Equation of State

Supercritical Fluid Extraction: A Study of Binary and Multicomponent Solid-Fluid Equilibria

by Ronald Ted Kurnik ~ B.S.Ch.E. Syracuse University (1976) M.S.Ch.E. Washington University (1977)

SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF SCIENCE at the MASSACHUSETTS INSTITUT.E OF TECHNOLOGY May, 1981

@Massachusetts Institute of Technology, 1981

Signature of Author Signature redacted ------""="------,------Department of Chemical Engineering May, 1981

Certified by Signature redacted Robert C. Reid i:cnesis Supervisor / Signature redacted Accepted by ARC~J\'ES (_ ;- . _ . . . = . _ . .. _ MASSACHUSEIT . Chairman, Departmental OFTECHN&&is7rrurE Committee on Graduate Students OCT 2 8 1981 UBRARlES SUPERCRITICAL FLUID EXTRACTION:

A STUDY OF BINARY AND

MULTICOMPONENT SOLID-FLUID

EQUILIBRIA

RONALD TED KURNIK

Submitted to the Department of Chemical Engineering on May 1981, in partial fulfillment of the requirements for the degree of Doctor of Science

ABSTRACT

Solid-fluid equilibrium data for binary and multicomponent systems were determined experimentally using two supercritical fluids -- carbon dioxide and ethylene, and six solid solutes. The data were taken for temperatures between the upper and lower critical end points and for pressures from 120 to 280 bar.

The existence of very large (106) enhancement (over the ideal gas value) of solubilities of the solutes in the fluid phase was.observed with these systems. In addition, it was found that the solubility of a species in a multicomponent mixture could be significantly greater (as much as 300 percent) than the solubility of that same pure species in the given supercritical fluid (at the same temperature and pressure).

Correlation of both pure and multicomponent solid-fluid equilibria was accomplished uiing the Peng-Ronbinson equation of state. In the case of multicomponent solid-fluid equilibrium it was necessary to introduce an additional binary solute-solute interaction coefficient.

The existence of a maximum in solubility of a solid in a supercritical fluid was observed both theoretically and experimentally. The reason for this maximum was explained. Energy effects in solid-fluid equilibria were studied and it was shown that in the retrograde solidification region that the partial molar enthalphy difference for the solute between the fluid and solid phase is exothermic.

Thesis Supervisor: Robert C. Reid

Title: Professor of Chemical Engineering Department of Chemical Engineering Massachusetts Institute of Technology Cambridge, Massachusetts 02139

May, 1981

Professor George C. Newton Secretary of the Faculty Massachusetts Institute of Technology Cambridge, Massachusetts 02139

Dear Professor Newton:

In accordance with the regulations of the Faculty I herewith submit a thesis entitled "Supercritical Fluid Extraction: A Study of Binary and Multicomponent Solid-Fluid Equilibria" in partial fulfillment of the requirements for the degree of Doctor of Science in Chemical Engineering at the Massachusetts Institute of Technology.

Respectfully submitted,

Ronald Ted Kurnik 5

ACKNOWLE DGEMENTS

The author gratefully acknowledges the support and

advice of Professor Robert C. Reid.

Many thanks are due to Dr. Val J. Krukonis for his

enthusiastic support of this work and for his help in the

experimental design of the equipment used in this thesis.

The help of Mike Mullins in constructing the equipment

is gratefully acknowledged.

Dr. Herb Britt, Dr. Joe Boston, Dr. Paul Mathias, Suphat

Watanasiri, and Fred Ziegler of the ASPEN project are

thanked for their many helpful discussions.

The members of my thesis committee, Professor Modell,

Professor Longwell, Professor Daniel I. C. Wang and Dr.

Charles Apt provided many helpful comments and suggestions.

Samuel Holla was helpful in obtaining some of the equilibrium data used in this thesis.

The Nestle's Company is gratefully acknowledged for their financial support in terms of a three year fellowship.

Financial support of the National Science Foundation is appreciated.

To my many friends at MIT, especially those in the LNG lab, thanks for good advice, endless encouragement, and many fun filled hours when we were together. I wish you all 6 success, happiness, and lasting friendship in the years to come.

Finally, I am most indebted to my brother, parents, and grandmother for their continuous confidence and support throughout my schooling.

Ronald Ted Kurnik

Cambridge, Massachusetts

May, 1981 7

CONTENTS

Page

1. SUMMARY 20

1-1 Introduction 20 1-2 Background 22 1-3 Thesis Objectives 27 1-4 Experimental Apparatus and Procedure 28 1-5 Results and Discussion 30 1-6 Recommendations 54

2. INTRODUCTION 57

2-1 Background 57 2-2 Phase Diagrams 85 2-3 Thermodynamic Modelling of Solid-Fluid Equilibria 115 2-4 Thesis Objectives 128

3. EXPERIMENTAL APPARATUS AND PROCEDURE 130

3-1 Review of Alternative Experimental 130 Methods 3-2 Description of Equipment 131 3-3 Operating Procedure 134 3-4 Determination of Solid Mixture Composition 135 3-5 Safety- Considerations 136

4. RESULTS AND DISCUSSION OF RESULTS 137

4-1 Binary Solid-Fliud Equilibrium Data 137 4-2 Ternary solid-Fluid Equilibrium Data 159 4-3 Experimental Proof that T < Tq 189

5. UNIQUE SOLUBILITY PHENOMENA OF SUPERCRITICAL FLUIDS 193

5-1 Solubilitv Minima 193 5-2 Solubility Maxima 194 5-3 A Method to Achieve 100% Solubility of a Solid in a Supercritical Fluid Phase 201 5-4 Entrainers in Supercritical Fluids 202 5-5 Transport Properties of Supercritical Fluids 206

lo I a Page

6. ENERGY EFFECTS 208

6-1 Theoretical Development 208 6-2 Presentation and Discussion of Theoretical Results 210

7. OVERALL CONCLUSIONS 214 217 8. RECOM ENDATIONS FOR FUTURE RESEARCH 8-1 Solid-Fluid Equilibria 217 8-2 Liquid-Fluid Equilibria 218 8-3 Equipment Design 219

APPENDIX I. Partial Molar Volume Using the Peng-Robinson Equation of State 220

APPENDIX II. Derivation of Slope Equality at a Binary Mixture Critical Point 222

APPENDIX III. Derivation of Enthalpy Change of Solvation 225

APPENDIX IV. Freezing Point Data for Multicom- ponent Mixtures 227

APPENDIX V. Physical Properties of Solutes Studied 236

APPENDIX VI. Sources of Physical Properties of Complex Molecules 244

APPENDIX VII. Listings of Pertinent Computer Programs 246

APPENDIX VIII. Detailed Equipment Specifications and Operating Procedures 281

APPENDIX IX. Operating Conditions and Calibra- 286 tions for the Gas Chromatograph 304 APPENDIX X. Sample Calculations

Standardization and APPENDIX XI. Equipment 307 Error Analysis

Location of Original Data, APPENDIX XII. 314 Computer Programs, and Output

NOTATION 315 9 Page

LITERATURE CITED 320

BIOGRAPHICAL SKETCH 332 10

LIST OF FIGURES

Page

1-1 Equipment Flow Chart 29

1-2 The Pressure-Temperature-Composition Surfaces for Equilibrium Between Two Pure Solid Phases, A Liquid Phase and a Vapor Phase 32

1-3 P-T Projection of a System in Which the Three Phase Line Does Not Cut the Critical Locus 33

1-4 P-T Projection of a System in which the Three Phase Line Cuts the Critical Locus 35

1-5 Solubility of Benzoic Acid in Supercritical Carbon Dioxide 36

1-6 Solubility of 2,3-Dimethylnaphthalene in Supercritical Carbon Dioxide 37

1-7 Solubility of 2,3-Dimethylnaphthalene in Supercritical Ethylene 38

1-8 Solubility of Naphthalene in Supercritical Nitrogen 40

1-9 P-T Projection of a Four Dimensional Surface of Two Solid Phases in Equilibrium with a Fluid Phase 42

1-10 Solubility of Phenanthrene from a Phenanthrene-Naphthalene Mixture in Supercritical Carbon Dioxide 44

1-11 Solubility of Naphthalene from a Phenanthrene-Naphthalene Mixture in Supercritical Carbon Dioxide 45

1-12 Selectivities in the Naphthalene- Phenanthrene-Carbon Dioxide System 47 11

Page

1-13 Solubility of Naphthalene in Supercritical Ethylene-Indicating Solubility Maxima 49

1-14 Experimental Data Confirming Solubility Maxima of Naphthalene in Supercritical Ethylene 51

1-15 Partial Molar Volume of Naphthalene in Supercritical Ethylene 55

2-1 Solubility of Naphthalene in Supercritical Ethylene 65

2-2 Reduced Second Cross Virial Coefficients of Anthracene in C0 2 , C 2 H 4 , C2 H6 , and Temperature 67 CH 4 as a Function of Reduced 2-3 Kerr-McGee Process to De-ash Coal 72

2-4 Phase Diagrams for a Ternary Solvent- Water-Fluid Type I System 75

2-5 Phase Diagrams for a Ternary Solvent- Water-Fluid Type II System 77

2-6 Phase Diagrams for a Ternary Solvent- Water-Fluid Type III System 78

2-7 Phase Equilibrium Diagram for Ethylene- Water-Methyl Ethyl Ketone

and

Schematic Flowsheet for Ethylene Dehydration of Solvents 2-8 Supercritical Fluid (SCI) Operating Regimes for Extraction Purposes 82 2-9 The Pressure-Temperature-Composition Surfaces for the Equilibrium Between Two Pure Solid Phases, A Liquid Phase and a Vapor Phase 86

2-10 A Pressure Composition Section at a Constant Temperature Lying Between the Melting Points of the Pure Components 88

2-11 A Pressure Composition Section at a 12 Page

Constant Temperature above the Melting Point of the Second Component 89

2-12 P-T Projection of a System in Which the Three Phase Line Does Not Cut the Critical Locus 90

2-13 P-T Projection of a System in Which the Three Phase Line Cuts the Critical Locus 93

2-14 A P-T Projection Indicating Where the Isothermal P-x Projections of Figure 2-15 are Located 94

2-15 Isothermal P-x Projections for Solid- Fluid Equilibria 95

2-16 Naphthalene-Carbon Dioxide Solubility Map Calculated from the Peng-Robinson Equation 98

2-17 Solubility of Phenanthrene in Supercritical Carbon Dioxide 99

2-18 Space Model in the Case Where the Critical Locus and the Three Phase Line Intersect 100

2-19 P-T Projection for Ethylene-Naphthalene 103

2-20 T-x Projection for Ethylene-Naphthalene for Temperatures and Pressures above the Critical Locus 104

2-21 P-T Projection of a Four Dimensional Surface of Two Solid Phases in Equilibrt ium with a Fluid Phase 106

2-22 Solubility of CO2 in Air at 143 K 122

3-1 Equipment Flow Chart 132

4-1 Solubility of 2,3-Dimethylnaphthalene in Supercritical Carbon Dioxide 147

4-2 Solubility of 2,3-Dimethylnaphthalene in Supercritical Ethylene 148

4-3 Solubility of 2,6-Dimethylnaphthalene in Supercritical Carbon Dioxide 149 13

Page

4-4 Solubility of 2,6-Dimethylnaphthalene in Supercritical Ethylene 150

4-5 Solubility of Phenanthrene in Supercritical Carbon Dioxide 151 4-6 Solubility of Phenanthrene in Supercritical Ethylene 152

4-7 Solubility of Benzoic Acid in Supercritical Carbon Dioxide 153 4-s Solubility of Benzoic Acid in Supercritical Ethylene 154

4-9 Solubility of Hexachloroethane in Supercritical Carbon Dioxide 155

4-10 Solubility of Benzoic Acid in Supercritical Carbon Dioxide 158

4-11 Solubility of Naphthalene in Supercritical Nitrogen 160

4-12 Solubility of Naphthalene from a Phenanthrene-Naphthalene Mixture in Supercritical Carbon Dioxide at 308 K 172

4-13 Solubility of Phenanthrene from a Phenanthrene-Naphthalene Mixture in Supercritical Carbon Dioxide at 308 K 173

4-14 Solubility of 2,3-Dimethylnaphthalene from a 2,3-Dimethylnaphthalene- Naphthalene Mixture in Supercritical Carbon Dioxide at 308 K 174

4-15 Solubility of Naphthalene from a 2,3-Dimethylnaphthalene-Naphthalene Mixture in Supercritical Carbon Dioxide at 308 K 175

4-16 Solubility of Benzoic Acid from a Benzoic Acid-Naphthalene Mixture in Supercritical Carbon Dioxide at 308 K 176

4-17 Solubility of Naphthalene from a Benzoic Acid-Naphthalene Mixture in Supercritical Carbon Dioxide at 308 K 177 14 Page

4-18 Solubility of 2,6-Dimethylnaphthalene from a 2,6-Dimethylnaphthalene; 2,3-Dimethylnaphthalene Mixture in Supercritical Carbon Dioxide at 308 K 178

4-19 Solubility of 2,3-Dimethylnaphthalene from a 2,6-Dimethylnaphthalene; 2,3-Dimethylnaphthalene Mixture in Supercritical Carbon Dioxide at 308 K 179

4-20 Solubility of 2,3-Dimethylnaphthalene from a 2,3-Dimethylnaphthalene; 2,6-Dimethylnaphthalene Mixture in Supercritical Ethylene at 308 K 180

4-21 Solubility of 2,6-Dimethylnaphthalene from a 2,3-Dimethylnaphthalene; 2,6-Dimethylnaphthalene Mixture in Supercritical Ethylene at 308 K 181

4-22 Solubility of 2,3-Dimethylnaphthalene from a 2,3-Dimethylnaphthalene; 2,6-Dimethylnaphthalene Mixture in Supercritical Carbon Dioxide at 318 K 182

4-23 Solubility of 2,6-Dimethylnaphthalene from a 2,3-Dimethylnaphthalene; 2,6-Dimethylnaphthalene Mixture in Supercritical Carbon Dioxide at 318 K 183

4-24 Selectivities in the Naphthalene- Phenanthrene-Carbon Dioxide System 185

4-25 Selectivities in the Naphthalene- 2,3-Dimethylnaphthalene-Carbon Dioxide System 186

4-26.. Selectivities in the Naphthalene- Benzoic Acid-Carbon Dioxide System 187

4-27 A Close Examination of the System Naphthalene-Ethylene Near the Upper Critical End Point 191

5-1 Solubility of Naphthalene in Supercrit- ical Ethylene-Indicating Solubility Maxima 195

5-2 Experimental Data Confirming Solubility Maxima of Naphthalene in Supercritical Ethylene 197 15

Page

5-3 Partial Molar Volume of Naphthalene in Supercritical Ethylene 200

5-4 P-T Projection for Ethylene- Naphthalene 203

5-5 T-x Projection for Ethylene- Naphthalene for Temperatures and Pressures above the Critical Locus 204

11-1 The Molar Free Energy of Mixing as M a Function of Mole Fraction, When g is a Continuous Function of x 223

IV-i Phenanthrene-Naphthalene Freezing Curves 234

VIII-l Extractor Design 282

IX-1 Gas Chromatograph Calibration Curve for Phenanthrene/Benzoic Acid Mixtures 297

IX-2 Gas Chromatograph Calibration Curve for Naphthalene/Benzoic Acid Mixtures 298

IX-3 Gas Chromatograph Calibration Curve for 2,3-Dimethylnaphthalene/Phenan- threne Mixtures 299

IX-4 Gas Chromatograph Calibration Curve for 2,6-Dimethylnaphthalene/2,3-Dimethyl- naphthalene Mixtures 300

IX-5 Gas Chromatograph Calibration Curve for Naphthalene/Phenanthrene Mixtures 301

IX-6 Gas Chromatograph Calibration Curve for Phenanthrene/2,6-Dimethylnaphthalene 302

IX-7 Gas Chromatograph Calibration Curve for Naphthalene/2,3-Dimethylnaphthalene 303

XI-1 Positions of Solid in Extractor for Test of Isothermality 312 16

LIST OF TABLES

PAGE

1-1 Comparison Between Experimental and Theoretical Solubility Maxima and the Pressure at these Maxima 52

2-1 Solubility Data for Solid-Fluid Equilibria Systems 59

2-2 Phase Diagrams Solid-Fluid Equilibria 63

2-3 Critical Point Data for Possible Mobile Phases for Supercritical Fluid Chromatography 83

2-4 Comparison of Critical End Points for the System Supercritical Ethylene- Naphthalene with the System Supercri- tical Ethylene-Naphthalene-Hexachloro- ethane 108

2-5 Comparison of Experimental vs Theoretical Values of the Critical End Points for the System Naphthalene-Ethylene 114

4-1 Co 2 ; 2,3-Dimethylnaphthalene Data 138

4-2 C2 H 4 ; 2,3-Dimethylnaphthalene Data 139

4-3 CO 2 ; 2,6-Dimethylnaphthalene Data 140

4-4 C2 H4 ; 2,6-Dimethylnaphthalene Data 141

4-5 CO2 ; Phenanthrene Data 142

4-6 C2 R4 ; Phenanthrene Data 143

4-7 CO2 ; Benzoic Acid Data 144

4-8 C 2 H 4 ; Benzoic Acid Data 145

4-9 CO 2 ; Hexachloroethane Data 146

4-10 C02; Benzoic Acid; Naphthalene Mixture Data at 308 K 161 17 PAGE

4-11 CO2 ; Benzoic Acid; Naphthalene Mixture Data at 318 K 162

4-12 C0 2 ; 2,3-Dimethylnaphthalene; Naphthalene Mixture Data at 308 K 163

4-13 CCe; Naphthalene; Phenanthrene Mixture Data at 308 K 164

4-14 CO 2 ; 2,3-Dimethylnaphthalene; 2,6- Dimethylnaphthalene Mixture Data at 308 K 165

4-15 C02 ; 2,3-Dimethylnaphthalene; 2,6- Dimethylnaphthalene Mixture Data at 318 K 166

4-16 C2H 4 ; 2,3-Dimethylnaphthalene; 2,6- Dimethylnaphthalene Mixture Data at 308 K 167

4-17 CO 2 ; Benzoic Acid; Phenanthrene Mixture Data at 308 K 168

4-18 CO2 ; 2,6-Dimethylnaphthalene; Phenanthrene Mixture Data at 308 K 169

4-19 CO2 ; 2,3-Dimethylnaphthalene; Phenanthrene Mixture Data at 308 K 170

4-20 CO2 ; 2,3-Direthylnaphthalene; Phenanthrene Mixture Data at 318 K 171

5-1 Comparison Between Experimental and Theoretical Solubility Maxima and the Pressure at these Maxima 198

6-1 Differential Heats of Solution for Phenanthrene-Carbon Dioxide at 328 K 211

6-2 Differential Heats of Solution for Phenanthrene-Ethylene at 328 K 212

6-3 Differential Heats of Solution for Benzoic Acid-Carbon Dioxide at 328 K 213

IV-1 Comparison of Melting Point Curve from Literature vs. Experimental Data for the System o-Chloronitrobenzene (1), 228 with p-Chloronitrobenzene (2) 18

PAGE

IV-2 Experimental Freezing Curves for Phenanthrene with Naphthalene 229

IV-3 Experimental Freezing Curves for Phenanthrene with 2,6-Dimethylnaphthalene 230

IV-4 Experimental Freezing Curves for Naphthalene with 2,6-Dimethylnaphthalene 231 IV-5 Experimental Freezing Curves for 2,3- Dimethylnaphthalene with 2,6-Dimethyl- naphthalene 232

IV-6 Melting Points and Heats of Fusion 235

V-1 Physical Propertities of Solutes Studied 237

V-2 Vapor Pressure of Solutes Studied 238

VI-i Vapor Pressures of Solid Substances 245

VII-l Computer Program PENG 247

VII-2 Computer Program MPR 252

VII-3 Computer Program KIJSP 262

VII-4 Documentation for Subroutine GENLSQ 268

IX-1 Temperature Programmed Conditions and Response Factors for Chromatography 287

IX-2 Sigma 10 Software for 2,6-DMN/2,3-DMN Analysis 290

IX-3 Sigma 10 Software for Naphthalene/ Phenanthrene Analysis 291

IX-4 Sigma 10 Software for 2,3-DMN/ Phenanthrene Analysis 292

IX-5 Sigma 10 Software for 2,6-DMN/ Phenanthrene Analysis 293

IX-6 Sigma 10 Software for Benzoic Acid/ Phenanthrene Analysis 294

IX-7 Sigma 10 Software for Naphthalene/ 2,3-DMN Analysis 295 19

PAGE

IX- 8 Sigma 10 Software for Naphthalene- Benzoic Acid Analysis 296

XI-1 Equilibrium Solubilities of Naphthalene in Carbon Dioxide as a Function of Flow Rate and Extractor Charge at 191 Bar and 308 K 308

XI-2 Solubility of Naphthalene in Supercritical Carbon Dioxide (Experimental Values vs. Literature) 310 20

1. SUMMARY

1-1 Introduction

Supercritical fluid extraction (SCF) is a rediscovered unit

operation for purification of solid and/or liquid mixtures.

It is of current interest and has potential utility in the

chemical process industry due to six reasons:

I. Sensitivity to all Process Variables

For supercritical fluid extraction, both temperature

and pressure may have a significant effect on the equilibrium

solubility. Small changes of temperature and/or pressure,

especially in the region near the critical point of the

solvent, can affect equilibrium solubilities by two or three

orders of magnitude. In liquid extraction, only temperature

has a strong effect on equilibrium solubility.

II. Non-Toxic Supercritical Fluids can be Used

Carbon dioxide, a substance which is non-toxic, non-

flammable, inexpensive, and has a conveniently low critical

temperature (304.2 K), can be used as an excellent solvent

for extracting substances. It is for this reason that many

food and pharmaceutical industries are involved in supercritical CO2 extraction research. 21

III. High Mass Transfer Rates Between Phases

A supercritical fluid phase has a low viscosity (near

that of a gas) while also having a high mass diffusivity

(between that of a gas and a liquid). Consequently, it is

currently believed that the mass transfer coefficient (and

hence the flux rate) will be higher for supercritical fluid

extraction than for typical liquid extractions.

IV. Ease of Solvent Regeneration

After a given supercritical fluid has extracted the

desired components, the system pressure can be reduced to a

low value causing all of the solute to precipate out. Then,

the supercritical fluid is left in pure form and can be easily

recycled. In typical liquid extraction using an organic solvent,

the spent solvent must usually be purified by a distillation

train.

V. Energy Saving

When compared to distillation, supercritical fluid ex-

traction is usually less energy intensive. For example, it

has been shown that dehydrating ethanol-water solutions is

more energy efficient using supercritical carbon dioxide than

azeotropic distillation (Krukonis, 1980).

VI. Sensitivity of Solubility to Trace Components

Solubility of components in supercritical fluids can

sometimes be affected by several hundred percent by the

addition to the fluid phase of small quantities (circa one mole percent) of a volatile, often polar, material (entrainer). 22

In addition, selectivities in the extraction can be significantly affected by an entrainer.

1-2 Background

Historical Summary

The earliest SCF extraction experiments were conducted by Andrews (1887)* who studied the solubility of liquid carbon dioxide in compressed nitrogen. Shortly thereafter,

Hannay and Hogarth (1879, 1880) found that the solubilities of crystalline I2, KBr, CoCL2 , and CaCl2 in supercritical ethanol were in excess of values predicted from the vapor pressures of the solutes modified by the Poynting (1881) correction. There have been many other studies since these pioneering papers as summarized in the main body of this thesis. In most of the investigations until recently, emphasis was placed on developing phase diagrams for the fluid- solute systems investigated. The use of theory to correlate the experimental data began with the application of the virial equation of state, but the principal object was to employ the extraction data to determine interaction second virial coefficients (see, for example, Baughman et al., 1975;

Najour and King 1966, 1970; King and Robertson, 1962).

Applications to the Food Industry

The most often cited example of SCF in the food industry

*The paper describing Andrew's work was publIshed after his death. The experiments were carried out in the 1870's. 23

is in the decaffeination of green coffee (Zosel, 1978).

British and German patents have been issued (Hag, A.G., 1974;

Vitzthum and Hubert, 12'75). While no data have been pub-

lished, it is believed that the supercritical C02 is rela-

tively selective for caffeine.

A patent has been issued to decaffeinate tea in a

similar manner (Hag, A.G., 1973). SCF has also been suggest-

ed to remove fats from foods, prepare spice extracts, make

cocoa butter, and produce hop extracts. These four applica-

tions are covered by patents of Hag, A.G. (1974b, 1973b,

1974c, 1975). In all these suggested processes, supercriti-

cal CO2 is recommended as a non-toxic solvent that may be

used in the temperature range where biological degradation

is minimized. It is suspected that extensive in-house,

non-published research is being conducted by the major food

industries.

Other Applications

Hubert and Vitzthum (1978) suggest the use of super-

critical CO2 to separate nicotine from tobacco. Desalina-

tion of sea water by supercritical Ci and C12 paraffinic

fractions has been successfully accomplished (Barton and

Fenske, 1970; Texaco, 1967). Other applications include de-asphalting of petroleum fractions with supercritical propane/propylene mixtures (Zhuze, 1960), extraction of lanolin

from wool fat (Peter et al. , 1974), and the recovery of oil

from waste gear oil CStudiengesselschaft Kohle M.B.H., 1967). 24 Holm C1959) discussed the use of supercritical CO2 as a

scavenging fluid in tertiary oil recovery. These and other

processes are noted in reviews by Paul and Wise (1971),

Wilke L1978), Irani and Funk (1977) and Gangoli and Thodos

(1977).

Supercritical extraction in coal processing is being

studied by a number of companies. In Great Britain, the

National Coal Board has examined the de-ashingof coal with

supercritical toluene and water (Bartle et al., 1975). The

Kerr-McGee Company is said to have an operational process to de-ash coal using pentane or proprietary solvents CKnebal and Rhodes, 1978; Adams et al., 1978).

Modell et al., C1978, 1979) has proposed to regenerate activated carbon with supercritical CO2. Phase separations may be accomplished in some instances by contacting a liquid. mixture with supercritical fluids.

CSnedeker, 1955; Elgin and Weinstock, 1959; Newsham and

Stigset, 1978; Balder and Prausnitz, 1966). The use of a supercritical fluid as the "third" component in a binary liquid mixture is analogous to the phase splits caused in the salting out process. The advantages of the use of a supercritical fluid over a soluble solid relate to the ease whereby the supercritical fluid may be removed by a pressure reduction. A current commercial venture is exploiting this technology to separate ethanol-water mixtures (Krukonis,

1980). 25

Supercritical-Fluid Chromatography

One quite promising application of SCF is in chromato-

graphy. While no commercial equipment is yet available,

several investigators have fabricated their own prototype

units CSie et al., 1966; van Wasen et al., 1980; Klesper,

1978). Due to the higher operating pressures, there are

significant problems in developing detectors and sample-

injection techniques. The often drastic variation in solu-

bility with pressure allows one to employ both temperature

and pressure to optimize separations. Also, with the use of

supercritical fluids with low critical temperatures, it would

appear that separations could be made of high molecular weight

thermodegradable biological materials. Ionic species which

decompose in gas chromatography have been stabilized in

supercritical fluids CJentoft and Gouw, 1972).

Finally, supercritical chromatography has been employed

to obtain a variety of physical and thermodynamic properties

for infinitely dilute systems, e.g. diffusion coefficients,

activity coefficients, and interaction second. virial coefficients

Van Wasen et al., 1980; Bartmann and Schneider, 1973).

Theoretical Work

There are two ways to model solid-fluid equilibria:

Ca) the compressed gas model; Ob1 the expanded liquid model.

The compressed gas model assumes that an equation of state can be used to estimate the fugacity coefficient of component i in a fluid phase. With the assumptions that 26 1. solid density is independent of pressure and

and composition

2. solubility of the fluid phase in the solid is sufficiently small S so that 1y and x. 1

3. no solid solutions form

4. vapor pressure of solid is sufficiently small so that

s ~l and P-P ~ P vpi ~vpi

the model can be written for component i as

P v .PV. -S. y =P F'exp (1-1.1) i

Using the expanded liquid approach to solid-fluid

equilibria, the solute activity in the fluid phase is expressed

in terms of an activity coefficient. As a result, the mole

fraction of component i in a supercritical fluid is

7R s (P-PR)V." fS (PR) exp ( = _iRT R.= ~p~(1-1.2) Yi 'Y(i'"P )fi Pr iR

exp PR[RJ dP

which can be simplified to give

eR FUSp

T J i IRT t % Y- = -t _T(1-1.3)

ie Y ix p P R( d YP 27 Mackay and Paulaitis (1979) have used a reference pressure of

R P = Pc,c

with P c the critical pressure of the pure fluid phase, and

the assumption that

Y(yPR (1-1.4) i. i- i c

.(yPR -(1-1.5) Si- i c

VT would then be found from an applicable equation of state

and y. would be treated as an adjustable parameter. Of the two methods to model solid-fluid equilibria, the

first method (Equation 1-1.1) is preferred because it requires only one adjustable parameter, k . (whereas Equation

1-1.3 requires two: k3. . and y" (PC) Also, it is much easier to generalize Equation 1-1.1 to a multicomponent system

than it is to generalize Equation 1-1.3.

1-3 Thesis Objectives

The objectives of this thesis can be divided into three parts: experimental, theoretical, and exploratory. Experi- mentally, equilibrium solubility data for both polar and non- polar solid solutes in supercritical fluids were to be measured over wide ranges of temperature and pressure. In addition, ternary equilibrium data (two solids, one fluid) were to be measured. Carbon dioxide and ethylene were the two supercritical fliuds to be used. 28 Theoretically, correlation of equilibrium solubility

data of both binary and multicomponent systems using rigorous

thermodynamics was to be done.

Finally, after obtaining equilibrium solubility data

and developing a thermodynamic model, it was desirable to use

this modelto explore the physics of solid-fluid equilibrium.

Using the model that was to be developed, such phenomena as

enthalpy changes of solvation of the solute in the supercrit-

ical solvent and changes in equilibrium solubility over wide

ranges of temperature and pressure were to be studied.

1-4 Experimental Apparatus and Procedure

The experimental method used in this thesis to measure

equilibrium solubilities was a one-pass flow through system.

A schematic is shown in Figure 1-1.

A gas cylinder was connected to an AMINCO line filter, (odel

49-14405) which feeds into an AMINCO single end compressor, (model

46-13411). The compressor was connected to a two liter magne-

drive packless autoclave (Autoclave Engineers) whose purpose

was to dampen the pressure fluctuations. In addition, an

on/off pressure control switch, Autoclave P481-P713 was used

to control the outlet pressure from the autoclave.

Upon leaving the autoclave, the fluid entered the

tubular extractor (Autoclave, CNLXl60121 which consisted of

a 30.5 cm tube, 1.75 cm in diameter. In the tube were alter-

nate layers of the solute species to be extracted and Pyrex wool. The Pyrex wool was used to prevent entrainment. A PC Heoig-01C Hua te0d lope I Valve ELdDHetn lTI Go s Compressor Surge - lank Ex t ractor Cy linder

Vent Key TC Dry - Temperoture Cont roler Test - Meter PC - Pressure Cont roller U - lubes Rotometer P - Pressure Gouge

I- lermocoople

Equipment Flow - Chort

Figure 1-1 30

LFE 238 PID temperature controller attached to the heating

tape kept the extractor isothermal. The temperature was

monitored by an iron-constantan thermocouple (Omega SH48-

ICSS-ll6U-15) housed inside the extractor. At the end of

the extraction system was a regulating valve (Autoclave

30VM4882), the outlet of which was at a pressure of 1 bar.

All materials of construction were 316 stainless steel.

Following the regulating valve were two U-tubes in

series (Kimax 46025) which were immersed in a 50% ethylene

glycol-water/dry ice solution. Complete precipation of the

solids occurred in the U-tubes, while the fluid phase was

passed into a rotameter and dry test meter (Singer DTM-ll5-3)

and finally vented to a hood. An iron constantan thermocouple

(Omega ICSS-l6G-6) at the dry test meter outlet recorded

the gas temperature. All thermocouple signals were displayed

on a digital LED device (Omega 2170A). Analysis of the solid

mixtures was done on a Perkin Elmer Sigma 2/Sigma 10 chromato-

graph/data station.

1-5 Results and Discussion

Phase Behavior for Binary Systems

Phase behavior resulting when a solid is placed in contact with a fluid phase at high pressures (Pr >> ) and at temperatures near and above the critical point of the pure fluid are of key importance. The phase diagram provides guidance to the possible operating regimes that exist in 31 supercritical fluid extraction.

In order to establish a basis, a general binary P-T-x

diagram for the equilibrium between two solid phases, a liquid

phase, and a vapor phase is shown in Figure 1-2. This dia-

gram is drawn for the case of a solid of low volatility

and high melting point and one of high volatility and slight-

ly lower melting point. On the two sides of this diagram

are shown the usual solid-gas and liquid-gas boundary curves

for the two pure components. These boundary curves meet,

three at a time, at the two triple points A and B. The line

CDEF is an eutectic line where solid 1 CC), solid 2 (F),

saturated liquid (E) and saturated vapor (D) join to form an

invariant state of four phases. A projection of ABCEF on

the T-x plane gives the usual solubility diagram of two im-

miscible solids, a miscible liquid phase, and a eutectic

point that is the projection of point E. This projection is

shown as the "cut" at the top of the figure, since pressure has little effect on the equilibrium between condensed phases.

In Figure 1-3 is shown a P-T projection of this P-T-x

surface, indicating the three-phase locus (AFB) and the critical locus (MN) . In this figure, the only region where solid is in equilibrium with a gaseous mixture is under the three- phase line AFB. Between the line AFB and MN, is a liquid- vapor region and above the locus MN is a one phase unsaturated fluid region. Consequently, if the pressure is raised iso- thermally starting at a pressure below the locus AFB, the solid will liquefy due to the presence of the fluid phase. 32

I- ______-

G H

I I I I

The Prcssure - Temperature - Composition Surfaces for the Equilibrium Between Two Pura Solid Phases, A Liquid Phase and a Vapor Phase

( Rowlinson and Richardson,1959 )

Figure 1-2 33

b N441 P ANI

B 1~

P-T Projaction of a System in Which thc Thre2 Phase Linc Does Not Cut thc Critical Locus

Figure 1-3 34 For some extractions, it is often desirable to keep the solute

a solid phase, and so Figure 1-3 is an undesirable situation.

Fortunately, Figure 1-3 in general, does not represent the

usual situation,as discussed below.

When a high molecular weight solid is in equilibirum

with a low molecular weight gas, the P-T projection that norm-

ally exists is as shown in Figure 1-4. Here, because the dif-

ferences in temperature between the triple points and criti-

cal points of these substances is large, the three phase line

AFB of Figure 1-3 can actually intersect the critical locus,

so as to "cut" it at two points: p- the lower critical end

point, and q- the upper critical end point. See Figure 1-4.

In this figure, M and N are the critical points of the super-

critical fluid and solid respectively. Critical end points

are mixture critical points in the presence of excess solid,

i.e., a liquid and gas of identical composition and proper-

ties in equilibrium with a solid.

The major consequence of a gap in the critical locus as

shown in Figure 1-4 is to allow at least a region in temper-

ature between T and T where one solid phase is in equlibrium

with one fluid phase with no liquid phase present.

Presentation and Discussion of Data

In Figures 1-5 to 1-7 are shown experimental data and acorrelation for the systems benzoic acid/CC2 , 2,3- dimethylnaphthalene (DMN)/CO2 , and 2,3-dimethylnaphthalene

(DMN)/C2 H4 respectively. In all cases, there are three pressure regimes: At low pressures an increase in temperature 35

q N N P N C-F.O A

P -T Projection of a System in Which the Three Phose Linc Outs th(2 Critical Locus

Figure 1-4 36

10 - ,- [ I I I I I

338 10K 318K

318 K

10 ~ 328K

/ 338

SYSTEM: BENZOIC ACID-CO 2 a i~4-- PR EQUATION OF STATE rEMPERATURE S(K) SYSOL 318 2 328 a

10 5 3 -3

3283K 10- 318 K

IDEAL GAS

a-,338 K

3 28 K 10-76-

i t1 1i 1,- -8 i 1 1 1 1

0 40 80 120 160 200 240 280 PRESSURE (BARS) Solubility of Benzoic Acid in Supercritical Carbon Dioxide

Figure 1-5 37

1 -amI lI

-2 328 10 - 318 K

308

-. 3 10 - -- 30 8 K - - z318 K- 328 K-

-4 10 SystOM C02- 2,3 DM N -- PR Equation of State.

Temper at ure (K) symbol k 12

328 K 30 08 .0996 - _ g 3 IS O.t O2 10 .. 3 2 8 j.1 7- -318 K-

308 K

10 0 40 80 120 160 20 0 24 0 280 PRESSURE ( BARS)

Solubili-ty of 2,3-Dimethylnaphthalene in Super- critical CarPon Dioxide

Ficure 1-6 38

328

318

30 -2 10

-3 308K 10-- 10318 K 32 8 K

S ys tem C2H4 -2,13 D M N

-2 K- PR Equa tion of Sto t4? Temp4?rature Symbol k 12

0 .0246 105-21-8 K 308 3 t8 0 .0209 328 0 .0147 308 K

-6 t0

0 40 80 120 160 200 240 280 PRESSURE (BARS)

Solubility of 2,3-Dimethylnaphthalene in Super- critical Ethylene

Figure 1-7 39

increases solubility; at intermediate pressures, an increase

in temperature decreases solubility (retrograde solidifica-

tion) -- more apparent for carbon dioxide than ethylene; and

at high pressures an increase in temperature enhances slu-

bility. The reason the retrograde solidification region is

more significant for carbon dioxide than ethylene is because

CO2 is at a lower reduced temperature and therefore the den-

sity dependence on pressure is larger.

In all cases, the Peng-Robinson equation of state is able

to correlate the data well providing that the proper binary

interaction parameter is used. Although the binary parameters

were independent of pressure and composition, they have a weak

linear dependence on temperature.

