Compressibility Factors for Natural and Sour

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COMPRESSIBILITY FACTORS FOR NATURAL AND SOUR

RESERVOIR GASES BY CORRELATIONS AND

CUBIC EQUATIONS OF STATE

NEERAJ KUMAR, B.Tech.

A THESIS

PETROLEUM ENGINEERING

Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of

MASTER OF SCIENCE

PETROLEUM ENGINEERING

Approved

Akanni Lawal Chairperson of the Committee

Paulus Adisoemarta

Accepted

John Borrelli Dean of the Graduate School

December, 2004 ACKNOWLEDGEMENTS

There are many people who were associated with this thesis who deserve recognition. I would like to thank Dr. Akanni S. Lawal for his direction, support and training. Thanks to Dr. James F. Lea for helping me with industrial approach towards this thesis. I would also like to thank Dr. Paulus Adisoemarta for serving on my committee and for his guidance.

ii TABLE OF CONTENTS

ACKNOWLEDGEMENTS ii ABSTRACT vi LIST OF TABLES vii LIST OF FIGURES viii LIST OF ABBREVIATIONS xii CHAPTER 1. INTRODUCTION 1 1.1 Background Information 1 1.2 Use of Compressibility Factors in Engineering Analysis 2 1.2.1 Z-Factor for Sour and Acid Gases 2

1.2.2 Z-Factor for Geologic CO2 Storage 2 1.3 Significance of the Project 3 1.4 Objective of the Project 4

2. COMPRESSIBILITY FACTOR PREDICTION TECHNIQUES 5 2.1 Theoretical Analysis of Gas Law-Based Z-Factors 5 2.2 Experimental Method for Compressibility Factors 5 2.3 Empirical Correlation Methods 5 2.3.1 Standing-Katz Compressibility Factor Chart 5 2.3.2 Hall-Yarborough Z-Factor Correlation 6 2.3.3 Wichert -Aziz Z-Factor Correlation 7 2.3.4 Dranchuk-Abou-Kassem Z-Factor Correlation 7 2.3.5 Beggs-Brill Equation for SK Z-Factor Chart 8 2.3.6 Amoco Company Equation for SK Z-Factor Chart 9 2.3.7 Gopal Best-Fit Equation for SK Z-Factor Chart 9 2.3.8 Shell Oil Company Equation for SK Z-Factor Chart 10

2.3.9 Physical Properties of C7+ Fractions Correlations 11

iii 2.4 Corresponding State Prediction Methods 12 2.5 Equations of State Prediction Methods 19

3. STANDING-KATZ Z-FACTOR CORRELATION 20 3.1 Standing-Katz Representation of Z-Factor Chart 20 3.2 Best-Fit Equations for SK Z-Factor Chart 20 3.3 Mixture Critical Property Prediction Methods 23 3.3.1 Heptane-Plus Fraction Correlation Methods 25 3.3.2 Pseudocritical Mixing Parameter Methods 27 3.3.3 Pseudocritical Gas Gravity Correlation Methods 33 3.3.4 van der Waals Theory of Pseudocritical Methods 37 3.3.5 Improved Theory for Pseudocritical Mixture Parameter 37 3.4 Designed Scaling Parameter for Standing-Katz Z-Factor Chart 38 3.4.1 Design Procedure for Scaling Parameter 38

3.5 Designed PR/Z Versus Z-Factor Chart 42 3.6 Prediction Results for Z-Factor of Natural Gases 43 3.7 Prediction Results for Z-Factor of Reservoir Gases 45

4. Z-FACTOR PREDICTIONS FROM CUBIC EQUATIONS OF STATE 53 4.1 Selection of Cubic Equations-of-State 53 4.2 Lawal-Lake-Silberberg Equation of State 54 4.3 van der Waals Equation of State 56 4.4 Redlich-Kwong Equation of State 57 4.5 Soave-Redlich-Kwong Equation of State 58 4.6 Peng-Robinson Equation of State 61 4.7 Schmidt-Wenzel Equation of State 62 4.8 Patel-Teja Equation of State 63 4.9 Trebble-Bishnoi Equation of State 65

iv 4.10 Transformed Cubic Equations to the LLS EOS Form 66 4.11 Generalized Reduced State of Cubic Equations-of-State 67 4.12 Prediction Results for Z-Factor of Pure Substances 71 4.13 Development of Binary Interaction Parameters 74 4.14 Prediction Results of Z-Factor of Mixtures 75 4.15 Prediction Results for Z-Factor of Natural Gases 77 4.15. 1 Results for Excelsior Laboratory Data 78 4.15. 2 Results for TTU Laboratory Data 80 4.15. 3 Results for UCalgary Data 81 4.15. 4 Results for Elsharkawy Gas Data 88 4.15. 5 Results for Elsharkawy Miscellaneous Data 90

5. CONCLUSIONS AND RECOMMENDATIONS 94 5.1. Conclusions 94 5.2. Recommendations 95

REFERENCES 96 APPENDICES 106 A. REDUCED FORM OF CUBIC EQUATIONS OF STATE 106 B. PREDICTION RESULTS FOR PSEUDOCRITICAL PARAMETERS 117 C. SCALING FACTOR DEVELOPMENT AND RESULTS 122 D. PREDICTION OF Z-FACTOR FOR PURE SUBSTANCES 127 E. EXPERIMENTAL Z-FACTOR FOR MISCELLANEOUS GASES 137 F. PREDICTION OF Z-FACTOR FROM LLS EOS 171 G. FORTRAN PROGRAMS 174

v ABSTRACT

Compressibility factor (z-factor) values of natural gases are necessary in most petroleum engineering calculations. The most common sources of z-factor values are experimental measurement, equations of state method and empirical correlations. Necessity arises when there is no available experimental data for the required composition, pressure and temperature conditions. Presented here is a technique to predict z-factor values of pure substances, natural gases and sour reservoir gases regardless of the composition of the acid gases at all temperatures and pressures. Eight equations of state have been thoroughly examined and the results suggest that the Lawal-Lake-Silberberg (LLS-EOS) equation of state is capable of predicting z- factor values of both pure substances and mixtures of gases. This equation of state

method allows the determination of reduced temperature (TR) and reduced pressure (PR) instead of the pseudo-reduced temperature (TPR) and pseudo-reduced pressure (PPR) both for pure substances and mixtures of gases. This EOS is robust and the results are accurate even if of acid gases present in high concentration. A comparative z-factor prediction result of the various EOS methods for different gas samples is presented fortifying the capability of the LLS-EOS method. Another method of predicting z-factor values is based on the famous Standing-Katz (S-K) Chart (empirical methods). Law of Corresponding States principle has formed the basis to develop a universal adjustable parameter. This developed adjustable parameter forms the basis for using LLS-EOS to be able to use S-K Chart to predict accurate z-factor values of pure substances and mixtures of gases regardless of the concentration of acid gases. In contrast to the existing methods derived from other equations of states (EOS methods) and S-K Chart (empirical methods), this project provides a simple and universal technique for predicting z-factor values for pure substances, natural gases and sour reservoir gases.

vi LIST OF TABLES

2.1 Heavy Fraction Property Correlations. 10 3.1 Coefficients of Cavett’s correlation. 25 3.2 Sources of Experimental Z-Factor for Pure Substances 36 3.3 Rich Gas Condensate Composition (Elsharkawy) 45 3.4 Highly Sour Gas Composition (Elsharkawy) 46 3.5 Carbon Dioxide Rich Composition (Elsharkawy) 47 3.6 Very Light Gas Composition (Elsharkawy) 48 3.7 Property Prediction for Gas Composition Data (Elsharkawy) 49 4.1 Common Specialization Cubic Equation of State 66 4.2 Sources of Experimental Z-Factor 77 4.3 Gas Composition Data for Excelsior 6 Laboratory Data. 78 4.4 Gold Creek Gas Composition. 81 4.5 Results of Elsharkawy Gas Data. 88 4.6 Z-Factor Results for Miscellaneous Gases. 90 B.1 Gas Composition Description. 118 E.1 UCalgary Z-Factor Data. 137

vii LIST OF FIGURES

1.1 Critical compressibility factor for pure hydrocarbons (alkanes). 3

2.1 Z-Factor of Pure Substances at Reduced Conditions(TR=0.65). 22

2.3 Z-Factor of Pure Substances at Reduced Conditions (TR=0.85). 24

2.4 Z-Factor of Pure Substances at Reduced Conditions (TR=1.02). 24

2.5 Z-Factor of Pure Substances at Reduced Conditions (TR=1.07). 25

2.6 Z-Factor of Pure Substances at Reduced Conditions (TR=1.13). 25

2.7 Z-Factor of Pure Substances at Reduced Conditions (TR=1.24). 26

2.8 Z-Factor of Pure Substances at Reduced Conditions (TR=1.55). 26

2.9 Z-Factor of Pure Substances at Reduced Conditions (TR=1.98). 27

2.10 Z-Factor of Pure Substances at Reduced Conditions (TR=2.03). 27 3.1 Comparison of Six Correlations for Pseudocritical Pressure Parameters. 35 3.2 Compare of Six Correlations for Pseudocritical Temperature Parameters. 35 3.3 Scaled Z-Factor for Buxton & Campbell Data (Mix-5) at 160 oF. 40 3.4 Scaled Z-Factor for Buxton and Campbell Data (Mix-5) at 130 oF. 40 3.5 Scaled Z-Factor for Buxton and Campbell Data (Mix-5) at 100 oF. 41 3.6 Scaled Z-Factor for Satter Data (Mix-E) at 160 oF. 41 3.7 SK Z-Chart Developed Based on Computation SK Technique. 42 3.8 Amount of gas produced. 43 3.9 Scaled Z-Factor Buxton & Campbell, Mix-2 Result, @ T = 130 oF. 43 3.10 Scaled Z-Factor Buxton & Campbell, Mix-2 Result, @ T = 100 oF 44 3.11 Scaled Z-Factor Buxton & Campbell, Mix-3 Result, @ T = 100 oF 44 3.12 Scaled Z-Factor for Very Light Gas Composition. 50 3.13 Scaled Z-Factor for Carbon Dioxide Rich Gas Composition. 50 3.14 Scaled Z-Factor for Rich Gas Condensate Composition. 51 3.15 Scaled Z-Factor for Highly Sour Gas Composition. 51 4.1 Z-Factor comparison for LLS-EOS for Methane. 71 4.2 Z-Factor comparison for LLS-EOS for Carbon dioxide. 72

viii 4.3 Z-Factor comparison for LLS-EOS for Nitrogen. 72 4.4 Z-Factor comparison for vdW-EOS for Methane. 73 4.5 Z-Factor comparison for vdW-EOS for Carbon dioxide. 73 o 4.6 Z-Factor comparison for CO2-C1 mixture at 49 F. 75 o 4.7 Z-Factor comparison for CO2-C1 mixture at 70 F. 75 o 4.8 Z-Factor comparison for CO2-C1 mixture at 90 F. 76 o 4.9 Z-Factor comparison for CO2-C1 mixture at 90 F. 76 4.10 Z-Factor for Sweet Natural Gas, Data from Excelsior 6 (FPP) at 581 oR. 79 4.11 Z-Factor Comparison Chart at 90 oF (Simon et. al.). 79 4.12 Z-Factor Comparison Chart at 120 oF (Simon et. al.). 80 o 4.13 75% CO2 - Dry Gas at 100 F for CO2 Sequestration. 80 o 4.14 25% CO2 - Dry Gas at 160 F for CO2 Sequestration. 81 4.15 Z-Factor for sour natural gas, data from Excelsior 6 (FPP) at 581 oR. 82 4.16 Z-Factor comparison for sour natural gas mixture at 84 oF. 82 4.17 Z-Factor comparison for sour natural gas mixture at 73 oF. 83 4.18 Z-Factor comparison for sour natural gas mixture at 198 oF. 83 4.19 Z-Factor comparison for sour natural gas mixture at 50 oF. 84 4.20 Z-Factor comparison for sour natural gas mixture at 100 oF. 84 4.21 Z-Factor comparison for sour natural gas mixture at 125 oF. 85 4.22 Z-Factor comparison for sour natural gas mixture at 150 oF. 85 4.23 Z-Factor comparison for sour natural gas mixture at 175 oF. 86 4.24 Z-Factor comparison for sour natural gas mixture at 200 oF. 86 4.25 Z-Factor comparison for sour natural gas mixture at 219 oF. 87 4.26 Z-Factor comparison for sour natural gas mixture at 250 oF. 87 B.1 Critical temperature prediction for Gore Data (Mix 47-1). 118 B.2 Critical pressure prediction for Gore Data (Mix 47-1). 119 B.3 Critical pressure prediction for Gore Data (Mix 26-1). 119 B.4 Critical temperature prediction for Gore Data (Mix 26-2). 120 B.5 Critical pressure prediction for Gore Data (Mix 26-2). 120

ix B.6 Critical temperature prediction for Gore Data (Mix 26-3). 121 B.7 Critical pressure prediction for Gore Data (Mix 26-3). 121 C.1 Scaled z-factor result for Buxton & Campbell Data at 160 oF (Mix-4). 123 C.2 Scaled z-factor result for Buxton & Campbell Data at 130 oF (Mix-4). 123 C.3 Scaled z-factor result for Buxton & Campbell Data at 160 oF (Mix-3). 124 C.4 Scaled z-factor result for Buxton & Campbell Data at 130 oF (Mix-3). 124 C.5 Scaled z-factor result for Buxton & Campbell Data at 100 oF (Mix-3). 125 C.6 Scaled z-factor result for Buxton & Campbell Data at 130 oF (Mix-2). 125 C.7 Scaled z-factor result for Buxton & Campbell Data at 160 oF (Mix-1). 126 D.1 Z-Factor comparison for vdW-EOS for Nitrogen. 127 D.2 Z-Factor comparison for RK-EOS for Methane. 127 D.3 Z-Factor comparison for RK-EOS for Carbon dioxide. 128 D.4 Z-Factor comparison for RK-EOS for Nitrogen. 128 D.5 Z-Factor comparison for SRK-EOS for Methane. 129 D.6 Z-Factor comparison for SRK-EOS for Carbon dioxide. 129 D.7 Z-Factor comparison for SRK-EOS for Nitrogen. 130 D.8 Z-Factor comparison for PR-EOS for Methane. 130 D.9 Z-Factor comparison for PR-EOS for Carbon dioxide. 131 D.10 Z-Factor comparison for PR-EOS for Nitrogen. 131 D.11 Z-Factor comparison for SW-EOS for Methane. 132 D.12 Z-Factor comparison for SW-EOS for Carbon dioxide. 132 D.13 Z-Factor comparison for SW-EOS for Nitrogen. 133 D.14 Z-Factor comparison for PT-EOS for Methane. 133 D.15 Z-Factor comparison for PT-EOS for Carbon dioxide. 134 D.16 Z-Factor comparison for PT-EOS for Nitrogen. 134 D.17 Z-Factor comparison for TB-EOS for Methane. 135 D.18 Z-Factor comparison for TB-EOS for Carbon dioxide. 135 D.19 Z-Factor comparison for TB-EOS for Nitrogen. 136 F.1 Z-factor for pure substances (Methane). 171

x F.2 Z-factor for pure substances (n-Decane). 171 F.3 Z-factor for pure substances (Carbon Dioxide). 172 F.4 Z-factor for pure substances (Hydrogen Sulfide). 172 F.5 Z-factor for pure substances (Nitrogen). 173

xi LIST OF ABBREVIATIONS

Symbol Definition a Attraction Parameter in EOS ⎛ a(T)P ⎞ A Dimensionless Constant ⎜ ⎟ ⎝ R 2T 2 ⎠ ACF Acentric Factor AF Acentric Factor API Oil Gravity b van der Waals co-volume ⎛ bP ⎞ B Dimensionless Constant ⎜ ⎟ ⎝ RT ⎠ BIN Binary Interaction Number BIP Binary Interaction Parameter EOS Equation of State G Gibbs Free Energy k Parameter of SRK EOS LLS Lawal-Lake-Silberberg m Parameter of SRK EOS

Mw Molecular Weight Mw Molecular Weight p Pressure in psia P Pressure in psia PR Peng Robinson R Universal Gas Constant (10.73 psiD.ft3/ (lb- mol. oR)) RK Redlick-Kwong SRK Soave-Redlich-Kwong

xii SW Schmidt-Wenzel t Inverse Absolute Temperature (1/T) T Absolute Temperature TB Trebble-Bishnoi V Volume in cubic feet vdW van der Waal x Mole Fraction z Compressibility Factor Z Compressibility Factor

Greek Letter α Parameter of LLS EOS

αij Binary Interaction Term β Parameter of LLS EOS Ω Dimensionless EOS Parameter ω Acentric Factor

γg Specific Gravity

Subscripts c Critical Property pr Pseudo Reduced Property Identification pc Pseudo Critical Property Identification r Reduced Property Identification m Mixture Definition R Reduced State i, j Component Identification 1, 2 Index for components 1 and 2

xiii CHAPTER 1

INTRODUCTION

1.1 Background Information Compressibility Factor is a measure of the amount the gas deviates from perfect behavior. It is more commonly called as the gas deviation factor, represented as z (or) Z. It is a dimensionless quantity and by definition the ratio of the volume actually occupied by a gas at a given pressure and temperature to the volume it would occupy if it behaved ideally. Therefore, a value of z = 1 would represent an ideal gas condition. V Actual volume of n moles of gas at T and p z = a = Vi Ideal volume of n moles at same T and p The kinetic theory of gases (basis for Ideal gas law) assumes that there are neither attractive forces nor repulsive forces between the gas molecules. In nature, ideal gases do not exist instead real gases exist. All molecules of real gases are under two kinds of forces: (a) to move apart from each other because of their constant kinetic motion, and (b) to come together because of electrical attractive forces between the molecules. At normal conditions, the molecules are quite far apart and the attractive forces are negligible and same is the condition at high temperatures because of the greater kinetic motion. Under these above mentioned conditions, the gas tends to approach ideal behavior. While, at high pressures, the molecules come very close to each other resulting in significant attractive forces. These theories qualitatively explain the behavior of non- ideal (real) gases and a general representation of the gas law is as follows: Ideal Gas Law: PV = nRT (1.1). Real Gas Law: PV = znRT (1.2).

1 1.2 Use of Compressibility Factors in Engineering Analysis Accurate information of compressibility factor values is necessary in engineering applications like gas metering, pipeline design, estimating reserves, gas flow rate, and material balance calculations. Some of the petroleum engineering applications which involve use of z-factor values of gases are as follows:

1.2.1 Z-Factor for Sour and Acid Gases If hydrogen sulfide is present in a natural gas mixture it is termed as sour natural gas. The existing methods of calculating z-factor values when significant amounts of acid gases like carbon dioxide (CO2) and hydrogen sulfide (H2S) are present in the natural gas mixtures incur high deviations from the actual values.

1.2.2 Z-Factor for Geologic CO2 Storage

A high content of CO2 gas present in the atmosphere is the major cause for global warming. A method to capture CO2 from the atmosphere or other sources of CO2 production and be able to store it into abandoned wells is called as CO2 sequestration.

CO2 gas in various concentrations can be required to be stored. Engineering this method needs z-factor values. Knowledge of accurate critical z-factor value for pure substances and mixtures is essential in the determination of accurate z-factor values. Critical z-factor is unique for each component and system. Figure 1.1 illustrates the capability of various equations-of- states in predicting critical compressibility factor values.

2 0.38 VDW

0.36 or

t 0.34

c RK ity Fa 0.32 ibil PR ss SW 0.30

Compre Twu PT al

Critic 0.28 TB EXP LLS 0.26

0.24 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 Pure Substances

Figure 1.1: Critical compressibility factor for pure hydrocarbons (alkanes).

1.3 Significance of the Project Today’s standard treatment of phase behavior in reservoir simulation is still based on formation volume factors (FVF’s) and surface gas/oil ratios (GOR’s) which requires the determination of z-factor and critical properties of mixtures, more importantly. As more and more, sour environment reservoirs are discovered, it becomes a necessity to have a simple and robust technique to be able to determine z-factor values accurately. This project presents methods that allow accurate determination of z-factor values both for pure components and gas mixtures including significant amounts of non-hydrocarbon components for all ranges of pressures and temperatures.

3 1.4 Objective of the Project This research project provides improved predictive techniques for z-factors based on the approaches of cubic Equations-of-State (EOS) and empirical correlation of Standing-Katz5 Chart. Eight EOS that are routinely used in reservoir calculations and improved pseudocritical property methods for Standing & Katz (SK) Chart are utilized to match experimentally determined z-factors for pure substances, natural and sour reservoir gases. The experimental z-factors data for 3100 gas samples, including highly sour gases

(H2S), acid gases (CO2 and N2) and rich gas condensates (with significant amount of C7+) are used to establish the improved predictive techniques for z-factors.

4 CHAPTER 2

COMPRESSIBILITY FACTOR PREDICTION TECHNIQUES

2.1 Theoretical Analysis of Gas Law-Based Z-Factors The magnitude of deviation of real gases from the conditions of the ideal gas law increases with increasing pressure and temperature and varies widely with the composition of the gas. Numerous equations-of-state have been developed in the attempt to correlate the pressure-temperature-volume variables for real gases with experimental data. In order to express a more exact relationship between the variables p, V, and T, z-factor must be introduced into the ideal gas equation to account for the departure of gases from ideality. This forms the basis for the real gas law and is represented as: pV = zRT (1.2). To account for this deviation factor (z-factor), numerous equations-of-state have been proposed.

2.2 Experimental Method for Compressibility Factors Among the existing method of determination of z-factors, experimental measurement is one of the most accurate methods. It is hard to determine experimentally measured z-factor values for all compositions of gases at all ranges of pressures and temperatures. At the same time, this method is expensive and most of the time these measurements are made at reservoir temperatures only.

2.3 Empirical Correlations Methods

2.3.1 Standing-Katz Compressibility Factor Chart Standing and Katz5 presented a generalized z-factor chart, which has become an industry standard for predicting the volumetric behavior of natural gases. To be able to

5 use this chart, knowledge of reduced temperature and reduced pressure are required, which further needs determination of critical properties (namely, critical pressure and critical temperature of the system). Numerous methods have been suggested to predict pseudocritical properties of the gases as a function of their specific gravity. The point to be noted here is that these methods predict pseudo critical values which are evidently not accurate values of the gas mixtures. The existing methods fail to predict accurate values of pseudocritical values when non-hydrocarbon components are present in significant amounts. Improved technique to predict critical properties have been discussed in the Chapter 3 of this thesis report.

2.3.2 Hall-Yarborough Z-Factor Correlation Hall and Yarborough8 (1973) presented an equation-of-state that accurately determined the Standing and Katz z-factor chart. This is based on the Starling-Carnahan21 equation-of-state. Best fit mathematical expressions were determined based on the data taken from Standing and Katz z-factor chart. The mathematical form of the equation is:

⎡0.06125p pr t ⎤ 2 Z = ⎢ ⎥EXP[]−1.2()1− t Y ⎣ ⎦ (2.1). where pPR = pseudo-reduced pressure

⎛ Tpc ⎞ t = reciprocal of the pseudo-reduced temperature ⎜= ⎟ ⎝ T ⎠

2 3 4 2 Y + Y + Y − Y F(Y) = −0.06125p pr T[]−1.2()1− t + ()1− Y 3 2 3 2 2 3 ()2.18+2.82t − ()14.76t − 9.76t 4.58t Y + (90.7t − 242.2t + 42.4t )Y = 0 (2.2). Hall and Yarborough pointed out that the method is not recommended for application if the pseudo-reduced temperature is less than one.

6 2.3.3 Wichert-Aziz Z-Factor Correlation

Sour natural gases (containing H2S) and/or CO2 frequently exhibit different compressibility factor behavior than do sweet natural gases. Wichert and Aziz22 (1972) developed a calculation procedure to account for these differences. Wichert and Aziz developed a pseudo-critcal temperature adjustment factor which is a function of the

concentration of CO2 and H2S in the sour gas. This correction factor is then used to adjust the pseudo-critical temperature and pressure according to the following expressions:

Tpc′ = Tpc − ε (2.3). p T′ p′ = pc pc pc T + B 1− B ε pc () (2.4). o where Tpc = pseudo-critical temperature, R

ppc = pseudo-critical pressure, psia o Tpc′ = corrected pseudo-critical temperature, R

p pc = corrected pseudo-critical pressure, psia

B = mole fraction of H2S in the gas mixture ε = pseudo-critical temperature adjustment factor and is defined mathematically by the following expression

0.9 1.9 0.5 4.0 ε = 120(A − A )+15(B − B ) (2.5).

where the coefficient A is the sum of the mole fraction of H2S and CO2 in the gas mixture, or A = y + y H2S CO2 (2.6).

2.3.4 Dranchuk-Abu-Kassem Z-Factor Correlation Dranchuk and Abu-Kassem23 (1975) proposed an eleven-constant equation-of- state for calculating the gas compressibility factors. The equation is as follows:

7 ⎡ ⎤ A 2 A 3 A 5 z = ⎢A1 + + 3 + 5 ⎥ρr ⎣⎢ Tpr Tpr Tpr ⎦⎥ ⎡ ⎤ ⎡ ⎤ A 7 A8 2 A 7 A8 5 + ⎢A 6 + + 2 ⎥ρr − A 9 ⎢ + 2 ⎥ρr ⎣⎢ Tpr Tpr ⎦⎥ ⎣⎢Tpr Tpr ⎦⎥ ρ2 + A ()1+ A ρ2 r EXP[]− A ρ2 +1 10 11 r T 3 11 r pr (2.7). where ρ r = reduced gas density and is defined by the following relationship: 0.27p ρ = pr r zT pr (2.8).

The constants A1 through A11 were determined by fitting the equation, using nonlinear regression models, to 1,500 points from the Standing and Katz z-factor chart. The coefficients values:

A1 = 0.3262 A2 = -1.0700 A3 = -0.5339 A4 = 0.01569

A5 = -0.05165 A6 = 0.5475 A7 = -0.7361 A8 = 0.1884

A9 = 0.1056 A10 = 0.6134 A11 = 0.7210 This method is applicable over the ranges

0.2 ≤ p pr < 30

1.0 < Tpr ≤ 3.0 with an average absolute error of 0.585 percent.

2.3.5 Beggs-Brill Equation for SK Z-Factor Chart Beggs and Brill25 (1973) proposed a best-fit equation for the Standing and Katz z- factor chart and is as follows:

()1− A D z = A + B + Cp pr e (2.9). where

0.5 A = 1.39()Tpr − 0.92 − 0.36Tpr − 0.101

8 ⎡ ⎤ 0.066 2 0.32 6 B = ()0.62 − 0.23Tpr p pr + ⎢ − 0.037⎥p pr + p pr 9()Tpr −1 ⎣⎢()Tpr − 0.86 ⎦⎥ 10

C = (0.132 − 0.32log(Tpr ))

()0.3016−0.49T +0.1824T2 D = 10 pr pr

This method is cannot be used for reduced temperature ( Tpr ) values less than 0.92.

2.3.6 Amoco Company Equation for SK Z-Factor Chart Amoco Company uses the Hall and Yarborough z-factor determination method and can be defined as follows:

⎡0.06125p pr t ⎤ 2 Z = ⎢ ⎥EXP[]−1.2()1− t Y ⎣ ⎦ (2.10). where ppr = pseudo-reduced pressure

⎛ Tpc ⎞ t = reciprocal of the pseudo-reduced temperature ⎜= ⎟ ⎝ T ⎠

2 3 4 2 Y + Y + Y − Y F(Y) = −0.06125p pr T[]−1.2()1− t + ()1− Y 3 2 3 2 2 3 ()2.18+2.82t − ()14.76t − 9.76t 4.58t Y + (90.7t − 242.2t + 42.4t )Y = 0 (2.11). It should be noted that this method is not recommended for application if the pseudo-reduced temperature is less than one.

2.3.7 Gopal Best-Fit Equation for SK Z-Factor Chart Gopal’s33 correlation for z-factor estimation was developed by dividing the

Standing-Katz chart into two parts by drawing a line isobarically for PR up to 5.4. For various Tr values, several z-factor values were tabulated isobarically for Pr up to 5.4 because, for any Pr,, the z-factor values show a uniform trend. His objective was to come

9 up with two noniterative equations, one for Pr less than or equal to 5.4, and the other for

Pr greater than 5.4. To describe the chart accurately, the chart was further divided into 12 parts24. A general equation was developed and is of the form: Z = P AT + B + CT + D r ()r r (2.12).

The values of constants A, B, C, and D for various combinations of PR and TR are 33 available in the reference . For Pr greater than 5.4, harmonic equations are suggested to be a good fit.

2.3.8 Shell Oil Company Equation for Z-Factor Chart

4 ⎛ p ⎞ Z = ZA + ZB× p + (1− ZA) × EXP(−ZG) − ZF× ⎜ pr ⎟ pr ⎜ 10 ⎟ ⎝ ⎠ (2.13). where,

ZA = −0.101− 0.36×Tpr +1.3868× (Tpr − 0.919)

0.04275 ZB = 0.021+ (Tpr − 0.65)

ZC = 0.6222 − 0.224×Tpr 0.0657 ZD = − 0.037 (Tpr − 0.86)

ZE = 0.32× EXP(−19.53× (Tpr −1))

ZF = 0.122× EXP(−11.3× (Tpr −1))

4 ZG = ppr *(ZC + ZD× ppr + ZE× ppr )

2.3.9 Physical Properties of C7+ Fractions Correlation

Table 2.1: Heavy Fraction Property Correlations.

6084 API = + 5.9 MW

141.5 SG = 131.5 + API

e e e o e1 2 1 2 e3 Tbp ()R = e0MW SG C = e0 MW SG Tbp

e e 1 2 e3 e4 p c ,(psi) = e0 MW SG Tbp C

e e o 1 2 e3 e 4 Tc ()R = e0MW SG Tbp C

e e 1 2 e3 e4 ω = e0 MW SG Tbp C

0.293 0.361 Z = Ω = c ()1+ 0.375ω w ()1+ 0.0274ω

Parameters Property e0 e1 e2 e3 e4

Tbp 108.701661 0.42244800 0.42682558 0.000000 0.000000

C 0.83282122 0.09255911 -0.0413045 0.12621158 0.000000

Pc 237031780 -0.028484 2.755309 -1.374444 -2.947221

Tc 6.206640 -0.059607 0.224357 0.968332 -0.802538

ω 1.5790E-13 -1.453063 -2.811708 4.883921 2.109476

ω 2.22065E-10 -0.45908 -2.25373 3.4452 0.000000

11 2.4 Corresponding States Prediction Methods The theory of Corresponding States proposes that all gases will exhibit the same behavior, e.g. z-factor, when viewed in terms of reduced pressure, reduced volume, and reduced temperature. Mathematically, this principle can be defined as: z = z c Ψ(p R ,TR ) (2.14). The mathematical derivation of the above expression is as follows: Real gas law is, PV = zRT (2.15).

