THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING VAPOR-LIQUID EQUILIBRIUM RATIOS IN HYDROGEN HYDROCARBON MIXTURES Howard Fo Silver A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The University of Michigan Department of Chemical and Metallurgical Engineering 1961 May, 1961 IP-B

Doctoral Committee: Professor G. Brymer Williams, Chairman Associate Professor Lee 0, Case Professor Donald L, Katz Professor Joseph J. Martin ii

ACKNOWIEDGMNT I would like to take this opportunity to express my appreciation to those who have given me support and encouragement during the period of time that I have worked on this dissertation. Mr. J. J. Merrill of the California Research Corporation was one of the first to encourage me to undertake graduate research on the doctors~ al level. Professor Wayne C. Edmister, formerly of California Research Corporation, participated actively in the initial phases of this work. Without his encouragement, this work would most likely have remained unattempted. At the University of Michigan, I am particularly indebted to my doctoral committee chairman, Professor G. Brymer Williams for his interest and support throughout my entire graduate school career. I also appreciate the support of the members of my committee; Associate Professor Lee 0. Case, Professor Donald L. Katz, and Professor Joseph J. Martin. Frank Drogosz, of the Chemical and Metallurgical Engineering Department staff, not only played an indispensable role in the construction of the experimental apparatus, but also worked beyond any reasonable expectation to provide the best possible analytical results from the mass spectrometer. Further, the staff of the Computing Center at the University of Michigan provided a substantial amount of time on the IBM 704 computer for correlation purposes. Finally, I am indebted for the financial support provided me by the Chemical and Metallurgical Engineering Department in the form of funds iii

for experimental equipment, for hydrocarbons and hydrogen used in this work, and for the use of the department mass spectrometer, by the Shell Oil Company in the form of a fellowship, and by the Esso Research and Engineering Company in the form of a research grant. iv

TABLE OF CONTENTS Page ACKNOWLEDTDG MENT l, *..,... v.. 4 *.,.... *, *.... iii LIST OF TABLES,..,,...................................,. vii LIST OF FIG ES U.............................,..........ix LIST OF APPEN DICES,.....e.**.........................., x NOMENCLATURE............... * e..... O 4.... *......... i ABSTRACT..,........#......,......... a... *. * e * * * * * * *xiv INTRODUCTION..........................i............,........,1 EXPERIMENTAL CONDITIONS OF STUDY. *........................... 5 MATERIALS USED IN STUDY................................... 6 EQUIPMENT DESIGN.............*.......,................. 7 DESCRIPTION OF THE EQUIPMENT................................... 9 Feed System............................................9 Equilibrium Section.................e.....i. 9 Sampling System....................................... 13 PROCEDURE,.....................................,..........,....15 Feeding Components........................ 15 Equilibriwun.*..*.............. o.................. 15 Sampling...*. 4,.* * *....... e * * *..*. * * 16 ANALYSIS.. t. t a a............................. 19 DISCUSSION OF ERRORS *.......*............................rr 20 Measurement of Temperature and Pressure.,.~.....,... 20 Sampling Errors,,.**,,....... e....... e......... 2o 1.21 SMIOOHEDD EXPERBIMENAL DATA....**....o.,****, 24 CORRELATION... a a. a........ +. * * a....... * 30 Introduction... r. *.............. *........ * a, o 30 Single Equation of State Method,. *...............,..... 31 Two Equations of State Method,,**,.,...**..*......... 36 v

TABLE OF CONTENTS CONT'D Page Vapor Phase Fugacity Coefficient............. 77 Liquid Activity Coefficient.................. 46 Fugacity Coefficient of the Pure Liquid Component.......................................... 49 Phase Rule Considerations.,,......................., 51 Outline of Correlation Procedure........................ 54 CONCLUSIONS.................................................... 63 APPENDICES.................................................. 66 BIBLIOGRAPHY........ o............................................. 130 vi

LIST OF TABLES Table Page I Purity of Materials................................... 6 II Summary of Experimental Results........................ 26 III Summary of Experimental Results at 100~F.............. 27 IV Summary of Experimental Results at 200~F............. 28 V Interaction Virial Coefficients for HydrogenHydrocarbons...................................... 46 VI Coefficients in the Pure Liquid Fugacity Coefficient Equations...<......,....*............... 51 VII Physical Constants................................... 51 VIII Vapor-Liquid Equilibrium Ratios for Benzene Using the Virial Equation of State....................... 58 IC Vapor-Liquid Equilibrium Ratios for Cyclohexane Using the Virial Equation of State........................ 59 X Vapor-Liquid Equilibrium Ratios for Hexane Using the Virial Equation of State............................... 60 XI Vapor-Liquid Equilibrium Ratios for Hydrogen Using the Virial Equation of State,....................... 61 XII Solubility Parameters........................... 70 XITI Thermocouple Calibration Data............. 72 XIV Gauge Tester Evaluation............................... 73 XV Equilibrium Data Sources for Hydrogen-Hydrocarbon Systems............................................ 74 XVI Equilibrium Data Sources for Hydrocarbon-Hydrocarbon Systems................ o.... o. o...... o....... 74 XVII Tabulated Calculation Results........................ 77 XVTI2 AAnalyses of Cyclohexane on Hyd2ogen-F-,e Basis,., 9 vii

LIST OF TABLES CONT'D Table Page XIX Analysis of Hydrogen Compositions for Run 33........ 94 XX Complete Experimental Data Results.,.............. 95 XXI Repetitive Analyses Results........................ 99 XXII Fortran Program for Prediction of Experimental Results Using IBM 704 Digital Computer..,......., 126 viii

LIST OF FIGURES Figure Page 1 Flow Diagram of Experimental Equipment................. 10 2 Sketch of Equilibrium Cell and the Magne-Dash Shaker Assembly...................................... 11 3 Solubility of Hydrogen in the Liquid Phase at Constant Temperature................................... 29 4 Second Virial Coefficient of Benzene,....,.,,.... 40 5 Second Virial Coefficient of Cyclohexane,............. 41 6 Second Virial Coefficient of Hexane.................... 42 7 Second Virial Coefficient of Hydrogen.,............. 43 8 Second Virial Interaction Coefficient for Hydrocarbon Mixtures,,. * v.o..................................... 44 9 Generalized Second Virial Interaction Coefficients for Hydrogen Systems......................~..... 45 10 Hydrogen Vapor-Liquid Equilibrium Composition Ratios in Hexane-Benzene............,.................... 102 11 Hydrogen Vapor>Liquid Equilibrium Composition Ratios in Hexane-Cyclohexane,............................ 103 12 Hydrogen Vapor-Liquid Equilibrium Composition Ratios in Benzene "Cyclohexane................. 104 13 Hydrogen Vapor-Liquid Equilibrium Ratios at 500 Psi as a Fumaction of UOP K Factors of Hydrogen Free Solvent... 105 r14 1Hydrogen Vapor-Liquid Equilibrium Ratios at 1000 Psi as a F-iction of UOP K Factors of Hydrogen Free Solvent... 106 15 Vapor-Liquid Equilibrium Composition Ratios of Hydrogen as F-nction of the Solvents UOP K Factor............ 107 16 Benzene Vapor-Liquid Equilibrium Composition Ratios.... 109 17 Cyclohexane VaporLiquid Equilibrium Composition Ratios 110 18 Hexane Vapor-Liquid Equilibrium Composition Ratios..... 111 19 Vapor-Liquid Equilibrium Composition Ratios of Hydrocarbons in Presence of Hydrogen as a Function of the System Pressure and the Ratio of Hydrocarbon Boiling Point Temperature to System Temperature............. 112 ix

LIST OF APPENDICES Page SOLUBILITY PARAMETER ESTIMATION,.................... 67 THERMOCOUPLE CALIBRATION......................................... 71 CHANDLER GAUGE TESTER CALIBRATION................................ 73 EQUILIBRIUM DATA SOURCES FOR BINARY SYSTEMS...................... 74 CALCULATION RESULTS............................................. 75 EXPERIMENTAL DATA...................................... 92 GRAPHICAL PRESENTATION OF THE DATA............................... 100 SAMPLE CALCULATION............................................... 114 x

NOMENCLATURE AN constant in Chao's equation A,B constants in Redlich-Kwong Equation of State AB constants in Van Laar Equation B(T) second virial coefficient C(T) third virial coefficient D vapor product stream flow rate E internal energy F feed stream flow rate F. Fahrenheit (G Gibbs Free Energy H enthalpy K vapor-liquid equilibrium composition ratio K. Kelvin L liquid product stream flow rate N number P pressure PoE. probable error R gas constant S entropy T temperature V volume a,b constants in van der Waal's Equation of State a,b constants in the Redlich-Kwong Equation of State n moles xi

x mole fraction in the liquid phase y mole fraction in the vapor phase z compressibility factor A difference A constant in hydrogen second virial coefficient quantum mechanical correlation ~a coefficient of thermal expansion 6 solubility parameter 7 liquid activity coefficient G function relating virial coefficients to volume V pure component liquid fugacity coefficient p density a standard deviation CP vapor phase fugacity coefficient.x accentric factor wt pseudo-accentric factor Subscripts B second virial coefficient C critical property F property of feed stream M mixture Mix mixing N component designation V vaporization ij,k component designation xii

r reduced property molar quantity Superscripts L liquid V vapor ~- partial molal quantity o pure component property xiii

ABSTRACT This research was undertaken for the purpose of providing vapor-liquid equilibrium composition data in multi-component mixtures of hydrogen and hydrocarbons of varying molecular structure. The experimental results have been used to evaluate the applicability of one of the more promising current analytical correlations, based on experimental vapor-liquid equilibrium data for binary systems, for use in predicting equilibrium compositions in multi-component systems. Experimental equipment was built to operate at pressures to 5000 psi and at temperatures to 4000F. The equilibrium cell was internally agitated and had sample ports through which samples of multicomponent liquid phase and vapor phase were withdrawn for analysis on a mass spectrometer. Compounds studied in this work were hydrogen, benzene, cyclohexane and hexane. Data was taken on three ternary systems and on one quaternary system at temperatures of 100~ and 200~F. and at pressures of 500 and 1000 psi. All systems contained hydrogen. A total of 170 vapor and 170 liquid samples, representing 28 different equilibrium mixtures, was obtained. The correlation evaluated in this work was modified to improve the prediction of experimentally obtained hydrogen equilibrium composition ratios. The modified equation gave results comparable to existing correlations for hydrocarbon equilibrium composition ratios. Parameters xiv

used in this correlation were evaluated from pure component data as well as from experimental data on binary systems which had been reported in the literature. The vapor-liquid equilibrium composition ratios of all components in the multi-component mixtures were predicted to within approximately 20% of the measured ratios despite the relatively low hydrogen liquid and hydrocarbon vapor concentrations encountered in this work. This suggests that correlations developed from binary vapor liquid equilibrium data can be applied to multicomponent data. However, further efforts in this area are indicated in order to reduce the deviation of the predicted from the measured equilibrium ratios. xv

IiNTRODUCiTOi\T At. present, engineers are utilizing vapor-liquid equilibriwu composition ratios obtained from such generalized, correlat ions as the NGAA K-Value charts( and the Kellogg Charts0) for design work. These charts are the culmination of over thirty years work, which began with the recognition that a combination of Raoult s and Dalton's Laws were inadequate to describe a vapor-liquid system in equilibriumn over ranges of pressure and temperat-ure of interest. A basic parameter in the NGAA charts is a parazmneter called "convergence pressure." The concept of convergence pressure evolved throiugh a realization that the phase rul.e variables in two compolnlent systems are completely defined by the specificat-ion of two of1 the vaviables generally known to the design engineer -- namely, the system temperature and pressure. Furt-her, it was recognized. that there is a unique critical point locus for any two component system. This ledr to an attempt to classify any multi-component system as a pseudo-binary system consisting of a pseudo-light and a pseudo-heavy componenti It was found that the composition of the pseu-.do-binary system could be specified with satisfactory accuracy if the system temperature an.d pressure were extrapolated along a constant temperature line to te7 critical locus of the system, rather thanl along a constant conmposition line. The intersection of this isothermral extension of the system pressure and temperature with the critical locus is used as a coxr-ie'aing pressure2 called the convergence press-ure,

-2The NGAA charts are based on experimental data for aliphatic hydrocarbons,, and as the physical properties of this homologous group happen to have a definite regularity, this correlation method seemed (56) to meet with success. However, Solomon( has shown that these charts may give results in error by as much as 250% for hydrocarbon mixtures containing aromatics. Further, as more experimental data has become available, it has been found that these charts are less and less reliable as the convergence pressure parameter increases. For example, the convergence pressure of close boiling mixtures such as toluene and hexane may be less than 500 psi, whereas the convergence pressure for wide boiling mixtures such as hydrogen and hexane will generally be greater than 10,000 psi. The concept of convergence pressure has always been a difficult concept to apply. In order to improve the usefulness of the existing NGAA charts, a considerable amount of effort has been expended on improving the prediction of convergence pressures. Lenoir and White(36'37) developed an empirical method of estimating convergence pressures using effective boiling temperatures and weighting factors. They found that each component contributed to the effective boiling points of the pseudobinary components, and proposed the use of weighting factors to account for the fact that the lightest component in the mixture contributed more to the effective boiling temperature of the pseudo-light component than some intermediate component, whereas the heaviest component had the greatest effect on the pseudo-heavy component boiling point. This method presupposes a knowledge of liquid phase composition. In order to improve the predictability of wide boiling mixtures, Lenoir and Hipkin( 5 developed a generalized convergence pressure

correlation for systems containing hydrogen and aliphatic hydrocarbonso This correlation was based on the data existing at the time of their paper, but failed to predict experimental convergence pressures for the system hydrogen-hexane that were later reported by Nichols, Reamer and Sage (41) Another set of charts currently in use is the "Kellogg Charts" (3 developed from the Benedict-Webb-Rubin Equation of State( 2'3) by Benedict, Webb, Rubin and Friend (45). These charts utilize the molal average boiling point for each phase as the composition parameter. Vaporliquid equilibrium values for 12 aliphatic hydrocarbons, from methane to heptane, are represented on 324 charts, including pressures between 14.7 and 3600 psi and temperatures from -100~ to 400~F. However, these charts do not include aromatic compounds, and interpolation is tedious and often inaccurate. DePriester(l3) has attempted to consolidate the charts to show the effect of all the variables continuously. He has reduced the number of graphs required for each hydrocarbon to two, while retaining almost the same accuracy contained in the original charts. At present, further efforts are being made to develop vapors liquid equilibrium correlations based on the use of equations of stateo These correlation techniques may be programmed for a modern computer2 or they may be drawn up in the form of nomographs and charts. However2 most of the work thus far is based on experimental data from binary systems. This research has been undertaken to provide vapor-liquid equilibrium data on wide-boiling, multi-component mixtures. The light

-4component studied is hydrogen, while the heavy components are hydrocarbons with relatively similar physical properties, but different molecular structure; namely, benzene, cyclohexane and hexane. The data thus obtained has been used to evaluate the applicability of one of the more promising current analytical correlation methods to multi-component mixtures, and an attempt has been made to improve this correlation.

EXPERIMENTAL CONDITIONS OF STUDY Ternary and quaternary mixtures of hydrogen, benzene, cyclohexane and hexane have been studied at 100~ and 200~F. and at pressures of 500 and 1000 psi. The equipment built to study these systems was theoretically capable of operating at pressures to 5000 psi and at temperatures to 4000F. The equipment was statically pressure tested to 7500 psi. Although the experimental apparatus was located near large windows in the laboratory, there was no means provided for holding and venting fumes directly from the temperature control bath, As glycerine, the heat transfer medium, gives off heavy vapors at elevated temperatures, the operating temperatures in this experiment were arbitrarily limited to 2000F. A gas compressor unit was incorporated into this equipment, but in this experiment, hydrogen was used directly from the high press-are supply cylinders. The maximum operating pressure studied was approximately 1100 psi. J O

MATERIALS USED IN STUDY The hydrocarbons used in this study were obtained from the stock of the Chemistry Department at the University of Michigan. Hydrogen was obtained through the University Plant Department. The manufacturers of these raw materials and the approximate purity of the components, as measured by means of a mass spectrometer, are tabulated below. TABLE I PURITY OF MATERIALS Component Manufacturer Analyzed Purity Benzene Phillips Petroleum Co., 99.5% Pure Cyclohexane Merck Chemical Co., 99.67% Reagent Grade Hexane Eastman Kodak Co., 99.51q Red Label Hydrogen Mathieson Co., 99.5% Electrolytic, water pumped -6

EQUIPMENT DESIGN As a first step in the study of vapor-liquid equilibrium in systems containing hydrogen, attention was directed to the many different types of experimental apparatus that might be used. The initial criteria used in examining possible designs was that the equipment be simple and that analysis of the sample be relatively fool-proof. A glass bubble-point dew-point apparatus, similar to that used by Professor Webster B. Kay at Ohio State University, was first considered, as this is probably one of the less complex types of apparatus, and the analysis of vapor and liquid samples is simple and accurate. The apparatus (27,28) is described in detail by Kay. However, the utility of such apparatus for determining vapor-liquid equilibrium is limited to binary mixtures for which complete phase diagrams may be drawn. Further, the entire scheme is dependent upon the fact that the composition of the sample charged to the cell be known accurately at all times. Professor Kay has pointed out that hydrogen is difficult to contain within a glass system at high temperatures. (29) Soft glass seems to be best, but it is also the least able to withstand large temperature variations. If a component, such as hydrogen, should leak out of this apparatus during the run, the data obtained would be worthless. After considering the limitations of this type of apparatus and considering the fact that multi-component systems would be of interest, attention was directed to systems in which samples could be withdrawn and analyzed independently of the equilibrium apparatus. Here, the choice was between a dynamic type of system, perhaps similar to a recirculating type -7

-8still, and a static type system, in which samples would be withdrawn from the cell itself, after they had come to equilibrium. Little effort was devoted to investigating a dynamic type equilibrium cell, because of the questionability of attaining true equilibrium in such apparatus. Generally, the maintenance of steady state conditions in a dynamic type cell over a period of time is considered to be equivalent to the attainment of equilibrium. Yet the process of flow itself suggests that potentials exist within the system. Entrainment also appears to be a major problem in such systems. Therefore, attention was directed toward a static type equilibrium cell. Considering the equipment that was available within the University for use on this project, the choice of an equilibrium cell narrowed to a decision between a rocking bomb apparatus, and an Autoclave Engineering Magne-Dash cell, which was designed by Standard Oil Co. of Indiana. Because of possible problems with moving parts and connections at the high pressures anticipated for the rocking bomb, and because the Magne-Dash cell lends itself to use with a liquid temperature control bath, the decision was made to use the Magne-Dash cell as the equilibrium cell in the vapor-liquid equilibrium equipment.

DESCRIPTION OF THE EQUIPMENT The system finally decided upon may logically be divided into three main parts; a feed system, an equilibrium section, and a sampling system. These are shown in the schematic diagram in Figure 1 Feed System The feed system consisted of a source of high pressure gas and a means of compressing gas to pressures above those available in the source cylinder. It also contained a gravity flow feed tank, through which liquid hydrocarbons were introduced. The compressor was designed and built by H. J. Aroyan and, Riki Kobayashi. It has been described in detail by Benham(6) and by (10) Cosway. (10) Equilibrium Section The equilibrium cell consisted of an Aminco Micro Reaction Vessel, made of type 316 stainless steel, modified to contain the stirring mechanism provided. by an Autoclave Magne-Dash stirrerr The approximate volume of the cell was 200 cubic centimeters. Agitation of the cell contents was produced by the reciprocating motion of the dasher assembly, shown in Figure 2. This motion was made possible by the thrust induced on a magnetic core, when the solenoid surrounding this core was energized. By the use of two coils, a positive thrust in either direction was possible. This action was controlled by a timer which regulated the current flow to both coils, energizing them alters nately. -9

FLOW DIAGRAM OF EXPERIMENTAL EQUIPMENT () LEGEND C X I A A. HIGH PRESSURE GAS CYLINDER B. COMPRESSOR C. GRAVITY FLOW FEED TANK D) +~ gTO VENT E D. PRESSURE GAUGE ---------- (o) E. DEAD WEIGHT TESTER r,,~~~~~~~1.~ n~ IF. EQUILIBRIUM CELL FEED SYSTEM EQUILIBRIUM G. SOLENOID HOUSING'StG _ SECTION H. MIXER — rn' E.y/A ~)P _i -I. TEMPERATURE CONTROLLER L I L / I J. THERMISTOR SENSOR:F 1/..K. IMMERSION HEATER L. HIGH PRESSURE LOCK M. RUPTURE DISC. IN,/ r I — N. TEMPERATURE CONTROL BATH _ B _ I < gK 0~ I 1 O. SAMPLE BOTTLE,- — \TTZ P~~P. EXPANSION BOTTLE Q. MERCURY MANOMETER O'/w//// t^ 7.7777 7777 777) R. CATHETOMETER TO VENT ~-'-S. MERCURY McLEOD GAUGE T. COLD TRAP 0 () ~ U. VACUUM PUMP a a RSAMPLE SYSTE iSAMPLE SYSTEM Fig-ure 1. Flow Diagram of Experimental Equipment.

-11PRESSURE GAUGE PLUG,- > = -PRESSURE GAUGE CONNECTION UPPER SPRING MAGNETIC CORE SOLENOID HOUSING MAGNETIC CORE HOUSING SOLENOID SUPPORT- CABE O CABLE TO TIMER LOWER SPRING SOLENOID COIL WATER OUTLET WATER INLET FEED INLET CENTERING SPRING.^v ^>>. COLLAR: -— GASKET COLLAR NUT GLAND RETAINING RING LIQUID SAMPLE "^^^ COUTLET 1s I RSAMPLE OUTLETS /"^<<^ ^ ~ COVER SECTION A-A r — BEARING PLATE VAPOR SAMPLE OUTLET RETAINING CAP — S^, ^ ^^ GASKET SECTION VIEW OF 1/4 " AMINCO HIGH PRESSURE FITTING OPENINGS CELL BODY LIQUID SAMPLE LINE DASHER SHAFT UPPER DASHER DISC LOWER DASHER DISC NOT TO SCALE Figure 2. Sketch of Equilibrium Cell and Magne-Dash Shaker Assembly.

-120 The duration of each stroke and hence the degree of agitation was controlled by the rheostats on the timer. This action could be regulated from about 4 cycles per second to one cycle approximately every 4 seconds. The dasher moved back and forth over a linear distance of approximately 1 1/2-inches to accomplish the required agitation. The agitation could be further modified by changing the position of the disks on the dasher shaft, by adding disks, or by using perforated disks. The upper and lower springs acted as stops for the magnetic core. The centering spring positioned the dasher assembly, supported the weight of the magnetic core, and aided the lower spring on the upward stroke. The magnetic coils were contained within a water jacket, which was used to remove excess heat from the coils during operation of the agitator. This cell was immersed up to the top of the retaining cap in a temperature control bath. Insulated heating tapes were wrapped around those portions of the equilibrium cell that protruded above the bath, up to the solenoid housing. The temperature of the glycerine, the heat transfer medium, was controlled by means of a Fenwal Thermistor Temperature Indicating Control Unit. A thermistor sensor, which had a resistance that was extremely sensitive to temperature, was used in a simple bridge circuit. This controller was supplied with three modes of control; on-off control, on-off control with fully adjustable differential, and proportional control with broadly adjustable proportional band limits. The unit was insensitive to stray magnetic fields, vibration

-13 and shock, and contact potential in the thermistor leads. Heat was supplied to the bath by means of a set of General Electric hairpin type electric immersion heaters. In addition to the temperature indicated by this control unit, a series of chromel-alumel thermocouples were placed at various strategic positions on the apparatus, both in the equilibrium section and in the sampling section. The feed inlet line and the sample outlet lines from the cell were wrapped with heavy-duty electrical heating tapes. Pressure within the cell was indicated by means of a pressure gauge located above the Magne-Dash shaker assembly, and was measured by means of a pressure gauge tester, No. D3-13, supplied by the Chandler Engineering Company. A monel rupture disc, rated at 3175 psi at 720F., was used in this section. Sampling System Both vapor and liquid samples were withdrawn through pressure locks, each consisting of two high-temperature, high-pressure Aminco valves made of super alloy N-155. This alloy consisted of 20o nickel, 21% chromium, 3% molybdenum, 20 tungsten, 2~0 cobalt, 0.15% carbon, with the balance iron. The valves were designed to operate at temperatures to 1000~F. and at pressures to 25,000 psi. The pressure on the samples was reduced from elevated cell pressure to subatamospheric pressures in these locks, which were totally immersed in the temperature control bath. The sampling system up to the valves marked "a" in Figure 1 had a volume of approximately 20 cc. and was constructed of stainless

-14steel. This section was provided with pressure gauges and a means of venting the sample, should the high pressure lock system fail. From valves "a" on, the system was made of pyrex glass. Expansion bottles were used to receive the sample expanded from the high pressure lock. Sample bottles were attached to the sample system by means of tapered glass joints. Mercury manometers and a mercury McLeod Gauge were used to measure the pressure within the sample system. A Central Scientific Company Cathetometer was used to measure the height of the mercury legs in the manometers. Heating tapes and heating lamps provided temperature differentials within the sample system in order to provide convective currents for mixing of the samples.

PROCEDURE The experimental procedure followed in this work can be divided into three parts -- feeding components to the cell, approaching equilibrium, and sampling. Feeding Components Liquid hydrocarbons were first introduced into a clean equilibrium cell at atmospheric conditions. Approximately 150 ml. of a mixture of hydrocarbons were mixed thoroughly in the feed tank, and 10 to 20 ml. of this solution were allowed to flow by gravity into the equilibrium cell. The cell was then valved off, and the hydrocarbon in the cell was evacuated into the cold trap. When the pressure in the equilibrium cell had been less than 0.05 mm. of mercury for at least two hours, the cell was considered to be flushed and clean. Approximately 120 ml. of solutionwere then admitted to the cell. Next, hydrogen was introduced to raise the pressure, and heat was applied to the temperature control bath to raise the temperature of the cell to the desired operating levels. If the pressure in the cell appeared to be too high after the operating temperature had been reached, hydrogen was bled from the cell through the high pressure valve lock system. The MagneDash stirrer was then activated. Equilibrium It was felt that equilibrium should be reached within two or three hours after operating conditions had been attained. However, -15

-16-. to insure that equilibrium was reached, the sampling schedule followed was conservative. The Magne-Dash stirrer was set for approximately one stroke per second, and was allowed to operate for a minimum of 12 hours. At the end of this period, at least three liquid and three vapor samples were taken in order to flush out the sample lines. Generally, hydrogen vapor was found present in the liquid sampling line. This operation reduced the pressure in the equilibrium cell. In order to counteract this pressure drop, the contents of the cell were then allowed to remain without agitation in the equilibrium cell, including the high pressure lock, for periods ranging from two to twelve hours. Each time a sample was taken thereafter, this same procedure was followed. Sampling Before any sample was withdrawn from the equilibrium cell, the sampling system was evacuated. The pressure in the sampling system was less than 0.05 mm. of mercury at this time. The first step in sampling, after the vacuum had been attained, was to close the inner valve, closest to the equilibrium cell in the high pressure lock system, and to allow the sample trapped within the lock to expand into the all metal safety volume. If the total pressure in the safety system did not increase with time, the sample was then allowed to expand into the glass portion of the sampling system. The total pressure in the sampling system after the sample had been expanded into the glass expansion bottles was

-17approximately 3 cm. of mercury as measured on a manometer by means of a cathetometer. This pressure was approximately 25% of the vapor pressure of the heaviest hydrocarbon present at room temperature. The expanded sample was then allowed to mix by diffusion for periods ranging from three to twelve hours. During some runs, convection currents were set up in the sampling system by applying heat to spots on the outer surface of the system, in an attempt to determine if any improvement in sample mixing took place. At the end of the mixing period, the sample was allowed to expand further into a 15 ml. sample bottle for a period of ten minutes. The sample bottle and the glass expansion bottle were then valved off, and the sample bottle was removed from the system. A second sample bottle was placed in the system and evacuated to a pressure less than 0.05 mm. of mercury. The remaining 97% of the original sample that had been held in the glass expansion bottle was then allowed to re-expand up to the second sample bottle. At the end of one to three hours, the second sample bottle was opened for ten minutes. The entire procedure was repeated at least three times. Hydrogen was then added to or removed from the equilibrium cell in order to establish a new pressure level, and the temperature of the cell was readjusted. The same sampling techniques were then repeated after the mixture had been allowed to come to a new equilibrium. After samples had been taken at 100~ and 200~F., and at 500 and 1000 psi, the equilibrium cell was cleaned and a new hydrocarbon

-18mixture was added. A total of 170 vapor and 170 liquid samples, representing 28 different equilibrium mixtures, was obtained.

