EPA/600/7-87/004
February 1987
VAPOR/LIQUID EQUILIBRIA OF CONSTITUENTS FROM COAL
GASIFICATION IN REFRIGERATED METHANOL
by
Te Chang. R. M. Rousseau, and J. K. Ferrell
North Carolina State University
Department of Chemical Engineering
Raleigh, North Carolina 27695-7905
Cooperative Agreement No. CR-809317
EPA Project Officer: N. Dean Smith
Air and Energy Engineering Research Laboratory
Research Triangle Park, NC 27711
AIR AND ENERGY ENGINEERING RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELGPMENl
U.S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, NC 27711
-------
TECHNICAL REPORT DATA.
(Please read Instructions on the reverse before completing)
1. REPORT NO. 2.
EPA/600/7-87/004
3. RECIPIENT'S ACCESSIOMNQ. ~ „
PBS 'f 16 Silt®
4. TITLE AND SUBTITLE
Vapor/Liquid Equilibria of Constituents from Coal
Gasification in Refrigerated Methanol
5* R-EFOfiT DATE
February 1987
6. PERFORMING ORGANIZATION CODE
7.AUTHOfiiS)
Te Chang, R. M. Rousseau, and J. K. Ferrell
8. PERFORMING ORGANIZATION REPORT NO.
S. PERFORMING ORGANIZATION NAME AND ADDRESS
North Carolina State University
Department of Chemical Engineering
Raleigh, North Carolina 27695
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
EPA Cooperative Agreement
CR809317
12. SPONSORING AGENCY NAME AND ADDRESS
EPA, Office of Research and Development
Air and Energy Engineering Research Laboratory
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED j
Final Reoort: 0/84 - 12/85
14. SPONSORING AGENCY CODE
EPA/600/13
15. supplementary NOTES AEERL project officer is N. Dean Smith, Mail Drop 62, 919/541-
2708. \
is. abstract report describes a thermodynamic framework, established for the
development of a model of the phase equilibria of mixtures of methanol and the major;
constituents found in gases produced from cosl. Two approaches were used to model
the equilibrium behavior:- (1) an equation of state was used to describe both gas and
liquid phases, and (2) an, equation of state was used to describe the gas while a solu-
tion model involving activity coefficients was used to describe the liquid. The appro-
ach chosen for each species was based on the component volatility. An experimental
apparatus was constructed to obtain data against which the model predictions could
be tested. The apparatus was evaluated by comparison of experimental F-T-x data
on mixtures of carbon dioxide (C02) and methanol with those from the literature.
The comparison was favorable. P-T-x-y data on mixtures of C02, methanol, and
water, and mixtures of C02, nitrogen,, and methanol at temperatures in a range of
-SO to 25 C pressures up to 54 atm (5472 kPa) were obtained. Comparisons of
the calculated and measured.values.of. bubble point pressures and/or liquid composi"
tions of the dissolved gases were satisfactory. .
17.
KEY WORDS AND DOCUMENT ANALYSIS
a. '
'DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS
c. cosati FieM/Croop
Pollution
Coal
Coal Gasification
Carbinols
Equilibrium
Vapors
Liquids
Volatility
Carbon Dioxide
Nitrogen
Pollution Control
Stationary Sources
Vapor/Liquid Equilibria
20 M
07B
QIC
14G
07D
18. DISTRIBUTION STATEMENT
Eelease to Public
1S. SECURITY CLASS (Tax Report)
Unclassified
21. NO. OF PAGES
148
20. SECURITY CLASS (Thitpage)
Unclassified
22. PRICE
SPA Form 222B-1 <9-73}
1
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NOTICE
This document has been reviewed in accordance with
U.S. Environmental Protection Agency policy and
approved for publication. Mention of trade names
or commercial products does not constitute endorse-
ment or recommendation for use.
ii
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ABSTRACT
A thermodynamic framework was established for the development of a model of the
phase equilibria of mixtures of methanol and the major constituents found in gases pro-
duced from coal. Two approaches were used to model the equilibrium behavior. In one,
an equation of state was used to describe both gas and liquid phases, and in the other
an equation of state was used to describe the gas while a solution model involving
activity coefficients was used to describe the liquid. The approach chosen for each
species was based on the component volatility.
The equation of state used in this work was an extended Soave-Redlich-Kwong
(SRK) equation; four-suffix Margules, Wilson, and UNIQUAC equations were used to
express activity coefficients. Vapor-liquid equilibrium data obtained in the present
study and from the literature were used to obtain parameters in the extended SRK
equation and Margules, Wilson, and UNIQUAC equations.
The SRK equation and associated sets of parameters obtained by fitting equilibrium
data on binary mixtures can be used to describe the vapor-liquid equilibrium behavior
of a multicomponent system in the composition, temperature, and pressure ranges
found in an absorption-stripping process coupled with a coal gasifier. A gas solubility
calculation using the equation greatly simplifies an equilibrium calculation without
significantly distorting the capability of the equation.
The parameters for the Four-Suffix Margules, Wilson, and UNIQUAC equations,
which are used'to describe the liquid phase nonideality, were obtained for many binary
systems formed from constituents of coal gas and methanol. The liquid reference state
fugacities were calculated from various sources. When using this approach to describe
the liquid phase, the SRK equation of state is used to describe the vapor phase.
Ail exerimental apparatus was constructed to obtain data against which the model
predictions could be tested. The apparatus was evaluated by comparison of experimen-
tal P-T-x data on mixtures of carbon dioxide and methanol with those from the litera-
ture. The comparison was favorable. P-T-x-y data on mixtures of carbon dioxide,
methanol and water, and mixtures of carbon dioxide, nitrogen and methanol at tem-
peratures in a range of -30 to 25°C and pressures up to 54 atm were obtained. Com-
parisons of the calculated and measured values of bubble point pressures and/or liquid
compositions of the dissolved gases were satisifactory.
i ii
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TABLE OF CONTENTS
Page
ABSTRACT i ii
FIGURES v-iii
TABLES x
1. INTRODUCTION . 1
2. LITERATURE REVIEW 4
SOLUBILITIES OF GASES IN A PHYSICAL SOLVENT 4
Binary Correlations for Gas Solubilities 4
Generalized Correlations for Gas Solubilities 6
VAPOR-LIQUID EQUILIBRIUM 8
Equation of State Method (Phi Method) 9
Activity Coefficient Method (Gamma Method) 10
PHYSICAL PROPERTIES AND BINARY DATA SETS 13
PRINCIPLES OF BINARY VLE DATA REDUCTION 15
3. RESEARCH SYSTEMS, APPROACHES, AND OBJECTIVES 17
4. MODELING PHASE EQUILIBRIA WITH AN EQUATION OF STATE 20
THE EXTENDED SRK EQUATION OF STATE 20
EVALUATION OF THE POLAR CORRECTION FACTOR 23
BINARY PHASE EQUILIBRIUM AND INTERACTION 25
PARAMETER EVALUATION
Methanol-Supereritical Gases 31
Methanol-Hydrogen System 32
Methanol-Carbon Monoxide System 32
Methanol-Methane System 32
Methanol-Nitrogen System 32
Binary Parameters k>, and C-tJ- 38
=, V
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Methanol-Light Hydrocarbon Gases 38
Methanol-Ethylene System 38
Methanol-E thane System 38
Methanol-Propylene System - 43
Methanol-Propane System 43
Binary Parameters k\j and C±j 43
Methanoi-Acid Gases 46
Methanol-Carbon Dioxide System 46
Me than o H lydroge n Sulfide System 49
Methanol-Carbo nyi Sulfide System 49
Methanol-Mercaptan and Methanol-Sulfide Systems 52
Binary Parameters ki}- and C,j 52
Systems Containing Water 56
Comparison of Results Using a Full Parameter Set to Those 56
Using a Reduced Parameter Set
Gas-Gas Systems 60
PHASE EQUILIBRIA IN MULTICOMPONENT SYSTEMS 64
Methanol-Hydrogen-Nitrogen System 64
Methanol-Hydrogen-Carbon Monoxide System. 66
Methanol-Hydrogen-Hydrogen Sulfide System 66
GAS SOLUBILITY CALCULATIONS USING AN EQUATION OF STATE 66
5. MODELING PHASE EQUILIBRIA WITH ACTIVITY COEFFICIENT 73
EQUATIONS
VAPOR PHASE FUGACITY COEFFICIENTS 73
ACTIVITY COEFFICIENTS 74
Four-Suffix Margules Equation 75
The Wilson Equation 76
UNIQUAC Equation 78
LIQUTO REFERENCE'STATE WGACITIES 83
Subcritical Components 83
Supercritical and Near-CriticalComponents 85
EVALUATION OF BINARY PARAMETERS IN ACTIVITY 87
COEFFICIENT EQUATIONS
Evaluation Method and Procedure 87
Binary Correlation Results 88
Effects of Reference Fugacity 102
MULTICOMPONENT VLE CALCULATIONS 102
vi
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6. EXPERIMENTAL
108
QUALITY ASSURANCE AND EXPERIMENTAL PROCEDURE 106
Vapor-Liquid Equilibrium Apparatus 108
Sampling Procedure 108
Sample Analysis 108
Cixemieals 112
EXPERIMENTAL RESULTS AND DISCUSSION 112
Methanol-Carbon. Dioxide Binary System 113
Methanol-Carbon Dioxide-Water System 114
Mettanol-Carboa Dioxide-Nitrogen. System 118
7. SUMMARY OF CONCLUSIONS 123
8. REFERENCES 128
9. LIST OF SYMBOLS 134
vii
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LIST OF FIGURES
Page
Figure 1. Classification and Interaction Relationships of 18
Constituents from Coal Gasification and Methanol
Figure 2. Logic Flow Chart for Polar Correction Factor Evaluation 24
Figure3. Logic Flow Chart for Binary Interaction Constant 27
Evaluation in the Phi Method
Figure 4. Logic Flow Chart for Bubble Point Pressure Calculation 29
in the Phi Method
Figures. Methanol-Hydrogen Equilibria 34
Figure 6. Methanol-Carbon Monoxide Equilibria 35
Figure 7. Methanol-Methane Equilibria 38
Figure 8. Methanol-NItrogen Equilibria 37
Figure 9. Binary Interaction Parameters for Methanol- 39
Supercritical Gases
Figure 10. Binary Interaction Parameters for Methanol- 40
. Supercritical Gases
Figure 11. Methanol-Ethylene Equilibria 41
Figure 12. Methanol-Ethane Equilibria 42
Figure 13. Methanol-Propane Equilibria 44
Figure 14. Binary Interaction Parameters for Methanol- 45
Light Hydrocarbon Gases
Figure 15. Binary Interaction Parameters for Methanol- 47
Light Hydrocarbon Gases
Figure 18. Methanol-Carbon Dioxide Equilibria 48
Figure 17. Methanol-Hydrogen Sulfide Equilibria 50
Figure 18. Methanol-Carbonyl Sulfide Equilibria 51
Figure 19. Methanol-Methyl Mercaptan Equilibria 53
Figure 20. Methanol-Dimethyl Sulfide Equilibria 54
Figure 21. Binary Interaction Parameters for Methanol- 55
Acid Gases
Figure 22. Binary Interaction Parameters for Methanol- 57
Acid Gases
Figure 23. Methanol-Water Equilibria 58
Figure 24. Carbon Dioxide-Hydrogen Sulfide Equilibria 62
vi ft
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Figure 25. Carbon Dioxide-Nitrogen Equilibria 62
Figure 28. Logic Flow Chart for Gas Solubility Calculation 69
Figure 27. Calculated and Measured Solubilities of Nitrogen 71
and Hydrogen in Methanol at 298,15 K
Figure 28. Calculated and Measured Solubilities of Carbon 72
Monoxide and Hydrogen in Methanol at 303.15 K
Figure 29. Logic Flow'Chart for Binary Parameters Evaluation 89
in the Gamma Method
Figure 30. Logic Flow Chart for Bubble Point Pressure 90
Calculation in the Gamma Method
Figure 31. Comparison of the Correlated Results by Wilson and 98
Margules Equations for Methanoi-CQS Equilibria
Figure 32. Residual Ratios (Pe — Pcai)/Pe of Fitting 97
Margules and UNIQUAC Equatiuons for Methanol-C02 VLE
Figure 33. Methanol-Propane Equilibria with Predictions calculated 98
by the UNIQUAC Equation
Figure 34. Methanol-Methyl Mercaptan Equilibria with Predictions 99
calculated by the UNIQUAC Equation
Figure 35. Methanol-Dimethyl Sulfide Equilibria with Predictions 100
calculated by the Margules Equation
Figure 36. Diagram of Methanol-Dimethyl Sulfide Equilibria at 288.15 F 101
Figure 37. Comparison of Using Lee-Erbar-Edmister and Robinson-Chao 104
Models in Margules Equation Activity Coefficient
Correlations for Methanol-C02 System
Figure 38. Vapor-Liquid Equilibrium Apparatus 107
Figure 40. GC Calibration Curve for Methanol-Nitrogen System 110
Figure 41. GC Calibration Curve for Methanol-Water System 111
Figure 42. Methanol-Carbon Dioxide-Water Equilibria at r=0.2 115
Figure 43. Methanol-Carbon Dioxide-Water Equilibria at 273.15 K 116
Figure 44. Calculated and Measured Solubilities of Carbon Dioxide 119
and Nitrogen hi Methanol
ix
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LIST OF TABLES
Table 1. Composition of Gaa from NCSU Fluidized Bed Gasifier
Texas Lignite Coal
Table 2. Check List of Binary Data Sets Including Major
Components from Coal Gasification
Table 3. Polar Correction Factor
Table 4. Pure Component Physical Properties
Table 5. Correlations of VLB Binary Pairs Containing
Methanol or Water
Table 6. Comparison of Correlated Results for VLB Binary
Pairs Using a Full Parameter Set to a Reduced
Parameter Set
Table 7. Correlations of Four Binary Gas-Gas Systems
Table 8. Recommended Binary Interaction Parameter in the
SRK Equation of State for Gas-Gas Systems
Table 9. Predicted and Experimental VLE Results for
Methano!-H2—N2 System at 25°C
Table 10. Predicted and Experimental VLE Results for
Methanol-H2-CO System at 30°C
Table 11. Binary Interaction Parameters in the SRK Equation
of State for Systems Containing Methanol
Table 12. Relationships of Multicomponent Margules Parameters
to Binary and Ternary Parameters
Table 13. Liquid Molar Volumes of Gases from Various Sources
Table 14. Uniquac Structure Parameters
Table 15. Vapor Pressure Constants for Equation 49
Table 16. Coefficients for Equation 51c
Table 17. Constants in Equation 53
Table 18. Binary VLE Data Used in Evaluation of Parameters
in Activity Coefficient Equations
Table 19. Recommended Margules Parameters in the Activity
Coefficient Correlations
• Table 20. Recommended Wilson Parameters in the Activity
Coefficient Correlations
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Table 21. Recommended UNIQUAC Parameters in the Activity
Coefficient Correlations
Table 22. Activity Coefficient Correlations with.
Robmson-Chao Reference Fugacity Mode for
C02andH2S
Table 23, Experimental Vapor-Liquid Equilibrium P-T-x.
Data for the Methanol(l)-C02 (2) System
Table 24, Experimental Vapor-Liquid Equilibrium P-T-x
Data for the Methanol(l)-C02—N2 (3) System
Table 25. Experimental Vapor-Liquid Equilibrium P-T-x
Data for the Methanol(l) C02(2)— H2(3) System,
at r = 0.2
Table 26. Calculated and Experimental Carbon Dioxide
Solubilities, x(C02), in the Mixture of Methanol
and Water at r = 0.2 '
Table 27. Calculated and Experimental Solubility Results
for Methanol(l)-C02—(2)—N2(3) System
xi
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INTRODUCTION
Since the energy crisis of 1973, much attention has been given'to coal utilization. In
1978, North Carolina State University (NCSU) began a study of the environmental
aspects of coal gasification under the sponsorship of the Environmental Protection
Agency. One of the main objectives of the project was to study processes by which the
synthetic gas was cleaned.. The gas produced from coal gasification contains carbon
dioxide, hydrogen sulfide and other sulfur gases, in addition to the desired gases: car-
bon monoxide, hydrogen and methane. The acid gases lower the heating value of the
product gas and are toxic and corrosive; the sulfur gases also have an offensive odor.
