University Microfilms, A XEROX Company , Ann Arbor, Michigan

II

71-22,520

PAK, Sung Chun, 1932-THE CRITICAL PROPERTIES OF HYDROCARBON MIXTURES: HIGH MOLECULAR WEIGHT BINARYSYSTEMS.

The Ohio State University, Ph.D., 1971 Engineering, chemical

University Microfilms, A XEROX Company , Ann Arbor, M ichigan

THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED

THE CRITICAL PROPERTIES OF HYDROCARBON MIXTURES! HIGH MOLECULAR WEIGHT ElNARY SYSTEMS

DISSERTATIONPresented in Partial Fulfillment of the Requirements for the

Degree Doctor of Philosophy in the Graduate School ofThe Ohio State University

BySung Chun Pakt B.S., M,3e,

# -H

The Ohio State University 19?1

Approved by

Advisor Department- of

Chemical Engineering

. ACKNOWLEDGMENT

I would like to express my sincere appreciation to Dr, Webster B, Kay for his assistance, understanding, and patience throughout the course of this work. It has been a great privilege and pleasure for me to work with him.

This work was supported by a grant from the American Petroleum Institute which was administered by the Ohio State University Research Foundation. This financial assistance is deeply appreciated.

I also wish to thank Dr. Kreglewski for the suggestion on the determination of the critical constants of unstable compounds and Dr. Hershey for the aid in the use of the Chemical Engineering Library Program.

The staff of the Ohio State University Numerical Computation Center were very helpful in providing the IBM 360 computer time and assistance in debugging the programs.

Thanks are due to the Aluminum Company of America for the loan of Gallium for the study of the effect of mercury on the critical properties of hydrocarbons and to the Phillips Petroleum Company for the donation of the high purity hydrocarbon samples.

Finally, but by no means least, 1 am very gratefulto my wife and our families whose understanding andencouragement have made this work possible,

ii

VITA

November 25» 1951 - 1959 196^

196*+ - 1967

1967 - 1968

1968

1968 - 1971

1932 Born - Kyonggi-Do, KoreaMilitary Service (Korean Navy)B.S, in Chemical Engineering University of California Berkeley, CaliforniaChemical Engineer Cutter Laboratories Berkeley, CaliforniaTeaching Assistant Department of Chemical Engineering The Ohio State University Columbus, OhioM*Sc. in Chemical Engineering The Ohio State University Columbus, OhioResearch AssociateDepartment of Chemical Engineering The Ohio State University Columbus, Ohio

FIELDS OF STUDY

Major Field 1 Chemical EngineeringStudies in Chemical Engineering Thermodynamics

Professor Webster B, Kay

TABLE OF CONTENTSPage

ACKNOWLEDGMENT iiVITA iiiLIST OF TABLES viLIST OF FIGURES ixLIST OF SYMBOLS xiiChapter

I. INTRODUCTION 1II. RELATED LITERATURE 6III. APPARATUS AND EXPERIMENTAL PROCEDURE 16IV. EX PERIMENTAL RESULTS 23V. PRECISION AND ACCURACY OF RESULTS 48

VI. THE EFFECT OF MERCURY ON THE CRITICALCONSTANTS AT HIGH TEMPERATURE 58

VII. DISCUSSION OF RESULTS 74Systems Whose Components Belong tothe Same Homologous Series 76Systems Whose Components Belong tothe Different Homologous Series 77

VIII. THEORETICAL APPROACHES TO THE CRITICALPROPERTIES OF MIXTURES 84

Use of the Thermodynamic Conditions atthe Critical State 84

Fundamental Equations for Binary Mixtures 84-Equations of State 86Calculation of the Critical Locus 90

iv

TABLE OF CONTENTS (CONT'D)PageCorrelation of the Reduced Interaction

Parameters 116Test of Correlations 148

The Application of the Theory of Conformal Solution Using the Revised Theorem of Corresponding States 151

IX. CONCLUSIONS 168X. RECOMMENDATIONS 170

APPENDIXA. APPARATUS AND EXPERIMENTAL PROCEDURE 172

Sample Confined Over Mercury 172Sample Confined Over Gallium 189

B. CALIBRATION OF EQUIPMENT 197Thermocouple 197Pressure Gauge 199

C. DATA REDUCTION AND SAMPLE CALCULATION 203, Data Reduction Procedure 203Sample Calculation 210

D. MISCELANEOUS TABLES 214E. COMPUTER PROGRAMS 25*4-

Expressions for the Derivatives in theEquations of the Thermodynamic Conditionsat the Critical Point 25^FORTRAN IV Statement Listings of theComputer Programs 259

Critical Locus Calculation 259Comparison with Experimental Values 27Ôptimization of Reduced Interaction Parameters 295

BIBLIOGRAPHY 321

LIST OF TABLES

Table1 Critical Properties of

n-Hexane - n-Decane System2 Critical Properties of

n-Hexane - n-Tridecane System3 Critical Properties of

n-Hexane - n-Tetradecane System^ Critical Properties of

n-Hexane - cis-Decalin System5 Critical Properties of

n-Nonane - n-Tridecane System6 Critical Properties of

n-Decane - n-Dodecane System7 Critical Properties of

Benzene - n-Decane System8 Critical Properties of

Benzene - n-Tridecane System9 Critical Properties of

Benzene - n-Kexadecane System10 Critical Properties of

Benzene - cis-Decalin System11 Critical Properties of

Ethylbenzene - cis-Decalin System12 Critical Properties of

o-Xylene - cis-Decalin System13 Critical Properties of

Cyclohexane - n-Decane Systemlh- Critical Properties of

Cyclohexane - n-Tridecane System15 Critical Properties of

Cyclohexane - cis-Decalin Systemvi

Page

25

25

26

26

2?

27

28

28

29

29

30

30

31

31

32

LIST OF TABLES (CONT'D)Table16

171819

20

21

22232*4-

25

26

27

28

Comparison of Pure Compound Data with Literature Values

Repeatability of ResultsEstimated Precision and AccuracyComparison of the Critical Constants Measured

with Gallium and MercuryComparison of the Critical Point Determined

with Gallium and Mercury When the Mercury-Hydrocarbon Interface at Room Temperature

Comparison of the Critical Point Determined with Mercury V/hen the Mercury- Hydrocarbon Interface at Room and Sample Temperature

Comparison of Optimization RoutinesClassification of Binary SystemsTotal Binary Systems StudiedOptimum Interaction Parameters for

Redlich-Kwong Equation of StateOptimum Interaction Parameters for

Redlich-Ngo Equation of StateStatistical Deviation Data on the Critical

Loci Calculated Using the Optimum Interaction Parameters for the Redlich-Kwong (RK OPTM) and Redlich- Ngo (RN OPTM; Equations of State

Comparison of Statistical Deviation Data on the Critical Loci Calculated Using the Reduced Interaction Parameters Predicted by the Various Correlations for the Redlich-Kwong Equation of State

Page

**95556

65

69

7199102103

106

108

110

123

LIST OF TABLES (CONT'D)Table29 Comparison of Statistical Deviation Data on

the Critical Loci Calculated Using the Reduced Interaction Parameters Predicted by the Various Correlations for the Redlich-Ngo Equation of State

30 Comparison of Critical Temperatures Predictedby Various Methods

31 Comparison of Statistical Deviation Data onthe Critical Loci Calculated by the Equation of State and the Revised Corresponding States Methods

32 Thermocouple Calibration (Iron-Constantan)33 Thermocouple Calibration (Chromel-Constantan)34 Pressure Gauge Calibration35 Comparison of the Experimental and Calculated

Critical Properties Using Optimum Interaction Parameters

36 Comparison of the Experimental and CalculatedCritical Properties Using the Predicted Reduced Interaction Parameters

37 Purity and Source of Samples38 Pure Component Constants Used in the Corre

lation39 Uncorrected Critical Properties for the

Effect of Mercury

Page

135

149

160200201202

215

229243

244

246

viii

LIST OF FIGURESPage

Apparatus for Tc-Pc Measurement 20Method of Stirring Sample 21Determination of Critical Points;

Extrapolation to Zero Time 22P-T Critical Locus of the System

n-Hexane - n-Decane 33P-T Critical Locus of the System

n-Hexane - n-Tridecane 34P-T Critical Locus of the System

n-Hexane - n-Tetradecane 35P-T Critical Locus of the System

n-Hexane - cis-Decalin 3°P-T Critical Locus of the System

n-Nonane - n-Tridecane 37P-T Critical Locus of the System

n-Decane - n-Dodecane 38P-T Critical Locus of the System

Benzene - n-Decane 39P-T Critical Locus of the System

Benzene - n-Tridecane **0P-T Critical Locus of the System

Benzene - n-Hexadecane ^P-T Critical Locus of the System

Benzene - cis-Decalin ^2P-T Critical Locus of the System

Ethylbenzene - cis-Decalin ^3P-T Critical Locus of the System o-Xylene - cis-Decalin 44P-T Critical Locus of the System

Cyclohexane - n-Decane ^5

LIST OF FIGURES (CONT'D)Fig.17

18

19

20

21

22

232425

26

27

28293031

P-T Critical Locus of the SystemCyclohexane - n-Tridecane

P-T Critical Locus of the SystemCyclohexane - cis-Decalin

Schematic P-T Diagram of Partially Miscible Systemi Hydrocarbon-Mercury

Experimental Tube for Mercury-Hydrocarbon Interface at Room Temperature

log10P P ^ Versus l/T for the Partial Pressureof Mercury Over the Hydrocarbon- Mercury System

P-T Critical Loci of Binaries of Different Homologous Series

Excess Critical Temperature vs. CompositionExcess Critical Pressure vs. CompositionEffect of Relative Size and Absolute Molecular

Weight on the Excess FunctionsComparison of Calculated vs. Experimental

Critical Volume-Composition Relationships >Propane - n-Pentane System

Electric Furnace for Determination of Critical Points

Experimental Tube for Electric FurnaceCross Sectional View of Compressor BlockHigh Vacuum LineMock-up for the Measurement of Temperature

Difference

Page

46

47

63

68

72

808182

83

147

174175176 181

187

x

LIST OF FIGURES (CONT'D)Fig. . Page32 Plot of Temperature Correction vs.

Temperature 18833 Schematic Diagram of Apparatus for

Gallium Experiments 1933^ Experimental Tube and Adapter (Gallium

Experiments) 19535 Electric Furnace 19636 Division of Mercury Head 207

Aa

a12

A12SR AVAB, AVG. B b

B12SRBIASCC0R1COR2COR3DD, DEV

D2GXD3GXEemff

LIST OF SYMBOLS

Correlating constantConstant in equation of state

. Interaction parameter for equation of stateReduced interaction parameter of a^2

ABS Absolute average deviation = ^SllDlCorrelating constantConstant in equation of stateInteraction parameter for equation of stateReduced interaction parameter of b^gBias deviation -Correlating constantCorrelation 1Correlation 2Correlation 3Correlating constantDeviation = difference between experimental and calculated values(5zs/ax^)p>T ( 3 ^p( jCorrelating constant Electromotive force Energy parameter

xii

G

gHISSONG

JKK# KK 0.99

KREGKL

InlogM

mrnNnNSYSOFOPTMP

A function in the Redlich-Ngo equation of stateMolar Gibbs free energyHissong's correlations for A12SR and B12SRJacobianRevised corresponding states method with V =1 and y = 0,99t respectivelyRevised corresponding states methodA function in the Redlich-Ngo equation of stateNatural logarithmCommon logarithmMolecular weightRatio of molecular weightsMolecular weight correlating parameterNumber of data pointsNumber of componentsSystem numberObjective functionOptimum interaction parametersPressureCritical pressure Excess critical pressure Vapor pressureRoot-mean-square pressure deviation

* * • xxii

PR Ratio of critical pressures

P?Hg Partial pressure of mercuryPEXP Experimental critical pressureR Universal gas constantr Intermolecular distanceRK, R-K, RK-EQ The Redlich-Kwong equation of stateRN, R-N, RN-EQ The Redlich-Ngo equation of stateRMS Root-mean-square deviationT, t TemperatureTc Critical temperature

Te Excess critical temperature

td Root-mean-square temperature deviationTR Ratio of critical temperaturesTB, Tb Normal boiling pointTBr Ratio of normal boiling pointsTEXP Experimental critical temperatureu Pair potentialu Total pair potentialV VolumeVc Critical volumeV* Liquid molar volume at T/Tc = 0,6

VR Ratio of critical volumes

VPHg Vapor pressure of mercuryX(A) Mole fraction of component AX Mole fraction

xiv

Height of mercury or gallium columnCritical compressibility factorRatio of critical compressibility factors

Ratio of acentric factors Weighting factor Association factor Minimum pair potentialSurface fraction or interaction parameter Correlating parameter for critical volume DensityCorrelating parameter for critical temperatureFugacity coefficient or interaction parameterSurface fractionCritical propertiesExcess critical propertiesacentric factor

Subscriptbar Barometriccal CalibrationGa GalliumHg Mercuryi f j Components i and j1 f 2 Components 1 and 2rt Room temperaturest Sample temperatureo 0 °Coo Reference substance

xvi

CHAPTER X

INTRODUCTION

For the process engineer who must design and operate process equipment involving the heating of vapor-liquid mixtures at high temperatures and pressures, a knowledge of the critical properties of the mixture is of practical importance in setting the limits of temperature and pressure wherein the two phases can coexist. Another important application of critical constants of pure substances and their mixtures is the prediction of thermodynamic properties which have not been measured heretofore by the application of the theorem of corresponding states. According to the theorem of corresponding states, all fluids at the same reduced temperature and pressure have the same reduced volume,

Wany correlations for predicting the critical temperatures and pressures of mixtures, particularly hydrocarbon mixtures, have appeared in the literature. However, most of these correlations are essentially empirical and of limited applicability. Such correlations should be based as much as possible on scientific principles so that the methods will be applicable over a wide range of conditions. Of the

available correlations, two methods seem to be worthy of further study. They are the Hissong-Kay method based on the classical thermodynamics and the Kreglewski-Kay method based on the statistical thermodynamics.

Hissong and Kay (38) have developed a correlational method for predicting the critical locus of binary systems, based on the rigorous thermodynamic relations that define the critical state of a binary mixture and an equation of state. The Redlich-Kwong and the Dieterici equations of state were studied. It was found that the former was superior to the latter for predicting the critical temperatures and pressures of binary hydrocarbon systems. Since satisfactory combining rules were not available, the interaction parameters resulting from the application of the equation of state to mixtures were determined by minimizing the sum of the squares of the deviations using a nonlinear estimation technique for the twenty-one binary hydrocarbon systems for which critical data had been experimentally

determined. The binary systems studied involved aliphatic, naphthenic and aromatic compounds having 5 to 9 carbon atoms. The optimum values of the interaction parameters were then correlated as functions of the ratio of molecular weights of the components so that the values of the interaction parameters could be determined for the systems for which no critical data are available. They have shown that these correlations could be used with considerable success

3in predicting the critical properties of the lower molecular weight binary systems.The completely analytical procedure for the solution of the thermodynamic equations distinguishes the Hissong-Kay method from previous methods which involved the use of both graphical and analytical techniques for the solution.

Longuet-*Higgins (59) developed the theory of conformal solutions, according to which all thermodynamic properties of a mixture can be evaluated from those of the pure components if components conform to certain simple postulates of statistical mechanics. The application of the theory requires a knowledge of a general principle of corresponding states. According to the classical principle of corresponding states, the applicability of the theory was limited to small spherical molecules such as Ar, Kr, CH^, and CO, Kreglewski and Kay (55) have shown, however, that when the classical principle of corresponding states is properly modified, satisfactory agreement with experimental data is obtained for mixtures of molecules that differ in both size and shape over a wide range. The binary systems used for this study were limited to mixtures containing 5 to 9 carbon atoms.

To test the applicability of these methods of calculation of the critical constants to systems of higher molecular weight, an experimental investigation was undertaken on binary systems in which at least one or both compo-

nents were hydrocarbons with 10 to 14 carbon atoms. This involved some experimental problems which were not present in the investigation of the low molecular weight compounds* i.e., the effect of mercury on the critical constants and thermal decomposition of the sample in the region of the critical temperature.

The objectives of this work, therefore, are four-fold*1, The development of a method for measuring the

critical constants of hydrocarbon mixtures in which one or both components are unstable at their critical temperatures,

2. The investigation of the effect of mercury on the critical constants,

3* Modification of the Hissong-Kay method*a. Using a new equation of state proposed by

Redlich and Ngo (75)»b. Applying the non-linear optimization technique

to more diverse systems in order to establish, with greater certainty, the interaction parameters as functions of the relative size, structure, and chemical nature of the molecules of the mixture, and

4. Test of the validity of the Kreglewski-Kay method by .the evaluation of critical temperatures and pressures of higher molecular weight hydrocarbon mixtures.

As in the case of Hissong*s work, this study was also restricted to hydrocarbon mixtures. In selecting the binary mixtures for this study, the size, structure, and chemical

nature of the molecules composing the mixture were taken into consideration. As revealed in the study of lower molecular weight hydrocarbon mixtures, those are the factors upon which the critical properties of hydrocarbon mixtures

CHAPTER II

RELATED LITERATURE

The earliest methods for predicting the critical pressure and temperature of mixtures of known composition were developed by Edmister and Pollock (23)* Mayfield (6l) Organic (65)* Roess (79)» and Smith and Watson (86). The correlational methods by the above investigators are essen tially graphical and empirical. They used API gravity, various average boiling points, or/and the pseudocritical temperatures and pressures , as defined by Kay (47), as correlating parameters. These methods are usually of limited applicability.

Grieves and Thodos (32) developed a method of the prediction of the critical tempertures and pressures of mixtures based on the data for binary hydrocarbon mixtures available in the literature. They introduced two di- mensionless parameters which accounted for the mixture composition and for the nature of the components involved. These parameters were defined by the molar average boiling point, the boiling point, and the dew point, all at atmospheric pressure*

Grieves and Thodos (33*34) also proposed a method for6

finding critical temperatures and pressures for all types of hydrocarbon mixtures including both methane and nonmethane systems. The suggested relationship for the critical temperature is

n T?me _ 5— (1)

“ "T, 1 nl “ 1 + X A i i x ii 3-1 1 J 3

j*i

where Tc = critical temperature of the mixture,°R,T? = critical temperature of ith component,x^ = mole fraction of ith component,x. = mole fraction of jth component,JA. . = correlating constant for binary system consist- 1J

ing i and j components.For binary system, this expression reduces to

k

1 2 T = -------------- + (2)

The constants, A. ., were calculated using literature1 Jexperimental data and plotted against the ratio of the pure component boiling points. The relationship permitting the determination of the critical pressure of two or more components is based on the number of moles of the low- boiling component in the mixture. The critical pressure is

8determined from the graph relating the ratio of critical pressure and pseudocritieal pressure to the ratio of the molar average boiling point and the atmospheric boiling point of the mixture. The atmospheric boiling point of the mixture is calculated using the expression

nP = 1 it.7 = 51 x.P* (3)

i=l 1 1

where = mole fraction of ith component,«■P^ = vapor pressure of ith pure component, psia.

Depending upon the type of mixture under consideration the boiling point ratio should be corrected for systems containing aromatic or naphthenic components. Wilson et al (92J pointed out that although the Grieves and Thodos correlation of critical properties of mixtures represented very well the data upon which it was based, its application to other systems was subject to some uncertainty and it was also inconvenient to use,

Etter and Kay (2?) proposed a method for correlating the critical temperature and pressure of light hydrocarbon binary systems, based on a plot of critical properties vs. weight-average molecular weight with composition as a parameter. From these graphs, empirical equations for critical temperature and pressure were developed as functions of weight-average molecular weight, weight frac-

tiori, and mole fraction* The method applies only to normal and light hydrocarbon mixtures.

Ekiner and Thodos (24,25) proposed expressions for the critical temperatures and pressures of multicomponent mixtures of methane-free aliphatic hydrocarbons, utilizing a mathematical treatment based on an interaction model*This model postulates an infinite series expansion of the excess critical properties, defined by the difference between the actual critical properties and its corresponding pseudocritical values; i.e.,

if* = £ * 1 + l/'e wi=l

where = critical properties of mixture,^ = critical properties of ith component, x^ - mole fraction of ith component, and ê = excess critical properties.

The infinite series has been truncated beyond the third order interactions for temperature, and beyond the fourth order interactions for pressure. For a binary systems, the expression for critical temperature is

=s T - (xiTi + x 2T2^ = x 1x2Â12 + B12xl^ ^

and for critical pressure

10

(6)

where B^, C^, Di2* and E12 are b^nary interactioncoefficients, and x is mole fraction of pure component.A similar expression was later developed for methane- aliphatic hydrocarbon mixtures (26). These methods based on an interaction model, are of limited applicability to aliphatic hydrocarbon mixtures.

Chueh and Prausnitz (15) presented correlations for the critical temperatures and volumes of mixtures as quadratic functions of the surface fraction 0 defined by

e (7)

where x^ = mole fraction of component i , and

V? = critical volume of component i.For a binary mixture, the critical temperature is expressedfey

T° = Q l * &z?l * 20& ZTj1 2 12 (8)

and the critical volume is given by

(9)

where T° and Vc - the critical temperature and volume of themixture, respectively, and

a n d ^ ^ = correlating parameters for the critical temperature and volume characterizing the 1-2 interaction.

For a given family of chemical systems, the correlating parameters ^2, and ^ 1 2 were rec*uced to 2and 2 V^g/tV^+Vg) * and these were correlated with

|(Tj - T^)/(Tj + t | ) J and |<v£)2/3-(V°)2/3 / (vj)2^3+(V^)2^ ,

respectively. Since no quadratic function was adequate for the critical pressure, they proposed to calculate the critical pressure by substituting the calculated critical temperature and volume into a slightly modified form of the Redlich-Kwong equation of state.

Most of the correlational methods that have been discussed so far are essentially empirical. Some of the more recent methods are based on the rigorous thermodynamic relations that define the critical state of a binary mixture* that is

( % - ) = 0V c* x2 / P.T

(10)

12where g = Gibb*s free energy, and

x = mole fraction.Upon suitable transformation, Eqs, (10) and (11) can be expressed in terms of measurable variables P, V, T, and x. Given an equation of state the transformed equations of Eqs, (10) and (11) can be solved simultaneously for the critical properties of a binary mixture.

Redlich and Kister (73) used this thermodynamic approach for the first time using the Redlich-Kwong equation of state. Instead of solving Eqs. (10) and (11) simultaneously, they developed a short-cut method for predicting the critical locus of binary mixtures. The limiting slopes of the critical locus v/ere calculated as the mixture approached its two pure component limits and logarithmic-hyperbolic interpolation function was used to predict the critical locus over the entire composition range. The binary mixture parameters, a and b used in their investigation, were obtained from the following mixing rule

where a^, b^, a2, and b^ are the Redlich-Kwong constants of the respective pure components.

Since it was expected that a more elaborate equation of state would furnish a much better prediction of the critical

(12)

b - blXl + b2x2 (13)

13locus, Ackerman and Redlich (2 ) repeated the short-cut method using the Benedict, Webb, and Rubin equation of state (lO )• However, an extensive comparison of the two equations of state did not reveal a clear advantage for either one.They concluded, therefore, that the use of the Benedict,Webb, and Rubin equation for the calculation of the critical properties could be recommended only if a more definite method for the determination of the coefficients is found,

Joffe and Zudkevitch (45) also used the same thermodynamic approach using the Redlich-Kwong equation of state. However, the following mixing rules are used for the constants a and b;

where a ^ and b ^ are interaction parameters which were computed from the pseudocritical data, A graphical procedure was used to solve the transformed equations of Eqs, (10) and (11) simultaneously for critical temperature and volume.The critical pressure was calculated from the Redlich-Kwong equation of state by substituting the calculated critical temperature and volume. Quantitative results were reported for the ethane-carbon dioxide and n-butane-carbon dioxide systems,

Spear et al (87) also used the Redlich-Kwong equation

(14)

(15)

14in conjunction with Eqs, (10) and (11). They used the same mixing rules given in Eqs. (14) and (15)» hut a12 and b12 were related to the pure component parameters by

a i 2 = d V v T ( l 6 )

bi2 - <P V v T <w>

where Q and (j> v;ere interaction parameters associated with a and b, respectively. Graphical interpretation of Eqs. (10) and (11) in conjunction with an isothermal volume-composition diagram of a simple mixture is as follows, Eq.(lO) defines the material instability boundary separating the unstable state from the stable and metastable state of a homogeneous phase, Eq„ (11) expresses the coalescence of the two branches of the instability boundary at the critical state. Realizing that the critical state of simple mixtures is known to be the point of maximum pressure along the material instability boundary of a constant temperature system, they developed a numerical search procedure for the critical point along the the conditions defined by Eq, (10), Since the critical pressure was found to be the most difficult to predict and most sensitive to 0 , the optimum value of 0 was obtained for each system using the usual statistical test, while ^ was kept at a constant value of unity. However, they did not attempt to correlate 0 •

15As can be seen from the above discussion, an advantage

of the equation of state approach to the prediction of critical properties of mixtures, is that a single calculation yields values for critical temperature, pressure, and volume#

CHAPTER III

APPARATUS AND EXPERIMENTAL PROCEDURE

The apparatus used in this work, originally developed by Andrew ( 8 ) and subsequently modified by Young (93) and Kay (52) for the measurement of the P-V-T relations by visual observation, is shown schematically in Fig. 1.

For the determination of the critical constants, a small amount of sample was confined over mercury in a thick- walled glass capillary tube of approximately 2 mm. bore.The tube was fastened in one leg of a mercury-in-steel U tube, with the other leg connected through amanifold to a source of high pressure nitrogen gas for pressurizing the system. To the manifold was attached a precision spring gauge to measure the pressure and a surge tank to stabilize the pressure. The precise adjustments of the gas pressure were made through the two valve systems on the high pressure nitrogen inlet and the vent line.

The sample was heated by an electric furnace similar to that used by Ambrose and Grant (5 )• The furnace consisted essentially of a copper rod l£" in diameter by 10" long with a hole drilled through the axis of the cylinder to take the experimental tube. Two diametrically

16

17opposed slits, with a third slit at right angles to the two, were cut in the copper bar and the bar positioned in the furnace with the slits in line with corresponding windows built into the wall of the furnace. By passing a beam of light through the sample and observing the sample through the window at right angles, the intense light scattering, characteristic of the critical state, could easily be detected. The furnace was mounted vertically with a pulley and counterweight so that it could be raised or lowered over the experimental tube.

The temperature of the sample was measured by an iron- constantan thermocouple located in a tiny well sealed to the top of the experimental tube. The thermocouple had been calibrated against a platinum resistance thermometer certified by the National Bureau of Standards, The thermocouple emf was recorded on a Leeds & Northrup Speedomax H, continuously adjustable AZAR Recorder reading to 0,002 mv, equivalent to O.Oh °C. The sample was observed during the heating and when the critical point appeared, a mark was made on the trace, and the pressure was read to within 0o2 psi on a sensitive spring gauge. The gauge was calibrated by means of a high-precision dead-weight gauge, manufactured by Ruska Instrument Corporation,

During the heating, the sample was agitated by a special stirrer consisting of a stainless steel plunger of slightly smaller diameter than the bore of the glass

18capillary tube, to which was spot-welded a length of a small drill rod. The plunger was located in the tube just above the compressor block with the drill rod extending into the sample at the top of the tube. The stirrer was moved up and down rapidly by two solenoind coils energized alternately by a manually operated two-way microswitch.A schematic drawing of how the sample was stirred is shown in Fig, 2.

Because high molecular weight hydrocarbons are unstable at their critical temperatures, a special technique must be used for these determinations. The incipient temperature of decomposition of the n-alkane hydrocarbons is about 3^0 °C, This means that beginning with n-decane there was measurable change in the critical constants with time.To obtain the true critical constants of the undecomposed sample, the apparent values were plotted against the elapsed time and the best curve through points was extrapolated to zero time. The procedure is illustrated for n-tridecane in Fig. 3. This method of extrapolation is not sufficiently definitive. Therefore, an effort to extrapolate the curve on the basis of the chemical kinetics was made but was unsuccessful. This inability to measure accurately the critical temperature and pressure of a rapidly decomposing sample limited our study in the n-alkane series to n-tetradecane.

In all determinations, the furnace was preheated to

19the estimated critical temperature of the sample. Then, as the furnace was lowered around the experimental tube a stopwatch was started, and observations of the apparent critical temperature and pressure were made as a function of time as the temperature was alternately raised and lowered through the critical point. If the rate of decomposition was not great, the observations were repeated a number of times before the experiment was terminated.

Details of the apparatus and experimental procedure are given in Appendix A,

Pressure Gauge

]Surge Tank

ElectricFurnace

ColdJunctionTemperature

Recorder

Auto-To 115 Volts Transformer Power Supply -—

t - i — f b V

Vent

ExperimentalTube

Compressed NitrogenCompressor BlockVoltage Regulator

Fig. 1 - Apparatus for Tc-Pc Measurement

Thermocouple Well

Experimental Tube

Sample

Tiny Steel Drill RodsMercury

Stainless Steel Plunger

AC Solenoid Coil

Fig. 2 - Method of Stirring Sample

CRITICAL

TEMPERATURE

(°C)

Pure Tridecane320

300

280

260

ZkO

390 220160120TIME (MIR)

Fig* 3 - Determination of Critical Points; Extrapolation to Zero Time

CRITICAL

PRESSURE

(psia)

CHAPTER IV

EXPERIMENTAL RESULTS

The binary hydrocarbon systems studied in this work were as followi

n-Hexane -- n-Decanen-Hexane -- n-Tridecanen-Hexane -- n-Tetradecanen-Hexane — - cis-Decalin

n-Nonane -— n-Tridecane n-Decane -- n-Dodecane

Benzene — - n-DecaneBenzene n-TridecaneBenzene --- n-Hexadecane Benzene cis-Decalin

Ethylbenzene -- cis-Decalin0-Xylene -- cis-Decalin

Cyclohexane -- n-DecaneCyclohexane -- n-TridecaneCyclohexane -- cis-Decalin

For each binary systems studied, measurements of thecritical temperature and pressure were made for the purecomponents and for five mixtures having approximately

23

0.1, 0.3» o, 5, 0.7» and 0.9 mole fraction. The critical temperatures and pressures were plotted against composition on large scale graphs, and smooth curves were drawn through the experimental points. From these curves the critical constants were read at regular intervals of composition;1.e., Ool mole fraction.

The smoothed values of the critical constants are tabulated in Tables 1 through 15* The excess critical values are also shown in these tables.

The experimental data were also plotted to give the P-T critical locus curves of the systems and these curves are shown in Figs. k through 18,

25

T A B L E 1 C R I T I C A L P R O P E R T I E SS Y S T E M ’ N U M B E R li~ •.... . . . .N - H E X A N E ( A ) N - D E C A N E ( B )

X .<A> T ( D E G . C ) P ( P S I A ) E X C E S S . T _ _ _ E X C E S S P0 . 0 3 4 3 . 6 3 1 0 . 1 0 . 0 0 . 00 . 1 0 3 3 6 . 4 3 3 4 . 5 3 . 8 1 1 . 20 . 2 0 3 2 8 . 9 3 5 8 . 6 7 . 2 2 2 . 20 . 3 0 3 2 1 .2 3 8 2 . 2 1 0 . 5 3 2 . 60 . 4 0 3 1 2 . 3 4 0 5 . 8 1 2 . 5 4 3 . 00 . 5 0 3 0 3 .1 4 2 7 . 0 1 4 . 3 5 1 . 10 . 6 0 2 9 2 .3 4 4 4 . 9 1 4 . 4 5 5 . 80 . 7 0 2 8 0 .1 4 5 7 . 2 1 3 . 2 5 4 . 90 . 8 0 2 6 6 . 4 4 6 2 . 6 1 0 . 4 4 7 . 10 . 9 0 2 5 1 .2 4 5 8 . 9 6 . 2 3 0 . 31 . 0 0 2 3 4 . 1 4 4 1 . 8 0 . 0 0 . 0

T A B L E ’ 2 . . . . . . . C R I T I C A L P R O P R T I E SS Y S T E M N U M B E R 1 8N - H E X A N E ( A ) - - - N - T R I D E C A N E ( B ).... ... - *- - - ---- • " * ' ' ' - - ’■ - - - -- - - - - - — • — - — * —X {A ) T ( D E G . C ) P ( P S I A ) E X C E S S T E X C E S S P0 . 0 4 0 1 . 7 2 5 0 . 2 0 . 0 0 . 00 . 1 0 3 9 3 . 0 2 8 8 . 7 8 . 1 1 9 . 30 . 2 0 3 8 4 . 0 3 2 8 . 1 1 5 . 8 3 9 . 60 . 3 0 . . . ' 3 7 4 . 1 ' 3 6 7 . 0 2 2 . 7 " . . . . . ' 5 9 . 30 . 4 0 3 6 3 . 8 4 0 4 . 9 2 9 . 1 7 8 . 10 . 5 0 3 5 1 . 1 4 4 1 . 1 3 3 . 2 9 5 . 10 . 6 0 3 3 6 . 1 4 7 5 . 4 3 5 . 0 1 1 0 . 20 . 7 0 3 1 8 . 3 4 9 9 . 5 3 3 .9 1 1 5 . 20 . 8 0 2 9 6 . 8 5 1 0 . 0 2 9 . 2 1 0 6 . 50 . 9 0 ... 2 6 9 . 0 4 9 9 . 2 . 1 8 . 1 7 6 . 61 . 0 0 2 3 4 . 1 4 4 1 . 8 0 . 0 0 . 0

26

T A B L E 3 C R I T I C A L P R O P E R T I E S

SYSTEM_""NUMBER’ ’ 19 :N - H E X A N E ( A ) - - - N - T E T R A O E C A N E { B )

X ( A ) T ( D E G . C ) P ( P S I A ) E X C E S S . T E X C E S S P0 . 0 4 2 3 . 7 2 0 8 . 5 0 . 0 0 , 00 . 1 0 4 1 6 . 0 2 5 4 . 9 1 1 . 3 2 3 . 10 . 2 0 4 0 7 . 6 3 0 1 . 2 2 1 . 8 4 6 . 00 . 3 0 3 9 7 . 1 3 4 7 . 5 3 0 . 3 6 9 . 00 . 4 0 3 8 4 . 7 3 9 3 . 8 3 6 . 8 9 2 . 0 _0 . 5 0 3 7 0 . 0 4 3 8 . 2 4 1 . 1 1 1 3 . 10 . 6 0 3 5 3 . 3 4 7 9 . 9 4 3 . 4 1 3 1 . 40 . 7 0 3 3 2 . 8 5 1 4 . 0 4 1 . 8 1 4 2 . 20 . 8 0 3 0 7 . 6 5 3 2 . 0 3 5 . 6 1 3 6 . 90 . 9 0 2 7 5 . 0 5 1 7 . 5 2 1 . 9 9 9 . 01 . 0 0 2 3 4 . 1 4 4 1 . 8 _ 0 , 0 _ _ _ _ _ _ _ _ _ _ 0 , 0 _

T A B L E V " C R I T I C A L P R O P E R T I E SS Y S T E M N U M B E R 2 0N - H E X A N E ( A ) C I C - D E C A L I N ( B )

X (A ) T ( D E G . C ) P ( P S I A ) E X C E S S T E X C E S S P0 . 0 4 3 1 . 8 4 6 5 . 1 0 . 0 0 . 00 . 1 0 4 1 8 . 5 5 0 1 . 8 6 . 5 3 9 . 00 . 2 0 _ _ _ __ 4 0 3 . 6 5 3 3 . 4 1 1 . 3 7 3 . 0 _0 . 3 0 3 8 7 . 3 " 5 5 8 . 3 1 4 . 8 1 0 0 . 20 . 4 0 3 6 9 . 5 5 7 5 . 9 1 6 . 8 1 2 0 . 10 . 5 0 3 5 0 . 0 5 8 4 . 0 1 7 . 1 1 3 0 . 60 . 6 0 3 2 8 . 7 5 8 2 . 1 1 5 . 5 1 3 1 . 00 . 7 0 3 0 6 . 1 5 6 9 . 8 1 2 . 7 1 2 1 . 00 . 8 0 _ 2 8 3 . 0 _ 5 4 3 . 6 9 . 4 _ _ _ 9 7 . 1O'. 9 0 . . . ... "2 5 8 . 8 . . . . ’ 4 9 8 . 4 ' 4 . 9 5 4 . 31 . 0 0 2 3 4 . 1 4 4 1 . 8 0 . 0 0 . 0

27

T A B L E 5 C R I T I C A L P R O P E R T I E SS Y S T E M N U M B E R " 2 1 ' ' ...-- - ■ ---—— — .—

N - N D N A N E ( A ) — - N - T R I D E C A N E ( B)

X (A) T ( D E G . C ) P ( P S I A ) E X C E S S T E X C E S S P0 . 0 A O 1 . 7 2 5 0 . 2 0 . 0 0 . 00 . 1 0 3 9 6 .A 2 6 A . 3 2 . 8 5 . 80 . 2 0 3 9 1 .5 2 7 8 . 1 6 . 0 11 . A0 . 3 0 3 8 5 .6 2 9 1 . 8 8 . 2 1 6 . 80 . A O 3 7 9 . 0 3 O A . 9 9 . 7 2 1 . 70 . 5 0 3 7 1 . 5 3 1 6 . 6 1 0 . A 2 5 . 10 . 6 0 3 6 3 .2 3 2 6 . 2 1 0 . 2 2 6 . 50 . 7 0 3 5 3 .6 3 3 3 . 0 8 . 7 2 5 . 1o . a o 3 A 3 .A 3 3 7 . 0 6 . 6 2 0 . 80 . 9 0 3 3 2 .3 3 3 6 . 9 3 . 6 1 2 . 51 . 0 0 3 2 0 . 6 3 3 2 . 7 0 . 0 0 . 0

TARLE 6 " C R I T I C A L ‘PROPERTIES

SYSTEM NUMBER 2 2

N - D E C A N E {A ) N - D O D E C A M E (B )

X (A ) T ( D E G . C ) P ( P S I A ) E X C E S S T E X C E S S P0 . 0 3 8 5 .8 2 6 9 . 8 0 . 0 0 . 00 . 10 3 8 2 .1 2 7 6 . 2 0 . 5 2 . 30 . 2 0 3 7 8 . 3 2 8 1 . 9 0 . 9 A. 00 . 3 0 3 7 A . 3 2 8 6 . 9 1 . 2 A . 9O . A O 3 7 0 . A 2 9 1 . 6 1 . 5 5 . 50 . 5 0 3 6 6 .A 2 9 5 . 7 1 . 7 5 . 60 . 6 0 3 6 2 .3 2 9 9 . 5 1 . 8 5 . 30 . 7 0 3 5 B . 1 3 0 2 . 8 1 . 8 A . 50 . 8 0 3 5 3 . 6 3 0 5 .7 1 . 6 3 . 30 . 9 0 3 A 8 • 7 .. . " 3 0 8 . 3 " 0 . 9 .. . 1 . 9 ~1 . 0 0 3 A 3 . 6 3 1 0 . 5 0 . 0 0 . 0

28

T A R L E 7 C R I T I C A L P R O P E R T I E S

S Y S T E M N U M B E R 2 8 -B E N Z E N E ( A ) - - - N - D E C A N E ( B )

X (A) _ _ _ _ T ( D E G . C ) ___ P ( P S I A ) ___ e x c e s s T E X C E S S P0 . 0 3 4 3 . 6 3 1 0 . 2 0 . 0 0 . 00 . 1 0 3 4 1 .2 3 4 1 . 9 3 . 2 - 8 . 50 . 2 0 3 3 7 . 0 3 7 5 . 2 5 . 3 - 1 5 . 40 . 3 0 3 3 3 .6 4 1 1 . 4 6 . 7 - 1 9 . 40 . 4 0 3 2 8 . 9 4 4 9 . 6 7 . 5 - 2 1 . 40 . 5 0 . . '3 2 3 .6 4 8 9 . 8 7 . 8 - 2 1 . 30 . 6 0 3 1 7 . 9 5 3 2 . 3 7 . 6 - 1 9 . 00 . 7 0 3 1 1 .7 5 7 7 . 0 7 . 0 - 1 4 . 50 . 8 0 3 0 4 . 0 6 2 1 . 7 5 . 6 - 1 0 . 00 . 9 0 2 9 6 .9 6 6 6 • 7 3 . 3 - 5 . 21 . 0 0 2 8 8 . 1 _7 1 2 . 1 _ 0 . 0 0 . 0

T A B L E 8 C R I T I C A L ' P R O P E R T I E SS Y S T E M N U M B E R 2 9B E N Z E N E ( A ) - - - N - T R I D E C A N E { P)

X (A ) T ( D E G . C ) P ( P S I A ) E X C E S S T E X C E S S P0 . 0 4 0 1 . 7 2 5 0 . 2 0 . 0 0 . 00 . 1 0 3 9 7 . 8 2 8 8 . 0 7 . 5 - 8 . 40 . 2 0 3 9 3 . 0 3 2 9 . 9 1 4 . 0 - 1 2 . 70 . 3 0 . . . . 3 8 7 . 3 “ 3 7 6 . 3 * 1 9 . 7 - 1 2 . 50 . 4 0 3 8 0 . 3 4 2 5 . 8 2 4 . 0 - 9 . 20 . 5 0 3 7 1 . 7 4 7 9 . 3 2 6 . 8 - 1 . 80 . 6 0 3 6 1 .5 5 3 8 . 7 2 8 . 0 1 1 . 40 . 7 0 3 4 8 . 7 6 1 2 . 2 2 6 . 5 3 8 . 70 . 8 0 3 3 2 .7 6 7 4 . 9 2 1 . 9 5 5 . 20 . 9 0 . . . " 3 1 3 . 0 ' 7 0 4 . 0 . . . . 1 3 . 5 3 8 . 11 . 0 0 2 8 8 . 1 7 1 2 . 1 0 . 0 0 . 0

T A R L E 9 C R I T I C A L P R O P E R T I E S

B E N Z E N E ( A } N - H E X A P E C A N E (B >

_X (A )____ T ( D E G . C ) P ( P S I A ) E X C E S S T E X C E S S P0 . 0 4 5 0 . 0 ( 6 3 ) 2 0 6 . 0 ( 6 0 ) 0 . 0 0 . 00 . 10 4 4 5 . 2 2 6 0 . 0 1 1 . 4 - 3 . 40 . 2 0 4 3 9 . 1 3 1 0 . 2 2 1 . 5 - 3 . 00 . 3 0 4 3 1 .6 3 6 5 .8 3 0 . 2 8 . 00 . 4 0 4 2 2 .6 4 2 7 . 6 3 7 . 4 1 9 . 20 . 5 0 4 1 2 .2 4 9 1 .8 4 3 . 2 . . . . 3 2 . 80 . 6 0 3 9 9 . 7 5 6 0 . 7 4 6 . 8 5 1 . 00 . 7 0 3 8 4 . 2 6 3 1 . 9 4 7 . 5 7 1 . 60 . 8 0 3 6 2 . 5 7 0 6 . 2 4 2 . 0 7 5 . 30 . 9 0 3 3 1 . 4 7 6 2 .4 2 7 . 1 1 0 0 . 91 . 0 0 2 8 8 . 1 7 1 2 . 1 0 . 0 0 . 0

TARLE 10 " 'CRITICAL PROPERTIESS Y S T E M N U M B E R 3 7B E N Z E N E ( A ) ----- C I S - 0 E C A L I N { B )

X (A ) T ( D E G . C ) P ( P S I A ) E X C E S S T E X C E S S P0 . 0 4 3 1 . 8 4 6 5 . 1 0 . 0 0 . 00. 10 4 2 2 . 6 5 1 4 . 5 5 . 2 2 4 . 70 . 2 0 4 1 2 . 5 5 6 0 . 5 9 . 4 4 6 . 0O'. 3 0 4 0 1 .6 .. " ”6 0 4 . 2 ' ~ 1 2 . 9 6 5 . 00 . 4 0 3 9 0 . 0 6 4 4 . 5 1 5 . 7 8 0 . 60 . 5 0 3 7 6 . 9 6 8 0 . 9 1 7 . 0 9 2 . 30 . 6 0 3 6 2 . 4 7 1 1 . 1 1 6 . 8 9 7 . 80 . 7 0 3 4 6 .3 7 3 1 . 6 1 5 . 1 9 3 . 60 . 8 0 3 2 8 . 4 7 4 0 . 1 1 1 . 6 7 7 . 40 . 9 0 3 0 8 . 9 ' 7 3 4 . 3 6 . 4 4 6 . 9 "1 . 0 0 2 8 8 . 1 7 1 2 . 1 0 . 0 0 . 0

T A R L E 1 1 C R I T I C A L P R O P E R T I E S

S Y S T E M ’ N U M B E R ' 44"E T H Y L B E N Z E N E (A ) - - - C I S - D E C A L I N ( B >

X (A ) T ( D E G . C ) P { P S I A )___ E X C E S S T _ _ _ E X C E S S0 . 0 4 3 1 . 8 4 6 5 . 1 o.o 0 . 00 . 1 0 4 2 3 . 9 4 8 9 . 5 0 . 9 1 8 . 00 . 2 0 4 1 5 . 9 5 0 7 . 2 1 . 7 2 9 . 30 . 3 0 4 0 7 . 6 5 1 9 . 3 2 . 3 3 5 . 00 . 4 0 3 9 9 . 1 5 2 8 . 6 2 . 6 3 7 . 90 . 5 0 3 9 0 .2 5 3 5 . 2 2 . 5 3 8 . 10 . 6 0 3 8 1 . 0 5 3 9 . 7 2 . 1 3 6 . 10 . 7 0 3 7 1 . 8 5 4 1 . 4 1 . 7 3 1 . 40 . 8 0 3 6 2 . 4 5 3 9 . 8 1 . 2 2 3 . 40 . 9 0 3 5 3 .2 5 3 5 . 4 0 . 8 1 2 . 6A - Q Q .... _ _ _ _ , 3 4 3 . 6 . . . . . 5 2 9 . 2 _ _ _ _ _ . 0 . 0 _ _ _ _ _ ___ 0 . 0

T A B L E 1 2 ‘ C R I T I C A L P R O P E R T I E S ________________ - ____ ________

S Y S T E M N U M B E R 4 5O - X Y L E N E ( A ) - - - C I S - D E C A L I N ( B )

XI A) T ( D E G . C ) P ( P S I A ) E X C E S S T E X C E S S0 . 0 4 3 1 . 8 4 6 5 . 1 0 . 0 0 . 00 . 1 0 4 2 4 . 8 4 8 5 . 3 0 . 6 1 2 . 30 . 2 0 _ 4 1 7 . 7 5 0 2 . 0 1 . 0 _ _ 2 1 . 00 . 3 0 " . . . . 4 1 0 . 4 5 1 5 . 7 1 . 3 2 6 . 00 . 4 0 4 0 3 . 0 5 2 7 . 8 1 . 4 3 0 . 90 . 5 0 3 9 5 . 5 5 3 7 . 2 1 . 5 3 2 . 40 . 6 0 3 8 7 . 8 5 4 3 . 5 1 . 4 3 0 . 00 . 7 0 3 8 0 . 1 5 4 7 . 2 1 . 2 2 6 . 50 . 8 0 3 7 2 . 2 _ 5 4 8 . 6 0 . 9 2 0 . 00 . 9 0 . . . . . . 3 6 4 . 2 ' 5 4 7 . 7 0 . 4 . . . . 1 1 . 11 . 0 0 3 5 6 . 2 5 4 4 . 5 0 . 0 0 . 0

31

T A B L E 1 3 C R I T I C A L P R O P E R T I E S

S Y S T E M N U M B E R " 6 0 7 C Y C L O H E X A N E ( A ) - - - N - D E C A N E ( B )

X {A ) T ( D E G . C ) P ( P S I A ) E X C E S S T E X C E S S P0 . 0 3 4 3 . 9 3 1 0 . 5 0 . 0 0 . 00 . 1 0 3 4 1 . 1 3 3 5 . 6 3 . 6 - 3 . 30 . 2 0 3 3 7 . 6 3 6 2 . 2 6 . 5 - 5 . 00 . 3 0 3 3 3 . 6 3 9 0 . 2 8 . 9 - 5 . 4O . A O 3 2 9 . 1 4 2 0 . 0 1 0 . 8 - 4 . 00 . 5 0 3 2 3 . 8 4 5 1 . 7 1 1 . 9 - 0 . 60 . 6 0 3 1 7 . 4 4 8 4 . 5 1 2 . 0 3 . 80 . 7 0 3 1 0 . 0 5 1 8 . 1 1 1 . 0 9 . 00 . 0 0 3 0 1 .7 5 5 1 . 3 9 . 1 1 3 . 80 . 9 0 2 9 1 .9 5 7 6 .8 5 . 7 1 1 . 01 . 0 0 2 7 9 . 8 5 9 4 . 2 0 . 0 0 . 0

T A B L E " ' C R I T I C A L P R O P E R T I E SS Y S T E N N U M B E R 6 1C Y C L O H E X A N E ( A ) ------ N - T R I D E C A M E ( B )

--- - ^ - • -- - - - - - --- - - - - • • • • • — . . . . . . . _ . ’X (A ) T ( O E G . C ) P ( P S I A ) E X C E S S T E X C E S S P0 . 0 4 0 1 . 7 2 5 0 . 2 0 . 0 0 . 00 . 1 0 3 9 7 . 4 2 8 6 .9 7 . 9 2. 30 . 2 0 3 9 2 .2 3 2 4 . 2 1 4 , 9 5 . 20 . 3 0 3 8 6 . 0 3 6 3 . 4 2 0 . 9 1 0 . 0 "

0 . 4 0 3 7 8 . 4 4 0 6 . 3 2 5 . 5 1 0 . 50 . 5 0 3 6 9 . 3 4 5 1 . 7 2 8 . 6 2 9 . 50 . 6 0 3 5 8 . 4 4 9 8 . 3 2 9 . 8 4 1 . 70 . 7 0 3 4 5 .4 5 4 5 . 4 2 9 . 0 5 4 . 40 . 8 0 3 2 9 . 5 5 8 7 . 2 2 5 . 3 6 1 . 00 . 9 0 3 0 8 . 4 6 1 1 . 0 1 6 . 4 . . . 5 1 . 21 . 0 0 2 7 9 . 8 5 9 4 . 2 0 . 0 0 . 0

32

TARLE 15 CRITICAL PROPERTIESSYSTEM NUMhTr* 63 ~~CYCLOHEXANE(A) -- CIS-DECALIN(R)

X (A)______ T(DEG.C).. P(PSIA) EXCESS T ___EXCESS P0 . 0 431 . 8 4 6 5 • 1 0 . 0 0 . 00 . 1 0 422 . 0 5 0 2 . 8 5 . 4 2 4 . 8o . a o 411 . 4 5 3 9 . 1 1 0 . 0 4 8 . 20 . 3 0 3 9 9 . 6 5 7 1 . 9 1 3 . 4 6 8 . 1O.AO 3 8 7 . 1 6 0 0 . 6 1 6 . 1 8 3 . 96 . 5 0 373 . 1 6 2 2 . 6 1 7 . 3 9 3 . 00 . 6 0 3 5 7 . 6 6 3 7 . 9 1 7 . 0 9 5 . 30 . 7 0 3 4 0 . 7 6 4 4 . 4 1 5 . 3 8 8 . 90 . 8 0 322 . 6 6 4 1 . 4 1 2 . 4 7 3 . 00 . 9 0 302 . 7 6 2 7 . 7 7 . 7 4 6 . 41 . 0 0 2 7 9 . 8 5 9 4 . 2 0 . 0 . . . o . o _ _

CR

ITIC

AL

P

RE

SS

UR

E

(psi

a)

33

4 6 0

4 4 0

4 2 0

4 0 0

3 8 0

M O L E % N - H E X A N E

3 6 0

3 - 3 0 , 3

4 - 5 2 , 35 - 6 9 . 4

6 - 8 9 . 9

7 - 1 0 0 . 0

3 4 0

3 2 0

3 0 0

2 3 0 2 5 0 2 7 0 2 9 0 3 1 0 3 3 0 3 5 0

C R I T I C A L T E M P E R A T U R E ( ° C )

Fig. - P-T Critical Locus of the Systemn-Hexane -- n-Decane

CRIT

ICA

L PR

ESS

UR

E

(psi

a)

34

5 0 0

4 6 0

4 2 0

M O L E % N - H E X A N3 8 0

2 - 10.13 - 3 0 .1

4 - 4 9 , 9

5 - 6 9 . 5

6 - 8 9 . 6

7 - 1 0 0 . 0

3 4 0

3 0 0

2 6 0

2203 8 0 4 2 02 6 0 3 0 0 3 4 0220


Fig* 5 - P-T Critical Locus of the Systemn-Hexane -- n-Tridecane

CRIT

ICA

L PR

ESSU

RE

(psi

a)

35550

5 0 0

4 5 0 - T

4 0 0

M O L E % N - H E X A N E

2 - 10.2 3 - 2 9 . 64 - 5 0 . 25 - 6 9 . 96 - 8 9 . 87 - 1 0 0 . 0

3 5 0

3 0 0

2 5 0

2002 2 0 2 6 0 3 0 0 3 4 0 3 8 0 4 2 0 4 6 0


Fig. 6 - P-T Critical Locus of the Systemn-Hexane — - n-Tetradecane

CR

ITIC

AL

PRE

SSU

RE

(p

sia)

610

5 9 0

5 5 0

5 1 0

4 7 0

4 3 0

AH

\ 3

/M O L E % N

1 -

- H E X A N E

0 . 0

/62 - 1 0 . 2 ^

3 - 3 0 . 2

4 - 5 0 . 3

5 *- 6 9 . 4

2

\,1 6

6 ~ <

7 - 1C

5 0 .1

5 0 . 0

220 2 6 0 3 0 0 3 4 0 3 8 0 4 2 0 4 4 0

C R I T IC A L T E M P E R A T U R E ( ° C )

Fig. 7 - P-T Critical Locus of the System n-Hexane -- cis-Decalin

CRIT

ICA

L PR

ESS

UR

E

(psi

o)

37

340

3 2 0

3 0 0

M O L E % N - N O N A N E2 8 0

2 - 10,6 3 - 3 0 . 0

4 - 5 0 , 2

5 - 6 9 , 7

6 - 8 9 , 8

7 - 1 0 0 . 0

2 6 0

2 4 0

2203 9 03 7 0 4 1 03 1 0 3 3 0 3 5 0


Fig. 8 - P-T Critical Locus of the Systemn-Nonane --- n-Tridecane

CRIT

ICA

L PR

ESS

UR

E

(psi

o)

38

320

3 1 0

3 0 0

2 9 0

M O L E % N - D E C A N E

2 - 10,22 8 0

4 - 5 0 . 0 -

5 - 6 9 , 9

6 - 9 0 , 0

7 - 1 0 0 . 02 7 0

2 6 03 8 0 3 9 03 6 0 3 7 03 5 03 4 0


Fig. 9 - P-T Critical Locus of the Systemn-Decane --- n-Dodecane

CRIT

ICA

L PR

ESS

UR

E (p

sia)

39

7 0 0

6 0 0

M O L E % B E N Z E N E5 0 0

2 - 1 3 .3

3 - 2 9 . 9

4 - 4 9 . 9

5 - 6 9 . 7

6 - 8 8 . 3

7 - 1 0 0 . 04 0 0

3 0 02 8 0 3 0 0 3 2 0 3 4 0


Fig. 10 - P-T Critical Locus of the SystemBenzene --- n-Decane

CRIT

ICA

L PR

ESS

UR

E (p

sia)

ko

700

6 0 0

5 0 0

4 0 0

o -Y

\5

—~ IVIVJL-u. to D l. IN C.C. INC.

1 - 0 . 0 2 - 1 3 .43 - 27 .14 - 4 6 . 05 - 6 6 . 96 - 8 9 . 97 - 1 0 0 . 0

V

\3\ 4? _______

3 0 0

2 4 02 8 0 3 0 0 3 2 0 3 4 0 3 6 0 3 8 0 4 0 0


Fig. 11 - P-T Critical Locus of the SystemBenzene --- n-Tridecane

CRIT

ICA

L PR

ESSU

RE

(p

sia)

800

7 0 0

6 0 0

5 0 0M O L E % B E N Z E N E

1 - 0.02 - 3 0 . 63 - 5 0 ,14 - 7 0 . 65 - 8 0 . 06 - 9 0 . 07 - 1 0 0 . 0

4 0 0

3 0 0

• L E S S R E L IA B L E P O I N T S

2 - E X P E R I M E N T A L

I - L I T E R A T U R E

200

1004 0 0 4 5 02 5 0 3 0 0 3 5 0


Fig. 12 - P-T Critical Locus of the SystemBenzene n-Hexadecane

CRIT

ICA

L PR

ESS

UR

E

(psi

o)

750kz

7 0 0

6 5 0

6 0 0

5 5 0

5 0 0

4 5 0

6 .

l /

\ 5

\ 4

M O L E % R E N Z E fME 6 3

1 “ 0 . 02 - 1 0 . 5

3 - 2 9 . 94 - 4 9 . 6 5 - 7 0 .1

— (5 - 8 9 . 3r - t o o . o

o 2

\ l

2 8 0 3 2 0 3 6 0 4 0 0 4 4 0


Fig. 13 - P-T Critical Locus of the SystemBenzene -- cis-Decalin

CR

ITIC

AL

PRE

SSU

RE

(p

sia)

540

5 2 0

5 0 0 —

M O L E % E T H Y L B E N Z E N E

4 8 0 —

4 6 0

1 - 0 . 0

2 - 9 . 9

3 - 3 0 .1

4 - 5 0 . 2

5 - 6 9 . 9

6 - 8 9 . 5

7 - 1 0 0 . 0

3 4 0 3 6 0 3 8 0 4 0 0 4 2 0 4 4 0


Fig. 14 - P-T Critical Locus of the System Ethylbenzene --- cis-Decalin

CRIT

ICA

L PR

ESS

UR

E (p

sia)

44

560

5 4 0

5 2 0

M O L E % 0 - X Y L E N E

I - 0.05 0 0

3 - 3 0 . 5

4 - 5 0 . 7

5 - 7 0 . 2

6 - 8 9 . 5

7 - 1 0 0 . 0

4 8 0

4 6 03 4 0 3 6 0 3 8 0 4 0 0 4 2 0 4 4 0


Fig. 15 - P-T Critical Locus of the Systemo-Xylene -- cis-Decalin

CRIT

ICA

L PR

ESSU

RE

(psi

a)

45

6 0 0

5 0 0

M O L E % C Y C L O H E X A N E

I - 0.02 - 10.63 - 3 0 . 34 - 5 0 . 1 5 - 6 9 . 76 - 8 9 . 77 - 1 0 0 . 0

4 0 0

3 0 03 4 0 3 6 03 2 03 0 02 8 02 6 0


Fig, 16 - F-T Critical Locus of the SystemCyclohexane -- n-Decane

CRIT

ICA

L PR

ESS

UR

E

(psi

c)

I* 47• • • 46

6 0 0

5 5 0

5 0 0

M O L E % C Y C L O H E X A N E

4 5 02 - 9 . 93 - 3 0 . 34 - 5 0 . 15 - 7 0 . 06 - 8 9 . 77 - 1 0 0 . 0

4 0 0

3 5 0

3 0 0

2 5 0

2 8 0 3 0 0 3 2 0 3 4 0 3 6 0 3 8 0 4 0 0


Fig, 17 - P-T Critical Locus of the SystemCyclohexane --- n-Tridecane

CR

ITIC

AL

PRE

SSU

RE

(p

sia)

650

6 0 0

5 5 0

5 0 0

4 5 0 2 7 0

c

7 /

6 ^

n o

_ M O L E % CYC: l o h e x a N F

\ > 3 -

1 - 0 . 0 2 - 1 0 .2 3 - 2 9 . 84 - 4 9 . 65 - 6 9 . 8 \ 26 - 7 - 1

8 9 . 40 0 . 0

2 9 0 3 1 0 3 3 0 3 5 0 3 7 0 3 9 0 4 1 0 4 3 0


Fig. 18 - P-T Critical Locus of the System Cyclohexane — - cis-Decalin

CHAPTER V

PRECISION AND ACCURACY OF RESULTS

There are several factors to consider in estimating the precision and accuracy of resultst calibration, temperature gradient, radiation, visual identification of the critical phenomena, uncertainty of extrapolation, effect of dissolved-air, effect of mercury, and repeatability.

The critical properties of the pure compounds determined in this work are listed in Table 16 and compared with the literature values. The literature values used for comparison were selected as among the most reliable values after a comparison of the available data on each compound,

1. CalibrationThe thermocouple was calibrated by

comparing it to a platinum resistance thermometer certified by the National Bureau of Standards. The details of calibration are given in Appendix B. The recorder connected tothe platinum thermometer could be read to + 0.002 ohms,

owhich corresponded to + 0.02 C. The precision of the recorder connected to the thermocouple was + 0.002 mv,

48

TABLE 16

COMPARISON OF PURE COMPOUND DATA WISH LITERATURE VALUES

Crit. Temperature(°C) Crit, Pressure(psia) Ref.Compound This Worka Literature13 Diff. This Worka Literature13 Diff.

Stablen-Hexane 234.1 234.7 -0.6 441.8 440,0 1.8 70Cyclohexane 279.8 279.8 0.0 594,2 591.5 2.7 50Benzene 288.1 289.0 -0.9 712.1 710.1 2.0 85n-Nonane 320,6 321.4 -0.8 332.7 331.8 0.9 7Ethylbenzene 343.6 344.0 -0.4 529.2 523.4 5.8 4n-Decane 343.6 344.2 -0.6 310.2 306.8 3.4 37o-Xylene 336,2 357.1 -0.9 544.5 541.4 3.1 4

Absolute Average Difference 0.6 2,8Unstablen-Dodecane 385.8+0.2° 385.1+0.1° 269.8+0.5° 264,5 7384,6+0.3 63n-Tridecane 401,7+0.8 403.0+0.5 250.2+4.0 63n-Tetradecane 423.7+1,5 419.4+0,4 208.5+9.0 63421 +1 3cic-Decalin 431.8+0.7 429.0+1.0 465,1+2.0 13

Note 1 a. Air-saturated Samplesb. Degassed Samplesc. The estimated uncertainty of the extrapolation of

the temperature-time and the pressure-time curvesvo

50equivalent to + 0.04 °C. Thus, the precision of the thermocouple calibration is estimated to be + 0.04 °C. The accuarcy of the thermocouple calibration is assessed to be +0.1 °Cf based on the standard deviation of the equation used to express the temperature-emf relationship0

The Ruska dead-weight gauge used to calibrate the Heise pressure gauge was accurate to within + 0.05 psi. However, since the Heise gauge could be read only to + 0.2 psi, the precision of the calibration was limited to this level. The accuracy of the gauge calibration is estimated to be + 0.5 psi.

2. Temperature GradientNo attempt was made to determine the temperature

gradient that might have existed along the inner surface of the furnace or along the experimental tube. It was found, however, that there existed temperature difference between that indicated by the thermocouple and the sample« This temperature difference was a measure of the temperature lag attributable to the difference in thickness of the sample tube and the thermocouple well. The method and procedure used in the determination of the temperature difference are given in Appendix A. The temperature read from the recorder was corrected, therefore, for the temperature difference.

The temperature gradient in the sample should be negligible because the sample was stirred and the section

of the tube occupied by the sample was only about 4 cm at the critical point,

3. RadiationIt is difficult to estimate the error caused by the

radiation of the thermocouple through the viewing slits, but the error should be very small. Cherry (l4) estimated the error due to the radiation of the platinum resistance thermometer through the sighting slits in a silvered vapor jacket by measuring the change in temperature when the jacket was completely covered with aluminum foil. He found that the error was less than 0,02 °C for the maximum temperature difference, i.e., a vapor bath temperature of 230 °C and an ambient temperature of 23 °C. This gives an order of magnitude of the radiation effect.

4. Visual Identification of the Critical PhenomenaThe critical point was determined by visual obser

vation of the disappearance of the meniscus as the temperature was raised and reappearance of the meniscus as the temperature lowered. The values of the critical point determined in this way may vary, depending upon the precision with which the critical phenomena could be defined visually. For example, in the determination of the critical point of naphthalene, three observers read the critical temperature independently with the following resulti

5 2

Observer Temperature

C

AB

476.1 °C 476.3 °C476.2 °C

This indicates the importance of the personal factor involved in the determination of the critical point.

5. Uncertainty of ExtrapolationFor the thermally unstable samples, apparent critical

temperatures and pressures were determined at the shortest intervals possible over a period of 1 to hours. The true critical point was then estimated by plotting the apparent critical properties against time elapsed and extrapolating to zero-time. This method was not sufficiently definitive. Therefore, an effort was made without success to extrapolate the temperature-time and the pressuretime curves theoretically assuming that the rate of decomposition was a first order reaction. The range of uncertainty of the extrapolation depended upon the rate of decomposition. As the critical temperature of the sample increased the rate of decomposition increased and the accuracy of the measurement decreased. Consequently, the critical properties obtained by extrapolation were subject to an indeterminate error. Since it is difficult tc assess absolute accuracy, only the estimated uncertainty of extrapolation is given for each unstable compound in Table 16.

536. Effect of Dissolved-airNo effort was made to remove the air dissolved in the

hydrocarbons at room temperature. The sample prepared in this manner is called "air-saturated". Previous measurements on the air-saturated samples (37) showed that the absolute average difference between the air-saturated and the degassed (literature) samples in the critical pressure was 2.0 psi and that in the critical temperature was about 0,4 °C.

Table 16 shows that the absolute average differences for the stable compounds are 2,8 psi in the critical pressure and 0,6 °C in the critical temperature. The pressure obtained in this study are consistantly higher than the literature values, and the critical temperatures are lower in all cases. This consistant difference is expected because the samples were air-saturated, whereas the literature values were for degassed-samples. The difference in the pressure varied from 0,9 to 5*8 psi and that in the temperature ranged from 0.0 to -0.9 °C. This wide range suggests that the solubility of air in the hydrocarbon sample may depend on the nature of the compound. Based on these result, the error due to the dissolved-air is estimated to be about 0,3 °C in the temperature and about 2.0 psi in the pressure.

5**7« Effect of MercuryIn the determination of the critical constants of

hydrocarbons in the presence of mercury, it has been customary to substract the vapor pressure of the mercury at the sample temperature from the total pressure to obtain the true critical pressure. This is based on the assumption that the mercury and hydrocarbon are completely immiscible. However, the experimental work has definitely shown that the partial pressure of the mercury in the sample is not equal to the vapor pressure of the mercury at the sample temperature when it is above about 320 °C. Consequently, a corrective equation was obtained and the data in this work have been corrected for the effect of mercury.A detailed description of the study on the effect of mercury on the critical properties is given in the following chapter.

8. RepeatabilityIn the course of this work, repeatability tests were

conducted to provide an experimental assessment of the precision of the critical properties being measured. These tests were made by loading identical samples in separate tubes and then measuring the critical properties. Some results are shown in Table 17. The average values of the differences between the two measurements were 0.3 °C in the critical temperatures and 1.0 psi in the critical pressures. These results provide an indication of the

TABLE I?

REPEATABILITY OF RESULTS

CompoundFirst Measurement Tc(°C) Pc(psia)

Second Measurement Tc(°C) Pc(psi?)

Difference Tc(°C) P°(psi)

Benzene 288.2 712.0 288.0 712.3 0.2 0.3Cyclohexane 279.7 594.2 280.0 594.1 0.3 0.1Ethylbenzene 343.6 529.1 343.5 530.7 0.1 1.6n-Decane 343.6 310.1 343.9 310.9 0.3 0.8n-Dodecane 385.8 270.0 386.3 269.6 0.5 0.6n-Tridecane 401.7 250.2 401.8 248.2 0.1 2.0cis-Decalin 431.8 *4-65.1 432.4 463.3 0.6 1.8Mixture 333.6 411.4 333.1 410.9 0.5 0.5(Benzene - n-Decane System* 30,04 mole % benzene) Average Difference 0.3 1.0

precision of the critical property measurements of this work.

As evident from the above discussion, it is not possible to assess accurately the individual error caused by each factor. Therefore, the precision of the measurements was estimated on the basis of the repeatability tests given in Table 17 and the accuracy of the measurements, on the basis of comparison with literature values presented in Table 16, The estimated precision and accuracy of the results for the stable samples (pure and mixture) are summarized in Table 18.

TABLE 18

ESTIMATED PRECISION AND ACCURACY

Temperature(°C) Pressure(psi)Precision Accuracy Precision Accuracy

Calibration +0.04- +0.1 +0.2 +0.5Measurement ±0.3 -0.6 +1.0 +2.8

The uncertainty of extrapolation given in Table 16 provides a good basis for estimating the accuracy of the thermally unstable samples. However, the estimated precision presented in Table 18 applies equally well to the unstable samples.

The composition of the mixtures were determined by

57weighing the amounts of the components by difference on an analytical balance. The weights could be recorded to the nearest 0,1 mg. The loss of the sample due to the evaporation might have occurred during the preparation and loading processes. On the basis of these, the accuracy of the sample composition is estimated to be within + 0,1 mole %%

CHAPTER VI

T H E E F F E C T O F M E R C U R Y O N T H E C R I T I C A L C O N S T A N T S A T H I G H T E M P E R A T U R E

In the determination of the critical constants of hydrocarbons in the presence of mercuryt it has been a usual practice to subtract the vapor pressure of mercury at the sample temperature from the observed total pressure to obtain the true critical pressure. The basic assumption for this practice is that the mercury and hydrocarbon are completely immiscible; i.e., the partial pressure of mercury is equal to its vapor pressure at the given temperature.

In 1955t however, Jepson and Rowlinson (AA) raised some questions concerning the validity of this practice and the effect which the dissolved mercury might have upon the critical temperature. Applying the virial equation of state of the mixture and assuming that the system is at equilibrium, they derived equations to be used for correcting the observed total pressure in the presence of mercury.

In order to show the order of magnitude of the corrections predicted by the equations, Hissong (37) made some calculations for the n-paraffins from propane throughn - D e c a n e a n d f o r c y c o h e x a n e a n d b e n z e n e . T h e r e s u l t s o f

58

59hie calculation showed that the corrections v/ere considerably larger than the vapor pressure of mercury. The equations derived by Jepson and Rowlinson require the knowledge of the second virial coefficient of the pure hydrocarbon(Bj^) and the second and third virial coefficients for the interaction of, respectively, one and two molecules of the hydrocarbon with one atom of mercuryi i.e., Bj2 and Hissong concluded that the accuracyof the predicted correction was questionable because of the uncertainty in the estimation of the intermolecular forces on which these calculations v/ere based.

Later, Jepson, Richardson, and Rowlinson (^3) measured the solubility of mercury in propane and n-butane at pressure up to 30 atm from lf& to 256 °C and showed that the concentrations of mercury v/ere up to 35 f° greater than the concentrations in pure mercury vapor at the same temperature. Richardson and Rowlinson (77) reported the results of measurements of the solubility in n-butane at temperature up to 300 °C and at pressures up to kOO atm which showed that the concentration of mercury in the mercury-hydrocarbon system exceeded that calculated from the saturated vapor pressure by factors of up to 3*7*In the same article they reported some observations of the effect of mercury on the measurement of the critical temperatures of cyclohexane and o-xylene. Their results showed that the critical point of the cyclohexane-mercury

system was very nearly the same as that of the pure compound but for o-xylene-mercury system it was 0.4 °C below the critical point of pure o-xylene. They concluded, therefore, that critical temperatures could not be measured reliably in the presence of mercury at temperatures above about 300 °C. The effect of mercury on the pressure was not investigated. The results were interpreted as evidence that the critical temperature observed was, in reality, the critical end point of a binary mixture of mercury and the hydrocarbon. Considering the results reported by Rowlinson et al (43, 4*1*, 77), it is believed that the partial pressure exerted by the mercury would be different from the vapor pressure of mercury at this temperature by some unknown amount which would be difficult to estimate with the present knowledge of the intermolecular forces between mercury atoms and hydrocarbon molecules. Since the critical temperatures of most of the pure compounds studied in this work were above 300 °C, it is important to estimate the magnitude of this difference.

In order to determine the true partial pressure of mercury experimentally, the critical pressure of the hydrocarbon must first be determined using a confining liquid which is inert to the hydrocarbons and has a negligible vapor pressure at their critical temperatures. Then, the partial pressure will be the difference between the total pressure with and without mercury. Of the possible liquids

available, gallium which has a very high boiling point was chosen to replace mercury. Gallium (89) belongs in the boron-aluminum family along with indium and thallium. Metallic gallium, however, shows little resemblance to aluminum in physical properties. It melts at 29.75 °C and its normal boiling point is 1983 °C. Since the vapor pressure of gallium at 1315 °G is only 1 mm Hg, it is negligible at the critical temperatures of the hydrocarbons of interest.

Through the courtesy of the Aluminum Company of America a quantity of gallium was made available on a loan basis for this investigation. In order to minimize the possible loss if the experimental tube should burst and to improve the handling problem, a new apparatus, similar to that used by Connolly and Kandalic (17), was constructed in which a hand-operated pressure generator filled v/ith gallium was used to develop the pressure on the sample, instead of using compressed nitrogen gas. A schematic drawing of the apparatus is shown In Fig. 33 in Appendix A. Since gallium, unlike most metals but like water, expands on freezing (3*2fo), the heat lamps were used to keep the temperature of the entire apparatus above the freezing point of gallium. In case of a power failure, an auxiliary heating system was provided in which the metal lines with gallium were wrapped with heating tapes connected to a 12-volt storage battery through a relay. In order to

prevent the temperature of the apparatus from falling below the freezing point of gallium at any time, an on-off temperature controller, activated by an iron-constantan thermocouple, was also provided so that the auxiliary heating system would be operated even if there was no power failure. The temperature controller had an adjustable set-point which was normally set at about 35 °C. The experimental tube is shown in Fig. 3*+ in Appendix A, The temperature of the sample was measured by a chromel- constantan thermocouple inserted in the we11 at the top of the tube and recorded continuously on a temperature recorder and the pressure was measured by means of a high precision Heise bourdon gauge. Details of the apparatus and experimental procedure are given in Appendix A.

The experimental results has definitely shown that when high molecular weight hydrocarbons are heated in the presence of excess mercury to temperature above 320 °C, the solubility of mercury in the liquid hydrocarbon increases. The critical point of the hydrocarbon measured under such circumstances, therefore, is not that of the pure hydrocarbon but the critical end-point of a mixture of hydrocarbon and mercury. This situation can be easily shown by a P-T diagram of the partially miscible systems.

Fig. 19 shows schematically the vapor pressure curve of a pure hydrocarbon ending at the critical point A (line A#A) and that of the system hydrocarbon + mercury,

PRESSURE

6 3

C r i t . P t . H g

AP

B *

A *

- > J K - A TC *

T E M P E R A T U R E

Fig. 19 - Schematic P-T Diagram of Partially Miscible System. Hydrocarbon-Mercury

ending at the critical end-point B (line B*B)« The dashed line AB represents the critical locus of the hydrocarbon- mercury system which terminates in the critical end-point B. The curve C^C is the vapor pressure curve of puremercury ending at the critical point C.

The critical constants of n-nonane, 1,2,4-trimethyl- "benzene, and naphthalene have been determined with gallium and with mercury, and are shown in Table 19, It is assumedthat the critical constant measured with gallium is reallythat of the pure hydrocarbon because the vapor pressure of gallium is insignificant in this temperature range. The subscript notation used in Table 19 corresponds to that in Fig, 19, That is, the critical constants measured with gallium and with mercury corresponds, respectively, to point A and B, It is to be noted from Table 19 that T° for the mixture of hydrocarbon ana mercury is less than T^ for the pure hydrocarbon, whereas Pg is greater than P^, This confirms the existance of critical end-point of the hydrocarbon-mercury system as reported by Richardson and Rowlinson (7?)•

The problem is to correct the critical end-point B of the hydrocarbon-mercury system to give the true critical point A of the pure hydrocarbon. Table 19 ndicates that

Tc is very small up to a temperature of 320 °C and less than 1 °C for hydrocarbons with T^ below ^00 °C, whereas A P C is large. If our assumptions about gallium; i.e.,

TABLE 19

COMPARISON OF THE CRITICAL CONSTANTS MEASURED WITH GALLIUM AND MERCURY

With Gallium Point A

With Mercury Point B A T C V]EW PPH«r (PI>calc

(psia)4 pA

Compound T°(°C) P^(psia) Tb (°C) Pg(psia) (°C) (pall (psi!A

(psi)n-nonane 322.7 332.3 322.5 340.3 0.2 7.7 -8.0 332.6 -0.31,2,4-trimethy1- benzene

377.4 475.3 376,7 490.6 0.7 20.9 -15.3 469.7 5.6

naphthalene 476.3 594.3 473.4 665.8 2.8 86.1 -71.5 579.7 14.6

Note* AT0 = T® - T°, VP^g = Vapor pressure of mercury at Tg t

P F ^ = P^ - Pg = Partial pressure of mercury =ilpcf

<PI>calc = PS - VPHg ’ 311(1 . AP£ = P1 - <PPcalc

o\Ui

1

66inertness and negligible solubility, are correct, AP° should be equal to the partial pressure exerted by mercury at Tg. A Pc should be also equal to the vapor pressure of mercury (VP^) at Tg» if mercury and hydrocarbon were completely immiscible. Then, (p^calc would be the true critical pressure of the hydrocarbon and A P^ would be zero. However, zero as can be seen fromTable 19* The data presented here definitely show that the customary practice of correcting for the effect of mercury by simply subtracting the vapor pressure from the observed total pressure is not correct when the temperature is above about 320 °C,

More critical data using gallium as the confining liquid are needed to devise a correction that can be applied to the critical constants that have already been determined. However, gallium is more susceptible to oxidation in the presence of air than mercury. Y/hen small amount of oxide is present the gallium wets the walls of experimental tube and makes it very difficult to observe the phase change in the sample. In addition to the wetting, a stirring problem was encountered because the density of gallium was less than that of the steel ball which was used to stir the sample•

In order to get around these problems with gallium, the method used by Ambrose and co-workers (4,6) has been tried as an alternative for solving the pressure problem.

