THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING THE EXPERIMENTAL DETERMINATION OF THE ENTHALPY OF MIXING OF BINARY GASEOUS MIXTURES UNDER PRESSURE Arun V. Hejmadi: A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Chemical Engineering) in The University of Michigan December, 1970 IP-836

Arun Vasudev Hejmadi 1970 All Rights Reserved ii

To Ahalya iii

ACKNOWLEDGMENTS I wish to express my appreciation to the people and organizations who contributed to the success of this research: To Professor John E. Powers, the chairman of my thesis committee, for his constant encouragement and guidance. To Professor Donald L. Katz for his help, advice and encouragement during this work. To the members of my thesis committee, Professors Joseph J. Martin, Richard E. Sonntag and Edgar F. Westrum, Jr., for their advice and assistance. To Andre W. Furtado for many helpful discussions some of which involved this research. To Dr. David T. Mage and Dr. Millard L. Jones for contributing to the initial phases of design and construction of' the equipment. To others who helped in various phases of this research: Donald Barber, Vasant Bhirud, Peter Fodor, Donald Gatza, Joseph Golba, Vijay Khanna, Dr. Alan Mather and Dr. Victor Yesavage. To the members of the ORA Instrument Shop: William Rekewitz, Edward Rupke and Herbert Senecal. To the members of the Instrument Shop of the Chemical and Metallurgical Engineering Department: Cleatis Bolen, Douglas Connell, Erwin Muehlig, Peter Severn and John Wurster. To the National Science Foundation for two grants without which the project would not have proceeded. To the Cities Service Oil Company for fellowship support in the latter phases of the work. To the Chemical and Metsllurgical E.ngriering Deparrtment for providing computer time. iv

To Professor Edgar F. Westrum, Jr., for the use of equipment. To the National Bureau of Standards for the calibration of standard cells and thermopiles. To my wife and family for their faith in me. v

TABLE OF CONTENTS Page ACKNOWLEDGMENTS........................ iv LIST OF,' TABLES........................ x LIST OI' I'I(URES........................iii NOMECLATU.......................... xv ABSTRACT............................ ix INTRODUCTION...............1....... 1 EXPERIENCE OF PREVIOUS INVESTIGATORS....... 3 Excess Property Measurements on Liquids........ 3 Discussion of Closed-System Calorimeters...... 7 Discussion of Flow Calorimeters..... 8 Excess Enthalpy Measurements on Gases....... 10 Comparison of Flow Calorimetric Techniques for Gases 12 Calorimeter Design.............. 12 Flow and Composition Measurement......... 13 Mode of Operation.............. 14 Interpretation and Smoothing of Data....... 15 Prediction Methods.................. 16 Review of Thermodynamic Properties........ 17 Nitrogen..................... 18 Carbon Dioxide............... 19 Ethane..................... 21 Oxygen..................... 22 Nitrogen-Carbon Dioxide Mixtures........ 22 Nitrogen-Ethane Mixtures............. 24 Nitrogen-Oxygen Mixtures.............24 vi

TABLE OF CONTENTS (Continued) Page THERMODYNAMIC RELATIONS..................... 28 Thermodynamic Definitions................ 28 Correlation of Excess Enthalpy with Composition... 31 Relations for the Benedict-Webb-Rubin Equation of State....................... 32 Application of First Law of Thermodynamics....... 35 Primary Corrections................... 39 Corrections for Impurities............... 40 Nitrogen-Carbon Dioxide System........... 41 Nitrogen-Ethane System.........44 Secondary Corrections and Smoothing of Data....... 47 APPARATUS AND EXPERIMENTS....................... 50 APPARATUS.......................... 50 Calorimeter...................... 50 Flow Calorimetric Facility...........55 Flow System.................. 56 Gas Supply Assembly................ 60 Constant Temperature Baths............ 61 Control Panel................... 63 MEASUREMENTS AND CALIBRATIONS................65 Pressure...................... 65 Pressure Level................... 65 Differential Pressure.............. 66 Temperature...................... 67 Power...................68 vii

TABLE O0' CONTENTS (Continued) Page Voltage Drop across Calorimeter Heater.......68 Current in Calorimeter Heater......... 70 Flow Rate...............71 High Pressure Flow Meters........... 71 Low Pressure Flow Meter.............80 Gas Composition.................... 81 Can Volume Determination..............82 Gas Density Measurement........... 83 PROCEDURE......................... 84 Preparation of the Apparatus..............84 Startup......................... 85 Measurements at Steady State.............. 85 Data and Data Reduction................. 86 RESULTS.............................. 89 Interpretation of Calorimetric Data.........89 Nitrogen-Carbon Dioxide System........ 89 Nitrogen-Ethane System............104 Nitrogen-Oxygen System.............111 Discussion of Results.................114 Check on the Assumption of Adiabaticity......114 Accuracy of the Results.............117 Comparisons..................120 RECOMMENDATIONS FOR IMPROVEMENT OF EXPERIMENTAL TECHNIQUES IN SUBSEQUENT STUDIES.....................123 SUIMMARY AND CONCLUSIONS..................... 125 viii

TABLE OF CONTENTS (Continued) Page APPENDIX A. ERROR ANALYSIS.................... 127 Compounding of Errors................. 127 Power Input Measurement................... 128 Flow Rate Measurement.................. 128 Gas Composition.................... 135 Excess Enthalpy Determinations............. 138 APPENDIX B. CALIBRATIONS..................... 143 APPENDIX C. TABULATED EXPERIMENTAL DATA AND RESULTS....... 157 APPENDIX D. SAMPLE CALCULATIONS................ 171 Volume Determination of Calibration Tank....... 171 Flow Meter Calibration.......................177 Enthalpy of Mixing Measurement............. 184 Nomenclature for Appendix D..............196 BIBLIOGRAPHY.............. 202

LIST OF TABLES Table Page I Investigations of Excess Thermodyramic Properties of Binary Mixtures in the Liquid State at Low Temperatures...................... 4 II Experimental Investigations of the Enthalpy of Mixing of Gases.................... 11 III Experimental Investigations on the Binary System Nitrogen-Carbon Dioxide under Pressure......... 23 IV Experimental Investigations on the Binary System Nitrogen-Ethane under Pressure............ 25 V Some Experimental Investigations on the Binary System Nitrogen-Oxygen under Pressure............. 27 VI Key to Sketch of Calorimeter in Figure 2....... 53 VII Key to Flow Diagram in Figure 3........ 59 VIII Systems Studied and Conditions of Experimental Investigation of this Research........... 87 IX Impurity Analyses of Gases Used in This Research.... 88 X Examples of Corrections Involved in Data Reduction for the Nitrogen-Carbon Dioxide System......... 90 XI Excess Enthalpy Data on Nitrogen-Carbon Dioxide System........................ 92 XII Regression Coefficients for Smoothing Nitrogen-Carbon Dioxide Excess Enthalpies Versus Composition..... 96 XIII Excess Enthalpy Data on Nitrogen-Ethane System.... 107 XIV Regression Coefficients for Smoothing Nitrogen-Ethane Excess Enthalpies Versus Composition......... 111 XV Excess Enthalpy Data on Nitrogen-Oxygen System..... 113 XVI Estimated Limit of Accuracy of the Experimental Measurements...................... 118 XVII Errors in Determination of Power Input to Calorimeter. 129 XVIII Errors in Volume Determination of Calibration Tank... 130 XIX Errors in Flow Meter Calibration Measurements..... 132 x

LIST OF TABLES (Continued) Table Page XX Errors in Gas Density Analysis Measurements....... 137 XXI Estimated Errors Introduced by Primary Corrections for Nitrogen-Carbon Dioxide Mixtures......... 140 XXII Estimated Errors Introduced by Secondary Corrections for Nitrogen-Carbon Dioxide Mixtures.......... 141 XXIII Results of Volume Determinations on Calibration Tank.. 143 XXIV Data of Calibrations for Nitrogen Flow Meter...... 144 XXV Data of Calibrations for Carbon Dioxide Flow Meter... 146 XXVI Data of Calibrations for Ethane Flow Meter....... 148 XXVII Data of Calibrations for Nitrogen and Oxygen Flow Meters Used in Measurements on Nitrogen-Oxygen System.. 150 XXVIII Calibration of Dead Weight Gauge............ 151 XXIX Calibration of Mercury Barometer............ 152 XXX Calibration of Mercury-in-Glass Thermometer....... 153 XXI Calibration of Thermopile................ 154 XXXII Calibrated Resistances of Standard Resistors...... 155 XXXIII Calibration of Potentiometer Standard Cells....... 156 XXXIV Characteristics of Leeds and Northrup Model K-3 Null Potentiometer................... 156 XXXV Experimental Enthalpy of Mixing Data on NitrogenCarbon Dioxide System.................. 157 XXXVI Experimental Enthalpy of Mixing Data on NitrogenEthane System................158 XXXVII Experimental Enthalpy of Mixing Data on NitrogenOxygen System..................... 158 XXXVIII Primary Corrections for Data on Nitrogen-Carbon Dioxide System.................... 159 XXXIX Secondary Corrections for Data on Nitrogen-Carbon Dioxide System.....................160 XL Primary Cor rections for Data on Nitrogen-Ethane System. 161 xi

L-8J''I.' 0F TAiBLE[]J (Continued) Table Page XLI Secondary Corrections for Data on Nitrogen-Ethane System........................ 162 XLII Primary Corrections for Data on Nitrogen-Oxygen System.. 163 XLIII Values of Heat Capacities and Isothermal Joule-Thompson Coefficients used for Primary Corrections..... 164 XLIV Formulae Derived from Benedict-Webb-Rubin Equation of State Used in Calculating Properties........16 XLV Constants for the Benedict-Webb-Rubin Equation of State. 166 XLVI Sample Results of Volume Determinations on Cans Used for Gas Density Analysis............... 167 XLVII Gas Density Analyses of Gravimetrically Prepared Samples. 168 XLVIII Second Virial Coefficients Used in Gas Density Analysis Computations................. 168 XLIX Comparison of Compositions from Flow Meter Calibrations and from Gas Density Analysis.................. 169 L Conversion Factors for SI Units............. 170 LI Molecular Weights Used in Computations.......... 170 LII Formulae for Properties of Nitrogen Used in Computer Programs......................... 172 LIII Sample Data for Volume Determination of Calibration Tank. 173 LIV Sample Flow Meter Calibration Data............ 178 LV Sample Data on Enthalpy of Mixing Measurement..... 186 xii

LIST OF FIGURES Figure Page 1 Schematic for Enthalpy of Mixing Measurements in a Flow Calorimeter................... 36 2 Enthalpy of Mixing Calorimeter (Key: Table VI)...... 52 5 Flow Diagram of the Facility (Key: Table VII)...... 58 4 Control Panel....................... 64 5 Electrical Power Input System for Calorimeter....... 69 6 Photograph of High Pressure Flow Meter.......... 73 7 Excess Enthalpy Data on Nitrogen-Carbon Dioxide System at 40~C..................... 97 8 Excess Enthalpy Data on Nitrogen-Carbon Dioxide System at 40~C and 500 psia, and Comparisons with Data of Lee and Mather and with B-W-R Equation of State Predictions.................. 98 9 Excess Enthalpy Data on Nitrogen-Carbon Dioxide System at 40~C and 950 psia, and Comparisons with Data of Lee and Mather and with B-W-R Equation of State Predictions.................... 99 10 Excess Enthalpy Data on Nitrogen-Carbon Dioxide System at 31~C................100 11 Excess Enthalpy Data on Nitrogen-Carbon Dioxide System at 31~C and 500 psia, and Comparisons with B-W-R Equation of State Predictions..........101 12 Excess Enthalpy Data on Nitrogen-Carbon Dioxide System at 31~C and 950 psia, and Comparisons with B-W-R Equation of State Predictions...... 102 13 Excess Enthalpy Data on Nitrogen-Ethane System...... 109 14 Excess Enthalpy Data on Nitrogen-Ethane System and Comparisons with B-W-R Equation of State Predictions.................. 110 15 Excess Enthalpy Measurements on Nitrogen-Carbon Dioxide System as a Function of Reciprocal Flow Rate........................... 116 l (, l'ow Motor Calibrations for Nit:rOgent r...........145:.. I:1.

LIST OF FIGURES (Continued) Figure Page 17 Flow Meter Calibrations for Carbon Dioxide........ 147 18 Flow Meter Calibrations for Ethane............ 149 xiv

NOMENCLATURE A, B Pure components A and B A0,BOCO Constants in the Benedict-Webb-Rubin equation of state a, b,c Constants in the Benedict-Webb-Rubin equation of state an,bn,cn Constants in equation for smoothing excess enthalpies with respect to composition ao,bco Constants in equation for smoothing the enthalpy difference AkHo with respect to composition BllBN Second virial coefficient of nitrogen B22 Second virial coefficient of carbon dioxide B12 Interaction virial coefficient CaC Connections in power input circuit to calorimeter Cp Isobaric heat capacity CV Isochoric heat capacity d Internal diameter of tubing used for flow meter e(z) Error in variable z ec Voltage across calorimeter heater F Flow rate f Friction factor H Enthalpy per unit mass or per unit mole H Partial molal enthalpy AHo Experimentally measured enthalpy difference at calorimeter outlet conditions AIcorr Correction for impurities ic Current in calorimeter heater KE Kinetic Energy AKEM Correction for kinetic energy differences L Length of flow path in flow meter M Molecular weight xv

m,n Constants in derivation of equation for correlating results of flow meter calibrations m Mass P Pressure AP Pressure drop or difference APcorr Correction for pressure drop Q Rate of heat leakage to calorimeter R Gas constant Rc Calorimeter heater R25 Resistance of standard resistor at 25~C RT Resistance of standard resistor at Tres ~C res ReRiRs Standard resistors RfRg Rheostats Rh Helipot Re Reynolds Number SaSb Switches in power input circuit to calorimeter T Temperature AT Correction for temperature difference corr Tres Temperature of standard resistors u Mean Velocity V Volume per unit mass or per unit mole Ve Voltage drop across standard resistor Re Vi Voltage drop across standard resistor Ri W Electrical energy input to calorimeter (W/F) Power to flow ratio or power per unit flow w Mass fraction x Mole fraction Y CGroup used for error analysis of flow meter calibrations y Fraction of impurity in inlet stream to calorimeter xvi

Z Dependent variable in error analysis z Independent variable in error analysis Subscripts A,B Pure component A and pure component B AB Mixture of A and B AM, ABM Impure A and impure AB ac Aerosol can used for gas density analysis C2H6 Ethane C02 Carbon dioxide c Critical property ct Calibration tank F Flow meter I Impurities N Nitrogen n Nominal experimental conditions O Oxygen o Conditions at calorimeter outlet P Constant pressure r Reduced property T Constant temperature V Constant volume 1 Conditions at calorimeter inlet 1 2 Conditions at calorimeter inlet 2 Suer s cr ipts E Excess property M Mixing function xvii

M- Ideal mixing function 0 Zero pressure property Greek Letters 7, y Constants in Benedict-Webb-Rubin equation of state a, B Temperature coefficients of standard resistor F'6F pConstants in correlation equation for flow meter calibrations r\ Viscosity ~a ~ Time period of gas collection [t Adiabatic Joule-Thompson coefficient p Density Cr Standard deviation cp Isothermal Joule-Thompson coefficient xviii

ABSTRACT THE EXPERIMENTAL DETERMINATION OF THE ENTHALPY OF MIXING OF BINARY GASEOUS MIXTURES UNDER PRESSURE by Arun Vasudev Hejmadi Chairman: John E. Powers Reliable and accurate data on the thermal properties of mixtures are essential for the design of equipment and the testing of enthalpy prediction methods. The importance of the enthalpy of mixing is that it directly measures the solution effect —that is the difference between the enthalpy of the mixture and the enthalpy of its constituents. Thus, the objectives of this research were (1) to design and construct a flow calorimetric facility for the experimental measurement of the enthalpy of mixing of binary gaseous mixtures at elevated pressures, (2) to calibrate and test the equipment and (5) to obtain data on systems of industrial significance and in regions of theoretical importance. In this flow calorimetric facility, the system brings two gases at the same pressure and temperature to the calorimeter where they are mixed. If there is a decrease in the temperature of the resultant mixture, electrical energy is supplied to the gases to minimize the temperature difference between the inlet pure gases and the outlet mixture stream. If there is an increase in the temperature of the mixture, the calorimeter may be operated without the electrical energy input. The flow rate of each gas is metered prior to entering the calorimeter. Each flow meter was calibrated tby flowing for a measured period of time under 8teuliy s ta'te coildit:ions into a tank of measured volume. The accuracy of xix

the hflow meterA:i ng was check(ed by comparing compositions calculated from the flow rates of the two gases with the results of a gas density analysis. Data were obtained on the following systems at the nominal conditions listed: (1) Nitrogen-carbon dioxide mixtures at 531C, p'00 psia and 950 psia, and at 40~C at the same pressures at a minimiun of four compositions. (2) Nitrogen-ethane mixtures at 32.58~C and 401 psia at four compositions. (3) Nitrogen-oxygen mixtures at 250C and 1001 psia at one composition. The data on the nitrogen-carbon dioxide system at 31~C and on the nitrogen-ethane system at 32.538C represent the first enthalpy of mixing measurements made at a reduced temperature of unity of one of the components in a mixture. The experimental measurements on these three systems were interpreted to yield values of the excess ent halpy at the measured conditions of pressure and temperature at the calorimeter outlet. The excess enthalpies were then normalized to nominal experimental conditions and, finally, smoothed with respect to composition. Results on the nitrogen-carbon dioxide system at 40~C and 500 psia were used to check on the adiabaticity of the experimental measurements. Ten repetitive measurements made at 0.5 mole fraction nitrogen over a range of flow rates indicated that the heat leak in the calorimeter was less than the experimental precision (0.3 percent). The estimated accuracy of the data is 0.8 to 2.1 percent for the data on the nitrogen-carbon dioxide and nitrogen-ethane mixtures and ten percent for the data on the nitrogen-oxygen mixtures. Comparisons were made with experimental results on the nitrogencarlbon dioxide system of another investigator at 40~C and at the same pressures as the present measurements. The excess enthalpy values agreed xx

within the combined experimental error of both investigations. Excess enthalpy values were calculated from the original Benedict-Webb-Rubin equation of state and were found to deviate five percent or less from the experimental results for the mixtures of nitrogen with ethane and with carbon dioxide. xx3i

INTRODUCTION Most process streams encountered in industry are mixtures of two or more components. Hence, it is important to obtain information on the thermal properties of mixtures. Very limited quantities of data are available on the enthalpies of mixtures because of the experimental difficulties and the considerable expense involved. Therefore, it is preferable to obtain data in limited and crucial regions —near the two phase envelope or close to the critical point of one of the components —where substantial deviations from ideal solution behavior are anticipated. The thermal property which yields the most information in such regions is the enthalpy of mixing or the excess enthalpy because by definition it measures the deviation from ideal solution behavior. For the reasons stated earlier, it is not possible to obtain data on the unlimited number of mixtures which may exist. A feasible alternative is to employ an enthalpy prediction method. Before such a method is used, however, it is necessary that its reliability be proved. This may be accomplished by comparing predicted excess enthalpies with the experimentally determined quantities. The enthalpy of mixing is obtained from a prediction method as the difference of two quantities — the enthalpy of the mixture and the enthalpy of the ideal solution of its constituents —both of which are of the same order of magnitude. Hence such a comparison constitutes an extremely severe test of' the applicability of a prediction method. Therefore, the objectives of this research are (1) to design and build a flow calorimetric facility for the experimental determination of the enthalpy of mixing of binary mixtures in the gas phase and under -1-_

-2pressure (2) to calibrate ard( test -the equipment (5) to obtain data on systems of industrial sigrl,'icar(c and inl relions of' theoretical imortanct I c.

EXPERIENCE OF PREVIOUS INVESTIGATORS This review covers both sources of data and experimental techniques. References are given to excess property measurements of mixtures of relatively simple molecules in the gaseous and liquid phase. Calorimetric techniques for enthalpy of mixing measurements of liquids and gases are discussed. Enthalpy prediction methods are considered very briefly. A review is presented on the thermodynamic properties of those pure components and mixtures which are relevant to this research. Excess Property Measurements on Liquids The measurement of the enthalpy change on mixing liquids at ambient conditions preceded the work at low temperatures. Recently, calorimetric data have been obtained for systems with endothermic (Mrazek (122) (146) and Van Ness, Savini, Winterhalter, Kovach and Van Ness, ) Savini, Winterhalter and Van Ness(147)) or exothermic enthalpies of mixing (Winterhalter and Van Ness(l82)). The systems so investigated generally consist of components (alcohols, aromatics) whose behavior does not approximate that of simple molecules, e.g. argon, krypton, etc. Measurements of excess properties at low temperatures and low pressures occurred next in chronological order. Table I lists investigations of excess volume, excess enthalpy and ex:c(s Jfree energy of binary systems of liquid mixtures of relat1.ve(ly simrplel mrolec(ules. All of these experiments have been performed below -240O~]' arid at pressures lower than 200 psia. In the references listed in Table I, excess free energies were calculated from volumetric and phase behavior measurements. There have been three different approaches used in excess volume investigations. -3

TABLE I INVESTIGATIONS OF EXCESS THEERMODYINAMIC PROPERTIES OF BINARY MIXTURES IN THE LIQUID STATE AT LOW TEMPERATURES System Property Year Author Reference He3-He4 HE 1953 Sommers, Keller, Dash 157 CO-CH VE, GE 1956 Mathot, Staveley, Young, Parsonage 105 Ar-CH4 VE, HE 1957 Jeener 70 CO-CH HE 1957 Pool, Staveley 131 c-i4 i 13~ N2-02, Ar-02 VE 1958 Blagoi, Rudenko l8 Ar-CH4 VE, HE 1958 Mathot 103 N2-02 VE, R 196o0 Knobler, Knaap, Beenakker 8o H2-D2 VYE, HE 1960 Lambert 88 02-N2, 02-Ar VE, GE 1961 Knaap, Knoester, Beenakker 79 nH2-nD2, nH2-pH2 nD2-oD2 Ar-02, N2-02 HE 1961 Knobler, Van Heijningen, Beenakker 81 H2-D2, H -HD, HE 1962 Knaap 78 HD-D2 Ar-CH4, CO-CH4 VE, HE 1962 Lambert, Simon 89

TABLE I (Continued) System Property Year Author Reference Ar-02, Ar-N2, VEIHEGE 1962 Pool, Saville, Herrington, 130 N2-02, N2-CO, Shields, Staveley Ar-CO CO-CH4, Ar-CH4 VEHEGE 1963 Mathot 104 He-nD2 GE 1963 Simon 154 CHq-CRH4 CE 1965 Cutler, Morrison 31 Ar-CO, L2-O0 VEHRE GE 1966 Duncan, Staveley 36 CO-N2 \j1 CO-CH4, Ar-CH4 GE 1966 Sprow, Prausnitz 158 N2-02, Ar-N2 N2-CH4 Ar-Kr VE GE 1967 Davies, Duncan, Saville, Staveley 33 CH4-Kr, CH4-N2 VE 1967 Fuks, Bellemans 47 N2-HR vE 1967 Mastinu 100 oH2-pH2, oD2-pD2 VE, H 1968 Bakx, Knaap 7 Binary mixtures of VE 1968 Shan'a, Canfield 152 CH4, C2R6, C3Ri and nC4Ho10 He3-He4 HE 1969 Seligmann, Edwards, Sarwinski, 150 Tough Kr-CH4 VE 1969 Calado, Staveley 23

-6Knaap, Knoester and Beenakker(79) directly measured the volume change which accompanies the mixing of the pure components. In the calorimeter of Jeener(70) constant pressure is maintained in the mixing chamber by cxtcrlrll mcaul, anuld ex(cess volul(me and xc(ss crthalpy are determined simultanleously. The third and most commonly used technique involves calculating excess volumes from density studies on pure components and their mixtures using a pyknometer (e.g. Pool et al.(130)). The calorimeters employed in making enthalpy of mixing measurements have certain common features. They are all "closed-system" calorimeters. The two pure components are charged into separate chambers which share one common wall made of thin aluminum or copper foil. The liquids are brought into contact by breaking the aluminum or copper foil partition and mechanically stirring the mixture. The cooling which accompanies the mixing process is compensated for by applying a measured potential difference to a resistance wire wound around the mixing chamber. The mixing chamber is enclosed by a vacuum jacket and the entire unit located in a constant temperature bath during the measurements. The main objective of this basically unsteady state technique is to minimize heat losses from the calorimeter to the surroundings by adding a controlled quantity of electrical heat input so as to maintain isothermal conditions in the calorimeter throughout the experiment. Sommers, Keller and Dash(17) made one of the first enthalpy of mixing measurements. They brought He3 and He4 together by breaking a glass vessel containing one component within a flask containing the other pure component. The first enthalpy of mixing calorimeters were reported at about the same time by Pool and Staveley( 3) and Jeener. (7 Pool, Saville, Herringtozn, Shields and Staveley(130) subsequently published

-7the design of a modified version of their original calorimeter. (13) Knobler, Van Heijningen and Beenakker(81) reported measurements on a calorimeter that eliminated the vapor spaces which existed in calorimeters of other investigators. Knaap(78) modified the calorimeter of Knobler et al. (1) for measuring small values of excess enthalpy such as in the hydrogen-deuterium system. Discussion of Closed-System Calorimeters Some of the design and operational problems encountered with closed system calorimeters are outlined in this section. This account is not intended to be exhaustive since detailed discussion of such types of calorimeters are available.(106) The object of this section is to provide a basis on which to compare closed-system calorimeters with flow calorimeters (discussed in next section) with a view to applying them for excess enthalpy measurements under pressure on gases. There are three areas in which difficulties arise with a closedsystem calorimeter. They are: 1. Need for mechanical stirring: The energy injected into the system by mechanical stirring must be accounted for when calculating excess enthalpies. Magnetic stirrers have been used in all calorimeters thus bypassing the need for stirrer shaft packing suitable for low temperatures. In all but the calorimeter of Pool et al.(130 131) the rotor on which the magnetic field acts is separated from the paddle by a long stirrer shaft. To eliminate field effects, Pool et al.(131) switch off the stirrer when making temperature measurements. 2. Constancy of pressure during mixing: Volume changes accompany the mixingllt process and maintain li qt. the pressure or volume constant introduces errors. The c-alorimelLers ol Pool et a-. 3 3) Koer el J ( l)

-8and Knaap(78) are essentially constant volume devices. Jeener (7) maintains constant pressure by adding or withdrawing measured quantities of material from the calorimeter. He, therefore, has to make corrections for the mass withdrawn but he also simultaneously determines excess volumes. 3. Corrections for vapor spaces: Some evaporation or condensation of material accompanies the mixing process if there are vapor spaces in the calorimeter. Both Pool et al.(130,131) and Jeener(70 ) make substantial corrections for this effect when calculating excess enthalpies. Closed-system calorimeters may be used for measurements on gases without corrections for vapor spaces. However, working with gases introduces some unique problems. Excess enthalpies of gas mixtures are smaller than for liquids except near the critical temperature of one of the components. Hence, large masses of the two gases are necessary to increase the magnitude of the overall heat effect to bring it into a measurable range. This implies larger calorimeters than are used for liquids since gases occupy larger molar volumes than liquids. Mechanical stirring of large volumes of gases and the design and construction of a large calorimeter for high pressure usage introduces considerable difficulty. Discussion of Flow Calorimeters A flow calorimeter eliminates or reduces the magnitude of these problems: 1. Need for mechanical stirring: A flow calorimeter can be built with devices (e.g. baffles) which facilitate internal mixing without the need for externally introduced devices (e.g. stirrers). Such devices

-9usually cause a pressure drop across the calorimeter which must be accounted for when interpreting the data. However, they can be designed to minimize this effect. 2. Constancy of pressure during mixing: The nature of the flow process is such that the calorimeter is at essentially constant pressure regardless of any volume change on mixing. 3. Corrections for vapor spaces: This can be solved by eliminating any dead spaces in the calorimeter where the flowing material can accumulate. The magnitude of the heat effect (Btu/minute) can be amplified by increasing the flow rate of the two gases rather than increasing the size of the calorimeter. The residence time of the gases can be increased by lengthening the flow path of the gases within the calorimeter. Flow calorimeters suffer from certain disadvantages. The factor which limits accuracy is the determination of the flow rate. Also, once they are mixed, the gases cannot be recycled to the calorimeter via a compressor without a separation facility. This once-through facility requires large quantities of gases. This entails considerable operational expense especially with costly materials. Design and construction of a suitable calorimeter presents few special problems especially since generalized criteria for the design and construction of flow calorimeters have been discussed by other investigators. ()5 The advantages of a flow calorimeter so outweigh the alternative closed-system calorimeter for measurements under pressure that all such enthalpy of mixing determinations on gas mixtures have employed flow calorimetric systems.

-10Excess Enthalpy Measurements on Gases Pioneering work was done at Leiden, Netherlands, by Beenakker and associates. (10l82l70) They investigated a variety of systems all of which are listed in Table II. Of perticular interest are their excess enthalpy measurements on the nitrogen-hydrogen, nitrogen-argon and hydrogen-argon systems because Zandbergen and Beenakker(187) measured excess volumes of the same systems at very similar conditions of pressure and temperature. He utilized a technique closely resembling that of Knaap, Knoester and Beenakker.(79) Lee and Mather(90) report that their results on the nitrogen-hydrogen system agree within three percent with the excess enthalpy values measured by Knoester et al.(82) Table II presents references to all the excess enthalpy data currently available. The accuracy of this data is believed to be three to five percent with the exception of the data of Kotousov and Baranyuk.(85) The latter are the only investigators among those listed in Table II who did not employ a flow calorimeter. They allowed the counter-current diffusion of the two pure gases along the axis of a tube and recorded temperature and composition profiles with time. Though direct comparison at identical conditions is not possible, their excess enthalpy values are an order of magnitude higher than the extrapolated results of Knoester(82) and Van Eijnsbergen.(l70) A flow facility which is under development but from which no data has been reported has been described by Jacobsen and Barieau.9) This facility is designed to measure excess enthalpies and excess heat capacities of helium-nitrogen mixtures. This review would be incomplete without the mention of some indirect determinations of excess properties of industrially significant systems: Ernst(42) calculated excess heat capacities of freon mixtures

TABLE II EXPERIMENTAL INVESTIGATIONS OF THE ENTHALPY OF MIXING OF GASES System Temperature Pressure Year Author Reference __OF __ psia H2-N2 68 440-1200 1962 Beenakker, Coremans 10 H2-N2, H2-Ar, -196 to 66 120-1900 1965 Beenakker, Van Eijns- 11 N2-Ar, CH4-H2 bergen, Knoester, Ar-CH4 Taconis, Zandbergen H2-N2, K2 -Ar -196 to 66 450-1900 1967 Krnoester, Taconis, 82 H2-Ar, H2-i-2-Ar Beenakker H2-CH4, He-CH4, -154 to 66 120-1800 1968 Van Eijnsbergen, 170 CH4-N, He-Ar Beenakker N2-CH4 -108 to 104 250-1500 1969 Klein 77 H~-Ar,, Hi-K, 72 4.4-14.7 1969 Kotousov, Baranyuk 85 H~-CO2 N2-CO, 104 140-1800 H-2 -100 to68 140-2000 1970 Lee, Mather 90 2 -N~. -loo to 68 14o-2000

-12from his own measurements of heat capacities on the pure components and their mixtures. Mather(11) plot;ted cxcess enthalpies of a methanenitrogen mixture between -,2-0 uand +40.1C' at 1000, 1500 and 2000 psia. He calculated these values from his experimentally determined enthalpy values for that mixture and the enthalpy values of the pure components determined by previous investigators. Bhirud and Powers(16) report excess heat capacities of methane-propane mixtures derived from measurements on the mixture and the pure components. Comparison of Flow Calorimetric Techniques for Gases The similarities and differences between the experimental and data interpretation techniques used by various investigators are described in this section. The object of these descriptions is to facilitate comparison of previously done work with the present research as it is described in later chapters. The descriptions will be under the following headings: 1. Calorimeter Design 2. Flow and Composition Measurement 3. Mode of Operation 4. Interpretation and Smoothing of Data Calorimeter Design The same design principle is used by all investigators. The temperatures of the two pure gases are monitored as they enter the calorimeter. On mixing, a controlled quantity of heat is added to maintain the exiting gas mixture at the same temperature as that of the two inlet gases. All but Beenakker and coworkers (10'11 170) use a similar mixing capsule. Mixing of the two pure gases is accomplished by Beenakker

-13and coworkers (l 82 170) with perforated baffles placed at right angles to the direction of flow of gas. Heat is supplied via a resistance wire that is wound on the outside of the mixing chamber. The resistance windings are suitably shielded from radiating heat to the surroundings. The (77,90) mixing capsules used by the other investigators(77'9 ) consist of concentric cylindrical baffles with the gas being introduced in the innermost baffle. Gas flow is parallel to the cylinder axes and the direction of its flow is reversed when it goes from one baffle to another. The resistance wire for supplying heat is wound on the inner baffles and is in direct contact with the gas. All the calorimeters except Klein's(77) employ a vacuum jacket for overall insulation. Klein's(77) calorimeter is distinctive in its usage of bakelite and nylon for insulation and for reducing the heat capacity of the calorimeter. Flow and Composition Measurement All the investigators measure flow rates by collecting the mixture at atmospheric pressure in a gasometer over a measured period of time. Beenakker and coworkers( 7 ) use an ingenious flow system which allows them to calculate and control the mixture composition: The gases are stored separately in cylinders of differing internal volumes. One cylinder is charged with gas at a slightly higher pressure than the other Flow is commenced by opening the valve on the cylinder with the higher pressure in it. Adjustment of a valve downstream from the calorimeter sets the operating pressure in the latter. When the pressure in the two cylinders is equal, the valve on the previously isolated cylinder is opened. The composition of the gas mixture may be calculated from

-14the ratio of internal volumes of the cylinders and the densities of the gases contained in them. (90) The flow system employed by Lee and Mather is similar to that of Beenakker and associates. Hence they use the same technique to'al'ulate tfhe composit:liorl of the rln trogren-hylrogCen mixture. THowever, the lquarntitative analysis of their nitrogen-(cartbon dioxid(l mixtures was done by gas chromatography. Klein(77) also employed the latter method for analyzing methane-nitrogen mixtures. Mode of Operation Beenakker and associates(l0' 1182'170) vary the pressure in the calorimeter by allowing the supply cylinders to exhaust continuously. Hence data is obtained at constant temperature with unsteady conditions of pressure in the calorimeter. Excess enthalpy measurements are made at closely spaced values of pressure from 1900 down to 120 psia, which are then corrected for the heat capacity of the calorimeter. Further, with a given set of cylinders, the composition of the gas mixture varies if the ratio of the isothermal compressibilities -(( -V of the two components changes with pressure. For the gases studied by Beenakker and coworkers (11128017 ) this correction is small since the gases in the tanks at room temperature are at high reduced temperatures. Lee and Mather(90) encountered difficulties with their excess enthalpy measurements on nitrogen-carbon dioxide mixtures because the carbon dioxide supply tanks were at room temperature where, due to the proximity of the critical temperature, the compressibility varies rapidly with pressure. For every set of cylinders used, they obtained data at scattered values of pressure and composition.