The outstanding feature of all the data and simulations

is the extreme sensitivity of equilibrium solubility to temp-

erature and pressure. For example, consider Figure 1-5

(benzoic acid-carbon dioxide). There is about a two order of

magnitude change in solubility when decreasing pressure and

simultaneously increasing temperature from (318K, 180 bar)

to (338K, 90 bar). Also shown for convenience in Figure 1-5

is the solubility predicted by the ideal gas law:

ID P / y. = /PC1-5.l) i vp C"5.1

The ratio of real to ideal solubilities is called the enhancement factor and can take on values of 106 or larger.

Figure 1-8 shows a simulation of the case naphthalene 40

,52 10

System: Nitrogen - Nophthalone -- PR Equation of State

k 12 =Q.1 -.3 10

LLid z Lid

10 - 328K

31 SK -=MOK

0 40 80 120 160 200 240 280 PRESSURE ( BARS)

Solubility of Naphthalene in Supercritical Nitrogen

Figure 1-8 41

in supercritical nitrogen. At no pressure does the isothermal

solubility of naphthalene even equal the solubility at one

bar pressure. The reason is because under these temperature

and pressure conditions, nitrogen is nearly an ideal gas with

fugacity coefficients and compressibility factors near unity.

Also, the density of nitrogen at high pressures is approxim-

ately 0.1 gm/cm3 as compared to 0.8 gm/cm3 for carbon dioxide

under the same conditions of temperature and pressure. The

dissolving power of supercritical fluids depends both on the

density Cthe higher the greater) and the nonideality (fugacity

coefficient) of the fluid phase.

Ternary Solid-Fluid Equilibrium

As in the case of binary solId-fluid equilibrium, it is

useful to examine the P-T projection that results when two

solids that form a eutectic solution (not a solid solution)

are in equilibrium with a fluid phase. Such a P-T projection

of the four dimensional surface is shown in Figure 1-9. In

this diagram, K and K{ are the first and second lower critical-end points. These end points are the intersection with

the critical locus of the three-phase line formed by the solids

in equilibrium, with a liquid and a gas phase. Similarly,

K2 and K' are the first and second upper-critical end points.

In the case where no solid solutions form, there will exist two eutectic points, and hence a four-phase line connecting them. However, the four phase line may intersect the critical locus at a lower double critical-end point and at a upper

I K 2

K N K, p q N, KA/4K

P ,

L i N /

600

P-T Projection of a Four Dimensional Surface of Two Solid Phases in Equilibrium with a Fluid Phase

Figure 1-9 43 double critical-endpoint -- shown as p and q respectively.

Only for temperatures between those corresponding to TP and

Tq , for any pressure, is one guaranteed that there are two

solid phases in equilibrium with a fluid phase with no liquid

phase forming.

Presentation and Discussion of Data

In Figures 1-10 and 1-11 are shown experimental data and a

correlation for the ternary system naphthalene-phenanthrene-

co2. The open circles represent the experimental solubilities

of the pure component in supercritical CO2, whereas the closed

circles represent the solubilities of that component from a

solid mixture in supercritical CO2' The most important conclusion that can be drawn from Fig-

ures 1-10 and 1-11 is, that by adding a more volatile component

(naphthalene) to phenanthrene the solubilities of both compo-

nents in the supercritical phase are increased. Component solubilities of phenanthrene in the supercritical fluid are about a maximum of 75% higher in the mixture than the pure phenanthrene alone in carbon dioxide; naphthalene concentrations in the mix-

ture increase a maximum of about 20%. Similar findings were made on the following ternary systems with supercritical CO2 with maximum increases of: benzoic acid (280% increase); naphthalene (107% increase) and 2,3-dimethylnaphthalene (144 % increase); naphthalene (46% increase).

There is one set of ternary data available in the literature (Van Gunst, 1950) for the system hexachloroethane- 44

..- 10

C, 4 H1 o MIXTUREPR EQUATION

IQ-3

C14H IO PUR E, PR EQUA TION

10-4

0 r 10-5! 0 SYS TE M: C02-CIOHB -C14H 10 () (2) (3) TEMPER ATURE =308.2K 0 PURE C(4Hjo IN C02

10-6. 0 MIXTURE C14 HIOIN CO2 -- PR EQUAT"'ION OF STATE k 20 .09w'59 k 13=0. 115 k23=0.05

10~7

I I C0- ) 40 80 120 160 200 240 280 PRESSURE (BARS) Solubility of Phenanthrene from a Phenanthrene- Naphthalene Mixture in Supercritical Carbon Dioxide

Figure 1-10 45

10- -

Cio H8 MIXTURE, PR EQUATw1iu-N

10-2 ~CioH8 PURE, PR EQUATION

SYSTEM: CO 2-C 0 H8 -C 1 4 H1 O (1) (2) (3) 10-4 TEMPERATURE= 308.2K

0 PURE CfOH IN C 0 2 t * MIXTURE CIo H8 IN CO2 -- PR EQUATION OF STATE

k 12 =0.0959 10-5 k 13 =0.-11

k 2 3 =0.05 +DATA OF TSEKHANSKAYA et al. (1964)

0 40 80 120 160 200 240 280 PRESSURE (BARS) Solubility of Naphthalene from a Phenanthrene- Naphthalene Mixture in Supercritical Carbon Dioxide

Figure 1-11 46

naphthalene-ethylene. Both the naphthalene and hexachlor-

ethane solubilities increased by about 300% when they are

used in a binary solid system as compared to a pure solid

system.

For one case studied in this thesis, however, there was

a slight (10%) decrease in component solubilities in a

ternary mixture as compared to the binary system. This case was the system phenanthrene; 2,3-DMN; CO2 . In most experiments, the ternary data were well corre-

lated by the Peng-Robinson equation of state and Equation 1-1.

There are two solute-solvent interaction parameters that are fixed from binary experiments and one solute-solute interaction coefficient that must be introduced. The solute-solvent interaction coefficients are those obtained by a nonlinear regression from binary data. Only for the solute-solute interaction coefficient is ternary data required.

To check whether there was physical meaning in the solute-solute parameter, the isomer system 2,3-DMN; 2,6-DMN was examined in both supercritical carbon dioxide and ethylene. Correlation of the resultant data showed that k23 was dependent on the supercritical fluid (component 1). Thus, it can be concluded that k23 is an adjustable parameter -- not a true binary constant.

Selectivities in the naphthalene-phenanthrene-Co2 system are shown in Figure 1-12. At 1 bar, the selectivity is the ratio of solute vapor pressures. Increasing the system presure dramatically decreases the selectivity until 47

-F- mmmmlmp I I I I I I 480- System: C02- Naphthalene -Phenanthrenc 440- (1) (2) (3) - Temperature = 30B K

400.- - PR Equation of State k 12 = 0.0959 360- k 13 =0.1 15

k 2 3 = 0.05 320 0:< Naphtholene /Phenanthrane

280 -

a- 240- 9 z 0~

Ii 200 0~ 4 8 z 160 - II 7

120- 46 80 E xpcndcd

Admk -M Aduk k 01 I K w~9@9@9#T 0 40 80 120 160 200 240 280 PRESSURE (BARS)

Selectivities in the Naphthalene-Phenanthrene-Carbon Dioxide System

Figure 1-12 48

it levels off at a nearly constant value just above the

solvent critical pressure. This type of selectivity curve

was found for all the ternary systems studied.

In conclusion, if in a given application, component

solubilities of a solid in a supercritical fluid are not large,

it may be possible to add to the original mixture a more

volatile solid component which causes substantial increases

in component solubilities of all species. Although this ef-

fect was shown only for solids in this thesis, it is believed

that volatile liquids (entrainers) can also be added to ac-

complish the same effect.

Solubility Maxima

Of the data and correlations shown in Figures 1-5 to 1-7,

the highest pressure attained was 280 bar. As these figures

indicate, the isothermal solubilities are still increasing with pressure. It is interesting, therefore, to perform computer simulations to very high pressures (Kurnik and

Reid, 1981). The results of such simulations are shown in

Figure 1-13 for the solubility of naphthalene in supercritical ethylene for pressures up to 4 kbar and for several temperatures. Experimental data are shown only for the 285 K isotherm to indicate the range covered and the applicability of the Peng-Robinson equation.

For the naphthalene-ethylene system, the solubility attains a minimum value in the range of 15 to 20 bar and a maximum at several hundred bar. 49

to-I

318K 308 K a.8K 285 K z

C z SYSTEM: 1K NAPHTHALENE- ETHYLENE 308 K -- PENG - ROB INSON EQUATION J OF STATE 29Kk, 2 .02

285 KEXPERIMEN ITAL DATA OF TSEKHANSIKAYA (1964); T: 285 K

-6 I --- mmmwvmFvmwlm I I - I - F

I 10 100 1000 10,000 PRESSURE (BARS)

Solubility of Naphthalene in Supercritical Ethylene- Indicating Solubility Maxima

Figure 1-13 50

The existence of the concentration maxima for the

naphthalene-ethylene system is confirmed by considering the

earlier work of Van Welie and Diepen (1961). They also

graphed the mole fraction of naphthalene in ethylene as a

function of pressure and covered a range up to about I kbar.

Their smoothed data (as read from an enlargement of their

original graphs), are plotted in Figure 1-14. At temperatures close to the upper critical end point (325.3 K), a maximum in

concentration is clearly evident. At lower temperatures, the maximum is less obvious. The dashed curve in Figure 1-14 represents the results of calculating the concentration maximum from the Peng-Robinson equation of state. This simula-

tion could only be carried out to 322 K; above this tempera-

ture convergence becomes a problem as the second critical end point is approached and the formation of two fluid phases is predicted. Table 1-1 compares the theoretical versus experimental maxima.

Concentration maxima have also been noted by Czubryt et al. C1970) for the binary systems stearic acid-CO2 and l-octadecanol-CO2 . In these cases, the experimental data were all measured past the solubility maxima -- which for both solutes occurred at a pressure of about 280 bar. An approximate correlation of their data was achieved by a solubility parameter model.

Theoretical Development

The solubility minimum and maximum with pressure can be 51

-- Vn Welie and Diepen , 1961 COMPUTER SIMULATION OF WU MAXIMUM CONCENTRATION Z 3Q USING THE PENG- ROBINSON EQUATION OF STATE a. 20

C 10 - C, LU / 3

200 400 600 800 1000 PRESSURE (BARS)

NUMBER TEMPERATURECK) 1 -303.2 2 308.2 3 313.2 4 318.2 5 321.2 6 323.2 7 324.2 8 325.3

Experimental Data Confirming Solubility Maxima of Naphthalene in Supercritical Ethylene

Figure 1-14 Table 1-1

Comparison between Experimental and Theoretical Solubility and Maxima and the Pressure at these Maxima

E T E (bar) Pa (bar) % error, P % error, y T (K) max max Ymax Ymax -2 303 612 680 11.1 4. 31x10 4.83x10 -2 12.1 308 590 648 9.8 5.68x10-2 6.06x10-2 6.9

2 2 313 576 576 0.0 7. 84x10- 8. 4 3x10- 7.5

318 477 472 1.0 1.17x10 1 1. 19x10~ 1.7 Ln N~ 1 321 398 357 10.3 1. 35x10 1 1. 60x10~ 18.5

Notes: 1. Calculations were done using the Peng-Robinson Equation of State, k1 2=0.02

2. Experimental Data are from van Welie and Diepen (1961).

3. PE = experimental value of maximum pressure. max P T = theoretical value of maximum pressure. 4. max 53

related to the partial molar volume of the solute in the

supercritical phase. With subscript 1 representing the solute,

then with equilibrium between a pure solute and the solute

dissolved in the supercritical fluid,

dlnfj = dlnfs (1-5.2)

Expanding Eq. 1-5.2 at constant temperature and assuming that

no fluid dissolves in the solute,

~7F 3nF e SdP + nf 1 dlny = dP (1-5.3) RT L alnyJ TP -RT

Using the definition of the fugacity coefficient,

$ F == f/yF P (1-5.4)

Then Eq. 1-5.3 can be rearranged to give

31nylRT T IT ~(1-5.5) T L ln$ olnylT

may be expressed in terms of y1 , T, and P with an equation of state (Kurnik et al., 1981). For naphthalene as the

solute in ethylene, (31nI/9lnyl)T,P was never less than -0.4 over a pressure range up to the 4 kbar limit studied. Thus

the extrema in concentration occur when V1s= 54

Again using the Peng-Robinson equation of state, 9I

for naphthalene is ethylene as a function of pressure and

temperature was computed. The 318 K isotherm is shown in

Figure 1-15. At low presures, V' is large and positive; it

would approach an ideal gas molar volume as P -+ 0. With an

increase in pressure, ~I decreases and becomes equal to V5

(111.9 cm3/mole) at a pressure of about 20 bar. This corres-

ponds to the solubility minimum. VY1 then becomes quite negative. The minimum in 9' corresponds to the inflection point

in the concentration-pressure curve shown in Figure 1-13.

At high pressures, I'increases and eventually becomes equal

to VS; this then corresponds to the maximum in concentration

described earlier.

In conclusion, the existence of a solubility maximum

gives one a reference number that is useful to decide if a

certain extraction scheme is economical. Furthermore, if it

has been determined to perform a certain extraction, then it

can be quickly ascertained what the optimal extraction pressure

is.

1-6 Recommendations

The next research area for supercritical fluids should be in the area of multicomponent liquid -- SCF extraction --

since most industrial separations are with liquids. Some

equilibrium data is available in the literature on binary liquid-fluid systems up to relatively low pressures (100 55

800

600

400 SOLUBILITY SOLUBILITY 200 MINIMA MAXIMA d1b, 0 - Is d -200 -F

X -400

-600

;-800 F o-1000

-1200, SYSTEM: NAPHTH ALENE-ETHYLENE

-1400 -- PE NG - ROBINSON EC)UATION OF STATE -1600 TEAMPERATURE=318 K k 12=0.02 -1800

I I -2000 =now 10 100 100 10,000 PRESSURE (BARS)

Partial Molar Volume of Naphthalene in Supercritical Ethylene

Figure 1-15 56 bar), but little is known about higher pressure solubilities and selectivities in multicomponent systems.

A rewarding research program in this area would include obtaining precise experimental data, correlating it with thermodynamic theory, and evaluating the selectivities as a function of temperature and pressure. 57

2. INTRODUCTION

2-1 Background

Supercritical fluid extraction can be considered to be a unit operation akin to liquid extraction whereby a dense gas is contacted with a solid or liquid mixture for the purpose of separating components from the original mixture.

Advantages in using supercritical fluids over liquid extraction or distillation are many. Compared to distillation, supercritical fluid extraction has shown to be more energy efficient (Irani and Funk, 1977). The advantage of supercritical fluid extraction over liquid extraction is that

(1) solvent recovery is much easier (the pure supercritical fluid can be obtained by expanding it to 1 bar pressure).

(2) Mon-toxic supercritical fluids can be used, such carbon dioxide, to perform the extraction with solubilities comparable to those by using liquid extraction. (3) Solu- bility of the condensed phase in the supercritical fluid is strongly controlled by the temperature and pressure of the system, whereas in distillation and liquid extraction, the major independent variable to control is only temperature.

Historically, the use of supercritical fluids dates back to 1875 with the work of Andrews (1887). Although his work was not published until after his death, Andrews was the true pioneer in this field as a result of the data he obtained 58 on the system liquid carbon dioxide in supercritical nitrogen.

Shortly thereafter, Hannay and Hogarth (1879, 1880) found

that the solubility of the crystals I2, KBr, CoC 2 , and CaCl2 in supercritical ethanol were in considerable excess of that

predicted from the vapor pressure of the solute species and

the Poynting (1881) correction.

This increase in solubility of solids in the supercriti-

cal phase after the discovery of Andrews has led to many

studies, both experimental and theoretical, of solid fluid

equilibrium. In Table 2-1 there is shown a compilation of

available solid-fluid equilibrium data.

As is discussed in more detail in section 2-1, the phase

diagrams for solid-fluid equilibria are of great importance.

The reason for this is that there is only a selected temper-

ature interval where it is feasible to carry out supercritical

fluid extraction. For convenience, Table 2-2 provides a

compilation of all available solid-fluid equilibrium phase

projections.

The basic features of supercritical fluid extraction can be ascertained by studying the data of Diepan and

Scheffer (1948a, 1948b, 1953) and Tsekhanskaya (1964). They measured the solubility of naphthalene in supercritical ethylene over a wide range of temperatures and pressures.

Figure 2-1 shows a plot of their combined data. Many important trends can be observed. First, it is apparent that there are three regimes of pressure. In the low pressure region, an increase in temperature results in an increase in

-11,11,11,11,11flF Table 2-1 Solubility Data for Solid-Fluid Equilibria Systems

Solute Solvent T (K) Tr (Solvent) P (bar) Pr (Solvent) Reference

CO Air 77-163 2 0.58-1.23 1-200 0.03-5.28 Webster (1950) Co Air 115-1,50 0.87-1.13 4-49 29 2 0.11-1. Gratch (1945) Neopentane Ar 199-258 1.32-1.71 na Baughman et al. (1975) Naphthalene Ar 298-347 1.98-2.30 1-1100 0.02-22. 57 King and Robertson (1962) Co 112 31-70 0.93-2.11 1-50 0.08-3.86 Dokoupel et al. (1955) N 25-70 2 H2 0.75-2.11 1-50 0.08-3.86 Dokoupel et al. (1955) CO 35-66 1.05-1.99 5-15 0.39-1.16 + N2 Dokoupel et al. (1955) Xenon 155 112 4.67 4-8 0.31-0.62 Ewald (1955) uL k0 Co 190 5.72 5-16 0.39-1.23 2 "2 Ewald (1955) 0.63-1.66 0 2 2 21-55 3-102 0.23-7.86 McKinley (1962) Naphthalene 295-343 2 8.89-10.33 1-1100 0.08-84.81 King and Robertson (1962) 80-170 2.14-5.12 1-130 0. 08-10.02 Hiza et al. (1968) C2"4 H"2 0 Quartz 653-698 1.01-1.08 112 0 300-500 1.36-2.27 Van Nieuwenbur9 and Van Zon (1935) Quartz 423-873 0.65-1.35 1-1000 0-4.54 Jones and Staehle (1973) Na 2CO3 32 3-623 0.50-0.96 na Waldeck et al. (1932) Na CO3+ NaHCO 373-473 0.58-0.73 na Waldeck et 3 20 al. (1934) UO 112 0 773 2 120 1.19 1020 4.63 Morey (1957) Al2 03 773 1.19 1020 4.63 Morey (1957) SnO23 11 20 773 2 1.19 1020 4.63 Morey (1957) NiO Ho 773 1.19 2040 9.25 Morey (1957 Table 2-1 (cont'd)

Solute Solvent T(K) Tr (Solvent) P (bar) Pr (Solvent) Re ference

Nb2 05 773 1.19 1020 4.63 Morey (1957) Ta2 05 H20 773 1.19 1020 4.63 Morey (1957) H20 FeO I2 0 773 1.19 1020 4.63 Morey (1957) 3 BeO H20H20 773 1.19 1020 4.63 Morey (1957) 11 2 0 GeO H 20 773 1.19 1020 4.63 Morey (1957) 2 CaSO I20 773 1.19 1020 4.63 Morey (1957) 4 HIf200 BaSO 2 773 1.19 1020 4.63 Morey (1957) 4 120 PbSO 773 1.19 1020 4.63 Morey (1957) 4 Na 2SO4 ii 0 773 1.19 1020 4.63 Morey (1957) a' H20 0 Silica HHe 0 883 1.36 1-1750 0-7.94 Kennedy (1950) lie0 Silica 493-693 0.76-1.07 303 1.37 Kennedy (1944) Xenon 155 29.87 4-13 1.76-5.73 Ewald (1955) CO He 190 36.61 4-9 1.76-3.96 Ewald (1955) 2 Air He 66.5-77.6 12.81-14.95 52-448 22.9-197.4 Zellner et al. (1962) N2 Neopentane lie 199-258 38.34-49.71 na Baughman et al. (1975) Naphthalene Ilie 305-347 58.77-66.86 1-1100 0.44-485 King and Robertson (1962) Xenon N 155 1.23 4-9.5 0.12-0.28 Ewald (1955) 2 CO N 140-190 1.11-1.51 5-100 0.15-2.95 Sonntag and Van Wylen (1962) 2 2 Neopentane N 199-258 1.58-2.04 na Baughman et al. (1975) 2

Naphthalene N2 295-345 2.34-2.73 1-1100 0.03-32.41 King and Robertson (1962) CH Ne 44-91 0.99-2.05 10-100 0.36-3.63 fliza and Kidnay (1966 4 Table 2-1 (cont'd)

Solute Solvent T(K) Tr (Solvent) P (bar) Pr (Solvent) Reference

Phenanthrene 313 1.38 138-551 3.69-14. 74 Eisenbeiss (1964) CF4 Naphthalene 294-341 1.54-1.79 1-130 0.02-2.83 Najour and King (1966) C' 4 Naphthalene 296-348 1.55-1.83 1-1100 0.02-23.91 King and Robertson (1962) CH'4 An thracene Cl 4 339-458 1.78-2.40 1-100 0.02-2.17 Najour and King (1970) Neopentane 199-258 1.04-1.35 na Baughman et al. (1975) CR Phenanthrene CH 4 313 1.64 138-551 3.00-11.98 Eisenbeiss (1964) CH Naphtha le ne 4 285-308 1.01-1.09 40-100 0. 79-1. 99 Diepen and Schef f er (1948) C2 4 Naphtha lene C H 318-338 1.13-1.18 40-270 0.79-5.36 Diepen and Scheffer (1953) 2 4 Naphthalene 296-308 1.05-1.09 1-130 0.02-2.58 Najour and King (1966) a' C 2 14 Van Gunst Naphthalene C2 4 289.5-296.5 1.03-1.05 1-170 0.02-3.38 (1950) Naphthalene 285-318 1.01-1.13 50-300 0.99-5.96 Tsekhanskaya et al. (1964)

Anthracene C 2 H4 338-453 1.20-1.60 1-100 0.02-1.99 Najour and King (1970) Anthracene C2 323-358 1.14-1.27 103-480 2.04-9.53 Johnston and Eckert (1981) C 2 l44 c2 313-323 1.11-1.14 na Holder and Maass (1940) 4 c 2 289.5-296.5 1.03-1.05 1-170 0.02-3.38 Van Gunst (1950) C22 ci6C1 6 4

C2 C16+ 289.5-296.5 1.03-1.05 0.02-3.38 Van Gunst Napththalene Cc2 2Hi 4 1-170 (1950) p-chloroiodo- c214 benzene C2 4 286-305 1.01-1.08 21-101 0.42-2.01 Ewald (1953)

Phenanthrene 313 1.11 138-551 2.74-10.94 Eisenbeiss (1964) Coal tar 298 1.06 310 6.16 Wise (1970) Table 2-1 (cont'd)

Solute Solvent T (f) T (Solvent) P (bar) rT (Solvent) Reference

Anthracene 336-448 1.10-1.47 1-100 0.02-2.05 26 Najour and King (1970) Naphthalene 296-337 0.97-1.10 1-1100 0.02-22.52 C2 6 King and Robertson (1962) Phenanthre ne C2U 313 1.02 138-551 2.83-11.28 Eisenbeiss (1964) Naph tha lene CO26 297-346 0.98-1.14 1-130 0.01-1.76 Najour and King (1966) Naphthalene Co 308-328 1.01-1.08 60-330 0.81-4.47 Tsekhanskaya et al. (1964) 2 Carbowax 4000 Co 313 1.03 300-2500 4.07-33.88 2 Czubyrt et al. (1970) Carbowax 1000 Co 313 1.03 300-2500 4.07-33.88 Czubyrt et al. (1970) 2 1-Octadecanol co 313 1.03 300-2500 4.07-33.88 Czubyrt et al. (1970) 2 Stearic Acid CO 313 1.03 300-2500 4.07-33.88 03 2 Czubyrt et al. (1970) Phenanthrene Co 313 1.03 138-551 1.87-7.47 Eisenbeiss (1964) 2 Diphenylamine Co 305-310 1.00-1.02 50-225 0.68-3.05 Tsekhanskaya et al. (1962) 2 Phenol Co 309- 333 1 .02-1.09 78-246 1.06-3.33 Van Leer and Paulaitis (1980) 2 p-chlorophenol CO 309 1.02 79-237 1.06-3.21 Van Leer and Paulaitis (1980) 2 2, 4-dichloro- phenol CO 309 1.02 79-203 1.06-2.75 Van Leer and Paulaitis (1980) 2 Bipheny l 308.8-328.5 co 2 1. 02-1. 08 105-484 1. 42-6. 56 McHugh and Paulaitis (1980) Table 2-2 Phase Diagrams for Solid-Fluid Equilibria

Solute Solvent T(K) Tr (Solvent) P (bar) Pr (Solvent) Reference

N H 10-130 2 0.30-3.92 0.01-10,000 0-771 Dokoupel et al. (1955) Co C11 173-303 0.91-1.59 2 4 1-90 0.02-1.96 Rowlinson and Richardson (1959) Co CH 89- 311 0. 47-1. 63 2 4 1-95 0.02-2.06 Agrawal and Laverman (1974) Naphthalene 258-350 0.91-1.24 10-75 C2 4 0.20-1.49 Dipen and Scheffer (1948) Naphthalene 285-333 c 2 14 1.01-1.18 40-270 0.79-5.36 Diepen and Scheffer (1953) Naphthalene 0.93-1.25 C 2 i4 263-353 1-179 0.02-3.55 Van Gunst et al. (1953) 1, 3, 5-trichlorobenzene 0.93-1.14 C 2 14 263- 323 31-67 0.62-1.33 Diepen and Scheffer (1948) p-dichlorobenzene C 2 i4 258-318 0.91-1.13 31-95 0.61-1.89 Diepen and Scheffer (1948)C p-ch lorobromoben ze ne c 2 14 263-327 0.93-1.16 31-82 0.62-1.63 Diepen and Scheffer (1948) p-chloroiodobenzene 263-319 0.93-1.13 c 2 i4 24-68 0.48-1.35 Diepen and Scheffer (1948) 263-353 p-dibromobenzene C 2 14 0.93-1.25 32-82 0.64-1.63 Diepen and Scheffer (1948) octacosane C 2 H4 260-327 0.92-1.16 29-87 0.58-1.73 Diepen and Scheffer (1948) hexiatriacontane c 2H4 263-343 0.93-1.21 32-88 0.64-1.75 Diepen and Scheffer (1948) biphenyl C2 4 278-328 0.98-1.16 43-85 0.85-1.69 Diepen and Scheffer (1948) benzophone C2 263-310 4 0.93-1.10 30-87 0.60-1.72 Diepen and Scheffer (1948) (1948) menthol c2 0.91-1.06 4 258-300 21-92 0.42-1.82 Diepen and Scheffer C 4 313-323 1.11-1.14 na Holder and Maass C2 C 6 2 (1940) Table 2-2 (cont'd)

Solute Solvent T(K) Tr(Solvent) P(bar) Pr(Solvent) Reference c2 6 C2H 263-285.4 0.93-1.01 32-53 0.64-1.05 Van Gunst et al. (1953) Anthracene C2 4 263-488 0.93-1.73 1-72 0.02-1.43 Van Gunst et al. (1953) Ilexaethylbenzene 263-401 0.93-1.42 0.02-1.27 2 4 1-64 Van Gunst et al. (1953) Hexamethylbenzene c2 4 263-438 0.93-1.55 1-83 0.02-1.65 Van Gunst et al. (1953) Stilbene C2 4 263-395 0.93-1.40 1-78 0.02-1.55 Van Gunst et al. (1953) in-Dinitrobenzene C2 4 263-362.9 0.93-1.29 1-78 0.02-1.55 Van Gunst et al. (1953) Polyethylene C2L1I 533 1.89 1-2000 2H4 0.02-39.71 Bonner et al. (1974) c2 4 Naphthalene 263-328 0.93-1.16 1-180 0.02-3.57 Van Gunst + C 2C16 et al. (1953) a' &6 65

Solubility of Naphthalene in Supercritical Ethylene

101

_Low Middle High Pressure Ragame. m - .- Prassurz P r assur U - S A 2 _R g M C Regime a A 0 I 0 10

004. 0 . z 10-3 Sa" C

Systam : Naphtholana - Ethylene 2. 08 K I OU Timcpratur ( K) Symbol

-4 0 10 285 298 A 308

10 A cData of DeP3n ona Scaffar (1948) and Tsakhc ns kcyc (1964)

10 I I - - 0 40 80 120 160 200 240 280 PRESSURE (BARS)

Solubility of Naphthalene in Supercritical Ethylene

Figure 2-1 66

solubility; in the middle pressure regime, an increase in

temperature results in a decrease in solubility, and finally

in the high pressure regime, an increase in temperature re-

sults in an increase in solubility. It is also apparent that

the solubility covers a wide range in magnitude -- about 104.

By operating an extraction process, say at point A, one can

achieve the extract in pure form by changing the process

conditions to point B. Going from point A to point B results

in a two-order magnitude change in solubility for a small

increase in temperature and simultaneous decrease in pressure.

This, in short, is the significant feature of supercritical

fluid extraction.

Second Interaction Virial Coefficients

Several investigators (Baughman et al., 1975; Najour and

King; 1970, 1966; and King and Robertson, 1962) have calcu-

lated second interaction virial coefficients for solid-fluid

equilibria systems. The virial equation of state is appli-

cable to systems where the gas phase density is less than

about one-half of the critical density of the gas phase. The

study of Najour and King (1970) is typical of all the investi-

gations performed and so their work will be discussed in more

detail. They examined the sys.tem solid anthracene or solid

phenanthrene in the supercritical fluids methane, ethylene,

ethane, and carbon dioxide. Figure 2-2 shows the result of

their calculations in the form of the reduced virial coeffi- H H cient B2* versus reduced mixture temperature TR 2 **. The data 67

-10 -i CnH 4- RR 12 -20 _ C2H6

-30 I ==mad .5 0.7 0.9 1.1 R

Reduced Second Cross Vi rio I Coefficiants of Anthraccna in C02 ,C2 H 4 ,C2 H 6 ,and CH 4 as a Function of Reduced F2mpcraturz

R = 1(7)/V 6 1i2 B12 ( 12 I;T 12 =T/T1

( Najour and King , 1970 )

Figure 2-2 68 for all four gases, except for carbon dioxide coincide on a

smooth curve. If, however, calculations are done to correct

the pure component critical temperature and critical volume

of carbon dioxide to those values that would exist without

the quadrupolar moment, then the carbon dioxide data can be

made to coincide with the other gases (Najour and King, 1970).

Also, it is interesting to note that Najour and King found

the reduced second interaction virial coefficients of

phenanthrene to be identical to those of anthracene.

Applications of Supercritical Fluid Extraction

Food Industry

One of the most active research areas in supercritical

fluid extraction is in the decaffination of coffee. Processes are described in a review article by Zosel (1978) and in two patents: a British patent granted to the German Company

Hag Aktiengesellschaft (1974) and a German patent granted to

Vitzthum and Hubert (1975). Basically, coffee is decaffin- ated by contracting moist green coffee beans before roasting with supercritical carbon dioxide. In a wet, unroasted coffee bean it is caffeine that has the highest vapor pressure of all substances present and is therefore selectively extracted by the carbon dioxide. In a similar manner, a

R C C I C 1/3+ C) 1 / 3 12 B1 2 (T1/V 2 , where V1 2 T + 2

TR C C C C1/2 12 = 1 2 ' where T 2 1 2 69 caffeine-free black tea can also be produced (Hag

Aktiengesellschaft, 1973).

Other food. related applications of supercritical fluid

extraction are removing of fats and oils from vegetables,

obtaining spice extracts, producing cocoa butter, and hop

extracts. These four applications are covered under the

patents of the German company Hag Aktiengesellschaft C1974b,

1973b, 1974c, 1975) respectively. The major reason for the

great interest in using supercritical carbon dioxide in the

food industry is due to the non-toxic properties of carbon

dioxide. Most other methods of purifying foods rely on using

organic solvents such as dichloromethane (Hubert and Vitzhum,

1978) which may pose toxicological problems.

Some food applications, however, rely on liquid carbon dioxide CLCO2 ) for extraction. For example, Schultz et al.

(1967a, 1967b, 1970a, 1970b). Schultz and Randall (1970), and Randall et al. C1971) have studied the extraction of aromas and fruit juices from concord grapes, applies, oranges, and pineapples. The major emphasis of these studies was to find out the key chemical constituents which comprise the flavor of a given species. For instance, although concord grapes have over 100 chemical species, only one constituent; methyl anthranilate is principally responsible for its characteristic aroma. One reason to use LCO2 extraction versus SCF extraction with carbon dioxide is that the selectivity is improved at the lower temperatures of LCO2 Cat the cost of lower solubilities), (Sims, 1979), see also Chapter4-2. 70

Non-Food Industry

Other applications of supercritical fluid extraction

industry are as follows. It has been suggested that a good

way to remove nicotine from tobacco is by the use of super-

critical carbon dioxide extraction (Hubert and Vitzthum,

1978; Hag Aktiengesellschaft, 1974). Desalination of sea

water by supercritical C1 1 and C1 2 paraffinic fractions has

been successfully accomplished (Barton and Fenske, 1970;

Texaco, 1967). Other uses include de-asphalting of petroleum

fractions using a supercritical propane/propylene mixture

(.Zhuze, 1960), extraction of lanolin from wool fat (Peter

et al., 1974), and recovery of purified oil from waste gear

oil (Studiengesellschaft Kohle M.B.H., 1967). Holm (1959)

discusses the use of supercritical carbon dioxide (T = 311 K,

P = 180 bar) as a scavenging fluid in tertiary oil recovery.

The SCF carbon dioxide aids in displacing the oils from the

pores of the reservoir rocks. Some of these applications

are also discussed in the review articles by Paul and Wise

(.19 71) , Wilke (1978), Irani and Funk (1977) , and Gangoli and Thodos (1977).

Application to Coal

Supercritical extraction of coal is under study by at least two industrial concerns. In England, the National Coal

Board (NCB) has done extensive work on de-ashing coal CBartle et al., 1975), with supercritical toluene and supercritical 71 water. In the United States, the Kerr-McGee Company is also

interested in de-ashing coal CKnebel and Rhodes, 1978; and

Adams et al. 19781.

A flow sheet of the Kerr-McGee process is shown in Fig-

ure 2-3. The feed consists of coal dissolved in pentane or

proprietary solvents after having undergone hydrogenation.

After the feed pump, ash-containing liquified coal is mixed

with the recycled propietary solvent (under supercritical

conditions). In the first stage settler, mineral matter and

undissolved coal separate from the coal solution as a heavy

phase. This heavy phase (ash) is then stripped of solvent

in Solvent Separator No. 1. The light phase from the first

stage settler then flows to the second stage settler(while

simultaneously heated to decrease the density of the solvent).

This heating decreases the solubility of the coal in the fluid phase and therefore the deashed coal precipates out and the supercritical fluid is recycled tin Solvent Separator No.

2). If necessary, an additional stage settler and solvent separator can be added to the process. Starting with an 11.7% ash content of Kentucky #9 coal, Kerr-McGee has been able to obtain a de-ashed coal of 0.1% ash by weight.

Regeneration of Activated Carbon

Modell et al. (1978, 1979) has studied the use of supercritical carbon dioxide to regenerate activated carbon.

Granular activated carbon CGAC) is widely used to remove organic contaminents from water. After a given adsorption 72

Karr - McGee Process to De-osh Cool Adams et al. 1978

Fee d

Su rga T nk

SOVont Tank

F Q cd M ixer Pump 21st 2 nd Stag a Staga Sat tler Sat t I ar

Sol v(2n t Solvent Se parator Seporoto r No I No 2

Ash Deoshed Concentrate Cool

Figure 2-3 73

time period, however, the GAC must be taken out of service

and re-activated.

Present technology for desorption of solutes is either

by thermal regeneration, or by use of liquid solvents.

Thermal regeneration has the drawback of significant loss of

carbon during treatment due to oxidation of the carbon and

attrition of fines. Liquid solvent regeneration suffers from

the problems of very slow desorption, expensive solvent regen-

eration equipment, expensive solvents, and toxicity of sol-

vents.

Most of the shortcomings can be overcome by using SCF

carbon dioxide to re-activate the spent carbon. Supercritical

fluids have a sufficiently high density to obtain liquid like

solubilities, but with diffusivities about two order of mag- nitudes larger than for liquids. These properties give favor- able mass transfer coefficients so that the desorption time to regerate GAC with a supercritical fluid is less than for ordinary liquids. Also, if carbon dioxide is chosen as the

SCF, it is inexpensive and nontoxic.

Dehydration of Organic Liquids

(Salting Out Effect)

Another application of supercritical fluids is their use to perform phase separations in binary liquid mixtures. When binary liquid systems which are either partially or completely miscible are subjected to a supercritical fluid, the mutual solubility of the two liquid components is usually reduced 74

(Elgin and Weinstock, 1955, 1959; Snedeker, 1956; Weinstock

1954; Todd 1952; Close 1953). This use of a third component

(.the supercritical fluid) to induce immiscibility is analogous

to adding a solid solute, normally an inorganic salt

(Costellan, 1971), to cause phase splits between organic

liquids and water. Thus, the name salting out effect. The

advantages of using a supercritical fluid over a solid to

"salt out" are obvious when the simplicity of separating and

recovering the fluid from both phases, contrasted with removing

a solid solute is considered. A current commercial venture

to exploit this technology is the dehydration of ethanol-

water solutions by supercritical solvents (Krukonis, 1980).

A better understanding of the salting out effect can be

obtained by considering typical phase behavior for ternary

systems of two liquids and a supercritical component. Elgin

and Weinstock (1959), and Newsham and Stigset (1978) have

shown that three types of phase behavior can be anticipated.