Removal of these acid gases is carried, out in an acid gas removal system (AGRS) that
involves absorption-stripping operations which utilize either a physical or chemical sol-
vent.
Physical solvents have been shown to be good bulk removers of acid gases (Rivas
and Prausnitz, 1979), and have a better capacity than chemical solvents when the acid
gases are at high concentrations or high partial pressures. Also, physical solvents are
easier to regenerate and cost less than chemical solvents. A physical solvent that has
shown promise is methanol; it has been used in the NCSU acid gas removal system and
several commercial coal gasification facilities.
Absorption of acid gases in methanol is favored at low temperatures and high pres-
sures, while stripping methanol of acid gases must be accomplished at elevated tem-
peratures and reduced pressures. The NCSU acid gas removal system operates In a tem-
perature range from 230 K to 300 K and a pressure range from 1 to 35 atm (1 atm —
101 kPa). Table 1 lists a typical composition of the crude gas produced from the NCSU
fiuidized bed gasifier when using a Texas Lignite coal and operating at 795°C.
The primary difficulty associated with conditioning gases having a composition
similar to that shown in Table 1, is the significantly greater amounts of carbon dioxide,
sulfur gases, hydrocarbons, and nitrogen compounds than usually found in natural gas.
In addition, the water, hydrocarbons, and nitrogen compounds may alter the behavior
of the solvent, especially if It Is methanol. This alteration In properties may cause pro-
duct gas contamination and may complicate the separation of sulfur compounds from
carbon dioxide in an absorption operation. Also, hydrocarbons tend to accumulate in
- 1-
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the solvent (Rousseau et al., 1981b) and cause potential problems with, methanol regen-
eration in a stripping operation.
TABLE 1
COMPOSITION OF GAS FROM NCSU FLUIDIZ1D BED GASIFIER
TEXAS LIGNITE COAL
Compound
Mole % Dry Basis
or ppm
TT
2
34.28%
CO
13.58
C02
28.87
N2
19.42
CH4
4.98
h2s
1608 ppm
COS
35
Methyl Mercaptan.
31
TMopkene
17
c2h4
1812
/"I TT
2 6
2S09
c3H6
777
°3H8
390
C4H8
359
Benzene
568
Toluene
179
o~Xyleae
15
m-Xyleiie
30
p-Xylene
6
Ethylbenzene
13
The phase equilibrium, behavior of mixtures consisting of methanol and compounds
produced in the gasification of coal is the fundamental information required for design
and analysis of the components of an AGRS using methanol as a solvent. A mathemati-
cal model of each component of the operation can be used to predict the effects of vary-
ing feed composition, temperature, and pressure with considerable reliability, and the
model can be used to avoid an inefficient over-design. Moreover, other economically
important factors, such as the solubility of sweet gas (including H2, CO. and CH4) in
methanol and the solubility of methanol in the sweet or stripping gas (Lazalde-Crabtree
et al.. 1979), can be evaluated with a properly constructed model of the system.
. 2 -
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Although processes and associated equipment using refrigerated methanol in an acid
gas removal system hare been designed successfully by some companies (for example,
the Rectisoi process by Lurgi GmbH) much of the experience and data required for
design remain proprietary. Despite the availability of gas solubility data, little infor-
mation has been published on vapor-liquid equilibria for multicomponent systems
which contain methanol (Weber and Knapp, 1980; Weber, 1981; Rousseau et al.,
1981a; Takeuchi et al.7 1983). As a result, the available equilibrium correlations have
been found inadequate for describing the phase equilibrium behavior between refri-
gerated methanol and the coal gas constituents at elevated pressures. Thus, vapor-
liquid equilibrium modeling of constitutents from coal gasification in refrigerated
methanol has been initiated at NCStJ (Bass, 1978; Matange, 1980), where the search for
better methods and further extensions continues.
' The work reported here is concerned primarily with the equilibrium behavior of
individual gas components in methanol at conditions corresponding to an acid gas
removal system. The collected data and resulting correlations characterize the solubili-
ties of each species in methanol over a wide range of temperatures and pressures, and
account for all the interactions between the existing species in the system/ The goal of
the study is to construct models that can be included in a simulation package and used
to predict the performance of gas-liquid processing units such as absorbers, strippers,
and flash tanks. These models are to be based on a limited amount of vapor-liquid
equilibrium data and correlations of pure-component data, and they are to be tested
against experimental multicomponent vapor-liquid equilibrium data. In addition to
these very important and practical benefits, the information obtained and evaluated in
this study may be of fundamental importance in understanding the factors that
influence phase equilibria and the models that describe such behavior.
In the sections that follow a review of the fundamentals of the thermodynamic rela-
tionships that exist between coexisting phases is presented. These principles are formu-
lated to provide two types of expressions relating temperature, pressure, and composi-
tion of vapor and liquid phases. One uses an equation of state to describe both gas and
liquid phases; the other uses an equation of state to describe the gas and a solution
model descibing a deviation from ideal behavior to describe the liquid. Binary experi-
mental data obtained In the present study and from the literature were used to obtain
parameters In both of these model formulations, and to provide the framework for a
model that can be used to describe multicomponent phase equilibrium behavior.
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LITERATURE REVIEW
Several thermodynamic approaches may be applied to the phase equilibrium
behavior of a coal gas-methanol system. When a single gas component is dissolved in a
physical solvent, a conventional gas solubility treatment may be useful. However,
description of the behavior of a multicomponent system involving a wide variety of
species dictates that a more fundamental approach be taken.
It has been shown (Prausnitz, 1989) that the basic equation relating temperature,
pressure, and compositions in coexisting phases at equilibrium is given by equating the
fugacities for each component i in these phases. For vapor-liquid equilibrium,
si - (l)
This equation is not useful, however, until it is known how the fugacity of component i
in each phase can be estimated or related to temperature, pressure and composition in
that phase. Relationships among these quantities will be developed in the sections that
follow.
SOLUBILITIES OF GASES IN A PHYSICAL SOLVENT
Equation I is fundamental to gas solubility calculations, which can be greatly
simplified by assuming Ideality of the gas phase or of both gas and liquid phases. In
solubility calculations, Equation 1 is solved for each gas component, and the solvent In
the vapor phase is neglected.
Binary Correlations for Gas Solubilities
If the solubility of a gas In a liquid is proportional to its partial pressure in the gas
-4-
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phase, the system follows Henry's law:
ll =fk = VlP = #2,1*2 (2)
where subscript 2 refers to the solute, subscript 1 refers to the solvent, and H2ji is the
Henry's law constant for the dissolution of component 2 in component 1. For a given
solute and solvent, this constant depends only on temperature at low or moderate pres-
sures. Rigorously, the Henry's law constant is defined as
H%1 = lim/2/x2 (3)
xz ~co
Equation 2 is not expected to apply when the partial pressure exceeds 10 atm or the
solubility exceeds 3 mole%.
The Krichevsky-Kasarnovsky equation (Krichevsky and Kasarnovsky, 1935)
represents the effect of pressure on the fugacity of a dissolved solute. It has the form
£ -X
In — = la (p Pi ) (4)
where
P* i
II2Jj_ = Henry1 s law constant evaluated at the
saturated vapor pressure of the solvent
V2 — partial molar volume of solute 2 at infinite dilution
pI = vapor pressure of solvent at the system temperature
and where 1 denotes solvent and 2 denotes a gas solute.
Equation 4 can be further extended to include an additional "composition effect"
term that is embodied in an activity coefficient. When this term is assumed fco follow a
two-suffix Margules equation. Equation 4 becomes the Kr i c he vs ky-Il i ask ay a equation
(Krichevsky and Ilinskaya, 1945)
In = In ffP2\ + [xf - 1) + {P ~ p{ ) (5)
2
RT ' ' RT
where A is an empirical constant determined from solubility data. A good example of
-5-
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the application of these correlations for a C02—H20 system has been given by Van
Ness and Abbott (1982).
In. order to find the solubility of a gas in a mixed solvent, the Henry's law constant
may be approximated in an ideal mixture as
M
i2 (6)
3=1,}^i
Henry's law constant for a gaseous solute in a nonideal solvent mixture is given by
0'Cornell (1984) as
M ilf-1 M
ln = £ x] - 2 E ajkxj*k (7)
j-l.j-r-i j=lk>j,kri
where is a binary constant of the jk pair in a two-suffix Margules equation.
Generalized Correlations for Gas Solubilities
A generalized correlation for nonpolar systems was described by Prausnitz and
Shair (1981) and a similar correlation has been given by Ten and McKetta (1962). They
used the regular solution theory in a symmetrical convention activity coefficient
approach. The basic equation has the following form:
1 f\ v2 ($1 — S2) #i
exp
fi RT
xs
where
Sj = solubility parameter of solvent
S2 = solubility parameter of solute
$j_ = volume fraction of solvent
v\ = liquid molar volume of solute
Using' both the liquid molar volumes and the solubility parameters at 25°C, coupled
with the solubility data at 1 atm, the fugacities of a hypothetical pure liquid, f\ , were
calculated and correlated in a corresponding-states plot (/1 /P, vs. T/Tc). Prausnicz
and Shair (1981) have also suggested that an empirical function of the activity
-6-
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coefficient may be used. with, a polar solvent instead of using regular solution theory.
TWs gas solubility correlation for a polar solvent has the form
1 J 2
2 / 2
liry2 = t'j F (T, h2,properties of solvent)
where /f may be the same as in a nonpolar solvent. The correlations are shown in plots
of
ln72 / v\ vs S2
in different solvents. If the solution is under high pressure (greater than 1 atm), the
Poynting correction (earpft/f (P — l)/i2T]) should, be applied to the pure liquid fugacity
/f . The technique of Prausmtz and Shair can be extended readily to mixed solvents by
substituting an average solvent solubility parameter for the pure solvent parameter.
Recently, Sebastian, Lin and Chao (1981a, 1981b) developed a solubility
parameter-based correlation for the solubility of gases in hydrocarbon solvents that
does not require evaluation of the reference state fugacity. Instead, the logarithm of
the undefined activity coefficient (f/x) is expressed as
In (f/x) = In (f/x)p=Q + Pv/RT
The zero-pressure activity coefficient is given as a function of the solubility parame-
ter of the solution, and the temperature T:
ln(//jC)jp —Q ~ +¦ A•,T/E + AgT + A^TS + A5+ Ag(S/T)2 (12)
The coefficients in this equation were determined by correlating the Henry's law con-
stants of the gas in various solvents, and the molar volume (v) in Equation 11 was
determined from high-pressure equilibrium data. This correlation is a form of the
Krichevsky-Kasarnovsky equation (Equation 4). A generalized Henry's constant at
zero-pressure (Equation 12) was used instead of the individual Henry's constant -at the
solvent saturated vapor pressure. This correlation has the capability to correlate with
reasonable accuracy the solubility of a gas in various hydrocarbon solvents.
The use of a group-contribution method to predict gas solubilities has gained atten-
tion recently. When successful, these methods can predict gas solubilities in a varity of
solvents using only a few group parameters. Sander et al. (1983) has shown that the
(9)
(10)
11)
-7-
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UNJFAC method can be applied to predict tlie solubilities of gases in pure and mixed
solvents at low pressures and low solubilities. Antunes and Tasslos (1983) used a
modified UNIFAC model for the prediction of Henry's constant. Tochig and Kojima
(1982) predicted non-polar gas solubilities in water, alcohol, and aqueous alcohol solu-
tions by a modified ASOG method.
VAPOR-LIQUID EQUILIBRIUM
A rigorous way to describe the phase behavior of a gas-solvent system is by applying
a vapor-liquid equilibrium (VLE) approach. This approach applies the fundamental
equilibrium relationships to all of the components in the system, including the solvent.
The range of pressures that are of interest in gas-liquid equilibria or high pressure
vapor-liquid equilibria are from atmosphere pressure to the critical pressure of the sys-
tem under consideration. Hence, the nonidealities of vapor and liquid phases must be
estimated over this range of pressures as a function of temperature, pressure, and com-
positions of vapor and liquid. An excellent discussion of vapor-liquid equilibria at high
pressure has been given by Re id, Prausnitz, and Sherwood (1977).
The vapor-liquid equilibrium working equation has been shown in Equation 1, and
for an N-compoaent system, there are N equilibrium relations. There are 2N variables:
temperature T, pressure P, vapor-phase mole fractions , and liquid-phase mole frac-
tions xt- . Therefore, N variables must be specified to formulate each of the four types of
VLE calculations, which are as follows:
1. Bubble point pressure calculation (BUBLP). This calculation obtains P and y(-
frorn given T and . The calculation starts with an initial estimate of system
pressure and proceeds iteratively by adjusting pressure until the sum of calcu-
lated vapor mole fractions is within a specified tolerance of 1.
2. Bubble point temperature calculation (BUBLT). This calculation obtains
T and wt- , from given P and xi . The calculation starts with an initial estimate
of system temperature and proceeds iteratively by adjusting temperature until
the sum of calculated vapor mole fractions is within a specified tolerance of 1.
3. Dew point pressure calculation (DEWP). This calculation obtains P and from
given T and yi . The calculation starts with an initial estimate of system pressure
and proceeds iteratively by adjusting pressure until the sum of calculated liquid
mole fractions is within a specified tolerance of 1.
-8-
-------
4, Dew point temperature calculation. (DEWT). This calculation obtains T and from
given P and yt- . The calculation starts with, an initial estimate of system tempera-
ture and proceeds iteratively by adjusting temperature until the sum of calculated
liquid mole fractions is within a specified tolerance of 1.
Thermodynamics provides two methods to calculate the fugacities in Equation 1.
The first is based entirely on an equation of state for both the vapor and liquid phases.
The second uses an equation of state for the vapor phase, and a solution model that
uses activity coefficients to express deviations of the liquid from ideal behavior as
defined by either Raoult's or Henry's law. An excellent comparison of these two
methods has been given by Prausnitz (1977); the details of the methods are discussed in
the next two sections.
Kouation-of-S tale Method (Phi Method)
The application of an equation of state to the description of vapor-liquid equilibria
was pointed out a century ago by van der Waals. The first step in such, descriptions is
rewriting the criterion for vapor-liquid equilibrium, shown in Equation 1, in the form
y&i = (13)
where and are fugacity coefficients of vapor and liquid phases, respectively.
These coefficients may be calculated from the following thermodynamic relationships:
CO ru rr*
In t- = -±- f [( — )rr,.. - ]dV In z (14)
1 RT > dn{ V
or
(is)
Equation 14 is more useful than Equation 15 because most equations of state are
pressure-explicit. Equation 14 can be used to calculate the fugacity coefficients of a
component both in the vapor and liquid phases at equilibrium by substituting the
appropriate vapor-phase or liquid-phase volume in the integration. The calculation is
done by iterations until the equilibrium criterion is satisfied.
-9-
-------
The most successful equations of state applied to the calculation of vapor-liquid
equilibria are the Benedit-Webb-Rubiii (33WR) and Redlich-Kwong (RK) modifications.
Recently, Soave (1972) and Peng and Robinson (1976) have modified the Redlich-
Kwong equation, to improve greatly the vapor-liquid equilibrium calculations for hydro-
carbons and simple gases. Extensions of these equations to polar and hydrogen-bonding
components, such as water, have been tested by few researchers (Wenzel and Rupp,
1978; Won and Walker, 1979; Evelein and Moore, 1976; Peng and Robinson, 1980). The
modifications focused on the intermolecular attraction force parameter a in the equa-
tions and the binary interaction parameter in the mixing rules. Vidal (1978), and
Huron and Vidal (1979), however, using a new mixing rule in a two-parameter cubic
equation of state, achieved good correlations of vapor-liquid equilibria of strongly
nonideal mixtures, including a methanol-COg system. Recent developments using
density-dependent local composition (DDLC) mixing rules (Mollerup, 1981; Whiting
and Prausnitz, 1982; Won, 1983; Mathias and Copeman, 1983) offer great promise for
the extension of cubic equations of state to highly nonideal mixtures. The DDLC model
may be useful in the future for gas mixtures obtained from coal which contain com-
ponents covering a wide density range.