-15(77) Klein's calorimetric measurements were at steady state conditions. Pressure regulators controlled the pressure of the gas entering the system from the supply cylinders. Interpretation and Smoothing of Data Different techniques are used to compensate for operational variations in pressure, temperature and composition in the data obtained from the three facilities. Beenakker and associates(10 182170 ) present their raw experimental data in tabular and graphical form and do not attempt to smooth the data. Recently, Hsi and Lu(6) published values of excess enthalpies, excess entropies and excess free energies obtained by graphically smoothing excess enthalpy data of Beenakker et al.( )' ) and (82) (187) Knoester() and excess volume data of Zandbergen 7on the nitrogenhydrogen, nitrogen-argon and hydrogen-argon systems. (77) Klein(77) took data as a function of composition at constant temperature and at slightly varying values of pressure. Smoothing this data for pressure and composition variation involved the use of a virial equation of state. The latter was mathematically manipulated and equated to the excess enthalpy. Constants for the equation were determined by a least squares analysis. The equation of state with the regression coefficients was then used to generate smoothed values of excess enthalpy. This approach requires a large number of data points. For example, approximately 40 excess enthalpy values at a given temperature required the evaluation of 16 constants (using up to hhe fifth virial coefficient) before the standard deviation was less than tha experimental uncertainty (3 to 6 percent). The calorimetric data obtained by Lee and Mather(90) require smoothing over pressure and composition at a given temperature. Their r HE pressure interpolation method involves plotting | ( —--- versus pressure. At low pressures where molecular interactions are purely binary in

nature, the ordinate is independent of pressure. Even at elevated pressures, this technique reduces the variation of excess enthalpy with pressure by an order of magnitude. It loses its efficacy, however, in high pressure regions where the excess enthalpy versus pressure curve goes through a maximum. For smoothing with respect to composition, they use plots of HE1-x) versus mole fraction, x. This method reduces the error due.x(l-x)J to composition interpolation because it changes the parabolic plot of HE against x to a monotonic variation in.L.. versus x!x(l-x)J Prediction Methods Methods for the prediction of the enthalpies of pure components and mixtures have been reviewed by Hobson and Weber, (6061) Nathan(123) and Mather.01) Curl and Pitzer(30) developed an enthalpy correlation based on the principle of corresponding states which utilizes three macroscopic parameters: reduced pressure, reduced temperature and acentric factor. A corresponding states treatment based on two molecular parameters was suggested independently by Prigogine33) and by Scott.( Various equations of state, such as the Benedict-Webb-Rubin(12) or the virial equation of state can also be used to determine enthalpies. Powers(132) and Sehgal et al.(l49) have shown by comparisons with other prediction methods and with experimental data that the B-W-R equation(l2) is one of the better methods for predicting enthalpy departures, H-H0, in the gaseous phase for both pure components and mixtures. Hence, it is chosen as the method by which excess enthalpies may be predicted for comparison with the experimental results of this research. This equation is pressure explicit: P = RTp + (BoRT-A - _~)p2 + (bRT-a)p3 + C p3(l+yp)e "P + aap (1) P TRTp + r 3 2YTP 2~~~~~~~~~ ao i

-17and contains eight constants which are usually determined from a least squares fit of PVT data. These constants have been determined for a large number of pure substances —as may be seen in the compilation of constants for 58 compounds by Cooper and Goldfranck. (25) For mixtures, however, constants are less readily available and therefore it is necessary to estimate them from constants for pure substances with mixing rules such as those suggested by Benedict, Webb and Rubin.(13) Review of Thermodynamic Properties Raw calorimetric data normally do not directly yield values of the enthalpy of mixing. Some corrections have to be made to the raw data for effects such as Joule-Thompson cooling due to pressure drop across the calorimeter. These corrections, which are discussed in detail in later chapters, require values for the thermodynamic properties of pure components and their mixtures. The object of this review is to give references to work on pure components and mixtures which are relevant to this research. This consists mainly of references to thermal properties with some mention of more recent investigations of other thermodynamic properties. Unless specified, the references given in this review are to measurements of properties under pressure. This review covers the properties of: 1. Nitrogen 2. Carbon dioxide 3. Ethane 4. Oxygen 5. Nitrogen-carbon dioxide mixtures N). Nitrogen-ethane mixtures'. i\:i itro;tetl-oxyp:eIl mixtures

-18There are several excellent general reviews available. Reviews of experimental measurements of the thermal properties of pure components have been reviewed by Masi(99) and of mixtures by Mage, Jones, Katz and Roebuck(97) and more recently by Ycsavage, Mather, Katz and Powers.(l84) Investigations into PVT, thermal and transport properties of several pure components have been reviewed by Wilson, Clark, and Hyman.(181) Nitrogen A literature review and compilation of the properties of nitro(34) (94) gen has been made by Din. Lunbeck, Michels and Wolkers calculated the PVT and thermal properties from -193~F to 302~F and up to 90,000 psia. More recently Tsiklis(l66) and Tsiklis and Polyakov(168) studied the PVT behavior up to 750~F and 147,000 psia of nitrogen by two different techniques and calculated the thermodynamic properties(169) to the same limits of pressure and temperature. Second virial coefficients of nitrogen have been reported by (126) (128) (65) Otto, Pfefferle, Goff and Miller and Huff and Reed. Values at low temperatures (-328~F to -185~F) have been listed by Din(34) and measured by Brewer(20) to -240~F. Heat capacities at constant pressure were measured at and above room temperatures and at high pressures by Workman(183) and Mackey and (95) Krase. The former measured the ratio of the heat capacity at the experimental pressure to the heat capacity at one atmosphere at 78.8~F and 140~F. Mage et al.(97) give enthalpies of nitrogen from 0 to 2000 psia and -250~F to 500F. Roebuck and Osterberg( ) measured Joule-Thompson coefficients for nitrogen which were subsequently corrected for an experimental error. Ahlert also measured integral Joule-Thompson coefficients

-19over a wide range of pressure (0-2400 psia) and temperature (-100~F to +100~F). Data on isothermal Joule-Thompson coefficients have been reported by Ishkin and Kaganer,(68) Gusak,(54) Charnley, Isles and Townley,(24) and Mather, Katz and Powers.(l02) Michels and Gibson(112) give viscosity as a function of pressure (200-15,000 psi) and temperature (78~F-1700F). Kestin and Leidenfrost(74) obtained viscosities of nitrogen at 680F as a function of pressure on the oscillating-disk viscometer. Constants for the Benedict-Webb-Rubin equation of state,(12) are reported by Stotler and Benedict, 160 Bloomer and Rao, (1) and rain and (27) Sonntag. (27 Carbon Dioxide (91) Liley(9) reviewed the data up to 1957 and presented tabulations of high temperature and high pressure properties. Subsequently, Newitt, Pai, Kuloor and Huggill(124) compiled and calculated the properties of carbon dioxide between -112~F and 302~F and up to 44,000 psia. Volumetric data on carbon dioxide were obtained by Michels and coworkers(l07,108,113) and thermodynamic properties calculated from them have been published by Michels and DeGroot.(lll) The most recent compilation and review is the book coauthored by Vukalovich and Altunin.(172) They describe experimental techniques, evaluate the accuracy of the data, and then present tables of thermodynamic and transport properties from the triple point to 1830~F and up to 9100 psia. A considerable amount of work has been done on carbon dioxide in the USSR. A large volume of work is published in Teploenergetika (Thermal Engineering). A number of density measurements have been reported in that journal since the publication of book by Vukalovich and Altunin(172) but are not directly referred to here as they are too numerous.

-20Low pressure volumetric data have been reviewed by Vukalovich (172) and Altunin.( ) Second virial coefficients at several temperatures above ambient conditions have been given by Huff and Reed.(65) Pfefferle, Goff and Miller report second and third virial coefficients at 86~F. The data used in this research is that of Michels and Michels.( l3) Constant pressure heat capacities of carbon dioxide were measured by Shrock(53) from 15 to 1000 psia and 150 to 950~F. Koppel and Smith 84) obtained enthalpy differences and heat capacities close to the critical point. Vukalovich and associates(175-179) report heat capacities of carbon dioxide between 68 to 932~F and 76 to 3300 psia. Extremely precise determinations of heat capacity between 50 to 2660F and 1300 to (136) 3700 psia were obtained by Rivkin and Gukov. A total of 171 data points within this range of pressure and temperature permits the accurate determination of the maxima in plots of' isobaric heat capacity versus (3) temperature. Recently Altunin and Kutznetsov( measured isobaric heat capacities between 62 and 140~F and 150 to 750 psia. Isochoric heat capacity measurements other than those listed by Yesavage et al.(184) are those of Amirkhanov. (4,5 6) Roebuck, Murrel and Miller(139) measured Joule-Thompson coefficients of carbon dioxide between -60~F and 5700F and up to 3000 psia. Isothermal Joule-Thompson coefficients have been reported by Charnley, (24=) Isles and Townley() between 32~F and 113~F and 59 and 660 psia. Vukalovich, Altunin, Bulle, Rasskozov and Ertel(173) describe a calorimeter for measuring isothermal Joule-Thompson coefficients for carbon dioxide and report some data.(17) Viscosity measurements have been made by Michels, Botzen and Schurman(l10) by the transpiration method. They review all the work done previous to their own.

-21Constants for the Benedict-Webb-Rubin equation of state(12) (37) have been calculated by Eakin and Ellington for use in mixture pro(29) perty calculations. Cullen and Kobe give two sets of constants each of which is to be used in a different temperature range. Sass, Dodge and Bretton(l44) calculated B-W-R constants for carbon dioxide, ethylene and their mixtures by regressing on compressibility factor data obtained between 122~F to 257~F and up to 7350 psia. Ethane Tester(162) has reviewed and compiled the thermodynamic properties of ethane. Michels, Van Straaten and Dawson(116) report PVT data and Michels and Nederbragt(l14) report compressibility factors of ethane. Other PVT data on ethane are those of Reamer, Olds, Sage and Lacey,(134) Beattie, Hadlock and Poffenberger(8) and Beattie, Su and Simard.(9) Early work on second virial coefficients have been reviewed by Tester. ) Hoover, Nagata, Leland and Kobayashi(62) reviewed the more recent work and presented their own accurate measurements. Data have been reported by Huff and Reed (65) and Michels, Van Straaten, and Dawson.(l16) (143) Sage, Webster and Lacey obtained a large quantity of PVT data. They also determined isochoric heat capacities and Joule-Thompson coefficients but over a small range of pressure and temperature. Saurel(144) has given a single plot of Cp/CV versus pressure at the critical temperature of ethane. Tsaturyants, Mamedov and Eivazova(l65) report isothermal Joule-Thompson coefficients abcYe 116~F. Furtado et al.(48) have measured the effect of both pressure and temperature on the enthalpy of ethane but have not published their results. Viscosity data on ethane have been reviewed, and selected values (3)ict, We giUven by Eakin, Starling, Dolian and Ellington. " Benedict, Webb and

-22(12,14) (12A)) (43) Rubin tl, i') Opfell,',chlinger and u:te (L'- and Eubtank and lt'ort I3) have evaluated constants for the Benedict-Wetbb-Ruhirn equation of state. Oxygen Hust(66) has authored a bibliography of thermophysical properties of oxygen. Another NBS publication, Circular 564 by Hilsenrath et al.(59) presents calculated thermophysical property values. The volumetric properties of oxygen have been measured by Michels, Schamp and de Graaf,(115) Otto and Hoborothers.(49 ) Weber(180) and Goodwin(50) have published calculated values of the thermodynamic functions of oxygen up to 4800 psia and from its triple point to 80~F. The only measurements of isobaric heat capacity under pressure have been those of Workman.(183) Voronel' Chaskin, Popov and Simkin(171) and, more recently, Goodwin and Weber (51,52) have measured isochoric heat capacities in the region surrounding the critical point. Joule-Thompson coefficients have been measured by Brilliantinov(21) at low pressures and by Bennewitz and Andreewa(l5) near the critical point of oxygen. Viscosities in the gas phase under pressure have been reported bydLeidenfrost(7)v4) ( Cntt for by Kestin and Leidenfrost(74) and Luken and Johnson. (92) Constants for the B-W-R equation of state(l2) have been calculated by Seshadri, Vishwanath and Kuloor (151) Nitrogen-Carbon Dioxide Mixtures The major experimental investigations of the thermodynamic properties are given in Table III. The ice point is the lowest temperature at which PVT work has been done.(87) Low temperature vapor liquid equilibria have been reported by several investigators.(32'72'129) Smith,

TABLE III EXPERIMENWTAL IlNVESTIGATIONS ON THE BINARY SYSTEM NITROGEN-CARBONT DIOXIDE UNDER PRESSURE Property Temperature Pressure Year Author Reference OF psia P-V-T-x 32 to 392 76o-7500 1940 Krichevsky, Markov 87 P-V-T-x 77 to 257 440-7350 1944 Haney, Bliss 56 p-V-T-x 86 5-1000 1955 Pfefferle, Goff, Miller 128 g-V-T-x 59 to 90 820-2000 a1965 iazanova, LensevskaTa 76 7 —L ~-60 to 71 up to 2400 19214- Pol itzer, Strebel 129 (Q V-L up to 86 up to 2900 1939 Abdullaev 1 V-L 43 to 68 150-1600 1945 Mills, Miller 120 V'-L 59 to 86 740-1500 1962 Krichevsky, Khazanova, 86 Lensevskaya, Sandalova -L -65 to 32 180-2100 193 Dana, Zenner 32 V-L -40 to 77 290-2900 1966 Kaminishi, Toriumi 72 S-V -205 to -115 70-1500 1962 Smith, Sonntag, Van Wylen 155 Jcule- 77 to 167 15-290 1965 Grossman 53 Thompson Viscosity 68 15-310 1966 Kestin, Kobayashi, Wood 73

-24(155) Sonntag and Van Wylen ) studied solid-vapor phase behavior. Grossmanl(3) made Joule-Thompson coefficient measurements on nitrogen-carbon dioxide mixtures over a limited range of pressure and temperature. Precise values of the vLrcositics of several binlary- mixtures have been measured bty Kestin, Kobayashi and Wood(73 using the oscillating-disk viscometer. Volumetric properties at low pressures were made initially by Fuchs(46) and Trautz and Emert.(4) Measurements of interaction virial coefficients at single values of temperatures were made by Edwards and (41) ( ( ) l iohls Roseveare() Lunbeck and Boerboom,(93) Miller and Gorski,(l9) Michels and Boerboom,(109) and Pfefferle, Goff and Miller.(128) Data on virial coefficients at several temperatures between -580F and 3920F have been reported by Zaalishvili,(l86) Cottrell et al.(26) Huff and Reed,(65) and (20) Brewer. () Nitrogen-Ethane Mixtures A list of experimental investigations of the nitrogen-ethane system under pressure are given in Table IV. Reamer, Selleck, Sage and Lacey35) made PVT measurements up to extreme pressures and from ambient temperatures to 464~F. Sage and Lacey(142) have published tables of thermodynamic properties of nitrogen-ethaine mixtures based on that work. The only investigations of thermal properties have been the Joule-Thompson measurements of Head(7) and Stockett ard Wenzell.(l59) Huff and Reed(65) report virial coefficients of nitrogen-ethane mixtures. Nitrogen-Oxygen Mixtures Of the three mixtures of interest here, the largest amount of work has been done on nitrogen-oxygen mixtures. The majority of the investigations have been on mixtures with the composition of air. An

TABLE ITV EXPERIMENTAL INVESTIGATIONS ON THE BINARY SYSTEM NITROGEN-ETHANE UNDER PRESSURE Property Temperature Pressure Year Author Reference OF psia P-V-T-x 40-464 15-10,000 1952 Reamer, Selleck, Sage, Lacey 135 P-V-T-x, -290 to 110 50-4000 1955 Eakin, Ellington, Gami 38 V-L V-L -310 to 90 110-2100 1957 Fastovski, Petrovski 44 V-L -260 to 90 100-1850 1959 Ellington, Eakin, Parent, 40 Gamni, Bloomer V-L -255 to -220 up to 591 1969 Yu, Elshayal, Lu 185 JouleThompson 10 to 190 25 to 590 1960 Head 57 JouleThompson -148 to 77 up to 2500 1964 Stockett, Wenzel 159

-26extensive bibliography of the thermophysical properties of air have been authored by Hall.(5) Of the few experimental investigations listed in Table V, only the work of Kuenen, Verschoyle and Van Urk(75) and Dodge (35) and Dunbar are not on air. Virial coefficients of nitrogen-oxygen mixtures near room temperature have been given by Miller and Gorski. (19)

TABLE V SOME EXPERI14ENTAL INVESTIGATIONS ON THE BINARY SYSTEM NITROGEN-OXYGEN UNDER PRESSURE Property Temperature Pressure Year Author Reference ~F psia P-V-T-x -220 to 68 440-740 1923 Kuenen, Verschoyle, Van Urk 75 P-V-T(air) -256 to -13 14,700 1954 Michels, Wasenaar, Levelt, 117 de Graaf V-L -320 to 236 0-440 1927 Dodge, Dunbar 35 Joule-Thompson 14 to 542 0-3200 1925 Roebuck 137 (air) - Joule-Thompson -274 to 32 0-3200 1930 Roebuck 138 (air) Joule-Thompson 53 15-1500 1959 Koeppe 83 (air)

THERMODYNAMIC RELATIONS This chapter presents the mathematical relations which are required to calculate the enthalpy of mixing from measurements such as pressures, temperatures, composition, mixture flow rate and power input in a flow calorimeter. Basic definitions of mixing and excess functions are presented. Mathematical relations are given for calculating thermodynamic properties from the Benedict-Webb-Rubin equation of state. The first law of thermodynamics is applied to a flow calorimeter in which two reasonably pure gases are mixed. Corrections for impurities are detailed. The expressions used to normalize excess enthalpies to nominal experimental conditions and subsequent smoothing with respect to composition are described. Thermodynamic Definitions The enthalpy of mixing and excess enthalpy are defined along with the excess heat capacity and the excess isothermal Joule-Thompson coefficient. The excess enthalpy and excess heat capacity are expressed in terms of enthalpy departures and heat capacity departures -for use with the Benedict-Webb-Rubin equation of state. (2) Thermodynamic mixing functions of binary solutions define the changes in various state functions (e.g. enthalpy, entropy) on mixing pure components at constant pressure and temperature. The enthalpy change on mixing two pure components A and B to form the mixture AB is HM = AB ~- AHA - BHB (2) where xA and xB are the mole fractions of A and B respectively. This definition is independent of the nature of the pure components and their molecular interactions. -28

-29For ideal solutions, the mixing function is * = O (3) where the superscript star signifies ideal solution behavior. Excess functions are obtained by subtracting the mixing function of an ideal solution from the value of the mixing function itself. The excess enthalpy at constant pressure and temperature is therefore: H = M - HM* (4) Substituting for the enthalpy of mixing, HM of Equation (2), and the enthalpy of mixing of the ideal solution, HM of Equation (3), into the last equation yields HE = B - xA - BHB (5) The excess enthalpy and the enthalpy of mixing defined as in Equation (5) and (2), respectively, are identical. The excess enthalpy of a binary mixture at zero pressure, (HE)O, may be written in terms of the zero pressure enthalpies of its constituents as (HE)O = - x AH xBH (6) Subtracting (HE)O from the definition of the excess enthalpy, Equation (5), gives HE _ (kAB-SA) - xA(LA-I) - xB(jXB-HI) (7) noting that the excess enthalpy at zero pressure has the value zero. By comparing the last equation with the definition of excess enthalpy, Equatioll (')), it may 1)( seen that tlcl (Y'G(S enlth-alpy my Lbe evaluated, either

-30from enthalpies or from enthalpy departures for the pure components and the mixture. Written in this form, the excess enthalpy can be calculated, from Equation (7), with an equation of state which yields values of enthalpy departure for the pure components and the mixture. The excess heat capacity and the excess isothermal Joule-Thompson coefficient are obtained starting with the definitions of the heat capacity and isothermal Joule-Thompson coefficient: Cp =(a- (8) ~=^~~~( aHa~ )(9) -P/T where the latter may be related to the volumetric properties by the identity: = V - T (10) ^T, and where the heat capacity and isothermal Joule-Thompson coefficient may be related to the adiabatic Joule-Thompson coefficient,, by the identity: _= _ L (11) Cp The last two equations will be used later for calculating isothermal Joule-Thompson coefficients for data interpretation. The excess heat capacity is the derivative of the excess enthalpy with respect to temperature P ( aT EPx (12) Substituting for the excess enthalpy from Equation (5) into the last equation gives

-31CP =< aTR -x^ A T -XBt T- (13) The partial differentials in this equation may be replaced by the heat capacity of the mixture and of the pure components according to Equation (8) c = Cp - xACp - xBCp (14) The excess heat capacity may be expressed in terms of the heat capacity departures by a procedure similar to the one utilized with excess enthalpies. The expression obtained is C = -xA(CP-CP) XB(C- PB-0PB (15) where the excess heat capacity is zero at zero pressure. By comparing the last equation with the definition of excess heat capacity, Equation (14), it may be seen that the excess heat capacity, too, may be calculated from either heat capacities or heat capacity departures. The excess isothermal Joule-Thompson coefficient is the derivative of the excess enthalpy with respect to pressure: = (p,x (16) Utilizing a procedure similar to the one used in obtaining Equation (14) for the excess heat capacity, the excess isothermal Joule-Thompson coefficient may be written as: E = pAB - XAA - XBB (17) Correlation of Excess Enthalpy with Composition The variation of the excess enthalpy with composition at constant pressure and temperature may be correlated with a mathematical expression

which satisfies the Gibbs-Duhem type relation:,,E /7-\ <s )A B) (18) A/p T /p,T where and H are the partial molal enthalpies of A and B The simplest expression which may be used is the one for regular solutions given by Hildebrand and Scott(58) HE (1 x(1-x) where a plot of excess enthalpy versus the mole fraction of one of the comporents is a parabola symmetrical about a line through x = 0.5. Since most gas mixtures approximate this behavior, the excess enthalpies may be fitted to a curve which simultaneously represents deviations from regular solution behavior and satisfies the Gibbs-Duhem type relation, Equation (18). One such curve is represented by the equation: HE rx(-xT = an + b((x- )05) (20) Relations for the Benedict-Webb-Rubin Equation of State This equation of state is used to calculate three thermodynamic properties: enthalpy departure, isothermal Joule-Thompson coefficient and heat capacity departure. The enthalpy departure is used in making corrections for impurities in the nitrogen-ethane mixture data and in calculating excess enthalpies for comparison with the experimental results of this research. The heat capacity departure is utilized in determining the heat capacity of the ethane used in these experiments. Excess isothermal Joule-Thompson coefficients and excess heat capacities used in data interpretation are evaluated from the heat capacity departures and isothermal Joule-Thompson coefficients for pure components and mixtures.

-33In the following paragraphs, expressions will be given for the three thermodynamic properties, mentioned in the last paragraph, which are suitable for use with a pressure-explicit equation of state (see Equation (1)). That is, the expressions will have only derivatives of pressure with respect to temperature or volume e.g. (a~T or (7 The expression for the enthalpy departure, H-H~, has been derived by Hougen, Watson and Ragatz(63) as V H - H = PV - RT - [P-TP) ]dV (21) 00 - The relation for the enthalpy departure obtained after performing the mathematical manipulations given in the last equation on the B-W-R equation of state is given in Table XLIV in Appendix C. The isothermal Joule-Thompson coefficient, c, has been given in Equation (10) in terms of the differential of volume with respect to temperature, (KT) T This equation may be rewritten to handle the pressure explicit B-W-R equation as P= V + \ TK T (22) Perl'orming the dil'Irc.ir(2t;:itofls of' tihe last (Iquat;.in (,r the Ib-W-R (:quation gives the equation i'or the isothermal Joule-Thompoorn coefficient given in Table XLIV in Appendix C. The expression for the heat capacity departure is obtained starting with the relation between isobaric and isochoric heat capacities given by Hougen, Watson and Ragatz (63 Cp - CV = i (23) S.plittilng the dlilfferential (5VJLT)p as before, the last equation may be wrri, Lel:

~3~(6 C C: (j k:~II PH V al (6 Hougen et al.(3 also give the derivative of the isochoric heat capacity with respect to volume as ( T (2-) (25) Integrating this relation isothermally gives C C + T / (V (26) At zero pressure, the isochoric and isobaric heat capacities are related as shown: CV = C - R (27) Substituting the zero pressure isochoric heat capacity from the last equation into Equation (26) gives V = Cp - R + T f( dV (28) Substituting for Cv from the last equation into Equation (23) and transposing terms in the resultant expression gives V Cp - Cp = - - T( ) ( + T ) dV (29) Carrying out the differentiations and integrations indicated in the last equation on the B-W-R equation, Equation (1), yields the expression for the heat capacity departure in Table XLIV. The three expressions for the thermodynamic properties given in Table XLIV require values for the eight empirical B-W-R constants. For the pure components used in this research the constants are given in Table XLV. For mixtures the constants are estimated by combining the pure component constant.s according to the mixing rules of Benedict et al. (13)

-35In calculating the excess properties for binary mixtures, for example excess enthalpy, first the enthalpy departures for the mixture and for the two pure components axe calculated and then they are subtracted according to Equation (7) given earlier. The excess heat capacity is similarly determined from Equation (15) and the excess isothermal Joule-Thompson coefficient obtained from Equation (17). Application of First Law of Thermodynamics The experimental scheme is illustrated in Figure 1. Gas A at flow rate FA and gas B at flow rate FB enter the calorimeter at almost identical conditions (P1,T1) and (P2,T2) respectively. If the gases cool on mixing then enough electrical heat input, W, is supplied to make the temperature of the exiting gas mixture, To, almost identical with the inlet gas temperatures, T1 and T2. This is the case for the nitrogen-carbon dioxide and nitrogen-ethane systems but when nitrogen and oxygen are mixed there is evolution of heat and the outlet temperature is higher than the inlet temperatures. For measurements with the latter system, the calorimeter may be operated without any power input i.e. W = 0. There is a small pressure drop across the calorimeter hence the outlet pressure, P0, is slightly lower than inlet pressures, Pi and P2 The mathematical derivation which follows is applicable to all three systems. Since the gases used contained some impurities, relations are obtained here for mixing two impure gases and corrections for impurities made later. Henceforth the added subscript M refers to the impure gas stream and the absence of M implies that the gas stream is assumed to be pure, e.g., the subscript A is pure A and the subscript AM is impure A.

Gas A Flow Calorimeter at (Pi,T) Flow rate FA Enthalpy HY, Ent hl (p) UA GasMixture ___ _________' A+ B at (Po,To) L Flow rate FAB Gas B -- -- Enthalpy HABo at (P2,T2) Flow rate FB Enthalpy HB,2 Electrical Heat Input,W Figure 1. Schematic for Enthalpy of Mixing Measurements in a Flow Calorimeter.

-37Neglecting potential energy effects, the first law of thermodynamics when applied to the system illustrated in Figure 1, at steady state, yields W-Q FAM FBM FAM FM FABM iAM,1 FABM HBM,2 BM,o + F AMB 1 FABM ABM AB + FM T - KBM,o (30) ABM where FA is the total flowrate of both gases and Q is the rate of heat leakage to the calorimeter. The heat leak term is the most difficult term to evaluate numerically in Equation (30). Hence the prime criterion in the design and operation of the enthalpy of mixing calorimeter is to make the heat leak negligible. For purposes of calculation, the assumption is made that the experiments are carried out under adiabatic conditions: Q 0 (31) The results of the experimental verification of this assumption of adiabaticity are discussed in the chapter entitled "Results." The kinetic energy, KE, of a given stream is calculated per unit mass of that stream and expressed in terms of the average velocity, u, of the stream. For example, the kinetic energy of the impure stream B at (T2,P2) is 1_~ KEBM 1 M 2 where FBM UBM2 = (PBM,2)(cross-sectional area of flow) (32) and pBM,2 is the density of impure B at (P2,T2). Substituting the assumed value of Q = 0 and abbreviating the differences in kinetic energy by

1,AM'BM AnM- FA K 1 AM, +: nKM, - KABM, (3) ABM FABM ABM reduces Equation (30) to FM F W FABM H AM, FBM HBM,2 -ABMo ( 34 FSABM FABM_ 1 FABM. B Y The first three terms on the right hand side of Equation (34) represent an enthalpy difference between three streams that are at differing pressures and temperatures. A similar enthalpy difference can be defined at the outlet conditions of the calorimeter, (ToPo), as FAM FBM ZT T - TTH --- (3 — o -= ABMo FABM AM,0o FA BMo (M ) Adding Equation (34) to (35) and transposing {/FABM gives FAM FBM + (H -+ ( -0 F" FAB ABM 1 M F BM ) + (36) The two terms on the right hand side of Equation (36) that represent enthalpy differences can be expressed in terms of the calorimeter inlet and outlet pressures and temperatures: W + FAMH FAM?l A\H = (.....P)T1 + (C dT) o F+ABM FASB P o FM pJ4 o P2 T2 FBM BM 4- ABM (PBdp PT2 + AKE (37) PO To The energy balance as expressed by Equation (37) may be used directly if power is supplied to the calorimeter. If there is no power input, then the energy balance, Equation (37),may be used after setting the power input to zero, W =.

-39Primary Corrections Experimental measurements give values of the power input, W, and the flow rate of the mixture, FABM, from which may be calculated the power per unit flow or the power/flow ratio, (W/F) (W/F) = W (38) FABM The excess enthalpy at calorimeter outlet conditions, H is obtained by applying four corrections to the power/flow ratio. Collectively, these corrections are called primary corrections. They are: 1. Correction for pressure drop across the calorimeter expressed by FAM FBM Pcorr = FM'AM[ P1-P] + FAB BM[P2 -Po (39) The two terms in this equation are the integrated forms of the terms involving pressure drop in the energy balance, Equation (37). 2. Correction for temperature difference across the calorimeter described by F F ATcorr AM C M[T-TD + FBM C [T2-T (40) FA M[ BM BM which are the integrated forms of the terms involving temperature difference in the energy balance equation. The pressure and temperature differences are sufficiently small (maximum values of about 0.1~C and 0.4 psi) to justify assuming that the values of Cp and cp are constant during the integration. The numerical values of the properties are obtained at nominal experimental conditions from literature sources which will he referred to irl the chapter entitled "Results." Only for oxygen,the isothermal JouleThompson coefficient is calculated from a slightly different form of Equation (10)

c- [ - V T)1p/(1 using the tabulations by Weber(180) of volume and the differentials, (6-P) and ( ), obtained from his own PVT data. 3. Correction for kinetic energy differences between incoming and outgoing gases, AKEM, detailed in Equation (33). This term, too, occurs in the energy balanceEquation (37). Density data is needed on impure A and B and on their mixture. These three corrections are applied to (W/F), the power to flow ratio, to obtain the enthalpy difference, AHo. This enthalpy difference is the enthalpy change which takes place with the isothermal, isobaric mixing of the impure streams of A and B at calorimeter outlet conditions, (To,PO). To determine the enthalpy of mixing of pure A and B it is necessary to make one more correction. 4. Correction for impurities in the substances under study. This correction is applied to the enthalpy difference, AHo, to obotain the excess enthalpy, H, of the mixture of the two major components in the stream exiting the calorimeter. HE=o + AIc (42) = o + corr where AIcorr is the correction for impurities. The nitrogen-carbon dioxide system uses the experimentally obtained enthalpy differences, AH, whereas the nitrogen-ethane system requires an enthalpy prediction technique to make this correction. Corrections for Impurities The mathematical manipulations required to extract the excess enthalpy, _, from the measurable enthalpy difference, AHo, will be derived in this section. The two cases of the nitrogen-carbon dioxide

-41system and the nitrogen-ethane system will be considered separately. To maintain continuity with the previous development, the subscripts used will be A and B. A is assumed to signify nitrogen and B the other component, ethane or carbon dioxide. Nitrogen-Carbon Dioxide System As indicated in Table IX, the nitrogen used in this research contains only 0.02 mole percent oxygen and the carbon dioxide contains 0.05 and 0.09 mole percent nitrogen and oxygen, respectively. Both streams are relatively pure and contain one principal impurity —oxygen. As will be described, the impurity corrections for the data on the nitrogen-carbon dioxide system are based on certain assumptions regarding the major impurity oxygen, and the implementation of these corrections require the experimental results of this very research. The enthalpy change on mixing nitrogen and oxygen was measured in the course of this research and found to be at least two orders of magnitude smaller than the excess enthalpy values of the other two systems. Therefore, since the amount of oxygen impurity is small, the nitrogen stream is assumed to be pure. Based on the same results, it seems reasonable to assume that the excess enthalpy of the oxygen-carbon dioxide system is very similar to that of the nitrogen-carbon dioxide system at the conditions of experimental measurements of the present research. Since the fraction of oxygen impurity in the carbon dioxide is small, for purposes of making impurity corrections, the oxygen is lumped with the nitrogen ard the carbon dioxide stream is assumed to contain only one impurity —.l14 mole percent nitrogen. For this system, the measurable quantity, AH, which was defined in Equation (35) for mixing impure A and B streams must be

-42modified to o BM FA ABAMo -A,O (43) ~o- L-Bo -A^ -B kM, o - FAB -A, o where A is pure nitrogen, BM is carbon dioxide with only nitrogen as impurity, and AB is the nitrogen-carbon dioxide mixture. The enthalpies of the impure carbon dioxide and the nitrogencarbon dioxide mixtures may be defined in terms of the excess enthalpies (as in Equation (5)) E and HE respectively: I~DMo -o ~ HBM, o = BM, o + YAA,o + YB (44) HABO =!~ + xA C ) + xH4o5 where YA and YB are the mole fractions of nitrogen and carbon dioxide in the latter feed stream. Substituting for BMo and B from Equation (44) and (45) in the expression for AH, Equation (43), and collecting coefficients of HO and HBO yields E FBM [rE + [ y FBM FA 0o - F L] - F.Mo +,o xA-YA F F FBM + HB,o [XBYB FAB (46) A mass balance on A and B entering and leaving the system gives FA + A FBM A FAB 47 YB FBM = XB NAB (48) Substituting for the mole fraction of A, xA from Equation (47), and the mole fraction of B, xB from Equation (48), into the expression

.43for iHo, Equation (46), reduces the coefficients of HA,o and Ho to zero. Transposing terms in Equation (46), the excess enthalpy of the exit stream, HE, may be expressed as =Ho +BM [BMo] (49) BE Comparing this equation with Equation (42) in which the application of the impurity correction was originally expressed yields AIcorr = FAB [oZM The excess enthalpy of the impure carbon dioxide stream, HM o required to estimate the impurity correction is obtained from the experimentally determined enthalpy difference, oAl. The enthalpy difference is fitted to an equation similar to Equation (20). AH xN(l-xN) = a + bo(xN-0.5) + cO(xN-O.5) (51) where xN is the mole fraction of nitrogen and ao, bo and co are determined by a least squares analysis. Since the carbon dioxide stream is assumed to contain only nitrogen uand since the fractio of'f this impurity is small, the excess enlthalpy of the impure cartborn dJioxide stream, 1M O is equated to the enthalpy difference, AlU), mand substituted in the last equation along with mole fraction impurity xN = YA: HM = Y-A(l-yA)[ao + bo(yA-0.5) + co(YA 0.5)2] (52) The excess enthalpy of the impure darbon dioxide feed stream HMo is evaluated by substituting the mole fraction impurity nitrogen, (in this caCe its value iL yA = 0.0014), in the last equation and the impurity correit0iol, AI(.1r,., determined from lquation (90).