In Figure 2-4 are shown three isobaric, isothermal sections

for a type 1 system. In these diagram, S is the organic solvent, F is a fluid phase, and the supercritical fluid is considered to be ethylene. At a moderately low pressure P1 ,

(and also for higher pressures), the mutual solubility of ethylene and water are very low. At a fixed temperature, however, the solubility of ethylene in the organic solvent increases markedly with pressure so that at an intermediate pressure P2 ' the solvent rich phase contains about 50% ethylene. At a still higher pressure (above the critical S S

P P2L

L-V L -V

H20 F H 20 F (a) (b)

p >p >pP P>Pp (F) 3 2 1 3 c -4 S

Phose Diagroms or aoTernary Solvent -Woter - Fluid Type I p 3 F Sys tem ([Elgin & Wainst oc k ,1959)

L -F

2 F (c )

Figure 2-4 76 pressure of ethylene, the binary pair (organic solvent --

ethylene) become completely miscible.

In Figure 2-5 are shown three isobaric sections for a

type 2 system. The only difference between a type 2 system

and a type 1 system is the existance of a liquid phase misci-

bility gap within the pressure composition prism which does not extend to the ethylene-solvent face of the prism. Type

2b and 2c phase behavior are also typical for water-solvent- salt systems.

Finally, when the miscibility gap in the three component system is large enough to intersect the water-solvent face of the pressure-composition prism, a type 3 system is obtained.

Three isobaric sections for this system are shown in Figure

2-6. The system methyl ethyl ketone-water-supercritical ethylene exhibits this type of behavior and will be used as an example for further discussion.

In Figure 2-7 is shown the pressure-composition prism for the ternary type III system methylethyl ketone (MEK)- water-ethylene at 35.5 bar and 288.1 K. MEK is an important industrial solvent which is used in lubricating oil and de- waxing and is also difficult to dehydrate to a low water content by conventional means. Using high pressure ethylene, however, the two liquid phases which exist in the invariant three-phase region have the following ethylene-free composition: 6.5% MEK in the heavy liquid and 98% MEK in the light liquid. Higher pressure would allow an even wider split, so that dehydration to a water content of less than 1% should S S

2 L2~ L -v LL -L 2-V L, -V H 0O F 2 H 2 0 F (a) (b)

s P33 > P22 >FPj1 ;P3 >IPc (F)(F)

Phase Diogrom5 for a Ternory P 3 Solvent - Woter - Fluid Type II F System ( Elgin & Weinstock, 1959)

L - F

H 20 F (c)

Figure 2-5 S S

Pi L2 P2 L 2

L, -L 2 -V L 2 -V L -V L1 -L 2

L1 -L2-V L1I -L 2 -V L 1 . L 1-V

H20 F H20 L1 -V F (b)

Phose Diagroms for a Ternory 3 F Solvent -Wotar - Fluid Type IR System ( Elgin & WeInstock, 1959)

Ll -L 2 or -F

H 20 F (c )

Figure 2-6 SolvmWntp--+ Pump ------+MixA Qr

Methyl Ethyl P Rec ycle Ketone E thyle Wot er Solvent Fla sh Flosh Tank Tank U, L - v 2 E thy lene Com pr essor Was te Water Dried SOIVent

L, -L2 -V Schematic Flowsheet for Ethylene Dehydrotion of Solvents (Elgin & Wei nstock,.1959 )

H-20 - L, - v C2H4

Phose Equilibrium Diogrom for Ethylene -Woter - Methyl Ethyl Ketone at 35.5 BOr and 288.1K ( Elgin ond Wainstock.1959)

Figure 2-7 80

be relatively easy to accomplish. A possible flowsheet for

a dehydration facility for MEK is shown in Figure 2-7.

The phase behavior for two liquid components and a super-

critical component can be modelled with standard thermodyn-

amics (Balder and Prausnitz, 1966). Using a two suffix

Margules equation for liquid phase activity coefficients,

they have been able to obtain qualitative agreement for the

seven systems studied by Elgin and Weinstock (1959). More

theoretical work, however, needs to be done in this interest-

ing area using more accurate models for the activities of the

liquid phase and the fugacity of the fluid phase.

Supercritical Fluid Chromatography

Another application of supercritical fluid extraction that

has developed is the use of supercritical fluids in chromato-

graphy. While no commercial equipment is yet available in

this area, several investigators (Sie et al., 1966; van Wasen,

et al., 1980; Klesper, 1978) have fabricated their own equipment. Major problems of the design of these chromatographs lie with the design of the detectors and the operation of a system capable of injecting a small sample into a column at pressures up to 300 bar.

The basic concept lying behind SCF chromatography is that if a supercritical fluid is used as the mobile phase, then by operating at sufficiently high pressures, the capacity ratioCSTAT STATA k. i (2-1.1) I CMB MOB 81

where CSTAT and CMOB are the concentrations of component i

in the stationary (stat) and mobile (mob) phase and VSTAT

and VMOB are the total volume of the stationary and mobile

phase in the column, will undergo a significant decrease with

increasing pressure. Whereas in gas chromatographyonly

temperature has a significant role in determining the capacity

ratio, in SCF chromatography, temperature and now, most signi-

ficantly pressure, has a great effect on the capacity ratio.

As a result, lower temperatures can be used so that high

molecular weight thermodegradeable biological materials as

complex as DNA may now be separated in SFC. Also, ionic

species (Jentoft and Gouw, 1972) which would decompose in gas

chromatography can be solubilized in a SCF and thus are amend-

able to supercritical chromatography.

The operating conditions where SFC will have its poten-

tial application is shown in Figure 2-8 in the form of a

reduced pressure, reduced density plot. Table 2-3 lists a

series of possible mobile phases for SFC. The "proper"

supercritical phase to choose is one whose critical tempera-

ture is close to, but slightly below the desired temperature

of operation.

An example application of SFC is in the resolution of

oligomers. For instance, stryene oligomers of nominal mole-

cular weight, NM = 2200 were separated into more than 30

fractions (Klesper and Hartmann, 1978) using a supercritical phase of 95% n-pentane and 5% methanol.

Finally, SFC can be used to obtain thermodynamic 82

30 20

Lu D 5

LU c-C. Cr -2

u 1 nQ LUJ NL 0.5

0.1 0 1.o 2.0 REDUCED D EN"S IT Y (GIDDINGS ET AL,1968)

SupercrIcal Fluid ( SCF) Operating Regimes for Extraction Purposes

Figure 2-8 83 Table 2-3

Critical Point Data for Possible Mobile Phases for Supercritical Fluid Chromatography

Compound c c(bar)

Nitrous Oxide 309.7 72.3 Carbon Dioxide 304.5 73.9 Ethylene 282.4 50.4 Sulfur Dioxide 430.7 78.6 Sulfur Hexafluoride 318.R 37.6 Ammonia 405.5 112.8 Water 647.6 229.8 Methanol 513.7 79.9 Ethanol 516.6 63.8 Isopropanol 508.5 47.6 Ethane 305.6 48.9 n-Propane 370.0 42.6 n-Butane 425.2 38.0 n-Pentane 469.8 33.7 n-Hexane 507.4 30.0 n-Heptane 540.2 27.4 2,3-Dimethylbutane 500.0 31.4 Benzene 562.1 48.9 Diethyl ether 466.8 36.8 Methyl ethyl ether 437.9 44.0 Dichlorodifluoromethane 384.9 39.9 Dichlorofluoromethane 451.7 51.7 Trichlorofluoromethane 469.8 42.3 Dichlorotetrafluoroethane 419.3 36.0 84

properties for the materials being used as the supercritical

phase. van Wasen et al. (1980) and Bartmann and Schneider

(1973) describe the proper data reduction to obtain partial molar volumes at infinite dilution, interaction second vivial

coefficients, and diffusion coefficients.

Rules of Thumb as to What can be Extracted

Stahl et al. (1980) presents some "rules of thumb" as to what can be extracted into SCF carbon dioxide at 313 K. These

rules were obtained by performing qualitative studies on many

types of solid constituents.

1. Hydrocarbons and other typically lipophilic organic

compounds of relatively low polarity, e.g., esters,

lactones and epoxides can be extracted in the

pressure range 70-100 bar.

2. The introduction of strongly polar functional groups

(e.g. -OH, -COOH) makes the extraction more difficult.

In the range of benzene derivatives, substances with

three phenolic hydroxyls are still capable of extrac-

tion, as are compounds with one carboxyl and two

hydroxyl groups. Substances in this range that

cannot be extracted are those with one carboxyl and

three or more hydroxyl groups.

3. More strongly polar substances, e.g. sugars and amino

acids, cannot be extracted with pressures up to 400

bar. 85

2-2 Phase Diagrams

Binary Phase Behavior for Similar Components at Low

Pressures

Phase behavior resulting when a solid is placed in con-

tact with a fluid phase at temperatures near and above the

critical point of the pure fluid are of key importance. The

phase diagram provides guidance to possible operating regimes

that exist in supercritical fluid extraction.

In order to establish a basis, a general binary P-T-x diagram for the equilibrium between two solid phases, a

liquid phase, and a vapor phase is shown in Figure 2-9. This diagram is drawn for the case of a substance of low volatil-

ity and high melting point and one of high volatility and

slightly lower melting point. On the two sides of the diagram are shown the usual solid-gas, solid-liquid, and liquid- gas boundary curves for the two pure components. These boundary curves meet, three at a time, at the two triple points A and B. The line CDEF is an eutectic line where solid 1(C), solid 2(F), saturated liquid (E), and saturated vapor (D) join to form an invariant state of four phases. A projection of

ABCEF on the T-x plane gives the usual solubility diagram of two immiscible solids, a miscible liquid phase, and a eutectic point that is the projection of point E. This projection is shown as the "cut" at the top of the figure, since pressure has little effect on the equilibrium between condensed phases. 86

G H

The Pressure - Temperature - composition Surfacas for the Equilibrium Between -Two Pure Solid Phases, A Liquid Phase and a Vapor Phase

( Rowlinson and Richardson,1959 )

Figure 2-9 87

It is also interesting to examine the P-x projections

of this three dimensional surface. Below the eutectic temp-

erature, the P,x projection is given by GHIJK, where H and

K are the vapor pressures of the two pure solids. The total

pressure of the two solids in equilibrium with the mixed

vapor is given by GIJ which is very close to the sum of the

vapor pressures of the two pure components. At temperatures

above the melting point of component 1, a P-x projection has

the shape shown by the dashed lines Cof the isothermal cut)

in Figure 2-9 and is drawn in more detail in Figure 2-10.

Notice that there are two homogeneous regions, liquid and gas,

and three heterogeneous regions, liquid + gas-, solid + gas,

and solid + liquid. At temperatures above the melting point

of the second component, an increase in temperature causes

points W and Y to move towards point Z. For temperatures

between the melting point of the second component and the

critical temperature of the light component, one obtains a

P-x cross section similar to that shown in Figure 2-11. The

locus (M-N) of the maxima of the (P,x) loops is the gas-

iqui critca1 pint 4ne of the binary mixture Finally, in Figure 2-12 there is shown a P-T projection

indicating the three-phase (AFB) locus and the critical

locus (MN). In this figure, the only region where solid is

in equilibrium with a gaseous mixture is in the area under the three-phase line AFB. Similarly, solid-gas equilibrium in Figure 2-9 exists on the curves HI and KI and in Figure

2-10 on the curve WX. Up until now, all of these diagrams 88

L S+ L p V, x I' z I

G0 S G w x

A Pressure Compositlo n Sect ion at a Constant Temperature Lying Between The Melting Points of the Pure Components ( Rowlinson and Richordson, 1959 )

Figure 2-10 89

A Pressure - Composition SQctiOn at a Constant Tampc raturc above the Melting Point of the Second Component

Figure 2-11 90

N P

P-T Projection of a System in Which the Three Phase Line Does Not Cut the Critical Locus

Figure 2-12 91

have been for similar substances and for relatively low pres-

sures. The next section discusses the case of very dissim-

ilar components and for very high pressures.

Binary Phase Behavior for Dissimilar Components at High

Pressures

Supercritical fluid extraction of solid solutes usually

operates with two very dissimilar substances (one is usually

a low molecular weight gas at room conditions; one a high mole-

cular weight solid at room conditions). Under these circum-

stances, the phase behavior discussed previously is not valid.

Instead, entirely new phenomena exist in the P-T-x phase

space. This phenomena, which is of most importance in

understanding the use and limitations of supercritical fluid

extraction, will be the topic of this section.

High pressure phase equilibria among dissimilar components has been previously investigated by Rowlinson (1969),

Rowlinson and Richardson (1959), van Welie and Diepen (1961), van Gunst et al. (1953a, 1953b), Diepen and Scheffer (.1948a,

1953)., Morey (1957), Smits (1909), and Zernike (1955). The best way to introduce this subject is to reconsider the diagram shown in Figure 2-12. If the two components are so dissimilar that one is a low molecular weight gas at room conditions and one is a high molecular weight solid, then the difference in temperature between the triple points and critical points of these substances is so large that the three phase line AFB in Figure 2-12 can actually intersect 92 the critical locus so as to "cut" it into two points: p-

the lower critical end point, and q- the upper critical end

point. See Figure 2-13. In this figure, M and N are the

critical points of the supercritical fluid and solid respec-

tively. Critical end points are mixture critical points in

the presence of excess solid. Following the notation of

Morey (1954), these critical end points are commmonly written

as follows:

p : (G ELi) + S

q : (G EL2 ) + S

i.e., a liquid and gas of identical composition and proper-

ties in equilibrium with a pure solid.

The major consequence of a gap in the critical locus as

shown in Figure 2-13 is to allow at least* a region in

temperature between Tp and T where cne solid phase is in

equilibrium with one fluid phase with no liquid phase present.

In order to have a better visualization for the P-T projection of the P-T-x surface, it is necessary to under-

stand various P-x and T-x projections. Figure 2-14 shows a

P-T projection indicating where isothermal P-x projections are located in Figure 2-15. At T1 , the projection is

*A more general statement is discussed later in this section. 93

P N N v I

A0 c- F BN

P -T Projaction of a System in Which the Three Phas a Line Cuts the Critical Locus

Figure 2-13 I I I I I I P I I 1I

I A I

T5 T 1 2 Ty Ti T6

A P-T Projection Indicating Where the Isothermol P-x Projections of Figure 2-15 ore Located

Figure 2-14 95

T, T2 T3-

F 5+ F Influence L S+L1 p or of 0E2 S +L .. -.F Inf luencc CEP, S.F orStV of CEPi S +V x *F or +L2 S+ L 2 p CE P 2 S+ F or S+L2 V+'2 5+L1

T4 Tz2 T6

T7 T8

5-L2

P Lz 2

p. I i

( after Hong ,1980)

Isothermal P-X Projections For Solid-Fluid Equilibria

Figure 2-15 96 identical to Figure 2-10, i.e., equilibrium exists between

two similar compounds. Isotherm T2, the lower critical end

point temperature, shows that the L-V branch has disappeared

so that there is one homogeneous region -- which for conven-

ience has been divided into two fictious regions correspond-

ing to the L-V equilibrium position that exists an infinitesi-

mal position to the left. T3 is a projection in the "window"

between Tp and Tq. Here, the solubility is unity at the

vapor pressure of the solute, then decreases with increasing

pressure, reaches a minimum, increases, reaches a maximum,

and then decreases again. At T4 , the upper critical end point

temperature, again there is one homogeneous fluid phase pre-

sent, which for convenience has been divided into two ficti-

tious regions corresponding to the top of the critical locus

that exists an infinitesimal position to the right. T5 is

an isotherm between the upper critical end point and the

triple point of the solid. Note the existence of a discon-

tinuity in the two solid + liquid regions. This discontinuity

is important from an experimental point of view in predicting the upper critical end point temperature. Also, the binary critical point for the mixture is located at the apex of the liquid-liquid equilibria region. At the triple point, the liquid-liquid region must disappear, and so there are now two homogeneous regions: (S+L2 ) and (V+L2). At T7 , the

CS+L2 1 phase has broken off from the liquid-vapor region and will continue to shrink, until at some temperature before the critical point of the solid, only a liquid-vapor 97

equilibrium region remains.

Construction of a T-x and P-x Diagram

Modell et al. (1979) has constructed a T-x diagram for

the system naphthalene-carbon dioxide as shown in Figure 2-16.

Several important features should be brought out. First, the

tie-lines connecting the three phase locus are isothermal

lines. Second, in the region between the first and second

critical end points, there exists a region of retrograde

solidification, i.e., a region where an increase in temperature

causes a decrease in solubility.

An analogous diagram for carbon dioxide-phenanthrene is

shown in P-x coordinates in Figure 2-17. In this figure the

extreme sensitivity of the equilibrium solubility to temper-

ature and pressure is more apparent and the retrograde solid-

ification region is clearly shown. All of these two-

dimensional projections aid in providing a picture of the

actual three-dimensional surface of this complex equilibria

system.

P-T-x Diagram for Solid-Fluid Equilibria

Zernike C1955) and Smits (1909) have provided isometric,

three-dimensional drawings for the case of solid-fluid equil-

ibria. With the help of the many projections shown previously, a clear understanding of these diagrams is now possible. As both sketches are similar, only the diagram of

Zernike will be discussed. Figure 2-18, shows this equilibrium surface. While the diagram indicates a perpendicular 98

280 290 300 310 320 330 340 350 360 0 --

UCEP Mir

-~1- S- L-F

S-F o 2150 at\ -2-

0 -3

5- L-V

55 atm - 4-

(Af ter Hong,1981)

Nophthalene - Carbon Dioxide Solubility Mop Calculated from the Peng - Robinson Equation; k12 = 0.11

Figure 2-16 99

-2 10

328 K

-3 10

- 318K

328 K 33S K

-4

-5 System CO2 -Phenanthrene -PR Equation of Statq Temperature (K) Symbol k12 318 0 0.113 338 K 328 A O008 338 U 0.106 10 -6328 K

318 K

-7 '0f 0 40 80 120 160 200 240 280 PRESSURE (BARS)

Solubility of Phenanthrene in Supercritical Carbon Dioxide

Figure 2-17 100

Space Model in the Case Where the Critical Locus and the Thre!e Phase Line Intersect ( Ze r n ike,1955 )

Figure 2-18 101

dividing surface extending infinitely upward at the upper and

lower critical end point temperatures -- this surface is

fictitious because there is no phase transition to the left

or right of these critical end point temperatures. The div-

iding surface only indicates the uniqueness of the region

between TP and T . It is also apparent that the isothermal

P-x projections shown in Figure 2-15 "fit" nicely into the three-dimensional surface. Note in Figure 2-18 that the

critical points of the two species and the upper and lower critical end points are on different planes of this surface.

This is not obvious from two dimensional projections.

Solid-Fluid Equilibria Outside The Critical End Point

Bounds

As is clearly shown by the many P-T projections of Figure

2-15, there exist regions of temperature other than

T < T < T for which there is solid-fluid equilibrium. p - - q These other regions of temperature, therefore, offer unique possibilities for supercritical fluid extraction, but suffer from the drawback that the pressure must be kept between minimum and maximum bounds in order to guarantee that no liquid phase will form. A major advantage, however, of operating in these regions is that much higher solubilities of the solid in the fluid phase can be achieved compared to the solubilities that can be achieved in the region

T < T < T . p q This particular phase behavior can be best understood 102

from Figure 2-15 isotherms, T 3 , T4 and T 5 . Since the (S+F)

isotherm T5 and the apex of the CL1 +L 2 ) isotherm T5 is on

the critical locus of the binary mixture, then it follows

that as long as the system pressure is greater than the maxi-

mum pressure on the critical locus connecting the upper ,

critical end point with the critical point of the solid com-

ponent, it is possible to operate with high solubilities in

the S+F region for temperatures T > T,. As the

P-x diagrams of Figure 2-15 show, the solubilities in this

region of solid-fluid equilibria will of necessity be higher

than the solubility in the region of temperatures Tp < T < T . Consequently one can theoretically approach a solubility of

100 mole percent of solute in the fluid phase.

As an example, consider the system naphthalene-ethylene.

Figure 2-19 shows experimental P-T data for the critical locus, the three-phase line and the upper critical end point.

From this figure, it can be concluded that if the system pressure is greater than about 250 bar, that it is possible to operate in a solid-fluid regime for T > T . Verification of these ideas is shown in Figure 2-20. This is a graph of temperature versus mole percent at a constant pressure of

274 bar. The large change in solubility occurs near the upper critical end point temperature C52.1 C). Also note the excellent agreement between the experimental data and theory Cthe solid line calculated from the Peng-Robinson equation of state,which is discussed later). 103

Critical 250 Locus c1 200 V) -UC E P 150 \B Ld --- Fusion Line LJ 100 Ur

CL ThrI I I oo Phasa 50 I I Line

I 0 = I iiiiiiinsop k .- . - -- I - 373 473 573 673 T (K)

P-T Projection for Et hylene - Naphthalene (Van Welie and Diepen, 1961)

Figure 2-19 104

90 -U

80 K

70 U -0 60 0 LU I 50 System Ethylene -Naphthalene 0 CL Pressure= 274 Bar I- 40 -PR Equation of State

k, 2 =0.02 30 0 Experimental Data of Diepen and Scheffer (1953 ) * Melting Point of Nophthalene 20 at 274 Bar

10: K- I 0 20 40 60 80 100 NAPHTHALENE (MOLE %/)

T-x Projection for Ethylene-Naphthalene for Temperatures and Pressures above the Critical Locus

Figure 2-20 105 Phase Behavior in Multicomponent Systems

Multicomponent systems (two or more solid phases in

equilibrium with a fluid phase) have essentially the same

type of phase behavior as binary systems with, however,.

a few peculiarities. Assuming the interesting case where

the critical locus is broken into lower and upper critical

end points, the P-T projection of a ternary phase diagram

will appear similar to that shown in Figure 2-21. (Note:

P-X projections cannot be drawn because the phase diagram is

four dimensional).

Key points to be noted about Figure 2-21 are as follows.

First, there are now six critical end points. K1 and Ki are

the first and second lower critical end points. These end

points are the intersection with the critical locus of the

three phase line formed by the two solids in equilibrium with

a liquid and a gas phase. Similarly, K2 and K' are the first

and second upper critical end points. In the case where no solid solutions form, there will exist two eutectic points and hence a four phase line connecting them. However, the four phase line may intersect the critical locus at a lower double critical end point and at an upper double critical end point -- shown as p and q respectively. The reason for calling these double critical end points is that they are actually formed by the intersection of the two first and second lower and upper critical end points respectively.

There are important physical implications that make the ternary system different from the binary system. As the I

q Kiv G K1 p KA K;

P P/0/ (9 't H L /

P-T Projection of a Four Dimensional Surface of Two Solid Phases In Equilibrium with a Fluid Phase

Figure 2-21 107

upper double critical end point is formed by the intersection

of the four phase line with the critical locus -- and the

four phase line starts at the eutectic point of the two

solids, then it is apparent that the temperature of the upper

double critical end point will be lower than either of the

temperatures corresponding to the first and second upper crit-

ical end points.

As an example, consider the system supercritical fluid

ethylene with the two solids naphthalene and hexachlorethane

in comparison to the binary system supercritical ethylene with naphthalene. The critical end points of these .two systems are shown in Table 2-4. Note the significant lowering of the upper critical end point temperature by 26.6 K.

Mathematical Representation of Binary Phase Behavior

By molecular thermodynamics, one can generate a binary- phase diagram for solid-fluid equilibria. All that is needed is an applicable mixture equation of state for the fluid phase, the vapor pressure, and the molar volume of the solid phase. The exact methodology to follow to generate such a phase diagram which includes the critical locus, the three phase line, and the critical end points is discussed in this section.

Thermodynamics of the Binary Critical Locus

A critical point is a stable position on a spinodal curve. Using the Legendre transform notation of Reid and

Beegle (1977) and Beegle et al. (1974), the critical locus 108

Table 2-4

Comparison of Critical End Points for the System Super- critical Ethylene-Naphthalene with the System Supercri- tical Ethylene -Naphthalene -Hexachloroethane

T (K) Tq(K) System ethy lene-naphtha lene 1 283.9 325.3 ethylene-naphthalene-hexachloroethane2 288.5 298.7

1. Diepen and Scheffer (1953).

2. van Gunst et al. (1953). 109 are those states that satisfy

(n) = 0 (2-2.1) Y(n+l) (n+l)

and

Y(n) = 0 (2-2.2) (n+l) (n+l) (n+l)

In terms of the Helmholtz free energy, these transforms can be written (for a binary mixture) in terms of the two deter- minants

Avv Av L = AV1 A

=A A -Ai =0 (2-2.3) vvll VI where

A a=A(2-2 .4) vv [WVJTx

A11 3t2jC2.S T,x

2 A 2 (2-2.6) vi = DVDx T,x 110

A A and MII = 0 (2-2.7) F3L1 (3L1 av J T,x L axTV

or, 2 =A A A +A A -JAA VA A 1 M 1 vvllvvl vvlll vvvlVll

-A A A + 2A2 A =0 (2-2.8) 11 vI vvv vlVV 1

Equations 2-2.3 and 2-2.8 are most conveniently solved sim-

ultaneously by a pressure explicit equation of state.

Modell et al. (1979) have derived these critical criteria

using the Peng-Robinson equation of state.

Determination of the Three Phase SLG Line

Thermodynamics requires that on the three-phase SLG line

that the following equalities must be satisfied:

fI(T,P) = fL (TPx1)(2-2.9)

f1(T,P) = fV (TPfyl)(2-2.10)

fj(T,P,y1 ) -fI(T,P,x1 ) (2-2.11)

f>(T,P,y1 ) =--TPx1)(2-2.12)

Of these four equations, only three are independent and a convenient set to chose is the last three. The fugacity of the solid phase is given by ill

V' P .sI(T, P) = PVP-*exp (2-2.13) and the fugacity of the liquid and vapor phase by

f = x L$ (2-2.14)

(2-2.15) fV = y1Pc where the fugacity coefficients L and $vare found from an applicable equation of state. An iterative solution of Equa- tions (2-2.10) through (2-2.12) coupled with the mass balance

X + X2 = 1 (2-2.16) is sufficient to define the three-phase line. Numerical techniques helpful in solving for the three phase line are discussed by Francis and Paulaitis (1980).

Determination of Binary Critical End Points

There are two convenient methods whereby the upper and lower critical end points may be calculated. One is to generate the entire critical locus and the entire three-phase line, then plot the results on a P-T projection and graphi- cally determine the end-points.

An easier way, however, is as follows. At a binary mixture critical point, the following thermodynamic equality must be satisfied.*

*See Appendix II for a derivation. 112

ap I =0 (2-2.17) 1a0 Tx l a

where x1 is the mole fraction of component 1 in the liquid

phase and subscript a denotes differentiation along the

three-phase curve. Thus, when the three phase curve is gen-

erated on the computer, a numerical check can be performed to

test for the equality of Equation 2-2.17. There will exist

two such equalities -- one at the upper critical end point

and one at the lower critical end point. Numerical techniques

helpful in solving for the binary critical end points are

discussed by Francis and Paulaitis (1980).

Experimental Methods to Determine Critical End Points

of Binary Systems

There are two methods whereby one can determine experi-

mentally the critical end points for binary systems. The

first method makes use of the rigorous thermodynamic relation-

ship that at a critical end point (see Appendix II).

=0 (2-2.18) dyjT

Thus, if careful experimental data are taken of isothermal solubilities versus pressure, then two isotherms will exhibit the zero slope criteria of Equation 2-2.18. These two conditions will be the upper and lower critical end points.

Extremely precise solubility data must be taken for this 113 method to be reliable -- for the solubility is very sensitive

to temperature and pressure near the critical end points.

Alternatively, one can make use of the special nature

of the phase behavior near the critical end points to deter-

mine their values. Consider the isotherms T4 and T5 shown in

Figure 2-15. These figures imply that if isothermal solu-

bility data are taken at many pressures, that as the isotherm

just exceeds the upper critical end point temperature (or is

just less than the lower critical end point temperature), then

there will be a discontinuity in the isothermal solubility

curve. The temperature and pressure at which the discontin-

uity first occurs are the critical end point temperature and

pressure respectively. McHugh and Paulaitis (1980) have ob-

tained experimental values of the upper critical end points

for a few systems by the second method.

Comparison of Experimental Critical End Points

to Those Predicted by Theory

To date, there is only one system for which there are both experimental measurements of critical end points and also theoretical calculations of the critical end points. This system is naphthalene-ethylene. Diepen and

Scheffer -1948a) and van Gunst et al. (1953) found the critical end points experimentally while Modell et al. (1979) calculated them using the Peng-Robinson (1976) equation of state. A comparison of experimental and theoretical results is shown in Table 2-5. The agreement is satisfactory. Table 2-5

Comparison of Experimental vs Theoretical Values of the Critical End Points for the System Naphthalene-Ethylene

Lower CEP Upper CEP System T (K) P(bar) y T (K) P (bar) y

Naphthalene-ethylene, experimentall 283.9 51.9 0.002 325.3 176.3 0.17

Naphthalene-ethylene, Peng-Robinson 282.8 50.6 0.0004 314.3 160.9 0.12

H 1 Diepen and Scheffer (1953) H 115

2-3 Thermodynamic Modelling of Solid-Fluid Equilibrium

Equilibrium Conditions Using Compressed Gas Model

The criterion of equilibrium between a solid phase (pure

or mixture) and a fluid phase for any component i is

^-S f% f^F%= (2-3.1)

Using a compressed gas model for the fluid phase, the fugac-

ity coefficient in the fluid phase can be written

^F F f. = FyP$ (2-3.2)

where $ is determined from an equation of state by the

definition (Modell and Reid, 1974).

ST a P ln$ = K- 3j dV - lnZ (2-3.3) - T,V,N. [il-

Assuming that

1. solid density is independent of pressure and compo-

sition

2. no solid solutions form

3. solubility of the fluid in the solid is sufficiently S small so that y. land x. = 1

4. vapor pressure of the solid is sufficiently small

so that $s5 ~land P -P s vp.- vpi

Then, the solid phase fugacity can be written 116

PVs fs = P exp (2-3.4) i vp.RT

Combining Equations 2-3.2 and 2-3.3 gives the equilibrium mole fraction of a component i in a supercritical fluid as

s ---- s - exp (2-3.5) y. = S P 0F RT

Equation 2-3.5 conveniently divided into three terms shown in brackets. The first bracketed term is the equilibrium solubility assuming the ideal gas law to be valid. The second term accounts for the nonideality of the fluid phase.

The third term is the Poynting (1881) correction.

It is also often convenient to speak of the enhancement factor which is defined as the actual solubility compared to that assuming an ideal gas. Solving for the enhancement factor from Equation 2-3.5 gives

PV.s expLRT E. e= (2-3.6) F i

Equilibrium Condition Using Expanded Liquid Model

Instead of treating the supercritical fluid phase as a compressed gas it may be advantageous to consider it as an expanded liquid. With this approach, at constant temperature, the fugacity of component i in the fluid phase can be 117

expressed as

'R V.

f(y.,P) = y y.(y ,P )f(P )exp dP (2-3.7)

pressure and f9 is a hypothetical where PR is a reference 1 fugacity of pure liquid i at the system temperature and at

the reference pressure PR. The solid phase fugacity can be

written as

'PV %s s R (PR) dP (2-3.8)

where fs (PR) is the fugacity of pure solid at the system

temperature and at the reference pressure PR. Making the

following assumptions: (1) the solid density is independent of pressure and composition; (2) the solubility of fluid in the solid is sufficiently small so that ys = 1 and xi_ and (3) no solid solutions form, then equation 2-3.8 can be written as

Rs f S = f(pR Kex RT)(2-3.9) 1 1 )ep' RT

Combining Equations 2-3.7 and 2-3.9 gives

(P-PR)V. f3(P )exp RT yi = R Lf R - P'- - (2-3.10) 1 1' exp B[}dP IpR RT, 118 It can be shown (Prausnitz, 1969) that to a very good approxi-

mation

fL(PR) AH N A C P- 'TT in (R R T]

AC I T i t + R in T23.1 (2-3.11)

where Tt .is the triple point temperature of component i.

Furthermore, the last two terms on the right of Equation

2-3.11 are about equal in magnitude and opposite in sign.

Thus, Equation 2-3.11 can be approximated as

rAH rT exp R-T [ PRs exL t.LI.jj exp R y.=RRTP i(2-3 .12)

exp dP

An accurate representation of y. (yF,P ) and V must now be obtained. Mackay and Paulaitis (1979) have used a reference pressure of

p R =c with Pc the critical pressure of the pure fluid phase, and the assumptions that

R 00 Yi cy ,P }~YiCPc) (2-3.13) 119

S (Y. ,P R) V~00 (P )(2-3.14)

V7I(P ) then can be found from an applicable equation of state i c by the definition

r(3V = im 1 (2-3.15) N10 3N T,PCN

Y (P ) is treated as an adjustable constant. 1 C Using the Peng-Robinson (1976) equation of state, Mackay and Paulaitis (1979) were able to correlate naphthalene solubilities in supercritical carbon dioxide and supercritical ethylene at a constant value of the binary interaction parameter and for a temperature dependent infinite dilution activity coefficients. The infinite dilution activity coefficients they obtained, however, are quite large.

Applicable Equations of State

Both the compressed gas and the expanded liquid model approach to solid-fluid equilibrium require an equation of state to evaluate fluid phase fugacity coefficients (former case and partial molar volumes (later case). This section will discuss the types of equations of state applicable to determine these thermodynamic quantities in the mixture state.

Virial Equation of State

The virial equation of state is applicable to the 120 correlation of the solubility of solids in compressed gases,

but only for relatively low pressures. When the pressure is

such that the density of the gas is less than about one-half

of the critical density, the virial equation of state,

truncated to the third term can be used. The virial equation

can be written

B CM = 1 + V + 9 + .* (2-3.16) where:

BM i=yyB. C(.2-3.17) 1J

(2-3.18) CM=ikaijk ijk

A major advantage of the virial equation is that the virial coefficients have a physical meaning in that they are related

to the intermolecular potential function. Under conditions where the virial equation of state is applicable, the enhancement factor has been calculated for the compressed gas model

(Ewald, 1955), (Ewald, et al., 1953) as:

Vs 2 ln E = 0B(P-P2)+ 2 - 2BB+x B 2 -2x 2 B ) RT P92 + -x1 B1 1 -2 1 B1 2 2 2 2 22 RT

2 1 P4 2 3 4BB ) + x 3C + 2 F-x43B2-x3(2C1111111- 1112 1 112

3 2 2 +x x 2 12B 1 B 2 xix(6C2 1 1 2 +4B 1 B 2 2 +8B$ 121 2 +x X 2 6C1 2 2 - xx2 (6C 1 1 2 +12B1 B 2 2 )

13 12-12 12 2 42 +x x 3 2B B +X 2 (2 B 2 +BB x4B2 1 2 12 22 1 2 (12B1 2 11+62 2 )+x2 B2 2

2 -x3(2C 2 2 2 +4B 2 )+X 2 3C2 2 2 J f (2-3.19)

where: subscript 2 is the solid

subscript 1 is the fluid

0 P2 is the vapor pressure of the solid 5 V2 is the molar volume of the solid

As an example, consider the application of the virial

equation to solid-fluid equilibrium calculations in the corre-

lation of solid carbon dioxide solubility in supercritical

air. The resultant plot is shown in Figure 2-22. Clearly, for

an accurate correlation past the solubility minimum, the third

virial coefficient must be taken into account. As the virial

equation is not valid for densities greater than about one-

half of the critical density of the mixture, one has to

resort to empirical equations of state for the high pressure

region.

Cubic Equations of State

Of all the equations of state used today, the cubic equations of state are probably the most widely used. Evi- dence of this is in the continuing effort to produce modifications of the original cubic equation of state: that of van der Waals (1873). After the development of van der Waals 122

-2 10 S 1 VIric 6 Second Coeff. Only ix 4 -/ CL

42 z 2 /

N Second and Third 0 Virnai Coeff. L) 10 z 0 6

LL Data 2 - C Webster (1952) -j 0 a Gr(OtCh (1945) 7 1(54 8 - Nc 6

I I ' s 0 20 40 60 80 100 120 PRESSUREal Lm (gauge)

Solubility Of C02 in Air ( Prousnitz,1969 ) Ot 143 K

Figure 2-22

ff 123

equation, the most significant advance was the Redlich-Kwong

(1949) equation which modified the attractive term of van der

Waals. After Redlich-Kwong, Soave (19 72) made the next major advance by introducing a temperature dependence on the

attractive term. Following Soave, many other equations of

state were developed (Peng and Robinson, 1976; Fuller, 1976;

Won, 1976; and Graboski and Daubert, 1978). Also, two review articles on cubic equations of state were written (Abbott,

1973; Martin, 1979).

At the present time, it is believed that the best cubic equation of state is that of Peng and Robinson (1976). Their equation is:

aCT) P RT_ (2-3. 20) V-b V (V+b) + b CV-b)

R 2T2 where a. T ) = RT (2-3.21) i c a P.i

RT b (T ) = 2 c C2-3. 221 i c b P.ci

a. (T) = a.(Tc) . a.CT ,w.) (2-3.23) I c

C2-3. b.(T)x = b.x CTc)c 24)

1 2 .(T u) Li + K. (1-T / ) (2-3.25) x C ri 124

. = 0.37464 + 1.54226w. - 0.269922. (2-3.26)

a = Zcl-k ).)a}/2 ah/ 2 x x. (2-3.27) iJ

b= Zb.x. (2-3.28) 1.

By definition of the fugacity coefficient (Modell and Reid,

1974)

l = fVFI- F4J32 dv - InZ (2-3.29) ;0 %.1JT, Pt% [i]j

The fugacity coefficient of component i can be calculated as

b.A lnt. = (Z-l) - ln(Z-B) -A b 2Y/IB

-22x.a.. S13 bo nz +(CL+42)B (2-3. 30) a b Z -(1- D)B, where A = aP/R2T2 (2-3. 31)

B = bP/RT (2-3. 32)

Benedict-Webb-Rubin Equation of State

The Benedict-Webb-Rubin (BWR) equation of state (Benedict et al., 1951, 1942, 1940), is another equation of state which is often used. Originally, the BWR constants were tabulated for only the light hydrocarbon systems. Later, Edmister et al. (1968) expressed the eight parameters in terms of critical 125

pressures, temperatures, and acentric factors. Starling and

Han C1971, 1972a, 1972b) added three more parameters to the

original BWR equation of state and developed a correlation

for these parameters in terms of critical temperature, critical

volume, and acentric factor. Yamada (1973) developed a

fourty four parameter BWR equation and a correlation of these

parameters in terms of critical temperature, critical pres-

sure, and acentric factor. Lee and Kesler (1975) developed

a modified BWR equation within the context of Pitzer's three

parameter correlation.

