prediction of coexistence vapor-liquid densities

PREDICTION OF COEXISTENCE VAPOR-LIQUID DENSITIES

FOR SUBSTANCES AND MIXTURES

by

ANDREAS SOEFAJIN, B.S.M.E.

A THESIS

IN

PETROLEUM ENGINEERING

Submitted to the Graduate Faculty of Texas Tech University in

Partial Fulfillment of the Requirements for

the Degree of

MASTER OF SCIENCE

IN

PETROLEUM ENGINEERING

Approved

Akanni Lawal Chairperson of the Committee

Paulus S. Adisoemarta

Accepted

John Borrelli Dean of the Graduate School

May, 2005

ACKNOWLEDGEMENTS

I am indebted to my supervisor Professor Akanni S. Lawal for guiding me

through all the phases of this thesis project. He has spent countless invaluable time, day

and night, and attention to mentor and support my effort in finishing the project. He was

extremely patient in explaining challenging materials. I am also indebted to Dr. Paulus S.

Adisoemarta and Dr. Lloyd Heinze for making a constructive suggestion and giving the

necessary support for this project. I am also very grateful to the financial support

received from the Center for Applied Petrophysical and Reservoir Studies and the

Department of Petroleum Engineering at Texas Tech University.

I also want to thank my colleagues Neeraj Kumar, Kaijuan Zou, Akindele Tododo

for the valuable discussions and insight to improve this work and to make my stay more

enjoyable.

Finally, I reserve my greatest gratitude to my family. I thank my father and

mother for giving the opportunity to study in Texas Tech University and for always

supporting my academic career, financially and psychologically. I also thank my brother

and sister for encouragement and support that have been given until this moment.

ii

TABLE OF CONTENTS

ACKNOWLEDGEMENT ii

ABSTRACT v

LIST OF TABLES vi

LIST OF FIGURES xii

NOMENCLATURES xv

CHAPTER

I. INTRODUCTION 1

1.1 Background Information 3

1.2 Statement of the Problem 6

1.3 Significance of the Project for Reservoir Simulation 7

1.4 Objective of the Project 8

II. REVIEW OF EQUATIONS-OF-STATE TECHNIQUES 10

2.1 Concepts of Cubic Equations-of-State 10

2.2 Lawal-Lake-Silberberg Equation-of-State 13

2.3 Selection of Equations of State for Reservoir Models 15

2.4 Transformed Cubic Equations of State 19

2.5 Resolving Near-Critical Fluid Phase Behavior 20

2.6 Generalized Fugacity Coefficient for Pure Substances 21

2.7 Generalized Fugacity Coefficient for Substances in Mixtures 22

III. ORTHOBARIC DENSITIES FOR SUBSTANCES 24

3.1 Algorithm for Resolving Phase Densities for Pure Substances 24

3.2 Estimation of Van der Waals Constant Parameter (Ωw) 26

3.3 Designed Attractive Temperature Functions 31

3.4 Second Virial Coefficient Calculation 38

3.5 Prediction of Phase Densities for Pure Hydrocarbons 43

3.6 Prediction of Phase Densities for Non-Hydrocarbons 46

3.7 Prediction of Phase Densities for Polar Substances 48

3.8 Prediction of Phase Densities for Miscellaneous Substances 50

iii

3.9 Prediction of Critical Densities for Pure Substances 53

3.10 Designed van der Waals Critical Limit for Pure Substances 54

3.11 Prediction of Virial Coefficient for Substances 55

IV. CRITICAL DENSITIES FOR BINARY MIXTURES 59

4.1 Critical Point for Mixtures by Analogy to Pure Substances 59

4.2 Critical Volume Prediction Methods 62

4.3 Critical Volume for Binary Hydrocarbon Systems 65

4.4 Critical Volume for Binary Non-Hydrocarbon Systems 66

4.5 Analysis of Prediction Results for Mixture Critical Volumes 66

V. CONCLUSIONS AND RECOMMENDATIONS 78

5.1 Conclusions 78

5.2 Recommendations 79

REFERENCES 80

APPENDICES 87

A. LAWAL-LAKE-SILBERBERG EQUATIONS OF STATE

A.1 Transformed LLS Equation of State.

A.2 Fugacity for LLS Equation of State.

A.3 Critical Volume Calculation Method.

B. FORTRAN PROGRAMS FOR VOLUMETRIC PROPERTIES

B.1 FORTRAN Program for Van Der Waals Limit (Ωw)

B.2 FORTRAN Program for Coexistence Densities

B.3 FORTRAN Program for Second Virial Coefficients

B.4 FORTRAN Program for Critical Densities of Mixtures

C. PREDICTION RESULTS FOR PURE SUBSTANCES

C.1 Results for the Lawal-Lake-Silberberg Equation of State

C.2 Results for the Peng-Robinson Equation of State

C.3 Results for the Soave-Redlich-Kwong Equation of State

87

87

90

92

95

95

101

118

125

137

137

178

214

iv

ABSTRACT

Knowledge of the critical state is important in any study of phase behavior;

therefore, the applications of critical state prediction methods can be found in many areas

of the petroleum and chemical industries. However, the vapor-liquid and volumetric

computations for reservoir fluid systems in the retrograde and near-critical regions still

remain a challenge. As a precursor in establishing a predictive equation of state for

compositional reservoir processes, a previously established four-parameter cubic

equation of state reported by Lawal-Lake-Silberberg (LLS) is used to predict orthobaric

densities, second virial coefficient and critical volumes of pure substances (hydrocarbon,

non-hydrocarbon, polar and non-polar fluids). The prediction results are generally within

0.5% of the experimental measurements.

A framework of the attractive temperature function is established for two

parameter (Peng-Robinson and Soave-Redlich-Kwong) and four parameter LLS

equations of state. The temperature function is demonstrated to be internally consistent

with the critical behavior of fluids at sub- and super-critical conditions and the function

does not suffer the difficulty encountered with Soave-type of temperature function which

hitherto has been major source of research in equations of state development.

An analysis of the thermodynamic constraint criteria of the critical state of pure

substances and binary mixtures is used to establish a theoretical expression for the van

der Waals critical point. The theoretical expression for the van der Waals criticality is

validated by the prediction results of binary critical volumes of asymmetric substances

and mixtures. This project offers an insight to the phase behavior of ternary and

multicomponent mixtures and the challenge for the future work is to apply this robust

method to the near-critical flash routine in ternary and multicomponent systems.

v

LIST OF TABLES

2.1 Common Specialization Cubic Equations 1 and 2 14

3.1 Estimation of Van der Waals Constant Parameter (Ωw) 29

3.2 Models for Attractive Temperature Function in Cubic Equations 33

3.3 Theta (Θ) Values for Equations of State 39

3.4 AAPDL and AAPDV for Hydrocarbon Substances 43

3.5 AAPDL and AAPDV for Non-Hydrocarbon Substances 46

3.6 AAPDL and AAPDV for Polar Substances 48

3.7 AAPDL and AAPDV for Refrigerant Substances 50

3.8 AAPDL and AAPDV for Miscellaneous Substances 53

3.9 AAPD for Critical Densities Prediction of Pure Substances 58

C1.1

C1.2

C1.3

C1.4

C1.5

C1.6

C1.7

C1.8

C1.9

C1.10

C1.11

C1.12

C1.13

C1.14

C1.15

C1.16

C1.17

C1.18

Densities Prediction for Methane

Densities Prediction for Ethane

Densities Prediction for Propane

Densities Prediction for n-Butane

Densities Prediction for i-Butane

Densities Prediction for n-Pentane

Densities Prediction for i-Pentane

Densities Prediction for n-Hexane

Densities Prediction for n-Heptane

Densities Prediction for n-Octane

Densities Prediction for n-Decane

Densities Prediction for Cyclohexane

Densities Prediction for Carbon Dioxide

Densities Prediction for Nitrogen

Densities Prediction for Hydrogen Sulfide

Densities Prediction for Carbon Monoxide

Densities Prediction for Chlorine

Densities Prediction for Benzene

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

153

154

vi

C1.19

C1.20

C1.21

C1.22

C1.23

C1.24

C1.25

C1.26

C1.27

C1.28

C1.29

C1.30

C1.31

C1.32

C1.33

C1.34

C1.35

C1.36

C1.37

C1.38

C1.39

C1.40

C1.41

C1.42

C1.43

C1.44

C1.45

C1.46

C1.47

Densities Prediction for Fluorobenzene

Densities Prediction for Bromobenzene

Densities Prediction for Chlorobenzene

Densities Prediction for Iodobenzene

Densities Prediction for 1,3 Butadiene

Densities Prediction for Xenon

Densities Prediction for Helium

Densities Prediction for Argon

Densities Prediction for Hydrogen

Densities Prediction for Ammonia

Densities Prediction for Acetic Acid

Densities Prediction for Acetone

Densities Prediction for Methanol

Densities Prediction for Ethanol

Densities Prediction for Propanol

Densities Prediction for Steam

Densities Prediction for Acetylene

Densities Prediction for Ethylene

Densities Prediction for Oxygen

Densities Prediction for Bromine

Densities Prediction for Sulfur Dioxide

Densities Prediction for Methyl Propionate

Densities Prediction for Ethyl Propionate

Densities Prediction for Methyl n-Butyrate

Densities Prediction for Methyl i-Butyrate

Densities Prediction for Methyl Acetate

Densities Prediction for Ethyl Acetate

Densities Prediction for Propyl Acetate

Densities Prediction for Methyl Chloride

154

155

155

156

156

157

157

158

158

159

160

160

161

161

162

163

164

164

165

165

166

167

167

168

168

169

169

170

170

vii

C1.48

C1.49

C1.50

C1.51

C1.52

C1.53

C1.54

C1.55

C1.56

Densities Prediction for Ethyl Chloride

Densities Prediction for Methyl Ether

Densities Prediction for Methyl Ethyl Ether

Densities Prediction for Refrigerant 11




Densities Prediction for Refrigerant 152a

Densities Prediction for Refrigerant C318

171

171

172

173

174

175

176

176

177

C2.1

C2.2

C2.3

C2.4

C2.5

C2.6

C2.7

C2.8

C2.9

C2.10

C2.11

C2.12

C2.13

C2.14

C2.15

C2.16

C2.17

C2.18

C2.19

C2.20





















179

180

181

182

183

184

185

186

187

188

189

190

191

192

193

194

194

195

195

196

viii

C2.21

C2.22

C2.23

C2.24

C2.25

C2.26

C2.27

C2.28

C2.29

C2.30

C2.31

C2.32

C2.33

C2.34

C2.35

C2.36

C2.37

C2.38

C2.39

C2.40

C2.41

C2.42

C2.43

C2.44

C2.45

C2.46

C2.47

C2.48

C2.49






























196

197

197

198

198

199

199

200

201

201

202

202

203

204

205

205

206

206

207

208

208

209

209

210

210

211

211

212

212

ix

C2.50 Densities Prediction for Methyl Ethyl Ether 213

C3.1

C3.2

C3.3

C3.4

C3.5

C3.6

C3.7

C3.8

C3.9

C3.10

C3.11

C3.12

C3.13

C3.14

C3.15

C3.16

C3.17

C3.18

C3.19

C3.20

C3.21

C3.22

C3.23

C3.24

C3.25

C3.26

C3.27

C3.28





























215

216

217

218

219

220

221

222

223

224

225

226

227

228

229

230

230

231

231

232

232

233

233

234

234

235

235

236

x

C3.29

C3.30

C3.31

C3.32

C3.33

C3.34

C3.35

C3.36

C3.37

C3.38

C3.39

C3.40

C3.41

C3.42

C3.43

C3.44

C3.45

C3.46

C3.47

C3.48

C3.49

C3.50






















Densities Prediction for Methyl Ethyl Ether

237

237

238

238

239

240

241

241

242

242

243

244

244

245

245

246

246

247

248

248

249

249

xi

LIST OF FIGURES

1.1 Classifications of Petroleum Fluids 3

1.2 Prediction of Density for Hydrocarbon 5

1.3 Prediction of Density for Pure Substances 5

2.1 Pressure-Composition Diagram of Methane-Kensol 16 System 16

2.2 Critical Locus of Methane-Kensol 16 System 16

2.3 Prediction of ZC-Factor for Pure Substances 18

2.4 Prediction of ZC-Factor for Mixtures 18

3.1 Systematic Algorithm to Calculate Orthobaric Densities 25

3.2 Internal Tuning Parameter (Ωw) Effect on Densities Prediction of Methane 26

3.3 Systematic Algorithm to Estimate Ωw 27

3.4 Regression Analysis of Ωw 28

3.5 Attractive Functions for Soave-Redlich-Kwong Equation of State 34

3.6 Attractive Functions for Peng-Robinson Equation of State 34

3.7 New Attractive Functions for Peng-Robinson Equation of State 35

3.8 New Attractive Functions for Soave-Redlich-Kwong Equation of State 36

3.9 Attractive Functions for Lawal-Lake-Silberberg Equation of State 36

3.10 Slope of Reduced Pressures against Reduced Temperatures 37

3.11 Second Virial Coefficients for Substances 41

3.12 Second Virial Coefficients for n-Octane 41

3.13 Second Virial Coefficients for Argon 42

3.14 Second Virial Coefficients for Hydrogen 42

3.15 Second Virial Coefficients for HFC-114 43

3.16 Prediction of Phase Densities for Methane 44

3.17 Prediction of Phase Densities for n-Pentane 44

3.18 Prediction of Phase Densities for n-Hexane 45

3.19 Prediction of Phase Densities for n-Decane 45

3.20 Prediction of Phase Densities for Carbon Dioxide 46

3.21 Prediction of Phase Densities for Hydrogen Sulfide 47

xii

3.22 Prediction of Phase Densities for Nitrogen 47

3.23 Prediction of Phase Densities for Steam 48

3.24 Prediction of Phase Densities for Propyl Acetate 49

3.25 Prediction of Phase Densities for Methanol 49

3.26 Prediction of Phase Densities for Ethanol 50

3.27 Prediction of Phase Densities for Refrigerant 32 51

3.28 Prediction of Phase Densities for Refrigerant 152a 51

3.29 Prediction of Phase Densities for Refrigerant 134a 52

3.30 Prediction of Phase Densities for Refrigerant 227 52

3.31 Prediction of Phase Densities for Argon 53

3.32 Prediction of Phase Densities for Sulfur Dioxide 54

3.33 Prediction of Critical Densities for Hydrocarbon Substances 56

3.34 Prediction of Critical Densities for Non-Hydrocarbon Substances 56

3.35 Prediction of Critical Densities for Polar Substances 57

3.36 Prediction of Critical Densities for Refrigerant Substances 57

4.1 Pressure-Temperature Diagram for Pure Substances 59

4.2 Pressure-volume Diagram for Pure Substances 60

4.3 Pressure-Temperature Diagram for Mixtures 61

4.4 Pressure-volume Diagram for Mixtures 61

4.5 Predicted Critical Volume in Methane-Propane System 67

4.6 Predicted Critical Volume in Methane-n-Butane System 67

4.7 Predicted Critical Volume in Methane-n-Pentane System 68

4.8 Predicted Critical Volume in Methane-n-Decane System 68

4.9 Predicted Critical Volume in Ethane-n-Butane System 69

4.10 Predicted Critical Volume in Ethane-n-Heptane System 69

4.11 Predicted Critical Volume in Ethane-n-Decane System 70

4.12 Predicted Critical Volume in Propane-n-Butane System 70

4.13 Predicted Critical Volume in Propane-n-Pentane System 71

4.14 Predicted Critical Volume in Propane-n-Hexane System 71

xiii

4.15 Predicted Critical Volume in Propane-n-Octane System 72

4.16 Predicted Critical Volume in Propane-n-Decane System 72

4.17 Predicted Critical Volume in n-Butane-n-Pentane System 73

4.18 Predicted Critical Volume in n-Butane-n-Hexane System 73

4.19 Predicted Critical Volume in n-Butane-n-Heptane System 74

4.20 Predicted Critical Volume in n-Butane-n-Octane System 74

4.21 Predicted Critical Volume in n-Butane-n-Decane System 75

4.22 Predicted Critical Volume in Carbon Dioxide-Hydrogen Sulfured System 75

4.23 Predicted Critical Volume in Carbon Dioxide-n-Butane System 76

4.24 Predicted Critical Volume in Carbon Dioxide-Hexane System 76

4.25 Predicted Critical Volume in Carbon Dioxide-Decane System 77

xiv

NOMENCLATURES

Symbol Definition

a Attractive Term of EOS

A Dimensionless Attractive Term

b van der Waals co-Volume

B Dimensionless Critical Volume

f Fugacity

n Number of moles

M Molecular Weight

P Pressure

R Universal Gas Constant

T Temperature

v Molar Volume

x Mole Fraction

Z Compressibility Factor

Fugr Fugacity Ratio

AAPDL Average Absolute Percentage Deviation of Liquid

AAPDV Average Absolute Percentage Deviation of Vapor

DEVL Liquid State Deviation

DEVG Vapor State Deviation

Subscript

i, j Component Code

1,2 Component Index

C Critical Property

l Liquid Phase

v Vapor Phase

m Mixture

w van der Waals Volume Limit Representation

xv

R Reduced property

Greek Letter

α LLS EOS Parameter

αij Binary Interaction Parameter of α

β LLS EOS Parameter

βij Binary Interaction Parameter β

θa Dimensionless parameter of Attrative Term

ρ Density

ω Acentric Factor

Ωw Van der Waals Constant Parameter

xvi

CHAPTER I

INTRODUCTION

A complete knowledge of phase behavior of substances and multi-component

mixtures is imperative in the petroleum and chemical processes. The reservoir fluid

characterization, reservoir simulation practices and fluid separation processes are some of

the fields where those phase behavior knowledge can be applied. Particular emphasizes

have been given for the phase behavior equilibrium of vapor and liquid in two-phase and

near critical point regions. Two-phase is the region where both the vapor and liquid have

distinct properties such as densities, compressibility factors and viscosities; while the

critical point is the point where there are no properties separations between two phases.

Of interest for petroleum engineers are the vapor and liquid phases. All known substances

have one point where properties distinction between vapor and liquid no longer exist.

This point is the critical point for that component.

Vapor and liquid properties such as volume and density of pure substances and

multi component mixtures at a fixed temperature and pressure can be determined

experimentally or analytically. Due to the high cost, time constraint and apparatus

limitation associated with experimental testing, especially those dealing with multi-

component mixtures at high pressure, laboratory measurement is no longer the preferred

way to measure the thermodynamic properties. Furthermore, in the absence of

experimental data, a robust analytical method is required to supply those values. Hence,

analytical solution has been given more attention to predict or estimate these properties.

Analytical approach ranges from a simple empirical correlation through detailed

thermodynamic approach have been studied. Analytical vapor-liquid equilibrium can be

studied by applying fundamental principle of Gibbs’ free energy,26 65 Wilson

renormalization22 and Van der Waals’ type cubic equations of state.92 Of those

fundamental principles, the van der Waals-derived cubic equation of state has been the

most commonly used and reported in the physical properties calculation. Van der Waals

also introduced law of corresponding states principles which stated that intermolecular

1

forces dependent properties in equilibrium relates with the critical properties

universally.65 The law is the single most significant foundation to develop the analytical

tools for vapor and liquid properties prediction. The van der Waals- type cubic equation

of state is a very valuable prediction method for the binary mixtures and can be extended

to analyze the multi-component hydrocarbon mixtures which of interest to the petroleum

engineer.

In most instances, petroleum industry deals with vapor and liquid phases. The

knowledge of volumetric properties for vapor and liquid phases in equilibrium is an

important tool for any part of petroleum operation. In upstream operation that includes

fluid reserves estimation, reserves depletion techniques, reservoir simulation practices, a

better understanding of vapor and liquid phases can improve the estimation and recovery

of the prospective reserve in the subsurface. For enhance recovery technique practices

such as miscible flooding of CO2 or chemical injections, with several assumptions, the

knowledge of reliable convergence of vapor and liquid properties can be applied to make

multi contact miscibility (MCM) computation. The knowledge can also be extended for

Constant Volume Depletion (CVD) and Constant Composition Expansion calculations.

The vapor and liquid properties prediction can also serve as a tool to determine the

economic prospect of the reserves. The benefit of a better vapor-liquid prediction for the

midstream and downstream operation is determining the size of the separator, heat

exchanger and pipeline to deliver the recovered hydrocarbon. The accurate estimation

reduces many of unnecessary expenses. It is vital to have a robust technique to determine

thermodynamic vapor and liquid properties.

At present, research interests are focused to make accurate prediction of liquid

density and critical properties, to find the extrapolation of a-function to supercritical

temperatures (TR>1), to analyze phase behavior in a high pressure thermodynamic

equilibria and to make a predictive equation of state for transport properties (Viscosity

and Thermal Conductivity) based on the thermodynamic model. One tool to solve these

problems is Equations of State. The most celebrated Equations of State was introduced by

Johannes Didderick van der Waals in 1873. Since that moment, many modifications and

2

alterations of the van der Waals Equations of State have been made, such as the one by

Redlich-Kwong, Soave, Peng-Robinson and Lawal-Lake-Silberberg. Thousands of

papers and publications have been published regarding the prediction of thermodynamic

properties for substances and mixtures using Equations of State method. Yet, the current

available methods still have shortcomings predicting the thermodynamic properties of

pure substances and multi-component mixtures especially those at or near critical point at

high pressure.

This project shows a robust method to predict the thermodynamic properties for

pure substances and multi-component mixtures in equilibrium using the Lawal-Lake-

Silberberg equation of state.

1.1 Background Information

Allen classified the petroleum fluid based on the critical properties. This

classification can be seen in Figure 1.1.

Dry Gas e

l

3

Crude Oi

Volatile Oil

Gas Condensat

Figure 1.1 Classifications of Petroleum Fluids. (Allen1)

Figure 1.1 shows that each petroleum fraction has a unique phase envelope. This

envelope is constructed by the bubble-point and dew-point lines. The pressure of bubble-

point and dew-point can be described as the pressure at which the first drop of liquid is

noticed and the pressure at which a minute liquid presents respectively.55 The

convergence point of these bubble-point and dew-point lines is the critical point.

Petroleum fluid types were classified based on the critical pressure and temperature of the

compounds. For a maximum recovery factor, each of those petroleum fluids requires

different recovery method. An accurate prediction tool for thermodynamic behavior of

vapor and liquid fraction of petroleum fluid is needed.

Cubic EOS is the most attractive method and has been given the most attention to

predict the thermodynamic properties. The most celebrated type of cubic EOS was

introduced by van der Waals in 1873. Many modifications have been made throughout

the year. Currently, cubic EOS has many forms ranging from 2-, 3-, 4-, until 7-

parameters. Polling et al. reviewed many types of equations of state and pointed out that

cubic equations of state have often been chosen as the optimal forms because the

accuracy is adequate and the analytic solution for the phase densities is not too

demanding. Eubank et al. 17 18 stated that the cubic equation of state must have ability to

predict pure component substances; including the near critical region and to ultimately be

applied for physical properties approximation of multi-component mixtures. Multi-

component mixtures in this case hydrocarbon mixtures are of interest for the petroleum

engineer.

The most commonly used cubic equations of state in petroleum industry are the

Redlich-Kwong, 69 Soave80 modification of Redlich-Kwong and Peng-Robinson.62

However, these cubic Equations of state still have shortcomings predicting the properties

in the near and super critical region. Otto Redlich68 even stated, “The illustration near or

at the critical point is the most difficult to obtain. Using critical compressibility ratio as

one parameter is the most potential way to solve the problem. However, discrepancy

should be expected and can be eliminated by addition of another term.” The shortcoming

4

of those cubic equations of state prediction can be quantified in Figure 1.2 and Figure 1.3.

20

28

36

44

52

C7 C9 nC11 nC13 nC15 nC17 nC20COMPONENT IDENTITY

DEN

SITY

(lb/

ft3 )

VDW SRKPR SWPT EXPLLS

P=7267 PSIAT=302 F

Figure 1.2 Prediction of Density for Hydrocarbon.

20

35

50

65

120 170 220 270 320 370MOLECULAR WEIGHT OF FRACTION

DEN

SITY

(lb/

ft3 )

VDW SRKPR SWPT EXPLLS

P=14.7 PSIAT=60 F

Figure 1.3: Prediction of Density for Pure Substances.

5

Figure 1.2 shows the density prediction for several hydrocarbon substances while

Figure 1.3 shows the density prediction as a function of molecular weight. In both

figures, the experimental density has an increasing trend as the molecular weight

increases. The LLS EOS is the only one that follows the same trend as the experimental

values; every other cubic equation of state has a decreasing trend. This inverse trend

magnified the discrepancies between experimental data and cubic equation of state

prediction as the molecular weight increases.

1.2 Statement of the Problem

A reliable method that can approximate the coexistence of vapor-liquid densities

is invaluable in all aspect of petroleum industry. Buxton et al. said that the principle of

corresponding states has been the most widely used of predicting volumetric properties of

gas. The law of corresponding states was introduced by van der Waals. Ever since the

introduction by van der Waals in his famous dissertation about cubic equation of state

many adjustment have been made to predict the thermodynamic properties of substances.

Polling et al. stated that due to the substance’s pressure and temperature sensitivity,

reliable experimental data and EOS predictions in near critical and high pressure region

are hard to attain. Kaliappan et al.35 stated, “Petroleum engineer is interested in the P-T

envelope that describes the fluid existing in a given reservoir.”

The current methods of predicting the volumetric properties near the critical point

and at supercritical region still have limitations. In the near critical region, limitations can

be caused by the fixed values of some parameters use in the calculation (P-R, S-R-K, and

VDW). Sims et al.76 stated that cubic equation of state such as the Peng-Robinson and

Redlich-Kwong fail to converge or are inaccurate in the critical region. Yang et al.97

stated, “Current methods to predict the coexistence of vapor-liquid densities, especially

those for mixtures cannot yield accurate and continuous density-predictions, especially in

the near critical region.” Firoozabadi et al. 20 stated, “All van der Waals-type equation of

state fail to perform satisfactorily in the critical region for binary and multicomponent

systems with a widespread volatility.” Chou et al.7 pointed out that the “classical” cubic

6

EOS such as Redlich-Kwong and Peng-Robinson derivation of van der Waals equation of

state failed to correctly represent thermodynamic properties in the near critical area. In

the supercritical region, some of the shortcomings can be attributed to the inaccuracy of

the temperature dependent attractive function. The most popular attractive function was

proposed by Soave. Many modifications have been made to the original Soave attractive

function, yet the limitation still exists. Segura et al.78 argue that there is a physical

inconsistency for Soave-type attractive function. Twu et al. 89 90 stated that although the

Soave-type attractive function is the most widely used, it becomes zero at finite

temperature and then increases as the temperature reaches infinity. Also, the Soave

function is not suitable for polar component.

1.3 Significance of the Project for Reservoir Simulation

Reservoir simulation has become so popular in petroleum industry that all current

and future oil production can be evaluated by a reservoir simulation package. Keith

Coats8 stated that in reservoir simulation practices, the question is not whether, but how

and how much. A reliable and accurate calculation of vapor-liquid equilibrium is

essential for the compositional 70 and enhanced oil recovery (EOR) 76 simulation. This

calculation can widely range from the two-phase region to at or near critical point.

Reservoir fluids, whether that is dry gas, wet gas or condensate, consist of many

components that do not always have a complete quantitative density data. Although these

data sets can be measured through a laboratory experiment, it is not be cost effective. The

equation of state is an attractive tool to supply those values and has been the backbone of

reservoir fluid properties prediction in reservoir simulation software package. Rowe

pointed out that to predict the phase composition; the correlation has to be internally

consistent, reasonably accurate and reliable, without discontinuity and must not require

excessive computer time. Saeedi et al.74 stated that a necessary condition, for

compositional simulation to be meaningful, is that the oil and gas phase densities and

viscosities should approach the critical point in a consistent and stable manner. However,

the current equation of state methods, which are employed in many simulation packages,

7

cannot accurately and continuously predict these properties, especially when dealing with

high molecular weight substances and mixtures such as C7+. Failing to accurately predict

these properties can result in inaccuracy reserves estimation and misinterpretation of the

reservoir fluid types.

1.4 Objective of the Project

The purpose of the project is to provide a robust calculation technique for

predicting the volumetric properties of substances, binary and ternary mixtures. To

accomplish this goal, several objectives have been set and listed:

1. To gather experimental data sets for pure substances and multi component

mixtures.

2. To determine the Van der Waals critical limit parameter (Ωw) for pure substances

that is consistent with the coexistence vapor-liquid phase densities.

3. To utilize Lawal-Lake-Silberberg equation of state as the foundation in building a

closed form van der Waals density prediction in subcritical, critical and

supercritical region.

4. To resolve the near critical saturation densities calculation for pure substances.

5. To design a robust attractive-temperature function for cubic equations of state.

6. To predict the vapor pressure for pure substances.

7. To predict the critical volume of multi-component mixtures.

To achieve those objectives, this report has been divided into five chapters.

Following a brief introduction of the problem, the proposed solution method and equation

of state technique is reviewed in Chapter 2. This chapter discusses the available method,

explains the concept of equations of state and stated reasoning behind the selection of the

Lawal-Lake-Silberberg equation of state. The prediction results of orthobaric densities

for pure substances are stated in Chapter 3, followed by the prediction of critical volume

8

for mixtures in Chapter 4. Finally, project conclusions and recommendations for future

work are stated in Chapter 5.

9

CHAPTER II

REVIEW OF EQUATIONS-OF-STATE TECHNIQUES

Thermodynamic properties can be predicted experimentally or analytically. Due

to the cost and difficulty associated in conducting the experiment, analytical solutions

have become the more preferred way to predict thermodynamic properties such as density

and vapor pressure. The analytical solutions can be based by Gibbs excess energy,

empirical solution and Equations of State. There are many types of equation of state such

as cubic, virial, empirical, crossover, chemical theory and perturbation model. Poling et

al. 65 reviewed many types of equation of state and stated “cubic Equations of State have

often been chosen as the optimal forms because the accuracy is adequate and the analytic

solution for the phase densities is not too demanding.” The most celebrated type of

equation of state is the van der Waals-derived equation of state. This chapter reviews the

equations of state techniques.

2.1 Concepts of Equations-of-State

Equation of state is an equation relating pressure, temperature and volume of

substance. The simplest equation of state is the ideal gas equation that was introduced in

19th century and can be expressed as follows:

nRTPv = (2.1)

This ideal gas equation was then developed to calculate real gas properties by setting the

value of n = 1 and incorporating a compressibility factor. The equation is expressed as:

ZRTPv = (2.2)

The real gas equation has limitation in predicting the volumetric behavior of

substances. Due to this limitation of real gas equation to further improvement, Johannes

Didderick Van der Waals introduced Equations of State (EOS) in 1873 to show the

continuity of vapor and liquid phase behavior and to predict the volumetric properties.

This EOS can be expressed as:

2va

bvRTP −−

= (2.3)

10

The boundary conditions or stability constraints at the critical point are set as:

0=⎟⎠⎞

⎜⎝⎛∂∂

CTvP (2.4)

02

2

=⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

CTvP (2.5)

Van der Waals separated Equation 2.3 into repulsive term and

attractive function of . Using the boundary conditions, parameters , which are

constant values and were calculated based on PVT experiment, can be expressed as:

)/( bvRT −

2/ va ba and

C

CC P

TRTa

22

421875.0)( = (2.6)

C

C

PRT

b81

= (2.7)

This EOS was originally developed for pure substances and was good enough to predict

the thermodynamic properties of substances at region far from the critical.

Since the van der Waals introduction of EOS, many adjustments have been made

to better predict the gas and liquid properties of substances. The adjustment can be

classified to so-called “classical” and “non-classical” EOS. The “classical” Equations of

state are the Redlich-Kwong, Peng-Robinson and Soave modification of Redlich-Kwong.

In 1949, Otto Redlich and J.N.S Kwong proposed a new EOS. By this time, there

are already 200 EOS available and most of them are Van der Waals modifications.91

Redlich-Kwong EOS can be described as:

)()(

bvvTa

bvRTP C

+−

−=

α (2.9)

At the critical point by applying the boundary conditions of Equation 2.4 and Equation

2.5 parameters yielded the following: ba and

C

CC P

TRTa

5.22

4278.0)( = (2.10)

( ) )()( TTaTa iCi α= (2.11)

11

5.0)( TaTi =α (2.12)

C

C

PRT

b 0867.0= (2.13)

After Redlich-Kwong EOS, the interest for EOS was rejuvenated. In 1972, Giorgio Soave

proposed a modification of the Redlich-Kwong EOS. Soave incorporated the acentric

factor as the third parameter. The Soave modification of Redlich-Kwong EOS

generalized the modified correlation parameter. This EOS can be shown as:

)()(bvv

Tabv

RTP+

−−

= (2.14)

Applying the boundary condition at the critical condition yielded the following:

C

CC P

TRTa

22

42747.0)( = (2.15)

),()()( ωα RiCi TTaTa = (2.16)

C

C

PRT

b 08664.0= (2.17)

Following Soave modification, Ding Yu Peng and Donald B. Robinson introduced their

modification in 1976. Their EOS can be expressed:

)()()(

bvbbvvTa

bvRTP

−++−

−= (2.18)

Applying the boundary conditions at critical temperature yielded the following:

C

CC P

TRTa

22

45724.0)( = (2.19)

),()()( ωα RiCi TTaTa = (2.20)

C

C

PRT

b 0778.0= (2.21)

These so-called “classical” EOS are the most widely used in petroleum industry. It can be

seen that every other state equation mentioned have a temperature dependent attractive

function (α) except for van der Waals EOS. This function is discussed further in Chapter

3.

12

In addition to those Equations of state, many more modifications to van der Waals

EOS were made such as Patel-Teja, Trebble-Bishnoi, Schmidt-Wenzel, Twu-Sim-

Tassone and Guo-Du. Judicious selection of EOS methods is required and many of those

EOS methods still have difficulty predicting thermodynamic properties near or at critical

point, especially at high pressures. A simple yet robust method is still needed to

accurately predict volumetric phase behavior of substances.

2.2 Lawal-Lake-Silberberg Equations-of-State

The Lawal-Lake-Silberberg Equations of State (LLS-EOS) is another derivation

of Van der Waals-type Equations of State. It was introduced in 1983 by Lawal and was

explained in literature. 43 The LLS EOS is expressed as:

22

)(bbv

Tabv

RTPβα −+

−−

= (2.22)

Parameters βα and ,,ba are established as:

C

CCw

C

CaC P

TRZ

PTR

Ta22

322

])1(1[)( −Ω+=Ω= (2.23)

),()()( ωγ RC TTaTa = (2.24)

C

CCw

C

Cb P

RTZ

PRT

b ][Ω=Ω= (2.25)

Cw

Cw

ZZ

Ω−Ω+

=)3(1

α (2.26)

Cw

CwCwwC

ZZZZ

2

232 )31(2)1(Ω

−Ω+Ω+−Ω=β (2.27)

Where P is the pressure in psia, T is the temperature in degree Rankine, is the molar

volume in cu-ft/lb-mole, R = 10.73 is the universal gas constant in psia cu-ft/lb-mole

voR,

Z is the compressibility factor and Ωw is a component based LLS EOS constant which is

further discussed in Chapter 3. In the absence of critical compressibility factor (ZC),

Rowlinson method was proved to be superior in supplying the appropriate value. The

13

Rowlinson method relates critical compressibility factor (ZC) and acentric factor and can

be expressed as:

ω375.01

293.0+

=CZ (2.28)

The LLS EOS is so flexible that it can be correlated with other EOS by changing

the value of α and β. For example, to show the van der Waals EOS from Equation 2.3 the

value of α and β must be set at 0. Table 2.1 displays the values of α and β for several

EOS.

Table 2.1 - Common Specialization of LLS Equation of State

Authors Year Coefficients of the Quadratic

α β α + β

Two -Constant Equations:

van der Waals 1873 0 0 0

Dieterici 1898 0 0 0

Berthelot 1990 0 0 0

Redlich – Kwong 1949 1 0 1

Peng – Robinson 1976 2 – 1 1

Harmens 1977 3 – 2 1

Zakharov 1977 c 0 c

Three -Constant Equations:

Clausius 1881 2c/b – c2/b2 1 (c =b)

Martins 1979 2 – t2/b2 1 (t = b)

Schmidt – Wenzel 1980 1 + 3ω – 3ω 1

Harmens – Knapp 1980 c – (c – 1) 1

Heyen 1981 (b + e)/b – e/b 1

Joffe – Martins 1981 2c/b – c2/b2 1 (c = b)

Patel – Teja 1982 (b + c)/b – c/b 1

Kubic – Martins 1982 2c/b – c2/b2 1 (c = b)

Table 2.1 (Continued)

14

Yu – Lu 1987 3 + ω – ω 3

Yu – Lu – Iwai 1987 (3b + c)/b – c/b 3 (c = b)

Guo – Du 1989 2c/b – c/b 1 (c = b)

Four -Constant Equations:

Himpan – Danes – Gaena 1979 2d/b – (d2 + c)/b2 1 (c = 0, d = b)

Lawal – Lake – Silberberg 1983 α – β α – β

Adachi – Lu 1983 b2 (b2 + b3)/b2 – b2b3/b2 1 (b2 = b3 = b)

Trebble – Bishnoi 1987 (b + c)/b – (bc + d2)/b2 1 (c = b, d = 0)

The LLS EOS can also be extended for predicting the multi-component mixtures and

shown as:

22mmmm

m

m bba

bRTP

βνανν −+−

−= (2.29)

The mixture parameters for use in Equation 2.28 are specified by the following mixing

rules:

(2.30) ijji

n

ij

n

jim aTaTaxxa 2/12/1 )()(∑∑=

(2.31) 3

3/1 ⎟⎠

⎞⎜⎝

⎛= ∑

n

iiim bxb

(2.32) ijji

n

ij

n

jim xx αααα 2/12/1∑∑=

(2.33) ijji

n

ij

n

jim xx ββββ 2/12/1∑∑=

Binary interaction parameters are denoted by ijijija βα , , for parameters βα , ,a .

2.3 Selection of Equations of State for Reservoir Models

Rzasa et al. made measurements of binary system Methane-Kensol 16 which can

be seen in Figure 2.1 and Figure 2.2. Figure 2.1 shows the vapor pressure measurement

15

against composition while Figure 2.2 shows the critical locus of the Methane-Kensol 16

system.

Figure 2.1: Pressure-Composition Diagram of Methane-Kensol 16 System 72

Figure 2.2: Critical Locus of Methane-Kensol 16 System 72

16

Both figures illustrated that the pressure can be up to about 13,000 psia which is

much higher than the critical values of each component for this binary mixture. From this

experiment, Rzasa stated, “Two phases can coexist at pressure of 13,000 psia and as the

drilling operation become deeper and deeper, the amount of methane in the reservoir

increases. In the case of the two phases are present, it is a possibility that a more

complicated production and operating technique is considered. The experimental results

also nullify the notion that in depth of 12,000 to 15,000 ft there is only be one phase exist

due to the high bottom-hole pressure.”

Prediction of critical densities depends on critical pressure, critical temperature,

and critical Z-factor. The critical pressure and critical temperature are accurately obtained

from experimental data while the critical Z-factor is an analytical value. The Z-factor

value can be obtained from EOS. Figure 2.3 shows the prediction and experimental

results of ZC-factor for several single components. The prediction values were obtained

from Van der Waals (VdW), Peng-Robinson (PR), Soave-Redlich-Kwong (SRK) and

Lawal-Lake-Silberberg (LLS) EOS. In this figure, VDW, PR and SRK EOS predicted

universal constant ZC-factor values are shown, which is one of the shortcomings of these

equations of state, while LLS EOS duplicates the value of experimental ZC-factor for

every component. Thus, the LLS EOS predicts a component based ZC-factor.

When the prediction methods are extended for multi-component mixtures, the

same shortcomings as pure component prediction are encountered. Figure 2.4 shows the

shortcomings of the VDW, PR and SRK EOS methods while LLS EOS illustrates the

effect of mixtures composition and follows the experimental data trend. Therefore, the

LLS EOS is selected for this project as a basis to make robust closed form solutions in

predicting the thermodynamic properties for pure substances and mixtures.

17

0.240

0.290

0.340

0.390

C1 C3 nC5 nC8Components

Z C-F

acto

rS

S

Figure 2.3: Prediction of ZC-Factor for Pure Substa

0.24

0.26

0.28

0.30

0.32

0.34

0.36

0.38

0.40

0 0.2 0.4 0.6 Mole Fraction of n-Butane

Z C- C

ritic

al C

ompr

essi

bilit

y Fa

ctor

nC5nC6nC7nC8nC10

VDW

SRK

PR LLS

LLS

Figure 2.4: Prediction of ZC-Factor for Mixture

18

PR EO
SRK EOS
S

nc

0

s.

LLS EO

VdW EO

nC10

es.

.8 1

LLS

2.4 Transformed Equations of State

The LLS EOS of Equation 2.22 shows the relation between pressure, temperature

and molar volume ( v ). In calculating the volumetric behavior, it is more convenient to

write this equation into the Z form. Equation 2.22 can be transformed into Z-form as:

0432

23

1 =Θ−Θ+Θ−Θ ZZZ (2.34)

Where parameters Θ1, Θ2, Θ3, Θ4 are:

11 =Θ (2.35)

[ B)1(12 ]α−+=Θ (2.36)

])([ 23 BBA αβα +−−=Θ (2.37)

)]([ 324 BBAB −−=Θ β (2.38)

Parameters were defined as: B andA

22TRaPA = (2.39)

RTbPB = (2.40)

Similarly Equation 2.22 can be written in form−v as:

0432

23

1 =Θ−Θ+Θ−Θ vvv (2.41)


11 =Θ (2.42)

⎥⎦⎤

⎢⎣⎡ +−=Θ

PRTbb α2 (2.43)

⎥⎦⎤

⎢⎣⎡ +−−=Θ 2

3 )( bP

RTbPa βαα (2.44)

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ +−=Θ β

PRTbb

Pab 23

4 (2.45)

Using mixing rules stated in Equation 2.30 to Equation 2.33 the Equations of State can be

extended for mixtures. The Z-form for mixtures is expressed as:

19

(2.46) 0)]([])([])1(1[ 32223 =+−−+−−+−+− BBABZBBAZBZ mmmmm βαβαα

Similarly, the LLS EOS can be expressed in v-form for mixtures as:

0

)(

23

223

=⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ +−−

⎥⎦⎤

⎢⎣⎡ +−−+⎟

⎠⎞

⎜⎝⎛ +−−

mmmmm

mmmmmm

mmm

PRTbb

Pba

vbP

RTbPa

vP

RTbbv

β

βααα (2.47)

Detailed derivation for the Z-form and v-form can be seen in Appendix A.

The solution of Equation 2.34 and Equation 2.41 can be either one or three real

roots. When three real roots are available, the highest real root is for vapor and the lowest

real root that larger than the value of B is for liquid. The other root is discarded as it

carries no physical meaning. An accurate determination of these roots helps resolve the

near critical region phase behavior.

2.5 Resolving Near-Critical Fluid Phase Behavior

The properties of substances are strongly affected by the presence of critical

point. Anisimov et al. defined critical region as 0.96< T/TC < 1.04. At the critical point,

the properties of liquid and vapor phases are indistinguishable while near the critical

point the properties of liquid and vapor are fairly similar. Although the critical point of

each component is widely varied, the behavior of the substances is not change. The

approach of simple extrapolation must not be used in predicting the phase behavior at the

near critical region condition. This is because as the condition draws nearer to the critical

point, the sensitivity and fluctuation of the properties calculation increases widely as

temperature or pressure is minutely changed. Research showed although properties

universality exists, substance-dependent variables play a significant role in this region.

Polling et al. stated that many adjustments have been made to resolve the

prediction near the critical point. These adjustments range from introduction of switching

20

function which does not required any iteration by Chapel and Rowlinson in 1974,

renormalization TC and ρC such as by Fox (1983) Pitzer et al. (1988) and Chou et al.

(1989), and the crossover functions by Sengers and colleague.

According to van der Waals theory, the EOS must have two-constant parameters.

These parameters which are represented by are the attractive and repulsive term

of the molecule. Resolving the near critical region, non temperature and pressure

dependent parameters are needed. The LLS EOS introduced the neither non temperature

nor pressure dependent parameters of alpha (α) and beta (β). The parameters α and β are

functions of Ω

b and a

w and ZC. These parameters force the prediction to converge consistently at

the critical point. Thus, resolving the near critical region.

The thermodynamic equilibrium condition should be expressed in experimental

quantity of pressure, temperature, volume and composition. The thermodynamic

equilibrium condition can be quantified by the fugacity term which was introduced G.N

Lewis and denoted by f. When there are vapor and liquid phases in the system, the

condition for thermodynamic equilibrium can be shown as: l

iv

i ff = (2.48)

Where v is the vapor state, l is the liquid state and i is the substance name.

2.6 Generalized Fugacity Coefficient for Pure Substances

Fugacity coefficient for pure component was developed for LLS EOS and can be

expressed as:

( ) ( ) QBZZPfi −−−−=⎟⎠⎞

⎜⎝⎛ ln1ln (2.49)

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

+−+

+++

⎭⎬⎫

⎩⎨⎧

+=

2)4(

2)4(

ln)4( 5.02

5.02

5.02 BZ

BZ

BAQ

βαα

βαα

βα (2.50)

Detailed derivations can be seen in Appendix A. This fugacity function can be extended

to calculate multi-component mixtures thermodynamic equilibrium condition.

21

2.7 Generalized Fugacity Coefficient for Substances in Mixtures

The general fugacity equation for components in multi-component mixture can be

expressed as:

∫ −=⎟⎟⎠

⎞⎜⎜⎝

⎛ P

Pi PdPZ

Pxf

*

)1(ln_

(2.51)

The mixture fugacity equation for LLS EOS was expanded as:

( ) ( )

⎭⎬⎫

⎩⎨⎧

+−⎭⎬⎫

⎩⎨⎧

−+−++

⎭⎬⎫

⎩⎨⎧

+−−−−−−=⎟⎟⎠

⎞⎜⎜⎝

⎛

∑∑

∑

k m

ikk

k m

ikk

kmi

m

ikkmi

i

i

xWHBSK

xWHBSGWHBGS

bbaax

QBZbbZPx

f

ββ

αα

)()(2)1(

2]/[32ln2]/[31ln 3/13/1

(2.52)

Where the parameters are:

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

+−+

+++

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

+=

2)4(

2)4(

ln)4( 5.02

5.02

5.02 BZ

BZ

BAQ

mmm

mmm

mm βαα

βαα

βα (2.53)

⎭⎬⎫

⎩⎨⎧ −−

−= QZ

BZZS (2.54)

( )⎥⎥⎦

⎤

⎢⎢⎣

⎡

+

+

⎭⎬⎫

⎩⎨⎧ −−

−=+

mm

mmQZBZ

ZGSβαβα

4)2(2

1 2

2

(2.55)

⎥⎥⎦

⎤

⎢⎢⎣

⎡

+⎭⎬⎫

⎩⎨⎧ −−

−=

mm

mQZBZ

ZSGβα

α42

2

(2.56)

⎥⎥⎦

⎤

⎢⎢⎣

⎡

+⎭⎬⎫

⎩⎨⎧ −−

−=

mm

mQZBZ

ZSKβα

β4

42 (2.57)

⎥⎥⎦

⎤

⎢⎢⎣

⎡

+⎭⎬⎫

⎩⎨⎧ −

−=

mm

mmBBZ

BWHBβα

βα4

22 (2.58)

22

The mixture fugacity equations are using the mixing rules proposed in Equation 2.30

through Equation 2.33.

23

CHAPTER III

ORTHOBARIC DENSITIES FOR SUBSTANCES

A detailed algorithm and prediction results of orthobaric densities of pure

substances is shown in this chapter. The algorithm shows a robust closed-loop orthobaric

densities prediction. The LLS EOS is used as a basis to construct the solution. The

prediction of single component covers polar, non-polar, hydrocarbon, non hydrocarbon

and refrigerant substances. Internal tuning parameter for pure substances prediction is

also presented in this chapter. In addition, an improved and robust temperature dependant

attractive function is discussed.

3.1 Algorithm for Resolving Phase Densities for Pure Substances

The LLS EOS has been applied as a basis to solve the phase densities for pure

substances. Step by step procedure to calculate orthobaric densities is illustrated in Figure

3.1.

The methodology started by reading input properties of the component. These

properties are component’s critical values of temperature, pressure and compressibility

factor, molecular weight and acentric factor. Calculating cubic EOS parameters of

βα and , , ba is the next step. Parameters βα and , , ba are functions of for

the LLS-EOS. Further discussion about Ω

Cw Zand Ω

w is made later. The next step is calculating

appropriate vapor pressures using the Newton-Raphson iteration. Following the vapor

pressure calculation, compressibility factor and fugacity of vapor and liquid states were

calculated. Fugacity values are important in checking the equilibrium condition. Once the

equilibrium condition is satisfied, the orthobaric densities were calculated. Finally, the

average absolute percent deviations (AAPD) between experimental and prediction values

are calculated. FORTRAN code for the orthobaric densities prediction can be seen in

Appendix B.

24

Figure 3.1: Systematic Algorithm to Calculate Orthobaric Densities.

Start

Given Properties of Component: TC, PC, ZC, ω, M

Calculate EOS Parameter a,b,α,β

Calculate Vapor Pressure

Calculate Density

Calculate Z-factor and fugacity.

Equilibrium satisfied?

No

Calculate AAPD

Yes

End

25

3.2 Estimation of Van der Waals Constant Parameter (Ωw)

Van der Waals parameter (Ωw) was introduced in LLS EOS. Figure 3.2 shows the

prediction results for various Ωw values. Bigger value of Ωw leads to smaller phase

envelopes.

0

0.5

1

1.5

2

2.5

3

3.5

0.55 0.65 0.75 0.85 0.95

Reduced Temperature

Red

uced

Den

sity

Figure 3.2: Ωw Effect on Densities Prediction of Methane.

Predicting the appropriate Ωw values were made through an iterative process. The

methodology is as follows:

1. Read the necessary input parameter of the component such as critical temperature,

critical pressure, critical compressibility and acentric factor.

2. Set the Van der Waals constant parameter (Ωw) as 0.25.

3. Calculate parameters βα and , , ba at the critical condition.

4. Set the average absolute percent deviation (AAPD) between experimental and

prediction values of vapor and liquid density equal to 0.

5. Calculate temporary parameter (Tmp), compressibility factor, fugacity for

bisection iterative calculation.

26

6. Do iteration using bisection method for checking the equilibrium condition.

7. Calculate the vapor and liquid density and AAPD values.

8. Check if AAPD is bigger than the previous value. If current value is bigger,

update the Ωw by 0.0025. If current value is less, end the iteration.

Figure 3.3: Systematic Algorithm to Estimate Ωw.

Given Properties of Component: TC, PC, ZC, ω, M

Calculate Density, AAPDnew

Calculate EOS Parameter βα ,,, ba

Set Ωw = 0.25

Equilibrium satisfied?

End

Yes No

Set AAPD = 0

Calculate Tmp, Z, f

AAPDnew > AAPD?

Ωw = 0.25+0.0025Yes

No

Start

27

The Ωw values were calculated for hydrocarbon, non-hydrocarbon, polar, non-

polar and refrigerant substances. After these values were calculated, regression analysis

was conducted and generalized function was developed. Figure 3.4 showed the regression

results of the Ωw.

0.354

0.355

0.356

0.357

0.358

0.359

0.36

0.361

0.362

0.300 0.310 0.320 0.330 0.340 0.350 0.360 0.370 0.380 0.390Ωw Exp

Ωw

Cal

c

Ωw = 0.361/(1+0.0274*ω)

Figure 3.4: Regression Analysis of Ωw.

The van der Waals constant parameter (Ωw) was determined as a function of acentric

factor. The general form of Ωw is:

ω0274.01361.0

+=Ωw (3.1)

This general form is used as one of the parameter in predicting the thermodynamic

properties and vapor pressures of substances. The complete result of van der Waals can

be seen in Table 3.1.

28

Table 3.1: Estimation of Van der Waals Constant Parameter (Ωw).

Component N Ωw AAPDL AAPDV Ammonia 64 0.3125 2.2060 3.9239 Steam 56 0.3500 1.5995 0.9946 Carbon Monoxide 14 0.3250 4.2127 3.5192 Nitrogen 18 0.3700 1.2500 5.2399 Oxygen 11 0.3450 3.0424 2.0418 Phosphine 15 0.3800 1.4814 7.0468 Hydrogen Sulfide 61 0.3525 1.2950 2.9733 Hydrogen Chloride 16 0.3425 2.3836 4.2391 Fluorine 11 0.3025 9.7235 1.1074 Carbon Dioxide 90 0.3650 1.7766 8.4812 Nitrous Oxide 14 0.3525 1.9707 2.8377 Sulfur-Dioxide 80 0.3450 1.7986 4.8686 Chlorine 31 0.3300 1.5109 6.2249 Bromine 17 0.3100 21.5452 9.2864 Methane 24 0.3500 1.3885 7.0384 Ethane 87 0.3250 2.1446 1.8499 Propane 79 0.3500 1.1018 5.6092 n-Butane 61 0.3525 1.1898 1.4229 i-Butane 76 0.3400 0.6382 4.5334 n-Pentane 61 0.3550 1.6789 3.2732 i-Pentane 62 0.3550 1.4861 2.6268 n-Hexane 53 0.3625 1.9509 2.5967 n-Heptane 36 0.3325 2.0091 2.1427 n-Octane 31 0.3575 1.6908 2.7407 n-Decane 25 0.3025 6.5882 2.0183 Benzene 21 0.3575 1.8253 3.2176 Fluorobenzene 20 0.3625 1.9403 2.8326 Chlorobenzene 28 0.3500 1.5995 0.9946 Bromobenzene 13 0.3450 1.8006 1.5418 Iodobenzene 11 0.3400 0.9396 0.7317 Acetylene 13 0.3750 2.9034 1.8788 Ethylene 37 0.3625 2.3536 5.9072 1-3-Butadiene 28 0.3200 3.9697 0.4398 Cyclohexane 19 0.3550 1.7455 4.0981

29

Table 3.1: (Continued)

Component N Ωw AAPDL AAPDV Methyl Alcohol 21 0.3475 2.1619 4.4322 Ethyl Alcohol 19 0.3600 2.1275 2.4813 Propyl Alcohol 18 0.3600 2.0940 2.5167 Deuterium 11 0.3500 0.7903 3.8270 Methyl Propionate 19 0.3525 2.0904 4.7759 Ethyl Propionate 21 0.3475 2.1830 2.4639 Methyl-n-Butyrate 20 0.3550 2.1413 3.5107 Methyl-iso-Butyrate 20 0.3575 2.0822 2.1416 Methyl Acetate 21 0.3500 2.2060 3.0299 Ethyl Acetate 22 0.3550 2.2406 2.6838 Propyl Acetate 15 0.3550 2.0993 2.9729 Methyl Chloride 44 0.3450 2.0482 3.1154 Ethyl-Chloride 38 0.3250 1.4773 5.4424 Carbon Tetrachloride 22 0.3575 1.9547 3.6040 Stannic Chloride 15 0.3475 1.6593 2.0862 Methyl Ether 19 0.3100 2.1077 2.8099 Methyl Ethyl Ether 18 0.3575 1.6271 15.1199 Ethyl Ether 19 0.3575 1.9589 3.5870 Ethyl Propyl Ether 21 0.3375 1.5782 27.8560 Methyl Mercaptan 21 0.3600 2.1864 52.3604 Ethyl Mercaptan 21 0.3425 1.6890 19.2209 Acetonitrile 21 0.3460 5.0511 7.7746 Propionitrile 22 0.3600 5.6700 13.2096 Methyl Formate 20 0.3500 2.1838 2.7260 Ethyl Formate 21 0.3525 2.1183 3.7623 Propyl Formate 18 0.3525 2.0081 2.8995 Dimethyl Sulfide 21 0.3425 1.8915 25.1403 Diethyl Sulfide 20 0.3425 1.4705 33.6164 Diethylamine 19 0.3525 1.8288 13.0112 Triethylamine 21 0.3650 1.5865 18.7130 Carbon Tetrafluoride 20 0.3525 2.1724 2.9359 Phosgene 19 0.3425 1.4966 11.9289 Acetone 20 0.3575 2.6482 16.5952 Acetic Acid 23 0.3750 4.1394 26.6015 Propionic Acid 6 0.3400 0.6882 23.1920

30

3.3 Designed Attractive Temperature Functions

Another use of cubic equation of state is supplying the appropriate vapor pressure

values. An accurate vapor pressure and mixtures properties prediction are important

components for a cubic equation of state in correlating the mixtures phase equlibria.

Modifications have been made to accurately predicting the vapor pressures and mixtures

properties. Applying the stability constraint of Equation 2.4 and Equation 2.5 at the

critical point, any cubic and non-cubic EOS is able to duplicate vapor pressure values.

However, an accurate vapor pressures prediction over a wide range of temperatures

requires a flexible attractive function. Introducing a temperature dependant attractive

function is a way to improve the vapor pressure prediction without negating the

prediction of thermodynamics properties of the substances. The van der Waals cubic EOS

does not include a temperature dependant attractive function. Clausius was the first to

identify that the attractive term of Equations of State should be temperature dependant.

The inclusion of temperature dependant function that can predict the pure

component vapor-pressures was made by Redlich and Kwong for their modification of

the Van der Waals cubic EOS. 69 Redlich-Kwong cubic EOS was developed to predict

the thermodynamics properties of gaseous state. It has limitations when dealing with

liquid phase. The Redlich-Kwong proposal of the temperature dependant attractive

function is: 5.0/)( TaT =α (3.2)

Improving the vapor pressure prediction, Soave proposed a new function in 1972. Soave

made a modification to the attractive function of Redlich-Kwong cubic EOS by using

acentric factor as one of the parameters. Soave modification function is the most popular

model80 for vapor pressure prediction of hydrocarbon but not for polar compounds. Soave

attractive function was developed as: 25.0 )]1(1[),( RR TmT −+=ωα (3.3)

31

CR T

TT = (3.4)

2176.0574.1480.0 ωω −+=m (3.5)

Another commonly used cubic EOS was proposed by Peng and Robinson. They

also proposed a temperature dependant attractive function and can be shown as: 25.0 )]1(1[),( RR TmT −+=ωα (3.6)

CR T

TT = (3.7)

226992.054226.137464.0 ωω −−=m (3.8)

In addition, other models of temperature functions modification can be seen in Table 3.2.

Table 3.2 shows the variations of temperature dependant attractive functions.

Many of these functions are similar to Soave-type functions. Included in the list is

another temperature dependant attractive function by Soave which was introduced in

1979. The new function was claimed to perform better than the previous one.

Twu et al. 89 90 stated that there are three fundamental requirements for useful

temperature functions. These requirements are: First, the function must be finite and

positive for all temperatures. Second, the function equals to unity at critical point. Third,

the function approaches finite value as the temperature goes to infinity. Most

temperature functions in Table 3.2 do not satisfy one or more requirements stated by Twu

et al. Many of the functions have limitation in which the function is no longer decreasing

monotonically and resulted to a negative attractive function. Figure 3.4 and Figure 3.5

showed the Soave-Redlich-Kwong and Peng-Robinson attractive function respectively.

These figures illustrated the reduced temperature point at which the attractive functions

are no longer positive for various pure components.

32

Table 3.2: Models for Attractive Temperature Function in Cubic Equations.

Expression for α(T) Authors (Poling,Valderrama) )1( 1−+ rr mTT Wilson

2rr n/Tm/T + Barner et al.

TTm rr22 )1()]1( [1 −−+ Usdin and McAuliffe

n/T m -T rTα rr ))(1(1)( ++= Soave -TC m

r )]1(exp[ Heyen

]701)1(1[ 2. / TnTm rr −+−+ Raimondi

/TmT mm rr2

321 / ++ Ishikawa et al.

TC dr )]1(exp[ − Boston and Mathias

T.TpTm rrr2)]70)(1()1(1[ −−−−+ Mathias

TmTmTm rrr3

32

21 )1()1()1(1 −+−+−+ Mathias and Copeman

/)](l [1 2rr TTm −+ Bazua

/Tm/TmT mm rrr3

42

321 / +++ Adachi and Lu

TmTm rr )1()1(1 21 −+−+ Gibbons and Laughton

)] (l [1 2nrTm ++ Kabadl and Danner

T.TnTm rrr2)]70)(1()1(1[ −−−−+ Stryjek and Vera

22 )6.0()]1(1[ −+−+ rr TnTm Adachi and Sugie

TqTpTm rrr2)])(1()1(1[ −−−−+ Du and Guo

]) -exp[(l)](exp )]/[l(exp [1 2122 kmr

m-r

mr TT-kTn.-kn ++ Twu

])(l ) (l[exp 2rTnTm r −+− Melhem et al.

)]1(1) (l[exp 11 −+−− −− TqTTp rrr Almeida et al.

))/(( ,)](1 [1 2ptc ptr TTTTm −−=−+ θθ Nasrifar and Moshfeghian

33

1.0E-04

1.0E-02

1.0E+00

1.0E+02

0 4 8 12

Reduced Temperature

Attr

activ

e Fu

nctio

n

16

MethaneNitrogenEthaneCO2Ethylene Glycol

Figure 3.5: Attractive Functions for Soave-Redlich-Kwong Equation of State.

1.0E-07

1.0E-04

1.0E-01

1.0E+02

0 4 8 12Reduced Temperature

Attr

activ

e Fu

nctio

n

16


Figure 3.6: Attractive Functions for Peng-Robinson Equation of State.

34

As can be seen in Figures 3.5 and 3.6, the proposed attractive function does not

satisfy the monotonically decreasing trend as the temperature increases (supercritical

region). Addressing those limitations, a consistent temperature function that continuously

and monotonically decreasing, equals unity at the critical point and approaching a finite

value as the temperature increases is proposed for this project as: EOS

RR TT Θ−=)(α (3.9)

Where

M 0.0036 0.3571 0.0863 0.1971 2LLS ωωω +++=Θ (3.10)

M 0.0032 0.3354 0.69050.3803 2PR ωωω +++=Θ (3.11)

M 0.0029 0.1906 0.83820.4526 2SRK ωωω +++=Θ (3.12)

This new temperature dependant attractive function is applied to the Peng-Robinson,

Soave-Redlich-Kwong and Lawal-Lake-Silberberg. The results can be seen in Figure 3.7,

Figure 3.8 and Figure 3.9 respectively.

1.0E-02

1.0E-01

1.0E+00


Attr

activ

e Fu

nctio

n

16


Figure 3.7: New Attractive Functions for Peng-Robinson Equation of State.

35

1.0E-03

1.0E-02

1.0E-01

1.0E+00


Attr

activ

e Fu

nctio

n

16


Figure 3.8: New Attractive Functions for Soave-Redlich-Kwong Equation of State.

1.0E-02

1.0E-01

1.0E+00


Attr

activ

e Fu

nctio

n

16


Figure 3.9: Attractive Functions for Lawal-Lake-Silberberg Equation of State.

36

-5

-4

-3

-2

-1

0

1 1.2 1.4 1.6 1.81/TR

ln P

RMethaneXenonCarbon Dioxiden-PentaneWaterAcetonen-DecaneEthyl Alcohol

Figure 3.10: Slope of Reduced Pressures against Reduced Temperatures.

Application of the proposed temperature dependant attractive function is not limited to

hydrocarbon substances. Figure 3.10 shows the reduced vapor pressures of several fluids

plotted against reduced temperature. The plot illustrates that the vapor pressures are

almost linear for all substances with various slopes. It can be inferred that the shape of

the vapor pressure curve is not highly dependent of the substances’ structure; instead the

curve is affected by the acentric factor values. Elliott et al.13 stated that the slope can be

characterized with acentric factor (ω), which was first introduced by Pitzer et al., as the

third parameter. The acentric factor helps specify the vapor pressure curve which

consecutively correlates the thermodynamic variables. Thus, the vapor pressure

prediction using appropriate temperature dependant attractive function can be applied not

only for predicting properties of hydrocarbon substances but also for every substance.

37

3.4 Second Virial Coefficient Calculation

The trend of the proposed temperature dependant attractive function was checked

for consistency by calculating the second virial coefficient. The coefficient is derived

from virial equation of state which is a polynomial series in pressure. The virial

coefficient is a function of temperature and has a general form of:

⎟⎟⎠

⎞⎜⎜⎝

⎛ Ω−Ω= +Θ 1

R

ab

C

C

TRTBP

(3.13)

The dimensionless parameters, Ωa and Ωb, of Equation 3.13 have been defined for various

cubic equations of state in Chapter 2.

Figures 3.11 until 3.15 show the experimental and prediction results of the virial

coefficient using Equation 3.13 for Peng-Robinson, Soave-Redlich-Kwong and Lawal-

Lake-Silberberg Equations of State. The proposed temperature dependant attractive

function was shown to be relatively accurate in predicting the virial coefficient for the

various substances. These predictions cover polar, non-polar, hydrocarbon, inert gases

and refrigerant compounds. The complete temperature function coefficients for

substances can be seen in Table 3.3.

38

Table 3.3: Theta (Θ) Values for Equations of State.