67In this method, the sample was also confined over mercury but the volume of sample used was large enough so that the mercury-hydrocarbon interface was kept at room temperature below the furnace when heated to the critical temperature. It was, therfore, not necessary to correct for the partial pressure of mercury. This method is perfectly acceptable for studies on pure compounds but may not give accurate results on mixtures since temperature gradients along the sample may cause concentration gradients to develop, resulting in an error in the critical constant. To use Ambrose technique the experimental tube shown in Fig, 20 was constructed, replacing the tube shown in Fig. 28 in Appendix A, The top of the tube is identical with that shown in Fig, 34, The volume of the middle section is approximately. 2£ times the volume of the top. The two sections are connected by a 2 mm bore capillary which minimized the amount of sample required for the test. The tube was loaded as described in section A, Appendix A and heated by the glass furnace described in section B,Appendix A and shown in Fig, 35*

The method was used to determine the critical constants of n-nonane, 1,2,4-trimethylbenzene, and naphthalene.The results are shown in Table 20 and compared with the values obtained using gallium as the confining liquid. It is to be noted that the agreement between the values determined with gallium and with mercury when the mercury-

68

“i--15 mm

27 mm

43 mm

230 mm

658mm

— 5 mm I.D.

itf- 2 -5 m mirtv

|25mm

|42mmu *76 mm

/ VI.STP 12/30

Fig. 20 - Experimental Tube for Mercury-Hydrocarbon Interface at Room Temperature

TABLE 20

COMPARISON OF THE CRITICAL POINT DETERMINED WITH GALLIUM AND MERCURY WHEN THE MERCURY-HYDROCARBON INTERFACE AT ROOM TEMPERATURE

Gallium Mercury DifferenceCompound Tc(°C) Pc(psia) Tc(°C) Pc(psia) Tc(°C) Pc(psi) -

n-nonane 322.7 332.3 322.7 332.2 o.u 0.11,2,4-trimethyl-benzene

377.4 475.3 377.2 474.2 0.2 1.1

naphthalene 4?6.3 594.3 475.7 589.5 0,6 4.8

7°hydrocarbon interface was held at room temperature is satisfactory, the largest deviation being 0.6 °C for temperature and 4.8 psi for pressure. Therefore, the latter method was chosen for further study of the effect of mercury on the critical constant.

As a basis for correcting the error in critical constant, the critical point of a series of hydrocarbons was determined using mercury as the confining liquid when the mercury-hydrocarbon interface was at the sample temperature and at the room temperature. The hydrocarbons used for this study were selected because of their thermal stability at their critical temperatures. Assuming then that the critical temperature and pressure observed when the mercury-hydrocarbon interface was at the room temperature was the true critical constant of the hydrocarbon, the correction that is to be used to the observed critical constant was calculated. The results are summarized in Table 21. Since Tc is relatively small, no correction for the temperature was attempted. Table 21 indicates that the partial pressure of the mercury is less than the vapor pressure of the mercury at the sample temperature.

In order to obtain a suitable equation for the pressure correction, the values of log^PPj^ were plotted against l/Tc as shown in Fig. 21 and a best straight line was drawn through the points.

TABLE 21

COMPARISON OP THE CRITICAL POINT DETERMINED WITH MERCURY WHEN THE .MERCURY-HYDROCARBON INTERFACE WAS AT ROOM AND SAMPLE TEMPERATURE

Compound

Mercury-Hydrocarbon Interface at Room Temu. Samule Terno. ^T

lj(°c) P^(psia) Tg(°C) Pj(psia) (°C)VP._,hg(psi)

PPnV<p«i7

n-nonane 322.5 334.4 322.6 341.9 -0.1 7.7 7.5n-decane 345.3 307.9 345.3 318.6 0.0 12,0 10.51»3»5-trimethylbenzene 365.5 458,6 365.2 472.1 0.3 17.2 13.51,2,4-trimethylbenzene 377.2 474.2 376.7 490.6 0.5 20.9 16.41,2,3-trimethylbenzene 392.4 499*3 391.7 523.7 0.7 26.8 24.4naphthalene 475.7 589.5 473.4 665.8 2.3 86,1 76.3

Notei ^ T c = T^ - Tg VPHg “ VaPor Pressure of mercury at T^ , and

P P ^ = Pg - P^ = Partial pressure of mercury.The subscripts used here correspond to the notation in Fig. 19.

PARTIAL

PRESSURE

OF Hg

(psia)

7 2

100

10.

loginPPHtr = 5.92822 - 3027*!i

1.6 1 . 81.3 1.5 1.7| x 103 (°K“X)

Fig. 21 - logôPPjjg versus l/T for the Partial Pressure of Mercury Over the Hydrocarbon-Mercury System

73The equation for the pressure correction* therefore, is

3037.61loS10pPHg = 5.92822 - — 5— (18)

where PPjjp. is partial pressure of mercury in psia, and Tcois critical temperature in °K when the mercury-hydrocarbon interface is at the sample temperature. The partial pressure calculated by Eq. (18) should be subtracted from the observed total pressure, instead of the vapor pressure of mercury when the sample temperature is above 320 °C.The experimental results presented in Chapter IV are corrected values using Eq, (18). For the purpose of future reference, however, the uncorrectod data are presented in Appendix D •

C H A P T E R V I I

D I S C U S S I O N O F R E S U L T S

Previous studies ( 1 , 37» 571 67) on binary systems composed of compounds 5 to 9 carbon atoms had shown that the critical locus curves and the excess critical properties v/ere affected in some complex manner by differences in size, structure, and chemical nature of the components. The molecular size is characterized by the molecular weight, the molecular structure is related to the shape of the molecule, and the chemical nature includes aliphatic, aromatic, and naphthenic compounds.

T h e c o n c e p t o f a n e x c e s s p r o p e r t y , w h i c h w a s i n d e p e n

d e n t l y c o n c e i v e d b y H i l d e b r a n d ( 3 9 ) a n d S c a t c h a r d ( 83 ) » c a n

b e e x t e n d e d t o a p p l y t o t h e c r i t i c a l t e m p e r a t u r e a n d

p r e s s u r e o f b i n a r y s y s t e m s . T h e e x c e s s c r i t i c a l p r o p e r t i e s

h a v e p r e v i o u s l y b e e n u s e d b y E t t e r a n d K a y ( 27 ) # L e e ( 5 7 ) »

A b a r a ( 1 ) t P a k ( 67 ) , a n d H i s s o n g ( 3 7 ) .

T h e e x c e s s c r i t i c a l p r o p e r t i e s a r e d e f i n e d a s f o l l o w s *

factual - îdeal + êxcess (19)

w h e r e ip i s t h e c r i t i c a l t e m p e r a t u r e o r p r e s s u r e , a n d

i d e a l d e f i n e d m ° l a l a v e r a g e c r i t i c a l

75properties! i.e.. ^ ideal = and l/»excess isa molecular interaction quantity equal to the difference between the actual and ideal values.

The excess critical properties are useful in studying the trends found in the critical property. Since they are difference quantities, the excess properties magnify the effects of the factors being studied. An increase in the excess critical properties indicate a greater nonideality of a mixture and a greater curvature of the critical locus curve.

It is interesting to find that binary systems with components of higher molecular weight follow the same patterns as found with the lower molecular weight binary systems. The evidence for this is revealed by an examination of the critical temperature and pressure data of a series of binary systems which have been arranged into four groups, each group composed of a common component with members of the same or different homologous series. The P-T critical locus curves, the excess critical temperature, and the excess critical pressure are shown, respectively, in Figs, 22, 23# and 2k. Fig. 25 shows the effect of relative size on the excess properties. For the purpose of meaningful interpretations, other systems that had been previously determined by others are included in these figures.

F r o m a n e x a m i n a t i o n o f F i g s , . 2 2 , 2 3 * 2 k , a n d 2 5 * t h e

f o l l o w i n g t r e n d s a r e t o b e n o t e d i n t h e c r i t i c a l l o c i a n d

t h e e : : c e s s c r i t i c a l p r o p e r t i e s i n s y s t e m s c o n t a i n i n g a

c o m m o n c o m p o n e n t .

A * S y s t e m s w h o s e c o m p o n e n t s b e l o n g t o t h e s a m e h o m o l o g o u s s e r i e s

1 . P - T c r i t i c a l l o c i

a . F i g . 2 2 a » W h e n t h e c o m p o n e n t s o f t h e s y s t e m

a r e o f a b o u t t h e s a m e s i z e ( s a m e m o l e c u l a r w e i g h t ) , t h e

c r i t i c a l l o c u s c u r v e a p p r o a c h e s a s t r a i g h t l i n e ,

k * F i g . 2 2 a i A s t h e r e l a t i v e s i z e i n c r e a s e s

t h e l o c u s c u r v e c h a n g e s t o a c u r v e d l i n e , c o n v e x d o w n w a r d ,

a n d a m a x i m u m p r e s s u r e p o i n t a p p e a r s . W i t h f u r t h e r i n c r e a s e

i n t h e r e l a t i v e s i z e , t h e m a x i m u m p r e s s u r e i n c r e a s e s a n d

m a y a t t a i n a v e r y h i g h v a l u e r e l a t i v e t o t h e c r i t i c a l

p r e s s u r e s o f t h e p u r e c o m p o n e n t s .

2 . E x c e s s t e m n e r a t u r e

a * F i g . 2 3 a i T h e p l o t o f e x c e s s c r i t i c a l t e m p e r

a t u r e v s c o m p o s i t i o n i s n o t n e c e s s a r i l y s y m m e t r i c a l , i n d i

c a t i n g t h a t o n e o f t h e c o m p o n e n t s e x e r t s a g r e a t e r e f f e c t

t h a n t h e o t h e r . T h e m a x i m u m T ° t e n d t o s h i f t t o w a r d t h ee

h i g h e r m o l e p e r c e n t o f m o r e v o l a t i l e c o m p o n e n t .

b . F i g s . 2 5 a a n d b i F o r a c o n s t a n t d i f f e r e n c e

i n m o l e c u l a r w e i g h t , t h e l o w e r t h e m o l e c u l a r

w e i g h t o f t h e c o m p o n e n t s , t h e g r e a t e r t h e m a x i m u m T ® .V

T h i s i s t o b e e x p e c t e d b e c a u s e a s t h e m o l e c u l e b e c o m e s

l a r g e r t h e d i f f e r e n c e b e t w e e n t w o c o n s e c u t i v e m e m b e r s o f

77a h o m o l o g o u s s e r i e s b e c o m e s l e s s i n t e r m s o f t h e i r

m o l e c u l a r s i z e .

c . F i g s . 2 5 a a n d b i A s t h e d i f f e r e n c e i n

m o l e c u l a r w e i g h t s o f t h e c o m p o n e n t i n c r e a s e s , t h e m a x i m u m

T c i n c r e a s e s f a s t e r t h e l o w e r t h e a b s o l u t e m o l e c u l a r e

w e i g h t o f t h e c o m p o n e n t s .

3* E x c e s s p r e s s u r e

F i g s . 2 ^ a a n d 2 5 c a n d d c l e a r l y s h o w t h e s a m e

t r e n d s a s w e r e o b s e r v e d i n e x c e s s c r i t i c a l t e m p e r a t u r e .

B . S y s t e m s w h o s e c o m p o n e n t s b e l o n g t o t h e d i f f e r e n t h o m o l o g o u s s e r i e s

1 . P - T c r i t i c a l l o c i

a . F i g s 2 2 b a n d c i T h e t r e n d s a r e g e n e r a l l y t h e

s a m e a s r e g a r d s s i z e , a l t h o u g h d i f f e r e n c e s i n c h e m i c a l

n a t u r e a n d m o l e c u l a r s t r u c t u r e p l a y s o m e p a r t w h i c h i s n o t

c l e a r l y , d i s c e r n a b l e . B e c a u s e t h e c r i t i c a l t e m p e r a t u r e s o f

n - h e x a n e a n d n - h e p t a n e a r e l o w e r t h a n t h a t o f c y c l o h e x a n e ,

t h e c r i t i c a l l o c i c r o s s o v e r f r o m o n e s i d e o f c y c l o h e x a n e

t o t h e o t h e r a s t h e m o l e c u l a r v / e i g h t o f t h e p a r a f f i n i s

i n c r e a s e d . T h e s a m e r e l a t i o n i s o b s e r v e d i n t h e b e n z e n e -

p a r a f f i n s e r i e s . H o w e v e r , t h i s s e r i e s i s d i f f e r e n t f r o m

t h e c y c l o h e x a n e - p a r a f f i n s e r i e s b e c a u s e t h e c r i t i c a l l o c u s

o f t h e b e n z e n e - n - o c t a n e h a s a m i n i m u m t e m p e r a t u r e p o i n t ,

v / h i c h s u g g e s t s t h e p r e s e n c e o f a c r i t i c a l a z e o t r o p e .

F i g . 2 2 d i n - H e x a n e , c y c l o h e x a n e , a n d b e n z e n e

a r e a p p r o x i m a t e l y o f t h e s a m e s i z e b u t b e l o n g t o c o m p l e t e l y

d i f f e r e n t h o m o l o g o u s s e r i e s . T h e r e f o r e , d i f f e r e n c e s i n

78their loci may be considered to be due, principally, to the differences in their molecular structure and chemical nature. The same is true for o-xylene and ethylbenzene which have the same molecular weight but different molecular structure.

2 , E x c e s s t e m p e r a t u r e

a. Figs. 22b and ci The plots are asymmetricaland show the transition from a minimum T^ (negative) to amaximum tJt (positive) as the difference in the size of the 6components increase.

b. Fig. 22di Maximum T^ are approximately the same when component molecules are of the same size even though the molecular structure or/and chemical nature are different. This indicates that the effect of size is greater than that of structure and chemical nature.

3 . E x c e s s p r e s s u r e

a. Figs. 2^b and ci The plots are highly asymmetric for the systems of cyclohexane and benzene with n-paraffins. As the molecular weight of the paraffin increases, the PQ becomes more negative and then reverses after the n-heptane binary, to become less negative again.As the size difference get larger, the curves show a transition in which a minimum P® and a maximum P® exist together.

Fig. 2^di Systems of cis-Decalin with n-hexane, cyclohexane, and benzene exhibit a maximum

V

(positive). Maximum tend to shift toward the higher mole percent of lower molecular component as observed in other

79binary systems. The maximum P° vaiue is greatest forc *

n-hexane but is almost the same for benzene and cyclohexane. This is to be expected because n-hexane differs from cis-decalin in size, structure, and chemical nature, whereas benzene and cyclohexane differ from it in size but have a similar structure, i.e., ring structure. The difference in chemical nature between benzene and cis- decalin seems to be negligible. The excess critical pressures are practically the same for the physical isomers ethylbenzene and o-xylene.

CRITICAL

PRES

SURE

(psia)

80800

6 0 0

4 0 0

200

D“Cjn-C

n-C,n-Ci

n-C

n-C.

8 0 0

BENZENE

6 0 0

n-Ci4 0 0 n-C

n-Cgn-C.

n-C,

n-Ci200 n-C

BENZENECYCLOHEXANE

Cis-DECALINn-HEXANE

2 2 0 3 0 0 3 8 0 4 6 0 2 2 0 3 0 0 3 8 0 4 6 0

CRITICAL T E M P E R A T U R E (°C)

F i g . 2 2 - P - T C r i t i c a l L o c i o f B i n a r i e s o f D i f f e r e n t H o m o l o g o u s S e r i e s

EXCE

SS

CRIT

ICAL

TE

MPE

RATU

RE

(°C)

81

n-H E X A N E40

20

CYCLOHEXANE

n-C

n-C

n-Cn-C,

n-C,

-B EN ZEN En -C

20

n - C,

n-C

0.2 1.00.6

-c is -DECALIN

CYCLOHEXANEn-C,

BENZENE

ETHYLBENZENE

O-XYLENE

0.2MOLE FRACTION

0.6 1.0

Pig. 23 - Excess Critical Temperature vs. Composition

EXCE

SS

CRITICAL

PRES

SURE

(psi)

CYCLOHEXANE

n-C

n-HEXANE120

8 0

4 0

-cis-DECALINn-

BEN7ENE

tYCLOHEXANE

ETHYLBENZENE _ 3

O-XYLENE

1.00.2 0.6

BENZENE120

8 0

n-Ccn-Ci

- 4 0

1.00.2 0.6

MOLE FRACTION

F i g . 2k - E x c e s s C r i t i c a l P r e s s u r e v s . C o m p o s i t i o n

EXCE

SS

CRIT

ICA

L PR

ESSU

RE

(psi

) EX

CESS

CR

ITIC

AL

TEM

PERA

TURE

(°

C)

83

2 5

0.2 0.6 1.0 0.2 0.6 1.0

1.00.6• 0.2

200

120

1.00.60.2M OLE RACTION OF LOWER MOL: WT. COM PONENT

Fig. 25 - Effect of Relative Size and Absolute Molecular Weight on the Excess Function

CHAPTER VIII

THEORETICAL APPROACHES TO THE CRITICAL PROPERTIES OF MIXTURES

A* Use of the Thermodynamic Conditions at the Critical

1• Fundamental Equations for Binary MixturesThe thermodynamic conditions for the existence of

the critical state of a mixture were originally derived by Gibbs (31) and have since been discussed by others (12,82). The conditions for a binary mixture are that the second and third partial derivatives of the Gibbs free energy with respect to the composition at constant temperature and pressure be zero? that is

State

(20)

(21)

Redlich and Kister (73) expressed the above equations in terms of the fugacity coefficients (f> and (f) 2 of the

Gk

components as

ax.

a2ln( s ^ / <p2 )

dxj

P,T xix2

xx-x2 P,T XjX2

= 0 ( 22)

= 0 (23)

In order to use these relations, it i3 necessary to express them in terms of measureable variables P, V, T, and x. Since this derivation has been given in detail elsewhere (37» 73)» only the final results will be presented here. Namely,

2* Equations of StateIn order to solve Eqs. (2k) and (25) simultane

ously, it is necessary to introduce an equation of state relating the variables P, V, T, and x. Although an equation of state may have been derived by some theoretical considerations, it is by no means rigorous and therefore essentially empirical. After a comparison of several equations of state, Shah and Thodos (8^) concluded that the two-constant Redlich-Kwong equation (74) possessed a combination of advantages in simplicity and the ability to predict reasonably well the PVT behavior. The Redlich- Kwong equation has been used by others (15, 38, ^5, 87) in attempts to calculate the critical properties of binary mixtures. The Redlich-Kwong equation is represented by

RT aP » ----- - — c------- (26)(V-b) TaV(V+b)

Hissong and Kay (38) have shown that the Redlich-Kwong equation was superior to the Dieterici equation (20) for use in the calculation of the critical temperatures and pressures of lower molecular weight hydrocarbon mixtures. Therefore, the Redlich-Kwong equation is chosen for further study for the higher molecular weight hydrocarbon mixtures.

Recently an improved equation of state was proposed by Redlich and Ngo (75). The primary objective of the

87Redlich-Ngo equation was to obtain an improvement in the region around the critical point and at the same time to conserve the good behavior of the Redlich-Kwong equation at high pressures and temperatures# Redlich and Ngo introduced the critical compressibility factor Zc as the third parameter, since the improvement around the critical point was a primary objective as previously mentioned. The Redlich-Ngo equation is represented by

RT(l-L) a(l-G)P ---------— T-------- (2?)

(V-b) T2V(V+b)

where L and G are functions of reduced temperature and volume. At the critical point the two functions L and G become

L - 1 - 3ZC (28)

G = 0 (29)

When Eqs. (28) and (29) are substituted in Eq. (2?), the Redlich-Ngo equation becomes

3Z°RT ap ---------------- (30)(V-b) T£V(V+b)

Hence, Eq. (30) can be used to calculate the critical properties.

88The constants a and b in Eqs, (26) and (30) can be ex

pressed in terms of the critical temperature and pressure of a pure substance by the application of the thermodynamic conditions at the critical point of a pure compoundj namely

*2P( — 2 } = 0 (32)

) T

The values of a and b calculated by Eqs. (3?.) and (32) are for the Redlich-Kwong equation

^2 2 a 5C 1 Ca = 0.4-274-80 --- — = h,93396RT;‘-?b (33)pC c

RTCb = 0.08664-0 ---- (34-)

Pc

and for the Redlich-Ngo equation

(3ZCR)ZT^ 5 , -a = 0.4-274-80------— 2— = 4-.93396(3ZcR)Ti°b (35)pC c

3Z°RTCb = 0.08664-0 ------

Pc(36)

89The application of an equation of state to mixtures

requires a "combination of constants", that is, a rule for computing constants a and b in Eqs, (26) and (30), In the application of these equations of state to mixtures the variation of the constants with composition is represented by the most commonly used equations

where a^, b^, a^, and b are the constants of the respective pure components and a ^ and b ^ are the "interaction parameters" between the molecules of components 1 and 2, The degree to which the calculated critical properties agree with the experimental values depends on the values assigned to these interaction parameters.

The critical compressibility factor Zc for a mixture was assumed to be linear in the mole fractions as suggested by Redlich and Ngoj that is

(37)

(38)

Z° = zjxj + z£ c2 (39)

903. Calculation of the Critical Locus

Since all the parameters in the equations of stateare defined for the binary system, the various partialderivatives in Eqs. (24) and (25) can be expressed in termsof the measureable variables T, V, and x. The expressionsfor these partial derivatives are presented in Appendix E for the Redlich-Kwong and the Redlich-Ngo equations of state# For the sake of the subsequent discussion, these transformed equations will be designated by the following functional notations*

D2GX(T,V) = 0

D3GX(T,V) = 0

where Eqs. (40) and (4l) are equivalent to Eqs. (24) and (25), respectively.

Provided that the values of a^g and b ^ a**fi given , the P-T critical locus curve of the binary system can now be calculated. At any given composition, Eqs. (40) and (4l) are solved simultaneously for the critical temperature and volume, and then the critical pressure is calculated by substituting them into the equation of state.

In solving the two thermodynamic equations (40) and (4l) simultaneously, a modified form of Newton's method for two equations was used by replacing the partial derivatives in Newton's method by the difference quotients because the

(40)

(41)

91n e c e s s a r y p a r t i a l d e r i v a t i v e s c o u l d n o t b e o b t a i n e d a n a l y t i

c a l l y .

S u c c e s s i v e a p p r o x i m a t i o n s a r e g e n e r a t e d f r o m t h e f o l l o w

i n g r e c u r s i o n f o r m u l a s * i . e . ,

f D2GX (T . ,V. ) (D 3 G X ) V-D 3G X (T . ,V. ) (D 2 G X ) V"|

V l = Ti - |_----- 1 ■■■ JdttMiDaGX) ----~ Jf D 3 G X ( T . ,V. ) ( D 2 G X ) qi-D 2G X (T . ,V. ) (D 3G X )qTl

V l - Vi ' [------- J(D3GX,D3GX) $Jw h e r e J ( D 2 G X , D 3 G X ) = J a c o b i a n o f t h e f u n c t i o n s D 2 G X a n d D 3 G X

= ( D 2 G X ) T ( D 3 G X ) V - ( D 3 G X ) T ( D 2 G X ) V (1j4 )

/ a n ? G X \ D 2 G X ( T . , V . ) - D 2 G X ( T . 1 , V . )(D2o x ) T = C a j ) v ~ ^ — — — " (1*5 )

(D2GX )y = (*3DyGX ) T

D 2 G X ( T i , V i ) - D 2 G X ( T i _ 1 , V i )y

T i - T i - 1

D 2 G X ( T i , V i ) - D 2 G X ( T i , V i _ 1 )

V .l

i < H* t h*

D 3 G X ( T i , V i ) - D 3 G X ( T i - 1 , V i )

T i- T . i

l - l

D 3 G X ( T i , V i ) - D 3 G X ( T i f V i - : l )

0*6)

(D3g x )t = ^ 2 S i ) v » ------1 ^ _ T.---- 1 1 1 (<*7)

✓ S n-iny U JGa \ I. , V . J — Dj UX 11. , V . ~ )(D3GX)V — V7 - V, , "

a n d t h e f u n c t i o n s D 2 G X a n d D 3 G X a r e e v a l u a t e d a t t h e i n d i

c a t e d p o i n t , r e s p e c t i v e l y .

92I n o r d e r t o s t a r t t h e i t e r a t i o n , t w o i n i t i a l a p p r o x i

m a t i o n s m u s t b e m a d e j i . e . , a n d ^ i - i ’ ^ i - l ^ *

G i v e n a n i n i t i a l a p p r o x i m a t i o n o f t e m p e r a t u r e , t h e

c o r r e s p o n d i n g i n i t i a l v a l u e o f t h e v o l u m e V ^ , w a s e s t i m a t e d

f r o m t h e e q u a t i o n

Z C R T C

w h e r e V ° =* c r i t i c a l v o l u m e ( c c / g - m o l e ) ,

T c = c r i t i c a l t e m p e r a t u r e ( ° K ) ,

P c = c r i t i c a l p r e s s u r e ( p s i a ) fR - g a s c o n s t a n t , a n d

Z c = c r i t i c a l c o m p r e s s i b i l i t y f a c t o r ,

T h e n , T . 1 a n d V . - w e r e o b t a i n e d b y m u l t i p l y i n g T . a n d V .J. ** 1 X I X Xb y c o n s t a n t s . T h e r e a f t e r , t h e l a s t t w o a p p r o x i m a t i o n s w e r e

u s e d t o o b t a i n t h e n e x t a p p r o x i m a t i o n ,

H i s s o n g (37) d e v e l o p e d a c o m p u t e r p r o g r a m t o s o l v e

E q s . (4o) a n d (4l) s i m u l t a n e o u s l y u s i n g t h e r e c u r s i o n

f o r m u l a s s h o w n i n E q s . (42) a n d (43) f o r t h e R e d l i c h - K w o n g

e q u a t i o n o f s t a t e . T h e c o m p u t e r p r o g r a m w a s m o d i f i e d ,

w h e r e v e r n e c e s s a r y , i n o r d e r t o u s e i t f o r t h e R e d l i c h - N g o

e q u a t i o n o f s t a t e . T h e e r r o r - c r i t e r i a t o s t o p t h e i t e r a t i o n

w a s a l s o c h a n g e d f r o m * h e r e l a t i v e - e r r o r t e s t s t o t h e a b s o -

l u t e - e r r o r t e s t s i n o r d e r t o r e d u c e t h e n u m b e r o f i t e r a t i o n s ,

a n d h e n c e t h e c o m p u t a t i o n t i m e . T h a t i s ,

93

Ti|< xl0“3

to K + i - ^ K ^ 10"3

These changes do not have any effect on the desired accuracy of the results* The method just described furnishes a completely analytical solution of the thermodynamic equations (40) and (41), The entire calculation was carried out on an IBM 360/75 digital computer*

As pointed out earlier, the agreement between the experimental and calculated critical properties depends on the values assigned to the interaction parameters* i*e., a^2 and’b^2* Hissong and Kay (38) investigated two sets of combining rules which could be obtained from the values of a and b for the pure components* Namely,

Set Ial2 = i(&1 + a2)bi2 = ifbj + b2)

Set II (40)

The results showed that, in general. Set II gave a considerably better prediction of the critical properties

than Set I* The results also showed, however, that the combining rules to calculate a^2 and ^ 2 from 'tlle constants a and b of the pure component might work satisfactorily for systems in which the components do not differ greatly, but not for the highly non-ideal systems.

Since the critical properties of a mixture are ultimately determined by the intermolecular forces existing in the solution, it is desirable to considerthe interaction parameters a^2 and as reâêd those forces. However, no satisfactory combining rules for a ^ and bj2 have been developed so far in terms of these forces.

The interaction parameters a^2 and b^2 can also be determined directly by fitting an equation of state to experimental PVT data for a mixture (78,91). Hissong adopted this method to obtain the best values of a^2 and b12 by fitting the available critical data on a binary system. This method eliminated the weakness of the existing combining rules by assuring that the best possible values of interaction parameters for the equation of state would be obtained. As Hissong pointed out, this approach provides a basis for developing a correlational method.That is, the best values of a^2 and bJ2 can be correlated in terms of the factors upon which the critical properties of mixtures depend 1 that is, the size, structure, and chemical nature of the molecules composing the mixture.From these correlations, the interaction parameters can

95be predicted for systems of interest on which no data are available.

The best values of and ^ 2 were calculated by minimizing the root-mean-squares of the residuals which was equivalent to minimizing the sum of squares of the residuals. The residual or deviation is defined as the difference between the experimental and calculated critical properties. The objective function (OF) was taken as a linear combination of the root-mean-square (hereafter abbreviated RMS) of the pressure and temperature deviations, namely,

OF - PD + fl(TD (50)

where P^ is the RMS pressure deviation in psi, T^ is the RMS temperature deviation in °C, and of is a weighting factor which is to balance the pressure ana temperature deviation. Seven different values of Of were tried on three binary systems, The results were as follows*

of n"c6 " 3 1 0 n-C^ - ciS'-Decalin Cyclo-C^ - n

PD td PD td PD td

1 7.7 5.9 6.4 4.9 4.2 2.82 8.4 5.^ 9.5 2.6 4.6 2-53 9.1 5.1 10.6 2.2 4.9 2.44 10.0 4.9 ll-3 1.9 5.3 2.35 11.1 4.6 12.0 1.8 5.7 2.26 13.7 4.2 13.1 1.6 6.2 2.17 15.1 3.9 13.9 1.5 6.7 2.0

These results indicate that as Of is increased, the

9 6increases but the T^ decreases, and the values of o( becomes relatively insensitive to PD and TD when o( is larger than

Therefore, the value of 0( = 4 was selected for this work. Hissong also used 0( = 4 for his work.

Each evaluation of the objective function (OF) involved calculating the critical properties by solving the thermodynamic equations (^0) and (4l) simultaneously over the entire composition range, comparing these values with the experimental data by calculating and T^, and then combining these two deviations according to Eq. (50)*Therefore, the optimization of a ^ ar*d "îs approachwhich is a non-linear optimization problem, requires a large amount of computer time. A comparison of seven available optimization routines was, therefore, made in order to select the most efficient one for this particular problem.Two types of optimization routines were tested* that is,

a. The method of gradient, also called the method of sterpest descent or ascent. In this method, the minimum of the objective function is searched by evaluating the gradient of the optimization criterion with respect to each parameter at each point during the search. This information was used, then, to determine the direction of the next move,

b. The univariate, pattern search, or direct search method. In this method, the minimum of the objective function is seached by varying one parameter at a time, preserving those changes which improve the optimization

97criterion, and incorporating strategies for patterned approach to the optimum.

The Chemical Engineering Library Program prepared by Hershey (36) contains three types of non-linear optimization subroutines. The first two types, the OPT series and the GRAD series are used for this comparison. The OPT series, based on the pattern search method, consist of

OPT 1« The Hooke and Jeeves pattern search (*H), slightly modified to improve the search pattern#

OPT 2t Powell's method (71) that does not requir a gradient evaluation, and

OPT 3* Rosenbrock's rotating coordinate search (80) with modifications.The GRAD series , based on the gradient method, consist of

GRAD li The Davidson's method of search (18),GRAD 21 The Fletcher-Powell modification (28) of

Davidson's method, andGRAD 3t A copy of GRAD 2, with the conjugate gradient

algorithm of Fletcher and Reeves (29) replacing the Fletcher- Powell method of the first step of each iteration.The last optimization routine in the comparison was developed by Williamson (90) of this laboratory, Williamson*s program was taken from the sample program in the article by Hooke and Jeeves with very few alterations, Williamson stated that the major difference between Hooke and Jeeves program and his program was that individual step sizes were

98used for each parameter, so that each parameter was changed by an appropriate amount at each iteration.

In this comparison, the initial guesses of the parameters and the initial step sizes to be used in the pattern search were identical for all the optimization routines. The GRAD series did not require the initial step size specification. The results of optimization on three cases are summarized in Table 22 , It clearly shows that all routines reached practically the same optimum criterion and Williamson's direct search routine appears to be the most efficient one for the optimization of the interaction parameters a^2 and b^2*

Since it is usually more convenient to use dimension- less quantities for a correlation, the reduced interaction parameters of a^2 and b^2 were used in the following form as defined by Hissong

A12SR = ----— ---- (51)^(a1 + a2)

B12SR = ----— ---- (52)+ t>2)

In order to extend the range of application of the Hissong-Kay method, the optimization of the reduced inter action parameters was also performed on the critical data for 65 additional hydrocarbon binary systems which have

99

TABLE 22

COMPARISON OF OPTIMIZATION ROUTINES

Optimization Optimum No. of Funct. ExecutionRoutine Case Criterion Evaluation Time(sec)OPT 1 A 1.68 108 14.2

B 7.63 111 16.9C 2.48 106 28.8

325 59.9OPT 2 A 1.68 125 16.6

B 7.63 178 27.4C 2.48 169 42.9

■"4'72 86.9OPT 3 A 1.68 193 26.2

B 7.63 173 26.9C 2.70 . V^•63

GRAD 1 A 1.68 60 16.8B 7.63 69 19.6C 2.48 2? 9.4

156 45.8GRAD 2 A 1.68 111 19.5B 7.63 75 22.0

C 2.48 5123728.469.9

GRAD 3 A 1.68 114 28.7B — -----C 2.15 87201 62.2

Williamson A 1.68 57 7.2B 7.63 74 10.7C 2.75 46

17714. 5 32.4

100been studied by other investigators in this laboratory.Table 23 shows a classification of the binary systems according to the chemical families of their componentsj i.e., aliphatics, aromatics, and naphthenics, The system numbers and component names for a total of 79 binary systems are shown in Table 2*K The system numbers are used to facilitate system identification in the subsequent discussion.

The results of the optimization for the 79 systems using the Redlich-Kwong and the Redlich-Ngo equations are shown in Table 25 and 26, respectively. Note that values for some systems are missing. For these systems no optimum values of A123R and B12SR could be obtained because of non-convergence.

Table 27 presents the statistical deviation data on the critical loci calculated using the optimum values of the interaction parameters for the Redlich-Kwong and Redlich- Ngo equations of state. Table 27 shows that the equation of state method can predict the critical temperatures and critical pressures of even highly non-ideal systems quite precisely if the proper values of the interaction parameters are used. The large deviations of the extremely non-ideal systems are considered to be due not to the weakness of the equation of state method but to the limitation of the Redlich-Kwong and Redlich-Ngo equations. Therefore, it is highly desirable that a better equation of state be

101developed.

The point by point comparison between the experimental and calculated critical temperatures and critical pressures for the systems studied in this work is given in Table 35 , Appendix D *

102

TABLE 23

CLASSIFICATION OF BINARY SYSTEMS

Number of Systems System This Work Contributed Total

Aliphatic - Aliphatic 5 29 3Âliphatic - Aromatic 2 9 11Aliphatic - Naphthenic 3 11 1Âromatic - Aromatic 6 6Aromatic - Naphthenic 3 k 7Naphthenic-Naphthenic 1 6 J L

Total Ik 65 79

103TABLE 2k

TOTAL BINARY SYSTEMS STUDIED

System No.(NSYS) System Ref.1 Ethane(A) - n-Heptane(B) k82 Propane(A) - n-Butane(B) 93 - n-Pentane(B) 66k - n-Hexane(B) 705 - n-Heptane(B) 6k6 - n-Octane(B) 307 - 2-Methylpentane(B) 168 - 3-Methylpentane(B) 169 - 2,3-Dimethylbutane(E) 16

10 n-Butane(A) - n-Pentane(B) 1911 - n-Hexane(B) . 1912 - n-Heptane(B) 1913 - n-Octane(B) 19lk n-Pentane(A) - n-Noxiane(B) 3715 n-Hexane(A) - n-Heptane(B) 5716 - n-Octane(B) 5717 - n-Decane(B)18 - n-Tridecane(B)19 • n-Tetradecane(B)20 - cis-Decalin(B)21 n-Nonane(A) - n-Tridecane(B)22 n-Decane(A) - n-Dodecane(B)23 Benzene(A) - Ethane(B) 512k - n-Hexane(B) 5725 - n-Heptane(B) 5726 - n-Octane(B) 5727 - n-Nonane(B) 3728 - n-Decane(B)29 - n-Tridecane(B)30 - Cyclopentane(B) 3731 - Cyclohexane(B) 3732 - Methylcyclopentane(B) 3733 - Methylcyclohexane(B) 373k - Toluene(B) kz

TABLE 24 (CONT'D)104

System No.(NSYS) System Ref.35 Benzene(A) - o-Xylene(E) 4236 - Ethylbenzene(B) 4237 - cis-Decalin(B)38 Ethylbenzene(A) - n-Pentane(B) 3739 - n-Hexane(B) 3740 - n-Heptane(B) 374l - n-Octane(B) 3742 - Toluene(B) 4243 - o-Xylene(B) 4244 - cis-Decalin(B)45 o-Xylene(A) - cis-Decalin(B)46 - Toluene(B) 4247 Cyclopentane(A) - n-Pentane(B) 3748 - n-Hexane(B) 3749 - n-Heptane(B) 3750 - n-Octane(B) 3751 - n-Nonane(B) 3752 - Cyclohexane(B) 3753 - LTethylcyclopentane (B) 3754 - Methylcyclohexane(3) 3755 Cyclohexane(A) - Ethane(B) 5056 - n-Hexane(B) 3757 - n-Heptane(B) 3758 - n-Octane(B) 3759 - n-Honane(B) 376o - n-Decane(E)6l - n-Tridecane(B)62 - Kethylcyclohexane(B) 3763 - cis-Decalin(B)64 Methylcyclopentane(A) - n-Hexane(B) 37

- Cyclohexane(B) 3766 - Methylcyclohexane(B) 3767 2,2-Dimethylbutane(A)

- 2,2-Dimethylpentane(B) 6768 - 2 ,2-Dimethylhexane(B) 6769 - 2,2-Dimethylheptane(B) 6?

TABLE 2*f (CONT’D)105

System Ho. (NSYS) System Ref.70 2,2-Dimethylpentane(A)

- 2,2-Dimethylhexane(B) 6771 - 2,2-Dimethylheptane(B) 6772 2,2-Dimethylhexane(A )

- 2,2-DimethyIheptane(B) 6773 2-Methylpentane(A) - 2-Methylhexane(3) 17^ - 2-MethyIheptane(B) 175 - 2-Methyloctane(B) 176 2-Methylhexane(A) - 2-Methylheptane(B) 177 - 2-Methyloctane(B) 178 2-Methylheptane(A) - 2-Methyloctane(B) 180 n-Heptane(A) - n-Octane(B) 57

“ 106T A B L E 2 5

_ _ _ _ _ _ _ _ _ n P T J M U M _ I N T E R A C J I Q N _ P A R A M E T £ R S _ F Q R _ _ _ _ _ _ _R E D L I C H - K W O N G E O U A T I H M O F S T A T E

N S Y S A 1 2 S R B 1 2 S R 1_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 5 6 8 2 2 8 6 6 _ _ _ _ _ _ _ _ _ 0 . 8 6 2 4 7 9 5 12 0 . 9 6 1 6 8 7 8 0 0 . 9 8 8 1 5 3 8 73 0 . 8 6 1 3 9 3 8 1 0 . 9 4 2 7 5 5 1 0* 0 . 8 0 0 7 7 8 6 3 0 . 9 2 1 4 9 4 0 75 0 . 7 2 2 2 7 4 0 1 0 . 8 9 4 4 9 9 4 86 0 . 6 5 6 5 2 5 5 5 0 . 8 6 3 1 6 4 4 8 7_ _ _ _ _ _ _ _ _ _ _ _ _ _ 0 . 8 0 4 7 9 9 6 8 _ _ _ _ _ _ _ _ _ _ _ _ _ 0_. 9 2 2 4 9 4 1 78 0 . 7 9 6 6 6 8 5 3 0 . 9 1 9 7 9 1 8 29 0 . 8 1 5 3 6 2 2 2 0 . 9 3 2 6 6 7 4 3

1 0 0 . 9 6 5 9 9 5 8 5 0 . 9 8 2 2 1 3 5 01 1 0 . 9 1 2 9 4 3 4 8 0 . 9 5 8 3 3 6 4 71 2 0 . 8 2 1 6 4 6 3 9 0 . 9 1 1 0 1 8 6 1

1.3 __ _ _ 0 . 7 6 8 9 9 8 2 7 8 9 0 9 4 7 1.0..1 4 0 . 8 4 9 0 5 7 3 8 0 . 9 1 5 0 7 5 9 01 5 0 . 9 8 1 4 3 1 9 6 0 . 9 8 9 1 3 9 8 01 6 0 . 9 5 2 7 3 8 5 2 0 . 9 7 2 6 8 5 8 11 7 0 . 8 4 3 2 1 4 0 4 0 . 9 0 7 9 2 6 9 21 8 0 . 7 1 5 6 6 4 0 9 0 . 8 3 7 4 7 3 8 2

1 9 ___ __ ___ __ 0 . 6 5 8 4 5 2 2 1 _ _ 0 . 3 4 5 6 5 9 9 72 0 0 . 8 1 9 7 7 7 7 9 0 . 9 1 3 4 1 4 9 62 1 0 . 8 P 9 1 2 2 3 1 0 . 9 1 2 4 8 ^ 2 92 2 0 . 9 6 8 7 8 1 1 1 0 . 9 7 9 2 8 3 1 52 3 0 . 6 7 0 3 9 8 9 1 0 . 8 6 1 7 8 5 5 92 42 5 0 . 9 5 5 5 9 9 9 0 0 . 9 7 6 5 1 3 5 62 6 0 . 9 2 6 0 9 2 4 5 0 . 9 6 1 6 0 5 9 12 7 0 . 8 9 2 2 1 4 7 8 0 . 9 4 3 0 6 7 0 12 8 0 . 8 3 4 2 8 3 3 0 0 . 9 0 5 9 8 6 1 92 9 0 . 6 9 4 2 0 5 2 8 0 . 8 1 9 3 9 3 8 13 0 0 . 9 8 1 7 1 5 9 8 0 . 9 9 8 6 7 9 8 2

_ 3 1__ _ _ _ _ __ ____ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _3 23 3 0 . 9 6 2 4 1 0 0 9 0 . 9 8 9 4 3 8 3 53 4 0 . 9 8 2 5 4 6 3 1 0 . 9 9 1 2 4 3 6 03 5 0 . 9 4 3 3 6 8 6 1 0 . 9 7 2 4 6 0 5 73 6 0 . 9 4 6 8 2 6 3 4 0 . 9 7 1 4 6 2 6 1

_ 3 7 0 . 7 9 9 0 0 6 5 2 0 . 9 1 0 5 4 0 1 63 8 0 . 8 9 4 0 4 3 5 1 ' 0 . 9 4 9 3 6 5 7 43 9 0 . 9 4 4 9 0 8 3 2 0 . 9 6 9 0 6 2 3 34 0 0 . 9 8 7 0 0 2 1 3 0 . 9 9 5 3 2 3 3 0

107T A B L E 2 5 ( C O M T ' D )

N S Y S _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ A 1 2 S R _____ B 1 2 S R4 14 2 0 . 9 8 4 7 8 9 9 7 0 . 9 8 7 5 7 4 9 34 34 4 0 . 8 8 0 8 9 8 7 7 0 . 9 2 2 3 1 2 9 74 5 0 . 8 9 1 4 3 9 8 0 0 . 9 2 7 7 3 2 6 54 6 “ o . 9 8 2 3 7 7 4 1 ' 0 . 9 8 9 6 9 9 9 64 74 8 0 . 9 8 7 4 3 0 4 5 0 . 9 8 9 8 7 1 0 84 9 0 . 9 4 3 0 7 2 2 6 0 . 9 6 5 8 7 1 5 15 0 0 . 9 2 0 8 3 9 6 1 0 . 9 6 1 6 6 2 4 15 1 _ _ 0 . 8 4 5 8 4 7 8 5 _ 0 . 9 1 2 1 8 4 7 25 2 . . . . .. . . . . . . . . . . . 0 . 9 8 1 5 6 0 0 5 0 . 9 9 0 0 4 1 ] 45 3 0 . 9 8 2 1 7 9 7 0 0 . 9 8 8 7 4 9 8 05 4 0 . 9 4 8 8 4 3 9 0 0 . 9 7 4 9 6 5 3 95 5 0 . 8 4 0 1 5 6 2 6 0 . 9 2 8 0 1 9 8 25 65 7 0 . 9 4 8 5 9 3 6 8 0 . 9 4 9 9 9 9 9 95 8” ’ . . . . ” 0 . 9 5 6 3 3 4 8 9 0 . 9 6 8 7 5 3 4 65 9 0 . 9 2 7 6 6 1 0 0 0 . 9 5 4 6 4 7 4 86 0 0 . 8 8 8 2 4 9 1 0 0 . 9 3 3 0 1 0 2 86 1 0 . 7 4 3 4 5 7 2 6 0 . 8 4 5 5 1 8 3 56 2 0 • 9 9 7 3 6 8 Q 7 1 . 0 0 2 2 2 1 1 16 3_ _ _ _ _ _ _ _ 0 . 8 4 1 4 1 5 1 1 __ . 0 . 9 2 4 9 6 5 6 2 .64 " .....6 56 6 0 . 9 8 0 0 7 5 7 2 0 . 9 8 8 1 3 1 1 16 7 0 . 9 8 0 8 9 3 6 7 0 . 9 8 7 8 0 5 5 56 8 0 . 9 5 0 4 1 2 8 1 0 . 9 7 i 0 9 2 8 8

_ j 6 9 __ 0 . 9 1 2 5 7 7 5 7 0 . 9 5 1 1 4 8 0 37 0 ’ 0 . 9 8 5 9 1 2 0 2 0 . 9 9 1 5 3 0 1 27 1 0 . 9 6 1 5 2 6 5 1 0 . 9 7 9 6 2 3 6 27 2 0 . 9 8 8 6 8 1 7 9 0 . 9 9 2 5 1 4 6 17 3 0 . 9 8 2 3 5 7 2 0 0 . 9 8 5 8 2 9 0 07 4 0 . 9 1 5 8 1 1 1 2 0 . 9 3 4 9 7 5 8 07 5 0 . 9 1 6 4 7 5 0 6 0 . 9 4 1 8 7 3 9 17 6 ” " " O'. 9 8 7 5 5 5 9 8 ” 0 . ' 9 8 6 1 6 4 2 17 7 0 . 9 7 7 3 8 3 7 9 0 . 9 7 6 2 8 8 6 87 8 0 . 9 9 2 1 6 0 5 0 0 . 9 8 7 6 9 0 7 58 0 0 . 9 8 5 8 6 0 8 8 0 . 9 9 0 1 1 2 4 2

108

O P T I M U M I N T E R A C T I O N P A R A M E T E R S F O R R E D L I C H - N G O E Q U A T I O N O F S T A T E

T A B L E 2.6

N S Y S _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ A 1 2 S R B 1 2 S R12 0 . 9 5 5 7 5 4 8 2 0 . 9 6 6 2 2 4 4 33 0 . 8 4 7 0 1 6 6 3 0 . 8 6 2 4 7 7 6 04 0 . 7 7 9 0 6 7 4 0 0 . 8 1 8 3 6 8 2 0 5_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 0 . 6 9 5 5 2 0 8 8 _ _ _ _ _ _ _ _ 0 . 7 6 6 6 4 5 4 96 " o . 6 6 3 1 0 1 0 2 " ~0. 8 6 2 1 0 9 9 0

. 7 . . . . . . . . 0 . 7 2 1 0 0 4 9 6 0 . 8 1 9 2 7 7 9 48 0 . 7 7 1 3 2 8 5 7 0 . 8 4 5 7 5 5 8 29 0 . 7 9 2 0 6 3 5 3 0 . 8 4 9 0 1 1 4 8

1 0 0 . 9 5 3 7 4 1 8 5 0 . 9 4 9 6 5 0 5 9__11_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 0 . 9 0 4 0 9 0 8 8 _ _ _ _ _ 0 . 9 1 6 _ 9 8 7 4 8

1 2 0 . 7 9 7 4 3 1 0 5 0 . 8 3 8 8 1 6 8 81 3 0 . 7 4 2 1 6 9 7 4 0 . 7 8 9 2 1 9 9 81 4 0 . 8 3 0 2 6 3 6 1 0 . 8 4 0 2 3 1 1 8

. 1 5 0 . 9 8 7 9 4 4 7 8 0 . 9 9 2 4 7 7 0 61 6 0 . 9 4 7 0 6 0 8 8 0 . 9 5 3 8 0 2 7 6

__1_7_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 0 . 8 2 6 0 2 6 8 6 _ _ _ _ _ _ _ _ _ 0 . 0 3 1 3 0 6 4 01 8 0 . 6 7 7 8 2 2 2 9 " o ' . 6 8 4 7 8 2 7 41 9 ' 0 . 5 6 9 7 5 5 2 6 0 . 5 9 2 4 1 9 9 22 0 0 . 7 8 2 8 9 0 5 6 0 . 8 6 6 1 2 5 0 521 222 3_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 0 . 6 6 0 1 7 1 0 9 _ _ _ _ _ 0 . 8 1 7 5 3 3 6 12 4 *2 5 0 . 9 5 7 0 9 9 8 5 0 . 9 7 6 5 1 3 5 62 6 0 . 9 1 2 5 0 7 7 7 0 . 9 2 0 1 5 6 0 02 7 0 . 8 9 7 6 5 3 5 8 0 . 8 9 2 0 7 1 3 12 8 0 . 8 5 8 5 9 2 6 3 0 . 8 5 8 7 1 2 8 52 9 _ _ _ _ _ _ _ _ ,__ 0 . 7 1 6 8 8 1 4 5 _ _ _ _ _ _ _ _ _ _ 0 . 7 1 0 1 3 5 1 03 0 0 . 9 9 0 7 6 9 9 8 0 . 9 9 0 7 9 9 9 63 13 2 ' . . . . . . . . . . .3 3 0 . 9 6 0 4 8 7 3 7 0 . 9 8 4 6 7 5 1 73 4 0 . 9 8 9 4 6 6 1 3 0 . 9 8 9 9 3 3 6 1

_3_5__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 0 . 9 3 9 5 6 4 3 5 _ _ _ _ _ _ _ _ _ 0 . 9 4 9 _ 1 3 9 0 6 _3 6 “ 0 . 9 4 5 9 8 9 9 7 “ ‘6'.95 2 9 0 9 9 43 7 0 . 7 5 3 8 1 1 7 3 0 . 8 7 1 3 9 9 8 83 8 .... ' 0 . 8 6 8 4 8 0 2 1 0 . 9 1 4 1 5 6 0 83 9 0 . 9 5 1 3 7 6 8 0 0 . 9 6 8 3 7 1 6 94 0 0 . 9 8 0 7 4 9 6 2 0 . 9 9 6 0 4 9 8 2

T A B L E 26 ( C O N T • D )

M S Y S A 1 2 S R B 1 2 S R4 14 3 . . . . . .

_ 4 2 _ _ _ _ _ _ _ _ _ _ _ _ _ __ 0 . 9 8 4 9 8 0 2 9 0 . 9 8 7 5 7 4 8 24 4 " 0 . 8 7 6 2 1 3 1 9 " 0. ' 9 2 1 6 2 2 1 64 5 0 . 8 7 5 0 4 5 3 0 0 . 9 3 5 6 9 5 1 14 6 0 . 9 8 0 1 7 8 7 1 0 . 9 8 5 2 4 5 5 94 7 1 . 0 0 5 3 8 1 5 8 1 . 0 0 3 5 1 1 4 34 84 9 0 . 9 4 3 0 7 2 2 6 0 . 9 6 4 3 7 1 5 05 0 ' 6 . 8 9 8 7 8 6 7 8 “ 0 . ' 8 9 8 2 7 6 2 15 1 0 . 8 5 9 7 3 9 0 1 0 . 8 4 3 4 3 1 8 95 2 0 . 9 8 3 5 0 5 1 3 0 . 9 8 6 3 8 3 4 45 3 0 . 9 8 0 6 3 2 0 7 0 . 9 8 3 4 5 2 2 05 4 0 . 9 4 4 7 0 6 4 4 0 . 9 5 4 3 5 7 6 85 5 0 . 8 2 9 9 1 2 0 1 0 . 9 2 3 8 0 2 2 05 6 " " 1 . 0 0 2 7 5 6 1 2 " " ™ “ l . 0 0 T l ' 4 2 5 05 7 5 0 5 9

' 6 0 0 . 9 0 6 0 1 1 6 4 0 . 8 7 7 0 9 3 2 66 1 0 . 7 6 4 7 7 2 7 1 0 . 7 3 2 5 5 4 2 0

~ 6 2 ~ “ ' 0 . 9 9 8 9 7 1 1 0 ' ‘“ ''0,9 9 9 9 2 3 1 76 3 0 . 8 1 7 7 2 8 3 4 0 . 8 6 8 9 2 4 2 06 46 56 6 0 . 9 7 8 2 2 8 3 3 0 . 9 8 1 2 3 7 6 5

_ 6 7 _ _ _ _ _ _ _ _ _ _ _ _ _ _ 0 . 9 7 9 9 7 2 6 0 _ _ 0 . 9 8 1 0 7 2 2 56 8 " 0 . 9 4 5 8 9 6 6 3 ""* '* " 0 . 9 4 8 8 1 4 2 1 "6 9 0 . 9 0 9 1 5 4 4 2 0 . 8 9 4 3 2 2 9 37 0 0 . 9 8 6 2 6 4 5 9 0 . 9 8 8 1 0 0 5 97 1 0 . 9 4 2 7 6 8 2 8 0 . 9 3 1 0 9 6 1 47 27 3 0 . 9 8 2 0 5 4 8 9 0 . 9 7 8 3 5 5 7 77 4 . . . . . . . . . . . O'. 9 0 7 9 9 9 5 8 ' 0 . 9 1 2 7 0 9 4 77 57 6 0 . 9 8 3 6 0 3 3 6 0 . 9 8 1 4 9 9 9 77 7

' 7 8 . . . . .8 0 0 . 9 8 5 1 7 4 4 8 0 . 9 8 5 2 7 0 4 4

110

T A 3 L E 2 7

S T A T I S T I C A L D E V I A T I O N D A T A D M T H E C R I T I C A L L D C I C A L C U L A T E D U S I N G T H E O P T I M U M I N T E R A C T I O N P A R A M E T E R S F O R T H E

R E D L I CHI K W O N G I R K O P T M ) A N D R E D L I C H - M G O ( R M O P T M )E O U A T I O N S O F S T A T E

N S Y S P R E S S U R E D E V . ( P S I ) T E M P E R A T U R E D E V . ( C)A V A B B I A S R M S A V A B B I A S R M S

1 R K O P T M 2 3 . 3 2 3 . 3 3 2 . 5 ' 2 . 8 - 2 . 0 3 . 81 R N O P T M2 R K O P T M 1 . 1 0 . 1 1 . 2 0 . 1 - 0 . 1 0 . 22 R N O P T M 1 . 1 0 . 0 1 . 2 0 . 2 - 0 . 1 0 . 23 R K O P T M 2 . 2 1. 1 2 . 9 1 . 0 - 0 . 5 1 . 13 R N O P T M 1 .7 1 . 2 2 . 5 0 . 9 - 0 . 3 1 . 04 R K O P T M 3 . 1 2 . 1 4 . 7 1. 5 - 1 . 2 1 . 74 R N O P T M 3 . 2 2 . 8 5 . 6 1 . 5 - 0 . 8 1 . 65 R K O P T M P .3 8 . 2 1 2 . 8 3 . 5 - 2 . 5 3 . 75 R N O P T M 1 0 . 4 9 . 6 1 5 . 1 3 . 2 - 1 . 7 3 . 36 R K O P T M 1 6 . 4 1 4 . 8 2 0 . 3 5 . 5 - 3 . 4 6 . 06 R N O P T M 7 5 . 9 7 5 . 9 8 7 . 4 1 2 . 7 1 2 . 7 1 5 . 37 R K O P T M 2 . 9 2 . 7 4 . 2 1 . 6 - 1 . 4 2 . 17 R N O P T M 5 . 4 - 5 . 2 7 . 0 2 . 7 2 . 7 3 . 58 R K O P T M 4 . 2 2 . 8 5 . 0 1 . 8 - 1 . 4 2 . 18 R H O P T M 5 . 3 3 . 5 6 . 0 1 . 8 - 1 . 2 2 . 19 R K O P T M 4 . 9 4 . 1 6 . 0 1 . 3 - 1 . 1 1 . 69 R M O P T M 5 . 6 4 . 8 7. 1 1 . 4 - 0 . 8 1 . 5

1 0 R K O P T M 0 . 9 - 0 . 2 0 . 9 0 . 1 0 . 0 0 . 11 0 R N O P T M 3 . 9 - 3 . 9 4 . 0 0 . 2 - 0 . 2 0 . 31 1 R K O P T M 1 . 4 0 . 8 1 . 8 0 . 6 - 0 . 3 0 . 711 R N O P T M 1 . 3 0 . 8 1 . 7 0 . 6 - 0 . 4 0 . 71 2 R K O P T M 3 . 8 3 . 7 6 . 3 1 . 9 - 1 . 1 2 . 11 2 R N O P T M 3 . 7 3 . 3 6 . 1 1 . 8 - 0 . 8 1 .9

Ill

T A B L E 2 7 ( C O N T ' D )

N S Y S P R E S S U R E D E V . ( P S I ) T E M P E R A T U R E D E V . (C)A V A B B I A S R M S A V A B B I A S R M S

1 3 R K O P T M 4 . 8 __ 4 . 8 _ _ 7 . 3 _ 2 . 6 _ _ _ - 1 . 6 _ _ _ __ 2_.7 _1 3 R N O P T M 5 . 1 4 . 8 7 . 6 2 . 3 - 1 . 1 2 . 51 4 R K O P T M 2 . 5 2 . 1 3 . 7 0 . 8 - 0 . 4 1 . 01 4 R N O P T M 3 . 1 2 . 4 4 . 5 1 . 0 - 0 . 3 1 . 21 5 R K O P T M 1 . 2 - 1 . 2 1 . 2 „ 0 . 1 0 . 1 _ _ _ _ 0 . 2 _ _

" 1 5 ” " R N O P T M 0 . 1 - 0 . 1 0 . 2 0 . 1 - 0 . 0 6 . 11 6 R K O P T M 0 . 3 0 . 1 0 . 4 0 . 1 - 0 . 0 0 . 11 6 R N O P T M 0 . 3 0 . 2 0 . 4 0 . 1 - 0 . 0 0 . 11 7 R K O P T M 2 . 8 2 . 4 4 . 1 _ 1 . 5 _ “ 0 . 8 _ 1 . 7 _

’ ’l 7 R N O P T M ’ 2 . 0 * ’ 1 . 2 ' 2 . 9 * " 1 . 2 - 0 . 5 1 . 31 8 R K O P T M 8 . 2 8 . 2 1 0 . 0 4 . 5 - 2 . 3 4 . 91 8 R N O P T M 4 . 9 3 . 5 5 . 9 3 . 7 - 1 . 3 4 . 01 9 R K O P T M 2 8 . 2 2 8 . 2 2 8 . 9 3 . 4 - 1 . 9 _ 3 . 8_

” 1 9 R N O P T M 1 1 . 5 8 . 1 ” 1 3 . 0 3 . 5 ‘" ' " - 0 . 8 4 . 02 0 R K O P T M 8 . 1 8 . 1 1 1 . 3 1 . 8 - 0 . 9 1 . 92 0 R N O P T M 8 . 2 8 . 2 1 1 . 6 2 . 2 - 1 . 0 2 . 421 R K O P T M 1 .3 0 . 8 1 . 6 0 . 5 ,_“ 0 . 2 _ 0 ,_5_2 1 R N ’O P T M . . . . . . . . . . . ” . . . . . . . . . . . . . . . .2 2 R K O P T M 0 . 3 0 . 3 0 . 4 0 . 3 - 0 . 1 0 . 32 2 R N O P T M2 3 R K O P T M 5 3 . 5 - 3 5 . 3 8 4 . 7 _ 1 2 . 0 - 1 0 . 0 _ 1 3 . 9 _

‘> 3 ” R N O P T M 3 5 . 3 2 9 . 7 3 9 . 4 ’ * 3 . 1 * ’- 1 . 5 3 . 72 4 R K O P T M2 4 R N O P T M2 5 R K O P T M 1 .2 0 . 5 1 . 6 0 . 1 0 . 1’2 5 R N O P T M ' " 0 . 5 .. ' 0 . 3 * 0 . 6 . . . . . . . . 1 . 0 ‘ 1 . 0 1 . 12 6 R K O P T M 1 . 1 0 . 4 1 . 2 0 . 1 - 0 . 0 0 . 12 6 R N O P T M 8 . 8 - 8 . 8 9 . 1 0 . 9 - 0 . 9 0 . 9

112

T A B L E 2 7 ( C O N T ' D )

N S Y S P R E S S U R E D E V . ( P S D T E M P E R A T U R E D E V . (C)A V A B B I A S

2 7 R K □ p t m 0 . 4 - 0 . 12 7 R(^ D P T M 5 . 9 - 5 . 92 8 R K □ P T M 0 . 7 0 . 42 8 R N D P T M 1 . 9 - 0 . 82 9 R K □ P T M 4 . 4 0 . 22 9 R N □ P T M 3 . 9 " - 0 . 13 0 R K G P T M 1 . 4 1 . 43 0 R N □ P T M 1 . 7 - 0 . 83 1 R K □ P T M3 1 R M □ P T M3 2 R K □ P T M3 2 R N □ P T M3 3 R K □ P T M 0 . 5 - 0 . 03 3 R N n P T M 0 . 3 - 0.13 4 R K □ P T M 1 . 3 - 1 . 33 4 R M O P T M 0 . 2 - 0 . 03 5 R K □ P T M 0 . 9 0 . 53 5 ' R N O P T M 0 . 9 0 . 53 6 R K O P T M 0 . 8 0 . 23 6 R N O P T M 1 .0 0 . 43 7 R K 0 P T M 4 . 2 3 . 63 7 ' R N O P T M 8 . 4 .. 8 . 43 8 R K O P T M 2 . 1 1 . 93 8 R N O P T M 2 . 0 1 . 93 9 R K O P T M 0 . 6 0 . 339' R N O P T M4 0 R K O P T M 3 . 3 3 . 34 0 R N O P T M 4 . 2 4 . 2

R M S A V A B B I A S R M S0.5 _ J _ 0 . 3 0 . 1 _ _ 0 . 36 . 5 " " 0 . 8 “ 0 • 6 0 . 90 . 8 0 . 6 - 0 . 1 0 . 72.2 0.1 .0.1 0.2

5 . 5 2 . 5 - 1 . 7 2 . 64 . 7 0 . 5 0 . 1 0 . 61.5 0.2 - 0.1 0.21 . 7 1 . 4 - 1 . 4 1 . 6

0.6 0.1 - 0.0 _ _ 0.10 . 3 0 . 1 ' ' 0 . 0 ' ' 0 . 11.5 0.1 0.0 0.10.2 0.0 - 0.0 0.01 . 1 0 . 2 - 0 . 1 _ 0 . 31.1 0.2 ' - 0 . 1 ' 0.2

1.0 0.1 - 0.0 0.11.2 0.1 - 0.0 0.15 . 2 2 . 1 - 1 . 0 2 . 39.3. 3 . 8 ' 3 . 8 5 . 03 . 1 0 . 8 - 0 . 4 0 . 93 . 2 0 . 9 - 0 . 5 1 . 00 . 7 0 . 4 _ - 0 . 1 _ ____ 0 . 5

3 . 4 0 . 1 - 0 . 1 0 . 14 . 4 0 . 0 - 0 . 0 0 . 0

T A B L E 2 7 ( C O N T ' D )

M S Y S P R E S S U R E D E V .A V A B B I A S

4 1 R K O P T M4 1 R N - O P T M4 2 R K O P T M 1 .9 - 1 . 94 2 R M O P T M 1 . 2 - 1 . 24 3 R K 0 P T M'43 R N O P T M '4 4 R K O P T M 2 . 1 1 . 34 4 R N O P T M 3 . 1 3 . 14 5 R K O P T M 1 . 0 0 . 54 5 R M O T P M 4 • 4 4 . 44 6 R K O P T M 0 . 2 0 . 04 6 R M O P T M 0 . 2 0 . 14 7 R K O P T M4 7 R N O P T M 0 . 3 " O.'l4 8 R K O P T M 0 . 2 1 o • O

4 8 R N O P T M4 9 R K O P T M 0 . 5 - 0 . 34 9 R N O P T M 4 . 9 4 . 95 0 R K O P T M 7 . 2 1 . 25 0 R N O P T M 0 . 8 0 . 251 R K O P T M .1 ° * 5.51 " R N " O P T M5 2 R K O P T M 0 . 4 - 0 . 35 2 R M O P T M 0 . 7 0 . 65 3 R K O P T M 1 . 1 - 1 . 15 3 R N * O P T M 1 . 2 "* - 1 . 25 4 R K O P T M 0 . 4 0 . 35 4 R M O P T M 0 . 5 0 . 3

( P S I ) T E M P E R A T U R E D E V . (C)R M S A V A B B I A S R M S

2 . 0 0 . 2 - 0 . 1 0 . 21 . 2 0. 1 0 . 0 0 . 1

2 . 5 1 . 0 - 0 . 3 1 . 13 . 5 0 . 8 - 0 . 1 0 . 91 . 2 1 . 0 - 0 . 4 1 . 14 . 7 2 . 2 2 . 2 2 . 60 . 3 0 . 0 - 0 . 0 0 . 10 . 3 0 . 0 - 0 . 0 0 . 1

o . 0 . 0 o . o ' " " b ; r0 . 2 0. 1 c•o 0 . 1

0 . 6 0 . 3 0 . 0 0 . 3" 5 . 4 2 . 8 2 . 8 .. 3 . 01 0 . 1 1 . 2 - 0 . 1 1 .90 . 9 0 . 2 0 . 0 . 0 . 31 . 9 ___ “ 0 . 2 0 . 8

0 . 6 0 . 2 0 . 1 0 . 30 . 8 0 . 2 - 0 . 1 0 . 21 . 2 0. 1 - 0 . 0 0 . 11 . 4 0 . 1 " 0 . 0 " " 0 . 10 . 6 0 . 3 - 0 . 1 0 . 30 . 6 0 . 2 - 0 . 1 0 . 3

ii¥

T A B L E 2 ? ( C O N T ' D )


5 5 R K O P T M l 2 2 .1 1 2 2 . 1 1 3 4 . 6 2 4 . 6 - 2 4 . 6 2 6 . 8' 5 5 R M 0 P T M 1 6 8 . 8 1 5 7 . 5 1 8 5 . 7 1 7 . 8 ' - 1 7 . 8 1 8 . 45 6 R K O P T M5 6 R N O P T M 1 . 4 - 1 . 4 1 . 6 0 . 1 0 . 0 0 . 15 7 R K O P T M 7 . 4 - 7 . 4 7 . 7 0. 1 0 . 1 0 . 25 7 R N O P T M5 8 R K O P T M 0 . 6 0 . 0 0 . 7 0. 1 0 . 0 0 . 15 8 R M O P T M5 9 R K O P T M 1 . 1 - 0 . 3 1 . 4 _ 0 . 2 0. 1 0 . 35 9 R N O P T M6 0 R K O P T M 1 . 3 0 . 4 1 . 7 0 . 1 - 0 . 0 0 . 26 0 R N O P T M 1 . 9 - 1 . 4 2 . 2 0 . 5 - 0 . 5 0 . 56 1 R K O P T M 4 . 2 4 . 1 5 . 3 2 . 1 - 0 . 9 2 . 36 1 R N O P T M 3 . 3 1 . 8 3 . 8 0 . 8 - 0.0 ' 0 .96 2 R K O P T M 0 . 9 0 . 9 1 . 0 0 . 1 - 0 . 0 0 . 16 2 R N O P T M 1 . 1 1 . 1 1 . 2 0. 1 - 0 . 1 0 . 16 3 R K O P T M 3 . 1 2 . 8 4 . 1 1 . 7 - 0 . 6 1 . 86 3 R N O P T M 3 . 3 2 . 7 4 . 2 1 . 7 - 0 . 5 1 . 96 4 R K O P T M6 4 R N O P T M6 5 R K O P T M6 5 R N O P T M6 6 R K O P T M 0 . 4 0 . 1 0 , 5 0 . 1 - 0 . 0 0 . 16 6 R N O P T M 0 . 5 0. 1 0 . 5 0 . 1 - 0 . 0 0 . 16 7 R K O P T M 0 . 2 - 0 . 1 0 . 3 0. 1 0 . 0 0 . 26 7 R N O P T M 0 . 2 - 0 . 1 0 . 3 0.1 ‘ 0 . 0 0 . 26 8 R K O P T M 0 . 5 0 . 2 0 . 6 0 . 2 - 0 . 1 0 . 26 8 R M O P T M 0 .4 0 . 2 0 . 6 0 . 2 - 0 . 1 0 . 2

U 5

T E M P E R A T U R E D E V . (C) A V A B B I A S R M S

6 9 R K O P T M 1 . 3 1 . 0 _ 1 . 9 _ 0_._5_ _ _ _ - 0 . 2 _ _ _ _ _ 0_.6_6 9 ' .. R N O P T M 1 . 3 *" 0 . 7 1 . 9 0 . 5 - 0 . 1 0 . 57 0 R K O P T M 0 . 5 - 0 . 0 0 . 6 0 . 0 - 0 . 0 0 . 07 0 R N O P T M 0 . 5 0 . 4 0 . 7 0 . 0 - 0 . 0 0 . 0 .7 1 ___ R K O P T M 1 . 0 0 . 3 1 . 1 _ _ _ _ _ _ _ .0 ._4___ - 0 ._ 1_ _ _ _ _ _ 0_.4_7 1 R N O P T M ' 2 . 8 " - 2 . 8 3 . 2 ’ 0 . 4 ' " 0 . 0 l 1 ?! In j

7 2 R K O P T M 0 . 5 - 0 . 2 0 . 6 0 . 1 - 0 . 0 0 . 17 2 R N O P T M7 3 R K O P T M 0 .1 - 0 . 1 0 . 2 0 . 1 0 . 1 0 . 17 3 ' R N O P T M 0 . 4 0 . 1 0 . 6 0 . 1 0 . 0 ' o . i7 4 R K O P T M 0 . 9 0 . 5 1 . 3 0 . 8 - 0 . 2 0 . 97 4 R N O P T M 0 . 8 0 . 4 1. 1 0 . 8 - u . 1 0 . 87 5 R K O P T M 0 . 3 - 0 . 0 __ 0 . 3 _ _ _ 0 . 5 1I"J°!1ii . . Ci. 57 5 R N O P T M7 6 R K O P T M 0 . 5 0 . 5 0 . 5 0. 1 0 . 0 0 . 17 6 R N □ P T M 0 . 3 0 . 3 0 . 4 0 . 1 0 . 1 0 . 27 7 R K O P T M P .4 . 0 . 1 0 . 5 _ _ _ _ _ _ 0 . 6 . ___ 0 • 4 .... 0 . 7_7 7 R N u p t m

7 8 R K □ P T M 2 . 6 2 . 6 2 . 8 0 . 2 - 0 . 1 0 . 27 8 R N □ P T M -8 0 R K O P T M 0 . 5 0 . 5 0 . 6 0 . 0 - 0 . 0 0 . 08 0 R N O P T M 0 . 3 0 . 3 0 . 4 . 0 . 0 " - 0 . 0 0 . 0

T A B L E 2 7 ( C O N T ' D

N S Y S P R E S S U R E D E V . ( P S I )A V A B B I A S R M S

116Correlation of the Reduced Interaction Parameters As mentioned earlier it is possible to calculate

the critical locus of a binary system provided that the values of the interaction parameters a ,, ant* b ^ are

given0 Therefore, it is desirable to generalize the results of optimization so that the values of the interaction parameters could be predicted for the systems for which no critical data are available. The critical properties of mixtures are related to the non-ideality of the systems as discussed in Chapter VII. The factors affecting the non-ideality were the molecular size, structure, and chemical nature of the components comprising the mixture. Therefore, in the development of a mathematical model for the prediction of the reduced interaction parameters, these factors should be taken into considerations•

As a set of potential variables which represent these factors, the following independent variables were selected; i,e., molecular weight ratio, critical temperature ratio, critical pressure ratio, critical volume ratio, normal boiling point ratio, critical compressibility factor ratio, and accentric factor ratio. Since some of the plots of the reduced interaction parameters against the independent variables showed non-linearity, the jquare and cross- product terms of the above variables were added for consideration* In order to select the best regression

117equation* the method of multiple regression analysis was used. Multiple regression is usually used in data analysis to obtain the best fit of a set of observations of independent and dependent variables by an equation of the formt

Y = bQ + bjXj + b2X2 + . . . . + bnXn (53)

where Y is the dependent variables X^* Xp, are theindependent variables; and b^* bp, ..... are the coefficients to be determined. Multiple regression (72) can also be used to fit nonlinear equations of the form;

Y = b^ H* b^Z^ + bpZp + b^(2^Zp) + ••••

* V n (V Z2 V W

Eq, (5*0 can be made equivalent to Eq. (53) by the substitutions

Xn s

The computer program, REGRES, prepared by Hershey (36) v/as adopted for the calculation. The routine REGRES was patterned after BMD02R, a stepwise regression routine in the Biomedical Computer Programs (21) which was supported

118

in part by the Ohio State University Computer Center.The routine REGRES computes a sequence of multiple linear regression equations in a stepwise manner. At each step, one variable is added to the regression equation, that is,

2 2> 2 * 2 + * 3 X 3

Y = *0 + V iY = b0 + bJXiY = b0 + bi'xl

The variable added is the one which makes the greatest reduction in the error sum of squares. In other words, it is the variable which has the highest partial correlation with the dependent variable partialed on the variables which have already been added to the regression. The coefficients represent the best values when the equation is fitted by the specific variables included in the equation. An important property of the stepwise procedure is based on the fact that (l) a variable may be indicated to be significant in any early stage and thus enter the equation, and (2) after several other variables are added to the regression equation, the initial variable may be indicated to be insignificant.The insignificant variable will be removed from the regression equation before adding an additional variable.Thus, only significant variables are included in the final regression equation. For the detailed discussion of this procedure, books by Ralston and Wilf (72) and Draper and Smith (22) are recommended.