-44Nitrogen-Ethane System The ethane used in this investigation has ethene, propene and propane as impurities as indicated in Table IX. Whereas it was possible to make use of binary enthalpy of mixing data to account for nitrogen as an impurity in carbon dioxide, the presence of several impurities other than nitrogen necessitates another approach, which is outlined below. The enthalpy difference, AHo, for this system is defined in a similar way as for the nitrogen-carbon dioxide system, Equation (43), FA BM ABM ABM o - _ABM,o - FABM A,o -FABM BM,o (53) assuming that the nitrogen. is pure and that the impurities are in the ethane feed and in the nitrogen-ethane mixture stream. The excess enthalpy of the nitrogen-ethane mixture, as defined in Equation (5), may be written in terms of the molar flow rates of A and B as HE H - FA H -JLH (54) FA FB where x -_ and xB F F FAB AB FABM Multiplying the expression for ALH, Equation (53), by F-' AB subtracting it from Equation (54) for, and writing the resultant expression explicitly in H gives E FB FABM FABM FBM - AB,o - FA f,o O FAB 0 FaAB FMn0 BMo The flow rates of the impure ethane and nitrogen-ethane streams mnlv be written as the stun of the flow rate of impurities, FI, and the flow rate of the remainder FBM = FAB + F ( 6)

FBM = FB FF (57) where FB is the flow rate of pure ethane and FAB is the flow rate of the impurity-free binary nitrogen-ethane stream. Substituting for FABM and FBM from the last two equations in the expression for H, Equation (55) and regrouping terms gives HE F I+t -FB t F B ~ I 1 OS = AHo FA B + F Mo - H~,oj + KAo-0 - _ABMo FAB Mo AB + r Mo - 5tBM,o] (38) By transposing terms in Equation (42), the correction for impurities, AIcorr, may be expressed as the difference between the excess enthalpy, HE, and the enthalpy difference, AHo — 0D AIcorr= o - Ho (59) Substituting for the excess enthalpy at calorimeter outlet conditions, HE, from Equation (58) in the last equation and performing the subtraction of Equation (59) gives the impurity correction: FI FB Alcorr F [AH,] + F [!BMo - B, + ABMo + 3M, ABM, (60) Evaluation o the impuity correction, requies value or the Evaluation of the impurity correction, requi'res values for the enthalpy difference, ALHo, and the six enthalpy terms in Equation (60). The former is determined experimentally. The six enthalpy terms are (12 131 14) estimated from the Benrediet-Wetlb-Rubin equation of state. (' An eq(al ioll of1 sl.aLet, however,.viliJ.] v,:lues o:' the enthalpy departure rather than values of the enthalpy itself (See Equation (21)). As will be shown, it is sufficient to use enthalpy departures in place of the six enthalpy terms in Equation (60) to evaluate the impurity correction.

-46The equation for the impurity correction, Equation (60), was derived from Equation (53) fo:r the enthalpy difference, AHHo,;md from Equation (54) for the excess enthalpy. Earlier in the chapter, it was shown that the excess enthalpy can be calculated from enthalpy departures. It will now be shown that the enthalpy difference, ZHo, can also be calculated from enthalpy departures. The enthalpy difference at zero pressure is AHo H FA H~ FPBM 0 6B) AUO = MO- H3M-o (61) o F o 0 FB o FI FABM FABM ABM subscript I refers collectively to all the impurities. In a similar way the zero pressure enthalpy of the impure ethane may be written as C) FI HBMo = FB + -,o (63) F B H o, o FBM — ABMIBM Substituting for H andB o from the last two equations into -ABMo M Equation (61) for the zero pressure enthalpy difference gives _ F 0 FB FI + FA 0 AHo + __ — H + H H - - A FI FABM ABM ABM ABM,AltI - t, +'BM All t;te terms il the last; equation clacel out reducing the zero pressure elit.llalpy! ii lt't.'erence to':cro. T.his implies tliat the enthalpy difference, AIll, likellt the excess etltthalpy\, n, ma be calc:ulated with enthalpy.departures o.nly, an; d flurtlher implies that the impurity correction, AICorr requires only elt;halpy departures for its evaluation.

-47Therefore, the impurity correction for the nitrogen-ethane mixtures is determined by substituting the values lfor the enthalpy departures, calculated from the B-W-R equation, instead of the enthalpy terms in Equation (60). The expression for the enthalpy departure for the B-W-R equation of state is given in Table XLIV. The B-W-R constants for the pure components are given in Table XLV and the mixture constants are determined from them using the mixing rules of Benedict et al.(13) Secondary Corrections and Smoothing of Data The primary corrections described in the previous sections of this chapter serve to yield values of H, the excess enthalpy at the experimentally determined conditions of pressure and temperature at the calorimeter outlet. It is necessary to make a second set of adjustments to the excess enthalpy H, to obtain a normalized excess enthalpy. These adjustments, called secondary corrections, compensate for the operational variation in temperature and pressure level (-I 0.050C and ~ 3 psi) at the calorimeter outlet. The normalized excess enthalpy at nominal experimental conditions (Tn,Pn) is obtained from the excess enthalpy at calorimeter outlet conditions (To,Po) using the equation P TT n r IE HE- + i (E dP / (. ilr) (i') P E'n where Cp and Ep have been defined earlier in J':quations (14) and (17), respectively. The actual calculations are carried out on the integrated form of the last equation HE =E HE + pE[Pu-P ] + C[T -T ] (66) — ri -o P 1 O with the thermodynamic excess properties being assumed constant over the integration.

-48As explained, thlrmnodynrlamic dtLa a;re' required oll the vurialti(ro of excess enthalpy with temperature and pressure, respectively. IIL the absence of experimental data, these quanlt;ies are estimated using the Benedict-Webb-Rubin equation of state. The heat capacity and the isothermal Joule-Thompson coefficient are estimated from the equations in Table XLIV for the pure components with the constants given in Table XLV. For the mixtures, the equations in Table XLIV are used with the mixture constants being calculated from the pure component constants using the mixing rules of Benedict et al. (3) The excess heat capacity and the excess Joule-Thompson coeiificiernt are calculated by substituting the values of the thermodynamic properties so obtained in the expressions given earlier in this chapter for these quantities, Equation (15) and (17) respectively. The excess properties predicted by the B-W-R equation are believed to be of doubtful accuracy (estimates of accuracy will be given in chapter entitled "Results"). The thermodynamic properties are evaluated at the nominal experimental conditions and are assumed to be constant over the pressure and temperature differences of Equation (66). In the chapter entitled "Results," the experimental results on the nitrogen-ethane mixtures are presented both with and without impurity corrections. When impurity corrections are made, the secondary corrections on the binary nitrogen-ethane mixtures are made as described. For the case where impurity corrections are not made, the "excess" heat capacity mad "excess" Joule-Thompson coefficient are calculated from the following equations at nominal experimental conditions: Ct= c FA c FBM C a ='c, -----— c, (67) P ABM,n FABM A,n FABM BM,n FA FBM v = ~ABM,n F. CA, n F B BM,n (68) ABM ABM

-49where A is pure nitrogen, BM is impure ethane and ABM is the impure nitrogen-ethane mixture. The heat capacities and the isothermal JouleThompson coefficients in the above equations are the derivatives at nominal experimental conditions of the enthalpy terms in Equationl ('j) I.)or the enthalpy difference, AHo, of nitrogen-ethane mixtures. The prime in the above equations indicates that these are not true excess properties. However, they are used just like "true" excess properties for normalizing the data as described in earlier paragraphs. The values of excess enthalpy normalized to nominal temperature and pressure are correlated with the mole fraction of nitrogen, xN using Equation (20) written previously XN(lxN) = an x 5+ bn(xN-O50) + (69) xN(l-xN) where xN is the mole fraction of nitrogen. The constants an, bn and cn are obtained by a regression analysis.

APPARATUS AND EXPERIMENTS In this flow calorimetric facility, the system brings two gases at the same temperature and pressure to the calorimeter where they are mixed. A measured quantity of electrical energy is added to the gases in the calorimeter to minimize the temperature difference between the incoming pure gases and the exiting mixture stream. Each pure gas stream is metered individually, hence both the flowrate and the composition of the mixture are determined simultaneously. The experimental details of these measurements are given in this chapter. The design of the flow calorimeter used to make these measurements is presented. The facility in which it is incorporated is described. An account is given of the mode of operation of this facility. APPARATUS A description is given here of the calorimeter and the flow calorimetric facility. Measurements and procedures are presented in later sections. Calorimeter The design of the calorimeter is based on several factors. The heat leak to and from the calorimeter must be minimized. The calorimeter must have a low heat capacity so it can respond quickly to changes in experimental conditions. The pure gases which enter the calorimeter must be adequately mixed so that the exit mixture is of uniform composition. Simultaneously, the pressure drop generated by internal mixing devices must be small. Differences in kinetic energy between the pure gases entering and the mixture leaving the calorimeter must be minimized. The experience of previous investigators(45'71'96'9 ) with flow calorimeters -50

-51for isobaric heat capacity measurements heavily influenced the design and construction of this calorimeter. Especially valuable was the work of Faulkner (45) who in his thesis gives an excellent review of various aspects of calorimeter design and instrumentation. A sketch of the calorimeter is given in Figure 2 with the key on Table VI. The pure gases A and B enter the calorimeter through ports 1 and 2, respectively, via 3/8-inch tubing union tees. The temperature difference between the gases entering is measured by duplicate six junction copper-constantan thermopiles which are inserted in thermowells 4. The temperature difference between the gas entering port 1 and the outlet mixture is monitored by similar duplicate thermopiles inserted in thermowells lla and llb. The bottoms of the thermowells are packed with Apiezon-N grease to improve thermal contact. The pressure is measured via 1/8-inch tubing pressure taps 5 and 6 for the inlet gases and 10 for the outlet mixture. The 1/8-inch tubes are welded to sleeves which are concentric to the 3/8-inch tubing carrying the gas. The gas pressure is transmitted to the sleeves through six 1/32-inch diameter holes equally spaced on the eircumference of the 3/8-inch tubing. The six holes are at the same location along the axis of the 3/8-inch tubing as the multiple junctions of the thermopiles inserted in the coaxial thermowells,in order that the pressure and temperature be measured at the same point. The pure gases flow through two concentric tubes and are mixed at the point labeled 7 within the mixing chamber. Reversing the direction of flow, the gas mixture then passes into the annular space, 8, between the outer most or' the two conclentric tube.- arid a thin (0.01 inch lh icRk) copp~epr cyli rdeir.''The Jal,!,Or is the It'irst o,.fbu r corlncentric (A/ lii(i drical b[af'l.t (; (oL,}eir I,'r(, l,; li' lot nliowri iii ll lI'i,;u'r'c ) o:ve:r

-521 1 2 112 3 c712 16 16 i 17K Fi g u l i I 10 4- Ilao I 8 123 23, ~I I I I I_11 1 I # I Ir i 4 INCH L.===:^= — m^- 2 _SCALE2 21 21 20 1lb. II' 4i Fgr12 11ta14 I i,~ SCALE Figure 2. Enthalpy of Mixing Calorimeter. (Key: Table VI)

-53irA13LE VI KEY TO SKETCH 01' CALORIMETER IN FIGURE 2 1. Gas inlet A 2. Gas inlet B 3. 3/8-inch tubing union tees 4. Thermocouple wells to measure differential temperature at inlet 5. Inlet pressure tap —Gas A 6. Inlet pressure tap —Gas B 7. Mixing point of Gases A and B 8. Annular space for flow of gas mixture 9. Helical tubes carrying mixed gases to outlet tubes 10. Outlet pressure tap —mixture A+B lla. Outlet thermocouple well llb. Inlet thermocouple well to measure temperature differential between gas inlet and gas outlet. Thermocouple junctions placed in wells lla and llb 12. Gas outlet tube 13. Heater leads 14. Tube for housing thermocouple lead 15. Tube for housing heater leads 16. Outer vacuum jacket 17. Vacuum line 18. Bottom flange 19. Teflon gasket 20. Teflon mechanical partition 21. Brass collar with coarse interrupted threads. Collar attached to outer jacket 22. Gold-plated thin copper shield 23. Silver-plated thin copper shield Note: Sketch on right shows details of inlet assembly and mixing chamber.

-54which the gas mixture flows back and forth. In passing from one baffle to the next the mixture flows through approximately 30 symmetrically distributed holes of 1/32-inch diameter located at alternate ends of the hemispherical ends of the baffles. Detailed drawings of similar baffles have been given by Faulkner.(45) The only difference is that the cluster of holes in each of these baffles are located at the opposite end of the baffles shown by Faulkner. From the top of the outermost baffle, the gas mixture passes into a helical 1/4-inch diameter tube, 9, which leads it to the outlet measuring station. The gas mixture exits the calorimeter via tube 12. This tube is made as long as possible to minimize heat conduction along it. The first two of these baffles is wound with 180 ohms of insulated Nichrome wire. Heater leads, 13, are brought into the mixing capsule through a conax gland. The two remaining baffles and the helical tube serve to equilibrate the mixture. An externally goldplated copper radiation shield, 22, is in contact with the helical tube and facilitates regenerative heat transfer. A silver plated copper shield, 23, completely surrounds the mixing chamber and the outlet measuring station and isolates them from the line of sight of the surroundings as well as the gas inlet assembly. A single junction copper-constantan thermocouple measures the temperature difference between the skin of the shield and the exit tube, 12. The shield, 23, is supported by three small copper pins which rest on the teflon partition, 20. Very little, if any heat is conducted away from the shield through these supports and through the teflon partition. The partition is bolted to a circular brass ring. Interrupted threads on the brass ring mate with similar threads on a brass collar, 21, which is attached to tile outer jacket, lot, of the calorimeter.

-55A vacuum jacket, 16, surrounds the mixing chamber, aid the measuring stations. The vacuum serves to minimize conductive and convective heat transfer between the calorimeter and the surroundings. Twelve symmetrically placed socket head screws squeeze a teflon gasket, 19, between the bottom flange, 18, and the flange on the vacuum jacket. An operational vacuum level of one to four microns Hg is maintained within the jacket with a vacuum pump. Conductive heat transfer along the thermopile wires is minimized by using 30-gauge wire and making the distance between the two sets of six junctions about four feet in length. The 30-gauge copper lead wires are brought out of the calorimeter bath through a 1/4-inch O.D. stainless tube, 14, about three feet long welded to the bottom flange, 18. The copper wires are threaded through teflon tubing before inserting them in the 1/4-inch tube. At the end of the 1/4-inch tube, the wires are soldered to the Covar sealed pins of an octal plug. A vacuum tight seal is maintained by soft-soldering the octal plug and the tubing to an annular stainless steel cylindrical adaptor. The 22-gauge copper lead wires from the calorimetric heater are brought out of the calorimeter via a similar stainless steel tubing, 15, and octal plug arrangement. Flow Calorimetric Facility The flow calorimetric facility supplies the two gases to the calorimeter where measurements are made under steady state corditions. The flow system is described by tracing the path followed by the two gases from the supply cylinders to the exhaust system. Details of the gas supply assembly, the conditioning baths and the control panel follow separately.

-56Flow System A flow diagram is presented in Figure 3 with the key on Table VII. The two gases under; investigation a;re suppliedi from cylinders, 1 and 2. These cylinders are manifolded, as shown, to dampen the rate of decrease of supply pressure caused by continuous withdrawal of gas. Manually operated pressure regulators, 3, set the pressure of the gas entering the flow metering section at about 1100 psia (except for ethane flow metering pressure of 500 psia). In the case of ethane and carbon dioxide only, the gas is heated with heating tapes wound onto the pressure regulator and gas supply tubing to prevent it from condensing when it is throttled from supply to flow metering pressure. The flow rate of each gas is metered separately in high pressure flow meters, 5 and 6, which are located in the flow meter bath. The temperature of the bath is maintained at 25~C for the nitrogen-oxygen system and at 45~C for the other two systems. The gases are preconditioned prior to entering the bath by heating tapes wrapped onto the tubing. The power input to the heating tapes is adjusted to maintain the gas temperature within ~ 1 to 20C of the bath temperature. Gas temperatures are monitored by single junction copper-constantan thermocouples, 13, inserted into the gas streams through conax glands. On entering the bath, the gases flow through 50 feet of copper conditioning coils. Traces of oil and gross particles are filtered out by passing the gases through glass-wool filled bombs (not shown in Figure 3) before they enter the bath. Micron filters, 4, on the gas inlet, outlet and pressure taps to the flow meter further cleanse the gas and prevent depositionl Cof particles within the flow meters.

-57The gases are throttled from the flow metering pressure to the required pressure in the calorimeter by metering valves, 21. Preheating by heating tapes on the tubing, 12, prevents condensation. Ball valves, 22, are used as on-off valves as they provide negligible resistance to flow. They occur at this and other points in the flow path of the gases wherever throttling or metering valves are located. The temperatures of the gases entering the calorimeter bath, which are measured by thermocouples, 13, are brought to within j 1 to 2~C of the bath temperature by controlling electrical power input to heating tapes, 12, wound on the tubing. Gas temperatures are equalized with the bath temperature by passing each of the gases through 50 feet of copper coils in the bath. The two gases are mixed within the calorimeter. The difference in temperature between the mixture exiting the calorimeter and the two pure gases entering it is rendered negligible by passing the mixture over heated resistance wire within the calorimeter. On leaving the calorimeter bath, the gas mixture is preheated with heating tape, 12,to prevent condensation when it is throttled to 75 psia pressure by pressure reducing valve, 18. Valving is provided at this point to withdraw mixture samples at a pressure of 75 psia for composition analysis. Again, the mixture is preconditioned as described earlier before entering the flow meter bath. The two flow meter baths in Figure 3 are in reality a single bath. They are drawn as shown for clarity in the flow diagram. The low pressure flow meter, 19, is not calibrated but used only for operational:orntrol. A glass wool bomb located prior to enlt;ering w tlle thalih, ani m:i(ro l:ilIters, I, at lthe.:low me lr( r emove oi ul tI ( parti-:ulate matter from the gas mixtulre.

12 13 7 ^,7,9 1 2 i 12 4& &4 ^22 "s/ /S -y 22 4 11 q 20 12 " 23 - =Z - -3 ~~~~~~~~~~~~C _ *-0-^12 21 9 7 EXHAUST TO ATMOSPHERE OR 1 4 9 8 TO CALIBRATION TANK -- nir\ n~~~~r ^ ^ ~~ 6 4 ^ rI ro110 1 4422 4 FLOWMETER BATH (NOTE) 13 12 _____ 5 22 18 12 14 tn- F __ CALORIMETER, g. __ __ ^__ —j I10 I11 17^^ -:= —." FLOWMETER BATH (NOTE) 15 16 10 CALORIMETER BATH Figure 3. Flow Diagram of the Facility. (Key: Table VII)

-59TABLE VII KEY TO FLOW DIAGRAM IN FIGURE 3 1. Gas A tanks 2. Gas B tanks 3. Pressure regulator 4. Micron filter 5. High pressure flow meter 6. High pressure flow meter 7. Pressure taps 8. Thermometer 9. Stirrer 10. Controlled heat input 11. Cooling water or compressed air 12. Heating tapes 13. Thermocouples 14. Thermometer 15. Inlet pressure tap —Gas A 16. Inlet pressure tap —Gas B 17. Mixture outlet pressure tap 18. Pressure reducing valve 19. Meriam flow meter —mixture A+B 20. Flow metering valves 21. Metering valves 22. Ball valves 23. Two-way outlet solenoid. valve

-6oThe mixture is throttled to atmospheric pressure through flow metering valves, 20. It is then vented through a two way solenoid valve, 23. During normal operation, with the solenoid valve switch off, the gas mixture is vented to a tunnel located beneath the laboratory floor. A fan at the end of the tunnel exhausts the gas mixture to the air outside the building. When the solenoid valve switch is thrown, the mixture is diverted to a calibration tank. The latter is a tank whose volume (about six cubic feet) has been measured accurately. It is used only during flow meter calibrations to measure flow rate by collecting the gas in it over a measured period of time. Gas Supply Assembly Each of the nitrogen and oxygen supply cylinders are filled with about 250 standard cubic feet of gas at approximately 2300 psig. Seven cylinders are connected to the supply manifold of each gas. Gas is withdrawn from the manifolded cylinders with a resultant decrease in pressure level of 30 to 40 psi/hour till an internal pressure of 1200 to 1300 psig is reached after which they are replaced with fresh cylinders. Both the ethane and carbon dioxide in the supply cylinders are in coexisting liquid and gaseous phases. The ethane cylinders contain about 30 pounds at 350 psig whereas there is 50 pounds of carbon dioxide at about 850 psig. The cylinders after manifolding are heated with heating tapes to raise the gas pressure to the required level. The four manifolded ethane cylinders are kept at 700 psig. The carbon dioxide in t lhe s:lx t'y1liiitr i is manlt;ainled at about 1300 psig. Variacs control the power input to the heat:ing - tapes to sustain the pressures at these levels within -+ 50 psi.

-61Constant Temperature Baths There are three constant temperature baths: The cooling water bath, the flow meter bath, and the calorimeter bath. 1. Cooling Water Bath: This bath, as its name implies, supplies cooling water at a controlled temperature. Water is recirculated by a floormounted centrifugal pump to a 50-gallon drum, fastened to the wall near the roof. Cooling water is tapped from the exhaust of this pump. An overflow drain on the drum maintains a constant head of water. The temperature of the water draining from the bottom of the drum into the pump is measured by a temperature sensing probe. A pneumatic error signal is transmitted by it to an air-pressure controlled valve which regulates the amount of water entering the drum to control the temperature of the water in the recirculating system. A constant amount of heat is supplied by a 2000-watt immersion heater in the drum. Once steady conditions are achieved, the cooling water temperature does not vary by more than a few tenths of a degree. 2. Flow Meter Bath: It consists of a 27-inch long by 15-inch wide by 25-inch deep stainless steel bath insulated with 2-inch thick styrofoam blocks on the side and bottom and with 1 1/2-inch thick styrofoam on the top. The assembly is enclosed in a 1/2-inch thick plywood box. The bath fluid water is stirred by a Lightnin' 10X mixer. A 100-watt tubular heater, used ftr on-off control, and a 300-watt tubular heater, for continuous heat input, are immersed in the water. These two low lag heaters consist of a resistance wire packed with high thermal conductivity material within 5/16-inch copper tubing. The temperature of the bath is sensed by a mercury-to-wire Philadelphia

-62 - Scientific and Glass thermoregulator. Lead wires from the thermoregulator are connected to a Fisher transistor relay. Cooling water tapped from the centrifugal pump is returned to the cooling water bath after it is circulated through a copper coil (50 feet in length) submerged in the flow meter bath. The constant flow rate and relatively invariant temperature of the cooling water provides for a fixed heat removal rate. The heat input from the continuous-input heater can be controlled with a variac till it provides slightly less heat than can be extracted by the cooling source. The temperature of the bath can then be maintained within ~ 0.01~C with on-off mode control by regulating the heat input from the on-off heater to 10-20 watts. 3. Calorimeter Bath: The working space in the calorimeter bath is an 18-inch long by 12-inch wide by 22-inch deep stainless steel tank. Eight-inch thick styrofoam insulation on the sides and bottom of the tank is supported by a 1/2-inch thick plywood box. The top consists of a stainless steel plate divided into two halves and covered with four inches of styrofoam. Since all the measurements are close to room temperature, the only bath fluid used is water. Stirring is accomplished by an explosion proof Lightnin' Molel NC-4 portable mixer with an EVS unit for varying the agitation rate. Cooling for the bath is provided by passing compressed air at an inlet pressure of 50 psig through a submerged copper coil 50 feet in length. A 300-watt knife heater connected to a powerstat supplies a constant heat input to the bath. The variable heat input is supplied to a 100-watt tubular heater by a Bayley Model 121 proportional controller. The temperature sensor for this controller

-63is a nickel resistance thermometer in a stainless steel sheath. In the bath described, the controller was capable of operating at a band width of 0.010C without temperature instability once the gas streams (e.g. nitrogen, ethane, etc.) had attained steady flow and temperaturre conditions. Thq degree of contrnl achieved is -~ 0.002~C. Control Panel The constant temperature baths and much of the high pressure tubing is enclosed by a 10-foot high, L-shaped, 1/4-inch thick steel barricade. Almost all the instruments used are either fastened to or are located in front of the long arm of the L-shaped barricade which is termed the control panel. A photograph of this control panel is given in Figure 4. Four separate pressure manifolds consisting of flush-mounted valves connected by 1/8-inch copper tubing are located on the face of the long arm of the L-shaped barricade. Two of these manifolds connect the two high pressure flow meters to their individual high pressure manometers and Heise gauges. One manifold is for measuring the pressure and pressure drop in the calorimeter. The fourth one is connected to the instrumnentation for the low pressure flow meter. The switches for the 110-volt electrical power are mounted on a transite board bolted to the control panel. The electrical measuring equipment (power supply, K-3 potentiometer, etc. described later) are placed separately on a wooden table. A 12-position Leeds and Northrup type 31-3 rotary selector switch which is mounted on the transite board permits the reading of voltages from several sources (e.g. four thermopiles in calorimeter) on the K-3 potentiometer. The pressure regulators and valves for controlling the pressure and flow rate of the flowing gas

i-i--i:i:,~: i::i:,:-ii:i:'-::-ii':::::II:-.::::: i:: I:::iii;i'i:(i:i:: i -::'ii::,i,:-,i:,,~::i:l::::'j:l::::::ji::::.:::l::i~:::::i.ii:::::;:i:::::;::-l::':ll:i:::::i::i::lli:::=:;:i:l:ii'i:': i:::ilii:i i:::'i:i-i::.:.;::i'-::i-:::::::::;:::i-i-:':::i::i::::i:.:.-:..;::.:. r::::-:: ag ii i a b: ii::i,..:.::;::-:.-:: i:_: ~- -..... g ib j a:iXi-i"-ikJ::::: -- i i::::3_ i:::":::2:::::ii::::::::i::ai::i::*: i, ~"" i:~s:~i i ii-::;'::: i?:C:::::::i::::i:::::':: 1 -,~ L ~: Q::z::.:r:: B I::8 iFiii: i::i: 1 -,::::I::i- i.i-r-:: i:::::::::':i:: Y:i:: i::: i;::ii:j::::l:i:i::~l:::i::::::i::i.: :::::*rrr* i::::: ii i i::~::::;;:: i:: * C-_:::: _: -' ~ d B: I.-ii-:~ i i j " ~.iai g;:g i:ii~ Figure 4. Con-trol Panel.

-65streams are mounted on an auxiliary aluminum panel board beside the control panel and at right angles to it. MEASUREMENTS AND CALIBRATIONS The prime measurements are pressure, temperature, power, flow rate and composition. Pressure Both pressure level and pressure drop are measured in the calorimeter. Pressure Level The pressure is measured at the calorimeter outlet tap, 10 (Figure 2), with a Mansfield and Green type 13Q dead weight gauge with a smallest measurable pressure increment of 0.1 psi. The nominal pressure reading on the dead weight gauge is corrected by a procedure outlined by Cross(28) (See Appendix D for sample calculation), which accounts for local gravity, air bouyancy on the brass weights and thermal expansion of the piston. Local gravity is 980.314 gals at the Natural Science Building on the Main Campus of the University of Michigan. After being corrected for latitude and elevation(22) of the Automotive Laboratory on North Campus, gravity is taken to be 980.317 gals. Effects due to elastic distortion (less than.01 psi) and surface tension of the oil (0.002 psi) are neglected. Corrections are also made from a calibration certificate traceable to the National Bureau of Standards provided by the manufacturer (See Appendix B, Table XXVIII). The oil which lubricates the piston-cylinder assembly of the dead weight gauge is separated from the gas in the system by a mercuryr'-i l Init 11-1(:.'t l m' n -ury is v-iinl):(a 1 1 tnwo'Pcner thr'y X-%'00 si );ht?;l asses

-66mounted on the end of a U-shaped stainless steel tube. Differences in the mercury levels can be read to 1/16-inch off transparent graduated scales fastened to the sight glasses. When making pressure measurements, the (dtierl'lcr(ce ii mnercury levels in the twoe armis i always kept at less than 1/16-inch (0.03 psi) by pumping in or draining oil. Metering valves on both the oil and gas side facilitate the gradual increase or decrease of pressure applied to the column of mercury. Traps are provided to prevent the mercury from blowing over into the system. The measurements on the dead weight gauge are corrected for oil head (0.075 psi) but not for the small difference in mercury levels (less than 0.03 psi) or for the gas head between the calorimeter and the U-leg (less than 0.01 psi). After accounting for uncertainties in the various corrections to the gauge pressure measurement the precision is believed to be + 0.2 psi and the accuracy + 0.3 pNi. The gauge pressure readings are converted to absolute pressure readings with atmospheric pressure measurements on an Eberbach catalog No. 5070 Fortin-type mercury barometer with a vernier scale with 0.01 inch smallest division. Pressure readings are corrected for scale and mercury expansion, local gravity and zero error using standard techniques (22) described by Brombacher, Johnson and Cross. The zero error was determined by calibrating the barometer against a standard barometer (see Appendix B, Table XXIX). The accuracy of the measurement after accounting for uncertainties in the corrections and including capillarity error is estimated as + 0.02 inches Hg. This error contributes negligibly to the absolute pressure value. Differential Pressure Pressure drops between pairs of taps 5, 6 and 10 in the calorimeter (Figure 2) are read in a Meriam high pressure manometer with dibutyl

-67phthalate manometric fluid (specific gravity 41.04) and measured by a telescope-cathetometer arrangement to + 1 cm. Temperature The temperature of the calorimeter bath is measured with a mercury-in-glass Fisher Scientific thermometer (No. 3C3642) graduated in 0.1~C intervals between -1~C and 51~C. Emergent stem corrections (161) were made as outlined by Swindells. An accompanying National Bureau of Standards calibration certificate (See Table XXX, Appendix B) estimates the inaccuracy of the corrections as less than ~ 0.03~C. Based on the 0.1~C graduations, it is estimated that a temperature change of + 0.025~C within a + 0.05~C band is detectable on this thermometer. The temperature of the gas stream entering the port labelled 1 in the sketch of the calorimeter (Figure 2) is assumed to be equal to the bath temperature. Temperature differences are measured between the two inlet streams by a pair of six junction copper-constantan thermopiles. Likewise the temperature difference between the inlet and outlet gases are measured by duplicate six junction copper-constantan thermopiles. One of the latter thermopiles was calibrated by the National Bureau of Standards (See Appendix B, Table XXXI) with an accuracy of ~ 0.5 microvolt. The output from the thermopiles is measured on a K-3 null potentiometer with a No. 9834 D.C. Null Detector both of which are manufactured by the Leeds and Northrup Company. The limit of accuracy on these instruments is ~ 0.5 microvolts (Table XXXIV) which corresponds to a temperature difference of ~ 0.0020C which is equal to the thermopile calibration accuracy. (iomete r witi:i -'; h( (.0020l crtlol'.lntr 1, l-lrtto 1( c alIc ratrocy of thetiometer with the + 0.002~C calorimnclcr bath control, the accuracy of the

-68temperature difference measurement is bel ieved to be ~ (O.00(~C.'Ihe estimated inaccuracy in the measurement of the temperature of the gas at the calorimeter outlet is + (0.03+0.006) q- about ~ 0.040C with differences in temperature being detectable to + (0.025+0.006) or about ~ 0.03~C. Power The power to the calorimeter is supplied by a Kepco CK40-0.8M D.C. power supply with output voltage regulation of + 0.01 percent. The scheme used to supply and measure the power to the calorimeter heater is shown in Figure 5. A pot within the Kepco power supply unit (not shown in Figure 5) is used for coarse adjustment of its power output. Fine adjustments are achieved by varying the setting on the 40-turn helipot, Rh. The degree of resolution on the final adjustments can be changed by altering the resistance of the rheostats, Rf and Rg The power input to the calorimeter is W = (ec)(ic) (70) where ec is the voltage drop across and ic is the current flowing through the calorimeter heater. Voltage Drop across Calorimeter Heater The potential drop, Ve, is measured across the standard resistor, Re. The accurate evaluation of the voltage drop across the calorimeter, ec, requires values for the resistance of the wires connecting the calorimeter heater, Rc, to the standard resistors, Re and Rs. The connections, Ca and Cb are made close to where the heater leads emerge from the conax gland within the calorimeter, 13 (in Figure 2). The resistance of the lead wires between the calorimeter heater, Rc,

Power 4 Supply - LEGEND Sb Co, Cb Connections soldered within calorimeter Cb Rc Calorimeter heater, 180 ohms Re Standard resistor, 10 ohms nominal, Rf Air-cooled rheostat, lOohmse S Rg Air-cooled rheostat, 1000 ohms Rh 40-Turn helipot, 125 ohms Ri Standard resistor, lohm nominal Ve Rs Standard resistor, 10,000 ohms nominal So, Sb Switches Ve Voltage drop across Re measured with K-3 potentiometer Vj Voltage drop across Ri measured with K-3 potentiometer Figure 5. Electrical Power Input System for Calorimeter.

