THE MEASUREMENT AND PREDICTION OF THE ENTHALPY OF FLUID MIXTURES UNDER PRESSURE by Victor Francis Yesavage A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the University of Michigan 1968 Doctoral Committee: Professor Associate Professor Professor Profes sor John E. Powers, Chairman Professor Robert H, Kadlec Donald Lo Katz Joseph J. Martin Richard E. Sonntag

ACKNOWLEDGMENTS The author wishes to express his appreciation and gratitude for the assistance of many people during the course of this research. I would like to thank Professor John E. Powers, chairman of my thesis committee, for his encouragement and guidance. I would like to thank Professors Donald L. Katz, Richard E. Sonntag, Joseph J. Martin, and Robert H. Kadlec for serving on the doctoral committee. I especially would like to thank Alan E. Mather and Joseph C. Golba who contributed greatly to this work by their efforts on the enthalpy project. Thanks are also due to Joseph Boisseneault, and Andre Furtado for their efforts while working on the project. In addition thanks are due to J. C. Golba, Jr., I.J.S. Sehgal, C. Albright, S. Engel, and R,. Giszczak for reduction of the data and preparation of diagrams. Many thanks are due to members of the ORA Instrument Shop, particularly E. Rupke and H. Senecal. I would also like to thank members of the Department of Chemical and Metallurgical Engineering staff including C. Bolen, D. Connell, and F. Drogoss for their assistance in solving mechanical and analytical problems. I also wish to thank N. Prodany and A. Hedjmadi for many useful discussions during the course of this work. I wish to thank Mrs. Margo Kaplin and Miss Patricia Williams for their efforts in the preparation of this manuscript. In addition I would also like to thank the following organizations for their equipment and financial support. ii

The Natural Gas Processors Association for support of the research and for fellowships. The American Petroleum Institute for additional support of the research. The Southern California Gas Company for the supply of methane used in this work. The Dow Chemical Company for the gift of a large quantity of Styrofoam. The National Bureau of Standards for the calibration of thermocouples ahd standard cells. Finally, I would like to thank my parents for all they have given me. iii Z G

TABLE OF CONTENTS Page ACKNOWLEDGMENTS................................................. ii LIST OF TABLES............................................. Viii LIST OF FIGURES................................................. xiii NOMENCLATURE.. XVe................................... xvii ABSTRACT................................................ xxi INTRODUCTION.......................................... 1 SECTION I - PRELIMINARY CONSIDERATIONS.......................... 4 Flow Calorimeters.......................................... 4 Isobaric Effect of Temperature on Enthalpy............ 4 Isothermal Effect of Pressure on Enthalpy............. Isenthalpic Effect of Pressure on Temperature......... 6 Previous Experimental Data................................6 Methane.................................7............. 7 Propane........................................... 7 Methane-Propane Mixtures.............................. 8 Interpretation of Data.................................. 9 Graphical Interpretation............................. 10 Computer Reduction............................12 Extension to Low Pressures........................... 14 Enthalpy Change on Vaporization....................... 15 SECTION II - METHODS OF PREDICTION..........0.................. 17 Statistical Mechanics Background................. 17 Fundamental Equation of State........................ 17 Intermolecular Potential Functions................. 18 Partition Functions................................ 18 iv

Page Physical Models................................... 20 Direct Calculations....******. **........ 20 Pair Distribution Functions............................ 21 Methods of Prediction Based on Thermodynamic Data.......... 23 Estimation of Partial Enthalpies..................... 23 Equivalent Pure Component Method..................... 25 Application of PVT Data.............................. 26 Application of Equations of State................... 27 Generalized Corresponding States Correlations......... 29 SECTION III - THE MODIFIED FLOW SYSTEM.....e............ 39 Description of Equipment....................... 42 Calorimeters................... 56 Measuring Instruments............................. 57 Electrical Measurement.......................... 59 Procedure...............*..... ****. 00 61 SECTION IV - THE ENTHALPY OF PROPANE UNDER PRESSURE............ 63 Regions of Measurement..................................... 63 Composition of Gas............oo........... 6 65 Flowmeter Calibrations........................... 66 Results.o...........0..................*....<.. 69 Enthalpy Change on Vaporization.................. 69 Isobaric Data............................... 71 Isothermal Data............................ 76 Isenthalpic Data................................... 83 Analysis and Comparison of Results......................... 83 Isobaric Data................................ 83 Isothermal Data..........................**...** 88 v

Page Isenthalpic Data.................................. 88 Enthalpy Diagram and Tables................................ 91 SECTION V - THE ENTHALPY OF METHANE-PROPANE MIXTURES UNDER PRESSURE............. o................. o o...................... o 106 The 76.6 Mole Percent Propane in Methane Mixture.......... 106 Composition of Gas.................................... 106 Regions of Measurement................................ 107 Flowmeter Calibrations................................ 110 Check on Assumption of Adiabaticity................. 112 Interpretation of Results.................................. 11 Isobaric...................................O........ 113 Isothermal............................................ 125 Isenthalpic......................................... 130 The 50.6 Mole Percent Propane in Methane Mixture........... 130 Composition of Gas 15...................... 130 Regions of Measurement............................... 130 Flowmeter Calibrations............................... 135 Check on Assumption of Adiabaticity................ 139 Interpretation of Results................................. 139 Isobaric............................................. 139 Isothermal.............................. 142 Isenthalpic.........................................154 Consistency Checks.................*.................. 156 Enthalpy Diagrams......................................... 156 The 76.6 Mole Percent Propane in Methane Mixture...... 156 The 50.6 Mole Percent Propane in Methane Mixture...... 167 Comparison with Other Published Data................... 167 vi

Page Enthalpy Data.................................... 167 Phase Behavior..................................... 172 Enthalpy of the Methane-Propane System..................... 172 SECTION VI EVALUATION AND EXTENSION OF METHODS OF PREDICTION.. 177 Comparison of Methods of Prediction........................ 177 Isobaric Enthalpy Differences........................ 178 Enthalpy Departure Comparisons....................... 184 Conclusions e o o..................e a......................... 187 Application of the Corresponding States Principle to Fit Experimental Enthalpy Data.............................. 188 Development of the Reference Substance Enthalpy Departures.......e e................................ 189 Application of Reference Sustance Equations to Pure Components............,................... 193 Application of the Correlation to Mixtures............ 197 Comparison with Other Mixing Rules.............................. 206 Extension to a Mixture of Nitrogen in Methane......... 215 Discussion of Results................................... 218 SUMMARY AND CONCLUSIONS...................................... 220 RECOMMENDATIONS FOR FUTURE WORK........................ o..... 222 APPENDIX A - Calibrations............... o................ 223 APPENDIX B - Experimental Data............................. 226 APPENDIX C - Computer Programs......................... 240 APPENDIX D - Data and Results of Corresponding States Correlation.. o o... o.......................................... 257 BIBLIOGRAPHY............ o...o..........................o..... 275 vii

LIST OF TABLES Table Page I. Impurity Content of Propane...................... 65 II. Calibration Table Used In Interpreting Experimental Results................................. 68 III. Illustration of Consistency of Calibration Equations for High and Low Flow Rates at Intermediate Flow Rates.................................... 68 IV. Experimental Values of Latent Heats of Vaporization for Propane............................. 71 V. Maximum Values of C for Propane................. 7 p VI. Experimental Values of Isobaric Heat Capacity, C, for Propane.................................. 77 P VII. Experimental Values of Isobaric Heat Capacity, C, Near the Saturation Curve and in the Vicinity oY C (T) Maxima.................................. 78 VIII. Experimental Values of the Isothermal Throttling Coefficient for Propane......................... 81 IX. Experimental Values of the Joule-Thomson Coefficient for Propane.............................. 83 X. Test of Consistency of Data Based on Equation (8). 92 XI. Tabulated Values of Enthalpy for Propane at Saturation Conditions.......................... 102 XII. Tabulated Values of Enthalpy for Propane......... 103 XIII. Composition of Nominal 77 Mole Percent Propane in Methane Mixture.............................. 107 XIV. Calibration Data Used in Interpreting Experimental Results.............................. 112 XV Tabulated Values of Isobaric Heat Capacities for a Nominal 77 Mole Percent Propane in Methane Mixture 1........................... 16 XVI. Supplemental Table of Experimental Values of Isobaric Heat Capacity........................... 120 viii

Table Page XVII. Properties of the Nominal 77 Mole Percent Propane in Methane Mixture at the Phase Boundaries........................... 124 XVII. Experimental Values of the Isothermal Throttling Coefficient, p, for a Nominal 77 Mole Percent Propane in Methane Mixture............. 127 XIX. Experimental Values of the Joule-Thomson Coefficient,, at -96.2~F, for the-Nominal 77 Mole Percent Propane in Methane Mixture............... 132 XX. Composition of Nominal 51 Mole Percent Propane in Methane Mixture as Determined by Chromatographic Analysis..................................... 135 XXI. Calibration Data Used in Interpreting Experimental Results........... o...... o..................... 138 XXII. Effect of Calibration Equation on Isobaric Heat Capacity Results............................. 138 XXIII. Tabulated Values of Isobaric Heat Capacities for a Nominal 51 Mole Percent Propane in Methane Mixture.............................. 143 XXIV. Supplementary Table of Experimental Values of Isobaric Heat Capacity.....o................ 146 XXV. Properties of the Nominal 51 Mole Percent Propane in Methane Mixture at the Phase Boundaries.. 149 XXVI. Experimental Values of the Isothermal Throttling Coefficient, p, for a 51 Mole Percent Propane in Methane Mixture................e.................. 152 XXVII, Experimental Values of the Joule-Thomson Coefficient,., at -149.0~F for the 51 Mole Percent Propane in Methane Mixture....................... 154 XXVIII. Tabulated Values of Enthalpy for the Nominal 77 Mole Percent Propane in Methane Mixture.......... 159 XXIX. Tabulated Values of Enthalpy for the Nominal 51 Mole Percent Propane in Methane Mixture.......... 162 XXX. Test of Consistency of Data Based on Equation (8). 171 XXXI. Test of Consistency of Data Based on Equation (8). 173 ix

Table Page XXXII. Correction Made in Jones' Table to Agree With Douslin's Enthalpy Departures.................... 192 XXXIII. Parameters Used in Corresponding States Calculations............................ 194 XXXIV. Test of Three Parameter Corresponding States Principle Using Data for Nitrogen................ 196 XXXV. Original Optimum Values for the Three Pseudoparameters in the Search Calculations............ 199 XXXVI. Optimum Values of Parameters After Fitting Pseudocritical Temperature and Holding it Constant in Optimization........................ 203 XXXVII. Final Fit Optimum Parameter Values............... 203 XXXVIII. Root Mean Square Deviations of the Results of This Study and Numerous Mixing Rules for the Methane-Propane System........................... 204 XXXIX. Differenced Results for the 5.1 Mole Percent Mixtures....................................... 207 XL. Optimum Values of Pseudocritical Parameters with Third Parameters, W, Held Constant............... 210 XLI. Root Mean Square of Deviations of the Results of This Study and Numerous Mixing Rules For a Methane-Nitrogen Mixture......................... 216 XLII. Thermopile M-3 Calibration for Isobaric Calorimeter...................................... 224 XLIII. Thermopile M-4 Calibration for Isobaric Calorimeter............................... 224 XLIV. Thermopile M-5 Calibration for Throttling Calorimeter.................................... 225 XLV. Thermopile M-6 Calibration for Throttling Calorimeter..................................... 225 XLVI. Tabulated Experimental Isobaric Data for Propane. 227 XLVII. Tabulated Experimental Isothermal Data for Propane.............................. 229 XLVIII. Tabulated Experimental Joule-Thomson Data for Propane.......................................... 230 x

Table Page XLIX. Flowmeter Calibration Equation Constants Used for Propane............................. 230 L. Tabulated Experimental Isobaric Data for the Nominal 77 Percent Mixture..,..............o.... 231 LI. Tabulated Experimental Isothermal Data for the Nominal 77 Percent Mixture...................... 234 LII. Tabulated Experimental Joule-Thomson Data for the Nominal 77 Percent Mixture.,................ 235 LIII. Flowmeter Calibration Equation Constants Used For the Nominal 77 Percent Mixture................ 235 LIV. Tabulated Experimental Isobaric Data for the Nominal 51 Percent Mixture...........,...... 236 LV. Tabulated Experimental Isothermal Data for the Nominal 51 Percent Mixture....,o..o...o.......... 238 LVI. Tabulated Experimental Joule-Thomson Data for the Nominal 51 Percent Mixture................. 239 LVII. Flowmeter Calibration Equation Constants Used for the Nominal 51 Percent Mixture.................. 239 LVIII. Program for Fitting Isobaric Data............... 241 LIX. List of Variables for Isobaric Data Fitting Programoo........................................ 245 LX. Program for Optimization of Parameters in Corresponding States Correlation................. 248 LXIo List of Variables for Corresponding States Calculation and Parameter Optimization Program...... 253 LXII. Reduced Enthalpy as a Function of Reduced Temperature and Reduced Pressure for Propane.... 258 LXIII. Reduced Enthalpy as a Function of Reduced Temperature and Reduced Pressure for Methane..... 259 LXIV. Results of Corresponding States Correlation for Methane-Propane Mixtures Using Optimum Values Determined for the Parameters.................... 260 LXVo Results of Corresponding States Correlation for Methane-Propane Mixtures Using Optimum Parameters with Smooth Pseudocritical Temperatures......... 265 xi

Table Page LXVI. Results of Corresponding States Correlation for Methane-Propane Mixtures Using Smoothed Optimum Parameters................................. 270 xii

LIST OF FIGURES Figure Page 1. Vapor-Liquid Equilibrium Envelope of the MethanePropane System............................. 41 2. Flow Diagram of Modified Recycle System.............. 44 3. View of Storage Tanks with the Front of the Insulated Box Removed.................................0. *........ 46 4. View of Calorimeter Bath Area.................... 48 5. Valve Panel with the Front of Insulated Box Removed,.. 53 6. View of Insulated Valve Panel*..................... 54 7. Control Area of Modified Flow System................ 55 8. Wiring Diagram of Power Measurement Circuit.......... 60 9. Temperatures and Pressures of Measurement for Propane. 64 10. Results of Flowmeter Calibrations for Propane......... 67 11. Enthalpy Differences for Propane in the Two-Phase Region............................................... 70 12. Isobaric Heat Capacity for Propane at 1000 psia in the Upper Temperature Range...................... 72 13. Isobaric Heat Capacity in the Critical Region at the Critical Pressure for Propane......................... 74 14. Isobaric Heat Capacity at 500 psia in the Gaseous Region for Propane..............................* 74 15. Isobaric Heat Capacity for Propane................... 75 16. Isothermal Throttling Coefficient for Propane Above the Critical Temperature............................ 80 17. Isothermal Throttling Coefficients for Propane....... 82 18, Isenthalpic Curves for Propane with a 21.2~F Initial Temperature...................................... 84 19. Pressure-Enthalpy Isotherm Generated from Isenthalpic and Isobaric Data................,...,... e..o...... 85 20. Experimental Data at 700 psia and Comparison with Results of Finn...,,........o.00,................ 87 xiii

Figure Page 21. Comparison of Experimental Heat Capacities with Tabulated Values of Kuloor et al. (69)............... 88 22. Comparison of Isothermal Enthalpy Departure with Data for Yarborough and Edmister..og.....o.......... 90 23. Range of Tables and Charts of Thermodynamic Properties of Propane....................................... 93 24. Range of Calorimetric Data Used in Preparation of Pressure-Enthalpy-Temperature Table for Propane....... 94 25. Checks of Thermodynamic Consistency of Thermal Data for Propane................................. 97 26. Pressure-Temperature-Enthalpy Diagram for Propane..... 100 27. Comparison of Tabulated Enthalpies of This Investigation with Those of Canjar and Manning................. 105 28. Composition of the Nominal 77 Percent Mixture as a Function of Time...................................... 108 29. Temperatures and Pressures of Measurement for the Nominal 77 Percent Mixture.......................... 109 30. Results of Flowmeter Calibrations for the Nominal 77 Percent Mixture............................. 111 31. Heat Capacity as a Function of Reciprocal Flow Rate for the Nominal 77 Percent Mixture.................... 114 32. Isobaric Heat Capacity at 1000 psia in the Upper Temperature Range for the Nominal 77 Percent Mixture.. 115 33. Isobaric Heat Capacity at 500 psia in the Gaseous Region for the 77 Percent Mixture...................... 119 34. Isobaric Heat Capacity for the Nominal 77 Percent Mixture............................................... 122 35. Enthalpy Differences for the 77 Percent Mixture in the Two-Phase Region.................................. 123 36. Isothermal Throttling Coefficient for the 77 Percent Mixture at 201~F.........o,. e,000....0,,........ 126 37. Isothermal Throttling Coefficient for the 77 Percent Mixture............................................... 128 xiv

Figure Page 38. Isothermal Enthalpy Differences Through the Two-Phase Region at 100~F for the 77 Percent Mixture............ 129 39. Joule-Thomson Coefficient for the 77 Percent Mixture at -96 2~F......9.. * 00 000a o... *o.0@0..*0 0 0 151 40. Composition of the Nominal 51 Percent Mixture as a Function of Time.................................. 153 41. Temperatures and Pressures of Measurement for the Nominal 51 Percent Mixture........................... 154 42. Results of Flowmeter Calibrations for the Nominal 51 Percent Mixture 13......6....................... 156 43. Heat Capacity as a Function of Reciprocal Flow Rate for the Nominal 51 Percent Mixture.................... 140 44. Isobaric Heat Capacity at 1500 psia in the Upper Temperature Range for the Nominal 51 Percent Mixture.. 14L 45. Isobaric Heat Capacity for the Nominal 51 Percent Mixture........................................ 147 46. Enthalpy Differences for the 51 Percent Mixture in the Two-Phase Region......................... 148 47. Isothermal Throttling Coefficient for the 51 Percent Mixture at 152.2~F.......1....... 0 *.** 0..000.... 150 48. Isothermal Throttling Coefficient for the 51 Percent Mixture............................................... 155 49. Joule-Thomson Coefficient for the 51 Percent Mixture at 149 0~F.... O00..... 0 * 4................ 0000 155 50. Checks ofT Thermodynamic Consistency of Thermal Data for the 77 Percent Mixture.......................... 1557 51. Checks of Thermodyn-amic Consistency of Thenral Data for the 51 Percent Mixture.........................** 158 52. Pressure-Temperature-Enthalpy Diagram for the 77 Percent Propane in Methane Mixture.................... 160 55. Pressure-Temperature-Enthalpy Diagram for the 51 Percent Propane n Methane Mixture................... 61 xV

Figure Page 54. The Effect of Pressure on C at Low Temperatures Including Comparison with Data of Cutler and Morrison (23)..A............8.......................... 168 55. The Effect of Pressure on C at High Temperatures Including Comparison with Published Values of Rossini et al.(118)............................. 170 56. Comparison of Experimental Isothermal Enthalpy Departures with the BWR Equation of State for the 50.6 Percent Mixture......................... 175 57. Comparison of Isobaric Enthalpy Differences with Numerous Methods of Prediction........................ 182 58. Comparison of Isothermal Enthalpy Departures with Numerous Methods of Prediction for the 77 Percent Mixture ****.*.*** *aa..........**....o..... 185 59. Comparison of Enthalpy Departure of Methane at 32~F Obtained Using Original BWR Equation (7) with Results Calculated by Douslin (34,35)*................**......o 191 60. Optimum Mixing Rules for the Methane-Propane System.o. 200 61. Comparison of Experimental Enthalpy Departures for the Methane-Propane System with the Results from the Corresponding States Correlation and Mixing Rules of this Investigation.................... a............... 205 62. Comparison of Experimental Enthalpy Departures for the Methane-Propane System with Results from the Corresponding States Correlation of This Investigation and Mixing Rules of Leland-Mueller (74)................... 209 63. Mixing Rules for Pseudocritical Temperature for the Methane-Propane System...................... 212 64. Mixing Rules for the Pseudocritical Pressure for the Methane-Propane System............................ 213 65. Mixing Rules for the Third Parameter for the MethanePropane System....................... 214 66. Comparison of Experimental Enthalpy Departures for a Methane-Nitrogen Mixture with Results from the Corresponding States Correlation of this Investigation Using Several Mixing Rules........................... 217 xvi

NOMEMCLATURE o, c, d, e a,b, c A A,B,C,D Af B' C D' E' A",B",C"'D",E" B BoP. C P D e E f F F g(2) H J k K M.A.B.P. Constants used in Equation (18) Constants in BWR Equation Helmholtz free energy Constants in flowmeter calibration equation Constants in BWR Equation Empirical constants for mixing rules Empirical constants for mixing rules Second virial coefficient Normal boiling point Isobaric heat capacity Correction term of Lydersen, Greenkorn, Hougen correlation Base of natural logarithm Total energy Symbol for a functional relationship Mass flow rate Root mean square deviation of enthalpy departure Pair distribution function Specific enthalpy Partial molal enthalpy Expression in mixing rule of Joffe-Stewart, Burkhardt, Voo Boltzmann constant Expression in mixing rule of Joffe-Stewart, Burkhardt, Voo Molal average boiling point xvii

N Number of molecules P Pressure Rate of transfer of heat Q Configurational integral r Correction factor in mixing rule of Prausnitz, Gunn r Distance R Gas constant s Correction factor in mixing rule of Prausnitz-Gunn T Temperature u Configurational energy U Specific internal energy V Volume V Specific volume w Rate of transfer of work W Third parameter used in this investigation x Mole fraction y Mole fraction z Compressibility factor Z Canonical ensemble partition function a Constant in mixing rule of Leland-Mueller ay Constants in BWR Equation B3y Expression in mixing rule of Prausnitz, Gunn A Difference ~e~ ~Molecular energy parameter p. Joule-Thomson coefficient ~p.?~ Viscosity xviii

p CP Subscripts c i,j m mix r r t v x 0 1 1 11 12 2 2 22 Superscript 0 Density Molecular distance parameter Summation Isothermal throttling coefficient Intermolecular potential energy Accentric factor Critical point property Components in a mixture Energy state Mean Value Mixture property Rotational contribution Reduced property Translational portion Vibrational portion Mixture property Reference substance property Component 1 Inlet condition Component 1 Interaction between component 1 and component 2 Component 2 Outlet condition Component 2 Zero pressure value xix

Conversion 1 Btu 1 lb 1 psi 1~R 0~F Factors for Units Used in This Study 1054.6 J(kg ms 2) 0.45359 kg 1.48907x10 kg m-1-2 oK/1.8 459.6~R XX

ABSTRACT THE MEASUREMENT AND PREDICTION OF THE ENTHALPY OF FLUID MIXTURES UNDER PRESSURE by Victor Francis Yesavage Chairman: Professor John E. Powers The objectives of this research are (1) to modify the existing recycle flow calorimetry system in order to extend its capabilities to mixtures with higher critical temperature, (2) to complete the experimental investigation of the effects of pressure and temperature on the enthalpy of the methane-propane system at elavated pressures, (3) to use the data obtained as a basis for comparison of methods of prediction of enthalpies of mixtures, and (4) to extend methods of prediction to represent the available data. Before obtaining measurements of enthalpy for propane and propane rich methane-propane mixtures with the recycle flow system, it was necessary to eliminate the possibility of severe composition and flow upsets. These upsets were caused by large parts of the system being at room temperature, and the presence of two-phase flow in parts of the system where liquid holdup was present. The modified flow system uses a steam heated/cooled Corblin diaphragm compressor for recycling the fluid. The valve panels, buffer tanks, and connecting lines are maintained at temperatures of 250~F. The calorimeter bath section consists of a series of baths connected such that the fluid, which may be a twophase mixture in this part of the system, always flows in a downward direction. Two calorimeters, an isobaric and a throttling calorimeter, are used interchangeably in the system. The throttling calorimeter is xxi

used isothermally at higher temperatures and as a Joule-Thomson device for liquids. The effects of pressure and temperature on the enthalpy of propane, and 76.6 and 50.6 mole percent propane in methane mixtures were measured. Data were obtained at temperatures from -250 to +300~F at pressures from 100 to 2000 psia in the liquid, two-phase, critical, and gaseous regions. The data were internally self consistent for each mixture to about ~0.2 percent. Enthalpy-pressure-temperature tables and diagrams were prepared at pressures up to 2000 psia vwith the aid of data from the literature. For propane the table extended from -280 to +500~F and for the mixtures from -280 to +300~F. These tables are believed to be accurate to 1 Btu/lb. These results together with the previous experimental results for methane and a 5.1, 11.7, and 28.0 mole percent propane in methane mixture should adequately represent the methane-propane binary system. Direct experimental data of this type and accuracy are rare in the literature. Experimental data were used to compare results from several published methods of prediction. This study indicated that the corresponding states principle is a fruitful approach for extending methods of prediction to represent enthalpy behavior. A three parameter corresponding states correlation was developed which uses reference reduced enthalpy tables developed from data for methane and propane. The correlation is valid between reduced temperatures of 0.5 and 1.5 at values of reduced pressure up to 3.0. Values of enthalpy departures for nitrogen calculated from the correlation agreed with experimental results to within the experimental uncertainty of the data. This supports the validity of the three parameter corresponding xxii

states principle for pure component enthalpy departures. The correlation was extended to methane-propane mixtures by determining an optimum set of mixing rules containing six empirical constants. This correlation predicted enthalpy departures for the mixtures -which agreed with experimental results almost to within experimental uncertainty (generally 1 Btu/lb), This established the validity of the principle of corresponding states for mixtures of nonpolar, mutually nonconformal components. The mixing rules obtained were compared with other rules available in the literature, and the correlation was successfully applied to a methane-nitrogen mixture. xxiii X.Xll

INTRODUCTION A knowledge of enthalpies of fluid mixtures over a wide range of pressure and temperature is necessary for accurate engineering designs of thermal processes. The goal of this research is to increase this knowledge by obtaining accurate experimental data and extending the available methods of prediction of enthalpies of fluids making maximum use of the experimental data. In the past most enthalpies of fluids at elevated pressures have been calculated by differentiation of volumetric data, However, this method limits the accuracy of the enthalpy data obtained. In addition, accurate volumetric data for mixtures are not in great abundance and the determination of enthalpy changes across the two-phase region involves the use of not only volumetric data and derivatives but also vapor-liquid equilibrium data and derivatives. For these reasons it is desirable to have direct experimental determinations of the enthalpy behavior of fluid mixtures under pressure. These data are quite scarce in the literature, IDue to the unlimited number of mixtures which may exist and the limited amount of reliable data, an experimental approach must be used which allows considerable generalization. The Thermal Properties of Fluids Laboratory at the University of Michigan has in the past accurately measured enthalpies of fixed gases and their mixtures over a wide range of conditions by direct flow calorimetry. Systems investigated have included methane, nitrogen, one methane-nitrogen mixture, and several mixtures of methanesrich methane-propane mixtures. A specific purpose of this research has been to expand the capabilities -1

of the calorimetric facility so that data could be obtained for propane and propane-rich methane-propane mixtures. Determinations for these mixtures and propane would result in an accurate knowledge of the enthalpy behavior of a binary system with two components of considerably different molecular type. In addition the modified system could be used in the future to make additional measurements of mixtures or pure components with critical temperatures less than that of propane. Hopefully, such an approach would permit evaluation and extension of methods of prediction so that eventually further experimental determinations of light hydrocarbon and fixed gas mixtures could be calculated a priorio There are many different methods of prediction which have been 140 proposed for enthalpies of fluid mixtures. A comparison study has been made by the American Petroleum Institute of these numerous enthalpy correlations. The data used in the investigation, however, were not plentiful and consisted mainly of data derived from volumetric properties. Data were especially lacking in the critical region. Therefore, current methods of prediction are still limited to questionable uncertainty at least in the critical region. The availability of more accurate enthalpy data based on calorimetric determinations provides an improved basis for comparison of available methods of prediction. Such comparisons serve to focus attention on methods that have potential both for accurate prediction of enthalpy data and extension to systems for which data are not available. Therefore, the specific goals of the present research were (1) to extend the capabilities of the recycle flow system, (2) to make experimental enthalpy determinations on propane and two propane-rich methanepropane mixtures, (3) to evaluate the available methods of prediction,

-3and (4) to select a potentially fruitful method and extend it to accurately represent tie available data over a wide range of conditions.

SECTION I - PRELIMINARY CONSIDERATIONS This introductory section presents a discussion of flow calorimetry and the necessary equations which are applied, a discussion of the data in the literature, and a summary of the techniques used in interpreting the experimental data obtained in this investigation. Flow Calorimeters The measurement of enthalpies of fluids at elevated pressures has been made by a number of methods. A review of experimental methods published recently by Barieau3 supplements earlier work by Masi and 40 Faulkner. Flow calorimeters have many advantages and have been used widelyo The calorimeter may be designed to operate in a number of differing modes depending upon the type of enthalpy data desired. In general they are used to measure the isobaric effect of temperature on enthalpy, the isenthalpic effect of pressure on temperature, the isothermal effect of pressure on enthalpy, and the effect of composition on enthalpy at constant temperature and pressure, In the present investigation the first three of the above effects have been studied, The first law of thermodynamics, applied to a flow calorimeter with negligible potential and kinetic energy effects, is IH T2,P2 -= - (1) T -2 -T1 P F where q is the rate of heat transfer, w the rate of work done, and F is the mass flow rate. Isobaric Effect of Temperature on Enthalpy To measure the isobaric effect of temperature on enthalpy the

-5pressure difference P - P is made as small as possible, and energy is added to the fluid to change its temperature. A small correction is made for the fact that the pressure is not constant. For a calorimeter with electrical energy input, -., and negligible heat leak, q, Equation (1) becomes P T 2 T) P, F1() dP1 T (2) Several types of flow calorimeters have been developed to determine the isobaric effect of temperature on enthalpy,. Partington and 98 Shilling98 present a review of the early designs. The isobaric calorim40 eter of Faulkner, which is used in this investigation, utilizes electrical heating in the internals of the calorimeter followed by passage of the fluid through a series of concentric shells to ensure uniformity of temperature. Heat leakage is reduced to negligible proportions by heating a radiation shield located in the vacuum jacket to the temperature of the exiting gas, Isothermal Effect of Pressure on Enthalpy The measurement of the effect of pressure on enthalpy can be accomplished by causing a pressure drop in the flowing fluid. Energy is added so that the inlet temperature is equal to the outlet temperature. From a knowledge of the flow rate, the energy input, and the pressure drop, the isothermal effect of pressure on enthalpy can be determined by P 2 P C T I (3) T (~~ ~P ~ 2 ~ d~p2(5

-6 where q is assumed to be negligible and the integral term is a correction for any slight difference between inlet and outlet temperatures. The calorimeter recently developed by Mather5 and used in this study uses a capillary coil to induce the pressure drop with an insulated heating wire coaxially inserted into the capillary. The gas exiting from the capillary is passed through a series of concentric baffles to ensure uniformity of temperature, and the input of electrical energy to the internal heating wire is adjusted to make the outlet temperature of the fluid equal to the inlet temperature, therefore making the entire process very nearly isothermal, Isenthalpic Effect of Pressure on Temperature The isenthalpic mode of flow calorimetry was first studied by 64 Joule and Thomson, In this type of experiment the fluid is throttled from a high pressure to a low pressure in an isenthalpic expansiono Equation (1) becomes H -H= 0 (4) T2,P2 iP1 56 Hoxton gives a good summary of the experimental work in this 59 area prior to 1920. Johnston and White review the Joule-Thomson determinations from 1920 to 1948. These summaries have been brought up to date (1967) by Yesavage et al. Previous Experimental Data All of the above methods have been used to obtain thermal data of fluids at elevated pressures. Most of the results have been for pure 84 5 components, Reviews of data have been prepared by Masi, Barieau Johnston and White9 Potter5 77A recent reviewof the availJohnston and White, Potter, and Mage, A recent review of the avail

-7 able mixture data at elevated pressures has been presented by Yesavage 152 85 et al. and Mather. Methane For methane a compilation of thermodynamic properties including a 159 comprehensive literature search is presented by Tester et al.9 Since this compilation was published additional determinations were made 62 g129 18.142 by Jones, Sahgal et al. Colwell, Gill, and Morrison, Vennix, Douslin et al.3 and Huang.57 Propane A similar compilation of the thermodynamic properties of propane 69 is presented by Kuloor, Newitt, and Bateman. Since that time additional determinations have been made by Dittmar, Schulz, and Strese3 51 l148 59 57 Helgeson and Sage5 Yarborough and Edmister, Ernst, Huang, and 42 Finn. Several of these previous determinations are similar to the present investigation in that they contain experimental measurements of the thermal properties of propane. Gaseous heat capacities at atmospheric pressure have been reported by Kistiakowski and Rice,7 Dailey and 25 128 Felsing25 and Sage Webster, and Lacey. Saturated liquid heat 66 26 capacities are given by Kemp and Egan, and Dana et al. JouleThomson coefficients have been measured by Sage, Kennedy, and Lacey125 in the gaseous region. The isothermal effect of pressure on enthalpy 148 has been measured by Yarborough and Edmister8 at pressures up to 1000 psia at temperatures between 200 and 400~F. Latent heats of vaporiza26 66 tion have been reported by Dana et al., Kemp and Egan, Sage, Evans, 124 51 and Lacey24 and Helgeson and Sage. The specific heat at constant pressure at 700 psia, about 80 psi above the critical point, has been

-8 reported by Finn. Gaseous heat capacities have been measured by Erns9 between temperatures of 68 and 176~F at pressures up to 118 psia. Methane-Propane Mixtures A review of the physical properties data available for the methanepropane system, including vapor-liquid equilibrium, compressibilities, Joule-Thomson coefficient, enthalpy changes on vaporization, heat capacities, viscosities, thermal conductivities, and surface tension has 85 been presented by Mather. For these mixtures a few experimental thermal properties investigations have been made. Joule-Thomson coefficients have been reported for three mixtures of methane-propane by Budenholzer et al. at pressures up to 1500 psia in the temperature range between 70 and 310~F. Head50 measured Joule-Thomson coefficients for a mixture of 51.1 mole percent propane in methane at pressures up to 40 atm between 260 and 3600K in the single phase region. 23 Cutler and Morrison have measured the vapor pressures and heat capacities of saturated liquid mixtures of methane-propane in the temper52 ature range of 90 to 110~K. Dillard presents values of the isothermal effect of pressure on enthalpy for two methane-propane mixtures in the region between 90 and 200~F at pressures up to 2000 psia. Manker obtained isobaric data on a nominal 5 percent propane in methane mixture at temperatures from -245 to 87~F at pressures from 250 to 2000 psia. Mather5 obtained data on the isothermal effect of pressure on enthalpy for this mixture at pressures up to 2000 psia in the temperature range of -147 to 2010F and extended the isobaric data to +257 In addition5reports isobaric data for a 12 percent to +257~Fo In addition, Mather reports isobaric data for a 12 percent

-9 and a 28 percent propane in methanemixture at pressures between 250 and 2000 psia and temperatures between -230 and 150~F. Interpretation of Data The basic data are recorded in terms of quantities that can be readily measured, such as microvolts, height of a fluid and weight. These quantities are converted to temperatures, pressures, power input and flow rate in the manner discussed by previous authors.62885 At this point Equations (2), (3), and (4) can be used to determine integral changes of enthalpy. In the single phase region these data may be interpreted to yield the derivative properties, heat capacity, C, Joule-Thomson coefficient,., and isothermal throttling coefficient, cp: H -H H -T - T lim (5) P 5T P x T-0 T2 T1 aT lim T2 T1 (6) = _ aP = SZP-+0 - P Hx P - L1 Hx H P lim P2 1 PThe t e drivtivsP2 -P1 x These three derivatives are related by the mathematical identity = -p.C (8) These derivitive properties are obtained from the integral data by several techniques. Both graphical and computer methods are used with the choice depending upon the type of data and the region where the data are taken.

-10 Graphical Interpretation Graphical interpretation is used to obtain differential properties for isothermal and isenthalpic data and for isobaric data in the regions of rapid change of heat capacity with respect to temperature and in regions where extrapolation is required. As an example one may consider determining C at constant pressure as a function of T. The data available from the experimental determinations are reported as sets of P. T1, T2, and (H T2 P - TP over a wide range of temperature. For any one data point T2 H TT- H TC P dT (9) T2P P P or T r2 C dT P HT - T H TP T TC P TL'P T1 (10) T T = C = T -(10) T2 - T1 Pm 2 1- T where C is the mean heat capacity between temperatures T1 and T2. Pm Values of C are plotted as horizontal lines as shown in Figure 12. Pm The smooth C curve is obtained by satisfying Equation (10): the area under the horizontal line segments, C *(T2 - T1), should equal the m area under the smooth heat capacity curve. This same technique is used to determine the isothermal throttling coefficient as a function of pressure. For determining p as a function of P, however, this technique can be applied only if all of the data points obtained are on the same line of constant enthalpy. This type of an experimental approach is not practical with the present facility and some other procedure must

-11 - be usedo In this investigation for isenthalpic determinations data at different pressures were obtained with the same inlet temperature, T1. The inlet pressure was continually reduced as data points were taken, One approximate technique can be used if the temperature difference, T - T s is small and if p is not a strong function of temperature. This is to assume that T2 T1 (T2 i, aH where Am is the mean Joule-Thomson coefficient between pressures P and P at an arithmetic average temperature, T = (T + T )/2. From.1 m 1 2 values of p m P2, and P1, the function i versus P at an average temperature, Tm, can be approximated by the equal area graphical technique described above, A second technique relates the isenthalpic temperature and pressures to the isothermal throttling coefficient. For an isenthalpic determination Equation (4) applies, and if H is added to both sides (Hp 2 p | = H-(T -H T (12) ( P2 -1 T - T2 -T (12)p 1 1P2 By dividing both sides by P2 - P1 H 2 - 1 T2 - 1 P2 T T P -P T -T P- - P 2 1 2 1 2 - 1 but Hp - H p P2 1 1 T,, I TL P2 - P1

-12 |( T H- T P ~2 1 15) P 2 T2 T and T - T A-= P (16) ~m 2 - 1 where pm is the average Joule-Thomson coefficient measured in the experiment, C is the average heat capacity which is determined m 2 from isobaric data, and cp T is the average isothermal throttling coefficient at temperature T1, thus Pm T1 - Cpm 2 m (17) The smooth isothermal throttling coefficient can be obtained as a function of pressure at temperature T1 by the same graphical technique described above. Computer Reduction The above graphical procedures are extremely time consuming, and in addition the equal area construction can easily lead to errors. Therefore, a computer program was developed for the interpretation of integral data. The equations used in the program are obtained as follows. Let us assume that the enthalpy at any temperature and a given pressure can be well represented over a limited temperature range by a truncated power series. H = a + bT + cT2 + dT3 + eT4 (18) For any two temperatures 2 1 1 T2+ eT 4 H = a + bT + cT +dT +eT1 (19) 2 = a + c2 + dT2 + eT24 2 = a + bT 2 + cT 2 + dT3 4(20)

-13 Subtracting Equation (19) from Equation (20) yields 2 2 H - H1 = b(T2 - Tl) + c(T2 - T ) + d(T23 - T13) + e(T2 - T ) (21) Factoring (T2 - T1) from the left hand side and dividing, results in - - = =C = b +c(T )+ (T + + T2) + ) + T2 -T1 Pm12 "~2 1 T 3 + e(T3 + T2 + T12 T2) (22) From data sets ofH T2 - H T I, T1, and T2, the constants b, c, d, and e can be determined by amultivariable least squares regression. H can then be determined from Equation (18) relative to a base enthalpy, a, Differentiating Equation (18) results in C = b + 2cT + 3dT2 + 4eT3 (23) p Thus in this way C can be determined as a function of temperature over p a given temperature range. Since data are obtained over a wide range of temperatures and it would not be expected of Equations (18) and (23) to accurately represent the data over such a range, the computer program was written to use the following approach. All experimental data for a given isobar are read in, and the program sorts the data in ascending order of the average temperature. Values of the enthalpy (relative to an arbitrary base) and the heat capacity are calculated at equal temperature intervals between a set initial and final temperature. The constants are determined at a temperature by fitting only eight data points. The data points used are the four nearest points below and above the temperature of the calculation. At the ends of the interval the first

-14 or last eight data points are used to determine the constants. The constant a is selected to make the enthalpy a continuous function of temperature. The constants in the fitting equation are continually changing from calculation to calculation. This procedure ensures that the equation will more closely fit the experimental data. However, this will cause the heat capacity to be discontinuous. This is not a serious drawback in regions where there are abundant data and the heat capacity is not a strong function of temperature. Nonetheless, in obtaining the final heat capacity values the results from the computer output are plotted and a smooth curve drawn through these points. Where the heat capacity is a strong function of temperature the fit is generally so poor that the graphical technique must still be used. In addition, it has been found that the equations do a poor job of extrapolating and when this is necessary again graphical methods are used. Although the program does not eliminate graphical methods, it does reduce the amount of equal area curve fitting which can lead to error. It also eliminates much of the graphical integration needed to determie enthalpy; and even when it cannot be applied it still can be used as a check of the graphical results. A listing of the MAD computer program which determines H and C is given in Table LVIII of p Apendix C. Extension to Low Pressures Since the lower limit in pressure of the recycle flow system is 100 psia, data from the literature are used in extending the enthalpy results to zero pressure. Isobaric enthalpy differences at zero

-15 pressure can be determined from ideal gas heat capacities which are related to the rotational, vibrational, and translational motion of a single moleculeo In addition, experimental values of heat capacities at elevated pressures when plotted versus pressure should extrapolate to the ideal gas heat capacity at zero pressure. The effect of pressure on enthalpy is determined at low pressures using PVT data and second virial coefficients. The isothermal throttling coefficient can be related to volumetric properties by cp = V - T I (24) At zero pressure this equation can be used to relate cp to the second virial coefficient =B -T( dB (25) The second virial coefficient is related to the interaction of two molecules. For binary mixtures B is of the form Bix = xB11 + 2 2B12 + x2 2 (26) where Bll and B22 are the pure component second virial coefficients and B12 is the interaction virial coefficient. Also dB dB dB dB mix 2 + 2x12 (27)2 dT 1 dT + l2 dT ) 2 dT The experimental isothermal throttling coefficients obtained at elevated pressure should extrapolate to the zero pressure values derived from the second virial equation using Equation (25). The resulting curve is integrated to determine the effect of pressure on enthalpy at low pressure. Enthalpy Change on Vaporization For pure component data in the two-phase region Equation (2) and

(3) can be used directly to determine enthalpies of vaporization. For pure components vaporization occurs at constant pressure and temperature so that the resulting enthalpy change of either an isobaric or isothermal experiment should be identical. For mixtures, however, vaporization must cause change of temperature, pressure, or both and thus the enthalpy of vaporization will depend on both the initial and final conditions. Equation (2) can be used to interpret isobaric data through the two-phase region and thus one obtains an isobaric enthalpy of vaporization for a mixture. If the inlet temperature, T1, is such that a condition in the two-phase region results, an appropriate value of p must be used in the pressure correction term. Equation (3) is used to reduce isothermal data, and, therefore, one obtains an isothermal enthalpy of vaporization for a mixture. An appropriate value of C must be used if the outlet fluid is in the two-phase region. P

SECTION II - METHODS OF PREDICTION This section presents a review of the methods of prediction of thermodynamic properties and particularly enthalpy of mixtures. As indicated a limited number of accurate enthalpy data are available for mixtures. However, the number of mixtures which have been investigated is infinitesimal relative to the number of systems of interest so that it is fruitless to contemplate the possibility of obtaining data for all such systems. Therefore, it is essential that reliable methods of predicting enthalpy behavior be developed. Statistical Mechanics Background With the advent of advanced calculational techniques including electronic computers, one would hope to be able to calculate enthalpy data for mixtures from a detailed knowledge of the behavior of individual molecules and of the interaction between molecules. Statistical mechanics has been applied with some success in this endeavor especially with respect to the behavior of gases containing relatively simple molecules. However, for mixtures in the liquid or dense fluid region this approach has not been extremely successful in obtaining quantitative representation of the macroscopic behavior. A brief discussion of the advances and problems in this endeavor will now be presented. Fundamental Equation of State The statistical mechanical theory relevant to the determination of thermodynamic properties of fluid mixtures at elevated pressure has been 52 derived and discussed in numerous textbooks and reviews, e.g., Hill5 107 120 47 Prigogine, Rowlinson, Guggenheim. The main goals of statistical -17

-18 mechanics in this endeavor are the determination of the potential energy of interaction of molecules, and the derivation of an equation of state which relates the thermodynamic properties of mixtures to the intermolecular potential. Intermolecular Potential Functions There are numerous discussions of the methods used in the determi120 nation of intermolecular potential functions, such as Rowlinson, Hirschfelder, Curtiss, and Bird, and more recently Klein. These functions can in principle be calculated from quantum mechanics. However, except for the most simple molecules, such an approach is not mathematically feasible since it involves a detailed knowledge of the behavior of every electron for each molecule. Thus, the potential energy function must be obtained from macroscopic data by use of a simplified equation of state in a region where the equation applies accuarately. A functional form is assumed for the potential energy and the parameters fit to represent the macroscopic data.5 Such an approach is often quite arbitrary, especially for non-spherical molecules where the potential is a function of orientation as well as distance. In addition, the potential energy function between two molecules is effected by the presence of additional molecules. Most studies of intermolecular potentials, however, are limited to systems which assume pairwise additivity and ignore this effect. If a knowledge of this potential energy function were available it would then be necessary to substitute it into an equation of state in order to determine macroscopic properties. The basic equations of statistical mechanics are the expressions for the partition functions. Partition Functions An example of such an equation which can be used for the determination

of thermodynamic properties is the expression for the canonical ensemble partition function, Z(N,V,T) Z(N,VT) = eEj(NV)/kT (28) J where E. is the total energy of a system in an energy state j, and k is J the Boltzmann constant. This partition function can be related to macroscopic thermodynamic functions by A = -kT~nZ(N,V,T) (29) where A is the Helmholtz free energy If it is assumed that the different contributions to the partition function are independent then Z(N,V,T) = ZtZrZvQ (30) where Zt, Z, and Z are the contributions of the partition function for translational rotational and vibration motion, and Q is the configurational integral. If the configurational portion is assumed to obey the laws of classical mechanics then Q = Je dr..drN (31) where u is the configurational energy of a molecular arrangement. This can be readily generalized to mixtures by. 1 10.01 eu/kT -d-..d1> (52) Q = iNi J e drl...drN (32) where = N (33) 1

-20 I. designates the I product and there are i species. Physical Models Since the evaluation of the above expression even for the simplest potential is extremely complex a simplified physical model is often assumed to represent the behavior of a fluid. An example of such a model is -the cell theory of the liquid where it is assumed that each liquid molecule occupies a single cell or lattice site. Next an assumption is made regarding the potential energy at positions inside the cell. The partition function and then the thermodynamic properties can thus be evaluated. This procedure can be similarly applied to mixtures often by making a random mixing assumption and can be applied to elongated molecules by assuming that a molecule can occupy more than one site. Additional refinements can be made to improve the physical model itself. Several attempts have been made to apply these methods to the determination of heats of mixing of simple fluids at low pressures with 6, 49,23 reasonable success. This is, however, partly due to the fact that heats of mixing represent only a very small part of the configurational enthalpy and may in fact be easier to represent07 In general, however, due to the number of approximations involved such methods give only a qualitative description of the properties of fluids. In addition, it is felt that due to the basic error in the physical assumption itself such methods can never be improved to the point of quantitatively predicting thermodynamic properties of fluids.07 Finally, such methods which incorporate physical assumptions must be limited to narrow regions of applications. Direct Calculatins A more direct approach is the solution for the macroscopic properties

-21 from the individual properties of a system of several hundred particles on a digital computer. There are two basic approaches. The method of molecular dynamics uses the classical equations of motions for each 2 particle and averages over time. The Monte Carlo method uses a statistical sampling process to select configurations in the canonica' e-nemble 119 and averages over these configurations with equal weight. Due to the complex calculations involved, these methods have, however, only been applied to the simplest type of molecular arrangements and potential functions which cannot be expected to represent the behavior of actual systems. Their main value has been in testing physical and mathematical models4 o Pair Distribution Functions A third approach uses the pair distribution function, g(2)(r), defined as the probability of finding a molecule in a volume element dr and a second molecule in a second volume element dr2. For molecules with a force field depending only on r (spherical pairwise additive molecules) this expression can be related directly to the configurational energy U Np - g (r) (r)(41r dr (34) 0 where p is the density and+(r) the potential function. Knowledge of the distribution function can be obtained from diffraction experiments3 89 121 or calculated by various approximate techniques. The above expression can be readily generalized to mixtures. Again, however, the method has severe limitations in accurately predicting the thermodynamic behavior of fluids. If the molecule is not spherical the distribution function

-22 and potential function must be made functions of orientation. Little or no progress has been made in the solution of such a problem. In addition calculation of thermodynamic functions are very sensitive to 114 small errors either in the distribution function or potential function. Recently an interesting approach to the calculation of thermodynamic properties of simple fluids, limited to moderate densities, has been 94,95 developed by Orentlicher and Prausnitz'95 Simplifying models for the distribution function and potential function in terms of three parameters are made. These models are substituted into an equation for enthalpy departure analogous to Equation 34. The three parameters are then empirically fit to best represent the thermodynamic data. Although the parameters have no physical significance, the flexibility of the expressions which are developed allow the authors to claim a minimum accuracy of 10 percent. Such an approach is similar to both equation of state methods and corresponding states correlations which are discussed in later sections. Although advances have been made in the area of predicting macroscopic enthalpy behavior from a study of microscopic properties it appears that for some time to come less sophisticated methods of prediction must play an important role. In the first place, the mathematical difficulties encountered not only make exceedingly difficult the solution of an equation of state, based on statistical mechanics, but also prevent the determination of accurate intermolecular potential functions. The simplifying assumptions which have been made are quite often themselves extremely complex mathematical problems, usually give only qualitative results, and are in general limited to narrow regions of application. To obtain quantitative representation of thermodynamic

-23 properties assumptions are required which make use of experimental data and contain parameters or functional forms having no direct fundamental significanceo These approaches and other methods developed from correlating thermodynamic data will now be discussed. Methods of Prediction Based on Thermodynamic Data A review of the available methods of prediction of enthalpi-es of fluid mixtures at elevated pressures has been published recently by 92 Nathan9 The predictive methods in common use can be classified in five categories 1) Estimation of partial enthalpies 2) Equivalent pure component method 3) Application of PVT data 4) Application of equations of state 5) Generalized corresponding states correlations This classification is somewhat arbitrary since first of all, the application of PVT data can be used to determine enthalpies for all of the other methods. In addition, corresponding states and equations of state methods can be difficult to distinguish and fundamentally are the same. However, for the sake of classification the five categories and examples of each will now be summarized. Estimation of Partial Enthalpies The enthalpy per mole of a mixture, H, can be determined exactly from a knowledge of the partial molal enthalpies of the individual components, Hi, by application of the expression

-24 H m= x.H. (35) i The partial molal enthalpy of a component is generally a function of composition and is, therefore, truly a mixture property. Accurate enthalpy data are available at low pressure for a large num118 ber of pure compounds, e.g., Rossini et al. For gases at zero pressure the assumption that the enthalpy of a component in a mixture is the same as the enthalpy of the pure component is an accurate one. Therefore, Equation (35) can be applied rigorously to establish the enthalpy of gaseous mixtures at zero pressure. In general, however, partial molal data are not abundant and, therefore, several methods of estimation have been suggested. For non-polar fluids either as gases or as liquids it is often adequate to assume that the partial molal enthalpy H i is independent of composition, ike., that the enthalpy of the component in the mixture is the same as the enthalpy of the pure component at the same temperature and pressure. However, extreme care must be taken when applying this procedure since as Mather has shown extreme values of the heat of mixing do exist, especially in the critical region. For this and other reasons, this method has been discouraged by the prediction 14o evaluation study conducted by the American Petroleum Institute. 99 89 Peters99 and Maxwell9 suggest a modification of this procedure in applying data from their published enthalpy diagrams to predict the enthalpy of gaseous mixtures. In applying this general procedure to liquid mixtures, one is faced with the problem of estimating the partial molal enthalpy of a component as a liquid above the critical temperature of the component. Peters relates the partial molal enthalpy of hydrocarbons above their critical temperatures to the molal average boiling

-25 point of the mixture and plots values of liquid partial molal enthalpies on enthalpy diagrams for the pure components. Unfortunately the method cannot be applied for pressures above 600 psia. Maxwell includes a single line on the enthalpy diagrams of pure components to represent the partial molal enthalpy of the component in the liquid phase above its critical. In general, the plots presented by Peters are limited to a temperature range between -260 and +420~F at pressures up to 600 psia. Similarly, Maxwell's plots extend between -200 and +1200~F at pressures below 150 atm. A major drawback of this method is the fact that an enthalpy diagram must be available for every component present in a mixture. This diagram is constructed by relying primarily on empiricism and would be difficult to extendo Equivalent Pure Component Method Application of this method is the simplest, generally only involving one parameter and is usually restricted to mixtures of components of homologous series. Scheibel and Jenny 3present nomographs based on the average molecular weight of a hydrocarbon mixture, 97 Papadopoulos et al. showed that the molal average boiling point of a mixture defined as M.A ooBoPo = xi(B.P. ) (36) where the (BPo.)o s are the pure component boiling points, for lighter hydrocarbons served to correlate values of a partial molal enthalpies calculated from an equation of state. Similar results were obtained at about the same time by Canjar and Edmister, Canjar and Peterka15 prepared plots of the isothermal enthalpy departure as a function of

-26 temperature and pressure for mixtures with different molal average boiling points. The plots of Canjar and Peterka are restricted to the temperature range -200 to + 500~F at pressures below 1500 psia for mixtures with molal average boiling points from -270 to +190~F, Application of PVT Data As mentioned earlier accurate PVT data can be used to calculate the effect of pressure on the enthalpy of fluids and fluid mixtureso In general, the enthalpy of a mixture at a specified temperature and zero pressure, H(T,O), can be determined for most simple fluids. This is evaluated from ideal gas enthalpies of pure fluids either from statistical mechanics or from measured data. The mixture enthalpy is determined by applying Equation (35) as already described, Thus, if accurate volumetric data are available for the mixtures, the enthalpy can be calculated by use of the relation P H(T,P) = H(T 0) + - T dP (7 0 - In principle, the use of this relation in the single-phase region is fairly straightforward. In contrast to pure components for which () T is infinite in the two-phase region, this derivative is finite in the two-phase region for mixtures (with the exception of mixtures of azeotropic composition). Thus Equation (37) applies throughout the twophase region for mixtures in which case V is the total volume per mole of the mixture. In application, the use of Equation (37) is not quite so straightforward. The term in brackets under the integral sign involves the difference between two terms, one of which includes a derivativeo As

-27 a result, extremely accurate volumetric data are required to yield reliable estimates of the effect of pressure on enthalpy. A reduction of accuracy of one order of magnitude is to be expected, Volumetric data for mixtures of the required accuracy are available but somewhat rare, Direct experimental determination of the volumetric behavior of twophase mixtures is even more rate. The total volume, V, can be related to the properties of the individual equilibrium phases. Strickland1538 Constable has presented the resulting equations which demonstrate that in order to make use of the properties of the individual phases, extremely accurate vapor-liquid equilibrium data are required in addition to the volumetric data. Another practical consideration is the method of obtaining accurate values of the derivative in Equation (37) from experimental data. In general, some method of curve fitting is applied. Quite often an equation of state is used for this purpose. The next section describes the application of equations of state in the determination of enthalpies of mixtures, Application of Equations of State Reviews dealing with equations of state have been presented by Van 141 83 122 Ness, Martin, and Rowlinson. In general most equations of state serve to relate pressure, P, as the dependent variable to temperature, T. and specific volume, V. as independent variables. As a result it is convenient to transform Equation (37) to V H(T,Po) - H(TV) = RT - PV + t P - T (T dVT (38) j \01 10

-28 The Benedict-Webb-Rubin (BWR) equation of state is commonly used to fit volumetric data and thereby estimate the enthalpy of fluids at elevated pressures. In terms of the eight constants which are used in this equation of state Equation (38) becomes 1 4c0 H(T,V) = H(T,o) + VBRT -2Ao - +. [2bRT 3a] + 6 a 2V2 V2 V ~ 32 "2 2 + - - e -e - e (39) The eight constants required for application of this relation are usually determined from volumetric data. It is risky to use the equation to extrapolate beyond the range of the original data. Experimental data are quite extensive in some cases as is illustrated by the fact that 22 Crain and Sonntag recently published BWR constants for nitrogen which apply fairly well to reduced densities of approximately 2. The BWR constants are only extremely rarely determined directly from volumetric data for mixtures. Instead, empirical rules have been developed for estimating values to be applied to a mixture from a knowledge of the constants for the pure components and the composition of the mixture. Combining rules for the eight constants have been suggested by Benedict, 8 Webb, and Rubin. Constants for the BWR equation of state are available for a considerable number of pure components, and therefore Equation (39) together with the appropriate mixing rules provides a convenient means of

-29 estimating the effect of pressure on enthalpy for mixtures, 75 Recently constants for the BWR equation of state or a modification of it 33 2 11 5have been determined by fitting volumetric and enthalpy relations simultaneously. This ensures thermodynamic consistency of both types of data. Other equations of state have been used to calculate enthalpies of fluid mixtures. The virial equation can be derived from statistical mechanics considerations5 The nth virial coefficient is related to an n particle interaction system, Unfortunately neither accurate thermodynamic data nor constants for equations of state such as the BWR are available for many components. 112 Several equations of state such as the Redlich-Kwong equation and 55,54 the equations due to Hirschfelder et al. 5use constants which are directly related to macroscopic constants for the individual components, These equations analytically represent a generalized correlation. Such correlations were developed to permit one to approximate the enthalpy of materials at elevated pressures using a very limited amount of available data. These corresponding states correlations will be described in the following paragraphs. Generalized Corresponding States Correlations Recently reviews of the application of the corresponding states 157 74 principle have been presented by Stiel7 and Leland and Chappelear. The principle of corresponding states was first applied in its simplest form to develop generalized correlations of PVT behavior by Cope, Lewis, and Weber and Brown, Souders, and Smith1 The law was stated as z = f(PT) (40) r r P where P is the reduced pressure, p-, and T is the reduced temperature, T 100 c T o Later Pitzer derived the expression from statistical mechanics c

-30 limiting its validity to spherical molecules having a potention function depending on only two parameters. In addition the translational and configuration portions of the partition function are assumed to be independent of quantum effects. This eliminates light molecules such as H2, He, and Ne. In addition the canonical ensemble partition function is assumed to be separable into independent internal and external factors. As expressed by Pitzer z = (,) |: (41) where f is a universal function. The C and a can be related directly 107 to the critical constants7 by applying Equation (41) at the critical point. To account for the nonconformity of compounds, which do not satisfy the above restrictions later contributors have suggested use of a third correlating parameter in addition to the critical temperature 76 and pressure. Lydersen, Greenkorn, and Hougen made use of the critical 102 compressibility factor, z. Pitzer et al. employed the accentric factor, W, which is related to the shape of the reduced vapor pressure curve. Substances with the same value of the third parameter are thus mutually conformal. The validity of the insertion of a third parameter from statistical mechanical considerations has been established by 104 19 Pople and Cook and Rowlinson. The correlations of Lydersen et al. and Pitzer et al. of PVT data have been used as the basis for generalized correlations of the isothermal effect of pressure on enthalpy. The total effect is considered to be the sum of two factors. The first factor gives the reduced enthalpy departure for a fluid with a standard value of the third correlating parameter and the second factor represents the influence of the deviation

-51 of this correlating parameter from the standard value. The correlation of Lydersen, Greenkorn, and Hougen has the form H(T,0) - H(T,P) HO- H] cTO)-(T ) = [.+ (z - 0.27) [D] (42) c c where the bracketed terms are presented as generalized functions in tabular form by the authors. The conditions covered include P 5 30 for r 150 0.5 _T' 15. Yen and Alexander have published revisions of these functions in equation and graphical form. The data used to develop these revised correlations include enthalpy data at elevated pressures and extend the upper limit on T to 30. A recent further modification 149 by Yen49 applies for P 5100 for 0.4ST e 60. r r 24 The correlation of Curl and Pitzer is given in the form H(To) - (T,P) Ho - H H H 1^ j2 O) == —=, IWO H p+- ~[HO + C (43) RT RT RT ( c c 0 c where the bracketed terms are somewhat different generalized functions presented in tabular form by the authors. These tables cover the range of pressures for P 9 for o.8 T'4. Revisions of the original correlations which incorporate enthalpy data at elevated pressures in addition to PVT data have been presented recently (Yarborough47). The range of conditions include P4 -10 for 0.5- T r 4, An approach for incorporation of the third parameter which is equivalent to the Curl-Pitzer method is used later in this investigationo This involves the use of two reference substances instead of the correction term. In this case the departure is represented as IH(TO) - (TP) H -. H] [H0 H] RT RT RT 2 c c c i J1 2

where W2 = W (45) and the bracketed terms are actual reduced enthalpy functions of reduced temperature and reduced pressure for two substances which are not cons formal. The normalized third parameter, W1, has a value of 1 for component one and 2 for component two. These factors weigh the reduced enthalpy departure for a substance according to its relative conformity to component one or component two. These weighing factors W1 and W2 can be related to another third parameter such as C by W = _- (46) 1 C - C1 X - X W 2 = (47) where w and w2 are the values of X for the two reference components, This latter approach was most convenient in this investigation, since accurate enthalpy data were availalbe for two reference components, methane and propane. This will be discussed further in the section on extensions of methods of prediction. Another approach used in the application of the corresponding states principle to non-conformal substances has been developed by Leach and 70, 71 Leland7'7 Shape factors for a given species are introduced which adjust the reduced temperature and pressure to force the component to conform to a reference substance. Its main disadvantage is that it requires the addition of two more parameters even for components which differ only slightly from a reference substance, In applying these correlations to mixtures it is assumed that the reduced functions for a mixture behave in the same manner as those for

-33 a pure component. It is necessary to establish values of the three parameters for a mixture. The actual critical properties of a mixture are in general not used, since, as is shown in several texts such as 108 Prigogine and Defay, the critical properties of a mixture do not have the same physical and thermodynamic significance as those for a pure component. Therefore, some kind of mixing rule must be developed which relates the mixture parameters to the parameters of the pure components. l40 The study conducted by the American Petroleum Institute4 however, does recommend use of the true critical properties in the vicinity of the mixture critical, Since heat capacity is infinite for a pure component but not for a mixture at the critical, as is pointed out in later sections, it seems doubtful that a reduced enthalpy function developed from pure component data would, at the critical, represent the mixture at its critical, Under certain conditions the generalization of the corresponding states principle to mixtures can be justified from theoretical considerations and mixing rules suggested. For molecules of equal size with a Lennard-Jones type potential function molecular pseudoparameters can be determined from pure component parameters. This development is given 120 in numerous texts, e.ogo Rowlinson. This approach uses a random mixing assumption which is not valid for molecules of different size, 75 Leland, Chappalear, and Gamson7 use an approximate technique based on expansion of the distribution function to determine equations for pseudomolecular parameters. This technique is limited to mixtures of mutually conformal molecular species. However, little is known about the molecular properties of non-conformal mixtures and since the statistical mechanics equations for such systems are extremely complex there

is no fundamental basis for the application of mixing rules to such complex systems. Thus, empirical methods must be used for substantiation and application of the corresponding states principle for such mixtures. A number of mixing rules have been developed for use in applying the corresponding states principle to mixtures. The simplest mixing rules used to define mixture pseudoparameters are those suggested by Kay which combine the pure component properties in a linear fashion with regard to mole fraction Tcx ci xi (48) P = Pcix. (49) i Wx= X W.x. (50) i 24 101 Curl and Pitzer recommend the rules of Pitzer and Hultgren for their correlation. These rules add a third empirical interaction term for each parameter which is a function of the components in the mixture Tcx =1Tcl + 2T2 + 2XlX2(2Tcl2 - Tl Tc) (51) cx Pcl X2 c2 2( c12 cl c2 (5 =x 1= X + x2 + x 2(z 12 -1 2) (53) These rules produce pseudoparameters having deviations from Kay's rule which are symmetrical with respect to composition. A generalization of these rules can be made by increasing the number of constants in the equation in order to better represent mixture behavior. Such an approach

-35 was used in this investigation and will be discussed more fully in a later section. The equations which were used are T = Zx.T i + x.x.[AT' + (1 - 2x.) B + (1 - 2x)2 C] (54) ex./ i ci I j i = x.P + xx[D +(1 - 2x) E'] ( Cx i ci 1 j and again W Z x.W. + F'x. (56) x a 1 1 1 j In addition there are several other mixing rules which have been proposed in the literature. The Joffe-Stewart, Burkhardt, Voo 6 6 3 equations are given as x KJ T Pcx = x (58) 2 T 2 | X l in the Vani d Wiaa (60) i cj / E Yi c Lci These rules were originally suggested by the mixing rules for the constants in the Van der Waals equation. Since the Van der Waals equation is a two parameter equation, the strict development is limited to mutually conformal substances. However, the rules can be applied to other mixtures by assuming a linear variation in the third parameter. The

-36 74 rules due to Leland and Meuller are given as 1 TZ 3 PcxT =. |T T 3 rwhere is afunctin of T ) x.P x T. x P P ~ i ci P) x.T o /. i ci i I Tci and is tabulated by the authors. The equation for the pseudocritical pressure is given as T cx x.z. eCX /. 1 ci i -i (62) cx 3 l l 3 13 i 3 L j 2 P 2 Pi j ~ / - These rules are obtained by equating terms of a second virial coefficient expression for mixtures with those of a pure component and making appropriate simplifying assumptions. Again, since the development was limited to mutually conformal substances the third parameter zc is given as z c x.z e (63) CX i 1 Ci i

-37 The mixing rules of Prausnitz and Gunn 6 are also suggested from relations for the second virial coefficient of conformal substances. These rules are given by +V' 2 + rV 7 T = -(64) cx 2sV - CX Vc = y.iy V- cij (65) i j RT:' c x'i X = E Yii (67) i The z c can be obtained from ci zc = 0.291 - 0.08 u (68) The quantities 3 and 7 are computed = E YiYY(T c)ij (69) i9j Y E YiYj( cc)c j (70) iJ where cij (Tci Tj -Tci (71) V (V + V.) -.. (72) - cij 2 ci -cj - cij where the A terms are small correction terms depending upon individual

-38 mixtures. Finally the quantities r and s are functions of T and C tabulated by the authors. Prausnitz and Gunn also recommend a simplified rule x= Y (73) i Tcx YiTc (74) px = x E i ci' i RT cxx -.yiz (75) ci ci ci Finally, Reid and Leland15 have obtained molecular mixing rules from the general expressions developed by Leland, Chappalear, and 73 Gamson7 for mutually conformal mixtures. Molecular rules can be obtained which are equivalent to the equations of Joffe-Stewart, 136 74 106 Buikhardt, and Voo, Leland and Mueller7 and Prausnitz and Gunn, depending on the assumptions used for approximating higher order terms,

SECTION III - THE MODIFIED FLOW SYSTEM 85 r80 The flow calorimetry facility as described by Mather, Manker, 62. and Jones was capable of making accurate determinations of the effect of pressure and temperature on the enthalpy of pure gases and mixtures behaving as fixed gases in the liquid two-phase, critical, and gaseous 40 62 states. As originally developed by Faulkner and Jones it was capable of measuring the isobaric effect of temperature on the enthalpy of pure fluids under pressure. It could operate between temperatures of -250 and +50~F and at pressures between 250 and 2000 psia. Such a system as described by Jones required in addition to the calorimeter itself, a series of baths to obtain constant temperature in the calorimeter, a compressor to enable recycle at a steady flow, a flow metering section, numerous buffer tanks to maintain stable pressures, storage tanks to enable adjustment of operating pressure, metering valves, and a host of accurate measuring devices. Thus, the calorimeter was only a small part of a large and complex system. When modifying the system 8O to enable measurements on mixtures behaving as fixed gases Manker8 and Mage77 found that a major problem was preventing fractionation and other sources of composition upsets throughout the system. In addition in order to complete a pressure-temperature-enthalpy network for any pure or mixed system it was necessary to determine the isothermal effect of temperature on enthalpy. Thus, Mather85 incorporated a throttling calorimeter into the system. In addition Mather increased the maximum operating temperature to +300~F. The next step in the process was to obtain measurements on more complex systems other than pure or mixed fixed gases. Since data were -39

available for mixtures of methane-rich methane and propane and, in addition, this system is of great practical interest, the completion of the methane-propane system was a logical direction in which to proceed. This required making measurements on pure propane as well as several mixtures of methane-propane. The phase behavior of the methane-propane system is shown in Figure 1. It can be noted that at room temperature mixtures which are greater than 30 mole percent propane are in the two-phase region over quite a range of pressures. The desired measurement pressures are between 250 and 2000 psia and the operating pressures would thus be between 95 and 2500 psiao Much of the original system (tanks, compressor, throttling valves) was at room temperature. Therefore, it would be impossible to maintain a constant composition for mixtures which were heavy in propane in this facility. In addition for mixtures with large propane content the temperature range covered by the two-phase region at pressures below 1000 psia is as large or larger than 200~F. That is complete vaporization of a liquid at constant pressure requires at least a 200~F temperature rise. It would be very desirable to obtain isobaric enthalpy data over the complete temperature range between -250 and +300~F including the two-phase region at specified pressures. The system as decribed by Mather could not be used to obtain data all of the way across the two-phase region for mixtures with large propane content. The available energy from the power supply was not great enough at lowest flow rates to vaporize as well as heat a mixture 200~F. Also, flow and composition instabilities would not allow the fluid to enter the calorimeter in the two-phase region. Finally even with pure propane where composition fluctuations are no problem there would still