Component N ΘPR ΘSRK ΘLLS

Ammonia 64 0.6271 0.7172 0.3599 Steam 56 0.9544 1.0763 0.3322 Carbon Monoxide 14 0.3805 0.4643 0.2556 Nitrogen 18 0.3804 0.4659 0.1640 Oxygen 11 0.3415 0.4126 0.1722 Phosphine 15 0.3877 0.4716 0.1059 Hydrogen Sulfide 61 0.4741 0.5751 0.2121 Hydrogen Chloride 16 0.4865 0.5742 0.2059 Fluorine 11 0.3775 0.4690 0.2488 Carbon Dioxide 90 0.6463 0.7712 0.2640 Nitrous Oxide 14 0.5279 0.6214 0.2727 Sulfur-Dioxide 80 0.6366 0.7167 0.3887 Chlorine 31 0.4223 0.5730 0.2004 Bromine 17 0.4567 0.5310 0.2696 Methane 24 0.3393 0.4187 0.1398 Ethane 87 0.4467 0.5018 0.2379 Propane 79 0.5279 0.6214 0.2727 n-Butane 61 0.5964 0.7350 0.2880 i-Butane 76 0.5750 0.6773 0.3218 n-Pentane 61 0.6569 0.6638 0.3122 i-Pentane 62 0.5970 0.7077 0.3249 n-Hexane 53 0.7218 0.8045 0.4341 n-Heptane 36 0.7368 0.8397 0.3952 n-Octane 31 0.8580 0.9130 0.4417 n-Decane 25 0.8539 0.9468 0.6272 Benzene 21 0.6059 0.7134 0.2935 Fluorobenzene 20 0.6476 0.7509 0.2870 Chlorobenzene 28 0.6532 0.6667 0.3202 Bromobenzene 13 0.6424 0.7421 0.3200 Iodobenzene 11 0.6341 0.7304 0.3336 Acetylene 13 0.5684 0.6645 0.2578 Ethylene 37 0.4444 0.5321 0.1902 1-3-Butadiene 28 0.5493 0.6231 0.3849 Cyclohexane 19 0.6863 0.7009 0.3413

39

Table 3.3(Continued)

Component N ΘPR ΘSRK ΘLLS

Methyl Alcohol 21 0.9907 1.1076 0.4468 Ethyl Alcohol 19 1.0742 1.1966 0.5841 Propyl Alcohol 18 1.0424 1.1655 0.5524 Methyl Chloride 44 0.5271 0.6088 0.2819 Ethyl-Chloride 38 0.5597 0.6405 0.3401 Carbon Tetrachloride 22 0.5818 0.6809 0.2722 Stannic Chloride 15 0.6610 0.7629 0.3401 Deuterium 11 0.1268 0.1932 0.0223 Methyl Propionate 19 0.7643 0.8726 0.3749 Ethyl Propionate 21 0.8184 0.9314 0.4192 Methyl-n-Butyrate 20 0.8091 0.9223 0.4042 Methyl-iso-Butyrate 20 0.7893 0.9016 0.3915 Methyl Acetate 21 0.7327 0.7867 0.3507 Ethyl Acetate 22 0.7820 0.8919 0.3668 Propyl Acetate 15 0.8221 0.9368 0.3899 Methyl Ether 19 0.5887 0.6107 0.4098 Methyl Ethyl Ether 18 0.6196 0.7476 0.2938 Ethyl Ether 19 0.6810 0.8383 0.3132 Ethyl Propyl Ether 21 0.7193 0.8278 0.4346 Methyl Mercaptan 21 0.5169 0.6850 0.2176 Ethyl Mercaptan 21 0.5728 0.6558 0.3054 Acetonitrile 21 0.7175 0.4000 0.0825 Propionitrile 22 0.7644 0.6197 0.1773 Methyl Formate 20 0.6476 0.7037 0.2878 Ethyl Formate 21 0.6835 0.8207 0.3131 Propyl Formate 18 0.7251 0.8324 0.3511 Dimethyl Sulfide 21 0.5610 0.7189 0.2772 Diethyl Sulfide 20 0.6697 0.7742 0.3681 Diethylamine 19 0.7141 0.7538 0.3532 Triethylamine 21 0.7240 0.8270 0.3661 Carbon Tetrafluoride 20 0.5501 0.6407 0.2954 Phosgene 19 0.5818 0.6771 0.3505 Acetone 20 0.7065 0.8722 0.2563 Acetic Acid 23 0.8771 0.9894 0.2683 Propionic Acid 6 0.9540 1.0635 0.5410

40

-1.5

-1.1

-0.7

-0.3

0.5 0.6 0.7 0.8 0.9Reduced Temperature

BP C

/RT C

Methyl BromidePropanenButaneSRKPRLLS

Figure 3.11: Second Virial Coefficients for Substances.

-1.6

-1.2

-0.8

-0.4

0

0.4 0.8 1.2 1.6 2 2.4Reduced Temperature

BP C

/RT C

ExpSRKPRLLS

Figure 3.12: Second Virial Coefficients for n-Octane.

41

-1.2

-0.8

-0.4

0

0.4 0.8 1.2 1.6 2 2.4Reduced Temperature

BP C

/RT C

ExpSRKPRLLS

Figure 3.13: Second Virial Coefficients for Argon.

-1.2

-0.8

-0.4

0

0.4

0 2 4 6 8 10 12Reduced Temperature

BP C

/RT C

14

ExpSRKPRLLS

Figure 3.14: Second Virial Coefficients for Hydrogen.

42

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.4 0.9 1.4 1.9Reduced Temperature

BP C

/RT C

2.4

ExpSRKPRLLS

Figure 3.15: Second Virial Coefficients for HFC-114.

3.5 Prediction of Phase Densities for Pure Hydrocarbons

Densities of defined pure hydrocarbon substances were predicted based on LLS

EOS. Figure 3.16 until Figure 3.19 show densities prediction of methane, n-pentane, n-

hexane and n-decane respectively. The average absolute percent deviations of liquid

(AAPDL) and vapor (AAPDV) for methane, n-pentane, n-hexane and n-decane were

calculated and summarized in Table 3.4. In most cases the liquid average deviation is less

than vapor average deviation. More densities prediction of pure hydrocarbon can be seen

in Appendix C.

Table 3.4: AAPDL and AAPDV for Hydrocarbon Substances.

Component AAPDL AAPDV Methane 2.403 10.208 n-Pentane 1.810 7.225 n-Hexane 3.753 2.588 n-Decane 6.846 7.879

43

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

150 200 250 300 350Temperature (oR)

Den

sity

(lbm

ol/ft

3 )

ExpPred

Figure 3.16: Prediction of Phase Densities for Methane.

0

0.1

0.2

0.3

0.4

0.5

0.6

520 570 620 670 720 770 820 870

Temperature(oR)

Den

sity

(lbm

ol/ft

3 )

ExpPred

Figure 3.17: Prediction of Phase Densities for n-Pentane.

44

0

0.15

0.3

0.45

500 600 700 800 900 1000Temperature (oR)

Den

sity

(lbm

ol/ft

3 )

ExpPred

Figure 3.18: Prediction of Phase Densities for n-Hexane.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

550 650 750 850 950 1050 1150Temperature(oR)

Den

sity

(lbm

ol/ft

3 )

ExpPred

Figure 3.19: Prediction of Phase Densities for n-Decane.

45

3.6 Prediction of Phase Densities for Non-Hydrocarbons

Densities of non hydrocarbon substances have been predicted. Figure 3.20

through Figure 3.22 show densities prediction of Carbon Dioxide (CO2), Hydrogen

Sulfide (H2S) and Nitrogen (N2). The AAPDL and AAPDV were calculated and

summarized in Table 3.5. The results show average deviation for liquid density prediction

is less than the vapor phase. More densities prediction of non-hydrocarbon substances

can be seen in Appendix C.

Table 3.5: AAPDL and AAPDV for Non-Hydrocarbon Substances.

Component AAPDL AAPDV Carbon Dioxide 1.824 5.515

Hydrogen Sulfide 2.720 5.488 Nitrogen 2.194 4.865

0

0.6

1.2

1.8

370 420 470 520 570Temperature (oR)

Den

sity

(lbm

ol/ft

3 )

ExpPred

Figure 3.20: Prediction of Phase Densities for Carbon Dioxide.

46

0

0.4

0.8

1.2

1.6

2

370 410 450 490 530 570 610 650 690Temperature (oR)

Den

sity

(lbm

ol/ft

3 )

ExpPred

Figure 3.21: Prediction of Phase Densities for Hydrogen Sulfide.

0

0.4

0.8

1.2

1.6

2

110 130 150 170 190 210 230Temperature (oR)

Den

sity

(lbm

ol/ft

3 )

ExpPred

Figure 3.22: Prediction of Phase Densities for Nitrogen.

47

3.7 Prediction of Phase Densities for Polar Substances

Polar substances densities prediction is challenging for many available Equations

of State. The LLS EOS was used to predict densities of polar substances. Figure 3.23

through Figure 3.26 show densities prediction of Steam (H2O), Propyl Acetate (C5H10O2),

Methanol (CH4O) and Ethanol (C2H6O) respectively. The AAPDL and AAPDV were

calculated and summarized in Table 3.6. The results show average deviation for liquid

density prediction is less than the vapor phase. More densities prediction of polar

substances can be seen in Appendix C.

Table 3.6: AAPDL and AAPDV for Polar Substances.

Component AAPDL AAPDV Steam 2.518 2.514

Propyl Acetate 2.833 5.191 Methanol 2.493 3.913 Ethanol 5.057 9.217

0

0.5

1

1.5

2

2.5

3

3.5

580 680 780 880 980 1080 1180Temperature (oR)

Den

sity

(lbm

ol/ft

3 )

ExpPred

Figure 3.23: Prediction of Phase Densities for Steam.

48

0

0.1

0.2

0.3

0.4

0.5

660 710 760 810 860 910 960 1010Temperature (oR)

Den

sity

(lbm

ol/ft

3 )

ExpPred

Figure 3.24: Prediction of Phase Densities for Propyl Acetate.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

600 650 700 750 800 850 900 950Temperature (oR)

Den

sity

(lbm

ol/ft

3 )

ExpPred

Figure 3.25: Prediction of Phase Densities for Methanol.

49

0

0.2

0.4

0.6

0.8

1

1.2

610 660 710 760 810 860 910 960Temperature (oR)

Den

sity

(lbm

ol/ft

3 )

ExpPred

Figure 3.26: Prediction of Phase Densities for Ethanol.

3.8 Prediction of Phase Densities for Refrigerant Substances

The LLS EOS was also applied to predict densities of refrigerant substances.

Figure 3.26 through Figure 3.29 show densities prediction of Refrigerant-32, Refrigerant

134a, Refrigerant 152a and Refrigerant 227. The AAPDL and AAPDV were calculated

and summarized in Table 3.7. The results show average deviation for liquid density

prediction is less than the vapor phase. More densities prediction of refrigerant

substances can be seen in Appendix C.

Table 3.7: AAPDL and AAPDV for Refrigerant Substances.

Component AAPDL AAPDV Refrigerant-32 1.833 3.190

Refrigerant 134a 3.025 N/A Refrigerant 152a 3.026 6.127 Refrigerant 227 1.751 12.865

50

0

5

10

15

20

25

220 240 260 280 300 320 340 360Temperature (K)

Satu

rate

d D

ensi

ty (k

g/m

3 )

ExpPred

Figure 3.27: Prediction of Phase Densities for Refrigerant 32.

0

0.2

0.4

0.6

0.8

1

420 470 520 570 620 670 720Temperature(oR)

Den

sity

(lbm

ol/ft

3 )

ExpPred

Figure 3.28: Prediction of Phase Densities for Refrigerant 152a.

51

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

400 450 500 550 600 650 700Temperature (oR)

Den

sity

(lbm

ol/ft

3 )

ExpPred

Figure 3.29: Prediction of Phase Densities for Refrigerant 134a.

0

0.1

0.2

0.3

0.4

0.5

0.6

470 500 530 560 590 620 650 680Temperature (oR)

Den

sity

(lbm

ol/ft

3 )

ExpPred

Figure 3.30: Prediction of Phase Densities for Refrigerant 227.

52

3.9 Prediction of Phase Densities for Miscellaneous Substances

In addition, the LLS EOS was applied to predict densities of miscellaneous

substances such as inert gases. Figure 3.30 and Figure 3.31 show densities prediction of

Argon and Sulfur Dioxide. The AAPDL and AAPDV were calculated and summarized in

Table 3.8. The results show average deviation for liquid density prediction is less than the

vapor phase. More densities prediction of miscellaneous substances can be seen in

Appendix C.

Table 3.8: AAPDL and AAPDV for Miscellaneous Substances.

Component AAPDL AAPDV Argon 2.006 10.310

Sulfur Dioxide 2.568 3.050

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

570 620 670 720 770 820 870 920Temperature (oR)

Den

sity

(lbm

ol/ft

3 )

ExpPred

Figure 3.31: Prediction of Phase Densities for Argon.

53

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

500 550 600 650 700 750 800Temperature (oR)

Den

sity

(lbm

ol/ft

3 )

ExpPred

Figure 3.32: Prediction of Phase Densities for Carbon Dioxide.

3.10 Designed van der Waals Critical Limit for Pure Substances

The van der Waals EOS can be expressed as follows:

2va

bvRTP −−

= (3.14)

where:

P

RTvb

PTR

aC

CC

C

C

83 ,

6427 22

=== (3.15)

Based on Equation 3.14 and Equation 3.15 the following parameters can be deduced:

T

vPRZ

C

CCC 3

8 ,

83 vdw == (3.16)

Fixing the value of ZC limits the EOS capabilities in predicting the true critical properties

of pure components or mixtures as not all pure components has the same value of ZC.

54

Improving the ability of equation of state in predicting the critical properties, LLS

EOS established ZC as a function of α and β and can be shown as:

)1(3

1−Ω+

=αw

CZ (3.17)

Parameter ΩW is a function of acentric factor and can be seen in Equation3.1.

Equation 3.17 was deduced from the coefficient comparison of LLS EOS for pure

substances (Equation 2.22) and expansion of ( ) 03 =− Cvv . The limit for the LLS EOS at

the critical point was developed as:

(3.18)

C

C

C

TTLimPPLimbvLim

→→→

3.11 Prediction of Critical Densities for Pure Substances

Applying the Van der Waals critical limit to the LLS EOS the critical densities of

pure substances can be calculated. Figure 3.32 through Figure 3.35 show the prediction of

critical densities of hydrocarbon, non-hydrocarbon, polar and refrigerant substances. The

absolute average percent deviations (AAPD) for these components were summarized in

Table 3.9.

55

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

C1 C2 C3 n-C4 n-C5 n-C6 n-C7 n-C8 n-C10

Component Name

Crit

ical

Den

sitie

s (lb

mol

/ft3 )

ExpPred

Figure 3.33: Prediction of Critical Densities for Hydrocarbon Substances.

0.62

0.64

0.66

0.68

0.7

0.72

0.74

HCl N2 CO2 H2S

Component Name

Crit

ical

Den

sitie

s (lb

mol

/ft3 )

ExpPred

Figure 3.34: Prediction of Critical Densities for Non-Hydrocarbon Substances.

56

0

0.2

0.4

0.6

0.8

1

1.2

H2O NH3 HCl CO PH3 C3H8OComponent Name

Crit

ical

Den

sitie

s (lb

mol

/ft3 )

ExpPred

Figure 3.35: Prediction of Critical Densities for Polar Substances.

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

R 32 R152a R134a R12 R11 R227Component Name

Crit

ical

Den

sitie

s (lb

mol

/ft3 )

ExpPred

Figure 3.35: Prediction of Critical Densities for Refrigerant Substances.

57

Table 3.9: AAPD for Critical Densities Prediction of Pure Substances.

Component AAPD Methane 0.763116 Ethane 1.848341 Propane 0.259994 n-Butane 0.203998 n-Pentane 2.873843 n-Hexane 0.058893 n-Heptane 0.138889 n-Octane 0.235849 n-Decane 0.1 Hydrogen Chloride 0.013774 Nitrogen 0.575954 Carbon Dioxide 1.108917 Hydrogen Sulfide 0.922884 Steam 2.479188 Ammonia 4.436702 Carbon Monoxide 1.833358 Phosphine 0.181521 Propanol 1.021127 Refrigerant 32 0.981147 Refrigerant 152a 0.983392 Refrigerant 134a 0.002831 Refrigerant 12 0.242887 Refrigerant 11 0.437202 Refrigerant 227 0.091324

58

CHAPTER IV

CRITICAL DENSITIES FOR BINARY MIXTURES

The LLS cubic equation of state method for predicting the orthobaric densities for

pure component was developed and discussed in the previous chapters. The LLS cubic

equation of state can be extended to predict the binary, ternary and multi-component

mixtures by applying the appropriate mixing rules proposed by Lawal et al. 42 to the

mixing parameters. These mixing rules relate the pure component parameters to the

composition of the mixture.

This chapter discusses the analogy of critical point between pure component and

mixtures and shows the phase equilibrium for mixtures. In addition, the flash routine is

discussed and prediction results for binary, ternary and multi-component systems are

shown for critical volumes and densities.

4.1 Critical Point for Mixtures by Analogy to Pure Substances

Understanding the pressure-temperature-volume relationship of a pure component

is a fundamental basis of predicting mixtures behavior. The pressure-temperature and

pressure-volume behavior of a pure substance can be seen in Figure 4.1 and Figure 4.2

respectively.

Figure 4.1: Pressure-Temperature Diagram for Pure Substances.

Pres

sure

Liquid

T

Pc C

Solid Gas

TcTemperature

59

Tc

Pres

sure

Volume Figure 4.2: Pressure-volume Diagram for Pure Substances.

The behavior of a two or more component mixture is more complex than a pure

compound. Binary, ternary and multi-component mixtures are formed by combination of

pure substances which has one point in the Pressure-Temperature and Pressure-volume

diagrams for their critical point. As described in Chapter 1, the critical point for a pure

substance is defined as a point where there is no more properties distinction between two

phases. This definition is no longer valid for mixtures because it is possible that both the

vapor and liquid phase exist after the critical point.

Combination of several pure substances forms a mixture. This mixture has a

unique point as the critical state. The critical point for mixtures is defined simply as a

conjunction point of bubble- and dew-point line. Bubble-point is the pressure condition at

which the first bubble is formed while dew-point is the pressure where the amount of

liquid is minute. The Pressure-Temperature and Pressure-volume relation for mixtures

can be seen in Figure 4.3 and Figure 4.4 respectively. In Figure 4.3, the term

cricondenbar means the highest pressure above which no gas can be formed for that

mixture while the term cricondenterm means the highest temperature above which a

liquid cannot occur for a particular mixture.

60

Figure 4.3: Pressure-Temperature Diagram for Mixtures (McCain55)

Figure 4.4. Pressure-volume Diagram for Mixtures (McCain55).

61

4.2 Critical Volume Prediction Methods

The detail methods for predicting critical volume of pure substances and mixtures have

been described by the books published by Elliot-Lira13 and Poling et al.65; the methods

range from empirical to corresponding state to group contribution techniques to equations

of state techniques. The equation of state technique that is based on the LLS EOS is used

in this project to demonstrate the robustness of near-critical flash routine and the stable

convergence of vapor-liquid densities (or coexistence densities) at the fluid and fluid

mixture critical point.

The following derivation is implemented in Section 3.11 for predicting the critical

volume of pure substances. Equation A.50 of Appendix A can be simplified for pure

substances as:

0432

23

1 =Θ+ΩΘ+ΩΘ+ΩΘ bbb (4.1)

where the coefficients Θ1, Θ2, Θ3, Θ4 of Equation 4.1 can be expressed as:

8612 321 +++=Θ ααα (4.2)

22 3271515 αβα −−+=Θ (4.3)

α363 +=Θ (4.4)

(4.5) 14 −=Θ

Equations 4.1-4.5 can be rearranged as in Equation 4.6:

23

2231

271)31515(

b

bbb

Ω

−ΩΘ+Ω−++ΩΘ=

ααβ (4.6)

62

The critical compressibility factor equation derived in Appendix A from the LLS EOS

can be expressed for pure substances as in Equation 4.7:

0012

23

3 =+++ θθθθ ccc ZZZ (4.7) where the coefficients of Equation 4.7 are expressed as

)(

6663

)9912123(

6128

20

21

22

323

βαβαθ

βαβααθ

βαβααθ

αααθ

−+−=

−++=

−+++−=

+++=

Equation 4.7 can be arranged in terms of Zc and αm as in Equation 4.8:

)1(66)99()63()12123()6128(

2

2222332

ααααααααααα

β−++−−

−++++−+++=

ccc

ccc

ZZZZZZ

(4.8)

By expressing Equation 4.6 and Equation 4.8 in terms of Zc and α, the following function

can be formed, as in Equation 4.9:

),(),()( bcc ZfZ Ω−=Φ αψα (4.9)

Equation 4.9 provides a unique value for Zc factor from a guess value of α via Newton-

Raphson iterative algorithm. The parameter Ωb has been expressed in term of Zc in

Chapter 2 (Equation 2.25). Knowing the Zc factor from Equation 4.9, critical volume of

defined pure substances (Pc and Tc are known) can be derived from Equation 4.10:

c

ccc P

RTZv = (4.10)

63

The prediction results for the critical volumes of pure substances are shown in Figures

3.33-3.35. The results are generally within 1% of the experimental values.

Similar process can be performed form the critical volumes of mixtures. In that case, the

mixture forms of Equations 4.1 - 4.7 are applied. Equation A.50 of Appendix A can be

simplified as:

0432

23

1 =Θ+Θ+Θ+Θ CCC BBB (4.11)

where the coefficients are Θ1, Θ2, Θ3, Θ4 of Equation 4.11 defined by:

8612 321 +++=Θ mmm ααα (4.12)

22 3271515 mmm αβα −−+=Θ (4.13)

mα363 +=Θ (4.14)

14 −=Θ (4.15)

It can be seen from Equation 4.11that ),( mmC fB βα= . It is therefore imperative to solve

βm as a function of BC and αm as shown in Equation 4.16, solving for βm yields:

23

2231

271)31515(

C

CCmmCm B

BBB −Θ+−++Θ=

ααβ (4.16)

64

Equation 4.7 can also be used for the composition dependent critical compressibility

factor can be expressed as in Equation 4.17.60

001

22

33 =+++ θθθθ ccc ZZZ (4.17)

where

)(

6663

)9912123(

6128

20

21

22

323

mmmm

mmmmm

mmmmm

mmm

βαβαθ

βαβααθ

βαβααθ

αααθ

−+−=

−++=

−+++−=

+++=

Equation 4.17 can be arranged in terms of Zc and αm as in Equation 4.18:

)1(66)99()63()12123()6128(

2

2222332

mcmccm

mcmmcmmcmmmm ZZZ

ZZZααα

ααααααααβ−++−−

−++++−+++= (4.18)

Equation 4.9 provides a unique value for the mixture Zc factor from a guess value of αm

via Newton-Raphson iterative algorithm. Also, by judiciously selecting the interaction

parameters for parameters αm and βm, Equation 4.17 is readily resolved for the Zc factor

of mixture. That technique is used in this project to derive the critical volumes for

mixtures.

4.3 Critical Volume for Binary Hydrocarbon Systems

Figures 4.5 - 4.8 show the prediction results from the critical volumes of methane binary

systems. Expect for the scatters in the experimental data, the prediction results are within

1.5% of the experimental data. Figures 4.9 - 4.11 show the prediction results from the

critical volumes of ethane binary systems. The prediction results are within 1.6% of the

65

experimental data. Figures 4.12 - 4.16 show the prediction results from the critical

volumes of propane binary systems. The prediction results are within 2.1% of the

experimental data. Figures 4.17 - 4.21 show the prediction results from the critical

volumes of n-butane binary systems. The prediction results are within 1.9% of the

experimental data.

4.4 Critical Volume for Binary Non-Hydrocarbon Systems

Figure 4.22 shows the prediction results from the critical volumes of carbon dioxide in

hydrogen sulfide binary systems. The prediction results are within 3.5% of the

experimental data because of the scatter in the measured data. Figures 4.23 - 4.25 show

the prediction results from the critical volumes of carbon dioxide in paraffin hydrocarbon

binary systems. Expect for the scatters in the experimental data, the prediction results are

within 2.5% of the experimental data.

4.5 Analysis of Prediction Results for Mixture Critical Volumes

The prediction results shown in Sections 4.3 - 4.4, show that technique described in

Section 4.2 can be an aid to the experimentalists, particularly where measurement of

critical volumes are difficult due to thermal decomposition of the substance: such as

unstable substances and petroleum fractions.

66

1.5

2

2.5

3

3.5

4

4.5

1.5 2 2.5 3 3.5 4 4.5VC Experimental(ft3/lbmol)

V C C

alcu

late

d(ft3

/lbm

ol)

Figure 4.5: Predicted Critical Volume in Methane-Propane System

1

1.5

2

2.5

3

3.5

4

1 1.5 2 2.5 3 3.5 4VC Experimental(ft3/lbmol)

V C C

alcu

late

d(ft3 /lb

mol

)

Figure 4.6: Predicted Critical Volume in Methane-n-Butane System

67

1

2

3

4

5

6

1 2 3 4 5VC Experimental(ft3/lbmol)

V C C

alcu

late

d(ft3 /lb

mol

)

6

Figure 4.7: Predicted Critical Volume in Methane-n-Pentane System

1

1.5

2

2.5

3

3.5

4


VC C

alcu

late

d(ft3 /lb

mol

)

Figure 4.8: Predicted Critical Volume in Methane-n-Decane System

68

2

2.5

3

3.5

4

2 2.5 3 3.5VC Experimental(ft3/lbmol)

VC C

alcu

late

d(ft3 /lb

mol

)

4

Figure 4.9: Predicted Critical Volume in Ethane-n-Butane System

2

2.5

3

3.5

4

4.5

5

5.5

6

2 2.5 3 3.5 4 4.5 5 5.5VC Experimental(ft3/lbmol)

VC C

alcu

late

d(ft3 /lb

mol

)

6

Figure 4.10: Predicted Critical Volume in Ethane-n-Heptane System

69

1

1.5

2

2.5

3

3.5

4


VC C

alcu

late

d(ft3 /lb

mol

)

Figure 4.11: Predicted Critical Volume in Ethane-n-Decane System

3

3.5

4

4.5

3 3.5 4 4VC Experimental(ft3/lbmol)

VC C

alcu

late

d(ft3 /lb

mol

)

.5

Figure 4.12: Predicted Critical Volume in Propane-n-Butane System

70

3

3.5

4

4.5

5


VC C

alcu

late

d(ft3 /lb

mol

)

5

Figure 4.13: Predicted Critical Volume in Propane-n-Pentane System

3

3.5

4

4.5

5

5.5

6


VC C

alcu

late

d(ft3 /lb

mol

)

Figure 4.14: Predicted Critical Volume in Propane-n-Hexane System

71

3

4

5

6

7

8

3 4 5 6 7VC Experimental(ft3/lbmol)

VC C

alcu

late

d(ft3 /lb

mol

)

8

Figure 4.15: Predicted Critical Volume in Propane-n-Octane System

3

3.2

3.4

3.6

3.8

4

4.2

4.4

4.6

4.8

5


VC C

alcu

late

d(ft3 /lb

mol

)

5

Figure 4.16: Predicted Critical Volume in Propane-n-Decane System

72

4

4.2

4.4

4.6

4.8

5

4 4.2 4.4 4.6 4.8 5VC Experimental(ft3/lbmol)

VC C

alcu

late

d(ft3 /lb

mol

)

Figure 4.17: Predicted Critical Volume in n-Butane-n-Pentane System

4

4.5

5

5.5

6

6.5

4 4.5 5 5.5 6 6VC Experimental(ft3/lbmol)

VC C

alcu

late

d(ft3 /lb

mol

)

.5

Figure 4.18: Predicted Critical Volume in n-Butane-n-Hexane System

73

4

4.5

5

5.5

6

6.5

7


VC C

alcu

late

d(ft3 /lb

mol

)

Figure 4.19: Predicted Critical Volume in n-Butane-n-Heptane System

4

4.5

5

5.5

6

6.5

7

7.5

8


VC C

alcu

late

d(ft3 /lb

mol

)

8

Figure 4.20: Predicted Critical Volume in n-Butane-n-Octane System

74

4

4.2

4.4

4.6

4.8

5

4 4.2 4.4 4.6 4.8 5VC Experimental(ft3/lbmol)

VC C

alcu

late

d(ft3 /lb

mol

)

Figure 4.21: Predicted Critical Volume in n-Butane-n-Decane System

1.4

1.45

1.5

1.55

1.6

1.4 1.45 1.5 1.55VC Experimental(ft3/lbmol)

VC C

alcu

late

d(ft3 /lb

mol

)

1.6

Figure 4.22: Predicted Critical Volume in Carbon Dioxide-Hydrogen Sulfide System

75

2

2.5

3

3.5

4


VC C

alcu

late

d(ft3 /lb

mol

)

4

Figure 4.23: Predicted Critical Volume in Carbon Dioxide-n-Butane System

1

1.5

2

2.5

3

3.5

4

4.5

5


VC C

alcu

late

d(ft3 /lb

mol

)

5

Figure 4.24: Predicted Critical Volume in Carbon Dioxide-n-Hexane System

76

1

1.5

2

2.5

3

3.5

4


VC C

alcu

late

d(ft3 /lb

mol

)

Figure 4.25: Predicted Critical Volume in Carbon Dioxide-n-Decane System

77

CHAPTER V

CONCLUSIONS AND RECOMMENDATIONS

The primary objective of this project is to develop a reliable and robust method to

predict the density of pure component and mixtures. The method used in predicting phase

densities for pure components is used as a foundation to analyze critical densities of

binary, ternary and multi-component mixtures.

5.1 Conclusions

The conclusions drawn from the results of this project can be stated as:

1. A robust technique is developed for predicting the volumetric

properties of pure substances and critical densities of binary systems.

2. A comprehensive experimental data sets on vapor pressures and

orthobaric densities data for pure substances (hydrocarbons, non-

hydrocarbons, polar, non-polar and refrigerants) have been tabulated

into the data bank of the Center for Applied Petrophysical and

Reservoir Studies.

3. The Van der Waals critical limit parameter (Ωw) correlation for pure

substances (hydrocarbons, non-hydrocarbons, polar, non-polar and

refrigerants) that is consistent with the coexistence vapor-liquid phase

densities has been developed for use in thermodynamic and transport

property correlations.

4. A new attractive-temperature function has been designed for cubic

equations of state, the framework of the temperature function is used

to predict second virial coefficient of pure substances. The prediction

results shown for three cubic equations of state (SRK, PR and LLS)

show the temperature function is applicable to sub- and super-critical

78

fluid behavior. The temperature function is also consistent with the

mathematical constraint established for the theory of cubic equations

of state: as reduced temperature 0)( →Ta .∞→RT

5. Vapor pressures for pure substances and saturated vapor-liquid

volumes of pure substances are accurately predicted with the

temperature function; the prediction results are generally within 0.5%

of the experimental data.

6. Near-critical flash computations for phase densities are resolved for

pure substances and binary mixtures by accurately predicting critical

densities of the fluid and fluid mixture with analytical solution derived

from the LLS EOS. The prediction results are generally within 0.5%

to 3.5% of the experimental measurements.

7. The Lawal-Lake-Silberberg equation of state is also demonstrated as

the foundation for developing a closed-form van der Waals critical

density routine for the prediction of subcritical, critical and

supercritical regions volumetric properties.

5.2 Recommendations

It is recommended that the method developed for the phase densities of pure substances

and the critical volumes of binary systems be extended to ternary and multicomponent

systems. The success of the techniques would provide a basis for the development of a

predictive equation-of-state for reservoir fluids.

79

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86

APPENDIX A

LAWAL-LAKE-SILBERBERG EQUATION OF STATE

A.1 Transformed LLS Equation of State.

The LLS EOS has been introduced in Equation 2.22 as:

( )22 bbvv

Tabv

RTPβα −+

−−

=

The real gas equation can be expressed as:

RTPvZ = (A.1)

Multiplying Equation A.1.1 byRTv :

⎟⎟⎠

⎞⎜⎜⎝

⎛−+

−−

= 22

)(bbvv

Tabv

RTRTv

RTvP

βα (A.2)

Rearranging and putting in terms of the Z-form for : v

22

)(

bP

ZRTbP

ZRTP

ZRTRTTa

bP

ZRTP

ZRT

Zβα −+⎟

⎠⎞

⎜⎝⎛

−−

= (A.3)

Multiplying byRTP :

22

2

2)(

⎟⎠⎞

⎜⎝⎛

⎥⎥⎦

⎤

⎢⎢⎣

⎡−+⎟

⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛

−−

=

RTPb

PZRTb

PZRT

RTP

PZRT

RTTa

RTPb

RTP

PZRT

RTP

PZRT

Z

βα

(A.4)

Rearranging yield:

( )2

2

2)(

⎟⎠⎞

⎜⎝⎛−+

−−

=

RTbPZ

RTbPZ

ZRT

PTa

RTbPZ

ZZβα

(A.5)

87

Assume:

( )2)(

RTPTaA = (A.6)

RTbPB = (A.7)

Inserting Equation A1.7 and Equation A1.8 to Equation A1.6 yield:

22 BBZZAZ

BZZZ

βα −+−

−= (A.8)

Dividing each side with Z:

22

11BBZZ

ABZ βα −+−

−= (A.9)

Multiplying each side with , Equation 2.22 can be expressed in

Z-form as:

))(( 22 BBZZBZ βα −+−

ABAZBBZZBBZZBZ −−−+=−+− 2222 ))(( βαβα (A.10)

Rearranging:

0432

23

1 =Θ−Θ+Θ−Θ ZZZ (A.11)


11 =Θ (A.12)

[ ]B)1(12 α−+=Θ (A.13)

])([ 23 BBA αβα +−−=Θ (A.14)

)]([ 324 BBAB −−=Θ β (A.15)

Similarly, The LLS EOS that has been introduced in Equation 2.22 can be expressed in

the v-form by expanding Equation 2.22 into the molar volume term yield:

( ) )()())(( 2222 bvTabbvvRTbbvvbvP −−−+=−+− βαβα (A.16)

Grouping the appropriate terms yield:

0432

23

1 =Θ−Θ+Θ−Θ vvv (A.17)


88

11 =Θ (A.18)

⎥⎦⎤

⎢⎣⎡ +−=Θ

PRTbb α2 (A.19)

⎥⎦⎤

⎢⎣⎡ +−−=Θ 2

3 )( bP

RTbPa βαα (A.20)

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ +−=Θ β

PRTbb

Pab 23

4 (A.21)

89

A.2 Fugacity for LLS Equation of State.

The fugacity equation for LLS EOS can be shown as:

dPPRT

vPf p

p 1ln

*∫ ⎟⎠⎞

⎜⎝⎛ −= (A.22)

The real gas law equation used in the derivation can be shown as:

(A.23) ZRTPv =

Equation A.22 can be separated into 2 integration:

∫∫ −=P

P

P

P PdPdP

RTv

Pf

**ln (A.24)

Starting the integration procedure

****ln

*1ln

PPdvPvP

TRPf v

v

pv

vp−⎥⎦

⎤⎢⎣⎡ ⋅−= ∫ (A.25)

**

**

ln 1lnPPdvP

RTRTPv

RTvP

Pf v

v−⋅−−= ∫ (A.26)

At the condition of P* is equal 0, Z is equal to 1. Applying Equation 2.22 yield:

** 22 ln11lnPPdv

bbvva

bvRT

RTZ

Pf v

v−⎟⎟

⎠

⎞⎜⎜⎝

⎛−−

−−

−−= ∫ βα (A.27)

** 22*ln111ln

PPdv

bbvva

RTdv

bvZ

Pf v

v

v

v−

−−+

−−−= ∫∫ βα

(A.28)

( )

( )( ) ( )( )dv

bvbvRTa

PPbvZ

Pf

v

v

v

v

24

24

1

lnln1ln

* 5.025.02

**

∫⎥⎦⎤

⎢⎣⎡ +−+⎥⎦⎤

⎢⎣⎡ +++

+

−−−−=

βααβαα

(A.29)

( )( ) ( )( ) ⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

⎥⎦⎤

⎢⎣⎡ +−+

−

⎥⎦⎤

⎢⎣⎡ +++

++−⎟

⎠⎞

⎜⎝⎛

−−

−−=

∫ ∫v

v

v

vdv

bvdv

bv

bRT

a

PP

bvbvZ

Pf

* * 5.025.02

5.02**

24

1

24

1

)4(lnln1ln

βααβαα

βα

(A.30)

90

( )( )

v

v

bv

bv

bRT

a

PP

RTRT

bvbvZ

Pf

*

5.02

5.02

5.02

**

2)4(2)4(

ln)4(

lnln1ln

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

+−+

+++

++

−⎟⎠⎞

⎜⎝⎛ ÷

−−

−−=

βαα

βαα

βα

(A.31)

The value of v* is a lot bigger than b, thus b can be neglected.

( )( ) ⎟⎟

⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

+−+

++++

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

×

−

−−=RT

PRT

P

bv

bv

bRT

a

PP

RTvRT

bv

ZPf

2)4(2)4(

ln22

ln1ln5.02

5.02

** βαα

βαα (A.32)

( )( ) ⎟⎟

⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

+−+

+++

++

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛−

−−=

RTP

RTP

bv

bv

RTP

RTP

bRT

aRT

vPRTbP

RTPv

ZPf

2)4(2)4(

ln)4(

ln1ln

5.02

5.02

5.02

**

βαα

βαα

βα

(A.33)

Assuming that:

22TRaPA = (A.34)

RTbPB = (A.35)

The above equation can be rewritten as:

( )( )

( ) ⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

+−+

+++

++−−−=

2)4(

2)4(

ln)4(

ln1ln5.02

5.02

5.02 BZ

BZ

BABZZ

Pf

βαα

βαα

βα (A.36)

91

A.3 Critical Volume Methods for Mixtures.

The LLS EOS for mixtures has been established and shown in Equation 2.28 as:

22mmmm

m

m bba

bRTP

βνανν −+−

−=

This equation can be expanded into molar volume terms as:

( )( ) ( ) ( mmmmmmmmmmm babbRTbbbP −−−+=−+− νβνανβνανν 2222 ) (A.37)

It can be simplify to a cubic equation as:

0432

23

1 =Θ−Θ+Θ−Θ vvv (A.38)


11 =Θ (A.39)

PRTbb mmm +−=Θ α2 (A.40)

( ) 23 mmmmm

m bP

RTbPa

βαα +−−=Θ (A.41)

mmmmm

PRTbb

Pba

β⎟⎠⎞

⎜⎝⎛ +−=Θ 23

4 (A.42)

The criticality condition in terms of molar volume and critical volume is:

( ) 03 =− Cvv (A.43)

Expanding yield:

(A.44) 033 3223 =−+− CCC vvvvvv

Comparing the molar volume (v) coefficient of Equation A36 to Equation A.42 yield:

P

RTbbv mmmC +−= α3 (A.45)

( 223 mmmmmm

C bP

RTbPa

v βαα +−−= ) (A.46)

mmmmm

C PRTbb

Pba

v β⎟⎠⎞

⎜⎝⎛ +−= 233 (A.47)

The dimensionless parameter at critical condition for mixtures was defined as:

92

22C

CmC TR

PaA = (A.48)

C

CmC RT

PbB = (A.49)

The real gas law at critical condition was defined as:

C

CCC P

RTZv = (A.50)

Substituting Equation A.48 through Equation A.50 to Equation A.45 through Equation

A.47 yield:

CmCC BBZ α−+= 13 (A.45)

(A.46) ( 223 CmmCmCC BBAZ βαα +−−= )

( ) mCCCCC BBBAZ β233 +−= (A.47)

Rearranging Equation A.45, the critical compressibility factor (ZC) for particular mixture

can be solved as:

3)1(1

31 CmCmC

CBBBZ αα −+

=−+

= (A.48)

Substituting Equation A.48 to Equation A.46, parameter AC can be calculated as:

( ) ( ) CmCmmCmC

C BBBBA αβαα

+++−+

= 22

31 (A.49)

Substituting Equation A.48 and Equation A.49 to Equation A.27 yield the following:

( ) ( )

( ) mCC

CCmCmmCmCCmC

BB

BBBBBBB

β

αβααα

23

223

31

31

+−

⎥⎥⎦

⎤

⎢⎢⎣

⎡+++

−+=⎟

⎠⎞

⎜⎝⎛ −+

(A.50)

Equation A.50 can be simplified as:

0432

23

1 =Θ+Θ+Θ+Θ CCC BBB (A.51)


93

8612 321 +++=Θ mmm ααα (A.52)

22 3271515 mmm αβα −−+=Θ (A.53)

mα363 +=Θ (A.54)

14 −=Θ (A.55)

It can be seen that ),( mmC fB βα= . It is imperative to solve βm as a function of BC and

αm. This is an iterative process with the αm value is guessed at the starting point.

Rearranging Equation A.51 to solve for βm yield:

23

2231

271)31515(

C

CCmmCm B

BBB −Θ+−++Θ=

ααβ (A.56)

By rearranging Equations A.45 to A.47, the composition dependent critical

compressibility factor can be expressed as in Equation A. 57.60

0012

23

3 =+++ θθθθ ccc ZZZ (A.57) where

)(

6663

)9912123(

6128

20

21

22

323

mmmm

mmmmm

mmmmm

mmm

βαβαθ

βαβααθ

βαβααθ

αααθ

−+−=

−++=

−+++−=

+++=

Equation A. 57 can be arranged in terms of Zc and αm as in Equation A.58:

)1(66)99()63()12123()6128(

2

2222332

mcmccm

mcmmcmmcmmmm ZZZ

ZZZααα

ααααααααβ−++−−

−++++−+++= (A.58)

Equations A.57 to A.58 can be resolved for Zc from a guess value of αm.

94

APPENDIX B

FORTRAN PROGRAM

B.1 Internal Tuning Parameter Approximation

! Program LLSpredsat_pure ! Input: Tc, Pc, Zc, densV, densL ! Input Units: Tc=R, Pc=psia, Zc=null, densV=lb-mole/cu-ft, densL=lb-mole/cu-ft ! Input Units: T = R, P = psia Character(Len=40)CName real, allocatable, dimension(:):: Pr,Tr,T, P, DLE, DGE, DLC, DGC, ZVC, ZLC, & DEVL, DEVG, Fugr,Gam, B open(unit=5,file='input.txt',status='old') open(unit=6,file='output.txt',status='old') read(5,*)NCOMP Do IC = 1,NCOMP AAPDL = 1.0E+05 AAPDV = 1.0E+05 ITMAX = 250 read(5,*)CName read(5,*)Tc,Pc,Zc,ACF read(5,*)NDT write(6,*)NDT,Tc,Pc,Zc,ACF allocate(DLE(NDT),DGE(NDT),P(NDT),T(NDT),DLC(NDT),DGC(NDT), & Gam(NDT), ZVC(NDT), ZLC(NDT), Fugr(NDT), DEVL(NDT), DEVG(NDT), & Pr(NDT), Tr(NDT),B(NDT)) write(6,*)CName R = 10.73 DO 60 I =1,NDT read(5,*)DLE(I),DGE(I),P(I),T(I) 60 continue Omw=0.25 write (6,20) 'IT',' OmW',' AAPDL',' AAPDV' 20 Format(2A10,2A15) Do 200 IT=1,ITMAX Call Crtpar(Tc, Pc, Zc, R, ACF, Omw, AC, BC, Alp, Bet) APDL = 0.0 APDV = 0.0 Do 100 J=1,NDT VL = 1/DLE(J) If (J.EQ. 1) Tmp = (((R*T(J))/(VL-BC))-P(J))*((VL**2+Alp*BC*VL-Bet*BC**2)/AC) RT = T(J)/Tc

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if (RT.GE.0.9999) ZV = Zc if (RT.GE.0.9999) ZL = ZV if (RT.GE.0.9999) FugrC = 0.0 if (RT.GE.0.9999) Tmp = 1 if (RT.GE.0.9999) GO TO 35 XR = 0.0 XL = 0.0 50 Continue XC1 = XR XC2 = XL If (XC1.NE.0.0 .and. XC2.NE.0.0) GO TO 130 AT= Tmp*AC Call Zfactr(Alp, Bet, AT, BC, P(J), T(J), R, BB, ZV, ZL) If (ZV.NE.ZL) GO TO 55 If (ZV.EQ.ZL) Tmp = Tmp*1.0005 GO TO 50 55 Call fugacty (Alp, Bet, P(J), T(J), R, AT, BB, ZV, ZL, AB, FugrC) if (FugrC.GT.0.0) GO TO 120 if (FugrC.LE.0.0) GO TO 125 120 Continue If (FugrC.GT.0.0) XR = Tmp If (FugrC.GT.0.0) FXR = FugrC If (FugrC.GT.0.0) Tmp = Tmp*0.75 If (XC2.EQ.0.0) Go to 50 125 Continue If (FugrC.LE.0.0) XL = Tmp If (FugrC.LE.0.0) FXL = FugrC If (FugrC.LE.0.0) Tmp = Tmp*1.05 If (XC1.EQ.0.0) Go to 50 130 Continue Tr(J)=T(J)/Tc Pr(J)=P(J)/Pc If(Tr(J).GT.0.97) EPS=1.0E-02 If(Tr(J).LE.0.97) EPS=1.0E-07 Call BISECT (XL, XR, FXL, FXR,EPS, T(J),Tc, P(J), Pc,Alp, Bet, BC, BB, & AC,R,ZV,ZL,Tmp,FugrC) 35 Continue Pr(J) = P(J)/Pc Tr(J) = T(J)/Tc Fugr(J)= FugrC ZVC(J) = ZV ZLC(J) = ZL Gam(J) = Tmp B(J) = BB

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! Calculating the fluid density. If (DLE(J).GT.0) Call Apdev (P(J), ZLC(J), DLE(J), T(J), R, DEVL(J), DLC(J)) If (DLE(J).EQ.0) DEVL(J) = 0.0 If (DGE(J).GT.0) Call Apdev (P(J), ZVC(J), DGE(J), T(J), R, DEVG(J), DGC(J)) If (DGE(J).EQ.0) DEVG(J) = 0.0 APDL = APDL + ABS(DEVL(J)) APDV = APDV + ABS(DEVG(J)) 100 Continue DN=NDT APDL=APDL/DN APDV=APDV/DN write(6,*)IT,Omw,APDL,APDV If (APDL .GE. AAPDL) Go to 300 If (AAPDL .GT. APDL) AAPDL = APDL Omw = Omw + 0.0025 200 Continue 300 Continue write(6,10) 'Pr','Tr','Gam','ZVC','ZLC','Fugr','BB','DLE','DGE','DLC','DGC','DEVL',& 'DEVG' 10 Format(2A6, 2A8,2A10, A9, 4A8, 2A7) DO 800 J=1,NDT write(6,19) Pr(J),Tr(J),Gam(J),ZVC(J),ZLC(J),Fugr(J),B(J),DLE(J),DGE(J),& DLC(J),DGC(J),DEVL(J),DEVG(J) 800 Continue 19 Format(2F6.3,2F8.4,3E10.2,4F8.4,2F7.2) deallocate(DLE, DGE, P, T, DLC, DGC, ZVC, ZLC,B, Fugr, DEVL, DEVG,Gam,Pr,Tr) end do close(5) close(6) Stop End SUBROUTINE Apdev (P, ZV, DGE, T, R, Pdev, Den) Den = P/(ZV*T*R) Dev = Den - DGE Pdev = 100.0*(Dev/DGE) RETURN END

SUBROUTINE BISECT (XL, XR, FXL, FXR,EPS,T, Tc, P, Pc,Alp, Bet, BC, & BB, AC, R, ZVC, ZLC, XFIT, FIT) IMAX=50

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! EPS=1.0E-07 ! Check for Presence of a Root if(FXL*FXR)50,30,80 30 IT=1 if(FXL.NE.0.0)go to 40 XFIT=XL FIT=0.0 go to 80 40 XFIT=XR FIT=0.0 go to 80 ! Begin Bisection Method 50 do 70 IJ=1, IMAX XFIT=(XL*FXR-XR*FXL)/(FXR-FXL) AT=XFIT*AC Call Zfactr (Alp, Bet, AT, BC, P, T, R, BB, ZVC, ZLC) Call fugacty (Alp, Bet, P, T, R, AT, BB, ZVC, ZLC, AB,FIT) ! Check for Convergence with Tolerance IF(ABS(FIT).LE.EPS) go to 80 ! Keep Right or Left Subinterval IF(FIT*FXL<0) go to 60 XL=XFIT FXL=FIT go to 70 60 XR=XFIT FXR=FIT 70 continue 80 RETURN END Subroutine Crtpar(Tc, Pc, Zc, R, ACF, Omw, AC, BC, Alp, Bet) AC = (1.+(Omw-1.)*Zc)**3*(R**2*Tc**2/Pc) BC = (Omw*Zc)*R*Tc/Pc Alp= (1.+(Omw-3.)*Zc)/(Omw*Zc) Bet= (Zc**2*((Omw-1.)**3)+2.*Omw**2.*Zc+Omw*(1.-3.*Zc))/(Omw**2*Zc) Return End Subroutine Zfactr (Alp, Bet, AT,BC, P, T, R, BB, ZV, ZL) Dimension Coef(4),RT(3) ! write(6,*) 'Root=',RT ,BB AA = AT*P/(R**2*T**2) BB = BC*P/(R*T)

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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) 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 fugacty (Alp, Bet, P, T, R, AT, BB, ZV, ZL, AA, Fugr) AA = AT*P/(R**2*T**2) B2 = BB/2. D = sqrt(Alp**2 + 4.*Bet) Fir = ZV - ZL Sec = alog((ZL - BB)/(ZV - BB)) Zf = ((ZV + Alp*B2 + D*B2)/(ZV + Alp*B2 - D*B2)) Zs = ((ZL + Alp*B2 - D*B2)/(ZL + Alp*B2 + D*B2)) Thi = (AA/(D*BB))*alog(Zf*Zs) Fugr = Fir + Sec - Thi Return End Subroutine Dervfug (Alp, Bet, P, T, R, AT, BB, ZV, ZL, AC, DFugr) AA = AC*P/(R**2*T**2) B2 = BB/2. D = sqrt(Alp**2 + 4.*Bet) Zf = ((ZV + Alp*B2 + D*B2)/(ZV + Alp*B2 - D*B2)) Zs = ((ZL + Alp*B2 - D*B2)/(ZL + Alp*B2 + D*B2)) DFugr = (AA/(D*BB))*alog(Zf*Zs) Return End SUBROUTINE Cubic (MTYPE, A, Z) ! Program Dimensioned for 4 Coefficients ! a3*X^3 + a2*X^2 + a1*X + a0 = 0

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! a3 MUST be greater or equal to 1 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

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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 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

B… Temperature Dependent Attractive Functions

! Program Saturated Vapor Pressure and Density ! Input: Tc, Pc, Zc, densV, densL ! Input Units: Tc=R, Pc=psia, Zc=null, densV=lb-mole/cu-ft, densL=lb-mole/cu-ft ! Input Units: T = R, P = psia Character(Len=40)CName Real wtm,Tc,Pc,Zc,ACF,Omw real, dimension(:):: Pr(50),Tr(50),T(25), P(50), ZVC(50), ZLC(50), B(50) Dimension RT(3) open(unit=5,file='input.txt',status='old') open(unit=6,file='output.txt',status='old') read(5,*)NCOMP,NT read(5,*)(Tr(I), I=1,NT) Do IC = 1,NCOMP AAPDL = 1.0E+05 AAPDV = 1.0E+05 read(5,*)CName read(5,*) Tc,Pc,Zc,ACF,wtm ! read(5,*)NDT write(6,*)CName R = 10.73 write(6,110) 'Tr','T(K)','Alp','Bet','BSRK','BS78','BSRKOld','BPR','BPROld','BLLS' 110 Format(4(A7,1x),6(A10,1X))

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Do 200 I = 1,NT Call BVirial(Tc,Tr(I),P,Pc,Zc,R,ACF,wtm,BSRK,BS78,BSOld,BPR,BPOld,BLLS,& ZRK,ZPR,ZLLS,Alp,Bet,Omw) write (6,1)Tr(I),(Tr(I)*Tc),Alp,Bet,BSRK,BS78,BSOld,BPR,BPOld,BLLS 1 Format (2(F7.2,1x),2(F7.4,1x),6(F10.4,1X)) 200 Continue write(6,1) Tc,Pc,Zc,ACF,wtm,Omw end do close(5) close(6) Stop End Subroutine BVirial(Tc,TR, P, Pc, Zc, R, ACF, wtm, BSRK, BS78, BSOld, BPR,& BPOld, BLLS, ZRK, ZPR, ZLLS,Alp,Bet,Omw) Omw = ((0.361)/(1+0.0274*ACF))*0.9 ! Omw = ((0.361)/(1+0.0274*ACF))*1.1 ! Omw = ((0.361)/(1+0.0274*ACF)) ! CoefLLS = 0.1778+0.2287*ACF+0.1710*ACF**2+0.0034*(ACF*wtm) ! CoefSRK =0.4604+0.7775*ACF+0.2146*ACF**2+0.0032*(ACF*wtm) ! CoefPR =0.3588+0.8562*ACF+0.1213*ACF**2+0.0028*(ACF*wtm) ! CoefLLS = 0.1971+0.0863*ACF+0.3571*ACF**2+0.0036*(ACF*wtm) ! CoefSRK =0.4604+0.7775*ACF+0.2146*ACF**2+0.0032*(ACF*wtm) ! CoefPR =0.3588+0.8562*ACF+0.1213*ACF**2+0.0028*(ACF*wtm) CoefLLS = 0.132239978 CoefPR = 0.321378375 CoefSRK =0.399954468 ! CoefLLS = -0.10988 ! CoefPR = 0.0136 ! CoefSRK =0.07092 CoefS78 =(1+(0.48508+1.55171*ACF-0.156136*ACF**2)*(1-sqrt(TR)))**2 CoefSOld =(1+(0.480+1.574*ACF-0.176*ACF**2)*(1-sqrt(TR)))**2 CoefPOld = (1+(0.37464+1.54226*ACF-0.26992*ACF**2)*(1-sqrt(TR)))**2 Alp = (1.+(Omw-3.)*Zc)/(Omw*Zc) Bet = (Zc**2*((Omw-1.)**3)+2.*Omw**2.*Zc+Omw*(1.-.*Zc))/(Omw**2*Zc) OmaLLS =(1.+(Omw-1.)*Zc)**3 OmbLLS = Omw*Zc OmaSRK = 0.42747 OmbSRK = 0.08664 OmaPR = 0.45724 OmbPR = 0.07780 BPR = (OmbPR-(OmaPR*TR**(-(CoefPR+1)))) BPOld =(OmbPR-(OmaPR*TR**(-(CoefPOld+1)))) BSRK = (OmbSRK-(OmaSRK*TR**(-(CoefSRK+1))))

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BSOld=(OmbSRK-(OmaSRK*TR**(-(CoefSOld+1)))) BS78=(OmbSRK-(OmaSRK*TR**(-(CoefS78+1)))) BLLS =(OmbLLS-(OmaLLS*TR**(-(CoefLLS+1)))) ZSRK =1+((PR/TR)*(BSRK*Pc/(R*Tc))) ZPR =1+((PR/TR)*(BPR*Pc/(R*Tc))) ZLLS =1+((PR/TR)*(BLLS*Pc/(R*Tc))) Return End

B…. Density Prediction by Lawal-Lake-Silberberg EOS

! Program Saturated Density and Vapor Pressure Prediction with LLS EOS ! Input: Tc, Pc, Zc, densV, densL ! Input Units: Tc=R, Pc=psia, Zc=null, densV=lb-mole/cu-ft, densL=lb-mole/cu-ft ! Input Units: T = R, P = psia Character(Len=40)CName Real wtm,Tc,Pc real, allocatable, dimension(:):: Pr,Tr,T, P, DLE, DGE, DLC, DGC, & VPD, ZVC, ZLC, FUGR, DEVL, DEVG, B Dimension RT(3) open(unit=5,file='input.txt',status='old') open(unit=6,file='output.txt',status='unknown') read(5,*)NCOMP Do IC = 1,NCOMP AAPDL = 1.0E+05 AAPDV = 1.0E+05 read(5,*)CName read(5,*) Tc,Pc,Zc,ACF,wtm read(5,*)NDT write(6,*)CName write(6,1)'Tc=',Tc,'Pc=',Pc,'Zc=',Zc,'ACF=',ACF,'wtm=',wtm 1 Format (A5,F8.2,A5,F8.2,A5,F8.2,A5,F8.2,A5,F8.2) allocate(Pr(NDT),Tr(NDT),P(NDT),T(NDT),DLE(NDT),DGE(NDT),DLC(NDT),& DGC(NDT),VPD(NDT),ZVC(NDT),ZLC(NDT),FUGR(NDT),DEVL(NDT),& DEVG(NDT),B(NDT)) R = 10.73 DO 60 I =1,NDT read(5,*)DLE(I),DGE(I),P(I),T(I) write (6,*)DLE(I),DGE(I),P(I),T(I) 60 continue APDL = 0.0 APDV = 0.0 ! VP=1 If (P(1).GT.0.0) VP = P(1)

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If (DGE(1).EQ.0.0 .and. P(1).EQ.0.0) VP=1 If (DGE(1).GT.0.0) VP = (R*T(1)*DGE(1))/2 PCal = VP Do 100 J=1,NDT Call ParaLLS(T(J),wtm,Tc, Pc, Zc, R, ACF, AC, AT, BC, Alp, Bet) Tcal=T(J) If (Tcal .Eq. Tc) ZV = Zc If (Tcal .Eq. Tc) ZL = Zc If (Tcal .Eq. Tc) FugrC = 0 If (Tcal .Eq. Tc) BB = BC If (Tcal .Eq. Tc) VP = Pc If (Tcal .Eq. Tc) Go to 75 Call XNewton (Tcal, VP, Alp, Bet, BC, BB, AT,R, ZV, ZL,FugrC,DFug,RT) Call Zfactr(Alp, Bet, AT, BC, VP, T(J), R, BB, ZV, ZL,RT) Call fugacty (Alp, Bet, VP, T(J), R, AT, BB, ZV, ZL, AB, FugrC) 75 Continue Pr(J) = VP/Pc Tr(J) = T(J)/Tc FUGR(J)= FugrC ZVC(J) = ZV ZLC(J) = ZL VPD(J) = VP B(J) = BB ! Calculating the fluid density. Call Apdev (VP, ZLC(J), DLE(J), T(J), R, DEVL(J), DLC(J)) If (DLE(J).EQ.0) DEVL(J) = 0.0 Call Apdev (VP, ZVC(J), DGE(J), T(J), R, DEVG(J), DGC(J)) If (DGE(J).EQ.0) DEVG(J) = 0.0 APDL = APDL + ABS(DEVL(J)) APDV = APDV + ABS(DEVG(J)) 100 Continue DN=NDT AAPDL=APDL/DN AAPDV=APDV/DN write(6,10)'VP','P','T','ZVC','ZLC','FUGR','BB','DLE','DGE','DLC','DGC' 10 Format(3A10, 2A10,2A10,4A12) DO 800 J=1,NDT write(6,19) VPD(J),P(J), T(J), ZVC(J), ZLC(J), FUGR(J),B(J), DLE(J), & DGE(J),DLC(J),DGC(J) 800 Continue 19 Format(3F10.2,2F10.3,2F10.5,4E12.4) write(6,119) 'AAPDL=',AAPDL,'AAPDV=',AAPDV 119 Format(A9,F9.4,A9,F9.4)

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deallocate(Pr,Tr,T,P,DLE,DGE,DLC,DGC,ZVC,ZLC,DEVL,DEVG,FUGR,VPD,B) end do close(5) close(6) Stop End SUBROUTINE Apdev (P, ZV, DGE, T, R, Pdev, Den) Den = P/(ZV*T*R) Dev = Den - DGE Pdev = 100.0*(Dev/DGE) RETURN END Subroutine BISINIT(Alp,Bet,XL,XR,FXL,FXR,T,PCal,AT,BC,R) ! To initialize the Bisection Method XR = 0.0 XL = 0.0 50 Continue XC1 = XR XC2 = XL If (XC1.NE.0.0 .and. XC2.NE.0.0) GO TO 130 Call Zfactr(Alp, Bet, AT, BC, PCal, T, R, BB, ZV, ZL,RT) ! write (6,*) Alp, Bet, AT, BC, PCal, T, R, BB, ZV, ZL If (ZV.NE.ZL) GO TO 55 If (ZV.EQ.ZL) PCal = PCal*1.005 GO TO 50 55 Call fugacty (Alp, Bet, PCal, T, R, AT, BB, ZV, ZL, AB, FugrC) if (FugrC.GT.0.0) GO TO 120 if (FugrC.LE.0.0) GO TO 125 120 Continue If (FugrC.GT.0.0) XR = PCal If (FugrC.GT.0.0) FXR = FugrC If (FugrC.GT.0.0) PCal = PCal*0.75 If (XC2.EQ.0.0) Go to 50 125 Continue If (FugrC.LE.0.0) XL = PCal If (FugrC.LE.0.0) FXL = FugrC If (FugrC.LE.0.0) PCal = PCal*1.005 If (XC1.EQ.0.0) Go to 50 ! write(6,*)'J=',J,' XL=',XL,' XR=',XR,' XC1=',XC1,' FXL=',FXL,' FXR=',FXR 130 Continue RETURN END

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SUBROUTINE BISECT (XL, XR, FXL, FXR,T, Tc, P, Pc,Alp, Bet, BC, BB, & AC, AT, R, ZVC, ZLC, XFIT,FGV,FGL, FIT,RT) Dimension RT(3) IMAX=50 EPS=1.0E-07 ! Check for Presence of a Root if(FXL*FXR)50,30,80 30 IT=1 if(FXL.NE.0.0)go to 40 XFIT=XL FIT=0.0 go to 80 40 XFIT=XR FIT=0.0 go to 80 ! Begin Bisection Method 50 do 70 IJ=1, IMAX XFIT=(XL*FXR-XR*FXL)/(FXR-FXL) P=XFIT Call Zfactr (Alp, Bet, AT, BC, P, T, R, BB, ZVC, ZLC,RT) Call fugacty (Alp, Bet, P, T, R, AT, BB, ZVC, ZLC, AB, FIT) ! Check for Convergence with Tolerance IF(ABS(FIT).LE.EPS) go to 80 ! Keep Right or Left Subinterval IF(FIT*FXL<0) go to 60 XL=XFIT FXL=FIT go to 70 60 XR=XFIT FXR=FIT 70 continue 80 RETURN END SUBROUTINE XNewton (T, P, Alp, Bet, BC, BB, AT,R, ZVC, ZLC,Fugr,DFug,RT) Dimension RT (3) IMAX=50 DFR = 1.0E-05 EPS = 1.0E-03 ! Begin Newton-Raphson Method DP = 0.005 Do 70 IJ=1, IMAX

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60 Continue Call Zfactr (Alp, Bet, AT, BC, P, T, R, BB, ZVC, ZLC,RT) ! If (ZVC .EQ.ZLC) write (6,*) 'T=',T,'P=',P,'ZVC=',ZVC,'ZLC=',ZLC If (ZVC .NE. ZLC) Go to 65 ! If (ZVC.GT. 0.1) P=P-0.001 ! If (ZVC .LE. 0.1) P = P+0.001 P= P*1.005 Go to 60 65 Continue Call fugacty (Alp, Bet, P, T, R, AT, BB, ZVC, ZLC, AB, Fugr) PDP = P + DP Call Zfactr (Alp, Bet, AT, BC, PDP, T, R, BBD, ZVDC, ZLDC,RTD) Call fugacty (Alp, Bet, PDP, T, R, AT, BBD, ZVDC, ZLDC, AB, DFugr) ! ...... Perform Derivative of the Fugacity ....... Call Dervfug (DP, Fugr, DFugr, DFug) ! Check for Convergence with Tolerance Pnew = P - (Fugr/DFug) RFDgr = Fugr/DFug DEVP= (Pnew-P)/P ! write (6,1)'P=',P,'ZV=',ZVC,'ZL=',ZLC,'Fugr=',Fugr,'DFug=',DFug,'RFDgr=',RFDgr,'DEVP=',DEVP,'BB=',BB !1 Format (2(A4,F9.5),6(A7,E12.3)) ! write(6,*) 'Root=',RT ! IF(RFDgr.GE.P) go to 80 IF (ABS(DEVP) .LE. EPS) Go to 80 P=Pnew ! .... Keep New P ..... 70 continue 80 RETURN END Subroutine ParaSRK(T,P,wtm,Tc, Pc, R, ACF, AC, AT, BC, Alp, Bet) TR = T/Tc ! tmp = 0.480+1.574*ACF-0.176*ACF**2 ! GamT= (1+tmp*(1-sqrt(TR)))**2 ! theta = 0.457+0.721*ACF+0.322*ACF**2+0.0038*(ACF* wtm) GamT= (TR)**(-theta) Oma = 0.42747 Omb = 0.08664 AC = Oma*(R**2*Tc**2/Pc) BC = Omb*R*Tc/Pc AT = AC*GamT

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Alp = 1 Bet = 0 Return End Subroutine ParaPR(T,P,wtm,Tc, Pc, R, ACF, AC, AT, BC, Alp, Bet) TR = T/Tc ! tmp = 0.37464+1.54226*ACF-0.26992*ACF**2 ! GamT= (1+tmp*(1-sqrt(TR)))**2 theta = 0.38+0.691*ACF+0.335*ACF**2+0.00315*(ACF*wtm) GamT= (TR)**(-theta) Oma = 0.45724 Omb = 0.07780 AC = Oma*(R**2*Tc**2/Pc) BC = Omb*R*Tc/Pc AT = AC*GamT Alp = 2 Bet = 1 Return End Subroutine ParaLLS(T,wtm,Tc, Pc, Zc, R, ACF, AC, AT,BC, Alp, Bet) ! Omw = (0.327)/(1.+0.0513*ACF) ! Sensitivity Analysis for Omw at +/- 10% ! Omw = ((0.361)/(1+0.0274*ACF))*0.9 ! Omw = ((0.361)/(1+0.0274*ACF))*1.1 ! Omw = 0.31 Omw = ((0.361)/(1+0.0274*ACF)) TR = T/Tc PR = P/Pc AC = (1.+(Omw-1.)*Zc)**3*(R**2*Tc**2/Pc) BC = (Omw*Zc)*R*Tc/Pc theta = 0.19708+0.08627*ACF+0.35714*(ACF**2)+(3.59015E-03)*(ACF*wtm) GamT= (TR)**(-theta) AT = AC*GamT Alp = (1.+(Omw-3.)*Zc)/(Omw*Zc) Bet = (Zc**2*((Omw-1.)**3)+2.*Omw**2.*Zc+Omw*(1.-3.*Zc))/(Omw**2*Zc) ! write(6,*) AC, AT,GamT, BC, Alp, Bet,Omw Return End Subroutine Zfactr (Alp, Bet, AT,BC, P, T, R, BB, ZV, ZL,RT)