-70and the connections, Ca and Cb, is negligible (less than 0.01 ohms) compared to the resistance of' the heater:itself (180 ohms). The wires t)cetweerl the.taindardi rcs:i sl;or d Lrd the conu ccti ons, C at Id Cb a'C chosen so that they contribute negligibly (about 0.1 ohms) to the overall resistance of that arm (approximately 10,010 ohms). Neglecting the resistance of the connecting wires, the voltage drop across the combined standard resistors, Re and Rs, can be calculated from Ve and equated to the voltage drop, ec (Rs~Re) ec = (RR V (71) Re Current in Calorimeter Heater Inspection of the power input system, Figure 5, reveals that the current passing through the one ohm standard resistor, Ri, is divided between the calorimeter heater and the arm with standard resistors, Re and R. The current flowing through the two standard resistors, Re and Rs, is equal and it is iR, =Ve (72) Re where i = iR Subtracting the current, iR, in the arm parallel to the calorimeter heater from that flowing through the one ohm standard resistor yields ic, the current in the calorimeter heater: Vi Ve ic = Ri R (73) The electrical energy input to the calorimeter is calculated by substituting the expression for ic, Equation (73), and ec, Equation (71), in the relation for the power input, Equation (70) w = - VRe watts (74) 1t< K^/ \ e

-71The two voltages Ve and Vi are measured on the K-3 potentiometer. Its operating characteristics are given in Table XXXIV in Appendix B. A Leeds and Northrup 7309 standard cell used in these measurements is checked at frequent intervals against a similar standard cell calibrated by the National Bureau of Standards (See Appendix B, Table XXXIII). All the measurements made during this research were at calorimeter power input levels which caused a rise in temperature of the resistors of only 3~C to 4~C. The temperature of each standard resistor is measured by single junction thermocouples inserted in tubes that penetrate the oil which submerges the resistance coils. Both the values of the resistances and the temperature coefficients are listed in Table XXXII, Appendix B. Flow Rate Metering of the flow rate is the most critical of all the measurements since it is the factor which limits the accuracy of the entire set of measurements. The high pressure flow meters and the low pressure flow meter are described separately. High Pressure Flow Meters The two high pressure flow meters and their workings are discussed under four separate headings: 1. Description 2. Measurements 3. Calibration 4. Correlation Description: Each of the high pressure flow meters is made out of 1/8-inch O.D. x 0.040-inch I.D. stainless steel tubing 13 inches long. The pressure

-72drop is measured across two #80 drill holes 6 inches apart and 3 1/2 inches from the ends of the tubing. Two lengths of 1/8-inch O.D. x 1/16inch I.D. tubes heliarc welded to the tubing at the location of the #80 drill holes serve as pressure taps. Argon is blown through all the tubing while heliarc welding to prevent the formation of blisters. To maintain a uniform inner surface, after the welding operation, the whole length of the tube is smoothed with medium lapping compound on music wire. A photograph of the flow meter is given in Figure 6. In the bath, the flow meter is held rigid sandwiched between two brass plates to prevent any change in flow pattern which would cause a change in its flow characteristics. Two Nupro micron in-line filters are attached to the ends of the flow tubing with Swagelok fittings. The filter brackets and flow meter sandwich are bolted to a common base plate. There are micron filters on the pressure taps as well. Measurements: The pressure at the inlet pressure tap is measured on a 0-1500 psi temperature-compensated Heise Bourdon tube gauge with 1 psi smallest division. The Heise gauge is calibrated frequently against the dead weight gauge described earlier. The accuracy of the pressure measurement with the Heise gauge is estimated to be + 1 psi. The pressure drop is registered with di butyl phthalate manometric fluid (specific gravity'1.04) in a Meriam high pressure manometer. Only in the case of the nitrogen-oxygen system, mercury was used as the manometric fluid. A maximum pressure drop of 100 cm is measurable with a telescope-cathetometer arrangement capable of reading differences in heights of ~ 0.01 cm. The Meriam Instrument Company who supplied the di butyl phthalate also supplied data on its thermal expansion characteristics. The temperature

:i::~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ lii-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ii ~~~~~~~~~~~~~~~~~~~~~~~~~":g;I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.e~~ ~~~ ~~~~~~~~~~~~~~~~~~~~~iJ11!~~! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~"~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~"~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~i!iii!i Figre6.Phtorah f ig Pesur FowMeer

-74of the fluid is measured by a mercury thermometer taped with insulation onto the outside of the well on the manometers. As both manometers operate at room temperatures, this does not introduce substantial error. The accuracy of the pressure drop is estimated to be ~ 0.04 cm. At the conditions of 1100 psia and 45~C (bath temperature) in the flow meters, the carbon dioxide is in the gaseous state but it is poossible for condensation to occur in the pressure tap lines that are at room temperature. Hence the 15 feet of pressure tap lines that lead from the flow meters to the manifold are wrapped with electrical heating tape. To prevent condensation inside the manifold and the high pressure manometer, they are filled with nitrogen under pressure instead of being heated. Occasional flushing with nitrogen is required wIhie setting the flow rates during the initial phases of operating the flow meters but not when steady conditions are approached. Calibr) at;i on: The calibration of the flow meters may be divided into three phases. The first phase consists of developing a means for measuring the flow rate of the gas through the flow meter. The second phase consists of calibrating the flow meter with this device and the third consists of correlating the pressure and pressure drop with the flow rate. 1. Fl@ Rate Determination: The device chosen is a copper tank (henceforth called calibration tank) whose volume is about six cubic feet. First the instrumentation used on the calibration tank will be described. Then the procedure for determining its volume and finally the manner in which it is utilized for measuring flow rates will be detailed. The tank is located in a stirred water bath. The temperature of' the water bath is measured with a mercury-in-glass thermometer which

-75has been calibrated against the NBS certified thermometer. Gas temperatures are measured at two vertical locations in the tank with calibrated copper-constantan thermocouples inserted in a 1/4-inch stainless steel tube. The output from the thermocouples is read on the K-3 potentiometer. When it is used to calibrate the flow meters, the absolute pressure of 20 mm Hg in the initially evacuated tank is measured by a mercury vacuum manometer to + 0.5 mm Hg. After the tank is filled with gas, the pressure of about 30 inches of water gauge is read to ~ 0.05 inches on a 36-inch King manometer filled with di butyl phthalate manometric fluid. During the volume determination of the calibration tank, the vacuum manometer is replaced by a McLeod gauge, and the pressure above atmospheric read on the 36-inch King manometer with mercury as the manometric fluid. The absolute pressure in the tank is determined from the gauge pressure in the tank and atmospheric pressure read on the Eberbach barometer described earlier. The first step in determining the volume of the calibration tank is to evacuate the tank to about 20 microns Hg. The pressure and temperatures are noted when the temperature of the gas and of the stirred water differ by less than 0.05~C. Two aluminum cylinders containing pure nitrogen are used to charge 320 g of gas into the tank. Both cylinders are weighed before and after releasing nitrogen. Pressures and temperatures are again recorded when the three temperature measurements agree within 0.050C. The volume of the tank is calculated from the pressures, temperatures, (126) mass of nitrogen and virial coefficient data of Otto. ) Four such volmeIB measulre t ells ('ete'I'a,:l X-X-TI, ApperLndix i) y:i.eld(ed( an a'cvera.,ge V(olme of ().L' ('H) Wii,1a iL tld LAr. l J'V.iation of.( 0.th pere n. When -the calibration tbank is utilized for calibration of the flow meters a procedure is used which is similar to the one described

for determining the volume. The gas in the system is allowed to enter the tank through a two-way solenoid valve, (23 in Figure 3) via a short length of copper tubing. A timer capable of measuring time intervals of 10,000 seconds to 0.1 second is connected To the switch for the solenoid valve. The tank is initially evacuated to <ibout 20 mm Hg and pressures and temperatures noted after thermal equilibration between the gas in the tank and the water in the bath. When steady state conditions are achieved in the flow meters, the switch on the solenoid valve is thrown. This simultaneously starts the timer and allows gas to enter the calibration tank. When the tank is full, the solenoid valve is deactivated which stops the timer as well. When the gas temperature differs from the water temperature by less than 0.05~C, values of the temperatures and pressure are recorded. 2. Calibration Procedure: Each flow meter is calibrated separately. The pressure in the flow meter is adjusted to about 1100 psia by regulators, 3 (Figure 3). The level of pressure in the calorimeter section is varied till there is sonic flow through metering valve, 21, and pressure reducing valve, 18, while maintaining 60 psi at the low pressure flow meter. Critical flow is also maintained across each of the two metering valves that comprise the flow metering valves, 20. The need for two flow metering valves was dictated by experience. Originally only one flow metering valve was used. Before the solenoid valve switch is thrown there is atmospheric pressure in the tank (20 mm Hg). During calibration the pressures in both the tank and at the valve exit rise from the initial pressure (20mm Hg) to just above atmospheric pressure. With one valve, this change in back pressure caused the flow rate and hence the pressure and pressure drop in the flow meters to change continuously.

-77To combat this affect, two flow metering valves were used with the pressure in the line between them being maintained at about 30 psig which assisted in sustaining critical flow across both valves. This worked satisfactorily with the nitrogen flow meter. To maintain steady conditions in the carbon dioxide flow meter, however, it was found necessary to continuously adjust the second valve so as to hold constant the pressure level in the low pressure flow meter section. The degree of adjustment required decreased when two vacuum pumps were attached in parallel to the atmospheric exhaust Ionrt of the two-way solenoid valve. When steady state conditions have been achieved in the flow meters, the switch on the solenoid valve is thrown and the flow rate determined as described earlier. During the period of gas collection, readings of pressure level and pressure drop in the flow meters are taken every minute. The readings on the various instruments are punched on IBM cards and fed to a computer program which calculates values for the flow rate, pressure and pressure drop and values of viscosity and density of the gas at the conditions in the flow meter. 3. Correlation: The results from the computer program are correlated by a modified version of the universal friction factor law:(17) 1_ _ 4.07 log10 Re ff - 0.40 (75) The modification consists of lumping all the dimensional constants (tube length, diameter, etc.) and the unit conversion factors together into two unknown constants, pF and 5F, and expressing the previous equation in terms of the flow rate, pressure, pressure drop, viscosity and density.

-78-'I'he unknowri constants in the modified equation axe determined from the f'low meter calibration results. The derivation of the modified equation is described below: The friction factor is defined as i d F f =1 d. PF (76) 2L -i PFu in terms of the tube diameter, d, the tube length, L, the pressure drop, APF, density, PF, and mean velocity,. The mean velocity is written in terms of the flow rate, F, d2 and the density, PF, and the cross-sectional area of flow, -, as u_ - (77) PFjrd2 Substituting for u from (77) in the previous equation for friction factor gives 1 d AF 2 2d4 ( f -- PF (7) 2L PF F216 Collecting the constant terms into a single constant, n yields f-=n2 (= 4F where n= 1 d5 2 (79) F2n 2 L 16 The Reynolds number is Re = PF (8o) rIF Substituting for the mean velocity, u from Equation (77) into the last equation gives 4F d Re = PF p PF2d qF 4 ~ (F_) (81) jtd. ^riF7~ ~ ~ ~~si

-79Substituting for Reynolds number, Re, and friction factor, f, from Equations (81) and (79) respectively into the friction factor Equation (75) gives F 1 = 407 log1O n ) - o.4o (82) ^ p^AP, n I0 L \ F / 0td (jd The constants within the log10 term may be combined thus: 1 m2 = n4 (83) jrd and the base 10 logarithm term written in terms of natural logarithms. Making these changes in Equation (82) yields F 1 = 4.07 in m2 f. f - 0.40 (84) pAPF n 2.303 - lF This expression is further modified by squaring the term within the square brackets and collecting all the constant terms F 0= 3. 1n PFPF + 7.07 n ln[m]- 0.40} (85) f; *2.505 2 J I.3 1i2.30 2 This equation expresses a linear relationship between the two measurable F PFAPF variables and in. This linear relation may also be PFAPF 2 written as F'PF'^sPF — P= F in L 1+ 6F (86) \ 4 PPF FF where PF and 6F are the two coistant terms in the previous Equation (85). The last equation is the modified friction factor equation used to correlate the results. Data from the following sources are used to correlate the results of flow meter calibrations: cl(rbol diioxi(e: D.,lsc.i~ty arid secondIl( virial coefficient data of Michels anldi M:i chels(13) ad viscosity data of Michels, Botzen anld Schurmanl. (l)

-80Ethane: Densities from tabulations by Tester, (62) viscosity values given by Eakin, Starling, Dolan and Ellington(39) and second virial coefficients reported by Michels, Van Straaten and Dawson.(l16 Nitrogen: For the calibrations used with the nitrogen-carbon dioxide (34) system, density tabulations by Din, viscosity data of Michels and Gibson(12) and second virial coefficients reported by Otto.(26) Oxygen: For the flow meter calibrations utilized for the nitrogen-oxygen system, data on compressibility factors and second virial coefficients given by Hilsenrath et al.(59) and data on viscosity reported by Kestin and Leidenfrost74) on both nitrogen and oxygen. The computer program for data reduction calculates values for F, PFAPF the two variables --- and 2.. A regression analysis on all the OpPpF T12 flow meter calibrations yields the two constants PF and. The results of the flow meter calibrationsfor all the gases are presented in Appendix B in a series of Tables XXIV through XXVII and Figures 16 through 18. The flow meters for all the gases are calibrated at a nominal pressure of 1100 psia except ethane for which nominal flow metering pressure is 500 psia. Low Pressure Flow Meter This is a laminar flow device made by the Meriam Instrument Company. The pressure drop across it is read to + 0.006 inches by a National Instrument Laboratory 20-inch water manometer. The pressure in the flow meter is read on a King 130-inch manometer to ~ 0.05 inches Hg. The low and high pressure flow meters can be calibrated simultaneously by a procedure described earlier. During calibration of the carbon dioxide flow meter, the second of the two flow metering valves,:20 ill Figure 53, is adjusted continuously so as to maintain constant

-81pressure at the low pressure flow meter as mentioned earlier. However, the response of the water manometer is too slow to give correct values of the pressure drop across it. Therefore, the low pressure flow meter was not calibrated. It was used only to check on steady state conditions during the enthalpy of mixing measurements and during the flow meter calibration. Gas Composition The composition of the mixture which exits the calorimeter can be calculated from the flow rates of the two gases entering it. In order to provide an independent check on this calculated composition, samples of nitrogen-carbon dioxide mixtures were collected during enthalpy of mixing measurements and analyzed by a modified gas density technique. The sample bomb is a 570 cc capacity aerosol can to which is soft soldered a small, light valve. Before collecting the sample, the can is evacuated to about 50 microns Hg with the pressure being read on a thermocouple vacuum gauge. The mixture sample at about 60 psig is tapped just downstream of the pressure reducing valve, 18 in Figure 5. Gas pressure in the can is measured to + 0.05 inches Hg on a 130-inch King manometer. During the pressure measurement, the can is held at a fixed temperature by immersion in a constant temperature water bath. The temperature of this bath is set at 250C with the NBS calibrated thermometer and regulated to 0.1~C with on-off control. Each can weighs about 160 g and holds approximately 1.8 g of nitrogen at 100 inches Hg gauge. The can is weighed on a Christian Becker balance whose weights have been corrected against a set of NBS cali brated weights.

Can Volume Determination Before analyzing the mixture sample it is necessary to determine the internal volume of the aerosol can. This procedure is initiated by evacuating the can and filling it to 120 inches Hg gauge pressure with nitrogen. The can is brought to 25~C by immersing it in the bath for about half an hour. The copper line between the manometer and the aerosol can is flushed out with the gas in the can to prevent impurities from diffusing into the nitrogen. As a further precaution, the pressure in the manometer is set slightly below the can pressure, which is now about 100 inches Hg gauge. After the valves connecting the manometer and the can are opened, the pressure on the manometer is noted every minute. Five minutes after the pressure reaches a steady level, atmospheric pressure is noted and the valves on the can and in the pressure manifold are closed. The can is removed from the bath, detached from the copper line, rinsed with acetone, dried and weighed. The can is evacuated to 30 microns Hg and reweighed. To ensure thermal equilibration with the room conditions, the can is placed in the balance room for 30 minutes prior to each weighing. Two successive weighings are made which usually differ by less than 0.4 mg. An identical can with an internal pressure of 15 psia is weighed along with the sample can to check for changes in atmospheric conditions. The change in weight of the identical can (about 0.5 mg) gives the buoyancy correction which should be applied to the sample can. The volume of the can is calculated from the mass of gas, its (109) pressure, temperature and the virial coefficient of nitrogen. The change in internal volume with pressure of several cans was also determined. The can is placed in a large mouthed jar completely filled with water. The level of water is noted in a graduated 5 cc pipette inserted in the rubber stopper of the jar. The change of the water level in the

-83pipette with pressure in the can is noted and the change in can volume with pressure calculated as 0.007 cc/psi. Repeated pressurizing also showed that the can does not suffer any permanent expansion at pressures up to 65 psig. The results of volume determinations on two aerosol cans are given in Table XLVI, Appendix C. The volumes reported have been normalized to 70 psia. Measurement Number 2 on can 30 and can 31 was done with the carbon dioxide used in the enthalpy of mixing measurements. Difficulties were encountered in a number of cans due to leaks (mostly vacuum leaks) in the soft solder and at the valves and fittings. For this reason and because each can volume measurement takes four to six hours, the volume of the remaining cans was determined just once. Gas Density Measurement The technique used for gas density analysis is identical with that used for can volume measurements. The can with the sample is immersed in the bath. Gas pressure is adjusted to within ~ 3 inches Hg of the pressure of can volume determination and its value is measured on the 130-inch manometer. The second virial coefficients of nitrogen,(l09) carbon dioxide(19) and its mixtures(93) used in calculating the compositions are given in Table XLVIII in Appendix C. A check was performed on the analytical technique before it was used. A mixture of known composition was made up by gravimetric analysis. Two cans were evacuated and weighed. They were filled simultaneously with nitrogen from a pressure regulator on a nitrogen cylinder to a predetermined pressure and both cans weighed. Carbon dioxide was piitroduced ito the two cans so that both cans were at the same final pressTure and the canls recwv-eilhel(i.'The g.ases were mixed for 48 hours by

-84placing the cans under a heat lamp. After making buoyancy corrections, the composition in the cans was calculated with a maximum inaccuracy of 0.08 percent from the mass of nitrogen and carbon dioxide introduced. Because of the filling proc(edurc used, the composition in both cans was almost equal. The gas in the cans was then analyzed by the gas density technique. The results are presented in Table XLVII, Appendix C. The volume of can 14 was determined just once whereas the volume of can 30 was measured three times (Table XLVI). The probable accuracy of the gas density measurements is discussed in Appendix A. PROCEDURE There are three phases into which the operation of the facility may be divided: 1. Preparation of the Apparatus 2. Startup 3. Measurements at Steady State These will be described briefly and followed by a section entitled 4. Data and Data Reduction Preparation of the Apparatus Preparations start a day previous and continue to the time that gas flow is commenced. Valves and fittings are tested for leaks under pressure. The baths are controlled at the required temperature. The heating tapes, calorimeter power input circuit and all the thermocouples and thermopiles are checked for open circuits and for shorts to ground. The aerosol cans are evacuated continuously for several hours till the time that they are used to collect samples.

-85Prior to starting gas flows, the Heise gauges are calibrated against the dead weight gauge. Readings are then taken of the level of fluids in all the manometers at zero pressure drop and the calorimeter bath temperature is checked with the NBS calibrated thermometer. Micrometer vernier handles on all the valves which control flows are set at predetermined values. Startup The valves on the nitrogen cylinders are opened and the pressure in the flow meter set at about 1100 psia with regulators, 3 (Figure 3). The flow rate is fixed approximately with metering valve, 21, on the nitrogen line. The calorimeter pressure is set at about the value of the partial pressure of nitrogen in the desired mixture. The flow of carbon dioxide is initiated similarly. Further simultaneous adjustments are required in both the metering valves, 21, and the pressure reducing valve, 18, to achieve the desired pressure and composition in the calorimeter. The latter can be set to within + 1-2 mole percent of a preselected value. The pressure level at the calorimeter outlet is set at ~ 3 psi of the preselected nominal pressure. Next, the power supply is switched on and adjusted to a precalculated setting. Measurements at Steady State Steady conditions are achieved one to two hours after commencing gas flows. Several minor checks and adjustments (e.g. valve settings, bath temperatures, etc.) are made towards the end of this period. Invariance of the flow rate of the two gases as determined by the pressure and pressure drop in the high pressure flow meters (5 and 6) can be checked by similar readings on the low pressure mixture flow meter, 19.

-86The final adjustments consist of varying the power input to the calorimeter. A desk calculator is used to calculate settings on the power supply and the helipot. The calorimeter itself can attain steady state within 15 to 20 minutes after a change in the input power setting if the initial values of the inlet-outlet gas temperatures differ by no more than 0.5~C. Data is taken under steady state conditions when the temperature difference between the inlet and outlet gases to the calorimeter is less than about 0.05~C. Readings on all instruments are taken every two minutes over a four- to six-minute period. For the nitrogen-carbon dioxide system, the gas mixture is sampled for analysis. Readings of power input and pressure drop in the calorimeter are taken at the conclusion of the other measurements. When the gas flow is stopped, several measurements are repeated: The Heise gauges are recalibrated against the dead weight gauge; the temperature of the calorimeter bath is rechecked with the NBS calibrated thermometer; and zero level readings are made on all the manometers. Data and Data Reduction After the measurements described are complete, all instrument readings are transferred to punched cards. The reduction of the data is then carried out on the IBM 360/67 computer. Several computer programs are used which perform the calculations outlined in the chapter entitled "Thermodynamic Relations." Measurements of the enthalpy of mixing were performed on three systems which along with the conditions of experimental measurements are listed in Table VIII. The purity of the gases used is listed in Table IX. The data obtained on these three systems is listed in Tables XXXV, XXXVI

-87and XXXVII in Appendix C. The results after interpretation of calorimetric measurements are given in the series of Tables XXXVIII to XLII in Appendix C. A sample calculation is detailed in Appendix D. TABLE VIII SYSTEMS STUDIED AND CONDITIONS OF EXPERIMENTAL INVESTIGATION OF THIS RESEARCH System Nominal Number of ExperiExperimental Conditions mental Measurements at Each (Pn,Tn) Temperature Pressure Tn Pn ~C ~F psia N2- CO2 40 104 500 15 40 104 950 4 31 87.8 500 4 31 87.8 950 4 N2 - C26 32.38 90.28 401 4 N2 - 02 25 77 1001 5

-88TABLE IX IMPURITY ANALYSES OF GASES USED IN TTIS RESEARCH Gas Constituent Mole Percent Nitrogen Nitrogen 99.98 Oxygen 0.02 Total 100.00 Carbon dioxide Carbon dioxide 99.86 Oxygen 0.09 Nitrogen 0.05 Total 100.00 Ethane Ethane 99.22 Propene 0.41 Propane 0.32 Ethene 0.05 Total 100.00 Oxygen Oxygen 99.80 Argon 0.11 Nitrogen 0.09 Total 100.00

RESULTS This chapter presents details o~ the interpretation of calorimetric data on the nitrogen-carbon dioxidce, nitrogen-ethane and nitrogenoxygen systems. The results are given in both tubular and graphical form, and are compared with available data on the systems as well as with values calculated from an equation of state. The precision and accuracy of the measurements are considered. Interpretation of Calorimetric Data Direct calorimetric measurements give the pressures and temperatures of the two gases entering and the mixture exiting the calorimeter. These are then combined with the power input and flow rate measurement through a set of primary and secondary corrections to yield values of the excess enthalpy. This data interpretation is discussed separately for each system. Nitrogen-Carbon dioxide System Two examples are given in Table X of the primary and secondary corrections involved in data reduction for the nitrogen-carbon dioxide system. The numerical values of the corrections (in Btu/lb) are given in Tables XXXVIII and XXXIX in Appendix C. Primary Corrections: Heat capacity data are required to make the correction for nonisothermal operation of the calorimeter (See Equation (40)). The tabulations by Din() lor nitrogen arid Vukalovich and Altunin (2) for carbon dtioxidec tae enmploved. for this ipurpose;'. This correction averages about 0.', lpercelnt with a m.niodImun ol 1..2 p'ercent.

-90-'I'AI1'T,',:'X EXAIMVPLES 01' CORRECT'IO}CN'., _I-NVUOIV.1D) IN DA'1.A RliDUlC'TION'OR THE NIITRO(l EN-CARI0OJ\N DIOXI]DE SYST~EM Nominal Experimental Conditions Tn~C 40 31 Pn psia 500 950 Actual Experimental Conditions To C 40.033 31.010 (Conditions at outlet of calorimeter) PO psia 498.5 952.6 Mole fraction Nitrogen 0.518 0.725 Electrical heat input to calorimeter, 82.3 259.0 (W/F), Btu/mol Percent Corrections Primary corrections: Applied to(W/F) (a) For pressure drop across calorimeter -0.22 -0.03 (b) For non-isothermal operation -0.07 -0.10 (c) For kinetic energy difference of incoming and outgoing gases -0.8xlO 4 0.5x10-5 (d) For impurities in carbon dioxide 0.37 0.48 Total 0.08 0.55 HE at experimental conditions (ToPO), 82.3 259.9 Btu/mol Secondary Corrections: Applied to Ho at (To Po) (e) For normalizing to Pn 0.34 -0.86 (f) For normalizing to Tn 0.03 0.04 Total 0.57 -0.82 HE normalized to (TnPn)Btu/mol 82.6 257.8 n n.9Pn)AtU/mo1

-91Joule-Thompson coefficients of carbon dioxide and nitrogen reported by Roebuck et al. (139'1 4) are combined with the above mentioned heat capacities values according to Equation (11) to obtain the isothermal Joule-Thompson coefficients used in making the pressure drop correction (See Equation (39)). The values of the thermodynamic properties are given in Table XLIII in Appendix C. This correction decreases with increased density of the gases flowing through the calorimeter as can be seen in the two examples in Table X. The pressure drop correction ranges between 0.03 and 0.22 percent with an average value of 0.1 percent. Kinetic energy corrections (See Equation (33)) are calculated (54) using the density tabulations on nitrogen by Din,(3 tabulations on carbon dioxide by Newitt et al.(124) and mixture compressibility factor (56) data of Haney and Bliss. As illustrated in Table X this correction is always very small with a maximum contribution to the power/flow ratio -4 of 10 percent. Impurities are accounted for by a technique, detailed in the chapter entitled "Thermodynamic Relations," which utilizes the experimental measurements of this very research. The impurity analysis of nitrogen and carbon dioxide is done with a mass spectrometer and the results are given in Table IXo Corrections calculated, assuming the nitrogen to be pure and the carbon dioxide to contain 0.14 mole percent nitrogen, range between 0.5 and 0.8 percent with an average contribution of 0.5 percent. Numerical values of the four corrections which comprise the primary corrections are listed in Table XXXVIII, Appendix C. Their sum is listed as a percent correction to the power per unit flow, (W/F), in Table XI along with the resultant excess enthalpy at calorimeter outlet conditions after primary corrections.

TABLE XI EXCESS EINTHALPY DATA ON NITROGEN-CARBON DIOXIDE SYSTEM Power. E E.E Mol Fr Flow Primary S at Secondary at ( mooth.ot, smoothe)O Nitrogen (W/F) Corrections (To, P) Corrections (Tn,Pn) E Btu/mol Percent Btu/mol Percent Btu/mol Percent Nominal Experimental Conditions: Tn = 400C Pn= 500 psia O.?88 76.8 0.35 77.0 -0.58 76.6 0.47 n. 339 80.4 0.12 80.5 0.02 80.5 -0.49 0.437 84.5 -0.48 84.1 0.11 84.2 -0.33 0.481 83.7 -0.00 83.7 -0.02 83.7 -0.38 0.482 83.9 -0.55 83.4 0.46 83.8 -0.16 0,484 84,0 0.34 84.3 -0.31 84.0 0.11 0.491 83.9 0.00 83.9 -0.14 83.8 0.08 0.503 8?.9 0. 1 83.0 0.16 83.1 -0.21 n.508 84.3 -0.89 83.5 0.04 83.5 0.47 n. 509 83.? -0.29 83.0 0.59 83.5 0.45 0.510 83.3 -0.60 82.8 0.79 83.4 0.44

TABLE XI (CONTINUED) Power (H oothed)x100 I —- -IE m-Smoothed Mol r Flow Primary HE at Secondary a t.E Nitrogen (W/P) Corrections (To, P) Corrections (TnPn) Btu/mol Percent Btu/mol Percent Btu/mol Percent n.5l 82.'3 0.08 82.3 0.37 82.6 -0.09 0.5?5 82.4 0.10 82.5 0.20 82.6 0.31 0.575 79.9 -0.29 79.7 0.01 79.7 0.56 0.670 69.5 -0.15 69.4 0.01 69.4 -0.35 No.iinal Experimental Conditions: Tn = 40~C P = 950 psia. 220 269.1 -0.32 268.2 0.45 269.4 0.76 0.358 302.9 0.92 305.7 -0.86 303.0 -0.64 0.516 281.8 -0.33 280.9 1.36 284.7 0.94 0.732 187.7 0.59 188.8 1.02 190.7 -0.14 Nominal Experimental Conditions: T = 51~C P = 500 psia.22 8 77.6 -0.15 77.4 0.04 77.5 -0.02 0.363 95.7 0.16 95.8 -0.78 95.1 0.35

TABLE XI (CONTIiU D) Power E(_ moothed )xlOO Mol Fr F'l-o Primary H at Secondary ab moothed Nitrogen (w/F) Corrections (TiP) Corrections (TnPn) HE Btu/mol Percent Btu/mol Percent Btu/mol Percent 0n4R5 97.1 0.33 97.4 -0.96 96.5 -0.29 0.729 70.? 0.38 70,5 0.55 70.9 0.02 Nominal Experimental Conditions: Tn = 310C Pn = 950 psia 0,239 419.1 -0.01 419.0 1.63 425.9 1.17 0.310 440.1 0.54 442.4 0.20 443.3 -0.76 0.489 409,5 0.18 410.2 0.70 413.1 0.93 0.725 259.0 0.35 259.9 -0.82 257.8 -0.06

-95Secondary Corrections and Tabulated Results: Secondary corrections compensate for operational variations in calorimeter outlet pressure level of ~ 3 psi and outlet temperature level of + 0.05~C. There are no experimental data available on the excess heat capacity and the excess isothermal Joule-Thompson coefficient of nitrogen-carbon dioxide mixtures. Hence, these properties are calcu(12) lated using the original Benedict-Webb-Rubin equation( of state with Bloomer and Rao's (9) constants for nitrogen and Cullen and Kobe's (29) constants for carbon dioxide (See Table XLV, Appendix C) and with the mixing rules suggested by Benedict et al.(l^) for their mixtures. Values of cpE calculated in this manner at 40~C agree within ten percent at 500 psia and 30 percent at 950 psia with values obtained by differentiating Lee and Mather's data. (90) The average contribution of the correction for pressure level at 500 psia which is about 0.2 percent at 400C and 0.5 percent at 310C increases to about 0.7 percent at 950 psia at both temperatures. This increase is due to the rise in the value of the excess properties caused by the increased proximity of the critical point of carbon dioxide. For example at 31~C and 0.49 mole fraction nitrogen, the value of pE is 0.32 Btu/(mol psi) at 500 psia and 1.5 Btu/(mol psi) at 950 psia. However, the percent correction does not reflect the five-fold rise in the value of cpE because the magnitude of the excess enthalpy also increases with pressure. The contribution for normalizing temperature levels averages 0.03 percent at 500 psia and 0,2 percent at 950 psia at both temperatures. The percent contribution due to the application of secondary corrections to the excess enthalpy at calorimeter outlet conditions and the resultant normalized excess enthalpies, H, are listed in Table XI. The numerical values of the corrections are given in Table XXXIX, Appendix C.

-96Values of the excess enthalpies are smoothed with respect to composition by a least squares analysis of the data after primary and secondary corrections have been applied. The equation used is one which has been given in the chapter entitled "Thermodynamic Relations": xN(l_-xN + bn) = + bn(xN-O.5) + 52 (69) Coefficients for this equation are listed in Table XII along with the average and standard deviations. The percent deviation of every individual experimental point from this curve is listed in the last column of Table XI. Graphical Results: The results of the excess enthalpy measurements are plotted in the Figures 7 through 9 for the data at 400C and in Figures 10 through 12 for the data at 31~C. The open and solid circles in these figures are experimental values of the normalized excess enthalpy,. In Figures 7 and 10, the excess enthalpy is plotted as a function of composition. The solid lines in these figures are obtained from TABLE XII REGRESSION COEFFICIENTS FOR SMOOTHING NITROGEN-CARBON DIOXIDE EXCESS ENTHALPIES VERSUS COMPOSITION Nominal Experimental Regression Percent Arithmetic Conditions Coefficients Average Absolute Deviation from a T P an bn cn Experimental Points Percent 40 500 333.909 -140.093 181.668 0.32 0.40 40 950 1147.29 -1082.50 1457.65 0.57 1.29 31 500 384.931 -155.828 185.099 o.19 O.45 31 950 1617.85 -2023.96 2623.85 0.70 1.72

-97-' I I" I I "' 0 Experimento/Data o 40~C -Least Squares Fit of Data, 300 / /0% 200 LJ I / 950psio 0 r100 H -/ \ coj / A6Represents Three Almost Identical Podints 0 0.2 0.4 0.6 0.8 1.0 XN, MOLE FR. N2 IN CO2 - V'ifyurIe'. Ixcess i-'jitrhalpy Data o.an it;ro.ert-Carbo)i Dbioxi.de,v nl, em (at )>0~C.