1000 / \/ )I00- ~800- / I, ) r 600-PURE C \O7 400 200 / 0t I I I I -200 -150 -100 -50 0 +50 TEMPERATURE, ~F I I I I I +100 +150 +200+250 Figure 1. Vapor-Liquid Equilibrium Envelope of the Methane-Propane System

be problems of flow and pressure instabilities caused by operating the system with the fluid in the dense gas or liquid state. In addition the gas compressor could nctbe used to pump propane without modification. It was therefore necessary to modify the original system in'light of the above considerations. Basically the main modifications consisted of placing all parts of the system which could be in the two-phase region in a high temperature environment, with the exception of the calorimeter bath section itself since it was desirable to obtain data at temperatures as low as -250~F. The calorimeter bath section consisted of a series of cooling coils and baths arranged so that the flow was always downward since in this section two-phase flow would occur. The baths bring the fluid to the desired temperature where it enters the calorimeter. Thus the high temperature environment would eliminate composition and pressure instability. The downward flow in the baths would in addition to removing instabilities allow for measurements with the fluid entering the calorimeter in the two-phase region. The final result would be the creation of a facility capable of accurately measuring enthalpies of mixtures as heavy as propane and as light as any fixed gas over a wide range of temperature and pressure. Accurate data of this type for mixtures over a wide range of conditions, where one component is a fixed gas and the other a heavier component, are at present almost entirely nonexistant in the literature. Description of Equipment The modified recirculating system capable of operating with propane as the test fluid and incorporating both isobaric and throttling

calorimeters for direct experimental determinations of the effects of both temperature and pressure on enthalpy is illustrated in Figure 2. Important features of the facility are described below. A Corblin A2CCV50-250 two stage-diaphragm compressor is used to provide recycle capabilities. Either water or steam can be used to cool or heat the heads ensuring that only a gas phase is compressed. Additional heating can be applied to the gas leaving the high pressure stages as well as between stages. The compressor is located in a transite enclosed area on the floor above the laboratory. The compressed fluid flows through two large bombs situated in an insulated metal box heated to 250~F. The first bomb contains glass wool with a layer of copper filings in the center. The glass wool is used to trap any oil which may have leaked into the system from the compressor. The copper filings are used to remove any oxygen in the system as copper oxide. Before installation of the copper filings, particles of copper oxide would form in the calorimeter bath coils and eventually plug up the calorimeters. The second bomb is filled with dehydrite and is used to remove any water from the system. When operating the calorimeter at low temperatures water in the bath coils would freeze and plug up the coils. The compressor is operated at a constant volume rate of 4 SCFM and a bypass line is provided to permit variatL on in flow rate through the calorimeter. The fluid passes in a heated line from the bomb box to the valve panel which is also located in an insulated box. The fluid is heated by a heating tape and throttled by a metering valve to approximately the calorimeter inlet pressure. Although the fluid is located in a heated box the auxiliary heater is needed to prevent condensation

I NLET HIGH BUFFER I PRESSURE SCAVENGER I BUFFER " BOMBS 77777 I ^y ^ ____ w_ __ _ __ _ _ I COOI NG _/////, ___, __, STORAGE [. -— COOLING I-~~~~~~~~~ X ~~WATER TANKS COIL r —-J (_ DRY ICE B4 A I~TH IBATH AI H.... OL _ H E HEAT BATH FILTER EXCHANGER LOW ~, ~ / - BATH PRESSURE ) GLASS., _ BUFFER WOOL; BOMB U CALORIMETER / --------; | E |BATH / ^?<- SECOND FLOOR I I,/ t/ - FIRST FLOOR FLOWMETER t -( —-IC-IuHO --- - HEATED BOXES HOT BATH OIL,,',-/' HEATED LINE' ( | I e BATH o FILTER Figure 2. Flow Diagram of Modified Recycle System

-45 caused by the cooling effect on throttling. The fluid then enters a high pressure manifold in the valve panel. The fluid which is bypassed is first heated with a heating tape and then throttled by a metering valve to the compressor suction pressure, This gas is then recycled. A bank of five storage tanks located in another heated box is provided to allow operation of the calorimeter at various pressures up to 2000 psia. Figure 3 is a photograph of this box with the cover removed, The calorimeter high pressure buffer tank is located in the controlled temperature box with the storage tanks. The fluid entering the calorimeter section first passes through this buffer tank and then goes through a micron filter at the entrance to the calorimeter section, Should temperatures get too high in the heated section and decomposition occurs this filter acts to prevent any decomposition products from entering the calorimeter sectiono The fluid at elevated temperature enters the calorimeter section at a height of about eleven feet above the floor level. As condensation and/or boiling may occur within the calorimeter section every effort has been made to reduce holdup in this section and to arrange piping such that flow of fluid is downward throughout this section, A water cooling coil is used when operating a calorimeter below room temperature and may be bypassed. A dry ice bath provides a convenient means of reducing the temperature of the recycle gas to about -100~F when operating a calorimeter at low temperatures. This bath contains 175 feet of 3/16" O.D. copper tubing. The bath is constructed of stainless steel and is contained in a wooden box with a layer of Styrofoam insulation between the bath and the woodo

ru 0 tf4 41) 0M. 41) td 0 ~. 4aj 0 4),d lJ a 0 0~~

The heat exchanger bath is designed to bring the temperature of the fluid close to that of the calorimeter bath. In this bath the fluid passes through 325 feet of 3/16" O.D. copper tubing. Cooling is provided by use of liquid nitrogen at low temperature and compressed air at elevated temperatures. The bath is well stirred and the temperature is controlled to within +0.5~F by a Bailey electronic controller driving a 50 watt immersion knife heater. The fluid from the heat exchanger bath passes through 100 feet of 3/16" O.D. copper tubing in the calorimeter bath before entering either the isobaric or throttling calorimeter, Four packless valves with stainless steel bellows (Hoke TY-445) located within the bath make it possible to operate either calorimeter with only minor adjustments. The calorimeter bath is well stirred and a Honeywell proportional-reset controller is used to obtain stable temperatures within +0,10~F A photograph of the outside of this bath is shown in Figure 4. The hot oil bath at the exit of the calorimeter bath serves the purpose of ensuring that the fluid leaves the calorimeter section as a single phase, The temperature of this bath is controlled to within +2~F by a Fenwal controller driving a coil immersion heater. When operating at low temperatures additional immersion heaters are used to supply a sufficient heat input in order to vaporize all of the flowing fluid, After leaving the calorimeter section the fluid returns to the valve panel where it is heated by a heating tape and throttled to approximately 80 psig, the flow meter pressure. The fluid next passes througha second glass wool bomb just outside of the flowmeter bath and then is brought to 27PC, +0o02~C in the water filled flowmeter bath. The temperature is controlled by a mercury contact switch and a Fisher relay. The

Figure 4. View of Calorimeter Bath Area

-49 flowmeter is further isolated from the rest of the system by two micron filers. After leaving the flowmeter the fluid passes through several buffer tanks and is recycled back to the compressor to maintain a steady flowo The heat exchanger bath and calorimeter bath are both contained in the same wooden structure. The baths were designed to operate at temperatures up to 300~F. Both are of double wall stainless steel construction in order to provide a vacuum jacket. They are each seated on 16 inch diameter transite pipe and are covered with a 1 inch layer of glass wool insulation. The wooden framework is filled with styrofoam insulation providing at least 5 inches around each bath. In addition when assembling several inches of urethane foam was formed between each bath and the styrofoam. This provides adequate insulation at bath temperatures in the range from -250 to about +275~F. Three bath fluids are used depending upon the bath temperature. Between -250 and -50~F isopentane is used, between -50 and +125~F kerosene and above +125~F industrial oil. To ensure adequate mixing at any condition a variable speed Lighnin1 mixer is used for stirring. With operation of much of the system at temperatures as high as 3000F it was found that propane or one of the trace components was decomposing and leaving a brownish black residue in the system. Since the flowmeter is the element in the system most affected by fouling, it was necessary to isolate that part from the rest of the system. In addition oil soluble in compressed propane could condense at the low flowmeter pressure. Thus the glass wool bomb was required right before the flowmeter bath. In case of backflow during startup and shutdown the low pressure buffer could act as a knockout for oil. In addition a

-50 sight glass was incorporated right before entry into the flowmeter bath so that oil could be visually detected if present. Finally the two filters, one before and one after the flowmeter, were required to eliminate solid matter which passed through the bombs. After leaving the flowmeter buffer the fluid passes through the compressor inlet buffer located in the laboratory. When the revised system was first tested with the compressor located on the floor above the laboratory, the compressor was connected to this inlet buffer by a long 1/2" O.D. stainless steel piece of tubing. Operating under these conditions the compressor suction pressure would drop to a very low level during the intake stage, and the compressor discharge pressure would not build up. That is the compressor did not have an ample enough supply of fluid to accept during the intake stage for it to operate in a satisfactory fashion. The 1/2 inch line was, therefore, replaced with a 3/4" O.D. line and a small suction bomb was placed upstairs, located physically near the compressor. After these modifications the compressor discharge would build up significantly and the gas could be compressed at a reasonable rate, however, a regulating valve was located between this second buffer tank and the compressor in order to eliminate large oscillations of pressure in the flowmeter section. A low vacuum in the calorimeters is obtained by use of a Hyvac 7 vacuum pump in series with an oil diffusion pump and a liquid nitrogen cold trap. The vacuum jacket of either or both calorimeters could be connected to the vacuum system by opening or closing two Veeco vacuum valves. Duplicate vacuum measurements can be made with both an ionization vacuum gauge and a McLeod gauge. Pressure must be transmitted from the calorimeter to the pressure

-51 measuring devices, The 1/8 inch taps for each calorimeter come out of the calorimeter bath containing the test fluid. All four lines are connected to shutoff valves after which the two high pressure taps and the two low pressure taps are combined. The two lines then enter a heated conduit and above the baths the conduit and lines are teed. One heated conduit and one set of lines go to a Meriam high pressure mercury manometero This manometer is located in a heated box and is used to measure the small pressure drops occuring in the isobaric calorimeter. The second conduit and the second set of lines lead toa.heated valve manifold. The high pressure tap passes through the manifold and into the gas leg of a Ruska diaphragm pressure null detector. The low pressure line passes through a mercury knockout bomb located in the heated box and into one leg of a mercury U-leg. The leg extends below the box and is insulated along the part which normally contains the system fluid, The U-leg is used to transmit pressure from fluid to oil. The mercury in both legs is kept at the same level by addition or removal of oil, The mercury levels are detected by a series of iron electrical contact wires on both sides of the leg. In addition, since the temperature of many parts of the system can be a critical factor in obtaining accurate data, it was necessary to install many thermocouples into the system. For example, when a fluid is throttled additional heat froma heating tape is generally required. There is normally one thermocouple located before the fluid is heated, one after the fluid is heated to ensure that the fluid temperature has not become too hot, and one after the fluid is throttled to ensure that the fluid is not too cold and therefore fractionating. In such a system operating over a wide range of temperature and

-52 pressure leaks become a severe source of trouble. In order to minimize this problem heliarc welds were used to connect joints wherever possible. Valves, however, were connected into the system with standard high pressure connectors so that they could be readily removed in case of failure. As an example the valve panel was heliarced together to eliminate 38 trouble spots. A photograph of the valve panel is given in Figure 5. The photograph illustrates the high and low pressure manifolds which are heliarced together, numerous thermocouples and the neat valve arrangement. The various U-bends which are seen are wrapped with heating tapes and are located in the system right before a throttling operation. Figure 6 shows the valve panel with cover on and again illustrates the neat valve arrangement. Figure 7 shows an overall view of the control panel area of the laboratory. The flowmeter calibration system is similar to that described by 62 Jones with several modifications necessary for running with propane and propane rich mixtures. The fluid to be collected is taken from one of several of the storage tanks and is throttled to flowmeter pressure in a special Tescom pressure regulator inside the heated valve panel box, The Tescom is a precision single stage regulator with a special viton diaphragm for withstanding the elevated temperature. Due to the temperature coefficient of pressure on the regulator and the severe effect of throttling propane near the critical point it is necessary to reach a steady state condition in the regulator before calibrating. This is accomplished by flowing through the regulator and flowmeter at approximately the desired flow rate for a short period before actually beginning the calibration. This produces a much more stable pressure and flow

-535 Figure 5. Valve Panel with the Front of Insulated Box Removed

Figure 6. View of Insulated Valve Panel

4.J Pi) U) 03 0 rA 4J 0 0 0 /. E:::::::::::: ~:i~~;..'............ i:::ii-

-56 rate of fluid through the flowmeter. The flow rate and pressure in the flowmeter are regulated by this pressure regulator, and the fluid passes through the meter and is collected in aluminum bombs as described by 62 Jones. Calorimeters The isobaric calorimeter used in this investigation is the one used by Faulkner4 and Jones with several minor modifications. The throttling calorimeter is that used by Mather modified to allow for Joule-Thomson measurements in the compressed liquid region. In the isobaric calorimeter new six-junction copper-constantan 8o 85 thermocouples replaced the ones used by Manker and Mathero The width of the inlet thermowell was increased to allow for removing and inserting the duplicate thermocouples more readily without damage. The lead wires to the nicrome heating wire in the calorimeter capsule was insulated with teflon to permit higher temperature operation without shorting. The previous vacuum electrical seals were replaced with Cervac vacuum electrical seals to facilitate removing the calorimeter and to prevent leakage. The vacuum line from the calorimeter was replaced with a one piece construction line to eliminate the possibility of leaks, For the isothermal calorimeter the stainless steel O-ring and mylar sheets used for a high pressure seal were replaced with a teflon coated stainless steel O-ring. Several additional capillary coils were made for the calorimeter to enable measurement over a larger range of mixture compositions and temperatures at reasonable flow rates. To operate the throttling calorimeter in the liquid region where throttling causes a temperature rise the radiation shield was wound

-57 with a nicrome heating wire in order to act as a guard heater. In addition a thermocouple was added between the guard heater and the outlet line to measure the temperature difference between the calorimeter body and the radiation shield. Measuring Instruments A detailed description of the measuring instruments has been given 62 80 85 by Jones as modified by Manker and Mather. Changes made from the above works and important features are listed below. (1) The inlet temperature to the calorimeter is assumed to be equal to the temperature of the calorimeter bath which is measured using a platinum resistance thermometer. The calibration constants 62 are given by Jones. The thermometer was checked at the ice point and found to agree with the original calibration to ~0.1~C. (2) The temperature rise in each calorimeter is measured by duplicate six-junction copper constantan thermocouples. These were calibrated at the oxygen and nitrogen points and compared with a platinum resistance thermometer at 20~C intervals by the National Bureau of Standards. These thermocouples are calibrated from -196 to +150~C and the calibration data are given in Tables XLII through XLV of Appendix A. The accuracy of the temperature rise measurement is about +0,05 percent. (3) The electrical energy input to the calorimeter is supplied by a regulated DC power supply. The energy input is measured by a K-3 potentiometer using standard resistors to scale the voltage to the range of the Potentiometer. This measurement circuit is described below, The accuracy of the electrical energy determination is +0.05 percent. (4) The mass flow rate of gas is determined by the measurement of pressure drop by a 10 inch precision water manometer across a Meriam

-58 laminar flow element together with the temperature and pressure of the elemento These data are used to obtain the mass flow rate, F, from the equation + A F C D (76) The calibration constants A, B, C, D are obtained by a least squares fit of the calibration data. As indicated by Equation (76) small density, p, and viscosity, Ki corrections must be applied for minor variations in 44 45 flowmeter conditions. In this investigation the results of Giddings4445 were used to correct for viscosity and the density data of Reamer, Sage, and Lacey and the BWR equation used for the density correction, The accuracy of the mass flow rate determination is about +0.2 percent, (5) The pressure at the inlet of the calorimeter is measured with a calibrated Mansfield and Green dead weight gauge. The calibration data for this gauge are given by Mather, and it is accurate to 0,03 percent, The pressure is checked with a calibrated Heise gauge during measurements. The accuracy of the gauge is 1 percent of full scale, In addition the dead weight gauge is occasionally checked with the dif116 ferential dead weight gauge of Roebuck. The pressure is transmitted from the calorimeter fluid to the oil in the pressure measurement system by means of a Ruska differential pressure indicator, (6) The pressure drop across the isobaric calorimeter is measured with a 40 inch high pressure mercury manometer. The manometer is located in a special heated box to prevent condensation and fractionation within it. The pressure measurement is accurate to ~ 0.1 inch of mercury pressure drop. (7) The pressure drop across the throttling calorimeter is measured

-59 over the differential dead weight balance due to Roebuck and modified 85 by Mather. The inlet pressure, as already mentioned, is transmitted to the oil in the pressure measurement system by means of a Ruska differential pressure indicator. The outlet pressure is transmitted by a 36 inch mercury U-leg. The level of mercury in the U-leg is sensed by iron electrical probes sealed into each leg. It was found that the Viton O-ring dynamic pressure seal used by Mather for the Roebuck differential pressure balance would become defective after a short period of time. The Viton was extruded by the motion of the piston and eventually the seal would blow and oil would burst out into the laboratory. The seal was replaced with a teflon O-ring and backup ring set-up which worked satisfactorily. The sensitivity of the Roebuck pressure balance at higher pressures with the new seal is about 1 psia. This limits the lower pressure drop measurements to an accuracy of 1 percent. Electrical Measurement The electrical measurement system for the isobaric calorimeters has 62 been described by Jones. The electrical system for the isothermal calorimeter is essentially the same as that used for the isobaric calorimeter. In fact both calorimeters have been connected to the same measuring system where a series of switches can connect either one or the other. The fact that the isothermal calorimeter heater is grounded forced some modifications to prevent ground loops. Measurements of power input, temperature, and temperature difference are obtained from voltages recorded with a K-3 potentiometer. The power measurement circuit used to eliminate the possibility of more than one ground is shorn in Figure 8,

ISOTHEMAL CALORIMETER CONNECTOR POWER SUPPLY + ISOTHERMAL CALORIMETER HEATER R I ISOBARIC CALORIMETE HEATER R= 20,000 S TO K3 HIGH ~ ISOBARIC CALORIMETER CONNECTOR POWER SUPPLY R=.Ia IS2 Figure 8. Wiring Diagram of Power Measurement Circuit

-61 When operating the isobaric calorimeter (the one used most frequently) double pole double throw switch Sl is connected to the positive side of the measurement and power leads of the isobaric calorimeter. Each calorimeter heater can be connected from the electrical system to the heater leads in the vacuum jacket by an electrical vacuum connector. During operation of the isobaric calorimeter the plug for the isobaric calorimeter is connected and the plug for the throttling calorimeter must be disconnected. Switch S2, which can be grounded, is open. Readings are then made for current (related to El) and voltage (related to E3). At the same time readings are made of the voltages across the thermocouples and the current through and voltage across the platinum resistance thermometer (see Jones6). The low side of the K-3 potentiometer is the only point of the circuit that is grounded. When the isothermal calorimeter is in operation S1 is connected to the positive side of the isothermal calorimeter heater. The isothermal calorimeter connector is connected and the isobaric vacuum connector may or may not be connected. Switch S2 is closed and the current through the heating wire passes through ground. When reading El and E35 the ground on the low side of the K-3 potentiometer must be disconnected in order to prevent a ground loop. Such a loop creates an error of as large as 20 percent in the power measurement. When making the other readings with the potentiometer the ground is again connected. Procedure In obtaining data, inlet conditions of temperature and pressure are established and flow rate and power input are adjusted to desired values. Readings are taken and adjustments made as necessary until the condition of steady state operation is obtained and maintained for at least 15

-62minutes. A single determination generally lasts from one to two hours depending on the magnitude of the changes made between determinations.

SECTION IV - THE ENTHALPY OF PROPANE UNDER PRESSURE After modifying the recycle flow facility the first system investigated was propane for several reasons. First of all it would permit testing the facility with the heaviest system that could possible be investigated. Thus, if propane could be investigated any system with a lower critical temperature could also. Secondly, it would allow checks of the results obtained by the new system with data in the literature. Finally, data could be obtained for propane in regions where at present they are nonexistant. Thus, the final result would be to obtain an accurate knowledge of the enthalpy of propane over a wide region of temperature and pressure. The data obtained would hopefully be used as a standard for investigations in the future. Regions of Measurements The range of experimental determinations is indicated on a PT diagram in Figure 9. In the single phase region isobaric measurements were usually made in groups of four runs each having the same inlet temperature rises of approximately 10, 20, 40, and 80~F. In regions where C varied significantly with temperature (such as near the critical point) much smaller temperature rises were investigated (as small as 1~F). Isobaric determinations across the two-phase region included determinations of the heat capacities of both liquid and vapor at temperatures respectively below and above the saturation temperatures. These runs are indicated by asterisks on Figure 9. The number of isobars was reduced at low temperatures because it was found that C did not vary apprecia ably with pressure in this region and values of C are available below P -63

2000 J500 36 35 34 38 40 29 6R IR 28 5 3I i 16 4R 10 13 3R 23 _ 22 43 24 0) CC w U) U) an a. 1000 37 39 30 4 12 33 EQ g 5 21 \ j 2R 500 5R 31 6' 45 32 27 ^ --— I I I -- ~ 14 15 118 9 I 01\ Op! -44,47 I 46 7R 19 8 ~L — It r I 0 I - 250 -200 I -150 -100 -50 0 +50 +100 +150 +200 +250 +300 TEMPERATURE ( F) Figure 9. Temperatures and Pressures of Measurement for Propane

-65 atmospheric pressure for the saturated liquid. Isothermal determinations were made mainly in the single-phase region. One isothermal enthalpy change on vaporization was obtained. Pressure drops between 100 and 500 psia were used. Isenthalpic determinations were made at conditions of constant inlet temperature for different inlet pressures. In general, pressure drops of approximately 300, 600, and 900-1000 psia were used at two different inlet pressures. The isobaric results for individual runs in the single- and twophase region are given in Table XLVI of Appendix Bo The basic isothermal and Joule-Thomson data are given in Tables XL;VII and XLVIII of Appendix B, respectively. Composition of Gas Phillips Instrument Grade propane was used. This material contained approximately 1/4 percent impurities as determined by mass spectrometer analysis and reported in Table I. TABLE I IMPURITY CONTENT OF PROPANE Mass Spectrometer Nitrogen 0.15% Oxygen 0,04% Methane 0.02% Ethane 0. 03 Propylene o 01% Propane (by difference) 99,75% 100.00%

-66 Flowmeter Calibrations Seven sets of flowmeter calibration runs (usually ten determinations to a run) were made during the course of this investigation of propane. In contrast to previous experience with other pure components and with mixtures5'9 13 the calibration function was decidedly nonlinear with marked curvature in the middle of the operating range as shown in Figure 10. Therefore, one set of constants in Equation (76) was used to represent the calibration data at low-flow rates (0.1 to 0.25 lb/min) and another for higher flows (0.25 to 0.4 lb/min). Data from the calibration runs were correlated in three groups. The results of the first two runs were in excellent agreement. These were fit with the lower curve in Figure 10. A third set showed deviations of as much as 1 percent from this pair at high flow rates (the upper curve on Figure 10). After cil was found in the flowmeter, the glass wool bomb described in the previous section was installed. The flowmeter was cleaned ultrasonically, and subsequently, four sets.of calibration runs were made which yielded results in excellent agreement. These sets are fit by the middle line in Figure 10. A single correlating equation represents the data from these four runs in the high flow region with an average deviation of ~0.17 percent. Another equation serves to correlate the data at low flows with an average deviation of +0.22 percent. In processing the data some improvement in precision was obtained by using correlating equations based on the two sets of calibration data obtained preceding and following a run when the calibration did not change. When the calibration changed, repeat runs were made to determine which calibration equation would most adequately represent the flow rate at the time of an experimental run.

0.23 0.22 0.21 FLOWMETER CALIBRATIONS FOR PROPANE. - / IL 0.19 0 0.1 - -- K) / 0. 16 - o 0 SERIES MAYUG. 1, 1967 O 0.17 - o/ a 20 SERIES MAY 15, 1967 Q- sr0.15^v 30 SERIES JUNE 7, 1967 TO 4 0 SERIES JUNE 30, 1967 0.16 - -<:./',~j,"o ~ 50 SERIES AUG. I, 1967 _.~,.,*..,;.~.~'.~-y x 60 SERIES AUG. 25, 1967 -— 30 SERIES CURVE 0.14 - -— 40 TO 70 SERIES CURVE 0.13 - 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 F/..I (LB/MIN) / ( POISE) x 103 YI Figure 10. Results of Flowmeter Calibrations for Propane

-68 TABLE II Calibration Data Used in Interpreting Experimental Results Experimental Runs Calibration Runs Number of Calibration Points High: 14 Low: 7 Average Deviation 1-7 10,20 0.14% 0.01% 0.10% o.06% 8-10 30 High: Low 6 6 11-20 21-31 40, 50 50,60 6o, 70 High: 15 Low: 12 High: 15 Low: 12 High: 16 Low: 12 0.14% o.14% 0.07% 0.11% 0.17% 0.17% 32-47 1R-7R TABLE III Illustration of Consistency of Calibration Equations for High and Low Flow Rates at Intermediate Flow Rates Flow Rate lb/min Mean Heat Capacity Btu/lb ~F Run Calibration Equation Used High Low Low 20.010 20.020 0.29304 0.29367 0.29276 0.29336 0.29251 1.4773 1.2523 High 1.4787 1.2335 20.0o30 0.292 78 0.9889 0.9898

69 - A summary of the calibration equations which were used to interpret specefic data is presented in Table II, together with values of the total number of points included in the calibration sets and the standard deviation of each set from the calibration equation. The high and low flow rate correlating equations appear to give reasonable results in the region of overlap. For example, Run 20 was obtained in the middle of the flow rate region and both correlating equations were used to calculate the flow rate. Table III shows the small effect (0.1 percent) of calculating flow rates by either equation for this run. All of the sets of calibration constants of Equation (76) used to interpret experimental data are presented in Table XLIX of Appendix B. Results Enthalpy Change on Vaporization Isobaric determinations were made across the two-phase region at 250, 400) and 500 psia as indicated by asterisks on the vapor pressure curve of Figure 9~ Results from the run at 500 psia are presented on Figure 11o Note that the transition is not isothermal because of the presence of impurities. (See Table I.) This factor was taken into account by extending the horizontal portion of the curve to intersect with an extension of the liquid phase curve to determine the equivalent initiation of vaporization. Estimation of the point of complete vaporization was complicated by the fact that some scattering of points in the vapor region resulted bacause relatively high rates of electrical energy input were required to span the two-phase region and as a result very.small changes in the flow rate caused very large changes in tempera ture. The data in the vapor region (difference values) were used together

UL 0-1 cr w F0 0 I -8 20 30 40 50 60 70 80 90 100 ENTHAPY DIFFERENCE (BTU/LB) Figure 11. Enthalpy Differences for Propane in the Two-Phase Region 120

with other runs made entirely in the vapor region to estimate C = f(T) p for the vapor near the saturation line. A linear relation served to represent the data and upon integration yielded the curve drawn on Figure 11. The resulting value for the latent heat of vaporization is listed in Table IV together with experimental values at 250 and 400 psia. TABLE IV EXPERIMENTAL VALUES OF LATENT HEATS OF VAPORIZATION OF PROPANE Btu/lb Other Investigators Pressure This Helgeson & Kuloor et Sage, Evans, Dana et psia Work Sage (51) al_ (69T & Lacey (124) al. (2-) 250 122.60 122.35b 123.82a 124.25b 127.87c 400 93.07 94.5b 93.20 98.0b 500 70.45 71.7c 67.56a 80.5c 588 44 49 42.3d 55.63a -2 a Calculated from equation fit to experimental data published prior to 1965. b Interpolated based on plot of experimental values. c Extrapolation based on vapor pressure data. d Calculated from equation given by authors. Isobaric Data Typical isobaric data in the single phase region are presented in Figure 12. Mean values of C determined both from the direct measurep ments (solid horizontal lines) and by differencing experimental data (dashed horizontal lines) are plotted versus temperature. A curve is constructed to determine point values of C = f(T) as indicated by the solid curved line. In regions where the heat capacity does not vary greatly with temperature Equations (18) and (23) are used to obtain the point values of heat capacity and enthalpy with the aid

-72 m L -7- \ LiL I / in.70.60.50 50 100 150 200 250 3( TEMPERATURE OF Figure 12. Isobaric Heat Capacity for Propane at 1000 psia in the Upper Temperature Range

-73 of a digital computer. The smooth curve is obtained by fitting the calculated point values of the heat capacity, Where C is a strong function p of temperature the fit of Equation (18) and (23) of eight data points becomes quite poor. In this region the graphical technique using Equation (10) is used. Also extrapolation to temperatures above and below the region of data, is done graphically. A distinct maximum in C of 1.47 Btu/lb-~F was located at 257~F for p this isobar, Data at lower temperatures showed less dependence of temperature on heat capacity (see Table VI). Maximum values of C were determined at several pressures above the critical. The results are summarized in Table Vo TABLE V MAXIMUM VALUES OF C FOR PROPANE p Pressure Temperature at Maximum Value of C psia Maximum, ~F Btu/lb-~F P 617 206 z 60 700 219 5.4 1000 257 1.47 1200 284 1.18 69 An isobaric run was made at the critical pressure, 617 psia. The results are presented in Figure 13. A very large value of C (a 60 Btu/lb-~F) was determined. From these data, it was determined that the maximum value of C occured at a temperature of 206.3 +0.53~F This is p in good agreement with the accepted value of 206,3~F as the critical 69 temperature. As can be seen by Figure 14, there is a strong variation in the heat capacity with respect to temperature at pressures below the critical

70 60 II m u a 41 CD) 4 50 40 3C Mean Heat Capacity for Pre Propane @ 87 PSIA Data Points —--- Difference Points — I_ IC I I IV,-_=.~_: ------ ----- --— I —------ ---— L —--- -- X) 2J0 zw 2u0 Temperature ~F 208 210 212 Figure 13. Isobaric Pressure for Propane Heat Capacity in the Critical Region at the Critical i.30k 1.20 LS: Lc 0 I 1.10 1.00o 500 PSIA PROPANE - Data Point --- Difference x x x Benedict, \ Extens I T Point Webb, Rubin ion 0.90 0.80 0.70k 150 200 250 300 350 T - TEMPERATURE, ~F 400 450 Figure 14. Isobaric Heat Capacity at 500 psia in the Gaseous Region for Propane.

-75 U. IL 0..1 Ia. (L IV.Vr=!;T 9. o -. Im i i' 8. o 9.......... ii:::::::................ 6.( i' 5.0 - 4.0 — —.. ~~1*~ ~ I-t::: I~~~~~~~~~~~~~~~~~c~~~~~~ i. 1 iiii~~........... LO~~~~~~~~~~~~~~~~~6. ~~~~~~~~~~~~~~~~~~~................... ~ ~ ~ ~ ~ ~ ~' j II 4. ~ ~ ~ ~ ~ ~ E 1.0 I em i II ~~I U. -FT- I TI L' I.:...... * +, T....,............ i..... 40 16!9 %I 9-'.L......., T -: q.... _.1 -........ (4. *.* -. I:-.. K 7.....:... I. ~c.: il:::l::::'::.....: - I - -...... -'..:.................................................................... -.............................. - ij.. w, Y, f o.0:;." 00...: a I i'...... I f..... I...... - I \t — A k e — i 7 -. rF ii,ara _ v L.......:N raotb t -, N'& s i:-............... -Li N — i;-wv.... "yA vH.6.-..... PAM':..1. -....: r nl 1.000 K J7-5oo, mlic: 00 I i i i..;...-^.. 2r —F% )i R14-l.: a:: j.v.. a. 4.... l ---- ) nais T........ h h - S | I c........ - - - -....:,' I,....... I.- j:: +100 i - i.............. — ++z........ +200. tI -F-4 1 r - -t -. + —-!f:i'i,: i.,!.' i:. *+00 *400 * 500 +30 +400 0. I - TEMPERATURE,'* Figure 15. Isobaric Heat Capacity for Propane

-76 alsoo At 500 psia the heat capacity of the liquid as well as the gas changes by a factor of 2 in the region near the saturation point. A table of C values is presented in Table VI. Interpolated values P are indicated underlined. Additional experimental values of the isobaric heat capacity, Cp, determined from data obtained in regions of rapid change with respect to temperature are presented in Table VIIo Figure 15 summarizes all of the experimental values of isobaric heat capacity for propane. Isothermal Data Typical isothermal data are presented in Figure 16. Average values of (p = (tH/AP)T are plotted as horizontal lines and the graphical equal area method was used to determine point values of cp = f(P) as illustrated by the solid curveo This was necessary because of the large variations in cp with pressureo In extrapolating the results of the experimental investigation to zero pressure it was necessary to use Equation (32) for ~ 0 cp in terms of the second virial coefficient. Values of cp were calculated from the virial coefficients given by Diaz-Pena and Cervena30'31 and Huff and Reed8 Both results are plotted on Figure 16o In addition the value of cp obtained from the BWR equation of state7 using the original constants for propane is also plotted. There are significant differences in the results (~7 percent) and heavy reliance was placed on the value of Diaz-Pena since it was the intermediate value. A table of cp values for all of the experimental isotherms is presented as Table VIII. These results are summarized in Figure 17, One isothermal run was made through the two-phase region at 201~F (see Figure 22). The estimate of the heat of vaporization at this temperature (588 psia) is listed in Table IV.

-77 Table VI Experimental Values Heat Capacity, Cp, (Btu/lb - (Pressure ps of Isobaric for Propane ~F) ia) Temperature OF a -250 0.4651 -225 0.4697 -200 0.4751 -175 0.4812 -150 0.4878 -125 0.4962 -100 0.5060 -75 0.5173 -50 0.5307 -25 0 +25 +50 +75 +100 +125 (po)b +150 0.4434 +175 0.4590 +200 0.4744 +225 O.4898 +250 0.5050 +275 0.5199 +300 0.5343 250 o.465 0.470 0.475 o.480 0.487 0.495 0.505 0.517 0.530 0.546 0.564 o.585 0.611 o.645 0.696 0.755(1) 0.552(g) 0.542 0.536 0.540 0.553 0.569 500 o.466 0.470 0.475 O.480 0.486 0.493 0.503 0.516 0.529 0.543 0.561 0.583 0.608 0.637 0.673 0.754 0.815 0.987(1) 0.854(g) 0.711 0.662 o.634 0.618 1000 0.466 0.470 0.475 o.48o o.485 0.492 0.502 0.514 0.526 0.540 0.557 0.576 0.597 0.619 o.644 0.677 0.722 0.780 0.863 1.026 1.45 1.250 0.956 1500 0.467 0.471 0.476 0.481 0.487 0.493 0.501 0.513 0.524 0.537 0.553 0.570 0.588 0.607 0.631 0.657 o.684 0.715 0.755 0.807 0.867 0.928 o.963 2000 0.467 0.472 0.477 o.483 0.489 0.494 0.501 0.511 0.522 0.535 0.549 0.568 0.581 0.597 0.617 o.640 0.664 0.687 0.713 0.743 0.792 _ _ _ _ a Values for saturated liquid at p < 15 and Egan (66). psia from Kemp b Values for ideal gas at zero pressure (118).

-78Table VII Experimental Values of Isobaric Heat Capacity, Cp, Near the Saturation Curve and in the Vicinity of Cp(T) Maxima Temperature (OF) Pressure (psia) 250 4oo 500 617 617 100 105 110 115 119.9 122.4 125 (1) (g) Cp (Btu/lb~F) 0.696.7047.7159.7290.7424.5794.575t Temperature (OF) 160 161.1 163.5 165 170 175 180 (1) (g) _p (Btu/lb~F).912.945.8214.8078.7693.7399.715' Temperature (OF) 165 170 175 180 185.3 186.0 190 (1) (g) Cp (Btu/lb~F).8970.9347.9889 1.11 (1.54) 1.32 Temperature (~F) 202 203 204 205 206 206.3 207 (c.p.) Cp (Btu/lb~F) 1.84 2.57 3.09 4.3 29 - 6.5 Temperature (~F) 212 214 217 220 225 230 235 Cp (Btu/lb~F) 130 135 140 6.5684.5629.5586 190 200 220 7.6769.6478.6130 195 200 205.985.8543.8069 208 209 210 4.0 2.95 2.55 240 245 250 1.88 1.68 1.30 1.17 1.06 0.97 0.90 0.84 0.79 0.76

-79Table vtI (continued) Pressure (psia) Temperature (~F) 200 207 213 217 219 220 225 230 240 250 700 Cp (Btu/lb~F) 1.265 1.410 2.150 3.795 5.280 3.910 2.018 1.351 1.061.986 Temperature (OF) 220 235 245 250 255 257 260 265 270 280 1000p _(Btu/lb~F).980 1.134 1.272 1.345 1.436 1.466 1.439 1.377 1.314 1.189 Temperature (~F) 255 260 270 275 280 284 285 290 295 300 1200 _p (Bt/lb~F) 1.050 1.077 1.121 1.139 1.161 1.177 1.172 1.118 1.070 Temperature (~F) 220 230 240 250 260 270 280 290 295 300 1500 p (Btu/lb~F).796.819.843.867.891.914.938.956.961.963

-80 (f) m 11ID H H LU LL LL 0 0 2 F-J C) rr r I 2i Ctl: LL 0 (f -e PRESSURE (PSIA) Figure 16. Isothermal Throttling Coefficient for Propane Above the Critical Temperature.

Table VIII Experimental Values of the Isothermal Throttling Coefficient for Propane 0 x 102 (Btu/lb-psia) Temperature - ~F Pressure ps ia 2000 1800 1600 4oo00 1200 1000 800 600 4oo 200 ob 21.2a +0.253 +0.248 +0.244 +0.239 +0.235 +0.230 +0.226 +0.221 +0.217 160.5 -o. oo009 -0.059 -0.110 -0.167 -0.239 -0.350 -0.518 -0.802 201.0 -0.207 -o.304 -o.410 -0.567 -o.843 -1.292 -2.198(1) 249.9 -0.57 -0.87 -1.16 -1.79 -3.18 -8.28 -17.69 -9.90 -7.o9 -5.70 -3.84 -lo.41(g) -6.58 -4.7 a Estimated from Figure 18 b Based on 0~ = B - T(dB/dT)

.a _J I aS 0 -9 I...........................c~. ~. +17 L~. c +16 H++ H~ ~~~~-+~~-~~ +13 tt y~~~~~~~~~~~~~r THE UNIVERSIT cC-c~t~ +12..... I I I J IPAN I I T:,+93 THE. UNOVERSITV — ~......... +8........~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.~, +7......~ ~ ~ ~ ~ ~ ~ ~~~~~~96, —L~f:: 4+4 —H 1 1 1 -T~ 1 -~.T~~ +11 ~ ~ ~ ~ ~ ~ ~ ~ ~............. +r -+ri++ 111- I... -T- #1~~~~~~~~~~~~~~~~~~~~~~~~~~LT,..'~ — ~ +4.....~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~iritcr t+1r —-t-rt~rt-~ — ~~-~~. fail! + ~ ~ ~ ~ ~ -t HTH 7~~~~~~~- 44;t ~ iij +1 249.9"F-~~~L. 201.OOFc~l0 160.611F~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~,c~-t~i- ~ 21.311F —.,HL.... ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ i-t ~ ro s I 500 1000 1500 PRESSURE (psia) Figure 17. Isothermal Throttling Coefficients for Propane -13 ^A ff% CuuU

-83 Isenthalpic Data Isenthalpic determinations were made at an inlet temperature of 21.2~F and inlet pressures of 2000 psia and 1100 psia. The basic results are presented on Figure 18. Values of t - (aT/?P)H estimated from a plot of (AT/AP)H versus P are presented in Table IX. The isenthalpic data were used together with C data in Equation (17) to generate an isotherm m at 21.2~F. The results of these calculations are summarized on Figure 19. Values of. estimated from these data are included in Table IX. TABLE IX EXPERIMENTAL VALUES OF THE JOULE-THOMSON COEFFICIENT OF PROPANE Pressure Temperature -I x 103 psia ~F ~F/psi 2000 21.20 4.61 1700 22.50 4.49 1300 24.23 4.12 1000 25,50 3.99 1000 21.58 3.99 700 22.74 3.71 300 24,15 3.27 150 24.61 3o08 Analysis and Comparison of Results Isobaric Data Values of AH at 250, 400, and 500 psia and at 201~F (588 psia) -v which have been estimated from other published data are also presented in Table IV. Results from the present investigation are in reasonable agreement with values reported in 1967 by Helgeson and Sage1 The discrepancies between the experimental values obtained using the isobaric

26 25 ur 24 0 LJ cr\ a-\ EJ 223 w 23 — 22 21_ I 0 500 1000 PRESSURE (PSIA) Figure 18. Isenthalpic Curves for Propane with a 21,2~F Initial Temperature

2000 - 1500 a) 0 / w 1000 U) U) n Propane Temperature=21.2~F 500 -4 -3 -2 -1 0 ENTHALPY DIFFERENCE (BTU/LB) Figure 19. Pressure-Enthalpy Isotherm Generated from Isenthalpic and Isobaric Data

-86 calorimeter in this investigation and experimental values recently reported by Helgeson and Sage5 are within the 1.5 Btu/lb which is the uncertainty the latter claimed. At 588 psia (2010F) the value of this investigation is about 2 Btu/lb (4 percent) higher than the calculated value which appears in their publication. Values from the other sources vary from these results by as much as 10 Btu/lb (11 percent). Isobaric heat capacity data at pressures in excess of 1 atm have 59,42 only recently become available3 Figure 20 summarizes the results 42 of Finn and of this investigation at 700 psia, only 80 psi or so above the critical point, There is excellent agreement between the two investigations with respect to the temperature of the maximum in C (219~F) but the values reported by Finn are between 7 and 26 percent P higher than those reported in this contribution with the maximum deviation occurring at the peak. Ernst39 reports values of C in the temperature range from 68 to ~p 176~F at pressures up to 118 psia. This is below the lowest pressure used for isobaric determinations in the present investigation (250 psia) and also at temperatures lower than any used in the determination of cp for propane as a gas (201oF) so that direct comparisons cannot be made. However, when values of C from the two investigations were plotted versus either T or P, smooth isobaric and isothermal curves could be passed through all the data. Values of C presented in Table VI were compared with values P estimated by Kuloor, Newitt, and Bateman69 using low pressure C values and PVT data. The results of this comparison are summarized in Figure 21o Sciance et al3 recently published calculated values of the properties of the saturated phases of propane. Comparison of his reported

-87 PROPANE P = 700 psia / 6.0 Data of this investigation I BASIC 5.. BY DIFFERENCES —- A J 5.2 I SMOOTHED VALUES 4.8 - OF FINN (42) - / I /0 co 4.8 o 4.4 - 4.0 / — <:K o 3.6 o 3.2 2.4 2.0 I I I I I I I I I I\ I I I 210 212 214 216 218 220 222 224 2 TEMPERATURE, "F Figure 20. Experimental Data at 700 psia and Comparison with Results of Finn

Deviation, d LId < 2 % <: 0. r) C) Q: Ld 500 S 2 < d < 5 50/0%< d Comparison Not Possible ) -150 -100 -50 0 +50 +100 +150 +200 +250 +300 TEMPERATURE F Figure 21. Comparison of Experimental Heat Capacities with Tabulated Values of Kuloor et al. (69) O I I I I I 111 -250 -20(

-89 values with values of C for the saturated vapor determined in the course P of this study and reported in Table VII together with a value from the:9 investigation of Ernst9 indicates that the values reported by Sciance et alo are uniformly high by about 0.02 Btu/lb-~F (-4 percent). Isothermal Data 148 Yarborough and Edmister report results of isothermal throttling experiments for propane at 200, 300, and 400~F. Their results at 200 and 300~F are plotted as points on Figure 22. Data from Runs 4R, 5R at 201~F, and 7R at 200.5~F were interpreted to yield values of the isothermal enthalpy departure and the results are represented by a solid line in Figure 22. When corrected to 200~F the results of the two investigations differ by about 5 Btu/lb above the boiling point (about 4 percent). This agreement seems reasonable when it is considered that the determinations are made through the twophase region within 5~F of the critical temperature. Isothermal measurements were not made at 300~F but isobaric determinations extended to this temperature. Therefore the isothermal data at 249,9~F (see Table VIII) were used in conjunction with isobaric results at elevated temperatures (see Table VI) to calculate values of enthalpy departure at 300~F. The results are plotted as a dashed line on Figure 22. The agreement at this temperature is good with a deviation of about 3 Btu/lb (5 percent at 1000 psia)o Isenthalpic Data Unfortunately, it was not possible to make a direct comparison with 125 other published experimental Joule-Thomson data5 because the isenthalpic data of the investigation were obtained in the liquid region. However, it is possible to apply Equation (8) to check the consistency

1000 x x\ iooo ~ \ \ 800 + (I) I\ L -AHvp =449 —> H x 300 OF 200 This Work 3 x o + 200 ~F \ \ x 300 ~F 200 This Work;k - 300 ~F (Calculated From Experimental Data 250-3000~F) -150 -100 -50 0 ENTHALPY DEPARTURE (BTU/LB) Figure 22. Comparison of Isothermal Enthalpy Departure with Data for Yarborough and Edmister

-91 of p and C data from this investigation with experimental values of [ from Reference 125. Smoothed experimental values of these properties are listed in Table X together with the ratio (-tCp /cp) which, according to Equation (8) should have a value of 1.0. The agreement is on the order of +10 percent. Enthalpy Diagram and Table A number of tables and charts of thermodynamic properties of propane,, 12, 14,.1726 69, 103127 1355,153 have been published 14172669101271 15 The ranges in temperature and pressure covered by these published tables are indicated in Figure 23. The values of the thermal properties, enthalpy, and entropy, presented in these tables were calculated using heat capacity data at low pressure 25'2666'67 and volumetric (PVT) data. This general procedure has been followed because there have been very few other experimental data at elevated pressures with the exception of data on the latent heat of vaporization26 51,24 and results of Joule-Thomson experi125 ments. The pressure-temperature-enthalpy diagram developed in this investigation, although developed mainly from the experimental portion of this research, summarizes all published experimental data on the thermal properties of propane over the range -250 to +500~F and 0 to 2000 psia. Figure 24 presents a list of the data used and the regions covered. The reference for enthalpy was taken as H = 0 at T = -280~F for liquid propane at its saturation pressure. This is consistent with the reference previously used in reporting enthalpy values for mixtures of methane and propane.8 85 868788 Values of the enthalpy of propane as a gas at zero pressure were calculated using data on the liquid phase

-92 Table X Test of Consistency of Data Based on Equation (8) 200OF Pressure ps ia 500 450 400 350 300 250 200 150 50 0 C.p Btu/lb~F 0.854 0.730 0.652 0.599 0.563 0.536 0.515 0.502 0.491 0.482 0.4744b Btu/lb psi 0.172 0.127 0.104 0.0903 0.0802 0.0723 0.0662 0.o614 0.0580 0.0555 0.0536c a P51 O F/ps i 0.1846 0.1752 0.1677 0.1613 0.1537 0.1470 0.1407 0.1370 0.1259 0.1165 -kL C p 0.919 1.005 1.051 1.070 1.079 1.090 1.095 1.120 1.o66 1.012 a Interpolated from data in Table I in Reference (125) b Value for ideal gas at zero pressure (118) c Based on 0~ = B - T (dB/dT)

C 0L I 0o NOTE CHANGE OF I iii i __(135).._._. 1,000 SCALE ON ORDINATE I | i f) CHUetol.(17) e 80D 0 1 1__9 |.i! | u!|h) CANJAR 8 MANNING, co 800-.I (14) ILJ 0l [c80 C i ) YORK DIVISION BW, 600-I i ( ~- |~oo-~ j~ fe~: i ~ 15e~ I~ ~THIS CONTRIBUTION 400- i i' o1 1 I f I I I I i_ i I i. [ I'i ~ i *l gi o,c _ _,hde bf a eb d c _T _ ig _ -4 0 -200 6 260 400 600 1000 1400 1800 2200 TEMPERATURE F Figure 23. Range of Tables and Charts of Thermodynamic Properties of Propane

V AL 2000 _,,, — - a) DAILY 8 FELSING (latm.;159to788~F)* * b) DANA et al. (Sat. Iiq. +7 to 64~F) 1500 500 c) ERNST d) KEMP a EGAN (Sat. liq. - 305 to -45~F) * e) KISTIAKOWSKY & RICE ~0 (latm, 30 to 193~F) "" 1000 * -* I Lu r |f) YARBOROUGH 8 EDMISTER 03 I I I I I - t L * YESAVAGE et al. * * nr plus this contribution H f~ f 500 — *e 7,/ - /* /. c,,! I I-! I o d --- J -280 -200 -100 0 +100 +200 +300 +400 +500 TEMPERATURE ~F Figure 24. Range of Calorimetric Data Used in Preparation of PressureEnthalpy-Temperature Table for Propane

-95 66 66 heat capacity, the latent heat of vaporization at 1 atmosphere, the 7 BWR equqtion of state to correct from 1 atm to zero pressure at the normal boiling point, and values of the ideal gas heat capacity to account for a change in temperature from the normal boiling point to other temperatures at zero pressure. The calculations of the enthalpy at 250~F and zero pressure are summarized below, H(Btu/lb) Saturated liquid (at -280~F) 0 Saturated liquid (-280 to -43i7~F) 115.30 Enthalpy change on vaporization (at -4357~F) 183517 Effect of pressure on enthalpy (14 7 to 0 psia) 2.70 Effect of temperature on zero pressure enthalpy (-43.7 to +250~F) 121.93 H (Propane at zero pressure and +250~F) 423.1 Isobaric enthalpy differences at elevated pressures were calculated 39 from the data presented in Table VI plus other published values of C 3 The pressures at which such data are available are indicated by horizontal lines on Figure 24. The values of C recently reported by Ernst39 are p in excellent agreement with those at 1 atm previously published by 62 Kistiakowsky and Rice. Above 100 psia, values of cp from this investigation were used to determine the effect of pressure on enthalpy. These basic data were supplemented by published experimental values of enthalpy departures, (H - H),4, The temperatures as which such data are available are indicated by vertical lines on Figure 24, As already mentioned the effect of pressure on enthalpy at low pressures (100 psia) was estimated

-96 using published experimental values of the pressure dependence of enthalpy 146148 together with values of cp estimated from published correlations of the second virial coefficient, B, and its temperature dependence30'31 58 (see Equation (32)) and estimates made using the BWR equation of state7 with primary reliance placed on the correlation of experimental values of B as made available by Diaz-Pena. 3 The interpreted isenthalpic data yielding isothermal differences in enthalpy as shown in Figure 19 was used in the compressed liquid region. In establishing the enthalpy change on vaporization, experimental 26 data from Dana et al. and this investigation were used together with "critically chosen values" reported by Helgeson and Sage5 The values from Helgeson and Sage are in excellent agreement (better than 1 percent) with the results of this investigation in the region of overlap as already shown in Table IV. No attempt was made to correlate the extensive vapor pressure data reported in the literature. Instead values were taken from recent 14,69 tabulations.6 As indicated by Figure 9 redundant thermal data are available between 21 and 300~F at pressures up to 2000 psia. Consistency checks were made as permitted by these redundancies and the results are summarized in Figure 25. Consider the loop between the pressures of 500 and 1000 psia and the temperatures of 21.2and 160.5~F. As indicated on the figure there is some error in the constituent experimental determinations because the algebraic sum of the enthalpy differences around the complete loop, 1A' is not zero but instead is -0.64 Btu/lb. The percentage deviation, defined as

27 28 29 30 2000 1500 aL 1000 Qn D 3U) ur L0 05 500 I I.15 +0.024 +0.01% -0.138 -0.23% 24 +0.086 +0.10% 25 -0.233 -0.08% 22 23 16 17 +0.223 +0.12 % -0.092 -0.14% 19 +0.13 +0.11% 20 18 21 -I I +0.09 -0.04% 13 -0.64 -0.34 % +0.83 +0.42% 14 -0.52,-0.23% 10 II I I I 121 I — I I 8 9 / 4 +1.72 -0.37 o // +0.03 +0.03%. 6 7I 7, 5 I I I +0.156 +0.20% 2i 3 31 I I, n r L L-L I I I - 5 -0 I - - - -- - -- - "250 -200 -150 -100 -50 0 +50 +100 +150 +200 +250 +300 TEMPERATURE (OF) Figure 25. Propane Checks of Thermodynamic Consistency of Thermal Data for

-98 ZLi percentage ZiX0 (77) =- X100 (77) deviation 1- ii i is determined to be -0.34. The maximum percentage deviation for any loop is +0.42 percent and the average absolute deviation of all such checks is 0.18 percent. It is felt that this is indicative of the accuracy of the enthalpy differences in this region. The differences in enthalpy at a point calculated from different experimental data are small but nevertheless it was necessary to make minor adjustments in preparing the final compilation. This was done by adjusting individual values of isobaric and isothermal enthalpy differences to make each loop thermodynamically consistent. These adjustments were made within the limits of experimental uncertainty of the data. In general, the uncertainty in zA p is +0.3 percent except near the critical region. The uncertainty in AH is ~1 percent except at pressures below 200 psia. In extending the calculations of enthalpy down to -280~F use was made of experimental values of C for the saturated liquid and values at 1000 and 2000 psia at temperatures of -240~F and above were extrapolated graphically to the lower temperatures. The variation in value of C over the range of extrapolation was about +1 percent. Above 300~F primary reliance was placed on the C data of Daily and sing25 at atm. Between 300 and 400F and at elevated pressures Felsing at 1 atm. Between 500 and 400~F and at elevated pressures smoothed curves were drawn to blend experimental values at 300~F with values calculated using the BWR equation of state with the low pressure data. The blending was carried out so that the results were consistent

-99 146 148~ with the experimental values of Yarborough and Edmister at 400~F. Between 400 and 500~F enthalpy departures were calculated using the BWR 7 equation of state. After all adjustments and extrapolations had been made as described above. a skeleton table of values of enthalpy was prepared. These values were then plotted on a diagram and smooth curves drawn to connent all points and to represent interpolated values. The results are presented as Figures 26a and 26b. Values were then read from the master plot and are reported in Tables XI and XII. From -250 to +300~F at the temperatures and pressures of measurement as indicated in Figure 9, little or no interpolation is involved and therefore the numbers listed for these temperatures and pressures can be considered to be smoothed experimental values. Since the values in Table XII are based on extensive data on the thermal properties of propane between -240 and +300~F at pressures up to 2000 psia, the values in this region are believed to be accurate enough to permit determinations of enthalpy to within ~1 Btu/lb or less. The graphical representation is slightly less accurate. Extrapolation of C data to -280~F was carried out by graphical means. Extension of P the values of +500~F was based on a combination of limited experimental data on the thermal properties and the BWR equation of state, and the uncertainty in these regions may be somewhat greater. A comparison of the results of this table has been made with the results of a most recent compilation by Canjar and Manningl and is given in Figure 27. The deviations are quite significant in the region right above the critical temperature (as large as 7 Btu/lb).

O:OSZ ~0, 84 Jo CK i~~~~~~~~ir~~~~L C T v, crz =rrr~~~~~~~~~~~~~~~~~f -T~~~~~~; -— I -ttttttt-M~ ~ ~~~~~tI~:!t 081~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. 9' 91 O 1 091~~~~~~~~~~~~l ---! ---- -:. — - o~~ ~~~~~~~LO I,- Ia -, ----- C~~~~~~~j~C C\Ji i id L4~O~ ON. 7F-~~~~~~~~~~~~~~~~~~~~~~~~a P-1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~H Is~~~~~~~~~~~~~~~I 7-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Q it~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i ~~lt~"~~~~~~~~tttt~~~~#~~####F~~~I mg 9,091~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~e try.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~r 001 I t ~ ~ ~ ~ t s In t n N = o on 0 r (9 {n, d- n N -~~~~~~~Mt!.9 1- F 081-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~4 00Z- O~~~~~ 0 0 0 0 0 0 0 0 0 0 0 0~~~~~~~~~~~~d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~iiit-iif~~ —~ -t~ 10 lqj- r~~~~~~~~~~~~~~~~~o 0 co LO C~~~~~~~~~~~~~~~~~~~~jj (VISd ) 38nSS38d

-101 2000 1900 1800 1700 -1030 1600....-oi 1500 N-H CIOt CDs OD~~~~ LO 71hEl ~~~~r~~tttl-!t-t~~~~~~~~titl~ ~~~1 - I I a I I I a I I -+UHaALLfTw 8 rt~tttt~tttt;!, - - " I I I II I I - - - - - -- - - - 1~ JO pro. IF r^EL I I I; I I oo ~-0>i II0 ll - -F- - - FI11 - 0 -:'il; 0 - - N I II I LI I I 1inn PROPANE DATUM: H=0 forI saturated liquid at -280~F|;.UNIVERSITY OF II;MICHIGAN - NGPA 1968 1300 1200 cn a_ 1100 " 1000 r> fl 900 a: a 8 700 600 500 400 300 I 200 I EE I260 280 300 320 340 360 380 400 420 440 460 480 500 520 540 560 I ENTHALPY (BTU/LB) Figure 26b. Pressure-Terperature-Enthalpy Diagram for Propane

o0o t7~*7~ 0'"89 8'36 17' TC o " Cr 9'3l7T c *11 L F, * Co9'Z9T c -Lg[ (ql/nqg) UOTqe ZTaOdeA JO V eSH 4usaBG o * L'o^~ 8'0^( L *1 occs Vccc -E 0 LCC 8;08f rg~ 8 *tt 9 * tt (qi/nag) ^'d'[BL4uat jodeA p9 " jn-0 9 * 0-; L * Fcc L 5z9FC i7 e 66F, (ql/nqg) fdleqquSq jod'eA P~q eanqes t7 96F L *68z He 6Lz 8~6ZgZ o'o~g 9'+70g i7 e 17 -E o6-c.Ed'-[eqqug p* 061 ( ql/nS ~ ) YSdTeq~ua plnbTli P@4 BanV B; * 90F O' lOg 5; oZ't70^6 8'W8 0 6Z 17 e -1761 8 o 081 5'91 9 * L~ Ol 5*TZI G 0019 L * Ci7 (9o ) qaJ nq ea 9 d'u-ig, ZT9 9o9 885 007 oo5 00i7 ong 00C oST 051E 001 09 L * tvi (eTsd') awnssgacj[ I OJ 0 r-1 I SNOI ICINMOD aCLZYvuvgs IV amo doadOd HC 7dlVHLHMa Jo SanlqVA UHLI`9LV Ix gTqvL

-103 TABLE XII TABULATED VALUES OF ENTHALPY FOR PROPANE H (Btu/lb) Pressure, psia Tempera ture (~F) 0 100 200 250 300 350 400 450 500 550 -280 -270 -260 -250 -240 -230 -220 -210 -200 -190 -180 -170 -160 -150 -140 -130 -120 -110 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 21.3 30 40 50 60 70 80 90 100 110 120 130 140 150 160 160.6 170 180 190 200 201.0 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490. 500 242.9 245.4 248.0 250.5 253.1 255.7 258.3 261.0 263.7 266.4 269.2 272.0 274.8 277.7 280.6 283.6 286.6 289.7 292.8 296.0 299.2 302.5 305.8 309.2 312.6 316.1 319.7 323.3 327.0 330.7 334.5 338.3 342.2 346.2 350.2 354.3 358.5 362.7 367.0 371.3 375.7 380.2 384.7 389.3 394.0 398.7 399.2 403.5 408.3 413.2 418.1 423.1 428.2 433.3 438.5 443.7 449.0 454.4 459.8 465.3 470.9 476.5 482.1 487.9 493.6 499.5 505.4 511.3 517.3 523.4 529.5 535.6 541.8 548.0 554.3 560. 7 567.1.1.2.3 4.8 4.9 5.0 9.3 9.5 9.6 14.0 14.1 14.2 18.5 18.6 18.8 23.2 23.3 23.4 28.0 28.1 28.2 32.9 33.0 33.0 37.5 37.6 37.6 42.2 42.3 42.4 46.9 47.0 47.1 51.7 51.8 51.9 56.7 56.8 56.9 61.5 61.6 61.6 66.5 66.6 66.6 71.4 71.5 71.6 76.4 76.5 76.6 81.4 81.5 81.5 86.5 86.7 86.7 91.5 91.7 91.7 96.5 96.6 96.6 101.8 101.9 102.0 106.8 106.9 107.0 112.2 112.2 112.3 117.5 117.5 117.5 123.0 123.0 123.0 128.5 128.5 128.5 133.9 134.0 134.0 139.2 139.4 139.5 145.1 145.2 145.3 150.4 150.5 150.6 151.2 156.5 156.5 156.5 162.5 162.5 162.5 169.0 168.8 168.7 327.6 174.9 174.8 332.9 181.5 181.3 337.5 187.8 187.6 342.1 195.0 194.4 346.6 201.3 201.0 351.3 340.5 208.2 355.5 346.0 215.5 360.2 351.2 344.8 364.7 356.1 350.6 369.1 361.0 356.0 373.7 366.3 361.7 368.2 363.8 378.6 371.7 367.5 383.3 376.4 372.5 388.1 381.6 378.1 392.9 386.6 383.4 393.5 387.5 384.0 398.0 392.1 388.8 403.0 397.3 394.2 408.2 402.7 399.7 413.1 407.9 405.0 418.3 413.3 410.6 423.5 418.7 416.0 428.7 424.0 421.5 434.1 429.6 427.2 439.6 435.1 432.8 445.2 440.8 438.5 450.7 446.4 444.1 455.9 451.8 449.9 461.7 457.7 455.6 467.2 463.4 461.5 473.0 469.3 467.3 478.8 475.2 473.3 484.5 481.1 479.2 490.5 487.0 485.2 496.3 492.9 491.2 502.2 498.9 497.3 508.3 505.1 503.5 514.4 511.3 509.7 520.4 517.4 515.9 526.7 523.7 522.3 532.9 530.0 527.5 539.3 536.4 535.0 545.4 542.7 541.3 551.7 549.2 547.8 558.2 555.6 554.3 564.7 562.2 561.0.4 5.0 9.7 14.3 18.9 23.5 28.3 33.1 37.7 42.5 47.2 52.0 57.0 61.7 66.7 71.7 76.7 81.6 86.8 91.8 96.7 102.0 107.0 112.4 117.5 123.0 128.5 134.0 139.5 145.3 150.7 151.3 156.6 162.6 168.5 174.8 181.2 187.5 194.1 200.7 207.9 215.2 223.1 344.7 350.4 356.6 358.7 362.3 368.1 374.1 379.7 380.3 385.2 390.8 396.3 401.8 407.5 413.3 419.0 424.6 430.3 436.1 441.7 447.5 453.4 459.4 465.3 471.3 477.3 483.3 489.4 495.4 501.8 508.0 514.3 520.7 527.0 533.5 539.8 546.5 553.o 559..5 5.0 9.6 14.3 19.0 23.5 28.4 33.0 37.8 42.5 47.3 52.0 57.0 61.7 66.8 71.8 76.8 81.7 86.8 91.8 96.7 102.0 107.0 112.3 117.7 123.1 128.6 134.1 139.6 145.3 150.8 151.4 156.7 162.7 168.4 174.8 181.1 187.3 193.9 200.5 207.6 214.9 222.5 230.8 240.0 350.5 352.5 356.5 363.0 369.5 375.6 376.4 381.2 387.1 392.8 398.6 404.3 410.3 416.2 421.8 427.7 433.5 439.2 445.2 451.1 457.2 463.1 469.2 475.4 481.4 487.5 493.6 500.0 506.3 512.7 519.1 525.5 532.0 538.4 545.1 551.6 558.3.6 5.1 9.7 14.4 19.1 23.6 28.5 33.1 37.9 42.7 47.5 52.1 57.1 61.8 66.9 71.976.9 81.8 86.9 91.9 96.8 102.0 107.1 112.4 117.8 123.1 128.7 134.1 139.6 145.3 150.8 151.5 156.8 162.7 168.4 174.8 181.1 187.2 193.7 200.4 207.3 214.5 222.0 229.9 238.5 248.9 249.8 349.6 356.7 363.9 370.8 371.4 376.7 383.0 388.8 395.0 401.0 407.0 413.1 418.9 425.0 430.9 436.6 442.8 448.8 455.0 460.9 467.1 473.3 479.4 485.7 491.7 498.3 504.6 511.0 517.5 523.9 530.5 536.9 543.7 r, 556.9 2 556.9.7.8 5.1 5.2 9.8 10.0 14.5 14.5 19.2 19.4 23.8 23.9 28.6 28.7 33.2 33.4 38. o 38.o 42.8 43.0 47.6 47.7 52.2 52.4 57.2 57.4 62.0 62.1 67.0 67.1 72.0 72.1 76.9 77.0 81.8 81.9 87.0 87.0 91.9 92.0 96.9 97.0 102.0 102.1 107.2 107.4 112.5 112.6 117.8 118.0 123.2 123.4 128.7 128.7 134.1 134.2 139.7 139.8 145.3 145.4 150.9 151.1 151.6 151.7 156.9 157.0 162.7 162.8 168.3 168.4 174.8 174.9 181.1 181.1 187.2 187.2 193.7 193.7 200.3 200.2 207.1 206.9 214.3 214.0 221.6 221.3 229.2 228.8 237.4 236.8 246.4 245.2 247.0 245.9 256.4 254.2 348.2 264.3 356.8 347.1 364.8 356.9 365.4 357.8 371.5 365.2 378.4 372.7 384.6 379.6 391.2 386.8 397.3 393.3 403.6 399.8 409.9 406.3 415.8 412.6 421.9 418.8 428.1 425.2 434.0 431.2 440.3 437.7 446.3 443.9 452.7 450.2 458.7 456.4 464.9 462.8 471.3 469.1 477.4 475.3 483.7 481.7 489.8 487.8 496.5 494.6 502.8 501.1 509.4 507.6 515.7 514.0 522.4 520.7 528.9 527.3 535.5 534.0 542.3 540.8 548.8 547.4 555.5 554.1.9 5.4 10.1 14.7 19.5 24.0 28.9 33.5 38.2 43.0 47.9 52.5 57.5 62.4 67.2 72.3 77.0 82.0 87.0 92..o 97.1 102.3 107.5 112.8 118.1 123.5 128.9 134.3 139.9 145.5 151.2 151.9 157.1 162.9 168.4 175.0 181.1 187.3 193.8 200.2 206.8 214.0 221.1 228.6 236.5 244.8 245.3 253.2 262.3 274.5 345.9 347.0 357.1 366.2 374.0 381.9 389.1 395.5 402.4 409.0 415.5 422.2 428.4 435.1 441.4 447.8 454.1 460.5 467.1 473.3 479.8 486.1 492.8 499.3 506.0 512.5 519.1 525.8 532.5 539.4 546.0 552.8

