Signature redacted - DSpace@MIT

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

Certified by

May, 1981

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

by

RONALD TED KURNIK

Submitted to the Department of Chemical Engineeringon May 1981, in partial fulfillment of the

requirements for the degree of Doctor of Science

ABSTRACT

Solid-fluid equilibrium data for binary and multicom-ponent systems were determined experimentally using twosupercritical fluids -- carbon dioxide and ethylene, and sixsolid solutes. The data were taken for temperatures betweenthe upper and lower critical end points and for pressures from120 to 280 bar.

The existence of very large (106) enhancement (over theideal gas value) of solubilities of the solutes in the fluidphase was.observed with these systems. In addition, it wasfound that the solubility of a species in a multicomponentmixture could be significantly greater (as much as 300 per-cent) than the solubility of that same pure species inthe given supercritical fluid (at the same temperature andpressure).

Correlation of both pure and multicomponent solid-fluidequilibria was accomplished uiing the Peng-Ronbinson equationof state. In the case of multicomponent solid-fluid equil-ibrium it was necessary to introduce an additional binarysolute-solute interaction coefficient.

The existence of a maximum in solubility of a solid ina supercritical fluid was observed both theoretically andexperimentally. The reason for this maximum was explained.

Energy effects in solid-fluid equilibria were studiedand it was shown that in the retrograde solidification regionthat the partial molar enthalphy difference for the solutebetween the fluid and solid phase is exothermic.

Thesis Supervisor: Robert C. Reid

Title: Professor of Chemical Engineering

Department of Chemical EngineeringMassachusetts Institute of TechnologyCambridge, Massachusetts 02139

May, 1981

Professor George C. NewtonSecretary of the FacultyMassachusetts Institute of TechnologyCambridge, Massachusetts 02139

Dear Professor Newton:

In accordance with the regulations of the FacultyI herewith submit a thesis entitled "SupercriticalFluid Extraction: A Study of Binary and MulticomponentSolid-Fluid Equilibria" in partial fulfillment ofthe requirements for the degree of Doctor of Sciencein Chemical Engineering at the MassachusettsInstitute 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 equil-

ibrium 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 201-2 Background 221-3 Thesis Objectives 271-4 Experimental Apparatus and Procedure 281-5 Results and Discussion 301-6 Recommendations 54

2. INTRODUCTION 57

2-1 Background 572-2 Phase Diagrams 852-3 Thermodynamic Modelling of Solid-Fluid

Equilibria 1152-4 Thesis Objectives 128

3. EXPERIMENTAL APPARATUS AND PROCEDURE 130

3-1 Review of Alternative Experimental 130Methods

3-2 Description of Equipment 1313-3 Operating Procedure 1343-4 Determination of Solid Mixture

Composition 1353-5 Safety- Considerations 136

4. RESULTS AND DISCUSSION OF RESULTS 137

4-1 Binary Solid-Fliud Equilibrium Data 1374-2 Ternary solid-Fluid Equilibrium Data 1594-3 Experimental Proof that T < Tq 189

5. UNIQUE SOLUBILITY PHENOMENA OF SUPERCRITICALFLUIDS 193

5-1 Solubilitv Minima 1935-2 Solubility Maxima 1945-3 A Method to Achieve 100% Solubility of

a Solid in a Supercritical Fluid Phase 2015-4 Entrainers in Supercritical Fluids 2025-5 Transport Properties of Supercritical Fluids 206

lo I

a

6. ENERGY EFFECTS

6-1 Theoretical Development6-2 Presentation and Discussion of

Theoretical Results

7. OVERALL CONCLUSIONS

8. RECOM ENDATIONS FOR FUTURE RESEARCH

8-18-28-3

Solid-Fluid EquilibriaLiquid-Fluid EquilibriaEquipment Design

APPENDIX I.

APPENDIX II.

APPENDIX III.

APPENDIX IV.

APPENDIX V.

APPENDIX VI.

APPENDIX VII.

APPENDIX VIII.

APPENDIX IX.

APPENDIX X.

APPENDIX XI.

APPENDIX XII.

Partial Molar Volume Using thePeng-Robinson Equation of State

Derivation of Slope Equality at aBinary Mixture Critical Point

Derivation of Enthalpy Changeof Solvation

Freezing Point Data for Multicom-ponent Mixtures

Physical Properties of SolutesStudied

Sources of Physical Propertiesof Complex Molecules

Listings of Pertinent ComputerPrograms

Detailed Equipment Specificationsand Operating Procedures

Operating Conditions and Calibra-tions for the Gas Chromatograph

Sample Calculations

Equipment Standardization andError Analysis

Location of Original Data,Computer Programs, and Output

NOTATION

Page

208

208

210

214

217

217218219

220

222

225

227

236

244

246

281

286

304

307

314

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-CompositionSurfaces for Equilibrium Between TwoPure Solid Phases, A Liquid Phase anda Vapor Phase 32

1-3 P-T Projection of a System in Which theThree Phase Line Does Not Cut theCritical Locus 33

1-4 P-T Projection of a System in whichthe Three Phase Line Cuts the CriticalLocus 35

1-5 Solubility of Benzoic Acid inSupercritical Carbon Dioxide 36

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

1-7 Solubility of 2,3-Dimethylnaphthalenein Supercritical Ethylene 38

1-8 Solubility of Naphthalene inSupercritical Nitrogen 40

1-9 P-T Projection of a Four DimensionalSurface of Two Solid Phases in Equilibriumwith a Fluid Phase 42

1-10 Solubility of Phenanthrene from aPhenanthrene-Naphthalene Mixture inSupercritical Carbon Dioxide 44

1-11 Solubility of Naphthalene from aPhenanthrene-Naphthalene Mixture inSupercritical Carbon Dioxide 45

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

11

Page

1-13 Solubility of Naphthalene inSupercritical Ethylene-IndicatingSolubility Maxima 49

1-14 Experimental Data ConfirmingSolubility Maxima of Naphthalenein Supercritical Ethylene 51

1-15 Partial Molar Volume of Naphthalenein Supercritical Ethylene 55

2-1 Solubility of Naphthalene inSupercritical Ethylene 65

2-2 Reduced Second Cross Virial Coefficientsof Anthracene in C02 , C 2 H 4 , C2 H6 , and

CH 4 as a Function of Reduced Temperature 67

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 EthyleneDehydration of Solvents

2-8 Supercritical Fluid (SCI) Operating

Regimes for Extraction Purposes 82

2-9 The Pressure-Temperature-CompositionSurfaces for the Equilibrium BetweenTwo Pure Solid Phases, A Liquid Phaseand a Vapor Phase 86

2-10 A Pressure Composition Section at aConstant Temperature Lying Between theMelting Points of the Pure Components 88

A Pressure Composition Section at a2-11

12

Page

Constant Temperature above theMelting Point of the Second Component 89

2-12 P-T Projection of a System in Whichthe Three Phase Line Does Not Cut theCritical Locus 90

2-13 P-T Projection of a System in Whichthe Three Phase Line Cuts the CriticalLocus 93

2-14 A P-T Projection Indicating Where theIsothermal P-x Projections of Figure2-15 are Located 94

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

2-16 Naphthalene-Carbon Dioxide SolubilityMap Calculated from the Peng-RobinsonEquation 98

2-17 Solubility of Phenanthrene inSupercritical Carbon Dioxide 99

2-18 Space Model in the Case Where theCritical Locus and the Three Phase LineIntersect 100

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

2-20 T-x Projection for Ethylene-Naphthalenefor Temperatures and Pressures abovethe Critical Locus 104

2-21 P-T Projection of a Four DimensionalSurface of Two Solid Phases inEquilibrt ium with a Fluid Phase 106

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

3-1 Equipment Flow Chart 132




13

Page


4-5 Solubility of Phenanthrene inSupercritical Carbon Dioxide 151

4-6 Solubility of Phenanthrene inSupercritical Ethylene 152


4-s Solubility of Benzoic Acid inSupercritical Ethylene 154

4-9 Solubility of Hexachloroethane inSupercritical Carbon Dioxide 155


4-11 Solubility of Naphthalene inSupercritical Nitrogen 160

4-12 Solubility of Naphthalene from aPhenanthrene-Naphthalene Mixture inSupercritical Carbon Dioxide at 308 K 172

4-13 Solubility of Phenanthrene from aPhenanthrene-Naphthalene Mixture inSupercritical Carbon Dioxide at 308 K 173

4-14 Solubility of 2,3-Dimethylnaphthalenefrom a 2,3-Dimethylnaphthalene-Naphthalene Mixture in SupercriticalCarbon Dioxide at 308 K 174

4-15 Solubility of Naphthalene from a2,3-Dimethylnaphthalene-NaphthaleneMixture in Supercritical Carbon Dioxideat 308 K 175

4-16 Solubility of Benzoic Acid from aBenzoic Acid-Naphthalene Mixture inSupercritical Carbon Dioxide at 308 K 176

4-17 Solubility of Naphthalene from a BenzoicAcid-Naphthalene Mixture in SupercriticalCarbon Dioxide at 308 K 177

14

Page

4-18 Solubility of 2,6-Dimethylnaphthalenefrom a 2,6-Dimethylnaphthalene;2,3-Dimethylnaphthalene Mixture inSupercritical Carbon Dioxide at 308 K 178


4-20 Solubility of 2,3-Dimethylnaphthalenefrom a 2,3-Dimethylnaphthalene;2,6-Dimethylnaphthalene Mixture inSupercritical Ethylene at 308 K 180

4-21 Solubility of 2,6-Dimethylnaphthalenefrom a 2,3-Dimethylnaphthalene;2,6-Dimethylnaphthalene Mixture inSupercritical Ethylene at 308 K 181



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

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

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

4-27 A Close Examination of the SystemNaphthalene-Ethylene Near the UpperCritical End Point 191

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

5-2 Experimental Data Confirming SolubilityMaxima of Naphthalene in SupercriticalEthylene 197

15

Page

5-3 Partial Molar Volume of Naphthalenein Supercritical Ethylene 200

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

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

11-1 The Molar Free Energy of Mixing as Ma Function of Mole Fraction, When gis a Continuous Function of x 223

IV-i Phenanthrene-Naphthalene FreezingCurves 234

VIII-l Extractor Design 282

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

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

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

IX-4 Gas Chromatograph Calibration Curve for2,6-Dimethylnaphthalene/2,3-Dimethyl-naphthalene Mixtures 300

IX-5 Gas Chromatograph Calibration Curvefor Naphthalene/Phenanthrene Mixtures 301

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

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

XI-1 Positions of Solid in Extractor forTest of Isothermality 312

16

LIST OF TABLES

PAGE

1-1 Comparison Between Experimental andTheoretical Solubility Maxima andthe Pressure at these Maxima 52

2-1 Solubility Data for Solid-FluidEquilibria Systems 59

2-2 Phase Diagrams Solid-Fluid Equilibria 63

2-3 Critical Point Data for Possible MobilePhases for Supercritical FluidChromatography 83

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

2-5 Comparison of Experimental vs TheoreticalValues of the Critical End Points forthe System Naphthalene-Ethylene 114

4-1 Co2 ; 2,3-Dimethylnaphthalene Data 138

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

4-3 CO2 ; 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 C2H 4 ; Benzoic Acid Data 145

4-9 CO2 ; Hexachloroethane Data 146

4-10 C02; Benzoic Acid; Naphthalene MixtureData at 308 K 161

17

PAGE

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

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

4-13 CCe; Naphthalene; PhenanthreneMixture Data at 308 K 164

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

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

4-16 C2H4 ; 2,3-Dimethylnaphthalene; 2,6-Dimethylnaphthalene Mixture Data at308 K 167

4-17 CO 2 ; Benzoic Acid; PhenanthreneMixture 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 andTheoretical Solubility Maxima and thePressure at these Maxima 198

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

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

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

IV-1 Comparison of Melting Point Curve fromLiterature vs. Experimental Data forthe System o-Chloronitrobenzene (1), 228with p-Chloronitrobenzene (2)

18

PAGE

IV-2 Experimental Freezing Curves forPhenanthrene with Naphthalene 229

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

IV-4 Experimental Freezing Curves forNaphthalene 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 andResponse Factors for Chromatography 287

IX-2 Sigma 10 Software for 2,6-DMN/2,3-DMNAnalysis 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 Naphthalenein Carbon Dioxide as a Function of FlowRate and Extractor Charge at 191 Bar and308 K 308

XI-2 Solubility of Naphthalene in SupercriticalCarbon 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 supercrit-

ical 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 signifi-

cantly 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, empha-

sis 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 pro-

pane/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 super-

critical fluid over a soluble solid relate to the ease where-

by 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 compon-

ent 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

Sso 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 ~ Pvpi ~vpi

the model can be written for component i as

P -S.v .PV.

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 iR Pr

exp PR[RJ dP

which can be simplified to give

eR FUSp

IRT t % T J i

Y- = -t _T(1-1.3)

Y i ( Y ie x p P R d P

27

Mackay and Paulaitis (1979) have used a reference pressure of

RP = 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 re-

quires 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 te0dlope I Valve

ELdDHetn lTICompressor Surge - lank Ex t r actor

Vent

DryTest - Meter

Rotometer

Key

TC - TemperotureCont roler

PC - Pressure

Cont roller

P - PressureGouge

I - lermocoople

Equipment Flow - Chort

Go sCy linder

U - lubes

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 con-

tact with a fluid phase at high pressures (P r >> ) 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 crit-

ical 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- ________-

I II 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

P

GH

ANI

B1~

Projaction of a System in Which thc

Thre2 Phase Linc Does Not Cut thc

Critical Locus

Figure 1-3

33

PN441

N

P-T

b

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

AC-F.O

qN

NN

T

P -T Projection of a System in

the Three Phose Linc Outs th(2

Locus

Which

Critical

Figure 1-4

P

36

10 - ,- [ I I I I I

33810K 318K

318 K

10 ~ 328K

/ 338

SYSTEM: BENZOIC ACID-CO2a i~4 -- PR EQUATION OF STATE

rEMPERATURES(K) SYSOL

3182

328 a

10 5 -3 3

3283K

318 K10-

IDEAL GAS

a-,338 K

10-76- 3 28 K

-8 i 1 1 1 1 i t 1 1i 1 , -

0 40 80 120 160 200 240 280

PRESSURE (BARS)

Solubility of Benzoic Acid in SupercriticalCarbon Dioxide

Figure 1-5

37

-am I lI1

-2 32810 - 318 K

308

-. 310 - -- 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 O210 .. 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

1

328

318

30-2

10

-3 308K10--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

105-21-8 K 308 0 .0246

3 t8 0 .0209

328 0 .0147308 K

-6t0

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 en-

hancement factor and can take on values of 106 or larger.

Figure 1-8 shows a simulation of the case naphthalene

40

,5210

-.310

10

10

0 40 80 120 160 200 240

PRESSURE ( BARS)

Solubility of Naphthalene in Supercritical

Figure 1-8

280

Nitrogen

System: Nitrogen - Nophthalone

-- PR Equation of State

k 12 =Q.1

- 328K

31 SK

-=MOK

LLid

zLid

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 criti-

cal-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, p

KA/4K

/

q

K 2

K

,

L i

NN,

600

*1

P-T Projection of a Four Dimensionalin Equilibrium with a Fluid Phase

Surface of Two Solid Phases

Figure 1-9

P

N

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 solu-

bilities 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 liter-

ature (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

10-5!

SYS TE M: C02-CIOHB -C14H 10() (2) (3)

TEMPER ATURE =308.2K0 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) 40 80 120 160 200 240C0-

280

PRESSURE (BARS)

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

Figure 1-10

0r

0

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 =0.095910-5 k 13 =0.-11

k 2 3 =0.05

+DATA OF TSEKHANSKAYAet 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 interac-

tion 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 inter-

action 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 ethyl-

ene. 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

480-

440-

400.-

360-

320

280 -

240-

200

160 -

120-

80

40

01 I

-F- I I I I I I

System: C02- Naphthalene -Phenanthrenc(1) (2) (3) -

Temperature = 30B K

- PR Equation of State

k 12 = 0.0959

k 13 =0.1 15

k 2 3 = 0.05

0:< Naphtholene /Phenanthrane

0~

E xpcndcd

K w~9@9@9#T

90~

8 z

II

7

46

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

Selectivities in the Naphthalene-Phenanthrene-CarbonDioxide System

Figure 1-12

a-

z

Ii

4

mmmmlmp

-M Aduk Admkk

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 com-

puter 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 supercriti-

cal ethylene for pressures up to 4 kbar and for several temp-

eratures. Experimental data are shown only for the 285 K iso-

therm to indicate the range covered and the applicability of

the Peng-Robinson equation.

For the naphthalene-ethylene system, the solubility at-

tains a minimum value in the range of 15 to 20 bar and a

maximum at several hundred bar.

318K

308 Ka.8K285 K

SYSTEM:1K NAPHTHALENE-

308 K -- PENG - ROBEQUATION

29Kk, 2 .02

285 KEXPERIMENTSEKHANSIT: 285 K

ETHYLENE

INSONJ OF STATE

ITAL DATA OFKAYA (1964);

10 100

PRESSURE

Solubility of Naphthalene inIndicating Solubility Maxima

1000

(BARS)

Supercritical Ethylene-

Figure 1-13

49

to-I

z

C

z

-6

10,000I --- mmmwvmFvmwlm I I - I - F

I

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 maxi-

mum 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 experi-

mental 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 sol-

ubility parameter model.

Theoretical Development

The solubility minimum and maximum with pressure can be

51

-- Vn Welie and Diepen , 1961COMPUTER SIMULATION OF

WU MAXIMUM CONCENTRATIONZ 3Q USING THE PENG- ROBINSON

EQUATION OF STATE

a. 20

C 10 -C,LU / 3

200 400 600 800 1000PRESSURE (BARS)

NUMBER TEMPERATURECK)

1 -303.22 308.23 313.24 318.25 321.26 323.27 324.28 325.3

Experimental Data Confirming Solubility Maximaof Naphthalene in Supercritical Ethylene

Figure 1-14

Table 1-1

Comparison between Experimental andTheoretical Solubility and Maxima and

the Pressure at these Maxima

E (bar)max

612

590

576

477

398

Pa (bar)max

680

648

576

472

357

% error, P

11.1

9.8

0.0

1.0

10.3

EYmax

-24. 31x10

5.68x10-2

7. 84x10-2

1.17x10 1

1. 35x10 1

TYmax

-24.83x10

6.06x10-2

8. 4 3x10-2

1. 19x10~

1. 60x10~ 1

% error, y

12.1

6.9

7.5

1.7

18.5

Notes: 1.

2.

3.

4.

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

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

PE = experimental value of maximum pressure.max

P T = theoretical value of maximum pressure.max

T (K)

303

308

313

318

321

LnN~

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 eSdP + nf1 dlny = dP (1-5.3)RT L alnyJ TP -RT

Using the definition of the fugacity coefficient,

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

Then Eq. 1-5.3 can be rearranged to give

31nylRT L T IT ~(1-5.5)T 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. VY then becomes quite nega-1

tive. 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 bin-

ary liquid-fluid systems up to relatively low pressures (100

55

800

600

400

200

0

d -200

X -400

-600

;-800

o-1000

-1200,

-1400

-1600

-1800

-2000

SOLUBILITYMINIMA

SOLUBILITYMAXIMA

- Is

F

-F

NAPHTH

-- PEEC

TEA

10

Partial MolarEthylene

SYSTEM:

ALENE-ETHYLENE

NG - ROBINSON)UATION OF STATEMPERATURE=318 K

k 12=0.02

100 100PRESSURE (BARS)

10,000

Volume of Naphthalene in Supercritical

Figure 1-15

d1b,

=nowII

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 pur-

pose of separating components from the original mixture.