0 Exper/nento/ Dotoar 500psio, 40~ C - HE/X, ( -XNt ) -=333.909 -/40.093 390 (XN - 0. 5) +/8 1,6 68(XI -0.5)2 \\ o0-0.40% \ -- Predicted by B- W- R 380 0\ Lee 8 Mother 370 F-J T m 350- 1% X \ W 320 \ Figure. xcss I;thalp Data or N\itrogen-Carbon Dioxide 1 340- ( 33o0 —Sy stem at; 4o~C ajnd 500 psia, and Compariisons -with Data of leo awnd Mather and with B-W-R Equation of State.Predictions.

-9917 7. X10I2 x _ 0 Experimental Dta ot950psia, 40~C -h _H/ (/-XN ) = //47.29-/082.50 (x -05) 16 +/45.765(XN -0.5 ao-= /.29.% \1 \ - - Predicted by B-W-R 15 -\ 0 Lee a Mother wI 14 I NC K N! - _ K 13, 1%? L \ 10 X9_ o I0 0.2 0.3 0.4 0.5 0.6 0.7 XN, MOLE FR. N2 IN CO2 Figure 9. Excess Enthalpy Data on Nitrogen-Carbon Dioxide System at 40~C and 950 psia, and Comparisons with Data of Lee and Mather and with B-W —: ti.quation of State Predictions.

-i ( )()600 r 1' I' l' l' 0 Exper/mental Doto at 3/~C -L east Squares Fi ofDof a, 500 4/0% 400 \' 300t~ -/6?% ^^> —Q ^ 950ps/a \ 200 co II] 100 /0 % 500psi 0 0 0.2 0.4 0.6 0.8 1.0 XN, MOLE FR. N2 IN CO2 Figure 10. Excess'riLthalpy Data on Nitrogen-Carbon Dioxide System at 31~C.

-101440, I I I I o Exper/mentalData ot 500psio, 3/ ~C - HXN (/ -XN - 384.93/ -/55.828 470- (XN -0.5) +/85099 (XN -0 5) - = 0.45% -— Predicted by B-W-R 450 430 0 m 410- 2 390- 270 z -l 350 330 0.2 0.3 0.4 0.5 0.6 0.7 XN, MOLE FR. N2 IN CO2 Figure 11. Excess Enthalpy Data on N\itrogen-Caxbon Dioxide System at 31~C arnd 500 psia, and Comparisons with Bt-W-R Equation of State rTedictions.

-1(027 I I, I I I x 102 0 Exper/mento/ Dato at 950ps/o, 3/~C -— _H/XN (/-XN = 16/785-2023.85 26- (XN -0.5) 1+262396 (XN -0.5) 2 o=/.72% 24 *' —Predicted by B-W-R 22 \ o 20I II 18 - 12 0 -, MOLE.R N IN CO ><X 16 N X K 14 121 I 0.2 0.3 0.4 0.5 0.6 0.7 XN, MOLE. FR. N2 IN CO2 Figure 12. Excess Enthalpy Data on Witrogen-Carbon Dioxide System at 31~C and 950 psia, aid Comparisons with B-W-R Equation of State Predictions.

-103the equation 1 = X N(l-x)(an 5)+ + n(XN-0.5)2) (87) with the constants listed in Table XII. In the same two figures, the effect of the relative vicinity of the critical point of carbon dioxide (Tc = 31~C and Pc = 1071 psia) may be seen by examining the location and value of the maxima in the curves which represent the composition-smoothed results. Within experimental accuracy, the excess enthalpies at 500 psia (Pr = 0.47 of carbon dioxide) at both 40~C(Tr = 1.15) and 31~C(Tr = 1.0) reach a maximum value at the same mole fraction value of 0.443. The corresponding value of the peak at this composition increases from 84.5 Btu/mol to 97.3 Btu/ mol with the decrease in temperature. The deviation from the symmetrical parabola increases with increasing pressure and decreasing temperature. For the data at the higher pressure of 950 psia (Pr = 0.89) the location at which this peak occurs shifts from 0.370 mole fraction at 40~C to 0.340 at 310C. The value of the peak rises from 306.0 to 450.8 Btu/mol — a sharper increase than at 500 psia for the same temperature change. The results are presented in different but related plots in Figures 8, 9, 11 and 12. The abscissae in these plots are the same as - HE in the previously discussed ones but the ordinates are L (1-x). The curves in these figures are obtained from Equation (69) with the constants from Table XII. r HE 1 In plots of _XN (XN) against xN, the intercepts at N = 0 and x = 1 are the slopes of the curves of H versus xN at the same mole fractions. The values of the intercepts cannot be determined from the plots in Figures 8, 9, 11 and 12 because the curves are

-lo4not drawn to those limits of composition. However, the intercepts may be evaluated from Equation (69) by substituting these mole fraction values: HE bn cn (88) xN(-x) = an - + (88) at xN = O, and a a + n + n (89) 2 4 at N = 1. x(1-X) + The effect of the critical point of carbon dioxide may be seen in these figures as well. The regression line through the data points is skewed most for the conditions closest to the critical point of carbon dioxide. Nitrogen-Ethane System The methods used for the reduction of the data on the nitrogenethane system are identical with the ones outlined for the nitrogen-carbon dioxide system with the exception of the technique for correcting for impurities. Primary Corrections: The sources of data used for nitrogen are the same ones referred to earlier in the discussion of the nitrogen-carbon dioxide system. In the absence of experimental data at elevated pressures, ethane heat capacities used in correcting for non-isothermal operation are obtained from the Benedict-Webb-Rubin equation of state(2) with zero pressure heat capacity tabulations of Rossini et al.(41) The B-W-R constants used for the impure ethane are obtained using the mixing rules of Benedict et al.(14) on the constants listed in Table XLV in Appendix C. Adiabatic Joule-Thompson coefficients of Sage, Webster and Lacey 4; for

-105ethane axe combined with the heat capacity values according to Equation (11) to obtain isothermal Joule-Thompson coefficients for making the pressure drop correction. The pressure drop correction varies between 0.11 to 0.15 percent and the temperature difference correction ranges from 0.43 to 0.58 percent. (162) Tabulations of density by Tester( on ethane and by Sage (142) and Lacey on nitrogen-ethane mixtures are employed for the kinetic energy difference correction. This correction never exceeds 10-4 percent. The enthalpy change on mixing the impure nitrogen and ethane streams at calorimeter outlet conditions, AHo (obtained by applying corrections for pressure drop, temperature difference and kinetic energy difference to the power/flow ratio), is listed in the fourth column of Table XIII under the heading "Multicomponent System." Henceforth this enthalpy change will be referred to as the excess enthalpy of the multicomponent system signifying that no corrections have been made for the ethene, propene and propane in the ethane used in this research (which amount to about 0.8 mole percent —See Table IX). The enthalpy change on mixing pure nitrogen and pure ethane, termed the "Binary System," is obtained by applying impurity corrections to the excess enthalpies at calorimeter outlet conditions for the multicomponent system. The method employed in making impurity corrections has been described in the chapter entitled "Thermodynamic Relations." The equation for the impurity correction derived there is Fi[zAHo] FB AI crr = ] [Mo-HBo] + [ ABo'-HABM,o] Cr FAB AB FI + - [ HBM,o- ABM,o] (60) FAB

-106which assumes that the nitrogen is pure and corrections are made for the impurities in ethane only. In this equation, the flow rates and the enthalpy difference, AHo, are obtained experimentally but a prediction method is required to estimate the enthalpies of the various streams. The enthalpy departures, H - HO, may alao be used in place of the enthalpies (as explained in the chapter "Thermodynamic Relations") and these are obtained from the Benedict-Webb-Rubin equation of state(2) with the constants(l4) listed in Table XLV and with the mixing rules suggested by Benedict et al.(13) The last term is the one that contributes the most (about 60 percent) to the impurity correction, Icorr. The magnitude of this term increases with the increase in the fraction of impurities in ethane and with an increase in the difference between the enthalpy of the impure ethane, HMo, and the enthalpy of the impure nitrogen-ethane mixture, H * In this case the substantial fraction of the impurities and the proximity of the ethane to its two-phase region causes the impurity correction to range from 0.9 to 1.6 percent. This is reflected in the increased contribution of the primary corrections for the "Binary System" over those for the "Multicomponent System" given in column three of Table XIII. The excess enthalpies after primary corrections for the nitrogen-ethane mixtures are listed in the fourth column of the same table. The interpreted results with and without impurity corrections are presented for three reasons. First, because the interpreted results on the binary system are less accurate than those on the multicomponent system because of the estimated 30 percent uncertainty in the impurity correction introduced by the enthalpy prediction method (the accuracy of the results is discussed in Appendix A and summarized later in this chapter),

TABLE XIII EXCESS ENTHALPY DATA ON NITROGEN-ETHATNE SYSTEM Pow~er ( E - E,7 n0 ^el- -E _s~~~~~~~~~~~~H (-H-moothed)10 Mol Fr Fow Primary at Secondary H (cmoo ted )xl —-- Nitrogen (x7F) Corrections (TQP^) Corrections (Tn1Pn) — I Btuf/mol Percent Btu/mol Percent Btu/mol Percent Multicomponent System, Nominal Experimental Conditions: T, = 52.580C, Pn = 401 psia 0*767 90.4 -0.69 89.8 -0.02 89.8 0.03 0.576 133.7 -0.57 133.0 0.17 133.2 -0.10 0.423 146.4 -0.61 145.5 -0.05 145.4 0.11 H n,276 131.8 -0.56 131.0 -0.29 130.7 -0.04 Binary System, Nominal Experimental Conditions: Tn = 2.580C, Pn = 401 Olpsia 0.769 90.4 -2.33 88.2 -0.02 88.2 0.03 n.578 133.7 -1.93 131.0 0.17 131.2 -0.11 0.425 146.4 -1.73 143.5 -0.05 143.5 0.12 n.?77 131.8 -1.47 129.5 -0.28 129.2 -0.04

-108Second, this procedure demonstrates that corrections can be made for impurities in the feed stream on which enthalpy of mixing data is not available. Finally, using cheaper, less pure gas, results of diminished accuracy may be obtained with considerably lower operating costs. Secondary Corrections and Tabulated Results: For both the binary and the multicomponent systems, the values for the excess heat capacities and the excess Joule-Thomlpson coefficients are obtained from the B-W-R equation(12 13) with the constants listed in Table XLV. The uncertainty in these values are estimated to be + 30 percent. The variation in the calorimeter outlet pressure is ~ 0.5 psi and outlet temperature is ~ 0.006~C as may be seen in Table XXXVI, Appendix C. This variation is much smaller than for the data on the nitrogencarbon dioxide system. Hence, the maximum correction for pressure level is 0.28 percent and the correction for temperature level never exceeds 0.02 percent. The secondary corrections along with the normalized excess enthalpies, F, are listed in Table XIII. The latter values are smoothed with respect to composition by fitting the data to Equation (69). The regression coefficients as well as the average and standard deviation are listed in Table XIV. The deviation of each experimental point from the regression curve is listed in the last column of Table XIII. Graphical Results: The results are presented graphically in Figures 13 and 14 in plots similar to those employed for the nitrogen-carbon dioxide data. fri both'igures the excess enthalpies of the binary system as well as the multicomponent system are shown. The circles represent the data, after primary and secondary corrections, on the multicomponent system and the squares represent similarly treated data on the binary system. The curves

-109Data on Nitro en-Ethane Mixtures at 27.29 am,3238 C 0 Multicomponent System 150 L - Least Squares Fit of Data 5% Binary -p — Multicomponent System System 100.-J -50 0 0.2 0.4 0.6 0.8 1.0 XN, MOLE FR. N2 IN C2H6 Figure 13.,,xc'ess Enthalpy Data orl Nit;roge:i- i-Lhatle System.

-110Nitrogen-Ethane Mixtures Multicomponent System 0 Experimental Data at 401 psia, 32.38~C HE/X(I -X) =568.74/ - 32068 3 (X- 0.5) +276.033 (XN-0.5); - 0. 16 % - -Predicted by B-W-R. \T | Binary System o Experimental Data at 401 psia, 3238~C _J 700-HEXN(I - XN) =56f.293 -315.004(XN-0.5) O +269.254 (XN- 05)2; -= 0.17% x2 C -- Predicted by B-W-R. \,\ 600 z | / —Multicomponent System w /% -- 10^T Binary -. 500- System 0.20 0.30 0.40 0.50 0.60 070 0.80 XN, MOLE FR. N2 IN C2H6 Fi'.re 14. excess Enthalpy Data orn itroven -Ethjie'.rstem and Comparisons with B-W-R Equation of State Predictions.

-111(solid lines) in Figures 13 and 14 are calculated using Equations (87) and (69) respectively with the constants listed in Table XIV. Based on the critical point for ethane of 708 psia and 32.3~C, this data is at a reduced pressure of 0.57 and at a reduced temperature of unity. TABLE XIV REGRESSION COEFFICIENTS FOR SMOOTHING NITROGEN-ETHANE EXCESS ENTHALPIES VERSUS COMPOSITION Regression Percent Arithmetic System Coefficients Average Absolute Deviation from a an bn cn Experimental Points Percent Binary 568.741 -320.683 276.033 0.07 0.16 Multicomponent 561.293 -315.004 269.254 0.07 0.17 Nitrogen-Oxygen System This is the first system on which enthalpy of mixing measurements were made in this research. There is a greater uncertainty in the accuracy of these measurements than on those on the nitrogen-carbon dioxide and nitrogen ethane systems because the measured excess enthalpies of nitrogenoxygen mixtures are at least two orders of magnitude smaller than the excess enthalpies of the other two systems. However, the results are included because measurements revealed that unlike the other systems heat is evolved when the two gases are mixed, with a resultant increase in temperature of the exiting gas mixture over the temperature of the inlet gases to the calorimeter. Five measurements were made at the same value of composition, calorimeter outlet pressure and bath temperature of which two were made with and three were made without power input to the calorimeter. The calometric data are detailed in Table XXXVII in Appendix C.

-112Other differences exist between the measurements on this and the other systems. Improper positioning of a heater resulted in a temperature difference of about 0.01~C between the two inlet gases. Further, the pressure at the calorimeter outlet pressure tap was measured with a Heise bourdon tube gauge and not with the dead weight gauge. Calculation of the excess enthalpy requires values for the heat capacity and the isothermal Joule-Thompson coefficient of both nitrogen and oxygen. The heat capacities for both nitrogen and oxygen at 26~C are obtained by combining the data of Workman(3) on the ratio of heat capacity under pressure to the heat capacity at one atmosphere, (54) with the tabulated heat capacities at one atmosphere of Din() for nitrogen and Weber( for oxygen. The variation of heat capacity values with temperature calculated from Din's and Weber's tabulations of heat capacity are employed to correct the heat capacities to 25~C. The isothermal Joule-Thompson coefficient for nitrogen is obtained by combining Roebuck's (40) Joule-Thompson coefficient value with the he t capacity for nitrogen. For oxygen, the isothermal Joule-Thompson coefficient is determined from Equation (41), from tabulated values of the volume and the differentials (PP/6p)T and (aP/6T)p calculated by Weber(l80) from his own accurate PVT measurements. The values for the thermodynamic [)ro)pF rtli.V(: (let(ermine(d in this way are listed in Table XLIII in Appendix (1.'I'1e accuracies ol' the Cp and cp values are believed to be three percent and five percent respectively. Details of the reduction of the nitrogen-oxygen data are given in Table XLII and the results are summarized in Table XV. The mean value of the excess enthalpy based on the five measurements is -1.6 Btu/mole.

-113The accuracy of the experimental measurements is limited by the small temperature rise of 0.12~C across the calorimeter. Based on an uncertainty of 0.008~C, the accuracy of the temperature difference measurement is estimated to be seven percent. As discussed in Appendix A, the accuracy of the excess enthalpy data on the nitrogen-oxygen system is believed to be 10 percent. As described, two enthalpy of mixing measurements were made with power being supplied to the calorimeter. The heat capacities of the mixture calculated from the data on these runs are listed in the last column of Table XV. They are based on an average calorimeter outlet temperature of 25.1160 ~ 0.0030C and are assessed to be accurate to 23 and 77 percent for the low and high power input runs respectively (See Appendix A). TABLE XV EXCESS ENTHALPY DATA ON NITROGEN-OXYGEN SYSTEM Mole Power Measured Fraction Flow Temperature H Heat Capacity Nitrogen (W/F) Rise Bt /lb of Mixture Btu/lb OC Btu/lb OF Nominal Experimental Conditions: 25~C and 1001 psia 0.522 0.0 0.117 -0.0548 0.522 0.0 o.l9 -0.0554 0.522 0.0070 0.128 -0.0529 0.318 0.522 0.0214 0.159 -0.0532 0.277 0.522 0.0 o.113 -0.0530 Mean _ = -0.054 Btu/lb or -1.6 Btu/mol a = 2.2%

-114Linear interpolation with respect to composition between the heat capacities of nitrogen and oxygen in Table XLIII yields 0.262 Btu/lb~F. The discrepancy of 21 percent and 5.7 percent between this and the measured value of heat capacity is within the estimated experimental accuracy of the heat capacity measurement. Discussion of Results Part of the data that have been obtained on the nitrogen-carbon dioxide system are used to check on the performance of the calorimeter. The probable maximum inaccuracy of the results is summarized based on the error analysis of Appendix A. Comparisons are made with a prediction method and with the experimental results cf other investigators. Check on the Assumption of Adiabaticity In the mathematical development which utilizes the first law of thermodynamics in the chapter entitled "Thermodynamic Relations," it is assumed that the measurements are made under adiabatic conditions. Mathematically this is expressed by Equation (31) as Q = 0 (31) implying that there is zero heat transfer between the calorimeter and its surroundings. The check on this assumption of adiabaticity is based on a principle suggested by Montgomery and DeVries. They show that for measurements in a flow calorimeter, if the heat capacity, or as in this case the excess enthalpy, is independent of flow rate then the heat leak is negligible. Ten measurements were made as a function of flow rate at 40~C and 500 psia on the nitrogen-carbon dioxide system between 0.481 and 0.525

-115mole fraction nitrogen. The results are listed in Table XI and may be seen as the cluster of points at 0.50 mole fraction in Figures 7 and 8. After normalization to 0.50 mole fraction nitrogen, the excess enthalpy values are plotted as a function of reciprocal flow rate in Figure 15. The mean value of the ten points in Figure 15 is 83.48 Btu/mol and the standard deviation is 0.31 percent. The same data were fitted by a regression analysis to a linear equation: HE 83.74. 021 Btu (90) F mol with a standard deviation of 0.31 percent —which represents no improvement over the standard deviation of the ten points from the mean value. The effect of heat leak should vanish at infinite flow rate: at 1/F = 0 the intercept is 83.74 Btu/mol. The intercept differs from the mean value by 0.31 percent and this percent difference is the same as the experimental precision. Hence it seems reasonable to draw a horizontal line as shown in Figure 15 and assume that the heat leak, Q, is smaller then experimental uncertainty of these measurements. It is possible to obtain the minimum operating flow rate for a flow facility from this kind of flow rate dependency study. This minimum flow rate is chosen so that the heat leak does not affect the accuracy of the results and, simultaneously, the cost of operating the facility is minimized. For the present experiments, this flow rate independence study was only partially completed. The lowest flow rate that could be achieved on this facility was limited not by the heat leak but by a practical difficulty encountered with the equipment. At low flow rates, the response time of the system to changes in conditions decreased disproportionately with the decrease in flow rate. Consequently the economic benefit of operating at low flow rates was cancelled by the longer

0 Experimental Doto Points ot500ps/a, 400C Normolised I 84.0 to 0.50 Mole Froction N2 in CO2 *0.3per cent o 0 2 A5 Average 83.48 3 835 — D -0.3 per centf ~ M 0 w 83.0 II 0 5 10 15 I/F (LB/MIN)- I Figure 15. Excess Euthalpy Measurements on riitrogen-Carbo:- Dioxide System as a Function of Reciprocal Flow Rate.

-117operating times required to attain steady state conditions. Hence, the measurements of the excess enthalpy of nitrogen-carbon dioxide mixtures and nitrogen-ethane mixtures were performed at flow rates of about 0.1 lb/minute (1/F = 10). For the nitrogen-oxygen system, the mixture flow rate was about 0.3 lb/minute. Accuracy of the Results There are two factors which affect the accuracy of the experimental measurements. They are: 1. Inaccuracies in the instruments and the experimental techniques, and 2. Errors introduced by data interpretation. The four prime experimental measurements are pressure, temperature, electrical power input and flow rate. The techniques for measuring pressures, temperatures and electrical power are well established and their application to flow calorimetry have been discussed here and by previous investigators.(4571,11) The estimated accuracies of the pressure and temperature measurement have been described in the chapter entitled "Apparatus and Experiments" and are listed in Table XVI. The accuracy of the power and flow measurements are discussed in Appendix A. The estimated accuracy of the composition and power per unit flow depend on the latter two measurements and are given in Table XVI. The measurement of flow rate poses the greatest uncertainty. Hence a gas density analytical technique was used to check on the compositions calculated from the flow meter calibrations for the nitrogen-carbon dioxide system. The results of the comparison are given in Table XLIX in Appendix C. The accuracy of the composition calculated from a knowledge o' tLhe flow rates is is elev-i to e ().)002 -to 0.003 mole fraction whereas t.he iimiiit.i H'; ac(ur'acs(' eiO liIal-e(J to be 0. 0C)()) mle01. traction for the gas

TABLE XVI ESTIMATED LIMIT OF ACCURACY OF THE EXPERIMENTAL MEASUREMENTS Uncertainty In Power Primary Secondary System Pressure Temperature Composition Flow Corrections Corrections psia ~C mol fr N2 Percent Percent Percent Nitrogen-Carbon 0.3 0.04 0.002-0.003 0,7 0.1-0.3 0.1-1,1 Nitrogen-Carbon 0.3 0.04I~ 0.002-0.003 0.7 0.1-0O3 0.1-1.1 dioxide Nitrogen-Ethane 0.3 0.04 0.003 0.8-1.1 0.2 0.3-0.4 (Multicomponent) Nitrogen-Ethane 0.3 0.04 0.003 0.8-1.1 0.6-0.7 0.3-0.4 (Binary) N.itrogen-Oxygen 1 0.04 0.007 1.5 10

-119density technique. The estimation of the accuracy of both methods'or compo),r::;itionr meaLsuremenrts are, di-c'ussed in detail in Appendix A. There i s good agreement between the two tabulated sets of compositions in Table XLIX within the combined accuracy of the two sets of measurements. There are two sources from which errors may stem while applying primary and secondary corrections during data interpretation. One is the inaccuracies in the experimental measurements of pressure, pressure drop, temperature and temperature difference in the calorimeter. The other is the inaccuracies in the thermodynamic properties used in making corrections. These have been estimated (neglecting the effect of the uncertainty in composition) and the resultant range of errors due to primary and secondary corrections given in Table XXI and XXII in Appendix A and are summarized in Table XVI. The accuracy of the enthalpy of mixing data on the nitrogenoxygen system is believed to be ten percent. For the other two systems, if the errors in the primary and secondary corrections are added to the errors in the power/flow ratio (See Table XVI) then the range of accuracies of the excess enthalpies at outlet conditions,', and the normalized excess enthalpies,, are 1. For the nitrogen-carbon dioxide system: 0.8 to 1.0 percent for HE and 0.9 to 2.1 percent for HE 2. For the nitrogen-ethane system: 1.0 to 1.3 percent for _ and 1.3 to 1.7 percent for HE of the multicomponent system, and 1.4 to -n 1.8 percent for H and 1.7 to 2.2 percent for H of the binary system. There are two other factors which affect the accuracy of the results. The first one is the uncertainty introduced by heat leak to the surroundings from the calorimeter. An upper bound has been placed on

-120this quantity by the flow rate independence check described in the previous section. The other factor is inhomogenities in the gas mixture at the calorimeter outlet due to inadequate mixing in the calorimeter. The reversal of flow and especially the sparging of the gas mixture from one baffle to the other along with additional time for equilibration in the helical tube leading to the calorimeter outlet is designed to eliminate composition gradients in the outlet mixture. The flow rate independence study furnishes some proof since the residence time varies from two to six seconds over the range of flow rates illustrated in Figure 15. It is felt that in the future an independent test should be made for further confirmation. It is suggested that a coiled length of tubing be used to extend the flow path of the gas before it leaves the vacuum chamber. If the gas temperature is the same at the end of this coil as the gas temperature at the outlet measuring station then the mixture exiting the mixing chamber is homogeneous. Ultimately, however, there is only one method by which the accuracy of these measurements may be checked and that is to compare this data with the data obtained independently in another laboratory. It would be preferable if a different method is used —for example the closedsystem technique used in measuring excess enthalpies of liquids. Comparisons There is no data available in the literature on the nitrogenethane system. The data on the nitrogen-oxygen system may be compared with the measurements of Knoester et al,(8) on a similar system. They report the excess enthalpy of a mixture containing 52 mole percent argon in nitrogen to be -2 Btu/mol at 1320 psia and 20~C. This suggests that the excess enthalpy of the nitrogen-oxygen system measured in this research is of the correct sign and magnitude.

-121For the data on nitrogen-carbon dioxide mixtures, a more accurate comparison can be made with the data of Lee and Mather(9) at 40~C. The excess enthalpy values, which they estimate to be better than four percent accurate, are plotted in Figures 8 and 9. As described in an earlier chapter entitled "Experience of Previous Investigators" these data were taken under relatively unsteady state conditions and smoothed versus pressure and composition at a given temperature. The values plotted as squares in Figures 8 and 9 are their reported values and were not interpolated by this author. Based on the interpolation technique for composition, it is felt that errors due to it are least at 0.5 mole fraction where the excess enthalpy does not vary excessively with composition. Further, since the excess isothermal Joule-Thompson coefficient is smaller at 500 psia than at 950 psia, the errors from pressure smoothing should be correspondingly lesser at the lower pressure. As anticipated, the agreement between the two sets of data is better at 500 psia than at 950 psia and is best at 0.50 mole fraction nitrogen at both pressures. Comparisons are also made with excess enthalpies calculated by the original Benedict-Webb-Rubin equation of state using various sets of constants for the nitrogen-carbon dioxide system: For nitrogen the con(27) (160) stants of Crain and Sonntag, Stotler and Benedict and Bloomer (19) i 37) and Rao;(19) for carbon dioxide the constants of Eakin and Ellington(37) (29) and Cullen and Kobe. The mixing rules used are those suggested by Benedict et al.(13) Various combinations of the constants predicted approximately similar values oi' the excess enthalpy. However, the con(19) (29) stanlts of Bloomer and Rao f'or nitrogen, and Cullen and Kobe for carbon dioxide (See Table XLV) give values that are closestto the experimental data reported here. The dotted lines in Figures 8, 9, 11 and 12

-122represent calculations using these constants. The constants used for predicting the excess enthalpies of both the binary and the multicomponent nitrogen-ethane system are those of Bloomer and Rao(19) for nitrogen and Benedict et al.(15) for ethane (See Table XLV).

RECOMMENDATIONS FOR IMPROVEMENT OF EXPERIMENTAL TECHNIQUES IN SUBSEQUENT STUDIES 1. It is felt that flow rates should be reduced by an order of magnitude in order to reduce operating costs. Flow meters suitable for use at low flow rates have already been designed and built. However, before incorporating them in the facility, it will be necessary to make improvements in the system to reduce the time required to achieve steady state conditions. It is believed that the four suggestions that follow this one will remedy the present situation. 2. The preconditioning of the gases before they enter constant-temperature baths or before they are throttled should be carried out in coils immersed in controlled temperature baths rather than with the present arrangement of wrapping electrical heating tapes around the tubes that convey the gas. 3. The valves and pressure regulators used in controlling flows should be placed in a heated box whose temperature is thermostatically controlled. 4. Automatic control on the D.C. power supply which provides the electrical energy input to the calorimeter will reduce the time required to achieve isothermal conditions in the calorimeter and will also assist in reducing the magnitude of the correction for temperature differences across the calorimeter. 5. The accuracy and speed of the measurement of pressure level in and pressure drop across the calorimeter should be improved by using null and differential transducers, respectively. 6. Bath temperatures should be measured with a more accurate device such as a platinum resistance or a quartz crystal thermometer. -123

-1247. Tests should be performed to confirm that the mixture exiting the calorimeter is of uniform composition.. A data interpretation technique should be developed to replace the secondary corrections which are used tQ normalize the data. It is suggested that a numerical method be used which relies on the experimental measurements of this very research and does not need an enthalpy prediction technique to predict excess properties. This will necessitate taking a larger volume of data over a finer grid of pressures and temperatures but would eliminate the inaccuracies introduced by the predicted excess properties.

SUMMARY AND CONCLUSIONS 1. A flow calorimetric facility was designed and built for the measurement of the enthalpy of mixing of binary gaseous mixtures at elevated pressures. 2. Data was obtained on three systems: (a) The nitrogen-carbon dioxide system at 31~C, 500 and 950 psia, and at 40~C at the same pressures at a minimum of four compositions. (b) The nitrogen-ethane system at 32.38~C and 401 psia at four compositions. (c) The nitrogen-oxygen system at 250C and 1001 psia at one composition. The systems investigated are of both industrial and theoretical importance: Mixtures of nitrogen with oxygen and carbon dioxide can be used to evaluate engine and fuel performance of combustion engines; nitrogen, ethane and carbon dioxide are constituents of natural gas. The data on the nitrogen-carbon dioxide system at 31~C and on the nitrogen-ethane system at 32.38~C represent the first direct calorimetric data obtained at a reduced temperature of unity of the heavy component in the mixtures. 35. Ten repetitive measurements on the nitrogen-carbon dioxide system at 40~C, 500 psia and 0.5 mole fraction nitrogen were shown to be independent of flow rate indicating that the heat leak was less than the experimental precision (0..3 percent). 4. The accuracy of the data is believed to be between 0.8 and 2.1 percent for the data on mixtures of nitrogen with ethane and carbon dioxide and ten percent for the data on nitrogen-oxygen mixtures. -125

-1265. It was concluded that before obtaining further data on this facility, the operating flow rates should be reduced by an order of magnitude. However, modifications should be made to improve the time required to achieve steady state conditions before low flow rates are used.

APPENDIX A ERROR ANALYSIS The accuracy of data of the kind obtained in this research is difficult to evaluate. However, an estimate can be made of the maximum errors caused by the measuring techniques and the data interpretation. To perform a detailed error analysis, it is necessary to assess the uncertainties in the instruments as well as the inaccuracies in data obtained from the literature. The latter is much more difficult than the former, hence this error analysis is based largely on instrument error with the inaccuracies in the data being accounted for wherever possible. Compounding of Errors Various techniques for compounding errors have been discussed (45) (71) (98) by Faulkner,^ Jones, and Manker for heat capacity measurements with a flow calorimetric method very similar to the present one. If a dependent variable Z is related to a number of independent variables (Zl, Z2,... Zn) by the equation Z W Z(zl, z2,... Zn) (91) (118) then the absolute error e(Z) in Z is given by e(z) =E i Q i e(zi)| (92) ii ii=l Zj~i where e(zi) is the absolute error in the variable zi. Dividing through by Z, the fractional error is obtained: z 1 _ e(zi) l (93) z i=l Z - i.Zji In this analysis, the errors are assumed to be random errors. This method of compounding errors does not allow for the subtraction of -1' 7

-128errors of opposite sign alnd it estimates Uhe ]imit of accuracy of the experimental results. Power Input Measurement The scheme employed in supplying electrical energy input to the calorimeter has been described earlier and the equation for calculating the power input, W, has already been derived as - /Rg+R +R V. ^ w = Se Ve - ) (74) \Re i Re/ Ve Vi The quantity R is much smaller than - and R is much larger than Re, hence the purposes of error analysis, this equation is approximated as Rs W = R- ViVe (94) ReRi Performing the manipulation described in Equation (93) on the last equation yields e(W) e(Rs) e(Vi) e(V) e(Re) e(Ri) W) - - + + + + (95) W Rs Vi Ve Re Ri The estimated maximum percent errors in the independent variables are listed in Table XVII. Compounding the errors as indicated in the last equation and adding the uncertainty in the power supply regulation and standard cell voltage yields an estimated accuracy of 0.1 percent. Flow Rate Measurement The measurement of the flow rate of the two gases to the calorimeter involves three steps. The first one is the volume determination of the calibration tank. The next is the calibration of the flow meters and the final step is calculating the flow rate of each gas from the correlation of the calibration data and the measurements on the flow meters.