Multiply and divide the LHS of the above equation by PcVc and RHS by zcTc, we get, PV zRT P V = z T c c P V z T c c c c c c (2.16). PV T T = = zR c P V P V T c c c c c (2.17). By definition P T P = & T = R P R T c c (2.18). z z T = P V = c c T R R z P V R c c c (2.19). we have from real gas law, z T 1 c c = P V R c c (2.20). z P V = P V = R R R R z T c R (2.21).

TR = z = z c PR VR z = z c Ψ(p R ,TR ) (2.22). Based on the above derivation, the following relationship can be established,

12 p V p V R1 R1 = R 2 R 2 Z T Z T R1 R1 R 2 R 2 (2.23).

4 r o ct

Fa 3 y t

i Exp l i b i nC7 TR = 0.65 ss

e nC9 r 2 p

m nC10 o

C vdW SRK 1 LLS PT PR 0 0 5 10 15 20 25 30 Reduced Pressure

Figure 2.1: Z-Factor of Pure Substances at Reduced Conditions (TR=0.65).

13 5

4 or

Fact 3 Exp y t i l nC4 bi nC5 ssi TR = 0.75 e r 2 nC6 p

m nC9 o

C vdW SRK 1 LLS PT PR 0 0 5 10 15 20 25 30 Reduced Pressure

Figure 2.2: Z-Factors of Pure Substances at Reduced Conditions (TR = 0.75).

14 5 Exp C3 iC4 4 nC4 nC5

r nC6 o nC7 ct

a nC9 3

y F nC10 t i

l vdW i

b SRK T = 0.85 LLS R essi

r 2 PT p PR m o C

0 0 5 10 15 20 25 30 Reduced Pressure

Figure 2.3: Z- Factor of Pure Substances at Reduced Conditions (TR=0.85).

1.8

1.4 r o t c a F

y Exp lit i CO2

ib 1

s H2S s e

r C2 p TR = 1.02 C3 m

o nC5 C 0.6 vdW SRK LLS PT PR 0.2 0481216 Reduced Pressure

Figure 2.4: Z-Factor of Pure Substances at Reduced Conditions (TR=1.02).

15 2.25

1.85 r acto 1.45

ility F Exp C2

ressib 1.05 C3 p nC4 m TR = 1.07 o iC4 C nC5 vdW 0.65 SRK LLS PT PR 0.25 0 5 10 15 20 Reduced Pressure

Figure 2.5: Z-Factor of Pure Substances at Reduced Conditions (TR=1.07).

2.03

1.75 or t

c 1.47 Exp Fa y

t CO2 i l H2S bi

i 1.19 s C2 s

e TR = 1.13

r C3 p nC4 m 0.91 o iC4 C vdW SRK 0.63 LLS PT PR 0.35 0 5 10 15 20 Reduced Pressure

Figure 2.6: Z-Factor of Pure Substances at Reduced Conditions (TR=1.13).

16 1.9

1.55 r o ct a

F Exp y t i l

i CO2 b i 1.2 H2S

ss C2 e r C3 p

m TR = 1.24 nC4 o

C iC4 0.85 vdW SRK LLS PT PR 0.5 0 5 10 15 20 Reduced Pressure

Figure 2.7: Z-Factor of Pure Substances at Reduced Conditions (TR=1.24).

1.64 r o t

c 1.31 a F

y Exp lit i CO2 ib

s TR = 1.55 C1 s e

r C2 p C3 m 0.98 o

C vdW SRK LLS PT PR 0.65 0 5 10 15 20 Reduced Pressure

Figure 2.8: Z-Factor of Pure Substances at Reduced Conditions (TR=1.55).

17 1.60 r o t 1.36 c a F y t Exp ili

ib CO2 s s C1 re p C2 m 1.12 o TR = 1.98

C vdW SRK LLS PT PR 0.88 0 3 6 9 12 15 18 Reduced Pressure

Figure 2.9: Z-Factor of Pure Substances at Reduced Conditions (TR=1.98).

2.00

1.73 r o t c a F y it il

ib 1.45 Exp s s

e N2 r

p TR = 2.03 C1 m

o vdW C 1.18 SRK LLS PT PR 0.90 0 5 10 15 20 25 30 Reduced Pressure

Figure 2.10: Z-Factor of Pure Substances at Reduced Conditions (TR=2.03).

18 2.5 Equations of State Prediction Methods Cubic equations of state (EOS’s) are simple equations relating pressure, volume, and temperature (PVT). They accurately describe the volumetric and phase behavior of pure compounds and mixtures, requiring only critical properties and acentric factor of each component. The same equation is used to calculate the properties of all phases, thereby ensuring consistency in reservoir processes that approach critical conditions.

Multiple phase behavior, such as low-temperature CO2 flooding, can be treated with an EOS, and even water-/hydrocarbon-phase behavior can be predicted accurately with a cubic EOS. Volumetric behavior is calculated by solving the simple cubic equation, usually pV expressed in terms of z = , RT

3 z + A 2 z + A1z + A 0 = 0 (2.24). where constants A0, A1, and A2 are functions of pressure, temperature, and phase composition. Chapter 4 presents a detailed use of equations-of-state method for solving z- factors.

19 CHAPTER 3

STANDING-KATZ Z-FACTOR CORRELATION

3.1 Standing-Katz Representation of Z-Factor Chart The z-factor in the Standing and Katz5 (SK) chart is a function of reduced pressure and temperature. To be able to predict z-factor using the SK chart requires the appropriate reduced temperature and pressure. Information on the composition of the gas used to design the Standing-Katz z-factor chart is not provided. A close study and comparison of the experimental data with that of SK chart z-factor values suggests that the SK chart was developed based on the natural gas mixture without any significant amounts of non-hydrocarbon components and C7+ in it.

3.2 Best-Fit Equations for SK Z-Factor Chart Many empirical equations and EOSs have been fit to the original Standing-Katz z- factor chart. Some of the commonly used methods in the petroleum industry are:

Hall & Yarborough11 Best Fit Equation:

⎡0.06125ppr t ⎤ 2 Z = ⎢ ⎥exp[−1.2(1− t)] (3.1) ⎣ Y ⎦

where ppr = pseudo-reduced pressure

⎛ Tpc ⎞ t = reciprocal of the pseudo-reduced temperature ⎜= ⎟ ⎝ T ⎠

2 3 4 2 Y + Y + Y − Y F(Y) = −0.06125p pr T[]−1.2()1− t + ()1− Y 3 2 3 2 2 3 ()2.18+2.82t − ()14.76t − 9.76t 4.58t Y + (90.7t − 242.2t + 42.4t )Y = 0 (3.2).

20 Beggs-Brill25 Best-Fit Equation:

()1− A D z = A + B + Cp pr e (3.3) where

0.5 A = 1.39()Tpr − 0.92 − 0.36Tpr − 0.101

⎡ 0.066 ⎤ 0.32 B = ()0.62 − 0.23T p + ⎢ − 0.037⎥p 2 + p6 pr pr pr 9()Tpr −1 pr ⎣⎢()Tpr − 0.86 ⎦⎥ 10

C = (0.132 − 0.32log(Tpr ))

()0.3016−0.49T +0.1824T2 D = 10 pr pr

Dranchuk-Abu-Kassem23 Best-Fit Equation:

⎡ ⎤ A2 A3 A5 z = ⎢A1 + + 3 + 5 ⎥ρ r ⎣⎢ Tpr Tpr Tpr ⎦⎥ ⎡ ⎤ ⎡ ⎤ A7 A8 2 A7 A8 5 + ⎢A6 + + 2 ⎥ρ r − A9 ⎢ + 2 ⎥ρ r ⎣⎢ Tpr Tpr ⎦⎥ ⎣⎢Tpr Tpr ⎦⎥ ρ 2 + A ()1+ A ρ 2 r EXP[]− A ρ 2 +1 10 11 r T 3 11 r pr (3.4) where ρ r = reduced gas density and is defined by the following relationship:

0.27p pr ρr = zTpr The constants A1 through A11 were determined by fitting the equation, using non-linear regression models, to 1,500 points from the Standing and Katz z-factor chart. The coefficients values:

A1 = 0.3262 A2 = -1.0700 A3 = -0.5339 A4 = 0.01569

A5 = -0.05165 A6 = 0.5475 A7 = -0.7361 A8 = 0.1884

A9 = 0.1056 A10 = 0.6134 A11 = 0.7210

Dranchuk-Purvis-Robinson Method:

21 Dranchuk, Purvis, and Robinson’s (1974) correlation was developed based on Benedict-Webb-Rubin57 type of equation of state. It consists of eight coefficients which were obtained based on a best-fit of 1500 data points from Standing-Katz Z-factor chart. The correlation is, ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ A 2 A 3 A 5 2 A 5A 6 5 Z = 1+ ⎢A1 + + 3 ⎥ρr + ⎢A 4 + ⎥ρr + ⎢ ⎥ρr ⎣⎢ Tpr Tpr ⎦⎥ ⎣⎢ Tpr ⎦⎥ ⎣⎢ Tpr ⎦⎥ ⎡A ⎤ + ⎢ 7 ρ2 ()1+ A ρ2 EXP(− A ρ2 )⎥ T 3 r 8 r 8 r ⎣⎢ pr ⎦⎥ (3.5)

0.27p pr where ρr = and the coefficients A1 to A8 have the following values: ZTpr

A1 = 0.31506237 A2 = -1.0467099 A3 = -0.57832729 A4 = 0.53530771

A5 = -0.61232032 A6 = -0.10488813 A7 = 0.68157001 A8 = 0.68446549 This method is valid with in a temperature and pressure range of:

1.05 ≤ Tpr < 3.0

0.2 ≤ Ppr ≤ 3.0.

Shell Oil Company Best-Fit Equation:

4 ⎛ p ⎞ ⎜ pr ⎟ Z = ZA + ZB× ppr + (1− ZA) × exp(−ZG) − ZF× ⎜ ⎟ (3.6) ⎝ 10 ⎠ where,

ZA = −0.101− 0.36× TR +1.3868× (TR − 0.919) 0.04275 ZB = 0.021+ (TR − 0.65)

ZC = 0.6222 − 0.224× TR 0.0657 ZD = − 0.037 (TR − 0.86)

ZE = 0.32× exp(−19.53× (TR −1))

22 ZF = 0.122× exp(−11.3× (TR −1))

4 ZG = PR *(ZC + ZD× PR + ZE× PR )

3.3 Mixture Critical Property Prediction Methods Numerous correlations and methods have been suggested in the past to predict mixture critical properties. These methods predict pseudocritical properties and do not represent a correct estimation of the properties for various ranges of composition. In most cases, each of the correlations are designed for a limited reduced pressure, reduced temperature and a fixed range of composition of gases (in Chapter 2 is discussed the procedure to calculate properties of C7+). This calls for a need to have a generalized method to calculate mixture critical properties and presented here is a generalized method to calculated pure component and mixture critical properties. The expressions for mixture critical point (Pc and Tc) are established in the following equations: a B2 P = m c c b 2 [3Z2 + (α + β )B2 + α B ] m c m m c m c (3.7) a B T = m c c b R[3Z2 + (α + β )B2 + α B ] m c m m c m c (3.8). The parameters going into the Equations 3.7 and 3.8 are calculated as shown below:

The critical equation-of-state parameter Bc is obtained by solving the following cubic equation: φ B3 + φ B2 + φ B + φ = 0 3 c 2 c 1 c 0 (3.9) where

2 3 φ3 = 8 +12αm + 6αm + αm φ = 15 +15α − 27β − 3α2 2 m m m φ1 = 6 + 3αm

φ0 = −1

Similarly, the expression for Zc (critical Z for mixtures) in terms of αm and βm are shown in Equations 3.7 and 3.8 is obtained by solving the following cubic equation:

23 θ Z3 + θ Z2 + θ Z + θ = 0 3 c 2 c 1 c 0 (3.10) where

2 3 θ3 = 8 +12α m + 6α m + α m θ = − (3 +12α +12α 2 + 9β − 9α β ) 2 m m m m m 2 θ1 = 3α m + 6α m + 6βm − 6α mβm 2 θ0 = − (α m + βm − α mβm ) where the mixture parameters am, bm, αm and βm are prescribed as

n n 1/ 2 1/ 2 a m = ∑∑x i x ja(T)i a(T) j a ij i==1 j 1 (3.11) n 3 ⎛ 1/ 3 ⎞ b m = ⎜∑ x i bi ⎟ ⎝ i=1 ⎠ (3.12). n n 1/ 2 1/ 2 α m = ∑∑x i x jα i α j α ij i==1 j 1 (3.13) n n 1/ 2 1/ 2 βm = ∑∑x i x jβi β j βij i==1 j 1 (3.14). The temperature function essential in the determination of the mixture equation of state parameter (attractive term ‘a’) is defined as: R 2T 2 R 2T 2 a(T) = Ω c = [1+ (Ω −1)Z ]3 c T −θ a P w c P R c c (3.15) where θ = 0.19708+0.08627ω+0.35714ω2 +3.59015e −03ωM w . The pure component parameters are defined as follows: RT RT b = Ω c = Ω Z c b P w c P c c (3.16) 1+ Ω Z − 3Z α = w c c Ω Z w c (3.17) Z2 (Ω −1)3 + 2Ω 2 Z + (1− 3Z )Ω β = c w w c c w Ω 2 Z w c (3.18) 0.361 Ω w = 1+ 0.0274ω (3.19).

24 A brief description of the previously used empirical correlations suggested is given in the following paragraphs. It should be noted that only the commonly used correlations are mentioned.

3.3.1 Heptane-Plus Fraction Correlation Methods Cavett’s Correlation:

Cavett (1962) proposed correlations for estimating the critical pressure and temperature of hydrocarbon fractions.

T = a + a T + a T 2 + a (API)(T ) + a (T )3 c 0 1 b 2 b 3 b 4 b (3.20) 2 2 2 + a 5 (API)(Tb ) + a 6 (API) (Tb ) Log()p = b + b (T ) + b (T ) 2 + b (API)(T ) + b (T )3 c 0 1 b 2 b 3 b 4 b (3.21). 2 2 2 + b5 (API)(Tb ) + b 6 (API) (Tb ) + b 7 (Tb ) The coefficients in the above equations are tabulated below:

Table 3.1: Coefficients of Cavett’s correlation.

I ai bi 0 768.07121 2.8290406 1 1.7133693 0.94120109*10-3 2 -0.0010834003 -0.30474749*10-5 3 -0.0089212579 -0.20876110*10-4 4 0.38890584*10-6 0.15184103*10-8 5 0.53094290*10-5 0.11047899*10-7 6 0.32711600*10-7 -0.48271599*10-7 7 - 0.13949619*10-9

25 Kesler-Lee Correlations:

Kesler and Lee (1976) proposed a set of equations to estimate the critical temperature, critical pressure, acentric factor, and molecular weight of petroleum fractions.

Critical Pressure:

0.0566 ⎛ 2.2898 0.11857 ⎞ ln p = 8.3634 − − ⎜0.24244 + + ⎟10−3 T ()c ⎜ 2 ⎟ b γ ⎝ γ γ ⎠ ⎛ 3.648 0.47227 ⎞ ⎛ 1.6977 ⎞ + ⎜1.4685 + + ⎟10−7 T 2 − ⎜0.42019 + ⎟10−10 T 3 ⎜ γ γ 2 ⎟ b ⎜ γ 2 ⎟ b ⎝ ⎠ ⎝ ⎠ (3.22) Critical Temperature:

105 Tc = 341.7 + 811.1γg + ()0.4244 + 0.1174γg Tb + (0.4669 − 3.26238γg ) (3.23) Tb Molecular Weight:

M W = −12272.6 + 9486.4γ g + (4.6523 − 3.3287γ g )Tb ⎛ 720.79 ⎞107 2 ⎜ ⎟ + (1− 0.77084γ g − 0.02058γ g )⎜1.3437 − ⎟ (3.24). ⎝ Tb ⎠ Tb ⎛ 181.98 ⎞1012 + 1− 0.80882γ + 0.02226γ 2 ⎜1.8828 − ⎟ ()g g ⎜ ⎟ 3 ⎝ Tb ⎠ Tb Winn-Sim-Daubert Correlation:

Sim and Daubert (1980) represented the critical pressure, critical temperature, and molecular weight as follows:

9 −2.3177 2.4853 pc = 3.48242×10 Tb γg (3.25)

0.08615 0.04614 Tc = exp[3.994718Tb γg ] (3.26)

−5 2.3776 −0.9371 Mw = 1.4350476 ×10 Tb γg (3.27)

o where Tb is the boiling point in R.

26 Watansiri-Owens-Starling Correlation

Watansiri (1985) developed a set of correlations to estimate the critical properties and acentric factor of coal compounds and other hydrocarbons and their derivatives.

Critical Temperature:

ln(Tc ) = −0.0650504 − 0.0005217Tb + 0.03905ln(Mw ) +1.11067ln(Tb ) 1 1 (3.28) M ⎡0.078154γ 2 − 0.061061γ 3 − 0.016943γ ⎤ w ⎣⎢ g g g ⎦⎥ Critical Volume: ln(V ) = 76.313887 −129.8038γ + 63.1750γ2 −13.175γ3 c g g g (3.29) +1.10108ln(Mw ) + 42.1958ln(γg ) Critical Pressure:

0.8 ⎛ T c ⎞ ⎛ M w ⎞ ⎛ T b ⎞ ln(P ) = 6.6418853 + 0.01617283⎜ ⎟ − 8.712⎜ ⎟ − 0.08843889⎜ ⎟ c ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ V c ⎠ ⎝ T c ⎠ ⎝ M w ⎠ (3.30) Acentric Factor:

⎡ ⎛ T ⎞ 382.904 ⎤ −4 ⎜ b ⎟ ⎢5.1236667 ×10 Tb + 0.281826667⎜ ⎟ + + ⎥ ⎢ ⎝ Mw ⎠ Mw ⎥ ⎢ 2 ⎥ ⎢ ⎛ T ⎞ ⎥⎛ 5T ⎞ ω = 0.074691×10−5 ⎜ b ⎟ − 0.12027778×10−4 T M + 0.001261γ M ⎜ b ⎟ ⎢ ⎜ γ ⎟ b w g w ⎥⎜ 9M ⎟ ⎢ ⎝ g ⎠ ⎥⎝ w ⎠ ⎢ 1 2 ⎥ T 3 T 3 ⎢+ 0.1265×10−4 M2 + 0.2061×10−4 γ M2 − 66.29959 b − 0.00255452 b ⎥ ⎢ w g w M γ2 ⎥ ⎣ w g ⎦ (3.31)

3.3.2 Pseudocritical Mixing Parameters Methods

Empirical Methods

Gpc = Gideal + Gexcess (3.32)

27 n P = x P + Φ (P x ) (3.33) pc ∑ i ci ∑ i ci(IDEAL)i i=1 n T = x T + Φ (T x ) (3.33) pc ∑ i ci ∑ i ci(IDEAL)i i=1

Kay’s Rule (1936) n Ppc = ∑ x i Pci (3.34) i

n Tpc = ∑ x i Tci (3.35) i

Joffe Method64 (1947)

⎛ ⎞ n ⎛ ⎞ ⎜ Tpc ⎟ Tc = x ⎜ ⎟ ⎜ 1 ⎟ ∑ i ⎜ 1 ⎟ ⎜ 2 ⎟ i 2 Ppc ⎝ Pc ⎠ ⎝ ⎠ m i (3.36) 1 1 3 ⎛ T ⎞ 1 n n ⎡⎛ T ⎞ 3 ⎛ T ⎞ 3 ⎤ ⎜ pc ⎟ = x x ⎢⎜ c ⎟ + ⎜ c ⎟ ⎥ ⎜ P ⎟ 8 ∑∑ i j ⎢⎜ P ⎟ ⎜ P ⎟ ⎥ ⎝ pc ⎠ i j ⎝ c ⎠i ⎝ c ⎠ j ⎣ ⎦ (3.37)

Prausnitz-Gunn (1958) n Tpc = ∑ x i Tci i=1 (3.38) ⎛ n ⎞ ⎛ n ⎞ ⎜∑ x i Zci ⎟R⎜∑ x i Tci ⎟ P = ⎝ i=1 ⎠ ⎝ i=1 ⎠ pc ⎛ n ⎞ ⎜∑ x i Vci ⎟ ⎝ i=1 ⎠ (3.39)

Stewart-Burkhardt-Voo Method61 (1959) 2 ⎡ c ⎛ T ⎞ ⎤ ⎢ x ⎜ c ⎟ ⎥ ∑ i ⎜ 1 ⎟ ⎢ i P 2 ⎥ ⎣ ⎝ c ⎠i ⎦ Tpc = 1 2 ⎡ 2 ⎤ 1 c ⎛ T ⎞ 2 nc ⎛ T ⎞ x ⎜ c ⎟ ⎢ x ⎜ c ⎟ ⎥ ∑∑i ⎜ ⎟ + i ⎜ ⎟ 3 i ⎝ Pc ⎠ 3 ⎢ i ⎝ Pc ⎠ ⎥ i ⎣ i ⎦ (3.40)

28 2 ⎡ nc ⎛ T ⎞ ⎤ ⎢ x ⎜ c ⎟ ⎥ ∑ i ⎜ 1 ⎟ ⎢ i P 2 ⎥ ⎣ ⎝ c ⎠i ⎦ Ppc = 2 1 2 ⎡ ⎡ 2 ⎤ ⎤ 1 nc ⎛ T ⎞ 2 nc ⎛ T ⎞ ⎢ x ⎜ c ⎟ + ⎢ x ⎜ c ⎟ ⎥ ⎥ ⎢3 ∑∑i ⎜ P ⎟ 3 ⎢ i ⎜ P ⎟ ⎥ ⎥ ⎢ i ⎝ c ⎠i ⎣ i ⎝ c ⎠i ⎦ ⎥ ⎣ ⎦ (3.41)

Leland-Mueller Method (1959) 1/ γ ⎡ 1/ 3 1/ 3 3 ⎤ n n ⎡ ⎛ ⎞ ⎤ ⎢ γ / 2 1 ZcTc 1 ⎛ ZcTc ⎞ ⎥ x i x j []Tc Tc ⎢ ⎜ ⎟ + ⎜ ⎟ ⎥ ⎢∑∑ i j ⎜ ⎟ ⎜ ⎟ ⎥ i j ⎢2 ⎝ Pc ⎠ 2 ⎝ Pc ⎠ ⎥ ⎢ ⎣ i j ⎦ ⎥ Tpc = ⎢ 1/ 3 1/ 3 3 ⎥ n n ⎡1 ⎛ Z T ⎞ 1 ⎛ Z T ⎞ ⎤ ⎢ x x ⎢ ⎜ c c ⎟ + ⎜ c c ⎟ ⎥ ⎥ ⎢ ∑∑ i j ⎜ ⎟ ⎜ ⎟ ⎥ i j ⎢2 ⎝ Pc ⎠ 2 ⎝ Pc ⎠ ⎥ ⎣ ⎣ i j ⎦ ⎦ (3.42) ⎡ ⎤ ⎢ n ⎥ T x Z ⎢ c ∑ i ci ⎥ ⎢ i ⎥ Ppc = ⎢ 1/ 3 1/ 3 3 ⎥ n n ⎡1 ⎛ Z T ⎞ 1 ⎛ Z T ⎞ ⎤ ⎢ x x ⎢ ⎜ c c ⎟ + ⎜ c c ⎟ ⎥ ⎥ ⎢∑∑ i j ⎜ ⎟ ⎜ ⎟ ⎥ i j ⎢2 ⎝ Pc ⎠ 2 ⎝ Pc ⎠ ⎥ ⎣ ⎣ i j ⎦ ⎦ (3.43) where ⎡ n ⎤ ⎢P∑ x i ()Tc i ⎥ ⎢ i=1 ⎥ γ = Ψ n ⎢T x P ⎥ ⎢ ∑ i ()c i ⎥ ⎣ i=1 ⎦ (3.44) Leland and co-workers later reported the following relationship, ⎡ n ⎤ x T ⎢∑ i ci ⎥ ⎢ i ⎥ γ = −0.75 n + 2.44 ⎢ x P ⎥ ⎢∑ i ci ⎥ ⎣ i ⎦ (3.45).

Satter-Campbell Method46 (1963) n n 1 1 2 2 Tpc = ∑∑x i x jTci Tcj i==1 i 1 (3.46)

29 n Tc ∑ x i Zci i Ppc = 1 1 3 n n ⎡1 ⎛ Z T ⎞ 3 1 ⎛ Z T ⎞ 3 ⎤ ⎢ ⎜ c c ⎟ ⎜ c c ⎟ ⎥ ∑∑x i x j ⎜ ⎟ + ⎜ ⎟ i==1 j 1 ⎢2 ⎝ Pc ⎠ 2 ⎝ Pc ⎠ ⎥ ⎣ i j ⎦ (3.47).

Lee-Kesler Method54 (1975)

Zci = 0.2905 − 0.085ωi (3.48) Z RT V = ci ci ci P ci (3.49). 1 n n 1 1 3 V = x x ⎜⎛V 3 + V 3 ⎟⎞ pc ∑ ∑ i j ⎝ ci cj ⎠ 8 i=1 j=1 (3.50) 1 n n 1 1 3 T = x x ⎜⎛V 3 + V 3 ⎟⎞ T T pc 8V ∑ ∑ i j ⎝ ci cj ⎠ ci cj c i=1 j=1 (3.51) T Θ = b T c (3.52) −1 6 − ln Pc (atm) − 5.92714 + 6.09648Θ +1.28862ln Θ − 0.169347Θ ωi = −1 6 15.2518 −15.6875Θ −13.4721ln Θ + 0.43577Θ (3.53). n ω = ∑ x i ωi i=1 (3.54) ()0.2905 − 0.085ω RT P = c pc V c (3.55)

Van Ness-Abbot Method63 (1982) 4 1 1 3 ⎡ 5 2 5 2 ⎤ n n ⎛ 2 ⎞ ⎛ 2 ⎞ ⎢ Tc Tc ⎥ x x ⎜ ⎟ ⎜ ⎟ ⎢∑∑ i j ⎜ ⎟ ⎜ ⎟ ⎥ i==1 j 1 Pc Pc ⎢ ⎝ ⎠i ⎝ ⎠ j ⎥ 2 ⎣ ⎦ Tpc = 2 3 ⎡ n n ⎛ T ⎞ ⎛ T ⎞ ⎤ ⎢ x x ⎜ c ⎟ ⎜ c ⎟ ⎥ ∑∑ i j ⎜ ⎟ ⎜ ⎟ ⎢ i==1 j 1 ⎝ Pc ⎠ ⎝ Pc ⎠ ⎥ ⎣ i j ⎦ (3.56)

30 4 1 1 3 ⎡ 5 2 5 2 ⎤ n n ⎛ 2 ⎞ ⎛ 2 ⎞ ⎢ T T ⎥ x x ⎜ c ⎟ ⎜ c ⎟ ⎢∑∑ i j ⎜ ⎟ ⎜ ⎟ ⎥ i==1 j 1 Pc Pc ⎢ ⎝ ⎠i ⎝ ⎠ j ⎥ 2 ⎣ ⎦ Ppc = 5 3 ⎡ n n ⎛ T ⎞ ⎛ T ⎞ ⎤ ⎢ x x ⎜ c ⎟ ⎜ c ⎟ ⎥ ∑∑ i j ⎜ ⎟ ⎜ ⎟ ⎢ i==1 j 1 ⎝ Pc ⎠ ⎝ Pc ⎠ ⎥ ⎣ i j ⎦ (3.57)

Pedersen-Fredenslund-Christensen-Thomassen Method55,56 (1984) 1 1 3 n n ⎡⎛ T ⎞ 3 ⎛ T ⎞ 3 ⎤ x x ⎢⎜ c ⎟ + ⎜ c ⎟ ⎥ ∑∑ i j ⎢⎜ P ⎟ ⎜ P ⎟ ⎥ i j ⎣⎝ c ⎠i ⎝ c ⎠ j ⎦ Tpc = TciTcj 1 1 3 n n ⎡⎛ T ⎞ 3 ⎛ T ⎞ 3 ⎤ ⎢⎜ c ⎟ ⎜ c ⎟ ⎥ ∑∑x i x j ⎜ ⎟ + ⎜ ⎟ i j ⎢⎝ Pc ⎠ ⎝ Pc ⎠ ⎥ ⎣ i j ⎦ (3.58) 1 1 3 n n ⎡⎛ T ⎞ 3 ⎛ T ⎞ 3 ⎤ 8 x x ⎢⎜ c ⎟ + ⎜ c ⎟ ⎥ ∑∑ i j ⎢⎜ P ⎟ ⎜ P ⎟ ⎥ i j ⎣⎝ c ⎠i ⎝ c ⎠ j ⎦ Ppc = 2 TciTcj ⎡ 1 1 3 ⎤ n n ⎡⎛ T ⎞ 3 ⎛ T ⎞ 3 ⎤ ⎢ x x ⎢⎜ c ⎟ + ⎜ c ⎟ ⎥ ⎥ ⎢∑∑ i j ⎢⎜ P ⎟ ⎜ P ⎟ ⎥ ⎥ ⎢ i j ⎣⎝ c ⎠i ⎝ c ⎠ j ⎦ ⎥ ⎣ ⎦ (3.59) Teja-Thurner-Pasumarti Method (1985) T n n T pc = x x cij P ∑∑ i j P pc i==1 j 1 cij (3.60) T 2 n n T 2 pc = x x cij P ∑∑ i j P pc i==i j 1 cij (3.61) where 1 2 Tcij = ξij (TciTcj ) (3.62)

8Tcij Pcij = 1 1 3 ⎡⎛ T ⎞ 3 ⎛ T ⎞ 3 ⎤ ⎢ c c ⎥ ⎜ ⎟ + ⎜ ⎟ ⎢⎝ Pc ⎠ ⎝ Pc ⎠ ⎥ ⎣ i j ⎦ (3.63)

Sutton Method62 (1985)

31 2 ⎡ c ⎛ T ⎞ ⎤ ⎢ x ⎜ c ⎟ − E ⎥ ∑ i ⎜ 1 ⎟ k ⎢ i P 2 ⎥ ⎣ ⎝ c ⎠i ⎦ Tpc = 1 2 ⎡ 2 ⎤ 1 c ⎛ T ⎞ 2 nc ⎛ T ⎞ x ⎜ c ⎟ ⎢ x ⎜ c ⎟ ⎥ E ∑∑i ⎜ ⎟ + i ⎜ ⎟ − J 3 i ⎝ Pc ⎠ 3 ⎢ i ⎝ Pc ⎠ ⎥ i ⎣ i ⎦ (3.64) 2 ⎡ nc ⎛ T ⎞ ⎤ ⎢ x ⎜ c ⎟ − E ⎥ ∑ i ⎜ 1 ⎟ k ⎢ i P 2 ⎥ ⎣ ⎝ c ⎠i ⎦ Ppc = 2 1 2 ⎡ ⎡ 2 ⎤ ⎤ 1 nc ⎛ T ⎞ 2 nc ⎛ T ⎞ ⎢ x ⎜ c ⎟ + ⎢ x ⎜ c ⎟ ⎥ − E ⎥ ⎢3 ∑∑i ⎜ P ⎟ 3 ⎢ i ⎜ P ⎟ ⎥ J ⎥ ⎢ i ⎝ c ⎠i ⎣ i ⎝ c ⎠i ⎦ ⎥ ⎣ ⎦ (3.65)

Lawal-Lake-Silberberg65 (2002) a B T = m c c b R[3Z2 + α + β B2 + α B ] m c ()m m c m c (3.66)

a B2 P = m c c b 2 [3Z2 + α + β B2 + α B ] m c ()m m c m c (3.67) n n 0.5 a m = ∑∑xi x j (ai a j ) a ij i j (3.68)

n 3 ⎛ 1/3 ⎞ b m = ⎜∑ x i bi ⎟ ⎝ i ⎠ (3.69)

n n 0.5 αm = ∑∑xix j (αi α j ) αij i j (3.70)

n n 0.5 β m = ∑∑x i x j (β i β j ) β ij i j (3.71)

3 2 Θ3Zc + Θ2Zc + Θ1Zc + Θ0 = 0 (3.72) where,

32 3 2 Θ3 = (α m + 6α m +12α m + 8) Θ = −3(1+ 4α 2 + 4α + 3β − 3α β ) 2 m m m m m 2 Θ1 = 3(2α m + 2β m − 2α mβ m + α m ) 2 Θ0 = (α mβ m − β m − α m )

3 2 θ3Bc + θ2Bc + θ1Bc + θ0 = 0 (3.73) where, 3 2 θ3 = (α m + 6α m +12α m + 8) θ = −3(α 2 − 5α + 9β − 5) 2 m m m θ1 = 3(α m + 2)

θ 0 = −1

Redlich-Kwong-Abbott 4 1 3 ⎡ 5 2 ⎤ n ⎛T 2 ⎞ ⎢ x ⎜ c ⎟ ⎥ ∑ i P ⎢ i ⎜ c ⎟ ⎥ ⎣⎢ ⎝ ⎠i ⎦⎥ Tpc = 2 (3.74) 3 ⎡ n T ⎤ x ⎛ c ⎞ ⎢∑ i ⎜ P ⎟ ⎥ ⎣⎢ i ⎝ c ⎠i ⎦⎥

4 1 3 ⎡ 5 2 ⎤ n ⎛T 2 ⎞ ⎢ x ⎜ c ⎟ ⎥ ∑ i P ⎢ i ⎜ c ⎟ ⎥ ⎣⎢ ⎝ ⎠i ⎦⎥ Ppc = 5 (3.75) 3 ⎡ n T ⎤ x ⎛ c ⎞ ⎢∑ i ⎜ P ⎟ ⎥ ⎣⎢ i ⎝ c ⎠i ⎦⎥

3.3.3 Pseudocritical Gas Gravity Correlation Methods The Standing90 gas gravity correlation is stated as: 2 Ppc (psia) = 706 − 51.7Sg −11.1Sg (3.76)

o 2 Tpc ( R) = 187 + 330Sg − 71.5Sg (3.77)

33 The Sutton90 gas gravity correlation is stated as: 2 Ppc (psia) = 756.8 −131.0Sg − 3.6Sg (3.78)

o 2 Tpc ( R) = 169.2 + 349.5Sg − 74.0Sg (3.79)

Elsharkawy-Hashem-Alikhan90 gas gravity correlation is stated as: 2 Ppc (psia) = 787.06 −147.34Sg − 7.916Sg (3.80)

o 2 Tpc ( R) = 149.18 + 358.14Sg − 66.976Sg (3.81)

Hankinson-Thomas-Philips91 gas gravity correlation is stated as:

Ppc (psia) = 709.604 + 58.718Sg (3.82)

o Tpc ( R) = 170.491+ 307.344Sg (3.83) Brill-Beggs102 gas gravity correlation is stated as:

Ppc (psia) = 708.75 − 57.5Sg (3.84)

o Tpc ( R) = 169.0 + 314.0Sg (3.85) This work: 2 Ppc (psia) = 659.94 + 57.306Sg − 63.012Sg (3.86)

o 2 Tpc ( R) = 165.95 + 321.82Sg + 0.7924Sg (3.87)

2 The R for Ppc is 0.9821 and that for Tpc is 0.9999.

700 Stan Sutt ElHA HaTPh 680 BrBe ThisWork a)

i 660 s p ( ed at l u c l a C

c 640 P

620

600 600 620 640 660 680 700 Pc Experimental (psia)

Figure 3.1: Comparison of Six Correlations for Pseudocritical Pressure Parameters.