Advantages in using supercritical fluids over liquid extrac-

tion or distillation are many. Compared to distillation,

supercritical fluid extraction has shown to be more energy

efficient (Irani and Funk, 1977). The advantage of supercrit-

ical 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 import-

ant 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

CO2

Co2

Neopentane

Naphthalene

Co

N2

CO + N2Xenon

Co2

0 2Naphthalene

C2"4

Quartz

Quartz

Na 2CO3

Na CO3+ NaHCO3

UO2

Al2 03

SnO23

NiO

Solvent T (K)

Air

Air

Ar

Ar

112

H2

112

"2

2

H 0

2

"2

112 0

20

12011 2 0

11 2 0

Ho2

77-163

115-1,50

199-258

298-347

31-70

25-70

35-66

155

190

21-55

295-343

80-170

653-698

423-873

32 3-623

373-473

773

773

773

773

Tr (Solvent) P (bar) Pr (Solvent)

0.58-1.23

0.87-1.13

1.32-1.71

1.98-2.30

0.93-2.11

0.75-2.11

1.05-1.99

4.67

5.72

0.63-1.66

8.89-10.33

2.14-5.12

1.01-1.08

0.65-1.35

0.50-0.96

0.58-0.73

1.19

1.19

1.19

1.19

1-200

4-49

na

1-1100

1-50

1-50

5-15

4-8

5-16

3-102

1-1100

1-130

300-500

1-1000

na

na

1020

1020

1020

2040

0.03-5.28

0.11-1. 29

0.02-22. 57

0.08-3.86

0.08-3.86

0.39-1.16

0.31-0.62

0.39-1.23

0.23-7.86

0.08-84.81

0. 08-10.02

1.36-2.27

0-4.54

4.63

4.63

4.63

9.25

Reference

Webster (1950)

Gratch (1945)

Baughman et al. (1975)

King and Robertson (1962)

Dokoupel et al. (1955)



Ewald (1955)

Ewald (1955)

McKinley (1962)


Hiza et al. (1968)

Van Nieuwenbur9 and Van Zon(1935)

Jones and Staehle (1973)

Waldeck et al. (1932)

Waldeck et al. (1934)

Morey (1957)

Morey (1957)

Morey (1957)

Morey (1957

uLk0

Table 2-1 (cont'd)

Solute

Nb2 05

Ta2 05

FeO3

BeO

GeO2

CaSO4

BaSO4

PbSO4

Na 2SO4

Silica

Silica

Xenon

CO2

Air

Neopentane

Naphthalene

Xenon

CO2

Neopentane

Naphthalene

CH 4

Solvent T(K)

H20H20

H20

I2 0

11 2 0H20

H20

H 20

I20

ii 0

If20

He 0

120

H 0H20

lie0

He

HeN2

lie

Ilie

N2

N2

N2

N 2

Ne

773

773

773

773

773

773

773

773

773

883

493-693

155

190

66.5-77.6

199-258

305-347

155

140-190

199-258

295-345

44-91

Tr (Solvent)

1.19

1.19

1.19

1.19

1.19

1.19

1.19

1.19

1.19

1.36

0.76-1.07

29.87

36.61

12.81-14.95

38.34-49.71

58.77-66.86

1.23

1.11-1.51

1.58-2.04

2.34-2.73

0.99-2.05

P (bar)

1020

1020

1020

1020

1020

1020

1020

1020

1020

1-1750

303

4-13

4-9

52-448

na

1-1100

4-9.5

5-100

na

1-1100

10-100

Pr (Solvent)

4.63

4.63

4.63

4.63

4.63

4.63

4.63

4.63

4.63

0-7.94

1.37

1.76-5.73

1.76-3.96

22.9-197.4

0.44-485

0.12-0.28

0.15-2.95

0.03-32.41

0.36-3.63

Re ference

Morey (1957)

Morey (1957)

Morey (1957)

Morey (1957)

Morey (1957)

Morey (1957)

Morey (1957)

Morey (1957)

Morey (1957)

Kennedy (1950)

Kennedy (1944)

Ewald (1955)

Ewald (1955)

Zellner et al. (1962)



Ewald (1955)

Sonntag and Van Wylen (1962)



fliza and Kidnay (1966

a'0

Table 2-1 (cont'd)

Solute

Phenanthrene

Naphthalene

Naphthalene

An thracene

Neopentane

Phenanthrene

Naphtha le ne

Naphtha lene

Naphthalene

Naphthalene

Naphthalene

Anthracene

Anthracene

C 2 C16c 2 ci6

C2 C16+Napththalene

p-chloroiodo-benzene

Phenanthrene

Coal tar

Solvent T(K)

CF4

C' 4

CH'4

Cl 4

CR4CH

C2 4CH 4

C H2 4

C 2 14C2 4

C 2 H4

C 2 l4C2 4

c2 42 4

c2 4

C2 4

C 2Hic214

313

294-341

296-348

339-458

199-258

313

285-308

318-338

296-308

289.5-296.5

285-318

338-453

323-358

313-323

289.5-296.5

289.5-296.5

286-305

313

298

Tr (Solvent)

1.38

1.54-1.79

1.55-1.83

1.78-2.40

1.04-1.35

1.64

1.01-1.09

1.13-1.18

1.05-1.09

1.03-1.05

1.01-1.13

1.20-1.60

1.14-1.27

1.11-1.14

1.03-1.05

1.03-1.05

1.01-1.08

1.11

1.06

P (bar)

138-551

1-130

1-1100

1-100

na

138-551

40-100

40-270

1-130

1-170

50-300

1-100

103-480

na

1-170

1-170

21-101

138-551

310

Pr (Solvent)

3.69-14. 74

0.02-2.83

0.02-23.91

0.02-2.17

3.00-11.98

0. 79-1. 99

0.79-5.36

0.02-2.58

0.02-3.38

0.99-5.96

0.02-1.99

2.04-9.53

0.02-3.38

0.02-3.38

0.42-2.01

2.74-10.94

6.16

Reference

Eisenbeiss (1964)

Najour and King (1966)




Eisenbeiss (1964)

Diepen and Schef f er (1948)

Diepen and Scheffer (1953)


Van Gunst (1950)

Tsekhanskaya et al. (1964)


Johnston and Eckert (1981)

Holder and Maass (1940)

Van Gunst (1950)

Van Gunst (1950)

Ewald (1953)

Eisenbeiss (1964)

Wise (1970)

a'

Table 2-1 (cont'd)

Solute Solvent T (f)

Anthracene

Naphthalene

Phenanthre ne

Naph tha lene

Naphthalene

Carbowax 4000

Carbowax 1000

1-Octadecanol

Stearic Acid

Phenanthrene

Diphenylamine

Phenol

p-chlorophenol

2, 4-dichloro-phenol

Bipheny l

26

C2 U

C2 6

CO26

Co2

Co2

Co 2

co2

CO2

Co2

Co2

Co2

CO2

CO2

co 2

336-448

296-337

313

297-346

308-328

313

313

313

313

313

305-310

309- 333

309

309

308.8-328.5

T (Solvent)

1.10-1.47

0.97-1.10

1.02

0.98-1.14

1.01-1.08

1.03

1.03

1.03

1.03

1.03

1.00-1.02

1 .02-1.09

1.02

1.02

1. 02-1. 08

P (bar) r T (Solvent)

1-100

1-1100

138-551

1-130

60-330

300-2500

300-2500

300-2500

300-2500

138-551

50-225

78-246

79-237

79-203

105-484

0.02-2.05

0.02-22.52

2.83-11.28

0.01-1.76

0.81-4.47

4.07-33.88

4.07-33.88

4.07-33.88

4.07-33.88

1.87-7.47

0.68-3.05

1.06-3.33

1.06-3.21

1.06-2.75

1. 42-6. 56

Reference



Eisenbeiss (1964)



Czubyrt et al. (1970)




Eisenbeiss (1964)


Van Leer and Paulaitis (1980)



McHugh and Paulaitis (1980)

03

Table 2-2

Phase Diagrams for Solid-Fluid Equilibria

Solute Solvent T(K)

N2

Co2

H

C11 4

Co2

Naphthalene

Naphthalene

Naphthalene

1, 3, 5-trichlorobenzene

p-dichlorobenzene

p-ch lorobromoben ze ne

p-chloroiodobenzene

p-dibromobenzene

octacosane

hexiatriacontane

biphenyl

benzophone

menthol

CH 4

C2 4

c 2 14

C 2 i4

C 2 14

C 2 i4

c 2 14

c 2 i4

C 2 14

C 2 H4

c 2 H4

C2 4

C2 4c2 4

10-130

173-303

89- 311

258-350

285-333

263-353

263- 323

258-318

263-327

263-319

263-353

260-327

263-343

278-328

263-310

258-300

Tr (Solvent) P (bar)

0.30-3.92

0.91-1.59

0. 47-1. 63

0.91-1.24

1.01-1.18

0.93-1.25

0.93-1.14

0.91-1.13

0.93-1.16

0.93-1.13

0.93-1.25

0.92-1.16

0.93-1.21

0.98-1.16

0.93-1.10

0.91-1.06

0.01-10,000

1-90

1-95

10-75

40-270

1-179

31-67

31-95

31-82

24-68

32-82

29-87

32-88

43-85

30-87

21-92

Pr (Solvent)

0-771

0.02-1.96

0.02-2.06

0.20-1.49

0.79-5.36

0.02-3.55

0.62-1.33

0.61-1.89

0.62-1.63

0.48-1.35

0.64-1.63

0.58-1.73

0.64-1.75

0.85-1.69

0.60-1.72

0.42-1.82

Reference


Rowlinson and Richardson

(1959)

Agrawal and Laverman (1974)

Dipen and Scheffer (1948)

Diepen and Scheffer (1953)

Van Gunst et al. (1953)

Diepen

Diepen

Diepen

Diepen

Diepen

Diepen

Diepen

Diepen

Diepen

Diepen

and

and

and

and

and

and

and

and

and

and

Scheffer

Scheffer

Scheffer

Scheffer

Scheffer

Scheffer

Scheffer

Scheffer

Scheffer

Scheffer

(1948)

(1948)C

(1948)

(1948)

(1948)

(1948)

(1948)

(1948)

(1948)(1948)

C2 C 6C2 4 313-323 1.11-1.14 na Holder and Maass (1940)

Solute

c2 6Anthracene

Ilexaethylbenzene

Hexamethylbenzene

Stilbene

in-Dinitrobenzene

Polyethylene

Naphthalene + C2C16

Table 2-2 (cont'd)

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

C2H

C2 4

2 4c2 4

C2 4C2

4

2H4C 2L1Ic2 4

263-285.4

263-488

263-401

263-438

263-395

263-362.9

533

263-328

0.93-1.01

0.93-1.73

0.93-1.42

0.93-1.55

0.93-1.40

0.93-1.29

1.89

0.93-1.16

32-53

1-72

1-64

1-83

1-78

1-78

1-2000

1-180

0.64-1.05

0.02-1.43

0.02-1.27

0.02-1.65

0.02-1.55

0.02-1.55

0.02-39.71

0.02-3.57







Bonner et al. (1974)


a'&6

High Pressure Ragame.

aU

SA

0

m

A0

65

Solubility of Naphthalene in Supercritical

Ethylene

MiddleP r assurRegime

-

I

04.0

0 .

Sa"

08OU

A

cData of DeP3n ona Scaffar

(1948) and Tsa khc ns kcyc (1964)

I I - -

Systam : Naphtholana - Ethylene

Timcpratur ( K) Symbol

285298308

0

0 40 80 120 160 200 240 280

PRESSURE (BARS)

Solubility of Naphthalene in SupercriticalEthylene

Figure 2-1

101

-

2

10

_Low.-Prassurz_R g M C

I

z

C

2.K

-310

-410

10

10

A

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 Hcient B2* versus reduced mixture temperature TR 2 **. The data

67

0

-10

R R12

-20

-30

I

-i Cn H 4-

_ C2H6

0.7 0.9 1.1R

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

6 R = 1(7)/V ;T1i2 B12 ( 12 I 12 =T/T1

( Najour and King , 1970 )

Figure 2-2

==mad

.5

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 ex-

tracted 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 C1/212 = 12 ' 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 selec-

tivity 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 super-

critical 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 rgaT nk

SOVontTank

F Q cd M ixer

Pump 21st 2 nd

Stag a StagaSat tler Sat t I ar

Sol v(2n t Solvent

Se parator Seporoto rNo I No 2

Ash DeoshedConcentrate 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 sol-

vent, 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

L

P

L-V

(a)

S

p 3 F

L -F

2

p >p >p P p P>P (F)3 2 1 3 c

Phose Diagroms or a oTernary

Solvent -Woter - Fluid Type I

Sys tem ([Elgin & Wainst oc k ,1959)

F

Figure 2-4

S

P2L

L -V

H20 F H 20

(b)

F

-4

(c )

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 composi-

tion: 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

L

L -v

H2 0O

(a)

s

P3

F

L - F

H20

F

S

P2

2 L2~

LL -L 2-V

L, -VH 20 F

(b)

P3 > P2>FPj ;P >IP (F)3 2 1 3 c (F)

Phase Diogrom5 for a Ternory

Solvent - Woter - Fluid Type II

System ( Elgin & Weinstock, 1959)

F

Figure 2-5

(c)

S

Pi L2

L, -L 2 -V L 2 -V

L1 -L2-V

L1 . L1-V

H20 F

S

3 F

Ll -L 2 or-F

H 20 F(c )

S

P2 L 2

L1 -L L2 -V

L1I -L 2 -V

H20 L1 -V F

(b)

00

Phose Diagroms for a Ternory

Solvent -Wotar - Fluid Type IR

System ( Elgin & WeInstock, 1959)

Figure 2-6

Methyl EthylKetone

L2- v

L, -L2 -V

H-20 - L, - v C2H4

Phose Equilibrium Diogrom for

Ethylene -Woter - Methyl EthylKetone at 35.5 BOr and 288.1K

( Elgin ond Wainstock.1959)

SolvmWntp--+

Pump------- +MixA Qr

P Rec ycleE thyle

Wot er Solvent

Fla sh Flosh

Tank Tank

E thy lene

Com pr essor Was te Water Dried SOIVent

Schematic Flowsheet for Ethylene Dehydrotionof Solvents (Elgin & Wei nstock,.1959 )

U,

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 equip-

ment. 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

ratioCSTATSTATA

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

1.oREDUCED

(GIDDINGS

2.0D EN"S IT Y

ET AL,1968)

SupercrIcal Fluid ( SCF) Operating Regimesfor Extraction Purposes

Figure 2-8

30

20

10

5

1

0.5

LuD

LUc-C.

uQnLUJ

-2

Cr

NL

0.10

83

Table 2-3

Critical Point Data for Possible Mobile Phasesfor 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 dia-

gram are shown the usual solid-gas, solid-liquid, and liquid-

gas boundary curves for the two pure components. These bound-

ary 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

p

GH

T

The Pressure - Temperature - composition Surfacasfor the Equilibrium Between -Two Pure Solid

Phases, A Liquid Phase and a Vapor Phase

( Rowlinson and Richardson,1959 )

Figure 2-9

FI

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

p

L

V,

x

G0

I'

S G

x

A Pressure Compositlo

Constant Temperature

The Melting Points of

z

w

n Sect ion at a

Lying Between

the Pure Components

( Rowlinson and Richordson, 1959 )

Figure 2-10

S+ L

I

89

A Pressure - Composition SQctiOn

at a Constant Tampc raturc above

the Melting Point of the Second

Component

Figure 2-11

B

r

P-T Projection of

Three Phase Line

Critical Locus

a System

Does Not

in Which the

Cut the

Figure 2-12

90

PN

N

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 compon-

ents 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 dia-

gram 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.

A0c- F

N N

BN

P -T Projaction

the Three Phas

of a System in Which

a Line Cuts the Critical

Locus

Figure 2-13

93

Pv

T

I

I

1 2Ti

IIIIIIIIII

1I

T5 T

TyT6

T

A P-T Projection Indicating Where the Isothermol P-x

Projections of Figure 2-15 ore Located

Figure 2-14

P

A

95

T,

L S+L1

S +V

x* For

S+ L 2

CE P2S+ For

5+L1

T4

T7

5-L2

Lz

T2

5+ For

S +L

CEP, S.F orStV

+L2

S+L2

Tz2

T8

2

T3-

F

Influenceof 0E2

.. -.FInf luenccof CEPi

V+'2

T6

( after Hong ,1980)

Isothermal P-X Projections For Solid-FluidEquilibria

Figure 2-15

p

p

P

p. I i

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 previ-

ously, a clear understanding of these diagrams is now pos-

sible. As both sketches are similar, only the diagram of

Zernike will be discussed. Figure 2-18, shows this equili-

brium surface. While the diagram indicates a perpendicular

98

TK

280 290 300 310 320 330 340 350 3600 --

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

-210

328 K

-310

- 318K

328 K 33S K

-4

00

-5 System CO2 -Phenanthrene-PR Equation of Statq

Temperature (K) Symbol k12

318 0 0.113338 K 328 A O008

338 U 0.106-6328 K10

318 K

-7'0f

0 40 80 120 160 200 240 280

PRESSURE (BARS)

Solubility of Phenanthrene in Supercritical CarbonDioxide

Figure 2-17

100

I

Space Model in theLocus and the Thre

Case Where the Critical

!e Phase Line Intersect

( Ze r n ike,1955 )

Figure 2-18

KB

P

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 pres-

sure 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

-UC E P

--- FusionLine

Thr oo

CriticalLocus

\B

PhasaLine

373 473 573

T (K)

P-T Projection for Et hylene -

Naphthalene (Van Welie and

Diepen, 1961)

Figure 2-19

V)

c1

Ld

LJUr

CL

250

200

150

100

50

0673

= I iiiiiiin sop k .- . - -- I -

I I I I I

I

104

90

80

70

60

50

40

30

20

10:0 20 40 60 80

NAPHTHALENE (MOLE %/)

T-x Projection for Ethylene-Naphthalene forTemperatures and Pressures above the CriticalLocus

Figure 2-20

U

0

LU

0

I

CLI-

-U

K

-0

System Ethylene -Naphthalene

Pressure= 274 Bar

-PR Equation of State

k, 2 =0.02

0 Experimental Data of Diepenand Scheffer (1953 )

* Melting Point of Nophthalene

at 274 Bar

K - I100

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

K1 p

KA K;

P/0/ (9

/

q Kiv G

't

L

T

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

Figure 2-21

P

H

I

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

System

ethy lene-naphtha lene 1

ethylene-naphthalene-hexachloroethane2

1. Diepen and Scheffer (1953).

T (K) Tq(K)

283.9 325.3

288.5 298.7

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 AvL =

AV1 A

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

where

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

A11 3t 2jC2.ST,x

2A = 2 (2-2.6)vi DVDx

T,x

110

A A

and MII = 0 (2-2.7)

F 3L1 (3L1

av J T,x L axTV

or,

2M =A A A +A A -JA A VA A 11 vvllvvl vvlll vvvlVll

-A A A + 2A 12 A =0 (2-2.8)11 vI vvv vlVV

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

illV' 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)

fV = y1Pc (2-2.15)

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 gen-

erate 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 mix-

ture critical point, the following thermodynamic equality

must be satisfied.*

*See Appendix II for a derivation.

=0

112

ap Ia x 1 0 T l a

(2-2.17)

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).

dyjT=0 (2-2.18)

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 condi-

tions 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 criti-

cal 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 theCritical End Points for the System Naphthalene-Ethylene

Lower CEP Upper CEP

T (K) P(bar) y T (K) P (bar) y

Naphthalene-ethylene, experimentall 283.9

Naphthalene-ethylene, Peng-Robinson 282.8

1 Diepen and Scheffer (1953)

51.9 0.002 325.3 176.3

50.6 0.0004 314.3 160.9

System

0.17

0.12

HH

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 ^Ff% %= 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 Ff. = FyP$ (2-3.2)

where $ is determined from an equation of state by the

definition (Modell and Reid, 1974).