Calculation of vapor-liquid equilibria from an equation of state is attractive pri-
marily because it avoids the need to estimate a fugaeity for a liquid reference state for
supercritical components. Secondly, equations of state are readily extended to mul-
ticornponent systems. Unfortunately, no truly satisifactory equation of state has been
established for all kinds of systems and thermodynamic properties. Simple cubic equa-
tions of state with semi-empirical parameters receive more attention because of their
accuracy, simplicity, and applicability over a wide range of conditions.
Activity Coefficient Method (Gamma Method)
The use of the activity coefficient method to calculate vapor-liquid equilibria of a
system containing gas components at high pressures Is an extension of the method
applied at low pressure. Liquid and vapor phases are treated separately in this method.
The vapor phase fugaeity is evaluated from the following equation:
fi=$iViP (is)
The fugaeity coefficient ,- is evaluated from an appropriate equation of state, and it
expresses the deviation of the vapor from ideal gas behavior.
The liquid phase fugaeity is calculated with an activity coefficient that expresses the
- 10-
-------
deviation of that liquid component from an ideal liquid reference state. When activity
coefficients are defined with reference to an ideal solution in the sense of Raoult's law,
the liquid phase fugacity can be expressed by
ff = lA7* (17)
where 7, is the activity coefficient of component i in the liquid solution. This activity
coefficient is defined so that 7t- — 1 as r,- — 1 . The activity coefficient in the expression
is assumed to be a function of temperature and liquid composition, but independent of
pressure.
Activity coefficients can be calculated from many activity coefficient equations
derived from different solution models, such as the Seatchard-Hildebrand, Van Laar,
Margules, Wilson, NRTL and UNIQUAC equations. The Seatchard-Hildebrand equa-
tion does not need binary parameters for most simple fluids that form regular solutions.
The other model equations contain parameters that are determined from binary phase
equilibrium data. The accuracy with which these equations can express equilibrium
behavior depends on the equation used and the polar and/or nonpolar species in the
solution. A group-contribution method such as ASOG or UTNIFAC is particularly useful
when no experimental VLE data are available. However, it should not be used in place
of good data (Wilcox, 1983).
A pure liquid reference state fugacity // for a subcritical component can be calcu-
lated from an exact thermodynamic relationship:
// = Pi 4>i exp
P vL
J — dP
jR 7'
(18)
where p, and are functions of temperature, and vf is a function of temperature and
pressure.
For a supercritical component such as methane or nitrogen, a hypothetical reference
state fugacity must be defined. It is common practice to extrapolate pure liquid fugaci-
ties to a temperature above the critical (Hoffman et al., 1982). The most common
method of extrapolation is to assume that a semi-logarithmic plot of the fugacity versus
reciprocal temperature is a straight line. Chao and Seader (1981), Robinson and Chao
(1971), and Lee et al. (1973) evaluated hypothetical liquid fugacity functions from
large sets of binary VLE data containing supercritical components by using an activity
coefficient equation derived from the regular solution theory. These empirical equations
are expressed as functions of reduced temperature, reduced pressure and a Pitzer acen-
tric factor. The use of these hypothetical liquid fugacity models to evaluate parameters
- 11-
-------
in other activity coefficient equations, however, may be inaccurate.
Another possibly satisfactory method for the use of activity coefficients on supercrit-
ical components is to define a reference state in the sense of Henry's law:
fi = "iUift (19)
where // equals m, the Henry's constant of i in solvent m at the system temperature
and pressure. The effect of pressure on the Henry's law constant, i?,- can be evaluated
from the equation
(20)
where E*m is the Henry's law constant evaluated at pressure and the system tem-
perature. (The Kriehevsky-Kasaraovsky equation is a simplified version of Equation
20.) The activity coefficient is defined so that 7,- -»1 as — 0 , and it must be calcu-
lated by using a corrected equation for the original For an expression of excess
Gibbs free energy gE, there exists a correction gE which yields the correct 7,-
(O'Connell, 1977). The following relationship exists between yi and :
In 7; = In 7j- - lim In 7,- (21)
%i ~o
Prausnitz and Chueh (1968) successfully used a dilated Van Laar model for hydrocar-
bons and simple gases, but no work has been done on polar compounds. Although it is
relatively easy to use a Henry's law reference state for the solute of a binary mixture
(known as the unsymmetrical convention), severe difficulties exist in multicomponent
systems. Because Henry's law constants depend on both the solute and the solvent,
care must be exercised in the definition of reference states and corresponding activity
coefficients when several solvents are present so that they are defined in a thermo-
dynamlcally consistent way (Prausnitz, 1977). Also, some uncertainties exist on how to
define a solute and a solvent, and how to estimate the Henry's law constant in a mixed
solvent. Hence, the Henry's law reference state is not yet practically accepted in appli-
cation to a multicomponent system.
Prausnitz et al. (1980) have developed a computer program chat uses the virial
equation of state to describe the vapor phase and optional activity coefficient equations
such as UNIQUAC, Wilson, NRTL, Margules, and van Laar to describe the liquid
phase. The Raoult's law reference state was used when the component was condensible,
and an arbitrary function was used when the component was noncondensible. The
&ifm = H,;,m exp
P 00
vi
f
KT
dP
- 12-
-------
program gave good multicomponent results when system temperatures were well below
the critical temperature of each component. However, when system temperatures were
near or above the critical temperature of one or more of the components, the multicom-
ponent predictions were in error, even though data on all the binary pairs were fit well.
Davis and Kcrrnode (1977/1978), using a computer program of Prausnitz et al.
(1987), evaluated Wilson parameters for systems containing H2, N2, CO,
C02. CH4, H2S, CH3OH, and H20. They suggested that the minor constituents having
low solubility might be lumped with the major constituents having low solubility in a
cold methanol absorption process. The necessary binary parameters would be reduced
greatly to the number of parameters between all the binary combinations of methanol,
C02. H2S and major low-solubility components such as H2. Although assumptions were
reasonable, no practical calculation was shown.
PHYSICAL PROPERTIES AND BINARY DATA SETS
Physical properties for pure components and binary VLE data are necessary in
almost all the vapor-liquid equilibrium calculations. Physical property data and their
correlations for gases and liquids are well presented by Reid et al. (1977), and by Yaws
(1977). Critical PVT properties, the Pitzer acentric factor, the solubility parameter,
liquid molar volume, and vapor pressure are some of the important physical properties
in vapor-liquid equilibrium correlations. Wichterle, Li nek and I la I a (1973/1983) have
compiled four volumes of the "Vapor-Liquid Equilibrium Data Bibliography" which list
the VLB literature published before 1983.
Many efforts have been devoted to binary systems involving methanol, carbon diox-
ide, nitrogen, hydrogen, carbon monoxide, sulfur gases, hydrocarbon gases, and water.
Most of the methanol-gas and water-gas binary mixtures provide P-F-ardata or solubil-
ity data. Excellent discussions of converting solubility data to a useful form of vapor-
liquid equilibrium data are given by Friend and Adler (1957), and Adler (1983a. 1983b).
Unfortunately, there is no way to check the thermodynamic consistency of these data.
Although some sources of data report vapor-phase compositions, methanol and water
concentrations in the gas are usually very low and often inaccurately measured.
Discrepancies between the data of different laboratories are often found, and selection
of data from the literature is achievied primarily by eliminating obviously erroneous
information. Table 2 gives a list of binary mixtures formed from species present in most
acid gas removal systems that process gases from coal. Binary data for each of these
binary mixtures are required for model development, and Table 2 shows those systems
for which such data were found in the literature.
-13-
-------
Table 2. Check List of Binary Data Sets Including Major Components from Coal Gasification.a
MeOH
MeOH
CO?
H2S
N2
COS
CH4
H2
CO
C2H6
C3H8
H2O
C2H4
CH3SH
CH3SCH3
C2H5SH
C02 H2s
n2
COS CH4
H?
CO
C2H6
c3H8
h2o
C2H4 CH3SH CH3SCH3 C2H5SH
X X
X
x +
X
+
0
0
X
X
XXX
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
+
X
X
X
+
X
X
X
X
X
X
X
X
X
X
+
+
+
+
X
X
X
X
X
X
+
a Symbols: x
0
+
= P-x-T or P-x-y-T data available
= Not enough Isothermal data available
= Only solubility data available
-------
PRINCIPLES OF BINARY VLE DATA REDUCTION
Vapor-liquid equilibrium calculations, either by the equation-of- state method or by
the activity coefficient method, require binary parameters in most of the models to
predict multicomponent behavior. The binary parameters must be obtained from
experimental VLE data fit by an appropriate model. Poor fit of a model to binary data
can result from three possible sources; (1) inaccurate data, (2) an inappropriate model,
(3) the method of reducing the data. There are various ways to reduce VLE data, rang-
ing from simple curve fitting to the application of sophisticated statistical principles.
Prausnitz (1977) has pointed out that the procedure used to obtain model parameters
from limited experimental data was often more important than details within the
model. However, Van Ness and Abbott (1982) have a different point of view. They
recognize that the improvement of parameters from a sophisticated data reduction
method still depends on the quality of data and the appropriateness of the model.
A static equilibrium cell is often used in measuring vapor-liquid equilibrium data.
Because direct sampling of the vapor phase in such systems usually upsets the equili-
brium condition, vapor-phase data are often neglected in the literature. The Gibbs-
Dtihem theorem allows the use of a set of P-T-x data to calculate corresponding values
of y. The method of Barker (1953) uses this thermodynamic theorem, and it is it is easy
to use, efficient, and in some cases the only way to correlate binary vapor-liquid equili-
brium data for the system of interest. For these reasons, the Baxker method was
adopted in the present work
Originally, Barker (1953) introduced a procedure to evaluate activity coefficient
model parameters in the Scatchard equation from total pressure measurements.. The
two essentials of the Barker method are (1) only P- T-x data are necessary, and (2) a
least squares routine is applied. Others, such as Of ye and Prausnitz (1985), Renon and
Prausnitz (1968), Holmes and Winkle (1970), and Nagahama, Suzuki and Hirata (1971),
used the Barker method with different objective functions and P-T-x-y data to evaluate
van Laar, Margules, Wilson or XR.TL parameters. Abbott and Van Ness (1975) did a
series of vapor-liquid equilibrium parameter searches on the Margules equation with
both numerical and Barker method. They concluded that reliable P-x data only were
required to provide reliable VLE relationships. Moreover, the use of the reported y
values along with P-x data in the data reduction process distorted the ¦ correlation of
both P-x and y-x relationships.
In recent years, VLE data reduction has focused on the maximum likelihood princi-
ple (see Fabries and Renon, 1975; Peneloux et al., 1976: Sutton and Macgregor, 1977;
Anderson et al., 1978; Nean and Peneloux, 1981; 1982; Kemeny et al., 1982: Patino-
Leal and Reilly, 19S2). This statistical principle considers errors in all measured vari-
ables and it weights the data properly. The estimated deviation method and the
observed deviation method are both based on the maximum likelihood principle. These
- 15-
-------
two methods lead to the same model parameters and the values do not depend on the
fitting functions when an appropriate weighting method is used (Nean and Peneloux,
1981). The observed deviation method has advantages over the estimated deviation
method, one of which is that it is easier to implement. Actually, the application of the
maximum likelihood principle is achieved by calculating the appropriate weighting fac-
tor for every measured variable of each data point in an objective function. The vali-
dity of the techniques rests on the presumptions that the data set is free of systematic
error and that the correlating equation does not itself introduce error (Van Ness and
Abbott, 1982); random error is corrected by system statistics. However, the presump-
tions in these statistical treatments are often not met by VLE data.
- 16-
-------
RESEARCH SYSTEMS, APPROACHES, AND OBJECTIVES
The compounds, shown in Table 1, found in an acid gas removal system used to
condition gases from a coal gaaifier can be classified according to volatility into three
groups. The first group contains the supercritical components hydrogen, nitrogen, car-
boa monoxide, and methane; the second group contains gases that are condensable at
the system conditions, such as carbon dioxide, hydrogen sulfide, carbonyl sulfide,
ethylene, ethane, propane, etc.; the third group includes components that are typically
liquids at system conditions, such as methanol, water, mercaptans, and aromatic hydro-
carbons. Figure 1 shows this arbitrary classification in terms of fluid density and molec-
ular interactions. The most important interactions in the liquid of an acid gas removal
system are those between methanol and the rich components having high solubilities,
followed by those between methanol and the lean components with high solubilities and
rich gaseous components with lovsr solubilities. Although the interactions between the
gaseous solutes in the liquid will be relatively less important than other interactions, a
rigorous model includes all interactions in both the liquid and vapor phases. Methanol,
carbon dioxide, hydrogen sulfide and other sulfur species may be considered the key
components in an acid gas removal system because they are the primary subjects in the
process. Because there are no chemical reactions and no electrolyte species present,
only physical interactions between component molecules in the vapor and liquid phases
were considered in developing a model of mixtures containing these components.
Both the equation-of-state and the activity coefficient approaches were used to
describe the equilibrated systems containing methanol. An extended Soave-Redlich-
Kwong equation of state was chosen for use in the first approach because of its simpli-
city and its capability in describing hydrocarbons and gases. The equation has been
further extended to describe systems containing polar components. UNIQUAC, Wilson,
and Four-Suffix Margules equations were used in the second approach. These equations
are well known for their capabilities in handling strongly nonideal liquid mixtures and
require well-defined liquid reference states. All of the components in Group HI and
some components in Group II can be handled by an activity coefficient equation.
The primary objective of this research is to develop generalized thermodynamic
models to describe the vapor-liquid equilibrium behavior of systems containing
methanol and the constituents from coal gasification. The specific tasks of this study
are as follows:
- 17 -
-------
Figure 1. Classification and Interaction Relationships of
Constituents from Coal Gasification and Methanol.
18
-------
¦1. Develop parameter estimation methods for the extended SRK equation of state
and for the activity coefficient equations.
2, ¦ Collect the necessary binary VLE data and evaluate the binary model parameters.
3. Develop multicomponent bubble point calculation programs with both the
equation-of-state and the activity coefficient methods, and compare the model cal-
culations with the binary and ternary VLE data.
4, Formulate a gas solubility calculation using the extended SRK equation of state
that will be a practical and useful method for the estimation of solubility of each
component in methanol or a mixed solvent.
5. Design and construct a high-pressure vapor-liquid equilibrium apparatus.
8. Test the apparatus and experimental procedure by measuring VLE data for
methanol-carbon dioxide mixtures and comparing with data from the literature.
7. Obtain ternary methanol-carbon dioxide-nitrogen P-T-x-y data at 243.15 and
273.15 K to evaluate the mixed gas solubility calculation.
8.' Obtain the ternary methanol-carbon dioxide-water P-T-x data at 243.15, 258.15,
273.15, and 298.15 K to evaluate the bubble pressure calculation and the gas solu-
bility calculation in a mixed solvent.
- 19-
-------
MODELING PHASE EQUILIBRIA WITH AN
EQUATION OF STATE
An equation of state that can be used to describe all fluid phases has many adyan-
tages in phase equilibrium calculations. Most importantly, it eliminates the troublesome
necessity of defining a reference state for a multicomponent mixture that includes one
or more supercritical components. Simple cubic equations of state, such as the Soare-
Redlieh-Kwong (Scare, 1972) and the Peng-Robinson (1976), hare been useful in phase
equilibrium calculations. The SRK equation of state was originally deyeloped to
describe the phase equilibrium behavior of hydrocarbons, and the inclusion of a binary
interaction parameter in the equation has extended its range to include nonhydroear-
bons. Incorporating a temperature dependence of the binary interaction parameters
and/or a polar correction factor may further extend its application to systems contain-
ing polar compounds (Eyelein and Moore, 1976; Chang et al., 1983; Mathias, 1983). An
extended SRK equation of state with a Mathias (1983) polar correction factor was
employed in this work. It is described in the following section.