Stan 530 Sutt ElHA HaTPh BrBe 490 ThisWork R) o (

ed 450 at l u c l a C c T 410

370

330 330 370 410 450 490 530 Tc Experimental (oR)

Figure 3.2: Compare Six Correlations for Pseudocritical Temperature Parameters.

35 Table 3.2: Sources of Experimental Z-Factor for Pure Substances.

Authors Year System Reference No.

Sage-Lacey 1950 C1 8

Sage-Lacey 1950 C2 8

Sage-Lacey 1950 C3 8

Sage-Lacey 1950 iC4, nC4 8

Sage-Lacey 1950 iC5, nC5 8

Stewart-Sage-Lacey 1954 nC6 10

Sage-Reamer- Nichols 1955 nC7 9

Sage-Lacey 1950 H2S 8

Sage-Lacey 1950 N2 8

Sage-Lacey 1950 CO2 8

36 3.3.4 van der Waals Theory of Pseudocritical Methods

Criticality Theory

1. van der Waals Pseudocritical Theory3 (1873)

⎛ ∂P ⎞ ⎜ ⎟ = 0 ⎝ ∂V ⎠ T at T = Tc and P = Pc (3.88) ⎛ ∂ 2 P ⎞ ⎜ ⎟ = 0 ⎜ ∂V 2 ⎟ ⎝ ⎠T at T = Tc and P = Pc (3.89) 2. Gibbs Criteria (1928) ⎛ ∂G ⎞ ⎜ ⎟ = 0 (3.90) ⎝ ∂x ⎠T,P

⎛ ∂ 2G ⎞ ⎜ ⎟ = 0 ⎜ ∂x 2 ⎟ ⎝ ⎠T,P (3.91) 3. Wilson Renormalization Theory (1982)

3.3.5 Improved Theory for Pseudocritical Mixture Parameter Mixture rules significantly affect the accuracy of mixture property determination. Weighted average based on mole fraction has been the general rule since Kay but this method is an approximate method and more rigorous methods are required for accurate determination of mixture properties. Numerous methods have been proposed but none of them present a generalized method for critical property prediction with high accuracy. Most of the methods are either statistical or empirical and therefore are bound by errors. In this project a method is presented which is based on LLS EOS. This method is capable of predicting critical properties of mixtures irrespective of the component and its composition. Prediction method of binary interaction number is an essential parameter in mixture critical property determination. The BIN can be function of molecular weights, acentric factor or product of molecular weight and acentric factor. Care must be taken in

37 applying these rules of predicting BIN with gas mixtures containing very light and heavy components. Other occasions of concern could be when isomers are present in a gas mixture. It should be noted that in BIN can be equal to 1 only in case of pure composition.

3.4 Designed Scaling Parameter for Standing-Katz Z-Factor Chart In order to extend the use of SK chart to the prediction of z-factors for sour and acid gases without resorting to the Wichert-Aziz2 correction formula for pseudocritical pressures and temperatures parameters, a universal scaling parameter has been established. This scaling parameter is developed by overlaying the experimental z-factor curves for the same range of pressures and temperatures as that of SK chart and measuring the deviation from of the SK chart curves. A mathematical quantification of this deviation for hydrocarbon compounds, non-hydrocarbon compounds, and sour reservoir gases resulted in a similar modification (or scaling) parameter requirement. This observation establishes the fact that the SK chart is designed perfectly but most of the time, it is used wrongly. The error is in the method of calculation of the pseudocritical pressures and temperatures.

3.4.1 Design Procedure for Scaling Parameter The scaling parameter for hydrocarbon components is developed based on wide range of available experimental data and measuring the deviation of SK computational methods from experimental data. In the design of a scaling parameter, non-hydrocarbon components that are commonly found in the reservoir gases like nitrogen, hydrogen sulfide, and carbon dioxide were considered. A wide range of experimental z-factor data for natural gases containing significant amounts of acid gases, sour gas, and C7+ fraction were collected and used in this project to develop the scaling parameter.

38 The step-by-step procedure for obtaining the scaling factor is as follows: zSK 1. zSF = × z . z Expt. c 2. A regression analysis of the reduced pressure and ZSK scaled z-factor (based on step 1) is performed to obtain a quadratic expression for scaling factor at each temperature of the mixture. The equation describing it is Equation 3.78.

3. The coefficients a0, a1 and a2 for each mixture is collected and is subjected to linear regression analysis. 4. The general expressions for these coefficients are obtained by performing regression analysis as functions of product of molecular weight and acentric

factor (ωMw). 5. The equations describing the final expressions are presented below.

2 SF = a0 + a1PR + a 2PR (3.92) where 0.31 a = 0 1.04518 − 0.15675(ωM ) w (3.93)

9.40E − 05 a = 1 1.2722E − 02 − 4.4852E − 03(ωM ) w (3.94)

− 3.54E − 04 a = 2 0.83084 − 0.41702(ωM ) w (3.95) The prediction results using the scaling factor technique is presented below. More results on this can be seen in the Section C.1 of Appendix C.

39 1.42 Expt.

SK 1.32 Scaled

1.22

1.12 or t c Fa

Z- 1.02

0.92

0.82

0.72 0 2,000 4,000 6,000 8,000 Pressure (Psia)

Figure 3.3: Scaled Z-Factor for Buxton & Campbell Data (Mix-5) at 160 oF.

1.41

Expt. 1.31 SK

Scaled 1.21

1.11 or t Fac

Z- 1.01

0.91

0.81

0.71 0 2,000 4,000 6,000 8,000 Pressure (psia)

Figure 3.4: Scaled Z-Factor for Buxton and Campbell Data (Mix-5) at 130 oF.

40 1.35

Expt.

1.25 SK

Scaled 1.15

1.05 or t c Fa

Z- 0.95

0.85

0.75

0.65 0 2,000 4,000 6,000 8,000 Pressure (Psia)

Figure 3.5: Scaled Z-Factor for Buxton and Campbell Data (Mix-5) at 100 oF.

1.2

Expt. Scaled 1.1 SK r o t c 1 Fa Z-

0.9

0.8 036912 Pressure (Psia)

Figure 3.6: Scaled Z-Factor for Satter Data (Mix-E) at 160 oF.

41 3.5Designed pR/z Versus Z-Factor Chart This section provides a clear view of an ideal z-chart and the eventually the capability of predicting amount of gas produced by a graphical means. Figure 3.5 is a z- chart developed based on computation techniques developed based on a correlation developed for SK Z-Chart.

1.1

0.9

Tr=1.0 Tr=1.05 Tr=1.1 Tr=1.2 0.7 Tr=1.3 Tr=1.4 Tr=1.5 Tr=1.6 Tr=1.7

Z-Factor Values Tr=2.0 0.5 Tr=2.2 Tr=2.4 Tr=2.6 Tr=2.8 Tr=3.0 Tr=1.8 0.3 Tr=1.9 Tr=1.15 Tr=1.25 TR = 1.0 Tr=1.35 Tr=1.45 0.1 02468 Reduced Pressure

Figure 3.7: SK Z-Chart Developed Based on Computation SK Technique.

42 Tr=1.0 Tr=1.05 1.00 Tr=1.1 Tr=1.15 Tr=1.2 Tr=1.25 0.80 Tr=1.30 Tr=1.35 Tr=1.40 Tr=1.45 or 0.60 t Tr=1.50 Fac Tr=1.6 Z- Tr=1.7

0.40 Tr=1.8 Tr=1.9 Tr=2.0 Tr=2.2

0.20 Tr=2.4 T =1.0 R Tr=2.6 Tr=2.8 Tr=3.0 0.00 024681012

PR/z

Figure 3.8: Amount of gas produced.

3.6 Prediction Results for Z-Factor of Natural Gases

1.4 Exp

Standing-Katzl 1.3 Scaledt

1.2

1.1 or t c Fa

Z- 1

0.9

0.8

0.7 0 2,000 4,000 6,000 8,000 Pressure (psia)

Figure 3.9: Scaled Z-Factor Buxton & Campbell, Mix-2 Result, @ T = 130 oF.

43 1.3 Exp Standing-Katz Scaled 1.2

1.1 r o ct Fa Z- 1

0.9

0.8 0 2,000 4,000 6,000 8,000 Pressure (psia)

Figure 3.10: Scaled Z-Factor Buxton & Campbell, Mix-2 Result, @ T = 100 oF.

1.26 Exp Standing-Katzl Scaled 1.16

1.06 or t c a F Z- 0.96

0.86

0.76 0 2,000 4,000 6,000 8,000 Pressure (psia)

Figure 3.11: Scaled Z-Factor Buxton & Campbell, Mix-3 Result, @ T = 100 oF.

44 45 3.7 Prediction Results for Z-Factor of Reservoir Gases Scaling is done based on the law of corresponding states principle as follows:

⎡ZScaled ⎤ ⎡ZSK ⎤ ⎢ ⎥ = ⎢ SF ⎥ (3.96). Zc Z ⎣ ⎦ PR ,TR ⎣ ⎦ PR ,TR

Table 3.3: Rich Gas Condensate Composition (Elsharkawy71). Serial No. 39 Rich gas Condensate

IND 281 282 283 284 285 286 287

H2S 0 0 0 0 0 0 0

CO2 0.0231 0.0242 0.0248 0.0253 0.0258 0.0262 0.0266

N2 0.0137 0.0155 0.0161 0.0166 0.0163 0.0155 0.0143

C1 0.6583 0.7074 0.738 0.7559 0.7583 0.7485 0.7292

C2 0.0803 0.0817 0.0821 0.0839 0.0863 0.0905 0.0944

C3 0.0417 0.0411 0.0404 0.0402 0.0415 0.0447 0.0495

iC4 0.0078 0.0073 0.007 0.0069 0.0073 0.0082 0.0091

nC4 0.0184 0.017 0.0162 0.0159 0.0167 0.0186 0.0208

iC5 0.0075 0.0067 0.0062 0.006 0.0062 0.007 0.008

nC5 0.0108 0.0097 0.0089 0.0084 0.0086 0.0096 0.0107

nC6 0.0116 0.011 0.0103 0.0086 0.0078 0.0082 0.0092

C7+ 0.1268 0.0784 0.05 0.0323 0.0252 0.023 0.0282

Mw+ 191 154 139 128 120 115 113 Sg+ 0.831 0.804 0.789 0.778 0.77 0.765 0.763

Pc C7+, (psia) 324.6 378.4 404.3 427.5 447.2 461.0 466.9 o Tc C7+, ( R) 1264.0 1177.7 1136.4 1105.1 1081.6 1066.6 1060.5 T(oF) 313 313 313 313 313 313 313 P (psia) 6010 5100 4100 3000 2000 1200 700 Z (Expt.) 1.212 1.054 0.967 0.927 0.93 0.952 0.97 ρ(lb/cu.ft.) 26.3 18.97 14.17 9.79 6.27 3.68 2.19 ZSK 1.0982 0.9806 0.9224 0.8964 0.9054 0.9311 0.9531 Scaled Z (This Study) 1.0213 1.0931 0.5793 0.0725 0.4924 0.8660 0.9835

46 Table 3.4: Highly Sour Gas Composition (Elsharkawy71). Serial No. 57

Highly sour gas condensate

IND 439 440 441 442 443 444 445

H2S 0.282 0.277 0.272 0.27 0.273 0.289 0.318

CO2 0.0608 0.0644 0.0669 0.0685 0.0694 0.0699 0.0679

N2 0.0383 0.0455 0.0476 0.0473 0.0461 0.0434 0.0394

C1 0.4033 0.4382 0.4641 0.4807 0.4844 0.4688 0.4331

C2 0.0448 0.0471 0.0481 0.0487 0.0493 0.0496 0.0494

C3 0.0248 0.0243 0.0239 0.0237 0.0239 0.0252 0.0277

iC4 0.006 0.0055 0.0051 0.0049 0.0049 0.0055 0.0067

nC4 0.0132 0.012 0.0111 0.0106 0.0106 0.0114 0.014

iC5 0.0079 0.0068 0.006 0.0055 0.0053 0.0058 0.0074

nC5 0.0081 0.0069 0.006 0.0054 0.0052 0.0057 0.0071

nC6 0.0121 0.0096 0.0078 0.0066 0.006 0.0063 0.0077

C7+ 0.0991 0.063 0.0412 0.0286 0.0217 0.0192 0.0214

Mw+ 165 121 116 112 109 107 107 Sg+ 0.818 0.778 0.773 0.768 0.764 0.762 0.762

Pc C7+, psia 365.4 453.2 467.1 477.8 486.0 492.7 492.7 o Tc C7+, R 1209.7 1090.7 1075.7 1062.7 1052.5 1046.3 1046.3 T(oF) 250 250 250 250 250 250 250 P (psia) 4190 3600 3000 2400 1800 1200 700 Z (Expt.) 0.838 0.806 0.799 0.809 0.842 0.888 0.935 ρ(lb/cu.ft.) 27.34 19.52 15.06 11.3 7.95 5.06 2.91 SK Z 0.8295 0.9299 0.9615 0.9744 0.9755 0.9734 0.9742 Scaled Z (This Study) 0.7981 0.8974 0.9347 0.9564 0.9709 0.9853 1.0020

47 Table 3.5: Carbon Dioxide Rich Gas Composition (Elsharkawy71). Serial No. 124 Carbon Dioxide Rich Gas

IND 926 927 928 929 930 931 932

H2S 0.003 0.003 0.003 0.003 0.003 0.003 0.004

CO2 0.6352 0.6395 0.6514 0.6579 0.6639 0.6706 0.6716

N2 0.0386 0.0399 0.041 0.0417 0.0421 0.0411 0.0388

C1 0.1937 0.1988 0.2008 0.207 0.2084 0.2037 0.1994

C2 0.0303 0.0307 0.0308 0.0309 0.0313 0.0315 0.0318

C3 0.0174 0.0172 0.017 0.0169 0.017 0.0175 0.0184

iC4 0.0033 0.0032 0.0031 0.003 0.003 0.0032 0.0035

nC4 0.0093 0.0088 0.0085 0.0082 0.0082 0.0088 0.0097

iC5 0.0039 0.0036 0.0033 0.0031 0.003 0.0033 0.0039

nC5 0.0047 0.0042 0.0038 0.0036 0.0035 0.0038 0.0046

nC6 0.0051 0.0049 0.0046 0.0042 0.0036 0.003 0.0034

C7+ 0.0551 0.0458 0.0324 0.0202 0.0127 0.0101 0.0113 Mw+ 170 153 139 128 118 110 106 Sg+ 0.811 0.797 0.783 0.773 0.763 0.755 0.751

Pc C7+, psia 347.8 373.9 397.8 421.7 446.3 469.4 482.4 o Tc C7+, R 1211.6 1169.4 1131.0 1100.6 1071.2 1046.9 1034.5 T(oF) 219 219 219 219 219 219 219 P (psia) 4825 4100 3300 2600 1900 1200 700 Z (Expt.) 0.851 0.777 0.72 0.719 0.775 0.851 0.915 ρ(lb/cu.ft.) 34.88 30.9 25.58 19.39 12.87 7.38 4.03 SK Z 0.7935 0.7739 0.7884 0.8247 0.8653 0.9084 0.9434 Scaled Z (This Study) 0.7151 0.7028 0.7233 0.7661 0.8151 0.8685 0.9125

48 Table 3.6: Very Light Gas Composition (Elsharkawy71). Very light gas 125

Serial No. IND 933 934 935 936 937 938 939

H2S 0 0 0 0 0 0 0

CO2 0.0033 0.0033 0.0034 0.0035 0.0035 0.0036 0.0038

N2 0.0032 0.0033 0.0033 0.0033 0.0033 0.0033 0.0033

C1 0.942 0.9438 0.9451 0.9461 0.9468 0.9473 0.9467

C2 0.0231 0.023 0.023 0.0231 0.0232 0.0233 0.0236

C3 0.0082 0.0082 0.0082 0.0082 0.0082 0.0082 0.0083

iC4 0.0023 0.0023 0.0023 0.0023 0.0023 0.0023 0.0023

nC4 0.0025 0.0025 0.0025 0.0025 0.0025 0.0025 0.0026

iC5 0.0012 0.0012 0.0012 0.0012 0.0012 0.0012 0.0012

nC5 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0009

nC6 0.0014 0.0013 0.0013 0.0013 0.0013 0.0012 0.0013

C7+ 0.012 0.0103 0.0089 0.0077 0.0069 0.0063 0.006 Mw+ 143 133 126 120 116 114 114 Sg+ 0.787 0.777 0.769 0.763 0.76 0.758 0.758

Pc C7+, psia 390.5 409.7 423.9 438.6 450.5 456.2 456.2 o Tc C7+, R 1142.1 1114.1 1093.0 1075.4 1064.3 1058.3 1058.3 T(oF) 209 209 209 209 209 209 209 P (psia) 4786 4000 3300 2600 1900 1300 700 Z (Expt.) 1.019 0.974 0.945 0.933 0.933 0.947 0.969 ρ(lb/cu.ft.) 12.13 10.42 8.76 6.92 5.03 3.37 1.78 SK Z 1.1235 1.0726 1.0375 1.0119 0.9955 0.9884 0.9883 Scaled Z (This Work) 1.0007 0.9565 0.9310 0.9179 0.9170 0.9264 0.9458

Table 3.7: Property Prediction for Gas Composition Data (Elsharkawy71). o o Data No. T, R P,psia TR PR Tc, R Pc, psia Zc ZExpt Rich Gas Condensate 281 773 6010 1.6602 9.545 465.6188 629.6467 0.3137 1.212 282 773 5100 2.346 9.9547 329.4974 512.3187 0.3111 1.054 283 773 4100 2.679 8.5429 288.5443 479.9311 0.3093 0.967 284 773 3000 2.8195 6.3235 274.1664 474.4191 0.3079 0.927 285 773 2000 2.8615 4.2224 270.1407 473.6642 0.3077 0.93 286 773 1200 2.8533 2.5324 270.9140 473.8606 0.3083 0.952 287 773 700 2.7923 1.4711 276.8299 475.8504 0.3095 0.97 Highly Sour Gas 439 710 4190 1.4904 5.6376 476.3853 743.2255 0.3176 0.838 440 710 3600 1.8906 5.459 375.5364 659.4605 0.317 0.806 441 710 3000 2.0593 4.7129 344.7844 636.5490 0.3167 0.799 442 710 2400 2.156 3.8496 329.3079 623.4470 0.3163 0.809 443 710 1800 2.1873 2.8831 324.5952 624.3326 0.3162 0.842 444 710 1200 2.1462 1.8854 330.8097 636.4649 0.3161 0.888 445 710 700 2.0284 1.0567 350.0302 662.4678 0.3161 0.935

CO2 Rich Gas 926 679 4825 1.3607 5.5574 499.0157 868.2062 0.3012 0.851 927 679 4100 1.4475 4.8577 469.0735 844.0239 0.3014 0.777 928 679 3300 1.5372 3.9986 441.7072 825.2834 0.3013 0.72 929 679 2600 1.6176 3.2057 419.766 811.0509 0.3016 0.719 930 679 1900 1.6622 2.3661 408.4864 803.0142 0.3016 0.775 931 679 1200 1.6632 1.4895 408.2512 805.6412 0.3011 0.851 932 679 700 1.6418 0.8669 413.5822 807.5066 0.3006 0.915 Very Light Gas 933 669 4786 2.3565 8.9693 283.8983 533.5994 0.2935 1.019 934 669 4000 2.3535 7.4526 284.2594 536.7226 0.2933 0.974 935 669 3300 2.3506 6.1209 284.603 539.1324 0.2932 0.945 936 669 2600 2.3480 4.8043 284.9245 541.1855 0.2931 0.933 937 669 1900 2.3460 3.5019 285.1668 542.5596 0.2930 0.933 938 669 1300 2.3445 2.3914 285.3522 543.6069 0.2930 0.947 939 669 700 2.3454 1.288 285.2353 543.4760 0.2930 0.969

50 1.15 Expt. SK Scaled 1.1

1.05 or ct Fa - Z 1

0.95

0.9 0246810 Pressure (Psia)

Figure 3.12: Scaled Z-Factor for Very Light Gas Composition.

Expt. SK Scaled

0.9 or Fact Z-

0.8

0.7 0246 Pressure (Psia)

Figure 3.13: Scaled Z-Factor for Carbon Dioxide Rich Gas Composition.

51 1.4

1.2

0.8 or t c Fa

Z- 0.6

0.4 Expt. SK 0.2 Scaled

0 1357911 Pressure (Psia)

Figure 3.14: Scaled Z-Factor for Rich Gas Condensate Composition.

1.05

0.95 or t c Fa Z- 0.9

0.85 Expt.

Scaled 0.8 0246 Pressure (Psia)

Figure 3.15: Scaled Z-Factor for Highly Sour Gas Composition.

52 CHAPTER 4

Z-FACTOR PREDICTION FROM CUBIC

EQUATIONS OF STATE

4.1 Selection of Cubic Equations-of-State Some phase behavior applications require the use of an equation of state to predict properties of petroleum reservoir fluids. Since the introduction of the van der Waals4 EOS, many cubic EOS’s have been proposed like the Redlich and Kwong13 EOS (RK EOS) in 1949, the Peng and Robinson12 EOS (PR EOS) in 1976, to name only a few. RT Most of these equations retain the original van der Waals repulsive term , ()V − b modifying only the denominator in the attractive term. With the advent of simulation techniques in petroleum engineering, accuracy was the priority but a universal equation- of-state method was required as most of the EOSs worked best in a certain range of pressures and temperatures and compositions. Most petroleum engineering relied on the PR EOS or a modification of the RK EOS. Soave’s19 modification (SRK EOS) was the simplest and most widely used. A major drawback of the SRK EOS was the poor liquid density prediction. PR EOS reported that their EOS predicts better liquid densities than the SRK EOS but not accurate enough for all ranges of pressures and temperatures including other phases. Many other proposed equations of states relied on complex temperature functions to represent the highly nonlinear correction terms for EOS constants. The critical properties, acentric factor, molecular weight, and binary-interaction parameters (BIP’s) of components in mixture are required for EOS calculations. With the existing chemical-separation techniques, we usually cannot identify the many hundreds and thousands of components found in reservoir fluids. Another problem with the

53 existing EOS and other methods of predicting EOS parameters is that they cannot predict

properties of components heavier than approximately C20. Eight equations of state have been chosen which are commonly used in the reservoir simulation and calculation purposes in the petroleum industry. Each of these equations of state has been thoroughly examined in their ability to be able to predict z- factor both for pure substances and gas mixtures (including natural gases and sour natural

gases with significant amounts of C7+). It is observed that the prediction of z-factor is significantly dependent on the accuracy of the critical properties supplied/predicted. Based on this observation, LLS29 EOS was observed to be capable of predicting accurate critical properties for gas mixtures and therefore, more accurate z-factor prediction is possible with this method for a wide range of pressures and temperatures and for any gas composition. Hence, LLS EOS method can be adopted as a universal method for z-factor determination.

4.2 Lawal-Lake-Silberberg Equation of State

RT a(T) P = − (4.1) V − b V2 + αbV −βb2 where 1+ Ω Z − 3Z α = w c c (4.2) Ωw Zc

2 3 2 Zc (Ωw −1) + 2Ωw Zc + (1− 3Zc )Ωw β = 2 (4.3) Ωw Zc

3 Ωa = (1+ (Ωw −1)Zc ) (4.4)

2 2 R Tc a = Ωa (4.5) Pc

Ω RT (4.6) b = b c Pc

54 Z-Form of the EOS:

3 2 Φ3Z +Φ2 Z + Φ1Z + Φ0 = 0 (4.7) where,

Φ3 =1.0 Φ2 = −[]1+ (1− α)B

2 Φ1 = [A − αB − (β + α)B ]

2 3 Φ0 = −⎡AB−β(B + B )⎤ where, a(T)P bP A = 2 2 , B = R T RT . Mixing Rules:

1 1 2 2 a m = ∑∑xi x jai a j aij (4.8) ij

3 1 ⎡ 3 ⎤ bm = ⎢∑xibi ⎥ (4.9) ⎣ i ⎦

ωi aij = for ωi ≤ ωj (4.10) ωj

ωj aij = for ωi > ωj (4.11) ωi

1 1 0.5 2 2 αm = ∑∑xi x jαi α j (αiα j ) (4.12) ij

1 1 0.5 2 2 βm = ∑∑x i x jβi β j (βiβ j ) (4.13) ij a ij = (a i a j ) = (α i α j ) = (β iβ j ) (4.14)

55 4.3 van der Waal Equation of State van der Waals4 proposed the first cubic EOS in 1873. The van der Waals EOS gives a simple, qualitatively accurate relation between pressure, temperature, and molar volume. It can be mathematically expressed as: RT a p = − (4.15) V − b V2 where a = attraction parameter b = repulsion parameter as compared to the ideal gas law, van der Waals EOS provides two important improvements. First, the prediction of liquid behavior is more accurate because volume approaches a limiting value, b, at high pressures, lim V(p) = b (4.16) p→∞ where be is referred to as the covolume. a/V2 term in the vdW EOS represents the non-ideal gas behavior and is interpreted as the attractive component of pressure. van der Waals also stated that the critical criteria that are used to define the two EOS constants a and b which are the first and second derivatives of pressure with respect to volume equal to zero at the critical point of a pure component.

⎛ ∂p ⎞ ⎛ ∂ 2 p ⎞ = ⎜ ⎟ = 0 (4.17) ⎜ ⎟ ⎜ 2 ⎟ ⎝ ∂V ⎠ ∂V pc ,Tc ,Vc ⎝ ⎠ pc ,Tc ,Vc

3 Martin and Hou show that this constraint is equivalent to the condition (z − z c )= 0 at the critical point. The constants a and b are given by: 27 R 2T 2 a = c 64 p c 1 RT and b = c (4.18) 8 p c 3 The critical compressibility results in z = = 0.375. c 8

56 van der Waals EOS in terms of z can be written as: z3 − ()B +1 z 2 + Az − AB = 0 (4.19)

p 27 p R where A = a 2 = 2 (4.20) ()RT 64 TR p 1 p B = b = R (4.21) RT 8 TR vdW EOS has a fixed zc (=0.375) for all components which is not true and no temperature function which is a drawback of vdW EOS.