ANALYS IS The samples obtained from this work were analyzed on a Consolidated Engineering Company 21-103B Mass Spectrometer. The theory and routine operation of this instrument have been discussed. in great detail by Benham(6) and by Cosway. (10) All hydrogen-rich vapor samples were run in a group before the hydrocarbon-rich liquid samples were run. This reduced the effect of possible molecular adsorption from one sample and desorption into the next sample in the mass spectrometer. Sample standards were rei at least once during each set of analyses. The sensitivity of the Instrument to these standards was found to vary not only from day to day, but also to vary during the same day. Efforts were made to establish the best method of introducing the sample into the mass spectrometer in order to eliminate a possible throttling effect. It was feared that as a result of the wide molecuilar weight difference in the components to be analyzed, throttling would cause a certain amount of separation between the molecules. No one method of introducing the sample into the mass spectrometer appeared to give better results than any other method. Several samples were analyzed at least twice -- some during the same day, and others on different days. The spread in the results of the analysis of the same sample was at least as great as the spraad between different samples of the same set. -19

DISCUSSION OF ERRORS Two groups of errors were involved in this experiment. The first group involved the measurement of the conditions under which equilibrium was attained, while the second group involved the sampling procedure and analysis of the equilibrium samples. Measurement of Temperature and Pressure The reported temperature of the glycerine bath was measured by means of a chromel-alumel thermocouple used in conjunction with a L,eeds-Northrup portable type potentiometer. This system was calibrated against mercury thermometers which had previously been calibrated by the U.S. Bureau of Standards. The temperature-EMF relationship for this thermocouple was found to be: E = - 0.69005 + 0.0213531T + 6.59597T2 x 10where T is the temperature in degrees Fahrenheit. The temperature of the bath was known to within approximately 0.1~F. The annulus between the Magne-Dash dasher shaft and the solenoid support and equilibrium cell cover, the feed line and portions of the sample lines were outside of the temperature control bath. This accounted for approximately 5% of the total volume of the equilibrium cell. All lines that protruded above the bath level, except for the annulus beneath the solenoid housing and the bourdon tube in the pressure gauge above the cell, were wrapped with a heavy duty heating tape. The temperature of the wrapped lines was measured by means of a second -20

-21l thermocouple, and was maintained approximately 1~F. above the bath temperature in order to reduce condensation of hydrocarbons in the vapor-phase. Pressure in the cell was measured by means of a Chandler Engineering Company pressure gauge tester, No. D3-13. This instrument had an absolute accuracy of + 3 psi, in the pressure range studied here. Sampling Errors The most significant errors involved in this work consisted of those errors which occurred in the sampling and in the analysis of the equilibrium sample. The effect of these errors could not be measured individually, but appeared as a total error found in running duplicate samples, A 1% expansion of the equilibrium cell was introduced when samples were admitted to the high pressure valve lock system, During the experiment, the time during which the sample was allowed to remain in this lock under pressure from the unagitated equilibrium ce(ll was varied from two to twelve hours. However, analyses did not indicate that the composition of the phases was effected by this change in length of time. The pressure composition diagram of the binary hydrogen systems also indicated that the change in pressure experienced during sampling would produce a composition change beyond the accuracy of the analysis. The possibility of selective adsorption within the sample system also was investigated. Experimentally, no adsorption effect could be found. This finding was confirmed by data measured by

-22Van Voorhis. (61) At 25~ C., Van Voorhis found that hexane, cyclohexane and benzene were physically adsorbed on silica in an amount asymptotically approaching zero at pressures below one-half the vapor pressure of the hydrocarbon. To insure that selective adsorption would not occur in this work, the pressure in the sample system was maintained at one-third the vapor pressure of the heaviest component in the mixture, or lower. Lack of complete mixing of samples withdrawn from the equilibrium cell was also a possible source of error. The liquid sample was withdrawn as a liquid, and had to evaporate and mix in the sample system. Evaporation of the liquid sample was followed as a pressure increase by measuring heights of the mercury legs in the sample system manometers, and was completed within one hour. A simplified mathematical model of the system indicated that at the pressures involved, essentially complete mixing by diffusion would have occurred within one hour after the sample had been completely vaporized. Samples were therefore allowed to mix by diffusion.for periods ranging from 2 1/2-hours to one week. No effect of mixing time -could be found from the results of the analysis. As one further attempt to study the effect of mixing, heat was applied at points to the sample system. This should have caused further mixing by means of heat convection, but did not affect the results. The main source of error in running duplicate samples has been experimentally determined to be in the analysis obtained from the mass spectrometer. Duplicate analyses of the same sample bottle

-23showed as much variation as the analyses of six different sample bottles. With such large variations in the mass spectrometer results, possible errors from the sources already discussed have been masked. It is believed that the reason for this discrepancy in the analyses of duplicate samples from the same sample bottle may be attributed to the extreme size variation in the molecules being analyzed. Several different experiments were attempted in an effort to eliminate this source of error, but the only successful method was to run a minimum of six samples for each pressure-temperature-composition point studied. These results have been analyzed statistically, and the results of this type of analysis are summarized in the discussion of the data. It is believed that the maximum probable error found occurred in the analysis of the hydrogen in both the liquid and the vapor phases, and is less than 0.5 mole per cent. The average spread in the results of analyses for all components is approximately 1 mole per cent.

SMOOTHED EXPERIMENTAL DATA Ternary and quaternary equilibrium mixtures of hydrogen, benzene, cyclohexane and hexane have been studied at temperatures of 100~ and 200~F., and at pressures of 500 and 1000 psi. At least six samples of each phase have been obtained at each pressure-temperaturecomposition point studied. A material balance and statistical techniques have been used in order to eliminate gross errors from the results reported here. Since of the approximately one mole of liquid hydrocarbon added to the equilibrium cell, only 0.001 to 0.005 moles vaporized, it seemed reasonable to assume that the composition of the liquid phase on a hydrogen-free basis might be the same as the composition of the hydrocarbon mixture added to the equilibrium cell. Further, approximately 20% or less of the liquid hydrocarbon charged to the cell was removed during sampling over the complete temperature and pressure range studied. The possibility that there was no significant change in the hydrogen-free liquid compositions between additions of hydrocarbon to the cell was examined statistically. It was found that this assumption was valid within a 99% confidence level. Scattered data points that fell outside this limit have been deleted from the results reported here. A similar analysis of the vapor phase results revealed that there was no significant difference in it.s hydrocarbon composition on a hydrogen-free basis. These results imply that over the range of conditions studied, the relative volatilities of the hydrocarbons were constant for a given hydrogen-free mixture. -24

-25The results of this analysis are summarized in Table II. The analyses of the hydrogen compositions did not allow the use of a similar statistical treatment. In this case, solubility data on the three binary hydrogen-hydrocarbon systems was used to reject obvious errors. Hydrogen in the liquid phase appeared to follow Henry's Law over the entire range of conditions studied. This permitted the interpolation of hydrogen concentrations in the liquid phase from hydrogen binary data reported by different experimentalists. However, at these relatively low pressures, the vapor phase hydrogen concentrations in binary mixtures did not appear to lie on a straight line between the results of different authors. Thermodynamic calculations confirmed this hypothesis. Consequently, only the system hydrogen-hexane could be used as an estimate of the hydrogen solubility in the vapor phase. The results of hydrogen analyses from the mass spectrometer have been examined by means of small sample statistical techniques. These techniques are based on the number of samples, the sample mean, and the range between the lowest and the highest sample values. (62) The reported values of hydrogen compositions are based on a combination of experimental results statistical analyses and data from the literature. Analysis of the final results indicated that an azeotrope reported at 0. 502 mole fraction benzene in the benzene-cyclohexane system at atmospheric pressure has been shifted to lower benzene concentrations at higher pressures(57,65) in the presence of hydrogen. Tables III and IV summarized the smoothed experimental results obtained in this work. Hydrogen solubility in the liquid phase at constant temperature is plotted in Figure 53 Complete experimental results are appended.

TABLE II 2iJ4MiKIEY OF EXPERIMENTAL RESULTS (Hydroc -. i Analysis on a Hydrogen Free Basis) Liquid Phase Vapor Phase Mole Fraction(l) Mole Fraction(l) Runs BZ CX HX N(2) a(3) P.E. (4) BZ CX HX N(2) a(3) P.E. 4) 18,19,20,21.219 13.0078.0015.239 21.0182.0026 22,23,24,25.217 10.0055.0013.250 11.0169.0036 30,51,32,33.200 15.0023.0004.200 20.0051.0008 34,55,36,37.179 20.0128.0020.258 22.0518.0078 40,41,42,43.299 23.0065.0009.298 22.0100.0015 44,45,46,47.139 14.0086.0016.157 14.0133.0024 50,51,52,53.500 35.0317.0037.455 33.0456.0054 50,51,52,53.173 35.0176.0020.168 33.0266.0031 50,51,52,53.327 35.0279.0032.377 33.0547.oo65 NOTES: (1) Mole fraction of hydrocarbon solute on hydrogen free basis (2) Number of samples.. (5) Standard deviation, a =J(x-)~2(N-l) (4) Probable error, P.E. = 0.674a/ N

TABLE III SUMMARY OF EXPERIMENTAL RESULTS AT 100 ~F Mole Fraction In Liquid Phase In Vapor Phase Press. Run (psia) BZ CX HX H2 P.E.(1) BZ CX HX H2 P.E.(1) 18 567.210.751.039.002.004.011.985.002 22 580.763.211.026.004.010.003.987.001 21 1100.203.724.072.004.003.008.989.001 25 1102.741.205.053.005. oo6.002.992.001 30 577.193.771.036.003.003.013.984.00oo 32 106o.188.750.062.005.002.oo6.992.005 34 563.803.175.022.001.007.002.991.002 35 1106.783.171.046.002.oo4.001.994.001 40 582.293.686.021.002.oo4.010.986.001 44 588.845.136.019.004.008.002.990.005 41 1122.286.670.044.005.002.005.993.001 45 1088.836.135.029.004.005.001.994.003 50 544.487.168.318.027.001.005.002.oo4.989.001 51 1074.471.163.308.058.005.oo4.002.oo4.990.001 NOTE: (1) Probable error of hydrogen analysis, based on small sample statistics

TABLE IV SUMMARY OF EXPERIMENTAL RESULTS AT 200 OF. Mole Fraction In Liquid Phase In Vapor Phase Press. Run (psia) BZ CX HX H2 P.E.(l) BZ CX HX H2 P.E.(1) 19 588.209.745.046.002.014.046.940.005 20 1057.201.717.082.00oo4.010.050.960.00o 25 570.756.209.035.005.042.014.944.005 24 1067.752.205.o66.005.022.007.970.oo4 ro 51 568.191.765.046.002.012.047.941.005 3355 1089.185.754.082.001.007.028.965.005 36 1067.762.166.072.005.022.oo008.970.002 57 574.787.172.o4l.001.03355.012.955.006 43 579.289.676.055.001.012.028.960.005 47 589.841.156.024.005.034.oo6.960.005 42 1076.279.655.o66.002.008.018.974.005 46 110o8.822.13355.045.002.019.oo006.975.002 52 1085.46o.159.500.o8l.005.012.oo4.010.974.002 53 541.482.167.515.06.002.027.010.025.940.001 NOTE: (L) Probable error of hydrogen analysis, based on small sample statistics

H2- Hx, NICHOLS (41) - — LEG H2 - Bz KRICHEVSKII(311- CONNOLLY (9) ----— H - Cx KRICHEVSKII(32) PRESENT INVESTIGATION 100 ~F 200 ~F I I I I I i I I i I I RUN2^ HEXANE- BENZENE RUN2 U RU 1000 / — 21 RUN22 HEXANE RICH RUN23 EXANE RICH 500 ^ RUN I- RUN 19 RUN 3E RUN 2 HEXANE CCLOHEXANE RUN 36 -1000 ~1000 -^ ^RUN 33 0- 5HEXANE RICH - CYCLOHE HEXANE RICH 500 RUN 30 RUN 31 RUN 34 RUN 37 --- I. I I I JI I I I I I I I I I I I I I I RUN4 RUN4 RUN46 RUN4 RUN4 R BENZENE- CYCLOHEXANE RUN - 1000 <CLOHEXANE,-'-CYCLOHEXANE RICH CCLOHEXANE RICH,,, 5o0o// RUN4o -- 40.w RUN43 n- RUN 44 RUN 47 a. RUN 51 R0 0051 BENZENE -CYCLOHEXANE- HEXANE RUN 52 500 R { RI 5CRUN 50 RUN 53 0.01.02.03.04.05.06.07.08.09.01.02.03.04.05.06.07.08.09.10 MOLE FRACTION HYDROGEN Figure 3. Solubility of Hydrogen in the Liquid Phase at Constant Temperature.

CORRELATION Introduction In developing any method of correlating experimental variables, much insight can be gained by making use of theoretical models. Theory must be judged, however, on how well it represents actual data. But it can provide direction to an experimentalist, and it can insure that the maximum amount of utility is obtained from the experimental data. In the field of vapor-liquid equilibrium, a considerable amount of theory does exist, which should be accounted for by any correlation. From the second law of thermodynamics, it can be shown that for a constant temperature process: State 2 AG= VdP State 1 f2 RT in 1 At equilibrium, there should be no available work between the liquid phase, state 1, and the vapor phase, state 2. This condition is satisfied if the difference in the Gibbs Free Energy, AG, between the states is zero. The Gibbs Free Energy can be evaluated directly from the second law of thermodynamics, if some relationship between pressure, volume and temperature is known. The relationship may be in the form of experimental data, or it may be in the form of an equation of state. The equation of state has the advantage of providing an analytical tool for the evaluation of the free energy of the state. -50

-31Equations which relate pressure, volume and temperature for the vapor phase have been studied extensively. Most of these equations have been developed in studying single component systems. The same forms of the equations are used to predict properties of mixtures of gases, although the methods of predicting mixture coefficients have remained substantially empirical. Equations of state contain parameters that are generally evaluated from experimental data. In order to eliminate the necessity of having experimental data available before the equation can be used for a specific component, considerable attention has been directed toward generalizing these equation coefficients. The theory of corresponding states has been developed to the point that experimental data for one component can be used with relative confidence to predict the coefficients in an equation of state for a different, but similar, pure component. Although equations of state have been rather highly developed to predict the behavior of vapors, they are of questionable validity when applied to the liquid state. Knowledge of the liquid state is limited. For example, although the shear strength of a liquid is more nearly like that of a vapor than of a solid, its compressibility and its density are more nearly like that of a solid. Neither a theoretical model based entirely on a solid model nor a theoretical model based entirely on the vapor will predict all the aspects of the liquid phase. Single Equation of State Methods A method of predicting vapor-liquid equilibrium ratios that is again receiving attention is the single equation of state method.

-32One equation is used to predict the Gibbs Free Energy in both the vapor and the liquid phases. This method is limited, however, to the range of the validity of the equation of state. One of the better equations of state, the Benedict-Webb-Rubin Equation(1 23 ) is valid only up to twice the critical density of the component being studied. This equation is the basis of the Kellogg Charts.( A major limitation to an equation of state as involved as the Benedict-Webb-Rubin equation has been that experimental data was required before it could be applied to a specific component. (42) Opfell, Sage and Pitzer ) made a definite contribution to the elimination of this problem by showing that a three parameter theory of corresponding states could be used to define reduced BenedictWebb-Rubin coefficients. However, although the reduced coefficients predicted thermodynamical properties of pure components as well as the specific coefficients for the same components, neither set of coefficients was as satisfactory in predicting properties as the compressibility factors tabulated by Pitzer.(45) This indicated a need for a more precise analytical representation of the P-V-T behavior of pure components. A generalized equation of state proposed by Hirschfelder, Buehler, McGee and Sutton(2l) has been proposed to fill this need. Other equations of state, such as the Re;dlich-Kwong Equation of State(5), are more easily applied than the Benedict-Webb-Rubin Equation with reduced coefficients, in that their empirical coefficients are given directly in terms of reduced physical properties. In their present form, however, these latter equations have a range of applicability

55-3 that is limited to densities less than half of the critical density of the component of interest. The Redlich-Kwong Equation of State is: RT a -b T1/2V(V + b) Constants for this equation are readily derivable from a knowledge of the critical properties of the component, and are given by the following relationships: 2.5 A2 = a 0.4278 TC R2 T7. P T2.5 C b Ta B o 0.o867RT P T C where PC is given in atmospheres. For mixtures: AM= ZxiAi and BM = XiBi It can be shown that at a constant temperature, the fugacity coefficient of a component in a mixture is given rigorously by the equation(52): 00 f' 7 P RT V M RTln = [(-)p - - ] dV_ - RTln x.P n.,Tnj V ] RT Redlich and Kwong show that the integration of the above equation, using their relationship, gives the result:

-34lo -B. A P A 2Ai Bi log o = 0.4343(z-l) 1 log (z-BMP) - [i - ] log (1 + xiP BM BMAM B z where the compressibility factor, z, is defined by the relationship: PVM z = M RT At moderate pressures, Redlich and Kwong find that: f_ 2 2 in = [Bi - Ai + (Ai - A) ] P xiP Upon substitution of assumed compositions of one phase into the integrated equation, the value of the fugacity of the component of interest is found. This may be compared with the fugacity of that same component in the second phase, calculated in a similar manner. The assumed initial phase compositions are adjusted until the difference in these fugacities is as small as desired. An equation of state that is theoretically capable of being used under all conditions is the Virial Equation of Statee A sufficient number of virial coefficients can be used to describe the properties of a substance to any desired density. However, data on coefficients greater than the second is limited. The Virial Equation of State can be written in the form: PV 1+ M(T) + C(T +.. RT V V? where the second virial coefficient of the mixture, BM(T), is given by the equation: M(T) = Z xiXjBij(T)

-35and the third virial coefficient of the mixture, CM(T), is given by the equation: CM(T) xixxkCijk(T) The first term in this infinite series can be considered to represent the kinetic energy contributions of the molecules to the equation of state. For an ideal gas, in which there are no forces of attraction or repulsion between molecules, the equation may be terminated after the first term. The second virial coefficient accounts for potential force interactions between pairs of molecules. At densities less than half the critical density, the Virial Equation of State terminated after the second virial coefficient adequately represents the behavior of real gases. Third and higher virial coefficients represent simultaneous potential force interactions between three or more molecules. The Virial Equation of State can be integrated at constant temperature to give: In i = F2 Z x.Bij(T) + XjXkCi.k(T) +..-.. n ln xiP YM j RT Several equations of state can be derived by expressing the second virial coefficient analytically, and then substituting the resulting expression into the Virial Equation of State. For example, van der Waal's equation: _ RT a V-b V2

-56is equivalent to assuming that: B(T) b - RT The Redlich-Kwong Equation is equivalent to assuming that: B(T) = 0.0867 [1. - 4.93 (T)15 P T Thus, a study of the interaction coefficients in mixtures, using the Virial Equation of State, should yield results that are directly applicable to other equations of state. Two Equations of State Method Chao, Edmister and Prausnitz(49) have suggested that two equations of state be used in predicting vapor-liquid equilibrium. This method has the advantage of requiring a relatively simple equation of state for predicting fugacity coefficients in the vapor phase, since this phase is generally at a relatively low density as compared to the liquid phase. The proposed correlation has the form: Ki = Yi - Yi K. i= Vi Xi CPi where yi is the liquid activity coefficient, and is defined: _L o i f= /xifi The parameter pi is the vapor-phase fugacity coefficient, and is defined: Pi f i/yP

-37while vi is the pure component liquid fugacity coefficient, and is defined: V. f /P I i The activity and fugacity coefficients required to evaluate K-values using this correlation will be discussed in the following sections. Vapor Phase Fugacity Coefficient In certain areas of general interest, the density of the vapor phase is less than half the critical density of the component being considered. Consequently, in this case the two equations of state method does not place extreme limitations on the exact vapor phase equations of state to be used. In this work vapor densities were relatively low, so that the integrated form of the Redlich-Kwong Equation for moderate pressures: in cp = [Bi - A2 + (A -AM)2] P i i as well as the integrated form of the Virial Equation of State through the second virial: V v % j RT has been used to evaluate vapor phase fugacity coefficients. (45) Using the Theory of Corresponding States, Pitzer and Curl( 5 have developed a generalized correlation for pure component second virial coefficients, of the form: B(T) = (BoT) + (OB1T) Bii(T) B (T) + eoBii(T) 11 ii~~~.

-38where (o) RT 2 3 8 B. (T) = (0.073 + 0.46/Tr - 050/Tr - 0.097/T - 0073/T B.~)(T) = p.70 7/T C and B()(T) = - (0.1445 - 0.330/Tr -0.1358/T2 - 0.0121/T3) ii p r The acentric factor,co, is defined by the relationship: = - log10 Pr(Saturated at Tr = 0.7) - 1.00 and is a measure of the forces that contribute to the nonideality of a gas. The acentric factor is related, through the Clausius-Clapeyron Equation, to the entropy of vaporization of a component. If nonideal forces exist between molecules of a component, these forces should tend to have an orienting effect, which will show up directly in the entropy of the component. Prausnitz has extended this form of correlation to interaction virial coefficients. (47) He assumes that the critical volume of a mixture is the arithmetic average critical volume of the components: V = 1/2 (V c +V ) Cij ci j and that the characteristic acentric factor is the arithmetic average of the component acentric factors:.ij =1/2 (oi + o) He also presents rules which correct for the deviation from the geometric mean critical temperature of the actual critical temperature of the mixture;

-391/2 TCij = kij(TCiTCj ) where kij is a function of the properties of the interacting molecules. For the hydrocarbons studied here, ki, is essentially unity, while for the hydrogen-hydrocarbon interactions, k.. is approximately equal to mj 0.85. Prausnitz tabulates the function B', where: BiL = B (T' Oj cij Tij The generalized pure virial coefficients predicted by using the method of Pitzer and Curl have been compared to experimental data. This work is shown on Figure 4, 5 and 6. Figure 7 shows virial coefficients for hydrogen that were used in this work. Prausnitz's correlation compares favorably with experimental data for the system benzene-cyclohexane as shown on Figure 8. However, an attempt was made to calculate second virial interaction coefficients for hydrogen and hydrocarbons from data obtained in this work for further verification of Prausnitz's correlations. Unfortunately, the accuracy of the variables assumed to be known quantities in these calculations is apparently insufficient to provide a definite check on his correlation for molecules of widely differing sizes. Results of this calculation are summarized in Table V. Hydrogen-hydrocarbon interaction virial coefficients predicted by Prausnitz's correlation are shown in Figure 9.

-4o~-EXPERIMENTAL VIRIAL ^' COEFFICIENTS C -1000 E E -2000 v / / I -— GENERALIZED VIRIAL n /y f —- ~ COEFFICIENTS SECOND VIRIAL COEFFICIENT OF BENZENE -3000 -- X PITZER (45) O DAVID (12) E ORGANICK (43) 0 HIRSCHFELDER (22) - + SCOTT(55) * LAMBERT(34) * WAELBROECK(63) -4000... ____.... 0 100 200 300 T,~C Figure 4. Second Virial Coefficient of Benzene.

-41o0 i _ _ GENERAUZED VIRIAL XA COEFFICIENTS l l -1000 EXPERIMENTAL VIRIAL COEFFICIENTS -2000 0 ~S;~ lj |~ |~ |~ ISECOND VIRIAL COEFFICIENT to /l FOR CYCLOHEXANE o -3000 l l - -- * DAVID (12) co X PITZER (45) 0 WAELBROECK (63) 0 LAMBERT (34) -4000 - 5000 0 100 200 300 T(~C) Figure 5. Second Virial Coefficient for Cyclohexane.

-42_ ~X. -1000 E -2000 I, / ^^ —-,GENERALIZED VIRIAL o / COEFFICIENT 1O -3000 SECOND VIRIAL COEFFICIENT OF HEXANE X PITZER (45) E BENEDICT (2) -4000 -4000 T0,O LAMBERT(34) -5000 O -0 0 100 200 300 T,~C Figure 6. Second Virial Coefficient.

-4316.. - EXPERIMENTAL. VALUES 15 C —-- ALCULATED CURVEBH2 F (A) 14 0 0 SECOND VIRIAL COEFFICIENT OF HYDROGEN 0 HIRSCHFELDER, (21) i./_______ _______________ ____ X CHANG,(7) _ __ 1.... 0 100 200 300 T, C -- Figure 7. Second Virial Coefficient of OIydrogen.

GENERALIZED VIRIALCOEFFICIENT -1000 EXPERIMENTAL VIRIAL.__ __ COEFFICIENT 0 O -2000 m /.... ----- — SECOND VIRIAL INTERACTION COEFFICIENTS / / FOR HYDROCARBON MIXTURES X BENZENE- CYCLOHEXANE,PRAUSNITZ (47 o BENZENE - HEXANE, PRAUSNITZ (47) ~~~~/ 0 ~/ ~~V CYCLOHEXANE-HEXANE, PRAUSNITZ (47) -3000 / 0 BENZENE-CYCLOHEXANE, WAELBROECK (63) / BENZEZENE-CYCLOHEXANE, (EXPERIMENTAL) COX (II) -4000 I —-- ---- 0 100 200 300 T (~C) Figure 8. Second Virial Interaction Coefficients for Hydrocarbon Mixtures.

70 60 -0__ E 50 HYDROGEN - HEXANE ________________ HYDROGEN -CYCLOHEXANE cut 40 30 20 t^- ~/^^^^^v-n HYDROGEN - BENZENE -100l 100 200 300 -10 T ~C --- - - -40 -50 -60 - 0 Figure 9. Generalized Second Virial Interaction Coefficients for Hydrogen Systems. Reference: Prausnitz (47)

-46TABLE V TINERACTION VIRIAL COEFFICIENTS FOR HYDROGEN-HYDROCARBONS Run BH2-Bz B12.-Cx BH2-HxX Set Temp. (cm3/gm-nmole) (cm3/gm-mole) (cm3/gm-mole) (1) (2) (1) (2) (1) (2) 20 1000 F. -4.0 -140.6 -7.0 7.0 -51.1 30 - 97.2 -52.1 40 -116.6 -150.8 50 - 80.0 -171.1 -35.4 20 200~F. 13.0 2.5 12.0 27.0 76.0 30 14.9 39.1 40 59.2 - 6.7 50 46.1 - 8.1 66.3 NOTE; 1. Predicted by method of Prausnitz. (47) 2. Calculated by method of least squares from experimental data. Liquid Activity Coefficient Attention has recently been directed to solubility theory as a means of predicting the liquid activity coefficients. Chao, Edmister, and Prausnitz have recommended that the Hildebrand-Scott regular solution theory correlation for multi-component mixtures: RT In i V ( V~ (~t - 3M) be used. ( 9) Here: _L i! f! = xp?

-47VL Molar liquid volume of component i -i 6. = Solubility parameter of component i = (Evi/V L)/ 2 where = A - Isothermal molar change in energy of component i Vi in going from liquid to the ideal gas state and SM = Solubility parameter of the mixture = xi Vii /ZxiVL An equation of this form was first developed by Van Laar for a liquid that obeyed the van der Waal Equation of State.(59,60) Hildebrand has shown that this equation can be applied to a broader class of mixtures, called "regular solutions." (20) A regular solution, as defined by Hildebrand, is a solution in which the entropy of mixing is given by the equation: Smix = -R(nlln xl + n2ln x2 +''' + nNln xN) All the nonideality of the mixture is attributable to its enthalpy. Although no real solution can be expected to be a regular solution, the Hildebrand theory has been surprisingly successful. Flory(16,17) and Huggins(25) independently considered the properties of mixtures of two kinds of molecules sufficiently similar to mix in all proportions without any heat of mixing, but differing widely in size. Such a solution is called an "athermal solution," and the entropy of mixing, based on a lattice type model, is given by: nlVL n2VL ASmix = R(nlln nl1L + n in n2V ) mix n 1 ^hnVL^ 2 nVL+nV Extending this to multi-component mixtures: Aix = - R(nln L + n2ln L+' )

-48so that L L N a(mix) x.(^o. -- (Smix) = - R(ln- L + 1.0 V4 = _M - V where L L V = Zx.V. If this expression defines the change in the partial molal entropy of a component, and if the change in its partial molal enthalpy in the multi-component mixture is given by the relationship developed by Hildebrand for a regular solution: = -1 ( - M) the partial molal change in the Gibbs Free Energy is given by the equation: AG1 = RT ln - flL L = VL ( V - 5M) -1 ( 5M) + RT in + RT(l.0 -L ) or L L ( )2 VL l 7n = ln =-V + iL 1-M} + 1.0 l 1VL RT vL -M -M If V1= VL = VL -1 -2 3- -N this equation reduces to Hildebrand's equation for mixtures. This volumetric correction has not previously been applied to multi-component mixtures in the form presented here. Prausnitz has pointed out that the assumptions used by Hildebrand in developing the theory of regular solutions do not necessarily apply to a gaseous solute in a liquid solution.

-49The definitions of a solubility parameter and liquid molar volume, as given, cannot be readily applied to a component at a temperature above its critical temperature. Chao, Edmister and Prausnitz(49) do suggest the use of effective solubility parameters and effective molar volumes for gaseous solutes, however. These factors have been back-calculated from vapor-liquid equilibrium data. The results of this work have been applied directly to the correlation of data obtained in the present investigation. Fugacity Coefficient of the Pure Liquid Component At low pressures, the fugacity coefficient of the pure liquid component, v., is equal to the ratio of the component vapor pressure, P~, to the total pressure. At higher pressures, vi is given by: fi V i(P-P0)'n vi = In P + In (-) o + pP P P RT f. where (pL)pO is a function of reduced vapor pressure and temperature. f. At the conditions encountered in this work, ( —)pO was essentially unity. Generalized fugacity coefficients have been presented with (38) the critical compressibility factor as a third parameter. (8) (46) Pitzer has correlated this coefficient analytically using the acentric factor as a third parameter. For components that do not (8) exist as liquids at the system temperature and pressure, Chao( has proposed effective fugacity coefficients, which were determined from experimental data. He proposes that the relationship: (o) (1) log v = log v + Ca' log v

-50be used to represent both actual and effective fugacity coefficients, where 1' is a pseudo -acentric factor calculated to give the best fit for the largest amount of experimental vapor-liquid equilibrium data. It varies from Pitzer's acentric factor. The factor v(~) is the pure liquid fugacity coefficient of a "simple fluid" and is given by the equation: log v~o y A + A+/Tr + A2Tr + A3T + A4T r 2 3 l r + (A AT + AT )Pr + (A8 + AT)P -log P while the factor v () is given by: log v 4) - 4.23893 + 8.65808T - 1.22060/Tr.15224Tr - 0.025 (Pr - 0.6) and may be considered to be a correction term. Tables VI and VII give values of constants recommended by Chao for use in this correlation, as well as Pitzer's acentric factor, w. Phase Rule Considerations If an estimate of the vapor-liquid equilibrium phase compositions can be made, the correlations that have been presented thus far can be used to provide improved estimates of vapor-liquid equilibrium composition ratios. However, for multi-component systems, the Gibbs Phase Rule indicates that additional information must be provided before these ratios can in turn be used to provide improved estimates of equilibrium compositions. The Gibbs Phase Rule may be deduced from elementary algebraic considerations. Any set of N independent variables is said to be

-51TABLE VI COEFFICIENTS IN PURE LIQUID FUGACITY COEFFICIENT EQUATIONS Simple Fluid Hydrogen A0 5.75748 1.96718 A1 -3.01761 1.02972 A2 -4.98500 -0.054009 A3 2.02299 0.0005288 A4 0 0 A5 0.08427 0.008585 A6 0.26667 0 A7 -0.31138 0 A8 -0.02655 0 A9 0.02883 0 TABLE VII PHYSICAL CONSTANTS Component TC(~R) PC(psia) V(cc/gm-mole) (cal)1/2 Benzene 1012.7 714.0 89.4 9.158.2130 0.215 Cyclohexane 997.7 561.0 108.7 8.196.2032 0.158 Hexane 914.2 440.0 131.6 7.266.2972 0.300 Hydrogen 60.2 190.8 31.0 3.250.0000 0.000

-52completely defined by N independent relationships between these variables. If the number of independent relationships between the variables is greater than the number of independent variables, statistical methods can be used to determine the best values of the independent variables that will satisfy all the relationships. If, however, the number of relationships is less than the number of variables, the number of independent.variables can only be reduced by the number of relationships. This fundamental idea underlies the Gibbs Phase Rule. For a two phase, N-component, noninteracting system consisting of vapor and liquid at equilibrium, the variables in the liquid phase are: x. x2o x)... xN] PT while the variables in the vapor phase are: y1l Y2, Y3 ", YN'P'T In this case, there are 2N + 2 independent variables, as the pressure and temperature in both phases are equal. The relationships between these variables include: Zx = 1.0 Yi = 1.0 and L Gi = G. so that there is a total of N + 2 relationships.