TABLE XII (continued) TABULATED VALUES OF ENTHALPY FOR PROPANE H (Btu/'lb) Pressure, psia Temperature (~F) 600 617 700 800 900 1000 1250 1500 1750 2000 -280 -270 -260 -250 -240 -230 -220 -210 -200 -190 -180 -170 -160 -150 -14o -130 -120 -110 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 21.3 30 40 50 60 70 80 90 100 110 120 130 140 150 160 160.6 170 180 190 200 201.0 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500 1.0 1.1 5.5 5.5 10.2 10.3 14.9 15.0 19.7 19.8 24.3 24.4 29.0 29.0 33.7 33.7 38.5 38.5 43.3 43.4 48. o 48.1 52.7 52.8 57.7 57.8 62.5 62.5 67.4 67.5 72.4 72.5 77.2 77.2 82.0 82.1 87.1 87.2 92.1 92.2 97.3 97.4 102.5 102.5 107.6 107.7 113.0 113.0 118.2 118.3 123.5 123.6 129.0 129.0 134.4 134.5 140.0 140.0 145.6 145.7 151.3 151.4 152.1 152.1 157.3 157.3 163.0 163.0 168.5 168.6 175.1 175.2 181.2 181.2 187.3 187.4 193.9 193.9 200.2 200.2 206.8 206.8 213.9 213.9 221.0 220.9 228.4 228.4 236.2 236.1 244.3 244.2 244.9 244.8 252.5 252.3 261.1 260.8 272.7 272.1 286.3 285.2 287.8 286.6 345.3 340.3 357.8 354.7 367.6 365.3 576.3 374.5 384.2 382.5 391.0 389.3 398.2 396.7 405.2 403.8 412.2 411.1 419.0 418.0 425.5 424.5 432.4 431.5 438.8 437.8 445.3 444.4 451.6 450.8 458.3 457.5 464.9 464.2 471.2 470.5 477.7 477.0 484. o 483.5 491.0 490.3 497.4 496.8 504.3 503.6 510.8 510.2 517.6 517.0 524.2 523.7 535-! 1 530.6 538.0 537.5 544.6 544.1 551.3 550.9 1.4 1.7 6.0 6.3 10.5 10.9 15.1 15.5 20.0 20.5 24.7 25.1 29.4.29.7 34.0 34.5 38.7 39.] 43.6 44.0 48.4 48.6 53.1 53.5 58.0o 58.4 62.9 63.1 67.8 68.1 72.8 73.1 77.6 78.0 82.5 82.8 87.5 87.8 92.5 92.9 97.6 98.0 102.8 103.1 108.0 108.4 113.3 113.6 108.5 108.9 123.9 124.2 129.3 129.6 134.8 135.0 140.3 140.7 146.0 146.3 151.7 152.0 152.5 152.7 157.6 157.9 163.4 163.6 168.9 169.3 175.4 175.6 181.4 181.6 187.6 187.9 194.1 194.2 200.4 200.6 207.0 207.1 214.0 214.1 220.8 220.8 228.2 228.0 235.8 235.4 243.7 243.2 244.3 243. 7 251.4 250.7 259.8 258.9 269.9 268.1 280.8 277.6 282.4 278.5 295.1 289.1 326.2 303.1 350.5 318.8 362.4 3142.5 372.9 357.4 381.2 369.3 389.1 378.6 397.1 388.5 405.2 397.4 412.5 405.3 419.5 413.0 426.8 420.8 433.3 427.5 440.1 434.7 446.6 441.6 453.5 448.6 460.5 455.8 467.0 462.6 473.6 469.4 480.1 476.1 487.1 483.2 493.7 489.9 500.7 497.2 507.4 504.0 514.2 511.0 521.2 518.0 528.0 525.0 535.0 532.0 541.7 538.8 548.6 545.8 1.9 6.7 11.4 15.9 20.8 25.5 30.0 34.9 39.5 44.3 49.0 53.8 58.7 63.5 68.5 73.5 78.3 83.2 88.2 93.2 98.3 103.4 108.7 113.9 109.2 124.5 129.9 135.4 141.0 146.6 152.4 153.0 158.1 163.9 169.6 175.9 181. 9 188.1 194.5 200.9 207.4 214.1 220.9 227.9 235.1 242.6 243.1 250.3 258.1 267.0 275.6 276.6 285.6 296.4 308.0 321.9 339.2 355.2 367.1 378.9 388.5 397.4 406.0 414.1 421.5 429.0 436.3 443.6 451.0 458.1 465.1 472.0 479.3 486.2 493.6 500.6 507.6 514.8 521.8 531.5 536.0 543.0 2.5 7.1 11.7 16.3 21.1 25.8 30.4 35.3 39.8 44.7 49.4 54.1 59.0 63.9 68.9 73.8 78.6 83.5 88.5 93.5 98.6 103.7 109.0 114. 3 119.5 124.9 130.3 135.8 141.2 146.9 152.5 153.2 158.3 164. 2 170.0 176.1 182.2 188.4 194.6 201.0 207.5 214.2 220.9 228.0 235.0 242.4 242.9 250.0 257.5 266.0o 274. 1 275.1 283.1 292.6 302.8 314.2 326.8 341.0 354.7 367.2 378.4 388.6 398.0 406.6 415.0 423.0 430.8 438.4 445.8 453.3 460.7 467.8 475.4 482.5 490.0 497. 1 504.2 511.5 518.6 525.9 533.0 540.1 3.4 8.o 12.6 17.2 22.0 26.8 31.4 36.1 40.8 45.7 50.4 55.2 60.2 65.0 69.8 74.6 79.6 84.5 89.5 94.5 99.7 104.7 110.0 115.4 120.6 125.8 131.1 136.5 142.0 147.6 153.1 153.8 158.9 164.9 170.8 176.9 182.9 188.9 194.9 201.3 207.5 214.3 221.0 228.0 234.7 241.5 242.0 249.2 256.5 264.0 271.5 272.6 279.6 287.9 296.2 305.7 315.3 326.0 337.0 348.2 358.6 368.1 378.6 388.3 398.1 407.1 416.3 424.7 432.7 441.0 449.1 456.9 465.o 472.8 480.5 488.1 495.6 503.1 510.6 518.2 525.7 533.0 4.0 8.8 13.3 18.0 22.6 27.5 32.0 36.9 41.4 46.3 51.0 55.9 60.8 65.5 70.4 75.3 80.3 85.4 90.3 95.3 100.5 105.5 110.7 115.9 121.2 126.5 131.7 137.1 142.6 148.1 153.5 154.0 159.4 165.3 171.3 177.2 183.2 189.3 195.4 201.6 208.0 214.5 221.0 227.8 235.5 241.2 241.7 248.4 255.6 262.7 270.1 271.1 277.9 285.7 293.8 302.1 310.5 319.3 328.4 337.8 347.1 356.8 366.4 375.8 385.3 394.6 403.9 412.7 421.4 430.1 438.5 446.7 455.0 463.2 471.2 479.2 487.0 494.9 502.6 510.5 518.2 525.9 4.4 9,2 13.7 18.5 23.1 27.7 32.5 37.2 42.0 46.8 51.5 56.3 61.3 66.1 71.0 75.8 80.9 85.9 90.8 95.8 100.9 106.1 111.3 116.4 121.7 127.0 132.3 137.7 143.0 148.5 154.0 154.6 160.0 165.9 171.7 177.4 183.2 189.5 195.8 201.8 208.0 214.6 221.0 227.6 234.2 240.8 241.5 247.9 255.0 261.9 269.2 270.0 276.7 284.3 291.9 299.6 307.8 315.8 324.1 332.9 341.4 350.8 359.7 368.5 377.5 386.5 395.2 403.9 412.8 421.5 430.0 438.4 447.2 455.3 463.5 471.5 479.5 487.5 495.7 503.8 511.6 519.5 4.6 9.3 13.9 18.6 23.3 27.9 32.6 37.4 42.2 47.0 51.8 56.6 61.5 66.5 71.3 76.2 81.2 86.0 91.0 96.2 101.3 106.5 111.7 116.9 122.0 127.5 132.7 138.1 143.5 149.0 154.6 155.2 160.4 166.2 171.9 177.7 183.5 189.5 195.8 201.9 208.0 214.5 220.8 227.4 233.9 240.4 241.1 247.4 254.4 261.4 268.4 269.3 275.6 283.0 290.3 298.1 305.8 313.7 321.8 330.0 338.3 346.5 355.0 363.4 371.8 380.3 388.7 397.4 405.8 414.2 422.7 431.1 439.7 448.1 456.2 464.8 473.0 481.2 489.3 497.5 505.5 513.5

2000 PROPANE X, \ CAN JAR and MANNI'NG l d evia t iona-H C I -, = 00, 0 < IHI < 2 1500 -I D 1000 -I LLJ 0'0 TEMPERATURE, OF Figure 27. Comparison of Tabulated Enthalpies of This Investigation with Those of Canjar and Manning

SECTION V - THE ENTHALPY OF METHA]NE-PROPANE MIXTURES UNDER PRESSURE As already mentioned the enthalpy of a 5l1 mole percent, 985 a 12 and a 28 mole percent 5 mixture of propane in methane had already been obtained over a wide range of temperature and pressure before the start of this investigation. Thus, to complete the methane-propane system data for two additional mixtures with propane as the major component were obtained. The 76o6 Mole Percent Propane in Methane Mixture After completing the experimental investigation of propane, methane was added to the fluid in the system to obtain a nominal 77 mole percent propane in methane mixture, Composition of Gas The methane used in the investigation of the mixture was obtained from the Southern California Gas Company. The same instrument grade propane as obtained from the Phillips Petroleum Company was used for the mixtures as was used for the determinations of pure propane. The composition of this mixture as determined by mass spectrometer and chromatographic analyses are reported in Table XIIIo A chromatograph which is incorporated as part of the recycle flow facility was used for frequent checks on the composition of the gas in the system. The chromatograph was calibrated using samples of known composition prepared by direct weighing. From time to time the fluid composition did change. This was most frequent during periods of excessive leakage of fluid from the system, The composition was re-established within reasonable limits by the

-107 TABLE XIII COMPOSITION OF NOMINAL 77 MOLE PERCENT PROPANE IN METHANE MIXTURE Chromatograph (mole percent) Nitrogen 0.20 Methane 23.16 Ethane 0.05 Carbon Dioxide 0.,05 Propane 76.53 Butane 0 11 100.10 a Sample taken from system in March 19bU, b Sample taken from system in October 1967. Mass Spectrometer (mole percent) w 0,05 24,23 - 0,05 a 0o05 75077 c 0,05 4 100o20 addition of one component of the mixture and remixing the entire system, The chromatographic analyses on a day to day basis are summarized in Figure 280 There is no indication of a change in average composition with time. Regions of Measurement Experimental measurements of isobaric, isothermal^ and isenthalpic changes in enthalpy for the mixture containing 7.66 mole percent propane in methane were made in the liquid, two-phase, critical, and gaseous regions at temperatures between -240 and +300~F and pressures between 100 and 2000 psiao The ranges of pressures and temperatures covered by these experiments are indicated by lines drawn on a pressure versus temperature diagram in Figure 29. In addition to the mixture data normally obtained with the recycle facility the first successful attempt to obtain an isothermal enthalpy of vaporization was madeo Experimental results for each run are presented in Appendix B, The isobaric single phase and

77.5 Nov. I,'67 Dec. I Jan.1,'68 Feb. I March I 77.0 w z a. 0 I — LL 0 I -J 0 s 0 0 o 0 0 0 0 )o1 0, 0@~ 0 76.51 0 P. Oo Oc03 o0 A6Q9 oco dD 0o 0 o o I 0 S 0 76.0 * System in Two- Phase Region o System in Single Phase Region 1 2700 Figure 28, of Time 2900 3100 3300 COMPRESSOR HOURS 3500 3700 Composition of the Nominal 77 Percent Mixture as a Function

-109 44. 40 36 22 13 2 9 2000 134" 35 33 37 21 1500 - C 12 -2829, 27 3 <* 4 —--- 32 0 t 3 IR 4 d 8 2R 2R 0 Q. C.I u) w (0) Q 4R d 48 r 3R 14 10 45 41, 47,38,18,19 20 1/ )2 16,. e f 46 39 23 26 /I 49 51 -r C _ I _ I 500-250 4 so - 4l I 04 I P 7F- __,/,i m /. __ /50 /1 g 25 49 31 6 5 43 24 15..+. — — V - 200 -100 0 +100 + 200 + 300 TEMPERATURE ~F Figure 29. Temperatures and Pressures of Measurement for the Nominal 77 Percent Mixture

-110 two-phase data are listed in Table L. The isothermal and Joule-Thomson data are presented in Table LI and Table LII, respectively. Flowmeter Calibrations The first three calibration runs made for the 77 percent propane in methane mixture were very successful and yielded reproducible results which are presented as the lowest curve in Figure 30. All curves illustrate that as with propane the flow is not strictly laminar in the flowmeter; if it were, the results would lie on a horizontal line on this type of plot. The calibration data for the first three calibration runs lie essentially on a single curve. Two sets of constants for Equation (76) were used to fit the calibration curve. The average deviations of the experimental calibration points from the correlating equation was +0.16 for the 19 points in the low flow rate range and +0.18 for the 19 points at high flow rates. The success of these early calibrations led to a deviation from standard practice and no recalibration was- made between Runs 26 to 46. During this interval of nine weeks, the calibration changedo Calibrations were then made after Run 46 and before Run 49. These calibrations are represented by the upper curve on Figure 50 and are fairly consistent (average deviation ~0.17 for the 12 low flow rate points and ~0.25 for the 13 points at high flow rate points). Runs 47 and 48 are repeats of previous runs and were made in an attempt to establish when the flowmeter calibration changed. Following the calibration after Run 48, the flowmeter was removed from the system, cleaned ultrasonically, and recalibrated. Additional check runs were mae to aid in the interpretation of the previous data and new data were obtainedo Data from the last calibration agreed well

.20.19.1 8 I O 0 _ * -. _. LL z U --.1 7.1I ) 5Il3 Flowmeter Calibrations 76.6 % Propane in Methane.1I I% o 10 SERIES-OCT. 26, 1967 [ 20 SERIES NOV. 6, 1967 v 30 SERIES DEC. 8, 1967 A 40 SERIES FEB. 8, 1968 o 50 SERIES FEB. 13, 1968 * 60 SERIES FEB. 17, 1968 0 70 SERIES MARCH I, 1968 I I p.1I I F.1.10.15.20.25.30 F//t (LB/MIN) / (L POISE) x 103.35.40 Figure 30. Mixture Results of Flowmeter Calibrations for the Nominal 77 Percent

-112 with the one made subsequent to ultrasonic cleaning as illustrated by the middle curve on Figure 30 (average deviation +0.08 for 10 low flow rate points and ~0,12 for 12 high flow rate points). In using the results of flowmeter calibrations to establish the experimental values of the flow rate, results from the pair of calibration runs which bracket the experimental runs are usually used. The calibration runs used to interpret specific data for this mixture are indicated in Table XIV together with values of the total number of points included in the calibration sets and the average deviation of each set from the calibration equation. The calibration constants used in Equation (76) obtained for each set are presented in Table LII of Appendix B. I TABLE XIV CALIBRATION DATA USED IN INTERPRETING EXPERIMENTAL RESULTS Number of Average Experimental Calibration Calibration Deviation Runs Runs Points (percent) 1 - 26, 10,20,30 high 19 0o18 1R - 3R low 19 16 27 - 47 40[50 high 13 0 25 low12 0"17 4)51 60 70 high 12 0,16 4R 10 low 10 0,08'' - —-—' —U —--- I —------- ----- ---- ------ Check on Assumption of Adiabaticity In applying Equation (2) to interpret experimental data, it is assumed that-the calorimeter is adiabatic. It has been established for the isobaric mode9 that this condition is satisfied if the heat capacity determined using the calorimeter is independent of the flow rate. Therefore, a series of isobaric determinations (Runs 18 and 20) was made at

-113 four different flow rates to test the assumption of zero heat leakage. As illustrated in Figure 31, the heat capacity obtained is essentially independent of flow rate within the limits of precision of the measurements (~0o3 percent). Interpretation of Results Isobaric The isobaric data in the single phase region were again interpreted using Equation (2). Typical results are shown as Figure 52 on which average values of heat capacity calculated from experimental results are plotted versus temperature. Again solid lines indicate basic results obtained in accordance with the procedure described previously and dashed lines are values obtained by difference from the basic resultso Point values of heat capacity were obtained in the same manner as the method used for propane, implementing both a graphical and computer techniqueo Figure 32 illustrates the broad maximum in the heat capacity which occurs in the region just above the critical point for the mixture, which closely resembles the curve for propane at 1000 psia (Figure 12). A majority of the values of heat capacity, Cp, obtained from interpretation of isobaric data in the single phase region. are summarized in Table XV for equal intervals of temperature and pressure. Significant changes in the value of the heat capacity as with pure propane occur not only in the region above the critical point for the mixture but also near the two-phase locus. Figure 33 illustrates typical values of experimental data with the smoothed curve through the data representing values of the heat capacity near the two-phase region. Table XVI lists values of heat capacity in the regions of significant

m QD m I C) CL C) ui H 0.650 0.645 O Run 18 0 Run 20 m m m m mm _m _ m I _ _ _ o o Cp =0.6477 0'30/o i ii ie ii i i ii i i!!'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 0.3%/ _.~._ -_ _- m Q, m o Pressure: 1000psia H H I z L< UJ Inlet Temp:+ 24.3~F Outlet Temp: + 55.5 F I I 0.640'0 I 2 3 4 5 6 7 I/F RECIPROCAL FLOW RATE Figure 31, Heat Capacity as a Function of Reciprocal Nominal 77 Percent Mixture (MIN/LB MASS) Flow Rate for the

76.6 % Propane in Methane 1000 PSIA Isobar I -- X' " I 1.0 o0.9 w 0 In 0 50 100 150 200 250 300 TEMPERATURE ~F Figure 32. Isobaric Heat Capacity at 1000 psia in the Upper Temperature Range for the Nominal 77 Percent Mixture

TABLE ( XV) TABULATED VALUES OF ISOBARIC HEAT CAPACITIES FOR A NOMINAL 77 MOL PERCENT PROPANE IN METHANE MIXTURE Temperature ~F -280 -270 -260 -250 -240 -230 -220 -210 -200 -190 -180 -170 -160 -150 -140 -130 -120 -110 -100 - 90 - 80 __ ~I J_ _ [ J _ 0 0.485** 0.487** 0.489** C (Btu/lb - ~F) Pressure, 250 500 0.490 0.492 0.493 0.493 0.495 0.497 0.496 0.499 0.498 0.501 0.501 0.504 0.503 0.506 0.507 0.509 0.510 0.512 0.513 0.515 0.517 0.518 0.521 0.521 0.525 0.524 0.529 0.527 0.533 0.533 0.538 0.534 0.543 0.538 0.549 0.542 0.555 0.546 0.561 0.551 - psia 1000 0.492 0.494 0.495 0.496 0.498 0.500 0.502 0.504 0.506 0.509 0.511 0.513 0.515 0.518 0.522 0.527 0.532 0.537 0.542 0.546 0.550 1500 0,486 0.488 0.489 0.491 0.494 0.497 0.500 0.504 0.508 0.512 0.520 0.528 0.538 0.545 2000 0.484 0.486 0.487 0.490 0.493 0.495 0.499 0.501 0.504 0.506 0.508 0.510 0.512 0.514 0.517 0.520 0.523 0.527 0.531 0.535 0.540 - - -

-117 TABLE (XV) - (Cont.) Temperature OF - 70 - 60 - 50 - 40 - 30 - 20 - 10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 i0. -250 Pressure, 500 0.557 0.564 0.572 0.580 0.588 0.597 0.607 0.617 0.738. _ - psia 1000 0.555 0.559 0.564 0.570 0.576 0.584 0.593 0.604 0.616 0.628 0.640 0.652 0.665 0.680 0.696 0.716 0.738 0.766 0.801 0.847 0.904 0.980 1.088 1500 A ~1 0.553 0.558 0.565 0.571 0.577 0.584 0.592 0.601 0.611 0.621 0.630 0.642 0.653 0.664 0.676 0.689 0.704 0.721 0.744 0.768 0.794 0.819 2000 0.546 0.551 0.557 0.563 0.569 0.576 0.583 0.591 0.597 0.604 0.611 0.619 0.627 0.636 0.645 0.655 0.665 0.676 0.687 0.700 0.714 0.728 0.743 0.425* 0.431* 0.437* 0.443* 0.449* 0.455* 0.601 0.567 0.541 0.530 0.525 0.523

-118TABLE (XV) - (Cont.) Temperature Pressure, psia ~F 0 250 500 1000 1500 2000 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 0.461* 0.467* 0.473* 0.479* 0.485* 0.491* 0.497* 0.503* 0.509* 0.514* 0.520* 0.526* 0.532* 0.538* 0.543* 0.523 0.523 0.523 0.525 0.528 0.531 0.535 0.539 0.544 0.548 0.553 0.559 0.565 0.571 0.577 0.718 0.679 0.652 0.633 0.621 0.613 0.608 0.603 0.601 0.601 0.602 0.604 0.606 0. 609 0.612 1.233 1.360 1.407 1.388 1.259 1.115 1.011 0.940 0.884 0.839 0.801 0.776 0. 756 0. 741 0. 729 0.845 0.870 0.899 0.922 0.948 0.976 1.001 1.002 0.984 0.960 0.940 0.916 0.896 0.879 0.864 0.758 0.773 0.786 0.800 0.813 0.827 0.840 0.854 0.868 0.881 0.886 0.875 0.855 0.834 0.812 *Ideal Gas Values of Rossini et. al. (118) **Experimental Data of Cutler and Morrison (25)

-119 76.6% Propane in Methane 500 PSIA Isobar in Gaseous Region.I.. >-.68 - IW r a.66< w.64.62 Dew Point Temperature 147.2~F —--.60 J 100 150 200 250 300 TEMPERATURE F Figure 33. Isobaric Heat Capacity at 500 psia in the Gaseous Region for the 77 Percent Mixture

-120TABLE XVI Supplemental Table of Experimental Values of Isobaric Heat Capacity, Cp (Btu/lb) Pressure ( psia ) Temperature(~F) -45 -40 -35 - -25 -24.0 1) ~.; 135 140 145 4oo C p (Btu/lb) 0.579 0.586 0.594 0.601 0.609 0.610 0.736 0.701 0.655 o.610 Temperature (~F) 50 55 60 65 70 75 170.1 175 180 185 700 C (Btu/lb) 0.678 0.688 0.698 0.708 0.719 0.729 1.276 1.153 1.028 0.906 Temperature (OF) 190 200 210 220 230 240 245 250 255 260 1200 Cp (Btu/lb) 1.169 1.166 1.153 1.118 1.061 0.983 0.943 0.903 0.834 0.764 Temperature (OF) 220 225 230 235 240 245 250 260 270 280 1700 C (Btu/lb) 0.915 0.9 25 0.9 33 0.937 0.936 0.933 0.927 0.915 0.901 0.889

-121 change such as near the maxima in the heat capacity and near the saturation curves. The results of all heat capacity determinations are summarized on Figure 34. A typical enthalpy traverse of the two-phase region at constant pressure is illustrated in Figure 35. Note that the traverse was made as two runs. Run 17 had an inlet temperature of about 50~F and was terminated with the two-phase region at about 140~F. In Run 16 a twophase mixture at about 100~F was fed to the calorimeter and the run was terminated after the exiting fluid was totally vaporized at about 190~F. The results of the two runs are consistent in the region of overlap as illustrated in Figure 35. This procedure was followed so that enthalpy traverses could be made across the two-phase regions at larger flow rates than would be possible if the entire change were experienced in one run. This is necessary due to a limitation on the power available from the constant voltage power supply at low temperatures and the possibility of overheating and burning up the insulation of the nicrome heating wire in the calorimeter capsule at higher temperatures. Determination of the points of discontinuity in slope of the curve yields values of the bubble point and dew point. For mixtures containing a majority of propane it is relatively difficult to determine the bubble point whereas the dew point is the more difficult determination for mixtures containing high mole fractions of methane. Experimentally determined values of the isobaric enthalpy change on vaporization are listed in Table XVII together with the experimentally determined values of the bubble point and the dew point for the mixture.

-122 -q I i i II I ~ii!~!:i ~i ~~~~~~~~~~~~~~~~.........;........;.........: ~~~~~~~~~~~ii~:il!!ili...........~~~~~~~~...................................,......................... i.;.~~~~~~~~~~~~~~................................. tnnx......... 7 t:.-t1 - ".... f.....;' -.;''- t'; & U;; + t' o I;' s, l'..........'-.................. _:;.;......................_..,., tt i-g...........................,,,..........., -'.......,.-''!tt -,.-.....~ *'.' *.1 t:.....;..::.:::........:::.::..: <:: A:; t:.:::: -~ t - 2.o. x;~:::::::::::::::::I ir L,,:;:,,, t! ti-tX t..............'.::: -..-....'....... ~~~~~~~~~~~~~..:.:.................................... *...tv ~, 4 i - e t -.......~..........*.._ *_ _ * t* —-..,..-.....|t *ntt- ~,4:-:; +i::;:': i:::.,- -t' "-'-..... i.i i~...... t.............. 1~t:~~~~~~ ~ ~ " —:" —:'~~ - "- t -',-','- ~.......-.......... -..........................., ~ ~. t ~' _ ~ i - t - - tt I I tt, _._..._.... j X t-tt *! * *. +...i *,.......!..t...i. -.,... 4- z................. i " t.! t: i i..;;............... i -t- t'~.,; t; t;':::::: I, - |'' l.,,_ t,!; s4 1-j t _ -*t...... _; * *.;.......i......... t t~i-t.~*Ii~~-+,t,4 o,, ~I~ ~~~ t;|s_,4-, f +Ht-t4 i ~'1'''' 1~ ~ rC i'- ~ *''' t4't -' 4v..;...t.. t6. i |............ -t |..... t.,............., -................. t i i,,~, t~~~~~~~~~~~~~~~~~~~~~tLJ....... t....... -........,..'t -; —.r _. i..i I 1.,~~ 1~~ ~ ~ i'~'~ I ~ ~-! ~,I-~ Cf i r tct t i;i rtt;tt:Fr-f: c., t ~i~i- cl +1~~-;~t~i-' ~~ (~C1; —it. Si'-~ t-~-i1~1-+ —1-1 1 —t-~ etcr 1C~t ii iC-k L ii t I 4 I.,., + I. -. I..-1 14 t~-!1 iti:tI,i~. 144114 tt ii-'-Fi Zb 0~-0 WM 0ob oS (0~ W co 41 4 I4 1. i. -. I''-..-. 4:t'. i rre i Ii ~ i ~ r I j 1 ii i t rti ~ / iii I:- 1i" t r I i!t.. *^:m~ilii -1 I 1'-II - -~- t I — I I1 * * Ii t II- i I wit —i t:' t. - 4 f. f:.i I -i i. I -et I., t ",llfm bjll it~-t Iism t 0 8 8 0),4 4. LL 0 0 al:: -, Z 111 X HQ: k o 4.. H r' t 0'-' C),4'4 to 0 I1-:4 c0 rX i i,i + i. c, t ft it-* i:t I idt —: itE ":.. I I I I,...1, 1- I.~ jt —XtlI I., I I 1. j.. I,,- i..;! I:...,..;.. I i i i' 4 -t;t I ----; -~, I ti -,i +-; I'I "I I+; i -.l 1I i II:t-HtiTf I tt-t: I si FT- -1 TT T-r-TI -71 i Ttt t t- -1T I I f'T- I f I I I 141- I I ~ t t t 4t I. j 1 T' F 1: T' 4 1.Jt i t i 4 ~ t 8!- ~ ~ ~ ~ ~ ~ ~ N (Q I C) t t ~ -:iirlt!L~ f, ~ ~ ~.1 6j i i., LO o n N- - 0 o o r (Jo-a /nl ) 3 ~I- (D. 1 It.I 0 0 o 0

LL 0 LLJ:D cr LUi 0_ LJ I H ro!LI 0 50 100 150 ENTHALPY DIFFERENCE (BTU/LB) 200 Figure 35. Enthalpy Differences for the 77 Percent Mixture in the Two-Phase Region

TABLE XVII Properties of the Nominal 77 Mole Percent Propane in Methane Mixture at the Phase Boundaries Pressure (psia) ] I 250 4oo 500 700 -( vap) 232.1 208.0 183.2 132.2 (Btu/lb) Bubble Dew Bubble Dew Bubble Dew Bubble Dew Phase Point Point Point Point Point Point Point Point Boundaries (OF) (~F) (OF) (~F) (OF) (~F) (OF) (~F) This Investigation -81.0 95.7 -24.0 131.2 12.2 147.0 75.0 170.1 Akers,Burns and Fairchild(l) -73.2 -- -2.5 -- 11.0 Price and Kobayashi (109) -79.0 -- -21.0 -- 11.7 -- -- - Reamer,Sage and Lacey (111) -- 100.8 -- 131.0 -- 147.1 75.8 173.0 Sage,Lacey and Schaafsma (126) -- 97.0 -- 132.0 -- 148.0 64.0 175.8

-125 Isothermal The isothermal data obtained in the single phase region were interpreted in accordance with Equation (3) and plots made of the average value of the isothermal throttling coefficient as a function of pressure. Typical results are shown in Figure 36. Point values of the isothermal coefficient were obtained graphically. As the lower limit on pressure is about 100 psia, it was necessary to estimate cp = f(P) at low pressures. To aid in this estimation, values were calculated using the BWR equation of state with the original constants for methane and propane7 together with mixing rules as originally 8 suggested8 Typical results are presented as a center line on Figure 36. In addition, Equations (32) to (34) were used with published values of the second virial coefficient for methane and propane and the interaction term5 to estimate cp. The resulting value at 201~F is plotted on Figure 36. As another check, PVT data for the mixture as inter57 r(H0 -H) 1i preted using Equation (24) yielded values of ( - between zero pressure and 200 psia. A typical value is presented as a dashed line on Figure 36. A solid line (such as shown on Figure 36) was drawn to be consistent with the data obtained at elevated pressures and the estimates based on data from the literature in the low pressure range. Values of the isothermal throttling coefficient, cp, obtained by interpreting the data (including values of qP established as outlined above) are reported for each of the experimental isotherms in Table XVIII. These values are summarized in Figure 37. As previously mentioned one experimental isothermal run was made across the two-phase region. The results of this run are presented in Figure 38. Breaks in the curve indicate both the upper pressure at which vaporization started and the lower pressure

-126-.12.1 I.10.09.08 On.07 m I-.06 a. I <3 76.6 % Propane in Methane 201 ~F Isotherm.05.04.03 --— B.W.R \ o HUFF and REED.02 --- EDMISTER and YARBOROUGH.01 500 1000 1500 PRESSURE (PSIA) Figure 36. Isothermal Throttling Coefficient for the 77 Percent Mixture at 201~F 2000

-127 TABLE XVIII Experimental Values of the Isothermal Throttling Coefficient, 0, for a Nominal 77 Mole Percent Propane in Methane Mixture 0 x 102 (Btu/lb. psia) Pressure psia ob 100 200 500 400 500 6oo 700 800 900 1000 1100 1200 1300 l4oo 1500 1600 1700 1800 1900 2000 -96.8a +0.301 +0.302 +0.303 +0.304 +0.304 +0.305 +0.306 +0.307 +0.308 +0.308 +0.309 +0.310 +0.311 +0.313 +0.316 +0.321 +0.328 +0.339 Tempera ture 99.9 -0.734 -0.596 -o.483 -0.396 -0.325 -0.265 -0.214 -0.170 -0.1350 -0.101 -0.071 -o.044 -0.017 -OF 201.0 -4.39 -4.76 -5.19 -5.70 -6.33 -7.01 -7.86 -9.13 -10.81 -11.60 -10.66 -8.77 -6.45 -4.54 -3.39 -2.62 -2.10 -1.72 -1.42 -1.19 -1.00 251.0 -3.76 -4.03 -4.30 -4.56 -4.83 -5.11 -5.43 -5.79 -6.18 -6.58 -6.77 -6.70 -6.56 -5.89 -5.16 -4.39 -3.70 -3.05 -2.53 -2.22 -1.98 a Calculated using Equation (8) b Extrapolation to zero pressure based primarily on PVT data

-128 a) t3 _J 0 -D x 400 800 1200 1600 2000 PRESSURE (PSIA) Figure 37. Isothermal Throttling Coefficient for the 77 Percent Mixture

2000 1800 1600 TEMPERATURE =99.9 ~F 76.6 MOLE PERCENT PROPANE IN METHANE 1400I1200W 800- 792 PSIA 600400---— x — _._.___ 255 PSIA 200- (AHv)r= 120.8 BTU/LB C I I I I, I I I I I I 1 I -150 -140 -130 -120 -110 -100 -90 -80 -70 -60 -50 -40 -30 0 -20 -10 0 ENTHALPY DEPARTURE - BTU/LB Figure 38. Isothermal Enthalpy Differences Through the Two-Phase Region at 100~F for the 77 Percent Mixture

-150 at which vaporization was complete. Isenthalpic Seven determinations were made with the throttling calorimeter under conditions such that a drop in pressure resulted in an increase in temperature (Run 4R on Figure 29). The inlet temperature was constant at -96,8~F in all cases. The data as interpreted using Equations (4) and (11) are illustrated in Figure 39. The values of the Joule-Thomson coefficient determined from these data are summarized in Table XIX. These data are used in conjunction with Equation (17) to obtain isothermal enthalpy differences, The 50.6 Mole Percent Propane in Methane Mixture After completion of the 76e6 mole percent propane in methane mixture the fluid in the system was diluted further with methane to obtain a 50.6 mole percent propane in methane mixture. Composition of Gas The composition of the system as obtained by a chromatographic analysis is reported in Table XX. Again any small changes in composition which occurred were balanced by adding quantities of the deficient component. The chromatographic analyses on a day to day basis are summarized in Figure 40o Regions of Measurement The ranges of pressures and temperatures covered in the experimental investigation of this mixture are indicated by lines drawn on a pressure versus temperature diagram in Figure 41. The isobaric results for individual runs in the single and two-phase region are given in Table LIV of Appendix B, The isothermal and Joule-Thomson data are presented

-151 cA. I a I...,..trI I I I I I I I I I INLET TEMPERATURE:- 96.8 OF AVERAGE TEMPERATURE:-96.2 ~F 76.6 PERCENT PROPANE IN METHANE I I 6.2 0,. e0 o Iz'-' 6.0 0 IL ULJ 0 0 z 0 U) o 5.8 x li - I rO o 5.6 I I% T 5.4 - I I I I I I I I I 0 200 400 600 800 1000 1200 PRESSURE (psia) 1400 1600 1800 2000 Figure 39. Joule-Thomson Coefficient for the 77 Percent Mixture at -96.2~F

-132 TABLE XIX Experimental Values of the Joule-Thomson Coefficient, 4, at -96.2~F, for the Nominal 77 Mole Percent Propane irn Methane Mixture Pressure ps ia 300 400 600 800 1000 1200 1400 1600 -[ x 103 ~F/p s i 5.50 5.52 5.57 5.62 5.67 $.72 5.78 5.85 1800 6.02

51.0 8 0 uj z 0~ 0.. 0 90B Oo0 0 0 0 O O 0 0 0 50.5 _ z 0I 0 Q _J O 0 O 0 0 0 I. 0 APRIL I MAY I 1968 50.0 k 0 <A -V 3600 3700 3800 3900 4000 4400 4200 COMPRESSOR HOURS Figure 40. Composition of the Nominal 51 Percent Mixture as a Function of Time

27 22 34 17 I I I 27UUU M --- ---- -- - -- k^ ---- -= ---- ^ ^ -- -- ---- a 24 I- I I t~utuu - -- A -z _i 4 12 37 23 35 18 13 7 2 1500 15 38 a. a: C) Ll 0: 0rr' n3 ro1 19 C: Co 29 24 36 1000 8 3. 16 I I 25 /; y 30 32 20 10 4 50 A 31 26 21 _ 14 - 9 5 r~ - I I I I I I I I - -250 -150 -50 0 50 150 150 250 300 TEMPERATURE -OF Figure 41. Temperatures and Pressures of Measurement for the Nominal 51 Percent Mixture

-135 in Tables LV and LVI, respectively. TABLE XX COMPOSITION OF NOMINAL 51 MOLE PERCENT PROPANE IN METHANE MIXTURE AS DETERMINED BY CHROMATOGRAPHIC ANALYSES Mole Fraction Nitrogen 0. 05 Methane 49. 4 Ethane 0.o05 Carbon Dioxide - 0.05 Propane 50.6 Butane 0.05 100.2 Flowmeter Calibrations Again there were shifts in flowmeter calibration from series to series. The first two calibrations made were very successful and yielded results lying essentially on a single curve. These results are illustrated as the solid line on Figure 42. Again the flow is not laminar in the flowmeter. The average deviations of the experimental calibrations points from the correlating equation for these two runs is ~0,20 percent for the 20 experimental points. The third calibration was found to differ by about 0.5 percent from the results of the first two. The curve for this calibration is shown as a center line of Figure 42. The flowmeter was removed from the system and ultrasonically cleaned. In addition the entire section around the flowmeter was cleaned. The flowmeter was replaced and three sets of calibrations made. These gave reproducible resultso The results are represented by the dashed line on Figure 42. The increased curvature of this last line made it necessary to fit the single curve with two

Flowmeter Calibrations 50.6% Propane in Methane. 17.16.1% L J.14- t 0 K) SERIES MAR. 17, 1968 U-1!$~~~ |u.EL~~ I.-~o ~ 20 SERIES APRIL 2, 1968 v 30 SERIES APRIL 24, 1968 40 SERIES MAY 1, 1968 I~~~~~~.13~~~ - *^S~ ~50 SERIES MAY 13, 1968 o 60 SERIES MAY 27 1968 -- 10 AND 20 SERIES J2- -- -30 SERIES ---— 40, 50 AND 60 SERIES.05.10.15.20.25.30.35 F/g (LB/MIN) /(/Z POISE) x103 Figure 42. Results of Flowmeter Calibrations for the Nominal 51 Percent Mixture

-137 calibration equations, one for low and the other for high flow rates. The average deviations of the experimental calibrations points from the correlating equation for these three runs is ~0.13 percent for 17 points in the low flow rate region and ~0.18 percent for the 20 points at higher flow rates. In using the results of flowmeter calibrations to establish the experimental values of the flow rate, results are used which most adequately represent the flow rate at the time of an experimental run. In cases where the flowmeter calibrations changed between runs (in this case between series 20 and 30 or runs 10 and 21) a somewhat arbitrary decision must be made in order to determine when the calibration most likely changed. This is accomplished by carefully investigating the interpreted experimental runs in light of all the data obtained. The calibrations runs used to interpret specific data for this mixture are indicated in Table XXI, together with values of the total number of points for each set from the calibration equation. For the case of this mixture the correlating equations do not yield identical values of the flow rate in the region of overlap. For example, Runs 37 and 38 were obtained in the region of overlap and both correlating equations-were used to calculate the flow rate. Table XXII shows the results of calculating flow rates by both equations for these runs. It shows that the effect of the choice of equation in this case is not insignificant (0.3 percent). All of the flowmeter calibration constants used in Equation (76) are presented in Table LVII of Appendix B. After completion of the three mixtures it now appers that the flowmeter is one of the main sources of uncertainty and trouble in the modified recycle system. It is affected by both physical upsets and impurities.

-138 TABLE XXI Calibration Data Used in Interpreting Experimental Results Experimental Runs 1 - 21 1 - 3R Calibration Runs Number of Calibration Points Average Deviation (percent) 10,20 20.20 22 - 38 )-,50,60 Low: 17.13.18 High: 20 TABLE XXII Effect of Calibration Equation on Isobaric Heat Capacity Results Inlet Pressure Temperature Run (psia) ( ~F) 37 1700 38 1300 1351.0 131.1 31 5.2 Outl]et Tempera ture ( F) I 44.6 158.3 172.0 ] 44.8 158.7 171.7 0.965 0.961 0.964 0.965 0.962 0.963 Cp(Btu/l bF) High Flow Equation C.(Btu/lb~F) Low Fl ow Equation 135.2 131.4 1.31.3 1.o88 1.050 1.085 1.C47 1.017 1.014

-139 The flowmeter calibration can be changed by either small amounts of oil or solid materials, overpressurization, removing it from the system for any length of time, and mechanical handling. Check on Assumption of Adiabaticity For this mixture a special flowmeter calibration was made to increase the range of possible flow rates in order to test the assumption of adiabaticity. Normally, the range of possible flow rates is determined by the pressure drop across the water manometer. The reading is usually allowed to vary between 2 and 10 inches of water. For this test a special calibration was made with only 1 inch of water pressure drop. This essentially doubles the range of reciprocal flow rate. Four of the points including the point at highest flow rate and the one at lowest flow rate are plotted on Figure 43. A fifth point differed significantly from the other four indicating the probability of a recording error and is not plotted. The figure as well as the results for the 77 percent mixture indicates that the heat capacity obtained is essentially independent of flow rate within the limits of precision of the measurements (~o,3 percent), These results are consistent with those of other studies of 80, 85 this effect8 Interpretation of Results Isobaric The isobaric data for this mixture in the single phase region were interpreted in the same way as the d(ata for propane and the 76.6 mole percent mixture. Results right above the critical region at 1500 psia are presented in Figure 44. This curve illustrates the broad maximum which occurs in the heat capacity in the region right above the critical

.795 h o I 790 a. 0 w I w LU 0 0 0 0 I 0.785 PRESSURE: 1500 PSIA INLET TEMP: +22.7~F OUTLET TEMP: +68.5~F BAND= ~.3 % I I.780 I 0 5 10 15 I/F RECIPROCAL FLOW RATE (MIN/LB MASS) 20 Figure 43. Heat Capacity as a Function of Reciprocal Flow Rate for the Nominal 51 Percent Mixture

1.2 MEAN HEAT CAPCITY 50.6 Mole-Percent Propane in Methane At 1500 PSIA 1.1 I -DATA POINT ---— DIFFERENCE POINT B.W.R. EQUATION OF C4'1A',1P -- _ 1.0 - it 0 _r m. -J I-.8 >II.7:!: IMI - -- I - _ 1 /0-000-r X —-~ - - - - -— 7 a F ~- --— 0 —-- I _Fl.6 -.5 —.4 10 50 100 150 TEMPERATURE OF 200 250 300 Figure 44. Isobaric Heat Capacity at 1500 psia Range for the Nominal 51 Percent Mixture in the Upper Temperature

-142 point for the mixture. This peak is much less sharp than the peaks either for the 76.6 percent mixture (Figure 32) or for pure propane (Figure 12) both at 1000 psia. It resembles the peaks at higher pressures for these systems (Figures 34 and 15). This suggests that the two-phase envelope for a mixture tends to "cover up" regions where there are drastic changes in the physical properties of a single component. It further suggests that it may actually be easier to represent the behavior of a mixture than of a pure component because the regions most difficult to reproduce or predict for the pure component do not exist for the mixture, A majority of the values of heat capacity, C, obtained from interpretation of isobaric data in the single phase regions are summarized in Table XXIII for equal intervals of temperature and pressure, Table XXIV lists supplementary values of heat capacity in the regions of significant change such as near the maxima in the heat capacity and near the saturation curves, All of the experimental heat capacity results are summarized in Figure 45. A typical enthalpy traverse of the two-phase region for this mixture at constant pressure is illustrated in Figure 46. Note the large temperature change between dew point and bubble point (almost 2000F)o Experimentally determined values of the isobaric enthalpy change on vaporization are listed in Table XXV together with the experimentally determined values of the bubble point and the dew point for the mixture, Isothermal Again it was necessary to estimate cp = f(P) at low pressures. This procedure is illustrated for this mixture in Figure 47. Values were calculated using the BWR equation of state with the original constants

-143 TABLE XXIII Tabulated Values of Isobaric Heat Capacities for a Nominal 51 Mole Percent Propane in Methane Mixture Cp (Btu/lb - ~F) Pressure, psia Temperature P sur, OF 0 250 500 1000 1500 2000 -280 -270 -260 -250 -240 -230 -220 -210 -200 -190 -180 -170 -160 -150 -149. -140 -130 -120 -110 -]00 -90 -80 -70 -60 -50 -40 -30 -20 -1.0 0 0.546** 0.548** 0.551** 0.545 0.547 0.549 0.552 0.554 0.557 0.560 0.565 0.566 0.569 0.572 0.576 0.581 0.586 0.586 0.592 0.545 o.548 0.550 0.553 0.555 0.558 0.560 0.563 0.565 0.568 0.571 0.574 0.577 0.581 0.581 0.585 0.590 o.595 0.602 0.611 0.627 0 0.543 0.544 o.546 0.548 0.550 0.553 0.555 0.559 0.562 o0.565 0.568 0.572 0.576 0.579 0.580 o.584 o.588 0.593 0.598 0.604 0.610 o.6.8 0.627 0.637 o.649 0.661 0.675 0.690 0.708 0.730 0.543 0.545 o.546 0.548 0.550 0.552 0.555 0.557 0.561 0.564 0.567 0.570 0.573 0.577 0.577 0.581 o.585 0.589 0.594 0.599 0.605 0.611 0.618 0.626 0.635 o.634 0.653 0.664 0.677 0.692 0.544..546 o..548 0.549 0.551 0.554 0.556 0.558 0.561 0.563 0.566 0.568 0.571 0.574 0.574 0.577 0.581 0.585 0.589 0.593 0.597 0.602 0.608 0.613 0.620 0.627 0.635 0.643 0.652 0.662

Table XXIII continued Tempera tu re OF Pressure, 500 psia 1000 0 250 1500 2000 3..5 10 20 30 40 50 60 70 80 90 100 1.10 120 130 1.40 150 151.2 160 170 180 190 200 210 220 230 240 250 251.3 260 0.741. 0.771 0.419* 0.425* o.430* 0. 44i-5* 0.446* 0.451* 0.457* 0.462* 0.468* 0. 4735 0.475* 0.479* o0.485* 0.490* 0. 496* 0.502* 0.507* 0.5135* 0.519* 0.524* 0.530* 0.53-1* 0.536* 0.507 o.508 0.509 0.510 0.511 0.512 0.514 0.516 0.518 0.518 0.520 0.523 0.525 0.529 0.537 0.536 0.540 0.545 0.549 0.554 0.555 0.560 0.664 0.62] 0.605 0.596 0.589 0.588 0.583 0.580 0.577 0.575 0.575 0.575 0.576 0.578 0.579 0.582 0.582 0.585 1.009 0.904 0.887 0.790 0.756 0.730 0.71.0 0.695 o.684 0.675 0.669 o.664 0.663 0.661 0.697 0.708 0.726 0.746 0.770 0.800 0.833 0.870 0.907 0.944 0.979 1.012 1.031 1.037 1.030 1.009 1.003 0.980 0.948 0.916 0.885 0.857 0.831 0.808 0.788 0.771 0.756 0.754 0.743 0.666 0.673 0.686 0.700 0.715 0.732 0.749 0.768 0.787 0.805 0.821 0.837 0.852 0.866 0.879 0.889 0.891 0.895 0.891 0.882 0.873 0.862 0.850 0.837 0.825 0.814 0.8o4 0.803 0.795

-145 Table XXIIIcontinued Temperature Pressure, psia OF 0 250 500 1000 1.500 2000 270 280 290 300 0.541* 0.565 0.589 0.547* 0.570 0.592 0.55* 0.574 0.596 0.558* 0.579 0.600 0.658 0.733 0.787 0.656 0.726 0.780 0.655 0.720 0.773 0.655 0.718 0.767 ( 18) *X Ideal gas values of Rossini et al Experimental data of Cutler and Morrison (23)

TABLE XXIV Supplementary Table of Experimental Values of Isobaric Heat Capacity, C (Btu/lb) Pressure 700 psia 1300 psia 1700 psia Temp. Temp. C Temp. (OF) P (oF) p (OF) p -50 (P).659 50.8623 110.9247 135 (g).740 60.90]3 120.9489 140.724 70.9390 ]30.9581 145.707 8o.9889 140.9609 150.692 90 3.0635 ]50.9602 155.676 100 1.1320 160.9570 130 1.1597 170.9532 120 1.1486 140 1.1.71 150 1.0208 i60.9678 370.9141

-147 1.2 1.1 I.0 1i -— i —it --— r-c — ICL c -i I I 1 r I it- rtt;':'' — t-r'r~ 7i; t~ _L. L 50.6 MOL PERCENT'-+ PROPANE IN METHANE 7t' UNIVERSITY OF MICHIGAN I- - t-,1968 i -* SATURATED LIQUID OR VAPOR'0 PSIA FROM ROSSINI ET AL. - ---- 1 ~ r g * I _ -I fr- 4l -ri f Iit tI r rrrrr:LL,,, if-C i-t-;-tt —--- ~ ~ i —it-i i —'-~-:'~-t-; ~ -— i —;-C-;;-: i -? I;~f —-; j:...cci..;.-; —I~~ —~I - i;r ii t ~ —-t —-- —; —i~-: --c-ri —-i-i'-~-'- ~ ~ —--- i;r -r: — t J —-- i —~-t —-. —-t -i — -fl -;-ci:.T.'7 f~ TI -Li-i- l~ i' i t-. —:-.i L. o CL El, i:71 V1F^ i5' _t. - I I!; it —-. _. ~-.4_+ 1._ ~-~-,~ q 4 I:.4 t tR ft-,Itl i!-i i. I. - 1 -t.- _.,. r!r-l i ~ —i — "-~l.t-1 —---- ~— i.-;"-1 —; tii-i-L. —IL.-..;..:.I.. tri~~ir I —l-1" —e — i~-' —~ -. -1: L... f I -— r - I. t-. t-l'?!c.. - I. i... 1. -.. i... ztz42t2K4z~ l OIL 1:21:24I. -:; 1/: - I zt ~.....-. i-;.... V... ---- -L I — i:- t - _ t 4 i- -i-. - - _.._, __ t j- -- — I - t r -1::_ PSIA' -../ -.50 - P: L 1500 P 0.8 0.7 0.6 0.5 I i C ~,I:. ~! 1 )lo.. i -L;-i t-' r- I- 1.. - -- * -- -- r — i I~r I. i 4:, +t-t'e i -- - — ff. _ i.4 I- I -t I -;; I *~ i;a b - -:-!' I -l.i 30: SIA-.i^ i1 - l_._ - ti-.!:'..I -. -L — 4-tL — -t~-~ H I -H 11 -f* I — ~~ ~ ~fttT.: i -.-. 1~ i,-e+r-j —-t — — -rci ir-~- ~ C-II-C.;: i cc;.. -1-t-i-if — 1-: -- L+31-ti ri — i I I... i. — ~ ii _I 4-: _ F __.;. _ _. -...~. _. _,_.. — | 7 4_1 _{ s 4~~''-w;~-. ~ ~ 1 — -c-.. -, - / ~- @{-L / -4 t 4,4i 4 ii—'- -r —~ —-~ I —~ —-— r-t~ — ~ —— 1~~ — t'i i-r —.~? -t r~~ —-'~:+ C — i.,-...; — -( —C-i-~i — —~:~-~~t —:-i.I. 100( _:... IT_ ) PSIA - -- - -r r...1 I I- -t r --.I — i-qt- c -7 E -cr~ ~i --- -1 i, 1 4 —— " -- * -.t.~ ii - F. i'-5 -~ -t-i —,. _! -; -.: I,.; Fi -~-t-C — i — r F.-i'- e|-*.1 — ~-t-~!- - -_. ^i~ --. — -7 - 00 PS i-'-hri S.) EI -.m ) PSIA"'-":../. );psi: -.5.T::'I'~-:...C -!- -7t _.i... I it~t- ~ i 1 t-l T"17 I i ct ---- i i -~i CL- 1 i... -- II-;- i LTt-t -i-i i+t- t-t ^..I _. — t 2:000 PSIA.1 -L 1500 PSIA /4i ~ * —4 —: - -- -, _ __ i._ I::T:7 T661000 PSIA I Is~ t 1: I I i!: I I I. - -147 A II x. ji7 4 t 7 -t:_t; rlt+_ -j'4'crnn DqI.A:L -'~ 2~~~~~~~~~~~~~~~~~~~~~~~~~~50 PSIA -' —. iLrcV I _ _ t r? i I;.._ c. i -+T I I 4-:L L 1 -.- -1 -- 4. Elti~4 E4 z:. 14.iI- I; —:l ri i 4 k 4L; 4, 0.4 -3'. rl i~;_. -.- i,. - -... -- - - - rt — el I. - l-7 -i t-i —: ~-' ~r t, i Li~ r - /i - I'-f i I- I i-i'- -~..- -1 -t - i - 7. -- — r...... t -' t -.-H 0 PSIA - -T tLrfl i-1:t: -ii rr i —C —~rlT'L —-i jl- ~t-i7-j i —-i-i:it. —-' ——' —' —'I- - —. t-.(..ii. i -i.L:-il t — -~l-~ —-1-.-i "-'.i-i-!-cLI.,.L. i-- ci -~ eI 1! i i, — t L fe-i —;- {!-ti t - -.i-. - e — -..'.L, _ 1-,'1....;''~-' —'t%: i _' - -"*'.~ - - - i;-'....i. i; * - -I-r — -— i-i ——; — -- t t _:.-::' —- ----: —r r _ -& — t I 7.i-1 — i=....L':- - +- "-'-f-' t' - t-T-'-' +-e __ a~~ I - -_, —8-t TFl.ih i'L 00 -200 -100 0 100 200 300 400 TEMPERATURE (~F) Figure 45. Isobaric Heat Capacity for the Nominal 51 Percent Mixture

110 Dew Point 104.1 OF 100 50.6% Propane in Methane 500 PSIA 80_n ~~~0 Run 20 80 - o Run 32 60 - 40 -20 l l c 20 O.r u, -20 - -40 - -60 -60 Bubble Point (-82.9~F) -80 ~- 0 t/ —--------------— (AHV)p 225.0 Btu/lb _ 50 100 150 200 250 ENTHALPY DIFFERENCE (BTU/LB) Figure 46, Enthalpy Differences for the 51 Percent Mixture in the Two-Phase Region I I

TABLE XXV Properties of the Nominal 51 Mole Percent Propane in Methane Mixture at the Phase Boundaries Pressure (psia) 500 700 250 1000 (AH vap )' i (Btu/a 2253.4 225.0 197.5 138.2 (Bt u/lb - _ Phase Boundaries This Investigation Bubble Point ( ~F) -136.0 Dew Point ( 62.0 OF) Bubble Point ( OF) -82.9 Dew Point ( ~ o104.1 F) Bubb le Point ( ~F) -46.4 Dew Point ( ~F) 123.6 Bubble Point ( ~F) 11.1 Dew Point ( 0F) 132.7 Akers, Burns -125.0 -80.9 -46.2 11.1 and. Fairchild Price and -136.3 Kobayashi 1356.3 -83.4 -46.1 11.1 Kob aya -..- - Reamer,S age 63.8 104.6 123.5 - 140.5 and Lacey | _, - - - -. _,, _..................... H! \O! Sage, Lacey and Schaafsma 6o.5 103.9 123.5 137.7

-150-.075 070 \ sotnerm.065 1%.060 _.055.. I 050 I'a-.045 -.040.035 A DANTZLER ET. AL..030 o HUFF AND REED 0 B.W.R. --- EDMISTER AND YARBOROUGH.025 -L * HEAD.020 I I 0 500 1000 1500 2 PRESSURE (PSIA) Figure 47. Isothermal Throttling Coefficient for the 51 Percent Mixture at 152.2~F;000

-151 7 for methane and propane together with mixing rules as originally sug8 gested. Typical results presented as open circles on Figure 47. Note that the agreement between the BWR equation and the experimental values is good throughout the entire region of pressure. Again PVT data for the mixture1 as interpreted37 using Equation (43) yielded values of v i T between zero pressure and 200 psia. J T This value is presented as a dashed line on Figure 47. Also Equations (532) to (34) were used with published values of the second virial coefficient for methane and propane and the interaction term 75 to estimate cp, The resulting values at 152 5~F are plotted on Figure 47. Values from the two sources disagree by over 15 percent, Finally values of p, the Joule-Thomson coefficient, have been measured by Head for a 51.1 mole percent propane in methane mixture at low pressureso By combining experimentally measured heat capacities from this investigation and Joule-Thomson coefficient data as indicated by Equation (8) values of p can be calculated. These results are presented as solid circles on Figure 47. There is considerable disagreement between the results of the various methods. The solid line on Figure 47 was drawn to be consistent with the data obtained at elevated pressures and the estimates based on data from the literature in the low pressure range. In the low pressure region the line was drawn to agree with the BWR equation of state because of its excellent agreement with the high pressure data. This line was also reasonably consistent with volumetric data. Values of the isothermal throttling coefficient, cp, obtained by interpreting the data (including values of c and other values at low pressure determined as outlined above) are reported for each of the experimental isotherms in Table XXVI. These results are summarized in Figure 48.

-152 TABLE XXVI Experimental Values of the Isothermal Throttling Coefficient, 0, for a 51 Mole Percent Propane in Methane Mixture 0 x 102 (Btu/lb. psia) Pressure psia 0b 100 200 300 400 500 6oo 700 8oo 900 1000 1100 1200 1300 14oo00 1500 1600 1700 1800 1900 2000 Temperature (~F) -149.0a 3.5 +0,305 +0.306 - +0.307 +0.308 +0.309 +0.310 +0.312 +0.313 -0.1904 +0.314 -0.1463 +0.315 -0.1069 +0.317 -0.0745 +0.318 -0.0474 +0.319 -0.0240 +0.321 -0.0030 +0.322 +0.01562 +0.324 +0.0320 +0.325 +o.o466a +0.326 +.o0593 a 152.2 -4.44 -4.67 -4.90 -5.16 -5.46 -5.81 -6.20 -6.62 -7.05 -7.45 -7.61 -7.44 -6.80 -6.08 -5.31 -4.52 -3.82 -3.23 -2.75 -2.35 -2.01 251.3 -3.21 -3.30 -3.38 -3.46 -3.53 -3.60 -3.67 -3.73 -3.79 -3.83 -3.85 -3.83 -3.80 -3.75 -3.67 -3.56 -3.42 -3.26 -3.09 -2.90 -2.72, a Calculated using Equation (8) bExtrapolated to zero pressure based primarily on PVT data

-153 --.,.-. I I" iI. -J CI —...:..: t — 7.1-.., 4 -i1-+-1-,P-tl t —-4 -o.j:.~c~r~-.-..!~-q [ ~Crnm'4 I...... I ~:.: ~.... - -..1-11;..!.- —.; -i- - —-i —~-i' i --; —~ ——; t —-e -r -- -; ~-; —-( r..4-. — i.. A.. t I.-, [ [f.... t I... Ml --?. -1: — 1. lU i. _ _',; —;'. —~-C-lt l....:-. - ~-,-~~-ti- ~ I~~~-;~h;-~~~~~~~~~~~~~~ -~-.'-~.... -l~-V -' p~~ ~ ~~ _ _ _ _ _ __~ 50.6 MOL PERCENT PROPANE IN METHANE UNIVERSITY OF MICHIGAN 1968 * SATURATED LIQUID i - i -I -4 -1I iI 4 — 44| -tI Ii t j >1r — 7 II (.) 0 x -t9;.1 —; I L.;:I-.~.,.~~~.~..~ ~ I I-t-' —!:- -- i-_ _ _ -- -— ~~~I~~.- ~I-~;. i. I 152l.2 0 F' d....... -- - - I..- c — ------- -~l-T: j-_.;-.; ——. —;-i —---- I —-l r —--- I ~ ~i-.. - I. - - I~- ~ ~;! ~~ 3 c -~ -- ~-~ -- ~-i -~ -- -- T -- -~ ~l: i I II I I j - i. L ki... i -—,-~. - i-~~l ~ ~- ~ i ~-.~-. I -~ c.. ~c-: — ~ —-- ~ - I - ~ ~ ~ ~ ( —I-~ I- _L.. .(.._.. I.!._ ~-~ — ~.~ ~ ~ I ~ ~; - — I —- ~1 —~':-:~7-1~-' ~~-r 1-~- ---- —~ —~,~.~I ~-~~; —--~ ~-;- i —-.; —-.~~~ —: ----— I,-~~. i.:I...,.; ~-~t —T.- -~:. — 1~ i -— r~-. ~~i.... I -— r i -—: iL; —-; —;~-~-~^ —....;...:.ii-;-~ i... 51.3 iOFi -— L 41 4- T I J I 4 I 4~-i,; I I ---— Irll I''I:. --- -.. —.- L —-— 4.. -. 1 4.~ tI - - — T -7 --- 7- -. t....._.. -I:...f....._. (........,...;.1..;....,,.:...l.i..j.......:..i i-.1...L' ~~: i-: ~1 ~-, —— -~... ~~ — -— i.. ( — C.. i-;- l ~ — I +3.5oF+4,: -149.00 T-: -4-: i: i H-:2:-*=::...... i!;. I I a i.. I 7 ~-:-L-i —_l~__!~ .' — t L..... —1 r -:-.j —r-_ .i-i _.. _.,_...... 1._..,.-.;..1.,.:.., i_ ~-'7'' -' — i~-i i. T`!T t"'r-~ —- 1 L ------ ~ =~-, -- - -.. - I -!:-t.... - (- i 1'. I Li iI -I i 0 400 800 1200 1600 2000 PRESSURE, PSIA Figure 48. Isothermal Throttling Coefficient for the 51 Percent Mixture

-154 One experimental isothermal run was made into the two-phase region at 3.5~F. A break in the curve was obtained at 966 psia. This break indicated the upper pressure at which vaporization starts. Isenthalpic Twelve determinations were made with the throttling calorimeter under conditions such that a drop in pressure resulted in an increase in temperature (Run 4R on Figure 41). The inlet temperature was constant at -149.0OF in all cases. The scatter in the data of greater than 1 percent as illustrated in Figure 49 is the result of the measurement of unusually small temperature differences due to the small JouleThomson effect at these conditions'When this effect is related to an enthalpy difference by Equation (17) and used in the preparation of a PTH diagram or table the error involved in this scatter becomes extremely insignificant. The values of the Joule-Thomson coefficient determined from these data are summarized in Table XXVII. TABLE XXVII EXPERIMENTAL VALUES OF THE JOULE-THOMSON COEFFICIENTJ, t, AT -149.0~F FOR THE 51 MOLE PERCENT PROPANE IN METHANE MIXTURE Pressure -i x 103 psia ~F/psi 300 5.24 400 5.26 600 5.30 800 5.35 1000 5.40 1200 5.44 1400 5.48 1600 5.53 1800 5.57 2000 5.62

6.0 - 5.5 <: a. o =k I% _ L I J1 n 5.0 - I I 200 500 1000 1500 PRESSURE (PSIA) Figure 49. Joule-Thomson Coefficient for the 51 Percent Mixture at -149.0~F 2000

-156 Consistency Checks As illustrated for propane, if isobaric, isothermal, and isenthalpic data are obtained for a system at properly selected values of pressure and temperature, it is possible to check the thermodynamic consistency of such data. For the 77.6 mole percent propane in methane mixture experimentally determined isobars and isotherms intersect forming closed loops which are shown in Figure 50. As can be seen, the largest percentage deviation is 0.47 percent for a loop which included both isobaric and isothermal data within the two-phase region. The average absolute deviation for the 14 loops was found to be 0.18 percent. This should give some indication of the accuracy of the data presented, Figure 51 shows the results of consistency checks for the 50.6 mole percent propane in methane mixture. The largest percentage deviation is 0,74 percent for a loop which included both isobaric and isothermal data within the twophase region. This is the largest deviation obtained using the present recycle flow facility. The average absolute deviation for the 13 loops was found to be 0.23 percent. Enthalpy Diagrams The data reported in previous sections have been used to prepare skeleton tables of values of the enthalpy for these mixtures at selected values of pressure and temperature as reported in Tables XXVIII and XXIX. In addition, enthalpy- pressure - temperature diagrams have been prepared and are presented as Figures 52a and 52b, and 53a and 53bo The 76.6 Mole Percent Propane in Methane Mixture The following procedure was used in preparing the skeleton table and diagram for the 76.6 mole percent propane in methane mixture.