4.4 Redlich-Kwong Equation of State Redlich and Kwong13 (1948) developed an adjustment in the van der Waals’ attractive pressure term (a/V2), which could considerably improve the prediction of the volumetric and physical properties of the vapor phase. This attractive pressure term has a temperature dependence term and their equation can be represented as: RT a(T) p = − V − b V(V + b) (4.22) where T is the system temperature in oR. The authors in their development of the equation, noted that as the system pressure becomes very large, i.e., p → ∞, the molar volume V of the substance shrinks to about 26% of its critical volume regardless of the system temperature. The Equation 2.17 was accordingly constructed to satisfy the following condition: b = 0.26Vc (4.23) Applying the critical point conditions (as expressed by Equation 4.17) on Equation 4.19, and solving the resulting equations simultaneously, gives

2 2.5 R Tc a = Ωa a(TR ) (4.24) pc

RTc b = Ω b (4.25) pc where

57 Ω = 0.42748 a Ω b = 0.08664 Equating Equation 4.18 with Equation 4.21 gives pc Vc = 0.333RTc (4.26) The above expression shows that Redlich-Kwong EOS produces a universal critical compressibility factor (Zc) of 0.333 for all substances. Replacing the molar volume V in Equation 4.20 with ZRT/p gives p A = a 2 2 R T (4.27) bp B = (4.28). RT Redlich and Kwong extended the application of their equation to hydrocarbon liquid or gas mixtures by employing the following mixing rules:

n 2 ⎡ 0.5 ⎤ a m = ⎢∑ x i a i ⎥ (4.29) ⎣ i=1 ⎦ ⎡ n ⎤ b m = ⎢∑ x i bi ⎥ (4.30) ⎣ i=1 ⎦

The Redlich-Kwong value of zc=1/3 is reasonable for lighter hydrocarbons but is unsatisfactory for heavier components.

4.5 Soave-Redlich-Kwong Equation of State A significant development of cubic equations of state was the publication by Soave19 (1972) of a modification in the evaluation of the parameter a in the attractive pressure term of the Redlich-Kwong equation of state (Equation 4.22). Soave replaced the term (a/T0.5) in Equation 4.22 with a more general temperature-dependent term as demonstrated by (aα), to give RT aα(T) p = − (4.31) V − b V(V + b)

58 where α is a dimensionless factor which becomes unity at T = Tc. At temperatures other than critical temperature, the parameter α is defined by the following expression:

0.5 2 α = (1+ m(1− Tr )) (4.32) The parameter m is correlated with the acentric factor, to give m = 0.480 +1.574ω − 0.176ω2 (4.33) where ω is the acentric factor of the substance. For any pure component, the constants a and b in Equation 4.31 are found by imposing the classical van der Waals’ critical point constraints (Equation 4.17), on Equation 4.31 and solving the resulting equations, to give R 2T 2 a = Ω c a p c (4.34) RT b = Ω c b p c (4. 35) where Ωa and Ωb are the Soave-Redlich-Kwong (SRK) dimensionless pure component parameters and have the following values:

Ωa = 0.42747 (4.36)

Ωa = 0.08664 (4.37) The Z-Form of the Equation 4.31 is: Z3 − Z2 + (A − B − B2 )Z − AB = 0 (4.38) where ()aα p A = 2 (RT) (4.39) bp B = (4.40) RT To use the Equation 4.38 with mixtures, the following mixing rules were proposed by Soave: 0.5 (4.41) ()aα m = ∑∑[x i x j ()a i a jα i α j (k ij − 1)] ij

59 b m = ∑[]x i bi i (4.42) with ()aα p A = m (4.43) (RT) 2

b p B = m (4.44) RT

The parameter kij is an empirically determined correction factor called the binary interaction coefficient, characterizing the binary formed by component i and component j in the hydrocarbon mixture.

Modifications of the SRK EOS Groboski and Daubert37 (1978) proposed a new expression for calculating the parameter m of Equation 4.32 to improve the pure component vapor pressure predictions by the SRK EOS. The proposed relationship has the following form: m = 0.48508 + 1.55171ω − 0.15613ω2 (4.45) Elliot and Daubert38 (1985) stated that the evaluation of optimal interaction coefficients of asymmetric mixtures (components with significant difference in chemical behavior), proposed the following set of expressions for calculating kij,

• For N2 systems:

∞ k ij = 0.107089 + 2.9776k ij

• For CO2 systems:

∞ ∞ 2 k ij = 0.08058 − 0.77215k ij −1.8407(k ij )

• For H2S systems:

∞ k ij = 0.07654 + 0.017921k ij • For Methane systems with compounds of 10 or more:

∞ ∞ 2 k ij = 0.17985 + 2.6958k ij +10853(k ij ) where, for the above expression:

60 ∞ 2 k ij = −(εi − ε j ) /(2εiε j ) (4.46) and

0.5 εi = (a i loge (2)) / bi (4.47). The major drawback in the SRK EOS is that the critical compressibility factor takes on the unrealistic universal critical compressibility of 0.333 for all substances. Consequently, the molar volumes are typically overestimated, i.e., densities are underestimated.

4.6 Peng-Robinson Equation of State Peng and Robinson12 (1975) conducted a comprehensive study to evaluate the use of SRK equation of state for predicting the behavior of naturally occurring hydrocarbon systems. The authors showed emphasis on the ability of the equation to predict liquid densities and other fluid properties particularly in the vicinity of the critical region. They proposed the following expression: RT aα(T) p = − (4. 48) V − b (V + b)2 − cb2 Equation 4.48 can be rewritten as: RT aα(T) p = − (4.49) V − b V(V + b) + b(V − b) Imposing the classical critical point conditions (Equation 4.17) on Equation 4.48 and solving for the parameters a and b, yields

2 2 R Tc a = Ωa (4.50) pc RT b = Ω c b p c (4.51) where

Ω a = 0.45724 Ω = 0.07780 b .

61 This equation predicts a universal critical gas compressibility factor of 0.307 compared to 0.333 for the SRK model. Peng and Robinson also adopted Soave’s approach for calculating the parameter α:

0.5 2 α = (1+ m(1− TR )) (4.52) where m = 0.3746 +1.5423ω − 0.2699ω2 (4.53) This was later expanded by the investigators (1978) to give the following relationship: m = 0.379642 +1.48503ω − 0.1644ω2 + 0.016667ω3 (4.54) Rearranging Equation 2.37 into the compressibility factor form gives Z3 + (B −1)Z2 + (A − 3B2 − 2B)Z − (AB − B2 − B3 ) = 0 (4.55) The mixing rules for PR EOS are defined as follows:

1/ 2 1/ 2 a m = ∑∑x i x ja i a j a ij (4.56) b m = ∑ x i bi (4.57) i Although PR EOS is another widely used cubic EOSs in petroleum engineering calculations, it underpredicts saturation pressure of reservoir fluids compared with SRK EOS.

4.7 Schmidt-Wenzel Equation of State Schmidt and Wenzel24 (1980) proposed an attractive pressure term that introduces the acentric factor ω as a third parameter. The SW EOS has the following form: RT a(T) p = − (4. 58) V − b V3 + (1+ 3ω)bV − 3ωb2 with

⎛ R 2T2 ⎞ ⎜ c ⎟ a = Ωa ⎜ ⎟α (4.59) ⎝ pc ⎠

62 ⎛ RT ⎞ ⎜ c ⎟ b = Ωb ⎜ ⎟ (4.60) ⎝ pc ⎠ where

3 Ωa = (1− ζ c (1− βc )) (4.61)

Ω b = βcξc (4.62)

The βc is given by the smallest positive root of the following equation:

3 2 ()6ω +1 βc + 3βc + 3βc −1 = 0 (4. 63) and 1 ξc = (4.64) 3(1+ βcω)

4.8 Patel-Teja Equation of State Patel and Teja20 (1982) proposed the following three-parameter cubic equation: RT a(T) p = − (4.65) V − b V2 + (b + c)V − bc In this equation “a” is a function of temperature, and b and c are constants characteristic of each component. Equation 4.65 was constrained to satisfy the following conditions: ∂p = 0 (4.66) ∂V TC

∂ 2 p = 0 (4.67) ∂V 2 TC p c Vc = ξc (4.68) RTc Patel and Teja pointed out that the third parameter c in the equation allows the empirical parameter ξc to be chosen freely. Application of Equation 4.66 to Equation 4.67 yields:

63 2 2 R Tc 0.5 2 a = Ωa [1+ m(1− TR )] (4.69) pc

RTc b = Ω b (4.70) p c

RTc c = Ωc (4.71) p c where

Ωc =1− 3ξc (4.72)

2 2 Ωa = 3ξc + 3()1− 2ξc Ωb + Ωb + (1− 3ξc ) (4.73) and Ωb is the smallest positive root of the following equation:

3 2 2 3 Ωb + (2 − 3ξc )Ωb + 3ξc Ω b − ξc = 0 (4.74)

Equation 4.74 can be solved for Ωb by using the Newton-Raphson iterative method with an initial value for Ωb as given by

Ω b = 0.32429Zc − 0.002005 (4.75)

For non-polar fluids, the parameters m and, ξc are related to the acentric factor by the following relationships: m = 0.452413 +1.30982ω − 0.295937ω2 (4.76) ξ = 0.329032 − 0.0767992ω + 0.0211947ω2 c (4.77) In terms of Z, Equation 4.65 can be rearranged to produce Z3 + ()C −1 Z2 + (A − 2BC − B − C − B2 )Z + (BC + B2C − AB) = 0 (4.78) where, for mixtures a p A = m (4.79) (RT)2 b p B = m (4.80) RT c p C = m (4.81) RT with

64 0.5 a m = ∑∑[x i x j (a i a j ) (1− k ij )] (4.82) bm = ∑[xibi ] (4.83) i cm = ∑ [xici ] (4.84) i

An improved relationship for undefined components such as C7+, the parameters 40 m and ξc was proposed by Willman and Teja (1986) in terms of the boiling point Tb and specific gravity γ. Therefore, a major drawback of PT EOS is that additional information is required to be able to determine volumetric properties of composition involving C7+.

4.9 Trebble-Bishnoi-Salim Equation of State Trebble and Bishnoi26 proposed a four parameter equation of state and it can be represented as follows: RT a(T) p = − (4.85) V − b V2 + (b + c)V − bc − d2 Parameters “a” and “b” are temperature dependent while “c” and “d” are independent of temperature. Therefore, new temperature functions for “a(T)” and “b(T)” have been proposed. The value of “d” was determined for all the components available in the database along the critical isotherm. “d” values for the remaining components were calculated from a linear fit of optimized “d” values versus the critical volume. The value of “c” was directly determined from the experimental value of the critical compressibility. Once the parameters “c” and “d” are set, optimal values of “a” and “b” are then calculated. This TB EOS offers increased correlational flexibility and allows for significant improvements in PVT predictions. Trebble and Bishnoi do mention that the quality of an equation-of-state largely depends on the data used in its preparation

65 4.10 Transformed Cubic Equations to the LLS EOS Form Lawal-Lake-Silberberg EOS is represented as: RT a(T) P = − 2 2 V − b V + αbV − βb (4.1) It is the most general form of the EOSs described in this study. This can be observed by substituting the values of α and β with numerical constants as described in the Table 4.1.

Table 4.1: Common Specialization Cubic Equation of State

4.11 Generalized Reduced State of Cubic Equations-of-State Described below is the derivation of reducing the general LLS EOS to the Z- form:

66 RT a(T) P = − 2 2 V − b V + αbV − βb (4.1) V Multiply on both sides of Equation 4.1 by , we get RT V a(T) V RT V RT P = − 2 2 RT V − b RT V + αbV − βb (4.86) Real Gas Equation: PV = ZRT (4.87) Using the real gas law, Equation 4.86 becomes, a(T)V V RT Z = − 2 2 V − b V + αbV − βb (4.88) ZRT Simplifying Equation 4.88 using the real gas law: V = , P

a(T) ZRT P 1 Z = − RT b ()ZRT 2 αbZRT 1− + − βP 2 ZRT P 2 P P (4.89) Further simplifying Equation 4.89,

a(T) ZRT P P 2 1 Z = − RT bp (ZRT) 2 ZbPRT (bP) 2 1− + α − β RTZ (4.90) a(T)P A = 2 Defining (RT) (4.91) bP B = and RT (4.92) 1 Using these definitions in Equation 4.90 and dividing the 2nd part of RHS by ,we ()RT 2 get,

a(T)P Z 1 ()RT 2 Z = − B (ZRT) 2 αZbPRT β(bP) 2 1− + − Z 2 2 2 ()RT ()RT (RT) (4.93)

Simplifying Equation 4.93, a(T)P Z 1 ()RT 2 Z = − B αZbP β(bP) 2 1− Z2 + − Z RT 2 ()(RT) (4.94) Using the definitions of A and B and further simplifying Equation 4.94, we get Z AZ Z = − 2 2 Z − B Z + αBZ − βB (4.95) Canceling Z on the numerators on both sides in Equation 4.95, we get 1 A 1 = − 2 2 Z − B Z + αBZ − βB (4.96) Simplifying Equation 4.96 by cross-multiplication, we get

3 2 2 2 3 2 2 Z + ()− B + αB Z + (− βB − αB )Z + βB = Z + αBZ − βB − AZ + AB (4.97) = Z3 + ()−1− B + αB Z2 + (A − αB − βB2 − αB2 )Z + (βB3 + βB2 − AB) = 0 (4.98)

The reduced form of the real-gas law can be expressed as Z = Z f (P , T ) c R R (4.99) In order to use Equation 4.99 to predict Z-factors of pure substances, natural and sour gases by utilizing cubic equations of state, the computation of Z-factor from the reduced form of Equation 4.1 requires composition-dependent critical compressibility factor as well as mixture critical pressure, temperature and volume for the reduced parameters (PR, νR, TR). The task is accomplished in the next paragraph

68 The reduced compressibility factor (ZR) equation for pure substances can be derived from Equation 4.1 by dividing the expression of Equation 4.100 by Zc: 1+ Ω Z − 3Z α = w c c Ω Z w c (4.100)

θ Z3 + θ Z2 + θ Z + θ = 0 3 R 2 R 1 R 0 (4.101) where

θ3 = 1 ⎛ 1 Ω P ⎞ ⎜ b R ⎟ θ2 = − ⎜ + (1− α) ⎟ ⎝ Zc ZcTR ⎠ ⎛ 2 ⎞ ⎜ Ωa PR Ω b PR ⎧Ω b PR ⎫ ⎟ θ1 = − α − (α + β)⎨ ⎬ ⎜ Z2T 2+θc Z2T Z T ⎟ ⎝ c R c R ⎩ c R ⎭ ⎠ ⎛ 2 ⎡ 2 3 ⎤⎞ ⎜ Ωa Ω b PR 1 ⎧Ω b PR ⎫ ⎧Ω b PR ⎫ ⎟ θ0 = − − β⎢ ⎨ ⎬ + ⎨ ⎬ ⎥ ⎜ Z3T3+θc Z Z T Z T ⎟ ⎝ c R ⎣⎢ c ⎩ c R ⎭ ⎩ c R ⎭ ⎦⎥⎠ The reduced compressibility factor (ZR) equation for mixtures can be derived from Equation 4.101 by replacing pure substance parameters with mixture parameters:

θ3 = 1 ⎛ 1 B P ⎞ ⎜ c R ⎟ θ2 = − ⎜ + (1− α m ) ⎟ ⎝ Zc ZcTR ⎠ ⎛ 2 ⎞ ⎜ A c PR Bc PR ⎧Bc PR ⎫ ⎟ θ1 = − α m − (α m + βm )⎨ ⎬ ⎜ Z2T 2+θm Z2T Z T ⎟ ⎝ c R c R ⎩ c R ⎭ ⎠ ⎛ 2 ⎡ 2 3 ⎤⎞ ⎜ A c Bc PR 1 ⎧Bc PR ⎫ ⎧Bc PR ⎫ ⎟ θ0 = − − βm ⎢ ⎨ ⎬ + ⎨ ⎬ ⎥ ⎜ 3 3+θm ⎟ ZcTR ⎢Zc ⎩ZcTR ⎭ ⎩ZcTR ⎭ ⎥ ⎝ ⎣ ⎦⎠ (4.102)

In Equations 4.102, the composition-dependent parameters Ac, Bc and Zc are defined by Equations 4.103-4.105.

69 A = (α + β )B2 + α B + 3Z2 c m m c m c c (4.103)

θ Z3 + θ Z2 + θ Z + θ = 0 3 c 2 c 1 c 0 (4.104) where 2 3 θ3 = 8 +12α m + 6α m + α m θ = − (3 +12α +12α 2 + 9β − 9α β ) 2 m m m m m 2 θ1 = 3α m + 6α m + 6βm − 6α mβm 2 θ0 = − (α m + βm − α mβm )

φ B3 + φ B2 + φ B + φ = 0 3 c 2 c 1 c 0 (4.105) where 2 3 φ3 = 8 +12α m + 6α m + α m φ = 15 +15α − 27β − 3α 2 2 m m m φ1 = 6 + 3α m

φ0 = −1

The expressions for mixture critical pressure and temperature are thereby established in Equations 4.99 and 4.102 a B2 P = m c c b 2 [3Z2 + (α + β )B2 + α B ] m c m m c m c (4.106) a B T = m c c b R[3Z2 + (α + β )B2 + α B ] m c m m c m c (4.107)

4.12 Prediction Results for Z-Factor of Pure Substances A graphical comparative result of the eight EOSs is shown with the experimental values for the components as shown below. More results on this can been seen in Appendix D.

70 Z-Factor Comparison Graph (Expt. vs. LLS-EOS)

1.35

1.25

1.15

1.05 Factor LLS 560 R Z-

LLS 680 R

0.95 LLS 920 R

Expt. T=560

Expt. T=680 0.85 Expt. T=920

0.75 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Pressure, P (Psia)

Figure 4.1: Z-Factor comparison for LLS-EOS for Methane.

Z-Factor Comparison Graph (Expt. vs. LLS)

1.13

1.03

0.93

0.83

or 0.73 t Fac - LLS 560 R Z 0.63 LLS 680 R

0.53 LLS 920 R

Expt. T=560 0.43 Expt. T=680

0.33 Expt. T=920

0.23 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Pressure, P (Psia)

Figure 4.2: Z-Factor comparison for LLS-EOS for Carbon dioxide.

71 Z-Factor Comparison Graph (Expt. vs. LLS-EOS)

1.45

1.35

or 1.25 t c Fa LLS 560 R Z-

LLS 680 R 1.15 LLS 920 R

Expt. T=560

1.05 Expt. T=680 Expt. T=920

0.95 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Pressure, P (Psia)

Figure 4.3: Z-Factor comparison for LLS-EOS for Nitrogen.

1.7 Z-Factor Comparison (Expt. Vs. VdW-EOS)

1.6

1.5

1.4

1.3 or t c 1.2 Fa Z- 1.1 VdW-EOS T=100 F 1 VdW-EOS T=220 F VdW-EOS T=460 F 100 F EXP 0.9 220 F EXP 460 F EXP 0.8

0.7 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Pressure (psia)

Figure 4.4: Z-Factor comparison for vdW-EOS for Methane.

72 1.6 Z-Factor Comparison (Expt. Vs. vdW-EOS)

1.4

1.2

1 or t Fac Z- 0.8

VdW-EOS T=100 F 0.6 VdW-EOS T=220 F VdW-EOS T=460 F 100 F EXP 0.4 220 F EXP 460 F EXP

0.2 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Pressure, (psia)

Figure 4.5: Z-Factor comparison for vdW-EOS for Carbon dioxide.

4.13 Development of Binary Interaction Parameters

Binary Interaction Coefficient/Number (BIN): These binary interaction coefficients are used to model the intermolecular interaction through empirical adjustment of the (aα)m term as represented mathematically by Equation 4.38. They are dependent on the difference in molecular size of components in a binary system and they are characterized by the following properties, as summarized by Slot-Petersen39 (1987): • The interaction between hydrocarbon components increases as the relative difference between their molecular weights increases:

k,j+1 > ki,j • Hydrocarbon components with the same molecular weight have a binary interaction coefficient of zero:

ki,j = 0

• The binary interaction coefficient matrix is symmetric:

ki,j = kj,i

4.14 Prediction Results for Z-Factor of Mixtures

Z-Factor Comparison Chart at 49 oF (Simon et. al.)

1.0 Expt. Measured Corresponding states BWR EOS 0.9 VdW LLS PR 0.8 PT RK SRK 0.7 SW r TB o t

Fac 0.6 Z-

0.5

0.4

0.3

0.2 1000 1250 1500 1750 2000 2250 2500 2750 3000 Pressure (Psia)

o Figure 4.6: Z-Factor comparison for CO2-C1 mixture at 49 F.

74 Z-Factor Comparison Chart at 70 oF (Simon et. al.)

1.0 Expt. Measured Corresponding states 0.9 BWR EOS VdW LLS 0.8 PR PT RK 0.7 SRK SW r o TB

act 0.6 F - Z

0.5

0.4

0.3

0.2 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 Pressure (Psia)

o Figure 4.7: Z-Factor comparison for CO2-C1 mixture at 70 F.

Z-Factor Comparison Chart at 90 oF (Simon et. al.)

1.0 Expt. Measured Corresponding states BWR EOS 0.9 VdW LLS TB PR PT 0.8 RK SRK SW or t 0.7 TB Z-Fac 0.6 VdW RK SRK

0.5 PT PR

LLS 0.4

0.3 1250 1500 1750 2000 2250 2500 2750 3000 Pressure (Psia)

o Figure 4.8: Z-Factor comparison for CO2-C1 mixture at 90 F.

75 Z-Factor Comparison Chart at 120 oF (Simon et. al.)

1.2 Expt. Measured Corresponding states 1.1 BWR EOS VdW LLS 1.0 PR PT 0.9 RK SRK SW 0.8 TB or t TB Fac

Z- 0.7

VdW 0.6 SRK PT 0.5 LLS PR

0.4

0.3 500 1000 1500 2000 2500 3000 Pressure (Psia)

o Figure 4.9: Z-Factor comparison for CO2-C1 mixture at 90 F.

4.15 Prediction Results for Z-Factor of Natural Gases

Table 4.2: Sources of Experimental Z-Factor. Authors Year System Reference No.

Sage-Reamer-Lacey 1950 C1-C2 8

Sage-Lacey-Schfaasma 1934 C1-C3 79

Reamer-Olds-Sage-Lacey 1944 C1-CO2 75

Reamer-Sage-Lacey 1951 C1-H2S 80

Reamer-Olds-Sage-Lacey 1942 C1-nC10 82

Reamer-Olds-Sage-Lacey 1945 C2-CO2 76

Reamer-Selleck-Sage-Lacey 1952 C2-N2 83

Reamer-Sage 1962 C2-nC10 84

Sage-Reamer-Lacey 1951 C3-CO2 77

Reamer-Olds-Sage-Lacey 1949 nC4-CO2 78

Reamer-Selleck-Sage-Lacey 1953 nC10-H2S 81

Wichert 1970 CO2-H2S-N2-C1-C2-C3-iC4-nC4- 86 iC5-nC5-nC6-C7+

Elsharkawy 2002, 2004 CO2-H2S-N2-C1-C2-C3-iC4-nC4- 41, 71 iC5-nC5-nC6-C7+

Elsharkawy-Foda 1998 CO2-H2S-N2-C1-C2-C3-iC4-nC4- 74 iC5-nC5-nC6-C7+

Satter-Campbell 1963 H2S-C1-C2 46

Buxton-Campbell CO2-N2-C1-C2-C3

Simon-Fesmire-Dicharry-Vorhis 1977 CO2-N2-C1-C2-C3-nC4-nC5-nC6 87

Fluid Prop. Package (Shell) 2003 CO2-N2-C1-C2-C3-iC4-nC4-iC5- Private nC5-nC6-C7+

77 4.15.1 Results for Excelsior Laboratory Data

Table 4.3: Gas Composition for Excelsior 6 Laboratory Data. COMPARISON OF LABORATORIES AND FLUID PROPERTIES PACKAGE Pressure (Psia) 3317 2615 Fluid Prop. Core Fluid Prop. Core Lab. Package Lab. Package BHT, oF 121 0.802 0.7942 0.768 0.7767 Z-Factor 0 0 0.171 0.2048 Produced Fraction of Dew Point Gas 0 0 0.042 0.05 Liquid Saturation Vapor Phase Composition 0.0005 0.0005 0.0005 0.0005 Carbon Dioxide 0.0069 0.0069 0.0073 0.0071 Nitrogen 0.813 0.813 0.8321 0.8325 Methane 0.063 0.063 0.0625 0.0627 Ethane 0.0343 0.0343 0.0325 0.0334 Propane 0.0195 0.0195 0.0179 0.0185 iso-Butane 0.0153 0.0153 0.0137 0.0143 n-Butane 0.0102 0.0102 0.0085 0.0091 iso-Pentane 0.0052 0.0052 0.0042 0.0045 n-Pentane 0.0079 0.0079 0.0059 0.0063 Hexane (s) 0.0242 0.0242 0.0149 0.0111 Heptane plus 0 0 0 0

1.20 Lab. vdW

LLS PR

PT RK 1.09 SRK SW r o t c 0.98 Fa Z-

0.87

0.76 715 1235 1755 2275 2795 3315 Pressure(psia)

Figure 4.10: Z-Factor for Sweet Natural Gas, Data from Excelsior 6 (FPP) at 581 oR

Z-Factor Comparison Chart at 90 oF (Simon et. al.)

Expt. Measured 1.0 Corresponding states BWR EOS VdW 0.9 LLS PR TB PT 0.8 RK SRK SW TB or

t 0.7 c a F Z- 0.6 VdW RK SRK

0.5 PT PR

LLS 0.4

0.3 1250 1500 1750 2000 2250 2500 2750 3000 Pressure (Psia)

Figure 4.11: Z-Factor Comparison Chart at 90 oF (Simon et al.).

79 Z-Factor Comparison Chart at 120 oF (Simon et. al.)

1.2 Expt. Measured Corresponding states 1.1 BWR EOS VdW LLS 1.0 PR PT 0.9 RK SRK SW 0.8 TB or t TB Fac -

Z 0.7

VdW 0.6 SRK PT 0.5 LLS PR

0.4

0.3 500 1000 1500 2000 2500 3000 Pressure (Psia) Figure 4.12: Z-Factor Comparison Chart at 120 oF (Simon et al.).

4.15.2 Results for TTU Laboratory Data

0.9 LLS EOS

PE Lab.

0.8 r o act F - Z 0.7

0.6

0.5 0 1000 2000 3000 4000 5000 Pressure, psia

Figure 4.13: 75% CO2 - Dry Gas at 100 oF for CO2 Sequestration.

80 1

LLS

PE Lab.

0.95 or t c a F Z-

0.9

0.85 0 1000 2000 3000 4000 5000 Pressure, psia

o Figure 4.14: 25% CO2 - Dry Gas at 160 F for CO2 Sequestration.

4.15.3 Results for UCalgary Data

Table 4.4: Gold Creek Gas Composition. GOLD CREEK 10-5

T (210 P (Psia) oF) 4496 0.93 4815 0.948 4515 0.966 5015 0.984 5215 1.003 5515 1.032 6015 1.061 CO2 H2S N2 Total Acid Gas 0.0318 0.0704 0.0401 0.1022 C1 C2 C3 IC4 NC4 IC5 NC5 C6 C7+ 0.7069 0.0303 0.0209 0.0057 0.0109 0.006 0.0057 0.0093 0.046 C7+ Mole. Sp. Gr. 0.785 Fraction Wt. 131

1.7 Expt. VdW LLS PR PT VdW RK 1.5 SRK SW

RK or

t SRK c

a 1.3

F PT

Z- SW

1.1

LLS

0.9 4400 4700 5000 5300 5600 5900 6200 Pressure (Psia)

Figure 4.15: Z-Factor for sour natural gas, data from Excelsior 6 (FPP) at 581 oR

Shell Marmattan 10-33 @ 84 oF

1.6

Expt. VdW-EOS 1.4 LLS-EOS PR-EOS PT-EOS 1.2 RK-EOS SRK-EOS SW-EOS 1.0

or TB-EOS

ct TB

Fa VdW Z- 0.8

SRK RK 0.6 SW

PR PT LLS 0.4

0.2 2014 2514 3014 3514 4014 4514 5014 Pressure (Psia)

Figure 4.16: Z-Factor comparison for sour natural gas mixture at 84 oF.

82 Shell Marmattan 10-33 @ 73 oF

1.6

Expt. VdW-EOS 1.4 LLS-EOS PR-EOS PT-EOS 1.2 RK-EOS SRK-EOS SW-EOS TB

or TB-EOS 1.0

Fact VdW Z-

0.8 SRK RK SW

PR PT 0.6 LLS

0.4 2014 2514 3014 3514 4014 4514 5014 Pressure (Psia)

Figure 4.17: Z-Factor comparison for sour natural gas mixture at 73 oF.

Sutte Plant, H,P Injection Line

1.23 VdW Expt. SW 1.18 LLS TB PR PT 1.13 RK PT RK SRK SW 1.08 SRK TB VdW 1.03 PR Z-Factor

0.98 LLS

0.93

0.88

0.83 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Pressure (Psia)

Figure 4.18: Z-Factor comparison for sour natural gas mixture at 198 oF.

83 Fina WindFall Processing Plant (510 oR)

1.12

VdW 1.02 TB

SW SRK 0.92 PR r o RK LLS t 0.82

Fac PT Z- 0.72 Expt. LLS-EOS VdW-EOS 0.62 PR-EOS RK-EOS SRK-EOS 0.52 PT-EOS SW-EOS TB-EOS 0.42 1014 1514 2014 2514 3014 3514 4014 4514 5014 Pressure (Psia)

Figure 4.19: Z-Factor comparison for sour natural gas mixture at 50 oF.

Fina WindFall Processing Plant (560 oR)

1.18

TB VdW 1.08

SW SRK 0.98 RK or t c

a LLS F 0.88 PR Z- PT Expt. LLS-EOS 0.78 VdW-EOS PR-EOS RK-EOS SRK-EOS 0.68 PT-EOS SW-EOS TB-EOS 0.58 1014 1514 2014 2514 3014 3514 4014 4514 5014 Pressure (Psia)

Figure 4.20: Z-Factor comparison for sour natural gas mixture at 100 oF.

84 Fina WindFall Processing Plant (585 oR)

1.19

TB VdW 1.09

SW SRK 0.99 RK r o t

c LLS

Fa PT 0.89 PR Z- Expt. LLS-EOS 0.79 VdW-EOS PR-EOS RK-EOS SRK-EOS 0.69 PT-EOS SW-EOS TB-EOS 0.59 1014 1514 2014 2514 3014 3514 4014 4514 5014 Pressure (Psia)

Figure 4.21: Z-Factor comparison for sour natural gas mixture at 125 oF.

Fina WindFall Processing Plant (610 oR)

1.20

1.15

1.10 TB VdW

1.05 SW SRK

1.00 RK r o 0.95 Fact PT Z- LLS 0.90 PR Expt. LLS-EOS 0.85 VdW-EOS PR-EOS 0.80 RK-EOS SRK-EOS PT-EOS 0.75 SW-EOS TB-EOS 0.70 1014 1514 2014 2514 3014 3514 4014 4514 5014 Pressure (Psia)

Figure 4.22: Z-Factor comparison for sour natural gas mixture at 150 oF.