THE EXTENDED SRK EQUATION OF STATE
The SRK equation of state has the form
p _ —KH.— _ (22)
(v — b) v(v + b)
For any pure component, the constants a and b are found at the critical point to be
0.42747 R2Tc
«(Tt) = = p (23)
0.08664 RT,
b = (24)
Pc
- 20 -
-------
Soaye (1972) expressed a as a function of temperature and held b constant, so that
a(T) = aca(T) (25)
where the quantity a is a function of temperature. An expression used here is given by
Mathias (1983) as
<*0.5 = 1 + m(l - rr0-3) p(i rr)(0.7 TV) (28)
The first and second terms on the right side of Equation 28 were introduced by Soave
to correlate m as a function of the acentric factor and reproduce the vapor pressures of
nonpolar hydrocarbons. Graboski and Daubert (1978a) used a regression program to
evaluate m based on a large API vapor pressure data set for hydrocarbons and gases to
obtain
m = 0.48508 + 1.55171 to - 0.15613 to2 (27)
Although use of the Soave a temperature function calculates vapor pressures of hydro-
carbons and gases accurately, it can not do the same for vapor pressures of polar com-
pounds such as water and alcohols. Mathias (1983) introduced the third term on the
right side of Equation 26 for this purpose; it uses a correction term p that is obtained
by fitting the equation to the vapor pressure data of the system component. This polar
correction factor uses only one temperature-independent parameter and enables accu-
rate calculation of the vapor pressures of the polar compounds.
The extended Soave-Redlich-Kwong equation can be applied to mixtures using the
mixing rules
N N
a = 2 2^¦xjaij
i=ij=i
and
N M
b = 2 2^/%
where the cross parameters are given by
a,-j = (tt.-fl,)0'5 (1 - Ktj) (30)
- 21 -
(28)
(29)
-------
(bt +¦ b,)
0-- c{j)
(31)
and K^j and Cty are interaction parameters.
In a previous study (Chang et aL, 1983), KtJ- was expressed as a function of tem-
perature for systems containing methanol:
K,i = + K,l,T(K)
(32)
Mathias (1983) has suggested that Ci} should also be expressed as a function of tem-
perature;
C;j = Cj} + Ci)-T(K)
(33)
The evaluation of fugacity coefficients from the SRK equation of state is made
easier with the definitions
z =
A =
Pv
RT
aP
R2T2
bP
RT
(34)
(35)
(36)
Equation 22 then can be written as
zz — (A — B — D'2)~ — AB = 0
(37)
A generalized treatment of the system allows evaluation of the fugacity coefficient of
any component in a mixture from Equation 14
in = /
R T JF
, dP x _ RT_
drij y
In
(14)
Using the extended SRK equation in Equation 14 gives
-22-
-------
In 4>i
6,-(* - 1)
In (z B)
A in (1 + Biz)
B
N XjGij
k
/ = !
a
(38)
Equation 38 can be used to calculate the fugacity coefficients of a component in
both, liquid and gas phases at equilibrium. In these calculations, the compressibility fac-
tor z is obtained by solving Equation 37. The largest root of Equation 37 is used to
evaluate gas-phase fugacity coefficients: the smallest root is used to evaluate liquid-
phase fugacity coefficients. The advantage of solving Equation 37 rather than using
Equation 22 is. that'the compressibility factor is, in most cases, between 0 and 1, while
the volume, v, is unbounded. Equation 37 can be solved by a Newton convergence tech-
nique with initial estimates of the compressibility factor being set at 1 for the gas phase
and 0 for the liquid phase. The iteration proceeds until the absolute value of the left
side of Equation 37 is less than 10"14. This tight tolerance is essential for calculation of
liquid phase behavior where compressibility is very small (< 0.03).
EVALUATION OF THE POLAR CORRECTION FACTOR
Successfully predicting multieomponent VLE behavior begins with a procedure for
accurately calculating pure-component vapor pressures. Soave (1972) introduced a gen-
eralized temperature function in the SRK equation that forces the equation to correlate
accurately the vapor pressures of nonpolar and slightly polar substances. Mathias
(1983) added a polar correction term in the Soave temperature function. Although this
term has only one temperature-independent polar correction factor, p, Mathias was
unable to correlate this factor with other molecular properties. Therefore, this polar
correction factor must be evaluated for each polar component in the system of interest
before applying the extended SRK equation to binary or multieomponent systems.
The polar correction factor can be evaluated by matching the calculated vapor pres-
sures from the equation with vapor pressure data of the polar compound. Figure *2
shows a logic flow diagram for evaluating this factor. An optimized value of p can be
obtained by minimizing an objective function of the sum of vapor pressure variances
for n temperatures using a Fibonacci search technique. As the polar correction factor is
expected to be close to zero, setting p equal to zero is an excellent place to start the
search for this quantity. A vapor pressure calculation corresponds to evaluating a
pure-component vapor-liquid equilibrium condition; this is done by adjusting pressure
until the ratio of liquid-phase fugacity coefficient to vapor-phase fugacity coefficient is
one. A computer program ASAIN (see Chang 1984) is available for the polar correction
factor evaluation.
-------
Figure 2. Logic Flow Chart for Polar Correction Factor
Evaluation.
24
s
-------
Table 3 lists several values of p for polar components of interest for this study. The
vapor pressure data were calculated from the Antoine equation with, constants from
Reid et al. (1977). Table 3 also lists the values of p for methanol and water that were
given by Mathias (1983). The polar correction factors are large for methanol and water,
and the improvements in fitting their vapor pressures are significant. However, the
polar correction factor is relatively small for methyl mercaptan. The p values for ethyl
mercaptan and dimethyl sulfide are near zero, so that the correction to the SRK equa-
tion may not he necessary for these two compounds. The polar correction factors for
hydrocarbons and other gases are assumed to be zero because the SRK equation calcu-
lates their vapor pressures very well.
TABLE 3
POLAR CORRECTION FACTOR
Compound
Optimal p Value
Temp. Range
*
Avg % Dev.
Mathias
This Work
K
P—0
p fitted
MeOH
0.2359
0.2208
213-513
11.92
1.18
h2o
0.1277
0.1282
273-843
7.18
1.05
CHgSH
C2fLSH
CHgSCHg
-
0.0237
200-300
3-83
1.85
-
0.0010
-0.0012
225-330
225-330
1.05
0.96
1.03
0.98
* Where the average % deviation is defined by,
» I p - f , I
Avg Dev = 2 — £ffLi
l n
and n equals the number of data points.
BINARY PHASE EQUILIBRIUM AND INTERACTION
PARAMETER EVALUATION
The use of the SRK equation to perform binary vapor-liquid equilibrium calcula-
tions for a hydrocarbon-hydrocarbon system has been found to be very accurate. When
a binary system contains a non-hydrocarbon, the SRK equation must include at least a
-25-
-------
temperature-independent binary interaction parameter (/T,in Equation 30). For a sys-
tem containing a polar component, temperature-dependent binary parameters are
necessary. Evaluation of these parameters is from binary mixture data, and preferably
from phase-equilibrium data. According to Graboski and Daubert (1978b), the best cri-
terion for selecting the optimal interaction parameter is a minimization of the bubble
point pressure variance, as defined by the equation
cr"
ml
(39)
k = l
This criterion was used in two optional search procedures to evaluate the binary
interaction parameters in the extended SRK equation. In the first procedure, a single-
variable Fibonacci search technique was used to determine a temperature-independent
optimal interaction parameter. The experience in this study suggests two ranges of this
parameter to begin the search procedure. One is from 0 to 0.25 and the other is from
-0.3 to 0. A computer program BFAIN (see Chang 1984) is available to evaluate a
temperature-independent binary interaction parameter such as Ki}- by fixing % equal
to zero. In the second procedure, a multivariable pattern search was used to determine
the optimal A'A, 0$, and Ct) . Zero is a good starting value in the estimation of
these parameters. However, the search for the first two may take the values reported
previously (Chang et at., 1983) as initial estimates. The parameter search may need a
small initial step size (0-0001) to prevent the parameters from jumping out of the range
in which the equation of state can perform the calculation using that adjusted parame-
ter set. Hence, the pattern search takes a very long computing time (30 to 120 minutes
on VAX 11/780, depending on the system and the number of data points). A computer
program PTAIN is available for the above purpose (see Chang 1984). Figure 3 gives a
schematic diagram outlining the calculations.
Binary P-T-x data were used in the parameter evaluations. The calculated pressure
for each data point was evaluated through a bubble point computational routine using
the given values of temperature and mole fraction. The'criterion for this equilibrium
calculation has been shown to be
Vib? = Xi$i (13)
xr r
where <}>,- and (|>t- are obtained from Equation 17. Iterations proceed until mote frac-
tions in the vapor phase sum up to one. Double precision and tight tolerances in both
the Newton convergence technique, the absolute magnitude of the left hand side of
Equation 37 < 10-14) and bubble point pressure calculations ( 1 2/s- — JL I
-------
Figure 3. Logic Flow Chart for Binary Interaction constant
Evaluation in the Phi Method.
27.
-------
pressure computational technique is given in Figure 4.
In addition to the binary parameters referred to above, the extended SRK equation
of state requires critical temperature, critical pressure, acentric factor, and polar correc-
tion factor for each of the components of a mixture. Table 4 lists the values of these
properties for the components of interest in this study.
Interaction parameters for the binary mixtures formed by methanol, carbon diox-
ide, hydrogen sulfide, nitrogen, carbonyl sulfide, hydrogen, carbon monoxide,' methane,
ethane, ethylene, propane, propylene, methyl mereaptari. dimethyl sulfide and water
were evaluated from binary equilibrium or solubility data that cover the operating tem-
perature and pressure ranges for an acid gas removal system that uses refrigerated
methanol as a solvent. The interaction parameters of gas-gas systems were assumed to
be independent- of system temperature, but the interactions parameters in methanol-gas
systems were assumed to be linearly dependent on temperature.
-------
I
Output Ps y-j4 FB
Figure 4. Logic Flow Chart for Bubble Point Pressure Calculation
in the Phi Method.
-------
TABLE 4
PURE COMPONENT PHYSICAL PROPERTIES2"
Component
Tc (K)
Pc (atm)
V (ml/mole)
ft)
P
H2
33.19b
12.98b
65.0
-0.220
0.00
N2
CO
126.2
33.5
89,5
0.040
0.00
132.9
34.5
93.1
0.049
0.00
ch4
190.8
45.4
99.0
0.008
0.00
c2h4
282.4
49.7
129.0
0.085
0.00
C3H8
C H
305.4
48-2
148.0
0.098
0.00
385.0
45.6
181.0
0.148
0.00
389.8
41.9
203.0
0.152
0.00
co2
H.,S
304.2
72.8
94.0
0.225
0.00
373.2
88.2
98.5
0.100
0.00
COS
378.8C
62.88°
135.0C
0.099
0.00
CH..SH
C2HgSH
470.0
71.4
145.0
0.155
0.0237®
499.0
54.2
207.0
0.190
0.0010®
CH3SOH3
MeOH
503.0
512.8
54.6
79.9
201.0
118.0
0.190
0.559
-0.0012e
0.2359d
h2°
647.3
217.6
56.0
0.344
G.1277d
a Reid et al. (1977)
b Lin (1980)
c Robiasoa and Seaturk (1979)
d Mafchlas (1983)
e Evaluated by program ASAIN
-30-
-------
Methanol-Supercritical Gases
Supercritical gases that are present in large amounts in the raw gas from coal
gasification include hydrogen, nitrogen, carbon monoxide and methane. The quantities
of these gases can sum to 70 to 75 mole% of the total produced gas. These gases are
classified in Group I, as shown in Figure 1, because they have low fluid densities and
similar molecular properties. The solubilities of these gases in methanol may be
sufficiently large to represent a significant economic loss at an extremely low tempera-
ture and high pressure. An accurate description of the binary phase equilibria of these
gases in methanol is necessary for the development of an extended SRK equation that
can be used to describe the phase equilibria of multicom.pon.enfc systems containing coal
gas and methanol.
Several modified versions of the SRK equation of state can be used in phase equili-
brium calculations involving supercritical components, especially hydrogen. Hydrogen
creates specical problems because it is a quantum fluid. Grabosfci and Daubert (1979)
replaced the temperature function a in the SRK equation with an exponential function
to be used with the "classical" critical constants Te = 41.67 K, Pc = 20.75 aim, and co
= 0. These constants are estimated on the basis of classical mechanics which do not
take quantum effects into account. Boston and Mathias (1980) have suggested a gen-
eralized extrapolation of a at a supercritical temperature for a supercritical substance.
However, Lin (1980) used the original temperature function a, even for hydrogen, with
the true critical constants and acentric factor: Tc = 33.19 K, Pc = 12.98 atrn, and to
= -0.22. Lin's approach was used in this work because it is simple and it may be the
best way to handle supercritical components. Since the function a proposed by Soave is
well behaved, the adoption of other a functions for supercritical components is
unnecessary.
The solubility data of hydrogen, carbon monoxide, and methane were read from the
chart prepared by Landolt-Bornstein et al. (1978) and were converted to Henry's con-
stants (see Chang 1984) at four temperatures. A set of P-T-s data was then generated
by using Henry's law calculations for each gas component. Under the absorption
operating conditions, the solubilities of these gases follow Henry's law very well. The
data from this source cover a broad range of temperatures, and they are believed to be
reliable because they match the data from other sources (Krichevskii et al., 1937; Kri-
chevskii and Efremova, 1951; Michels et al., 1953) at room temerature.
The generated data were used to evaluate the binary interaction parameters in the
-31-
-------
extended SRK equation of state for the methanol-hydrogen, methanol-earbon monox-
ide, and methanol-inethane systems. The four parameters in the equation for each
binary" system were determined simultaneously, and the resulting optimal parameter
sets are listed in Table 5. The generated data sets coyer a temperature range from 223
to 303 K and a pressure range from 1 to 60 aim; each data set has a total of 18 calcu-
lated points.
Methanol-Hydrogen System-
Figure 5 shows an excellent fit of the calculated bubble point pressures to the gen-
erated data. The root mean square deviation of bubble pressures (RMSD%) is less than
1%. The solubility of hydrogen in methanol increases with increasing temperature. The
temperature effect on gas solubility can be qualitatively obtained by analyzing the
terms' in partial molar entropy or enthalpy change. A detailed discussion has been given
by Prausnitz (1969). Generally, the solubility for a sparsely dissolved gas increases with
temperature.
Methanol-Carbon Monoxide System-
Figure 6 shows a good fit of the calculated values to the generated data. The root
mean square deviation of bubble pressures is less than 3%. The solubility of carbon
monoxide increases as the temperature decreases.
Methanol-Methane System-
Figure 7 shows an excellent fit of the calculated results to the generated data. About
a 2% deviation was found in the fitting process. The solubility of methane in methanol
obviously increases as the temperature drops.
Methanol-Nitrogen System—
The data of Weber and Knapp (1978) were used to evaluate the interaction parame-
ters in this system. The data cover a temperature range from 225 to 300 K and a pres-
sure range from 20.7 to 177 atm. Although a previous paper (Chang ei al., 1983) used
only the temperature-dependent interaction parameter iTt-y to fit the data, both
temperature-dependent parameters Ki}- and C,-y are included in this work. The results
of fitting the data are shown in Table 5 for a total of 21 data points; the root mean
square deviation of bubble pressures was 2.24%. Figure 8 shows the excellent fit of the
calculated results to the data.
- 32-
-------
Table (5. Correlations of VI.E Binary Pairs Containing Methanol or Water.
. Ka1 _ Kb1 RMSDa Ranges No.
System Kau _ «bU - % EyD of Ref.
(10~J) (10~T, K P, atm data
MeOH-H2
-1,
.4849
3.3560
-2
.0324
6.4330
0.87
-
223-
-303
1.0-60.2
16
c
MeOH-CO
-0,
.4455
0.6615
-0
.4702
0.8860
2.60
-
223-
-303
1.0-60.2
16
c
MeOH-N2
-0,
.3537
0.5240
-1
.1193
4.2590
2.24
-
225
-300
20.7-177.0
21
d
MeOH-CH4
-0,
.2650
0.7882
0
.0228
-0.7030
2.11
-
223-
-303
1.0-60.2
16
c
MeOH-C2H4
-0,
.2655
0.8885
0
.2765
-1.1000
2.36
-
228-
-248
1.0-18.0
18
e
MeOH-C2H6
-0.
.2318
0.8925
0
.0887
-0.4030
4.79
-
248-
-323
10.0-60.0
21
f,
.g
MeOH-C3H6
-0,
.2349
0.8434
0
.0840
-0.0510
2.44
-
228-
-303
1.0-1.2
9
c
MeOH-C3Ha
-0,
.1140
0.4066
-0
.2349
0.9930
8.90
-
238-
-303
1.0-7.9
19
C,
,h
Me0H-C02
-0.