These many types of BWR equations have proved to be very

successful for light hydrocarbon systems at conditions far

removed from the critical point. Near the critical point,

however, the BWR equations are less accurate as they do not

satisfy the two pure component stability criteria at a critical

point.

Perturbed Hard Sphere Equation of State

All of the cubic equations of state developed to date

have used the same repulsive term that van der Waals used in

1893, i.e.,

P - (2-3.33) and have emphasized modifications on the attractive term.

It can be shown, however, (Carnahan and Starling, 1972) , that a more accurate representation of the repulsive term is 126

2 3~ Pa_ RT 1++_- (2-3. 34) R V -(_ 3

where E = b/4V (2-3.35)

Equation 2-3.34 is quite precise since its virial expan-

sion closely agrees with the exact expression for rigid

spheres (Ree and Hoover, 1967). The equation of'state that

results when the repulsive term is replaced by Equation 2-3.34

is called a perturbed hand sphere (PHS) equation of state

(Oellrichet al., 1978). Preliminary use of the PHS equation of state, augmented

by density dependent attractive forces (Alder et al., 1971)

for solid-fluid equilibria has been encouraging (Johnston and

Eckert, 1980). More development work, however, needs to be

done.

Conclus ions

The two general types of equation of state -- cubic and

Benedict-Webb-Rubin (BWR) have been tested for their ability to correlate solid-fluid equlibrium data. For the cubic equations of state, the Peng-Robinson (1976) and Soave (1972) equations of state were used. Also, the Starling and Han

(1971, 1972a, 1972b) modifications of the BWR equation of state were tried. In all cases the correlational ability of these equations were tested on the systems naphthalene- carbon dioxide and naphthalene-ethylene using the data of

Tsekhanskaya (1964). 127

Extensive testing of the Starling and Han modification

of the BWR equation of state showed that the solid-fluid equil-

ibrium data could not be accurately correlated unless the

binary interaction parameter was a function of both temper-

ature and pressure. In the case of the two cubic equations

of state (.Soave and Peng-Robinson), the solid-fluid equili-

brium data could be well correlated for a binary interaction

parameter that is a weak function of temperature. The ability

of both the Peng-Robinson and Soave equations of state to

correlate the solubility data was essentially identical, but

the two equations required different values of the binary

interaction parameter.

Clearly, it is more desirable to have the binary inter-

action parameter a function of as few variables as possible --

and so the two cubic equations prove to be superior to the

BWR equation. Of the two cubic equations of state, the Peng-

Robinson equation predicts molar volumes of the liquid phase

more accurately than the Soave equation of State (.Peng and

Robinson, 1976) and so the Peng-Robinson equation was chosen

as the equation to use in this thesis.

A possible reason for the better predictive abilities

of the cubic-type equation of state over the BWR-type equation

of state can be explained as follows. Cubic equations of

state contain two adjustable parameters. Typically, these

adjustable parameters are found by forcing the cubic equations of state to satisfy the two pure component stability criteria: 128

C J =0 (2-3.36) 3VT c [2 ' a- =P0(2-3.37)

Consequently, isotherms for cubic equations of state have the correct slope in the critical region. BWR type equations, however, have typically eight to eleven adjustable parameters.

These parameters are obtained by fitting the BWR equation to

P-V-T data by use of a non-linear regression routine. Thus, the BWR equations may not satisfy pure component stability criteria and thus,will tend not to correlate data well in the critical region.

2-4 Thesis Objectives

The objectives of this thesis can be divided into three parts: experimental, theoretical, and exploratory. Experi- mentally, equilibrium solubility data for both polar and non- polar solid solutes in supercritical fluids were to be measured over wide ranges of temperature and presure. In addition, ternary equilibrium data (two solids, one fluid) were to be measured. Carbon dioxide and ethylene were the two supercritical fluids to be used.

Theoretically, correlation of equilibrium solubility data of both binary and multicomponent systems using rigorous thermodynamics was to be done. 129

Finally, after obtaining equilibrium solubility data and developing a thermodynamic model, it was desirable to use this model to explore the physics of solid-fluid equilibria. Using the model that was to be developed, such phenomena as enthalpy changes of solvation of the solute in the supercritical solvent and changes in equilibrium solubility over wide ranges of temperature and pressure were to be studied. 130

3. EXPERIMENTAL APPARATUS AND PROCEDURE

3-1 Review of Alternative Experimental Methods

Experimentally, there are three feasible methods to

determine equilibrium solubilities of slightly volatile solids

in supercritical fluids. These are static methods, flow

methods, and tracer methods.

Static Method

In the static method, the solute species to be extracted

is contacted with the supercritical fluid in a batch vessel.

After a sufficient length of time has passed so that an equil-

ibrium solubility has been obtained, fluid samples are removed

for analysis. Special care must be taken that no appreciable

pressure perturbations occur during sampling. This is

accomplisehd by taking very small samples or by a volumetric

compensation technique (such as mercury displacement).

Eisenbeiss (1964), Tsekhanskaya et al. (1962, 1964), and

Diepen and Scheffer C1948b) measured equilibrium solubilities

by this method.

Flow Method

In the flow method, the supercritical fluid is contacted with the solute species to be extracted in a flow extractor.

The fluid stream exciting the extractor is then analyzed for

composition. In order to assure that an equilibrium 131 solubility has been achieved, the solubility is determined

at various flow rates and as long as the solubility is inde-

pendent of flow rate, it can be assured that equilibrium is

acheived. Several authors (Kurnik et al., 1981; Johnston

and Eckert, 1981; McHugh and Paulaitis, 1981) have success-

fully used this method.

Tracer Method

Tracer methods of determining solubility are done typi-

cally by using a radioactive isotope of the desired solute

species to be extracted. Using a static method, a Geiger

counter is then attached to the fluid portion of the equili-

brium cell. By careful calibration, the number rate of radio-

active counts can be converted to an equilibrium solubility.

Ewald et al. (1953) used this method to determine the equili-

brium solubility of iodine in supercritical ethylene.

3-2 Description of Equipment The experimental method used in this thesis to measure equilibrium solubilities was a one-pass flow system. A schematic is shown in Figure 3-1. Details of various sections of the equipment are discussed in Appendix VII.

A gas cylinder was connected to an AMINCO line filter, rodel

49-14405) which feed into an AMINCO single end compressor, model

46-13411). The compressor was connected to a two liter magnedrive packless autoclave (Autovlave Engineers) whose purpose was to dampen the pressure fluctuations. In addition, PCHetn -- 0 TC Hoe

------lope a Valve

GO 5 Compressor Surge -lonk Ex troctor Cylinder

I P Vent Key TC - Temperoture Dry Cont roller Test- Meter PC - Pressure Cont roller U - Tubes Rota meter P - Pressure Gouge

T - ThermocoOple Equipment Flow - Chort

Figure 3-1 133 an on/off pressure control switch, Autoclave P481-P713 was

used to control the outlet pressure from the autoclave.

Upon leaving the autoclave, the fluid entered the tubu-

lar extractor (Autoclave, CNLXJ6012) which consisted of a

30.5 cm tube, 1.75 cm in diameter. In the tube were alternate

layers of the solute species to be extracted and Pyrex wool.

The Pyrex wool was used to prevent entrainment. A LFE 238

PID temperature controller attached to the heating tape kept

the extractor isothermal. The temperature was monitored by

an iron-constantan thermocouple (Omega SH48-ICSS-ll6U-15)

housed inside the extractor. At the end of the extraction

system was a regulating valve (Autoclave 30VM4882), the outlet

of which was at a pressure of I bar. All materials of con-

struction were 316 stainless steel.

Following the regulating valve were two U-tubes in series

(Kimax 46025) which were immersed in a 50% ethylene glycol- water/dry ice solution. Complete precipitation of the solids occurred in the U-tubes, while the fluid phase was passed

into a rotameter and dry test meter (Singer DTM-115-3) and

finally vented to a hood. An iron-constantan thermocouple

(Omega ICSS-116G-6) at the dry test meter outlet recorded

the gas temperature. All thermocouple signals were displayed on a digital LED device (Omega 2170A). Analysis of the solid mixtures was done on a Perkin Elmer Sigma 2/Sigma 10 chromatograph/data station. 134

3-3 2eratingProcedure

Approximately 40 gm of solid or solid mixture to be

extracted was inserted into the extractor between alternate

layers of glass wool. In order not to damage the thermocouple

which was lodged in the center of the extractor, a 0.6 cm O.D.

copper tube was inserted around the thermocouple while the

extractor was being filled. Finally, the extractor was closed

with an Autoclave coupling 20F41666.

The extraction assembly was mounted on the specially

designed mounting bracket and all connections fastened.

Heating tape was carefully wrapped around the extractor and

connected to the temperature controller. The pressure con-

troller switch was set to the desired operating pressure and

the compressor started. Heating tape was also wrapped around

the depressurization valve and attached to a variac to maintain a temperature greater than the melting point of the

solid.

The data recorded was (1) the initial and final weights of both U-tubes; (2) the initial and final reading on the dry test meter; (3) the extraction temperature and pressure; (4) the barometric pressure, and (5) the temperature of the gas leaving the dry test meter.

To start the experiment, the depressurization valve was opened so that a steady flow rate of about 0.4 standard liters* per minute is obtained. The extraction was then continued

*At 1 atm pressure and 294 K. 135

until the amount of solid collected gave no more than one

percent error in the experimental solubility. During this

time, no operator intervention was necessary since the extrac-

tion temperature and pressure were automatically controlled.

3-4 Determination of Solid Mixture Composition

After precipating solid mixtures in the U-tubes, it was

necessary to determine their composition. In all cases, this

was done by dissolving the solids in methylene chloride and

injecting the sample into a gas chromatograph. A Perkin-Elmer

Sigma 2/Sigma 10 chromatograph/data station was used with a

FID detector. In Appendix VIII there is given complete

documentation for using the gas chromatograph for all of the

solid mixtures studied.

It was imperative to show that the solid mixtures ex-

tracted formed an eutectic solution -- not a solid solution.

First, a metling point analysis was done on all of the solid mixtures and, in each case, an eutectic solution was found

(see Appendix III). The extraction temperature for a given solid mixture was always below the eutectic temperature.

Then, 50/50 solid mixtures of naphthalene and phenanthrene were melted, recrystalized, and then extracted. The extracted mixture had identical component solubilities as when the solids were physically mixed.

Also, the system phenanthrene-2,3-DMN was extracted with different ratios (50/50 and 30/70) of the two solids changed to the extractor. The extracted mixture had component 136 solubilities independent of the ratio charged. Thus, it can be concluded that eutectic solutions were formed for the solid systems studied.

3-5 Safety Considerations

Due to the high pressures used in this research (350 bar), special safety precautions had to be observed. These are as follows:

* The autoclave was fitted with a rupture disk rated for

411 bar at 295 K; the outlet was vented to a hood.

* Hydrocarbon leak detectors were used at all times when

ethylene was used as the supercritical fluid.

In addition, care must be exercised that rapid pressure reductions do not occur. A rapid release in pressure of carbon dioxide has the potential of creating vapor explosions and shock waves. For details, see Kim-E (1981), Kim-E and

Reid (1981) and Reid (1979). 137

4. RESULTS AND DISCUSSION OF RESULTS

In this section, experimental solid-fluid equilibrium

data are given for both binary and multicomponent systems.

Also, graphs of the data points correlated with the Peng-

Robinson equation of state are shown.

4-1 Binary Solid-Fluid Equilibrium Data

Presented in Tables 4-1 through 4-9 are experimental equilibrium data for the solubility of pure component solids in supercritical carbon dioxide and ethylene at several temperatures and pressures. Also shown with the data are isothermal Peng-Robinson binary interaction coefficients obtained by use of a non-linear least squares regression. Figures 4-1 through 4-9 show the experimental data are correlated with the Peng-Robinson equation of state.

Binary Interaction Coeffients

In modelling the binary solid-fluid equilibrium problem using the Peng-Robinson equation of state, there exists an unknown binary interaction parameter, ki 1 , which must be determined from experimental data (refer to Eq. 2-3.27).

The binary interaction parameter has been found to be a weak function of temperature, but independent of pressure and composition -- at least over the range studied here. One Table 4-1

Co2 ; 2,3-Dimethylnaphthalene Data

T=308 K T=318 K T=328K

P(bar) y P(bar) P(bar) y

99 2. 20x10-3 99 1.28x10-3 99 3. 41x10~ 4

143 4. 40x10 3 145 4.79x10-3 146 4.46x10-3

194 5. 42x10-3 195 6. 37x10- 3 197 7.14x10 3

242 5. 83x10-3 242 6. 89x10-3 241 8.48x10-3

3 3 3 H 280 6.43x10- 280 7.19x10- 280 9. 01x10 LA) OD

k12 0.0996 0.102 0.107 Table 4-2

2,3-Dimethylnaphthalene 2H4; Data

T=308 K T=318 K T=328 K P(bar) y P(bar) y P(bar) y 77 3.13x10~ 4 80 3. 67x10~ 4 80 3. 00x10~ 4

120 2.59x10-3 120 2.59x10-3 122 3.18x10-3

159 6.02x10-3 160 7.18x10- 3 160 8.79x10-3

200 9.66x10 3 200 1.22x10-2 200 l.89x10-3 Hj U) 240 1.27xl0-2 240 1.84x10-2 240 3.22x10-2 ko

280 1.51x10-2 280 2.42x10 2 280 5.25x10-2

0.0246 0.0209 0.0147 Table 4-3

Co 2 ; 2,6-Dimethylnaphthalene Data

T=308 K T=318 K T=328 K P(bar) y P (bar) y P(bar) 4 97 1.91x10-3 98 7. 57x10 4 96 3.06x10

3 3 145 2.97x10 3 146 3. 95x10- 146 4. 32x10- 3 195 3. 83x10-3 194 5.09x10-3 195 6. 16x10-

3 3 245 4. 01x10-3 244 6. 27x10- 246 7. 99x10- 3 H 47x10-3 6.77x10 3 9. 21x10- 280 4. 280 280 0

0.102 0.0989 0.100 Table 4-4

C211 4 ; 2,6-Dimethylnaphthalene Data

T=308 K T=318 K T=318 K P(bar) P(bar) y P(bar)

80 4. 84x10~ 4 78 1. 89x10~ 4 78 2. 36x10'4

120 2. 35x10-3 120 2. 20x10-3 120 2.20x10-3

159 4. 62x10-3 160 5. 56x10-3 160 6.74x10-3

H 200 6. 95x10-3 200 9. 08x10-3 200 1.30x10-2

240 9. 28x10-3 240 1.39x10-2 240 2.00xlO'2

280 1. 10x10-2 280 1. 71x10-2 280 2.75x10-2

k12 0.0226 0.0201 0.0167 Table 4-5

CO2 - Phenanthrene Data

T=308 K T=318 K T=328 K P (bar) y P(bar) y P(bar) y

120 7. 86x10~ 4 120 8. 50x10~ 4 120 4.65x10~ 4 160 1. 38x10- 3 160 1.40x10- 3 160 1. 52x10- 3 200 1.58x10-3 200 1. 71x10- 3 200 2. 14x10- 3 240 1. 70x10- 3 240 2. 23x10- 3 240 2.79x10- 3 280 1. 78x10- 3 280 2. 29x10- 3 280 3. 20x10- 3

H- k12 0.115 0.113 0.108

T=338 K

P (bar) y

120 3. 29x10 4 160 1.19x10 3 200 2. 37x10- 3 240 3. 28x10-3 280 3.84x10 3

0.106 Table 4-6

C2 H - Phenanthrene Data

T=318 K T=328 K T=338 K P(bar) y P(bar) -Y P(bar) 120 8. 16x10~ 4 120 7. 38x10~ 4 120 7.44x10~ 4

160 1. 7 5x10- 3 160 1. 76x10-3 160 1. 84x10 3

200 2. 67x10- 200 3. 33x10-3 200 3.65x10-3 -3 240 3. 71x10-3 240 5. 34x10-3 240 6.39x10-3

3 3 2 280 4. 56x10- 280 8. 29x10- 280 1.07x10- LJ

k 12 0.0459 0.0356 0.0318 Table 4-7

CO - Benzoic Acid Data

T=308 K T=318 K T=328 K

P(bar) y P(bar) y P(bar) y

120 1. 38x10-3 120 1. 15x10-3 120 4. 90x10 4 160 2. 37x10-3 160 2. 38x10-3 160 2.27x10-3 200 3. 01x10-3 200 3. 18x10-3 200 3.86x10-3 240 3. 10x10-3 240 4.21x10-3 240 5. 16x10- 3 280 3. 31x10-3 280 4. 39x10-3 280 7. 35x10-3

H 0.0183 0.00994 -0.00172 k12

T=338 K P(bar) y 120 3.21x10~ 4 160 1. 72x10- 3 200 4. 11x10-3 240 6.96x10-3 280 9. 84x10-3

-0.0124 Table 4-8

C 24 - Benzoic Acid Data

=3T=318 K T=328 K T=338 K P(bar) y P (bar) P(bar)

120 5.76x10~ 4 120 5. 48x10~ 4 120 5. 44x10-4

160 1.36x10-3 160 1.61x10- 3 160 1. 93x10-3

200 1.90x10 3 200 2.61x10-3 200 3. 51x10-3

240 2.90x10-3 240 3.61x10-3 240 4.94x10-3 H- ,P 3 3 280 2.91x10- 280 4. 01x10- 280 6. 19x10-3 (J1

k12 -0.0563 -0.0642 -0.0756 Table 4-9

Co - Hexachloroethane Data

T=308 K T=318 K T=328 K P(bar) y P(bar) y P(bar)

99 1.45x10-2 100 1.04x10- 2 97 3.80x10- 3

149 1.86x10-2 148 2.40x10- 2 145 2.32x10-2

199 1.97x10-2 198 2.60x10- 2 195 3.89x10-2

2 2 2 248 2.00x10- 247 2.78x10- 245 3.94x10- H a'6 280 1.80x10- 2 280 2.71x10- 2 280 3.90x10-2

k12 0.129 0.123 0.116 147

-2 328 10 318 K

308 K-

-3 10 308 K

Z 318 K - 328 K

-4 10System C02 2,3 DM N -PR Equction of Statc'

Temp2ratur4?(K) Symbol k 2

328K 308 0 0.0996 53 1 8 & 0.102 10 328 O.107 - -318 K _

3 08 K

10 1| 1 | Il 0 40 s 120 '60 200 240 280 PRESSURE (BARS)

Solubility of 2,3-Dimethylnaphthalene in Super- critical Carbon Dioxide

Figure 4-1 148

- 1

318

-2 30 10

-3 10 308 K Z r318K- 328 K

-4 10

System C2H4 - 2,3 DMN State 328 K - PR Equation of -Tampqraturc- Symbol k12 -5 K308 0.0246 10 IL K3 18 0 .0209 328 0.0147 308K

-6 10 ti| 0 40 80 120 160 200 240 280 PRESSURE (BARS)

Solubility of 2,3-Dimethylnaphthalene in Super- critical Ethylene

Figure 4-2 149

-2 10 -- 328 31 - 0308

-3 z 10 308 K-

318 K- 328K

-4 0 Systlm CO2 -2,6 DMN PR Equation of Statc-

Temperature(K) Symbol k, 2 308 0 0102 5 328 318 A 0.0989 1 .- 328 U 0.100 .3118 K

-308

-6

0 40 80 120 160 200 240 280 PRESSURE (BARS) Solubility of 2,6-Dimethylnaphthalene in Super- critical Carbon Dioxide

Figure 4-3 150

328

-2 308 K 10 -

-3\

-3 318 K- z -0 308K 328-

-4 '0 S YSteM C 2 H4 -2,6 0M N PR Equation of Stcte

- 328 Temperature(K) Sym bol k12 308 0 0.0226 -5 31 & 0.0201 0 -318 328 0.0167

~08~

-6 10 I l 0 40 80 120 160 200 240 280 PRESSURE ( BARS)

Solubility of 2,6-Dimethylnaphthalene in Super- critical Ethylene

Figure 4-4 1531

-2 10

318 K- -3 10

- 318K

328 K 3 3 BK

-4 10

~0 System C0 2 -Phenanthrenc' -PR Equation of State Temper-oture(K) Symbol k12 3 1 8 0.113 338K 328 4 0.108 338 U 0.106 -6'0 328 K

.318 K

-7 10 0 40 80 120 '60 200 240 280 PRESSURE (BARS)

Solubility of Phenanthrene in Supercritical Carbon Dioxide

Figure 4-5 152

-2 10 338

-3 10

318 K- 328K v~ 338K

- 4

1 0

Systarm C2H4 -Phenanthrenm 2 -- PR Equation of St a t e-

- 338 Tqrmp ratur e(K) Symbol k12- -318 0 0.0459 - -6 328 328 0 .0356 10 -- 338 0 .0 318 -

.318

10 0 40 80 120 160 200 240 2830 PRESSURE ( BARS )

Solubility of Phenanthrene in Supercritical Ethylene

Figure 4-6 153

-2 10 -233A8

328 328K3K2

-3 10

318 K

328 K- 338 K

-4 10 ItS 31099 'a

N C -5 338 K 09 l0 >1 Syst C2 - ACid [BenZoiC - -PR E qu at io n of St ate- -328 K Tempqra tur e(K) Symbol k12 3 8 K 31 8 0 .0994 -6 10 328 0.00172 3 38 -0.0124

-7 10 0 40 80 120 '60 200 240 280 PRESSURE (BARS)

Solubility of Benzoic Acid in Supercritical Carbon Dioxide

Figure 4-7 154

-2

- to3

u -4 10 z LL) System C 2H4 - Benzoic Acid PR Equation of State

Temperoture(K) Symbol k1 2 -5 338 K 3 18 9 -0.0563 10 328 A -0.0642 338 a -0.0756 -328K-

.318 K -6 to 0 40 80 120 160 200 240 280 PRESSURE (BARS)

Solubility of Benzoic Acid in Supercritical Ethylene

Figure 4-8 155

-1

328K-

A318 K

&308

10308-2 K

318K- 328 K

-3 10 .- -- 4

328K-

318Systcm CO2 -C2 C16 - PR Equation of Statce 308 TempraturQ (K) Symbol!k12

- 4 -308 0 0.129 -_ 318 & 0.123 328 0.116

-5 10 _ _L1 ... l .I l II i 0 40 80 120 160 200 240 280 PRESSURE (BARS)

Solubility of Hexachloroethane in Supercritical Carbon Dioxide

Figure 4-9 156 data point is sufficient (mathematically) to determine the

value of k..(T) at each temperature, but an optimum value of IJ k.'J (T) can be found by regressing isothermal experimental data. It has been found that minimizing the objective func-

tion J, where

0 -2 lny.-Iny J = min IE J(4-1.1)

subject to

f = f (4-1.2)

where y.0 = mole fraction of component i predicted from

Peng-Robinson equation of state E y = experimental value of mole fraction. enables one to obtain k.'a .(T) from isothermal experimental data. The computer software necessary to perform these calculations is given in Appendix VI.

Holla (1980) has shown that if it is desired to model isothermal binary solid-fluid equilibrium data, one experimental compositional datum point is sufficient to determine an accurate value of k. (T) if this one point is measured at a pressure P', where

P' ~3.8/Pclc2 (4-1.3)

If kI..T) is calculated at P', then the complete isotherm 'J 157

can be generated almost as accurately as if k. (T) were ob-

tained by regressing all isothermal data.

Discussion of Binary Solid-Fluid Equilibrium Results

As Figures 4-1 through 4-9 show, the effects of temperature and pressure solubility for all the solid species are similar. There are three pressure regimes: At low pressures an increase in temperature increases solubility; at intermed-

iate pressures, an increase in temperature decreases solubility (retrograde solidification) -- more apparent for carbon dioxide then ethylene; and at high. pressures an increase in temperature enhances solubility. The reason that retrograde solidification region is more significant for carbon dioxide than ethylene is because CO2 is at a lower reduced temperature and therefore the density dependence on pressure is larger.

In all cases, the Peng-Robinson equation of state is able to correlate the data well providing that the proper binary interaction parameter is used. Although the binary parameters were independent of pressure and composition, examination of Tables 4-1 through 4-9 shows a weak linear dependence on temperature.

The outstanding feature of all the data and simulations is the extreme sensitivity of equilibrium solubility on temperature and pressure. For example, consider Figure 4-10

(benzoic acid-carbon dioxide). There is about a two order of magnitude change in solubility when decreasing pressure and simultaneously increasing temperature from (318 K, 180 bar)

a l 158

338

318K

-O- 328K

/ 338

SYSTEM: BENZOIC AC!O-CO 2 90 -4 - -PR EQUATION OF STATE TEMPERATURE o (K) SYMSOL 318 328 338 * S10-5 338K

328K

318 K

1006 - IDEAL GAS

- -338 K

3 28 K 10~ -

.3 18 K

0 40 so 120 160 200 240 280 PRESSURE (BARS)

Solubility of Benzoic Acid in Super- critical Carbon Dioxide

Figure 4-10 159

to (338 K, 90 bar). Also shown for convenience in Figure 4-10

is the solubility predicted by the ideal gas law:

.i (4-1.41 yIDI - P

The ratio of real to ideal solubilities is called the enhancement factor and can take on values of 106 or larger.

Figure 4-11 shows a simulation of the case naphthalene in supercritical nitrogen. In no case does the isothermal solubility of naphthalene even equal the solubility at one bar pressure. The reason is because under these temperature and pressure conditions, nitrogen is nearly an ideal gas with fugacity coefficients and compressibility factors near unity.

Also, the density of nitrogen at high pressures is approximately 0.1 gm/cm3 as compared to 0.8 gm/cm3 for carbon dioxide under the same conditions. The dissolving power of supercritical fluids depends both on the density (the higher the greater) and the nonideality (fugacity coefficient) of the fluid phase.

4-2 Ternary Solid-Fluid Equilibrium Data

Presented in Tables 4-10 through 4-20 are experimental equilibrium data for the solubility of solid mixtures in supercritical carbon dioxide and ethylene at several temperatures and pressures. Also shown with the data are isothermal binary solute-solute interaction coefficients.- Figures 4-12 through 4-23 show the experimental data correlated with the 160

-2 10 -_ I I I I I I -

Sys tem: NitroQen - Naphthol2ne - - PR Eqution of StatQ4

3 k12 :0.1

uJ zJ

328 K z 3 1K

W3OWf8 K -5 10

0 40 80 120 160 200 240 280 PRESSURE ( BARS)

Solubility of Naphthalene in Supercritical Nitrogen

Figure 4-li 161

Table 4-10

CO2 (1); Benzoic Acid (2); Naphthalene (3) Mixture Data

T=308K

P (bar) y(Benzoic acid). y (Naphthalene)

120 2. 93x10-3 1. 44x10-2

160 4. 01x10-3 1. 73x10-2

200 5.22x10-3 2.06x10-2

240 5.46x10-3 2. 08x10-2

280 5. 61x10-3 2. 12x10-2

k12= 0.0183

k13= 0.0959

k 23= 0.000 162

Table 4-11

CO2 (1); Benzoic Acid (2); Naphthalene (3) Mixture Data

T=318K

P (bar) y(Benzoic acid) y(Naphthalene)

120 3.49x10-3 1.76x10-2

160 6.96x10-3 2.61x10-2

200 1. 00x10-2 3.25x10-2

240 1.21x10-2 3.67x10-2

280 1.26x10-2 3.66x10-2

k12= 0.00994

k13= 0.0968

k 23= 0.015 163

Table 4-12 co2 (1); 2,3-DMN (2); Naphthalene (3) Mixture Data

T=308K

P (bar) y(2, 3-DMN) y (Naphthalene)

120 6. 32x10-3 1.85x10-2

160 8.80x10- 3 2.41x10-2

200 9. 34x10-3 2. 39x10 -2

240 9.95x10-3 2.58x10-2

280 9.90x10-3 2.62x10-2

k 12=0.0996

kl3= 0.0959

k 23= 0.04 164

Table 4-13

Data CO 2 (1); Naphthalene (2); Phenanthrene(3) Mixture T=308K

P (bar) y (Naphthalene) y(Phenanthrene)

2 3 120 1. 47x10- 1.65x10- 2 140 1. 62x10- 1.92xl0-3 2 160 1. 76x10- 2.32x10-3 3 180 1. 84x10- 2 2.54x10- 2 3 200 1. 88x10- 2.59x10- 2 3 220 2. 08x10- 2.90x10- 3 240 2. 14x10-2 2.93x10-

2 3 260 2. 13x10- 3. 01x10- 3 280 2. 14x10 2 3. 21x10-

k 12=0.0959

k13= 0.115

k23= 0.05 165

Table 4-14

CO2 (1); 2,3-DMN (2); 2,6-DMN (3) Mixture Data T=308K

P (bar) y (2,3-DMN) y(2,6-DMN)

3 120 3. 92xi0-3. 3. 04x10-

3 140 4. 34x10 -3 3. 36x10-

160 4. 94xl0-3 3. 87x10 3

180 5. 21x10-3 4. 02x10-3

200 5.68x10-3 4. 38x10 3

220 6. 00x10-3 4.62x10-3

240 6.03x10-3 4.57x10-3

3 260 6. 16x10-3 4. 62x10-

3 280 6 . 40x10-3 4. 74x10-

k12= 0.0996

k3 = 0.102

k23= 0.20 166

Table 4-15

Co 2 (1); 2,3-DMN (2); 2,6-DMN (3) Mixture Data

T=318K

P (bar) y(2,3-DMN) y(2,6-DMN)

120 3. 67x10- 3 3. 40x10- 3

140 5. 18x10-3 4.47x10- 3

160 6. 51x10-3 5. 48x10-3

180 7. 36x10-3 6.14x10- 3

200 7. 95x10- 3 6. 59x10- 3

220 8. 24x10-3 6. 78x10- 3

240 9. 01x10-3 7. 39x10-3

260 9. 45x10-3 7. 58x10-3

280 1. 01x10-3 8.13x10-3

k 2= 0.102

k13= 0.0989

k 23= O 167

Table 4-16

C 2 H 4 (1); 2,3-DMN (2); 2,6-DMN (3) Mixture Data T=308K

P (bar) y(2,3-DMN) y(26-DMN) 3 3 120 5. 35x10- 4. 41x10 3 3 140 7. 46x10- 5.97x10- 3 160 9. 70x10- 7. 73x103 2 3 180 1. 19x10- 9. 45x10- 2 2 200 1. 40x10- 1.08x10- 2 2 220 1. 62x10- 1. 24x10- 2 240 1. 62x10- 1.25x10-2 2 2 260 1. 76x10- 1. 34x10- 2 2 280 1. 85x10- 1. 40x10-

k2 0.0246

k 3= 0.0226

k 23= 0.05 168

Table 4-17

CO2 (1); Benzoic Acid (2); Phenanthrene(3) Mixture Data T=308K

P (bar) y(Benzoic acid) y(Phenanthrene)

120 1. 84x10- 3 1. 02x10- 3

160 2.44x10-3 1. 36x10-3

200 2. 95x10-3 1. 63x10-3

240 3.28x10-3 1. 87x10-3

280 3. 70x10-3 2. 05x10-3

k12= 0.0183

k13= 0 115

k23= 0.2 169

Table 4-18

Co2 ; 2,6-DMN; Phenanthrene Mixture Data

T=308K

P (bar) y(2,6-DMN) y(Phenanthrene)

120 2. 92xl0-3 1.06x10-3

160 3.46x10-3 1.49x10-3

200 4. 18x10-3 1.85x10-3

240 4. 25x10-3 2. 05xl03

280 4.23xl 0-3 2.07x10-3

The correlation of mixture data by the Peng-Robinson Equation of State is not possible. 170

Table 4-19

co2; 2,3-DMN; Phenanthrene Mixture Data

T=308K

P (bar) y (2, 3-DMN) y (Phenanthrene)

120 2. 89x10- 3 7. 33x4Q4

160 3.56x10- 3 1. 00x10 3

200 4. 23x10-3 1. 24xl0-3

240 4. 43x10-3 1. 43x10 3

280 4. 50x10- 3 1. 48x10-3

The correlation of mixture data by the Peng-Robinson equation of state is not possible. 171

Table 4-20

Co 2 ; 2,3-DMN; Phenanthrene Mixture Data T=318K

P (bar) y(2,3-DMN) y (Phenanthrene)

120 2. 47x10-3 5. 27x10~ 4

160 4. 33xl0-3 1. 19x10-3

200 5. 54x10-3 1. 71x10 3

240 5. 85x10-3 1. 96x10-3

280 6.97x10-3 2. 33x10-3

The correlation of mixture data by the Peng-Robinson equation of state is not possible. 172

10-1

Cio HseMIXTUR E, PR EQUATION

10-2 CioH8 PURE, PR EQUATION

10-

SYSTEM: CO-Cgo He8 0C14 HfQ (1) (2) (3) TEMPERATURE= 308.2 K

o PURE COH8 IN C02t e MIXTURE CIO H8 IN CO2 -PR EQUATION OF STATE

ka=0.0959 10-5k3= k13=O.I.l IS k 2 3z0.05 t DATA OF TSEKHANSKAYA et al. (1964)

1011I I1 6--I-I 0 40 80 120 160 200 240 280 PRESSURE (BARS)

Solubility of Naphthalene from a Phenanthrene-Naphthalene Mixture in Supercritical Carbon Dioxide

Figure 4-12 173

C14 HIO MIXTURE,PR EQUATION 100

10-3 io- -

0C4 HIO PURE,PR EQUATION

= 5 '1~ 10- C)

SYSTEM: CO 2 -CoHe-0C 4 H1 o (I) (2) (3) TEMPERATURE =308.2K 0 0 PURE C14 HIO IN C 2 0 -_ * MIXTURE C 1 4 HIOIN C 2 -PR EQUATION OF STATE ki=0.0 9 5 9

k 13=0.115 k23=0.05

10-7-1-

io- 8 4 0 40 80 120 160 200 240 280 PRESSURE (BARS)

Solubility of Phenanthrene from a Phenanthrene- Naphthalene Mixture in Supercritical Carbon Dioxide Figure 4-13 173

C14 H i MIXTURE, PR EQUA TION

10-3

C14HIO PURE,PR EQUATION

io-4

\0-5

SYSTEM: C0 2 -CIOH 8 --C14H10 (1) (2) (3) TEMPERATURE =308.2K 0 PURE C14 HIO IN C02 0 10-6 0 MIXTURE C 14 HIOIN C 2 -PR EQUATION OF STATE

k 2=0.0959

k 13 =0.115 k23=0.05

10~7

10-81 0 40 80 120 160 200 240 280 PRESSURE (BARS)

Solubility of Phenanthrene from a Phenanthrene- Naphthalene Mixture in Supercritical Carbon Dioxide Figure 4-13 174

102

-3 10

Sys tzm C02; 2 3 -DM N; Nophthalnca - (1) (2) (3) N 4 > 10F---qmperature =308 K 0 Pure 2,3 -DMN in C02 * Mixture 2,3 -DMN In CO2 -- PR Equation of State k12=z-0.0996

k13 =:0.0959 0 _k 2 3 = 0.04

-6 10 1I I I 0 40 80 120 160 200 240 280 PRESSURE (BARS) solubility of 2,3-Dimethylnaphthalene from a 2,3-Dimethylnaphthalene-Naphthalene Mixture in Supercritical Carbon Dioxide at 308 K.

Figure 4-14 175

-1 10

-2 10

z 10 --J

>1Sys t2m C02; 2,3-DMN; Nophthalana 10 -- ( ) (2) (3)

Tempercit ure = 308 K-

- O0 Pur(2 Naphthalene in C02 0Mixtur- Naphthalana In C02

PR Equation of Stata -5 k12 = 00996 10 k13 = 0.0 959

k 23= 0.0 4

~ t Datao of Tse khonskaya (2t al (1964)

-6 10

0 40 80 120 160 200 240 280 PRESSURE (BARS) Solubility of Naphthalene from a 2,3-Dimethyl- naphthalene-Naphthalene Mixture in Supercritical Carbon Dioxide at 308 K.

Figure 4-15 176

10-2

-3 10

-4 10 0 u- Bcnzoi c u SystemCOM;Naphtholn;2 Acid (1) (2) (3) NJ z Temperature = 308 K uiJ -5 -+ 10 o Pure Benzoic Acid in C02 * Mixture Ben zoic Acid in C02 z~ - PR Equation of State k12 =0.0959 k,3 0.0183

-6 k 23 = 0.Z00 10

-7 I I I I I I I I I I 10 I I I I I I I I I I I- - I 0 40 80 120 160 200 240 280 PRESSURE (BARS) Solubility of Benzoic Acid from a Benzoic Acid- Naphthalene Mixture in Supercritical Carbon Dioxide at 308 K.

Figure 4-16 177

-2 10

- -3 z 10

z ~Banzoi c System: C0 2 ;Naphthalcne;ACid 0(1) (2) (3) Temperature = 308 K o Pure Naphthalene in C02 t * Mixture Naphtholene in 002 - PR Equation of State

- k 12 =0-0959 10 k13 =0.0183

k23 =0.000 t Data of Tsekhonskaya et a.(1964)

-6 10 _. 1iiI i 1 0 40 80 120 160 200 240 220 PRESSURE (BARS)

Solubility of Naphthalene from a Benzoic Acid- Naphthalene Mixture in Supercritical Carbon Dioxide at 308 K.

Figure 4-17 178

-2 10

2,16 - DMN ( MIxturq),,.