-157 2000 1500 1 AH = AT +3.91 Btu/Ib SAHi = + 0.43 Btu/lb I ZAHi I AH I x 100 = +0.18% I +0.08 +0.05% -0.35 -0.31% -0.44 -0.20% -0.08 -0.06% -0.06 -0.05% 0't) Q. UL r n AL or Q_ 1000 AHT = +1.49 Btu/Ib +1.36 +0.47% / -.- -0.89 -0.28%/ +0.56 +0.35% 500- ------ +2.00/ -0.10 -0.12 +0.41% / -0.03% -0.14% H = 156 Btu/lb I +0.03 +0.02% -0.05 0.06% 0 -200 -100 0 TEMPERATURE OF +100 +200 +300 Figure 50. Checks of Thermodynamic Consistency of Thermal Data for the 77 Percent Mixture

<.. -.092 -.253 +.313 -.05%.08 / +.15% / + 1000 C) d / +2.710. ~ +.74 % -.479 c -3 3 3 OZ59 -.26% +.07%/ 500 +1.411 1 -352 +.23% 1 -.27% -.382 -.31% -250 -150 -50 50 150 250 TEMPERATURE (OF) Figure 51. Checks of Thermodynamic Consistency of Thermal Data for the 51 Percent Mixture

-159 TABLE XXVIII TABULATED VALUES OF ENTHALPY FOR THE NOMINAL 77 MOL PERCENT PROPANE 1IN METHANE MIXTURE Temperature, F Saturated Saturated Latent Heat Pressure Bubble Dew Liquid Enthalpy Vapor Enthalpy Of Vaporization (psia) Point Point (Btu/lb) (Btu/lb) (Btu/lb) 100 -144 +36 69.0 325.0 256.0 200 -100 +83 93.6 335.7 242.1 300 -62 +110 115.3 342.6 227.3 400 -24 +132 137.2 344.7 207.5 500 12 147 159.2 342.7 183.5 600 47 160 181.3 338.7 157.4 700 76 170 201.6 333.4 131.8 800 102 178 221.6 326.5 104.9 H (Btu/lb) Temperature Pressure, psia (~F) 0 250 500 750 1000 1250 1500 1750 2000 -280 234.9 1.2 2.1 3.1 4.2 5.2 5.9 6.9 8.0 -270 237.7 6.1 7.1 8.2 9.2 10.0 10.7 11.6 12.9 -260 240.4 11.1 12.0 13.3 14.2 15.0 15.6 16.5 17.8 -250 243.1 16.1 17.1 18.3 19.2 20.0 20.5 21.4 22.7 -240 245.9 21.1 22.0 23.2 24.0 24.9 25.5 26.5 27.7 -230 248.6 26.0 27.0 28.2 29.0 30.0 30.7 31.6 32.6 -220 251.4 30.9 32.1 33.2 34.0 34.9 35.7 36.5 37.6 -210 254.2 35.9 37.0 38.1 39.0 39.9 40.7 41.5 42.6 -200 257.1 40.9 42.0 43.2 44.0 44.9 45.8 46.6 47.6 -190 259.9 45.9 47,1 48.4 49.2 50.0 5,0.8 51.5 52.6 -180 262.8 50.9 52.3 53.5 54.4 55.2 55.9 56.7 57.6 -170 265.7 56.1 57.5 58.5 59.4 60.4 61.0 61.9 62.7 -160 268.7 61.3 62.7 63.8 64.6 65.5 66.1 67.0 67.8 -150 271.7 66.6 68.0 67.0 69.8 70.6 71.4 72.,2 73.0 -140 274.7 71.8 73.2 74.2 75.0 75.7 76.6 77.4 78.2 -130 277.7 77.0 78.5 79.4 80.2 80.8 81.7 82.5 83.3 -120 280.8 82.3 83.8 84.8 85.5 86.0 86.9 87.6 88.4 -110 284.0 87.9 89.0 90.2 90.8 91.5 92.3 93.0 93.6 -100 287.1 93.7 94.4 95.5 96.2 97.0 97.7 98.4 98.9 - 96.8 288.2 95.7 96.1 97.2 98.0 98.6 99.3 100.0 100.5 - 90 290.4 99.4 100.0 100.9 101.6 102.2 103.0 103.6 104.2 - 80 293.6 105.0 105.5 106.3 107.0 107.6 108.3 109.0 109.5 - 70 296.9 112.3 111.0 111.9 112.5 113.0 113.7 114.5 114.9 - 60 300.3 119.3 116.7 117.4 118.0 118.6 119.5 120.1 120.4 - 50 303.7 126.5 122.4 123.0 123.6 124.4 125.1 125.7 125.9 - 40 307.1 133.8 128.2 128.6 129.3 130.1 130.8 131.3 131.4 - 30 310.6 140.9 134.0 134.3 134.9 135.7 136.4 136.9 137.1 - 20 314.2 148.2 139.9 140.1 140.6 141.4 142.2 142.8 143.0 - 10 317.8 156.2 145.8 146.0 146.3 147.1 148.0 148.5 148.8 0 321.4 163.7 152.0 152.1 152.1 152.9 153.9 154.3 154.7 10 325.2 172.5 158.3 158.2 158.3 159.0 159.9 160.3 160.7 20 328.9 181.2 165.0 164.4 164.5 165.2 165.9 166.4 166.8 30 332.7 191.1 173.1 170.6 170.7 171.5 172.0 172.6 173.0 40 336.6 201.8 181.4 176.9 177.3 177.9 178.4 178.7 179.0 50 340.5 214.7 189.7 183.4 183.9 184.4 184.9 185.0 185.1 60 344.5 229.4 198.8 190.5 190.8 191.0 191.4 191.5 191.4 70 348.6 249.1 207.9 197.6 197.7 197.8 197.9 197.9 197.8 80 352.7 276.2 218.1 204.8 204.6 204.9 204.5 204.4 204.2 90 356.9 312.0 228.6 212.3 212.0 211.7 211.4 211.0 210.7 100 361.1 340.7 240.5 221.9 219.3 218.7 218.3 217.7 217.5 110 365.4 346.9 254.2 231.6 227.2 226.0 225.4 224.8 224.2 120 369.7 352.3 271.1 242.0 235.4 233.9 233.0 232.0 231.2 130 374.1 357.5 292.0 253.4 243.6 241.9 240.6 239.5 238.3 140 378.6 362.8 317.0 266.5 253.4 250.3 248.4 246.9 245.5 150 383.1 368.1 345.0 281.5 263.6 259.6 256.4 254.3 253.0 160 387.7 373.3 352.6 299.0 275.1 268.9 264.5 262.0 260.5 170 392.3 378.5 359.2 318.8 288.2 278.9 273.0 269.6 268.1 180 397.0 383.8 366.0 337.7 302.6 288.9 282.0 278.3 276.0 190 401.8 389.1 372.6 347.7 316.1 298.8 291.0 286.7 283.8 200 406.6 394.2 378.7 356.6 329.5 309.0 300.0 295.0 291.9 201.0 407.1 394.8 379.4 357.5 330.7 310.2 301.0 295.8 292.8 210 411.5 399.6 384.8 365.1 341.2 320.3 309.4 303.6 300.2 220 416.4 404.9 391.0 372.8 351.5 331.5 319.4 312.9 308.8 230 421.4 410.3 397.0 380.5 361.4 342.2 329.4 322.1 317.3 240 426.4 415.7 403.0 387.9 370.6 352.7 339.6 331.3 326.0 250 431.5 421.3 409.0 395.2 378.9 362.6 349.4 340.1 334.7 251.0 432.0 421.9 409.8 396.1 379.8 363.6 350.3 341.2 335.6 260 436.7 426.7 415.0 402.0 387.2 372.4 359.2 349.6 343.4 270 441.9 432.2 421.2 408.7 395.0 381.0 368.0 358.3 352.2 280 447.2 437.7 427.3 415.4 402.4 389.0 376.9 367.9 360.8 290 452.5 443.5 433.2 421.6 409.4 397.2 385.8 376.8 369.3 300 457.9 449.3 440.2 427.7 416.0 404.8 394.5 385.6 377.6

-16o 2000 1900.. (.| (|'' II Methane- Propane 1800^11 |* Mole Fraction C3H8=0.766 Mole Fraction CH4=0.234 1700 Datum: H=O For Pure Methane and Propane 1600 111 l || I|1|| |I| 1 || IIgl Saturated Liquids at -280~F 1500 T-| | |1 gI||HI|I|I 11 The University of Michigan 1968 1400.. O O iC 01~0::0 1300 0 20o'0 M 14 1 16 9 2 1 a i: 900' 12 00 7) 4000 U'~) o00o ENTHALPY (BTU/LB) Figure 52a. Pressure-Temperature-Enthalpy Diagram for the 77 Percent Propane in Methane Mixtur 300~~iri;ii illt -i200~~~~~~~~~~~~~Ijin;i//' ~ iiiiii lB 0 1020 3 40 0 6070 0 90100 10 20 30 10 15 160170180 90 2o $0P-2 300 r~~~~~~~~~~~~NHAP (T/L8 Figre 2a.Presur-Tepertur-Enhaly Dagrm fr te 7 Pecen I 240 300 30

Ado;. e 1ruuu 1900 1800 1700 1600 -1 L I I~: e-i ~ ~ ~ ~ ~ ~ ~ E I II NSIII - El I -+~~~~~~~~~~~~~~~~~~~~~~~~II 0, 4 00 0 o p 0000 00 0o( c~~~~~~~~~~~~~~~~l ~ ~ ~ ~ ~ ~ \ pr) Q C C L r I A Ol Cs~i Li =: C\1 J:5:ri:r l I IL i rr x1i ILT 1 I i IT I~l I IL I I' 1 E lI I I L 1I fl I! cW CW ffl\1 1T ", I t f 4: t c rl. 0 1:. TT. lllj T - I.... 1 O' |F||E|| Methane- Propane t > t l X XMole Fraction C'H9=0.766 % p 9 Xl||ll Moie Fraction CH4=0.234:| aS X1| W Datum: H=0 For Pure g: 5 S 4 Methane and Propane.% T _ Saturated Liquids at - 280~F > f Ao og'' The University of Michigan 14V -....;I I -'!!U I r. 14 < Ir LU cn iija I n JO c w Z 0( E I.I 1C; ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ II ul it~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~ ~~~~~~~~~~~~~~~~~i JOO~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~' ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ I'00~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~L too.i ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~~~~Ll 50 II LI i 1+4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ M-~~~~~~~~~ ~~~~~~ 7-T-T-)1&...6.... _4'i — i SHEL L. I IOLL j v vu I~~~~~~~~~~~~~~~~~~~~~i ~ ~ ~ ~ ~ ~ ~ ~ - L Ws &I s X t lk t t I I~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~~I I IL~ ~ ~ ~ ~ ~ ~ ~~~~.L.i;.I.i MX~~t NLI-Wt 1\11L 1'LI XI a d I I L I I~~~~~~~~~~~~~~~~~~~~ti~L IL. I I~~~~~~~~~~~~~~~~~~~~~~ C z t %. 140 150 160 170 180 190 200 210 220 230 240 250'260 270 280 290 300 310 320 330 340 350 360 370 380 39 t0 400 410 220 430 440 450 460 ENTHALPY (BTU/LB) Figure 52b. Pressure-Temperature-Enthalpy Diagram for the 77 Percent Propane in Methane Mixture

-162 TABLE JXO:X TABULATED VALUES OF ENTHALPY FOR THE NOMINAL 51 MOL PERCENT PROPANE IN METHANE MIXTURE Temperature ~F Saturated Saturated Latent Heat Pressure Bubble few' Liquid Enthalpy Vapor Enthalpy of Vaporization (psia) Point Point (Btu/3b) (Btu/lb) (Btu/lb) 0loo -80 200 -149 300 -125 400 -103 500 -85 600 -66 700 -46 800 -27 go900 -9 3000 11 1100loo 51 1200 51 300 79 13 56.6 50 74.8 73 89.7 91 102.9 104 115.4 116 127.8 124 140.0 132 152.7 337 165.8 137 180.0 136 194.5 13 210.2 114 235.4 327.0 335.5 339.6 341.3 341.5 340.6 338.4 335.6 530.4 322.2 312.3 299.6 276.5 270.4 260.7 249.9 238.4 226.1 232.8 198.4 182.9 164.6 142.2 117.6 89.4 41.1 H (Btu/lb) Temperature 20 50 Pressure, psia 170 20 (~F) ~~0 250 500 750 16000 1250 60 1750 2100 -280 234.0 1.5 2.1 2.9 3.9 4.9 6.o 6.7 7.5 -270 237.1 7.0 7.5 8.4 9.6 10.4 11.4 12.1 13.1 -260 240.2 12.3 12.9 3.9 15.1'16.0 16.7 17.6 18.5 -250 243.4 17.7 ]8.5 19.5 20.4 21.3 22.2 23.0 24.0 -240' 246.5 23.4 24.0. 24.9 26.0'26.8 27.7 28.5 29.5 -230 249.7 28.9 29.6 30.5 31.5 32.3 33.3 34.1 34.9 -220 252.9 34.6 35.4 36.3 37.0 37.6 38.7 39.6 40.4 -210 256.1 40.2 40.9 43.8 42.5 43.3 44.4 45.2 46.1 -200 259.3 45.9' 46.5 47.4 48.2 49.0 49.9 50.7 51.7 -]go 262.5 51.4 52.3 52.9 53.6 54.6 55.5 56.4 57.2 -180 265.8 57.0 57.9 58.8 59.6 60.4 61.3 62.1 62.8 -170 269.1 62.8 63.6 64.3 65.2 65.9 66.9 67.7 68.6 -160- 272.4 68.6 69.5 70.2 71.0 71.7 72.5 73.3 74.4 -150 275.7 74.4 75.1 75.8 76.7 77.5 78.3 79.o 80.0 -149.0 276.0 75.0 75.7 76.5 77.2 78.0 78.9 79.7 80.5 -140 279.1i 80.4 80.8 81.4 82.6 83.5 84.3 85.o 85.8 -]30 282.5- 93.5 86.7 87.4 88.4 89.3 90.0 90.7 9.6 -120 285.9 107.0 92.7 93.6 94.3- 95.0 95.8 96.5' 97.4 -110 289.4 118.2 98.6 99.2 100.2 o101.0 101.2 302.4 103.3 -100 292.9 127.1 104.8 105.5 106.2 107.0 307.6 108.3'109.2 -90 296.4 136.0 310.8 131.5 ]]2.3 113.0 313.6 114.3 115.1 -80 300.0 144.2 119.0 ]18.1 138.5 118.9 119.6 120.3 32i.2 -70 303_6 152.7 130.5 124.6 124.5 125.1 225.9 126.4 127.2 -60 307;2 160.7 140.6 351.3 131.0 131.3 132.0 132.5 133.3 -50 310.9 168.6 149.9 337.6 37.4 337.6 138.2 138.8 139.5 -40 314.7 177.4 359.3 34.9 143.9 344.2 i44.7 145.? 145.7 -30 18.4 186.4 368.3 153.3 150.6 150.7 153.1'153.4 151.9 -20 322.3 195.7 176.7 ]63.4 157.5 157.6 157.9 158.0 158.4 -30 326.1 205.7 185.5 ]735.3 164;6 164.2 164.4 164.5 165.0 0,'5 330.1 2}7.5194.7 182.1 173.5 371.3 171.3 171.2 171.6 3.5 31.4 197.9 185.1 174.1 373.9'173.7 173.6 173.8 10 334.0 230.'0 204.2 191.5 179.2 378.5 378.2 178.2,178.4 20 338.0 244.3 233.7 200.8 188.3 185.6'185.2 185.0 185.0'Temperature ( F) 30 40 50 60 70 80 90 100 310 120 330 140 150 152.2 160 170 180 190 200 230 220 250 240 250 251.3 260 270 280 290. w;300 Pressure, psLa 50 1000 125-C 342.1 260.4 224.0 210.6 198.3 193.0 192.5 192.3 346.2 278.2 254.9 220.2 208.1 201.1 o00.1 199.3 350.4 301.9 247.0 229.7.217.6 209.3 208.2 207.2 354.6 330.5 260.0 239.8 227.6238.3 216.3 214.6 358.9 341.7 274.2 251.1 237.6 228.1 224.8 222.8 363.2 347.0 290.8 263.0 248.4-238.4 233.8 231.0 367.6 352.0 309-4 276.2 259.5 248:5 242.9 239.3 372.0 357.5 330.5 290.2 271.7 259.9 252.2 247.8 376.5 362.4 345.1 306.2 284.7 271.5 262.3 256.7 381.0 367.7 351.3 323.8 298.7 283.4 272.5 266.0 385.6 372.9 357.6 338.5 333.6 295.4 282.7 275.3 390;3 377.9 363.7 346.1 325.8 306.7 293.1 284.7 395.0 383.2 369.5 353.7 335.3 317.2 303.3 294.0 396.0 384.5 371.0 355.0 337.2 319.2 305.5 296.1 399.8 388.5 375.6 360.8 344.1 327.1 313.2 303.6 404.6 393.7 383.4 367.3 351.8 336.1 323.0 313.2 409.5 398.9 387.3 374.2 359.8 345.0 332.0 322.5 414.4 404.2 393.2 380.8 367.1 353.5 341.1 333.4 419.4 409.6 398.7 387.1 374.5 361.7 350.1 340.6 424.4 434.8 404.7 393.6 383.6 369.8 358.5 349.0. 429.5 420.2 420.3 399.9 388.7 377.35 366.5 357.3 434.7 425.7 416.1 406.0 395.3 384.7 374.5 365.7 439.9 435.2 421.9 412'.4 402.'3'392.1 382.2 373.7 445.'1 436.6 427.9 418.2 408.7 399.0 390.0 381.6 445.8 437.2 428.5 419.2 409.6 399.9 390.8 382.5 450.5 442.2 433.7 424.9 435.4 407.2 397.4 389.3 455:8 447.9 439.5 431.0 422.0 413.3 404.7 397.1 46l 3. 453.4 445.5 437.3 428.5'420.1 411.9 404.6 466.8 459.2 453.3 443.3'435.2'42T7.1 419.3 412.3 472.5'465.1 457.4 449.7 441.6~ 434.1 426.5 419.7 192.0 199.0 206.5 213.7 221.5 229.1 237.0. 245.1 253.5 262.0 270.5 279.5 288.2 290.1 297.1 306.0 314.9 323.7 332.5 341.0 349.5 357.3 366.0 374.0 375.0 382.1 390.1 397.7 405.5 413.2

-LO5 2000 1900 1800 1700 1600 1500 1400 1300 1200 < 1"00 Fn w 1000 cr I 900 LUf 0- 800 700 600 500 400 300 200 100 0 Methane - Propane Mole Fraction C3He= 0.506 Mole Fraction CH,4= 0.494 Datum: H =0 For Pure Methane and Propane Saturated Liquids at -280~ The University of Michigan IQ9 dft 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 ENTHALPY (BTU/LB) Figure 53a. Pressure-Temperature-Enthalpy Diagram for the 51 Percent Propane in Methane Mixture 230 240 250 260 270 280 290 300

alnqxTr auevqSal UT auvdoaj uaajd T9S aq3 Jog mUeSeTCI aAdTvqIug-ainaeadaaI-eaalnsseaj l *q9g ajnsTl 08b OLZ 097 0V OVtV O0~b OZ 017 00 062 08~ 0~ 09~ 02 O2 02~~ OZ2~ 01~ 00~ 062 082 O0< 7 092 OSZ 072 ~ OZ OI2 0 00Z - I I t a \I I V- \- - I rI I! I W a - - 1 as I T K K I - I a, N, X m: \ v. I V i - \- I:: 7- 0 is X V: A mI I\:\.. i:\ 7 - T> 0 -:-0 - -:X-. -: \. \: Of i- - - i'' i - A - I VI \-' -\-.-. - - - -:::-.. —-- 0:: -a: i_ _' —- -~ —- - 0-a —i - ff — -- -i- _ —------ A C,:: -:-I i ": \ \::-:-0:\:: A — 0 —N \- - - - \ 1 | r- V'. _ s 4.\u _ 1 i_. X,.. a\.. HI_. j __ _\1_.._.. \.. ^\ -.:\I M\ "A V- \; 001 oo002 k - \' i~ 7.A' q S I - i - -.:X... -].._..: —: v — 00~ 0017 009 OOS 009 OOL 008 -a m rl3 006 c co C: 0001 m 0011 1 _> _ r\'SAi,^ A; H l:, ii:i,- _.. m-._iiCI. *$ Hi! 1- [_ ^n EFS. l.. Z0021 00~1..._l-. V -- 4 n i..._...4a C r i., I — I..!j lk.. r - L — I, Nl t- -- in0 -e - i( r r_. t C Caro~~~~~~~~~~~il ~i lu S I rllr asp'o o o -1 E _...i.!-~ —9 O; i —9~l-l I.L 4 1) l T_>_LA,__'t_,; —+@ —; |-inch -i- Ianl |;~te ~ te-m0 e-ffi~~~~~~~~~~~~~.9 M w -'4 — -L,,L1 OOb I ) I -iI _L A, I- _j _j_ -4 - ----: --:i.- OOSI t,:", - - :. ' -1 -:. 8961 uD6!q3!oi 10 A!sJa!Aun aqLW Jo082- ID sp!nb! pgsDjnlDS auodoJd pUD auoyqla\ aind joj o=H:wnloa - 767'OHO uo!po3DJJ alo|i -90S'0 = 8H~3 L uo!0iDJJ a9o|0 auDdoJd- auolqWY 0091 OOL I 0081 I-! — I -- l —:\; - S 01 i f 0061 OZ0002 I; -_W

-165 1. Reference states were taken to be H = 0 Btu/lb for the pure components as saturated liquids at -280~F. This choice is consistent with that previously used for pure methane63 pure propane and for other mixtures of propane and methane which have been investigated80,82)85,87,88 2. The enthalpy of pure methane as a gas at zero pressure and +201.0~F was calculated using published data on the latent heat of 43 vaporization at 5 psia, the BWR equation of state with the original constants7 to correct from 5 psia to zero pressure at -280~F and published values of the ideal gas heat capacity8 between -280 and +201.0~Fo These calculations are summarized below. H(Btu/lb) Enthalpy change on vaporization at -280~F +228.27 Effect of pressure on enthalpy (5 to 0 psia) +1.43 Effect of temperature on zero pressure enthalpy (-280 to +201.0~F) +248.67 H (Pure methane at zero pressure and +201.0~F) 478.37 - C1 3. The enthalpy of pure propane as a gas at zero pressure and 66 201.0~F was calculated using data on the liquid phase heat capacity, 66 the latent of heat of vaporization at 1 atmosphere, the BWR equation 7 of state to correct from 1 atmosphere to zero pressure at the normal boiling point, and values of the ideal heat capacity1 to account for a change in temperature from the normal boiling point of propane to 201o00Fo These calculations are summarized below. H(Btu/lb) Saturated liquid (-280 to -4357~F) 115.30 Enthalpy change on vaporization at -43.7~F 183.17 Effect of pressure on enthalpy (14.7 to 0 psia) 2.70

-166 Effect of temperature on zero pressure enthalpy (-43.7~F to +201.O~F) 97.99 H C (Pure propane at zero pressure and +201.O~F) 399.16 3- C 4. The enthalpy of the propane-methane mixture at zero pressure and 201.0~F was calculated assuming negligible heat of mixing under these conditions. The molecular weight of methane was taken to be 16.042 and that of propane as 44.094. The resulting value for the mixture is 407.08 Btu/lb. 5. The isothermal effect of pressure on the enthalpy of the mixture at 201.0~F was established from the basic experimental data obtained at this temperature (see Figure 36). As indicated previously, extrapolation of the experimental data to zero pressure was necessary and involved application of data from the literature7 37'5'111 6. Isobaric data reported in this manuscript were used at various pressures to determine the isobaric effect of temperature on enthalpy in both the gaseous and liquid regions as well as within the two-phase envelope. The limits of the two-phase region were determined using results from the traverses of the two-phase regions which were made during the course of this investigation (Table XVII and Figures 35 and 1,109.111.117.125.126 38) supplemented by data from the literature' 9'' 7'' 7. A skeleton table of values determined in this manner was prepared. Slight adjustments were made in the values such that all deviations reported in Figure 50 were reduced to zero. The final results are presented as Table XXVIII. 8. Values from the skeleton table were plotted on graph paper and a smooth plot of the results was prepared by graphical methods. The PTH diagram is presented as Figures 52a and 52b.

-167 The 50.6 Mole Percent Propane in Methane Mixture Essentially the same procedure was used for this mixture as for the 76.6 mole percent mixture. However, the enthalpy at zero pressure and 152.2~F was calculated from the data of the pure components. The resulting value for the ehthalpy of the mixture under these conditions is 396.05 Btu/lb. The isothermal effect of pressure on the enthalpy at 152.2~F was established from the basic experimental data and extrapolated to zero pressure by application of data from the literature7'82733 50, 58,111 for this mixture. A skeleton table of values determined for this mixture is given in Table XXIX. Values from the skeleton table are presented as a smooth plot on Figures 53a and 53b. Comparison with Other Published Data Enthalpy Data There are some data in the literature which permit direct comparison 25 with the data reported here. Cutler and Morrison report data on the heat capacity of liquid mixtures of methane and propane at temperatures around -280~F as well as data on the heat of mixing of liquid methane and propane at -280~F. The values of the heat capacity at -260 and -2800F for the saturated liquid based on data reported by Cutler and Morrison are plotted on Figure 54 together with values obtained by extrapolation to lower temperatures of isobaric determinations at elevated pressures. The data from these independent investigations illustrate the effect of pressure on the isobaric heat capacity in the dense fluid region. There may be some question regarding the difference in the curvature

LL 0 -o 111 3 I >O m 0 I (. 0C.57k 51 PERCENT PROPANE AND METHANE.1% 1 -2000F LL 0.QQ -o m 0 CL I 0 0 x m 0 0.56k \ A - F -22noF A.55.55 On\ A soLo P CUTR OPEN PONTS T60H0F SOLID POINTS: CUTLER & MORRISON (23) OPEN POINTS: THIS INVESTIGATION I H fc 00 OI OD.54~ 500 1000 1500 2000 PRESSURE psia PRESSURE psia (a) (b) Figure 54. The Effect of Pressure on C at Low Temperatures Including Comparison with Data of Cutler and Morrison (23)

-169 between the results for the two mixtures. The curvature, however, is difficult to determine because of the small variation in heat capacity with respect to pressure (note the 1 percent band). Values of heat capacity of the mixtures can be calculated at zero 118 pressure from published values of ideal heat capacities. Values for both mixtures thus determined are plotted on Figure 55 together with values obtained during the course of this investigation. These values from independent sources are consistent and illustrate the effect of pressure on the isobaric heat capacity in the gaseous region at temperatures just above the two-phase envelope. Data on the Joule-Thomson coefficient, A, have been published for a 51l1 mole percent propane in methane mixture at 1520F at pressures up to 600 psia by Head50 In addition, data on the Joule-Thomson coefficient have been published for several binary mixtures of methane and propane 11 over a wide temperature range and up to 1500 psia. These latter values were interpolated with respect to composition to establish the values reported in Table XXX. In addition to both sets of. values, values of - iC C and cp for the 50.6 mole percent mixture and the ratio of -iP lo00 P are also listedo The values of p. obtained by both experimental investigators are reasonably self consistent, however, they differ from the experimental results of this investigation by as much as 10 percent, The data of Head when combined with experimental heat capacities from this investigation and ideal gas heat capacities reported in the literature by Rossini give the results as shown in Figure 47. These results do not agree well with values of isothermal throttling coefficient obtained from PVT data or the BWR equation of state. The JouleThomson results 11mentioned above must be used with The Joule-Thomson results mentioned above must be used with

m I >o 0 LU I 0 Q m 0 U) I Q. o LL 0 -D:3 I >o 0 U) L I 0 I 0 500 1000 1500 2000 PRESSURE - psia (a) PRESSURE - psia (b) Figure 55. The Effect of Pressure on Cp at High Temperatures Including Comparison with Published Values of Rossini et al. (118)

-171 TABLE XXX Test of Consistency of Data Eased on Equation ( 8) Temperature (~F) 152.2 251.3 Pressure (psia) 0 200 400 600 0 200 400 600 800 1000 1250 1500 cB (Btu/lb~F).475.509.558.635.530.547.570 * 597.628.664.712.754 0 (Btu/lbpsi) -. o440 -.0490 -. 0546 -. 0620 -.0321 -.0338 -.0353 -. 367 -.0379 -.0385 -. 03578 -.0356 (F - - Cp (~F/psi) -.o859.0979.1030.1039.0592.0614.0627 o0633.0627.0608.0569.0525 b (~F/psi).0856.0978.1038.1068 pbC.924 1.016 1.061 1.093.927 1.017 1.053 1.064.977.994 1.012 1.030 1.0359 1.049 1.072 1.112 a Interpolated with et. al ( 11). respect to composition using values of pi from Budenholzer, b Values for |p for a 51.1 mole percent propane in methane mixture from Head (50).

-172 Joule-Thomson results for propane125 in order to obtain interpolated results for the 77 percent propane in methane mixture. The results for propane25 extend only to moderate pressures (600 psia) but can be extended to elevated pressures by applying Equation (8) with values of C and p from this investigation. These values were interpolated with respect to composition to establish the values reported for a 76.6 mole percent propane in methane mixture in Table XXXI. Also listed in this table are values of C and cp for the 76.6 mole percent mixture from this investigation and p the ratio -C p/cp. These interpolated values of i are consistent with experimental results of this investigation to +3 percent. Phase Behavior A number of independent investigators have reported data on the 1,109,111,126 vapor-liquid equilibrium of the methane-propane system.' "' Data from these sources were used to estimate bubble and dew points corresponding to the pressures of investigation for both the 76.6 and the 50.6 mole percent propane in methane mixtures. These results are included in Tables XVII and XXV for the 76.6 and 50.6 mole percent mixtures, respectively. The results indicate not only the variation among the various investigators, but give some indication of the accuracy of the vapor-liquid equilibrium measurements made in the course of the present investigation. Enthalpy of the Methane-Propane System The isobaric effect of temperature and the isothermal effect of pressure on the enthalpy have been obtained for propane, a 76.6 mole percent and, a 50.6 mole percent propane in methane mixture. Skeleton enthalpy tables and diagrams have been presented for these mixtures,

-173 TABLE XXXI Test of Consistency of Data Based on Equation ( 8) Temperature (~F) 201~F 250 F Pressure Cp (psia) (Btu/lb ~F) 0 200 400 0 200 400 600 800 o.486 0.517 0.579 0.514 0.541 0.577 0.631 0.705 (Btu/lb psi) -0.0438 -0.0519 -o. o653 -0.0376 -0.0430 -0.0483 -0.0543 -0.0618 4 - 4Cp ( F/p si) 0 0. 104a 1.030 0.1115a 1.02 o. 0807b o0.0837b 0.0874b o0.o874b 1.015 1.000 1.016 0.997 a - Interpolated with respect to composition using values of i for propane from (125) and for methane-propane mixtures from (11) b - Interpolated with respect to composition using values of k. for the methane-propane mixtures from (11) and values of i for propane calculated using Equation (8 ) and data for C and 2. g p

In addition both isothermal and isobaric effects on enthalpy have been 80 85 measured by Manker and Mather for a 5.1 mole percent propane in 85 methane mixture) and an enthalpy diagram has been constructed by Mather, The isobaric effect of temperature on the enthalpy for a 12 and 28 mole 85 percent mixture has been measured also by Mather, In constructing the enthalpy diagram for the 11.7 mole percent mixture Mather 5used the averaged data of Dillard32 and the BWR equation of state with the original constants78 and mixing rules to determine the effect of pressure on enthalpy. These results were in agreement with each other for the 11o7 mole percent mixture, and for the 5.1 mole percent propane in methane mixture, both results agreed with the data of Mather, For the 28 mole percent mixture, however, no experimental data were available and Mather used the BWR equation of state alone above the twos phase region to establish the effect of pressure on enthalpyo His justification was based on the agreement of the equation with experimental data for the 5,2 and 11o7 mole percent mixtures. Figure 56 shows the smoothed enthalpy departures obtained above the two-phase region for the 50~6 mole percent mixture at 152.2 and 25130~Fo The points are values of the enthalpy departure obtained using the BWR equation of state. The agreement of the BWR: equation with the experimental data is excellent for both isotherms (less than 0.5 Btu/lb or 1 percent). Since the BWR equation with the original mixing rules agrees with experimental data for both an 11.7 and 50.6 mole percent mixture, the use of the equation by Mather is most probably valid for the effect of pressure on enthalpy for the 28 percent mixture. Thus, accurate results for enthalpy as a function of pressure and temperature are available for a 5o2, 11,7, 28o0, 50.o6 and a7606 mole percent propane in methane mixture and complete the

2000 - U \ \ 1500 a, w 1000 r). 500 \ ~ BWR EQUATION AT 152.2~F * BWR EQUATION AT 251.3~F ~- SMOOTHED EXPERIMENTAL DATA 500 I I -100 -80 -60 -40 -20 0 ENTHALPY DEPARTURE (BTU/LB) Figure 56. Comparison of Experimental Isothermal Enthalpy Departures with the BWR Equation of State for the 50,6 Percent Mixture

-176work on the methane-propane system.

SECTION VI - EVALUATION AND EXTENSION OF METHODS OF PREDICTION The thermal data obtained for the methane-propane system and other data obtained at the Thermal Properties of Fluids Laboratory permits a direct evaluation and an extension of the current methods of prediction of the enthalpy of fluid mixtures at elevated pressures, which were discussed in Section II. This section presents the results of comparison studies and an extension of the corresponding states principle which was suggested from the results of these studies. The various methods of prediction were compared with experimentally determined enthalpy data. The results of these comparisons indicated that the method of corresponding states looked most promising for representing enthalpy behavior of fluid mixtures. Empirical mixing rules were obtained for a three-parameter corresponding states correlation which. accurately represented the enthalpy of the methane-propane binary system. The mixing rules were compared with generalized rules available in the literature and the technique extended to a mixture of nitrogen in methane. Comparisons of Methods of Prediction There have been several comparison studies of methods of prediction of mixture enthalpies. Most have been based mainly on volumetric data. The most extensive of these is the one conducted by the American 140 Petroleum Institute. The recommendations of the authors, however, are restricted for mixtures due to the lack of direct experimental data available when the study was conducted. Since that time there have been several papers which have compared methods of prediction of enthalpies -177

-178 of mixtures which are based on the more recent thermal data. These 87 6 144 41 include Mather et al. Barner and Schreiner, Wiener, Findley et alo, 132 151 Sehgal et al,, and Yesavage et al. All of the above comparisons have used experimental data obtained at the Thermal Properties of Fluids Laboratory. The last two of the above which are the most extensive, were conducted as a part of the present investigation and are summarized in the following pages. Two separate techniques were used to make comparisons of the data with methods of prediction. The techniques used were determined by the data available at the time comparisons were made. The first set of comparisons were based on enthalpy differences resulting from 100~F isobaric temperature differences. This comparison was based on isobaric data made available for mixtures before operation of the isothermal calorimeter. In the second set of comparisons results for isothermal enthalpy departures were utilized, basing the comparisons on the most recent data. Isobaric Enthalpy Differences The data available and used in the first set of comparisons includes the results of isobaric determinations made on the following mixtures: 80,8 85 Nominal 5 percent propane in methane; Manker et al., Mather, 85 86 Nominal 12 percent propane in methane; Mather, Mather et al. Nominal 28 percent propane in methane; Mather8 Mather et al87 85 87 Nominal 43 percent nitrogen in methane; Mather, Mather et al 77 79 Nominal 25 percent helium in nitrogen; Mage, Mage and Katz7 77 79 Nominal 50 percent helium in nitrogen; Mage, Mage and Katz.

-179 Most of the data from the references cited above have been obtained with an isobaric flow calorimeter in the temperature range from -250~F to about 250~F. Some data have been extended to 250~F from about 100~F using low pressure C data and corrections for pressure calculated from p the BWR equation. This extrapolation was made only when experimental values of C at 100~F agreed with predicted values within 1/2 percent p and showed the same trend with temperature. Six methods of prediction were compared with the above data. These included three three-parameter corresponding states methods. The corre24 147 lations of Curl and Pitzer, and modified by Yarborough, the correla149 76 tion of Yen and that of Lydersen, Greenkorn and Hougen. The BWR 7 8 equation of state with the original constants and mixing rules was 96 applied as an example of an equation of state which was compared with experimental data. Finally, comparisons were made with the empirical methods of Peters99 and Canjar and Peterka 5 for hydrocarbon mixtures. In applying these correlations to predict enthalpy changes, pseudocritical properties and values of the correlating parameters for the mixtures must be estimated. A variety of mixing rules have already been suggested. The simplest of these are the linear mixing rules based on mole fraction as originally suggested by Kay5 for estimation of pseudocritical temperatures and pressures. This rule has been extended to 101 estimation of the third parameter for mixtures. Pitzer and Hultgren make use of a quadratic term in predicting correlating parameters for mixtures. Gunn, Chueh and Prausnitz have suggested mixing rules 48 applicable to mixtures containing quantum gases.4 For the helium-nitrogen mixtures, the mixing rules of Gunn, Chueh

48 and Prausnitz were used for all mixtures. In applying the methods of 76 l49 Lydersen, Greenkorn and Hougen, and Yen for the remaining mixtures 65 linear mixing rules were applied. In connection with the Curl and Pitzer method2 the mixing rules suggested by Pitzer and Hultgren1 were applied for the methane-propane mixtures and those of Prausnitz and Gunn were used with the methane-nitrogen mixture. As mentioned previously, several of the procedures use a combination of experimental enthalpy data at low pressures with estimations of the effect of pressure on enthalpy. In order to make these comparisons as meaningful as possible, common sets of low pressure data were used for all methods. For the light hydrocarbons, values were taken from the compilation of API Project 44. Values for nitrogen are 46 those of Goff and Gratch4 For helium, calculations were made using C 0 = (5/2)R. p To estimate enthalpy changes within and in the vicinity Of the two-phase region of a mixture, it is essential that the limits of this region be established accurately. For purposes of obtaining the most meaningful comparison the experimental data of Price and Kobayashi l9 were used to establish these limits for the methane-propane mixtures, the data of Bloomer and Rao were used for the methane-nitrogen mixture and those of DeVaney et al., and Mage7 for the helium-nitrogen mixture. For purposes of comparison isobaric enthalpy changes at pressures of 500, 1000, 1500 and 2000 psia were calculated for five temperature intervals of 100~F and compared with experimental data. The pressures selected were those for which actual experimental enthalpy determinations were made. The large temperature interval of 100~F was selected to

dampen out regions of rapid change in the heat capacity and to reduce round off error involved in reading charts. A percentage deviation was defined as: [H(T2) -H(T)( P(predicted) [H( T)-H( T1 )P(experimental) T2)-H( T1)] P(experimental) Results of the comparison are presented in graphical form for the six mixtures in Figure 57. The figures represent the percentage deviation on a pressure-temperature diagram. Lines corresponding to zero percent deviation between calculated and experimental values are sketched in much the same manner one might draw a contour line from survey determinations on a topographic map. In a similar manner contour lines corresponding to + 5 percent,~ 10 percent and +20 percent deviation were sketched in. Suitable coding was developed to distinguish these regions and to identify regions in which comparison was not possible. From the results of the comparison several observations can be noted. The procedures based on use of molal average boiling point by Canjar 15 99 and Peterka5 and partial molal diagrams by Peters99 yield results which are comparable to other methods. However, they are limited to a smaller region of pressure and temperature and to fewer systems than the other methods as was mentioned in Section II. The BWR equation of state (using the original constants derived from a variety of data) is adequate in the gaseous and critical region but predicts erroneous results in the liquid region. This results, in part, from the fact that limited data were available in this region when the original constants were evaluated and illustrates that empirical equations of state should not be used for purposes of extrapolation. Again it is

-182 a) 5 MOL PERCENT PROPANE IN METHANE b) 12 MOL PERCENT PROPANE IN METHANE 200( 1500 tL I': I i t., II l'.. 2000 \l - N \ I xT I I500 \\ I-F 150 < \ 50( tI> I lr(zIV-V 1- 200( I.000 500 -,,-' -250 -150 - TEM;II;.-i 0 + PERATUI iiiliiH i/!iiii{''i:: t""::. iO +150 +250 E, ~F -250 -150 -50 +50 +150 +250 TEMPERATURE, ~F 1500 —,500 —-./ —^F__ 0 -250 -150 -50 +50 +150 +250 TEMPERATURE, ~F -250 -150 -50 +50 +150 +250 TEMPERATURE, ~F 2,00C ~ I 0 I -250 -150 -50 +50 +150 +250 TEMPERATURE, PF c) 28 MOL PERCENT PROPANE IN METHANE 2o.'..........,~S::0^^-250 -150 -50 +50 +150 +250 TEMPERATURE, ~F 2000 ='\\\':1 qp^ -^, l 1500 I11 w... / _ 250 - 0 5 5 1 -250 -150 -50 +50 +150 +250 TEMPERATURE, TF I -250 -150 -50 +50 +150 +250 TEMPERATURE, ~F d) 43 MOL PERCENT NITROGEN IN METHANE 200( S I 00 500 a_50:.,i l\ +.. —-......... —. J I. /.'-y~.'. I= - -:''''1i.. TEMPERATURE, ~F TEMPERATURE, ~F 2000 --- --- z 500 ---- +,....i....... 200 150 1000 50 71 / -250 -150 -50 +50 +150 +250 TEMPERATURE, ~F -250 -150 -50 +50 +150 +250 TEMPERATURE, ~F e) 25 MOL PERCENT HELIUM IN NITROGEN f) 50 MOL PERCENT HELIUM IN NITROGEN 2000:: —-- I / -:;::::::::::: II -I,~ 1':'-.' ffi:.................. 1500.-. —-. — -...-. 0i0 - 4 — + | _ 1 1 -2% -250 -150 -50 +50 +150 +250 TEMPERATURE, ~F i',S ir::, 1500+ i\_: ~t'Hi -250 -150 -50 +50 +150 +250 TEMPERATURE, ~F METHOD OF CURL AND PITZER (24) AND YARBOROUGH (147) I Tl IiE-ERTUR,,-, 1 I ooo............ -250 -150 -50 +50 +150 +250 -250 -150 -50 +50 +150 +250 TEMPERATURE, ~F CORRELATION OF YEN (149) -250 -150 -50 +50 +150 +250 TEMPERATURE, ~F CORRELATION OF YEN (149) 2000'": k\c. I','!' li;91 o I+ 1 500...''.....':. -250 -150 -50 +50 +150 +250 TEMPERATURE, ~F METHOD OF LYDERSEN, GREENKORN, AND HOUGEN (76) LEGEND DEVIATION ------ 0% LI > 0%;< 5% \\\" "\\\ > 5% < 10% > 10%; < 20%._ _> 20% I! i,1' 1ii i ll NO COMPARISON | w!HH POSSIBLE Figure 57. Comparison of Isobaric Enthalpy Differences with Numerous Methods of Prediction

-183 a) 5 MOL PERCENT PROPANE IN METHANE b) 12 MOL PERCENT PROPANE IN METHANE c) 28 MOL PERCENT PROPANE IN METHANE d) 43 MOL PERCENT NITROGEN IN METHANE 20( 15( 15C 20C gC 1 100 50 200 150 100 50 I I' I \ I 200( 1504 loo 504 -250 -150 -50 +50 +150 +250 TEMPERATURE, F -50 +50 TEMPERATURE, *F i I I 0 +150 +250 E,F 2004 150 a I=0 200 150 100 50 -250 -150 -50 +50 +150 TEMPERATURE,. METHOD OF PETERS (99) g X l[-tl m I - ) -150 -50 +50 +150 +250 TEMPERATURE, T CALCULATIONS USING B-W-R (7, 8) METHOD OF CANJAR AND PETERKA (15) LEGEND DEVIATION 0% I > 0%;< 5% > 5%; < 10% / //% 7> 10%;< 20% ~_ -________> 20% ~~ m:,,::::~NO COMPARISON POSSIBLE Figure 57. Comparison of Isobaric Enthalpy Differences with Numerous Methods of Prediction

more limited with regard to the number of systems which can be predicted than the corresponding states methods. Procedures based on the principle of corresponding states can be applied with some degree of confidence to predict enthalpy departures for mixtures of nonpolar compounds over a wide range of temperatures 149 and pressures. The recent correlation of Yen9 yields results which are slightly better than those obtained from the correlation of Curl 24 and Pitzer and represent a considerable improvement over that of Lydersen, Greenkorn, and Hougen. This is not too surprising since the latter two correlations are based primarily on PVT data whereas the former incorporates enthalpy data. Enthalpy Departure Comparisons In this set of comparisons the results of the investigation of the 76.6 mole percent propane in methane system of Table XXVIII was used as an example to determine enthalpy departures. These departures were compared with various methods of prediction with more emphasis on corresponding states correlations. Again the methods compared with include the BWR equation, the methods of Canjar and Peterka5 and 99 Peters9 The same three corresponding states methods were studied in 149 this comparison as in the previous one. For the correlations of Yen49 and 147 24 Yarborough's extension of Curl and Pitzer, two-mixing rules, Kay's rule5 and the Pitzer-Hultgren rule, were used to permit comparison with each other. In addition an equation of state (Hirschfelder, Bueller, McGee, Sutton53'5 which is based on an extended theorem of corresponding states was also studied. In making comparisons in the two-phase region it is necessary to

-185 200 150.OO I 100.S ~ I\ - / I / 7-t I / -+.g I:5100C w 8r -- __ -100 0 +100 TEMPERATURE ~F (a) +200 + 300 ( V TEMPERATURE ~F (C) 2000uO \\\ \\\ -....... - \ I PETERS (99): -_._AA \\\\\\\\ /. \ -: TTT(llll~tTttt 1500 1500 ~. oirJii —'",'/? i'-"=. lklla........ii A - /,+/ \. + I 1 I000 \\\I 1,000 X w\E~~~~~r\11111,lllll -200 -100 0 +100 +200 +300 TEMPERATURE ~F (d) I 4 — 100 0 TEMPERATURE ~F (f) TEMPERATURE ~F (e) i 2000 1500:ooo EN (149) WITH HULTGREN (101) 500 0 -200 -100 0 +100 + 00 +300 TEMPERATURE ~F (h) LEGEND DEVIATION, d BTU/Ib d=O Exceeds limits If correlot I 0 < d < 20 20< d of correlation 1500 i I o 0 +100 +200 +300 TEMPEIRAURE ~F (i) Figure 58. Comparison of Isothermal Enthalpy Departures with Numerous Methods of Prediction for the 77 Percent Mixture

-186 145 make some sort of flash calculation, and the NGPA Chao-Seader program5 and data in the literature were used to generate the vapor-liquid equili99 brium data. In using the method of Peters99 which is not based on an enthalpy departure it was necessary to determine the departure by substraction. Results of the comparisons are presented in graphical form in Figure 58. These graphs were obtained by plotting the difference between the experimental and calculated enthalpy departures. (H - H) - (H - H) deviation (H)(Btu/lb) (78) (- - 0exp - - calc on a pressure-temperature diagram. Percentage errors between any two points on the pressure-temperature diagram can be obtained by referring to the enthalpy table for the 76.6 percent mixture (Table XXVIII). Figures 58a and 58b show the results of the comparisons of the data with the original BWR equation78 and a recently modified BWR equation.33 Both results indicate good agreement in the gaseous and critical region but much poorer agreement for the liquid. Figures 58c and 58d show the results of the comparisons for the 15 99 correlations of Canjar and Peterka5 and Peters9 Again both methods show fair agreement but are limited in their region of application. Figures 58e and 58f are the results for the Curl and Pitzer and 147 Yarborough method using two different mixing rules. Figures 58g and l49 58h are the results for the Yen correlation using two different rules. It appears that both of these correlations show a distinct improvement when used with the nonlinear Pitzer-Hultgren mixing rule as opposed to Kay's rule. For this mixture the method of Curl and Pitzer, and Yarborough is somewhat better than that of Yen and both are better than that of Lydersen Greenkorn and Hougen76 (Figure 58i). Figure 58 is a that of Lydersen, Greenkorn, and Hougen (Figure 58i). Figure 58j is a

-187 comparison of the data with the equation of state of Hirschfelder et al53'54 It is an empirical corresponding states equation with up to five parameters. It is fit by three analytical functions which are forced to conform at their boundaries. By comparing Figure 58j with Figures 58f and 58h it appears that a five parameter corresponding states analytical equation of state cannot reproduce the data as accurately as a three parameter corresponding states tabular function. This implies that the reduced enthalpy is (to a reasonable degree of accuracy) a function of pseudoreduced temperature, pressure, and a third parameter. However, when trying to fit the tabulated function to one or a set of analytical equations it is at present necessary to add additional parameters. Even with these additional parameters the results of the equation of state do not compare as favorably as the tabulated correlations with experimental data. This is also demonstrated by Figure 58a and 58b where the eight constant BWR equations very poorly reproduce the enthalpy departure in the liquid region. Conclusions A goal of this research was to extend methods of prediction to the point of accurately reproducing the enthalpy data obtained in this investigation with the hope of using an approach that would result in considerable generalization. In light of this goal and the results of the comparison studies it was decided to develop a three parameter corresponding states tabular correlation to describe the behavior of the enthalpy departures of the methane-propane system. There were many considerations which influenced this decision. In the first place, methods such as Peters99 and Canjar and Peterka15

although reproducing the data quite effectively, do not lend themselves easily to extension and generalization. This is in part due to the fact that there is no fundamental justification for such an approach other than success in their region of application. Equations of state also can be made to reproduce the data accurately over their region of application. However, they also cannot be readily generalized to systems for which data are not available. A more fruitful approach appears to be a generalized equation of state based on the corresponding states principle. However, at present, the use of an analytical form appears to require the use of additional parameters. A corresponding states graphical correlation has numerous advantages. It can represent the results to a reasonable degree of accuracy and at the same time has some grounds for fundamental validity. It can be used to represent the enthalpy departure of systems for which data, other than a knowledge of the parameters, is not available. It is generally valid over a wide range of conditions, and can be improved for mixtures by the use of improved mixing rules. Finally, if an analytical form is desirable, the tabular functions themselves can eventually be fit by one or a series of equations. For these advantages a three parameter corresponding states tabulation was utilized. Application of the Corresponding States Principle to Fit Experimental Enthalpy Data In applying the corresponding states principle it was first necessary to develop a tabular function of the reduced enthalpy

-189 departure. This was accomplished using Equation (44) with reference H~-H 1 H~-H 1 substance enthalpy departure functions, RT~- and R- 1 2 developed from enthalpy data for methane and propane. Next, the corresponding states principle was tested for pure components by comparison of calculated results with experimental data for nitrogen. The reference substance tables were interpolated with respect to reduced temperature and pressure to determine the two reduced enthalpies. Next, Equation (44) was used to determine the departure for nitrogen, and the results compared with experimental data. After proving to be successful for. pure components, the results were extended to the methane-propane system by developing mixing rules which best fit the experimental data. First an optimization technique was developed which would search to find a set of optimum values over a wide range of conditions of the three parameters for a given mixture. The individual optimum values of each parameter for each mixture were then fit with respect to composition to obtain smooth mixing rules. Development of the Reference Substance Enthalpy Departures Reduced enthalpy departure tables are available.from most three parameter corresponding states correlations. These tables have, however, been generated in the most part from volumetric data and may be of questionable accuracy. Since accurate enthalpy data have been obtained at the Thermal Properties of Fluids Laboratory for methane and propane, it was decided to develop reference reduced enthalpy functions from these results. In generating the tabular reduced enthalpy function for propane the values of enthalpy, temperature, and pressure presented in Table XII

-190 H -H were used to determine reduced quantities: RT, T/T and P/P l cl *? c c The resulting reduced table is presented as Table LXII of Appendix D. The second substance reduced enthalpy departure table was based 62 on values of enthalpy for methane as reported by Jones. In obtaining Jones' table his isobaric heat capacity data were used to determine the effect of temperature on enthalpy at numerous pressures. The effect of pressure on enthalpy was determined by the BWR equation of state with the original constants7 Recently accurate volumetric results for methane by Douslin et al35 have been used in Equation (38) to determine the 54 48a effect of pressure on enthalpy for methane at 320~F 4' The values for enthalpy departure at 32~F obtained from both the BWR and Douslin are plotted on Figure 59. This figure shows a significant difference between the two results especially at high pressure. The differences are reported in Table XXXII. Since it is believed that the differentiated volumetric data are likely to be more accurate than the BWR equation with the original constants, the Jones' table was adjusted. This was accomplished by adjusting the enthalpy at all pressures in the table by the difference between the results of Douslin34,48a and the BWR results. The resulting corrected table amounts essentially to the table that Jones would have obtained had he used the departures of Douslin348a instead of the BWR. This table was put in reduced form and the results are presented in Table LXIII of Appendix D. Values of the three parameters used in this investigation for methane and propane as well as those for nitrogen are the ones presented in the NGPSA data book and are listed in Table XXXIII. The range of the methane table is for 0.52=T c 1.49 and P _ 2.99 and the propane r r

80 0 70 - 60w 7 a: 40 30- Y I 7 20W' DEPARTURE OF JONES 10 - - DEPARTURE OF DOUSLIN 5 z 0 500 1000 1500 2000 PRESSURE (PSIA) Figure 59. Comparison of Enthalpy Departure of Methane at 32~F Obtained Using Original BWR Equation (7) with Pesults Calculated by Douslin (34,35)

-192 TABLE XXXII CORRECTION MADE IN JONES' TABLE TO AGREE WITH DOUSLIN'S ENTHALPY DEPARTURE Pressure psia 50 100 150 200 250 300 350 400 450 500 550 6oo 625 680 700 800 900 1000 1200 1500 2000 [H(Jones) -H(Douslin) ] Btu/lb 0.00 0.18 0.27 0.35 0.39 0.42 0.49 0.54 0.52 0.40 0.62 0.58 0.64 0.67 0.64 0.56 0.70 0.82 0.94 1.45 1.64

-193 table for 0.27-T 1.44 and P 3.24. In order to obtain departures for r r a third substance both tables must be applied and, therefore, the range of application of the present method is 0.52'Tr 1.44 and P 2.99. This includes much of the liquid and gaseous region as well as the region around the critical. The method can be applied in the two-phase region for mixtures if vapor-liquid equilibrium data is generated from some other source. Application of Reference Substance Equations to Pure Components If the three parameter corresponding states principle is valid for non-polar fluids then it should be possible to predict the enthalpy departure for a substance such as nitrogen from the tabulated departures developed for methane and propane and the three additional parameters only. An enthalpy table developed from experimental data has been presented by Mage et al7'78 and from it enthalpy departures were obtained for comparison. This procedure permitted a check of the three parameter corresponding states theory and the accuracy of the experimentally determined reduced functions. A third order interpolating polynomial was used to determine reduced enthalpy departures from the methane table and the propane table for a given reduced temperature and pressure. The values of reduced enthalpy from the two functions along with a value of the third parameter, W, were used in Equation (44) to obtain enthalpy departures for nitrogen. The values of the three parameters used for nitrogen are listed in Table XXXIIII Equation (48) was used to determine the value of W from c. As can be seen from Table XXXIII the third parameter for nitrogen falls between methane and propane about 1/3 of the way from methane.

-194 TABLE XXXIII PARAMETERS USED IN CORRESPONDING STATES CALCULATIONS Critical Critical Temperature Pressure Accentric Component (OR) (psia) Factor Methane 343.3 67301 0o010 Propane 666.0 617.4 0.152 Nitrogen 226.9 492.9 0.047 Enthalpy departures were obtained for nitrogen throughout the region of application of the reduced tables. Calculations were obtained at pressures of 500, 1000, and 1500 psia and at 20~F temperature intervals between -300~F and -120~F. A computer program subroutine (DEV) was used to perform the numerical calculations. The subroutine searches the reduced enthalpy tables to find the grid points which center a given data point. After selecting the points on which the interpolation is to be based a second subroutine is called which uses Newton's third order interpolating polynomial. The program is called four times to interpolate with respect to reduced temperature and once with respect to reduced pressure for each table to determine enthalpy departures. This subroutine was essentially the one 16 given by Carnahan et al. and converted to the FORTRAN language. The calling subroutine then calculates the enthalpy departure for the points and also the deviation and percent deviation between the calculated and experimental value. The subroutine repeats the process for the next input condition. When the departures and deviations are calculated for all of the conditions desired, the root mean square difference between the experimental and calculated enthalpy departures is determined. A simplified main

-195 program can be used to transmit data and print results. As will be discussed later, however, this subroutine was used as part of the optimization scheme applied for mixtures. The complete program is given in Table LX of Appendix C. A major disadvantage of the calculation procedure is its inability to correctly interpolate (or extrapolate) the tables in the vicinity of two-phase region. The search procedure arrives at a series of grid points on which the interpolation is based which contain both gaseous and liquid points. Since there is a natural discontinuity at the twophase region which the interpolation does not consider, the interpolation is likely tc be in error. This is, however, a limitation only for pure components, since for mixtures the two-phase envelope, in which the mixture is not stable as a single phase, extends to prohibit the possibility of calculations near the single component reduced two-phase region. For the 32 conditions which were compared for nitrogen, the sum of the squares deviation is 0.52 Btu/lb. The maximum deviation is 1.5 Btu/lb but this occurred at -120~F (T = 1.50) slightly outside of the region of application of the tabulated functions. The results of this comparison are presented in Table XXXIV. The agreement is good especially when considering the possible uncertainties of 1 Btu/lb present in each of the tables for the three pure components. Thus, in this instance it appears that the three component principle of corresponding states can be used to predict enthalpy departures for non-polar pure components almost to the degree of uncertainty of the measured quantities. The parameters that are used are quantities that have definite physical meaning and thus knowledge of these quantities alone is enough to

TABLE XXXIV TEST OF THREE PARAMETER CORRESPONDING STATES PRINCIPLE USING DATA FOR NITROGEN PPESSURE...... - TEMPERATi -EXPER. DEPARTURE.CALC. DEPARTURE DiFE1aNCE =-PERCENT DIFEPRENCE (psia).(.o. u/lb_ (Btu/lb)(Btu/lb) (Btu/lb)_ a nr r a nL:::: LIr'- -I oC) 1 7 f. - hr IN.A n B/l.b) L....... I >,Y) J~ *j UUUU J! 1.> 9 ~.D %-) -) 9':J),U — Ld.UO D -U u. 5 4b'-OU -U.'*44t'O 500.0000000 5 00. 0000000 500.0000000 500.0000000 500.0000000 500.0000000 500.0000000 500. 000000 50no-nnnno 17-i. 5999')08 1 99,4. 599 9 0^ ______ 21'9.5999903) 239. 590I- 3____ 259 593.)8535 279. 9) 85 3 5 2 99. 599353 5 31 9. i, 9 3'5 - 7o.60 000 1 -70. 39 993 9 -o0. 0 )00031. -i. 70)00122 -it. 3. 0. 31 -12. C9-99c 9 -1G. i;.'J. 1 -76. 9572449 -70.9122925 -61.5042419 -22.22o0132 -16.12136834 -13. 271521 -10.980)2246 -9.4131461 0.3572388 0.5122986 0.7042389 0.5260010 -0. 1786346 0.3271551 0.3802185 0.41 81461 -0.4663691 -0.7276967 -1. 1582870 -2.4239655 1.0959177 -2.5760241 -3.5869646 -4. 64606A7 I \O kON 0I! 500.0000000 1000. 0000000 1000.0000000 1000.0000000 1000.0000000 1300.0000000 1000. 000000 10.00.000000 1000.0000000 1000. 0000000 1000.0000000 1000. 000000 1500.0000000 150000000000 1500. 000000 1500.0000000 1500.0000000 1500.0000000 1500.0000000 1500.0000000 1500.0000000 1500.0000000 1500.0000000 339. 5998535 159. 5999903 179. 599990 9 199 599999) q 21 9. 5O 0:Q999) 229. 5999908 239.5999:9) 259. 5993535 279.5998535 299.5998535 319.5998535 339.5998535 159.59999)8 179. 599998 199. 599908 219. 9'99903 229.5999903 239. 5999908 259. 5998535 279.5998535 299.5998535 319. 5998535 339.5998535 -/ o. 9- 939 -6.4066436 o4-"-'.)fl..-4 7. -80). 705581. 7 -.000000 0 -75.8509827 -7 0.) 0U00 31 -70.5439453 -o4. J9'993 9 -64. 1234637 -6C. 1 )0006 1 -60.2589264 -55. 8000031 -55.4396057 _-41. 3_00031 __ -41.4095459 _ -30.;10UO o 1 -30.1832428 -23. 6T0006 1 -23.8399963 -19.o 99969 -19. 3444977 -1. 8999939 -17.2372894 -80. 5'99756 -79.6332338 -75.9c)(0092 -75. 1092224 - t. 5999908 -70. 2011 371 -65.3999939 -64.7862701 -62.1000061 -61.7879486 -58. 8000031 -58.7319031 -51.1000061 -50.9752350 -42. 19999069 -42. 7993927 -35. 000000 -35.2981567 -29.0999908 -29.4218597 -24. 999939 -23.7418671 -1. 4933453 -0.2944031 -0.1490173 -0.2560577 -0.2715302 0.1589203 -0.3603973 0. 1095428 0.0332367 0.2399902 0. 1445007 0.3372955 -0.969741 -0.790786 7 -0.3988037 -0.6137233 -0.3120575 -0.0681300 -0.1247711 0.5993958 0.2981567 0.3218689 -1.1581268 18.9031067 0.3634606 0.1960754 0.3616634 0.4216306 -0.2644264 0.6458733 -0.2652369 -0.2765338 -1.0169067 -0.7335063 -1.9958315 1.2031536 1.0418787 0.5648777 0.9384155 0. 5025077 0.1158162 0. 2441704 -1.4203682 -0.8518763 -1.1060781 4.6511126

-197 interpolate accurate reference substance functions to accurately predict enthalpies of fluids under pressure. Application of the Correlation to Mixtures When attempting to apply this technique to mixtures, the critical properties of the mixtures cannot be used in the reduced enthalpy function, since mixture critical properties do not have the same physical and thermodynamic significance as those for the pure components. In addition for nonconformal mixtures, such as mixtures of methanepropane, the principle of corresponding states has at present no funcamental justification. This also eliminates the possibility of developing mixing rules from relatively rigorous theoretical analysis. Thus, an empirical approach is essential. It was, therefore, assumed that the reduced enthalpy of methane-propane mixtures does behave the same as that of a pure substance. Empirical mixing rules containing a total of six constants were determined which represent the methane-propane data to within ~lBtu/lb which is of the order of the uncertainty of the data. The success of these results justified the validity of the corresponding states principle when applied to mixtures of this type. The pure component reference substance enthalpy departures obtained from the methane and the propane enthalpy data were used to calculate mixture enthalpy data for values of the three parameters of the given mixture. These parameters were determined by a direct search procedure which found values of the three parameters which minimized the root mean square difference between the calculated and experimental departures for each mixture. Calculations were made with the aid of the computer program previously mentioned. The program assumes initial values of T, P, and W. The 1 CX ~ CX X

-198 enthalpy departures are calculated using the subroutine described above for a wide variety of conditions including the gaseous, liquid, and critical regions. Input points were selected at pressures of 500, 1000, 1500, and 2000 psia where actual experimental determinations were usually made. Temperatures at 20~F intervals were used when the point fell in the single phase region. The range of temperature was determined usually by the range of the reference tables or occasionally by the limits of the experimental data. The root mean square deviation for all points was calculated. Root mean square deviations were then calculated with each parameter incremented in both the positive and negative direction. The base values of P, T, and W would shift CX CX X to the point which had the lowest root mean square deviation. The procedure would continue until the root mean square deviation of the base value was lower than that of any of the six points surrounding it. Due to limits on computer execution time minimum step sizes of AP = 3.0 psia, AT = 1.5~F and AW = 0.002 were used. If initial condix x x tions far away from reasonable values (Kay's rule is a normal "reasonable" initial value) were used the calculation would not necessarity converge to the optimum. This indicated that the function was not unimodalo However, reasonable but different initial conditions would usually converge to the same optimum. Due to the large computer execution times involved a more complete analysis of the different optimums was not undertaken. It was, however, noted that the minimum in the temperature direction was in a relatively steep valley. A gradient search was originally used, instead of the direct search, but it would not converge to the optimum. The valley in the temperature direction had too much of an effect on the gradient when using reasonable step sizes.

-199 The technique was used to determine optimum parameters for all five experimentally determined methane-propane mixtures. The original optimum values, the sum of the squares deviations, and the number of data points used for each mixture are given in Table XXXV, The actual comparisons for each data point are given in Table LXIV of Appendix D for all five mixtures. The A's represent departures from Kay's rule as for example pseudo critical temperature. cT =- T - T (79) cx cx cKay TABLE XXXV ORIGINAL OPTIMUM VALUES FOR THE THREE PSUEDOPARAMETERS IN THE SEARCH CALCULATIONS P AP T AT Mole Fraction cx cx x Tx c F Propane psia psi (R) () x x Btu/lb 0.052 664.2 -6.o 361.5 1.7 0.032 -0.020 0.964 0.117 667.5 +0.9 388.0 7.0 0.175 0.058 0.776 0.280 654.0 -3.4 447.0 13.4 0.359 0.019 0.966 0.506 632.4 -12.5 521.5 14.6 0.618 0.108 0.709 0.766 6.914 -11.0 596.5 6.0 0.855 0.089 0.644 The three parameters are plotted on Figure 60 as deviations from Kay's rule. The figure indicates that the results for critical temperature are the smoothest and most regular. This is again due to the fact that the optimum pseudocritical temperature lies in a very steep valley and has the strongest effect on the magnitude of the error. It can also be noted that these points are not symmetrical and thus cannot be represented by a single empirical correction term as was suggested by 101 Pitzer and Hultgren. In order to fit the points to a smooth curve to within the value of the minimum step size, AT = 1.5~F, it was necescx sary to use a three constant empirical equation.

-20016 o I- 8 0. 0 0 4 0 oORIGINAL OPTIMUM - * *OPTIMUM AFTER TC FIT S -16:3z0 12 0 8 a / \ O:.10.08 ~.06 0.04 0.02 -- O. 0 0 0.2.4.6.8 MOLE FRACTION PROPANE - Figure 60. Optimum Mixing Rules for the Methane-Propane System

-201 T = x.T + xix[A' + (l-2xi)B' + (1-2xi)C'] (54) i c i i j The values of the constants obtained by a least squares fit were: A' = 59.454 B' = 50.868 C' = -35,880 The resulting fitting curve is shown on Figure 60, Since the root mean square deviations were so sensitive to small temperature changes it was felt that changes in the optimum critical temperature caused by the fit could significantly effect the optimum values of the remaining two parameters. Thus, values of T were calculated by Equation (54) cx for the five mixtures and a second search procedure performed, Using these values for the pseudocritical temperature, P and W for each cX x mixture were allowed to vary and new optimum values found. The resulting optimum parameters along with the root mean square deviations are presented in Table XXXVI. The enthalpies calculated and compared with experimental results for each tested condition are presented in Table LXV of Appendix D, The results of this procedure are shown as the solid points on Figure 60o Since there is considerable uncertainty in the results obtained for these two parameters, there was some question regarding the choice of fitting equation. Because these two parameters do not significantly effect the root mean square deviation it was decided to use simple equations for the fit. For P it appears that the results show a definite asymmetry Therefore, a two constant equation was used asymmetry. Therefore, a two constant equation was used. Pc = xiPi + x.x.[D' + E' (l-2x.)] cx 1i ci 11 i (55)

-202 For Wx, however, any asymmetry, if present, cannot be observed due to scatter in the results. Therefore, the simple one constant equation was used. = x.W.i + xx.j F' (56) x 11 1 J The values of the constants were obtained by least squares fitting. The points for the 5.2 percent mixture differed significantly from the trend of the data for the other mixtures and were not used in determining the constants, The values of these constants are given as D' = 43.448 E' = -46.590 F' = 0.44250 The parameters for each mixture were calculated using Equations (55) and (56) with Tx from Equation (54). The fit parameters were then used to Cx calculate enthalpy departures and compared with experimental results. The root mean square of the deviations are presented in Table XXXVII. Fitting the calculated optimum values for the parameters does cause some increase in the average deviation for all of the mixtures. This is illustrated in Table XXXVIII where columns A, B, and C present respectively the root mean square deviations obtained using the original parameters, using the smooth pseudocritical temperature values with adjusted values of the other parameters, and using the final smooth mixing rules for each parameter. The worst case (except for the 5.1 percent mixture which was not used in the final fit) was for the 11.7 percent mixture where the root mean square deviation for all data points increased from 0.776 to 0.937.

-205 TABLE XXXVI OPTIMUM VALUES OF PARAMETERS AFTER FITTING PSEUDOCRITICAL TEMPERATURE AND HOLDING IT CONSTANT IN OPTIMIZATION P PP T AT Mole Fraction Px ex Tx Ax F Propane psia psi (OR) (F) x x Btu/lb 0.052 674.2 +14.4 362.6 2.8 0.012 -0.040 0.999 0.117 663.5 -3.1 387.5 6.4 0.183 0.066 0.703 0.280 645.0 -3.4 447.0 13.3 0.359 0.079 0.966 0.506 634.4 -10.5 521.7 14.8 0.610 0.104 0.720 0.766 617.4 -13.0 596.4 5.9 0.855 0.089 0.648 TABLE XXXVII FINAL FIT OPTIMUM PARAMETER VALUES P APT LT Mole Fraction cx cx Tx cx F Propane psia psi (~R) (OF) x x Btulb 0.052 670.1 -0.1 362.6 2.8 0.072 +0.021 2.100 0.177 665.7 -0.8 387.5 6.4 0.163 0.046 0.937 0.280 652.9 -4.6 447.0 13.3 0.370 0.089 1.010 0.506 633.9 -ll.0 521.7 14.8 0.617 0.111 0.744 0.766 618.2 -12.2 596.4 5.9 0.845 0.079 0.709 The results of the final smooth mixing rules are also presented on topographic pressure-temperature charts for each mixture in Figure 61. Deviations are represented as Btu/lb as obtained from Equation (79). The tabulated, calculated, and experimental departures for each data point are presented in Table LXVI of Appendix D. The root mean square deviations are on the order of 1 Btu/lb or less for all mixtures with the exception of the 5.2 mole percent propane in methane mixture. These deviations are in the range of uncertainty of the experimental data and thus, the proposed mixing rules and departure function represent the data well.