.0740
0.3767
0
.2332
-0.5905
4.61
-
223-
-313
1.0-79.5
130
i-
¦o
MeOH-H2S
-0,
.0502
0.3286
0
.1710
-0.0190
4.84
-
248-
-273
2.0-10.0
22
1
MeOH-COS
-0,
.1418
0.6720
0
.0585
0.1690
6.23
0.0011
233-
-293
0.38-11.1
51
P
MeOH-CH3SH
0.
.0197
0.1500
-0
.1334
1.0770
5.55
-
263-
-288
0.19-1.38
18
q
MeOH-CH3SCH3
-0.
.0272
0.2140
-0
.1511
1.1120
6.88
-
263-
-288
0.08-0.45
24
q
MeOH-H20
-0.
.1638
0.2090
-0
.0733
0.3280
2.44
0.0141
298-
-338
0.04-1.02
72
r-
¦u
H20-C02
-0,
.5135
1.2492
0
.3694
0.0673
4.40
-
273-
-298
1.0-36.0
93
V
RMSD % = { e [(Pe - Peal)/Pe3/n}^ x 100 % , where n = no. of data points,
h n 1
Ey = [ e |yie - yicall^/n. c Landolt-Bornsteln et al. (1976).
^ Weber and Knapp (1978). . e Shenderel et al. (1962). ^ Ma and Kohn (1964).
9 Ohgaki et al. (1976). n Nagahama et al. (1971). Krichevskii and Lebedeva (1947).
J Bezdel and Teodorovich (1958). Shenderel et al. (1959). Yorizane et al. (1969).
¦" Katayama et al. (1975). n Ohgaki and Katayama (1976). 0 This work. p Oscarson (1981).
J Jackowskl (1980). r Butler et al. (1933). s Ratcllff and Chao (1969).
McGlashan and Williamson (1976). 11 Kooner et al. (1980). v Houghton et al. (1957).
-------
Mole Fraction x CH2)
Figure 5. Methanol-Hydrogen Equilibria.
34
-------
o
o
Figure 6. Methanol-Carbon Monoxide Equilibria.
35
-------
Figure 7.' Methanol-Methane Equilibria.
36
-------
o
LO
cy
o
o
W
£ o
*
CO °
Data of Ueber and Knapp (1978)
B . 22SK
X 2S0K
A. 275K
• 4- 30 OK •, 3QQK
'«]' w»j
250IC
225K
27 EK
SRK with Fitted KM> C;i
U3
o
o
©
C
3
m
®
L
P-
cc
if °
O o
I— U3
0.00 0.01 0.02 0.03 0.04
Hole Fraction x
-------
Binary Parameters Ki}- and
-------
Figure 9. Binary Interaction Parameters for Methanol-
Supercritical Gases.
39
-------
Temperature , K
Figure 10, Binary Interaction Parameters' ; for Methanol-
Supercritical Gases.
40
-------
o
Hole Fraction x CC2H4)
Figure 1U Methanol-Ethylene Equilibria.
41
-------
o
*
o
CD
m
Data of.He and Kohn (19S4)
Data of Qhgaki et el.. C197£>
SRK with Fltied Kjj, C-jj_
323.1SK
0.0 0.2 0.4 0.6 0.8
Mole Fraction x, y (C2H6)
Figure 12, Methanol-Ethane Equilibria.
42
-------
each, of the isotherms in Figure 12 at ethane mole fractions of about 0.23 in the
methanol-rich phase, although the experimental data show phase separation at ethane
mole fraction of 0.4. The portions of calculated equilibrium curves which show local
maxima and minima represent metastable phase equilibrium conditions. Figure 12 gives
the P-x plot at 323.15 K, a temperature above the critical point of ethane. The vapor
(ethane-rich) curve has detached from the pure ethane edge, and it shows a large
change in curvature. Detailed phase diagram calculation near the critical region is
beyond the scope of this work, but Hong et al. (1983) and Streett (1983) have given
good discussions and diagrams for similar systems at high pressure.
Methanol-Propylene System—
The converted P-T-x data from the solubility chart (Landolt-Bornstein et al., 1978)
were used to evaluate the binary parameters. These converted data have a temperature
range from 228 to 303 K and pressures around 1 atm. Table 5 lists the optimal set of
parameters. Because the extended SRK equation can be applied to a wide range of tem-
peratures and pressures, the evaluated parameters are believed sufficient to extend the
application of the available data to pressures higher than 1 atm.
Metfaanol-Propane System—
The data of Nagahama et al. (1971) at 293.05 K and the P-T-x data calculated
from the solubility chart (Landolt-Bornstein et al,, 1976) were used together to obtain
binary parameters in the extended SRK equation. The optimal values of the parameters
are listed in Table 5. The root mean square deviation of bubble pressures is high, about
8.9%, because the calculated values do not agree with the experimental data at pro-
pane mole fractions in the liquid exceeding 0.3. Figure 13 shows the calculated bubble
pressures and the experimental data of Nagahama et al. (1971). The calculated results,
which show local maximum and minimum, may belong to metastable state solutions,
and they imply that a LLC equilibrium condition is predicted by the equilibrium calcu-
lation from the cubic equation of state. Another justication for this discrepancy
between the data and calculated values is that the quadratic mixing rule in the equa-
tion may be insufficient for a mixture of methanol and propane at high pressure. The
system cannot be correlated by the quadratic mixing rule since' a large miseibility gap
would be predicted.
Binary Parameters K{,- and
Figure 14 shows the dependence of Ki}- on temperature for the binary systems
methanol-ethylene, methanol-ethane, methanol-propylene, and methanol-propane over
the range of temperatures from 220 to 320 K. The values are between -0.07 to 0.05, and
-43-
-------
m Data of Nagahama et el. CI9715
— SRK with Ffiled Kjjf Gjj
0.0 0.2 0.4 0.6 0.8
¦ Mole Fraction x CC3H8)
Figure 13, Methanol-Propane Equilibria.
44
-------
Temperature , K
Figure 14. Binary Interaction Parameters for Methanol-Light
Hydrocarbon Gases.
45
-------
they increase with increasing temperature. Figure 15 shows the dependence of C,-y on
temperature. All values of (7,-y are between -0.08 and 0.08. Note that the temperature
dependence of both parameters for the methanol-C3H8 system is quite different than it
is for the other three systems. This could simply be the result of a relatively poor fit of
the binary data by the equation of state for the methanol-C3Hg system at high pres-
sures.
Methanol-Acid Gases
Carbon dioxide, hydrogen sulfide, carbonyl sulfide, and mercaptans are the primary
components whose removal is desired in an acid gas removal system. The phase equili-
brium behavior of these acid gases in methanol has great importance in the
absorption-stripping operations of acid gas removal systems. Optimal operation of the
system may be geared to maximize the removal of these acid gases and to separate the
sulfur species from carbon dioxide. Conditions leading to optimal operation can be
determined by using an appropriate model of the phase equilibrium behavior in the
design of the system. 'The data from the binary systems presented here cover a broad
range of temperatures and pressures, including those found in acid gas removal systems
using methanol as a physical solvent. The data are used to evaluate all four binary
interaction parameters in the extended SRK equation, and thereby develop a model
useful for the prediction of multicomponent phase equilibrium behavior.
Methanoi-Carbon Dioxide System—
This binary system is the most important system under consideration, since carbon
dioxide occupies about 20 to 35 mole% of the product gas from coal gasification, and it
has a very large solubility in methanol. The data of Krichevskii and Lebedeva (1947),
Bezdel and Teodorovich (1958), Shenderei et al. (1959), Yorizane et al. (1969), Katay-
ama et al. (1975), Ohgaki and Katayama (1976), and the data generated in this labora-
tory (see experimental) were used to evaluate binary interaction parameters. These
data have a temperature range from 223 to 313 K and a pressure range from 1.0 to 79.5
atm. The data of Krichevskii and Lebedeva (1947) at 298.15 K were not used because
they have large deviations from model calculations; these deviations are over five times
the average error of the data of Katayama et al. (1975), and Ohgaki and Katayama
(1976) from model calculations.
Table 5 lists the values of the optimal binary interaction parameters. The root
mean square deviation of bubble pressures was less than 5% for a total of 130 data
points. The pressure-liquid composition diagram of Figure 16 shows the fit of the calcu-
lated values to the data. Small discrepancies exist between the literature data at 298
-46-
-------
o
Temperature ,K
Figure 15. Binary Interaction Parameters for Methanol-Light
Hydrocarbon Gases.
47
-------
o
Hole Fraction x(C02)
Figure 16. Methanol-Carbon Dioxide Equilibria.
48
-------
and 273 K. As shown in Figure 18, the calculated bubble pressures at 298 K are higher
than, the literature data when the carbon dioxide mole fraction in the liquid is less than
0.6, while the calculated bubble pressures at 273 K are lower than the literature data.
On the other hand, the experimental data from the present work seem to be fit well by
the model calculations. Although Figure 16 does not show the predicted vapor-phase
compositions, the extended SRK equation of state gives very good agreement with the
21 data points for which vapor compositions were measured; the average deviation of
carbon dioxide mole fractions in the vapor phase was 0.0007. The data used for com-
parison with the SRK equation were taken at 298.15 K by Katayama et al. (1975) and
Ohgaki and Katayama (1976).
Methanol-Hydrogen Sulfide System—
The data of Yorizane et al. (1969) were used exclusively in this study to determine
the interaction parameters for this binary system. The data include liquid-phase com-
positions at temperatures of 248, 258, and 273 K and at pressures from 2 to 10 atm.
Table 5 lists the binary parameters in the extended SRK equation that provided the
best fit to the equilibrium data. The fit to the data resulted in less than 5% root mean
square deviation between bubble pressures of the 22 data points and the equation of
state. Figure 17 shows an excellent fit of the calculated values to the data for liquids
containing less than a 0.6 to 0.7 mole fraction of hydrogen sulfide.
Figure 17 also shows three dotted curves that correspond to the bubble pressures
calculated by setting all the binary interaction parameters in the extended SRK equa-
tion to zero. The dotted curves are nearly straight lines between the 'two pure-
component vapor pressures at the system temperatures. Although the extended SRK
equation is able to calculate pure-component vapor pressures accurately, computations
involving the binary mixture provide results that are close to those obtained from
Raoult's law when the quadratic mixing rule is applied without a binary interaction
parameter. The four binary interaction parameters correct for deviations from ideal
behavior that result from mixing the pure components. However, these corrections seem
insufficient for liquids containing a hydrogen sulfide mole fraction larger than 0.6 to
0.7.
Methanol-Carbonyl Sulfide System—
The data of Oscarson (1981) reported to the Design Institute for Physical Property
Research were used in the binary interaction parameter evaluation for the methanol-
carbonyl sulfide system. The data cover a temperature range from 233 to 293 K and a
pressure'range from 0.38 to 11.1 atm. The binary interaction parameters determined
from the data are listed in Table 5, which also shows a 6.2% root mean square devia-
tion of babble pressures for a total of 51 data points. Figure 18 shows that the
-49-
-------
115
0 Data of Yorizame el al. (1SSS)
—— SRK w J th FI tied Kjj> Cjj-
SRK w l th Kjj =0 end Cjj—O
£ °
-P
m
m
L.
3
m
m
m
£_ O
w
m
o
0.0
T
0.2 0.4 0.6 0.8
Hole Fraction x CH2S)
i.O
Figure 17,- Methanol-Hydrogen Sulfide Equilibria.
50
-------
€3
U5
e Data of Oscarson C1S81)
SRK with Fitted KVp Cy
^ t r 1 1 1 1 1 1 1 1
0.0 0.2 0.4 0.6 0,8 1.0
Hole Fraction x (COS)
Figure 18. Hethanol-Carbonyl Sulfide Equilibria.
51
-------
calculated results fit the data very well for liquids having a carbonyl sulfide mole frac-
tion of less than a 0,5. Oscarson also reported vapor-phase compositions for this binary
system. By comparing these values with the predicted vapor-phase compositions from
the bubble point pressure calculations, the average error in mole fraction of the vapor is
0.0011. The calculated equilibrium pressures do not fit the data well for liquids contain-
ing a carbonyl sulfide mole fraction of more than 0.5 at temperatures of 273 and 293 K.
In addition, the exhibition of local maxima and minima in the equation of state calcula-
tions indicates the existence of metastable solutions, and the concomitant formation of
two liquid phases. The data, do not show liquid-phase separation.
Methanol-Methyl Mercaptan and Methanol-Dimethyl Sulfide Systems—
The P-T-ardata reported by Jackowski (1980) were used to evaluate the interaction
parameters for both methanol-methyl mercaptan and methanol-dimethyl sulfide mix-
tures. The data cover a temperature range from 263 to 288 K. The methanol-methyl
mercaptan data have a pressure range from 0.19 to 1.38 atm, and the methanol-
dimethyl sulfide data range in pressure from 0.08 to 0.45 atm. Table 5 lists the optimal
binary interaction parameter sets for both systems. The root mean square deviations in
bubble pressures were 5.6% and 6.9% for the fittings of 18 data points from the
methanol-methyl mercaptan system and 24 data points from the methanol-dimethyl
sulfide system, respectively.
Figures 19 and 20 show the pressure-composition diagrams for the methanol-methyl
mercaptan system and the methanol-dimethyl sulfide system, respectively. There was
good agreement between calculated and experimental bubble pressures for both systems
as long as the methanol mole fraction was at least 0.5. The predicted vapor-phase com-
positions for methanol-methyl mercaptan mixtures compare favorably up to a vapor-
phase methyl mercaptan mole fraction of 0.95 (compared with the results from an
activity coefficient correlation "of Chapter 5). The predicted vapor-phase compositions
for methanol-dimethyl sulfide are good up to a 0.8 mole fraction of dimethyl sulfide in
the vapor phase (compared with the results from an activity coefficient correlation of
Chapter 5). Both Figure 18 and Figure 19 show local extrema in both vapor- and
liquid-phase equilibrium curves. The methanol-dimethyl sulfide data of Jackowski
(1980) exhibits an azeotrope at each temperature; however, the cubic equation used
with quadratic mixing rule incorrectly predicts phase splitting. A similar result was
given by Huron and Yidal (1979) for an ace tone-water system.
Binary Parameters K,-j and
Figure 21 shows the values of K.n- for methanol-earbon dioxide, methanol-hydrogen
sulfide, methanol-carbonyl sulfide, methanol-methyl mercaptan, and • methanol-
dimethyl mercaptan mixtures. These results cover the temperature range from 220 to
- 52 -
-------
in
Hole Fraction x, y (CH3SH)
Figure 19. Methanol-Methyl Mercaptan Equilibria.
53-
-------
LD
Hole Fraction x, y (CH3SCH3)
Figure 20. Methanol-Dimethyl Sulfide Equilibria.
54
-------
CD
Temperature , K
¦Figure 21. Binary Interaction Parameters for Methanol-Acid Gases.
55
-------
320 K. and the parameters vary between 0 and 0.07. The parameters increase with
increasing temperature for all the binary systems. Figure 22 shows the Tallies of C^,
which vary from 0.04 to 0.20 in a temperature range of 220 to 320 K.
Systems Containing Water
Systems containing water provide a good test of any model since they generally
exhibit significant nonideality. In the experimental part of this study, a water and
methanol mixture was used as a solvent to study the solubilities of carbon dioxide.
Therefore, binary systems of methanol-water and carbon dioxide-water are examined
here.
The methanol-water vapor-liquid equilibrium data of Butler et al. (1933), Ratal iff
and Chao (1969), McGlashan and Williamson (1976), and Kooner et al. (1980) were
used to develop extended SRK correlations. The data cover a temperature range from
298 to 338 K and a pressure range from 0.04 to 1.02 atm. The interaction parameters
were obtained for the carbon dioxide-water system by using the data compiled by
Houghton et al. (1957). The data used in the calculations were in a temperature range
from 273 to 298 K and pressure range from 1 to 36 atm. Table 5 lists the optimal
binary parameters, and it also shows good agreement between caicuated and measured
bubble pressures for both binary systems. Figure 23 demonstrates that the extended
SRK can correlate equilibrium data for the methanol-water system. The interaction
parameters K- and Qy increase with increasing temperature for both binary systems,
but the effect of temperature on C,y for mixtures of carbon dioxide and water is slight.