119Three different correlations were investigated* First,

all of the systems that converged were included in the correlation! secondly, outliers were not considered in the correlation! and thirdly, separate correlations for the aliphatic-aliphatic systems and for the cyclic systems (i«e*, one or both components are either aromatic or naphthenic) were studied. The final equations with the number of systems considered for each correlation, were as follows*

HEDLICH-KWONG EQUATION

Correlation 1 i (RK C0R1) (70 systems)

A12SR = 1.323494? - 0.3321?129MR + 0.03278483MR2 (55)B12SR = 1.1796816 - 0.3440?676MR + 0.07023001MR2

+ 0,l45776l2VR - 0.041826o6Vr2 (56)

Correlation 2 1 (RK C0R2) (64 systems)

A12SR = 1.3402386 - O.36l06543MR + 0.030?6067MR2+ 0.02043529^R (57)

B12SR - 0.88286268 - 0.178lll66MR + 0.02635322MR2+ 0.28433690Zr (58)

Correlation 3 * (RK C0R3)Aliphatic (34 systems)

A12SR = 1,0248616 - 0.32355906VR + 0.0195094MRVR+ 0.31471218Zr (59)

B12SR - 0.65059709 + 0.37384345Pr (60)

Cyclic (30 systems)

A12SR = 1 .2 7 0 3 1 0 1 - 0 .0 ^ 5 2 3 9 0 1 MrVr -

B12SR = 0 .9 8 1 0 0 ^ 8 3 - 0 .0 5 H 2 0 9 6 M rVr

- 0 .0 1 4 1 0 8 5 3 -Q r

REDLICH-NGO EQUATION

Correlation I 1 (RN CORi) (55 systems)

A12SR = 1 .4 2 3 3 1 4 4 - 0 .453 3 5 4 8 1 MR + 0

B12SR = 0 .2 9 1 3 8 3 7 7 - 0 .52580653V r + I

+ 0 .0 5 5 0 9 3 2 6 jQ r + 1. 259^071 Zj

- 0.13438522PR2

Correlation 2 1 (RN C0R2) (51 systems)

A12SR = 1 .7 6 4 4 1 9 2 - 0,32917764Mr + 0,

- 0.^54l0531ZRB12SR = 1 .2 4 5 4 9 1 9 - 0.22509280M dli

Correlation 3 1 (HN C0R3)Aliphatic (24 systems)

A12SR = 1 .0 6 0 9 2 8 9 - 0 .40548950M r + 0.

B12SR = 0 .0 9 2 4 8 0 3 0 + 0 .2 2 0 7 0 9 3 2 P R +

- 0 .04571294V R2

0.21442805Tr0.07927359Vr

06l38679MR2.08315749Vr2

03620706i R

36681503Tr.76279946z r

121Cyclic (22 systems)

A12SR = 0.22114569 + 0 . 0 3 9 9 5 0 8 M r 2 - 1.0478193?Br2 + 0.00292810 ^ H2 - 0.472000l6TR + 2.4323436TBR - 0.17039590Vr ( 69 )

B12SR = 0.86185026 - 0.10654015 M r 2

- 0.03374359MRVR + 0.22795463ZR ( 70 )

where MR = ratio of melecular weights,P = P c / P c R V 2, ratio of critical pressures,Tr = T^/Tg, ratio of critical temperatures,TBr = TB^/TBg, ratio of normal boiling points,VR = V^/Vg, ratio of critical volumes,ZR = Zj/Z°, ratio of critical compressibility

factors, and■nH = a / /«/ ratio of acentric factors(68 ).

Hissong and Kay ( 38 ), however, correlated the reducedinteraction parameters as polynomials in the ratio ofmolecular weights of the components. The final equationsbased on the twenty-one binary systems v/ere as follows 1

A12SR = 0.977543 - 0.004949Ti ~ 0.280326 T ± Z+ 0.0987983vl 3 ( 71 )

B12SR = 0.995^8 - 0.082779jtf (72 )

where = fÂlg ~ ranSe of 2<L wasbetween 0.1 and 1.6.

Tables 28 and 29 present the statistical deviation data on the critical loci calculated by using the reduced interaction parameters calculated by the various correlations for the Redlich-Kwong and Redlich-Ngo equations, respectively. The results show that agreement between the critical loci calculated with the predicted interaction parameters and those calculated with the optimum interaction parameters is quite satisfactory. Tables 28 and 29 clearly indicate that as the relative size difference of the components increases, the calculated values show greater deviations from the experimental values.It is also to be noted in these tables that the deviations for the extremely non-ideal systems, i.e., n-heptane, benzene, and cyclohexane with ethane as a common component, whose molecular weight ratios are greater than 2.5» are unusually large. These systems acted like outliers when the reduced interaction parameters were plotted against

jthe independent variables. Therefore, the equation of state method is not recommended for the systems whose molecular weight ratios are greater than 2,5* In addition to the three systems, the systems with cis-decalin as a common component did not follow the trend shown by other binary systems. Consequently, these systems were not taken into account in Correlation 2 and 3* However, the deviations for the systems with cis-decalin as a common component are not too large.

T A B L E 2 8

C O M P A R I S O N O F S T A T I S T I C A L D E V I A T I O N D A T A O N T H E C R I T I C A L L O C I C A L C U L A T E D U S I N G T H E R E D U C E D I N T E R A C T I O N P A R A M E T E R S P R E D I C T E D B Y T H E V A R I O U S C O R R E -L A T I O N S F O R T H E R E D L I C H - K W O N G E Q U A T I O N O F S T A T E

N S Y S P R E S S U R E D E V . ( P S I ) T E M P E R A T U R E O F V . (C)A V A B B I A S R M S A V A B B I A S R M S

1 R K O P T M 2 3 . 3 2 3 . 3 3 2 . 5 2 . 8 - 2 . 0 - 3 . 8i R K e m u 2 7 . 8 2 7 . 8 3 5 . 9 2 . 3 - 2 . 3 3 . 21 R K C O R 2 2 7 . 6 2 7 . 6 3 1 . 1 4 . 5 - 0 . 2 5 . 4l R K C H R 3 2 6 . 1 2 6 . 1 3 2 . 1 3 . 2 - 1 . 2 4 . 1l H I S S O N G 1 3 2 . 8 - 4 5 . 2 1 5 1 . 6 2 8 . 6 - 2 8 . 6 3 1 .32 R K IIPTM 1 .1 0 . 1 1 . 2 0. 1 - o . 1 0 . 22 R K C D R l 5 . 9 - 5 .9 6 . 3 0 . 5 - 0 . 5 0 . 62 R K C O R ? 4 . 1 - 4 . 1 4 . 5 0 . 3 - 0 . 1 0 . 32 R K C O R 3 1 . 2 - 0 . 8 1 . 5 0 . 2 - 0 . 1 0 . 22 H I S S O N G 5 . 5 - 5 . 5 5 . 7 0 . 9 - 0 . 9 0 . 93 R K (1 P T M 2 . 2 1 . 1 2 . 9 1 . 0 - 0 . 5 1 . 13 R K C O R 1 4 . 5 ' - 4 . 5 5 . 1 2 . 5 - 2 . 5 2 . 93 R K C O R 2 5 . 1 - 5 . 1 5 . 8 2 . 5 - 2 . 5 2 . 93 R K C O R 3 1 . 7 1 . 2 2 . 0 2 . 0 - 2 . 0 2 . 43 H I S S O N G 2 . 6 - 0 . 9 3 . 1 3 . 0 - 3 . 0 3 . 34 R K O P T M 3 . 1 2 . 1 4 . 7 1 . 5 - 1 . 2 1 . 74 R K ' C D R l 5 . 5 - 5 . 2 6 . 4 3 . 2 ' " - 3 . 2 ‘ 3 . 54 R K C O R 2 6 . 2 - 4 . 8 6 . 8 2 . 4 - 2 . 2 2 . 74 R K C O R 3 2 . 5 0 . 5 3 . 7 1 . 8 - 1 . 6 2 . 04 H I S S O N G 2 . 1 0 . 2 2 . 8 2 . 1 - 2 . 0 2 . 35 R K O P T M 8 . 3 8 . 2 1 2 . 8 3 . 5 - 2 , 5 3 . 7

~ 5 ' R K C O R 1 7 . 8 3 . 7 8 . 6 " 5 . 6 - 5 . 6 “6 . 35 R K C O R 2 7 . 0 2 . 9 9 . 4 4 . 7 - 4 . 4 5 . 35 RK c m * , 3 7 . 7 7 . 0 1 1 . 2 3 . 8 - 3 . 2 4 . 25 H I S S O N G 7 . 5 6 . 5 1 1 . 9 3 . 7 - 2 . 8 4 . 0

6 R K O P T M 1 6 . 4 1 4 . 8 2 0 . 3 5 . 5 - 3 . 4 6 . 0... R K C O R I 1 9 . 5 1 9 . 5 2 2 . 1 6. 1 - 5 . 7 6 . 9

6 R K C O R 2 1 6 . 4 1 4 . 9 1 9 . 3 5 . 8 - 4 . 7 6 . 56 R K C O R 3 1 7 . 5 1 6 . 8 2 2 . 4 5 . 2 - 2 . 3 5 . 66 H I S S O N G 1 6 . 6 1 5 . 2 2 0 . 3 5 . 5 - 3 . 5 6 . 0

T A B L E 2 8 ( C O N T ' D )

N S Y S P R E S S U R E D E V . ( P S I ) T E M P E R A T U R E D E V . ( C)... A V A R B I A S R M S A V A B B I A S R M S

7 R K O P T M 2 . 9 2 . 7 4 . 2 1 . 6 - 1 . 4 2 . 17 R K C D R l 3 . 4 - 5 . 1 6 . 9 3 . 0 - 3 . 6 3 . 57 R K C 0 R 2 5 . 3 - 2 .6 6 . 3 2 . 0 - 1 . 8 2 . 67 R K C 0 R 3 9 . 0 9 . 0 1 0 . 4 1 . 2 - 0 . 1 1 . 37 H I S S O N G 2 . 7 0 . 4 3 . 2 2 . 0 - 1 . 9 2 . 58 R K O P T M 4 . 2 2 . 8 5 . 0 1 . 8 - 1 . 4 2 . 18 "RK C 0 R 1 7 . 3 — 5 • 6 8 . 5 3 . 7 - 3 . 7 3 . 98 R K G 0 R 2 5 . 0 0 . 4 5 . 5 1 . 9 - 1 . 4 2 . 28 R K C 0 R 3 4 . 4 2 . 2 4 . 9 2 . 9 - 2 . 9 3 . 28 H I S S O N G 3 . 7 0 . 3 4 . 1 2 . 5 - 2 . 5 2 . 99 . RK. O P T M . 4 . 9 4 . 1 6 . 0 _ _ _ _ _ 1 . 3 ___ “ 1 . 1 1 . 6 __9 R K C O R 1 7 . 9 - 6 . 5 1 0 . 4 2 . 5 - 2 . 5 3 . 19 R K C 0 R 2 9 . 9 - 2 . 5 1 1 . 1 1 . 8 - 0 . 6 1 . 89 R K C 0 R 3 2 . 8 0 . 5 2 . 9 2 . 5 - 2 . 5 2 . 3Q✓ H I S S O N G 6 . 1 - 1 . 0 6 . 9 1 . 7 - 1 . 5 2 . 1

1 0 R K n P T M 0 . 9 - 0 . 2 0 . 9 0 . 1 0 . 0 0 . 11 0 R K C 0 R 1 2 . 0 - 2 . 0 2 . 2 0 . 3 - 0 . 3 0 . 31 0 R K C 0 R 2 2 . 7 - 2 . 7 3 . 0 0 . 8 - 0 . 8 0 . 81 0 R K C 0 R 3 1 .0 - 0 . 3 1 . 1 0 . 2 - 0 . 2 0 . 21 0 H I S S O N G 1 . 3 - 1 . 8 2 . 1 0 . 2 - 0 . 2 0 . 311 R K n P T M 1 .4 0 . 8 1 -s .. 0 . 6 - 0 . 3 0 . 711 ~ R K C O R 1 2 .6 - 1 . 8 2 . 9 0 . 8 - 0 . 4 0 . 811 R K C 0 R 2 2 . 4 - 0 . 6 2 . 6 0 . 7 0 . 1 0 . 811 R K C O R 3 2 .6 - 0 . 8 2 . 8 0 . 7 0 . 1 0 . 81 1 H I S S O N G 1 . 0 - 0 . 9 1 . 2 1 . 5 - 1 . 5 1 -71 2 R K O P T M 3 . 8 3 . 7 6 . 3 1 . 9 - 1 . 1 2 . 11 2 R K C D R l 5 . 6 5 . 6 5 . 9 2 . 9 - 2 . 8 3 . 21 2 R K C.0R2 7 .4 7 . 4 7 .9 2. 1 - 1 . 9 2 . 31 2 R K C 0 R 3 5 . 7 5 . 7 6 . 6 2 . 0 - 1 . 7 2 . 31 2 H I S S O N G 8 . 9 8 . 9 9 . 1 3 . 1 - 3 . 1 3 . 41 3 R K O P T M 4 . 8 4 . 8 7 . 3 2 . 6 - 1 . 6 2 . 71 3 R K C 0 R 1 7 . 0 7 . 0 7 . 2 3 . 8 - 3 . 8 4 . 21 3 R K C 0 R 2 8 . 2 3 . 2 8 . 5 2 . 9 - 2 . 7 3 . 213 R K C 0 R 3 6 . 3 6 . 3 3 . 3 2 . 4 - 1 . 3 2 . 51 3 H I S S O N G 1 1 . 9 1 1 . 9 1 2 . 2 2 . 5 - 2 . 3 2 . 7

T A B L E 2 8 ( C O N T ' D )

N S Y S P R E S S U R E D E V . ( P S D T E M P E R A T U R E D E V . (C)A V A B B I A S R M S A V A B B I A S R M S

1 4 R K O P T M 2 . 5 2 . 1 3 . 7 0 . 8 - 0 . 4 1 . 014 R K c r m i 4 . 1 3 . 4 6 . 3 ‘ 1 . 5 " 1 . 5 2 . 01 4 R K C O R 2 5 . 3 4 . 7 8 . 2 2 . 7 2 . 7 3 . 114 R K C 0 R 3 7 . 3 1 . 8 9 . 1 3 . 6 3 . 6 " 4 . 314 H I S S O N G 6 . 7 6 . 6 8 . 1 1 . 6 1 . 6 1 - 91 3 R K O P T M 1 . 2 - 1 . 2 1 . 2 0 . 1 0 . 1 0 . 21 5 R K C D R l 1 . 6 “ 1 . 6 ' 1 . 6 0 . 1 - o • i..... " 0 . 115 R K C 0 R 2 0 . 3 - 0 . 3 0 . 3 0 . 1 0 . 1 0 . 21 5 R K C 0 R 3 1 .7 - 1 . 7 1 . 8 0 . 6 — 0 . 6 0 . 61 5 H I S S O N G 2 . 1 - 2 . 1 2 . 1 5 0 . 5 0 . 61 6 R K O P T M 0 . 3 0 . 1 0 . 4 0 . 1 - 0 . 0 0 . 11 6 R K C 0 R 1 ' 0 . 9 - 0 . 3 ' 1 . 0 0 . 8 'O'. 8 ' 0 . 91 6 R K C 0 R 2 0 . 9 0 . 7 1 . 2 1 . 0 1 . 0 1 . 116 R K C D R 3 2 .4 - 2 . 4 2 . 7 0 . 2 - 0 . 1 0 . 21 6 H I S S O N G 0 . 7 - 0 . 6 0 . 8 0 . 2 - 0 . 2 0 . 21 7 R K O P T M 2 . 8 2 . 4 4 . 1 1 . 5 - 0 . 8 1 . 717 R K C 0 R 1 6 . 5 6 . 5 7 . 2 1 . 1 - 0 . 7 1 . 31 7 R K C 0 R 2 5 . 5 5 . 5 5 . 9 1 . 8 - 1 . 7 2 . 01 7 R K C D R 3 3 .6 3 . 6 5 . 1 1 . 4 - 0 . 4 1 . 51 7 H I S S O N G 8 . 3 8 . 3 8 . 8 1 . 5 - 1 . 5 1 . 71 8 R K O P T M 8 . 2 3 . 2 1 0 . 0 4 . 5 - 2 . 3 4 . 91 8 ’ R K C 0 R 1 1 9 . 8 1 9 . 8 2 0 . 3 .. “3 . 0 - 2 . 1 3 . 31 8 R K C 0 R 2 1 8 . 1 1 8 . 1 1 8 . 7 3 . 0 - 1 . 5 3 . 31 8 R K C 0 R 3 1 4 . 5 1 4 . 5 16 . 4 4 . 2 1 . 4 5 . 11 8 H I S S O N G 2 4 . 2 2 4 . 2 2 5 . 4 3 . 5 2 . 3 4 . 31 9 R K O P T M 2 8 . 2 2 8 . 2 2 8 . 9 3 . 4 - 1 . 9 3 . 8

-~ig- R K C 0 R 1 3 7 . 6 3 7 . 6 3 9 . 7 6 . 7 - 6 . 7 7 . 21 9 R K C 0 R 2 3 4 . 5 3 4 . 5 3 6 . 1 6 . 3 - 6 . 3 6 . 91 9 R K C 0 R 3 2 5 . 1 2 5 . 1 2 6 . 3 6 . 7 - 6 . 7 7 . 71 9 H I S S O N G 4 1 .3 4 1 . 3 4 2 . 8 2 . 7 - 2 . 7 3 . 12 0 R K O P T M 8 . 1 8 . 1 1 1 . 3 1 . 8 - 0 . 9 1 .92 0 R K C 0 R 1 1 1 . 1 1 1 . 1 1 1 . 6 6 . 5 - 6 . 5 . . . 6 . 92 0 R K C 0 R 2 1 9 . 2 1 9 . 2 1 9 . 9 1 . 0 - 1 . 0 1 . 12 0 R K C 0 R 3 2 1 . 8 2 1 . 8 2 2 . 5 1 . 6 - 1 . 6 1 . 72 0 H I S S O N G 1 5 . 9 1 5 . 9 1 6 . 7 6 . 5 - 6 . 5 7 . 0

T A B L E 2 8 ( C O N T ' D )


21 R K O P T M 1 . 3 0 . 8 1 . 6 ■' 0 . 5 - 0 . 2 0 . 521 R K C D R l 7 . 0 7 . 0 7 . 7 2 . 4 2 . 4 2 . 621 R K CC1R2 7 . 1 7 . 1 7 . 7 2 . 6 2 . 6 2 . 92 1 R K C O R 3 3 . 8 3 . 8 4 . 3 1 . 1 1 . 0 1 . 22 1 H I S S O N G 7 . 1 7 . 1 7 . 7 0 . 9 0 . 8 1 . 02 2 R K O P T M 0 . 3 0 . 3 0 . 4 0 . 3 - 0 . 1 0 . 32 2 R K C O R 1 0 . 6 0 . 6 0 . 7 . . 0 . 3 - 0 . 1 0 . 32 2 R K C O R 2 0 . 5 0 . 5 0 . 6 0 . 3 - 0 . 0 0 . 32 2 R K C O R 3 0 . 6 - 0 . 4 0 . 7 0 . 0 - 0 . 8 0 . 92 2 H I S S O N G 0 . 4 0 . 4 0 . 4 0 . 4 0 . 4 0 .62 3 R K O P T M 5 3 . 5 - 3 5 . 3 8 4 . 7 1 2 . 0 - 1 0 . 0 1 3 . 92 3 R K C O R 1 4 6 .4 - 2 2 . 3 6 5 . 9 1 0 . 0 - 9 . 6 1 2 . 123 RK CORl45^6.8 -^537.5 11016.0 ((4.0 26.3 86.82 3 R K C O R 3 5 4 .3 - 3 6 . 7 8 7 . 4 1 2 . 4 - 1 0 . 1 1 4 . 22 3 H I S S O N G 1 4 0 . 2 5 0 . 5 2 3 7 . 9 1 7 . 1 - 2 . 4 2 1 . 72 4 R K O P T M2 4 R K C 0 R 12 4 R K C 0 R 22 4 R K C 0 R 32 4 H I S S O N G2 5 R K O P T M 1 . 2 0 . 5 1 . 6 0 . 1 0 . 1 0 . 22 5 R K C 0 R 1 1 . 1 0 . 9 1 . 3 1 . 0 1 . 0 1 . 22 5 R K C 0 R 2 1 .8 - 1 . 5 2 . 0 1 . 1 - 1 . 1 1 . 12 5 R K C 0 R 3 0 . 9 0 . 2 1 . 2 1 . 0 - 1 . 0 1 . 02 5 H I S S O N G 1 , 7 - 1 . 3 1 . 8 0 . 6 - 0 . 6 0 . 6 ...2 6 R K OPTf-i 1 . 1 0 . 4 1 . 2 0 . 1 - 0 . 0 0 . 12 6 R K C 0 R 1 1 . 5 — 0 , 4 1 . 7 1 . 3 ‘ " 1 . 3 1 . 42 6 R K C 0 R 2 2 . 3 - 2 . 1 2 . 9 0 . 3 - 0 . 3 0 . 32 6 R K C 0 R 3 1 . 1 0 . 6 1 . 2 0 . 1 - 0 . 1 0 . 12 6 H I S S O N G 1 . 5 - 0 . 9 1 . 8 0 . 5 - 0 . 5 0 . 52 7 R K O P T M 0 . 4 - 0 , 1 0 . 5 0 . 3 0 . 1 0 . 3

" 2 7 ~ R K ' C 0 R 1 2 . 9 - 2 . 9 ' 3 . 3 1. 3 1 . 3 1 . 42 7 R K C 0 R 2 4 . 5 - 4 . 5 4 . 8 0 . 5 - 0 . 4 0 . 62 7 R K C 0 R 3 0 . 8 - 0 . 8 0 . 9 0 . 3 0 . 2 0 . 32 7 H I S S O N G 0 . 9 o * 1 . 1 1 . 0 1 . 0 1 . 1

T A B L E 2 8 ( C O N T ' D )


2 8 R K O P T M 0 . 7 0 . 4 0 . 8 0 , 6 - 0 . 1 0 . 72 8 R K C 0 R 1 1 . 4 - 1 . 2 1 . 8 0 . 7 - 0 . 1 " 0 . 8 "2 8 R K C 0 R 2 1 .4 - 0 . 5 1 . 5 1 . 1 - 1 . 1 1 . 42 8 R K C 0 R 3 1 .0 0 . 9 1 . 3 0 . 8 - 0 . 7 1 . 02 8 H I S S O N G 6 . 8 6 . 8 7 . 5 2 . 4 2 . 4 2 .62 9 R K O P T M 4 • 4 0 . 2 5 . 5 2 . 5 - 1 . 7 2 . 62 9 R K C 0 R 1 3 . 8 - 0 . 2 4 . 5 5 . 9 - 5 . 9 " ' 6 . 42 9 R K C 0 R 2 1 3 . 9 1 3 . 9 1 7 . 5 1 . 8 1. 8 2 . 72 9 R K C 0 R 3 5 . 6 1 . 2 7 . 3 2 . 3 - 1 . 2 2 . 52 9 H I S S O N G 1 8 . 2 1 8 . 2 2 5 . 6 7 * ° 7 . 0 8 * 3 ..

3 0 R K O P T M 1 . 4 1 . 4 1 . 5 0 . 2 - 0 . 1 0 . 230' ’ R K C D R l 7 . 8 ' - 7 . 6 7 . 8 3 . 7 - 3 . 7 3 • 73 0 R K C 0 R 2 3 . 1 - 3 . 1 3 . 3 2 . 5 - 2 . 5 2 . 73 0 R K C 0 R 3 4 . 1 - 3 . 9 4 . 5 1 . 8 - 1 . 8 2 . 03 0 H I S S O N G 2 . 7 - 2 . 6 3 . 0 0 . 7 - 0 . 7 0 . 83 1 R K O P T M'31 " R K C 0 R 13 1 R K C 0 R 23 1 R K C 0 R 33 1 H I S S O N G3 2 R K O P T M3 2 ' R K C O R 13 2 R K C O R 23 2 R K C O R 33 2 H I S S O N G3 3 R K O P T M 0 , 5 - 0 . 0 0 . 6 0 . 1 - 0 . 0 0 . 13 3 . ' R K C 0 R 1 2 . 7 - 2 . 7 . . 2 . 8 0.6' - 0 . 6 0 . 63 3 R K C 0 R 2 1 . 8 - 1 . 8 2 . 0 0 . 3 - 0 . 3 0 . 43 3 R K C 0 R 3 2 .3 - 2 . 3 2 . 5 1 . 6 - 1 . 6 1 . 73 3 H I S S O N G 5 . 2 “ 5 . 2 . 5 . 5 1 * 7 - 1 . 7 1 . 63 4 R K O P T M 1 . 3 - 1 . 3 1 . 5 0 . 1 0 . 0 0 . 13 4 R K C 0 R 1 2 . 1 ' - 2 . 1 2 . 3 * 0 . 2 " 0 . 2 0 . 23 4 R K C 0 R 2 3 . 5 - 3 . 5 3 . 8 0 . 8 - 0 . 8 0 . 83 4 R K C 0 R 3 3 . 0 - 3 . 0 3 . 3 0 . 3 - 0 . 3 0 . 33 4 H I S S O N G 3 . 2 - 3 . 2 3 . 5 0 . 5 0 . 5 0 . 6

128

T A B L E 2 8 ( C O N T ' D )

^lSYS P R E S S U R E D E V . ( P S I ) T E M P E R A T U R E D E V . (C)A V A B B I A S R M S A V A B B I A S R M S

3 5 R K O P T M 0 . 9 0 . 5 1 . 1 0 . 2 - 0 . 1 0 . 33 5 R K C D R l 1 . 9 - 1 . 1 2 . 2 0 . 5 0 . 3 0 . 53 5 R K C O R 2 1 . 8 - 0 . 6 2 . 0 0 . 3 0 . 7 0 , 93 5 R K C O R 3 2 . 9 2 . 9 3 . 1 0 . 9 0 . 9 1 . 03 5 H I S S O N G 2 . 5 - 2 . 3 2 . 9 1 * 2 - 1 . 2 . 1 * 23 6 R K O P T M 0 . 8 0 . 2 1 . 0 0 . 1 - 0 . 0 0 . 13 6 R K C O R 1 0 . 9 - 0 . 3 1 . 0 1 . 1 1 . 1 1 . 23 6 R K C O R 2 1 . 1 - 0 . 8 1 . 3 0 . 5 0 . 5 0 . 63 6 R K C O R 3 1 . 3 1 . 3 1. A 0 . A 0 . A 0 . 53 6 H I S S O N G 1 . 9 - 1 . 6 2 . 2 0. A - 0 . A 0 . 53 7 R K O P T M A . 2 3 . 6 5 . 2 .2 . 1__ - 1 . 0 2 . 33 7 R K C D R l 7 . 2 3 . 2 8 . 0 6 . 0 - 6 . 0 6 . 33 7 R K C 0 R 2 9 . A 9 . A 9 . 6 2 . 2 - 2 . 1 2 . 53 7 R K C 0 R 3 11 . A 11 .A 1 2 . 8 A. 2 - A . 2 A . A3 7 H I S S O N G 9 . 7 ( .9 1 1 . 1 5 . 9 - 5 . 9 6 . 23 8 R K O P T M 2 . 1 1 . 93 8 R K C 0 R 1 1 . 9 - 1 . 63 8 R K C 0 R 2 6 . 0 6 . 03 8 R K C 0 R 3 7 . 1 7 . 13 8 H I S S O N G 2 . A 2 . 13 9 R K O P T M 0 . 6 0 . 33 9 R K C 0 R 1 2 . A - 2 . 13 9 R K C 0 R 2 3 . 7 3 . 73 9 R K C 0 R 3 3 . A 3 . A3 9 H I S S O N G 1 .2 0 . 9A O R K O P T M 3 . 3 3 . 3A O ” R K C 0 R 1 2 . 7 - 2 . 7A O R K C 0 R 2 A . 7 A . 7A O R K C 0 R 3 2 . 0 2 . 0A O H I S S O N G 3 . 5 3 . 5A 1 R K O P T MA 1 " R K C 0 R 1A 1 R K C 0 R 2A 1 R K C 0 R 3A 1 H I S S O N G

3. 1 0 . 8 - 0 . A 0 . 92 . A 3 . 0 -3 ."o"'6 . 6 0 . 7 0 • A 0 . 87 . 6 0 . 5 0 . 3 0 . 63 . 0 3 . 2 - 3 . 2 3 . A0 . 7 0. A - 0 . 1 0 . 52 . 8 ’3 . 0 - 3 . 0 3 . 2A . 0 0 . A - 0 . A 0 . 53 . 6 0 . 5 0 . A 0 . 61 • A 1 . 5 - 1 . 5 1 .63. A 0 . 1 - 0 , 1 0 . 12 . 7 3 . 6 - 3 . 6 3 . 65 . 0 1 . 7 - 1 . 7 1 . 72 . 2 0 . A - 0 • A " 0 . 53 . 5 0 . 7 0 . 7 0 . 7

1 2 9

T A B L E 2 8 ( C O N T ' D )

N S Y S P R E S S U R F D E V . ( P S I ) T E M P E R A T U R E D E V . (C)A V A B B I A S R M S A V A B B I A S R M S

4 2 R K O P T M 1 .9 - 1 . 9 2.0 0.2 - 0 . 1 0.242' R K C O R 1 o . B ... - 0.8 0 . 9 " " 0 . 4 0 . 4 6 7 44 2 R K C O R 2 0.8 0.8 0.8 0.6 0.6 0.64 2 R K C O R 3 1 .7 - 1 . 7 1 . 7 0 . 1 - 0.0 0.14 2 H I S S n N G4 3 R K O P T M4 3 R K C D R l4 3 R K C 0 R 24 3 R K C 0 R 34 3 H I S S O N G

4 4 R K O P T M 2.1 1 . 34 4 ' "' R K C 0 R 1 9 . 5 9 . 54 4 R K C 0 R 2 1 4 . 6 1 4 . 64 4 R K C 0 R 3 1 3 . 9 1 3 . 94 4 H I S S O N G 9 . 1 9 . 14 5 R K O P T M 1.0 0 . 54 5 R K C O R 1 8 . 3 8 . 34 5 R K C 0 R 2 1 3 . 0 1 3 . 04 5 R K C 0 R 3 1 1 . 8 11.84 5 H I S S O N G 7 . 6 7 . 64 6 R K O P T M 0.2 0.04 6 R K C D R l 0 . 3 - 0.24 6 R K C 0 R 2 1 . 7 1 . 74 6 R K C 0 R 3 0.2 0.24 6 H I S S O N G 1.0 - 1.04 7 R K O P T M4 7 R K C O R 14 7 R K C 0 R 24 7 R K C 0 R 34 7 H I S S O N G4 8 R K O P T M 0.2 - 0.04 8 R K C D R l4 8 R K C 0 R 2 3 . 4 - 3 . 44 8 R K C 0 R 3 1.2 - 1.24 8 H I S S O N G

2 . 5 1.0 - 0 . 3 1.11 0 . 3 2 . 9 - 2 . 9 “ 3 . 11 5 . 1 0 . 3 0.2 0 . 414 .5 0 . 9 - 0 . 9 1.010. 1 3 . 9 - 3 . 9 4 . 11.2 1.0 - 0 . 4 1.18 . 7 ' 2.2 ... _ 2- 2 - 2 . 3

1 3 . 6 0 . 7 0 . 7 0.81 2 . 3 1.0 - 1.0 1.18.1 3 . 3 - 3 . 3 3 . 40 . 3 0.0 - 0.0 0.10 . 4 0 . 3 - 0 . 3 0 . 31 . 7 0.2 0.2 0 . 30 . 3 0.1 0 . 1 0.11.0 0.8 0.8 0.8

111ir\j•o ___ 0.1 0.0__ 0.1

3 . 4 0.1 - 0.0 0.11.2 0 . 3 0 . 3 0 . 3

130

T A B L E 2 8 ( C O N T ' D )


4 9 R K O P T M 0 . 5 - 0 . 3 0.6 ' 0 . 3 0.0 0 . 34 9 R K C 0 R 1 1 .8 0.6 2.2 2 . 5 2 . 5 2.84 9 R K C 0 R 2 2.2 - 2.1 2 . 5 0.8 0.8 0 . 94 9 R K C 0 R 3 0 . 9 0.6 1.0 0.8 0.8 0 . 94 9 H I S S O N G 1.1 - 0 . 7 1.2 0 . 7 0 . 7 0 . 95 0 R K O P T M 7 . 2 1.2 10.1 1.2 - 0 . 15 0 R K C 0 R 1 5 . 5 - 2.6 1 0 . 4 2.8 2.85 0 R K C 0 R 2 5 . 2 - 4 . 3 11.2 1.6 1 . 55 0 R K C 0 R 3 5 . 2 - 1 . 4 10. 0 1 . 3 1 . 35 0 H I S S O N G 5 . 4 - 0 . 9 9 . 9 1 . 9 1 . 95 1 R K O P T M 1 . 4 0 . 5 1 . 9 0 . 7 - 0.251 R K C 0 R 1 3 . 6 0.8 4 . 6 1 . 9 1 . 95 1 R K C 0 R 2 3 . 1 - 1.0 3 . 4 0 . 9 0 . 751 R K C 0 R 3 3 . 1 2 . 5 3 . 6 0.6 0 . 35 1 H I S S O N G 6.8 6.1 S . 4 3 . 0 3 . 05 2 R K O P T M 0 . 4 - 0 . 3 0.6 0.2 0.15 2 R K C O R 1 2.1 - 2.1 2.2 0 . 3 0.25 2 R K C 0 R 2 1.2 0 . 3 1 . 3 1.2 1.252 R K C 0 R 3 1.0 0 . 1 1.0 0.8 0.85 2 H I S S O N G 2.8 - 2.8 2.8 0 . 5 0 . 55 3 R K O P T M 1.1 - 1.1 1.2 0.1 - 0.053 R K C 0 R 1 1 .6 - 1.6 1.8 0. 5 0 . 55 3 R K C 0 R 2 0 . 7 - 0 . 7 0.8 0 . 5 0 . 55 3 R K C 0 R 3 1 . 5 - 1 . 4 1.8 0.2 - 0.05 3 H I S S O N G 2 . 5 - 2 . 5 2 . 7 0 . 5 0 . 55 4 R K O P T M 0 . 4 0 . 3 0.6 0 . 3 - 0 . 15 4 “ R K C 0 R 1 3 . 2 - 2 .6’ 3 . 5 1.1 1.15 4 R K C 0 R 2 2.6 - 0.8 2.8 1 . 9 1 . 95 4 R K C 0 R 3 1 .0 1.0 1 . 5 0.8 0.85 4 H I S S O N G 2.8 - 2.8 3 . 2 0 . 4 - 0.25 5 R K O P T M l 2 2 . 1 122. 1 1 3 4 . 6 2 4 . 6 - 2 4 . 65 5 R K C O R 1 4 4 . 1 l . o ’” 5 0 . 0 9.3 - 9 . 35 5 R K C O R 2 1 6 8 . 1 1 6 2 .6 3 1 4 . 3 2 0 . 7 5 . 45 5 R K C 0 R 3 6 9 4 . 8 - 6 8 1 .5 1 6 3 8 . 3 4 0 . 5 1 3 . 55 5 H I S S O N G 6 9 . 7 - 4 6 . 1 9 3 . 7 1 2 . 9 - 1 2 . 3

O.B2 . 21.20 . 73 . 30 . 30 . 41 . 3 0 . 9 0 . 7

0.60 . 70.20 . 5°-3_* 1.'4 2.2 1.0 0 . 4

2 6 . 0 10 . 9 2 7 . 8 7 3 . 1 1 4 . 4

131

T A B L E 28 t C O N T 'D)

N S Y S P R E S S U R E D E V . ( P S I ) T E M P E R A T U R E D E V . ( C)A V A B B I A S R M S A V A B B I A S R M S

5 6 R K O P T M5 6 R K C D R l5 6 R K C O R 2 ■5 6 R K C O R 35 6 H I S S O N G - - - ■5 7 R K OPTII 7 . 6 - 7 . 6 7 . 7 0. 1 _ _ _ _ 0 . 1; 0 15 7 R K C O R 15 7 R K C O R 25 7 R K C O R 3 2 .6 - 2.6 2 . 7 0.8 CO.01 0.85 7 H I S S O N G5 8 R K O P T M 0.6 0.0 0 . 7 0.1 0.0 0.15 8 R K C O R 1 1 .2 1.2 1.6 2 . 7 2 . 7 2 . 95 8 R K C O R 2 2.2 -2 . 2 2 . 5 0.6 - 0.6 0 . 75 8 R K C-OR3 0.6 - 0 . 3 0.8 0.2 0.2 0.25 8 H I S S O N G 0 . 6 0.6 0 . 9 1 . 3 1 . 3 i * -J5 9 R K O P T M 1.1 - 0 . 3 1.6 0.2 0 . 1 G . 35 9 R K C O i U 3 . 5 0 . 5 3 . 9 3 . 6 . ' 3 . 6 3 . 05 9 R K C O R 2 6.6 -6 .6 6 . 7 0 . 3 - 0.0 0 . 35 9 R K C O R 3 1 .6 - 0 . 1 1 . 9 0 . 9 0 . 9 0 . 95 9 H I S S O N G 2 . 3 0.6 2 . 7 1 . 9 1 . 9 2.0

6 0 R K O P T M 1 . 3 0.6 1 . 7 0.1 - 0.0 0.26 0 R K C D R l 6.2 0.8 5 . 1 3 . 6 3 . 6 ' 3". 76 0 R K C O R 2 6 . 5 - 6 . 5 5 . 0 1 . 9 - 1 . 9 2.06 0 R K C 0 R 3 2 . 3 - 2.0 2 . 7 0.6 - 0.6 0 . 76 0 H I S S O N G 3 . 8 3 . 6 5 . 6 3 . 0 3 . 0 3 . 26 1 R K O P T M 6.2 6.1 5 . 3 2.1 - 0 . 9 2 . 361 R K ' C D R l 9 . 0 " ' 9 . 0 9 . 7 "1.5"" 0 . 5 2.06 1 R K C 0 R 2 9 . 8 9 . 8 10.1 1 . 5 - 0.2 1 .76 1 R K C 0 R 3 5 . 6 5 . 6 5 . 9 2.2 - 1 . 9 2.66 1 H I S S O N G 1 8 . 9 1 8 . 9 22.6 7 . 5 7 . 5 8.6

6 2 R K O P T M 0 . 9 0 . 9 1.0 0.1 - 0.0 0.16 2 " R K C O R i 1.2 - 1.2 1 . 3 0.2 0.2 ' 0.26 2 R K C 0 R 2 1 .5 - 1 . 5 1.6 0.2 - 0.2 0.26 2 R K C 0 R 3 3 . 6 - 3 . 6 3 . 5 0 . 3 - 0.8 0.86 2 H I S S O N G 1 .6 - 1.6 1.6 0 . 3 0 . 3 0 . 3

1 3 2

T A B L E 2 8 ( C O N T ' D )

N S Y S P R E S S U R E D C V . ( P S I ) T E M P E R A T U R E D E V . (C)A V A B B I A S R M S A V A B B I A S R M S

6 3 R K O P T M 3 . 1 2.8 4 . 1 1 . 7 - 0.6 1 .86 3 R K C D R l 4 . 2 2 . 7 4 . 8 3 . 6 - 3 . 6 3 . 96 3 R K C O R 2 6 . 4 6 . 4 6 . 7 1 . 9 - 1 . 7 2.16 3 R K C O R 3 9 . 1 9 . 1 9 . 7 2 . 4 - 2 . 4 2.66 3 H I S S O N G 6 . 4 5 . 7 7 . 9 4 . 5 - 4 . 5 4 . 8

._J&4 R K O P T M6 4 R K C O R 16 4 R K C O R 26 4 R K C O R 36 4 H I S S O N G6 5 _ R K O P T M6 5 R K C O R 16 5 R K C O R 26 5 R K C O R 36 5 H I S S O N G66 R K O P T M 0 . 4 0.1 0 . 5 0.1 - 0.0 0.166 R K C 0 R 1 0.6 - 0.6 0 . 7 0 . 3 - 0 . 3 0 . 466 R K C 0 R 2 0.8 0 . 7 0 . 9 0.1 0 . 1 0.166 R K C 0 R 3 0 . 7 0 . 5 0 . 7 0.2 0.2 0.266 H I S S O N G 1.0 - 0.8 1.1 0.6 0.6 0 .66 7 R K O P T M 0.2 - 0 . 1 0 . 3 0.1 0.0 0.26 7 R K C O R 1 0 . 3 - 0 . 3 0. 4 0 . 1 - 0.1 0.2. " "6 7 R K C O R 2 0 . 4 0 . 3 0 . 5 0.2 - 0.2 0 . 36 7 R K C O R 3 0 . 4 - 0 . 4 0.6 0 . 5 - 0 . 5 0 . 56 7 H I S S O N G 0 . 5 - 0 . 5 0 . 5 0 . 7 0 . 7 0 . 76 0 R K O P T M 0 . 5 0.2 0.6 0.2 - 0 . 1 0.2

* 6 0 R K C O R 1 1 . o ’ ~ 0 . 0 1.1 "0.6 0.6 0 . 768 R K C O R 2 1.0 0 . 5 1.2 0.8 0.8 0 . 968 R K C O R 3 1 .7 - 1 . 3 1 . 9 0.6 0 . 5 0 . 76 8 H I S S O N G 0.6 - 0 . 4 0 . 7 0 . 3 - 0 . 3 0 . 36 9 R K O P T M 1 .3 1.0 1 . 9 0 . 5 - 0 . 2 0.66 9 R K C O R 1 2.0 0 . 5 2.6 0 . 7 0 . 5 0 . 9 * .. .6 9 R K C O R 2 2 . 4 - 1.0 2.6 0 . 7 - 0.0 0 . 76 9 R K C O R 3 3 . 2 - 2.0 3 . 4 0 . 7 - 0.1 0.86 9 H I S S O N G 1 . 4 1 . 4 1.8 0 . 7 - 0.6 0.8

133

T A B L E 2 8 { C O N T ' D )

N S Y S P R E S S U R E D E V . ( P S D T E M P E R A T U R E D E V . (C)A V A B B I A S R M S A V A B B I A S R M S

7 0 R K O P T M 0 . 5 - 0.0 0.6 0.0 - 0.0 0.07 0 R K C 0 R 1 0.6 - 0.0 0.6 " ' 0 . 2 ' . . . - 0.2 " 0 . 37 0 R K C 0 R 2 0.6 0.6 0.8 0 . 3 - 0 . 3 0 . 37 0 R K C D R 3 0 . 5 0.0 0.6 0 . 4 - 0 . 4 0 . 47 0 H I S S O N G 1.1 - 1.1 •1- 1 0.6 0.6 0 . 771 R K O P T M 1.0 0 . 3 1.1 0 . 4 - 0 . 1. 0 . 47 1 R K C D R l 1 . 5 - 1.0 1 . 7 0 . 5 ‘ - 0.1 0 • 57 1 R K C 0 R 2 2.2 - 2.2 2 . 5 0 . 9 - 0 . 9 1 .07 1 R K C 0 R 3 2 . 5 - 2 . 5 2.8 1.0 - 1.0 1.171 H I S S O N G 1.2 - 0 . 9 1 . 4 0 . 4 - 0 . 4 0.6

7 2 R K O P T M 0 . 5 - 0.2 0.6 0 . 1 - 0.0 0.17 2 R K C 0 R 1 0 . 7 - 0 . A 0 . 7 0 . 5 ■■■■■ - 0 . 5 .. " 0 . 5"7 2 R K C 0 R 2 0 . 9 - 0 . 9 1.2 1 . 4 - 1 . 4 1 . 57 27 2

R K C 0 R 3 H I S S O N G

0 . 5 0 . 1 0.6 0 . 3 - 0 . 3 0 . 3

7 3 R K O P T M 0.1 - 0 . 1 0.2 0.1 0.1 0.17 3 R K C 0 R 1 0 . 3 0 . 3 0 . 4 0 . 3 ' " 0 . 3 “ 0 . 37 3 R K C 0 R 2 0.8 0.8 0 . 9 0.1 0 . 1 0.17 37 3


0 . 4 0 . 3 0 . 5 0 . 3 - 0 . 3 0 . 3

7 4 R K O P T M 0 . 9 0 . 5 1 . 3 0.8 - 0.2 0 . 97 4 R K C 0 R 1 6 . 5 6 . 5 6 . 9 0 . 7 0 . 7 1 .07 4 R K C 0 R 2 7 .4 7 .4 7 . 9 1.1 1.1 1 .37 4 R K C 0 R 3 4 . 7 4 . 7 4 . 9 0.6 0.1 0 . 77 4 H I S S O N G 6.1 6.1 6 . 4 0 . 5 - 0 . 2 0.67 5 R K O P T M 0 . 3 - 0.0 0 . 3 0 . 5 0.2 0 . 575— ■ " R K C 0 R 1 2 . 4 2 . 3 3 . 1 2 . 7 2 . 7 .. 2 .8“7 5 R K C 0 R 2 1 . 9 1.8 2.6 2 . 4 2 . 4 2 . 47 5 R K C 0 R 3 1.6 - 0 . 3 1.6 1 . 7 1 . 7 1.87 5 H I S S O N G 3 . 1 3 . 1 3 . 4 1 . 5 1 . 5 1 . 57 6 R K O P T M 0 . 5 0 . 5 0 . 5 0.1 0.0 0.176' R K C 0 R 1 " 2.0 2.0 2.0 .. 0 . 9 0 . 9 ' 0 . 97 6 R K C 0 R 2 3 . 7 3 . 7 3 . 7 1 . 3 1 . 3 1 .37 67 6


1 . 5 1 . 5 1 . 5 0 . 3 0 . 3 0 . 3

13

T A B L E 2 8 ( C O N T ' D )

N S Y S P R E S S U R E D E V . ( P S I ) T E M P E R A T U R E D E V . (C)A V A B B I A S R M S A V A R B I A S R M S

7 7 R K O P T M 0 . 4 0 . 1 0 . 5 0 . 6 0 . 4 0 . 77 7 ' R K C O R 1 1.1 1.1 1 . 4 3 . 5 " 3 . 5 3 . 57 7 R K C O R 2 1 . 1 1.1 1 . 3 3 . 1 3 . 1 3 . 27 7 R K C O R 3 0 . 9 - 0 . 7 1.0 2 . 3 2 . 3 2 . 37 7 H I S S O M G 0 . 9 0 . 9 1.2 3 . 0 3 . 0 3 . 07 8 R K O P T M 2.6 2.6 2.8 0.2 - 0 . 1 0.27 8 ’ R K C 0 R 1 " 3 . 0 3 . 0 3 . 2 0 . 3 ' "“ 0 . 3 " “ ' “6 . 47 8 R K C D R 2 3 . 2 3 . 2 3 . 3 0 . 4 - 0 . 4 0 . 57 8 R K C 0 R 3 3 . 9 3 . 9 4 . 0 0 . 3 - 0 . 3 0 . 37 8 H I S S O M G8 0 R K O P T M 0 . 5 . 0 . 5 __ lIc*o 0.0 - 0.0 0.08 0 R K c n R i 0 . 4 0 . 4 0.6 0.2 - 0.2 0.28 0 R K C 0 R 2 0.8 0.8 0 . 9 0 . 3 - 0 . 3 0 . 48 0 R K C 0 R 3 0 . 5 - 0.2 0.6 0.8 - 0.8 0 . 98 0 H I S S O M G 0.8 0.8 0.8 0 . 4 0 . 4 0 . 4

135

T A B L E 2 9

C O M P A R I S O N O F S T A T I S T I C A L D E V I A T I O N D A T A O N T H E C R I T I C A L L O C I C A L C U L A T E D U S I N G T H E R E D U C E D I N T E R A C T I O N P A R A M E T E R S P R E D I C T E D B Y T H E V A R I O U S C O R R E L A T I O N S F O R T H E R E D L I C H - N G O E Q U A T I O N O F S T A T E

N S Y S P R E S S U R E D E V . ( P S D T E M P E R A T U R E D E VA V A R B I A S R M S A V A R B I A S

1 R M O P T M1 R N C D R 1 7 0 . 4 7 8 . 4 88 .5 2.1 - 1 . 31 R M C 0 R 2 3 6 4 . 3 - 3 6 2 .6 4 9 7 . 9 1 4 . 9 - 1 4 . 91 R M C O P . 3 3 8 3 . 1 - 3 0 2 . 0 5 3 0 . 2 1 0 . 5 - 7 . 6.2.. ... R M O P T M 1 . ] 0.0 _. . . J .. 2 ...... 0.2 ___ - 0..12 R M C O R 1 2 . 3 - 0 . 7 2.6 1.2 1.22 R M C 0 R 2 3 . 7 - 3 . 7 4 . 2 0 . 3 0.22 R M C 0 R 3 1 .4 - 0.8 1.6 0 . 3 0.23 R M O P T M 1 . 7 1.2 2 . 5 0 . 9 - 0 . 33 R M C O R 1 5 .2 5 . 2 6.0 _ _ _ 0 . 8. 0 . 73 R M C 0 R 2 5 . 4 5 . 4 5 . 6 0.8 - 0 . 53 R N C 0 R 3 4 . 7 4 . 7 5 . 0 0.8 - 0 . 54 R N O P T M 3 . 2 2.8 5 . 6 1 . 5 - 0.84 R N C 0 R 1 8 . 3 8 . 3 1 1 . 5 1 . 4 1 . 34 R M C 0 R 2 6.0 - 0 . 9 7 . 1 1 . 5 - 0.64 R M C 0 R 3 3 . 7 2.1 6 . 3 1 . 3 - 0 . 55 R M O P T M 1 0 . 4 9 . 6 1 5 . 1 3 . 2 - 1 . 75 R M C 0 R 1 2 3 .2 2 3 . 2 2 5 . 8 1 . 9 0 . 75 R M C 0 R 2 1 3 . 8 - 4 . 0 1 7 . 4 4 . 5 - 3 . 45 R M C O R 3 .12.0 - 0 . 5 1 6 . 3 . _ _ _ _ 4 . 0. _ _ _ _ —.2.46 R M O P T M 7 5 .9 7 5 . 9 8 7 . 4 1 2 . 7 1 2 . 76 R M C O R 1 4 4 . 9 4 4 . 9 4 8 . 5 4 . 0 3 . 06 R N C 0 R 2 2 6 . 3 - 4 . 9 31 . 5 6.2 - 2 . 96 R M C 0 R 3 2 8 . 9 - 7 . 8 3 5 . 9 6 . 3 - 1.8

RM" O P T M 5 .4 - 5 . 2 7 . 0 2 . 7 2 . 77 R M C 0 R 1 6.6 6.6 - 9 . 0 1 . 4 0 . 47 R M C 0 R 2 7 . 4 - 4 . 0 9 . 4 2.2 - 1.67 R M C D R 3 8 . 9 B . 9 12.2 1 . 9 1 . 7

(C)RMS

2 . 5 1 6 . 9 12.2

„_0 . 2______1 .3 0 . 4 0 . 31.0

_ 1 . 1________0 . 90 . 91 .62 .0 1 . 7 _ _ _1 . 53 . 32 . 54 . 9

4 ^ 2 __________1 5 . 35 . 66 . 96 . 9

■'3.5' “

1.6 2.62 . 4

T A B L E 2 9 ( C O N T ' D )

N S Y S P R E S S U R E D E V . ( P S I ) T E M P E R A T U R E D E V . (C)A V A R B I A S R M S A V A R B I A S R M S

8 R N 0 PT M 5 . 3 3 . 5 6.0 1.8 - 1.2 2.18 R N C H R 1 12.1 12.1 1 3 . 3 1.8 0.8 2.28 R N C 0 R 2 11.0 10.6 15 .2 2 . 9 - 2.8 3 . 48 R N C 0 R 3 5 . 7 4 . 2 6.6 1.8 - 0 . 9 2.09 R N D P T M 5 . 6 4 . 8 7 . 1 1 . 4 - 0 . 3 1 . 59 R N C O R 1 9 . 5 7 . 8 12.2 1.6 1 . 4 2.09 R N C 0 R 2 12.6 -6 .6 " 1 5 . 4 2.1 - 0 . 5 2.19 R M C 0 R 3 9 . 8 7 . 2 12.8 1 . 9 2 . 3

10 R N O P T M 3 . 9 - 3 . 9 4 . 0 0.2 - 0.2 0 . 310 R N C 0 R 1 4 . 1 - 4 . 1 4 . 3 0 . 5 - 0 . 5 0 . 510 R N C D R 2 0 . 3 - 0 . 3 0 . 4 0.2 0.2 0.210 R N C 0 R 3 ' 3 . 5 - 3 . 5 " ' 3 . 8 0 . 9 ’ - 0 . 9 ' 1 .011 R N O P T M 1 . 3 0.8 1 . 7 0.6 - 0 . 4 0 . 71 1 R N C O R 1 2.6 0 . 9 3. 1 1.1 1.1 1 . 411 R N C O R 2 2 . 3 0.8 2 . 7 0.8 0 . 7 1 .011_ _ _ R N C 0 R 3 . .2*1 -1 - 4 2 . 3 0 .8 - 0 . 712 R N O P T M 3 . 7 3 . 3 6.1 1.8 - 0.8 1 . 912 R N C 0 R 1 1 3 . 1 1 3 . 1 1 4 . 0 1.1 0 . 5 1 .412 R N C 0 R 2 7 . 0 7 . 0 7 . 6 2.1 - 1 . 7 2 . 312 R N C 0 R 3 4 . 9 4 . 9 5 . 4 3 . 0 - 2.8 3 . 31 3 R N O P T M 5 . 1 ' 4 . 8 " 7 . 6 2 . 3 ' - i . r " 2 . 51 3 R M C 0 R 1 1 7 . 2 1 7 . 2 1 8 . 2 1 . 4 0 . 9 1 . 91 3 R N C 0 R 2 8.1 8.1 8.8 2 . 4 - 1.8 2 .61 3 R N C 0 R 3 4 . 3 3 . 2 5 . 5 3 . 3 - 2 . 9 3 . 61 4 R N O P T M 3 . 1 2 . 4 4 . 5 1.0 - 0 . 3 1.21 4 " R N C 0 R 1 ‘8.2 8 .2 1 0 . 3 4 . 7 “ “" ' 4 . 7 . . . . 4 . 91 4 R M C 0 R 2 5 . 7 5 . 7 8.2 3 . 8 3 . 8 4 . 01 4 R N C 0 R 3 4 . 8 - 1.2 5 . 3 1.6 ' 1 . 4 1 . 91 5 R N O P T M 0.1 - 0 . 1 0.2 0.1 - 0.0 0.11 5 R N C 0 R 1 2 .6 2.6 2.6 2 . 1 2.1 2.115"' R N C 0 R 2 0 . 9 - 0 . 9 " 0 .9 ' . . . . . 0.8 ' 0.8. . . . 0.81 5 R N C 0 R 3 0.2 0.1 0.2 0 . 7 0 . 7 0.8

137

T A B L E 2 9 ( C O N T ' D )


1 6 R N O P T M 0 . 3 0 . 2 0 . 4 0 . 1 - 0 . 0 0 . 11 6 R N C 0 R 1 2 . 3 " 2 . 3 2 . 7 2 . 5 2 . 5 2 . 71 6 R N C D R 2 0 . 3 - 0 . 2 0 . 9 0 . 9 0 . 9 1 . 01 6 R M C 0 R 3 1 . 9 - 1 . 9 2 . 1 0 . 2 - 0 . 0 0 . 21 7 R N O P T M 2 . 0 1 . 2 2 . 9 1 . 2 - 0 . 5 1 .317 R N C O R 1 1 3 . 8 1 3 . 8 1 5 . 1 4 . 7 4 . 7 5 . 31 7 " R N C 0 R 2 9 . 6 9 . 6 1 0 . 1 ™ ~ 0 . 7 - 0 . 3 0 . 81 7 R N C 0 R 3 2 .6 2 . 6 3 . 4 1 . 3 - 1 . 0 1 . 518 R M O P T M A-. 9 3 . 5 5 . 9 3 . 7 - 1 . 3 4 . 01 8 R M C O R 1 2 5 . 7 2 5 . 7 2 6 . 1 4 . 0 3 . 7 5 . 01 8 R M C 0 R 2 2 6 . 1 2 6 . 1 2 6 . 7 5 . 5 5 . 5 _ 6 . 81 8 ~~RN C 0 R 3 9 . 9 9 . 9 1 0 . 7 3 . 5 1 . 9 4 . 61 9 R N O P T M 1 1 . 5 8 . 1 1 3 . 0 3 . 5 - 0 . 8 4 . 01 9 R M C 0 R 1 4 6 .0 4 6 . 0 4 6 . 4 2 . 1 2 . 1 2 . 41 9 R N C 0 R 2 4 6 . 6 4 6 . 6 4 7 . 0 5 . 2 5 . 2 5 . 61 9 R N C 0 R 3 2 2 .7 22.1 _ 2 3. 5 __ 3 . 5 - 1 . 7 _ 3 . 7_2 0 R N O P T M 8 . 2 8 . 2 1 1 . 6 2 . 2 - 1 . 0 2 . 42 0 R N C 0 R 1 2 3 . 0 2 3 . 0 2 3 . 6 2 . 6 - 2 . 6 2 . 82 0 R N C 0 R 2 1 2 .4 1 2 . 4 1 3 . 1 3 . 0 - 2 . 9 3 . 42 0 R N C 0 R 3 1 4 . 2 1 4 . 2 1 5 . 0 ■ 2 . 1 - 1 . 9 2 . 42 1 ~ W 0 P T M — ■ - .. .. . . . . . — — — . . . — -— ---------------- ------ - ------- " - —- - - - -21 R N C 0 R 12 1 R M C 0 R 221 R N C 0 R 3 . , .

2 2 R M 0 PT M2 2 R N C 0 R 12 2 R N C 0 R 22 2 R M C 0 R 32 3 R N O P T M 3 5 . 3 2 9 . 7 " 3 9 . 4 3 . 1 - 1 . 5 3 . 72 3 R N C 0 R 1 4 5 .7 3 0 . 5 5 1 . 3 4 . 7 - 3 . 8 5 . 923 " RN C0R23252.1 ‘ -3231.^ 7686.1 39.4 21.3 74.22 3 R N C 0 R 3 1 2 8 . 8 - 1 2 8 . 8 1 2 0 . 8 9.0 - 9 . 0 9 . 0

138

T A B L E 2 9 ( C O N T ' D )

N S V S P R E S S U R E D E V . ( P S I ) T E M P E R A T U R E D E V . (C)A V A B B I A S R M S A V A B B I A S R M S

2 4 _ R N O P T M _ _ ___ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _2 4 " R N C O R 1 '. . . .. . . . . . . . . . . . . . . . . . . .2 4 R N C G R 22 4 R N C O R 32 5 R N O P T M 0 . 5 0 . 3 0 . 6 1 . 0 1 . 0 1 . 12 5 R N C G R 1 _ _ .....2 5 R N C 0 R 2 . . . . . . . . . .2 5 R N C 0 R 3 1 . 8 1 . 8 2 . 2 1 . 6 1 . 6 1 . 62 6 R N D P T M 8.8 - 8.8 9 . 1 0 . 9 - 0 . 9 0 . 92 6 R N C 0 R 1 2 9 . 0 - 2 9 . 0 2 9 . 0 7 . 4 - 7 . 4 7 . 426_ R N C D R 2 1 0 . 3 - 1 0 . 3 1 0 . 7 _ _ _ _ _ _ _ _ 2 . 3 _ _ _ _ - 2 - . 3 .. , _ 2 ._32 6 R N C 0 R 32 7 R N O P T M 5 . 9 - 5 . 9 6 . 5 0 . 8 - 0 . 6 0 . 92 7 R N C 0 R 1 2 6 . 1 - 2 4 . 1 2 6 . 6 4 . 5 - ^ . 5 5 . 12 7 R N C 0 R 2 9 . 4 - 9 . 4 1 0 . 4 1 . 3 - 1 . 2 1 . 52 7 R N _ C 0 R 3 2 . 5 _ - 2 . 4 3 . 0 ._ _ _ _ _ _ V *0 _____ 1 • I2 8 R N O P T M 1 . 9 - 0 . 8 2 . 2 0 . 1 0 . 1 0 . 22 8 ' R N C D R 1 2 1 . 3 - 2 1 . 3 2 1 . 7 2 . 0 - 2 . 0 2 . 12 8 R N C 0 R 2 8 . 1 - 8 . 1 8 . 7 2 . 5 - 2 . 5 2 . 62 8 R N C 0 R 3 2 . 4 - 0 . 5 2 . 7 • 0 . 4 - 0 . 2 0 . 4Z9 R N ' O P T M . . . 3 . 9 - 0.1 " " 4 7 7 " “ ‘ "'6.5.... O.T 0.62 9 R N C D R 1 6 . 1 2 . 7 7 . 3 4 . 2 4 . 2 4 . 2

" 2 9 R N C 0 R 2 8.6 6 . 9 1 1 . 2 7 . 1 7 . 1 7 . 22 9 R N C 0 R 3 3 . 8 - 0 . 2 4 . 8 0 . 5 0 . 3 0 . 63 0 R N O P T M 1 . 7 - 0 . 8 1 . 7 1 . 4 - 1 . 4 _ _ _ _ _ 1 .63 0 ' R N C 0 R 1 4 . 1 - 4 . 1 ’ 4 . 1 ‘ 2 . 3 - 2 . 3 2 . 33 0 R N C 0 R 2 1 . 2 1 . 2 1 . 6 T .6 - 1 . 6 1 . 63 0 R N C 0 R 3 1 . 6 - 1 . 1 1 . 6 1 . 7 - 1 . 7 1 . 83 1 R N O P T M3 1 R N C 0 R 1

" " 3 1 R N C 0 R 2 ' . . . . . .3 1 R N C 0 R 3

139

T A B L E 2 9 ( C O N T ' D )


3 2 R N O P T M . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _:_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _3?. R N C D R 13 2 R N C O R 23 2 R N C O R 33 3 R N O P T M 0 . 3 - 0.1 0 . 3 0 . 1 0.0 0.13 3 RN. C 0 R 1 6 . 3 - 6 . 3 6.8 1 . 8 _ - 1.8 1 . 93 3 R N C 0 R 2 5 .5 - 5 . 3 5 . 8 0 . 3 - 0 . 3 0 . 33 3 R N C 0 R 3 3 . 0 - 3 . 0 3 . 1 1.6 - 1.6 1 .63 4 R N O P T M 0.2 - 0.0 0.2 0.0 - 0.0 0.03 4 R N C O R 1 3 . 2 - 3 . 2 3 . 2 0 . 4 0 . 4 0 . 53 4 R N C O R 2 2 . 9 . . . . - 2 . 9 3 . 0 0 . 2 _ _ _ _ - 0 . 2 _ _ _ __ 0 . 23 4 R N C 0 R 3 1 . 4 - 1 . 4 1 . 5 0.2 on 2 0.2

3 5 R N O P T M 0 . 9 0 . 5 1. 1 0.2 - 0.1 0.23 5 R N C O R ) 8 . 3 - 8 . 3 9 . 2 1 . 5 - 1 . 5 1.63 5 R N C 0 R 2 1 .7 - 0 . 3 1 . 9 1 . 5 1 . 5 1 .73 5 R N C 0 R 3 1 . 5 .1 *5 .. 1 . 7 _ _ _ 0 . 4 0 . 4 0 . 53 6 R N O P T M 1.0 0 . 4 1.2 0 . 1 - 0.0 0.13 6 R N C 0 R 1 2 . 4 - 2 . 3 2.8 1 . 3 1 . 3 1 .43 6 R N C 0 R 2 2 . 7 - 2.6 3. 1 0 . 3 0.2 0 . 33 6 R N C 0 R 3 1 . 5 - 0 . 4 1.6 0.6 - 0.6 0 . 73 7 R N O P T M 8 .4 8 . 4 9 . 3 3 . 0 3 ^ 8 ’ 5 . 03 7 R N C 0 R 1 7 . 9 - 0 . 4 8.6 7 . 0 - 7 . 0 7 . 43 7 R N C 0 R 2 5 . 5 - 1 . 4 6 . 4 4 . 2 - 4 . 2 4 . 63 7 R N C 0 R 3 8 . 4 1.8 9 . 0 7 . 2 - 7 . 2 7 . 63 8 R N O P T M 2.0 1 . 9 3 . 2 0 . 9 - 0 . 5 1 .03 8 R N C 0 R 1 1 3 . 4 1 3 . 4 1 4 . 2 1 . 9 1 . 9 2.23 8 R N C 0 R 2 2 . 3 2 . 3 3 . 4 1-0 - 0.6 I .13 8 R N C 0 R 3 4 . 5 4 . 5 5 . 6 1.0 0.6 1.2

3 9 R N O P T M 4 . 1 4 . 1 4 . 4 0.2 - 0.0 0 . 33 9 R N C 0 R 1 4 . 2 4 . 2 4 . 5 0 . 7 - 0 . 7 0 . 73 9 R N C 0 R 2 5 . 3 5 . 3 5 . 3 0 . 5 0 . 5 . . 0.63 9 R N C 0 R 3 5 . 3 5 . 3 5 . 3 0.2 0 . 1 0 . 3

T A B L E 2 9 ( C O N T ' D )

^!SYS P R E S S U R E D E V . ( P S I ) T E M P E R A T U R E D E V . (C)A V A B B I A S R M S A V A B B I A S R M S

4 0 R M O P T M 4 . 2 4 . 2 4 . 4 0.0 - 0.0 0 . 0__4 0 R M C O R 14 0 R M C O R 2 7 . 0 7 . 0 7 . 2 0.0 0.8 0.84 0 R N C O R 3 5 . 8 5 . 8 5 . 9 0 . 5 0 . 5 0 . 54 1 R M O P T M4 1 R M C O R 14 1 R N C O R 24 1 R M C O R 34 2 R M O P T M 1 .2 - 1.2 1.2 0.1 0.0 0.14 2 R M C O R 14 2 R M C 0 R 2 0 . 5 - 0 . 5 0.6 1.6 1.6 1 .64 2 R M C 0 R 3 0.8 0.8 0 . 9 0 . 7 0 . 7 0 .74 3 R M O P T M4 3 R M C 0 R 14 3 R M C 0 R 24 3 R M C 0 R 3 . ...... ......... . — . *4 4 R M O P T M 3 . 1 3 . 1 3 . 5 0.8 - 0 . 1 0 . 94 4 R M C 0 R 1 1 3 . 1 1 3 . 1 1 3 . 7 1.2 - 1.2 1 . 34 4 R M C 0 R 2 10.6 10.6 10.6 0 . 5 - 0 . 4 0.64 4 R M C 0 R 3 1 1 . 5 1 1 . 5 12.2 2 . 5 - 2 . 5 2.6

4 5 R M O T P M 4 . 4 4 . 4 4 . 7 2.2 2.2 .. . . 2 .6~4 5 R M C 0 R 1 12.6 12.6 1 3. 1 0 . 4 0.0 0 . 54 5 R N C 0 R 2 7 . 5 7 . 5 7 . 7 0 . 7 0.1 0.84 5 R N C 0 R 3 9 . 1 9 . 1 9 . 7 2 . 9 - 2 . 9 3 . 04 6 R N O P T M 0.2 0.1 0 . 3 0.0 - 0.0 0.14 6 " " " R N ‘ C 0 R 1 3 . 3 3 . 3 ' " 3 . 4 1.2 1.2 1 .2"'4 6 R N C 0 R 2 1 .6 1.6 1.6 1 . 5 1 . 5 1 . 54 6 R N C 0 R 3 2 . 4 2 . 4 2 . 5 0 . 7 0 . 7 0.84 7 R N O P T M 0 . 3 o . r 0 . 4 0.0 0.0 0.14 7 R N C 0 R 14 7 R N C 0 R 24 7 R N C 0 R 3 1 .1 i . i 1.2 0 . 4 0 . 4 0 . 4

141

T A B L E 2 9 ( C O N T ' D )


j 4 8 R N O P T M _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _" 4 8 R N C O R 14 8 R N C O R 24 8 R N C O R 34 9 R N O P T M 4 . 9 4 . 9 5 . 4 2 . 8 2 . 8 3 . 0

_ 4 9 R N C 0 R 1 1 0 . 7 - 1 0 . 7 _ 1 1 . 5 0 . 3 _ - 0 . 1 0 . 4 _4 9 R N C 0 R 2 5 . 3 - 5 . 3 5 . 8 .. . . 0 . 3 " - 0.1 0 . 3 '4 9 R N C 0 R 3 1 . 6 - 1 . 4 1 . 7 0 . 2 0 . 2 0 . 35 0 R N O P T M 0 . 8 0 . 2 0 . 9 0 . 2 0 . 0 0 . 35 0 R N C O R 1 1 1 . 8 - 1 1 . 8 1 2 . 1 0 . 5 0 . 4 0 . 75 0 R N C n R 2 4 . 0 - 4 . 0 _ 4 . 4 _ _ 0 . 3 ____ 0 . 1 _ _ __.0. 45 0 R N C 0 R 3 1 . 0 - 0 . 2 1 . 1 0 . 3 - 0 . 1 0 . 35 1 R N O P T M 0 . 9 0 . 3 1 . 2 0 . 3 0 . 0 0 . 35 1 R N C 0 R 1 1 3 . 9 - 1 3 . 9 1 5 . 1 0 . 9 0 . 8 1 . 251 R M C 0 R 2 2 . 1 1 . 0 2 . 9 2 . 9 2 . 9 2 . 9

_ 5 1 ___ R N C 0 R 3 _ 1 . 1 _ _ _ _ _ 0 . 4 _ _ . 1 . 4 „ . ____ 0 . 7 . . . __0.7. . .. 0 . 8_5 2 R N O P T M 0 . 7 0 . 6 0 . 8 0 . 2 - 0 . 1 0 . 25 2 R M C 0 R 1 2 . 6 - 2 . 6 2 . 7 0 . 3 0 . 2 0 . 45 2 R N C 0 R 25 2 R N C 0 R 3 0 . 5 - 0 . 0 0 . 7 0 . 4 0 . 4 0 . 553 RN OPTM 1 . 2 - 1 . 2 1 . 4 0 . 1 0 . 0 0 . 153 RN C0R1 1 . 0 1 . 0 1 . 0 1 . 6 1 . 6 1 . 753 R N C0R2 2 . 2 - 2 . 2 2 . 3 1 . 1 1 . 1 1 . 253 RN C0R3 1 . 7 - 1 . 7 1 . 9 0 . 5 - 0 . 5 0 . 6

5 4 R N OPTM 0 . 5 _ 0 . 3 _ 0 . 6 0 . 2 - 0 . 1 0 . 354 ' RN C0R1 4 . 7 ........... - 4 . 7 ........ 5 . 0 1 . 5 1 . 5 " ’ 1 . 754 RN C0R2 5 . 2 - 5 . 2 5 . 4 2 . 2 2 . 2 2 . 454 " RN C0R3 4 . 7 ' - 4 . 7 " 5 . 2 2 . 0 - 2 . 0 2 . 1

55 RN 0PTM16 8 . 8 1 5 7 . 5 1 8 5 . 7 1 7 . 8 - 1 7 . 8 1 8 . 455 RN C0R1 4 8 . 3 2 . 2 5 4 . 0 1 0 . 0 - 1 0 . 0 1 1 . 35 5 RN COR22389.5 - 2 3 8 8 . 0 6 0 7 2 . 6 3 1 . 2 7 . 6 5 6 . 855 RN C 0 R 3 1 8 4 . 3 - 1 8 4 . 3 2 1 1 . 9 1 4 . 8 - 1 4 . 8 1 6 . 1

142

T A B L E 2 9 ( C O N T ' D )

N S Y S P R E S S U R E D E V . ( P S I } T E M P E R A T U R E D E V . ( C )A V A B B I A S R M S A V A B B I A S R M S

5 6 R N h p t m 1 . 4 - 1 . 4 1 . 6 0. 1 0 . 0 0 . 15 6 R N C O R 1 1 . 5 - 1 . 5 2 . 0 1 . 8 - 1 . 8 1 . 85 6 R N C D R 25 6 R M C 0 R 3 2 . 4 2 . 4 2 . 8 1 . 4 1 . 4 1 . 45 7 R N d p t m5 7 R M C O R 15 7 R N C 0 R 25 7 R M C 0 R 3 -5 8 R N O P T M5 8 R M C O R 15 8 R M C 0 R 2 5 . 5 ___ - 5 . 5 5 . 5 2 . 2 _ - 2 . 2 2 . 35 8 R N C 0 R 35 9 R N O P T M5 9 R N C O R 15 9 R N C 0 R 2 4 . 1 - 4 . 1 4 . 1 0 . 4 - 0 . 4 0 . 55 9_ R M C 0 R 3 1 . 2 - 1 . 2 1 . 2 0 . 3 0 . 3 _ _ _ 0 . 36 0 R N O P T M 1 . 9 - 1 . 4 2 . 2 0 . 5 - 0 . 5 0 . 56 0 R N C 0 R 16 0 R N C 0 R 2 7 . 0 - 7 . 0 7 . 2 3 . 3 - 3 . 3 3 . 46 0 R N C 0 R 3 2 . 2 - 2 . 2 2 . 8 0 . 7 - 0 . 7 0 . 86 1 R N O P T M 3 . 3 1 . 8 3 . 8 " 0 . 8 ' - 0 . 0 0 . 96 1 R N C O R 1 8 . 0 8 . 0 8 . 0 1 0 . 0 1 0 . 0 1 0 . 16 1 R M C 0 R 2 1 0 . 5 1 0 . 5 1 1 . 1 4 . 8 4 . 8 4 . 96 1 R M C 0 R 3 3 . 7 3 . 4 4 . 5 0 . 7 0 . 6 1 . 06 2 R N O P T M 1 . 1 1 . 1 1 . 2 0 . 1 - 0 . 1 0.16 2 " R M ' C 0 R 1 0 . 8 0 . 8 0 . 8 0 . 9 O'. 9 ‘ 0 . 9'6 2 R M C 0 R 2 2 . 5 - 2 . 5 2 . 5 0.1 0. 1 0 . 16 2 R N C 0 R 3 1 .7 - 1 . 7 1 . 8 0 . 5 - 0 . 5 0 . 56 3 R N O P T M 3 . 3 2 . 7 4 . 2 1 . 7 - 0 . 5 1 . 96 3 R N C 0 R 1 1 3 . 9 1 3 . 9 1 4 . 2 1 . 4 1 . 3 1 . 96 3 ~ R N C 0 R 2 3 . 7 3 . 0 4 . 4 2 . 9 - 2 . 8 3 . 26 3 R N C 0 R 3 5 . 3 5 . 3 6 . 2 3 . 0 - 3 . 0 3 . 3

143'

T A B L E 2 9 ( C O N T ’ D)


6 4 _ R N O P T M ____ _ _ _ _ _ _ _ ___ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _” 6 4 " R N C O R 1 ...6 4 R N C O R 26 4 R N C O R 36 5 R N O P T M

_ 6 5 _ R N C O R l _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _6 5 R N C 0 R 26 5 R N C O R 366 R N O P T M 0 . 5 0 . 1 0 . 5 0 . 1 - 0 . 0 0 . 166 R N C 0 R 1 0 . 6 - 0 . 6 0 . 7 0 . 2 - 0 . 2 0 . 266_ _ R N C 0 R 2 _ _ __ _ _ _ _ _ _ _ _ _66 “ R N C O R 3 1 .8 1 . 8 1 . 8 0 . 3 0 . 3 0 . 36 7 R M O P T M 0 . 2 - 0 . 1 0 . 3 0 . 1 0 . 0 0 . 26 7 R M C 0 R 1 0.6 0 . 6 0 . 7 0 . 4 0 . 4 0 . 46 7 R N C 0 R 2 0 . 6 0 . 6 0 . 7 0 . 4 0 . 4 0 . 46_7 _ R N C 0 R 3 0 . 5 0 . 6 _ 0.2 - 0 ._2 _ _ _ _ _ 0 .368 R N O P T M 0 . 4 0 . 2 0 . 6 0 . 2 - 0 . 1 0 . 268 R N C D R 1 1 . 1 - 0 . 3 1 . 2 0 . 9 0 . 9 1 . 168 R N C D R 2 1 . 2 0 . 9 1 . 5 1 . 3 1 . 3 1 . 468 R N C 0 R 3 2 . 7 - 2 . 7 2 . 9 0 . 6 - 0 . 6 0 . 76 9 R N O P T M 1 . 3 0 . 7 1, 9*' 0 . 5 - 6".“ ' ' '6.5'6 9 R N C 0 R 1 3 . 2 - 1 . 8 3 . 4 0.8 0 . 7 1 . 16 9 R N C 0 R 2 5 . 5 5 . 5 6 . 3 2 . 8 2 . 8 3 . 06 9 R N C 0 R 3 3 . 8 - 3 . 2 4 . 2 0 . 8 - 0 . 4 . 0.87 0 R N O P T M 0 . 5 _ 0 . 4 0 . 7 _ 0.0 - 0 . 0 _ _ _ _ _ 0 . 0“Yd"' R M C O R l 1 .8' 1.8 1 . 9 0.8 0.8 0.87 0 R N C 0 R 2 0 . 9 „ 0 . 9 1 . 1 0 . 9 0 . 9 0 . 97 0 R N C 0 R 3 0.6 0 . 5 0 . 8 0 . 1 0 . 0 0 . 17 1 R N O P T M 2 . 8 - 2 . 8 ' 3 . 2 0 . 4 0 . 0 0 . 5

__ 71_ R N C O R l 3 . 3 _ - 3 . 3 _ 3 . 5 0 . 4 _ - 0 . 2 „ 0 . 57 1 ' “ R N C 0 R 2 2 . 8 ' 2 . 8 3 . 0 . . . . . . . 1 . 7 “ 1 . 7 1 . 871 R N C 0 R 3 3 . 7 - 3 . 7 3 . 9 0 . 9 - 0 . 9 0 . 9

T A B L E 2 9 ( C O N T ' D )

NSYS PRESSURE DEV. (PSI) TEMPERATURE DEV. (C)AVAB BIAS

72 RN OPTM72 RN CORl '72 RN C0R272 RN C0R373 RN OPTM 0.4 0. 173 RN CORl 1.9 1.973 RN C0R2 2.1 2.173 RN C0R3 0.4 0.2

RMS AVAB BIAS RMS

0.6 0. 1 0.0 0.11.9 1.1 1.1 1.12.1 1.1 1.1 1.'20.6 0.2 0.2 0.2

74 RN OPTM 0.8 0.4 1.1 0.8 -0. 1 0.874 RN CORl 8.4 8.4 8.9 2.1 2. 1 2.374 RN C0R2 7.1

.. . 7 *! . . 7.5 1.4 1.4 1 .674 RN C0R3 4.6 4.6 4.9 0.6 -0.3 ”0.775 RN OPTM75 RN CORl75 RM COR275 RN C0R376 RN OPTM 0.3 0.3 0.4 0.1 0.1 0.276 RN CORl76 RN C0R276 RN C0R3 3.9 3.9 3.9 1.9 1.9 1.9

77 RN OPTM77 RN CORl77 RN C0R277 RN C0R378 RN OPTM78 RN CORl78 RM C0R278 RN C0R380 RN OPTM 0.3 0.3 0.4 o.o c*o0 .c1

80 RN CORl80 RN C0R2 1 .5 ' 1.5 1.5 0.6 0.6 0.780 RN C0R3 0.4 0.4 0.5 0.0 -0.0 0.0

The overall absolute average deviations excluding the systems with ethane as a common component are summarized as followst

Overall. Absolute Average Deviations■Ngo Eq.