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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 ,' BB=',BB 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 fugacty (Alp, Bet, P, T, R, AT, BB, ZV, ZL, AA, Fugr) AA = AT*P/(R**2*T**2) B2 = BB/2. D = sqrt(Alp**2 + 4.*Bet) Fir = ZV - ZL Sec = alog((ZL - BB)/(ZV - BB)) Zf = ((ZV + Alp*B2 + D*B2)/(ZV + Alp*B2 - D*B2)) Zs = ((ZL + Alp*B2 - D*B2)/(ZL + Alp*B2 + D*B2)) Thi = (AA/(D*BB))*alog(Zf*Zs) FGV = (ZV-1)-alog(ZV-BB)-(AA/(D*BB))*alog(Zf) FGL = (ZL-1)-alog(ZL-BB)-(AA/(D*BB))*alog(1/Zs) Fugr = Fir + Sec - Thi ! write(6,*) 'ZV=',ZV,'ZL=',ZL,'BB',BB Return End Subroutine Dervfug (DP, Fugr, DFugr, DFug) DFug = (DFugr-Fugr)/DP Return End SUBROUTINE Cubic (MTYPE, A, Z)

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! Program Dimensioned for 4 Coefficients ! a3*X^3 + a2*X^2 + a1*X + a0 = 0 ! a3 MUST be greater or equal to 1 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

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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 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

B…..Density Prediction by Soave-Redlich-Kwong EOS

! Program SatDSRK ! Input: Tc, Pc, Zc, densV, densL ! Input Units: Tc=R, Pc=psia, Zc=null, densV=lb-mole/cu-ft, densL=lb-mole/cu-ft ! Input Units: T = R, P = psia Character(Len=40)CName real, allocatable, dimension(:):: Pr,Tr,T, P, DLE, DGE, DLC, DGC, ZVC,ZLC,& DEVL, DEVG, Fugr,Gam open(unit=5,file='input.txt',status='old') open(unit=6,file='output.txt',status='old') read(5,*)NCOMP Do IC = 1,NCOMP AAPDL = 1.0E+05 AAPDV = 1.0E+05 ITMAX = 250 read(5,*)CName read(5,*)Tc,Pc,Zc,ACF read(5,*)NDT write(6,*)NDT,Tc,Pc,Zc,ACF

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allocate(DLE(NDT),DGE(NDT),P(NDT),T(NDT),DLC(NDT),DGC(NDT),Gam(NDT)& ,ZVC(NDT),ZLC(NDT),Fugr(NDT),DEVL(NDT),DEVG(NDT),Pr(NDT),Tr(NDT)) write(6,*)CName R = 10.73 DO 60 I =1,NDT read(5,*)DLE(I),DGE(I),P(I),T(I) 60 continue ZCRK = 1.0/3.0 Omw=0.08664/ZCRK write (6,20) 'IT',' OmW',' AAPDL',' AAPDV' 20 Format(2A10,2A15) IT=1 Call Crtpar(Tc, Pc, Zc, R, ACF, Omw, AC, BC, Alp, Bet) APDL = 0.0 APDV = 0.0 Do 100 J=1,NDT VL = 1/DLE(J) If (J.EQ. 1) Tmp = (((R*T(J))/(ABS(VL-BC)))-P(J))*((VL**2+Alp*BC*VL-& Bet*BC**2)/AC) RT = T(J)/Tc

if (RT.GE.0.9999) ZV = ZCRK if (RT.GE.0.9999) ZL = ZV if (RT.GE.0.9999) FugrC = 0.0 if (RT.GE.0.9999) Tmp = 1 if (RT.GE.0.9999) GO TO 35 XR = 0.0 XL = 0.0 50 Continue XC1 = XR XC2 = XL If (XC1.NE.0.0 .and. XC2.NE.0.0) GO TO 130 AT= Tmp*AC Call Zfactr(Alp, Bet, AT, BC, P(J), T(J), R, BB, ZV, ZL) If (ZV.NE.ZL) GO TO 55 If (ZV.EQ.ZL) Tmp = Tmp*1.0005 GO TO 50 55 Call fugacty (Alp, Bet, P(J), T(J), R, AT, BB, ZV, ZL, AB, FugrC) if (FugrC.GT.0.0) GO TO 120 if (FugrC.LE.0.0) GO TO 125 120 Continue If (FugrC.GT.0.0) XR = Tmp If (FugrC.GT.0.0) FXR = FugrC If (FugrC.GT.0.0) Tmp = Tmp*0.75 If (XC2.EQ.0.0) Go to 50

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125 Continue If (FugrC.LE.0.0) XL = Tmp If (FugrC.LE.0.0) FXL = FugrC If (FugrC.LE.0.0) Tmp = Tmp*1.05 If (XC1.EQ.0.0) Go to 50 130 Continue Tr(J)=T(J)/Tc Pr(J)=P(J)/Pc If(Tr(J).GT.0.97) EPS=1.0E-02 If(Tr(J).LE.0.97) EPS=1.0E-07 Call BISECT (XL, XR, FXL, FXR,EPS, T(J),Tc, P(J), Pc,Alp, Bet, BC, BB, & AC,R,ZV,ZL,Tmp,FugrC) 35 Continue Pr(J)=P(J)/Pc Tr(J)=T(J)/Tc Fugr(J)=FugrC ZVC(J) = ZV ZLC(J) = ZL Gam(J)= Tmp ! Calculating the fluid density. If (DLE(J).GT.0) Call Apdev (P(J), ZLC(J), DLE(J), T(J), R, DEVL(J), DLC(J)) If (DLE(J).EQ.0) DEVL(J) = 0.0 If (DGE(J).GT.0) Call Apdev (P(J), ZVC(J), DGE(J), T(J), R, DEVG(J), DGC(J)) If (DGE(J).EQ.0) DEVG(J) = 0.0 APDL = APDL + ABS(DEVL(J)) APDV = APDV + ABS(DEVG(J)) 100 Continue DN=NDT APDL=APDL/DN APDV=APDV/DN write(6,*)IT,Omw,APDL,APDV write(6,10) 'Pr','Tr','Gam','ZVC','ZLC','Fugr','DLE','DGE','DLC','DGC','DEVL',& 'DEVG' 10 Format(2A6, 2A8,2A10, 4A8, 2A7) DO 800 J=1,NDT write(6,19) Pr(J),Tr(J),Gam(J),ZVC(J),ZLC(J),Fugr(J),DLE(J),DGE(J),& DLC(J),DGC(J),DEVL(J),DEVG(J) 800 Continue 19 Format(2F6.3,2F8.4,F10.4,E10.2,4F8.4,2F7.2) deallocate(DLE, DGE, P, T, DLC, DGC, ZVC, ZLC, Fugr, DEVL, DEVG,Gam,Pr,Tr) end do close(5)

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close(6) Stop End SUBROUTINE Apdev (P, ZV, DGE, T, R, Pdev, Den) Den = P/(ZV*T*R) Dev = Den - DGE Pdev = 100.0*(Dev/DGE) RETURN END SUBROUTINE BISECT (XL, XR, FXL, FXR,EPS,T, Tc, P, Pc,Alp, Bet, BC, BB, AC, & R, ZVC, ZLC, XFIT, FIT) IMAX=50 ! EPS=1.0E-07 ! Check for Presence of a Root if(FXL*FXR)50,30,80 30 IT=1 if(FXL.NE.0.0)go to 40 XFIT=XL FIT=0.0 go to 80 40 XFIT=XR FIT=0.0 go to 80 ! Begin Bisection Method 50 do 70 IJ=1, IMAX XFIT=(XL*FXR-XR*FXL)/(FXR-FXL) AT=XFIT*AC Call Zfactr (Alp, Bet, AT, BC, P, T, R, BB, ZVC, ZLC) Call fugacty (Alp, Bet, P, T, R, AT, BB, ZVC, ZLC, AB,& FIT) ! Check for Convergence with Tolerance IF(ABS(FIT).LE.EPS) go to 80 ! Keep Right or Left Subinterval IF(FIT*FXL<0) go to 60 XL=XFIT FXL=FIT go to 70 60 XR=XFIT FXR=FIT 70 continue 80 RETURN

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END SUBROUTINE XNewton (T, P, Alp, Bet, BC, BB, AC,R, ZVC, ZLC, tmp, Fugr) IMAX=50 EPS=1.0E-07 ! Begin Newton-Raphson Method oldtmp = tmp do 70 IJ=1, IMAX 30 continue AT=tmp*AC 20 continue Call Zfactr (Alp, Bet, AT, BC, P, T, R, BB, ZVC, ZLC) if (ZVC.NE.ZLC) GO TO 50 if (ZVC.EQ.ZLC) Tmp = Tmp*1.005 GO TO 20 50 Call fugacty (Alp, Bet, P, T, R, AT, BB, ZVC, ZLC, AB,Fugr) ! ...... Perform Derivative of the Fugacity ....... Call Dervfug (Alp, Bet, P, T, R, AT, BB, ZV, ZL, AC, DFugr) tmp = tmp - Fugr/DFugr ! Check for Convergence with Tolerance Ptmp = (tmp-oldtmp)/oldtmp IF(ABS(Ptmp).LE.EPS) go to 80 ! .... Keep New tmp ..... oldtmp = tmp 70 continue 80 RETURN END Subroutine Crtpar(Tc, Pc, Zc, R, ACF, Omw, AC, BC, Alp, Bet) Oma=0.42747 Omb=0.08664 AC = Oma*(R**2*Tc**2/Pc) BC = Omb*R*Tc/Pc Alp = 1 Bet = 0 Return End Subroutine Zfactr (Alp, Bet, AT,BC, P, T, R, BB, 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)

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Coef(3) = AA-(Alp*BB)-(Bet+Alp)*BB**2 Coef(4) = -(AA*BB-Bet*(BB**2+BB**3)) 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 Return End Subroutine fugacty (Alp, Bet, P, T, R, AT, BB, ZV, ZL, AA, Fugr) AA = AT*P/(R**2*T**2) B2 = BB/2. D = sqrt(Alp**2 + 4.*Bet) Fir = ZV - ZL Sec = alog((ZL - BB)/(ZV - BB)) Zf = ((ZV + Alp*B2 + D*B2)/(ZV + Alp*B2 - D*B2)) Zs = ((ZL + Alp*B2 - D*B2)/(ZL + Alp*B2 + D*B2)) Thi = (AA/(D*BB))*alog(Zf*Zs) Fugr = Fir + Sec - Thi Return End Subroutine Dervfug (Alp, Bet, P, T, R, AT, BB, ZV, ZL, AC, DFugr) AA = AC*P/(R**2*T**2) B2 = BB/2. D = sqrt(Alp**2 + 4.*Bet) Zf = ((ZV + Alp*B2 + D*B2)/(ZV + Alp*B2 - D*B2)) Zs = ((ZL + Alp*B2 - D*B2)/(ZL + Alp*B2 + D*B2)) DFugr = (AA/(D*BB))*alog(Zf*Zs) Return End SUBROUTINE Cubic (MTYPE, A, Z) ! Program Dimensioned for 4 Coefficients ! a3*X^3 + a2*X^2 + a1*X + a0 = 0 ! a3 MUST be greater or equal to 1 DIMENSION B(3), A(4), Z(3)

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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

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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

B…. Density Prediction by Peng-Robinson EOS

! Program SatDPR ! Input: Tc, Pc, Zc, densV, densL ! Input Units: Tc=R, Pc=psia, Zc=null, densV=lb-mole/cu-ft, densL=lb-mole/cu-ft ! Input Units: T = R, P = psia Character(Len=40)CName real, allocatable, dimension(:):: Pr,Tr,T, P, DLE, DGE, DLC, DGC, ZVC, ZLC, & DEVL, DEVG, Fugr,Gam open(unit=5,file='input.txt',status='old') open(unit=6,file='output.txt',status='old') read(5,*)NCOMP Do IC = 1,NCOMP AAPDL = 1.0E+05 AAPDV = 1.0E+05 ITMAX = 250 read(5,*)CName read(5,*)Tc,Pc,Zc,ACF read(5,*)NDT write(6,*)NDT,Tc,Pc,Zc,ACF allocate(DLE(NDT),DGE(NDT),P(NDT),T(NDT),DLC(NDT),DGC(NDT),Gam(NDT)& , ZVC(NDT),ZLC(NDT),Fugr(NDT),DEVL(NDT),DEVG(NDT),Pr(NDT),Tr(NDT)) write(6,*)CName R = 10.73 DO 60 I =1,NDT

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read(5,*)DLE(I),DGE(I),P(I),T(I) 60 continue ZCPR=0.3074 Omw=0.07780/ZCPR write (6,20) 'IT',' OmW',' AAPDL',' AAPDV' 20 Format(2A10,2A15) IT=1 Call Crtpar(Tc, Pc, ZCPR, R, ACF, Omw, AC, BC, Alp, Bet) APDL = 0.0 APDV = 0.0 Do 100 J=1,NDT VL = 1/DLE(J) If (J.EQ. 1) Tmp = (((R*T(J))/(abs(VL-BC)))-P(J))*((VL**2+Alp*BC*VL-Bet*BC**2)/AC) RT = T(J)/Tc if (RT.GE.0.9999) ZV = ZCPR if (RT.GE.0.9999) ZL = ZV if (RT.GE.0.9999) FugrC = 0.0 if (RT.GE.0.9999) Tmp = 1 if (RT.GE.0.9999) GO TO 35 XR = 0.0 XL = 0.0 50 Continue

XC1 = XR XC2 = XL If (XC1.NE.0.0 .and. XC2.NE.0.0) GO TO 130 AT= Tmp*AC Call Zfactr(Alp, Bet, AT, BC, P(J), T(J), R, BB, ZV, ZL) If (ZV.NE.ZL) GO TO 55 If (ZV.EQ.ZL) Tmp = Tmp*1.0005 GO TO 50 55 Call fugacty (Alp, Bet, P(J), T(J), R, AT, BB, ZV, ZL, AB, FugrC) if (FugrC.GT.0.0) GO TO 120 if (FugrC.LE.0.0) GO TO 125 120 Continue If (FugrC.GT.0.0) XR = Tmp If (FugrC.GT.0.0) FXR = FugrC If (FugrC.GT.0.0) Tmp = Tmp*0.75 If (XC2.EQ.0.0) Go to 50 125 Continue If (FugrC.LE.0.0) XL = Tmp If (FugrC.LE.0.0) FXL = FugrC If (FugrC.LE.0.0) Tmp = Tmp*1.05 If (XC1.EQ.0.0) Go to 50

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130 Continue Tr(J)=T(J)/Tc Pr(J)=P(J)/Pc If(Tr(J).GT.0.97) EPS=1.0E-02 If(Tr(J).LE.0.97) EPS=1.0E-07 Call BISECT (XL, XR, FXL, FXR,EPS, T(J),Tc, P(J), Pc,Alp, Bet, BC, BB, & AC,R,ZV,ZL,Tmp,FugrC) 35 Continue Pr(J)=P(J)/Pc Tr(J)=T(J)/Tc Fugr(J)=FugrC ZVC(J) = ZV ZLC(J) = ZL Gam(J)= Tmp ! Calculating the fluid density. If (DLE(J).GT.0) Call Apdev (P(J), ZLC(J), DLE(J), T(J), R, DEVL(J), DLC(J)) If (DLE(J).EQ.0) DEVL(J) = 0.0 If (DGE(J).GT.0) Call Apdev (P(J), ZVC(J), DGE(J), T(J), R, DEVG(J), DGC(J)) If (DGE(J).EQ.0) DEVG(J) = 0.0 APDL = APDL + ABS(DEVL(J)) APDV = APDV + ABS(DEVG(J)) 100 Continue DN=NDT APDL=APDL/DN APDV=APDV/DN write(6,*)IT,Omw,APDL,APDV write(6,10) 'Pr','Tr','Gam','ZVC','ZLC','Fugr','DLE','DGE','DLC','DGC','DEVL',& 'DEVG' 10 Format(2A6, 2A8,2A10, 4A8, 2A7) DO 800 J=1,NDT write(6,19) Pr(J),Tr(J),Gam(J),ZVC(J),ZLC(J),Fugr(J),DLE(J),DGE(J),& DLC(J),DGC(J),DEVL(J),DEVG(J) 800 Continue 19 Format(2F6.3,2F8.4,F10.4,E10.2,4F8.4,2F7.2) deallocate(DLE, DGE, P, T, DLC, DGC, ZVC, ZLC, Fugr, DEVL, DEVG,Gam,Pr,Tr) end do close(5) close(6) Stop End SUBROUTINE Apdev (P, ZV, DGE, T, R, Pdev, Den)

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Den = P/(ZV*T*R) Dev = Den - DGE Pdev = 100.0*(Dev/DGE) RETURN END SUBROUTINE BISECT (XL, XR, FXL, FXR,EPS,T, Tc, P, Pc,Alp, Bet, BC, & BB, AC, R, ZVC, ZLC, XFIT, FIT) IMAX=50 ! EPS=1.0E-07 ! Check for Presence of a Root if(FXL*FXR)50,30,80 30 IT=1 if(FXL.NE.0.0)go to 40 XFIT=XL FIT=0.0 go to 80 40 XFIT=XR FIT=0.0 go to 80 ! Begin Bisection Method 50 do 70 IJ=1, IMAX XFIT=(XL*FXR-XR*FXL)/(FXR-FXL) AT=XFIT*AC Call Zfactr (Alp, Bet, AT, BC, P, T, R, BB, ZVC, ZLC) Call fugacty (Alp, Bet, P, T, R, AT, BB, ZVC, ZLC, AB,& FIT) ! Check for Convergence with Tolerance IF(ABS(FIT).LE.EPS) go to 80 ! Keep Right or Left Subinterval IF(FIT*FXL<0) go to 60 XL=XFIT FXL=FIT go to 70 60 XR=XFIT FXR=FIT 70 continue 80 RETURN END SUBROUTINE XNewton (T, P, Alp, Bet, BC, BB, AC,R, ZVC, ZLC, tmp, Fugr) IMAX=50 EPS=1.0E-07 ! Begin Newton-Raphson Method

121

oldtmp = tmp do 70 IJ=1, IMAX 30 continue AT=tmp*AC 20 continue Call Zfactr (Alp, Bet, AT, BC, P, T, R, BB, ZVC, ZLC) if (ZVC.NE.ZLC) GO TO 50 if (ZVC.EQ.ZLC) Tmp = Tmp*1.005 GO TO 20 50 Call fugacty (Alp, Bet, P, T, R, AT, BB, ZVC, ZLC, AB,Fugr) ! ...... Perform Derivative of the Fugacity ....... Call Dervfug (Alp, Bet, P, T, R, AT, BB, ZV, ZL, AC, DFugr) tmp = tmp - Fugr/DFugr ! Check for Convergence with Tolerance Ptmp = (tmp-oldtmp)/oldtmp IF(ABS(Ptmp).LE.EPS) go to 80 ! .... Keep New tmp ..... oldtmp = tmp 70 continue 80 RETURN END ! Oma=(1.+(Omw-1.)*Zc)**3 ! Omb=(Omw*Zc) Subroutine Crtpar(Tc, Pc, Zc, R, ACF, Omw, AC, BC, Alp, Bet) Oma=0.45724 Omb=0.07780 AC = Oma*(R**2*Tc**2/Pc) BC = Omb*R*Tc/Pc Alp= 2 Bet= 1 ! Alp= (1.+(Omw-3.)*Zc)/(Omw*Zc) ! Bet= (Zc**2*((Omw-1.)**3)+2.*Omw**2.*Zc+Omw*(1.-3.*Zc))/(Omw**2*Zc) Return End Subroutine Zfactr (Alp, Bet, AT,BC, P, T, R, BB, 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)

122

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 fugacty (Alp, Bet, P, T, R, AT, BB, ZV, ZL, AA, Fugr) AA = AT*P/(R**2*T**2) B2 = BB/2. D = sqrt(Alp**2 + 4.*Bet) Fir = ZV - ZL Sec = alog((ZL - BB)/(ZV - BB)) Zf = ((ZV + Alp*B2 + D*B2)/(ZV + Alp*B2 - D*B2)) Zs = ((ZL + Alp*B2 - D*B2)/(ZL + Alp*B2 + D*B2)) Thi = (AA/(D*BB))*alog(Zf*Zs) Fugr = Fir + Sec - Thi Return End Subroutine Dervfug (Alp, Bet, P, T, R, AT, BB, ZV, ZL, AC, DFugr) AA = AC*P/(R**2*T**2) B2 = BB/2. D = sqrt(Alp**2 + 4.*Bet) Zf = ((ZV + Alp*B2 + D*B2)/(ZV + Alp*B2 - D*B2)) Zs = ((ZL + Alp*B2 - D*B2)/(ZL + Alp*B2 + D*B2)) DFugr = (AA/(D*BB))*alog(Zf*Zs) Return End SUBROUTINE Cubic (MTYPE, A, Z) ! Program Dimensioned for 4 Coefficients ! a3*X^3 + a2*X^2 + a1*X + a0 = 0 ! a3 MUST be greater or equal to 1

123

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

124

! 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

B.1 FORTRAN Program for Critical Densities of Mixtures

Program CrtVol

Dimension T(100),X(20),rMw(20),ZC(20),AF(20),omgW(20),PC(20),

&TC(20),acLLS(20),bcLLS(20),acVDW(20),bcVDW(20),ALP(20),BET(20),

&Compstn(20),PCM(20),TCM(20),VCM(20),acPR(20),bcPR(20),acSRK(20),

&bcSRK(20)

Character* (30) MixName(20),Compnt(10)

OPEN (UNIT=5,FILE='InputA.TXT',STATUS='old')

OPEN (UNIT=6,FILE='OutputA.TXT',STATUS='unknown')

R=10.73

Read (5,*)NMix

Do 120 J=1,NMix

Read (5,*)NCMP

Read(5,*)MixName(J)

Write(6,*) MixName(J)

Do 14 I=1,NCMP

Read(5,*)Compnt(I)

125

Read(5,*)TC(I),PC(I),ZC(I),AF(I),rMw(I)

C Compute a(I),b(I),ALP(I),BET(I) (by calling para)

Call Para(X(I),ZC(I),AF(I),omgW(I),PC(I),TC(I),

& ALP(I),BET(I),acLLS(I),bcLLS(I),acVDW(I),bcVDW(I),

& acPR(I),bcPR(I),acSRK(I),bcSRK(I))

14 Continue

C write(6,*)J,rMw(11)

C Compute am,bm (by calling Mixrule)

Read (5,*)NDT

write(6,300)"Compstn","PCM","TCM","VCM"

300 Format(4(A10))

Do 10 IJ=1,NDT

Read(5,*)Compstn(IJ),PCM(IJ),TCM(IJ),VCM(IJ)

10 write(6,310)Compstn(IJ),PCM(IJ),TCM(IJ),VCM(IJ)

310 Format(4(F10.3))

C Call EOSrule(Ncomp,X,AF,rMw,acLLS,bcLLS,acVDW,bcVDW,acPR,bcPR,

C &acSRK,bcSRK,amLLS,bmLLS,amVDW,bmVDW,amPR,bmPR,amSRK,bmSRK)

C Call

EOSPCTC(Ncomp,X,Pci,Tci,amVDW,bmVDW,amPR,bmPR,amSRK,bmSRK,

C &PCVDW,TCVDW,PCPR,TCPR,PCSRK,TCSRK,PCKay,TCKay)

C Write(6,50)J,Tc,Pc,PCKay,TCKay,PCVDW,TCVDW,PCPR,TCPR,PCSRK,

C &TCSRK

50 Format(1X,I3,10(F8.2,1X))

Call Volume(NDT,NCMP,Compstn,ALP,BET,AF,rMw,TCM,PCM,VCM)

18 Format(2I8,8(F10.4,X))

120 Continue

Close(5)

Close(6)

Stop

126

END

Subroutine Volume (NDAT,NCMP,Z,ALP,BET,AF,wm,TCE,PCE,VCE)

Implicit None

Real ALP(10),BET(10),AF(10),wm(10),TCE(10),PCE(10),VCE(10),

& Z(20),ZCE(10),IDX(10),Exx,Ex,Alpm,RZC(3),X(10),ZCOEF(4),R,VC(10),

& Betm,wmI,wmJ,aIJ,bIJ,AL,BE,ZC,RMIN,RMAX,MTYPE,APD,Dev,VEC

Integer I,J,IE,ID,KI,KJ,NDAT,NCMP

Data IDX/0.1,0.125,0.2,0.25,0.333,0.375,0.4,0.5,0.625,0.875/

R=10.73

C Write(6,80) "I","J","Exx","Ex","VC","APD","ALP","BET"

80 Format(2(A3),6(A11,x))

Do 10 I=1,10

Do 10 J=I,10

Exx = IDX(I)

Ex = IDX(J)

APD=0.0

Do 30 ID = 1, NDAT

Alpm=0.0

Betm=0.0

X(1) = Z(ID)

X(2) = 1.0-Z(ID)

Do 20 KI=1,NCMP

Do 20 KJ=1,NCMP

wmI=AF(KI)*wm(KI)

wmJ=AF(KJ)*wm(KJ)

if (wmI .LE. wmJ) aIJ=(wmI/wmJ)**Exx

if (wmI .GT. wmJ) aIJ=(wmJ/wmI)**Exx

if (wmI .LE. wmJ) bIJ=(wmI/wmJ)**Ex

127

if (wmI .GT. wmJ) bIJ=(wmJ/wmI)**Ex

Alpm=Alpm+X(KI)*X(KJ)*sqrt(Alp(KI)*Alp(KJ))*aIJ

Betm=Betm+X(KI)*X(KJ)*sqrt(Bet(KI)*Bet(KJ))*bIJ

20 Continue

C.....Computation of Mixture Critical ZC........

AL=Alpm

BE=Betm

ZCOEF(1) = 8.0 +12.0*AL + 6.0* AL*AL + AL*AL*AL

ZCOEF(2) = -(3.0 + 12.0*AL + 12.0*AL*AL + 9.0*BE*(1.0-AL))

ZCOEF(3) = 3.0*AL + 6.*AL*AL + 6.*BE - 6.*AL*BE

ZCOEF(4) = -(BE + AL*AL - AL*BE)

C

CALL CUBIC (MTYPE, ZCOEF, RZC)

C.......Select Real Root........

RMIN = 1.0E+10

RMAX = 1.0E-10

DO 21 IE = 1,3

IF(RZC(IE) .LT. 0.0) GO TO 21

IF(RZC(IE) .LT. RMIN) RMIN = RZC(I)

IF(RZC(IE) .GT. RMAX) RMAX = RZC(I)

21 CONTINUE

ZC = RMAX

VC(ID)=ZC*R*TCE(ID)/PCE(ID)

ZCE(ID)=PCE(ID)*VCE(ID)/(R*TCE(ID))

Dev=(VC(ID)-VCE(ID))/VCE(ID)

APD=APD+abs(Dev)

write(6,250) I,J,Exx,Ex,VCE(ID),VC(ID),Alpm,Betm

250 Format(2(I3),2(F8.3),4(F10.4))

C

128

30 Continue

write (6,100)"I=",I,"J=",J,"APD=",APD

100 Format(2(A5,I3),(A5,F10.4,X))

10 Continue

Return

End

Subroutine Predict (NDAT,NCMP,Z,ALP,BET,AF,wm,TCE,PCE,VCE)

Implicit None

Real ALP(10),BET(10),AF(10),wm(10),TCE(10),PCE(10),VCE(10),

& Z(20),ZCE(10),IDX(10),Exx,Ex,Alpm,RZC(3),X(10),ZCOEF(4),R,

& Betm,wmI,wmJ,aIJ,bIJ,AL,BE,VC,ZC,RMIN,RMAX,MTYPE,APD,Dev,VEC

Integer I,J,IE,ID,KI,KJ,NDAT,NCMP

Data IDX/0.1,0.125,0.2,0.25,0.333,0.375,0.4,0.5,0.625,0.875/

R=10.73

Write(6,80) "I","J","Exx","Ex","APD","ALP","BET"

80 Format(2(A3),5(A11,x))

Do 10 I=1,10

Do 10 J=I,10

Exx = IDX(I)

Ex = IDX(J)

APD=0.0

Do 30 ID = 1, NDAT

Alpm=0.0

Betm=0.0

X(1) = Z(ID)

X(2) = 1.0-Z(ID)

Do 20 KI=1,NCMP

Do 20 KJ=1,NCMP

129

wmI=AF(KI)*wm(KI)

wmJ=AF(KJ)*wm(KJ)

if (wmI .LE. wmJ) aIJ=(wmI/wmJ)**Exx

if (wmI .GT. wmJ) aIJ=(wmJ/wmI)**Exx

if (wmI .LE. wmJ) bIJ=(wmI/wmJ)**Ex

if (wmI .GT. wmJ) bIJ=(wmJ/wmI)**Ex

Alpm=Alpm+X(KI)*X(KJ)*sqrt(Alp(KI)*Alp(KJ))*aIJ

Betm=Betm+X(KI)*X(KJ)*sqrt(Bet(KI)*Bet(KJ))*bIJ

20 Continue

C.....Computation of Mixture Critical ZC........

AL=Alpm

BE=Betm

ZCOEF(1) = 8.0 +12.0*AL + 6.0* AL*AL + AL*AL*AL

ZCOEF(2) = -(3.0 + 12.0*AL + 12.0*AL*AL + 9.0*BE*(1.0-AL))

ZCOEF(3) = 3.0*AL + 6.*AL*AL + 6.*BE - 6.*AL*BE

ZCOEF(4) = -(BE + AL*AL - AL*BE)

C

CALL CUBIC (MTYPE, ZCOEF, RZC)

C.......Select Real Root........

RMIN = 1.0E+10

RMAX = 1.0E-10

DO 21 IE = 1,3

IF(RZC(IE) .LT. 0.0) GO TO 21

IF(RZC(IE) .LT. RMIN) RMIN = RZC(I)

IF(RZC(IE) .GT. RMAX) RMAX = RZC(I)

21 CONTINUE

ZC = RMAX

VC=ZC*R*TCE(ID)/PCE(ID)

ZCE(ID)=PCE(ID)*VCE(ID)/(R*TCE(ID))

130

Dev=(VC-VCE(ID))/VCE(ID)

APD=APD+abs(Dev)

C

30 Continue

write (6,100)I,J,Exx,Ex,APD,Alpm,Betm

100 Format(2(I3),5(F11.4,X))

10 Continue

Return

End

Subroutine Para(X,Zc,AF,omgw,Pc,Tc,

& Alp,Bet,acLLS,bcLLS,acVDW,bcVDW,acPR,bcPR,acSRK,bcSRK)

Implicit None

Real X,Zc,AF,Pc,Tc,Alp,Bet,acLLS,bcLLS,

&acVDW,bcVDW,acPR,bcPR,omgw,acSRK,bcSRK,omgb,omga,R

R=10.73

omgw = 0.361/(1.0+0.0274*AF)

Alp = (1.0+omgw*Zc-3.0*Zc)/(omgw*Zc)

Bet = (Zc*Zc*(omgw-1.0)**3.0+(2.0*Zc*omgw

&*omgw)+omgw*(1.0-3.0*Zc))/(omgw*omgw*Zc)

omga = (1.0+(omgw-1.0)*Zc)**3.0

omgb = omgw*Zc

bcLLS = omgb*R*Tc/Pc

acLLS = omga*R**2*Tc**2/Pc

acVDW=0.4218*R**2*Tc**2/Pc

bcVDW=0.125*R*Tc/Pc

acPR=0.4572*R**2*Tc**2/Pc

bcPR=0.0778*R*Tc/Pc

acSRK=0.4275*R**2*Tc**2/Pc

131

bcSRK=0.0866*R*Tc/Pc

Return

End

Subroutine EOSrule(NComp,x,AF,wm,acLLS,bcLLS,acVDW,bcVDW,

&acPR,bcPR,acSRK,bcSRK,SumamLLS,bmLLS,SumamVDW,SumbmVDW,SumamPR

,

&SumbmPR,SumamSRK,SumbmSRK)

Implicit None

Integer I,J,NComp

Real SumamLLS,bmLLS,SumamVDW,SumbmVDW,SumamPR,SumbmPR,

&SumamSRK,SumbmSRK,SumAlpm,SumBetm

Real SumbmLLS,wmI,wmJ,BIN,exx

Real x(20),acLLS(20),bcLLS(20),acVDW(20),bcVDW(20),acPR(20),

&bcPR(20),acSRK(20),bcSRK(20),Alp(20),Bet(20),AF(20),wm(20)

SumamLLS=0.0

SumbmLLS=0.0

SumamVDW=0.0

SumbmVDW=0.0

SumamPR=0.0

SumbmPR=0.0

SumamSRK=0.0

SumbmSRK=0.0

SumAlpm = 0.0

SumBetm = 0.0

Do 16 I = 1,NComp

SumbmVDW = SumbmVDW + x(I)*bcVDW(I)

SumbmLLS = SumbmLLS + x(I)*bcLLS(I)**(1.0/3.0)

132

SumbmPR = SumbmPR + x(I)*bcPR(I)

SumbmSRK = SumbmSRK + x(I)*bcSRK(I)

16 Continue

bmLLS = (SumbmLLS)**3.0

Return

End

Subroutine

EOSPCTC(NComp,X,PC,TC,amVDW,bmVDW,amPR,bmPR,amSRK,

&bmSRK,VCVDW,VCPR,VCSRK,VCKay)

Implicit None

Integer NComp,I

Real amVDW,bmVDW,amPR,bmPR,amSRK,R,SumPC,SumTC,SumVC,X,

&bmSRK,PCVDW,TCVDW,VCVDW,PCPR,TCPR,VCPR,PCSRK,TCSRK,VCSRK,

&PCKay,TCKay,VCKay

Real Dimension X(20),TC(20),PC(20),VC(20)

R=10.73

SumPC=0.0

SumTC=0.0

SumVC=0.0

DO 10 I=1,NComp

SumPC=SumPC+X(I)*PC(I)

SumTC=SumTC+X(I)*TC(I)

SumVC=SumVC+X(I)*VC(I)

10 Continue

C Critical Parameters for Kay's Rule

PCKay=SumPC

TCKay=SumTC

133

VCKay=SumVC

C Critical Parameters for Peng-Robinson EOS

PCPR=(1.0/62.6)*amPR/bmPR**2

TCPR=(5.56/27.0)*amPR/(R*bmPR)

VCPR=3.94*bmPR

C Critical Parameters for Soave-Redlich-Kwong EOS

PCSRK=(1.0/58.8)*amSRK/bmSRK**2

TCSRK=(5.48/27.0)*amSRK/(R*bmSRK)

VCSRK=3.84*bmSRK

C Critical Parameters for Van der Waals EOS

PCVDW=(1.0/27.0)*amVDW/bmVDW**2

TCVDW=(8.0/27.0)*bmVDW/(R*bmVDW)

VCVDW=3.0*bmVDW

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

134

SQBOV=BETOV**2

DEL=SQBOV+CUAOV

IF (DEL) 90,10,40

10 MTYPE = 0

C 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

C 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

135

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

PEI=PEI+2.0943951


PEI=PEI+2.0943951


130 CONTINUE

IF (MTYPE .EQ. 1) Z(2) = -99.99

IF (MTYPE .EQ. 1) Z(3) = -99.99

RETURN

END

136

APPENDIX C

DENSITY PREDICTION RESULTS FOR PURE SUBSTANCES

C.1 Results for the Lawal-Lake-Silberberg Equation of State.

137

Table C1.1: Densities Prediction for Methane.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG0.02 0.59 1.0749 0.9654 4.30E-03 0.00E+00 1.653 0.007 1.5771 0.007 -4.591 0.130.03 0.61 1.0659 0.9534 6.20E-03 -3.00E-07 1.623 0.0101 1.5613 0.0101 -3.804 0.060.04 0.63 1.0619 0.9457 7.40E-03 0.00E+00 1.602 0.0122 1.5518 0.0122 -3.133 -0.220.05 0.64 1.0574 0.9369 8.90E-03 2.40E-07 1.586 0.0147 1.5417 0.0146 -2.792 -0.010.06 0.66 1.0535 0.9275 1.10E-02 -1.80E-07 1.57 0.0174 1.5313 0.0174 -2.468 0.150.07 0.67 1.0503 0.9175 1.20E-02 2.40E-07 1.551 0.0204 1.5204 0.0205 -1.97 0.20.08 0.68 1.0472 0.9067 1.40E-02 -3.00E-07 1.532 0.0239 1.509 0.024 -1.5 0.41

0.1 0.7 1.0436 0.8947 1.70E-02 2.40E-07 1.513 0.0279 1.4967 0.028 -1.076 0.480.11 0.71 1.0406 0.8821 1.90E-02 2.40E-07 1.495 0.0322 1.4839 0.0324 -0.741 0.610.13 0.73 1.0386 0.8691 2.20E-02 1.20E-07 1.477 0.0369 1.4709 0.0372 -0.413 0.850.15 0.74 1.0339 0.8535 2.50E-02 0.00E+00 1.456 0.0428 1.4554 0.0432 -0.043 1.140.17 0.76 1.0314 0.8382 2.90E-02 6.00E-08 1.436 0.0488 1.4401 0.0495 0.289 1.36

0.2 0.77 1.0288 0.8219 3.30E-02 1.20E-07 1.417 0.0555 1.4238 0.0565 0.481 1.70.22 0.79 1.0261 0.8044 3.70E-02 -2.40E-07 1.394 0.063 1.4063 0.0644 0.879 2.140.25 0.8 1.0237 0.7859 4.10E-02 -1.20E-07 1.373 0.0714 1.3875 0.0732 1.053 2.540.29 0.82 1.021 0.766 4.70E-02 1.80E-07 1.352 0.0808 1.3669 0.0832 1.104 3.020.32 0.83 1.0187 0.7452 5.20E-02 -1.20E-07 1.329 0.0911 1.3451 0.0943 1.215 3.480.36 0.84 1.0169 0.7236 5.80E-02 0.00E+00 1.304 0.1024 1.3219 0.1066 1.373 4.080.44 0.87 1.013 0.676 7.30E-02 0.00E+00 1.252 0.1294 1.2684 0.1365 1.313 5.480.49 0.89 1.0112 0.6498 8.10E-02 -1.80E-07 1.222 0.1455 1.2376 0.1547 1.278 6.290.55 0.9 1.0091 0.6215 9.10E-02 1.20E-07 1.192 0.1644 1.2027 0.1761 0.9 7.13

0.6 0.92 1.0076 0.5916 1.00E-01 -8.90E-08 1.159 0.1854 1.1644 0.2005 0.462 8.140.66 0.93 1.0064 0.5601 1.10E-01 -1.20E-07 1.119 0.2094 1.1217 0.2288 0.241 9.280.72 0.95 1.0053 0.5254 1.30E-01 -3.00E-08 1.077 0.2379 1.0721 0.2631 -0.456 10.580.79 0.96 1.0042 0.4866 1.50E-01 -8.90E-08 1.029 0.2727 1.013 0.3059 -1.552 12.160.86 0.98 1.0031 0.442 1.70E-01 -6.30E-05 0.968 0.3172 0.9391 0.3619 -2.989 14.09

1 1 1 0.286 2.90E-01 0.00E+00 0.629 0.629 0.6338 0.6338 0.755 0.76

138

Table C1.2: Densities Prediction for Ethane.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG0.001187 0.47 1.212 0.9968 2.50E-04 -1.40E-03 1.246 0.0003 1.2051 0.0003 -3.283 0.690.004719 0.53 1.1775 0.99 9.00E-04 6.00E-08 1.192 0.0011 1.1962 0.0011 0.355 -1.44

0.01 0.55 1.167 0.9864 1.30E-03 4.80E-07 1.175 0.0016 1.1895 0.0016 1.236 -0.260.01 0.58 1.1472 0.9763 2.50E-03 -2.40E-07 1.147 0.003 1.173 0.003 2.266 -0.730.02 0.6 1.1376 0.9696 3.30E-03 0.00E+00 1.131 0.004 1.1642 0.004 2.932 -0.360.02 0.6 1.1343 0.9678 3.50E-03 0.00E+00 1.127 0.0043 1.162 0.0043 3.102 -0.670.03 0.62 1.1271 0.9616 4.40E-03 -6.00E-08 1.116 0.0053 1.1545 0.0053 3.454 -0.410.04 0.65 1.1099 0.9421 7.20E-03 6.00E-08 1.083 0.0087 1.1337 0.0087 4.682 -0.460.06 0.67 1.1017 0.9303 9.00E-03 -2.40E-07 1.069 0.011 1.1223 0.0109 4.983 -0.610.07 0.69 1.094 0.9172 1.10E-02 4.20E-07 1.052 0.0136 1.1101 0.0135 5.524 -0.390.11 0.73 1.0792 0.8863 1.70E-02 2.40E-07 1.02 0.0204 1.0831 0.0203 6.189 -0.250.13 0.75 1.0721 0.8684 2.00E-02 2.40E-07 1.005 0.0246 1.0681 0.0246 6.278 0.120.16 0.76 1.0654 0.8489 2.40E-02 -2.40E-07 0.987 0.0295 1.0519 0.0296 6.574 0.380.19 0.78 1.0587 0.8275 2.80E-02 -2.40E-07 0.972 0.0353 1.0343 0.0355 6.408 0.680.23 0.8 1.0524 0.8044 3.40E-02 6.00E-08 0.953 0.0418 1.0152 0.0423 6.523 1.080.27 0.82 1.0462 0.7792 3.90E-02 6.00E-08 0.934 0.0494 0.9943 0.0502 6.451 1.590.31 0.84 1.0404 0.7521 4.60E-02 3.00E-07 0.916 0.0582 0.9714 0.0595 6.047 2.20.36 0.85 1.0349 0.7228 5.40E-02 0.00E+00 0.896 0.0683 0.9462 0.0703 5.602 2.890.42 0.87 1.0295 0.6909 6.30E-02 0.00E+00 0.873 0.0802 0.9181 0.0831 5.164 3.70.55 0.91 1.0196 0.6189 8.50E-02 2.40E-07 0.825 0.1105 0.8508 0.1169 3.133 5.760.62 0.94 1.0273 0.5816 9.80E-02 6.00E-08 0.776 0.1248 0.8137 0.1373 4.852 9.980.71 0.95 1.0108 0.5317 1.20E-01 6.00E-08 0.763 0.1551 0.7609 0.1684 -0.273 8.580.75 0.95 1.0087 0.5063 1.30E-01 -1.80E-07 0.742 0.1699 0.7327 0.1861 -1.256 9.52

0.8 0.96 1.0068 0.4788 1.40E-01 1.80E-07 0.72 0.187 0.701 0.2069 -2.635 10.60.84 0.97 1.0049 0.4487 1.60E-01 -7.70E-05 0.693 0.2071 0.6643 0.2318 -4.145 11.950.89 0.98 1.0031 0.4138 1.80E-01 -1.80E-05 0.66 0.2316 0.6206 0.2639 -5.971 13.95

1 1 1 0.279 2.80E-01 0.00E+00 0.422 0.422 0.4298 0.4298 1.85 1.85

139

Table C1.3: Densities Prediction for Propane.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG0.13 0.75 1.0787 0.8731 2.00E-02 4.80E-07 0.743 0.0159 0.7301 0.0169 -1.738 6.21

0.2 0.8 1.0611 0.8213 3.10E-02 3.00E-07 0.708 0.026 0.7039 0.0268 -0.582 3.060.31 0.84 1.0447 0.7568 4.70E-02 1.20E-07 0.669 0.0408 0.6706 0.0415 0.243 1.80.32 0.85 1.0426 0.746 5.00E-02 -1.20E-07 0.662 0.0434 0.6649 0.0443 0.433 1.990.44 0.89 1.0302 0.678 6.90E-02 4.20E-07 0.624 0.0616 0.627 0.0637 0.486 3.520.49 0.9 1.0267 0.6542 7.60E-02 -1.20E-07 0.61 0.0686 0.613 0.0715 0.497 4.170.62 0.93 1.0172 0.5795 1.00E-01 0.00E+00 0.568 0.0935 0.5658 0.0995 -0.381 6.50.65 0.94 1.0158 0.565 1.10E-01 -1.20E-07 0.56 0.0987 0.556 0.1057 -0.709 7.110.81 0.97 1.0075 0.4709 1.50E-01 -6.00E-08 0.501 0.1383 0.4863 0.1534 -2.943 10.920.85 0.98 1.0058 0.4452 1.60E-01 -8.10E-05 0.484 0.1452 0.4648 0.169 -3.961 16.42

1 1 1 0.281 2.80E-01 0.00E+00 0.308 0.3077 0.3069 0.3069 -0.369 -0.29

140

Table C1.4: Densities Prediction for n-Butane.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG0.06 0.69 1.1128 0.9312 9.20E-03 4.80E-07 0.625 0.0059 0.6006 0.0059 -3.911 -0.160.09 0.73 1.0949 0.9017 1.40E-02 1.80E-07 0.6 0.0092 0.5888 0.0093 -1.861 0.530.09 0.73 1.0932 0.8993 1.50E-02 1.80E-07 0.599 0.0095 0.5879 0.0096 -1.855 0.980.11 0.74 1.0873 0.8871 1.70E-02 4.20E-07 0.592 0.011 0.5833 0.0111 -1.476 0.750.15 0.77 1.0756 0.8598 2.20E-02 1.20E-07 0.577 0.0145 0.573 0.0147 -0.695 1.170.15 0.77 1.0749 0.8587 2.20E-02 -6.00E-08 0.577 0.0146 0.5726 0.0149 -0.764 1.50.18 0.79 1.0661 0.8341 2.70E-02 -1.20E-07 0.564 0.0181 0.5634 0.0185 -0.105 1.650.22 0.81 1.0578 0.8086 3.30E-02 -4.80E-07 0.552 0.0219 0.5538 0.0225 0.324 2.520.23 0.81 1.0571 0.8039 3.40E-02 -3.60E-07 0.549 0.0228 0.552 0.0233 0.551 1.90.27 0.83 1.0496 0.7751 4.10E-02 1.80E-07 0.53 0.0276 0.541 0.0283 2.068 2.650.36 0.87 1.038 0.7204 5.40E-02 6.00E-08 0.508 0.0375 0.5191 0.039 2.186 4.20.44 0.89 1.0287 0.6747 6.70E-02 1.80E-07 0.493 0.0463 0.4996 0.0495 1.345 6.840.54 0.92 1.022 0.6175 8.40E-02 1.20E-07 0.467 0.0601 0.4734 0.0646 1.368 7.42

0.6 0.93 1.0171 0.5864 9.50E-02 3.60E-07 0.454 0.0673 0.4581 0.074 0.895 9.840.73 0.95 1.0116 0.5153 1.20E-01 1.20E-07 0.42 0.0893 0.4198 0.099 -0.053 10.860.79 0.97 1.0084 0.4762 1.40E-01 -1.80E-07 0.4 0.1029 0.3965 0.1153 -0.864 12.060.91 0.99 1.0035 0.3983 1.80E-01 -1.20E-04 0.346 0.1364 0.3436 0.155 -0.707 13.58

1 1 1 0.274 2.70E-01 0.00E+00 0.245 0.2451 0.2446 0.2446 -0.145 -0.19

141

Table C1.5: Densities Prediction for i-Butane.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG0.14 0.76 1.0934 0.869 2.10E-02 -2.40E-07 0.577 0.0137 0.5714 0.0138 -0.977 0.140.15 0.77 1.0885 0.8581 2.30E-02 -1.80E-07 0.571 0.0153 0.5668 0.0153 -0.74 0.040.19 0.79 1.078 0.8323 2.90E-02 1.80E-07 0.558 0.0193 0.556 0.0192 -0.364 -0.350.21 0.8 1.0735 0.8202 3.10E-02 3.00E-07 0.553 0.0211 0.5509 0.0211 -0.384 0.410.24 0.82 1.0673 0.8018 3.60E-02 -1.80E-07 0.544 0.0243 0.5432 0.0242 -0.155 -0.240.28 0.84 1.0583 0.7727 4.30E-02 -2.40E-07 0.53 0.0276 0.5308 0.0295 0.147 6.930.31 0.84 1.0545 0.7598 4.60E-02 2.40E-07 0.524 0.0314 0.5252 0.0319 0.23 1.520.38 0.87 1.0442 0.7175 5.80E-02 1.20E-07 0.505 0.04 0.5065 0.0407 0.298 1.760.43 0.88 1.038 0.6875 6.60E-02 -1.80E-07 0.491 0.0461 0.4927 0.0476 0.35 3.220.57 0.92 1.0251 0.613 9.10E-02 1.20E-07 0.459 0.0629 0.4563 0.0675 -0.583 7.330.59 0.93 1.0229 0.5986 9.60E-02 1.80E-07 0.453 0.0664 0.4489 0.0719 -0.912 8.160.76 0.96 1.0123 0.5073 1.30E-01 3.00E-08 0.406 0.0893 0.3977 0.1043 -2.039 16.760.79 0.97 1.0104 0.4851 1.40E-01 0.00E+00 0.393 0.0974 0.3842 0.1136 -2.237 16.62

1 1 1 0.283 2.80E-01 0.00E+00 0.238 0.2377 0.2371 0.2371 -0.391 -0.24

142

Table C1.6: Densities Prediction for n-Pentane.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG0.03 0.66 1.1482 0.9559 5.20E-03 6.00E-07 0.525 0.0027 0.5023 0.0027 -4.318 0.120.04 0.68 1.138 0.9468 6.50E-03 6.00E-08 0.518 0.0034 0.4989 0.0034 -3.689 0.420.05 0.7 1.1318 0.9354 8.20E-03 5.40E-07 0.509 0.0044 0.4949 0.0044 -2.777 -0.30.06 0.71 1.1212 0.9273 9.50E-03 -6.00E-08 0.505 0.005 0.4921 0.005 -2.557 0.960.08 0.73 1.109 0.9094 1.20E-02 -6.00E-08 0.495 0.0066 0.4862 0.0067 -1.768 0.390.09 0.73 1.1065 0.9051 1.30E-02 1.80E-07 0.493 0.007 0.4849 0.0071 -1.646 0.4

0.1 0.75 1.1002 0.8927 1.50E-02 -6.00E-08 0.487 0.0082 0.481 0.0083 -1.236 0.670.12 0.76 1.0917 0.8767 1.80E-02 -1.20E-07 0.479 0.0098 0.4761 0.0099 -0.615 0.680.13 0.77 1.0903 0.8706 1.90E-02 -3.00E-07 0.476 0.0104 0.4742 0.0105 -0.379 0.860.16 0.79 1.079 0.8467 2.40E-02 5.40E-07 0.467 0.0131 0.4669 0.0132 -0.022 1.160.19 0.8 1.0727 0.827 2.80E-02 1.20E-07 0.458 0.0155 0.4609 0.0156 0.627 0.44

0.2 0.81 1.0688 0.8185 3.00E-02 1.20E-07 0.455 0.0163 0.4583 0.0166 0.722 1.80.26 0.83 1.0579 0.7851 3.70E-02 0.00E+00 0.442 0.0206 0.4479 0.0211 1.335 2.530.28 0.84 1.0551 0.7729 4.00E-02 -1.80E-07 0.438 0.0222 0.4441 0.0228 1.382 2.80.31 0.85 1.0501 0.7533 4.40E-02 -6.00E-08 0.43 0.025 0.4378 0.0258 1.806 3.110.38 0.88 1.0404 0.7098 5.50E-02 -1.20E-07 0.415 0.0316 0.4233 0.0329 1.998 4.080.41 0.88 1.0372 0.6927 6.00E-02 1.20E-07 0.41 0.0346 0.4174 0.036 1.798 4.150.51 0.91 1.0273 0.6345 7.60E-02 2.40E-07 0.39 0.0449 0.3962 0.0476 1.583 6.10.61 0.93 1.0197 0.5768 9.50E-02 -6.00E-08 0.369 0.0571 0.3731 0.0614 1.107 7.590.67 0.95 1.0159 0.5429 1.10E-01 8.90E-08 0.356 0.0649 0.3584 0.0706 0.68 8.860.82 0.97 1.008 0.4572 1.40E-01 -5.10E-04 0.321 0.0885 0.3158 0.0991 -1.624 12.020.87 0.98 1.0057 0.42 1.60E-01 -1.20E-04 0.305 0.1007 0.2963 0.1141 -2.847 13.31

1 1 1 0.27 2.70E-01 0.00E+00 0.205 0.2053 0.1994 0.1994 -2.721 -2.88

143

Table C1.7: Densities Prediction for i-Pentane.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG0.000408 0.48 1.3039 0.9982 1.20E-04 2.80E-02 0.6 0.0001 0.5923 0.0001 -1.276 0.03 0.000612 0.49 1.2902 0.9976 1.70E-04 6.10E-03 0.595 0.0001 0.583 0.0001 -2.011 -2.020.000877 0.51 1.2791 0.9968 2.40E-04 -1.60E-04 0.59 0.0001 0.5727 0.0001 -2.926 -1.410.001264 0.52 1.2672 0.9957 3.30E-04 3.60E-04 0.585 0.0002 0.5762 0.0002 -1.497 -0.330.003324 0.55 1.2359 0.9909 7.70E-04 2.90E-05 0.57 0.0004 0.5723 0.0004 0.403 1.31

0.01 0.57 1.2262 0.9886 1.00E-03 4.80E-07 0.566 0.0006 0.57 0.0006 0.708 -0.750.01 0.58 1.2166 0.9859 1.30E-03 4.20E-07 0.559 0.0007 0.5674 0.0007 1.495 0.630.01 0.59 1.2074 0.9828 1.60E-03 3.00E-07 0.554 0.0009 0.565 0.0009 1.988 -0.530.01 0.6 1.1986 0.9792 2.00E-03 3.60E-07 0.55 0.0012 0.5623 0.0012 2.243 0.140.02 0.62 1.1898 0.9751 2.50E-03 4.80E-07 0.546 0.0014 0.5598 0.0014 2.52 -0.530.02 0.63 1.1812 0.9705 3.00E-03 4.80E-07 0.541 0.0018 0.5569 0.0017 2.935 -0.590.02 0.64 1.173 0.9653 3.70E-03 3.00E-07 0.537 0.0021 0.554 0.0021 3.158 -0.120.03 0.65 1.1648 0.9595 4.40E-03 6.00E-08 0.531 0.0026 0.5509 0.0025 3.739 -0.550.03 0.66 1.1569 0.9531 5.30E-03 1.20E-07 0.527 0.003 0.5476 0.003 3.913 -0.350.04 0.68 1.1491 0.946 6.30E-03 -1.80E-07 0.521 0.0036 0.5442 0.0036 4.459 -0.120.06 0.7 1.134 0.9298 8.60E-03 -1.80E-07 0.511 0.005 0.5369 0.005 5.071 -0.050.08 0.72 1.1199 0.9106 1.20E-02 0.00E+00 0.502 0.0067 0.5289 0.0067 5.354 0.260.11 0.75 1.1064 0.8883 1.50E-02 -3.00E-07 0.491 0.0089 0.52 0.009 5.899 0.660.14 0.77 1.0934 0.8625 2.00E-02 -1.80E-07 0.481 0.0117 0.51 0.0118 6.024 1.030.18 0.8 1.0811 0.8331 2.60E-02 4.20E-07 0.47 0.015 0.4988 0.0153 6.125 1.780.23 0.82 1.0693 0.7997 3.20E-02 -1.20E-07 0.457 0.0192 0.4861 0.0197 6.36 2.540.29 0.84 1.0582 0.7622 4.10E-02 2.40E-07 0.444 0.0243 0.4716 0.0252 6.207 3.610.36 0.87 1.0478 0.7201 5.10E-02 -2.40E-07 0.43 0.0306 0.4548 0.0321 5.767 4.880.54 0.92 1.0285 0.6186 7.90E-02 0.00E+00 0.396 0.0487 0.4113 0.0528 3.853 8.450.66 0.94 1.0189 0.555 1.00E-01 6.00E-08 0.375 0.0625 0.381 0.0692 1.6 10.720.78 0.96 1.011 0.4812 1.30E-01 0.00E+00 0.345 0.0816 0.3422 0.0928 -0.81 13.73

1 1 1 0.27 2.70E-01 0.00E+00 0.204 0.204 0.2042 0.2042 0.081 0.08

144

Table C1.8: Densities Prediction for n-Hexane.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG0.00149 0.53 1.318 0.9964 2.50E-04 2.10E-04 0.502 0.0001 0.4688 0.0001 -6.621 -0.940.00357 0.56 1.2854 0.9925 5.80E-04 -3.00E-05 0.49 0.0003 0.4631 0.0003 -5.484 -0.44

0.01 0.59 1.264 0.9886 9.40E-04 3.00E-07 0.479 0.0004 0.4607 0.0004 -3.813 -0.550.01 0.6 1.2536 0.986 1.20E-03 1.20E-07 0.476 0.0006 0.4585 0.0005 -3.679 -1.860.01 0.62 1.2334 0.9798 1.80E-03 4.80E-07 0.468 0.0009 0.4546 0.0008 -2.854 -0.890.02 0.63 1.2238 0.9761 2.20E-03 6.00E-08 0.464 0.001 0.4525 0.001 -2.473 -0.150.02 0.65 1.2051 0.9671 3.20E-03 0.00E+00 0.455 0.0015 0.4479 0.0015 -1.554 -0.810.02 0.66 1.2044 0.9649 3.50E-03 1.80E-07 0.453 0.0016 0.447 0.0016 -1.335 0.040.05 0.7 1.1699 0.9425 6.30E-03 -2.40E-07 0.438 0.003 0.4376 0.0029 -0.102 -0.350.07 0.73 1.1452 0.9173 9.90E-03 2.40E-07 0.425 0.0046 0.4284 0.0046 0.791 -0.220.08 0.74 1.1378 0.9077 1.10E-02 1.20E-07 0.422 0.0053 0.4251 0.0053 0.725 0

0.1 0.75 1.1304 0.8972 1.30E-02 -6.00E-08 0.417 0.0061 0.4216 0.0061 1.095 0.120.11 0.76 1.1233 0.8861 1.50E-02 -1.80E-07 0.413 0.0069 0.4179 0.007 1.189 0.30.16 0.79 1.102 0.8475 2.10E-02 1.80E-07 0.399 0.0101 0.4055 0.0102 1.638 1.030.18 0.81 1.0957 0.8331 2.40E-02 1.20E-07 0.395 0.0114 0.401 0.0115 1.522 1.370.26 0.84 1.0761 0.7835 3.40E-02 6.00E-08 0.379 0.0162 0.3853 0.0166 1.665 2.570.35 0.87 1.0584 0.725 4.70E-02 6.00E-08 0.361 0.0226 0.3663 0.0236 1.469 4.510.47 0.91 1.0425 0.6561 6.40E-02 -1.80E-07 0.342 0.0313 0.3427 0.0335 0.196 7.310.52 0.92 1.0375 0.6303 7.10E-02 -1.20E-07 0.334 0.0348 0.3333 0.0378 -0.196 8.540.68 0.95 1.0223 0.5392 1.00E-01 3.00E-08 0.305 0.0492 0.298 0.0558 -2.298 13.290.74 0.96 1.0183 0.5052 1.10E-01 3.00E-08 0.292 0.0552 0.2837 0.0639 -2.86 15.75

0.8 0.97 1.0136 0.4665 1.30E-01 -3.90E-04 0.274 0.0627 0.2658 0.0744 -3.006 18.540.87 0.98 1.0089 0.4186 1.50E-01 -1.00E-04 0.247 0.0728 0.2435 0.0892 -1.42 22.41

1 1 1 0.264 2.60E-01 0.00E+00 0.139 0.139 0.1594 0.1594 14.661 14.66

145

Table C1.9: Densities Prediction for n-Heptane.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG0.00184 0.54 1.3015 0.9957 3.20E-04 -4.30E-05 0.425 0.0001 0.4035 0.0001 -5.068 -0.830.00315 0.56 1.2812 0.9933 5.30E-04 -2.10E-04 0.419 0.0002 0.3975 0.0002 -5.128 1.54

0.01 0.58 1.2603 0.9898 8.50E-04 8.40E-06 0.412 0.0003 0.3963 0.0003 -3.816 0.570.01 0.59 1.2503 0.9877 1.10E-03 -6.50E-06 0.409 0.0004 0.3953 0.0004 -3.35 -0.870.01 0.6 1.2407 0.9852 1.30E-03 -1.90E-06 0.406 0.0005 0.3939 0.0005 -2.977 -0.780.01 0.61 1.2317 0.9824 1.60E-03 -6.00E-08 0.402 0.0006 0.3921 0.0006 -2.461 0.30.01 0.00080.62 1.2223 0.9792 2.00E-03 2.40E-07 0.399 0.0008 0.3907 -2.092 0.010.02 0.64 1.2042 0.9716 2.80E-03 -1.80E-07 0.393 0.0011 0.3876 0.0011 -1.378 -0.290.02 0.65 1.1955 0.9671 3.40E-03 2.40E-07 0.39 0.0013 0.3859 0.0013 -1.059 00.03 0.66 1.1871 0.9622 4.00E-03 1.20E-07 0.387 0.0016 0.3841 0.0016 -0.747 -0.380.03 0.67 1.1787 0.9567 4.70E-03 -6.00E-08 0.384 0.0019 0.3823 0.0019 -0.438 -0.390.04 0.69 1.1704 0.9507 5.40E-03 -1.80E-07 0.381 0.0022 0.3804 0.0022 -0.154 00.04 0.7 1.1624 0.9442 6.30E-03 -3.00E-07 0.377 0.0025 0.3784 0.0025 0.371 0.290.05 0.71 1.1545 0.937 7.30E-03 -1.20E-07 0.374 0.0029 0.3763 0.0029 0.619 0.360.06 0.72 1.1468 0.9293 8.40E-03 -3.00E-07 0.371 0.0034 0.3741 0.0034 0.845 0.370.07 0.73 1.1393 0.921 9.70E-03 -6.00E-08 0.367 0.0039 0.3718 0.0039 1.316 0.510.08 0.74 1.1319 0.912 1.10E-02 -2.40E-07 0.364 0.0044 0.3694 0.0045 1.492 0.570.13 0.78 1.1041 0.8692 1.80E-02 -6.00E-08 0.35 0.0073 0.3585 0.0074 2.418 1.330.17 0.8 1.0913 0.8435 2.30E-02 2.40E-07 0.343 0.0093 0.3521 0.0094 2.639 1.720.21 0.82 1.0794 0.8148 2.80E-02 -1.80E-07 0.335 0.0116 0.3449 0.0119 2.957 2.370.32 0.86 1.0576 0.7474 4.20E-02 -6.00E-08 0.318 0.0178 0.3277 0.0186 3.053 4.190.38 0.88 1.047 0.7072 5.20E-02 3.60E-07 0.309 0.022 0.317 0.0232 2.579 5.360.46 0.9 1.0366 0.6618 6.30E-02 -1.20E-07 0.298 0.0273 0.3042 0.0291 2.087 6.770.55 0.92 1.0268 0.6105 7.80E-02 0.00E+00 0.286 0.034 0.2889 0.0369 1.009 8.340.65 0.94 1.0175 0.552 9.70E-02 -6.00E-08 0.271 0.0429 0.2699 0.0473 -0.409 10.230.77 0.96 1.0082 0.4816 1.20E-01 1.20E-07 0.251 0.0561 0.2446 0.0627 -2.56 11.83

1 1 1 0.263 2.60E-01 0.00E+00 0.144 0.144 0.1438 0.1438 -0.158 -0.16

146

Table C1.10: Densities Prediction for n-Octane.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG0.05 0.71 1.1573 0.9425 6.70E-03 -2.40E-07 0.3318 0.0023 0.317 0.0023 -4.462 -1.630.06 0.73 1.1445 0.9295 8.60E-03 5.40E-07 0.3264 0.003 0.3143 0.0029 -3.697 -3.190.08 0.74 1.1321 0.9147 1.10E-02 6.00E-07 0.3211 0.0037 0.3114 0.0037 -3.009 -0.4

0.1 0.76 1.1193 0.8974 1.40E-02 -1.20E-07 0.3154 0.0046 0.3082 0.0047 -2.292 1.190.12 0.78 1.1078 0.8784 1.70E-02 -6.00E-08 0.3097 0.0058 0.3047 0.0058 -1.63 -0.030.15 0.8 1.0973 0.8574 2.00E-02 -1.20E-07 0.3036 0.0072 0.3008 0.0071 -0.918 -0.70.18 0.81 1.087 0.834 2.50E-02 -3.00E-07 0.2974 0.0088 0.2965 0.0088 -0.291 -0.310.22 0.83 1.0767 0.8077 3.00E-02 6.00E-08 0.2906 0.0107 0.2917 0.0107 0.374 0.390.26 0.85 1.067 0.7786 3.60E-02 0.00E+00 0.2836 0.0129 0.2862 0.0131 0.927 1.590.31 0.87 1.0575 0.7465 4.30E-02 -6.00E-08 0.2761 0.0157 0.28 0.016 1.41 1.760.37 0.88 1.0487 0.7113 5.10E-02 1.20E-07 0.2678 0.019 0.2729 0.0194 1.902 2.320.44 0.9 1.0396 0.6714 6.10E-02 1.20E-07 0.2586 0.0232 0.2644 0.0238 2.246 2.70.51 0.92 1.0313 0.6278 7.20E-02 1.20E-07 0.2489 0.028 0.2545 0.0293 2.248 4.5

0.6 0.94 1.0234 0.5789 8.70E-02 2.10E-07 0.2385 0.034 0.2425 0.0363 1.661 6.660.69 0.95 1.0157 0.5225 1.10E-01 2.10E-07 0.2253 0.0422 0.2272 0.0458 0.829 8.51

0.8 0.97 1.0081 0.457 1.30E-01 -5.10E-04 0.2087 0.0537 0.2064 0.0594 -1.102 10.651 1 1 0.259 2.60E-01 0.00E+00 0.1272 0.1272 0.1269 0.1269 -0.259 -0.26