Comparison of Results Using a Full Parameter Set to Those
Using a Reduced Parameter Set
Binary systems of methanol-carbon dioxide, methanol-water, and carbon dioxide-
water are discussed here. Table 6 gives binary parameters obtained when either the
complete extended SRK equation (optimal A"I; and C,-y) or a reduced form of the equa-
tion (C,y set to zero) were fit to data on these systems.
Numerical comparisons in Table 6 show that better fits to the methanol-carbon
dioxide and carbon dioxide-water equilibrium data were obtained when both K;; and
Qy were included in the equation of state. Note that the improvement in the fit when
both are used is slight for the methanol-water system; this may be because is more
important than in a symmetric mixture such as that formed by methanol and
-56-
-------
220.0 240.0 260.0 280.0 300.0 320.0
Temperature , K
Figure 22, Binary Interaction Parameters „::V-for Methanol-Acid Gases.
57
-------
Hole Fraction x, y (H20)
Figure 23. Methanol-Water Equilibria.
58
-------
Table 6. Comparison of Correlated Results for VLE Binary Pairs Using a Full Parameter
Set to a Reduced Parameter Set.
System
Ka°
K ^
Ka
(1CT3)
Kb°
Kb1
(10~3)
RMSDa
%
Eyb
Ranges
T, K P, atm
No.
of
data
Ref.
Me0H-C02
-0.0740
0.3767
0.2332
-0.5905
4.61
223-313
1.0-79.5
130
c-1
-0.0586
0.3551
0.
0.
8.32
-
Me0H-H20
-0.1638
0.2090
-0.0733
0.3280
2.44
0.0141
298-338
0.04-1.02
72
j-m
-0.1873
0.3050
0.
0.
2.95
0.0106
co2-h2o
-0.5135
1.2492
0.3694
0.0673
4.40
-
273-298
1.0-36.0
93
n
-0.4820
1.1831
0.
0.
12.61
~
RMSD % = { £ [(Pe - Pcal)/Pe] /n} x 100 , where n = no. of data points.
, n 1
Ey = [ e tyie - yical^/n« C Krlchevskli and Lebedeva (1947).
^ Bezdel and Teodorovlch (.1958). e Shenderel et al. (.1959). ^ Yorizane et al. (1969).
9 Katayama et al. (1975). n Ohgakl and Katayama (1976). 1 This work.
¦J Butler et al. (1933). * Rate!Iff and Chao (1969). McGlashan and Williamson (1976).
Kooner et al. (1980). n Houghton et al. (1957).
-------
water. As iC,y modifies the parameter in. the SRK equation that accounts for inter-
molecular attractive forces, the hydrogen bonding in the methanol-water system could
make K,, even more important. C,y is more significant in the slightly asymmetric
rnethanol-carbon dioxide system (RMSD improved from 8.32% to 4.61%), and of even
greater importance in the asymmetric carbon dioxide-water system (RMSD improved
from 12.81% to 4.40%).
For a mixture of close boiling components, such as methanol and water, values of a
for both components are similar (1.778 for methanol and 1.769 for water at 0°C). An
adjustment on the parameter set, which expresses a deviation from a geometric
mean of ac a of the pure components, will be enough'to correlate the bubble point pres-
sures of the mixture. However, values of a are 1.088 for carbon dioxide and 1.769 for
water at 0°C. The large difference between these values may indicate that adjustment
on the Ktj parameter set is insufficient to fit the data for mixtures of these compounds.
Although a related discussion was given by EI-Twaty and Prausnitz (1980) for the
extremely asymmetric system of hydrogen and a heavy hydrocarbon, the temperature
function a becom.es small for hydrogen and causes Kt,; msensitivity.
Gas-Gas Systems
Graboski and Daubert (1978b) observed that the interaction parameter in the Soave
modification of the Redlich-Kwong equation of state did not play a strong role in equili-
brium calculations for permanent gas components. Hence, in the present work the
parameters in the extended SRK equation were set for gas components (defined in Fig-
ure 1) as follows: K{j independent of temperature and C,y equal to zero. Additionally,
by setting the polar correction factor equivalent to zero for all the gases described here,
the equation was reduced to a Graboski-Daubert (GD) version SRK equation of state.
The interaction parameters for gas-gas pairs were calculated from equilibrium data.
Table 7 gives the parameter values for carbon dioxide-hydrogen sulfide, carbon
dioxide-nitrogen, carbon dioxide-propane3 and nitrogen-hydrogen sulfide systems.
These values are slightly different from those determined by Graboski and Daubert
(1978b), apparently because different data were used in their evaluation. However,
there are no significant differences in the results calculated with the parameters from
the present work and those from the work of Graboski and Daubert. The root mean
square deviations of bubble point pressures were less than 4% for the carbon dioxide-
hydrogen sulfide and carbon dioxide-propane mixtures. For the carbon dioxide-
nitrogen and nitrogen-hydrogen sulfide mixtures, the deviations were between 6% and
7%.
-60-
-------
TABLE 7
CORRELATIONS OF FOUR BINARY GAS-GAS SYSTEMS
Optimal
Ranges
No.
Binary
This
RMSD
of
Sef
system
Graboske
work
%
T, K
P, atm
data
GOg-HgS
0.102
0.1036
2.00
224.82/313.15
8.8/60.0
78
b,c
COg-Ng
-0.022
-0.0295
8.32
218.15/273.15
12.8/137.1
34
d-i
go2-c3h8
0.1018
0.1358
3.62
244.26/310.95
3.30/37.43
68
H
n2-h2s
0.140
0.1727
7.00
227.98/300.04
3.30/204.14
40
where
RMSD %
and o equals the number of data points.
b. Blerlein and Kav (1953). c. Sobocinski and Kurata (1959).
d. Aral et al. (1971). e. Krichevskii and Lebedeva (1982).
f. Kaminishi and Toriumi (1963).. g. Muirbrook and Prausnitz (1965).
h. Yorizane et al. (1970). L Zenner and Dana (1963).
j. Hamam and Lu (1976). k. Nagahama et al. (1974).
L Reamer et al. (1951). m. Besserer and Robinson (1975).
n. Kalra et al. (1976).
1/2
E ilF* ~ Pr.al)/PS? X 100%
x
Figure 24 gives isothermal pressure composition diagrams for carbon dioxide-
hydrogen sulfide mixtures. Excellent agreement is noted over the range of compositions
and temperatures studied. Similar agreement was noted for carbon dioxide-propane
mixtures.
Figure 25 shows good agreement between experimental and model predictions of
bubble point pressures and vapor compositions for carbon dioxide-nitrogen mixtures,
except for those close to the critical regions. Similar results were obtained for mixtures
of hydrogen sulfide and nitrogen.
Table 8 summarizes the evaluated binary parameters % for all gas-gas systems,
including those from the present work as well as values from the literature. Values from
the literature are the result of either using the original 8RK equation or a GD version of
the SRK equation (which has a slightly different set of constants in the m function).
-61-
-------
o
Hole Fraction x, y (002)
Figure 24. Carbon Dioxide-Hydrogen Sulfide Equilibria.
62
-------
0.0 0.2 0.4 0.6 0.8
Hole Fraction x, y
-------
Parameters from these sources may be used directly or they may simply be assumed
equal to zero in a vapor-liquid equilibrium calculation without introducing serious
errors. For a mixed gas-methanol system the gas-gas interactions in the liquid are
small, Lin's approach (see Section on Methanol-Supercritical Gases) was used for
hydrogen-containing systems in this work, and some results are shown in Table 8.
PHASE EQUILIBRIA IN MULTICOMPONENT SYSTEMS
A program EQNBP for calculation of bubble point pressure in multieomponent sys-
tems has been developed and'is presented by Chang, 1984. This program was used to
calculate the binary phase equilibrium diagrams described in the previous sections. In
this section, two methanol-containing ternary mixtures are used to demonstrate the
bubble point pressure calculations. These multieomponent phase equilibrium calcula-
tions use only the pure and binary parameters determined earlier. The bubble point
pressure calculation procedure for a multieomponent system is the same as for a binary
system (see Figure 4). The subroutine DVLFGM2 was replaced by DYLFGMN for the
dimensional expansion.
Methanoi-Hvdrogeii-Nitrogeii System
The data reported by Kriehevskii and Efremova (1951) at 25°C were used in the
evaluation. Liquid-phase composition and temperature were used in the model to calcu-
late bubble point pressure and vapor-phase composition for each data point. Table 9
lists the results for the 11 data points. The average error in the predicted bubble point
pressures is about 6%. The absolute average errors in the hydrogen and nitrogen vapor
phase compositions are 2.8% and 3.1%, respectively.
- 64 -
-------
TABLE 8
' RECOMMENDED BINARY INTERACTION PARAMETER IN THE
SRK EQUATION OF STATE FOR GAS-GAS SYSTEMS
Binary
co„-h9s
co2-n2
co2-ch4
C02-h2
CO^-CO
go2-c2h6
CO,,-C0IL
CO,
-C2H4
C02-CoH,
H S-H„
h2s-co
H2s-N2
H2s-cn4
H2S-C„H„
6
Nn-CHj
N,
-H2
n9-co
N2"G2He
%C3H8
CH4"H2
CH.-CO
4
C%'
CH,-C„H.
4 2 4
Hg-CO
HP TT
2* 2 o
Hg-Cgllg
CO-C„H„
2 8
co-c3hs
-C3HS
0.1036"
-0.0295®
0.09 73 b
-0.08833
-0.0372s
0.1348b
0.1358a
0.0S82a
0.0914b
-0.3002a
0.08883
0.17273
0.0830fc
0.0829b
H2S-C3H8 0.0831
0.0319
0.10163
0.0460b
0.0388b
0.0807b
0.0050c
G.0300b
0.0U0d
0.0440d
0.0904a
o.oaso13
0.1880c
0.000ftb
0.0200 ¦"
K
0.102
-0.0221
0.134°
-0.064b
0.1018b, 0.134d
0.140" i
0.0850°
O.OSS11
a Evaluated by program BFAIX.
b Graboski and Daubert (1978b).
c Lin (1980).
d Pannovic et al. (1981).
- 65-
-------
Metfaaiipl-Hydrogeii-Carbon Monoxide System
Table 10 lists the experimental data of Krichevskii et al. (1937) and the predicted
results from the model at 30°C. For a total of 12 data points, the average error in the
predicted bubble point pressures was 4.4%. The absolute average errors in the hydro-
gen and carbon monoxide vapor-phase compositions were 6.4% and Q.7%, respectively.
Methanol-Hvdrogeii-Hvdrogen ' Sulfide System
The predicted results for the methanol -hydrogen-hydrogen sulfide system do not
compare satisfactorily with , the data of Yorizane et al. (1989). This is believed to be
caused by the fact that the solubility of hydrogen in methanol reported by Yorizane et
al. (1969) is almost double that shown by the chart of Landolt-Bornatein et al. (1976). A
different binary parameter set is required for the methanol-hydrogcn. system in order to
have a satisfactory comparison of this hydrogen-containing ternary data set. Similar
difficulties with nitrogen solubilites are encountered by taking the data on an apparatus
similar to the one used by Yorizane et al. This problem will be discussed in the experi-
mental section.
GAS SOLUBILITY CALCULATIONS USING AN EQUATION OF STATE
A gas solubility calculation, which is useful in the analysis of absorption-stripping
processes, neglects the presence of solvent in the vapor phase, and it calculates the
solute mole fraction in the liquid phase from the temperature, pressure, and composi-
tion of the vapor phase. The fundamental relationship used in such calcuations is
i!=f< : (i)
A solubility calculation uses the equilibrium relationship in Equation 1 for each gas
component. Moreover, using an equation of state that accurately describes the influence
of temperature, pressure, and composition on the fugacities in both the vapor and
liquid phases accounts for all the nonidealities in the mixture.
A solubility calculation program SOLMAN (see Chang 1984) has been developed by
using the extended SRK equation of state with the binary parameters evaluated as
described earlier. Figure 26 shows the logic flow diagram for this calculation. Since the
- 66-
-------
Table 9. Predicted and Experimentala VLE Results for Methanol-H2-N2 System at 25°C.
x(Exp.)
P.
atm
y(MeOH)
y(H?)
y(N2)
MeOH
H2
n2
Exp.
Cal.
Cal.
Exp.
Cal.
Exp.
Cal.
0.9782
0.0143
0.0075
135.
125.68
0.0035
0.750
0.7474
0.250
0.2490
0.9757
0.0142
0.0101
129.
136.73
0.0036
0.672
0.6847
0.328
0.3116
0.9725
0.0047
0.0228
135.
130.82
0.0048
0.217
0.2353
0.783
0.7599
0.9750
0.0167
0.0083
142.
145.69
0.0034
0.750
0.7577
0.250
0.2389
0.9720
0.0186
0.0094
163.
164.46
0.0035
0.750
0.7520
0.250
0.2446
0.9696
0.0179
0.0125
166.
174.49
0.0036
0.672
0.6845
0.328
0.3119
0.9640
0.0062
0.0298
166.
178.99
0.0052
0.217
0.2296
0.783
0.7652
0.9588
0.0072
0.0340
188.
210.74
0.0056
0.217
0.2284
0.783
0.7660
0.9639
0.0210
0.0151
203.
210.21
0.0038
0.668
0.6741
0.332
0.3222
0.9625
0.0254
0.0121
224.
227.09
0.0036
0.750
0.7579
0.250
0.2385
0.9437
0.0103
0.0460
268.
313.13
0.0073
0.217
0.2261
0.783
0.7666
Avg.
error P^
= 6.03%
Avg.
error yc
= 2.82%
3.09%
a Krichevskii and Efremova (1951)
, 11
D Avg. error P =[ s I (Pe - PCal )/pe I J/11 x 100&
c Avg. error y =[ £ | (ye - ycai )/Ye I ]/H * 100^
1
-------
Table 10. Predicted and Experimental5 VLE Results for Methanol-H2"C0 System at 30°C.
x(Exp.)
P.-
atm
y'(MeOH)
y(H2)
y (CO)
MeOH
H2
CO
Exp.
Cal.
Cal.
Exp.
Cal.
Exp.
Cal.
0.9865
0.0022
0.0139
50.
48.87
0.0077
0.270
0.2559
0.730
0.7363
0.9682
0.0048
0.0270
100.
99.67
0.0062
0.270
0.2715
0.730
0.7223
0.9533
0.0078
0.0389
150.
148.29
0.0063
0.270
0.2872
0.730
0.7064
0.9389
0.0108
0.0503
200.
195.01
0.0070
0.270
0.2947
0.730
0.6983
0.9248
0.0138
0.0614
250.
240.07
0.0078
0.270
0.2978
0.730
0.6944
0.9104
0.0171
0.0724
300.
286.10
0.0088
0.270
0.3026
0.730
0.6886
0.9865
0.0055
0.0080
50.
54.86
0.0065
0.638
0.6028
0.362
0.3907
0.9744
0.0113
0.0144
100.
107.88
0.0050
0.638
0.6258
0.362
0.3692
0.9639
0.0170
0.0191
150.
156.87
0.0048
0.638
0.6493
0.362
0.3459
0.9539
0.0231
0.0230
200.
206.57
0.0049
0.638
0.6694
0.362
0.3257
0.9432
0.0301
0.0267
250.
262.85
0.0051
0.638
0.6899
0.362
0.3049
0.9323
0.0374
0.0302
300.
321.59
0.0055
0.638
0.7050
0.362
0.2895
Avg.
error P*3
= 4.39%
Avg.
error yc
= 6.37%
6.69%
a Krlchevskii et al. (1937).
h 12
D Avg. error P =[ e |(Pe - PCal)/pe13/12 x 100%
c Avg. error y =[ l I(ye - yCal)/Ve13/12 x 100%
-------
Start
Figure 26. Logic Flow Chart for Gas Solubility Calculation
-------
liquid-phase fugacity is a strong function of temperature and pressure, but not the
liquid phase compositions, a direct-substitution method can be used to aehieve conver-
gence easily. The gas solubility calculation program has the ability to calculate mixed-
gas solubilities in pure and mixed solvents. For a mixed solvent, the ratio of solvent
mole fractions must be specified.
The data from the methanol-hydrogen-nitrogen system at 25°C reported by Kri-
ehevskii and Efrenova (1951) were used to test these calculations. Figure 27 compares
the calculated hydrogen and nitrogen solubilities in methanol to measured values. The
average deviations of these values were 7.4% and 3.7% for hydrogen and nitrogen,
respectively.