2,6 - OMN( Pur e) -0

-4 10 - -- S Osysteom C02 ;2,3-DM N; 2,6 -OMN (1) (2) (3) Temperoture = 308 K o PurQe 2,3 - DMN in CO, *Mixture 2,3-DMN in C02

1----PR Equation of S tct - k12 = 0.0996

k13 0-102 k 23 z0.20

-6 10 .ii 0 40 80 120 160 200 240 280 PRESSURE (BARS)

Solubility of 2,6-Dimethylnaphthalene from a 2,6- Dimethylnaphthalene; 2,3-Dimethylnaphthalene Mixture in Supercritical Carbon Dioxide at 308 K.

Figure 4-18 179

-2 10 =-2,3 -OMN (Mixtura -

23 -D0M N( Pu r 4)

-3 10-

System C0 2 ;2,3-DMN ;2,6-DMN S(1) (2) (3) Temporoture =308K 0 Pure 2,3-DMN in C02 -5 *Mixturc' 2,3-DMN in C02 10 k 22-0.0996

k, 3 =O.102

k23=0.2 0 PR Equation of StotQ

106 0 40 _80 120 160 200 240 280 PRESSURE (BARS) Solubility of 2,3-Dimethylnaphthalene from a 2,6- Dimethylnaphthalene; 2, 3-Dimethylnaphthalene Mix- ture in Supercritical Carbon Dioxide at 308 K.

Figure 4-1.9 180

10-

-2 10

-3 10 z-

N System C 2 H4 ;2,3-DMN;2,6-DMN (i) (2) (3) -4 10 Temperature = 308 K

o Pure 2.3-DMN in C 2H4

* Mixture 2,3-DMN in C2 H 4 -PR Equation of Stata

k1 2 =0.0246

-5 k13=0.0226 10 -- k 23 =0.0 5 ~ -

106 0 40 80 120- 160 200 240 280 PRESSURE ( BARS) Solubility of 2,3-Dimethylnaphthalene from a 2,3- Dimethylnaphthalene; 2,6-Direthylnaphthalene Mixture in Supercritical Ethylene at 308 K.

Figure 4-20 181

-1 10 - 1- 1 1 1 1 1 1

-3 id 2- z 15 - ----

System: C2 H 4 ;2,3 DMNi 2,6 DMN 10 (1) (2) (3) Temperature = 308 K o Pure 2,6-DMN in C2H4 *Mixture 2,6-DMN in C2 H 4 -PR Equation of State

k1 2 =0.0246 10 T.k13 -- =0.02 26 ~~

10 1i i i . I 0 40 $0 120 160 200 240 280 PRESSURE ( BARS) Solubility of 2,6-Dimethylnaphthalene from a 2,3- Dimethylnaphthalene; 2,6-Dimethylnaphthalene Mix- ture in Supercritical Ethylene at 308 K.

Figure 4-21 182

-1 10 -1 1 1 t

-2 10

-3 10

-4 10 System: C02 ;;2,3-DMN ; 2,6 -DMN (1) (2) (3) Temperature = 318 K o Pure 2,3 - DMN in C02 * Mix ture 2,3-DMN in CO2 10- PR Equation of Sttate

k12 =0.102 k1,= 0.0989

k 23 :0.1

-6 1 0 t_ I I I I I I I I I I I I 0 40 80 120 160 200 240 280 PRESSURE (BARS) Solubility of 2,3-Dimethylnaphthalene from a 2,3- Dimethylnaphthalene; 2,6-Dimethylnaphthalene Mix- ture in Supercritical Carbon Dioxide at 318 K.

Figure 4-22 183

-1 10 1 I I

-2 10

-3 10 z

- 2,6-DMN -4 System:C0 2 ;2,3-DMN -0 (1) (2) (3) - Temperature =318 K (3) o Pure 2,6-DMN in C02 * Mixtura 2,6 - DMN in C02 PR Equation of State

1(55--k 12= 0.102

k 3 =:0.09 89

k23 =O,1

-6

0 40 80 120 160 200 240 280 PRESSURE (BARS)

Solubility of 2,6-Dimethylnaphthalene from a 2,3- Dimethylnaphthalene; 2,6-Dimethylnaphthalene Mix- ture in Supercritical Carbon Dioxide at 318 K.

Figure 4-23 184 Peng-Robinson equation of state.

Binary Solute-Solute Interaction Coefficients

In modelling ternary solid-fluid equilibrium problems

using the Peng-Robinson equation of state, it was found that

in most cases the ternary data could not be well correlated

unless non-zero values of the binary solute-solute interac-

tion coefficients (k23 ) were used. For an appropriately deter-

mined pressure, and composition independent solute-solute

parameter, correlation of isothermal ternary data was generally successful. The evaluation of the solute-solute parameter was done by a trial and error procedure.

Selectivities in Ternary Solid-Fluid Equlibria Systems

Selectivities (ratios) of component solute concentrations in supercritical fluids have been found to have the characteristic shape as shown in Figure 4-24 for the system naphthalene-phananthrene-CO2 and Figure 4-25 for the system naphthalene-2,3-DMN-CO2 . At 1 bar, the selectivity is just the vapor pressure ratio. As the pressure increases, there is a sharp drop in selectivity, especially near the solvent critical point. Finally, at pressures well above the solvent critical point, the selectivity is nearly constant -- at a relatively low value. The effect of temperature on selectivity is shown in Figure 4-26 for the system naphthalene-benzoic acid. Only at pressures at and below the critical pressure does temperature have an effect on selectivity.

The conclusion to be drawn from the selectivity curves 185

I I I I I 480 Syste I 00 C2- Nap ht hale ne -Phencnt hrenc 440 (1) (2) (3) Temperature = 30% K

400 - PR Equation of State k 12 = 0.0959 360- k 13 = 0.11 5 k 2 3 = 0.05 3 2 0

0< NOphtholene /Phenanthrene 280

C- 240 z 0 C- I' 200- y S z 160 -

120- -46 80- Expandad

lah Adh 1 a 1 40 00I 0 IF w 40 -9r o 40 80 120 160 200 240 280 PRESSURE (BARS)

Selectivities in the Naphthalene-Phenanthrene-Carbon Dioxide System

Figure 4-24 186

221 I .- I I I

System - Naphthalana - 2,3 -DMN 201 C02 (1) (2) (3)

Temperature = 308 K 181 -- PR Equation of State k12 =0.0959 16 k 13 =0.0996 k 23 =0.04

Naphthalena / 2,3-DMN 14

z 12. 2 0

C 10

~t. z 8 II '6 ~- p p-

0 I I ILII 0 40 80 120 160 200 240 280 PRESSURE (BARS) Selectivities in the Naphthalene-2,3-Dimethyl- naphthalene-Carbon Dioxide System

Figure 4-25 187

110

System C2 -Naphtholene - Benzoic 100 Acid (1) (2) (3) 90 T=308K T =318 K Symbol 0 k12 0.0959 0.0968 80-k,3 0.0183 0.00994 k23 0.000 0.015

70 PR Equation of State ( 308 K) - -PR Equation of State( 318 K)

60 - z% "Benzolc Acid

40L

2o --

10 10

0 40 80 120 160 200 240 280 PRESSURE C BARS)

Selectivities in the Naphthalene-Benzoic Acid- Carbon Dioxide System

Figure 4-26 188

is that at high reduced pressures (Pr '1).the selectivity

is low and therefore, both "high" and "low" volatile species

will be extracted. In order to get a good separation of

solute materials, the pressure must be kept less than the

solvent critical pressure, but here, the solubilities are also

low. (At pressures of about 1000 bar, computer simulations

predict that selectivities increase slightly.)

Discussion of Ternary Solid-Fluid Equilibrium Results

Ternary solid-fluid equilibria exhibits similar phenom-

ena to binary solid-fluid equilibrium. There are, however,

some unique characteristics: component solubilities in ternary

systems can be significantly higher than the solubility of

the pure component in a supercritical fluid under identical

operating conditions.

Careful examination of the ternary solid-fluid equili-

brium data taken shows that component solubilities are signi-

ficantly increased when an additional solid component of high

solubility C> 10- mole fraction) is added to the first

solid. If, however, the solubilities of both pure components are low C< tO-3 mole fraction), then the solubility of the components in the mixture will be almost identical to the pure component solubilities. If the solubilities of both components are high (> 10- mole fraction), then the solubilities of both components in the mixture are significantly increased.

Physically, what seems to be happening is that a high 189 concentration of a hydrocarbon solute in the supercritical fluid phase aids in dissolving other hydrocarbon solutes -- by using the rule that "like dissolves like." In one case studied in this thesis, however, there was a slight (10%) decrease in component solubilities in a ternary mixture as compared to the binary system. This case was the system phenanthrene; 2,3-DMN; CO2. In most cases, the ternary data can be correlated well by the Peng-Robinson equation of state. Correlation of these ternary systems requires, however, the use of a solute-solute interaction coefficient (k23 ). To check the physical meaning of this solute-solute parameter, the isomer system 2,3-DMN;

2,6-DMN was examined in both supercritical carbon dioxide and ethylene. Correlation of the resultant data showed that k23 was dependent on the supercritical fluid (component 1). Thus it can be concluded that k2 3 is an adjustable parameter -- not a true binary constant.

4-3 Experimental Proof that T < Tq

As discussed in Chatper 2-2, it is only for system temperatures less than the upper critical end point temperature

(T ) that one is guaranteed that no liquid phase will form.

Since all of the thermodynamic modelling used in this thesis incorporated the assumption of T < Tq, it is necessary to obtain experimental proof that this assumption was valid.

Such a proof can be inferred with experiments using the system naphthalene-ethylene. For this system (Diepen and 190

Scheffer, 1953):

T = 325.3 K

P = 176 BAR

Experimental data at 318 K and 328 K and for many pres-

sures are shown for naphthalene in supercritical ethylene in

Figure 4-27. At 318 K, the solubility data agree well with

(Tsekhanskaya, 1964). At 328 K, however, T > T and the

experimental isothermal data show entirely different behavior.

By examining the P-T space for this isotherm, the large dis-

continuinity in concentration can be explained and the lack

of such a discontinuinity in concentration in the binary and

ternary systems studied in this thesis suggest that T < T.

Explanation of the discontinuity in. concentration is

as follows. Consider isotherms T3 and T5 of Figure 2-15.

Upon raising the system pressure on isotherm T3 ' which is

below Tq, there is a continuous change in concentration for

a saturated solution. However, for temperature T5 ' which is

greater than T , it is apparent that upon increasing the

system pressure while keeping the fluid phase saturated with

solid, that the concentration will have a discontinuity because of the L 1 +L2 region which is "jumped". Furthermore,,

for T 5T , the discontinuity will occur at a pressure P-P .

This discontinuity predicted by P-T phase space is what was

found experimentally for the system ethylene-naphthalene at

328 K in Figure 4-27. Scattering of the data at high 0.30 I I I I I I I I I I I I I I

0.28 0 S 0

0.22 S w System: Ethylene - Nophtholene z w 0.18 Temperoture K I Sym bol 4 CL 318 0 328 a. 0.14 I H H z T (UCEP) 325.3 K 0.10 P (UCE P)=176 BAR

0.06 ~0

0.021 I I I I I I 1 I I I i I I I 1 1 1 1 1 1 1 4- f I t 0 40 80 120 160 200 240 280 PRESSURE ( BARS)

A Close Examination of the System Naphthalene-Ethylene Near the Upper Critical End Point

Figure 4-27 192 pressures (and concentrations) results because of plugging problems in the pressure let-down value. Finally, the lack of such a discontinuity in the binary (and by analogy ternary) systems studied in this thesis certainly indicates that in all cases T < T q 193

5. UNIQUE SOLUBILITY PHENOMENA OF SUPERCRITICAL FLUIDS

Solubility of solids in supercritical fluids exhibit several unique phenomena not present in typical phase equilibria situations. These pheneomena are the existance of a maximum in isothermal solubilities at high pressures, a solubility minimum at low pressures, and a method to achieve essentially 100% solubility of a solid in a supercritical phase. Solubility maxima (Kurnik and Reid, 1981) and a method to achieve 100% solubilities of a solid in a supercritical phase are new findings in this thesis.

5-1 Solubility Minima

As is clearly shown in typical isothermal solubility diagrams of mole fraction versus pressure, a definite solubility minimum exists at relatively low pressures (10 - 30 bar). At these pressures, the virial equation of state is applicable and so it is possible to solve analytically for the pressure and mole fraction at the solubility minimum.

As is shown by Hinckley and Reid (1964), the pressure and mole fraction at the solubility minimum for binary systems is:

2 eB1 2 PV1 (5-1.1) y(min) =- RT 194

P(y.) RT (5-1.2) min B 22 + 2B12

Knowing the pressure for the minimum solubility is important

in deciding optimum operating pressures for low temperature

purification systems such as in heat exchangers used to

remove carbon dioxide from air.

5-2 Solubility Maxima

Of the data and correlations shown in Figures 4-1 to 4-9,

the highest pressure attained was 280 bar. As these figures

indicate, the isothermal solubilities are still increasing

with pressure. It is interesting, therefore, to perform com-

puter simulations to very high pressures (see Kurnik and

Reid, 1981). The results of such simulations are shown in

Figure 5-1 for the solubility of naphthalene in supercritical

ethylene for pressures up to 4 kbar and for several tempera-

tures. Experimental data are shown only for the 285 K isotherm

to indicate the range covered and the applicability of the

Peng-Robinson equation.

For the naphthalene-ethylene system, the solubility attains a minimum value in the range of 15 to 20 bar and a maximum at several hundred bar.

The existence of the concentration maxima for the naphtha-

lene-ethylene system is confirmed by considering the earlier work of Van Welie and Diepen (1961). They also graphed the mole fraction of naphthalene in ethylene as a function of 195

100

3 18 K 308 K 298 K 285 K z u-I 10 C z SYSTEM: 3 18K NAPHTHALENE- ETHYL ENE

308 K - PENG -ROBINSON EQUATION OF STATE 298K I k12 :O .02 285 K * EXPERIMENTAL DATA OF TSEKHANSKAYA (1964); T=:285 K

io-6 - II -mm m m m w ------I I -I

I 10 100 1000 10,000 PRESSURE (BARS)

Solubility of Naphthalene in Supercritical Ethylene- Indicating Solubility Maxima

Figure 5-1 196 pressure and covered a range up to about 1 kbar. Their

smoothed data (as read from an enlargement of their origional

graphs), are plotted in Figure 5-2. At temperatures close

to the upper critical end point (325.3 K), a maximum in con-

centration is clearly evident. At lower temperatures,the

maximum is less obvious. The dashed curve in Figure 5-2

represents the results of calculating the concentration maxi-

mum from the Peng-Robinson equation of state. This simulation

could only be carried out to 322 K; above this temperature

convergence becomes a problem as the second critical end point

is approachedand the formation of two fluid phases is pre-

dicted. Table 5-1 compares the theoretical versus experimental

maxima.

Concentration maxima have also been noted by Czubryt

et al. (1970) for the binary systems stearic acid-CO2 and

1-octadecanol-CO2 In these cases, the experimental data

were all measured past the solubility maxima -- which for both

solutes occurred at a pressure of about 280 bar. An approxi-

mate correlation of their data was achieved by a solubility parameter model.

Theoretical Development

The solubility minimum and maximum with pressure can be rel 4ted to the partial molar volume of the solute in the supercritical phase. With subscript I representing the solute, then with equilibrium between a pure solute and the solute dissolved in the supercritical fluid, 197

- Van Welie and Diepen, 1961 COMPUTER SIMULATION OF j 30-MAXIMUM CONCENTRATION USING THE PENG-ROBINSON EQUATION OF STATE

20 =8

Ca 5

LU -J- CIO -j 0 0 a 200 400 600 800 1000 PRESSURE (BARS)

NUMBER TEMPERATURE(K) I 303.2 2 308.2 3 313.2 4 318.2 5 321.2 6 323.2 7 324.2 8 325.3 Experimental Data Confirming Solubility Maxima of Naphthalene in Supercritical Ethylene

Figure 5-2 Table 5-1

Comparison between Experimental and Theoretical Solubility Maxima and the Pressure at these Maxima

E (bar) T (bar) E T T(K) max max % error,P Ymax Ymax % error,y

303 612 680 11.1 4. 31x10- 2 4.83x10-2 12.1

308 590 648 9.8 5.68x10-2 6.06x10-2 6.9

313 576 576 0.0 7.84x10 2 8.43x10-2 7.5

318 477 472 1.0 1.17x10 1 a.19x10 1 1.7 H k0 321 398 357 10.3 1. 35x10 1 1.60x10 1 18.5 OD

Notes: 1. Calculations were done using the Peng-Robinson Equation of State, kl2=0.02. 2. Experimental Data are from Van Welie and Diepen (1961). E 3. PEx= experimental value of maximum pressure. max 4. pT = theoretical value of maximum pressure. max 199

dmn4 = dlnfs (5-2.1)

Expanding Eq. 5-2.1 at constant temperature and assuming that

no fluid dissolves in the solute,

VF nF + lny1dP dlny1 =T dP (5-2.2) 1T,P

Using the definition of the fugacity coefficient,

F ^F $ -- f1 /yP (5-2.3)

Then Eq. 5-2.2 can be rearranged to give

Vs_

alnyl'RT H I [ (5-2.4) T + ll +[alny Tf,P-

an equation $K may be expressed in terms of y1 , T, and P with of state (Kurnik et al., 1981). For naphthalene as the solute

in ethylene, (aln$,/3lnyl)T,P was never less than -0.4 over a

pressure range up to the 4 kbar limit studied. Thus the

extrema in concentration occur when Vs=

Again using the Peng-Robinson equation of state, 1 for naphthalene in ethylene as a function of pressure and tempera-

ture was computed. The 318 K isotherm is shown in Figure 5-3. At low pressures, 4 is large and positive; it would approach 200

800

600

400 [ SOLUBILITY SOLUBILITY MAXIMA 200 MINIMA

0 - Is

-F / -200

Ct -400

- -600 C-) -800 o -1000

SYSTEM: - I 200 NAPHTH ALENE-ETHYLENE

- I 400 - PEtNG-ROBINSON E( OUATION OF STATE

- I 600 TE MPERATURE =318 K k =0.02 -1800

-'Qn I - . S 'W; I mmmm I 10 100 1000 10,000 PRESSURE (BARS)

Partial Molar Volume of Naphthalene in Supercritical Ethylene

Figure 5-3 201

an ideal gas molar volume as P -+- 0. With an increase in pres-

sure, decreases and becomes equal to Vs (111.9 cm3/mole)

at a pressure of about 20 bar. This corresponds to the solu-

bility minimum. V4 then becomes quite negative. The minimum

in 9'corresponds to the inflection point in the concentra-

tion-pressure curve shown in Figure 5-1. At high pressures,

eventually becomes equal to this then VF1 increases and Vs; thste corresponds to the maximum in concentration described earlier.

5-3 A Method to Achieve 100% Solubility of a Solid in

a Supercritical Phase

Due to the unusual phase behavior of the solid-supercrit-

ical fluid surface described in Chapter 2-2, it is possible

to delineate regions of solid-fluid equilibria other than

between the lower and upper critical end points. Moreover,

in these regions, one can obtain significantly higher solu-

bilities than between the critical end points and actually

approach a solubility of 100% mole fraction. These unique

features of supercritical fluids are discussed in this section.

Consider the P-x isotherms shown in Figure 2-15 of the

P-T projection shown in Figure 2-14. These projections are

for the case where the three phase line intersects the critical locus. On isotherms T 5, T 6 and T7 , there is a distinct solid + fluid (S+F) region existing for temperatures greater

than the upper critical end point temperature (T4).

One can, nevertheless, operate in the (S+F) region, provided that the pressure is greater than the highest 202

pressure on the critical locus connecting the critical point

of the solute with the upper critical end point. In this

situation, a limiting composition of 100% solubility of the

solute in the supercritical phase may be achieved when the

temperature just equals the pure solid melting point temper-

ature at the operating pressure.

Consider the system naphthalene-ethylene. The maximum

pressure on the critical locus connecting the critical point

of the pure solid to the upper critical end point is approxi-

mately 250 bar (see Figure 5-4). Thus, at an operating

pressure greater than 250 bar, say 274 bar, one can achieve

100% solubility of a solid in a supercritical fluid by chosing

the operating temperature equal to the melting point temper-

ature of pure naphthalene at 274 bar. Diepen and Scheffer

(.1953) give the melting point of pure naphthalene at 274 bar as 363 K.

A computer simulation of the ethylene-naphthalene system at a constant pressure of 274 bar and for temperatures between

285 K and 363 K is shown in Figure 5-5. For comparison, experimental data of Diepen and Scheffer (1953) under these conditions is also shown. The Peng-Robinson equation appears to simulate these extremely concentrated solutions quite well.

5-4 Entrainers in Supercritical Fluids

Solubilities of desired species in supercritical fluids may not always be sufficiently large enough for certain applications. In order to further increase component 203

Critical 250 Locus 200 I 4l: --UCEP '4 1~~ 150 Lo - Fusion 100 Line CL -Thr ec Phose 50 Line

0 - r 373 473 573 673 T (K)

Projection for Et hylene - Naphthalene (Van Welia and Diepen, 1961)

Figure 5-4 204

90- U

60 0

LU 50 System Ethylene - Na phthalene CL Pressure = 274 Bar 40 -PR Equation of St ate

k12 = .02 30 . Experimental Datc of Diepen and Schaffer (195 3 ) * Melting Point of' Naphtholaene 20 at 274 Bar

I I 101 - I-- 0 20 40 60 80 100 NAPHTHALENE (MOLE /0 )

T-x Projection for Ethylene-Naphthalene for Tempera- tures and Pressures above the Critical Locus

Figure 5-5 205 solubilities in supercritical fluids, it is possible in some

circumstances to add an additional component of higher

solubility -- called an entrainer.

At present, there is only one published case where en-

trainers were systematically used. This case is the separa-

tion of glyceride mixtures using supercritical carbon dioxide.

Quoting from Panzer et al. (1978): "Little separation was

achieved using pure carbon dioxide, but considerable improve- ments resulted by the addition of the entrainers carbon

tetrachloride and n-hexane." Peter and Brunner (1978) made

similar observations with the system carbon dioxide- glycer- ides, but with acetone as the entrainer. Selectivities of the glycerides were different, however, with the different entrainers.

Brunner (1980) has also noted that entrainers can significantly change the retrograde temperature region.

Some exploratory investigations done in this thesis have also shown the effect of entrainers. Several experiments were performed whereby the solubility of natural alkaloids in supercritical carbon dioxide were determined. Upon adding water as an entrainer Cabout one weight percent in the fluid phase), component solubilities of the alkaloids could be increased from 10 to 50 percent.

Finally, the ternary solid-fluid systems that were systematically studied in this thesis show that small amounts of a volatile component in a supercritical phase can significantly effect the solubility of all components in the supercritical 206 phase.

Little is really known about the important topic of

entrainers in supercritical fluids. Clearly much more research

remains to be done.

5-5 Transport Properties of Supercritical Fluids

Mass transfer in supercritical fluids is of importance

for the design engineer in sizing equipment -- for rarely will

industrial applications operate at equilibrium. Very little

work has been done in this area -- a few binary diffusion

and self diffusion coefficients have been measured and flux

rates for one system have been measured.

It is the purpose of this section of the thesis to review

the literature on transport properties in supercritical

fluids and to make suggestions for further research.

Tsekhanskaya (1968, 1971) has made measurements of the

diffusivity for the systems p-nitrophenol-water and naphthal-

ene-carbon dioxide near the critical region. In dense fluids,

the diffusivities are slightly larger than those of liquids

2 (D 1 2 ~ 10~4cm /s), but when the critical point is approached, the binary diffusivity approaches zero as suggested by theory

(Reid et al., 1977).

Iomtev and Tsekhanskaya C1964) and Morozov and Vinkler

C1975) have made extensive measurements on the diffusivity of naphthalene in ethylene, carbon dioxide, and nitrogen.

Except for the measurements of Morozov and Vinkler, all diffusivities were measured in static diffusion cells. 207

Morozov and Vinkler designed a dynamic method to obtain dif-

fusion coefficients which appears to give good results and

is also quite simple to construct and use.

Finally, Rance and Cussler (1974) measured flux rates of iodine into supercritical carbon dioxide. Their data are interesting as it suggests that there is no retrograde solidification region with this system. Also, if equilibrium solubility measurements are made on the system iodine-carbon dioxide, then it would be possible to calculate mass transfer coefficients from their flux data.

Suggestions for further research are to obtain binary diffusivity data for additional solid-fluid systems and to measure mass transfer coefficients to these systems. A generalized correlation of the Sherwood number as a function of the

Reynold and Schmidt number would then be obtained. 208

6. ENERGY EFFECTS

Enthalpy changes when a solid dissolves in a supercriti-

cal fluid are of importance in evaluating the energy require-

ments of a supercritical fluid extractor. Although no work

has been previously reported in this field, and no calori-

metric measurements were made in this thesis, it is possible

to obtain quantitative values of the differential heat of

solution by applying an equation of state to model systems.

6-1 Theoretical development

Consider the situation where solute (1) is added to ori-

ginally pure fluid (2) at constant temperature and pressure.

Applying the First Law:

dUF =dQ - dW + H dN (6-1.1)

dHF -PdVF= dQ - PdV+ HsdN1(6-1.2)

dHF = dQ + HsdN (6-1.3)

But, for the fluid mixture,

H-= NIH +N F (6-1.4)

dHFH =(N(N1 dHH1 +"NZ+ 2 dHd 2F) + (H1 dNI+H1 2 dN 2 ) (6-1.5) 209

At constant temperature and pressure,

N1dH1 + H 2 dH 2 = 0

by the Gibb's Duhem Equation. Since only solid is added to the mixture,

dH_F =F dN(6-1.6)

Combining Eq. (6-1.3) and (6-1.6) gives

Hs dQ =--F (6-1.7) dN (H1 - H)

or, the differential heat of solution is equal to the differ-

ence between the partial molar enthalpy of component 1 in the

fluid phase minus the enthalpy of pure solid 1. As shown in

Appendix III, this enthalpy difference is given by

F 1~31ny 3 ln$ (- - Hs) = -R [ + (6-1.8) T P -M

The integral heat of solution is defined as I'N Q = (( - Hs)dN 1(6-1.9)

Equation (6-1.9) can be simplified to give 210

Q = N 2 { (H4 - H)d[(6-1.10)

Physically, the molar differential heat of solution is the

heat interaction with the system by dissolving 1 mole of

solute in an infinite amount of fluid; the integral heat of

solution is total heat interaction with the system for a given

amount of solute and solvent.

6-2 Presentation and Discussion of Theoretical Results

Using an equation of state, the differential heat of

solution can be evaluated for the model systems studied in

this thesis. These simulations were made for many cases and

several numerical results are shown in Tables 6-1 to 6-3.

In the low pressure region, the enthalpy difference

(if - H ) AHsusi as expected. In the high pressure region

2 (P 300 bar), (H1 - H1 ) AHFUS, and in the retrograde region (where an increase in temperature decreases solubility),

(HF - H ) is exothermic. This exothermic enthalpy difference may prove beneficial in minimizing the energy requirements of a supercritical fluid (SCF) extraction plant. Table 6-1

Differential Heats of Solution for Phenanthrene-Carbon Dioxide at 32 8K1

31ny1 )ln$ (H -H1),cal./mole P (bar) Sal/T P 3lnyj 328t,P 20, 734 1 20,734 0 20, 382 5 20 ,382 0 19,930 10 19,930 0 -11,540 120 -11,087 -0.03928 H 8,110 H 300 6,849 -0.1555

AII(fusion) 2 = 4,456 cal./mole

AH(submlimation) 3 = 20,870 cal./mole

Notes: 1. Calculations were done using the Peng-Robinson Equation of State; k1 2 =k1 2 (T) as given in Table 4-5.

2. Date from Perry and Chilton (1973).

3. Calculated from vapor pressures of de Kruif et al. (1975). Table 6-2

Differential Heats of Solution for Phenanthrene-Ethylene at 328K1

alny Bn

P(bar) (-R)l/TJlny 2 P (5-H),cal./mole

1 20,724 0 20,724

5 20,339 0 20,339

10 19,834 0 19,834

120 -1,951 -0.04224 -2,037

300 7,706 -0.2819 10,731

AH(fusion) 2 = 4456 cal./mole

AH(sublimation)'3 = 20,870 cal./mole

Notes: 1. Calculations were done using the Peng-Robinson Equation

of State; k1 2=k1 2 (T) as given in Table 4-6.

2. Data from Perry and Chilton (1973)

3. Calculated from vapor pressures of de Kruif et al. (1975) Table 6-3

Differential Heats of Solution for Benzoic acid-Carbon Dioxide at 328K'

3 lny I)3 l1$ R) 131/TJ (3nyj1328,P (H. -Hf ) ,cal. /mole P(bar) 1 )1

1 21,030 0 21,030

5 20,766 0 20,766

10 20,436 0 20,436

120 -10,114 -0.04245 -10,562 H 300 7,191 -0.2236 9,262 WA

AH(fusion) 2 = 4,139 cal./mole

AH (sublimation) 3 = 21,096 cal./mole

Notes: 1. Calculations were done using the Peng-Robinson Equation of State, k 1 2=k1 2 (T) as given in Table 4-7.

2. Data of Perry and Chilton (1973).

3. Calculated from vapor pressures of de Kruif et al. (1975). 214

7. OVERALL CONCLUSIONS

Supercritical fluid extraction processes are seeing a

resurgence of interest -- both in academic institutions and

in industry. In academia, many of the phase equilibrium and

transport propertities of a condensed phase in equilibrium

with a fluid phase are being studied. In industry, the empha-

sis is on process development and solving the design and

engineering problems.

There are six major reasons why supercritical fluids are receiving a widespread interest.

* High Mass Transfer Rates Between Phases

A supercritical fluid phase has a low viscosity (near that of a gas) while also having a high mass diffusivity (between that of a gas and a liquid). Consequently, it is currently believed that the mass transfer coefficient (and hence the flux rate) will be higher than for typical liquid extractions.

* Ease of Solvent Regeneration

After a given supercritical fluid has extracted the desired components, the system pressure can be reduced to a low value (20-30 bar) causing all of the solute to precipate out. Then, the supercritical fluid is left in pure form and can be easily recycled. In typical liquid extractions, using an organic solvent, the spent solvent must usually be purified by distillation. 215

. Sensitivity to all Process Variables

For supercritical fluid extraction, both temperature and pressure have a significant effect on the equilibrium solubility. Small changes of temperature and/or pressure -- especially in the region near the critical point of the solvent, can affect equilibrium solubilities by two or three orders of magnitude. In liquid extraction, only temperature has a strong effect on equilibrium solubility.

* Non-Toxic Supercritical Fluids Can Be Used

Carbon dioxide -- a chemical which is non-toxic, non-flammable, inexpensive, and has a low critical temperature (304.2 K) can be used as a solvent for extracting substances. It is for this reason that many food and pharmaceutical industries are quite interested in supercritical CO2 extraction research.

* Energy Saving

When compared to distillation, supercritical fluid extraction is usually less energy intensive. A study by Arthur D.

Little, Inc. on dehydrating ethanol-water solutions by using than supercritical CO2 has shown to be more energy efficient azeotropic distillation (Krukonis, 1980).

. Sensitivity of Solubility to Trace Components

Solubility of components in supercritical fluids can be changed by several hundred percent by the addition to the fluid phase of small quantities (Cone mole percent) of a volatile, often polar, material (entrainer). In addition, selectivities of the extraction can be significantly affected by the entrainer. More research on entrainers in multicomponent 216 systems will give a better physical understanding of the en- hanced solubility as well as to enable one to develop guide- lines to chose the best entrainer.

New developments in supercritical fluid extraction discovered in this thesis are (1) the existance of a maximum in isothermal solubilities with increasing pressure; (2) enhancement of component solubilities in supercritical fluids by the addition of a second volatile solid component; (3) differential heats of solution from solid to fluid phase changing from endothermic in the low pressure regime to exothermic in the middle pressure regime back to endothermic in the high pressure regime; and (4) correlation and prediction of equilibrium solubilities of binary and multicomponent solids in supercritical fluids by use of rigorous thermodynamic theory. 217

8. RECOMMENDATIONS FOR FUTURE RESEARCH

8-1 Solid-Fluid Equilibria

In the area of solid-fluid equilibria, there are several

research topics which warrant further study. First, in this

thesis, only ternary systems were studied (two solids, one

fluid). It would be interesting to extend this work to even

higher order systems (more solid components) to answer sev-

eral questions:

a) Does the "temperature window" between p and q close?

b) Can one model a complex equilibria problem like coal

in supercritical CO2 by considering it to be made

up of many model compounds?

c) Do component solubilities in multicomponent systems

keep increasing in value over their value in a binary

system (when they do increase)?

Along with the experimental data of these higher order systems,

it would be interesting to examine the Peng-Robinson equation

(and others, such as Perturbed-Hard-Chain) to test their

ability to correlate higher order systems.

As solid-fluid extractions are most conveniently per-

formed in the region between the upper and lower critical end points, a convenient way of theoretically and experimentally determining these end points for multicomponent systems is a topic for further study. 218 Correlation of the solid-fluid equilibrium data taken in

this thesis and the data available in the literature proved

satisfactory by using the Peng-Robinson model for the fluid

phase fugacity coefficient. A drawback of this model, how-

ever, is that there is a temperature dependent binary parameter,

k.., which up to now, cannot be determined apriori. Perhaps

correlation methods to predict k.(T) could be developed, or

better yet, a model for the fluid phase fugacity coefficient

that has a more theoretical framework (and without adjustable

parameters) than the Peng-Robinson equation of state could be

developed.

As discussed in Chapter 5-3 of this thesis, there are

temperature and pressure regimes other than those between the

upper and lower critical end points where solid is in equilibrium with a fluid phase. Furthermore, in these other regimes,

it is possible to reach extremely high solubilities of solid components in the fluid phase. As the experimental equipment was designed in this thesis, however, it was impossible to obtain reproducible data for high solubilities (30 percent mole fraction or higher) due to plugging problems inside the let-down valve. Perhaps with a refinement of the experimental apparatus, equilibrium data in this very interesting regime could be obtained (and correlated with theory).

8-2 Liquid-Fluid Extraction

The area of liquid-fluid extraction has much wider applications in industry than solid-fluid extraction -- since most 219 industrial separation problems are with liquids. Some

equilibrium data is available in the literature on binary

liquid-fluid systems up to relatively low pressures (100 bar),

but little is known about higher pressure solubilities and

solubilities in multicomponent systems.

An interesting research program would be to determine

experimentally the solubility of multicomponent liquids in

supercritical fluids and successfully model and correlate the

data. The effect of temperature and pressure on the distri-

bution coefficients in multicomponent systems could then be

examined.

8-3 Equipment Design

A visual observation extraction would be useful in

locating critical end points (in the case of solid-fluid

equilibria) by observing the appearance and disappearance of a liquid phase.

As discovered in this thesis, there exists an isothermal solubility maxima (with pressure) of component solubilities of solids in supercritical fluids. This maxima however, exists at relatively high pressures (600 bar), and so it would be useful to have the capability to take solubility measurements in this region, and therefore give more support to this finding. A similar solubility maxima will probably exist with some liquid-fluid equilibria systems -- and this may be of value to test. 220

APPENDIX I

PARTIAL MOLAR VOLUME USING THE PENG-

ROBINSON EQUATION OF STATE

The partial molar volume of component i in a fluid is

by definition

S= (I-I) J

The partial molar volume can be evaluated from an equation

of state for the fluid mixture. Since most equations of

state are explicit in pressure, rather than in volume, it

is convenient to rewrite Equation (I-1):

' P

T,P,N. i] V(i= 3P (1-2)

JT,N.

Evaluating Equation (I - 2) using the Peng-Robinson Equation of State gives n 2ab. (V-b)

-_2T1bja - V(V+b) + b(V-b) I V-b V-bJ V(V+b) + b(V-b)

22 (aI(V+b)2(1-3) L(v-b ) [V(V+b)+b(V-b] 221

A similar derivation has been made by Lin and Daubert

(1980). 222

APPENDIX II

DERIVATION OF SLOPE EQUALITY

AT A BINARY MIXTURE CRITICAL POINT

Consider a binary mixture of two substances that has a molar Gibbs energy of mixing as shown in Figure II-I.

Compositions x' and xf correspond to points on a binodial curve while points B and C correspond to the limits of material stability of this system. If, however, points A,

B, C, and D of Figure II-1 were made to coincide to form a stable point E, then E is called a critical point and satisfies the relations:

c=0,g = Qgc>0 (11-1) 2 x 3x 4 x

where gc _ [tij

TP, CRITICAL POINT

By performing a Taylor expansion of g (in terms of P and x) around the critical point, it can be shown (Rowlin- son, 1969) that for component 1 that:

c -1-94x (11-2) LT 6V T , c T,a C2x

where Ax = x - x 223

xi X1

m g

The Molar Free Energy of Mixing as a Function of Mole Fraction , When g' is a Continuous Funtion of X

( Rowlinson, 1969 )

Figure II-1 224

a = at saturation

Thus, at the binary mixture critical point,

SI- = 0 (I1-4) T,cr

More meaningfully, Equation 11-4 can be written for the case of solid (1) fluid (2) equilibrium by

3 =0 (11-5)

as an equality at the binary critical end points. The differentiation can be conveniently performed along the three- phase locus. 225

APPENDIX III

DERIVATION OF ENTHALPY CHANGE

OF SOLVATION

The derivation of Equation (6-1.8):

-F ' Dny,~ 'aln$ (i-Hs) = -RL + [ait1]

i .1P T, -

is as follows:

With subscript 1 representing the solute, then with equilibrium between a pure solute and a solute dissolved in the supercritical fluid,

dlnfF = dlnfs 1 1 I1l-i)

Expanding Eq. III-i at constant pressure and assuming that no fluid dissolves in the solute,

iHF-Hr 3ln^F -H -H* - dT + LY 1 dlny2 =- dT (111-2) RT2 y1RT TP

Using the definition of the fugacity coefficient,

F -^F I = fI/ yP then Eq. 111-2 can be rearranged to give 226

= -r3]ny 11 (F Hs) [1 + +31nyBln }TP 4 R -R 1 j 9l-y - T - TrPj 227

APPENDIX IV

FREEZING POINT DATA

FOR MULTICOMPONENT MIXTURES

A Fisher-Johns melting point apparatus (Fisher

Scientific, Model 12-144) was used to determine if the solid mixtures used in this research formed solid solutions or an eutectic mixture with the solid phases as pure components.