147

Table C1.11: Densities Prediction for n-Decane.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG0.001 0.53 1.667 0.998 9.20E-05 -1.50E-02 0.3092 0 0.3271 0 5.796 0.2370.001 0.557 1.4013 0.9969 2.00E-04 1.60E-04 0.3028 0.0001 0.3036 0.0001 0.272 -1.1250.003 0.584 1.3703 0.9943 4.00E-04 -2.70E-06 0.2965 0.0001 0.3004 0.0001 1.309 -0.2610.005 0.611 1.34 0.9902 7.30E-04 3.00E-07 0.2904 0.0002 0.2992 0.0002 3.04 -0.2440.009 0.638 1.3161 0.9846 1.20E-03 -2.40E-07 0.2845 0.0004 0.2961 0.0004 4.049 -1.2430.017 0.665 1.2775 0.9748 2.20E-03 -1.20E-07 0.2789 0.0007 0.2923 0.0007 4.809 -0.6220.028 0.692 1.2419 0.9614 3.70E-03 1.80E-07 0.2729 0.0011 0.288 0.0011 5.513 -1.50.044 0.719 1.2164 0.9454 5.50E-03 1.20E-07 0.2672 0.0017 0.2836 0.0017 6.13 -1.7980.068 0.746 1.1862 0.9233 8.40E-03 0.00E+00 0.2601 0.0026 0.2782 0.0025 6.969 -0.80.102 0.773 1.1557 0.8946 1.20E-02 6.60E-07 0.2524 0.0038 0.2718 0.0038 7.722 0.1390.152 0.8 1.121 0.8557 1.90E-02 -1.80E-07 0.2445 0.0056 0.2636 0.0057 7.835 1.7780.211 0.827 1.0969 0.814 2.60E-02 0.00E+00 0.2365 0.0079 0.255 0.0081 7.831 2.0750.235 0.836 1.0886 0.7979 2.90E-02 6.00E-08 0.231 0.0089 0.2517 0.009 8.948 1.6010.294 0.854 1.0689 0.7592 3.60E-02 -3.60E-07 0.225 0.0113 0.2436 0.0116 8.264 2.7310.343 0.872 1.0626 0.7294 4.30E-02 -6.00E-08 0.2175 0.0142 0.2373 0.0138 9.081 -2.5350.408 0.89 1.051 0.69 5.10E-02 0.00E+00 0.21 0.0175 0.2286 0.0171 8.865 -2.5480.474 0.908 1.044 0.6521 6.10E-02 2.40E-07 0.2 0.0214 0.22 0.0205 10.011 -3.9040.572 0.926 1.0275 0.5939 7.70E-02 0.00E+00 0.19 0.0269 0.2061 0.0267 8.468 -0.9890.657 0.944 1.0211 0.5451 9.20E-02 -8.90E-08 0.179 0.0333 0.1936 0.0327 8.157 -1.710.752 0.962 1.0149 0.489 1.10E-01 0.00E+00 0.164 0.045 0.1782 0.041 8.68 -8.9530.869 0.98 1.0055 0.4125 1.50E-01 -4.70E-04 0.1443 0.06 0.1542 0.0551 6.833 -8.115

1 1 1 0.2563 2.60E-01 0.00E+00 0.1 0.1 0.1001 0.1001 0.009 0.009

148

Table C1.12: Densities Prediction for Cyclohexane.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG0.03 0.64 1.1492 0.9636 4.20E-03 6.00E-08 0.534 0.0022 0.5099 0.0022 -4.52 1.40.03 0.66 1.1391 0.9552 5.40E-03 1.80E-07 0.5265 0.0028 0.5064 0.0029 -3.811 2.360.04 0.67 1.1285 0.9446 7.00E-03 0.00E+00 0.5183 0.0036 0.5024 0.0037 -3.069 2.890.06 0.69 1.1181 0.9325 8.80E-03 0.00E+00 0.5106 0.0047 0.4981 0.0047 -2.457 0.560.07 0.71 1.109 0.9191 1.10E-02 0.00E+00 0.5025 0.0059 0.4935 0.0059 -1.797 0.50.09 0.73 1.0998 0.9038 1.40E-02 1.20E-07 0.4945 0.0074 0.4884 0.0074 -1.225 -0.230.11 0.75 1.0898 0.8861 1.70E-02 1.80E-07 0.4861 0.0091 0.4828 0.0092 -0.679 0.80.14 0.77 1.0802 0.8664 2.10E-02 -3.00E-07 0.4773 0.0111 0.4766 0.0113 -0.141 1.820.17 0.78 1.0715 0.8451 2.50E-02 4.20E-07 0.4683 0.0136 0.47 0.0138 0.355 1.350.24 0.82 1.055 0.7955 3.50E-02 3.00E-07 0.4495 0.0197 0.4544 0.0202 1.085 2.70.28 0.84 1.0477 0.7675 4.20E-02 -1.20E-07 0.4389 0.0235 0.4454 0.0243 1.477 3.460.33 0.86 1.0414 0.7377 4.90E-02 0.00E+00 0.4282 0.0282 0.4355 0.0291 1.706 3.030.39 0.87 1.0351 0.7049 5.80E-02 -3.00E-07 0.4164 0.0334 0.4243 0.0348 1.888 4.060.45 0.89 1.0297 0.67 6.70E-02 1.20E-07 0.4037 0.0396 0.4117 0.0415 1.985 4.730.52 0.91 1.024 0.6308 7.90E-02 1.20E-07 0.3899 0.0469 0.3969 0.0499 1.783 6.32

0.6 0.93 1.0188 0.588 9.30E-02 8.90E-08 0.3752 0.0553 0.3796 0.0602 1.164 8.840.68 0.95 1.0142 0.5407 1.10E-01 6.00E-08 0.3578 0.0665 0.3589 0.0733 0.319 10.180.78 0.96 1.0094 0.4851 1.30E-01 6.00E-08 0.3365 0.0814 0.3324 0.0913 -1.227 12.170.88 0.98 1.0044 0.416 1.70E-01 -1.10E-04 0.3081 0.1039 0.2947 0.1189 -4.348 14.4

1 1 1 0.273 2.70E-01 0.00E+00 0.2025 0.2025 0.2015 0.2015 -0.475 -0.48

149

Table C1.13: Densities Prediction for Carbon Dioxide.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG0.07 0.71 1.1074 0.9194 1.10E-02 0.00E+00 1.623 0.0195 1.5957 0.0195 -1.682 -0.060.08 0.72 1.1034 0.9123 1.20E-02 -6.00E-08 1.611 0.0217 1.5884 0.0217 -1.402 0.02

0.1 0.74 1.0934 0.8955 1.50E-02 -4.20E-07 1.589 0.0271 1.5717 0.0272 -1.088 0.190.11 0.75 1.0886 0.8864 1.70E-02 3.60E-07 1.567 0.0302 1.5628 0.0303 -0.27 0.30.12 0.76 1.0836 0.8767 1.90E-02 -5.40E-07 1.556 0.0335 1.5533 0.0337 -0.174 0.430.15 0.78 1.0752 0.8563 2.30E-02 3.00E-07 1.535 0.041 1.5336 0.0412 -0.089 0.680.17 0.78 1.0713 0.8455 2.50E-02 2.40E-07 1.525 0.0451 1.5232 0.0454 -0.119 0.860.18 0.79 1.0673 0.8341 2.80E-02 1.80E-07 1.515 0.0496 1.5121 0.0501 -0.192 1.030.22 0.81 1.059 0.809 3.30E-02 1.80E-07 1.485 0.06 1.4877 0.0608 0.179 1.410.24 0.82 1.0549 0.7954 3.60E-02 -1.80E-07 1.475 0.0659 1.4743 0.067 -0.047 1.670.26 0.83 1.0509 0.7813 3.90E-02 6.00E-08 1.457 0.0723 1.4603 0.0737 0.223 1.890.31 0.85 1.0442 0.752 4.70E-02 -1.20E-07 1.429 0.0863 1.4304 0.0885 0.095 2.510.34 0.86 1.0408 0.7363 5.00E-02 1.20E-07 1.411 0.0943 1.414 0.0969 0.21 2.840.36 0.87 1.0375 0.7197 5.50E-02 -1.20E-07 1.403 0.103 1.3963 0.1063 -0.477 3.180.42 0.89 1.0317 0.6853 6.40E-02 1.80E-07 1.369 0.1224 1.3582 0.1273 -0.786 3.980.46 0.89 1.0284 0.6661 7.00E-02 3.00E-07 1.353 0.134 1.3362 0.1399 -1.239 4.440.49 0.9 1.0256 0.6465 7.60E-02 -6.00E-08 1.337 0.1463 1.313 0.1536 -1.793 4.960.57 0.92 1.0202 0.6044 8.90E-02 1.20E-07 1.298 0.1748 1.2606 0.1856 -2.878 6.210.61 0.93 1.0172 0.5809 9.70E-02 -6.00E-08 1.277 0.1922 1.2296 0.2054 -3.712 6.860.66 0.94 1.0135 0.5544 1.10E-01 -2.10E-07 1.255 0.2136 1.193 0.2295 -4.942 7.450.75 0.96 1.0094 0.5019 1.30E-01 1.50E-07 1.202 0.2576 1.1149 0.2833 -7.244 9.980.79 0.97 1.0081 0.4741 1.40E-01 -1.80E-07 1.171 0.2816 1.0703 0.3156 -8.596 12.10.85 0.98 1.0065 0.4425 1.60E-01 -7.90E-05 1.136 0.3096 1.0156 0.3563 -10.596 15.09

1 1 1 0.274 2.70E-01 0.00E+00 0.664 0.6644 0.6649 0.6649 0.131 0.07

150

Table C1.14: Densities Prediction for Nitrogen.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG0.09 0.7 1.0536 0.8978 1.70E-02 -1.20E-07 1.668 0.0299 1.6198 0.0301 -2.892 0.66

0.1 0.71 1.0522 0.8933 1.80E-02 2.40E-07 1.66 0.0316 1.615 0.0318 -2.713 0.80.12 0.72 1.0475 0.8781 2.10E-02 3.60E-07 1.637 0.0375 1.599 0.0379 -2.323 1.060.12 0.73 1.0472 0.8769 2.10E-02 2.40E-07 1.63 0.038 1.5977 0.0384 -1.983 1.080.15 0.75 1.0417 0.8562 2.60E-02 -6.60E-07 1.601 0.0465 1.5761 0.0472 -1.555 1.490.16 0.76 1.0393 0.8462 2.80E-02 -4.20E-07 1.586 0.0508 1.5658 0.0516 -1.274 1.670.18 0.77 1.0361 0.8318 3.10E-02 -2.40E-07 1.566 0.0572 1.5508 0.0583 -0.97 1.97

0.2 0.78 1.0336 0.8198 3.40E-02 -1.20E-07 1.545 0.0627 1.5383 0.0642 -0.436 2.270.23 0.79 1.0308 0.8051 3.80E-02 -1.80E-07 1.525 0.0698 1.5227 0.0716 -0.148 2.60.27 0.81 1.0258 0.7757 4.60E-02 -6.00E-07 1.487 0.0847 1.4914 0.0875 0.293 3.34

0.3 0.83 1.023 0.7568 5.10E-02 3.00E-07 1.463 0.0948 1.4707 0.0984 0.528 3.830.33 0.83 1.0212 0.7437 5.40E-02 1.80E-07 1.451 0.1022 1.4561 0.1064 0.35 4.190.39 0.86 1.017 0.7088 6.50E-02 1.80E-07 1.405 0.1228 1.4161 0.1292 0.788 5.180.41 0.86 1.016 0.6992 6.80E-02 -3.00E-07 1.394 0.1288 1.4048 0.1358 0.773 5.440.46 0.88 1.0132 0.6706 7.70E-02 -2.40E-07 1.357 0.1475 1.3702 0.1567 0.975 6.280.51 0.89 1.0108 0.6418 8.60E-02 -1.20E-07 1.317 0.1676 1.3338 0.1796 1.278 7.170.53 0.9 1.0099 0.6289 9.10E-02 0.00E+00 1.303 0.177 1.3169 0.1905 1.069 7.60.61 0.92 1.0072 0.5867 1.10E-01 8.90E-08 1.248 0.2101 1.2593 0.229 0.901 90.62 0.92 1.007 0.5829 1.10E-01 -3.00E-08 1.244 0.2134 1.2537 0.2328 0.783 9.110.71 0.94 1.0046 0.5311 1.30E-01 -6.00E-08 1.17 0.2592 1.1765 0.2876 0.552 10.930.81 0.97 1.0029 0.4747 1.60E-01 -1.20E-07 1.092 0.317 1.0834 0.3578 -0.788 12.860.82 0.97 1.0028 0.4707 1.60E-01 0.00E+00 1.088 0.3216 1.0765 0.3632 -1.061 12.940.93 0.99 1.0013 0.3912 2.10E-01 -2.80E-05 0.978 0.4265 0.925 0.487 -5.423 14.2

1 1 1 0.289 2.90E-01 0.00E+00 0.694 0.6945 0.6985 0.6985 0.651 0.58

151

Table C1.15: Densities Prediction for Hydrogen Sulfide.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG0.01 0.58 1.1464 0.9774 2.50E-03 -2.40E-07 1.747 0.0042 1.6498 0.0042 -5.562 00.02 0.6 1.1409 0.9725 3.10E-03 -7.70E-07 1.726 0.0053 1.6408 0.0053 -4.936 0.070.03 0.63 1.1266 0.9601 4.90E-03 0.00E+00 1.677 0.0083 1.6212 0.0083 -3.33 0.380.03 0.64 1.1187 0.9525 6.10E-03 1.20E-07 1.658 0.0102 1.6103 0.0103 -2.88 0.290.05 0.67 1.1033 0.9342 9.00E-03 -6.00E-08 1.621 0.0152 1.5865 0.0153 -2.13 0.550.06 0.68 1.0959 0.9236 1.10E-02 1.80E-07 1.595 0.0183 1.5735 0.0185 -1.351 0.870.08 0.7 1.0889 0.9119 1.30E-02 -6.60E-07 1.578 0.0219 1.5598 0.0221 -1.156 1.080.09 0.71 1.0821 0.8992 1.50E-02 6.00E-08 1.553 0.0259 1.5452 0.0262 -0.502 1.410.11 0.73 1.0744 0.8848 1.80E-02 -1.80E-07 1.536 0.0305 1.5291 0.0312 -0.449 2.450.13 0.74 1.0697 0.8707 2.10E-02 1.20E-07 1.513 0.0356 1.5135 0.0363 0.035 2.060.15 0.76 1.0639 0.8548 2.40E-02 1.80E-07 1.489 0.0413 1.4962 0.0424 0.483 2.530.18 0.77 1.0584 0.8378 2.80E-02 1.80E-07 1.467 0.0478 1.4777 0.0492 0.73 3

0.2 0.79 1.0532 0.8197 3.20E-02 3.60E-07 1.438 0.055 1.458 0.057 1.389 3.590.23 0.8 1.0483 0.8004 3.70E-02 6.00E-08 1.418 0.0631 1.4368 0.0657 1.326 4.170.27 0.82 1.0435 0.7798 4.20E-02 -6.00E-08 1.391 0.072 1.414 0.0756 1.657 4.88

0.3 0.83 1.039 0.7579 4.70E-02 6.00E-08 1.365 0.0821 1.3895 0.0867 1.793 5.670.34 0.85 1.0347 0.7346 5.40E-02 -1.20E-07 1.334 0.0933 1.3628 0.0994 2.16 6.50.39 0.86 1.0306 0.7098 6.10E-02 1.20E-07 1.304 0.1059 1.3337 0.1139 2.281 7.50.44 0.88 1.0267 0.6834 6.80E-02 2.40E-07 1.276 0.1202 1.3019 0.1305 2.026 8.580.49 0.89 1.0229 0.6551 7.70E-02 6.00E-08 1.243 0.1363 1.2666 0.1496 1.9 9.780.54 0.91 1.0193 0.6248 8.80E-02 -6.00E-08 1.203 0.1547 1.2273 0.172 2.021 11.17

0.6 0.92 1.0159 0.5921 9.90E-02 1.20E-07 1.164 0.1759 1.183 0.1984 1.631 12.780.67 0.94 1.0126 0.5564 1.10E-01 -2.10E-07 1.12 0.2008 1.1322 0.2302 1.087 14.60.74 0.95 1.0095 0.517 1.30E-01 -8.90E-08 1.071 0.2307 1.0726 0.2695 0.152 16.810.81 0.97 1.0065 0.4721 1.50E-01 1.20E-07 1.015 0.268 1.0002 0.3203 -1.459 19.520.89 0.98 1.0035 0.4186 1.80E-01 -1.50E-04 0.947 0.3179 0.9038 0.3913 -4.562 23.08

1 1 1 0.284 2.80E-01 0.00E+00 0.639 0.6393 0.6334 0.6334 -0.876 -0.92

152

Table C1.16: Densities Prediction for Carbon Monoxide.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG0.03 0.61 1.1306 0.9588 5.30E-03 1.20E-07 1.7897 0.0098 1.7666 0.0098 -1.289 -0.410.03 0.63 1.1302 0.9528 6.20E-03 -3.60E-07 1.7696 0.012 1.7552 0.0115 -0.812 -4.150.09 0.7 1.0919 0.9016 1.60E-02 6.00E-07 1.6671 0.029 1.6709 0.0289 0.227 -0.190.19 0.77 1.068 0.8312 3.10E-02 -1.20E-07 1.5535 0.0602 1.5697 0.0594 1.044 -1.370.36 0.85 1.0463 0.735 5.80E-02 6.00E-08 1.4242 0.1025 1.4343 0.1133 0.709 10.540.61 0.93 1.0278 0.6055 1.00E-01 -1.20E-07 1.2481 0.1961 1.2389 0.213 -0.735 8.62

1 1 1 0.299 3.00E-01 0.00E+00 0.6709 0.6709 0.6586 0.6586 -1.826 -1.83

Table C1.17: Densities Prediction for Chlorine.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG0.01 0.56 1.1223 0.9815 1.90E-03 3.00E-07 1.3895 0.0025 1.3192 0.0025 -5.06 0.20.01 0.57 1.1154 0.9771 2.40E-03 6.00E-08 1.3759 0.0032 1.313 0.0033 -4.574 0.280.03 0.61 1.0978 0.9617 4.50E-03 2.40E-07 1.3368 0.006 1.2937 0.006 -3.228 0.530.04 0.64 1.0868 0.9479 6.50E-03 -2.40E-07 1.3095 0.0086 1.279 0.0087 -2.331 0.770.05 0.67 1.0765 0.9312 9.00E-03 -1.20E-07 1.281 0.0121 1.263 0.0123 -1.406 1.140.08 0.69 1.067 0.9115 1.20E-02 -1.80E-07 1.2525 0.0166 1.2452 0.0168 -0.585 1.48

0.1 0.72 1.0581 0.8886 1.60E-02 -6.00E-08 1.2221 0.0222 1.2255 0.0226 0.279 1.960.14 0.75 1.0499 0.8622 2.10E-02 -2.40E-07 1.1902 0.0291 1.2036 0.0299 1.128 2.520.18 0.77 1.0423 0.8324 2.70E-02 6.00E-08 1.1579 0.0377 1.1789 0.0389 1.815 3.20.23 0.8 1.0353 0.7988 3.50E-02 0.00E+00 1.1229 0.0482 1.151 0.0502 2.502 3.990.29 0.83 1.0289 0.7611 4.40E-02 1.20E-07 1.0865 0.0612 1.119 0.0642 2.986 4.920.44 0.88 1.0177 0.6722 6.70E-02 -6.00E-08 1.0059 0.0971 1.0383 0.1041 3.219 7.280.54 0.91 1.0129 0.6193 8.40E-02 1.20E-07 0.9588 0.1224 0.9858 0.1332 2.824 8.790.65 0.93 1.0086 0.5591 1.00E-01 0.00E+00 0.9046 0.1562 0.9206 0.1723 1.761 10.350.77 0.96 1.0048 0.4878 1.30E-01 1.20E-07 0.837979 0.204394 0.8346 0.2289 -0.406 12.01

1 1 1 0.275 2.80E-01 0.00E+00 0.5037 0.5037 0.5045 0.5045 0.17 0.17

153

Table C1.18: Densities Prediction for Benzene.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG0.03 0.65 1.1429 0.961 4.60E-03 1.80E-07 0.6426 0.0029 0.6102 0.0029 -5.047 -0.340.05 0.68 1.1214 0.9403 7.60E-03 0.00E+00 0.6241 0.0048 0.6009 0.0048 -3.718 0.730.08 0.60480.72 1.102 0.9136 1.20E-02 3.00E-07 0.0077 0.5902 0.0077 -2.421 -0.480.12 0.75 1.0847 0.8803 1.80E-02 1.80E-07 0.5842 0.0115 0.5776 0.0116 -1.125 1.220.17 0.79 1.0688 0.8397 2.60E-02 -2.40E-07 0.5629 0.0167 0.5627 0.0172 -0.033 2.840.21 0.81 1.062 0.8169 3.00E-02 -1.80E-07 0.5519 0.0199 0.5543 0.0206 0.437 3.590.34 0.86 1.0429 0.735 4.90E-02 1.20E-07 0.514 0.0336 0.523 0.0351 1.755 4.450.46 0.9 1.0306 0.6663 6.80E-02 1.20E-07 0.4847 0.0478 0.4944 0.0502 1.996 5.070.69 0.95 1.0151 0.5363 1.10E-01 -3.00E-08 0.4258 0.083 0.431 0.0888 1.222 6.940.78 0.97 1.0104 0.4807 1.30E-01 1.20E-07 0.3983 0.1029 0.399 0.1106 0.188 7.5

1 1 1 0.271 2.70E-01 0.00E+00 0.2398 0.2398 0.2427 0.2427 1.221 1.22

Table C1.19: Densities Prediction for Fluorobenzene.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG0.03 0.65 1.1401 0.9622 4.20E-03 6.00E-08 0.6084 0.0025 0.5766 0.0025 -5.223 1.180.06 0.7 1.1119 0.9301 8.80E-03 -6.60E-07 0.5817 0.0054 0.5641 0.0053 -3.022 -1.140.07 0.72 1.0988 0.9144 1.10E-02 6.00E-08 0.5724 0.0068 0.5587 0.0069 -2.397 1.040.14 0.77 1.0724 0.86 2.10E-02 -4.20E-07 0.5433 0.0129 0.5406 0.013 -0.488 0.540.21 0.81 1.0578 0.8142 2.90E-02 6.00E-08 0.5221 0.0189 0.5257 0.019 0.685 0.70.29 0.85 1.044 0.7587 4.10E-02 -1.20E-07 0.4983 0.0272 0.5069 0.0276 1.725 1.520.46 0.9 1.0269 0.6562 6.70E-02 2.40E-07 0.4571 0.0457 0.4686 0.0477 2.527 4.320.54 0.92 1.0216 0.615 7.80E-02 6.00E-08 0.441 0.0546 0.4515 0.0576 2.371 5.530.62 0.93 1.0165 0.569 9.30E-02 -8.90E-08 0.4225 0.0655 0.4307 0.0703 1.944 7.310.71 0.95 1.0117 0.5171 1.10E-01 3.00E-08 0.4004 0.0796 0.405 0.087 1.155 9.240.81 0.97 1.007 0.4566 1.40E-01 -2.50E-04 0.3728 0.0997 0.3708 0.1104 -0.529 10.75

1 1 1 0.263 2.60E-01 0.00E+00 0.23 0.23 0.2306 0.2306 0.244 0.24

154

Table C1.20: Densities Prediction for Bromobenzene.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG0.02 0.65 1.1538 0.9636 3.90E-03 1.20E-07 0.5166 0.0021 0.5009 0.002 -3.037 -3.640.03 0.66 1.1437 0.9559 4.90E-03 -1.20E-07 0.5108 0.0026 0.4978 0.0025 -2.537 -1.930.04 0.68 1.1351 0.9474 6.00E-03 3.60E-07 0.5048 0.0032 0.4946 0.0032 -2.018 -1.410.05 0.69 1.1259 0.9376 7.40E-03 -2.40E-07 0.4983 0.0039 0.491 0.0039 -1.456 -0.280.07 0.72 1.1097 0.9149 1.10E-02 -4.20E-07 0.4854 0.0058 0.4834 0.0057 -0.409 -1.490.11 0.75 1.0935 0.8869 1.50E-02 3.60E-07 0.4722 0.0083 0.4745 0.0082 0.489 -10.13 0.77 1.0858 0.8708 1.80E-02 -2.40E-07 0.4647 0.0099 0.4695 0.0098 1.04 -1.280.18 0.8 1.0704 0.8338 2.50E-02 2.40E-07 0.4497 0.0136 0.4582 0.0137 1.884 0.680.21 0.81 1.0632 0.8129 2.90E-02 3.00E-07 0.4413 0.016 0.4517 0.0161 2.367 0.7

1 1 1 0.263 2.60E-01 0.00E+00 0.1821 0.1821 0.1926 0.1926 5.76 5.76

Table C1.21: Densities Prediction for Chlorobenzene.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG0.03 0.65 1.1506 0.9605 4.40E-03 -2.40E-07 0.5393 0.0024 0.5192 0.0024 -3.725 -1.270.04 0.67 1.1405 0.9519 5.50E-03 1.20E-07 0.5324 0.003 0.5157 0.003 -3.13 0.090.05 0.69 1.1305 0.9421 6.90E-03 1.20E-07 0.5258 0.0038 0.512 0.0038 -2.618 -0.910.06 0.7 1.1215 0.9312 8.50E-03 -1.20E-07 0.5188 0.0047 0.5081 0.0047 -2.061 -0.920.09 0.73 1.1048 0.9057 1.30E-02 1.80E-07 0.5042 0.0069 0.4995 0.0069 -0.93 0.32

0.1 0.75 1.0965 0.8907 1.50E-02 5.40E-07 0.4967 0.0084 0.4947 0.0084 -0.412 -0.450.15 0.78 1.0809 0.8561 2.10E-02 -1.20E-07 0.481 0.0119 0.4837 0.012 0.566 0.720.18 0.8 1.0735 0.8364 2.50E-02 -1.20E-07 0.4724 0.0141 0.4775 0.0143 1.085 1.070.21 0.81 1.0663 0.8149 2.90E-02 4.80E-07 0.4634 0.0166 0.4708 0.0169 1.587 1.670.28 0.84 1.0514 0.765 4.00E-02 -6.00E-08 0.4446 0.0231 0.4547 0.0237 2.263 2.550.33 0.86 1.0444 0.7369 4.60E-02 6.00E-08 0.4345 0.0273 0.4452 0.028 2.474 2.57

1 1 1 0.265 2.60E-01 0.00E+00 0.2027 0.2027 0.2026 0.2026 -0.07 -0.07

155

Table C1.22: Densities Prediction for Iodobenzene.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG0.02 0.64 1.1621 0.9655 3.70E-03 0.00E+00 0.4785 0.0018 0.4674 0.0018 -2.328 -1.420.03 0.66 1.1538 0.9589 4.50E-03 6.00E-08 0.4734 0.0022 0.4647 0.0022 -1.838 -0.60.04 0.67 1.145 0.9513 5.50E-03 4.80E-07 0.4681 0.0027 0.4619 0.0027 -1.332 -0.610.04 0.68 1.136 0.9426 6.70E-03 -1.80E-07 0.4628 0.0033 0.4588 0.0033 -0.869 -0.810.05 0.7 1.1275 0.9331 8.10E-03 0.00E+00 0.4572 0.004 0.4555 0.004 -0.366 -1.110.07 0.71 1.1191 0.9225 9.70E-03 2.40E-07 0.4518 0.0048 0.4521 0.0047 0.058 -1.10.08 0.73 1.1106 0.9107 1.20E-02 3.00E-07 0.4462 0.0057 0.4483 0.0057 0.478 -0.450.09 0.74 1.1026 0.8978 1.40E-02 2.40E-07 0.4401 0.0067 0.4444 0.0067 0.973 0.510.11 0.75 1.0947 0.8837 1.60E-02 - 42 -0.541.80E-07 0.43 0.008 0.4401 0.008 1.363

1 1 1 0.265 2.60E-01 0.00E+00 0.1779 0.1779 0.1776 0.1776 -0.156 -0.16

Table C1.23: Densities Prediction for 1,3 Butadiene.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.000525 0.47 1.313 0.9984 1.10E-04 2.60E-02 0.8384 0.0001 0.7697 0.0001 -8.197 00.000798 0.48 1.2782 0.9978 1.50E-04 2.00E-02 0.8313 0.0001 0.8276 0.0001 -0.438 -0.040.001709 0.51 1.252 0.9958 3.20E-04 6.80E-05 0.8177 0.0003 0.8106 0.0003 -0.867 -0.070.004575 0.55 1.2212 0.9905 7.90E-04 -5.30E-05 0.7969 0.0006 0.8032 0.0006 0.794 -0.12

0.01 0.57 1.202 0.985 1.40E-03 -3.60E-07 0.7827 0.0011 0.7939 0.0011 1.428 -0.140.01 0.6 1.1839 0.9775 2.20E-03 4.80E-07 0.7684 0.0018 0.7865 0.0018 2.358 -0.160.03 0.65 1.1504 0.955 5.00E-03 0.00E+00 0.7386 0.004 0.7678 0.004 3.955 -0.120.06 0.69 1.1275 0.9304 8.40E-03 -6.00E-08 0.7152 0.0068 0.7515 0.0068 5.085 0.050.13 0.76 1.0932 0.8726 1.80E-02 -1.20E-07 0.673 0.0146 0.7181 0.0148 6.7 0.70.22 0.81 1.0693 0.809 3.00E-02 0.00E+00 0.6355 0.0251 0.6834 0.0255 7.531 1.670.28 0.84 1.0582 0.7705 3.90E-02 6.00E-08 0.6148 0.0323 0.6623 0.0331 7.717 2.480.35 0.86 1.048 0.7272 4.90E-02 2.40E-07 0.5924 0.0414 0.6379 0.0428 7.685 3.41

1 1 1 0.27 2.70E-01 0.00E+00 0.2826 0.2826 0.2826 0.2826 0 0

156

Table C1.24: Densities Prediction for Xenon.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.1 0.7 1.0476 0.8894 1.70E-02 6.00E-08 1.3276 0.0228 1.3041 0.0253 -1.769 11.14

0.15 0.74 1.0388 0.8567 2.40E-02 -2.40E-07 1.2834 0.0376 1.2719 0.0357 -0.893 -5.080.2 0.77 1.0334 0.8206 3.20E-02 0.00E+00 1.2387 0.0514 1.237 0.0485 -0.137 -5.7

0.27 0.8 1.0239 0.7753 4.30E-02 -1.80E-07 1.194 0.0651 1.1927 0.0667 -0.111 2.440.35 0.84 1.0242 0.7328 5.50E-02 0.00E+00 1.1459 0.0856 1.1501 0.0861 0.363 0.540.46 0.87 1.0119 0.6689 7.40E-02 -1.20E-07 1.0898 0.1132 1.0826 0.1201 -0.664 6.060.55 0.91 1.0199 0.624 8.90E-02 -1.80E-07 1.0314 0.1488 1.0322 0.1478 0.075 -0.640.71 0.94 1.0073 0.5352 1.20E-01 -1.20E-07 0.9448 0.2002 0.9232 0.2146 -2.291 7.18

1 1 1 0.287 2.90E-01 0.00E+00 0.5487 0.5487 0.5325 0.5325 -2.949 -2.95

Table C1.25: Densities Prediction for Helium.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.02 0.42 0.7102 0.9522 8.00E-03 0.00E+00 2.2782 0.0192 2.2812 0.0191 0.13 -0.640.04 0.46 0.7341 0.9349 1.20E-02 1.80E-07 2.2644 0.0281 2.261 0.0279 -0.152 -0.670.05 0.5 0.757 0.915 1.60E-02 -4.20E-07 2.2466 0.0392 2.2393 0.039 -0.324 -0.590.08 0.54 0.779 0.8925 2.10E-02 -6.60E-07 2.2251 0.0529 2.2155 0.0527 -0.432 -0.370.11 0.58 0.8002 0.8675 2.70E-02 -6.00E-08 2.2003 0.0694 2.1893 0.0693 -0.497 -0.020.14 0.62 0.8206 0.84 3.50E-02 1.80E-07 2.1721 0.089 2.1604 0.0894 -0.541 0.390.18 0.65 0.8405 0.81 4.30E-02 -6.00E-08 2.1406 0.1123 2.128 0.1133 -0.589 0.880.23 0.69 0.8597 0.7774 5.30E-02 -4.20E-07 2.1051 0.1399 2.0914 0.142 -0.654 1.490.29 0.73 0.8784 0.7422 6.40E-02 -1.20E-07 2.0652 0.1724 2.0497 0.1762 -0.753 2.180.36 0.77 0.8968 0.7041 7.60E-02 0.00E+00 2.0199 0.2111 2.0015 0.2173 -0.91 2.950.44 0.81 0.9148 0.6629 9.10E-02 6.00E-08 1.9676 0.2574 1.945 0.2671 -1.147 3.770.52 0.85 0.9324 0.618 1.10E-01 -6.00E-08 1.9059 0.3142 1.8772 0.3287 -1.505 4.620.62 0.88 0.9497 0.5683 1.30E-01 -1.20E-07 1.830201 0.386092 1.7931 0.4068 -2.026 5.36

1 1 1 0.301 3.00E-01 0.00E+00 1.0862 1.0862 1.0916 1.0916 0.501 0.5

157

Table C1.26: Densities Prediction for Argon.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.01 0.56 1.0866 0.9756 2.90E-03 -6.00E-08 2.2106 0.0063 2.1221 0.0063 -4.003 0.010.02 0.56 1.084 0.9729 3.30E-03 3.00E-07 2.2 0.0072 2.1162 0.0072 -3.809 -0.040.03 0.6 1.0732 0.9593 5.30E-03 -1.80E-07 2.1519 0.0116 2.0891 0.0116 -2.918 0.070.04 0.63 1.0632 0.942 8.20E-03 3.00E-07 2.1019 0.0179 2.0594 0.018 -2.025 0.210.07 0.66 1.0541 0.9207 1.20E-02 3.00E-07 2.0495 0.0264 2.0261 0.0265 -1.141 0.37

0.1 0.7 1.0459 0.8951 1.70E-02 -4.80E-07 1.9952 0.0377 1.9889 0.0379 -0.316 0.630.14 0.73 1.0384 0.8652 2.30E-02 4.80E-07 1.9378 0.0522 1.9469 0.0527 0.472 1.020.19 0.76 1.0316 0.8306 3.10E-02 1.80E-07 1.8766 0.0707 1.8991 0.0718 1.201 1.530.25 0.8 1.0256 0.7912 4.10E-02 1.20E-07 1.8123 0.0941 1.8442 0.0962 1.761 2.170.32 0.83 1.0201 0.7465 5.30E-02 -3.00E-07 1.7424 0.1238 1.7801 0.1275 2.165 30.41 0.86 1.0153 0.6958 6.90E-02 -3.00E-07 1.6643 0.1619 1.7039 0.1683 2.377 40.52 0.89 1.011 0.6379 8.80E-02 -3.00E-07 1.5769 0.2118 1.6109 0.2226 2.151 5.130.65 0.93 1.007 0.5704 1.10E-01 -3.00E-08 1.4721 0.2804 1.4921 0.2983 1.36 6.41

0.8 0.96 1.0035 0.4875 1.50E-01 -6.00E-08 1.3335 0.3861 1.328 0.4139 -0.407 7.211 1 1 0.291 2.90E-01 0.00E+00 0.8372 0.8372 0.8379 0.8379 0.083 0.08

Table C1.27: Densities Prediction for Hydrogen.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.009 0.451 0.9156 0.9799 2.60E-03 -5.40E-07 2.363 0.0062 2.3386 0.0061 -1.03 -0.970.019 0.496 0.926 0.9659 4.80E-03 -4.20E-07 2.3206 0.0118 2.3062 0.0115 -0.62 -2.480.068 0.601 0.9445 0.9139 1.50E-02 -1.20E-07 2.2091 0.0359 2.2139 0.0361 0.22 0.440.168 0.701 0.9594 0.8376 3.30E-02 1.20E-07 2.0822 0.0818 2.0973 0.0833 0.73 1.83

1 1 1 0.305 3.10E-01 0.00E+00 0.9606 0.9606 0.9557 0.9557 -0.51 -0.51

158

Table C1.28: Densities Prediction for Ammonia.

Pr Tr Tmp ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.003377 0.55 1.2411 0.9927 5.20E-04 -1.80E-07 2.5777 0.0013 2.4648 0.0013 -4.378 -0.770.004666 0.56 1.2304 0.9904 7.10E-04 0.00E+00 2.5541 0.0018 2.4539 0.0018 -3.926 -0.83

0.01 0.58 1.22 0.9877 9.50E-04 -8.90E-07 2.5289 0.0024 2.4372 0.0023 -3.624 -0.990.01 0.59 1.2098 0.9845 1.20E-03 2.40E-07 2.504 0.0031 2.4259 0.0031 -3.122 -1.140.01 0.6 1.1998 0.9807 1.60E-03 -2.40E-07 2.4787 0.004 2.4133 0.004 -2.639 -1.190.01 0.61 1.195 0.9786 1.80E-03 1.70E-06 2.4652 0.0045 2.4062 0.0045 -2.39 -1.360.02 0.62 1.1853 0.9738 2.30E-03 -3.00E-07 2.4395 0.0057 2.3919 0.0057 -1.954 -1.490.02 0.63 1.1805 0.9711 2.60E-03 -1.20E-07 2.4274 0.0064 2.3855 0.0063 -1.73 -1.470.02 0.64 1.1712 0.9652 3.20E-03 -5.40E-07 2.4007 0.008 2.3698 0.0079 -1.287 -1.680.03 0.65 1.1666 0.9619 3.60E-03 1.80E-07 2.387 0.009 2.3622 0.0088 -1.039 -1.740.03 0.66 1.1621 0.9585 4.00E-03 6.00E-08 2.3735 0.0099 2.3542 0.0098 -0.812 -1.780.04 0.67 1.1532 0.9509 4.90E-03 1.20E-07 2.3488 0.0117 2.3376 0.0119 -0.475 2.160.04 0.68 1.1445 0.9424 5.90E-03 -1.80E-07 2.3182 0.0148 2.3198 0.0145 0.071 -1.940.05 0.7 1.136 0.933 7.10E-03 1.20E-07 2.2902 0.0178 2.3012 0.0175 0.481 -2.010.07 0.71 1.1277 0.9226 8.50E-03 -1.20E-07 2.2611 0.0213 2.2813 0.0209 0.894 -2.070.08 0.73 1.1196 0.9112 1.00E-02 -6.00E-08 2.231 0.0254 2.2604 0.0249 1.316 -2.130.11 0.75 1.1041 0.885 1.40E-02 -6.00E-08 2.1692 0.0354 2.2144 0.0346 2.084 -2.190.15 0.78 1.0894 0.8541 1.90E-02 1.80E-07 2.1047 0.0482 2.1621 0.0473 2.729 -20.17 0.79 1.0823 0.8368 2.20E-02 0.00E+00 2.0705 0.0561 2.1332 0.055 3.025 -1.940.19 0.8 1.0788 0.8276 2.30E-02 1.80E-07 2.0531 0.0603 2.1179 0.0593 3.153 -1.820.23 0.82 1.0687 0.798 2.80E-02 -1.80E-07 1.998 0.0752 2.0685 0.0738 3.531 -1.75

0.3 0.85 1.0561 0.7535 3.70E-02 1.20E-07 1.9208 0.0996 1.9933 0.0983 3.774 -1.260.38 0.88 1.0443 0.7025 4.80E-02 1.80E-07 1.8356 0.1313 1.9042 0.1306 3.741 -0.530.48 0.9 1.0333 0.6439 6.20E-02 -2.40E-07 1.7398 0.1734 1.7964 0.1742 3.253 0.48

0.6 0.93 1.0231 0.5758 8.20E-02 1.80E-07 1.6266 0.2311 1.6617 0.2354 2.156 1.880.74 0.96 1.0137 0.4939 1.10E-01 1.20E-07 1.4866 0.3167 1.4829 0.3285 -0.244 3.72

1 1 1 0.255 2.50E-01 0.00E+00 0.861 0.861 0.8228 0.8228 -4.435 -4.43

159

Table C1.29: Densities Prediction for Acetic Acid.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.02 0.66 1.1283 0.9718 2.2E-03 0.0E+00 0.9751 0.0033 0.8687 0.002 -10.91 -39.430.03 0.69 1.1069 0.9531 4.0E-03 1.2E-07 0.9451 0.0057 0.8607 0.0036 -8.934 -36.150.07 0.75 1.082 0.9148 8.1E-03 -4.8E-07 0.9038 0.0113 0.8463 0.0075 -6.366 -33.670.11 0.78 1.0665 0.8791 1.2E-02 1.2E-07 0.8746 0.0175 0.8338 0.0116 -4.667 -33.450.13 0.8 1.059 0.8576 1.5E-02 1.2E-07 0.8592 0.0213 0.8264 0.0144 -3.823 -32.380.24 0.85 1.0378 0.7758 2.6E-02 0.0E+00 0.8071 0.0377 0.797 0.0268 -1.251 -29.010.34 0.88 1.0253 0.7045 3.7E-02 -2.4E-07 0.7655 0.0537 0.7686 0.0403 0.406 -24.96

0.4 0.9 1.0197 0.6629 4.4E-02 3.6E-07 0.7418 0.0641 0.7502 0.0497 1.132 -22.520.55 0.93 1.0101 0.5658 6.2E-02 3.0E-07 0.6891 0.0918 0.7002 0.077 1.61 -16.120.64 0.95 1.0063 0.509 7.5E-02 -1.8E-07 0.6584 0.1115 0.6651 0.0976 1.013 -12.420.75 0.96 1.0033 0.4446 9.1E-02 -1.5E-07 0.6185 0.1384 0.6182 0.127 -0.053 -8.220.86 0.98 1.001 0.3693 1.2E-01 -1.7E-04 0.5637 0.1786 0.55 0.1729 -2.439 -3.2

1 1 1 0.211 2.1E-01 0.0E+00 0.3645 0.3645 0.3462 0.3462 -5.02 -5.02

Table C1.30: Densities Prediction for Acetone.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.02 0.65 1.1299 0.9669 3.10E-03 3.60E-07 0.8061 0.0021 0.7544 0.0024 -6.411 13.780.05 0.69 1.1039 0.9402 6.20E-03 3.60E-07 0.7728 0.0043 0.7419 0.0049 -4.001 12.95

0.1 0.75 1.0734 0.8881 1.30E-02 -6.00E-08 0.7298 0.0097 0.7208 0.0106 -1.228 9.250.2 0.81 1.0474 0.8116 2.50E-02 -1.80E-07 0.6815 0.0172 0.6913 0.0212 1.44 23.070.3 0.85 1.0322 0.744 3.70E-02 6.00E-08 0.646 0.0258 0.6639 0.0328 2.769 27.18

0.43 0.89 1.019 0.6607 5.40E-02 -6.00E-08 0.6105 0.0419 0.6263 0.0508 2.592 21.30.6 0.93 1.0079 0.5565 7.90E-02 -1.20E-07 0.5525 0.0699 0.5708 0.0809 3.319 15.750.7 0.95 1.0039 0.4955 9.70E-02 -6.00E-08 0.5181 0.0914 0.5324 0.1039 2.77 13.69

0.82 0.97 1.0001 0.4219 1.20E-01 1.80E-07 0.4762 0.1182 0.4785 0.1393 0.474 17.881 1 1 0.2376 2.40E-01 0.00E+00 0.2934 0.2934 0.2934 0.2934 -0.012 -0.01

160

Table C1.31: Densities Prediction for Methanol.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.01 0.66 1.2111 0.9791 1.60E-03 -2.40E-07 1.4632 0.0024 1.3897 0.0023 -5.02 -4.180.02 0.69 1.1866 0.9668 2.80E-03 -2.10E-06 1.433 0.0041 1.3771 0.0039 -3.904 -4.150.06 0.75 1.1392 0.9275 6.90E-03 1.20E-07 1.3677 0.0105 1.3455 0.01 -1.624 -4.43

0.1 0.79 1.11 0.8872 1.20E-02 -1.80E-07 1.319 0.0183 1.3169 0.0175 -0.161 -4.540.17 0.82 1.0832 0.8327 1.90E-02 -1.20E-07 1.2654 0.0304 1.2795 0.0293 1.113 -3.620.34 0.88 1.0479 0.7184 3.70E-02 -1.20E-07 1.1651 0.0621 1.1962 0.0616 2.67 -0.830.41 0.9 1.0375 0.6698 4.60E-02 2.40E-07 1.1242 0.0781 1.1566 0.079 2.883 1.21

0.5 0.92 1.0281 0.6147 5.70E-02 0.00E+00 1.0774 0.0989 1.1076 0.1022 2.803 3.360.72 0.96 1.0118 0.4793 9.00E-02 0.00E+00 0.9547 0.1682 0.9612 0.1808 0.676 7.520.78 0.97 1.0081 0.4382 1.00E-01 -4.50E-04 0.9108 0.1954 0.9052 0.2135 -0.612 9.240.85 0.98 1.0051 0.391 1.20E-01 -1.40E-04 0.8592 0.2313 0.8374 0.2578 -2.539 11.46

1 1 1 0.224 2.20E-01 0.00E+00 0.5303 0.5303 0.5196 0.5196 -2.018 -2.02

Table C1.32: Densities Prediction for Ethanol.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.02 0.68 1.2618 0.976 2.30E-03 -6.00E-07 0.998 0.0022 0.956 0.0022 -4.208 0.80.02 0.7 1.2358 0.9656 3.50E-03 3.00E-07 0.9826 0.0034 0.9482 0.0034 -3.505 -0.340.07 0.76 1.173 0.9237 8.90E-03 4.80E-07 0.9384 0.0089 0.9232 0.0089 -1.624 -0.130.09 0.78 1.1538 0.9039 1.20E-02 -1.20E-07 0.92 0.0119 0.9127 0.0119 -0.793 -0.260.12 0.8 1.1353 0.8807 1.50E-02 -1.80E-07 0.8986 0.0156 0.9008 0.0157 0.248 0.330.25 0.86 1.0857 0.7882 3.10E-02 -6.00E-08 0.8354 0.0331 0.8536 0.034 2.177 2.720.31 0.88 1.071 0.7485 3.90E-02 1.20E-07 0.8109 0.0422 0.8323 0.0436 2.636 3.330.38 0.9 1.0573 0.7037 4.90E-02 -1.20E-07 0.7835 0.0538 0.8069 0.0559 2.985 3.870.67 0.96 1.0217 0.5286 9.50E-02 3.00E-08 0.6719 0.1157 0.6868 0.1237 2.222 6.91

0.8 0.97 1.0111 0.4496 1.20E-01 -9.20E-04 0.6166 0.1538 0.6136 0.17 -0.479 10.51 1 1 0.2488 2.50E-01 0.00E+00 0.3733 0.3733 0.3733 0.3733 -0.012 -0.01

161

Table C1.33: Densities Prediction for Propanol.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.02 0.69 1.2432 0.9711 2.80E-03 7.20E-07 0.7636 0.0022 0.732 0.0021 -4.139 -3.90.02 0.7 1.2376 0.9688 3.10E-03 6.00E-08 0.7609 0.0023 0.7308 0.0023 -3.954 0.650.03 0.71 1.215 0.9582 4.30E-03 6.00E-08 0.75 0.0033 0.7253 0.0033 -3.298 -0.990.04 0.73 1.1932 0.9453 5.90E-03 -6.00E-08 0.7386 0.0046 0.7192 0.0045 -2.628 -1.740.06 0.75 1.1727 0.9298 8.00E-03 -4.20E-07 0.7266 0.0063 0.7125 0.0061 -1.947 -2.660.08 0.77 1.1531 0.9114 1.10E-02 -4.80E-07 0.7142 0.0084 0.7049 0.0082 -1.303 -2.470.11 0.79 1.1346 0.89 1.40E-02 -4.80E-07 0.7002 0.011 0.6964 0.0108 -0.541 -1.910.14 0.81 1.1172 0.8653 1.80E-02 1.80E-07 0.6856 0.0143 0.6868 0.014 0.179 -1.840.18 0.83 1.1009 0.8371 2.20E-02 6.00E-08 0.67 0.0184 0.6759 0.0181 0.883 -1.720.22 0.84 1.0857 0.8053 2.80E-02 -6.00E-08 0.6529 0.0234 0.6634 0.0231 1.616 -1.280.27 0.86 1.0716 0.7695 3.50E-02 -3.60E-07 0.6347 0.0293 0.649 0.0294 2.259 0.180.34 0.88 1.0586 0.7296 4.30E-02 2.40E-07 0.615 0.0367 0.6322 0.0372 2.804 1.240.41 0.9 1.0467 0.6851 5.30E-02 2.40E-07 0.5937 0.0459 0.6124 0.047 3.142 2.460.49 0.92 1.0359 0.6357 6.40E-02 -6.00E-08 0.5698 0.0578 0.5885 0.0596 3.29 3.170.58 0.94 1.0262 0.5802 7.90E-02 6.00E-08 0.5433 0.0731 0.5592 0.0763 2.92 4.320.69 0.96 1.0174 0.5172 9.80E-02 8.90E-08 0.5111 0.0939 0.5216 0.0991 2.059 5.540.81 0.97 1.0094 0.4438 1.30E-01 -5.60E-04 0.4701 0.1226 0.4693 0.1329 -0.161 8.38

1 1 1 0.248 2.50E-01 0.00E+00 0.284 0.284 0.2869 0.2869 1.013 1.01

162

Table C1.34: Densities Prediction for Steam.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.001159 0.52 1.2448 0.997 1.70E-04 7.30E-04 3.3965 0.0006 3.3438 0.0006 -1.552 -0.350.001478 0.53 1.2366 0.9963 2.20E-04 4.50E-04 3.3857 0.0007 3.2994 0.0007 -2.55 -0.420.002911 0.56 1.2171 0.9935 4.10E-04 1.80E-05 3.3496 0.0014 3.2871 0.0013 -1.864 -0.540.004402 0.57 1.2046 0.9908 6.00E-04 1.40E-05 3.3229 0.002 3.2662 0.002 -1.707 -0.65

0.01 0.58 1.1985 0.9892 7.20E-04 5.40E-05 3.309 0.0024 3.2578 0.0024 -1.55 -0.710.01 0.6 1.1865 0.9854 1.00E-03 6.60E-07 3.2795 0.0034 3.243 0.0034 -1.114 -0.810.01 0.62 1.1748 0.9806 1.40E-03 -2.40E-07 3.2482 0.0047 3.2259 0.0047 -0.688 -0.910.02 0.63 1.1634 0.9748 1.90E-03 6.00E-07 3.2153 0.0064 3.2076 0.0064 -0.24 -1.010.02 0.65 1.1523 0.9677 2.60E-03 3.00E-07 3.181 0.0086 3.1869 0.0085 0.183 -1.090.03 0.67 1.1416 0.9593 3.40E-03 2.40E-07 3.1432 0.0113 3.1649 0.0112 0.69 -1.160.04 0.69 1.1311 0.9494 4.40E-03 6.00E-08 3.1063 0.0147 3.1417 0.0145 1.141 -1.20.05 0.7 1.121 0.9379 5.60E-03 3.00E-07 3.0651 0.0188 3.1163 0.0185 1.669 -1.220.06 0.72 1.1111 0.9247 7.00E-03 0.00E+00 3.0234 0.0238 3.0884 0.0235 2.152 -1.20.08 0.74 1.1016 0.9097 8.80E-03 -1.80E-07 2.978 0.0298 3.0582 0.0295 2.694 -1.14

0.1 0.76 1.0924 0.8927 1.10E-02 2.40E-07 2.9308 0.037 3.025 0.0366 3.214 -1.030.15 0.79 1.075 0.8523 1.60E-02 -4.20E-07 2.8307 0.0558 2.9484 0.0555 4.161 -0.610.18 0.81 1.0667 0.8286 1.90E-02 -4.20E-07 2.7755 0.0679 2.9039 0.0677 4.629 -0.280.25 0.84 1.0514 0.7737 2.80E-02 2.40E-07 2.6547 0.0992 2.7989 0.0999 5.432 0.67

0.3 0.86 1.0443 0.7421 3.30E-02 1.80E-07 2.5866 0.1193 2.7363 0.1209 5.785 1.320.35 0.88 1.0375 0.7073 3.90E-02 1.20E-07 2.5151 0.1434 2.6651 0.1464 5.961 2.110.41 0.89 1.0312 0.6693 4.60E-02 -2.40E-07 2.4357 0.1723 2.5833 0.1776 6.062 3.060.48 0.91 1.0253 0.6274 5.50E-02 6.00E-08 2.3481 0.2075 2.4883 0.2163 5.969 4.20.56 0.93 1.0197 0.5811 6.50E-02 1.20E-07 2.251 0.2514 2.3758 0.2653 5.545 5.550.64 0.94 1.0146 0.5295 7.80E-02 2.10E-07 2.1391 0.308 2.2396 0.3296 4.699 70.74 0.96 1.0098 0.4707 9.50E-02 6.00E-08 2.0054 0.3847 2.0683 0.4183 3.137 8.740.84 0.98 1.005 0.4012 1.20E-01 -3.60E-04 1.8278 0.4993 1.8324 0.552 0.255 10.54

1 1 1 0.229 2.30E-01 0.00E+00 1.0931 1.0931 1.1202 1.1202 2.48 2.48

163

Table C1.35: Densities Prediction for Acetylene.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.02 0.62 1.1245 0.9683 3.60E-03 3.00E-07 1.462 0.0052 1.3837 0.0052 -5.358 -0.42 0.05 0.68 1.0952 0.9379 8.00E-03 -1.80E-07 1.422 0.0116 1.3556 0.0116 -4.672 0.56 0.08 0.72 1.0788 0.9083 1.30E-02 3.00E-07 1.3751 0.019 1.3318 0.0189 -3.149 -0.32 0.11 0.75 1.0682 0.8818 1.80E-02 1.80E-07 1.3368 0.0264 1.3115 0.0262 -1.892 -0.82 0.16 0.78 1.0569 0.8454 2.50E-02 1.20E-07 1.2898 0.0377 1.2842 0.0374 -0.44 -0.9 0.24 0.82 1.0422 0.7901 3.60E-02 3.00E-07 1.2265 0.0571 1.2419 0.0571 1.259 -0.08 0.32 0.85 1.0325 0.7392 4.80E-02 3.00E-07 1.1735 0.0776 1.201 0.0783 2.349 0.84 0.41 0.88 1.0275 0.6915 6.00E-02 1.80E-07 1.1248 0.0997 1.16 0.1013 3.126 1.6 0.49 0.9 1.0231 0.6452 7.30E-02 0.00E+00 1.0763 0.1241 1.1172 0.1269 3.796 2.23 0.57 0.92 1.0177 0.5993 8.70E-02 -6.00E-08 1.0353 0.1508 1.0711 0.156 3.455 3.46 0.65 0.94 1.0138 0.5536 1.00E-01 1.50E-07 0.9925 0.181 1.0209 0.1894 2.858 4.66 0.81 0.97 1.0074 0.4589 1.40E-01 -5.40E-04 0.8893 0.2569 0.8972 0.2764 0.895 7.59

1 1 1 0.268 2.70E-01 0.00E+00 0.5529 0.5525 0.5671 0.5671 2.563 2.65

Table C1.36: Densities Prediction for Ethylene.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.02 0.6 1.1099 0.9688 3.70E-03 6.00E-08 1.2649 0.0046 1.1975 0.0046 -5.329 -0.340.03 0.63 1.0972 0.9557 5.70E-03 2.40E-07 1.239 0.0071 1.1845 0.0071 -4.398 -0.780.05 0.67 1.0815 0.9325 9.50E-03 -2.40E-07 1.2026 0.0119 1.1644 0.0118 -3.177 -0.880.09 0.71 1.0666 0.9025 1.50E-02 6.00E-07 1.1418 0.019 1.1409 0.0188 -0.075 -0.840.14 0.75 1.0536 0.8656 2.20E-02 -6.00E-08 1.1213 0.0206 1.1134 0.0286 -0.701 39.03

0.2 0.78 1.0423 0.8211 3.20E-02 0.00E+00 1.0776 0.0416 1.0808 0.0421 0.304 1.270.39 0.86 1.0228 0.7057 6.20E-02 -1.80E-07 0.9734 0.0851 0.9914 0.087 1.854 2.290.52 0.9 1.0153 0.6324 8.50E-02 1.80E-07 0.9112 0.1184 0.9277 0.1243 1.817 4.970.68 0.94 1.0093 0.5441 1.20E-01 1.80E-07 0.8305 0.1681 0.8404 0.1812 1.185 7.79

1 1 1 0.282 2.80E-01 0.00E+00 0.5092 0.5092 0.4812 0.4812 -5.499 -5.5

164

Table C1.37: Densities Prediction for Oxygen.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.0012 0.45 1.1525 0.9966 2.90E-04 -5.20E-04 2.4091 0.0007 2.28 0.0007 -5.359 -0.37

0.01 0.52 1.1218 0.9877 1.30E-03 -4.80E-07 2.3198 0.0029 2.2542 0.0029 -2.827 0.050.02 0.58 1.0964 0.9687 3.80E-03 -1.20E-07 2.2268 0.0086 2.2038 0.0086 -1.035 -0.010.02 0.58 1.0959 0.9682 3.80E-03 -4.80E-07 2.2256 0.0087 2.2024 0.0087 -1.042 0.020.05 0.65 1.0742 0.9361 8.90E-03 -5.40E-07 2.1275 0.0204 2.1411 0.0204 0.637 0.210.11 0.71 1.0551 0.8875 1.80E-02 -3.00E-07 2.0189 0.0415 2.0634 0.0418 2.201 0.71

0.2 0.78 1.0388 0.8212 3.30E-02 -2.40E-07 1.8984 0.0766 1.964 0.0779 3.454 1.660.34 0.84 1.0251 0.7347 5.50E-02 3.60E-07 1.7586 0.1332 1.8317 0.1375 4.16 3.180.49 0.9 1.04 0.6606 7.80E-02 0.00E+00 1.5844 0.2274 1.7098 0.2016 7.915 -11.35

1 1 1 0.288 2.90E-01 0.00E+00 0.8322 0.8322 0.8561 0.8561 2.881 2.88

Table C1.38: Densities Prediction for Bromine.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.000406 0.45 1.2641 0.9987 8.00E-05 6.90E-02 1.2577 0.0001 1.5192 0.0001 20.789 -0.68 0.001199 0.48 1.2199 0.9968 2.30E-04 1.70E-05 1.2331 0.0003 1.4679 0.0003 19.043 -0.18

0.01 0.55 1.1734 0.987 1.10E-03 -1.70E-06 1.1798 0.0016 1.4272 0.0016 20.967 0.34 0.01 0.58 1.1542 0.9778 2.10E-03 -4.20E-07 1.154 0.003 1.4088 0.003 22.081 0.64 0.04 0.65 1.1201 0.9477 5.80E-03 0.00E+00 1.1004 0.0082 1.3644 0.0084 23.992 2 0.06 0.68 1.104 0.9253 9.00E-03 3.00E-07 1.0711 0.0126 1.3375 0.013 24.869 3.09 0.14 0.75 1.0738 0.8635 1.90E-02 1.20E-07 1.0055 0.0264 1.2714 0.0282 26.442 6.69

0.2 0.79 1.0602 0.823 2.70E-02 -3.60E-07 0.971 0.0366 1.2304 0.04 26.71 9.25 0.36 0.86 1.0357 0.7199 5.00E-02 6.00E-08 0.8923 0.0664 1.1245 0.0776 26.024 16.92 0.47 0.89 1.0251 0.6554 6.70E-02 -1.20E-07 0.845 0.0878 1.0542 0.1075 24.753 22.5 0.61 0.92 1.0158 0.5797 9.00E-02 1.20E-07 0.7911 0.1159 0.9651 0.1506 22.003 29.94 0.77 0.96 1.0078 0.4872 1.30E-01 -6.00E-08 0.7277 0.1559 0.8447 0.2185 16.069 40.17

1 1 1 0.269 2.70E-01 0.00E+00 0.4609 0.4607 0.494 0.494 7.168 7.23

165

Table C1.39: Densities Prediction for Sulfur Dioxide.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.03 0.65 1.1644 0.9617 4.30E-03 0.00E+00 1.3779 0.0062 1.3221 0.0059 -4.053 -5.090.04 0.67 1.1522 0.9519 5.60E-03 -3.00E-07 1.3574 0.0082 1.3114 0.0078 -3.386 -5.410.04 0.68 1.1463 0.9464 6.40E-03 -4.20E-07 1.3476 0.0095 1.3058 0.0089 -3.105 -6.80.04 0.69 1.1435 0.9435 6.80E-03 -1.80E-07 1.3418 0.01 1.3029 0.0094 -2.901 -5.610.06 0.7 1.1322 0.9307 8.70E-03 -1.80E-07 1.3213 0.0129 1.2907 0.0121 -2.313 -60.07 0.72 1.1239 0.92 1.00E-02 0.00E+00 1.3038 0.0156 1.2809 0.0145 -1.756 -6.960.08 0.73 1.1185 0.9123 1.20E-02 3.00E-07 1.2931 0.0178 1.274 0.0163 -1.476 -8.370.11 0.75 1.1052 0.8907 1.50E-02 -6.00E-08 1.2619 0.024 1.2553 0.0216 -0.522 -9.960.11 0.76 1.0993 0.8842 1.60E-02 -2.40E-07 1.2561 0.0252 1.2499 0.0233 -0.495 -7.670.13 0.77 1.0916 0.869 1.90E-02 -6.00E-08 1.2376 0.0292 1.2371 0.0273 -0.038 -6.360.15 0.78 1.0866 0.8582 2.10E-02 -2.40E-07 1.2239 0.032 1.2281 0.0304 0.344 -5.070.16 0.79 1.0818 0.8469 2.30E-02 -1.80E-07 1.2111 0.0348 1.2186 0.0337 0.623 -3.20.18 0.8 1.0796 0.8367 2.50E-02 0.00E+00 1.1976 0.0378 1.2102 0.0367 1.054 -2.81

0.2 0.81 1.0724 0.8224 2.80E-02 -1.20E-07 1.184 0.0409 1.1983 0.0412 1.204 0.820.25 0.83 1.0615 0.7884 3.60E-02 0.00E+00 1.1479 0.0513 1.1696 0.0527 1.894 2.72

0.3 0.85 1.0533 0.7584 4.20E-02 1.20E-07 1.1177 0.0625 1.1438 0.0638 2.333 2.150.36 0.87 1.0437 0.7234 5.10E-02 0.00E+00 1.0855 0.0753 1.1127 0.0781 2.509 3.72

0.4 0.88 1.0383 0.7001 5.70E-02 -1.80E-07 1.064 0.0847 1.0913 0.0885 2.568 4.440.44 0.89 1.033 0.6754 6.30E-02 -2.40E-07 1.0416 0.0945 1.0679 0.1002 2.528 6.050.48 0.9 1.0281 0.6492 7.10E-02 -1.20E-07 1.0182 0.1064 1.0423 0.1136 2.367 6.80.53 0.91 1.0235 0.6215 7.90E-02 -1.80E-07 0.992 0.1206 1.0141 0.129 2.229 6.950.58 0.92 1.0192 0.5923 8.80E-02 1.20E-07 0.9637 0.1378 0.983 0.1466 2.003 6.42

0.7 0.95 1.0122 0.5287 1.10E-01 6.00E-08 0.8974 0.1835 0.91 0.1909 1.401 4.060.76 0.96 1.0095 0.4939 1.20E-01 -8.90E-08 0.8576 0.214 0.8666 0.2192 1.046 2.420.82 0.97 1.0073 0.4568 1.40E-01 -1.70E-04 0.8108 0.251 0.8162 0.2531 0.663 0.850.88 0.98 1.0061 0.4154 1.60E-01 -1.90E-05 0.7474 0.2993 0.7579 0.2961 1.411 -1.07

1 1 1 0.269 2.70E-01 0.00E+00 0.5048 0.5048 0.5109 0.5109 1.215 1.21

166

Table C1.40: Densities Prediction for Methyl Propionate.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.03 0.67 1.1719 0.9635 3.80E-03 4.80E-07 0.596 0.0022 0.5661 0.0022 -5.019 1.710.05 0.7 1.1439 0.9407 6.80E-03 2.40E-07 0.5766 0.004 0.5569 0.004 -3.412 0.29

0.1 0.76 1.1063 0.8914 1.40E-02 2.40E-07 0.5459 0.0086 0.5399 0.0086 -1.107 -0.480.13 0.78 1.0949 0.8702 1.80E-02 -2.40E-07 0.5352 0.0108 0.5329 0.0108 -0.421 -0.160.16 0.8 1.0841 0.8465 2.20E-02 6.00E-08 0.5236 0.0135 0.5253 0.0135 0.316 -0.18

0.2 0.82 1.0737 0.82 2.70E-02 1.20E-07 0.5116 0.0167 0.5166 0.0167 0.985 0.20.29 0.85 1.0546 0.758 3.90E-02 -2.40E-07 0.4858 0.0252 0.4959 0.0255 2.072 1.080.42 0.89 1.0374 0.6819 5.60E-02 1.20E-07 0.4567 0.03 0.4683 0.0386 2.549 28.750.67 0.95 1.0156 0.5324 9.90E-02 -2.10E-07 0.3993 0.0685 0.4036 0.0752 1.07 9.720.84 0.98 1.0065 0.4295 1.40E-01 -1.10E-04 0.3526 0.1005 0.3468 0.1128 -1.644 12.28

0.9 0.99 1.0038 0.3848 1.60E-01 -1.30E-05 0.3298 0.1187 0.3185 0.134 -3.413 12.921 1 1 0.256 2.60E-01 0.00E+00 0.2214 0.2214 0.2204 0.2204 -0.462 -0.46