85 Fina WindFall Processing Plant (635 oR)

1.24 Expt. 1.19 LLS-EOS VdW-EOS VdW 1.14 PR-EOS TB RK-EOS 1.09 SRK-EOS PT-EOS SRK SW-EOS SW RK 1.04 TB-EOS

0.99 Z-Factor 0.94 PT LLS PR 0.89

0.84

0.79

0.74 1014 1514 2014 2514 3014 3514 4014 4514 5014 Pressure (Psia)

Figure 4.23: Z-Factor comparison for sour natural gas mixture at 175 oF.

Fina WindFall Processing Plant (660 oR)

1.24 Expt. 1.19 LLS-EOS VdW-EOS PR-EOS VdW 1.14 TB RK-EOS SRK-EOS 1.09 PT-EOS SRK SW-EOS SW 1.04 TB-EOS RK or t c 0.99 Fa

Z- PT 0.94 LLS PR 0.89

0.84

0.79

0.74 1014 1514 2014 2514 3014 3514 4014 4514 5014 Pressure (Psia)

Figure 4.24: Z-Factor comparison for sour natural gas mixture at 200 oF.

86 Fina WindFall Processing Plant (679 oR)

1.24 Expt. 1.19 LLS-EOS VdW-EOS PR-EOS VdW 1.14 TB RK-EOS SRK-EOS 1.09 PT-EOS SRK SW-EOS SW RK 1.04 TB-EOS or

ct 0.99 Fa

Z- PT 0.94 LLS PR 0.89

0.84

0.79

0.74 1014 1514 2014 2514 3014 3514 4014 4514 5014 Pressure (Psia)

Figure 4.25: Z-Factor comparison for sour natural gas mixture at 219 oF.

Fina WindFall Processing Plant (710 oR)

1.24 Expt. LLS-EOS 1.19 VdW-EOS PR-EOS TB VdW 1.14 RK-EOS SRK-EOS PT-EOS 1.09 SW-EOS SRK TB-EOS SW r RK

acto 1.04 F - Z

0.99 PT

LLS 0.94 PR

0.89

0.84 1014 1514 2014 2514 3014 3514 4014 4514 5014 Pressure (Psia)

Figure 4.26: Z-Factor comparison for sour natural gas mixture at 250 oF.

87 4.15.4 Results for Elsharkawy Gas Data

Table 4.5: Results of Elsharkawy Gas Data. IND 1 84 416 439 504 752 817

H2S 0 0.0708 0.0383 0.2816 0 0.1693 0.1047

CO2 0.0017 0.0096 0.0058 0.0608 0.0097 0.0576 0.0163

N2 0.015 0.0064 0.002 0.0383 0.0041 0.0011 0.0244

C1 0.7284 0.6771 0.7564 0.4033 0.8616 0.6619 0.7352

C2 0.0847 0.0871 0.0706 0.0448 0.0355 0.0412 0.0498

C3 0.0418 0.0384 0.0336 0.0248 0.0154 0.0188 0.0181

IC4 0.011 0.005 0.0104 0.006 0.0046 0.0044 0.0059

NC4 0.0171 0.0156 0.0135 0.0132 0.0046 0.0076 0.0073

IC5 0.0088 0.0056 0.0072 0.0079 0.0026 0.0032 0.004

NC5 0.0084 0.0082 0.0055 0.0081 0.002 0.0036 0.0037

C6 0.0124 0.0083 0.0077 0.0121 0.0035 0.0052 0.0053

C7+ 0.0707 0.0656 0.049 0.0991 0.0564 0.0261 0.0253 Mw+ 152 154 158 165 253 144 132 Sg+ 0.81 0.776 0.783 0.818 0.85 0.788 0.774 o Tc C7+, R 1179.581 1151.75 1165.19 1209.73 1368.64 1144.9 1109.426

Pc C7+, 381.99 350.86 373.99 398.74 487.02 362.72 409.55 psia T (oF) 221 296 325 250 271 255 290 P (psia) 4973 4669 5095 4190 11830 4050 4255 Z (Expt.) 0.997 0.97 1.011 0.838 1.775 0.914 0.968 LLS (This Study) 1.0052 0.9883 1.0651 0.7349 1.5917 0.9749 1.0172

88 Table 4.5 (Contd.) Component Mole Fraction IND 1275 1277 1280 1714 1788 1866

H2S 0.068 0.1078 0.1826 0.2327 0.273 0.5137

CO2 0.0209 0.0616 0.0866 0.0287 0.0451 0.0319

N2 0.1019 0.004 0.0037 0.0304 0.0061 0.0258

C1 0.6857 0.7414 0.5213 0.5601 0.6459 0.4241

C2 0.059 0.0327 0.1165 0.082 0.0084 0.0024

C3 0.0282 0.0121 0.0142 0.0345 0.0093 0.0007

iC4 0.0047 0.0022 0.0039 0.0085 0.0027 0.0002

nC4 0.0116 0.0061 0.0083 0.011 0.002 0.0003

iC5 0.0085 0.0057 0.0095 0 0.002 0.0002

nC5 0 0 0 0.0071 0.001 0.0001

nC6 0.0035 0.0046 0.0103 0.0028 0.0012 0.0002

C7+ 0.008 0.0218 0.0431 0.0022 0.0032 0.0004 Mw+ 125 125 125 145 103 120 Sg+ 0.75 0.75 0.75 0.85 0.7 0.75 o Tc C7+, R 1074.0 1074.02 1074.0 1202.56 983.27 1063.8

Pc C7+, psia 405.26 405.26 405.26 394.76 272.93 422.82 T (oF) 157 189 216 120 250 230 P (psia) 2347 5065 5385 1000 5014 3514 Z (Expt.) 0.823 0.95 0.942 0.802 0.931 0.711 LLS (This Study) 0.9151 1.0328 0.9984 0.8768 1.0095 0.8330

89 4.15.5 Results for Elsharkawy Miscellaneous Data

Table 4.6: Z-Factor Results for Miscellaneous Gases. Rich Gas Condensate Serial No. 281 282 283 284 285 286 287

H2S 0 0 0 0 0 0 0

CO2 0.0231 0.0242 0.0248 0.0253 0.0258 0.0262 0.0266

N2 0.0137 0.0155 0.0161 0.0166 0.0163 0.0155 0.0143

C1 0.6583 0.7074 0.738 0.7559 0.7583 0.7485 0.7292

C2 0.0803 0.0817 0.0821 0.0839 0.0863 0.0905 0.0944

C3 0.0417 0.0411 0.0404 0.0402 0.0415 0.0447 0.0495

iC4 0.0078 0.0073 0.007 0.0069 0.0073 0.0082 0.0091

nC4 0.0184 0.017 0.0162 0.0159 0.0167 0.0186 0.0208

iC5 0.0075 0.0067 0.0062 0.006 0.0062 0.007 0.008

nC5 0.0108 0.0097 0.0089 0.0084 0.0086 0.0096 0.0107

nC6 0.0116 0.011 0.0103 0.0086 0.0078 0.0082 0.0092

C7+ 0.1268 0.0784 0.05 0.0323 0.0252 0.023 0.0282 Mw+ 191 154 139 128 120 115 113 Sg+ 0.831 0.804 0.789 0.778 0.77 0.765 0.763

Pc C7+, 324.60 378.39 404.34 427.52 447.21 460.98 466.85 psia o Tc C7+, R 1264.023 1177.662 1136.436 1105.09 1081.6 1066.586 1060.503 T (oF) 313 313 313 313 313 313 313 P (psia) 6010 5100 4100 3000 2000 1200 700 Z (Expt.) 1.212 1.054 0.967 0.927 0.93 0.952 0.97 ρ (lb/cu.ft.) 26.3 18.97 14.17 9.79 6.27 3.68 2.19 LLS (This Study) 1.0614 1.0612 1.0239 0.9815 0.9595 0.9588 0.9675

Table 4.6 (Contd.) Highly Sour Gas Condensate Serial No. 439 440 441 442 443 444 445

H2S 0.282 0.277 0.272 0.27 0.273 0.289 0.318

CO2 0.0608 0.0644 0.0669 0.0685 0.0694 0.0699 0.0679

N2 0.0383 0.0455 0.0476 0.0473 0.0461 0.0434 0.0394

C1 0.4033 0.4382 0.4641 0.4807 0.4844 0.4688 0.4331

C2 0.0448 0.0471 0.0481 0.0487 0.0493 0.0496 0.0494

C3 0.0248 0.0243 0.0239 0.0237 0.0239 0.0252 0.0277

iC4 0.006 0.0055 0.0051 0.0049 0.0049 0.0055 0.0067

nC4 0.0132 0.012 0.0111 0.0106 0.0106 0.0114 0.014

iC5 0.0079 0.0068 0.006 0.0055 0.0053 0.0058 0.0074

nC5 0.0081 0.0069 0.006 0.0054 0.0052 0.0057 0.0071

nC6 0.0121 0.0096 0.0078 0.0066 0.006 0.0063 0.0077

C7+ 0.0991 0.063 0.0412 0.0286 0.0217 0.0192 0.0214 Mw+ 165 121 116 112 109 107 107 Sg+ 0.818 0.778 0.773 0.768 0.764 0.762 0.762

Pc C7+, 365.42 453.28 467.1 477.79 486.02 492.70 492.70 psia o Tc C7+, R 1209.732 1090.741 1075.735 1062.661 1052.522 1046.28 1046.28 T (oF) 250 250 250 250 250 250 250 P (psia) 4190 3600 3000 2400 1800 1200 700 Z (Expt.) 0.838 0.806 0.799 0.809 0.842 0.888 0.935 ρ(lb/cu.ft.) 27.34 19.52 15.06 11.3 7.95 5.06 2.91 LLS (This Study) 0.8055 0.8698 0.8837 0.8920 0.9009 0.9156 0.9361

91 Table 4.6 (Contd.) Carbon Dioxide Rich Gas Serial No. 926 927 928 929 930 931 932

H2S 0.003 0.003 0.003 0.003 0.003 0.003 0.004

CO2 0.6352 0.6395 0.6514 0.6579 0.6639 0.6706 0.6716

N2 0.0386 0.0399 0.041 0.0417 0.0421 0.0411 0.0388

C1 0.1937 0.1988 0.2008 0.207 0.2084 0.2037 0.1994

C2 0.0303 0.0307 0.0308 0.0309 0.0313 0.0315 0.0318

C3 0.0174 0.0172 0.017 0.0169 0.017 0.0175 0.0184

iC4 0.0033 0.0032 0.0031 0.003 0.003 0.0032 0.0035

nC4 0.0093 0.0088 0.0085 0.0082 0.0082 0.0088 0.0097

iC5 0.0039 0.0036 0.0033 0.0031 0.003 0.0033 0.0039

nC5 0.0047 0.0042 0.0038 0.0036 0.0035 0.0038 0.0046

nC6 0.0051 0.0049 0.0046 0.0042 0.0036 0.003 0.0034

C7+ 0.0551 0.0458 0.0324 0.0202 0.0127 0.0101 0.0113 Mw+ 170 153 139 128 118 110 106 Sg+ 0.811 0.797 0.783 0.773 0.763 0.755 0.751

Pc C7+, 347.8288 373.929 397.8203 421.6873 446.3173 469.4246 482.3509 psia Tc C7+, 1211.601 1169.445 1131.005 1100.627 1071.227 1046.943 1034.515 oR T (oF) 219 219 219 219 219 219 219 P (psia) 4825 4100 3300 2600 1900 1200 700 Z (Expt.) 0.851 0.777 0.72 0.719 0.775 0.851 0.915 ρ(lb/cu.ft.) 34.88 30.9 25.58 19.39 12.87 7.38 4.03 LLS (This Study) 0.7551 0.7276 0.7222 0.7483 0.7882 0.8437 0.8975

Table 4.6 (Contd.) Very light gas Serial No. 933 934 935 936 937 938 939

H2S 0 0 0 0 0 0 0

CO2 0.0033 0.0033 0.0034 0.0035 0.0035 0.0036 0.0038

N2 0.0032 0.0033 0.0033 0.0033 0.0033 0.0033 0.0033

C1 0.942 0.9438 0.9451 0.9461 0.9468 0.9473 0.9467

C2 0.0231 0.023 0.023 0.0231 0.0232 0.0233 0.0236

C3 0.0082 0.0082 0.0082 0.0082 0.0082 0.0082 0.0083

iC4 0.0023 0.0023 0.0023 0.0023 0.0023 0.0023 0.0023

nC4 0.0025 0.0025 0.0025 0.0025 0.0025 0.0025 0.0026

iC5 0.0012 0.0012 0.0012 0.0012 0.0012 0.0012 0.0012

nC5 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0009

nC6 0.0014 0.0013 0.0013 0.0013 0.0013 0.0012 0.0013

C7+ 0.012 0.0103 0.0089 0.0077 0.0069 0.0063 0.006 Mw+ 143 133 126 120 116 114 114 Sg+ 0.787 0.777 0.769 0.763 0.76 0.758 0.758

Pc C7+, psia 390.4827 409.7106 423.93 438.5907 450.5163 456.162 456.162 o Tc C7+, R 1142.133 1114.075 1093.042 1075.419 1064.345 1058.3 1058.3 T (oF) 209 209 209 209 209 209 209 P (psia) 4786 4000 3300 2600 1900 1300 700 Z (Expt.) 1.019 0.974 0.945 0.933 0.933 0.947 0.969 ρ(lb/cu.ft.) 12.13 10.42 8.76 6.92 5.03 3.37 1.78 LLS (This Study) 1.0018 0.9569 0.9252 0.9046 0.8995 0.9113 0.9411

93 CHAPTER 5

CONCLUSIONS AND RECOMMENDATIONS

5.1 Conclusions This project establishes the need and a solution for a simple and robust technique of predicting z-factor values for sour reservoir gases and natural reservoir gases.

1. Z-factor from Equations of state has been established. Eight equations-of-state routinely used in the reservoir simulators have been examined and the most general EOS has been established. 2. LLS EOS is the most generalized EOS. Every other EOS can be derived from LLS EOS by substituting for α and β. 3. Best-fit equations for Standing and Katz Z-Chart have been established. Eight computational techniques available has been examined and Beggs and Brill computation technique has been used in the development of the scaling factor. 4. A universal scaling factor has been developed for S-K Z-Chart which is capable of predicting z-factors of a. Natural gases b. Sour reservoir gases 5. Determination of accurate critical parameters of mixtures is an essential step to obtain accurate z-factor values. 6. Improved technique for mixture critical property has been established. 3100 experimental data from various sources were used in the development of scaling factor and also used for comparison purposes.

5.2 Recommendations The following points can be based for further studies: 1. design of a generalized chart for predicting the amount of gas produced, 2. improvement in the generalized scaling of z using Standing-Katz chart based on law of corresponding principles.

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105 APPENDIX A

REDUCED FORM OF CUBIC EQUATIONS OF STATE

A.1 Lawal-Lake-Silberberg Reduced Equation of State RT a(T) P = − 2 2 V − b V + αbV − βb (A.1)

1+ Ω Z − 3Z α = w c c Ω Z w c (A.2) Z2 (Ω −1)3 + 2Ω 2 Z + (1− 3Z )Ω β = c w w c c w Ω 2 Z w c (A.3) Ω = (1+ (Ω −1)Z )3 a w c (A.4) R 2T2 a = Ω c a P c (A.5) Ω RT b = b c P c (A.6) −θc 2 a(T) = aTR (A.7) where, ω θ = 0.309833+1.763758ω+ 0.720661ω2 −1.363589ω3 − 4.005783 c M w (A.8)

Z-Form of the LLS-EOS is as follows: Φ Z3 +Φ Z 2 + Φ Z + Φ = 0 3 2 1 0 (A.9) where, Φ = 1.0 3 (A.10) Φ 2 = −[1+ (1− α)B] (A.11) 2 Φ1 = [A − αB − (β + α)B ] (A.12) Φ = − AB −β(B2 + B3 ) 0 ⎡ ⎤ (A.13)

106 a(T)P A = 2 2 R T (A.14) bP B = RT (A.15)

Mixing Rules 1 1 2 2 a m = ∑∑x i x ja i a j a ij ij (A.16) 3 1 ⎡ 3 ⎤ bm = ⎢∑ xibi ⎥ ⎣ i ⎦ (A.17) ω a = i for ω ≤ ω ij ω i j j (A.18) ω a = j for ω > ω ij ω i j i (A.19) 1 1 0.5 2 2 αm = ∑∑xi x jαi α j ()αiα j ij (A.20) 1 1 0.5 2 2 βm = ∑∑x i x jβi β j ()βiβ j ij (A.21) a = a a = α α = β β ij ( i j ) ( i j ) ( i j ) (A.22)

A.2 van der Waals Reduced Equation of State RT a(T) P = − 2 V − b V (A.23) α = 0 (A.24) β = 0 (A.25) Ω = (1+ (Ω −1)Z )3 = (1+ (Ω −1)0.375)3 a w c w (A.26) a(T) = a (A.27) R 2T2 a = Ω c a P c (A.28) Ω Z RT b = w c c P c (A.29) Z-Form of the vdW-EOS is as follows:

107

Φ Z3 +Φ Z 2 + Φ Z + Φ = 0 3 2 1 0 (A.30) where, Φ = 1.0 3 (A.31)

Φ 2 = −[1+ (1− α)B]= −[1+ B] (A.32) 2 Φ1 = [A − αB − (β + α)B ] = [A] (A.33) Φ = − AB −β(B2 + B3 ) = −[AB] 0 ⎡ ⎤ (A.34) where a(T)P A = 2 2 R T (A.35) bP B = RT (A.36)

Mixing Rules:

1 1 2 2 a m = ∑∑xi x jai a j aij ij (A.37) bm = ∑ xibi i (A.38) ω a = i for ω ≤ ω ij ω i j j (A.39) ω a = j for ω > ω ij ω i j i (A.40) 1 1 0.5 2 2 α m = ∑∑x i x jα i α j ()α i α j ij (A.41) 1 1 0.5 2 2 βm = ∑∑x i x jβi β j ()βiβ j ij (A.42) a = a a = α α = β β ij ( i j ) ( i j ) ( i j ) (A.43)

A.3 Redlich-Kwong Reduced Equation of State RT a(T) P = − 2 V − b V + bV (A.44)

108 α =1.0 (A.45) β = 0.0 (A.46) Ω = 0.42751 a (A.47) R 2T2 a = 0.42747 c P c (A.48) RT b = 0.08664 c P c (A.49) 1 a(T) = a T R (A.50)

Z-Form of the RK-EOS is as follows: Φ Z3 +Φ Z2 + Φ Z + Φ = 0 3 2 1 0 (A.51) where, Φ = 1.0 3 (A.52) Φ2 = −1.0 (A.53) 2 Φ1 = [A − B − B ] (A.54) Φ = −[AB] 0 (A.55) where, a(T)P A = 2 2 R T (A.56) bP B = RT (A.57)

Mixing Rules 1 1 2 2 a m = ∑∑xi x jai a j aij ij (A.58) bm = ∑xibi i (A.59) ω a = i for ω ≤ ω ij ω i j j (A.60) ω a = j for ω > ω ij ω i j i (A.61)

109 1 1 0.5 2 2 αm = ∑∑xi x jαi α j ()αiα j ij (A.62) 1 1 0.5 2 2 βm = ∑∑x i x jβi β j ()βiβ j ij (A.61) a = a a = α α = β β ij ( i j ) ( i j ) ( i j ) (A.62)

A.4 Soave-Redlich-Kwong Reduced Equation of State

RT a(T) P = − 2 V − b V + bV (A.63) α =1.0 (A.64) β = 0.0 (A.65) Ω = 0.42751 a (A.66) R 2T2 a = 0.42747 c P c (A.67) RT b = 0.08664 c P c (A.68) 2 0.5 2 a(T) = [1.0 + (0.48 +1.574ω− 0.176ω )(1.0 − TR )] a (A.69)

Z-Form of the SRK-EOS is as follows Φ Z3 +Φ Z2 + Φ Z + Φ = 0 3 2 1 0 (A.70)

Φ3 = 1.0

Φ 2 = −1.0 2 Φ1 = [A − B − B ]

Φ 0 = −[AB] where, a(T)P bP A = , B = R 2T 2 RT Mixing Rules: 1 1 2 2 a m = ∑∑xix jai a j aij ij (A.71)

bm = ∑xibi i (A.72)

110 ω a = i for ω ≤ ω ij ω i j j (A.73) ω a = j for ω > ω ij ω i j i (A.74) 1 1 0.5 2 2 αm = ∑∑xi x jαi α j ()αiα j ij (A.75) 1 1 0.5 2 2 βm = ∑∑x i x jβi β j ()βiβ j ij (A.76) a = a a = α α = β β ij ( i j ) ( i j ) ( i j ) (A.77)

A.5 Peng-Robinson Reduced Equation of State RT a(T) P = − 2 2 V − b V + 2bV − b (A.78) α = 2.0 (A.79) β = 1.0 (A.80) Ω = 0.45724 a (A.81) Ω = 0.07780 b (A.82) R 2T 2 a = 0.45724 c P c (A.83) RT b = 0.07780 c P c (A.84) 2 0.5 2 a(T) = [1.0 + (0.37464 +1.54226ω− 0.26992ω )(1.0 − TR )] a (A.85) Z-Form of the PR-EOS Φ Z3 +Φ Z2 + Φ Z + Φ = 0 3 2 1 0 (A.86)

Φ3 = 1.0

Φ2 = −[1− B]

2 Φ1 = [A − 2B − 3B ]

2 3 Φ0 = −[AB − (B + B )] a(T)P bP A = , B = R 2T2 RT

111 Mixing Rules

1 1 2 2 a m = ∑∑xix jai a j aij ij (A.87) bm = ∑ xibi i (A.88) ω a = i for ω ≤ ω ij ω i j j (A.89) ω a = j for ω > ω ij ω i j i (A.90) 1 1 0.5 2 2 βm = ∑∑x i x jβi β j ()βiβ j ij (A.91) a = a a = α α = β β ij ( i j ) ( i j ) ( i j ) (A.92)

A.6 Schmidt-Wenzel Reduced Equation of State RT a(T) P = − 2 2 V − b V + (1+ 3ω)bV − 3ωb (A.93) (6ω +1)β3 + 3β2 + 3β −1 = 0 c c c (A.94)

βc = smallest positive root of the above equation. 1 ζ = c 3(1+ β ω) c (A.95) Ω = ζ β b c c (A.96) 3 Ω a = (1− ξc (1− βc )) (A.97) R 2T2 a = Ω c a P c (A.98) R.T b = Ω c b P c (A.99) a(T) = aα(TR ,k) (A.100) 2 α (TR ,k) = (1+ k(TR ,k 0 )(1− TR )) (A.101) where, k = 0.465 +1.347ω − 0.528ω2 0 (A.102)

112 2 (5TR − 3k0 −1) k(TR ,k0 ) = k0 + , for TR ≤1.0 70 (A.103) k(T ,k ) = k(1,k ) for T > 1.0 R 0 0 R (A.104)

Z-Form of SW-EOS: Z3 −[1.0 + (1.0 − (1.0 + 3ω))B]Z2 + [A − (1.0 + 3ω)B − (1+ 6ω)B2 ] 2 3 −[AB − 3ω(B + B )] = 0 (A.105)

Φ1 : 1.0

Φ 2 : −[1.0 + (1.0 − (1.0 + 3ω))B]

2 Φ 3 : A − (1.0 + 3ω)B − (1+ 6ω)B

2 3 Φ 0 : −[AB − 3ω(B + B )] a(T)P A = (RT)2 bP B = RT Mixing Rules:

1 1 2 2 a m = ∑∑xix jai a j aij ij (A.106) bm = ∑xibi i (A.107) ω a = i for ω ≤ ω ij ω i j j (A.108) ω a = j for ω > ω ij ω i j i (A.109) αm =1+ 3ωm (A.110) βm = −3ωm (A.111)

∑ xiωi ()M w i ω = i m x ()M i w i (A.112) where Mwi is the component’s molecular weight.

113 A.7 Patel-Teja Reduced Equation of State

RT a(T) P = − 2 V − b V + (b + c)V − cb (A.113) Z-Form of PT-EOS

3 2 2 2 Z − (1.0 − C)Z + (A − 2BC − B − B − C)Z −[AB− (B + B )C] = 0 (A.114)

Φ1 : 1.0

Φ 2: -(1.0-C)

2 Φ 3: A − 2BC − B − B − C 2 Φ 0: - AB + (B + B )C where,

1/ 2 2 α (TR ) = [1+ F(1− TR )] (A.115) 2 F = 0.452413 +1.30982ω − 0.295937ω (A.116) Z = 0.329032 − 0.076799ω + 0.0211947ω2 c (A.117) Ω =1− 3Z c c (A.118) Ω ,solve Ω3 + (2 − 3Z )Ω2 + 3Z2Ω − Z3 = 0 b b c b c b c (A.119) Ω = 3 Z 2 + 3(1− 2Z )Ω + Ω2 +1− 3Z a c c b b c (A.120)

pick the smallest positive root = Ω b

a(T) = aα(TR ) (A.121) 2 a(T)P Ωa (RTc ) A = 2 a = (RT) Pc bP Ω RT B = b = b c RT Pc cP Ω RT C = c = c c RT Pc Mixing Rules:

1 1 2 2 a m = ∑∑xix jai a j aij ij (A.122)

bm = ∑ xibi i (A.123)

c m = ∑ x ici i (A.124)

114 ω a = i for ω ≤ ω ij ω i j j (A.125) ω a = j for ω > ω ij ω i j i (A.126) 1 1 0.5 2 2 αm = ∑∑xi x jαi α j ()αiα j ij (A.127) 1 1 0.5 2 2 βm = ∑∑x i x jβi β j ()βiβ j ij (A.128) a = a a = α α = β β ij ( i j ) ( i j ) ( i j ) (A.129)

A.8 Trebble-Bishnoi-Salim Reduced Equation of State

RT a(T) P = − 2 2 V − b V + (b + c)V − bc − d (A.130)

Z-Form of the TB-EOS Equation 3 2 2 2 2 2 Z − (1− C)Z + (A − 2BC − B − B − C − D )Z −[AB− (B + B )C − (B +1)D ] = 0 (A.131)

Φ1 : 1.0

Φ2 : − (1− C) 2 2 Φ3 : (A − 2BC − B − B − C − D ) 2 2 Φ0 : −[AB − (B + B )C − (B +1)D ] where, a(T) P bP cP dP A = ; B = ; C = ; D = R 2T2 RT RT RT where, 2 2 R Tc Ω b RTc Ω c RTc Ω d RTc a(T) = Ω a α(TR ) ;b = ;c = ;d = Pc Pc Pc Pc

2 m = 0.662 + 3.12ω− 0.854ω + 9.3(Z − 0.3) C (A.132) -1 p = 0.475 + 2.0ω for M ≤128 g mol (A.133) 2 -1 p = 0.613+ 0.62ω+ 4.06ω for M > 128 g mol (A.134) 1/ 2 1/ 2 1/ 2 1/ 2 α (TR ) = [[1+ m(1− TR )] + p{(0.7) − (TR ) }{1− (TR ) }] (A.135) ξ =1.063× Z c c (A.136)

115 Ω =1.0 − 3.0ξ c c (A.137) Ω3 + (2.0 − 3.0ξ )Ω2 + 3.0ξ2Ω − (Ω2 + ξ3 ) = 0 b c b c b d c (A.138)

Ω b = the smallest positive root in the above equation.

2 2 2 Ωa = 3ξc + 2ΩbΩc + Ωb + Ωc + Ωb + Ωd V Ω = c d 3.0 Mixing Rules

1 1 2 2 a m = ∑∑xix jai a j aij ij (A.139) 1 1 2 2 b m = ∑∑x i x jbi b j bij ij

1 1 2 2 c m = ∑∑x i x jci c j cij ij

ωi a ij = for ωi ≤ ω j ω j

ω j a ij = for ωi > ω j ωi

1 1 0.5 2 2 αm = ∑∑xi x jαi α j ()αiα j ij

1 1 0.5 2 2 βm = ∑∑x i x jβi β j ()βiβ j ij a ij = b ij = cij = (a ia j ) = (α i α j ) = (βiβ j )

116 APPENDIX B

PREDICTION RESULTS FOR

PSEUDOCRITICAL PARAMETERS

B.10 Pseduocritical Parameter Results

Table B.1: Gas Composition Description.

Mix No. 47-1 26-1 26-2 26-3 47-2 26-4 26-5

CO2 0.0120 0.0109 0.0100 0.0091 0.0044 0.0030 0.0020

N2 0.0000 0.0884 0.1611 0.2441 0.0000 0.1130 0.2400 C1 0.9089 0.8286 0.7625 0.6870 0.9668 0.8580 0.7364

C3 0.0191 0.0174 0.0160 0.0144 0.0070 0.0060 0.0053

iC4 0.0033 0.0030 0.0028 0.0030 0.0014 0.0012 0.0010

nC4 0.0060 0.0055 0.0051 0.0040 0.0020 0.0018 0.0015

iC5 0.0021 0.0019 0.0018 0.0016 0.0007 0.0006 0.0005

nC5 0.0013 0.0012 0.0011 0.0010 0.0005 0.0004 0.0004

nC6 0.0015 0.0014 0.0012 0.0011 0.0005 0.0004 0.0004

C7+ 0.0018 0.0016 0.0015 0.0014 0.0007 0.0006 0.0005 He 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Table B.1 (Contd.)

Mix No. 26-6 26-7 26-8 Mix-1 Mix-2 Mix-3 Mix-4

CO2 0.0013 0.0020 0.0025 0.0069 0.0069 0.0079 0.0079

N2 0.1146 0.1350 0.0705 0.0150 0.0148 0.0149 0.0143 C1 0.7665 0.7515 0.8532 0.9027 0.8906 0.8313 0.7961

C3 0.0335 0.0327 0.0198 0.0134 0.0139 0.0365 0.0399

iC4 0.0035 0.0038 0.0037 0.0037 0.0040 0.0080 0.0101

nC4 0.0090 0.0060 0.0039 0.0034 0.0039 0.0108 0.0149

iC5 0.0017 0.0000 0.0000 0.0019 0.0023 0.0033 0.0065

nC5 0.0015 0.0020 0.0022 0.0012 0.0019 0.0023 0.0052

nC6 0.0000 0.0000 0.0000 0.0020 0.0038 0.0028 0.0087

C7+ 0.0033 0.0000 0.0000 0.0029 0.0110 0.0029 0.0171 He 0.0100 0.0060 0.0031 0.0000 0.0000 0.0000 0.0000

117 Table B.1 (Contd.)

Mix No. Mix-5 Mix-6 Mix-7

CO2 0.0079 0.0079 0.0014

N2 0.0138 0.0135 0.0000 C1 0.7644 0.7507 0.4534

C3 0.0430 0.0443 0.1961

iC4 0.0120 0.0128 0.0936

nC4 0.0186 0.0202 0.0825

iC5 0.0094 0.0106 0.0542

nC5 0.0078 0.0089 0.0343

nC6 0.0140 0.0164 0.0129

C7+ 0.0299 0.0355 0.0011 He 0.0000 0.0000 0.0000

Mixture 47-1 (Gore Data) 500

400 LM LLS Expt. Joffe LK SBV VNA Pedersen Kay PG SC Sutton R) o TTP 300 re ( u t a er p m e T l a c

i 200 t i r C

100

0 Critical Property Methods Kay Joffe PG LK SBV TTP VNA Pedersen LM SC Sutton LLS Expt. Figure B.1: Critical temperature prediction for Gore Data (Mix 47-1).