ST a Pln$ = 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

Ssmall so that y. land x. = 1

4. vapor pressure of the solid is sufficiently small

so that 5 $s ~land P -P svp.- vpi

Then, the solid phase fugacity can be written

116

PV s

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 ----

sy. = - exp (2-3.5)

S P 0F RT

Equation 2-3.5 conveniently divided into three terms

shown in brackets. The first bracketed term is the equili-

brium 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

expLRTE. e= (2-3.6)

Fi

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)

where PR is a reference pressure and f9 is a hypothetical1

fugacity of pure liquid i at the system temperature and at

the reference pressure PR. The solid phase fugacity can be

written as

'P V%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 P- A C 'TTin (R R T]

AC I Ti t

+ R in T23.1

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 rTexp R-T [ PRsexL t. LI.jj exp R

y.=RRTP i(2-3

exp dP

.12)

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

(2-3.11)

119

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

V7 I(P ) then can be found from an applicable equation of statei 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 solu-

bilities in supercritical carbon dioxide and supercritical

ethylene at a constant value of the binary interaction para-

meter and for a temperature dependent infinite dilution acti-

vity 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

CM=ikaijk (2-3.18)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 enhance-

ment factor has been calculated for the compressed gas model

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

Vsln E = 0B(P-P2) + 2 2B - B+x 2 B 2 -2x2 B )RT P92 + -x1 B11 -2 1 B12 2 2 2 22 RT

1 P4 2 3 2+ F-x43B2-x3(2C 4BB ) + x 3C2 1111111- 1112 1 112

3 2 2+x x 212B 1 B 2 xi 2x(6C1 1 2 +4B 1 B 2 2 +8B$

121

2+x X 2 6C1 2 2 - xx2 (6C1 1 2 +12B1 B 2 2)

13 12-12 12 2 42

+x x3 2B B +X 2 (2 B 2 +BB x4 B21 2 12 22 1 2 (12B1 2 1+61 2 2 )+x2 B2 2

-x3(2C 2 2 2 +4B 2 )+X2 3C2 2 2 J f 2 (2-3.19)

where: subscript 2 is the solid

subscript 1 is the fluid

P 0 is the vapor pressure of the solid2

V5 is the molar volume of the solid2

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 modifi-

cations of the original cubic equation of state: that of

van der Waals (1873). After the development of van der Waals

122

-210

S 1

6

4

2

10

6

4

2

1(548

6

0 20 40 60PRESSUREal

80 100 120Lm (gauge)

SolubilityOt 143 K

Of C02 in Air ( Prousnitz,1969 )

Figure 2-22

ix

CL

42zN

0L)

z0

LL

-j07

Second VIricCoeff. Only

-/

/Second and ThirdVirnai Coeff.

Data

- C Webster (1952)

a Gr(OtCh (1945)

- Nc

I I ' s

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:

P RT_ aCT)V-b V (V+b) + b CV-b)

R 2T2a. T ) = RT

i c a P.i

RTb (T ) = 2 c

i c b P.ci

(2-3. 20)

(2-3.21)

C2-3. 221

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

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

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

where

(2-3.25)

124

. = 0.37464 + 1.54226w. - 0.269922.

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

(2-3.26)

(2-3.27)

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

By definition of the fugacity coefficient (Modell and Reid,

1974)

l = fVFI- F4J32;0 %.1JT, Pt% [i]j

dv - InZ (2-3.29)

The fugacity coefficient of component i can be calculated as

b.Alnt. = (Z-l) - ln(Z-B) -A

b 2Y/IB

-22x.a..S13 bo nz +(CL+42)B

a b Z -(1- D)B,(2-3. 30)

A = aP/R2T2

B = bP/RT

(2-3. 31)

(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

where

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 cri-

teria:

128

C J =0 (2-3.36)3VT

c

[ 2 'a- =P0(2-3.37)

c

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 equili-

bria. 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 solubil-

ity 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

Compressor Surge - lonk Ex t roctor

I PVent

DryTest- Meter

U - Tubes Rota meter

Key

TC - TemperotureCont roller

PC - PressureCont roller

P - PressureGouge

T - ThermocoOple

Equipment Flow - Chort

Figure 3-1

GO 5Cylinder

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 chroma-

tograph/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 temp-

eratures and pressures. Also shown with the data are iso-

thermal 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

2,3-Dimethylnaphthalene

T=308 K

y

2. 20x10-3

4. 40x10 3

5. 42x10-3

5. 83x10-3

6.43x10- 3

T=318 K

P(bar)

99 1.

145 4.

195 6.

242 6.

280 7.

T=328K

28x10-3

79x10-3

37x10- 3

89x10-3

19x10- 3

P(bar)

99

146

197

241

280

y

3. 41x10~4

4.46x10-3

7.14x10 3

8.48x10-3

9. 01x10 3

k12 0.0996

Co2 ; Data

P(bar)

99

143

194

242

280HLA)

OD

0.102 0.107

Table 4-2

2,3-Dimethylnaphthalene Data

T=308 K

P(bar) y

77 3.13x10~ 4

120 2.59x10-3

159 6.02x10-3

200 9.66x10 3

240 1.27xl0-2

280 1.51x10-2

T=318 K

P(bar) y

80 3. 67x10~ 4

120 2.59x10-3

160 7.18x10- 3

200 1.22x10-2

240 1.84x10-2

280 2.42x10 2

T=328 K

P(bar) y

80 3. 00x10~ 4

122 3.18x10-3

160 8.79x10-3

200 l.89x10-3

240 3.22x10-2

280 5.25x10-2

0.0147

2 H4;

HjU)ko

0.0246 0.0209

Table 4-3

2,6-Dimethylnaphthalene Data

T=308 K

y

1.91x10-3

2.97x10 3

3. 83x10-3

4. 01x10-3

4. 47x10-3

T=318 K

P (bar)

98 7.

146 3.

194 5.

244 6.

280 6.

T=328 K

y

57x10 4

95x10-3

09x10-3

27x10-3

77x10 3

P(bar)

96

146

195

246

280

3.06x10 4

4. 32x10- 3

6. 16x10- 3

7. 99x10-3

9. 21x10-3

0.0989

Co 2 ;

P(bar)

97

145

195

245

280H

0

0.1000.102

Table 4-4

C211 4 ; 2,6-Dimethylnaphthalene Data

T=308 K T=318 K

4. 84x10~ 4

2. 35x10-3

4. 62x10-3

6. 95x10-3

9. 28x10-3

1. 10x10-2

P(bar)

78

120

160

200

240

280

y

1. 89x10~ 4

2. 20x10-3

5. 56x10-3

9. 08x10-3

1.39x10-2

1. 71x10-2

T=318 K

P(bar)

78 2. 36x10'4

120 2.20x10-3

160 6.74x10-3

200 1.30x10-2

240 2.00xlO'2

280 2.75x10-2

k12 0.0226

P(bar)

80

120

159

200

240

280

H

0.0201 0.0167

Table 4-5

CO2 - Phenanthrene Data

T=318 K

y

7. 86x10~ 4

1. 38x10- 3

1.58x10-3

1. 70x10-3

1. 78x10- 3

P(bar)

120

160

200

240

280

P (bar)

120

160

200

240

280

k12

y

8. 50x10~ 4

1.40x10- 3

1. 71x10- 3

2. 23x10- 3

2. 29x10- 3

P(bar)

120

160

200

240

280

0.113

y

4.65x10~ 4

1. 52x10-3

2. 14x10-3

2.79x10-3

3. 20x10- 3

0.108

T=338 K

y

3. 29x10 4

1.19x10 3

2. 37x10- 3

3. 28x10-3

3.84x10 3

0.106

T=308 K

0.115

T=328 K

P (bar)

120

160

200

240

280

H-

Table 4-6

C2 H - Phenanthrene Data

T=318 K

y

8. 16x10~ 4

1. 7 5x10- 3

-3

2. 67x10-

3. 71x10-3

4. 56x10-3

P(bar)

120

160

200

240

280

T=328 K

-Y

7. 38x10~ 4

1. 76x10-3

3. 33x10-3

5. 34x10-3

8. 29x10-3

T=338 K

P(bar)

120 7.44x10~ 4

160 1. 84x10 3

200 3.65x10-3

240 6.39x10-3

280 1.07x10-2

0.0356

P(bar)

120

160

200

240

280 LJ

k 12 0.0459 0.0318

Table 4-7

CO - Benzoic Acid Data

T=318 K

y

1. 38x10-3

2. 37x10-3

3. 01x10-3

3. 10x10-3

3. 31x10-3

0.0183

P(bar)

120

160

200

240

280

y

1. 15x10-3

2. 38x10-3

3. 18x10-3

4.21x10-3

4. 39x10-3

P(bar)

120

160

200

240

280

0.00994

y

4. 90x10 4

2.27x10-3

3.86x10-3

5. 16x10- 3

7. 35x10-3

-0.00172

T=338 K

y

3.21x10~ 4

1. 72x10- 3

4. 11x10-3

6.96x10-3

9. 84x10-3

-0.0124

T=308 K

P(bar)

120

160

200

240

280

T=328 K

P(bar)

120

160

200

240

280

H

k12

Table 4-8

C 24 - Benzoic Acid Data

=3 T=318 K

P(bar) y

120 5.76x10~ 4

160 1.36x10-3

200 1.90x10 3

240 2.90x10-3

280 2.91x10-3

T=328 K

P (bar)

120

160

200

240

280

T=338 K

5. 48x10~ 4

1.61x10- 3

2.61x10-3

3.61x10-3

4. 01x10-3

P(bar)

120

160

200

240

280

5. 44x10-4

1. 93x10-3

3. 51x10-3

4.94x10-3

6. 19x10-3

k12 -0.0563

H-,P(J1

-0.0642 -0.0756

Table 4-9

Co - Hexachloroethane Data

T=308 K

P(bar) y

99 1.45x10-2

149 1.86x10-2

199 1.97x10-2

248 2.00x10-2

280 1.80x10-2

T=318 K

P(bar) y

100 1.04x10- 2

148 2.40x10- 2

198 2.60x10- 2

247 2.78x10-2

280 2.71x10-2

T=328 K

P(bar)

97 3.80x10- 3

145 2.32x10-2

195 3.89x10-2

245 3.94x10-2

280 3.90x10-2

k12 0.129

Ha'6

0.1160.123

147

1

-2 32810 318 K

308 K-

-310 308 K

Z 318 K - 328 K

-410System C02 2,3 DM N

-PR Equction of Statc'

Temp2ratur4?(K) Symbol k 2

328K 308 0 0.099653 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

32

318

-2 3010

-3 308 K10Z r318K- 328 K

-410

System C2H4 - 2,3 DMN

328 K - PR Equation of State

-Tampqraturc- Symbol k12

-5 K308 0.024610 IL K3 18 0 .0209

328 0.0147308K

-610 ti|

0 40 80 120 160 200 240 280

PRESSURE (BARS)


Figure 4-2

149

10

-210 -- 328

31 -

0308

-3z 10 308 K-

318 K- 328K

-40

Systlm CO2 -2,6 DMNPR Equation of Statc-

Temperature(K) Symbol k,2

308 0 01025 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

10

328

-3\

-2 308 K10 -

-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 & 0.02010 -318 328 0.0167

~08~

-610 I l

0 40 80 120 160 200 240 280

PRESSURE ( BARS)


Figure 4-4

1531

-210

33

318 K-

-310

- 318K

328 K 3 3 BK

-410

~0 System C0 2 -Phenanthrenc'-PR Equation of State

Temper-oture(K) Symbol k12

3 1 8 0.113338K 328 4 0.108

338 U 0.106-6 328 K'0

.318 K

-710

0 40 80 120 '60 200 240 280

PRESSURE (BARS)

Solubility of Phenanthrene in SupercriticalCarbon Dioxide

Figure 4-5

152

-210

338

-310

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 .035610 -- 338 0 .0 318 -

.318

100 40 80 120 160 200 240 2830

PRESSURE ( BARS )

Solubility of Phenanthrene in SupercriticalEthylene

Figure 4-6

153

0 40 80 120 '60 200 240 280

PRESSURE (BARS)

Solubility of Benzoic Acid in SupercriticalCarbon Dioxide

Figure 4-7

-210

-310

-410

'a

V

NC09

>1

-5l0

-610

-710

-233A8

ItS 31099

328 328K3K2

318 K

328 K- 338 K

338 K

Syst C2 - [BenZoiC ACid- -PR E qu at io n of St ate-

-328 K

Tempqra tur e(K) Symbol k12

3 8 K 31 8 0 .0994

328 0.00172

3 38 -0.0124

154

-2

10

- 3to

0 40 80 120 160 200 240 280

PRESSURE (BARS)

Solubility of Benzoic Acid in Supercritical Ethylene

Figure 4-8

u

zLL)

-410

System C 2H4 - Benzoic Acid

PR Equation of State

Temperoture(K) Symbol k1 2

338 K 3 18 9 -0.0563328 A -0.0642338 a -0.0756

-328K-

.318 K

-510

-6to

155

-1

328K-

A318 K

&308

-210308 K

318K- 328 K

-34

10 . - --

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

-510 _ _L 1 .. .l .I l I I i

0 40 80 120 160 200 240 280

PRESSURE (BARS)

Solubility of Hexachloroethane in SupercriticalCarbon Dioxide

Figure 4-9

156

data point is sufficient (mathematically) to determine the

value of k..(T) at each temperature, but an optimum value ofIJ

k. (T) can be found by regressing isothermal experimental'Jdata. It has been found that minimizing the objective func-

tion J, where

0 -2lny.-Iny

J = min IE J(4-1.1)

subject to

f = f (4-1.2)

0where y. = mole fraction of component i predicted from

Peng-Robinson equation of state

Ey = experimental value of mole fraction.

enables one to obtain k. .(T) from isothermal experimental'adata. The computer software necessary to perform these cal-

culations is given in Appendix VI.

Holla (1980) has shown that if it is desired to model

isothermal binary solid-fluid equilibrium data, one experi-

mental 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 temper-

ature 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 solubil-

ity (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 temp-

erature 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

318K

-O - 328K

/ 338

SYSTEM: BENZOIC AC!O-CO 290 -4 - -PR EQUATION OF STATE

TEMPERATUREo (K) SYMSOL

318328

S10-5 338K 338 *

328K

318 K

1006 -IDEAL GAS

- -338 K

10~ - 3 28 K

.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:

P

yID - .i (4-1.41I P

The ratio of real to ideal solubilities is called the enhance-

ment 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 approxi-

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

under the same conditions. The dissolving power of super-

critical 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 temper-

atures 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

0 40

SolubilityNitrogen

80 120 160 200 240

PRESSURE ( BARS)

of Naphthalene in Supercritical

Figure 4-li

-210

-

3

10

-510

uJ

zJ

z

-_ I I I I I I -

Sys tem: NitroQen - Naphthol2ne

- PR Eqution of StatQ4

k12 :0.1

328 K

3 1K

W3 OWf8 K

280

161

Table 4-10

CO2 (1); Benzoic Acid (2); Naphthalene (3) Mixture Data

T=308K

y(Benzoic acid).

2. 93x10-3

4. 01x10-3

5.22x10-3

5.46x10-3

5. 61x10-3

y (Naphthalene)

1. 44x10-2

1. 73x10-2

2.06x10-2

2. 08x10-2

2. 12x10-2

k12= 0.0183

k13= 0.0959

k 23= 0.000

P (bar)

120

160

200

240

280

162

Table 4-11

CO2 (1); Benzoic Acid (2); Naphthalene (3) Mixture Data

T=318K

y(Benzoic acid)

3.49x10-3

6.96x10-3

1. 00x10-2

1.21x10-2

1.26x10-2

y(Naphthalene)

1.76x10-2

2.61x10-2

3.25x10-2

3.67x10-2

3.66x10-2

k12= 0.00994

k13= 0.0968

k 23= 0.015

P (bar)

120

160

200

240

280

163

Table 4-12

co2 (1); 2,3-DMN (2); Naphthalene (3) Mixture Data

T=308K

y(2, 3-DMN)

6. 32x10-3

8.80x10- 3

9. 34x10-3

9.95x10-3

9.90x10-3

y (Naphthalene)

1.85x10-2

2.41x10-2

2. 39x10 -2

2.58x10-2

2.62x10-2

k 12=0.0996

kl3= 0.0959

k 23= 0.04

P (bar)

120

160

200

240

280

164

Table 4-13

CO 2 (1); Naphthalene (2); Phenanthrene(3) Mixture Data

T=308K

y (Naphthalene)

1. 47x10- 2

1. 62x10- 2

1. 76x10- 2

1. 84x10- 2

1. 88x10- 2

2. 08x10- 2

2. 14x10-2

2. 13x10-2

2. 14x10 2

y(Phenanthrene)

1.65x10-3

1.92xl0-3

2.32x10-3

2.54x10-3

2.59x10-3

2.90x10-3

2.93x10-3

3. 01x10-3

3. 21x10-3

k 12=0.0959

k13= 0.115

k23= 0.05

P (bar)

120

140

160

180

200

220

240

260

280

165

Table 4-14

CO2 (1); 2,3-DMN (2); 2,6-DMN (3) Mixture Data

T=308K

y (2,3-DMN)

3. 92xi0-3.

4. 34x10 -3

4. 94xl0-3

5. 21x10-3

5.68x10-3

6. 00x10-3

6.03x10-3

6. 16x10-3

6 . 40x10-3

y(2,6-DMN)

3. 04x10- 3

3. 36x10-3

3. 87x10 3

4. 02x10-3

4. 38x10 3

4.62x10-3

4.57x10-3

4. 62x10-3

4. 74x10-3

k12= 0.0996

k3 = 0.102

k23= 0.20

P (bar)

120

140

160

180

200

220

240

260

280

166

Table 4-15

Co2 (1); 2,3-DMN (2); 2,6-DMN (3) Mixture Data

T=318K

y(2,3-DMN)

3. 67x10- 3

5. 18x10-3

6. 51x10-3

7. 36x10-3

7. 95x10- 3

8. 24x10-3

9. 01x10-3

9. 45x10-3

1. 01x10-3

y(2,6-DMN)

3. 40x10- 3

4.47x10- 3

5. 48x10-3

6.14x10- 3

6. 59x10- 3

6. 78x10- 3

7. 39x10-3

7. 58x10-3

8.13x10-3

k 2= 0.102

k13= 0.0989

k 23= O

P (bar)

120

140

160

180

200

220

240

260

280

167

Table 4-16

C2 H4 (1); 2,3-DMN (2); 2,6-DMN (3) Mixture Data

T=308K

y(2,3-DMN)

5. 35x10-3

7. 46x10-3

9. 70x10-3

1. 19x10-2

1. 40x10-2

1. 62x10-2

1. 62x10-2

1. 76x10-2

1. 85x10-2

y(26-DMN)

4. 41x103

5.97x10-3

7. 73x103

9. 45x10-3

1.08x10-2

1. 24x10-2

1.25x10-2

1. 34x10-2

1. 40x10-2

k2 0.0246

k 3= 0.0226

k 23= 0.05

P (bar)

120

140

160

180

200

220

240

260

280

168

Table 4-17

CO2 (1); Benzoic Acid (2); Phenanthrene(3) Mixture Data

T=308K

y(Benzoic acid)

1. 84x10- 3

2.44x10-3

2. 95x10-3

3.28x10-3

3. 70x10-3

y(Phenanthrene)

1. 02x10- 3

1. 36x10-3

1. 63x10-3

1. 87x10-3

2. 05x10-3

k12= 0.0183

k13= 0 115

k23= 0.2

P (bar)

120

160

200

240

280

169

Table 4-18

Co2 ; 2,6-DMN; Phenanthrene Mixture Data

T=308K

y(2,6-DMN)

2. 92xl0-3

3.46x10-3

4. 18x10-3

4. 25x10-3

4.23xl 0-3

y(Phenanthrene)

1.06x10-3

1.49x10-3

1.85x10-3

2. 05xl03

2.07x10-3

The correlation of mixture data by the Peng-RobinsonEquation of State is not possible.

P (bar)

120

160

200

240

280

170

Table 4-19

co2; 2,3-DMN; Phenanthrene Mixture Data

T=308K

y (2, 3-DMN)

2. 89x10- 3

3.56x10- 3

4. 23x10-3

4. 43x10-3

4. 50x10- 3

y (Phenanthrene)

7. 33x4Q4

1. 00x10 3

1. 24xl0-3

1. 43x10 3

1. 48x10-3

The correlation of mixture data by the Peng-Robinsonequation of state is not possible.

