444.70 441.40 437.94 434.69 429.65 427.93 424.41 2ou.0 404.75 4o1.93 457.38 455.88 452.87 449.64 446.54 441.91 44G.39 437.06. Oug.O 475.10 473.04 468.62 407.23 464.48 461.44 458.47 454.17 452.83 449.66

492 TABLE K-7 (CONTINUED) EhrdALPY OF TEiiiiARBI ai14l IN B.T.U. FEB POUND USING POWERS GElERALBZE D CORBELATIOI PRaSSURB (T/Si.IN.) TBEPERATUiE F 1300.0 11Cl.0 1250.0 J1JO.C 1400.0 1500.0 1600.0 1750.0 1900.C 200C.0'2.94 3.56 4.52 4.83 5.27 5,66 6.C2 6.61 7.24 7.66 -.80.C 13.d1 14.36 15.1c 15.46 15.91 16.33 16.74 17.36 17.99 18.41 -2bO.C 24.d2 25.30 26.01 26.25 26.72 27.19 27.65 28.29 28.90 29.32 -24C.C 27.72 28.19 28.83 49.11 29.59 30.07 30.54 31.18 31.79 32.21 -234.9 3i.4 1 3b6.5 37.32 J7.55 38.04 38.53 39.02 39.66 40.26 40.67 -22".0 47.7d 4d.z3 d4.97 49.23 49.73 50.22 50.69 51.33 51.90 52.29 -20c., 59.,2 o3.C9 60.88 o1.15 61.65 62.13 62.58 63.18 63.71 64,07 -18C.0 71.53 72.00 72.78 73.04 73.52 73.97 74.39 74.91 75.35 75.65 -160.0 d3.29 d3.76 84.50 d4.75 85.20 85.62 86.01 86.46 d6.83 87.09 -14C.r 95.14 95.bC 96.3; 96.56 96.98 97.37 97.74 98.20 98.60 98.87 -120.C 107.17 117.61 1C8.29 1J8.52 108.91 109.27 109.61 110.09 110.54 110.83 -1CC.O 119.46 119.86 120.49 1L0.70 121.05 121.39 121.70 122.1i 122.62 122.96 -80.0 132.09 1J2.45 133. 0 133.17 133.49 133.79 134.07 134.48 134.85 135.08 -6C.O 145.13 145.40 145.80 145.93 146.19 146.44 146.68 147.01 147.3G 147.48 -4v.C 159.17 159.34 159.48 159.55 159.95 160.29 16C.38 160.54 160.77 160.88 -2r.0 161.54 161.6C7 161. 01.85 162.07. 162.28 162.44 162.65 162.85 162.97 -16.C 173.1b 173.34 173.41 113.41 173.64 173.82 173.79 173.74 173.77 173.83 G.C 188.22 188.17 188.CC 167.92 187.87 187.81 187.66 187.45 187.31 187.30 2C.r 204.31 203.45.J33.26 20.84 202.46 202.15 201.87 201.78 201.74 40C. i14.95 213.34 ^12.87 212.10 211.63 211.29 210.72 210.22 209.91 52.C i22.85 221.11.;-0.60 219.53 218.6C 218.15 217.39,16.62 216.14 6(." 242.67 239.09 J,8.23 236.84 235.81 234.85 233.28 231.93 231.25 8C.C;69.55 261.7C,9,.97 256.79 254.27 252.29 250.C9 248.34 247.34 10'.C J11.1)b 99.66 286.e8G 44.29 279.49 275.08 271.34 267.52 265.26 264.11 120.C 31d.J1 33d.17 "294.97 zi1.77 286.37 281.55 277.45 273.27 270.83 269.56 126.2 333.32 324.37 311.70 JJ7.97 301.41 295.99 291.64 286.87 283.67 281.95 14'.C 350.15 343.OC 332.25 3Z8.85 322.61 317.13 312.38 3C6.69 302.39 299.98 160.0 365.41 359.64 350.dl 347.91 342.25 336.97 332.14 325.93 320.86 317.96 18C.O 374.24 368.67 360.84:58.20 352.90 347.88 343.27 337.12 331.84 328.78 192.( 379.48 374.78 367.21 Jo4.74 359.68 354.86 350.45 344.41 339.07 335.94 200.0 394.%1 369.38 382.65 o03.72 376.11 371.60 367.48 361.70 356.46 353.34 220.C 437.o0 403.50 397.81 3o5.93 391.69 387.47 383.60 378.18 373.24 370.28 24C.c 423.32 417.21 412.,9 41C.38 406.53 402.67 399.09 394.09 389.56 386.82 260.C 433.65 430.51 425.0d 4Z4.03 420.70 417.41 414.20 409.69 405.55 403.01 28C.0 446.39 443.E6 438.9 437.38 434.54 431.78 428.94 424.90 421.15 418.80 30C.C

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