-129TABLE XVII ERRORS IN DETERMINATION OF POWER INPUT TO CALORIMETER Percent Variable Instrument Reading Error Error Power Supply Kepco Power Supply 0.01 Resistance Standard Resistors Ri=l ohm 0.01 Re=10 ohms 0.01 RS=10,000 ohms 0.01 Standard Leeds and Northrup 0.01 Cell #7309 Calorimeter K-3 Potentiometer 0.022 5 micro 0.023 Heater and Resistor, Re volts volts Voltage, Ve Calorimeter K-3 Potentiometer. 16 36 micro 0.023 Heater and Resistor, Ri volts volts Current, Vi Measurement of Volume of Calibration Tank For purposes of this analysis, the relation used to determine the volume of the calibration tank, Vct, may be approximated by the ideal gas law. The experimental measurements along with estimated errors are listed in Table XVIII. Excluding uncertainties in the second virial coefficient of nitrogen the errors in the individual measurements sum to 0.27 percent. At the low final pressure in the calibratioll talk ()15 inches Hg), it is unlikely that errors in the reliable volumetric data of Otto( will appreciably affect the accuracy of the results. A check on the present measurements is the volume measurement on the same tank performed by Mage.(9) He determined the volume to be 6.416 - 0.002 ft3 by weighing the amount of water required to fill the tank at a measured temperature. Adding 0.0041 ft3 for the volume of the

-130TABLE XVIII ERRORS IN VOLUME DETERMINATION OF CALIBRATION TANK Percent Measurement Instrument Reading Error Error Pressure, PCt 36-inch King 15 inches Hg 0.05 inches 0.16* Manometer Barometer 30 inches Hg 0.02 inches Vacuum McLeod Gauge 20 microns 5 microns 0.0007* Hg Hg Temperature, Thermometer 20 ~C 0.3~.043 Tct Thermocouples 0.10~ Mass, met Balance 320g 0.2g 0.07 Percent error based on 45 inches Hg final pressure in tank. manometer well and the gas lines outside the tank to the calibration tank volume measured by Mage yields 6.420 ft3. The excellence of the agreement of this value with the mean value of Vct = 6.422 ft3 given in Table XXIII may be fortuitous. However, it provides some justification for assuming the probable error in the measurement of the volume of the calibration tank to be ~ 0.2 percent. Flow Meter Calibration Four quantities are required for the correlation of the results of flow meter calibrations using Equation (86) given earlier. They are: the pressure drop across the flow meters, APF, the flow rate, F, obtained from measurements on the calibration tank, and the density, PF and viscosity, TIF, of the gas in the flow meters. For purposes of this error analysis, the quantity.F is equated to Y

-131Y F (96) Also, for this analysis the relation for determining the mass of gas in the calibration tank is approximated by the ideal gas law. The flow rate may then be calculated from the approximate equation: 1 (Pctf-Pcti)Vct F = -............ (97) G R Tct where 9 is the time period of gas collection, Pcti is the pressure in the initially evacuated tank and Pctf is the final pressure in the filled tank. Substituting for the flow rate F from the last equation into Equation (96) yields: = 1 1 (Pctfcti)ct (98 PLPF AP R Tct Using the method of analysis described by Equation (93), the fractional error in Y is given by e(Y) 1 e(PF) 1 e(1PF ) e () e(Pctf) __ ~+ e -( a _ (Ptf) ++ Y 2 PF 2 APF (Pctf-Pcti) +e(Pcti) e(Vct) e(Tct) (99) + —.... —..-.. + --... (99) (Pctf-Pcti) Vct Tct noting that the error in the density has been replaced by the error in the measurement of pressure in the flow meter. The estimated error in the various measurements are listed in Table XIX. The Heise pressure gauges are calibrated against the dead weight gauge before and after every calibration or enthalpy of mixing run. The 1 psi variation of Table XIX includes this deviation as well as the uncertainty of' ~ 0.02 inches Hag in the barometric pressure measurement. The fluctuations of pressure and pressure drop during a calibration run are less than the uncertainties listed in Table XIX. The measurements

-132TABLE XIX ERRORS IN FLOW METER CALIBRATION MEASUREMENTS Percent Errors Measurement Instrument Reading Error Low High Flows Flows Measurements on Flow Meters Pressure, PF Heise Gauge 1100 psia 1 psi 0.09 0.09 Pressure Drop, Manometer and 15 to 95 cm 0.04 cm 0.26 0.04 APF Cathetometer Flow Meter Bath Mercury-in-Glass 45~C 0.03~C Temperature Thermometer Flow Rate Determination Time of flow Timer 1000 to 400 sec 0.1 sec 0.01 0.03 through Solenoid Valve, 9 Pressure in Manometer 28 in di butyl 0.05 in dbp Calibration phthalate (sp. Tank, Ptf gr. 1.04) 007* 0.07 Barometer 30 in Hg 0.02 in Hg Pressure in Vacuum 20 mm Hg 0.5 mm Hg 0.07* 0.07* Evacuated Calibra- Manometer tion Tank, Pcti Temperature in Thermometer 20~C 0.050C 0,4 0. Calibration Tank, Thermocouples 0.10C Tct *Percent error based on approximately 30 inches Hg final pressure in tank.

-133on the calibration tank for determination of flow rate are similar to those listed in Table XVIII with two exceptions: the vacuum in the tank is measured with a vacuum manometer and a timer is used to measure the time interval of gas collection, G. The volume of the calibration tank is taken as fixed for all the calibration runs. Therefore,it affects the accuracy but not the precision of the measurements. Neglecting the error in the volume of the calibration tank and substituting the percent errors from Table XIX in the last equation yields an estimated precision for the experimental measurements of 0.28 to 0.537 percent between high and low flow rates, respectively. Indeterminacies in the viscosity (IF) and density (PF) of the gas in the flow meters have so far been neglected. Since the flow meters have been calibrated at the conditions at which they will be used in the calorimetric measurements, errors in the absolute values of these quantities will not affect the accuracy of the results appreciably. The effect of pressure on the density of di butyl phthalate is also eliminated by replicating conditions in this way. Errors in the second virial coefficient data on nitrogen,(126) carbon dioxide(13) and ethane( 16) do not appreciably alter the precision or accuracy of the results because the data is believed to be reliable and because at the approximately atmospheric pressure in the calibration tank there is only a small deviation from ideal gas behavior. There are two more factors which can affect the precision of the flow calibration results. The first represents deviations from the friction factor relation, Equation (75), chosen to correlate the data. The second is drifts in the true calibration line with time which has (48,101) The latter effect is been experienced by other investigators. The latter effect is

-134minimized by repeating calibration runs over the period of time that the enthalpy of mixing runs are performed. In the case of the carbon dioxide flow meter, however, it is believed that the true calibration line drifted upwards. The combined affect of all the factors on the precision of the flow rate is reflected in the standard deviation from the regression line. For the nitrogen and carbon dioxide flow meters this standard deviation is 0.18 and 0.25 percent respectively (See Tables XXIV, XXV and Figures 16, 17 in Appendix B). This is less than the estimated upper limit of errors in the experimental measurements hence the maximum precision of these calibrations is taken to be 0.28 to 0.57 percent for the nitrogen-carbon dioxide system. Four ethane flow meter calibration points give a standard deviation of 0.65 percent (See Table XXVI and Figure 18 in Appendix B). This large value is due to one calibration point which deviates by 0.68 percent from the regression line. This point was not repeated because of an insufficient supply of ethane. Hence the precision of the ethane flow meter calibrations is taken as 0.65 percent. For the nitrogen-oxygen system it is felt that due to the limited number of calibration points (See Table XXVII in Appendix B) a reasonable estimate of the precision is one percent for each gas. The accuracy of the flow rate measurements depends not only on the flow meter calibrations but on the accuracy of the calibration tank volume determination. Combining the estimated 0.2 percent error in the latter with the error in the flow meter calibrations yields: 1. Nitrogen-carbon dioxide system: The accuracy of the flow meter calibrations for each gas should be 0.48 to 0.57 percent.

-1352. Nitrogen-ethane system: The accuracy of the nitrogen flow meter calibrations is 0.48 to 0.57 percent and the corresponding value for ethane is 0.85 percent. 3. Nitrogen-oxygen system: The accuracy of each flow meter calibration is 1.2 percent. Calculation of Flow Rate The error in the flow rate calculation is determined by compounding the errors in the pressure and pressure drop measurements on the flow meter with the estimated errors in the flow meter calibrations. This error is obtained from the equation e(F) e(Y) 1 e(PF) 1 e(PF) F Y 2 APF 2 PF For the nitrogen and carbon dioxide flow meters, the error at low flow rates is 0.75 percent and at high flow rates is 0.55 percent. Similar calculations on the ethane flow meters which operated at 500 psia yield estimates of 0.97 to 1.1 percent which may be rounded off to one percent. For the nitrogen-oxygen system the pressure drop in each of the flow meters was about 20 cm Hg during enthalpy of mixing determinations and the resultant accuracy is estimated as 1.4 percent for each gas flow rate. Gas Composition The error in the composition determination due to inaccuracies in the flow rate calculation and the error in the gas density technique are estimated. Coxmposi tionl from "l'low Rates The mass fraction of componlent A, wA, is calculated from the mass flow rates of the two constituents A and B of the mixture:

-136wA = (101) FA+FB Performing the manipulations in Equation (92), the absolute error in the mass fraction is expressed as e ( )B e(FA)1 e(wA) = A(l-A) [ + FA (102) For the nitrogen-carbon dioxide qyptem the mass fraction of nitrogen varies between 0.23 and 0.75. When combined with the accuracy of the flow rate determinations for the two gases, the error for nitrogenlean mixtures is 0.0023 mass fraction and for nitrogen-rich mixtures is *.0026 mass fraction. The corresponding absolute error in the mole fraction is 0.003 to 0.002 mole fraction, respectively. In the case of the nitrogen-ethane system, the error is 0.005 mass or mole fraction. The uncertainty in the composition of the nitrogen-oxygen system is 0.007 mass or mole fraction. Composition from Gas Density Analysis The error in the composition is obtained by compounding the error in the initial step of can volume determination with the error in the final step of gas density measurements. The estimated instrument errors are listed in Table XX. The mathematical relation for calculating the volume of the aerosol can may be simplified to the ideal gas relation. The overall maximum error of 0.14 percent is obtained as the sum of the errors in the individual measurements listed in Table XX. Gas density measurements yield the molecular weight, M, of the unknown mixture m RTC M ac ac(105) PacVac

-137TABLE XX ERRORS IN GAS DENSITY ANALYSIS MEASUREMENTS Percent Measurement Instrument Reading Error Error Determination of Can Volume Mass, mac Balance 1.8g 1 mg 0.056 Pressure, Pac Manometer 100 in Hg 0.05 in 0.054 Barometer 30 in Hg 0.02 in Temperature, Tac Thermometer 250C 0.1 0.033 Gas Density Determination Mass, mac Balance 2.5g* 1 mg 0.4 Pressure, Pac Manometer 100 in Hg.05 0.054 Barometer 30 in Hg 0.02 Temperature, Tac Thermometer 25~C 0.1 0.033 *For equimolar mixture of nitrogen and carbon dioxide. again assuming ideal gas behavior for the purpose of error analysis. The fractional error in the molecular weight e(M)/M is the sum of the errors in the individual measurements for gas density determinations given in Table XX combined with the uncertainty in the volume of the can. Evaluated thus, the estimated accuracy is 0.27 percent. The composition of the gas mixture is dependent on its molecular weight XN = (M-MC2)/(MN-MC02) (104) where MN and MCO are molecular weights of nitrogen and carbon dioxide respectively. The absolute error in composition measurement obtained by performing the operations in Equation (92) on the last equation is

-138e(x N) (105) For an average molecular weight of M = 36 the maximum error J:ir composition is ().006 mole fraction. The second virial coefficients used in these calculations are given in Table XLVIII in Appendix C. It is difficult to estimate the error in these low pressure volumetric properties. However, it seems likely that the error introduced is small compared to the uncertainties in the experimental measurements. Excess Enthalpy Determinations The errors introduced by the data reduction procedure are evaluated for the nitrogen-carbon dioxide and the nitrogen-ethane systems. The nitrogen-oxygen system is treated separately. Power per Unit Flow The power/flow ratio is determined from the equation (W/F) = wF (106) Using the previous analysis, the fractional error in the power/ flow ratio is e(W/F) e(W) FA ) e(FA) (FB e(FB), — JA+- + + (107) (W/F) W FA+FB FA FA+FB FB where the terms with the ratio of flow rates represent the mass fractions of the two components. For the nitrogen-carbon dioxide system, the mass fraction of nitrogen varies between 0.23 and 0.73. The corresponding error in power/flow ratio should then be 0.71 to 0.72 percent. The range of error for nitrogen-ethane mixtures is estimated to be 1.1 to 30.75 percent for

-139nitrogen-lean and nitrogen-rich mixtures respectively. For an estimated error of 0.1 percent in the power input for the nitrogen-oxygen system, the inaccuracy in the power/flow ratio is 1.5 percent. Primary Corrections The estimated errors due to primary corrections for the data on nitrogen-carbon dioxide mixtures at 400C and 500 psia are detailed in Table XXI(a). All the percent errors listed are based on the power/flow ratio, (W/F). The estimated range of error of 0.19 to 0.27 percent are the sum of the columns of minimum and maximum errors, respectively. The estimated errors in the primary corrections at the other experimental conditions, are summarized in Table XXI(b). The error in the individual variables, e(z), is assumed to be identical with the estimates in Table XXI(a) except for a 15 percent uncertainty in the isothermal Joule-Thompson coefficient at 31~C and 950 psia. Based on the uncertainties in the individual variables, e(z), in Table XXI(b), the estimated errors in the primary corrections for the multicomponent nitrogen-ethane system are 0.22 to 0.23 percent. The additional inaccuracy in the binary nitrogen-ethane system due to an estimated 30 percent uncertainty in the impurity correction causes this error estimate to rise to 0.55-0.71 percent. Secondary Corrections The errors due to the variables that affect the secondary corrections for the nitrogen-carbon dioxide system are listed in Table XXII in a manner similar to the previous Table XXI for primary corrections. The percent errors in this table are based on the excess enthalpy at outlet conditions, HE. For the data at 500 psia, both at 51~C and 40~C, the uncertainty in the excess propertics, cpE and CE, is believed to P

TABLE XXI ESTIMATED ERRORS INTRODUCED BY PRIMARY CORRECTIONS FOR NITROGEN-CARBON DIOXIDE MIXTURES (a) For measurements at 400C and 500 psia Percent Estimate of Error in H Correction Correction to Error in Percent for Power/Flow Ratio Variable Variable, Fractional Error min max z e(z) Contribution min max Pressure 0.05 0.22 cp 5% AP e(p)/(W/F) 0.002 0.011 Drop AP 1 cm di butyl e(AP)cp/(W/F) 0.025 0.025 phthalate* Temperature 0.04 1.20 Cp 5% AT e(Cp)/(W/F) 0.002 O.OO Difference AT D.006~C e(AT)Cp/(W/F) O.149 0.149 Impurities 0.50 0.58 Composition 5% e(AIcorr)/(W/F) 0.0215 0.09 Range of Errors due to Primary Correction: 0.19% 0.27% (sum of minimum and maximum errors) (b) For measurements at other conditions Experimental Conditions Percent Error in E Tn Pn min max 0C psia 40 950 0.12 0.19 31 500 0.26 0.27 31 950 0.13 0.19 *1 cm di butyl phthalate = 0.015 psi.

TABLE XXII ESTIMATED ERRORS INTRODUCED BY SECOINDARY CORRECTIONS FOR NITROGEN-CARBON DIOXIDE MIXTURES (a) For measurements at 400C and 500 psia Error in H Correction Percent Correction Variable Estimate of Percent for of H z Error in Fractional Error min max Variable z Contribution min max e(z) Pressure 0.01 0.58 cpE 10% e(cpE)AP / 0.001 0.058 Level AP0 0.5 psi pEe(AP,)/ 0.071 0.071 Temperature 0.00 0.07 CE % e(CE)ATO/E 0.000 0.007 PP Ho Level AT0 0.040C Cpe(AT0)/I 0.072 0.072 Range of Errors due to Secondary Corrections: 0.14 0.21 (sum of minimum and maximum errors) (b) For measurements at other conditions Experimental Conditions Percent Error in E Tn P 0C psia min max 40 950 0.54 0.72 51 500 0.25 0.3355 51 950 0.65 1.1

-ll-2be 10 percent. For the remainder of the data and also for the nitrogenethane system the errors in the excess properties are estimated to be 30 percent. The range of error is estimated to be 0.26 to 0.36 percent for both the binary and the multicomponent nitrogen-ethane data. Nitrogen-Oxygen System The maximum possible error in the measurement of the temperature difference between the inlet oxygen and outlet mixture is 0.006~C (See chapter entitled "Apparatus and Experiments"). The error in the temperature difference between the inlet gases, nitrogen and oxygen, is 0.00o4C as the 0.0020C error in the bath temperature control can be neglected. Hence the uncertainty in the temperature difference between inlet nitrogen and outlet mixture is 0.010~C. The Average uncertainty for the equimolar mixture is + 0.008~C which corresponds to a 6.9 percent error. Compounded with a three percent uncertainty in the heat capacity values, the estimated uncertainty in the excess enthalpy measurement is about 10 percent. The accuracy of the heat capacity values is also limited by the ~ 0.0030C uncertainty in the mixture outlet temperature and the + 0.006oc uncertainty in the temperature difference measurement. Compounded with the 1.5 percent inaccuracy in the power/flow ratio, the uncertainty for the measurement at the low power input is estimated at 77 percent and at 23 percent. The error due to heat leakage in the calorimeter is estimated to be less than the experimental uncertainties for both the excess enthalpy and the heat capacity measurements.

APPENDIX B CALIBRATIONS TABLE XXIII RESULTS OF VOLUME DETERMINATIONS ON CALIBRATION TANK Determination Measured Percent Deviation Number Volume from Average ft3 Volume 1 6.412 -o. l6% 2 6.436 0.22% 3 6.429 0.11% 4 6.411 -0.17% Average Volume = 6.422 ft3 = 0.20% -143

-144TABLE XXIV DATA OF CALIBRATIONS FOR NITROGIEN FLOW METER.. -....... -lina,, |... - x L0) D)aL 10.8581 o.47348 Oct 12, 1969 11.1328 0.48046 Feb 22, 1969 11.4457 0.49192 Jan 8, 1970 11.6912 0.49946 Feb 23, 1969 11.7095 0.49881 Apr 10, 1969 11.7183 0.50144 Nov 16, 1969 11.9434 0.50709 Mar 28, 1970 12.3812 0.52123 Feb 25, 1969 12.7131 0.53304 Feb 25, 1969 12.9873 0.54245 Sep 8, 1969 FN. = 0.118757 x 10 + 0.525670 x 10 (nL P F ) Averge Deviation; = 8 Average Deviation = 0.14% a = O.18%

0.54 - Nitrogen Flow Meter Calibrations t 0.52 F APF~ A 1% 0.50 T 0.48 0.46 x 10Y2 10.6 11.0 11.4 11.8 12.2 12.5 13.0 fO PF -F in 2 Figure lo 1Fow Meter Calibrations for K'i-trogen.

-111 6TABLE XXV DATA OF CALIBRATIONS FOR CARBON DIOXIDE FLOW METER ln A7 x 102 Date 11.9286 0.51121 Oct 13, 1969 12.0813 0.51833 Feb 14, 1969 12.4421 0.52793 Nov 27, 1969 12.4434 0.53062 Feb 15, 1969 12.4528 0.52853 Dec 10, 1969 12.4982 0.53019 Jan 7, 1970 12.5352 0.53106 Apr 5, 1969 13.0713 0.54743 Feb 16, 1969 13.5173 0.56004 Apr 4, 1969 13.5313 0.55767 Jan 7, 1970 13.8371 0.56796 Feb 17, 1969 135.9072 0.56901 Sep 8, 1969 FC02 -2 P /-3pFi FC;2 = 0.174145 x 10 + 0.284626 x 10-3 (in Pn Average Deviation = 0.17% a = 0.25%

0.58 Carbon Dioxide Flow Meter Calibrations F PF-F 0.54 1 t 0.52 0.50 x 102 _________ I__ 11.8 12.2 12.6 13.0 13.4 13.8 PFAPF __ Fur17 2 Figure 17. ow Meter Calibrations for Carbon Dioxide.F Fiot-re 17. Flow Me er Calibratiorns for Carbon Dioxide.

-1)18-'IPAlILE XXVI DATA OF CALIBRATIONS FOR ETHANE FLOW METER r<Ap1 F -2 lnK j x 10 x2 Date 12.1287 0.51777 Mar 18, 1970 13.1561 O.55060 Mar 23, 1970 13.6413 0.56044 Mar 24, 1970 13.8746 0.56342 Mar 19, 1970 F. F; = 0.194744 x 10- + 0.267658 x 1-3 In Average Deviation = 0.39% a = 0.63%

0.58 I 1 1 I 1 Ethane Flow Meter Calibrations 0.56 F -L o F/APF 0.54 ~ ~ 0.52 0.50 x 10'2. I 11.8 12.2 12.6 13.0 13.4 13.8 t PF APF ie1n f 2 igure 13. -Flow Meter Calibrations for Et-hane.

-150T'ABLE XXVII DATA OF CALIBRATIONS FOR NITROGEN AND OXYGEN FLOW METERS USED IN MEASUREMENTS ON NITROGEN-OXYGEN SYSTEM Gas In S —- x 10-1 Date Nitrogen 11.4665 0.20152 May 22, 1968 12.3205 0.20676 May 21, 1968 Oxygen 11. 3686 0.20354 May 24, 1968 12.2762 0.20838 May 24, 1968 Nitrogen: N = 0.131085 x 101 + 0.614258 x 10 -3 (In <PF P APF i JF Oxygen: =0.14300 x 101 + 0.532507 x 10 n ^P PaF v 12j

-151TABLE XXVIII CALIBRATION OF DEAD WEIGHT GAUGE Type: Mansfield and Green WG-13Q Serial No.: 1872 Calibrated by: Mansfield and Green Nominal Pressure True Pressure Difference Percent psi psi psi Deviation 200 199.978 -0.022 -0.011 400 399.978 -0.022 -0.006 600 600.004 +0.o44 +0.007 800 800.044 +0.o44 +0.o006 1000 1000.o04 +.4 +0044 +0.4 1200 1200.044 +0.o44 +0.004 1400 1400.o88 +0.088 +0.003

-152TABLE XXIX CALIBRATION OF MERCURY BAROMETER Measured Pressure* True Pressure** Difference inches Hg inches Hg inches Hg 29.24 29.192 -0.048 29.23 29.195 -0.035 29.24 29.197 -0.043 29.24 29.194 -0.046 29.23 29.194 -0.036 29.24 29.192 -0.048 29.24 29.191 -0.049 29.30 29.263 -0.037 29.30 29.267 -0.033 29.31 29.262 -0.048 29.31 29.253 -0.052 29.31 29.2c62 -0.048 Zero Error = -0.04 + 0.006 inches Hg *Both the measured and the true atmospheric pressure noted here have been corrected for mercury and scale expansion. **True pressure is read on a calibrated mercury barometer manufactured by H. J. Green Company, New York, belonging to the Meteorology and Oceanography Department, University of Michigan.

-153TABLE XXX CALIBRATION OF MERCURY-IN-GLASS THERMOMETER Type: Fisher Scientific Mercury-in-glass thermometer Marked: Fisher 3C3642 Range: -1 to +51~C in 0.1~C Calibrated by: NBS Thermometer Reading True Temperature oC ~C +0.02 0.00 10.00 9.97 20.00 19.97 30.00 30.03 4o0.00oo 40.02 50.00 50.00 Estimated uncertainties do not exceed 0.03~C up to 51~C.

-154TABLE XXXI CALIBRATION OF THERMOPILE Tagged G2'(724-A axd (355)350 Temperature EMF ~C microvolts -196 -33550 -185 -52004 -120 -25627 -100 -20545 -80 -16795 -60 -12971 -4o -8890 -20 -4568 0 0 +20 4776 +40 9764 +6o 14948 +80 20525 +100 25886 +120 3.-613 Calibrated by: NBS

TABLE XXXII CALIBRATED RESISTANCES OF STANDARD RESISTORS Designation Leeds and Northrup Resistance Accuracy Date of Temperature Coefficients in Figure 5 Catalog No. Serial No. at 250C, R25 R25 Calibration a abs ohms (Percent) Rj_ ~ 4020-B 1745750 1.000008 0.001 Dec 68 +0.00000oo6 -0.0000005 Re 4025-B 1648097 10.0000 0.005 Jun'64 +0.000009 -0.0000005 Rs 4040-C 1227969 9999.8 0.005 Apr'57 +0.000001 -0.0000005 Resistance, RT, at temperature Tres OC given by res es RTres R25(1+(Tres-25)+P(Tres-25)2

-156TABLE XXXIII CALIBRATION OF POTENTIOMETER STANDARD CELLS Eppley Serial No. EMF Date Calibrated by 768338 1.01930 @ 23~C Oct'63 Eppley Lab. 1.01926 @ 230C Aug'66 NBS 1.01923 @ 24~C Apr'69 NBS 813229 1.01926 @ 23~C Dec'67 Eppley Lab. TABLE XXXIV CHARACTERISTICS OF LEEDS AND NORTHRUP MODEL K-3 NULL POTENTIOMETER Measuring Ranges High (X1) Range 0 - 1.6110 volts Medium (XO.1) Range 0 - 0.16110 volts Low (XO.01) Range 0 - 0.016110 volts Limits of Error* High Range (Xl): ~ (0.01% + 20 microvolts) Medium Range (XO.01): ~ (0.015o + 2 microvolts) Low Range (XO.01): + (0.015% + 0.5 microvolts) Thermal emf On operation of switches: Less than 0.1 microvolts of very short duration. On operation of slide wire: Not more than 0.3 microvolts of very short duration. Residual emf: Not more than 0.3 microvolts. Guarding and Shielding 1. The potentiometer is guarded for high humidity operation. 2. The potentiometer is shielded to eliminate electrostatic problems. *Values apply for both measuring and standardizing, and include the effect of residual thermal emf's at 90% relative humidity.

TABLE XXXV EXPERIMENTAL ENTHALPY OF MIXING DATA ON NITROGEN-CARBON DIOXIDE SYSTEM Temperature Temperature Run Flow Rate Power N2 Inlet Outlet Difference Pressure Drop Pressure Number N2 C2 (W) (T1) (To) (T-T) N2 Inlet C02 Inlet at Outlet b/mi lb/min watts ~C~C C -Outlet -Outlet PO (P1-Po) (P2-Po) psia psi psi 4.n00 0.03567 0.05549 3.696 40.03 40.037 -0.007 0.089 0.063 499.5 5.nn1 0.03578 0.0542? 3.678 40.02 40.064 -0.044 0.088 0.062 496.9 5.n0? 0,n3577 0.05432 3.678 40.0? 40.049 -0.029 0.088 0.062 497.7 5.03n 0.03579 0.05470 3.7R8 40.01 40.068 -0.058 0.088 0.063 500.2 6.0N1 n.n2896 0.1R130 4.869 40.00 40.001 -0.002 0.142 0.144 503.1 6, 6.n n0.03073 n0.09437 4.589 40.00 40.011 -0.011 0.121 0.113 5000 0 6.03 n0.n4073 0.08251 4.951 40.00 40.037 -0.037 0.137 0.112 499.7 h.nn04 0.04338 0.07075 4.6hO 40.00 40.014 -0.014 0.131 0.097 500.7 > 7.001 n0.4956h n0.S77 4.3B1 40.01 40.036 -0.026 0.136 0.088 500.1 7.nn0? n.n701 n0.0543 4.h66 40.00 40.015 -0.015 0.217 0.120 500.0 9.O01 0.n7170 n.n10233 7. 84 40.01 40.013 -0.003 0.311 0.225 499.2 9.00? 0.n7177 n0.1531 7.174 40.03 40.033 -0.003 0.317 0.232 498.5 11.1 0.09437 O.04144 2.668 40.00 40.017 -0.017 0.050 0.034 500.2 11.? 0.02432 n.04111 2.661 39.99 40.033 -u.043 0.049 0.034 498.1 11.3 0.02423 0.04075 2.648 40.00 40.001 -0.001 0.049 0.033 501.4 13.1 0.0n149 0.1203n 16.589 40.00 40.08 -0.088 0.059 0.062 949.6 13.2.0n3339 0. n9425 17.77? 39.99 39.955 0.035 0.063 0.054 952.5 c 13.3 0.05799 0.08564 19.919 40.02 40.105 -0.085 0.107 0.074 946.1 13.4 0. 7?62 0.04184 11.705 40.01 39.991 0.019 0.110 0.054 945.8 14.1 n.0?264 0.12150 4.873 30.99 31.023 -0.033 0.128 0.139 500.0 14.2 0.03311 0.09146 5.491 31.00 31.009 -0.009 0.119 0.107 502.4 14.3 0.05549.0n9267 6.983 31.00 30.994 0.006 0.204 0.155 502.9 14.4 n0.7252 0.04232 4.387 31.00 30.990 0.010 0.204 0.102 498.2 15.1 0.0,529 0.12695 27.942 31.00 31.064 -0.064 0.064 0.064 94(.1 15.2 0.02603 0.09135 23.277 30.99 31.003 -0,013 0,046 0.041 949.5 15.3 r.n5343 n0.0804 78.166 31.01 31.047 -0.037 0.094 0,067 948.7 15.4 0.07231 0.04317 16.236 31.00 31.010 -0.010 0.107 0.052 952.5

TABLE XXXVI EXPERIMENTAL EN.THALJPY OF MIXING DATA ON NITROGEN-ETHANE SYSTEM Run Flow Rate Power Temperature Temperature Pressure Drop Pressure Number Nitrogen Ethane () N2 Inlet Outlet Difference N2 Inlet C2H6 Inlet at Outlet b/min Ilb/min watts (T1) (TO) (T1-T ) -Outlet -Outlet P ~C 0C aC (P1-P0) (P2-Po) ps]a psi psi 16.1 0.07279 0.02375 5.385 32.34 32.370 -0.030 0.234 0.103 401.0 16.2 0.05500 0.f4358 8.020 32.34 32.369 -0.029 0.180 0.107 400.6 16.3 0. 0983 0.05845 8.653 32.35 32.380 -0.030 0.141 0.106 401.1 16.4 0.02292 0.n6482 6.880 32.36 32.381 -0.021 0.093 0.086 401.6 TABLE XXXVII 00 EXPERIMENTAL ENTHALPY OF MIXING DATA ON NITROGEN-OXYGEN SYSTEM Run Flow Rate Power Temperature Temperature Pressure Drop Pressure Number Nitrogen Oxygen (W) 02 Inlet Outlet Difference Difference Np Inlet 02 Inlet at Outlet Ib/min Ib/min watts (T1) (TO) 02 Inlet N2 Inlet -Outlet -Outlet P ~C ~C -Outlet -Outlet (P1-P 0) (P2-Po) psia (T1-T0)0C (T2-T0)OC psi psi 17.1 0.1268 0.13?5 0.0 25.00 25.117 -0.117 -0.108 0.2R 0.39 1001.0 17.2 0.168 0.1325 0.0 25.00 25.119 -0.119 -0.108 0.28 0.39 1001.0 17.3 0.1268 0.1325 0.03188 25.00 25.128 -0.128 -0.118 0.28 0.39 1001.0 17.4 0.!268 0.1325 0.09771 25.00 25.159 -0.159 -0.150 0.28 0.39 1001.0 17.7 0.1268 0,132 0.0 25.00 25.113 -0.113 -0.104 0.29 0.39 1000.8

TABLE XXXVIII PRIMARY CORRECTIONS FOR DATA ON NITROGEN-CARBON DIOXIDE SYSTEM Run Mole Power Corrections for^ at (T0,P,) Number Fraction Flow Pressure Temperature Kinetic En- Impurities after Primary Nitrogen (W/F) Drop Difference ergy Diff. Btu/lb Corrections Btu/lb Btu/lb Btu/lb Btu/lb Btu/lb Btu/mol 4.001 0.503 2.304 -0,0014 -0.0035 -0.5E-06 0.0087?.308 83.0 5.001 0.510 2.3?? -0.0014 -0.0211 -0. 5FE-06 0.0086 2.308 82.8 5.00 I0.509 2.320 -0.0(14 -0.0140 -0.5E-06 0.0086 2.313 83.0 5.003 n0.508 2.347 -0.0014 -0.0281 -0.5E-06 0.0086 2.326 83.5 6.001 0.288 1.948 -0.00fn37 -0.0007 0.1E-05 0.01.13 1.955 77.0 6.002 0.339 2.085 -0.0028 -0.0054 0.4F-06 0.0107 2.087 80.5 6.003 0.437?.?P3 -0.0026 -0.0179 -0.6E-06 0.0095 2.272 84.1 6.0r04 0.491?.3?0 -0.o?22 -0.0066 -0.7E-06 0.0088 2.320 83.9 7,001 0. 575 2.?95 -0.0018 -0.0126 -0.6E-06 0.0077 2.288 79.7 7.o0 0.2 6.70 O2.09 -0.00?P3 -0.0071 0.4E-06 0.0062 2.085 69.4 9.001 0.5n5 2.313-0.0048 -0.0013 -0.2E-05 0.0084 2.315 82.5 9.002 0.518e 2.3 -0.0050 -0.0015 -0.2E-05 0.0085 2.304 82.3 11.1 0.481j 23l4 -0.0008 -0.0083 -0.2E-06 0.0090 2.304 83.7 11.2 0.482 2.311 -0.0008 -0.0209 -0.2E-06 0.0089 2.299 83.4 11.3.44 2.315 -0.0008 -0.0004 -0.2F-06 0.0089 2.323 84.3 13.1 ".2 6.646 -0.0031 -0.0730 0.2E-06 0. 0 545 6. 625 268.2 13.2? 0.358 7.913 -0.0024 0.0278 -0.2F-06 0.0474 7.985 305.7 13.3 0.51.6 7.P81 -0.0028 -0.0617 -0.5F-06 0.0383 7.855 280.9 13.4 0.732 5.811 -0.0015 0.0122 0.5E-06 0.0235 5.845 188.8 14.1 0.2??q8 1.9?1 -0.0048 -0.0116 0.2E-05 0.0135 1.918 77.4 14.? 0.363 2505 -0.0033 -0.0044 -0.3F-07 0.0118 2, 509 95.8 14.3 0.4R85?.678 -0,0043 0.0032 -0.1E-05 0.0100 2, 687 97.4 14.4 0.7?9 2.171 -0.0023 0.0047 0.IE-05 0.0059 2.179 70.5 15.1 0.239 10.429 -0.00 n54 -0.0808 -0. 5-08 0.0856 10.429 419.0 15.2 0.310 11.269 -0.0032? -0.0157 -0.1F-06 0.0798 11.330 442.4 15.3 0.48R 11.314 -0. 0044 -0.0390 -0.5E-06 0.0639 11.334 410.2 15.4 0.725 7.989 -0. 003 -0. 0082 0.4E-06 0.0384 8.017 259.9

-l6oTABLE XXXIX SECONDARY CORRECTIONS FOR DATA ON NITROGEN-CARBON DIOXIDE SYSTEM Run Corrections for H at (Tn,Pn) Number Pressure Temperature after Secondary Level Level Corrections Btu/lb Btu/lb Btu/lb Btu/mol 4.001 0.0028 0,0009 2.312 83.1 5,001 0.0166 0,0016 2.326 83.4 5.00? 0.0124 0,0012 2.327 83.5 5.003 -0.0008 0.0017 2.327 83.5 6.001 -0.0113 0.0000 1.944 76.6 6.002 0.0001 0. On02 2.087 80.5 6.003 0,0017 0.0009?.274 84.2 6.004 -0.0035 0.0003 2.317 83.8 7.001 -0,0006 0.0009 2,288 79.7 7.002 -0.0001 0.0003 2.086 69.4 9.001 0.0044 0.0003 2.320 82.6 9.002 0.0078 0.0008 2.313 82.6 1.1 -0.0008 0.0004 2.304 83.7 11.2 0.0099 0.0008?.309 83.8 11.3 -0.0073 0.0000 2.316 84.0 13.1 0.0083 0.0214 6.654 269.4 13.2 -0.0567 -0.0118 7.917 303.0 13.3 0.0823 0.0247 7.962 284.7 13,4 0.0609 -0.0015 5.905 190,7 14. 1 -0.0001 0.0008 1.919 77.5 14. -0.0199,0004 2.489 95.1 14. 3 -0.0256 -0. 0003 2.661 96. 5 14.4 0.0122 -0.0003?.191 70.9 15.1 0 1 306 0.0394 10.599 425.9 15.2 0.0209 0.0018 11.352 443.3 15.3 0.054 00.0251 11.414 413.1 1.5.4 -0.0688 0.00344 7.952 257,8

TABLE XL PRIMARY CORRECTIONS FOR DATA ON NITROGEN-ETHANJE SYSTEM Run Mole Power Corrections for EH at (T Po) Number Fraction Flow Pressure Temperature Kinetic En- Impurities after Primary Nitrogen (W/F) Drop Difference ergy Diff. Btu/lb Corrections ~3tu/lb Btu/lb Btu/lb Btu/lb Btu/lb Btu/mol Multicomponent System 16.1 0.767 3.170 -0.0r33 -0, 0185 0.4E-05 -0.0000 3.148 89.8 16.? 0.576 4.6?23 -0.0049 -0.0213 -0.7E-06 -0.0000 4.597 133.0 16.3 0.423 5.0P3 -0,0061 -0.0244 -0.LE-05 -0.0000 4.972 145.5 16.4 0.?76 4.456 -0,0059 -0.0190 0.6E-06 -0.0000 4.431 131.0 Ci^ Binary System 16.1 0.769 3.170 -0.0033 -0.0185 0.4E-05 -0.0519 3.096 88.2 16.2 0.578 4.623 -0.0049 -0.0213 -0.7E-06 -0.0628 4.534 131.0 16.3 0.425 5.003 -0.0061 -0.0244 -0.1E-05 -0.0560 4.916 143.5 16.4 0.277 4.456 -0.0059 -0.0190 0.6E-06 -0.0404 4.391 129.5

-162TABLE XLI SECONDARY CORRECTIONS FOR DATA ON NITROGEN-ETHANE SYSTEM Run Corrections for at (Tn Pn) Number Pressure Temperature after Secondary Level Level Corrections Btu/lb Btu/lb Btu/lb Btu/mol Multicomponent System 16. 1 -0.0001 -0.0005 3.148 89.8 h6.2 0.0084 -0.0008 4.605 133.2 16.3 -0.0024 -0.n000 4.970 145.4 16.4 -0.0127 0.0001 4.419 130.7 Binary System 16.1 _-0.0 1 -0,0004 3.096 88 2 16. 2 o0.03 -0 0008 4,542 131.2 1h.3 -0.0024 -0.0000 4*914 143.5 16,4 -0 01?5 0 000 4.379 129.2

TABLE XLII PRIMARY CORRECTIONS FOR DATA ON NITROGEN-OXYGEN SYSTEM Run Mole Power Corrections for HE at (T P) Number Fraction Flow Pressure Temperature Kinetic En- after Primary Nitrogen (W/F) Drop Difference ergy Diff. Corrections Btu/lb Btu/lb Btu/lb Btu/lb Btu/lb Btu/mol 0% 17.1 0.522. -0.2 - 0. 052 -052 -0.9E-06 -0.0548 -1.65 17.7 0.52? 0.0 -0.0022 -0.0532 -0.9E-06 -0,0554 -1.67 1 7.3 0. 5?2 0. 070 -0. 0022 -0.0576 -0.9E-06 -0.0529 -1.59 17.4 n. 522 0.? 14 -0.0022 -0.0724 -0.9E-06 -0.0532 -1.60 17.5 0.522 0.0 -0.0022 -0.0508 -0.9E-06 -0.0530 -1.60

-164TABLE XLIII VALUES OF HEAT CAPACITIES AND ISOTHERMAL JOULE-THOMPSON COEFFICIENTS USED FOR PRIMARY CORRECTIONS Component Temperature Pressure Heat* Isothermal* ~C psia Capacity, Joule-Thompson Cp Coefficient, cp Btu/(lb~F) Btu/(lb psi) Oxygen 25 1001 0.247 -0.00697 Nitrogen 25 1001 0.275 -0.00603 31 500 0.259 -0.00592 950 0.270 -0.00538 40 500 0.258 -0.00550 950 0.268 -0.00501 Carbon Dioxide 31 500 0.287 -0.0395 950 0.782 -0.086 40 500 0.275 -0.0312 950 0.497 -0.0575 Ethane 32.4 401 0.597 -0.0904 *Literature sources for these values given in chapter "Results."