P (bar)

120

160

200

240

280

171

Table 4-20

Co2 ; 2,3-DMN; Phenanthrene Mixture Data

T=318K

y(2,3-DMN)

2. 47x10-3

4. 33xl0-3

5. 54x10-3

5. 85x10-3

6.97x10-3

y (Phenanthrene)

5. 27x10~ 4

1. 19x10-3

1. 71x10 3

1. 96x10-3

2. 33x10-3

The correlation of mixture data by the Peng-Robinsonequation of state is not possible.

P (bar)

120

160

200

240

280

172

10-1

Cio HseMIXTUR E, PR EQUATION

10-2CioH8 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=0.095910-5k3= .lk13=O.I IS

k23z0.05

t DATA OF TSEKHANSKAYAet al. (1964)

10 6 11I I1 -- I -I0 40 80 120 160 200 240 280

PRESSURE (BARS)

Solubility of Naphthalene from a Phenanthrene-NaphthaleneMixture in Supercritical Carbon Dioxide

Figure 4-12

173

C14 HIO MIXTURE,PR EQUATION

10-3

100

io- -0C4 HIO PURE,PR EQUATION

10- 5

SYSTEM: CO 2 -CoHe-0C 4 H1 o(I) (2) (3)

TEMPERATURE =308.2K0 PURE C14 HIO IN C0 2

-_ * MIXTURE C1 4 HIOIN C0 2


ki=0.0 9 5 9

k 13=0.115

k23=0.05

10-7-1-

io- 8 40 40 80 120 160 200 240 280

PRESSURE (BARS)


Figure 4-13

0=

'1~C)

173

C14 H i MIXTURE, PR EQUA TION

10-3

C14HIO PURE,PR EQUATION

io-4

\0-5

SYSTEM: C0 2 -CIOH 8 --C14H 10(1) (2) (3)

TEMPERATURE =308.2K0 PURE C14 HIO IN C02

10-6 0 MIXTURE C14 HIOIN C0 2


k 2=0.0959

k 13 =0.115

k23=0.05

10~7

10-810 40 80 120 160 200 240 280

PRESSURE (BARS)


Figure 4-13

174

102

-310

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

-610 1I I I

0 40 80 120 160 200 240 280

PRESSURE (BARS)

solubility of 2,3-Dimethylnaphthalene from a2,3-Dimethylnaphthalene-Naphthalene Mixture inSupercritical Carbon Dioxide at 308 K.

Figure 4-14

175

-110

-210

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)

-610

0 40 80 120 160 200 240 280

PRESSURE (BARS)Solubility of Naphthalene from a 2,3-Dimethyl-naphthalene-Naphthalene Mixture in SupercriticalCarbon Dioxide at 308 K.

Figure 4-15

176

Bcnzoi cSystemCO 2M;Naphtholn; Acid

(1) (2) ( 3)

Temperature = 308 K

o Pure Benzoic Acid in C02* Mixture Ben zoic Acid in C02


k12 =0.0959

k,3 0.0183

k 23 = 0.Z00

I I

0 40 80 120 160 200 240 280

PRESSURE (BARS)

Solubility of Benzoic Acid from a Benzoic Acid-Naphthalene Mixture in Supercritical CarbonDioxide at 308 K.

Figure 4-16

-210

-310

0u-

u

NJzuiJ -+

z~

-410

-510

-610

-710

I II I I I I I I I I I I- - I

I II I I I

177

1

-210

- -3z 10

z ~Banzoi c

System: C0 2 ;Naphthalcne;ACid0(1) (2) (3)

Temperature = 308 K

o Pure Naphthalene in C02 t

* Mixture Naphtholene in 002- PR Equation of State

- k 12 =0-095910 k13 =0.0183

k23 =0.000

t Data of Tsekhonskaya et a.(1964)

-610 1ii _. I i 1

0 40 80 120 160 200 240 220PRESSURE (BARS)

Solubility of Naphthalene from a Benzoic Acid-Naphthalene Mixture in Supercritical CarbonDioxide at 308 K.

Figure 4-17

178

-210

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 = 0.0996k13 0-102

k 23 z0.20

-610 .ii

0 40 80 120 160 200 240 280

PRESSURE (BARS)

Solubility of 2,6-Dimethylnaphthalene from a 2,6-Dimethylnaphthalene; 2,3-Dimethylnaphthalene Mixturein Supercritical Carbon Dioxide at 308 K.

Figure 4-18

179

-210 =-2,3 -OMN (Mixtura -

23 -D0M N( Pu r 4)

-310-

System C0 2 ;2,3-DMN ;2,6-DMNS(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 0PR 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-

-210

-310

z-

N System C 2 H4 ;2,3-DMN;2,6-DMN(i) (2) (3)

-410 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=0.022610 -- k 23 =0.0 5 ~ -

106

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

Solubility of 2,3-Dimethylnaphthalene from a 2,3-Dimethylnaphthalene; 2,6-Direthylnaphthalene Mixturein Supercritical Ethylene at 308 K.

Figure 4-20

181

-110 1- - 1 1 1 1 1 1

10

-3id 2-

15 - ----z

System: C2 H 4 ;2,3 DMNi 2,6 DMN

10 (1) (2) (3)

Temperature = 308 Ko 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 280PRESSURE ( 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

-110 -1 1 1 t

-210

-310

-410 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,= 0.0989k 23 :0.1

-61 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

-110 1 I I

-210

-310

z

-4 System:C0 2 ;2,3-DMN - 2,6-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 State1(55--k 12= 0.102

k 3 =:0.09 89

k23 =O,1

-6

0 40 80 120 160 200 240 280PRESSURE (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 charac-

teristic 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 selectiv-

ity 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

480

440

400

360-

3 2 0

280

240

200-

160 -

120 -

80-

40

0

Syste I

I I I I I

00 C2- Nap ht hale ne -Phencnt hrenc(1) (2) (3)

Temperature = 30% K


k 12 = 0.0959k 13 = 0.11 5

k 2 3 = 0.05

0< NOphtholene /Phenanthrene

0

Expandad

IF w

C-

S z

-46

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

Selectivities in the Naphthalene-Phenanthrene-CarbonDioxide System

Figure 4-24

C-

z

I'

y

40 1 a 1 40 00lahI

Adh

-9r

186

221

201

181

16

14

I I ILII0 40 80 120 160 200 240 280

PRESSURE (BARS)

Selectivities in the Naphthalene-2,3-Dimethyl-naphthalene-Carbon Dioxide System

Figure 4-25

System

I .- I I I

C02 - Naphthalana - 2,3 -DMN

(1) (2) (3)

Temperature = 308 K

-- PR Equation of Statek12 =0.0959

k 13 =0.0996

k 23 =0.04

Naphthalena / 2,3-DMN

~- p p-

12.

10

z20

C

~t.

z

II

'6

8

4

2

0

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

50

40L

30

2o --

10

10

0 40 80 120 160 200 240 280PRESSURE 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 solubil-

ities 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 temp-

eratures 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 sys-

tem 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

I I I I I I I I I I I I

0

S0

System: Ethylene - Nophtholene

Temperoture K I Sym bol

318

328 I 0

T (UCEP) 325.3 K

P (UCE P)=176 BAR

0.22

0.18

0.14

0.10

0.06

I I 1 I I I i I I I1 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

0.30

0.28

wzw

CL4

a.

z

S

~0

0.021

H

H

I I I

I I

I

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 tern-

ary) systems studied in this thesis certainly indicates that

in all cases T < Tq

193

5. UNIQUE SOLUBILITY PHENOMENA OF SUPERCRITICAL FLUIDS

Solubility of solids in supercritical fluids exhibit

several unique phenomena not present in typical phase equil-

ibria situations. These pheneomena are the existance of a

maximum in isothermal solubilities at high pressures, a solu-

bility 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 solu-

bility 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

y(min) =- (5-1.1)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

I

100

1

zu-I

10

C

z

10

3 18 K

308 K298 K285 K

SYSTEM:NAPHTHALENE- ETHYL

- PENG -ROBINSON

ENE

EQUATION OF STATEk12 :O .02

* EXPERIMENTAL DATA OFTSEKHANSKAYA (1964);T=:285 K

100 1000 10,000

PRESSURE (BARS)

Solubility of Naphthalene inIndicating Solubility Maxima

Supercritical Ethylene-

Figure 5-1

3 18K

308 K

298K

285 K

io-6 - I I -m m m m m w - - ---- -- I I -I

I

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, 1961COMPUTER SIMULATION OF

j 30-MAXIMUM CONCENTRATIONUSING THE PENG-ROBINSONEQUATION OF STATE

20=8

5C

-J-

a

LU

CIO-j0 0a 200 400 600 800 1000

PRESSURE (BARS)

NUMBER TEMPERATURE(K)

I 303.22 308.23 313.24 318.25 321.26 323.27 324.28 325.3

Experimental Data Confirming Solubility Maxima ofNaphthalene in Supercritical Ethylene

Figure 5-2

Table 5-1

Comparison between Experimental and TheoreticalMaxima and the Pressure at these Maxima

Solubility

T (bar)max

680

648

576

472

357

% error,P

11.1

9.8

0.0

1.0

10.3

EYmax

4. 31x10-2

5.68x10-2

7.84x10 2

1.17x10 1

1. 35x10 1

TYmax

4.83x10-2

6.06x10-2

8.43x10-2

a.19x10 1

1.60x10 1

% error,y

12.1

6.9

7.5

1.7

18.5

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).E3. P Ex= experimental value of maximum pressure.max

4. pT = theoretical value of maximum pressure.max

T(K)

303

308

313

318

321

E (bar)max

612

590

576

477

398Hk0OD

199

dmn4 = dlnfs (5-2.1)

Expanding Eq. 5-2.1 at constant temperature and assuming that


VF nF1dP + lny dlny1 =T dP (5-2.2)

1T,P


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-

$K 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, (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

200

0

/ -200

Ct -400

- -600C-)

-800

o -1000

- I

- I

- I

200

400

600

-1800

-'Qn- . S 'W;

SOLUBILITYMINIMA

SOLUBILITYMAXIMA

- Is

-F

NAPHTH

- PEtE(

TE

10 100

SYSTEM:ALENE-ETHYLENE

NG-ROBINSONOUATION OF STATEMPERATURE =318 K

k =0.02

1000PRESSURE (BARS)

Partial Molar Volume of Naphthalene in SupercriticalEthylene

Figure 5-3

10,000I mmmm

400 [

I

I

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,

VF increases and eventually becomes equal to Vs; this then1 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 criti-

cal locus. On isotherms T5, T6 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

CriticalLocus

--UCEP '41~~

- FusionLine

-Thr ec PhoseLine

373 473 573T (K)

Projection for Et hylene -

Naphthalene (Van Welia and

Diepen, 1961)

Figure 5-4

4l:

Lo

CL

I250

200

150

100

50

0 - r

673

204

90-

0

System Ethylene - Na

Pressure = 274 Bar

-PR Equation of St

k12 = .02

. Experimental Datc

and Schaffer (195

* Melting Point of'

at 274 Bar

I I

80

70

60

50

40

30

20

101

0 20 40 60 80NAPHTHALENE (MOLE /0

U

phthalene

ate

of Diepen

3 )Naphtholaene

100

)

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

Figure 5-5

0

LU

CL

- I- -

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 signi-

ficantly 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 in-

creased from 10 to 50 percent.

Finally, the ternary solid-fluid systems that were system-

atically 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

(D 1 2 ~ 10~4cm2 /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 solid-

ification region with this system. Also, if equilibrium solu-

bility 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 gener-

alized 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)

dHF =(N dH + d FH (N1 H1 +"NZ 2dH2) + (H 1dN 1I+H 2dN 2 ) (6-1.5)

209

At constant temperature and pressure,

N1dH1 + H2 dH2 = 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

dQ =--F HsdN (H1 - H) (6-1.7)

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'NQ = (( - 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

(P 300 bar), (H1 - H1 ) 2 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 SolutionPhenanthrene-Carbon Dioxide at

31ny1 )ln$

S al/T P 3lnyj 328t,P

20,734 0

20 ,382 0

19,930 0

-11,087 -0.03928

6,849 -0.1555

for32 8K1

(H -H1),cal./mole

20, 734

20, 382

19,930

-11,540

8,110

Notes: 1.

2.

3.

AII(fusion) 2 = 4,456 cal./mole

AH(submlimation) 3 = 20,870 cal./mole

Calculations were done using the Peng-Robinson Equation of

State; k1 2 =k1 2 (T) as given in Table 4-5.

Date from Perry and Chilton (1973).

Calculated from vapor pressures of de Kruif et al. (1975).

P (bar)

1

5

10

120

300HH

Table 6-2

Differential Heats of Solution forPhenanthrene-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)

P(bar)

1

5

Table 6-3

Differential Heats of Solution forBenzoic acid-Carbon Dioxide at 328K'

3 lny I)3 l1$R) 131/TJ (3nyj 1328,P (H.

21,030 0

20,766 0

-H f ) ,cal. /mole1 )1

21,030

20,766

10 20,436 0 20,436

120 -10,114 -0.04245 -10,562

300 7,191 -0.2236 9,262

AH(fusion) 2 = 4,139 cal./mole

AH (sublimation) 3 = 21,096 cal./mole

Notes: 1. Calculations were done using the Peng-Robinson Equation ofState, k1 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).

HWA

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 solubil-

ity. Small changes of temperature and/or pressure -- especi-

ally 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

supercritical CO2 has shown to be more energy efficient than

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 vola-

tile, often polar, material (entrainer). In addition, selec-

tivities 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 dis-

covered in this thesis are (1) the existance of a maximum in

isothermal solubilities with increasing pressure; (2) enhance-

ment of component solubilities in supercritical fluids by the

addition of a second volatile solid component; (3) differen-

tial 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 equili-

brium 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 equili-

brium 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 appli-

cations 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 iso-

thermal 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 _ [tijTP, 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 CT , c T,a 2x

where Ax = x - x

223

xi X1

A

mg

D

The Molar Free Energy of Mixing asa 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 dif-

ferentiation 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 I1l-i)1 1

Expanding Eq. III-i at constant pressure and assuming that


iHF-Hr 3ln^F -H -H*

- dT + LY 1 dlny2 = - dT (111-2)RT2 y1RT

TP


F -^FI = fI/ yP

then Eq. 111-2 can be rearranged to give

(F Hs) = -r3]nyR -R 1 j

- T -

226

[1 + Bln }TP 11+31ny9l-y TrPj

4

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 temper-

atures 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)

T(K) ,Literature*x2

0.035

0.110

0.165

0.210

0.250

0.290

0.330

0.350

0.400

0.450

0.500

0.560

0.620

0.670

0.720

0.780

0.840

0.900

0.960

T (K) ,Experimental

304.2

301.2

298.2

297.2

295.2

291.2

288.2

292.2

300.2

307.2

315.2

321.2

326.2

331.2

336.2

341.2

345.2

349.2

353.2

*Prigogine and Defay (1954)

304.7

301.5

298.5

296.7

294.7

291.5

288.2

292.0

300.0

307.2

315.0

321.2

326.2

330.9

336.4

340.7

345.0

349.2

352.9

229

Table IV-2

Experimental Freezing Curves forPhenanthrene 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 forPhenanthrene 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


T. liquidus curve

T B eutectic line

232

Table IV-5

Experimental Freezing Curves for2,3-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


T. liquidus curve

T eutectic line

233

1969)

1 1lx ln (1-x 1 IV2--- = VnH AH(I-

T1 T LtHFUS,I I FUS,2]

where T and T2 are the melting points of comopnents 1 and 2

and AH FUS,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 phenan-

threne/benzoic acid, only the final melting temperature (Tf)was measured. For both cases, Tf was constant, and withinone percent of the value predicted from ideal solutiontheory.

234

Phcncnthrcne - Naphtholene Freezing

C u rvs

0 0.2 04 0.6 o8 1.0

MOLE FRACTION

* Experimental First

PHENANTHRENE

Freezing

0 Experimental Second Freezing

Poin t

Point

--- Ideal Solution Theory

Figure IV-1

SI I I

LUJ

:D

LUCL2LUjH=

373.2

363.2

353.2

343.2

333.2

323.2

235

Table IV-6

Melting Points andHeats of Fusion

Component

Phenanthrene

Naphthalene

2,3-DMN

2,6-DMN

Benzoic Acid

T NMP(K)

373.7

353.5

376.2

383.3

395.6

AHFUS (cal/mol)

4456

4614

5990

5990

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 ccName __C

Carbon Dioxide 0.2251 304.2

11Ethylene 0.0851 282.4

2,3-Dimethylnaphthalene 0.424036 7855

2,6-Dimethylnaphthalene 0.42013 7775

Phenanthrene 0.440 8781

Benzoic Acid 0.621 7521

7Hexachloroethane 0.255 698.4

Naphthalene 0.3021 748.4

REFERENCES

1. Reid et al. (1977)

2. Estimated by Lydersen's method, see

Reid et al. (1977).

3. Reid et al. (1977) for vapor pressures

and definition of acentric factor.

4. Weast (1975)

c gmoli

73.81

50.361

32.1695

32.27 5

28.992

45.61

33.42

40.531

L

156.36 4

156.36 4

181.9 4

96.474

113.224

111.9434

Supplier

Matheson

Matheson

Aldrich

Aldrich

Eastman Kodak

Aldrich

Aldrich

Fisher

Purity

99.8%

C.P., 99.5%

99%

99%

98%

99%

99%

99.9%

5. Dreisbach (1955).

6. Dreisbach (1955) for vapor pressures, and

definition of acentric factor.

7. Perry and Chilton (1973) for vapor pressures, and

definition of acentric factor.

LA)

238

Table V-2

Vapor Pressures of Solutes Studied

I. Naphthalene

Diepen and

T (K)

285.2

298.2

308.2

Scheffer (1948)

vp (bar)

3. 0701x10 -5

1. 0943x10 4

2. 7966x10~ 4

Fowler et al. (1968)

2619.91log1 0 P(mm) = 9.58102 (t(0 C)+220. 651)

40*C < t < 800C

239

Table V-2 (cont 'd)

II. Benzoic Acid

de Kruif et

T (K)

293.2

298.2

303.2

308.2

313.2

318.2

323.2

328.2

al. (1975)

P (bar)VP

4. 49x10~ 7

8. 27x10

1. 49x10-6

2. 64x10 -6

4. 57x10-6

7. 80x10-6

1. 31x10 -5

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

303.2 3.00x10 7

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 3.386x10C4

348.2 5.093x10~ 4

353.2 7.653x10~ 4

358.2 1.136x10-3

363.2 1.649x10-3

368.2 2.376x10-3

373.2 3.382x10-3

242

Table V-2 (cont'd)

V. 2,6-Dimethylnaphthalene

Osborn and

T (K)

348.2

353.2

358.2

363.2

368.2

373.2

378.2

383.2

Douslin (1975)

P (bar)

5. 360x10 4

8.146x10o 4

1. 236x10- 3

1. 823x10 -3

2. 650x10- 3

3. 850x10-3

5. 488x10-3

7. 709xlO 3

w

243

Table V-2 (cont'd)

VI. Hexachloroethane

Sax (1979)

T (K)

305.9

459. 8

vp (m)

1

76 0*

*sublimes

244

APPENDIX VI

SOURCES OF PHYSICAL PROPERTIES OF COMPLEX MOLECULES

Required physical property data for simulating equil-

ibrium 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

acenaphthene

fluorene

1, 8-dimethylnaphthalene

2 , 7-dimethy3naphtha lene

monuron (a herbicide)

p-acetophenetidide

anthracene

benzoic acid

benzoic acid

a-oxalic acid

benzophenone

trans tilbene

anthracene

acridine

phenazine

phenanthrene

pyrene

2, 2-dimethylpropanoic acid

nicotine

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)

Temperature Range (K)

338. 2-366 .4

348.2-387.2

328.2-335.7

333.2-368.2

303.5-379.1

312.4-387.8

290.1-358.0

290.4-315.5

293.2-328.2

293.2-338.2

293.2-318.2

298.2-343.2

313.2-343.2

293.2-338.2

293.2-338.2

293. 2-338.2

398.2-458.2

241. 62-256. 77

293.2-323.2

Reference

2

2

2

2

3

3

3

3

3

3

3

3

4

5

6

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 para-

meter for solid-fluid equilibria. The interaction para-

meters are those for the Peng-Robinson equation of state.