CorrelationRedlich--Kwong Eq. Redlich-P(psi) T(°C) P(psi) T(°C)

OPTM 2.6 0.8 4.1 1.1CORl 4.5 2.0 10.0 • 00

C0R2 5.1 1.4 6.7 1.9C0R3 4.2 1.3 4.4 1.4HISSONG 5.5 1.9

Notei OPTM = Optimum interaction parametersKESSONG = Interaction parameters calculated

from the Hissong-Kay correlation

A comparison of the overall absolute deviations show the following* 1) The critical temperatures and pressures calculated by using the reduced interaction parameters predicted by the correlation 3 for both the Redlich-Kwong and Redlich-Ngo equations, i.e., RK C0R3 and RN C0R3, deviate least from the experimental values. 2) The equation of state method can predict, on the average, the critical temperature and critical pressure of a hydrocarbon system to within 2°C and 10 psi, respectively.3) The new correlations of the reduced interaction parameters for the Redlich-Kwong equation, i.e., RK C0R3, are somewhat better for the prediction of the critical temper-

146ature and critical pressure than the Hissong-Kay correlation, 4) The critical temperature and critical pressure predicted by the Redlich-Kwong and Redlich-Ngo equations are of about the same accuracy.

It should be pointed out, however, that the Redlich- Ngo equation predicts the critical volume more accurately than the Redlich-Kwong equation. This is shown in Fig, 26, where the calculated critical volume -composition curves are compared with the experimental data for the propane - n-pentane system ( 66 ),

The point by point comparison between the experimental and the calculated critical properties using the reduced interaction parameters predicted by RK C0R3 and RN C0R3 for the systems studied in this work, is presented in Table j6. Appendix D,

CRITICAL VOLUME

(cc/g-mole)

147

O Experimental Points (66)

350

Redlich-Kwong Equation

300

Redlich-Ngo Equation

200

0.6 0.8 1.00.20.0MOLE FRACTION PROPANE

Fig. 26 - Comparison of Calculated vs. Experimental Critical Volume - Composition Relationships! Propane - n-Pentane System

1 85. Test of Correlations

Chueh-Prausnitz method ( 1 5 ) predicting critical constants of mixtures is somewhat different from that proposed here. The values of the critical constant predicted by this method for the 1^ binary systems that were studied, are shown in Table 30 and are compared with those obtained by the equation of state method. Included in the table are values predicted by another method developed by Li ( 58 ). In a study of the various methods for predicting the critical properties of hydrocarbon binary systems which did not include the equation of state method, Spencer (88) concluded that the methods of Chueh-Prausnitz and Li showed the smallest deviations from the experimental values. Table 30 shows that all methods give about the same values but that the equation of state method is best for the systems with cis-Decalin.

To test further these correlations, the critical loci of five binary systems which were not included in the study, were calculated using the interaction parameters predicted by RK C0R3 and RN C0R3 and were compared with the experimental values.

TA3L2 30

COMPARISON OF CRITICAL TEMPERATURES PREDICTED BY VARIOUS METHODS

SystemAbsolute Average Deviation (°C)

RK C0R3 RN COR3 Chueh-Prausnitz Li

n-Hexane - n-Decane 1.4 1.3 1.0 0.6- n-Tridecane 4.2 3.5 4.4 2.2- n-Tetradecane 6.7 3.5 9.5 6.4- cis-Decalin 1.6 2.1 21.0 12.6

n-Nonane - n-Tridecane l.l 1-5 1.4n-Decane - n-Dodecane 0.8 0.3 0.2Benzene - n-Decane 0.8 0.4 0.4 3.3- n-Tridecane 2.3 0.5 8.3 2.5- cis-Decalin it-.2 7.2 18.6 10.0Ethylbenzene - cis-Decalin 0.9 2.5o-Xylene - cis-Decalin 1.0 2.9Cyclohexane - n-Decane 0.6 0.7 2.0 0.5- n-Tridecane 2.2 0.7 5.0 1.3- cis-Decalin 2.4 3.0 21.5 12.4

The results were as followsi150

Average DeviationSystem Ref. Method Pc(psi) Tc(°C)

Ethane - n-Butane 1+9 RK COR3 '*

RN COR35.66.1 3.1+1.2

C02 - H2S 11 RN C0R3 8.1+ 3.1- Ar 1+6 RN COR3 1+81.1+ 10.3

Propane - H2S 52 RK COR3 5*+. 3 1.1+

co2- n-Butane 69 RK COR3 75.1+ l+.l

The above results show that the calculated critical temperatures are in satisfactory agreement with the observed except for the CH^ - Ar system but the critical pressures for the hydrocarbon - non-hydrocarbon systems are in poor agreement with the experimental values. However, the results indicate that the equation of state method is capable of calculating the critical properties of binary systems other than hydrocarbon-hydrocarbon systems.

Therefore, to calculate the critical properties of systems other than hydrocarbon-hydrocarbon systems with higher accuracy, the correlations for the reduced interaction parameters should be improved by applying the optimization technique to all types of binary systems available in the literature.

151B. The Application of the Theory of Conformal Solution

Using the Kevised Theoxêm of Corresponding States

Longuet-Higgins (59) developed the theory of con-formal solutions, according to which all thermodynamicproperties of a mixture can be evaluated from those ofthe pure compounds if the components conform to certainpostulates of statistical mechanics.

A conformal solution is one whose pair potential asa function of intermolecular distance, u. .(r), is related— Jto those of a reference substance, u , byoo

“ fijuoo(®ij’r) (73)

where f. . = ./£. . = energy parameter,-L J X J J. J

g. . = roD/r?-i ~ size parameter,1 J OO X jr* = the intermolecular distance at which u(r) has

its minimum,<£* = the minimum depth of u.

In order to apply the theory of conformal solutions, a knowledge of a general principle of corresponding states is required. According to the classical principle of corresponding states, the applicability of the theory was limited to small spherical molecules such as Ar, CO, CH^, and However, Kreglewski and Kay (55) have shown thatwhen the classical principle of corresponding states is properly modified, satisfactory agreement with experimental data is obtained for both small and large molecules.

152The basic assumptions were that the total pair potential (u. .) and the force constant per equivalent surface (£. .) could be expressed by means of the general principle of corresponding states, namely

u12

* vl/3^11u TC \V* / OO 00 ' oo

u22 T2 ( V2° /v* \ 1/3

u Tc \V .oo oo\ oo* . st- \ 1/3W MTC I V# /o n V n n *uoo “OO ' 00

c ✓ * vl/3 " T f V'11 X1 f 00w

€ Tc Vv.oo oo\ 1* x-1/3

22 x2 f ’ooT„ / V1 *if£- T \ Vfcoo oo\ 2

s- t # \l/3^12 W V >

" o o = To o U 2

(7*0

(75)

(76)

(77)

(78)

(79)

c ^where T^ and are the critical temperatures and the liquidmolar volumes at the reduced temperature T/T? - 0.6 of the

*pure components, T^2 is the characteristic temperature for mixed interaction, and V^2 measures the size involved in a

153mixed collision. Two other assumptions were that l) the configurational properties of mixtures, that is, those depending on u. . are functions of surface fractions, and

X J2) a pure fluid behaves approximately as a system of rigid spheres in the critical state. Since an accurate and generally valid combining rule for u^^ could not be found, it is approximated by the harmonic mean

2 yu12 -------------------- (80)

For mixtures of two inert liquids, is also obtainedby taking a harmonic mean of anc* ^22

2 y

C^7 + 4 )

£ 12 ^ (81)

The value of y appearing in Bqs. (80) and (8l) is unity for a mixtures of two inert liquids, but may be different from unity in the presence of specific (doner-accepter) interactions, either between one or both of the components.

On the basis of the above mentioned assumptions, Kreglewski and Kay ( 55 ) derived the equations, utilizing the relations for the critical and pseudocritical constants given by Kowlinson ( 82 ), which could be used to predict the critical properties of conformal mixtures.

15This method makes use of the theory of conformal solutions, slightly modified in that it employs surface fractions instead of mole fractions. A feature of this method is that the calculation can he made by using the data on the pure components alone. From now on this method will be called "Revised Corresponding States method". Since the details of derivation have been described in ( 55 )» the final relations needed for the calculation of the critical properties of binary mixtures are presented here.

1. Critical Temperature (Eq. (8) in Ref. 55 )

2+ 1 , 2 (82)

where Tc = the critical temperature of the mixture in °K, T? = the critical temperature of the pure component

(i = 1,2) in °Kf = the pseudo-critical temperature of the mixture

* Om K*^ = the surface fractions of the pure components,

■u- #= Vx = the molar pseudo-volume of a mixture of rigid spheres at the reduced temperatureT/Tc =0.6,

-e o

= the liquid molar volumes of the pure components at T/fc = 0.6. and

for all systems involving inert (non-associated) liquids.

2, Critical Pressure (Eq, (15) in Ref. 55 )

= the pseudo-critical pressure of the mixture in psia,

3. Pseudo-critical Temperature (Eq. (12) in Ref. 55 )

Y = association factor or constant equal to unity

where

156Pseudo-critical Pressure (Eq. (1*0 in Ref. 55 )

r c t s ; p ^ i + ,86)P t 1/3 c c (oo;P (Vp )V3 T 1<?Z

W 75

5, Molar PseudQ"Volume of a Mixture of Rigid Spheres (Eqs. (3) and (4) in Ref. 55 )

< “ Vlxl + V* + (2Vrr ' V1 - VP X1X2 <6?>3

V = i--------- £---- i— (88)rr 8

= the mole fractions of the pure components corresponding to the surface fractions <p in all the remaining relations.

6* The Surface Fractions

■* \ 2/3- 1 (89)\v^/ xi

and ? Z = 1 “ ?i <Ref* 53)

1577. The Logarithmic Slope of the Vapor Pressure Curve

at Critical PointThis slope is approximated from the equation for

pure fluids due to Pitzer and coworkers (68 ). That is,

( a l H L = 5.808 + k.93«j (90)

where a) = the acentric factor of a mixture. tO is calculated from the following relation (Eq. (17) in Ref. 55 ),

€aJ + ^ 2 $ 2 +

h r

-JL - + J L _ (a)\

- b)1 - a) 2 Pi P 2 ^l)

where c*j is the acentric factors of the pure components, defined by Pitzer and coworkers as

P.i = - log “ - 1 Pj

(92)

where P^ is the vapor pressure at T/Tc = 0,7t

158For a quick comparison, the statistical deviation

data on the critical loci calculated using the equation of state and the revised corresponding states methods are summarized in Table 31. In these calculations, for the first method the reduced interaction parameters predicted by RK C0R3 and RN C0R3 were used; in the second method, the association factor Y = 1 was used for systems of two inert components and Y = 0,99, for systems of an inert component with a doner-acceptor compound, i.e., aromatic- n-alkane and aromatic-naphthenic systems, as suggested by Kreglewski and Kay, The use of a value of / less than unity did improve the critical temperature and critical pressure prediction for the aromatic-naphthenic systems, but not for the aromatic-n-alkane systems. Unfortunately, at the present time, we are not in a position to predict the Y value accurately.

It is to be noted in Table 31 that as the relative size difference of the components increases, the calculated values by the revised corresponding states method, show greater deviations from the experimental values.This was also the case with the equation of state method. The revised corresponding states method also predicts, on the average, the critical temperature and critical pressure within 10 psi and 2°C, respectively. However, the equation of state method predicts the critical pressure slightly better than the revised corresponding states

159method by about b psi. It is remarkable that the calculated critical temperatures and critical pressures from two entirely different approaches agree so closely.

The point by point comparison between the experimental and the calculated critical properties for the systems studied in this work is given in Table 36,Appendix D.

l6o

T A B L E 3 1

COMPARISON OF STATISTICAL DEVIATION DATA ON THE CRITICAL LOCI CALCULATED BY THE EQUATION OF STATE

AND THE REVISED CORRESPONDING STATES METHODS

N S Y S P R E S S U R E DE'' . ( P S I ) T E M P E R A T U R E D E V . (C)A V A B B I A S R M S A V A B B I A S R M S

1 R K C G R 3 2 6 . 1 2 6 . 1 3 2 . 1 3 . 2 - 1.2 4 . 1i R H C O R 3 3 8 3 . 1 - 3 0 2 . 0 5 3 0 . 2 1 0 . 5 - 7 . 6 12.21 K K 4 2 . A - 2 1 . 9 5 2 . 6 3 . 2 - 3 . 2 4 . 12 R K C D R 3 1 .2 - 0.8 1 . 5 0.2 - 0.1 0.22 R N C 0 R 3 1 .4 - 0.8 1.6 0 . 3 0.2 0 . 3

_ _ _ 2 . K K . ...1 1 1.6 . 0.2_ _ _ _ „ 0.2_ _ _ _ _._0.2 _ _ _ _ _ _3 R K C O R 3 1 . 7 1.2 2.0 2.0 - 2.0 2 . 43 R N C G R 3 4 . 7 4 . 7 5 , 0 0.8 - 0 . 5 0 . 93 K K 5 . 0 5 . 0 5 . 8 0 . 5 0 . 5 0.6

_ _ _ 4 _ R K C O R 3 2 . 5 0 . 5 . 3 . 7 . . . . . 1.8 “ 1*6 2.04 R N C 0 R 3 3 . 7 2.1 6 . 3 1 . 3 - 0 . 5 1 . 5A K K 7 . 7 - 2 . 7 8 . 4 1 . 7 1 . 7 1.8

5 R K C G R 3 7 . 7 7 . 0 11.2 3 . 8 - 3 . 2 4 . 25 R N C 0 R 3 12.0 - 0 . 5 1 6 . 3 4 . 0 - 2 . 4 4 . 2

K K 1 4 . 5 .......“ 5 , 7 1 6 . 6 1.1. . . 1.0_ _ _ _ _1 .6_____6 R K C O R 3 1 7 . 5 1 6 . 8 2 2 . 4 5 . 2 - 2 . 3 5 . 66 R N C O R 3 2 8 . 9 - 7 . 8 3 5 .9 6 . 3 - 1.8 6 . 96 K K 21 .6 - 10.0 2 6 . 0 2 . 3 1 . 7 3 . 37 R K C 0 R 3 9 . 0 9 . 0 1 0 . 4 1.2 - 0.1 1 . 37 R N C O R 3 8 . 9 0 . 9 12.2 1 . 9 1 . 7 2 . 47 K K 4 . 2 - 4 . 1 5 . 4 0 . 3 - 0 . 3 o . ?8 R K C O R 3 4 . 4 2.2 4 . 9 2 . 9 - 2 . 9 3 . 28 R N C G R 3 5 . 7 4 . 2 6.6 1.8 - 0 . 9 2.0

_ _ _ 8 __ K K ___ 3 .2 - 1 . 3 3 . 4 1.2 - 0 . _ _ _ 1 .6_ _ _ _ _ _9 R K C O R 3 2.8 0 . 5 2 . 9 2 . 5 - 2 . 5 2.89 R N C G R 3 9 . 8 7 . 2 12.8 1 . 9 1 . 7 2 . 39 K K 4 . 9 - 4 . 3 6.8 0 . 4 - 0 . 3 0.6* * * * * * * * * * * *KK = T h e R e v i s e d C o r r e s p o n d i n g S t a t e s M e t h o d w i t h Y = 1 .

l6l

T A B L E 3 i ( C O M T * D)

JS Y S P R E S S U R E D E V . ( P S I ) T E M P E R A T U R E 1A V A B B I A S R M S A V A R B I A S

10 R K C O R 3 1.0 - 0 . 3 1.1 0.2 - 0.210 R N C 0 R 3 3 . 5 - 3 . 5 3 . 8 0 . 9 * -0 . 910 K K 1 .7 1 . 7 2.2 0 . 4 0 . 411 R K C 0 R 3 2 .6 I o • CO 2.8 0 . 7 0 . 111 R N C 0 R 3 2.1 - 1 . 4 2 . 3 0.8 - 0 . 711 K K ! .4 0 . 7 1 . 7 .... 0 . 8 _ 0.812 R K C D R 3 5 . 7 5 . 7 6.6 2.0 - 1 . 712 R N C 0 R 3 4 . 9 4 . 9 5 . 4 3 . 0 - 2.812 K K 5 . 5 5 . 5 6.2 0 . 4 0 . 41 3 R K C D R 3 6 . 3 6 . 3 8 . 3 2 . 4 - 1 . 31 3 R M C O R 3 4 . 3 3 . 2 5 . 5 . . 3 . 3 - 2 . 91 3 K K 4 . 1 0 . 4 5 . 1 1 . 3 1 . 31 4 R K C O R 3 7 . 3 1.8 9 . 1 3 . 6 3 . 61 4 R M C O R 3 4 . 8 - 1.2 5 . 3 1.6 11 4 K K 6 . 5 — A. 0 A 7 . 1 3 . 9 3 . 91 5 R K C 0 R 3 1 . 7 - 1 . 7 1.8 0.6 - 0.615 R N C O R 3 0.2 0. 1 0.2 0 . 7 0 . 715 K K 0 . 9 - 0 . 9 0 . 9 0.2 0.21 6 R K C 0 R 3 2 .4 - 2 . 4 2 . 7 0.2 - 0.11 6 R M C 0 R 3 1 . 9 . . . - 1 . 9 2.1 0.2 - 0.01 6 K K 0 . 4 - 0.0 0 . 5 1.0 1.017 R K C 0 R 3 3 . 6 3 . 6 5 . 1 1 . 4 - 0 . 41 7 R N C 0 R 3 2.6 2.6 3 . 4 1 . 3 - 1.017 K K 2 .4 i. 1 2 . 9 1.2 1.21 8 R K C D R 3 1 4 . 5 1 4 . 5 1 6 . 4 4 . 2 1 . 41 8 R N C O R 3 9 . 9 9 . 9 1 0 . 7 3 . 5 1 . 91 8 K K 4 . 6 - 0 . 9 5 . 5 3 . 6 3 . 61 9 R K C O R 3 2 5 . 1 2 5 . 1 2 6 . 3 6 . 7 - 6 . 71 9 R N C O R 3 2 2 . 7 2 2 . 7 2 3 . 5 .. “ '3 . 5 - 1 . 71 9 K K 6 . 7 5 . 9 8 . 3 4 * 6 ^.6

(C)R M S0.2 1 .0 0.40.00 . 90 . 92 . 33 . 3 0.6

2*53 . 61 . 54 . 3 1 .94 . 00.60.00.20.20.21 . 1

1 . 51 . 51 . 45 . 14 . 64 . 27 . 73 . 74 . 8

162

T A B L E 3 1 ( C O N T ' D )

IS Y S P R E S S U R E D E V . ( P S I ) T E M P E R A T U R E D E V . ( C)A V A R R I A S R M S A V A R B I A S R M S

20 R K 0 0 R 3 21.8 2 1.8 2 2 . 5 1.6 - 1.6 1 .720 R M C 0 R 3 1 4 . 2 1 4 . 2 1 5 . 0 2.1 - 1 . 9 2 . 420 K K 2 6 . 0 2 6 . 0 2 7 . 4 1 . 7 1.6 2.0

21 R K C 0 R 3 3 . 8 3 . 8 4 . 3 1.1 1.0 1.221 R N C O R 321 ---- K K . .4 . 3 . . 1COS • :!j 4 . 7 ... 2 . 4 . 2 . 4 2 . 722 R K C G R 3 0.6 - 0 . 4 0 . 7 0.8 - 0.8 0 . 922 R M C O R 322 K K 0.6 0 . 4 0 . 7 0.2 0.0 0.22 3 R K C n R 3 5 4 . 3 - 3 6 . 7 8 7 . 4 1 2 . 4 - 10. 1 1 4 . 22 3 R M C n R 3 1 2 8 . 8 -12 8.8 1 2 8 . 8 9 . 0 - 9 . 0 9 . 02 3 K K 0 . 9 9 8 5 .5 8 5 .5 1 0 2 . 7 1.0 0 . 7 1 . 32 4 R K C 0 R 32 4 R M C 0 R 32 4 K K 0 . 9 9 4 . 8 - 4 . 8 5 . 3 1 . 3 1 . 3 1 . 42 5 R K C O R 3 0 . 9 0.2 1.2 1.0 - 1.0 1.02 5 R M C O R 3 1.8 1.8 2.2 1.6 1.6 1 .62 5 K K 0 . 9 9 12.0 - 12.0 1 2 . 9 0.8 0.8 0 . 92 6 R K C 0 R 3 1.1 0.6 1.2 0 . 1.____- 0 . 1_____ 0.12 6 R M C O R 32 6 K K 0 . 9 9 2 0 . 4 - 2 0 . 4 2 2 . 3 1.1 1.1 1.1

2 7 R K C 0 R 3 0.8 - 0.8 0 . 9 0 . 3 0.2 0 . 32 7 R M C 0 R 3 2 . 5 - 2 . 4 3 . 0 1.0 1.0 1.12 7 K K 0 . 9 9 2 9 . 1 - 2 9 . 1 3 1 . 3 2.0 2.0 2.12 8 R K C 0 R 3 1 . 0 0 . 9 1 . 3 0.8 - 0 . 7 1 . 02 8 R M C 0 R 3 2 . 4 - 0 . 5 2 . 7 0 . 4 - 0 . 2 0 . 42 0 K K 0 . 9 9 3 6 . 1 - 3 6 . 1 3 9 . 4 2 . 5 2 . 5 2 . 62 9 R K C 0 R 3 5 . 6 1 . 2 7 . 3 2 . 3 - 1 . 2 2 . 52 9 R M C 0 R 3 3 .8 . . - 0 . 2 ' " 4 . 8 0 . 5 " ' " 0 . 3 " ' 0 .62 9 K K 0 . 9 9 6 1 . 4 - 6 1 . 4 6 9 . 0 4 . 0 4 . 0 4 . 2

**************KK 0.99 - The Revised Corresponding States Method with

y = 0.99.

T A B L E 3 1 ( C O N T ' D )

---------- — - • - * * *• -------- . — — ........... " '..................

N S Y S P R E S S U R E D b V . ( P S I ) T E M P E R A T U R E D E V . ( C)A V A R B I A S R M S A V A R B I A S R M S

3 0 R K C H R 3 4 . 1 - 3 . 9 4 . 5 1.8 - 1.8 2.0” 3 0 R M C 0 R 3 1.6 - 1. 1 1.6 1.7" - 1 . 7 1 .8” '

3 0 K K 0 . 9 9 3 . 9 3 . 9 4 . 0 0 . 9 0 . 9 0 . 93 1 R K C D R 33 1 R M C 0 R 33 1 K K 0 . 9 9 3 . 9 - 3 . 9 4 . 0 0 . 3 - 0 . 3 0 . 33 2 R K C D R 33 2 R M C H R 33 2 K K 0 . 9 9 2.2 - 2.2 2 . 4 0 . 4 0 . 4 0 .43 3 R K c nti3 2 . 3 - 2 . 3 2 . 5 1.6 - 1.6 1 .7

” 3 3 ” R M C H R 3 3 . 0 - 3 . 0 3 . 1 1.6 1 .63 3 K K 0 . 9 9 7 . 7 - 7 . 7 8.2 0 . 3 - 0 . 3 0 . 33 4 R K C D R 3 3 . 0 - 3 . 0 3 . 3 0 . 3 - 0 . 3 0 . 33 4 R M C H R 3 1 .4 - 1 . 4 1 . 5 0.2 0 . 2 0.23 4 K K 0 . 9 9 1 .0 - 0.6 1.2 2.2 2.2 2 . 3 _3 5 R K L O R 3 2 . 9 2 . 9 3. 1 0 . 9 0 . 9 1 .03 5 R M C 0 R 3 1 . 5 1 . 5 1 . 7 0 . 4 0 . 4 0 . 5 '3 5 K K 0 . 9 9 2 . 5 - 1.6 2 . 9 2.6 2.6 2.8

3 6 R K C 0 R 3 1 .3 1 . 3 1 . 4 0 . 4 0 . 4 0 . 53 6 R M C 0 R 3 1 . 5 - 0 . 4 1.6 0.6 - 0.6 0 . 73 6 K K 0 . 9 9 2 . 5 - 2 . 5 2 . 9 2 . 5 2 . 5 2.6

3 7 R K C D R 3 11 .A 1 1 . 4 12.8 4 . 2 - 4 . 2 4 . 43 7 R M C 0 R 3 8 . 4 1.8 9 . 0 7 . 2 - 7 . 2 7 . 63 "L K K 0 . 9 9 9 . 5 - 8 . 4 11.2 0 . 9 - 0 . 9 _1 . o _ _3 8 R K C 0 R 3 7 . 1 7 . 1 7 . 6 0 . 5 0 . 3 0.63 8 R M C 0 R 3 4 . 5 4 . 5 5 . 6 1.0 0.6 1 .2 '3 8 K K 0 . 9 9 1 4 . 0 1 4 . 0 1 5 . 5 4 . 1 4 . 1 4 . 33 9 R K C 0 R 3 3 . 4 3 . 4 3 . 6 0 . 5 0 . 4 0.6

" 3 9 ' R N C 0 R 3 5 . 3 5 . 3 5 . 3 0.2 0.1 0 . 3 ...3 9 K K 0 . 9 9 9 . 5 9 . 5 1C . 1 3 . 2 3 . 2 3 . 4

T A B L E 3 1 C C n ft T 1 n )

J S Y S P R E S S U R E D E V . ( P S I ) T E M P E R A T U R E D E V . (C)A V A B B I A S R M S A V A B B I A S R M S

A O R K C H R 3 2 .0 2.0 2.2 ■ 0. A - 0 . A 0 . 5A O " R M c n R 3 5 . 8 5 . 8 5 . 9 . . . . “ 0. 5 0. 5 ~ '0. 5A O K K 0 . 9 9 A . 7 A . 7 A . 9 2.2 2.2 2 . 3A 1 ' R K C 0 R 3A 1 R M C D R 3Al_ K K 0 . 9 9 0 . 7 “ 0 • A _ _ 0.8_ _ _ _ _ _ 1 . 8 ____ 1.8____ _1_._9A 2 R K C 0 R 3 1 .7 - 1 . 7 1 . 7 0 . 1 - 0.0 0.1A 2 R M C 0 R 3 0.8 0.8 0 . 9 0 . 7 0 . 7 0 . 7A 2 K K 0 . 9 9 1.1 0 . 9 1 . 3 2. A 2. A 2 . 5A 3 R K C 0 R 3A 3 R M C D R 3A 3 K K 0 . 9 9 2 .1 2.1 2.2 2. A 2. A 2 . 5A A R K C H R 3 1 3 . 9 1 3 . 9 1A . 5 0 . 9 - 0 . 9 1 .0A A R M C D R 3 1 1 . 5 1 1 . 5 12.2 2 . 5 - 2 . 5 2 .6A A K K 0 . 9 9 11 •! 11*1... 11.6 _.o* i. _ -0.0___ 0.1

A 5 R K C 0 R 3 11 .8 11.8 1 2 . 3 1.0 - 1.0 1.1A 5 R M C 0 R 3 9 . 1 9 . 1 9 . 7 2 . 9 - 2 . 9 3 . 0A 5 K K 0 . 9 9 9 . 0 9 . 0 9. A 0.2 - 0 . 1 0.2

A 6 R K C 0 R 3 0.2 0.2 0 . 3 0.1 0.1 0.1A 6 R M C 0 R 3 2 .A 2 . A 2 . 5 0 . 7 0 . 7 0 . 3A 6 K K 0 . 9 9 2 .3 2 . 3 2 . 5 2 . 3 2 . 3 2 . AA 7 R K C 0 R 3A 7 R M C 0 R 3 1.1 1.1 1.2 0 . A 0. A O . AA 7 K K . .... __ . 0.8 0 . 9 ___ 0.8 __ 0.8 _ 0 .8A 8 RK C 0 R 3 1.2 - 1.2 1.2 0 . 3 0 , 3 0 . 3A 8 R M C 0 R 3A8 K K 6.6 —6 • 6 6 . 9 0 . 7 0 . 7 0 . 7A9 RK C D R 3 0 . 9 0.6 1.0 0.8 0.8 0 . 9A 9 '"*RN C 0 R 3 ' 1.6 — 1 • A . 1 . 7 " 6 . 2 " 0.2 0. 3 'A 9 KK 1 0 .9 1 0 . 9 1 1 . 7 0,8 0.8 0 . 3

165

T A B L fr 3 1 ( COI'JT 1 D )

N S Y S P R E S S U R E D E V • ( P S I ) T E M P E R A T U R E D E V . (C)A V A R B I A S R M S A V A B BI A S R M S

5 0 R K C 0 R 3 5 . 2 - 1 . 4 10.0 1 . 3 1 . 3 2.65 0 R N C 0 R 3 1.0 - 0.2 1.1 0 . 3 - 0 . 1 “ ' 0 . 35 0 K K 1 9 . 1 - 1 9 . 1 2 3 . 6 2 . 1 2.1 3 . 05 1 R K C G R 3 3 . 1 2 . 5 3 . 6 0.6 0 . 3 0 . 751 R M C 0 R 3 1 . 1 0 . 4 1 . 4 0 . 7 0 . 7 0.851 K K 21 .8 -2 1.8 2 3 . 4 2 . 5 2 . 5 2 . 55 2 R K CC1R3 1.0 0.1 1.0 0.8 0.8 0 . 95 2 R N C 0 R 3 0 . 5 - 0.0 0 . 7 0 . 4 0 . 4 0 . 55 2 K K 0 . 4 - 0.2 0 . 5 0 . 4 0 . 4 0 . 55 3 R K C 0 R 3 1 .5 - 1 . 4 1.8 0 . 2 - 0.0 0.25 3 R M C 0 R 3 1 . 7 - 1 . 7 1 . 9 " 0 . 5 " “ - 0 . 5 " 0 .65 3 K K 1 . 4 - 1 . 3 1.6 0.2 0.1 0.2

5 4 R K C D R 3 1.0 1.0 1 . 5 0.8 0.8 1.05 4 R N C D R 3 4 . 7 - 4 . 7 5 . 2 2.0 - 2.0 2.15 4 K K 4 . 0 - 4 . 0 4 . 4 0 . 3 0 . 3 0 . 45 5 R K C H R 3 6 9 4 .8 - 6 8 1 .5 1 6 3 8 . 3 4 0 . 5 1 3 . 5 7 3 . 15 5 R N C O R 3 1 8 4 . 3 - 1 8 4 . 3 2 1 1 . 9 1 4 . 8 - 1 4 . 8 1 6 . 15 5 K K 3 6 . 9 3 6 . 9 4 9 . 9 2 . 4 - 2.2 2 . 95 6 R K C 0 R 35 6 R N ' C D R 3 2 . 4 2 . 4 2.8 1 . 4 1 . 4 “ 1 . 45 6 K K 2.8 - 2.8 2 . 9 0 . 7 0 . 7 0 . 75 7 R K C D R 3 2 . 4 - 2 .4 2 . 7 0.8 - 0.8 0.85 7 R M C D R 35 7 K K __ 5 . 4 - 5 . 4 5 . 8 0 . 5 0 . 5 0.65 8 R K C 0 R 3 0.6 - 0 . 3 0.8 0.2 0.2 0.25 8 R M C 0 R 35 8 K K 7 . 9 - 7 . 9 8 . 4 1.1 1.1 1.1

5 9 R K C H R 3 1.6 - 0.1 1 . 9 0 . 9 0 . 9 0 . 95 9 R N C 0 R 3 ' 1.2 - 1.2 1.2 0 . 3 0 . 3 0 . 35 9 K K 1 3 . 0 - 1 3 . 0 1 3 . 6 2.0 2.0 2.0

T A B L E 3 1 ( C O N T ' D )

IS YS PRESSURE DEV. ( P S I ) TEMPERATURE DEV. (C)

A VAB BIAS RMS AVAB BIAS RMS

60606 0

RK CDR3 RM COR3

KK

2 . 3 2 . 2

1 8 . 0

- 2 . 0- 2 . 2

- 1 8 . 0

2 . 7 •2 . 8

1 9 . 5

0 . 60 . 73 . 0

- 0 . 6- 0 . 7

3 . 0

0 . 70 . 83 . 1

6161

j 6 1_______

RK C0R3 RM COR3

___ KK_____

5 . 6 3 . 7

2 8 . 8

5 . 63 . 4

- 2 8 . 8

5 . 9 4 . 5

3 2 . 9 _____

2 . 2 0 . 7

__ 4 . 9

- 1 . 90 . 6

____ 4 . 9 ______

2 . 6 1 . 0 5 . 0

626262

RK C0R3 RM C0R3

KK

3 . 4 1 . 7 1 . 9

- 3 . 4- 1 . 7- 1 . 9

3 . 51 . 82 . 0

0.80 . 50 . 0

- 0 . 8 - 0 . 5 - 0 . 0

0 . 80 . 50 . 1

63 RK C0R3 9 . 1 9 . 1 9 . 7 2 . 4 - 2 . 4 2 . 66363

RN C0R3 KK

5 . 37 . 7

5 . 37 . 7

6 . 27 . 9

3 . 00 . 9

- 3 . 00 . 9

3 . 3' 1 . 0

666464 _

RK C0R3 RN C0R3

KK 1 . 5 ... “ 1*^. 1 . 7 ______ _ _ 0 . 2 _ 0 . 2 0 . 2

656565

RK C0R3 RM CC1R3

KK 0 . 6 - 0 . 5 0 . 6 0 . 1. 0 . 1 0 . 1

666666

RK CnR3 RN C0R3

KK

0 . 71 . 80 . 5

0 . 51 . 80 . 5

0 . 71 . 80 . 6

0 . 20 . 30 . 0

0 . 20 . 3 ...........

- 0 . 0

0 . 20 . 30 . 0

676 767

RK C0R3 RN C0R3

_______KK

0 . 40 . 5

- 0 . 4- 0 . 5

0 . 60 . 6

0 . 5 0 . 2

- 0 . 5- 0 . 2

0 . 50 . 3

686 868

RK C0R3 RN C0R3

KK

1 . 72 . 7

- 1 . 3- 2 . 7

1 . 92 . 9

0 . 60 . 6

0 . 5 — 0 . 6

0 . 7 0 . 7

6 9 6 9 ' 69

RK C0R3 RN C0R3

KK

3 . 2 3 . 8

- 2 . 0 ~ —3 • 2

3 . 44 . 2

0 . 7' 0 . 8

- 0 . 1" —0 . 4

0 . 80 . 8

16?

N S Y SA V A B B I A S

7 0 R K C 0 R 3 0 . 5 0.07 0 ..... R N C 0 R 3 0 .6 ' 0 . 57 0 K K7 1 R K C D R 3 2 . 5 - 2 . 57 1 R N C 0 R 3 3 . 7 - 3 . 771 K K7 2 R K C D R 3 0 . 5 0 . 17 2 R N C 0 R 37 2 K K7 3 R K C 0 R 3 0 . 4 0 . 37 3 R N C 0 R 3 0 . 4 0.27 3 K K7 4 R K C 0 R 3 4 . 7 4 . 77 4 R N C 0 R 3 4 . 6 4 . 67 4 K K

. _ ..

7 5 R K CC1R3 1.6 - 0 . 37 5 R N C 0 R 37 5 K K7 6 R K C 0 R 3 1 .5 1 . 57 6 R N C 0 R 3 3 . 9 3 . 97 6 K K7 7 R K C D R 3 0 . 9 1 o • -si

7 7 R N C 0 R 37 7 K K ... ________

7 8 R K C D R 3 3 . 9 3 . 97 8 R N C 0 R 37 8 K K

T A B L E 3 1 ( C O N T ' D )

P R E S S U R E D E V . ( P S I )R M S0 . 6_ 0.8

T E M P E R A T U R E D E V . (C) A V A B B I A S R M S0 . 4 - 0 . 4 0 . 4

2.83 . 9

0.6

0 . 5O.V

4 . 94 . 9

1.6

1 . 53 . 9

0.1

1.00 . 9

0.0

■ 1.0• 0 . 9

0.1

1 . 10 . 9

0 . 3 - 0 . 3

0 . 3 ___ - 0 . 3 0.2 ' 0.2

0.6 0.10 . 6 - 0 . 3

0 . 3

0 . 3

1 . 7

0 . 3 1.9

2 . 3

0 . 3

1 . 7

0 . 31 . 9

2 . 3

* 0 . 3

0.2

0 . 70 . 7

1 . 8

0 . 3 1 . 9

2 . 3

0 . 3

8 0 R K C D R 3 0 . 5 - 0.2 0 . 6 CO.o CO.01 0 . 98 0 R N C 0 R 3 0 . 4 0 . 4 0 . 5 0.0 - 0.0 0.08 0 K K 0 . 9 0 . 9 1.0 0 . 2 0 . 2 0 . 3

CHAPTER IX

C O N C L U S I O N S

1 . A s t h e c r i t i c a l t e m p e r a t u r e o f t h e s a m p l e

i n c r e a s e d t h e r a t e o f d e c o m p o s i t i o n i n c r e a s e d a n d t h e

a c c u r a c y o f t h e m e a s u r e m e n t d e c r e a s e d . T h i s i n a b l i l i t y

t o m e a s u r e a c c u r a t e l y t h e c r i t i c a l t e m p e r a t u r e a n d

p r e s s u r e o f a r a p i d l y d e c o m p o s i n g s a m p l e l i m i t e d o u r

s t u d y i n t h e n - a l k a n e s e r i e s t o n - T e t r a d e c a n e .

2 . W h e n h i g h m o l e c u l a r w e i g h t h y d r o c a r b o n s a r e

h e a t e d i n t h e p r e s e n c e o f m e r c u r y t o t e m p e r a t u r e a b o v e

3 2 0 ° C , t h e s o l u b i l i t y o f m e r c u r y i n c r e a s e s . T h e c r i t i c a l

p o i n t m e a s u r e d u n d e r s u c h c i r c u m s t a n c e i s , i n r e a l i t y ,

t h e c r i t i c a l e n d - p o i n t o f a h y d r o c a r b o n - m e r c u r y m i x t u r e .

T h e a c t u a l p a r t i a l p r e s s u r e e x e r t e d b y m e r c u r y i n t h e

h y d r o c a r b o n i s a b o u t 1 0 t o lk% l e s s t h a n t h e v a p o r

p r e s s u r e o f p u r e m e r c u r y b e t w e e n 3 0 0 a n d 476 ° C ,

3. T h e e q u a t i o n 01 s t a t e a n d t h e r e v i s e d c o r r e s

p o n d i n g s t a t e s m e t h o d s c a n p r e d i c t , o n t h e a v e r a g e , t h e

c r i t i c a l t e m p e r a t u r e a n d p r e s s u r e o f a h y d r o c a r b o n s y s t e m

t o w i t h i n 2 ° C a n d 1 0 p s i , r e s p e c t i v e l y . H o w e v e r , t h e

e q u a t i o n o f s t a t e m e t h o d p r e d i c t s t h e c r i t i c a l p r e s s u r e

168

169slightly better by about ^ psi than the revised corresponding states method,

*f# Finally, binary systems with components of high molecular weight follow the same pattern as was found with the lower molecular weights binary systems# The effect of the relative size of molecules on the critical properties of hydrocarbon mixtures appears to be greater than the effect of the structure and chemical nature of molecules# As the relative size difference of the components increases, the calculated values by both the equation of state and the revised corresponding states methods, show greater deviations from the experimental values.

CHAPTER X

RECOMMENDATIONS

1. The Redlich-Kwong equation is recommended for the calculation of the critical temperature and pressure of a binary system and the Redlich-Ngo equation, for the calculation of the critical volume,

2 . The separate correlations for the aliphatic- aliphatic systems and for the cyclic systems, i.e.,RK C0R3 and RW C0R3, are recommended for the prediction of the reduced interaction parameters for systems for which no critical data are available.

3. The optimization of the interaction parameters should be performed on the data for all types of binary systems available in the literature, i.e., systems with methane, alkenes, and non-hydrocarbons and systems whose molecular v/eight ratios are greater than 2,5* It would then be possible to establish, with greater certainly, the interaction parameters as functions of the relative size, structure, and chemical nature of the molecules of the mixture. In this way, the equation of state method

170

171could be used with greater confidence in the calculation of the critical properties of more diverse systems.

4. The equation for the partial pressure of mercury in hydrocarbons was obtained based mainly on the data for aromatic compounds. This equation could be improved by conducting some more experiments with compounds other than aromatic, i.e., aliphatic and naphthenic.

APPENDIX Af

APPARATUS AND EXPERIMENTAL PROCEDURE

A. Sample Confined Over Mercury 1• Apparatus

a. The Electric FurnaceIn the determination of the critical points

of low molecular compounds, the sample in the experimental tube was surrounded by a.jacket and heated to a constant temperature by the vapors of a series of pure organic compounds. The extension of the studies to h.igh molecular weight compounds, however, necessitated substituting an electric furnace for heating the sample because no stable organic compounds above 350 °C were available.

The furnace was designed specifically for determination of the critical properties of a liquid by visually observing the liquid as it is heated under pressure. It was constructed by the Marshall Product Co., a subsidiary of National Research Corporation, Columbus, Ohio.

The furnace was similar to that used by Ambrose and Grant ( 5 )• The principal features of the furnace which are pertinent to the determination of the critical point are shown schematically in Pig. 27. The copper bar (10" long x 1-5/8" diameter) which acts as a heat sink was

172

173drilled to receive both the thermocouple and the experimental tube. Parallel to this hole, a second hole was drilled to a depth of 3a*1 "to take a second thermocouple which actuated the temperature controller for the furnace. Three slits, 2 -" long x l/8" wide, were cut through the copper bar, as shown in Fig. 2? , so that the tip of the experimental tube could be observed during the experiment. The copper bar occupied a position in the middle of thefurnace with 6" cylinders of insulating material at the topand the bottom. The bar was rotated until the slits were aligned with the slits through the furnace. Transparent quartz windows were used to cover the observation slits atthe outside of the furnace.

The furnace was mounted on a stand and equipped with a counterweight and lock so that it could be moved vertically and thus brought into position around the experimental tube. The furnace was equipped with an automatic temperature controller and also with an auto-transformer connected in series with a voltage regulator for manual control of the furnace temperature.

b. Experimental Tube and Compressor BlockThe experimental tubes used in this work

were thick-walled glass tubes. The approximate dimensions of the tube are shown in Fig, 28 .

Fig. 29 is a cross sectional view of the compressor block showing its construction and the method of holding

Thermocouple to Controller

+-To Tem perature Recorder

Compressor Block

6Section A -A

I. Electric Furnace2 2 in. Long x lOin. Dia.

2 . Insulating Ceramic Plug3. Copper Bar lOin. Long x

I 5 / 8 in. Dia.4. Thermocouple5. Experimental Tube6. V iew ing Slit7. Support For 2 B 38. Controlling Thermocouple

Fig. 2? - Electric Furnace for Determination of Critical Points

7mm

8. Omm 2,0mm

0.D1.D

O.D, = 18mm 5mmI.D

20cm

Fig. 28 - Experimental Tube for Electric Furnace

176

Detail of G

Pig, 29 - Cross Sectional View of Compressor Block

177the experimental tube. The pressure applied, at the mercury surface in back legf B, was transmitted through the mercury to the sample in the tube. D was a safty check valve which would stop the flow of mercury in the event that the tube burst under high pressure. The steel ball, E, due to the difference in the density of mercury and steel, did not interfere with the normal flow of mercury. In case of breakage of the tube under pressure, the sudden rush of mercury drove the steel ball into the valve seat, F, and prevented further loss of mercury.

The experimental tube was held in front leg, A, of the compressor block in the following way. An enlarged shoulder, I, was formed which was rested on a small rubber washer, H, in the split ring assembly, G. Surrounding the tube above the shoulder were first a rubber washer, J, a loose-fitting steel ring, K, and a rubber cylinder, L, which effected the stuffing box seal. On top of this rubber cylinder v/as a thin steel washer, M, and gland, 0, which, when forced down by a hand-tightened cap, N, compressed the rubber cylinder, thus making the seal.

c. Sample Preparation and FillingThe hydrocarbons were research-grade

samples. They, however, undoubtedly dissolved a small amount of air when allowed to stand in the presence of air at room temperature. Also, since the air was moist, a certain amount of water evidently dissolved in them.

178In order to remove the dissolved water, a sample of hydrocarbons was transferred from the source bottles into 20 cc stoppered bottles containing about one half gram of silica gel.

No effort was made to remove the dissolved air in the hydrocarbons at room temperature. Sample prepared in this way are called "air-saturated". Previous study on air- saturated samples by Hissong (37) showed that the dissolved air added up to 3 psi to the critical pressures and up to 0.5 °C to the critical temperatures measured for the hydrocarbons. Since it was the trends in the data which were being sought, as Hissong pointed out, the precision or consistency of the measurements was more important than the absolute accuracy.

The critical constants of mixtures of approximately 10» 30, 50, 70, and 90 mole percent composition of each system were measured. Approximate volume ratios of the pure components of each mixture were calculated from the densities and molecular weights. A clean dry 3 cc glass- stoppered weighing bottle was weighed on an analytical balance to the nearest 0.1 milligram. Transfers of pure components were made with one milliliter hyperdemic syringes. The desired quantity of the less volatile components was first transferred to the weighing bottle and the bottle v/as reweighed. The more volatile component was then added and the bottle was weighed again. The amount

179of the components used were then determined by the difference. The total quantity of a mixture prepared was at least 1 milliliter. The mixture prepared in this manner was swirled around to make sure of complete mixing.

The experimental tube was inverted and clamped in astable position. Several glass capillaries smaller than the tube bore were prepared by heating and drawing pieces of 8 mm glass tubing. One of these capillaries was insertedinto the tube. About 0.15 cc of the sample, which wasenough to occupy a length of about 2 cm in the closed end of the tube, was then transferred from the weighing bottle to the capillary funnel with a clean hyperdemic syringe.Then the capillary was removed.

Then, a small amount of mercury, enough to occupy a length of 10 cm, was introduced into the experimental tube. Due to the capillary effect and high surface tension of mercury, the mercury came to rest trapping a column of air between it and the sample. This column was then lowered carefully through the tube by slowly pushing another capillary down the tube and rotating it. As the mercury column reached the sample in the bottom of the tube, the capillary action caused the first liquid touched to pass through the mercury column and collect on top of it. The mercury column was lowered until the sample height was about from the closed end of the tube. Extreme care was taken not to trap any air bubbles between the sample and the

180mercury column or "between the mercury column and the wall of the tube. This was done by slowly rotating capillary around the tube.

The capillary was then taken out of the tube, attached to an aspirator, and re-inserted into the tube. The tip of the capillary was lowered gradually to suck out the excess sample above the mercury. After all of the excess sample was removed, the capillary was held just above the mercury surface for about a minute to evaporate any remaining liquid. Then the capillary was removed. At this time the total height of sample and mercury column was approximately 10 cm.

Then the sample and mercury column were frozen by immersing the tip of the tube into a Dewar flask with either liquid nitrogen or a slurry of dry ice in acetone. The choice of freezing agent depended upon the freezing point of the sample. As soon as the sample and the mercury column were frozen, a stirring rod, which has been immersed in actone, was washed with ether, waved through a flame, and inserted into the experimental tube.

The experimental tube v/as then attached to a high vacuum line through a mercury-sealed standard taper joint as shown in Fig. 30, which is a schematic drawing of the high vacuum line. The system has been operating for some time with V-2 closed. Therefore, the system was in high vacuum up to V-2, After connecting the tube, V-2 v/as

ex}VI

ADiffusion Pump

O

LiquidNitrogenTrap

MacLeod Gauge

Vacuum Pump

Fig, 30 ~ High Vacuum Line

V2

MercuryReservoir

ExperimentalTube

181

182slowly opened to pump the air out from the tube. During the pumping period, the sample and mercury were kept frozen and the stirring rod was lifted by a permanent magnet to separate the tip of the stirring rod from the surface of the mercury column. The pressure of the system was checked regularly with the built-in Macleod gauge.When the pressure in the system was reduced to better than 1(T6 mm Hg (stick vacuum), the mercury reservoir was tilted so that the mercury would flow through a hair-size capillary into the experimental tube. After the tube v/as completely filled with mercury up to the open end, the tube was ready to be transferred to the compressor block.

The back leg of the compressor block was plugged and the front leg was completely filled with mercury. After the necessary compression fittings had been placed on the tube as shown in Fig. 29 • an index finger was placed over the open end of the tube, and the tube v/as inverted and placed in the front leg of the compressor block. The plug was removed form the back leg and the tube assembly was forced into place with the gland and cap. While the above step was carrying out, the frozen mercury and sample were thawed slowly by hand. The mercury column was thawed first from bottom up in order to prevent the cracking of the tube due to the expansion of liquid sample. The mercury in the back leg was removed to a level of 5 to 7 cm below the top. The distance is referred to as the

183"back leg head" which was needed for pressure correction. The back leg was then connected to the manifold.

Great care was taken to avoid the possibility of cantaminating the samples throughout the procedure. Before beginning the experimental work, all glass equipment v/as cleaned thoroughly with cleaning solution (a mixture of potassium dichromate and concentrated sulfuric acid).After each experimental run, the tubes, the weighing bottles, syringes, and needles were rinsed with acetone and anhydrous reagent grade ether, and dried in anelectric oven at 100 - 150 °C for overnight. The mercuryused as the pressure transmitting medium was thoroughly cleaned by washing it with water and acetone, contacting it with air in a rotating oxidizer, pinholing it through filter paper, and finally distilling under vacuum.

d. Operation of the ApparatusThe furnace was preheated to the estimated

critical temperature of the sample by means of the automatic temperature controller. Since the system response to a unit step change in set-point was very slow, the automatic controller was not adequate for the determination of critical point. Hence, when the furnace temperature became constant at the estimated critical temperature of the sample, the automatic temperature controller was disconnected and the current to the furnace was controlled manually by an auto-transformer connected to a voltage

18/fregulator. The preheated furnace was then lowered in place around the experimental tube as shown in Fig. 2? , The rapid heating of the sample was necessary in order to reduce the amount of decomposition before the critical point was reached. The rate of heating did not, however, exceed 0.7 °C/minute. The pressure on the sample was increased so that the meniscus remained constant near the middle of the section of the tube occupied by the sample and the sample was stirred intermittently. When the critical phenomena were observed, the temperature was marked by means of an event-marking switch on the temperature recorder and pressure was read from the pressure gauge.

e* Determination of the Critical PointThe critical point was determined by

visual observation of the disappearance of the meniscus as the temperature was raised and of the reappearance of the meniscus as the temperature was lowered through the critical point. The sample was observed by both transmitted and reflected light. When the sample was thermally stable, the critical point was checked and the mean of, on the average, two or three appearances and disappearances of meniscus was reported as the true value.

Because high molecular weight hydrocarbons are unstable at/or near their critical temperatures, a special procedure must be used for the determinations.

185The n-alkanes through n-nonane are thermally stable at their critical point* However, compounds above n-nonane are definitely unstable at/or near their critical temperatures. For the unstable compounds, observations were continued at the shortest intervals permissible with the furnace over a period of 1 to 2£ hours. The apparent critical temperatures and pressures were then plotted against the time elapsed, beginning with the time when the furnace was lowered over the experimental tube. Then, the true critical temperature and pressure were determined by extrapolating the temperature-time and pressure-time curves to zero-time as illustrated in Fig. 3*

f. Temperature CorrectionAs mentioned earlier in Chapter V, there

existed temperature difference between the temperature indicated by the thermocouple and the true sample temperature. This temperature difference is considered to be due to the finite rate of heat transfer through the glass walls of the sample tube, whereas the thermocouple response was almost instantaneous even if the thermocouple was placed in the well. To determine the temperature difference, a capillary tube of the same shape and dimensions was constructed and placed in the furnace with the thermocouple inside the tube and a platinum resistance thermometer on the top of the tube as shown in Fig. 31 . Observations of the difference in temperature,A T, v/ere

186then carried out for a series of heating and cooling rates up to 0,7 °C/ minute as in an actual measurement of the critical point, at approximately 200, 250, 300, 350, ^00, and ^30 °C, Then the average of the values of AT at each temperature was plotted against the corresponding temperature and a best straight line was drawn through the points as shown in Fig, 32 . The equation for the straight line was

4 T = -0,'I8 + 0.007385T (93)

and the above equation was used to correct all observed critical temperature.

To Recorder

Platinum Resistance Thermometer

Experimental Tube

■Thermocouple

To Recorder

18?

Fig, 31 - Mock-up for the Measurement of Temperature Difference

TEMPERATURE

CORRECTION

(°C)

A T = -O.iJ-8 + 0.007385T

2.0

0.0200 250100 300 350

TEMPERATURE (°C)

Fig. 32 - Plot of Temperature Correction vs. Temperature

189B. Sample Confined Over Gallium

1• ApparatusThe apparatus for determining the critical

constants of a pure compound with gallium as the confining liquid is shown schematically in Fig, 33. Experimental tube 5 was constructed from a thick-walled glass capillary of about 0,25 cm bore with an expanded section at the top containing a tiny thermocouple well. Details of the construction are shown in Fig, 34, With the thermocouple in the well surrounded by the sample, the response to temperature changes in the sample was greatly improved over that shown in Fig, 28. The bottom of the tube was shaped in the form of a flange and a glass-to- metal seal was made to adapter 6 by a small 0-ring in the manner shown in Fig. 34 .

The experimental tube was connected through valves 29 and 30 to the gallium pressure generator 2 and through valves 31 and 32 to oil pressure generator 1^. The pressure developed in the experimental tube was indicated by pressure gauge 8 when the gallium-oil interface was kept at a fixed point in 9. The interface was located by means of an electric probe operating with a 1.5 volts drycell with a small flashlight bulb. Gauge 8 was a high- precision Heise Bourdon gauge with a 16" dial, graduated in 2 psi divisions from 0 to 2000 psi. It was evacuated and filled with oil and calibrated at 20 psi intervals with a

190precision dead weight gauge reading to 0.05 psi.

Electric furnace **, shown in detail in Fig. 35 » consisted of a quartz tube 1-1/8" O.D. coated with a metallic film which served as an electric resistor and was jacketed by a 1-7/8" O.D. pyrex tube. The inner and outer tubes were held tight by means of a rubber 0-ring. At the middle, two windows 3§" long and l/8" wide, diametrically opposed with a third window of the same size at 90° to the axis of the other two, were provided in order to observe the sample during the heating process. The current was regulated by means of an auto-transformer with a voltage regulator to maintain a constant power supply. The maximum rating for the furnace was 60 volts and 8 amperes. The low heat capacity and the uniform distribution of heat along the quartz tube made it possible to raise the temperature to ^00 °G in 15 to 20 minutes. The furnace was constructed to order by the Ace Glass Co.

The temperature was measured with a chrome1-constantan thermocouple calibrated by comparing it with a platinum resistance thermometer which had been certified by the National Bureau of Standards. The millivolt reading v/as recorded continuously with a Leeds & Northrup Speedomax H recorder with a chart speed of 12" per minute and a sensitivity equivalent to 0.0^ °C.

Difficulties were encountered in stirring the sample during the experiment. The steel ball which had been used

191so successfully with mercury was "wet" by the gallium because of the presence of small quantities of gallium oxide and the density of the gallium was less than the steel ball, with the result that the steel ball sank in the gallium. The problem is of concern only for mixtures where the composition of the liquid and vapor phases are different and must be mixed in order to assure an equilibrium state,

2. Experimental Procedurea. Filling the Experimental Tube with a

Degassed SampleThe experimental tube with the adapter and

valve 29 were de tached from the apparatus and a small amount of the pure liquid, equal to slightly less than l/3 the volume of the upper part of the tube, was loaded into the tube. The tube was then attached to a high- vacuum line and the sample subjected to a freeze-pump-melt cycle under high vacuum until bubbles of gas were no longer observed during the melt cycle. With the sample frozen, the tube assembly was evacuated until the pressure was less than 10-6 mm Hg, then valve 29 was closed and the tube assembly removed to the high-pressure line, keeping the sample frozen in the top of the tube. With valves 29 and 30 closed and valve ? attached to the high-vacuum line, valve 7 was opened and the air in the line between valves 29» 3°» and 7 was evacuated. Valve 7 was then closed, and

192valve 30 opened in order to fill line with gallium.Finally, valve 29 was opened cautiously and gallium allowed to partially fill the tube, after which it was closed and the sample melted and warmed to a temperature above 29*75 °C, the freezing point of gallium. Valve 29 was then fully opened and the loading was completed,

b. Operation of the ApparatusThe furnace was put in place, making sure

that the windows of the furnace were in line with the section of the tube containing the sample, and the thermocouple inserted into the well of the tube. As the temperature rose and the sample began to evaporate, the pressure was increased so that the meniscus remained constant nearthe middle of the sample section. At the same time, thegallium and oil pressure generators, 2 and 1^ v/ere adjusted so as to keep the gallium-oil interface in 9 constant.As the temperature approached the critical temperature, the voltage was adjusted so as to hold the sample at the critical temperature. When the critical phenomena were observed, the temperature was marked on the chart and the pressure was read.

252 6

2 93 0 3 2 3 3

/20 22 2 3

19 OFig* 33 - Schematic Diagram of Apparatus for Gallium Experiments

Gallium ReservoirGallium Pressure GeneratorChrome1-Oonstantan ThermocoupleElectric FurnaceExperimental TubeTube AdapterTo High Vacuum I-ineHeise Pressure GaugeGallium-Oil Interface DetectorFlashlight Bulb1.5 Volts Dry CellVentOil ReservoirOil Pressure GeneratorOil Reservoir for Gauge Calibration 29,To Mercury Manometer &Dead Weight Gauge

Infra-red Heating Lamp (250 watts)Auto-TransformerTo 115 Volts, 60 Cycle AC Power SourceI ron-Cons tantan' ThermocoupleOn-Off Relay Actuated by Temperature Set-pointSingle-Pole Single-Throw Relay12 Volts Storage BatteryFour 60 Watts Heating Tapes. These are wrapped around the Gallium line.Hood Enclosing Entire ApparatusVoltmeterFine Voltage Controller Course Voltage Controller

30, 31» 32, and 33. Valves

Nomenclature for the Gallium Apparatus

17.

18 .19.

20,21.

22.

23.2*K

25.

26.

27.28.

2.5 c m

3.5 c m

195

4 0 c m

T H E R M O C O U P L E

T H E R M O C O U P L E W E L L 0 . 4 c m O.D.

S A M P L E0 . 5 5 c m I.D. & 0 . 8 c m O.D.

E X P E R I M E N T A L T U B E ( P Y R E X G L A S S )

G A L L I U M

0 . 2 5 c m I.D. 8i 0 . 8 c m O.D.

N Y L O N R I N G

A D A P T E R

R U B B E R O - R I N G

Fig. 3- - Experimental Tube and Adapter (Gallium Experiments)

Viewing Slits

1-7/8" Pyrex Tube Ton View7 - / 4

II1/8 ,HI

18 3 _|/2»

Section A-A

1-1/8" O.D. Quartz Tube

Three 3-1/2" x l/Q" Uncoated Viewing Slits

Coated Heating Element High Temperature Rubber RingsElectric Lead Wires

Fig* 35 - Electric Furnace

APPENDIX B

CALIBRATION OF EQUIPMENT

A. Thermocouple

Iron-constantan and chromel-constantan thermocouples were used and were calibrated by comparing them with a platinum resistance thermometer certified by the National Bureau of Standards. The calibration was carried out in an electric furnace designed for this purpose by Leeds & Northrup Co. The ernf of the thermocouple was read on a Leed & Northrup Speedomax H, continuously adjustable AZAR recorder and the resistance of the platinum thermometer, on a Leed & Northrup Speedomax 'Type G recorder. A simultaneous reading of the emf of the thermocouple and the resistance of the platinum thermometer v/ere made when the furnace was brought to a series of constant temperatures ranging from 120 to 500°C. For each resistance read, the corresponding temperature was calculated from the calibration equation recommended by the National Bureau of Standards for the resistance thermometer. The calibration data for the thermocouples are given in Tables yi and 33*

The calculated temperatures were then fitted as polynomials in the emf's by a least squares regression

197

analysis and the results were as followsi for the iron-constantan thermocouple

t = 5.12^9032 + l8.051^18emf - 0.001*4-188329emf 2 (9*0

with the standard deviation of the fit 0,0997°Cj and for the chromel-constantan thermocouple

t = *K9*100231 + I5.25l558emf - 0.096l*l-5205emf2+ 0.0009*J-772*i-6/iemf3 (95)

with the standard deviation of the fit 0.1008°C.The accuracy of the platinum resistance thermometer

and its recorder was checked against the melting point of zinc before the calibration of the thermocouple was made. The result was

Reading from the Recorder Literature ( 35 )*4-19.52°C (65.630ohms) *U9.*0°C

The accuracy of the calibration was also checked against the melting points of zinc and lead. The chromel-constantan thermocouple was used for this test.The temperatures of thermocouple were calculated from Sq.. (95) • The results were as follows!

Substance Calculated Value Literature Valuezinc *H9.5*^°C *KL9.*J-7°C (35)lead 327,*4-8°C 327.*0°C ( 35 )

199This test showed that the calibration technique used in this laboratory was quite satisfactory and reliable.

B. Pressure Gauge

During the period of this work, three precision Heise Bourdon gauges were used. They were calibrated by comparing them with a Ruska high-precision dead-weight gauge, manufactured by Ruska Instrument Corporation, Houston, Texas. The calibration data are given in Table 3^.

200

TABLE 32

THERMOCOUPLE CALIBRATION (iron-Constantan)

Resistance(Ohm) Temperature(°C) emf(mv)

37.^37 120.85 6.42038.590 130.57 6.96040.369 148.79 7.956iH. 698 162.47 8.71843.158 177.57 9.55844,806 194.69 10.49846.388 211,22 11.42647.938 227.49 12.33249.292 241.78 13.12651.008 259.98 14.13851.294 263.02 14.30853.107 282.38 15.38054.892 301.52 16.44856.621 320.22 17.48459.989 356.95 19.51861.643 375.16 20.52663.293 393.43 21.54665.139 414.01 22.68669.373 461.74 25.34470.914 479.30 26.32272.425 496.63 27.292

201

TABLE 33

THERMOCOUPLE CALIBRATION (Chrome1-Constantan)

Resistance(Ohm) Temperature(°C) emf(mv)

42,9 66 175.58 11.99844.328 189.72 13.04645.883 205.93 14.28047.255 220.31 15.38048.673 235.24 16.54450.073 250.05 17.69451.757 267.95 19.11253.312 284.58 20.42654.871 301.30 21.79256.4?2 318.60

334.6523.186

57.949 24,49459.448 351.02 25.83260.938 367.39 27.1746 2 . M 6 384.26 28.55863.983 401.11 29.95467.002 434.91 32.77868.354 450.18 34.04669.651. 464.90 35.26870.931 479.50 36.48672.374 496.05 37.874

TABLE 34 202

PRESSURE GAUGE CALIBRATION

Heise Gauge H-1715 Heise Gauge H-1542 Heise Gauge H-1543Reading Correction1* Reading Correction* Reading Correction* (psig) (psi) (psig) (psi) (psig) (psi)70.1 -0.1 70.4 -0.4 50.0 0.0111.0 -1.0 109.3 +0.7 89.5 0.5151.0 -1,0 150.0 0.0 129.4 0,6191.0 -1.0 190.4 -0.4 169.8 0.2231.5 -1.5 230,7 -0.7 209.7 0.3272.3 -2.3 270.9 -0.9 250.4 -0.4312.3 -2.3 3H.3 -1.3 291.0 -1.0352.1 -2.1 350.1 -0.1 331.9 -1.9393.2 -3.2 391.9 -1.9 351.8 -1.0433.1 -3.1 431.5 -1.5 371.6 -1.6473.1 -3.1 472.2 -2.2 391.6 -1.6513.5 -3.5 511.2 -1.2 412,3 -2.3554.3 -4.3 551.9 -1.9 432.4 0 ii— t_ • "T595.0 -5.0 591.6 -1.6 452.7 —2.7635.0 -5.0 631.6 -1.6 472.3 -2.3675.0 -5.0 672,0 -2.0 492.0 -2.0715.6 -5.8 711.5 -1.5 5U.5 -1.5750.0 0.0 531.3 -1.3

791.3 -1.3 551.5 -1.5830.5 -0.5 571.7 -1.7871.7 -1.7 591.5 -1.5912.0 -2.0 611.7 -1.7951.0 -1.0 652.0 -2.0992.0 -2.0 693.0 -3.01030.2 -2.0 733.5772.8

813.1853.9893.9 934.0

-3.5-2.8-3.1-3.9-3.9-4.0

* Should be added to the gauge reading.

APPENDIX C

DATA REDUCTION AND SAMPLE CALCULATION

A. Data Reduction Procedure

X, Sample confined over mercury

a* TemperatureThe observed sample temperature was calcu

lated from the iron-constantan thermocouple calibration equation given in Appendix B, i.e., Eq. (9*0» and corrected for the temperature difference between the indicated temperature by the thermocouple and the true sample temperature using Eq. (93) presented in Appendix A.

b. PressureThe absolute sample pressure was obtained

by correcting the pressure read from the gauge (Pgauge) for the following termsi 1) pressure gauge calibration (Pcai)» 2) barometric pressure (pâr)» 3) mercury head in sample tube (Pgt + and ^ partial pressure of mercury<pp„g>.

The observed gauge pressure was corrected by a linearinterpolation between adjacent calibration points presentedin Table y\ (Heise gauges H-l?15 and H-15^2).

203

The barometric pressure was measured at room temperature, The mercury head in the sample tube was equal to the difference between the meniscus and the level of mercury in the back leg as shown in Pig. 3 6, The calculation of this pressure is subject to some uncertainty because of the temperature gradient betv/een the hot and cold zones. However, it was assumed that the mercury column outside of the furnace remained at room temperature and that inside the furnace was at the temperature of the sample. The barometric pressure and the mercury head were measured as differences in mercury levels and corrected for the variation of the density of mercury with temperature using the following equationsi

p = psiabar 76.00cm Kg'p ' barp 1 0= 0.1933728(O&)zbar (9 6 )

pPst = 0.1933728 (97)

PPrt = 0.1933728(î)zrt (98)

barometric pressure in psia, barometric pressure in cm Hg, pressure due to the mercury head at sample temperature in psia,mercury head at sample temperature in cm Hg,

w h e r e P b a r

Z b a r

P s t

z s t

205P ^ = pressure due to the mercury head at room

temperature in psia,Zrt - mercury head at room temperature in cm Hg,Pst ~ density of mercury at sample temperature in

gm/cc,- density of mercury at room temperature in gm/cc,

f*o = density of mercury at 0 °C in gm/cc.

Davies ( 19) correlated the density ratio, fyPo' as a function of temperature over two temperature ranges and the results were as followsi

0 to 50 °C

Pp. - o.999999^ - 1.8l6^2xl0“^t + 2.5^7xl0"8t2 (99)r o

50 to 300 °c

= 0.9999835 - 1.81519x10"^t + 3.05*+xlO~8t23.195xlO“11t3 (100)

where t is the temperature in °C.Eq« (99) was used for mercury levels measured at room

temperature and Eq. (100), for mercury level at sample temperature. Since mercury density data were not available at high temperatures, Eq. (100) was used even when the temperature was above 300 °C.

It has been usually assumed that the partial pressure exerted by mercury in contact with the hydrocarbon is

/>,rt

equal to the vapor pressure of mercury at the temperature of the system, i.e., the mercury is insoluble in the hydrocarbon. As discussed in Chapter VI, this assumption was not valid when the sample temperature was above 320 °C. Therefore, when the sample temperature was above 320 °C, the partial pressure of mercury was calculated from theequation obtained in this work, i.e., Eq. (18) in>Chapter VI. Namely,

l0gPPHg 51 5.92822 - (18)

where PP1T„. - partial pressure of mercury in psia, andJ iQT° = critical temperature in °K.

When the sample temperature was below 320 °C, the partialpressure of mercury was calculated from the equation for the vapor pressure of mercury given by I.lenzies (62 ).That is,

logVPHg = 9.957094 - - 0,6652401ogT (101)

where " vapor pressure of mercury in mm Hg, andT = sample temperature in °K.

A force balance around the compressor block yields the following equation for the sample pressure,

Psample = Pgauge + Pcal “ PPHg + 0.1933728 [(Zbar

Electric Furnace

st (Hot zone)

■ (Cool zone)

Back leg head

. 36 - Division of Mercury Head

2. Sample confined over gallium

a* TemperatureThe sample temperature was calculated from

the chromel-constantan thermocouple calibration equation given in Appendix B, i.e., Eq. (9-5)*

b. PressureThe absolute sample pressure was obtained

by correcting the pressure read from the gauge (P )gaugefor the following terms* 1) pressure gauge calibration (pd > - 2 ) barometric pressure (pbar)» and 3) gallium headin sample tube +

The pressure gauge calibration data (for H-l5*1-3) a**e presented in Table 3^ in Appendix B, The observed gauge pressure was corrected by linear interpolation between calibration points.

The barometric pressure was measured at room temperature as difference in mercury levels and converted interms of psi using Eq. (96).

The gallium head was also divided into two zones as was done for the mercury head and converted in terms of psi in the following manner*

(103)

(10*0

209Substituting Eq. (10*0 into Eq. (103)» we obtain

Pt = 0.1933728(Zt)Ga (105)

where subscripts llg and Ga represent mercury and gallium, respectively.

Combining all these terms, the following equation for the sample pressure is obtained!

B. Sample Calculation1. Sample confined over mercury

The following is a sample calculation using the data for pure ethylbenzene.Data i

Pressure gauge reading 538.0 psigThermocouple emf 18,880 mvCathetometer reading

Hydrocarbon-mercury interface 59.62 cmBottom of hot zone 31.97 cmTop of back leg 15*15 cm

Back leg head 5,3 cm HgBarometric pressure 74.6? cm HgRoom temperature 30,13 °C

Temperatvire tObserved temperature

-t = 5.12^9032 + (18.051408) (18,800)- (0,0014188329)(18.880)2

= 3^5.63 °C Temperature correction

t ^ = -0.48 + (0,007385)(345.63) = 2.07 °Cv v iTrue critical temperature

211Pressure t

Gauge calibration!Pcal = -4.0 psi (by linear interpolation)

Partial pressure of mercury»Since tc is higher than 320°C, Eq. (18) should be

used.Tc = 343.56 + 273.16 = 616.72 °K

log PPHg = 5.92822 - = 1.00279PP^g = 10.1 psia

Mercury headiHot zone i Z ^ - 59.62 - 31*97 - 27,65 cmCool zonet Z t = 31.97 - 15.15 + 5*3

= 22.12 cm Mercury density ratio*

P = 0.9999994 - (1,81642x10) (30.13)+’ (2.547x10“®)(30.13)2 = 0.99455

£>— = 0.999984 - (1.81519x10"^)(343.6)P o + (3.054x10"®)(343.6)2 - (3.195xl0"n )(343.6)3

= 0.93993 True critical pressure*

sample = 538,0 " 4,0 “ 10,1 + 0.1933728 [(7 .67 - 22.12)(0.99 55) - (27.65)(0.93993)]

= 529.1 psia

2122, Sample confined over gallium

The following is a sample calculation using the data for pure 1,2,4-Tridmethylbenzene.Data i

Pressure gauge reading 468.0 psigThermocouple emf 27*998 mvCathetometer reading

Hydrocarbon-gallium interface 71.22 cmBottom of hot zone 45.12 cmGallium-oil interface 15.42 cm

Barometric pressure 74,88 cm HgRoom temperature 29.6°C

Temperature*tc = 4.9480231 + (15.251558)(27.998)

- (0.096145205)(27.998)2 + (0.000947725)(27.998)3 = 377.4 °C

Pressure 1Gauge calibration!

^cal = Psi (by linear interpolation)Gallium headi

Hot zone* (Zst^Ga ~ 71*22 - 45.12 = 26.10 cmCool zonet (Zrt^Ga “ ^5*12 - 15*^2 = 29.70 cm

True critical pressure!Sample = lt68-0 ' 2'3 + [(13.5)(7^.63)

(5*85)(26.1) - (6,09)(29.7)]

Densities of mercury and gallium were obtained from References (35) and (89)» respectively.

APPENDIX D

MESCELAN30US TABLES

This appendix contains the point by point comparison between the experimental and calculated critical temperatures and pressures of the systems studied in this work, using the optimum and predicted interaction parameters, the purity and source of samples, the pure component constants used in the correlation, and the uncorrected data for the effect of mercury. These are shown in Tables 35, 36, 37* 38, and 39, respectively.