-53The number of independent variables can be reduced by the number of relationships, so that there remain: (2N + 2) - (N + 2) = N independent variables that must be specified before the system is defined. For binary mixtures, the specification of pressure and temperature completely defines the system. Multi-component systems require that N - 2 additional variables be specified. If this problem is considered in relation to a physical application, material balance equations may be added. Along with a specified operating pressure and temperature, this will provide sufficient additional information so that the system will be completely defined. The variables in the feed stream to an equilibrium stage are compositions: x, xF2 XF,... XF F1 F2 5 FN the flow rate, pressure and temperature of the stream. The variables in the product streams are also compositions, pressure and temperature, so that the total number of independent variables is 3N + 7. In this case, the relationships between these variables include: Xi = 1.0 Zyi = 1.0 XFi= 1.0 -L -V Gi = Gi F = L+ D FXF = Ixi + DYi so that there are 2N + 3 relationships between the variables.

-54Generally, the composition, flow rate, pressure and temperature of the feed stream are specified. In this case, there would be 2N + 4 independent variables and 2N + 2 relationships between the variables. The number of independent variables remaining to be specified is 2: the pressure and temperature of the equilibrium stage. The energy balance can be used to determine the operating temperature of the equilibrium stage. Alternatively, if the operating temperature is specified, the energy balance determines the amount of heat that must be supplied or removed from the equilibrium stage in order to maintain this temperature. This type of analysis can be applied to the many types of equilibrium stage separation equipment found in a chemical or petroleum process plant. Outline of Correlation Procedure The concepts presented in this section have been combined to predict the experimental vapor-liquid equilibrium compositions measured in this work. The experimental compositions were used to calculate a complete material balance around the equilibrium cell. The hydrogen-free composition of the liquid phase and the calculated feed were assumed to be equal. This information was then used as a basis for predicting vaporliquid equilibrium ratios by means of the two equations of state method. For a specific example, consider the prediction of equilibrium compositions in a four component system. The feed composition to the cell has been estimated and the pressure and temperature of the run are specified. By a material balance, we have: F = L +D FXFI = Lxi + Dyi

-55Per mole of feed, we find: xFx2 x XF-X3 XF4-x4 2 2 3-x3 y4-x4 Solving for x2 and x3 in terms of x4: x4xF (K4-1) x2 = XF4(K2-1) + x4(K-K2) X4XF (K4-1) x =, -............. xF (K3-1) + x4(K4-K3) where Ki yi/xi The quantity x1 can be found from the relationship: x = 1.0 - x2 - x3 - x4 and the final equation relating these variables is found from the relationship: Y1 + Y2 + Y3 + Y4 = 1.0 so that x, (K 1-K+ XF2(K2-K3) x4(K4-l) -+ -- - (K1-l) + x4(K4-K1) xF (K2-1) + x4(K4-K2) + K3(l-x4) + K4x4 = 10 This last equation has been solved for x4 on a 704 IBM computer using Newton's method of approximation. The vapor-liquid equilibrium ratios, Ki, were found from the two equations of state method:

-56Ki = ii/(Pi where the liquid activity coefficient, yi, was given either by: L(si-^b)2 7i = exp(V(.. )R from Hildebrand's regular solution theory, or by: VL L(5i-5M)2 V V Vi3i3M) -i =L exp( - + 1. - ) Yi VL RT V -M -M from the present modification of this theory. Further, the vapor phase fugacity coefficient, cpi. was given either by: 2 2 ci = exp{[Bi - A2 + (Ai - AM) ]P} from the Redlich-Kwong Equation for moderate pressures, or by: RT 2exp[ jB y j] CPi 7T v J J i -M -M from the Virial Equation of State. The pure component liquid fugacity coefficients were found either from Chao's correlation, or from vapor pressure and liquid volume data on the pure hydrocarbons. A first estimate was made of all unknown compositions and these estimates were used to calculate activity and fugacity coefficients, from which K-values were calculated. The improved K-values were then used to re-estimate x4. When the integrated form of the Virial Equation of State was used, the equation of state was first solved for the largest root of V at constant pressure and temperature. In general, the number of positive

-57real roots of an equation of degree N is either equal to the number of its variations of sign or is less than that number by a positive even integer. The largest positive real root of the Virial Equation of State has been assumed to be the dew point volume, while the smallest root has been assumed to be the bubble point volume. The Virial Equation of State, terminated at the second virial, is a quadratic equation in volume, and so may be solved directly for the dew point volume. Having solved for x4, the values of xl, x2 and x3 were found. The vapor compositions were estimated from the relationship: y = K.x. The new values of compositions were then used to make new estimates of the activity and fugacity coefficients. This process was repeated until two successively calculated compositions agreed as closely as was desired. This method of calculation can be used for an N-component mixture. While it is tedious if computed by hand, it is easily programmed for a digital computer. Two different sets of parameters for these equations have been used to predict the measured vapor-liquid equilibrium composition ratios. In one set, the empirical solubility parameters, liquid volumes and pure liquid component fugacity coefficients recommended by Chao were used(8) Virial coefficients were predicted by the methods of Pitzer (45) (47)T and Curl(5) and of Prausnitz. (47) These results are reported as being calculated from generalized data in Tables VIII, IX, X and XI.

TABLE VIII VAPOR-LIQUID EQUILIBRIUM COMPOSITION RATIOS FOR BENZENE USING VIRIAL EQUATION OF STATE Volumetric Entropy Ideal Entropy Observed Calculae Calculate Calculate Calculaela Run K-Value K-Valuekl) % Dev(2) K-Value % Dev(2) K-Valuel) % Dev(2) K-ValueT ) Dev(2) 100~F. 18 0.019 0.011 - 42.1.012 - 36.9 0.011 - 42.1 0.013 - 31.6 22 0.013 0.007 - 46.2.009 - 30.8 0.007 - 46.2 0.009 - 30.8 21 0.015 0.007 - 53.4.008 - 46.7 0.007 - 53.4 0.008 - 46.7 25 o.oo8 0.005 - 37.5.006 - 25.0 0.005 - 37.5 0.006 - 25.0 40 0.014 0.007 - 50.0.009 - 35.7 0.007 - 50.0 0.009 - 35.7 44 0.009 0.007 - 22.2.008 - 11.1 0.007 - 22.2 0.008 - 11.1 41 0.007 0.005 - 28.6.006 - 14.3 0.005 - 28.6 0.006 - 14.3 45 0.005 0.004 - 20.0.005 0.0 o.oo4 - 20.0 0.005 0.0 50 0.010 0.008 - 20.0.010 0.0 o.008 - 20.0 0.010 0.0 51 0.008 0.005 - 37.5.006 - 25.0 0.005 - 37.5 o.oo6 - 25.0 Abs.sum of Deviations 357.5 225.5 357.5 220.2 Abs.avg.% Deviation 35.8(3) 22.6(3) 35.8(3) 22.0(3) 200"F. 19 0.067 0.072 + 7.4.070 + 4.5 0.074 + 10.5 0.072 + 7.4 20 0.050 o.045 - 10.0.46 - 8.0 0.046 - 8.0 0.047 - 6.0 23 0.056 0.051 - 8.9.052 - 7.1 0.051 - 8.9 0.052 - 7.1 24 0.030 0.031 + 3.3.033 + 10o. 0.031 + 3.3 0.033 + 10.0 43 0.042 0.050 + 19.0.051 + 21.4 0.050 + 19.0 0.051 + 21.4 47 0.041 o.o46 + 12.2.047 + 14.6 o.o46 + 12.2 0.047 + 14.6 42 0.029 0.030 + 3.5.033 + 13.8 0.031 + 6.9 0.033 + 15.8 46 0.023 0.027 + 17.4.030 + 30.5 0.028 + 21.7 0.030 + 30.5 52 0.026 0.034 + 30.8.036 + 38.5 0.034 + 30.8 0.036 + 38.5 53 0.056 0.058 + 3.6.058 + 3.6 0.059 + 5.4 0.058 + 3.6 Abs.sum of Deviations 116.1 152.0 126.7 152.9 Abs.avg. % Deviation 11.6(3) 15.2(3) 12.7() 15 ) NOTES: (1) Calculation based on specific data (2) Percent deviation = ((Kcalc - Kobs)/Kobs) x 100 (3) Absolute average percent deviation = (\1% dev. |)/number of samples (4) Calculation based on generalized data

TABLE IX VAPOR-LIQUID EQUILIBRIUM COMPOSITION RATIOS FOR CYCLOHEXANE USING VIRIAL EQUATION OF STATE Volumetric Entropy Ideal Entropy Observed Calculate2 Calculate Calculated Calculate4 Run K-Value K-Valuel) % Dev(2) K-Value 4) % Dev(2) K-ValueMl) % Dev(2) K-ValueW % Dev(2) 10~oF. 30.016.008 - 50.0.010 - 37.5.008 - 50.0.010 - 37.5 32.011.006 - 45.4.007 - 36.4.oo6 - 45.4.007 - 36.4 34.009.008 - 11.1.009 0.0.008 - 11.1.009 0.0 35.005.005 0.0.006 + 10.0.005 0.0.oo6 + 10.0 40.015.007 - 53.4.009 - 4o.o.007 - 53.4.009 - 40.o 44.015.008 - 46.7.009 - 40.0.008 - 46.7.009 - 40.o 41.007.oo4 - 42.8.oo6 - 14.3.005 - 28.6.oo6 - 14.3 45.007.005 - 28.6.006 - 14.3.005 - 28.6.007 0.0 50.012.008 - 33.3.009 - 25.0.008 - 33.3.009 - 25.0 51.012.005 - 58.4.006 - 50.0.005 - 58.4.006 - 50.0 Abs.sum of Deviations 369.7 267.5 355.5 253.2 Abs.avg. % Deviation 37.0(3) 26.8(3) 35.6(3) 25.5(5) 200~F. 31.063.058 - 7.9.055 - 12.7.059 - 6.4.055 - 12.7 33.038.036 - 5.2.037 - 2.6.036 - 5.2.037 - 2.6 36.029.030 + 3.5.032 + 10.0.030 + 3.5.032 + 10.0 37.042.049 + 16.7.048 + 14.3.049 + 16.7.048 + 14.3 43.042.047 + 11.9.047 + 11.9.047 + 11.9.047 + 11.9 47.045.047 + 4.5.049 + 8.9.048 + 6.7.050 + 11.1 42.027.028 + 3.7.031 + 14.8.028 + 3.7.031 + 14.8 46.045.028 - 37.8.032 - 28.8.029 - 35.6.033 - 26.6 52.025.029 + 16.0.032 + 28.0.050 + 20.0.032 + 28.0 53.o60.0 1.051 - 15..5251 - 10.0.52 -.051 - 15.o Abs.sum of Deviations 132.2 147.0 119.7 147.0 Abs.avg. % Deviation 13.2(3) 14.7(3) 12.0(3) 14.7(3) NOTES: (1) Calculation based on specific data (2) Percent deviation = ((Kcalc - Kobs)/Kobs) x 100 (3) Absolute average percent deviation = (Z*% devj)/number of samples (4) Calculation based on generalized data

TABLE X VAPOR-LIQUID EQUILIBRIUM COMPOSITION RATIOS FOR HEXANE USING VIRIAL EQUATION OF STATE Volumetric Entropy Ideal Entropy Observed Calculated Calculated Calculated Calculated Run K-Value K-Value(l) % Dev(2) K-Value(4) % Dev(2) K-Value 1) % Dev(2) K-Value(4) % Dev(2) 100~F. 18.015.011 - 26.6.013 - 13.3.011 - 26.6.013 - 133 22.014.014 0.0.017 + 21.4.015 + 7.1.018 + 28.6 21.011.007 - 36.4.009 - 18.2.007 - 36.4.009 - 18.2 25.010.008 - 20.0.011 + 10.0.009 - 10.0.012 + 20.0 30.017.011 - 35.3.013 - 23.6.011 - 35.3.013 - 23.6 32.008.007 - 12.5.009 + 12.5.007 - 12.5.009 + 12.5 34.011.012 + 18.2.014 + 27.3.012 + 18.2.014 + 27.3 35.006.007 + 16.7.009 + 50.0.007 + 16.7.009 + 50.0 50.013.013 o.0.015 + 15.4.013 o.o.016 + 23.1 51.013.007 - 46.1.010 - 23.1.008 - 38.4.010 - 23.1 Abs.sum of Deviations 211.8 214.8 201.2 239.7 Abs.avg. % Jh Deviation 21.2(3) 21.5(3) 20.1(3) 24.0(3) O 200~F. 19.062.071 + 14.5.072 + 16.1.073 + 17.8.074 + 19.4 20.042.042 0.0.047 + 11.9.043 + 2.4.048 + 14.3 23.067.085 + 26.9.088 + 30.4.091 + 35.8.094 + 40.3 24.034.048 + 41.3.055 + 61.8.052 + 53.0.061 + 79.5 31.062.070 + 12.9.071 + 14.5.071 + 14.5.072 + 11.6 33.038.o41 + 7.9.045 + 18.4.042 + 10.5.047 + 23.7 36.048.042 - 12.5.046 - 4.2.044 - 8.3.048 0.0 37.070.072 + 2.9.071 + 1.4.074 + 5.7.074 + 5.7 52.033.043 + 30.3.049 + 48.5.046 + 39.4.052 + 57.6 53.073.080 + 9.6.081 + 11.0.083 + 13.7.085 + 16.4 Abs.sum of Deviations 158.8 218.2 201.1 268.5 Abe.avg. % Deviation 15.9(3) 21.8(3) 20.1(3) 26.9(3) NOTES: (1) Calculation based on specific data (2) Percent deviation = ((Kcalc - Kobs)/Kobs) x 100 (3) Absolute average percent deviation = (Z|1 devl)/number of samples (4) Calculation based on generalized data

TABLE XI VAPOR-LIQUID EQUILIBRIUM COMPOSITION RATIOS FOR HYDROGEN USING VIRIAL EQUATION OF STATE Volumetric Entropy Ideal Entropy Observed Calculated Calculated Calculated Calculated Run K-Value K-Valuekl) % Dev(2) K-Value(4) % Dev(2) K-Value l) % Dev(2) K-Value4) % Dev(2) 100~F. 18 25.256 24.612 - 2.5 20.005 - 20.8 41.977 + 66.3 36.805 + 45.8 22 37.962 48.981 + 29.0 37.314 - 1.7 72.737 + 91.6 59.573 + 57.0 21 13.736 13.078 - 4.8 10.709 - 22.1 22.103 + 60.9 19.418 + 41.3 25 18.717 26.312 + 40.5 20.110 + 7.4 39.055 + 108.3 32.022 + 71.2 30 27.333 22.072 - 19.3 18.062 - 34.0 38.568 + 41.2 34.060 + 24.7 32 16.000 12.379 - 22.6 10.205 - 36.2 21.412 + 33.8 18.942 + 18.4 34 45.045 32.878 - 27.1 25.857 - 42.7 53.184 + 18.1 45.115 + 0.2 35 21.609 17.169 - 20.6 13.584 - 37.1 27.648 + 28.0 23.493 + 8.7 40 46.952 43.392 - 7.6 33.160 - 29.4 66.188 + 41.0 54.472 + 16.0 44 52.105 64.667 + 24.1 47.823 - 8.2 92.070 + 76.8 73.097 + 4o.4 41 22.568 23.012 + 2.0 17.657 - 21.8 35.057 + 55.4 28.886 + 28.0 45 34.276 35.610 + 4.1 26.391 - 23.0 50.735 + 48.0 40.304 + 17.7 50 36.630 39.659 + 8.6 30.931 - 15.6 61.860 + 69.0 51.963 + 41.9 51 17.069 20.543 + 20.8 16.101 - 5.7 31.967 + 87.4 26.891 + 57.6 Abs.sum of Deviations 232.7 305.7 825.8 468.9 Abs.avg. % Deviation 16.6(3) 21.8(3) 59.0() 3.6() 200~F. 19 20.435 19.497 - 4.6 14.402 - 29.5 31.874 + 51.0 26.284 + 28.6 20 11.707 10.612 - 9.3 7.946 - 32.2 17.165 + 46.7 14.198 + 21.3 23 26.971 37.086 + 37.4 24.818 - 8.0 52.807 + 95.9 39.480 + 46.4 24 14.697 20.169 + 37.2 13.592 - 7.5 28.697 + 95.3 21.501 + 46.3 31 20.457 17.806 - 12.9 13.143 - 35.6 29.745 + 45.3 24.564 + 20.0 33 11.768 9.611 - 18.4 7.206 - 38.8 15.843 + 34.7 13.128 + 11.6 36 13.472 14.519 + 7.8 9.720 - 27.8 22.142 + 65.4 16.625 + 23.4 37 23.293 26.415 + 13.4 17.471 - 25.0 40.456 + 73.6 30.285 + 30.0 43 27.429 35.161 + 28.2 22.137 - 19.3 50.846 + 85.5 36.206 + 32.0 47 40.000 48.104 + 20.2 30.189 - 24.5 65.533 + 63.7 46.033 + 15.0 42 14.758 19.264 + 30.6 12.234 - 17.1 27.826 + 88.5 19.859 + 34.6 46 21.667 26.009 + 20.0 16.405 - 24.3 35.458 + 63.6 24.946 + 15.1 52 12.025 15.652 + 30.5 10.821 - 9.8 23.265 + 93.5 17.894 + 48.9 53 26.111 30.673 + 17.9 20.987 - 19.4 45.747 + 75.2 35.088 + 34.4 Abs.sum of Deviations 287.7 319.3 977.9 407.6 Abs.avg. % Deviation 20.6(3) 22.8(3) 69.9(3) 29.1(3) NOTES: (1) Calculation based on specific data (2) Percent deviation = ((Kcalc - Kobs)/Kobs) x 100 (3) Absolute average percent deviation = (Zl1 dev|)/number of samples (4) Calculation based on generalized data

-62. In the second set, the solubility parameters of the hydrocarbons were calculated from the heat of vaporization data and density data. Chao's solubility parameter for hydrogen, reported at 25~ C, was corrected for use at 100~ and 200~F. Experimental density data was used for hydrocarbon liquid volumes,(15) and the Gamson-Watson Expansion Factor method was used to predict the liquid molal volume of hydrogen. (9) The pure hydrocarbon liquid fugacity coefficients were predicted from vapor pressure data. Experimental virial coefficients were used wherever available. These results are reported as being calculated from specific data in Tables VIII, IX, X and XI. For both sets of parameters, liquid activity coefficients were predicted using both the ideal liquid entropy relationship and the entropy predicted by the volumetric correlation. The results of using the second set of parameters with the volumetric entropy function are presented in Table XVII,taken directly from the IBM computer and placed in the Appendix. These tables include the calculated interaction virial coefficients for hydrogenhydrocarbon mixtures, and the vapor-liquid equilibrium composition calculations using these experimental interaction coefficients. Coefficients for the Redlich-Kwong Equation were estimated from the physical properties of the pure components.

CONCLUSIONS Examination of the data obtained in this work reveals that specification of the temperature and pressure of a hydrogen-hydrocarbon mixture does not completely define the vapor-liquid equilibrium composition ratios of the components studied. These ratios also depend upon the relative amounts and the physical properties of the other components in the mixture. The interaction of all variables is difficult to present in a concise graphical correlation. However, the experimental vapor-liquid equilibrium composition ratios have been correlated analytically by means of the two equations of state method: Ki = 7iVi/pi The fugacity and activity coefficients in this correlation have been predicted independently of the experimental data obtained in this research. This correlation predicts the benzene-cyclohexane azeotrope at the elevated pressures. The over-all consistency of the experimental and predicted results indicates that this method of predicting K-values has general applicability. The fugacity coefficients of components in the vapor phase have been estimated by means of integrated equations of state. The Virial Equation of State, terminated after the second virial, as well as the Redlich-Kwong Equation of State, integrated for moderate pressures,(50) has been used. Results from the two equations of state were consistent~ -65

-64Interaction virial coefficients for hydrogen-hydrocarbons were back-calculated from the data for comparison with values predicted by a method proposed by Prausnitz (47) The accuracy of the calculated hydrogenhydrocarbon interaction virial coefficients depended upon the accuracy to which all the other parameters used in predicting K-values were known. As experimental data did not exist for all the parameters required, the accuracy of the calculated hydrogen-hydrocarbon interaction virial coefficients may be insufficient to provide a definite check on Prausnitz's correlation for molecules of widely differing size. Chao and Seader(8) have used the Hildebrand Solubility Theory to predict activity coefficients in the liquid phase. Using the empirical solubility parameters and pure liquid component fugacity coefficients calculated by Chao from existing vapor-liquid equilibrium data, and generalized P-V-T data of Pitzer and Curl, 45) the average absolute deviation of predicted hydrogen equilibrium values from the measured values was 314%.4 This deviation increased to 64.5% when hydrocarbon solubility parameters based on physical properties of the pure liquid hydrocarbons were usedo Available experimental P-V-T data was used in this latter case to evaluate vapor phase fugacity coefficientso The Hildebrand Solubility Theory used by Chao is based on the assumption that, despite differences in molecular size, thermal agitation is sufficient to provide complete randomization of the molecules in the liquid phaseo(20) This implies ideal entropy of mixing. As the difference in the molecular size of hydrogen and the hydrocarbons studied in this work was appreciable, the Flory-Huggins type volumetric correction to the entropy of mixing was applied(16l17,25)

-65Hildebrand has used this correction for binary mixtures, but it has not previously been applied to multi-component mixtures in the form presented here. This change in the liquid activity coefficient correlation reduced the absolute average deviation of the hydrogen equilibrium values based on Chao's empirical solubility parameters and pure liquid component fugacity coefficients from 31.4 to 22.3%. When the proposed correlation was used with the solubility parameters calculated from pure liquid hydrocarbon physical properties, it reduced the deviation from 64.5 to 18.6%. As the molecular size of the hydrocarbons was approximately equal, this new correlation did not improve the predictions of the hydrocarbon vapor-liquid equilibrium ratios. These ratios had an average absolute deviation of 15.4% at 200~F. and an average absolute deviation of 27.35% at 100~F. At the relatively low hydrogen liquid and hydrocarbon vapor concentrations encountered in this work, these results indicate that compositions have been predicted to within approximately 0.005 mole fraction of the measured composition. Prediction of vapor-liquid equilibrium compositions may be improved further in the future. Work is needed to clarify and improve the prediction of mixture coefficients in equations of state, as well as the prediction of equilibrium compositions of mixtures containing polar components. The concept of ideal mixing of volumes i nthe liquid phase should also be re-examined. Finally, as physical chemists improve statistical methods of treating liquids, their results should be incorporated into generalized correlations for engineering use.

AP PEND I CE S -66

SOLUBILITY PARAMETER ESTIMATION The solubility parameter, 6, used in this work, can be estimated in at least four different ways. For components that exist as liquids under the conditions being studied, the solubility parameter can be estimated from the properties of the component. For example, an interpolation of data on heats of vaporization of benzene, reported by Rossini (53), indicates that at 100~Fo. AHV = 7.918 kcal/mole and from density data reported in the N.G.A.A. Data Book (1957)(15) PBz (100 F.) = O 859gms /c.c. By definition, it follows that: AEV 1/2 Bz(100~F.) = ( VL 7V8 - RT 1/2 ( VL (7918 - 1.9872 x 310.9)1/2 78/0.859 = 8.97 Table XII includes solubility parameters of the hydrocarbon mixtures which were calculated in this manner. A second method of calculating solubility parameters consists of considering the solubility parameter to be a correlating function -67

-68for liquid activity coefficients, similar to Van Laar's or Margules' constants. By comparing Van Laar's equations, as used by White for isobaric equilibria:(66) in 71 = A/T [1 + Axl/Bx2]2 and in Y2 = B/T [1 + Bx2/Axl]2 with Hildebrand's equation for liquid activity coefficients of binary mixtures: (20) L 2 RT in 71 = V(1l-52)1( L -----— + L ~ -~ ~2 Xl-V L 4. 12 RT in 72 = V2(62-81)2( 1_1 )2 x VL + x VL 1-1 22 Edmister(14) has shown that: A =v /R (68-82)2 B = v/R (61-62)2 Solubility parameters of substances that do not exist as liquids at the temperature of interest can be estimated from their Van Laar coefficients or calculated directly from vapor-liquid equilibrium data. Chao has calculated a number of solubility parameters from data on vapor-liquid equilibrium. The values he reports for the components of interest are also in Table XII.

-69Hildebrand and Scott report that the variation of solubility parameter with temperature is given approximately by the relationship: dln5 = -125a dT where a denotes the coefficient of thermal expansion. Over a moderate range of temperature, a may be taken as constant. For hydrogen at one atmosphere, a is 0.00366 from 0 to 100~C.(44) Using this value of a to evaluate the variation of solubility parameter with temperature gives the result: in 5H2[(cal/ml) l/] = 1.17865 - 0.004575(T(~C) - 25) for hydrogen. The value of the hydrogen solubility parameter, reported by Chao at 25~C., was extrapolated by means of this equation to 100~ and 2000F. and is tabulated as a calculated solubility parameter in Table XII. Still another method of obtaining solubility parameters is used by Hildebrand. From the thermal equation of state: aE 6P () =T() -P (av aT-v VT TV Hildebrand measures the slopes of a component's vapor-pressure curve at a series of pressures and temperatures in order to evaluate the right side of this equation. Then: aE 1/2 Values reported by Hildebrand are tabulated in Table XII Values reported by Hildebrand are tabulated in Table XII.

-70Finally, Van Laar(59,60) has shown that for a van der Waal fluid: VL where "a" is the van der Waal "a". Values of v are also in Table XII. VL TABLE XII SOLUBILITY PARAMETERS Calculated Reported by * Chao (8) Hildebrand(20) \fa Compound 100 F. 200~F. at 25 ~C. at 25 ~C. V Benzene 8.97 8.13 9.158 9.0 7.87 Cyclohexane 8.03 7.35 8.196 7.8 7.37 Hexane 7.09 6.31 7.266 7.2 6.22 Hydrogen 3.06 2.38 3.25 - 2.18 2 2 NNOTE~ a - 27 R2Tc 64 Pc

THERMOCOUPLE CALIBRATION The thermocouples used in this work were calibrated against standardized thermometers in a temperature control bath. The thermometers had been calibrated by the U.S. Bureau of Standards. Readings were taken at two elevated temperatures and at the ice point. This permitted evaluation of the constants in the equation: E = a + bT + cT2 By alternately reading the thermometer and the standardized portable potentiometer, a good estimate couldbe made of the actual temperature of the thermocouple at the instant the potentiometer was read. For the thermocouple used to indicate the equilibrium temperature, the constants in the temperature-EMF relationship were: a = -6.9005 x 10-1 b = 2.13531 x 10-2 c = 6.59597 x 10-6 for T in degrees Fahrenheit. At 100~F., this thermocouple gave the reading: E = 1.511 millivolts while at 200~F., it gave the reading: E = 3.844 millivolts Experimental calibration data obtained for the thermocouples used in this work is presented in Table XIII. -71

TABLE XIII tHERMOCOUPLE CALIBRATION DATA T.C. No. 0 T.C. No.2 T.C. No.3(4) T.C. No. 4 T.C. No.5 T.C. No.6 T.C. No.10 Temp. Milli Temp. Milli Temp. Milli Temp. Milli Temp. Milli Temp. Milli Temp. Milli Reading (~C) Volts (~C) Volts (~C) Volts (~C) Volts (~C) Volts (~C) Volts (~C) Volts (01W 0 0 0 0 0 0 0 0 0 0 0 0 0 0 o(l) o o o o o o o o o o o o o o 1(2) 64.48 62.80 65.33 64.17 63.82 64.80 65.10 2.614 2.539 2.651 2.591 2.577 2.615 2.658 -R 2 64.42 62.76 65.29 64.10 63.75 64.76 65.02 3(3) 103.7 103.6 10.6 6 1036 10103.7 103.7 103.7 4.283 4.281 4.290 4.278 4.278 4.277 4.276 4 103.7 103.6 103.6 103.6 105.7 103.7 103.7 NOTES: (1) Both junctions immersed in ice water (2) Calibrated with Princo thermometer 255197 (3) Calibrated with Princo thermometer 503944 (4) Thermocouple used to indicate temperature of bath

CHANDLER GAUGE TESTER CALIBRATION The absolute accuracy of the Chandler Gauge Tester, No. D3-13, has been determined in the pressure range of interest by comparing the calibration of a 1500 psi pressure gauge, No. C2-473, obtained by using the Chandler tester, with a calibration obtained using American Gauge Tester, No. 1315. These results, shown in Table XIV, indicate that the gauge tester used in this work is accurate to within + 3 psi in the pressure range studied. TABLE XIV GAUGE TESTER EVALUATION American Chandler Gauge Gauge Tester Pressure Tester Pressure No. 1315 Gauge Difference No. D3-13 Gauge Difference 525 535 -10 600 613 -13 700 709 - 9 775 783 -8 800 809 - 9 1000 1009 - 9 1025 1033 - 8 1100 1110 -10 1200 1211 -11 1275 1285 -10 1300 1311 -11 i400 1411 -11 1475 1484 - 9 1500 1510 -10 -73

EQUILIBRIUM DATA SOURCES FOR BINARY SYSTEMS Experimental vapor-liquid equilibrium data sources for the binary systems of components studied in this work are listed in Tables XV and XVI. TABLE XV EQUILIBRIUM DATA SOURCES FOR HYDROGEN-HYDROCARBON SYSTEMS Press.Range Temp.Range Phases Hydrocarbon Ref. Author psi ~F. Studied Benzene 9 Connolly 116-3050 320-500 Vapor,Liquid 26 Ipatieff 380-4420 77-212 Liquid 31 Krichevskii 15-3500 77 Liquid Cyclohexane 18 Frolich 0-1550 77 Liquid 32 Krichevskii 720-10,000 68-140 Vapor,Liquid HIexane 18 Frolich 0-1620 77 Liquid 41 Nichols 0-10,000 40-460 Vapor,Liquid TABLE XVI EQUILIBRIUM DATA SOURCES FOR HYDROCARBON-HYDROCARBON SYSTEMS (Data at one atmosphere) System Ref. Author BenzeneCyclohexane 19 Harrison 33 Kumarkrishna 51 Richards 54 Scatchard 57 Thornton 65 Weck Benzene - Hexane 33 Kumarkrishna 40 Myers 58 Tongberg -74

CALCULATION RESULTS The calculations shown in Table XVII were based on the two equations of state method of calculating K-values. This method is discussed in detail in the sub-section entitled "Outline of Correlation Procedure", Generalized data was used only where experimental data did not exist. Further, the entropy of the liquid solution has been assumed to be a function of component volumes. The "Initial Value" column contains the values of composition that were obtained experimentally, and the results of the first calculation of activity and fugacity coefficients. The K-values reported in this column are not the ratio of yi to xi, but rather are ratios of activity and fugacity coefficients. The "Virial Equation Values" columns are the summary of the results of this calculation using the Virial Equation of State to calculate the vapor phase fugacity coefficients. All data was supplied to the computer in the program for the results reported in the column, "Unadjusted". The data in the "Adjusted" virial column are the results of using hydrogenhydrocarbon interaction virial coefficients that were calculated from the data. In this calculation, the vapor phase activity coefficient was calculated from the relationship: Pi = YiVi/Ki where Ki is the experimentally determined equilibrium composition ratio. This step required the assumption that Yi and Vi were known exactly. -75

-76Then values of all variables, except those that were to be solved for, were substituted into the integrated virial equation: v 2 PYM In cpi - Z. yjBij(T) - In M lnp V_ =j- RT ese calculations were run in groups of four, and the desired interaction virials were solved for by a method of least squares. The data presented in the "Redlich-Kwong Values" column is based on the use of the Redlich-Kwong equation, integrated for moderate pressures, to estimate vapor-phase fugacity coefficients.