TABLE XXXVIII ROOT MEAN SQUARE DEVIATIONS OF THE RESULTS OF THIS STUDY AND NUMEROUS MIXING RULES FOR THE METHANE-PROPANE SYSTEM A B C D E F G H I J K Mole Fraction Propane 5.1 11.7 28.0 50.6 76.6 Optimum Parameters smooth all rlall original Tx smooth 0.964 0.999 2.100 0.776 0.703 0.937 0.966 0.966 1.010 0.709 0.720 0.744 0.644 0.648 0.709 Kay (65) 1.79 6.59 10.11 10.04 5.37 PH (101) 2.87 1.39 3.34 5.54 4.63 5.27 J-JBV (136) 1.31 3.45 5.04 5.01 0.91 LM (74) 2.78 1.62 2.34 2.21 2.63 PG (106) 4.46 3.10 2.52 1.94 2.87 SPG (106) 1.72 6.42 10.00 9.95 5.30 Optimum 2 Parameters original smooth 1.01 2.70 1.25 1.32 1.53 1.48 1.44 1.75 1.05 1.06 r o I

-205 Uj 5 I'" L ^/iW [t 111111 i 111:1: I-\^. I _3.5 ~~500 m; v \ t~~mllml[T mmlllt ~ 500 - Ill-lD8+\ IlJ llll I l 0 -200 - I00 0 +100 +200 +300 -200 -100 0 +100 +200 +300 TEMPERATURE'F TEMPERATURE ~F,,:ooo 1o| I oll -0 - 10 0 10 20 30-0 ~(c)I u I(d) 2000 76.6 MOLE PERCENT /I / / // LEGEND <r o C r. — eim a E < d < he 500 C-ITEMPERATURE ~F (e) < 20 < d I a+ 0 - 000 0 - 0 +d of correlation Figure 61. Comparison of Experimental Enthalpy Departures for the Methane-Propane System with the PResults from the Corresponding States Correlation and Mixing Rules of This Investigation Correlation and Mixing Rules of This Investigation

-206 By looking at Figure 61a, the comparison chart for the 5.2 mole percent mixture, it appears that a significant part of the deviations for this mixture is present in the liquid region and especially at lower pressures. There are several possible explanations for these large uncertainties in this region. By looking at the range of measurement for this mixture (Figure 5 in Mather's thesis (85)) it can be seen that at 500 psia it was necessary to interpolate heat capacity data to obtain enthalpy data at very low temperatures since there is a region where data was not taken for the liquid. In addition the pressure-temperatureenthalpy diagram (Figure 34 in Mather's thesis) appears to be constructed inconsistently in the low temperature liquid region. Table XXXIX presents the results at 500 and 1000 psia for the average heat capacities AH/AT obtained from this diagram. The strange behavior suggests the possibility of error in this region. In addition the -80~F isotherm appears to be drawn inconsistently. This suggests the large deviation obtained at -80 and 1000 psia on Figure 61a. Thus, the large deviations in this region may well be caused by errors made in constructing the pressure-temperature-enthalpy diagram for the mixture. Figures 61b, 61c, 61c, and 61e show that for the other mixtures the mixing rule proposed predicts enthalpy departures almost universally to within 2 Btu/lb or better. Thus, the proposed equations containing a total of six constants appear to be sufficient to predict the enthalpy of the entire methane-propane system over a wide rasnge of conditions. Comparison with Other Mixing Rules The mixing rules determined in the present investigation although truly representative of the mixture behavior are obtained by fitting a

-207 TABLE XXXIX DIFFERENCED RESULTS FOR 5.1 MOLE PERCENT MIXTURE Average (@ 500 psia) 1000 psia) Temperature AT AT (~F) (Btu/lb-~F) (Btu/lb-~F) -275 7.5 7.6 -265 7.5 7.7 -255 9.1 8.2 -245 8.0 8.1 -235 7.5 7.7 -225 7.8 7.6 -215 8 8. 8 -205 8.2 8.1 -195 7.9 7.8 -185 7.8 7.7 -175 9.9 9.5 -165 7.3 7.0 -155 9.4 8.8 large amount of experimental data. The generalized mixing rules which are available in the literature can be used to estimate mixture properties from a knowledge of pure component properties and minimal amount of mixture results if any. Thus, a comparison of the results of this investigation with the generalized mixing rules of Kay (K), Joffe-Stewart, Burkhardt, Voo (S-SBV), Leland, Mueller (LM), Prausnitz, Gunn (PG), io6 and a simplified rule of Prausnitz, Gunn (SPG) was undertaken. The rules were used in conjunction with the reference enthalpy tables of this investigation to determine enthalpy departures for the mixtures at the same conditions as were calculated using-the empirical 74 mixing rules of this investigation. Both the rules of Leland, Muller and Prausnitz, Gunn show a dependence of the pseudoparameters on temperature and pressure. It was found that for the system studied in

-208 this investigation the effects were minor. Therefore, the variations were not considered. Table XXXVIII presents the results of these calculations. It gives the root mean square deviation obtained for each mixture for each rule in columns D through I. As can be seen the empirical rule is a considerable improvement over the other available generalized rule even when the new reference enthalpy departure tables are used. The generalized mixing rules which give the best agreement with experimental results for the methane-propane system are those due to 74 106 Leland and Mueller and Prausnitz and Gunn. The results of the comparisons for the best rule, that of Leland and Mueller, is illustrated graphically on Figure 62. As can be seen the discrepancies between the calculations using this rule and the experimental data is as large as 10 Btu/lb in some regions. It should be remembered from Section II that all of the mixing rules 101 tested with the exception of the Pitzer-Hultgren rule assume that the third parameter is a linear function of composition. In addition it has been shown that if a two parameter corresponding states principle is valid these mixing rules have some theoretical justification. Thus, in order to more realistically compare these mixing rules with an optimum rule, the original optimization program was modified to search only for an optimum pseudocritical temperature and pressure with the third parameter held constant. The program was run for each mixture using a linear variation of the third parameter, W, with composition to obtain optimum values for the remaining two parameters. This approach assumed that in effect the mixing rules for pseudocritical temperature and pressure are not altered by mixing two nonconformal substances, Table XL lists the

-209 ct Vf) - 1 a: tn LU w r a2 rn a: nIt tL a: CL uz a. w ul a: a. TEMPERATURE ~F U (a) (b) -, cr LI!ATURE ~F TEMPERATURE'F (c) (d) ^'77.:7n\ "\\^\-^,N^..",L^_,,_^N X_ L N^ - DLEGEND a. w a. DEVIATION, d BTU/lb d=O | d < 2 \\\m\\inni2 < d < 5c 5 < d < 10 vm ~ I10< d< 20 20< d Exceeds limits of correlation (e) Figure 62. Comparison of Experimental Enthalpy Departures for the Methane-Propane System with Results from the Corresponding States Correlation of This Investigation and Mixing Rules of Leland-Mueller (74)

-210 TABLE XL OPTIMUM VALUES OF PSEUDOCRITICAL PARAMETERS WITH THIRD PARAMETER, W, HELD CONSTANT Mole Fraction Propane 0.052 0.117 0.280 0.506 0.766 Original Optimum Values P AP T ZT c c c c F 662.0 -8.0 361.1 1.3 1.01 689.0 22.4 390.5 9.5 1.25 675.0 17.5 450.0 16.5 1.53 659.4 14.5 526.2 19.3 1.44 643.4 13.0 600.9 10.4 1.05 Smoothed Optimum Values 0.052 0.117 0.280 0.506 0.766 676.6 679.3 678.5 664.1 638.5 6.4 12.8 21.0 19.2 8.1 364.3 390.5 450.6 525.0 601.5 4.6 9.5 16.9 18.4 11.0 2.70 1.32 1.48 1.75 1.06 optimum temperatures and pressures obtained for each mixture along with the root mean square deviations. Again the results obtained for the 5.2 mole percent propane in methane mixture did not agree with the other results and were not used to obtain the empirical equations. The two parameters could each be fit in this instance with two constant equations cx- c + A"xix [1+ (1 - 2xi)B"] cx EPcixi i xj ) pcx Z PciX i + D"x x[l + (1 - 2x)E,"-] (80) (81) The constants obtained by a least squares fit of the optimization results

-211 are given as A" = 735749 B" = 23.289 D" = 77.417 E" = 60.490 Values of pseudocritical temperature and pressure were calculated for each mixture from the above equations and these results used to obtain enthalpy departures. These results were compared with experimental values and the root mean square deviations for each mixture are listed in column K of Table XXXVIII. Although these results are not as good a fit as the results for the three parameter optimization they are still considerably more in agreement with experimental data than the generalized mixing rules. Next the actual values of the parameters were compared. Figure 63 shows the pseudocritical temperatures as a function of composition for the various mixing rules..including both the linear and nonlinear third parameter mixing rules of this investigation. All of the mixing rules show a positive deviation in temperature with respect to Kay's rule. Inclusion of a variable third parameter causes the departure from Kay's rule to decrease. Figure 64 shows the pseudocritical pressure as a function of composition. Inclusion of a nonlinear third parameter causes a change in 101 sign in the departure from Kay's rule. The Pitzer-Hultgren mixing rule seems to overdo the deviation in pressure from Kay's rule. Also the optimum curve obtained with the two parameter search does qualitatively agree with the generalized mixing rules in magnitude as well as in shape, Finally, Figure 65 presents the third parameter deviation from

-212 30 28 26 24 22 20 18 a 3 PARAMETER OPTIMIZATION * 2 PARAMETER OPTIMIZATION -LEAST SQUARES CURVES - PITZER HULTGREN (101) - JOFFE-~TEWART, BURKHARDT, vo0 (136) -- LELAND,MUELLER 74) - PRAUSNITZ, GUNN (106), ^ _ _. 4001 ** / / // 0 I/ I 0 I 16 14 S 12 10 8 6 4 2 O0 0 l --,Y I I.2.4.6.8 1.0 X Figure 63. Mixing Rules for Pseudo-Critical Propane System Temperature for the Methane

-213 80 ~'. _ 60 - * 3 PARAMETER OPTIMIZATION * 2 PARAMETER OPTIMIZATION -LEAST SQUARES CURVES - PITZER, HULTGREN (101) JOFFE -STEWART, BURKHARDT, VOO (136) -- LELAND, MUELLER (74) - PRAUSNITZ, GUNN (106) - m m mmmm ~ b,m-,- m 401 I,___ ___!/ "s9c4,% 20 0 L() 0x x <3 0 m I -20 -40 -60 ~~~~l\ I - \ //:\ \ / \ / -80 / I. / 0 I I I I -1001k 0.2.4.6.8 MOLE FRACTION PROPANE 1.0 Figure 64. Mixing Rules Propane System for the Pseudo-Critical Pressure for the Methane

.30 * 3 PARAMETER OPTIMUM --- LEAST SQUARES CURVE ---- PITZER, HULTGREN (101) / \ / \ / I \ I.25.20 x. 15 a~~~~~~~~~ I I / I.10.05 0 / / \ I I I.2.4.6 MOLE FRACTION PROPANE.8 1.0 Figure 65. Mixing Rules for the Third Parameter for the Methane-Propane System

-215 linearity as a function of Kay's rule. Again it appears that that the rule due to Pitzer and Hultgren overemphasizes the diviation. Extension to a Mixture of Nitrogen in Methane As a final step both the two parameter and three parameter optimization techniques were applied to correlate data for a mixture containing 43.3 mole percent nitrogen in methane. An enthalpy diagram and table based on isobaric enthalpy determinations for this mixture are found in the thesis of Mather5 In addition departures were obtained. using the various mixing rules described above. The results of the optimization and mixing rule enthalpy departure comparisons in terms of a root-meansquare deviation are given in Table XXXXI, It can be noted that in this case the deviation of pseudocritical temperature is negative. Also there is hardly any effect on varying the third parameter. This seems reasonable in view of the relative similarity between methane and nitrogen, Also Table XXXXI is arranged in such a way that the root-mean-square deviation increases from left to right for the various mixing rules. At the same time the difference between the optimum pseudocritical temperature also increases in the same fashion regardless of the effect of the other parameters. This shows the strong sensitivity of the deviations to the value of the temperature parameter. Figure 66 presents the results of estimations based on the various mixing rules. All of the rules appear to differ from the experimental results mainly in the liquid region. The results with the optimized parameters are in much better agreement than the generalized rules. It must, however, be pointed out that the diagram of Mather5 can be in error in the compressed liquid region since it is based entirely on isobaric data with the effect of pressure on enthalpy estimated from the

TABLE XXXXI ROOT MEAN SQUARE DEVIATIONS OF THE RESULTS OF THIS STUDY AND NUMEROUS MIXING RULES FOR A METHANE-NITROGEN MIXTURE Pcx( psia) Tcx( R) W x F optimum parameters 558.0 286.1.0981 0.649 optimum 2 parameters 558.0 286.1.1131 0.675 J-SBV (136) 596.4 291.2.1131 2.54 PG (106) 599.5 292.8.1131 3.53 Kay (65) SPG (106) LM (74) 602.5 549.9 599.9 292.8.1151 3.60 293.5.1131 3.99 294.0 1I H O\ I.1131 4.30

-217 cn a w mi 0, cn Q. I a UJ QC 0 TEMPERATURE OF TEMPERAUt (a) (b) LEGEND DEVIATION, d BTU/lb d=O l -I 111T11J 1 i111 iii't', ~,,' JJIJ < d <2 2 < d < 5 5 < d <10 n a n vL w 03 03, n. a 0L 10< d < 20 20< d Exceeds limits of correlation RATURE F TEMPERATURE ~F (c) (d) < n' cn D a. n uL gc a. RATURE OF TEMPERATURE'F (e) (f) Figure 66. Comparison of Experimental Enthalpy Departures for a MethaneNitrogen Mixture with Results from the Corresponding States Correlation of This Investigation Using Several Mixing Rules

-218 BWR equation at room temperature. Cumulative errors could produce results in the liquid region which are considerably in error. This may in part account for the reversal in the deviation from Kay's rule of the optimum pseudocritical temperature. It is somewhat disappointing that the deviation from Kay's rule of the parameters obtained from the mixing rules in general differ in sign from the optimum rule for this mixture. It must be remembered, however, that for the methane-nitrogen system departures from Kay's rule for all parameters are quite small in all cases. Thus, the effect of even an incorrect sign in the departure from Kay's rule is not necessarily that important. In addition the mixing rules which apply most successfully to the methane-propane system are not the best for the methane-nitrogen system. If this were not the case, it might have been possible to make a more definite recommendation of a mixing rule which could be used for systems not experimentally investigated. Discussion of Results As has been illustrated the theorem of corresponding state can be used to accurately fit the enthalpy of simple fluid mixtures. From a table of reference substance functions and empirically fit mixing rules the enthalpy of a binary mixture can be calculated almost to within the experimental uncertainty of the experimental data. Although this method was applied to the methane-propane system using data for pure methane and propane it appears that the procedure could be applied to other systems using the same methane-propane reference functions. This is in part justified by the ability of the method to calculate the enthalpy of nitrogen under pressure and of a nitrogenmethane mixture, In fact although a smaller range of temperature and

-219 pressure was considered, the root-mean-square deviations for the methanenitrogen mixture was smaller than those obtained for any of the methanepropane mixtures. One could therefore accurately represent the enthalpy behavior of a wide variety of mixtures from two reference substance reduced enthalpy functions and a maximum of six constants for each mixture, In addition) by use of the reference substance function constants for these mixtures could probably be developed from a much smaller amount of new experimental data. The above procedure need not be limited to the enthalpy function but can be extended to other thermodynamic properties as well. If a thermodynamically consistent and accurate series of reference substance functions were developed for all of the thermodynamic properties of nonpolar fluids under pressure then:.mixing rules could be obtained by an optimization using all of the available thermodynamic data. Of course actual data cannot be obtained for every mixture and in some cases generalized mixing rules must be used. At present these rules, although not extremely accurate, can be applied with a knowledge that no gross errors will result, If more empirical mixing rules were available, however, such results could be used to test mixing rules developed from theoretical considerations,

-220 SUMMARY AND CONCLUSIONS 1. The recycle flow facility as described by Mather was modified to allow for measurements of fluids of lower volatility than that for which the equipment was originally designed. 2. The effects of pressure and temperature on enthalpy were determined experimentally for propane, a nominal 77 percent and a 51 percent mixture of propane in methane. Measurements were made in the liquid, two-phase, critical, and gaseous regions at temperatures from -250 to +300~F at pressures from 100 to 2000 psia. The data are self consistent to about 0.2 percent. 3. An enthalpy-pressure-temperature table is presented for propane between -280 and +500~F at pressures up to 2000 psia. The table was prepared with the aid of supplementary data in the literature. 4. From the data for the two mixtures, enthalpy-pressure-temperature tables in the regions between -280 and +300~F and pressures up to 2000 psia were developed. These results plus those obtained by Jones, Manker, and Mather adequately represent the enthalpy behavior of the methanepropane binary system. 5. The data obtained in the course of this investigation plus data in the literature were used to compare several of the available methods of prediction. This comparison study indicated that the corresponding states principle would be a most fruitful appxrach for extending methods of prediction to represent the available data.

-221 6. A three parameter corresponding states correlation was developed which used reference tables derived from enthalpy data for methane and propane. The correlation is valid between T of 0.5 and 1,5 at values r of P up to 3.0. The three parameter corresponding states principle was r tested for enthalpy departures by comparing the results of the correlation with data for nitrogen. The correlation predicted the enthalpies of nitrogen to within the experimental uncertainty of the data. 7. The correlation was extended and justified for mixtures by developing a set of mixing rules containing six empirical constants to represent the behavior of the methane-propane binary system. The correlation predicted departures for the mixture to almost within experimental uncertainty in the single phase region over the entire region of its validity,

APPENDIX A CALIBRATIONS

-224 TABLE XLII THERMOPILE M-3 CALIBRATION FOR ISOBARIC CALORIMETER Electromotive Force as a Function of Temperature of Measuring Junction (reference junctions at 0~C) Degrees C Absolute Degrees C Absolute (Int. 1948) Microvolts (Int. 1948) Microvolts -196 -33328 20 4774 -183 -31987 40 9761 -100 -20336 60 14946 - 80 -16778 80 20320 - 60 -12954 100 25877 - 40 - 8876 120 31600 - 20 - 4556 140 37486 0 0 160 43533 TABLE XLIII THERMOPILE M-4 CALIBRATION FOR ISOBARIC CALORIMETER Electromotive Force as a Function of Temperature of Measuring Junction (reference junctions at 0~C) Degrees C Absolute Degrees C Absolute (Int. 1948) Microvolts (Int. 1948) Microvolts -196 -33332 20 4774 -183 -31990 40 9762 -100 -20330 60 14947 - 80 -16778 80 20322 - 60 -12956 100 25882 - 40 - 8874 120 31606 - 20 - 4551 140 37494 0 0 160 43543

-225 TABLE XLIV THERMOPILE M-5 CALIBRI'ATION FOR THROTTLING CALORIMETER Electromotive Force as a Function of Temperature of Measuring Junction (reference junctions at 0~C) Degrees C Absolute Degrees C Absolute (Int. 1948) Microvolts (Int. 1948) Microvolts -196 -33331 20 4774 -183 -31990 40 9760 -100 -20338 60 14946 - 80 -16779 80 20326 - 60 -12955 100 25872 - 40 - 8878 120 31596 - 20 - 4556 140 37486 0 0 160 43530 TABLE XLV THERiOPILE M-6 CALIBRATION FOR THROTTLING CALORIMETER Electromotive Force as a Function of Temperature of Measuring Junction (reference junctions at 0~C) Degrees C Absolute Degrees C Absolute (Int. 1948) Microvolts (Int. 1948) Microvolts -196 -33330 20 4775 -183 -31986 40 9761 -100 -20338 60 14944 - 80 -16781 80 20322 - 60 -12956 100 25868 - 40 - 8877 120 31593 - 20 - 4557 140 37484 0 0 160 43530

APPENDIX B EXPERIMENTAL DATA -226

-227 TABLE XLVI TABULATED EXPERIMENTAL ISOBARIC DATA FOR PROPANE INLET INLET OUTLET' FOWEK -\ RUN PRESSURE TEMPERATURE TEMPERATURE POWER FLr! CORR. FLOW A Hp (sia) (~F) (F) (Btu/min) (b/m ubin ) (Btu/lb ) (Btu/lb) (Btu/lb- F) 1.010 400.6 158.06 158.92.257 o.3f6..~ -.756.753.87033 - 1.020 399.4 158.06 15987.559.3454 -003 1.618 1.616.8921 1.030 400.6 158.07 160.80.850.3466 -.003 2.451 2.449.8964 1.040 400.2 158.07 161.21 1.216.3460 -.003 3.516 3.513 * 1.050 399.8 158.07 161.42 1.704.3474 -.003 4.906 4.903 * 1.060 399.9 158.07 161.58 2.188.3441.-003 6.359 6.356 * 1.070 399.7 158.07 161.79 2.875.3444 -.003 8.346 _ 8.343 1.080 399.7 158.07 162.23- 4.659.3448 -.004 13.514 13.510 - 1.090 399.1. 58.07 162.55 7.232.3447 -.005 20.977 20.973 1.100 399.0 158.07 162.80 310.852.3443 -.006 31.515 31.510 * 1.110 399.1 158.07 163.17 16.486.3440 -.007 47.930 47.923 * 1-120 398.8 -T5 07. - 163.26 21-649.3424 -.009.-.. 3..223 63.214 - * 1.130 398.5 158.07 163.27 21.641.3155 -.008 68.588 68.581. 1.140 397.8 158.07 163.31 24.629 -.3141 -.009 78.410 78.401 1.150 397.7.1568.07 163.30 26.563.3136 -.009 84.697 84.688 * 2.010 399.5 158607 163.12.- 4796 489. 26M -.003 24.449'g"'- 24.446 ~ 2.020 400.0 158.06 163.38 9.120.1998 -.000 45.6374 45.637 2.030 398.8 157.98 163.39 15.830.1995 -.003 79.358 79.355 * 2.040 399.4 158.09 163.65 16.07E.1994 -.004 90.671 90.667 * 2.050 399.3 158.09 163.59 19.197.1996 -.004 96.174 96.170. * 2.060 399.4 15806 16'4.76 19.767.1994 -.004 99.150 99.145 * 2.070 398.5 158.06 166.54 20.064.1995 -.005 100.576 100.571. * 2.080 399.6 158.01 170.12 20.663.1998 -.005 103.402 103.397 * 2.090 400.8 156.09 178.67 21.957.2002 -.005 109.691 109.686 * 3.012 2000.3 10210 112.51 2.183 -.3353..001 6.51 6.i. 253 3.011 2000.3 102.11 112.79 2.205.3304.001 6.673 6.673.6246 3.010 2001.7 - 0-2.16 112.89 2..205.3214.001.66 6.694.6238 3.020 2001.9 102.15 122.83 4.319.3326.001 12.980 12.988.6280?3.030 2002.2 102.09 — --- 142.43 8.595.3341.ol- 25...26 25.727 637U 3.041 2002.8 102.109 184.41 17.831.328.001' 54.231 54.232 *6588 3.040 1998.7- 102.09 184.61 17X832.318 0. —01 54056U 54.570.6613 4.010 999.1 102.02 112.47 2.360.34*0.000 6.819 6.819.6S234.020 999.8 - I$2.03[..122.90 4.834.3498.000..81. 13.819. 6619 4.030 999.9 101.93 145.24 9.846.3354.000 29.352 29.352.6778 4.040 999.8 102.02 182.94 - 19.174.3322.000 -- 572-.. 724.7134 5.010 1498.9 102.05 113.08 2.340.3313 -.000 7.066 7.065.6406 5.020 1498.5 102.05 124.79 4.822 —-.2.. —7000 14.687 14.686.6456'5.030 1499.1 102.06 145.27 9.341 3289 -.000 28.404'28.404.6573'5.040 1499.5 102.06 185.32 18.359.3234 -.000 56.76 — 56.764.6817....6.010 499.2 102.04 112.24 2.340.3342 -.001 7.002 7.001.6868 6.020 501.9 101.97 124.06 4.966.3232 -.001 15.366 15.365.6955 6.030 498.9 102.17 144.47 9.710 ___.3173__ -.001 30.603 30.602.7234 6.040 500.4 102.29 183.12 21.630.3212 -.002 67.342 67.340.8331 7.010 251.6 102.16 111.89 2.305.3325 -.000 6.933 6.933.7125 7.040 7.050 250.7 101.94 118.87 3.932.3233 -.000 12.160 tii —,7183 251.2 102.27 116.00 3.172.3233 -.000 9.811 o.6A.7147 * e _ _ --------— X ----- --- e - - - - - - -, r.U0I 29.3J 1U".UO 10U.3 4. 15.8*90 -.UUU 14.3JJ34 t.o. 7.020 249.3 102.03 119.87 4.713.3250 -.000 14.499 14.499 * 7.030 251.2 102.00 121.28 -6.285 -.3251- -.001 19.333. —-— 3 — * 7.060 250.0 1 02.08 120.59 5.643.3209 -.001 17.585 I___17.5S * 7.070 250.8. 101.85 - 121.71 8.391.3224.-.001 26054~ -- 7.080 250.7'102.08 121.75 5.647.1906 -.000 29.630 29630. 7.090 252.4 102.08 122.85 8.400.1912 -.000 43.927 43.926 * 7.100 251.2 102.11 122.71 11.832.1906 -.000 62.094 62.094 * 7.110 250.1 101.96 122.16 15.51C.1894 -.001 _81.888 _ 81.887 6.' * 7.120 249.4 152.08 122.28 19.724.1887 -.001 104.519 104.518 * 7.130 248.9 102.08 122.15 22.161.1880 -.001 117.888 117.887 * 7.140 249.0 102.11 122.21 - 23.340 ".1880 -.001 124.156 124.15- * 7.150 248.7 102.08 122.23 25.366.1876 -.001 135.201 135.199 * 7.160 247.8 102.11 125.79 26.020.1871 -.001 139.095 139.094 * 7.170 248.6' 102.14 129.49 26.513.1879 -.001 141.090 141.089 * 7.180 _ 249.3 102.11 - 133.52.- 27.036e.1886 -.001 143.346 143.345 _8.010_ 246.5 201.59 212.22 228.3363 -.300 6.032 5.732.5393 8.020 246.6 201.54 222.03 3.822.3368 -.310 11.350 11.039.5388 8.031 245.9, 201.53 241.05 7.230.3315 -.317 21.810 21.493.5438 8.030 245.7, 201.53 241.12 7.23C.3309 -.317 21.850 21.533.5439 _8.040,_ 245.6 _ 201.67 277.55 13.898.3309 -.337 41.999 41.662,.5490 9.010 500.2 201.48 210.71 2.622.3385 -.295 7.746 7.451.8068 9.020 499.5 201.54 221.28 5.188.3358 -.313 15.451 15.137.7670 9.031 499.5 201.44 239.53 9.483.3360 -.331 28.220 27.889.7321 9.030 499.2 201.46 239.60 9.482.3359 -.340 28.227 27.887.7312 9.041 498.7 201.46 277.26 17.662.3349 -.389 52.732 52.343.6905 9.040 498.9 201.48 277.13 17.659.3356 -.394 52.618 52.225.6904 10.011 1502.6 201.41 210.89 2.375.3201 -.002 7.420 7.418.7823 10.010 1502.1 ___201,45 211.09 2.354.3184 -.002 7.393 7.391.7661 11.013 246.2 201.35 211.37 - 1.978.3454 -.317 5.727 5.410.5404 11.020 243.9 2-I. — 0 " -221.19 - 3.781.3429 -.320 "-11.024 13.74.. — 541T 11.030 245.1 201.33 240.14 7.405.3439 -.334 21.532 21.198.5463 11.043 Z43.4 201.44 279.16 —.T4-.727.3435 -- -.-35-. —-.-5~235~ —-42.884.5518 12.011 999.1 201.48 212.11 2.954.3136 -.037 9.511 9.504.8947 1Z.015o —' -rO. — 201.57 - 212.24 -'2.954.3089 -.007 9.564 - 9.558....8957 12.020 999.4 201.50 221.93 5.935.3141 -.008 18.893 18.885.9245 12.031 10000.3. 201.52- -- - 242.85 13.523.3203 -.009 42.214 -'' 42.205...' -1213 12.030 1002.1 201.55 243.08 13.519.3188 -.009 42.410 42.401 1.0209 13.011 1500.9 zTI.9- 21 2.- 2.'597'.3159 -... — -.T --.T....191. 7721 13.013 1500.2 201.49 212.36 2.597.3191 -.032 8.140 8.138.7704 13.023 -— T5021.T' 201.51.- -' 222.91 5.441.3255 -.002 16.714 16.717 -'" —.7n-1 13.021 1500.7 201.51 223.12 5.442.3219 -.002 16.906 16.904.7824 13030 1 98.3 -'- 201.48.-" -—. 242.20 - 11.1338.3397 -.003 32.788 32.785 --.8'05114.010 700.2 201.49 210.52 ~+.044.3235 -.015 12.619 12.605 1.3956 14.011 700.0- zO.53 —-— 210.-54 -' 4.045.3217 -. 015. --- TT 12.558 -- 1.3948 14.023 701.2 201.54 220.75 7 14.327.3184 -.023 44.997 44.9777 2.3545 15.011 699.3 201.53 2?31.1 _ 13.596.1943 -.0_9 69.977 69.968 2.3577 15.010 700.3 201.5? 230.70 13.997.1955 -.009 69.539 69.530 2.3822 15.021 702.3 29].54 242.85 16.658.2004 -.009 83.136 83.127 2.0122 15.020 701.? 201.49 244.25 16.656.1969 -.009 84.607 84.598 1.9785 15.030 701.1 201.56 2'7.71 18.040.1842 -.009 97.912 97.902 1.7437

-228 TABLE XLVI (CONTINUED) -- INLET INLET OUTLET —-- WERUN PRESSURE TEMPERATURE TEMPERATURE POWER FLOW'CORR. FLOW Hp p....... _ (paia).. (oF) (oF) (Btu/min) (lb/min). (Bt/lb) (Btu/lb) (Btu/lb) (Btu/lb-~F) L'- U.'0 zoo.o u.U 20..0.. —-; 21132. —- 2.289.3227:.001: —— T.09..-.7.095.72.16.020 23003.6 201.46 221.49 4.567.3122 -.001 14.629 14.628.7304.. T6..030 — 2001.2......-201.-58.....240.49 8.863.3056 - -.001 -- 289 - 28.97 — — 7454~16,042 2000.2 201.46 277.15 17.582.3025 -.001 O58.123 58.122.7679 l16.041 1999.r 20 - -27 z3 ----— 72T.-8 i;580 ~. 3-0T -TO..58.288 5.Z..8 —7686 16.040 2001.8 201.58 277.68 17.580.2973 -.001 59.134 59.134.7771 17.013 -- 6I7.4 -202.15 203.44..1-.008 3417 -.039 2.950 2.911 2.2572. 17.020 616.8 202.14 204.75 2.437.3429 -.029 7.107 7.078 2.7151 18.010 - -- T.5 — -203.79 — 205.09 -.53 -327 -. 073 --—..4.595 -4.- 52 - - 3.459393 18.020 618.1 203.83 206.18 7.353.3309 -.092 22.223 22.131 9.4276 18.030 617.8 20'-3.79 20. 30 —— 1_.7118 -' —.3335 -- -I2-'- 30-32.30.231. 1Z.UZ..42. 18.040 618.5 203.84 207.30 11.834.3052 -.097 38.651.- 38.553 11.1487 18.053 618.1...2 03.8-~~~~208.48... 11.831.2712 —.-097. ----— 43.-625.-.52.1. 3b40 - 18.060__.618.0... --- 2 --- 2 10.?. 11.687.2414 -.0784...8.450' 48.342.......7.5280 18.070. 618.4',..93.82 211.74 11.43?__.2227 -.078 51.336 51.258 6.4771 19.010 498.2 203.88 213.11 2.223.3013 -.170 7.378 7.208.7814 19.020 499.2 203.87 223.23 ___4.478.3015 - 1-_79 14.853 14.674.7583 19.030 499.5 203.87 242.53 6 8.485 -.3010.. -.197.28.186 27.989.7240 19.040 499.6 203.944 260.87 12.057.3003 -.206 40.146 39.940.7016...i19.051~.....-499.?: 203.77 280.50 11.884.2255 -.134 52.693 52.558.6850 19.050 499.4 203.79 280.33 11.884.2257 -.134 52.661: 52.526.6862 20.0103' 617.9 212.22 218.17 2.597...2928 -.070 8.871 8.800. 1.4787 220.020 - 5517.5-..212.-2-0....227.83 -5.694 2934 3 —-.23 p.... -r1-.279 — - 1.2335 20.030 617.1 212.14 253.11 11.910.2925 -.163' 40.717 40.554.9898 21.010 995.3 251.29 260.23' 3258.1339 -.527 24.883 24.357..2.7268 21.021 999.8 251.34 270.00 6.074.1250 -.656 48.579 47.923 2.5686 21.020 1000.1 251.35 270.10 6.074.1245 -.689 48.804 48.115 2.5667 21.030 998.6 251.34 282.52 8.468.1158 -.661 73.124 72.463 2.3243 22.011 1199.8 251.32 262.11 2.027.1078 -.003 18.807 18.804 1.7416 22.010 1199.-8... 251.28' 62.96 2.028.1027 -.003. 19.750 19.747 1.6915 22.021 1201.3' 251.28 276.94 4.550.1020 -.003 4:4.628 44.626 1.7391 22.020 1201.4 251.28. 276.93 4.549.1020 -.004 44.622 44.618 1.7397 22.030 1200.9 251.31 294.55 7.975.1034_ -.004 ___ 77.111 77.107___ 1.7833 23.010 1500.4 251.34 264.43 2.115.1095 -.001 19.320 19.319.4760 23.020 1502.4 251.34 276.63 3.999.1071 - -.001 37.331 37.330 1.4761 23.030 1499.2 251.41.294.50 6.804.1053 -.001 64. 635 64.634 + 1.4998 24.010 1001.4 251.34 293.85 8.543.1008 -.010 84.798 84.788 1.9943 25.010 998.9 231.39 241.43 2.886.1322 -.005. 21.821 21.816 2.1743 25.020' 1000.8 231.46 250.42 5.612.1304 -.005 43.038 43.033 2.2696 _ 25.030 999.2 231.44 260.47 7 7.764.1185 -.005 65.505 65.500 2.2559 26.010 498.5 171.47 174.22.640.1301 -.001 4.924 4.923 1.7895 -26.020.........498.8 ~3......171.39 176.43 1.193.1300 -.001 9.177 9.176 i.8203 26.030 499.3 171.46 178.71 1.749.1302 -.001 13.439 13.438 1.8533 26.040 499.8 171.46 180.94 2.337.1299 -.001 17.986 17.984 1.8962 26.050 500.6 171.44 180.58 2.243 __.1302 -.001 17.233 17.232 1.8856 26.060 498.6 171.42 180.05 2.091.1294 -.001 16.156 16.155 1.8721 26.070 500.0 171.43 181.60 2.530.1301 -.001 19.443 19.441 1.9114 26.6680 0.- 1.. 171.47 184.00 3.203.1299 -.001 24.659. 24.657. 1.9690 26.090 500.5 171.62 185.11 3.928.1299 -.001 30.233 30.232 * 26.100 500.9 -171.27 185.38 4.787.1302 -.002 36.776 36.774 * 26.110 500.9' 171.36 185.36 5.631 __.1299 -.002 43.345 43.343 * 26.120 500.7 171.34 185.26 4.773..1298.-..002 36.774 36.772 *' _26.130 _ __500.6.. 171.37 185.35 6.540.1298 -.003 50.405 50.402. 26.140 501.0 171.56 185.63 7.972.1298 -.003 61.419 61.416 * 26.150 500.8 171.31 185.44 7.970.1170 -.003 68.136 68.133 * 26.160 500.0 171.33 185.34 7.968.1058 -.001 75.286 75.285 * 26.170 __ 501.4 171.33 185.65 9.986.1061 ___-.003 94.127 94.124 * 26.180 501.0 171.35 185.62 12.130.1059 -.002 114.500 114.498 * 26.190 501.1 171.33 185.59 14.761.1059 -.003 139.430 139.427 * 26.200 501.0 171.33 188.30 15.366.1061 -.003 144.886 144.883 * 26.210 499.2 171.34 192.78 16.254.1055 -. 00 154.097 154.095 * — 26.220'....... 498."9...........171.37. 202.78 17.786.1056 -.003 168.498 168.495 * 27.050 250.2 136.13 176.50 5.457.1305 -.124 41.799 41.674 _ 1.0322 27.060 249.5 136.16 176.60 3.184.0940 -.042 33.857 33.814.8361 27.010' 250.3 136.05 146.49 1.880.3123 -.216 —.6.026 5.809.5564 27.0 20 -- 249.3..... — — 136..3...I.57;'00...3..637 -.3137.225 —.I....706......-.4I...... 553 27.030 250.1 136.26 177.14 7.123.3117 -.233 22.852 22.619 g 5533 Z7.040 24R. 3.- 136,36 -177.09 -— 8 294-' 64~.3-"- --- 32 22.76 —-- 22.438.5509 27.071 248.3 136.17 203.75 10.759.2896 -.220 37.158 36.937.5466 27.070T0' —- - S? —,' — -- n 7..... —-2 03*9 424 —-—..1 —;76.....-'9'............-21T — —..37. 07 —9 — 36.862..5480 —28.010 1498.4 22.71 34.40 2.069.3079.000 6.722 6.722.5749 28.020 - - 1498.5 22.2 --- 47.00-..-4;.233 - -..3016 —...000.. —- T4;035.. —- 036.,5779 -- 28.033 1499.7 22.93 68.13 8.070.3055.030 26.413 256.413.5844 28.041 1498.5 ZZ8.55 -.0..71- 5 325 -- 3114.-.00 -----— 492I-..9.-2T —-— 5990U 28.040 1497.7 22.53 104.95 15.327.3103.000 49.389 49.389.5993 ~2 9.'010. —. 20U0.90 — 22. 64 —--- 34.74~.2. 124 -.3077. OOc - 6.903 6.903 -'570-429.020 1998.9 22.62 46.31 4.183.3080.000 13.583 13.583.5735 — 29 330 — 1998.8 2 —--- 7......67.27 - -7.938..3075.000 - 258 25.81-6.......7 29.041 1999.4 22.61 107.59 15.338.3040.000 50.455 50.455.5937 29.0430 1999.3 3 88 22~ 62 1081.....15'.339 —...3027.033.. 50'66' —-- ---—..5 66.59200 30.010 1001.3 22.63 34.13 2.132.3159.000 6.656 6.656.5790 30.020 T 002. ——' 0. 2750- 45.20 - 4..173.3164.000. 13.19 — 3..13~191-7....5836 ---- 30.030 1001.5 22.63 68.59 7.952.2922.000 27.246 27.247.5927 30.040 998.-4....22_- 7.... —---- 10 8.41. 15.169.2894.000 -.52.42-1 ----— 52.4-2-2 - -- --- 31.010 502.2 22.55 33.73 2.023.3094.003 6.539 6.539.5847 31.020 5501.1 82.58...573 — 4.478.3062-..000- I 3-365-.-. 45 -.5918 31.030 499.9 22.60 67.70 8.245.3038.000 27.142 27.143.6019 _3'.00 —.... —501;r.....~ Z....22-,-61..... 103.78 15.343.3033.000 50.572' 50.572 -.6230 32.010 251.8 22.32 33.64 2.035.3016.000 6.747 6.747.5965 32.020. 248.4 22.32 45.76 4.214.2999.000 14.049 14.050.5993 32.030 248.5 22.38 67.88 8.255.2973.000 27.762 27.762.6102 32.040 250.1 22.36 104.97 15.485.2953.000 52.445 52.446.6348: 33.010 1001.9 22.33 67.93 IC.205.3769.000 27.075 27.075 -.5937..33.020 - -1000.4 22.32 67.47 8.271.3095..000 26.747 26.747.5924.33.03). -.. 1:.0.0.'3.. 22,.29.-. 68.46 6.56Q.2421.000 27.253 27.263.5905. 33.040 1].02.0 22.24 67.18 4.056.1 543.000 26.286 26.286 5848'34.010 -- 999.6 -236.75 -223.33 2.305.3641.002 6.332 6.334.4720 35... 010 1000.7 -236.25 -209.59 4.345.3461.001 12.553 12.554 4708 35.021 998.5 -236.23 -186.89 8.429.3603.001 23.394 23.395.4741 35.020 998.4 -236.26 -186.74 8.418 -.3588.001 23.465 23.466.47316 35.031 1001.9 -236.24 -186.00 6.883.2913.001 23.628 23.629 ___.4703'35.'030 — 998.9 -236.22 -- -185.73 6.879.2887.001 23.825 - 23. 826 74719 35.040 1001.4 -236.21 -142.60. 14.799.3307.001 __ 4.752 44.753..4761__

-229TABLE XLVI (CONTINUED) --- — N'~ T- TET NLEOET Z T"oU-E'T f —- ~_ —- --- RUN PRESSURE TEMPERATURE TEMPERATURE POWER FLOW CORR. FLOW I' p " (psia) (~F) (oF) (Btu/min) (lb/_min) (Btu/lb) (Btu/lb) (Btu/lb) (Btu/lb-~F) 36.010 2001.5 -236.22 -222.89 2.134.3406.001 6.266 6.26T.4701 36.024 2003.9 -236.23 -209.11 4.13S.3219.001 12.859 12.860.4741 36.023 2002.2 -236.24 -2C9.20 4.139.3248.001 12.744 12.745.4713 36.022 1999.4 -236.21 -209.21 4.139.3231.001 12.810 12.811.4745 ~ 36.021 2000.6 -236.22 -2C8.69 4.13S -.3172.001 13.047 13.048.47_41 36.020 1998.7 -236.23 -2C8.10 4.139.3098.001 13.360 13.361.4749 - 36.031 2001.3 -236.20 -185. 15 7.727.3184.001 24.267 24.268.474~ 36.030 2002.6 -236.20 -184.92 7.727.3182.001 24.286 24.286.4736 36.041 2001.5 -236.20 -141.02 14.090.3081.001 45.730 45.731.4805 36.040 2003.2 -236.20 -138.95 14.090.3012.001 46.775 46.775.4810 37.010 1000.9 -136.72 -126.74 1.697.3470.001 4.890 4.890 -.4902 37.020 1001.7 -136.72 -116.40 3.495.3488.001 10.022 10.022.4931 37.031 1001.4 -136.72 -96.02 6.940.3436.001 20.201 20.201.4964 37.030 1001.4 -136.72 -96.03 6.940.3433.001 20.214 20.214.4968 37.042 1001.1 -136.73 -60.90 13.611.3557.001 38.263 38.263.5046 37.041 999.4 -136.73 -60.60 ~ 13.609.3542.001 38.428 38.429.5048 37.040 1000.5 -136.73 -60.37 13.610.3534.001 38.510 38.511' -.5044 38.010 2000.7 -136.73 -126.39 1.761.3456.001 5.096 5.097.4932 38.020 1999.3 -136.72 -115.79 3.532.3380.001 10.450 10.451.4994 38.030' 2001.1 -136.68 -96.69 7.013,3541.001 19.804 19.804,.4952 38.040 2000.9 -136.69 -59.13 13.689.3501.001 39.099 39.099.5041 39.010 1000.5 -56.94 -48.15 1.640.3533.001 4.641 4.642..5282 39.020 999.3 -56.97 -39.48 3.257.3518.001 9.260 9.260.5294 39.030 1000.7 -57.06 _ -42.02 6.554.3508.001 18.685 18.686.5333 39.040 999.0 -56.90 11.12 12.757.3451.001 36.962 36.963.5434 40.010 2000.5 -56.98 -48.09 1.587.3420.001 4.639 4.640.5218 40.020 1999.3 -56.92 -38.84 3.243.3422.001 9.477 9.477..5242 40.030 1999.9 -56.98 -21.75 6.275.3374.001 18.601 18.602.5279 ~ 40.040 _ 2001.1 -56.96.11.36 12.513.3415.001 36.641 36.642.5363 43.010 1201.3 267.58 269.45 --.514.24?3 -.0O.1. 2.122 __._2.121 1.1352 43.020 1201.5 267.59 272.19 1.259.2385 -.001 5.278 5.277 1.1460 43.030 1200.9 267.17 274.555 1.976.2343 -.001 8.433 8.432 1.1406'43.040 1200.5 267.29 277.48 2.686.2324 -.001 11.557 11.556 1.1344 43.050.1197.6 267.49 280.25 3.326.2289 -.001 14.532 14.532 1.1389 43.060 1199.7 267.53 282.96 4.119.2331 -.001 17.656 17.655 1.1443 44.010 700.5 211.94 212.87 -.481.2522 -.076 1.907 1.831 1.9577 44.020 702.0 211.94 213.87 1.054.2535' -.076 4.1-. 57 4.081 2.1108 44.030 700.2 211.94 214.77 1.720.2581 -.080 6.662 6.583 2.3226 44.040 701.8 212.02 215.92 2.418.2505 -.O0O 9.653 9.574 2.4526 44.050 701.4 212.00 216.74 3.188.2513 -.080 12.685 12.605 2.6602 44.060 700.2 211.98 217.73 4.143.2499 -.080 16. 578 16.498 2.8696 44.070 701.3 212.03 218.68 5.115.2495 -.080 20.503_ 20.423 3.0709 44.080 702.1 212.09 219.76 6.319.2496 -.080 25. 319 25.240 3.2931 45.010 400.6 181.84 191.73 1.992.2830 -.193 7.040 6.847.6916 45.020 399.8 181.80 201.37 3.857.2881 -.202 13.388 13.186.6736 45.0-30 397.5 181.93 211.13 5.589.2864 -.214 19.513 19.298.6608 46.010 449.0 191.46 201.25 2.109.2810 -.277 7.504 7.227.7389 46.020 448.9 191.38 210.85 4.058.2816 -.292 14.411 14.119.7252 47.010 701.1 218.37 219.30 1.275.2696..-.-055 4.729 4.674 5.0303 47.020 700.6 218.40 220.26 2.524.2704 -.072 9.335 9.263 4.9774 47.030 701.2 218.40 221.24 3.601.2693 -.079 13.374 13.295 4.6680 47.040 699.4 218.40 222.26 4.569.2692 -.085 16.972 16.887 4.3663 TABLE XLVII TABULATED EXPERIMENTAL ISOTHERMAL DATA FOR PROPANE T." INL.ET INLET PRESSURE ~"j RUN TEMPERATURE PRESSURE DROP POWER FLOW- CORR. HUT (Hg/ P)T (~F) (psia) (psi) (Btu/min) (ib/!i~:(Btu/ib) (Btu/lb) (Btu/b-pzi),-, 3.020 250.0 2005.6 339.2.985.3540.13 2.769.o008163 3.040 249.9 1821.3 360.4 1.473.3607 -.010 4.094 -.011358 3.060 250.0 1581.2 365.0 2.475.3543 -.028 7.014 -.019219 _3.080 249.9 1333.7,-.40.2.3...7.294_.__._,3499 _ -.105 -_20.951. _-.0520844 3.010 250.1 2010.2 181.5.338.2564.023 1.296 -.007141 3.030. 250.0 1809.4 186.7.474.2546.003 1.858 -.009954 3.050 250.0 1586.4 213.8.884.2689 -.005 3.292 -.015398 3.070 250.0 1347.8 232.9 1.890.2723 -.040 6.982 -.C29980 3.090 249.9 1046.8 2S7.4 10.751.2524 -.039 42.635 -.143372 3.100 249.9 829.4 333.4 8.046.1936 -.011 41.566 -.124686 3.110 249.9 659.8 316.6 3.879.1463.001 26.518 -.083768 3.120 249.9 654.6 136.6 6.311.1625 -.012 38.847 -.072402 4.010 201.0 2024.8 17C.9.101.2608 -.023.409 -.002393 4.030 201.0 1826.4 192.2.175.2750 -.028.662 -.003446 4.050 201.0 1544.9 181.2.238.2558.022.909 -.005016 4.070. 201.0 1284.7 188.7.428.2666 -.026 1.632 -.008650 4.020 201.0 2025.0' 319.2.315.3623 -.006.876 -.002744 4.040 231.0 1828.2 333.6.472.3688 -.003 1.283 -.003846.. 4.060 231.0 1530.4 340.6.834.37T2 -.004 2.216 -.006507 _4.080 201.0. 1273.7 345.1 1.288 _____.362__ -.048..__3,605 _.. 10448 5.020 201.0 1018.5 1354.5 2.896.3642.042 7.911 -.022317 5.01C 201.0 1021.2 160.4.472.2395 -.037 2.007 -.012512 5.030 201.0 720.6 77.9.565.1568.020 3.584 -.046012 5.04C 201.0 721.6 89.4.739.1682.641 4.354 -.048707 5.050 201.0 822.7 104.5 1.047.1834.039 5.669 -.054254 5.060 201.0 719.3 119.9 1.48.1940 -.033 7.696 -.064189 5.07C 201.0 726.0 176.6 13.530.1968.052 68.707 -.389091 5.080 200.9 722.1 190.6 14.381.2001.036 71.844 -.376971 5.090 201.0 717.7 205.2 15.203.2022 -.031 _ 75.235 -.366674 5.100. 201.0 555.3 52.6 5.575.1421.006 39.241 -.11131 5.110 201.0 551.3 44C.9 6.652.1479 -.019 45.004 -.102084 6.010 161.7 2019.8 202.9.011.2911 -.021.059 -.000293 6.020 160.6 1877.5 2C1.5.039.2912 -.003.135 -.000672 6.030 160.6 1710.4 203.0.063.2889.004.216 -.001062 6.040 160.6 1567.5 202.0.087.2900 -.002.301 -.001493 -6.050....16o.4 1386.4 210.5.126.2914.o07.42- 7 -.002027 6.060 160.5 1217.9 220.0.199.3025 -.000.657 -.002987 6.070 160.5 1024.4 223.0.290.3012.026.938 -.004205 6.080 160.5 827.9 232.4.452.3053.001 1.479 -.006364 6.090 160.6 638.3 210.8.589.2874.013 2.037 -.009665 7.010: 200.6 _ 562.8 163.7 4.844.1814 -.024 26.725 -.163271 7.020 - 200.5 470.6 256.2 4.129.1733.010 23.820 -.092981 7.030 200.5 447.8 331.2 4.762.1751.010 27.186 -.082091

-230 TABLE XLVIII TABULATED EXPERIMENTAL JOULE-THOMSON DATA FOR PROPANE Inlet Temperature Run (OF) 0.011 0.010 2,010 2.020 2.050 2.040 2,050 21.2 21.3 2.153 21.3 21.2 21,1 21.2 Inlet Pressure (psia) 1992.1 1992.5 2026.0 2020,5 1082.2 1071.7 1099o.6 Temperature Difference (~F) 1.524 3.3554 4.281 1.837 2.580 35.5372 Pressure Drop (psi) 381.2 352.0 773.9 01o6.6 481.5 697.7 941.9 (OF psi)xlo1 4.668 4.371 4.357 4,262 3.853 35.738 35.622 TABLE XLIX FLOWMETER CALIBRATION EQUATION CONSTANTS USED FOR PROPANE Flow Meter Series B A C D low 0.045462835 94,.606418 -34925.556 5060329.4 10 - 20 low high 0.4390828 -270.13652 263753522 -6141762.4 30 high 0.86077077 -610.80764 166847.2 -153993813.0 4 low 0.045505256 9355971 -34102.569 4941925.4 high 0.50686614 -320.16109 88793.802 -7156188.0 low 0.057971521 81.50558 30315,252 4554907,9 high 0.49223719 -308.87943 86038.184 -6942817.9 6o - 70 low 0.050889514 89.836006 -33417.221 4928000.5 high 0.50108158 -316.88119 88371.262 -7159948.1

-231TABLE L TABULATED EXPERIMENTAL ISOBARIC DATA FOR THE NOMINAL 77 PERCENT MIXTURE MOriljA ~3LT' INLE.T U=LiT PO- UWE1 RU^ FRACTION PRESSURE TEMPERATURE TEMPERATURE POWER FLOW CORR. FLOW. AHpP C3H (psia) CF) _ () (Btu/min)L (Ib/min) (Btu/lb) (Btu/lb) (Btu/lb) (Btu/lb~~F- _ 1.oo100..767 1409.8 199.49 215.81 3i.869.2454 -.004 15.764 15.759.9659 1.0200.767 1501.6 200.72 233.44 8.091.2496 -.005 32.420 32.415.9905 1.0300.767 1502.1 200.98 249.09 11.598.2441 -.005 47.504 47.499.9872 2.0100.767 2001.2 200.99 216.69 3.114.2410 -.001.12.917 12.916.8228 2.0200.767 2001.0 200.99 234.89 6.420.2252 -.001 28.514, 28.512.8412 2.0310.767 1999.5 201.02 252.32 8.974.2049 -.001 43.792 43.791.8537 -2.0300.767 2000.9 200.99 252.61 8.974.2041 -.001 43.971 43.970.8517 3.0100.767 1199.6 201.0? 216.85 4.045.2202 -.009 18.375__ 18.366 1.____ 1601 3.0200.766 1199.4 201.12 234.14 7.967.2158 -.012 36.921 36.909 1.1179 3.0310.767 1202.0 201.06 249.54 11.123.2137 -.011 52.056 52.045 1.0735 3.0300.767 1201.6 200.94 249.92 11.123.2121 -.012 52.432 52.419 1.0701 4.0100.767 999q.9 201.04 210.36 2.302.2085 -.019 __11.043 11.024 1.1819 4.0210.767 1001.8 200.84 220.02 4.440.2069 -.021 21.456 21.435 1.1173 4.0200.767 1002.0 200.82 219.94 4.440.2060 -.021 21.550 21.530 1.1264 4.0300'.768 998.9 200.56 239.72 7.926,1972 -.021 40.196 40.175 1.0260 4.0400.768 _1001.8 201.05 257.72 10.338.,1884 -.020 54.887 54.867.9682 4.0500.766 998.9 200.99 276.17 13.043.1855 -.015 69.201 69.186.9202 5.0100.766 497.8 201.00 210.83 1.267.2073 -.026 6.112 6.086.6192 5.0200.766 498.2 201.18 220.77 2.503.2075 -.032 12.060 12.028.6142 5.0300.766 408.4 200.92 240.09 4.968.2072 -.032 23.975 23.943.6114 5.0400.766 498.1 201.02 258.49 7.244.2071 -.037 34.989 34.952.6081 5.0500.766 498.0 201.39 277.07 9.496.2066 -.036 45.971 45.935.6069 6.0100.770 246.8 199.22- 209.08 1.132.2128 -.082 5.317 5.235.5305 6.0200.770 247.5 200.61 220.54 2.280.2138 -.084; 10.662 10.579.5307 6.0300.767 247.7 201.03 239.95 4.478.2137 -.088 20,952 20.864.5362 6.0400.767 247.3 201.04 259.02 6.705.2135 -.089 31.402 31.314.5401 6.0500.767 247.8 201.03 276.47 8.780.2133 -.092 41.160 41.068.5444 7.01.10.767 1499.0 251.54 261.21 1.986.2165 -.007 9.169 9.162.9475 7.0100,766 1498.6 251.02 260.60 1.996.2185 -.007 9.134.9.126.9529 7.0210.766 1499.8 251.04 260.93S 3.832.2158 -.007 17.754 17.747.9394 7.0200.766 1498.2 251.02 270.09 3.832.2134 -.007 17.950 17.944.9409 7.0300.766 1499.0 251.12 282.32 6.032.2099 -.007 28.745 28.738.9210 7.0400.766 1498,5 251.02 299.64 6.859.1556 -.005 44.086 44.081.9067 8.0100.767 1697.9 250.61 263.00 2.499.2190 -.004' 11.413 11.409.9208 8.0200.767 1701,2 251.17 276.97 4.994.2149 -.005 23.236 23.232,9007 8.0300.767 1698.1 250.39 293.12 8.124.2105 -.005 38.598 38.593.9032 9.0100.767 2000.9. 251.02 264.72 2.412.2012 -.002 11.989 11.987.8751 9.0210.767 2000.9 251.02 275.70 4.530.2120 -.002 21.374 21.371.8657 9.0200.767 1999.1 251.02 278.40 4.530.1883 -.001 24.062 24.061.8788 10.0100.766 101.9 151.73 165.64 3.713.2220 -.004 16.727 16.723 1.2019 10.0200.766 999.9 151.70 178.86 7.685.2192 -.004 35..055 35.051 1.2902 10.0300.766 1001.9.151.67 192.58 11.871.2188 -.006 54.262 54.256 1.3264 10.0400.765 999.6 151.61 205.28 15.196.2163 -.006 70.271 70.265 1.3092 11.0100 _.765 501.58 156.63 173.26 2.539.2195 -.045 11.566 11.521.6930 11.0200.765 501.8 156.59 189.69 4.884.2198 -.058 22.215 22.157.6694 110300.76 501.2 156.58 206.68 74:82.2195 -.054 32.727 32.673.6522 12.0200.766 1500.9 102.03 123.61 4.010.2561 -.000 15.656 15.656.7256 12.0300 -.165 1498.1 102.C - 144.61 - t.046.(-00 -.000 32.186 32.1E6.1169 12.0400.765 1498.4 101.S3 183.53 16.446.2506 -.000 65.636 65.636.8043 13.0100.1764 199-.4 101.69S 112.00 - 1.131.281.000 1.01 71.0178.6866 13.0200.764 1998.7 101.74 123.49 3.548.2364.000 15.011 15.011.6900.U jo'uU. — rr164 iY991.4 1II.24 144.4/1 1.4- 4.418-.000 9.b884 29.8y2 -.040 F3.0400.764 1998.2 101.67 184.37 14.766.2424.000 60.921 60.921.7367 14.0100.t~5 998.3 101.11 119.43 3.58 -.26151 -.001 - 13.719 13.718.1142 14.0200.765 99.0 101.67 136.51 7.519.2564 -.001 29.330 29.330.8419 14.0300.165 1000.1 101.68 113.31 12.130.2600 -.001 - 46.646- 46.645.9028 15.0100.768 246.4 112.28 122.71 1.557.2714 -.224 5.736 5.512.5281 1i.0200.176 2460.4 - -112.254 133.-18 -3.060 L.27 11 -.228 - 11.290 11.063.5285 15.0300.768 246.5 112.26 154.76 6.126.2712 -.201 22.586 22.385.5266 15.0400.768 246.6. 112.26 180.11 9.623.2713 -.239 30.203 35.963.52016.0100.766 700.0 102.47 113.25 2.175.1933 -.000 11.254 11.254 16.0200.767 699.5 102.48 124.22 4.604.1933 -.000 23.820 23.820 * 16.0300.767 698.7 102.43 134.81 7.2P4.1939 -.000 37.571 37.571 16.0400.767 697.4 102.46 145.87 10.491 _.1930 -.000 54.365 54.365 * 16.0500.766 699.1 102.44 154.92 13.609.1927 -.000 70.633 70.633 16.0600.766 699.8 102.49 164.82 13.597.1459 -.000 93.193 93.193 * 16.0700.766 700.9 102.44 170.06 15.608.1460 -.000 106.912 106.912 16.0800.766 701.0 102.45 175.10 16.498.1460 -.000 113.033 113.033 * 16.0900.766 698.4 102.46 182.22 17.480.1449 -.000 120.622 120.622 16..1000.766 699.4 102.46 189.96 18.529.1454 -.000 127.405 127.405 * 17.0100.769 698.7 47.35 51.14.543.2195.000 2.473 2.473.6539 17.0200 *.76Q 69 8. 47.49 53.59,.856,.2131.000 4.016 4.016.6588 17.0300 *769 699.4 47.48 55.98 1.236.2126.000 5.815 5.815.6842 17.0400.769 698.7 47.48 58.61 1.613.2115.000 7.626 7.626.6854 17.0500.768 698.6 47.50 61.36 2.011.2111.000 9.526 9.526.6875 17.0600.768. 699.? 47.50 63.62 2.356.2112.000 11.155 11.155.6921 17.07nO.768 6Q9.0 47.50 66.14 2.718.2102.000 12.931 12.931.6937 -17.0800.768 699.8 47.48 68.16 3.044.2119.000.14.366 14.366.6947 -17.0900.768 698.6 47.50 72.55 3.727.2116.000 17.609 17.609 17.1000.769 699.6 - 47.50 77.72 4.580.2123.000. 21.570. 21.570 * 17.1100.769 699.4 47.51 75.42 4.177.2121.000 19.697 19.697 17.1200 -. 769 ___699. 1 47.51. 882.81.54.46.2073...000 ____26.0.83..__ 26.0826 17.1300.769 699.3 47.51 96.49 5.420.1396.000 38.822 38.822 17.1400.760 698.7 47.52 110.28 7.321.1394.000 52.528 52.528 * 17.1500.769 700.7 47.51 124.88 9.566.1390.000 68.812 68.812 17. 1600.769 700.2 47.50 137.86 11.991.1387.000 86.431 — __86.431..* 17.1700.769 699.1 47.53 155.03 15.891.1382.000'- 114.962 114.962 * ____ 18.0100" ".764" 998.5 — 22.91 30.80 1.478.2945.000 5.019 5.019.6363 18.0200.164 -10UU.1 44.5Z9 - - 3.93.031.2951 * 000 10.411 10.40.6i05 18.0300.764 1000.0 22.82 53.07 6.-29.3266.000 19.564 19.564.6467 -9.1U.1100 1 991.24 24.426 51.02 0.144.310E.00 19.111 7 1. 77I1.6431 20.0100.766 998.3 24.26 55.45 6.354.3136.000 20.261 20.261.64 20.0200.110 999.4 4.4.31 1.9 141.01.0 011 4.1 01 20.0500.766 998.2 24.32 84.48 11.852.2926.000 40.507 40.507.6733 20.0300.766 998.7?4.23 55.62 3.73.18 -.0007 20.344 20.3.6 *636 20.0400 -.766 093.7 24. 27 56.19C 2.203.1128 -.000 20.326 20.326 66

-232 TABLE L (CONTINUED) RUN FRACTION PRESSURE TEMPERATURE TEMPERATURE POWER FLOW CORR. FLOW A MR 0 3 H 8 (psia) (OF) ( (Btu/min), (lb/min) (Btu/lb) (Btu/lb) (Btu/lb) (Btu/lb-~F) _ "21.011)0.166 1*)UZ.( Z'4. JU 32.24 1.41 -".2,960.0UU 4.y3b 4.935.62. -, 21.0200.766 1498.7 24.26 39.82 2.823.2905.000 9.717 9.718.6253 21.03-00.100 10I1.1 24.31 54.18 - -.55 -.2883.100 19.269 19.270.6324 21.0400.766 1501.1 24.32 84.32 11.026.2837.000 38.867 38.868.6478 22.010I ----.T675 --- 999.7 --- 24V.2 ---- 32.02 --- 1.371 ----. V07 ----.0J ---- 4.71 ---- 4.716 ----.6098 22.0200.766 1999.1 24.28 40.45 2.789.2812.000 9.919 9.920.61.32 -.8& 00 ---.75 - 19.4 44'y.- 00_-b.0 _ 0 —--. 2J/ I.2/08.000 19.343 19.343 --.61 22.0400.765 1999.2 24.31 65.06 10.381.2705.000 38.378 38.378.6317 23.0100.766 499.4 9-.94.61.495.2162. 2. 2-292.962020 23.0200.766 500.? -.09 6.06.821.2151.000 3.817 3.817.6204 23.0300.766 4499.8 -.09 8.69 _1.170.2149__ 000 5 446 5__4_5.44.6206 23.0400.766 498.6 -.06 11.23 1.513.2143.000 7.058 7.058.6250 23,0500.766 49877 -.07 14.00 1.928.2142.000 9.002 9.002 __23.0600.765 500.9 -.08 16.92 2.402.2147.000 11.189 11.189 * 23.0700.765 499.5 -.08 19.77 2.873.2142.000 13.415 13.415 * ____ 23.0800.765 498.3 -.08 31.89 4.887.2132.001 22.921 22.922 * 23,0900.766 499.7 -.09 47.39 7.583.2134.001 35.540 35.541 * 23.1000.766 498.5 -.09 69.78 11.815.2132.001 55.408 55.409 * 23.1100'.766 498.3 -.077 91.41 16.564.2129.000 77.798 77.799 * 24.0100.766 250.1 -.09 15.98 2.319.1697.001 13.663 13.664 * 24.0200.766 248.1 -.07 31.02 4.722.1676.001 28.181 28.182 * 24.0300.766 248.9 -.09 46.53 7.686.1675.001 45.879 45.880k * 24.0400.766 249.8 -.07 61.77 11.422.1678.001 68.053 68.054 * 24.0500.766 249.6 -.05 76.45 16.483.1674.001, 98.472 98.473 * 24.0600.767 247.8 -.05 88.62 23.385.1658.001 141.005 __141.006 * 24.0700.767 248.4 -.14 91.82 19.053.1228.001 155.196 155.197 * 74.0800.767 251.0 -.08 94.90 20.724.1239.001 167.296 167.296 4 ___ 24.0900.767 250.0.01 102.15 21.781.1234.001 176.548 176.549 * 24.1000.767 __ 249.7.01 113.42 22.561.1232.001 183.066 183.067 * 24.1100.767 248.9.0p 118.18 22.820.1227.001 185.920 185.921 * 25.0100 ____._~_765 ______ 399.0 58.70 69.97 1.602.1345 -.0,00 ___113.913 11.913______ * 25.0200.765 398.5 58.65 80.93 3.346.1358 -.000 24.648 24.648 * 25.0300.765 399.9 58.66 91.95 5.381.1365 -.000 39.411 39.411 * 25.0400.765 399.4 58.66 102.68 7.799.1364.000 57.178 57.178 * -25.0500.766 398.8 58.70 113.32 10.838.1359 -.000, 79.731 _ 79.731 __*__ 25.0600.766 399.16 58.61 124.29 15.309.1359 -.000 112.693 112.692 * 25.0700.766 398.3 58.62 129.87 18.457.1354 -.000 136.288 136.288 * 25.0800.766 399.7 58.63 130.87 18.819.1360 -.000 138.385 138.385 * 25.0900 _ 766 399.4 58.63 135.38 19.514.1359 -.000 143.592 143.592 * 25.1000.767 398.5 58.73 141.26 19.965.1355 -.000 147.391 147.391 * 25. 1100.767 398.9 58.67 145.84 20.418.1358 -.000 150.333 150.3331.. * 26.0100.767 502.1 82.72 93.51 1.611.1344 -.001 11.983 11.983 * 26.0200.767 498.6 82.52 104.26 3.434.1327 -.000 225.868 25.5$8.68 ______ ~_ 26.0300.767 498.9 82.52 114.94 5.540.1335 -.000 41.493 41.493 * 26.0400.765 498.6 82.49 125.63 8.164.1328 -.001 61.475 61.474 * 26.0500.765 499.1 82.49 135.60 11.197.1324 -.001 84.549 84.548 * 26.0600.765 500.7. 82.61 145.99 15.504.1330 -.001 116.574 116.574 * 26.0700.765 501.2 82.63 147.50 16.168.1327.000 121.806 121.806 *,.26.0800.765 501.0 82.71 150.61 16.572.1324 -.001 125.133 125.132 * o't6.0900.765 500.2 82.57 154.79 16.922.1320 -.001 1 28.213 128.212 * 2^'1000.765 499.5 82.56 159.26 17.369..1320 -.001 131:58.0. 131.57q * 2770100w.764 1302.1 139.72 153.36?.87i.1864 -.002 15.406 15.404 1.1297 27.0200.765 1300.0 140.06 168.20 5.717 —.1793 -.002 31.886 31.884 1.1332 2:7,0300.765 1300.0 140.18 181.49 8.715.1767 -.002 49.328 49.326 1.1940: 27.0400 -.765,130.1 139.99 193.18 11.676.1755 -.003 66,549 66.547 1.2511 28.01UU.166- 14v.8 l07.1i 161.77 1.844.Zu88 -.U17 8.7a 2 8.700.8337 28.0210.766 1497.9 158.13 178.64 3.496.1988 -.016 17.583 17.566.8563 28.0200.16 - 14591. - 158.13 1t.4- 3.49 -.1973 -.016 -17.716 11.699.87111 29.0100.766 1500.4 181.71 191.65 A.820.2001 -.016 9.098 9.081.9134 29.0200.166 1498.60 81.10 400.90 3.671.2067 -.0-U 11.706 - 11.140 -.9241 30.0100.766 1198.4 191.74 198.40 1.506.1924 -.078 7.827 7.749 1.1629 0.002U.100-'1199.24 1-1.10 4204.94 2.5 -.185I -.0U8l - - l0.387 I 15.306 -1.1599 31,0100.765 495.5 199.S4 219.23 2.420.1983 -.423 12.205 11.781.6107 31.U4U1 0.165 493.1 I9. -8 4238.16 4.650.1911 -.459 -23.585 23.126.6051 32.0100.765 1499.6 213.8C 220.43 1.263.1906 -.037 6.626 6.589.9936 32.0200.165 1497.7 - 213.13 226.15 2.408.1855 -.0319 12.980 12.941 --- 941.22.0300.765 1499.7 213.15 232.85 3.746.2004 -.047 18.688 18.641.9762 32.0400.T l5-.5 1498.4 213.13- -239.47 5.050.1975 —.-050 25.565 -- 25.516 -.9915 33.0100.765 1701.1 221.24 230.68 1.765.2008 -.027 8.790 8.763.9280 3 200 -.1065 - 1697.9 -221.20 - 240.10 3.509 -.2000 -.029 - 11.53 17.510 --.9268 33.0300.765 1698.6 221.23 249.65 5.279.1994 -.031 26.482 26.451.9307 34.01100 ------ 0~TE5 - 1998.0 5 4231.71 240.55 1.146.2133 -.016 8.183 8.1671.8607 34.0200.766 1998.6 231.C2 249.95 3.430.2096 -.018 16.368 16.350 *8638.34.03-00.b0 42C01.0 4230. 1 I 0259.33 5.la!).2079 - -.0119 24.5571 24.538.8652 34.0400.766. 1997.3 231.04 268.58 6.569.2012 -.019 32.644 32.624.8689 34.0500.166 1999.2 4231.01 277.43 8.067.2002 -.020 40.293 -40.273.8681 34.0600.766 2000.1 230.95 286.43 9.670.2007 -.021 48.185.48.164 *8682 35.0100.616 106197. 4221. 40258.560 7.285.2092 -.029 34.817 - 34.188 - 9282 35.0210.766 1697.7 220.32 267.08 9.048.2100 -.038 43.075. 43.037.9203 35.02001.10 - 1700.5 220.3 - 0267.18 9.1047.2094 - -.038 -43.207 - 43.169.9213 36.0300.766 1998.9 -57.38 -21.58 4.218.2090.000 20.183 20.183.5638 i0..0400.106 2002.1- — 5.3 9.51 17.241.1885.000 38.405 38.406.5147 106.U11O ~.166 1599.1 -S7.4C -48.51 1.100.213A.000 4.541 4.543.0~5feU 34.0200.766 2001.9 -57.38 -38.74 2.476.2388.000 10.370 10.370.5563 37.0100.765 1498.2 -57.43 -48.95 1.309.2771.000 4.724 4.72g.5573 17.021 0 ---—. 5 -- 1D 1458.8 -51I.41 -40.31 -2.11.2839 -.100- -.580 - 59.580 - *003 37.0300.765 1499.5 -57.39 -23.16 5.369.2771.000 19.374 19.375.5660 37.0400.76 1 10U0.2 -57.30 9.958 10.627.27318.01100 J1.818 38.818.0710 35.0111001..1600 55.4 -57.37 -40.38 ---— 02..916.3X —.110 ------ 9T5.2 ---— 31.542.506Lb 38.0300.765 1000.0 -57.38 -22.93 6.020.3075.000 19.578 19.578.5683 38. 0400 — —. 1k0 998.1 -517.1359 10.04 11.1901 7.3040.000 39.167 39.10af.5830 38.0100.T65 -999.0 -57.29 -47.08 - 1.201-.2077.000 5.781 5.781.5662 39.0100 ---- 65 -— 499.3 --- -7.5 -- 4 8.83 1.3 --- 2695.6650 4.967 497 59 39.0200 --.1B5 - 499.0 -51.4C -39.050 2.845.2690 -.000 10.511 10.518.5165 39.0300.765 499.3 -57.51 -22.68 5.452.2689.000 20.278 20.278.5821 40.0i11.10046-2002.4. —.147.5 1 1 -111.51 1.411 -.2710.1000 - 5.206.5 206 -.51761 40.0200.765 1999.8 -147.56 -126.99 2.868.2680.000 10.700 10.700.5202, 40.0300 --.1065 1998.8 -147.56 -101.33 5.712.2721 -.000 120.996 - -20.996 -521i9 40.0400.765 2000.5 -147.56 -68.43 11.050.2646.000 41.759 41.760.5277 41.01111.100566 998.5 -141.60 -137.68 1.494.29045 -.010 5.145 5.145 -.5185 41.0200.766 999.5 -147.60 -126.72 3.119.2878.000 10.836 10.836.5190 41.011 ---.105 -1001.1 - -147.01 -101.98 06.128.29471.00 420.7960 20.796 -.261 41.0400.766 1001.3 -147.52 -69.52 12.258.2940.000 41.690 41.690.5345