Table C1.41: Densities Prediction for Ethyl Propionate.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.03 0.68 1.1793 0.9584 4.40E-03 6.00E-08 0.4868 0.0021 0.4651 0.0021 -4.467 1.570.04 0.7 1.1637 0.9463 6.00E-03 0.00E+00 0.4782 0.0029 0.461 0.0029 -3.602 0.060.07 0.74 1.1362 0.9181 9.90E-03 -1.80E-07 0.4614 0.0049 0.4523 0.0049 -1.966 -0.330.14 0.79 1.0996 0.8594 1.90E-02 -3.00E-07 0.4349 0.0099 0.4359 0.0098 0.239 -1.170.26 0.85 1.0676 0.7772 3.50E-02 -1.20E-07 0.4049 0.0184 0.4132 0.0184 2.042 0.240.38 0.88 1.049 0.707 5.00E-02 6.00E-08 0.3816 0.0273 0.3924 0.0277 2.836 1.570.45 0.9 1.0402 0.6659 6.00E-02 -6.00E-08 0.3684 0.0332 0.3794 0.0341 2.977 2.790.72 0.96 1.0161 0.5086 1.10E-01 3.00E-08 0.3167 0.063 0.3205 0.0675 1.204 7.210.83 0.98 1.0084 0.438 1.40E-01 -6.10E-04 0.29 0.0817 0.2865 0.0893 -1.209 9.270.89 0.99 1.0052 0.393 1.60E-01 -1.70E-04 0.2726 0.0955 0.2639 0.106 -3.187 11.05

1 1 1 0.256 2.60E-01 0.00E+00 0.1812 0.1812 0.1798 0.1798 -0.785 -0.79

167

Table C1.42: Densities Prediction for Methyl-n-Butyrate.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.03 0.68 1.1753 0.9596 4.30E-03 6.00E-07 0.4911 0.0022 0.4662 0.0021 -5.067 -4.140.06 0.73 1.1381 0.9264 8.90E-03 6.00E-08 0.4697 0.0045 0.4558 0.0044 -2.951 -2.750.13 0.78 1.1026 0.8728 1.70E-02 3.60E-07 0.4444 0.0089 0.4411 0.0088 -0.733 -1.440.16 0.8 1.0919 0.8505 2.10E-02 6.00E-08 0.4353 0.011 0.4352 0.0109 -0.025 -1.160.28 0.85 1.0623 0.7673 3.70E-02 6.00E-08 0.4054 0.02 0.4126 0.0201 1.784 0.52

0.4 0.89 1.0448 0.6961 5.30E-02 1.80E-07 0.3821 0.0295 0.3918 0.03 2.539 1.80.47 0.91 1.0365 0.6546 6.40E-02 0.00E+00 0.3678 0.0357 0.3786 0.0369 2.944 3.270.54 0.93 1.0286 0.6083 7.60E-02 0.00E+00 0.3529 0.0437 0.3629 0.0456 2.827 4.240.74 0.96 1.0142 0.4962 1.10E-01 0.00E+00 0.3158 0.0667 0.3188 0.0726 0.936 8.870.85 0.98 1.0073 0.424 1.40E-01 -3.10E-04 0.2886 0.0866 0.2837 0.0964 -1.688 11.270.91 0.99 1.0044 0.3774 1.70E-01 -9.10E-06 0.2681 0.1034 0.2597 0.1152 -3.139 11.37

1 1 1 0.257 2.60E-01 0.00E+00 0.1835 0.1835 0.1831 0.1831 -0.192 -0.19

Table C1.43: Densities Prediction for Methyl-iso-Butyrate.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.03 0.68 1.1708 0.9592 4.50E-03 -1.80E-07 0.4914 0.0022 0.4656 0.0022 -5.247 -1.350.06 0.73 1.1337 0.9245 9.30E-03 -1.20E-07 0.4694 0.0047 0.4549 0.0046 -3.09 -2.330.13 0.78 1.0979 0.8687 1.80E-02 2.40E-07 0.443 0.0094 0.4397 0.0093 -0.749 -0.980.16 0.8 1.0872 0.8453 2.30E-02 1.80E-07 0.4337 0.0116 0.4335 0.0116 -0.046 -0.250.29 0.86 1.058 0.7587 4.00E-02 3.60E-07 0.403 0.0213 0.4099 0.0216 1.723 1.250.35 0.88 1.0492 0.7234 4.80E-02 -1.80E-07 0.3919 0.0258 0.3998 0.0264 2.01 2.430.42 0.89 1.0408 0.6845 5.70E-02 0.00E+00 0.379 0.0314 0.388 0.0324 2.369 3.230.57 0.93 1.0254 0.593 8.20E-02 -1.20E-07 0.3478 0.0472 0.3572 0.0495 2.703 4.960.67 0.95 1.0182 0.5382 1.00E-01 1.80E-07 0.3292 0.0588 0.3362 0.0624 2.129 6.070.77 0.97 1.0116 0.4744 1.20E-01 -6.00E-08 0.3069 0.0744 0.3088 0.0805 0.612 8.16

1 1 1 0.259 2.60E-01 0.00E+00 0.1841 0.1841 0.1842 0.1842 0.043 0.04

168

Table C1.44: Densities Prediction for Methyl Acetate.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.02 0.65 1.1691 0.9677 3.20E-03 -1.80E-07 0.745 0.0024 0.7102 0.0024 -4.675 -0.830.05 0.7 1.1371 0.9421 6.50E-03 -6.00E-08 0.7179 0.0047 0.6969 0.0048 -2.921 1.76

0.1 0.76 1.1 0.8914 1.40E-02 1.80E-07 0.6792 0.0104 0.6749 0.0105 -0.639 1.070.16 0.8 1.0782 0.8447 2.20E-02 -2.40E-07 0.6502 0.0166 0.6558 0.0168 0.866 1.250.25 0.83 1.0586 0.7862 3.30E-02 1.80E-07 0.6185 0.0255 0.6318 0.0261 2.145 2.5

0.3 0.85 1.0496 0.7519 4.00E-02 -2.40E-07 0.6011 0.0314 0.6171 0.0324 2.667 3.260.43 0.89 1.0331 0.6717 5.80E-02 3.00E-07 0.5622 0.0479 0.5804 0.0499 3.237 4.10.51 0.91 1.0257 0.6248 7.00E-02 1.80E-07 0.5402 0.0589 0.5568 0.0621 3.08 5.51

0.7 0.95 1.0126 0.5123 1.00E-01 2.40E-07 0.4838 0.0919 0.4917 0.1001 1.64 8.90.82 0.97 1.0066 0.4411 1.30E-01 -2.80E-04 0.445 0.1193 0.4416 0.1326 -0.756 11.18

1 1 1 0.254 2.50E-01 0.00E+00 0.2741 0.2741 0.2737 0.2737 -0.151 -0.15

Table C1.45: Densities Prediction for Ethyl Acetate.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.03 0.67 1.1661 0.9622 3.90E-03 1.20E-07 0.5869 0.0023 0.5578 0.0023 -4.95 -1.870.04 0.69 1.1484 0.9481 5.70E-03 -6.60E-07 0.5748 0.0033 0.5524 0.0033 -3.903 0.020.05 0.71 1.1349 0.9348 7.40E-03 -1.20E-07 0.5649 0.0044 0.5476 0.0044 -3.059 -0.870.09 0.75 1.1097 0.9014 1.20E-02 3.60E-07 0.5444 0.0073 0.5366 0.0073 -1.432 0.10.14 0.79 1.0868 0.8581 1.90E-02 0.00E+00 0.5228 0.0117 0.5231 0.0117 0.052 0.170.27 0.85 1.0565 0.7713 3.50E-02 -1.20E-07 0.4852 0.0224 0.4957 0.0226 2.163 1.050.39 0.89 1.0392 0.6965 5.10E-02 3.60E-07 0.4564 0.0337 0.4701 0.0346 3.001 2.740.46 0.9 1.0311 0.6525 6.20E-02 1.80E-07 0.44 0.0411 0.4537 0.043 3.122 4.630.64 0.94 1.0169 0.5486 9.10E-02 -2.10E-07 0.4002 0.0631 0.4098 0.0679 2.387 7.630.74 0.96 1.0107 0.4852 1.10E-01 -8.90E-08 0.3742 0.0801 0.3783 0.0878 1.09 9.550.86 0.98 1.0047 0.4086 1.50E-01 -3.90E-04 0.3385 0.1062 0.3325 0.1186 -1.772 11.65

1 1 1 0.252 2.50E-01 0.00E+00 0.218 0.218 0.2181 0.2181 0.05 0.05

169

Table C1.46: Densities Prediction for Propyl Acetate.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.03 0.68 1.1686 0.958 4.40E-03 -4.20E-07 0.4878 0.0021 0.4612 0.0021 -5.452 0.910.04 0.7 1.1571 0.9489 5.60E-03 1.20E-07 0.4786 0.0027 0.4583 0.0027 -4.237 -0.520.09 0.75 1.1179 0.9047 1.20E-02 2.40E-07 0.4545 0.0058 0.4459 0.0058 -1.895 0.050.14 0.79 1.0946 0.864 1.80E-02 -3.00E-07 0.437 0.0091 0.4353 0.0092 -0.387 0.920.21 0.82 1.0736 0.8132 2.70E-02 -3.60E-07 0.4178 0.0139 0.4222 0.0141 1.048 1.48

0.3 0.86 1.0548 0.7506 3.90E-02 6.00E-08 0.3966 0.0207 0.4054 0.0213 2.218 2.940.36 0.88 1.0461 0.7143 4.70E-02 4.20E-07 0.3851 0.0252 0.3951 0.0261 2.594 3.760.43 0.9 1.0377 0.6739 5.70E-02 3.60E-07 0.3721 0.0307 0.383 0.0322 2.93 4.77

0.5 0.92 1.0299 0.6291 6.80E-02 6.00E-08 0.3579 0.0376 0.3686 0.0398 3.001 5.740.68 0.95 1.0156 0.5221 1.00E-01 -1.20E-07 0.3233 0.0574 0.3293 0.0628 1.848 9.390.79 0.97 1.0089 0.4559 1.20E-01 -5.00E-04 0.3 0.0737 0.2995 0.0818 -0.17 10.99

1 1 1 0.252 2.50E-01 0.00E+00 0.1807 0.1807 0.1809 0.1809 0.097 0.1

Table C1.47: Densities Prediction for Methyl Chloride.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.01 0.56 1.1987 0.9864 1.20E-03 1.60E-05 1.2764 0.0016 1.2254 0.0015 -3.994 -0.720.02 0.6 1.1724 0.9749 2.60E-03 -1.20E-07 1.2405 0.0032 1.2057 0.0032 -2.801 -0.980.04 0.65 1.1405 0.9506 5.80E-03 -6.00E-08 1.1905 0.0072 1.1757 0.0071 -1.248 -1.360.05 0.68 1.1259 0.9341 8.20E-03 -6.00E-08 1.1633 0.0103 1.1584 0.0102 -0.418 -1.490.06 0.69 1.119 0.9247 9.70E-03 -4.80E-07 1.1498 0.0122 1.1491 0.012 -0.056 -1.550.12 0.75 1.0938 0.8788 1.80E-02 -3.00E-07 1.0964 0.0225 1.1073 0.0221 0.997 -1.730.18 0.79 1.0777 0.8354 2.60E-02 1.80E-07 1.0505 0.0337 1.0699 0.0333 1.848 -1.190.21 0.8 1.0729 0.8192 2.90E-02 2.40E-07 1.0351 0.0382 1.056 0.0378 2.019 -0.930.26 0.83 1.0639 0.7841 3.70E-02 6.00E-08 1.0021 0.0487 1.0258 0.0486 2.364 -0.210.29 0.84 1.0598 0.7651 4.20E-02 2.40E-07 0.9837 0.0549 1.0093 0.0549 2.603 0.05

1 1 1 0.276 2.80E-01 0.00E+00 0.4365 0.4365 0.4365 0.4365 0 0

170

Table C1.48: Densities Prediction for Ethyl Chloride.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.02 0.62 1.1715 0.9701 3.10E-03 6.60E-07 0.8767 0.0028 0.8463 0.0027 -3.469 -1.870.05 0.68 1.1346 0.9383 7.50E-03 -6.00E-08 0.8354 0.0067 0.8215 0.0066 -1.659 -1.460.07 0.7 1.1223 0.9229 9.90E-03 1.20E-07 0.8198 0.0089 0.8111 0.0087 -1.058 -1.990.11 0.75 1.099 0.8846 1.60E-02 -3.60E-07 0.7871 0.0147 0.7873 0.0146 0.024 -0.790.18 0.79 1.0777 0.8358 2.60E-02 -3.00E-07 0.7519 0.0228 0.7583 0.0233 0.858 2.340.22 0.81 1.0686 0.8077 3.20E-02 1.20E-07 0.7325 0.0284 0.7418 0.029 1.274 2.210.33 0.85 1.049 0.7395 4.70E-02 6.00E-08 0.6919 0.0416 0.7009 0.045 1.303 8.19

0.4 0.88 1.0402 0.7 5.80E-02 -1.20E-07 0.6687 0.0503 0.6763 0.0558 1.131 10.940.48 0.9 1.0319 0.6562 7.00E-02 -1.80E-07 0.6435 0.0619 0.6477 0.0693 0.649 11.980.57 0.92 1.0244 0.6077 8.50E-02 0.00E+00 0.6154 0.0764 0.6143 0.0864 -0.178 13.080.78 0.96 1.0102 0.4869 1.30E-01 1.20E-07 0.5409 0.1239 0.5211 0.1414 -3.662 14.12

1 1 1 0.274 2.70E-01 0.00E+00 0.3203 0.3203 0.3112 0.3112 -2.831 -2.83

Table C1.49: Densities Prediction for Methyl Ether.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.02 0.62 1.2161 0.9711 3.20E-03 -1.80E-07 0.9787 0.0033 0.9623 0.0031 -1.68 -4.860.03 0.66 1.1914 0.9555 5.30E-03 6.00E-08 0.954 0.0053 0.9451 0.0053 -0.93 -0.690.07 0.71 1.1533 0.9226 1.10E-02 0.00E+00 0.9159 0.0103 0.9149 0.0105 -0.106 1.480.13 0.76 1.1198 0.8772 1.90E-02 -3.00E-07 0.8747 0.0192 0.8787 0.0189 0.455 -1.380.22 0.81 1.0892 0.8173 3.20E-02 -1.20E-07 0.8288 0.0327 0.8338 0.0324 0.605 -0.910.42 0.88 1.0494 0.6957 6.40E-02 0.00E+00 0.7476 0.0656 0.742 0.0684 -0.743 4.310.52 0.91 1.0384 0.6455 8.00E-02 1.80E-07 0.7124 0.0844 0.702 0.0873 -1.46 3.430.75 0.96 1.0165 0.5169 1.30E-01 -3.00E-08 0.62 0.1436 0.5899 0.1498 -4.861 4.320.82 0.97 1.0115 0.4771 1.50E-01 -3.90E-04 0.5895 0.1656 0.55 0.1746 -6.704 5.440.89 0.98 1.0067 0.4273 1.80E-01 -9.70E-05 0.5475 0.1985 0.5007 0.2097 -8.543 5.62

1 1 1 0.287 2.90E-01 0.00E+00 0.3678 0.3678 0.3446 0.3446 -6.321 -6.32

171

Table C1.50: Densities Prediction for Methyl Ethyl Ether.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.03 0.65 1.1499 0.9632 4.10E-03 6.00E-08 0.7407 0.0042 0.7129 0.0031 -3.75 -26.960.05 0.69 1.1166 0.9347 8.20E-03 3.60E-07 0.7137 0.0083 0.6984 0.0061 -2.15 -25.940.07 0.72 1.1031 0.9168 1.10E-02 -6.60E-07 0.6981 0.0104 0.6901 0.0083 -1.139 -200.17 0.78 1.0652 0.8431 2.40E-02 -2.40E-07 0.6524 0.0197 0.6588 0.019 0.978 -3.770.21 0.81 1.0547 0.812 3.10E-02 2.40E-07 0.6357 0.0239 0.6456 0.0243 1.563 1.670.33 0.85 1.0357 0.7378 4.70E-02 -1.80E-07 0.6015 0.0353 0.6131 0.0392 1.927 11.15

0.4 0.88 1.0281 0.6952 5.80E-02 -1.20E-07 0.5817 0.0416 0.5931 0.0494 1.961 18.770.48 0.9 1.0209 0.6472 7.10E-02 2.40E-07 0.561 0.0519 0.5691 0.0625 1.444 20.40.58 0.92 1.0144 0.5936 8.70E-02 2.40E-07 0.536 0.0665 0.54 0.0795 0.747 19.52

0.8 0.97 1.0051 0.4635 1.40E-01 -1.80E-07 0.4675 0.1132 0.4566 0.1346 -2.341 18.91 1 1 0.267 2.70E-01 0.00E+00 0.2826 0.2826 0.2824 0.2824 -0.059 -0.06

172

Table C1.51: Densities Prediction for Refrigerant 11.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.000561 0.47 1.3029 0.9983 1.20E-04 -5.90E-02 0.7482 0.0001 0.674 0.0001 -9.911 -0.160.001162 0.5 1.2702 0.997 2.30E-04 5.40E-07 0.7375 0.0002 0.7103 0.0002 -3.694 -0.210.00223 0.52 1.2504 0.9948 4.30E-04 4.90E-04 0.7265 0.0003 0.7034 0.0003 -3.18 -0.27

0.004004 0.54 1.2316 0.9916 7.40E-04 1.10E-05 0.7151 0.0005 0.6984 0.0005 -2.337 -0.340.004593 0.55 1.2271 0.9906 8.50E-04 1.80E-07 0.7123 0.0006 0.6962 0.0006 -2.254 -0.36

0.01 0.55 1.2226 0.9895 9.60E-04 -3.60E-07 0.7095 0.0007 0.6951 0.0007 -2.026 -0.370.01 0.57 1.2138 0.9871 1.20E-03 3.00E-07 0.704 0.0009 0.6924 0.0009 -1.657 -0.410.01 0.58 1.2052 0.9843 1.50E-03 -5.40E-07 0.6986 0.0011 0.6898 0.0011 -1.269 -0.450.01 0.59 1.1969 0.981 1.90E-03 -3.60E-07 0.6926 0.0013 0.6863 0.0013 -0.92 -0.480.01 0.6 1.1887 0.9773 2.30E-03 4.80E-07 0.6868 0.0017 0.6831 0.0016 -0.539 -0.510.02 0.61 1.1807 0.9732 2.90E-03 0.00E+00 0.681 0.002 0.68 0.002 -0.149 -0.530.03 0.64 1.1607 0.9599 4.60E-03 3.60E-07 0.6654 0.0033 0.6707 0.0032 0.798 -0.550.04 0.66 1.1504 0.9512 5.90E-03 -2.40E-07 0.6564 0.0041 0.6653 0.0041 1.349 -0.530.05 0.68 1.1363 0.9367 8.10E-03 -4.80E-07 0.6442 0.0057 0.657 0.0057 1.988 -0.450.07 0.71 1.1228 0.9196 1.10E-02 4.80E-07 0.6308 0.0076 0.6479 0.0076 2.714 -0.290.09 0.73 1.11 0.8997 1.40E-02 -1.20E-07 0.6174 0.0101 0.638 0.0101 3.323 0.020.12 0.75 1.0976 0.8768 1.80E-02 -1.20E-07 0.6036 0.0132 0.6269 0.0132 3.86 0.30.16 0.78 1.0859 0.8508 2.40E-02 2.40E-07 0.589 0.0169 0.6146 0.017 4.358 0.76

0.2 0.8 1.0747 0.8214 3.00E-02 3.60E-07 0.5736 0.0214 0.6009 0.0217 4.747 1.370.26 0.83 1.064 0.7884 3.70E-02 -6.00E-08 0.5574 0.027 0.5854 0.0276 5.018 2.130.32 0.85 1.0538 0.7515 4.60E-02 -1.80E-07 0.54 0.0338 0.5677 0.0348 5.123 3.060.39 0.87 1.0441 0.7103 5.70E-02 1.80E-07 0.5211 0.0421 0.5473 0.0439 5.034 4.190.47 0.9 1.0349 0.664 7.00E-02 -1.80E-07 0.5 0.0525 0.5234 0.0554 4.694 5.560.56 0.92 1.0262 0.6117 8.70E-02 -6.00E-08 0.4764 0.0657 0.4949 0.0705 3.87 7.160.67 0.94 1.0179 0.5516 1.10E-01 1.20E-07 0.4483 0.0833 0.4594 0.0908 2.493 9.01

0.8 0.97 1.0102 0.4794 1.40E-01 6.00E-08 0.4124 0.1087 0.4127 0.1206 0.069 11.011 1 1 0.278 2.80E-01 0.00E+00 0.2516 0.2516 0.2527 0.2527 0.424 0.42

173


Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.00239 0.52 1.2351 0.9944 4.80E-04 -9.30E-05 0.8287 0.0004 0.7778 0.0004 -6.14 -0.380.00483 0.55 1.213 0.9902 9.20E-04 -1.20E-05 0.814 0.0007 0.7717 0.0007 -5.198 -0.5

0.01 0.58 1.1922 0.9838 1.60E-03 6.60E-07 0.7983 0.0013 0.7649 0.0013 -4.186 -0.630.02 0.61 1.1726 0.9749 2.70E-03 -4.20E-07 0.7832 0.0021 0.7571 0.0021 -3.333 -0.740.03 0.63 1.1542 0.963 4.30E-03 8.90E-07 0.7665 0.0034 0.7481 0.0034 -2.403 -0.810.04 0.66 1.1368 0.9477 6.50E-03 -3.00E-07 0.7498 0.0051 0.7381 0.0051 -1.563 -0.820.04 0.67 1.1326 0.9434 7.20E-03 -3.00E-07 0.7458 0.0057 0.7355 0.0056 -1.381 -0.810.05 0.68 1.1285 0.9387 7.90E-03 1.20E-07 0.7411 0.0062 0.7327 0.0062 -1.128 -0.80.06 0.69 1.1204 0.9288 9.50E-03 3.00E-07 0.7319 0.0075 0.727 0.0075 -0.668 -0.750.07 0.71 1.1126 0.9178 1.10E-02 2.40E-07 0.723 0.009 0.7209 0.0089 -0.278 -0.670.09 0.72 1.105 0.9058 1.30E-02 -4.20E-07 0.7136 0.0107 0.7145 0.0106 0.13 -0.56

0.1 0.74 1.0976 0.8927 1.60E-02 0.00E+00 0.7039 0.0126 0.7077 0.0126 0.542 -0.420.12 0.75 1.0905 0.8785 1.90E-02 0.00E+00 0.6944 0.0148 0.7004 0.0148 0.863 -0.240.14 0.76 1.0836 0.8632 2.20E-02 -6.00E-08 0.6841 0.0173 0.6926 0.0173 1.25 -0.020.17 0.78 1.0769 0.8466 2.50E-02 -6.00E-08 0.6735 0.0201 0.6843 0.0202 1.608 0.240.18 0.79 1.0729 0.8361 2.70E-02 -1.80E-07 0.667 0.022 0.6791 0.0221 1.81 0.430.19 0.79 1.0704 0.8288 2.90E-02 -1.20E-07 0.6627 0.0233 0.6754 0.0234 1.917 0.550.22 0.81 1.0641 0.8097 3.30E-02 -6.00E-08 0.6517 0.0269 0.6658 0.0271 2.161 0.910.29 0.84 1.0522 0.7674 4.30E-02 3.00E-07 0.628 0.0355 0.6443 0.0361 2.591 1.780.37 0.87 1.0411 0.7191 5.60E-02 6.00E-08 0.6015 0.0465 0.6187 0.0478 2.866 2.880.47 0.89 1.0308 0.6638 7.20E-02 -1.20E-07 0.5724 0.0608 0.5879 0.0634 2.711 4.230.58 0.92 1.0213 0.5998 9.30E-02 -6.00E-08 0.5385 0.0792 0.5494 0.0847 2.03 6.950.72 0.95 1.0126 0.5238 1.20E-01 1.80E-07 0.4964 0.1078 0.4987 0.1159 0.457 7.57

1 1 1 0.279 2.80E-01 0.00E+00 0.2882 0.2882 0.2875 0.2875 -0.245 -0.25

174


Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0 0.48 1.3503 0.9982 1.20E-04 2.90E-01 1.21 0.0001 1.1246 0.0001 -7.056 -7.10 0.51 1.2843 0.9962 2.60E-04 2.30E-03 1.188 0.0003 1.136 0.0003 -4.382 -7.160 0.54 1.2583 0.9928 5.50E-04 1.40E-04 1.1658 0.0007 1.1254 0.0006 -3.466 -7.24

0.01 0.57 1.2338 0.9874 1.10E-03 6.00E-06 1.1422 0.0013 1.1146 0.0012 -2.416 -7.330.01 0.6 1.2104 0.9794 1.90E-03 5.40E-07 1.1185 0.0023 1.1008 0.0021 -1.59 -7.420.02 0.63 1.1881 0.9682 3.10E-03 6.00E-07 1.0939 0.0038 1.0851 0.0035 -0.808 -7.480.03 0.66 1.1669 0.9534 4.90E-03 -6.00E-08 1.0685 0.006 1.068 0.0055 -0.05 -7.50.05 0.69 1.1468 0.9345 7.50E-03 4.20E-07 1.0417 0.0091 1.0488 0.0084 0.687 -7.450.06 0.7 1.1419 0.9291 8.20E-03 -2.40E-07 1.0347 0.01 1.0437 0.0093 0.866 -7.430.07 0.71 1.1371 0.9234 9.10E-03 -6.00E-08 1.0279 0.011 1.0384 0.0102 1.021 -7.40.08 0.72 1.1278 0.911 1.10E-02 -8.30E-07 1.0136 0.0133 1.0273 0.0123 1.348 -7.3

0.1 0.74 1.1187 0.8975 1.30E-02 1.20E-07 0.9998 0.0159 1.0155 0.0147 1.571 -7.180.12 0.75 1.1098 0.8826 1.50E-02 -6.00E-08 0.9847 0.0189 1.0029 0.0176 1.848 -7.020.14 0.77 1.1013 0.8664 1.80E-02 1.20E-07 0.9693 0.0223 0.9895 0.0208 2.077 -6.820.16 0.78 1.093 0.8488 2.10E-02 3.00E-07 0.9537 0.0263 0.9751 0.0246 2.245 -6.580.19 0.8 1.085 0.8298 2.50E-02 -6.00E-08 0.9379 0.0308 0.9597 0.0288 2.33 -6.290.22 0.81 1.0773 0.8093 2.90E-02 -1.80E-07 0.9212 0.0359 0.9432 0.0338 2.387 -5.940.24 0.82 1.0728 0.7963 3.20E-02 6.00E-08 0.9104 0.0393 0.9327 0.0371 2.444 -5.70.25 0.83 1.0698 0.7872 3.40E-02 2.40E-07 0.9038 0.0417 0.9254 0.0394 2.387 -5.530.29 0.84 1.0626 0.7635 3.90E-02 -6.00E-08 0.8851 0.0484 0.906 0.0459 2.364 -5.060.38 0.87 1.049 0.7106 5.10E-02 2.40E-07 0.8459 0.0646 0.8621 0.0621 1.908 -3.880.49 0.9 1.0363 0.6494 6.80E-02 -1.20E-07 0.8007 0.0862 0.8089 0.0842 1.02 -2.340.62 0.93 1.0245 0.5774 9.00E-02 8.90E-08 0.7473 0.1161 0.742 0.1157 -0.708 -0.350.77 0.96 1.0134 0.4888 1.20E-01 -6.00E-08 0.678 0.1618 0.6516 0.1653 -3.894 2.14

1 1 1 0.268 2.70E-01 0.00E+00 0.407 0.407 0.3776 0.3776 -7.229 -7.23

175


Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0 0.49 1.2825 0.9982 1.00E-04 7.10E-02 1.6297 0.0002 1.5104 0.0002 -7.321 -0.28

0.01 0.57 1.2076 0.9898 7.30E-04 -1.80E-07 1.5385 0.0011 1.5179 0.0011 -1.334 2.660.01 0.6 1.1855 0.9824 1.40E-03 -2.30E-06 1.4908 0.0021 1.5009 0.0021 0.678 -0.960.05 0.69 1.126 0.9372 6.10E-03 -1.20E-07 1.3736 0.0095 1.44 0.0094 4.834 -1.60.11 0.76 1.0919 0.8815 1.30E-02 -6.00E-08 1.2907 0.0212 1.3823 0.0209 7.102 -1.640.16 0.79 1.0765 0.8442 1.90E-02 -1.80E-07 1.2407 0.0303 1.346 0.0299 8.491 -1.31

0.3 0.85 1.049 0.7469 3.50E-02 1.80E-07 1.1447 0.0594 1.2509 0.0592 9.281 -0.320.4 0.88 1.0368 0.6849 4.80E-02 -4.20E-07 1.0865 0.0818 1.1865 0.0827 9.209 1.08

0.67 0.95 1.0156 0.5233 8.90E-02 3.00E-07 0.929 0.1616 0.993 0.1697 6.886 50.85 0.98 1.0065 0.409 1.30E-01 -2.20E-04 0.8013 0.2465 0.8221 0.2667 2.597 8.17

1 1 1 0.243 2.40E-01 0.00E+00 0.5156 0.5198 0.5147 0.5147 -0.174 -0.98

Table C1.55: Densities Prediction for Refrigerant 152a.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.000207 0.45 1.394 0.9992 4.30E-05 1.50E+00 1.0853 0 0.9489 0 -12.571 -0.080.000799 0.55 1.177 0.9924 6.10E-04 1.50E-04 1.0223 0.0006 0.9105 0.0006 -10.932 -0.1

0.01 0.6 1.149 0.9802 1.80E-03 3.60E-07 0.9831 0.0017 0.8978 0.0017 -8.679 -0.090.05 0.69 1.1067 0.9398 6.80E-03 1.20E-07 0.9198 0.0063 0.8723 0.0063 -5.165 0.14

0.1 0.75 1.0797 0.8919 1.40E-02 1.80E-07 0.8721 0.013 0.8485 0.0131 -2.705 0.640.19 0.8 1.0548 0.8223 2.50E-02 -5.40E-07 0.8179 0.0248 0.8157 0.0252 -0.269 1.750.33 0.86 1.0333 0.7268 4.40E-02 0.00E+00 0.754 0.045 0.7682 0.0468 1.881 3.850.43 0.89 1.0241 0.6675 5.80E-02 -3.60E-07 0.7162 0.0603 0.7354 0.0636 2.686 5.440.55 0.92 1.0162 0.599 7.50E-02 0.00E+00 0.6717 0.0814 0.6933 0.0871 3.212 7.040.68 0.95 1.0097 0.5185 1.00E-01 8.90E-08 0.6167 0.1142 0.636 0.1221 3.136 6.970.76 0.96 1.007 0.472 1.20E-01 -6.00E-08 0.5821 0.152 0.5982 0.1471 2.774 -3.22

1 1 1 0.25 2.50E-01 0.00E+00 0.3486 0.3486 0.3514 0.3514 0.8 0.8

176

Table C1.56: Densities Prediction for Refrigerant C318.

Pr Tr Gam ZV ZL Fugr DSL DSV DL DV DEVL DEVG 0.01 0.6 1.2877 0.9875 1.20E-03 0.00E+00 0.5376 0.0006 0.5147 0.0006 -4.251 -0.370.01 0.63 1.2592 0.9798 2.10E-03 -2.40E-07 0.5268 0.0011 0.5097 0.0011 -3.239 -0.430.02 0.66 1.2316 0.9689 3.50E-03 -4.20E-07 0.5159 0.0018 0.5036 0.0018 -2.388 -0.460.02 0.66 1.2249 0.9657 3.90E-03 -1.20E-07 0.5127 0.0021 0.5021 0.0021 -2.084 -0.460.04 0.69 1.2051 0.9544 5.60E-03 1.80E-07 0.5045 0.0029 0.4969 0.0029 -1.505 -0.440.05 0.7 1.1897 0.9437 7.20E-03 -2.40E-07 0.4969 0.0038 0.4925 0.0037 -0.904 -0.390.05 0.71 1.1797 0.9356 8.40E-03 3.00E-07 0.4921 0.0044 0.4893 0.0044 -0.565 -0.330.08 0.74 1.1555 0.9121 1.20E-02 3.00E-07 0.4798 0.0065 0.4805 0.0065 0.158 -0.120.12 0.77 1.1327 0.8834 1.80E-02 -6.00E-07 0.4659 0.0094 0.4705 0.0094 0.987 0.270.13 0.78 1.1262 0.8737 1.90E-02 -1.80E-07 0.4616 0.0104 0.4672 0.0104 1.213 0.390.17 0.8 1.1114 0.849 2.40E-02 5.40E-07 0.4516 0.0131 0.4589 0.0132 1.615 0.790.23 0.83 1.0914 0.8086 3.30E-02 1.80E-07 0.4359 0.018 0.4453 0.0183 2.169 1.54

0.3 0.86 1.073 0.7615 4.40E-02 -1.20E-07 0.4187 0.0244 0.4292 0.0251 2.506 2.560.4 0.89 1.0561 0.7069 5.90E-02 -1.20E-07 0.3996 0.0329 0.4097 0.0342 2.53 3.88

0.51 0.92 1.0406 0.6434 7.80E-02 0.00E+00 0.3773 0.0442 0.3856 0.0467 2.188 5.580.65 0.94 1.0263 0.5682 1.00E-01 -1.50E-07 0.3503 0.0602 0.3541 0.0648 1.073 7.720.74 0.96 1.0182 0.5145 1.30E-01 6.00E-08 0.3302 0.0737 0.3294 0.0805 -0.241 9.30.81 0.97 1.0127 0.4737 1.50E-01 -4.30E-04 0.3138 0.0858 0.3083 0.0944 -1.776 10.05

1 1 1 0.279 2.80E-01 0.00E+00 0.1924 0.1924 0.1924 0.1924 0 0

177

C.2 Results for the Peng-Robinson Equation of State.

178

Table C2.1: Densities Prediction for Methane.

Pr Tr Gam ZVC ZLC Fugr DSL DSG DL DV DEVL DEVG0.022 0.586 1.1946 0.9671 0.0037 -2.40E-07 1.653 0.007 1.8507 0.007 11.96 -0.040.033 0.612 1.1786 0.9558 0.0053 -4.20E-07 1.623 0.0101 1.8153 0.0101 11.85 -0.190.049 0.641 1.1624 0.9403 0.0077 1.80E-07 1.586 0.0147 1.7729 0.0146 11.78 -0.370.058 0.655 1.1546 0.9315 0.0092 6.00E-08 1.57 0.0174 1.7508 0.0173 11.52 -0.280.069 0.67 1.1477 0.9222 0.0109 -1.20E-07 1.551 0.0204 1.7285 0.0204 11.45 -0.310.097 0.699 1.1334 0.901 0.0149 1.80E-07 1.513 0.0279 1.6811 0.0278 11.11 -0.220.113 0.714 1.1266 0.8893 0.0173 -1.80E-07 1.495 0.0322 1.6564 0.0322 10.79 -0.20.131 0.728 1.1187 0.8762 0.02 3.60E-07 1.477 0.0373 1.6296 0.0373 10.33 -0.190.13 0.728 1.121 0.8772 0.0198 6.00E-08 1.477 0.0369 1.6317 0.0369 10.47 -0.08

0.151 0.743 1.112 0.8628 0.023 -1.20E-07 1.456 0.0428 1.6028 0.0428 10.08 0.060.173 0.757 1.1056 0.8486 0.0263 2.40E-07 1.436 0.0488 1.5753 0.0489 9.7 0.130.198 0.772 1.099 0.8334 0.03 -1.20E-07 1.417 0.0555 1.5464 0.0557 9.13 0.290.225 0.786 1.0924 0.8172 0.0342 1.20E-07 1.394 0.063 1.5161 0.0634 8.76 0.530.254 0.801 1.0859 0.8 0.0387 1.20E-07 1.373 0.0714 1.4845 0.0719 8.12 0.720.287 0.815 1.079 0.7816 0.0439 1.20E-07 1.352 0.0808 1.4509 0.0816 7.32 0.960.322 0.83 1.0727 0.7623 0.0496 -2.40E-07 1.329 0.0911 1.4163 0.0922 6.57 1.160.359 0.845 1.0667 0.7421 0.0559 -6.00E-08 1.304 0.1024 1.3804 0.1039 5.86 1.48

0.4 0.859 1.0606 0.7206 0.0629 0.00E+00 1.277 0.1151 1.3422 0.1172 5.11 1.840.445 0.874 1.0543 0.6975 0.0709 -6.00E-08 1.252 0.1294 1.3014 0.1323 3.95 2.220.493 0.888 1.0481 0.6729 0.0799 -6.00E-08 1.222 0.1455 1.258 0.1494 2.95 2.640.545 0.903 1.0415 0.646 0.0904 1.80E-07 1.192 0.1644 1.2106 0.1694 1.56 3.06

0.6 0.917 1.0354 0.6176 0.1023 0.00E+00 1.159 0.1854 1.1603 0.1921 0.11 3.60.659 0.932 1.0298 0.5872 0.1158 -3.00E-08 1.119 0.2094 1.1064 0.2182 -1.12 4.230.722 0.947 1.0239 0.5535 0.1321 6.00E-08 1.077 0.2379 1.0462 0.2497 -2.86 4.950.789 0.961 1.0181 0.5154 0.1522 -3.00E-08 1.029 0.2727 0.9776 0.2888 -5 5.890.861 0.976 1.0119 0.4716 0.179 -3.00E-04 0.968 0.3172 0.8937 0.3392 -7.67 6.94

1 1 1 0.3074 0.3074 0.00E+00 0.629 0.629 0.5896 0.5896 -6.26 -6.26

179


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.002 0.491 1.3445 0.9953 0.0004 -2.00E-04 1.227 0.0005 1.3133 0.0005 7.03 -4.280.003 0.509 1.3333 0.9934 0.0005 2.20E-05 1.209 0.0007 1.3083 0.0007 8.21 -3.160.005 0.527 1.3116 0.9904 0.0008 -3.00E-07 1.192 0.0011 1.2927 0.0011 8.45 -1.480.007 0.545 1.2961 0.9869 0.0012 -6.00E-08 1.175 0.0016 1.2792 0.0016 8.87 -0.320.01 0.564 1.2811 0.9826 0.0017 -3.60E-07 1.163 0.0022 1.265 0.0022 8.77 -0.81

0.014 0.582 1.2664 0.9774 0.0023 -2.40E-07 1.147 0.003 1.2496 0.003 8.94 -0.840.019 0.6 1.2519 0.9712 0.0031 -1.20E-07 1.131 0.004 1.2336 0.004 9.07 -0.520.021 0.604 1.2474 0.9694 0.0034 4.80E-07 1.127 0.0043 1.2297 0.0043 9.11 -0.840.034 0.636 1.2227 0.9551 0.0054 -1.80E-07 1.098 0.0069 1.1997 0.0068 9.26 -0.90.057 0.673 1.1964 0.9345 0.0087 -6.00E-08 1.069 0.011 1.1632 0.0109 8.81 -1.050.072 0.691 1.1839 0.9223 0.0109 -6.00E-08 1.052 0.0136 1.1437 0.0135 8.72 -0.950.133 0.745 1.1475 0.8772 0.0198 -3.00E-07 1.005 0.0246 1.0795 0.0244 7.41 -0.890.16 0.764 1.1359 0.8593 0.0238 -1.80E-07 0.987 0.0295 1.0559 0.0293 6.98 -0.83

0.191 0.782 1.1243 0.8396 0.0285 1.80E-07 0.972 0.0353 1.0309 0.035 6.05 -0.770.227 0.8 1.113 0.8183 0.0339 -2.40E-07 0.953 0.0418 1.0044 0.0416 5.39 -0.650.267 0.818 1.1018 0.7951 0.0401 -6.00E-08 0.934 0.0494 0.9762 0.0492 4.52 -0.450.362 0.854 1.0802 0.743 0.0556 -1.20E-07 0.896 0.0683 0.9143 0.0684 2.04 0.080.48 0.891 1.0591 0.6815 0.0767 6.00E-08 0.851 0.094 0.8423 0.0948 -1.02 0.8

0.548 0.909 1.0488 0.6463 0.0903 1.80E-07 0.825 0.1105 0.8013 0.1119 -2.88 1.280.585 0.918 1.0437 0.6273 0.0981 -1.20E-07 0.811 0.12 0.7791 0.1218 -3.94 1.50.623 0.936 1.0517 0.6111 0.1051 6.00E-08 0.776 0.1248 0.76 0.1307 -2.06 4.690.706 0.945 1.0287 0.5633 0.1272 3.00E-08 0.763 0.1551 0.7038 0.1589 -7.76 2.480.75 0.954 1.0238 0.5388 0.1397 0.00E+00 0.742 0.1699 0.6747 0.1749 -9.07 2.91

0.796 0.963 1.0189 0.5121 0.1541 8.90E-08 0.72 0.187 0.6427 0.1934 -10.73 3.430.844 0.973 1.0138 0.483 0.1718 -3.00E-04 0.693 0.2071 0.6055 0.2154 -12.62 4.020.894 0.982 1.009 0.4483 0.1939 -1.80E-04 0.66 0.2316 0.5632 0.2436 -14.67 5.18

1 1 1 0.3074 0.3074 0.00E+00 0.422 0.422 0.3901 0.3901 -7.56 -7.56

180


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.009 0.571 1.3153 0.9841 0.0015 4.80E-07 0.8557 0.0014 0.9123 0.0014 6.61 0.590.012 0.586 1.3031 0.9802 0.002 -6.00E-08 0.8462 0.0018 0.9034 0.0018 6.77 0.520.016 0.601 1.2905 0.9756 0.0025 -3.60E-07 0.839 0.0023 0.8948 0.0023 6.65 0.630.026 0.631 1.2665 0.9644 0.0041 0.00E+00 0.8207 0.0037 0.8759 0.0037 6.72 00.033 0.646 1.2538 0.9575 0.0051 -1.20E-07 0.8116 0.0045 0.8657 0.0046 6.66 1.120.041 0.661 1.2423 0.9499 0.0062 -3.00E-07 0.8025 0.0056 0.8553 0.0056 6.59 00.061 0.691 1.2177 0.9317 0.0092 1.80E-07 0.7839 0.0083 0.8328 0.0082 6.25 -0.660.074 0.706 1.2054 0.9211 0.0111 6.00E-08 0.774 0.0099 0.8209 0.0099 6.06 0.110.089 0.721 1.1939 0.9097 0.0132 -1.80E-07 0.7635 0.0117 0.8085 0.0117 5.89 -0.090.107 0.736 1.1817 0.8969 0.0157 1.80E-07 0.7531 0.0142 0.7954 0.0139 5.61 -1.70.126 0.751 1.17 0.8832 0.0186 6.00E-08 0.7423 0.0171 0.7817 0.0164 5.31 -3.70.149 0.766 1.1585 0.8683 0.0218 6.00E-08 0.7313 0.0199 0.7675 0.0193 4.95 -3.20.174 0.781 1.1472 0.8523 0.0255 1.20E-07 0.7199 0.023 0.7525 0.0225 4.53 -2.460.202 0.796 1.1358 0.8348 0.0297 2.40E-07 0.7067 0.0266 0.7367 0.0262 4.25 -1.40.233 0.811 1.1248 0.8162 0.0344 -1.20E-07 0.6937 0.0304 0.7201 0.0304 3.81 -0.250.268 0.826 1.1139 0.7962 0.0398 -3.00E-07 0.6812 0.0353 0.7027 0.0351 3.16 -0.440.306 0.841 1.1032 0.7748 0.0459 -1.20E-07 0.6689 0.0406 0.6842 0.0405 2.28 -0.270.349 0.856 1.0927 0.7518 0.0528 0.00E+00 0.6569 0.0466 0.6646 0.0467 1.17 0.330.395 0.871 1.0823 0.7271 0.0607 -3.00E-07 0.6421 0.0532 0.6438 0.0538 0.27 1.040.446 0.886 1.0724 0.7008 0.0698 6.00E-08 0.6278 0.0613 0.6216 0.0619 -0.98 0.960.501 0.901 1.0625 0.6723 0.0801 -6.00E-08 0.6126 0.0709 0.5978 0.0712 -2.41 0.540.561 0.916 1.0527 0.6413 0.0923 -3.00E-07 0.5941 0.0816 0.5718 0.0823 -3.75 0.870.625 0.931 1.0434 0.608 0.1064 -1.20E-07 0.5724 0.0945 0.5437 0.0952 -5.01 0.740.692 0.946 1.0355 0.5728 0.1226 -1.80E-07 0.5488 0.109 0.514 0.11 -6.34 0.90.768 0.961 1.0258 0.5299 0.1443 1.20E-07 0.5193 0.126 0.4774 0.13 -8.07 3.210.85 0.976 1.0161 0.4812 0.1735 -4.90E-04 0.4813 0.1522 0.4326 0.156 -10.11 2.47

1 1 1 0.3074 0.3074 0.00E+00 0.312 0.312 0.2804 0.2804 -10.12 -10.12

181


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.021 0.627 1.2997 0.9701 0.0033 6.00E-08 0.647 0.0023 0.6882 0.0023 6.37 -0.870.027 0.641 1.286 0.9641 0.0041 3.00E-07 0.64 0.0029 0.6808 0.0029 6.37 -0.560.032 0.653 1.2754 0.9587 0.0049 6.00E-08 0.635 0.0035 0.6745 0.0034 6.22 -0.990.039 0.666 1.2624 0.9518 0.0059 -1.20E-07 0.63 0.0042 0.6671 0.0041 5.9 -0.550.047 0.679 1.2505 0.9444 0.0071 6.00E-08 0.623 0.005 0.6596 0.0049 5.88 -0.650.057 0.692 1.2386 0.9363 0.0084 -2.40E-07 0.619 0.0059 0.6519 0.0059 5.31 -1.020.067 0.705 1.2269 0.9274 0.01 4.80E-07 0.612 0.007 0.6438 0.0069 5.19 -0.830.093 0.731 1.2048 0.9075 0.0136 4.80E-07 0.602 0.0095 0.6269 0.0094 4.14 -0.830.109 0.744 1.1924 0.8957 0.016 6.00E-08 0.595 0.0111 0.6176 0.011 3.79 -0.890.127 0.758 1.1813 0.8835 0.0185 4.20E-07 0.589 0.0128 0.6081 0.0127 3.25 -0.870.147 0.771 1.1703 0.8703 0.0213 -4.20E-07 0.581 0.0148 0.5983 0.0147 2.98 -0.870.169 0.784 1.1595 0.8562 0.0245 -3.60E-07 0.575 0.017 0.588 0.0168 2.27 -0.670.193 0.797 1.1489 0.8412 0.0281 0.00E+00 0.568 0.0194 0.5774 0.0193 1.65 -0.630.22 0.81 1.1385 0.8252 0.0321 6.00E-08 0.562 0.0221 0.5662 0.022 0.74 -0.53

0.249 0.823 1.1283 0.8081 0.0365 1.20E-07 0.553 0.0252 0.5545 0.0251 0.27 -0.440.281 0.836 1.1181 0.79 0.0415 1.20E-07 0.546 0.0286 0.5422 0.0285 -0.69 -0.30.354 0.862 1.0987 0.7503 0.0533 -1.20E-07 0.529 0.0366 0.5159 0.0366 -2.48 0.090.395 0.875 1.0891 0.7285 0.0603 -1.80E-07 0.52 0.0414 0.5015 0.0415 -3.55 0.320.439 0.888 1.0801 0.7056 0.0681 -2.40E-07 0.511 0.0466 0.4866 0.0469 -4.78 0.620.487 0.901 1.0707 0.6806 0.077 -2.40E-07 0.499 0.0528 0.4703 0.0532 -5.75 0.860.54 0.914 1.0611 0.6534 0.0874 6.00E-08 0.487 0.0599 0.4526 0.0606 -7.07 1.13

0.596 0.927 1.0518 0.6242 0.0994 6.00E-08 0.474 0.0681 0.4334 0.069 -8.56 1.430.723 0.953 1.033 0.5561 0.1308 0.00E+00 0.44 0.0897 0.3886 0.0914 -11.67 1.90.794 0.966 1.0236 0.5151 0.1524 -1.20E-07 0.417 0.1049 0.3613 0.1069 -13.35 1.910.87 0.98 1.0139 0.4671 0.1821 -3.70E-04 0.381 0.1261 0.327 0.1275 -14.17 1.08

1 1 1 0.3074 0.3074 0.00E+00 0.245 0.2451 0.2181 0.2181 -10.99 -11.03

182


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.001 0.497 1.4279 0.9968 0.0002 1.30E-03 0.702 0.0002 0.747 0.0002 6.42 0.950.004 0.537 1.3816 0.9924 0.0006 -2.10E-05 0.685 0.0005 0.7272 0.0005 6.17 0.780.005 0.551 1.3664 0.9902 0.0009 -6.00E-07 0.677 0.0006 0.7228 0.0006 6.77 0.450.009 0.578 1.3374 0.9844 0.0015 -4.80E-07 0.667 0.0011 0.7107 0.0011 6.55 -0.070.012 0.592 1.3236 0.9808 0.0019 -7.70E-07 0.662 0.0014 0.7044 0.0014 6.41 -0.750.022 0.626 1.2903 0.9691 0.0034 3.60E-07 0.647 0.0024 0.6876 0.0024 6.27 -0.810.027 0.639 1.2774 0.9633 0.0042 4.20E-07 0.64 0.003 0.6804 0.003 6.32 -0.470.034 0.653 1.2649 0.9569 0.0051 -6.00E-07 0.633 0.0036 0.6731 0.0036 6.34 -0.390.041 0.667 1.2525 0.9497 0.0062 6.00E-08 0.628 0.0044 0.6655 0.0044 5.97 -0.410.05 0.68 1.2404 0.9418 0.0075 1.80E-07 0.621 0.0053 0.6576 0.0052 5.9 -0.36

0.072 0.708 1.2169 0.9235 0.0106 1.20E-07 0.608 0.0074 0.641 0.0074 5.43 -0.240.085 0.721 1.2056 0.9132 0.0125 4.80E-07 0.6 0.0087 0.6322 0.0087 5.37 -0.160.117 0.748 1.1836 0.8901 0.0171 4.20E-07 0.585 0.0118 0.6137 0.0118 4.91 0.030.136 0.762 1.1727 0.8771 0.0199 3.60E-07 0.577 0.0136 0.6038 0.0137 4.65 0.290.181 0.789 1.1517 0.8483 0.0264 1.20E-07 0.56 0.018 0.5829 0.0181 4.09 0.680.207 0.803 1.141 0.8322 0.0303 -6.00E-08 0.551 0.0207 0.5715 0.0208 3.73 0.80.268 0.83 1.1203 0.7968 0.0396 1.20E-07 0.533 0.0269 0.5473 0.0272 2.68 1.280.342 0.857 1.1001 0.7563 0.0514 0.00E+00 0.511 0.0347 0.5203 0.0354 1.82 1.960.384 0.871 1.0902 0.7341 0.0585 -1.20E-07 0.499 0.0394 0.5056 0.0403 1.33 2.310.479 0.898 1.0706 0.6844 0.0756 -6.00E-08 0.471 0.0507 0.4732 0.0523 0.46 3.220.533 0.912 1.0609 0.6567 0.0861 -6.00E-08 0.455 0.0575 0.4551 0.0597 0.02 3.750.654 0.939 1.0418 0.5936 0.1129 1.80E-07 0.416 0.075 0.4137 0.0787 -0.55 4.970.721 0.952 1.0324 0.5569 0.1304 -6.00E-08 0.391 0.0863 0.3895 0.0912 -0.39 5.660.794 0.966 1.023 0.5149 0.1526 -6.00E-08 0.361 0.1006 0.3615 0.1071 0.13 6.450.872 0.98 1.0134 0.4658 0.1831 -3.90E-04 0.326 0.1199 0.3263 0.1282 0.08 6.94

1 1 1 0.3074 0.3074 0.00E+00 0.238 0.2377 0.2183 0.2183 -8.3 -8.16

183


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.022 0.639 1.3213 0.9698 0.0033 1.20E-07 0.533 0.0019 0.5526 0.0019 3.67 -0.710.032 0.662 1.2971 0.9593 0.0048 2.40E-07 0.523 0.0027 0.5424 0.0027 3.71 -0.70.038 0.674 1.2848 0.9532 0.0057 6.00E-08 0.519 0.0032 0.5371 0.0032 3.48 -0.750.054 0.698 1.2605 0.9391 0.0079 -1.20E-07 0.51 0.0045 0.5258 0.0044 3.09 -0.360.064 0.709 1.2485 0.9311 0.0093 6.00E-08 0.504 0.0052 0.5198 0.0052 3.14 -0.770.087 0.733 1.2253 0.9131 0.0126 -2.40E-07 0.495 0.007 0.5073 0.007 2.49 -0.5

0.1 0.745 1.214 0.9031 0.0145 6.00E-08 0.49 0.0081 0.5007 0.008 2.19 -0.560.133 0.769 1.1917 0.8807 0.0191 1.80E-07 0.48 0.0106 0.4868 0.0105 1.42 -0.430.151 0.78 1.1809 0.8684 0.0218 1.20E-07 0.473 0.0121 0.4795 0.012 1.36 -0.370.172 0.792 1.1703 0.8553 0.0247 -1.20E-07 0.468 0.0137 0.4718 0.0137 0.81 -0.280.194 0.804 1.1598 0.8414 0.0281 -6.00E-08 0.462 0.0155 0.4638 0.0155 0.4 -0.240.219 0.816 1.1494 0.8265 0.0318 -3.60E-07 0.456 0.0175 0.4555 0.0175 -0.1 -0.10.246 0.828 1.1393 0.8108 0.0358 -1.80E-07 0.45 0.0198 0.4469 0.0198 -0.7 0.020.276 0.84 1.1292 0.7941 0.0404 -1.80E-07 0.443 0.0222 0.4378 0.0223 -1.18 0.160.308 0.851 1.1193 0.7764 0.0454 -1.20E-07 0.437 0.025 0.4283 0.0251 -2 0.310.342 0.863 1.1093 0.7575 0.0511 -3.00E-07 0.429 0.0281 0.4182 0.0282 -2.52 0.450.38 0.875 1.0996 0.7376 0.0573 0.00E+00 0.421 0.0315 0.4076 0.0317 -3.17 0.670.42 0.887 1.09 0.7163 0.0644 1.80E-07 0.414 0.0353 0.3964 0.0356 -4.24 0.86

0.464 0.899 1.0805 0.6936 0.0723 1.20E-07 0.405 0.0396 0.3846 0.0401 -5.04 1.110.511 0.91 1.071 0.6693 0.0813 0.00E+00 0.396 0.0446 0.3718 0.0452 -6.1 1.310.562 0.922 1.0613 0.6428 0.0917 -1.80E-07 0.385 0.0503 0.3579 0.0511 -7.03 1.490.615 0.934 1.0525 0.6151 0.1033 -6.00E-08 0.373 0.0567 0.3434 0.0577 -7.93 1.730.674 0.946 1.0432 0.5842 0.1172 8.90E-08 0.358 0.0644 0.3271 0.0656 -8.63 1.880.736 0.958 1.0341 0.5501 0.1338 -6.00E-08 0.341 0.0737 0.309 0.0752 -9.39 2.020.802 0.97 1.0249 0.5112 0.1546 -8.90E-08 0.316 0.0856 0.2882 0.0871 -8.81 1.830.874 0.981 1.0153 0.466 0.183 -3.90E-04 0.269 0.102 0.2619 0.1028 -2.62 0.85

1 1 1 0.3074 0.3074 0.00E+00 0.205 0.2053 0.1752 0.1752 -14.56 -14.69

184


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.000408 0.47 1.5856 0.9987 0.0001 3.90E-01 0.605 0.0001 0.5731 0 -5.27 -20.24

0.001 0.482 1.4918 0.9983 0.0001 1.40E-02 0.6 0.0001 0.6166 0.0001 2.77 0.020.001 0.495 1.477 0.9977 0.0002 2.80E-03 0.595 0.0001 0.6208 0.0001 4.34 -2.030.001 0.507 1.4598 0.9969 0.0002 1.00E-04 0.59 0.0001 0.6098 0.0001 3.36 -1.430.002 0.519 1.4444 0.9959 0.0003 1.20E-07 0.585 0.0002 0.6097 0.0002 4.22 -0.350.002 0.531 1.4293 0.9947 0.0004 1.80E-07 0.58 0.0003 0.6049 0.0003 4.29 -1.720.004 0.555 1.3995 0.9913 0.0007 7.20E-07 0.57 0.0004 0.5963 0.0004 4.61 1.260.006 0.567 1.3852 0.9892 0.001 -1.20E-07 0.566 0.0006 0.5924 0.0006 4.66 -0.810.008 0.579 1.3712 0.9866 0.0012 -1.80E-07 0.559 0.0007 0.5877 0.0007 5.14 0.550.01 0.591 1.3576 0.9837 0.0016 -6.00E-07 0.554 0.0009 0.5832 0.0009 5.27 -0.63

0.012 0.603 1.3445 0.9804 0.0019 0.00E+00 0.55 0.0012 0.5785 0.0012 5.19 0.020.015 0.615 1.3313 0.9766 0.0024 -6.00E-08 0.546 0.0014 0.5734 0.0014 5.02 -0.690.019 0.627 1.3185 0.9723 0.003 6.00E-08 0.541 0.0018 0.5684 0.0017 5.06 -0.780.024 0.639 1.3061 0.9676 0.0036 -3.60E-07 0.537 0.0021 0.5633 0.0021 4.89 -0.340.029 0.651 1.2937 0.9622 0.0044 3.60E-07 0.531 0.0026 0.558 0.0025 5.08 -0.820.042 0.675 1.2695 0.9498 0.0062 0.00E+00 0.521 0.0036 0.5469 0.0036 4.97 -0.520.059 0.7 1.246 0.9349 0.0086 3.00E-07 0.511 0.005 0.535 0.0049 4.7 -0.60.081 0.724 1.2237 0.9175 0.0117 -6.00E-08 0.502 0.0067 0.5224 0.0067 4.06 -0.490.142 0.772 1.1805 0.8739 0.0206 -1.80E-07 0.481 0.0117 0.4942 0.0116 2.74 -0.290.184 0.796 1.1598 0.8474 0.0266 2.40E-07 0.47 0.015 0.4784 0.015 1.78 0.060.234 0.82 1.1395 0.8172 0.0341 -1.80E-07 0.457 0.0192 0.4611 0.0193 0.9 0.340.364 0.868 1.1006 0.7453 0.0549 1.20E-07 0.43 0.0306 0.4215 0.031 -1.98 1.330.447 0.893 1.0819 0.7022 0.0692 6.00E-08 0.415 0.0385 0.3983 0.0393 -4.02 2.030.543 0.3960.917 1.0631 0.6525 0.0878 -1.20E-07 0.0487 0.3716 0.05 -6.15 2.810.655 0.941 1.0438 0.5933 0.113 -2.70E-07 0.375 0.0625 0.3398 0.0647 -9.39 3.580.781 0.965 1.0262 0.523 0.1481 1.80E-07 0.345 0.0816 0.3015 0.0854 -12.61 4.62

1 1 1 0.3074 0.3074 0.00E+00 0.204 0.204 0.1793 0.1793 -12.1 -12.1

185


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.001 0.53 1.508 0.9965 0.0003 1.70E-03 0.502 0.0001 0.4687 0.0001 -6.64 -0.960.003 0.552 1.4759 0.9943 0.0004 1.80E-07 0.494 0.0002 0.4619 0.0002 -6.49 -0.920.006 0.585 1.4307 0.9892 0.001 2.00E-06 0.479 0.0004 0.4518 0.0004 -5.67 -0.620.008 0.596 1.4158 0.9869 0.0012 -6.00E-08 0.476 0.0006 0.4487 0.0005 -5.74 -1.940.01 0.607 1.4009 0.9842 0.0015 -6.00E-08 0.472 0.0007 0.4456 0.0007 -5.6 0.52

0.015 0.629 1.3727 0.9777 0.0023 5.40E-07 0.464 0.001 0.4386 0.001 -5.47 -0.310.018 0.64 1.359 0.9738 0.0028 -1.80E-07 0.459 0.0012 0.4352 0.0012 -5.19 -0.60.022 0.651 1.3453 0.9694 0.0034 -3.00E-07 0.455 0.0015 0.4315 0.0015 -5.16 -1.050.039 0.685 1.3058 0.9534 0.0057 -6.00E-08 0.443 0.0025 0.4198 0.0025 -5.24 -1.020.046 0.696 1.293 0.947 0.0067 6.00E-08 0.438 0.003 0.4156 0.0029 -5.11 -0.820.073 0.729 1.2555 0.9241 0.0105 -1.20E-07 0.425 0.0046 0.4023 0.0046 -5.34 -0.960.085 0.74 1.244 0.9154 0.0121 4.20E-07 0.422 0.0053 0.3977 0.0053 -5.77 -0.850.097 0.751 1.2325 0.9061 0.0139 0.00E+00 0.417 0.0061 0.3928 0.006 -5.8 -0.860.127 0.773 1.2095 0.8852 0.0181 0.00E+00 0.409 0.0079 0.3825 0.0078 -6.47 -0.80.164 0.795 1.1875 0.8615 0.0233 1.80E-07 0.399 0.0101 0.3715 0.0101 -6.9 -0.610.184 0.806 1.177 0.8487 0.0263 1.80E-07 0.395 0.0114 0.3657 0.0113 -7.41 -0.490.232 0.828 1.155 0.8199 0.0334 -3.60E-07 0.384 0.0144 0.3531 0.0144 -8.04 -0.170.289 0.85 1.1341 0.7878 0.0421 6.00E-08 0.373 0.0181 0.3394 0.0182 -9 0.220.392 0.883 1.1039 0.7324 0.059 2.40E-07 0.356 0.0252 0.3164 0.0255 -11.12 1.140.431 0.894 1.0946 0.7121 0.0658 -1.80E-07 0.35 0.028 0.3081 0.0285 -11.97 1.570.473 0.905 1.085 0.6901 0.0736 -6.00E-08 0.342 0.0313 0.2991 0.0319 -12.56 2.040.567 0.927 1.0666 0.642 0.092 0.00E+00 0.326 0.0388 0.2794 0.04 -14.3 3.30.679 0.95 1.0461 0.5826 0.118 -8.90E-08 0.305 0.0492 0.255 0.0516 -16.41 4.840.737 0.961 1.0374 0.5507 0.1335 -2.40E-07 0.292 0.0552 0.2417 0.0586 -17.23 6.180.801 0.972 1.0275 0.5144 0.154 -7.20E-04 0.274 0.0627 0.2253 0.0674 -17.78 7.510.872 0.983 1.0175 0.4682 0.1815 -4.00E-04 0.247 0.0728 0.2057 0.0797 -16.73 9.44

1 1 1 0.3074 0.3074 0.00E+00 0.139 0.139 0.1369 0.1369 -1.53 -1.53

186


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.002 0.545 1.5197 0.9959 0.0003 -1.40E-04 0.425 0.0001 0.4163 0.0001 -2.05 -0.860.003 0.565 1.4897 0.9937 0.0005 3.00E-07 0.419 0.0002 0.4144 0.0002 -1.1 1.50.005 0.586 1.4588 0.9905 0.0008 -6.00E-08 0.412 0.0003 0.4104 0.0003 -0.38 0.50.007 0.596 1.4439 0.9885 0.001 -3.00E-07 0.409 0.0004 0.4073 0.0004 -0.41 -0.950.01 0.617 1.4157 0.9837 0.0016 0.00E+00 0.402 0.0006 0.4019 0.0006 -0.01 0.17

0.015 0.637 1.3876 0.9774 0.0023 1.20E-07 0.396 0.0009 0.3962 0.0009 0.05 -0.040.022 0.658 1.3607 0.9697 0.0033 2.40E-07 0.39 0.0013 0.39 0.0013 0 -0.260.027 0.668 1.3476 0.9652 0.0039 6.00E-08 0.387 0.0016 0.3868 0.0016 -0.05 -0.690.032 0.678 1.3346 0.9602 0.0046 -5.40E-07 0.384 0.0019 0.3835 0.0019 -0.13 -0.760.038 0.689 1.3217 0.9548 0.0055 6.00E-08 0.381 0.0022 0.3801 0.0022 -0.23 -0.430.044 0.699 1.3091 0.9489 0.0064 1.20E-07 0.377 0.0025 0.3766 0.0025 -0.1 -0.210.051 0.709 1.2967 0.9425 0.0074 -1.20E-07 0.374 0.0029 0.373 0.0029 -0.27 -0.220.069 0.73 1.2724 0.9281 0.0098 6.00E-08 0.367 0.0039 0.3655 0.0039 -0.42 -0.270.103 0.761 1.2379 0.9025 0.0146 2.40E-07 0.356 0.0057 0.3533 0.0057 -0.77 -0.420.133 0.781 1.2149 0.8821 0.0188 6.00E-08 0.35 0.0073 0.3443 0.0073 -1.63 -0.150.168 0.802 1.1931 0.8594 0.0238 -1.20E-07 0.343 0.0093 0.3348 0.0093 -2.4 -0.160.21 0.822 1.1723 0.8341 0.0299 1.20E-07 0.335 0.0116 0.3246 0.0116 -3.11 0.01

0.257 0.843 1.1535 0.8067 0.0369 0.00E+00 0.327 0.0143 0.3139 0.0144 -4 0.350.315 0.863 1.1325 0.7745 0.046 -1.20E-07 0.318 0.0178 0.3016 0.0179 -5.14 0.540.382 0.884 1.1126 0.7389 0.0569 -1.20E-07 0.309 0.022 0.2883 0.0222 -6.7 0.840.459 0.905 1.0926 0.6984 0.0706 1.20E-07 0.298 0.0273 0.2733 0.0276 -8.3 1.160.548 0.925 1.0728 0.6523 0.0879 -6.00E-08 0.286 0.034 0.2562 0.0345 -10.41 1.40.65 0.946 1.0533 0.5989 0.1105 8.90E-08 0.271 0.0429 0.2364 0.0436 -12.76 1.59