TABLE XVII TABULATED CALCULATION RESULTS -77

-78RUN NUMBE__R 18 TEMFIERi TURE 1 00. 00 DEGREES FHRENHET —------- PRESSURE 567. PSIA VIRIAL EQUATION VALUES REDLICH -KWONG INIIIAL VALUE ADJUSTED UNADJUSTED VALUES ----—, —----— _-_-_-__-_. ____,____ __Jll~ -^ —— J____ —----------------------- VOLUfi1E OF LIQUID (CC PER GM MOLE) 1 1.LCi 2 120.975 120.899 120.890 V.OLUdE OF VAPOR (CC' PER GM r1MOLE- 5.4.0 661 582 675. 695______ BEiE INZ EE Y 0.004 ~0.0020 0.002 L0.002.1 2 1 0 ~ 10. 20 O. AUE 0.017 0.010 0.2011 0.10 ACTIVITY COEFFICIENT,LIQUID PHASE 1423 1 4.24 1 425 1~.425 FbUA RIT', PURE OL 00L 0I007 L0 L. 07, ~ 0007 FUG!iC:IT'IT COEFFICIENT, VAF'OR PHfSE 0.9 04 ~ 0.988 0. 922 0.928 CYCLOHEXRNE Y O'. Ci. 0 0 _ ^ - - -- -- - — _______ _ -_ — ____ -____ ~- __ ______ _ __ _ __P._ ___ - -__-0 i____ _________ -____-__________ — — _- ____'K.ILUE. 008.008 0. 008 _ iCTTI:ITY COEFFICIENT, LIQ-UID FPHSE 1~ I04 1.084 1.0 - 1. 085 108.5 FUGRCITY, PURE'~ ~ A:.17' 0007 0.007 O~ 0.7 L0.007 FUGiC I TY CO:EFF I C IET, VPF'OR PHFISE.0. 9 979 ~ 91 3 0.937 HE i-.A E................ O~0 11 0.08 UO~ 0 0.008 0. 7.51 0.750 0.750 0.750 _K'Fli LU E iI Lii L' III U _ _ _ _ _ 01 _ 1 i_ _ Ri 1 _ FKGIVAL.T UE 0.015 0.010 0.011 0.0110 -I TI:IT COEFFICIENTPLIQUID FHASE 1. 0I0I 1 ~IU 8 1. 008 1 U008 F IIXJ C I T., F'URE 0.1 H OI 1 0 ~01L 0I ~ 0110 F UGi CITY'V COEFFICIENT, VAFPOR PHPASE 0.32 1.021 0.5' 1 0. 60 H Y D'F R O- i3E N 0.0'_ 0.:-.i! -.I 0.040 O.040 K VRLUE"'"" - -_ - 25.51 8. 1 7 9 24 61 2 24.591 ACTI,.IT COEFFICIENT,LIQUID PHAFSE 1. 1.661.. 686 FF,: IT, F.PUR E 14. 929 14.929 14.929 14. 929 FUGFiC: ITV COEFFICIENT, VAPOR F'HASE 1.02. 000'3 1. 0 024 I'TER.FCTIOON VIF I RIL C:OEFF I CIENTS BCH LROGEN-BENZENE. -140.588 -4.000 H Y R I: G E It - BCL HE ZE fil EE 1. - - 2 7.:Ci 000 E,HD'.ROGEN-HEXi:NE.) -51.052 7.000 RUN-F' Ei^i~i~TII'^Si —-------------- -- - - ----— _ —---------— ___ —-----— ____ —----— _-. —------ TE'P'EF TURE 1 00. 00 DEGRFEES Fr':HRENHE I Tf P RESE I E 580. F'S I A VIR IAL EQUFRTION', L U E S FR E D L I C: H - b.I ON G INIiTIL VALUE DA 1J -E UNDJU STEE UA' -i E yRLLIES',OLU'iE OF LE I L I,IQUID CCC: PER GiM MiLE) 8.540. 50 9. 20 9 919 DiLU 1'iE OF VUP0R P__C_: F''EFR GM _ "I'"lLE: " 5 S _ R_84' 6_ __1 6_60.88: - " _ bEl B.. Z El'..E'_0 O. Ci 1 0 Ii. 005 - 0 Li' f.I It 0 0L: X A. 7 ":, 0.763 0. 768 0.77'.7 K'VA LUE Ii. Ii' I' 0 I I'. l 07 "CTI.ITY COEFFICIENT, LIQUID FPRSE 1.05 Fi. 1 48 ~ 1.i 48 1. 04 FUGC:I TYP COEFFICIENT.IVPOR PHRSE.95 0. 0.3'.1.9 C'' L 0 H E XN r.. E "FU-G RFCIT',PURE ~ 0-i 007 0. 0 7 0. 007. 0 07 FUG FCITv. C TOEFFICIENT.. VFRPGR PHfiSE:.9."9 0. n Ci i'. 943 HEXAit'E K V'LUE 0.05 0 3 0. 1 4 i01 NC TIkVIT. COEFFICIENT, LIQUIID PHASZE 1. 1.369 1.~:-~ 1.368 FUGACITY'., PURE O.'010 1. 0 1 O. 0010. I010 FPUGi C ITY COEFFICIENT,V APOR PHfSE o.39 1 22. 95.967 HYDROGEN _X O. 0.026::', 0.020J 0.020 0.020 K ",-LU~E 1 - - 2 51.5 48. —------— 1 —-1.9.5 ACTIV'ITV COEFFICIENTT LIQUID PHASE'3415 3.431 3.429 3.4291 FUGiNTITV,PURE 14. 14 14.,14 14.614 14.614 FUC:ITV ITYCOEFFICIEfNTTVRP R F'HPSE 1~ 2L 1. I0iO 1._23 1.024 INTERCTION V'IRIPLL COEFFICIENTS B' HYDROI3EN-BENZE'.-E) -1 40. 588 -4.000 E,: H Y R E N - H YE L I E:: - E. - -~ 000 B CH' DROGEN-HEXIFtNE:: -51.052'7. 000J

-79RUN NMi'MBER 21 fEMFERRTURE 100.00 DEGREE5S FRHRENHEIT PRESSURE 1100. PSIA VIRIAL EQUFi TIOrT'l V'RLUES REDLICH-KWONG IFITIAL VALUE ADJUSTED LIHARDJ ISTED VALUES Ui~~T~ii-,,tl',,,,,J^__~3-c^U^l[E.Qr — -- VOLFUi E OF LIQUID (CC. FPER GM M1 LE:;, 18027 17.990 7.702 7 117.' 17. 702 11 7. 687 VOLUME OF VRFPOR CCC PER GMt MOLE) Z:: 1;'-'.4. 14 1 1O 20 3 5.09 BENZENE Y 0.003 Ci0.001 -0.001 i i i0. 001 X ~* ]0.20.3 0.203 0.2$ ] - i 2 0 2 0.202 1K H- R L UE 0. 0.1 0. i.007 0. C0 07!lP:TI',,IT'-, COEFFICIEHT, LIQUID PHASE 1.463 144.4 1.4.468 F i G -i C: I T- YI' U IR E. Ci-i 4. 0.__04 0. O I HH04 -- 00 UFiUG3' I' —,' C OEFICI NT, F PFO fR F-F' i H S E 0. 85 5' 0.8 7 C'CLOH fE A:R E Y'0. 0. 0. 0. K V'., " R i E 0. 0.005 0.005 -" 0.005 RCTI'I T'. C OEFF ICI ENT, L I Ol PFHAgS0E t1. 0 -.0 i 1. 1 t.874 1 l0.0C F UI G C T C EFFICIE N T,'.FCR F HASE Si.:L:. I- HE i'R.iE Y i- i t C"_i —: i ID. C C, 4 I- 0 I i 5 I-CiC 0 Fi 5,:':, I-i. 7-';4 ". 72 O'72 4D. 722 K VO.LU8E 0.012042 O.0, C!.0057 0.007 Kr: ifLU _FF I C I' --------- --------------------------------------------— ^ F T I TY I'COEFFCIENT, L IQUID 1 1 1.FH EC 1 1. It000 1. 000 F Ui'J-3i, I T'.'IifE0 6 i0..0.-0.0 - 0. 0012, F UG C ITV I OEFF IIENT,'lFGR FFPHSE.-. 042 i': 4 0950 H Y D R I E EN K1'V L! -V'~.'S, _-,- "."_"-..q';_.", -----------— o' —-------—. — - f "1' HE I IF.'8 ~ 1'J C:TI' Ii', OEFFI C IE T, LIQI: D F'SEi1. 2.I8t1.6 79 1.I6, 1 6 79 FU IG CFF:IT' "F FiE T IR F 0 F' F IS E T 1 - 4 1 U00' 14044 1.46 I NTER C-i TIO'N I RIRjLUIFrrnT11"~ f H T E R K iS T l U'H" ij i F.:'i'l~i L' _.,.: ~-. r r i _. l =, 1-,: F i DRO IEi-BENZErE -140.58 -4. 00 E: - i T'E R T 0 E I HE' C' L HE,;L:: - 1.05r,... -7. 000 — - B: C Y D R 0 G E H - H E::: Z H E N:' -L51.4-52 7. C 0IRU-.i UI BERE PRE FSSURf.'E 1 02 P. 1S 1IR''VI R L E:! UTi L IE S R E D I H - I ) I C O G "V!_-I L I1 f"i EOi 0 F L i i;',: U I D ( C: C: "F' E F.: GM MO0 L E::' S F-',. -;;' 29':-.:6. 97.:-:889: 97.78I3 97?. 777', 0LI LIQ U i E C F:CE R G M M 0LE';,..:,.34l. 47 5. 6 VOLLUME OF`WFPOR CCC PER GM J'-lp0LE _ _ _ _ 5 J4 _ __4 _ _ _ 374.4 4 BEHNZEM-E y CO. 0. 1 0 0 0.7 3 0 -.3 K LU E 0.U ti,-_ iLi. 00 -. 0-5 LI.t'05 RCTIV IT COEFFICIENT, LIQUID FPFiSE T.F,2 1.054 1H.055 1.05 F U G R I T V, F'U F:RE _ _. _ _ _ 4. 40L114 0 U L4. 0-04 FUGFiCIT COEFFICIEHttT,RPPOR F:HRSE.T —: - —. — 7 —---— i- -------- -- CYCLOiEXRI'iE X 0. L. 0. I0. i<- V -L-U-E - - t - - - 0.004. 0. 0-05 0. 004C. fCTI,,'IT" COEFFICIENT, LIL:UID PHFSE 1'.Ci,. 1.11 1.0 11 1. 011 FURG ITFr I. F; 4 I.F UE I.. L I. 0 0 44. 0 0 4 0.004 FUGRFCITY COEFFICIENiT, VF'FPOR FPHSE H0.82 0.. -0. L 0.83 —'. 0. 1 3I Y' 0. L2-0 0. l 02 0. OI 2I 0.002 RCTI.ITV'- COEFFICIENT, LI -II D FHPASE. 1. 1 —--------- ------------ --- F U f R C I T'~, F.: r__E i__0. 006: __ 0. 006 __ O. 00i6 __ O. 006 FtUC-.C I IT' C'0EFFICIENHT, VA'F.:R PHASE E. 9.301. 042. 954 I 58 H. IFI E. -: i. E IC V 0.05;.3 0.036 0.03 0.038 AC:TIVITV COEFFICIENT, LIQUID FHAfSE _ 3.343_.~ 3.387 3..38 3.33 FU-fiCITVPURE —-------------------------— 8. 119 ------— ^7TT5 ------— 87TT^ --------- 8.119 —FLUG R- C I TY-, PURE.1 O 1-.,1' 1 100 FUGCF ITV COEFFICIENT, VAPOR PHASE 1.04 1 00 1.044 1.046 IHTERFiCTIOi N VIRIPL CO EFFICIENTS BCHYDFOGEN-BENZENE) -1.-.588 -4. 0Li B ( H-DR UEN —"!t"-l!" —. E"E-0 B <HVDROGEN-HEXftE).LI-51.05217.000

-80RUN NULMBER 30 TEMF;ER ITULRE, 100. 00 DEGREES FREHEIT —-------------- PRESSURE 577. PSIA VIRIAL EQUATION VALUES REDLICH-KWONG INI.TIL VIALUE ADJUSTED rUNDJUSTED VALUES'VOLUME OF LIQUID (CC PER GF;N MOLE) f~25.782 125.081 124.988 124.984 VOLUME OF vfIPOR_ (CC: FER GM MOLE) 6,63.886 650.113 664.255 BENZENEHE V O. I. 0. 0. X O. flD. 0. 0. K V'A.LLIE. 0.010 0.011 0.011 PI:TI'ITY COEFFICIENT, LIQUID FHRSE 1.506 1.-515 1.517 1.517 FUGI:: ITY, FPURE n. C07 O. 007 0.007..007 ------------ FJJR ____ ___________ ____ ____________ __ i007. _____ __CI^.P-7 -_ —----- ^ J - --- 7 --- -- FIURf'; IL TS.:OEFFIrCI EHT, VPFOF. F'HF-iSE.I9:-.9 0. 922 0.928 C,' C: L i FE X A,'R'i E'. O. 000 3 C. 002 0. ~002 0.002',-":,' O. _1' L. 19'1 O1. 1'1 0. 191 K V'ALU E O. Fil 7 0.008.008 0.008'R - F TF IJ, I TV,:EF F Ii C IET, D E 1. 1 1 1 1 3 124_______________ 1. F PU i':: IT'~; F':E P..... 0i.07.00 7 0. 007 0. 007 FUGf I I TYV CI EFF IC I Ei T. P 0 R P FHiSE 0.S0. 7: O.914 _ 0.937 H E;i i E ~'~~~~~~ ~ ~ ~~~..'F.r i O. 1 0008 0.. 008 Ii 008 V _______-~ _ ~_ _ _` _ _____-_-______~Q —-------------- ---— 0 — - - - - --------------- --- -------- ~.................................1. 771 076f,5 0. 7, 4 0.764 K VALUE I.1i 1 C. 0 1:0 0.011 I.011 K...t~. Vf~iUI~E..~_.. ~~ ~~ ~~_~~~_~~_ ~ ~~_ ~ ~__~~~~~_~~~ __~~_~_________ _______ Uj —-- ---- ---- RI:TI IITY Fi:OEFFICIENLT, LIQUrDI C FHiSE I 0 1 i 1.0001 1 i 1 1.000 FUG -RC I TY, F'PURE I. 1 iCi. O! - l.0 0O1 1. 1. 01 FUGlClIT Y COEFFICIEHT V'IPFOR PHASE 0.27 1.02 0.95 0.9 61 H V R: G E J.V.9s4 0.991 0L.90 0.9 0::. O. 0d.0 500 44 0.L045 0 ~ 045 K',:iLUE';-'7. Fi.':': 22.5A S8 22. 072 22. 052 IOT I VIT' COEFFICIEiT., LIQUID FHiSE' 1. 538 1.51 51.538 FU G FiC I T, P U RE Li5.:5 1 4. 5 14. 685 FUHGf'iCT,'"Y CrOEFF I I E!"NT, I',. PHCFORJ PHSE 1 f.i4 1 1. 0 1 0LI1 1.024 IrN-tTERfICTIoI-'IF.IPIL' " EFFIC I ENTS EB,:' I.,` FiR,' 0 G E l - E EfH- Z E N:. -4. 00 B H; R 0 GEN I" CC LH H E i E 0 - 97. -7.0 0 B:'H -,F.:OGEN-HEXHNE":, -52. e 4.3 7.000 RUN U' B E R 32 TEMF:ERTUE-.' 1 Icii. EG EES F:iHRENHE IT F RE S SR U F. E 1e 6 1. P S i A VIR!IFL EQU' TION I'FLUES RE E DL I C:H-K IiiONG I__ iT'il. _VA __iUE j I I U C.D L i.J USTESD -V'OiL E- CLI Qi I'D: ER G'I fFIt MOLE) i'.'":. 2. 77 i 12 1. 9 121.6 1,'-4. 6' LILUME _OF: yP'OFIFR (IC I ER Gt L__ MOLE:'-' F.i. 0. 0.0 VK i L U E. i.Ci 0 L.0 E 1.i. 0 _-VO'__ Or-_R C C C- F' E R G — - tl _ - ) - -------------- J -~ _- ------- ---------- ---- -------------------- i: C: T I V I T'"'" C IEI E F F i C! E HT" L' I gI! l' E1'52;'5 1 5' —~ 5 ~'': I 1i 1 5 I' 4 FUI CIT' U R E iD 0.:4 0.0 4 E0. 4 0.0 I'; -iF I T Y f':V r F F I C 33. I E H T, L I P Li F.: P I ~'E / i. O..3I O. I',', 1; ri. A!"'i 2 0 ~ i-~0 Ii C - IE, 1 O" 0 0 14 K V ""' 0 1: L7. 0.73 0 L! I- iEI.736 0. 35 FUG AfiCIT, PU RE I'.00_i f L0. I04 I.i004 I-.04 F U I'i.CIT "L' OEF FICIENT., V U R PF H i SE.''ii 1. 1. i fI-li. TURE I.40 F.F404T L-.404 8H 1 1. 1 1-C. 0 i- Fl Ui-kiC' IT'~, F'U R E LI-. 0 0 7 r. I L- 0.004 I:THTERFCETI.I VIRIF':L CO-EFFIC:IENTS 1~3F I G A C I T',,, EEF IF. ENE ) -. 4.4 L A' 04III B.y':! "',' E: R 0 G E. - EOE'-. Z E l.ri E, O. - 40 FI- O 0 B,:"'. D R 0 _;E "i - CS-,' C: L HO' HE' E:.:;'Fi -E - 7. 207 - 7 -i i- i 0 B::HVE:ROGE-HE.NE - 52. 143 7.0 I0 0

-81R UN I"i U ri E R 34 ________________________ TE-E.RtiTURE 100.00 DEGREES FPHRENHEiT F'RESSUELI:.E =563. F'PS IT A VIRIRL EQUTIOA H',.:lLUE S REDL ICH-KWONG I._ _ T I AL',I:iLLIE A.i USi 1TED U "iND E_ US TED E,, ALUES 6nL'U'i lE 0 F LIQUID CC C PER G n LE:: 11 8 112.26.3 11 2.211 11 2.208 VO0LUM1iE OF V A F'0R CC: PFER GO I'I iJI0L E )_ ______b::, ^____^ ^j -- 3 1 C 8 60.. 359 B' E!"-i Z7 E.r.t',~'-','~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~ 0. 0. Fi. K V iL E Et _.. i ID:_. I"_ _ _.00V_ F:''i-".T.T,.:""-i-EFFIC'i-E.i"TLIci_ — "'HiE 1.1 1:':7 1. 202. 1.. 1. 203U7 —----- FU,. TC I T'.,:: F IU F.'CE F_. I]C7 i'"; I i"'i. L.I 7. F " E 0. -! 0.1-1-7 FU~~~ftOITV~ ~r LOF I I"TV P R P hb"""" U -"" J^ O ".8 j9 4" -~" "*3^ 6 FFL- I IFE 9J9 I Il LI _ E_ _ _ _ _ H'iJ ii;^ _ _ _ _ _ _2 ~ 2 - - -___________^2? _ _ _ G- P I T 007~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ii.....:...:.-.......00.'.'-007': ]" A0.0':. ". 007 "," i'IT. iOEFFICIENT^ VflPO.:i F('SE____________ L.'7 9 ~ i" 1 90. d' Ui. — I Ci O2'. HE~~~~fihE """"" "'" " ~~~~~~~~ —----------------------------------------------------- 0j!' 0 ill7 A,' T I.T F I' I L0'-,: 1 1 - L.01 i012: 1. 1 L U Ci-C.JC I T Fl Li.' E J 1'" 0 I 0. 0 1 0 F I_; G A C: I T ",:', F' t ~ ~ ~~~~~ i J ]';C'? i -.il0' 1_-.0liIi - F C I I- i T1': 0 1 F F I C I A'F; FHSE n.: A' i C: T Ii' - 9..:- 5H'E:-: 14'i F....... ","^~~~~~~~ 0~~~~~~ ~~.1 C *: C. *. 22 C0. i 0. C 0 0. 0;:'::~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~ 1".i.: 5 O.17. n 4 -71 74. K..j_!E t:'.i.1 I 1-f I_ 1-f F U Ci; P, C I'.,"., P RO.']' I ":i O. 01 0'.11 2 I. 0 0 K'.. L U E - --- "'. —... — -.-,-.. —. —.^ ^ -—. —--- -- ------— ^ — ---.- -- - - - -- - - - - I-h. I-I i-r,~~~~~~LI( 1[ Fif-'I3 1 0'If1i'- l) F' I 1 i Ci F IE - - F- -..: 1.. 9 F U -1 11D 0 1 0 0 o 1 n~~~~~1 ~j F C" I, " I........... 0.' 91..-29.'029', — "-. 3-: FUGHL.T1.i' -IOI I [ V i4FIP R PLIH E.0 1.000.102 1.023',:'.',' r). R 0 2 r'E, I.: 0 E. H 7E E 0 F. 4.00 0 K',,'i::: L i EM..................................-.....:;"."-.'":!,' 2.?_..-'.-.-._-;-...'.,:.,_, -._'"r:-: —------— _-_____________; _ ~'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-1 0...,- i I-R1 C I T'.'" P i HiF.:a E.., _ ________________5. 1 3 ___. OO_________ TEM~~~~PERATURE "~~~~~~~~~~' 10. EGE'':.)H 1 E- -i 29 I 5 I" — 29-l —---------- PRES LiRi 06 F SIf,_ _______________________________________________________________ FR L I E" L ikT I I-iLlE0 REEL I 7H-KiiDNI 11~t. ^ -1. i tk — H- i r il[: TViL^ -_ _U'*yJED'-m~LHES,,.. F:i. I 0T'.' ":; 23 0 I': F.' I- I C L F E E ":' LI. I P..-.-: 1 202- 7.0 1'i 1 0 BEMZEME - ~~~~~... -^.-.... - - -..-. - - - - - - - _ - - -.....-..-..-._....._._......^_ _.._ _ _. FiUt'-I':' -I E E i.L..; —TEMFl L- F.:I:T i~i;: E FF-CIE T [).IFi ~[,EiD PH.;4:.S'i: ~:iHF; E:'i' 1T I 1 L iFi L I' i-' JK'i lE i,I iiiAD' iiT. flCji',iE. CT.UI N,:L-.'- -- —:';EFF- 1.216..4 -- -—. —------ - --—.. [2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ E'-; 1'? I OI- PU lE __ i.00 0.004 01.004 1.0 r TU i: I T i C FL iE F F I'C: E N T, L I O L I I D P H RS O. 1 1 1 — - - - - - - --- - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - ","* 0. O 4. 0030. 004.0 4' K _:'.. -.... _... ~...-....-...... _.. -... ~..... i'"i 1 "} i-l.I-i._- _ - _ _ J ^ _ _ _ _ _ U J Z ^ _ _ _ _ _ ^ 7 ^ _ _ - _ _ P ^ K V'AL.U E C"i 0.006 0 5F.00 t9 - i 5 O. F i 0 G —— 1~ o c-~ F U~~~h O I T S^ P U R E " "' " "" —- - - - - - - - --— O. O G — - - - - - - - ----- - - - - - — 7D 0 " -- - - - - - - - - - - - - - - -4 - - - - - -T E i'i, iEi'T I -l-i-' -.-E F UrA-'' I0 i'F I E T F'-,.' F'hI_ RE F.1" ").i. L0. - I-16 9 1 il 0.';16U-9 - I -'.1i-f ~NF:~ I'-.ii' F IC E. LIQUID i'KE 1:. -0 ARE. 0T hA U-S- EALUE''E.-. 0L.!'E R E -t 0. 5 0.05 A1 "-L:.'IT' L: C F C C C FEER H.L;!Ii!D F: ".i ~L. IZ t ~U!4 1. i i. - KU A'z L' U?,-Fi:E...... J! C 4. IF i { C; U Flo,.0 -!' -^ -V RLU' —" —" " —~~- -— " —----— ~ —- --------- —?T ---------- 7 —- - - - - -- - - - - -- - - - - -- - - - - - FT I.. T C: I T.'-,: E F- F ]' IC- I E I L T: C L' P F'F.:F H i'SE}.:::'.3 Z"-. E, 2G 0 -.'-G-.1' "E v, PUE.::-CX093E -7. 071 -. 0 9. 000 A CHYIT' COEFFICIE NT,) LIU D PHASE 1.044 i.07 7 1.07 5 1.075 F~~~~~~~~~~~~~~~~~~~~ - -3 -A'- - -'-,-, F' - - --- M- ~Z 7 -': -' ] - " -3 -, -l - -t,- -. -l — 0,2, ---------- ---------- FL F; r- I T'; ":0E F1 F I C I ENIT-i'". V A P C,':: F~.-'':'4 F1-.. 0'2 P. E5 S, 9 4 C'.L,-': RO E H~.At!C K V A ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~~~~~~~~~~~~L U E..:..,7,_,!7: 0!7,S. 1 3 IATER-: T I',.,'IT ",''. T E'FFICEHTL.!!_tIDPHAS E. 22.21 7 2.21 5. ~ ---------— /-5 —--- K IL "I E R LF: C:-, 0H V IFLC: U Li F4 U I: i "FS AL.'' H I, D IF.: 0 IS E F - FB C i" rE. l ". IE ) L f"!. 1,1-4 I4 0 n 51 I...B't'';.0i]!f'-C " C: -:'iD. [3'GEi-.TENZ ^::,__ -97.2 0. -47.000 B,:' H V [- R I-i J E I'"1 -CV OH E A t-E-' -: — i —-------------------- E'C H V D R O G E N - H E ~ ~~fl H E:)____________________________________- 5 2. 1 4 3________ 7. 0 0 0_________________~~~~0 F C

-82RULN NiLliBEE R 40_________ _____ TEMF PER kITURE 1 00. 00 DEGREES FAHRENHEIT PRESSURE 582. PSIfl VIRII L EQUATION','PLUES REDLICH-KWilONG ItflTI'L _L_____LlE_ A ___ IJ USTED UNHD-J USTED'V'ALLUES VOLUME OF LIQUID CCC PER Gt'M MOLE.) 10.3.087 10. 019 12.984 l2.981'OL__ME OIF _ PFOR (CC PER GM, NOLE) -:. 1I6 1 644._361 65-, 65.3 _ BENZ EE B E -I" Z E'-i U.E'' 0. 001"4 U. 002 O. OQ2 0 02d0. 002 \ FI I- tE. -I ft t7 }i' 0.293 0~i. 292 0.292 O. 292 T" T'. TY CEFF I C I ENT: L. 1 UID PHRSE E 1.04 1.07 1.075 1.075 FU~~~fi~~ifS^'CuEF~~~~~fCI'EHT, VfipOR PHHSE~ ~ ~ ~~~Ci ~" i.-. i-.90 0.9880 I 0.937 i' i i 0.937i I'L'I-E~litE___________ ______________________________________________________________ IC' —':L0FI El'-':RI"E' IT CO.FFICIENT, LIQUID PH0E _ 1 1l. 0 1 1'.t005, I-.Li' E L Li E 0. 0 4.7 0.007 0.001' U. 0.007 -------------—. —-—. —-. —-------------- -— j ----- — = —---- i — ------ -:* -, F t' -I I' ~; ~,.,~ l T'.,: r: i_-i S F F.'[ C Z E!"i T, L. i::.! U i D F' H-I E 1 ~ 13 I35 I 0i.' 1 I't75 Ft I'6 FI F:. TY'-,-".. F' LI'(:rtF_' I.!E~ [0T';'IF Oc[ -'7 0' ~F U G'i~i' "I T ['"' U:IE t:: R F' i':PH~. U.;'i}ol ID- i~.-i'?j Ci' —---—'i?. 4' H E;.:Ft'IE "," - o. n.. ~ 0. i:. L tUE Ai, __ __.i 13.1 E -1 TI IT.O 1F]Fi ET: LIQfi'"iDtF Hti:E "' E 1 21 1.27' f 1 27 1 78 _F L; - FiC i' T';::- F'!PF.: E ___________ 01 ii i C l 0.010t ]!"i C!. 0 1 t Oi. 0105 Ft i.......T...... I.' t - - Fv'' T rFEVFFILN'7'f4UR F.' 0 5:.022 - 0.99.971 HVDrOGE V ~ - -.- — ^^ ^ ^ ------------ ----- ---- ----- ---- --------— ^- ---- ---- -- - -- ^ I F~~~~~~~~~~~~ F'O Kk':{ L IO. 02 I. 0.0'2F. 0'. 2 O. 02.:!,} tZt......................... 4'?.5 44.51G 43..39' 4.351 R7 I.~: T l'.; [T L C F F I I L IU D A H i.;E.:.:'. 100- 4 -.041 A. Z,~~~~~~~~~~~~~~~~~~~~~~~~~4 6 F U GC:T, P R E U, 5. i T.5 r 7 [.4 ~ 56 7 1 4. 5 F 7 I G ITI CEFFICIEiN. T'I.: FI" H' E 1 2"..00. W-.__FS4 I I SRE EC: I F.:' FF -1!-'-1 -4.i HEr Fi3 FYI IHE I: (iF.l' —' "', -"} - i-.j - E- H- -: E.1'ti; -E I, 3 -- t':: 2 --. 0 -- C i " B H S T - O G E N C V C L H E ~ h E ^ " **- *-*- -- - - -- - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - -- - - - - - - - - - - - -- - - - - -- - - - - - - - - - - - - - - - - F':. i i - I'.: I'-,,:l'.F_; F.fGE. — HI D E:Fl.'7. I Ili Ill_ T,_A__r__iA R Ut- i U:E: R 44 TEMFE.::UF. cE i0. - DEGF.:EES FH.:EHEil"I Ft RE.SSU. 5E 5';',:,. F''S_____F I t:,,:I-'-L E UfiT 10 H,.RLtiES REDL I C:H-K lt CNI vC!Lut',-i~ ~ ~ ~ ~~~~H I E o-HTTF'Iit;HjD- I:c PTE. r I',iLE:E,''LUME OF LIQUID CC PER GMMOLE:.":-.-i.. 9'.7E'71 92.710 92.71, V- L UL I F E OtF.F.:Hof_'.'CtF'F: GI'I'0L E.: 11i,E ZEE -' -Ei".! S*_________"_____________________O_________Q. - -:-: - _ ——. 0- 0 5- -- —. 0 0 _ -U —- -. 0 j —-—,. s 45.848 0.' E.8 4 R C ~~~~~~~~~~~~~ T I":, T J.:C0EFFI Ca Eh T.. _'' H iS E t ~0C 5I~0Ci 0 I~5'' " F I ITC! FT FICE.T, LQUID- HSE 1'" 15 1'.00'.'005 7.' F UC I T —': T.' -:E F C I E. —'. -` F::IHU.9. FUT TITl COEFFICIENT' POR PHfiE C' I 0 H E::E Fi HF,:i"1'" L'i 2 i'.001 i-. F 1 0i! r. 0 i0i 1i -1 L. T I_~~~~~~~~~~~~' 6'. Fk,'.' RS i.!6D 1.!':7" H0t. 1A' r' 15;7 J F -..-.'^ —---- -- --- -.- --- - -- - - --------------— lr L — _ —--—:i —------------ --— 137 —--------------------- K'., RL UE t/ ~ — "0 015 0.'.07.- 1? Ili.U Il:: f ] 0/C07 L:T, T E FF.'III-. 0 E R I E F............ _KYR-':Y-F;Gi:ltV........ 0.' C -':, O. 0.006 0.006-, ~~~. o i~ o,'_:, A ^ ^ -^ —------------------------------ --— ^ —-------------— _ —--- -_ —— _ —-- F' TIITY COEFFICIENT, LI ID PH iS E 1. 17 5 1 1. 7 2'-.7 I. Ft OF IT' COEFFICIENT.'R PHlS E 1.: 9U"' H:CRI GEN - - ^ ~-.._ _. —. -..~ - _ _-.. — - -- - - -- -.- - - - - - - - - - - - - - - - - - - - - - _- - - - - - - - - - - — _ - -__ _ _ _ _ - --- - _ _.._-. _K b'RL U E 1ll}.. 016 4.1 O. tI H' TI ITY COIEFFICIENCT, LIQUID PHSE. Fj R: T; I TY CV:C:tEFF IC: I E-NT..- L - I-U -----------— H-SE 1' 1 ---- LI 1 L 2._-:-', 1 -L -2._4 FU'C:H CITF I:EELI E -I: 0 I.. 1::'1 of. F LU G A Cs: I T'.," FCI0E FF I C I Et-IT,',.,AF-tF' P FiRS E.9:H.:i 2 1 ~0''. 9K' -.9E_-.::"~ 0 ~ 01 0 i'll ~ 01 5 C,'~~~~~ ~ ~ ~~~~~~. 01 O.0 FUGERRC: IOTN C:IEFF COI EHT:, k,~RF'CiR FICI-E 1 - — 2- - - - - - -2._ —:' - - -'2 —-- B CHPCI'"D.:GE!-i- cCLBHEiEC -1 50.809' - 7. 21 - 4 ~ 000 BEC T:,:H'.,RO CEt-HE F E:H- C:..: U"L I H C'-.:R'E:,- 17. E:0. Oi.: E:' -' v ID R 0 G IS H-HEX: H E:..