118 Mixture 47-1 (Gore Data) 1000

LLS Expt.

800

LM LK Pedersen Kay Joffe PG SBV VNA SC Sutton a) i s p

( 600

re TTP u s res P al c i 400 t i r C

200

0 Kay Joffe PG LK SBV CritTicalTP ProVNAperty PMedeethrsenods LM SC Sutton LLS Expt. Figure B.2: Critical pressure prediction for Gore Data (Mix 47-1).

Mixture 26-1 (Gore Data) 1000 LLS Expt.

800

LM LK Pedersen Kay Joffe PG SBV VNA SC Sutton ) sia p 600 ( e r u s TTP s e r P l a 400 itic r C

200

0 Kay Joffe PG LK SBV CritTicalTP ProVNAperty PMedeethrsenods LM SC Sutton LLS Expt. Figure B.3: Critical pressure prediction for Gore Data (Mix 26-1).

119 Mixture 26-2 (Gore Data) 400

LM LLS Expt. Kay Joffe PG LK SBV VNA Pedersen Sutton SC

300

TTP R) o re ( u erat

p 200 m e T al c i t i r C

100

0 Kay Joffe PG LK SBV CrTitTicalP PropVNeArty MethPedersodens LM SC Sutton LLS Expt. Figure B.4: Critical temperature prediction for Gore Data (Mix 26-2).

Mixture 26-2 (Gore Data) 1000 LLS Expt.

800

LM Joffe LK SBV Pedersen Sutton Kay PG VNA SC a) i s

p 600 ( re su TTP res P al c

i 400 t i r C

200

0 Kay Joffe PG LK SBV CritTicalTP ProVNAperty PMedeethrsenods LM SC Sutton LLS Expt. Figure B.5: Critical pressure prediction for Gore Data (Mix 26-2.

120

Mixture 26-3 (Gore Data) 400

LM LLS Expt. Kay Joffe PG LK SBV VNA Pedersen Sutton SC

300 R) o TTP re ( u erat

p 200 m e T al c i t i r C

100

0 Kay Joffe PG LK SBV CritTicaTPl PropVNertyA PMethoedersends LM SC Sutton LLS Expt. Figure B.6: Critical temperature prediction for Gore Data (Mix 26-3).

Mixture 26-3 (Gore Data)

1075

LLS Expt.

860 ) a i

s LM

p LK Pedersen ( Kay Joffe PG SBV VNA Sutton 645 SC e r u s s e r P l TTP a

ic 430 it r C

215

0 Kay Joffe PG LK SBV CritTicalTP ProVNAperty PMedeethrsenods LM SC Sutton LLS Expt. Figure B.7: Critical pressure prediction for Gore Data (Mix 26-3).

121 APPENDIX C

SCALING FACTOR DEVELOPMENT

AND RESULTS

The following three forms of the scaling parameter were tested and the exponential form was selected based on its prediction and matching capability:

SF 2 Z = [1+ k(1− TR )] … (3.18).

SF θ Z = TR … (3.19).

SF Z = aEXP(bTR ) … (3.20). The step-by-step procedure for obtaining the scaling factor is as follows: zSK 1. zSF = × z z Expt. c SF 2. Plot z vs. TR graph; obtain the best fit-curve and the corresponding equation in the form of zSF = a × e −bTR for each pure component. Obtain a and b for each component.

3. Plot a vs. ωMw graph; obtain the best fit-curve and the corresponding equation of

−coeff2 the form a = coeff1 (ωM w ) . 4. Plot b vs. ω graph; obtain the best fit-curve and the corresponding equation of the form b = [Aω2 + Bω + C] where A, B, and C are constants. 5. The scaling factor expressions for: a. Pure Components

SF z = a exp(bTR ) where,

coeff2 a = coeff1 (ωM w ) b = [Aω2 + Bω + C] b. Mixtures follow the following Mixing rule:

122 n 2 n 2 ⎛ 0.5 ⎞ ⎛ 0.5 ⎞ ω m = ⎜ ∑ x i ωi ⎟ []ωM w = ⎜ ∑ x i [ωM w ]i ⎟ ⎝ i ⎠ ⎝ i ⎠ where a, b, A, B, and C belong to the above described procedure only.

C.1 Scaled Z-Factor Results

Buxton & Campbell at 160 oF (Mix-4) 1.45 Expt. SK 1.35 Scaled

1.25

1.15 r o t c Fa

Z- 1.05

0.95

0.85

0.75 0 2,000 4,000 6,000 8,000 Pressure (Psia) Figure C.1: Scaled z-factor result for Buxton & Campbell Data at 160 oF (Mix-4).

123 Buxton & Campbell, Mix-4, T = 130 F, Quadratic

1.42 Exp SK 1.32 Scaled

1.22

1.12 or t c Fa

Z- 1.02

0.92

0.82

0.72 0 2,000 4,000 6,000 8,000 Pressure (psia)

Figure C.2: Scaled z-factor result for Buxton & Campbell Data at 130 oF (Mix-4).

Buxton & Campbell, Mix-3, T = 160 F 1.4 Exp SK

1.3 Scaled

1.2 or t c

a 1.1 F Z-

0.9

0.8 0 2,000 4,000 6,000 8,000 Pressure (psia)

Figure C.3: Scaled z-factor result for Buxton & Campbell Data at 160 oF (Mix-3).

124 Buxton & Campbell, Mix-3, T = 130 F 1.36 Exp

1.26 Scaled

1.16 r o t c 1.06 Fa Z-

0.96

0.86

0.76 0 2,000 4,000 6,000 8,000 Pressure (psia)

Figure C.4: Scaled z-factor result for Buxton & Campbell Data at 130 oF (Mix-3).

Buxton & Campbell, Mix-3, T = 100 F, Quadratic

1.36 Exp SK

Scaled

1.21 or t c 1.06 Fa Z-

0.91

0.76 0 2,000 4,000 6,000 8,000 Pressure (psia)

Figure C.5: Scaled z-factor result for Buxton & Campbell Data at 100 oF (Mix-3).

125

Buxton & Campbell, Mix-2, T = 130 F,Quadratic 1.2

Exp SK

1.1 Scaled or t c 1 Fa Z-

0.9

0.8 0 2,000 4,000 6,000 8,000 Pressure (psia) Figure C.6: Scaled z-factor result for Buxton & Campbell Data at 130 oF (Mix-2).

Buxton and Campbell Data, Mix-1, Quadratic 160 oF 1.35 Expt. SK 1.25 Scaled

1.15 Z-Factor

1.05

0.95

0.85 0 2,000 4,000 6,000 8,000 Pressure (Psia)

Figure C.7: Scaled z-factor result for Buxton & Campbell Data at 160 oF (Mix-1).

126 APPENDIX D

PREDICTION OF Z-FACTOR FOR PURE SUBSTANCES

D.1 Prediction Results by Equations of State Method

Z-Factor Comparison (Expt. Vs. vdW-EOS) 1.55

1.45

1.35 r

o 1.25 act F - Z 1.15

VdW-EOS T=100 F 1.05 VdW-EOS T=220 F VdW-EOS T=460 F 100 F EXPT. 0.95 220 F EXPT. 460 F EXPT.

0.85 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Pressure (psia) Figure D.1: Z-Factor comparison for vdW-EOS for Nitrogen.

Z-Factor Comparison Graph (Exp. vs. RK-EOS)

1.37

1.29

1.22

r 1.14 o act F -

Z RK-EOS 560 R 1.07 RK-EOS 680 R

RK-EOS 920 R 0.99 Expt. T=560

Expt. T=680 0.92 Expt. T=920

0.84 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Pressure, P (Psia)

Figure D.2: Z-Factor comparison for RK-EOS for Methane.

127 Z-Factor Comparison Graph (Expt. vs. RK-EOS)

1.13

0.98

0.83 or t c

a 0.68 F

Z- RK-EOS 560 R

RK-EOS 680 R 0.53 RK-EOS 920 R

Expt. T=560

0.38 Expt. T=680 Expt. T=920

0.23 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Pressure, P (Psia)

Figure D.3: Z-Factor comparison for RK-EOS for Carbon dioxide.

Z-Factor Comparison Graph (Expt. vs. RK-EOS)

1.43

1.36

1.28 or ct 1.21

Z-Fa RK-EOS 560 R

RK-EOS 680 R

1.13 RK-EOS 920 R

Expt. T=560

1.06 Expt. T=680 Expt. T=920

0.98 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Pressure, P (Psia)

Figure D.4: Z-Factor comparison for RK-EOS for Nitrogen.

128 1.5 SOAVE-REDLICH-KWONG(C1) vs. Experimental Z-Factor Plot

1.4

1.3

1.2 or t Fac - Z 1.1 T=100 F T=220 F T=460 F 1 100 F EXP 220 F EXP 460 F EXP 0.9

0.8 0 2000 4000 6000 8000 10000 Pressure(psia)

Figure D.5: Z-Factor comparison for SRK-EOS for Methane.

1.3 SOAVE-REDLICH-KWONG(CO2) vs. Experimental Z-Factor Comparison Plot

1.08

0.86 or t c a F Z-

0.64 T=100 F T=220 F T=460 F 100 F EXP 0.42 220 F EXP 460 F EXP

0.2 0 2000 4000 6000 8000 10000 Pressure(psia)

Figure D.6: Z-Factor comparison for SRK-EOS for Carbon dioxide.

129 SOAVE-REDLICH-KWONG(N2) vs. Experimental Z-Factor Comparison Plot 1.55

1.45

1.35 or t c

Fa 1.25 Z-

T=100 F

T=220 F 1.15 T=460 F

100 F EXP

220 F EXP

1.05 460 F EXP

0.95 0 2000 4000 6000 8000 10000 Pressure(psia)

Figure D.7: Z-Factor comparison for SRK-EOS for Nitrogen.

Z-Factor Comparison Graph (Expt. vs. PR-EOS)

1.25

1.20

1.15

1.10

1.05 or t c Fa

Z- 1.00 PR-EOS 560 R

PR-EOS 680 R 0.95 PR-EOS 920 R

Expt. T=560 0.90 Expt. T=680

0.85 Expt. T=920

0.80 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Pressure (Psia)

Figure D.8: Z-Factor comparison for PR-EOS for Methane.

130 Z-Factor Comparison Graph (Expt. vs. PR-EOS)

1.0

0.9

0.8

0.7 r o t

0.6 T = 560 R Z-Fac

T = 680 R 0.5 T = 920 R

Expt. T=560 0.4 Expt. T=680

0.3 Expt. T=920

0.2 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Pressure, P (Psia)

Figure D.9: Z-Factor comparison for PR-EOS for Carbon dioxide.

Z-Factor Comparison Graph (Expt. vs. PR-EOS)

1.4

1.3

1.2 or t c

Fa 1.2 Z-

1.1 PR-EOS 560 R PR-EOS 680 R 1.1 PR-EOS 920 R Expt. T=560 1.0 Expt. T=680 Expt. T=920

1.0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Pressure (Psia)

Figure D.10: Z-Factor comparison for PR-EOS for Nitrogen.

131 1.5 Z-Factor Comparison (Expt. Vs. SW-EOS)

1.4

1.3

1.2 or t c a F Z- 1.1

SW-EOS 100 F

SW-EOS 220 F 1 SW-EOS 460 F

100 F EXP

220 F EXP 0.9 460 F EXP

0.8 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 P (psia)

Figure D.11: Z-Factor comparison for SW-EOS for Methane.

1.2 Z-Factor Comparison (Expt. Vs. SW-EOS)

1.1

0.9

0.8 r o

act 0.7 F Z-

0.6

SW-EOS 100 F 0.5 SW-EOS 220 F SW-EOS 460 F 0.4 100 F EXP 220 F EXP 0.3 460 F EXP

0.2 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Pressure (psia)

Figure D.12: Z-Factor comparison for SW-EOS for Carbon dioxide.

132 Z-Factor Comparison (Expt. Vs. SW-EOS) 1.55

1.45

1.35 or t

Fac 1.25 Z-

SW-EOS 100 F

1.15 SW-EOS 220 F

SW-EOS 460 F

100 F EXP 1.05 220 F EXP

460 F EXP 0.95 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 P (psia)

Figure D.13: Z-Factor comparison for SW-EOS for Nitrogen.

Z-Factor Comparison Graph (Exp. vs. PT-EOS)

1.33

1.23

1.13 or t Fac - PT-EOS 560 R Z

1.03 PT-EOS 680 R

PT-EOS 920 R

Expt. T=560

0.93 Expt. T=680

Expt. T=920

0.83 0 100020003000400050006000700080009000 Pressure, P (Psia)

Figure D.14: Z-Factor comparison for PT-EOS for Methane.

133 Z-Factor Comparison Graph (Exp. vs. PT-EOS)

1.13

1.03

0.93

0.83

or 0.73 t c a F

Z- 0.63 PT-EOS 560 R PT-EOS 680 R

0.53 PT-EOS 920 R

Expt. T=560 0.43 Expt. T=680

0.33 Expt. T=920

0.23 0 100020003000400050006000700080009000 Pressure, P (Psia)

Figure D.15: Z-Factor comparison for PT-EOS for Carbon dioxide.

Z-Factor Comparison Graph (Expt. vs. PT-EOS)

1.46

1.36

1.26 or t

Z-Fac PT-EOS 560 R

1.16 PT-EOS 680 R

PT-EOS 920 R

Expt. T=560

1.06 Expt. T=680

Expt. T=920

0.96 0 100020003000400050006000700080009000 Pressure, P (Psia)

Figure D.16: Z-Factor comparison for PT-EOS for Nitrogen.

134 TB-EOS (METHANE) 1.35

1.25

1.15 r acto F - 1.05 Z

100 F 0.95 220 F 460 F 100 F EXP 0.85 220 F EXP 460 F EXP

0.75 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Pressure (psia)

Figure D.17: Z-Factor comparison for TB-EOS for Methane.

1.1 TB-EOS (CO2)

0.9

0.8

0.7 or t c Fa

Z- 0.6 T=100 F T=160 F 0.5 T=220 F 100 F EXP 0.4 220 F EXP 460 F EXP 0.3

0.2 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 P(psia)

Figure D.18: Z-Factor comparison for TB-EOS for Carbon dioxide.

135 1.5 TB-EOS (NITROGEN)

1.4

100 F 220 F 1.3 460 F 100 F EXP 220 F EXP 460 F EXP or 1.2 Fact Z-

1.1

0.9 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Pressure (psia)

Figure D.19: Z-Factor comparison for TB-EOS for Nitrogen.

136 APPENDIX E

EXPERIMENTAL Z-FACTOR FOR

MISCELLANEOUS GASES

Table E.1: UCalgary Z-Factor Data.

Thesi Cmp CO nC nC nC C7 o s T ( F) nt. 2 H2S N2 C1 C2 C3 iC4 4 iC5 5 6 + Mcle od- Mole 0.5 0.4 0.7 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Mix-1 40 % 0 22.60 6 75.61 1 8 2 2 0 0 0 0 P Zexpt (psia) . 600 0.847 1000 0.748 1500 0.639 2000 0.586 2500 0.595 3000 0.632 4000 0.732 5000 0.845

Com Thesi pone CO nC nC nC C7 o s T ( F) nt 2 H2S N2 C1 C2 C3 iC4 4 iC5 5 6 + Mcle od- Mole 0.5 0.4 0.7 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Mix-1 100 % 0 22.60 6 75.61 1 8 2 2 0 0 0 0 P Zexpt (psia) . 600 0.895 1000 0.836 1500 0.779 2000 0.731 2500 0.713 3000 0.722 4000 0.783 5000 0.876

137 Table E.1 (Contd.)

o Thesis T ( F) Cmpnt. CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

Mcleod-Mix-1 40 Mole % 0.50 22.60 0.46 75.61 0.71 0.08 0.02 0.02 0.00 0.00 0.00 0.00 P (psia) Zexpt. 600 0.847 1000 0.748 1500 0.639 2000 0.586 2500 0.595 3000 0.632 4000 0.732 5000 0.845

o Thesis T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

Mcleod-Mix-1 100 Mole % 0.50 22.60 0.46 75.61 0.71 0.08 0.02 0.02 0.00 0.00 0.00 0.00 P (psia) Zexpt. 600 0.895 1000 0.836 1500 0.779 2000 0.731 2500 0.713 3000 0.722 4000 0.783 5000 0.876

o Thesis T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

Mcleod-Mix-1 175 Mole % 0.50 22.60 0.46 75.61 0.71 0.08 0.02 0.02 0.00 0.00 0.00 0.00 P (psia) Zexpt. 600 0.933 1000 0.9 1500 0.865 2000 0.839 2500 0.826 3000 0.825 4000 0.856 5000 0.914

o Thesis T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

Mcleod-Mix-2 40 Mole % 0.30 14.38 0.46 84.14 0.59 0.08 0.03 0.02 0.00 0.00 0.00 0.00 P (psia) Zexpt. 626 0.866 848 0.82 1022 0.787 1521 0.706 2021 0.662 2521 0.663 3021 0.69 4021 0.781 5021 0.887

o Thesis T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

Mcleod-Mix-2 65 Mole % 0.30 14.38 0.46 84.14 0.59 0.08 0.03 0.02 0.00 0.00 0.00 0.00

138 Table E.1 (Contd.)

P (psia) Zexpt. 624 0.889 823 0.859 1022 0.828 1521 0.763 2021 0.722 2522 0.716 3022 0.732 4022 0.807 5022 0.903

o Thesis T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

Mcleod-Mix-2 100 Mole % 0.30 14.38 0.46 84.14 0.59 0.08 0.03 0.02 0.00 0.00 0.00 0.00 P (psia) Zexpt. 607 0.911 625 0.909 824 0.886 1023 0.864 1522 0.815 2021 0.783 2521 0.773 3021 0.781 3521 0.805 4021 0.837 4521 0.876 5021 0.919

o Thesis T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

Mcleod-Mix-2 135 Mole % 0.30 14.38 0.46 84.14 0.59 0.08 0.03 0.02 0.00 0.00 0.00 0.00 P (psia) Zexpt. 655 0.926 824 0.911 1023 0.894 1522 0.858 2021 0.834 2521 0.826 3021 0.83 4021 0.873 5021 0.941

o Thesis T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

Mcleod-Mix-2 175 Mole % 0.30 14.38 0.46 84.14 0.59 0.08 0.03 0.02 0.00 0.00 0.00 0.00 P (psia) Zexpt. 565 0.946 823 0.93 1023 0.918 1522 0.891 2021 0.874 2521 0.867 3021 0.869 4021 0.903 5021 0.958

139 Table E.1 (Contd.)

o Thesis T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

Mcleod-Mix-3 40 Mole % 1.31 5.70 0.52 91.51 0.84 0.08 0.02 0.02 0.00 0.00 0.00 0.00 P (psia) Zexpt. 600 0.892 1000 0.819 1500 0.751 2000 0.711 2500 0.707 3000 0.73 4000 0.814 5000 0.918

o Thesis T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

Mcleod-Mix-3 100 Mole % 1.31 5.70 0.52 91.51 0.84 0.08 0.02 0.02 0.00 0.00 0.00 0.00 P (psia) Zexpt. 600 0.913 1000 0.883 1500 0.843 2000 0.816 2500 0.808 3000 0.815 4000 0.867 5000 0.945

o Thesis T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

Mcleod-Mix-3 100 Mole % 1.31 5.70 0.52 91.51 0.84 0.08 0.02 0.02 0.00 0.00 0.00 0.00 P (psia) Zexpt. 600 0.913 1000 0.883 1500 0.843 2000 0.816 2500 0.808 3000 0.815 4000 0.867 5000 0.945

o Thesis T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

Mcleod-Mix-3 175 Mole % 1.31 5.70 0.52 91.51 0.84 0.08 0.02 0.02 0.00 0.00 0.00 0.00 P (psia) Zexpt. 600 0.951 1000 0.929 1500 0.909 2000 0.896 2500 0.892 3000 0.897 4000 0.932 5000 0.986

o Thesis T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

Mcleod-Mix-22 88 Mole % 1.80 0.00 0.81 84.99 6.64 2.67 1.07 0.91 0.82 0.00 0.19 0.10 P (psia) Zexpt. 500 0.902

140 Table E.1 (Contd.)

1000 0.823 1500 0.756 2000 0.725 2500 0.728 3000 0.755 3500 0.787

o Thesis T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

Mcleod-Mix-22 113 Mole % 1.80 0.00 0.81 84.99 6.64 2.67 1.07 0.91 0.82 0.00 0.19 0.10 P (psia) Zexpt. 500 0.925 1000 0.862 1500 0.811 2000 0.775 2500 0.772 3000 0.797 3500 0.821

o Thesis T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

Mcleod-Mix-22 200 Mole % 1.80 0.00 0.81 84.99 6.64 2.67 1.07 0.91 0.82 0.00 0.19 0.10 P (psia) Zexpt. 500 0.96 1000 0.927 1500 0.9 2000 0.884 2500 0.882 3000 0.891 3500 0.91

o Thesis T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

Mcleod-Mix-24 81 Mole % 0.61 0.00 0.00 85.00 6.00 3.32 0.85 1.29 0.57 0.66 1.09 0.62 P (psia) Zexpt. 500 0.918 1000 0.842 1500 0.777 2000 0.742 2500 0.739 3000 0.765 3500 0.802

o Thesis T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

Mcleod-Mix-24 152 Mole % 0.61 0.00 0.00 85.00 6.00 3.32 0.85 1.29 0.57 0.66 1.09 0.62 P (psia) Zexpt. 500 0.947 1000 0.903 1500 0.868 2000 0.848 2500 0.843 3000 0.853 3500 0.877

o Thesis T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

141 Table E.1 (Contd.)

Mcleod-Mix-24 200 Mole % 0.61 0.00 0.00 85.00 6.00 3.32 0.85 1.29 0.57 0.66 1.09 0.62 P (psia) Zexpt. 500 0.96 1000 0.929 1500 0.906 2000 0.892 2500 0.89 3000 0.889 3500 0.916

o Thesis T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

Mcleod-Mix-25 91 Mole % 0.40 0.00 0.00 94.32 3.90 1.17 0.08 0.13 0.00 0.00 0.00 0.00 P (psia) Zexpt. 500 0.929 1000 0.875

o Thesis T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

Mcleod-Mix-25 110 Mole % 0.40 0.00 0.00 94.32 3.90 1.17 0.08 0.13 0.00 0.00 0.00 0.00 P (psia) Zexpt. 500 0.939 1000 0.895

o Thesis T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

Mcleod-Mix-25 150 Mole % 0.40 0.00 0.00 94.32 3.90 1.17 0.08 0.13 0.00 0.00 0.00 0.00 P (psia) Zexpt. 500 0.958 1000 0.925

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ S & B T4 160 Mole % 0.00 10.00 0.00 90.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 600 0.955 1000 0.929 1500 0.899 2000 0.879 3000 0.874 4000 0.911 5000 0.969

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ S & B T4 220 Mole % 0.00 10.00 0.00 90.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 600 0.971 1000 0.953 1500 0.937 2000 0.926 3000 0.924 4000 0.955 5000 1.002

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ S & B T4 280 Mole % 0.00 10.00 0.00 90.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

142 Table E.1 (Contd.)

P (psia) Zexpt. 600 0.981 1000 0.972 1500 0.963 2000 0.957 3000 0.96 4000 0.989 5000 1.027

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ S & B T4 160 Mole % 0.00 20.00 0.00 80.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 600 0.945 1000 0.909 1500 0.87 2000 0.842 3000 0.825 4000 0.863 5000 0.925

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ S & B T4 220 Mole % 0.00 20.00 0.00 80.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 600 0.963 1000 0.941 1500 0.917 2000 0.899 3000 0.887 4000 0.912 5000 0.959

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ S & B T4 280 Mole % 0.00 20.00 0.00 80.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 600 0.976 1000 0.963 1500 0.948 2000 0.937 3000 0.931 4000 0.953 5000 0.99

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Mix-2-API-PRJ- 37 157 Mole % 2.09 6.80 10.19 68.57 5.90 2.82 0.47 1.16 0.85 0.00 0.35 0.80 P (psia) Zexpt.

2115 0.829 MC7+ 125

2347 0.823 SgC7+ 0.7500

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Mix-17-API-PRJ- 37 189 Mole % 6.16 10.78 0.4 74.14 3.27 1.21 0.22 0.61 0.57 0 0.46 2.18 P (psia) Zexpt.

4915 0.938 MC7+ 125

5065 0.95 SgC7+ 0.7500

143 Table E.1 (Contd.)

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Mix-25-API-PRJ- 37 191 Mole % 4.16 9.13 0 78.77 2.97 1.27 0.27 0.6 0.43 0 0.43 1.97 P (psia) Zexpt.

4945 0.955 MC7+ 125

SgC7+ 0.7500 o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Mix-2-API-PRJ- 37 216 Mole % 8.66 18.26 0.37 52.13 11.65 1.42 0.39 0.83 0.95 0.00 1.03 4.31 P (psia) Zexpt.

4515 0.852 MC7+ 125

5385 0.942 SgC7+ 0.7500

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Mix-402-API- PRJ-37 230 Mole % 2.06 2.44 10.70 70.72 6.91 3.38 0.52 0.67 0.64 0.00 0.37 1.59 P (psia) Zexpt.

3000 0.903 MC7+ 125

3270 0.91 SgC7+ 0.7500 3400 0.914 3600 0.918 3800 0.925 4000 0.934 4200 0.946 4400 0.954 4600 0.97 4800 0.981 5130 1.006

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Mix-601-API- PRJ-37 276 Mole % 6.61 4.53 15.58 41.72 7.12 5.42 2.23 3.10 2.85 0.00 2.68 8.17 P (psia) Zexpt.

4000 0.875 MC7+ 125

5000 0.98 SgC7+ 0.7500

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Mix-705-API- PRJ-37 190 Mole % 4.24 2.90 0.98 70.90 7.34 2.84 0.66 1.40 1.43 0.00 1.13 6.18 P (psia) Zexpt.

4720 0.948 MC7+ 125

4743 0.95 SgC7+ 0.7500 4774 0.955 4815 0.959 4915 0.969 5015 0.981 5115 0.991 5315 1.014 5515 1.039

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Mix-707-API- PRJ-37 218 Mole % 3.17 18.5 2.18 56.22 4.83 2.5 0.56 1.49 1.48 0 1.15 7.82 P (psia) Zexpt.

4475 0.884 MC7+ 125

4515 0.887 SgC7+ 0.7500 4565 0.893

144 Table E.1 (Contd.)

4615 0.899 4715 0.91 4915 0.933 5215 0.97 5515 1.006 6015 1.067

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Mix-722-API- PRJ-37 179 Mole % 2.30 13.21 8.71 65.57 3.07 1.77 0.35 1.00 1.01 0.00 0.78 2.23 P (psia) Zexpt.

3025 0.812 MC7+ 125

3115 0.814 SgC7+ 0.7500 3215 0.818 3315 0.824 3515 0.834 3815 0.853 4215 0.883 4615 0.916 5015 0.951

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Mix-727-API- PRJ-37 143 Mole % 2.06 6.21 10.15 70.52 5.38 2.8 0.37 0.95 0.64 0 0.3 0.62 P (psia) Zexpt.

2399 0.831 MC7+ 125

2415 0.831 SgC7+ 0.7500 2515 0.832 2615 0.834 3015 0.844 3515 0.868 4015 0.903 4515 0.943 5015 0.986

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Mix-729-API- PRJ-37 181 Mole % 5.11 6.56 4.52 77.85 2.50 0.77 0.12 0.45 0.42 0.00 0.31 1.39 P (psia) Zexpt.

3099 0.859 MC7+ 125

3115 0.859 SgC7+ 0.7500 3215 0.861 3515 0.872 3586 0.875 4115 0.906 4415 0.927 4715 0.946 5015 0.968

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Mix-735-API- PRJ-37 206 Mole % 5.05 2.05 25.15 49.35 6.49 3.22 1.05 1.7 1.59 0 1.18 3.17 P (psia) Zexpt.

4430 0.987 MC7+ 125

4515 0.994 SgC7+ 0.7500 4715 1.011

145 Table E.1 (Contd.)

4915 1.029 5215 1.056 5515 1.083

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Shell-Et.Al- Marmattan-10- 33 73 Mole % 3.19 51.37 2.58 42.41 0.24 0.07 0.02 0.03 0.02 0.01 0.02 0.04 P (psia) Zexpt.

2114 0.402 MC7+ 120

2514 0.438 SgC7+ 0.7500 3014 0.495 3514 0.553 4014 0.612 4514 0.67 5014 0.728

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Shell-Et.Al- Marmattan-10- 33 84 Mole % 3.19 51.37 2.58 42.41 0.24 0.07 0.02 0.03 0.02 0.01 0.02 0.04 P (psia) Zexpt.

2114 0.426 MC7+ 120

2514 0.454 SgC7+ 0.7500 3014 0.507 3514 0.562 4014 0.62 4514 0.677 5014 0.734

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Shell-Et.Al- Marmattan-10- 33 95 Mole % 3.19 51.37 2.58 42.41 0.24 0.07 0.02 0.03 0.02 0.01 0.02 0.04 P (psia) Zexpt.

2114 0.458 MC7+ 120

2514 0.478 SgC7+ 0.7500 3014 0.526 3514 0.578 4014 0.632 4514 0.685 5014 0.737

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Shell-Et.Al- Marmattan-10- 33 110 Mole % 3.19 51.37 2.58 42.41 0.24 0.07 0.02 0.03 0.02 0.01 0.02 0.04 P (psia) Zexpt.

2114 0.495 MC7+ 120

2514 0.485 SgC7+ 0.7500 3014 0.534 3514 0.586 4014 0.639 4514 0.693 5014 0.747

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

146 Table E.1 (Contd.) Shell-Et.Al- Marmattan-10- 33 147 Mole % 3.19 51.37 2.58 42.41 0.24 0.07 0.02 0.03 0.02 0.01 0.02 0.04 P (psia) Zexpt.

2114 0.61 MC7+ 120

2514 0.568 SgC7+ 0.7500 3014 0.585 3514 0.619 4014 0.662 4514 0.707 5014 0.756

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Shell-Et.Al- Marmattan-10- 33 186 Mole % 3.19 51.37 2.58 42.41 0.24 0.07 0.02 0.03 0.02 0.01 0.02 0.04 P (psia) Zexpt.

2114 0.69 MC7+ 120

2514 0.665 SgC7+ 0.7500 3014 0.651 3514 0.666 4014 0.696 4514 0.731 5014 0.77

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Shell-Et.Al- Marmattan-10- 33 230 Mole % 3.19 51.37 2.58 42.41 0.24 0.07 0.02 0.03 0.02 0.01 0.02 0.04 P (psia) Zexpt.