0.767 0.966 1.0334 0.5334 0.1425 1.20E-07 0.251 0.0561 0.2118 0.0566 -15.61 0.971 1.005 1 0.3074 0.3074 0.00E+00 0.144 0.1444 0.123 0.123 -14.58 -14.82

187


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.00025 0.495 8.0862 0.9963 0.0037 -3.60E+00 0.389 0 0.0041 0 -98.96 -25.16

0.0005 0.515 2.6381 0.9978 0.0021 -4.20E+00 0.384 0 0.014 0 -96.36 -4.20.001 0.535 1.599 0.9977 0.0002 5.40E-03 0.379 0 0.3306 0.0001 -12.78 3.790.002 0.554 1.5641 0.9963 0.0003 -2.20E-04 0.376 0.0001 0.3287 0.0001 -12.59 0.220.003 0.574 1.5301 0.9942 0.0005 -4.20E-07 0.371 0.0002 0.3225 0.0002 -13.08 0.210.005 0.594 1.5013 0.9914 0.0007 6.90E-06 0.366 0.0002 0.3197 0.0002 -12.64 -2.080.008 0.614 1.467 0.9874 0.0011 -3.60E-07 0.363 0.0004 0.3153 0.0004 -13.13 -0.840.011 0.634 1.4372 0.9824 0.0017 -1.20E-07 0.359 0.0005 0.3114 0.0005 -13.26 -1.090.017 0.653 1.4074 0.9759 0.0025 1.20E-07 0.354 0.0008 0.3067 0.0008 -13.37 -0.370.024 0.673 1.3788 0.968 0.0036 0.00E+00 0.35 0.0011 0.302 0.0011 -13.72 -0.120.034 0.693 1.3505 0.9582 0.0049 1.80E-07 0.345 0.0015 0.2969 0.0015 -13.95 -0.570.047 0.713 1.3238 0.9467 0.0067 0.00E+00 0.341 0.0021 0.2916 0.0021 -14.5 -0.20.064 0.733 1.2974 0.9331 0.009 -4.80E-07 0.335 0.0028 0.2859 0.0027 -14.67 -0.580.084 0.752 1.2717 0.9173 0.0118 6.00E-08 0.33 0.0036 0.2797 0.0036 -15.23 -0.50.109 0.772 1.2467 0.8991 0.0153 6.00E-08 0.325 0.0047 0.2732 0.0046 -15.94 -0.170.14 0.792 1.2227 0.8785 0.0195 -2.40E-07 0.319 0.0059 0.2662 0.0059 -16.54 -0.14

0.176 0.812 1.1993 0.8553 0.0248 -1.20E-07 0.314 0.0075 0.2587 0.0075 -17.6 0.240.218 0.832 1.1782 0.8301 0.0309 2.40E-07 0.307 0.0093 0.2509 0.0093 -18.28 0.720.269 0.851 1.1557 0.8008 0.0385 0.00E+00 0.3 0.0115 0.2421 0.0116 -19.31 1.210.298 0.861 1.1447 0.7849 0.043 -1.20E-07 0.296 0.0128 0.2373 0.013 -19.81 1.460.328 0.871 1.1337 0.768 0.0479 6.00E-08 0.292 0.0142 0.2324 0.0145 -20.41 1.86

0.4 0.891 1.1105 0.7297 0.0599 1.20E-07 0.282 0.0177 0.2213 0.0182 -21.53 2.570.479 0.911 1.09 0.6885 0.0741 0.00E+00 0.271 0.0217 0.2094 0.0225 -22.72 3.710.571 0.931 1.0691 0.6407 0.0926 1.80E-07 0.256 0.0269 0.1957 0.0283 -23.56 5.160.676 0.95 1.0487 0.585 0.1169 -6.00E-08 0.231 0.0334 0.1796 0.0359 -22.25 7.260.797 0.97 1.0268 0.5175 0.1531 -1.30E-03 0.199 0.0426 0.1583 0.0469 -20.44 9.93

1 1 1 0.3074 0.3074 0.00E+00 0.101 0.101 0.0961 0.0961 -4.89 -4.89

188


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.001 0.53 1.6553 0.9984 0.0001 2.20E-02 0.3092 0 0.2841 0 -8.13 0.20.001 0.557 1.6174 0.9971 0.0002 -9.60E-04 0.3028 0.0001 0.2815 0.0001 -7.02 -1.140.003 0.584 1.5729 0.9946 0.0004 1.50E-05 0.2965 0.0001 0.2799 0.0001 -5.6 -0.290.005 0.611 1.5299 0.9908 0.0008 3.00E-07 0.2904 0.0002 0.277 0.0002 -4.63 -0.310.009 0.638 1.4946 0.9856 0.0013 -4.20E-07 0.2845 0.0004 0.2726 0.0004 -4.19 -1.350.017 0.665 1.441 0.9767 0.0024 -1.20E-07 0.2789 0.0007 0.2668 0.0007 -4.33 -0.810.028 0.692 1.391 0.9645 0.004 -6.00E-08 0.2729 0.0011 0.2606 0.0011 -4.52 -1.820.044 0.719 1.3534 0.9501 0.0062 -6.00E-07 0.2672 0.0017 0.2545 0.0017 -4.76 -2.280.068 0.746 1.3098 0.9303 0.0094 -1.20E-07 0.2601 0.0026 0.2473 0.0025 -4.93 -1.550.102 0.773 1.2655 0.9048 0.0141 -1.80E-07 0.2524 0.0038 0.239 0.0037 -5.28 -0.990.152 0.8 1.2156 0.8704 0.0213 -1.20E-07 0.2445 0.0056 0.2289 0.0056 -6.36 0.060.211 0.827 1.1785 0.8337 0.0299 1.20E-07 0.2365 0.0079 0.2189 0.0079 -7.45 -0.340.235 0.836 1.1657 0.8196 0.0335 6.00E-08 0.231 0.0089 0.2151 0.0088 -6.88 -1.080.294 0.854 1.136 0.7855 0.0428 1.20E-07 0.225 0.0113 0.2063 0.0112 -8.31 -0.710.343 0.872 1.1231 0.7593 0.0505 -1.80E-07 0.2175 0.0142 0.1996 0.0133 -8.22 -6.360.408 0.89 1.1031 0.7244 0.0617 0.00E+00 0.21 0.0175 0.1908 0.0162 -9.13 -7.170.474 0.908 1.0889 0.6907 0.0733 1.20E-07 0.2 0.0214 0.1824 0.0194 -8.79 -9.270.562 0.926 1.0669 0.6443 0.0911 1.20E-07 0.19 0.0269 0.1708 0.0242 -10.08 -10.290.65 0.944 1.0507 0.5979 0.1109 1.50E-07 0.179 0.0333 0.1592 0.0295 -11.05 -11.29

0.752 0.962 1.0337 0.5417 0.1381 1.20E-07 0.164 0.045 0.145 0.037 -11.57 -17.831 1 1 0.3074 0.3074 0.00E+00 0.1 0.1 0.0834 0.0834 -16.62 -16.62

189


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.025 0.64 1.2959 0.9659 0.0038 -3.00E-07 0.534 0.0022 0.5606 0.0022 4.99 1.150.033 0.657 1.2792 0.9582 0.0049 -4.20E-07 0.5265 0.0028 0.5532 0.0029 5.07 2.030.043 0.675 1.2616 0.9485 0.0064 -6.00E-08 0.5183 0.0036 0.5447 0.0037 5.1 2.470.055 0.693 1.2444 0.9374 0.0082 -2.40E-07 0.5106 0.0047 0.5359 0.0047 4.96 0.030.07 0.711 1.2285 0.9252 0.0103 -2.40E-07 0.5025 0.0059 0.5268 0.0059 4.84 -0.16

0.088 0.729 1.2125 0.9113 0.0129 -6.00E-08 0.4945 0.0074 0.5172 0.0073 4.58 -1.050.11 0.747 1.1953 0.8953 0.016 1.80E-07 0.4861 0.0091 0.5066 0.0091 4.22 -0.23

0.136 0.765 1.1785 0.8775 0.0198 -1.20E-07 0.4773 0.0111 0.4955 0.0112 3.8 0.540.166 0.783 1.1629 0.8582 0.0241 1.20E-07 0.4683 0.0136 0.4838 0.0136 3.32 -0.20.24 0.819 1.132 0.8135 0.0351 1.20E-07 0.4495 0.0197 0.4581 0.0198 1.92 0.42

0.284 0.837 1.1176 0.7883 0.042 -1.20E-07 0.4389 0.0235 0.4441 0.0237 1.19 0.740.333 0.855 1.1042 0.7613 0.0499 3.00E-07 0.4282 0.0282 0.4294 0.0282 0.28 -0.160.389 0.873 1.0907 0.7316 0.0593 -6.00E-08 0.4164 0.0334 0.4133 0.0335 -0.74 0.280.45 0.892 1.0781 0.6997 0.0701 -2.40E-07 0.4037 0.0396 0.3962 0.0397 -1.85 0.280.52 0.91 1.0648 0.6637 0.0834 -1.20E-07 0.3899 0.0469 0.3769 0.0474 -3.33 1.05

0.597 0.928 1.0521 0.624 0.0995 1.80E-07 0.3752 0.0553 0.3556 0.0567 -5.21 2.570.681 0.946 1.0398 0.5795 0.1194 0.00E+00 0.3578 0.0665 0.3317 0.0684 -7.3 2.810.776 0.964 1.0268 0.5262 0.1464 6.00E-08 0.3365 0.0814 0.3027 0.0842 -10.06 3.42

1 1 1 0.3074 0.3074 0.00E+00 0.2025 0.2025 0.179 0.179 -11.61 -11.61

190


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.07 0.712 1.2316 0.9255 0.0103 -1.20E-07 1.623 0.0195 1.7451 0.0194 7.52 -0.72

0.078 0.721 1.2243 0.919 0.0115 2.40E-07 1.611 0.0217 1.73 0.0216 7.38 -0.710.099 0.739 1.2068 0.9038 0.0143 -6.00E-08 1.589 0.0271 1.6958 0.0269 6.72 -0.730.11 0.748 1.1982 0.8956 0.016 1.20E-07 1.567 0.0302 1.678 0.0299 7.09 -0.73

0.123 0.757 1.1895 0.8868 0.0178 4.20E-07 1.556 0.0335 1.6595 0.0333 6.65 -0.710.15 0.776 1.1738 0.8684 0.0218 1.20E-07 1.535 0.041 1.6222 0.0407 5.68 -0.72

0.166 0.785 1.1663 0.8586 0.024 -1.80E-07 1.525 0.0451 1.6029 0.0448 5.11 -0.680.182 0.794 1.1586 0.8483 0.0264 6.00E-08 1.515 0.0496 1.5827 0.0492 4.47 -0.670.219 0.812 1.1428 0.8257 0.032 0.00E+00 1.485 0.06 1.5397 0.0596 3.68 -0.640.24 0.821 1.1348 0.8135 0.0351 6.00E-08 1.475 0.0659 1.5169 0.0655 2.84 -0.58

0.262 0.83 1.1271 0.8008 0.0385 6.00E-08 1.457 0.0723 1.4934 0.0719 2.5 -0.590.31 0.849 1.1128 0.7743 0.046 6.00E-08 1.429 0.0863 1.4451 0.0859 1.13 -0.44

0.336 0.858 1.1057 0.7601 0.0503 0.00E+00 1.411 0.0943 1.4195 0.0939 0.61 -0.370.364 0.867 1.0985 0.7451 0.0549 4.20E-07 1.403 0.103 1.3926 0.1027 -0.74 -0.330.424 0.885 1.0852 0.7137 0.0653 6.00E-08 1.369 0.1224 1.3367 0.1222 -2.36 -0.160.458 0.894 1.0778 0.6962 0.0714 0.00E+00 1.353 0.134 1.3056 0.1339 -3.5 -0.070.492 0.903 1.071 0.6782 0.0779 2.40E-07 1.337 0.1463 1.2737 0.1464 -4.73 0.060.568 0.922 1.0576 0.6393 0.0931 6.00E-08 1.298 0.1748 1.2048 0.1755 -7.18 0.420.61 0.931 1.0504 0.6173 0.1024 -6.00E-08 1.277 0.1922 1.1657 0.1933 -8.71 0.56

0.656 0.94 1.0422 0.5923 0.1135 -1.20E-07 1.255 0.2136 1.1212 0.2148 -10.66 0.570.748 0.958 1.0298 0.5422 0.1379 8.90E-08 1.202 0.2576 1.0311 0.2623 -14.22 1.80.795 0.967 1.0246 0.5152 0.1524 -1.20E-07 1.171 0.2816 0.9822 0.2904 -16.13 3.150.845 0.976 1.0185 0.4847 0.1709 -3.40E-04 1.136 0.3096 0.9227 0.3253 -18.78 5.07

1 1 1 0.3074 0.3074 0.00E+00 0.664 0.6644 0.5926 0.5926 -10.75 -10.8

191

Table C2.14: Densities Prediction for Nitrogen.

Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.094 0.703 1.147 0.9036 0.0144 -1.80E-07 1.668 0.0299 1.8786 0.0299 12.63 0.03

0.1 0.708 1.144 0.8994 0.0152 6.00E-08 1.66 0.0316 1.8685 0.0316 12.56 0.120.119 0.725 1.1347 0.8852 0.0181 -3.00E-07 1.637 0.0375 1.8354 0.0376 12.12 0.260.121 0.726 1.1339 0.884 0.0184 -2.40E-07 1.63 0.038 1.8327 0.0381 12.44 0.260.15 0.747 1.1225 0.8647 0.0226 -2.40E-07 1.601 0.0465 1.7895 0.0467 11.77 0.49

0.164 0.756 1.1174 0.8555 0.0247 0.00E+00 1.586 0.0508 1.7693 0.0511 11.56 0.570.185 0.769 1.1105 0.8421 0.0279 2.40E-07 1.566 0.0572 1.7406 0.0576 11.15 0.730.203 0.779 1.105 0.8309 0.0306 2.40E-07 1.545 0.0627 1.7171 0.0633 11.14 0.90.226 0.791 1.0987 0.8172 0.0342 0.00E+00 1.525 0.0698 1.6885 0.0706 10.72 1.080.273 0.813 1.0871 0.7899 0.0416 1.20E-07 1.487 0.0847 1.6327 0.0859 9.8 1.490.305 0.826 1.0804 0.7722 0.0466 -6.00E-08 1.463 0.0948 1.5973 0.0965 9.18 1.760.327 0.835 1.0759 0.7599 0.0503 -6.00E-08 1.451 0.1022 1.5727 0.1042 8.39 1.960.389 0.857 1.0649 0.7272 0.0607 -3.00E-07 1.405 0.1228 1.5079 0.1259 7.32 2.510.406 0.862 1.0621 0.7182 0.0637 -6.00E-08 1.394 0.1288 1.4901 0.1322 6.89 2.650.458 0.879 1.0542 0.6913 0.0731 2.40E-07 1.357 0.1475 1.4372 0.152 5.91 3.110.511 0.894 1.0469 0.664 0.0833 -1.20E-07 1.317 0.1676 1.3836 0.1736 5.06 3.60.535 0.901 1.0439 0.6517 0.0881 -1.20E-07 1.303 0.177 1.3594 0.1839 4.33 3.850.613 0.921 1.0346 0.6112 0.105 -2.40E-07 1.248 0.2101 1.2798 0.2198 2.55 4.630.62 0.923 1.0339 0.6075 0.1066 6.00E-08 1.244 0.2134 1.2724 0.2234 2.29 4.69

0.715 0.945 1.0242 0.5572 0.1303 -1.20E-07 1.17 0.2592 1.1726 0.2741 0.22 5.740.812 0.965 1.0154 0.5013 0.1602 -1.20E-07 1.092 0.317 1.0603 0.3388 -2.9 6.870.819 0.967 1.0149 0.4974 0.1625 1.50E-07 1.088 0.3216 1.0523 0.3438 -3.28 6.9

1 1 1 0.3074 0.3074 0.00E+00 0.694 0.6945 0.6567 0.6567 -5.37 -5.44

192


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.01 0.566 1.28 0.9821 0.0017 1.20E-07 1.768 0.0034 1.8942 0.0034 7.14 0.04

0.013 0.581 1.2731 0.9784 0.0022 1.80E-07 1.747 0.0042 1.8786 0.0042 7.53 -0.110.017 0.595 1.2638 0.9738 0.0028 6.00E-08 1.726 0.0053 1.8606 0.0053 7.8 -0.060.022 0.61 1.2529 0.9684 0.0035 4.80E-07 1.706 0.0067 1.8413 0.0066 7.93 -0.150.028 0.625 1.2411 0.9621 0.0044 -1.80E-07 1.677 0.0083 1.8206 0.0083 8.56 0.180.043 0.655 1.2168 0.9468 0.0067 -6.00E-08 1.639 0.0125 1.7765 0.0126 8.39 0.20.053 0.67 1.2048 0.9378 0.0082 0.00E+00 1.621 0.0152 1.7531 0.0153 8.15 0.170.065 0.685 1.193 0.9279 0.0099 -6.00E-08 1.595 0.0183 1.7288 0.0184 8.39 0.40.078 0.7 1.1816 0.917 0.0118 -3.60E-07 1.578 0.0219 1.7036 0.022 7.96 0.520.094 0.715 1.1705 0.9052 0.0141 -2.40E-07 1.553 0.0259 1.6776 0.0261 8.02 0.740.112 0.729 1.1582 0.8919 0.0167 6.00E-08 1.536 0.0305 1.6492 0.031 7.37 1.640.153 1.4890.759 1.1394 0.8641 0.0227 1.20E-07 0.0413 1.5932 0.0419 7 1.430.177 0.774 1.1297 0.8483 0.0264 0.00E+00 1.467 0.0478 1.5629 0.0486 6.53 1.720.205 0.789 1.1202 0.8315 0.0305 0.00E+00 1.438 0.055 1.5312 0.0562 6.48 2.110.268 0.819 1.1019 0.7945 0.0403 -6.00E-08 1.391 0.072 1.4634 0.0742 5.2 2.930.305 0.834 1.093 0.7742 0.0461 0.00E+00 1.365 0.0821 1.4269 0.0849 4.53 3.440.344 0.849 1.0843 0.7526 0.0526 3.00E-07 1.334 0.0933 1.3884 0.097 4.08 3.960.388 0.863 1.0757 0.7295 0.06 -2.40E-07 1.304 0.1059 1.3476 0.1108 3.35 4.60.435 0.878 1.0672 0.7047 0.0684 0.00E+00 1.276 0.1202 1.3042 0.1265 2.21 5.280.487 0.893 1.0589 0.6782 0.0779 0.00E+00 1.243 0.1363 1.2578 0.1445 1.19 6.040.542 0.908 1.0506 0.6496 0.089 1.80E-07 1.203 0.1547 1.2077 0.1654 0.39 6.930.603 0.923 1.0424 0.6185 0.1019 6.00E-08 1.164 0.1759 1.1531 0.1899 -0.93 7.960.668 0.938 1.0343 0.5843 0.1172 1.80E-07 1.12 0.2008 1.0929 0.2192 -2.42 9.140.738 0.953 1.0262 0.546 0.1359 -1.80E-07 1.071 0.2307 1.025 0.2551 -4.29 10.60.813 0.968 1.0181 0.5019 0.1599 -6.00E-08 1.015 0.268 0.9459 0.3013 -6.81 12.420.894 0.982 1.0099 0.4486 0.1939 -2.20E-04 0.947 0.3179 0.8447 0.3651 -10.8 14.83

1 1 1 0.3074 0.3074 0.00E+00 0.639 0.6393 0.5852 0.5852 -8.42 -8.46

193


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.029 0.61 1.1973 0.9598 0.0047 -6.00E-08 1.7897 0.0098 1.9854 0.0098 10.93 -0.510.035 0.625 1.1953 0.954 0.0056 6.00E-08 1.7696 0.012 1.9668 0.0115 11.14 -4.260.093 0.7 1.1445 0.9044 0.0142 -1.80E-07 1.6671 0.029 1.8347 0.0289 10.05 -0.510.194 0.775 1.1091 0.8365 0.0293 -6.00E-08 1.5535 0.0602 1.6865 0.059 8.56 -20.359 0.85 1.0752 0.7436 0.0554 -6.00E-08 1.4242 0.1025 1.5026 0.112 5.5 9.260.606 0.925 1.0439 0.6174 0.1023 -6.00E-08 1.2481 0.1961 1.2603 0.2089 0.98 6.54

1 1 1 0.3074 0.3074 0.00E+00 0.6709 0.6709 0.6407 0.6407 -4.51 -4.51


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.048 0.655 1.1946 0.9419 0.0075 2.40E-07 1.2925 0.0113 1.3606 0.0108 5.27 -4.250.065 0.679 1.1805 0.9272 0.01 -3.60E-07 1.2661 0.0154 1.3327 0.0143 5.26 -6.870.087 0.703 1.1646 0.9098 0.0132 -1.20E-07 1.2397 0.0199 1.3019 0.0189 5.02 -5.130.115 0.727 1.1471 0.8891 0.0173 -6.00E-08 1.2124 0.0264 1.2679 0.0247 4.58 -6.460.149 0.751 1.1305 0.8658 0.0223 -1.80E-07 1.1833 0.0338 1.2318 0.0318 4.1 -5.920.193 0.775 1.11 0.8372 0.0291 0.00E+00 1.1534 0.0428 1.1895 0.0413 3.13 -3.430.234 0.799 1.1036 0.8135 0.0351 -1.80E-07 1.1226 0.0528 1.1556 0.0499 2.94 -5.490.302 0.823 1.0772 0.7731 0.0464 -1.80E-07 1.0918 0.0652 1.0994 0.0659 0.7 1.150.346 0.847 1.0798 0.7509 0.0531 6.00E-08 1.0557 0.0801 1.0689 0.0756 1.25 -5.590.453 0.871 1.0444 0.6912 0.0731 -6.00E-08 1.0178 0.0991 0.988 0.1046 -2.92 5.50.49 0.895 1.0589 0.6764 0.0786 -1.20E-07 0.9764 0.1197 0.968 0.1125 -0.86 -6.04

0.668 0.919 1.0072 0.5755 0.1214 -6.00E-08 0.9324 0.1444 0.8311 0.1753 -10.86 21.381 1 1 0.3074 0.3074 0.00E+00 0.5045 0.5045 0.4515 0.4515 -10.51 -10.51

194


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.027 0.646 1.2925 0.9636 0.0042 4.20E-07 0.6426 0.0029 0.6675 0.0029 3.88 -0.610.06 0.699 1.2397 0.9334 0.0089 6.00E-08 0.6147 0.0062 0.637 0.0061 3.63 -1.89

0.076 0.717 1.2231 0.9205 0.0112 -6.00E-08 0.6048 0.0077 0.6259 0.0076 3.49 -1.220.117 0.753 1.1918 0.8905 0.017 1.20E-07 0.5842 0.0115 0.602 0.0115 3.05 0.070.173 0.788 1.1619 0.854 0.0251 1.20E-07 0.5629 0.0167 0.5754 0.0169 2.23 1.120.206 0.806 1.1482 0.8335 0.03 1.20E-07 0.5519 0.0199 0.5613 0.0202 1.69 1.530.337 0.86 1.1077 0.7599 0.0503 3.00E-07 0.514 0.0336 0.5125 0.0339 -0.3 1.020.455 0.895 1.0803 0.6977 0.0708 6.00E-08 0.4847 0.0478 0.4724 0.048 -2.53 0.340.601 0.931 1.0543 0.6225 0.1001 3.60E-07 0.4483 0.0683 0.4243 0.0682 -5.36 -0.080.686 0.948 1.0412 0.5773 0.1205 -3.00E-08 0.4258 0.083 0.3951 0.0825 -7.21 -0.640.781 0.966 1.0281 0.524 0.1475 -6.00E-08 0.3983 0.1029 0.3604 0.1015 -9.51 -1.38

1 1 1 0.3074 0.3074 0.00E+00 0.2398 0.2398 0.214 0.214 -10.77 -10.77


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.026 0.649 1.3085 0.9651 0.0039 1.20E-07 0.6084 0.0025 0.617 0.0025 1.41 0.870.045 00.685 1.2706 0.9466 0.0067 2.40E-07 0.5909 0.0042 .5986 0.0043 1.31 1.350.058 2 1.2568 0.93 1.80E-07 0.5817 0.0054 0.5897 0.0053 1.37 -1.790.70 63 0.00840.116 0.756 1.2008 0.892 0.0167 -6.00E-08 0.5534 0.0106 0.556 0.0104 0.47 -1.690.172 0.792 1.1689 0.855 0.0248 0.00E+00 0.5329 0.0157 0.5311 0.0154 -0.33 -1.770.247 0.827 1.138 0.8102 0.036 6.00E-08 0.5104 0.0227 0.5029 0.0223 -1.47 -1.580.464 0.899 1.081 0.6938 0.0722 2.40E-07 0.4571 0.0457 0.4332 0.0451 -5.23 -1.330.536 0.917 1.0669 0.6567 0.0862 1.80E-07 0.441 0.0546 0.4113 0.054 -6.73 -1.170.706 0.952 1.0385 0.5665 0.1257 1.20E-07 0.4004 0.0796 0.3578 0.0794 -10.65 -0.280.807 0.97 1.0235 0.5099 0.1569 -9.30E-04 0.3728 0.0997 0.3213 0.0989 -13.81 -0.84

1 1 1 0.3074 0.3074 0.00E+00 0.23 0.23 0.1973 0.1973 -14.23 -14.23

195


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.025 0.646 1.3121 0.9664 0.0038 6.00E-08 0.5166 0.0021 0.5165 0.002 -0.02 -3.910.05 0.691 1.2651 0.9428 0.0073 -4.20E-07 0.4983 0.0039 0.4972 0.0039 -0.21 -0.84

0.061 0.706 1.2505 0.9331 0.009 -1.80E-07 0.4924 0.0048 0.4904 0.0047 -0.41 -20.09 0.736 1.2219 0.9106 0.013 1.80E-07 0.4786 0.0069 0.4756 0.0068 -0.62 -1.3

0.108 0.751 1.2078 0.8976 0.0156 1.80E-07 0.4722 0.0083 0.4677 0.0081 -0.94 -2.170.129 0.766 1.1938 0.8833 0.0185 -1.80E-07 0.4647 0.0099 0.4594 0.0096 -1.14 -2.680.152 0.781 1.1799 0.8677 0.0219 -1.20E-07 0.4576 0.0116 0.4506 0.0114 -1.52 -1.90.179 0.796 1.1655 0.8505 0.0259 3.60E-07 0.4497 0.0136 0.4412 0.0134 -1.88 -1.30.21 0.811 1.1518 0.8321 0.0304 -1.20E-07 0.4413 0.016 0.4314 0.0157 -2.24 -1.61

1 1 1 0.3074 0.3074 0.00E+00 0.1821 0.1821 0.1648 0.1648 -9.52 -9.52


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.028 0.653 1.3063 0.9635 0.0042 3.00E-07 0.5393 0.0024 0.5446 0.0024 0.98 -1.570.045 0.685 1.2726 0.9468 0.0067 1.80E-07 0.5258 0.0038 0.5301 0.0037 0.82 -1.40.057 0.701 1.257 0.937 0.0083 2.40E-07 0.5188 0.0047 0.5225 0.0046 0.72 -1.530.086 0.733 1.2273 0.9141 0.0124 -6.00E-08 0.5042 0.0069 0.5064 0.0069 0.43 -0.60.125 0.764 1.1982 0.8861 0.0179 1.80E-07 0.4889 0.01 0.4886 0.0099 -0.07 -1.080.149 0.78 1.1836 0.8699 0.0214 3.60E-07 0.481 0.0119 0.4789 0.0118 -0.45 -0.880.177 0.796 1.1695 0.8524 0.0254 1.80E-07 0.4724 0.0141 0.4687 0.014 -0.79 -0.830.208 0.812 1.1556 0.8334 0.03 1.20E-07 0.4634 0.0166 0.4579 0.0165 -1.18 -0.580.244 0.827 1.1411 0.8122 0.0355 -6.00E-08 0.4546 0.0196 0.4463 0.0195 -1.83 -0.610.285 0.843 1.1266 0.7891 0.0418 1.20E-07 0.4446 0.0231 0.4337 0.023 -2.44 -0.570.33 0.859 1.1124 0.7641 0.0491 3.00E-07 0.4345 0.0273 0.4204 0.027 -3.25 -1.08

1 1 1 0.3074 0.3074 0.00E+00 0.2027 0.2027 0.1746 0.1746 -13.85 -13.85

196


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.023 0.642 1.3152 0.9679 0.0036 -4.20E-07 0.4785 0.0018 0.4814 0.0018 0.6 -1.680.029 0.656 1.3015 0.9619 0.0044 0.00E+00 0.4734 0.0022 0.4762 0.0022 0.6 -0.910.036 0.67 1.287 0.955 0.0054 -3.60E-07 0.4681 0.0027 0.4708 0.0027 0.58 -10.045 0.684 1.2723 0.9472 0.0066 0.00E+00 0.4628 0.0033 0.4651 0.0033 0.5 -1.280.055 0.698 1.2581 0.9385 0.008 -5.40E-07 0.4572 0.004 0.4592 0.0039 0.44 -1.690.066 0.712 1.2442 0.929 0.0097 1.80E-07 0.4518 0.0048 0.4531 0.0047 0.29 -1.790.08 0.726 1.2299 0.9184 0.0116 0.00E+00 0.4462 0.0057 0.4466 0.0056 0.09 -1.29

0.095 0.739 1.2162 0.9069 0.0137 6.00E-08 0.4401 0.0067 0.4399 0.0067 -0.04 -0.490.113 0.753 1.2026 0.8943 0.0162 -6.00E-08 0.4342 0.008 0.4329 0.0079 -0.31 -1.71

1 1 1 0.3074 0.3074 0.00E+00 0.1779 0.1779 0.1531 0.1531 -13.93 -13.93


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.000016 0.444 1.6567 0.9992 0.0001 3.60E-01 0.852 0 0.7024 0 -17.55 -0.36

0.001 0.497 1.4383 0.997 0.0002 -2.30E-04 0.8246 0.0002 0.8408 0.0002 1.96 -0.120.002 0.523 1.407 0.9946 0.0004 4.20E-07 0.8108 0.0004 0.836 0.0004 3.1 -0.110.006 0.562 1.3633 0.9886 0.001 -1.80E-07 0.7897 0.0008 0.8181 0.0008 3.6 -0.210.011 0.588 1.3357 0.9826 0.0017 -3.00E-07 0.7755 0.0014 0.8046 0.0014 3.76 -0.270.014 0.601 1.3224 0.9788 0.0021 3.00E-07 0.7684 0.0018 0.7977 0.0018 3.81 -0.290.033 0.653 1.2716 0.958 0.005 6.60E-07 0.7386 0.004 0.767 0.004 3.84 -0.430.081 0.719 1.2131 0.9168 0.0119 -1.20E-07 0.699 0.0094 0.7225 0.0093 3.37 -0.510.128 0.758 1.1805 0.8829 0.0186 3.00E-07 0.673 0.0146 0.6918 0.0146 2.79 -0.480.169 0.784 1.1596 0.856 0.0246 1.20E-07 0.6549 0.0193 0.6692 0.0192 2.19 -0.440.219 0.81 1.1394 0.8254 0.032 -2.40E-07 0.6355 0.0251 0.6447 0.025 1.44 -0.360.352 0.862 1.1006 0.7514 0.0529 -6.00E-08 0.5924 0.0414 0.5881 0.0414 -0.72 0.07

1 1 1 0.3074 0.3074 0.00E+00 0.2826 0.2826 0.2482 0.2482 -12.17 -12.17

197


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.103 0.701 1.1226 0.8954 0.016 6.00E-08 1.3276 0.0228 1.4075 0.0252 6.02 10.390.147 0.736 1.1059 0.8648 0.0226 1.20E-07 1.2834 0.0376 1.3549 0.0354 5.57 -5.97

0.2 0.77 1.093 0.8311 0.0306 0.00E+00 1.2387 0.0514 1.3003 0.0479 4.97 -6.890.272 0.805 1.0748 0.7887 0.0419 -1.20E-07 1.194 0.0651 1.2344 0.0656 3.38 0.690.346 0.839 1.0681 0.749 0.0537 1.80E-07 1.1459 0.0856 1.1742 0.0842 2.47 -1.620.459 0.874 1.0458 0.6887 0.0741 0.00E+00 1.0898 0.1132 1.0843 0.1166 -0.51 3.010.548 0.908 1.0479 0.6461 0.0904 0.00E+00 1.0314 0.1488 1.0209 0.1428 -1.02 -4.030.708 0.943 1.0241 0.5605 0.1286 -3.60E-07 0.9448 0.2002 0.8927 0.2049 -5.52 2.34

1 1 1 0.3074 0.3074 0.00E+00 0.5487 0.5487 0.4972 0.4972 -9.39 -9.39


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.023 0.423 0.8098 0.9542 0.0055 -3.60E-07 2.2782 0.0192 3.2823 0.0191 44.08 -0.850.037 0.462 0.8303 0.9379 0.0081 2.40E-07 2.2644 0.0281 3.2025 0.0278 41.43 -0.980.054 0.5 0.8494 0.9192 0.0114 1.20E-07 2.2466 0.0392 3.1207 0.0388 38.91 -1.040.077 0.538 0.8671 0.898 0.0155 6.00E-07 2.2251 0.0529 3.0361 0.0524 36.45 -0.980.106 0.577 0.8835 0.8746 0.0204 1.20E-07 2.2003 0.0694 2.9481 0.0688 33.99 -0.820.141 0.615 0.8988 0.8488 0.0263 -1.20E-07 2.1721 0.089 2.8564 0.0884 31.5 -0.650.183 0.654 0.913 0.8207 0.0333 -6.00E-08 2.1406 0.1123 2.7601 0.1118 28.94 -0.440.233 0.692 0.9262 0.79 0.0415 6.00E-08 2.1051 0.1399 2.6581 0.1397 26.27 -0.130.291 0.731 0.9384 0.7568 0.0513 -1.80E-07 2.0652 0.1724 2.5498 0.1728 23.46 0.20.358 0.769 0.9498 0.7208 0.0629 0.00E+00 2.0199 0.2111 2.4337 0.2122 20.49 0.570.435 0.808 0.9603 0.6814 0.0767 6.00E-08 1.9676 0.2574 2.3078 0.2599 17.29 0.950.523 0.846 0.97 0.638 0.0937 2.40E-07 1.9059 0.3142 2.1689 0.3184 13.8 1.340.622 0.885 0.9788 0.5893 0.1149 -8.90E-08 1.8302 0.3861 2.0124 0.3923 9.95 1.6

1 1 1 0.3074 0.3074 0.00E+00 1.0862 1.0862 1.0689 1.0689 -1.59 -1.59

198


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.014 0.555 1.2007 0.9765 0.0024 0.00E+00 2.2106 0.0063 2.5352 0.0063 14.68 -0.090.016 0.563 1.1963 0.9739 0.0028 6.60E-07 2.2 0.0072 2.5224 0.0072 14.66 -0.150.027 0.596 1.1776 0.961 0.0045 7.20E-07 2.1519 0.0116 2.4631 0.0116 14.46 -0.10.044 0.63 1.1598 0.9446 0.007 -6.00E-08 2.1019 0.0179 2.3999 0.0179 14.17 -0.070.066 0.663 1.1428 0.9244 0.0105 2.40E-07 2.0495 0.0264 2.3323 0.0264 13.8 -0.040.097 0.696 1.1267 0.9004 0.015 -3.00E-07 1.9952 0.0377 2.2597 0.0377 13.26 0.040.136 0.729 1.1113 0.8723 0.0209 6.00E-08 1.9378 0.0522 2.1814 0.0523 12.57 0.20.186 0.762 1.0966 0.8399 0.0284 3.00E-07 1.8766 0.0707 2.0965 0.071 11.72 0.410.248 0.795 1.0824 0.8029 0.038 2.40E-07 1.8123 0.0941 2.0039 0.0948 10.57 0.690.323 0.828 1.0687 0.7608 0.0501 0.00E+00 1.7424 0.1238 1.9016 0.1251 9.14 1.060.414 0.861 1.0552 0.7129 0.0655 -6.00E-08 1.6643 0.1619 1.7871 0.1643 7.38 1.510.521 0.895 1.042 0.6577 0.0857 -6.00E-08 1.5769 0.2118 1.6563 0.2159 5.03 1.970.647 0.928 1.0288 0.5926 0.1134 1.20E-07 1.4721 0.2804 1.5011 0.2872 1.98 2.420.795 0.961 1.0156 0.511 0.1547 -6.00E-08 1.3335 0.3861 1.3043 0.3949 -2.19 2.28

1 1 1 0.3074 0.3074 0.00E+00 0.8372 0.8372 0.7932 0.7932 -5.26 -5.26


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.009 0.451 1.0034 0.9803 0.002 -2.40E-07 2.363 0.0062 3.0577 0.0061 29.4 -1.010.019 0.496 1.0086 0.9666 0.0037 1.20E-07 2.3206 0.0118 2.9739 0.0115 28.15 -2.550.068 0.601 1.0136 0.9164 0.0119 1.20E-07 2.2091 0.0359 2.7582 0.036 24.86 0.170.168 0.701 1.0141 0.8427 0.0277 -1.80E-07 2.0822 0.0818 2.5152 0.0828 20.8 1.21

1 1 1 0.3074 0.3074 0.00E+00 0.9606 0.9606 0.9482 0.9482 -1.29 -1.29

199


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.001 0.489 1.5013 0.9982 0.0001 -1.90E-03 2.6793 0.0003 2.3884 0.0003 -10.86 -5.850.001 0.501 1.4844 0.9975 0.0002 3.30E-05 2.6585 0.0004 2.3584 0.0004 -11.29 0.830.004 0.551 1.4223 0.9927 0.0006 1.00E-05 2.5732 0.0014 2.271 0.0014 -11.75 -1.080.005 0.563 1.4077 0.9908 0.0008 3.00E-07 2.5514 0.0018 2.2557 0.0018 -11.59 0.570.006 0.575 1.3933 0.9885 0.001 1.40E-05 2.5292 0.0024 2.2383 0.0023 -11.5 -2.630.008 0.588 1.3791 0.9858 0.0013 -4.80E-07 2.5067 0.003 2.2201 0.003 -11.43 -0.690.011 0.6 1.3651 0.9827 0.0017 3.00E-07 2.4839 0.0038 2.2027 0.0038 -11.32 -1.20.013 0.612 1.3512 0.9792 0.0021 -6.00E-08 2.4609 0.0048 2.1844 0.0047 -11.24 -2.410.017 0.625 1.3377 0.9751 0.0026 -6.60E-07 2.4377 0.0059 2.1657 0.0058 -11.16 -1.960.026 0.649 1.3112 0.9655 0.0039 -3.00E-07 2.3898 0.0088 2.1262 0.0086 -11.03 -2.360.031 0.662 1.2982 0.9597 0.0047 4.20E-07 2.3655 0.0106 2.1051 0.0103 -11.01 -2.360.046 0.686 1.2728 0.9464 0.0068 2.40E-07 2.3154 0.0151 2.0612 0.0147 -10.98 -2.610.055 0.698 1.2604 0.9388 0.008 -2.40E-07 2.2898 0.0178 2.0381 0.0174 -10.99 -2.440.065 0.711 1.2481 0.9304 0.0094 -3.00E-07 2.2637 0.0209 2.0141 0.0204 -11.03 -2.430.076 0.723 1.2361 0.9214 0.011 1.80E-07 2.237 0.0245 1.9894 0.0238 -11.07 -2.770.089 0.735 1.2241 0.9115 0.0129 0.00E+00 2.2098 0.0285 1.9636 0.0277 -11.14 -2.830.103 0.748 1.2124 0.9009 0.0149 3.00E-07 2.1819 0.0331 1.9368 0.0321 -11.23 -3.130.12 0.76 1.2008 0.8895 0.0172 6.00E-08 2.1533 0.0382 1.9089 0.037 -11.35 -3.23

0.138 0.772 1.1893 0.8773 0.0198 -1.80E-07 2.1241 0.044 1.88 0.0425 -11.49 -3.470.158 0.785 1.178 0.8641 0.0227 0.00E+00 2.0941 0.0505 1.8498 0.0486 -11.67 -3.680.18 0.797 1.1669 0.8501 0.026 -2.40E-07 2.0632 0.0578 1.8184 0.0555 -11.87 -3.9

0.232 0.822 1.145 0.8192 0.0336 1.20E-07 1.9986 0.0751 1.751 0.0719 -12.39 -4.250.294 0.846 1.1236 0.7841 0.0432 1.20E-07 1.9292 0.0972 1.677 0.0924 -13.07 -4.920.367 0.871 1.1025 0.7441 0.0553 -1.20E-07 1.8537 0.1251 1.5944 0.1184 -13.99 -5.350.454 0.896 1.082 0.6986 0.0705 -3.00E-07 1.7701 0.1608 1.5016 0.1516 -15.17 -5.720.555 0.92 1.0619 0.6462 0.0903 -1.80E-07 1.6749 0.2083 1.3952 0.195 -16.7 -6.37

1 1 1 0.3074 0.3074 0.00E+00 0.8558 0.8558 0.6794 0.6794 -20.62 -20.62

200


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.018 0.659 1.414 0.9755 0.0026 1.20E-07 0.9751 0.0033 0.7579 0.002 -22.27 -39.660.033 0.695 1.3638 0.9598 0.0047 4.20E-07 0.9451 0.0057 0.7364 0.0036 -22.08 -36.60.055 0.728 1.3214 0.9403 0.0077 -1.80E-07 0.9178 0.0092 0.7146 0.0059 -22.15 -36.070.135 0.796 1.2386 0.8827 0.0187 1.20E-07 0.8592 0.0213 0.662 0.014 -22.95 -34.30.288 0.863 1.1564 0.7914 0.0411 -1.20E-07 0.787 0.045 0.592 0.0308 -24.78 -31.640.342 0.88 1.1362 0.7618 0.0498 -6.00E-08 0.7655 0.0537 0.5705 0.0373 -25.48 -30.610.404 0.896 1.116 0.7287 0.0602 1.80E-07 0.7418 0.0641 0.5467 0.0452 -26.3 -29.520.555 0.93 1.0765 0.6501 0.0888 1.20E-07 0.6891 0.0918 0.4908 0.067 -28.78 -27.010.644 0.947 1.0574 0.6027 0.1088 8.90E-08 0.6584 0.1115 0.457 0.0825 -30.59 -26.040.745 0.964 1.0385 0.5469 0.1355 -8.90E-08 0.6185 0.1384 0.4169 0.1033 -32.6 -25.39

1 1 1 0.3074 0.3074 0.00E+00 0.3645 0.3645 0.2376 0.2376 -34.81 -34.81


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.021 0.647 1.3448 0.9704 0.0032 -1.80E-07 0.8061 0.0021 0.7161 0.0024 -11.16 13.370.034 0.675 1.3124 0.9578 0.005 1.20E-07 0.7889 0.0032 0.7004 0.0037 -11.22 14.30.045 0.694 1.2919 0.9472 0.0066 1.80E-07 0.7728 0.0043 0.6888 0.0048 -10.87 12.110.102 0.753 1.2272 0.9029 0.0145 -4.80E-07 0.7298 0.0097 0.6481 0.0104 -11.2 7.460.162 0.793 1.1866 0.8627 0.0231 1.80E-07 0.6987 0.014 0.6163 0.0165 -11.79 17.650.298 0.852 1.128 0.7823 0.0437 6.00E-08 0.646 0.0258 0.5585 0.0312 -13.54 20.960.429 0.891 1.0905 0.7122 0.0658 1.20E-07 0.6105 0.0419 0.5104 0.0471 -16.39 12.530.511 0.911 1.0713 0.6695 0.0812 1.20E-07 0.5804 0.0537 0.4815 0.0584 -17.04 8.740.601 0.93 1.0537 0.6225 0.1002 1.20E-07 0.5525 0.0699 0.4495 0.0723 -18.64 3.480.702 0.95 1.0368 0.5682 0.1248 -6.00E-08 0.5181 0.0914 0.4125 0.0906 -20.39 -0.850.818 0.97 1.0192 0.5 0.161 6.00E-08 0.4762 0.1182 0.3652 0.1176 -23.31 -0.54

1 1 1 0.3074 0.3074 0.00E+00 0.2934 0.2934 0.2268 0.2268 -22.72 -22.72

201


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.013 0.659 1.4797 0.9813 0.0018 3.60E-07 1.4632 0.0024 1.2239 0.0023 -16.35 -4.40.022 0.688 1.4331 0.9708 0.0032 2.40E-07 1.433 0.0041 1.1967 0.0039 -16.49 -4.540.06 0.747 1.3417 0.9375 0.0082 -3.60E-07 1.3677 0.0105 1.1339 0.0099 -17.1 -5.45

0.105 0.786 1.2834 0.904 0.0143 -3.60E-07 1.319 0.0183 1.0837 0.0171 -17.84 -6.320.135 0.805 1.255 0.8832 0.0185 1.20E-07 1.2937 0.0237 1.0556 0.0222 -18.41 -6.490.272 0.864 1.1732 0.8014 0.0384 -6.00E-08 1.2004 0.0492 0.9549 0.0457 -20.45 -7.080.336 0.883 1.1468 0.7664 0.0484 6.00E-08 1.1651 0.0621 0.9141 0.0577 -21.54 -7.040.716 0.961 1.0466 0.5646 0.1266 6.00E-08 0.9547 0.1682 0.6845 0.1535 -28.3 -8.730.78 0.971 1.0339 0.5284 0.1464 -1.00E-03 0.9108 0.1954 0.6389 0.177 -29.86 -9.4

0.849 0.981 1.0223 0.4847 0.1715 -5.90E-04 0.8592 0.2313 0.5877 0.208 -31.6 -10.081 1 1 0.3074 0.3074 0.00E+00 0.5303 0.5303 0.3786 0.3786 -28.6 -28.6


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.016 0.681 1.4904 0.9781 0.0022 -1.80E-07 0.998 0.0022 0.9692 0.0022 -2.89 0.590.025 0.704 1.4481 0.9688 0.0034 -3.00E-07 0.9826 0.0034 0.9512 0.0034 -3.2 -0.670.035 0.723 1.4126 0.9588 0.0049 -6.60E-07 0.9698 0.0048 0.9347 0.0047 -3.62 -1.310.067 0.762 1.3443 0.932 0.0091 3.00E-07 0.9384 0.0089 0.8976 0.0088 -4.34 -1.020.09 0.781 1.3115 0.9148 0.0122 1.20E-07 0.92 0.0119 0.877 0.0117 -4.68 -1.46

0.119 0.801 1.2797 0.8949 0.0161 1.80E-07 0.8986 0.0156 0.8546 0.0154 -4.89 -1.260.248 0.859 1.1901 0.8156 0.0346 1.20E-07 0.8354 0.0331 0.7753 0.0329 -7.2 -0.730.38 0.897 1.1347 0.7432 0.0555 0.00E+00 0.7835 0.0538 0.7082 0.0529 -9.61 -1.65

0.561 0.936 1.0821 0.6485 0.0894 6.00E-08 0.717 0.0888 0.6225 0.0858 -13.18 -3.360.673 0.955 1.057 0.5889 0.115 -1.20E-07 0.6719 0.1157 0.5685 0.111 -15.4 -4.050.802 0.975 1.0309 0.5166 0.1539 -1.40E-03 0.6166 0.1538 0.4966 0.1479 -19.46 -3.83

1 1 1 0.3074 0.3074 0.00E+00 0.3733 0.3733 0.3021 0.3021 -19.07 -19.07

202


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.02 0.69 1.4642 0.9737 0.0028 1.20E-07 0.7636 0.0022 0.7356 0.0021 -3.67 -4.16

0.022 0.695 1.4551 0.9716 0.0031 6.00E-08 0.7609 0.0023 0.7327 0.0023 -3.71 0.350.031 0.714 1.4185 0.9623 0.0043 2.40E-07 0.75 0.0033 0.7204 0.0033 -3.95 -1.410.044 0.732 1.383 0.9509 0.006 1.20E-07 0.7386 0.0046 0.7071 0.0045 -4.27 -2.320.06 0.751 1.3489 0.9374 0.0082 -3.60E-07 0.7266 0.0063 0.693 0.0061 -4.63 -3.44

0.081 0.77 1.3159 0.9214 0.011 -6.00E-08 0.7142 0.0084 0.6778 0.0081 -5.1 -3.530.106 0.788 1.2842 0.9029 0.0145 2.40E-07 0.7002 0.011 0.6615 0.0106 -5.52 -3.320.138 0.807 1.2538 0.8817 0.0189 -2.40E-07 0.6856 0.0143 0.644 0.0138 -6.06 -3.670.176 0.826 1.2245 0.8576 0.0242 -1.80E-07 0.67 0.0184 0.6252 0.0176 -6.69 -4.080.221 0.844 1.1965 0.8305 0.0308 -6.00E-08 0.6529 0.0234 0.6048 0.0224 -7.37 -4.270.274 0.863 1.1696 0.7999 0.0388 -6.00E-08 0.6347 0.0293 0.5826 0.0282 -8.2 -3.630.336 0.881 1.1439 0.7658 0.0485 -6.00E-08 0.615 0.0367 0.5584 0.0354 -9.2 -3.540.408 0.9 1.1191 0.7276 0.0606 -1.80E-07 0.5937 0.0459 0.5317 0.0443 -10.45 -3.530.489 0.919 1.0955 0.6847 0.0755 -1.20E-07 0.5698 0.0578 0.502 0.0554 -11.9 -4.220.583 0.937 1.0727 0.6359 0.0945 6.00E-08 0.5433 0.0731 0.4682 0.0696 -13.82 -4.820.689 0.956 1.0507 0.5792 0.1196 -1.80E-07 0.5111 0.0939 0.4287 0.0885 -16.12 -5.760.808 0.974 1.0285 0.5122 0.1561 -1.20E-03 0.4701 0.1226 0.3777 0.1151 -19.66 -6.08

1 1 1 0.3074 0.3074 0.00E+00 0.284 0.284 0.2314 0.2314 -18.51 -18.51

203


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.000528 0.498 1.5709 0.9986 0.0001 2.60E-03 3.4257 0.0003 3.0067 0.0003 -12.23 -0.260.000901 0.515 1.5399 0.9977 0.0002 4.80E-03 3.4069 0.0005 2.8616 0.0004 -16.01 -0.35

0.003 0.558 1.4807 0.994 0.0005 3.00E-07 3.3496 0.0014 2.8086 0.0013 -16.15 -0.60.005 0.577 1.4559 0.9914 0.0007 -7.20E-06 3.3201 0.0021 2.7793 0.0021 -16.29 -0.750.005 0.583 1.447 0.9902 0.0009 -1.10E-05 3.309 0.0024 2.7702 0.0024 -16.29 -0.810.006 0.592 1.436 0.9886 0.001 0.00E+00 3.2945 0.0029 2.7492 0.0028 -16.55 -0.880.009 0.609 1.4142 0.9848 0.0014 -1.20E-07 3.2526 0.004 2.7221 0.004 -16.31 -1.030.013 0.626 1.3929 0.9801 0.002 0.00E+00 3.232 0.0055 2.6901 0.0055 -16.77 -1.190.015 0.635 1.3824 0.9774 0.0023 2.40E-07 3.2153 0.0064 2.6731 0.0063 -16.86 -1.280.021 0.652 1.3616 0.9712 0.0031 -6.00E-08 3.181 0.0086 2.6403 0.0085 -17 -1.460.028 0.669 1.3411 0.964 0.0041 -6.00E-08 3.1432 0.0113 2.605 0.0111 -17.12 -1.640.037 0.686 1.321 0.9555 0.0054 1.20E-07 3.1063 0.0147 2.5679 0.0144 -17.33 -1.830.061 0.721 1.2818 0.9345 0.0087 -1.80E-07 3.0234 0.0238 2.4882 0.0232 -17.7 -2.230.096 0.755 1.2439 0.9075 0.0136 -2.40E-07 2.9308 0.037 2.3994 0.036 -18.13 -2.640.119 0.772 1.2253 0.8915 0.0168 -5.40E-07 2.8821 0.0456 2.351 0.0443 -18.43 -2.850.146 0.789 1.2071 0.8738 0.0206 1.80E-07 2.8307 0.0558 2.2996 0.0541 -18.76 -3.060.176 0.807 1.1891 0.8542 0.025 6.00E-08 2.7755 0.0679 2.2449 0.0657 -19.12 -3.260.212 0.824 1.1714 0.8326 0.0302 -6.00E-08 2.717 0.0822 2.1864 0.0794 -19.53 -3.47

0.3 0.858 1.1368 0.7826 0.0436 -1.80E-07 2.5866 0.1193 2.0562 0.1147 -20.51 -3.920.353 0.875 1.1199 0.7538 0.0522 1.80E-07 2.5151 0.1434 1.983 0.1374 -21.16 -4.180.413 0.892 1.1032 0.722 0.0624 0.00E+00 2.4357 0.1723 1.9032 0.1646 -21.86 -4.470.481 0.909 1.0867 0.6868 0.0747 3.00E-07 2.3481 0.2075 1.8153 0.1975 -22.69 -4.820.557 0.927 1.0703 0.6475 0.0898 1.80E-07 2.251 0.2514 1.7171 0.2381 -23.72 -5.270.642 0.944 1.054 0.6028 0.1087 1.50E-07 2.1391 0.308 1.6052 0.2895 -24.96 -6.010.737 0.961 1.0378 0.5505 0.1336 0.00E+00 2.0054 0.3847 1.4732 0.3576 -26.54 -7.040.844 0.978 1.0206 0.4873 0.1703 -7.60E-04 1.8278 0.4993 1.3 0.4544 -28.88 -9

1 1 1 0.3074 0.3074 0.00E+00 1.0931 1.0931 0.8345 0.8345 -23.66 -23.66

204


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.019 0.62 1.2987 0.9717 0.0031 4.80E-07 1.4817 0.005 1.561 0.0049 5.35 -2.010.036 0.657 1.2622 0.9549 0.0054 6.00E-08 1.4409 0.0086 1.5159 0.0086 5.21 0.270.056 0.69 1.2338 0.9362 0.0084 1.80E-07 1.4026 0.0134 1.4738 0.0133 5.08 -1.030.086 0.722 1.205 0.9126 0.0127 -3.00E-07 1.3618 0.0204 1.427 0.0198 4.79 -2.980.177 0.787 1.1528 0.8508 0.0258 -1.80E-07 1.2755 0.0408 1.3207 0.0401 3.55 -1.780.242 0.819 1.1291 0.8119 0.0355 4.20E-07 1.2276 0.0575 1.2596 0.0551 2.61 -4.120.325 0.851 1.1046 0.7657 0.0486 6.00E-08 1.1748 0.0791 1.1894 0.0755 1.24 -4.550.427 0.884 1.0807 0.7114 0.0661 1.20E-07 1.1125 0.1079 1.1087 0.1029 -0.34 -4.590.55 0.916 1.0581 0.6476 0.0897 1.20E-07 1.0429 0.1439 1.0147 0.1406 -2.7 -2.29

0.7 0.948 1.0354 0.5688 0.1246 -6.00E-08 0.959 0.1966 0.8977 0.1966 -6.4 0.011 1 1 0.3074 0.3074 0.00E+00 0.5538 0.5538 0.4931 0.4931 -10.97 -10.97


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.02 0.599 1.2456 0.9705 0.0032 1.20E-07 1.2662 0.0049 1.3987 0.0046 10.46 -5.6

0.025 0.613 1.236 0.9652 0.0039 8.30E-07 1.2551 0.0058 1.3851 0.0056 10.36 -2.730.066 0.683 1.1857 0.9265 0.0101 1.20E-07 1.1883 0.014 1.3058 0.0142 9.89 1.68

0.1 0.719 1.1633 0.9003 0.015 -6.00E-08 1.1505 0.0207 1.2613 0.0211 9.63 1.840.146 0.754 1.1414 0.8686 0.0217 3.60E-07 1.1126 0.0296 1.2123 0.0303 8.96 2.410.206 0.789 1.1199 0.8311 0.0306 -1.20E-07 1.0704 0.0423 1.158 0.0426 8.18 0.820.281 0.825 1.0999 0.7877 0.0422 6.00E-08 1.0259 0.0556 1.0979 0.0588 7.02 5.760.374 0.86 1.0807 0.7375 0.0574 -1.80E-07 0.9769 0.0757 1.0304 0.0802 5.47 5.890.49 0.895 1.0602 0.6769 0.0784 -1.20E-07 0.9213 0.1024 0.95 0.1101 3.11 7.50.63 0.931 1.0407 0.6045 0.108 1.20E-07 0.8545 0.138 0.854 0.1525 -0.06 10.52

0.802 0.966 1.02 0.5089 0.1559 -6.00E-08 0.7677 0.1958 0.7253 0.2221 -5.52 13.451 1 1 0.3074 0.3074 0.00E+00 0.4673 0.4673 0.4428 0.4428 -5.24 -5.24

205


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.001 0.452 1.2932 0.9967 0.0002 -4.70E-04 2.4091 0.0007 2.768 0.0007 14.9 -0.380.006 0.517 1.2463 0.9881 0.0011 2.40E-07 2.3198 0.0029 2.6394 0.0029 13.78 0.010.02 0.581 1.2051 0.97 0.0033 -6.00E-08 2.2268 0.0086 2.5311 0.0086 13.67 -0.140.02 0.583 1.2043 0.9696 0.0033 1.20E-07 2.2256 0.0087 2.5292 0.0087 13.64 -0.110.05 0.646 1.1675 0.9392 0.0079 -1.80E-07 2.1275 0.0204 2.4078 0.0203 13.17 -0.12

0.107 0.711 1.133 0.8936 0.0164 -1.20E-07 2.0189 0.0415 2.2656 0.0415 12.22 0.020.201 0.775 1.101 0.8316 0.0305 -1.80E-07 1.8984 0.0766 2.0991 0.0769 10.57 0.380.344 0.84 1.071 0.7506 0.0532 -1.20E-07 1.7586 0.1332 1.8984 0.1345 7.95 0.990.489 0.905 1.0748 0.6808 0.077 1.80E-07 1.5844 0.2274 1.7302 0.1957 9.2 -13.97

1 1 1 0.3074 0.3074 0.00E+00 0.8322 0.8322 0.8021 0.8021 -3.61 -3.61



0.003 0.514 1.3457 0.9934 0.0005 -1.20E-07 1.2087 0.0008 1.4474 0.0008 19.75 -0.010.013 0.582 1.2834 0.9791 0.0021 -2.40E-07 1.154 0.003 1.3896 0.003 20.42 0.510.023 0.616 1.2563 0.9672 0.0037 -3.60E-07 1.1277 0.0051 1.357 0.0051 20.33 0.940.039 0.65 1.2297 0.9512 0.006 1.20E-07 1.1004 0.0082 1.3213 0.0083 20.07 1.610.062 0.685 1.2037 0.9308 0.0094 -3.60E-07 1.0711 0.0126 1.2823 0.0129 19.71 2.480.138 0.753 1.1535 0.8746 0.0204 -3.00E-07 1.0055 0.0264 1.1923 0.0278 18.58 5.320.195 0.787 1.1297 0.8381 0.0289 -1.80E-07 0.971 0.0366 1.1401 0.0393 17.41 7.290.36 0.856 1.0842 0.7448 0.055 -6.00E-08 0.8923 0.0664 1.0155 0.075 13.81 13.01

0.472 0.89 1.0628 0.6861 0.075 1.20E-07 0.845 0.0878 0.9393 0.1027 11.16 17.030.607 0.924 1.0422 0.6161 0.1029 1.20E-07 0.7911 0.1159 0.8488 0.1417 7.29 22.250.768 0.959 1.0226 0.5288 0.145 -6.00E-08 0.7277 0.1559 0.7344 0.2013 0.91 29.16

1 1 1 0.3074 0.3074 0.00E+00 0.4609 0.4607 0.4323 0.4323 -6.22 -6.16

206


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.027 0.653 1.3115 0.9644 0.0041 3.00E-07 1.3779 0.0062 1.3965 0.0059 1.35 -5.350.036 0.672 1.2919 0.9554 0.0054 1.20E-07 1.3574 0.0082 1.3756 0.0077 1.34 -5.750.051 0.695 1.2683 0.9421 0.0075 -6.00E-08 1.3321 0.0113 1.3478 0.0107 1.18 -5.630.084 0.732 1.2317 0.9157 0.0121 2.40E-07 1.2872 0.0191 1.2994 0.0171 0.94 -10.310.089 0.737 1.2272 0.9119 0.0128 3.00E-07 1.2805 0.0203 1.2929 0.0181 0.97 -10.740.105 0.75 1.2137 0.8999 0.0151 6.00E-08 1.2619 0.024 1.273 0.0214 0.88 -10.890.148 0.778 1.1831 0.8708 0.0212 -1.20E-07 1.2239 0.032 1.2274 0.0299 0.28 -6.440.178 0.797 1.1693 0.8515 0.0256 -6.00E-08 1.1976 0.0378 1.1987 0.0361 0.09 -4.490.219 0.815 1.1495 0.8269 0.0317 -1.80E-07 1.1694 0.0444 1.1633 0.0446 -0.53 0.350.251 0.829 1.1373 0.8082 0.0365 -1.20E-07 1.1479 0.0513 1.137 0.0514 -0.95 0.210.262 0.834 1.1334 0.8017 0.0383 1.80E-07 1.1401 0.0537 1.1279 0.0539 -1.07 0.350.274 0.839 1.1294 0.795 0.0401 0.00E+00 1.1323 0.0565 1.1187 0.0565 -1.2 -0.050.286 0.843 1.1254 0.7881 0.0421 1.80E-07 1.1255 0.0595 1.1093 0.0592 -1.44 -0.530.299 0.848 1.1216 0.7812 0.044 1.20E-07 1.1177 0.0625 1.0998 0.062 -1.6 -0.840.312 0.853 1.1178 0.7741 0.0461 5.40E-07 1.1098 0.0655 1.0901 0.0649 -1.78 -0.920.325 0.857 1.1139 0.7669 0.0482 1.80E-07 1.1011 0.0686 1.0802 0.068 -1.9 -0.940.356 0.867 1.1039 0.7498 0.0534 1.20E-07 1.0855 0.0753 1.0571 0.0754 -2.62 0.070.396 0.878 1.0933 0.7288 0.0602 -1.20E-07 1.064 0.0847 1.0287 0.085 -3.31 0.330.438 0.89 1.0829 0.7064 0.0678 -1.80E-07 1.0416 0.0945 0.9987 0.0958 -4.12 1.40.484 0.901 1.0728 0.6826 0.0763 -6.00E-08 1.0182 0.1064 0.9669 0.1081 -5.04 1.580.584 0.925 1.0536 0.6303 0.0968 1.20E-07 0.9637 0.1378 0.8969 0.1378 -6.93 00.639 0.936 1.0446 0.6016 0.1093 0.00E+00 0.9326 0.1585 0.8583 0.1559 -7.96 -1.630.696 0.948 1.0362 0.5708 0.1236 1.50E-07 0.8974 0.1835 0.8168 0.1768 -8.98 -3.620.756 0.959 1.0284 0.5377 0.1403 -2.10E-07 0.8576 0.214 0.7717 0.2013 -10.01 -5.920.817 0.971 1.021 0.5024 0.1605 -5.00E-04 0.8108 0.251 0.7202 0.2301 -11.18 -8.310.879 0.983 1.015 0.4618 0.1853 -2.70E-04 0.7474 0.2993 0.6639 0.2663 -11.17 -11.01

1 1 1 0.3074 0.3074 0.00E+00 0.5048 0.5048 0.4471 0.4471 -11.43 -11.43

207


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.025 0.665 1.3517 0.9666 0.0037 -3.60E-07 0.596 0.0022 0.5755 0.0022 -3.44 1.380.062 0.722 1.2813 0.9337 0.0089 -6.00E-08 0.5666 0.0053 0.5466 0.0052 -3.54 -2.090.103 0.76 1.2376 0.9028 0.0145 4.20E-07 0.5459 0.0086 0.5245 0.0085 -3.93 -1.740.161 0.798 1.1961 0.8636 0.0228 6.00E-08 0.5236 0.0135 0.4994 0.0132 -4.62 -2.160.292 0.854 1.1376 0.7866 0.0425 1.20E-07 0.4858 0.0252 0.4545 0.0245 -6.45 -2.60.416 0.892 1.1004 0.7201 0.0631 1.20E-07 0.4567 0.03 0.4175 0.0366 -8.59 21.920.673 0.948 1.047 0.5859 0.1164 8.90E-08 0.3993 0.0685 0.3437 0.0683 -13.93 -0.310.78 0.967 1.0297 0.525 0.147 6.00E-08 0.3699 0.0876 0.3097 0.0867 -16.28 -1.03

0.839 0.977 1.0207 0.4897 0.1683 -5.20E-04 0.3526 0.1005 0.2881 0.099 -18.3 -1.50.901 0.986 1.0123 0.4454 0.1961 -2.30E-04 0.3298 0.1187 0.263 0.1158 -20.26 -2.47

1 1 1 0.3074 0.3074 0.00E+00 0.2214 0.2214 0.1835 0.1835 -17.11 -17.11


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.03 0.682 1.3526 0.962 0.0044 1.80E-07 0.4868 0.0021 0.4657 0.0021 -4.33 1.18

0.042 0.702 1.3266 0.9512 0.006 0.00E+00 0.4782 0.0029 0.4576 0.0029 -4.31 -0.460.055 0.72 1.3029 0.9396 0.0079 -1.80E-07 0.4702 0.0038 0.4497 0.0038 -4.37 -0.940.092 0.757 1.2578 0.911 0.013 6.00E-08 0.4531 0.0063 0.4324 0.0061 -4.56 -2.40.145 0.793 1.2154 0.8748 0.0204 0.00E+00 0.4349 0.0099 0.413 0.0096 -5.03 -2.90.264 0.848 1.1551 0.8032 0.0379 -1.20E-07 0.4049 0.0184 0.3784 0.0178 -6.54 -30.377 0.885 1.1173 0.7419 0.056 1.80E-07 0.3816 0.0273 0.3504 0.0264 -8.18 -3.20.446 0.903 1.0985 0.7057 0.068 1.20E-07 0.3684 0.0332 0.3341 0.0322 -9.3 -3.010.715 0.958 1.0427 0.5635 0.1271 -2.40E-07 0.3167 0.063 0.2702 0.061 -14.68 -3.240.83 0.976 1.0234 0.4974 0.1645 -9.50E-04 0.29 0.0817 0.2377 0.0786 -18.04 -3.78

0.893 0.986 1.0145 0.453 0.1913 -2.90E-04 0.2726 0.0955 0.2179 0.092 -20.06 -3.651 1 1 0.3074 0.3074 0.00E+00 0.1812 0.1812 0.1497 0.1497 -17.37 -17.37

208

Table C2.42: Densities Prediction for Methyl n-Butirate.

Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.029 0.678 1.3525 0.963 0.0042 -3.60E-07 0.4911 0.0022 0.4771 0.0021 -2.84 -4.480.063 0.727 1.2893 0.9335 0.0089 -6.00E-08 0.4697 0.0045 0.4559 0.0043 -2.94 -3.490.102 0.763 1.2466 0.904 0.0143 -1.20E-07 0.4532 0.0071 0.4383 0.0069 -3.3 -2.30.127 0.781 1.2261 0.8864 0.0179 -2.40E-07 0.4444 0.0089 0.4286 0.0086 -3.55 -2.950.157 0.799 1.2061 0.8669 0.0221 0.00E+00 0.4353 0.011 0.4183 0.0107 -3.9 -3.040.233 0.835 1.1673 0.8211 0.0331 -3.60E-07 0.4156 0.0165 0.3956 0.016 -4.82 -3.210.334 0.871 1.1298 0.7649 0.0488 1.20E-07 0.3941 0.0243 0.369 0.0236 -6.36 -3.080.395 0.889 1.1114 0.7322 0.0591 2.40E-07 0.3821 0.0295 0.3539 0.0286 -7.38 -3.220.545 0.926 1.075 0.6543 0.0871 -1.20E-07 0.3529 0.0437 0.3182 0.0424 -9.84 -3.090.736 0.962 1.0391 0.5516 0.1331 1.20E-07 0.3158 0.0667 0.2708 0.0653 -14.24 -2.07

1 1 1 0.3074 0.3074 0.00E+00 0.1835 0.1835 0.1531 0.1531 -16.56 -16.56

Table C2.43: Densities Prediction for Methyl i-Butirate.

Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.029 0.676 1.3452 0.9626 0.0043 -1.80E-07 0.4914 0.0022 0.4832 0.0022 -1.68 -1.70.037 0.69 1.3278 0.9554 0.0054 -3.60E-07 0.4856 0.0027 0.4774 0.0027 -1.68 -0.640.106 0.764 1.2386 0.9008 0.0149 3.00E-07 0.4521 0.0075 0.4423 0.0073 -2.16 -2.220.133 0.783 1.2179 0.8824 0.0187 -2.40E-07 0.443 0.0094 0.4322 0.0092 -2.44 -2.520.201 0.82 1.1782 0.8392 0.0286 1.80E-07 0.4238 0.0143 0.4099 0.014 -3.29 -2.360.294 0.857 1.1403 0.7862 0.0426 1.20E-07 0.403 0.0213 0.3841 0.0208 -4.69 -2.30.351 0.875 1.1218 0.7553 0.0517 2.40E-07 0.3919 0.0258 0.3695 0.0253 -5.72 -1.890.416 0.894 1.1036 0.721 0.0628 6.00E-08 0.379 0.0314 0.3534 0.0308 -6.74 -20.573 0.931 1.0678 0.6393 0.0931 1.20E-07 0.3478 0.0472 0.3155 0.046 -9.29 -2.630.668 0.949 1.0501 0.5892 0.1149 -6.00E-08 0.3292 0.0588 0.2921 0.057 -11.27 -3.10.774 0.968 1.0325 0.5293 0.1447 -3.00E-08 0.3069 0.0744 0.2639 0.0721 -14.01 -3.06

1 1 1 0.3074 0.3074 0.00E+00 0.1841 0.1841 0.1552 0.1552 -15.71 -15.71

209


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.022 0.652 1.354 0.9704 0.0032 1.80E-07 0.745 0.0024 0.7141 0.0024 -4.14 -1.120.045 0.697 1.2989 0.9477 0.0066 3.00E-07 0.7179 0.0047 0.6874 0.0048 -4.25 1.170.079 0.736 1.2536 0.92 0.0113 0.00E+00 0.6928 0.0081 0.6609 0.0081 -4.6 0.110.162 0.795 1.1904 0.8625 0.0231 2.40E-07 0.6502 0.0166 0.6145 0.0165 -5.49 -0.84

0.3 0.855 1.1316 0.7821 0.0438 -6.00E-08 0.6011 0.0314 0.5568 0.0312 -7.36 -0.720.361 0.874 1.1128 0.749 0.0537 4.20E-07 0.5821 0.0387 0.5341 0.0383 -8.25 -1.030.431 0.894 1.0943 0.7121 0.0658 -6.00E-08 0.5622 0.0479 0.509 0.047 -9.46 -1.80.703 0.953 1.041 0.5689 0.1245 -6.00E-08 0.4838 0.0919 0.4118 0.0901 -14.87 -1.940.819 0.973 1.0226 0.5031 0.1611 -9.70E-04 0.445 0.1193 0.3631 0.1163 -18.39 -2.52

1 1 1 0.3074 0.3074 0.00E+00 0.2741 0.2741 0.2261 0.2261 -17.5 -17.5

Table C2.45: Densities Prediction for Ethyl Acetate.

Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.026 0.67 1.3536 0.9656 0.0039 1.80E-07 0.5869 0.0023 0.5597 0.0022 -4.64 -2.220.04 0.694 1.3225 0.9531 0.0057 -1.80E-07 0.5748 0.0033 0.5482 0.0033 -4.64 -0.510.07 0.732 1.2755 0.9278 0.0099 -2.40E-07 0.5549 0.0057 0.5282 0.0056 -4.82 -1.260.09 0.751 1.2528 0.9122 0.0127 2.40E-07 0.5444 0.0073 0.5172 0.0072 -4.99 -1.08

0.144 0.79 1.2094 0.8746 0.0204 2.40E-07 0.5228 0.0117 0.4932 0.0115 -5.66 -1.730.18 0.809 1.1886 0.8524 0.0254 -6.00E-08 0.5109 0.0147 0.4799 0.0143 -6.07 -2.58

0.325 0.866 1.1286 0.7692 0.0476 6.00E-08 0.4714 0.0275 0.4332 0.0268 -8.1 -2.610.388 0.885 1.1095 0.7351 0.0581 -3.00E-07 0.4564 0.0337 0.4148 0.0328 -9.12 -2.660.462 0.904 1.0904 0.6967 0.0712 0.00E+00 0.44 0.0411 0.3942 0.0403 -10.4 -2.010.545 0.923 1.0719 0.6537 0.0873 -6.00E-08 0.4212 0.0505 0.3712 0.0496 -11.87 -1.780.639 0.942 1.0536 0.6042 0.1081 0.00E+00 0.4002 0.0631 0.3447 0.0617 -13.87 -2.270.745 0.962 1.0356 0.5459 0.136 6.00E-08 0.3742 0.0801 0.3131 0.078 -16.33 -2.61

1 1 1 0.3074 0.3074 0.00E+00 0.218 0.218 0.1788 0.1788 -17.98 -17.98

210

Table C2.46: Densities Prediction for Propyl Acetate.


0.039 0.698 1.333 0.9538 0.0056 0.00E+00 0.4786 0.0027 0.4551 0.0027 -4.92 -1.030.087 0.752 1.2636 0.9151 0.0122 -4.20E-07 0.4545 0.0058 0.4306 0.0057 -5.27 -1.080.137 0.789 1.2203 0.8798 0.0193 1.80E-07 0.437 0.0091 0.4116 0.009 -5.81 -0.890.302 0.861 1.1403 0.782 0.0438 2.40E-07 0.3966 0.0207 0.3651 0.0205 -7.95 -1.190.36 0.88 1.1213 0.7505 0.0532 0.00E+00 0.3851 0.0252 0.3509 0.0249 -8.88 -1.26

0.427 0.898 1.1025 0.7155 0.0647 0.00E+00 0.3721 0.0307 0.3352 0.0303 -9.91 -1.310.685 0.952 1.0473 0.58 0.1192 3.00E-08 0.3233 0.0574 0.275 0.0565 -14.94 -1.530.794 0.971 1.0282 0.5194 0.1519 -1.30E-03 0.3 0.0737 0.2455 0.0718 -18.18 -2.58

1 1 1 0.3074 0.3074 0.00E+00 0.1807 0.1807 0.1483 0.1483 -17.94 -17.94


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.015 0.599 1.2945 0.9765 0.0024 7.70E-07 1.2328 0.0032 1.2526 0.0031 1.61 -2.310.038 0.656 1.2474 0.9525 0.0058 -6.00E-08 1.1808 0.0074 1.2 0.0073 1.63 -1.240.053 0.68 1.2284 0.9389 0.008 1.80E-07 1.1586 0.0101 1.1757 0.01 1.48 -1.150.126 0.752 1.173 0.8833 0.0185 -6.00E-08 1.0856 0.0234 1.0925 0.0229 0.63 -2.110.162 0.776 1.156 0.8597 0.0237 -1.80E-07 1.0584 0.0299 1.0611 0.0293 0.25 -2.010.206 0.8 1.1382 0.8325 0.0303 -1.20E-07 1.0288 0.0396 1.0264 0.0373 -0.23 -5.80.322 0.848 1.1025 0.7669 0.0482 6.00E-08 0.9682 0.0606 0.9466 0.0595 -2.23 -1.730.393 0.872 1.0863 0.7288 0.0602 0.00E+00 0.9348 0.0742 0.9016 0.0744 -3.55 0.320.476 0.897 1.0698 0.6855 0.0753 1.20E-07 0.8965 0.0927 0.8507 0.0934 -5.11 0.740.574 0.921 1.053 0.6353 0.0948 1.20E-07 0.8532 0.1162 0.7918 0.1181 -7.19 1.670.683 0.945 1.0372 0.5777 0.1203 8.90E-08 0.8 0.1484 0.724 0.1507 -9.5 1.560.807 0.969 1.0216 0.5069 0.157 -1.20E-07 0.732 0.1966 0.6393 0.1981 -12.66 0.74

1 1 1 0.3074 0.3074 0.00E+00 0.4365 0.4365 0.3918 0.3918 -10.24 -10.24

211


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.019 0.62 1.2994 0.9718 0.003 -4.80E-07 0.8767 0.0028 0.8787 0.0027 0.23 -2.040.036 0.659 1.2632 0.9547 0.0055 -1.80E-07 0.8506 0.005 0.8526 0.0049 0.23 -2.230.066 0.702 1.2242 0.9281 0.0098 4.20E-07 0.8198 0.0089 0.8199 0.0087 0.01 -2.550.144 0.767 1.1695 0.8722 0.0209 3.60E-07 0.7701 0.0184 0.7629 0.0183 -0.93 -0.540.18 0.789 1.152 0.8487 0.0263 4.80E-07 0.7519 0.0228 0.7412 0.023 -1.42 0.79

0.275 0.832 1.1177 0.7929 0.0407 -1.20E-07 0.7132 0.0339 0.6923 0.0356 -2.93 4.90.401 0.876 1.0858 0.7248 0.0615 1.80E-07 0.6687 0.0503 0.635 0.0539 -5.04 7.140.479 0.898 1.07 0.6844 0.0756 3.00E-07 0.6435 0.0619 0.6015 0.0665 -6.53 7.350.566 0.919 1.0549 0.6394 0.0931 -6.00E-08 0.6154 0.0764 0.5641 0.0821 -8.33 7.460.665 0.941 1.0399 0.5875 0.1157 6.00E-08 0.5825 0.0958 0.5208 0.1025 -10.59 7.030.777 0.963 1.0247 0.5247 0.1471 -6.00E-08 0.5409 0.1239 0.4679 0.1312 -13.5 5.89

1 1 1 0.3074 0.3074 0.00E+00 0.3203 0.3203 0.2774 0.2774 -13.39 -13.39


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.028 0.659 1.3167 0.9633 0.0042 2.40E-07 0.5864 0.0027 0.5883 0.0026 0.32 -4.970.047 0.692 1.2789 0.9454 0.0069 4.20E-07 0.5697 0.0043 0.5716 0.0042 0.33 -2.70.085 0.735 1.2341 0.9149 0.0122 -1.80E-07 0.5501 0.0075 0.5478 0.0073 -0.42 -2.40.142 0.778 1.1919 0.8749 0.0203 -1.80E-07 0.5264 0.0124 0.5206 0.0121 -1.1 -2.420.18 0.799 1.1715 0.8509 0.0258 0.00E+00 0.5142 0.0157 0.5055 0.0153 -1.69 -2.42

0.277 0.842 1.132 0.7938 0.0405 -6.00E-08 0.4855 0.0247 0.4714 0.024 -2.91 -2.670.41 0.885 1.0941 0.7222 0.0624 -1.80E-07 0.4535 0.0378 0.4304 0.0372 -5.08 -1.66

0.584 0.928 1.058 0.6315 0.0963 0.00E+00 0.4166 0.0582 0.3792 0.0579 -8.98 -0.60.809 0.97 1.0226 0.5085 0.158 -1.10E-03 0.3595 0.0956 0.3061 0.0951 -14.85 -0.490.874 0.981 1.0148 0.4651 0.1833 -3.30E-04 0.3384 0.1112 0.2819 0.1111 -16.69 -0.07

1 1 1 0.3074 0.3074 0.00E+00 0.2223 0.2223 0.1887 0.1887 -15.12 -15.12

212


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.023 0.641 1.3153 0.9683 0.0035 3.00E-07 0.7438 0.0031 0.7717 0.0028 3.76 -9.710.025 0.647 1.3093 0.9659 0.0038 2.40E-07 0.7407 0.0042 0.7683 0.0031 3.73 -27.160.037 0.67 1.2817 0.9542 0.0055 3.00E-07 0.7272 0.0062 0.7533 0.0044 3.59 -29.380.053 0.692 1.2549 0.94 0.0078 -3.00E-07 0.7137 0.0083 0.7373 0.0061 3.3 -26.360.072 0.715 1.2314 0.9238 0.0106 -3.00E-07 0.6981 0.0104 0.7208 0.0083 3.25 -20.610.098 0.738 1.2071 0.9045 0.0142 3.60E-07 0.6835 0.0135 0.7026 0.011 2.79 -18.260.128 0.761 1.1858 0.8831 0.0186 -1.20E-07 0.669 0.0166 0.6838 0.0144 2.22 -13.40.166 0.784 1.1636 0.8581 0.0241 -6.00E-08 0.6524 0.0197 0.663 0.0186 1.63 -5.440.211 0.807 1.1432 0.8304 0.0308 -1.20E-07 0.6357 0.0239 0.641 0.0238 0.83 -0.580.263 0.829 1.1252 0.8004 0.0386 -1.80E-07 0.6191 0.0301 0.6179 0.0298 -0.2 -0.880.327 0.852 1.1041 0.7643 0.049 -1.20E-07 0.6015 0.0353 0.5908 0.0379 -1.78 7.30.399 0.875 1.0865 0.7262 0.0611 -1.20E-07 0.5817 0.0416 0.5625 0.0473 -3.3 13.710.482 0.898 1.069 0.6829 0.0762 0.00E+00 0.561 0.0519 0.5307 0.0592 -5.4 14.110.576 0.921 1.0521 0.6339 0.0954 6.00E-08 0.536 0.0665 0.4947 0.0744 -7.7 11.920.682 0.944 1.0363 0.5778 0.1202 -6.00E-08 0.5059 0.0852 0.4534 0.0943 -10.38 10.71

0.8 0.966 1.0216 0.5112 0.1546 -6.00E-08 0.4675 0.1132 0.4035 0.122 -13.68 7.811 1 1 0.3074 0.3074 0.00E+00 0.2826 0.2826 0.2453 0.2453 -13.19 -13.19

213

C.3 Results for the Soave-Redlich-Kwong Equation of State.

214

Table C3.1: Densities Prediction for Methane

Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.022 0.586 1.2424 0.9684 0.0042 5.40E-07 1.653 0.007 1.6367 0.007 -0.99 -0.170.026 0.597 1.2347 0.9641 0.0049 -3.60E-07 1.64 0.0082 1.6232 0.0082 -1.03 -0.30.033 0.612 1.2236 0.9576 0.006 -2.40E-07 1.623 0.0101 1.6044 0.0101 -1.15 -0.380.04 0.626 1.2143 0.9507 0.0073 -1.80E-07 1.602 0.0122 1.5858 0.0121 -1.01 -0.75

0.058 0.655 1.195 0.9346 0.0104 1.20E-07 1.57 0.0174 1.5465 0.0173 -1.5 -0.610.069 0.67 1.1866 0.9258 0.0123 0.00E+00 1.551 0.0204 1.5265 0.0203 -1.58 -0.690.082 0.684 1.1783 0.9162 0.0144 -6.00E-08 1.532 0.0239 1.506 0.0237 -1.7 -0.630.097 0.699 1.1692 0.9057 0.0169 -1.20E-07 1.513 0.0279 1.4842 0.0277 -1.9 -0.740.113 0.714 1.1609 0.8947 0.0196 -4.20E-07 1.495 0.0322 1.4623 0.032 -2.19 -0.80.131 0.728 1.1513 0.8824 0.0227 -4.20E-07 1.477 0.0373 1.4386 0.037 -2.6 -0.890.13 0.728 1.1538 0.8833 0.0225 1.20E-07 1.477 0.0369 1.4404 0.0366 -2.48 -0.77

0.173 0.757 1.1351 0.8564 0.0298 -1.80E-07 1.436 0.0488 1.3908 0.0484 -3.15 -0.780.198 0.772 1.127 0.8421 0.034 -1.80E-07 1.417 0.0555 1.3655 0.0551 -3.64 -0.740.225 0.786 1.1188 0.8268 0.0387 -6.00E-08 1.394 0.063 1.339 0.0626 -3.94 -0.640.254 0.801 1.1106 0.8107 0.0439 6.00E-08 1.373 0.0714 1.3115 0.0709 -4.48 -0.60.287 0.815 1.1021 0.7933 0.0497 -2.40E-07 1.352 0.0808 1.2823 0.0803 -5.15 -0.540.322 0.83 1.0941 0.7752 0.0561 1.20E-07 1.329 0.0911 1.2523 0.0907 -5.77 -0.520.359 0.845 1.0864 0.7562 0.0632 4.20E-07 1.304 0.1024 1.2213 0.102 -6.34 -0.41

0.4 0.859 1.0787 0.7359 0.0711 3.00E-07 1.277 0.1151 1.1884 0.1147 -6.94 -0.280.493 0.888 1.0627 0.6909 0.0901 1.20E-07 1.222 0.1455 1.1162 0.1455 -8.66 -0.020.545 0.903 1.0543 0.6654 0.1017 -6.00E-08 1.192 0.1644 1.0756 0.1645 -9.76 0.06

0.6 0.917 1.0464 0.6383 0.1149 1.80E-07 1.159 0.1854 1.0327 0.1859 -10.9 0.230.659 0.932 1.039 0.6093 0.1299 1.50E-07 1.119 0.2094 0.9867 0.2103 -11.82 0.450.722 0.947 1.0313 0.577 0.1478 -2.70E-07 1.077 0.2379 0.9355 0.2396 -13.14 0.690.789 0.961 1.0235 0.5402 0.1697 3.00E-08 1.029 0.2727 0.877 0.2755 -14.77 1.030.861 0.976 1.0154 0.4977 0.1987 -3.50E-04 0.968 0.3172 0.8052 0.3214 -16.81 1.32

1 1 1 0.3333 0.3333 0.00E+00 0.629 0.629 0.5438 0.5438 -13.55 -13.55

215


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.000692 0.436 1.4745 0.9988 0.0001 3.00E-02 1.279 0.0001 1.236 0.0001 -3.36 4.97

0.001 0.454 1.4475 0.9981 0.0002 2.20E-03 1.26 0.0002 1.1923 0.0002 -5.37 -8.490.002 0.491 1.4091 0.9955 0.0004 -6.00E-05 1.227 0.0005 1.167 0.0005 -4.89 -4.30.003 0.509 1.396 0.9936 0.0006 -4.20E-07 1.209 0.0007 1.1585 0.0007 -4.18 -3.170.005 0.527 1.3717 0.9907 0.0009 -5.50E-06 1.192 0.0011 1.145 0.0011 -3.95 -1.510.01 0.564 1.3366 0.9832 0.0019 3.00E-07 1.163 0.0022 1.1195 0.0022 -3.74 -0.87

0.014 0.582 1.3197 0.9782 0.0026 -1.20E-07 1.147 0.003 1.1056 0.003 -3.61 -0.930.019 0.6 1.303 0.9723 0.0035 2.40E-07 1.131 0.004 1.0913 0.004 -3.51 -0.630.034 0.636 1.2693 0.957 0.0061 0.00E+00 1.098 0.0069 1.0604 0.0068 -3.43 -1.090.045 0.654 1.2538 0.9478 0.0078 -2.40E-07 1.083 0.0087 1.0442 0.0086 -3.58 -1.060.057 0.673 1.2387 0.9374 0.0099 3.60E-07 1.069 0.011 1.0274 0.0108 -3.89 -1.360.072 0.691 1.224 0.9258 0.0123 -4.20E-07 1.052 0.0136 1.01 0.0134 -3.99 -1.330.109 0.727 1.1952 0.8989 0.0185 0.00E+00 1.02 0.0204 0.9729 0.0201 -4.62 -1.640.16 0.764 1.1673 0.8664 0.027 -1.80E-07 0.987 0.0295 0.9322 0.029 -5.56 -1.65

0.227 0.8 1.1399 0.8279 0.0383 -1.20E-07 0.953 0.0418 0.887 0.0411 -6.92 -1.790.312 0.836 1.1133 0.7825 0.0535 0.00E+00 0.916 0.0582 0.8366 0.0572 -8.67 -1.780.362 0.854 1.1003 0.7571 0.0628 -1.80E-07 0.896 0.0683 0.8089 0.0671 -9.72 -1.770.418 0.873 1.0873 0.7293 0.0737 1.80E-07 0.873 0.0802 0.7792 0.0788 -10.75 -1.750.48 0.891 1.0745 0.699 0.0865 6.00E-08 0.851 0.094 0.747 0.0924 -12.22 -1.72

0.548 0.909 1.0617 0.6656 0.1016 2.40E-07 0.825 0.1105 0.7119 0.1087 -13.71 -1.660.585 0.918 1.0554 0.6476 0.1103 0.00E+00 0.811 0.12 0.693 0.118 -14.55 -1.670.623 0.936 1.0625 0.6321 0.118 2.40E-07 0.776 0.1248 0.6767 0.1263 -12.8 1.20.75 0.954 1.0304 0.5628 0.156 -6.00E-08 0.742 0.1699 0.604 0.1674 -18.6 -1.48

0.796 0.963 1.0242 0.537 0.1717 2.10E-07 0.72 0.187 0.5768 0.1845 -19.89 -1.370.844 0.973 1.0177 0.5088 0.1909 -3.40E-04 0.693 0.2071 0.545 0.2045 -21.36 -1.260.894 0.982 1.0116 0.4748 0.2146 -2.00E-04 0.66 0.2316 0.5089 0.23 -22.89 -0.69

1 1 1 0.3333 0.3333 0.00E+00 0.422 0.422 0.3597 0.3597 -14.75 -14.76

216


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.002 0.495 1.4656 0.9964 0.0003 4.40E-04 0.879 0.0003 0.8466 0.0003 -3.69 -2.370.003 0.525 1.4293 0.9932 0.0006 0.00E+00 0.862 0.0005 0.8341 0.0005 -3.23 0.780.007 0.555 1.3949 0.9883 0.0012 -1.80E-07 0.843 0.001 0.8169 0.001 -3.1 0.450.009 0.57 1.3785 0.9851 0.0017 -2.40E-07 0.837 0.0014 0.8091 0.0014 -3.34 -1.130.016 0.601 1.3463 0.9767 0.0028 -1.20E-07 0.822 0.0023 0.7925 0.0023 -3.59 -1.320.024 0.625 1.321 0.9679 0.0042 -6.00E-08 0.807 0.0034 0.7779 0.0034 -3.61 -0.590.033 0.646 1.3002 0.959 0.0058 1.20E-07 0.796 0.0047 0.7651 0.0046 -3.88 -1.140.051 0.676 1.2709 0.9432 0.0087 2.40E-07 0.779 0.007 0.7454 0.0069 -4.31 -1.420.062 0.691 1.2567 0.934 0.0106 -2.40E-07 0.771 0.0085 0.735 0.0083 -4.67 -1.610.091 0.721 1.229 0.9129 0.0152 1.20E-07 0.754 0.0121 0.7131 0.0119 -5.42 -1.660.128 0.751 1.2023 0.888 0.0212 0.00E+00 0.734 0.0168 0.6895 0.0165 -6.06 -1.710.15 0.766 1.1893 0.8741 0.0249 1.20E-07 0.725 0.0196 0.677 0.0193 -6.62 -1.83

0.202 0.796 1.1638 0.843 0.0337 -2.40E-07 0.704 0.0265 0.6504 0.026 -7.62 -1.860.233 0.811 1.1513 0.8257 0.039 4.80E-07 0.694 0.0306 0.6361 0.0301 -8.34 -1.890.347 0.856 1.1146 0.7661 0.0594 0.00E+00 0.657 0.0465 0.5887 0.0457 -10.4 -1.850.393 0.871 1.1027 0.7433 0.0682 1.20E-07 0.643 0.0533 0.571 0.0524 -11.19 -1.80.443 0.886 1.0907 0.7186 0.0781 -2.40E-07 0.628 0.0611 0.5521 0.06 -12.08 -1.690.498 0.901 1.0788 0.6919 0.0896 2.40E-07 0.611 0.07 0.5318 0.0689 -12.96 -1.610.589 0.923 1.061 0.6471 0.1105 1.80E-07 0.583 0.0863 0.498 0.085 -14.59 -1.470.657 0.938 1.0492 0.6133 0.1277 -8.90E-08 0.56 0.0998 0.4724 0.0984 -15.63 -1.370.693 0.946 1.0433 0.5948 0.1377 6.00E-08 0.547 0.1076 0.4585 0.1062 -16.18 -1.370.73 0.953 1.0373 0.575 0.1489 0.00E+00 0.531 0.1165 0.4435 0.1149 -16.48 -1.39

0.769 0.961 1.0313 0.5535 0.1616 1.50E-07 0.513 0.1265 0.4273 0.1247 -16.71 -1.40.81 0.968 1.0254 0.5301 0.176 1.80E-07 0.493 0.138 0.4096 0.136 -16.92 -1.41

0.852 0.976 1.0191 0.5046 0.1937 -3.10E-04 0.467 0.1518 0.3887 0.1492 -16.76 -1.720.896 0.983 1.0131 0.4743 0.215 -2.00E-04 0.433 0.1691 0.3655 0.1657 -15.59 -2.04

1 1 1 0.3333 0.3333 0.00E+00 0.308 0.3077 0.2587 0.2587 -16.01 -15.94

217


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.021 0.627 1.3524 0.9712 0.0037 0.00E+00 0.647 0.0023 0.6087 0.0023 -5.92 -0.980.032 0.653 1.3247 0.9604 0.0055 2.40E-07 0.635 0.0035 0.5963 0.0034 -6.09 -1.170.039 0.666 1.3099 0.9539 0.0067 -6.00E-08 0.63 0.0042 0.5896 0.0041 -6.41 -0.760.047 0.679 1.2963 0.9468 0.008 6.00E-08 0.623 0.005 0.5828 0.0049 -6.45 -0.90.057 0.692 1.2826 0.9391 0.0095 3.00E-07 0.619 0.0059 0.5758 0.0058 -6.97 -1.320.067 0.705 1.2691 0.9306 0.0113 4.20E-07 0.612 0.007 0.5686 0.0069 -7.1 -1.180.08 0.718 1.2558 0.9215 0.0133 0.00E+00 0.608 0.0082 0.5611 0.0081 -7.72 -1.41

0.093 0.731 1.2436 0.9118 0.0154 3.60E-07 0.602 0.0095 0.5535 0.0094 -8.05 -1.310.127 0.758 1.2166 0.8892 0.0209 6.00E-08 0.589 0.0128 0.5369 0.0126 -8.85 -1.510.147 0.771 1.2038 0.8768 0.0242 4.80E-07 0.581 0.0148 0.5282 0.0146 -9.09 -1.610.169 0.784 1.1913 0.8636 0.0278 2.40E-07 0.575 0.017 0.5192 0.0167 -9.71 -1.510.193 0.797 1.1789 0.8494 0.0318 4.80E-07 0.568 0.0194 0.5098 0.0191 -10.25 -1.590.22 0.81 1.1667 0.8343 0.0363 1.80E-07 0.562 0.0221 0.5 0.0218 -11.03 -1.62

0.249 0.823 1.1547 0.8183 0.0414 2.40E-07 0.553 0.0252 0.4898 0.0248 -11.43 -1.680.281 0.836 1.1427 0.8012 0.047 1.20E-07 0.546 0.0286 0.4791 0.0281 -12.25 -1.70.316 0.849 1.1311 0.7831 0.0533 -3.00E-07 0.538 0.0324 0.468 0.0318 -13.01 -1.680.354 0.862 1.1197 0.7639 0.0602 1.80E-07 0.529 0.0366 0.4563 0.036 -13.74 -1.70.395 0.875 1.1083 0.7434 0.0681 -2.40E-07 0.52 0.0414 0.444 0.0407 -14.62 -1.690.439 0.888 1.0974 0.7218 0.0768 6.00E-08 0.511 0.0466 0.4311 0.0459 -15.64 -1.640.487 0.901 1.0861 0.6982 0.0868 0.00E+00 0.499 0.0528 0.4171 0.0519 -16.41 -1.670.54 0.914 1.0746 0.6724 0.0984 1.80E-07 0.487 0.0599 0.4019 0.0588 -17.47 -1.73

0.596 0.927 1.0634 0.6446 0.1118 1.80E-07 0.474 0.0681 0.3856 0.0669 -18.65 -1.790.657 0.94 1.052 0.6139 0.1274 1.20E-07 0.459 0.0778 0.3676 0.0763 -19.91 -1.910.723 0.953 1.0406 0.5795 0.1463 -6.00E-08 0.44 0.0897 0.3474 0.0877 -21.04 -2.210.794 0.966 1.0291 0.5399 0.1699 -6.00E-08 0.417 0.1049 0.3242 0.102 -22.26 -2.770.87 0.98 1.0172 0.4934 0.202 -4.30E-04 0.381 0.1261 0.2948 0.1207 -22.63 -4.3

1 1 1 0.3333 0.3333 0.00E+00 0.245 0.2451 0.2011 0.2011 -17.92 -17.95

218


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.001 0.469 1.5399 0.9985 0.0001 1.80E-02 0.714 0.0001 0.6548 0.0001 -8.29 -12.820.001 0.497 1.4979 0.9969 0.0003 1.70E-05 0.702 0.0002 0.6613 0.0002 -5.79 0.940.003 0.524 1.4623 0.9944 0.0005 4.10E-05 0.691 0.0003 0.6525 0.0003 -5.57 0.240.005 0.551 1.4288 0.9905 0.001 7.70E-07 0.677 0.0006 0.6405 0.0006 -5.4 0.420.007 0.565 1.412 0.988 0.0013 6.00E-07 0.672 0.0008 0.635 0.0008 -5.51 -0.860.012 0.592 1.3803 0.9815 0.0022 -1.80E-07 0.662 0.0014 0.6233 0.0014 -5.85 -0.820.022 0.626 1.3424 0.9703 0.0038 -7.70E-07 0.647 0.0024 0.6082 0.0024 -6 -0.930.027 0.639 1.3278 0.9648 0.0047 -4.20E-07 0.64 0.003 0.6016 0.003 -6 -0.620.034 0.653 1.3134 0.9587 0.0058 3.00E-07 0.633 0.0036 0.595 0.0036 -6 -0.570.05 0.68 1.2854 0.9443 0.0085 6.00E-08 0.621 0.0053 0.581 0.0052 -6.44 -0.630.06 0.694 1.2718 0.936 0.0101 -4.20E-07 0.614 0.0063 0.5737 0.0062 -6.57 -0.64

0.072 0.708 1.2583 0.927 0.012 0.00E+00 0.608 0.0074 0.5661 0.0074 -6.9 -0.620.085 0.721 1.2452 0.9173 0.0142 2.40E-07 0.6 0.0087 0.5583 0.0086 -6.96 -0.6

0.1 0.735 1.2325 0.9068 0.0166 -6.00E-08 0.593 0.0101 0.5502 0.0101 -7.21 -0.480.136 0.762 1.207 0.8832 0.0225 -1.20E-07 0.577 0.0136 0.5331 0.0136 -7.61 -0.40.181 0.789 1.1824 0.8561 0.0299 0.00E+00 0.56 0.018 0.5146 0.018 -8.1 -0.240.207 0.803 1.1699 0.8409 0.0343 0.00E+00 0.551 0.0207 0.5047 0.0206 -8.41 -0.240.268 0.83 1.1456 0.8076 0.0449 -2.40E-07 0.533 0.0269 0.4835 0.0269 -9.28 -0.080.342 0.857 1.1216 0.7696 0.0582 2.40E-07 0.511 0.0347 0.4602 0.0348 -9.95 0.20.384 0.871 1.1098 0.7486 0.0661 -1.20E-07 0.499 0.0394 0.4475 0.0395 -10.32 0.320.429 0.884 1.098 0.726 0.0751 6.00E-08 0.486 0.0446 0.434 0.0449 -10.7 0.490.479 0.898 1.0863 0.7018 0.0853 -6.00E-08 0.471 0.0507 0.4196 0.051 -10.91 0.670.533 0.912 1.0746 0.6755 0.097 6.00E-08 0.455 0.0575 0.4041 0.058 -11.19 0.870.654 0.939 1.0514 0.6154 0.1267 0.00E+00 0.416 0.075 0.3688 0.0759 -11.35 1.240.794 0.966 1.0285 0.5397 0.17 1.20E-07 0.361 0.1006 0.3243 0.1022 -10.16 1.560.872 0.98 1.0166 0.4919 0.203 -4.00E-04 0.326 0.1199 0.2943 0.1214 -9.73 1.25

1 1 1 0.3333 0.3333 0.00E+00 0.238 0.2377 0.2013 0.2013 -15.43 -15.31

219


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.022 0.639 1.3749 0.9709 0.0037 -6.00E-07 0.533 0.0019 0.4886 0.0019 -8.32 -0.830.03 0.659 1.3515 0.9627 0.0051 6.00E-07 0.525 0.0026 0.481 0.0026 -8.39 -0.95

0.032 0.662 1.3473 0.961 0.0054 -1.20E-07 0.523 0.0027 0.4795 0.0027 -8.32 -0.870.046 0.686 1.3194 0.9488 0.0076 6.00E-08 0.513 0.0038 0.4696 0.0038 -8.45 -0.870.054 0.698 1.3057 0.9418 0.009 -5.40E-07 0.51 0.0045 0.4645 0.0044 -8.93 -0.650.064 0.709 1.2921 0.9342 0.0105 5.40E-07 0.504 0.0052 0.4591 0.0052 -8.9 -1.10.087 0.733 1.2656 0.9172 0.0142 -1.20E-07 0.495 0.007 0.448 0.0069 -9.5 -0.940.116 0.757 1.2397 0.8975 0.0189 -6.60E-07 0.485 0.0093 0.436 0.0092 -10.1 -1.020.133 0.769 1.227 0.8866 0.0216 -1.80E-07 0.48 0.0106 0.4297 0.0105 -10.47 -1.090.151 0.78 1.2145 0.875 0.0247 1.80E-07 0.473 0.0121 0.4233 0.0119 -10.52 -1.130.172 0.792 1.2023 0.8627 0.028 -6.00E-08 0.468 0.0137 0.4165 0.0135 -11 -1.130.194 0.804 1.1901 0.8495 0.0318 1.80E-07 0.462 0.0155 0.4095 0.0153 -11.35 -1.20.219 0.816 1.178 0.8356 0.036 1.20E-07 0.456 0.0175 0.4023 0.0173 -11.78 -1.190.246 0.828 1.1661 0.8208 0.0406 1.20E-07 0.45 0.0198 0.3947 0.0195 -12.29 -1.20.308 0.851 1.1427 0.7885 0.0514 3.00E-07 0.437 0.025 0.3785 0.0247 -13.38 -1.220.342 0.863 1.1311 0.7707 0.0578 2.40E-07 0.429 0.0281 0.3698 0.0277 -13.79 -1.270.38 0.875 1.1196 0.7519 0.0648 1.20E-07 0.421 0.0315 0.3607 0.0311 -14.32 -1.250.42 0.887 1.1083 0.7318 0.0727 -2.40E-07 0.414 0.0353 0.3511 0.0349 -15.2 -1.28

0.464 0.899 1.097 0.7104 0.0816 -4.20E-07 0.405 0.0396 0.3409 0.0391 -15.83 -1.290.511 0.91 1.0857 0.6874 0.0916 -1.80E-07 0.396 0.0446 0.33 0.044 -16.68 -1.360.562 0.922 1.0741 0.6623 0.1032 0.00E+00 0.385 0.0503 0.3181 0.0496 -17.38 -1.50.615 0.934 1.0635 0.636 0.116 -6.00E-08 0.373 0.0567 0.3057 0.0558 -18.05 -1.610.674 0.946 1.0523 0.6065 0.1314 6.00E-08 0.358 0.0644 0.2918 0.0632 -18.5 -1.850.736 0.958 1.0413 0.5737 0.1496 -2.40E-07 0.341 0.0737 0.2764 0.0721 -18.96 -2.180.802 0.97 1.0302 0.5361 0.1722 1.20E-07 0.316 0.0856 0.2586 0.0831 -18.16 -2.90.874 0.981 1.0186 0.4922 0.2029 -4.10E-04 0.269 0.102 0.2362 0.0974 -12.18 -4.52

1 1 1 0.3333 0.3333 0.00E+00 0.205 0.2053 0.1615 0.1615 -21.2 -21.33

220


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.000612 0.482 1.5697 0.9983 0.0001 -8.50E-03 0.6 0.0001 0.526 0.0001 -12.34 0.02

0.001 0.495 1.5506 0.9978 0.0002 1.50E-03 0.595 0.0001 0.5445 0.0001 -8.49 -2.040.001 0.507 1.5316 0.997 0.0003 -2.40E-07 0.59 0.0001 0.5422 0.0001 -8.1 -1.430.002 0.519 1.5144 0.996 0.0003 3.00E-07 0.585 0.0002 0.54 0.0002 -7.7 -0.360.002 0.531 1.4975 0.9948 0.0005 2.40E-07 0.58 0.0003 0.5371 0.0003 -7.4 -1.730.004 0.555 1.464 0.9916 0.0008 4.80E-07 0.57 0.0004 0.5281 0.0004 -7.34 1.230.006 0.567 1.448 0.9895 0.0011 -1.20E-07 0.566 0.0006 0.5241 0.0006 -7.4 -0.840.008 0.579 1.4321 0.9871 0.0014 0.00E+00 0.559 0.0007 0.5201 0.0007 -6.95 0.50.01 0.591 1.4169 0.9843 0.0018 -3.60E-07 0.554 0.0009 0.5162 0.0009 -6.83 -0.68

0.012 0.603 1.4021 0.9811 0.0022 -1.20E-07 0.55 0.0012 0.5119 0.0011 -6.93 -0.050.019 0.627 1.3726 0.9734 0.0034 2.40E-07 0.541 0.0018 0.5028 0.0017 -7.06 -0.890.024 0.639 1.3585 0.9688 0.0041 0.00E+00 0.537 0.0021 0.4981 0.0021 -7.24 -0.470.029 0.651 1.3444 0.9637 0.0049 -6.00E-08 0.531 0.0026 0.4933 0.0025 -7.09 -0.980.035 0.663 1.3306 0.9581 0.0059 -6.00E-08 0.527 0.003 0.4884 0.003 -7.32 -0.870.042 0.675 1.3169 0.9519 0.007 4.20E-07 0.521 0.0036 0.4833 0.0036 -7.24 -0.740.059 0.7 1.2901 0.9378 0.0098 -6.00E-08 0.511 0.005 0.4726 0.0049 -7.52 -0.910.108 0.748 1.2393 0.9021 0.0177 -1.20E-07 0.491 0.0089 0.4492 0.0088 -8.51 -0.890.142 0.772 1.2146 0.8801 0.0233 -2.40E-07 0.481 0.0117 0.4362 0.0115 -9.3 -10.184 0.796 1.1907 0.8552 0.0302 1.80E-07 0.47 0.015 0.4223 0.0149 -10.14 -0.850.234 0.82 1.1669 0.8269 0.0387 -6.00E-08 0.457 0.0192 0.4072 0.019 -10.89 -0.830.294 0.844 1.1439 0.795 0.0491 -2.40E-07 0.444 0.0243 0.3909 0.0241 -11.97 -0.660.364 0.03050.868 1.1212 0.7592 0.062 1.20E-07 0.43 0.0306 0.3729 -13.28 -0.520.447 0.893 1.099 0.7186 0.0781 6.00E-08 0.415 0.0385 0.3529 0.0384 -14.95 -0.290.543 0.917 1.0765 0.6715 0.0989 0.00E+00 0.396 0.0487 0.3301 0.0486 -16.64 -0.10.655 0.941 1.0535 0.6151 0.1268 0.00E+00 0.375 0.0625 0.3029 0.0624 -19.22 -0.10.781 0.965 1.032 0.5476 0.1652 1.20E-07 0.345 0.0816 0.2703 0.0815 -21.65 -0.07

1 1 1 0.3333 0.3333 0.00E+00 0.204 0.204 0.1654 0.1654 -18.93 -18.93

221


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.001 0.53 1.5815 0.9966 0.0003 2.30E-04 0.502 0.0001 0.4126 0.0001 -17.8 -0.970.004 0.563 1.5296 0.9931 0.0007 -4.80E-07 0.49 0.0003 0.4064 0.0003 -17.07 -0.50.006 0.585 1.4955 0.9896 0.0011 1.80E-07 0.479 0.0004 0.4004 0.0004 -16.42 -0.650.008 0.596 1.4788 0.9873 0.0014 -2.40E-07 0.476 0.0006 0.3974 0.0005 -16.51 -1.990.015 0.629 1.4305 0.9785 0.0026 6.00E-08 0.464 0.001 0.3882 0.001 -16.34 -0.390.022 0.651 1.3998 0.9706 0.0038 0.00E+00 0.455 0.0015 0.3816 0.0015 -16.13 -1.170.024 0.658 1.3969 0.9686 0.0041 -3.00E-07 0.453 0.0016 0.3801 0.0016 -16.09 -0.350.039 0.685 1.3553 0.9553 0.0064 4.20E-07 0.443 0.0025 0.371 0.0025 -16.25 -1.220.046 0.696 1.3407 0.9492 0.0075 -1.20E-07 0.438 0.003 0.3673 0.0029 -16.15 -1.050.073 0.729 1.2983 0.9276 0.0119 0.00E+00 0.425 0.0046 0.3553 0.0046 -16.4 -1.330.097 0.751 1.2721 0.9105 0.0157 6.00E-08 0.417 0.0061 0.3468 0.006 -16.83 -1.340.127 0.773 1.2458 0.8908 0.0205 -1.80E-07 0.409 0.0079 0.3377 0.0078 -17.43 -1.430.164 0.795 1.2205 0.8685 0.0264 6.00E-08 0.399 0.0101 0.328 0.01 -17.8 -1.420.184 0.806 1.2085 0.8565 0.0298 6.00E-08 0.395 0.0114 0.3229 0.0112 -18.25 -1.390.232 0.828 1.1832 0.8294 0.0379 0.00E+00 0.384 0.0144 0.3119 0.0142 -18.79 -1.310.289 0.85 1.1588 0.7992 0.0477 -3.00E-07 0.373 0.0181 0.3 0.0179 -19.58 -1.210.321 0.861 1.1467 0.7826 0.0534 3.00E-07 0.368 0.0203 0.2936 0.02 -20.22 -1.160.392 0.883 1.1236 0.747 0.0667 1.80E-07 0.356 0.0252 0.28 0.025 -21.33 -0.840.519 0.916 1.09 0.6849 0.0927 1.20E-07 0.334 0.0348 0.2569 0.0348 -23.09 -0.110.621 0.939 1.0672 0.6346 0.1167 1.20E-07 0.316 0.0436 0.2384 0.0439 -24.57 0.60.679 0.95 1.0551 0.6049 0.1322 0.00E+00 0.305 0.0492 0.2275 0.0497 -25.43 0.980.737 0.961 1.0447 0.5743 0.1493 -1.80E-07 0.292 0.0552 0.2162 0.0562 -25.97 1.820.801 0.972 1.0328 0.5394 0.1716 -7.90E-04 0.274 0.0627 0.2021 0.0643 -26.23 2.530.872 0.983 1.0209 0.4944 0.2013 -4.30E-04 0.247 0.0728 0.1854 0.0755 -24.93 3.65

1 1 1 0.3333 0.3333 0.00E+00 0.139 0.139 0.1262 0.1262 -9.19 -9.19

222


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.002 0.545 1.5932 0.9961 0.0003 7.20E-07 0.425 0.0001 0.3718 0.0001 -12.52 -0.870.003 0.565 1.56 0.9939 0.0006 -5.70E-05 0.419 0.0002 0.367 0.0002 -12.4 1.480.005 0.586 1.5256 0.9908 0.0009 -6.00E-08 0.412 0.0003 0.3633 0.0003 -11.81 0.470.007 0.596 1.5089 0.9889 0.0012 -1.30E-06 0.409 0.0004 0.3607 0.0004 -11.82 -0.990.008 0.606 1.4928 0.9867 0.0014 -1.20E-07 0.406 0.0005 0.3584 0.0005 -11.72 -0.920.01 0.617 1.4775 0.9842 0.0018 2.40E-07 0.402 0.0006 0.3559 0.0006 -11.47 0.12

0.015 0.637 1.4459 0.9782 0.0026 -6.00E-08 0.396 0.0009 0.3506 0.0009 -11.47 -0.120.022 0.658 1.4158 0.9708 0.0038 4.80E-07 0.39 0.0013 0.3449 0.0013 -11.56 -0.380.027 0.668 1.4011 0.9666 0.0045 1.80E-07 0.387 0.0016 0.342 0.0016 -11.62 -0.830.032 0.678 1.3865 0.9618 0.0053 1.80E-07 0.384 0.0019 0.339 0.0019 -11.71 -0.920.038 0.689 1.372 0.9567 0.0062 2.40E-07 0.381 0.0022 0.336 0.0022 -11.82 -0.620.044 0.699 1.3578 0.9511 0.0072 2.40E-07 0.377 0.0025 0.3328 0.0025 -11.72 -0.440.051 0.709 1.3438 0.945 0.0084 -6.00E-08 0.374 0.0029 0.3296 0.0029 -11.88 -0.480.06 0.72 1.33 0.9384 0.0097 -1.80E-07 0.371 0.0034 0.3262 0.0034 -12.07 -0.6

0.069 0.73 1.3164 0.9313 0.0111 -2.40E-07 0.367 0.0039 0.3228 0.0039 -12.05 -0.620.103 0.761 1.2772 0.9071 0.0165 1.20E-07 0.356 0.0057 0.3119 0.0057 -12.39 -0.930.133 0.781 1.251 0.8879 0.0213 -6.00E-08 0.35 0.0073 0.3039 0.0073 -13.16 -0.80.168 0.802 1.2261 0.8665 0.027 0.00E+00 0.343 0.0093 0.2955 0.0092 -13.84 -0.980.21 0.822 1.2022 0.8427 0.0338 6.00E-08 0.335 0.0116 0.2866 0.0115 -14.45 -1.02

0.257 0.843 1.1804 0.817 0.0418 1.80E-07 0.327 0.0143 0.2773 0.0142 -15.2 -0.910.315 0.863 1.1562 0.7867 0.052 -1.20E-07 0.318 0.0178 0.2666 0.0176 -16.15 -1.020.382 0.884 1.133 0.7532 0.0643 3.00E-07 0.309 0.022 0.2551 0.0218 -17.44 -1.070.459 0.905 1.1096 0.715 0.0796 0.00E+00 0.298 0.0273 0.2422 0.027 -18.73 -1.180.548 0.925 1.0864 0.6713 0.0989 -6.00E-08 0.286 0.034 0.2276 0.0335 -20.42 -1.470.65 0.946 1.0634 0.6205 0.124 -1.80E-07 0.271 0.0429 0.2107 0.0421 -22.26 -1.94

0.767 0.966 1.0398 0.5576 0.1591 -6.00E-08 0.251 0.0561 0.1897 0.0541 -24.41 -3.411 1.00 1 0.3333 0.3333 0.00E+00 0.144 0.1444 0.1134 0.1134 -21.22 -21.45

223


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.00025 0.495 1.8181 0.9993 0.0001 -3.30E-01 0.389 0 0.235 0 -39.59 -25.39

0.0005 0.515 1.7207 0.9987 0.0001 3.50E-02 0.384 0 0.294 0 -23.45 -4.290.000938 0.535 1.6782 0.9978 0.0002 2.60E-05 0.379 0 0.2951 0.0001 -22.14 3.78

0.002 0.554 1.6403 0.9964 0.0003 1.50E-04 0.376 0.0001 0.2909 0.0001 -22.64 0.210.003 0.574 1.6027 0.9944 0.0005 -3.00E-07 0.371 0.0002 0.2861 0.0002 -22.88 0.190.005 0.594 1.5706 0.9917 0.0008 2.40E-07 0.366 0.0002 0.283 0.0002 -22.67 -2.110.008 0.614 1.5326 0.9878 0.0013 0.00E+00 0.363 0.0004 0.2792 0.0004 -23.08 -0.890.017 0.653 1.4662 0.9768 0.0028 -3.60E-07 0.354 0.0008 0.2714 0.0008 -23.34 -0.460.024 0.673 1.4343 0.9692 0.004 6.60E-07 0.35 0.0011 0.267 0.0011 -23.7 -0.250.034 0.693 1.4026 0.9599 0.0056 1.80E-07 0.345 0.0015 0.2624 0.0015 -23.93 -0.750.047 0.713 1.3726 0.949 0.0076 -6.00E-08 0.341 0.0021 0.2576 0.0021 -24.45 -0.440.064 0.733 1.343 0.9361 0.0101 3.00E-07 0.335 0.0028 0.2525 0.0027 -24.63 -0.90.084 0.752 1.3141 0.9211 0.0133 -6.00E-08 0.33 0.0036 0.247 0.0036 -25.14 -0.910.109 0.772 1.2858 0.9039 0.0173 3.60E-07 0.325 0.0047 0.2412 0.0046 -25.78 -0.710.14 0.792 1.2586 0.8846 0.0221 6.00E-08 0.319 0.0059 0.235 0.0059 -26.32 -0.81

0.176 0.812 1.232 0.8627 0.028 1.80E-07 0.314 0.0075 0.2284 0.0074 -27.26 -0.610.218 0.832 1.2078 0.8389 0.0349 1.80E-07 0.307 0.0093 0.2215 0.0092 -27.83 -0.340.269 0.851 1.1821 0.8114 0.0436 0.00E+00 0.3 0.0115 0.2138 0.0115 -28.72 -0.120.298 0.861 1.1694 0.7964 0.0486 0.00E+00 0.296 0.0128 0.2098 0.0128 -29.14 -0.010.328 0.871 1.1568 0.7806 0.0542 -6.00E-08 0.292 0.0142 0.2055 0.0143 -29.64 0.22

0.4 0.891 1.1301 0.7445 0.0677 6.00E-08 0.282 0.0177 0.1959 0.0178 -30.55 0.530.479 0.911 1.1063 0.7056 0.0836 -4.20E-07 0.271 0.0217 0.1857 0.022 -31.48 1.20.571 0.931 1.0819 0.6603 0.1041 0.00E+00 0.256 0.0269 0.1739 0.0274 -32.06 2.040.676 0.95 1.0579 0.6072 0.131 -1.20E-07 0.231 0.0334 0.1602 0.0346 -30.65 3.340.797 0.97 1.0321 0.5425 0.1707 -1.40E-03 0.199 0.0426 0.142 0.0447 -28.63 4.86

1 1 1 0.3333 0.3333 0.00E+00 0.101 0.101 0.0886 0.0886 -12.29 -12.29

224


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG6.57E-05 0.504 1.8936 0.9993 0.0001 6.60E-02 0.3159 0 0.2156 0 -31.74 1.31

0.001 0.53 1.7382 0.9985 0.0001 4.00E-03 0.3092 0 0.2492 0 -19.41 0.20.001 0.557 1.6969 0.9971 0.0002 5.30E-04 0.3028 0.0001 0.2521 0.0001 -16.74 -1.150.003 0.584 1.6478 0.9948 0.0005 -4.20E-07 0.2965 0.0001 0.2491 0.0001 -16.02 -0.310.005 0.611 1.6001 0.9911 0.0009 6.00E-07 0.2904 0.0002 0.2456 0.0002 -15.44 -0.340.009 0.638 1.5605 0.9861 0.0015 1.20E-07 0.2845 0.0004 0.2414 0.0004 -15.17 -1.40.017 0.665 1.5014 0.9776 0.0027 -2.40E-07 0.2789 0.0007 0.2361 0.0007 -15.34 -0.90.028 0.692 1.4461 0.9659 0.0046 0.00E+00 0.2729 0.0011 0.2304 0.0011 -15.57 -1.960.044 0.719 1.4039 0.9522 0.007 -1.80E-07 0.2672 0.0017 0.2249 0.0017 -15.83 -2.50.068 0.746 1.3554 0.9334 0.0107 -3.60E-07 0.2601 0.0026 0.2184 0.0025 -16.03 -1.880.102 0.773 1.3059 0.9093 0.016 -3.00E-07 0.2524 0.0038 0.211 0.0037 -16.37 -1.480.152 0.8 1.2504 0.8769 0.0241 -6.00E-08 0.2445 0.0056 0.2021 0.0056 -17.33 -0.680.211 0.827 1.2085 0.8424 0.0339 3.60E-07 0.2365 0.0079 0.1933 0.0078 -18.28 -1.360.235 0.836 1.1941 0.829 0.038 1.80E-07 0.231 0.0089 0.19 0.0087 -17.76 -2.210.294 0.854 1.1606 0.797 0.0484 -6.00E-08 0.225 0.0113 0.1823 0.0111 -18.98 -2.140.343 0.872 1.1453 0.7723 0.0572 0.00E+00 0.2175 0.0142 0.1765 0.0131 -18.84 -7.950.408 0.89 1.1222 0.7395 0.0696 1.80E-07 0.21 0.0175 0.1689 0.0159 -19.55 -9.070.474 0.908 1.1053 0.7077 0.0827 -1.20E-07 0.2 0.0214 0.1617 0.0189 -19.14 -11.440.562 0.926 1.0799 0.6637 0.1025 -1.20E-07 0.19 0.0269 0.1518 0.0234 -20.1 -12.920.65 0.944 1.0607 0.6195 0.1245 1.20E-07 0.179 0.0333 0.1419 0.0285 -20.73 -14.38

0.752 0.962 1.0405 0.5656 0.1543 -1.50E-07 0.164 0.045 0.1298 0.0354 -20.85 -21.31 1 1 0.3333 0.3333 0.00E+00 0.1 0.1 0.0769 0.0769 -23.1 -23.1

225


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.025 0.64 1.3475 0.9673 0.0043 -1.20E-07 0.534 0.0022 0.4957 0.0022 -7.17 1.010.033 0.657 1.3286 0.9599 0.0056 5.40E-07 0.5265 0.0028 0.489 0.0029 -7.12 1.850.043 0.675 1.3085 0.9507 0.0073 -1.80E-07 0.5183 0.0036 0.4814 0.0037 -7.12 2.240.055 0.693 1.2887 0.9402 0.0093 1.80E-07 0.5106 0.0047 0.4734 0.0047 -7.28 -0.260.07 0.711 1.2705 0.9286 0.0117 -1.20E-07 0.5025 0.0059 0.4653 0.0059 -7.41 -0.53

0.088 0.729 1.252 0.9154 0.0146 2.40E-07 0.4945 0.0074 0.4566 0.0073 -7.66 -1.50.11 0.747 1.2323 0.9003 0.0182 1.80E-07 0.4861 0.0091 0.4473 0.009 -7.99 -0.79

0.136 0.765 1.213 0.8836 0.0224 -1.80E-07 0.4773 0.0111 0.4374 0.0111 -8.36 -0.150.166 0.783 1.1949 0.8654 0.0273 2.40E-07 0.4683 0.0136 0.4271 0.0135 -8.79 -1.030.24 0.819 1.159 0.8233 0.0398 -1.20E-07 0.4495 0.0197 0.4046 0.0195 -9.98 -0.78

0.284 0.837 1.1421 0.7996 0.0475 1.80E-07 0.4389 0.0235 0.3925 0.0233 -10.58 -0.70.333 0.855 1.1262 0.7742 0.0565 -6.00E-08 0.4282 0.0282 0.3797 0.0277 -11.33 -1.830.389 0.873 1.1101 0.7463 0.067 0.00E+00 0.4164 0.0334 0.3658 0.0328 -12.15 -1.70.45 0.892 1.095 0.7162 0.0791 -1.80E-07 0.4037 0.0396 0.3511 0.0388 -13.03 -2.030.52 0.91 1.079 0.6821 0.094 1.80E-07 0.3899 0.0469 0.3346 0.0461 -14.19 -1.68

0.597 0.928 1.0636 0.6444 0.1119 1.80E-07 0.3752 0.0553 0.3164 0.0549 -15.67 -0.680.681 0.946 1.0486 0.6019 0.1339 8.90E-08 0.3578 0.0665 0.296 0.0658 -17.28 -1.030.776 0.964 1.0328 0.5506 0.1633 1.80E-07 0.3365 0.0814 0.2713 0.0804 -19.39 -1.17

1 1 1 0.3333 0.3333 0.00E+00 0.2025 0.2025 0.1651 0.1651 -18.49 -18.49

226


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.07 0.712 1.2738 0.9289 0.0116 2.40E-07 1.623 0.0195 1.5412 0.0193 -5.04 -1.08

0.078 0.721 1.2653 0.9228 0.013 -1.20E-07 1.611 0.0217 1.5277 0.0215 -5.17 -1.110.099 0.739 1.2452 0.9084 0.0162 -2.40E-07 1.589 0.0271 1.4972 0.0268 -5.78 -1.230.11 0.748 1.2354 0.9006 0.0181 -6.00E-08 1.567 0.0302 1.4815 0.0298 -5.46 -1.28

0.123 0.757 1.2253 0.8923 0.0202 -6.00E-08 1.556 0.0335 1.4651 0.0331 -5.84 -1.330.15 0.776 1.2072 0.875 0.0247 1.20E-07 1.535 0.041 1.432 0.0403 -6.71 -1.47

0.166 0.785 1.1985 0.8658 0.0272 4.20E-07 1.525 0.0451 1.4151 0.0444 -7.21 -1.50.182 0.794 1.1895 0.8561 0.0299 1.20E-07 1.515 0.0496 1.3974 0.0488 -7.76 -1.570.219 0.812 1.1711 0.8348 0.0362 -4.80E-07 1.485 0.06 1.3597 0.059 -8.44 -1.730.24 0.821 1.1619 0.8233 0.0398 -6.00E-08 1.475 0.0659 1.3398 0.0647 -9.17 -1.77

0.262 0.83 1.1528 0.8114 0.0436 -1.20E-07 1.457 0.0723 1.3193 0.0709 -9.45 -1.890.31 0.849 1.136 0.7865 0.0521 6.00E-08 1.429 0.0863 1.2774 0.0846 -10.61 -1.98

0.336 0.858 1.1276 0.7731 0.0569 -1.80E-07 1.411 0.0943 1.2553 0.0923 -11.04 -2.050.364 0.867 1.1191 0.759 0.0621 -6.00E-08 1.403 0.103 1.232 0.1008 -12.19 -2.150.424 0.885 1.1031 0.7294 0.0737 6.00E-08 1.369 0.1224 1.1839 0.1196 -13.52 -2.310.458 0.894 1.0945 0.7128 0.0805 3.00E-07 1.353 0.134 1.1572 0.1307 -14.47 -2.410.492 0.903 1.0863 0.6958 0.0879 0.00E+00 1.337 0.1463 1.1298 0.1427 -15.49 -2.480.568 0.922 1.0702 0.6589 0.1048 6.00E-08 1.298 0.1748 1.0709 0.1703 -17.5 -2.580.61 0.931 1.0615 0.638 0.115 -1.80E-07 1.277 0.1922 1.0375 0.187 -18.75 -2.71

0.656 0.94 1.0518 0.6142 0.1273 6.00E-08 1.255 0.2136 0.9995 0.2071 -20.36 -3.020.748 0.958 1.0366 0.5661 0.1541 1.20E-07 1.202 0.2576 0.9228 0.2512 -23.23 -2.490.795 0.967 1.0301 0.54 0.1698 1.80E-07 1.171 0.2816 0.8812 0.2771 -24.75 -1.580.845 0.976 1.0225 0.5105 0.1899 -4.00E-04 1.136 0.3096 0.8301 0.3088 -26.92 -0.25

1 1 1 0.3333 0.3333 0.00E+00 0.664 0.6644 0.5465 0.5465 -17.69 -17.74

227

Table C3.14: Densities Prediction for Nitrogen

Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.094 0.703 1.1835 0.9082 0.0163 3.60E-07 1.668 0.0299 1.6586 0.0298 -0.56 -0.48

0.1 0.708 1.18 0.9042 0.0172 1.80E-07 1.66 0.0316 1.6496 0.0315 -0.63 -0.410.119 0.725 1.1687 0.8908 0.0205 2.40E-07 1.637 0.0375 1.6203 0.0373 -1.02 -0.380.121 0.726 1.1678 0.8897 0.0208 -6.00E-08 1.63 0.038 1.6179 0.0378 -0.74 -0.380.15 0.747 1.154 0.8716 0.0256 -1.20E-07 1.601 0.0465 1.5798 0.0464 -1.33 -0.3

0.164 0.756 1.1479 0.8629 0.028 2.40E-07 1.586 0.0508 1.562 0.0507 -1.51 -0.290.185 0.769 1.1395 0.8503 0.0316 1.20E-07 1.566 0.0572 1.5369 0.0571 -1.86 -0.240.203 0.779 1.1329 0.8397 0.0347 -1.20E-07 1.545 0.0627 1.5163 0.0627 -1.86 -0.160.226 0.791 1.1252 0.8268 0.0387 -3.60E-07 1.525 0.0698 1.4913 0.0698 -2.21 -0.10.273 0.813 1.111 0.8011 0.047 1.80E-07 1.487 0.0847 1.4427 0.0847 -2.98 0.060.305 0.826 1.1027 0.7845 0.0528 1.20E-07 1.463 0.0948 1.412 0.095 -3.49 0.170.327 0.835 1.0972 0.773 0.0569 -1.20E-07 1.451 0.1022 1.3907 0.1024 -4.15 0.240.389 0.857 1.0835 0.7421 0.0686 0.00E+00 1.405 0.1228 1.3348 0.1234 -5 0.450.406 0.862 1.08 0.7336 0.072 0.00E+00 1.394 0.1288 1.3195 0.1295 -5.34 0.490.458 0.879 1.0701 0.7082 0.0825 1.20E-07 1.357 0.1475 1.2741 0.1484 -6.11 0.640.511 0.894 1.0609 0.6824 0.0939 0.00E+00 1.317 0.1676 1.2282 0.1689 -6.75 0.80.535 0.901 1.057 0.6707 0.0992 6.00E-08 1.303 0.177 1.2075 0.1786 -7.33 0.90.613 0.921 1.0453 0.6323 0.1179 0.00E+00 1.248 0.2101 1.1395 0.2125 -8.69 1.150.62 0.923 1.0442 0.6287 0.1197 -6.00E-08 1.244 0.2134 1.1332 0.2158 -8.91 1.16

0.715 0.945 1.0317 0.5805 0.1457 0.00E+00 1.17 0.2592 1.0482 0.2631 -10.41 1.490.812 0.965 1.0202 0.5265 0.1783 -6.00E-08 1.092 0.317 0.9526 0.3226 -12.77 1.750.819 0.967 1.0195 0.5227 0.1808 6.00E-08 1.088 0.3216 0.9457 0.3271 -13.08 1.72

1 1 1 0.3333 0.3333 0.00E+00 0.694 0.6945 0.6056 0.6056 -12.74 -12.79

228


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.01 0.566 1.3353 0.9828 0.002 -8.90E-07 1.768 0.0034 1.6769 0.0034 -5.15 -0.03