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-84RN NUMBER L " r u E 5 0 TE'PE-[E'.'TI-RE 100."1....EGREES F REH E IT PRE S SUR LF.E. 544. PSIP:I A'.'I RF I L E I U A T I H'.'iLES LE EDL I CH- KIONG I H I I'I f L'LI E HD J: TED U NAD JUS TED',LU IES FELE -O TI MIT CF LI:EFICID E TCC PER G F MiOLE -1 1 1 1G6 1 1.34I -, 1.538 11.4 49 FOL- L 0 F R P 0 R:_C FE R G_ IT' M L E7,. 5 4 7,'__9.4:___ 7','BENZ~~~~hE -* " ---- - " " - - ------------------- - --- ------- - -- ------------- B E 2", Ei"~ E Y "i LC__i E' 5 i.Ei._ t_____0______.________0_ _ f05',f': i 0 f_____l_ _ C _ 4_______0. 00 ___4::-"^~~~~~ 0F!. 4 E;~.~ 7 0r'. 4 8~ 8~0. 4:880. 4 - 18 K L Fi L U E n. "0 i- " " O_,__ g _. O _-_ 8_'-___ - O: _ _ _:: DiE: T IV IT'.?- CO!EFF IC-i~.ENT: L I L.'.iUiIDi'FTHN R'EE 1"~ 1.135 1.133 1.14 F 1.3,- 1. 1 34 Er FI IlL IH F U GC I T'-. iRE 0. 7 0.0'7 0.T L C. 7 FUGi-RFIT';:':OEFF I C'IE'NiT,,"': i.i FHS'......... O.PO'::,;:?."":'" o. s,""'.:^""""""^:, o.'-,zt.....i-.-~.i i~~5..... C: Y t.E: L L-Hi E'e' AX R E''*'~~~~~~ ~ ~~~~~ ~ ~~~~~ ~ ~~~~~~~~~~~~~~~~~~~~ O.0 0 01 0.001 0001 I!".IT 1COEFF ICIENTI. P SE-C! I_ 1 __tE. _C -.9 _____ P`:;'., RL. L E. i 2 O. UU," O-_C..............-7'A T! L I T'Y. F I C I EN T L I C.!.. -. 9' 5i. U..'9 8!.E. 921 9'-4 HE I' IF I *i ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I x'1IIIi ^ V l-L U E ~ ~....,........................................... _ S S l _ _ _ _J ^ J L - _ 0. 0 3 O, 0 9 0 1 _ _ IF I'. E U. 0' i'1. "1 10 Ii' FU~h~l F ICIENT,'1P4IF C HSE. FI'.*' F:0.:. F: i*-'EFFiF:IEi" ".L/:4F0RF" 9 C:::. 9) 91; i0. 9', - 0 0. 9' 91 - H;:-::........:. i...................... C C T I I T F/ C. 1E:: F I C I E l-1 T L. I.Q U: I,' F;!h -!_. i:.3 i. G 1,':,.5; I2.61,'3 t". 1 T 5 FT;F' T'.,F'4_ F: I' O.C-' 1 F i,7 7. C, I 1 T F.'.. 9-, H}F4f: T -'r RE A N 5 B'.,.'. R:'.... -..-...........5":-!T:~' " o.'.::,o.'. —,..............-.-..-..... ^.;:,.-..- - -.-:-;,: _ —I..... IT:: (Ti.:.';.:~:::'';,FO, F) 2 I: C. IE -5'" —i..~J "_ —,A 1' JI M F E~_:,. I T'.."Ci~ F; I E: i E ". T. L.' C U I E G r F; E.':. S.'i F";! {.:::'. n 1 E.,- 1'-: 1 FFESUR'I_, _I1__ I F.___._____________________________________ _______________________ i.. - fL R REL I' C l4llNG F 0i_ E OF LI'; I L:' C 1' T.,: i F.. E. 1 i:'4.5.:,'".'1 C:E-. 1.4 ~.! 1 4.':;6 E I F TF LI: I I T'T: C O:.. -'E I:'. 2L. I -.. 11 4 3. 11 2 T I-!, U P,F_1 J:,E 1'- F'i - E' F H. E H: V. -- -- -- - -- --- - - -- - -j:-j~~~~~~~~~~~~~~~~~~~~~~i-j7 47- " F:^"n 7 BK (!- L Li E':-i-: (:.C L 0 0' 5 0E 0: 51...... 0.5 J 1,~I iTV C E P I T LIUk CH S I- *- *- * *** —- I -- I E NT L. I C 1 15 I..-'I" D I I T IT. iIIITLI''i F-~ F U 1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~"-~.-i-:.-....... IT` FFICIET..................... Fl: U E R I:I.'P U R:E ____.O'' 1- JE~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~7 -'r 1]'IT' " _ E: EFFI I T LUI F;L T E: F H S. E 04:.9' F'_'-'_IYEPRjE _________________________________________________________ ______________________________ Fl 1-~~~~~~~~~~~~~~~~~~~~~~~~i: IT;:OE~CET'.EOCF r HOSE i., "' I' F. IL'U'I. P E l0. __j< _ ____ __~~____ ___ _9 ^ ^ ___ G.1^ 0.165 0. 1 65 _ _~~~~~~~~~~~~~~~~~~~~~~~~~.71M. 4 1 ---—'FI..E' T' ",.,2 -------!' q' L U':E: -- - 0.t —004"-i —. FU 1' iCIT"^ PURE'.................... -. - - -......^...... -_._ _.:7!_...':L";:::L.T..:. —......1....HC _Fl-F-" IT' l OE FICIEENT.'.'HfIIF Fl- 1ni E______ 0 14_____. 6 ___ _. 8 lI-____.12l -I0 TE. I'; TE iF'IFC!U II I I'r:':F: FF1.: F-:l',ihT0L.E:, i 04 0': ~4 -'',4! C.::'4...': r... HE ~ c' E'E' -::''F.';E 1 0.00 7I.0-7,':.007 11.1 — R:' i,, I'/ F: -Fii!T: L'U "R"E.................... —:!i::3..........42'. 1.S_-I 1.-E'.......... -F UGP'!;C IT"',: C:O!E FF I L: I Er-iT',}'- R P:F:F H!::'5EO'J.9 61 i. 8 u:-: 1 -----.951' —----—.95 K 0.,0 5::LiiEii "ii2 i ) i- i.0. 4 6' - 0.0 4i i - j.. 0 ~IEIi'4.9.qF,IT"/K: FiE F[L: E HT L- ^ -.181.-.-..^. --..;! F:'H R E -',x^ - - - - ^ ^ ^ ^ - - ^ ^ ^ ^ ^.. 9,n-. BUT~ ~ ~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~O I:-,' TV,OFIINTLQI PhE _____ 2. 56O____.8 _____.'-57-9 ___O_. 59'- FI i:..H- ITS'' PURE.........................8i-,:~".....307: ~i''......30 8.3074 8..307i...... F i,]"P "" I T'-,": OE FF I CI ENi-iT:,~ F' CF.; F' P H R''-;E Ci_;i::: 1.0:3 1'.000':.043,I i:: - 1.04 HINE:-:RCIO i'.r " Ui^~ CElrT - - - - - - - - - - - - - - -- - - ---- - - - _EC,'":HV ROGE -BE'E";r i-80.047 t -4.i.I11j2Ci - iE —';.<........................................ Ki..{';8........i-?-':'i-...............-..' — i.................?"i"'Zi'i.......... K H,., U G EHL IK t E C__________._______i__- 3 5 i. 3 6 i___i. 0i"0__li_-?_i"__._i-_Ci _?

-85_RUN NU tIMBER 19 _________________.............. fTEMFErR:TURi: T'i.E' OC DEGREES' FAHRENHEIT PRES' SURE 5;.55S. PS I'U'IRIAL EQUATIOH''VAiLUES REDL ICH-KWONG I Hi T I [L VRL LIE RD..L USEID iHADJ ISTED iALLIES' - OU E" PO LIQUID.''C:: 1.PER GM M..LE: 1- 1. 13 ~ 13 O'LU'E. OF P,' R COCC FER G Q __ _,'g l. 3 L E _::,;..,. Fl HCI I Il PL URE _ t _~ H —-------—.-..JrL~'iL --------- I-I.JrL6 I —- — k^*-i —- ---- -------- - B E f'-r E ki E 0 i. 0. 0.:.' 0.20.": y.''."....... r""'; *- --- - - ------- - - - --------- --- ------------------ - F U:R:IT. T' Y P - I"0. 004S l"0.05 0I.054 V1 IITS:OEFEICIENT- LIQI ~ c i114- 11 —---— 1 —11 —---------- ----- - ------- F'..........R................................ 44 0 4 0. - - II T"/ CO FOIE.F I C I E..: F H E. 1 f I19 1:0 F -HE 1 91t HE F.: 1 "1i1 E F:ill i:,. l L 1 1-:'I I T":' COEFFZ::EhT;LI i.:!"i'-HRSE i"-. 4 C I I'4 1.0 L'4 1. 004 H- Y E: F. 0N. EU-E --' - - -'R -'T]:'I 1"'~T-1 OEFFICIE HT: LIQ.- I I.! *Ii. DF'iiiS E' I. 6'20 1. E-20 1.20 1. 6214* F -U G.IT'. PUF i-'2.355. ------ 12.3 5.5 - --- 12. 355 -- -- 12.35.5 ---- F L!G T CI L EFFI T EIC I ET,'F:.i —. FH'E i.25 0. 1 025 E:': F. 0 IID (G ECH- E:EFHZEHE: 2.4: — 1 1 3. 100 E:':;:,-' E:: 0.: 0 7.': E1. ___ LE; _i]_. F.E:!'i___ - I:-:::'75.954I27.000 ~~RUNl~~i t'.i ~ f ~ih':r ~E:R ~Q H:-'1 20 i 0 tT i IT.E 2i E LI EGRES F E;1: 1; T 1 H: F' i IET 1:JE FFFIC3 0.i. F E 1 t; I. H 1" T,.,' l F;:! R L E [.;! U gi 7' li 0 ['i',.,; RLi F I C I E'F~~~'.'I I. -E D I C A.:i0 IS FMOLUE OF LTSUI IT I E PE R LI-QUiD H O LE~1::: 1''u.-;::I2. i,!:.', 127.582' 12. 6 3. 2 F: EOL IT LIE LI C E Fl","_______________ O. 0i0 10tO__. 007EFFI E T. 009F_ f E 1 L. I- t. 4 0 - _: II ['2 1 i.20 0. 9 I 419 S 9i A::'I.L iUE I: L F I C I E 7 0 1j T: 45:I I14EC:-:4o.iTTIIT. COEFFIC.IE;T, LIQ': " U'' 1. 1 5..395 1. 3995.. FU I: IT V CI EFFIC.:ENT PLIF PSE 5'.058 0. 0. I2. 02 FRlTI'.IT'~ EIEFFICIErIT, IILUID PHFHSE 10 12 2 1.0 15 1. 105 1.61, F IC I I T I PUREF I A, L C UitFHR: E.08;7 0.08:' 0.3 0 Fli< IT R OUEFiF1. -'-.T:-P 1R PHS.E03 -2 -. —-- 1 2 —- 1. --— 0. —_ - - --- RCTIvIT: COEFFICIENT. LIQIID F.H SE i ~F',12 1.611 1.610 1.610 INTEF.:iCTIOl',IRIf:L CI:I3EFFICIErTS~$ EB f R::H YrF.:nEN -E: — EH-ZEH-E)- _2,481 1. L00I0 I E,: H D RF GEH-HEXM H E:: F'CL75. 9- 54 27.000

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-87-'TEEM'ER FTIUE. E 2O.0 DEGREES FAHREHHEIT PRESFSUREI.E 5:_:'. PFS I _ VIR IHL EQL.UATION',iALUES REDLICH-KWONG I!ITIAL V'PLUE ADJUSTED LIUNHOADJUSTED, ALI-IES VOLUMEE OF LIQUID C.C FER GulM HOLE) 1 35. 4 4.964 1. 4 4. 871 1.34. 869'.,.' Fl O 0. 0 5. 0.,'.'.:: n. u. 0 ~ O. -'' HLU E L I. 0I_7 4 F_ 0P-072-Z TCT IVIT'. COEFFICIEH", LIQUID FHfSE 1.4 6 1.412 1.413 1.413 FiUGCIT' PUIRE' -_ ~ 0,':i. I5T.'I 0'Efl Q 4H' 10 14 5' 0I 0 I495- F;i R': I Ti:? - C::'E-eF i I'E' T-VRFR E l. 87i:::';5 1. 2. 5 0i. 88'4 i-I';.'. L U. - - E::T; I''T:i R 1i Fi 1 1 1. 1 1 1 F, I I i..0 F.09 0.0.11 0 11 I: R:F FIIT,'4':F: FIH-~i-E -.5 1 9 1"::O 19 C'-!. I__~ I T _Y r U PI E __~ — - _ - — L^l l - - --------- -J:L*-l^-^ ---------— L - I <'-F F-:F C —"....... 0.06 P':: 1 0. 04. 9 0.05: -'.8 Fl aI- IH T UO EF _ I cI1 J __ _ _ _ __ _ _ _ _ __ _ _ 1 _ _ _ _ _. __. LI' 5 _ F: T I,i IT' C E - Fi: T I E..E 1 —- 1.I.7.44 0.041 0.i 0' FTI- IT'd (EFFICIE~;T?' FlO. PEl..............0. 7'!. -. L2I4LIIU. S62E_1_'" 1i[4. 184. 1 114 FlR~ C ~I~~~ f ~~i ~ -I IT F_;~~~~~~~~~lP~~~~~~~C. 1 1 0 1 1.1 51 F ii- L- T ","'- F E T I CI'-'F.: F "i iE. 1.2 1E —-------------- -. -----------. —--- L H E1 - 1..1-u. 7.3 0.F759 0. 75:8 I. 758 K;i'Li E f I LICI`BUIE'__'2121 F'_F:_ I_ NLE)- _u 3 --------— I13'1q'l: —-- 13 —' 1 — ------- FE Elt'i E H C ITi (iTEFF IE!'T, LJ' FHR E 1.F'. F U a. t-i: I T. FP LI:: E -. i -. 0G —,2_ F C C I T' CI IEFFI C I E T V.FI PH FiE..0 0. -- 0 0. 91 Hi TV IlT'':OEFFIC:IENIT, LIFiL PHIiSE U.011 1 1 L 1.016 1 1.90 V''~" " " "" "" 0~~-.9......41 0.9:46, 0.9 6 0'.f 3937::.-:: 0. 050: 2 0.53 OrO, 3 -. 0 5 K UfiLUE -~?, - ^^^~- ^^ ^ -. -.. ^^ — --------- - -- - - ---------- - - - -- -------- ----- — 1- 7. -S 1-5 K' L LI E...-I.: 1. 1.:- 1141 CT T II T C EFF I C I E T. L I QU I F H SEqE 1.5 1.51 504 Fl G I T," PURE 2. 1512.15112.5112. 1 51 FLahL ITY COEFFICIENT, VRFI:'H^8E___________ 1 1 4 LI'1 I — - - - - - - -- - - - - _ — -------- --------------- - --------- INTER —CTION EiRI'L U. OEFF I T E E,: H "D R. 0 G E N- B E Z E' E: _ ________________________ -------- -------------- B C H'- [: R,.C E H - H E:.:RE.-39. 123 27. 000 R.: u N r it a E- E I~i LI, r! E! 1E1 5 1. I:. T E fi F E i: T LI RE 200. i D'EG REtES F H F. i E lT RES'S U R E I',-'0-.'PS I A VIR I f I E Q U R T I -E, i LUES R. E D L I C H - K 1 1i- N3G iITTIL VALiE ADJU _STED L DJUEED'-.'A L F_ E-. VOLUME OF L IEQNELEUID':F PER'LE" 1 3 L.8-2 130 1.50 1'0.L 1 3.22 FOLUME'- OF-flrEH I L CUH fE R GIIE) 1 I___- -_ll-__ —---- --- -------- ---------— __-ll BE HZ EEE;.-' 0. oU cf. I. ^K -JiBL'-ii - -.-_-____-____ _-__ —------------------------------------------ --------— __ —-o.................________ F I7i T I i- I T" _ N E F F I C I E r —I T, 46 I P L-I F.: F" H I 1,.4 1. 470? 0.00-i i —!'7 1' - i. [10.005 I -!.006 0'-i!'] f:, i. I- 0 0 6' K V R L U E 0~i, I~i.038:-: i - I, [I'.02." 9 0.036 0.0 5 FLiGAC I T'Y COEFF I dI ENT, VAPOR PHASSE ID. 055i'.' -, 0 I86!-i55 O. 188'T— AR':TI,'IT",' -O: E FFICIEt-]T, LIQUID PHAiSE 0. 0 _.9 4 0. 99-4 0. i 4.99 FU G i ITY, PURE O.: E -i. 0.8 F-: O'i. 0-38 _ 7. 0. 0 8 0.038 _ FUGAiCIT" COEFFI CIENT,V:F'-..F HR PHSE 0.922 4 1.34. 0.91 9 0.2916 -: 0.9 —:,-5 0.'.971 0. 0,S -.964.' OS 4 X O. 0.082 0.09, C4 O?i 0 1 0 0.10 O R'TIIT'T" EFF I C I ENT, L I QU I D PH'iSE 1.501 1.C4.9'-)'i 1. 498 4 1. 4- 98 FUGiLO-IT.,PURE U. E,2. 689 6.689:.6 89,60.068: 9 B CH' DR OGEN -BE HEHE) 1.93.000

-88R U'i',E R 3, —.: —-— ______ —------------ TEFER. iTUREE 200 -i. DEGREES FAHRENHEIT FRESSURE 1 O1 07. FPS I V I RIL EQUIT ION fLLIES REDL I CH-KWONG _HINITIAL. VAHLUE ADJ JSTED IUNHDJUSTED ALIIES YOLUI' E F LIfQtUID 0::C PER G1 MOLE) ~ 157'921' 1.54 116.36- 11. 36I1 VLli ME OF'2FA:r:R, C C PEF G5 1 HO - -LE 2::- 4 B E I"; ZE l- E'-' O. -. 0. 0. K,'L LI E 0- --- -i —--- -i —-'-RT. T C EF I CI T E H T, L I: I U D F H S E 1. 1, I 1 1, 4 1 1 64 F U i.R 0.. 0 O.02 02 -F P- IT CI F FF-iE' T.' R I i''PHSE 1.'1 L. 0 56r. S S-i...'v' I-i. 0 2 2 k~i-i. 0!?J I't. Ci 2; O. CI O',."-',' L.! 7! i'":, 2~l;E F~CIE~l~-ii~ ~~ O1FiPOE 7'HRSE E1Ei"`C I-!.. i 7 tS,5 FTIK vIT E U 0. OE". L U 1. CR T,I TI'. C- i"iE F I C I E T, L I Fh I- E.i D 1. 0. 0,-', IV I' l -k~ i R......................................... —i —....- ---- -- --- - e C* O0 0.0'67 0 t'I. i -3 O. i 0.0 I I- 0 1 1 0.0 1 E' y M L' U E..-.- --.....^- - -.- - -................... =' i[3.9 —`'- - - 1LIf-Ii lA iTY COEFFICIE LIEQIUID0 PF.HOSE ___ 2.213 _____ - 2.2 21 2.219 F i "I" T', E.'i1 16 16. 1 16. S 1 ~ A C: T I I T ",:CFl EF F I C I E I T L I C F HR SE' 1 I. 121'471 2 1.02 0 BF U C, CR',:C I T -. F i. 1 7. 00 0 0 "~~~~~~~~~TEl' M~~~~~~~~~Fl~~-TiURE~ ~ ~ ~ ~ ~ ~ ~p - -—.- E: —-1 -1F U.HE i T FPF~^ LG.::i E F. F ICE_____-i___.___F:_H__RS__EI_~__0_4_______'___._________'T I'L"i T EQ F-.'I C: I E N I- F.-ii [ TI'O-' Pi-LU'-ES REDL I C:H -Ki HTS,i- F:';'' IL T -L'UE -RF'i'EJ,-"'STEi"4 LLE2 F'F.: I SSi. 54IAET,.EFr-CDE F'-HOS i R r-i T~ IT I 1OE Fi IEN-T! LIQUID UfiOSE 1.14 1 1. Li U 1.14 CFiiU IT Y U I'.. "S i. 1 8 9,.-:C EF4fT 5 -S1L5 K t. L UE LI 0.04 0 4,- i 0 E H T ITY COEFFICIENT. LIiUpR PHSE I. I4': i.02 8iE. 920 1. 9091' F E F-S IT - F E F'U U 44. LI. - - U T A 0ffCTy.PRC.03':50. F.0 05 F UI'', IUE 02~ Ci 4.2 t7.1 04.~ 2.415 26.416 F'i IT- L R- F2. 0E L; H1E 1 2.99 1 1 1. - 120 L 2.0 BCHVDROGEH —----- - -. - - -. - 7 - ------ - -__1. -—.-. ----- F ERHlI T'; Fr IU A E 14. 932 1. Ii 0' -i ECHYDROGUEi-HE* HiHE:'_________________________________39 12T_ 2710__.i

-89RUN NIIUMBER 4___.__- _- _ ____ _ _____ ____ ___ _ — - - - - - ___ TEMPERRTURE 200.00 DEGREES FRHRENHEIT PRESSURE _ 5?79.. PSIA VIRIRL EQLIURT I C AH'LUES REDL I CH-KWONG.- - - - - - - -- - - - - ----— _ —— __ —-__ _ _ __ _ _ __ _ _ __ _ _ _JA L Iiii_EL- S DLu~ —- 11- I J!J1 ----— _LLtt J^U- -- - RL E -- - - VOLUME OF LIQUID CCC FER G'1N MOLE) 1 F. i 98 1 0 I4" 1. 1 4. 10i. 942 VOLir1E. OF V POR C:: PFER. GM, OLE) _ 7.423,. 4 77 776.: - B E I.Z E' E' O 01 2 i0 13 n -i. I-1 4 Ci 014 _J)^_________________________________________0.012 ________ 0. 0 1 3 ________ Q.Q14 _________ Q,014-i 1 If' i"0i. 289 0 —"i'-.iI-I.'29'.:..I 1 C 0. 291 0l. 291 K.R LU E.i1 f. Ot i 0.05-i-. 04_ U.:9.i. TI' IT':' COEFFICIENTLIQUID PHFSE 1 H 1 1.48 1.048 1. 048 F UiS,:: C:I ",'..,F' ~i R E O. El3 O.. f 12 5. 0 C. 043.0. 0 43. FVF~ j-r-IT', PURE I _ _ -___ H_______________JrLJll^ —- — ______ ------ ----- _ —--— _ - _ —- - - - F U Fi C- IT' CEFFICIE T, FAPOR':'HRSE -i.' -21 I. -i2 H. 1 -08 C. 9H1 5 CYVIjLHEfl-rE'k__________ _ _____ __________________________________________________________________________ C ", C: L F"~ FiE:-' A H E ","'***'~~~~ i].- I~- ~ 0.0~28 0.. 0r28 0.0Fl.3:2. 03 1 K'hVfiLUE~~~~~~~~~~~~............. U..............-................6 K V R L LiE O. 0I,-:: - 2". "41 C i.0i4 7 i-! O 4!:'-'TIl.ITV' FOEFFICIEINTLIFIjZD P:HASEi 1 ~i[L! _t ~ t " _ I _ 1. 0 _ 1 1 _ _ lPi 1 F U iSR F' T",'',P U F:E -..-...-F'.. r 0.042 r 0.0i]42 0'. 042 O. 0.42 FH E;..:ii I FiREi I i i-.i ",.' Fi. UR0-C. OO. ID 20 4..: F f'CITY COEFFICIENT,''lPOR PHISE. 1.161 H 110 0 2-ii HEf XA lv! - _ ~ _ _ ~~~~~~~~~~~~~~ — - - - - --- --- ---- _ -_ _ *- -- - - - ----- _ 0 — - -- -- --- -__ _ — -- -- --- - -- - < ~~'.iL i. 70 i 0 1 I-. l 8 II RCTIITV T'.EFF'ICIE:IHT, LIC!LIiD T Z"F'"nTLIU FHRi'S2-E. 1.26- 1269.. 1 2. FUIti -ifi:IT",, PI lU FRE.J05.: 9CH9I. Ci 5.5 L: ~~ ~ ~ ~~~~~~~~~~~~~~~~~~~~. 3 0 5 3.:..F -"i::I T' I E FF IE T, RF R C S E u.; 7 109 1,0-.." O..8 H' DLF.: 0 i El V' -..-.-... ---—.... —------------- --- ---------------- ------------- --- ------------- -- ---- -'-," I::i. 9 6 0 C!. _ _5 _ _ nr ^ 0 ^ 5 - - -... - -. 9 5 4 O.,0 ^ ^! _ _ _ _ _ _ _ _ _ _ S:L 0 55 —O',... I:.02 i 7 0 ~ F' 2 7 J'I.'I 2 K Pi'F:.,...... 7 36. 50 35. 161.35. 13 RFTI, IT." F:OEFFICIENT:, L I CQUI D PH SE Hi L32.9993.'. 1 F U G PZIT F'./P 1.R. F i9 1.33 1. 93.1 11 933 F UGiC IT'.,. rV"' EF F i C I E 1" iP T. F, O-;R P H R S E! 23 i 9'1 ~ ClO__ _4 1 ~__. 0 4 INTEFfFCTIIOtf JIRIAL COEFFICIEliTr' -- B,:i ____GE 59. 177 1.3. 000 E.. H HU -9 *"L 0 H E " E5' 1 1 —------ --------------------- E:,:. H'-. D R 0 G E N'- - H E:'''ft H E:.:,_______________0,___Q_ _____ 27. 000________ E., C,i E', E L iH-' — -- -- - -- -iT EM EF::iTU!E. 200. E 0 DEGRE-'-' -:HE Hill FilNI HEF T~rE r I,[-ir —S fiHrHH FPRESSrE. i':~:. F.' 1kH'I RiT F L I EQUT I I:LUES - ELICH-K W 0 N-i3 I N k T i iL L'-AL UE kLJ U] TED -i i'AD J US TE D ARLUES 1 L.~~~~~~~ 0 L IiLiE F LI 98.820 99.0 ri 71 99.04 5 9.044 I LTU' I E 0 F:.:'AT L' R, C: FC'E 1 MOi 1LE ", P E- 7 Hg4 1Hl4 BE — HZEIT E F 0IFF I. V'" FH0.0 4 O 0.0314! -. C0.- 9 A i. 0.0 9::y.~~': 0.84 — "1 1 10:. 44 0. 44 8I 4 4!<~.' AL. iE Ci Ci.':;: Ci! ". i" 4 I] C! i_1412. i _ i. 4 I6" - K _'*!? L- -!^ _ _ _ _ -- - - - - - - - - - - - - - - - - - - - - --- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -_ _ _ _ _ _ -*-l~ ~ b _ _ _ RFCTI'I.T'IT COEFFICIENT, LILUID FHRSE. 4 1 004 1.004 Hf 1.l4 Fi GRF CI T'"C", P U RE O 10 O. i0l-f 2 H'i~! 0.0H41 F UiGfR- I T 0 E F F I C I E N T V R' PO R FPH RSE 0 15.92 1. Li "1 2P.91 C E C L 0 i E.' A X 0i.002':6 0.00126 0.006 0. O 6 -J —-- - - - - - - -- ----— __ _ —----- -----------— _ — __ -_ —----- J1 __ ------— ___ __l^ ^ — ----- - _Jl K'.,-iLUE..046 0i.041.047 0.04 RACT I V I TY~ iS0E FF I C I ENHT., L I Qg! UD E F' H,Q S E I ~ 0Ci 44' 1 047 1, 046 1. "E,. F UTGCl: I T';' PU RE 0 1. 04 1 O. 041 0.041. 041 F L I k I. T'Y' C 0 F OEFFICIENT, V P 0 R PH R SE Ci.9151.030 I. C4090.3 70. 925_ HEXAiNE HY O F-. 0 E. -- - - -- - - -- - - - -- - - -- - ----- ---— ___ _ _ -_ _ _ __ _ _ -- -- -- - _ Jl- _ _ —------ --------------------------------: —---------: U. 0. 0. U. Li 1 %1 I i I 58 I K Vi-iLHUE -Ill.i I-I.E l 5 0~0 -, li-f. 4 11.1 RCTIVIT"," COEFFICIENT, LIQUID F'HRSE 4.571- 1. 1.:.:58 - — 4 1.: —-- FUGRCITT, PURE 0 58 5 i-. 058. 05i — 81 0. 058 FUGICITY COEFFICIENT,V.POR PHRSE 0.946 1.070 0.933 0.944 HYDROGEN BC"VD0l.N-E91':: 0. 9270I-. 9.i 5 0' XV O,0 4 O 0 9 2 0. 020-~~ - ~ OT 0~~ ~~~'^^ ^ - - -"- -'7 5 -'K U 14L UE'4 t 40.678:, 49.33 S6' 48.:,104 4',.,110 IfiCTIk.IT'~' C:OEFFICIEI"T, LI QUID F'HRSE _____ 4. 177/ ____ 4.19'5 ___ 4. 19'4 ___' _ 4. 19'4 FUGRiCITVy, PURE 11.7?43 11.7 43 11. 743 11.743 If'.T-E-ElgCTIOI'" VIRIRlL COEFFICIEHTS B HD- OGEH~r^ ^Fl -BEH Z -fiE 5'"_,L77 13. 000l~ B(H'vDROGEN-CY'CLOHE,'.:!iHE:) -6.6F-74! 2. 000 - -- --- B (H'DROGEr,-HE:>Rfl E':, O. __________________ _____ 27.~000________