2114 0.749 MC7+ 120

2514 0.722 SgC7+ 0.7500 3014 0.71 3514 0.711 4014 0.73 4514 0.755 5014 0.786

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

147-Sutte-Plant 198 Mole % 4.2 3.32 1.06 77.91 7.74 2.99 0.58 1.45 0.25 0.23 0.16 0.11 P (psia) Zexpt.

200 0.991 MC7+ 125

500 0.968 SgC7+ 0.7340 1000 0.924 1500 0.895 2000 0.878 2500 0.869 3000 0.876 3500 0.893 4000 0.918 4500 0.951 5000 0.988

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ 147-Waterton 156 Mole % 8.03 29.66 1.04 52.75 3.48 0.82 0.15 0.6 0.22 0.23 0.45 2.57 P (psia) Zexpt.

147 Table E.1 (Contd.)

3914 0.749 MC7+ 130

4014 0.757 SgC7+ 0.8340 4214 0.774 4414 0.792 4714 0.82 4914 0.839 5064 0.853 5114 0.858 5214 0.868 5414 0.888 5714 0.917 6014 0.948

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Gold Creek 210 Mole % 3.18 7.04 4.81 70.69 3.83 2.09 0.57 1.09 0.60 0.57 0.93 4.60 P (psia) Zexpt.

4496 0.938 MC7+ 131

4615 0.948 SgC7+ 0.7850 4815 0.966 5015 0.984 5215 1.003 5515 1.032 6015 1.061

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ HOME-ET.AL-6- 8(L) 77 Mole % 3.08 49.35 2.66 44.47 0.23 0.06 0.02 0.03 0.02 0.01 0.03 0.04 P (psia) Zexpt.

1014 0.667 MC7+ 125

1514 0.455 SgC7+ 0.7500 2014 0.421 2514 0.457 3014 0.408 3514 0.562 4014 0.618 4514 0.674 5014 0.73

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ HOME-ET.AL-6- 8(L) 120 Mole % 3.08 49.35 2.66 44.47 0.23 0.06 0.02 0.03 0.02 0.01 0.03 0.04 P (psia) Zexpt.

1014 0.75 MC7+ 125

1514 0.622 SgC7+ 0.7500 2014 0.537 2514 0.529 3014 0.557 3514 0.597 4014 0.643 4514 0.691 5014 0.74

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ HOME-ET.AL-6- 8(L) 144 Mole % 3.08 49.35 2.66 44.47 0.23 0.06 0.02 0.03 0.02 0.01 0.03 0.04 P (psia) Zexpt.

148 Table E.1 (Contd.)

1014 0.802 MC7+ 125

1514 0.692 SgC7+ 0.7500 2014 0.612 2514 0.584 3014 0.596 3514 0.626 4014 0.665 4514 0.707 5014 0.752

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ HOME-ET.AL-6- 8(L) 230 Mole % 3.08 49.35 2.66 44.47 0.23 0.06 0.02 0.03 0.02 0.01 0.03 0.04 P (psia) Zexpt.

1014 0.884 MC7+ 125

1514 0.832 SgC7+ 0.7500 2014 0.786 2514 0.751 3014 0.739 3514 0.74 4014 0.757 4514 0.78 5014 0.809

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ DICK-LAKE-A- 15(SMOOTHED- DATA) 93 Mole % 1.23 1.62 2.52 77.48 10.32 3.94 0.54 1.30 0.27 0.24 0.54 0.00 P (psia) Zexpt. 615 0.882 715 0.872 815 0.861 915 0.849

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ DICK-LAKE-A- 15(SMOOTHED- DATA) 105 Mole % 1.23 1.62 2.52 77.48 10.32 3.94 0.54 1.30 0.27 0.24 0.54 0.00 P (psia) Zexpt. 615 0.888 715 0.878 815 0.868 915 0.858

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ DICK-LAKE-A- 15(SMOOTHED- DATA) 120 Mole % 1.23 1.62 2.52 77.48 10.32 3.94 0.54 1.30 0.27 0.24 0.54 0.00 P (psia) Zexpt. 615 0.896 715 0.888 815 0.879 915 0.87

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ RIMBEY-GAS- PLANT 84 Mole % 1.21 1.50 2.08 78.14 10.29 4.05 0.62 1.23 0.29 0.29 0.30 0.00

149 Table E.1 (Contd.) DICK-LAKE-A- 15(SMOOTHED- DATA) P (psia) Zexpt. 500 0.926 750 0.885 1000 0.841 1250 0.805 1400 0.787

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ RIMBEY-GAS- PLANT 95 Mole % 1.86 3.29 2.28 80.34 6.56 3.02 0.52 1.07 0.37 0.34 0.35 0.00 DICK-LAKE-A- 23(SMOOTHED- DATA) P (psia) Zexpt. 500 0.945 750 0.911 1000 0.873 1250 0.842 1500 0.816

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ HOMEGLEN- RIMBEY-A- 25(SMOOTHED- DATA) 83 Mole % 1.61 3.26 2.75 80.52 6.61 2.92 0.42 0.99 0.21 0.21 0.50 0.00 P (psia) Zexpt. 615 0.881 715 0.872 815 0.862 915 0.853 1015 0.844

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ HOMEGLEN- RIMBEY-A- 25(SMOOTHED- DATA) 100 Mole % 1.61 3.26 2.75 80.52 6.61 2.92 0.42 0.99 0.21 0.21 0.50 0.00 P (psia) Zexpt. 615 0.892 715 0.883 815 0.874 915 0.865 1015 0.856

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ HOMEGLEN- RIMBEY-A- 25(SMOOTHED- DATA) 120 Mole % 1.61 3.26 2.75 80.52 6.61 2.92 0.42 0.99 0.21 0.21 0.50 0.00 P (psia) Zexpt. 615 0.905 715 0.896 815 0.887 915 0.878 1015 0.869

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

150 Table E.1 (Contd.) SHELL-LOW- WATERTON- NO.5-17 156 Mole % 3.48 16.03 0.97 65.49 3.93 1.53 0.32 0.92 0.52 0.50 1.12 5.19 P (psia) Zexpt.

4560 0.864 MC7+ 140

4596 0.868 SgC7+ 0.9050 4650 0.874 4714 0.881 4814 0.892 4914 0.903 5114 0.926 5514 0.973 6014 1.03

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ SHELL-NO.3- BURNT- TIMBER 196 Mole % 5.78 6.42 0.33 81.87 3.64 0.74 0.22 0.19 0.10 0.07 0.13 0.51 P (psia) Zexpt.

936 0.935 MC7+ 118

1058 0.929 SgC7+ 0.7580 1203 0.923 1363 0.915 1557 0.906 1733 0.899 1912 0.894 2275 0.886 2772 0.885 3199 0.893 3506 0.901 3781 0.912 3827 0.914 3851 0.915 4014 0.923 4514 0.95 5014 0.981 5514 1.014 6014 1.051

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ SHELL-NO.4- W.J.P.2-23 120 Mole % 6.17 5.40 0.49 81.07 3.74 0.94 0.32 0.34 0.18 0.12 0.23 1.00 P (psia) Zexpt.

4279 0.882 MC7+ 127

4295 0.883 SgC7+ 0.8050 4314 0.885 4330 0.886 4346 0.887 4414 0.893 4514 0.902 5014 0.948 5514 0.995 6014 1.044 6514 1.094

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

151 Table E.1 (Contd.) WIMBORNE- NO.6-11- (UPPER) 162 Mole % 2.06 12.96 9.63 66.34 3.11 1.80 0.34 0.94 0.33 0.45 0.56 1.48 P (psia) Zexpt.

2899 0.82 MC7+ 115

2916 0.82 SgC7+ 0.7610 2945 0.821 2984 0.823 3014 0.823 3064 0.825 3114 0.827 3214 0.831 3314 0.836 3514 0.846 4014 0.878 4514 0.916 5014 0.958 5514 1.003 6014 1.048

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ ROYALITE- EDSON-6-4-52- 17 160 Mole % 4.34 1.04 0.17 90.31 2.70 0.66 0.16 0.18 0.09 0.07 0.11 0.17 P (psia) Zexpt.

514 0.959 MC7+ 125

1014 0.925 SgC7+ 0.7500 1514 0.898 2014 0.88 2514 0.873 3014 0.878 3514 0.896 4014 0.918

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ ROYALITE- EDSON-6-4-52- 17 220 Mole % 4.34 1.04 0.17 90.31 2.70 0.66 0.16 0.18 0.09 0.07 0.11 0.17 P (psia) Zexpt.

514 0.975 MC7+ 125

1014 0.955 SgC7+ 0.7500 1514 0.939 2014 0.929 2514 0.926 3014 0.931 3514 0.943 4014 0.961

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ HB-UNION- KAYBOS-S-7- 14 250 Mole % 3.13 16.82 1.12 60.09 7.72 3.12 1.00 1.44 0.41 0.63 1.10 3.42 P (psia) Zexpt.

3542 0.94 MC7+ 124

4014 0.971 SgC7+ 0.7940 4514 1.009 5014 1.051

152 Table E.1 (Contd.)

5514 1.096 6014 1.144

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ HB-UNION- KAYBOS-S-11- 1 230 Mole % 3.12 15.62 1.01 60.12 7.85 3.28 0.82 1.56 0.67 0.75 1.11 4.09 P (psia) Zexpt.

3457 0.821 MC7+ 125

4014 0.848 SgC7+ 0.7950 4514 0.89 5014 0.936 5514 0.984 6014 1.033 6514 1.082

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ PANTHER- RIVER-5-23 50 Mole % 12.86 35.99 1.54 49.53 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 434 0.851

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ PANTHER- RIVER-5-23 50 Mole % 12.01 38.37 2.35 46.98 0.29 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 464 0.85

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ PANTHER- RIVER-5-23 50 Mole % 10.77 30.28 3.09 55.80 0.06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 764 0.778

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

R&J-Mixture-17 200 Mole % 1.18 20.27 0.23 76.30 1.29 0.73 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 246 0.979 363 0.97 532 0.956 776 0.938 1125 0.915 1623 0.846

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

R&J-Mixture-18 100 Mole % 7.44 7.35 0.61 83.03 1.30 0.07 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 252 0.967 369 0.952 536 0.931 772 0.902 1101 0.864 1556 0.821

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

153 Table E.1 (Contd.)

R&J-Mixture-19 100 Mole % 15.55 14.91 0.41 67.92 1.11 0.10 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt.

194 0.968 MC7+

285 0.953 SgC7+ 414 0.932 597 0.903 849 0.863 1188 0.812 1640 0.854

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

R&J-Mixture-20 100 Mole % 2.87 23.27 3.04 56.01 8.20 3.45 0.85 1.10 0.00 0.71 0.28 0.22 P (psia) Zexpt.

400 0.912 MC7+

600 0.867 SgC7+ 800 0.82 1000 0.874

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

R&J-Mixture-20 120 Mole % 2.87 23.27 3.04 56.01 8.20 3.45 0.85 1.10 0.00 0.71 0.28 0.22 P (psia) Zexpt. 400 0.922 600 0.883 800 0.842 1000 0.902

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

R&J-Mixture-11 150 Mole % 22.30 0.00 0.50 75.59 1.40 0.21 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 250 0.975 360 0.964 538 0.949 783 0.927 1130 0.9 1622 0.869

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

R&J-Mixture-12 200 Mole % 28.14 0.00 0.82 69.93 1.06 0.05 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 233 0.962 344 0.974 505 0.963 739 0.947 1076 0.927 1559 0.903

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

R&J-Mixture-13 100 Mole % 0.08 4.09 0.96 89.26 1.54 0.07 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 231 0.972 339 0.959

154 Table E.1 (Contd.)

495 0.941 717 0.916 1029 0.883 1464 0.845

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

R&J-Mixture-14 100 Mole % 1.44 16.30 0.77 79.48 1.53 0.48 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 258 0.962 377 0.945 547 0.921 785 0.889 1111 0.847 1558 0.798

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

R&J-Mixture-15 100 Mole % 2.10 26.96 0.68 68.68 1.15 0.43 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 197 0.965 288 0.95 418 0.927 600 0.894 848 0.851 1178 0.794 1609 0.829

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

R&J-Mixture-16 150 Mole % 1.27 18.99 0.77 77.26 1.32 0.39 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 255 0.972 375 0.959 547 0.941 791 0.916 1135 0.884 1617 0.846

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

R&J-Mixture-5 100 Mole % 10.18 10.33 10.66 49.06 9.55 10.22 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 248 0.965 363 0.949 526 0.926 754 0.895 1074 0.854 1511 0.808

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

R&J-Mixture-6 100 Mole % 0.04 0.00 0.95 97.48 1.53 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 352 0.964 515 0.948 749 0.926

155 Table E.1 (Contd.)

1000 0.898 1550 0.867

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

R&J-Mixture-7 100 Mole % 5.36 0.00 0.84 92.22 1.49 0.09 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 342 0.963 500 0.946 726 0.924 1049 0.894 1496 0.86

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

R&J-Mixture-8 100 Mole % 11.46 0.00 0.68 86.16 1.46 0.04 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 256 0.97 376 0.956 548 0.937 792 0.911 1134 0.877 1614 0.84

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

R&J-Mixture-9 100 Mole % 19.72 0.00 0.55 78.30 1.39 0.04 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 254 0.967 371 0.952 540 0.931 779 0.902 1111 0.865 1570 0.822

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

R&J-Mixture-10 100 Mole % 54.46 0.00 0.26 44.60 0.68 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 154 0.97 225 0.956 328 0.935 473 0.907 672 0.866 937 0.811 1275 0.843 1703 0.867

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

B&C-Mixture-1 100 Mole % 5.06 0.00 0.53 89.77 4.64 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 1026 0.861 1526 0.844 2026 0.816 2526 0.811 3026 0.822

156 Table E.1 (Contd.)

3526 0.846 4026 0.878 4526 0.917 5026 0.959 6026 1.05 7026 1.146

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

B&C-Mixture-1 130 Mole % 5.06 0.00 0.53 89.77 4.64 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 1026 0.904 1526 0.875 2026 0.855 2526 0.851 3026 0.857 3526 0.877 4026 0.904 4526 0.937 5026 0.974 6026 1.056 7026 1.143

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

B&C-Mixture-1 160 Mole % 5.06 0.00 0.53 89.77 4.64 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 1026 0.925 1526 0.899 2026 0.885 2526 0.874 3026 0.905 3526 0.901 4026 0.923 4526 0.954 5026 1.009 6026 1.064 7026 1.143

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

B&C-Mixture-2 100 Mole % 10.13 0.00 0.57 85.20 4.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 1026 0.881 1526 0.838 2026 0.812 2526 0.864 3026 0.875 3526 0.908 4026 0.921 4526 0.96 5026 1.002 6026 1.095 7026 1.19

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

157 Table E.1 (Contd.)

B&C-Mixture-2 130 Mole % 10.13 0.00 0.57 85.20 4.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 1026 0.904 1526 0.872 2026 0.85 2526 0.844 3026 0.851 3526 0.879 4026 0.897 4526 0.93 5026 0.969 6026 1.052 7026 1.139

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

B&C-Mixture-2 160 Mole % 10.13 0.00 0.57 85.20 4.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 1026 0.923 1526 0.899 2026 0.882 2526 0.877 3026 0.883 3526 0.899 4026 0.921 4526 0.949 5026 0.983 6026 1.058 7026 1.139

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

B&C-Mixture-3 100 Mole % 20.16 0.00 0.52 74.58 4.74 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 1026 0.865 1526 0.814 2026 0.878 2526 0.862 3026 0.878 3526 0.904 4026 0.938 4526 0.979 5026 0.923 6026 1.114 7026 1.214

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

B&C-Mixture-3 130 Mole % 20.16 0.00 0.52 74.58 4.74 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 1026 0.889 1526 0.852 2026 0.925 2526 0.914 3026 0.92

158 Table E.1 (Contd.)

3526 0.939 4026 0.967 4526 1.002 5026 1.041 6026 1.126 7026 1.214

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

B&C-Mixture-3 160 Mole % 20.16 0.00 0.52 74.58 4.74 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 1026 0.91 1526 0.882 2026 0.86 2526 0.95 3026 0.955 3526 0.97 4026 0.993 4526 1.024 5026 1.056 6026 1.134 7026 1.215

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

B&C-Mixture-4 100 Mole % 10.91 0.00 0.00 75.93 0.00 13.16 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 1026 0.913 1526 0.85 2026 0.814 2526 0.814 3026 0.837 3526 0.875 4026 0.821 4526 0.971 5026 1.023 6026 1.131 7026 1.241

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

B&C-Mixture-4 130 Mole % 10.91 0.00 0.00 75.93 0.00 13.16 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 1026 0.951 1526 0.899 2026 0.87 2526 0.863 3026 0.878 3526 0.906 4026 0.945 4526 0.989 5026 1.036 6026 1.035 7026 1.136

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

159 Table E.1 (Contd.)

B&C-Mixture-4 160 Mole % 10.91 0.00 0.00 75.93 0.00 13.16 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 1026 0.974 1526 0.934 2026 0.91 2526 0.904 3026 0.913 3526 0.936 4026 0.967 4526 1.003 5026 1.045 6026 1.136 7026 1.228

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

B&C-Mixture-5 100 Mole % 12.92 0.00 0.00 58.41 28.67 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 1026 0.893 1526 0.815 2026 0.776 2526 0.778 3026 0.808 3526 0.851 4026 0.901 4526 0.955 5026 1.01 6026 1.124 7026 1.138

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

B&C-Mixture-5 130 Mole % 12.92 0.00 0.00 58.41 28.67 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 1026 0.93 1526 0.872 2026 0.836 2526 0.83 3026 0.848 3526 0.882 4026 0.924 4526 0.971 5026 1.021 6026 1.125 7026 1.231

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

B&C-Mixture-5 160 Mole % 12.92 0.00 0.00 58.41 28.67 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 1026 0.961 1526 0.913 2026 0.883 2526 0.875 3026 0.886

160 Table E.1 (Contd.)

3526 0.911 4026 0.947 4526 0.989 5026 1.033 6026 1.129 7026 1.227

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ FINA-ET.AL- Creek-10-7 236 Mole % 3.4 16 1.15 59.09 7.59 3.09 0.78 1.69 0.67 0.78 1.2 4.56 P (psia) Zexpt. 3514 0.914 4014 0.955 4514 0.999 5014 1.042 5514 1.092 6014 1.142 6514 1.193

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

FINA- WINDFALL-T-3 219 Mole % 7.74 11.83 1.62 63.00 4.20 2.69 0.69 1.80 0.70 0.79 0.92 4.02 P (psia) Zexpt.

3814 0.843 MC7+ 139.0

3854 0.845 SgC7+ 0.7880 3914 0.849 4014 0.857 4514 0.901 5014 0.946

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ FINA- WINDFALL- PILOT-PLANT- INJECTION- GAS-T-3 150 Mole % 5.13 15.67 2.68 66.84 4.55 3.01 0.47 0.83 0.22 0.23 0.15 0.22 P (psia) Zexpt.

3014 0.764 MC7+ 125.0

3514 0.787 SgC7+ 0.7500 4014 0.82 4514 0.859 5014 0.901

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ FINA- WINDFALL- PILOT-PLANT- INJECTION- GAS-T-3 200 Mole % 5.13 15.67 2.68 66.84 4.55 3.01 0.47 0.83 0.22 0.23 0.15 0.22 P (psia) Zexpt.

3014 0.824 MC7+ 125.0

3514 0.839 SgC7+ 0.7500 4014 0.864 4514 0.894 5014 0.928

161 Table E.1 (Contd.)

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ FINA- WINDFALL- PILOT-PLANT- INJECTION- GAS-T-3 250 Mole % 5.13 15.67 2.68 66.84 4.55 3.01 0.47 0.83 0.22 0.23 0.15 0.22 P (psia) Zexpt.

3014 0.877 MC7+ 125.0

3514 0.888 SgC7+ 0.7500 4014 0.907 4514 0.931 5014 0.96

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ FINA- WINDFALL- PILOT-PLANT- INJECTION- GAS-T-3 300 Mole % 5.13 15.67 2.68 66.84 4.55 3.01 0.47 0.83 0.22 0.23 0.15 0.22 P (psia) Zexpt.

3014 0.912 MC7+ 125.0

3514 0.922 SgC7+ 0.7500 4014 0.939 4514 0.96 5014 0.985

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ FINA- WINDFALL- PROCESSING- PLANT- INJECTION- GAS-T-3 50 Mole % 4.51 27.30 0.61 64.59 0.84 0.93 0.27 0.20 0.20 0.11 0.12 0.32 P (psia) Zexpt.

1014 0.714 MC7+ 103.0

2014 0.63 SgC7+ 0.7000 2514 0.655 3014 0.7 4014 0.715 5014 0.834

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ FINA- WINDFALL- PROCESSING- PLANT- INJECTION- GAS-T-3 100 Mole % 4.51 27.30 0.61 64.59 0.84 0.93 0.27 0.20 0.20 0.11 0.12 0.32 P (psia) Zexpt.

1014 0.816 MC7+ 103.0

2014 0.764 SgC7+ 0.7000 2514 0.752 3014 0.769 4014 0.748 5014 0.846

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

162 Table E.1 (Contd.)

FINA- WINDFALL- PROCESSING- PLANT- INJECTION- GAS-T-3 125 Mole % 4.51 27.30 0.61 64.59 0.84 0.93 0.27 0.20 0.20 0.11 0.12 0.32 P (psia) Zexpt.

1014 0.847 MC7+ 103.0

2014 0.722 SgC7+ 0.7000 2514 0.703 3014 0.708 4014 0.771 5014 0.857

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ FINA- WINDFALL- PROCESSING- PLANT- INJECTION- GAS-T-3 150 Mole % 4.51 27.30 0.61 64.59 0.84 0.93 0.27 0.20 0.20 0.11 0.12 0.32 P (psia) Zexpt.

1014 0.871 MC7+ 103.0

2014 0.768 SgC7+ 0.7000 2514 0.747 3014 0.747 4014 0.795 5014 0.869

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ FINA- WINDFALL- PROCESSING- PLANT- INJECTION- GAS-T-3 175 Mole % 4.51 27.30 0.61 64.59 0.84 0.93 0.27 0.20 0.20 0.11 0.12 0.32 P (psia) Zexpt.

1014 0.895 MC7+ 103.0

2014 0.809 SgC7+ 0.7000 2514 0.788 3014 0.784 4014 0.819 5014 0.885

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ FINA- WINDFALL- PROCESSING- PLANT- INJECTION- GAS-T-3 200 Mole % 4.51 27.30 0.61 64.59 0.84 0.93 0.27 0.20 0.20 0.11 0.12 0.32 P (psia) Zexpt.

1014 0.913 MC7+ 103.0

2014 0.842 SgC7+ 0.7000 2514 0.824 3014 0.818 4014 0.844 5014 0.902

163 Table E.1 (Contd.)

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ FINA- WINDFALL- PROCESSING- PLANT- INJECTION- GAS-T-3 225 Mole % 4.51 27.30 0.61 64.59 0.84 0.93 0.27 0.20 0.20 0.11 0.12 0.32 P (psia) Zexpt.

1014 0.925 MC7+ 103.0

2014 0.865 SgC7+ 0.7000 2514 0.848 0.748 3014 0.841 0.741 4014 0.864 0.764 5014 0.914 0.814

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ FINA- WINDFALL- PROCESSING- PLANT- INJECTION- GAS-T-3 250 Mole % 4.51 27.30 0.61 64.59 0.84 0.93 0.27 0.20 0.20 0.11 0.12 0.32 P (psia) Zexpt.

1014 0.944 MC7+ 103.0

2014 0.894 SgC7+ 0.7000 2514 0.88 3014 0.873 4014 0.889 5014 0.931

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ CHEVRON- CLARK-LAKE- 11-33 228 Mole % 3.44 17.6 1.02 57.41 7.55 3.24 0.87 1.63 0.63 0.79 1.31 4.51 P (psia) Zexpt.

3366 0.79 MC7+ 150.0

3414 0.793 SgC7+ 0.8000 3469 0.797 3514 0.8 3814 0.822 4214 0.857 4514 0.883 4672 0.899 4714 0.902 4814 0.912 5014 0.931 5514 0.982 6014 1.034 6514 1.086 7014 1.139

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ NEVIS-NO.110- 30 143 Mole % 2.06 6.21 10.15 70.52 5.38 2.8 0.37 0.95 0.29 0.35 0.3 0.62 P (psia) Zexpt.

2354 0.832 MC7+ 125.0

164 Table E.1 (Contd.)

2404 0.832 SgC7+ 0.7500 2414 0.832 2514 0.832 2614 0.834 3014 0.844 3514 0.869 4014 0.903 4514 0.944 5014 0.987

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Panther River5- 23 50 Mole % 10.67 31.08 3.37 54.78 0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 864 0.759

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Panther River5- 23 50 Mole % 9.67 27.72 4.34 58.21 0.06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 1114 0.702

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Panther River5- 23 50 Mole % 9.29 26.77 4.63 59.24 0.07 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 1189 0.674

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Panther River5- 23 100 Mole % 11.27 63.57 1.09 23.90 0.17 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 664 0.779

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Panther River5- 23 100 Mole % 10.53 50.44 1.98 36.86 0.19 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 984 0.7

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Panther River5- 23 100 Mole % 11.10 49.80 1.80 37.18 0.12 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 1014 0.697

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Panther River5- 23 100 Mole % 10.22 45.47 2.56 41.64 0.11 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 1344 0.613

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Panther River5- 23 100 Mole % 10.13 44.74 2.75 42.26 0.12 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 1454 0.589

165 Table E.1 (Contd.)

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Panther River5- 23 150 Mole % 7.96 73.85 0.75 17.27 0.17 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 714 0.758

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Panther River5- 23 150 Mole % 8.74 69.95 0.89 20.27 0.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 1064 0.635

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Panther River5- 23 150 Mole % 9.14 67.16 1.04 22.53 0.13 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 1374 0.543

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Panther River5- 23 150 Mole % 9.12 66.84 1.06 22.85 0.13 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 1414 0.518

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Panther River5- 23 150 Mole % 9.14 65.87 1.08 23.73 0.18 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 1594 0.452

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+ Panther River5- 23 175 Mole % 8.65 70.03 0.92 20.24 0.16 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 664 0.829 1014 0.726 1364 0.606

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

Jeff Lake Et.Al Cross 11-25-25- 29 W4M (Smoothed Data) 100 Mole % 10.16 33.16 2.16 53.41 1.11 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 200 0.958 600 0.871 1000 0.786 1500 0.681 2000 0.611 2500 0.598 3000 0.619 3500 0.656 4000 0.7

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

166 Table E.1 (Contd.)

Jeff Lake Et.Al Cross 11-25-25- 29 W4M (Smoothed Data) 176 Mole % 10.16 33.16 2.16 53.41 1.11 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 200 0.972 600 0.92 1000 0.873 1500 0.816 2000 0.77 2500 0.744 3000 0.74 3500 0.752 4000 0.776

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

Jeff Lake Et.Al Cross 6-32-25- 28 W4M (Smoothed Data) 100 Mole % 9.23 26.59 2.64 59.57 1.97 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 200 0.956 600 0.876 1000 0.804 1500 0.719 2000 0.66 2500 0.645 3000 0.66 3500 0.695 4000 0.735

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

Jeff Lake Et.Al Cross 6-32-25- 28 W4M (Smoothed Data) 176 Mole % 9.23 26.59 2.64 59.57 1.97 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 200 0.972 600 0.924 1000 0.883 1500 0.837 2000 0.801 2500 0.78 3000 0.78 3500 0.795 4000 0.816

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

167 Table E.1 (Contd.)

Jeff Lake Et.Al Cross 11-3-25- 28 W4M (Smoothed Data) 100 Mole % 13.47 10.38 3.00 70.69 2.46 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 200 0.963 600 0.902 1000 0.851 1500 0.795 2000 0.755 2500 0.74 3000 0.749 3500 0.775 4000 0.809

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

Jeff Lake Et.Al Cross 11-3-25- 28 W4M (Smoothed Data) 176 Mole % 13.47 10.38 3.00 70.69 2.46 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P (psia) Zexpt. 200 0.976 600 0.942 1000 0.915 1500 0.884 2000 0.86 2500 0.846 3000 0.849 3500 0.863 4000 0.884

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

Imperial FINA Wildcat Hills 6- 35-27-6 W5M (Smoothed Data) 75 Mole % 6.60 3.95 0.68 83.74 2.86 0.75 0.25 0.23 0.06 0.08 0.08 0.72 P (psia) Zexpt. 513 0.913 1013 0.835 7+ Fraction Mole Wt. 139 1513 0.772 Sp. Gr. 0.7860 2013 0.736 2513 0.73 3013 0.748 3513 0.781 4013 0.825

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

168 Table E.1 (Contd.)

Imperial FINA Wildcat Hills 6- 35-27-6 W5M (Smoothed Data) 99 Mole % 6.60 3.95 0.68 83.74 2.86 0.75 0.25 0.23 0.06 0.08 0.08 0.72 P (psia) Zexpt. 513 0.928 1013 0.863 7+ Fraction Mole Wt. 139 1513 0.808 Sp. Gr. 0.7860 2013 0.773 2513 0.762 3013 0.774 3513 0.801 4013 0.837

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

Imperial FINA Wildcat Hills 6- 35-27-6 W5M (Smoothed Data) 132 Mole % 6.60 3.95 0.68 83.74 2.86 0.75 0.25 0.23 0.06 0.08 0.08 0.72 P (psia) Zexpt. 513 0.934 1013 0.882 7+ Fraction Mole Wt. 139 1513 0.845 Sp. Gr. 0.7860 2013 0.82 2513 0.812 3013 0.821 3513 0.842 4013 0.872

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

Imperial FINA Wildcat Hills 6- 35-27-6 W5M (Smoothed Data) 189 Mole % 6.60 3.95 0.68 83.74 2.86 0.75 0.25 0.23 0.06 0.08 0.08 0.72 P (psia) Zexpt. 513 0.949 1013 0.912 7+ Fraction Mole Wt. 139 1513 0.889 Sp. Gr. 0.7860 2013 0.878 2513 0.874 3013 0.876 3513 0.89 4013 0.914

o Reservoir T ( F) Component CO2 H2SN2 C1 C2 C3 iC4 nC4 iC5 nC5 nC6 C7+

Imperial Mobil Brazeau River 6-11 (Smoothed Data) 210 Mole % 3.66 2.16 0.00 89.34 3.52 0.50 0.21 0.23 0.10 0.08 0.20 0.00 P (psia) Zexpt.