TABLE XLIV FORMULAE DERIVED FROM BENEDICT-WEBB-RUBIN EQUATION OF STATE USED IN CALCULATING PROPERTIES Enthalpy Departure 2 2~~~~~~~ 2 H-H - V B RT-2A, - p + (2bRT-3a) 2 + __5 + 2 -(le )-_ + 2 e-yp2] 0 0 2 2j 2 5 L2 2 - ~~~T 5 T 7p2 Isothermal Joule-Thompson Coefficient (BQRT - 2Ao - ) + (2bRT-5a)p + 6aap4 + y [5cp + 5c7p - 2c72p5] 2 cp~ ~ ~ ~ ~ ~~c 5 ----. —---— 2 —— 4 —-----------— 6 RT + 2p(BRT - AO -) + 3p2(bRT-a) + 6aap5 + e — [5cp2+ )cyp - ec7p6] T T Heat Capacity OP 6c -p2 6 2 c - C -R +- - - -7 + ce7 - + TrRp + 3R2 +bR+ 2Cp2 2( 2cp3 2cyp- ) 5 T3 2AOp3 2Cp 4 7 2 Rp2 + 2BORp3 - - + bRp4 -ap + 6aap e-YP [cp 4 + 6 cy pT T3 T [p 2cT3p8

TABLE XLV CONSTANTS FOR THE BENEDICT-WEBB-RUBIN EQUATION OF STATE Units: psia, ft5, lb mole, OR R = 10.7555 TOR = T~F + 459.65 Constants Nitrogen* Carbon Dioxide Ethylene Ethane Propylene Propane Bo 0.0407426 0.799496 0.891980 1.00554 1.56265 1.55884 A0 1.055642 10522.8 12595.6 15670.7 25049.2 25915.4 C0 8059. 1695.01 x 106 1602.28 x 106 2194.27 x 106 5565.97 x 106 6209.95 x 6 b 0.0025277 1.0582 2.20678 2.85595 4.79997 5.77555 a 0.025102 8264.46 x o106 15645.5 20850.2 46758.6 57428.0 c 728.41 2919.71 x 106 4155.60 x 106 6413.14 x 106 20085.0 x 106 25247.8 ~a 0.0001272 0.348 0.751661 1.00044 1.87512 2.49577 7r 0.0055 1.584 2.56844 5.02790 4.69525 5.64524 Author Bloomer & Rao Cullen & Kobe Benedict, Webb Benedict, Webb Benedict, Webb Benedict, Webb & Rubin & Rubin & Rubin & Rubin Reference (19) (29) (14) (14) (14) (14) *Units: atm, 1, g mol, OK

-167TABLE XLVI SAMPLE RESULTS OF VOLUME DETERMINATIONS ON CANS USED FOR GAS DENSITY ANALYSIS Data on Can No. 30 Measurement Volume Percent of Can Difference cc from Average Volume 1 372.97 0.13 2 372.21 -0.08 3 372.32 -0.05 Average Volume 372.50 cc 0.09% Data on Can No. 31 1 371.92 0.10 2 371.28 -0.07 3 371.44 -.0o3 Average Volume 371.55 cc 0. 11

-168TABLE XLVII GAS DENSITY ANALYSES OF GRAVIMETRICALLY PREPARED SAMPLES Can Number Mole Fraction Nitrogen Gravimetric Gas Density Difference Analysis Analysis 14 0.4023 0.4053 +0.0030 30 0.4022 0.4Q03 -o.oo19 TABLE XLVIII SECOND VIRIAL COEFFICIENTS USED IN GAS DENSITY ANALYSIS COMPUTATIONS Temperature = 250C Constituent Second Virial Reference Coefficient cc/mol Nitrogen, Bll -4.71 (109) Carbon Dioxide, B22 -123.6 (109) Nitrogen-Carbon-Dioxide, B12 -42.6 (93) (Interaction Coefficient)

-169TABLE XLIX COMPARISON OF COMPOSITIONS FROM FLOW METER CALIBRATIONS AND FROM GAS DENSITY ANALYSIS Run Nominal Conditions Mole Fraction Nitrogen from Difference Number Tn Pn Flow Meter Gas Density ~C psia Calibrations Analysis 6.003 40 500 0.437.441 o.oo004 11.1 0.481 o.484 0.003 11.2 0.482 o.486 o.oo4 o.483 0.001 11.3 0.484 0.482 -0.002 0.485 0.001 6.004 0.491 0.495 0.004 4.001 0.503 0.506 0.003 5.001 0. 0.510 0.000 9.001 0.525 0.524 -0.001 7.002 0.670 o.669 -0.001 15.1 40 950 0.220 0.222 0.002 0.224 O.004 15.2 0.358 0.359.001l 0.362 o.oo4 13.3 o.516 0.519 0.003 13.4 0.752 0.732 0.000 0.753 o.o001 14.1 31 500 0.228 0.230 0.002 14.2 0.363 0.363 0.000 14.3 0.485 0.483 -0.002 14.4 0.729 0.728 -0.001 15.1 31 950 0.239 0.242 0.003 15.2 0.310 0.307 -0.002 15.3 0.489 o.493.o004 15.4 0.725 0.720 -0.005

TABLE L CONVERSION FACTORS FOR SI UNITS English Units SI Units 7) 1 Btu = 1055.87 Joules 1 psi = 101325/14.696 Nm-2 1 lb = 0.453592 Kg TABLE LI MOLECULAR WEIGHTS USED IN COMPUTATIONS Substance Molecular Weight Carbon Dioxide 44.011 Ethane 30.07 Ethene 28.05 Nitrogen 28.016 Propane 44.10 Oxygen 32.00 Propane 44.10 Propene 42.08

APPENDIX D SAMPLE CALCULATIONS One sample calculation of each of the following are presented here: 1. The volume determination of the calibration tank utilized in calculating the flow rate during flow meter calibrations. 2. Flow meter calibrations on the nitrogen flow meter 3. Enthalpy of mixing measurements on the nitrogen-carbon dioxide system and the impurity correction for the nitrogen-ethane system. The equipment and procedures used have been described in detail in the chapter entitled "Apparatus and Experiments." The literature sources for the thermodynamic and transport properties used in reducing the flow meter calibration data are referred to in the same chapter. The viscosity data(12) and low pressure(126) and high pressure(3) volumetric data on nitrogen were fit graphically. The resultant formulae used in calculating these properties are given in Table LII. A tabulation of the nomenclature used here is given at the end of this appendix. Volume Determination of Calibration Tank The calculation of the volume of the tank from the data in Table LIII involves six steps. They are the calculation of the 1. Temperature in the tank, Tctf 2. Atmospheric pressure, PR 3. Pressure in the tank, Pctf 4. Compressibility factor of nitrogen, ZN 5. Mass of nitrogen in the tank, mct 6. Volume of the tank, Vct -171

-172TABLE LII FORMULAE FOR PROPERTIES OF NITROGEN USED IN COMPUTER PROGRAMS Independent Property Variable Formula Compressibility 70 < P atm < 80 ZN = ZL + (ZH-ZL)(T-290)/30 Factor 290 < T ~K < 320 where ZL = 0.993974 + 7.98_10 -(P-70) and ZH = 1.0074 + 2.57x10 (P-70) Viscosity, poise 70 < P atm < 80 N = (183.2 + 0.22P)106 Second Virial 283 < T ~K < 318 BN = -301.3 + 51.94 ln T Coefficient, cc g mol Temperature in Tank Calculated from data on tank filled with nitrogen Tth = Tef + (108) Cth = 20.80 + (-38.5 microvolts) (4o mi C \40 microvoltsJ = 19,,84~C Tthtf Tctf = (109) 2 19.84+19.80 2 - 19.820C Atmospheric Pressure Equation suggested by Brombacher et al. (22) PR = (P-0.04)(G) l + (sexp mexp)(TR-211l) (1) L l4-m^(TR-21.l)

-173TABLE LIII SAMPLE DATA FOR VOLUME DETERMINATION OF CALIBRATION TANK Variable Value Mass of Nitrogen Discharged Full Cylinder No. 1, mcl 2807.810 g Empty Cylinder No. 1, mc2 2651.080 g Full Cylinder No. 2, mc3 2876.917 g Empty Cylinder No. 2, mc4 2715.338 g Evacuated Tank Room Pressure just prior to evacuation, PRi 28.95 in Hg Room Temperature just prior to evacuation, TRi 20.2~C Pressure in evacuated tank,* P llxl 3 mm Hg ct 1 mm Hg Thermocouple reading, AE -44.1 microvolts Reference junction temperature, Tref 20.85~C Bath fluid temperature, Tc 19.75~C Tank Filled with Nitrogen Tank Pressure,* Pctf 15.88 in Hg gauge Thermocouple reading*, AE -58.5 microvolts Reference Junction temperature,* Tref 20.80~C Bath fluid temperature* (Corrected for emergent 19.80~C stem), T' Room Pressure, P 29.12 in Hg Room Temperature,% TR 18.5~C Equipment Constants Thermocouple calibration constant, Cth 40 microvolts/~C Coefficient of expansion of aluminum, sexp 24.5x10-6/~C Coefficient of expansion of mercury, mexp 1. 82x10-/~C Ratio of local to standard gravity, G 0.999645 Volume of 36-inch King manometer well, Vwell 4.7 in3 Volume of connecting line, Vline 0.79 in3 Approximate volume of tank, V 6.43 ft3 Volume of union between calibration tank and solenoid valve, Vu 0.00017 ft3 Cross-sectional area of indicating column of 36-inch King manometer, Am 0.038 in2 Coe.fficient of expansion of copper vexp 5x10-5/~C XAvcrage (o1 three mneasur(1e I(nto made over a time period of 15 minutes.

-174PR = (29.12-0.04 in Hg)(O.999645) l + (24.5xlO16-1.82xlO-4)(18.5-21.1) j 1 + 1.82xlO( 18.5-21.1) = 29.08 in Hg Pressure in Tank tf = PR+ (Pctf )(G)1 + Sexp(TR-20)-mexp(TR-0) (111) Pctf -P + (P1 + mexp(TR-0) (. = 29.08 in Hg + (15.88 in Hg)(0.999645)[1 + 24.5x10-(18.5-20)-l.82xlo-4(!85) j 1 + 1.82x10 (18.5) = 44.90 in Hg Compressibility Factor of Nitrogen Z= +BN Pctf (1) ZN =1+ (l~) R Tctf where BN = -6.0 cc/g mol is calculated from the formula in Table LII at T = Tctf + 273.15~K or 292.97~K (-6 CC )(44.90 in Hg) g mOl ZN = 1 +...... ZN ~l+in Hg cc (2455 gi K); 19.82+273.150K) g mol 0K = 0.9998 Mass of Nitrogen in Tank mct = Napp + Nwell + Nl + N+ vac (113) Intermediate calculations: 1. Mass of gas discharged from cylinders, Na Npp = (m l-m2) + (1mc-mc4) (114) = (2807.810-2651.080) + (2876.917-2715.338)g

-1753183509 g ( lb = 0.70175 lb 2. Residual gas in manometer well, Nwe well N N PRi Vwell (115) well- TRi R where PRi = 28.90 is calculated by substituting Pi = 28.95 in Hg and TRi = 20.2~C in Equation (110). lb (28.016 m-)(28.90 in Hg)(4.7 in3) Nwell = (20.2+273.15~K)(67961 in3 in Hg) mol ~K = 0.00019 lb of nitrogen 5. Mass of residual gas in line connecting cylinders to calibration tank, Nline Vline MN Nline = R R-int - Pctf] (116) where (mcl-mc2) R TR pint = Vapp MN ft5 in Hg) (156.73g) (18.5+273.15~K)(39.33 ft3 in H) mol OK (6.43 ft3)(28.016 m )l(453.59 g) = 22 in Hg Hence (0.79 in3)(28.016 lb) line M 7-) [2(29.0o8)-22-44.90] (18.5+273.15 K)(67961 in in Hg) mol OK - -.'X)00Q 11) ol' nAi Lrogcn

-1764. Mass of gas in evacuated tank, Nvac MN cti Vapp (117) vac R T R cti where Ttti = 19.75~C is calculated from data on the evacuated tank using procedure detailed in Equations (108) and (109) for calculating Tctf (28.016 mol)( 1x10l3 mm Hg)(6.43 ft3) vac= (999 mm Hg ft)( 1975+27315~K) mol ~K = 0.000007 lb of nitrogen 5. Mass of gas discharged, mct, calculated from Equation (113) met = 0.70175 + 0.00019 - 0.000008 + 0.000007 = 0.70194 lb of nitrogen Volume of Tank mct ZN R Tctf ( Pctf MN in Hg ft5 (0.70194 lb)(0.9998)(19.82+273.15~K)(39.33 mol ~K ) (44.90 in Hg)(28.016 l-) 6.4292 ft3 at Tctf = 19.82~C The volume, Vt, calculated above is corrected for (a) volume of manometer fluid displaced into the indicating column from the well (b) volume of union, V, connecting calibration tank to two-way solenoid valve (23 in Figure 3) and (c) thermal expansion to 20~C Vtf = Vt + Vu - (An)(Pctf) (119) = 6.4292 + 0.00017 - (0.038 in2)(15.88 in) (1728 in3/ft3 )

-177= 6.4290 ft3 Vct = ctf[l + Vexp (20-Tctf) (120) = 6.4290[1 + 5x10-5(20-19.82)] = 6.429 ft3 Flow Meter Calibration Sample data taken on a single flow meter calibration run with nitrogen are given in Table LIV. Two parameters are calculated from these datad hese data: Tese parameters along with 4 PFAPF - TIF J the parameters calculated from other calibration runs are used in correlating the results of the flow meter calibrations. The steps described below are followed in calculating these parameters from the data given in Table LIV. 1. Pressure at the flow meter inlet pressure tap, PF 2. Pressure drop across the flow meter, APF. 3. Mean pressure, Pm, in the flow meter calculated from PF and ALPF 4. Density of nitrogen, pF, in the flow meter at pressure P 5. Viscosity of nitrogen, rF, in the flow meter at pressure Pm 6. Flow rate, F, calculated from measurements on the calibration tank. 7. Calculation of parameters. Pressure at Flow Meter Inlet G....- pair Intermediate calculations: 1. Ieise g;auge calibratioil corruct.ion, Pi. I...( 10'8. 1lO).)(L01.)l.5-l092.2) _ -1.4 psi

-178TABLE LIV SAMPLE FLOW METER CALIBRATION DATA Temperature of Flow Meter bath (corrected for emergent 45~C stem), TF Pressure in Flow Meter Average pressure in flow meter read on Heise gauge, Phs 1084.8 psig Heise gauge calibration data: Heise gauge reading prior to run 1089.5 psig Nominal dead weight gauge pressure prior to run 1087.6 psig Heise gauge reading after run 1092.2 psig Nominal dead weight gauge pressure after run 1091.3 psig Temperature of dead weight gauge (assumed room temperature), TR 27.4~C Pressure Drop across Flow Meter Average cathetometer reading of fluid height, hH 22.08 cm Average cathetometer reading of zero, hL 1.44 cm Temperature of cathetometer, T ath 26.2~C Temperature of manometer fluid (assumed room temperature) TR 27.4~C Flow Rate Determination Evacuated Tank Filled Tank ti -22.2 m Hg P 28.95 in dbp** Pressure* P_ ci= 22,2 mm Hg P f = 28.95 in dbp Thermocouple reading,* ZE -56.5 microvolts -5 microvolts Reference junction temperature* Tref 26.26~C 26.34~C Bath fluid temperature* (corrected for emergent stem) T tf 24.83~C T. = 25.04~C Room Pressure,* c 2~.13 in Hg Room Temperature, TR 27.4~C Time period of gas collection, 9 931.6 seconds Equipment Constants Density of air, Pai 0.0012 g air cc Density of brass weights (dead weight gauge), Pbrass 8.4 g Expansion coefficient of stainless steel (dead weight gauge), sexp 1.65x10-5/C Head of oil between dead weight gauge and U-leg, Ph 0.075 psi * Average of three measurements made over a time period of 15 minutes. **dbp = di butyl phthalate

-179TABLE LIV (Continued) Dead weight gauge calibration correction (Table XXVIII), Pcorr 0.044 psi Expansion coefficient of aluminum (cathetometer scale) s 24.5xl0-5/oc Well factor for high pressure manometer, Aw 0.99077 Values of G, vexp, Vwell and Am given in Table LIII and Vct from Table XXIII. 2. True barometric pressure, PR PR = 29.05 inches Hg by substituting P~ = 29.13 inches Hg and TR = 27.4~C from Table LIV in Equation (110). Hence from Equation (121) 0.0012 0.999645(1 - 8. c) P? = (1084.8 psig) P = (1084.8 psig)| — 8 —l —.4- 7+ 0.075 psi + 0.044 psi F- ~~-1 + 1. 65x10-5(274.4-23) - 1.4 psi + (29.05 in Hg)(0.4912 ps ) = 1097.2 psia Pressure Drop across Flow Meter APF = (a() [Pdbp - PN] (122) Pdbp where Ah = (hH-hL)[l+sexp(Tcath-21,l)]/AW Intermediate calculations: [1 + 24.5xl 6(26.2-21.1)] 1. Ah = (22.08-1.44 cm) (-99 + 2450-77) (4 c n) (0.99077)(2.54 cm/in) = 8.203 in dbp 2. Variation of density of di butyl phthalate with temperature Pdbp = P [1l - 6.16xl- (T -23.3)] c (123)

-180= l.o408 [ 1 - 6. l6xlO (27.4-23.3) ] = 1.0382 g cc 3. Density of nitrogen, PN. Compressibility factor calculated from formulae in Table LII at PF = (1097.2/14.696)atm and TR = 27.4 + 273.15~K is ZN = 0.9994 PN MN MP (124) ZN R TR (28.016 lb) (1097.2 psia) (0.9994)(27.4+273. 15K)(19.317 psiaoft3) mol OK lb = 5.298 fb ft3 Hence from Equation (122) F (8.203 in dbp)(O.999645) ( l.0582 g) - (5.298 I _ )(o0.0o62 t3 (1.0408 ) cc ft5 cc lb = 7.511 in dbp Mean Pressure in Flow Meter APF ^ - ^ + -- (125) Pm = PF + (125) (7.511 in dbp)(1.040o8 inches dbp 0.4912 psi) m = 1097.2 psia - inches H20 inches Hg inches Hg (2( 13. 595 inches'H20 ) = 1097.1 psia Density of Nitrogen in Flow Meter Compressibility factor of nitrogen from formulae in Table LII at Pm = 1097.1 psia and T = TF + 273.15~C or 318.15~K is ZN = 1.008

-181p = N -m (126) PF ZN R TF (28.016 I-) (1097.1 psia) mol (1.008)(45+273. 15~K) ( 19.517 psia t) mol OK = 4.962 lb ft3 Viscosity of Nitrogen in Flow Meter Calculated from the formula in Table LII at P = (1097.1/14.696)atm rF = 199.6x10-6 poise Flow Rate Determination The four steps consist of calculating: (a) Mass of gas in initially evacuated in tank, Ni (b) Mass of residual gas in manometer well, Nwell (c) Mass of gas in tank after stopping gas flow, Nf (d) Flow rate of nitrogen, F (a) Mass of gas in evacuated tank Ni Pcti Vcti (127) R Tcti Intermediate calculations: 1. Temperature, Tcti, calculated as in Equations (108) and (109) OC Tth = 26.26 + (-56.5 microvolts)( -- C ) 40 microvolts = 24.85~C = 4.85+24.83 = 24.84~C Tcti= 2

-1822. Volume oi' calibrat ion talk, Vcti: corrected for thermal expansion of copper tank to Tcti and for volume of manometer well Vcti = Vct[l + Vexp(Tcti-20)] - Vwell (128) = 6.422[1 + 5x10-5(24.84-20) - (4 7 in3) (1728 ) ft3 = 6.421 ft3 Hence from Equation (127): (28.016 lT)(22.2 mm Hg)(6.421 ftP) Ni = m f (24.84+273. 15K)(999 mo H ft3) mol ~K = 0.0134 lb of nitrogen (b) Mass of gas in manometer well MN PR Vwell Nwell = R el (129) R T (28.016 b- )(29.05 in Hg)(4.7 in3) (27.4+275.15~K)(67961 in3 in Hg) mol OK = 0.0002 lb of nitrogen (c) Mass of gas in filled tank N MN Pctf Vctf (10) ZN Tctf R Intermediate calculations: 1. Temperature, Tctf, calculated P.s in Equations (108) and (109) Tth = 26.34~C + (-52.0 microvolts) (4- m10crov0t) thn =40 microvolts = 25.04~C Ttf =- 25.04+25.04 = 25.04~C Tctf = o2

-1832. Pressure, Pctf Pctf = PR + Ptf b G (131) 0 PHg (28.95 in dbp)(1.0382 g) (0.999645) Pctf = 29.05 in Hg + (13.5951 C) = 31.26 inches Hg 3. Compressibility factor, ZN. The second virial coefficient calculated from the formula in Table LII at T = Tctf + 273.15~K or 298.19~K is BN = - 5.3 cm g mol BN Pctf ZN 1+ tR t (132) (-5.3 )(3.)( 26 in Hg) (25.04+273.15~K)(2455 cc in Hg) g mol 0K = 0.9998 4. Volume of calibration tank, Vctf: corrected for thermal expansion to Tctf and for volume of manometer fluid displaced in well Vctf = Vct[l + exp(Tctf-20)] + (Am)(Potf) (133) = 6.422[l + 5x10-5(25.04-20)] + (0.038 in2)(28.95 in) (1728 in3/ft3) = 6.424 ft3 Hence, from Equation (130) (28.016 m-)(31.26 in Hg)(6.424 ft3) Nf = 2ol (o.9998)(25.o4+275.1:K)(59.529 in t3 )

-184(d) Flow rate of nitrogen Nf-Ni-Nwell (1) F. (i34) (0.4798 - 0.0134 - 0.0002)lb 60 sec (931 sec) nute lb = 0.03003 - minute Calculation of Parameters lb F 0o. 003 minute \Tp^pp (4.962.b )(7.511 inches dbp) f7t 0.4919x10-2 PFP F (4.962 -~)(7.511 inches dbp) PE=, ft3 T2 (199.6x10 poise)2 - 0.9552xl05 In FF = 11.446 lF Enthalpy of Mixing Measurement Sample data on run number 4.001 on the nitrogen-carbon dioxide system at the nominal experimental conditions of 400C and 500 psia are given in Table LV. The equations which will be used for making primary and secondary corrections are those that have been derived in the chapter entitled "Thermodynamics Relations." The necessary heat capacity and isothermal Joule-Thompson coefficient data are given in Table XLIII. Calculations made are: 1. Flow rates 2. Composition

-1853. Power input 4. Pressure at calorimeter outlet 5. Pressure drops across calorimeter 6. Temperature at calorimeter outlet 7. Excess enthalpy at calorimeter outlet conditions 8. Normalized excess enthalpy 9. Impurity correction for a nitrogen-ethane mixture Flow Rates (a) Flow rate of nitrogen stream The measurements on the nitrogen flow meter are given in Table LV. The density, PF, the pressure, APF, and the viscosity, TF, are calculated from this data utilizing the procedures described in the previous sections. The flow rate of nitrogen calculated from the calibration equation given in Table XXIV is FA = 0.05567 2 A mmin (b) Flow rate of carbon dioxide stream The flow rate of carbon dioxide uncorrected for impurities, FCO, calculated from the measurements on the flow meter in Table LV and the calibration equation in Table XXV is F = 0.05552 -l CO min The flow rate of impure carbon dioxide corrected for impurities is F (F ^MBM BM (FC02)( M ) Co02 (0.05552) (43988 lb/mol) (44.011 Ib/mol) = o,05549 Ibmmn

-186TABLE LV SAMPLE DATA ON ENTHALPY OF MIXING MEASUREMENT Variable Value Run Number 4.oo01 Nominal Temperature, Tn 40~C Nominal Pressure, Pn 500 psia Room Pressure, Pr 29.46 in Hg Room Temperature, TR 22.5~C Nitrogen Flow Meter Pressure on Heise gauge, Phs 1080.1 psig Heise gauge calibration, Pdiff 0.5 psi Measured pressure drop, (hH-hL) 28.03 cm dbp* Temperature of cathetometer, Tcath 23.8~C Carbon Dioxide Flow Meter Pressure on Heise gauge, Phs 1058.0 psig Heise gauge calibration, Pdiff 1.2 psi Measured pressure drop, (hH-hL) 23.55 cm dbp Power Input Voltage drop across 1 ohm resistor, Vi 0.147704 volts Voltage drop across 10 ohm resistor, Ve 0.025439 volts Temperature of resistors, Tres 26.8~C Calorimeter Pressure at calorimeter outlet pressure tap, P1 485.2 psig Measured pressure drop between: Nitrogen inlet and mixture outlet, APN 6.28 cm dbp Carbon dioxide inlet and mixture outlet, APC2 4.44 cm dbp Measured temperature, Tb 4o.oo0C Temperature of emergent stem, t 32~C Length of emergent stem, n 10~C Average reading on thermopile between inlet and outlet, AE -1.7 microvolts Average reading on thermopile between inlet gases 0.2 microvolts Additional Data Molecular weight of impure inlet CO2 stream, MBM 43.988 Mass fraction of impurities in inlet CO2 stream, wI 0.001 Dead weight gauge calibration correction (See Table XXVIII), Pcorr 0.0 psi Differential expansion coefficient for mercury-inglass in thermometer 0. 00016/~C

-187TABLE LV (Continued) Variable Value Thermometer calibration correction (See Table XXX), +0.02~C T Isoti&iMal Joule-Thompson coefficient of N2 p -0.0055 B lb psi Isothermal Joule-Thompson coefficient of CO2, B -0.0312 Btu lIb psi Heat capacity of N2, C 0.258 b B CPA lb OF Heat capacity of C02, CPB 0.275 Btu B - lb OF Excess isothermal Joule-Thompson coefficient, cpE 0.0053 Btu Ib psi Excess heat capacity, CE -0.024 Btu lb OC Cross sectional area of calorimeter inlet gas tubes, Ain 0.106 in2 Cross sectional area of calorimeter outlet gas tube, Aout 0.197 in2 Density of Nitrogen, PN 2.74 lb ft3 Density of Carbon dioxide, PCO2 4.30 lb ft3 Density of mixture containing 0.503 mole fraction nitrogen, PAB 3.15 ft3 Note: See Table LIV for values of sexp, Pair, Pbrass, Ph. Aw *dbp is dibutyl phthalate.