Table VII-4 gives detailed documentation of the non-

linear 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.

OSSOON3d (SOW ) WU0 ot

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

O9vOONad N~td0O1I Sr 00

OSOOON~d OS NIOd VIVO 3bfSSfld 0 b39wfN 314 SI N 3

OVVOON~d (ri) vwuo siOCPOON3d 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

O9CO0N3d *~Ss*S**S*#*@

OLCOON~d '3 liOS 3ml 2 0 3WYN 314 SI SS 'SV0 N3A1OS 3

OSCOON~d 3M14 0 3KVN 314 SI VS 'SNDIO 31 IOW 3Dn3AN03 0 O3Sfl 3

OSCOON~d S IV 11 OM1001 KNOI Vb31333Y N13 S03M 314 NI Q3Sfl SNOIZDYbi 3

OCDCON3d 310W .0 SnifVA 3 VIC3W83 NI 3ml OA'3A'9A'VA 3

OCCOON~d *3511d SYD 314 NI N3A1OS 314 0 NOI 31n 310W 314 SI CA 3

OCCOON~d *3SV14d SIC 314 NI 3 fl10S 314 AD 0 NI 3Vb 310W 314 SI A 3

O&COON~d IIW0NA10d 5SIMI 0 SIOOb X31dW0O3H 314 3 I12 'iIIWONA1Od 3

COCOON~d 5114 0 SICOonIV~b 314 mY fl SbD 3Y AII9ISS38dW03 3

O6ZO0N3d 0 SW63 NI N3 IbM 31 S 0 NoIuvrIONSNI90b 3

CerOON~d -DN3d 314 : 0 lYIWONAlOd 319113 314 0 S N3131 30:)3H3 I0

OLZOON3d DN3d 'SlVAU3 NI bnASS~bd 0JO IBIAAAN 314 51 N 3n314M 3

OSCOON~d WN "C'rl d NO tf3 Nfl03 N3bAO3H34 I 'r3

CcGr00N3d LNY 5N03 SIC) 314 SI b '31 5 0 NOXivnCI N0SNI90U 3

OvZOON~d -Om~d 314 NI S NV 5N0O3 mV 019'9D19r'311'90'I0 3

OCE00N3dOrrooN~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)ANOISNIINICOSLOON~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

OtODON~d ' @ *.. ... .. .......... .. 3

C9000N3d 3

0OOON~d DNIh33NIDN3 1W3143 0 N3W~dVdlO 30

OVOOON3d AD0I0N1433 0 31Ani iSNI S 35111431551W 3C000N3d )INunl. *1 IN0b 3

oroOwNd 3

C I CON~d .*p@...... * U.. ... ............. ..3

N31SAS NOIC W VNOI VSU3AN03 V NVtl W0 (mid :3114

DN3d we.A5o-ad.aa;ndwoc,

-ILA aLqej

LAVZ

248Table VlI-1 (cont.)

Computer Program PENG

FILE: PENG FORTRAN A CONVERSATIONAL MONITOR SYSTEM

READ (5.50) W2,PC2,TC250 FOR!.0AT (F4O.5)

C ZI,PCI,TCI ARE THE ACCENTRIC FACTORS.CRITICALC PRESSURES.,AND CRITICAL TEMPERATURES. UNITS:C DEG. K.AND EARS.c- ***, W --A ****** -U ***

READ (5,60) PIVAP60 FORMAT(1EI1.5)

C PIVAP IS THE VAPOR PRESSURE IN BARS.READ (5,70) VI

70 FCRMAT(F10.5)C VI IS THE OLAR VOLUME OF THE SOLUTE IN CC/GR.MOL.

READ (5.90) K12!0 FORMAT (FIO.5)

C K12 IS THE BINARY INTERACTION COEFFICIENT.DATA CA,0B.R/0.45724DO,0.0778000,83.1400/

C END OF CATA INPUTC CWWU ** *- * * $ * 3 *

C CALCULATION OF THE CONSTANT PROPERTIES IN THE PENG-C ROBINSON EQUATION OF STATE.C S*...*-a.*****.SSS***

B1=03'wR-TCI/IPC1B2=0S*P.-TC2/PC2TP1=T,/TCTR2=T/ TC2K1=0.3746400+1.54226DOw1-0.26992OsW1*W1K2=0.3746400+1.54226.O*W2-0.2699200-W2*W2GAM1AI=(I.D0-A1w(I.00-TR1**0.5D0))*s2.O0GA IA2=(I.I0.e2 (1.00-TR2**0.5DO))*2.DO0ALIEI=OAR*RSTC1'TC1/PC1A,-!E2=CA-RRTC2vTC2/ PC2ALIE1 =ALIEICwGAMV.AIALIE2=ALIE2*GAMMA2M= 1U=1L=1TWRITE(6,30)

90 FORMAT(35X' PENS-ROBINSON EQUATION OF STATE')WprTE(6,100) (SG(K),K=l,5)

100 FORMAT(35X.' SOLVENT GAS:',5A4)WRITE (6,110) (SS(K),K=1,5)

110 FORMAT(35X.' SOLUTE:',5A4).ITE (6,120) T1

120 FORMAT (35X, ' TEMPERATURE=',F6.,' K' )WRITE(6,130) PiVAP

130 FORMAT(35X,' VAPOR PRESSURE =' ,E0.5.' BAR')w;ITE(6.131 W1

131 FO RAAT(36X,'W1=',F10.5)WPATE(6.132) W2

132 FORMAT(36X.'W2=',F10.5)WRITE(6.133)TC1

133 FCRAT(36X.'TC1=',Fl0.5)WRITE(6.134) TC2

134 FORMAT(36X.'TC2=',F10.5)

PENOO560PENOO570PENOO580PEN00590PENOO600PENOO610PEN00620PENOO630PENOO640PEN00650PENO0660PENOO670PENOO6SOPENOO690PENOO700PENOO710PENOO720PENOO730PENOO740PENOO750PEN00760PENOO770PENO0780PENCO 790PENOOBOOPEN0810PENOOS20PEN0O830PENOO4OPENOO850

PENOo60PENOO870PENOOSSOPENOO890PENO0900PEN00910PENOO920PENO930PENO094OPEN0O950PENCO960PENOO70PENOOSSOPENOO990PENO1000PENO1010PENO1020PEN01030PENO1040PENO1050PENO1060PENO1070PENO1080PENO1090PEN01100

249

Table Vll-1 (cont.)



WRITE(6.135) PC1 PENO1110135 FoRMAT(36X,'PC1=',F10.5) PENO1120

WRITE(6.136) PC2 PENO1130136 FORMAT(36X.'PC2=',F10.5) PEN1140

WRITE(6,137) Vi PENO1150137 FORMAT(26X.'V1='.F10.5) PEN01160

WRITE(6.140) K12 PEN01170140 FORMAT (35X,' K12=',FIO.5,/) PENO1180

WRITE(6,150) PENO1190150 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) PENO1230160 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 PENO12SOC 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 PENO1350170 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

PENG(4)=(-1.CO)(ABIG-BBIG-BBIGvBSIG-BBIG**3 .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.)



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) PENO18OOC PENGI 610

C THE FOLLOWING SECTION COMPUTES THE FUGACITY PENO1820

C COEFFICIENT OF THE SOLID. PHI TO PH6 ARE THE PENO1830

C COMPONENTS OF THE FUGACITY. PH IS THE LOG OF THE FUGACITY PEN01840

C COEFFICIENT. PT IS TME POYNTING TERM. PENOl 85

C p SS-- * - $* * S * * W * P E N O 1 6 6 0

Z=P(J)sV/R/T PENO1870

PH1=B1*(Z-1.00)/B PENO1880

PH2=(-1.DOP-L1Z-BBIG)PPH3=L-1.DO).ABtG'2.DO/BSIG/0SQRT(2.DO) PENO1900

PH4=(2.DO-Y1(J)PALIE1+2.DO*Y2(J)*(1.00-K12)* PENO1910

1( (ALIEI.-ALIE2)--0.5DO))/ALIE PEN01920

PH5=(-1.D00) 61/8 PEN01930

PH6=DLOG((Z+2.414DO-BBIG)/(Z0-.414O*BIG)) PENO1940

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 *PENO1990C IN THIS SECTION OCCURS THE ACCELERATED wEGSTEIN PEN02000

C CONVERGENCE r,'ETHOD TO GET CONVERGENCE ON MOL. PENO2OI0

C FRACTIONS. PENO2200PENO2C3O0

IF (L .EQ. 2) GO TO 240 PENO2040

YA(.j =Y1 (J) PENO2050

YB(J)=ENTwP1VAP/P(J) PENO2060

Y1(J)=Y(J) PENO2070

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

ERRO;=1.34*CAsS((YC(J)-YB(J))/YC(J)) PENO2140

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.)



260 Y1(d)=YD(J) PENO2210L=1 PEN02220GO TO 180 PEN02230

270 Y1(U)=YD(J) PEN02240Y2(J)=1.DO-Y1(4) PENO22SOYIDEAL(J)=PIVAP/P(U) PEN02260

C...... .................................................................PENO2270C.......................................................................PENO2280C IN THIS SECTION OCCURS THE CALCULATIONS FOR THE PARTIAL MOLAR VOLUMES,PEN02290C THE DIFFERENCE BETWEEN THE PARTIAL MOLAR VOLUME AND THE SOLID PENO2300C VOLUME, AND THE CAPACITY OF THE FLUID PHASE. VPM IS THE PEN02310C PARTIAL MOLAR VOLUME(CC/G.MOL), CAP IS THE CAPACITY(G.MOL/CC) PEN02320C PEN02330C PENO2340

Q1=RsT/(V-8) PENO235002=1.DO+B1/( V-B) PEN02360Q3=Q1 02 PEN02370Q4=2.DO'(Yl(J)-ALIE1+Y2(J)*((ALIE1*ALIE2)**0.500)s(1.0-K12)) PEN02380Q5=2.DO*ALIE*81*(V-S) PEN02390QS=V*(V+B)+BS(V-B) PENO240007=05/06 PENO241006=04-07 PEN02420Q9=V*(V+3)+B*(V-B) PENO2430010=08/09 PEN02440011=03-010 PENO2450Q12=R-T/(V-B)/(V-B) PEN02460Q13=2.DOALIE-(V+B) PEN02470Q14=(V*(V+)+*B(V-B))*s2.0 PENO248O15=Q12-013/014 PEN02490

016=011/015 PENO2500VPM(J)0=G16 PENO2510

C........................................................................PENO2520C............. .. ............. -....................................... PENO2530

CAP(J)=Y1(J)/V PENO254OWRITE(6,280) P(J),Y1(U),YIDEAL(J),ENT,VZ,IPH,PT PENO2550

230 FORMAT(8E16.5) PEN02560888 J=J+1 PEN02570

N1=1 PENO2580L=1 PENO2590IF (d.LE. N) GO TO 180 PENO2600

WR:TE(6,774) PENO2610774 FORMAT (/////) PEN2C20

WRITE(6,776) PENO4630776 FORMAT(X,'O(BAR)',7X,'VPM(CC/G.ML)',4X,'(VS-VPM).(CC/G.MOL)', PEN02640

15X,'CAP(G.MOL/CC)') PENO2650DO 778 I=1,N PEN02660

778 VDIF(I)=V1-VPM(I) PEN02670DO 779 I=1,N PENO26OWRITE(6,775)((P(I)),(VPM(I)),(VDIF(I)),CAP(I)) PEN02690

775 FCRMAT(3D16.5,6X,D16.5,6X.016.5) PENO2700779 CONTINUE PEN02710999 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 MPROOOSOC 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**MPROO13OCss*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 MPR00250READ(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 MPROO33OGO 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 MPROO400IF (NP .EQ. 1 ) GO TO 999 MPROO410

DO 30 I=2,NP MPR00420P=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) MPROO470WRITE(6,40) MPROO480

40 FORMAT(///) MPR00490

REWIND 5 MPROO500

30 CONTINUE MPROO510

999 STOP MPROO520END MPROO530

Table Vl - 3 (cont.)


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

DIMENSION APHI(10),ERROR(10),AP(10,10) PEN040

DIMENSION PHl(l0),PH2(10),PH3(10),PH4(10),PHS(1O),PH7 (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) PENOO100COMMON /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 sQPENOO230C 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*esseePENOO280C 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 oor060 LONid NrzI ocr 00090 LCN3d IflNIZLNO3 OtOLD LON3d OLLC01DOSOLON~d ( I) A= (I)X 091090 LONUd N'11 091 CC OSL0O0 LONUd 666 01 CDOCO ONUdkL LOY'l4iOrOLONU (,SNCI 1n3lI ACI s NI C3Db3ANC3 ION A).VWUO.4 Of7L010 LONUd 1 (o00V9) 3116m000 LON3d 091 01 00 (Oocr*Ile1) -41O6600N3d 1+1=1OS600N~d OiL 0.1 CD (oc6L 31r wnss) Al0i600N3d(03)133IfS09600N3d (IX(IX())Sva' =I)C3 OctOSSOON~d NrZ=1 OCtOCOV600N3d (N'"A)IAwfs-o0 1 =(Li),A0C600N3d (I He. x) IHdl/d/ (I)evAe= CI A ortOr0OoNid N'r=IOC 00o t600N3d 666 Cio!CD(Lt0030 Dviii) .i100600N3d (Z'AIlHdY 'DISS'9DsrrV'Xd) 8063 111306900N3d 3IrlNI NCO OI1LoBBOON~d 3flN1 N03 SOtOL900N3d (N"x)vuns-o L(L)XOSSOON~d d/(1)e1Ad2(1)X 001OSBOON~d N'r=I 001 CCOVS0ON~d 89063 1113OtBOON3d *W83 DNIINAOd 3HZ sI ide 3OCSOON3d (18b/ ()SA~d)dxbo= CI lie 0o IBOONUd N'r=I 06 00OOBOON3d (zioti.)lvwoi riO66.00N3d PIS (r22S) 0138Oe 00N3 d..............................................................OLLOONUd AIND SW31SAS A81N831 804 C03Sfl MON b313W1b1d 3OSLOONUd NCI13Z"NI A8YNIS 3ifllCS-3nDcS 3HZ I snrs oOSLO0N~d...............................................OVLtOON3d (suaILoa) Lrj oA oLOCtOON3d i19' . ari~riiOs'ti3tno0s 3H 40o S38flSS3bd 8CdYA:dlAeOrL~oN3d (N'r =I I) dvAe) (oz ' S)ovb0 ILOON~d (Lz0tp L i) vilO:4 OSOOL00N3d i1CrD/OO'*o'r3if1CS't3fl1CS 3HZ 40 3Ifl1CA 81101N:SA 306900N3d (N"'ZVI(I)SA) (O9'S)03809900N3d ('taL ji) .1 wJ80i4 09OL900N~d 6 (N3A1CSr3flCS)'(ZINSA-1CS-L~Inf1S) 3O9900N3d U804 lN3101JJ303 NCIIV313lNlI .NA1OS-SlfllCS 30SSOON~d (N'0'(~ne O9)ov38Ot900N3d (l.vLjLIvw8Ci CsOC900N3d *onr 31nlOS'131nnoCsIN3AlCS 3HZ 880 014314 318.1dN33V 14:Or0ooNid (N 6 L =I(IM ) (09"S)01V380 L900N3d (Lvt'LlWtlC4 Ot'00900N3d tzfl1CoS' ,L~iCS' INIAlOS 3HZ 40 S38flZY83eIN3J I 131 183 306S00N3d (N :1l'(z)3 ) (ot"S)C13tOSSOON~d (L ovLi) 11i80i QoCOLSOON3d 0 ''r*3 rfl0s'ti 1CStlN3A1OS 3HZ 40 S38flSS38e 1131 183 :3d 3OSSOONid (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.)


FILE: PENGMR FORTRAN A CONVERSATIONAL MONITOR SYSTEM

DO 210 I=2,N PEN01110

210 E(I)sY(I)/YID(1) PENO1120Z=P*V/R/T PENO1130

999 RETURN PENO1140

END PEN0I150

256Table Vl-2 (cont.)


FILE: VPSP FORTRAN A CONVERSATIONAL MONITOR SYSTEM

SUBROUTINE VPSP (ABIG,BBIG,V,IERIFLAG,T,PR) VPS00010

IMPLICIT REAL*B (A-HO-Z) VPS00020

Css**s.*****5.ss *****e**s********ss*s****esees t***t*** te **sVPS0003O

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 VPSOO140PENG(1 )=1.D0 VPSOOI54PENG(2)=(-1.DO)*(1.DO-BBIG) VPSOOIS0

PENG(3)=(ABIG-3.D0*BBIG*SBIG-2.D0*BBIG) VPSOO16O

PENG(4)=(-1.DO)*(ABIGBBIG-BBIG*BBIG-BBIGtBBIG*BBIG) VPSOO170

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

5 ZR(1)zREAL(ZCCMP(1)) VPS00240

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

IF(ZI(I) .EQ. 0.00) GO TO 10 VPSOO310

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 VPSOO410END VP500420

257Table VlI-2 (cont.)


FILE: ESOSR FORTRAN A CONVERSATIONAL MONITOR SYSTEM

SUBROUTINE ESOSR (P,X,A,ABIG,BBBIGAPHI,VZ) ES000010IMPLICIT 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. ES000060C 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) E000120DIMENSION 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) ES000150COMMON /03/ KIJ,PVAP(10),VS(10),PHI,AP.SId ES000160COMMON /Q4/ NIFLAG,LIJ E5000170COMMON/Q7/ PH1,PH2,PH3,PH4,PH5,PH7,PH8 ES0001805=0.00 ES000190DO 10 I1,N E5000200

10 5=B+Bl(I)*X(I) E5000210

M=N-1 E5000220C IN ALL CALCULATIONS,'1' IS THE SOLVENT E5000230C PHASE AND 2 THRU 10 ARE THE SOLUTES ES000240

PLUS=O.DO ES000250DO 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) ES000280A=PLUS E5000290ABIG=A*P/R/R/T/T E5000300

BBIG=B*P/R/T ES000310CALL 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 ES000350C...... ...................................... ......................... 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) ES000500DO 90 Is2,N ES000510

90 APHI(I)=DEXP(PHI(I)) ES000520

999 RETURN E5000530

END E000540

258Table V1L-2 (cont.)


FILE: ESO6R FORTRAN A CONVERSATIONAL MONITOR SYSTEM

SUBROUTINE ESO6R 5000010C.----- ------------- ---------.................. E....................................5000020C THIS PROGRAM INITIALIZES THE PARAMETERS A AND B 5000030C REQUIRED IN PENG-ROBINSON EOS. E5000040C ......................................... 5000050

IMPLICIT REALs8(A-H,O-Z) E5000060REAL*6 KIJ(10),LIJ(10,10) E5000070DIMENSION PHI(10),AP(10,10) E5000080COMMON /Q1/R.TTC(10),PC(10),W(10) E5000090COMMON /02/ A1(10),81(10),TR(10) ES000100COMMON /Q3/ KIJ.PVAP(10),VS(10),PHI,AP,SIJ E5000110COMMON /04/ N,IFLAGLIJ ES000120DIMENSION A2(10),ALPHA(10) 5000130REAL*8 M(10) 5000140CO 10 I=1,N 5000150

10 81(I)=0.07780DOsR*TC(I)/PC(I) 500016000 20 I=1,N ES000170

20 A2(I)sO.4572400*R*R'TC(I)*TC(I)/PC(I) 5000180DO 30 I1,N E5000190

30 M(I)=0.3746400+1.5422600*W(I)-0.2699200*w(I)*W(z) 5000200DO 40 I=1.N ES000210

40 TR(I)=T/TC(I) E5000220DO 50 I=1,N E5000230

50 ALPHA(I)=1.DO+M(I)*(1.D0-(TR(I)*0.500)) ES000240DO 60 I=1,N E5000250

60 ALPHA(I)=ALPHA(I)*ALPHA(I) ES00026000 70 1=1,N 5000270

70 A1(I)=A2(I)*ALPHA(I) E000280DO 80 I=1,N E000290DO 90 J=1,N 5000300LIJ(I,d)=0.DO E000310

90 CONTINUE E5000320so CONTINUE E000330

DO 100 J=2,N 5000340LIJ(1,J)=KIJ(J) ES000350LIJ(J,1))KIJ(J) ES000360

100 CONTINUE ES000370LIJ(2,3)=SIJ 5000380LIJ(3,2)&SIJ ES000390RETURN ES000400END ES000410

259Table Vll-2 (cont.)