. . . . . . . . . . T A B L E 3 5 215C O M P A R I S O N O B T H E E X P E R I M E N T A L A N D C A L C U L A T E D C R I T I C A L P R O P E R T I E S U S I N G O P T I M U M I N T E R A C T I O N

P A R A M E T E R S S Y S T E M N U M B E R 1 7

N - H E X A N E ' — — N - D E C A N E ( B ) S . C . PAICR E D . I N T . P A R . R - K A 1 2 S R = 0 . 8 4 3 2 1 4 0 4 B 1 2 S R = 0 . 9 0 7 9 2 6 9 2R E D . I N T . P A R . R - N A 1 2 S R = 0 . 8 2 6 0 2 6 8 6 B 1 2 S R = 0 . 8 3 1 3 0 6 4 0

T E M P E R A T U R E ( C )X (A ) T E X P R K - E P D E V R N - E O D E V K R E G K D E V0.0 3 4 3 .6 3 A 3 • 6 0.0 3 4 3 . 6 0.0 3 4 3 . 6 0.00 . 10 3 3 6 . 4 3 3 7 . 9 - 1 . 5 3 3 7 . 6 - 1.2 3 3 6 . 4 0.00.20 3 2 8 . 9 3 3 1 . 2 - 2 . 3 3 2 8 . 6 0 . 30 . 3 0 3 2 1 . 2 3 2 3 .6 - 2 . 4 3 2 3 . 1 - 1 . 9 3 2 0 . 3 0 . 90 . 4 0 3 1 2 . 3 3 1 4 . 7 - 2 . 4 3 1 A . 2 - 1 . 9 3 1 1 . 2 1 .10 . 5 0 3 0 3 . 1 3 0 4 . 5 - 1 . 4 3 0 4 . 0 - 0 . 9 3 0 1 . 2 1 . 90 . 6 0 2 9 2 . 3 2 9 2 .8 - 0 . 5 2 9 2 . 4 - 0.1 2 9 0 . 2 2.10 . 7 0 2 8 0 . 1 2 7 9 . 6 0 . 5 2 7 9 . 3 0.8 2 7 8 . 2 1 . 90 . 8 0 2 66 . 4 2 6 5 . 1 1 . 3 2 6 5 . 0 1 . 4 2 6 4 . 8 1.60 . 9 0 2 5 1 . 2 2 4 9 . 7 1 . 5 2 5 0 . 2 1.01.00 2 3 4 . 1 2 3 4 . 1 0.0 2 3 4 . 1 0.0 2 3 4 . 1 0.0

A V G . A B S 1 . 5 1.2 1.2B I A S - 0 . 8 - 0 . 5 1.2R M S 1 . 7 1 . 3 1 . 4

P R E S S U R E ( P S I A )X ( A ) P E X P R K - E P D E V R N - E O D E V K R E G K D E V0.0 3 1 0 . 1 3 1 0 . 1 0.0 3 1 0 . 1 0.0 3 1 0 . 1 0.00 . 10 3 3 4 . 5 3 3 4 . 4 0 . 1 3 3 4 . 4 0.1 3 3 5 . 3 - 0.80.20 3 5 8 . 6 3 5 9 . 0 - 0 . 4 3 6 0 . 3 - 1 . 70 . 3 0 3 8 2 . 2 3 8 3 . 3 - 1.1 3 8 3 . 7 - 1 . 5 3 8 4 . 4 - 2.20 . 4 0 4 0 5 . 0 4 0 6 . 2 - 0 . 4 4 0 6 . 8 - 1.0 4 0 6 • 8 -1 .00 . 5 0 4 2 7 . 0 4 2 6 . 4 0.6 4 2 7 . 3 - 0 . 3 4 2 6 . 6 0 . 40 . 6 0 4 4 4 . 9 A A 2 . 4 2 . 5 4 4 3 . 5 1 . 4 4 4 2 . 6 2 . 30 . 7 0 4 5 7 . 2 4 5 2 . 4 ' 4 . 8 4 5 3 . 5 3 . 7 4 5 3 . 4 3 . 80 . 8 0 4 6 2 . 6 4 5 5 . 1 7 . 5 4 5 6 . 3 6 . 3 4 5 7 . 8 4 . 80 . 9 0 4 5 8 . 9 4 5 0 . 7 8.2 4 5 4 . 3 4 . 61.00 4 4 1 .8 4 4 1 .8 0.0 4 4 1 . 8 0.0 4 4 1 . 8 0.0

A V G . A B S 2.8 2.0 2 . 4B I A S " 2 . 4 1.2 1.1R M S 4 . 1 2 . 9 2 . 9

)|« f*| 3. .1. .1. .1. .1. V*. fc1# .1' . a>|. «i» »,* *|* ■ 3r« 1* v *!■ >!» v ;'*1 ;J: ;J; ;1' '1* '1' 1* '1* *1*. V V 't* v V V ••%■* •’i'. <*,. <,* «i» ' i * »i» »i* v n * *|» 'i> »|» #,» . . . »,« «,» «t i . ,» •)« r , i »,•

RK-EO = REDLICH-KWOMG EOUATI ON OF STATF RN-EO = REDLICH-NGO EOUATION OF STATF KREGK = KREGLEWSKI-KAY METHOD

216T A B L E 3 5 ( C O N T ' D )

S Y S T E M N U M B E R 1 8 N - H E X A H E ( A ) — N - T R I D E C A N E ( B ) " S . C . P A KR E D . I N T . P A R . R - K A 1 2 S R = 0 . 7 1 5 6 6 4 0 9 R 1 2 S R = 0 . 8 3 7 4 7 8 8 2R E D . I N T . P A R . R - N A 1 2 S R = 0 . 6 7 7 8 2 2 2 9 B 1 2 S R = 0 . 6 8 6 7 8 2 7 4

T E M P E R A T U R E ! C )X ( A ) T E X P P K - E O D E V R N - E O D E V K R E G K D E V0.0 4 0 1 . 7 4 0 1 . 7 0.0 4 0 1 . 7 0.0 4 0 1 . 7 0.00 . 10 3 9 3 . 0 3 9 6 . 1 - 3 . 1 3 9 2 . 8 0.20 . 20 3 8 4 . 0 3 3 9 . 2 - 5 . 2 3 8 7 . 9 - 3 . 9 3 8 3 . 3 0 . 70 . 3 0 3 7 4 . 1 3 8 0 . 7 - 6.6 3 7 8 . 9 - 4 . 8 3 7 2 . 7 1 . 40 . 4 0 3 6 3 . 8 3 7 0. 0 - 6.2 3 6 8 . 0 - 4 . 2 3 6 0 . 8 3 . 00 . 5 0 3 5 1 . 1 3 5 6 . 6 - 5 . 5 3 5 4 . 3 - 3 . 2 3 4 7 . 1 4 . 00 . 6 0 3 3 6 . 1 3 3 9 . 6 - 3 . 5 3 3 7 . 3 - 1.2 3 3 1 . 1 5 . 00 . 7 0 3 1 8 . 3 3 1 8 . 3 - 0.0 3 1 6 . 1 2.2 3 1 2 . 3 6.00 . 8 0 2 9 6 . 8 2 S 2 . 5 4 . 3 2 9 0 . 6 6.2 2 9 0 . 1 6 . 70 . 9 0 2 6 9 . 0 2 6 3 . 4 5 . 6 2 6 4 . 0 5 . 01.00 2 3 4 . 1 2 3 4 . 1 0.0 2 3 4 . 1 o.o 2 3 4 . 1 0.0

A V G . A P S 4 . 5 3 . 7 3 . 6B I A S - 2 . 3 - 1 . 3 3 . 6

-- R M S 4 . 9 _ 4 . 0 _ _ 4 . 2P R E S S U R E ( P S I A )

X (A ) P E X P R K - E O D E V R N - E O D E V K R E G K D E V0.0 2 5 0 . 2 2 5 0 . 2 0.0 2 5 0 . 2 0.0 _ 2 5 0 . 2 0.00.10 2 8 3 . 7 2 8 2 . 8 5 . 9 2 8 6 . 8 1 . 90.20 3 2 8 . 1 3 1 8 . 5 9 . 6 3 1 9 . 5 8.6 3 2 6 . 4 1 . 70 . 3 0 3 6 7 . 0 3 5 6 . 9 10. 1 3 5 9 . 3 7 . 7 3 6 7 . 9 - 0 . 90 . 4 0 4 0 4 . 9 3 9 7 . 2 7 . 7 4 0 1 . 1 3 . 8 4 0 9 . 6 - 4 . 70 . 5 0 4 4 1 . 1 4 3 7 . 3 3 . 8 4 4 2 . 4 - 1 . 3 4 4 9 . 0 - 7 . 90 . 6 0 4 7 5 . 4 4 *i 3 • 0 2 . 4 4 7 8 . 1 - 2 . 7 4 8 2 .1 - 6 . 70 . 7 0 4 9 9 . 5 4 9 7 . 2 2 . 3 5 0 0 . 6 - 1.1 5 0 3 . 8 - 4 . 30 . 8 0 5 1 0 . 0 5 0 0 . 1 9 . 9 5 0 0 . 7 9 . 3 5 0 7 . 9 2.10 . 9 0 4 9 9 . 2 4 7 7 . 3 2 1 . 9 4 8 8 . 4 10.81.00 4 4 1 .8 4 4 1 .8 0.0 4 4 1 . 8 0.0 4 4 1 . 8 0.0

A V G . A R S 8.2 4 . 9 4 . 6B I A S 8.2 3 . 5 “ " - 0 . 9R M S 10.0 5 . 9 5 . 5%<> *pV <1* v '*** •t" «■». at* a*. %t. .t, a «!« «.» «|» »,* *,» t 5,i #,« Jti I,£ * t1. .*• a'. a1, .t. a*.

* 'f* -|» ■*«* -1* -I* *1* '1'•(' V *1« 'i* V V -1“ *!» V ’■i. .i. .t. .i* . I' 1* T *|* “•«' -"i** ,C V *|. 5,. .i, .i. ,p, jP; ,

RK-FO = REDL]CH-KWDNG EOUATIDM OF STATERN-EO = REDLICH-NGO EOUAT IDM OF STATEKREGK = KREGLEWSKI-KAY METHOD

21?TABLE 35 (CONT'D)

S Y S T E M N U M B E R 1 9h’- H E X A N E ( A ) — - N - T E T . R A D E C A N E ( R ) S . C . P A KR E D . I N T . P A R . R - K A 1 2 S R = 0 . 6 5 8 4 5 2 2 1 B 1 2 S R = 0 . 8 4 5 6 5 9 9 7R E D . I N T . P A R . R - N A 1 2 S R = 0 . 5 6 9 7 5 5 2 6 R 1 2 S R = 0 . 5 9 2 4 1 9 9 2

T E M P E R A T I J R E ( C)X( A ) T E X P R K - E O D F V R N - E O D E V K R E G K D E V0.0 4 2 3 . 7 4 2 3 . 7 0.0 4 2 3 . 7 0.0 4 2 3 . 7 0.00.10 4 1 6 . 0 4 1 7 . 6 - 1.6 4 1 4 . 3 1 . 70.20 4 0 7 . 6 4 1 0 . 2 - 2.6 4 0 9 . 2 - 1.6 4 0 4 . 2 3 . 40 . 3 0 3 9 7 . 1 4 0 1 . 1 - 4 . 0 4 0 0. 0 - 2 . 9 3 9 3 . 1 4 . 00 . 4 0 3 8 4 . 7 3 8 9 . 6 - 4 . 9 3 88 .7 - 4 . 0 3 8 0 . 4 4 . 30 . 5 0 3 7 0 . 0 3 7 5 . 1 - 5 . 1 3 7 4 . 4 - 4 . 4 3 6 5 . 5 4 . 50 . 6 0 3 5 3 . 3 3 5 6 . 3 - 3 . 0 3 5 5 . 7 - 2 . 4 3 4 7 . 9 5 . 40 . 7 0 3 3 2 . 8 3 3 2 . 3 0 . 5 3 3 1 . 0 1.8 3 2 6 . 5 6 . 30 . 8 0 3 0 7 . 6 3 0 2 . 2 5 . 4 2 9 9 . 9 7 . 7 3 0 0 . 8 6.80 . 9 0 2 7 5 . 0 2 6 9 . 9 5 . 11.00 2 3 4 . 1 2 3 4 . 1 0.0 2 3 4 . 1 0.0 2 3 4 . 1 0.0

A V G . A P S 3 . 4 3 . 5 4 . 6B I A S - 1 . 9 - 0.8 4 . 6R M S 3 . 8 4. 0 4 . 8

P R E S S U R E ( P S I A )X ( A ) P E X P R K - E O D E V R N - E O D E V K R E G K D E V0.0 2 0 8 . 5 2 0 8 . 5 0.0 2 0 8 . 5 o . o 2 0 8 . 5 0.00 . 10 2 5 4 . 9 2 4 0 . 6 1 4 . 3 2 4 7 . 4 7 . 50.20 3 0 1 . 2 2 7 6 . 4 2 4 . 8 2 8 2 . 1 1 9 . 1 2 9 1 . 1 10.10 . 3 0 3 4 7 . 5 3 1 6 . 3 3 1 . 2 3 2 7 . 7 1 9 . 8 3 3 8 . 9 8.60 . 4 0 3 9 3 .8 3 5 9 . 9 3 3 . 9 3 7 8 . 8 1 5 . 0 3 8 9 . 2 4 . 60 . 5 0 4 3 8 . 2 4 0 5 . 9 3 2 . 3 4 3 3. 2 5 . 0 4 3 3 . 8 - 0.60 . 6 0 4 7 9 . 9 4 5 0 . R 2 9 . 1 4 8 4 . 8 - 4 . 9 4 8 2 . 9 - 3 . 00 . 7 0 5 1 4 . 0 4 8 6 . 5 2 7 . 5 5 2 0 . 9 - 6 . 9 5 1 4 . 0 - 0.00 . 8 0 5 3 2 . 0 4 9 9 . 3 3 2 . 7 5 2 2 . 2 9 . 8 5 2 3 . 1 8 . 90 . 9 0 5 1 7 . 5 5 0 0 . 8 1 6 .1.00 4 4 1 .8 4 4 1 .8 0.0 4 4 1 . 8 0.0 4 4 1 . 8 0.0

A V G . A B S 2 8 . 2 1 1 . 5 . 6 . 7B I A S 2 8 . 2 8.1 5 . 9R M S 2 8 . 9 1 3 . 0 8 . 3

»|. »(* »|* V »|« >|* r(i .t<i .,■> *ti #4t .k. «,* *,« r(i

RK-EO = REDLICK-KWONG EDUCTION OF STATERN-EO = REDLICI1-NG0 EOUAT ION OF STATEKREGK = KREGLEUSKI-KAY METHOD

218TABLE 35 (CONT'D)

SYSTEM NUMBER 20

N-HEXANE(A) — CIS-DECALIN(B ) S.C. PAK

R E D . I N T . P A R . R - K A 1 2 S R = 0 . 8 1 9 7 7 7 7 9 B 1 2 S R = O .19 1 3 4 1 4 9 *R E D . I N T . P A R . R - N A 1 2 S R “ 0 . 7 8 2 8 9 0 5 6 R 1 2 S R = 0 . 8 6 6 1 2 5 0

T E M P E R A T U R E ! C )X (A ) T E X P R K - E O D E V R N - E Q D E V K R E G K D E V0.0 4 3 1 .8 4 3 1 . 8 0.0 4 3 1 . 8 0.0 4 3 1 . 8 0.00 . 10 4 1 8 . 5 4 1 9 . 6 - 1.1 4 1 9 . 9 - 1 . 4 4 1 7 . 1 1 . 40.20 4 0 3 . 6 4 0 5 . 8 - 2.2 4 0 6 . 3 - 2 . 7 4 0 1 . 3 2 . 30 . 3 0 3 8 7 . 3 3 9 0 . 0 - 2 . 7 3 9 0 . 7 - 3 . 4 3 8 4 . 5 2.80 . 4 0 3 6 9 . 5 3 7 2 . 2 - 2 . 7 3 7 2 . 8 - 3 . 3 3 6 6 . 5 3 . 00 . 5 0 3 5 0 . 0 3 5 2 . 1 - 2.1 3 5 2 . 5 - 2 . 5 3 4 7 , 4 2.60 . 6 0 3 2 8 . 7 3 2 9 . 8 - 1 . 1 3 2 9 . 9 - 1.2 3 2 7 . 0 1 . 70 . 7 0 3 0 6 . 1 3 0 5 .8 0 . 3 3 0 5 . 5 0.6 3 0 5 . 4 0 . 70 . 8 0 2 8 3 .0 2 P 1 • 1 1 . 9 2 8 0 . 5 2 . 5 2 8 2 . 7 0 . 30 . 9 0 2 5 8 . 8 2 5 6 . 7 2 . 1 2 5 6 . 1 2 . 7 2 5 8 . 8 - 0.01.00 2 3 4 . 1 2 3 4 . 1 0.0 2 3 4 . 1 0.0 2 3 4 . 1 0.0

A V G . A B S 1 .8 2.2 1 . 7B I A S - 0 . 9 - 1.0 1.6R M S 1 . 9 2 . 4 2.0

P R E S S U R E ( P S I A )X ( A ) P E X P R K - E O D E V R N - E O D E V K R E G K D E V0.0 4 6 5 . 1 4 6 5 . 1 0.0 4 6 5 . 1 0.0 4 6 5 . 1 0.00.10 5 0 1 .8 4 9 8 . 4 3 . 4 4 9 8 . 0 3 . 8 4 9 2 . 4 9 . 40.20 5 3 3 . 4 5 2 9 . 2 4 . 2 5 2 8 . 9 4 . 5 5 1 5 . 7 1 7 . 70 . 3 0 5 5 8 . 3 5 5 5 . 7 2.6 5 5 5 . 6 2 . 7 5 3 3 . 8 2 4 . 50 . 4 0 5 7 5 .9 5 7 4 . 9 1.0 5 7 5 . 2 0 . 7 5 4 5 . 7 3 0 . 20 . 5 0 5 8 4 . 0 5 8 3 . 3 0 . 7 5 8 3 . 9 0 . 1 5 5 0 . 4 3 3 . 60 . 6 0 5 8 2 . 1 5 7 7 . 4 4 . 7 5 7 8 . 0 4. 1 5 4 6 . 9 3 5 . 20 . 7 0 5 6 9 . 8 5 5 5 . 5 1 4 . 3 5 5 5 . 6 1 4 . 2 5 3 4 . 5 3 5 . 30 . 8 0 5 4 3 . 6 5 2 0 . 4 2 3 . 2 5 1 9 . 8 2 3 . P 5 1 2 . 8 3 0 . 80 . 9 0 4 9 8 . 4 4 7 9 . 5 1 8 . 9 4 7 8 . 7 1 9 . 7 4 8 1 . 7 1 6 . 71.00 4 4 1 .8 * 4 1 .8 0.0 4 4 1 . 8 0.0 4 4 1 .8 0.0

A V G . A B S 8.1 8.2 2 6 . 0. . . B I A S 8.1 8.2 2 6 . 0

R M S 1 1 . 3 11.6 2 7 . 4v*'1* V *!» '1' 'C 'l* *J; ijs v *1" 'i;> v1. .1. O, .1. .1# .1. ■*.‘ *!• 3|» v *»* .1)1 ,t., J, s', ,tp .1, *1* «l'» 4*1• *«» 'i* *i’ 'i* *i' fr •»* 'i' *v■ V '.i. .t. .*« o, i*. .4.

■I" 'i* *1* -V '1' ■V "i" *i« -V '(■RK-FO = REDLJCH-KWONG EOUATION OF STATFRN-EO = REDLICH-IMGO EQUATION DF STATEKREGK = KREGLEl'SK I—KAY METHOD

219T A B L E 3 5 ( C O N T ' D )

S Y S T E M N U M B E R 21 M - N O N A M E ( A ) ■ M - T R I.D E C A N E ( B ) S . C . P A KR E D . I N T . P A R . R - K A 1 2 S R = 0 . 8 0 9 1 2 2 3 1 B 1 2 S R = 0 . 9 1 2 4 8 4 2 ‘R E D . I N T . P A R . P.-N A 1 2 S R = 0 . R 9 8 3 2 8 4 8 B 1 2 S R = 0 . 9 0 9 6 1 5 7 1

T E M P E R A T U R E " ! C)X ( A ) T E X P R K - E O D E V R N - E O D E V K R E G K D E V0.0 4 0 1 .7 403. . 7 0.0 4 0 1 . 7 0.00 . 10 3 9 6 . 4 3 9 7 . 3 - 0 . 9 3 9 5 . 7 0 . 70.2 0 3 9 1 . 5 3 5 2.2 - 0 . 7 3 8 9 . 4 2 . 10 . 3 0 3 8 5 . 6 3 8 6 . 3 - 0 . 7 3 8 2 . 6 3 . 00 . A O 3 7 9 . 0 3 7 9 . 5 - 0 . 5 3 7 5 . 5 3 . 50 . 5 0 3 7 1 . 5 3 7 1 .7 - 0 . 2 3 6 7 . 9 3 . 60 . 6 0 3 6 3 . 2 3 6 3 . 1 0 . 1 3 5 9 . 7 3 . 50 . 7 0 3 5 3 . 6 3 5 3 .4 0 . 2 3 5 0 . 9 2 . 70.00 3 4 3 . 4 3 4 3 . 0 0 . 4 3 4 1 . 5 1 . 90 . 9 0 3 3 2 . 3 3 3 1 .9 0 . 4 3 3 1 . 4 0 . 91 .00 3 2 0 . 6 3 2 0 . 6 0.0 3 2 0 . 6 0.0

A V G . A P S 0 . 5 2 . 4B I A S - 0. 2 2 . 4R M S 0 . 5 2 . 7

P R E S S U R E ( P S I A )X (A ) P E X P R K - E O D E V R N - E O D E V K R E G K D E V0.0 2 5 0 . 2 2 5 0 . 2 0.0 2 5 0 . 2 0.00 . 10 2 6 4 .3 2 6 4 . 7 - 0 . 4 2 6 3 . 3 1.00.20 2 7 F . 1 2 7 8 . 9 - O . R 2 7 6 . 2 1 . 90 . 3 0 2 9 1 . 8 2 9 2 . 5 - 0 . 7 2 88.6 3 . 20 . 4 0 3 0 4 . 9 3 0 5 . 0 - 0 . 1 3 0 0 . 1 4 . 80 . 5 0 3 1 6 . 6 3 1 6 . 0 0.6 3 1 0 . 6 6.00 . 6 0 3 2 6 . 2 3 2 4 . 8 1 . 4 3 1 9 . 6 6.60 . 7 0 3 3 3 . 0 3 3 0 . 9 2 . 1 3 2 6 . 7 6 . 30 . 8 0 3 3 7 . 0 2 2 4 . 1 2 . 9 3 3 1 . 6 5 . 40 . 9 0 3 3 6 . 9 3 3 4 . 5 2 . 4 3 3 3 , 7 3 . 21 .00 3 3 2 . 7 3 3 2 . 7 0.0 3 3 2 . 7 0.0

A V G . A P S 1 . 3 4 . 3R I A S O . R 4 . 3R M S

«,** V*. Sr» » »’«1.6

,1 ,*» •»>, i1, »'» O# ,'» »'# »'» i4 . 7

fc*. .

RK-EO = REDLICM-KUDNG EOUATI ON OF STATERN-EO = REDLICM-MGO EOUATION OF STATEKREGK = KREGLEUSKI-KAY METE'PD


SYSTEM NUMBER 22

N-DECANE(A ) --- N-DODECANE(B ) S.C. PAK

R E D . I N T . P A R . R - K A 1 2 S R = 0 . 9 6 8 7 8 1 1 1 B 1 2 S R = 0 . 9 7 9 2 8 3 1 5R E D . I N T . P A R . R - N A 1 2 S R = 0 . 9 6 8 6 0 4 3 3 B 1 2 S R = 0 . 9 4 6 8 1 0 7 2

T E M P E R A T U R E ( C )X I A ) T E X P P K - E Q D E V R N - E O D E V K R E G K D E V0.0 3 8 5 . 8 3 8 5 . 8 0.0 3 8 5 . 8 0.00.10 3 8 2 . 1 3 8 2 . 3 - 0 . 2 3 8 2 . 2 - 0.10.20 3 7 8 . 3 ? 7 f . 6 - 0 . 3 3 7 8 . 4 - 0.10 . 3 0 3 7 4 . 3 3 7 4 . 8 - 0 . 5 3 7 4 . 6 - 0 . 30 . 4 0 3 7 0 . 4 3 7 0 . 7 - 0 . 3 3 7 0 . 6 - 0.20 . 5 0 3 66 . 4 3 6 6 . 5 - 0 . 1 3 66.6 - 0.00 . 6 0 3 6 2 . 3 3 6 2 . 1 0.2 3 6 2 . 2 0.10 . 7 0 3 5 3 . 1 3 5 7 . 7 0 . 4 3 5 7 . 8 0 . 30 . 8 0 3 5 3 .6 3 5 3 . 2 0 . 40 . 9 0 3 ^ 8 . 7 3 4 8 . 3 0 . 4 3 4 8 . 5 0.21.00 3 4 3 .6 3 ^ 3 . 6 0.0 3 4 3 . 6 0.0

A V G . A B S 0 . 3 0,2R I A S - 0 . 1 0,0R M S 0 . 3 0.2

P R E S S U P E ( P S I A )X ( A ) P E X P R K - E P D E V R N - E O D E V K R E G K D E V0.0 2 6 9 . 8 2 6 9 . 8 0.0 2 6 9 . 8 0.00 . 10 2 7 6 . 2 2 7 5 . 6 0.6 2 7 5 . 4 0.80.20 2 8 1 . 9 2 8 1 . 2 0 . 7 2 8 0 . 8 1.10 . 3 0 2 8 6 . 9 2 8 6 . 3 0.6 2 8 5 . 9 1.00 . 4 0 2 9 1 .6 2 9 1 . 1 0 . 5 2 9 0 . 7 0 . 90 . 5 0 2 9 5 . 7 2 9 5 . 5 0.2 2 9 5 . 2 0 . 50 . 6 0 2 9 9 . 5 2 9 9 . 4 0. 1 2 9 9 . 3 0.20 . 7 0 3 0 2 . 8 3 0 2 . 9 - 0.1 3 0 3 . 0 - 0.20 . 8 0 3 0 5 . 7 3 0 6 . 1 - 0 . 40 . 9 0 3 0 8 . 3 3 0 8 . 4 - 0 . 1 3 0 8 . 6 - 0 . 31 .00 3 1 0 . 5 3 1 0 . 5 0.0 3 1 0 . 5 0.0

A V G . A B S 0 . 3 0.6B I A S 0 . 3 0 . 4R M S 0 . 4 0 . 7

V V *!*• 4* *Vi .4. .1. ,1. .4. ' 'I* *1* *r "'I* *4* «*l* "I* '!*•

.4. ,1. ,1. .4# .4. ,*«|. .p .1. , U ,1. « 1 w «l. ,1. ,1* »(V *|* •)> .,•» .4. .4. v1. .1,. .4 .4. .4. .1. .4# 4. .1. ,1. .4. .4d• |. .|i .|« P|4 .|, qi ,4# ,4. .4. ,4, .4 »|'

RK-EO = REDL ICH-K'-'OMG EOUAT I ON OF STATERN-EO = REDLICH-MGO EOUATION OF STATEKREGK = KREGLEWSKI-KAY METHOD


SYSTEM NUMBER 28

BENZENE(A) "N-DECANE(B) S.C PAK


T E M P E R A T U R E ( C )X ( A > T E X P 7D T' 1 m D E V R N - E O D E V K R E G K D E V0.0 3 4 3 . 6 3 * 3 . 6 0.0 3 4 3 . 6 0.0 3 4 3 . 6 0.00 . 10 3 4 1 . 2 3 4 0 . 9 0 . 3 3 3 9 . 1 2.10.20 3 3 7 . 8 3 3 7 . 8 0.0 3 3 6 . 3 1 . 5 3 3 4 . 6 3 . 20 . 3 0 3 3 3 . 6 3 3 4 . 1 - 0 . 5 3 3 2 . 3 1 . 3 3 3 0 . 2 3 . 40 . 4 0 3 2 8 . 9 3 2 9 . 7 - O . R 3 2 8 . 0 0 . 9 3 2 5 . 6 3 . 30 . 5 0 3 2 3 . 6 3 2 4 . 5 - 0 . 9 3 2 3 . 2 0 . 4 3 2 0 . 7 2 . 90 . 6 0 3 1 7 . 9 3 ) 8 . 5 - 0.6 3 1 7 . 8 0 . 1 3 1 5 . 5 2 . 40 . 7 0 3 1 1 . 7 3 1 1 . 6 0 . 1 3 1 1 . 7 - 0.0 3 0 9 . 6 2.10 . 8 0 3 0 4 . 8 3 0 3 . 9 0 . 9 3 0 4 . 8 - 0.0 3 0 3 . 1 1 . 70 . 9 0 2 9 6 . 9 2 9 5 .8 1. 1 2 9 7 . 0 - 0.1 2 9 5 . 0 1 .11 .00 2 8 0 . 1 2 8 8 . 1 0.0 2 8 8 . 1 0.0 2 8 8 . 1 0.0

A V G . A B S 0.6 0.6 2 . 5B I A S - 0 . 1 0 . 5 2 . 5R M S 0 . 7 0.8 2.6

P R E S S U R E ( P S I A )X( A ) P E X P R K - E O D E V R N - E O D E V K R E G K D E V0.0 3 1 0 . 2 3 1 0 . 2 0.0 3 1 0 . 2 o.o 3 1 0 . 2 0.00.10 3 4 1 . 9 3 4 1 . 0 0 . 9 3 4 9 . 3 - 7 . 40.20 3 7 5 . 2 3 7 4 . 3 0 . 9 3 7 1 . 9 3 . 3 3 9 2 . 2 - 1 7 . 00 . 3 0 4 1 1 . 4 4 1 0 . 4 1.0 4 0 7 . 4 4 . 0 4 3 8 . 5 - 2 7 . 10 . 4 0 4 4 9 .6 4 4 9 . 1 0 . 5 4 4 6 . 0 3 . 6 4 8 7 . 3 - 3 7 .70 . 5 0 4 8 9 . 8 4 9 0 . 1 - 0 . 3 4 0 7 . 5 2 . 3 5 3 7 . 3 - 4 7 . 50 . 6 0 5 3 2 . 3 5 3 3 . 1 - 0.8 5 3 1 . 8 0 . 5 5 8 6 . 4 - 5 4 . 10 . 7 0 5 7 7 . 0 5 7 7 . 1 - 0 . 1 5 7 7 . 0 - 0.8 6 3 1 . 0 - 5 4 . 00 . 8 0 6 2 1 . 7 6 2 1 . 3 0 . 4 6 2 4 . 5 - 2 .R 6 7 0 . 0 - 4 8 . 30 . 9 0 6 6 6 . 7 6 6 5 . 5 1.2 6 6 9 . 9 - 3 . 2 6 9 7 . 4 - 3 0 . 71.00 7 1 2 . 1 7 1 2 . 1 0.0 7 1 2 . 1 0.0 7 1 2 . 1 0.0

A V G . A B S 0 . 7 2.6 3 6 . 1B I A S 0 . 4 0 . 9 - 3 6 . 1R M S 0.8 2.8 3 9 . 4

RK-FO = RFDLICH-KNOMG EOUATION HE STATERN-EO = REDLICH-NGO EOUATION OF STATEKREGK = KREGLEWSKI—KAY METHOD


S Y S T E M N U M B E R 2 9B E N Z E N E * A ) M - T R I D E C A N E ( B ) S . C . P A K . . . . . . . . . . . . . . . . .R E D . I N T . P A R . R - K A 1 2 S R = 0 . 6 9 4 2 0 5 2 8 B 1 2 S R = 0 . 8 1 9 3 9 3 8 1R E D . I N T . P A R . R - N A 1 2 S R = 0 . 7 1 6 8 8 1 4 5 R 1 2 S R = 0 . 7 1 0 1 3 5 1 0

T E N P E R A T 1 'R r l C )X ( A ) T E X P R K - E P D E V R N - E O D E V K R E G K D E V0.0 4 0 1 .7 4 0 1 , 7 0.0 4 0 1 . 7 0.0 4 0 1 . 7 0.00.10 3 9 7 . 8 3 9 8 . 7 - 0 . 9 3 9 4 . 9 2 . 90.20 3 9 3 . 0 3 9 4 . 9 - 1 . 9 3 9 1 . 9 1. 1 3 8 8 . 3 4 . 70 . 3 0 3 8 7 . 3 3 9 0.0 - 2 . 7 3 8 6 . 2 1.1 3 8 1 . 6 5 . 70 . 4 0 3 8 0 .3 3 8 3 . 6 - 3 . 3 3 7 9 . 6 0 . 7 3 7 4 . 6 5 . 70 . 5 0 3 7 1 . 7 3 7 5 . 3 - 3 . 6 3 7 1 . 7 0.0 3 6 6 . 7 5 . 00 . 6 0 3 6 1 .5 3 6 4 . 3 -2 . 8 3 6 1 . 8 - 0 . 3 3 5 7 . 2 4 . 30 . 7 0 3 4 8 . 7 3 5 0 . 0 - 1 . 3 3 4 9 . 3 - 0.6 3 4 5 . 4 3 . 30 . 8 0 3 3 2 . 7 3 3 3 . 2 - 0 . 5 3 3 0 . 3 2 . 40 . 9 0 3 1 3 . 0 3 0 9 . 9 3. 1 3 1 2 . 7 0 . 3 3 1 1 . 1 1 . 91 .00 2 88 . 1 2 8 8 .1 0.0 2 8 8 . 1 0.0 2 8 8 . 1 0.0

A V G . A B 5 2 . 5 0.6 4 . 0B I A S - 1 . 7 0.2 4 . 0R M S 2.6 0 . 7 4 . 2

P R E S S U R E ( P S I A )X ( A ) P E X P R K - E P D F V R N - E O D E V K R E G K D E V0.0 2 5 0 . 2 2 5 0 . 2 0.0 2 5 0 . 2 0.0 2 5 0 . 2 0.00.10 2 0 8 . 0 2 8 6 . 7 1 . 3 2 9 6 . 7 - 8 . 70.20 3 2 9 . 9 - 2 8 . 1 1.8 3 2 5 . 2 4 . 7 3 5 1 . 6 - 2 1 . 70 . 3 0 3 7 6 . 3 3 7 5 . 0 1 . 3 3 7 1 . 6 4 . 7 4 1 5 . 1 - 3 8 . 80 . 4 0 4 2 5 . 8 4 2 7 * 5 - 1 . 7 * 2 4 . 4 1 . 4 4 8 6 . 8 - 6 1 .00 . 5 0 4 7 9 . 3 4 8 5 .6 - 6 . 3 4 8 3 . 5 - 4 . 2 5 6 4 . 2 - 8 4 . 90 . 6 0 5 3 8 . 7 5 4 7 . 5 - 8.8 5 4 7 . 2 - 8 . 5 6 4 2 . 0 - 1 0 3 . 30 . 7 0 6 1 2 . 2 6 0 8 . 9 3 . 3 6 1 1 . 7 0 . 5 7 1 0 . 6 - 9 8 . 4O . F O 6 7 4 . 9 668 .6 6 . 3 7 5 5 . 5 - 8 0 . 60 . 9 0 7 0 4 . 0 6 9 3 . 7 1 0 . 3 7 0 5 . 3 - 1 . 3 7 5 9 . 3 - 5 5 . 31 .00 7 1 2 . 1 7 ) 2 . 1 0 . 0 7 1 2 . 1 0.0 7 1 2 . 1 0.0

A V G . A R S 4 . 4 4 . 0 61 . 4B I A S 0.2 0 . 5 - 6 1 .'4R M S 5 . 5 4 . 7 6 9 . 0

,C ,1. *1, *i, V V T V , 5,1 v v ~r- v *|. ... .p. »|«: * :I,1. .1# hi. s', .1, .v .1, .If V 'l' '•’I* '1* “l* *1* 5,h ?|! 5,! ?,S ' %■* hi* .1. .1, **V .1. . 4 hi* hi,, ,p. rp, «•,» ,pt »,♦ .1. h*. ,1. hi* i1. .1* .1.*,h «►,. »,»

RK-EP = REDLICH-KUDNG EQUATION OF STATFRN-EO = REDL ICH-HGO EOUAT ION OF STATEKREGK = KPEGLEWSKI—KAY METHOD


SYSTEM NUMBER 37

BENZENE (A ) C. I S-DEC AL IN ( R ) S.C. PAK


T E M P E R A T U R E ! C)X ( A ) T E X P R K - E O D E V R N - E O D E V K R E G K D F V0.0 4 3 1 .8 4 3 1 . 8 0.0 4 3 1 . 8 0.0 4 3 1 . 8 0.00 . 10 4 2 2 . 6 4 2 4 . 1 - 1 . 5 4 2 2 . 5 0.1 4 2 2. 8 - 0.20.20 4 1 2 . 5 4 1 5 . 2 - 2 . 7 4 1 2 . 0 0. 5 4 1 3 . 1 - 0.60 . 3 0 40],. 6 4 0 5 . 0 - 3 . 4 4 0 0 . 2 1 . 4 4 0 2. 5 - 0 . 90 . 4 0 3 9 0 . 0 3 9 3 . 1 - 3 . 1 3 8 6 . 8 3 . 2 39). . 0 -1 .00 . 5 0 3 7 6 . 9 3 7 9. 3 - 2 . 4 3 7 1 . 8 5 . 1 3 7 8 . 1 - 1.20 . 6 0 3 6 2 .4 3 6 3 . 5 - 1 . I 3 5 5 .1 7 . 3 3 6 3 . 7 - 1 .30 . 7 0 3 4 6 . 3 3 4 5 . 8 0 . 5 3 3 7 . 1 9 . 2 3 4 7 . 5 - 1.20 . 8 0 3 2 8 . 4 3 2 6 . 5 1 .9 3 1 8 . 8 9 . 6 3 2 9 . 5 - 1.10 . 9 0 3 0 8 . 9 3 0 6 .6 2 . 3 3 0 9 . 6 - 0 . 71 .00 2 88.1 2 8 8 . I. 0.0 2 8 8 . 1 0.0 2 8 8 . 1 0.0

A V G . A B S 2 . 1 4. 6 0 . 9B I A S - 1.0 4. 6 - 0 . 9R M S 2 . 3 5 . 8 1.0

P R F S S U R E ( P S I A )X ( A ) P E X P P . K - E O D E V R N - E O D E V K R E G K D E V0.0 4 6 5 .1 7 ’- 6 5 . 1 0.0 4 6 5 . 1 0.0 4 6 5 . 1 0.00.10 5 1 4 . 5 5 0 9 . 3 5 . 2 5 0 8 . 7 5 . 8 5 1 1 . 2 3 . 30.20 5 6 0 . 5 5 5 4 . 7 5 . 8 5 5 3 . 4 7 . 1 5 5 8 . 8 1 . 70 . 3 0 6 0 4 . 2 6 0 0 . 0 4 . 2 5 9 7 . 7 6 . 5 6 0 6.6 - 2 . 40 . 4 0 6 4 4 . 5 6 ^ 3 . 4 1.1 6 3 9 . 3 5 . 2 6 5 2 . 4 - 7 . 90 . 5 0 6 8 0 . 9 6 8 2 . 1 - 1.2 6 7 4 . 9 6 . 0 6 9 3 . 8 - 1 2 . 90 . 6 0 7 1 1 . 1 7 1 2 . 5 - 1 . 4 7 0 0 . 8 1 0 . 3 7 2 7 . 2 - 1 6 .10 . 7 0 7 3 1 . 6 7 3 0 . 3 1 . 3 7 1 3 . 9 1 7 . 7 7 4 9 . 0 - 1 7 . 40 . 8 0 7 4 0 . 1 7 3 3 . 2 6 . 9 7 1 4 . 7 2 5 . 4 7 5 5 . 3 - 1 5 . 20 . 9 0 7 3 4 . 3 7 2 3 .7 10.6 7 4 3 . 2 - 8 . 91 .00 7 1 2 . 1 7 1 2 . 1 0.0 7 1 2 . 1 0.0 7 1 2 . 1 0.0

A V G . A B S 4 . 2 1 0 . 5 9 . 5” B I A S 3 . 6 1 0 . 5 - 8 . 4

R M S 5 . 2 1 2 . 5 11 .2iV *** *•» »'» »•* »*« »*» .*< »•. %.*. *■. «■. •»*. «■. .*• *•. >i. .<« »•.V *1* *1* ' I * *T* *1* ' | * ' i * *1* * |* »(• • )« . | . . ) • . | . »|» . j » » |* « |» »(« . t » . | . i*!* # | . t > r,m r , . . r , t *4% »,i

R K - E O = R E D L I C H - K W D N G E O U A T I O N O F S T A T ER N - E O = R E D L I C H - N G O E O U A T I O N O F S T A T EK R E G K = K R E G L E W S K I - K A Y M E T H O D


S Y S T E M N U M B E R 4 4

E T H Y L R E N Z E N E ( A ) ' C I S - D E C A L I N ( B ) S . C . P A KR E D . I N T . P A R . R - K A 1 2 S R = 0 . 8 8 0 8 9 8 7 7 B 1 2 S R = 0 . 9 2 2 3 1 2 9 7R E D . I N T . P A R . R - N A 1 2 S R = 0 . 8 7 6 2 1 3 1 9 R 1 2 S R = 0 . 9 2 1 6 2 2 1 6

X { A ) T E X P R K - E OT E M P E R A T U R E ( C ) D E V R N - E O D E V K R E G K D E V

0.0 4 3 1 .8 4 3 1 . 8 0.0 4 3 1 . 8 0.0 4 3 1 .8 0.00 . 10 4 2 3 . 9 4 2 4 . 9 - 1.0 4 2 4 . 7 - 0.8 4 2 4 . 0 -0 . 10.20 4 1 5 . 9 4 1 7 . 3 - 1 . 4 4 1 7 . 0 - 1.1 4 1 5 . 9 - 0.00 . 3 0 4 0 7 . 6 4 0 9 . 0 - 1 . 4 4 0 8 . 6 - 1.0 4 0 7 . 6 - 0.00 . 4 0 3 9 9 . 1 4 0 0 . ]. - 1.0 3 9 9 .6 - 0 . 5 3 9 9 . 0 0.10 . 5 0 3 9 0 . 2 3 9 0 . 6 - 0 . 4 3 9 0 . 1 0.1 3 9 0 . 2 0.00 . 6 0 3 8 1 . 0 3 8 0 . 7 0 . 3 3 8 0 . 3 0 . 7 3 0 1 .1 -0 . 10 . 7 0 3 7 1 . 8 3 7 0 . 6 1.2 3 7 0 . 3 1 . 5 3 7 1 . 9 - 0.10 . 8 0 3 6 2 .4 3 6 0 . 8 1.6 3 6 0 . 6 3 .8 3 6 2 . 5 - 0.10 . 9 0 3 5 3 . 2 3 5 1 . 7 1 . 5 3 5 1 . 6 1.6 3 5 3 . 0 0.21.00 3 4 3 .6 3 4 3 . 6 0.0 3 4 3 . 6 0.0 3 4 3 . 6 0.0

A V G .B I A SR M S

A B S 1.1 - 0 . 1 1 . 2

1.0 0.2 1. !

0.1- 0.00.1

X ( A ) P E X P R K - E OP R E S S U R E ( P S I A )

D E V R N - E O D E V K R E G K D E V0.0 4 6 5 .1 4 6 5 . 1 0.0 4 6 5 . 1 0.0 4 6 5 . 1 0.00.10 4 8 9 . 5 4 8 5 . 1 4 . 4 4 8 4 . 0 5 . 5 4 7 9 . 8 9 . 70.20 5 0 7 . 2 5 0 3 . 0 4 . 2 5 0 1 . 0 6.2 4 9 3 . 0 1 4 . 20 . 3 0 5 1 9 . 3 5 1 7 . 9 1 . 4 5 1 5 . 3 4 . 0 5 0 4 . 6 1 4 . 70 . 4 0 5 2 8.6 5 2 9 . 4 - 0.8 5 2 6 . 4 2.2 5 1 4 . 3 1 4 . 30 . 5 0 5 3 5 . 2 5 3 6 . 9 - 1 . 7 5 3 4 . 0 1.2 5 2 2 . 1 1 3 . 10 . 6 0 5 3 9 . 7 5 4 0 . 4 - 0 . 7 5 3 7 . 9 1.8 5 2 7 . 6 12.10 . 7 0 5 4 1 . 4 5 4 0 . 2 1.2 5 3 8 . 3 3 . 1 5 3 1 . 0 1 0 . 40 . 8 0 5 3 9 . 8 5 3 7 . 4 2 . 4 5 3 6 . 2 3 . 6 5 3 2 . 3 7 . 50 . 9 0 5 3 5 . 4 5 3 3 .2 2.2 5 3 2 . 8 2.6 5 3 1 . 6 3 . 81.00 5 2 9 . 2 5 2 9 . 2 0.0 5 2 9 . 2 0.0 5 2 9 . 2 0.0

.......A V G .B I A S

A R S 2.11 . 4 . . . .

3 . 43 . 4

11.111.1

R M SJ. .1. k*. .1. .1. «>. i1. .*# O. h1. .1. kj r|« rp #(• «|. V|. .4. f|i .|1 n » .|V >ak .(fc <•). .ak r,* .p.

2 . 5rj. .p «a. #p #|» .a% ri„ ..I, tia *i, .1,

3 . 7r .1. .C .1. O. kU/p kp *1* •>(. .p t"p k"j<l -p .I* .4. *,

11.6* 3'C j'* 1

RK-EO = REDLICH-KWOMG EOUATION OF STATFRN-EO = R E D LICH-NGO EOUATION OF STATEKREGK = KREGLEWSKI-KAY METHOD


S Y S T E M N U M B E R 4 5O R T H O - X Y L E N F . (A ) C I S - D E C A L I N ( B ) S . C . P A KR E D . I N T . P A R . R - K A 1 2 S R = 0 . 8 9 1 4 3 9 8 0 B 1 2 S R = 0 . 9 2 7 7 3 2 6 5R E D . I N T . P A R . R - N A 1 2 S R - 0 . B 7 5 0 4 5 3 0 B 1 2 S R = 0 . 9 3 5 6 9 5 1 1

T E M P E R A T U R E ( C)X ( A ) T E X P R K - E O D E V R N - E O D E V K R E G K D E V0.0 4 3 1 . 8 431. .8 0.0 4 3 1 . 0 0 . 0 4 3 1 . 8 0.00.10 4 2 4 . 8 4 2 5 . 7 - 0 . 9 4 2 4. 4 0 . 4 4 2 5 . 0 - 0.20.20 4 1 7 . 7 4 1 9 . 1 - 1 . 4 4 1 6 . 6 1.1 4 1 8 . 0 - 0 . 30 . 3 0 4 1 0 . 4 4 11 . 9 - 1 . 5 4 0 8 . 4 2.0 4 1 0 . 7 ' - 0 . 30 . 4 0 4 0 3 . 0 4 0 4 . 2 - 1.2 3 9 9 . a 3. 2 4 0 3 . 3 - 0 . 30 . 5 0 3 9 5 . 5 3 9 6 . 0 - 0 . 5 3 9 1 . 1 4 . 4 3 9 5 . 7 - 0.20 . 6 0 3 8 7 . 8 3 8 7 . 6 0.2 3 8 8 . 0 - 0.20 . 7 0 3 8 0 . 1 3 7 9 . 1 1.0 3 8 0 . 1 0.0O . R O 3 7 2 . 2 3 7 0 . P 1 . 4 3 7 2 . 1 0 . 10 . 9 0 3 6 4 . 2 3 6 3 . 1 1.1 3 6 4 . 1 0.11 .00 3 5 6 . 2 3 5 6 . 2 0.0 3 5 6 . 2 0 . 0 3 5 6 . 2 0.0

A V G . A B S 1.0 2.2 0.2B I A S - 0 . 2 2.2 - 0.1R M S 1.1 2 . 6 0.2

P R E S S I J R E ( P S I A )X ( A ) P E X P R K - E O D E V R N - E O D E V K R E G K D E V0.0 4 6 5 . 1 4 6 5 . 1 0.0 4 6 5 . 1 0.0 4 6 5 . 1 0.00.10 4 8 5 . 3 4 8 4 . 3 1.0 4 8 2 . 9 2 . 4 4 7 9 . 7 5 . 60.20 5 0 2 . 0 5 0 1 .6 0 . 4 4 9 8 . 7 3 . 3 4 9 3 . 2 8.80 . 3 0 5 1 5 . 7 5 1 6 . 5 - O . R 5 1 2 . 0 3 . 7 5 0 5 . 3 1 0 . 40 . 4 0 5 2 7 . 8 5 2 8.6 - 0.8 5 2 2 . 4 5 . 4 5 1 5 . 9 11 . 90 . 5 0 5 3 7 . 2 5 3 7 . 4 - 0.2 5 2 9 . 9 7 . 3 5 2 4 . 9 1 2 . 30 . 6 0 5 4 3 . 5 5 4 3 . 0 0 . 5 5 3 2 . 2 11 .30 . 7 0 5 4 7 . 2 5 4 5 . 7 1 . 5 5 3 7 . 7 9 . 50 . 8 0 5 4 8 . 6 5 4 6 . 2 2 . 4 5 4 1 . 4 7 . 20 . 9 0 5 4 7. 7 5 4 5 . 4 2 . 3 5 4 3 . 6 4 . 11 .00 5 4 4 . 5 5 4 4 . 5 0.0 5 4 4 . 5 0•c 5 4 4 . 5 0.0

A V G . A B S 1.1 4 . 4 9 . 0B I A S 0 . 7 4 . 4 9 . 0R M S 1 . 3 4 . 7 9 . 4

R K - E O = R E D L I C H - K H O M G E O L J A T I O N O F S T A T E R N - E O = R E D L I C H - N G O E Q U A T I O N O F S T A T E K R E O K = K R E G L E W S K I - K A Y M E T H O D


S Y S T E M N U M B E R 6 0" C Y C L O H E X A N E (A ) - - - M - D E C A N E ( R ) S . C . P A KR E D . I N T . P A R . R - K A 1 2 S R = 0 . 0 8 R 2 4 9 1 0 B 1 2 S R = 0 . 9 3 3 0 1 0 2 8R E D . I N T . P A R . R - N A 1 2 S R = 0 . 9 0 6 0 1 1 6 4 P 1 2 S R = 0 . 8 7 7 0 9 3 2 6

T E M P E R A T U R E ( C )X (A ) T E X P R K - E O D E V R N - E O D E V K R E G K D E V0.0 3 4 3 . 9 3 * 3 . 9 0 . 0 3 4 3 . 9 o • o 3 4 3 . 9 0.00.10 3 4 1 . 1 3 4 1 . 0 0 . 1 3 3 9 . 6 1 . 50.20 2 3 7 . 6 2 3 7 . 7 - 0.1 3 3 5 . 1 2 . 50 . 3 0 3 3 3 . 6 3 3 3 . 7 - 0 . 1 3 3 0 . 3 3 . 30 . 4 0 3 2 9 . 1 2 2 9 . 2 - 0 . 1 3 2 5 . 3 3 . 80 . 5 0 3 2 3 . 8 3 2 3 . 8 - 0 . 0 3 2 3 . 9 - 0 . 1 3 1 9 . 7 4 . 10 . 6 0 3 1 7 . 4 2 1 7 . 6 - 0.2 3 1 7 . 9 - 0 . 5 3 1 3 . 6 3 . 80 . 7 0 3 1 0 . 0 3 1 0 . 2 - 0 . 2 3 1 0 . 8 - 0 . B 3 0 6 . 7 3 . 30 . 8 0 2 0 1 . 7 2 01.6 0 . 1 3 0 2 . 3 - 0 . 6 2 9 8 . 8 2 . 90 . 9 0 2 9 1 . 9 2 9 1 . 5 0 . 4 2 9 2 . 1 - 0.2 2 8 9 . 9 2.01.00 2 7 9 . 8 2 7 9 . 8 0.0 2 7 9 . 8 0.0 2 7 9 . 8 0.0

A V G . A P S 0 . ] 0 . 5 3 . 0B I A S - 0.0 - 0 . 5 3 . 0R M S 0.2 0 . 5 3 . 1

P R E S S U R E ( P S I A 1X ( A ) P E X P x

i 1m D E V R N - E O D E V K R E G K D E V

0.0 3 1 0 . 5 2 1 0 . 5 0.0 3 1 0 . 5 0.0 3 1 0 . 5 0.00.10 3 3 5 . 6 3 3 5 . 6 - o . n 3 4 1 . 6 - 6.00.20 3 6 2 . 2 2 6 2 . 5 - 0.2 3 7 4 . 4 - 12.20 . 3 0 3 9 0 . 2 3 9 1 . 0 - 0 . 8 4 0 8 . 5 - 1 8 . 30 . 4 0 4 2 0 . 0 * 21.2 - 1.2 4 4 3 . 4 - 2 3 . 40 . 5 0 4 5 1 . 7 4 5 2 . 7 - 1.0 4 5 4 . 8 - 3 . 1 4 7 8 . 2 - 2 6 . 50 . 6 0 4 8 4 . 5 4 8 4 . 9 - 0 . 4 4 8 7 . 7 - 3 . 2 5 1 1 . 5 - 2 7 .00 . 7 0 5 1 8 . 1 5 1 7 . 0 1.1 5 2 0 . 2 - 2.1 5 4 1 . 9 - 2 3 . 8o . e o 5 5 1 . 3 5 4 7 . 5 3 . 8 5 5 0 . 6 0 . 7 5 6 7 . 4 - 1 6 . 10 . 9 0 5 7 6 . 8 5 7 4 . 2 2.6 5 7 6 . 4 0 . 4 5 8 5 . 7 - 8 . 91.00 5 9 4 . 2 5 9 4 . 2 0.0 5 9 4 . 2 0.0 5 9 4 . 2 0.0

A V G . A B S 1 . 3 1 . 9 1 8 . 0B I A S 0 . 4 - 1 . 4 - 1 8 . 0

.<1 R M S■ «J. J. v'f .1. »*. .

1 . 7.a. .a. .V V. H1.

2.2 Of Or .1. >1. .1. .1. .1 O. . U O. Of Or i

1 9 . 5RK-FQ = REDL JCH-KWONG EOUATION OF STATERN-EO = REDLICH-NGO EOUATION OF STATEKREGK = KREGLEWSKI-KAY METHOD


SYSTEM NUMBER 61

CYCLGHEXAME(A ) N-TRI DECANE(B ) S.C. PAK


T E M P E R A T U R E ( C)X ( A ) T F X P A 1 m -2 D F V R N - E O D E V K R E G K D E V0.0 6 0 1 . 7 6 0 1 . 7 0 . 0 6 0 1 . 7 0.0 6 0 1 . 7 0.00.10 3 9 7 . 6 3 9 8 . 2 - 0.8 3 9 5 . 0 2.60.20 3 9 2 .2 3 9 3 .8 - 1.6 3 8 8 . 2 6.00 . 3 0 3 8 6 . 0 3 8 8 . 3 - 2 . 3 3 0 5 . 8 0.2 3 8 0 . 9 5 . 10 . 6 0 3 7 8 . 6 2 8 1 . 2 - 2.8 3 7 8 . 7 - 0 . 3 3 7 2 . 8 5 . 60 . 5 0 3 6 9 . 3 3 7 2 . 3 - 3 . 0 3 7 0 . 2 - 0 . 9 3 6 3 . 7 5 . 60 . 6 0 3 5 8 . 6 2 6 0 . 8 - 2.6 3 5 9 . 5 - 1.1 3 5 2 . 9 5 . 50 . 7 0 3 6 5 . 6 3 6 6 . 2 - 0.8 3 6 6 . 0 - 0.6 3 3 9 . 8 5 . 60 . 8 0 3 2 9 . 5 2 2 7 . 7 1.8 3 2 8 . 6 0 . 9 3 2 3 . 6 5 . 90 . 9 0 3 0 8 . 6 3 0 5 . 1 3 . 3 3 0 6 . 7 1 . 7 3 0 3 . 8 6.61.00 2 7 9 . 8 2 7 5. 8 0.0 2 7 9 . 8 0.0 2 7 9 . 8 0.0

A V G . A B S 2.1 0.8 6 . 9B I A S - 0 . 9 - 0.0 6 . 9R M S 2 . 3 0 . 9 5 . 0

P R E S S U R E ( P S I A )X ( A ) P F X P R K - E O D E V R N - E O D E V K R E G K D E V0.0 2 5 0 . 2 2 5 0 . 2 0.0 2 5 0 . 2 0.0 2 5 0 . 2 0.00.10 2 8 6 . 9 2 8 2 . 6 6 . 3 2 9 0 . 2 - 3 . 30.20 3 2 6 . 2 3 1 8 . 8 5 . 6 3 3 5 . 6 - 11.20 . 3 0 3 6 3 . 6 3 5 8 . 9 6 . 5 3 5 7 . 8 5 . 6 3 8 5 . 3 - 2 1 . 90 . 6 0 6 0 6 . 3 6 0 2 . 9 3 . 6 6 0 2 . 5 3 . 8 6 3 9 . 1 - 3 2 . 80 . 5 0 6 5 1 . 7 6 5 0 . 1 1.6 6 5 0 . 7 1.0 6 9 6 . 5 - 6 2 . 80 . 6 C 6 9 8 . 3 6 9 8 .8 - 0 . 5 5 0 0 . 7 - 2.6 5 6 7 . 9 - 6 9 . 60 . 7 0 5 6 5 . 6 5 6 6 . 9 0 . 5 5 6 8 . 3 - 2 . 9 5 9 3 . 2 - 6 7 . 80 . 8 0 5 8 7 . 2 5 P ].. 5 5 . 7 5 8 6 . 6 0.8 6 2 2 . 6 - 3 5 . 20 . 9 0 6 1 1 .0 5 9 9 . 2 11.8 6 0 6 . 7 6 . 3 6 2 5 . 7 - 1 6 . 71 .00 5 9 6 . 2 5 9 6 . 2 0.0 5 9 6 . 2 0.0 5 9 6 . 2 0.0

A V G . A B S 6.2 3 . 3 2 8 . 8B I A S 6 . 1 1.8 - 2 8 . 8R M S 5 . 3 3 . 8 3 2 .9

»'* .r. »i. *•*v ' f v *t' «i' .i. »*» *’• .'■» .*«• .1. O. O#*i« «■,. '(« i» f,i f|» :;c ; -'■* sU *r. .V k(f O. »'f|» <|k fjk f|lf *|» f|k fl|.-V v 'i* 'i’ v t v .p. .p. .p. p. #|. .p. ■

R K - E O = R E D L T C H - K W G N G E O I J A T I O N O F S T A T F R N - E O = R E D L I C H - N G O E O U A T I O N O F S T A T E K R E G K = K R E G L F W S K I - K A Y M E T H O D


S Y S T E M N U M B E R 6 3C Y C L D H E X A M E (A) C I . S - D E C A L I N ( R ) S . C . P A KR E D . I N T . P A R . R - K A 1 2 S R = 0 . 8 4 1 4 1 5 1 1 B 1 2 S R = 0 . 9 2 4 9 6 5 6 2R E D . I N T . P A R . R - N A 1 2 S R = 0 . 8 1 7 7 2 8 3 4 B 1 2 S R = 0 . 8 6 8 9 2 4 2 0

T E M P E R A T U R E i C )X ( A ) T E X P R K - E O D E V R N - E O D E V K R E G K D E V0.0 4 3 1 .8 4 3 1 . 8 0.0 4 3 1 . 8 0.0 4 3 1 .8 0.00 . 10 4 2 2 .0 4 2 3 . 1 - 1. 1 4 2 3. 1 - 1.1 4 2 1 . 6 0 . 40.20 4 1 1 . 4 4 1 3 . 3 - 1 . 9 4 1 3 . 3 - 1 . 9 4 1 0 . 7 0 . 70 . 3 0 3 9 9 . 6 4 0 2 . 1 - 2 . 5 4 0 2 . 1 - 2 . 5 3 9 8 . 9 0 . 70 . 4 0 3 8 7 . 1 3 8 9 . 3 - 2.2 3 8 9 . 3 - 2.2 3 8 6 . 0 1 . 10 . 5 0 3 7 3 . 1 3 7 4 . 8 - 1 . 7 3 7 4 . 8 - 1 . 7 3 7 1 . 9 1.20 . 6 0 3 5 7. 6 3 5 8 .5 - 0 . 9 3 5 8 . 3 - 0 . 7 3 5 6 . 6 1.00 . 7 0 3 4 0 . 7 3 4 0 . 4 0 . 3 3 4 0 . 1 0.6 3 3 9 . 8 o .yO . P O 3 2 2 . 6 3 20.8 1.8 3 2 0 . 4 2.2 3 2 1 . 4 1 .20 . 9 0 3 0 2 . 7 3 0 0 . 2 2 . 5 2 9 9 . 9 2.8 3 0 1 . 4 1 . 31 . 0 0 2 7 9 . 8 2 7 9. 8 0.0 2 7 9 . 8 0.0 2 7 9 . 8 0.0

A V G . A B S 1 . 7 1 . 7 0 . 9B I A S - 0.6 - 0 . 5 0 . 9R M S 1.8 3 . 9 1.0

P R E S S U R E ( P S I A )X ( A ) P E X P R K - E O D E V R N - E O D E V K R E G K D E V0.0 4 6 5 . 1 * 6 5 . 1 0.0 4 6 5 . 1 0.0 4 6 5 . 1 0.00 . 10 5 0 2 . 8 5 0 0 . 4 2 . 4 4 9 9 . 9 2 . 9 4 9 8 . 9 3 . 90.20 5 3 9 . 1 5 3 5 . 3 3 . 8 5 3 4 . 7 4 . 4 5 3 1 . 8 7 . 30 . 3 0 5 7 1 . 9 5 6 8 .5 3 . 4 5 6 8 . 3 3 . 6 5 6 2 • 6 9 . 30 . 4 0 6 0 0 . 6 5 5 8 . 5 2.1 5 9 8 . 6 2.0 5 9 0 . 2 1 0 . 40 . 5 0 6 2 2 . 6 6 2 2 .9 - 0 . 3 6 2 3 . 4 - 0.8 6 1 2 . 9 9 . 70 . 6 0 6 3 7 . 9 6 3 9 . 0 - 1.1 6 3 9 . 7 - 1.8 6 2 9 . 2 8 . 70 . 7 0 6 4 4 • 4 6 4 4 . 0 0 . 4 6 4 4 . 6 - 0.2 6 3 7 . 2 7 . 20 . 8 0 6 4 1 , 4 6 3 6 . 6 4 • P 6 3 6 . 8 4 . 6 6 3 5 . 1 6 . 30 . 9 0 6 2 7 . 7 6 1 8 . 2 9 . 5 6 1 8 . 2 9 . 5 6 2 1 . 1 6.61 .00 5 9 4 . 2 5 9 4 . 2 0.0 5 9 4 . 2 0.0 5 9 4 . 2 0.0

A V G . A B S 3 . 1 3 . 3 7 . 7B I A S 2.8 2 . 7 7 . 7R M S 4 . 1 4. 2 7 . 9

J. .1. il* ' ■V ^ *1* V ■ ■‘i- 'i* *r -i* »i* "I* 5,* ; •r v *r V V V V.1. j. .i. .t1. ..p. ■» . .'(1 .1. . V s' i" 'i' 'r

. 1,1,1 s'#. *,» rfp. «■,. «r* i*. .*■ %*>•C -i* 't* *|* »)• v *|

RK-FO = REDL ICH-KWONG EOUAT I ON DF STATERN-EO = REDLICH-NGO EOUATION DF STATEKREGK = KREGLEWSKI-KAY METHOD

T A B L E 3 6 ' 2 2 9C O M P A R IS Of'1 O F T H E E X P E R I H E M T A L A N D C A L C U L A T E D C R I T I C A L P R O P E R T I E S U S I N G T H E P R E D I C T E D I N T E R

A C T I D N P A R A M E T E R S S Y S T E M N U M B E R 1 7

N - H E X A N E N - D E C A N E t B) S . C . P A K ‘R E D . I N T . P A R . R - K A 1 2 S R = 0 . 8 4 5 4 0 7 2 5 R 1 2 S R = 0 . 9 1 3 0 3 3 1 5R E D . I N T . P A R . R - N A 1 2 S R * 0 . 8 3 7 5 1 3 0 3 R 1 2 S R = 0 . 8 4 0 3 9 0 4 4

T E M P E R A T U R E ( C )X { A ) T E X P R K - E O D E V R N - E O D E V K R E G K D E V0.0 3 4 3 . 6 3 4 3 . 6 0.0 3 4 3 . 6 0.0 3 4 3 .6 0.00 . 10 3 3 6 . 4 3 3 7 . 7 - 1 . 3 3 3 7 . 7 - 1 . 3 3 3 6 . 4 0.00.20 3 2 8 . 9 3 3 1 .0 - 2 . I 3 3 0 . 9 - 2.0 3 2 8 . 6 0 . 30 . 3 0 3 2 1 . 2 3 2 3 . 2 - 2.0 3 2 3 . 2 - 2.0 3 2 0 . 3 0 . 90 . 4 0 3 1 2 . 3 3 1 4 . 2 -3. . 9 3 1 4 . 4 - 2.1 3 1 1 . 2 1 . 10 . 5 0 3 0 3 . 1 3 0 3 . 9 - 0.8 3 0 4 . 3 - 1.2 3 0 1 . 2 1 . 90 . 6 0 2 9 2 . 3 2 5 2.2 0 . 1 2 9 2 . 9 - 0.6 2 9 0 . 2 2 .10 . 7 0 2 8 0 . 1 2 7 9 . 1 1.0 2 7 9 . 9 0.2 2 7 8 . 2 1 . 90 . 8 0 2 66 . 4 2 6 4 . 7 1 . 7 2 6 5 . 6 0.8 2 6 4 . 8 1.60 . 9 0 2 5 1 . 2 2 4 9 . 4 1.8 2 5 0 . 1 1 . 1. 2 5 0 . 2 1 .01 .00 2 3 4 . 1 2 3 4 . 1 0.0 2 3 4 . 1 0.0 2 3 4 . 1 0.0

A V G . A P S 1 . 4 1 . 3 1.2B I A S - 0 . 4 - 0.8 1.2R M S 1 . 5 1 . 4 1 . 4

P R E S S U R E ( P S I A )X ( A ) P E X P R K - E O D E V R N - E O D E V K R E G K D E V0.0 3 1 0 . 1 3 1 0 . 1 0.0 3 1 0 . 1 0.0 3 1 0 . 1 0.00 . 10 3 3 4 . 5 3 3 4 . 2 0 . 3 3 3 3 . 8 0 . 7 3 3 5 . 3 - 0.80.20 3 5 8 . 6 3 5 8 . 5 C . 1 3 5 7 . 9 0 . 7 3 6 0 . 3 - 1 . 70 . 3 0 3 8 2 . 2 3 8 2 . 4 - 0 . 2 3 8 1 . 9 0 . 3 3 8 4 . 4 - 2.20 . 4 0 4 0 5 . 8 4 0 4 . 9 0 . 9 4 0 4 . 7 1.1 4 0 6 . 8 -1 .00 . 5 0 4 2 7 . 0 4 2 4 . o 2 . 1 4 2 5 . 0 2.0 4 2 6 . 6 0 . 40 . 6 0 A. A A , 0 4 4 0 . 7 4 . 2 4 4 1 . 4 3 . 5 4 4 2 . 6 2 . 30 . 7 0 4 5 7 . 2 4 5 0 . 6 6.6 4 5 2 . 0 5 . 2 4 5 3 . 4 3 . 80 . 8 0 4 6 2 . 6 ' ■ 5 3 . 6 9 . 0 4 5 5 .6 7 . 0 4 5 7 . 8 4 . 80 . 9 0 4 5 8 . 9 4 4 9 .8 9 . 1 4 5 1 . 7 7 . 2 4 5 4 . 3 4 . 61 .00 4 4 1 .8 4 4 1 . 8 0. 0 4 4 1 . 8 0.0 4 4 1 . 8 0.0

A V G . A P S 3 . 6 3. 1 2 . 4~ " B I A S 3 . 6 3 . 1 1.1

R M S 5 . 1 4 . 0 2 . 9RK-EP = REDLICH-KWOMG EPUATTON OF STATFRN-EO = REDLICH-NGn EOUATION OF STATEKREGK = KREGLEWSKI-KAY METHOD

230T A B L E 3 6 ( C O N T ' D )

S Y S T E M N U M B E R IBN - H E X A N E ( A ) N - T R I D E C A N E ( B ) S . C . P A K . . . . . .R E D . I N T . P A R . R - K A 1 2 S R = 0 . 7 1 5 6 2 2 R 4 B 1 2 S R = 0 . 8 6 2 1 9 2 4 5R E D . I N T . P A R . R - N A 1 2 S R = 0 . 6 8 1 0 4 5 5 3 B 1 2 S R = 0 . 7 0 4 6 0 2 3 0

T E M P E R A T U R E t C )1 L: 1-1 H r K A 1 U K h ( L )X( A ) T E X P R K - E O D E V R N - E O D E V K R E G K D E V0.0 4 0 1 .7 4 0 1 .7 0.0 4 0 1 . 7 0.0 4 0 1 . 7 0.00.10 3 9 3 . 0 3 9 5 .2 - 2.2 3 9 4 . 5 - 1 . 5 3 9 2 . 8 0.20.20 3 8 4 . 0 3 8 7 . 4 - 3 .4 3 8 6 . 2 - 2.2 3 8 3 . 3 0 . 70 . 3 0 3 7 4 . 1 3 7 7 .9 - 3 . 8 3 7 6 . 4 - 2 . 3 3 7 2 . 7 1 . 40 . 4 0 3 6 3 .8 3 6 6 . 3 - 2 . 5 3 6 4 . 8 - 1.0 3 6 0 . 8 3 . 00 . 5 0 3 5 1 . 1 3 5 1 . 9 - O . R 3 5 0 . 6 0 . 5 3 4 7 . 1 4 . 00 . 6 0 3 3 6 .1 3 3 4 . 3 1 . 8 3 3 3 . 2 2 . 9 3 3 1 . 1 5 . 00 . 7 0 3 1 8 . 3 3 1 2 . 8 5 . 5 3 1 2 . 1 6.2 3 1 2 . 3 6.00 . 8 0 2 9 6 . 8 2 8 7 . 5 9 . 3 2 8 7 . 3 9 . 5 2 9 0 . 1 6 . 70 . 9 0 2 6 9 . 0 2 6 0 . 1 8 . 9 2 6 4 . 0 5 . 0].. 00 2 3 4 . 1 2 7 4 . 1 0.0 2 3 4 . 1 0.0 2 3 4 . 1 0.0

A V G . A O S 4 . 2 3 . 3 3 . 6B I A S 1 . 4 1 . 5 3 . 6R M S 5 . 1 4 . 3 4 . 2

P R E S S U R E ( P S I A )X ( A ) P E X P R K - E O D E V R N - E O D E V K R E G K D E V0.0 2 5 0 .2 2 5 0 . 2 0.0 2 5 0 . 2 0.0 2 5 0 . 2 0.00.10 2 88 .7 2 8 2 .6 6.1 2 8 2 . 2 6 . 5 2 8 6 . 8 1 . 90.20 3 2 8 .1 3 1 7 . 7 1 0 . 4 3 1 7 . 7 1 0 . 4 3 2 6 . 4 1 . 70 . 3 0 3 6 7 .0 3 5 5 . 1 1 1 . 9 3 5 6 . 2 10.8 3 6 7 . 9 - 0 . 90 . 4 0 4 0 4 . 9 3 5 3 .8 11.1 3 9 6 . 4 8 . 5 4 0 9 . 6 - 4 . 70 . 5 0 4 4 1 . 1 4 3 1 .5 9 . 6 4 3 5 . 7 5 . 4 4 4 9 . 0 - 7 . 90 . 6 0 4 7 5 .4 4 6 4 . 2 11.2 4 6 9 . 4 6.0 4 8 2 . 1 - 6 . 70 . 7 0 4 9 9 . 5 4 8 5 .2 1 4 . 3 4 9 0 . 4 9 . 1 5 0 3 . 8 - 4 . 30 . 8 0 5 1 0 . 0 4 86 .6 2 3 . 4 4 9 1 . 0 1 9 . 0 5 0 7 . 9 2.10 . 9 0 4 9 9 . 2 4 6 7 . 0 3 2 . 2 4 8 8 . 4 10.81.00 4 4 1 . 8 4 4 1 . 8 0.0 4 4 1 . 8 0.0 4 4 1 .8 0.0

A V G . A P S 1 4 . 5 9 . 5 4 . 6R I A S 1 4 . 5 9 . 5 - 0 . 9R M S 1 6 . 4 1 0 . 3 5 . 5

bl* .1. b1. .L b*» b*« b*. b*. b*. b*» b*> b*. b*. b*> bt. ,1, b1. b*. bt. b1. b*. bl. b*. .1. at. *•. bl. b1. b1. a1, b*. bl. b<4 b*. «♦* bl. b<. bb*. b*. b*. b*. b*< b1. bl« b*. b*. b1. b*. b*# >*< b1* »*< b1. bl. b*. J.«|b .|b .|b .|b *,b *,» «,b »,b »(b #p. (b *|b <!> .|b «b *■)» r(» i(b <k« «(b .b *(b , «(b .,b |> »,» .(b «,» .p» .,b «,* *|b a( b *+b », i •»,» »*b .,b •*,. *,b .jb »j» »(» »j» »|» .|b

RK-EO = REDL ICH-KWONG EOUATIDN OF STATFRN-EO = REDLICH-NGO EOUATIDM DF STATEKREGK = KREGLEWSKI-KAY METHOD


S Y S T E M N U M B E R 1 9N - H F X A N F ( A ) - - - N - T E T R A D E C A N E ( B ) S . C . P A KR E D . I N T . P A R . R - K A 1 2 S R - 0 . 6 7 7 7 4 4 1 5 B 1 2 S R = 0 . 8 2 7 0 5 1 1 6R E D . I N T . P A R . R - N A 1 2 S R = 0 . 6 3 1 4 9 6 1 3 B 1 2 S R = 0 . 6 4 0 2 2 3 0 9

T E M P E R A T U R E t C)X (A ) T E X P R K - E O D E V R N - E O D E V K R E G K D E V0.0 4 2 3 . 7 4 2 3 . 7 0.0 4 2 3 . 7 0.0 4 2 3 . 7 0.00 . i n 4 1 6 . 0 4 1 R . 6 - 2.6 4 1 6 . 9 - 0 . 9 4 1 4 . 3 1 . 70.20 4 0 7 . 6 4 0 9 . 2 - 1.6 4 0 4 . 2 3 . 40 . 3 0 3 9 7 . 1 4 0 4 . 4 - 7 . 3 4 0 0 . 1 - 3 . 0 3 9 3 . 1 4 . 00 . 4 0 3 8 4 . 7 ? S 4 . 2 - 9 . 5 3 8 9 . 1 - 4 . 4 3 8 0 . 4 4 . 30 . 5 0 3 7 0 . 0 3 8 1 . 1 - 11.1 3 7 5 . 4 - 5 . 4 3 6 5 . 5 4 . 50 . 6 0 3 5 3 .3 3 6 3 . 9 - 10.6 3 5 7 . 7 - 4 . 4 3 4 7 . 9 5 . 40 . 7 0 3 3 2 . 8 3 4 1 . 2 - 8 . 4 3 3 4 . 7 - 1 . 9 3 2 6 . 5 6 . 30 . 8 0 3 0 7 . 6 3 1 1 . 5 - 3 . 9 3 0 5 . 3 2 . 3 3 0 0 . 8 6.80 . 9 0 2 7 5 .0 2 7 4 . 9 0 . 1 2 7 0 . 3 4 . 7 2 6 9 . 9 5 . 11 .00 2 3 4 . 1 2 2 4. 1 0.0 2 3 4 . 1 c.c 2 3 4 . 1 0.0

A V G . A B S 6 . 7 3 . 2 4 . 6B I A S - 6 . 7 - 1.6 4 . 6R M S 7 . 7 3 . 5 4 . 8

P R E S S U R E ( P S I A )X ( A ) P E X P R K - E O D E V R N - E O D E V K R E G K D E V0.0 2 0 8 . 5 2 0 8 . 5 0.0 2 0 8 . 5 0.0 2 0 8 . 5 0.00 . 10 2 5 4 . 9 2 3 9 . 7 1 5 . 2 2 3 9 . 9 1 5 . 0 2 4 7 . 4 7 . 50.20 3 0 1 . 2 2 7 6 . 3 2 4 . 9 2 9 1 .1 10.10 . 3 0 3 4 7 . 5 3 1 4 . 3 3 3 . 2 3 1 7 . 9 2 9 . 6 3 3 8 . 9 8.60 . 4 0 3 9 3 . 8 3 5 8 . 0 3 5 . 8 3 6 4 . 5 2 9 . 3 3 8 9 . 2 4 . 60 . 5 0 4 3 8 . 2 4 0 5 . 2 3 3 . 0 4 1 4 . 4 2 3 . 8 4 3 8 . 8 - 0.60 . 6 0 4 7 9 . 9 4 5 2 . 9 2 7 . 0 4 6 3 . 3 1 6 . 6 4 8 2 . 9 - 3 . 00 . 7 0 5 1 4 . 0 4 9 4 . 3 1 9 . 7 5 0 2 . 1 1 1 . 9 5 1 4 . 0 - 0.0O . F O 5 3 2 .0 5 1 5 . 2 1 6 . P 5 1 4 . 9 1 7 . 1 5 2 3 . 1 8 . 90 . 9 0 5 1 7 . 5 ^ 9 7 . 2 2 0 . 3 4 8 9 . 5 2 8 . 0 5 0 0 . 8 1 6 . 71 .00 4 4 1 . 8 ^ 4 1 . 8 0.0 4 4 1 . 8 0.0 4 4 1 . 8 0.0

A V G . A P S 2 5 . 1 2 1 . R 6 . 7B I A S 2 5 . 1 21.8 5 . 9R M S 2 6 . 3 2 2 . 7 8 . 3

?,« fp fp .|* V|. »|* .p. .p. »,« »,» .|. ... ... «p fi|> »,■. *(<» .,s r,« (,« rp »|. ... C,* »|.