-90Rj UN NULiV'EER, 42-.______._...:,-:;__ TErI'ERfLTUR.E 200.00 DEGREES FAHRENHEIT PRESSURE 1076. F'PS"IA. U.IRIfL EQCUTION',.' RLUES REDL ICH- Kb.IONG -_-_ —_ —------------------— _ —--------- I —-- -Jt'1'I..' —; L 1 E -- D J LI S T E L.DJ U.-;TED ALU ES V 0 L U I, E 0 F L I! U lI D: C F E R G M M1 0 L E.:1 11 1. 0 1. 2 7 07. 03 0.29 VOLUMIE OF -'AFIF.: (CC: PER GI', MfLE": 4'25. 4'2 411.41 5 425. 41'^.^IJ F ^^-^^f- ^ Ju L ------------' -------- ------------ ---------- EEZEEIE'H,' I'. E i 8ID I-. U0. 7 0 0~ 0' 0. 01091:F': 0-I.'27 0 O.2S4 T.2SE4. 2 28 4 It'! A L LiE 1 Iii I' i. LI6. I —- - - I,. 0 ~L03 1 14 i-: T I',,: I T'.,-" COrl E F F T C I E H T., L 1I:! U IDEl F' PHf, S E 1 ~ 06,I. 057 1 -.58 1 ~ 058 F-i TI'' IT'"' CiEFFICIEN "iT, LI I PH SE i. 1 1 2 1. 1.9 5 I T,": F U R C0 E:."::C i O E1 — *: —-- -__ _ _______ __ __ — -~_ _____-_- ___ — __ —-__ —-lA 5___________ —--— __________ —----— ___________ — -— J Ii ii.4 I' I'~iLI I I H TI IT i OE FICIEHT L ID FH E ______ __ _ ^ F'U C ITy C-EFFICI ENT! O HAE 1 O. 4 60 0.901- 1'0.904 I` C'-, T T' C L I I F I EI. E LFTllVCE,1 C~ T'Y~il"^^ I- U " oil:N5.. 1..2 35 E HI'- tUFI'. Ci H'It___________0. __3 _. Li__i _ D.03 "~~TErnj~~i'rV~~lT' CEFLTN.fO LIFE096. 135 0E1 F.955: I IL.'-: I T'F E F F I C I E HT V IA F FF'H A` E 1.':i.:' O "L' I f. i'i. I 0F0L0. 4..: f LLIE L. O I 4TI': I, IT'Z' I IE!FICIE-T].LIUIDI 2.I' —.970 11ILI.9 1 5. f I].I f.:, F U G CT I E -. - L: I R6. IT. 7. 6, I. 1.76 r.I IH I.: IJCIF Fr E 1'4 HITrI' IT" IO:IEF-FICIENT, LIQU IDI — R, - 1,-,,S 17I1 I,. 7I: 1 6.76,1 -:,:"Fi./ F.: n SEH:ELLIRO E 1:, I-; Zr-.'!:9 17 13. 000 -T-ECHVCROGEH-iE H'?F.!.........".:.'1t::'l"____________U.]':........ 0 00-_'_H_.F.; i0H~' P R CE'F I IS UR F 1. I F I EIT I Li;, UF:'IJ____- 114-'lE.T'RI'i, IFIL _CE S REDL I EF'H-Fi. T' 1_; hi e 0 F'.': P F':'':C —; F'" F': - -' —-------- -i -M- L -E - -: —----- i —----- ------ - - --------------------------- E' F-iU 1 FO lE UD E:-ENE::I PE I 1 1 E - 97.9'LI BE' F E -'E:'E:,^.E'i-J-1^ -- --.- _- -_ —------- ------- -- —.- - -- - --- --- - - ------- -_ — P F EESC L PE'F I1. A V.' l~i, I] l'-i fl.0' 0.00I] [IE3 0i,0 [ Li H4 I- 110 0 4 UL 0F U C, j:- I T C C I E 024- f. 024.. 024'- E 24:: I Li LIE U E. LiO. 9 8.-, C-0. 90i.55 O.925::'::yO. 0.045 f ~ i. 0.036 -,. 0.037 0.0.37 KCTI',IT: C:OE FFICIEIT. LI QIU.I D FH14SE -,.:i..079 4. 1 20 _ 4. 113 4.113 FUG_-.C: I T' COEFF I C I ENT, L'.: I PHfSE 1. 042 0. 999 1. E0 2 1.04.3 IT ERF::: iC:T rI v.~IF' 1 L OFF I L -:"-, P UR'TS:Z4

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F2 1 E.0 0.8- 2 0. 884 C'.'E L f-'-.; A[ — lE 1 Li E,S, (]. 0.00:i'4 0.004 0.005 0.005'i.'.IT: C',FF.!IEIET Li h -..1 f.3, 11 0.l. 1 E 2Ly, " * * **'''"~"~~ ~ ~~ "'- -"~ - ~'" -- -- 7:^^ 3 iD O -- -- -- -- -- ---- -' 7 ~ ~ ~ - ~ - ----- --- -- -- - - - - - --- K VRLUE 9 -P 3^ -- -..Jzll~~~~~~il -^ —.- - -^ J? —- ------- ---------... G...~i — l, I i.[E I.,....................... O.I C0: D L3. Oi2 F.029.02'C T I,: I T CE F F I C I E. T. L I L' IF H,q S E't, H i5,,E 1 ~ 0 G 1 ~ 0106 1.106 F I I T PU R. F_1F. i2:I 0:2.- 032GT.'4PCJ0 0-I 2:.0 Ij 1-:.; I~ ~ ~ ~ ~ ~ ~ ~~li il II ii C. I I6i -'. TT':0 C EFF I C I E I T.V.F'iH -E. 9A50 4 1. 10 7. 3 0 ~.937 H E::x'-::.i, CI -i E i 011 0.0i3 0.0L1 3 HVDRGCEH ___~__ _ _F I_- CI_.i Phi — - - 1 ------------------- - - -:::..................-.-...-...-............. F'.. (3 O.5 S 0. 72 ~. 0.9 6 6 0.9 66 F K LI~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ F U (- l:"V' t.., 1._ i". 0 S ( 0. 059 0.0 f T IH*'ITY. COEFFICIFENT,L LIrUI'i-gj-_______.C5 ____2E4 ____ 2 4 0 ____..43': TF:G I'T,.-.E I:I':- FI FU' -6.7'::' 1 1. 7. 1. CIE H.. F_' Ff i0~ iiiE jEt" R IN i. C I 1 I'- 0 O 3 6E2 0 0 3 2 K Jh,,~'F I............................'J 2.2 1 2'..7 5 3~.: IN~~~TE R-CiF Fh~~~~TI FE EONiI,~ —FE ]'T.?_H- C. z J EIE C VR O N- NZ N:__ _ __ C-____ - _-_ —--- — ~:-* —----------— ~ j —---------------------------'DiE I".T EL. i: iF?'.Ui' L F.:I I::!. _'""""'r R G: -SHOi:iE. 1 159 12 L.00 E:,:] Fi'-,' E, F~~~~~~~~~~ ~~~~~~~~~~~~~~.:. F) E2 H -O' Er E.r'': S'i 1 3 0C EB,:] "," [:, h T.F. OG E H.- H E::-: i~I'tE::,_:,_- - - - - 6..3 42 _____ 27.0 —00 — --- -- -- -- --- - KL U E~~~~~~~~~~~~~~~~~ F- U H I" U h E; E RF 5 3 9 __ PRF U E ____ 5 1 PS I Tt __________7________71__________1_ -- V'!: I RnL. E L]U PiT IiI-O,,H l. fL U ES F.'E DL I C H- KIt0!"iONG iL TE OF Liii D, E' GiCiI,'LE 13.9 5 i 1 1 114'. 1.6 11437 Fl i IT F ri CiILi-il...,! C _IJ[:_EY.....,Iq'_..' C....!:.: A F'C` Fr,! LI'iL E;.;:': I:?.'.... 0i.0:E',20.47 K'-B~r-iL _ - -.___ -_-_ -_ — -_- ------------------------ --- _ —------ l —---------------- - - - -- - - - - -- - - - - l i F D GIT iCiiEFFICIENT, LI ID: P HSE 1 1i 1 8rt; ElTVE i - E-i E. V -----— E —F r_3,:7 ~~~~~~~~~J _ Ii I 1 r i Fl iUf-irITV ICOEFFICIENIT,i i4PLR PHPSE 0.I8.2.8.9'.,-' 0.0 10' E. 0 0200 0.028 _ —------------ ------------ ----------------- ---------------- -----------—, —--— _~ — " K:,.V R L. iE ("i." 0 — - -':::. 0 r:.0 0. 04 0.05 1'-3 0.0 5 0 ^-S -L1'- ^' ^ iff1'li'iJLU lu~D-fMR E — -- -------— l —-------------- - - -- - - -- - - --- - - -- - - -- - - - u U N __~________ —_F_-R_- ---------------------------------— ^~L —---------—.- 0*0^ -----— 1:L-^ --- 0 1 I 112 m.~ ~ ~ ~ ~ ~ ~ ~~1LiL'..... R]": T I R,., IDI Ti"/': l".F'I7'- EI':T[-I T!_. F P FHFiRS E IN. iE3. 1 1 - 1.11b 1. 1 0 FtI]i-_' I TK F' U RE _i.ii4 i,'i.i 4I~_ _ lT II0t-. VA UE RF, C H - E 4 6 I -FL ICT'.i'v OIEFFICIENT, LA'L:IED PHiSE 1.129 1.1 4 1 1. 4 1 1. 4 F:i' T., PUEC L____________. F-i ITDINA i.06 E:: Ar0.-6 E "'~V 01 40..947. 00.938 0.93 X t-036i. i IS. I i-i 31 0'01 K U R L t _ 1 E O. ~~~~~~i], iL! i-. 1'}44[)1 e 1 1I-.i-5IT' IIT' CEFFIIET LI. FU I I D CPCF:HE R E 1 4 H 1 1 SE~ 72 4 6.47i. 02 7 1004 F IUia;Ii GIT'", PLRI- E.i —i —- 5- i-i. ~: —. —2.71 1 C.2 -1- — 72 — 1 F jl'IT', E H:U'Z E".: F F q'E.:';:'9I~2 EO: —', —---------'.,.'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 7: U 0.U2.1. 02 O, 0 21 =— F':-iIT" 1';..:FIi 5LET y.':: PHF.E1 i 51. 4 41 K AUF- L. Li_ E -- - - - - -- - - - - - -- - - - - - -- - - -- - - Ci_?5. 0i 0 i~,r a I.-.C8I' 1 C ~ 0'78 IIITEFf-TIimoirYIRIPL LiiEFFIL:IEITS~. H' ITEFiEN-.-? F'F I C IE. 12 I.14 1.0' 1.1' F t! i]I:i': I T Y',, P'U R.'E —-- ---- ---- --- ---- ---- ---- -—. ij' ~ I-i ~,.3e.0.: FU Al I TC 0 F I I C hI E - ------- 0 R'R E,:]-,,. 89ii -C'-,J H' C L -EP. CEi E -',:':: 1..i Ci. — - -- - - —: -- -- -- - O, 1 8 0. C l "EI-.:.1 ~, L VALU -iLL E 2.1 i 1. -—: —-----------— O.6 9 AC:TII'.,' IT'~e COCEFF I C I EH-T7I. L 19tii F'HAcE'.:,432 470 2470247 FIJF;RC:~~~~~~~~~~~~~~~~~ —--------- ---— RE!;.:'2 1 ID O2 4272 12 001 FUJGAF IT' CUOEF I C iET. R'OF F' S 1. 02 O. 5?9 1. ~ 04 15 ~ —i —IFTR. iC' I T -OH E, F F IIR CEF I c: I AE HTSF 0 8 "B,:'-.DR:OGEH-BELHZErt iHE} 4. 124 2:.0 BH'D.:GE.,HE',:.:: R H E::, - 8. 11 F! 6.34l I-t7 0 --—:F:OE- H E RE 0,, 31'2 27. 025

EXPERIMENTAL DATA As previously explained, the experimental data presented in Tables III and IV has been smoothed. All experimental data has been compared with data from the literature and has been analysed statistically. The results of this work have been summarized in these tables. An unexpected amount of difficulty has been encountered in reproducing the analyses of duplicate samples by means of the mass spectrometer. Therefore., this section has been appended to the dissertation in order to provide a more complete picture of the experimental data. It has been asserted previously that the main source of error in these analyses has been experimentally determined to be in the analysis of the hydrogen in the liquid and in the vapor. Table XVIII shows an example of the consistency of the hydrogen-free hydrocarbon analyses for both vapor and liquid. This data, as well as all the other hydrocarbon data. has been analysed by means of large sample statistical techniques. A Student "t" Test was used to reject sample analyses that deviated from an average value beyond a 99% confidence limit. Table XIX shows the analyses of the hydrogen data for Run 55. Small sample statistics, as well as comparison with literature data results, were used in this case. A sample calculation is given for Run 55 to show how the results of the data analyses have been applied to the experimental data. As analyses of this type may have been biased by human judgment, a complete set of all the data obtained in this work has been included in Table XX for future reference. -92

TABKE XVIII ANALYSES OF CYCLOBEXANE ON HYDROGEN-FREE BASIS LIQUID PHASE VAPOR PHASE _ SAMPIE x x-x| ( 1X-X)2 SAMPLE Y IY-Y (1 1) 30 202.002.000004 30.210.010.0C0100 30A.202.002.oo0oo4 30A.201.001.000001 30B.205.005.000025 31.208.008.oooo64 30C.202.002.000004 51A.212.012.000144 30D.208.008.oooo64 31B.208.008.oooo64 30E 204.004.000016 31D.203.003.000009 31F 198.002.000004 31E.200.000.000000 31G.198. 002.000004 31F.198.002.ooooo4 31H 199. 001.000001 32.194.oo6 000036 32.201. 001.000001 32A.198.002.000004 32A.201.001.000001 52B.192.008.0000641 32B.200.000.000000 52C.194.006.000036 32C.202.002.000o04 52D.19. 006.000036 321.203.003.000009 32E.197.003.000009 32E.204 oo4 oooo16 33 -199.001.000001 33.196:04.1000016 33A.198.002.000009 33A. 197. 003. 000009 33B.200O. 000. 000000 33B. 197.003.000009 33C.203.003.000009 330. 197. 003. 000009 33D). 200. 000. 000000 331).196. oo11. ooooi6 33E.197. 003.000009 33E.197.003.000009 S1241 4.209.000225 1.006.000493 AVERAGE:. 200.200 ('ii-1.0034.0051 P.E.2) = 0.674 cTNM.ooo4 *10008 1. Stand-ard deviation 2. Probable error

-94 ANAI3BS aF!DIROCN CCMPOSITI0lS FOR Kr 33 E X'jMETCAL DAMA SAIMPIB T(~y) P(psla) X3: XX2 Y YCX % 33 200.0 1089.7358.1787.0855.04350.0107.9464 3355A.7335 1793.0872.05308.0076.9616 335 1065.7394.1808.0797.0516.0129.9355 3355C.7389.1813.0797.0318.0081.9601 355D 10453. 7383.189.0807.0283.0071.9646 355.7274.1780. o946.0208.0051.9747 LIQID X2- 0.0846 Pange - 0.0946 - 0.0797 = 0.0149 At a 99% Confidence Level, % = 0.08146 + (0.628)(.0149) o.o0846 + 0.o0094 Discard Sample 33, which lies outside of this unit. \ - 0.082 The probable error in this analysis is: P.. - (0.674)(?ange)(.43o)/IiN - (o.674)(.0075)(.430)/$5 " 0.001 VAPOR Y2 - ~0 9571 Range -.9741 -.9355 0. 0386 At a 99% Confidence Level, Y - 0.9571 ~ (0.628)(.0386) - 0.9571 +.0245 Discard Sample 3355, which lies at this limit. Comparison of vapor-phase hydrogen analyses with other results from other experimental runs and from results in the literature indicates that sample 33 is low. The rank difference ratio is: Y. 49 Y33 - 33 The probability that this point is representative of the true value is approximately 10%. On the basis of this statistical test and on the basis of comparative data, discard sample 33. Then Y o2 = 0.965 The probable error in this analysis is: P.E. - (0.674)(Range)(.486)/,^ - (0.674)(.0146)(.486)/2 - 0.003 SAMPIE CAL ATI O SMOOTSED EXPEP TA REISUS F0O RN 33 PRAS XH2 -.082 -XC- a 0.200 XCX + X 0 - LO - 0.082 - 0.918 Xcx - 0.200 (XCX + XE) - 0.200 (.918) = 0.183 XEX a 0.918 - 0.183 - 0.734 VAPCR PHASE Y2 " 0.965 Y c = 0.200 YCX + EX Y= + Y~' 1 - 0.965 - 0.035 YC = 0.200 (Ycx + Ym) - 0.200 (.035) = 0.007 -x 0.055 " 0.007 o. 0028.SOMA.Y FOR 0m 355 T("F) P(psia) XEx XC YX n E V 200.0 1089.754.183.082 028.0 oo7.965

-95TAmuiZ XX CUPIZAB EPER DL DATA RESIS8 =IQD PHASE MOLE FaACTION?APQR PHASE MOLE F aACTI0 sAiz XBZ XC XB XJL Y Y Y YE2 18.2312.7237.0450.0036.0125.9838 laA.1923.7691.0387.0015. oo69.9915 18B.2212. 571.0417.0032. ou6.9852 18C.2057.7559.0384.0017.0084.9899 18D.2148.7790.0062.0058.0198.9744 18E.2004.7522.0470.0022.0107.9862 19.2178.7275.0547.0156.0506.9339 19A.2150.7441. 409.0120.0373.9507 19B.2409.7087.0504.0175.0592.9233 19C.2047.7490.0463.0115.0359.9526 1D.2389.7195.0416.0511.1414.8075 19.2080.7535.0385.0359.1232.8409 20.2 90.7111.0800.0153.0415.9431 20A.2021.7152.0827.0095.0295.9609 20B.2262.6921.0816.0111.0308.9581 20C.2095.7104.0801.oo67.0234.9699 23D.2218.6901.0881.0185.0468.9347 2CE.2019.7028.0953.0086.0265.9649 20F.0171.0482.9518 20o.2012.6981.1007.0085.0292.9623 21.2382.6879.0740.0075.0250.9675 21A.2019. 7159.0822.0030.0087.9883 21.2302.7092.0606.0050.0172.9778 21c.2102.7170.0728 212.2531.6892.0577.21 2053.7097.0849.0023.0071.9906 21-.oo84.o226.9689 22.8023.1772.0204.0241.0029.9692 22A.7350.2320.0329.0114. oo49.9838 22.8341.1548.0111.0093.0034.9873 22C.7459.2171.0370.0069.0029.9902 22D.7570.2145.0285.0105.0037.9858 22E.8213.1758.0029.0086.0037.9877 253.8195.1533.0272. o61.0184.9205 23A.7424.2096.0480.0361.0130.9509 23B.8093.1648.0259.029:.0107.9602 23C.7474.2148.0 o379.0325.0117.9558 23D.8140.1642.0218.0512.0162.9326 23E.7487.2070.o443.0428.0143.9429 24.7974.1466.0560.1055.0165.8780 24A.7246.1993.0761.0444.014i.9415 24B.8064.1740.0196.0593.0185.9222 24c.7310.2-)4o.o650.0153.0089.9758 24D.8017.1546.0437.0240.0088.9673 24E.7502.2028.0470.0194.0073.9733 25.7219.2422.0359.0070.0028.9902 25A.7315.2016.0669.0043.0017.9941 25B.8257.15341.0403.0088.0031.9881 25C.7262.2053.0686.0057.0021.9922 25D.8105.1496.0399.0oo36.0030.9933 25E.7440.1911.0649.0018.0020.9962 30.1930.7650.0420.0064.0241.9695 30A.1931.7648.0421.0066.0249.9685 30B.1984.7685.0331.0047.0220.9732 30C.1943.7668.0389.0029.0132.9837 3CD.2015.7643.0342.0077.0283.9640 35E.1963.7642.0395.0039.0169.9792 31.1565.8051.05384.0215.0817.8967 31A.1696.6826.1477.0204.0759.9037 31B.1579.7956.0465.0152.0578.9277 31C.1559.7778.0663.0130.0478.9391 35D.1579.8012.0409.0130.0510.9359 332.1595.7917.0488.0081.0324.9595 31F.1871.7608.0521.0068.0276.9656 31G.1887.7643.0471.0093.05304.9619 31H.1892.7646.0462 32.1846.7385.0769.0048.0200.9752 32A.1906.7581.0513.0031.0125.9844 32B.1876.7519.0605.0092.0388.9520 52C.1905.7500.0595.0104.04352.9464 52D.1951.7578.0490o.0047.0196.9757 52E.1982.7713.0305.00 oo15.0061.9925 5533.1787.7558. o855.0107.0430.9464 533A.1795.7335.0872. o0076.0308.9616 3355.1808.7594. o797.0129. 0516.9355 335C.1815.7389.0797.0081.0318.9601 53D.1809.7385. o807.0071.0285.9646 335.1780.7274. o0946.0051.0208.9741

-96TABI2 XX CONT'D LTQO PHASE MOIR FRACTION VAPOR PEASE MOLE FRACTION SAMPI Z XM XH2 ^B ^ 34.8477.1549.0174.0275.0288.9457 34A.7841.1805.0353.0116.0145.9741 54.8550.1215.0235.0211.0219.9570 54A.81C.9.1650.0241.0147.0157.9696 54B.8197.1614.0188.0261.0272.9467 54C.8021.1822.0157.oi6o.0186.9654 54D.8021.1890.008$.0070.0075.9855 548...81io.701.o0178.0042.0055.9905 34.0282.0071.9646 54A.0116.0070.9813 54.0214.0037.9748 34A.0149.0057.9814 34B.0267.0074.9659 34c.0162.0061.9777 34]).0070.0028.9901 34E.0042.0021.9956 35.7758.1756.0459 55A.7376.1866.0758.0o114.0118.9768 55B.7614.1778.0607.oo46.0051.9903 550.8235.1555.0229.0078.0142.9780 55D.8676.1059.0284.0044.0049.9906 352.8321 2.323.o446.0057.0037.9926 55C.9335.2242.0429 35D.7921.1547.0552 552.7416. 1788.0796 35A.0115.0025.9862 35B.00)L7.0013.9940 350.0079.0005.9916 35D.00o45.0015.9940 55E.00357.0009.9955 56.7717.1485.0800.0170.0185.9645 36A.7244.1723.1034.0144.0166.9690 36B.7956.1575.0492.0158.0168.9674 360.7672.1865.0463.0103.0114.9783 56D.7739.1559.0722.0183.0192.9624 36.7745.1566.0688.0112.0122.9767 36.0173.0050.9776 36A.0145.0087.9767 36B.0l60.0048.9792 56C.0103.0040.9800 36D.0186.0051.9765 36E.0113.0041.9846 37.7879.1925.0197.0214.0214.9572 37A.7762.1844.0594.0158.0163.9680 57B.8053.1532.0415.0231.0240.9529 370.8146.1648.0205.0131.0151.9739 37D.7957.1582.0460.0138.0oi44.9718 37E.7922,1681.0597.0166 0180.9654 40.2933.6803.0264.0162.0247.9591 40A.2926.6824.0249.0049.0111.9859 40B.2897.6825.0278.0033.0084.9883 400.2928.6922 o.0149.0036.0083.9880 40D.2951.6856.0193.00oo44.0111.9845 4GE.2955.6893.0152.0041.0092.9867 41.2796.6490 o714.0071.0164.9765 41A.2757.6450.0812.0011.0028.9960 4lB.2791.6470.0739.0028.0062.9910 4ic.2586.6928.0486.0025 o.0o46.9931 41D.2745.6337.0918.0031.0068.9901 41E.2881.6725.0594.0017.0040.9942 42.2866.6482.0652.o0098.0220.9683 42A.2913.6606.0481.0066.0152.9781 42B.2918.6608.0475.0124.0278.9597 42C.2861.6449.0690.0051.0118.9830 42D.2898.6623.0475.0065.0158.9776 42E.2854.6513.0652.0065.0148.9787 45.2776.6832.0592.0290.0711.8998 43A.2823.6940.0257.0055.0129.9819 43B.2771.6809.0421. o5314.0761.8926 43c.2790.6881.0529.0079.0182.9739 43D.2792.6867.0o340.0082.0206.9711 45E.2792.6874,0554.0068.0165.9767 44.8229.1406.0365.0425.0076.9499 44A.7500.1785.0714.0194.0097.9709 44B.7965.1681.0554.0084.0017,9899 44.0892.0125.8970 44c.7964.1713.0522 44D.7967.1788.0244.1689.0358.7955 442.8238.1566.0196 44.8456.1296.0577.0501.0083.9417 442.8417.1392.0189.0200.0045.9756 44A.7712.1774.0514

-97TABLE XX COIT'D LUID PHASE MOXI FACTION YAPOR PEASE MOLE FRACTION SAMPLE XBZ cHX ) ^ Y ^ Y 2 2 45.8446.1338,0216.0854.0149.8997 45A.7972.1664.0363.0817.0154.9028 45B.8611.1335.0055.2533. o404.7063 45c.7870.1559.0570 45D.8684.1224.0092.0091.0029.9885 45E.7873.1474.0653.0047.0013.9937 45.8175.1264.0560.0815,0131.9053 45A.7831.1650.0518.0973.0165.8861 45B.8548.1287.0165.3032.0o448.6520 46.7863.1189,0947 46A.7754.1323.0923.0487.0081.9431 46B.7161.1355.1484.2266.0368.7366 46C.2902,4814.2283.0201.0034.9764 46D.8326.1224.0450.0220.0041.9739 46E.7653.1306.1041.0252.0048.9700 47.8507.1357.0136.0112.0033.9856 47A.8288.1407.0305.0115.0035.9850 47B.8206.1296 o0499.0106.0029.9865 47C.8444.1331.0267.0170.0036.9794 47D.8224.1220.0556.0231.0047.9721 47E.7958,1291.0751.0151.0032.9817 47E.0244.0038.9718 50.4955.1738.2918.0389.0952.0357.0876.7815 50A.4845.1679.3078.0398.0310.0126.0370.9194 50B.5146.1754.2792.0307.0181.0075.0106.9638 50C.5039.1607.3123.0231.0079.0030.00oo60.9831 50D.5045.1655.3039.0261.0277.0092.0193.9437 5aE.4961.1771.3072. 0196. 0242.0089.0218.9451 50J.4822.1657.3317.0241 SOF.4790.1632.3266.0312 50G.4371.1497.3696.0436 50H.5031.1712.3040.0217 50D.4381.1634.2973.1012.0266.0108.0208.9419 5aE.0249.0100.0224.9428 5aE.0370.0139.0324.9166 5EF.0049.0018.0054.9879 5OG.0030.0010.0035.9924 50H.0023.0054.0058.9864 50J.0047.0019.0056.9878 51.5301.1148.3151. o4o0.0093.0019.0056.9832 5lA.5639.1137.2944.0280.0163.0026.0043.9769 51B.5715.1183.2800.0302.0076.0019.0048.9857 510.5457.1131.3085.0327.0078.0016.0039.9867 51D.5580.1214.2953.0295.0060.0017.0043.9881 51.4139.1772.3364.0724 51B.4489,.1785.3196.0529 51C.4239.1715.3561.0485 51T.0016.0036.0064.9884 51J.0019.0043.0071.9867 53T. o0016.0031.0052.9901 5]J.0012.0031. 0062.9893 52.4932.18o6.2777.0o485. o486.0206.0374.8935 52A.4174.1651.3170.1004.0365.0153.0342.9140 52B. 549.1769.3026.0656.0217.0092.0184.9507 52C.4224.1660.3320.0796.0109.0039.0109.9743 52D.4907.1678.2905.0509.0116.0043.0104.9736 52E.4335.1714.2964.0988.0085.0035.0085.9795 52C.4363.1734.3224.0678 52D.3645.1496.3370.1486 52E.3863.1698.3405.1034 53.5385.1678.2713.0224.0494.0165.0354.8987 53A.5235.1596.3122.OC47.0389.0128.0353.9131 53B.5478.1702.2751. OC.0062.0016.0016.9907 53C.4683.1519.3080.0718.0111.0035.0104.9750 53D.5398.1705.2557.0341.0104.0031.0079.9786 53E.5342.1453.2735.0470.0113.0034.0090.9763 53.45C2.0864.3806.0747 55A.4731.1902. 373.0296.0348.0153. o44.9155 53B.4679.2052.2800.0428.0044.0027.0017.9911 530.4428.1857.3000,0714.0105.0047.0105.9742 53D.5015.2063.2698.0222.0106.0045.0090.9758 53E,.4859.1771.2937.0432.0117.o0046.0096.9741 53E.5357.1513.2842.0286 55E.5231.1873.2683. 0212 53A.0489.0209.0393.8908 53F.4874.1759.2998.0368. 0o343.0129.0324.9203 53G.4444.1628.3473.0453.0265.0097.0239.9398 53E.4895.1772.2954.0380.0358.0140.0308.9195 53J.4333.1602.3575.0490.0296.0129.0276.9299

-98The results of repetitive analyses of the same samples have been summarized in Table XXI. It is believed that these results give the most accurate picture of the major definable source of experimental error. The cause of the observable deviations in the data has not been definitely established. However, the wide difference in the molecular weights of the substances analysed in this work is believed to be a contributing factor.