FILE: PENGF1 FORTRAN A CONVERSATIONAL MONITOR SYSTEM

SUBROUTINE PENGF1(WTCPC.KIJPVAPVS.NSOLVNSOLU,N,SIJ) PENOQO10C........................................................--...............PENOOO2OC OUTPUT FORMATTING PROGRAM NO. 1 PEN00030C...............................................................-..............PEN00040

IMPLICIT REAL*8 (A-H,O-Z) PENQOOSOREAL*8 KIJ(10) PENOOO60INTEGER NSOLU(45),NSOLV(5) PENOOO70DIMENSION W(1O),TC(10),PC(10),PVAP(1l),VS(10) PENCOOSO

WRITE(6,10) (NSOLV(K),Ks1,5) PENOOO9010 FORMAT (38X,5A4) PENOO100

WRITE(6,20) W(1) PENOO11020 FORMAT(30X,'W',14XD10.5) PENOO120

WRITE(6,30) TC(1) PEN0013030 FORMAT(30X,'TC(K)',10XD10.5) PEN00140

WRITE(6,40) PC(1) PENOQ15040 FORMAT(30X,'PC(BAR)',BX,D10.5,///) PENO0160

M=N-1 PENOO170CO 110 1=2,N PEN0180LI=(I-1)*5-4 PEN0O190J=LI+4 PEN00200WRITE(6,50) (NSOLU(K),KzL,J) PEN00210

50 FORMAT(40X.5A4) PEN00220WRITE(6,55) KIJ(I) PENOO230

55 FORMAT (30X,'KIJ',11X,D11.5) PEN00240WRITE(6,60) W(I) PENOO250

60 FORMAT(30X,'W',14X,D10.5) PEN00260WRITE(6,70) TC(I) PEN00270

70 FORMAT(30X,'TC(K)',10X,D10.5) PEN00280WRITE(6.80) PC(I) PENOO290

so FORMAT(30X,'PC(BAR)',8XD10.5) PENOO300WRITE(6.90) PVAP(I) PEN00310

90 FORMAT(30X,'PVAP(BAR)',6XDO.5) PEN00320WRITE(6,100) VS(I) PEN00330

100 FORMAT(30X,'VS(CC/GR.MOL)',2XDIO.5,///) PEN00340110 CONTINUE PEN00350

WRITE(6,120) SId PENOO360120 FORMAT(30X.'SOLUTE-SOLUTE INTERACTION COEFFICIENTS ,F10.5,///) PEN00370

RETURN PEN00380END PEN00390

260

Table V1I-2 (cont.)


FILE: PENGF2 FORTRAN A CONVERSATIONAL MONITOR SYSTEM

SUBROUTINE PENGF2 (KIJ,NSOLUNT,PV,Z,YYIO.E.APHI.PT.SIJ) PENOOO10

C0.-....-........--......--....-......--...----...------....-----..----PENOOO2C OUTPUT FORMATTING PROGRAM NO. 2 PENOOO30

c.----.... .... ............- PENOO04OIMPLICIT 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./) PENOC190WRITE(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 PEN00260J=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) ERCOCO10IMPLICIT REALsS(A-HO-Z) ERCOOO20DIMENSION ERROR(10) ERCOOO30ERCAL=DMAXI(ERROR(1),ERROR(2),ERROR(3),ERROR(4),ERROR(5), ERCOO401ERROR(6),ERROR(7),ERROR(B),ERROR(9),ERROR(10)) ERCOOO50

999 RETURN ERCOOC60END ERCOOO70

FILE: SUM FORTRAN A CONVERSATIONAL MONITOR SYSTEM

FUNCTION SUM(X,N) SUMOOO10IMPLICIT REAL*G (A-H,O-Z) SU41100020

C assssssssseseassssss*sssssssssssasssssassasss*ssssaasasstassssss*ss*e*SU.10030Ca*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. SUMOCOSOCss**s*assseesss*ssassaseassssssass*sssssa*sss****s****w**s***s**5sSUMOOO6

sa**e s a*s*es* se**e*w***sse*** *ssess* a*****s*s5***s****s* s*5 s~s e*msSUMOOODIMENSION X(10) SUMOO8QADD=0. o SUMOO090DO 10 I=2,N SUMOC 100

10 ADD=ADD+X(I) SUMOO110SUM=ADD -SUMOOI120

RETURN SUM0O130END SUMOO140

262Table Vl-3

Computer Program KlJSP

FILE: KIJSP FORTRAN A CONVERSATIONAL MONITOR SYSTEM

C........................................................... .............KIJOO10C KIdOOO2C RONALD T. KURNIK KIJ00030C MASSACHUSETTS INSTITUTE OF TECHNOLOGY KIJ00040C DEPARTMENT OF CHEMICAL ENGINEERING KIJOOSOC KI100060C...................KIJOOO70

IMPLICIT REAL*8 (A-H.O-Z) KIJOOOSOC...... ........................................ ......................... KIJOOO90C KIdOO100C THIS PROGRAM PERFORMS A NONLINEAR LEAST SQUARES REGRESSION - KIJOO110C ON (YP) DATA TO BACKTRACK OUT AN OPTIMAL BINARY INTERACTION KIJOO120C PARAMETER. THE FOLLOWING LIBRARIES MUST BE LINKED: KIJOO130C TESTBED AND PRODCTLB--BOTH AVAILABLE ON PROJECT KIJ00140C ASPEN. SEE HERB BRITT OF UNION CARBIDE FOR ADDITIONAL KIJOO150C INFORMATION. THE SUBROUTINES SVEP AND VSVEP ARE ALSO KIJOO160C REQUIRED. KIJOO170c KIJO0180C............ ....................... .... ............................... KIJOO190

EXTERNAL SVEP KIO200COMMON /GLOBAL/ KPFLG1 ,KPFLG2 ,KPFLG3 ,LABORT ,NH , KIJ00210

I LDIAG ,NCHAR ,IMISS ,MISSCI ,MESSC2 , KIJO2202 LPDIAG ,IEBAL ,IRFLAG ,MXBLKW ,ITYPRN , KIJ002303 LBNCP ,LBCP ,LSDIAG ,MAXNE ,MAXNPI , KJ002404 MAXNP2 ,MAXNP3 ,IUPDAT ,IRSTRT ,LSFLAG , KId002505 LRFLAG ,KSLKI ,KSLK2 ,KRFLAG ,IRNCLS , KIJ002606 LS THIS KIJ00270

C END COMMON /GLOBAL/ 10-11-79 KIJ00280DIMENSION 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), KIJ003002COVAR(100).MV(100),NCV(100) KId00310REAL*8 UB(5),L(S),LM(100,101) KIJOO320INTEGER NAME(5) KJO0330DATA MV/100*1/.NCV/100*1/ KIJ00340P(1)=0.00 KIJOO350READ (3,1) (NAME(K),Ks1,5) KJO0360

1 FORMAT(5A4) KIJ00370WRITE(6,2) (NAME(K),Ks1,5) KUO4030

2 FORMAT(SA4) KIJO0390C**S**S***S****S*****S***************SSS@**S*****S**S*S*S*K1400400

C K IS THE NUMBER OF EXPERIMENTAL DATA POINTS IN Y KIJ00410Caa*sse*es*c*s*ss*ss*s***s**s**sesssse****s*es**********ss*.*.*..sKIJ00420

READ (3,10) K KIJ0043010 FORMAT (12) KIJ00440Cass*sseseses*sSS*SSSSSS*S**S***S**********sseSS*****as**sessssKIJ0O450

C X(1,1)=P KIJ00460C ZM(1,I)=Y KIJ00470Csssas*ceea*s***************************s**Sss***ssss**s****seos*KIJOO4O

READ (3,15) T KIJOO49015 FORMAT (F10.5) KIJ00500

DO 40 I=1,K KIJ0510READ(3,30) X(I,I),ZM(I,I) KIJ00520

30 FORMAT(F11.5,D11.5) KIJOO53040 CONTINUE KIJOO540

DO 35 I=1,K KIJ00550


Computer Program KlJSP


35 ZM(1. I)=DLOG(ZM(1 I))00 20 1=1,K

20 Rf1,1)=ZVi(11), IREAD(5,200) TC1,TC2

200 FORMAT(F10.5)READ (5.210) PCl,PC2

210 FORMAT(F10.5)READ(5,220) WI,W2

220 F0*dAT(F10.5)READ(5.230) VS

230 FORIAT(F10.5)pEAD(5,240) PVP

240 FCRMAT(11.5)REA(5,2E0) T

250 FC..MAT(F10.5)

WVIE( 6,252)252 FZ~hAT( PENG-RCSINSON

WR:TE(6,260) TC1260 FQRMAT('T01= '.F0.5)

& sTE(6,Z70) TC2

270 FO;:AT'TC2= .F10.5)r7E(6,280) PC1

280 FCRT(c'PC=,IFlo.5)WR1ITE(6,290) PC2

290 F0rtA7('PC2=',F10.5)w~rTE(C,300) W1

300 FCPMAT('w1z',FO.5);.rTE(6,310) w2

310 FR4R.AT('W2='pr10.5)wITE6,32C) VS

320 FPMAT('VS=',RIO.5)-ITE(6,

2 3 0 ) PVP330 FR9MAT('PVP=',D11.5)

.RITE(6.340) T340 FORtAAT('T=',F10.5)

v3.1T(6,350) K350 FCRMAT('K=',I12)

N=1=1NC=1

Us, '1)=0.5LS 1)=-O.3ITER=501DE..=20,CUT= 1

NH=6IODS=155=0.000lEPS=1.0-6

SSNS=1 .0-4ISv=0N I C=0ISOUND1

EQUATION OF STATE')

KIJ00560KIJO570KlUO0580

KIJ00590KIJ00600KIJ00610KlOOC620KIJ00630KIJC0640KIJ00650KIJ00660KIJ00670KIJO0680KIJ00690KIJ00700KIJ00710K1JO0720KIJ00730KIJ00740KIJ00750

KIJ00760KIJ00770

KI 400780KIJ00790K10100800

KIJOOS10KIJOOE20KIJ00830KIJOO40KI00C50K1100860KIJ00870KIJO890KIJ0090KI OO900KIJOO910KIJO920K 1J00930

Kl1O0940KIJ00950KIJ00960KIJ00970KIJOC980KIJ00990Kj%101000KIJO1010KIJ01020KIJO1030KI101040KIJ01050KIJ01060KIJ01070KI01080Kl1O1090KIJ01100

264Table V11-3 (cont.)

Computer Program K1JSP


REWIND 5 KIJO1110

CALL GENLSQ (NM,,V.L,KNC,NCVP,ZMXRSVEPITERITERZ, KIJ01120

1 10E7,ICODS. S-, EPS, KOUTNDRTISSND. ISV,wORK, IWORK, Z, F,DE LZKIJ01130IwoKIJ011402SU SQ .SI3MA , COV AR , NFEVAL ,IER ,I8BOUNDLSUB ,LMNICC,) KIJ01 140

'-.WPJTE (6, 60) IER KIJ0116060 FORI:XT //.', 'ERROR CODE =I1)IJ010

W,2ITE(6,7D) KIJO118070 FORMAT(,//) KIJO1190

DO 72 I=1.K KIJUC20Z ( , )=DEXP (Z-1(1I . I) KIJ01210

72 Z(1,I)DEXP(Z(1,I)) KIJ01220DO 74 I=1,K0KIJO0;20

74 PE(I)=DAES(ZM(1 , I) -Z(1 , I ))/ZM(1,I)10 0

. KIJO1230

WPITE( 6,203 KIJOI1240

80 FCRMvAT(2GX,'PRESSURE,6X,'MCL. PRACTICN',3X,'MOL. FRACTION', KIJOI2SO

16x 'PERCENT') KIJO1260

WPTE( 6.62) KIJO1270KIJ01 280

82 FCRMTAT(42X,'(MEASURED)',5x,'(ESTIMATED)',8X,'ERROR') KIJ01290DO 100 I=1.K KIJ0120W'RITE(6,90) (X(1,I).ZM(1,1),Z(1,I),PE(I)) KIJO1300

90 FOR.AT (20X,4D16.5)4KIJOI310100 CONTINUE KIJO1320

STO0 P KIJO1w30

EIND KIJ0I1340

265Table VII-3 (cont.)


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), SVE000602PH6(100),PV(100),PV1(100),PV2(100),ZC(100), SVE00070

3v(100),X(1,100) SVEOOCOS

Cases5*sens* **ca*s******sn******ceasee*secant*eases cnacuuesseesseu eSVEOOO

C I IS SOLID, 2 IS FLUID SVEOOIOO

C*******a*** sc************ *s*****.e s* scsesssc at5 5S*SVEOO110

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/ SVE00250DATA OB/0.0778000/ SVE00260

C*****ce*sca**a*sass*** s**ans**************s***es asa c***ees ees 5VE00270

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

Ceue*u********se**s**m*su*s*ss*ss*a*as****maau**e*e*s*aeess**ssass esses cae sSVE00320C CALCULATION OF CONSTANT PROPERITIES IN PENG-ROBINSON EOS SVE00330CC55*********ess*assess*assess*sene e~aseesess ssecss assesseeeseeee S VE00340

B1=OB*RGASCTCi/PC1 SVEOO350

82=O*RGASwTC2/PC2 SVEOO36OA21=OA*RGASPRGAS*TC*TC1/PC1 SVEOO370

A22=0A*RGAS-RGAS-TC2-TC2/PC2 SVEOO380

Ml=0.3746400+1.54226DOW1-0.269920*W1W1 SVEOO390

M2=0.3746400+1.54226DO*W2-0.26992DO*W2*W2 SVE00400

TR1=T/TC1 SVE00410

TR2=T/TC2 SVE00420ALPHA11.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 SVE00470A2=A22*ALPHA2 SVEOO480

Cae****. a*e**a****s******e**es****s*********a***s*assess svsa ssses eee *SVEOO49O

C CALCULATION OF MIXTURE PROPERITIES SVEOO500

C ssseaa*.sn*u*ea*s*****ae***s**a*es**s****s***s***s***seesaessucsuesSVEOO O

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

266Table V1l-3 (cont.)


FILE: SVEP FORTRAN A CONVERSATIONAL MONITOR SYSTEM

AIJ=((Al*A2)**0.5DO)*(1.DO-P(1)) SVE00560DO 165 I=1,K SVE00570

165 A(I)=Z(1,I)*Z(iI)*AI+ SVE0058012.DO*Z('6,&)-(1.00-Z(1,I))*AIU+ SVE005902(1.Do-Z(1,I))*(1.00-Z(1,I))*A2 SVEOO600DO 180 I=1,K SVEOO610ABIG(I)=A(I)*X(1,I)/RGAS/RGAS/T/T SVEOO620

180 BBIG(I)=(I)*X(1,I)/RGAS/T SVE00630CALL VSVEP(ABIG,BBIGO,V,T,RGAS,KZM,X.Z) SVE00640DO 185 I=lK SVEOO650

185 ZC(I)=X(1,I)*V(I)/RGAS/T SVE00660C............................................................ .......... SVEOO670C SVE00680C CALCULATION OF FUGACITY COEFFICIENTS. SVEOO690C SVE00700C...............................................................................5VE00710

DO 190 1=1,K SVE00720PH1(I)=B1*(ZC(I)-1.DO)/B(I) SVE00730PH2(I)=(-1.00)*DLOG(ZC(I)-BBIG(I)) SVE00740PH3(I)=(-1.DO)ABIG(I)/2.DO/DSQRT(2.00)/BBIG(I) SVEOO750PH4(I)=2.DO* (Z(1,I)*A+(1.0O-Z(1I))*AI)/A(I) SVEOO760PHS(I)=(-1.D0)w81/8(I) SVE00770PH6(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) SVE00790DO 200 I=1,K SvEOOBOO

200 Pv2(I)=Z(1,1 )*X(1,I)*DEXP(PV1(I)) SVE0081000 205 I=1,K SVE00820

205 PV(I)=0LOG(PV2(I)) SVE00830DO 210 I=1,K SVE00840

210 F( I)=PV(I)-PS(I) SVEOOSSODO 220 I=1,K SVE00860

220 Z(1,I)=DLOG(Z(1,I)) SVEOO870REWIND S SVEOOS8ORETURN SVE00890END SVE00900



FILE: VSVEP FORTRAN A CONVERSATIONAL MONITOR SYSTEM

SUBROUTINE VSVEP (ABIG,BSIG,V,TRGAS,K,ZMX,Z) VSVOOOo1C.......................................................................VSVOOO2OC THIS SUBROUTINE CALCULATES THE SPECIFIC VOLUME OF THE FLUID PHASE. VSVO0030C THE IMSL SUBROUTINE ZPOLR IS REQUIRED. VSVOOO40C ................................................................................... VSVQOO50

IMPLICIT REAL*8 (A-HO-Z) VSVOOO00DIMENSION PENG(4).V(100),ZR(3),ZI(3),ZM(1,100),Z(1,100) VSVOOO70DIMENS ION ABIG( 100),v BBIG( 100),X(1 ,100) VSVOOO80COMPLEX-16 ZCOMP(3) VSVOO090RGAS=83.14 VSVOO10000 30 I=1,K vsV00110PENG(1)=1.DO VSVOO120PENG(2)=(-1.CO)*(1.DO-BBIG(I)) VSVOO130PENG(3)=ABIG(I)-3.D0*BBIG(I)*BBIG(I)-2.OO*BBIG(I) VSVO0140PENG(4)=(-1.D0)wBBIG(I)*(ABIG(I)-BBIG(I)-BBIG(I)*BBI(I)) VSVOO1SOCALL ZPOLR(PENG,3,ZCOMP,IER) VSVOO160DO 10 J=1,3 VSVOO170ZR(J)=REAL(ZCOMP(J)) VSV00180

10 ZI(J)=AIMAG(ZCOMP(J)) VSVOO19000 20 Jc1,3 VSVOO200IF (ZI(J) .EQ. 0.DO) GO TO 20 VSVOO210ZR(J)=0.DO VSVO0220

20 CONTINUE VSVO023030 V(I)=RGAS*T/X(1,t)*DMAXI(ZR(1),ZR(2),ZR(3)) VSVO0240

RETURN VSVO0250END VSVO0260

268

Table VII-4

Documentation of the Subroutine GENLSQ

Purpose

To fit an implicit nonlinear model of the form

f(z1 ... ,ZXm'l' '..'vX L'''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 2i=l j=1 r.

3i

subject to the constraints

f(z ... ,z ,x ,0, i=1,..,kI M n

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 pro-

gram.

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<ITER - Deming's method is used until con-

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.

- Work vector of length 2N + 3K + MK + NK +

3max(N,M)K + 3 N(N+l)

- Integer work vector of length N.

- Array of dimension (M,K).

- Vector of length K.

- Array of dimension (M,K).

- Vector of length N(N+1)/2.

- Vector containing the least squares parameter

estimates if converged or most recent values

if not converged.

- Number of iterations used.

- 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.

- Weighted sum of squares of residuals at P,

i.e., the minimized sum of squares value.

- Standard error of curve fit.

Outp.

WQRK

IWORK

z

F

DELZ

COVAR

at

p

ITER

z

SUMSQ

SIGMA

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

2been 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

2 2variance a 2r. 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 - BT+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.