From the freezing point behavior, it can be determined if the solids form a solid solution oran eutectic mixture.

Only in the latter case can the activity coefficient of the solid phase be neglected -- see Equation (2-3.8).

In order to test the accuracy of the equipment, a known eutectic mixture was examined: o-chloronitrobenzene with p-chloronitrobenzene (Prigogine and Defay, 1954). As Table

IV-1 shows, the agreement between the literature and experimental data for the melting point curve are within

+ 0.5 K.

Tables IV-2 through IV-5 give experimental freezing point data for four of the binary systems investigated.Y Listed in these tables are both T and Tf -- the initial and final freezing points. In each case, since Tf is constant, the formation of a eutectic composition is confirmed. Also listed in Tables IV-2 through IV-5 are the eutectic temperatures predicted from ideal solution theory (Prausnitz, 228

Table IV-

Comparison of Melting Point Curve from Literature* vs. Experimental Data for the System o-chloronitrobenzene(l), with p-chloronitrobenzene (2)

x2 T(K) ,Literature* T (K) ,Experimental

0.035 304.7 304.2 0.110 301.5 301.2 0.165 298.5 298.2 0.210 296.7 297.2 0.250 294.7 295.2 0.290 291.5 291.2 0.330 288.2 288.2 0.350 292.0 292.2 0.400 300.0 300.2 0.450 307.2 307.2 0.500 315.0 315.2 0.560 321.2 321.2 0.620 326.2 326.2 0.670 330.9 331.2 0.720 336.4 336.2 0.780 340.7 341.2 0.840 345.0 345.2 0.900 349.2 349.2 0.960 352.9 353.2

*Prigogine and Defay (1954) 229

Table IV-2

Experimental Freezing Curves for Phenanthrene with Naphthalene

Mole Fraction T. (K) Tf(K) Phenanthrene i f

0 352.2 352.2

0.1 348.2 326.2

0.2 342.2 326.2

0.3 335.7 326.2

0.4 328.2 326.2

0.5 335.2 326.2

0.6 344.2 326.2

0.7 353.2 326.2

0.8 360.7 326.2

0.9 367.2 326.2

1 369.2 369.2

TE(ideal solution) = 326.5 K T. E liquidus curve T.== eutectic line 230

Table IV-3

Experimental Freezing Curves for Phenanthrene with 2,6-DMN

Mole Fraction T. (K) T (K) Phenanthrene i f

0 382.2 382.2

0.1 378.7 344.2

0.2 374.2 344.2

0.3 367.2 344.2

0.4 360.2 344.2

0.5 352.2 344.2

0.6 344.2 344.2

0.7 352.2 344.2

0.8 360.2 344.2

0.9 367.2 344.2

1 369.2 369.2

TE(ideal solution) = 343.5K

Ti liquidus curve

Tf eutectic line 231

Table IV-4

Experimental Freezing Curves for Naphthalene with 2,6-DMN

Mole Fraction T (K) Tf(K) Naphthalene i f

0 382.2 382.2

0.1 378,7 334.2

0.2 374.2 334.2

0.3 367.2 334.2

0.4 360.2 334.2

0.5 353.2 334.2

0.6 343.7 334.2

0.7 336.2 334.2

0.8 343.2 334.2

0.9 348.7 334.2

1 352.2 352.2

TE(ideal solution) = 333.9K

T. liquidus curve

T B eutectic line 232

Table IV-5

Experimental Freezing Curves for 2,3-DMN with 2,6-DMN

Mole Fraction T (K) T (K) 2,3-DMN T (f

0 382.2 382.2

0.1 378.2 349.2

0.2 373.2 349.2

0.3 367.2 349.2

0.4 360.7 349.2

0.5 353.2 349.2

0.6 354.2 349.2

0.7 361.2 349.2

0.8 366.7 349.2

0.9 371.7 349.2

1 376.2 376.2

TE(ideal solution) = 349.3K

T. liquidus curve

T eutectic line 233

1969)

1 1lx ln (1-x 1 IV2 --- = VnH AH(I- T1 T LtHFUS,II FUS,2]

where T and T2 are the melting points of comopnents 1 and 2

and AHFUS,1and H FUS,2are the enthalpies of fusion of

components 1 and 2

Agreement between experimental eutectic temperatures and

eutectic temperatures predicted from ideal solution theory

is within one percent error.

Figure IV-1 shows the freezing point diagram for the

naphthalene-phenanthrene system and also a comparison with

the ideal solution model. In Table IV-6 are listed the

melting points and heats of fusion used in the ideal solu-

tion model.

*For the systems naphthalene/benzoic acid and phenanthrene/benzoic acid, only the final melting temperature (Tf) was measured. For both cases, Tf was constant, and within one percent of the value predicted from ideal solution theory. 234

Phcncnthrcne - Naphtholene Freezing C u rvs

373.2 SI I I

363.2 LUJ :D 353.2

LU CL 343.2 2 LUj H= 333.2

323.2 0 0.2 04 0.6 o8 1.0 MOLE FRACTION PHENANTHRENE

* Experimental First Freezing Poin t

0 Experimental Second Freezing Point --- Ideal Solution Theory

Figure IV-1 235

Table IV-6

Melting Points and Heats of Fusion

Component T NMP(K) AHFUS (cal/mol)

Phenanthrene 373.7 4456

Naphthalene 353.5 4614

2,3-DMN 376.2 5990

2,6-DMN 383.3 5990

Benzoic Acid 395.6 4140

T NMP = normal melting point temperature 236

APPENDIX V

PHYSICAL PROPERTIES OF SOLUTES STUDIED

In Table V-1 are listed physical properties of the supercritical fluids and the solutes studied in this research. Table V-2 lists vapor pressure data for all the solutes. Table V-1 Physical Properties of Solutes Studied

T (K) P (bar) Vs cc Name __C c gmoli Supplier Purity

Carbon Dioxide 0.2251 304.2 73.81 Matheson 99.8% 11 Ethylene 0.0851 282.4 50.361 Matheson C.P., 99.5%

2,3-Dimethylnaphthalene 0.424036 7855 32.1695 156.36 4 Aldrich 99%

2,6-Dimethylnaphthalene 0.42013 7775 32.27 5 156.36 4 Aldrich 99% L Phenanthrene 0.440 8781 28.992 181.9 4 Eastman Kodak 98% LA) Benzoic Acid 0.621 7521 45.61 96.474 Aldrich 99% 7 Hexachloroethane 0.255 698.4 33.42 113.224 Aldrich 99%

Naphthalene 0.3021 748.4 40.531 111.9434 Fisher 99.9%

REFERENCES

1. Reid et al. (1977) 5. Dreisbach (1955).

2. Estimated by Lydersen's method, see 6. Dreisbach (1955) for vapor pressures, and Reid et al. (1977). definition of acentric factor.

3. Reid et al. (1977) for vapor pressures 7. Perry and Chilton (1973) for vapor pressures, and and definition of acentric factor. definition of acentric factor.

4. Weast (1975) 238

Table V-2

Vapor Pressures of Solutes Studied

I. Naphthalene

Diepen and Scheffer (1948) vp (bar) T (K)

285.2 3. 0701x10 -5

298.2 1. 0943x10 4

308.2 2. 7966x10~ 4

Fowler et al. (1968) 2619.91 0 log1 0 P(mm) = 9.58102 (t( C)+220. 651)

40*C < t < 800C 239

Table V-2 (cont 'd)

II. Benzoic Acid

de Kruif et al. (1975) P T (bar) (K) VP 293.2 4. 49x10~ 7

298.2 8. 27x10

303.2 1. 49x10-6

308.2 2. 64x10 -6

313.2 4. 57x10-6

318.2 7. 80x10-6

323.2 1. 31x10 -5

328.2 2. 16x10 -5 240

Table V-2 (cont'd)

III. Phenanthrene

de Kruif et al. (1975)

T(K) PV (bar)

293.2 9.19x10 8

298.2 1.68x10 7

7 303.2 3.00x10

308.2 5.28x10 7

313.2 9. 09x10 7

318.2 1.55x10- 6

323. 2 2.57x10-6

328.2 4.23x10-6

333.2 6.83x10-6

338.2 1.09x10-5 241

Table V-2 (cont'd)

IV. 2, 3-Dimethylnaphthalene

Osborn and Douslin (1975)

TO(K) vp (bar)

333.2 1.400x10 4

338.2 2.200x10 4

343.2 3.386x10C 4

348.2 5.093x10~ 4

353.2 7.653x10~ 4 3 358.2 1.136x10-

363.2 1.649x10-3

3 368.2 2.376x10-

373.2 3.382x10-3 242

Table V-2 (cont'd)

V. 2,6-Dimethylnaphthalene

Osborn and Douslin (1975) w P (bar) T (K)

348.2 5. 360x10 4

353.2 8.146x10o 4

358.2 1. 236x10- 3

363.2 1. 823x10 -3

368.2 2. 650x10- 3

373.2 3. 850x10-3

378.2 5. 488x10-3

383.2 7. 709xlO 3 243

Table V-2 (cont'd)

VI. Hexachloroethane

Sax (1979) vp (m) T (K)

305.9 1

459. 8 76 0*

*sublimes 244

APPENDIX VI

SOURCES OF PHYSICAL PROPERTIES OF COMPLEX MOLECULES

Required physical property data for simulating equilibrium solubilities in binary and multicomponent solid- fluid equilibrium systems are: critical temperatures, critical pressures, and acentric factors for solute and solvent and vapor pressure and molar volumes of the solute.

Of these properties, those which are usually unknown are solid vapor pressures and solid critical properties. It is the purpose of this appendix to summarize these solid properties. This summary is not meant to be all-inclusive, but it covers physical property data found during the author's work. Table VI-I lists references containing solid vapor pressures along with the temperature range covered. Sources of critical property data are given by

Reid et al. (1977) and Ambrose and Townsend (1978). 245

Table VI-1

Vapor Pressures of Solid Substances

Solid Temperature Range (K) Reference

acenaphthene 338. 2-366 .4 fluorene 348.2-387.2 1, 8-dimethylnaphthalene 328.2-335.7 2 , 7-dimethy3naphtha lene 333.2-368.2 monuron (a herbicide) 303.5-379.1 2 p-acetophenetidide 312.4-387.8 2 anthracene 290.1-358.0 2 benzoic acid 290.4-315.5 2 benzoic acid 293.2-328.2 3 a-oxalic acid 293.2-338.2 3 benzophenone 293.2-318.2 3 trans tilbene 298.2-343.2 3 anthracene 313.2-343.2 3 acridine 293.2-338.2 3 phenazine 293.2-338.2 3 phenanthrene 293. 2-338.2 3 pyrene 398.2-458.2 4 2, 2-dimethylpropanoic acid 241. 62-256. 77 5 nicotine 293.2-323.2 6

References 1. Osborn and Douslin (1975) 2. Wiedemann (1972) 3. de Kruif et al. (1975) 4. Smith et al. (1979) 5. de Kruif and Oonk (1979) 6. Neghbubon (1959) 246

APPENDIX VII

LISTINGS OF THE PERTINENT COMPUTER PROGRAMS

In this appendix, three computer programs, written

in FORTRAN, are listed.

Table VII-l is the listing of the program PENG. This

program is used to calculate the equilibrium solubility of a solid in a fluid for binary systems. The Peng-Robinson

equation of state is used.

Table VII-2 lists the program MPR and eight subroutines.

This program calculates equilibrium solubilities for multi-

component solid-fluid equilibria with the Peng-Robinson

equation of state.

Table VII-3 lists the program KIJSP and two subroutines.

These programs call a non-linear least squares regression subroutine (GENLSQ) to determine a binary interaction parameter for solid-fluid equilibria. The interaction parameters are those for the Peng-Robinson equation of state.

Table VII-4 gives detailed documentation of the nonlinear least squares subroutine GENLSQ that performs the actual regression. This documentation is supplied courtesy of Dr. Herb Britt.

The input parameters for each of these programs are explained in the beginning of the respective programs. ot OSSOON3d (SOW ) WU0 ovBOON~d L1' 3'LS (010s) 0I3kf OCSOON3d w"N S33NO30 NI 3flfl Ib3dW3 3HI4 51 0 OCSCON3d ( s'o0L A) lvuW0 J or o LSOON3d (oc's) Oa~b 0OGOON~d StiV9 NI SmifSSatd 314 IUW d 3 06tOON3d InNIINDOD se O8VOON~d (r*OL L)L Ikio i Oc OLV0ON3d (d0011l)d (or's) Oaim N~td0O1I Sr 00 O9vOONad N 3 OSOOON~d OS NIOd VIVO 3bfSSfld 0 b39wfN 314 SI OVVOON~d (ri) vwuo si OCPOON3d N (GL'S) C3V~ CZV00N3d (oYs) vwb0 CL o LVOON3d ('LsuN'(N)SS) (OL'S)013b CCV00N3d (vl9) IW~D s O6EOON3d (S'- S('S) Oann *~Ss*S**S*#*@ O9CO0N3d 3 OLCOON~d '3 liOS 3ml 2 0 3WYN 314 SI SS 'SV0 N3A1OS 3M14 0 3KVN 314 SI VS 'SNDIO 31 IOW 3Dn3AN03 0 O3Sfl 3 OSCOON~d 3 OSCOON~d S IV 11 OM1001 KNOI Vb31333Y N13 S03M 314 NI Q3Sfl SNOIZDYbi OCDCON3d 310W . 0 SnifVA 3 VIC3W83 NI 3ml OA'3A'9A'VA 3 *3511d SYD 314 NI N3A1OS 314 0 NOI 31n 310W 314 SI CA 3 OCCOON~d 3 OCCOON~d *3SV14d SIC 314 NI 3 fl10S 314 AD 0 NI 3Vb 310W 314 SI A O&COON~d IIW0NA10d 5SIMI 0 SIOOb X31dW0O3H 314 3 I12 'iIIWONA1Od 3 5114 0 SICOonIV~b 314 mY fl SbD 3Y AII9ISS38dW03 3 COCOON~d 3 O6ZO0N3d 0SW63 NI N3 IbM 31 S 0 NoIuvrIONSNI90b -DN3d 314 : 0 lYIWONAlOd 319113 314 0 S N3131 30:)3H3 I0 CerOON~d 3 OLZOON3d DN3d 'SlVAU3 NI bnASS~bd 0JO IBIAAAN 314 51 N 3n314M WN "C'rl d NO tf3 Nfl03 N3bAO3H34 I 'r3 OSCOON~d 3 CcGr00N3d LNY 5N03 SIC) 314 SI b '31 5 0 NOXivnCI N0SNI90U OvZOON~d -Om~d 314 NI S NV 5N0O3 mV 019'9D19r'311'90'I0 3 OCE00N3d OrrooN~d Lr rdr'3'3'M/NOH/ S113WVN o trooNad (C)dwOO)Z SL*x31dW03 C0rOON3d rVWx14d1 'rLi 8BelVa C6LOON3d (C)IZiCE)bZ'(t')DN~d NOISNIWIO OSLOON~d (E'OCL))3314'(CL)1V3OIA'(OOL)O3A NOISNSWIC Ch&OON3d (C)A(O)A(OLV'CLr(o)ANOISNIINIC OSLOON~d (OOL)dV3'(OCL) IOA'(OO1)WdA'(COL)d NOISNIWIC OSLOON~d (S)DV'(S)SS bi03iNi OPLOON~d rMW'LMW 9.1I3b OCLOON~d (Z0'14-I) BalV~b L IIdWI CL LOON~d 3VI S j90 COLOON~d NOI 1fl03 NOSNI9OA-DN3d 314 VNISA ISY~d SIC)314 NI 3 O6000N3d 011051 A IAn 10iS 34 1f3 113 iinvowIE)Obd 51M 3

.. 3 ...... OtODON~d ' @ *.. C9000N3d 3 0OOON~d DNIh33NIDN3 1W3143 0 N3W~dVdlO 30 OVOOON3d AD0I0N1433 0 31Ani iSNI S 35111431551W 3 C000N3d )INunl. *1 IN0b 3 oroOwNd 3 .. 3 ...... C I CON~d .*p@...... * U.. .

N31SAS NOIC W VNOI VSU3AN03 V NVtl W0 (mid :3114

DN3d we.A5o-ad.aa;ndwoc, -ILA aLqej

LAVZ 248 Table VlI-1 (cont.) Computer Program PENG

FILE: PENG FORTRAN A CONVERSATIONAL MONITOR SYSTEM

READ (5.50) W2,PC2,TC2 PENOO560 50 FOR!.0AT (F4O.5) PENOO570 PENOO580 C ZI,PCI,TCI ARE THE ACCENTRIC FACTORS.CRITICAL PEN00590 C PRESSURES.,AND CRITICAL TEMPERATURES. UNITS: PENOO600 C DEG. K.AND EARS. PENOO610 c- ***, W --A ****** -U *** PEN00620 READ (5,60) PIVAP PENOO630 60 FORMAT(1EI1.5) PENOO640 C PIVAP IS THE VAPOR PRESSURE IN BARS. PEN00650 READ (5,70) VI PENO0660 70 FCRMAT(F10.5) PENOO670 C VI IS THE OLAR VOLUME OF THE SOLUTE IN CC/GR.MOL. PENOO6SO READ (5.90) K12 PENOO690 !0 FORMAT (FIO.5) PENOO700 C K12 IS THE BINARY INTERACTION COEFFICIENT. PENOO710 DATA CA,0B.R/0.45724DO,0.0778000,83.1400/ PENOO720 C END OF CATA INPUT PENOO730 C CWWU ***- * * $ * 3* PENOO740 C CALCULATION OF THE CONSTANT PROPERTIES IN THE PENG- PENOO750 C ROBINSON EQUATION OF STATE. PEN00760 C S*...*-a.*****.SSS*** PENOO770 B1=03'wR-TCI/IPC1 PENO0780 B2=0S*P.-TC2/PC2 PENCO 790 TP1=T,/TC PENOOBOO TR2=T/ TC2 PEN0810 K1=0.3746400+1.54226DOw1-0.26992OsW1*W1 PENOOS20 K2=0.3746400+1.54226.O*W2-0.2699200-W2*W2 PEN0O830 GAM1AI=(I.D0-A1w(I.00-TR1**0.5D0))*s2.O0 PENOO4O GA IA2=(I.I0.e2 (1.00-TR2**0.5DO))*2.DO0 PENOO850 ALIEI=OAR*RSTC1'TC1/PC1 PENOo60 A,-!E2=CA-RRTC2vTC2/ PC2 PENOO870 ALIE1 =ALIEICwGAMV.AI PENOOSSO ALIE2=ALIE2*GAMMA2 PENOO890 M= 1 PENO0900 U=1 PEN00910 L=1T PENOO920 WRITE(6,30) PENO930 90 FORMAT(35X' PENS-ROBINSON EQUATION OF STATE') PENO094O WprTE(6,100) (SG(K),K=l,5) PEN0O950 100 FORMAT(35X.' SOLVENT GAS:',5A4) PENCO960 WRITE (6,110) (SS(K),K=1,5) PENOO70 110 FORMAT(35X.' SOLUTE:',5A4) PENOOSSO .ITE (6,120) T1 PENOO990 120 FORMAT (35X, ' TEMPERATURE=',F6.,' K' ) PENO1000 WRITE(6,130) PiVAP PENO1010 130 FORMAT(35X,' VAPOR PRESSURE =' ,E0.5.' BAR') PENO1020 w;ITE(6.131 W1 PEN01030 131 FO RAAT(36X,'W1=',F10.5) PENO1040 WPATE(6.132) W2 PENO1050 132 FORMAT(36X.'W2=',F10.5) PENO1060 WRITE(6.133)TC1 PENO1070 133 FCRAT(36X.'TC1=',Fl0.5) PENO1080 WRITE(6.134) TC2 PENO1090 134 FORMAT(36X.'TC2=',F10.5) PEN01100 249 Table Vll-1 (cont.) Computer Program PENG

FILE: PENG FORTRAN A CONVERSATIONAL MONITOR SYSTEM

WRITE(6.135) PC1 PENO1110 135 FoRMAT(36X,'PC1=',F10.5) PENO1120 WRITE(6.136) PC2 PENO1130 136 FORMAT(36X.'PC2=',F10.5) PEN1140 WRITE(6,137) Vi PENO1150 137 FORMAT(26X.'V1='.F10.5) PEN01160 WRITE(6.140) K12 PEN01170 140 FORMAT (35X,' K12=',FIO.5,/) PENO1180 WRITE(6,150) PENO1190 150 FORMAT(SX.' P(BAR)'.5X,5X,'Y(PENG)',9X,Y(IDEAL)'.4X PENO1200 2,-3X2, 'ENHANCEMENT ' .4X. - V( CC/GR. MOL.),2X, 'COMPRESSIBILITY, PENO1210 14X,'FUGACITY',4X,4X,'POYNTING') PENO1220 V2ITE(6,160) PENO1230 160 FORMAT(53X, FACTOR ',24X,'FACTOR ', PENO1240 15X,' COEFFICIENT',SX,'TERM') PENO12SO C a..*...u..s...... PEN01260 C TR1,TR2 ARE THE REUCED TEMPOERATURES. K1,K2 PENO1270 C GAMMA1, GA.',A2,ALIE1.ALIE2 ARE THE CONSTANTS PENO12SO C IN THE PENG-RO5INSON EQUATION OF STATE. L IS A PENO1290 C COUNTER '!HICH IS EITHER 1 OR 2 AND IS USED IN THE PENO1300 C TWO STEPS OF THE wEGSTEIN ACCELERATION METHOD OF PEN0131o C C:%VERGING MCL FRACTIONS. M IS A COUNTER ON THE NUMBER OF PENO1J20 C ITERATIONS IN CONVERGING MOL FRACTIONS. PENO1330 C* PENO1340 00 170 K=1,N PENO1350 170 Y1(K)=0.DO PENO1360 C INITIAL GUESSES CN ALL MOL FRACTIONS IS ZERO PENO1370 180 Y2(J)=1.DO-YI(J) PENO1380 B=Y1(J)-E1+Y2(J) -92 PENO1390 ALIE=ALIE1-Y1(J)+Y1(J)+2.D0*((ALIEl* PENO1400 1AL'E2)--0.SDO)*(1.D0-K12)*Y1(J)*Y2(d)+ PENO1410 1ALIE2-Y2(J)-Y2(J) PENO1420 SELG=B-P(J)/R: T PENO1430 ABIG=ALIE*P(J)/R/R/T/T PENO1440 PENG(1 )=1.DO PENO1450 PENG(2)=(-1.DO)*(1.D00-BIG) PENO1460 PENC(3)=(ASIG-3.DO-BSIGBBIG-2.DO*BSIG) PENO1470 3 PENG(4)=(-1.CO)(ABIG-BBIG-BBIGvBSIG-BBIG** .DO) PENO1480 C CtU*catinssS ws.-mSeein-n PENO1490 C THE ABOVE SECTION CALCULATED THE COMPOSITION PENO1500 C OF THE DEPENDENT PROPERTIES IN THE PENG-ROBINSON EQUATION. PENO1510 C IN THE NEXT SECTION WILL BE CALCULATED THE MOLAR VOLUME PENO152O C OF THE GAS PHASE BY SOLVING PENO1530 C THE CUBIC FORM OF THE FENG-ROBINSON EQUATION OF PENO154O C STATE AND TAKING THE LARGEST ROOT IN THE CASE OF MULTIPLE PENO1550 C ROOTS. THE IMSL SUBROUTINE ZPOLR IS REQUIRED PENO1560 C *nssssasms*i*--ns*ni*.sk PENO1570 CALL ZPOLR(PENG,3,ZCOMP,IER) PENO1580 IF (IER .EQ. 0) GO TO 200 PENO1590 WRITE (6,190) IER PENO1600 190 FORMAT (' ON V ITERATION, IER='.13) PENO1610 GO TO 999 PENO1620 200 ZR(1)=REAL(ZCCMP(1)) PENO1630 ZR(2)=REAL(ZCOMP(2)) PENOI640 ZR(3)=REAL(ZCOMP(3)) PENO1650 250 Table Vll-l (cont.) Computer Program PENG

FILE: PENG FORTRAN A CONVERSATIONAL MONITOR SYSTEM

ZI(1)=AIMAG(ZCOMP(1)) PENOI660 ZI(2)=AIMAG(ZCCMP(2)) PENC0170 ZI(3)=AIMAG(ZCOMP(3)) PENO1660 DO 220 K=1,3 PEN01690 IF (ZI(K) .EQ. 0.00) GO TO 210 PEN01700 ZI(K)=0.DO PENO1710 GO TO 220 PENO1720 210 ZI(K)=1.DO PENO1730 220 CONTINUE PENO1740 DO 230 K=1.3 PENO1750 230 ZR(K)=ZR(K)ZI(K) PENO1760 CHECK(J,1 )=ZR(1) PENO1770 CHECK(J.2)=ZR(2) PENO1780 CHECK (J,3) =ZR(3) PENOI790 V=R-T. D0MAXI(ZR(IVZR(2),ZR(3)))/P(J) PENO18OO C PENGI 610 PENO1820 C THE FOLLOWING SECTION COMPUTES THE FUGACITY C COEFFICIENT OF THE SOLID. PHI TO PH6 ARE THE PENO1830 PEN01840 C COMPONENTS OF THE FUGACITY. PH IS THE LOG OF THE FUGACITY C COEFFICIENT. PT IS TME POYNTING TERM. PENOl 85 P E N O 1 66 0 C p SS--* - $** S * * W * Z=P(J)sV/R/T PENO1870 PH1=B1*(Z-1.00)/B PENO1880 PH2=(-1.DOP-L1Z-BBIG)P PH3=L-1.DO).ABtG'2.DO/BSIG/0SQRT(2.DO) PENO1900 PENO1910 PH4=(2.DO-Y1(J)PALIE1+2.DO*Y2(J)*(1.00-K12)* 1( (ALIEI.-ALIE2)--0.5DO))/ALIE PEN01920 61/8 PEN01930 PH5=(-1.D00) PENO1940 PH6=DLOG((Z+2.414DO-BBIG)/(Z0-.414O*BIG)) H=PH 1 PH2 PHS (PH4+PHS)PNPHE1950 !PH=DEXo(PH) PENO1960 P=DEXP( VI* (P(J)-P1VAP) /'R/T) PENO1970 ENT=PT/IPH PENO1980 C *PENO1990 C IN THIS SECTION OCCURS THE ACCELERATED wEGSTEIN PEN02000 C CONVERGENCE r,'ETHOD TO GET CONVERGENCE ON MOL. PENO2OI0 PENO2200 C FRACTIONS. PENO2C3O0 IF (L .EQ. 2) GO TO 240 PENO2040 PENO2050 YA(.j =Y1 (J) PENO2060 YB(J)=ENTwP1VAP/P(J) PENO2070 Y1(J)=Y(J) L=L+1 PENO-2080 GO TO 180 PENO2090 240 YC(J)=ENT*PIVAP/P(J) PEN02100 FP=(YC(U)-YS(J))/(YB(J)-YA(J)) PENO2110 ALPHA=1.D/(.OO-FP) PENO2120 YO(J)=YB(J)+ALPHA*(YC(J)-YB(J)) PENO2130 PENO2140 ERRO;=1.34*CAsS((YC(J)-YB(J))/YC(J)) IF (ERROR .LE. 1.00) GO TO 270 PEN02150 M= M+ I PEN02I160 IF 1 .LT. 15) GO TO 260 PEN02180 WRITE (6,250) M 250 FORMAT (' Y NOT CONVERGED IN '.12,' ITERATIONS') PENO2190 GO TO 888 PEN02200 251 Table Vl-1 (cont.) Computer Program PENG

FILE: PENG FORTRAN A CONVERSATIONAL MONITOR SYSTEM

260 Y1(d)=YD(J) PENO2210 L=1 PEN02220 GO TO 180 PEN02230 270 Y1(U)=YD(J) PEN02240 Y2(J)=1.DO-Y1(4) PENO22SO YIDEAL(J)=PIVAP/P(U) PEN02260 C...... PENO2270 C...... PENO2280 C IN THIS SECTION OCCURS THE CALCULATIONS FOR THE PARTIAL MOLAR VOLUMES,PEN02290 C THE DIFFERENCE BETWEEN THE PARTIAL MOLAR VOLUME AND THE SOLID PENO2300 C VOLUME, AND THE CAPACITY OF THE FLUID PHASE. VPM IS THE PEN02310 C PARTIAL MOLAR VOLUME(CC/G.MOL), CAP IS THE CAPACITY(G.MOL/CC) PEN02320 C PEN02330 C PENO2340 Q1=RsT/(V-8) PENO2350 02=1.DO+B1/( V-B) PEN02360 Q3=Q1 02 PEN02370 Q4=2.DO'(Yl(J)-ALIE1+Y2(J)*((ALIE1*ALIE2)**0.500)s(1.0-K12)) PEN02380 Q5=2.DO*ALIE*81*(V-S) PEN02390 QS=V*(V+B)+BS(V-B) PENO2400 07=05/06 PENO2410 06=04-07 PEN02420 Q9=V*(V+3)+B*(V-B) PENO2430 010=08/09 PEN02440 011=03-010 PENO2450 Q12=R-T/(V-B)/(V-B) PEN02460 Q13=2.DOALIE-(V+B) PEN02470 Q14=(V*(V+)+*B(V-B))*s2.0 PENO248O 15=Q12-013/014 PEN02490 016=011/015 PENO2500 VPM(J)0=G16 PENO2510 C...... PENO2520 C...... -...... PENO2530 CAP(J)=Y1(J)/V PENO254O WRITE(6,280) P(J),Y1(U),YIDEAL(J),ENT,VZ,IPH,PT PENO2550 230 FORMAT(8E16.5) PEN02560 888 J=J+1 PEN02570 N1=1 PENO2580 L=1 PENO2590 IF (d.LE. N) GO TO 180 PENO2600 WR:TE(6,774) PENO2610 774 FORMAT (/////) PEN2C20 WRITE(6,776) PENO4630 776 FORMAT(X,'O(BAR)',7X,'VPM(CC/G.ML)',4X,'(VS-VPM).(CC/G.MOL)', PEN02640 15X,'CAP(G.MOL/CC)') PENO2650 DO 778 I=1,N PEN02660 778 VDIF(I)=V1-VPM(I) PEN02670 DO 779 I=1,N PENO26O WRITE(6,775)((P(I)),(VPM(I)),(VDIF(I)),CAP(I)) PEN02690 775 FCRMAT(3D16.5,6X,D16.5,6X.016.5) PENO2700 779 CONTINUE PEN02710 999 STOP PEN02720 END PEN02730 252 Table Vl-2 Computer Program MPR

FILE: MPR FORTRAN A CONVERSATIONAL MONITOR SYSTEM

C...... ----..-...... * ... MPROOO10 C MPROOO20 C RONALD T. KURNIK MPROO30 C MASSACHUSETTS INSTITUTE OF TECHNOLOGY MPROOO40 C DEPARTMENT OF CHEMICAL ENGINEERING MPROOOSO C MPROOO60 C...... MPROOO70 IMPLICIT REAL*8 (A-H.O-Z) MPROOO80 Ceases. sans assss*asse*s eassa as*ess gatea** as*a**s**s* sa*a**asassess*sasMPROOO9O

C THIS IS THE PROGRAM THAT CREATES THE CALLING SEQUENCE FOR MPROO110 C THE MULTICOMPONENT PENG-ROBINSON EOS. MPROO120 Cse*ssee*ssawa*asss,*aea*a**a*s,************ssasa*asas*ss*,s**MPROO13O Css*sas**a***ass*ss***ass*a*s**s*a*s*ss********~*a******************sa*s**MPROOI4O DIMENSION PM(100) MPROO150 DIMENSION X(:0),Y(10),PT(10) MPROO160 DIMENSION APHI(10),ERROR(10),AP(10,10),PHI(1O) MPROO170 REAL'8 KIJ(10).LIJ(10,10) MPROO1IO INTEGER NSOLV(S),NSOLU(45) MPROO190 COMMON /01/ R,T,TC(10),PC(10),W(10) MPROO200 COMMON /Q2/ A1(10),B1(10),TR(10) MPROO210 COMMON /03/ KIJ,PVAP(10),VS(10),PHI,AP,SIJ MPROO220 COMMON /04/ N,IFLAG,LIJ,IFLAG1 MPR00230 COMMON /Q5/ VAPHI,Z,YID(10),E(10),PTY MPROO240 COMMON /06/ NSOLV,NSOLU MPR00250 READ(4,10) NP MPROO26O 10 FORMAT(I2) MPR00270 C NP IS THE NUMBER OF PRESSURE DATA POINTS MPROO20 READ(4,20) (PM(I),I=1,NP) MPROO290 20 FORMAT (F10.5) MPROO300 P=PM(1 ) MPROO310 CALL PENGMR(P) MPROO320 IF((IFLAG .EQ. 0) .AND. (IFLAG1 .EQ. 0)) GO TO 80 MPROO33O GO TO 999 MPROO34O 80 CONTINUE MPROO350 CALL PENGF1(W,TC,PC,KIJ,PVAP,VS.NSOLVNSOLU,N,SIJ) MPROO360 CALL PENGF2(KIJ,NSOLU,N,T,P,VZ.Y,YID,E.APHI.PT,SIJ) MPR00370 WRITE(6,50) MPROO380 50 FORMAT(///) MPR00390 REWIND 5 MPROO400 IF (NP .EQ. 1 ) GO TO 999 MPROO410 DO 30 I=2,NP MPR00420 P=PM(I) MPR00430 CALL PENGMR(P) MPROO440 IF ((IFLAG .EQ. 0) .AND. (IFLAGI .EQ. 0)) GO TO 70 MPROO450 GO TO 999 MPROO460 70 CALL PENGF2(KIJNSOLU,NT,P.V,Z,YYID,E,APHIPT.SIJ) MPROO470 WRITE(6,40) MPROO480 40 FORMAT(///) MPR00490 REWIND 5 MPROO500 30 CONTINUE MPROO510 999 STOP MPROO520 END MPROO530 Table Vl - 3 (cont.) Computer Program MPR

FILE: PENGMR FORTRAN A CONVERSATIONAL MONITOR SYSTEM

SUBROUTINE PENGMR(P) PENOOO10 IMPLICIT REAL8(A-H,O-Z) PENOO20 DIMENSION X(10),Y(10),PT(10) PENOOO3O PEN040 DIMENSION APHI(10),ERROR(10),AP(10,10) 7 DIMENSION PHl(l0),PH2(10),PH3(10),PH4(10),PHS(1O),PH (1O), PENOOO50 1PHB(10),PHI(10) PENOOO6 REAL *8 KIJ(10),LIJ(10,10) PENOOO70 INTEGER NSOLV(5).NSOLU(45) PENOOO80 COMMON /01/ R,TTC(10),PC(10),W(10) PENOOO90 COMMON /02/ A1(10),B1(10),TR(10) PENOO100 COMMON /Q3/ KIJ,PVAP(10),VS(10),PHI,AP,SIJ PENOO110 COMMON /04/ N,IFLAG,LIJIFLAG1 PEN0120 COMMON /05/ V,APHI,Z,YID(1O),E(10).PTY PENOO130 COMMON /06/ NSOLV,NSOLU PENO140 COMMON /07/ PH1,PH2,PH3,PH4,PH5,PH7,PH8 PENOO150 DO 5 I=1,10 PENOO160 ERROR(I)=0.DO PENOO170 KIJ(I)=0.DO PENO180 PVAP(I)=O.DO PENOO190 5 VS(I)=0.DO PENOO200 NAMELIST/RON/ PH1,PH2,PH3,PH4,PH5,PH7,PH8,V,Z,A1,B ,TRPHI,APHI, PENOO210 1PT,LIJ,AP PENO220 IFLAGi sQPENOO230 C ses* assess as*** am assess*** mesas***e****s******asses**e*s****seesses*essPENOO24O

C 1 IS ALWAYS THE SOLVENT. 2 THRU 10 ARE THE SOLUTES. PENOO260

Cs***sse**ssssss**ssssass*e*e*s*sSS****sss**e*******ssssss**eas*s*esseePENOO280 C THIS PROGRAM IS THE DRIVER PROGRAM FOR THE MULTICOMPONENT PENOC290 C PR EOS SOLID-FLUID EQUILIBRIA CALCULATIONS. AT PRESENT,2 PENOO300 C SOLUTES AND I SOLVENT CAN BE MODELLED, BUT THIS CAN BE EASILY PENOO310 C EXTENDED. BOTH SOLID-FLUID AND SOLID-SOLID BINARY PENOO320 C INTERACTIONS CAN BE MODELLED. DIRECT PENO330 C ITERATION IS USED FOR CONVERGENCE. PENO340