-188(c) Flow rate of impurities FI = IFBM (155) = (o.001)(o.05549 lb) min = o.000oooo6 lb min (d) Flow rate of mixture FABM - FA + FBM (136) = 0.03567 + 0.05549 = o. 09116 l min FBM = FA + FCO (137) = 0.03567 + 0.05552 = 0.9119 -l min Composition /FA+FI XN =FB \MB + Ib o. o3567+0.oooo6 min 0. 28.016 lb 43.988 28.016 lb mol mol = 0.503 Power Input wW r- R1 e R(R e Ve (74) where resistances Ri, Re, Rs calculated at Tre = 26.8~C from equation and constants given in Table XXXII. Hence

-189(.147704 volts 0.02549 volts 9999.8+10.00 ohms o.000 ohms 10.00 ohms 10.00 ohms5439 ot = 3.696 watts Pressure at Calorimeter Outlet Po = Pbal + PR (139) Intermediate calculations: 1. Pressure measured with dead weight gauge, Pbal. Calculated as in Equation (121) in "Pressure at Flow Meter Inlet" at Pbal = 485.2 psig. 0.0012 g 0.999645 - 8, cc Pbal = 485.2,cc 2 + 0.075 + 0.0 1 + 1.65x10-5(22.5-23) = 485.04 psig 2. True barometric pressure obtained by substituting P' = 29.46 in Hg and TR =22.5~C in Equation (110) PR = 29.40 in Hg Hence from Equation (139) Po = 485.04 psig + (29.40 in Hg)(0.4912 pH ) = 499.48 or 499.5 psia Pressure Drops across Calorimeter Pressure drops calculated are between (a) Nitrogen inlet and mixture outlet, (P1-Po) (b) Carbon dioxide inlet and mixture outlet, (PI-P0)

-190(a) Pressure drop between nitrogen inlet and mixture outlet (Pi - ) i ( [,p-PI/Aw (140) pIbp Intermediate calculations: Density of di butyl phthalate from Equation (123) dbp = 1.0408[1 - 6.16x10-4 (22.5-23.53)] 1 = 1.0413 g cc (6.28 cm dbp)(o.999645)[(l.0413 g)-(2.74 flb ) o1602 g ft (P1iPo) 1.0408 i (26.6 indb.54 Ct) c 2c psi' inch. = 0.089 psi (b) Pressure drop between carbon dioxide inlet and mixture outlet Calculated from APco2 = 4.44 cm dbp as in Equation (140): (P2-P ) = (4.44 cm dbp)(0.999645)[.o0413-(2.74)(0.01602)] (1.0408)(26.6)(2.54) = 0.063 psi Temperature at Calorimeter Outlet To = Tb + Te + Tcorr - (T1-To) (141) Intermediate calculations: 1. Emergent stem correction, Te Te = K n(Tb-t) (142) = (o.ooo00016(C)-)(10C)(40-32C) = 0.01~C 2. Temperature difference across calorimeter, (T1-To). The data between 20~C and 80~C in Table XXXIII are fitted to the equation

-191AE = -19.75 + 234.94T + 0.2419T2 (143) Temperature difference is calculated from the differentiated form of Equation (143 ) (T1-To) = 234.9+o.488T (144) -1.7 234.94+(0.4838)(40o.oo ) = -0.oo7c Hence from Equation (141) T = 40.00 + 0.01 + 0.02 - (-0.007) = 40.037~C Excess Enthalpy at Calorimeter Outlet Conditions HE (W/F)+A P * * * (145) -o corr Tcorr + AKEM + Icorr (45) Intermediate calculations: 1. Power/Flow ratio, (W/F) (W/F) = W (38) ABM 3.696 watts lb ( _ watts-minute_ (. 09116 inute 175978 wat.tu Btu = 2.304 - 2. Pressure drop correction, APcorr FA FCO0 APcorr = F PA[P1-Po] +, (PB[P-Po] (146) ABM F ABM

-192lb (=.57 min. (-0.0055 Btu (0.089 psi) (0.09119 lb-) lb psi (0'05552 -) / Btu \ +. ( -0.0312 -lb3 (o.o6 psi) (0.09119 lb > lb psi min' = -0.0014 Btu lb 3. Temperature difference correction, ATcorr ATcorr FAM CPA(T-To) + F CpT (T2-To) (147) ABM A -ABM 2B Intermediate calculations: Temperature difference (T2-To) is equated to (T1-To) as thermopile reading of 0.2 microvolts is less than the accuracy of potentiometer (+ 0.5 microvolts) F(0.05567 lb) 0 B tu \ (0.05552 l) / AT orr= lb (0.258 Btu) + (m (0in,275 Btu \ (-0.00C Btu (0.09119 n n) (0.09119 m) n (1.8 ) = -0.0055 BT 4. Kinetic energy difference, AKEM lFFA -2 FC02 2_.2 AKEM= Te. uA +- B - (148) 27A-) > A F2 02 FC02 2 I _J L ABM ABM22 2 4IFBM / (PNAin FAB \P02Ain Aout lb lb.03567 0mn 3567 (,n 2 mm min 0.0~5552 \ /.05552 b f\2 (.09119 L-)i (24. -3-)(0.106 in2 2 ft3

-193lb 2.4 (0.909119 n 2.3xlO-4 Btu min in (3-15 l)(0.197 in2) lb ft6 ftp -6 Btu = -o.5x1O b 5. Impurity correction, AICorr FBM [E A icorr [ o1 (50) where the excess enthalpy of the inlet carbon dioxide stream, HM, is given as in Equation (52) BM o 332.22 - 138.65(YA-0.5) + 187.48(YA-0.5)2 Btu YX( i-YA) ~b M-l -1 A ~~MBM Intermediate calculations: M = (.o0014)(0.9986) 32.22-138.65(0.0014-0o.5)+l87.48(o.001i4-05)2 2.90 (lM.988O v m = 0.0o1423 B Hence from Equation (50) /0.05549 lb AIm (o.o2~0l 5 P2 ) corr 0 l6) (0.01b3 lb \o. o9116 -o^ min = 0.0087 Bt Ib Hence from Equation (145) H = 2.304 - 0.0014 - 0.0035 - 0.5x10-6 + 0.0087 = 2.308 Btu lb

Normalized Excess Enthalpy nE= + P + c( ) + (T -T) (66) = 2.304 Bt + (0.0053 Btu )(500-499.48 psia) lb lb psi Btu + (-0.024 b )(40-40.0370c) lb OC = 2.308 + 0.0028 + 0.0009 Btu = 2.312 lb Impurity Correction for a Nitrogen-Ethane Mixture The example to be described is run number 16.2 on which data are given in Table XXXVI. The procedures used for all calculations other than the impurity correction are identical with those used on the nitrogencarbon dioxide mixtures. The interpreted data are given in Tables XL and XLI. The impurity correction is FI FB Acorr F= B ( H) + F (BM M,o-B,o) + (AB, o-_ABM,o) F AB 0 + F (BM,o->ABM,o) (60) Enthalpy departures are used in place of enthalpy values as discussed in the chapter entitled "Thermodynamic Relations." The data for Equation (60) are HBMo - 0o = -27.848 Btu -BM, o BM,o l- lb HB,o,O = -27.706 Btu,B.Yo.- L.Bo lb AB, o - _,o = - 8.959 Btu HBM,- = - 9.027 Bt -ABM, o -fAB3M, lb

-195AH = 4.597 Bt F - = 0.439 mass fraction FAB FT FI = 0.00482 mass ratio FAB Substituting the above values in Equation (60) yields: = (o.oo00482)(4.597)+ (0.439)[-27.848+27.706] + [-8.959+9.027] + (0.00482)[-27.848+9.027] = 0.022 - 0.062 + o.o68 - 0.091 -0o.63 Btu lb

-196Nomenclature for Appendix D Roman Alphabet Am Cross-scetional area o' indicating column of 3V-inch King manLometer AW Well factor for high pressure Meriam manometer. Needed to correct for depression of fluid level in well below measured zero level, hL, at finite pressure differences, hH-hL. Ain Cross-sectional area of gas inlet tubes in calorimeter Aout Cross-sectional area of mixture outlet tubes in calorimeter BN Second virial coefficient of nitrogen CPA Heat capacity of nitrogen CPB Heat capacity of carbon dioxide Cp Excess heat capacity Cth Calibration constant for thermocouples in calibration tank AE Microvolt reading on thermopiles or thermocouples F Flow rate FA Flow rate of nitrogen calculated from flow meter calibrations FAB Flow rate of impurity-free binary nitrogen-ethane mixture FABM Flow rate of impure nitrogen-carbon dioxide or nitrogen-ethane mixture F' Flow rate of impure nitrogen-carbon dioxide mixture calculated with uncorrected carbon dioxide flow rate, FCo FB Flow rate of impurity free etnane FBM Flow rate of impure carbon dioxide stream corrected for impurities FCO2 Flow rate of carbon dioxide uncorrected for impurities FI Flow rate of impurities G Ratio of local gravity (980.317 gals) to standard gravity (980.665 gals) HkCg O Enthalpy of impurity-free binary nitrogen-ethane mixture at (P0,T0) LH o Zero pressure enthalpy of impurity free binary nitrogen-ethane mixture at (P,,T.)

-197-ABM,o Enthalpy of impure nitrogen-ethane mixture at (Po,To) H0Mo Zero pressure enthalpy of impure nitrogen-ethane mixture at (Po,To) -ABM, o XH Enthalpy of pure ethane at (Po,To) Zero pressure enthalpy of pure ethane at (Po,To) Bo HBMo Enthalpy of impure ethane at (PoTo) 0Mo Zero pressure enthalpy of imrpure ethane at (Po0To) HE Excess enthalpy of impure carbon dioxide stream at (PoTo) -BM, o HE Excess enthalpy at nominal experimental conditions, (Pn,Tn) AHo Experimentally measured enthalpy difference obtained by applying pressure drop, temperature and kinetic energy difference corrections to the power/flow ratio HTE Excess enthalpy at experimentally measured calorimeter outlet conditions, (PO,To) Ah Measured pressure drop in flow meter corrected for scale expansion and for well factor, AW. hH Average cathetometer reading of fluid level in high pressure manometer hL Average cathetometer reading of zero level of fluid in high pressure manometer AIcorr Impurity correction applied to enthalpy difference, ALH K Differential coefficient of expansion of mercury-in-glass for thermometer AKEM Kinetic energy difference between inlet and outlet gases in calorimeter MBM Molecular weight of impure carbon dioxide stream MCO2 Molecular weight of carbon dioxide MN Molecular weight of nitrogen m 1 Weight of full cylinder number 1 min.,, Weight o(' empt. cyli.rlndr number 1 r~ We'.i.ht oP I' u'l..vl.i 1 r r' i bl'r 2 me4 Weight of empty cylinder number 2 mct Mass of gas in calibration tank during volume determinations

-198mexp Coefficient of volume expansion of mercury Napp Mass of nitrogen discharged from cylinders into calibration app tank Nf Mass of gas in filled calibration tank after stopping gas flow Ni Mass of gas in evacuated calibration tank prior to starting gas flow Nline Residual gas in line connecting cylinders to calibration tank Nvac Mass of gas in initially evacuated calibration tank Nwell Mass of gas in well of 56-inch King manometer n Length of emergent stem of thermometer P Pressure (P1-Po) Pressure difference between nitrogen inlet and outlet mixture in calorimeter (P2-Po) Pressure difference between carbon dioxide inlet and outlet mixture in calorimeter P' Nominal gauge pressure reading on dead weight gauge bal Pbal True gauge pressure reading on dead weight gauge Pcorr Calibration correction for dead weight gauge APcorr Pressure drop correction applied to power/flow ratio APc2 Measured pressure drop between inlet carbon dioxide and outlet mixture in calorimeter P' Measured gauge pressure in filled calibration tank ctf Pctf Absolute pressure in filled calibration tank Pcti Absolute pressure in initially evacuated calibration tank Pdiff Heise gauge calibration correction PF Pressure at flow meter inlet pressure tap APF Pressure drop across flow meter Ph Head of oil between dead weight gauge and U-leg Phs Average pressure in flow meter read on Heise gauge Pm Mean pressure in flow meter

-199AP Measured pressure drop between inlet nitrogen and outlet mixture in calorimeter Pn Nominal pressure PO Pressure at calorimeter outlet pressure tap Pt Room pressure measured on barometer R PR True barometric pressure obtained from PI Pti Room pressure measured on barometer prior to evacuating calibration tank PRi True barometric pressure obtained from PRi R Gas constant Re Standard resistor, 10 ohms -ominal Ri Standard resistor, 1 ohin nominal Rs Standard resistor, 10,000 ohms nominal sexp Linear coefficient of expansion T Temperature T1 Temperature of inlet nitrogen to calorimeter (T1-To) Temperature difference between inlet nitrogen and outlet mixture in calorimeter (T2-To) Temperature difference between inlet carbon dioxide and outlet mixture in calorimeter Tb Measured calorimeter bath temperature Tcath Temperature of cathetometer T Thermometer calibration correction corr ATcorr Temperature difference correction applied to the power/flow ratio Tt Temperature of bath fluid measured when calibration tank is ctf filled T'i t rtTemperatuIre ) of' as in filled calibration tank It'Icnir. cral,ur 1 atlah liluid measured. Wl.tln calibratioi tank is 1 1,. i e v acuat;ed Tat+ Temperature of gas in evacuated calibration tank

-200 - Te Emergent stem correction for thermometer TF Temperature of flow meter bath Tn Nominal temperature To Temperature at calorimeter outlet TR Room temperature Tref Temperature of reference junction for calibration tank thermocouples res Tres Temperature of standard resistors TRi Room temperature prior to evacuating calibration tank Tth Temperature measured by thermocouples in calibration tank t Temperature of emergent stem of thermometer _UA Mean velocity of inlet nitrogen in calorimeter UB Mean velocity of inlet carbon dioxide in calorimeter Mean velocity of outlet nitrogen-carbon dioxide mixture in calorimeter Vp Approximate volume of calibration tank Vct Volume of calibration tank normalized to 20~C VCt Volume of calibration tank at Tctf Vcti Volume of calibration tank at Tcti Ve Voltage drop across standard resistor Re Vi Voltage drop across standard resistor Ri Vline Volume of line connecting cylinders to calibration tank Vt Uncorrected volume of calibration tank at TCtf Vu Volume of union connecting solenoid valve to calibration tank Vwell Volume of well of 36-inch King manometer vexp Volume expansion coefficient W Power input to calorimeter (W/F) Power/flow ratio WI Mass fraction of impurity in carbon dioxide stream

-201XN Mole fraction nitrogen in mixture exiting calorimeter y/A Mole fraction nitrogen in carbon dioxide stream ZH Constant defined in Table LII ZL Constant defined in Table LII ZN Compressibility factor of nitrogen Greek Alphabet TIN Viscosity of nitrogen TIF Viscosity of nitrogen at conditions in flow meter Q Time period of gas collection PAB Density of nitrogen-carbon dioxide mixture Pair Density of air Pbrass Density of brass pCO2 Density of carbon dioxide po Density of dibutyl phthalate at 23.3~C dbp Pdbp Density o: dibutyl phthalate pF Density of nitrogen at conditions in flow meter p0 Density of mercury at 0~C PHg pN Density of nitrogen CPA Isothermal Joule-Thompson coefficient of nitrogen cPB Isothermal Joule-Thompson coefficient of carbon dioxide CPE Excess isothermal Joule-T.ompson coefficient of nitrogencarbon dioxide mixture

BI BILIO( ItAPHY 1. Abdullaev, Y. A., Zhur. I'Viz. Khim., 13, 986 (1939). 2. Ahlert, R. C., Ph.D. Thesis, Lehigh University (1964). 3. Altunin, V. V. and D. 0. Kutznetsov, Teploenergetika, 16 (8), 82 (1969). 4. Amirkhanov, K. I., A. M. Kerimov and B. G. Alibekov, The Application of Ultra-Sound to the Study of Matter, No. 13, Mosk. Obl. Ped. In-t. (1961) p. 89. 5. Amirkhanov, K. I., A. M. Kerimov and B. G. Alibekov, Critical Phenomena and Fluctuations in Solutions, Izd. Akad. Nauk. SSSR (1960) p. 5. o. Amirkhanov, K. I., N. G. Polikhronidi and R. G. Batyarova, Teploenergetika, 17 (3), 70 (1970). 7. Bakx, I. N. and H. F. P. Knaap, Physica, 39, 1 (1968). 8. Beattie, J. A., C. Hadlock and N. Poffenberger, J. Chem. Phys. 3, 93 (1935). 9. Beattie, J. A., G. J. Su and G. L. Simard, J. Am. Chem. Soc., 61, 926 (1939). 10. Beenakker, J.J.M. and J.M.J. Coremans, Second Symposiumn on Thermophysical Properties, ASME, New York (1962) p. 3, 11. Beenakker, J.J.M., B. Van Eijnsbergen, M. Knoester, K. W. Taconis and P. Zandbergen, Third Symposium on Thermophysical Properties, ASME, New York (1965) p. lk4. 12. Benedict, M., G. B. Webb and L. C. Rubin, J. Chem. Phys., 8, 334 (l_94o). 13. Benedict, M., G. B. Webb and L. C. Rubin, J. Chem. Phys., 10, 747 (1942). 14. Benedict, M., G. B. Webb and L. C. Rubin, Chem. Eng. Prog., 47, 419 (1951). 15. Bennewitz, K. and N. Andreewa, Z. Phys. Chem., A142, 37 (1929). 16. Bhirud, V. L. and J. E. Powers, Thermodynamic Properties of a 5 Mole Percent Propane in Methane Mixture, Report to the Natural Gas Processors Association, Tulsa, Oklahoma (1969). 17. Bird, R. B., W. E. Stewart and E. N. Lightfoot, Transport Phenomena, John Wiley, New York (1963). 18. Blagoi, Yu. P. and N. S. Rudenko, Izvest. Vysshikh. Ucheb. Zavedinii, Fiz., No. 6, 145 (1958). -202

-20319. Bloomer, 0. T. and K. N. Rao, Inst. Gas Tech. ies. Bull., 18, (1952). 20. Brewer, J, Determination of Mixed Virial Coefficients, CFSTI, AD 663-448 (1967. 21. Brilliantinov, N. A, Zhur. Tekh. Fiz., 18, 1113 (1948). 22. Brombacher, W. G., D. P. Johnson and J. L. Cross, Mercury Barometers and Manometers, Nat. Bur. Standards Monograph 8 (1964). 23. Calado, J.C.G. and L.A.K. Staveley, Rev. Port. Quim., 11, 65 (1969). 24. Charnley, A., G. L. Isles and J. R. Townley, Proc. Roy. Soc. (London), A218, 133 (1958). 25. Cooper, H. W. and J. C. Goldfranck, Hydrocarbon Process., 46 (12), 14 (1967) 26. Cottrell, T. L., R. A. Hamilton and R. P. Taubinger, Trans. Farad. Soc., 52, 1310 (1956). 27. Crain, R. W. and R. E. Sonntag, J. Chem. Eng. Data, 12, 73 (1967). 28. Cross, J. L., Reduction of Data for Piston Gage Pressure Measurements, Nat. Bur. Standards Monograph 65 (1964).. 29. Cullen, E. J. and K. A. Kobe, AIChE J., 1, 452, (1955). 30. Curl, R. F., Jr. and K. E. Pitzer, Ind. Eng. Chem., 50, 265 (1958). 31. Cutler, A.J.B. and J. A. Morrison, Trans. Farad. Soc., 61, 429 (1965). 32. Dana, L. I. and G. H. Zenner, Chem. Eng. Prog. Symp. Ser., 59 (44) 36 (1963). 33. Davies, R. H., A. G. Duncan, G. Saville and L.A.K. Staveley, Trans. Farad. Soc., 63, 855 (1967). 34. Din, F., Thermodynamic Functions of Gases, ed. F. Din, Vol. 3, Butterworths, London (1961). 35. Dodge, B. F. and A. K. Dunbar, J. Am. Chem. Soc., 49, 591 (1927). 36. Duncan, A. G. and L.A.K. Staveley, Trans. Farad. Soc., 62, 548 (1966). 37. Eakin, B. E. and R. T. Ellington First Symosium on Thermophysical Properties, ASME, New York (1959 P. 195. 38. Eakin, B. E., R. T. Ellington and D. C. Gami, Inst. Gas. Tech. Res. Bull., 26, (1955). 39. Eakin, B. E., K. E. Staxlling, J. P. Dolan and R. T. Ellington, J. Chem. Eng. Data, 7, 33 (1962).

-20440. EllingtonR.R T. B. Ea'kin, J. D. Parent, D. C. Gamri and 0. T. B1lo'omer-, First yImpos i1u 1m i' h:rmoph sical Properties, ASMI, New York (09fl) p. i8(o. 41. I'(dwardJs, A. E1. arid. IW. lo. ov(J:_ro, J. Am. Chem. oc.,, _,2816 ( 1) 42 ). 42. Ernst, G., Proceedings of First International Conference on Calorimetry and Thermodynamics, Warsaw, Poland (1969). 43. Eubank, P. T. and B. F. Fort, Can. J. Chem. Eng., 47, 177 (1969). 44. Fastovski, V. G. and Y. V. Petrovski, Zh. Fiz. Khim., 31, 2117 (1957). 45. Faulkner, R. C., Ph.D. Thesis, University of Michigan (1959). 46. Fuchs, P., Z. Physik. Chem., 92, 641 (1918). 47. Fuks, S. and A. Bellemans, Bull. Soc. Chim. Belg., 76, 290 (1967). 48. Furtado, A. W., D. L. Katz, and J. E. Powers, Personal communication, University of Michigan, Sept. (1969). 49. Goldman, K. and N. G. Scrase, Physica, 44, 555 (1969). 50. Goodwin, R. D., Jour. Res. Nat. Bur. Standards —A, 73, 25 (1969). 51. Goodwin, R. D. and L. A. Weber, Jour. Res. Nat. Bur. Standards —A, 73, 1 (1969). 52. Goodwin, R. D. and L. A. Weber, Jour. Res. Nat. Bur. Standards —A, 73, 15 (1969). 53. Grossman, E. D., Ph.D. Thesis, University of Pennsylvania (1965). 54. Gusak, I. M., J. Tech. Phys. (USSR), 7, 796 (1937). 55. Hall, L. A., Nat. Bur. Standards Tech. Note No. 383 (1969). 56. Haney, R.E.D., and H. Bliss, Ind. Eng. Chem., 36, 985 (1944). 57. Head, J. F., Ph.D. Thesis, University of London (1960). 58. Hildebrand, J. H. and R. L. Scott, The Solubility of Non-Electrolytes, Reinhold (1950). 59. Hilsenrath, J. T., et al., Tables of Thermal Properties of Gases, NBS Circular 564 (1955).. 60. Hobson, M. and J. H. Weber, Petroleum Process., 12 (9), 153 (1957). 61. Hobson, M. and J. H. Weber, Chem. Eng., 64 (12), 272 (1957). 62. Hoover, A. E., I. Nagata, T. W. Leland, Jr. and R. Kobayashi, J. Chem. Phys., 48, 2633 (1968).

-20563. Hougen, 0. A., K. M. Watson and R. A. Ragatz, Chemical Process Principles., Part II: Thermodynamics, John Wiley, New York (1962). 64. Hsi, C. and B. C-Y. Lu, J. Chem. Eng. Data, 14, 38 (1969). 65. Huff, J. A. and T. M. Reed, J. Chem. Eng. Data, 8, 306 (1963). 66. Hust, J. C., Nat. Bur. Standards Tech. Note No. 137 (1962). 67. International Union of Pure and Applied Chemistry, Info. Bull. No. 32 (1968). 68. Ishkin, I. P. and M. G. Kaganer, Soviet Phys. Tech. Phys., 1, 2255 (1956). 69. Jacobsen, J. A. and R. E. Barieau, Paper presented at the Symposium on Enthalpy of Mixtures, 159th National Meeting of ACS, Houston Texas, Feb. 22-24 (1970). 70. Jeener, J., Rev. Sci. Instr., 28, 263 (1957). 71. Jones, M. L., Jr., Ph.D. Thesis, University of Michigan (1961). 72. Kaminishi, G. and T. Toriumi, J. Chem. Soc. Japan, 9, 175 (1966). 73. Kestin, J., Y. Kobayashi and R. T. Wood, Physica, 32, 1065 (1966). 74. Kestin, J. and W. Leidenfrost, First Symposium on Thermophysical Properties, ASME, New York (1959) p. 321. 75. Keunen, J. P., T. Verschoyle and A. T. Van Urk, Proc. Roy. Soc. (London), 26, 49 (1923). 76. Khazanova, N. E. and L. S. Lensevskaya, Khim. Prom., 41, 344 (1965). 77. Klein, R. R., Ph.D. Thesis, Yale University (1969). 78. Knaap, H.F.P., Physica, 28, 343 (1962). 79. Knaap, H.F.P., M. Knoester and J.J.M. Beenakker, Physica, 27, 309 (1961). 80. Knobler, C. M., H.F.P. Knaap and J.J.M. Beenakker, Physica, 26, 142 (1960). 81. Knobler, C. M., R.J.J. Van Heijningen and J.J.M. Beenakker, Physica, 27, 296 (1961). 82. Knoester, M., K. W. Taconis and J.J.M. Beenakker, Physica, 33, 389 (1967). 83. Koeppe, W., Kaltetechnik, 11, 363 (1959). 84. Koppel, L. B. arl J. M. Smith, J. Chem. Eng. Data, 2, 437 (1960).

-20685. Kotousov, L. S. and V. V. Baranyuk, Zh. Tekh. Fiz., 39, 372 (1969). 86. Krichevskii, J. R., N. E. Khazanova, L. S. Lensevskaya and L. Yu. Sandalova, Khim. Prom., 38, 169 (1962). 87. Krichevskii, J. R. and V. P. Markov-, Zh. Fiz. Khim., 14, 101 (1940). 88. Lambert, M., Phys. Rev Letters, 4, 555 (1960). 89. Lambert, M. and M. Simon, Physica, 28, 1191 (1962). 90. Lee, J. I. and A. E. Mather, Personal Communication, University of Alberta, Jan. 23 (1970). 91. Liley, P. E., J. Chem. Eng. Data, 4, 238 (1959). 92. Luken, J. A. and J. Johnson, J. Chem. Eng. Data, 4, 176 (1959). 93. Lunbeck, R. J. and A.J.H. Boerboom, Physica, 17, 76 (1951). 94. Lunbeck, R. J., A. Michels and G. J. Wolkers, Appl. Sci. Res., A3, 197 (1952). 95. Mackey, B. H. and N. W. Krase, Ind. Eng. Chem., 22, 1062 (1930). 96. Mage, D. T., Ph.D. Thesis, University of Michigan (1964). 97. Mage, D. T., M. L. Jones, Jr., D. L. Katz and J. R. Roebuck, Chem. Eng. Prog. Symp. Ser., 59 (44), 61 (1963). 98. Manker, E. A., Ph.D. Thesis, University of Michigan (1964). 99. Masi, J. F., Trans. Am. Soc. Mech. Eng., 76, 1067 (1954). 100. Mastinu, G., J. Chem. Phys., 47, 338 (1967). 101. Mather, A. E., Ph.D. Thesis, University of Michigan (1967). 102. Mather, A. E., D. L. Katz and J. E. Powers, Trans. Farad. Soc., 64, 2939 (1968). 103. Mathot, V., Nuovo Cimento, 9, Suppl. No. 1, 356 (1958). 104. Mathot, V., Acad. Roy. Belg. Classe Sci., Mem., Collection in 8, 33, 32 (1963 105. Mathot, V., L.A.K. Staveley, J. A. Young and N. G. Parsonage, Trans. Farad. Soc., 52, 1488 (1956). 106. McCullough, J. P. and D. W. Scott, Experimental Thermodynamics. Volume I: Calorimetry of Non-Reacting Systems, Butterworths, London (196a8)... 107. Michels, A., A. Bijl and C. Michels, Proc. Roy. Soc. (London), A160, 376 (1937).

-207108. Michels, A., B. Blaise and C. Michels, Proc. Roy. Soc. (London), A160, 358 (1937). 109. Michels, A. and A.J.H. Boerboem, Bull. Soc. Chim. Belg., 62, 119 (1953). 110. Michels, A., A. Botzen and W. Schurman, Physica, 23, 95 (1957). 111. Michels, A. and S. R. De Groot, Appl. Sci. Res., Al, 94 (1948). 112. Michels, A. and R. 0. Gibson, Proc. Roy. Soc. (London), A134, 288 (1931). 113. Michels, A. and C. Michels, Proc. Roy. Soc. (London), A153, 201 (1935). 114. Michels, A. and G. W. Nederbragt, Physica, 6, 656 (1939). 115. Michels, A., H. W. Schamp and W. De Graaf, Physica, 20, 1209 (1954). 116. Michels, A., W. Van Straaten aiAd J. Dawson, Physica, 20, 17 (1954). 117. Michels, A., T. Wasenaar, J. M, Levelt and W. De Graaf, Appl. Sci. Res., A4, 381 (1954). 118. Mickley, H. S., T. K. Sherwood and C. E. Reed, Applied Mathematics in Chemical Engineering, McGraw-Hill, New York (1957. 119. Miller, J. G. and R. A. Gorski, J. Am. Chem. Soc., 75, 550 (1953). 120. Mills, J. R. and F.J.L. Miller, Can. Chem. Proc. Ind., 29, 651 (1945). 121. Montgomery, J. B. and T. De Vries, J. Am. Chem. Soc., 64, 2372 (1942). 122. Mrazek, R. V. and H. C. Van Ness, AIChE J, 7, 190 (1961). 123. Nathan, D. I., Brit. Chem. Eng., 12, 223 (1967). 124. Newitt, D. M., M. TU. Pai, N. R. Kuloor aLnd J.A.W. ITuggill, Thermodynamic Functions of- Gases, ed. I'. Din, Vol. -I, IButttrworths-, London (1962). 125. Opfell, J. B., W. (. Schlinger and B. H. Sage, Ind. Eng. Chem., 46, 1286 (1954). 126. Otto, J., Handbuch der Experimental Physik, Vol. III, Part 2, Akademische Verlogsgesellschaft M.B.H., Leipzig (1929). 127. Otto, J. and L. Holborn, Z. Physik., 10, 367 (1922). 128. Pfefferle, W. C., J. A. Goff and J. G. Miller, J. Chem. Phys., 23, 509 (1955).

129. Pollitzer, F. and E. Strebel, Z. Physik. Chem., 110, 768 (1924). 130. Pool, R.A.H., G. Saville, T. M. Herrington, B.C.D. Shields and L.A.K. Staveley, Trans. Farad. Soc., 58, 1692 (1962). 131. Pool, R.A.H. and L.A.K. Staveley, Trans. Farad. Soc., 53, 1186 (1957). 132. Powers, J. E., Proc. Ann. Cony., Nat. Gas Process. Assoc., Tech. Papers, 48, 16 (1969). 133. Prigogine, I., The Molecular Theory of Solutions, North Holland Publ., Amsterdam (1957). 134. Reamer, H. H., R. H. Olds, B. H. Sage and W. N. Lacey, Ind. Eng. Chem., 36, 956 (1944). 135. Reamer, H. H., F. T. Selleck, B. H. Sage and W. N. Lacey, Ind. Eng. Chem., 44, 198 (1952). 136. Rivkin, S. L. and V. M. Gukov, Teploenergetika, 15 (10), 109 (1968). 137. Roebuck, J. R., Proc. Amer. Acad. Arts and Sci., 60, 537 (1925). 138. Roebuck, J. R., Proc. Amer. Acad. Arts and Sci., 64, 287 (1930). 139. Roebuck, J. R., T. A. Murrel and E. E. Miller, J. Am. Chem. Soc., 64, 400 (1942). 140. Roebuck, J. R. and H. Osterberg, Phys. Rev., 48, 450 (1935). 141. Rossini, F. D., et al., Selected Values of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds, Carnegie Press, Pittsburgh (1953). 142. Sage, B. H. and W. N. Lacey, Some Properties of the Lighter Hydrocarbons, Hydrogen Sulfide and Carbon Dioxide, Am. Pet. Inst., Proj. 37, New York (1959). 143. Sage, B. H., D. C. Webster and W. N. Lacey, Ind. Eng. Chem., 29, 658 (1937). 144. Sass, A., B. F. Dodge and R. H. Bretton, J. Chem. Eng. Data, 12, 168 (1967). 145. Saurel, J. R., Genie Chim., 79 (12), 44 (1958). 146. Savini, C. G., D. R. Winterhalter, L. H. Kovach and H. C. Van Ness, J. Chem. Eng. Data, 11, 40 (1966). 147. Savini, C. G. and D. R. Winterhalter and H. C. Van Ness, J. Chem. Eng. Data, 10, 168, 171 (1965). 148. Scott, R. L., J. Chem. Phys., 25, 193 (1956).

-209149. Sehgal, I.J.S., V. F. Yesavage, A. E. Mather and J. E. Powers, Hydrocarbon Process., 47, No. 8, 137 (1968). 150. Seligmann, P., D. 0. Edwards, R. E. Sarwinski and J. T. Tough, Phys. Rev., 181, 415 (1969). 151. Seshadri, D. N., D. S. VishWanath and N. R. Kuloor, J. Chem. Eng. Data, 12, 70 (1967). 152. Shan'a, M. Y. and F. B. Canfield, Trans. Farad. Soc., 64, 2281 (1968). 153. Shrock, V. E., N.A.C.A. Tech. Note No. 2838 (1952). 154. Simon, M., Physica, 29, 1079 (1963). 155. Smith, G. E., R. E. Sonntag and G. J. Van Wylen, Advan. Cryogen. Eng., 8, 162 (1962). 156. Smithsonian Physical Tables, Publication 4169, Smithsonian Institute, Washington, D.C. (1954). 157. Sommers, H. S., Jr., W. E. Keller and J. G. Dash, Phys. Rev., 92, 1345 (1953). 158. Sprow, F. B. and J. M. Prausnitz, AIChE J, 12, 780 (1966). 159. Stockett, A. L. and L. A. Wenzel, AIChE J, 10, 557 (1964). 160. Stotler, H. H. and M. Benedict, Chem. Eng. Prog. Symp. Ser., 49 (6), 25 (1953). 161. Swindells, J. F., Calibration of Liquid-in Glass Thermometers, Nat. Bur. Standards Monograph 90 (1965). 162. Tester, H. E., Thermodynamic Functions of Gases, ed. F. Din, Vol. 3, Butterworths (1961). 163. Timrot, D. L. and V. P. Borisoglebskii, Soviet Phys. JETP, 11 (6), 1248 (1960). 164. Trautz, M. and 0. Emert, Z. Anorg. Chem., 150, 227 (1926). 165. Tsaturyants, A. B., A. R. Mamedov and R. G. Eivazova, Dokl. Akad. Nauk. Azerb. SSSR, 18, (11), 23 (1962). 166. Tsiklis, D. S., Dokl. Akad. Nauk. SSSR, 79, 289 (1951). 167. Tsiklis, D. S., and A. I. Kulikova, Russian J. Phys. Chem., 39 928 (1965). 168. Tsiklis, D. S. and E. V. Polyakov, Zh. Fiz. Khim., 41, 3145 (1967).

-_10 - Nlioi.'I'siklis, D. S. and ]E. V. Polyakov:,ov:i; t; Phys. Dokl., I1, 901 170. Van Eijnsbergen, 1. aud J.J.M. Beenakker, Physica, 39, 499 (1968). 171. Voronel1, A. V., Yu. R. Chaskin, V. A. Popov and V. G. Simkin, Soviet Phys. JETP, 18, 568 (1964). 172. Vukalovich, M. P. and V. V. Altunin, Thermophysical Properties of Carbon Dioxide, Collet's, London (19YI). 173. Vukalovich, M. P., V. V. Altunin, K. Bulle, D. S. Rasskozov and D. Ertel, Teploenergetika, 16 (11), 70 (1969). 174. Vukalovich, M. P., V. V. Altunin, K. Bulle, D. S. Rasskozov and D. Ertel, Teploenergetika, 17 (5), 60 (1970). 175. Vukalovich, M. P., V. V. Altunin and A. N. Gureev, Teploenergetika, 11 (9), 83 (1964). 176. Vukalov-ich, M. P., V. V. Altunin and A. N. Gureev, Teploenergetika, 12 (7), 75 (1965). 177. Vukalovich, M. P. and A. N. Gureev, Teploenergetika, 11 (8), 112 (1964). 178. Vukalovich, M. P. and Ya. F. Masalov, Teploenergetika, 11 (7), 103 (1964). 179. Vukalovich M. P. and Ya. F. Masalov, Teploenergetika, 11 (11), 91 (1964). 180. Weber, L. A., Nat. Bur. Standards Report No. 9710A (1968). 181. Wilson, G. M., R. G. Clark and F. L. Hyman, Ind. Eng. Chem., 60, 58 (1968). 182. Winterhalter, D. R. and H. C. Van Ness, J. Chem. Eng. Data, 11, 189 (1966). 183. Workman, E. J., Phys. Rev., 37, 1345 (1931). 184. Yesavage, V. F., A. E. Mather, D. L. Katz and J. E. Powers, Ind. Eng. Chem., 59 (11), 35 (1967). 185. Yu, P., I. M. Elshayal and B. C-Y. Lu, Can. J. Chem. Eng., 47, 495 (1969). 186. Zaalishvili, S. D., Uspekhii Khim., 24, 759 (1955). 187. Zandbergen, P. and J.J.M. Beenakker. Physica, 33, 343 (1967).

UNIVERSITY OF MICHIGAN 3 9011111 111011113026 8893 0302 8893s oz