169 Table E.1 (Contd.)

813 0.948 1063 0.934 7+ Fraction Mole Wt. 139 1516 0.913 Sp. Gr. 0.7860 2085 0.904 2513 0.898 2828 0.9 3013 0.901 3429 0.906 3743 0.919 4013 0.935

170 APPENDIX F

PREDICTION OF Z-FACTOR FROM LLS EOS

Methane Z-Factor (LLS EOS) 1.088

1.033

0.978 400 Expt. LLS 400 psia 1500 Expt. or t c 0.923 LLS 1500 psia Fa

- 2000 Expt Z LLS 2000 psia 3000 Expt 0.868 LLS 3000 psia 4000 Expt LLS 4000 Psia 0.813

0.758 1.5 1.7 1.9 2.1 2.3 2.5 2.7 Reduced Temperature

Figure F.1: Z-factor for pure substances (Methane).

n-Decane Z- Factor (LLS EOS) 2.5

2.0

400 Expt. LLS 400 psia 1.5 1500 Expt. or t

c LLS 1500 psia

Fa 2000 Expt Z- 1.0 LLS 2000 psia 3000 Expt LLS 3000 psia 4000 Expt 0.5 LLS 4000 Psia

0.0 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 Reduced Temperature

Figure F.2: Z-factor for pure substances (n-Decane).

171 Carbon Dioxide Z-Factor (LLS EOS) 1

0.8

400 Expt. LLS 400 psia

r 1500 Expt. o t c 0.6 LLS 1500 psia

Fa 2000 Expt Z- LLS 2000 psia 3000 Expt LLS 3000 psia 0.4 4000 Expt LLS 4000 Psia

0.2 0.9 1.1 1.3 1.5 1.7 Reduced Temperature

Figure F.3: Z-factor for pure substances (Carbon Dioxide).

Hydrogen Sulfide Z-Factor (LLS EOS) 0.9375

0.75

400 Expt. LLS 400 psia 0.5625 1500 Expt. or t

c LLS 1500 psia a

F 2000 Expt Z- 0.375 LLS 2000 psia 3000 Expt LLS 3000 psia 4000 Expt 0.1875 LLS 4000 Psia

0 0.74 0.83 0.92 1.01 1.10 1.19 Reduced Temperature

Figure F.4: Z-factor for pure substances (Hydrogen Sulfide).

172 Nitrogen Z-Factor (LLS EOS)

1.145

1.11

400 Expt. LLS 400 psia

r 1500 Expt.

o 1.075 t

c LLS 1500 psia

Fa 2000 Expt Z- LLS 2000 psia 1.04 3000 Expt LLS 3000 psia 4000 Expt LLS 4000 Psia 1.005

0.97 2.40 3.00 3.60 4.20 4.80 Reduced Temperature

Figure F.5: Z-factor for pure substances (Nitrogen).

173 APPENDIX G

FORTRAN PROGRAMS

! Z-FACTOR PROGRAM BY LLS EOS METHOD FOR MIXTURES DIMENSION root(3),coeff(4),XC(20),P(30), ac(20), bc(20), zc(20), omgw(20) Dimension PPR(40),TTR(20),PP(30),Zexpt(30,30),Corr(20),BWR(20),XCMP(20),BIJA(15,15),& BIJB(15,15),BIJC(15,15),BIJD(15,15) Dimension Alp(20), Bet(20), AF(20), wm(20), tc(20), pc(20),APDB(5),ZZV(5,30) Data PPR/0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0,1.1,1.2,1.3,1.4,1.5,1.6,1.7,1.8,1.9,2.0& ,2.5,3.0,3.5,4.0,4.5,5.0,5.5,6.0,6.5,7.0,7.5,8.0,8.5,9.0,9.5,10,15,20,25,30/ Data TTR/0.1,0.5,1,1.5,2,3,4,5/

OPEN (UNIT=5,FILE='Input_SageLaceyC1-C2_ZFactData.TXT',STATUS='old') OPEN (UNIT=6,FILE='OUTPUT_SageLaceyC1-C2_ZFactData.TXT',STATUS='unknown')

WRITE (6,*) 'LLS-MIXTURE-Sage and LaceyC1-C2_ZFactData' Read (5,*)NData do 20 I = 1,2 Read (5,*)wm(I),zc(I),AF(I),omgw(I),pc(I),tc(I) 20 Continue R = 10.73 ! BIJA = Average Acentric Factor ! BIJB = Average Molecular Weight ! BIJC = Average of Acentric Factor X Molecular Weight ! BIJD = Average of Tc / Sqrt(Pc) Do 100 K=1,NData Read (5,*)Ncomp,TT,NDataP Read (5,*) (XCMP(J),J=1,9) Do 220 I=1,2 ! Write (6,*)wm(I),zc(I),AF(I),omgw(I),pc(I),tc(I) Call Para(AF(I),zc(I),wm(I),tc(I),pc(I),R,TT,Alp(I),Bet(I),ac(I),bc(I)) ! write(6,*)I,TT,AF(I),zc(I),wm(I),tc(I),pc(I),Alp(I),Bet(I),ac(I),bc(I) ! write(6,*)I,TT,PP,Alp(I),Bet(I),ac(I),bc(I) 220 continue ! Computation of Binary Interaction Parameter Call BinIJ(Ncomp,AF,wm,tc,pc, BIJA,BIJB,BIJC,BIJD) ! If( K .GT. 1) GO TO 122 Do 121 I=1,Ncomp Do 121 J=1,Ncomp write(6,*) BIJA(I,J),BIJB(I,J),BIJC(I,J),BIJD(I,J) 121 Continue 122 Continue Do 120 J=1,NDataP Read (5,*)PP(J),(Zexpt(J,I),I=1,9) ! Write (6,*) TT,PP(J),(Zexpt(J,I),I=1,9) 120 Continue Do 160 J=1,9 AAPD=0.0 IT=0 XC(1)=XCMP(J) XC(2)=1.0-XC(1) Write (6,125) Write (6,*)' C1 Mole Fraction = ',XC(1),' C2 Mole Fraction = ',XC(2) 125 Format(/) Do 145 IB=1,4 IT=0 AAPD=0.0 Do 140 I=1,NDataP

174 If(IB .EQ. 1)Call Mixrule(Ncomp, XC, ac, bc,tc,pc, Alp, Bet, AF, wm,BIJA, am, bm, Alpm, Betm,wmix,AFmix) If(IB .EQ. 2)Call Mixrule(Ncomp, XC, ac, bc,tc,pc, Alp, Bet, AF, wm,BIJB, am, bm, Alpm, Betm,wmix,AFmix) If(IB .EQ. 3)Call Mixrule(Ncomp, XC, ac, bc,tc,pc, Alp, Bet, AF, wm,BIJC, am, bm, Alpm, Betm,wmix,AFmix) If(IB .EQ. 4)Call Mixrule(Ncomp, XC, ac, bc,tc,pc, Alp, Bet, AF, wm,BIJD, am, bm, Alpm, Betm,wmix,AFmix) call Zfactr (Alpm, Betm, am, bm, PP(I), TT, R, ZV, ZL) call TcPcMix(am,bm,Alpm,Betm,R,Tcm,Pcm) DenV=PP(I)*wmix/(ZV*R*TT) APD=((ZV-Zexpt(I,J))/Zexpt(I,J))*100.0 AAPD=AAPD+ABS(APD)

! write (6,*) ! write (6,15) TT,PP(I),ZV,ZL,Zexpt(I,J),APD ZZV(IB,I)=ZV 15 Format(2F8.1,5F8.4) 140 Continue DatP=NDataP AAPD=AAPD/DatP APDB(IB)=AAPD ! write(6,*)'End of Data = ',K ! write(6,*)'Average Absolute Percent Deviation = ',AAPD 145 Continue Do 146 I=1,NDataP write (6,15) TT,PP(I),(ZZV(N1,I),N1=1,4),Zexpt(I,J) 146 Continue write(6,51)(APDB(N1),N1=1,4) 51 Format(16X,5F8.2) write(6,25) 160 Continue 25 Format(/) 100 Continue close(5) close(6)

STOP END Subroutine Zfactr (Alp, Bet, AT, BC, P, T, R, ZV, ZL) Dimension Coef(4),RT(3) AA = AT*P/(R**2*T**2) BB = BC*P/(R*T) Coef(1) = 1. Coef(2) = -(1.+(1-Alp)*BB) Coef(3) = AA-(Alp*BB)-(Bet+Alp)*BB**2 Coef(4) = -(AA*BB-Bet*(BB**2+BB**3)) Call Cubic (MTYPE, Coef, RT) ! write(6,*) 'Root=',RT Rmin = 1.E+10 Rmax = 1.E-10 Do 70 I=1,3 if (RT(I).LE. 0.0) Go to 70 if (RT(I).LT. BB) Go to 70 if (RT(I).GT. Rmax) Rmax = RT(I) if (RT(I).LT. Rmin) Rmin = RT(I) 70 Continue ZV=Rmax ZL=Rmin Return End

Subroutine ZRedMix (Alp, Bet,AF,wm, Zc,Pr,tr, ZV, ZL) Dimension Coef(4),RT(3) w=AF theta = 0.309833 + 1.763758*w + 0.720661*w*w - 1.363589*w**3 - 4.005783*w/(sqrt(wm)) tmp = tr ** (-theta/2.0) omgW=0.361/(1.0+0.0274*w) omga=(1.0+(omgW-1.0)*Zc)**3 omgb = omgW*Zc

175 Coef(1) = 1.0 Coef(2) = -(1.0/Zc+(1.0-Alp)*omgb*Pr/(Zc*tr)) Coef(3) = omga*Pr/(Zc**2*tr**(2+theta))-Alp*omgb*Pr/(Zc**2*tr)-(Alp+Bet)*(omgb*Pr/(Zc*tr))**2 Coef(4) = -(omga*omgb*Pr**2/(Zc**3*tr**(3+theta))-Bet*(1.0/Zc*(omgb*Pr/(Zc*tr))**2+(omgb*Pr/(Zc*tr))**3)) Call Cubic (MTYPE, Coef, RT) ! write(6,*) 'Root=',RT Rmin = 1.E+10 Rmax = 1.E-10 Do 70 I=1,3 if (RT(I).LE. 0.0) Go to 70 if (RT(I).LT. BB) Go to 70 if (RT(I).GT. Rmax) Rmax = RT(I) if (RT(I).LT. Rmin) Rmin = RT(I) 70 Continue ZV=Rmax*Zc ZL=Rmin*Zc Return End

Subroutine Zcfactr (Alp, Bet, Zc, RT) Dimension Coef(4),RT(3) Coef(1) = Alp**3 + 6*Alp**2+ 12*Alp + 8. Coef(2) = -(12*Alp**2+12 *Alp + 9*Bet- 9*Alp*Bet+ 3.) Coef(3) = 6*Alp**2 + 3*Alp + 6*Bet - 6*Alp*Bet Coef(4) = -(Alp**2+Bet-Alp*Bet) Call Cubic (MTYPE, Coef, RT) Rmin = 1.E+10 Rmax = 1.E-10 Do 70 I=1,3 if (RT(I).LE. 0.0) Go to 70 ! if (RT(I).LT. BB) Go to 70 if (RT(I).GT. Rmax) Rmax = RT(I) if (RT(I).LT. Rmin) Rmin = RT(I) 70 Continue ZV=Rmax ZL=Rmin Zc = Rmax Return End

Subroutine Bcfact (Alp, Bet, Bc,RT) Dimension Coef(4),RT(3) Coef(1) = Alp**3 + 6*Alp**2+ 12*Alp + 8. Coef(2) = -(3*Alp**2-15 *Alp+27*Bet-15.) Coef(3) = 3*Alp+6. Coef(4) = -1. Call Cubic (MTYPE, Coef, RT) Rmin = 1.E+10 Rmax = 1.E-10 Do 70 I=1,3 if (RT(I).LE. 0.0) Go to 70 ! if (RT(I).LT. BB) Go to 70 if (RT(I).GT. Rmax) Rmax = RT(I) if (RT(I).LT. Rmin) Rmin = RT(I) 70 Continue ZV = Rmax ZL = Rmin Bc = Rmax Return End

Subroutine TcPcMix(am,bm,alpm,betm,R,Tcm,Pcm) Dimension RTB(3), RTZ(3) call Bcfact (alpm, betm, Bc,RTB) call Zcfactr (alpm, betm, Zc, RTZ) denom = 3*zc**2+(alpm+betm)*Bc**2+alpm*Bc

176 Pcm = (am*Bc**2)/(bm**2*denom) Tcm = (am*Bc)/(bm*R*denom) return End

Subroutine Para(AF,zc,wm,tc,pc,R,TT,Alp,Bet,ac,bc) omgww = 0.361/(1.0+0.0274*AF) Alp = (1.0+omgww*zc-3.0*zc)/(omgww*zc) Bet = (zc*zc*(omgww-1.0)**3.0+(2.0*zc*omgww**2)+& omgww*(1.0-3.0*zc))/(omgww**2*zc) omga = (1.0+(omgww-1.0)*zc)**3.0 omgb = omgww*zc tr = TT/tc theta = 0.309833 + 1.763758*AF + 0.720661*AF*AF - 1.363589*AF**3 - 4.005783*AF/sqrt(wm) tmp = tr ** (-theta/2.0) ! theta = 0.19708+0.08627*AF+0.35714*AF**2+3.59015E-03*AF*wm ! tmp = tr**(-theta) CB = omgb*R*tc/pc CA = omga*R**2*tc**2/pc ac = CA*tmp bc = CB Return End

Subroutine Mixrule(Ncomp, x, ac, bc,tc,pc, Alp, Bet, AF, wm,BIN, Sumam,bmLLS, SumAlpm, SumBetm,wmmix,AFmix) Dimension x(20), ac(20), bc(20), Alp(20), Bet(20), AF(20), wm(20),tc(20),pc(20),BIN(15,15) Sumam = 0.0 SumbmLLS = 0.0 SumAlpm = 0.0 SumBetm = 0.0 wmmix = 0.0 AFmix = 0.0 Do 10 I = 1,Ncomp Sumbm = Sumbm + x(I)*bc(I) AFmix=AFmix+x(I)*sqrt(AF(I)) wmmix=wmmix+x(I)*sqrt(wm(I)) SumbmLLS = SumbmLLS + x(I)*bc(I)**(1.0/3.0) Do 10 J = 1,Ncomp Sumam = Sumam + x(I)*x(J)*sqrt(ac(I))*sqrt(ac(J))*BIN(I,J) SumAlpm = SumAlpm + x(I)*x(J)*sqrt(Alp(I))*sqrt(Alp(J))*BIN(I,J) SumBetm = SumBetm + x(I)*x(J)*sqrt(Bet(I))*sqrt(Bet(J))*BIN(I,J) 10 Continue bmLLS = (SumbmLLS)**3.0 AFmix=AFmix**2 wmmix=wmmix**2 Return End Subroutine BinIJ(Ncomp,AF,wm,tc,pc, BIJA,BIJB,BIJC,BIJD) Dimension AF(20),wm(20),tc(20),pc(20) Dimension BIJA(15,15),BIJB(15,15),BIJC(15,15),BIJD(15,15) Do 10 I = 1,Ncomp Do 10 J = 1,Ncomp AFI=AF(I) AFJ=AF(J) WMI=wm(I) WMJ=wm(J) AFWI=wm(I)*AF(I) AFWJ=wm(J)*AF(J) TPCI=tc(I)/sqrt(pc(I)) TPCJ=tc(J)/sqrt(pc(J)) ! If(AFI.LE.AFJ) BIJA(I,J) = (AFI/AFJ)**0.5 If(AFI.GT.AFJ) BIJA(I,J)= (AFJ/AFI)**0.5 !

177 If(WMI.LE.WMJ) BIJB(I,J) = (WMI/WMJ)**0.5 If(WMI.GT.WMJ) BIJB(I,J) = (WMJ/WMI)**0.5 ! If(AFWI.LE.AFWJ) BIJC(I,J) = (AFWI/AFWJ)**0.5 If(AFWI.GT.AFWJ) BIJC(I,J) = (AFWJ/AFWI)**0.5 ! If(TPCI.LE.TPCJ) BIJD(I,J) = (TPCI/TPCJ)**0.5 If(TPCI.GT.TPCJ) BIJD(I,J) = (TPCJ/TPCI)**0.5 10 Continue Return End Subroutine Cubic(MTYPE,A,Z) DIMENSION B(3), A(4), Z(3)

B(1)=A(2)/A(1) B10V3=B(1)/3.0 B(2)=A(3)/A(1) B(3)=A(4)/A(1) ALF=B(2)-B(1)*B10V3 BBT=2.0*B10V3**3-B(2)*B10V3+B(3) BETOV=BBT/2.0 ALFOV=ALF/3.0 CUAOV=ALFOV**3 SQBOV=BETOV**2 DEL=SQBOV+CUAOV IF (DEL) 90,10,40 10 MTYPE = 0 ! Three Equal Roots GAM=SQRT(-ALFOV) IF (BBT) 30,30,20 20 Z(1) = -2.0*GAM-B10V3 Z(2) = GAM-B10V3 Z(3) = Z(2) GO TO 130 30 Z(1) = 2.0*GAM-B10V3 Z(2) = -GAM-B10V3 Z(3) = Z(2) GO TO 130 40 MTYPE = 1 ! One Real Root & 2 Imaginary Conjugate Roots EPS=SQRT(DEL) TAU=-BETOV RCU=TAU+EPS SCU=TAU-EPS SIR=1.0 SIS=1.0 IF (RCU) 50,60,60 50 SIR=-1.0 60 IF (SCU) 70,80,80 70 SIS=-1.0 80 R=SIR*(SIR*RCU)**0.3333333333 S=SIS*(SIS*SCU)**0.3333333333 Z(1)=R+S-B10V3 Z(2)=-(R+S)/2.0-B10V3 Z(3)=0.86602540*(R-S) GO TO 130 90 MTYPE = -1 ! Three Dissimilar and Real Roots QUOT=SQBOV/CUAOV RCOT=SQRT(-QUOT) IF (BBT) 110,100,100 100 PEI=(1.5707963+ATAN(RCOT/SQRT(1.0-RCOT**2)))/3.0 GO TO 120 110 PEI=ATAN(SQRT(1.0-RCOT**2)/RCOT)/3.0 120 FACT=2.0*SQRT(-ALFOV) Z(1)=FACT*COS(PEI)-B10V3

178 PEI=PEI+2.0943951 Z(2)=FACT*COS(PEI)-B10V3 PEI=PEI+2.0943951 Z(3)=FACT*COS(PEI)-B10V3 130 CONTINUE IF (MTYPE .EQ. 1) Z(2) = -99.99 IF (MTYPE .EQ. 1) Z(3) = -99.99 RETURN END

! Z-FACTOR PROGRAM BY LLS EOS METHOD FOR MIXTURES DIMENSION root(3),coeff(4),XC(20),P(20), ac(20), bc(20), zc(20), omgw(20) Dimension PPR(40),TTR(20),Zexpt(20),BIJA(15,15),BIJB(15,15),BIJC(15,15),BIJD(15,15) Dimension APDB(5,20),ZZV(5,30),DEV(5),TT(30),PP(30) Dimension Alp(20), Bet(20), AF(20), wm(20), tc(20), pc(20) Data PPR/0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0,1.1,1.2,1.3,1.4,1.5,1.6,1.7,1.8,1.9,2.0& ,2.5,3.0,3.5,4.0,4.5,5.0,5.5,6.0,6.5,7.0,7.5,8.0,8.5,9.0,9.5,10,15,20,25,30/ Data TTR/0.1,0.5,1,1.5,2,3,4,5/

OPEN (UNIT=5,FILE='Input-Elsh_SPE74369.TXT',STATUS='old') OPEN (UNIT=6,FILE='OUTPUT-LLS-Elsh-SPE74369.TXT',STATUS='unknown') WRITE (6,*) 'LLS-Elsh-SPE74369' Read (5,*)NData Read (5,*)(Zexpt(I),I=1,NData) R = 10.73 AAPD=0.0 ! BIJA = Average Acentric Factor ! BIJB = Average Molecular Weight ! BIJC = Average of Acentric Factor X Molecular Weight ! BIJD = Average of Tc / Sqrt(Pc) IT=1 Do 100 K=1,NData Read (5,*)Ncomp,PP(K),TT(K) ! Write (6,*) Ncomp,TT(K),PP(K) do 20 I = 1,Ncomp Read (5,*)XC(I),wm(I),zc(I),AF(I),omgw(I),pc(I),tc(I) ! Write (6,*)XC(I),wm(I),zc(I),AF(I),omgw(I),pc(I),tc(I) Call Para(AF(I),zc(I),wm(I),tc(I),pc(I),R,TT,Alp(I),Bet(I),ac(I),bc(I)) ! write(6,*)I,TT(K),AF(I),zc(I),wm(I),tc(I),pc(I),Alp(I),Bet(I),ac(I),bc(I) ! write(6,*)I,TT(K),PP(K),Alp(I),Bet(I),ac(I),bc(I) 20 continue ! Computation of Binary Interaction Parameter Call BinIJ(Ncomp,AF,wm,tc,pc, BIJA,BIJB,BIJC,BIJD) ! If(IT .GT. 1) GO TO 122 Do 121 II=1,Ncomp 121 write(6,126) (BIJA(II,JJ),JJ=II,Ncomp) write(6,127) Do 123 II=1,Ncomp 123 write(6,126) (BIJB(II,JJ),JJ=II,Ncomp) write(6,127) Do 124 II=1,Ncomp 124 write(6,126) (BIJC(II,JJ),JJ=II,Ncomp) write(6,127) Do 125 II=1,Ncomp 125 write(6,126) (BIJD(II,JJ),JJ=II,Ncomp) write(6,127) 126 Format(12F6.3) 127 Format(/) IT=IT+1 122 Continue ! write(6,*)'End of Data = ',K Do 145 IB=1,4 AAPD=0.0

179 If(IB .EQ. 1)Call Mixrule(Ncomp, XC, ac, bc,tc,pc, Alp, Bet, AF, wm,BIJA, am, bm, Alpm, Betm,wmix,AFmix) If(IB .EQ. 2)Call Mixrule(Ncomp, XC, ac, bc,tc,pc, Alp, Bet, AF, wm,BIJB, am, bm, Alpm, Betm,wmix,AFmix) If(IB .EQ. 3)Call Mixrule(Ncomp, XC, ac, bc,tc,pc, Alp, Bet, AF, wm,BIJC, am, bm, Alpm, Betm,wmix,AFmix) If(IB .EQ. 4)Call Mixrule(Ncomp, XC, ac, bc,tc,pc, Alp, Bet, AF, wm,BIJD, am, bm, Alpm, Betm,wmix,AFmix) ! call Mixrule(Ncomp, XC, ac, bc,tc,pc,Alp, Bet, AF, wm, am, bm, Alpm, Betm,wmix,AFmix) call Zfactr (Alpm, Betm, am, bm, PP(K), TT(K), R, ZV, ZL) call TcPcMix(am,bm,Alpm,Betm,R,Tcm,Pcm) ! DenV=PP*wmix/(ZV*R*TT(K)) APD=((ZV-Zexpt(K))/Zexpt(K))*100.0 AAPD=AAPD+ABS(APD) APDB(IB,K)=AAPD ! write (6,*);write (6,*) ! write (6,15) TT(K),PP(K),ZV,ZL,Zexpt(K),APD ZZV(IB,K)=ZV 15 Format(2F8.1,5F8.4) 145 Continue 100 continue Dat=NData AAPD=AAPD/Dat ! write(6,*)'Average Absolute Percent Deviation = ',AAPD Do 146 I=1,NData write (6,15) TT(I),PP(I),(ZZV(N1,I),N1=1,4),Zexpt(I) 146 Continue APDA2=0.0 APDB2=0.0 APDC2=0.0 APDD2=0.0 Do 147 I=1,NData APDA2=APDA2+APDB(1,I) APDB2=APDB2+APDB(2,I) APDC2=APDC2+APDB(3,I) APDD2=APDD2+APDB(4,I) 147 Continue DEV(1)=APDA2/Dat DEV(2)=APDB2/Dat DEV(3)=APDC2/Dat DEV(4)=APDD2/Dat write(6,51)(DEV(N1),N1=1,4) 51 Format(16X,5F8.2) close(5) close(6) STOP END Subroutine Zfactr (Alp, Bet, AT, BC, P, T, R, ZV, ZL) Dimension Coef(4),RT(3) AA = AT*P/(R**2*T**2) BB = BC*P/(R*T) Coef(1) = 1. Coef(2) = -(1.+(1-Alp)*BB) Coef(3) = AA-(Alp*BB)-(Bet+Alp)*BB**2 Coef(4) = -(AA*BB-Bet*(BB**2+BB**3)) Call Cubic (MTYPE, Coef, RT) ! write(6,*) 'Root=',RT Rmin = 1.E+10 Rmax = 1.E-10 Do 70 I=1,3 if (RT(I).LE. 0.0) Go to 70 if (RT(I).LT. BB) Go to 70 if (RT(I).GT. Rmax) Rmax = RT(I) if (RT(I).LT. Rmin) Rmin = RT(I) 70 Continue ZV=Rmax ZL=Rmin Return End

180 Subroutine ZRedMix (Alp, Bet,AF,wm, Zc,Pr,tr, ZV, ZL) Dimension Coef(4),RT(3) w=AF theta = 0.309833 + 1.763758*w + 0.720661*w*w - 1.363589*w**3 - 4.005783*w/(sqrt(wm)) tmp = tr ** (-theta/2.0) omgW=0.361/(1.0+0.0274*w) omga=(1.0+(omgW-1.0)*Zc)**3 omgb = omgW*Zc Coef(1) = 1.0 Coef(2) = -(1.0/Zc+(1.0-Alp)*omgb*Pr/(Zc*tr)) Coef(3) = omga*Pr/(Zc**2*tr**(2+theta))-Alp*omgb*Pr/(Zc**2*tr)-(Alp+Bet)*(omgb*Pr/(Zc*tr))**2 Coef(4) = -(omga*omgb*Pr**2/(Zc**3*tr**(3+theta))-Bet*(1.0/Zc*(omgb*Pr/(Zc*tr))**2+(omgb*Pr/(Zc*tr))**3)) Call Cubic (MTYPE, Coef, RT) ! write(6,*) 'Root=',RT Rmin = 1.E+10 Rmax = 1.E-10 Do 70 I=1,3 if (RT(I).LE. 0.0) Go to 70 if (RT(I).LT. BB) Go to 70 if (RT(I).GT. Rmax) Rmax = RT(I) if (RT(I).LT. Rmin) Rmin = RT(I) 70 Continue ZV=Rmax*Zc ZL=Rmin*Zc Return End

181 Return End

Subroutine TcPcMix(am,bm,alpm,betm,R,Tcm,Pcm) Dimension RTB(3), RTZ(3) call Bcfact (alpm, betm, Bc,RTB) call Zcfactr (alpm, betm, Zc, RTZ) denom = 3*zc**2+(alpm+betm)*Bc**2+alpm*Bc Pcm = (am*Bc**2)/(bm**2*denom) Tcm = (am*Bc)/(bm*R*denom) return End

Subroutine Mixrule(Ncomp, x, ac, bc,tc,pc, Alp, Bet, AF, wm,BIN, Sumam,bmLLS, SumAlpm, SumBetm,wmmix,AFmix) Dimension x(20), ac(20), bc(20), Alp(20), Bet(20), AF(20), wm(20),& tc(20),pc(20),BIN(15,15) Sumam = 0.0 SumbmLLS = 0.0 SumAlpm = 0.0 SumBetm = 0.0 wmmix = 0.0 AFmix = 0.0 Do 10 I = 1,Ncomp Sumbm = Sumbm + x(I)*bc(I) AFmix=AFmix+x(I)*sqrt(AF(I)) wmmix=wmmix+x(I)*sqrt(wm(I)) SumbmLLS = SumbmLLS + x(I)*bc(I)**(1.0/3.0) Do 10 J = 1,Ncomp Sumam = Sumam + x(I)*x(J)*sqrt(ac(I))*sqrt(ac(J))*BIN(I,J) SumAlpm = SumAlpm + x(I)*x(J)*sqrt(Alp(I))*sqrt(Alp(J))*BIN(I,J) SumBetm = SumBetm + x(I)*x(J)*sqrt(Bet(I))*sqrt(Bet(J))*BIN(I,J) 10 Continue bmLLS = (SumbmLLS)**3.0 AFmix=AFmix**2 wmmix=wmmix**2 Return End Subroutine BinIJ(Ncomp,AF,wm,tc,pc, BIJA,BIJB,BIJC,BIJD) Dimension AF(20),wm(20),tc(20),pc(20) Dimension BIJA(15,15),BIJB(15,15),BIJC(15,15),BIJD(15,15) Do 10 I = 1,Ncomp Do 10 J = 1,Ncomp AFI=AF(I) AFJ=AF(J) WMI=wm(I)

182 WMJ=wm(J) AFWI=wm(I)*AF(I) AFWJ=wm(J)*AF(J) TPCI=tc(I)/sqrt(pc(I)) TPCJ=tc(J)/sqrt(pc(J)) ! If(AFI.LE.AFJ) BIJA(I,J) = (AFI/AFJ)**0.5 If(AFI.GT.AFJ) BIJA(I,J)= (AFJ/AFI)**0.5 ! If(WMI.LE.WMJ) BIJB(I,J) = (WMI/WMJ)**0.5 If(WMI.GT.WMJ) BIJB(I,J) = (WMJ/WMI)**0.5 ! If(AFWI.LE.AFWJ) BIJC(I,J) = (AFWI/AFWJ)**0.5 If(AFWI.GT.AFWJ) BIJC(I,J) = (AFWJ/AFWI)**0.5 ! If(TPCI.LE.TPCJ) BIJD(I,J) = (TPCI/TPCJ)**0.5 If(TPCI.GT.TPCJ) BIJD(I,J) = (TPCJ/TPCI)**0.5 10 Continue Return End Subroutine Cubic(MTYPE,A,Z) DIMENSION B(3), A(4), Z(3)

183 ! Three Dissimilar and Real Roots QUOT=SQBOV/CUAOV RCOT=SQRT(-QUOT) IF (BBT) 110,100,100 100 PEI=(1.5707963+ATAN(RCOT/SQRT(1.0-RCOT**2)))/3.0 GO TO 120 110 PEI=ATAN(SQRT(1.0-RCOT**2)/RCOT)/3.0 120 FACT=2.0*SQRT(-ALFOV) Z(1)=FACT*COS(PEI)-B10V3 PEI=PEI+2.0943951 Z(2)=FACT*COS(PEI)-B10V3 PEI=PEI+2.0943951 Z(3)=FACT*COS(PEI)-B10V3 130 CONTINUE IF (MTYPE .EQ. 1) Z(2) = -99.99 IF (MTYPE .EQ. 1) Z(3) = -99.99 RETURN END

184 PERMISSION TO COPY

In presenting this thesis in partial fulfillment of the requirements for a master’s degree at Texas Tech University or Texas Tech University Health Sciences Center, I agree that the Library and my major department shall make it freely available for research purposes. Permission to copy this thesis for scholarly purposes may be granted by the Director of the Library or my major professor. It is understood that any copying or publication of this thesis for financial gain shall not be allowed without my further written permission and that any user may be liable for copyright infringement.

Agree (Permission is granted.)

______Neeraj Kumar______09-30-2005___ Student Signature Date

Disagree (Permission is not granted.)

______Student Signature Date