READ(5,10) T PENOO370 10 FORMAT(F14.7) PENOO380 C T IS THE SYSTEM TEMPERATURE,K PENO390 READ(5,20) N PENOO400 20 FORMAT(12) PENOO410 C N IS THE NUMBER OF PHASES, NOW RESTRICTED TO 2 OR 3. PENOO420 M=N-1 PENOO430 L=1 PENOO44O LM=5SM PENOO450 R=83.14 PENOO460 READ(5,21) (NSOLV(K),K*l,5) PENOO470 21 FORMAT(5A4) PENOO480 C NSOLV IS THE NAME OF THE SOLVENT, 20 CHARACTERS AT MOST. PENOO490 DO 23 I=1,LM,5 PENOOSQO J=I+4 PENOO510 READ(5,22) (NSOLU(K),K=I,J) PENOOS20 22 FORMAT (5A4) PENOO530 C NSOLU ARE THE NAMES OF THE SOLUTES,20 CHARACTERS AT MOST. PENOOS40 23 CONTINUE PENOOSSO OOL LON~d d/(I)dYAds(I)CXA oor 060 LONid NrzI ocr 00 090 LCN3d IflNIZLNO3 Ot OLD LON3d OLLC01D OSOLON~d ( I) A= (I)X 091 090 LONUd N'11 091 CC OSL 0O0 LONUd 666 01 CD OCO ONUdkL LOY'l4i OrOLONU (,SNCI 1n3lI ACI s NI C3Db3ANC3 ION A).VWUO.4 Of7L 010 LONUd 1 (o00V9) 3116m 000 LON3d 091 01 00 (Oocr*Ile1) -41 O6600N3d 1+1=1 OS600N~d OiL 0.1 CD (oc6L 31r wnss) Al 0i600N3d(03)133IfS 09600N3d (IX(IX())Sva' =I)C3 Oct OSSOON~d NrZ=1 OCtOC OV600N3d (N'"A)IAwfs-o0 1 =(Li),A 0C600N3d (I He. x) IHdl/d/ (I)evAe= CI A ort Or0OoNid N'r=IOC 00 o t600N3d 666 Cio!CD(Lt0030 Dviii) .i1 00600N3d (Z'AIlHdY 'DISS'9DsrrV'Xd) 8063 1113 06900N3d 3IrlNI NCO OI1L oBBOON~d 3flN1 N03 SOt OL900N3d (N"x)vuns-o L(L)X OSSOON~d d/(1)e1Ad2(1)X 001 OSBOON~d N'r=I 001 CC OVS0ON~d 89063 1113 OtBOON3d *W83 DNIINAOd 3HZ sI ide 3 OCSOON3d (18b/ ()SA~d)dxbo= CI lie 0 o IBOONUd N'r=I 06 00 OOBOON3d (zioti.)lvwoi ri O66.00N3d PIS (r22S) 0138 Oe 00N3 d...... OLLOONUd AIND SW31SAS A81N831 804 C03Sfl MON b313W1b1d 3 OSLOONUd NCI13Z"NI A8YNIS 3ifllCS-3nDcS 3HZ I snrs o OSLO0N~d...... OVLtOON3d (suaILoa) Lrj oA oL OCtOON3d i19' . ari~riiOs'ti3tno0s 3H 40o S38flSS3bd 8CdYA:dlAe OrL~oN3d (N'r =I I) dvAe) (oz 'S)ovb 0 ILOON~d (Lz0tp L i) vilO:4 OS OOL00N3d i1CrD/OO'*o'r3if1CS't3fl1CS 3HZ 40 3Ifl1CA 81101N:SA 3 06900N3d (N"'ZVI(I)SA) (O9'S)038 09900N3d ('taL ji) .1 wJ80i4 09 OL900N~d 6(N3A1CSr3flCS)'(ZINSA-1CS-L~Inf1S) 3 O9900N3d U804 lN3101JJ303 NCIIV313lNlI .NA1OS-SlfllCS 3 0SSOON~d (N'0'(~ne O9)ov38 Ot900N3d (l.vLjLIvw8Ci Cs OC900N3d *onr 31nlOS'131nnoCsIN3AlCS 3HZ 880 014314 318.1dN33V 14: Or0ooNid (N 6 L =I(IM ) (09"S)01V38 0 L900N3d (Lvt'LlWtlC4 Ot' 00900N3d tzfl1CoS' ,L~iCS' INIAlOS 3HZ 40 S38flZY83eIN3J I 131 183 3 06S00N3d (N :1l'(z)3 ) (ot"S)C13t OSSOON~d (L ovLi) 11i80i QoC OLSOON3d 0 ''r*3 rfl0s'ti 1CStlN3A1OS 3HZ 40 S38flSS38e 1131 183 :3d 3 OSSOONid (N=V0(z)0) (Or"S)013b

W31SAS U0 IN0W 11N01.LVS83ANO3 V N18Z8C4 8WDN3d :3114

EfdW WeJBOad Je4ndwo3 (t4uoz) Z-LLA eLqej 255 Table V1-2 (cont.) Computer Program MPR

FILE: PENGMR FORTRAN A CONVERSATIONAL MONITOR SYSTEM

DO 210 I=2,N PEN01110 210 E(I)sY(I)/YID(1) PENO1120 Z=P*V/R/T PENO1130 999 RETURN PENO1140 END PEN0I150 256 Table Vl-2 (cont.) Computer Program MPR

FILE: VPSP FORTRAN A CONVERSATIONAL MONITOR SYSTEM

SUBROUTINE VPSP (ABIG,BBIG,V,IERIFLAG,T,PR) VPS00010 IMPLICIT REAL*B (A-HO-Z) VPS00020 t***t*** te **sVPS0003O Css**s.*****5 .ss *****e**s********ss*s****esees C s*sesass*e a*ses*t*s**s*ss*****************555**** S55S***eesssssesssw*VPSO0040 C THIS PROGRAM CALCULATES THE VAPOR ROOT FOR THE PR EOS ONLY. VPSOOOS0 C IN THE CASE OF MULTIPLE ROOTS. IFLAG IS SET EQUAL TO 1 VPSooo60 C AND EXECUTATION TERMINATED. NOTE: THE IMSL SUBROUTINE ZPOLR VPSO0O70 C IS NEEDED. VPSOO080

DIMENSION PENG(4),ZR(3),ZI(3) VPSOO110 COMPLEX-16 ZCOMP(3) VPS0O120 IFLAG=O VPSOO140 PENG(1 )=1.D0 VPSOOI54 PENG(2)=(-1.DO)*(1.DO-BBIG) VPSOOIS0 PENG(3)=(ABIG-3.D0*BBIG*SBIG-2.D0*BBIG) VPSOO16O VPSOO170 PENG(4)=(-1.DO)*(ABIGBBIG-BBIG*BBIG-BBIGtBBIG*BBIG) CALL ZPOLR (PENG,3,ZCOMPIER) VPSOO180 IF (IER .NE. 131) GO TO S VPSOO190 WRITE(6,1) VPSOO200 I FORMAT(' ROOT FINDING ERRORIER=131') VPSOO210 IFLAG=1 VPS00220 GO TO 999 VPSOO230 VPS00240 5 ZR(1)zREAL(ZCCMP(1)) ZR(2)=REAL(ZCOMP(2)) VPS00250 ZR(3)=REAL(ZCOMP(3)) VPSOO260 ZI(1)=AIMAG(ZCOMP(1)) VPS0O270 ZI(2)=AIMAG(ZCOMP(2)) VPSOO280 ZU(3)=AIMAG(ZCOMP(3)) VPS00290 DO 20 1=1,3 VPS00300 VPSOO310 IF(ZI(I) .EQ. 0.00) GO TO 10 ZI(I)=0.DO VPS00320 GO TO 20 VPS00330 10 ZI(I)=1.00 VPS00340 20 CONTINUE VPSOO350 O 30 1=1,3 VPSOO360 30 ZR(I)=ZR(I)*ZI(I) VPSOO37O TOP=DMAX1 (ZR(1) ,ZR(i) ,ZR(3)) VPS00380 BOT=DMIN1(ZR(1),ZR(2),ZR(3)) VPS00390 50 V=R*T*TOP/P VPS00400 999 RETURN VPSOO410 END VP500420 257 Table VlI-2 (cont.) Computer Program MPR

FILE: ESOSR FORTRAN A CONVERSATIONAL MONITOR SYSTEM

SUBROUTINE ESOSR (P,X,A,ABIG,BBBIGAPHI,VZ) ES000010 IMPLICIT REALeB (A-H,O-Z) ES000020

C eses **S******$****ea************************$**** ****S eass 5000040 C THIS PROGRAM CALCULATES THE MIXTURE CONSTANTS ANO COMPONENT ES000050 C FUGACITIES FOR A N (NOW RESTRICTED TO 10) COMPONENT MIXTURE. ES000060 C THI IS DONE FOR PR EOS ONLY. COMMONS ARE LINKED WITH E000070 C PROGRAM ESO6R. ES000080

REAL*8 KIJ(10),LIJ(10,10) ES000110 DIMENSION AP(10,10),PHI(10),APHI(10),A2(10),X(10) E000120 DIMENSION PH1(10),PH2(10),PH3(10),PH4(10),PH5(10),PH7(10),PHS(10) E5000130 COMMON /01/ R,T,TC(I0),PC(10).W(10) ES000140 COMMON /Q2/ A1(10),B1(10),TR(10) ES000150 COMMON /03/ KIJ,PVAP(10),VS(10),PHI,AP.SId ES000160 COMMON /Q4/ NIFLAG,LIJ E5000170 COMMON/Q7/ PH1,PH2,PH3,PH4,PH5,PH7,PH8 ES000180 5=0.00 ES000190 DO 10 I1,N E5000200 10 5=B+Bl(I)*X(I) E5000210 M=N-1 E5000220 C IN ALL CALCULATIONS,'1' IS THE SOLVENT E5000230 C PHASE AND 2 THRU 10 ARE THE SOLUTES ES000240 PLUS=O.DO ES000250 DO 30 I=1,N E5000260 DO 30 J=1,N E5000270 30 PLUS=PLUS+(1.0E-LI5(I,J))*DSQRT(A1(I)*Al(J))*X(I)*X(J) ES000280 A=PLUS E5000290 ABIG=A*P/R/R/T/T E5000300 BBIG=B*P/R/T ES000310 CALL VPSP(ABIG,BBIGV,IER,IFLAGT.P,R) E5000320 IF (IFLAG .EQ. 1 .OR. IER .EQ. 131 ) GO TO 999 E5000330 C CALCULATION OF FUGACITY COEFFICIENTS ES000340 Z=P*V/R/T ES000350 C...... E5000360 C CALCULATION OF FUGACITY COEFFICIENTS E5000370 C...... --- -.--.-- -- E5000380 DO 70 I=2,N E5000390 PH1(I)zB1(I)=(Z-1.D0)/B E5000400 PH2(I)=(-1.D0)*DLOG(Z-BBLG) ES000410 PH3(I)=-(-1.DO)*ABIG/2.DO/BBIG/DSQRT(2.DO) E5000420 PLUS=0.DO ES000430 DO 80 J=1,N E5000440 PLUS=PLUS+(1.DO-LIJ(I,J))s((A1(I)*A(J))**o.5)*X(J) ES000450 80 CONTINUE E5000460 PH4(I)=2.DO*PLUS/A E5000470 P115(I) =(-1 .D0)a(I)/B E5000480 PH7(I)=DLOG((Z+2.414DOBBIG)/(Z-0.41400*BBIG)) E5000490 70 PHI(I)=PM1(I)+PH2(I)+PH3(I)*(PH4(I)+PH5(I))*PH7(I) ES000500 DO 90 Is2,N ES000510 90 APHI(I)=DEXP(PHI(I)) ES000520 999 RETURN E5000530 END E000540 258 Table V1L-2 (cont.) Computer Program MPR

FILE: ESO6R FORTRAN A CONVERSATIONAL MONITOR SYSTEM

SUBROUTINE ESO6R 5000010 C.------...... E...... 5000020 C THIS PROGRAM INITIALIZES THE PARAMETERS A AND B 5000030 C REQUIRED IN PENG-ROBINSON EOS. E5000040 C ...... 5000050 IMPLICIT REALs8(A-H,O-Z) E5000060 REAL*6 KIJ(10),LIJ(10,10) E5000070 DIMENSION PHI(10),AP(10,10) E5000080 COMMON /Q1/R.TTC(10),PC(10),W(10) E5000090 COMMON /02/ A1(10),81(10),TR(10) ES000100 COMMON /Q3/ KIJ.PVAP(10),VS(10),PHI,AP,SIJ E5000110 COMMON /04/ N,IFLAGLIJ ES000120 DIMENSION A2(10),ALPHA(10) 5000130 REAL*8 M(10) 5000140 CO 10 I=1,N 5000150 10 81(I)=0.07780DOsR*TC(I)/PC(I) 5000160 00 20 I=1,N ES000170 20 A2(I)sO.4572400*R*R'TC(I)*TC(I)/PC(I) 5000180 DO 30 I1,N E5000190 30 M(I)=0.3746400+1.5422600*W(I)-0.2699200*w(I)*W(z) 5000200 DO 40 I=1.N ES000210 40 TR(I)=T/TC(I) E5000220 DO 50 I=1,N E5000230 50 ALPHA(I)=1.DO+M(I)*(1.D0-(TR(I)*0.500)) ES000240 DO 60 I=1,N E5000250 60 ALPHA(I)=ALPHA(I)*ALPHA(I) ES000260 00 70 1=1,N 5000270 70 A1(I)=A2(I)*ALPHA(I) E000280 DO 80 I=1,N E000290 DO 90 J=1,N 5000300 LIJ(I,d)=0.DO E000310 90 CONTINUE E5000320 so CONTINUE E000330 DO 100 J=2,N 5000340 LIJ(1,J)=KIJ(J) ES000350 LIJ(J,1))KIJ(J) ES000360 100 CONTINUE ES000370 LIJ(2,3)=SIJ 5000380 LIJ(3,2)&SIJ ES000390 RETURN ES000400 END ES000410 259 Table Vll-2 (cont.) Computer Program MPR

FILE: PENGF1 FORTRAN A CONVERSATIONAL MONITOR SYSTEM

SUBROUTINE PENGF1(WTCPC.KIJPVAPVS.NSOLVNSOLU,N,SIJ) PENOQO10 C...... --...... PENOOO2O C OUTPUT FORMATTING PROGRAM NO. 1 PEN00030 C...... -...... PEN00040 IMPLICIT REAL*8 (A-H,O-Z) PENQOOSO REAL*8 KIJ(10) PENOOO60 INTEGER NSOLU(45),NSOLV(5) PENOOO70 DIMENSION W(1O),TC(10),PC(10),PVAP(1l),VS(10) PENCOOSO WRITE(6,10) (NSOLV(K),Ks1,5) PENOOO90 10 FORMAT (38X,5A4) PENOO100 WRITE(6,20) W(1) PENOO110 20 FORMAT(30X,'W',14XD10.5) PENOO120 WRITE(6,30) TC(1) PEN00130 30 FORMAT(30X,'TC(K)',10XD10.5) PEN00140 WRITE(6,40) PC(1) PENOQ150 40 FORMAT(30X,'PC(BAR)',BX,D10.5,///) PENO0160 M=N-1 PENOO170 CO 110 1=2,N PEN0180 LI=(I-1)*5-4 PEN0O190 J=LI+4 PEN00200 WRITE(6,50) (NSOLU(K),KzL,J) PEN00210 50 FORMAT(40X.5A4) PEN00220 WRITE(6,55) KIJ(I) PENOO230 55 FORMAT (30X,'KIJ',11X,D11.5) PEN00240 WRITE(6,60) W(I) PENOO250 60 FORMAT(30X,'W',14X,D10.5) PEN00260 WRITE(6,70) TC(I) PEN00270 70 FORMAT(30X,'TC(K)',10X,D10.5) PEN00280 WRITE(6.80) PC(I) PENOO290 so FORMAT(30X,'PC(BAR)',8XD10.5) PENOO300 WRITE(6.90) PVAP(I) PEN00310 90 FORMAT(30X,'PVAP(BAR)',6XDO.5) PEN00320 WRITE(6,100) VS(I) PEN00330 100 FORMAT(30X,'VS(CC/GR.MOL)',2XDIO.5,///) PEN00340 110 CONTINUE PEN00350 WRITE(6,120) SId PENOO360 120 FORMAT(30X.'SOLUTE-SOLUTE INTERACTION COEFFICIENTS ,F10.5,///) PEN00370 RETURN PEN00380 END PEN00390 260 Table V1I-2 (cont.) Computer Program MPR

FILE: PENGF2 FORTRAN A CONVERSATIONAL MONITOR SYSTEM

SUBROUTINE PENGF2 (KIJ,NSOLUNT,PV,Z,YYIO.E.APHI.PT.SIJ) PENOOO10 C0.-....-...... --...... --....-...... --...----...------....-----..----PENOOO2 C OUTPUT FORMATTING PROGRAM NO. 2 PENOOO30 c.----...... - PENOO04O IMPLICIT REAL*8 (A-HO-Z) PENOOSO REAL*8 KIJ(10) PENOOO6 INTEGER NSOLV(5),NSOLU(45) PENOOO7O DIMENSION W(10),TC(10),PC(10),PVAP(10),VS(10),Y(IO), PENOOO8O I Y(10(10),E(10),APHI (10),PT(10) PENOOO90 M=N-1 PEN0O100 L=M*5 PENOO110 WRITE(6,120) T PENOO12O 120 FORMAT(40X,' TEMPERATURE= ',D10.5,' K') PENOO130 WRITE(6,130) P PENOO140 130 FORMAT(40X,'PRESSUREz ',010.5,' BARS') PENOO150 WRITE(6,140) V PENOO16O 140 FORMAT(40X,'VOLUME= ',D10.5,' CC/GR.MOL') PENOO170 WRITE(6.150) z PENOO180 150 FORMAT(40X.'COMPRESSIBILITYs ',010.5./) PENOC190 WRITE(6,170) PEN0O200 170 FORMAT(42X,'Y(PENG)',9X,'Y(IOEAL)',6X,'ENHANCEMENT'USX, PENOO210 1'FUGACITY',8X,'POYNTING') PENO0220 WRITE(6,180) PENOO230 180 FORMAT(75XU'FACTOR',7X,'COEFFICIENT',SX,'TERM') PENOO24O 00 200 I=29N PEN00250 LIZ(I-I)*5-4 PEN00260 J=L1+4 PENOO27O WRITE(6,190) (NSOLU(K),K=LI,d),Y(I),YID(I),E(I),APHI(I), PENOO280 IPT(I) PENOO290 190 FORAAT(15X5A4,5016.5) PENOO300 200 CONTINUE PENOO310 RETURN PEN00320 END PENOO330 26I Table V1l-2 (cont.) Computer Program MPR

FILE: ERCAL FORTRAN A CONVERSATIONAL MONITOR SYSTEM

FUNCTION ERCAL (ERROR) ERCOCO10 IMPLICIT REALsS(A-HO-Z) ERCOOO20 DIMENSION ERROR(10) ERCOOO30 ERCAL=DMAXI(ERROR(1),ERROR(2),ERROR(3),ERROR(4),ERROR(5), ERCOO40 1ERROR(6),ERROR(7),ERROR(B),ERROR(9),ERROR(10)) ERCOOO50 999 RETURN ERCOOC60 END ERCOOO70

FILE: SUM FORTRAN A CONVERSATIONAL MONITOR SYSTEM

FUNCTION SUM(X,N) SUMOOO10 IMPLICIT REAL*G (A-H,O-Z) SU41100020 C assssssssseseassssss*sssssssssssasssssassasss*ssssaasasstassssss*ss*e*SU.10030 Ca*s*s** Ss**6*********asses.*assess***s*s s****** asse*** ***s*a*ss**s**SUMOOO4O C THIS PROGRAM WILL SUM N COMPONENTS OF A x VECTOR. SUMOCOSO Css**s*assseesss*ssassaseassssssass*sssssa*sss****s****w**s***s**5sSUMOOO6 sa**e s a*s*es* se**e*w***sse*** a*****s*s5***s****s**ssess* s*5 s~s e*msSUMOOO DIMENSION X(10) SUMOO8Q ADD=0. o SUMOO090 DO 10 I=2,N SUMOC 100 10 ADD=ADD+X(I) SUMOO110 SUM=ADD -SUMOOI120 RETURN SUM0O130 END SUMOO140 262 Table Vl-3 Computer Program KlJSP

FILE: KIJSP FORTRAN A CONVERSATIONAL MONITOR SYSTEM

C...... KIJOO10 C KIdOOO2 C RONALD T. KURNIK KIJ00030 C MASSACHUSETTS INSTITUTE OF TECHNOLOGY KIJ00040 C DEPARTMENT OF CHEMICAL ENGINEERING KIJOOSO C KI100060 C...... KIJOOO70 IMPLICIT REAL*8 (A-H.O-Z) KIJOOOSO C...... KIJOOO90 C KIdOO100 C THIS PROGRAM PERFORMS A NONLINEAR LEAST SQUARES REGRESSION - KIJOO110 C ON (YP) DATA TO BACKTRACK OUT AN OPTIMAL BINARY INTERACTION KIJOO120 C PARAMETER. THE FOLLOWING LIBRARIES MUST BE LINKED: KIJOO130 C TESTBED AND PRODCTLB--BOTH AVAILABLE ON PROJECT KIJ00140 C ASPEN. SEE HERB BRITT OF UNION CARBIDE FOR ADDITIONAL KIJOO150 C INFORMATION. THE SUBROUTINES SVEP AND VSVEP ARE ALSO KIJOO160 C REQUIRED. KIJOO170 c KIJO0180 C...... KIJOO190 EXTERNAL SVEP KIO200 COMMON /GLOBAL/ KPFLG1 ,KPFLG2 ,KPFLG3 ,LABORT ,NH , KIJ00210 I LDIAG ,NCHAR ,IMISS ,MISSCI ,MESSC2 , KIJO220 2 LPDIAG ,IEBAL ,IRFLAG ,MXBLKW ,ITYPRN , KIJ00230 3 LBNCP ,LBCP ,LSDIAG ,MAXNE ,MAXNPI , KJ00240 4 MAXNP2 ,MAXNP3 ,IUPDAT ,IRSTRT ,LSFLAG , KId00250 5 LRFLAG ,KSLKI ,KSLK2 ,KRFLAG ,IRNCLS , KIJ00260 6 LS T HIS KIJ00270 C END COMMON /GLOBAL/ 10-11-79 KIJ00280 DIMENSION P(1),PE(100),ZM(1,00),R(1,100),WORK(2000), KIJ00290 IIWORK(200).Z(1,100).DELZ(1,100),F(100),X(1,I00), KIJ00300 2COVAR(100).MV(100),NCV(100) KId00310 REAL*8 UB(5),L(S),LM(100,101) KIJOO320 INTEGER NAME(5) KJO0330 DATA MV/100*1/.NCV/100*1/ KIJ00340 P(1)=0.00 KIJOO350 READ (3,1) (NAME(K),Ks1,5) KJO0360 1 FORMAT(5A4) KIJ00370 WRITE(6,2) (NAME(K),Ks1,5) KUO4030 2 FORMAT(SA4) KIJO0390 C**S**S***S****S*****S***************SSS@**S*****S**S*S*S*K1400400 C K IS THE NUMBER OF EXPERIMENTAL DATA POINTS IN Y KIJ00410 Caa*sse*es*c*s*ss*ss*s***s**s**sesssse****s*es**********ss*.*.*..sKIJ00420 READ (3,10) K KIJ00430 10 FORMAT (12) KIJ00440 Cass*sseseses*sSS*SSSSSS*S**S***S**********sseSS*****as**sessssKIJ0O450 C X(1,1)=P KIJ00460 C ZM(1,I)=Y KIJ00470 Csssas*ceea*s***************************s**Sss***ssss**s****seos*KIJOO4O READ (3,15) T KIJOO490 15 FORMAT (F10.5) KIJ00500 DO 40 I=1,K KIJ0510 READ(3,30) X(I,I),ZM(I,I) KIJ00520 30 FORMAT(F11.5,D11.5) KIJOO530 40 CONTINUE KIJOO540 DO 35 I=1,K KIJ00550 263 Table Vll-3 (cont.) Computer Program KlJSP

FILE: KIJSP FORTRAN A CONVERSATIONAL MONITOR SYSTEM

35 ZM(1. I)=DLOG(ZM(1 I)) KIJ00560 KIJO570 00 20 1=1,K KlUO0580 20 Rf1,1)=ZVi(11), I READ(5,200) TC1,TC2 KIJ00590 200 FORMAT(F10.5) KIJ00600 READ (5.210) PCl,PC2 KIJ00610 210 FORMAT(F10.5) KlOOC620 READ(5,220) WI,W2 KIJ00630 220 F0*dAT(F10.5) KIJC0640 READ(5.230) VS KIJ00650 230 FORIAT(F10.5) KIJ00660 pEAD(5,240) PVP KIJ00670 240 FCRMAT(11.5) KIJO0680 REA(5,2E0) T KIJ00690 KIJ00700 250 FC..MAT(F10.5) WVIE( 6,252) KIJ00710 K1JO0720 252 FZ~hAT( PENG-RCSINSON EQUATION OF STATE') WR:TE(6,260) TC1 KIJ00730 260 FQRMAT('T01= '.F0.5) KIJ00740 KIJ00750 & sTE(6,Z70) TC2 270 FO;:AT'TC2= .F10.5) KIJ00760 r7E(6,280) PC1 KIJ00770 280 FCRT(c'PC=,IFlo.5) KI 400780 WR1ITE(6,290) PC2 KIJ00790 K10100800 290 F0rtA7('PC2=',F10.5) w~rTE(C,300) W1 KIJOOS10 300 FCPMAT('w1z',FO.5) KIJOOE20 ;.rTE(6,310) w2 KIJ00830 310 FR4R.AT('W2='pr10.5) KIJOO40 wITE6,32C) VS KI00C50 320 FPMAT('VS=',RIO.5) K1100860 2 3 0 -ITE(6, ) PVP KIJ00870 330 FR9MAT('PVP=',D11.5) KIJO890 .RITE(6.340) T KIJ0090 340 FORtAAT('T=',F10.5) KI OO900 v3.1T(6,350) K KIJOO910 350 FCRMAT('K=',I12) KIJO920 K 1J00930 Kl1O0940 N=1=1 KIJ00950 NC=1 KIJ00960 Us,'1)=0.5 KIJ00970 LS 1)=-O.3 KIJOC980 ITER=50 KIJ00990 1DE..=20 Kj%101000 ,CUT=1 KIJO1010 NH=6 KIJ01020 IODS=1 KIJO1030 55=0.000l KI101040 EPS=1.0-6 KIJ01050 KIJ01060 SSNS=1 .0-4 KIJ01070 ISv=0 KI01080 Kl1O1090 N IC=0 ISOUND1 KIJ01100 264 Table V11-3 (cont.) Computer Program K1JSP

FILE: KIJSP FORTRAN A CONVERSATIONAL MONITOR SYSTEM

KIJO1110 REWIND 5 KIJ01120 CALL GENLSQ (NM,,V.L,KNC,NCVP,ZMXRSVEPITERITERZ, 1 10E7,ICODS. S-, EPS, KOUTNDRTISSND. ISV,wORK, IWORK, Z, F,DE LZKIJ01130 IwoKIJ01140 2SU SQ.SI3MA , COV AR ,NFEVAL ,IER ,I8BOUNDLSUB ,LMNICC,) KIJ01 140 '-.WPJTE(6, 60) IER KIJ01160 60 FORI:XT //.', 'ERROR CODE =I1)IJ010 W,2ITE(6,7D) KIJO1180 70 FORMAT(,//) KIJO1190 DO 72 I=1.K KIJUC20 , )=DEXPZ (Z-1(1I( .I) KIJ01210 72 Z(1,I)DEXP(Z(1,I)) KIJ01220 DO 74 I=1,K0KIJO0;20 0 0 KIJO1230 74 PE(I)=DAES(ZM(1 , I) -Z(1 , I ))/ZM(1,I)1 . KIJOI1240 WPITE( 6,203 80 FCRMvAT(2GX,'PRESSURE,6X,'MCL. PRACTICN',3X,'MOL. FRACTION', KIJOI2SO 16x 'PERCENT') KIJO1260 WPTE( 6.62) KIJO1270 KIJ01 280 82 FCRMTAT(42X,'(MEASURED)',5x,'(ESTIMATED)',8X,'ERROR') KIJ01290 DO 100 I=1.K KIJ0120 W'RITE(6,90) (X(1,I).ZM(1,1),Z(1,I),PE(I)) KIJO1300 90 FOR.AT (20X,4D16.5)4KIJOI310 100 CONTINUE KIJO1320 KIJO1w30 STO0 P KIJ0I1340 EIND 265 Table VII-3 (cont.) Computer Program K1JSP

FILE: SVEP FORTRAN A CONVERSATIONAL MONITOR SYSTEM

SUBROUTINE SVEP(Z,ZM,X,P,K,M,MV.L,N,NC,NCVKEY,F) SVEOO0IO IMPLICIT REAL-8 (A-H,O-Z) SVEOOO20 REAL'S M1,M2 SVEOO3O DIMENSION ZM(1,100),Z(1,100),P(S),MV(100),NCV(100)LF(100) SVE00004 DIMENSION B(100),A(100),ASIG(100),SSIG(100). SVEOOOSO IPH1(100),PH2(100),PH3(100),PH4(100),PH5(100),PS(100), SVE00060 2PH6(100),PV(100),PV1(100),PV2(100),ZC(100), SVE00070 3v(100),X(1,100) SVEOOCOS eSVEOOO Cases5*sens* **ca*s******sn******ceasee*secant*eases cnacuuesseesseu C I IS SOLID, 2 IS FLUID SVEOOIOO at5 5S*SVEOO110 C*******a*** sc************ *s*****.e s* scsesssc READ (5,10) TC1,TC2 SVEOO120 10 FORMAT(F10.5) SVEOO130 READ(5,20) PC1,PC2 SVEOO140 20 FORMAT(F1O.5) SVEOO150 REAO(5,30) W1,W2 SVE016O 30 FORMAT(FI0.5) SVE00170 READ(5,40) VS SVEOO180 40 FORMAT(FIO.5) SVEOO190 READ(5,50) PVP SVEO0200 so FORMAT(DI1.5) S/EOO210 READ (5,60 ) T VE00220 60 FORMAT(F10.5) SVE00230 DATA RGAS/93.14/ SVE00240 DATA OA/0.4572400/ SVE00250 DATA OB/0.0778000/ SVE00260 5VE00270 C*****ce*sca**a*sass*** s**ans**************s***es asa c***ees ees C CALCULATION OF FUGACITY COEFFICIENT OF SOLID SVEOO280

DO 70 I=1,K SVEOO300 70 PS(I)=X(1,I)eVS/RGAS/T+DLOG(PVP) SVEOO310 cae Ceue*u********se**s**m*su*s*ss*ss*a*as****maau**e*e*s*aeess**ssass esses sSVE00320 C CALCULATION OF CONSTANT PROPERITIES IN PENG-ROBINSON EOS SVE00330 CC55*********ess*assess*assess*sene e~aseesess ssecssassesseeeseeee S VE00340 B1=OB*RGASCTCi/PC1 SVEOO350 82=O*RGASwTC2/PC2 SVEOO36O A21=OA*RGASPRGAS*TC*TC1/PC1 SVEOO370 A22=0A*RGAS-RGAS-TC2-TC2/PC2 SVEOO380 Ml=0.3746400+1.54226DOW1-0.269920*W1W1 SVEOO390 M2=0.37464 00+1.54226DO*W2-0.26992DO*W2*W2 SVE00400 TR1=T/TC1 SVE00410 TR2=T/TC2 SVE00420 ALPHA11.D+M1(1.D0-(TR1eO.500)) SVE00430 ALPHA2=1.D0+M2"(1.DO-(TR2**O.5D0)) SVE00440 ALPHA1=ALPHA1*ALPHAI SVEOO450 ALPHA2=ALPHA2*ALPHA2 SVE00460 AI=A21*ALPHAI SVE00470 A2=A22*ALPHA2 SVEOO480 Cae****. a*e**a****s******e**es****s*********a***s*assess svsa ssses eee *SVEOO49O SVEOO500 C CALCULATION OF MIXTURE PROPERITIES O C ssseaa*.sn*u*ea*s*****ae***s**a*es**s****s***s***s***seesaessucsuesSVEOO DO 140 I=1,K SVEOO520 140 Z(1,I)=DEXP(Z(1,I)) SVE00530 DO 150 I=1,K SVE00540 150 B(I)=BlaZ(1,I)+82*(1.00-Z(1,1)) SVEOO550 266 Table V1l-3 (cont.) Computer Program K1JSP

FILE: SVEP FORTRAN A CONVERSATIONAL MONITOR SYSTEM

AIJ=((Al*A2)**0.5DO)*(1.DO-P(1)) SVE00560 DO 165 I=1,K SVE00570 165 A(I)=Z(1,I)*Z(iI)*AI+ SVE00580 12.DO*Z('6,&)-(1.00-Z(1,I))*AIU+ SVE00590 2(1.Do-Z(1,I))*(1.00-Z(1,I))*A2 SVEOO600 DO 180 I=1,K SVEOO610 ABIG(I)=A(I)*X(1,I)/RGAS/RGAS/T/T SVEOO620 180 BBIG(I)=(I)*X(1,I)/RGAS/T SVE00630 CALL VSVEP(ABIG,BBIGO,V,T,RGAS,KZM,X.Z) SVE00640 DO 185 I=lK SVEOO650 185 ZC(I)=X(1,I)*V(I)/RGAS/T SVE00660 C...... SVEOO670 C SVE00680 C CALCULATION OF FUGACITY COEFFICIENTS. SVEOO690 C SVE00700 C...... 5VE00710 DO 190 1=1,K SVE00720 PH1(I)=B1*(ZC(I)-1.DO)/B(I) SVE00730 PH2(I)=(-1.00)*DLOG(ZC(I)-BBIG(I)) SVE00740 PH3(I)=(-1.DO)ABIG(I)/2.DO/DSQRT(2.00)/BBIG(I) SVEOO750 PH4(I)=2.DO* (Z(1,I)*A+(1.0O-Z(1I))*AI)/A(I) SVEOO760 PHS(I)=(-1.D0)w81/8(I) SVE00770 PH6(I)=DLOG((ZC(I)+2.41400*BBIG(I))/(ZC(I)-O.41400*'BIG(I))) SVEOO780 190 PV1(I)=PH1(I)+PH2(I)+PH3(I)*(PH4(I)+PHS(I))*PH6(I) SVE00790 DO 200 I=1,K SvEOOBOO 200 Pv2(I)=Z(1,1 )*X(1,I)*DEXP(PV1(I)) SVE00810 00 205 I=1,K SVE00820 205 PV(I)=0LOG(PV2(I)) SVE00830 DO 210 I=1,K SVE00840 210 F( I)=PV(I)-PS(I) SVEOOSSO DO 220 I=1,K SVE00860 220 Z(1,I)=DLOG(Z(1,I)) SVEOO870 REWIND S SVEOOS8O RETURN SVE00890 END SVE00900 267 Table Vll-3 (cont.) Computer Program K1JSP

FILE: VSVEP FORTRAN A CONVERSATIONAL MONITOR SYSTEM

SUBROUTINE VSVEP (ABIG,BSIG,V,TRGAS,K,ZMX,Z) VSVOOOo1 C...... VSVOOO2O C THIS SUBROUTINE CALCULATES THE SPECIFIC VOLUME OF THE FLUID PHASE. VSVO0030 C THE IMSL SUBROUTINE ZPOLR IS REQUIRED. VSVOOO40 C ...... VSVQOO50 IMPLICIT REAL*8 (A-HO-Z) VSVOOO00 DIMENSION PENG(4).V(100),ZR(3),ZI(3),ZM(1,100),Z(1,100) VSVOOO70 DIMENS ION ABIG( 100),v BBIG( 100),X(1 ,100) VSVOOO80 COMPLEX-16 ZCOMP(3) VSVOO090 RGAS=83.14 VSVOO100 00 30 I=1,K vsV00110 PENG(1)=1.DO VSVOO120 PENG(2)=(-1.CO)*(1.DO-BBIG(I)) VSVOO130 PENG(3)=ABIG(I)-3.D0*BBIG(I)*BBIG(I)-2.OO*BBIG(I) VSVO0140 PENG(4)=(-1.D0)wBBIG(I)*(ABIG(I)-BBIG(I)-BBIG(I)*BBI(I)) VSVOO1SO CALL ZPOLR(PENG,3,ZCOMP,IER) VSVOO160 DO 10 J=1,3 VSVOO170 ZR(J)=REAL(ZCOMP(J)) VSV00180 10 ZI(J)=AIMAG(ZCOMP(J)) VSVOO190 00 20 Jc1,3 VSVOO200 IF (ZI(J) .EQ. 0.DO) GO TO 20 VSVOO210 ZR(J)=0.DO VSVO0220 20 CONTINUE VSVO0230 30 V(I)=RGAS*T/X(1,t)*DMAXI(ZR(1),ZR(2),ZR(3)) VSVO0240 RETURN VSVO0250 END VSVO0260 268

Table VII-4

Documentation of the Subroutine GENLSQ

Purpose

To fit an implicit nonlinear model of the form

f(z1 ... ,ZXm'l' '..'vXL'''n) = 0 to a set of z-x data. The observed z data, zm, is assumed to contain random

experimental error while the x data is assumed to be error

free. This subroutine may be thought of as an extension of ordinary least squares to the case where some of independent variables, as well as the dependent variable, are subject to error.

An alternative interpretation is to think of GENLSQ as a routine for simultaneous data adjustment and model fitting.

Method

The generalized least squares algorithm of Britt and

Luecke. The values of p1 .. . ,p are found that minimize

k m(zm . - z. )2 L 2 i=l j=1 r. 3i subject to the constraints

f(z ... ,z ,x ,0, i=1,..,k n I M 269 where r. is the standard deviation of the error in zm. Ji Ji and k is the number of data points to be fit. The values of z are the estimates of the true values of the model variables whose observed values zm were assumed to be sub-

ject to error. The Deming approximate algorithm is used to generate starting values for the Britt-Luecke algorithm.

For reference, see Britt, H.I., and Luecke , R.H. , "The

Estimation of Parameters in Non Linear, Implicit Models,"

Technometrics, 15,2, 233 (1975), and Deming, EW.E., "Statis- tical Adjustment of Data," Wiley, New York, 1943.

Usage

The subroutine is called by the following statement:

CALL GENLSQ (NM,MVL,K,NCNCVP,ZM,X,R,SVEPITER,ITERZ,

IDEM, IODSSS, EPS , KOUTNDRIVSSND, ISVWORK, IWORK, Z , F, DELZ,

SUMSQ, SIGMA, C0VAR, NFEVAL, IER, IBUND ,LB, UB, LMNIC, C, D)

Description of Parameters

Input:

This is a double precision program. All floating point variables must be declared REAL*8 in the calling program.

N - Number of unknown model parameters to be

estimated.