0.013 0.581 1.327 0.9792 0.0025 1.20E-07 1.747 0.0042 1.662 0.0042 -4.87 -0.190.017 0.595 1.316 0.9748 0.0031 0.00E+00 1.726 0.0053 1.6458 0.0053 -4.64 -0.160.022 0.61 1.3034 0.9696 0.004 -2.40E-07 1.706 0.0067 1.628 0.0066 -4.57 -0.280.028 0.625 1.2898 0.9636 0.005 3.00E-07 1.677 0.0083 1.6096 0.0083 -4.02 0.020.043 0.655 1.2617 0.9491 0.0076 -4.20E-07 1.639 0.0125 1.5698 0.0125 -4.22 -0.040.053 0.67 1.2478 0.9405 0.0092 -4.20E-07 1.621 0.0152 1.5487 0.0152 -4.46 -0.120.065 0.685 1.2342 0.9311 0.0112 -3.00E-07 1.595 0.0183 1.5269 0.0183 -4.27 0.050.078 0.7 1.2209 0.9209 0.0134 -1.80E-07 1.578 0.0219 1.5044 0.0219 -4.66 0.10.094 0.02590.715 1.208 0.9097 0.0159 2.40E-07 1.553 0.0259 1.4811 -4.63 0.240.112 0.729 1.1938 0.8971 0.019 0.00E+00 1.536 0.0305 1.456 0.0308 -5.21 1.040.153 0.759 1.1714 0.8709 0.0258 -1.20E-07 1.489 0.0413 1.4065 0.0416 -5.54 0.630.177 0.774 1.1598 0.8561 0.0299 1.80E-07 1.467 0.0478 1.3798 0.0482 -5.94 0.80.205 0.789 1.1485 0.8403 0.0345 -1.80E-07 1.438 0.055 1.3521 0.0556 -5.98 1.050.235 0.804 1.1374 0.8235 0.0397 0.00E+00 1.418 0.0631 1.3232 0.0638 -6.69 1.250.268 0.819 1.1265 0.8055 0.0456 -6.00E-08 1.391 0.072 1.2929 0.0731 -7.05 1.530.305 0.834 1.1157 0.7864 0.0521 0.00E+00 1.365 0.0821 1.2613 0.0836 -7.6 1.840.344 0.849 1.1051 0.766 0.0595 -2.40E-07 1.334 0.0933 1.228 0.0953 -7.95 2.130.388 0.863 1.0947 0.7443 0.0678 -6.00E-08 1.304 0.1059 1.1928 0.1086 -8.52 2.520.435 0.878 1.0843 0.7209 0.0772 1.80E-07 1.276 0.1202 1.1555 0.1237 -9.44 2.920.487 0.893 1.074 0.6959 0.0879 1.80E-07 1.243 0.1363 1.1157 0.1409 -10.24 3.350.542 0.908 1.0637 0.6687 0.1002 -2.40E-07 1.203 0.1547 1.0728 0.1607 -10.82 3.870.603 0.923 1.0535 0.6392 0.1145 -2.40E-07 1.164 0.1759 1.0262 0.1838 -11.83 4.470.668 0.938 1.0433 0.6065 0.1314 -6.00E-08 1.12 0.2008 0.9749 0.2112 -12.96 5.140.738 0.953 1.0332 0.5698 0.1519 1.80E-07 1.071 0.2307 0.9171 0.2445 -14.37 5.990.813 0.968 1.023 0.5271 0.1779 6.00E-08 1.015 0.268 0.8497 0.2869 -16.28 7.05

1 1 1 0.3333 0.3333 0.00E+00 0.639 0.6393 0.5397 0.5397 -15.55 -15.58

229


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.029 0.61 1.2438 0.9614 0.0053 0.00E+00 1.7897 0.0098 1.7549 0.0097 -1.94 -0.680.035 0.625 1.2407 0.9559 0.0063 -1.20E-07 1.7696 0.012 1.7382 0.0115 -1.77 -4.460.093 0.7 1.181 0.909 0.0161 -2.40E-07 1.6671 0.029 1.6198 0.0287 -2.83 -1.010.194 0.775 1.1375 0.845 0.0331 -1.20E-07 1.5535 0.0602 1.4891 0.0584 -4.14 -2.980.359 0.85 1.0953 0.7575 0.0626 -2.40E-07 1.4242 0.1025 1.3294 0.1099 -6.66 7.240.606 0.925 1.0549 0.6381 0.115 -1.80E-07 1.2481 0.1961 1.1217 0.2021 -10.13 3.07

1 1 1 0.3333 0.3333 0.00E+00 0.6709 0.6709 0.5908 0.5908 -11.94 -11.94


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.048 0.655 1.2379 0.9444 0.0085 1.20E-07 1.2925 0.0113 1.202 0.0108 -7 -4.50.065 0.679 1.2212 0.9305 0.0113 -3.60E-07 1.2661 0.0154 1.177 0.0143 -7.04 -7.20.087 0.703 1.2024 0.914 0.0149 2.40E-07 1.2397 0.0199 1.1495 0.0188 -7.27 -5.570.115 0.727 1.1819 0.8945 0.0196 6.00E-08 1.2124 0.0264 1.1194 0.0245 -7.67 -7.020.149 0.751 1.1624 0.8725 0.0253 6.00E-08 1.1833 0.0338 1.0875 0.0316 -8.1 -6.650.193 0.775 1.1385 0.8456 0.0329 5.40E-07 1.1534 0.0428 1.0503 0.0409 -8.94 -4.390.234 0.799 1.1299 0.8233 0.0398 2.40E-07 1.1226 0.0528 1.0207 0.0493 -9.08 -6.620.302 0.823 1.0996 0.7854 0.0525 -6.00E-08 1.0918 0.0652 0.9718 0.0649 -10.99 -0.430.346 0.847 1.1005 0.7644 0.0601 -6.00E-08 1.0557 0.0801 0.9454 0.0743 -10.45 -7.260.453 0.871 1.0602 0.7082 0.0825 -5.40E-07 1.0178 0.0991 0.8759 0.102 -13.94 2.970.49 0.895 1.0739 0.6942 0.0886 1.80E-07 0.9764 0.1197 0.8588 0.1096 -12.05 -8.45

0.668 0.919 1.0156 0.5981 0.136 -1.80E-07 0.9324 0.1444 0.7419 0.1687 -20.43 16.791 1 1 0.3333 0.3333 0.00E+00 0.5045 0.5045 0.4164 0.4164 -17.47 -17.47

230


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.027 0.646 1.3435 0.9651 0.0047 -6.00E-07 0.6426 0.0029 0.5902 0.0029 -8.16 -0.760.06 0.699 1.2833 0.9363 0.0101 6.00E-08 0.6147 0.0062 0.5627 0.0061 -8.46 -2.2

0.117 0.753 1.2282 0.8958 0.0193 -1.80E-07 0.5842 0.0115 0.5315 0.0114 -9.02 -0.520.173 0.788 1.1934 0.8614 0.0284 6.00E-08 0.5629 0.0167 0.508 0.0167 -9.75 0.250.337 0.86 1.1296 0.773 0.0569 -3.00E-07 0.514 0.0336 0.4532 0.0334 -11.84 -0.680.393 0.877 1.113 0.7448 0.0675 3.00E-07 0.4999 0.0401 0.4365 0.0396 -12.68 -1.290.455 0.895 1.0971 0.7143 0.0799 -3.00E-07 0.4847 0.0478 0.4187 0.0468 -13.62 -1.990.601 0.931 1.0657 0.643 0.1125 -6.00E-08 0.4483 0.0683 0.3775 0.0661 -15.8 -3.270.686 0.948 1.0499 0.5998 0.135 -1.80E-07 0.4258 0.083 0.3526 0.0794 -17.19 -4.370.781 0.966 1.034 0.5485 0.1646 -8.90E-08 0.3983 0.1029 0.3231 0.0969 -18.89 -5.79

1 1 1 0.3333 0.3333 0.00E+00 0.2398 0.2398 0.1973 0.1973 -17.71 -17.71


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG0.026 0.649 1.3604 0.9665 0.0045 4.20E-07 0.6084 0.0025 56 250.54 0.00 -10.33 0.730.045 5 1.3174 0.94 0.0042 0.5289 0.0042 -10.48 1.10.68 88 0.0076 7.20E-07 0.59090.075 0.72 1.2763 0.9258 0.0123 1.20E-07 0.5724 0.0068 0.5107 0.0068 -10.77 -0.210.116 0.756 1.2376 0.8972 0.0189 6.00E-08 0.5534 0.0106 0.4909 0.0104 -11.3 -2.260.172 0.792 1.2008 0.8624 0.0281 1.20E-07 0.5329 0.0157 0.4689 0.0153 -12.01 -2.610.343 0.863 1.131 0.7706 0.0578 1.20E-07 0.4859 0.0323 0.4165 0.0312 -14.29 -3.33

0.4 0.881 1.1142 0.7421 0.0686 -2.40E-07 0.4719 0.0384 0.4009 0.0371 -15.04 -3.470.464 0.899 1.0975 0.7106 0.0815 -6.00E-08 0.4571 0.0457 0.384 0.044 -15.99 -3.660.616 0.935 1.0637 0.6356 0.1163 2.40E-07 0.4225 0.0655 0.344 0.0629 -18.57 -3.930.706 0.952 1.0467 0.5894 0.1407 2.40E-07 0.4004 0.0796 0.3196 0.0763 -20.19 -4.160.807 0.97 1.0285 0.5351 0.1748 -1.00E-03 0.3728 0.0997 0.2884 0.0942 -22.64 -5.5

1 1 1 0.3333 0.3333 0.00E+00 0.23 0.23 0.1819 0.1819 -20.91 -20.91


231

Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.025 0.646 1.3645 0.9677 0.0043 3.00E-07 0.5166 0.0021 0.4567 0.002 -11.59 -4.040.04 0.676 1.3289 0.9537 0.0067 6.00E-08 0.5048 0.0032 0.4454 0.0031 -11.77 -2.060.05 0.691 1.3111 0.9453 0.0083 -3.60E-07 0.4983 0.0039 0.4393 0.0039 -11.83 -1.09

0.074 0.721 1.2785 0.9261 0.0122 -4.80E-07 0.4854 0.0058 0.4268 0.0056 -12.08 -2.680.09 0.736 1.2617 0.9148 0.0148 -4.20E-07 0.4786 0.0069 0.42 0.0068 -12.25 -1.75

0.108 0.751 1.2456 0.9025 0.0176 1.20E-07 0.4722 0.0083 0.413 0.0081 -12.55 -2.710.129 0.766 1.2294 0.889 0.021 6.00E-08 0.4647 0.0099 0.4056 0.0096 -12.72 -3.30.152 0.781 1.2134 0.8744 0.0248 -1.80E-07 0.4576 0.0116 0.3978 0.0113 -13.06 -2.640.179 0.796 1.1968 0.8582 0.0293 6.00E-08 0.4497 0.0136 0.3896 0.0133 -13.37 -2.180.21 0.811 1.1809 0.8408 0.0344 1.20E-07 0.4413 0.016 0.381 0.0156 -13.68 -2.64

1 1 1 0.3333 0.3333 0.00E+00 0.1821 0.1821 0.152 0.152 -16.56 -16.56


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.028 0.653 1.3578 0.9649 0.0047 6.60E-07 0.5393 0.0024 0.4815 0.0024 -10.72 -1.720.045 0.685 1.3196 0.9491 0.0076 1.80E-07 0.5258 0.0038 0.4684 0.0037 -10.92 -1.640.07 0.717 1.2848 0.9295 0.0115 3.00E-07 0.5116 0.0057 0.4545 0.0056 -11.15 -1.2

0.104 0.748 1.2507 0.9054 0.017 -1.80E-07 0.4967 0.0084 0.4394 0.0082 -11.54 -2.070.125 0.764 1.2343 0.8917 0.0203 -1.20E-07 0.4889 0.01 0.4313 0.0098 -11.78 -1.70.149 0.78 1.2174 0.8764 0.0243 -3.60E-07 0.481 0.0119 0.4227 0.0117 -12.11 -1.610.177 0.796 1.2011 0.8599 0.0288 0.00E+00 0.4724 0.0141 0.4138 0.0139 -12.41 -1.70.208 0.812 1.185 0.842 0.034 6.00E-08 0.4634 0.0166 0.4044 0.0163 -12.74 -1.60.244 0.827 1.1682 0.8222 0.0401 -1.20E-07 0.4546 0.0196 0.3942 0.0192 -13.29 -1.810.285 0.843 1.1513 0.8004 0.0473 3.00E-07 0.4446 0.0231 0.3833 0.0226 -13.8 -1.980.33 0.859 1.1348 0.7768 0.0555 -1.20E-07 0.4345 0.0273 0.3717 0.0266 -14.46 -2.71

1 1 1 0.3333 0.3333 0.00E+00 0.2027 0.2027 0.161 0.161 -20.56 -20.56

232


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.023 0.642 1.3681 0.9692 0.004 3.00E-07 0.4785 0.0018 0.4257 0.0018 -11.04 -1.80.029 0.656 1.3524 0.9634 0.005 -6.00E-08 0.4734 0.0022 0.421 0.0022 -11.06 -1.070.036 0.67 1.336 0.9569 0.0061 -6.00E-08 0.4681 0.0027 0.4161 0.0027 -11.1 -1.190.045 0.684 1.3193 0.9494 0.0075 1.80E-07 0.4628 0.0033 0.411 0.0032 -11.2 -1.520.055 0.698 1.3032 0.9412 0.0091 0.00E+00 0.4572 0.004 0.4057 0.0039 -11.27 -1.970.066 0.712 1.2873 0.9322 0.0109 -2.40E-07 0.4518 0.0048 0.4002 0.0047 -11.43 -2.130.08 0.726 1.2711 0.9222 0.0131 -6.00E-08 0.4462 0.0057 0.3944 0.0056 -11.61 -1.69

0.095 0.739 1.2554 0.9113 0.0156 0.00E+00 0.4401 0.0067 0.3884 0.0066 -11.75 -0.980.113 0.753 1.2397 0.8994 0.0184 1.20E-07 0.4342 0.008 0.3822 0.0078 -11.99 -2.27

1 1 1 0.3333 0.3333 0.00E+00 0.1779 0.1779 0.1412 0.1412 -20.62 -20.62


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.001 0.47 1.5481 0.9985 0.0001 1.70E-03 0.8384 0.0001 0.7828 0.0001 -6.63 -0.010.002 0.51 1.4914 0.9961 0.0003 2.20E-04 0.8177 0.0003 0.7491 0.0003 -8.38 -0.10.006 0.562 1.4248 0.989 0.0011 -1.20E-07 0.7897 0.0008 0.7243 0.0008 -8.28 -0.240.014 0.601 1.3784 0.9796 0.0024 4.20E-07 0.7684 0.0018 0.7058 0.0017 -8.15 -0.370.048 0.679 1.293 0.9461 0.0081 -1.20E-07 0.723 0.0057 0.6627 0.0057 -8.34 -0.720.058 0.693 1.2797 0.9383 0.0097 -6.00E-08 0.7152 0.0068 0.6547 0.0068 -8.45 -0.790.095 0.732 1.2407 0.9108 0.0157 -6.00E-08 0.6903 0.0109 0.6292 0.0108 -8.86 -1.010.169 0.784 1.1913 0.8633 0.0279 -1.20E-07 0.6549 0.0193 0.5908 0.0191 -9.79 -1.280.219 0.81 1.1676 0.8346 0.0363 6.00E-08 0.6355 0.0251 0.5693 0.0247 -10.42 -1.450.28 0.836 1.1444 0.8019 0.0468 -6.00E-08 0.6148 0.0323 0.5459 0.0319 -11.21 -1.53

0.352 0.862 1.1217 0.765 0.0599 0.00E+00 0.5924 0.0414 0.5202 0.0407 -12.18 -1.71 1 1 0.3333 0.3333 0.00E+00 0.2826 0.2826 0.2289 0.2289 -19 -19

233


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.103 0.701 1.1574 0.9005 0.0181 -7.20E-07 1.3276 0.0228 1.2426 0.025 -6.4 9.780.147 0.736 1.137 0.8716 0.0256 -1.20E-07 1.2834 0.0376 1.1961 0.0351 -6.8 -6.71

0.2 0.77 1.1206 0.8399 0.0346 1.20E-07 1.2387 0.0514 1.1482 0.0474 -7.31 -7.870.272 0.805 1.0983 0.8001 0.0474 1.80E-07 1.194 0.0651 1.0908 0.0646 -8.64 -0.730.346 0.839 1.0884 0.7626 0.0607 0.00E+00 1.1459 0.0856 1.0387 0.0827 -9.36 -3.390.459 0.874 1.0614 0.7058 0.0835 0.00E+00 1.0898 0.1132 0.9613 0.1138 -11.79 0.510.548 0.908 1.0607 0.6654 0.1017 -1.20E-07 1.0314 0.1488 0.907 0.1387 -12.06 -6.820.708 0.943 1.0318 0.5837 0.144 8.90E-08 0.9448 0.2002 0.7977 0.1967 -15.57 -1.73

1 1 1 0.3333 0.3333 0.00E+00 0.5487 0.5487 0.4585 0.4585 -16.44 -16.44


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.023 0.423 0.8405 0.9561 0.0063 -6.00E-07 2.2782 0.0192 2.901 0.019 27.34 -1.050.037 0.462 0.8599 0.9406 0.0092 -2.40E-07 2.2644 0.0281 2.8292 0.0277 24.94 -1.270.054 0.5 0.8778 0.9229 0.0129 1.80E-07 2.2466 0.0392 2.7558 0.0387 22.67 -1.440.077 0.538 0.8942 0.9029 0.0175 -1.20E-07 2.2251 0.0529 2.6805 0.0521 20.46 -1.520.106 0.577 0.9091 0.8808 0.0231 0.00E+00 2.2003 0.0694 2.6026 0.0683 18.28 -1.530.141 0.615 0.9228 0.8565 0.0298 1.80E-07 2.1721 0.089 2.5218 0.0876 16.1 -1.550.183 0.654 0.9353 0.8301 0.0377 -1.80E-07 2.1406 0.1123 2.4376 0.1106 13.87 -1.570.233 0.692 0.9465 0.8013 0.047 -6.00E-08 2.1051 0.1399 2.3488 0.1377 11.57 -1.540.291 0.731 0.9568 0.7701 0.058 1.80E-07 2.0652 0.1724 2.255 0.1698 9.19 -1.520.358 0.769 0.966 0.7361 0.071 6.00E-08 2.0199 0.2111 2.1549 0.2078 6.68 -1.520.435 0.808 0.9742 0.6989 0.0865 -1.20E-07 1.9676 0.2574 2.0468 0.2534 4.02 -1.570.523 0.846 0.9814 0.6577 0.1054 0.00E+00 1.9059 0.3142 1.928 0.3088 1.16 -1.70.622 0.885 0.9877 0.6113 0.1288 0.00E+00 1.8302 0.3861 1.7944 0.3782 -1.95 -2.05

1 1 1 0.3333 0.3333 0.00E+00 1.0862 1.0862 0.9857 0.9857 -9.25 -9.25

234


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.014 0.555 1.251 0.9773 0.0028 -6.00E-08 2.2106 0.0063 2.2437 0.0063 1.5 -0.170.016 0.563 1.2457 0.9749 0.0031 0.00E+00 2.2 0.0072 2.2313 0.0072 1.42 -0.250.027 0.596 1.2235 0.9626 0.0051 -2.40E-07 2.1519 0.0116 2.1775 0.0116 1.19 -0.260.044 0.63 1.2022 0.947 0.008 -7.20E-07 2.1019 0.0179 2.1204 0.0179 0.88 -0.320.066 0.663 1.1818 0.9279 0.0119 2.40E-07 2.0495 0.0264 2.0597 0.0263 0.5 -0.410.097 0.696 1.1622 0.9052 0.017 -1.20E-07 1.9952 0.0377 1.9951 0.0375 -0.01 -0.490.136 0.729 1.1433 0.8786 0.0237 -1.20E-07 1.9378 0.0522 1.9258 0.0519 -0.62 -0.530.186 0.762 1.125 0.8481 0.0322 1.20E-07 1.8766 0.0707 1.8511 0.0703 -1.36 -0.570.248 0.795 1.1073 0.8133 0.043 6.00E-08 1.8123 0.0941 1.7702 0.0936 -2.32 -0.60.323 0.828 1.0899 0.7738 0.0566 3.60E-07 1.7424 0.1238 1.6815 0.123 -3.49 -0.630.414 0.861 1.0727 0.7286 0.074 1.20E-07 1.6643 0.1619 1.5828 0.1608 -4.9 -0.690.521 0.895 1.0556 0.6765 0.0966 0.00E+00 1.5769 0.2118 1.4707 0.2099 -6.74 -0.860.647 0.928 1.0383 0.6144 0.1272 -6.00E-08 1.4721 0.2804 1.3382 0.2769 -9.09 -1.220.795 0.961 1.0209 0.5359 0.1724 -3.00E-08 1.3335 0.3861 1.1706 0.3765 -12.21 -2.48

1 1 1 0.3333 0.3333 0.00E+00 0.8372 0.8372 0.7314 0.7314 -12.63 -12.63


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.009 0.451 1.0463 0.981 0.0022 3.00E-07 2.363 0.0062 2.7061 0.0061 14.52 -1.090.019 0.496 1.0489 0.9679 0.0042 -1.20E-07 2.3206 0.0118 2.6297 0.0115 13.32 -2.690.068 0.601 1.0472 0.9202 0.0135 2.40E-07 2.2091 0.0359 2.4356 0.0358 10.25 -0.250.168 0.701 1.0407 0.8508 0.0314 1.20E-07 2.0822 0.0818 2.2208 0.082 6.65 0.24

1 1 1 0.3333 0.3333 0.00E+00 0.9606 0.9606 0.8745 0.8745 -8.97 -8.97

235


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.001 0.489 1.5776 0.9983 0.0001 1.30E-03 2.6793 0.0003 2.1208 0.0003 -20.85 -5.860.002 0.526 1.5223 0.9957 0.0004 2.30E-05 2.6164 0.0008 2.0422 0.0008 -21.95 -3.110.004 0.551 1.4888 0.9929 0.0007 -6.10E-06 2.5732 0.0014 2.0075 0.0014 -21.98 -1.10.005 0.563 1.4723 0.9911 0.0009 -1.20E-07 2.5514 0.0018 1.9987 0.0018 -21.66 0.540.006 0.575 1.4561 0.9889 0.0012 1.80E-07 2.5292 0.0024 1.9823 0.0023 -21.62 -2.670.008 0.588 1.44 0.9863 0.0015 3.00E-07 2.5067 0.003 1.9669 0.003 -21.53 -0.740.011 0.6 1.4243 0.9834 0.0019 3.60E-07 2.4839 0.0038 1.9497 0.0038 -21.5 -1.260.013 0.612 1.4087 0.9799 0.0024 0.00E+00 2.4609 0.0048 1.9329 0.0047 -21.46 -2.480.017 0.625 1.3934 0.9761 0.0029 -1.80E-07 2.4377 0.0059 1.9163 0.0058 -21.39 -2.050.021 0.637 1.3783 0.9717 0.0036 0.00E+00 2.4139 0.0072 1.8984 0.0071 -21.35 -1.80.031 0.662 1.3486 0.9614 0.0053 3.00E-07 2.3655 0.0106 1.861 0.0103 -21.33 -2.520.038 0.674 1.3341 0.9553 0.0064 -6.00E-08 2.3407 0.0127 1.8415 0.0124 -21.33 -2.730.046 0.686 1.3197 0.9487 0.0076 -1.20E-07 2.3154 0.0151 1.8213 0.0147 -21.34 -2.840.055 0.698 1.3056 0.9415 0.0091 -3.60E-07 2.2898 0.0178 1.8005 0.0173 -21.37 -2.720.065 0.711 1.2916 0.9335 0.0107 1.20E-07 2.2637 0.0209 1.779 0.0203 -21.41 -2.760.076 0.723 1.2778 0.925 0.0125 1.20E-07 2.237 0.0245 1.7568 0.0237 -21.47 -3.150.089 0.735 1.2641 0.9157 0.0146 0.00E+00 2.2098 0.0285 1.7338 0.0276 -21.54 -3.260.12 0.76 1.2373 0.8949 0.0195 -1.80E-07 2.1533 0.0382 1.6853 0.0367 -21.73 -3.81

0.138 0.772 1.2241 0.8833 0.0224 0.00E+00 2.1241 0.044 1.6597 0.0422 -21.86 -4.140.158 0.785 1.2111 0.871 0.0257 1.80E-07 2.0941 0.0505 1.6331 0.0483 -22.02 -4.440.18 0.797 1.1982 0.8578 0.0294 1.80E-07 2.0632 0.0578 1.6054 0.055 -22.19 -4.76

0.232 0.822 1.1728 0.8287 0.0381 0.00E+00 1.9986 0.0751 1.5465 0.0711 -22.62 -5.350.294 0.846 1.1478 0.7957 0.0489 6.00E-08 1.9292 0.0972 1.482 0.0911 -23.18 -6.310.367 0.871 1.1231 0.758 0.0625 6.00E-08 1.8537 0.1251 1.4106 0.1162 -23.9 -7.090.454 0.896 1.0988 0.7151 0.0796 6.00E-08 1.7701 0.1608 1.3307 0.1481 -24.82 -7.90.555 0.92 1.075 0.6655 0.1017 0.00E+00 1.6749 0.2083 1.2396 0.1894 -25.99 -9.09

1 1 1 0.3333 0.3333 0.00E+00 0.8558 0.8558 0.6265 0.6265 -26.79 -26.79

236


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.018 0.659 1.4729 0.9764 0.0029 -6.00E-08 0.9751 0.0033 0.6707 0.002 -31.22 -39.720.033 0.695 1.4168 0.9614 0.0053 -3.00E-07 0.9451 0.0057 0.651 0.0036 -31.12 -36.710.055 0.728 1.3691 0.9429 0.0088 1.80E-07 0.9178 0.0092 0.6312 0.0059 -31.22 -36.240.088 0.762 1.3222 0.919 0.0138 1.80E-07 0.8893 0.0142 0.6093 0.0092 -31.49 -35.490.135 0.796 1.2755 0.8884 0.0211 -6.00E-08 0.8592 0.0213 0.5845 0.0139 -31.98 -34.720.288 0.863 1.182 0.8026 0.0465 1.80E-07 0.787 0.045 0.5231 0.0303 -33.54 -32.590.342 0.88 1.1588 0.7747 0.0563 -2.40E-07 0.7655 0.0537 0.5044 0.0366 -34.11 -31.760.404 0.896 1.1357 0.7436 0.068 6.00E-08 0.7418 0.0641 0.4839 0.0443 -34.76 -30.930.555 0.93 1.09 0.6692 0.0999 -1.20E-07 0.6891 0.0918 0.436 0.0651 -36.73 -29.090.644 0.947 1.0678 0.6241 0.1221 -6.00E-08 0.6584 0.1115 0.4071 0.0796 -38.16 -28.580.745 0.964 1.0456 0.5706 0.1514 -2.10E-07 0.6185 0.1384 0.3729 0.099 -39.7 -28.49

1 1 1 0.3333 0.3333 0.00E+00 0.3645 0.3645 0.2191 0.2191 -39.88 -39.88


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.021 0.647 1.3995 0.9715 0.0036 -1.80E-07 0.8061 0.0021 0.6334 0.0024 -21.42 13.240.045 0.694 1.3397 0.9495 0.0075 3.00E-07 0.7728 0.0043 0.6086 0.0048 -21.24 11.840.079 0.734 1.2911 0.9236 0.0128 2.40E-07 0.7449 0.0075 0.5852 0.0081 -21.43 8.010.129 0.773 1.2429 0.8897 0.0208 0.00E+00 0.7148 0.0118 0.5586 0.0131 -21.85 10.780.162 0.793 1.2198 0.8696 0.0261 -1.80E-07 0.6987 0.014 0.5441 0.0163 -22.13 16.710.247 0.832 1.1729 0.8212 0.0404 -3.60E-07 0.6643 0.0215 0.5112 0.0252 -23.04 17.10.429 0.891 1.1085 0.7279 0.0743 1.20E-07 0.6105 0.0419 0.4521 0.0461 -25.95 10.090.601 0.93 1.0652 0.643 0.1126 -6.00E-08 0.5525 0.0699 0.4 0.07 -27.61 0.180.702 0.95 1.045 0.5911 0.1398 3.00E-08 0.5181 0.0914 0.3684 0.0871 -28.9 -4.690.818 0.97 1.024 0.5252 0.1792 1.20E-07 0.4762 0.1182 0.3281 0.1119 -31.1 -5.32

1 1 1 0.3333 0.3333 0.00E+00 0.2934 0.2934 0.2091 0.2091 -28.73 -28.73

237


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.013 0.659 1.5434 0.982 0.0021 1.80E-07 1.4632 0.0024 1.0832 0.0023 -25.97 -4.470.022 0.688 1.4914 0.9719 0.0036 1.80E-07 1.433 0.0041 1.0585 0.0039 -26.13 -4.650.044 0.727 1.4231 0.9527 0.0069 1.20E-07 1.3911 0.0078 1.0218 0.0074 -26.55 -5.310.08 0.766 1.3567 0.9256 0.0124 0.00E+00 1.3443 0.0139 0.98 0.0131 -27.1 -5.93

0.173 0.825 1.2611 0.8665 0.027 1.80E-07 1.2654 0.0304 0.9049 0.0282 -28.49 -7.380.272 0.864 1.2 0.812 0.0434 1.20E-07 1.2004 0.0492 0.8436 0.0451 -29.73 -8.290.336 0.883 1.1701 0.779 0.0547 1.80E-07 1.1651 0.0621 0.8082 0.0568 -30.63 -8.550.498 0.922 1.1116 0.6984 0.0867 1.20E-07 1.0774 0.0989 0.7245 0.09 -32.75 -9.020.716 0.961 1.0547 0.5876 0.1417 -2.40E-07 0.9547 0.1682 0.6115 0.1475 -35.94 -12.310.78 0.971 1.0399 0.553 0.1634 -1.10E-03 0.9108 0.1954 0.5725 0.1692 -37.15 -13.42

0.849 0.981 1.0263 0.5105 0.1906 -6.20E-04 0.8592 0.2313 0.529 0.1975 -38.43 -14.621 1 1 0.3333 0.3333 0.00E+00 0.5303 0.5303 0.3492 0.3492 -34.16 -34.16


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.016 0.681 1.5533 0.9789 0.0025 -1.20E-07 0.998 0.0022 0.8574 0.0022 -14.09 0.510.035 0.723 1.4672 0.9605 0.0055 -5.40E-07 0.9698 0.0048 0.8262 0.0047 -14.81 -1.480.067 0.762 1.3913 0.935 0.0104 1.80E-07 0.9384 0.0089 0.7929 0.0088 -15.51 -1.340.119 0.801 1.3193 0.8999 0.0183 -4.20E-07 0.8986 0.0156 0.7545 0.0153 -16.03 -1.820.197 0.839 1.2512 0.8535 0.0307 -6.00E-08 0.8576 0.026 0.7099 0.0255 -17.22 -1.930.309 0.878 1.1868 0.7934 0.0497 3.00E-07 0.8109 0.0422 0.6571 0.0411 -18.97 -2.520.38 0.897 1.1558 0.7572 0.0628 2.40E-07 0.7835 0.0538 0.6266 0.0519 -20.03 -3.47

0.561 0.936 1.0955 0.6677 0.1006 6.00E-08 0.717 0.0888 0.553 0.0833 -22.87 -6.140.673 0.955 1.0665 0.611 0.129 -8.90E-08 0.6719 0.1157 0.5069 0.107 -24.56 -7.510.802 0.975 1.0362 0.5415 0.1715 -1.50E-03 0.6166 0.1538 0.4456 0.1411 -27.73 -8.26

1 1 1 0.3333 0.3333 0.00E+00 0.3733 0.3733 0.2786 0.2786 -25.37 -25.37

238


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.02 0.69 1.5247 0.9747 0.0032 0.00E+00 0.7636 0.0022 0.6508 0.0021 -14.77 -4.26

0.022 0.695 1.5146 0.9727 0.0035 -1.80E-07 0.7609 0.0023 0.6481 0.0023 -14.83 0.240.031 0.714 1.4741 0.9638 0.0049 2.40E-07 0.75 0.0033 0.6368 0.0032 -15.09 -1.560.044 0.732 1.4348 0.953 0.0068 1.80E-07 0.7386 0.0046 0.6249 0.0045 -15.4 -2.530.06 0.751 1.397 0.9402 0.0093 -2.40E-07 0.7266 0.0063 0.6122 0.0061 -15.75 -3.73

0.081 0.77 1.3603 0.925 0.0125 -5.40E-07 0.7142 0.0084 0.5986 0.0081 -16.19 -3.90.106 0.788 1.325 0.9076 0.0164 -1.80E-07 0.7002 0.011 0.5841 0.0106 -16.59 -3.820.138 0.807 1.291 0.8876 0.0214 3.00E-07 0.6856 0.0143 0.5686 0.0137 -17.07 -4.310.176 0.826 1.2582 0.8648 0.0274 -1.20E-07 0.67 0.0184 0.5519 0.0175 -17.62 -4.880.221 0.844 1.2267 0.8393 0.0348 -5.40E-07 0.6529 0.0234 0.5341 0.0222 -18.2 -5.280.274 0.863 1.1963 0.8106 0.0439 0.00E+00 0.6347 0.0293 0.5147 0.0279 -18.9 -4.90.336 0.881 1.167 0.7785 0.0549 -6.00E-08 0.615 0.0367 0.4937 0.0348 -19.72 -5.120.408 0.9 1.1387 0.7425 0.0685 0.00E+00 0.5937 0.0459 0.4706 0.0434 -20.73 -5.460.489 0.919 1.1116 0.702 0.0852 -6.00E-08 0.5698 0.0578 0.4451 0.054 -21.88 -6.580.583 0.937 1.0852 0.6558 0.1063 -6.00E-08 0.5433 0.0731 0.4162 0.0675 -23.39 -7.70.689 0.956 1.0596 0.6017 0.134 0.00E+00 0.5111 0.0939 0.3826 0.0852 -25.15 -9.280.808 0.974 1.0336 0.5372 0.174 -1.30E-03 0.4701 0.1226 0.339 0.1098 -27.88 -10.46

1 1 1 0.3333 0.3333 0.00E+00 0.284 0.284 0.2134 0.2134 -24.85 -24.85

239


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.001159 0.523 1.6033 0.9973 0.0002 1.90E-03 3.3965 0.0006 2.5517 0.0006 -24.87 -0.380.001478 0.532 1.5898 0.9967 0.0003 -5.30E-04 3.3857 0.0007 2.4997 0.0007 -26.17 -0.46

0.002 0.549 1.5637 0.9952 0.0004 1.40E-04 3.3622 0.0011 2.4937 0.0011 -25.83 -0.560.003 0.558 1.5508 0.9942 0.0005 -5.50E-06 3.3496 0.0014 2.4824 0.0013 -25.89 -0.620.004 0.566 1.5381 0.9931 0.0007 3.60E-07 3.3365 0.0017 2.4728 0.0016 -25.89 -0.690.004 0.575 1.5255 0.9919 0.0008 0.00E+00 3.3229 0.002 2.4616 0.002 -25.92 -0.760.006 0.592 1.5007 0.989 0.0012 3.60E-07 3.2945 0.0029 2.4373 0.0028 -26.02 -0.920.009 0.609 1.4763 0.9853 0.0016 -2.40E-07 3.2526 0.004 2.4087 0.004 -25.95 -1.090.011 0.618 1.4643 0.9832 0.0019 -1.20E-07 3.2482 0.0047 2.3951 0.0047 -26.27 -1.170.015 0.635 1.4405 0.9782 0.0026 2.40E-07 3.2153 0.0064 2.3657 0.0063 -26.43 -1.360.021 0.652 1.4171 0.9723 0.0035 -6.60E-07 3.181 0.0086 2.3349 0.0085 -26.6 -1.570.028 0.669 1.3941 0.9654 0.0047 -3.00E-07 3.1432 0.0113 2.3032 0.0111 -26.73 -1.790.037 0.686 1.3714 0.9573 0.0061 2.40E-07 3.1063 0.0147 2.2697 0.0144 -26.93 -2.020.048 0.704 1.3491 0.948 0.0078 -3.00E-07 3.0651 0.0188 2.2347 0.0183 -27.09 -2.270.061 0.721 1.3271 0.9374 0.0099 -1.20E-07 3.0234 0.0238 2.1979 0.0232 -27.3 -2.530.096 0.755 1.284 0.9119 0.0154 6.00E-08 2.9308 0.037 2.1185 0.0359 -27.71 -3.110.119 0.772 1.2629 0.8968 0.019 1.80E-07 2.8821 0.0456 2.0755 0.0441 -27.99 -3.420.146 0.789 1.242 0.8801 0.0233 -2.40E-07 2.8307 0.0558 2.0301 0.0537 -28.28 -3.750.176 0.807 1.2214 0.8616 0.0283 6.00E-08 2.7755 0.0679 1.9819 0.0651 -28.59 -4.1

0.3 0.858 1.1612 0.7943 0.0494 -1.20E-07 2.5866 0.1193 1.8172 0.113 -29.75 -5.340.353 0.875 1.1415 0.7672 0.059 -1.20E-07 2.5151 0.1434 1.7539 0.135 -30.27 -5.860.413 0.892 1.1221 0.7373 0.0705 1.80E-07 2.4357 0.1723 1.6851 0.1612 -30.82 -6.450.481 0.909 1.1028 0.704 0.0843 0.00E+00 2.3481 0.2075 1.6096 0.1927 -31.45 -7.140.557 0.927 1.0835 0.6668 0.1011 -1.20E-07 2.251 0.2514 1.5255 0.2313 -32.23 -8.010.642 0.944 1.0643 0.6242 0.122 6.00E-08 2.1391 0.308 1.43 0.2796 -33.15 -9.230.737 0.961 1.045 0.5741 0.1494 0.00E+00 2.0054 0.3847 1.3175 0.3429 -34.3 -10.86

1 1 1 0.3333 0.3333 0.00E+00 1.0931 1.0931 0.7696 0.7696 -29.6 -29.6

240


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.021 0.623 1.3484 0.9717 0.0036 6.00E-08 1.462 0.0052 1.3814 0.0052 -5.51 -0.760.032 0.651 1.3162 0.9598 0.0056 -1.20E-07 1.4518 0.008 1.3507 0.0079 -6.96 -0.860.049 0.678 1.2874 0.9455 0.0083 -3.60E-07 1.422 0.0116 1.3186 0.0115 -7.27 -0.240.081 0.717 1.2498 0.9203 0.0135 -1.20E-07 1.3751 0.019 1.27 0.0187 -7.64 -1.610.162 0.78 1.1943 0.8674 0.0267 -1.20E-07 1.2898 0.0377 1.1829 0.0365 -8.29 -3.410.324 0.852 1.1281 0.7786 0.0549 -3.00E-07 1.1735 0.0776 1.0549 0.0743 -10.1 -4.270.406 0.88 1.1078 0.7384 0.0701 -1.20E-07 1.1248 0.0997 0.9999 0.0949 -11.1 -4.860.487 0.903 1.0898 0.6991 0.0865 -6.00E-08 1.0763 0.1241 0.947 0.1171 -12.02 -5.640.568 0.923 1.0719 0.6593 0.1046 1.20E-07 1.0353 0.1508 0.8939 0.1418 -13.65 -5.950.649 0.941 1.0564 0.619 0.1248 0.00E+00 0.9925 0.181 0.8403 0.1694 -15.34 -6.40.811 0.972 1.0285 0.5334 0.1764 -1.30E-03 0.8893 0.2569 0.7191 0.2378 -19.14 -7.43

1 1.002 1 0.3333 0.3333 0.00E+00 0.5529 0.5525 0.4551 0.4551 -17.7 -17.63


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.02 0.599 1.2951 0.9716 0.0036 -3.00E-07 1.2649 0.0046 1.2333 0.0046 -2.5 -0.62

0.031 0.628 1.2699 0.9599 0.0056 -5.40E-07 1.239 0.0071 1.206 0.007 -2.66 -1.210.054 0.667 1.2373 0.9394 0.0095 -1.20E-07 1.2026 0.0119 1.1664 0.0117 -3.01 -1.60.088 0.706 1.2053 0.9132 0.0151 -3.00E-07 1.1418 0.019 1.1228 0.0186 -1.66 -1.990.136 0.745 1.1754 0.8811 0.023 1.80E-07 1.1213 0.0206 1.0753 0.0281 -4.1 36.58

0.2 0.785 1.147 0.8427 0.0338 -1.80E-07 1.0776 0.0416 1.0232 0.041 -5.05 -1.320.278 0.824 1.1251 0.8006 0.0472 -1.20E-07 1.0278 0.0601 0.9691 0.0572 -5.71 -4.870.391 0.863 1.0922 0.7427 0.0684 -1.20E-07 0.9734 0.0851 0.8979 0.0827 -7.75 -2.810.523 0.902 1.0663 0.6781 0.0958 0.00E+00 0.9112 0.1184 0.8205 0.1159 -9.95 -2.10.684 0.942 1.041 0.5981 0.1359 2.40E-07 0.8305 0.1681 0.7255 0.1649 -12.65 -1.94

1 1 1 0.3333 0.3333 0.00E+00 0.5092 0.5092 0.4071 0.4071 -20.05 -20.05

241


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.001 0.452 1.3565 0.9968 0.0003 1.10E-03 2.4091 0.0007 2.4381 0.0007 1.2 -0.390.006 0.517 1.3023 0.9885 0.0012 1.80E-07 2.3198 0.0029 2.3381 0.0029 0.79 -0.030.02 0.581 1.254 0.9712 0.0037 -3.00E-07 2.2268 0.0086 2.2389 0.0085 0.54 -0.260.02 0.583 1.2531 0.9707 0.0038 7.20E-07 2.2256 0.0087 2.2369 0.0087 0.51 -0.240.05 0.646 1.2094 0.9418 0.009 4.80E-07 2.1275 0.0204 2.1271 0.0203 -0.02 -0.41

0.107 0.711 1.168 0.8988 0.0186 0.00E+00 2.0189 0.0415 2.0002 0.0413 -0.93 -0.550.201 0.775 1.1289 0.8404 0.0345 2.40E-07 1.8984 0.0766 1.8535 0.0761 -2.36 -0.660.344 0.84 1.0914 0.7642 0.0601 0.00E+00 1.7586 0.1332 1.6792 0.1321 -4.52 -0.810.489 0.905 1.0903 0.6983 0.0868 -2.40E-07 1.5844 0.2274 1.5345 0.1907 -3.15 -16.13

1 1 1 0.3333 0.3333 0.00E+00 0.8322 0.8322 0.7397 0.7397 -11.11 -11.11



0.001 0.479 1.4488 0.997 0.0003 1.10E-03 1.2331 0.0003 1.3094 0.0003 6.19 -0.20.007 0.548 1.3715 0.9881 0.0013 0.00E+00 1.1798 0.0016 1.2577 0.0016 6.6 0.230.013 0.582 1.3379 0.9798 0.0024 0.00E+00 1.154 0.003 1.2298 0.003 6.56 0.430.039 0.65 1.2759 0.9533 0.0068 -1.80E-07 1.1004 0.0082 1.1676 0.0083 6.11 1.390.062 0.685 1.2457 0.9339 0.0106 -6.00E-08 1.0711 0.0126 1.1326 0.0128 5.74 2.140.138 0.753 1.187 0.8809 0.0231 0.00E+00 1.0055 0.0264 1.0526 0.0276 4.68 4.580.195 0.787 1.1588 0.8464 0.0327 1.80E-07 0.971 0.0366 1.0067 0.0389 3.67 6.230.36 0.856 1.1045 0.7587 0.0622 6.00E-08 0.8923 0.0664 0.8984 0.0736 0.68 10.93

0.472 0.89 1.0785 0.7033 0.0846 -2.40E-07 0.845 0.0878 0.8329 0.1002 -1.43 14.170.607 0.924 1.0532 0.6369 0.1156 -6.00E-08 0.7911 0.1159 0.7555 0.1371 -4.5 18.260.768 0.959 1.0287 0.5531 0.1618 0.00E+00 0.7277 0.1559 0.658 0.1925 -9.58 23.47

1 1 1 0.3333 0.3333 0.00E+00 0.4609 0.4607 0.3986 0.3986 -13.52 -13.46

242


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.027 0.653 1.3634 0.9658 0.0046 4.20E-07 1.3779 0.0062 1.2349 0.0059 -10.38 -5.490.036 0.672 1.3412 0.9572 0.0061 -2.40E-07 1.3574 0.0082 1.2158 0.0077 -10.43 -5.930.044 0.685 1.325 0.9499 0.0074 6.00E-08 1.3418 0.01 1.201 0.0094 -10.49 -6.240.054 0.699 1.3091 0.9418 0.009 -6.00E-08 1.3261 0.012 1.1856 0.0113 -10.59 -5.760.066 0.713 1.2933 0.9329 0.0108 -1.20E-07 1.3097 0.0146 1.1697 0.0135 -10.69 -7.230.079 0.727 1.2777 0.9231 0.0129 -6.00E-08 1.2931 0.0178 1.1531 0.0161 -10.83 -9.450.094 0.741 1.2622 0.9124 0.0153 -6.00E-08 1.2745 0.0215 1.1358 0.0191 -10.88 -11.30.113 0.755 1.2423 0.8992 0.0184 1.80E-07 1.2561 0.0252 1.1156 0.0229 -11.19 -9.20.119 0.76 1.2372 0.895 0.0195 3.00E-07 1.2503 0.0265 1.1094 0.0241 -11.27 -8.920.148 0.778 1.217 0.8772 0.0241 1.20E-07 1.2239 0.032 1.0835 0.0297 -11.47 -7.130.163 0.788 1.2071 0.8676 0.0267 0.00E+00 1.2111 0.0348 1.0701 0.0329 -11.65 -5.510.178 0.797 1.2009 0.8591 0.029 6.00E-07 1.1976 0.0378 1.0583 0.0358 -11.63 -5.340.219 0.815 1.1781 0.8359 0.0359 6.00E-08 1.1694 0.0444 1.0272 0.0441 -12.16 -0.740.312 0.853 1.141 0.7863 0.0521 1.80E-07 1.1098 0.0655 0.9636 0.0639 -13.18 -2.450.325 0.857 1.1365 0.7795 0.0546 -1.20E-07 1.1011 0.0686 0.955 0.0669 -13.27 -2.550.339 0.862 1.1321 0.7725 0.0571 3.00E-07 1.0933 0.0721 0.9463 0.0699 -13.45 -30.356 0.867 1.1249 0.7634 0.0604 -6.00E-08 1.0855 0.0753 0.935 0.074 -13.86 -1.720.396 0.878 1.1125 0.7436 0.068 0.00E+00 1.064 0.0847 0.9106 0.0833 -14.42 -1.680.438 0.89 1.1003 0.7225 0.0765 4.20E-07 1.0416 0.0945 0.8848 0.0937 -15.05 -0.860.533 0.913 1.0768 0.676 0.0968 0.00E+00 0.992 0.1206 0.8285 0.1186 -16.48 -1.670.584 0.925 1.0655 0.6504 0.1089 -2.40E-07 0.9637 0.1378 0.7977 0.1335 -17.23 -3.090.639 0.936 1.0548 0.623 0.1227 -6.00E-08 0.9326 0.1585 0.7647 0.1505 -18 -5.020.696 0.948 1.0445 0.5936 0.1384 -2.10E-07 0.8974 0.1835 0.7293 0.1701 -18.73 -7.330.756 0.959 1.035 0.5617 0.1567 -6.00E-08 0.8576 0.214 0.691 0.1927 -19.43 -9.950.817 0.971 1.0258 0.5278 0.1788 -5.90E-04 0.8108 0.251 0.6468 0.2191 -20.23 -12.720.879 0.983 1.0182 0.488 0.2054 -3.00E-04 0.7474 0.2993 0.5989 0.252 -19.87 -15.8

1 1 1 0.3333 0.3333 0.00E+00 0.5048 0.5048 0.4123 0.4123 -18.32 -18.32

243


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.025 0.665 1.4057 0.9679 0.0042 -1.20E-07 0.596 0.0022 0.5089 0.0022 -14.61 1.250.035 0.685 1.3784 0.9589 0.0058 -5.40E-07 0.5862 0.003 0.5005 0.003 -14.61 0.410.103 0.76 1.2769 0.9074 0.0165 1.20E-07 0.5459 0.0086 0.4631 0.0084 -15.18 -2.240.13 0.779 1.253 0.89 0.0207 -1.20E-07 0.5352 0.0108 0.4523 0.0105 -15.49 -2.37

0.161 0.798 1.2297 0.8705 0.0259 -1.80E-07 0.5236 0.0135 0.4409 0.0131 -15.8 -2.930.242 0.835 1.1844 0.8247 0.0393 1.80E-07 0.4992 0.0206 0.4156 0.0198 -16.74 -3.770.35 0.873 1.1405 0.7684 0.0586 1.20E-07 0.4717 0.0306 0.3863 0.0295 -18.1 -3.73

0.416 0.892 1.1191 0.7354 0.0713 0.00E+00 0.4567 0.03 0.3697 0.0358 -19.06 19.380.577 0.93 1.0771 0.6567 0.1059 2.40E-07 0.4207 0.0554 0.3305 0.0533 -21.44 -3.820.78 0.967 1.0357 0.5495 0.164 1.80E-07 0.3699 0.0876 0.2776 0.0828 -24.96 -5.44

0.839 0.977 1.0249 0.5153 0.1871 -5.60E-04 0.3526 0.1005 0.2591 0.0941 -26.52 -6.411 1 1 0.3333 0.3333 0.00E+00 0.2214 0.2214 0.1692 0.1692 -23.56 -23.56


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.03 0.682 1.4056 0.9635 0.005 -1.80E-07 0.4868 0.0021 0.4118 0.0021 -15.42 1.02

0.072 0.738 1.3239 0.9296 0.0115 -2.40E-07 0.4614 0.0049 0.3897 0.0048 -15.53 -1.560.145 0.793 1.2507 0.881 0.0231 1.20E-07 0.4349 0.0099 0.3646 0.0095 -16.16 -3.580.218 0.83 1.2045 0.8386 0.0351 2.40E-07 0.4153 0.0151 0.3452 0.0144 -16.89 -4.450.316 0.867 1.16 0.7865 0.0521 6.00E-08 0.3938 0.0225 0.3227 0.0214 -18.04 -5.050.377 0.885 1.1379 0.756 0.0632 0.00E+00 0.3816 0.0273 0.31 0.0259 -18.76 -50.614 0.94 1.0725 0.6389 0.1146 1.20E-07 0.3362 0.0503 0.2625 0.0471 -21.93 -6.440.715 0.958 1.0507 0.5866 0.1423 -1.20E-07 0.3167 0.063 0.2414 0.0586 -23.77 -7.050.83 0.976 1.0279 0.5228 0.183 -9.70E-04 0.29 0.0817 0.2137 0.0748 -26.31 -8.46

0.893 0.986 1.0173 0.4793 0.2117 -2.90E-04 0.2726 0.0955 0.1968 0.087 -27.79 -8.941 1 1 0.3333 0.3333 0.00E+00 0.1812 0.1812 0.1381 0.1381 -23.8 -23.8

244

Table C3.42: Densities Prediction for Methyl n-Butyrate.

Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.029 0.678 1.4057 0.9645 0.0048 0.00E+00 0.4911 0.0022 0.4219 0.0021 -14.1 -4.630.048 0.709 1.3599 0.948 0.0078 1.80E-07 0.4777 0.0035 0.41 0.0034 -14.17 -3.830.102 0.763 1.2864 0.9086 0.0162 -6.00E-08 0.4532 0.0071 0.3869 0.0069 -14.62 -2.790.157 0.799 1.2402 0.8736 0.025 -4.20E-07 0.4353 0.011 0.3693 0.0106 -15.16 -3.780.233 0.835 1.1958 0.8305 0.0375 -1.20E-07 0.4156 0.0165 0.3494 0.0158 -15.94 -4.310.334 0.871 1.1525 0.7777 0.0552 -1.20E-07 0.3941 0.0243 0.3263 0.0232 -17.21 -4.670.395 0.889 1.1312 0.7469 0.0667 6.00E-08 0.3821 0.0295 0.3132 0.028 -18.03 -5.120.545 0.926 1.0887 0.6732 0.0981 -6.00E-08 0.3529 0.0437 0.2826 0.0412 -19.93 -5.810.635 0.944 1.0677 0.6284 0.1199 1.80E-07 0.3365 0.0532 0.2641 0.0504 -21.51 -5.30.736 0.962 1.0465 0.5752 0.1488 1.20E-07 0.3158 0.0667 0.2422 0.0626 -23.31 -6.08

1 1 1 0.3333 0.3333 0.00E+00 0.1835 0.1835 0.1412 0.1412 -23.05 -23.05

Table C3.43: Densities Prediction for Methyl i-Butirate.

Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.029 0.676 1.398 0.9641 0.0049 3.00E-07 0.4914 0.0022 0.4272 0.0022 -13.06 -1.860.049 0.709 1.3522 0.9467 0.008 -1.80E-07 0.4777 0.0036 0.4147 0.0035 -13.19 -2.430.106 0.764 1.2777 0.9056 0.0169 3.00E-07 0.4521 0.0075 0.3905 0.0073 -13.62 -2.730.133 0.783 1.2541 0.8882 0.0212 1.20E-07 0.443 0.0094 0.3816 0.0091 -13.87 -3.160.201 0.82 1.2087 0.8475 0.0324 -3.60E-07 0.4238 0.0143 0.3619 0.0138 -14.61 -3.320.294 0.857 1.1651 0.7977 0.0482 -3.60E-07 0.403 0.0213 0.3394 0.0205 -15.78 -3.710.351 0.875 1.1436 0.7686 0.0585 -1.20E-07 0.3919 0.0258 0.3268 0.0249 -16.62 -3.590.416 0.894 1.1225 0.7363 0.0709 0.00E+00 0.379 0.0314 0.3129 0.0301 -17.43 -4.040.573 0.931 1.0805 0.659 0.1048 6.00E-08 0.3478 0.0472 0.2804 0.0446 -19.38 -5.540.668 0.949 1.0595 0.6112 0.1289 1.80E-07 0.3292 0.0588 0.2605 0.0549 -20.88 -6.590.774 0.968 1.0387 0.5537 0.1615 -6.00E-08 0.3069 0.0744 0.2365 0.069 -22.95 -7.32

1 1 1 0.3333 0.3333 0.00E+00 0.1841 0.1841 0.1431 0.1431 -22.27 -22.27

245


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.022 0.652 1.4091 0.9715 0.0036 4.20E-07 0.745 0.0024 0.6317 0.0024 -15.21 -1.230.033 0.677 1.3736 0.9604 0.0055 -1.20E-07 0.73 0.0035 0.6184 0.0035 -15.28 1.350.045 0.697 1.3469 0.9499 0.0074 3.00E-07 0.7179 0.0047 0.6074 0.0047 -15.39 0.930.13 0.776 1.2471 0.8896 0.0208 -1.80E-07 0.6652 0.0132 0.5571 0.013 -16.26 -1.17

0.162 0.795 1.2236 0.8694 0.0262 1.80E-07 0.6502 0.0166 0.5425 0.0163 -16.57 -1.630.247 0.835 1.1781 0.8217 0.0403 6.00E-08 0.6185 0.0255 0.5102 0.025 -17.51 -1.930.431 0.894 1.1124 0.7279 0.0743 6.00E-08 0.5622 0.0479 0.4508 0.046 -19.81 -3.930.601 0.934 1.07 0.644 0.112 -1.20E-07 0.5141 0.073 0.3995 0.0695 -22.28 -4.780.703 0.953 1.0493 0.5918 0.1394 1.80E-07 0.4838 0.0919 0.3678 0.0866 -23.98 -5.720.819 0.973 1.0273 0.5285 0.1794 -1.10E-03 0.445 0.1193 0.3262 0.1107 -26.7 -7.21

1 1 1 0.3333 0.3333 0.00E+00 0.2741 0.2741 0.2085 0.2085 -23.92 -23.92

Table C3.45: Densities Prediction for Ethyl Acetate

Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.026 0.67 1.4074 0.967 0.0044 1.20E-07 0.5869 0.0023 0.4949 0.0022 -15.67 -2.360.04 0.694 1.3725 0.9551 0.0065 -4.20E-07 0.5748 0.0033 0.4844 0.0033 -15.72 -0.710.07 0.732 1.3195 0.931 0.0112 -6.00E-08 0.5549 0.0057 0.4665 0.0056 -15.94 -1.60.09 0.751 1.2938 0.9163 0.0144 -6.00E-08 0.5444 0.0073 0.4567 0.0072 -16.11 -1.52

0.144 0.79 1.2445 0.8809 0.0231 -6.00E-08 0.5228 0.0117 0.4354 0.0114 -16.72 -2.420.221 0.828 1.1973 0.8366 0.0357 6.00E-08 0.4983 0.0183 0.4111 0.0175 -17.49 -4.210.325 0.866 1.1516 0.7817 0.0538 1.80E-07 0.4714 0.0275 0.383 0.0264 -18.75 -4.170.388 0.885 1.1295 0.7496 0.0657 -6.00E-08 0.4564 0.0337 0.3671 0.0322 -19.57 -4.540.545 0.923 1.0856 0.6726 0.0983 -6.00E-08 0.4212 0.0505 0.3297 0.0482 -21.73 -4.550.639 0.942 1.064 0.6256 0.1214 -2.40E-07 0.4002 0.0631 0.307 0.0596 -23.28 -5.610.745 0.962 1.0427 0.5696 0.152 -3.00E-08 0.3742 0.0801 0.2801 0.0748 -25.14 -6.67

1 1 1 0.3333 0.3333 0.00E+00 0.218 0.218 0.1649 0.1649 -24.36 -24.36

246

Table C3.46: Densities Prediction for Propyl Acetate


0.039 0.698 1.3836 0.9557 0.0063 -6.00E-08 0.4786 0.0027 0.4022 0.0027 -15.96 -1.230.052 0.716 1.3567 0.9451 0.0083 -1.80E-07 0.4708 0.0035 0.3952 0.0035 -16.05 -0.40.068 0.734 1.3304 0.9328 0.0108 6.00E-08 0.4628 0.0045 0.3879 0.0045 -16.19 -0.060.087 0.752 1.3053 0.919 0.0138 -1.80E-07 0.4545 0.0058 0.3802 0.0057 -16.35 -1.510.11 0.77 1.2806 0.9033 0.0174 -3.00E-07 0.446 0.0073 0.372 0.0072 -16.58 -1.55

0.137 0.789 1.2563 0.8857 0.0218 -3.00E-07 0.437 0.0091 0.3634 0.009 -16.85 -1.550.17 0.807 1.2329 0.8662 0.027 -1.80E-07 0.4277 0.0113 0.3542 0.0111 -17.18 -2.11

0.208 0.825 1.2096 0.8444 0.0333 -1.80E-07 0.4178 0.0139 0.3444 0.0136 -17.57 -2.270.251 0.843 1.1871 0.8204 0.0407 6.00E-08 0.4075 0.017 0.334 0.0166 -18.05 -2.520.302 0.861 1.1647 0.7937 0.0496 -4.20E-07 0.3966 0.0207 0.3226 0.0202 -18.65 -2.650.36 0.88 1.1428 0.7641 0.0602 -1.80E-07 0.3851 0.0252 0.3104 0.0244 -19.4 -3.01

0.427 0.898 1.1209 0.7311 0.073 -6.00E-08 0.3721 0.0307 0.2969 0.0297 -20.21 -3.420.503 0.916 1.0992 0.6939 0.0887 -6.00E-08 0.3579 0.0376 0.2819 0.036 -21.23 -4.140.588 0.934 1.0776 0.6516 0.1083 1.80E-07 0.3414 0.0463 0.265 0.0441 -22.38 -4.860.685 0.952 1.0562 0.6024 0.1336 1.80E-07 0.3233 0.0574 0.2454 0.0544 -24.1 -5.20.794 0.971 1.0336 0.5443 0.1694 -1.40E-03 0.3 0.0737 0.2201 0.0685 -26.62 -7.04

1 1 1 0.3333 0.3333 0.00E+00 0.1807 0.1807 0.1367 0.1367 -24.33 -24.33

247


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.015 0.599 1.3487 0.9773 0.0028 6.00E-08 1.2328 0.0032 1.1082 0.0031 -10.11 -2.40.038 0.656 1.2944 0.9545 0.0066 0.00E+00 1.1808 0.0074 1.0605 0.0073 -10.19 -1.440.053 0.68 1.2724 0.9416 0.009 0.00E+00 1.1586 0.0101 1.0387 0.01 -10.35 -1.430.096 0.728 1.2294 0.9091 0.0161 -4.20E-07 1.1104 0.0179 0.9908 0.0175 -10.77 -2.080.126 0.752 1.208 0.8891 0.021 -1.80E-07 1.0856 0.0234 0.9645 0.0228 -11.16 -2.740.206 0.8 1.1671 0.8412 0.0343 1.80E-07 1.0288 0.0396 0.9063 0.0369 -11.9 -6.780.259 0.824 1.1456 0.812 0.0434 3.00E-07 1.0003 0.0482 0.873 0.0467 -12.73 -3.150.393 0.872 1.1054 0.7437 0.068 0.00E+00 0.9348 0.0742 0.7981 0.073 -14.63 -1.680.476 0.897 1.0855 0.7027 0.0849 -1.20E-07 0.8965 0.0927 0.7543 0.0911 -15.86 -1.730.683 0.945 1.0459 0.6002 0.1348 -3.60E-07 0.8 0.1484 0.6461 0.1451 -19.23 -2.240.807 0.969 1.0267 0.5319 0.1749 6.00E-08 0.732 0.1966 0.574 0.1887 -21.58 -4

1 1 1 0.3333 0.3333 0.00E+00 0.4365 0.4365 0.3613 0.3613 -17.22 -17.22


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.019 0.62 1.3526 0.9729 0.0034 1.20E-07 0.8767 0.0028 0.7771 0.0027 -11.36 -2.150.049 0.68 1.2885 0.9449 0.0084 -1.20E-07 0.8354 0.0067 0.7392 0.0066 -11.52 -2.140.087 0.724 1.2449 0.9159 0.0145 6.00E-08 0.8037 0.0116 0.7082 0.0112 -11.88 -3.290.144 0.767 1.2032 0.8786 0.0237 -1.80E-07 0.7701 0.0184 0.6735 0.0182 -12.54 -1.260.18 0.789 1.1828 0.8564 0.0298 -2.40E-07 0.7519 0.0228 0.6544 0.0228 -12.97 -0.12

0.275 0.832 1.1425 0.8039 0.0461 -1.20E-07 0.7132 0.0339 0.6117 0.0351 -14.23 3.450.401 0.876 1.1047 0.7399 0.0695 1.20E-07 0.6687 0.0503 0.5621 0.0528 -15.93 4.960.479 0.898 1.0857 0.7018 0.0853 -3.60E-07 0.6435 0.0619 0.5334 0.0648 -17.12 4.70.665 0.941 1.0492 0.6096 0.1297 1.50E-07 0.5825 0.0958 0.4645 0.0988 -20.26 3.150.777 0.963 1.0306 0.5492 0.1642 0.00E+00 0.5409 0.1239 0.4194 0.1253 -22.47 1.17

1 1 1 0.3333 0.3333 0.00E+00 0.3203 0.3203 0.2558 0.2558 -20.13 -20.13

248


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.019 0.624 1.3636 0.9732 0.0034 -1.20E-07 0.9787 0.0033 0.9018 0.0031 -7.86 -5.070.049 0.683 1.297 0.9456 0.0082 5.40E-07 0.9357 0.0075 0.8581 0.0075 -8.3 -0.270.095 0.733 1.2416 0.9105 0.0158 -2.40E-07 0.8957 0.0141 0.815 0.0141 -9 0.050.167 0.783 1.1923 0.8645 0.0275 6.00E-08 0.8526 0.0255 0.7668 0.0244 -10.07 -4.250.274 0.833 1.1442 0.8045 0.0459 6.00E-08 0.8038 0.0415 0.7098 0.0405 -11.69 -2.410.344 0.858 1.1207 0.7684 0.0586 -6.00E-08 0.7771 0.0522 0.6771 0.0516 -12.86 -1.070.425 0.883 1.0986 0.7281 0.0742 1.20E-07 0.7476 0.0656 0.6415 0.0654 -14.19 -0.330.627 0.933 1.0557 0.6287 0.1197 6.00E-08 0.6708 0.1098 0.5551 0.1057 -17.24 -3.730.75 0.958 1.0351 0.5645 0.155 8.90E-08 0.62 0.1436 0.4995 0.1372 -19.43 -4.47

0.817 0.97 1.0245 0.5271 0.1793 -6.40E-04 0.5895 0.1656 0.4645 0.158 -21.2 -4.580.89 0.983 1.0143 0.4789 0.2119 -2.80E-04 0.5475 0.1985 0.4227 0.1871 -22.79 -5.76

1 1 1 0.3333 0.3333 0.00E+00 0.3678 0.3678 0.2967 0.2967 -19.34 -19.34


Pr Tr Gam ZVC ZLC Fugr DLE DGE DLC DGC DEVL DEVG 0.023 0.641 1.3682 0.9695 0.004 -1.20E-07 0.7438 0.0031 0.6825 0.0028 -8.25 -9.830.037 0.67 1.3303 0.9561 0.0063 -1.80E-07 0.7272 0.0062 0.6658 0.0044 -8.45 -29.520.053 0.692 1.3001 0.9426 0.0088 -1.80E-07 0.7137 0.0083 0.6514 0.0061 -8.74 -26.570.166 0.784 1.1956 0.8653 0.0273 1.20E-07 0.6524 0.0197 0.5853 0.0185 -10.28 -6.230.263 0.829 1.1508 0.811 0.0437 0.00E+00 0.6191 0.0301 0.5459 0.0294 -11.83 -2.180.327 0.852 1.1263 0.7771 0.0554 0.00E+00 0.6015 0.0353 0.5223 0.0373 -13.16 5.530.399 0.875 1.1055 0.7412 0.069 1.20E-07 0.5817 0.0416 0.498 0.0463 -14.4 11.410.482 0.898 1.0846 0.7003 0.0859 1.20E-07 0.561 0.0519 0.4706 0.0578 -16.11 11.280.682 0.944 1.045 0.6003 0.1347 -8.90E-08 0.5059 0.0852 0.4046 0.0908 -20.02 6.56

0.8 0.966 1.0268 0.5361 0.1723 -1.80E-07 0.4675 0.1132 0.3622 0.1164 -22.53 2.81 1 1 0.3333 0.3333 0.00E+00 0.2826 0.2826 0.2262 0.2262 -19.95 -19.95

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prediction of coexistence vapor-liquid densities

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