RK-EO = REDL ICH-Kl'DMG EOUAT ION OF STATERN-EO = REDL ICH-NGD EOIJAT ION OF STATEKREGK = KREGLEWSKI-KAY METHOD


S Y S T E M N U M B E R 2 0N - H E X A N « = ( A > -C I S - D E C A L I M ( B) S . C . P A KR E D . I N T . P A R . R - K A 1 2 S R = 0 . 8 7 6 4 8 4 5 1 R 3 . 2 S R ~ 0 . 9 6 2 5 5 8 1 5R E D . I N T . P A R . R - N A 1 2 S R = 0 . 8 1 2 9 7 6 1 8 R 1 2 S R = 0 . 8 8 9 2 9 7 3 1

T E M P E R A T U R E tZ)X I A ) T E X P R K - E O D E V R N - E O D E V K R E G K D E V0.0 4 3 1 . 8 4 3 1 . 8 0.0 4 3 1 . 8 0 . 0 4 3 1 . 8 0.00.10 4 1 8 . 5 4 1 8 . 9 - 0. 4 4 1 9 . 8 - 1 . 3 4 1 7 . 1 1 . 40.20 4 0 3 .6 4 0 4 . 6 -I . 0 4 0 6 . 1 - 2 . 5 4 0 1 .3 2 . 30 . 3 0 3 8 7 . 3 3 8 8.8 - 1 . 5 3 9 0 . 6 - 3 . 3 3 8 4 . 5 2.80 . 4 0 3 6 S’. 5 3 7 1 . 4 - 1 . 9 3 7 3 . 0 - 3 . 5 3 6 6 . 5 3 . 00 . 5 0 3 5 0 . 0 3 5 2 . 1 - 2 . 1 3 5 3 . 3 - 3 . 3 3 4 7 . 4 2.60 . 6 0 3 2 8 . 7 3 3 1 . 2 - 2 . 5 2 3 1 . 4 - 2 . 7 3 2 7 . 0 1 . 70 . 7 0 3 0 6 . 1 3 0 8 . 6 - 2 . 5 3 0 7 . 7 - 1.6 3 0 5 . 4 0 . 70 . 8 0 2 8 3 . 0 2 ( 4 . 6 - 1.6 2 r 2 . r, 0 . 2 2 8 2 . 7 0 . 30 . 9 0 2 5 8 . 8 2 5 9 . 6 - 0 . 8 2 5 7 . 0 1 . 0 2 5 8.8 - 0.01.00 2 3 4 . 1 2 3 4 . 1 0.0 2 3 4 . 1 0.0 2 3 4 . 1 0.0

A V O . A E S 1 • 6 2. 1 1 . 7B I A S - 1.6 - 1 . 9 1.6R M S ! . 7 2 . 4 2.0

P R E S S U R E ( P S I A )X( A) P E X P R K - E O D E V R N - E O D E V K R E G K D E V0.0 4 6 5 .1 4 6 5 . 1 0 . 0 4 6 5 . 1 0 . 0 4 6 5 . 1 0.00.10 5 0 1 .8 4 9 1 .6 1 0 . 2 4 9 4 . 8 7 . 0 4 9 2 . 4 9 . 40.20 5 3 3 . 4 5 1 5 . 7 1 7 . 7 5 2 2 . 5 1 0 . 9 5 1 5 . 7 1 7 . 70 . 3 0 5 5 8 . 3 5 3 6 . 2 2 2.1 5 4 6 . 5 11.8 5 3 3 . 8 2 4 . 50 . 4 0 5 7 5 . 9 5 5 1 . 2 2 4 . 7 5 6 ' . 2 1 1 . 7 5 4 5 . 7 3 0 . 20 . 5 0 5 8 4 . 0 5 5 8 . 6 2 5 . 4 5 7 2 . 7 1 1 . 3 5 5 0 . 4 3 3 . 60 . 6 0 5 8 2 . 1 5 5 6 . 3 2 5 . F 5 6 8 . 9 1 3 . 2 5 4 6 . 9 3 5 . 20 . 7 0 5 6 9 . 8 5 4 2 .5 2 7 . 3 5 5 0 . 7 1 9 . 1 5 3 4 . 5 3 5 . 30 . 8 0 5 4 3 . 6 5 1 7 . 0 2 6 . 6 5 1 9 . 4 2 4 . 2 5 1 2 . 0 3 0 . 80 . 9 0 4 9 8 . * - 4 8 2 . 0 1 6 . 4 4 8 0 . 4 1 8 . 0 4 8 1 . 7 1 6 . 71.00 4 4 1 .8 4 4 1 . P 0.0 4 4 1 . 8 0.0 4 4 1 .8 0.0

A V G . A B S 21.8 1 4 . 2 2 6 . 0B I A S 21.8 1 4 . 2 2 6 . 0R M S 2 2 . 5 1 5 . 0 2 7 . 4

V •r* n* 'i' “iR K - E O = R E D L I C H - K V O N G E O U A T I O N

*,* .|* 'i* •*»' 4O F 5 T A T p

•»). .|. *y* »,•» «i» *4* »,• *,• f,

R N - F . O = R E D L J C H - M G O E O U A T I O N D F S T A T EK R E G K = K R E G L E W S K I - K A Y M E T H O D

233T A B L E 3 6 ( C O N T ' D )

S Y S T E M N U M B E R 2 1 N - N O N A N E ( A ) - - - " M - T R I D E C A N E ( B ) S . C . P A KR E D . I N T . P A R . R - K A 1 2 S R = 0 . 9 0 1 0 8 6 5 7 B 1 2 S R = 0 . 9 3 1 7 2 7 3 !R E D . I N T . P A R . R - N A 1 2 S R = 0 . 8 9 6 9 0 3 6 2 B 1 2 S R = 0 . 8 9 3 2 9 6 2 ;

T E M P E R A T U R E t C )X ( A ) T E X P R K - E O D E V R N - E O D E V K R E G K D E V0.0 6 0 1 . 7 6 0 1 . 7 0.0 6 0 1 . 7 0.0 6 0 1 . 7 0.00.10 3 9 6 . 6 3 9 6 . P. - 0.6 3 9 5 . 7 0 . 70.20 3 9 1 . 5 ?C1 .2 0 . 3 3 8 9 . 6 2.10 . 3 0 3 0 5 . 6 3 3 6 . 9 0. 7 3 8 2 . 6 3 . 00 . 6 0 3 7 9 . 0 3 7 7 . 9 1 . 1 3 7 5 . 5 3 . 50 . 5 0 3 7 1 . 5 3 7 0. 1 1.6 3 7 0 . 3 1.2 3 6 7 . 9 3 . 60 . 6 0 3 6 3 . 2 3 6 1 .6 1.8 3 6 1 . 7 1 . 5 3 5 9 . 7 3 . 50 . 7 0 3 5 3 . 6 3 5 2 . 0 1.6 3 5 2 . 6 1.2 3 5 0 . 9 2 . 70 . G O 3 6 3 .6 ? M . 9 1 . 5 3 6 1 . 5 1 . 90 . 9 0 3 3 2 . 3 3 3 1 . 6 0 . 9 3 3 1 . 6 0 . 91.00 3 2 0 . 6 3 2 0.6 0.0 3 2 0 . 6 0.0 3 2 0 . 6 0.0

A V G . A R S I . I 1 . 3 2.6B I A S 1.0 1 . 3 2.6

. . . .R M S 3 . 2 1 . 3 2 . 7

t P R E S S U R E ( P S I A )X( A ) P E X P R K - E O D E V R N - E O D E V K R E G K D E V0.0 2 5 0 . 2 2 5 0 . 2 0.0 2 5 0 . 2 0.0 2 5 0 . 2 0.00 . 10 2 6 6 . 3 2 6 3 .7 0.6 2 6 3 . 3 1 .00.20 2 7 0 . 1 2 7 7 . 0 1 . 1 2 7 6 . 2 1 . 90 . 3 0 2 9 1 . 0 2 3 9 . 7 2.1 2 8 8 . 6 3 . 20 . 6 0 3 0 6 . 9 3 01.6 3 . 5 3 0 0 . 1 6.80 . 5 0 3 1 6 . 6 3 1 1 . 9 6 . 7 3 1 2 . 1 6 . 5 3 1 0 . 6 6.00 . 6 0 3 2 6 . 2 3 2 0 . 5 5 . 7 3 2 0 . 9 5 . 3 3 1 9 . 6 6.60 . 7 0 3 3 3 . 0 3 2 6 . 9 6.1 3 2 7 . 6 5 . 6 3 2 6 . 7 6 . 30 . 8 0 3 3 7 . 0 3 3 1 . 0 6.0 3 3 1 . 6 5 . 60 . 9 0 3 3 6 . 9 3 3 2 . 8 6 . 1 3 3 3 . 7 3 . 21.00 3 3 2 . 7 3 3 2 . 7 0.0 3 3 2 . 7 0.0 3 3 2 . 7 0 .0

A V G . A B S 3 . P 5 . 1 6 . 3B I A S 3 . 8 5 . 1 6 . 3R M S 6 . 3 5 .1 6 . 7

kl# .1. .1* .1. .V. .t* s*# sj: .U .6 : * V V *»' *1* 'I'# »•* O. .1. *♦* .1. «*. »•» v. #1% .|» #j • |* «|

RK-EO = REDL ICH-K.NONG EOUAT IDM DF STATERN-EO = REDLICH-MGO FOUATION OF STATEKREGK = KREGLEWSKI-KAY METHOD

TABLE 36 (CDNT1D J

SYSTEM NUMBER 22

N-DECANE(A ) — — N-DC1DECANE ( 8 ) S.C. PAK

R E D , I N T . P A R . R - K A 1 2 S R = 0 . 9 7 0 0 9 0 0 2 B 1 2 S R = 0 . 9 7 5 8 4 0 8 7R E D . I N T . P A R . R - N A 1 2 S R = 0 . 9 6 7 3 1 6 5 1 B 1 2S R = 0 . 9 5 4 7 7 5 1 5

T E M P E R A T U R E (C )X ( A ) T E X P R K - E P D F V R N - E O D E V K R E G K D E V0.0 3 8 5 .8 3 f 5 . 8 0.0 3 8 5 . 8 0.00 . 10 3 8 2 . 1 3 8 2 .6 - 0 . 5 3 8 2 . 2 - 0.10 . 2 0 3 7 R . 3 3 7 9 . 2 - 0 . 9 3 7 8 . 4 -0 . 10 . 3 0 3 7 4 . 3 3 7 5 .5 - 1.2 3 7 6 . 6 - 0 . 3c■'d"•c 3 7 0 . 4 3 7 1 . 6 - 1.2 3 7 0 . 6 - 0.20 . 5 0 3 6 6 . 4 3 6 7 . 5 - 1.1 3 6 6 . 4 - 0.00 . 6 0 3 6 2 .3 3 6 3 . 2 -0 . 9 3 6 2 . 2 0.10 . 7 0 3 5 8 . 1 3 5 0 . 6 - 0 . 5 3 5 7 . 8 0 . 3o. p . n 3 5 3 .6 3 5 3 . 8 - 0.2 3 5 3 . 2 0 . 40 . 9 0 3 4 8 . 7 3 4 0 . 8 - 0 . 1 3 4 8 . 5 0.21.00 3 4 3 .6 ? A 3 . 6 0.0 3 4 3 . 6 0.0

A V G . A R S 0 . 7 0.2B I A S - 0 . 7 0.0

— .. . . . R M S 0.0 0.2P R E S S U R E ( P S I A )

X ( A ) P E X P R K - E O D E V R N - E O D E V K R E G K D E V0.0 2 6 9 . 8 2 6 9 . 8 0.0 2 6 9 . 8 0.00.10 2 7 6 . 2 2 7 5 .0 0 . 4 2 7 5 . 4 0.80.20 2 8 1 . 9 2 8 1 . 6 0 . 3 2 8 0 . 8 1 . 10 . 3 0 2 8 6 . 9 2 0 7 . 0 - 0 . 1 2 8 5 . 9 1.00 . 6 0 2 9 1 . 6 2 9 2 . 0 - 0 . 4 2 9 0 . 7 0 . 90 . 5 0 2 9 5 . 7 2 9 6 . 5 - 0.0 2 9 5 . 2 0 . 50 . 6 0 2 9 9 . 5 3 0 0 . 5 - 1.0 2 9 9 . 3 0.20 . 7 0 3 0 2 . 8 3 0 3 . 9 - 1.1 3 0 3 . 0 - 0.20 . 8 0 3 0 5 . 7 3 0 6 . 7 - 1.0 3 0 6 . 1 - 0 . 40 . 9 0 3 0 8 . 3 3 0 0 . 9 - 0.6 3 0 8 . 6 - 0 . 31 .00 3 1 0 . 5 3 1 0 . 5 0.0 3 1 0 . 5 0.0

A V G . A P S 0.6 0.6B I A S - 0 . 5 0 . 4R M S 0 . 7 0 . 7.1. «A> »i. «i. .i. ,V|, rg, ^ |S ■ »•» »•. »•* .ip i 4* ,,v ,k‘. .'j *1. .1. vV »*«■ .1# ,1. *1. t*f ,1.«,« t-|, .4, n* *1' *1* n* *1" V r **» .4. .4# .4. .4. .1. k4p ,1. ,1. ,1. .4.1 ,|, .j. r(k «|« .j. .j. |, #|k .

R K - F P = REDI. I C H - K l ' O N G F O U A T I O M O F S T A T F R N - F O = R E D L I O H - N G O E Q U A T I O N O F S T A T E K R E G K = K R E G L F W S K I - K A Y M E T H O D

235TABLE 36 (COMT'D) SYSTEM NUMBER 28

BENZENE(A ) N-DECANE(B) S.C PAKRED. INT. PAR . R-K A12SR = 0.84309691 R12SR = 0.191031 39(RED. INT. PAR . R-N A 12 SR = 0.86074895 B1 2SR - 0. 85871 88:

TEMPERATURE(C)X (A ) TEXP RK-EP DEV RN-EO DEV KREGK DEV0.0 343 .6 ?'3.6 0.0 343.6 0.0 343.6 0.00.10 341 . 2 3 41 . 0 0.2 339. 1 2.10.20 33 7. n 32 8.0 -0.2 336.5 1.3 334.6 3.20.30 333.6 3 34.4 -0. R 332.6 1.0 330.2 3.40.40 328.9 330.2 -1.3 3 28. 3 0.6 325.6 3.30.50 323.6 325.3 -1.7 323.6 0.0 320.7 2.90.60 317. 9 3 3 9.5 -1.6 318.3 -0.4 315.5 2.40.70 311.7 312.7 -1.0 312.2 -0.5 309. 6 2.10.80 304 . 8 305. 0 -0.2 305 .3 -0. 5 303.1 1 .70.90 2 96.9 2 96.6 0.3 2 97. 3 -0.4 295.8 1.11.00 288 . 1 2 F fi. 1 0.0 288 . 1 0.0 2 88.1 0.0

AVG. AF S 0.8 0.6 2.5R IAS -0.7 0.2 2.5

... . RMS -------- - 1 . 0 0.7 2.6PRESSURE{PS I A)

X (A ) PEXP RK-EP DEV RN-EO DEV KREGK DEV0.0 310.2 3 3 0.2 0. 0 310.2 0.0 310.2 0.00.10 341.9 340.5 1.4 349. 3 -7.40.20 3 75.2 3 7 3.5 1.7 371.9 3.3 392.2 -17.00.30 411. 4 409.2 2. 2 407.4 4.0 438.5 -27.10.4 0 44 9. 6 447 . 7 1.9 446. 1 3.5 487.3 -37.70.50 4 8 9.3 *•38.7 1.1 4 87 .3 2.0 537.3 -47.50.60 532.3 532.0 0.3 532. 1 0.2 586.4 -54.10.70 577. 0 576.8 0. 2 57 8. 4 -1.4 631.8 -54.80.80 621 .7 622.0 -0.3 625.1 -3.4 670.0 -48.30.90 666.7 6 66.8 -0. 1 670. 5 -3.8 69 7.4 -30.71.00 712.1 7 3 2.1 0.0 712. 1 0.0 712.1 0.0

AVG. APS 1.0 2.7 36.1BIAS 0.9 0.6 -36.1RMS 1.3 3.0 39.4

1*; 5 V »'« **• ■ ** V1. «l* »•* «*. l'» »•* V1* .Vi •’» »<i .'i 4<i k1. .1. s'. .v. .■« «>i s'*. Oi «l« .*( .*» *•» »'i k'i »*. »*« .*« «*i .*» «*( %•« »*. .1. .1# tlj s*. S*. S*. >*f «*. k*i#|S «|« »,• pi,* pi,* «tf* Pf. *1' »|* *|» *■<’ v ■*«“ ■*!' '1’ V *|‘ *>» *1* '1' '|» *>* ■**» »,» *,» 'I* ‘I* p|* p(p P|* r,p »,* ■>,. 1,1 »,» Pî »,• *,1 fp *,p P|1 »,» f|. «|» ppfs *|* *,* i|i »,*

RK-EP a REQL ICH-KUPIMG E P t J A T I D M HE STATERN-EO = REDLICH-NGO EQUATION OF STATEKREGK = KREGLEV/SK I—KAY METHOD


S Y S T E M N U M B E R 2 9B E N Z E N E ( A ) N - T R I D E C A N E ( R ) S . C . P A K "R E D . I N T . P A R . R - K A 1 2 S R = 0 . 6 9 0 9 9 4 3 8 B 1 2 S R = 0 . 8 1 7 4 8 1 4 6R E D . I N T . P A R . R - N A 1 2 S R = 0 . 7 1 5 1 6 9 1 9 R 1 2 S R = 0 . 7 0 9 3 8 0 5 1

T E M P E R A T U R E ( C )X ( A ) T E X P I m o D E V R N - E O D E V K R E G K D E V0.0 4 0 1 . 7 4 0 1 . 7 0.0 4 0 1 . 7 0.0 4 0 1 . 7 0.00 . 10 3 9 7 . 8 3 9 8 . 7 - 0 . 9 3 9 4 . 9 2 . 90.20 3 9 3 . 0 3 9 4 . 9 - 1 . 9 3 9 1 . 8 1.2 3 8 8 . 3 4 . 70 . 3 0 3 8 7 . 3 3 9 0 . 0 - 2 . 7 3 8 6 . 0 1 . 3 3 8 1 . 6 5 . 70 . 4 0 3 8 0 . 3 3 f 3 . 6 - 3 . 3 3 7 9 . 4 0 . 9 3 7 4 . 6 5 . 70 . 5 0 3 7 1 . 7 3 7 5 . 1 - 3 . 4 3 7 1 . 5 0.2 3 66 . 7 5 . 00 . 6 0 3 6 1 . 5 3 6 4 . 1 - 2.6 3 6 1 . 6 - 0 . 1 3 5 7 . 2 4 . 30 . 7 0 3 4 8 . 7 3 4 9 . 7 - 1.0 3 4 9 . 1 - 0 . 4 3 4 5 . 4 3 . 3O . P O 3 3 2 . 7 3 ? 1 . 3 1 . 4 2 3 2 . 9 - 0.2 3 3 0 . 3 2 . 40 . 9 0 3 1 3 . 0 3 0 9 . 5 3 . 5 3 1 2 . 5 0 . 5 3 1 1 . 1 1 . 91 .00 2 8 8 . 1 2 8 8 . ]. 0 . 0 2 88.1 0.0 2 8 8 . 1 0.0

A V G . A P S 2 . 3 0.6 4 . 0B I A S - 1.2 0 . 4 4 . 0R M S 2 . 5 0 . 7 4 . 2

P R E S S U R E I P S I A )X (A I P E X P R K - E O D E V R N - E O D E V K R E G K D E V0.0 2 5 0 . 2 2 5 0 . 2 0.0 2 5 0 . 2 0.0 2 5 0 . 2 0.00 . 10 2 8 3 . 0 2 8 6 . 9 1. 1 2 9 6 . 7 - 8 . 70.20 3 2 9 . 9 ? 2 8 . 5 1 . 4 3 2 5 . 3 4. 6 3 5 1 . 6 - 2 1 . 70 . 3 0 3 7 6 . 3 3 7 5 . 6 0 . 7 3 7 1 . 7 4 . 6 4 1 5 . 1 - 3 8 . 80 . 4 0 4 2 5 . 8 * 2 8 . 4 - 2.6 4 2 4 . 6 1.2 4 8 6 . 8 - 6 1 .00 . 5 0 4 7 9 . 3 4 86.6 - 7 . 3 4 8 3 . 7 - 4 . 4 5 6 4 . 2 - 8 4 . 90 . 6 0 5 3 8 . 7 5 4 8 . 6 - 9 . 9 5 4 7 . 4 - 8 . 7 6 4 2 . 0 -• 1 0 3 . 30 . 7 0 6 1 2 . 2 6 0 9 . 7 2 . 5 6 1 1 . 8 0 . 4 7 1 0 . 6 - 9 8 . 40 . 8 0 6 7 4 . 9 6 6 1 . 3 1 3 . 6 66 8 . 4 6. 5 7 5 5 . 5 - 8 0 . 60 . 9 0 7 0 4 . 0 6 9 3 . 0 11.0 7 0 5 . 0 - 1.0 7 5 9 . 3 - 5 5 . 31.00 7 1 2 . 1 7 1 2 . 1 0.0 7 1 2 . 1 0.0 7 1 2 . 1 0.0

A V G . A R S 5 . 6 3 . 9 6 1 . 4B I A S 1.2 0 . 4 - 6 1 . 4R M S 7 . 3 A .8 6 9 . 0

.k# .v o.t rf* ri% * r ^ v.1. .f# «1. .1. *•• .L 4,1■•p »'» »*.r p .p #|l1 T 'h’ »i» *i* 'i;• .•» %*. . .p .p p|. ... .■ .k. .kj .1. .kf .4. .4r,. .i* ... .| .1. fc*. J. .1. .1. .1. .1. I« V '|' »|» '(• *1* 'I1* i

RK-EO = REDL ICH-KUONO EOIJ AT I DM OF STATERN-EO = REDLICH-NGO EQUATION OF STATEKREGK = KREGLEUSKI-KAY METHOD

237TABLE 36 (CDNT'D)

S Y S T E M N U M B E R 3 7 B E N Z E N E ( A ) - — C I S - D E C A L I M ( B ) S . C . P A KR E D . I N T . P A R . R - K A 1 2 S R = 0 . 8 5 0 0 4 5 6 8 R 1 2 S R = 0 . 9 3 9 8 3 8 4 7R E D . I N T . P A R . R - N A 1 2 S R = 0 . 8 2 2 0 6 6 7 8 B 1 2 S R = 0 . 8 6 4 8 1 6 3 1

T E M P E R A T U R E ( C)X ( A ) T E X P R K - E O D E V R N - E O D E V K R E G K D E V0.0 4 3 1 .8 4 3 1 .8 0.0 4 3 1 . 8 0.0 4 3 1 .8 0.00 . 10 4 2 2 . 6 4 2 4 .4 -l.fi 4 2 5 . 4 - 2.8 4 2 2 . 8 - 0.20.20 4 1 2 . 5 4 1 5 . 9 - 3 . 4 4 1 8 . 0 - 5 . 5 4 1 3 . 1 - 0.60 . 3 0 4 0 1 .6 4 0 6 .3 - 4 . 7 4 0 9. 2 - 7 . 6 4 0 2 . 5 - 0 . 90 . 4 0 3 9 0 .0 3 9 5 . 3 - 5 . 3 3 9 8 . 9 - 8 . 9 3 9 1 . 0 -1 .00 . 5 0 3 7 6 . 9 3 8 2 .6 - 5 . 7 3 0 6 . 7 - 9 . 8 3 7 8 . 1 - 1.20 . 6 0 3 6 2 . 4 3 6 8 . 1 - 5 . 7 3 7 2 . 3 - 9 . 9 3 6 3 . 7 - 1 . 30 . 7 0 3 4 6 . 3 3 5 1 . 4 - 5 . 1 3 5 5 . 3 - 9 . 0 3 4 7 . 5 - 1.2O . E O 3 2 8 . 4 3 3 2 . 5 - 4 . 1 3 3 5 .5 - 7 . 1 3 2 9 . 5 - 1.10 . 9 0 3 0 8 . 9 3 1 1 . 3 - 2 . 4 3 1 2 . 9 - 4 . 0 3 0 9 . 6 - 0 . 71 .00 2 8 8 . 1 2 8 8.1 0.0 2 8 8 . 1 0.0 2 8 8 . 1 0.0

A V G . A P S 4 . 2 7 . 2 0 . 9B I A S - 4 . 2 - 7 . 2 - 0 . 9R M S 4 • 4 7 . 6 1 .0

P R E S S U R E ( P S I A )X ( A ) P E X P R K - E O D E V R N - E P D E V K R E G K D E V0.0 4 6 5 .1 ^ 6 5 . 1 0.0 4 6 5 . 1 0.0 4 6 5 . 1 0.00 . 10 5 1 4 . 5 5 0 4 .3 10.2 5 0 5 . 5 9 . 0 5 ]. 1. 2 3 . 30.20 5 6 0 . 5 5 4 4 . 8 1 5 . 7 5 4 8 .0 1 2 . 5 5 5 8 . 8 1 . 70 . 3 0 6 0 4 . 2 5 8 6 . 0 1 8 . 2 5 9 1 . 9 1 2 . 3 6 0 6 • 6 - 2 . 40 . 4 0 6 4 4 . 5 6 2 6.6 17 .9 6 3 5 . 8 8 . 7 6 5 2 . 4 - 7 . 90 . 5 0 6 8 0 . 9 6 6 5 . 0 1 5 . 9 6 7 7 . 6 3 . 3 6 9 3 . 8 - 1 2 . 90 . 6 0 7 1 1 . 1 6 9 8 . 6 1 2 . 5 7 1 4 . 0 - 2 . 9 7 2 7 . 2 - 1 6 . 10 . 7 0 7 3 1 . 6 7 2 4 . 0 7 . 6 7 4 0 . 3 - 8 . 7 7 4 9 . 0 - 1 7 . 40 . 6 0 7 4 0 .1 7 3 6 . 8 3 . 3 7 5 0 . 9 - 10.8 7 5 5 . 3 - 1 5 . 20 . 9 0 7 3 4 . 3 7 3 3 .3 1.0 7 4 1 . 4 - 7 . 1 7 4 3 . 2 - 8 . 91.00 7 1 2 . 1 7 1 2 . 1 0.0 7 1 2 . 1 0.0 7 1 2 . 1 0.0

A V G . A P S 1 1 . 4 8 . 4 9 . 5B I A S 1 1 . 4 1.8 - 8 . 4

J. .'<■ t*. .*> R M S* .*» 12.8 9 . 0 11 .2*1* #1% . ,1 .a. /(l jfh .a. «|t .4f .|« .g. .|. *g« «|t f|l #|1 i|l »g*

R K - E P = R E D L I C H — K V J O N G E P U A T I 0 M O F S T A T E R N - E P = R E D L I C H - U G O E O U A T I D M O F S T A T E K R E G K = K R E G L E l ' S K I - K A Y M E T H O D


SYSTEM NUMBER 44

ETHYLRENZEME(A) • CI S - D E C AL I N ( B ) S . C . PAK

RED. I NT. PAR. R-K A12SR = 0 . 9 4 8 2 9 3 3 6 B12SR = 0 . 9 8 4 2 1 1 5 6RED. INT. PAR. R-N A12SR = 0 . 9 4 0 9 6 7 5 6 B12SR = 0 . 9 6 9 7 1 7 3 8

TFMPERATURE t C )

X ( A ) T E X P R K - E O D E V R N - E O D E V K R E G K D E V0.0 4 3 1 .8 4 3 1 .8 0.0 4 3 1 . 8 0.0 4 3 1 .8 0.00 . 10 4 2 3 . 9 ^ 2 4 . 5 - 0.6 4 2 5 . 1 - 1.2 4 2 4 . 0 - 0.10.20 4 1 5 . 9 i 1 6 . P - 0 . 9 4 1 8 . 0 - 2.1 4 1 5 . 9 - 0.00 . 3 0 4 0 7 . 6 4 0 8 . 7 - 1.1 4 1 0 . 4 - 2.8 4 0 7. 6 - 0.00 . 4 0 3 9 9 . 1 4 0 0 . 3 - 1.2 4 0 2. 2 - 3 . 1 3 9 9 . 0 0.10 . 5 0 3 9 0 . 2 3 9 1 . 4 - 1.2 3 9 3 . 6 - 3 . 4 3 9 0 . 2 0.00 . 6 0 3 8 1 . 0 3 8 2.2 - 1.2 3 8 4 . 4 - 3 . 4 3 8 1 . 1 -0 . 10 . 7 0 3 7 1 . 8 3 7 2 . 8 - 1.0 3 7 4 . 8 - 3 . 0 3 7 1 . 9 - 0 . i0 . 8 0 3 6 2 . 4 3 6 3 . 1 - 0 . 7 3 6 4 . 7 - 2 . 3 3 6 2 . 5 - 0.10 . 9 0 3 5 3 . 2 3 5 3 . 3 - 0 . 1 3 5 4 . 3 - 1.1 3 5 3 . 0 0.21.00 3 4 3 . 6 3 4 3 . 6 0.0 3 4 3 . 6 0.0 3 4 3 . 6 0.0

A V G . A P S 0 . 9 2 . 5 0.1B I A S - 0 . 9 - 2 . 5 - 0.0

. . _R M S 1.0 2.6 0.1

P R E S S U R E ( P S I A )X ( A ) P E X P R K - E O D E V R N - E O D E V K R E G K D E V0.0 4 6 5 . 1 4 6 5 . 1 0.0 4 6 5 . 1 0.0 4 6 5 . 1 0.00 . 10 4 8 9 . 5 4 7 8 . 3 11.2 4 7 8 . 8 1 0 . 7 4 7 9 . 8 9 . 70.20 5 0 7 . 2 4 9 0 . 5 1 6 . 7 4 9 1 . 6 1 5 . 6 4 9 3 . 0 1 4 . 20 . 3 0 5 1 9 . 3 5 0 1 .4 1 7 . 9 5 0 3 . 1 1 6 . 2 5 0 4 . 6 1 4 . 70 . 4 0 5 2 P. 6 5 1 0 . 7 1 7 . 9 5 1 3 . 2 1 5 . 4 5 1 4 . 3 1 4 . 30 . 5 0 5 3 5 . 2 5 1 8 . 3 1 6 . 9 5 2 1 . 4 1 3 . 8 5 2 2 . 1 1 3 . 10 . 6 0 5 3 9 . 7 5 2 4 . 0 15 .7 5 2 7 . 6 12. 1 5 2 7 . 6 12.10 . 7 0 5 4 1 . 4 5 2 7 . 9 1 3 . 5 5 3 1 . 5 9 . 9 5 3 1 . 0 1 0 . 40 . 8 0 5 3 9 . B 5 2 9 . 8 10.0 5 3 3 . 0 6.8 5 3 2 . 3 7 . 50 . 9 0 5 3 5 . 4 5 3 0 . 1 5 . 3 5 3 2 . 2 3 . 2 5 3 1 . 6 3 . 81 .00 5 2 9 . 2 5 2 9 . 2 0.0 5 2 9 . 2 0.0 5 2 9 . 2 0.0

A V G . A P S 1 3 . 9 1 1 . 5 11.1B I A S 1 3 . 9 1 1 . 5 11.1R M S 1 4 . 5 12.2 11.6

**»■' T 1 - I " V '■

R K - E O. .p . '( » - j . . p . . p . »,» 'p . rp i .p .

= R E D L I C H - K W D N G E O U A T I O N O F S T A T E.p . iy% .p* .p* •»,% f (* . . . ■>)

R N - E O = R E D L I C H - 1 1 G O E O U A T I O N O F S T A T EK R E G K = K R E G L F U S K I - K A Y M E T H O D


SYSTEM NUMBER 45

ORTHO-XYLENE(A) C I S-DFCALIN(B ) S.C. PAK

RED. INT. PAP.. R-K A12SR = 0 . 9 5 2 1 6 4 5 9 B12SR = 0 . 9 8 3 4 6 6 0 3RED. INT. PAR. R-N A12SR = 0 . 9 4 7 7 4 5 6 2 R3.2SR = 0 . 9 7 0 5 0 8 8 7

TEMPERATUREtC)

X C A ) TEXP RK-EO DEV RN-EO DEV KREGK DEV

0 . 0 4 3 1 . 8 4 3 1 . V 0 . 0 431 . 8 0 . 0 4 3 1 . 8 0 . 00 . 1 0 4 2 4 . J? 42 5 . 5 - 0 . 7 4 2 6 . 2 - 1 . 4 42 5 . 0 - 0 . 20 . 2 0 4 1 7 . 7 4 1 8 . P. - 1 . 1 4 2 0 . 2 - 2 . 5 4 1 8 . 0 - 0 . 30 . 3 0 4 1 0 . 4 4 1 1 . R - 1 . 4 4 1 3 . 7 - 3 . 3 4 1 0 . 7 - 0 . 30 . 4 0 4 0 3 . 0 4 0 4 . 5 - 1 . 5 4 0 6 . 8 - 3 . 8 4 0 3 . 3 - 0 . 30 . 5 0 3 9 5 . 5 3 9 6 . 9 - 1 . 4 3 9 9 . 5 - 4 . 0 3 9 5 . 7 - 0 . 20 . 6 0 3 8 7 . 8 38 9 . 0 - 1 . 2 3 9 1 . 6 - 3 . 8 3 8 8 . 0 - 0 . 20 . 7 0 3 8 0 . 1 3 8 1 . 0 - 0 . 9 3 R 3 . 3 - 3 . 2 3 8 0 . 1 0 . 0O.FO 3 7 2 . 2 372 . 7 - 0 . 5 2 7 4 . 6 - 2 . 4 3 7 2 . 1 0 . 10 . 9 0 3 64 . 2 3 6 4 . 4 - 0 . 2 3 6 5 . 6 - 1 . 4 3 6 4 . 1 0 . 11 . 0 0 3 5 6 . 2 3 5 6 . 2 0 . 0 3 5 6 . 2 0 . 0 3 5 6 . 2 0 . 0

AVG. A p S 1 . 0 2 . 9 0 . 2B I AS - 1 . 0 - 2 . 9 - 0 . 1RMS 1 . 1 3 . 0 0 . 2

PRESSURE < PS I A )

X { A ) PEXP RK-EO DEV T m DEV KREGK DEV

0 . 0 4 6 5 . 1 4 6 5 . 1 0 . 0 4 6 5 . 1 0 . 0 4 6 5 . 1 0 . 00 . 1 0 4 8 5 . 3 47 8 . 3 7 . 0 4 7 8 . 9 6 . 4 4 7 9 . 7 5 . 60 . 2 0 5 0 2 . 0 4 9 0 . 7 1 1 . 3 6 9 1 . 9 1 0 . 1 4 9 3 . 2 8 . 80 . 3 0 5 1 5 . 7 5 0 2 . 1 1 3 . 6 5 0 4 . 0 1 1 . 7 5 0 5 . 3 1 0 . 40 . 4 0 52 7 . 8 5 1 2 . 3 1 5 . 5 5 1 5 . 0 I 2 . 8 5 1 5 . 9 1 1 . 90 . 5 0 5 3 7 . 2 5 2 1 . 1 1 6 . 1 5 2 4 . 6 1 2 . 6 5 2 4 . 9 1 2 . 30 . 6 0 5 43 . 5 5 2 8 . 5 1 5 . 0 5 3 2 . 5 1 1 . 0 5 3 2 . 2 1 1 . 30 . 7 0 5 4 7 . 2 5 3 4 . 5 1 2 . 7 5 3 8 . 6 8c 6 5 3 7 . 7 9 . 50 . 8 0 5 4 8 . 6 53 9 . 0 9 . 6 5 4 2 . 6 6 . 0 5 4 1 . 4 7. 2.0 . 9 0 5 4 7 . 7 5 4 2 . 2 5 . 5 5 4 4 . 6 3 . 1 5 4 3 . 6 4 . 11 . 0 0 5 4 4 . 5 5 4 4 . 5 0 . 0 5 4 4 . 5 0 . 0 5 4 4 . 5 0 . 0

AVG. ARS 1 1 . 8 9 . 1 9 . 0BIAS 1 1 . 8 9 . 1 9 . 0RMS 1 2 . 3 9 . 7 9 . 4

J. .L«v* .' •'l* 'l* <V *|. .g. P|. .g> ... «i*. .*« .t. .i. .i* o. .ii■ .*« .i. .i. .i. s4. w*. sL. .I. .1. .1. .■# sV O..g. .gs 5|5 "

RK-EO = P.FDL ICH-KUDNG EOUATION OF STATFRN-FO = REDL1CH-NGO EOUATION OF STATEKREGK = KRFGLEV.'SK I-KAY METHOD

2k0TABLE 36 (CONT'D)

SYSTEM NUMBER 60

CYCLOHEXANE(A ) --- N-DECANE(B) S.C. PAK


T E M P E R A T U R E ( C )X( A ) T E X P R K - E O D E V R N - E P D E V K R E G K D E V0.0 3 4 3 . 9 3 4 3 . 9 0.0 3 4 3 . 9 0.0 3 4 3 . 9 0.00.10 3 4 1 . 1 3 4 1 . 2 - 0 . 1 3 3 9 . 6 1 . 50.20 3 3 7 . 6 3 3 8 . 1 - 0 . 5 3 3 7 . 5 0 . 1 3 3 5 . 1 2 . 50 . 3 0 3 3 3 . 6 3 3 4 . 4 — 0.8 3 3 3 . 6 - 0.0 3 3 0 . 3 3 . 30 . 4 0 3 2 9 . 1 3 2 9 . 9 - 0.8 3 2 9 . 3 - 0.2 3 2 5 . 3 3 . 80 . 5 0 3 2 3 . 8 3 2 4 . 7 - 0 . 9 3 2 4 . 2 - 0 . 4 3 1 9 . 7 4 . 10 . 6 0 3 1 7 . 4 3 1 8 . 4 -1 . 0 3 1 8 . 2 - 0.8 3 1 3 . 6 3 . 80 . 7 0 3 1 0 . 0 3 1 1 . 0 - 1.0 3 1 1 . 1 - 1.1 3 0 6 . 7 3 . 30 . 8 0 3 0 1 . 7 3 02 .2 - 0 . 5 3 0 2 . 6 - 0 . 9 2 9 8 . 8 2 . 90 . 9 0 2 9 1 . 9 2 9 1 .9 0.0 2 9 2. 3 - 0 . 4 2 8 9 . 9 2.01.00 2 7 9 . 8 2 7 9 . 8 0.0 2 7 9 . 8 0.0 2 7 9 . 8 0.0

A V G . A R S 0.6 0 . 5 3 . 0B I A S - 0.6 - 0 . 5 3 . 0

. . R M S 0 . 7 0.6 3 . 1P R E S S U R E ( P S ! A )

X (A ) P E X P R K - E O D E V R N - E O D E V K R E G K D E V0.0 3 1 0 . 5 3 1 0 . 5 0.0 3 1 0 . 5 0.0 3 1 0 . 5 0.00 . 10 3 3 5 . 6 3 3 6 . 2 - 0.6 3 4 1 . 6 - 6.00.20 3 6 2 . 2 3 6 3 . 7 - 1 . 5 3 6 3 . 1 - 0 . 9 3 7 4 . 4 - 12.20 . 3 0 3 9 0 . 2 3 9 3 . 0 - 2.8 3 9 2 . 2 - 2.0 4 0 8 . 5 - 1 8 . 30 . 4 0 4 2 0 . 0 * 2 3 . 8 - 3 . 8 4 2 3 . 2 - 3 . 2 4 4 3 ■ 4 - 2 3 . 40 . 5 0 4 5 1 . 7 4 5 5 . 9 - 4 . 2 4 5 5 . 5 - 3 . 8 4 7 8 . 2 - 2 6 . 50 . 6 0 4 8 4 . 5 * 8 8 . 5 - 4 . 0 4 8 R . 5 - 4 . 0 5 1 1 . 5 - 2 7 . 00 . 7 0 5 1 8 . 1 5 2 0 . 6 - 2 . 5 5 2 1 . 0 - 2 . 9 5 4 1 . 9 - 2 3 . 80 . 8 0 5 5 1 . 3 5 5 0 . 6 0 . 7 5 5 1 . 4 - 0.1 5 6 7 . 4 - 1 6 . 10 . 9 0 5 7 6 . 8 5 7 6 . 1 0 . 7 5 7 7 . 0 - 0.2 5 8 5 . 7 - 8 . 91.00 5 9 4 . 2 5 5 4 . 2 0.0 5 9 4 . 2 0.0 5 9 4 . 2 0.0

A V G . A P S 2 . 3 2.1 1 8 . 0B I A S - 2.0 - 2 . 1 - 1 8 . 0R M S 2 . 7 2.6 1 9 . 5

«|» «|» .j* *|« »,* «(• -|. .j. »,•* *|. >,i «4> r,< .|>< r(. .p a>|. .p .p .p »,» *,« <p *,«.

RK-EO = REDLICH-KUDNG EOUATION OF STATERN-EO = REDLICH-NGO EOUATION OF STATEKRE^K = KREGLEWSKI-KAY METHOD

2klTABLE 36 (CONT'D)

S Y S T E M N U M B E R 6 1C Y C L O H E X A N E ( A ) N - T R I D E C A N E (B ) S . C . P A KR E D . I N T . P A R . R - K A 1 2 S R = 0 . 7 5 7 6 4 0 4 2 B 1 2 S R = 0 . 8 5 3 1 1 5 5 6R E D . I N T . P A R . R - N A 1 2 S R = 0 . 7 6 6 7 9 9 3 3 B 1 2 S R = 0 . 7 3 7 3 6 4 0 3

T E M P E R A T U R E ( C )X( A ) T E X P R K - E P D E V R N - E O D E V K R E G K D E V0.0 4 0 1 . 7 4 0 1 . 7 0.0 4 0 1 . 7 0.0 4 0 1 . 7 0.00.10 3 9 7 . 4 3 9 8 . 3 - 0 . 9 3 9 5 . 0 2 . 40.20 3 9 2 . 2 3 9 4 . 0 - l . P 3 9 1 . 4 0.8 3 8 8 . 2 4 . 00 . 3 0 3 8 6 . 0 3 8 3 . 6 - 2.6 3 3 5 . 3 0 . 7 3 8 0 . 9 5 . 10 . A 0 3 7 8 . 4 3 3 1 . r - 3 . 4 3 7 8 . 1 0 . 3 3 7 2 . 8 5 . 60. 5 0 3 6 9 . 3 3 7 3 . 1. - 3 . 8 3 6 9 . 5 - 0 . 2 3 6 3 . 7 5 . 60 . 6 0 3 5 8 . 4 362 . 0 - 3 . 6 3 5 8 . 8 - 0 . 4 3 5 2 . 9 5 . 50 . 7 0 3 4 5 . 4 3 4 7 . 8 - 2 . 4 3 4 5 . 3 0.1 3 3 9 . 8 5 . 6o . p n 3 2 9 . 5 3 2 9 . 6 - 0 . 1 3 2 8 .0 1 . 5 3 2 3 . 6 5 . 90 . 9 0 3 0 8 . 4 3 0 6 . 9 1 . 5 3 0 6 . 3 2.1 3 0 3 . 8 4 . 61.00 2 7 9 . r 2 7 c . 8 0.0 2 7 9 . 8 0 . 0 2 7 9 . 8 0.0

A V G . A P S 2.2 0.8 4 . 9B I A S - 1 . 9 0.6 4 . 9R M S _ 2.6 1.0 5 . 0

P R E S S U R E ( P S I A )X ( A ) P E X P R K - E O D E V R N - E P D E V K R E G K D E V0.0 2 5 0 . 2 2 5 0 . 2 0.0 2 5 0 . 2 0.0 2 5 0 . 2 0.00 . 10 2 8 6 . 9 2 8 1 . 9 5 . 0 2 9 0 . 2 - 3 , 30.20 3 2 4 . 2 ? 1 7 . 3 6 . 9 3 1 7 . 1 7 . 1 3 3 5 . 4 - 11.20 . 3 0 3 6 3 , 4 3 5 6 . 6 6.8 3 5 7 . 0 6 . 4 3 8 5 . 3 - 2 1 . 90 . 4 0 4 0 6 . 3 ? c. 9 . 9 6 . 4 4 0 1 . 3 5 . 0 4 3 9 . 1 - 3 2 . 80 . 5 0 4 5 1 . 7 4 4 6.6 5 . 1 4 4 9 . 1 2.6 4 9 4 . 5 - 4 2 . 80 . 6 0 4 9 8 . 3 4 5 5 . 4 2 . 9 4 9 8 . 6 - 0 . 3 5 4 7 . 9 - 4 9 . 60 . 7 0 5 4 5 .4 5 4 2 .7 2 . 7 5 4 6 . 0 - 0.6 5 9 3 . 2 - 4 7 . 80 . 8 0 5 8 7 . 2 5 F 1 . 8 5 . 4 5 8 4 . 2 3 . 0 6 2 2 . 4 - 3 5 . 20 . 9 0 6 1 1 . 0 6 0 2 .2 8 . 3 6 0 3 . 1 7 . 9 6 2 5 . 7 - 1 4 . 71 .00 5 9 4 . 2 5 9 4 .2 0.0 5 9 4 . 2 0.0 5 9 4 . 2 0.0

A V G . A B S 5 . 6 4 . 1 2 8 . 8B I A S ' 5 . 6 3 . 9 - 2 8 . 8R M S » k .ri 5 . 9 i*. *4 %■, ,1. 4 . 9 k*f J. .If ,1, ,'i .1, .>* 1 3 2 . 9 1, ,1, .1. ,1. <*,» m

R K - E O = R E D L I C I - I - K U D M G E G I J A T I O N D F S T A T ER N - E O = R F D L I C H - N G O E O U A T I O N 01= S T A T E K R E G K = K R E G L E W S K I - K A Y M E T H O D

2^2T A B L F 3 6 ( C O N T ' D )

S Y S T E M N U M B E R 6 3C Y C L O H E X A N E (A ) - - - C I S - D E C A L I N (B ) . S . C . P A KR E D . I N T . P A R . R - K A 1 2 S R = 0 . 8 7 9 1 7 9 3 6 B 1 2 S R - 0 . 9 5 0 4 7 7 9 6R E D . I N T . P A R . R - N A 1 2 S R = 0 . 8 4 9 4 0 3 0 8 B 1 2 S R = 0 . 8 8 5 0 0 8 3 4

T E M P E R A T U R E [ C }X { A ) T E X P 73 1 m O D E V R N - E O D E V K R E G K D E V0.0 4 3 1 . 8 4 ? 1 . P 0.0 4 3 1 . 8 0.0 4 3 1 .8 0.00 . 10 4 2 2 . 0 4 2 3 . 2 - 1.2 4 2 3 . 6 - 1.6 4 2 1 . 6 0 . 40.20 4 1 1 . 4 4 1 3 . 5 - 2 . 1 4 1 4 . 3 - 2 . 9 4 1 0 . 7 0 . 70 . 3 0 3 9 9 . 6 4 0 2.6 - 3 . 0 4 0 3 . 7 - 4 . 3 3 9 8 . 9 0 . 70.^0 3 8 7 . 1 3 5 0 . 4 - 3 . 3 3 9 1 . 5 - 4 . 4 3 8 6 . 0 1 . 10 . 5 0 3 7 3 . 1 3 7 6.6 - 3 . 5 3 7 7 . 7 - 4 . 6 3 7 1 . 9 1.20 . 6 0 3 5 7 . 6 3 6 1 . 1 . 5 3 6 1 . 9 - 4 . 3 3 5 6.6 1 .00 . 7 0 3 4 0 . 7 3 4 3 . 7 - 3 . 0 3 4 4 . 0 - 3 . 3 3 3 9 . 8 0 . 9o . r o 3 2 2 . 6 3 2 4 . 3 - 1 . 7 3 2 4 . 2 - 1.6 3 2 1 . 4 1.20 . 9 0 3 0 2 . 7 3 0 2 . 9 - 0.2 3 0 2 . 6 0 . 1 3 0 1 . 4 1 .31 .00 2 7 9 . 8 2 7 9 . 8 0.0 2 7 9 . 8 0.0 2 7 9 . 8 0.0

A V G . A 5 5 2 . 4 3 . 0 0 . 9B I A S - 2 . 4 - 3 . 0 0 . 9R M S 2.6 3 . 3 1 .0

P R E S S U R E ( P S I A )X ( A ) P E X P P K - E O D E V R N - E O D E V K R E G K D E V0.0 4 6 5 . 1 4 6 5 . 1 0.0 4 6 5 . 1 0.0 4 6 5 . 1 0.00 . i n 5 0 2 . 8 4 9 6 . 6 6.2 4 9 7 . 5 5 . 3 4 9 8 . 9 3 . 90.20 5 3 9 . 1 5 2 7 . 9 11.2 5 3 0 . 2 8 . 9 5 3 1 . 8 7 . 30 . 3 0 5 7 1 . 9 5 5 8 . 3 1 3 . 6 5 6 2 . 1 9 . 8 5 6 2 . 6 9 . 30.^0 6 0 0 .6 5 F 6 . 4 14 . 2 5 9 1 . 7 8 . 9 5 9 0 . 2 1 0 . 40 . 5 0 6 2 2 . 6 6 1 0 . 7 1 1 . 9 6 1 7 . 1 5 . 5 6 1 2 . 9 9 . 70 . 6 0 6 3 7 . 9 6 2 5 .0 8 . 9 6 3 5 . 5 2 . 4 6 2 9 . 2 8 . 70 . 7 0 6 4 4 • 4 6 3 8 . 6 5 . 8 6 4 4 . 0 0 . 4 6 3 7 . 2 7 . 20 . 8 0 6 4 1 . 4 6 3 7 . 0 4 . 4 6 3 9 . 9 1 . 5 6 3 5 . 1 6 . 30 . 9 0 6 2 7 . 7 6 2 2 . 2 5 . 5 6 2 2 . 5 5 . 2 6 2 1 . 1 6.61.00 5 9 4 . 2 55 4 . 2 0.0 5 9 4 . 2 0.0 5 9 4 . 2 0.0

A V G . A P S 9 . 1 5 . 3 7 . 7B I A S 9 . 1 5 . 3 7 . 7R M S 9 . 7 6.2 7 . 9

4*# V*. H1-V 'i* <•»* *r’ V V V V V V 'iP# *1. «*. . *. .1. .1. 1. .V. 1* t rf, 1 . V V * i ' * i ' v *

O .1. .1. . 1 . . t« .1 . . f . |i , . r j . . «*« o . • . t i1 . | . .g . .g . F |. .|% > »*. . i . . i . « i . .,*J* V rl* 'I* *|% •** *(» *|* *(’ #|« T» .|. »|» F|* »|i .|» rj. #|k «t»

RK-EO = REDL ICH-KHONG EOIJATIOM OF STATERN-EO = REDLICH-NGO EOUATION OF STATEKREGK - KREGLEWSKI-KAY METHOD

2k3

TABLE 37

PURITY AND SOURCE OP SAMPLES

Compound Puri ty (mole %)

Source

n-Hexane 99.99 PPCon-Nonane 99.68 IIn-Decane 99.^9 IIn-Dodecane 99.70 IIn-Tridecane 99.82 IIn-Tetradecane 99.9 CSCoCyclohexane 99.99 PPCocis-Decalin 99.9 CSCoBenzene 99.91 PPCoEthylbenzene 99.92 II'o-Xylene 99.97 II1,3 ?5-^rimethylbenzene CSCo1,2,h-Trimethylbenzene tr1,2,3-Trimethylbenzene tiNaphthalene

PFCo i Furnished by Phillips Petroleum Co.CSCo t From Chemical Sample Co,, Columbus, Ohio

TABLE 38

PURE COMPONENT CONSTANTS USED IN THE CORRELATION

Tb Vc ZC (V*)1/3Compound Mol. tft. °K cc/g-mole

Ref.‘ Ref. Ref. Ref. Ref.Methane 16,04 111.7 76 99 56 0.288 56 0.013 76 3.373 54Ethane 30.07 184.6 76 148 56 0.285 56 0.105 76 3.800 54Propane 44.09 231.1 76 203 56 0.281 56 0.152 76 4,208 54n-Butane 58.12 272.7 76 255 56 0.274 56 0,201 76 4.543 54n-Pentane 72.15 309.3 76 304 56 0.262 56 0.252 76 4.797 54n-Kexane 86.17 341.9 76 370 56 0.264 56 0.290 76 . 5.102 542-Methylpentane 86.17 333.5 76 367 56 0.267 56 0.295 76 5.104 542 i2-Diraethylbutane 86.17 322.9 76 359 56 0.2?2 56 0.266 76 ' 5.101 54n-Heptane 100.20 371.6 76 432 56 0.263 56 0.352 7 6 5.341 542- Me thy1hexane 100.20 363.2 76 421 56 0.261 56 0.340 76 •

2i2-DimethyIpentane 100.20 352.4 76 4l6 56 0.267 56 0.300 76n-Octane 114.22 398.9 76 492 56 0.259 56 0.408 76 5.564 542-Methylheptane 114.22 390.8 76 488 56 0.261 56 0.384 762,2-Dime thylhe.xane 114.22 380.7 76 478 56 0.264 56 0,343 76n-Nonane 128.25 424.0 76 543 76 0.250 76 0.441 76 5.770 542-Me thylo c tane 128.25 4l6.1 a 529 b 0.252 c 0.453 d2,2-Dime thylheptane 128.25 404,0 a 514 b 0.250 c 0.372 dn-Decane 142,28 447.3 76 602 76 0,247 76 0.586 76 5.965 54n-Dodecane 170.33 489.5 76 718 76 0.238 76 0.553 76 6.325 54n-Tridecane 184,36 508.6 76 780 76 0.239 76 0.593 76 6.491 54n-Tetradecane 198.38 526.8 76 830 76 0.233 76 0.626 76 6.653 54

TABLE 38 (CONT'D)

Tb Vc Zc Cd (v*)l/3Compound Mol. Wt.

0 . cc/g-mole Ref. Ref. Ref. Ref. Ref.

Cyclopentane 70. 13 322.4 76 260 56 0.278 58 0,.193 76 ^.577 54Methylcyclopentane 84. 16 345.0 76 319 58 0.273 56 0,,234 76 4.881 54Cyclohexane 84. 16 353.9 76 308 58 0.273 58 0,,186 76 4.841 54Me thylcyclohexane 98. 18 374.1 76 368 56 0.269 56 0.,244 76 5.13^ 54cis-Decalin 138.26 467.8 76 488 78 0.267 76 0,,304 76 5.570 5^Benzene 78. 11 353.3 76 259 58 0.271 56 0,,215 76 4.546Toluene 92. 13 383.8 76 316 58 0.264 56 0,,279 •76 4.847 54o-Xylene 106.16 417.6 76 369 58 0.263 56 0,,300 76 5.085 54Ethylbenzene 106.16 409.4 76 374 58 0.263 56 0,,322 76 5.106 54Argon 39.94 87.5 76 75.2 76 0.290 76 -0,,002 76 3.077 54Hydrogen Sulfide 34.08 211.4 76 95 76 0.268 76 0,,100 78 3.304 54Carbon Dioxide 44. 01 194.7 76 94.0 56 0.274 56 0,,420 76 3.235 54

ai Calculated from Eq. (2-40) in Ref, 76,bi Calculated from Eq, (2-26) in Ref. 76.ci Calculated from Eq. (2-24) in Ref. 76.di Calculated from Eq. (2-28) in Ref, 76,V = Liquid molar volume of pure component at T/T = 0.6, cc/g-mole.

ro-e*

TABLE 39 UNCORRECTED CRITICAL PROPERTIES FOR THE EFFECT OF MERCURY

S Y S T EM E \T ITN-HEXA ME (A ) --- N—DECANE(B)

X ( A ) T ( D F G . C ) __ P C P SI A )_ _ _ E X C E S S T_ _ _ _ E X C E S S P0.0 3 A 3 .6 3 0 8 . 6 0.0 0.00 . 10 3 3 6 . A 3 3 3. A 3 . 8 11.60.20 3 2 8 . 9 3 5 8 . 0 7 . 2 22 . 80 . 3 0 3 2 1 .2 3 8 2 . 2 1 0 . 5 3 3 . 70 . A O 3 1 2 . 3 A 0 5 . 8 1 2 . 5 A A . 00 . 5 0 3 0 3 . 1 A 2 7 . 0 1 A. 3 5 1 . 90 . 6 0 2 9 2 .3 A A A . 9 1 A . A 5 6 . A0 . 7 0 2 8 0 . 1 A 5 7 . 2 1 3 . 2 5 5. A0 . 8 0 2 66 .A A 6 2 . 6 1 0 . A A 7 . 50 . 9 0 2 3 1 . 2 A 5 8 . 9 6.2 3 0 . A1 .00 2 3 A . 1 A A 1 .8 0.0 0.0

S Y S T E M N U M B E R 1 8N - H E X A N E (A ) — - M - T R I D E C A M E ( B )

X { A ) T ( D E G . C ) P ( P S I A ) E X C E S S T E X C E S S P0.0 A O 1 . 7 2 A A . 9 0.0 0.00 . 10 3 9 3 . 0 2 8 A . 0 8.1 1 9 . A0.20 3 8A .0 3 2 A . 0 1 5 . 8 3 9 . 70 . 3 0 3 7 A , 1 3 6 3 . 5 2 2 . 7 5 9 . 50 . A O 3 6 3 .8 A 0 2 . 0 2 9 . 1 7 8 . 30 . 5 0 3 5 1 . 1 A 3 9 . 1 3 3 . 2 9 5 . 80 . 6 0 3 3 6 . 1 A 7 A . 3 3 5 . 0 1 1 1 . 30 . 7 0 3 1 8 . 3 A 9 9 . 5 3 3 . 9 1 1 6 . 80 . 8 0 2 9 6 . 8 5 1 0 . 0 2 9 . 2 1 0 7 . 60 . 9 0 2 6 9 . 0 A 9 9 . 2 1 8 . 1 7 7 . 11.00 2 3 A • 1 A A 1. 8 0.0 0.0

TABLE 39 (CONT’D)2^7

S Y S T E M N U M B E R 1 9N - H E X A N E ( A ) N - T E T R A D E C A M E ( B )

X {A ) T ( D E G . C ) P f P S I A ) E X C E S S T E X C E S S P0.0 4 2 3 .1 201 .8 0.0 0.00 . 10 4 1 6 . 0 2 4 8 . 7 1 1 . 3 2 2 . 90.20 4 0 7 . 6 2 9 5 .6 21.8 4 5 . 80 . 3 0 3 9 7 . 1 3 4 2 . 5 3 0 . 3 6 8 . 70 . 4 0 3 8 4 . 7 3 8 9 . 6 3 6 .8 9-1.80 . 5 0 3 7 0 . 0 4 3 5 . 0 4 1 . 1 ... 1 1 3 . 20 . 6 0 3 5 3 .3 4 7 7 . 7 4 3 . 4 1 3 1 . 90 . 7 0 3 3 2 . 0 5 1 3 . 1 4 1 . 0 1 4 3 . 30.00 3 0 7 .6 5 3 2 . 0 3 5 . 6 1 3 8 . 20 . 9 0 2 7 5 . 0 5 1 7 . 5 2 1 . 9 9 9 . 71.00 2 3 4 . 1 4 4 1 .8 G . O 0.0

S Y S T E M N U M B E R 2 0N - H E X A N E ( A ) - - - C I S - D E C A L I N ( B >

X ( A ) T ( O E G . C ) P f P S I A ) E X C E S S T E X C E S S P0.0 4 3 1 .8 4 5 7 . 9 0.0 0.00 . 10 4 1 8 . 5 4 9 5 . 5 6 . 5 3 9 . 20.20 4 0 3 .6 5 2 8 . 0 1 1 . 3 7 3 . 30 . 3 0 3 8 7 .3 ' 5 5 4 . 0 1 4 . 8 1 0 0 . 90 . 4 0 3 6 9 . 5 5 7 2 . 7 1 6 . 8 121. 20 . 5 0 3 5 0 . 0 5 8 2 . 0 1 7 . 1 1 3 2 . 20 . 6 0 3 2 8 . 7 5 8 1 . 5 1 5 . 5 1 3 3 . 30 . 7 0 3 0 6 . 1 5 6 9 . 8 1 2 . 7 1 2 3 . 20 . 8 0 2 8 3 .0 5 4 3 . 6 9 . 4 9 8 . 60 . 9 0 2 5 8 . 8 ' 4 9 8 . 4 " 4 . 9 ' 5 5 . 01.00 2 3 4 . 1 4 4 1 . 8 0.0 0.0

TABLE 39 (CONT'D)

S Y S T E M N U M B E R 2 1 N - N O N A M E {A ) - - - N - T R I D E C A M E ( B)

X (A ) T ( D E G . C ) _ _ _ _ _ P ( P S I A ) E X C E S S T E X C E S S0.0 4 0 1 . 7 2 4 4 .9 0.0 0.00.10 3 9 6 . 4 25 9 . 4 2.8 5 . 70.20 3 9 1 .5 2 7 3 . 5 6.0 11.00 . 3 0 3 8 5 .6 2 8 7 . 6 8.2 1 6 . 40 . 4 0 3 7 9 . 0 3 0 1 . 1 9 . 7 21.10 . 5 0 3 7 1 . 5 3 1 3 . 3 . 1 0 . 4 ' '.. . 2 4. 50 . 6 0 3 6 3 .2 3 2 3 . 4 10.2 2 5 . 80 . 7 0 3 5 3 . 6 3 3 0 . 8 8 . 7 2 4 . 40 . 8 0 3 4 3 .4 3 3 5 . 4 6.6 2 0 . 30 . 9 0 3 3 2 .3 3 3 6 . 1 3 . 6 12.21 .00 3 2 0 .6 3 3 2 . 7 0.0 0.0

S Y S T E M N U M B E R 2 2N - D E C A M E (A ) - - - N - D U D E C A M E ( B )

X (A ) T I D E G . C ) P ( P S I A ) E X C E S S T E X C E S S0.0 3 8 5 .8 2 6 5 . 5 0.0 0.00.10 3 8 2 . 1 2 7 2 . 2 0. 5 2 . 40.20 3 7 8 . 3 2 7 8 . 1 0 . 9 3 . 90 . 3 0 3 7 4 . 3 " 2 8 3 . 4 1.2 4 . 90 . 4 0 3 7 0 . 4 2 8 8 . 3 1 . 5 5 . 40 . 5 0 3 6 6 . 4 2 9 2 . 7 1 . 7 5 . 50 . 6 0 3 6 2 .3 2 9 6 . 7 1.8 5 . 20 . 7 0 3 5 8 . 1 ' " 3 0 0 . 3 1.8 4 . 40 . 8 0 3 5 3 .6 3 0 3 . 5 1.6 3 . 30 . 9 0 . . . . 3 4 8 . 7 . . . . " " " 3 0 6 . 4 0 . 9 1.81.00 3 4 3 .6 3 0 8 . 6 0.0 0.0

TABLE 39 (CONT'D)

SYSTEM "NUMBER 2 8 -

B E N Z E N E ( A ) - - - N - D E C A M E ( B J

X (A ) T ( O E G . C ) P ( P S I A ) E X C E S S T E X C E S S P0.0 3 4 3 . 6 3 0 8 . 6 0.0 0.00.10 3 4 1 . 2 3 4 0 . 5 3 . 2 - 8 . 40.20 3 3 7 . 0 3 7 4 . 0 5 . 3 - 1 5 . 30 . 3 0 3 3 3 . 6 4 1 0 . 5 6 . 7 - 1 9 . 10 . 4 0 3 2 8 . 9 4 4 9 . 0 7 . 5 - 21.00 . 5 0 3 2 3 . 6 4 8 9 . 5 7 . 8 — 20 . 80 . 6 0 3 1 7 . 9 5 3 2 . 3 7 . 6 - 1 8 . 40 . 7 0 3 1 1 . 7 5 7 7 . 0 7 . 0 - 1 4 . 00 . n o 3 0 4 . 8 6 2 1 . 7 5 . 6 - 9 . 70 . 9 0 2 9 6 . 9 666 . 7 3 . 3 - 5 . 01 .00 2 88.1 7 1 2 . 1 0.0 0.0

S Y S T E M N U M B E R 2 9B E N Z E N E ( A ) N - T R I D E C A N E ( P-)

X (A ) T f D E G . C ) P ( P S I A ) E X C E S S T E X C E S S0.0 4 0 1 .7 2 4 4 . 9 0.0 0.00.10 3 9 7 . 8 2 8 3 . 0 7 . 5 - 8.60.20 3 9 3 . 0 3 2 5 . 2 1 4 . 0 - 1 3 . 10 . 3 0 3 8 7 . 3 3 7 2 . 0 '■ 1 9 . 7 - 1 3 . 10 . 4 0 3 8 0 . 3 4 2 1 . 9 2 4 . 0 - 9 . 90 . 5 0 3 7 1 . 7 4 7 5 . 9 2 6 . 8 - 2.60 . 6 0 3 6 1 . 5 5 3 6 . 0 2 8 . 0 10. 80 . 7 0 3 4 8 . 7 6 1 0 . 3 2 6 . 5 3 8 . 40 . 8 0 3 3 2 .7 6 7 4 . 0 2 1 . 9 5 5 . 30 . 9 0 " ■ 3 : 1 3 . 6 7 0 4 . 0 1 3 . 5 3 8 . 61 .00 2 8 8 . 1 7 1 2 . 1 0.0 0.0


B E N Z E N E ( A ) - - - N - H E X A D E C A N E ( B )

X ( A ) T ( D E G . C ) P ( P S I A ) E X C E S S T E X C E S S P0.0 4 5 0 . 0 (63) 2 0 6 . 0 (6 0 ) 0.0 0.00.10 A A 5 . 2 2 5 2 . 0 1 1 . A - A . 6o . ? o A 3 9 . 1 3 0 2 . 5 2 1 . 5 - A . 70 . 3 0 A 3 1 .6 3 5 8 . 6 3 0 . 2 0.80 . A O A 2 2 .6 A 2 1 . 0 3 7 . A 12.60 . 5 0 4 1 2 . 2 . . . A 8 5 ,8 ... ~ 4 3 -2 2 6 . 80 . 6 0 3 9 9 . 7 5 5 5 .5 A 6 . 8 A 5 . B0 . 7 0 3 8 4 . 2 6 2 7 . 7 A 7 . 5 6 7 . A0 . B O 3 6 2 . 5 7 0 3 . A A 2 . 0 9 2 . 50 . 9 0 3 3 1 . A 7 6 1 . 6 2 7 . 1 100 . 11 .00 2 8 B . 1 7 1 2 . 1 0.0 0.0

S Y S T E M N U M B E R 3 7B E N Z E N E ( A ) — - C I S - O E C A L I N ( B )

X (A ) T ( D E G . C ) P ( P S I A ) E X C E S S T E X C E S S P0.0 A 3 1 .8 A 5 7 . 9 0.0 0.00.10 A 2 2 . 6 5 0 7 . 9 5 . 2 2 A . 60.20 A 12 . 5 5 5 A . 6 9 . A A 5 . 90 . 3 0 A O 1 . 6 5 9 8 . 9 1 2 . 9 ' "" 6 4 . 70 • A O 3 9 0 . 0 6 A 0 . 0 1 5 . 7 8 0 . A0 . 5 0 3 7 6 . 9 6 7 7 . 2 1 7 . 0 9 2 . 20 . 6 0 3 6 2 . A 7 0 8 . 3 1 6 .8 9 7 . 90 . 7 0 3 A 6 . 3 ' 7 2 9 . 9 1 5 . 1 9 4 . 10 . 8 0 3 2 8 . A 7 3 9 . 5 11.6 7 8 . 20 . 9 0 3 0 8 . 9 7 3 A • 3 6 . 4 ' “ ' " 4 7 . 6 '1 .00 2 8 8 .1 7 1 2 . 1 0.0 0.0


S Y S T E M N U M B E R ” 4 4 ” "ETHYLBENZENE(A) ------ C I S - D E C A L I N ( B)

XJ A ) T J D E G . C ) I M P S I A ) E X C E S S T E X C E S S P0.0 4 3 1 .8 4 5 7 . 9 0.0 0.00.10 4 2 3 . 9 4 8 2 . 8 0 . 9 1 7 . 90.20 4 1 5 . 9 5 0 1 . 0 1 . 7 2 9 . 20 . 3 0 4 0 7 . 6 5 1 3 . 7 2 . 3 3 4 . 90 . 4 0 3 9 9 . 1 5 2 3 . 5 2.6 3 7 . 70 . 5 0 3 9 0 . 2 5 3 0 . 7 2 . 5 3 8 . 00 . 6 0 3 8 1 . 0 5 3 5 . 8 2.1 3 6 . 10 . 7 0 3 7 1 . 8 5 3 8 . 0 1 . 7 3 1 . 30 . 8 0 3 6 2 . 4 5 3 7 . 0 1.2 2 3 . 30 . 9 0 3 5 3 . 2 5 3 3 . 2 0.8 12.61.00 3 4 3 .6 5 2 7 . 6 0.0 0.0

S Y S T E M N U M B E R 4 5O - X Y L E N E ( A ) - 7- C I S - D E C A L I N { D )

X (A ) T ( D E G . C ) P ( P S I A) E X C E S S T E X C E S S P0.0 4 3 1 .8 4 5 7 . 9 0.0 0.00.10 4 2 4 . 8 4 7 8 . 6 0.6 1 2 . 30.20 4 1 7 . 7 4 9 5 .7 1.0 21.00 . 3 0 . . ' 4 1 0 . 4 5 0 9 . 9 1 . 3 2 6 . 70 . 4 0 4 0 3 . 0 5 2 2 . 5 1 . 4 3 0 . 90 . 5 0 3 9 5 . 5 5 3 2 . 3 1 . 5 3 2 . 30 . 6 0 3 8 7 .8 5 3 9 . 1 1 . 4 3 0 . 70 . 7 0 3 8 0 . 1 5 4 3 . 3 1.2 2 6 . 50 . 8 0 3 7 2 . 2 ‘ 5 4 5 . 2 0 . 9 1 9 . 90 . 9 0 3 6 4 . 2 5 4 4 . 8 0 . 4 .. * 11.11.00 3 5 6 . 2 5 4 2 . 1 0.0 0.0

TABLE 39 (COWT'D)252

SYSTEM"’NUMBER 66” " ’ ’ ""

CYCLDHEXANE(A) N-DE CANE(B )

X (A ) T ( D E G . C ) P ( P S I A )__ E X C E S S T _ _ _ e x c e s s p_0.0 3 4 3 . 6 3 O B . 6 0.0 0.00.10 3 4 1 . 1 3 3 4 . 2 3 . 6 - 3 . 20.20 3 3 7 . 6 3 6 1 . 0 6 . 5 - 5 . 00 . 3 0 3 3 3 . 6 3 8 9 . 3 8 . 9 - 5 . 20 . 4 0 3 2 9 . 1 4 1 9 . 4 10.8 - 3 . 60 . 3 0 3 2 3 . 0 4 5 1 . 4 1 1 . 9 " ' - 0 . 10 . 6 0 3 1 7 . 4 4 8 4 .5 12.0 4 . 40 . 7 0 3 1 0 . 0 5 1 8 . 1 11.0 9 . 5O . R O 3 0 1 .7 5 5 1 . 3 9 . 1 1 4 . 20 . 9 0 2 9 1 . 9 5 7 6 .8 5 . 7 11.11.00 2 7 9 . 0 5 9 4 . 2 0.0 0.0

S Y S T E M N U M B E R 6 1C Y C L O H E X A N E (A 1 - - - M - T R I D E C A N E ( B)

X (A ) T ( D E G . C ) P ( P S 1 A ) E X C E S S T E X C E S S P0.0 4 0 1 .7 2 4 4 . 9 0.0 0.00.10 3 9 7 . 4 2 8 1 . 9 7 . 9 2.10.20 3 9 2 .2 3 1 9 . 5 1 4 . 9 4 . 70 . 3 0 3 8 6 . 0 3 5 9 . 1 2 0 . 9 9 . 4 "0 . 4 0 3 7 8 . 4 4 0 2 . 5 2 5 . 5 1 7 . 90 . 5 0 3 6 9 . 3 4 4 8 . 5 2 8 . 6 2 9 . 00 . 6 0 3 5 8 . 4 4 9 5 .8 2 9 . 8 4 1 . 30 . 7 0 3 4 5 . 4 5 4 3 . 7 2 9 . 0 5 4 . 30 . 8 0 3 2 9 . 5 5 86 .5 2 5 . 3 6 2 . 20 . 9 0 . . . . . 3 0 8 . 4 .. 6 1 1 . 0 " 1 6 . 4 ' 5 1 . 7 " '1.00 2 7 9 . 8 5 9 4 . 2 0.0 0.0

TABLE 39 (CONT’D)253

S Y S T E M N U M B E R 6 3C Y C L O H E X A N E ( A ) - - - C I S - D E G A L I N ( B)

X (A ) T ( D E G . C ) P ( P S I A ) E X C E S S T E X C E S S P0.0 A 3 1 .8 A 5 7 . 9 0.0 0.00.10 A 2 2 . 0 A 9 6 . 2 5. A 2 A. 70.20 A l l . A 5 3 3 . 2 10.0 A 8 . 00 . 3 0 3 9 9 . 6 5 6 6 . 8 1 3 . A 68.00 . A O 3 8 7 . 1 5 9 6 . 3 1 6 . 1 8 3 . 90 . 5 0 3 7 3 . 1 6 1 9 . 2 1 7 . 3 9 3 . 20 . 6 0 3 5 7 . 6 6 3 5 . A 1 7 . 0 9 5 . 70 . 7 0 3 A 0 . 7 6 A 3 . 0 1 5 . 3 8 9 . 70 . 8 0 3 2 2 .6 6A 1 . 2 1 2 . A 7 A . 30 . 9 0 3 0 2 . 7 6 2 7 . 7 7 . 7 A 7 . 11 .00 2 7 9 . 8 5 9 A . 2 0.0 0.0

APPENDIX E

COMPUTER PROGRAMS

A. Expressions for the Derivatives in the Equations of the Thermodynamic Conditions at the Critical Point TiTe. , Kgs. (247 and T25U

The following expressions are the same for both the Redlich-Kwong and Redlich-Ngo equations of state.

a = a jX2 + 2a12XjX2 + a.,x2 = SjXj + a2x2 + A12Bxix2

b = b ^ 2 + 2b12xlX2 + b,,x2 = U1X1 + t»2X2 + B12I,x ix2

= DAX = ax - a2 + A12L(x2 - xjd 2 aS-f = -2A12L dxj

= DBX « bx - b2 + B12L(x2 - xx)

a -2B12Ldx^

where A12L « 2ai2 " al " a2 = (A12$R - l)(a1 + a2^B12L = 2bl2 - bx - b2 = (B12SR - lXbj + b2 )

254

1* The Redlich-Kwong Equation of State255

RT ap ----------------------------- 3— --------------

(V-b) TaV(V+b)

The following expressions were derived by Hissong (3?) and are presented here again to assist the user of the subsequent computer programs.

ripy — \ — T RT , a____"1 /db\DPX - dXj V,T - [(T.b)2 T#v(v+b)2j (dx>

- [ -tr1 - 1 Cgf >LT2V(V+b)J dxl

D2PX“ (L p v -T = 2 { [ ? v ‘!v+b ) ] A 1 2 L ■ L w

r l B 12L + ( | | ) - f r - r — -J dxi Ut2v(v-RTT 1,1 ”

(V-b)2 J dxl U T 2V(V+b)2

. f RT_________a 1 /db \ V 1L(V-b)3 T2V(V+b)3 J d x l J J

D3PX - «S5>v.t - 3 (s> [b7 (i>2 - 2B12L]

(— ) vdx'

2 •|b i2L(j|) + (f£)TaV(V+b) I axl QX1 (-- T - ? -SB12L( |) + <j|£) |A12L

2aB12L , 1 /dbx |*/da\ a /db*-|“ ( V + b ) ( v + b j (dx' L dXj " ( V + b ) (dx'J

dvx = (&) = -VA dx^P#T DPDV

DPDV =

D2VX =

z^DPDVv 1 ;

fdDPXvV fcx/P

D2PVX =

256

‘ H ’ x j . T = [ T* V ( V + b ) ] [ ^ + T V + b lJ - ^ S j 5

,d£Vx = DPX /3DPDV\ JL /SDPXxSx* P ’T “ (DPDV)2 * X1 P 'T " DPDV * V P ’T

P - T = [ # v ( v + b ) ] { & + (^ 1 ' 2 a ( D V X ) ( 7

+ T v T b T [ V + T v T b j ] } " T v + b T ( d x * [ v

* w M } * ^ [<™> - C > ]

•c ' [',:v/(v-ni]{ 2 { Mi!L * T W 5 T [f% !