For the mef.hanol-hycl rogen-carbon monoxide system, the data of Kricho.vslcii ei al.
(1937) at 30°C were examined. The average error for hydrogen solubilities was 5.8%,
while that for carbon monoxide solubilities was 9.2%. Figure 28 shows a good match of
calculated and measured values.
The solubility calculations for a methanol-carbon dioxide-nitrogen system and
methanol-water-carbon dioxide system are reported in the experimental section of this
report.
-------
Measured x
Figure 27. Calculated and Measured Solubilities of Nitrogen and
Hydrogen in Methanol at 298.15 K.
71
-------
Measured x
Figure 28. Calculated and Measured Solubilities of Carbon Monoxide
and Hydrogen in Methanol at 303.15 K.
72
-------
MODELING PHASE EQUILIBRIA- WITH ACTIVITY
COEFFICIENT EQUATIONS
Activity coefficients hare been used successfully to describe systems that exhibit
high, liquid-phase nonidealisy. This method works well for systems at low to moderate
pressure and at low reduced temperature. As described in the preceding section, cubic
equations of state also have been used for such systems, but they do not describe easily
the liquid-phase nonidealities for polar systems. Although density-dependent mixing
rules (Won, 1983; Mathias and Copeman, 1983) have promise of being able to treat all
systems, they need further testing. Hence, in the near future, the activity coefficient
method probably will continue to be used to describe systems containing polar com-
pounds.
The basic relationship used in the activity coefficient method is obtained by combin-
ing Equation 1, Equation 16, and Equation 17, to give
4yiViP = 7 iXifi (40)
In this expression, the fugacity coefficient activity coefficient yi} and reference fuga-
city f° must be calculated in terms of temperature, pressure, and/or composition. The
symmetric convention for the normalization of activity coefficients (defined with refer-
ence to Raoult's law) is adopted in this study. The methods used to obtain the quanti-
ties in Equation 40 are described in the following sections.
vapor phase fugacity coefficients
The fugacity coefficient t- which represents the deviation of the vapor-phase from
an ideal vapor phase for component i can be calculated from Equation 14 using a
pressure-explicit equation of state. The equation of state used for this purpose need not
be very complex because the vapor phase will not deviate greatly from the ideal gas at
low and moderate pressures. The most frequently used equations are the Redlich-
Kwong and virial equations of state. The nonideaiity of the vapor-phase becomes large
-T3-
-------
wlxen the system pressure is high, and under these conditions the accuracy of the
vapor-phase fugacity coefficient may have a significant effect on the vapor-liquid equili-
brium calculation. According to Tarakad et at. (1979), the most appropriate equation
of state depends upon the mixture. The Rediich-Kwong equation and its modifications
are found equally reliable.
The SRK equation of state was chosen to evaluate yapor-phase fugacity coefficients
in the present study because of the large number of binary parameters that haye been
evaluated as described earlier. (At high pressure, these binary interaction parameters
improve the predicted vapor-phase fugacity coefficients (Lin and Daubert, 1980)). The
SRK equation and the method for calculating fugacity coefficients were present in an
earlier section. Table 11 lists the binary parameters for systems containing methanol; as
these parameters have little impact at low and moderate pressures, they were set to
zero for the systems on which there were no data.
TABLE 11
BINARY INTERACTION PARAMETERS IN THE SRK EQUATION
OF STATE FOR SYSTEMS CONTAINING METHANOL*
Binary
MeOH-Hg
MeOH-Ng
MeOH-CO
MeOH-CH4
MeOH-C2H4
MeOH-CgHg
MeOH-CgHg
MeOH-CgHg
MeOH-C09
MeOH-HgS*
MeOH-COS
-1.7951 4.2830E-03
-0.5406 1.1180E-03
-0.8532 1.3445E-03
-0.3400 . 1.0G02E-G3
-0.2805 0.8895E-03
-0.2558 0.9005E-G3
-0.2420 0.8534E-03
-0-2235 0.7901E-03
-0.0972 0.4741E-03
-0.1074 0.5556E-03
-0.1436 0.702QE-03
The polar correction factor of methanol at zero.
ACTIVITY COEFFICIENTS
Activity coefficients cannot in general be predicted on an a priori basis. Rather,
-------
binary equilibrium data usually are used to evaluate parameters in a liquid solution
model that can be extended to multicomponent systems. Although a variety of equa-
tions has been used for to express activity coefficients as functions of temperature and
liquid composition, the four-suffix Mar gules, Wilson, and UNIQUAC equations are used
in the present study. They are believed to be better than others in vapor-liquid equili-
brium calculations on mixtures involving polar compounds and highly nonldeal solu-
tions. In addition, the Wilson and UNIQUAC equations can be directly extended to
multicomponent systems without simplifying assumptions.
Four-Suffix Mar gules Equation
This is a special case of the Wohl expansion model which was recommended by
Adler et al. (1968). The original Wohl polynomial is truncated so as to include terms
through the fourth order, and equal molar volumes of system constituents are assumed.
For a binary system, the activity coefficients can be expressed as a function including
three adjustable parameters;
In **yi ^2 12) ^ ~f~ 3 D-^2*^1
In ~ xl ^ ^21 -(A 12 ~ --4-21 — ® 12) % + 3 D12X2 j (41b)
The parameters A12, A21, and D12 are inversely proportional to temperature for a reg-
ular solution. These relationships have been used successfully by Adler et al, (1988)for
many binary mixtures of sub critical components.
In an N-component system, the activity coefficient of component i is given by
N N N
In 7,- = 4 J 2 ^xixkxi$ijU ¦ (42)
/ 1 k 1 / -1
N N N N
-3 S 2 E 1Lxixixkxl$ijkl
i -1 y 1 fc=i / 1
where the values of (3^ depend upon the binary parameters as given in Table 12.
Adler et al. (1966) studied the effect of C^, a parameter evaluated from ternary
equilibrium data, on the deviation of predicted vapor composition from estimated
(41a)
- 75-
-------
•f-
values for a a umber of ternary systems. They found C{j>K to be very near zero in all
cases. Based on this conclusion and the general lack of ternary data, was assumed
to be zero in this study.
TABLE 12
RELATIONSHIPS OF MULTICOMPONENT MARGULES PARAMETERS TO
BINARY AND TERNARY PARAMETERS
Combination
$ijki
i=j=k=l
0
i=j=k*I
11; /4
i=j=t]c—J
[ A-^k A _
- ®ikV6
i -J k 1
[(Ay i Aft
+" A'ki) ~ Cijk}/12 '
{Aijk + Aikl
+ Ajki)/24
where
2Aikl = Aik + Ah + A{1 -h Au + Aa + Alk
and
Cijk ~ ternary parameter
The Wilson Equation.
The equation developed by Wilson (1964) was the first solution model based on the
local composition theory. Because it has only two adjustable parameters and it is
mathematically simple, the Wilson equation is widely used, especially for solutions con-
taining alcohols. However, it is not applicable to mixtures that exhibit liquid-liquid mls-
cibility gaps. The activity coefficients for a binary system are given by the Wilson equa-
tion as
-------
In 7i = -In (a^ + Ai2x2) +
Ai2;F2
A21s2
x\ + ^i2x2 X1 + ^21^ 1
111 72 = ln ix2 + A21*2l) +
A-21^1
A. 12% 1
x2 A2iXl 2^1 + A12®g
(43b)
where
^ 1.2 —
exp
¦ AK.1 >i
12
RT
A,, = — exp
•AX
21
RT
The liquid molar volumes, yf and v\, used here are functions of temperature. They are
calculated at a pressure of 1 atmosphere using the Chueh-Prausnitz method, which will
be described in a later section. This method cannot be used when the reduced tempera-
ture is above 0.99. Additionally, the calculated liquid molar volumes for gas com-
ponents at reduced temperatures between 0.9 and 0.99 are usually high, as shown be
the comparison with the data listed in Table 13. Therefore, in the present study the
liquid molar volume at a reduced temperature of 0.9 is used whenever the reduced tem-
perature is larger than 0.9. The liquid molar volumes calculated from the Chueh-
Prausnitz method at the reduced temperature of 0.9 for various gases are listed in
Table 13. This Table also lists the liquid molar volumes at 25°C given by Prausnitz and
Shair (1981); Yen and McKetta (1962); Lee, Erbar, and Edmister (1973).
. The energy parameters AX
wide range of temperatures. However, A12 and A21
stable parameters to fit isothermal data.
12 and AX21 can be adjusted to fit equilibrium data over a
are often used as the two adju-
For a system containing N components, the activity coefficient of component i is
expressed by
N J£ xk&ki
In yt = -In jjj syAfj- + 1 - E ^
y k
f
(44)
- 77 -
-------
Note that this expression requires only the parameters obtained, by fitting binary
data.
TABLE 13
LIQUID MOLAR VOLUMES OF GASES FROM VARIOUS SOURCES
Liquid Molar Volume
ml/mole
Gas
Clrneh
-------
In = In
>1 , ,
h la
x,
f0 1
U1
V 1 >
+ 2
h* i
+ 9i'
/n (0/ + ©2't21)
©2?T21
0,'t
12
©i ' + ©2?t21 ©•?* + 0/
1 * 12
zq9
In 72 = In 1" In
4>,
hr2
ri
(45b)
+ «•>'
In (02' + 01't12) + 7—
0,'t
1 '12
0! T,
1 '21
©,' + ©i't12 ©/+-©/
2 '21
wkere
4ri -
-------
0,
xlr2
<7 1j?2
Coordination number = 10
Structural size parameters
Structural area parameters
Modified structural area parameters
The structure size parameter, r, and structure area parameters, q and q' are pure-
component physical properties. Prausnitz ef, al. (1930) hare listed these parameters for
a large number of condensable components. Breivi (1982) has calculated these parame-
ters for some simple polar and nonpolar components directly from their molecular
structure. Two methods can be used to estimate quantities that do not appear in the
above sources. Breivi (1982) has correlated the structure parameters as functions of
critical volume and radius of gyration. The r parameters are found proportional to van
der Waals volumes as suggested by Bond! (1968). The ratio {qjr) is a measure of the
shape of the molecule, and as r becomes very large, qjr approachs 2/3 for a linear
chain molecule (Donohue and Prausnitz, 1975). Hence, Prausnitz (1983) has suggested a
simple scaling of these parameters with critical volume:
- 80-
-------
I}cj
3L
f/
2/3
(47]
Jcj
Here the reference substance j is selected based on haying a molecular structure that is
similar to component i. Table 14 lists the structure parameters of the components of
interest in this study.
TABLE 14
UNIQUAC STRUCTURE PARAMETERS
Substance
r
q
«'
Source
h2
0.42
0.570
a
c
N2
0.94
0.99
a
c
°2
0.91
0.88
a
c
CO
1.06
1.07
a
c
CH4
1.54
1.38
a
c
1.57
1.49
a
b
C2H
1.80
1.70
a
b
CA
2.25
2.02
a
b
0I1 ^
2.48
2.24
a
b
co2
1.32
1.28
a
b
H2S
1.0
1.0
a
h
COS
1.90
1.83
a
d
CHgSH
1.76
1.64
a
d
O U On
2.62
2.27-
a
d
CHgSCH3
2.82
2.27
a
d
MeOH
1.43
1.43
0.96
b
11,0
0.92
1.40
1.0
b
-81-
-------
where
a q' = q
b Prausnitz et al. (1980),
c Breivi (1982).
d Estimated from the scaling hypothesis suggested
by Prausnitz (1983). Reference substances:
cos-co2, CH3 S11 — C 0 H. C2HsSH-C2H5OH.
Atf12 and Am2i are adjustable binary parameters that must be evaluated from
experimental data, which may cover a range of temperatures. Alternatively, Isothermal
data could be fit by choosing ri2 and t21 as adjustable parameters.
In an N-eomponent system, the activity coefficient of component I for the UNI-
QLJAC equation is given by
<£>• 2 ©,•
In y{ - In + —fcln — + k
X: 2 t
€>¦ N
- 2 - ft '1'
n
xi ]
N
2 ®/rji
j
(48)
N
+ 1i' - Qi' 2
i
(hI . f-r . .
KJj t
_
2 ®k 'Tkj
k
where
<6.
a -
N
2 rkxk
k
N
""ST*
2 rikxk
W
it xi
N ¦
2
k
- 82 -
-------
LIQUID REFERENCE STATE FUGACITIES
The reference state for the corresponding activity coefficient is defined here as the
pure component at the system temperature and pressure. The reference state fugacity
then is the pure component liquid fugacity // which can be calculated by Equation 18
for a subcritical component, or by a generalized correlation for a supercritical or near-
critical component.
Subcritical Components
Equation 18 was used for methanol, water, earbonyl sulfide, and propane. The
vapor pressures were estimated from the following expression which applies to a wide
temperature range:
log p*(mmllg) = A + B/T(K) + C log(T) + DT + ET2 (49)
Constanta A through E are listed in Table 15.
TABLE 15
VAPOR PRESSURE CONSTANTS FOR EQUATION 49
Compound
A
B
C
D
E
Source
MeOH
-42.629
-1188.2
23.279
-35.082E-3
17.578E-6
3,
h2o
16.373
-2818.6
-1.6908
-5.7546E-3
4.0073E-8
a
COS
10-222
-1255.8
0.00
-10.193E-3
11.376E-6 '
b
C.{HX
38.007
-1737.2
-11.668
8.5187E-3 .
0.00
a
a Yaws (1977).
b Robinson and Senturk (1979).
For other subcritical components, e.g. methyl mercaptan and dimethyl sulfide, the
vapor pressures can be estimated from the Antoine equation:
-------
lu p* (mmffg) — At — Bt/( T — Ct )
(50)
Reid at at. (1977) have listed the Antoine constants At, Bt, and Gt for a large number
of compounds.
The fugacity coefficient of component i, at the saturated vapor pressure in
Equation 18 was calculated bj the SRK equation of state. The liquid molar volume
used in Equation 18 was calculated from the following corresponding state correlation
of Chueh and Prausnitz, which is described in detail by Reid et al. (1977).
,L _
1 +
9zcNv{P -p*)
-1/9
(51)
where
Nv = (1.0 - 0.89w) [ exp (6.9547 - 76.2853 Tr
- 203.5472 Tr3 + 82.763111,4 ) ]
191.3060 Tr2
(51a)
|Vr(0)
+ co Vp + w2 Fi2)
(51b)
~ a, + bj Tr + c, Tr2 + d.- T? -f e}-/Tr + /, In (1 — Tr)
(51c)
The coefficients for Equations 51 are given in Table 16.
TABLE 16
COEFFICIENTS FOR EQUATION 51c
j
a.
b.
c.
„ d.
e.
f.
J
J
J
J
J
J
0
0.11917
0.009513
0.21091
-0.0S922
0.07480
-0-084476
1
0,98465
-1.60378
1.82484
-0.61432
-0.34548
0.087037
2
-0.55314
-0.15793
-1.01801
0-34095
0.46795
-0.239938
-84-
-------
Using the above correlations for the liquid molar volume and evaluating the integral
in Equation 18, the following expression is obtained for the reference fugacity of a sub-
critical component
f° = p**exp
8RTp.zc Nv
1 +
9zcNv (P - p*)
8/9
- 1
(52)
Supercritical and Near-Critical Components
The pure-component liquid fugacity coefficients of carbon dioxide, hydrogen sulfide,
nitrogen, methane, and hydrogen at system temperature and pressure can be estimated
by a generalized correlation developed by Lee, Erbar, and Edmister (1973). This corre-
lation, which can also be applied to ail the hydrocarbons, is
In LP (54)
- 85 -
-------
Table 17. Constants in Equation 53.
All hydrocarbons
Constant (N2 (CH4 CO2 H2S H2
included) excluded) Methane Nitrogen For all For all For all
Tr< 1.0 Tr> 1.0 Tr> 0.93 1.0 2.2 temp. temp. temp.