-99TA3BLE XXI REPETITIVE ANALYSES RESIS MASS SPEC. LIQD PHASE MOLE FRACTION VAPOR PBASE MOLE FRACTION SAMPLE DATE T NO. X XBZ XCX Xx YBZ YCg YEX 34v 8/11/60 (6582).9437.0275.0288 8/15/60 (6627).9570.0211.0219 34AV 8/11/60 (6583).9741.0116. 0143 8/15/60 (6628).9696.0157.0147 34L 8/11/60 (6584).0068.4932.5000 8/15/60 (6630).0109.4959.4932 34AL 8/11/60 (6585).0182.4742.5076 8/15/60 (6631).0117.4851.5032 44y 9/30/60 (6858).9499.0425.0076 10/6 /60 (6937).8970.0892.0125 10/11/60 (6954).9417.0501.0083 44BV 9/30/60 (6860).9899.0084.0017 10/11/60 (6956).9756.0200.0043 44L 9/30/60 (6864).o365.8229.1406 10/11/60 (6960).0377.8456.1296 44AL 9/30/60 (6865.).0714.7500.1785 10/11/60 (6961).0514.7712.1774 44BL 9/30/60 (6866).0354.7965.1681 10/11/60 (6962).0189.8417.1392 45V 9/30/60 (6861).8997.0854.0149 10/11/60 (6957).9053.0815.0131 45AV 9/350/60 (6862).9028.0817.0154 10/11/60 (6958).8861.0973.0165 45BV 9/30/60 (6863).7063.2573.o4o4 10/11/60 (6959).6520.3032. o448 45L 9/30/60 (6867).0216.8446.1338 o10/11/60 (6963).0560.8175.1264 45AL 9/30/60 (u868).0363.7972.1664 10/11/60 (6964).0518.7851.1650 45BL 9/30/60 (6869).0055.8611.1335 10/11/60 (6965).0165.8548.1287 50DV 10/13/60 (6982).9437.0277.0092.0193 10/16/60 (7016).9419.0266.0108.0208 50EV 10/13/60 (6983).9451.0242.0089.0218 10/16/60 (7017).9428.0249.0100.0224 5JZV 12/3/60 (7256).9884.0016. o0036.0o64 12/3/60 (7257).9867.0019.0043.0071 12/3/60 (7247).9901.0016.0031.0052 12/3/60 (7248).9893.0012.0031.0062 52DL 10/16/60 (7022).0509.4907.1678.2905 11/18/60 (7155).1486.3645.1496.3370 53AL 10/25/60 (7059).0047.5235.1596.3122 11/17/60 (7137).0296.4731.1902.3073 53AV 10/25/60 (7053).9131.0389.0128.0353 11/17/60 (7131).9155.0348.0153. o344 11/17/60 (7144).8908.0489.0209.0393 53DL 10/25/60 (7062).0341.5398.1705.2557 11/17/60 (7140).0222.5015.2063.2698 53DV 10/25/60 (7056).9786.0104.0031.0079 11/17/60 (7134).9758.0106.0o045.oo0090 53EL 0lo/25/60 (7063).0470.5342.1453.2735 11/17/60 (7141). 0432.4859.1771.2937 11/17/60 (7142).0286.5357.1513.2842 11/17/60 (7143).0212.5231.1873.2683 53EV 10/25/60 (7057).9763.0113.0034.oo0090 11/17/60 (7135).9741. 0117.0046.0096

GRAPHICAL PRESENTATION OF THE DATA Certain insights into the effect of aromaticity on the K-values of hydrogen and the effect of hydrogen on the K-values of hydrocarbons may be obtained from a graphical presentation of the experimental data obtained in this work. Figures 10, 11 and 12 show that the effect of solvent composition on hydrogen K-values is not a linear function of composition. The results of calculations based on the two equations of state method are shown to predict the curvature shown in these figures. Relative volatilities of the hydrocarbons from experimental data as well as from the literature are also shown as an indication of the hydrocarbon interactions. A graphical correlation of these results requires a parameter that indicates the composition of the solvent. One such parameter in common use is the U.O.P. K factor. Elbishlawi and Spencer(71) have shown that the K-values of methane at constant temperature and pressure may be correlated as a function of this parameter. The experimental hydrogen Kvalues, as well as hydrogen K-values from the literature, have been plotted in this manner in Figures 13 and 14. This correlation of hydrogen K-values has an average absolute percentage deviation of 10.8 at 200~F., and an average absolute percentage deviation of 17.2 at 100~F. The modified two equation of state method gave an average absolute percentage deviation of 20.6 at 200~F. and 16.6 at 100~F. for hydrogen K-values, This graphical correlation of hydrogen K-values brings out several points of interest. The K-values of hydrogen increase as the -100

-101aromaticity of the solvent increases, as the system pressure decreases, and as the system temperature increases. However, the U.O.P. K factor does not completely define the effect of the solvent on hydrogen Kvalues. Figure 15 shows two different solvents that have a U.O.P. K of 11.0. One is pure cyclohexane, while the other is a mixttire of hexane and benzene. Improved accuracy in the prediction of hydrogen K-values will require more specific information about the solvent than the U.O.P. K can provide.

-102110 ----- 100 LEGEND: El DATA FROM LITERATURE (15,41) 90 i0 EXPERIMENTAL RESULTS.] X CALCULATION RESULTS 80 - - 100 ~OF --— 200~F / 60 -- 40 tN o —---------—.0- 5 0 I 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 XBZ —--- RELATIVE VOLATILITY OF HEXANE-BENZENE 20 2.0N DATA AT I ATM (58)If 1 0.5................................. 0 0.1 02 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 XZ'" Figure 10. Hydrogen Vapor-Liquid Equilibrium Composition Ratios in Hexane-Benzene.

-103100 -- I i-i -|| LEGEND: 90..... 0 DATA FROM LITERATURE (32,41) 8 0 EXPERIMENTAL RESULTS X CALCULATION RESULTS 1000 F 0 ---'200~ F 60 50............. N O 0.m2~F —----- - 2.0'I500 PSI. 0.1.2.3.4.5.6.7.8.9 1.0 - a? I.o 0 --— 0.^...G 0 --- -- -- - - 0.1.2.3.4.5.6.7.8.9 1.0 XCX — Figure 11. ardrogen Vapor-Llquid Equilibriwn Compoition Ratios in Hexane-Cyolohexane.

-104100 — _-,,._._,_,_,,. _. - - LEGEND= 90 DATA FROM LITERATURE (15,32) 90... -- 0 EXPERIMENTAL RESULTS 80 - X CALCULATION RESULTS -/ —.- 100 F /x 70 - _~ ~70 — _-, 200~F x, ~'" z60 / x _0 __ ____ DTX 0..0......- - - 10 - -- ---- ----------------------------- 205o'0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 XBZ — Figre 122.0 Hydrogen Vapor-Liquid Equi-bu onpo-i0.1 0.2t 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 FgRELATIVyroEn VOAIIYa rL quid BNEE-ul'bu CYCOHEXAN f~ ~~~~~to Ratos nBnee'ylhx~

-105~100' _ _ E D-____ -200~F 100 9 8 _ 4 PRESEN INVSTGAIO o -"IO~ F ^-3 2 00~F LEGEND: _______ 20 9 8 ~ AUTHOR -200~F -IOOO F O~F IOOOF200OF 7 ~ PRESENT INVESTIGATION 0 I V L5 ENICHOLS (41) V DEAN (70) 0 0 4 - BURRIS (69) -, KRICHEVSKII (32) 0 3 - WILLIAMS (73) BENHAM (68) A A AROYAN (67) r 0 U 2 NELSON (72) 9 10 II 12 13 14 15 16 UOP K [(Tp/ /S.G.(6d/600)] - Figure 13. Hydrogen Vapor-Liquid Equilibrium Ratios at 500 Psi as a Function of UOP K Factors of Hydrogen Free Solvent.

14~~00~-106 9 0 0 >~10 | ILED0 |-0- -* —-0 F N 7, AUTHOR -2000F -100~F 0F I0OOF 200F 5 NICHOLS (41) v v DEAN (70) WILLIAMS (73) v BENHAM (68) A A A 3 ----— AROYAN (67) —NELSON (72) |2 o-KRICHEVSKII (32) - 9 10 11 12 13 14 15 16 UOP K- [(TB e) 3/S.G(6 6OO]F Figure 14 Hydrogen Vapor —Liqui Equilibrium Ratios at 1000 Psi as a Function of UOP K Factors of Hydrogen Free Solvent. Funiction of UOP K Factors of Hydrogen Free Solvent.

-107w z Z Z W Z ix N Z z 0J P: 500 PSIA < 100 -LEGEND: _ 9 1~ -— 0- 100 0F 8, ---— __immmr - 200oF - K~ \\ DDATA FROM LITERATURE(15, 6,. — -."- 32. 41) 5,,~ ____,'_ ___ ___.X Qy___ 0 EXPERIMENTAL RESULTS 5.0 20 -- -----—'"~-'- - -. - O 100.... —'............ 9 6 P=1000 PSIA LEGEND: 4 IOOOF I. s.~...... 200~F — 00o — ---- El DATA FROM LITERATURE1 2 ~,,,. < 32,_41) s^ E)^ EXPERIM'NTAL RESULT 2 -^10~~w'' - - -:-. 9.5 10 II 1213 UOP K [(TB.p.)1/3 /S.G.(60~/600)] Figure 15. Vapor-Liquid Equilibrium Composition Ratios of Hydrogen as Function of the Solvent's UOP K Factor.

-108In Figures 16, 17 and 18, the K-values of the hydrocarbons studied in this work are shown on a conventional log-log plot. At a given system temperature and pressure, the K-values of two different hydrocarbons in the presence of hydrogen appear to be proportional to their vapor pressures. That is: K - i K P0 J j at constant P and T. Data reported by Nichols(41) for the system hydrogen-hexane has been used to establish the validity of this relationship. All experimental hydrocarbon K-values were predicted to within approximately 25% in this manner. Another method of correlating hydrocarbon K-values is presented in Figure 19. Several simplifying assumptions are incorporated into this graph. Since the hydrocarbon K-values measured in this work appeared to be proportional to their vapor pressures, Raoult's and Dalton's Laws were assumed to give a first order approximation of these K-values, Ki = Yi/Xi = P /P or K.P = P0 1 i The vapor pressure of component "i" may be estimated from the ClausiusClapeyron Equation: log(P) = - AH [L - ] (Pi) 2.505R T2 i 2

-109-__I I__I_1______________1 0 ---- - - -.1 -- 0"\ 20\ 200 OF 3 x { 10 ---------- IOOF LEGEND' COMPOSITION ON A HYDROGEN FREE BASIS _- \ XBZ XcX XHX _______ ____ ______.219 -.781 5.783 -.217 ------.299.701 - - --... -.861.139 -.....500.173.327 3 -- 2 --- 100 200 300 400 500 1000 2000 PRESSURE (PSIA) — Figure 16. Benzene Vapor-Liquid Equilibrium Composition Ratios.

-11016i( —- -.-...5 2 —- -- - = ^;. —~ 2000~F.4~~X -2 do____ _ LEGEND: _ ____________ - COMPOSITION ON A HYDROGEN FREE BASIS 5 XBZ Xcx X HX 4 —-I_ -=.200.800 _ -.299.701 -_ ---.861.139 - 3 -—.500.173.327 -- - - 2 I k k IO O~ 100 200 300 400 500 1000 2000 PRESSURE (PSIA) - Figure 17, Cyclohexane Vapor-Liquid Equilibrium Composition RatiosJ

4 3 2 -_- _- -. < LEGEND:! iG D " COMPOSITION ON A I 5 | --- - — X BZ Xcx X HX —4 -.78_.217 - - --- _ _ __ _.2_00.800-L 2 I00 2-0 300 400 500 1000 2000 PRESSURE 200 300 400 500 1000 2000SIA) Figure 18. Hexane Vapor-Liquid Equilibrium Composition Ratios.

1011 —---------------------------- _ _ _ _ _ _~_ __ _ __ _ _ _ IO +S TO 4P'co +' N.p * ~~~ 1.0 A BUTANE, AROYAN (67)~~~~~~~~~~~~~~~~~~~~~~~~ 4:)4 10 - - - - - -^ - - - - -! - - - - g ^ <u~~~~~~~~~~~~~~~~~~~~~0 --- --- --- --- -hf- --- --- --- --- --- -— ~S IS-OCTA — -- -- — NEq, DEN(0 * lU CO 0 E EE / OEICD)EANE, WLAM (73) Id */ 1_ __ __ __ _ tr Pi 4'T I - U ---— fa -04~ ~ ~ ~ r -03EN -0 -0. 0. 2 03. 5 06 0... I 2 ^4 " *~~~~~~~~~~~~ ISO-OCTANE, DEAN (70) H?0 y[/ * *' Q~~~~~~~~~E BENZENE, EXPERIMENTAL,Q 0 ____ ____ / ____ ____ ____ ____ ___ ____ __ X CYCLOHEXANE. EXPERIMENTAL __ __ J? //* ~~~~~~~~~ ~~~~0 HEXANE, EXPERIMENTAL J ( ^//+ D~~~~~~~~ ~~ ~~~~ HEXANE. NICHOLS (4 1) (1 / / ~~~~~~~~~~~~~~+ PROPANE, WILLIAMS (73) cd^ Q^/ ^ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~0 P-1 _p id-1- - - -- - - - -- -- - - - 0 rd co,/f _________ —----- ^ a ^ ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~T 77, ___ ___ ___ ___ > ^-{ o3 CQ~~~~~~~G -H_ - ^ -- -- -- -- -- -- -- -- -- -- -- -- -- -- — ~~~~~~~~~~~~~~~~~~~~~r_

-115If the atmospheric boiling point of the component is chosen as a reference state, the vapor pressure of the component at any other temperature is given by the relationship: log P~ _ ~V [I - 1] i - 2.303R TB.p T Trouton's empirical ratio indicates that at atmospheric pressure: -HV = 21 TB.P. so that lo o _ 21. TB.P. log P~ = - (1 - ) 1 i 2.303R T or log KiP = 4.6 (1- T') This relationship is in a reduced form, and except for data on isomeric dodecane and iso-octane by Dean and Tooke(70), it appears to represent vapor-liquid equilibrium composition ratios of non-polar hydrocarbons in the presence of hydrogen to 1000 psia. The effect of pressure on the hydrocarbon molal heat of vaporization is reflected in the fact that the slope of the lines shown in Figure 19 is 4.2 rather than 4.6.

SAMPLE CALCULATION In order to further clarify the methods used to predict vapor-liquid equilibrium compositions in this dissertation, the following section has been added. Estimating Overall Composition The first step in calculations of this type is to estimate the overall composition of the phases. In industrial practice, the overall composition of the phases is the feed stream composition to an equilibrium stage. The overall composition of the phases present in the equilibrium cell in this work has been estimated from the experimental equilibrium composition data. By a material balance around the equilibrium cell: F = L+ D FxF Lxi + Dyi Per mole of feed: X = XFX xF X = xF x xF4-____ D 3 1 2 2 3 3 4 4 yl-X Y2'x2 Y3-x y4-x4 where subscript 1 indicates benzene, subscript 2 indicates cyclohexane, subscript 3 indicates hexane, and subscript 4 indicates hydrogen. Since hydrogen is present in all runs xF4 is solved for first(xF. x4)( YzxF -x xF -114

-115An additional restriction is required to provide a completely defined set of equations for the overall composition. In this work, the assumption was made that the hydrogen free composition of the liquid phase and calculated feed were equal. That is: XF. X 1-XF 1-x4 or for benzene: XF = ix4 XF4 (- ) Substituting this relationship into the equation for XF.: xF XF -xi _ ( )Yi-x xl x xF4 (y4-x4) 4( ) 1-x4- xF4 ( —-) - x= Rearranging xl Y+-Xi ~ x + x —-A_ ) _ xl -x44 Y!-xl XF4 = y4-x4 1-x4 then 1-xF XFp = X1 (-1-x4 XF2 2 1-x4 and x^ e= x3 (IX ) xF3 -x4 Sample Calculation The ideas and equations presented thus far will be combined to illustrate the calculation presented in Table XVII for Run 18.

-ll6. The given data is: Pressure = 567 Psia Temperature = 100~ F. x y Benzene 0.210 0. 004 Cyclohexane 0.000 0.000 Hexane 0.751 0.011 Hydrogen 0.039 0.985 The first step is to calculate the overall phase composition. From the preceding subsection: xBz + YBz-XBz xE + XH (y 2x2) - XBz x xHp H2 yH2-xH2 Bz H2 YBz' XBz xbz H2 H2 2 XF = 0.039 2 Then 1-xH ( ) 0210 XBz = x (-x E2) = o021o ^Bz - ^^2 and 1-xF xF x ( iI( - H2) 0.751 Hx Hx 1xH2 Vapor-Liquid Equilibrium Composition Ratios The vapor-liquid equilibrium composition ratios are calculated by means of the two equation of state method. Ki = ivi/i The vapor phase fugacity coefficienti, cp. and the liquid phase activity coefficient, 7Yi are functions of composition. Thus, a first estimate

-117of all compositions must be made. For this case, assume: x y Benzene 0.210 0.002 Hexane 0.750 0.oo8 Hydrogen 0.040 0.990 Calculations for each of the coefficients shown in the above relationship for the vapor-liquid equilibrium composition ratio follow. Liquid Phase Activity Coefficient The Hildebrand Solubility Theory is the basis for the prediction of liquid phase activity coefficients. The equations used are discussed in the main text of this dissertation. Physical data required for this particular calculation include the liquid phase composition, the liquid molal volume of each component, and the solubility parameter for each component. Liquid molal volumes have been estimated in two ways. The Watson Expansion factor has been used, where: V = (ViOi)(5.7 + 3.0 Tri) A compilation of (Vi0o) is given by Edmister(14) and the critical properties of the components studied here are tabulated in Table VII. At lO0~F. the following liquid volumes may be calqulated: VL = 11.64 (5.7 + 3.0 x 1560 ) = 85.7 cc/gm-mole -Bz 1012.7 V-L = 16.52 (5.7 + 3.0 x 560) = 124.6 cc/gm-mole L 5 560 VL = 1.05 (5.7 + 3.0 x -0 ) = 353 cc/gm-mole -H2 60.2 Specific physical data from the Engineering Data Book(l5) indicates that

-118for the hydrocarbons at 100~ F.: VL = 78/0.860 = 90.6 cc/gm-mole -Bz VL = 86/0.642 = 134 cc/gm-mole Hx From Table VII the liquid molal volumes recommended by Chao for all temperatures are found to be. VL = 89.4 cc/gm-mole'-Bz L Vx = 131.6 cc/gm-mole -x V = 31.0 cc/gm-mole -H2 Solubility parameters needed for this calculation are discussed in a special appendix on page 67. This information may now be substituted into the volumetric entropy equation: L L 2L + Vi (5i M) V. n y. = in +- + + 1.0 D1 v RT where V L Zx.V -M i 1-1 and L L M = xiVii xii By substituting specific data into these equations, the following liquid activity coefficients are found: B = 1.425 7 = 1.oo008 7H2 = 1. 686

kll9Pure Liquid Component Fugacity Coefficient The pure liquid component fugacity coefficient for hydrogen, VH, has been estimated by Chaots method from the data in Tables VI and VII: 2 log V = 1.96718 + 1.02972/Tr - 0.054009 Tr + 0. 0005288 Tr H2 + 0.008585 Pr log Pr Here Tr = 560/60.2 Pr: 567/190.8 and v = 14.929 H2 The pure liquid component fugacity coefficients for the hydrocarbons has been estimated from a knowledge of the hydrocarbons' vapor pressure and liquid molal volumes: in vi - ln +ln( )P + P P P. iRT 1 At 100~F., the following vapor pressures are found in the Data Book on Hydrocarbons by Maxwell(39): P = 0.215 atmospheres PO = O.343 atmospheres Hx fi For both hydrocarbons, (p-)pO is essentially unity. Thus: ~Bz = 0.007 = 0. 010 Hx Vapor Phase Fugacity Coefficient The vapor phase fugacity coefficient has been calculated in three different ways. The first method utilizes the Virial Equation of

-120State. From Figures 4 through 7, the following experimental virial coefficients are found at 100~F.: (100~F. ) BBB= - 1430 cc/gm-mole Bz. Bz (100~F. ) *Hx} Hx = - 1750 cc/gm-mole (100~F.) = B =(l00 F) = 14.50 cc/gm-mole Hz Hz From Figures 8 and 9, the following second virial interaction coefficients are found: (100~ F ) (oB ( 0 = - 1580 cc/gm-mole Bz, Hx (100~F )F B ( F = - 4.0 cc/gm-mole Bz, H2 (100~ F. ) Blx, H2 7.0 cc/gm-mole The virial equation must first be solved for its largest root, the vapor-phase volume::M i1 + V RT V where BM 2 B (T)+ 2 (T) 2 H (T) (T) M =YBz Bz Bz + YHxBHxXx + YH2BH2X + 2YBzYHxBBzH x + 2YBzYBBzH () + 2yryB~,H2(T) Upon substitution of values presented earlier, this equation yields the result: VV = 675.695 cc/gm-mole -M

-121Then 2 (100~E) (100~F.) (100~F.) in ~i - 7 (yBz i Bz + YHiHx + YH2Bi H2 ) - PVV ln --- RT Solving this equation gives the result: PBz = 0.922 THx = 0.951 TH2 = 1.023 The Redlich-Kwong Equation, integrated for moderate pressures, has also been used to predict vapor phase fugacity coefficients. 2 2 ln cp = [Bi - Ai + (Ai' AM) ] P where 2 Tc' A. = 0.'4278 c 1 P T2 5 B. = 0.0867 T_ 1 PT and AM = i Ai This equation gives the results cp = 0.928 Bz PHx = 0.960 H2 = 1.024 Calculation of K-Values and Improved Estimates of Equilibrium Phase Compositions The information calculated in the preceding sections may now be used to estimate the K-values for each component.

-122Using the vapor phase fugacity coefficients based on the Virial Equation of State, the following results are obtained: K 1.425 x 0.007 = 0.011 Bz 0.922 K1x = 0.010 = 0.011 x 0.951 K = 686 x 14.929 = 24.612 H2 1.023 These values, plus the overall composition, are used to improve the original estimates made of the equilibrium phase compositions. From the Outline of Correlation Procedure (see page 54ff): XF (KBz -Kx) XH (K2-1) ( Bz x(K KB) ) + K (1-x2) + K xH = 1. 0 2 2 xFII (KxBZ-) + xH (KH -KBz) ) x H2 H2 H2 Substituting the known values and solving for xH2 gives the result: xH = o.040 H2 Then xH2 xFH( K2 ) Hx = 12 X ( ^ KHxl) + ^xH2 KH2'KHx) Substituting into this equation gives the result: xHx = 0.750 Finally XBz = 10 - x H XHx = 0.210 The vapor phase compositions are found from the relationship: y K.x. 1 1

-125so that y = 0. 002 Bz y - o0.008 y 0.990 2 As these are the initial values assumed, the calculation is complete. This same procedure has been used to re-estimate equilibrium phase compositions in which vapor phase fugacity coefficients were estimated from the Redlich-Kwong Equation of State, integrated for moderate pressures. Calculation of Interaction Virial Coefficients This calculation is discussed in the section entitled "'Calculation Results" (page 75). The experimentally determined equilibrium phase compositions are assumed to be correct. Then: ci = 7ivi/Ki Substitution of the experimentally determined compositions into the equations previously discussed gives the results: )Bz = (1. 423)(0.007)(0.210)/0o.004 = 0.523 cp = (1. 009)(0. oo)(o. 751)/. oll = 0. 690 CH2 = (1.686)(14.929)(0.039)/0.985 = 0.999 The virial equation must be solved for the vapor-phase volume, giving the result: V _= 675. 430 cc/gm-mole for the experimental vapor phase compositio for the experimental vapor phase composition.

-124Assuming that a change in the hydrogen-hydrocarbon second virial interaction coefficients will not affect this last result, the equation for the vapor phase fugacity coefficient may be written: ln i = V (BzBi Bz (T) + HxiHx() + i (T)) -ln - V~ z 2x i B Hx ) H2 iH2 RT The values of Pi and ~, which have just been determined, plus experimentally determined values of vapor phase compositions and all second virial coefficients except the hydrogen-hydrocarbon second virial interaction coefficients, which are the variables in this calculation, are now substituted into the above relationship. In order to reduce experimental uncertainty, this set of equations from Run 18 has been combined with similar sets of equations utilizing data from Runs 21, 22 and 25. The combined set of equations has been solved by the method of least squares for the hydrogenhydrocarbon second virial interaction coefficients, giving the results: (100F. ) BBzH2H= 140.588 cc/gm-mole (lOo F.) HBx ~= - 51.052 cc/gm-mole The new estimates of the hydrogen-hydrocarbon second virial interaction coefficients have then been used in a second calculation of equilibrium phase compositions, giving as final results: x y Benzene 0O 210 0.002 Hexane 0.750 0 o008 Hydrogen 0. 039 0.990

-125 Computer Program The complete calculation that has just been described in detail has been programmed for a 704 IBM computer. This program is presented in Table XXII.