- aBizLJ } + [7 + Xvkr] (DVX)(ff>-■ T v + b T ^ { [ 7 + T v + t l ] (D V X ) + T v f b J ^ } ] "

' ' & ( B12L + ^ (^ > [ (DVX) - (5 % ] }

(av*q;)T = = [r^V(V+b)]{[7 + Tvtft]^^

a f"i . 2 1 /dbO SRT__,db,■ T v + b T L v T T v + b T j M x ' J ■ ( v _ b ) 3 dxl

1 t d v = “ T T f A 1 2 L l n ( ^ ) + a 6 1 2 L ( G 2 )Jv dx2 V,T bTa <> V

- • < e > [ ( G 2 ) ( a f > -

+ [t vTF7 <E>2 - 2B12L]

^ i | ( G 2 ) [ A 1 2 L ( f | ) + B 1 Z L < § £ ) ]

+ < f l > { < G3 > [ < a f > t E > - 2 a B * 2L ]

_ a ( d b ) 2 f M + ___1___ 1 •>!aldx' L b 3(v+b)3 J JJ

+ (v-b)2 (^ i [ tv T < ^ 2 " 6B12L]

n o - 1 i l T n / V + b NTv+bT “ ,b v *

ICO 0

( ^ )3 V,T dV =

G3 ~ T v + b T \_z(V+b J + b ] " ^2 l n ( V y b )

2582. The Redlich-Ngo Equation of State

3Z RT aP = ----- - at critical point,

(V-b) TaV(V+b)

2° = H zl + x22=

The other equations are exactly the same as those given for the Redlich-Kwong equation of state except that each term with "rt" should be multiplied by "32°,f•

259B. FORTRAN IV Statement Listings of the Computer Programs

1, Critical Locus Calculation

This program calculates the critical locus of a binary system using the Redlich-Kwong and Redlich-Ngo equations of state and the Revised Correponding states methods. As mentioned earlier, the equation of state method requires initial approximations of critical temperature and critical volume in order to start the iteration at each given composition. The program is arranged such that the revised corresponding states method is used to provide these initial approximations.

The program requires the following data cards for each binary systemi

(1) System number and reduced interaction parameters for the Redlich-Kwong equation, i.e., A12SR and B12SR,

(2) Reduced interaction parameters for the Redlich- Ngo equation,

(3) Name of the binary system,(h) Critical temperatures, critical pressures, and

critical compressibility factors of components A and B, and

(5) (V*)*^ and acentric factors for components A andB.

As many data sets may be run at one time as desired by arranging the data sets in the same order as shown above# The last card of the data sets should be a fictious system number “O" denoting the end of the data input#

The output of the program consists of a printed table of calculated critical properties by each method.

o n o o

C C R I T I C A L L O C U S C A L C U L A T I O N U S I N G T H E E Q U A T I O N O F S T A T E A N DC T H E R E V I S E D C O R R E S P O N D I N G S T A T E S M E T H O D S . S . C . P A K

I M P L I C I T R E A L * R ( A - H , 0 - Z )D I M E N S I O N T I T L E ( 2 0 )C O M M O N / T P X / X (9 ) , T K R E G ( 9 ) , P K R E G ( 9)C O M M O N / A B / A l , A 2 ,'b ) , R 2 , A 1 2 L , R 1 ? L C 0 (■: M 0 1'! / A 1 P 1 / A 11 , A 2 2 , R 1 1 , R 2 2 , A 1 2 L 1, R 1 2 L 1 C O M M f W Z / Z C A , Z C PC P M 1-1 P M / D O / P A , r m t O'A , O P , T K A , T K B , P C A , P C B

C A IS T H E C O M P O N E N T W I T H S M A L L E R M n L E C U L A R W E I G H T .5 0 0 R E A D ( 5 , 1 ) U S Y S , A 1 2 S R , R 1 2 S R

1 F O R M A T ( I 5 , 5 X , 2 F 2 0 . n )C A 1 2 S R F. B 1 2 S R F O R T H E P F P L 1 C H - K W 0 N G E O U A T I O M

I F ( N S Y S ) 5 0 I , 5 0 1 , 5 0 2 5 0 2 R F A D ( 5 , 2 ) A 1 2 S R 1 , B 1 2 S R I

2 F O R M A T ( 1 0 X , 2 F 2 0 . R )C A 1 2 S R 1 R R 1 2 S P . 1 F O R T H E R E D L I C H - N G O E Q U A T I O N

R E A D { 5 , 3 ) ( T I T L E ! I ) , I = 1 , 2 0 )C N A M E O F T H E B I N A R Y S Y S T F M

3 F O R M A T ( 2 0 A 4 )P E A DC 5 , 4 ) T C A , T C B , P C A , P C B , Z C A , Z C B

4 F O R M A T ( 6 F 1 0 . 5)T C A , T C R = C R I T I C A L T E M P E R A T U R E S O F C O M P O N E N T S A C B I N C , R E S P E C T I V E L Y P C A , P C P = C R I T I C A L P R E S S U R E S O F C O M P O N E N T S A £ B I N P S I A , R E S P E C T I V E L Y Z C A , Z C B = C R I T I C A L C O M P R E S S I B I L I T Y F A C T O R S O F C O M P O N E N T S A C B , R E S P E C T I V E L Y R E A D ( 5 , 5 ) D A , D R , O A , O B

5 F O R M A T ( 4 F 1 0 . 5 )C D A , D B = ( V - ) 1 / 3 O F C O M P O N E N T S A £ B, R E S P E C T I V E L YC O A ,0 B = A C E N T R I C F A C T O R S O F C O M P O N E N T S A G R , R E S P E C T I V E L Y

T K A = T C A + 2 7 3 . 1 6 D 0 B 1 = 1 0 4 . 4 B 0 0 3 D 0 * T K A / P C A A l = 5 9 4 9 . 3 8 9 9 D 0 * B l * T K A * n S 0 R T (T K A )B 1 1 = 3 1 3 . 4 4 0 1 0 6* Z C A * T K A / P C A 261

A11=17849.6686*B11*ZCA*TKA*DS0RT(TKA>TKB=TCB+273•1600B2 = 104.4R003D0:’:TKB/PCRA2=59A9.P099n0*B2*TKB*DS0RT(TKB)822=313. 440 106:::7.CR*TRB/ PCB .........A 22 = 1 7F49 . A6 8 6 2 2 * ZCB -TKR*DS0RT (TKB )A12L=(A12SR-l.DO}*(Al+A2)P12L=(B12SR-1.00 )*(Bl+P?)A1 2 L1 = ( AlZSRl-l.ODOl*t A11+A22 )F12L 1 = ( R12.SR1-1 .000 )* ( P11+R22 )X ( 1 ) = 0-1nn 6 1=2,9X ( I ) =X( 1-1I+O.l

6 c o n t i n u e on iooo i=iTgCALL EOKRcG(I)

iooo c o n t i n u e .........WRITEt6,100) MSYS , (TITLE(II , I =1, 201,A12SR,B12SR

100 FORMAT(1H1 / 14H SYSTEM NUMBER, 14, 20X, 20A4,///57H THERMODYNAMIC1-EOUAT ] ON OF STATE M E T H O D REDL I CH-KV’ONG/// 10X , 34HREDUCED2 INTERACTION PARAMETERS — , 10X, 7HA12SR ~y F13.8, 10X, 7HR12SR =, 3F13.F fit 29X, 23HREDLICH-KWONG CONSTANTS, 17X, 30HCALCULATED CRIT 4ICAL PROPERTIES, U X, 10H HERAT IONS // 1 2X , 2 H X A , 16X, 1 HA , 17X,5 1 H B , 1A X , 7 H P I P S I A ) , 5 X , 4 H T ( C ) , 5 X , 7 H V ( C C / r . ) , R X , 1 H Z / / )DO 2000 1=1,9 CALL RKEOST(I)

2000 CONTINUEWRITE(6,2 00 IMSYS,(TITLE{I I,1 = 1,20),A12 SP1,B12 S R1

200 FORMAT I1H1 / 14H SYSTEM NUMBER, 14, 20X, 20A4,///55H THERMODYNAMIC1 — EOIJATI ON OF STATE M E T H O D REDLICH-NGO///10X, 34HREDUCED2 INTERACTION PARAMETERS — , 10X, 7HA12SR “» F13.8, 10X, 7HB12SR =, 3F13.P- /// 29X, 23HREDLICH-NGD CONSTANTS, 17X, 30HCALCULATED CRIT 4 1CAL PROPERTIES, 11X, 10HITERATIONS // 12X, 2HXA, 16X, 1 HA, 17X,51HB , 14X, 7HP £ PS IA), 5X, 4HT(C), 5X, 7HV(CC/M), BX, 1HZ //)

262

" . . . D O 3 0 0 0 1 = 1 , 9C A L L R N E O S T ( I )

3 0 0 0 C O N T I N U EWRITE(6,300) MSYS, (T ITLE(I ),I = 1,20)

3 0 0 F O R M A T ( 1 H 1 / 1 4 H S Y S T E M M U M P E R , I * , 2 0 X , ? 0 A 4 / / / 5 7 H R E V I S E D C O R R E S P 1 0 M D I M G S T A T E S - C O H F O P . M A L S O L U T I O N T H E O R Y / / / 3 4 X , 2 H X A , 1 8 X , 1 5 H P R E S 2 S U R E ( P S IA }, 15,X , 1 5 H T E M P E R A T U P . E (C) //)W R I T E ( 6 , ^ 0 0 ) ( X ( I ) » P K R E G ( I ), T KP.EG ( I ) , I = 1, 9 )

4 0 0 F O R M A T t 3 3 X , F 4 . 2 , 1 B X , F 1 2 .1 , 1 P X , F 1 0 . 1 )G O T O 5 0 0

5 0 1 S T O P E N D

n o o o

S U B R O U T I N E R K E O S T ( I )C A L C U L A T I O N O F C R I T I C A L L O C U S F O R B I N A R Y S Y S T E M S U S I N G T H E R E D L I C H - K W O N G E Q U A T I O N O F S T A T EI T E R A T I O N B Y N E W T O N S M E T H O D F O R 2 E P S . » S E C A N T M O D I F I C A T I O N P R O G R A M E D B Y D.VJ. K I S S O N G A N D M O D I F I E D B Y S . C . P A K I M P L I C I T R E A L * 8 ( A - H . O - 7 )D I M E N S I O N A R T (3 J , A R V ( 3 } , D N G X t 2 , 3 ) T D M T ( 2 ) , D M V ( 2), P E X P I 9 ) , T E X P ( 9) D I M E N S I O N T ( 9 ) » P ( 9 )C O N , M O M / T P X / X ( 9 ) , T K R E G ( 9 ) T P K P. E G ( 9 )C O M M O N / A R / A 1 . A 2 » R 1 , R 2 TA 1 2 L , R 12 L D A T A E P S , M T M . A X t M 7 . M A X / 4 . 0 E - 3 , 7 , 5 /T F X P ( 1 ) = T K R E G ( I )PF.XP ( I ) = P K R E G ( I )

1 9 X 2 = 1 . 0 — X ( I )R A = 1 2 0 5 . 9 0 5 / ( X ( I ) * X 2 )R 7 = R 6 * ( X ( I )- X 2 I / ( X ( I ) * X 2 )A = A 1 * X ( I ) + X 2 * ( A 2 + A 1 2 L * X ( I ) ) " ' . . . . .B = B 1 * X ( I ) + X 2 :': ( R 2 + R 1 2 L * X ( I ) )D A X = A 1 - A 2 + A 1 2 L ::( X 2 - X ( I ) )D R X = B 1 - B 2 + R 1 2 L :M X 2 - X ( I ) )

C B E G I N I T E R A T I O N F O R T E M P E R A T U R E T K A N D V O L U M E VN N N = 0N T O T = 1 . . . . . . . . . . . .Z E S T = 0 . 3 5 G O T O i n o

2 0 0 Z E S T = 0 . 3 1 N T O T = 1 N N N = 1

1 0 0 T S T = T E X P ( I 1 + 2 7 3 . 1 6 D O 5 0 N T S T = 1 t N T M A X N E V D D = N T S T - 2 * ( N T S T / 2 )N T R = 1 N Z E S T = 1

21 N = 1I F ( M E V O D . E O . O ) A B T (1 ) = T S T - 0 . 2 5 * F L O A T ( N T S T )

I F t N E V O D . E G . l > A B T ( 1 ) = T S T + 0 . 2 5 - F L O A T ( N T S T - 1) A R V ( 1) = 1 2 0 5 . 9 0 5 * Z E S T * A R T ( 1 ) / P E X P ( I )IF ( M T R . E 0 . 2 ) Gfl T O 2 3 A P T ( ? ) = 0 . 9 9 9 * A B T ( I )A R V ( 2 ) = 0 . 9 9 8 :':A 3 V (1 )O T R = ?G O T O 2 2

■22 A R T ( 2 ) = 1 .Oni-'-'APT 1 1 )A F. V ( 2 ) = I . 0 0 2 :;:A P V ( I )'N T R = 3

2 2 D O 3 4 :<=1,3I F ( K . E 0 * 3 ) G O T O 2 6 T K = A R T (2)J F ( K . E P . 2 ) G O T O 2 P

2 4 V = A E V ( 2 )P T = 1 ? 0 5 . 9 0 5 * T K T H F = O S O R T ( T K )D 6= R 6 - T K D 7 = R 7 * T K G O T O 3 0

2 6 T K = A R T (1)G O T O 2 4

2 8 V = A B V (1)3 0 0 1 = R T / ( (V - B ) * * 2 )

I F ( K . M E . I ) G O T O 3 2 V S T = V R T S T = R T

3 2 r ? = I . O D O / ( T H F - V * ( V + B ) )0 3 = 0 2 / ( V + B )D P X = D B X * ( D 1 + A * D 3 ) - D A X * P 2 D P 0 V = A * D 2 * ( 1 - 0 0 0 / V + I , 0 0 0 / (V-s-B) ) - D 1 D V X = - D P X / D P D V D 5 = D L 0 G ( ' V + B ) / V )G 2 = l . 0 0 0 / ( V + R ) - l . 0 D 0 / B * D 5 G 3 = ( 0 . 5 D 0 / ( V + B ) + 1 . 0 0 0 / 3 ) / ( V + B ) - D 5 / ( 3 * 8 )

D4=A12L*D5+B12L*A*G2-DRX*{DAX*G2-0BX*A*G3)D4=2.*D4/1R*THF)+RT/(V-R)*((0BX**2)/ (V-B)-2.*B12L)DMGX{1,K)=06+04-DPX*0VX n2PX = A12L*r>2-P12L* 101+A*03 )D2PX=2.* (02 PX + DRX*( DA X*D3+DRX* (D 1 /(V-R)- A* D3/(V+B) ) ) )D4 = G?-(n AX-0R X-2 .* A * R 12 L )D4 = 04-A*(ORX**2) * ( G3/R +1.000/(3.ODD*(V + R )** 31) p^ = 04 *DB X*G2 * ( A 1 2 L*0P X + P. ]. 2 L *P AX )D 4= 6 .0 00 *04 /(R *T H F)+0 R X*D1*(2.*(0 R X ** 2 ) / ( V - B) -6 . 000* B12L )D2PVX=DAX* ( 1 .000 AM-1. .000/ I V + R) ) -0RX*A/ ( V + R )* ( 1. ODO/V+2. / ( V+B ) ) D2PVX = D2PVX*02-2.*m. / (V-RK-ORX C5=A12L+ ( nAX*DRX-A*R12l.)/ ('MB )D3=DVX* ( 2 . / ( V + R ) +1 .000/V ) +2 . *r)RX / ( V + R )02VX = 2.*03—A*DBX*03/(V + P )+0VX*0AX* ( 1. 000 / ( V+ R ) +1. 0 DO / V )0 2 VX=0 2 V X * 0 2 - 2 . * D 1 * ( B 12 L + D R X / { V - R ) * ( D V X - D R X ) )p? = i.ono/v+i.ono/iV+R)D5=OAX*D3-2.*A*DVX*(1.00 0/(V*V) +1 .000/(V+R)*03)-A*D5X/(V+B)*tD3 11.000/[V+B))05=05*02+2.*01/(V-B>*(DVX-ORX)D2VX=(DPX*05/0P0V-02VX ) /OPOV

34 DM GX ( 2 , K ) =0 7+04-DVX* ( D2 P VX*OVX + 2.*D2 PX) - DPX*02 VXr-n 36 K = 1, 2DMT( K ) = (DMGX(K ,1)-DMGX(K,3))/(ABT(2)-ART{ 1 ))

36 DMV ( K ) = ( DMGX ( K T1 )-DMGX(K ,2 } ) / ( ABV ( 2 )-ARV ( 1) )XJACOB = DNT(1)*OMV(2 J-DNT(2)*OMV{1)PELT-t DMGX(2,1)*DNV(1 )-OMGX(1,1)*0NV(2 ))/XJACOB DELV=(DMGX(1,1)*DNT(2)-DMGX(2,1)*ONT (1))/XJACOB APT(? )=ABT(2)+DELT ARV(3)=ABV(2)+DELVDTEST=OABS(DMGX(1,1))+OARS(DMGX(2,1))IF((DABS(DELT).LT.EPS).AMD.(OARS(OELV).LT.EPS)

1.AMD.(DTEST .LT.1.0E6)) GO TO 56 IF(M .GE.75) GO TO 48 JF(ABT(3).LT.O.O) APT(3)=ART(2)/2.IF(ARV(3 ) .LT.0.0) ARV(3)=A5V(2)/2.

THF=DSORT(RTS 1/ 1205.905D0)P I I ) = R T S T / I V S T - B ) - A / ( T F F * V S T * ( V S T + B ))IF ( (ART(2).LT.1.0).0R. (P( I J.LT.0.0) ) GO TO 43 7=p(])*VST/RTST M T O T = MTflT + lI F ( ['TOT . G E .3 00 ) G O T O 5 2I F ( ( N . F 0 . 2 ) . A N D . ( Z . G T . n . 4 5 )) G O T O 4 4r=r+iD O 3 « K = l , 2 A F T ( K ) = A P T {K + 1 )

3 3 A 3 V ( K ) = A P. V ( K + 1 )G O T O 2 2

4 4 N Z E S T - N Z E S T + 1 ? E S T = Z E S T + 0 . 0 2I F ( N Z E S T . L E . N Z M A X ) G O T O 2 1 .

4 3 I F ( M T R • E O •2) G O T O 2 1 5 0 C O N T I NlJE5 2 IF ( N N N . N E . 1) G O T O 2 0 0

U R IT E (6 » 5 4 ) X ( I ) , A , R * T K , V 5 4 F O R M A T (/ 4 X , 4 0 H I T E R A T I O M F O R T K A N D V H A S N O T C O N V E R G E D / 2 0 X T

1 6 H X ( I ) = T F 5 . 2 » 1 0 X » 3 H A =, E 1 6 . R , 1 0 X T 3 H P = E 1 6 . R / 2 0 X , 1 8 H L A S T 2 V A L U E O F T K = . E 1 6 . 8 , 2 H K , 2 0 X • 1 7 H L A S T V A L U E O F V =, E 1 6 . 8 ,3 5 H C C / M / / )G O T O 5 0 0

5 6 T K = A R T ( 3 )V = A B V (3)E N D I T E R A T I O N F O R T E M P E R A T U R E T K A N D V O L U M E V R T = 1 ? 0 5 . 9 0 5 * T K T ( I }= T K - 2 7 3 . 1 6P ( I } = R T / ( V — B ) — A / { D S O R T (T K ) # V * t V + B ) )z=pt n*v/pjI! R I T E ( 6 • 6 0 ) X ( I ) , A , B , P ( I ) » T t I ) fV r Z ?N T O T , N

6 0 F 0 R M A T ( F 1 5 . 2 T4 X , 2 E l 8 . 6 , F 1 4 . 1 f F 1 0 . 1 , F l l . l , F 1 2 . 4 , 1 1 2 , 2 H / , 1 3)5 0 0 R E T U R N

E N D

O o

o o

S U B R O U T I N E R N E O S T ( I )C A L C U L A T I O N O F C R I T I C A L L O C U S F O R B I N A R Y S Y S T E M S U S I N G T H E R E n L I C H - M G O F P U A T I O N O F S T A T EI T E R A T I O N B Y N F V ' T O N S f-iFTHOD F O R 2 E P S . T S E C A N T N O D I FI C A T I O N

“ P R fT G R A f ■ EI) R Y D . H . H I S S O N G A N O N p n i F I E O B Y S . C . P A K I M P L I C I T R E A L M S (AH-i,0 - 7 )D I M E N S I O N A R T IB ) , A R V I 3 ) ,n.VPX ( 2 » 3 ) , D M T t 2) , D N V ( 2 ) , P E X P t 9 ) , T E X P l 9) DI M E N S I O N T ( 9 ) , P ( 9 )C O M N i O N / T P X / X (Q ) ,TK-RFr, (9 ) , P K P E G I 9 )C O M M O N / A I R 1./A 13 , A 2 2 , E 11 ,R 2 2 * A 1 2 L 1. R 1 2 L 1 C 01 Hi Or! / Z / Z C A } Z C RO A T A E P S * N T H A >: f 0 Z H A X / * . 0 F - 3 , 7 ,5 /T F X P l I ) = T K P E P ( I }P E X P t I ) = P K F E G ( I )

1 9 X 2 = 1 . 0 - X ( I )F:6 = l ? 0 5 . 9 0 5 / (X( I ) * X 2 )R 7 = R 6M ( X ( I ) - X 2 ) / ( X ( I ) M X 2 )A = A 1 1 * X ( I ) + X 2 * ( A 2 2 + A ] 2 L l * X ( I ))B = 8 1 1 * X ( I ) + X 2 * ( R 2 2 + B 1 2 L l * X ( I ) ) f A X = A 11 - A 2 2 + A 1 2 L 1 M ( X X ( I ) )O R X = R 1 1 - R 2 2 + R 1 2 L 1 M ( X 2 - X ( I I J 7 C A B = X ( I ) * Z C A + X 2 * Z C R R Z = 1 2 0 5 . 9 0 5 D O M 3 . 0 0 0 M 7 X A B A3 2 L = A 1 2 L !B 1 2 L = B 1 2 L 1

C B E G I N I T E R A T I O N F O R T E M P E R A T U R E T K A N D V O L U M E VNNN = 0 r;T 0 T = l Z F S T = 0 . 2 9 G O T O 1 0 0

2 0 0 Z E S T = 0 • 2 7 fvTOT = 1 NNN = 1

1 0 0 T S T = T E X P ( 1 1 + 2 7 3 . 1 6

268

D P 5 0 N T S T = 1 » N T H A X H E V 0 D = M T S T - 2 -’M M l S T / 2) r-TR= l N Z E S T - 1

21 f'=lI F t P F V O D . E O . O ) A B T ( l ) = T S T - 0 . 2 5 * F L 0 A T ( M T S T )I F ( N E V O D . E O . ]. > A B T { 1) = T S T + 0 . 2 5 * F L O A T ( M T S T - 1 ) A R V I 1 ) = 1 2 0 5 . 9 0 5 * Z E S T * A R T ( 1 ) / P E X P t I ) I F t N T R . E O . 2 ) C-n T O '?_?A R T ( 2 ) = 0 • 9 9 9 * A R T ( 1 )A p V ( 2 ) = 0 • 9 9 8 * A R V (1 ) fv'TI-: = 2 G O T P 2 2

2 3 A R T ( 2 ) = 1 . 0 0 1 * A R T (1)A P V ( 2 ) = 1 • 00 2 A B V (1 )G! T FI = 3

2 2 P P 3 4 K = 1 t 3I F ( K • E 0 • 3 ) G O T O 2 6 T K = A R T ( 2 )I F t K . E 0 . 2 J G O T O 2 8

2 4 V = A B V (2)R T = R Z * T K T F F = P S O R T (T K )D 6= R 6* T KD 7 = R 7 - T KG O T O 3 0

2 6 T K = A R T ( 1)G O T O 2 4

2 E V = A R V ( 1 )3 0 D l = R T / ( t V - B ) * * 2 )

IFt K . K E . l ) G O T O 3 2V S T = VR T S T = R TX R T S T = R T / ( 3 . 0 D 0 * Z C A B )

3 2 D 2 = 1 . 0 D 0 / ( T H F * V * ( V + R ) )D ? = D 2 / ( V + R )D P X = D B X * ( D 1 + A * 0 3 ) - R A X * D 2 D P D V = A * 0 2 * ( 1 . 0 D 0 / V + 1 . 0 0 0 / ( V + R ) i - D ld v x = - d p x / o p d vD 5 = D L D G ( ( V+ R ) / ' / )G2= 1 . 0 0 0 / ( V + R ) - 1 . 0 0 0 / R * D 5C- ?=( 0 . 3 0 0 / ( V + P J + l . O D O / R ) / ( V + B ) - 0 5 / ( B * R )n 4 = A 1 2 L * D 5 + [ U 2 L * A * G 2 - 0 R X * ( 0 A X * G 2 - 0 B X * A * G 3 )DA = 2 . * 0 4 / ( 0 * 1 HI* ) + R T / ( V- P. ) * ( ( O R X * * 2 ) / ( V - B ) - 2 . * R 1 2 L )DMGX ( 1 , K ) = n 6 + ! K; - n p X= : : l )VX 0 2 PX = A 1 2 I . * 0 2 - R 1 2 L * ( 0 1 + 4 * 0 3 )D2 PX = 2 • * ( 0 2 P X + O R X * { R A X * 0 3 + 0 R X * ( 0 1 / ( V - R ) - A * 0 3 / ( V + B ) ) ) )0 4 = o ? * ( 0 AV * 0 P X - 2 . * A * P 1. 2L )D 4 = 0 4 - A * ( 0 3 X * * 2 ) * ( 0 3 / B + l . 0 0 0 / ( 3 . 000* ( V + B ) * * 3 ) )IV- = D 4 * f)BX + G2 * ( A 1 2 L * 0P X + P 1 2 L * 0 AX )D 4 = 6 * 0 0 0 * 0 4 / ( R * T I - ! F ) + 0 F > X * 0 1 * ( 2 . * { 0 P X * * 2 ) / ( V - R ) - 6 . O D O * R 1 2 L )r 2P v x = D A x * ( i . o n o / v + i . o n o / ( v + R ) ) - o r x * a / ( v + r ) * ( i . o n o / v + 2 . / ( v + r ) )02 PVX = 02P V X * O2- 2 . * n i / ( V —R ) * 0 RX r 5 = A 1 2 L + ( D A X * O R X - A + P ] 2 L ) / ( V + F )D 3 = D V X * ( 2 . / ( V + P ) + 1 . 0 i ) 0 / V ) + ? . * O R X / ( V + B )H 2 V X = 2 . * 0 5 - A * 0 r X * 0 3 / ( V + P-) + P ' ' X * 0 A X * ( 1 . 0 1) 0 / ( V + R ) + 1 . 0 D 0 / V )0 2 V X = D 2 V X * D 2 - 2 . * 0 1 * ( 0 1 2 L + DR X / ( V - R ) * ( D V X - P R X ) )0 3 = 1 . 0 0 0 / V+1 . 000 / ( V +F> )D 5 = D A X * D 3 - 2 . * A * O V X * ( 1 . 0 0 0 / ( V * V ) + 1 . 0 0 0 / ( V + B ) * 0 3 ) - A * D B X / ( V + B ) * ( D 3 +

l l . O P O / l V + P ) )0 5 = 0 5 * 0 2 + 2 . * D 1 / ( V - R ) * ( D V X - O B X )D2 VX = ( 0 P X * 0 5 / D P D V - 0 2 V'X ) / DPDV

3 4 D O G X { 2 » K ) = 0 7 + D 4 - D V X * ( 0 2 P V X * 0 V X + 2 . * D 2 P X ) - 0 P X * 0 2 V X 0 0 3 6 X = 1 t 2DOT ( ! ' ) = ( DMGX ( K T 1 ) - D M G X ( K , 3 ) ) / ( A P.T ( 2 ) - AR T ( 1 ) )

3 6 D D V ( K ) = { D M G X ( K , l ) - 0 N G X ( K f 2 ) ) / ( ARV ( 2 ) - ARV ( 1 ) )X J A C O B = D M T ( 1 ) * O N V ( 2 J - D M T { 2 ) * O M V ( 1 )D E L T = ( D M G X ( 2 , 1 ) * D U V ( 1 J - P N G X ( I t 1 ) * D M V ( 2 ) ) / X J A C O B

2?0

D E L V = ( D M G X { 1 T 1 ) * D N T I 2 ) - D M G X ( 2 * 1 ) '-’:D N T ( 1 ) ) / X J ACOP./ \ R T ( 3 ) = A B T f 2 ) + D E L T ATA/ ( 3 ) = A B V (2 ) + D E L VD T E S T = D A R S (D N G X ( 1 » 1 ) ) + D A R S ( D N G X ( 2 * 1 ) )]F{ ( n A B S ( D F L T ) . L T . E P S ) . A \ ' D . ( D A R S { D F L V ) . L T . E P S )

1 . A M D . ( D T F S T . L T . 1 . 0 F 6 ) ) G G T O 5 6 J F U\! • G E • 7 5 ) G O T n 48.I F ( A P T ( 3 ) . L T . n . 0 ) A R T ( 3 ) = A R T ( 2 ) / 2 .J F ( A R V ( 3 ) . L T . 0 .0 ) A B V ( 3 ) = A B V { 2 ) / 2 .T H F = D S r, R T ( X R T S T / 1 2 0 5 . 9 G 5 D 0 )F ( I ) = R T S T / ( V S T - R )~A / (T U F ^ V S T * ( V S T + R ] )I F ( ( A B T ( 2 ) . L T . l . 0 ) . D R . ( P ( I ) . L T . O . O ) ) G O T O 4 87 = P tI ) * V S T / X R T S TN T G T = N T 0 T + 11 F { U T O T . G F . 3 0 0 ) G O T O 5 2I F ( ( N . F 0 .2 ) . A N D . ( Z . G I . 0 . 4 5 ) ) G O T O 4 4N = N + 1D O 3 8 K = l » 2 A P T ( K ) = A ft T ( K + 1 )

3 8 A R V ( K ) = A R V ( K + l )G O T O 2 2

4 4 M Z E S T = N Z E S T + 1 Z F S T = Z E S T + 0 . 0 2 I F ( N Z E S T . L E . N Z M A X ) G O T O 2 1

4 8 I F ( N T R . E D . 2) G O T O 2 1 5 0 C O N T I N U E5 2 J F ( N N N . N E . l ) G O T O 2 0 0

W R I T E ( 6 f 5 4 ) X ( I ) , A , B , T K , V 5 4 F O R M A T (/ 4 X , 4 0 H I T E R A T 1 0 0 F O R T K A N D V H A S N O T C O N V E R G E D / 20X,'

1 6 H X U ) =» F 5 . 2 , l O X t 3 H A =, E 1 6 . 8 , 1 0 X , 3 H R = E 1 6 . 8 / 2 0 X » 1 8 H L A S T 2 V A L U E O F T K = , E 1 6 . 3 , 2 H K , 2 0 X , 1 7 H L A S T V A L U E O F V = , E 1 6 . 8 ,3 5 H C C / M / / )G O T O 5 0 0

5 6 T K = A B T (3)

V = A B V (3)C E N D I T E R A T I O N F O R T E M P E R A T U R E T K A N D V O L U M E V

R T = R Z * T K T C I ) = T K - 2 7 3 . 1 6P( I } = R T / ( V - P > > - A / ( D S O R T ( T K ) * V * ( V + B ) )R T = R T / ( 3 . 0 0 0 - Z C A P )Z = P ( I 1* V / R TUP IT F( 6,60) x m , A , R , P ( I ) » T ( I ) ?V,Z,NTOT,N

60 FnRM A T ( F 1 5 . 2 T 4 X , 2 E l 8 . 6 fF14.1,F10,l,Fll.l,F12.A,I 12.2H /,I3) 500 RETURN

E N D

rv)->3ro

o o S U B R O U T I N E E O K R E G ( I )

C R I T I C A L L O C U S C A L C U L A T I O N U S I N G K R E G L E W S K I ' S E O U A T I O N B A S E D O N T H E R E V I S E D C O R R E S P O N D I N G S T A T E S - C O M F R O M A L S O L U T I O N T H E O R Y I M P L I C I T R E A L * F ( A - H t P - Z )C O M M . O N / T P X / X (9 ), i:<r:EG(9 ) , P K P.EG (9)C P M H P K / D O / D A ,O B ,O A , O B , T K A , T K F P C A . P C BV A = D A * * 3V P - O R - * 3X B = 1 . O D O - X ( I )Z A - X t I ) / ( ( P B / D A ) * * 2 * X R + X ( I ) )Z B = l . C n O - Z AV A B = ( P A + O R 5 * * 3 / 8 . 0 0 0V Z = V A * X ( I ) + V 3 * X 8 + ( 2 . 0 D 0 * V A 6 - V A - V B ) * X ( I ) * X B E = 1 . 0 D 0 / 3 . O D O D Z = V7.**E G A M M A = 1 . 0 0 0D E Rl J = 2 .0 0 0 * G A M H A * ( Z B - Z A ) / (1. 0 0 0 / ( T K A * D A ) + 1 . 0 0 0 / { T K B * D B ) ) + T K A * D A * Z A

1 - T K B * 0 B * Z RV C = V Z - { 7 2 . 0 D O / 1 6 . 0 D O 5 * Z A * Z B * 0 Z / ( T K A * Z A + T K R * Z R ) * * 2 * ( D E R U * * 2 E A B = 2 .0 D O * G A M M A / ( D A / T K A + D R / T K B 5T 7. = 0 Z * ( T K A * Z A / OA+ T ! < . B * Z B / D R + ( 2 . 0 0 0 * E A B - T K A / D A - T K R / D R 5 * Z A * Z B )P Z = ( T Z / D Z ) * ! P C A * Z A +PC.P * Z P ) / ( TKA*7. A / P A + T K B * Z R / D B )T K R E G K = T Z + ( 3 n . 0[)0 / 1 6 • O D O ) * Z A * Z B / { T Z * D 7 * * 2 ) * ( O F F l.i** 2 ) 'T K R E G ( I 5 = T K R E G K - 2 7 3 . I 6 0 0O A B = 2 . O D O * G A M M A / ( 1 . 0 0 0 / 0 A + l . O D O / f l R )A L P H A = 5. 8 0 8 0 0 + 6 . 9 3 0 0 * ( O A * Z A + 0 B * 7 . R + ( 2. 0 0 0 * 0 A R - O A - O B 5 * Z A * Z B 5 E X = 2 . 0 D O / 3 . 0 D OP K R E G ( I) = P 7.* (1 . 0 D O + A L P H A * ( T K R E G K / T Z - 1 . 0 D O ) ) * ( V Z / V C ) * * E XR E T U R N "E N D

273

27^2* Comparison with Experimental Values

This program calculates the critical locus of a binary system and then compares the calculated v/ith the experimental values. The experimental values are used for the initial estimations of critical temperature and critical volume at each composition.


(1) System number and reduced interaction parameters for the Redlich-Kwong equation,

(2) System number and reduced interaction parameters for the Redlich-Ngo equation,

(3) Name of the binary system,(4-) Number of experimental points,<5) Experimental critical data for the system, i.e.,

composition, critical pressures, and critical temperatures,

(6) Critical compressibility factors for components A and B, and

(7) < v V / 3 and acentric factors for components Aand B.

As many systems may be run at one time as desired by arranging the data sets in the same order as shown above. The last card of the data sets should be a fictious system number "0" denoting the end of the data input.

275The output of the program consists of a printed table

of values comparing the calculated and experimental values for each method and a punched cards output as shown in Table 35 for each system.

o n CRITICAL LOCUS CALCULATION AND COMPARISON WITH THE EXPERIMENTAL

VALUES. S.C. PAK IMPLICIT RE AL-':B { A—H • O-Z )D I M E N S I O N T I T L E (2 0 ) , T D E V ( 1 1 ) , P D E V ( 1 1 ) , P C T D V 1 t i l ) , P C P D V 1 t i l ) ,

1 T D V K R G ( 1 1 ) » P D V K R G ( I I ) , P C T D V 2 t1 1 ) , P C P D V 2 ( 1 1 ) ,2TDEVRN( 11 ) tPDEVRI'M 11 ) »PCTDV3 t 11 ) »PCPDV3( 11 )C O H M O N / T P X / X ( 1 1 ) , P E X P ( 1 1 ) , T E X P ( 1 1 ) , T R N ( 1 1 ) , P R N ( 1 1 ) , P K R E G t 1 1 ) ,

1 T K R E G ( 1 1 )COMMOM/TP/ P(11)?T(11)C0MM0M/AB/A1,A2,B1,R2, TKA,TKR,NPT, M,NPTCON, NPTKRG,

1A12L1iB12Ll,A11,61!,A22,B22,NPTRM COMMON/A1B 1/ A 12L ,R12 L COMMON/Z/ ZCA,ZCB COMMON/DO/ DA,OB,OA,OB

500 READ(5,1) NSYS,A 12SR,B12SR C A12SR & B12SR FOR R-K EQUATION

1 FORMAT(I5,5X,2r20.8)] F{NSYS) 501,501 ,502

502 READ(5,1J NSYS1,A12SR1,B12SR1 C A12SR1 £ B12SR1 FOR R-N EOUATION

R E A D (5,3) (TITLE(I ),I=1,20)3 FORMAT(20A4)

READt 5,4) NPT,(X(I),PEXP(I ),TEXPtI),1=1,NPT)4 FORMAT{ 15/(3F10-5))

READ{5,5) ZCA, ZCB5 FORMAT(2F10.5)

READI5,20 >DA,DB,OA,OB20 FORMAT!4F10.5J

WRITE(6,8) NSYS,(TITLE!I),1=1,20),A12SR,B12SR 8 FORMAT(1H1 / 14H SYSTEM NUMBER, 14, 20X, 20A4,///57H THERMODYNAMIC1— EOUATION OF STATE M E T H O D REDLICH-KWONG///10X, 34HREDUCED2 INTERACTION PARAMETERS — , 10X, 7HA12SR = , F13.8, 10X, 7HB12SR = , 3F13.8 /// 29X, 23HREDLICH-KWONG CONSTANTS, 17X, 30HCALCULATED CRIT 4ICAL PROPERTIES, 11X, 10HITERATIONS If 12X, 2HXA, 16X, 1HA, 17X,

276

5 1 H B , l A X t 7 H P ( P S I A ) t 5 X , 4 H T ( C > , 5 X , 7 H V ( C C / M ) t 8X , 1 H Z / / ) T K A = T E X P {N P T ) + 2 7 3 . 1 6 D 0 B 1 = 1 0 4 . 4 8 0 0 3 D O * T K A / P E X P t N P T )A 1 = 5 9 4 9 . 8 8 9 9 0 0 - 8 1 * T K A S D S Q R T ( T K A )B ! l = 3 1 3 . 4 4 0 1 0 6 * Z C A * T K A / P E X P ( N P T 1 A 1 1 = 1 7 8 4 9 . 6 6 8 6 * 8 1 I * Z C A * T K A * D S O R T ( T K A )T K B = T E X P ( 1 J + 2 7 3 . 1 6 D 0 B 2 = 1 0 4 . 4 8 0 0 3 D 0 * T K B / P E X P ( 1 )A 2 = 5 9 4 9 . B 8 9 9 n o * B 2 * T K R * D S n R T ( T K B )B ? ? = 3 1 3 . 4 4 0 i n 6 $ 7 C P . * T K R / P E X P { 1 ) A 2 2 = 1 7 8 4 9 . 6 6 8 6 * B 2 2 * Z C B * T K B * n S Q R T ( T K B )A 1 2 L = { A 1 2 S R - 1 . 0 0 ) * ( A 1 + A 2 )B 1 2 L = < B 1 2 S P - 1 . D 0 J- ( P. 1+R2 )A 1 2 L 1 = ( A 1 2 S R 1 - 1 . 0 D 0 ) * ( A 1 1 + A 2 2 )E 1 2 L 1 = ( B 1 2 S R 1 - 1 . 0 0 0 ) * { R 1 1 + B 2 2 )M P T C 0 W = 0NPTPJ'! = 0A B T D V 1 = 0 . 0 0 0A B T D V 2 = 0 . 0 D 0A B T D V 3 = O . O D OA B P f} V 1 = 0 . 0 D OA 8 P D V 2 = 0 . 0 D 0A B P D V 3 = O . O D OT D E V 1 = 0 . 0 D 0T D E V 2 = O . O D OT D E V 3 = 0 . 0 D 0P D E V 1 = 0 . 0 D 0P O E V 2 = O . O D OP D E V 3 = 0 . 0 D 0T D V S G 1 = O . O D OT D V S P 2 = 0 . 0 D 0T D V S O 3 = 0 . 0 n 0P D V S O ! = O . O D OP D V S 0 2 = 0 • O D O

277

P D V S Q 3 = 0 . O D O f-'=f':P T - l D O I O O O 1 = 2 , M C A L L R K E Q S T ( I )T O E V ( I ) = T E X P ( I ) — T ( I ) - - - - -P O E V ( I )= P E X P ( I ) - P ( I )P C T D V I ( I ) = 10 0 . O D O * T D E V ( I ) / T E X P ( I )P C P D V 1 { I ) = 1 0 0 . 0 D 0 * P D E V ( I l / P E X P ( I )A B T D V 1 = A B T D V 1 +DA BS '( T D E V ( I ) )A F P D V 1= A B P P V 1 -i-DA B S { P D E V ( I) )T D E V 1 = T D E V 1 + T D E V ( I )P D E V 1 = P D E V 1 + P D E V ( I )T D V S 0 1 = T D V S 0 1 + T 01: V { I 1 * * 2 P D V S 0 1 = P D V S 0 1 -5-PDEV ( I 1 * * 2

1 0 0 0 C O N T I U I J E1 F ( 0 P T C O H . E O . 0 ) G O T O 3 0 X N P C 0 0 = F L O A T ( N P T C O N )A B T A V 1 = A B T D V 1 / XL! P C O NA R P A V 1 = A R P D V 1 / X M P C 0 NT B I A 5 1 = T D E V 1 / X M P C O NP R I A S 1 = P D E V 1 / X 0 P C 0 MT R K S 1 = D S O R T (T D V S 01/ X M P C O N )P R M S 1 = D S 0 R T ( P D V S Q 1 / X N P C 0 N )

30 WRITE( 6 , 9 )9 F O R M A T { / / 3 4 X » 1 4 H P R E S S U R E ( P S I ) , 3 7 X , 1 5 H T E M P E R A T U R E ( C ) / / 7 X ,

1 1 F X , 1 4 X , 5 H E X P E R , 7 X , 4 F C A L C , 7 X , 3 H D E V , 5 X , 7 H P C T D E V , 1 3 X , 5 H E X P E R , 7 X , 4 H C 2 A L C , 8 X , 3 H D E V , 6 X , 7 H P C T D E V / / )T (1 ) = T E X P {1)T R M ( 1 ) = T E X P {1)T K R E G ( 1 ) = T E X P (1 )P ( 1) = P E X P 1 1)P R N ( 1 ) = P E X P ( I )P K R E G f 1 ) = P E X P (1)T ( NPT ) = TE XP ( NPT )T R N t N P T ) = T E X P ( N P T )

2?8

T K R E G ( N P T ) = T E X P ( N P T )P {N P T ) = P E X P (N P T )P R N I N P T ) = P E X P ( M P T )P K R E G t N P T ) = P E X P ( M P T )T 0 E V ( 1 ) = 0 . 0 P O E V ( 1 ) = 0 . 0 T D E V R r J ( 1 ) = 0 . 0 P D E V R N ( 1 ) = 0 . 0 T D V K R G l 1 ) = 0 . 0 P D V K R G t 1. ) = 0.0 T D E V (N P T ) = 0 . 0 P O E V { T!P T ) = 0 . 0 T D E V R M ( N P T ) = 0 . 0 P D E V R K t N P T ) = 0.0 T D V K R G ( N P T ) = 0 .0 P D V K R G t N P T ) = 0 . 0 P C T D V 1 t 1 ) = 0 . 0 0 0 P C P D V K 1 ) = o . o n o P C T D V l ( N P T ) = 0 . 0 0 0 P C P D V 1 ( O P T ) = 0 . 0 D 0 P C T D V 2 t 1 ) = 0 . 0 0 0 P C T D V 2 1 N P T } = 0 . 0 D 0 P C P D V 2 ( 1 ) =0.000 P C P D V 2 ( M P T ) = 0 . 0 D 0 P C T D V 3 ( 1 ) = 0 . 0 P C P D V 3 ( 1 ) = 0.0 P C T D V 3 (M P T ) = 0 .0 P C P D V 3 ( N P T ) = 0 . 0W R I T E ! 6 , 1 0 ) ( X ( IJ r P E X P ( I ),P ( I ) T P D E V ( I ) ,P C P D V 1 ( I ) , T E X P ( I )» T ( I )»

1 T D E V ( I ) t P C T D V l ( I ) , 1 = 1 , N P T )1 0 F O R M A T ( F 1 0 . 2 , 6 X , 2 F U . 1 , F 1 0 . 1 , F I 2 . 2 , 6 X , 2 F 1 2 . 2 , F H . 2 , F 1 2 . 2 )

W R I T E ! 6 , 1 1 ) A C P A V I , A R T A Y 1 , P B I A S 1 , T B I A S 1 , P R M S 1 , T R M S 111 F O R M A T ( / / 6 X » 9 H A V G . A C S . , F 3 A . 2 , 1 1 X , F A 1 . 2 / 6 X , 4 H R I A G , F 3 9 . 2 , 1 2 X , F 4 0 .2

l / f c X , 3 H R M S t F 4 0 . 2 t 1 2 X , F 4 0 . 2 )

279

W R I T E ( 6 , 1 6 ) N S Y S , ( T I T L E ! I ) , I = 1 T 2 0 ) , A 1 2 S R 1 , B 1 2 S R 116 FORMAT(1H1 / 14H SYSTEM NUMRER, I * , 20X, 2 0 A 4 , / / / 5 5 H THERMODYNAMIC

1 — E O U A T I O N O F S T A T E M E T H O D - - - R E D L I C H - N G O / / / 1 0 X , 3 4 H R E D U C E D2 I N T E R A C T I O N P A R A M E T E R S — , 1 0 X , 7 H A 1 2 S R = , F 1 3 . 8 , 1 0 X , 7 H R 1 2 S R = , 3 F 1 3 . F / / / 2 ^ X , 2 3 H R E f1L I C H - N G O C O N S T A N T S , 1 7 X , 3 0 H C A L C U L A T E D C R I T 4 I C A L P R O P E R T I E S , U X , 1. O H I T E R A T Ii .IMS / / ! 2 X , 2 H X A , 1 6 X , 1 H A • 1 7 X ,5 1 H B , 1 A X , 7 H P ( P S I A )* 5 X , 4 H T ( C ) , E X , 7 H V ( C C / M ) , 8X , 1 H Z / / )

d o ? n n n t = ? . mr.A I I D M P n c T I T 'T D E V R N ( I )= T E X P ( I ) - T R M ( I )P D E V R N f I ) = P E X P ( I )-PRfl ( I )P C T D V 3 ( I ) = 100. 0 D 0 * 7 D E V R N ( I ) / T E X P ( I )P C P D V 3 ( I ) = 1 0 0 . O D O M p O E V R N ( I ) / P E X D ( I )A B T D V 3 = A R T D V 3 + D A B S (T D E V R N ( I ))A P P D V 3 = A R P D V 3 + D A B S ( P D E V R N ( I ) )T D E V 3 = T D E V 3 + T D p V R N ( I ) _P D E V 2 = P D E V 3 + P D E V R I J ( I ) 'T D V S 0 3 = T D V S 0 3 + T O F V R N ( I ) * * 2 P D V S 0 3 = P D V S 0 3 + P D E V R I ! ( I ) * * 2

2 0 0 0 C O N T I N U E1 F I N P T R N . E O . 0 ) G O T O 4 0 XNPTRi\! = F L O A T ( N P T K N )A B T A V 3 = A B T D V 3 / X N P T R N A B P A V 3 = A 3 PI) V 3 / X N P T R N T B 1 A S 3 = T D E V 3 / X N P T R N P R I A S 3 = P D E V 3 / X H P T R N TRi ' S 3 = D S 0 R T ( T D V S 0 3 / X N P T R N )P R M S 3 = D S 0 R T ( P D V S 0 3 / X N P T R N )

4 0 W R I T E ( 6 , 1 7 )1 7 F O R M A T ( / / 3 4 X , 1 4 H P R E S S U R E ( P S I ) » 3 7 X , 1 5 H T E M P E R A T U R E ( C ) / / 7 X ,

1 1 H X , 1 4 X , 5 H E X P E R , 7 X , 4 H C A L C , 7 X , 3 H D E V , 5 X , 7 H P C T D E V , 1 3 X , 5 H E X P E R , 7 X , 4 H C 2 A L C , 8 X , 3 H D E V , 6 X , 7 H P C T D E V / / )

WRITE( 6 , 1 8 ) ( X ( I ) , PEXP( I ) , PRN( I ) , PDEVRN( I ) , PCPDV3( I ) , TEXP( I ) ,1 T R N ( I ) , T D E V R N ( I ) , P C T D V 3 ( I ),1 = 1 , N P T )

280

18 F O R M A T ( F 1 0 . 2 , 6 X , 2 F 1 1 . 1 , F 1 0 . 1 , F 1 2 . 2 , 6 X » 2 F 1 2 . 2 , F l l . 2 , F 1 2 . 2 )WRIT E ( 6 , 1 9 ) A13 PA V3 , A BTA V3 , PB I AS3 , TBI AS3 , PRMS 3 , TR MS 3

19 FORMAT!/ / 6X, 9HAVG* ABS. , F 3 4 . 2 , 1 1 X » F 4 1 . 2 / 6 X » 4 H R I A S , F 3 9 . 2 » 1 2 X , F 4 0 . 2I / 6 X , 3 HRMS, F 4 0 . 2 , 1 2X , F 4 0 . 2 )

DO 3 0 0 0 1 = 2 fMCALL EOKRFG( I )TDVKRG( I )=TEXP( I ) -TKREG( I )PDVKRG( I)=PEXPI I J-PKREG( I )PCTDV2 ( I ) = ! OO.ODO*TOVKRG( I ) /TEXP ( I )PCPDV21I) = 100 . nn0- PDVKRG(I ) / PEXP( I )ARTDV2=ABTDV2+UARS(TDVKRG( I ))ABPDV2=AB PDV2+DABS( PDVKRG( I ) )TD E V2 = T0 E V2 +T D VK RG ( I )PDEV2 = PDEV? + PDVKRG( I )TDVS02 = TDVS02 +TDVKRG( I ) * * 2 PDVS02 = PDVS02 + PDVI'RG { I ) **2

3 0 0 0 CONTINUENPTKRG=NPT-2 XM = FLOAT! HPTK RG)AB T A V 2= AB T D V 2 / XM ADPAV2=ABPDV2/XM T R IA S 2 = TD E V2 / XM PBIAS2=PDEV2/XM TRMS2 = DS0RT t TDVSQ2/XM)PRMS2=DS0RT( PDVS02/XM)WRITE!A, 12) MS Y S , ( T I T L E ( I > , 1 = 1 , 2 0 )

12 FORMAT(1 Ml / 1AH SYSTEM NUMBER* I 4 , 2 0 A 4 / / / 5 7 H REVISED CORRESPONDI IMG STATES - COMFORMAL SOLUTION THEORY)

WRI TE( 6 , 13 )13 FORMAT!/ / SAX * 14HPRESSUPF ( PS I ) *3 7 X * 15HTEMPFRATURE (C) / / 7X,

I I MX, 1 4 X, BHE XPER » 7X »4HCALC, 7 X , 3 HOEV, 5 X »7HPCT DEV, 1 3 X, 5 HEXPER, 7 X, 4 HC 2ALC, LX» 3HDEV, 6 X , 7HPCT Oi:V / / )

WRITE!6 , 1 4 ) ( X ( I ) , P E X P ( I ) , PKRFG!I) , PDVKRG!I) , PCPDV2 t I ) , TEXP( I ) , 1TKRFG( I ) , TDVKRG( I ) , PCTPV2 t I ) , 1 = 1 , NPT)

281

14 F 0 R M A T ( F 1 0 . 2 , 6 X , 2 F 1 1 . 1 , F 1 0 . 1 , F 1 2 . 2 , 6 X , 2 F1 2 . 2 , FI 1 . 2 , F I 2 . 2 )WRITE!6 , 1 5 ) ABPAV2*ABTAV2.PBIAS2»TPIAS2»PRMS2»TRMS2

15 FORMAT!/ / 6X,9HAVG. A R S . , F 3 4 . 2 , 1 I X , F 4 1 . 2 / 6 X , 4 H B I A S , F 3 9 . 2 , 1 2 X , F 4 0 . 2 1 / 6 X , 3 H R M S , F 4 0 . 2 , 1 2 X , F 4 0 . 2 )

WRI TE( 7 , 2 0 0 ) N S Y S , ( T I T L E ! I ) , I = 1 , 1 7 ) , A l ? S R , B12SR200 FORMAT ( 33X, 14H SYSTEM NUMBER , 15 , / / 1 2 X , J. 7A4/ / 13X, 26HRED. I NT . PAR.

1 P-K A12SR = , F1 2 . 8 , 3 X, 7 1 ' P . 1 ? SR = , F ) 2 . 8 )WRITE!7 , 2 2 0 } A1 2SR 1 , B1 2SR1

220 FORMAT! 13X, 26HRED. ' U T . PAR. R-M A ] 2SR = , F 1 2 . 8 , 3 X ,17HB1 2S I! = f F 1 2 . R / )

WRITE( 7 , 2 0 1 )201 FORMAT!SAX,14HTEMPERATURE{ C) / )

W R I T E { 7 , 2 0 2 }202 FORMAT!I3X, 4HX(A) , 3X, 4HTEXP, 4X, 5HRK- EO, 4X, 3HDEV, 4X, 5HRN- E0,

14 X, 3 HD E V, 4 X » 5 HK RE GK, 4X, 3HDEV/ )WRITE!7 , 2 0 3 ) ( X( I ) ,TEXPI I ) , T ( I ) , T O E V ( I ) , T R N ! I ) , TDEVRN!I) , TKREG! I J ,

1TDVKR0!I ) , 1 = 1 ,MPT )203 FORMAT( F 1 7 . 2 , F 7 . 1 , F 9 . 1 , F 7 . 1 , F 9 . 1 , F 7 . 1 , F 9 . 1 , F 7 . 1 )

WRITE( 7 , 2 0 4 ) ABTAV1, ABTAV3, ARTAV2»TBIAS1»TBI AS 3 , TBI AS 2 , TRMS1, TRMS3 1 , TRMS2

204 FORMAT!/ 2 2X , 8I1AVG. ARS, F 1 0 . 1 , 2 F 1 6 . 1 / 2 2 X , 4HRI AS, F 1 4 . 1 , 2 F 1 6 . 1 / 2 2 X , 1 3 H RMS , F 1 5 . 1 , 2 FI 6 . 1 / )

WRITE!7 , 2 0 5 )205 FORMAT{ 3 6 X,14HPRESSURE!PS IA J/ )

WRITE!7 , 2 0 6 )2 0 6 FORMAT! 13X, 4HX( A ) , 3 X, 4HPEXP, 4X, 5 HRK- E0 , 4X, 3HDEV, 4X, 5HRN-E0,

14 X, 3MDEV, 4 X , 5HKREGK, 4 X , 3MDEV/)WRITE!7 , 2 0 7 ) ( X ( I ) , P E X P ( I ) , P ( I ) , P O F V ! l ) , P R M ( I ) , PDEVRN!I) , PKREG( I ) ,

1 PDVKRG!I) , 1 = 1 , MPT)20 7 F O R M A T ( F 1 7 . 2 » F 7 . 1 , F 9 . 1 , F 7 . 1 , F 9 . 1 , F 7 . 1 , F 9 . 1 , F 7 . 1)

WRITE!7 , 2 0 R) ARPAV1, ABPAV3, ABPAV2 , PBI AS1 , PRI AS 3 , PR I A S 2 , PRMSI, PRMS3 1, P R M S 2

208 FORMAT!/ ?2X»8HAVG. ABS , F 1 0 . 1 , 2 F 1 6 . 1 / 2 2 X , 4 H B I A S , F 1 4 . 1 , 2 F 1 6 . 1 / 2 2 X , 1 3 H R M S , F 1 5 . 1 , 2 F 1 6 . 1 / )

282

V'R ITE ( 7 » 209 )209 FORMAT( 13X

1 J* *»(» %** »'• «’i / %»|» »!’ '■f »|» *1' T' 'J' '|» / I

WRITE!7 , 2 1 0 }210 FORMAT( 13X*39HRK-EP = REOLICH-KKDNG EQUATION OF STATE/

1 13X t ? 7HRN-E0 = REDLICH-NGO EPUATJON OF STATE/2 1 3 X»29HKREGK = KREGLEWSKI-KAY METHOD)

GO TO 500 5 0 1 STOP

END

o o

o o

S U B R O U T I N E R K E O S T ( I )C A L C U L A T I O N O F C R I T I C A L L O C U S F O R B I N A R Y S Y S T E M S U S I N G T H E R E D L I C H - K W O N G E O U A T I O N O F S T A T EI T E R A T I O N B Y N E W T O N S M E T H O D F O R 2 E O S . , S E C A N T M O D I F I C A T I O N P R O G R A M E D B Y D . W . H I S S O N G A N D M O D I F I E D B Y S . C . P A K I M P L I C I T R F A L *F. t A - H . 0 - 7 )D I M FI'S I O N A B T ( 3 ) » A B Y 13 ) , D N G X ( 2 ,3 I , D N T t 2 ) , D N V ( 2 )C O M M O N / T P X / X t 1 1 J , P E X P ( 1 1 1 - T E X P l 1 1 ) , T R N ( 1 1 ) , P R N ( 1 1 ) , P K R E G t 1 1 ) ,

1 T K R E G ( 1 1 )C O M M O N / T P / P t 11 ) ? T ( 1 1 }C 0 M M 0 N / A B / A 1 , A 2 » B 1 , B 2 , T K A , T K B , N P T , M t M P T C O N , N P T K R G ,

1 A 1 2 1 I , 3 1 2 1 1 * A I I , B 1 1 , A 2 2 , R 2 2 , N P T R N C O M M O N / A 1 B 1/ A 1 2 1 , R 1 2 L D A T A E P S * N T M A X t N Z M A X / 4 . 0 E - 3 , 7 , 5 /

1 9 X ? = 1 . 0 - X ( I IR 6 = 1 2 0 5 . 9 0 5 / ( X ( I ) * X 2 )R 7 = Pn6* ( X ( I J - X 2 )/ ( X ( I ) * X 2 )A = A 1 * X ( I ) + X 2 * ( A 2 + A 1 2 L * X { I ))R = 8 1 * X ( I ) +X2'-;: ( B 2 + B 1 2 L * X ( I ) )D A X = A 1 - A 2 + A 1 2 L * I X 2 - X ( I ) )D R X = R 1 - B 2 + B 1 2 L * ( X 2 - X ( I ))

C B E G I N I T E R A T I O N F O R T E M P E R A T U R E T K A N D V O L U M E VN N N = 0 N T 0 T = 1 7 E S T = 0 . 3 5 G O T O 1 0 0

2 0 0 7 E S T = 0 . 3 1 N T O T = 1 N N N = 1

1 0 0 T S T = T E X P ( I ) + 2 7 3 . 1 6 D O 5 0 N T S T = 1 , N T M A X M E V O D = N T S T - 2 * I N T S T / 2 J NTR = 1 N Z E S T = 1

2 1 N - lJ F ( N E V O O . E O . O ) A B T t l } s T S T - 0 . 2 ! > * F L 0 A T ( N T S T )I F < N E V O D . E O . l ) A B T (1 ) = T S T + 0. 2 5 - = F L O A T ( N T S T - 1 J A B V ( 1 ) = 1 2 0 5 . 9 0 5 * Z E S T * A B T ( 1 J / P E X P ( I )I F ( N T R . F 0 . 2 ) G O T O 2 3 A B T ( 2 ) = 0 . 9 9 9 * A B T ( 1 )A B V ( 2 ) = 0 . 9 9 8 * A R V ( 1 )N T R = 2 G O T O 2 2

2 3 A B T ( 2 ) = 1 • 0 0 1 * A B T (1)A R V ( 2 ) = 1 . 0 0 2 * A R V ( 1 )N T R = 3

2 2 D O 3 4 K = 1 » 3I F ( K . E O - 3 J G O T O 2 6 T K = A R T (2)I F { K . E O . 2 ) G O T O 2 8

2 4 V = A B V (2)R T = 1 2 0 5 . 9 0 5 * T K T H F = D S Q R T {T K )D 6= R 6* T KD 7 = R 7 * T KG O T O 3 0

2 6 T K = A B T {1)C O T O 2 4

2 8 V = A B V t 1)3 0 D l = R T / ( I V ~ R ) 4 ^ 2 )

J F C K . B E . l ) G O T O 3 2 V S T = V R T S T - R T

3 2 D 2 = 1 . 0 D 0 / ( T H F * V * ( V + B ) )D 3 = D 2 / ( V + B )D P X = D B X * ( D 1 + A * D 3 ) - D A X * D 2 D P D V = A * 0 2 * ( l . O D O / V + l . O D O / (V + B) J - D l O V X = - D P X / D P D V

D 5 = D L 0 G ( ( V + B I / V )G 2 = 1 . 0 0 0 / ( V + B ) - 1 . 0 D 0 / R * D 5G 3 = ( 0 . 5 0 0 / ( V + B ) + l . O D O / P ) / t V + B ) - 0 5 / ( B * B )D 4 = A 1 2 L * D 5 - ? - B l 2 L * A * G 2 - P R X * ( D A X * G 2 - P R X :’:A * G 3 )D 4 = 2 . * D 4 / ( B * T H F ) + R T / ( V - R l * ( ( D 5 X * * 2 ) / ( V - 8 ) - 2 . * R 1 2 L )D M G X ( 1 » K ) = D 6 + D 4 - D P X * D V X 0 2 P X = A 1 2 L * 0 2 - B ). 2 L * ( D 1 + A * D 3 )Q 2 P X = 2 . * ( D 2 P X + n B X :M D A X * n 3 + O R X * ( n i / ( V - l 3 ) - A * D 3 / ( V + R ) ) ) ) p l = G 3 ( p A X * D R X - 2 . * A * P 1 ? L )D 4 = D 4 - A * ( O R X * * 2 ) * { 0 3 / R + ! . 0 0 0 / (3 . O n o * { V + R ) * * 3 ) )D ^ = D 4 * D B X + G 2 * ( A 12L*nr'X + B}.2L * D A X )D 4 = 6 . 0 n n * n 4 / ( B * T H F ) + D R X * 01 * ( 2. * (0 R X * * 2) / ( V - R ) - 6. 0 n 0 * R 12 L )P 2 P V X = D A X 4 (1 . n o n / V +1 .0 P rv I V + P ) ) “ 0 F- X * A / t V + R ) * ( 1. O D O / V + 2 . / t V + B ) )D 2 P V X = 0 2 P V X 40 2 - 2 . * PI / ( V - R ) * 0 R X r ? = A 1 2 L + ( D A X * D B X - A * R 1 2 L ) / ( V + B )D 3 = D V X * ( 2 . / ( V + R J + l . 0 0 0 / V ) + 2 . * f ) R X / < V + B)P 2 V X = 2 . * D 5 - A * D R X * D 3 / ( V + B ) + D V X * D A X * ( 1 . 0 0 0 / ( V + R ) + 1 . O D O / V ) D 2 V X = Q 2 V X * n 2 - 2 . * D L * ( R 1 2 L + D B X / (V - R ) * ( D V X - D B X ))D 3 = 1 . O D D / V + 1 . 0 0 0 / ( V + B }D 5 = D A X * D 3 - 2 . * A * O V X * ( l . D D O / ( V * V ) + 1 . 0 0 0 / (V + B > * D 3 ) - A * D B X / ( V + B ) * ( D 3 +

1 1 . O D D / ( V + B ) )D 5 = D 5 * D 2 + 2 . * D 1 / ( V - R ) * ( D V X - D B X )D 2 V X = ( P P X + D 5 / D P D V - D 2 V X ) / O P O V

3 4 D M G X (2 » K )= D 7 + D 4 - D V X * ( 0 2 P V X * 0 V X + 2 . * D 2 P X ) - 0 P X * D 2 V X D P 3 6 K = 1 t 2D M T (K } = ( D i ! G X ( K ,1 ) - D N G X ( K ,3 ) ) /< A B T ( 2 ) - A B T I 1 ) )

3 6 D M V ( K ) = ( D M G X ( K , 1 > - D M G X ( K , 2 ) ) / ( A B V ( 2 ) - A B V ( 1 ) )X J A C O B = D M T ( 1 ) * D M V (2 J - D H T ( 2 ) * O M V (1)D E L T = ( D M G X ( 2 i1 ) * D N V ( 1 ) - D M G X ( 1 , 1 ) * 0 N V ( 2 ) ) / X J A C O B D F L V = ( D M G X ( 1 » 1 ) * D N T ( 2 ) - D N G X ( 2 » 1 ) * D N T ( 1 ) ) / X J A C O B A R T ( 3 ) = A B T (2 ) + D E L T A R V ( 3 ) = A B V ( 2 ) + D E L VD T E S T = D A B S (D M G X ( 1 » 1 ) ) + D A B S (D M G X ( 2 , 1 ) )I F U D A B S ( D E L T ) . L T . E P S ) . A N D . ( D A B S ( D E L V ). L T . E P S )

1 . A M D • ( D T E S T . L T . 1 . 0 E 6 ) ) C-P T O 5 6

286

I F t N . G E . 7 5 ) G O T O 4 8I F ( A B T ( 3 ) . L T . 0 . 0 ) A B T ( 3 ) = A B T (.2) / 2 .I F t A B V ( 3 ) . L T . 0 . 0 ) A B V ( 3 ) = A R V ( 2 ) / 2 .T H F = D S O R T ( R T S T / 1 2 0 5 . 9 0 5 0 0 )P ( I ) = R T S T / ( V S T - R ) - A / ( T H F * V S T * t V S T + B ) )I F ( ( A B T 1 2 ) . L T . l .0 ) . O R . ( P ( T ) . L 1 . 0 . 0 ) ) G O T O 4 8Z = P( I ) * V S T / R T S TN T 0 T = N T 0 T + 1I F t N T O T . G F . 3 r i O ) GO- T O 5 2I F ( { M . E 0 . 2 ) . A N D . t Z . G T . 0 . 4 5 ) ) G O T O 4 4N = N + 1n o 3 8 K = l , 2 A R T ( K )= A 3 T (K + l )

3 8 A R V ( K ) = A R V t K + 1 )C-0 T O 2 2

4 4 M Z L - S T = (’Z F S T + 1 7 E S T = Z F S T + 0 . 0 2 I F ( N Z t i S T . L E . N Z M A X ) G O T O 21

4 F I F t M T R . E O . 2 ) G O T O 2 1 5 0 C O N T I N U E5 2 I F ( N N N . N E . l ) G O T O 2 0 0

U R I T F ( 6 , 5 4 ) X ( I ) , A , B » T K , V 5 4 F O R M A T ! / 4 X , 4 0 H I T E R A T I O N F O R T K A N D V H A S N O T C O N V E R G E D / 2 0 X T

I6 H X t I ) =, F 5 .2 T 1 0 X , 3 H A =, E 1 6 . 8 , 1 0 X , 3 H B = E 1 6 . 8 / 2 0 X , 1 8 H L A S T 2 V A L U E O F T K = , E 1 6 . 8 f 2 H l(, 2 0 X , 1 7 H L A S T V A L U E O F V =. E 1 6 . 8 ,3 5 H C C / M / / )T t I ) = T E X P ( I )P( I ) = P E X P t I )G O T O 5 0 0

5 6 T K = A R T (3)V = A B V ( 3 )

C E N D I T E R A T I O N F O R T E M P E R A T U R E T K A N D V O L U M E VR T = 1 2 0 5 . 9 0 5 - T K T t I ) = T K - 2 7 3 . 1 6

28?

P ( I ) = R T / ( V - B ) - A / { D S P R T (T K )❖V* (V+ B) )Z = P ( J ) * V / R TV.'R I T E { 6t 60 ) X I I ) , A f B t P < I ) » T ( I ) - V , Z , N T n T , N

60 F n R M A T ( F 1 5 . 2 » 4 X , 2 E l f i . 6 , F 1 4 . 1 t 2 f : 1 1 . 2 t F 1 1 . 4 , I 1 2 , 2 H /, 1 3 ) N P T C O N = M P T C O M +1

5 0 0 R E T U R N END

288

S U B R O U T I N E R M E O S T ( I )C A L C U L A T I O N O F C R I T I C A L L O C U S F O R B I N A R Y S Y S T E M S U S I N G T H E R E D L I C H - M G O E Q U A T I O N O F S T A T EI T E R A T I O N R Y N E W T O N S M E T H O D F O R 2 E O S . , S E C A N T M O D I F I C A T I O N P R O G R A M E D B Y D . W . H I S S O N G A N D M O D I F I E D B Y S . C . P A K I M P L I C I T R E A L * a ( A - H , 0 - 2 )D I M E N S I D M A BT 13 ) T A B V ( 3 ) t D N G X t 2 , 3 ) , D M T ( 2 ) . D N V ( 2 1 D I M E N S I O N P ( 111 ,T (11 IC O M M O U / T P X / X { I I )* P E X P ( 1 1 ) » T E X P t 1 1 ) » T R N { 11 )» P R N ( I I ) . P K R E G ( 1 1 ) ,

1 T K R E G I 11 )C O M M O N / A B / A 1, A 2 , B 1 » B 2 , T K A , T K 3 , N P T ? U , N P T C O M * M P T K R G ?

1 A 1 2 L 1 , 3 1 2 L 1 , A 1 1 , B 1 1 , A 2 2 , B 2 2 , N P T R N C O M M O N / 7./ Z C A , Z C BD A T A E P S , N T H iA X tN Z H A X / 4 . 0 E - 3 » 7 ,5 /

1 9 X 2 - 1 - 0 — X ( I )R 6 = 1 2 0 5 . 9 0 5 / ( X ( I ) * X 2 I R 7 = R 6 = M X m - X 2 ) / ( X ( I ) * X 2 )A = A 11 M X ( I1 + X 2 * t A 2 2 + A 1 2 L 1 * X ( I ))B = R 1 1 * X ( I ) + X 2 - ( B 2 2 + R 1 2 L l - X ( I ))D A X = A 1 1 - A 2 2 + A 1 2 L 1 * ( X 2 - X ( I ) J D B X = B 1 1 - B 2 2 + B 1 2 L 1 :': ( X 2 - X ( I ) )? C A R = X ( I ) * Z C A + X 2 * Z C B R Z = 1 2 0 5 . 9 0 5 0 0 - 3 . O D O - Z C A B A 1 2 L « A 1 2 L 1 B 1 2 L = B 1 2 L 1

C B E G I N I T E R A T I O N F O R T E M P E R A T U R E T K A N D V O L U M E VN N N =0 I'-’T C T = 1 Z E S T = 0 . 2 9 C-0 T O 1 0 0

2 0 0 Z E S T = 0 . 2 7 N T O T = 1 NNN = 1

1 0 0 T S T = T E X P ( I ) + 2 7 3 . 1 6

289

D O 5 0 N T S T = 1 , O T M A X - N E V 0 D = N T S T - 2 * (M T S T / 2 )NTR=*1N 2 E S T = 1

21 N=1I F ( N E V O D . E Q . O ) A R T ( 1 > * T S T - 0 . 2 5 * F L 0 A T ( N T S T ) ] F ( M E V 0 D . E 0 . 1 ) A R T ( 1 ) = T S T + 0 . 2 5 * F L O A T I U T S T - 1 ) A R V ( 1 ) = 1 2 0 5 . 9 0 5 * Z E S T * A R T ( 1 ) / P E X P f I ) I F ( N T R . F P * 2 ) G O T O '22 A R T ( 2 ) = 0 . 9 9 9 * A R T ( 1)A P V ( ? J = 0 . 9 9 8 * A P \ M 1 )MTR = 2 G O T O 2 2

2 3 A R T (2) = 1 • 0 0 1 - A R T (1)A P V ( 2 ) = 1 . 0 0 2 - A R V (1)N T R = 3

2 2 T O 3 k K - 1 , 3 I F ( K . E 0 . 3 ) G O T O 2 6 T K = A R T (2 )I F I K . E 0 .2 ) G O T O 2 8

2 A V = A R V (2 )R T = R Z * T K T H F = D S O R T ( T K )D 6 = R 6:'-'-TK D 7 = R 7 - T K G O T O 3 0

2 6 T K = A R T ( 1)G O T O ?A

2 8 V = A R V (1)3 0 0 1 = R T / ( ( V - R ) - * 2 J

J F ( K . O E . l ) G O T O 3 2V S T = VR T S T = R TX P T S T = R T / ( 3 . 0 D O * Z C A B )

290

3 2 0 2 = 1 . 0 D 0 / ( T H F * V * ( V + B ) )D 3 = D 2 / { V + R )D P X = D B X + ( D I + A + 0 3 ) - D A X + 0 2 P P D V = A + D 2 + ( 1 . 0 D 0 / V + 1 . 0 D 0 / ( V + R ) ) — D 1 D V X = - D P X / D P D V D 5 = D L 0 G ( ( V + B ) / V )G 2 = 1 . 0 0 0 / ( V + B )-]. . 0 D 0 / B + 0 5G 3 = (0 . 5 0 0 / ( V + B ) + 1 . 0 0 0 / R ) / ( V + B ) - 0 5 / ( B + B )0 4 = A 1.2 L + 0 5 + 01 2 L + A + 0 2 - 0 R X + ( 0 A X * G 2 - 0 B X * A * G 3)D 4 = 2 . + 0 4 / ( R * T M F J + R T / ( V - n } + ( ( n p X + + 2 ) / ( V - P ) - 2 . * R 1 2 L )D M G X ( 1 , K ) = 0 6 + D + - 0 P X + 0 V X 0 2 P X = A 1 2 L + D 2 - B 1 2 L + ( D l + A + 0 3 )0 2 P X = 2 . + ( n 2 P X + n R X + ( n A X + n 3 + D B X + ( n i / ( V - R ) “ A + D 3 / ( V + B ) )))(Vi = C- 3 * ( 0 A X + 0 R X - 2 . * A * f11 2 L )D 4 = 0 4 - A + ( L W X + + 2 ) + ( G 3 / B + 1 . 0 0 0 / ( 3 . 0 0 0 + ( V + R )+ + 3 ) )D 4 = 0 4 + 0 B X + 0 2 + ( A 1 2 L + 0 R X + R ] 2 L + 0 A X )0 4 = 6 . 0 0 0 + 0 4 / ( R + T H F ) + 0 0 X + F H + ( 2 . * (0 R X + + 2 ) / ( V - R ) -6 . O P O + B 1 2 L )0 ? P V X = 0 A X + ( 1 . O O O / V + l .000/ (V + R ) ) - O P X + A / ( V + B ) + ( 1 . 0 D 0 / V + 2 . / ( V + B ))0 2 P V X = 0 2 P V X + 0 2 - 2 . + 0 1 / ( V - R ) + O P X D 5 = A 1 2 L + ( 0 A X + 0 R X - A + P 1 2 L ) / (V + P)D 3 = 0 V X + ( 2 . / ( V + R ) + l . O D O / V ) + 2 . + O R X / ( V + R )D 2 V X = 2 . + 0 5 - A + n rj X + 0 3 / ( V + P ) + D V X + O A X + ( 1. 0 0 0 / t V + B ) + 1. O D O / V )D 2 V X = D 2 V X + 0 2 - 2 . + D 1 + ( R 1 2 L + 0 R X / ( V - R ) * ( 0 V X - O B X ) )D 3 = l . O D O / V + 1 . 0 0 0 / ( + + B )D 5 = D A X + P 3 - 2 • + A + D V X + ( 1 . 0 0 0 / ( V + V ) + 1 . 0 0 0 / ( V + B ) + 0 3 ) - A + D B X / ( V + B ) + ( 0 3 +

1 1 . 0 0 0 / ( V + B ) )0 5 = 0 5 + 0 2 + 2 . + 0 1 / ( V - B ) + ( O V X - O R X 5 D 2 V X = (D P X + 0 5 / D P O V - 0 2 V X ) / O P O V

3 4 0 O G X (2 t K ) = 0 7 + 0 4 - 0 V X + ( 0 2 P V X + O V X + 2. + 0 2 P X )- D P X + D 2 V X D P 3 6 K = 1 T 2D M T I X ) = ( O P G X ( K , 1 ) - D M G X ( K , 3 ) ) / ( A B T ( 2 ) - A R T ( 1) )

3 6 D N V ( K ) = ( D M G X (K » 1 )- D M G X (K , 2 ) ) / ( A B V ( 2 ) - A B V ( 1 ) )X J A C H B = D M T ( 1 ) + 0 M V ( 2 l - D N T ( 2 ) + O M V ( 1 )D H L T = (D M G X (2 11 ) + O H V ( 1 ) - O M G X ( 1 , 1 ) + D H V ( 2 ) ) / X J A C P R

D E L V = ( D N G X ( 1 , 1 ) * D N T ( 2 ) - D M G X ( 2 , 1 ) * D M T ( 1 ) ) / X J A C O B A B T ( 3 ) - A R T ( 2 ) + D E L T A R V ( 3 ) = A B V ( 2 J + D E L VD T E S T = O A B S { D M G X ( 1 , 1 ) ) + D A B S (D M G X ( 2 , 1 ) 1 I F ( ( D A B S ( OFfLT ) . L T . E P S ) . A ^ D . ( D A B S ( D E L V ) . L T . E P S )

1. A M D . ( D T E S T . L T . 1 . 0 F 6 ) ) G O T O 5 6 ] F ( W . G E . 7 5 ) G O I D 4 r I F ( A R T ( 3 ) . L T . O . O ) A B T ( 3 ) = A B T ( 2 ) / 2 .J F ( A R V ( 3 ) . L T . O . O ) A B V ( 3 ) = A R V ( 2 ) / 2 .J11F = D S ° R T ( X P . T S T / X P O B . o o f O o )P ( I ) - k T S T / ( V S T - n ) - A / ( T D F - V S T P ( V S T + B ) )I F ( ( A B T ( 2 ) . L T . 1 . 0 ) . O R . ( P ( I ) . L T . 0 .0 ) ) G O T O 4 8 Z = P( I ) * V S T / X R T S T M T O T — fJ TDT-f-1I F ( ( 'TOT . G E . 3 0 0 ) G O T O 5 2I F ( ( 0 . 0 0 . 2 ) . A H O . ( Z . G T . 0 . 4 5 ) ) G O T O 4 4f-l-i+1D n 3 8 K = 1 ,2 A F’ T ( K ) = A B T (K + 1 )

3 8 A R V { K ) = AiBV ( K + 1 )G O T O 2 2

4 4 N Z E S T = N Z E S T +1 Z E S T = Z E S T + 0 . 0 2 I F ( N Z E S T . L E . H Z U A X ) G O T O 2 1

4 E 1 F ( M T R . E 0 . 2 ) G O T O 2 1 5 0 C O N T I N U E5 2 I F ( M O D .N E .1) G O T O 2 0 0

W R I T E ( 6 , 5 4 ) X ( I ) , A , R , T K , V 5 4 F O R M A T (/ 4 X , 4 0 H I T E R A T I 0 0 F O R T K A M D V H A S M O T C O N V E R G E D / 2 0 X ,

1 6 H X ( I ) = , F 5 . 2 , 1 0 X , 3 H A = , EJ.6 .8 , 1 0 X , 3 H B = E 1 6 . 8 / 2 0 X , 1 8 H L A S T 2 V A L U E O F T K = , E 1 6 . 8 , 2 H K , 2 0 X , 1 7 H L A S T V A L U E O F V =, E 1 6 . 8 ,3 5 H C C / M / / )T R N ( I ) = T E X P ( I )P R N ( I ) = P F X P ( I )

292

G O T O 5 0 0 5 6 T K = A R T (3 )

V = A B V { 3 )C E N D I T E R A T I O N F O R T E M P E R A T U R E T K A N D V O L U M E V

R T = R Z * T K T { I ) = T K - 2 7 3 . 1 6P( I ) = R T / (V - B )- A / { O S O R T (T K )*'/*( V + B ) )R T = R T / ( 3 . 0 D 0 * Z C A R )Z = P ( I )* V / R Tl ' P IT F< 6 , 6 0 ) X ( I ) , A , B , P ( I ) , T ( I ) ,V , Z , N T O T , N

6 0 F 0 R U A T ( F 1 5 . 2 , 4 X , 2 E 1 8 . 6 , F 1 4 . 1 , 2 R 1 1 . 2 , F 1 1 . 4 , I 1 2 , 2 H /, 1 3 ) T R N ( I ) = T ( I )P R N ( I ) = P ( I )N P T R N = N P T R M +1

5 0 0 R E T U R N E N D

293

o o

S U B R O U T I N E E O K R E G t I )C R I T I C A L L O C U S C A L C U L A T I O N U S I N G K R E G L E W S K I 1 S E O U A T I O N B A S E D O N T H E R E V I S E D C O R R E S P O N D I N G S T A T E S - C O N F R O N A L S O L U T I O N T H E O R Y I M P L I C I T R E A L - 3 ( A - H t O-7.)C P N M O N / T P X / X ( II ) t P F X P ( 11 ) , T E X P ( 1 1 ) * T R W ( 11 ) ,PP.N( 1 1 ) , P K R E G ( 1 1 ) ,

1 T K R E G I 1 1)C T 01 / A B / A 1 , A 2 » R 1 * B 2 , T K A » T K B , N P T , N, N P T C O N , N P T K R G ,

1 A 1 2 L 1 , P 1 2 L 1 t A 1 1 , B 1 1 , A 2 2 , B 2 2 , N P T R N C P M N P N / D O / D A t D R ? O A t O B V A = D A :::-3 V B = D R - - 3 X B = 1 . O D O - X ( I )Z A = X ( I ) / ( t D R / D A )- - 2 - X B + X ( I ))Z R = 1 . O U O - Z AV A R = ( DA-f-DB ) - * 3 / 3 . O D DV Z = V A * X ( IJ + V R - X B + ( 2 . 0 D O - V A R - V A - V B )- X ( I ) * X B E = 1 . 0 0 0 / 3 .000 D Z = V Z * - E G A F M A = 1 . O D DD E R U = 2 .0 D O - G A N N A - ( Z B - Z A )/( 1 . O D O / { T K A - D A ) + 1 . O D O / ( T K B - D B '» ) + T K A - D A * Z A

1 - T K R = : = D R - Z BV C = V Z - f 7 2 . 0 D O / 1 6 . O D O ) * Z A - Z B - D Z / ( T K A - Z A + T K B - ‘:Z B ) * * 2 - ( D E R U * * 2 )E A B = 2 • O D O - G A M N A / ( D A / T K A + D B / T K 3 1T Z = D Z - t T K A - Z A / D A + T K B - Z R / D B + t 2 . O D O - E A B - T K A / D A - T X R / D R ) * Z A :’:Z B )P 7 = ( T Z / O Z )- ( P E X P (N P T ) * 7 A + P E X P ( 1 )-7.B)/ t T K A * Z A / D A + T K B * Z B / D B )T K R E G K = T Z + ( 3 6 . 0 D O / 1 6 . O D O ) - Z A ::=Z R / ( T Z - D Z * - 2 ) - ( D F R U * * 2 )T K R E G t 1 ) = T K R F G K - 2 7 3 . 1 6 D 0 0 A B = 2. 0 D 0 - G A M N A / t 1 - O D O / O A + l . O O f ' / O B )A L P H A = 5 . e 0 8 D O + A , 9 3 n o - t O A * Z A + O B « Z R + t 2 . O D O * O A B - O A - O B ) - Z A - Z B )E X = 2 . 0 D 0 / 3 . 0 D 0P K R E G ( I ) = P Z - ( 1 . 0 D O + A L P H A - ( T K R E G K / T Z - 1 . 0 D O ) ) * ( V Z / V C )- - E X R E T U R NE N D ' wVO■P-

2953* Optimization of Reduced Interaction Parameters

a* The Redlich-Kv/ong; Equation of StateThis program seeks the optimum values of the

reduced interaction parameters A12SR and B12SR for the Redlich-Kv/ong equation of state#


(1) RF = Reduction factor =0.5DELIN = Initial increment = 1.5x10“^STOP = Stopping increment = 1.0x10"ÎP =* Printing control variable = 1 KSTOP = Maximum iterations = 100 INPTS = Control variable for number of points = 1

The values given here are those used for this work.(2) System number and estimated reduced interaction

parameters**

(3) Name of the binary system,(4) Number of experimental points* and(5) Experimental critical data for the system, i.e.,

composition, critical pressures, and critic.' . temperatures.