ANTOIN 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

I

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 ex-

tractor and connected to a LFE 238 PID temperature control-

ler 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 F41666Autoclave "OD Nipple

CNLX16012

Wood Suppor ts

+--AutoclOve Coupling

(20 F41666)

Autoclave Tee( CTX 4 40 )

Special 1/16I Ferrule Required( Autoclave 1010 - 6850)

Omega Thermocouple

(CSH 48 -ICSS-I11SU,-15% )

'not drawn to scOle)

30 cm

FluidInlet

To

TempersturaCont roller

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 temp-

erature program conditions and with the response fac-

tors shown in Table IX-l. The response factors are for use

with an area normalization calibration as specified by

C= x 100 (IX-1)

Mixture

2,6-DMN / 2,3-DMN

Naphthalene / Phenanthrene

2,3-DMN / Phenanthrene

2,6-DMN / Phenanthrene

Phenanthrene / Benzoic Acid*

2,3-DMN / Naphthalene

Naphthalene / Benzoic Acid*

Table IX-l

Temperature Programmed Conditions andResponse Factors for Chromatography

Final Final Ramp

Temperature Temperature Rate

(0C) (C) (0C/min)

160 182 2

150 250 10

150 250 10

150 250 10

150 250 10

150 250 10

140 140 0

Injector & Detector

*Reacted with silyl

InitialHold(min)

0

0

0

0

3.5

0

0

FinalHold(min)

4

5

5

5

3.5

5

0

ResponseFactor

1/1.034

1/1.029

1/0.998

1/1.043

1/.097

1.038/1

1/1.071

Temperature = 300'C

reagent n-o-bis(trimethylsilyl)acetamide

NOD

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 25DET ZONE 1,2 65AUX TEMP 25FLOW RB 5 5INIT OVEN TEMPTIME

25

76 999-

DATA PROC

STD WT,5MP WTFACTORoSCALETIMES 15.0SENS-DET RANGEUNK.,AIR 8.80TOL 0.0000REF PK 1.000STD NAME 2 6-DMN

0 .00001.0000 01 o

1.90 327.67 327.67 327.67 327.6775 4 5.00 2 0 0

0.000.050 1.08.25 8.45 8.35

CONC47.268852.7296

NAME2 6-DMN2 3-DMN

EVENT CONTROL

ATTN-CHART-DELAY

TIME DEVICE

2.80 ATTN A2.10 CHART C

10 18

FUNCTION NAME64

RT8.359.29

RF1.001.034

8.01

291

Table 1X-3


Naphthalene/Phenanthrene Analysis

04ALYZER CONTROL

INJ TEMP 25

DET ZONE 1,2 65

AUX TEMP 25FLOW A,8 5 5

INIT OVEN TEMPTIME

25

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

CONC16.280083.7184

NAMENRPHTHALENEPHENANTHRENE

EVENT CONTROL

ATTN-CHART-DELAY

TIME DEVICE

2.10 CHART

6.89 ATTNCA

18 10 0.81

FUNCTION NAMEATTN A 6

44

RT3.96

10.52

RF1.000

1.929

292

Table 1X-4


2,3-DMN/Phenanthrene Analysis

RHALYZER CONTROL

INj TEMP 25DET ZONE 1,f2. 65AUX TEMP 25FLOW AB 5 5INIT OVEN TEMPTIME

25

76 999

DATA PROC

STD WTSMP WTFACTOP. SCALETIMES 15.00SENS-DET RANGE

UNKAIR 9.9000TOL 8.80000REF PK I;eloSSTD NAME 2 3-DMN

8w.eeee1.8099 8

1 01.99 327.67 327.67 327.67 327.67

75 4 5.8 2 0 89.80

8.858 I.e6.-68 6.78 6.73

CONC79. 497629. 5080

NAME2 3-DM4

PHENANTHRENE

EVENT CONTROL

ATTN-CHART-DELAY

TIME DEVICE-2.89 ATTN A

2.18 CHART C

8.58 ATTN A

10 19

FUNCTION NAME644

RT6.73

10.52

RF1 .8 OR90.998

8.91

293Table 1X-5


2,6-DMN/Phenanthrene Analysis

ANALYZER CONTROL

INJ TEMP 25

DET ZONE 1.2 65

AUX TEMP 25

FLOW A.B 5 5

INIT OVEN TEMPTIME

25

76 999

DATA PROC

STD WTaSMP WTFACTORoSCALETIMES 15.080SENS-DET RANGE

UNK.AIR 8.0003

TOL 8.0000REF PK 1.00STD NAME 2 6-DMN

8.0001 0

1.90750.80

8.8506.00

1.8800 8

327.67 327.67 327.67 327.67

4 5.00 2 0 8

1.86.40 6.22

CONC50.eeo850.0000

NAME2 6-DMNPHENANTHRENE

EVENT CONTROL

ATTN-CHART-DELAY

TIME DEVICE

2.80 ATTH2.18 CHART8.50 ATTN

ACA

18 10

FUNCTION NAME

644

RT6.2218.43

RF1.8001.843

0.081

I

294

Table 1X-6


Benzoic Acid/Phenanthrene Analysis

ANALYZER CONTROL

INJ TEMP 25DET ZONE 1,2 65AUX TEMP 25FLOW RB 5 5INIT OVEN TEMPPTIME

25

76 999

DATA PROC

STD WTSMP WTFACTORPSCALETIMES 17.00SENS-DET RRNGEUNKAIR 8.088TOL 8.8888REF PK 1.680STD NAME BENZOIC

8.888 1.8888 81 8

4.18 327.67 327.67 327.67 327.6775 4 5.80 2 0 88.88.858 1.85.88 6.28 6.83

ACID

CONC58.80058. 888

NAMEBENZOIC ACIDPHEMANTHRENE

EVENT CONTROL

ATTN-CHART-DELAY

TIME DEVICE4.28 ATTN A4.38 CHART C

18 18

FUNCTION NAME44

RT6.03

13.71

RF1.8988.971

8.81

295Table 1X-7


Naphthalene/2,3-DMN Analysis

ANALYZER CONTROL

INJ TEMP 25DET ZONE 1,2 65AUX TEMP 25FLOW AB 5 5INIT OVEN TEMPTIME

25

76 999

DATA PROC

STD WTSMP WT 0.88000FACTORSCALE 1 8TIMES 15.88 1.90SENS-DET RANGE 75

UNKAIR 8.880 8.88

TOL e.888 0.8518

REF PK 1.888 3.80

STD NAME NAPHTHALEHE

RT3.916.618

RF1.8881.838

CONC50.0800050.08000

1.8888 8

327.67 327.67 327.67 327.674 5.88 2 8 0

1.84.88 3.91

NAMENAPHTHALENE2 3-DMH

EVENT CONTROL

ATTN-CHART-DELAY

TIME DEVICE2.88 ATTN2.18 CHART6.8 ATTH

ACA

18 18

FUNCTION NAME64

4

8.81

296

Table 1X-8


Naphthalene/Benzoic Acid Analysis

#4ALYZER CONTROL

INJ TEMP 25DET ZONE 1,2 65AUX TEMP 25FLOW AB 5 5INIT OVEN TEMPTIME

25

76 999

DATA PROC

STD WTSMP WT 8.08000 i.00 0FACTORSCALE 1 0TIMES 15.0 4.88 327.67 327.67 327.67 327.67

SENS-DET RANGE 75 4 5.88 2 0 0UJNKAIR 8.800 8.88TOL 000080 8.850 1.8REF PK 1.800 7.18 7.38 7.18STD NAME NAPHTHALENE

CONC58.80058.8000

NAMENAPHTHALENEBENZOIC ACID

EVENT CONTROL

ATTN-CHART-DELAY

TIME DEVICE4.8 ATTN A4.81 CHART C8.80 ATTN A

18 18

FUNCTION NAME644

RT7.188.93

RF1.80I1.871

8.81

297

Gas Chromatograph Calibration Curve For

Phenanthrene I Benzoic Acid Mixture

I II |26

24

22 * Phcnanthrene0 Benzoic Acid

20

18

16-

14

LU

12

10

8

6-

4-* Reacted with Silyl ReagentN,O -bis (trimethyl silyl

ace tamide2

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Q9WEIGHT % OF COMPONENT IN SOLVENT

Figure IX-1

298

Gas Chromatograph Calibration Curve forNaphthalene / Benzoic Acid* Mixture

0 0.2 0.4 0.6 0.8 1.0 1.2 104

WEIGHT %OF COMPONENT IN SOLVENT

Figure IX-2

45

351

4wz4

5

Nophtholene

QBenzoic Acid

* Reacted with Silyl ReagentNO- bis (trimethyl siyl ) H

0 1ocatomid

I

299

Gas Chromatograph Calibration Curvafor 2,3 - DMN / Phananthrena Mix ture

70

60

50

40

30

20

10

01.2 1.6 2.0

COMPONENT IN

2.4

SOLVENT

Figure IX-3

LUI

0 0.4 0.8

WEIGHT % OF

-* 2,3 -D0MN

o Phinanthrena

Gas Chromotograph

2,3 - DMN Mixture

Colibrotion Curve for 2,6- DMN /

* 2,6- DMN

S2,3- DMN

0 0.1 0.2 0.3 0,4 0.5 0.6 0.7 0.8 09WEIGHT %Ol OF COMPONENT IN SOLVENT

Figure IX-4

50

40

30

4d

20

10

0

(A)

301

Gas Chromatograph Calibration Curve forNaphthclene I Phenanthrene Mixture

100

* Naphtholene90 0 Phenanthrene

80

70

60

< 50

40

30

20

10 /

00 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

90* 216-DMN

o Phenanthrena

707

60-

40-

30

20--

10 /

0IJ0 0.4 0.8 1.2 1.6 2.0 2.4WEIGHT / OF COMPONENT IN SOLVENT

Figure IX-6

303

Gas Chromotograph Colibration Curve

for Naphtholene / 2,3 - Dimethyinophthclene

.2 0.4 0.6 0.8 1.0 1.2

WEIGHT % OF COMPONENT IN SOLVENT

Figure IX-7

* Nophtholene

o 2,3 - Dimethyf ncphtholne

-=o-

50

40

30wA

20

10

C )

I -- - - slamommommomm

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 gmoln2 *(0. 083-14T(2-977.7- .37g

305

Moles of Phenanthrene Collected (n):

1.17 -3n1= = 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 gmoln1--(0.0 8314 (296 .8) = .829gl

306

Moles of 2,6-DMN Collected (n2

(0.4287) (1.40) -3n 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

n2 -3Y2 n +n2+n = 4.622 x 10

y n n3+n = 6.163 x 10-33 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 isotherm-

al 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 extrac-

tion 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 Naphthalenein Carbon Dioxide as a Function of FlowRate and Extractor Charge. P=191 bar;

T=308K yxl02

ExtractorCharge (gM)

28

20

Flow Rate* (1/min)

2.1

1.623

1.625

1.0

1.717

1. 711

Experimental Value of Tsekhanskaya (1964): y=1.701x10 2

*at 1 atm and 294K.

0.6

1.725

1.693

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 solu-

bility of 1.701 x 10- mole fraction. The average devia-

tion 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 inCarbon Dioxide at 328K

(Experimental Values vs. Literature)

y_(exp.)_

1.41x10-2

2. 92x10-2

4.0x1-24.OlxlQ-2

4 . 79x10 2

y(Tsekhanskaya)*

1.42x10-2

3.00x10-2

3.99x10-2

4.85x10-2

*Data of Tsekhanskaya (1964).

P(bar)

125

162

197

253

% error

0.70

2.67

0.50

1.24

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 dio-

xide 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 exam-

ine the consequences of the residence time. The solubility

data comparisons just examined were for a maximum experi-

mental 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

Quartz

30 cm Wool

7.4 cm

7.6 cm

Th ermocouple

(a)

Solid at Bottomof Extrac tor

30 cm Oaua tz

Woo

30 cm

7.6 cm

7.4 cm

15cm

( b)

Solid at Top

of Extractor

(c )Normal Position

Solid Evenly

Distributed

(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 ob-

tained from the author, or Professor Robert C. Reid.

Computer outputs are in the possession of the author.

315

NOTATION

a , a. .,IA

Avv' vI' A1

BMf B1 , B1 2 ,

CM

C

E

f

G

H

K1 , K{, K2 , K

KA, KB, Kc

L

L

N

P

Q

R

SB' Sc

T

U

parameters in Peng-Robinson Equation of State

derivatives of Helmholtz Free Energy

parameters in Peng-Robinson Equation of State

B22 second virial coefficients

third virial coefficient

heat capcity (cal/gmol K)

eutectic point; enhancement factor

fugacity (bar)

gas phase

enthalpy (cal/mole)

binary critical end points

critical points

Peng-Robinson binary interaction parameter

liquid phase

stability matrix

stability matrix

moles

pressure (bar)

heat (cal/mole)

gas constant

solid B, C

temperature (K)

internal energy (cal/mole)

1

2

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

component 1, 2, i

mixture property of components 1 and 2

lower critical end point

upper critical end point

1, 2, i

12

p

q

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

a Qb constants in the Peng-Robinson Equation of State

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," paperpresented at 71st AIChE meeting, Miami, Nov 15, (1978).

Agrawal, G.M. and R.J. Laverman, "Phase Behavior of theMethane-Carbon Dioxide System in the Solid-VaporRegion," 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 Augmentedvan der Waals Theory for the Square Well Fluid,"J. Chem. Phys., 56, 3013 (1972).

Ambrose, D. and R. Townsend, "Vapor-Liquid Critical Proper-ties," National Physical Laboratory, England (1978).

Andrews, "On the Properties of Matter in the Gaseous andLiquid States under Various Conditions of Temperatureand Pressure," Phil. Trans Roy. Soc. London, 178, 45(1887).

Balder, J.R. and J.M. Prausnitz, "Thermodynamics of TernaryLiquid-Supercritical Gas Systems with Applications forHigh Pressure Vapor Extraction," Ind. Eng. Chem. Fund,5, 449 (1966).

Bartle, K.D., T.G. Martin, and D.F. Williams, "ChemicalNature of a Supercritical-Gas Extract of Coal at 350 C,"Fuel, 54, 227 (1975).

Barton, P. and M.R. Fenske, "Hydrocarbon Extraction ofSaline Waters," Ind. Eng. Chem. Proc. Des. Dev., 9,18 (1970).

Bartmann, D. and G.M. Schneider, "Experimental Results andPhysico-Chemical ASpects of Supercritical Chromato-graphy with Carbon Dioxide as the Mobile Phase," J.Chromat., 83, 135 (1973).

Baughman, G.L., S.P. Westhoff, S. Dincer, D.D. Duston,and A.J. Kidnay, "The Solid + Vapor Phase Equilibriumand Interaction Second Virial Coefficients for Argon +

321

Nigrogen + Methane +, and Helium + Neopentane,"II. Analysis of Results", J. Chem. Thermo., 7, 875(1975).

Beegle, B.L., M. Modell, and R.C.Reid, "Legendre Transformsand their Applications in Thermodynamics," AIChE J.,20, 1194 (1974).

Benedict, M., G.B. Webb, and L.C. Rubin, "An EmpiricalEquation for Thermodynamic Properties of LightHydrocarbons and their Mixtures," I. Methane, Ethane,Propane, and n-Butane," J. Chem. Phys., 8, 334 (1940).

Benedict, M., G.B. Webb, and L.C. Rubin, "An EmpiricalEquation for Thermodynamic Properties of Light Hydro-carbons and their Mixtures. Constants for TwelveHydrocarbons," Chem. Eng. Prog., 47, 419 (1951)..

Benedict, M., G.B. Webb, and L.C. Rubin, "An EmpiricalEquation for Thermodymamic Properties of LightHydrocarbons and their Mixtures II. Mixtures ofMethane, Ethane, Propane, and n-Butane," J. Chem.Phys., 10, 747 (.19421.

Bonner, D.C., D.P. Maloney, and J.M. Prausnitz, "Calcula-tion of High Pressure Phase Equilibria and MolecularWeight Distribution in Partial Decompression ofPolyethylene-Ethylene Mixtures," Ind. Eng. Chem. Proc.Des. Dev., 13, 91 (1974).

Brunner, G., Discussion at the Supercritical Fluid Extrac-tion Symposium Electrochemical Meeting, St. Louis,Missouri, May 14-15 (1980).

Carnahan, N.F. and K.E. Starling, "Intermolecular Repulsionsand the Equation of State for Fluids," AIChE J., 18,1184 (1972).

Castellan, G.W., "Physical Chemistry," 2nd ed., Addison-Wesley, Mass. (1971).

Close, R.E., "Vapor-Liquid Equilibrium in the CriticalRegion: Systems of Alphatic Alcohols in the Propaneand Propylene," Ph.D. Thesis, Princeton University,(1953).

Czubryt, J.J., M.N. Myers, and J.C. Giddings, "SolubilityPhenomena in Dense Carbon Dioxide Gas in the Range 270to 1900 Atmospheres," J. Phys. Chem., 74, 4260 (1970).

de Kruif, C.G., and Oonk, H.A.J., "Enthalpies of Vaporiza-tion and Vapor Pressures of Seven Aliphatic CarboxylicAcids," J. Chem. Therm., 11, 287 (1979).

322

de Kruif, C.G., C.H.D. van Ginkel, and J. Voogel, "Torsion-Effusion Vapor Pressure Measurements of OrganicCompounds, "Quatrieme Conference Internationale de

Thermodynamique Chemique," 26 au 30, Aout, Montpellier,France (1975).

Diepen, G.A.M. and F.E.C. Scheffer, "On Critical Phenomenaof Saturated Solutions in Binary Systems," J. Am.Chem. Soc., 70, 4081 (1948a).

Diepen, G.A.M. and F.E.C. Scheffer, "The Solubility ofNaphthalene in Supercritical Ethylene," J. Am. Chem.Soc., 70, 4085 (1948b).

Diepen, G.A.M., and F.E.C. Scheffer, "The Solubility ofNaphthalene in Supercritical Ethylene II," J. Phys.Chem., 57, 575 (1953).

Dokoupel, Z., G. van Soest and M.D.P. Swenker, "On theEquilibrium Between the Solid Phase and the Gas Phaseof the Systems Hydrogen-Nitrogen, Hydrogen-CarbonMonoxide, and Hydrogen-Nitrogen-Carbon Monoxide,"App. Sci. Res., A5, 182 (1955).

Dreishbach, R.R., "Physical Properties of Chemical Com-

pounds," American Chemical Society, Washington, D.C.,p. 215 (1955).

Edmister, W.C., J. Vairags, and A.J. Klekers, "A GeneralizedBWR Equation of State," AIChE J., 14, 479 (1968).

Elgin, J.C., and J.J. Weinstock, "Phase Equilibria MolecularTransport Thermodynamics," J. Chem. Eng. Data, 4,3 (1959).

Eisenbeiss, J., "A Basic Study of the Solubility of Solidsin Gases at High Pressures, "Final Report, ContractNo. DA 18-108-AtMC-244(A), Southwest Research Institute,

San Antonio, August (1964).

Ewald, A.H., "The Solubility of Solids in Gases, Part III,The Solubility of Solid Xenon and Carbon Dioxide,"Trans. Far. Soc., 51, 347 (1955).

Ewald, A.H., W.B. Jepson, and J.S. Rowlinson, "The Solubil-ity of Solids in Gases," Disc. Far. Soc., A5, 238(1953).

Fowler, L., W. Trump, and C. Vogler, "Vapor Pressure of

Naphthalene," J. Chem. Eng. Data, 13, 209 (1968).

323

Francis, D. and M. Paulaitis, "Solid Solubilities in Super-critical Fuilds -- High Pressure Phase EquilibriumCalculations Near the Upper Critical End Point Usingthe Lee-Kesler Equation of State," submitted for

publication (1981).

Fuller, G.G. , "A Modified Redlich-Kwong-Soave Equation of

State Capable of Representing the Liquid State,"Ind. Eng. Chem. Fund. ,15, 254 (1976).

Gangoli, N. and G. Thodos, "Liquid Fuels and Chemical Feed-

stocks from Coal by Supercritical Gas Extraction,,"

Ind. Eng. Chem. Prod. Res. Dev., 16, 208 (1977).

Graboski, M.S. and T.E. Daubert , "A Modified Soave Equationof State for Phase Equilibrium Calculations.1. Hydrocarbon Systems," Ind. Eng. Chem. Proc. Des.