-233TABLE L (CONTINUES) ------- HLBE ---- FINT - INLET 4,W UTLET ----- ----- -POWER -__ RUN FRACTION PRESSURE TEMPERATURE TEMPERATURE POWE4. FLOW CORR. FLOW A Hp' (AT/p C3H8 (psia) (~F)- (OF) (Btu/min) (lb/min) (Btu/lb) (Btu/lb) (Btu/lb) (Btu/lb-0F) 42.0100U ~.75- 500.8- -1147 eV -137.48 -1.511-.28,46 —-- uuu 5.310 -5.3T1 -- 2f49 42.0200.765 500.8 -147.52 -126.14 3.217.2847.001 11.299 11.300.5285 42.030U -.15 --- 1.y —-147.5s —-107.b52 6.045 —.2841 -—.000 -21.276 -— 21.277 ---.5310 42.0400.765 498.3 -147.54 -70.08 11.815.2833.000 41.704 41.705.5384 43.0100 -----. 1 248.5 —-217.80 —-206.15 — 1.770 -.29S99 - 000 - 5.904- -5.904 -.5068 43.0200.765 248.3 -217.e2 -193.59 3.843.3097.000 12.410 12.411.5122 43.0300U ~5 -249.6- — 217.08 -170.05 17.349 -.3029 -.000 24.O263 - 24.263 u.503 43.0400.765 251.0 -217.78 -128.55 13.702.2977.000 46.020 46.020.5158 44.00U0.T6 2001.1 -236.16 -223.40 1.792.2791i.000 6.401 6.408 -.5021 44,0200.766 2000.9 -236.12 -209.98 3.597.2764.000 13.012 13.012 *.4978 494.0U132 -.T766 - 1999.JJ -236.1 -— 186.bO 0.167371.26840.000 -25.101 - -2b.101 - *0.1b 44.0400.766 2000.3 -236.C7 -142.71 12.458.2631.000 47.358 47.358.5073 45.0100. -6 -998. - -236.11 — 222.48 1.943.2855.U 000 6.806 06.8060.496 45.0200.766 998.7 -236.C7 -210.40 3.637.2836.000 12.825 12.825.4996 -45.0300.756 999. -236.11 -18/a.b54 6.971.2851.000 24.451 -24.451..5035 45.0400.766 1000.3 -236.C7 -141.99 13.633.2850.000 47.837 47.838.5084 46.0U1u0.g -499.0U -236.C -- -223.02 1.884.2884 -.000 06.532 6.533 -.b009 47.0100.765 1000.3 -57.14 -48.82 1.390.2975.000 4.672 4.672.5621 947.0200 -.7-65 -- 998.I - -b?.22-4 — 39.160 -3.0b88.30125 —.000- -10.142 - -10.142 --.56152 -,0300.765 998.7 -57.19 -20.91 5.971.2908.000 20.530 20.531.5659 48.0100.765. 1006.2 -147.07 -135.85 1.631.2789.000 5.847.5.847..5213 49.0200 _.766 1004.2 -147.05 -126.77 2,912.2749.000 10.594 10.595.5224 48.-0300.766 1006.2 -146.91 -106.93 5.825.2731.000 21.329 21.329.5281 49.l0400.766 1000.? -146.91 -68.85 11.4846.2730.000 4258 4258.538 49.0100.765 254.2 -107.37 -104.34.265 i623-.00 1.632 1.6Z.5400 49.0200.765 254.2 -107.38 -101.46.535.1622.000 3,.302 3.302.5574 49.0300..765 254.2 -107.38 -98.75.761.1618.000 4.704 4.704-..5446 49.0400.765 257.2 -107.38 -95.79 1.040.1637.000 6.353 6.353. 54 84 49.0500.765 256.2 -107.37 -93.05 1.284.1636.000 7,.847 7.847..5481 49.0600.765 257.2 -107.38 -89.95 1.562.1636.000 9.548 9.548.5477 49.0700.765 256.2 -107.36 -986.79 1.848.1627.000 11.358 11.358.5521 49.0800.767 256.2 -107.39 -83.92 2.108.1641.000 12.842 12.842.5471 49.0900 -.767 256.1 -107.39 -81.12 2.353.1624.000 14.490- 14.490.5516 49.1000.767 256.0 -107.62 -78.51 2.658.1630.001 16.311 16.312 49.1100 -.767 254.0 -107.54 -75.77 2.957.1612.001 18.338 18.338 8 - 49.1200.767 255.0 -107.38 -71.94 3.381.1617.001 20.910 20.910 49.1300.763 254.9 -107.38 -60.47 4.726.1606.001 29.426 -29.426 49.1400.763 253.9 -107.36 -34.39 7.718.1607.001 48.036 48.037 49.1500. 768 254.0 -107.37 -9.65 10.658.1608.001 66.293.- 66.294 49.1600.768 256.9 -107.38 13.81 13.874.1623.001 85.504 85.505 50.0100.764 406.1 -47.83 -42.46.514.1656.000 3.103 3.103.5781 50.0200.764 406.2 -47.76 -37.45.990..1653.000 5.989 5.990.5810 50.0300.764 407.1 -47.71 -32.11 1.518 -.1651.000 9.197 9.197.5892 50.0400.764 407.1 -47.77 -27.04 2.015.1651.000 12.204 12.204.5885 50.0500.764 408.1 -47.75 -22.15 2.541.1660.000 15.309 15.310 - 50.0600.764 408.1 -47.73 -17.20 3.141.1661.000 18.904 18.905 * 50.0700.764 - 408.1 -47.71 -11.84 3.803.1659.000 22.927 22.928 50.0800.764 408.1 -47.73 2.58 5.567.1655.000 33.649 33.649 * 50.0900.764 408.1 -47.69 18.72 7.614-.1655 -.000 45.995 45.995 50.1000.764 409.1 -47.69 40.74 10.665.1665.000 64.054 64.054 * 50.1100.764 408.1 -47.74 65.75 14.599.1652-.000 88.379 88.379 51.0100.765 501.0 200.63 211.78 1.446.2094 -.022 6.905 6.884.6175 51.0200.765 500.7 200.64 220.20 2.501.2086 -.016 11.989 11.973.6121 51.0300.765 498.7 200.60.239.17- 4.879.2075 -.025 23.512 - 23.487.6089 51.0400.765 498.6 200.74 275.97 9.351.2049 -.032 45.631___ 45.599.6061

TABLE LI TABULATED EXPERIMENTAL ISOTHERMAL DATA FOR THE NOMINAL 77 PERCENT MIXTURE Mole Inlet Inlet Pressure Power Flow Corr. A H (A H/AP) Fraction Temperature Pressure Drop T Run C3H8 (OF) (psi) (psi) (Btu/min) (Ib/min) (Btu/lb) (Btu/lb) (Btu/lb-psi) 1.010 1.020 1.030 1.040 1.050 1.060 1.070 1.080 1.090 1.100 1.110 1.120 1.130 1.140 2.010 2.020 2.030 2.040 2.050 2.060 2.070 2.080 2.090 2.100 2.110 3.010 3.020 3.030 3.040 3.050 3.060 3.070 3.080 3.090 3.100 3.110 3.120 3.130 3. 140 3.150 3.160 3.170.766.766.767.767.767.767.767.767.767.767.767.767.767.767.765.765.765.765.765.765.765.765.766.766.766.764.764.764.764.764.764.764.764.764.764.764.764.764.764.764.764.764 200.9 200.9 200.9 200.9 200.9 200.9 200.9 200.9 201.2 201.2 200.9 200.9 201.0 200.9 251.3 251.5 251.3 250.7 252.1 250.9 250.9 250.8 250.9 250.9 251.0 9918 99.8 99.8 99.8 100.0 100.0 99.9 99.8 99.9 99.8 99.8 100.0 99.9 99.9 99.9 99.8 99.8 2029.7 1893.1 1830.9 1731.1 1622.1 1529.9 1403.2 1277.0 I 1 1.9 950.7 801.2 657.3 482.2 361.0 2022.3 1904.7 1747.2 1632.3 1474.4 1315.7 1112.3 893.7 660.4 506.7 390.2 1998.7 1856.1 1701.9 1550.1 1388.2 1206.3 1005.1 990.5 1005.7 990.6 1006.1 640.0 640.9 641.4 519.2 474.8 476.7 105.6 112.1 117.3 127.1 131.9 137.1 144.3 158.7 161.0 169.4 149.5 239.3 285.0 251.5 144.3 154.4 158.2 176.0 179.1 204.2 233.4 201.5 187.5 212.8 283.2 179.7 178.5 192.0 205.0 204.6 211.2 145.0 177.6 254.2 291.6 396.2 140.0 236.2 324.8 242.8 307.5 369.4.3229.4105.5209.7158.9523 1.2340 1.8854 3.2092 4.5689 4.6841 2.7615 3.4539 2.6800 1.6074.9540 1.2602 1.6519 2.3237 2.8521 3.8209 4.2942 2.6726 1.6425 1.4416 1.5539.0200.0338.0558.0891.1265.1889.1464.2078.7678 1.3169 3.5425 1.4012 3.8363 8.7386 8.5695 12.1448 13.7217.29048.29500.29970.30957.31073.31175.31189.31026.28263.24350.19260.19618.15830.11916.31595.32102.31360.32310.30320.29632.27570.21480.16383.14012.12321.21569.21338.21979.22275.22348.22575.17960.20150.24986.26841.32087.12647.15380.17022.12230.11650.12532.0097.0137.0077.0052.0091 -.0232.0240 -.0315.0072.0215 -.0022.0017 -.0194.0108.0278.0157 -.0069.0182 -.0012.0001 -.0070.0178.0200.0132.0223.0158.0159.0121.0094 -.0012 -.0040 -.0154 -.0169 -.0080.0146.0269 -.0080 -.0164.0079.0125.0010.0042 1.112 1.392 1.738 2.312 3.065 3.958 6.045 0.343 16.166 19.236 14.338 17.605 16.929 13.490 3.019 3.926 5.268 7.192 9.407 12.894 15.576 12.442 10.026 10.289 12.612.093.158.254.400.566.837.815 1.031 3.073 4.906 11.040 11.079 24.943 51.336 70.068 104.244 109.493 -.010437 -.012292 -.014754 -.018154 -.023168 -.029044 -.041729 -.665'3a -.100374 -.113439 -.095927 -.073570 -.059475 -.053599 -.020733 -.025325 -.033344 -.040763 -.052533 -.063151 -.066770 -.061665 -.053368 -.048291 -.044459 -.000427 -.000799 -.001259 -.001906 -.002773 -.003980 -.005728 -.005904 -.012122 -.016777 -.027800 -.079202 -.105682 -.158044 -.288559 -.339032 -.296424 ro I I

-235 TABLE LII TABULATED EXPERIMENTAL JOULE-THOMSON DATA FOR THE NOMINAL 77 PERCENT MIXTURE Mole Inlet Inlet Temperature Pressure - -i1 Fraction Temperature Pressure Difference Drop H Run Propane (~F) (psia) (~F) (psi) (OF/psi)x103 4.010 0.761 -96.8 1942.3 1.285 221.0 6.00 4.020 0.761 -96.7 1796.2 1.331 226.0 5.89 4.030 0.761 -96.7 1451.8 1.269 220.2 5.77 4.040 0.761 -96.8 1173.6 1.229 216.0 5.69 4.050 0.761 -96.8 912.3 1.213 214.8 5.65 4.060 0.761 -97.0 694.5 1.183 213.2 5.55 4.070 0.761 -96.7 602.1 1.211 219.4 5.52,,,,, _,,,, TABLE LII FLOWMETER CALIBRATION EQUATION CONSTANTS USED FOR THE NOMINAL 77 PERCENT MIXTURE Flow Meter Series B A C D low 0.074556366 59.519280 -21616.839 3479232.9 10,20,30 high 0.12003127 16.100944 -8125.2457 2118787.9 low 0.10684014 15.203628 -1462.5168 535593.14 40 - 50 high -0.16666467 315.17891 -110295.06 1360895.0 low 0.087080753 43.093003 -14088.483 2339258.0 high 0.15376994 -13.008022 7.5220947 1395307.2

-236 TABLE LIV TABULATED EXPERIMENTAL ISOBARIC DATA FOR THE NOMINAL 51 PERCENT MIXTURE MOUM UINLET - INLET OUTLET - MPOWER -AH _ RUN FRACTION PRESSURE TEMPERATURE TEMPERATURE POWER FLOW CORR. PLOW A f ^ _________ C3R8 (psia) (~F) (~F) (Btu/min) (lb/min) (Btu/lb) (Btu/lb) (Btu/lb) (Btu/lb-~F) 1.0100.505 2000.1 200.54 209.92 1.641.2051 -.001 8.004 8.003.8529 1.0200.505 2002.1 200.51 220.02'3.408.2063 -.001 16.518 16.516.8465 1.0300.505 1998.3 200.54 238.76 6.559.2039 -.002 32.166 32.165.8414 1.0400.505 1998.6 200.57 275.92 12.500.2025 -.002 61.713 61.711.8190 2.0100.506 1502.0 200.58 209.96 1.564.1985 ---.003 7.877 7.874.8393 2.0200.5068 1499.9 200.56 220.06 3.186.1976 -.003 16.120 16.117.8265 2.0300.506 1501.3 200.57 238.69 6.099.1980 -.002 30.800 30.798 808060 2.0400.506 1500.4 200.56 275.69 11.571.1979 -.002 58.453 58.450.7780 3.0100.506 1000.1 200.54 210.69 1.425.1991 -.019 77156.-7.137.7032 3.0200.506 998.6 200.58 220.29 2.740.1988 -.021 13.780 13.759.6980 3.0300.506 998.0 200.46 238.91 57246.1989 -.022 26.378 26.356.6856 3.0400.506 998.0 200.48 275.62 10.065.1986 -.022 50.694 50.672.6744 4.0100.506 498.1 200.55 210.26 1.108.1983 -.018 5.588 —.-570-.5734 4.0200.506 4\98.4 200.57 220.10 2.236.1987 -.019 11.252 11.233.5752 4.0300 -.506 499.9 200.60 238.86.4.398.1988 -.019 22.1151 22.096 -.5715 * 4.0400.506 498.8 200.60 275.96 8.628.1970 -.021 43.798 43.777.5810 5.0110 7507 245.7 200.76 210.20 1.080 -.1990 —.116 5.426 5.309 -.5625 5.0100.507 251.0 200.74 210.68 1.067.2018 -.034 5.287 5.252..5284 5.0200.7507 251.3 200.77 220.57 2.144 o2016 -.032 10.632 -10.599 -.5355 5.0300.507 250.9 200.69 238.71 4.129.2014 -.031 20.503 20.472.5385 *5.0400.507 251.0 200.77.275.77 8.270.2012 -.024 41.107 41.082.5478 6.0100.506 1999.2 151.51 -161.22 1.795.2075 -.001 8.652 8.651.8912 6.0200.506 1999.0 151.53 171.21 3.643.2070 -.001 17.598 17.597- a.8940 6.0300.506 2001.1 151.56 181.08 5.442.2070 -.001 26.290 26.289.8903 6.0400.506 2001.8.151.51 191.19 7.290.2070 -.001 35.214 33.213.8874.6.0500..506 2002.1 151.54 201.44 9.097.2061 -.001 44.133 44.132.8844.7.0100.506 1500o.8 151.52 161.76 1.810.1793 -.005 10.095 -10.090 -.-9850 7.0200u.506 1498.7 151.57 172.30 3.572.1766 -.006 20.227 20.220.9753 7.0300.506 1499.4 151.57 181.52 57048.1765 -o008 28.597 28.589.9544:7.0400.506. 1498.5 151.58 191.33 6.606.1760 -.008 37.538 37.530.9440 7.0500.506 1498.9 -151.56 - 20L.05 -- 8.084.1756 -.009 46.C30 46.021 -.9299 8.0100.505 999.3 141.96 1i 71 2.982.1979 -.011 15.068. 15.057.1 8.0200.505 1001.7 141.97 -': — 3-02 ~ 5.639 71977 —.011 a-28.521 -- I 28.510 8.0300.505 999.1 141.99 193.24. 8.199.1961 -.013 41.822 41.809 _ IWV 9.0100.508 — 250.5 141.96 159.30 17792 7.1993 -.038 - 8.990 87952-.7562Z 9.0200.508 249.7 142.00 175.84 3.482.1984 -.039 17.54S 17.510.5175 9.0300.508 248.4 141.89 193.52 5.293.1965 -.039 26.934 26.894.5209 10.0100.505 501.4 112.16 122.39 1.267.1996 -.022 6.349 6.328.6187 10.0200.505 501.5 112.22 133.06 2.537.1977 -7024 12.833 -12.810.6148 10.0300.505 501.3 112.19 153.97 4.952.1969 -.024 25.146 25.123.6013 10.0400.505 501.2 112.35 193.73 9.433.1957 -.027 48.200 48.174 -.5919 11.0100.507 2002.3 101.72 111.92 1.663.1962 -.000 8.478 8.478.8317 11.0200.507 2000.0 101.76 122.71 3.407 -.1932 -.000 - 17.632 17.631.8413 11.0300.507 2001.2 101.73 133.54 5.173.1916 -.000 26.992 26.992.8486 11.0400.507 1999.3 101.79 143.24 6.733.1899 -.000 35.448 35.448 —.8552 11.0500.507 2000.2 101.85 154.56 8.498.1864 -.000 45.589 45.589.8649 12.0100.506 1699.4 101.78 112.02 1.707.1822 -.001 -- 367 97366 -.9146 12.0200.506 1699.0 101.75 122.83 3.531.1806 -.001 15.551 19.550.9273 12.0300.506 1698.5 101.75 133.19 57293 -- 1794 — 001 -25.495 29.498.9382 1.2.0400.506 1699.5 101.74 143.09 6.977.1789 -.001 38.994 38.993.9430 12.0500.506 1698e8 101.73 154.13 8.851.1781 -.001 49.704 49.704.9487 13.0100.507 1499.4 101.79 112.36 1.879.1775 -.001 10.588 10.587 1.0020 13.0200.507 1498.4 101.84 122.64 3.712.1758 -.002 21.111.-21.109 1.0149 13.0300.507 1498.7 _101.80 133.30 5.642.1753 -.002 32.179 32.177 1.0215 13.0400.507 1499.8 101.89 144.09 7.563.1747 -.002 43.290 43.288 1.0257 13.0500.507 1498.8 101.74 153.85 9.281.1741 -.002 53.317 53.315 1.0231:14.0100.503 249.4 72.26 84.05 1.083.1792 -.040 6.042 6.002.5089 14.0200.503 251.0 72.26 93.87 1.996.1804 -.040 11.C68 11.028.5104 14.0300.503 251.5 72.30 115.88 4.023.1804 -.042 22.303 22.261.5107 14.0400.503 251.1 72.30 156.38 7.692.1782 -.042 43.16C 43.118.5128 7?15.0100,-.506 1298.4 52.19 66.77 27445-..1871 -.000 13.C68 13.067.8960 15.0200.506 1298.5 52.11 81.96 5.253.1873 -.001 28.C52 28.051.9400 15.0300.506 1299.2 52.21 96.54 7.644.1808 -.001 42.284 42.283.9538 15.0400.506 1299.6 52.15 110.33 10.259.1761 -.001 58.272 58.271 1.0016 15.0500.506 1299.7 52.25 124.57 13.144.1768 -.001 74.354 74.353 1.0281 15.0600.506 1300.1 52.15 138.43 15.968.1776 -.001 85.897 89.896 1.0419 16.0100.506 701.1 52.29 63.07 2.127.1787 -.003 11.900 11.897 1.1033 16.0200.506 698.3 52.39 73.00 4.314.1850 -.002 23.312 23.310 1.1312 16.0300.506 698.3 52.45 81.92 4.439.1280 -.000 - 34.670 34.670 1.1765 16.0400.506 698.3 52.49 92.22 6.230.1276 -.000 48.832 48.832 1.2292 16.0500.506 - 698.7 52.47 102.04 8.148.1276 -.000 63.871 63.871 1.2885 16.0600.506 699.1 52.47 109.70 9.801.1277 -.003 76.737 76.734 1.34C9 16.0700.506 699.5 52.43 117.26 11.578.1277 -7003 9C.656 90.653 -13982 16.0800.506 699.5 52.43 125.70 13.370.1278 -.004 104.656 104.652 1.4283 -16.0900.506 700.1 52.44 134.61 14.193.1279 -.009 110.956 110.947 1.3502 16.1000.506 699.3 52.51 146.19 15.163.1272 -.000 119.249 119.249 1.2728 16.1100.506 699.8 52.50 155.79 16.003.1271 -.000 125.866 -125.866 1.2185 17.0100.506 1999.3 22.72 34.91 1.686.1971.000 8.553 8.553.7014 17.0200 - -.506 1998.6 22751 46.12 3.251.1941.000 16.755 -16.755 -.091 17.0300.506 1998.8 22.72 68.60 6.399.1921.000 33.321 33.321.7263 — 17.0400 --—.-7506 --— 1999.9 22.80 -111.91 12.962.1903.00U - 68.105 -68.105 -.7643 18.0100.506 1500.8 22.76 34.03 1.571.1883 -.000 8.347 8.347.7404 18.0200.506 1501.4 22.78 45.90 3.275.1882 -.000 17.403 -- 7.403.7527 18.0300.506 1499.7 22.78 68.80 1.939.0532 -.000 36.468 36.468.7925 18.0400.506 1500.3 22.78 68.46 3.178.0878 -.000 36.197 36.197.7924 18.0500.506 1499.8 22.71 68.16 5.803.1618 -.000 35.859 35.859.7889 18.0600.506 1499.6 22.71 68.71 8.253.2286 -.000 36.C97 36.097.-7847 18.0700 _.506 1498.5 22.73 68.53 10.596.2927 -.000 36.196 36.196.7903 18.0800.506 1499.9 22.82 111.89 14.631.1903 -.000 76.886 76.886.8632 19.0100.507 1000.8 2.69 6.03.477.1927 -.000 2.476 2.476.7406 19.0200.507 1000.2 2.76 -- 9.65.990.1921 -70003 5.155 5.155.7473 19.0300.507 1000.3 2.69 10.86 1.182.1916 -.000 6.166 6.166.7549 19.0400.507 998.6 2.69 12.89 1.565.1918 -.000 8.161 8.161 19.0500.507 999.8 2.71 16.08 2.140.1920 -.000 11.146 11.146 * 19.0600.507 998.8 2.68 19.45 2.781.1910 -.000 14.56C 14.559 19.0700.507 1000.8 2.74 26.66 4.077.1915 -.000 21.284 21.284 * 19.0800..507 998.4 2.74 42.08 3.883.1068 -.000 36.356 36.356 19.0900.507 999.8 2.75 64.68 6.284.1065 -.000 58.994 58.994 * 19.1000.507 1000.4 2.75 86.37 8.739.1064 -.000 82.145 82.145 -- 19.1100.507 999.8 3.91 102.02 10.554.1057 -.000 9S.851 9S.851 * 19.1200.507 999.2 3.97 115.20 12.341.1053 -.000 117.145 117.145 19.1300.507 998.8 3.93 122.07 13.320.1049 -.000 126.S31 126.931 *

-237 TABLE LIV (CONTINUED) I'iUJ.0 ll~tINLET I1LET UUTJLTj PUWEJR 9 RUN FRACTION PRESSURE TEMPERATURE TEMPERATURE POWER FLOW CORR. FLOW H Sp f79T p ____________ ^8 ____L~~(sia) ___(F) __ ~F __(tu/min) (lb/min) (Btu/lb)_ (Btu/lb) (Btu bj (Bul-OF) 19.1400.507 998.3 3.87 129.41 14.460.1046 -.00C ~83.177 138.177 19.1500.507 998.3 3.90 137.45 15.596.1045 -.000 14S.219 149.218 * 19.1600.507 998.7 3.90 145.53 16.394.1042 -.00C 157.273 157.273 * 19.1700.507 999.3 3.83 148.03 16.609.1041 -.000 159.596 159.596 * 20.0100.506 498.9 8.10 20.19 1.431.1214 -.000 11.785 11.784.9749 20.0200.536 498.7 8.11 31.88 2.895.1215 -.001 23.629 23.828 1.0023 20.0300.506 502.0 8.13 51.49 5.720.1230 -.001 46.486 46.486 1.C721 20.0400.506 501.8 8.16 70.32 8.877.1234 -.001 71.940 71.940 * 20.0500.506 501.5 8.16 88.71 12.726.1227 -.001 103.732 103.732 20.0600.506 501.0 8.24 105.79 17.077.1226 -.002 139.294 139.292 * 20.0700.506 500.7 8.23 113.02 17.687.1227 -.002 144.202 144.20 * 20.0800.506 500.5 8.18 101.10 15.938.1226 -.003 13C.041 130.038 * 20.0900.506 501.0 8.29 119.04 18.132.1226 -.003 147.935 147.932 * 21.3100.500 251.5 -26.52 -14.49 1.608.1352 -.074 11.892 11.818.9826 21.0200.500 251.4 -26.46 -2.15 3.417.1345 -.059 25.408 25.349 1.0424 21.0300..500 250.3 -26.49 17.87 6.4G4.1248 -.059 51.326 51.269 1.1557 21.0400.500 250.1 -26.49_ -37.19 10.470.1248 -.059 83.890 83.831 * 21.0500.500 250.2 -26.44 55.83 16.049.1246 -.C89 128.848 128.759 * 21.0600.500 -250.5 -26.33 68.18. 18.859.1245 -.074 151.465 151.391 21.0700.500 249.7 -26.42 78.87 19.516.1242 -.C89 157.C82 156.994 * 21.0800.500 250.4 -26.40 81.45 19.758.1248 -.096 158.312 158.216 21.0900.500 250.0 -26.39 59.57 17.404.1246 -.089 139.731 139.642 * 21.1000.500 250.60 -26.34 92.88 20.084.1221 -.096 164.459 164.363 __ 22.0100.509 2001.0 -147.77 -137.02 1.499.2419.000 6.196 6.196.5768 22.0200.509 1998.3 -147.77 -125.85 3.047.2413.000 12.628 12.628.5763 22.0300.509 1999.5 -147.71 -106.09 5.776.2393.000 24.133 24.134.5798 22.0400.509 2001.7 -147.66 -69.32 11.063.2402.000 46.C52 46.052.5878 23.0100.507 1499.2 -147.71 -136.91 1.542.2470.000 - 6.242 6.242.5781 23.0200.507 1499.8 -147.72 -126.50 3.045.2470.000 12.328 12.328.5810 23.0300.507 1499.3 -147.70 -107.06 5.872.2471.000 23.768 23.768.5848 23.0400.507 1499.6 -147.67 -69.57 11.472.2471.000 46.431 46.432.5945 24.0100.509 1000.0 -147.73 -137.24 1.534.2513.000 6.106 6.106.5824 24,0200.509 1000.5 -147.67 -126.85 3.052.2512.000 12.149 12.149.5834 24.0300.509 1000.2 -147.69 -107.00 6.024.2513.000 23.971 23.971.5891 24.0400.509 998.6 -147.68 -69.52 11.769.2510.000 46.887 46.887.5999 25.0100.508 499.8 -147.62 -131\85 2.151.2319.000 9.275 9.275.5883 25.0200.508 499.5 -147.57 -116. 2 4.204.2320.000 18.125 18.126.5895 25.0300.508 500.5 -147.56 -87.81 8.336.2323.000 35.883 35.883.6006 26.0100.506 249.1 -147.61 -144.08.253.1212.000 2.085 2.085.593C 26.0200.506 249.9 -147.59 -141.12.466.1217.000 3.827 3.827.5919 26.1300.506 249.7 -147.57 -137.56.718.1214.000 5.914 5.914.5909 26.0400.506 250.0 -147.58 -135.29 1.007.1216.000 8.284 8.284 * 26.1500.506 250.2 -147.57 -132.14 1.685.1214.001 13.881 13.681 26.1600.506 249.5 -147.56 -116.61 4.216.1210.001 34.852 34.853 * 26.0700.506 248.7 -147.58 -88.18 7.409.1208.001 61.353 61.354 26.07007.506 251.1 -147.49 -52.36 10.998.1218.001 9C.295 90.296 * 26.7900.506 250.5 -147.51 -19.74 14.492.1213.001 119.523 119.524 * 27.0100.504 19998.8 -241.75 -227.71 2.060.2648 -.000 7.181 7.781.5542 27.0200.534 1998.1 -242.11 -215.85 3.877.2681.000 14.460 14.461.5507 27.0300.504 1999.7 -242.11 -191.38 7.561.2691.000 28.102 28.103.5539 27.0400.504 1999.0 -242.12 -147.25 14.182.2660.000 53.314 53.314.5619 28.0100.504 1499.9 -242.13 -228.78 1.836.2496.001 7.356 7.357.5509 28.0200.504 1499.3 -242.12 -216.20 3.573.2494.001 14.324 14.325.5528 29.0100.504 1000.2 -242.12 -229.13 1.836.2556.001 7.185 7.186.5530 29.0200.504 998.5 -242.11 -215.23 3.790.2551.001 14.859 14.860.5528 29.0300.504 999.5 -242.09 -191.39 7.174.2549.001 28.149 28.150.5552 29.0400.504 998.1 -242.08 -146.51 13.491.2502.001 53.912 53.913.5641 30.0100.504 498.8 -242.13 -229.53 1.802.2553.000 7.C57 7.057.56C1 30.0200.504 498.4 -242.14 -215.79 3.755.2556.000 14.696.14.696.5577 30.0300.504 498.1 -241.30 -191.21 7.193.2555.000 28.158 28.158.5621 30.0400.504 500.0 -242.10 -146.99 13.833.2565.000 53.929 53.930.5671 31.0100.501 248.0 -242.12 -227.90 1.982.2503.000 7.920 7.920.5568 31.0200.501 249.4 -242.11 -214.68 3.868.2519.000 15.355 15.355.5597 31.0300.501 249.2 -242.11 -190.77 7.260.2511.000 28.910 28.910.5631 31.0400.501 250.5 -242.08 -146.64 13.734.2530.000 54.283 54.283.5687 32.0170.504 498.5 -97.84 -93.81.338.1361.000 2.481 2.481.6158 32.9200.574 498.5 -97.83 -89.97.664.1362.000 4.E79 4.879.6206 32.0300.504 498.8 -97.83. -86.30.982.1362.000 7.208 7.209.6250 32.0400.504 498.5 -97.80 -82.62 1.330.1363.000 9.757 9.757.6428 32.0500.574 499.0 -97.82 -78.83 1.967.1367.001 14.384 14.385 * 32.0600.504 499.1 -97.52 -74.46 2.684.1369.0T1 1s.606 19.606 * 32.0700.504 498.7 -97.81 -61.13 4.614.1364.000 33.819 33.819 * 32.0800 7504 499.5 -97.79 -25.78 8.934.1354.000 65.996 65.996 * 32.0900.504 499.5 -97.74 15.44 14.035.1355.001 103.593 103.593 * 33.0100.504 700.07 -57.29 -53.60.344.1395.000 2.468 2.468.6686 33.0200.504 699.1 -57.24. -50.33.634.1394.000 4.546 4.546 _____.6579 33.0307.504 700.3 -57.32 -46.30 1.013.1395.000 7.265' 7-265-.593 33.7400.5074 7707.3 -57.29__-43.57 1.389.1382.000 1C.C46 10.046 7 318 33.7500.504 699.1 -57.33 -39.17 2.034.1391.000 14.616 14.616 * 33.7607.504 701.1 -57.26 -24.01 4.099.1382.000 29.663 29.663 * 33.0700.504 700.4 -57.26 8.21 8.222.1387.000 59.276 59.277 * 33.0807.504 700.8 -57.22 40.96 12.519.1378.000 90.851 90.852 * 14.01.00.505 2000.8 -57.25 -48.11 1.391.2444.000 5.691 5.692.6224 34.0200.505 1998.4 -57.23 -39.19 2.712.2421.000 11.204 11.204.62C8 34.0300.505 1998.2 -57.27 -22.94 5.370.2477.000 21.678 21.679.6315 34.0400.505 1999.1 -57.25 9.91 10.633.2469.000 43.067 43.067.6413 39.0100 _____.505 1499.0 -57.28 -48.45 1.375.2472.000 5.564 5.564 (.306 35.0200.505 1501.3 -57.28 -40.03 2.700.2472.000 10.921 10.921.8333 35.0300.505 1499.6 -57.25 -22.56 5.268.2364.000 22.286 22.287.6424 35.0400.505 1498.0 -57.41 7.49 11.394.2558.000 44.548 44.548.6863 36.0100 _.05 1001.1 -57.42 -43.99 2.134.2454.000 8.695A 8.695.6472 36.0200.505 1000.1 -57.43 -30.12 4.404.2458.000 17.914 17.914.6561 36.0300.505 1000.2 -57.42 -5.62 8.725.2495.000 34.968 34.968.6750 37.0100.504 1698.6 131.04 144.64 2.896.2206 -.002 13.127 13.125.9649 37.n000 __.904 1699.7 131.13 158.35 5.793.2214 -.003 26.162 26.159.9612 37.0300.504 1698.1 131.21 171.99 8.146.2071 -.003 39.326 39.323.9642 38.0100.504 1301.2 131.18 144.84 2.906.1954 -.005 14.874 14.869 1.0882 38.0200.504 1298.3 131.38 158.75 5.604.1950 -.004 28.740 28.736 1.0500 8.70300.504 1300.6 131.27 171.68 8.014.1950 -.006 41.095 41.089 1.C166

-238TABLE LV TABULATED EXPERIMENTAL ISOTHERMAL DATA FOR THE NOMINAL 51 PERCENT MIXTURE MU- ~8- IN:LET INLET kfiRSSURE'- RUN FRACTION TEMPERATURE PRESSURE DROP POWER:Gbw CORR. a H (IH/ LP) C3H8 (OF) (psia) (psi) (Btu/mit), _^ain) (Btu/lb) (Btu/lb) (Btu/lb-psi) 1.010!.505 1 2.2 2C76. 1 198.0,'%o.9-05.1766.022 4.458 -.022519 1.020.505 12.?- 1839.0 207.0 1.115.1744.033 6.361 -.030732 1.030.505 1 —2.2 l647?. 2,)2-.8 1.36.1610.019 8.653 -.042670 1.040.505 152.2 1460. 7 210.4 1.811.1506.018 12.006 -.05'7069 1.050.505 5?.2 125..7 218.2 2.CS4.1341 -.027 15.648 -.071721 1.060.505 152.2 1049. 23.2 2.732,1301 -.003 21.0C7 -.074184 1.070.505 152.? 545. 8 278.2 1.938.1042.011 18.574 -.066772 1. 0 5t(05 152.? 655.5 420.0 2.116.0906 -.003 23.358 -.055619 1. 90.505r, 152.? 6hn. q 460.2 1.960.0807 -.002 24.281 -.052766_ 2.010.907 2=1.3 1 4. 6 195.0.852.1503.001 5.670 -.029078?. 0?70.5C7?71.3 1706.8 196.6.909.1 415.003 6.419- -.032654 2.030.507 251. 3 622. 206.4.993.1364.003 7.279 -.035268 2.040 i.7507 251.3 1450. p 212.2 1.020.12z5 -.011 7.889 -.037179 2.050.507 251.3 1^F. 8 219.2 1.C09.1213.011 8.3C8 -.037906 27T.06W ---- F 5"(7 — 251. l - i.7 3??9.4.q983.1114 -.004 8.826 -.038480 2.070.507 251.3 87.& 6 231.4.951.1005.009 9.455 -.040864 7. P0C.-'7 -507 51.? 666.2 299.4.952.0881.007 10.792 -.036048 2.090.507 251.2 594 5 491.6 1.475.0857.000 17.206 -.035003?3. oC.51?5 Z. 4 1 o6. 5 188.2.000.1818.083 -.083.0004423.02C.505 3.5 1813. R 198.0.000.1851.035 -.035.000179 3.010.505 3.5 163.. 3 207.6.00C.1887 -.051.051 -.00C248 3.040.50o 3.5 143?. 207.6.027.1875.004.141 -.000681. t05;0.CC5- 3.5 1231. 1 212.0.062.1891.017.313 -.001475 3.060.505 3.5 1098.6 113.2.028.1323.014.199 -.001754'.070.505 3. 11-^ l,. 2 159.6.243.1597 -.019 1.543 -.009669 3.OP8.'505. 5 1 100. 1 211.6.758.1833 -.014 4.151 -.019617 37n-.505 3.5 110 0.0 262.7 1.374.2074.008- 6.617 -.025191 3. 10.505 3.6 1100.4 346.6 2.663.2459 -.015 10.846 -.031295 3.110.t-5 3.5 10~. 7 434.6 4.263.2800 -.005 15.226 -.035037 3.1?0.505 3.6 699.5 6199.2 1.062,,. 1C49 -.030 10.153 -.050971

-239 TABLE LVI TABULATED EXPERIMENTAL FOR THE NOMINAL 51 JOULE-THOMSON DATA PERCENT MIXTURE Mole Fraction Run Propane 4.010 K+.020 4.030 4.040 4.050 4.060 4.070 4.080 4.090 4.100 4.110 4.120 0.507 0.507 0.507 0.507 0.507 0.507 0.507 0.507 0.507 0.507 0.507 0.507 Inlet Temperature __OF) -149.0 -149.1 -149.0 -149.0 -149.0 -149.0 -149.0 -149.0 -149.0 -149.o -149.0 Inlet Pressure (psia) 2011.1 1899.3 1800.6 1681.0 1540.9 1403.5 1291.6 1166.1 1005.6 827.2 630.7.453..8 Temperature Difference (~F) 0.713 0.753 0.725 0.956 0.933 0.759 0.763 0.961 0.995 1.050 1.075 0.998 Pressure Drop (psi) 128.4 134.o 132.2 170.7 166.7 138.3 140.8 176.4 186.0 196.6 201.2 191.2 lP H ("F/0psi)l03 5.55 5.62 5.48 5.60 5.6o 5.49 5.41 5.45 5.35 5.35 5.34 5.22 TABLE LVII FLOWMETER CALIBRATION EQUATION CONSTANTS USED FOR THE NOMINAL 51 PERCENT MIXTURE Flow Meter Series- B A C D 10 - 20 0.10331343 20.513388 -4137.6569 962875.55 low 0.10590242 18.503396 -2433.9077.630217.66 40,50,60 high 0.043650561 98.539795 -37002.100 5443353.1

APPENDIX C COMPUTER PROGRAMS -240

-241 TABLE LVIII PROGRAM FOR FITTING ISOBARIC DATA INTEGER N,I,J,K,L,M _ DIME.NSION CPBAR(200), T IN (200 ), TOUT.( 2.QO AQ.._P.. 21...__ _... 1 EX( (1...2. 00)*(C...3) ),X( (1...8)*(1...3)),Y(8), B(3) BOOLEAN IPO _.. BEGIN READ DATA NTO, iTFIPO _ TO=TC+460.._..___._____ TF=TF+460. THROUGH DO,FOR I=1,1,I.G.N _.............._..._.,,._ READ FORMAT INPUTCPBAR(I),TIN(I),TOUT(I) TIN( I)=TIN(I )+460. TOUT( I )=TOUT( I )+460. DO EX( I..)=TIN( I)+TOUT( I ).....____ -____ -- VECTOR VALUES INPUT=$3E14.8*$ THROUGH. GO,FOR I= 1,, I... G.N. K=l THROUGH ORDERFORJ=2,1,J.G.N_..__ ___ WHENEVER EX(K,C).G.EX(JO) K=J...................____ ORDER END OF CONDITIONAL EX( I, 1)=EX(K,O). CPARR( I )=CPBAR(K)...EX( I,2)=TIN(K).P.2+TIN(K)*TOUT(K)+TOUT(K).P.2 EX( I 3 )=TIN(K ). P.3+( TIN(K). P.2 )*TOUT(K )+TIN(K) *(TOUT( K).P.2) 1 +TOUT(K).P.3.____.... GO EX(K,C)=500C...-........,WH.ENEVER IPO,.PRINT RESULT-S CPARR(I)....CPAIR().LEX(L.1.,.... 1 EX(N,1) __ L=-O._......................... M= 1 bE [ H=0........ _. H 0.0........................_.....___. EXECUTE ZERO.B(R0)...B(3)) THROUGH ALL,FOR T'=TO,10.,T.G.TF WHENEVER L.E.I, TRANSFER TO SKIP HC=.0.0' -.._..............__ THROUGH TIL,FOR K=3,-1,K.L.0 TIL' HC=(C.+B (K) )*EX (M-l, 1 )/2.... HC.=HC+DELH'THROUGH RANGE,FOR I=M,..,T.., EX (I ri /2.OR.,G,N............ RANGE CONTINUE WHENEVER IL.5I=5... WHENEVER (I+3).G.N,I=N-3 K=. THROUGH HORSE, FOR J=I-4,1,J.G.I+3 X( K., 1) =EX (J, 1 ). X(K,2)=EX-(J,2) X(K,3)=EX ( J 3) Y(K)=CPARR(J) HORSE K=K+1 S=REGR.(X,Y,A,B,BAD,IPO).................. B i O )'= A HON=O.O THROUGH KIQ, FOR K=3,-1,K.L.O KIQ HON=(HON+B(K) )*EX(M-1, 1)/2.

-242 TABLE LVIII (CONTINUED) DELH=HO-HON __ ___ SKIP H=O.0 THROUGH D IM, FOR K=3,-1, K-.-O ___' _ DIM H=(H+B(K )*T H=H+DELH:P=B(O )+2. *B ) *T+3.*B(2)*T.P.2+4.*B(3)*T. P.3 TF AR=T-460. PRINT RESULTS TFAR,H,CPS TRANSFER TO JUMP BAD PRINT RESULTS T PRINT COMMENT$1FOR THE ABOVE TEMPERATURE, COEFFICIENT MATRIX 1 IS SINGULAR OR NEARLY SINGULAR$ JUMP M=I+I1 I =n - ALL - WHENEVER T.L.(EX(I I )/2. -10 ).OR.(I+3)._E.NL=! -TRANSFER TO BEGIN END OF PROGRAM

TABLE LVIII (CONTINUED) EXTERNAL FUNCTION (NAtX,EPS) NORMAL MODE IS INTEGER FLOATING POINT DETERAXEPS,BIGAAJCK DIMENSION IR<3),JC(3) ENTRY TO SIMUL* MAX=N+1 DETER=.0 THROUGH Ll, FOR K=Il.,K.G.N BIGA=O'. C THROUGH L2,FOR I=il,I.GG.N THROUGH L2,FOR J=1,1,J.G.N THROUGH L3,FOR I1=1,ll..E E.K __ THROUGH L3,FOR Jl=l,ltJ1.E.K L3 WHENEVER I.E.IR(I1).OR.J.E.JC(JI),TRANSFER TO L2 iHE NEVE RV."'.'AB-S""'-' " "-I3.A'J G -'" B I"-GA-" BIGA=.ABS.A(IJ) IR(K)=I JC(K)=J L2 END OF CONDITIONAL WHENEVER BIGA.L.EPS, FUNCTION RETURN O. BIGA=A(IR(K)7JC(K))'' DETER=DETER*BI GA THROUGH L4,FOR J=l,1,J.G.MAX L4 A( IRIK),J)=A(IR(K),J)/BIGA THROUGH L1, FOR I=l,I,I.G.N AJCK=A(I,JC(K) _ WHENEVER I.NE.IR(K) THROUGH L5, FOR J=1,1,J.G.MAX L5 WHENEVER J.NE.JC(K),A(I,J)=A(I,J)-AJCK*A(IR(K),J) LI END OF CONDITIONAL THROUGH L7., FOR I=I,1,I.G.N L. 7 __X__X(JC(I))=A( IR( I),MAXj__... FUNCTION RETURN DETER END OF FUNCTION

TABLE LVIII (CONTINUED) EXTERNAL FUNCT ION ( X Y AB, BAD, BOOL) STATEMENT LABEL BAD BOOLEAN BOOL INTEGER IJ,L __ DIMENSION SX (3), SYX( 3) CYX( 3 ) C( (1... 3) 1..4 ) ENTRY Tn R.EGP... _ _ __ EXECUTE ZERO.(SY,SYY, SX(1).SX(3),SYX(1)..SYX(3) ),_r__1_.:.___..._'THRO UGH OWN,.FO. R I.,... G.8...................... SY=SY+Y ( I ) ________SYY= SYY+Y ( I ).P.2 _____2_....... THROUGH OWN, FOR J=- 1,-', J.G-.3 _SX(J)=S X(J)+X( IJ) _ ____,J),_ OWN SYX(J) =SYX(J )+X(I, J )* Y( _.._ THROUGH COEFFOR J=1,ltJ.G.3 R.. THROUGH COEFFOR I=1,1,I.G.3 C(I,J)=-SX( I)*SX(J)/8.0C THROUGH COEF, FOR L=1,1,L.G.8 COEF C( I J)=C(I,J)+X(L, I *X(L,J) THROUGH LIP, FOR I=1,l,I.G 3 CYX(I)=-SX(I )*SY/8.0 THROUGH BIDFOR J=l 1, J.G 8 BID CYX(I)=CYX(I )+X(J,I)*Y(J) LIP C(I,4) =CYX(I) WHENEVER BOOL,PRINT RESULTS C(1,1)...C(3,4) CYY=SYY- ( SY).P.2/8.,0) DET=SIMUL. (3,C,B,1.OE-20) WHENEVER DET.E..C, TRANSFER TO BAD A=SY/8.C TEMP=CYY THROUGH GIN, FrR I=l,,I.G.3 A=A-B( I )*SX( I)/8. GIN TEMP=TEMP-B( I *CYX( I) S=SQRT. (.ABS. (TFMP/4.0 ) WHENEVER.00L, PRINT RESULTS A, ( 1 )...B( 3 ) D ET FUNCTION RETURN S END OF FUNCTION

-245 TABLE LIX LIST OF VARIABLES'FOR ISOBARIC'DATA FITTING PROGRAM Program Symbol A, B(I) CP CPARR CPBAR DELH EX H HO HON I, J, K IPO L, M N REGR S SIMUL T TO TF TFAR Main Program Definition Regression coefficients C. p Array of ordered values of C pm Array of C variables pm Enthalpy base correction Data input storage array H Original enthalpy base value Enthalpy base value for a new set of constants Counter variables Boolean conditional variable Defined in program Number of input data points Regression subroutine name Standard deviation Simultaneous equation subroutine name T(~F) Lower temperature interval limit Upper temperature interval limit T(~F)

-246 TABLE LIX CONTINUED TIN Inlet temperature of data point TOUT Outlet temperature of data point X Array containing regression independent variables, x. i Y Array containing dependent variable, y Subroutine REGR* BAD Error return dummy statement label BOOL Boolean conditional variable C Coefficient matrix, C.. ii CYX C. ly CYY C YY DET Determinant of matrix C.. 1j I, J, L Counter variables SX(I) EXi SYX(I) Ex. SY, SYY E, Y 2 TEMP Temporary iteration variable Subroutine SIMUL* A Coefficient matrix, A.. AJCK A. i,Jck BIGA Pivot element, AIR,JCk DETER Value of determinant of A.. 1J

-247 TABLE LIX CONTINUED EPS Tolerance value, I Row index, i I1 Index on the array IR during pivot element search IR Array containing row subscripts of pivot elements, in order J Column index, j J1 Index of the array JC during element search JC Array containing column subscripts of pivot elements, in order MAX Number of columns in the matrix A.. 13 N Number of equations TEMP Temporary location used in ordering CJ array X Vector containing the ordered solution values 16 * Subroutines are explained more fully in Carnahan et al. from which they were obtained with minor modifications.

-248 TABLE LX PROGRAM FOR OPTIMIZATION OF PARAMETERS IN CORRESPONDING STATES CORRELATION FORTRAN IV G COMPILER MAIN 10-09-68 12:36.37 PAGE 0Odo 0001 _ DIMENSION TABLE(11,11), 1H1(30,40),TI(40),P1(30),HLIQ1(20),HGASI(20),KEQ1(20,PLIQ(20), 2H2(20,79),T2(79),P2(20),F(7),PMIX(100),TMIX(100),HMIX(100), 3HOMIX(100),HEXP(100),HMIXC(100,7) 0002 COMMON' TABLEtHlTlPlH2,T2tP2tPMIX,TIXMIXHMIXtHOMIXHEXPtHMIXCt 1DELH,M1,N,M2,N2,F 0003 NAMELIST/NL/PECTEC,TEWGA INDF 0004 M2=20 0005 N2=79 0006 READ(8) (P2(J),J=l,10) 0007 READ(8)(P2(J},J=ll120) 0008 - READ(8)?T2(J),J=l,161]0009 READ(8)(T2(J),J=17,32) 0010 READ((T28(J),J= 333,48R) 0011 READ(8)(T2(J),J=49,64) 0012 READ(8)(T2(J),J=65,79) 0013 DO 122 J=1,79 0014 READ(8)(H2(I,J),I-l=,10) 0015 122 READ(8)(H2(I,J),I=11,20) 0016 READ(8)(P1(J),J=1,19) 0017 READ(8) (P(J),J=20,22) w0d18 - READ(8)(TI(J),J=l, 19) 0019 READ(8)(T1(J),J=20,38). 0020 REAOD8)(HLIQ1 (),J=1, 19) 0021 READ(8)(HGAS1(J) J=t,19) 0.022 READ8)'(KEQl(J),J=l,19) 0023 READ(8)(PLIQ1(J),J=1,19) 0024 READ(8)M1,NI,LIQVA1 0025 DO 121 J1l,38 0026 READ(8)(H1I,J),I =1,19) 0027 121 READ(8)(H1(I,J), I20,22) 0028 I READ(5,110) PC,TC,W,WM,DPC,DTCtOW,N, INEXNPR 0029 WRITE (6,110 )PC,TCWWMDPC,DTCDWN, tINDEX NPR 0030 110 FORMAT(2F6. 1,F6.4,F7.3,2F6.1, F64', 4, 4,13) 0031 DO 202 1lt,N 0032 201 READ (5,111)PMIX( I),TMIX t ),HMIX I),HOMIX( I) 0033 202 HEXP( I )HMtX( )-HOMIX() 0034 111 FORMAT (F6.0,3F6.1) 0035 PECuPC _003-' TEC"TC 0037 WGA WEPE00N 0038 ^D P-oC/20/6.0039 INDOl 0041 IF( INDEX-I)S2t3,52. 0042 3 00 2 1-2,7 0043 2 F(t)IF( 1 ). 0044' B TO go0,. 0045 _ 52 PEC"PEC+DPC — 0046 CALL nEV(PEC,TECWGA,WMN, 2 0047 _ P.ECPEC-DPC g-0-0-4 - T EC:TEC+OTC o0G04 90 CALL DEV (PEC TECWGAWM N,3) 0050 TGECTEC-WTC 0Q~ 1 O.WGAWGA+OW

-249TABLE LX (CONTI:ED) FORTRAN IV G COMPILER MAIN 10-09-68 12:36.37 PAGE 0002 0052 CALL DEV(PEC,TECWGAWM, N4) 0053 WGA=WGA-DW 0054 PEC=PEC-DPC 0055 CALL DEV(PEC,TEC,WGA,WMN,5) 0056 PEC=PEC+DPC 0057 TEC=TEC-DTC 0058 CALL DEV(PEC,TEC,WGA,WM,N,6! 0059 TEC=TEC+DTC 0060 WGA=WGA-DW 0061 CALL DEV(PECTECr,WGAWMN,7) 0062 WGA=WGA+DW 0063 I =1 0064 On 11 I=2,7 0065 11 IF(F(I).LT.F(II) )II=I 0066 IF(II.EQ.1) GO TO 50 0067 IF(II.EQ.2) PEC=PEC+DPC 0068 IF(II.EQ.3) TEC=TEC+DTC 0069 IF(II.EQ.4) WGA=WGA+DW 0070 IF(II.EQ.5) PEC=PEC-DPC 0071 IF(II.EQ.6) TEC=TEC-DTC 0072 IF(II.EQ.7) WGA=WGA-DW 0073 IF (NPR.GT.O) WRITE(6,NL) 0074 F(1)=F(II) 0075 00 53 1=1,N 0076 53 HMIXC(I, l=HMIXC(, I I) 0077 IND=IND+1 0078 IF (IND.GT.INDEX) GO TO 50 0079 GO TO 52 0080 50 WRITE(6,NL) 0081 WRITE(6,120) 0082 120 FORMAT(30X,' OPTIMUM CALCULATED ENTHALPY DEPARTURES'/e PRES 1SURE TEMPERATURE EXPER. DEPARTURE CALC. DEPARTU 2RE DIFFERENCE PERCENT DIFFERENCE'/) 0083 DO 54 I=1,N 0084 DELH=HEXP(I)-HMIXC I,1) 0085 DELHP=(HEXP(I)-HMIXC,1 ))/HEXP(I)*100. 0986 54 WRITE(6,123)PMIX(I),TMIX(I),HEXP(I),HMIXC(I,1),DELHDELHP 0087 123 FORMAT(1H,6F20.7) 0088 GO TO 1 0089 END

-250-TABLU LX (CONTINUEDI FORTRAN IV G COMPILER CEV 08-03-6 8 20:25.26 PAGE 0001 0001 SUBROUTINE DEV(PEC,TEC,W,WM,N,EF) 0002 INTEGER EF 0003 DIMENSIONTABLE(1,11 ),PTAB ( 11),HVEC(11),HTAB( 44),HOUT( 11), lTTAB(11),F(7),PMIX(100),TMIX(lCO),HMIX(100),HOIX(100),HEXP(100', 2HMIXC(100,7),Hl( 30,40),T1 (40),PI(30),H2(20,79) T2(79),P2(20-) 0004 COMMGN TABLE,H1,T1,P1,H2,T2,P2,PMIX,TMIX,HMIX,HOMIX,HEXPHMIXC, ___DELH,M1,N1,M2,N2,F 0005 F(EF)=0.0 0006 DO 416 L=1,N 0007 PR=PMIX(L)/PEC 0008 TR=TMIX( L/TEC 0009 D01 1=19,MI,1 0010 IY=I 0011. IF(PR-P1 (I) )3, 1, 1 0012 1 CONTINUE 0013 3 00 5 J=1,N1,1 0014 JAY=J 0015 IF (TR-TI(J) )401,5,5 0016 5 CUNTINUE 0017 401 IF( JAY.GT.N1-1 )JAY=N 1-1 0018 IF(IY.GT.MI-1) IY=M1-1 0019 IF ( JAY.LT.3)JAY=3 0020 CALL INT4(H1,T1,P1,HTAB,TTA8,PTAB, IY,JAY,30,40) 0021 DO 30 J=1,4 0022 00 21 1=1,4 0023 21 HVEC(I)=HTAB( I,J) 0024 CALL DTABLE(PTAe,HVEC,TABLE 3,3, &.5) 0025 30 CALL NEWTON(PTABPR,TAbLE,3,3,HOUT(J),3,&15) 0026 CALL DTABLE(TTAB,HOUTTABLE,3,3,&15) 0027 CALL NEWTON(TTAB,TRTABR BLE,3,3HINT1,3,&15) 0028 DO 10 I=l,M2,1 0029 IY=I 0030 IF(PR-P2(I))11,,ll 10, 0031 10 CONTINUE 0032 11 D012 J=1,N2,1 0033 JAY=J 0034 IF(TR-T2(J))402,12,12 0035 12 CONTINUE 0036 402 IF(JAY.GT.N2-1 )JAY=N2-1 0037 IF(JAY.LT.3)JAY=3 0038 IF( IY.GT.M2-1) IY=M2-1 0039 13 CALL INT4(H2,T2,P2,HTAB,TTA, PTAIY, JAY,M2,N2) 0040 DO 22 J=1,4 0041 DO 23 1=1,4 0042 23 HVEC(I)=HTAB( I,J) 0043 CALL DTABLE(PTAe,HVEC,TAbLE,3,3,&15) 0044 22 CALL NEWTON(PTABPR,TABLE,3.3,,HOUT(J),3&15) 0045 CALL DTABLE(TTAB, HOUT,TABLE, 3 3,&15) 0046 CALL NEWTON(TTAB,TR,TABLE,3,3,HINT2,3,&15) 0047 R=.1987/WM 0048 HMIXC(L,EF)=( 1.-W)*HINT.1+W*HINT2)*R*TEC 0049 DELH=HEXP(L)-HMIXC(LEF) 0050 F(EF)=F(EF)+DELH**2 0051 416 CONTINUE 0052 EN=N

-251-,1- U..t", FORTRAN IV G COMPILER nFV n7t~-!7- 0A I "IA Pt I I -___ ___ ^ - -- VI-41-OO_____, *-* 13 40*.~1C2 _ PAGE 0002 0053 0054 0055 F(EF)=SQRT(F(EF)/EN) 15 RETURN END:ORTRAN lV G COMPILER INT4 07-16-68 22:38,32 PAGE 0001 003!. ISUBROUTINE INT4 (H T, P HTAB TTABPTAB. IY, JAY, M,N) 0002 DIMENSION H(M,N),T(N),P(M),HTAB(4,4),TTAB(11),PTAB(11) 0003 ILOW=IY-3_ 0004 JLOW=JAY-3 0005 00DO 1 J14 __ 0006 1 TTAB( J)T(JLOW+J.) 0007 DO 2 11,4+ 0008 2 PTAB(I)=P(ILOW+I) 0009 DO 3 J=1,4 0010 DO 3 1=1',4 0011 3 HTAB(I J)=H( LOW+iJLOW+J) 0012 RETURN 0013 END... 7,

-252 TABLE LX (aoOMSu D). FORTRAN IV G COMPTILP DTA 1 F 07-16-68 72:381.6 PAGF- 000 00,1 i SSUBROUTINE DTABLE(X,YTABLE,.NM,*) 00O? INTEGER DEGREE 0003 DIMENSION X(ll),Y( 11),TABL F(lll ) 0004 IF(M-N)1,1,? 0005? WRITE(6,3) 0006 3 FORMAT(' SCREWED UP') 0007 RETURN 1_ 0008 1 no 4 J=1,M 0009 no 4 I=J,N 0010 IF(J-1)5,6,5 0011 6 TABLF(,)=(Y( I.+ )-Y( I ))/(X( I+l )-X( I )) 001? GO TO 4 00?3 5 TABLE( I J)=(TABLE( IJ-1 )-T ABLE( I-l,J-1))/(X( I+1)-X(I-J+l) ) 0014 4 CONTINUE 0015 RETURN 0016 ENTRY NEWTON(X,XARG,'TABLEN,M,YFST,DEGREE,*) 0017 IF(DEGREE-M 17,7,8 0018 8 WRITF(6,9) 001 9 9 FORMAT(' SCREWED UPPP') 0020 RETURN 1 002T 7 L=N+1 0022 00 10 I=I,L 0023 K=I 00n.4 IF (XARG.LE.X(K)) GO Tn!1 0025 10 CONTINUE 00'6 11 MAX=K+DEGREE/2 0027 IF (MAX.LT.DEGRFE+I. )MAX=DEGREE+1 00?R IF(MAX.GT. N-+ )MA XN+ 0029 gYEST=TABLE(MAX-1 EGRE)E) 0030 L=DEGREE-1 0031. IF(L.EQ.O) GO TO 13 003?. nO 12 I=l,L 0033 12 YEST=YEST*(XARG-X(MAX-I) )+TABLE(MAX-I-1 DEGR.EE-I)' 0034 1 3 YEST=YEST* (X ARG-X (MAX- DE E E) )+Y (MAX-DEGREF) 003C5 RETURN 0036 END

-253 TABLE LXI LIST OF VARIABLES FOR CORRESPONDING STATES CALCULATION AND PARAMETER OPTIMIZATION PROGRAM Program Symbol DELH DELHP DEV DPC, DTC, DW F HOMIX H1 H2 HEXP HMIX HMIXC I, J II IND INDEX M1 Main Program Definition Difference between experimental and calculated enthalpy Percent difference between experimental and calculated-enthalpy Enthalpy departure calculation and comparison subroutine name Step size of parameters in optimization procedure Root mean square deviation between experimental and calculated enthalpy departures Ideal gas enthalpy Reduced enthalpy departure for first reference substance Reduced enthalpy departure for second reference substance Experimental enthalpy Experimental enthalpy departure Calculated enthalpy departure Counter variables Variable indicating direction of maximum reduction in standard deviation Counter variable of search iterations Maximum number of search iterations Number of reduced pressure values for first reference substance table

-25:4 TABLE LXI CONTINUED M2 Number of reduced pressure values for second reference substance table N1 Number of reduced temperature values for first reference substance table N2 Number of reduced temperature values for second reference substance table NPR Conditional print index P1 Reduced pressure of first reference substance P2 Reduced pressure of second reference substance PC Initial critical pressure PEC Critical pressure PMIX Mixture pressure Tl Reduced temperature of first reference substance T2 Reduced temperature of second reference substance TABLE Storage matrix for difference table TC Initial critical temperature TEC Critical temperature TMIX Mixture temperature W Initial third parameter WGA Third parameter WM Molecular Weight of mixture Subroutines DEV and INT4 DTABLE Difference table calculation subroutine name EN Number of data points EF Subscript of F

-255 TABLE LXI CONTINUED HINT1 HINT2 HOUT HTAB HVEC I, J, L ILOW, JLOW IY, JAY NEWTON PR PTAB R TR TTAB DEGREE I, J K, L M Final interpolated enthalpy using first reference table Final interpolated enthalpy using second reference table Vector containing enthalpies interpolated with respect to pressure Matrix containing reduced enthalpies upon which interpolation is based Vector containing enthalpies from HTAB at the same reduced temperature Counter variables Defined in program Defined in program Interpolation subroutine name Reduced pressure of mixture Vector containing reduced pressures corresponding to HTAB values of reduced enthalpy Gas constant Reduced temperature Vector containing reduced temperatures corresponding to HTAB values of reduced enthalpy Subroutines DTABLE* and NEWTON* Degree of desired interpolating polynomial Counter variables Defined in program Maximum order of divided differences to be calculated by DTABLE

-256 TABLE LXI CONTINUED MAX Subscript of largest X value used in constructing the interpolating polynomial N Maximum subscript on X and Y TABLE Matrix containing divided difference table X An array containing abscissa values in ascending order XARG Interpolation argument Y An array containing ordinate values YEST Variable used to hold partially computed value of interpolant * Subroutines are more fully expla ined in Carnahan et al. from where they were obtained with minor modification.