As many systems may be optimized at one time as disired by arranging the data cards (2) through (5) for each system. The last card should be a fictious system number H0H

denoting the end of the data input.The output consists of the optimum reduced inter

action parameters and the execution time in second for each system.

D T P . E C T S F A R C H O P T I M I Z A T I O N C F A 1 2 S R A N D P 1 2 S R . D . F T S S C N G T H E P E D L I C H - K W C N G E G U A T I O N O c S T A T E . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _

M C D T F T F D R Y S . C . P A KO P T I M I Z A T I O N M E T H O D O F J. W I L L I A M S O Nn i M F N S I C N X ( 2 1 ) , P F X P ( 2 1 > , T E X P ( ? 1 ) , S ( I C O , 2 1 , S S R l 1 0 0 ) , F V U L T ( 2 ) ,

1 0 E L ( 2 ) , S 0 E L ( 2 ) , T ( 2 ) , T I T L F ( 2 0 )RFAl. L S C R ITN P A P = 2 . „ ..._ _ _ _ _ _ _PEAf) (>5,1) R F , D F L I N , S T O P , T P , K S T G P , I N P T S

1 F O R M A T ( F 5 . 1 , 2 E 1 C . 1 , 3 1 5 )C T P » n F O R C O N C E N S E D T U T P U T , I N P T S F O R F U N C T . F V A L . A T E V E R Y P T .

S W I T C H = 1 C . * S T C P W « I T F < <S , 1 0 1 ) N P A R

1 0 1 F O R M A T (1H 1 / / A 5 H T H I S IS A 0 1 P E C T . S E A R C h O P T IM IZ A T m N P R O G R A M . . / /1 fl 2 3« *=« O F P A P . A N F T F R S « , 1 2 //)W R I T F (6. ,10**) D E L IN, S T O P

1 0 5 F O R M A T ( / / / / 3 0 H T H E I N I T I A L I N C R E M E N T S I Z E I S , 1 P E I I S . 7 / / / / 2 6 H T I F F S T O P P I N G C R I T E R I O N IS , 1 P F 1 5 . 7 )W R I T F ( 6 , 1 1 2 ) R F

1 1 2 F O R M A T ( / / / / 2 5 H T H F R E D U C T I O N F A C T O R IS , 1 P F I 5 . 7 )W P I T F (6 , 1 1 3 ) K S T O P

1 1 3 F O R M A T ( / / / / 2 5 H T H I S R D M IS P R O G R A M M E D F O R , 1 3 , 3 R F I T E R A T I O N S U1 M L F S S 0 T H F R WI SE T E R M I N A T E D )IF ( I P . N E . O ) G C T C 1 1 4 W R I T F ( 6 , 1 1 5 )

_ 1 1 5 F O R M A T I / / / / 4 6 H T H T S R U N W I L L P R O V I D E A. C O N O E N S E D . O U T P U T O N L Y . ) . _____

G O T O 51 1 4 V R I T E ( 6 , 1 1 7 )1 1 7 F O R M A T ( / / / / 4 3 H T H I S R U M W I L L P R O V I D E A C O M P L E T E W R T T E - C U T )

8 P E A D ( 5 , 4 ) N S Y S , A 1 2 E S T , B 1 2 E S T 4 F O R M A T ( I 5 , 5 X , 2 F 2 C . F ).. I F ( M S Y S ) 2 0 6 , 2 0 6 , 1 3 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ___ _ _ _ _ _ _

1 3 R F A 0 ( 5 , 1 2 ) ( T I T L E ( I ) ,1 = 1 , 2 0 1 1 2 F O P M A T t 2 9 A 4 )

297

C A L L S C I C K 1 S C A L E = 1 . 0W R I T E ( 6 , 14) N S Y S , ( T I T L E ( I ) , I = 1 , 2 C )

1 4 F O R M A T t l H l / 1 4 H S Y S T E w N E W E E R , I 5, 2 0 X » 2 0 A V / )_ _ _ _ _ _ _ _ _ _ _ _ _ _R p A D ( 5 t 2 0 ) N P , ( X ( I ) , P E X P ( I ) , T F X P ( I ) , 1 = 1 , N P )

2 0 F C D M AT ( 1 5 / ( 3 F 1 0 . 5 ) )n n l s k = i , n p a rD F L ( K 1 = D E L I N . . . . . . . . .

15 S D E L ( K ) = S T O P. . . . . . T = I .....__________________

IF ( f I M P T S . N E . 0) . A N D . ( N P . G T . I D ) G C T O 2 2I L O = 2 . ...IT N C = 1 G O T O 2 4

2 2 I L O = 3 I T N G = . 2 ... _ _ _ _ . _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _

2 4 T K = T F X P ( N P ) + 2 7 3 . 16B1 = 1 0 ^ . 4 P 0 0 3 * T K / P E X P ( N P )A I = 5 0 4 5 . P A S O * R l * T K * S O R T ( T K )T K = T F X P ( l ) + 2 7 3 . 1 6 R 2 = 1 0 4 . 4 e 0 0 3 * T K / P E X P ( l )

_ _ _ _ _ A 2 = 5 9 4 5 . fi{?99*E? 2 * T K * S Q R T ( TK) ... .. . _ __ _C O 1 1 9 I = l , K S T O P S S R ( I ) = 0 . 0 D O 1 1 9 K = 1 » N P A R

. 1 1 9 S ( I , K ) = C . OC D 1 2 1 1 = 1 , N P A RT( I ) = 0 .

1 2 1 F M U L T ( I )=0 .S (I ,1 ) = A 1 2 E S T SI 1 ,2) = B I ? E S T

______ IF ( T P . E Q . 0) G O T O 1 3 3 . . „

W P I T F ( 6 , 2 5 ) N P2 5 F O R M A T ( / / 4 5 H N U M B F R O F D A T A P C I N T S ^ I N C L U D I N G F N D P T S . < H 13 / / )

298

W R I T E ( 6, 130)1 3 0 F C P M A T ( l H 0 t 3 6 H I N I T I A L V A L U F S C F T H E C O N S T A N T S W F R E )

WR I T F ( 6 , 1 3 2 ) SI 1 , 1 ) , S{ l r ?)1 3 2 F O R M A T t/ 1 5 X , 7 F A 1 2 S R «, E 1 6 . 8 / / 1 5 X , 7 H R 1 2 S R E L 6. B / /) __ _ _ _

W R T T E ( 6 , 1 6 0 )1 6 0 F O R M A T ( / / / 6 X, S H I T E R . , 8V, 5 H A 1 2 S R , 1 3 X , 5 H B 1 2 S R , 1 1 X , R H C P T C R I T

1 . , 1 3 X , 3 H 0 E L , 1 0 X , 4 F N F U N , 4 X , 4 H I I N C / / )G O T O 1 3 5

1 3 3 W R I T E < 6, 1 3 4 )1 3 4 F O R M A T (/ J O X , 5 1 F'R F S U L T S C F C T R F C T S E A R C H M T N T M T 7 A T I ON P R O C E D U R E

1- - - - / / 1 4 X, 6H P A R A M . , 2 5 X , 6H V A L U E S , 3 6 X , 1 O H I N C P F M E N T S // 1 6 X t? 2 U S X , 7 H I N IT I A L , 1 4 X , 5 H F I N A L ))

1 3 5 N F U N = 0 N O N O Q N = 0 K = 1

9 9 8 L S C R T T = F U N G P T ( X , P F X P , T E X P , N P , Al , A2 , El , 02 , S ( K , 1 ) , S ( K , 2 ) , I L O , _ I I I N C )N F U N = N FtJN + 1IF ( A R S ( L S C R I T - 5 0 . ) . L E . 1 . 0 E - 7 ) N C N C C N = N O N C C N + I S S R ( K )= L S O R I T I F ( K . F O . l ) G O r e 1 3 7IF ( S S R ( K ) - S S R ( K - l ) ) 1 3 7 , 1 4 6 , 1 4 6 ... ._ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

1 3 7 J l - 00 0 1 3 5 N = 1 , N P A RTl M) = S ( K , M )S (K., w ) = S ( K , M ) + O E L (M ) . . . . . .L S C R T T = F U N ' C P T (X , P F X P ,T EX P , N P , A 1, A 2, R l , R2, S ( K , 1 ) , S ( K , 2 > , I L O ,

i U N O .... . . . . . ... . . . . . . .. . . . . .N F U N = N F U N + 1IF ( A 3 S ( L S C R I T - 5 0 . ) . L E . 1 . 0 F - 7 ) N C N C O N = N D N C O N + 1 IF ( S S R ( K ) . G T . L S C . R I T ) G O T O 1 4 2S ( K , V ) = T { M 1_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _S( K , ^ ) = S ( X , M ) - O E L ( M )I . S C R T T = F U N O P T ( X, P E X° , T E XP , N P , A 1 ,A 2 ,B 1 ,B 2 ,. S ( K , 1) , _ S ( K ,2 ) t _I L C

1 U N O

299

N F U N = N F L N + IIF ( A G S ( L S C R I T - 5 0 . ) . L E . l . D F - 7 ) N O N C O N = N O N C O N + 1T F ( S S R (« I . L F . L S C P I T ) G C T T 1 4 1 . ...F M U L T{ M ) = - 1.

G D T D 1 4 4 . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _1 4 1 S ( K , w ) = T ( V )

. F M U L T ( M ) = c . . . . . . . . . - _ _ _ _ _J l = J l + lG O T O 1 3 ? '

1 4 ? fmijlt ( M ) = 1.1 4 4 S S P ( K ) - L S C R I T _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ... 1 _ _ _ _ _ _ _ _ _ _ _ _ _1 3 8 C H N T T N U E

IF ( N O N C O M . G E . 51 G O T O 2 1 CIF ( i o . M E . 0) W R I T E ( 6 , 1 3 5 1 K , S( K , I ) , S ( K , 2 > , S S R ( K ) , D E L ( l ) ,

1 N F U N , I T N C _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _1 3 9 F O R M A T ( 1 1 0 , 4 E 1 8 . 8 , 2 I P )

IF t ( C F L ( 11 . G T . S W I T C H ) . H R . ( I N P T S . E Q . 0 ) ) G C T C 1 4 0 T L O = 2 I I N C = 1

1 4 0 K = K + 1... IF ( K . C T . K S T C P ) G C T C 1 4 5 . . . . . . . ___ . ___ _ _ _ _ _ _ _

IF C J 1 . F Q . N P A R ) G C T O 1 4 6 C O 1 4 7 I = 1 , N P ARIF ( F M U L T ( I ) . E C . O . ) G C T C 1 ^ 8 S ( K , I ) = SI K- 1, I ) + < F M U L T U ) * D F L ( I) )G C T C 1 4 7

1 4 8 S t K . I ) - S ( K - 1 , 1 ) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _1 4 7 C O N T I N U E

G O T C 9 9 R 1 4 6 K = K - 1

N K = 00 0 1 5 0 1 = 1 , N P A R

... D E L m = D E L U ) * R F _ _. . . . . . . . . . . . . . . .. . . . . . . . . . . ... . „ . _ _IF ( D E L ( I ) . G T . S O E L I 1 ) ) G O T O 1 5 0

O E L ( IJ = S G E L ( I )N K = N K + 1

1 5 0 C O N T I N U E IF ( N K - N P A R ) 1 3 7 t 1 4 5 1 , 1 4 5 1

1 4 5 K - K - 1 . ... . .. . . . . . . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _1 4 5 1 IF ( I P . E C . 0 ) G O T C 3 0 0

W R I T E ( 6 , 1 3 9 ) K, S ( K , 1 ) , S ( K ,2 ) , S S R ( K ) , D F L ( l ) , N'F'JN, T I N CW R I T F ( 6 , 1 5 1 ) S S R ( K )

1 5 1 F O R M A T iff 4 ° H T H E F I N A L V A L U E O F T H E O P T I M I Z A T I O N C R I T E R I O N I S ,1 E 16. « )

W R I T E (6 , 1 5 2 ) K . . .. . . . . . . . . . .1 5 2 F O R M A T ( / / 4 0 H T H F N U M B E R O F I T E R A T I O N S P E R F O R M E D W A S , 1 3 )

W R I T E ( 6 , 1 5 4 ) N F U N1 5 4 F n R M AT (/ 4 0 H T H F N U ‘-‘3 E R O F F U N C T I O N E V A L U A T I O N S W A S , 1 4)

W R I T E (6 , 1 5 3 ) ....1 5 3 F O R M A T ( / / / 3 9 H T H E F I N A L V A L U E S C F T H E C O N S T A N T S W F R F )

W R I T E ( 6 , 1 3 2 ) S (K, I ), S (K, 2 ) _ _ _ _ _ _ _ _ _ ____ _ _ _ _ _ _ _ _ _ _ _ _ _TI VE = R C L C K 1 ( S C A L E )W R I T E ( 6 , 7 0 0 ) T I M E

7 0 0 F O R M A T ( 1 H 0 , 3 2 H F X F C U T I G M T I M F IN S E C O N D S W A S * , F 1 0 . 5 )W R I T E ( 7 , 4 CO) N S Y S , S ( K ,1) , S t K ,2) _ _

4 0 0 F O R M A T ( 1 5 , 5 X , 2 F 2 0 . P )G C T C 9 . . . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

3 0 0 WR I T E ( 6 , 3 C 2 ) A 1 2 F S T , S I K , 1) , D F I I N , D E L 1 1 )3 0 2 F O R M A T (/ 1 5 X , 5 H A 1 2 S R , ? ( 4 X , 2 E 2 0 . 8 ) )

WRI T E (5 ,3 04) B1 2 F S T , S (K , 2 ) , O F L ! N , D E L (2 ) , K , N F U N3 0 4 F O R M A T ( / L 5 X , 5 H S 1 2 S R , 2 ( 4 X , ? E 2 0 . P) ft 1 5 X , 2 2 H N U M B E R C F I T E R A T I

I O N S tf, 1 3 , 2 H ,, 1 0 X , 3 2 F N U M R F R O F F U N C T I O N E V A L U A T I O N S 1 4 //) G O T O 3 ....__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

2 1 0 W R I T E ( 6, 2 1 2 )2 1 2 F O P M A T ( / / / / 4 8 H O P T I M I Z A T I O N S T C P P F D R F C A U S F O F N O N - C O N V E R G E N C E )

G O TO 82 0 6 S T O P

F N O

non

F U N C T I O N F U N C P T (X, P F X P , T F X P , N P , A 1 , A 2 , R 1 , R 2 , A 1 2 S R , R 1 2 S P ,_ _ I I L O , M NC) ... . . . . . . . . . . . . . .

F U N C T I O N W H I C H I S T O R E M I N I M I Z E D O K HM R O I F I E D FY S . C . P A XI T E R A T I O N r-UP T K fl,NO V P Y N E W T O N S M F T K M F O R 2 E Q S . ♦ S E C A N T M O O I F . D I M E N S I O N P ( 2 i ) , T ( 2 1 ) , A R T ! ?) , A B V( 3) , D N G X( 2, 31 , P N T 1 ? ) , D N V 1 2 ) ,

I R N < ? ) , X S T ( ? 1 ) , P X S T ( ? 1 ) , T X 5 T ( ? 1 )C M A I N P R O G R A M M U S T . C O N T A I N D I M E N S I O N S T V N T , L I K E THE. F O L L O W I N G _ _ _ _ _

0 I M E N S I O N X ( ? l ) , P E X P ( 2 ] ), T c X P ( ? 1 )0 O U R LE P R E C I S I O N R T , 0 1 , 0 2 , 0 3 , 0 4 , 0 5 , 0 5 , 0 7 , C V * , C P X , D p D V ,0 ? P X , G 2 ,

1 O R , D ? P V X , D 2 V X , A R T , A B V , D M C , y , D N T , O N V , J A C O B , O F L T , O F L V , T K ,V2 ,Rl t M , 42 » R? , A 1 2 L » R 1 2 L , Rfit P 7 , A, E, H A X , D B X, T H F D A T A E P S , N T Y A X , N Z P A X / A . C F - R , 7 , 5 /

_____________ I H I = H P - 1 . ..___ ___________________

N M P T = ( I H I - I L C J / I I N C + I NT NN'PT = { N « P T + 1 ) /2 A 1 2 L = ( A 1 2 S R - 1 . C ) * ( A 1 + A 2 )P 1 2 L = ( H 1 2 S R - l . 0 > * ( R 1 + P 2 )D O 1 5 1 = 1 , N PX S T < I ) = X ( I ) .... .. . . . . . . . . . .p X 5 T ( I ) = P E X P U )

1 5 T X 5 T ( I) = TF XP( I )C B E G I N C A L C U L A T I O N A L L O O P O V F R M O L E F R A C T I O N S

1 = T L O1 9 X 2 = 1 . C - X( n

. . . . . . Pb = 12 0 5 .90 5 / 1 X 1 I ) * X 2 ) _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _R 7 = (?6 *[ V( I ) - X 2 ) / (X U ) * X 2 )A - A 1 * X { I ) + V 2 * 1 A 2 + A 121.* X { I ) )R = R l * x m + X ? * ( R ? + P 12L * X 1 1)1 r>A X = A 1 - A 2 + A 12L* ( X2 - X I I ) )O B X = B 1 - 6 2 + R 12L *1 X 2 - Xt T ) )

C R F G I N I T E R A T I O N F O R T E M P E R A T U R E T K A N D . V O L U M E V _N N N = Q NT O T = 1

Z E S T = 0 . 3 5G O T 0 I C O '

2 0 0 Z E S T = 0 . 3 1 N T Q T = 1 _ _ _ _ _ _ _ „ .... ___ .._ _ _ _

N N N = 11 0 0 T S T = T E X P U I + 2 7 3 . 1 6

0 0 5 0 N T S T * 1, N T P A XM E V O D = M T S T - 2 * t„N T S T / 25 . . . . . . . . . .M R = I

N Z E S T = 1 ..... _ _ _ _ _ _ _ _ _ _ _ _ ___ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _21 N * 1

IF ( N E V O C . F Q . 0 ) A P T Cl ) = T S T - 0 . 2 5 * F L 0 A T ( N T S T )IF ( NE V C D . E C . 1) Afl T (1 ) = T S T + 0 , 2 5 * F t . C AT ( M S T - 1 )A R V I L 1 = 1 2 C 5 . S C 5 * Z F S T * 4 3 T { l ) / f » E X P ( I )IF ( N T R . F C . 2 ) G C T C 2 3

... ...... A!\T[ 2) C . 9 S C * A F T ( 1 )A n v (2 ) = 0 . 9 9 R £ A R V I 1 )N T R = 2 GO T O 2 2

2 3 A B T (2) = 1 . 0 0 I * A R T (11 A R V ( 2) = 1 . 0 0 2 - A R V I 1 )

. . N T R = 322 00 34 K=113

IF { K . E Q . 31 G C T C 2 6 T K = A R T I 2 )IF ( K . E O . 2) G O T O 2 8

7 4 V = A QV 12 IR T = 1 2 0 5 . 9 0 5* T K T H F = D S O R T ( T K )06 = P 6 * T K D 7 = R 7 * T K

.. G O T O 3 02 6 T K = A.RT(l )

G O T O 2 4

2R V = A BV C t )3 0 01 = R T / l (V - P ) * * 2 )

TP < K . N F . I) G O T G 3 2. V S T = V ____________________________________________________________ ______________________________________________________________________________

P. T S T = R T 3 2 0 2 = 1. CO C/( T H F * V * ( V + B ) )

03 = D ? / ( V + B )D P X = 0 B X * ( D 1 + A * 0 3 ) - C A X + D 2O R Q V = * * 0 2 * 1 1 . 0 0 0 / V + 1 . C O C / l V + B ) ) - D 1n v x = - n p x / n p c v _ _ _ __ _ ___ _ _ _ _ _ _ _0 5 = 0 L O G { ( V + P ) /V) " . . . . .G 2 = l . O D C / ( V + R ) - l . C 0 C / R * P 5G 3 = ( 0 . 5 0 0 / ( V + fi ) + 1 , O C O / P ) / ( V + B) - 0 5 / ( B * B )D A = A 121.*0 5 + R 1 2 l * A * G 2 - 0 R X * ( n A X * G 2 - 0 R X * A * G 3 )0 4 = 2 . * 0 4 / ( R * T P F ) + R T / ( V - R } * ( ( 0 B X * * 2 ) / ( V - B ) - 2 . * B 1 2 L )

D M G X ( 1 , K ) = 0 6 + 0 4 - C P X * C V X . . . . . . . . . .D 2 P X = A 121.*0 2 - B l ? l * ( 0 1 + A * 0 3 >n ? p x = ? . * < o ? p x + c p x * ( r A x * r . 3 + c b x *( o i /( v - r ) - a * 0 3 / { v + r i )) )0 4 = 0 3 * { D A X * D P X - 2 . * A * P 1 2 L )n 4 = 0 4 - A * ( 0 R X * * 2 ) * ( G 3 / B + 1 . CO C/( 3. CD P * ( V + B ) * * 3 ) )0 4 = 0 4 * C O X + G? * { A1 21. * O C X + 8 1 ? L * D A X )0 4 = 6. C 0 C * 0 4 / ( P * T H F ) + O R X * D l * { ? . * ( O R X * * ? } / ( V - B ) - 4 . 0 0 0 * R 1 2 L ) D 2 P V X = 0 A X * ( 1 . 0 0 C / V + l . C O O / f V + P ) ) - O R X * A / ( V + B ) * f 1. 0 0 0 / V + 2 . /

1 ( V + B ) )D 2 P V X = 0 2P V X *0 2 - 2. * 0 1 / ( V - R ) * 0 R X0 5 = A 1 2 L + ( O A X * n R X - A * R 1 ?L ) / ( V + B )0 3 = O V X * ( ? . / ( V + R ) + 1 . 0 C O / V ) + 2 . * D B X / ( V + B )D 7 V X = ? . * 0 5 - A * 0 R x * D 3 / { V + R ) + 0 V X * DA X* ( 1 . 0 0 0 / ( V+ R) + 1 . 0 0 0 / V ) _0 ? VX = 0 7 V X * 0 2 - 2 . * 0 1 * ( R 1 2 L + O R X / ( V - R ) * ( 0 V X - D B X 1 )0 3 = l . O D C / V + 1. O O P / { V + P )0 5 = 0 A X * 0 3 - 2 . * A * D V X * ( l . O O C / t V * V ) + i . C 0 0 / ( V + B ) * 0 3 ) - A * D B X / ( V + B

1 )* ( 0 3 + L . O D 0 / ( V + P ) )0 5 = 0 5 * 0 ? + 2 . * D 1 / ( V - R ) * ( D V X - O R X )0 2 V X = ( O P X * 0 5 / GP D V - D 2 V X J / 0 P 0 V

3 4 D N G X ( 2 , K ) = D 7 + D 4 - D V X * ( C ? P V X * D V X + 2 . * D ? P X ) - D P X * D 2 V X 0 0 3 6 K = 1 , 2D N T ( K ) = ( O N G X ( K , l ) - D N G X ( K , ? ) ) / ( A R T ( 2) - A B T l l ) )

aftPNvco = (o no x ( k , n - o n g x i k ,?j)/(a r v (?j - a b v u ); .......JACOB = D N T t 1)*L)N V{ ?) - D N T ( ? ) *n NVC 1 )O c L T = ( D N G X r? , 1 ) * R N V Cl ) - r N('X ( 1, l l * O N V ( 2) ) / J A C O B D F I. V - ( O N G X l I T 1) * D N T ( ? ) - D N G X (2 ,1 ) * D N T ( 1 ) ) / J A C C B A R T (3) = A R T { 2 ) + P F L T A P V (3) = A R V ( 2 ) + * D F L VO T F S T = O A R S( O N G X ( 1, 1 ) ) + Q A B S ( 0 \ 0 X ( ? , 1 ) )IF ( ( D A B S ( C E L T } . L T . E P S ) . A N C . ( C A B S ( D F L V ) .L T . E P S

1) . A NO. ( D T E S T .LT. 1 . 0 F * ) > C C t c 5 4 _ _ _ _ _ _ _ _ _i f n . g f . ? p ) o n t o 4 eIF ( A R T f 3 } . L T . O . O ) A p r ( i ) = A H T ( 2 ) / ? .IF ( A B v m . L T . 0 . 0 ) A p v ( 3) = A R V ( 2 ) / 2 .T H E = S 0 R T ( R T S T / L 2 O 5 . F r 5 ) .. . .0 ( 1 ) = R T S T Z ( V S T - R ) - A / { T H F * V S 7 * ( V S T + B ) )IF ( (A B T (2) .LT. I .0 ) .OP. (P(T) .LT . 0.0)) GO TO 48Z = P(I)*VST/RTST NT CT = NTOT + 1 IF (NTQT .GE. 300) GO TO 52IF ( (N . G O . 2) . A N D . (Z . G T . 0 . 4 5 ) ) G C T C 4 4 . . . .N = N + 1 D O 3 R K = L ,2 A R T( K ) = A B T ( K + l )

3 8 A B V ( K ) = A B V (K + 11 G O T O 2 2

44 N 7 F S T = N 7 F S T + 1 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _Z F S T = Z E S T + 0 . 0 2 IF ( N 7 F S T . L E . N Z ^ A X ) G O T C 21

4 H IF ( N T R . F O . 2) G O T O 21 5 0 C O N T I N U E5 2 I F (N N N . N E . L) G O T O 2 0 0

IH I = IFT - I ___________ ________

Tp (I . G T . I H I ) G C T C 6 2 G O 6 6 K = I, I H T X { K } = X { K + l }P E X p (Kl = P E X P C K + l )

5 5 T F X P ( K ) = T F X t M K + U- I F ( I I N C - E C . 1 ) G O T G 19.... _ _ _ _ _ _ _ _ _ _ _ _ _ _ _T = I + I INC - IIF II - IH I ) 1° , .19, 6 2

5 6 T K = A B T H )V = A D V ( 3 )

C F N D I T E R A T I O N F O R T E M P E R A T U R E T K A N D V O L U M E V P T = 1 2 0 5 . 9 0 5 * T K .... . . .. .

T( I } = T K - 2 7 1 . 1 6P l I ) = R T / I V - R ) - A / ( C S O R T ( T K ) * V * ( V + B J )I = I + ! I NC.IF (I . L F . I H I } G O T C 19

C E N D C A L C U L A T 1 C N A L L O O P O V F R Mnj_ g F R A C T I O N S_ 6 2 NU'-’P T S = N M P T - '\P + I H I + 1 . .. ... .

IF { N I J M P T S . L T . M I N N P T ) G O T O 7 C D C 6 4 K = l , 2

6 4 R P I K 1 = 0 . 00 0 6 6 1= IL O * I H I , I I N CP M ( l ) = R M U ) + ( P I N - P E X P ( I ) ) * * 2

.. . 6 6 R M ( 2 ) = P w ( ?) + ( T ( I ) - T E X P f I ) ) * * 2 . . . .P T S N C = N'JMD T S D O 6 9 K = 1 , 2

6 9 R M ( K ) = S O R T I R M I K ) / P T S N D )T P R A T =4 .0F I IN O P T = R M ( 1} + T P R A T * P M (2)

G O T O 7 4 . ....7 0 I F ( M J M P T S . E C . - 0 } M J M P T S = 0

W R I T E ( 6 , 7 2 ) N M P T , N L M P T SVjJOo\

7 2 * = n R V A T (/ 1 0 X , 1 P H P G I N T S A T T F M F T E D # , 1 3 ,1 V E R G E D # f 1 3 , 2 H ,, 1 0 X , 4 1 F S T N C E T H I S IS2 5 0 . / / )F U N O P T = 5 0 .

lb D H lb I = 1 , \ P X( I } = X S T ( I )P F X P ( I ) = P X S TC I )

7 6 T E X P t I ) = T X S T { I ),PFTURN Emd

2 H ,, 1 0 X , 1. 8 H P 0 I N T S C O N T O O S M A L L , S F T F U N O P T H

VjJo-s3

b, The Redlich-Ngo Equation of State308

This program is exactly the same as the one for the Redlich-Kwong equation except minor alterations in order to account for the factor '^Z0” appearing in the Redlich-Ngo equation.

This program requires one more data card in addition to those needed for the Redlich-Kwong equation. Namely, the 6th card contains the critical compressibility factors for components A and B.

i

C D T P f r C T S E A R C H O P T IM TZ A T I O N O F A 1 2 S R A N D 3 1 2 S R . D. H T S S C N G... C ...THE R E D L I C H - N G C E C U AT I O N n r S T AT F . .. _ . _ _ _ _ _ _ _

C V n O T P T F D B Y S . C . PA KC O P T I M I Z A T I O N X E T H O D O F J . W I L L I A H S O N

O I M F N S r n N X ( ? l ) , P F X P (21 I , T F X P ( 2 t ) ,S ( 1 0 0 , 2 ), S S R ( 1 0 0 ) t F M HI. T( 21 , 1 P E L ( 2 ) , S D F L ( 2 ) ,T( 2 > . T I T L E ( 2 C )

C O P Y O N / If Z C A . 7 . C RPEAL L S C K I T _ ___ _ _ _ _ _ _ ___ _ _ _ _ _ _ _ _ _ _ _ _ _vp AP = 2PFAf) ( S , l ) R F f D E L IN. S T O P , IP, K S T O P , I N R T S

] F O R M A T (F *5. I , 2 E I 0 . 1 , 3 1=5)C IP *0 F O R C O N D F A ' S F Q O U T P U T , I N R T S « C F ^ R F I N C T. E V A l . A T E V F R Y P T .

S W I T C H = 1 0 . * S T C PW RT T r ( 6, in I) A F A R _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ____ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

10 | F O R M A T ( 1 H 1 / / 4 S H T H I S I S A D I R E C T S E A R C H O P T I M I Z A T I O N P R O G R A M }(\tf 2 3H N U N n F R O F P A R A M E T E R S I? //)W B I T E ( 6 , I C P ) D E L T N , S T O P

I O B F O R M A T { / / / / 30E T H E I N I T I A L I N C R E M E N T S I Z E I S , 1 P E 1*5.7 / / / / 2 6 H T 1 H c S T O O P I N G C R I T E R I O N I S , I P F 1 5 . 7 ). V R J T F ( 4 , 1 1 ? ) . . . . . . . . . . . .. . . . . . . . . . .

1 1 ? F O R M A T ( / / / / ? S H T H E P F C U C T I O N F A C T O R I S , 1 P E 1 5 . 7 1 W R I T F ( 6 , 1 1 3 ) K S T C P

1 1 3 F O R M A T ( / / / / 2 8 H T H I S R U N IS P R O G R A M M E D F C R , 1 3 , 3 9 H I T E P A T I C N S U 1 M . E S S O T H E R W I S E r r R M I N A T F C )IF d P . N F . C ) G O T O 1 1 A

..... . . W R I T F (6, 1 1 5 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... ....._ _ _ _ _ _ _ _ _ _ _ _ _ _1 1 6 F O R M A T ( / / / / 4 6 H T H I S R O N W I L L P R C V I D F A C O N O E N S F D O U T P U T O N L Y )

G O T O 31 1 4 W R I T E ( 6 , 1 1 7 )

1 1 7 F O R M A T ( / / / / 4 3 H T H I S R U N W I L L P R O V I D E A C O M P L F T F W R I T E - O U T )« R E A D ( S , 4 ) N S Y S . A 1 2 E S T . B 1 2 E S T

.. 4. F C R R A K I S , S X , ? F ? O . S ) ... . . . . . . . . . . . . . . . . . . . . . . . . .I F ( N S Y S ) 2 0 6 , 7 0 6 , 1 3 ^

. 1 3 P E A D (5, 1 2 ) ( T I T L E ! I), 1 = 1 , 2 0 ) vO

1 2 F C R M A T ( 2 0 A 4 )C A L L S C L 0 K 1 S C A L F=1 .0

ViRI T E l 6 11 4 ) N S Y S t ( T I T L E t l ) ,1 = 1 , 2 0 ) . ...... ...1 4 F P P " 1 A T ( 1 H 1 / I A H S Y S T E N M J Y " E R , I 5 f 2 O X , 2 0 A 4 / /)

P ! Z A D ( 5 , 2 0 ) N P t (X (I) , P E X P m . T E X f M I), I = 1 , N P ) 2 0 F 0 C Y A T{f 5 / ( 3F 1 0 . 5 ) )

R E A D ( 5, 3 0 ) Z C A, Z C 3 3 0 T C R V A T ( 2 F I O . 5 1

...... 0 0 15 K = 1 t N p A" ..r . F L ( K ) = C t L I N

. 1 5 SD EL f K . ) = S T C P I = 1IF ( ( TM P T S . N E . 0 ) - A N D . ( N P . G T . I D ) G C T G I L C = 2

I I N C - .1 ... _ _ _ ___ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _G O T O 2 4

2 2 I L Q = 3 I I N C = 2

2 4 T K = T E X P ( N P ) + 2 7 3 . 16R 1 = 313. 440106*7CA*TK/PEXP (NP)

.. . A 1 = 1 7 8 4 ^ . 6 6 3 6 * 8 1 * Z C A * T ' < * S Q P T{ TK.) . . . .T K = T F X P (1 ) + 2 7 3 .16B 2 = 3 13. 4 4 C 1 0 6 * Z C R * T K / PE X P (1 )A 2 = 1 7 3 4 9 . f 6 8 6 * B 2 * Z C R * T K * S O R T f T K )

... D G 1 1 9 r = i , K S T D P S S R C I ) = O . o D O 1 1 9 K = 1 , N P A R

1 1 9 S ( I , K 1 = 0 . 0D C 1 2 1 I = 1 , N P A P T { I ) = 0 .

121 FwU l T ( I )= 0 . ......................5 ( 1 ,1 ) = A 1 2 E S T S( If 2 ) = R 1 2 F ST

TF ( IP . E C . 0 ) G O T O I T ?W R I T E ( 6 , 2 5 ) N P

2 5 F O R M A T ( / / 4 5 H N U M R F R O F D A T A P O I N T S % I N C L L D I N G E N D P T S .< T3 / / )W ° I T E ( 6 , 1 3 0 ) . . . . . . . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

n o F n ? . V A T I L W 0 , 3 4 H f n i t i a l v a l u e s c e T H E C O N S T A N T S W E R E !V° I T E t 6, 1 3 2 1 S{ 1, 1) , S( It 2)

1 3 2 F E R M A T (/ l S X t 7 H A 1 2 S R FI#,.8 / / 1 5 X , 7 H R 1 2 S R *, Fife. 8 // )W P I TE 1 ^ , 1 6 0 )

1 6 0 F O R M A T ( / / / 6 X , 5HIT FP . 8 X , 6 H A 1 2 S R , l ? X , 5H R 1 2 S P , II X, P H C P T C R I T l . i 1 3 X f 3 H C F L , 1 0 X , A F N F U N , A X , A HI I N C / / )G O TO 1 R 5

1 3 ? W R I T E ( 6 , 1 3 4 )1 3 A F O R M A T (/ 1 Q X , 5 1 H R F S U L T S O F D I R E C T S F A R E. F M I N I M I Z A T I O N P R O C E D U R E

1- - / / 1 4 X , 5 H P A R A M . , 2 F X , feHVAl.UES, 3 6 X , 1 O H J N C P E M F N T S // 1 6 X ,7 ? (13 X , 7 H T M T I A L , 1 A X , 5 F F I N A L ))

1 3 5 N F U N = G _ . ...... _ _ _ _ _NONE. O N = 0 K = 1

9 9 8 L S C R I T = F U N O P T ( X , P F X P , T E X P , N P , Al , A 2 , Bl , B2 , S ( K , 1 ) , S ( K , 2 ) , T L O ,1 I I N C )N F U N = N F U N + 1

. . I F { 4 M S ( L S C R I T - 5 0 . I . LE . 1 . O F - T ) N C N C C N = N O N C G N _ _ + 1 S S R ( K J= L S ER IT I F ( K . F f ) . l ) G C T E 1 3 7 IF { S S R ( K I - S S R ( K - 1)) 1 3 7 , 1 ^ 6 , 1 4 6

1 3 7 J 1 = 0D O I 3 8 M = i t \ p A R

... T ( M ) = S ( K , M ) ____ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _S ( K , X ) = S ( K , V ) + C F L ( M )L S C R I T = F U N C P T ( X , P F X P , T E X P , N P , A l , A 2 , R L , 8 2 , S ( K , 1 ) , S ( K , 2 ) , ILO,..

I I I N C )N F U N = N F U N + II F ( A 3 S ( L S C R I T - 5 0 . ) . L E . 1. O E - 7 ) N C N C C N - N C N C C N + 1IF ( S S R ( K ) . O T . L S C R I T ) G O T O 1 A ? _ ... . _

St K t m ) = T( V)S ( K , M )= S ( K » M )—D F L ( M 1 . . . .L S C R I T = FU N G °T ( X, P F X 0, T F X P , N P t A 1, A 2, B I , B 2 , S ( K , 1 ) , S ( K , ? j , I L O

1 U N ON F U N = N F U N + IT F (A { L S C R I T -5 0 . ) .L p . 1 . 0 E - 7 ) N H N C D N = N O N C O N + I IF ( S S R t ' O . L F . L S C R T T ) G O T C 1 4 1

... . F'-TJLT (M ) = - l . ____________ _______________ ___________________________

G C T C 1 4 41 4 1 S ( K , m ) = T ( N » . . . . . . . . .

F P U L T ( M ) - 0 .JI - JI -M ______ _____________________G O T O 1 3 5

14? FPULT<M)=1.1 4 4 S S < M K ) = L S C R I T1 3 F C O N T I N'JF . . . . . _ _ _ _ _ _ _ _ _ _ _

IP ( N O N C O N , G F . 5) G C T p ? 1 0IF ( I P . N E . 0 ) W R I T E ( 6 , 1 3 0 ) K f S I K t lJ, S ( K , 2 ) , S S R ( K ) , D F Lf 1)

1 NF U N , I I N C 1 3 q F O R M A T ( 1 1 0 , 4 E 1 9 . 8 , 2 1 £ )

I P ( ( O c L (1 ) . G T . S W I T C H ) . O R . { I N P T S . F Q . 0 ) ) G O T O 1 4 0I L O = 2 ..._ _ _ _ _ _ _ _I I N C = 1

1 4 0 K = K + LTF ( K . G T . K S T O P ) G O T O 1 4 5 I F ( J1 . E Q . N ° A R ) G C T O 1 4 6 D O 1 4 7 I = 1 , N P A R

IF ( F M U L T { I } ■ F O . 0 *) G O T C 1 4 6 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _S ( K , I )=S ( K - l , I ) + { FN! JL T( I )* C F L f I ) )G O T O 1 4 7

1 4 B S ( K , I ) = S ( K — 1 , I)1 4 7 C O N T I N U E

G O T O o u r1 4 4 K = K — 1 ...............................

N K = 0D O 1 5 0 I = 1 , N P A R D F L ( I ) = n E L ( I I * P FIF { O G L ( I I . G T . S D F i m ) G C T C 1 5 0 P F L ( I ) = S 0 E L f I )N K = N K + I

1 5 0 C O N T I N U EIF ( N K - N P A R ) 1 3 7 , 1 ^ 5 1 , 1 4 5 1

1 4 5 K ^ K — 1 1 4 5 1 IF ( I P . E O . 0 ) GO TO 3 0 0

V;P I T F (fitn q ) K , S ( K , 1 ) , S ( K , 2 ) , S S R ( K ), O E L ( l ) , N F U N , I I N C. WR I I F ( 6, 1 5 1 ) S 5 R ( K) . ...

1 5 1 FCP'-’AT (// 4 ^ 1 T E C F I N A L V A L U E O F T H E O P T I M I Z A T I O N C P I T F R I O N I S ,1 E 1 6 . P )Vv9 I T E ( 6 , 1 5 2 1 K

1 5 2 F C R M AT ( / / 4 0 H T H F N U M B E R O F I T E R A T I O N S P E R F O R M E D W A S , 131■«RI TF ( f , 1 5 4 ) N F U N

. 1 5 4 F O R M AT (/ 4 0 H T F F N U M B E R O F F U N C T I O N E V A L U A TI CN'S > A S , . 1 4 )W R I T E ( 6 , 1 5 3 )

1 5 3 F O R M A T ( / / / 3 F H T H E F I N A L V A L U E S C F T H E C C N ' S T A N T S W E R E )W P I T F ( 5, L3 2 ) S ( K , I ), S ( K , 2 )TI N‘E =P.C L C K 1 ( S C A L E )W p IT E ( 6 , 7 0 0 ) T I M F

_.700 F O R M A T ( 1 H O t 3 2 H E X F C U T I O N T I M E IN S E C O N O S W A S. . ,F 1.0. 5 )_ _ _ _ _ _ _ _ _ _W R I T F ( 7 , 4 0 0 ) N S Y S , S ( K , 1 ) , S ( K , 2 )

4 0 0 F O R M A T ( 1 5 , 5 X , 2 F 2 C . 8 ) .. . . . ... .G C T C R

3 0 0 W R I T E ( 6 , 3 C ? ) A 1 2 E S T , S ( K , 1) , 0 F t T N , D E L (1)3 0 2 F O R M A T {/ 1 5 X , 5 F A 1 2 S R , 2 ( * X , 2 E 2 0 . P ) )

K P I T F ( 6 , 3 0 4 ) 3 1 2 F S T ,S ( K , 2 ) , C E I I N , E ' E L ( 2 ) » K , N F U N _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _ _3 0 4 FORMAT ( / 15X, 5 H M 7 S R , 2 ( 4 X , 2 F 2 0 . P ) / / 1 5 X, 2? HNUM8E R CF ITFRATI

I C N S « , 1 3 , 2 H , , 10X, 32KNUMRFR OF FUNCTION EVALUATIONS * , 1 4 / / )

G C TO P 210 WRITE t 6 , 2 1 2 )2 1 2 F 0 ° V AT ( / / / / ASH OPTIMIZATION STOPPED BECAUSE OF NON-CON VFROFNCE)

CO TO 8 - ■2 0 6 S T n °

F A D

FUNCTION FUNCPT ( X, PFXP, TFXP, NP, Al , A 2 * B 1 , R 2 , A12SR, B 1 2 S R ,.... 1 ILO, I I NC) . ........................ ... ........................ .............

FUNCTION WHICH IS TC PF MINTNIZFC nwHM0 9 1 FI F 0 liY S . C . PAKITFR AT 1 ON FOR TK A NO V BY NFV.TONS METHOD FOR 2 FOS. , SECANT VCDtF n v E N S I C N P { 2 I ) » t ( 2 1 ) , A3T f 3 ) , AEVI3 ) , 0NGX( 2 , 3 ) , DNTI 2) ,CNV( 2) ,

1 R M ( 2 ) , XST( 2 1 ) tPYST 1 2 ! ) , T X S T (21 }VAIN PROGRAM MUST CON TA 10 DIMENSION S T w \ T . LI KE.. THE. FCLLCWI NG_____DIMENSION X (21 ) PFXPI21 ) , TRXP( 21>COMMON/ / / ZC 4,7015DOUBLE PR FC IS ION RT, 0 1, 02» 0 3, 0 A, D 5, D £, 0 7 t 0 V X,OP X , DPD V ,0 2 D X , G2

I 0 3 , 02 PVX , 0 ? VX , AHT , ABV, CNGX, CAT , PNV , J A CO p, CELT, QF1. V,TK ,V 2 * R l , A l , A 2 t R ? t 4 1 2 L , P 1 2 L , R f t , P 7 , A , P , C A X , r P X , T H F

CAT A EPS , NT WAX, N7M AX / A . O F - ? , 7 , 5 / ....IHI = NP - 1NVPT = ( IHI - ILO) / I INC. + 1 PI NNPT = Il\YPT + 1 ) / ?A 1 2 L = l A 1 2 S R - 1 . 0 ) * I M + A?)P 12L= ( P 1 2 S P - I . 0 ) * I BI + B2)DC L5 1=1 ,NP ________ __ _______XST ( I ) = X U )PXST ( I ) = PFXP( I )

15 TXST( I ) = TEX P I I )BEGIN CALCULATIONAL LOOP OVFR PCLE FRACTIONS I = ILO

19 X2 = 1 . C - XI I ) ______________________ _____________ ________________RA = 1 2 0 5 . 9 0 5 / 1 XI I ) * X2 )R7 = R5 * IX I I )-X 2 ) / IX I I ) *X 2 )A = A 1* X( I } + X 2 U A 2 + A 1 2 L * X ( I I )B = B l * X{ I ) + X 2 U B2 4- B 12L*X( I ) )PAX = Al - A2 + A1?[_*(Y? - X I I ) )OB X = B I - 6 2 + P12L- ( X2 - XII ) ) . . ....__________ _ ____ _______7CAR=XI I )*ZCA + X2*ZCB PZ = 1 2 C 5 . ° C 5 * 3 . 0*7CAR

BEGIN ITERATION FOR TFNPFRATLRE TK AND VCLUPE VNMN=DNTCT = I

. Z E S T= C. 29 . ____ _________ ________ ___GC TC ICO

2 0 0 ZE ST = 0. 27 NTHT=L N N N = 1

LOO TST ^ T F X P t ! ) + 2 7 1 . 1 6... DO 50 NT ST = 1, NT* A*

NEVCO = KTST - 2 * ( N T S T / 2 )NTR = 1 N7FST = 1

21 N = 1IF (NFVOD . F O . 0) A WTd ) = T ST - 0 . 2 5* FL TAT ( NIST )

IF (NEVOO . FO. 1) f i OT( l ) = T5T + 0 . ? C-Ft_ nA T ( \\ j ST- 1)ABV (1 ) = I 2 03 . 0 0 5 ' -7FST* AHT (1 ) / PFX P 11 )TF (NT? . EO. 2) OC TC 2 3ART (7 ) = 0 .09o*ART(I)A B V t 2 > = C. 9 ° 1* ARV 11)NTO = 2

GC. TC 2 221 ABT( 2) = 1. 0 0 1 * ART (1 }

APV ( 2 ) = 1 . 0C2*APV( 1 )N TP = 1

2? DC 1 4 K - 1 f 1 . .___________________I c ( K • FO. 1) GC TC 26 TK = ART ( 2 )IF ( K . EC. 7 ) GC TC 2 P

24 V = ABV( 2)

THF =DS Q1T ( TK )________________________ _ ____ ____ __________0 6 = R6*TK D7 = P7*TK

317 ( d + A J / L U O M + A/ OOO* I = eu

U X S G - XAG } * <U-A ) / X y Q + l Z l b J ^ I G ^ ' Z - ZO^XAZO = XAZU ( A / O 0 G M + ( d + A ) / G G O * T ) *Xt f ( j *XAO + ( u + \ 1 / f .G*X 9 0 * V - S G * * Z = XAZC1

( d + A ) / X O U * * Z + ( A/ UJ 0* I + { d + A ) / ‘ ZJ *X AU = tCJ ( d+A 1/ ( I t X asV - XHG* XV3 ) + 1 Z I V = btl

X d 3 * ( d - A ) / 1 0 * ‘ Z - Z( l * XAdZG = XAdZO ' ( ( 0 + A J \ '

/• Z + A/ GGu * U s (d+A ) /V*X bQ - [ ( ‘d+A )/QGO *1 + A/0 00 *1 ) * X VO - XAdZJ C l Z I t i * G Q 0 * 9 - l a - A J / ( Z * * X b U > * * Z W l O ^ X d U + l d r i l * o > / ^ 0 « 0 t l 0 *9 =■ V/ U

( X V U * l Z I d + X v J G * l Z l V ) * Z 0 + X d U * +/G =( ( £ * * ( d +A) *000 * t J/OQO * I + a / £ 0 i * { Z * * X b G ) * 7 - VG = <70

( l Z l d * t f * * Z - X r f J * X v 3 ) * f c d = v U ( £ ( d + A ) 7 t U * V - ( d - A 1 / 1 0 ) * X 0 0 + I u * X V O ) * X d G + X d Z 3 ) * * Z = XdHG

( t a * V + I Q i ^ l Z l Q - Z G * 1 Z I V = XdZU XAG*XoO - VJ + 90 - O i M J X O N U

H Z i a * * Z - { t - A ) / ( Z * * X d a ) ) * ( b-A } / I d + I J H l * b ) / 9 0 * ’ Z - 90l t O * V * X d 3 - Z 3 * X V 3 ) * x a j - Z O * V * l Z l b + 9 G * 3 Z 1 V = 9 0

l a * a > / s u - t d + A ) / [ d / o o u * I + l y + A ) / 0 3 b * U = t o._ . S G* u / GGO* T (d+A ) / 0 G O *1 = Z0

I A / t ri+A ) ) BOia=*»U A G d G / X d O - = XA3

1 0 - t t d + A ) / 0 CJO *1 -f A / U C I O M ) * Z U * V - AG dO Z 3 * X * / 3 - I £ 0 * 9 + l G ) * X d O - X d U

( d + A ) / ZU — tG.................................................. t ( t i + M * A * d H i j / j a o * i = z a z e

( 3 7 3 Z ^ 0 #t)/lM-lSioX l b = l S l d

A - ISAZ£ 01 30 (I *3\l * X ) 31

(Z**l d-A ) )/l'd = IU U£■ ' n ) A9\/ - A »z

*7Z D1 00 (T )19V = *1 9Z

O t 01 0 0

2 ............ ...... ................. 12 31 JO IXVriZM * j T ISiZN) 3l2 u* 0 + 1S3Z = I b l Z I + IS 3Zfv ^ 1S3ZN *7*7

22 31 30 ( 1+ >t) A97 = t X) A3V &£(1+X119V = OIJIUV

. . . 2*l = >i &£ DQ ' '1 + !\ - N

*7*v 31 3D { ( S V O *13* Z) " t m * C2 *3 3* N) ) a I23 U1 JO ( uOt *30’ IL'UM) 31

i + iuiim = iniw15>ldX/TA=d I )d = Z

0i QQ ({0*0 --j- (i)c) * du* (0*1 * 13* ( 21 1 h V } } 31 ■'( O+lbA) *iSA*3Hi )/V - ( 1— iSA )/l5l a = d i d

{ S 0 6 ‘ b 0 2 I / l S i a X ) i f c 0 S = - d r t i * 2 / ( 2 ) A 9 t f = ( i ) A 9 V ( 3 * 0 * 1 3 * ( £ ) A £ v ) 31* 2 / ( 2 ) l t W = ( £ ) i q v 0 * 0 • I T t E ) 1 G V ) 31

ttv 31 3D ( bl * 3 0 * N ) 31. .. ^ ^ ( ( :y rj 0 -! 1 S 3 1 G ) ' O W (1S d J * I T ( A 33 3) S 3 V 3 ) * J\'V* O d d * I T (i13(! )D 9 V U } ) 31

( ( I* 2) x O M G ) Sdi/Q + ( ( T l l x £j \ u )S ‘J v (j = 1 S 3 1 UA3d 3 + ( 2 1 Ati ? — (£)AdVi 130 + (2 JidV = (t JldV

9 H J P / ( (11 IMG i ( I * 2)XQ 3 J - (2) IXOMC) - A3 3QBLiJVf/( (2 )ANu* (TI )Xj .\3 - ( 1 ) ANiO* ( I * 2 ) XJ\J J i = 1310'

( 1 >A\IG* (2 )1\U - 12 )AMG*(1 )1NU = bODVT llDAdV - (2 ) AbV ) /( I 2 * ») x333 - ( T,mO\lU) = U)Afcd 9£( (I )19V - (2 ) 1 GV )/ ( (t ‘ A )XONG - ( TXJXDMJ) = Oi)i.\0

.... 2 A1 = >i d£ uGXAZLOXdG - ( X d2 0* * 2 + X AG* X Ad23 ) * xAQ - */j + ZJ = OiA2)XGi\;U Vt

A GdG/(X A2 G - Au dG/5 3*Xo3 J = XA2u( Xd3 - X A 3) -rlb-Al/lU^'d + 20*50 = 50

I Iti + A) / u G J* I + £ G ) * ( 1 8 + A ) / X y G * 7 - ( £ 0 * ( 6 + A ) / 0 3 0 ' 1 + ( A * A ) / O G O *1 ) * X A G * V T 2 - £ G * X * G = 5 0

4 5 TF ( N T 0, „ F G . ?) B O T C 2 1 5 0 C C N T T N J F5 2 I F ( M N N . hf. 1) G C T C ? C 0

I H I = I H I — 1 I F { T . G T . I H I ) G C T C 6 2 o n 5 5 K - I , I H I X (K ) = X IK + L )PEXP(K) * PE X P ( K + l.}

55 T E X P ( K ) = T F X P t K + 1 )IF ( I IPviC . E C . 1 ) G C T O 15 I = I * I I N C - 1

IF { I - I H I ) IS, 1 9 1 6 2 . . . . . .5 6 T K = A G T H )

V - 4 ! W C 3 )C E N D I T E R A T I O N FOP. T E M P E R A T C P F T K A N O V O L U M E

P T = R Z * T KT ( I ) = T K - 2 7 3 . 1 6

_ _ _ _ _ _ P ( I ) = R T / ( V - 9 ) - A / ( D S Q R T ( T K ) * V * ( V + B l )I = I + IT N CI F I I . L E . I H I ) G O T C 1 9

C E N D C A L C U L A T I O N A L L O O P O V E R M O L E F R A C T I O N S6 2 N U M P T S = N M P T - N P + I H I + 1

IF ( N U M D T S . L T . MI N N P T ) G O T C 7 C D C 6 6 K = 1 ,2 . ___ _ _ _ _ _ _ _ _ _

66 RN{ K> = 0 . 000 66 1 = ILO, I H I , I INCP M f 1 1 = RM( U + ( P m - P E X P ( m * * 2

66 PMI2) = R v ( 2) f m i ) - TEXP { I ) ) **2PTSNO = NUWPT 5D C 6 3 K = l »2 . . . . . . .

6 R R M ( K ) = 5 C P T ( R M ( K ) / P T S N C )T P R A T = 4 • 0FUNOPT = ) + TPRAT*RN(?)G O T O 7 4

T O I F ( N U M P T S . E G . - 0 ) N U M P T S = 0... fcRI TE ( 6 , 7 2 ) N V FT , M J M P T S ___ ____ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _7 2 F O R M A T { / 1 0 X , l F n P O I N T S A T T F N P T F 0 * , 1 3 , ? H ,, 1 0 X , 1 R F P O 1 N T S C C N

1 V F P G E D H f 1 3 , 2 H ,, 1 0 X , 4 1 H S I N C E T H I S IS T O O S M A L L , SF T F U N O P T U 2 5 0 . / / )F U M O P T = 5 0 . ...... _... . .. . . . . . . . . . . . . ...

7 4 p n It I = 1 , N P X ( I) = X S T ( I )P F X P { I J = P X S T U )

7 6 TF X P ( IJ = T X S T t l )PETIJ R N

... F N D . . _ ...

BIBLIOGRAPHY

Abara, J. A., M.Sc, Thesis, The Ohio State University, 1967.

Ackerman, F, J., and 0. Redlich, "On the Thermodynamics of Solutions. IX. Critical Properties of Mixtures and the Equation of Benedict, Webb, and Rubin",J. Chem. Phys. ^8 , 2740(1963).

Ambrose, D., "Critical Temperatures of Some Phenols and Other Organic Compounds", Trans, Faraday Soc,

1988(1963).Ambrose, D., B. E. Broderick, and R. Townsend, "The

Vapor Pressures above the Normal Boiling Point and the Critical Pressures of Some Aromatic Hydrocarbons", J, Chem. Soc.(A) 4, 633(1967).

Ambrose, D. , and D, G. Grant, "The Critical Temperatures of Some Hydrocarbons and Pyridine Bases”, Trans. Faraday Soc. jQ, 771(1957).

Ambrose, D., and R. Townsend, "Thermodynamic Properties of Organic Oxygen Compounds, Part IX. The Critical Properties and Vapor Pressures, Above Five Atmospheres, of Six Aliphatic Alcohols", J. Chem, Soc. 361M 1963).

Ambrose, D., and R. Townsend, "Critical Temperatures and Pressures of Some Alkanes", Trans. Faraday Soc. 64, 2622(1968) .

Andrews, T,, Phil. Trans. 159. 575(1869).Barber, J. R., M.Sc. Thesis, The Ohio State University, 1964.

32210* Benedict, M,, G. B. Webb, and L. C. Rubin, "An Empi

rical Equation for Thermodynamic Properties of Light Hydrocarbons and Their Mixtures*I, Methane, Ethane, Propane, n-Butane", J. Chem, Phys, 8, 33*4(19*40); "An Empirical Equation for Thermodynamic Properties of Light Hydrocarbons and Their Mixtures* XI, Mixtures of Methane, Ethane, Propane, and n-Butane", J, Chem, Phys,10, 7*47(19*42).

11, Bierlein, J, A,, and W, B, Kay, "Phase-EquilibriumProperties of System Carbon Dioxide-Hydrogen Sulfide", Ind, Eng. Chem. *4j>, 618(1953)*

12, Boberg, T, C., and R, R, White, "Prediction ofCritical Mixtures* Use of Mathematical Representations for Molar Free Energy of Mixing",Ind. Eng. Chem. Fundamentals 1_, *40(l9o2).

13* Cheng, D. C-H, J. C. McCoubrey, and D. G. Phillips, "Critical Temperatures of Some Organic Cyclic Compounds", Trans, Faraday Soc, ^8, 22*4-(1962),

14, Cherry, Jr., R. H,, Ph.D. Dissertation, The Ohio State University, 1966,

15* Chueh, P. L,, and J. M, Prausnitz, "Vapor-Liquid Equilibria at High Pressures* Calculation of Critical Temperatures, Volumes, and Pressures of Non-Polar Mixtures", A.I.Ch.E. J, 12» 1107(1967),

16. Chun, S. W., Ph.D. Dissertation, The Ohio StateUniversity, 196*4,

17. Connolly, J, F., and G, A. Kandalic, "Virial Coefficients and Intermolecular Forces of Hydrocarbons", Physics of Fluids 2* *463(1960).

18. Davidson, W, C., "Variable Metric Method for Minimization", A.E.C. Research and Development Report, ANL-5990(1959).

19* Davies, 0. L., M.Sc, Thesis, The Ohio State University, 1965.

20, Dieterici, C., Ann. Phys. 6£, 685(1899).21. Dixson, W. J,, "BMD Biomedical Computer Programs",

University of California Publication No.2, P.2 3 3, University of California Press, Berkeley &Los Angeles, 196?,

32322. Draper, N. R., and H. Smith, "Applied Regression

Analysis", John Wiley & Sons, New York, 1967*23* Edmister, W. C., and D. H. Pollock, "Phase Relations

for Petroleum Fractions", Chem. Eng. Prog. 44,905(19^8).2k, Ekiner, 0., and G. Thodos, "Interaction Model for

Critical Temperatures of Multicomponent Mixtures of Methane-Free Aliphatic Hydrocarbons",A.I.Ch.E, J. U, 897(1965).

25. Ekiner, 0., and G. Thodos, "Interaction Model forCritical Pressures of Multicomponent Methane- Free Aliphatic Hydrocarbon Mixtures", Chem. Eng. Science 21, 353(1966).

26, Ekiner, 0., and G. Thodos, "Critical Temperatures ofMethane-Aliphatic Hydrocarbon Mixtures",Ind. Eng. Chem. Fundamentals 6, 222(1967),

27* Etter, D. 0., and V/. B. Kay, "Critical Properties of Mixtures of Normal Paraffin Hydrocarbons",J. Chem, Eng. Data 6, 409(1961),

28. Fletcher, R., and M. J. D. Powell, Computer Journal6, 163(1963).

29. Fletcher, R,, and C. M. Reeves, Computer Journal2, 149(1964).30. Genco, J. M., M.Sc. Thesis, The Ohio State University,1962.31. Gibbs, J. W., "The Collected Works", Vol. I, pp. 129-

13^, Longmans, Green, New York, 1928.32. Grieves, R. B., and G, Thodos, "The Critical Temper

atures and Pressures of Binary Systems» Hydrocarbons of All Types and Hydrogen", A.I.Ch.E. J.6, 561(1960).

33* Grieves, R. B., and G, Thodos, "The Critical Temperatures of Multicomponent Hydrocarbon Systems", A.I.Ch.E. J. 8, 550(1962).

34-. Grieves, R. B. , and G. Thodos, "The CriticalPressures of Multicomponent Hydrocarbon Mixtures and the Critical Densities of Binary Hydrocarbon Mixtures", A.I.Ch.E. J. £, 25(1963)*

32435* "Handbook of Chemistry and Physics", Chemical Rubber

Publishing Co., Cleveland, Ohio, i960.36. Hershey, H. C., "The Chemical Engineering Library

Program”, Department of Chemical Engineering,The Ohio State University, 1969*

37* Hissong, D, W., Ph.D. Dissertation, The Ohio State University, 1968.38. Hissong, D. V/,, and W. B. Kay, "The Calculation of

the Critical Locus Curves of a Binary Hydrocarbon Mixtures", A.I.Ch.E. J. 3 6, 580(1970).

39* Hildebrand, J. H., and R. L. Scott, "The Solubility of Nonelectrolytes", p*29» Dover Publication,1964.

1*0. Hirschfelder, J. 0. , et al, "Molecular Theory of Gases and Liquids", pp. 1^2-163, V/iley & Sons, New York, 1954.'

41. Hooke, R., and T. A. Jeeves, J. ACM 8, 212(1961).42. Jefferies, E. F., M.Sc. Thesis, The Ohio State

University, 1966*43. Jepson, W. B., M. J, Richardson, and J. S. Rowlinson,

"The Solubility of Mercury in Gases at Moderate Pressures", Trans, Faraday Soc. 1586(1957).

44. Jepson, W. B., and J, S. Rowlinson, "Calculation ofthe Correction to be Applied to Gas Isotherms Measured in the Presence of Mercury",J. Chem. Phys. 2^, 1599(1955).

45* Joffe, J., and D. Zudkevitch, "Prediction of Critical Properties of Mixtures 1 Rigorous Procedure for Binary Mixtures", Chem, Eng. Prog. Symp. Ser,No.81, 43(1967).

46, Jones, J. W,, and J. S. Rowlinson, "Gas-LiquidCritical Temperatures of Binary Mixtures", Trans. Faraday Soc, j>2» 1702(1963).

47, Kay, W, B,, "Density of Hydrocarbon Gases and Vaporsat High Temperature and Pressure", Ind. Eng. Chem. 28, 1014(1936).

32548. Kay, W. B., "Liquid-Vapor Phase Equilibrium Relations

in the Ethane - n-Heptane System", Ind, Eng. Chera. 30, **-59(1938).

49. Kay, W. B., "Liquid-Vapor Equilibrium Relations inBinary Systems1 The Ethane - n-Butane System",Ind. Eng, Chem. 22, 353(19^0).

50r Kay, W, B., and R, R. Albert, "Liquid-Vapor Equilibrium Relations in the Ethane - Cyclohexane System", Ind. Eng. Chem, 4§, 422(1956).

51 • Kay, W. B., and T. D, Nevens, "Liquid-Vapor Equilibrium Relations in Binary Systems* The Ethane - Benzene System", Chem. Eng. Prog. Symp. Ser.No. 3, 48, 108(1952).

52. Kay, \V, B., and G. M. Rambosek, "Vapor-Liquid Equilibrium Relations in Binary Systems* Propane- Hydrogen Sulfide System", Ind, Eng. Chem. 45, 221(1953).

53* Kreglewski, A., "A Semiempirical Treatment ofProperties of Fluid Mixtures. II. Estimation of the Effects of Molecular Sizes in Fluids and Fluid Mixtures", J. Phys. Chem. £2. 1897(19o8).

54. Kreglewski, A., "On the Second Virial Coefficient of Real Gases", J. Phys. Chem. 23.* 608(1969),

55* Kreglewski, A., and V/, B. Kay, "The CriticalConstants of Conformal Mixtures", J. Phys. Chem. 23* 3359(1969).

56. Kudchadker, A. P., G. H. Alani, and B. J0 Zwolinski,"The Critical Constants of Organic Substances", Chem. Rev« 68, 659(1968).

57. Lee, K. H., M.Sc. Thesis, The Ohio State University,1965.

58. Li, C. C., Allied Chemical Corporation, Morristown,New Jersy, Private Communication with Calvin F, Spencer, The Pennsylvania State University, University Park, Pennsylvania* 1969,

59. Longuet-Higgins, H. C., "The Statistical Thermodynamics of Multicomponent Systems", Proc. Royal Soc. 205A. 247(1951)

32660. Lyderson, A. L, , ‘'Estimation of Critical Properties of

Organic Compounds"* Coll. Eng., Univ. Wisconsin, Eng. Expt. Station Report 3, Madison, Wis., 1955*

61. Mayfield, F. D,, "Critical States of Two-ComponentParaffin Systems", Ind. Eng. Chem. 3ft» 843(1942).

62. Menzies, Alan W. C., "The Vapour Pressure of LiquidMercury", Z. Physik. Chem. 130, 90(192?).

63. Mogollon, E., M.Sc. Thesis, The Ohio State University,1969.

64. Ng, S. M. , M.Sc, Thesis, The Ohio State University,1961.

65. Organic, E. I., "Prediction of Critical Temperaturesand Critical Pressures of Complex Hydrocarbon Mixtures", Chem. Eng. Prog. Symp. Ser, No.6, 49, 81(1953).

66. Oxley, J. A., M.Sc. Thesis, The Ohio State University,1962.

67. Pak, S. C., M.Sc. Thesis, The Ohio State University,1988*

68. Pitzer, K. S., D. Z. Lippmann, R.F. Curl, Jr.,. C. M, Huggins, and D. E. Petersen, "The Volumetric and Thermodynamic Properties of Fluids. II. Compressibility Factor, Vapor Pressure and Entropy of Vaporization", J, Am. Chem, Soc, 22* 3^33(1955).

69. Poettmann, F. H. , and D, L. Katz, "Phase Behavior ofBinary Carbon Dioxide - Paraffin Systems",Ind. Eng, Chem, 32» 847(1945).

70. Porthouse, L, D., M.Sc, Thesis, The Ohio StateUniversity, 1962,?lo Powell, M. J. D,, Computer Journal 1_, 155(1964),72. Ralston, A., and H, S. Wilf, "Mathematical Methods for

Digital Computers", Chapter 17, John Wiley & Sons, New York, 1962.

73. Redlich, 0., and A. T. Kister, "On the Thermodvnamicsof Solutions. VII. Critical Properties of Mixtures", J, Chem. Phys. 36, 2002(1962).

32774. Redlich, 0,, and J. N. S. Kwong, "On the Thermo

dynamics of Solutions. V. An Equation of State. Fugacities of Gaseous Solutions", Chem. Rev. 44. 233(1949).

75. Redlich, 0. and Victoria B. T. Ngo, "An ImprovedEquation of State", Ind. Eng. Chem. Fundamentals£, 287(1970).

76. Reid, R. C., and T. K. Sherwood, "The Properties ofGases and Liquids 1 Their Estimation and Correlation", 2nd. Ed,, McGraw-Hill Boole Co., New York,1966.

77. Richardson, M, J., and J. S. Rowlinson, "The Solubility of Mercury in Gases at High Density",Trans. Faraday Soc. 22* 1333(1959).

78. Robinson, R. L., Jr., and R. H. Jacoby, "BetterCompressibility Factors", Hydrocarbon Process. Petrol. Refiner 44, No,*!-, 141(1965).

79. Roess, L, C,, "Determination of Critical Temperatureand Pressure of Petroleum Fractions by a FlowMethod", J, Inst. Petrol. Tech. 22, 665(1936).

80. Rosenbrock, H. H., Computer Journal 2* 175(1960).81. Rosenbrock, H. H., and Storey, "Computational

Techniques for Chemical Engineers", Pergamon Press, London, 1966.

82. Rov/linson, J. S., "Liquids and Liquid Mixtures",2nd Ed, pp.190-202, 342, Butterworths & Co. Ltd.,London, 1969.

83. Scatchard, G., "Change of Volume on Mixing and theEquations for Non-Electrolyte Mixtures",Trans. Faraday Soc, 22* 160(1937).

84. Shah, K. K., and G, Thodos, "A Comparison ofEquation of State", Ind. Eng. Chem. 2Z* 30(1965).

85. Skaates, J. M., and W. B. Kay, "The Phase Relationsof Binary Systems That Form Azeotropes N-Alkylalcohol - Benzene Systems* Methanol Through n-Butanol", Chem. Eng. Science 19. 431(1964).

328

86* Smith, R. L., and K. M. Watson, "Boiling Points and Critical Properties of Hydrocarbon Mixtures",Ind. Eng. Chem* 21408(193?).

87* Spear, R* R., R. L. Robinson, Jr., and K. C, Chao, "Critical States of Mixtures and Equations of State", Ind. Eng. Chem. Fundamentals 8, 2(1969)*

88. Spencer, C. F., Private Communication, The Pennsylvania State University, 1970,

89. Wagner, G. H., and V/, H, Gitzen, "Gallium",J. Chem. Education 2£, 162(1952).

90. Williamson, J. E,, Ph.D. Dissertation, The Ohio StateUniversity, 1968.

91. Wilson, G. M., "Vapor-Liquid Equilibria, Correlationby Means of a Modified Redlich-Kwong Equation of State", Adv. Cryog, Eng. 168(1964),

92. Wilson, R. F., et aj, "Documentation of the Basis forSelection of the Contents of Chapter 4 - Critical Properties in Technical Data Book - Petroleum Refining", Documentation Report No.4-66,American Petroleum Institute, 1966.

93° Young, Sci. Proc. Royal Dublin Soc. 12, 374(1910).

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