Dev., 17, 443 (1978).

Gratch, S., Proj G-9A, Univ. of Penn. ThermodynamicsResearch Laboratory, "Low Temperature Properties of

CO -Air-Mixtures by Means of a One Stage Experiment(1945-46).

Hag, A.G.,, "Method of Producing Hop Extracts," Br. 1 388581 (1975).

Hag, A.G. , "Method of Extracting Nicotine from Tobacco,"Br. 1 357 645 (1974).

Hag, A.G.,, "Method of Producing Caffeine-Free Coffee

Extract," Br. 1 346 134 (.1974).

Hag, A.G. "Method of Producing Caffeine-Free Black Tea,"

Br. 1 333 362 (1973).

Hag, A.G., "Method of Producing Vegetable Fats and Oils,,"

Br. 1 356 749 (1974).

Hag, A.G.,, "Method of Producing Cocoa Butter," Br. 1 356

750 (.1974) .

Hag, A.G., "Method of Producing Spice Extracts with a

Natural Composition," Br. 1 336 511 (1973).

Hannay, J.B. and J. Hogarth, "On the Solubility of Solids

in Gases," Proc. Roy. Soc. (London), 30, 178 (1880).

Hannay, J.B. and J. Hogarth, "On the Solubility of Solidsin Gases" Proc. Roy. Soc. (London),, 29, 324 (1879).

Hannay, J.B., "On the Solubility of- Solids in Gases,"Proc. Roy. Soc. (London), 30, 4t.4 (1880).

324

Hinckley, R.B. and R.C. Reid, "Rapid Estimation of MinimumSolubility of Solids in Gases," AIChEJ, 10, 416 (1964).

Hiza, M.J. and A.J. Kidnay, "Solid-Vapor Equilibrium inthe System Neon-Methane," Cryogenics, 6, 348 (1966).

Hiza, M.J., C.K. Heck, and A.J. Kidnay,, "Liquid-Vapor andSolid-Vapor Equilibrium in the System Hydrogen-Ethyl-ene," Chem. Eng. Prog. Symp. Ser., No. 88, 64, 57(1968).

Holder, C.H. and 0. Maass, "Solubility Measurements in.the Region of the Critical Point," Can. J. Res., 18B,293 (1940).

Holm. L.W. , "Carbon Dioxide Flooding for Increased OilRecovery," AIME Petro. Trans., 216, 225 (1959).

Holla, S.J. "Supercritical Fulid Extraction," M.S. Thesis,M.I.T., (1980).

Hong, G., personal communication, (1981).

Hubert, P. and 0. Vitzhum, "Fluid Extraction of Hops,Spices, and Tobacco with Supercritical Gases,"Angew. Chem. Int. Ed. Engl., 17, 710 (1978).

Iomtev, M.B. and Y.V. Tsekhanskaya, "Diffusion of Napthalenein Compressed Ethylene and Carbon Dioxide, " Russ. J.Phys. Chem., 38, 485 (1964) .

Irani, C.A. and E.W. Funk, "Separations Using SupercriticalGases," CRC Handbook: Recent Developments in SeparationScience, CRC Press, Boca Raton, Florida, (1977).

Jantoft, R.E. and T.H. Gouw, "Apparatus for SupercriticalFluid Chromatography with Carbon Dioxide as the MobilePhase," Anal. Chem., 44, 681 (1972).

Johnston, K.P. and C.A. Eckert, "An Analytical Carnahan-Starling-van der Waals Model for Solubility of Hydro-carbon Solids in Supercritical Fluids," submitted toAIChE J. (1981).

Jones, D. and R. Staehle, "High Temperature Electrochemistryin Aqueous Solutions," Central Electricity ResearchLaboratory, National Society of Corrosion Engineers,p. 131 (1973).

Kennedy, G.C. , "The Hydrothermal Solubility of Silica,"Economic Geology, 39, 25 C1944).

325

Kennedy, G.C., "A Portion of the System Silica-Water,"Economic Geology, 45, 629 (1950).

Kim-E, Miral, "The Possible Consequences of Rapidly Depres-surizing a Fulid," M.S. Thesis, MIT (1981).

Kim-E, M. and R.C. Reid, "The Rapid Depressurization ofHot, High Pressure Liquids or Supercritical Fluids,"paper presented at the AIChE Annual Meeting, NewOrleans, (1981).

King, A.R. and W.W. Robertson, "Solubility of Naphthalenein Comprssed Gases," J. Chem. Phys., 37, 1453 (1962).

Klesper, E. and W. Hartmann, "Apparatus and Separations in

Supercritical Fluid Chromatography," Eur. Polym. J., 1477 (1978).

Klesper, E., "Chromatography with Supercritical Fluids,"Angew. Chem. Int. Ed. Engl. 17, 738 (1978).

Knebel, A.H. and D.E. Rhodes, "Critical Solvent Deashingof Liquified Coal," paper presented at the 13thIntersociety Energy conversion Engineering Conference(1978).

Krukonis, Val, private communication C1980).

Kurnik, R.T. and R.C. Reid, "Solubility Extrema in Solid-Fluid Equilibria," accepted for publication inAIChE J, (.1981).

Kurnik, R.T., S.J. Holla, and R.C. Reid, "Solubility ofSolids in Supercritical Carbon Dioxide and Ethylene,"

J. Chem. Eng. Data. 26, 47 (1981).

Lee, B.E. and M.G. Kesler, AIChEJ, 21, 510 (1975).

Lin, C.T. and T.E. Daubert, "Estimation of Partial MolarVolume and Fugacity Coefficients of Components inMixtures from the Soave and Peng-Robinson Equationsof State," Ind. Eng. Chem.Proc. Des. Dev., 19, 51(1980).

Mackay, M. and M. Paulaitis, "Solid Solubilities of HeavyHydrocarbons in Supercritical Solvents," Ind. Eng.Chem. Fund., 18, 149 (1979).

Martin, J.J., "Cubic Equations of State -- Which?" Ind.Eng. Chem. Fund., 18, 81 (1979).

326

McHugh, M. and M. Paulaitis, "Solid Solubilities ofNaphthalene and Biphenyl in Supercritical CarbonDioxide," J. Chem. Eng. Data, 25, 326 (1980).

McKinley, C., J. Brewer, and E.S.J. Wang, "Solid-VaporEquilibria of the Oxygen-Hydrogen System," Adv. Cry.Eng., 7, 114 (1962).

Modell, M., R.P. deFilippi, and V. Krukonis, "Regenerationof Activated,Carbon with Supercritical Carbon Dioxide,"paper presented at ACS meeting, Miami, Sept. 14(1978).

Modell, M., R. Robey, V. Krukonis, R. de Felippi, and D.Oestreich, "Supercritical Fluid Regeneration ofActivated Carbon," paper presented at 87th Nationalmeeting AIChE, Boston (1979).

Modell, M., G. Hong, and A. Herba, "The Use of the Peng-Robinson Equation in Determining Supercritical Behav-ior," paper presented before 72nd Annual meeting AIChE,San Francisco, Nov. C1979).

Modell, M. and R.C. Reid, "Thermodynamics and its Applica-tions," Prentice Hall, Englewood, New Jersey, (1974).

Morey, G.W., "The Solubility of Solids in Gases," EconomicGeology, 52, 227 (1957).

Morozev, V.S.,and E.G. Vinkler, "Measurement of DiffusionCoefficients of Vapors of Solids in Compressed Gases.I. Dynamic Method for Measurement of Diffusion Coeffi-cients," Russ. J. Phys. Chem., 49, 1404 (1975a).

Morozev, V.S. and E.G. Vinkler, "Measurements of DiffusionCoefficients of Vapors of Solids in Compressed Gases,II. Diffusion Coefficients of Naphthalene in Nitrogenand Carbon Dioxide," Russ. J. Phys. Chem., 49, 1405(1975b).

Najour, G.C. and A.D. King, Jr., "Solubility of Anthracenein Comprssed Methane, Ethylene, Ethane, and CarbonDioxide: The Correlation of Anthracene -- Gas SecondVirial Coefficients Using Pseudo Critical Parameters,"J. Chem. Phys., 52, 5206 (1970).

Najour, G.C. and A.D. King, Jr., "Solubility of Naphthalenein Compressed Methane, Ethylene, and Carbon Dioxide,"J. Chem. Phys., 45, 1915 (1966).

Neghbubon, W. (ed.), "Handbook of Toxicology," Vol. III,Interscience, New York, (1959).

327

Newsham, D.M.T. and O.P. Stigset, "Separation ProcessesInvolving Supercritical Gases," J. Chem. E. Symp.Ser. No. 54, (1978).

Oellrich, L.R., H. Knapp and J.1M. Prausnitz, "A SimplePerturbed-Hard Chain Equation of State Applicable toSubcritical and Supercritical Temperatures," FluidPhase Equilibria, 2, 163 (1978).

Osborn, A.G., and D.R. Douslin, "Vapor Pressures and Der-ived Enthalpies of Vaporization for Some CondensedRing Hydrocarbons," J. Chem. Eng. Data, 20, 229 (1975).

Panzer, F., S.R.M. Ellis, and T.R. Bott, "Separation ofGlycerides in the Presence of Supercritical CarbonDioxide," Ind. Eng. Chem. Symp. Ser. No. 54, p. 165(1978).

Paul, P.F.M. and W.S. Wise, "The Principles of Gas Extrac-tion," Mills and Boon, Ltd., London, Monograph CE/5,(1971).

Peng, D.Y. and D.B. Robinson, "A New Two Constant Equationof State," Ind. Eng. Chem. Fund., 15, 59 (.1976).

Perry, R.H. and C.H. Chilton, (ed.)1" Chemical Engineers'Handbook," McGraw Hill, New York (1973).

Peter, S., G. Brunner,, and R. Riha, "Phasengleichgewichtebei holen Drtcken und Mbglichkeiten ihrer technischenAnwendung, "Chem. Ing. Tech. 46, 623 (1974).

Peter, S., and G. Brunner, "The Separation of NonvolatileSubstances by Means of Comprssed Gases in Countercur-rent Processes," Angew, Chem. Int. Ed. Eng. , 17, 746(1978).

Poynting, "Change of State: Solid-Liquid," Phil, Mag.,12, 32 (1881).

Prausnitz, J.M., "Molecular Thermodynamics of Fluid PhaseEquilibria," Prentice-Hall, Englewood Cliffs, N.J.(1969).

Prausnitz, J.M., "Solubility of Solids in Dense Gases,"Nat. Bur of Stds., Tech. Note 316, July (1965).

Prigogine, L. and R. Defay, "Chemical Thermodynamics,"Longmans Green and Co. Inc., London (1954).

Rance, R.W. and E.L. Cussler, "Fast Fluxes with Supercriti-

cal Solvents," AIChE J, 20, 353 (1974).

328

Randall, J.M., W.G. Schultz, and A.I. Morgan Jr., "Extrac-tion of Fruit Juices and Concentrated Essences withLiquid Carbon Dioxide," Confructa, 16, 10 (1971).

Redlich, 0. and J.N.S. Kwong, "On the Thermodynamics ofSolutions. V. An Equation of State. Fugacities ofGaseous Solutions," Cheri. Rev., 44, 233 (1949).

Ree, R.H. and W.G. Hoover, "Seventh Virial Coefficientsfor Hard Spheres and Hard Disks," J. Chem. Phys.,46, 4181 (1967).

Reid, R.C. and B.L. Beegle, "Critical Point Criteria inLegendre Transform Notation, " AIChE J, 23, 726(1977).

Reid, R.C., "A Possible Mechanism for Pressurized-LiquidTank Explosions or BLEVES, Science, 203, 1263 (1979).

Reid, R.C., J.M. Prausnitz, and T.K. Sherwood, "The Proper-ties of Gases and Liquids," McGraw Hill, New York(1977).

Rowlinson, T.S. and M.J. Richardson, "Solubility of Solidsin Compressed Gases," Adv. Chem. Phys., Vol. II, 85(1959).

Rowlinson, J.S., "Liquids and Liquid Mixtures," 2nd ed.,Butterworths, London Q1969).

Sax, N.I., "Dangerous Properties of Industrial Materials,"5th ed., Van Nostrand Reinhold Co., p. 718 (1979).

Schultz, W.G. and J.M. Randall, "Liquid Carbon Dioxide forSelective Aroma Extraction," Food Tech., 24, 94 (1970).

Schultz, T.H., D.R. Black, J.L. Bomben, T.R. Mon, andR. Teranishi, "Volatiles from Oranges. 6. Constituentsof the Essence Identified by Mass Spectra," J. FoodSci. , 32, 698 (1967al .

Schultz, T.H., R.A. Flath, D.R. Black, D.G. Gudagni, W.G.Schultz, and R. Teramishi, "Volatiles from DeliciousApple Essence -- Extraction Methods," J. Food Sci.,32, 279 (.1967b).

Schultz, W.G., T.H. Schultz, R.A. Carlson, and J.S. Hudson,"Pilot Plant Extraction with Liquid CO 2 ," Food Tech,24, 1282 (1970a).

Schultz, T.H., T.R. Mon, and R.R. Forrey, "Variations ofRelative Retention Times in Open-Tubular Gas-Chromato-

329

graphic Columns: Relevancy to Fruit Volatiles,"J. Food Sci., 35, 165 (1970b) .

Sie, S.T., W. Van Beersum, and G.W.A. Rijnders, "High-Pressure Gas Chromatography and Chromatography withSupercritical Fluids I. The Effect of Pressure onPartition Coefficients in Gas-Liquid Chromatographywith Carbon Dioxide as a Carrier Gas," Sep. Sci. , 1,459 (1966).

Sims, M., "Extracting Natural Materials with Liquid CO2 '"unpublished paper, (1979).

Smith, N.K., R.C. Stewart, Jr., A.G. Osborn, and D.W.Scott, "Pyrene, Vapor Pressure, Enthalpy of Combus-tion and Chemical Thermodynamic Properties," submittedto J. Chem. Thermodynamics (1979).

Smits, A., "The P-T-x-Spacial Representation of the SystemEther-Anthraquinone," Proc. Roy. Acad. Sci., Amsterdam,12, 231 (1909-10).

Snedeker, R.A. , "Phase Equilibria in Systems with Supercrit-ical Carbon Dioxide," Ph.D. Thesis, Princeton Univ.,(.1955).

Soave, G.,, "Equilibrium Constants from a Modified Redlich-Kwong Equation of State," Chem. Eng. Sci. , 27, 1197(.1972).

Sonntag, R.E. and G.J. Van Wylen, "The Solid-Vapor Equili-brium of Carbon Dioxide-Nitrogen," Adv. Cry. Eng.,, 7,99 (1962).

Stahl, E. et al. "Quick Method for the MicroanalyticalEvaluation of the Dissolving Power of SupercriticalGases," Angew. Chem. Int. Ed. Engl., 17, 731 (.1978).

Starling, K.E., "Thermo Data Refined for LPG," Hydro. Proc.51, 107 (1972a).

Starling, K.E. , "Thermo Data Refined for LPG," Hydro Proc.,51, 129 (.1972b).

Starling, K.E. , "Thermo Data Refined for LPG" Hydro Proc.,50, 101 (1971).

Studiengesellschaft, Kohle, M.B.H. , Br. 1 057 911 (.1967).

Texaco, U.S. 3 318 805 (1967).

Todd, D.B., "Phase Equilibria in Systems with SupercriticalEthylene," Ph.D. Thesis, Princeton Univ., (1952).

330

Todd, D.B. and J.C. Elgin, "Phase Equilibria in Systems withEthylene Above its Critical Temperature," AIChE J, 1,20 (1955).

Tsekhanskaya, Y.V., M.B. Iomtev, and E.V. Mushkina, "Solu-bility of Diphenylamine and Naphthalene in CarbonDioxide Under Pressure," Russ. J. Phys. Chem., 36,1177 (1962).

Tsekhanskaya, Y.V., M.B. Iomtev, and E.V. Mushkina, "Solu-bility of Naphthalene in Ethylene and Carbon DioxideUnder Pressure," Zh. Fiz. Khim., 38, 2166 (1964).

Van der Waals, "The Equilibrium Between a Solid Body and a

Fluid Phase, Especially in the Neighborhood of theCritical State," Proc. Roy. Acad. Sci., Oct 31, 439 (1903).

Van Gunst, C.A., F.E.C. Scheffer, and G.A.M. Diepen, "OnCritical Phenomena of Saturated Solutions in BinarySystems, II. J. Phys., Chem., 57, 581 (1953a).

Van Gunst, C.A., F.E.C. Scheffer, and G.A.M. Diepen, "OnCritical Phenomena of Saturated Solutions in TernarySystems," J. Phys. Chem., 57, 578 (1953b).

Van Gunst, "De Oplosbaarheid Van Mengsels Van VasteStoffen In Superkritische Gassen, "Dissertation, Delft(1950).

Van Leer, R.A. and M. Paulaitis, "Solubilities of Phenoland Chlorinated Phenols in Supercritical CarbonDioxide," J. Chem. Eng. Data., 25, 257 (1980).

Van Nieuwenburg, C.J. and P.M. Van Zon, "Semi-QuantitativeMeasurement of the Solubility of Quartz in Steam,,"Rec. Trav. Chim, 54, 129 (1935) .

Van Wasen, "Physicochemical Principles -and Applications ofSupercritical Fluid Chromatography," Angew. Chem. Int.Ed. Engl., 19, 575 (1980).

Van Welie, G.S.A. and G.A.M. Diepen, "The P-T-x Space Modelof the System Ethylene-Naphthalene," J. Recl. Trav.Chim., 80, 659 (1961).

Vitzthum, 0. and P. Hubert, Ger. Patent, 2 357 590 (1975).

Waldeck, W., G. Lynn, and A. Hill, "Aqueous Solubility ofSalts at High Temperatures. I. Solubility of SodiumCarbonate from 50 to 3480, " J. Am. Chem. Soc., 54928 (1932).

331

Waldeck, W., G. Lynn, and A. Hill, "Aqueous Solubility ofSalts at High Temperature. II. The Ternary SystemNa2CO3 -NaHCO3 -H20 from 100 to 2000,6" J. Am. Chem.Soc., 56, 43 (1934).

Weast, R.C. (ed.), "CRC Handbook of Chemstry and Physics,"CRC Press, Ohio, 55th ed. , (1975).

Webster, T.J., "The Effect of Water Vapor of SupercbmposedAir Pressure," J. Chem. Soc. (London),, 69,, 343 (1950).

Weinstock, J.J., "Phase Equilibria at Elevated Pressuresin Ternary Systems of Ethylene and Water with OrganicLiquids," Ph.D. Thesis, Princeton Univ., (1954).

Wiedmann, H. G. , "Applications of Thermogravimetry for VaporPressure Determination," Thermochimica Acta, 3, 355(1972).

Wilke, G., "Extraction with Supercritical Gases," Angew.Chem. Int. Ed. Eng., ,17 701 (1978).

Wise, W.S. , "Solvent Extraction of Coal," Chem. Ind. (London),950 (1970).

Won, K.W. "Predicted Solubilities of Methanol in CompressedNatural Gas at Low Temperatures and High Pressures,"Adv. in Cry. Eng.., Plenum Press,, 23, 544(1978).

Yamada, T.,, "An Improved Generalized Equation of State,,"AIChEJ, ,19 286 (1973) .

Zellner, M.G., C.J. Sterner, L.C. Claitor, and J.M. Geist,"Vapor Phase Solubility of Oxygen in Helium at LowTemperatures and Pressures up to 6500 psi," paperpresented at the AIChE meeting, Denver, Co., August(1962).

Zernike, J.,, "Chemical Phase Theory," Gregory Lounz, NewYork, p. 146 (1957).

Zhuze, T.P., "Compressed Hydrocarbon Gases as a Solvent,"Petroleum (London), 23, 298 (.1960).

Zosel, K., "Separation with Supercritical Gases: PracticalApplications," Angew. Chem. Int. Ed. Engl. , 17, 702(1978).

332

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.

Signature redacted - DSpace@MIT

Documents