APPENDIX D DATA AND RESULTS OF CORRESPONDING STATES CORRELATION -257

!_TABEX LXII #UCED ENM!ALPY AS A PUNCTION OF REDUCED DIPERATUEE AND REDUCED PRESSURE FOR TR PR 0.0 0.16198 0.32395 0.40494 3.48593,0.56691 0.64790 0.72889 0.80988 0.89086L0Q.97185 0.99939 1.13382 1.29580'1.457f7 1.61975 2.02469 2.42963 2.83456 3.23950 0.26969 O- 0.0 -7.84080 -7.83747 -7.83414 -7.83080 -7.82747 -7.82414 -7.82081 -7.81747 -7.81414 -1.081 -7.80748 -7.79748 -7.78748 -7. 8082 —7.76083 -7.73084-7.71884-7.69751 -7.69085 0.28471 0.0 -7.76749 -7.76416 -7.76083 -7.76083 -7.76083 -7.75749 -7.75749 -7.75416 -7.74750 -7.74416 -7.74416 -7.72750 -7.71751 -7.70418 -7.69085 -7.66086 -7.63420 -7.62087 -7.61754 0.29972 0.0 -7.70085 -7.69418 -7.69085 -7.68752 -7.69085 -7.68752 -7.68418 -7.67752 -7.67419 -7.67085 -7.66752 -7.66086 -7.64753 -7.63087 -7.62087 -7.59088 -7.56756 -7.55423 -7.54756 0.31474 0.0 -7.62754 -7.62420 -7.62087 -7.61754 -7.61754 -7.61421 -7.61087 -7.61087 -7.60421 7.59755 -7.59421 -7.59088 -7.57755 -7.56422 -7.55089 -7.52090 -7.49425 -7.47758 -7.47425 0.32975 0.0 -7.56089 -7.55756 -7.55089 -7.54756 -7.54423 -7.54090 -7.53757 -7.53090 -7.52757 7.52090 -7.51757 -7.51091 -7.49425 -7.48425 -7.47425 -7.44426 -7.42427 -7.40761 -7.40094 0.34477 0.0 -7.49091 -7.48758 -7.48425 -7.48092 -7.48092 -7.47758 -7.47092 -7.46759 -7.46426 7.45426 -7.45093 -7.44093 -7.42760 -7.41427 -7.40427 -7.37095 -7.34763 -7.34096 -7.33430 0.35979 0.0 -7.41427 -7.41094 -7.40761 -7.40427 -7.40094 -7.39761 -7.39428 -7.39095 -7.38428 7.38095 -7.38095 -7.36762 -7.35762 -7.34763 -7.33430 -7.30097 -7.28098 -7.26432 -7.26099 0.37480 0.0 -7.33763 -7.33430 -7.33430 -7.33097 -7.33430 -7.33097 -7.32763 -7.32097 -7.31764 7.31097 -7.31097 -7.30097 -7.28431 -7.27098 -7.25766 -7.23100 -7.20434 -7.19434 -7.18768 0.38982 0.0 -7.27098 -7.26765 -7.26765 -7.26432 -7.26099 -7.25766 -7.25432 -7.25432 -7.24766 7.23766 -7.23766 -7.23100 -7.21767 -7.20434 -7.19434 -7.16102 -7.14103 -7.12103 -7. 11437 0.40483 0.0 -7.20100 -7.1S767 -7.19434 -7.19100 -7.19100 -7.18434 -7.18101 -7.17434 -7.17434 -7.16435 -7.16101 -7.15435 -7.14102 -7.13102 -7.11769 -7.08437 -7.06438 -7.04772 -7.04105 0.41985 0.0 -7.13436 -7.13103 -7.12770 -7.12436 -7.12103 -7.11437 -7.11104 -7.10770 -7.10104 7.09771 -7.09438 -7.08438 -7.07771 -7.06438 -7.05106 -7.01773 -6.99774 -6.98108 -6.97108 0.43487 0.0 -7.06438 -7.06105 -7.05772 -7.05439 -7.05439 -7.05105 -7.04772 -7.04106 -7.03772 -7.03106 -7.02773 -7.01773 -7.00440 -6.99441 -6.98441 -6.94775 -6.92443 -6.91110 -6.90110 0.44988 0.0 -6.98774 -6.98441 -6.98108 -6.97774 -6.97774 -6.97441 -6.97108 -6.96441 -6,,%01 -6.95442 -6.95109 -6.94442 -6.S3109 -6.92109 -6.91110 -6.87111 -6.85112 -6.83446 -6.82779 0.46490 0.0 -6.92110 -6.91776 -6.91776 -6.91443 -6.91443 -6.91110 -6.90443 -6.90110 -6.89111 -6.88777 -6.88777 -6.87444 -6.86778 -6.85445 -6.84112 -6.80447 -6.78781 -6.76781 -6.75448 0.47992 0.0 -6.84779 -6.84446 -6.84446 -6.84112 -6.83779 -6.83446 -6.83113 -6.82780 -6.82446 -6.81780 -6.81447 -6.80447 -6.79447 -6.78114 -6.76781 -6.73782 -6.71783 -6.69784 -6.68784 0.49493 0.0 -6.77780 -6.77447 -6.77114 -6.76781 -6.76447 -6.76114 -6.75781 -6.75448 -6.4781-6.74448 -.6.74115 -6.73115 -6.72116 -6.70783 -6.69783 -6.67117 -6.64785 -6.63118 -6.61786 0.50995 0.0 -6.70783 -6.70450 -6.70117 -6.69783 -6.69450 -6.69117 -6.69117 -6.68784 -6.68784 6.68117 -6.68117 -6.66784 -6.65452 -6.64452 -6.63452 -6.60120 -6.57787 -6.55788 -6.54788 0.52496 0.0 -6.63785 -6.63452 -6.63452 -6.63119 -6.62785 -6.62452 -6.62452 -6.62119 -6.61786 -6.61786 -6.61452 -6.60120 -6.59120 -6.57787 -6.56787 -6.53455 -6.50456 -6.48790 -6.48457 0.53998 0.0 -6.56787 -6.56121 -6.56121 -6.55788 -6.55788 -6.55454 -6.55121 -6.55121 -6.55121 -6.54788 -6.54455 -6.53455 -6.52455 -6.51122 -6.50123 -6.46791 -6.44125 -6.42459 -6.41792 0.55500 0.0 -6.50123 -6.49456 -6.49456 -6.49123 -6.49123 -6.48790 -6.48790 -6.48457 -6.48457 6.48123 -6.47790 -6.46791 -6.45458 -6.44458 -6.43458 -6.40126 -6.37460 -6.35794 -6.34461 0.57001 0.0 -6.43792 -6.43459 -6.43459 -6.43125 -6.43125 -6.42792'-6.42459 -6.42126 -6.41792 6.41126 -6.40793 -6.40126 -6.38793 -6.37794 -6.36794 -6.33129 -6.30463 -6.29130 -6.27797 0.58503 0.0 -6.36460 -6.36127 -6.35794 -6.35794 -6.35794 -6.35794 -6.35794 -6.35461 -6.34794 -6.34128 -6.34128 -6.33128 -6.32129 -6.31129 -6.30129 -6.26797 -6.24131 -6.22132 -6.20799 0.60004 0.0 -6.30463 -6.30130 -6.29797 -6.29797 -6.29797 -6.29463 -6.29130 -6.28464 -6.28130 -6.27797 -6.27464 -6.26464 -6.25131 -6.24132 -6.23132 -6.19800 -6.17467 -6.15468 -6.14135 0.61506 0.0 -6.23132 -6.23132 -6.22799 -6.22465 -6.22799 -6.22465 -6.22132 -6.21799 -6.21133 -6.20466 -6.20466 -6.19466 -6.18467 -6.17467 -6.16134 -6.12469 -6.10803 -6.09136 -6.07470 0.63008 0.0 -6.16467 -6.16467 -6.16467 -6.16467 -6.15801 -6.15468 -6.15468 -6.14801 -6.14468 -6.14135 -6.13802 -6.13135 -6.11802 -6.10803 -6.09803 -6.06138 -6.04138 -6.02472 -6.C1472 0.64509 0.0 -6.09136 -6.09136 -6.09136 -6.09136 -6.08803 -6.08803 -6.08469 -6.07803 -6.07470 -6.07470 -6.07137 -6.06137 -6.C5137 -6.04138 -6.02805 -5.99806 -5.97473 -5.95807 -5.94141 0.66011 0.0 -6.02139 -6.02139 -6.02139 -6.02139 -6.01805 -6.01472 -6.01472 -6.01472 -6.00806 -6.00473 -6.00473 -5.99473 -5.98473 -5.97474 -5.96141 -5.93475 -5.91475 -5.89476 -5.88143 0.67513 0.0 -5.95474 -5.95141 -5.95141 -5.95141 -5.94807 -5.94807 -5.94807 -5.94474 -5.94141 -5.93808 -5.93474 -5.92475 -5.S1808 -5.90475 -5.89143 -5.86810 -5.84811 -5.82811 -5.81478 0.69014 0.0 -5.89476 -5.88809 -5.88476 -5.88476 -5.88143 -5.88143 -5.87810 -5.87476 -5.87143 -5.86810 -5.86810 -5.85810 -5.84477 -5.83478 -5.82811 -5.80145 -5.78146 -5.76813 -5.75147 0.70516 0.0 -5.81812 -5.81479 -5.81145 -5.81145 -5.81145 -5.81145 -5.81145 -5.80812 -5.80479 -5.80146 -5.79813 -5.78813 -5.77813 -5.76814 -5.75814 -5.73481 -5.71815 -5.70482 -5.68816 0.72017 0.0 -5.76147 -5.75813 -5.75480 -5.75147 -5.74814 -5.74814 -5.74480 -5.73814 -5.73481 -5.73148 -5.72814 -5.71815 -5.70815 -5.69482 -5.69149 -5.67149 -5.65817 -5.64150 -5.62151 0.73519 0.0 -5.68150 -5.68150 -5.68150 -5.67817 -5.67483 -5.67150 -5.66817 -5.66484 -5.66150 -5.65484 -5.65484 -5.64484 -5.63485 -5.62818 -5.62152 -5.60152 -5.58486 -5.56487 -5.55154 0.75021 0.0 -5.60485 -5.60485 -5.60485 -5.60152 -5.59819 -5.59819 -5.59819 -5.59486 -5.59153 -5.58819 -5.58819 -5.57486 -5.56820 -5.55820 -5.54821 -5.52488 -5.51155 -5.49156 -5.48156 0.76522 0.0 -5.51488 -5.52155 -5.52488 -5.53155 -5.53488 -5.53488 -5.53821 -5.53488 -5.53488 -5.53155 -5.52821 -5.51822 -5.50489 -5.49489 -5.48156 -5.45490 -5.43824 -5.42491 -5.41825 0.78024 0.0 -0.35655 -5.44490 -5.44823 -5.44823 -5.44823 -5.44823 -5.44823 -5.44490 -5.44157 -5.43824 -5.43490 -5.42824 -5.42158 -5.41158 -5.40491 -5.37826 -5.36826 -5.36160 -5.35160 0.79525 0.0 -0.30990 -5.35493 -5.36160 -5.36493 -5.36826 -5.36826 -5.36826 -5.36826 -5.36826 -5.36493 -5.36493 -5.35827 -5.35160 -5.34161 -5.33161 -5.30828 -5.29829 -5.29829 -5.28829 0.81027 0.0 -0.28990 -5.27829 -5.28496 -5.28829 -5.29496 -5.29829 -5.29829 -5.29829 -5.29496 -5.29496 -5.29162 -5.28496 -5.27496 -5.26830 -5.25830 -5.24164 -5.22831 -5.22164 -5.22164 0.82529 0.0 -0.26992 -5.17166 -5.19165 -5.20165 -5.20832 -5.21498 -5.21498 -5.21498 -5.21165 -5.20832 -5.20832 -5.20165 -5..19832 -5.18832 -5.18499 -5.17499 -5.15833 -5.14500 -5.14500 0.84030 0.0 -0.25658 -5.09835 -5.10834 -5.11834 -5.12500 -5.12834 -5.13167 -5.13500 -5.13500 -5.13500 -5.13500 -5.12834 -5.12167 -5.11168 -5.10834 -5.09835 -5.08835 -5.08169 -5.07835 0.85532 0.0 -0.23993 -0.59981 -5.00838 -5.01838 -5.02838 -5.03837 -5.04504 -5.05170 -5.05503 -5.05503 -5.05503 -5.04837 -5.C4504 -5.03504 -5.03171 -5.03171 -5.01505 -5.01505 -5.C1505 0.87034 0.0 -0.23992 -0.55649 -4.90508 -4.91508 -4.92507 -4.93840 -4.94507 -4.95506 -4.95506 -4.95840 -4.95840 -4.95506 -4.95173 -4.95173 -4.94840 -4.94507 -4.93840 -4.93507 -4.93840 0.88535 0.0 -0.22660 -0.52650 -0.73977 -4.79512 -4.81511 -4.83177 -4.84510 -4.85510 -4.86176 -4.86510 -4.86843 -4.87176 -4.87176 -4.86843 -4.86843 -4.86510 -4.86510 -4.86510 -4.87176 0.90037 0.0 -0.21992 -0.50650 -0.68978 -0.88638 -4.68181 -4.71180 -4.73513 -4.74846 -4.75512 -4.76179 -4.76179 -4.76845 -4.77512 -4.77845 -4.77512 -4.77512 -4.78178 -4.78845 -4.79511 0.91538 0.0 -0.21993 -0.48984 -0.65645 -0.84306 -4.52187 -4.57185 -4.60851 -4.62850 -4.63850 -4.64850 -4.65183 -4.661-83 -4.67515 -4.68515 -4.68848 -4.69848 -4.70514 -4.71514 -4.72514 0.93040 0.0 -0.21660 -0.46319 -0.61647 -0.78642 -0.98968 -4.37525 -4.45856 -4.49854 -4.51187 -4.52854 -4.53187 -4.54853 -4.56519 -4.58518 -4.59185 -4.62184 -4.63183 -4.64516 -4.65849 0.94542 0.0 -0.20327 -0.43319 -0.57315 -0.74643 -0.93969 -1.16963 -4.27529 -4.34859 -4.38192 -4.40524 -4.41191 -4.44190 -4.46522 -4.47855 -4.48855 -4.51521 -4.54186 -4.55853 -4.57519 0.96043 0.0 -0.19994 -0.42986 -0.55981 -0.70644 -0.87638 -1.08631 -1.36955 -4.16532 -4.23197 -4.27195 -4.28195 -4.31527 -4.34526 -4.37192 -4.39191 -4.42523 -4.45522 -4.47521 -4.49521 0.97545 0.0 -0.19661 -0.41320 -0.52983 -0.66312 -0.81640 -1.00301 -1.23961 -1.56283 -3.98205 -4.04203 -4.06203 -4.13533 -4.19532 -4.23197 -4.26529 -4.33193 -4.37525 -4.40191 -4.41858 0.99046 0.0 -0.19327 -0.40321 -0.50984 -0.63313 -0.76975 -0.92970 -1.12964 -1.39288 -1.75943 -3.74546-3.78211 -3.92874 -4.03537 -4.10201 -4.15199 -4.23863 -4.28528 -4.31527 -4.34193 1.00548 0.0 -0.18327 -0.37988 -0.48985 -0.60980 -0.74309 -0.89305 -1.06632 -1.27626 -1.54617 -1.93938 -2.10599 -3.61217 -3.81211 -3.92874 -4.01204 -4.12867 -4.18532 -4.22530 -4.26196 1.02050 0.0 -0.17660 -0.36655 -0.46984 -0.58314 -0.70644 -0.84305 -0.99634 -1.18628 -1.40287 -1.68279 -1.78608 -2.73578 -3.50553 -3.72679 -3.85542 -4.01203 -4.08534 -4.13200 -4. 17531 1.03551 0.0 -0.16661 -0.34989 -0.44985 -0.56316 -0.67979 -0.81308 -0.95303 -1.11964 -1.30624 -1.51951 -1.59616 -2.08932 -3.14565 -3.50553 -3.67882 -3.89874 -3.97872 -4.04203 -4.09535 1.05053 0.0 -0.16661 -0.33989 -0.43652 -0.54316 -0.64979 -0.76975 -0.89637 -1.04300 -1.20627 -1.39288 -1.45286 -1.85606 -2.51918 -3.20563 -3.46221 -3.74545 -3.86542 -3.94872 -3.99871 1.06555 0.0 -0.15995 -0.32656 -C.41653 -0.51983 -0.62647 -0.73642 -0.85972 -0.99301 -1.13297-1.29624 -1.35289 -1.67279 -2.18929 -2.79576 -3.20896 -3.59217 -3.75212 -3.84209- -3.90874 1.08056 0.0 -0.15661 -0.31656 -0.40653 -0.49651 -0.59648 -0.70644 -0.81974 -0.94637 -1.08965 -1.23960 -1.29625*-1.56616 -1.96270 -2.43255 -2.90573 -3.40556 -3.62883 -3.74546 -3. 81543 1.09558 0.0 -0.15328 -0.30989 -0.39320 -0.47651 -0.56981 -0.67311 -0.77974 -0.89971 -1.02966 -1.16962 -1.2.1960 -1.472.86 -1.82274 -2.,0595 -2.61915 -3.20896 -3.49553 -3.63882 -3.71547 1. 11059 0.0 -0.14662 -0.29658_-0.37655 -0.46319 -0.55649 -0.65313 -0.75643 -0.86306 -0.98302 -1.10964 -1.15630 -1.37956 -1.66613 -1.98603 -2.37590 -3.00903 -3.35559 -3.51887 -3.61550 1.12561 I-0.0 -0.13663 -0.28658 -0.36322 -0.44653 -0.53316 -0.62313 -0.72643 -0.82974 -0. 9396 -1.04966 -.08632 -1.28292 -1.54284 -1.83940 -2.1.1597 -2.83575 -3.21896 -3.40890-3.51220 1.14063 0.0 -0.12663 -0.27325 -0.34989 -0.42987-0.51650 -0.60314 -0.69645 -0.79308 -0.89305 -0.99968 -1.03300 -1.21627 -1.45620 -.1.71945 -2.01269 -2.69580 -3.07235 -3.27228 -3.41556 1.15564 0.0 -0.12329 -0.26658 -0.34322 -0.42320-0.50650 -0.59314 -0.67978 -0.77308 -0.86439 -0.96302 -0.99634 -1.16295 -1.37955 -1.61281 -1.87939 -2.52585 -2.93239 -3.15565 -3.31226 1.17066 0.0 -0.12995 -0.26658 -0.32989 -0.40986 -0.48650 -0.56648 -0.64979 -0.73642 -0. 82307 -0.91304 -0 94302 -1.09964 -1.29958 -1.52284 -1.77276 -2.38256 -2.79910 -3.04234 -3.21229 1.18567 0.0 -0.119S6 -0.25325 -0.32323 -0.39654 -0.47318 -0.54982 -0.63313 -0.71310 -0.79641 -0.88305 -0.91637 -1.06632 -1.25959 -1.45952 -1.67612 -2.23927 -2.66580 -2.92571 -3.11566 1.20069 0.0 -0.12329 -0.24992 -0.31323 -0.38321 -0.45652 -0.52983 -0.60647 -0.68978 -0.76975 -0.85306 -0.88305 -1.02634 -1.20627 -1.39621 -1.59615 -2.12598 -2.54251 -2.81242 -3.01903 1.21571 0.0 -0.11663 -0.23993 -0.30657 -0.37322 -0.44653 -0.51984 -0.59314 -0.66979 -0.74641 "-0.82974 -0.85640 -0.99635 -1.16296 -1.33957 -1.52285 -2.00602 -2.41922 -2.70913 -2.92572 1.23072 0;0 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-0.80640 -0.93636 -1.06632 -1.19628 -1.54283 -1.87605 -2.13597 -2.38589 1.32 82 0.0 -0.09663 -0.19994 -0.25325 -0.30989 -0.36655 -0.42320 -0.48318 -0.53982 -0.5.66 2 -.63 -.8641 -0.91304 -1.03633 -1.15962 -1.48285 -1.80275 -2.0660 -2.36 592 1;33584 0.0 -0.09997 -0.19994 -0.24992 -0.30324 -0.35655 -0.41320 -0.46652 -0.52650 -0.858' -0.63646 -0.65979. -0.75642 -0.87305 -0.99301-1.11297 -1.42953 -1.73944 -1.99602 -2.23927 1.35085 0.0 -0.09330 -0.19327-0.23993 -0.29324 -0.34656 -0.39987 -0.45985 -0.51650 -0.6 -.62 3 4 -0.64313 -0.7364 -.4973 -0.96303 -1.07966 -1.37956 -.6 63 -.932 1 -2.1559 1.36587 0.0 -0.08997 -0.18660 -0.23659 -0.28657 -0.33655 -0.38987 -0.43986 -0.49650 -0.549.*8.59981 -0.61979 -0.71310 -0.81973 -0.93303 -1.04632 -1.33290 -1.61947 -1.86939 -2.08599 1.38088 0.0 -0.08331 -0.17994 -0.22659 -0.27657 -0.32655 -0.37654 -0.42986 -0.48318 _-0. 5331 -g.58647 -0.60313 -0.68644 -0.79307 -0.89971 -1.00967 -1.28958 -1.56283 -1.80941 -2.01934 1.39590 0.0 -0.08664 -0.17661 -0.22327 -0.27325 -0.31990 -0.36988 -0.41653 -0.46652 -0.51650 -0.56316 -0.57982 -0.66645 -0.76642'-0.87306 -0.97969 -1.24627 -1.51285 -1.74277 -1.95604. 1.41092 0.0 -0.08663 -0.16994 -0.21660 -0.25991 -0.30657 -0.35321' -0.39987 -0.44985 -0.496 -o.4315 -0.55981 -0.64312 -0.74309 -0.84639 -0.94636 -1.20294 -1.45952 -1.68279 -1.89272 1.42593 0.0 -0.08331 -0.16995 -0.21327 -0.25658 -0.30324 -0.34989 -0.39654 -0.44319 -0.48964 -0.5*650 -0.55316 -0.63313 -0.72977 -0.82307 -0.92303 -1.16629 -1.41621 -1.63614 -1.83940 1.44095 0.0 -0.07997 -0.16328 -0.20326 -0.24658 -0.29324 -0.33989 -0.38654 -0.43319 -0.4761 -0.650 -0.53982 -0.61647 -0.70977 -0.80307 -0.89971 -1.13629 -1.37289 -1.58615 -1.78608 I \Jn 00 I

TABLE LXIlI REDUCED ENTHALPT AS A FUNCTION.01 RIZD=CD TEMPERATURE AND REDUCED PRESSURE FOR METHANE TR PR 0.0 0.07474 0.14948 0.22422 0.29895 0.37369 0.44843 0.52317 0.59791 0.67265 0.7473a[ 0 82252 0.89686 0.93423 1.01644 1.04634 1.19581 1.34529 1.49477 1.79372 2.242150 2.98954 0.52361 0.0 -5.32907 -5.33331 -5.33543~-5.33731 -5.33825 -5.33896 -5.33825 -5.33943 -5.33896 -5.33378 -5.33660 -5.33331 -5.33472 -5.33072 -5.32766 -5.31636 -5.30553 -5.29188 -5.24998 -5.20079 -5.14406 055277 0.0 -5.25610 -5.26034 -5.26246 -5.26434 -5.26528 -5.26599 -5.26528 -5.26646 -5.26599 -5.26808i-5.26363 -5.26034 -5.26175 -5.25775 -5.25469 -5.24339 -5.23256 -5.21891 -5.17701 -5.12782 -5.07109 0.58192 0 -5. 131 3 -5.18737 -5.18949 -5.19373 -5.19467 -5.19537 -5.19467 -5.19584 -5.19537 -5.19020 -5.19302 -5.18972 -5.19114 -5.18713 -5.18408-5.17278 -5.16195 -5.14830 -5.10640 -5.05720 -5.00048 0.61108 0.0 -5.10546 -5.10969 -5.11417 -5.11605 -5.11699 -5.11770 -5.11699 -5.11817 -5.11770 -5.112521-5.11534 -5.11205 -5.11346 -5.10946 -5.10640 -5.09745 -5.08663 -5.07297 -5.03343 -4.98423 -4.92751, 0.64023 0.0 -5.02543 -5.02966 -5.C3414 -5.03602 -5.03696 -5.03767 -5.03696 -5.03814 -5.03767 -5.032491-5.03531 -5.03202 -5.03343 -5.02943 -5.02637 -5.01978 -5.00895 -4.99530 -4.95811 -4.90891 -4.85219; 0.66939 0.0 -4.94069 -4.94493 -4.94940 -4.95128 -4.95222 -4.95293 -4.95222 -4.95340 -4.95293 -4.94775 -4.95293 -4.94963 -4.95105 -4.94940 -4.94634 -4.93975 -4.92892 -4.91762 -4.88043 -4.83359 -4.77686 0.69854 -0.12240 -4.85783 -4.866231 -4.86419 -4.86513 -4.86584 -4.86749 -4.86866 -4.86819 -4.86301 -4.86819 -4.86725 -4.86866 -4.86937 -4.86631 -4.86207 -4.85124 -4. 83994 -4.80275 -4.75591 -4.70054 0.72770. 00 - -0_12004 -4.76368 -4.76815 -4.77003 -4.77098 -4.77168 -4.77568 -4.77686 -4.77639 -4.775871-4.78110 -4.78016 -4.78057 -4.78227 -4.77921 -4.77498 -4.76415 -4.75521 -4.71801 -4.67353 -4.62386 0.75685 0.0 -0.1769 -0.24903 -4.66223 -4.66646 -4.66976 -4.67517 -4.67917 -4.68035 -.67988 -4.679411-4.68694 -4.68600 -4.68741 -4. 68812 -4.68741 -4.68553 -4.67470 -4.66576 -4.63092 74.58879 -4.54383: 0.78601 0.0 -0.11063 -0.23727 -4.55395 -4.56054 -4.56384 -4.56925 -4.57325 -4.57679 -4.57631 -4.58055-4.59044 -4.59185 -4.59326 -4.59397 -4.59326 -4.59138 -4.58055 -4.57396 -4.54148 -4.50170 -4.46145, 0.01516 0.0 -0.10592 -0.22550 -0.37356 -4.44756 -4.45556 -4.46098 -4.46733 -4.47557 -4.47510 -4.48169-4.48922 -4.49063 -4.49205 -4.49511 -4.49440 -4.49252 -4.48405 -4.47745 -4.44968 -4.41225 -4.37906 0.84431.-0 -0.-09886 -0.21138 -0.34295 -0.49077 -4.32610 -4.33387 -4.34022 -4.34846 -4.35270 -4.35929-4.37153 -4.37530 -4.37906 -4.38683 -4.38612 -4.38424 -4.37812 -4.37388 -4.35082 -4.31810 -4.29197.87347. -0.0918C -0.19961 -0.31471 -0.44605 -0.59529 -4.19029 -4.20606 -4.21430 -4.21853 -4.22512-4.23972 -4.24584 -4.25196-4.26443 -4.26373 -4.26655 -4.2 985 -4.26561 -4.244905-4.21924 -4.20-173.90262 0.0 -0_.08474 -0.18784 -0.29352 -0.41075 -0.53879 -0.69250 -0.88009 -4.04247 -4.06318 -4.07448 -4.09142 -4.10461 -4.11308 -4.12556 -4.129.56 -4.13709 -4.14745 -4.15027 -4.13426 -4.11567 -4.10361 0.93L78 0 - 3 -0.17842 -0.27705 -0.38249 -0.49407 -0.62424 -0.77417 -0.96601 -3.86310 -3.88617 -3.910108-3.93042 -3.93890 -3.55843 -3.96950 -3.98880 -4.00622 -4.01610 -4.01657 -4.00739 -4.00716. 0.96093 0.0 -0.07532 -0.16900 -0.25821 -0.35425 -0.45876 -0.56774 -0.69649 -0.85067 -1.03144 -1.26400 -3.65361 -3.69739 -3.71528 -3.75365 -3.76707 -3.81226 -3.83909 -3.85839 -3.87534 -3.88735 -3.90359. 0.97551 0.0 -0.07297 -0.16665 -0.25115 -0.34483 -0.44464 -0.54891 -0.66825 -0.81066 -0.96554 -1.16279 -1.44336 -3.51379 -3.55051 -3.62654 -3.64231 -3.71104 -3.74729 -3.77130 -3.80237 -3.82144 -3.849.45 0.99009 0.0___-0.07297 -0.16194 -0.24409 -0.33306 -0.42816 -0.52773 -0.63765 -0.76829 -0.91140 -1.08041 -1.28566 -1.59307 -1.65803 -3.43117 -3.47048 -3.58158 -3.63431 -3.67244 -3.72234 -3.75788 -3.79531 1.00000 0. -0.07297 -0. 8077 -0.23938 -0.32365 -0.41639 -0.50654 -0.61411 -0.73534 -0.89493 -1.04274 -1.22682 -1.47302-61.63214 -3.19814 -3.31513 -3.48978 -3.57076 -3.61830 -3.68468 -3.68727 -3.738w21.01924 0.0 -0.07061 -0.15488 -0.23232 -0.31424 -0.40227 -0.49007 -0.59057 -0.70238 -0.82195 -0.95095 -1.10441 -1.29178 -1.40147 -1.75289 -2.02288 -3.14612 -3.34714 -3.44177 -3.54580 -3.61666 -3.68233 1.03302 0.0 -0.06826 -0.15252 -0.22526 -0.30482 -0.39050 -0.47359 -0.56939 -0.67413 -0.78665 -0.90151 -1.048i6-1.19998 -1.29790-. 54576 -1.67922 -2.59297 -3.11176 -3.29583 -3.44459 -3.53662 -3.62348 1.04840 0.0 -0.06826 -0.14782 -0.22055 -0.29540 -0.37873 -0.45711 -0.54820 -0.64824 -0.75370 -0.86150 -0.98908 -1.12936 -1.21552 -1.42100 -1.50268 -2.04453 -2.80341 -3.12164 -3.32925 -3.45659 -3.56228 1.06297 0.0 -0.06826 -0.14311 -0.21584 -0.28834 -0.36931 -0.44534 -0.53073 -0.62706 -0.72310 -0.82384 -0.94436 -1.07052 -1.14490 -1.32450 -1.39205 -1.79738 -2.41738 -2.89568 -3.19744 -3.36 - 1.07755 0.0 -0.0659C -0.14075 -0.20878 -0.28128 -0.35990 -0.43122 -0.51289 -0.60587 -0.69720 -0.79089 -0.90434 -1.01638 -1.08606 -1.24211 -1.29790 -1.64438 -2.15140 -2.61792 -3.05150 -3.27535 -3.43517 1.10670 0.0 -0.06355 -0.13370-0.09937 -0.26716 -0.34107 -0.40768 -0.48465 -0.56821 -0.65012 -0.734394 -0.83137 -0. 93 165 -0.98719 -1.11501 -1.15902 -1.42312 -1.76772 -2.137T4^2770549370T15 -3.30101 1.13586 0.0 -0.q06120 -0.12899 -0.18995 -0.25539 -0.32223 -0.38885 -0.45876 -0.53526 -0.61011 -0.68731 -0.77253 -0.86103 -0.90952 -1.00605 -0.05546 -1.27483 -1.55117 -1.84116 -2.34770 -2.82577 -3.15507 1.16501 0 -508885 -0.12428 -0.18289 -0.24362 -0.30576 -0.37002 -0.43522 -0.50966 -0.57480 -0.644, -8.72545 -0.80218 -0.84596 -0.93847 -0.97542 -1.16185 -1.39347-1.62696 -2.05583 -2.57862 -2.99972 1.19417_ — - 0.0 -0.05649 -0.11957 -0.17347 -0.23185 -0.29164 -0.35119 -0.41404 -0.47876 -0.54420 -0.60944 -0.68308 -0.75275 -0.79183 -0.87492 -0.90716 -1.07240 -1.26636 -1.46219 -1.83928 -2.34323 -2.83730 10 1.22332 0.0 -0.05413 -0.11251 -0.16406 -0.22008 -0.27751 -0.33471 -0.39285 -0.45523 -0.51596 -0.57668 -0.6(307 -0.70803 -0.74004 -0.82078 -0.85067 -0.99943 -1.16043 -1.33509 -1.66981 -2.13375 -2.61253 \J3 0.25248 0.0 -0.05178 -0.10545 -0.15700 -0.20831 -0.26339 -0.31823 -0.37167 -0.43169 -0.48771 -0.54608 -8.60736 -0.67C37 -0.70238 -0.77370 -0.80124 -0.93588 -1.08276 -0.23387 -1.53328 -1.95721 -2.5077 1.28163.70 -010074 -0.14994 -0.19890 -0.25162 -0.30411 -0.35519 -0.41051 -0.46417 -0.5174 -8.57716 -0.63506 -0.66472 -0.72898 -0.75652 -0:87939 -1.01685 -1.14914 -1.42030 -1.80892 -2.35477 \J 1.31079 0.0 -0.04708 -0.09839 -0.14523 -0.19184 -0.24221 -0.29235 -0.34107 -0.39403 -0.44534 -0.49666: -0.55127 -0.60447 -0.63177 -0.69132 -0.71651 -0.83232 -0.95801 -1.08088 -1.32615 -1.68417 -2.21119 1 1.33994 0.086 -. -0 03817 -0.18478 -0.23279 -0.28058 -0.32695 -0.37755 -0.42652 -0.47547 -0.52538 -0.57622 -0.60352 -0.66072 -0.68356 -0.78995 -0.90388 -1.01968 -1.24377 -1.57825 -2.07938 1.36909 0.0 -0.04472 -0.08897 -0.13346 -0.17771 -0.22338 -0.26880 -0.31283 -0.36108 -0.40768 -0.45429 -0.50184 -0.55033 -0.57528 -0.63012 -0.65C60 -0.75228 -0.85915 -0.96554 -1.17550 -1.48880 -1.95932 13982 0.0 -0.04237 -0.08427 -0. 2640 -0.17066 -0.21396 -0.25704 -0.29870 -0.34460 -0.39021 -0.43546 -0.48065 -0.52443 -0.54938 -0.60188 -0.62000 -0.71698 -0.81443 -0.91611 -1.11195 -1.40641 -1.85105 1.42740 0.0 -0.04001 -0.08191 -0.12169 -0.16594 -0.20690 -0.24763 -0.28929 -0.33283 -0.37708 -0.41898 -0.46182 -0.50560 -0.52820 -0.57598 -0.59411 -0.68402 -0. 77677 -0.87139 -1.05545 -1.33344 -1.75219 1.45656 0.0 -0.03766 -0.07956 -0.11698 -0.16124 -0.19984 -0.24056 -0.27987 -0.32106 -0.36296 -.40258 -44299 -0.48677 -0.50701 -0.55245 -0.57056 -0.65342 -0.74146 -0.83137 -1.00367 -1.26753 -1.66275 1.48571 0.0 -0.03531 —0.07720 -0.11463 -0.15653 -0.19277 -0.23114 -0.27046 -0.30929 -0.34883 -0.38"63 -0.42651 -0.46794 -0.48583 -0.52890 -0.54703 -0.62518 -0.70850 -0.79371 -0.95660 -1.20633 -1.58036

-260TABLE LXIV RESULTS OF CORRESPONDING STATES CORRELATION FOR METHANE-PROPANE MIXTURES USING OPTIMUM VALUES OF THE PARAMETERS A. 5.1 PERCENT MIXTURE R1 pZSU E.RE —. TEMPERATURE --- EXPER. =DEPARTURE G-CAIC.z DEPARTURE. DIFFEENCE PERCENT DIFFERENCE _(psia)' (OR) (Btu/lb)- _ (Btu/lb) (Btu/lb) 50C.0000000 179.5999908 -223.5000C00 -223.8465271 0.3465271 -0.1550456 179 t.~I~~=~n7~-n~m~-~;-~~23.599990346527! -0.1550456.......... 500.0000000 199.5999908 -217.69;9969 -217.6114197 -0.08e5773 0.0406878... 500.0000000 219.5999908 -209.699,9S69 -211.7310486 2.0310516 -0.9685509.. 500.0000000 239.5999908 -203.7999573 -205.2352753 1.4353180 -0. 7042776.... 50C.000000 259.5998535 -196.9000092 -198.4780273 1.5780182 -0.8014310....... 500.0000000 279.5998535 -190.39SS634 -190.9170227 0.5170593 -G.2715648 500.0000000 299.5998535 -182. 3998566 -182.72 81189 0.3282623 -0.1799685. 500.0000000 319.5998535 -172.30CC031 -172.2226105 -0.0773926 0.0449173,.. 500.0000000 419.5998535 -27.8000488 -26.9967194 -0.8033295 2.889665........ 500.0000000 439.5998535 -24.9001465 -24.2286530 -0.6714935 2.6967449.. 500.0000'000 459.5998535 -22.5000000 -21.8375854 -0.6624146 2.9440641..... 500.0000000 479.5998535 -20.3999023 -20.0686493.-0.3312531. 1.6237965... 500.0000000 499.5998535 -18.6999512 -18.4226685 -0.2772827 1.4827986.. 500.0000000 519.5998535 -17.3000488 -17.0725708 -0.227478C 1.3148975 1COO.0000000 179.5999908 -221. 50CO00 -221.9775238 0.4775238. -0.2155863.,... 1C00.0000000 199.5999908 -215.40COC92 -215.8345032 0.4344940 -0.2017149.1C00.0000000 219.5999908 -208.1999969 -210.0275879 1.8275909 -0.8778054.... 1000.0000000 239.5999908 -202.2999573 -203.8572693 1.5573120 -0.7698033.... 1COO.0000000 259.5998535 -195.5000000 -197.5049744 2.0C49744 -1.0255613.. 1COO.0000000 279. 5998535 -189. 1999512 -190.4310455 1.2310944 -C.65C6841.. 1000.0000000 299.5998535 -182.0998535 -182.7608032 0.66C9497 -0.3629600..... 1000.0000000 319.5998535 -173.6000061 -174.2459564 0.6459503 -0.3720911 1000.0000000 335.5998535 -163.3999023 -163.9692383 0.5653359 -0.348431C 1000.0000000 359.5998535 -149.7998047 -150.3798218 0.5800171 -0.3871948...1C00.0000000 379.5998535 -125.4998169 -128.1374054 2.6375885 -2.1016665 1COO.0000000 399.5998535 -88.8999023 -89.5020294 0.6021271 -0.6773088 1000.0000000 419.5998535 -68.50C0000 -68.5833588 O.0833588 -0.1216916 COC. 0000000 439.5998535 -56.8000488 -56.5252686 -0.2747803 0.4837673 1000.0000000 459.5998535 -49.2001953 -48.7428894 -0.4573059 0.9294797 1 C0.0000000 479.5998535 -43.5000000 -43.3065186 -0.1934814 0.4447848 1000.0000000 499.5998535 -39.0998535 -38.9842224 -0.1156311 C.295732e 1 00. 0000000 519.5998535 -35.600C77 -35.4225464 -0.1775513 0.4987381 1500.0000000 179.5999908 -219.3999939 -218.2074738 -1.1S25201 0.543537C... 1500.0000000 199.5999908 -213.1999969 -212.1310272 -1.0689697 0.501392e 1500.0000000 219.5999908 -206.3999939 -206.4019775 0.0019836 -0.0009611 1500. 0000000 239.5999908 -200. 8999634 -200.4232788 -0.4766846 0.2372746 1500.0000000 259.5998535 -194.3000031 -194.1630C96 -0.1369934 0.0705061 150C.000000 279. 5998535 -187.8999634 -187.4026794 -0.4972839 0.2646535. 1500.0000000 299.5998535 -181.0998535 -180.2934113 -0.8064423 0.4453C22.. 1500.0000000 319.5998535 -173.7000122 -172.5238342 -1.1761780 0.6771315. 150C.0000000 339.5998535 -165.4999084 -164.0117950 -1.4881134.08991625... 1500.0000000 359.5998535 -155.3998108 -153.5645447 -1.8352661 1.1809959....... 1500.0000000 379.5998535 -143.0998077 -142.0413571 -1.0584106 0.7396311.. 1500.0000000 399.5998535 -127.4999084 -126.5802460 -0.9196625 0.7213041.... 1500.0000000 419.5998535 -108.8000031 -108.0916443 -0.7CE3588 0.6510649... 150C.0000000 439.5998535 -91. 1999512 -90.3188019 -0.8811493 0.9661726. 150C. 000000 459.5998535 -77.6000977 -76.8830719 -0.7170258 C.9240009 1500.0000000 479.5998535 -67.59S8535 -67.1749878 -0.4248657 0.62e500C..... 1500.0000000 499. 5998535 -60.C 000000 -59.9863129 -0.0136871 0.0228119.... 150C.0000000 519.5998535 -54.0000000 -54.1292572 0.1292572 -0.2393652 2CO0O00000 179.5999908 -217.2999878 -215.9124298 -1.3e75580 C.6385446. 2 CO0.0000000 199.5999908 -211.1000061 -209.8416138 -1.2583923 0.5961116 2000.0000000 219.5999908 -204.7999878 -204.1183624 -0.6816254 0.3328249 2000.0000000 239. 5999908 -199.5999603 -198.1295013 -1.47C4590 0.7367030. 2000.0000000 259.5998535 -193.1000061 -192.0975647 -1.0024414 0.5191303 2000.0000000 279.5998535 -186.6999512 -185.7134C94 -0.9865417 0.528411.. 2CO0.0000000 299.5998535 -180.1998596 -179.1232758 -1.0765839 0.5974386 2000.0000000 319.5998535 -173.2000122 -171.8867340 -1.3132782 0.7582433. 2000,0000000 339.5998535 -165.3999023 -164.2259216 -1.1739807 0.7097829 2CO0.0000000 359.5998535 -156.9998169 -155.5579681 -1.4418488 0.9183760... 2 CO. 0000000 379.59S8535 -147.4998169 -146.7535095 -0.746374 0.5059715 2COC. 0000000 399.5998535 -136.69'99054 -136.7344360 0.0345306 -0.0252602 2COC.0000000 419.5998535 -124.50C000 -124.3732452 -0.1267548 0.1018110 2000.0000000 439.5998535 -111.5999603 -111.8323975 0.2324371 0C.2082770 2000.0000000 459. 5998535 -99.0000000 -99.3701172 0.3701172 -0.3738557.. 2C00.0000000 479.5998535 -87. 5998535 -88.2673C35 0.6674500 -0.7619302 2C00.0000000 499.5998535 -78.0998535 -78.8437347 0.7438812 -C.9524744... 2C00.0000000 519.5998535 -70.3000488 -70.9891663 0.6891174 -0.98C2516...

-261TABLE LXIV (CONTINUED) B. 11.7 PERCENT MIXTURE -I.F.SURET -- -OSUR-.... [R~... P, I7JA'ITURE --'CALC. DEPARTURE: DIFFiRENCE- PERCENT DIFFERENCE (Psia)_______ (~IQ J ___(Btu/lb) _________(Btu/lb) (Btu/lb) 500.0000000 199.5999908 -223.659969 - C-222.9557190 -0. 7442780 0.3327125......... 500.0000000 219.5999908 -218.0999908 -217.0829010 -1.0170898 0. 4663408..... 500.0000000 239.5999908 -212.C999146 -211.0576172 -1.0422974 0.4914179-. 50C. 0000000 259.5998535 -205.7000122 -204.6004181 — 1.0995541 0.5345616,. 500.0000000 279.5998535 -198.7998657 -197.9979553 -0.8C19104 C.4033755. 500.0000000 299.5998535 -191.2999115 -190.7028503 -0.5970612 0.3121073... 500.0000000 319.5998535 -181.8999634 -182.8739929 0.9740295 -0.5354751............ 500.0000000 479.5998535 -24.5998535 -22.6493683 -1.9504852 7.9288483...... 500. 0000000 499.5998535 -20.9001465 -20.6938171 -0.2063293 0.9872146..-..,. 500.0000000 515.5998535 -18.6999512 -19.0550690 0. 3551178 -1.8990297 500.0000000 539.5998535 -17.3999023 -17.5503082 0.1504059 -0.8644063...... 500.0000000 559.5998535 -16.8000488 -16.3127899 -0.4872589 2.9003410.. 10CO. 0000000 199.5999908 -220.8999939 -221.2119751 0.3119 12 -0.1412318. 1000.0000000 219. 5999908 -215.C999908 -215.3538208 0.2538300 -0.1180055. 1COO.0000000 239.5999908 -209.2999115 -209.4137573 0.1138458 -0.0543936.. 1000.0000000 259. 5998535 -203.1000061 -203.2781982 0.1781921 -0.0877361........ 1C000.0000000 279.5998535 -196.2958657 -196.9353180 0.6354523 -0.3237150 —.. 1000.0000000 299.5998535 -189.2999115 -190.0705261 0.7706146 -0.4070863.......... 1000.0000000 319.5998535 -181.6999512 -182.6600189 0.9600677 -0.5283806....... 1 COO. 0000000 339.5998535 -172.9000092 -174.5535736 1.6535645 -0.9563703.......... 1COO. 0000000 355. 5998535 -163. 8000031 -165.1951599 1.3951 569 -0.851744C 0..... 1000.0000000 379.5998535 -150.2999115 -152.9467773 2.6468658 -1.7610559........... 1000.0000000 479.5998535 -52.8999023 -51.6362762 -1.2636261 2.388711c....... 1000, 0000000 499.5998535 -45.9001465 -45.4912415 -0.40 89050 O0.8908577........ 1COO.0000000 519.5998535 -40. 80C0488 -40.7847748 -0.0152740 0.0374363...... 1COO.0000000 539.5998535 -37.0998535 -36.9780884 -0.1217651 0.3282092 - 1 COO.0000000 559.5998535 -34.1999512 -33.8241577 -0.3757935 1.0988121.1500.0000000 199.5999908 -218.0000000 -217.8072357 -0.1927643 0.088424C..,. 1500.0000000 21S.5999908 -212.1999969 -211.9319611 -0.2680359 0.1263129............. 1500.0000000 239.5999908 -206.3999023 -206.1060028 -0.2938995 0.1423932........... 1500.0000000 259.5998535 -200.5000000 -200.1881104 -0.3118896 0.1555559...... 1500. 0000000 279.5998535 -193.8998566 -194.0115509 0.1116943 -0.0576041...... 1500.0000000 299.5998535 -187.3999023 -187.3063507 -O.CS35516 0,0499208.,, 150C. 0000000 319.5998535 -180.3999634 -180.4412384 0.0412750 -0.0228797....-.... 1500.0000000 339.5998535 -173.0CC000OOO -172.9879761 -0.0120239 0,0069502...... 15 CO. 0000000 359.5998535 -165.0000000 -164.9716949 -0.0283C51 0.0171546....... 1500.0000000 379.5998535 -155.5999146 -155.7413025 0.1413879 -C.0908663....... 1500. 0000000 39S.5998535 -144. 3000031 -145.0418549 0.7418518 -0.5141035.... 1500.0000000 419.5998535 -130.1998596 -131.7047424 1.5048828 -1.1558247............ 1500.0000000 439.5998535 -113.4998169 -114.8953552 1.3955383 -1.2295504.............. 1500.0000000 459.5998535 -97.50OOO000 -97.2541504 -0.2458496 0.2521534.... 1500. 0000000 479.5998535 -83. 5000000 -82.4559479 -1.0440521.1.2503614. 1500. COOOOOO 499.5998535 -72.5000000 -71.5027771 -0.9972229 1.3754787.. 1500.0000000 519.5998535 -64.1999512 -63.2568207 -0.9431305 1.4690514............ 1500.0000000 539.5998535 -57.3999023 -56.9259644 -0.4739380 0.8256770 -......... 150C. 0000000 559.5998535 -52.10CC977 -51.6867065 -0.4133.911 0.7934555 2000.0000000 199.5999908 -215.2999878 -215. 7004395 0.4C4 517 -0.1859970... 200C.00000 219.5999908 -209.3999939 -209.8628693 0.4628754 -0.2210484..-.. 2 CO0.0000000 239.5999908 -203.8999023 -204.0389252 0.1390228 -0.0681819.....,... 2COC. 0000000 259.5998535 -198.0000000 -198.0725403 0.0725403 -0.0366365........... 2 CO0.0000000 279.5998535 -191.5958535 -192.12 8558 0.5287323 -0.2759565-..... _20oo00.00000 299.5998535 -185.4999084 -185.7765656 0.2766571 -0. 1491413...... 2000.0000000 319. 5998535 -179. 2999573 -179.2699585 -0.0299988 0.0167311....... 2COO0.0000000 339.5998535 -172.6000061 -172.3524933 -0.2475128 0.1434025..... 2000.0000000 355.5998535 -165.4000092 -165.0437469 -0.3562622 0.2153943........ 2000.0000000 379. 5998535 -157.3999023 -157.0870209 -0.3128815 0.1987812 2C00.0000000 399. 599853'5 -148. 5000000 -148.4530792 -0.0469208 0.0315965......... 2000.0000000 419. 5998535 -138. 3998566 -138.9698334 0.5699768 -0.4118330............ 2000. 0000000 439.5998535 -127.C 098077 -128. 0904541 O.9SC6464 -0.7794238.,-,. 2CO0. 0000000 459. 5998535 -115. 199951'2 -116.2451935 1.0452423 -0.9073287..... 2000.0000000 479.5998535 -103.3000488 -104.2760315 0.9759827 -0.9448037-'.. 2 COC. 0000000 499.5998535 -92.5000000 -93.0516510 0.5516510 -0.5963791'..... 2000.0000000 519.5998535 -82.8999023 -83.1849213 0.2850189 -.34381C....... 2 CO0. 0000000 53. 5998535 -74.6999512 -74.8662415 0.1662 903 -0.2226110 2COC.0000000 559.5998535 -67.8000488 -67.8438416 0.0437927 -0.0645910.

-262 TABLE LXIV (CONTINUED) C. 28.0 PERCENT MIXTURE PRESSURE TEMPERATURE EXPER. DEPARTURE'.ALC. DEPARTURE DIFFERENCE - ERCENT DIFFERENCE (psia),,(,,(~R).... {Btu/lb), ( Btu/lb) Btu/lb). 500.0000000 219.5999908 -219.6999969 -219.7361450 0.0361481 -0.0164534... 500.0000000 239.5999908 -214.3999939 -213.9856720 -0.4143219 0.1932471....... 500.0000000 259.5998535 -209.COOOOOO -208.8074C36 -0.1925964 0.0921513...500.00295835 -202.80000310 279.5998535-203.2437439 0.4437408-0.218071 500.0000000 299.5998535 -197.2998657 -197.4878082 0.1879425-0.0952572 500.0000000 319.5998535 -190.5998077 -191.6642914 1.0644836 -0.5584914. 500. 0000000 339.5998535 -184.1998596 -185.4840851 1.2842255 -0.6971911... 50 0.00000000 __ 519.5998535 -27.C99S8535 -25.2987976 -1.8010559 6.6459951.. 500.0000000 539.5998535 -24.3000488 -23.0268860 -1.2731628 5.2393417. 500. 0000000 _ __ 559.5998535 -22.1000977 -21.0830688 -1.0170288 4.6019192..~ 500.0000000 579.5998535 -20.3000488 -19.5655518 -0.7344971 3.6182022....... 500. 0000000 599.5998535 -18.7998047 -18.1147308 -0.6850739 3.6440468 500.0000000 619.5998535 -17.3000488 -16.7906189 -0.509S4299 2.9446726.... 500.0000000 _ __ 639.5998535 -16. 1000977 -15.7055397 -0.3945580 2.4506550. 1000.0000000 - -- 219.5999908 -217.4000092 -217.8384857 0.4384766 -0.2016911 1CCO.0000000 239.5999908 -212.0999908 -212.2733154 0.1733246-0.081183 1000.0000000 259.5998535 -206.8000031 -207.0347900 0.2347870 -0.1135333 1000. 0000000 279.5998535 -201.0000000 -201. 5647888 0.5647888 -0.2809894 icoo-0000000 299-5998535.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~0.2809894......... 1CO0.0000000 - -- 299.5998535 -195.5998535 -196.0337372 0.4338837 -0.2218220. 100C.0000000 319.5998535 -189.4998169 -190.3890381' 0.8892212 -0.4692461 1COO.0000000 339.5998535 -183.6998596 -184.4388123 0.7389526 -0.4022605 1000.0000000 0.73e9526 ~~~~~~~~~~~~~~~~~~~~-0.4022605-.... 1000.0000000 359.5998535 -177.0CC0000 -178.0918274 1.0918274-0.6168514. 1C00.0000000 379.5998535 -170.3000031 -171.3118591 1.0118561 -0.5941607 1000.0000000. 1.0118561 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~-0. 5941607 —....... 1000.0000000 _ __ 399.5998535 -161.6998596 -163.9705963 2.2707367 -1.4042902......... 1COC.0000000 539.5998535 -55.8000488 -53.8077698 -1.92291 3.503888 1000.0000000 559.5998535 -48.6999512 -47.3797913 -1.3201599 2.7108030.......... 10C00.0000000 579.5998535 -43.8000488 -42.6066895 -1.1933594 2.7245607 - 1000. 0000000 _ 599.5998535 -39.7998047 -38.6299438 -1.1698608 2.9393625... 1COO.0000000 619.5998535 -36.3000488 -35.3710785 -0.9289703 25591431 1000.0000000 -0.92e9703 ~~~~~~~~~~~~~~~~~~~~~~~~2.5591431 —..... 1000.0000000 _ __ 639.5998535 -33.3999023 -32.6143951 -0.7855072 2.3518238......... 1500.0000000 219.5999908 -215.1000061 -214.9495850 -0.1504211 0.069930 150~~~~~~~~~~~~~~~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~0.000015410069930'7...... 1500.0000000 239.5999908 -209.8000031 -209.3151093 -0.4848938 0.2311219..... 1500.0000000 259.5998535 -204.7000122 -204.0634766 -0.6365356 0.3109602 150C. CO____0___0000 279.5998535 -199.4000092 -198.6932678 -0.7067413 0.3544339.. 1500.0000000 299.5998535 -194.C998535 -193.4026489 -0.6972046 0.3591989.. 1500. 0000000, _3139.5998535 -188.4998169 -187.9442444 -0.5555725 0.2947336...... 1500.0000000 339 5998535 -182.6998596 -182.0074005 -0.6924591 0.3790146......... 1500. 0000000 359. 5998535 -176. 5000000 -175.9835968 -0.516432 0.2925797........ 1500.0000000 379 5998535 -170.5000000 -169.7929535 -0.7070465 0.4146900..... 1500. 0000000 399. 5998535 -163.89S98566 -163.0111237 -0.8887329 0.5422413 -... 1500.0000000 419.5998535 -156.3999023 -155.8802948 -0.5196C75 0.3322300. 1500.0000000 439 5998535 -147.6998138. -147.9449615 0.2451477 -0.1659769..... 1500.0000000 459.5998535 -137.3998108 -138.6822968 1.2824 860 -0.9333968 150C. 0000000 479 5998535 -125.0000031 -127.5434113 2.2434C82 -1.7904291....... 150C.0000000 499. 5998535 -111.6998138 -114.0764008 2.3765869 -2.1276541.. 15CO. 0000000 519.5998535 -98.0998535 -99.8649902 1.7651367 -1.7993259.......... 1500.0000000 539.5998535 -85.9001465 -86.2155304 0.3153839 -0.3671517 1500. 0000000 559. 5998535 -75. 8C00488 -75.2431946 -0.5568542 0.7346354... 1500.0000000 579.5998535 -67.7001953 -66.7154541 -0.9847412 1.4545612.. 1500.0000000 599.5998535 -61.0000000 -59.9455566 -1.0544434 1.7285948..... 1500.0000000 619.5998535 -54.4001465 -54.5367737 0.1366272 -0.2511522...... 1500.0000000 639. 5998535 -49.6999512 -49.9396667 0.2397156 -0.4823253........ 2COC.0000000 219.5999908 -212.8000031 -213.1689758 0.36E9728 -0.1733894....-.. 2C000 0000000 239. 5999908 -207.5999908 -207.5888214 -0.0111694 0.0053803.. 2000.0000000 259.5998535 -202. 6000061 -202.2734833 -0.3265228 0. 1611662...... 2000.0000000 279.5998535 -197.7000122 -196.9940338 -0.7259784 oll60.3570957... 2CC.00000000 299.5998535 -192.5998535 -191.5930481 -1.0068C54 0.5227442.0 2000.0000000 319. 5998535 -187.2998047 -186.3367310 -0.9630737 0.5141880. 2COO.0000000 339.5998535 -181.8998566 -180.6253052 -1.2745514 0.7006884 2000.0000000 359.5998535 -176.2000122 -175.0912170 -1.1C87952 0.6292820..... 2000.0000000 379. 5998535 -170. 5000000 -169.1955261 -1.3044739 0.7650871. 2000.0000000C 399.5998535 -163.7998657 -162.8309326 -0.9689331 0.5915344.. 2000. COOOO 419.5998535 -157.0999146 -156.4238129 -0.6761017 C.4303638. 2000.0000000 _ __ 439.5998535 -149.8998108 -149.4604797 -0.4393311 020'0.2930831 20C0.0000000 459.5998535 -141.8S98108 -142.1370544 0.2372437 -0.1671909..... 2 C000.0000000 479 5998535 -133.2000122 -134.5644684 1.3644562 -1.0243654...... 2000.0000000 499. 5998535 -123.799847 -125.3279724 1.5281677 -1.2343855 2 COC. 0000000 _ __ 519.5998535 -113.7998047 -114.5359497 0.7361450 -0.6468769.. 2000C.0000000 539. 5998535 -103.8000488 -104.8703308 1.07C2820 -1.0310993 2000. 0000000 559.5998535 -94.3000488 -95.3125305 1.0124817 -1.0736799 2000.0000000 579. 5998535 -85.8000488 -86.3955078 0.5954590 -0.6940074... 2000.0000000 5S99. 5998535 -78.0998535 -78.4010773 0.3012238 -0.3856905....... 2C0.00000000 619.5998535 -71.0000000 -71.4418030 0.4418030 -0.6222576...... 2000.0000000_ /... 639.5998535 -64.8999C23 -65.3887939 0.4888916: -0.7533006......

-263 TABLE LXIV (CONTINUED) D. 50.6 PERCENT MIXTURE — PRESSURE - --- TEMPERATURE - EXPER. DEPARTURE CAL."DEPARTURE- DIFFERENCE PERCENT DIFFPEI:NCE (psia)..". (-~R) -.........(Btu/lb)' = (Btu/lb).......(Btu/lb) ____. (Btu/lb)_.... 500.0000000 259.5998535 -212.7998C47 -213.4365540 0.6367493 -0.2992245. 500.0000000 279.5998535 -207.8998108 -208.3826752 0.4828644 -0.2322582, 500.0000000 299.5998535 -202.8999023 -203.6472321 0.7473297 -0.3683243, 500.0000000 319.5998535 -198.2998657 -198.6600647 0.3601990 -0.1816435, 500.0000000 339.5998535 -193.1999054, -193.5580902 0.3581848 -0.1853959.. 500.0000000 359.5998535 -188.0999146 -188.4100800 0.3101654 -0,1648939. 500.0000000 579.5998535 -29.7001953 -27.8946075 -1.8055878 6.0793791. 500.0000000 59C.5998535 -26.5998535 -25.3979950 -1.2018585 4.5182896... 500.0000000 619.5998535 -24. 1999512 -23.2492371 -0.9507141 3.9285774 500.0000000 639.5998535 -22.2001953 -21.4089813 -0.7912140 3.5639944 500.0000000 659.5998535 -20.6999512 -19.9047089 -0.7952423 3.8417587 500.0000000 679.5998535 -19.2001953 -18.5703430 -0.6298523 3.2804470 500.0000000 699.5998535 -18.0000000 -17.3711395 -0.6288605 3.4936686 500.0000000 719.5998535 -16.8000488 -16.1923523 -0.6076965 3.6172304 500.0000000 739.5998535 -15.7998047 -15.0905466 -0.7092581 4.4890299 1000.0000000 259.5998535 -211.0998077 -211.5381470 0.4383392 -0.2076454. 1000.0000000 279.5998535 -206.1998138 -206.6434326 0.4436188 -0.2151402 1000.0000000 299.5998535 -201.3999023 -201.8343353 0.4344330 -0.2157066 1000.0000000 319.5998535 -196.4998627 -196.8405304 O 0.3406677. -0.1733679 1000.0000000 339.5998535 -191.5999146 -191.9116974. 0.3117828 -0.1627259 1000.0000000 359.5998535 -186.6999054. -186.9467773 0.2468719 -0.1322293 1000.0000000 379.5998535 -181.5000000 -181.8092346 0.3092346 -0.1703772 1000.0000000 399.5998535 -176.1999512 -176.5315399 0.3315887 -0.1861889 1000.0000000 419.5998535 -170.7999573 -170.8943787 0.0944214 -0.0552818 1000.0000000 439.5998535 -164.7998047 -165.0761566 0.2763519 -0.1676894 1000.0000000 459.5998535 -158.5998535 -158.8870087 0.2871552 -0.1810563 1000.0000000 599.5998535 -64.5000000 -63.9630127 -0.5369873 0.8325383 1000.0000000 619.5998535 -55.6999512 -55.1568909 -0.5430603 0.9749744 1000.0000000 639. 5998535 -49.7001953. -48.9238434 -0.7763519 1.5620699.. 1000.0000000 659.5998535 -44.8999023 -44.0820770 -0.8178253 1.8214407 1000.0000000 679.5998535 -40.8000488 -40.1949463 -0.6051025 1.4830923 1000.0000000 69. 5998535 -37.6000977 -36.8521881 -0.7479095 1.9891157 1000.0000000 719.5998535 -35.1000977 -34.0541229 -1.0459747 2.9799767 1000.0000000 739.5998535 -32.7998047 -31.5944824 -1.2053223 3.6747847 1500.0000000 259.5998535 -209. 3998108 -209.2494812 -0.1503296 0.0717907 1500.0000000 279.5998535 -204.4998169 -204.1678009 -0.3320160 0.1623551 1500.0000000 299.5998535 -199.8999023 -199.3116302 -0.5882721 0.2942833 1500.0000000 319.5998535 -194.7998657 -194.4917755 -0.3080902, 0.1581573 1500.0000000 339.5998535 -190.0999146 -189.6732025 -0.4267120 0.2244672 1500.0000000 359.5998535 -185.2999115 -184.8447876 -0.4551239 0.2456147 1500.0000000 379.5998535 -180.4000092 -180.0071259 -0.3928833 0.2177845 1500.0000000 399.5998535 -175.1999512 -174.5782013 -0.6217499 0.3548802 1500.0000000 419.5998535 -169.9999542 -169.2781677 -0.7217865 0.4245803 1500.0000000 439.5998535 -164.3998108 -163.9106445 -0.4891663 0.2975467 1500.0000000 459.5998535 -158. 7998657 -158.1855927 -0.6142731 0.3868221 1500.0000000 479.5998535 -152. 8000031 -152.1361237 -0.6638794 0.4344757 1500.0000000 499.5998535 -146.0999603 -145.5708466 -0.5291138 0.3621587. 1500.0000000 519.5998535 -138.2998657 -138.3458405 0.0459747 -0.0332428 1500.0000000 539.5998535 -129.3999634 -130.5618744 1.1619110 -0.8979220 1500.0000000 559.5998535 -119.8000031 -121.1949463 1.3949432 -1.1643925 1500.0000000 579.5998535 -108.5000000. -110.3257751 1.8257751 -1.6827412 1500.0000000 599.5998535 -97.1999512 -99.1565399 1.9565887 -2.0129519 1500.0000000 619.5998535 -86.5998535 -87.8372803 1.2374268 -1.4289007 1500.0000000 639.5998535 -77.5000000 -77.6985779 0.1985779 -0.2562295 1500.0000000 659.5998535 -69.3000488 -69.4961395 0.1960907 -0.2829589 1500.0000000 679.598535 -63.0000000 -62.8487396 -0.1512604 0.2400958 1500.0000000 699.5998535 -57.6999512 -57.2648468 -0.4351044 0.7540807 1500.0000000 719.5998535 -53.1000977 -52.5844574 -0.5156403 0.9710718 1500.0000000 739.5998535 -49.3999023 -48.5066986 -0.8932037 1.8081074 2000.0000000 259.5998535 -207.5998077 -207.8436737 0.2438660 -0.1174693 2000.0000000 279.5998535 -202.9998169 -202.9090576 -0.0907593 0.0447090 2000.0000000 299.5998535 -197.9999084 -197.9739075 -0.0260010 0.0131318 2000.0000000 319.5998535 -193. 2998657 -193.1004028 -0.19S4629 0. 1031883 2000.0000000 339.5998535 -188.4999084 -188.2640686 -0.2358398 0.1251140 2000.0000000. 359. 5998535 -183.6999054 -183.5434113 -0.1564941 0.0851901 2000.0000Q00 379.5998535 -178.8000031 -178.6508179 -0.1491852 0.0834368 2000.0000000 3.99.5998535 -173.8999634 -173.6158600 -0.2841034 0.1633717 2000.0000000 419.5998535 -168.9999542 -168.7568359 -0.2431183 0*1438569 2000.0000000 439.5998535 -163.8998108 -163.5118713 -0.3879395 0.2366930 2000.0000000. 459.5998535 -158.4998627 -158.0872192 -0.4126434 0.2603431 2000.0000000 479.5998535 -153.0000000 -152.6286469 -0.3713531 0.2427145 2000.00.00000 499.5998535 -147.1999512 -146.6492767 -0.5506744 0.3740996. 2000.0000000 519.5998535 -140.8998566 -140.9973907 0.0975342 -0.0692223 2000.0000000 539.5998535 -134.0999603 -134.6815338. 0.5E15735 -0.4336864 2000.0000000 559.5998535 -126.9000092 -128.5209351 1.6209259 -1.2773247 2000.0000000 579.5998535 -119.0000000 -120.7305603 1.7305603 -1.4542513 200C.0000000.599.5998535 -110.7998047 -110.8277435 0.0279388 -0.0252156 2000,0000000 619.5998535 -102.6999512 -102.6545715 -0.0453796 0.0441866 2000.0000000 639.5998535 -94.6000977. -95.1943207 0.5942230 -0.6281421 2000.0000000 659.5998535 -86,8999023 -87.7607880 0.8608856 -C.9906635 2000.0000000 679.5998535 -80.0000000 -80.5902405 0.59C2405 -0.7378004. 2000.0000000 699.5998535 -73.8999023 -74.2270966 0.3271942 -0.4427530 2000.0000000 71. 5998535 -68.4001465 -68.3797455 -0.0204010 0.0298260 2000.0000000 739.5998535 -63.5998535 -63.1242065 -0.4756470 0.7478740

-264TABLE LXIV (CONTINUED) E. 76.6 PERCENT MIXTURE RESSURE TEMPERATURE EXPER. DEPARURE AL. DEPARTURE D IFFjEREJN-eCE - PERCENT DIFFERENCE. (psia) (R() (Btu/lb) (Btu/lb) (Btu/lb) 500.0000000 259.5998535 -215.0998535 -216.0159760 0.9161224 -0.4259C53. 500.0000000 279.5998535 -210.4998169 -211.0794220 0.5796051 -0.2753471 500.0000000 299.5998535 -205.9999542 -206.1875153 0.1875610 -0.0910490 500.0000000 319.5998535 -201.4999542 -201.6920776 0.1921234. -0.0953466 500.0000000 339.5998535 -196.9908169 -197.3670197 0.13672028 -0.1863975 50C.COOOOOO 359.5998535 -192.6998596 -192.8692474 0.1693878 -0.0879024 500.0000000 379.5998535 -188.0998535 -188.2959747 0.1961212 -0.1042644 50C.0000000 399.5998535 -183.5998077 -183.8383789 0.2385712 -0.1299408. 500.0000000 419.5998535 -178.'8998566 -179.2449188 0.3450623 -0.1928801 500.0000000 439.5998535 -174.2999573 -174.4692841 0.1693268 -0.0971467 500.0000000 459.5998535 -169.3999023 -169.8678589 0.4679565 -0.2762437 500.0000000 619.5998535 -35.1000977 -34.1748047 -0.9252930 2.6361542. 500.COOOOO0, 639.5998535 -31.0000000 -30.2193756 -0.7806244 2.5181427 50C0.0000000 659. 5998535 -27.8999023 -27.2233734 -0.6765289 2.4248428 500. 0000000 679.5998535 -25. 3999023 -24.8325653 -0.5673370 2.2336187 500.0000000 699.5998535 -23.3999023 -22.8972473 -0.5026550 2.1481066 500.0000000 _ __ 719.5998535. -21.6999512 -21.3358612 -0.3640900 1.6778374 500.0000000 739.5998535 -19.9001465 -19.8022156 -0.0979309 0.4921112500.0000000 759.5998535 -17.6999512 -18.6399384 0.9399872 -5.3106766 10C0.0000000 259. 5998535 -213.0998535 -214.0740051 0.9741516 -0.4571.337 1000.0000000 279.5998535 -208.3998108 -209.1317596 0.7319489 -0.3512233 100C.0000000 299.5998535 -204.0999603 -204.4316711 0.3317108 -0.1625236 1000.0000000 319.5998535 -199.6999512 -200.0546722 0.3547211 -0.1776270 1CO.O00000000 339.5998i35. -195.2998047 -195.6636S63 0.3638916 -0.1863246 1000.0000000 359.5998535 -190.8998566 -191.1503754 0.2505188 -0.1312305 10CC.0000000 379.5998535 -186.5998535 -186.7207184 0.1208649 -0.0647722 1000.0000000 399.5998535 -182.2998047 -182.1741638 -0.1256409 0.0689198 1COC.0000000 419.5998535 -177.7998657 -177.7269287 -0.0729370 0.0410220 1C00O. 0000000 439.5998535 -173.5999603 -173.1340179 -0.4659424 0.2684000 1CO0.0000000 45. 5998535 -169.2999115 -168.4081879 -0.8917236 0.5267121 1COO. 0000000 479.5998535 -164.3999023 -163.4295044 -0.9703979 0.5902666 1000.0000000 499.5998535 -159.2998657 -158.4062347 -0.8936310 0.5609739 ICOO.0000000 519. 5998535 -153.7000122 -153.0404663 -0.6595459 0.4291121 1000.0000000 539.5998535 -148.0999603 -147.2147064 -0.8852539 0.5977407 1COC. 00000000 559.5998535 -141.7998657 -140.7905579 — 1.C093C79 0.7117830 1000.0000000 579.5998535 -134.2999573 -133.4449310 -0.8550262 0.6366540. 1COC. 0000000 599.5998535 -'-125.i98596 -124.8813477 -0.3185120 0.2544028 100C.0000000 619.5998535 -112.6000977 -113.3713989 0.7713013 -0.6849915 1000.0000000 639.5998535. -94.40C1465 -96.1907349 1.7905884 -1.8968058 1CCC.0000000 659.5998535 -77.0998535 -76.7966156 -0.3032379 0.3933053 1000.0000000 679.5998535 -65.3000488 -63.6920471 -1. 6080017 2.4624805 1COC.0000000 699.5998535 -55.80C0488 -55,2490692 -0.5509796. 0.9874176 1COO.0000000 719.5998535 -49.5000000 -49.2533264 -0.2466736 0.4983302 100C.000000000 739.5998535 -44.8000488 -44.6920166 -0.1080322 0.2411430 1000.0000000 759.5998535 -41.8999023 -40.8411102 -1.0587921 2.5269556 1500.0000000, 259.5998535 -211.2998657 -211.9787292 0.6788635 -0,3212796 1500.COOOOO0 279.5998535 -206.8998108 -207.2814789 0.3816681 -0.1844699 1500.0000000 299.5998535 -202.5999603 -202.5853119 -0.0146484 0.0072302 1500. 0000000 319.5998535 -198.0999603 -197.9884338 -0.1115265 0.0562981 1500.0000000 339.5998535 -193.8998108 -193.5381317 -0.3616791 0.1865288 150C.0000000 359.5998535 -189.3998566 -189.2272491 -0.1126074, 0.0911338 1500.0000000 379.5998535 -185.2998657 -184.8013611 -0.4985046 0.2690259 1500.0000000 399. 5998535 -180.7998047 -180.5911407 -0.2086639 00.1154116 1500.0000000 419.5998535 -176.2998657 -176.2270050 -0.0728607 0.0413277 1500.0000000 439.5998535 -171.9999542 -171.7733612 -0.2265930 0.1317401 1500.0000000 459.5998535 -167.4999084 -166.9301605 -0.5697479. 0.3401482 1500.0000000 479.5998535 -162.9999084 -162.2540436 -0.7458649 0.4575859 1500.COOOOO0 499.5998535 -158.1998596 -157.5592651 -0.6405945 0.4049271 150C. 0000000 519.5998535 -153.1000061 -152.5584564 -0.5415497 0.3537228 150C000000.COOOOO 539.5998535 -148.1999512 -147.2889099 -0.9110413 0.6147377 1500.0000000 559.5998535 -142.7998657 -142.0412140 -0.7586517 0.5312688 1500.0000000 579.5998535 -136.6999512 -136.2548065 -0.4451447 0.3256363 150C. 0000000 599. 5998535 -130.1998596 -129.7807159 -0.4191437 0.3219233 1500.0000000 619.5998535 -123.1999512 -122.8943024 -0.3056488 0.2480916 150C.0000000 639.5998535 -115.0000000 -115.0190887 0.0190887 -0.0165989 1500.0000000 659.5998535 -106.5998535 -105.9700928 -0.6297607 0.5907707 1500.00OO0000 679.5998535 -97.0000000 -96.5324860 -0.4675140 0.4819732 1500. 0000000 699.5998535 -86.8000488 -87.1248169 0.3247681 -0.3741565 1500. 0000000 6719.5998535 -77.500000 -78.2465820 0.7465820 -0.9633313 1500.0000000 739.5998535 -70.3000488 -70.6694489 0.3694000 -0.5254619 150C0. 0000000 75. 5998535 -63.3999023 -64.1792145 0.7793121 -1.2292004 2 CO0.0000000 259.5998535 -209.4998627 -210.9630432 1.4631805 -0.6984159 20C00. 0000000 279.5998535' -205.1998138 -206.0866547 0.8868408 -0.4321839 200C0.0000000 299.5998535 -200. 8999634 -201.4947968 0. 5948334 -0.2960843 2CO0.0000000 319.5998535 -196.4999542 -197.1403961 0.6404419 -0.3259246 200C.0000000 339.5998535 -192.3998108 -192.5645142 0.1647034 -0.0856047 2000.0000000 359.5998535 -188.1998596 -188.0761566 -0.1237030 0.0657296 2COC.COOO00 0 379.5998535 -184.0998535 -183.79C4205 -0.30S4330 0.1680788. 2000.0000000 399.5998535 -179.8998108 -179.4332886 -0.4665222 0.2593233 2CO0.0000000 419.5998535 -175.6998596 -175.2061157 -0.4937439 0.2810155 2000.0000000 439.5998535 — 171.1999512 -170.6735535 -0.5263977 0.3074753 2000.0000000 455.5998535 -166.6999054 -166.2579803 -0.4419250 0.2651021. 2000.0000000 479.5998535 -160.0999146 -161.9475708 1. 8476562 -1.1540642 200C.0000000 499.5998535 -157.5998535 -157.1962585 -0.4035950 0.2560884 2000.0000000 519.5998535 -153.1000061 -152.5149689 -0.5850372 0.3821275 2000.0000000 539.5998535 -148.4999542 -147.6849060 -0.8150482 0.5488541 2COC.0000000 559.5998535 -143.5998535 -142.9332275 -0.6666260 0.4642244 2000.0000000 579.5998535 -138.49S9542 -137.5990753 -0.9008789 0.65C4539. 2 CCC. 0000000 599.5998535 -133.0998535 ~ -132.6007233 -0.4991302 0.3750043 2000. 0000000 619.5998535 -127.1999512 -126.8971252 -0.3028259 0.2380707 2 COC. 0000000 639.5998535 -121.0000000 -121.1513214 0.1513214 / -0.1250589 200C.000000 659.5998535 -114.6999512 -114.6189880 -0.0809631 0.0705869 2000.0000000 679. 5998535 -107. 60CC00977 -106. 8897247 -0.7103729 0.66C1970 2000.0000000 699.5998535 -100.3999023 -99.7025604 -0.6973419 0.6945640 2000.0000000 719.5998535 -93.3000488 -93.3039856 0.0039368 -0.0042195 2 CO. 0000000 739.5998535 -86.4001465 -86.8682861 0.4681396 -0.5418271 20CC. 0000000 759. 5998535 -80.3000488 -80.8584290 -- 0.5583801 -0.6953667