TABLE XXII FORTRAN PROGRAM FOR PREDICTION OF EXDPERIMETAL RESULTS USING I.B.M. 7o4 DIGITAL COMPITEN EOR-^ ---— J^ B A -L L9 E-6a^E ^ ~/ ^ A ^QJ _.__. __-_______0______-______ ____________ ____Y LJ _00 - -------—, — -- _ --- 3-. - -- --------- ------------ ------------ ------— [VIC 2 FORMAT (8F6_2) VLE00020 C F 11_.3_3H- ~ 1.3t4H ACI;TY COEFFICIENT.LIQUI PHASE FVLEOO I FnRMAT(6F8.3) VLEOU030 16 FoRMAT(55H ATVYCOFIENLGUOVLEU0 4 FORMAT(I16*F10.2) VLEU0041 C11.3,3H F11.3,3H F11.394H F1.3,/ 5 FORMAT(7F10.4,/F10.4) VLE00050 Q55H FUGACI TYPJRE ----- 11-3 — HVLEOO3 l 6 FORMAT (7F-10.6./F1076-)- -- --- - ~~~~~~ —------------------------------------— V LE-C9DDV(5 —----------- ~ l.3,3 "F.3 ------------'F11.3,FllF ^6 FORMAT(I7Fl0.69,/FlO.6) VLE1OOOH6110 -4 7 FORMAT(FI.O) VLE00070 — 5 - -- ______FUGACITY COEFFICIENT,VAPOR-_PHASL Fllo3,3HVLE00IO 8" DIMENSION -B —--—.-S(4AVL(4), P C(4)Trl),IRUN P[- C F11.33H F11.3,4H F11.3) — EO-64O - C(8,4),XSAV(4,4),XSUV(4,4),XRKS(4,4),Y(8~4),YSAV(4,4),YSUV(494),YRKVLEOOO75 17 F')RMAT (23H - HYDROGEN / VLEOUI5O CS(4~4)~AKVALS(4~4),AKSAV(4~4)~AKSUV(4,4)~AKRKS(4,4),GS(4~4)~GSAV(4VLFOUO80 C55H Y F11.03HVL 6 C~4)~GSUV(4~4)~GRKS(4,4)~ANUS(4~4)~ANUSAV(4~4)~ANUSUV(4~4)~ANURKS(4VLE00090 C F11.3~3H F11.3l4H F1L.3s/ VLEOO67O C.4),FS( 4,4),FSAV( 494).FSUV( 9~F-F,-4 C55H ----- --------------— F113,ILTO0 - — ^^-^ ^-^-^^^-^^-^-^^^-^^^-^-^^ -- - - ^ F11 v~~~~~~~~~~~~~~~~~~~~ —---------!F n C~VLRKS(4)~VVS(4)~VVSAV(4)~VVSUV(4)~AKVAL(494)~XF(4~4),SVL(4)~VL(4)VLEOOU1O C F11.3~3H Fl1l.34H F11.39/ VLIOO69O C9VV(4).F(4.44 -— TC-4- )(- -R4,4)-AKVALCT4.4)Ac ---------- C55HVALUE - CT(1),VP(4),ARKM(4),BM(4),XS(4,4),YS(4,4)~BUVS(4~4~4),BAVS(4~4~4)~AVLE00130 C F11.3,3H F11.3~4H F11.3) VLIOO' — C(4.4).FC(4,4),R(4.4).ERR(4~,DERR(4) VLEOU1 — Q 18 FORMAT(55H ACTIVITY COEFFICIENT9LIQUID PHASE FVLEOU(I O 9 FORNAT(27H1 RUN NUMBER I 10U/ VLEOU150 ClL.3,3H F11.3,3H F11.3.4H F11_.3./ VI____O ~~C27H - - - - T M - U ~ ^ -, ~DFE-GTZEE3-S-ARl RE^-I ------ VEEUZ176 ---------- C5 5H FUGAC I Tf, PURE 3 C27H PRESSURE F1.O0,7H PSIA) VLEO170 C F11.3.3H F11.3~4H Fll.3~/ VLEOOi7S -O — FO-RMAT F1-H —----------- ----------- ------------ C —----------— 5 —---- f-5H 5FU-GHACrTT-cOE-rrff.VA7R-Tr`- - 3 C VIRIAL EQUATION VALUES REDLICH-KWONG / VLEOU190 C F113,3H F11~3~4H F11.3) VLEOO I 0 C106H IN1IAL VLtUO0U - 19 FORMAT(46H INTERACTION VIRIAL COEFFILIENTI/ VLEOU/O CVALUE ADJUSTED UNADJUSTED VALUES/ VLF00210 C69H B(HYDROGEN-BENZENEI VL —- 79O -- C55HVOUOFTtflDC-PWGW)OLT —---- ------ VDL2W2-CT —CI M-1CC-PETF-G CET —-----— Fl.3 3HVT^G2-U ------------------ - F11.33/ 9LEoo8 C F11.3.3H F11.3,4H F11.3,/ VLEOU230 C69H B)HYDROGEN-CYCLOHEXANE) VLEOO81O p ~C55H~ ~~~~ —----— ~ —V(5LUM^-OF-VAFP^-TCC-^~Tff-C^^^tr-E^ —-----— FIT.-3j-3HV-CFO^^OZ F 11.3.-3H F 11.3,1 V 8- - r?C F11.3,3H Fl1.3) VLE00250 c69H B(HYDROGEN-HEXANE) V 11 FORMAT (22H BENZENE 7 —-— VLEUU bU - C69H F VL C55H Y VLEUU~~~~~~~~~~~~~~bU ~~C 1. 3,3 H F11.3) 1,B2,9)B C55H Y F11.3,3HVLFOU27O 20 READ INPUT TAPE 7,1,B(1,1,1),B(1,2VLF0270,01RED)IBUT AP 7 91 9 l.3I.lI) 1 B)1B( 4 12) I B(2,2,1) 1 BVLEOO85O 4, ------ ---------- - - 9. —- - --- ---— l- ^ ^..,.?...^^ ^^,^ ^^ C F — PMl.^3H —l.^ ^ —T ----------------- ---------— F-l-h —--- pb(3, 1 C55 F133 F1Bi1 FT37~C Z8TC(2. 3,1.B(2,p4q1).B(3; 31),B 39.)B441)2lI BI;-TB1-vC~F ------ _ C55H Fl 1.3,3HVLEOU29O CF,1),B) 3,2,1).B(429.1),B(4,3.1) LE8 C55 FK VALUE 3R-E~OOREAD INPUT TAPE 792,51)115 )2).S)3).S 9) AV 1.9-2 9~L3,M1WEOTV C5F15H 3 K1.34 VALUE F11.3v3HVLFOU31O C) VLEOOTTS9O C F11.3.3H F11.3.4H F11.3) —-----------------------------— VLE003z!0 --------- READ INPUT TAPE 7,~3,VP ( 1 ),VP ( 2 ) ~VP I 3AP ~PC (P43)4~TC4 ),TT VCOO — 12 — -FORMAT55H ACTIVITY COEFFICIENTLIQUID PHASE FVLE00330 - DO22 M=l,~4 VL —---- --------------------------------------- O9 ~ 3C113,H Fi1.*33H F 1. 3,4H~~ -.937- V-T- READ INPUT TAPE 74tIRUN) M),PPIM) C55H FUGACITY.PURE F11.3,3HVLE00350 READ INPUT TAPE 7.5~X(1~M),X(2XM),X23,M),X(4,M)_Y_,^M).Y_2,M)Y,39VLEOO93 -— ~~~Z —-F~~r.3V3-H —— F~~l.-3T4H —~-Fll-.-3-.-7~ —---------------------------------— 7rVe-n30 ---- -C Y. —- " --------------- ------- 7rO C F —-11. 3,t3-H -— F-1. - 3-,4-H —---- LOO~OCM). Y(4. M) C55H FUGACITY COEFFICIENTVAPOR PHASE Fl1.3,3HVLEOU370 22 READ INPUT TAPE 796,ARK(1,M),ARK(2,M),ARK(3,M)~ARK(4,M)~BRK(1,M)~BVLE0O9B0 C F11.3.3H F11.3.4H F11.3) VLE00380 CRK(2~M),BRK(3,M),BRK(4~M) VLE096 13 FORMAT (26H CYCLOHEXANE / VLE0039O 21 READ INPUT TAPE 7,7,COND VLEO —--------------------------------------—' — T C55H Y F — - __ _[__ __ _ _ _ ^ Do 24 M= 1,4 VLEOO98O C —----- - F11.3,3H — F11.34H- F11.3,/ VLF00410 Do 23 L=14 -------------------------------------- C55H X 113vv~T4o5 LM.1SI.M1 C F11.393H F11.3,4H F11.3,/ VLEOU430 23 AKVAL(L*M)=Y(LgM)/X(LMM) VLEOO99O C55H K VALUE F11.3,3HVLEOU44o 24 CONTINUE VLEO100 C F11.3.3H F11.3~4H F11.3) VLEOU450 T=(TT-32.0)/1.8+273.l16 VLEO1Ol 14 FORMAT)55H ----- --— ACTIvrTY C-OEFFPNTLTUD PHASE --— FVf DO 25 M 1,4 - - -`VLE01020 C1l.3~3H F11.3,3H F11.3,4H F11.3./ VLEOU470 5 P_(M)=PP(M)/14.7 --— V-LEOO ----- " —— ~ —--- -~ -~-FGCTYPR~ — ------ ---------------- -Fr33VE0g —2Y 1=' ----— " —"VE^ C55H FUGACITVPURE F 11. 3,3HVCE0048 ——.- 27_ 1= VLO15 C F11.303H F11.3,4H F11.3,/ VLE00490 v-i ______________________________________- VLEO1O6O C55H FUGACITY COEFFICIENTVAPOR PHASE Fl1.3,3HVLE00500 J=l VLEO — C —-— C F_._33H F11.3_4H F11_3) VLEOU510 D.29.M=1.,4 VLEO1O8 15 FORMAT (21H HEXANE / VLE00520 DO 28 L=14 VLEO1100 ------- 5__ _ _ _-_____ —___-______- V F_11.3.3HVLEOU530 x OL, X -----— _ —------------- - - ----------------— I —-^ C F11.3.3H F11.3,4H F11.3./ VLE00540 YS(LM)=Y(L~M) VLEO11E C55H X Fl1.3.3HVLEOU550 28 AKVALS( L,M ) =AKVAL ( L*M) VLE ^A — C F11.3,3H F11.3,4H F11.3./ VLE00560 29 CONTINUE vLEO11BO C55H K VALUE Fll*3,3HVLEOU570 30 - Do 31 M=1.4 — L —------------------------------— E~ — - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - --- ~ — - - - - - - - - -~- -

TABLE XXII CONT'D BUVS( l~4~MY=B ~ --— l —----------------------------------------- ----— lO'' -yo"D-07MT4 -" ------------------------------------------ Q — BUVS(1,4,M):B(1,4,1) VLEO1140 300 DO 307 M=1,4 VLEO17O BUVS(2,4,M)=B( 2,4,1) VLE01150 301 IF(X(1,M)) 303,302,303 VLEO1775 31 2 —BUVS(3.4~M)=B(3~4,1)VL E11 — 302 AKVALC(1,M)=0.0000 VLEO1780 32 DO 40 M=1,4 VLEO1165 33iELkL2iMIJ 305,304,305 VLE01790 33 IF (X(l.M)) 3- 634 —--------------------------------------------------— VL-E01165O —- ------— 05304305 --------------— _ —... —-KL —M_30-,30 - VLE1 33 IF (X(1,M)) 34,36,34 VL7EO117O~ 304 AKVALC(2,M):O=.0000 VLEO1800 __34 — XF(4,MI)=(X(l1,M)/(1.*U-X(4,M))+(X(4,M)*( Y(1,M)-X(1,M) ) )/(Y(4,M)-X(4,VLE01180 310-IP(X( 3. 1 3I,30 7 VLE18 ~~~~~~~~~~~~~~~~~~~~~~~~__05__~LiJvl.. QTJ_9__VLEO1810 CM))-X (1M))/((Y(1,M)-X( 1M))/(Y(49M)-X(49M))I+ TIvT~7(]~-J-Fi —g[~ —ZA.. 306 AKVALC(3,M)=0.0000 VLE 35 GO TO 37 VLEO1210 307 CONTINUE VLEO1830 36 XF(4,M)=(X(2,M)/(1.0-X(4,M))+(X(4,M)*(Y(2,M)-X(2,M)))/(Y(4,M)-X(4,VLE0120 DO 316 M=1,4 VLE01865 CMJ)-X(2,1_))/((Y(2,M)-X(2,M_)/(Y(:,M)-X(4,M))+X(2,M)/(1.0-X(4,M))) VLE01230 308 ERR(M):X(4,M)(AKVALC(4,M)-1.0)((XF(1,M)(AKVALC(1,M)-AKVALC(3,M)))/VLEO1i70 37 XF(1,M)=X(1,M)*(1.0-XF(4,M))/(1.0-X(4,M)) — VLEr2O C(XF(4,M) AKVALC(1,M)-1. )+X 4,M)(AKVALC4,M)- AKVALC(1,M1V+1XF(,MVL-O8-7A 38 XF(2,M)=X(2,M)*(1.0-XF(4,M))/(1.U0-X(4,M)) VLEO1250 C)(AKVALC(2,M)-AKVALC(,3,M)))/(XF(4,M)(AKVALC(2,M)-1.0)+X(4,M)(AKVALVLE01872 39 XF(3,M)=X(3,M)*(1.0-XF(4,M))/( 1.0-X(4,M)) LV[-OT26 CC(4,M)-AKVALC( 2 M) ) ))+AKVALCI 3,M)C(1O -X 4 M9)+AKVALC(4,M)*XF4~M1-1VOLF?'17 40 CONTINUE VLEO1270 C.oo VLE01874 IF (COND-1.0) 53,73,53 VLE01427 309 IF(ABSF(ERR(M))-O.0001)?13~313,310 VLEO1880 73_____ 3 WRITE OUTPUT TAPE 6,191,((XF(LM),L=1,4),M=1,4) VLE01428 310~DERR(Mi=ERR(M)-AKVALC(3,M)+1.I/ 4M-X4 4M AKVALC4,M)-10(VLE89 Go TO 53 -V c 0TF429 -— 1/Il —-- --- --- ---- --- --- ~~GO TO 53'~VLC~EO^ —'I-~~9' ^ C(XF ( 1,M)*(AKVALC( 1,M )-AKVALC( 3,M ))(AKVALC(4,M)-AKVALC( 1,M)))/((XF(VLE 9 53 Do 55 M=1,4 VLEO1430 C4,MI(AKVALCI1,M)-1.0)+XI4,M)(AKVALC(4,M)-AKVALC(1,M)))**2)+(XF(2,MVLE01892 54 VL(M) =X (1,M )*AVL(1)+X(2,M)* AVL(2 ) +X(3,M *AVL ( T -AVT ---- VIEI40- C)(AKVALC(2M-AKVALC-A VL (3,M))(AKVA4ALC(4,M)-AKVALC( 2,M))I/( X-47M-) 1V-EIB 3 55 SVL(M)=X(1,M)*AVL(1)*S(1)+X(2,M)*AVL(2)*S(2)+X(3,M)*AVL(3)*S(3)+X(VLE0145O CALC(2,M)-1.0)+X(4,M)(AKVALC(4,M)-AKVALC(2,M)))**2)) VLF01894 C4.M)*AVL(4)*S(-4)1 —-------------- --— VLE014bO -- - 311 X(4,M)=X(4,M)-ERR(M)/DERR(M) VLE01900 — 56 IF (J-2) 57, 115,57 VLE01470 312 Go TO 306 VLE191 57 DO 62 M=1,4 --------------— V —-r- ---— Y —------------------------------------------------------------------ =X4,M -9_58 BM(M)=Y(1,M)*Y(1,M)*B(1,1,K)+Y(2,M)*Y(2,M)*B(2,2,K)+y(3,M)*Y(3,M)*VLE01490 314 X(5,M)=(X(8,M)*XF(1,M)*(AKVALC(4M)-1.0))/(XF(4M)(AKVALC(1,M)-1. VLE1921 C B ( 3. 3. K ) + Y ( 4, M ~ Y ( 4. M ) JQ91-4,9 4W V T2- 07^T w 7 f I 2*R^^^- 7.C+.a*7 V ^ -----------------— 8-~y —---------------- ~~~~~~~~~~~~~~~~ ~~~~~~~~~~9 19TCI+XI(8,MI)AKVALC(4,M)-AKVALCI 1,MI) HVLTE2 _ CM)*Y(3,M)*B(1,3,K)+2.Q*Y(1,M)*Y(4,M)*B(194,K)+2.0*Y(2,M)*Y(3,M)*BVLE0151O X(6,M)=(X(8,M)*XF(2,M)(AKVALC(4,M)-1.0))/(XF(4,M)(AKVALC(2,M)-1.0)VLE01923 C(2,3,K)+2.*0Y(2,M)*Y(4,M)*B(2,4,K)+2.0*Y(3,M)*Y(4,M)*Br,4,Kl VLEUIZ-U C+X($,M)(AKVALC(4,M)-AKVALCI 2,M))) -VLEOIl4 59 VV(M)=O.5(82.057*T/P(M)+SQRT((82.357*T/P(M)I)**2+328.228*T*BM(M)/P(VLEO1530 X7,Ml=1.O-X8,M-X(5,M-X6,M VLE --— ^ —— YyL~~~l^*5!8.2.",057^!^^^50^^^ ~~~X(7,M)=1.0-X(8,M)-X(5,M)-X(6,M) VLEO 1925J|f CMII) -~~-VWI-'3W ~~~CM)) VT — ~ - ----------— I —--— _ __y_-_315 Y(5,M)=AKVALC(11,M)*X(5,M) ----—' —-9 —-- -- --- ---- - 60 DO 61 L=1,4 VLEO1550 Y(6,M)=AKVALC(2M)*X(6M) VLE1931 C2,M) VLE01565 316 Y(8,M)=AKVALC( 4,M)*X( 8,M) VLE01933 K C*B(L,2,K)+Y(3,M)*B(L,3,K)+Y(4,M)*B(L,4,K))) VLEUI/fU IF (COND-1.O) 85,1l05,85 VLEUI4.62__ CONTINUE VLE01580 105 WRITE OUTPUT TAPE 6*192,((X(LM),Y(LM),ANU(LM),G(LM),F(LM),L=1VLE01842 63 DO 70 M=l,4 V. —------------------------------------------------------------ ----- - 64 ANU(4,M)=(PC(4)/P(M))*EXP((2.30258509)*(1.96718+(1.02972*TC(4))/T VLEO1600 GO TO 85 VLE01844 C( *054009*T)/TC(4)5 —---------— 5B-T —CT~ —----------—........ —-......D —--------------— 0 —65 DO 66 L=l13 VLE01602 86 DO 92 L=1,4 VLE01860 FP(LM)=VP(L)*EXP(VL(M)*(P(M)-VPIL))/(82.O57*T)) VLEO1610' 87 LL=L+4 VLEU1OU__66 — ANU(L,M)=FP(LM)/P(M) VLEO1620 88 IFIABSFIXILM)-XILLM))-O.0001) 91,91,89 VLE01880 67 DO 69 L=1,4 V[LE8-.......-; [-....X....xLu — E —-90 —-----------------------------------------— _VE_ -------- IF (COND-2.0) 68,400,68 VLE01635 Y(LM)=Y(LLM) VLEO1900 68 G(LM)=(AVL(L)/VL(M l)*EXP( (AVL(L)*(S(L)-SVL.lM/7VL[T-i I **/-I-8-~TV-* IT-Oz~.. —9o~0...G~-TO5~-)3 C)+1.O-AVL(L)/VL(M)) VLE1164-1 91 IF(ABSF(Y(LM)-Y(LLM))-U.UU01) 92992,89 VLE01920 GO TO 69 VLE11642 92 CONTINUE VLEU b 40 —40 G(LM)=EXP((AVL(L)*(S(L)-SVL(M)/VL(M))**2)/(1.987*T)) VLE11643 93 CONTINUE VLEO1930 69 AKVALC(LM)=G(LM)*ANU(L,M)/F(LM) -----— I.. F _J-23 95,- 120,-1 —_-67_- —.'. —--— 6-_ — 70 CONTINUE VLEO1660 95 DO 104 M=1,4 VLEO1950 71 IF 1I-1) 3-00.723 -00 ----------------- VT[- r67 V -------- VVSUV(M)=VV(M) t-r —-r9 72 DO 75 M=l,4 VLEO1680 96 VLSUV(M)=VL(M) VLEO1970 VLS(M)=VL(M) VLEO1690 97 DO 103 L=l,4 VLEO1980 -----— VVS(M)= VV(M) __ —------ --------- VLEO1700 98 AKSUV(L,M)=G(LM)*ANU(LMI/F(L,M) VLEO1990 DO 74 L=1,4 VLEOr71~ 99 FSUV(LM)=F(LM) E —------------------------- GS(L,M)=GLM VLEO1720 10 GSUV(LM)=G(LMM VLE02020 ANUS-L,M)=ANU(-L,M) VL — --- — 100 GSUVILM=G(LMI~VLEO2O2O 7VLANUSE(L0M~=ANU(LgM - - E —-— v-17TT376- 101 ANUSUVILM)=ANU(LM) --' —------------------------ E 74 FS(LM)=F(LM) VLE01740 102 XSUV(L~M)X(L~M) VLE24 75 CONTINUE VLEO1750 103 YSUV(LM)YlLMI VET _76. =IN+1. —---- VLEO1760 104 CONTINUE VLE02060 ~ —------------- ____ — ____________________________________~____________-_-_______________ —----- ____-p —p —---— _ —_-_________________________-_ ~_ _ — - - - - - - - - - - - -

TABLE XXII CONT'D 108 J-J+1 - - - - - - - -- ------— ^^ ^ ^ -^ — __ —-^ ^ —_^ ^ _^ ^ _ —___-______-__-_ -- -_ ----------------------------------------------- 108 J=J+l VLE0207O 143 CONTINUE VLE02480 109 Do 113 M=1l,4 VLE02080 =.0 VLE02490 110 DO 112 L=l,4 VLE02090 DO 144 M=1,4 VLE02500 1___X -_ iL_,MJ! )=XS ('__,M) VLE02100. D..__B___t_.(J_ LA-(_zMJ~Y_ LMJ_Aj4M) V4LE02510 112 Y(LM):YS(LM) VLE02110O — - - - - B - -- - - - - - - - - - - - -- 112 Y(LM)=YS(L~MI VLE02V10 144 CONTINUE VLE02520 113 CONTINUE VLEO212OC.D.___.D_ VLE02530 114 IF(K-2) 53,132953 VLEO2130 DO 145 M=1,4 VLE02540 115 DO 119 M=1,4 VLE02140 CD=CD+Y(4,M)*A(3,M)+Y(3,M)*A(4,M) VLE02550 116 ARKM(M)=Y(1,M)*ARK(l',M)+Y(2,M)*ARK(2,M)+Y(3,M)-ARK(3,M)+Y(4,M)*ARKVLE02150 145 CONTINUE VLE02560 C(4,M) VLE02160 AO-r.00 V 117 DO 118 L=l,4 - ~ VLEO27TT DO" 46 M:1-lQ,4 V D ~ LE025~~~O 118 F(LM)=EXP((BRK(LM)-ARK(LM)**2-',ARK(LM)-ARKM(M))**2)*P(M)) VLE02180 A=A:A+Y(4 M)**2+Y( 1,M)**2 VLE02585 119~- CON TI NUEC ~ - --------------— |FTTD- ~i^ —^^^ —----------------------------------------------------------- Vr 97 —----- -— 02'90119 CONTINUE VIE~O-T9 0' 146 CONTI NUE VLE0-2590' GO TO 63 VLE02195 AB=O.00 VLE02595 120 DO 129 M=l,4 VLEUZZUU DO 147 M=1,4 VLE02600 121 VLRKS(M)=VL(M) VLE02210 AB=AB+Y(i1,M)*Y(2,M) VLE02605 122 DO 128 L=1,4 V —- ----— 2 —------------------------ UZ20 —-- _ __14_ C NI N - ------ --------------- 12) XRKS(LM)=X(L,M) VLE02230 AC=O.00 VLE02615 124 YRKS (L-M)=Y(MT- --------------------— 1 —----------- ---------------- -- -------------------------------------------------------------— V 2 125 AKRKS(LM)=G( L,M)*ANU(LM)/F(LM) VLE02250 AC=AC+Y(1,M)*Y(3,M) VLE02625 126 GRKS(LM)=G(LM) VLEU226U 148 CONTINUE VLEUb3U'J 127 ANURKS(LM)=ANU(LM) VLE02270 BA=O.00 VLE02635 128 FRKS(LM) F( L M).....I-Z2 ---------- ------------- -- 1 —- ----— _- _ —----- --------------- --- - V_. 129 CONTINUE VLE02290 BA=BA+Y(1,M)*Y(2,M) VLE02645 130 ----------------------- ------------------------------------------ ^ Q —-^^-^^ ------- --- -- - - ----—. —. — -— ^ g^ 130 K=K+l VEE02300 ----— 1 NT-JU W2 —'v 131 GO TO 108 VLE02310 BB=O.00 VLE02655 132 DO 138 M='-4 VLEU232U DO 150 M=1,4 VLEU6OU L33 DO 137 L=l14 VLE02330 BB=BB+Y(4,M)**2+Y(zM)**2 VLE02665 134 G ( L, J M ) -}-9 — V —------------------------------------------------- E EVZ -— ^___-_^ —-(5-I —----------------------------------- ---------------- V 135 ANUILM)=ANUS(LM).LE02350 BC=O.00 VLE02675 -i Y —- f-6W A [ L- I-K-t 1 m7 VAL3TU-F~ l -------------------------------------— VI 137 FC(LM)=G(LM)*ANU(LM)/AKVAL(LM) VLE02370 BC=BC+Y(3,M)*v'22M) VLE02685 138 CONTINUE VLEU238U 151 CO.iTINU VLEU6U —v 139 DO 142 M=1,4 VLE02390 CA=O.00 VLE02695............ A(~-MT~vV-EM~7.~-;~)EI~-D.GTF-C-F~T~T-~q~TMT~x~T~T~-~-~5~TTZi TMT*.4T - T-41 — E.~2.T DO 152 M='i,4 - Oz' —— O —' CK) VLE02401 CA=CA+Y(1,M)*Y(3,M) VLE02705 140 - ------------------------------------------— V2402 —— 152 CONTINUE L 7 —-------------------------- 220 R(LM)=FC(LM)*P(M)*VV(M)/(82.057*T) VLE02403 CB=0.00 VLE0.2715 200 IF(X(1.M)) 202,201,202 VLEO240U5 DO 153 M=1,4 VLE 72' 201 R(1,M)=1.0000 VLE02406 sCB=CB+Y(2*M)*Y(3,M) VLE02725 202 IFX 2,M)) -l 204,2-03,204 V~-2-07 153 CONT I NUE WEf30 - 203 R(2,M)=1.0000 VLE02408 Cc=0.00 VLE02735..204- I F(X(3,M)) -1 i41,-0-0,141 L —-2W0 DO 154 M=l,9-4 — v F —' —W 205 R(3,M)=1.0000 VLE0241O CC=CC+Y(4,M)**2+Y(3,M)**2 VLE02745 141 A(LM)=VV(M)/2.0*ELOG(R(L,M))-Y(1,M)*B(L,1,K)-Y(2,M)*B(L,2,K)-Y(3,VLEOZ40Z 154 CONTINUE VLE02750 --- -CM)*B(L,3,K) VLE02430 155 EA=AA*BB<CC+AB*BC*CA+AC*CB*BA-AC*3B*CA-BA*AB*CC-AA*CB*BC VLE02760 142 CONTINUFK ~VDLEO -~ 1 56 - EB:=AD*BB*CC+AB*BC*CD+AC*CB*BD-AC*B*CD-BD*AB*CC-AD*CB*B- VLEO"V 70 209 DO 217 M=1,4 VLE02440 157 EC=AA*BD*CC+AD*BC*CA+AC*CD*BA-AC*BD*CA-BA*AD*CC-AA*CD*BC VLE02780 210 IF(X(1 M)) 212,221 --------- LE-244~ 158 E D=AA*BB*CD+AB*BD*CA+AD*CB* BA-AD* BB*CABA*B*CD-AA*CB*D VLE27211 A(1,M)=0.0000 VLE02442 159 B(I1,4,2)=EB/EA VLE02800 212 IF(X(2,M)) 214,213,214 VLE02443 160 B(2,4,2)=EC/EA VLE02810 213 A(2,M)=0.0000 ------- - - -------- ---- ---- VLE02444 __ 16___ BL3,4,2)=ED/EA -- VLE02820 214 IF(X(3.M)) 217,215,217 VLE02445 162 DO 163 M=1,4 VLE02830 215 A(3,M):0O 0000 VLE02446..BAVLli 4_,M) __B 1,4,2) VLE02840 217 CONTINUE VLE02448 BAVS(2,4,M)=B(2,4,2) VLE02850 218 AD=O.00 VLE02450 BAVS(3,4,M)=B(3,4,2) VLE02860 DO 143 M=1,4 VLE02460 B(4,1,2)=B(1,4,2) VLE02861 ---- AD:AD+Y(4,M)*A(1,M)+Y('1,M)*A(4,M) V —-— LE —-- -02470- ____J —__ _ VLE02862

-129TABLE XXII CONT'D 163 8(4,3,2)=8(3,4,2) VLE02863 165 K=K+1 VLE02870 16" GO TO 109 VLE02880 167 DO 177 M=1,4 VLE02890 168 VVSAV(M) VVMj V —------------ 169 VLSAV(M)=VL(M) VLE02910 170 DO 176 — o —4 —--------------------------— 92 171 AKSAV(L,M)=G(L,M)*ANU(L,M)/F(LLM) VLE02930 172 FSAV(LM)=F(LM) VLE02940 173 GSAV(L,M)_=G(L,M) VLE02950 174 ANUSAV(LM)=ANU(LgM) CVLE02""6-' 175 XSAV(L,M)=X(LM) VLE02970 176 YSAV(LM)=Y(LM) VLE02980 177 CONTINUE VLE02990 178 DO 189 M=1,4 VLE02995 179 WRITE OUTPUT TAPE 6,9,IRUN(M),TTPP(M) VLE03000 180 WRITE OUTPUT TAPE 6l109VLS(M),VLVLSAV(M)VLSUV(M) VLRKS(M)VVS(MVEO IO CSAV(M)gVVSUV(M) VLE03020 181 WRITE OUTPUT TAPE 6t11,YS(TM)Y-~PVT M),YS-0OV-1WTYRK-ST1-FT-xFTrVU'.-3O' — CM),XSAV(1,M),XSUV(1,M),XRKS(19M),AKVALS(19M)9AKSAV(l,M)9AKSUV(1~M)VLE03040 C,AKRKS(1,M) VLE03050 182 WRITE OUTPUT TAPE 6,129GS(1,M)gGSAV(1,M),GSUV(1,M),GRKS(19M),ANUS(VLE03060 Cl M),ANUSAV( 1M)~ ANUSUV( 1 M) ANURKS( 1 9M) FFS( 1T-) FAV(-1t )r-r V-E CM),FRKS(1,M) VLE03080 183 WRITE OUTPUT TAPE 6,13,YS(2,M),YSAV(2,M),YSUV(2,MJ)YRKS(2 M) XST2 VLEO-O-O CM),XSAV(2,M),XSUV(2,M),XRKS(2,M),AKVALS(2,M),AKSAV(2,M)9AKSUV(2~M)VLE03100 CAKRKS(2,M) VLE03110 -84 WRITE OUTPUT TAPE 6,14,GS(2,M),GSAV(2,M),GSUV(2,M),GRKS(2,M),ANUS(VLE03120 C2M) USAVANUSSAV(2M) ANUSUV(29M) ANU7KS(2,M) - -(C2- ) -FSAV( 2- TSOV-~2-VE-Trr3T CM),FRKS(2,M) VLE03140 85 WRI TE- OUTPUT - TAP~-1 —STT;-9-VT9-Tv3 FFY —,E T5 — CM),XSAV(3,M),XSUV(3,M),XRKS(3,M),AKVALS(3,M),AKSAV(3,M),AKSUV(39M)VLE03160 CtAKRKS(3,M) VLEO 310 186 WRITE OUTPUT TAPE 6,16,GS(39M),GSAV(3,M),GSUV( 3M)gGRKS(39M) ANUS(VLE03180 C3,M)iANUSAV(3,M),ANUSUV(3,M),ANURS ( 3 M ), Fs ( 3 ~-TAV (TF,) FS-T-ET3VD3OT CM),FRKS(3,M) VLE03200 187 WRITE OUTPUT TAPE 6,17,YS4,M),YSAV(4,M),YSUV(4XCM),XSAV(4,M),XSUV(4,M),XRKS(4,M),AKVALS(4,M),AKSAV(4,M),AKSUV(4,M)VLE03220 C,AKRKS(4,M) VLE03230 188 WRITE OUTPUT TAPE 6,18,GS(4,M),GSAV(4,M),GSUV(4,M),GRKS(4,M)ANUS(VLEO324O C4,M),ANUSAV(4,M),ANUSUV(4,M),ANURKS(4,M),FS(49M),FSAV(4,M),FSUV(49VLE03Z50 CM),FRKS(4,M) VLE03260 189 WRITE OUTPUT TAPE 6,19,BAVS(1,4,M)gBUVS(1,49M),BAVS(2,4,M),BUVS(2,VLE0320 C4,M) BAVS(3,4,M),BUVS(3,4,M) VLE03280 190 GO TO 20 VLE03290 191 FORMAT (1H 8F6.5/1H08F6.5//) VLE03300 192 FORMAT(1H 8F7.5//) VLE03310 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - - _ _ _ _ _ _ _ _- - _ _ _ _ _ _- _ _ _ _ _ _ _ _ _ _ _ _ _- _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _- - _ _ _ _ _ _ _ _ _ _

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