K - Number of data points to be fit (K > N)

L - Number of model independent variables (L > 1) 270

P - Vector of length N containing the initial

guesses of the unkonwn model parameters.

ZM - Vector of length K containing the observed

values of the model dependent variable, one

per data point.

X - Array of dimension L*K containing the values

of the model independent variables, L per data

point.

R - Vector of length K containing the standard

deviations of YM. These values may be thought

of as the inverse of the weighing factor for

each data point. For unweighted least squares,

set all elements of R equal to 1.0.

MODEL - Name of user supplied model subroutine des-

cribed below. Must be declared EXTERNAL in

the calling program.

ITER - Maximum number of iterations allowed. A good

choice is 50.

IDEM - Deming method parameter

IDEM

vergence is obtained or until IDEM

iterations have been made. The

program will then switch to the

Britt-Luecke method.

IDEM = -1 - Deming's method is used for all

iterations. The exact least

squares solution is obtained in 271

only certain special cases.

IODS - Key for one dimensional search during Deming

iterations. See Remark 2.

I4DS=O No one dimensional search. Take SS

times the predicted Gauss-Newton step

on each iteration.

lqDS=l Search for the minimum in the Gauss-

Newton direction on each iteration.

On the 1st iteration, begin the search

by taking SS times the predicted

Gauss-Newton step. On subsequent

iterations, begin the search with the

optimum value of SS from the previous

iteration.

lWDS=2 Search for the minimum in the Gauss-

Newton direction on each iteration.

Begin the search on each iteration by

taking SS times the predicted Gauss-

Newton step.

SS - Step size parameter. See lDS above and Remark 2.

EPS - Convergence tolerance. Convergence is declared

if the root mean square fractional change in P

is less than EPS. A good choice is 1.D-6.

KWUT - Print output key.

0 No printed output.

1 Final results only. 272

2 Minimum amount of information per

iteration and final results.

3,4 Relatively more output per iteration.

Used for debugging purposes.

NDRIV - Derivative key.

0 User supplied model subroutine evalu-

ates model and its first derivatives

with respect to P and Z.

I User supplied model subroutine evalu-

ates model only. Derivatives are

calculated numerically by GENLSQ.

SSND - Step size to be used in calculating numerical

derivatives. Applies only if NDRIV=l. A good

choice is l.D-4.

ISV - Variance-covariance matrix computation key.

See Remark 4.

ISV=0 It is assumed that the input values

(R) of the standard deviations of ZM

are proportional to the correct

values. The constant of proportion-

ality is estimated by the standard

error of curve fit (SIGMA) and R is

adjusted accordingly before the vari-

ance-covariance matrix (COVAR) of the

parameter estimates is computed.

ISV=l It is assumed that the input values

(R) of the stadnard deviations of ZM 273 are correct. Their values are not

adjusted by the standard error of

curve fit (SIGMA) before the variance-

covariance matrix (C0VAR) of the

parameter estimates is computed.

It is suggested that ISV=Q be used unless R is

known with a high degree of certainty.

WQRK - Work vector of length 2N + 3K + MK + NK + 3 max(N,M)K + 3 N(N+l)

IWORK - Integer work vector of length N.

z - Array of dimension (M,K).

F - Vector of length K.

DELZ - Array of dimension (M,K).

COVAR - Vector of length N(N+1)/2.

Outp. at

p - Vector containing the least squares parameter

estimates if converged or most recent values

if not converged.

ITER - Number of iterations used.

z - Array containing the estimates of the true values of the model variables whose observed

values (ZM) were assumed to be subject to ran-

dom experimental error.

SUMSQ - Weighted sum of squares of residuals at P, i.e., the minimized sum of squares value.

SIGMA - Standard error of curve fit. 274 COVAR - Vector representing the lower triangular part

of the (symmetric) variance-covariance matrix

of the parameter estimates, stored by columns.

For example, the order of storage is 1

2 4

3 5 6

for N=3. Parameter estimate standard deviations

are obtained by taking the square root of the

diagonal elements of this matrix.

NFEVAL- Number of times the user supplied subroutine

was called by GENLSQ.

IER - Error code.

0 - No error.

1 - Minimum not found in ITER iterations.

2 - Steps taken to overcome matrix

singularity have caused COVAR to be

modified. It is no longer the

variance-covariance matrix. This

problem is caused by highly corre-

lated model parameters. Reformula-

tion of the model with fewer, less

dependent parameters may help.

3 - Program stopped because of matrix

inversion problems. Comments for

IER=2 apply. 275 Subroutines Required

GENLSQ calls a user supplied routine to evaluate the model and, optionally, its first derivatives with respect

to the model parameters P. The form for NDRIV=O is:

SUBROUTINE MODEL (ZZMX,P,K,M,L,N,KEYF)

IMPLICIT REAL*8 (A-HO-Z)

DIMENSION Z (M,K),ZM(M,K),X(L,K),P(N),F(K),FZ(M,K)

FP(N,K)

DO 3 l=l,K

P(N))

C IF KEY=1 DERIVATIVES ARE NOT REQUIRED

IF (KEY.EQ.1) Go To 3

Do 1 J=l,N

1 FP(Jl)= 3f(Z(ll),...,Z(M,l),X(ll),...,X(L,l)

PCl),...,P(N))/3PCJ)

Do 2 J=l,M

2 FZ(J,1)=af(Z(1,1),...,Z(M,1),X(LI1),...,X(L,1),PCl)

... ,P(N))/9Z(J,

3 C&NTINUE

RETURN

END

The form for NDRIV=1 is

SUBROUTINE MODEL(Z, ZM,X,P,K,M,L,N,KEYF)

IMPLICIT REAL*8(A-H,0-Z)

DIMENSION Z(MK),ZM(M,K),X(L,K) ,P(N) ,F(K)

Do 1 I=l,K 276

1 F(1)=f(Z(l,1),...,rZ(Mrl),X(,1),...,X(L,1),P(l),

... ,PCN))

RETURN

END

NOTE: It is permissible for the model function to change

with 1.

The subroutine name (not necessarily MODEL) must appear

in the argument list of GENLSQ at the proper position and

must also appear in an EXTERNAL statement in the program

which invokes GENLSQ.

A subroutine LUEBRI, supplied by the catalogued pro-

cedure, is called by GENLSQ to do the actual calculations.

Space Requirement

? decimal bytes.

Remarks

1. For explicit models with significant error in only the dependent variable, use subroutine NLLSQ.

2. The Deming approximate algorithm is an excellent initialization method for the Britt-Luecke algorithm since it usually produces estimtaes very close to the exact

Britt-Luecke estimates and is less prone to convergence problems. The Britt-Luecke algorithm almost always con- verges rapidly from a converged Deming solution. Both algorithms are of the Gauss-Newton type; that is they are based on model linearization. 277

When convergence problems do arise during the Deming

initialization, they can often be overcome by step size

(SS) adjustment. GENLSQ uses the unmodified Deming method when 10DS=0 and SS=1.0. Setting SS=1.0 damps the search and is often helpful. Setting 10DS=1 or 2 causes a one- dimensional search to be made in the Gauss-Newton direction on each iteration to find a near-optimum value of SS. The following strategy is recommended:

(a) Make sure you are providing the program with the

best initial guesses of P 1 ...P. you can come up

with.

(b) Try using 1DS=0, SS=1.0. This should result in

rapid convergnece for most problems.

.c) If (b) fails, try damping the search. A range of

.1 to .5 is recommended for SS. Leave I0DS=0.

(d). If (c) fails, try 10DS=l, SS=.l.

(e) If (d) fails, contact H. 1. Britt, Applied Mathe-

matics and Computing Group.

The significance of Step (a) depends greatly on the particular model and data. In the event that you are having convergence problems that appear to be due to poor starting values, and you are unable to come up with better ones, a randomized start is recommended. A procedure for doing this is described on page 15 of the UCC R&D Report

"SIDEWINDER IV" by C.D. Hendrix, File No. 18454, dated

June 11, 1973. This tactic also provides some protection against converging to a local minimum rather than the global 278

minimum.

There is no one dimensional search during the Britt-

Luecke iterations, however the step size is adjusted by the

SS parameter.

3. The X array is not used by GENLSQ. It is only a ve-

hicle for passing data to the user supplied model subrou-

tine. As a result, it can be dimensioned any way the user

pleases, although X(L,K) is the normal case.

5. The weighing factors in the least squares criteria have 2 been denoted 1/r., rather than the more typical wi, to em-

phasize the statistical aspects of the curve fitting prob-

lem. If the errors in measuring the y's are independent of

each other and normally distributed with zero mean and

variance a2r. 2 2 then GENLSQ produces the maximum liklihood

estimate of p 1 ,...,p. The factor a2 need not be known. In other words, it is only the ratios of the standard

deviations that need be known. For example, it is often

assumed that the error in measuring pressure is proportional

to the pressure (constant relative error). Therefore, if

pressure were the dependent variable in a curve fitting

problem, it would be appropriate to set R=ZMir i1 . . k.

The output variable SIGMA would then be the estimated con-

stant of proportionality.

Example

Suppose it is desired to fit the Antoine equation

lnP=A - B T+c 279 to 100 data points using unweighted least squares with

lnP as the independent variable. Input to GENLSQ would be as follows:

N=3 A, B, and C are the unkonwn parameters

K=100 There are 100 sets of T-lnP data.

K=1 T is the single independent variable.

P(l, P(2), P(3) Are initial guesses of A, B, & C,

respectively.

ZM(l,l)-ZM(1,100)Are the 100 measured values of P.

ZM(2,1)-ZM(2,l00)Are the corresponding 100 measured

values of T.

X Not used since there are no model vari-

ables whose values are assumed to be

known exactly.

R(1,1)-R(l,l00) Are set equal to 0.OlP for the corres-

ponding 100 pressures.

R(2,l)-R(2,l00) Are all set equal to 0.01.

IANTOIN Is the name of the user supplied sub-

routine.

ITER=50 A maximum of 50 iterations will be al-

lowed, including Deming iterations.

IDEM=20 A maximum of 20 Deming iterations will

be made before switching to the Britt-

Luecke algorithm.

IODS=0, SS=l.0 The unmodified search will be tried.

EPS=1.D-6 Convergnece tolerance.

KOUT=l The program is to print the final 280 results.

NDRIV=l Numerical derivatives. SSND=l.D-4 Numerical derivative step size. The main program would include the following statements:

EXTERNAL ANTOIN DIMENSION P(3), ZM(2,l00), R(2L,00), WORK(1124),

IWORK(3), Z(2,100), F(100), DELZ.(2,l00), COVAR(6) The user supplied subroutine would be: SUBROUTINE ANTOIN(Z,ZM,X,P,K,M,L,N,KEYF)

IMPLICIT REAL*8 (A-H,0-Z) DIMENSION Z(M,K) ,ZM(MK) ,P(N) ,F(K) Do 1I=1, K

I F(I)=DLOG(Z(1,I) )-P(l)+P(2)/(Z(2,I)i+P(3)) RETURN END 281

APPENDIX VIII

DETAILED EQUIPMENT SPECIFICATIONS

AND OPERATING PROCEDURES

Extractor

The extractor used in this thesis consists of an

Autoclave CNLXl6012 medium pressure tube, 30.48 cm in length and 1.75 cm in diameter. Attached to the extractor inlet are openings for the thermocouple assembly and for the fluid inlet stream. Details of the extractor are shown in Figure VIII-1.

Temperature Control of Extractor

The extraction temperature was controlled by use of a heating tape (Fisher ll-463-55D) wrapped around the extractor and connected to a LFE 238 PID temperature controller with a 20 AMP integral power pack. The temperature sensor was an iron-constantan thermocouple (Omega SH48-

ICSS-ll6U-15) housed inside the extractor.

Optimal temperature control (+ 0.5 K) was obtained with the following settings on the temperature controller:

proportional control: proportional band = 10

integral control: 16 minutes

derivative control: off

cycle time: minimum 282

EXTRACTOR DESIGN

-+Fluid Exit

Autoclave Coupling (20 F41666 Autoclave "OD Nipple CNLX16012

Wood Suppor ts 30 cm

+--AutoclOve Coupling (20 F41666)

Autoclave Tee Fluid ( CTX 4 40 ) Inlet Special 1/16I Ferrule Required ( Autoclave 1010 - 6850)

Omega Thermocouple (CSH 48 -ICSS-I11SU,-15% ) To Temperstura Cont roller 'not drawn to scOle)

Figure VIII-1 283

With these controller values, the digital set point should

be put at a temperature 2 K below the desired extraction

temperature. Electronic reference junctions for the thermo-

couples were standard with the controller and digital

temperature readout.

Pressure Control of Extractor

Pressure was controlled in the extractor by an on/off

controller (Autoclave P481-P713) located at the surge

tank outlet. Control action was directly to the compressor.

As the system was configured, the controller was in the

high limit off mode. Positioning the set point at the

desired pressure (making use of the more accurate calibra-

tion from the Heise gauge Ct,400, with thermal compensation

and slotted link protection) enables the pressure to be

controlled to + 1 bar.

Surge Tank

A two liter magnedrive packless autoclave was used as

the surge tank. As the system is configured, there were

three Autoclave SW 2072 valves connected to the autoclave

-- one at the inlet, one at the outlet, and one for vent-

ing purposes. The purpose of the inlet and outlet valves were to enable the autoclave to be isolated from the rest

of the system. Isolation was necessary when changing gas

cylinders, depressurizing the extractor, and venting the

autoclave. 284 In addition to its use as a surge tank, the autoclave

is also useful as a device to pre-saturate the supercritical

fluid with a liquid solvent before the fliud contacts the

solute species. When used in this mode, the autoclave

must be preheated to the desired temperature. For this

purpose a LFE 232 10 Amp proportional controller was used

to control the power input to heating tape wrapped around

the autoclave. Also, the connecting tubing between the

autoclave and the extractor must be heated to prevent

condensation of the liquid species. A variac was conveni-

ently located for connection to heating tapes for this

purpose.

Start up Procedure

After the extractor is charged with the solute species

to be extracted, the outlet valve of the surge tank was

cracked open so that the pressure in the extractor was

slowly increased to the autoclave pressure. When the pres-

sures of the two vessels were equal (but below the desired

extraction pressure), the set point on the pressure con-

troller was adjusted to the desired value and the compres-

sor switch turned on.

Simultaneously, the temperature controller switch was

turned on. It takes about one-half hour for the system to

stabilize at the desired operating temperature and pressure.

After the system had stabilized, the extraction could be

started by opening the exist regulating valve until a steady 285 flow rate of about 0.4 standard liters per minute was achieved.

Shut Down Procedure

To shut down the extraction system, the compressor and temperature controller switches were turned off (but the thermocouple switch left on since this switch also turns the heating tape on the exit regulating value on and off).

Then, the exit value on the autoclave was completely shut off so as to isolate the autoclave from the rest of the system

After attaching the tygon tube vent pipe (connected to the hood) to the regulating valve outlet, the regulating valve was slowly opened until the extractor was depressurized. Finally, the thermocouple switch was turned off and the entire system disasembled and cleaned. 286

APPENDIX IX

OPERATING CONDITIONS AND CALIBRATIONS

FOR THE GAS CHROMATOGRAPH

To analyze the composition of the solid mixture pre-

cipated from the U-tube, a Perkin-Elmer Sigma 2/Sigma 10

gas chromatograph equipped with a flame ionization detec-

tor (FID) was used. In the FID configuration, three gas

cylinders are required at the following delivery pressures:

Air: 45 psig

*2: 85 psig

H2 : 30 psig

Presures for these gases on the gas chromatograph should be set at

Air: 30 psig

N2 : 69 psig, inlet A

Hi2 : 20 psig

Analysis of the solid systems was done under the temperature program conditions and with the response factors shown in Table IX-l. The response factors are for use with an area normalization calibration as specified by

C= x 100 (IX-1) Table IX-l Temperature Programmed Conditions and Response Factors for Chromatography

Final Final Ramp Initial Final Temperature Temperature Rate Hold Hold Response Mixture (0C) (C) (0C/min) (min) (min) Factor

2,6-DMN / 2,3-DMN 160 182 2 0 4 1/1.034

Naphthalene / Phenanthrene 150 250 10 0 5 1/1.029

2,3-DMN / Phenanthrene 150 250 10 0 5 1/0.998

2,6-DMN / Phenanthrene 150 250 10 0 5 1/1.043 N OD Phenanthrene / Benzoic Acid* 150 250 10 3.5 3.5 1/.097

2,3-DMN / Naphthalene 150 250 10 0 5 1.038/1

Naphthalene / Benzoic Acid* 140 140 0 0 0 1/1.071

Injector & Detector Temperature = 300'C

*Reacted with silyl reagent n-o-bis(trimethylsilyl)acetamide 288 where f . is the response factor

A. is the peak area

C. is the concentration in weight %.

Solid Preparation

The precipitated solid in all cases was dissolved in

methylene chloride at a concentration of about 0.5 weight

percent. This dilute solution was satisfactory for injec-

tion into the GC system. In the case of mixtures contain-

ing benzoic acid, however, a silyl reagent had to be added

to the solution in a 10% weight ratio to prevent severe

tailing of the acid peak. The reagent used was N,0-bis

(trimethylsilyl) acetamide, purchased from Supelco.

Gas Chromatograph Column and Septa

The column used for all separations was a 10% SP-2100 methyl silicone stationary phase on a 100/120 Supeloport support with the following dimensions:

length: 10 ft

O.D.: 1/8"

material: 316 SS

This column is a stock column from Supelco Inc. In all cases, nitrogen was the carrier gas at a flow rate of

30 ml/min.

For the injection conditions used in this thesis, the best septa was Supelco Thermogreen, LB-i, llmm. 289 Data Station Operating Methods

The Sigma 10 data station requires operating software for each sample. Software for each of the solid systems investigated are shown in Tables IX-2 through IX-3.

Detector Linearity and Response Factors

Calibration curves for each of the mixture species studied were examined to determine the range of linearity and the response factors of the detector. These curves are shown in Figures IX-1 through IX-7.

In all cases, the detector was linear over the range studied. Response factors are given in Table IX-l. 290 Table 1X-2 Sigma 10 Software for 2,6-DMN/2,3-DMN Analysis

ANALYZER CONTROL

INJ TEMP 25 DET ZONE 1,2 65 25 AUX TEMP 25 FLOW RB 5 5 INIT OVEN TEMPTIME 76 999-

DATA PROC

STD WT,5MP WT 0 .00001.0000 0 FACTORoSCALE 1 o TIMES 15.0 1.90 327.67 327.67 327.67 327.67 SENS-DET RANGE 75 4 5.00 2 0 0 UNK.,AIR 8.80 0.00 TOL 0.0000 0.050 1.0 REF PK 1.000 8.25 8.45 8.35 STD NAME 2 6-DMN

RT RF CONC NAME 8.35 1.00 47.2688 2 6-DMN 9.29 1.034 52.7296 2 3-DMN

EVENT CONTROL

ATTN-CHART-DELAY 10 18 8.01

TIME DEVICE FUNCTION NAME 2.80 ATTN A 6 2.10 CHART C 4 291 Table 1X-3 Sigma 10 Software for Naphthalene/Phenanthrene Analysis

04ALYZER CONTROL

INJ TEMP 25 DET ZONE 1,2 65 25 AUX TEMP 25 FLOW A,8 5 5 INIT OVEN TEMPTIME 76 999

DATA PROC

STD WTSMP WT 0.0899 1.089 9 FACTORSCALE 1 0 TIMES 15.99 1.98 327.67 327.67 327.67 327.&7 SENS-DET RANGE 75 4 5.00 2 0 0 UNKAIR 0.900 0.08 TOL 0.08e 8.950 1.8 REF PK 1.00 3.86 4.86 3.96 STD NAME NAPHTHALENE

RT RF CONC NAME 3.96 1.000 16.2800 NRPHTHALENE 10.52 1.929 83.7184 PHENANTHRENE

EVENT CONTROL

ATTN-CHART-DELAY 18 10 0.81

TIME DEVICE FUNCTION NAME ATTN A 6 2.10 CHART C 4 6.89 ATTN A 4 292 Table 1X-4 Sigma 10 Software for 2,3-DMN/Phenanthrene Analysis

RHALYZER CONTROL

INj TEMP 25 DET ZONE 1,f2. 65 25 AUX TEMP 25 FLOW AB 5 5 INIT OVEN TEMPTIME 76 999

DATA PROC

STD WTSMP WT 8w.eeee1.8099 8 FACTOP. SCALE 1 0 TIMES 15.00 1.99 327.67 327.67 327.67 327.67 SENS-DET RANGE 75 4 5.8 2 0 8 UNKAIR 9.9000 9.80 TOL 8.80000 8.858 I.e REF PK I;eloS 6.-68 6.78 6.73 STD NAME 2 3-DMN

RT RF CONC NAME 6.73 1 .8 OR9 79. 4976 2 3-DM4 10.52 0.998 29. 5080 PHENANTHRENE

EVENT CONTROL

ATTN-CHART-DELAY 10 19 8.91

TIME DEVICE- FUNCTION NAME 2.89 ATTN A 6 2.18 CHART C 4 8.58 ATTN A 4 293 Table 1X-5 Sigma 10 Software for 2,6-DMN/Phenanthrene Analysis

ANALYZER CONTROL

INJ TEMP 25 DET ZONE 1.2 65 25 AUX TEMP 25 FLOW A.B 5 5 INIT OVEN TEMPTIME 76 999

DATA PROC

STD WTaSMP WT 8.000 1.8800 8 FACTORoSCALE 1 0 TIMES 15.080 1.90 327.67 327.67 327.67 327.67 SENS-DET RANGE 75 4 5.00 2 0 8 UNK.AIR 8.0003 0.80 I TOL 8.0000 8.850 1.8 REF PK 1.00 6.00 6.40 6.22 STD NAME 2 6-DMN

RT RF CONC NAME 6.22 1.800 50.eeo8 2 6-DMN 18.43 1.843 50.0000 PHENANTHRENE

EVENT CONTROL

ATTN-CHART-DELAY 18 10 0.081

TIME DEVICE FUNCTION NAME 2.80 ATTH A 6 2.18 CHART C 4 8.50 ATTN A 4 294 Table 1X-6 Sigma 10 Software for Benzoic Acid/Phenanthrene Analysis

ANALYZER CONTROL

INJ TEMP 25 DET ZONE 1,2 65 25 AUX TEMP 25 FLOW RB 5 5 INIT OVEN TEMPPTIME 76 999

DATA PROC

STD WTSMP WT 8.888 1.8888 8 FACTORPSCALE 1 8 TIMES 17.00 4.18 327.67 327.67 327.67 327.67 SENS-DET RRNGE 75 4 5.80 2 0 8 UNKAIR 8.088 8.88 TOL 8.8888 .858 1.8 REF PK 1.680 5.88 6.28 6.83 STD NAME BENZOIC ACID

RT RF CONC NAME 6.03 1.898 58.800 BENZOIC ACID 13.71 8.971 58. 888 PHEMANTHRENE

EVENT CONTROL

ATTN-CHART-DELAY 18 18 8.81

TIME DEVICE FUNCTION NAME 4.28 ATTN A 4 4.38 CHART C 4 295 Table 1X-7 Sigma 10 Software for Naphthalene/2,3-DMN Analysis

ANALYZER CONTROL

INJ TEMP 25 DET ZONE 1,2 65 25 AUX TEMP 25 FLOW AB 5 5 INIT OVEN TEMPTIME 76 999

DATA PROC

STD WTSMP WT 0.88000 1.8888 8 FACTORSCALE 1 8 TIMES 15.88 1.90 327.67 327.67 327.67 327.67 SENS-DET RANGE 75 4 5.88 2 8 0 UNKAIR 8.880 8.88 TOL e.888 0.8518 1.8 REF PK 1.888 3.80 4.88 3.91 STD NAME NAPHTHALEHE

RT RF CONC NAME 3.91 1.888 50.08000 NAPHTHALENE 6.618 1.838 50.08000 2 3-DMH

EVENT CONTROL

ATTN-CHART-DELAY 18 18 8.81

TIME DEVICE FUNCTION NAME 2.88 ATTN A 6 2.18 CHART C 4 6.8 ATTH A 4 296 Table 1X-8 Sigma 10 Software for Naphthalene/Benzoic Acid Analysis

#4ALYZER CONTROL

INJ TEMP 25 DET ZONE 1,2 65 25 AUX TEMP 25 FLOW AB 5 5 INIT OVEN TEMPTIME 76 999

DATA PROC

STD WTSMP WT 8.08000 i.00 0 FACTORSCALE 1 0 TIMES 15.0 4.88 327.67 327.67 327.67 327.67 SENS-DET RANGE 75 4 5.88 2 0 0 UJNKAIR 8.800 8.88 TOL 000080 8.850 1.8 REF PK 1.800 7.18 7.38 7.18 STD NAME NAPHTHALENE

RT RF CONC NAME 7.18 1.80I 58.800 NAPHTHALENE 8.93 1.871 58.8000 BENZOIC ACID

EVENT CONTROL

ATTN-CHART-DELAY 18 18 8.81

TIME DEVICE FUNCTION NAME 4.8 ATTN A 6 4.81 CHART C 4 8.80 ATTN A 4 297

Gas Chromatograph Calibration Curve For Phenanthrene I Benzoic Acid Mixture

I II | 26

22 * Phcnanthrene 0 Benzoic Acid 20

16-

14 LU 12

Silyl Reagent 4-* Reacted with N,O -bis (trimethyl silyl ace tamide 2

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Q9 WEIGHT % OF COMPONENT IN SOLVENT

Figure IX-1 298

Gas Chromatograph Calibration Curve for Naphthalene / Benzoic Acid* Mixture

Nophtholene QBenzoic Acid

351

4 w z 4

I 5 * Reacted with Silyl Reagent NO- bis (trimethyl siyl ) H 0 1ocatomid

0 0.2 0.4 0.6 0.8 1.0 1.2 104 WEIGHT %OF COMPONENT IN SOLVENT

Figure IX-2 299

Gas Chromatograph Calibration Curva for 2,3 - DMN / Phananthrena Mix ture

40 LUI

20 -* 2,3 -D0MN o Phinanthrena 10

0 0 0.4 0.8 1.2 1.6 2.0 2.4 WEIGHT % OF COMPONENT IN SOLVENT

Figure IX-3 Gas Chromotograph Colibrotion Curve for 2,6- DMN / 2,3 - DMN Mixture

* 2,6- DMN 40 S2,3- DMN

4d (A) 20

0 0 0.1 0.2 0.3 0,4 0.5 0.6 0.7 0.8 09 WEIGHT %Ol OF COMPONENT IN SOLVENT

Figure IX-4 301

Gas Chromatograph Calibration Curve for Naphthclene I Phenanthrene Mixture

100

* Naphtholene 90 0 Phenanthrene

< 50

10 /

0 0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 WEIGHT % OF COMPONENT IN SOLVENT

Figure IX-5 302

Gas Chromatograph Calibration Curve for Phananthrene / 26 DMN Mixture

100

* 216-DMN o Phenanthrena

707

60-

40-

20--

10 /

0IJ 0 0.4 0.8 1.2 1.6 2.0 2.4 WEIGHT / OF COMPONENT IN SOLVENT

Figure IX-6 303

Gas Chromotograph Colibration Curve for Naphtholene / 2,3 - Dimethyinophthclene

I ---- slamommommomm

* Nophtholene - Dimethyf ncphtholne 50 o 2,3 -=o-

40 wA 30

C ) .2 0.4 0.6 0.8 1.0 1.2 WEIGHT % OF COMPONENT IN SOLVENT

Figure IX-7 304

APPENDIX X

SAMPLE CALCULATIONS

Sample calculations for converting raw experimental

data for binary and ternary systems into equilibrium solu-

bility data are shown below.

Binary Systems

Raw Data for Run R280.

System: Phenanthrene-Ethylene

Barometric Pressure = 1.0168 BAR

Weight of Sample Collected in First U-tube = 1.17 gm

Weight of Sample Colelcted in Second U-tube = 0.00 gm

Temperature of Extraction = 318 K

Pressure of Extraction = 280 BAR

Temperature of Gas Leaving Dry Test Meter = 297.4 K

Pressure of Gas Leaving Dry Test Meter = 0 BAR (guage)

Total Volume of Ethylene Passed = 34.84 Z

Molecular Weight of Phenanthrene = 178.23

Calculations

Moles of Ethylene Passed (n2

n= ({.0168) (34.84) 1.4327 gmol n2 *(0. 083-14T(2-977.7- .37g 305

Moles of Phenanthrene Collected (n):

1.17 -3 n1= = 6.5645 x 10 gmol

Y,= nn2=4.561 x 10 3

Ternary Systems

Raw Data for Run M58

System: Carbon Dioxide; 2,6-DMN; 2,3-DMN

Barometric Pressure = 1.0141 BAR

Weight of Sample Collected in First U-tube = 1.40 gm

weight of Sample Collected in Second U-tube = 0.00 gm

Temperature of Extraction = 308 K

Pressure of Extraction = 260 BAR

Temperature of Gas Leaving Dry Test Meter = 296.8K

Pressure of Gas Leaving Dry Test Meter = 0 BAR (gauge)

Total Volume of Ethylene Passed = 20.00

Molecular Weight of 2,6-DMN = 156.23

Molecular Weight of 2,3-DMN = 156.23

Composition of Mixture by Gas Chromatography: 42.87 wt. % 2,6-DMN

57.13 wt. % 2,3-DMN

Calculations

Moles of Carbon Dioxide Passed (n9:

= (1.0141) (20) 0.8219 gmol n1--(0.0 8314 (296 .8) = .829gl 306 Moles of 2,6-DMN Collected (n2

(0.4287) (1.40) -3 n 2 (156.23) = 3.8405 x 10 gmol

Moles of 2,3-DMN Collected (n3

n3 (0.573 (16.340) 5.1206 x 10O3 gmol

n 2 -3 Y2 n +n2+n = 4.622 x 10

n n3+n = 6.163 x 10-3 y 3 n1 n2 +n3 307

APPENDIX XI

EQUIPMENT STANDARDIZATION AND ERROR ANALYSIS

Equipment standardization and error analysis consists of verifying that the extraction was (within experimental error): isothermal, isobaric, and at equilibrium. As discussed in Appendix VIII the extraction is kept isothermal by means of a PID temperature controller and isobaric by means of an on/off pressure controller. The maximum deviation of the extraction temperature from the set point was 0.5 K. The on/off pressure controller kept the extraction isobaric to within + 1 bar.

Since a flow system is used to obtain solubility data, there are several key points to check to verify that the data obtained are equilibrium data. First, solubility has to be independent of flow rate. After showing this, the data has to reproduce accepted equilibrium data from the literature. Finally, comparisons of the system residence time to the extraction residence time must be made and shown not to matter.

Examining the first question of independence of flow rate, shown in Table XI-1 is the solubility of naphthalene in supercritical carbon dioxide at 191 bar and 308 K as a function of flow rate (and charge to the extractor). As the average deviation from the maximum solubility is low 308

Table XI-1

Equilibrium Solubilities of Naphthalene in Carbon Dioxide as a Function of Flow Rate and Extractor Charge. P=191 bar; T=308K yxl02

Flow Rate* (1/min) Extractor Charge (gM) 2.1 1.0 0.6

28 1.623 1.717 1.725

20 1.625 1. 711 1.693

2 Experimental Value of Tsekhanskaya (1964): y=1.701x10

*at 1 atm and 294K. 309

(2.8%), it is confirmed that the solubility is independent of flow rate. At the same conditions of temperature and pressure Tsekhanskaya (1964) reports and equilibrium solubility of 1.701 x 10- mole fraction. The average deviation of the experimental data from that obtained from

Tsekhanskaya is 2.07%. As all the experimental data taken in this thesis was at a flow rate of 0.4 liters per minute* or less, and at a reactor charge of at least 28 grams, equilibrium can be assured.

To further check the agreement between experimental data and that published in the literature, additional data on the system naphthalene - carbon dioxide were taken at

328 K and for various pressures as shown in Table XI-2. The average percent error of 1.28% confirms that equilibrium was achieved in the extractor.

Additional Isothermal Calibration

At the extraction conditions of 197 bar and 328 K, additional checks were performed on the isothermality of the extractor as follows. Transverses of the thermocouple inside the extractor (the set point thermocouple) were made. Equilibrium solubilities obtained by positioning the thermocouple at the top or bottom of the extractor

(the usual position was the middle) were within 2% of the

data of Tsekhanskaya (1964).

*At 1 atm and 294 K. 310

Table XI-2

Solubility of Naphthalene in Carbon Dioxide at 328K (Experimental Values vs. Literature)

P(bar) y_(exp.)_ y(Tsekhanskaya)* % error

125 1.41x10-2 1.42x10-2 0.70

162 2. 92x10-2 3.00x10-2 2.67

197 4.OlxlQ-24.0x1-2 3.99x10-2 0.50 2 253 4. 79x10 4.85x10-2 1.24

*Data of Tsekhanskaya (1964). 311

In addition, the solid naphthalene was congregated in just the uppermost and lowermost portion of the extractor

(usually it is spread evenly throughout the extractor) -- see Figure XI-1. Taking experimental data of the system carbon dioxide-naphthalene at 197 bar and 328 K with the naphthalene in the upper and lower configurations gave equilibrium solubilities no more than 0.4% different from the data of Tsekhanskaya. Thus, the isothermality of the extractor was confirmed.

Extractor Residence Time

A simple calculation on the extractor for carbon dioxide at 170 bar and 308 K shows that the superficial velo- city was 7.8 x 10-3 cm/s and that the mean residence time was 64 minutes. As extractions for naphthalene-carbon dioxide may only last 20 minutes,* it was necessary to examine the consequences of the residence time. The solubility data comparisons just examined were for a maximum experimental residence time of 20 minutes. Thus, it was apparent that equilibrium was rapidly achieved in order for the extraction time to be less than the mean residence time and still achieve equilibrium.

As expected,.experiments with naphthalene-carbon dioxide at 197 bar and 308 K at very low flow rates -- giving a residence time of over two hours -- show the

*Experiments with other solids (e.g. phenanthrene) last up to 4 hours. 312

Positions of Solid in Extractor for Test of Isothermality

(a) Solid at Bottom Quartz of Extrac tor 30 cm Wool

7.4 cm

7.6 cm

Th ermocouple

( b) 7.6 cm Solid at Top of Extractor 7.4 cm 30 cm Oaua tz Woo

(c ) Normal Position Solid Evenly Distributed 30 cm

15cm

(not drawn to scale)

Figure XI-1 313 experimental data to agree to within one percent of the data of Tsekhanskaya. 314

APPENDIX XII

LOCATION OF ORIGIONAL DATA,

COMPUTER PROGRAMS, AND OUTPUT

The original binary and ternary data obtained during this thesis are in the possession of the author. Duplicate copies of these data can be obtained from Professor Robert

C. Reid. Card decks for the computer programs can be obtained from the author, or Professor Robert C. Reid.

Computer outputs are in the possession of the author. 315

NOTATION

a , a. .,IA parameters in Peng-Robinson Equation of State derivatives of Helmholtz Free Energy Avv' vI' A 1 parameters in Peng-Robinson Equation of State

BMf B B22 second virial coefficients 1 , B1 2 , CM third virial coefficient

C heat capcity (cal/gmol K) E eutectic point; enhancement factor f fugacity (bar)

G gas phase

H enthalpy (cal/mole)

K , 1 binary critical end points 1 K{, K2 , K 2 KA, KB, Kc critical points

Peng-Robinson binary interaction parameter

L liquid phase

L stability matrix stability matrix

N moles P pressure (bar)

Q heat (cal/mole) R gas constant

solid B, C SB' Sc T temperature (K)

U internal energy (cal/mole) 316 v volume (cm3/mole) y mole fraction, Legendre Transform

Z compressibility factor 317

SUPERSCRIPTS

C critical point

E experimental

F fluid

FUS fusion

ID ideal gas

L liquid phase

M melting point

R reduced property

S solid phase

SUB sublimation t triple point

Vp vapor pressure

component property

partial molar property

at infinite dilution 318

SUBSCRIPTS

1, 2, i component 1, 2, i

12 mixture property of components 1 and 2

p lower critical end point q upper critical end point 319

GREEK LETTERS

parameter in Peng-Robinson Equation of State

Y activity coefficient

< parameter in Peng-Robinson Equation of State dimensionless density (b/V)

property to be evaluated at saturation

fugacity coefficient wo acentric factor

Equation of State a Qb constants in the Peng-Robinson 320

LITERATURE CITED

Abbott, M.M., "Cubic Equations of State," AIChE J, 19, 596 (1973).

Adams, R.M., Alfred H. Knebel, and Donald E. Rhodes, "Critical Solvent Deashing of Liquified Coal," paper presented at 71st AIChE meeting, Miami, Nov 15, (1978).

Agrawal, G.M. and R.J. Laverman, "Phase Behavior of the Methane-Carbon Dioxide System in the Solid-Vapor Region," Adv. In Cry. Eng., Vol. 19, (1974).

Alder, B.J., D.A. Young, and M.A. Mark, "Studies in Mole- cular Dynamics. X. Corrections to the Augmented van der Waals Theory for the Square Well Fluid," J. Chem. Phys., 56, 3013 (1972).

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BIOGRAPHICAL SKETCH

Ronald Ted Kurnik was born on May 2, 1954 in Bridge-

port, Connecticut. At Syracuse University, he obtained

the Bachelor of Science degree in Chemical Engineering;

at Washington University, he obtained the Master of Science degree in Chemical Engineering. In September 1977, he entered M.I.T. to pursue studies leading to the Sc.D. degree.

During his stay at M.I.T., he held an M.I.T. fellowship

(l year) and a Nestle fellowship (3 years). Upon gradua- tion, Mr. Kurnik will join the Corporate Research Staff of

General Electric Co., Schenectady, New York.

Mr. Kurnik is a member of the American Institute of

Chemical Engineers, the American Chemical Society, the

American Association for the Advancement of Science, and the Societies of Sigma Xi, Phi Kappa Phi, and Tau Beta Pi.

He is the author of eight technical papers and has one patent pending.