-265 TABLE LXV RESULTS OF CORRESPONDING STATES CORRELATION FOR METHANE-PROPANE MIXTURES USING OPTIMUM PARAMETERS WITH SMOOTH PSEUDOCRITICAL TEMPERATURES A. 5.1 PERCENT MIXTURE PRESSURT —- TEMPERATUE EXPER. EPRTURE CALC. DEPARTURE DI —NE P T DIFFERENCE (psia) (~K) (Btu/lb) (Btu/lb) (Btu/lb) 00. 0000000 179.5999908 -223.5000000 -223.6318359 0.1318359 -0.0589870 5Q0.0000000 199.5999908 -217.6999969 _ -217.4304962 -0.2695007 0.1237945 500.0000000 219.5999908 -209.6999969 -211.6576538 1.9576569 -0.9335510 500 0000000 239.5999908 -203.7999573 -205.2513428 1.4513855 -0.7121615 500.0000000 259.5998535 -196.9000092 -198.5638275 1.6638184 -0.8450065...,l.,.,.:,.. 500.0000000 279.5998535 -190.3999634 _ -191.0784302 0.6784668 -0.3563376 500.0000000 299.5998535 -182.3998566 -183.0291901 0.6293335 -0.3450295 500.0000000 319.5998535 -172.3000031 __ -172.6023102 0.3023071 -0.1754539 500.0000000 419.5998535 -27.8000488 -26.7770691 -1.0229797 3.6797762 500.0000000 439.5998535 -24.9001465 -24.0481415 -0.8520050 3.4216862 500.0000000 459.5998535 -22.5000000 -21.6835175 -0.8164825 3.6288109 500.0000000 479.5998535 -20. 3999023 -19.9320984 -0.4678040 2.2931671 500.0000000 499.5998535 -18.6999512 -18.3113556 -0.3885956 2.0780563 500.0000000 519.5998535 -17.3000488 -16.9819641 -0.3180847 1.8386345 1000.0000000 179.5999908 -221.5000000 -221.8489990 0.3489990 -0.1575616 1000.0000000 199.5999908 -215.4000092 -215.7433777 0.3433685 -0.1594096 1000.0000000 219.5999908 -208. 1999969 -210.0404816 1.8404846 -0.8839983 1000.0000000 239.5999908 -202.2999573 -203.9433899 1.6434326 -0.8123741........... 1000.0000000 259.5998535 -195.5000000 -197.6898346 2.1898346 -1.1201191 1000. 0000000 279.5998535 -189.1999512 -190.6936951 1.4937439 -0.7895052. 1000.0000000 299.5998535 -182.0998535 -183.1223145 1.0224609 -0.5614836 1000.0000000 319. 5998535 -173. 6000061 -174.7048492 1 ~ 1048431 -0.6364301 1000.0000000 339.5998535 -163.3999023 -164.5803680 1.1804657 -0.7224396 1000.0000000 359. 5998535 -149. 7998047 -150.9364166 1. 1366119 -0.7587537 3 7.... 1000.0000000 379.5998535 -125.4998169 -128.9161835 3.4163666 -2.7222080 1000.0000000 399.5998535 -88.8999023 -89.5667877 0.6668854 -0.7501528 1000.0000000 419.5998535 -68.5000000 -68.3029938 -0.1970062 0.2876003 1000. 0000000 439.5998535 -56.8000488 -56.2066345 -0.5S34143 1.0447416. 1000.0000000 459.5998535 -49.2001953 -48.4727478 -0.7274475 1.4785452 1000.0000000 479.5998535 -43.5000000 -43.0586243 -0.4413757 1.0146561 1000.0000000 499.5998535 -39.0998535 -38.7781219 -0.3217316 0.8228458 1000.0000000 519.5998535 -35.6000977 -35.2352295 -0.3648682 -1.0249071 1500.0000000 179.5999908 -219.3999939 -218.0461121 -1.3538818 0.6170835 1500.0000000 199.5999908 -213.1999969 -212.0303650 -1.1696320 0.5486078 1500.0000000 219.5999908 -206. 3999939 -206.4029541 0.0029602 -0.0014342 1500.0000000 239.5999908 -200.8995634 -200.5047607 -0.3952026 0.1967161 1500.0000000 259.5998535 -194. 3000031 -194.3301086 0.0301056 -0.0154944 1500.0000000 279.5998535 -187. 8995634 -187.6579742 -0.2419891 0.1287861. 150C.0000000 299.5998535 -181.0998535 -180.6305695 -0.4692841 0.2591299 1500.0000000 319.5998535 -173.7000122 -172.9298706 -0.7701416 0.4433743 1500.0000000 339.5998535 -165.4999084 -164.5115662 -0.988342-3 0.5971856 1500.0000000 359.5998535 -155.3998108 -154.4683075 -0.9315033 0.5994234;-..,... 1500.0000000 379.5998535 -143.0998077 -142.7532196 -0.3465881 0.2422003 1500.0000000 399.5998535 -127.4999084 -127. 3916321 -0.1082764 0.0849227 1500.0000000 419.5998535 -108.8000031 -108.2607117 -0.5392914 0.4956718 1500.0000000 439.5998535 -91.1999512 -90.2763367 -0.9236145 1.0127354 1500.0000000 459.5998535 -77. 6000977 -76.7010498 -0.8990479 1.1585646 1500.0000000 479.5998535 -67.5998535 -66.9355621 -0.6642914 0.9826816 1500.0000000 499.5998535 -60.0000000 -59.7538757 -0.2461243 0.4102070 1500.0000000 519.5998535 -54.0000000 -53.9082794 -0.0917206 0.1698529 2000.0000000 179.5999908 -217.2999878 -215.7217407 -1.5782471 0.7262986 2000.0000000 199.5999908 -211.1000061 -209.6983643 -1.4016418 O0.6639704 2000.0000000 219.5999908 -204.7999878 -204.0653229 -0.7346649 0.3587231 2CO0.0000000 239.5999908 -199.5999603 -198.1613159 _ -1.4386444 0.7207636...... 2000.0000000 259.5998535 -193. 1000061 -192.1994476 -0.9005585 0.4663687 2000.0000000 279.5998535 -186.6999512 -185.8863373 -0.8136139 O0.4357867............. 2000.0000000 299.5998535 -180.1998596 -179.3311768 -0.8686829 0.4820660 2000.0000000 319.5998535 -173.2000122 -172.1945801 -1.0054321 0.5805034 2000.0000000 339.5998535 -165.3999023 -164.5603638 -0.8395386 0.5075808 2000.0000000 359.5998535 -156.9998169 -156.0212555 -0.9785614 0.6232880 2000.0000000 379.5998535 -147.4958169 -146.8545380 -0.6452789 C.4374776...... 2000.0000000 399.5998535 -136.6999054 -136.3205414 -0.373 640 0.27'75159. 2000.0000000 419.5998535 -124.5000000 -125.2012177 0.7012177 -0.5632270 2000.0000000 QO 439.5998535 -111.5999603__ -112.2586365 0.6586761 -0.5902115 2000.0000000 459.5998535 -99.0000000 -99.3920441 0.3920441 -0.3960039 2000.0000000 479. 5998535 -87. 5998535 -88.1770325 _ _ _ 0.5771790 -0.65888CS 2000.0000000 499.5998535 -78.0998535 -78.7508850 0.6510315 -0.8335884 2000O.0000000 519.5998535 -70.3000488 -70.9214172 0___.6213684 -0.8838803

-266 TABLE LXV (CONTINUED)'B. 11.7 PERCENT MIXTURE PRESSURE: - TEMPERATURE " EXPER. DEPARTUREi -CALC. EPA RURE. DIFFERENCE PERCENT DIFFERENCE(psia)......(OR) _....... (Btu/lb) (Btu/lb) (Btu/lb) 500.0000000 199.5999908 -223.6999969 -223.0068207 -0.6931763 0.3098686 500 0000000 219.5999908 -218.0999908 -217.1113892 -0.9886017 0.4532788500.0000000 239.5999908 -212.0999146' -211.0460510 -1.0538635 0.4968710-...... 500.0000000 259.5998535 -205.7000122 -204.5604553 -1.1395569 0.5539894. 500.0000000 279.5998535 — 198.7998657 -197.9233704 -0.8764954 0.4408933 500.0000000 299.5998535 -191.2999115 -190.5954132 -0. 7044983 0.3682690 500.0000000 319.5998535 -181.8999634 -182.7186432 0.8186798 -0.4500713 500.0000000 479.5998535 -24.5998535 -22.7081757 -1.8916779 7.6897917 500.0000000 499.5998535 -20.9001465 -20.7657623 -0.1343842 0.642981.. 500.0000000 519.5998535 -18. 6999512 -19.1062469 0.4062 5 8 -2.1727095 500.0000000 539.5998535 -17.3999023 -17.5858459 0.1859436 -1.0686464 500.0000000 559.5998535 -16.8000488 -16.3319092 -0.4681396 2.7865372 1000.0000000 199.5999908 -220.8999939 -221.2240906 0.3240967 -0.1467164 1000.0000000 219.5999908 -215.0999908 -215.3415680 0.2415771 -0.1123092 1000.0000000 239.5999908 -209.2999115 -209.3639832 0.0640717 -0.0306124 1000.0000000 259.5998535 -203.1000061 -203.1998596 0.998535 -0.0491647... 1000.0000000 279.5998535 -196.2998657 -196.8235321 0.5236664 -0.2667685 1000. 0000000 299.5998535 -189.2999115 -189.9216919 0.6217804 -0.3284631 1000. 0000000 319. 5998535 -181.6999512 -182.4802399 0. 7802887 -0.4294376 1000.0000000 339.5998535 -172.9000092 -174.3420105 1.4420013 -0.8340086.... 1000.0000000 359.5998535 -163.8000031 -164.9284210 1.1284180 -0.6888996. 1000.0000000 379. 5998535 _ 1000.0000000 479.5998535 1000.0000000 499. 5998535 1000.0000000 519.5998535 1000. 0000000 539.5998535 1000.0000000 559.5998535 1500. 0000000 199. 5999908 1500.0000000 219.5999908 1500.0000000 239.5999908 1500.0000000 259.5998535 1500. 0000000 279.5998535 1500.0000000 299.5998535 1500.0000000 319.5998535 1500.0000000 339. 5998535 1500.0000000 359. 5998535 1500.0000000 379.5998535 1500.0000000 399.5998535 1500.0000000 419.5998535 1500.0000000 439.5998535 1500.0000000 459.5998535 150C. 0000000 479.5998535 1500. 0000000 499. 5998535 1500.0000000 519.5998535 1500.0000000 539.5998535 1500.0000000 559.5998535 2000.0000000 199.5999908 -150.2999115 -52.8999023 -45.9001465 -40.8000488 -37.0998535 -34. 1999512 -218.0000000 -212.1999969 -206.3999023 -200. 5000000 -193.8998566 -187. 3999023 -180.3999634 -173.0000000 -165.0000000 -155.5999146 -144.3000031 -130.1998596 -113. 4998169 -97. 5000000 -83.5000000 -72. 5000000 -64. 1999512 -57.3999023 -52.1000977 -215.2999878 -152.6010284 -51.7379303 -45.5902863 -40.8630066 -37.0459137 -33.8877258 -217.8262177 -211.9238281 -206.0637970 -200.1178741 -193.9117432 -187.1718597 -180.2784119 -172.7988586 -164.7543640 -155.5247192 -144.7363434 -131. 3392029 -114.7121124 -97.1982269 -82.4818115 -71.5636292 -63.3362732 -56.9979706 -51.7556305 -215.7375946.. 2.3011169 -1.1619720 -0.3098602 0.0629578 -0.0539398 -0.3122253 -0.1737823 -0.2761688 -0.3361053 -0.3821259 0.0118866 -0.2280426 -0.1215515 -0.2011414 -0.2456360 -0.0751953 0.4363403 1.1393433 1.2122955 -0.3017731 -1.0181885 -0.9363708 -0.8636780 -0.4019318 -0.3444672 0.4376068 -1.5310163 2.1965485 0.6750743 -0.1543080 0.1453909 0.9129409 0.0797166 C.1301455 0.1628418 0.1905864 -0.0061303 0.1216877. 0.0673789 0.1162666 T 0.1488702 0.0483260 -0.3023841 -0.8750725. -1.0681028.. 0.3095108 1.2193871 1.2915449. _ 1.3452930 C.7002305 0.6611637 -0.2032544 2 0UUUO. UUUUUUU 219. 5_999YU0 -209. 39-99939 -20g.U f4T!134 0O. 47493195 -O.ZZe.Af2 2000.0000000 239.5999908 -203.8999023 -204.0192261 0.1193237 -0.0585207 2000.0000000 259.5998535 -198.0000000 -198.0189514 0.0189514 -0.0095714.... 2000.0000000 279.5998535 -191.5998535 -192.0462036 0.4463501 -0.2329595... 2000.0000000 299.5998535 -185.4999084 -185.6760712 0.1761627 -0.0949664 2 COC.0000000 319.5998535 -179.2999573 -179.1514740 -0.1484833 0.0828127 2000.0000000 339.5998535 -172.6000061 -172.2033844 -0.3966217 0.2297924 2000.0000000 359.5998535 -165.4000092 -164.8913727 -0.5086365 0.3075190 2000.0000000 379.5998535 -157.3999023 -156.9180145 -0.4818878 0.3061551 2000.0000000 399.5998535 -148.5000000 -148.3316650 -0.1683350 0.1133568 2000.0000000 419.5998535 -138.3998566 -139.0845490 0.6846924 -0.4947204 2C00.0000000 439.5998535 -127.0998077 -127.8479462 0.7481384 -0.5886227 2 00. 0000000 459.5998535 - 115.1999512 -115.9387665 0.7388153 -0.6413329 2000.0000000 479.5998535 -103.3000488 -104.1500397 0.8499908 -0.8228365 2000.0000000 499.5998535 -92.5000000 -93.0359802 0.5359802 -0.5794380. 0000000000 519. 5998535 200. 0000000 539.5998535 2000.0000000 559.5998535 -82.8999023 -74.6999512 -67.8000488 -83.1945953 -74.8671112 -67.8381500 0*2946530 0.1671600 0.0381 012 -0.3554805 -0.2237753 -0.0561964

-267 TABLE LXV (CONTINUED) C. 28.0 PERCENT MIXTURE — PREESURE. —.-..-TEMPERTURE —---— EXPER.~FEPAR~TURE~ —6~T-rCEPST U -DIFFERE.DiFP~NmCE PERCENT DIFFERENCE_(psia)__ < (~R)_ (Btu/lb) (Btu/ib)_ (Btu/lb_ 500.0000000 219.5999908 -219.6999969 -219.7362C61 0.0362091 -0.0164812 500.0000000 239.5999908 -214.3999939.. _-213.9856720 -0.4143219 0.1932471 500.0000000 259.5998535 -209.0000000 -208.8074036 -0.1925964 0.0921513 500,0000000 279.5998535 -202.8000031 -203.2437439 0.4437408 -0.2188071 500.0000000 299,.5998535 -197.2998657 -197.4878082 0.1879425 -0.0952572 500. 0000000 319.5998535 -190.5998077 -191.46642914 1.0644836 -0.5584914 500.0000000 339.5998535 -184.1998596 -185.4840851 1.2842255 -0.6971911 500.0000000 519.5998535 -27.0998535 -25.2987976 -1. -8010559 6.6459951 500.0000000 539.5998535 -24.3000488 - 230268a6 0 -1.2731628 5.2393417.. 500.0000000 559.5998535 -22.1000977. -21.0830688 -1.0170288 4.6019192 500.0000000 579.5998535 -20.3000488 -19.5655518 -0.7344971 3.6182022 500.0000000 599.5998535 -18.7998047 -18.1147308 -0.6850739 3.6440468 500.0000000 619.5998535 -17.3000488 -16.7906189 -0.5094299 2.9446726 500.0000000 639.5998535 -16.1000C977 -15. 7055397 -0.3945580 2.4506550 1000.0000000 219.5999908 -217.4000092 -217.8384857 - 0.4384766 -0.2016911 1000.0000000 239.5999908 -212.0999908 -212.2733459_ 0.1733551 -0.0817327.... 1000.0000000 259.5998535 -206.8000031 -207.0347900 0.2347870 -0.1135333 1000.0000000 279.5998535 -201.0000000 -201.5647888 0.5647888 -0.2809894 1000.0000000 299.5998535 -195.5998535 -196.0337372 0.4338837 -0.2218220 1000. 0000000 319.5998535 -189. 4998169 -190. 3891144'0.8892975 -0.4692863. 1000.0000000 339.5998535 -183.6998596 -184.4388123 0.7389526 -0.4022605 1000.0000000 359.5998535 -177.0000000 __-178. 0918274 1.0918274 -0.6168514.. 1000.0000000 379.5998535 -170.3000031 -171.3119202 1.0119171 -0.5941964...... 1000.0000000 399.5998535 -161.6998596 ____ -163.9705811 2.2707214 -1.4042807.... 1000.0000000 539.5998535 -55.8000488 -53.8077698 - 1.9922791 3.5703888.. 1000.0000000 559.5998535 -48.6999512 _____ -47.3797913 -1.32C1599 2.7108030.. 1COO. 0000000 579.5998535 -43.8000488 -42.6066895 -1.1933594 2.7245607... 1000.0000000 599.5998535 -39.7998047 -38.6299438 -1.1698608 2.9393625-...... 1000.0000000 619.5998535 -36.3000488 -35.3710785 -0.9289703 2.5591431 1000.0000000 639.5998535 -33. 3999023 _-32. 6143951 -0.7855072 2.3518238... 1500.0000000 219.5999908 -215.1000061 -214.9496307 -0.1503754 0.0699095.... 1500.0000000 239.5999908 -209.800.0031 -209.3151C93 -0.4848938 0.231121 9__ 1500.0000000 259.5998535 -204.7000122 -204.0634766 -0.6365356 0.3109602 1500.0000000 279.5998535 -199.4000092 -198.6932678 -0.7067413 0.3544339... 1500.0000000 299.5998535 -194.0998535 -193.4026489 -0.6972046 0.3591989 1500.0000000 319.5998535 -188.4998169 -187.9442444 -0.5555725 0.2947336.... 1500.0000000 339.5998535 -182.6998596 -182.0074005 -0.6924591 0.3790146 1500.0000000 _ __ 359.5998535 -176.5000000 -175.9835968 -0.5164C32 0.2925797.... 1500.0000000 379.5998535 -170.5000000 -169.7929535 -0.7070465 0.4146900 1500. 0000000 399.5998535 -163.8998566 -163.0111542 -0.EE87C24 0.5422227... 1500.0000000 419.5998535 -156.3999023 -155.8802948 -0.5196075 0.3322300.. 1500.0000000 439.5998535 -147.6998138 -147.9449615 0.2451477 -0.1659769... 1500.0000000 459.5998535 -137.3998108 -138.6822 68 1.2824860 -0.9333968 1500.0000000 479.5998535 _ -125.3000031 -127.5434113 ___ 2.2434082 -1.7904291. 1500.0000000 499.5998535 -111.6998138 -114.0764008 2.3765E69 -2.1276541 1500.0000000 519.5998535 -98.0998535 -99.8649902 1.7651367 -1.7993259 1500.0000000 539.5998535 -85.9001465 -86.2155304 0.3153839 -0.3671517 1500.0000000 559.5998535 -75.8000488 -75.2431946 -0.5568542 0.7346354 1500.0000000 579.5998535 -67.7001953 -66.7154541 -0.9847412 1.4545612 1500.0000000 599.5998535 -61.0000000 -59.9455566'-1.0544434 1.7285948... 1500.0000000 619.5998535 -54.4001465 -54.5367737 0.1366272 -0.2511522 1500. 0000000 639. 5998535 -49.6999512 -49.9396667 0.2397156 -0.4823253. 2000.0000000 219.5999908 -212.8000031 -213.1689758 0.3689728 -0.1733894 200C.0000000 239.5999908 -207.5999908 __-207.5888214 -0.0111694 0.0053803. 2000.0000000 259.5998535 -202.6000061 -202.2735138 -0.3264923 0.1611511 2000.0000000 279.5998535 -197.7000122 - 6 - 1.969940338 -0.7059784 0.3570957 2000.0000000 299.5998535 -192.5998535 -191.5930481 -1.0068054 0.5227442 2000.0000000 319.5998535 -187.2998047 -186.3367310 -0.9630737 0.5141880 2000.0000000 339.5998535 -181.8998566 -180.6253357 -1.2745209 C.7006716 2000.0000000 359.5998535 -176.2000122 -175.0912170 -1.1087952 0.6292820 2000.0000000 379.5998535 -170.5000000 -169.1955566 -1.3044434 0.7650692 2000.0000000 399.5998535 -163.7998657 _ -162.8309326 -0. 9689331 0.5915344 2000.0000000 419.5998535 -157.0999146 -156.4238129 -0.6761017 0.4303638 2000.0000000 439.5998535 -149.8998108 -149.4604797 -0.4393311 0.2930831 2000.0000000 459.5998535 -141.8998108 -142.1370239 0.2372131 -0.1671694 2000.0000000 479.5998535 -133.2000122___ -134.5644989 1.3644867 -1.0243893 2000.000000 499.5998535 -123.7998047 -125.3279724 1.5281677 -1.2343855 2000.0000000 519.5998535 -113.7998047 -114.5359497 0.7361450. -C.6468769 200C.0000000 539.5998535 -103.8000488 -104.87033088 ~1.0702820e2 -1.0310993 2C0C. 0000000 --- 559.5998535 -94.3000488 -95.3125305 1.0124817 -1.0736799 2000.0000000 579.5998535 -85.8000488 -86.3955078 0.5954590 -0.6940074 2000. 0000000 599.5998535 -78.0998535 ______ _-78.4010315 0.301178C..-0.3856319 - 2000.0000000 619.5998535 -71.0000000 -71.4418030 0.4418030 -0.6222576 2000.0000000 639.5998535 -64.8999023 -65.3888245 0.4889221 -0.7533479

-268TABLE LXV (CONTINUED) D. 50.6 PERCENT MIXTURE -"PRSREh TEMPERATURE — EXPER.DEP'ITURE CJALG * DEPARTURE DIFFERENCE PERCENT DIFFERENCE (Psia) ((E) (Btu/lb) (Btu/lb)'(Btu/lb) 500 0000000 259.5998535 -212.7998047 -213.3624878 0.5626831 -0.2644190 500.0000000 279.5998535 -207.8998108 -208.3149261 0.4151154 -0.1996709 500.0000000 299.5998535 -202.8999023 -203. 5897675 O0.6898651 -0.3400027 500.0000000 319.5998535 -198.2998657 -198.6142731 0.3144073 -0.1585514 500.0000000 339.5998535 -193.1999054 -193.5208435 0.3209381 -0.1661171... 500. 0000000 359.5998535 -188.0999146 -188.3823090. 0.2823944 -0.1501300. 500.0000000 579. 5998535 -29.7001953 -27.8154144 -1.8847809 6.3460169.. 500.0000000 599.5998535 -26. 5998535 -25.3229980 -1.2768555 4.8002338 500. 0000000 619.5998535 -24.1999512 -23.1920776 -1.0078735 4.1647739 500.0000000 639.5998535 -22.2001953 -21.3625031 -0.8376923 3.7733545 500.0000000 659.5998535 -20.6999512 -19.8561401 -0.8438110 4.0763903 500.0000000 679.5998535 - -19.2001953 -18.5359192 -0.6642761 3.4597359. 500.0000000 699.5998535 -18.0000000 -17.3280334 -0.6719666 3.7331467 500.0000000 719.5998535 -16.8000488 -16.1573486 -0.6427002 3.8255844 500. 0000000 739.5998535 -15. 7998047 -15.0561409 -0.7436638 4.7067900 1000.0000000 259.5998535 -211.0998077 -211.4761200 0.3763123 -0.178-2627........ 1000.0000000 279.5998535 -206.1998138 -206.5892334 0.3894196 -0.1888554 1000.0000000 299.5998535? -201.3999023 -201.7908478 0.3909454 -0.1941140 1000.0000000 319.5998535 -196.4998627 -196.8105011' 0.3106384 -0.1580858 1000.0000000 339.5998535 -191.5999146 -191.8905334 0. 2906189 -0.1516801. 1000.0000000 359.5998535 -186.6999054 -186.9299469 0.2300415 -0.1232145. 1000.0000000 379.5998535 -181.5000000 -181.8016968 0.3016968 -0.1662241 1000. 0000000 399.5998535 -176.1999512 -176.5414581 0.3415070 -0.1938178_... 1000.0000000 419o 5998535 -170. 7999573 -170.9107666 0.1108093 -0.0648766 1000.0000000 439.5998535 -164.7998047 -165.0961456 0.2963409 -0.1798187.. 1000.0000000 459.5998535 -158.5998535 -158.9174194 0.3175659 -0.2002308 1000.0000000 599. 5998535 -64. 5000000 -63. 8252411 -0.6747589 1.0461369 1000.0000000 619.5998535 -55.6999512 -55.0355377 -0.6644135 1.1928434 1000.0000000 639.5998535 -49.7001953 __ -48.8198700 -0.8803253 1.7712708 1000.0000000 659.5998535 -44. 8999023' -43.9855652 -0.9143372 2.0363894 1000.0000000 679.5998535 -40.8000488 -40.1219482 -0.6781006 1.6620083 1000.0000000 699.5998535 -37.6000977 -36.7792511 -0.8208466 2.1830959 1000. 0000000 719.5998535 -35.1000977 r -33.9914856 -1.10 6121 3.1584291 1000.0000000 739.5998535 -32.7998047 -31.5339203 -1.2658844 3.8594255 1500.0000000 259.5998535. -209.3998108 -209.1833954 -0.2164154 0.1033503 1500.0000000 279.5998535 -204.4998169 -204.1105042 -0.3893127 0.1903731 1500.0000000 299.5998535 -199.8999023 -199.2641144 -0.6357880 0.3180531 1500.0000000 319.5998535 -194.7998657 -194.4530334 -0.3468323 0.1780454 1500.0000000 339.5998535 -190.0999146 -189.6434021 -0.4565125 0.2401434 1500.0000000 359.5998535 -185.2999115 -184.8253937 -0.4745178 0.2560809 1500.0000000 379.5998535: -180.4000092 -179.9970703 -0.4029388 0.2233585 1500.0000000 399.5998535 -175.1999512 -174.5775757 -0.6223755 0.3552372 1500. 0000000 419.5998535 -169.9999542 -169.2830811 -0.7168732 0.4216902 1500.0000000 439.5998535 -164.3998108 -163.9248199 -0.4749908 0.2889242.. 150000000 459. 5998535 -158. 7998657 -158.2054443 -0.5944214 0 0.3743210 1500.0000000 479.5998535 -152.8000031 -152.1599426 -0.6400604 0.4188876.. 1500.0000000 499.5998535 -146.0999603 -145.6017914 -0.4981689 0. 3409781. 1500.0000000 519.5998535 -138.2998657 -138.4087219 0.1088562 -0.0787103 1500. 0000000 539.5998535 -129.3999634 -130.6119843 1.2120209 -0.9366468 1500.0000000 559.5998535 -119.8000031 -121.2412872 1.4412842 -1.2030745 1500.0000000 579.5998535 -108.5000000 -110.3212433 o1.8212433 -1.6785650 1500.00000000 599.5998535 -97. 1999512 -99.1135864 1.9136353 -1.9687614 1500.0000000 619.5998535 -86.5998535 -87.7532349 1.1533813 -1.3318510. 1500. 0000000 639.5998535 -77. 5000000 -77.5964966 0.0964966 -0.1245117 1500.0000000 659.5998535 -69.3000488 -69.3953552 0.0953064 -0.1375272 1500.0000000 679.5998535 -63.0000000 -62.7524719 -0.2475281 0.3929015 1500.0000000 699.5998535 -57.6999512 -57.1692352 -0.5307159 0.9197857 1500.0000000 719.5998535 -53.1000977 -52.4980316 -0.6020660 1.1338310 1500.0000000 739.5998535 -49.3999023 -48.4240875 -0.9758148 1.9753370 _ 2000.0000000 259.5998535 -207.5998077 -207.7725830 0.1727753 -0.0832251 200. 0000000 279.5998535 -202.9998169 -202.8385620 -0.1612549 0.0794359 2000.0000000 299.5998535 -197.9999084 -197.9224548 -0.0774536 0.0391180 2000.0000000 319.5998535 -193.2998657 -193.0569916 -0.2428741 0.1256462 2000.0000000 339.5998535 -188.4999084 -188.2287598 -0.2711487 0.1438455 2 000. 0000000 359. 5998535 -183.6999054 -183.5183105 -0.1815948 0.0988541 2000.0000000'379.5998535 -178. 8000031 -178.6380920 -0.1619110 0.0905542 2000.0000000 399.5998535 -173.8999634 -173.6020966 -0.2978668 0.1712863 2000.0000000 419.5998535 -168.9999542 -168.7507019 -0.2492523 0.1474866 2000.0000000 439. 5998535 -163.8998108 -163. 5073700 -0.3924408 0.2394394 2000.0000000 459.5998535 -158.4998627 -158.0904541 -0.4094086 0.2583022. 2000.0000000 479.5998535 -153.0000000 -152.6328430 -0.3671570 0.2399718 2000.0000000 499.5998535 -147. 1999512 -146.6652832 -0.5346680 0.3632256 200. 0000000 519.5998535 -140.8998566 -140.9657898 O. 0659332 -0.0467944. 2000.0000000 539.5998535 -134.0999603 -134.6620483 0.5620880 -0.4191558 2000.0000000 559.5998535 -126.9000092 -128.4300385 1. 5300293 -1.2056961 2000.0000000 579.5998535 -119.0000000 -120.6824341 1.6824341 -1.413809 2000.0000000 599.5998535 -110. 7998047 -110.8658600 0.0660553 -0.0596168 2000.0000000 619.5998535 -102.6999512 -102.6687012 -0.0312500 0.0304284 2000.0000000 639.5998535 -94. 6000977 -95.1734467 0.5733490 -0.6060764 2000.0000000 659.5998535 -86.8999023 -87.6919403 0.7920380 -0.9114370 2000.0000000 679.5998535 -80.0000000 -80.5114899 0.5114899 -0.6393622 2000.0000000 699.5998535 -73.8999023 -74.1491852 0.2492828 -0.3373249 2 000. 0000000 719.5998535 -68.4001465____ -68.3155670 -0.0845795 0.1236539 2000.0000000 739.5998535 -63.5998535 -63.0513611 -0.5484924 0.8624114

-269TABLE LXV (CONTINUED) E. 76.6 PERCENT MIXTURE?'~PRESSUS RE TEMPERATURE EXPER. DEP-ATURE --- ALC. DEPARTURE - -DIFFERNCE -- PERCENT (psia).... (~R) (Btu/lb) (Btu/lb) (Btu/lb) 500.0000000 259. 5998535 -215.0998535 -215.9630890 0.8632355 -0.4013184 500.0000000 279.5998535 -210.4998169 -211.02 89612 0.5291443 -0.2513751 500.0000000 299.5998535 -205.9999542 -206.1390533 _. 139099_1 -0.0675238 500.0000000 319.5998535 -201.4999542 -201.6459351 0.1459808 -0.0724471 500.0000000 339. 5998535 -196.9998169 -197.3194733 0.3196564 -0.1622622~ 500.0000000 359.5998535 -192.6998596 -192.8189240 0.1190643 -0.0617874 500.0000000 379.5998535 -188.0998535 -188.2440186 _ 0.1441650 -0.0766428 500.0000000 399.5998535 -183.5998077 -183.7898560 0.1900482 - -0.1035122 500.0000000 419. 5998535 -178. 8998566 -179.1966705 0.2968140 -0.1659107 500.0000000 439.5998535 -174.2999573 -174. 4201050 0. 1201477 -0.0689315 500.0000000 459. 5998535 -169.3999023 -169.8145447 0.4146423 -0.2447712 500. 0000000 619.5998535 -35.1000977 -34.3142700 -0.7858276 2.2388182 500. 0000000 639.5998535 -31.0000000 -30.3339081 -0.6660919 2.1486826 500.0000000 659.5998535 -27.8999023 -27.3220062 -0.5778961 2.0713186 500. 0000000 679.5998535 -25. 3999023 -24. 9154816 -0.4844208 1.9071751 500.0000000 699.5998535 -23.3999023 -22.9706421 -0.4292603 1.8344526 500. 0000000 719.5998535 -21. 6999512 -21.4063873 -0.2935638 1.3528309 500.0000000 739.5998535 -19.9001465 -19.8648071 -0.0353394 0.1775833 500. 0000000 759.5998535 -17.6999512 -18.6975403 __ 0.9975891 -5.6361113 1000.0000000 259. 5998535 -213.0998535 -214.0125885 0.9127350 -0.4283130 1000.0000000 279.5998535 -208.3998108 -209.0690460 0.6692352 -0.3211304 1000.0000000 299.5998535 -204.0999603 -204,3749390 0.2749786 -0.1347274 1000.0000000 319.5998535 -199.6999512 -199.9977875 0.2978363 -0.1491418 1000.0000000 339.5998535 -195.2998047 -195.6057587 0.3059540 -0.1566586 1000.0000000 359.5998535' -190.8998566 -191.0912170 0.1913605 -0.1002412 1000.0000000 379.5998535 -186.5998535 -186.6613770 0.0615234 -0.0329708 1000. 0000000 399.5998535 -182.2998047 -182._1132355 _____ -'0.1865692 0.1023419 1000.0000000 419.5998535 -177.7998657 -177.6692047 -0.1306610 0.0734876. 1000.0000000 439.5998535 -173.5999603 -173.077652 0 -0.5223C83 0.3008689 100C.0000000 459.5998535 -169.2999115 -168,3477173 -0.9521942 0.5624301 1000.0000000 479. 5998535 -164.3999023 -163.3701935 -1.0297089 0.6263438 1000.0000000 499.5998535 -159.2998657 -158.3547974 -0.9450684 0.5932636 1000.0000000 519.5998535 -153. 7000122 -152.9866638 -0.7133484 0.4641171. 1000.0000000 539,5998535 -148.0999603 -147.1595001 -0.9404602 0.6350170 1000. 0000000 559.5998535 -141.7998657 -140. 7395935 -1.0602722 0.7477242 1000.0000000 579.5998535 -134.2999573 -133.4069977 -0.8929596 0.6648591 1000.0000000 599.5998535 -125.1998596 -124.8759003 -0.3239594 0.2587537 1000.0000000 619.5998535 -112.6000977 -113.3898468 0.7897491 -0.7013749 1000.0000000 639.5998535 -94.4001465 -96.4388885 2.0387421 -2.1596804 1000.0000000 659.5998535 -77. 0998535 -77.0856628 -0.0141907 0.0184056 1000.0000000 679. 5998535 -65. 3000488 -63.9251556 -1.3748932 2.1055002. 1000.0000000 699.5998535 -55.8000488 -55.4507446 -0.3493042 0.6259925 1000. 0000000 719.5998535 -49.5000000 -49.4138489 -0.0861511 0.1740426.. 1000.0000000 739.5998535 -44.8000488 -44.8408203 0.0407715 -0.0910076. 1000. 0000000 759.5998535 -41.8999023 -40.9667664 -0.9331360 2.2270594.... 1500.0000000 259.5998535 -211.2998657 -211.9204712 0.6206055 -0.2937084 1500.0000000 279.5998535 -206 89981'08 -207.2250214 0.3252106 -0.1571826 1500.0000000 299.5998535 -202.5999603 -202.5259705 -0.0739899 0.0365202 1500.0000000 319.5998535 -198.0999603 -197.9289093 -0.1710510 0.0863458. 1500.0000000 339.5998535 -193.8998108 -193.4789581 -0.4208527 0.2170464 1500.0000000 359.5998535 -189.3998566 -189.1691284 -0.2307281 0.1218206 1500.0000000 379.5998535 -185.2998657 -184.7435455 -0.5563202 0.3002269 1500.0000000 399.5998535 -180.7998047 -180.5327148 _..-0.2670898 0.1477268 1500. 0000000 419.5998535 -176.2998657__ -176.1721954 -0.1276703 0.0724165 1500. 0000000 439.5998535 -171.9999542 -171.7151031 -0.2848511 0.1656111 1500.0000000 459.5998535 -167.4999084 -166.8757019 -0.6242065 0.3726608 1500.0000000 479.5998535 -162.9999084 -162.2016907 -0.7982178 0.4897043 1500.0000000 499.5998535 -158.1998596 -157.5055847 -0.6942749 0.4388593 1500.0000000 519.5998535 -153._1000061 _-152..5.071259 _ -0.5928802 0.3872503 1500.0000000 539.5998535 -148.1999512 -147.2438507 -0.9561005 0.6451420 150C.0000000 559.5998535 -142.7998657 -141.9967957 -0.8030701 0.5623743 1500.0000000 579.5998535 -136.6999512 -136.2226715 -0.4772797 0.3491440 1500.0000000 599.5998535 -130.1998596 -129.7465363 -0.4533234 0.3481750 1500.0000000 619.5998535 -123.1'999512 -122.8667450 -0.3332062 0.2704597 1500.0000000 639.5998535 -115.0000000 -115.0187378 0.0187378 -0.0162937 1500.0000000 659.5998535 -106.5998535 -106.0254669 -0.5743866 0.5388249 1500. 0000000 679.5998535 -97.0000000 -96.6218567 -0.3781433 0.38983'84 1500.0000000 699.5998535 -86. 8000488 -87.2585297 0.4584808 -0.5282033 1500.0000000 719.5998535 -77.5000000 -78.3973999 __ 0.8973999 -1.1579351 1500.0000000 739.5998535 -70.3000488 -70.8262329 0.5261841 -0.7484831. 1500.0000000 759.5998535 -63.3999023 -64.3321075 O.0.9322052 -1.4703569... 2000.0000000 259.5998535 -209.4998627 -210.9001007 1.4002380 -0.6683714 2000.0000000 279.5998535 -205.1998138 -206.0324097 0.8325958 -0.4057485 2000.0000000 299.5998535 -200.8999634 -201.4397278 0.5397644 -0.2686732 2 00C. 0000000 319.5998535 -196.4999542 -197.0929565 0.59300C23 -0.3017824..... 2000.0000000 339.5998535 -192.3998108 -192.5046082 0.1047974 -0.0544685 2 COC. 0000000 - 359. 5998535 -188.1998596 -188.0214539 __ - 0.171 4058 0.0947959.. 2000.0000000 379.5998535 -184.0998535 -183.7349091 -0.3649445 0.1982318 2000.0000000 399.5998535 -179.8998108 -179.3813171 -0.5184937 0.2882124 2000.0000000 419.5998535 -175.6998596 -175.1452789 -0.5545807 0.3156409 2000.0000000 439.5998535 -171.1999512 -170.6218872 -_ _-0.5780640 0.3376542 2000.0000000 459.5998535 -166.6999054 -166.2076416 -0.4922638 0.2952994 2000.0000000 479.599535 ___-160.0999146 -161.8976135___ _-.... 1.1976990 -1. 122860C _ 2000.0000000 499.5998535 -157.5998535 -157.1539154 -0.4459381 0.2829559 2000.0000000 519.5998535 -153.1000061 -152.4760895 __. __ -0.6239166 C.4075221 2000.0000000 539.5998535 -148.4999542 -147.6445465 -0.8554077 0.5760319 2000.0000000 559.5998535 -143.5998535 -142.8975525 -0.7023010 0.4890680 2000. 0000000 579. 5998535 -138.4999542 -137.5681305 -0.9318237 0.6127971 2000.0000000 599.5998535 -133.0998535_ __ -132.6048889 -0.4949646 0.3718746 2000.0000000. 619.5998535 -127.1999512 -126.8992615 -0.3006897 0.2363913 2000.0000000 639.5998535 -121.0000000 __-121.2071686 0.2071686 -0.1712137 2000.0000000 659.5998535 -114.6999512 -114.6870728 -0.0128784 0.0112279 2000.0000000 679.5998535 -107.6000977 -106.9406891..-0.45.94C86 _ 0._6128326 2000.0000000 699.5998535 -100.3999023 -99.7528687 -0.6470337 0.6444562 2000.0000000 719.5998535 -93.3000488 -9_3.3932648 0.0932159 -C.0999098 2000.0000000 739.5998535 -86.4001465 -86.9765625 0.5764160 -0.6671469 2000.0000000. 759.5998535 -80.3000488 -80.9935608 - 0.6935120..__ -0.8636504

-270TABLE LXVI RESULTS OF CORRESPONDING STATES CORRELATION FOR METHANE-PROPANE MIXTURES USING SMOOTHED OPTIMUM PARAMETERS A. 5.1 PERCENT MIXTURE -ETSS~mw7mPRE..EXPER. DEPARlUE CALC. DEPARTURE - DIFFENCE PERCENT DIFFERENCE I ---- e \ (fO-> RQ.H /l h (Rtu/lb (/Rtu/lb) kpsia) x) U 60 i —-- \ — -- \- - 500. 0000000 179.5999908 -223.5000000 -226.9316864 3.4316864 5CC.0000000 1c9.5999908 -217.99998 -217.6999969 -220.4833527 2.7833557 50C.~0000000 219.599908 -209.6999969 -214.4564667 4.7564697 5CC. 0000000 23,59'9908 —''3, —779-9-573...- -707,-BSC7 23-99.. -.-.... -—.4' 00 c 8 26-7 5CC.0000000 259.5998535 -196.9000092 -200.9120026 4.0119934 50C.C OOOOO0... -.279. 5998535 3 -190.3999634 -193. 2441254 2.8441620 50C. 0000000 299.5998535 -182.3998566 -184. 9583282 2.554 717 50C.0000000 --'. 5998535"... -172.3000C31 -174..374755 9. 2.0747528 50C.0000000 419.5998535 -27.8000488 -27.0675659 -0.7324829 50C.C00000 4-5~8553-"5 — --- -2Z;.9001465-".....- -.24.2700500 -0.6300964 50C.0000000'59. 5998535 -22.5000000 -21.8718262 -0.62 1738 50. 0000000 -— 4797 5998535~ -- - -20.3999023 -20.0746 918 -0.3252106 500.0000000 44S.5998535 -18.6999512 -18.4159088 -0.2840424 50C0. CC000000 —.-19. 59985-35 - -17.3000488 -17.0569916 -0.2430573 1COC.0000000 179.5999908 -221.5000000 -225.1002960 3.60C2960 100C. 000000 IOO 1. 595-08 --''215.40'0092 -218.7625427 3.3625336 1000.0000000- 219. 5999908 -208.1999969 -212.7849884 4.5849915 1COC.0000000 2-;'. 5999908-. - -202.2999 573 -206.4502258 4.1502686 10C0.0000000 259.5998535 -195.50C000 O-199.9441681 4.4441681 1COC.0000000 -2T79. 59 8535.....- - -189.1999512 -192. 7454071 3.5454559 1COC.0000000 29. 5998535 -182.0998535 -184.9430542 2.8432007 1C.0000 00 310~ 59.98 535 --- 1 ~3. 60002....04-176.3085480 -.2.7085419 1CCC.000000 339.5998535 -163.3999C23 -165.9652100 2.5653C76 1COC.0000000 -- 555 9855 5 -I49.799 8047 -152.1031342 2.3033295 1COC.00000000 319.5998535 -125.4998169 -129.8916321 4.3918152 -CC.0000 o --- 3 5 -- 59-98535 - 88.8999023 -90.4928894 1.5929871 1C0C. 0000000 19. 5998535 -68.500000 -68.8716431 0.3716431 100a.0000000-o — o - 4 <.b98b3 - - -56. BU000488- - --'-56.701232'9....- -0.0988159 100C.0000000 459.5998535 -49.2001953 -48.8535004 -0.3466949 1COC. 0000000 4 -7975998535 -- -43. 5000000- - -43.3674469 -0.1325531 1000.0000000 499.5998535 -39.0998535 -38.9932098 -0.1066437 10CC. 0000000 00-19- 59 8's35. -.35.6000977 -3 5.4002533 -0.1998444 150C0.0000000 179.5999908 -219.3999939 -221.3976746 1.9976807 15Cl. uooooo S. 000000,999o8 -z13. 19-969- ~ — zr5s; 121 1853 1.9211884 1500.0000000 219.5999908 -206.3999939 -209.2149506 2. 8149567 1500C. 00U0000 - 29?. 59S99B -.__ - — 200. 899 634 -203.0811768 2.1812134 150C.0000000 259.5998535 -194.3000031 -196.6875610 2.3875580 1-50C. 00 -00 —00 T ~7 i.; 8535 -. —187T89-9934 -189.7619171 1.8619537 150C.0000000 299.5998535 -181.0998535 -182.5285339 1.4286804 150C. 000000 3O1s. 59b8535 -13.0ou0lz2 - -174;1910 -- -.9190979 150C0.0000000 339.5998535 -165.4999084 -165. 9848785 0.4849701 150C. 0-0-000 --- 3559-98535.. —-.-....5'39 810 8. — 155.7523804 0.3525696 150C.C000000 79.5998535 -143.0998C77 -143.7893066 0.6894989, 150C.0000000 3Cs.O9 —59 98535... —1-7, 49 c.C 84 -128.1256104 0.6257019 15CC.0000000 419.5998535 -108.8000031 -109.0628204 0.2628174 150(C.000o000 4 — 9.'598535 -91.71999512-. -. -90.9673615 - -0.2325897 150C.0000000 459.5998535 -77.6000977 -77.2834015 -0.3166962 -1CC.0 - 00000-0 —- 9759 535 --..-69535 -67.3894501 -0.2104034 150C0.0000000 499.5998535 -60.0000000 -60.0946655 0.0946655 15.COOOO 00000 51 9853500 -54.1584320 0.1584320 2COC.0000000 11S9.5999908 -217.2999878 -219.1347809 1.8347931 -200 C. 0000000 19.599908 —....... 01T.-I010 61 -212. 8544922 1.7544861 200C.OOOOOO000000 219.5999908 -204.7999878 -206.9452972 2.1453094 20C CC0. 0000000 z~.' ^' —-- -.............-199.599-9603 -200.8016663 1.2017C59 2000.0000000- 259. 5998535 -193.1000061 -194.6253204 1.5253143 2 CCC. 0000 000 -- 7~-59985 35 — - 18 6. 699 512 -188. 0641937 1. 3642 426 200C.0000000 299.5998535 -18C.1998596 -181.2850037 1.0851440 2 COC.0000000 315.5998535 - - -173 —2000172.....~. —.-.173%. 9479'065 0.7478 943 2COC. 0000000 3 39.5998535 -165.3999C23 -166.1320038 0.7321014 2000.0000000 359. 59798535~ ~.~-I3.. 99 9 8169.-1574232025 0.4233856 2000.0000000 31S.5S998535 -147.4998169 -148.1235962 0.6237793 200C0.000000 3 89c9. 5998535 -136.6999054 -137.5641785 0.8642731 2 COC.OO0000000 419.5998535 -124.5000000 -125.699081e4 1. 190 814 2 COC. 0000000 4O39.5998535 -111 59/9603 -...-112; 7542-72 1.1542 969 2000. 0000000 459.5998535 -99.00C0000 -99.9122620 0.9122620 2CCC.C0000000' 479.5998535 -— 87. 599853-5 -88.6198578 1.0200C43 200C. 0000000 499. 5998535 -78.0998535 -79.1157684 1.C159149 2 COC. 0000000 519.5998535 -730C0488 -71.1804657 0.8804169 -1.5354290 -1.2785273 -2.2682257.....-I 967533 -2.0375786 -1.4937820 -1.4026709 -1.2041512 2.6348257 2.53C4928 2.7918825 1.5941763 1.5189466 1.4049511 -1.6254148 -1.5610t38 - -2.2022047 -2.0515413 -2.2732315 -1.8739195 -1.5613413 -1.560218 " -1.5699558 -1.'5376043 -3.4994583 -1. 7918873 -0.5425445 0.17397 -1 0.7046614 0.3047197 0.2727470 0.5613587 -0.9105198 - -0.9011201 -1.3638353 -1.0857201 -1.2287989 -0.9909279 -0.7888909 -0. 521 294 -0.2930334 -0.2268790 -0.4818305 -0.4907466 -0.2415600 0.2550327 0.4081130 0.3112483 -0.1577758 -0.2933925 -0.8443594 -0.8311160 -1.047514C -0.6020568 -0.7899086 -0. 7307138 -0.6021891 -0.4318095 -0.4426248 -0.2696726 -0.4229016 -0.6322410 -0.9631175 -1.0343161 -0.9214766 -1.1643896 -1.30C7889 -1.2523699

-271 TABLE LXVI (CONTINUED) B. 11.7 PERCENT MIXTURE.PR'EURE TEMPERATURE. EXPER. DEPRTURE -- CALC. DEPARTURE -- DIFFERENCE PERCENT DIFFERENCE =(psia) (~B).. (Btu/lb)... (Btu/lb)...(Btu/lb).. 50C.00000000 1c55.599908 -223.6955569 -221.9612732 -1.7387238 0.7772568 5CC.COOOOOO9.y0 9 1 9.:-990*8 - -?-r-8-0,W O —g-g -216. 1458282 - -1.954162 6..895993 50C.C0OOOOO 235. 55999C8 -212.0999146 -210.1582794 -1.9416351 0.9154338 50C.COOOOOO0 -----—. 35.~..-20-. 7000122 -. 203.7401886 -1.9598236 0.9527579 500.0000000 279.5998535 -198.7998657 -197.1702118 -1.6256539 0.8197457 50C.0000000 2'5.. 55 8535 — 19 1.29 99T5- -- -I89620W84Z7-3-r.-643407 - 3-733 738t50C.000 000 319. 5998535._-181.8999634 -182.0914c17 0.1915283 -0.1052932 5CC. 0000000 41 5. 5998535 -24.5998535' -22.6095428 -i9903107 8.0907402 500.0000000 499.5998535 -20.9001465 -20.6689606 -0. 2311859 1.1061440 50C.0000000 519. 5998535- -- -18.-994512 — - -19.0365601. 0.3366C89....8000517 5CC.COOOOOO 329.5558535 -17.3999023 -17.5312042 0.1313019 -0.7546127 50C. 000000000. 559. 599853'5 -16.80CC488 — 16.2901306- - - — 5099182 -- -3.035'821CCC. COOOOO0 159.5999908 -220.8999939 -220.2052917 -0.6947021 0.3144872 1000C.0000000 2159.5999908 - 215. 0999908.....-214.4022217 -0.6977692 0.3Z47921000.0000000 239.5999908 -209.2999115 -208.5052032 -0.7947C83 0.3796983 -1CC.0000000 259.75998535 -203.1000061 - - 02.4145660 -0.6854401 - 0.3374-81CCC.0000000 2719.5998535 -196.295e657 -196.1113892 -0.1884766 0.0960146 1 CC. 0000000 i299. 5998535 -189.299'9115 -19272 2 --.' — 274353 0.014T4930 1000.0000000 319.5998535 -181.6999512 -181.8969421 0.1969910 -0.1084155 1C0C. 0000000 339.5998535 -172.9000092 — 173.8210297 0. 9210205 -- 0.5326-8-W ICOC.COOOdOO 0 355.5998535 -163.8000031 -164.4685669 0.6685638 -0.4081584 100CC.OO0000000 9.S98535 -150.299-911.5 -152.195861 1,8976746..-6-25-T4 1000.0000000 479.5998535 -52.8999023 -51.5134277 -1.3864746 2.6209393 100C.0000000 49.5998535 -45.9001465. 10-454022675 ~ -' ~-064978790 - --- 1.084696100C. 0000000 519.599853.5 -40.8000488 -40.7203217 -0.0797272 0.1954095 10C00.0000000 539.5998535 -37.099E535.-36.9300842 -0.1697693.571COC.0000000 559.5998535 -34.1999512 -33.7904205 -0.4095306 1.1974592 1500.0000000 199.5999908 -218.00COCOO -216.7839050 -1.2160950 --- 0.55WV4 — 15CC. 0000000~ 219.5999908 -212.1999969 -210.9642487 -1.2357483 0.5823504 1500.PO0000000 239. 59399098 T20.5.T`-47-7"' —------- u;.25I1.b588T12ze 150C.0000000 259.5998535 -200.5000000 -199. 3072205 -1.1927795 0.5949024 150C0. 0000000 279. 5998535 — 193.9-566 -—. - 193.1636047 -0.7362518.. 37970721500.0000000 299.5998535 -187.3999023 -186.5019379 -0.8979645 0.4791699 1500.0000000 ~3.59555~ —- — 1 T8039-9:634 -.. -179.6705322.. -0.7294312. -.-~.043477r 1500. 0000000 329.5998535 -173.0000000 -172.2507935 -0.7492065 0.4330672 1500. 0000000 359.598535 -165.0000000 - -164. 2658386 -0 -. I"6- 1'44-44946 1500.0000000. 3579.5998535 -155.5999146 -155.0887146 -0.5112CO0 0.3285348 150C.0000000 2 359.595985335 -- -144. 3S 7 C~3T — — 14'4-.3593-597 O- - 0.0593567 — 0. 0411341500.0000000 419.5998535- -130.1998596 -131.0386200 0.8387604 -0.6442096 150CC.0000000 439.5998535 7 — -113.4998169 -- 1.3-71-722. 0.8673553 —.76907 1500.0000000 459.5998535 -97.50C0000 -96.8395691 -0.6604309 0.6773646 1500.0000000 479.5998535 -83.5000000 -82.1640015 -1.3359985 l. 9991 150C.0000000 499.5998535 -72.5000000 -71.2907867 ___ -1.2092133 1.6678801 150C. 0000000!15.55598535 -64.1999512 -63.1142578 -1.0856934 1.6911116 15CC00.0000000 539.5998535 -57.3999023 -56.8190460 -0.5808563 1.0119457 1500. 000000 5 — 55-9 —-- - 535 -52.10C0977. - — 51.61-855.048924263..9390432 2000.0000000 199.5999908 -215.2999878 -214.6734314 -06265564 0.2910155 2CCC.CO000000 219.5999908 -209.3999939 -Z-08.88i9313 -0. iuee 0.24406U05 2COC.000000M0 235.5999908 -203.8999023 -203.1128387 -0.7870636 0.3860049 2CCC.0000000 25 O 0 —-99T575 —-- 198.0000.. —— 97-83Z4 -...-0. 8116760.. 0.4099373 2000CC.0000000 279.5998535 -191.5998535 -191.2792053 -0.3206482 0.1673530 2000C.0000000 2c9-5-3. 59-98535 - 1-85. 49-9V-84 —- - 14W.-9T'72 - -............ 5206757.-0.2806878 2000.0000000 319.5998535 -179.2999573 -178.5186462 -0.7813110 0.4357561 200CC.0000000::. 58535 -LZ. 60061.- T' —3183 -09689178.. 0.561653 2000.0000000 359.5998535 -165.40C0092 -164.3647919 -1.0352173 0.6258867 2000. 00000 0 -. 5598535-.399023....-l..- 156.4539337..-m. -0.9459686 0. 600-9966 200C.0000000 3i5.5998535 -148.5000000 -147.8839111 -0.6160889 0.4148744 - 2000.0000000 415.5998535 -i 3-138-.399Y6 - 1 —- I38. 5615234- -- -...0.1616669 -0.1168114 200C.0000000 439.5998535 -127.0998077 -127.5689240 0.4691162-0.3690928 2 ooo. ooooooo it s 9. bS as t 35 - 1.1' 52.. 99 - 115.755432T-'0.-52548 1-... 0.4821882 2COC.0000000 479.5998535 -103.3000488 -103.9051056 0.6050568 -0.5857274 -2000.0000000' 459.5998535 -92.500ZIOO0 ~....927773813 -.2783813 -C.3009528 2000. 0000000 5 19.5998535 -82.8999023 ~ -82.9710693 0.0711670 -0.0858468 200C. 0000000 539. 5998535 746999512 - i74?.6830292.......-0.0169220 0.0226533 2C00.0000000 555.5998535 -67.8000488 -67.6909790 -0.1090698 0.1608698

-272 TABLE LXVI (CONTINUED) C. 28.0 PERCENT MIXTURE PR;ESS RE....TEMPERATURE EXPER. DEPARTURE- CALC. DEPARTURE DIFFERENCE PERCENT DIFFERENCE (psia) (~O) (Btu/lb) (Btu/lb) (Btu/lb) 50C.0000000 219.5999908 -219.6999969 -220.2863007 0.5863037 -0.2668656 50C. 0000000ooo z3. 5999908 -214.39Y9939 -214. U4828 0. 1048889 -0.0489220 50C. 0000000 25 9. 9 98535 -209.0000000 -209.2912445 0.2912445 -0.1393514 50C. 0000000 279. 599 8535 -2 02. 8000071 — -203.6928406 -- 0. 8928375 ---. 4402552 50C.0000000 259.5998535 -197.2998657 -197.9077148 0.6078'491 -0.3080838 50C. 0000000 319. 5998535 -190. 5998077- -— 192. 05331 — - - 1.;4537354 — —.762 759 50C.0000000 339.5998535 -184.1998596 -185.8499756 1.6501160 -0.8958287 50C. 0000000 - 19. 5998535 -ZT-2. 0998 35 -25.3669434 -1.7329102 -6.3 94535 50C.0000000 539.5998535 -24.300C488 -23.0831146 -1.2169342 5.0079489 50C.COOOOO0 559.5998535 - -22.1000977 -21.3156-0.96884T16 -1-5 -4388787 500.0000000 579.5998535 -20.3000488 -19.6109467 -0.6891022 3.3945827 50C. 0000000 599. 5998535 -18.7998047 -8. 495Z72Z — -. 6502o075 3 — -~-345 5857 50C.0000000 619.5998535 -17.3000488 -16.8185883 -0.4814606 2.7830009 50C. 00000000 39. 598535 -16.100 091 7/ -15. 72 938T 7 -o 32.3 9 — 5 -— 53 100C.0000000 219.5999908 -217.4000092 -218.3764343 0.9764252 -0.4491374 CCOC. 0000000 239.5999908 -212.099990-8 -212.7g2T503- - -.6821 4 -U..32 216 1COC.0000000 259.5998535 -206.8000031 -207.5072327 0.7072296 -0.3419872 1 COC. 0000000 -201 0000000 - Z-2.OZT22736 r —-— 20022T 7 6 - -.49 6435 100.0000C000 299.5998535 -195.5998535 -196.4371185 0.8372650 -0.4280496 1000.0000000 319.5998535 -189.4958169 -190.760780 U1.2609 11 - - -.6654207 1CCC.0000000 339.5998535 -183.6998596 -184.7817688 1.0819092 -0.5889546 1000.OOOOOOC 359.59 98535 -177. 0000000 -1 8-7404 27 - - 9.40 43274, - 0-. 7934052 100C.C000000 379S 5998535 -170.3000031 -171.5980377 1.2980347 -0.7622044 1 CCC. 0000000 3cS. 5998535 -161. 699596 - -164.22 61353. 262756. 5-23236 1 CO.0000000 539.5998535 -55.80C0488 -53.9281158 -1.8719330 3.3547153 1 COC. 0000000 559.5998535 -48. 6999512 -47.4826508 - 1.21 7304.959 1000.0000000 579.5998535 -43.8000488 -42.6932068 -1.1068420 2.5270329 1 COC. 0000000 5S9.5998535 -39.7998047 - 3 —-3 6974-2 —- -... -1.10237254 2.7696753 1CCC.0000000 619.5998535 -36.3000488 -35.4270477 -0.8730011 2.4049578 1 00. 0000000 39 3.5998535 - 33.3999023 -- -32.6T9I~~ -0.T379 — 2. 2095604 150C.COOOOOO 219.5999908 -215.1000061 -215.5056000 0.4055939 -0.1885605 1500C. 000000 239.5S99908 -209.8000031 -209.8356171 - 0.0356140 — 0.u010992 150C.0000000 259.5998535 -204.7000122 -204.5474091 -0.1526031 0.0745496 15CC. 000000 279.5998535 -199.4000092 -199.1423035 - 0.T577057 0.1292405 150C.00.00000 299.5998535 -194.0998535 -193.8211975 -0.2786560 0.1435632 150C.0000000 319.5998535 -188.4998169 - 18 8.33483 - 0-.1'50085 085 53 7 1500.0000000 339.5998535 -182.6998596 -182.3637543 -0.3361053 0.1839658 1500.0000000 -39.5998535 -176. 5000000 -1/ 6.30b6314 A -0.1903687 U0.1078576 1500.0000000 379.5998535 -170.5000000 -170.0927734 -0.4072266 0.2388425 150.(O000000 399.5998535 -163.8998566 -163.28288Z7 -0.6169739 0.3764334............................................... 1500.0000000 1500. 000000 150C. 0000000 150C.0000000 150C.0000000 1500. 000000 150C. 0000000 1500.0000000 1500.00000000 150C. COOOOOO 1500. C0000000 2COC.0000000 200C.0000000 2COC.0000000 200. 0000000 2000.0000000 2000.0000000 200C.0000000 200C.0000000 20 C. 0000000 200C.0000000 2000. 0000000 2CO0. 0000000 2COC. OOOOOO 2C000. 0000000 2 000. 0000000 2COC. 0000000 2000.0000000 2COC. 0000000 2COC.0000000 2COC.0000000 200C. 0000000 2 000.0000000 2000.0000000 419.5998535 4 9. 59 98535 459.5998535 4 79. 5598535 499.5998535 s19. SSc 8535 539.5998535 55S. 5998535 579.5998535 55S. 5998535 619.5998535 639.5998535 219.5999908 23. 59999C8 59. 5998535 279. 5998535 299. 5998535 319.5998535 33-S.5998535 359.5998535 379. 5998535 3SS. 5998535 419.5998535 439.5998535 459. 5998535 479. 5998535 4S9. 5998535 51S.5998535 539.5998535 559.5998535 579.5998535 599. 5998535 619.5998535 639.5998535 - -156.3999C23 -147.6998138 -137.3998108 -125.30C00031 -111.6998138 -98.0998535' -85.9001465 -75.8000488 -67.7001953 -61.0000o000 -54.4001465 -49.6999512 -212.8000031 -207.5999908 -202.6000061 -197.7000122 -192.599E535 -187.2998047 -181.8998566 -176.2000122 -170.5000000 -163.7998657 -157. 0999146 -149.8998108 -141.8998108 -133.2000122-123. 7998C47 -113.795 8047 -103.8000488 -94.30-00488 -85. 8000488 -78.0998535 -71.0000000 -64.8999023. -156,1258392 -148.1684418 - -138.8779907 -127. 7117615 -114.2397308 -100.0403748 -86.3804779 -75.3906403 -66.8442688 -60.0529022 -54.6243286 -50.0119781 -213.7352905 -208.123977 -202. 7685394 -197.4569550 -192.0215454 -186. 7361603 -180.9917603 -175.4336548 -169.5098724 -163.1153717 -156.6856079 -149. 6936951 -142.3596497 -1-34. 8022W614 -125.5167C84 -114.6369171 -104. 9794312 -955..4340515 -86.5139618 — 78.5068C54 -71.5308990 -65.4637146 ____ -0.2740631 0.1752322 0.-466279 ----- -0.31 72840 1.4781799 - 1.0758228 2.4117584 -1.9247866 2.5399170 -2.2738771 ~~T. 55 21~~ - - -1.9781075 0.4803314 -0.5591739 -0.4094086 - 0. 5401164 -0.8559265 1.2642889 -0.9471078 1. 5526190 0.2241821 -0.4120983 0.3Tz20270- -- -0-.6 278213 0.93 2 875 -0.4395146 "0.- 5239~68- - -0, 2Z5240210.1685333 -0.0831852 -.~ Z430 573U. - ZZ294Z4 -0.5783081 0.3002640 -0. 563-444 30 3009316 -0.9080963 0.4992284 --.7663 574 - 0.4349358 -0.9901276 0.5807198 -0.68449-40 0-.4178841 -0.4143066 0.2637217 -L. 2Q615 T -.. —..1T375023 0.4598389 -C.3240588 T.'-022 9... —. -2W07944 1.71 69037 -1.3868380 0.83711Z24 — 0.7356007 1.1793823 -1.1362057 1.T34: -1.2025W47IT 0. 713913 0 -0.8320655 0-.06 0i9 - -7 C. 521 0-60.5308990. -0.7477451 0. 5638123 -. 8-68740 - - -

-273 TABLE LXVI (CONTINUFD) D. 50.6 PERCENT MIXTURE (psia) 5CC. 0000000 50C.0000000 500.0000000 50. 0000000 500.0000000 500. 0000000 500.00000000 500.0000000 50C. 0000000 50. 0000000 50. 0000000 50C. 0000000 500.0000000 500.0000000 50C.0000000 10 C. 0000000 1000.0000000 1COC. 0000000 1000.0000000 I CCC. 0000000 1000.0000000 1Coc.Coooooo 100. 0000000 1 co. 0000000 1000. 000000 1000. 0000000 1000.0000000 100C. 0000000 1000.0000000 1 COC. 0000000 1000. 0000000 1 COC. 0000000 150C. 0000000 1500. 0000000 150C. COOOOOO 150C.6000000 1500. 0000000 150CC. COOOOOO 150C. 00000o 1500. 0000000 150C. 0000000 ITEPER-TURE' EXPER. 5EP-TU CAI. IEPRTURE ( R) (Btu/lb) (Btu/lb) DIFFERENCE ('R-tn /11b -PERCENT DIFFERENCE ( RttL U/l. -. I - - - - - 1500.0000000 15CC. 0000000 1500.0000000 150C.0000000 150C.0000000 1500. 0000000 150C. 0000000 1500.0000000 1500.0000000 1500.0000000 150C.0000000 1500.0000000 15C0. 0000000 1500.0000000 1500. 0000000 1500.0000000 150C. 0000000 2000.0000000 20CC. 0000000 onn nnnnn 279.5998535 129.5998535 319.5998535 359. 5998535 3359.5998535 5 5. 5998535 5S9.5998535 619.5998535 2639.5998535 659.5998535 679.5998535 - 69. 5998535 719.5998535 739.5998535 2 9. 9< 8535 279.5998535 2c.59.98535 319.5998535 339.5998535 359.5998535 379.5998535 3S9. 5998535 419. 5998535 439.5998535 459.5998535,99. 5998535 619.5998535 6- 39. 55998535 659.5998535 679. 5998535 899.5998535 719. 5998535 139. 5998535 259.59S8535 279.5998535 299. 5998535 31S.5998535 339. 5998535 39. 5998535 379.5998535 399.5998535 4 19. 5998535 439.5998535 45. 59985 35 479.5998535 49 c9. 599853 5 51S9. 5998535 539.5998535 559.5998535 579.5998535 509.5998535 619. — 598535 639. 5998535 679. 5998535 6S9. 59-8535 719. 5998535 7.: -;m8535 259. 5998535, s275. 5598535 299. 5998535 3- 75S599H535 329. 5998535 3 c.597.9-5 15379. 5998535 315. 5598535 419. 5998535 439. 5998535 — 459. 5998535 479.5998535459.5998535 539.5998535 539.5998535 5. 59.5658535 579. 5998535 - c9g. 5g98535 619.5998535 659.5998535 699.5998535 719. 5998535 139.5998535 -2132.7.8-4 -2i3.'682262 -207.8998108 -208. 6192 322 -202. 8999C23 -203. 8759460 -198.2998657 -198.8828430 -193.7199905+4 —.. -193.7728424 -188.0999146 -188.6192627 - 29. 70 01953- T.-8566132-... -26.5998535 -25.3582458 -24.199S512 -23.2206879 -22.2001953 -21.3867645 -20.6999512 -19.8788452 -19.2001953 -18.5556488 -1 8'0'O''0000 - -17.3G444 824.. -16.8000488 -16. 1705322 -15. 7998047 -15.0652752 -211.0998077 -211.7926483 -206.1998138 -206.8906860 -201.3999023 -202.0738525 -196.4998627 -19-T. 042798 - -191.5999146 -192.1378326 -186.6999054 -187.1615143 -181.5000000 -182.0179138 -176. 199951 2 -176.7419586 -170.7999573 -171.0954132 -164. 7998C 4T --.-65. 2679'4-43 — -158.5996535 -159.0746307 -64.50000000 -63.8943329 -55.6999512 -55.0928802 -49. 7001-953.- -- -'' -48.8696289 -44.8999023 -44.02 97546 -40. 8000488'-W.1583405 -37.60100977 -36.8083344 -3 5.10 -OC97' --. — 34.0158081 -32.7998047 -31.5534515 -209.3998108 -209. 5099945 -204.4998169 -204.4188232 -199.8999023 -199.553 8C25 -194.7998657 -194.7259979 -190.0999146 -189. 8994751 -185.2999115 -185.0658569 - 80.400092. -180. 2243 805 -175.1999512 -174.7866974 -169. 9999542 -169.477'4O1-7 -164.3998108 -164.1054535 -15 8.-T90657 -158. 3721771 -152.8000C31 -152.3120880:-i46. — 0999603'- ~ -145.7399445 -138.2998657 -138.5391388 -i Z9.399q3-zF..-130. 7234344. -119.8000031 -121.3415680 -08.~-5000000 -110.4123230 -97.1999512 -99.1941223 -8i6.9 98535 -.-87. 83108'52 -77.5000000 -77.6684418 -6 9. 30U048-F — 6-.-459Z896.-. -63.0000000 -62.8094940 -5 7.699 5-1 2 —.. — -7. 2172394 -53.1000977 -52.5367432. -~.J99023........-48. 4553 986.. -207.5998077 -208.1056824 -20 Z.998169 ---— T03.579V — - -197.9999084 -198.2191925 - 193.2998657. -193.33499 -5 -188.4999084 -188.4903412 -1 83.69-905 ---- -183.7644043 -178.8000031 -178.8682861 -1 73.8995634 -173.817275- - -168.9999542 -168.9519806 -163.8998T108W - 163. 6926 70 - -158.4998627 -158.2630310 153. 00-000...-. —1-52.;792027 - -147.1999512 -146.8095093 -140. 89ES566 -.141.1 0 8606BO -134.0999603 -134.7816467 -126. 900092 — 128. 5346680 - - -119.0000000 -120.7703705 -110. 7 W998-04T —..1-0.-93 9956T — -102.6999512 -102.7336273 -94. 000U77S -95.2316284 -86.8999023 -87.7489014 -80.0000000 -805-35223 —-- -73.8999023 -74.1958618 -68.400UC 5 -68."352661- -63.5998535 -63.0837708 0.8824615 -0.4146907 0.7194214 -0.3460423 0.9760437 -0.4810467 0.5829773 -0.2939877 0.5729370 -0.2965513 0.5193481 -0.2761022..~I- 8435822 - -.. 6. 2073C59 -1.2416077 4.6677227 -0.9792 633 4.0465498 -0.8134308 3.6640701 -0.8211060 3.9667044 -0.6445465 3.3569784 -0. 6555176. 3.6417637 -0.62S5166 3.7471113 -0.7345295 4.6489782 0.6928406 -0.3282052 0.6908722 -0.3350498 0.6739502 -0. 3346328 0.5744171 -0.2923244 0.5379181 -0.2807506'0.4616089 -0. 2472464 0.5179138 -0.2853519.0.5420C74 -0-30760930.2954559 -0.1729836 0'. 46 81396.. -O 2.f406560.4747772 -0.2993554 -0.6056671 0.9390186 -0.6070709 1.0898943 -0.8305664 1. 671152I -0.8701477 1.9379711 -0. 6417084 1. 5728121 -0.7917633 2.1057472 -1.0842896 3.0891342 -1.2463531 3.7998791 0.1101837 -0.052-6T8-0.0809937 0.0396057 -;-.34z 609g- ---- 0.1731365 -0.0738678 0.0379198 -0.20C4395 0.1054389 -0.2340546 0. 1263112 -0.1756287 0.0973551 -0.4132538 0.2358755 -U-5'225525 U~0.3073839 -0.2943573 0.1790496 -0.4276886 - O.Z6-93255 -0.4879150 0.3193161 -0.3600159.. 0. 24-64175 0.2392731 -0.1730103 1.3234711 - -1.022774T1.5415649 -1.2887813 1.9123230 -1.76250931.9941711 -2.0516167 1.2312317 -1. 421472 0.1684418 -0.2173442. 0.-1592407 -0;-2974-4 -0. 19C5060 0. 3023904 -0.4827118 0.8365895 -0.5633545 1.0609283 -0.9445038 1.9119539 0.5058746 -0.2436777 -. 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