A1
6.2741
9.52326
9.55412
9.26614
6.82287
28.9284
13.94
0.43571
A2
-7.3401
-9.88046
-8.31211
-10.538
-8.9725
-20.01
-1.75213
5.34346
a3
-4.2751
-6.00351
-3.23962
-7.98618
-9.78514
-10.3989
14.0164
-0.46
A4
-0.22647
-0.41660
-2.26419
0.76209
2.67084
-12.5
-12.5
-0.1043
A5
0.93842
0.18150
0.46272
0.21677
0.0
3.52631
-0.00024
0.04794
a6
-0.23825
0.0
0.0
0.0
0.0
0.0
0.0
0.0
a7
0.03798
-0.02010
-0.09953
-0.05624
0.90970
-12.7
2.84127
0.35304
a8
-0.00344
0.10390
0.2516
0.18917
-1.01342
12.9708
-4.94796
-0.68039
a9
-0.21974
-0.06538
0.2727
0.12474
-0.40848
15.4946
-8.0
-0.10673
A10
0.10862
0.08916
0.01198
-0.00023
0.0
-0.94143
1.5889
-0.00023
A11
0.0298
0.0
0.0
0.0
0.0
0.0
0.0
0.0
A12
-0.00188
-0.00188
-0.00188
0.0
0.0
-0.22382
0.48453
0.0
a13
10.2920
-1.027
0.0
0.0
0.0
0.0
0.0
0.0
a14
-11.6780
-0.59264
0.0
0.0
0.0
0.0
0.0
0.0
a15
-1.6470
0.0
0.0
0.0
0.0
0.0
0.0
0.0
a16
-0.03885
-0.03885
0.0
0.0
0.0
0.0
0.0
0.0
a17
-0.00101
-0.00101
-0.00101
-0.05652
-0.05652
2.32463
-0.00101
0.0
-------
EVALUATION OF BINARY PARAMETERS IN ACTIVITY
COEFFICIENT EQUATIONS
The four-suffix Margules, Wilson, and UNIOUAC equations were used to describe
the dependence of activity coefficients on liquid composition and temperature. The
parameters in these activity coefficient equations must be evaluated through the reduc-
tion of vapor-liquid equilibrium data on binary mixtures. With these parameters, the
equations can be used to calculate binary vapor-liquid equilibrium conditions at tem-
peratures and pressures other than those covered by experiment. In addition, the
binary parameters can be used directly to predict the vapor-liquid equilibrium behavior
of a multicomponent system. Methods used to evaluate the binary parameters from
equilibrium data are described in the following-sections.
Evaluation Method and Procedure
The method used in the present study to evaluate model parameters from binary
equilibrium data is based on the principle developed by Barker (1953). A bubble point
pressure calculation procedure is included in the parameter search routine, which evalu-
ates total pressure as a function of the estimated parameters, the measured tempera-
ture, and the measured liquid-phase composition. This procedure does • not require
measurement of vapor-phase composition, which many binary VLE experimental data
sets do not have, but the mole fractions of each component in the vapor phase is calcu-
lated in the course of the parameter search routine. Ideal gas behavior is not assumed.
The objective function used in the present study is
OF =2
k=1
P. " Pad
P.
e
(55)
and it was minimized by a Gauss-Marquarat nonlinear regression procedure. It is
important in the use of the Gauss-Marquardt technique to derive the analytical formu-
las of the derivatives of the objective function with respect to each model parameter.
Careful manipulation is necessary to handle the nonlinear activity coefficient equations
involved. The manipulation of the necessary derivatives for the three activity coefficient
equations is listed by Chang 1984.
The' input information for the parameter search program includes the pure-
component physical properties, the binary P-T-x data, the parameters that control the
algorithm, and the initial estimates of the model parameters. An initial guess of total
pressure for each data point is assigned to start the bubble point calculation. The best
-------
choice of Initial pressure is the measured total pressure. The iterations will proceed
until the equilibrium criterion of Equation 40 is satisified; in addition, convergence
requires the mole fractions in the vapor phase to sum to one and that the calculated
total pressure does not change in subsequent iterations. After each data point has been
used to determine Psai, the objective function and its derivatives are calculated. New
estimates of the model parameters are evaluated by the Gauss-Marquardt technique,
and the whole process is repeated until the objective function is minimized. The outline
of this parameter-search procedure is given in Figure 29. Note that the procedure ia
similar to the evaluation of the binary interaction, parameters in the extended SRK
equation of state. Figure 30 shows the procedure for performing the bubble point pres-
sure calculations. A computer program GMACC (see Chang 1984) has been developed
to evaluate the binary parameters in the Mar gules, Wilson, and UNIQUAC equations.
The application of other objective functions and the use of the maximum likelihood
principle were also tested. In minimizing pressure deviation, Barker's method did a
better job. The maximum likelihood principle is attractive but requires much longer
computational time for results that are no better than were obtained with the objective
function in Equation 55.
It is desirable that a phase equilibrium model has an ability to estimate equilibrium
behavior over a range of conditions. In this study, two options were adopted in the
evaluation of model parameters which could then be used over a wide range of tem-
peratures. In the first option, the temperature-independent model parameters were
evaluated from all available data on the binary systems methanol-carbon dioxide,
methanol-carbonyl sulfide, methanol-hydrogen sulfide, methanoi-water, methanol-
propane, methanol-methyl mercaptan, methanol-dimethyl sulfide, and carbon dioxide-
hydrogen sulfide. Note that both components in each binary system are condensable.
For systems containing a supercritical component, such as methanol-nitrogen, carbon
dioxide-nitrogen, and hydrogen sulfide-nitrogen, the above option did not work, so the
second option was used. In this procedure the temperature-dependent model parame-
ters were evaluated at each available set of isothermal data. Selected parameter sets
were fit by an empirical temperature function (a / T + b). The selection of parameter
sets to be fit was based on the standard error associated with their estimation. However,
parameter sets with large standard errors were often in good agreement with the empir-
ical parameter function reduced from the parameter sets with small standard errors.
Binary Correlation Results
Table 18 lists the binary systems examined in this study accompanied by their
sources, conditions, and number of data points used. The optimal parameters in the
four-suffix Margules, Wilson, and UNIQUAC equations, with the deviations resulting
-88-
-------
Figure 29. Logic Flow Chart for Binary Parameters Evaluation
in the Gamma Method.
89
-------
Figure 30.. Logic Flow Chart for Bubble Point Pressure Calculation
in the Gamma Method.
90
-------
Table 18. Binary VIE Data Used in Evaluation of Parameters in
Activity Coefficient Equations.
Binary
No.
of
system data T, K
Ranges
P, atm
References
MeOH C02 101 223/313 1.0/79.53
MeOH-COS 51
HeOH-H2S 22
MeOH-CH3SH 18
MeOH-CH3SCH3 24
MeOH-C3H8 11
Me0H-H20 72
233/293
248/273
263/288
263/288
293.05
298/338
n2-h2s
0.38/11.11
2.0/10.0
0.1908/1.3809
0.0834/0.4533
2.67/7.94
0.0351/0.9569
C02-H2s
76
225/313
6.8/60.0
MeQH-N2
C02-N2
21
56
225/300
218/301
20.7/177.0
12.6/115.8
41 228/300 3.30/204.34
Bezdel & Teodorovich (1958);
Katayama et al. (1975);
Krichevskii & Lebedeva (1947);
Ohgaki & Katayama (1976);
Shenderer et al. (1959);
Yorizane et al. (1969).
Oscarson (1981).
Yorizane et al. (1969).
Oackowski (1980).
Jackowski (1980).
Nagaharna et al. (1971).
McGlashan & Williamson (1976);
Ratcliff & Chao (1969).
Kooner et al. (1980).
Butler et al. (1933).
Bierlein & Kay (1953);
Sobocinski & Kurata (1959).
Weber & Knapp (1978).
Aral et al. (1971);
Krichevskii & Lebedeva (1962);
Kamintshi & Toriuni (1966);
Muirbrook & Prausnitz (1965);
Yorizane et al. (1970);
Zenner & Dana (1963).
Besserer & Robinson (1975);
Kalra et al. (1976).
91
-------
from'the fitting procedures, are listed in Tables 19, 20, and 21, respectively. Generally,
the three activity coefficient correlations fit the data equally well; the root mean square
deviations of bubble point pressures vary considerably from one system to another, but
all are under or near 10%. ¦ ¦
The Wilson and UNIQUAC equations are superior to the Margules equation for the
methanol-carbonyl sulfide system. Figure 31 shows how well the Wilson equation fits
the data of Oscarson (1981). The four-suffix Mar gules equation incorrectly predicts
liquid-phase separation as indicated by local exirema in the F x diagram of Figure 31.
. The UNIQUAC and Margules equations are slightly better than the Wilson equation
for the methanol-carbon dioxide binary. However, in the correlations of the methanol-
carbon dioxide data, the Margules equation resulted in more systematic errors than the
Wilson and UNIQUAC equations. Figure 32 shows that the pressure deviations result-
ing from the Margules equation are positive at temperatures above 273 K and negative
below 273 K. That is, use of the Margules equation resulted in higher bubble pressures
in the low-temperature isotherms and lower bubble pressures in the high-temperature
isotherms, when the calculations are compared to data. Deviations between the UNI-
QUAC equation and the methanol-carbon dioxide data are more random than sys-
tematic, as is illustrated by Figure 32.
Figure 33 shows a good fit of the UNIQUAC equation to the data of Nagahama
et al. (1971) for the methano 1-propane system. The Wilson equation did as well as the
UNIQUAC equation, but the four-suffix Margules equation incorrectly predicted
liquid-phase separation for this system.
Figure 34 shows the pressure-composition diagram for the methanol-methyl mer-
captan system. It indicates that the UNIQUAC equation fits the P-T-x data of
Jacfcowski (1980) excellently, and it also gives the vapor-phase compositions predicted
from a bubble point pressure calculation. Figure 35 shows the pressure-composition
diagram for the methanol-dimethyl sulfide system. The three activity coefficient equa-
tions gave good agreement with the P-T-x data of Jackowski (1980), although the Mar-
gules equation was slightly better than the Wilson and UNIQUAC equations. All equa-
tions also predict an azeotrope at each isotherm. Figure 36 plots the calculated vapor-
phase composition vs. the liquid composition at 288.15 K for the methanol-dimethyl
sulfide system; an azeotrope is shown at the dimethyl sulfide mole fraction of 0.88.
Severe difficulty has been encountered in the evaluation of binary parameters for
systems containing a supercritical component. The workable parameters for these sys-
tems are bound to a very small region; if an initial parameter estimate" is not in that
region, the optimization procedure that is part of the parameter evaluation process can-
not be executed. Nevertheless, the binary parameters for three nitrogen-containing sys-
tems have been evaluated in this study using the method as described.
-------
Table 19. Recommended Margules Parameters In the Activity Coefficient Correlations.
Binary
Al2
A21
Dl2
RMSD^a
EPb
Eyc
system
atm
Me0H(l)-C02(2)
509.77/T
214.57/T
115.76/T
8.76
1.71
_
MeOH(1)-C0S(2)
742.01/T
454.89/T
425.27/T
9.07
0.278
0.0014
MeOH(l)-H2S(2)
175.14/T
130.13/T
-160.26/T
4.45
0.18
-
MeOH 1)-CH3SH(2)
696.32/T
442.69/T
344.38/T
1.18
0.0073
-
MeOH(l)-CH3SCH3(2) 720.61/T
534.50/T
451.29/T
0.87
0.0015
-
MeOH(l)-C3Hn(2)
851.87/T
673.69/T
336.36/T
5.62
0.15
-
Me0H(l)-H20(2)
185.10/T
140.36/T
-72.590/T
3.07
0.0045
0.0075
C02(1)-H2S(2)
-37.102/T
-136.18/T
-723.25/T
5.22
1.09
0.0408
MeOH(1)-N2(2)
-0.85837
3.8692
-4.1996
6.59
4.54
-
C02(l)-N2?2)
6134.7/T-23.418
1153.9/T-2.8897
8061.4/T-33.663
7.49
3.32
0.0898
N2tl)-H2S(2)
990.65/T-O.55020
-32089/T+83.371
-37934./T+95.060
9.99
5.33
0.0514
a RMSD % = { s [(Pe - Pcal)/'3e^/n^^ x 100 % , where n = no. of data points.
1
b EP = [ z |Pe - Pca113/n. c Ey = [ Myle - yicalI]/n.
-------
Table 20. Recommended Wilson Parameters 1n the Activity Coefficient Correlations.
Binary
AA12
A^21
RMSD%a
EPb
Eyc
system
atm
Me0H(l)-C02(2)
48.604
-0.62504
11.00
1.52
—
Me0H(l)-C0S(2)
110.35
7.9072
1.84
0.049
0.0011
Me0H(l)-H2S(2)
15.645
3.5334
4.88
0.20
-
Me0H(l)-CH3SH(2)
61.796
8.2665
1.45
0.0061
-
MeOH(l)-CH3SCH3(2)
61.299
7.8623
1.64
0.0026
-
MeOH(l)-C3H«(2)
124.89
13.919
5.87
0.22
-
Me0H(l)-H20(2)
-8.9306
25.150
3.31
0.0043
0.0079
C02(1)-H2S(2)
13.057
-3.4196
6.43
1.33
0.0445
A12
a21
MeOH(1)-Np(2)
-1.0151
0.15410
6.61
4.64
_
C02(l)-N2{2)
-111.23/T+0.35348
-314.71/T+1.
,7771
6.22
2.31
0.0927
N2(1)-H2S(2)
150.74/T-O.19793
-1265.0/T+3.
4689
9.86
5.48
0.0484
n
a RMSD % = { E [(Pe -
1
Pcal)/Pe]2/n}1/2 x
100 % , where n =
no. of data points
•
b EP = [ " IPe - Peal
1
1]/n. c Ey = [ "
1
Ivie ~ Vlcal1
]/n.
-------
Table 21. Recommended UNIQUAC Parameters in the Activity Coefficient
Correlations.
Binary &uj_2 ^u21 RMSD%a EP^ Eyc
system atm
Me0H{l)-C02(2)
MeOH(l}-COS{2)
Me0H(l)-H2S{2)
MeOH(l)-CH3SH(2)
HeOH(i)-CH3SCH3(2)
MeOH(l)-C3H8(2)
Me0H(l)-H20(2)
C02(1)-H2S(2)
-5.7734
88.471 .
8.13
1.10
-
-0.50644
1672.3
1.65
0.049
0.0010
3.5301
18.081
4.89
0.21
-
-0.25523
70.519
1.45
0.0066
-
-2•7289
70.140
1.85
0.0030
-
2.3676
116.35
5.73
0.18
-
-10.652
15.107
2.70
0.0033
0.0066
5.0145
1.8468
6.60
1.42
0.0450
a RMSD % = { £ l(Pe - PCal)/Pe]2/n}1/2 x 100 %
1
where n = no. of data points,
n
EP = [ z |Pc - PcaiI]/n.
[ S
1
n
c Ey = [ I lyie - yicalH/n.
1 '
95
-------
o
Mole Fraction xCCOS)
Figure 31, Comparison of the Correlated Results by Wilson and Margules
Equations for Methanol-COS Equilibria.
96
-------
to
CM
o
p-
X.
i—I
(0 ®
O o
p_
© •
p- ?
(VI
•
o
I
Margules
X X
x X
X
M
X
X
¦ '
¦ J?
X *
1
* xrf<
V
v ^
J*
X
Kg X
X
X
*<
V gm
a m
ff ¦¦
0
* fa
• * • ¦ .
¦ X
¦
^ • «¦ #
¦ ¦
¦
¦
¦ < 273.15
K* > 273.15 K
0.0 o.s
x(C02)
1.0
(VI
*
o
CD <=»
P-
X
i—i
(0 °
(J o
p_
® '
p_ «f
CVI
«
O
i
UNIQUAC
a
¦
¦ <
273.15 K
* 2
273.15 K
X
¦ X
X
X
a
X
X
X
¦
® ¦! X _ X
w m x ¦ x
¦ ;
X
X
X Xjh
*
X
X X ¦
¦ X ¦
¦
m *
>
¦
¦ X
¦
¦
¦
X
* X
**
X
w
¦
H
0
1
O.S
1.
x
-------
Figure 33. Methanol-Propane Equilibria with Predictions calculated by
UNIQUAC Equation.
98
-------
w
El Dele of Jsckowskl (1530)
— UNI6URC Eqn.
0.0 0.2 0.4 0.6 0.8
Mole Fraction x, y (CH3SH)
1.0
Figure 34. Methanol-Methyl Nercaptan Equilibria with Predictions
calculated by UNIQUAC Equation.
99
-------
us
Figure 35. Methanol-Dimethyl Sulfide Equilibria with Predictions
calculated by Margules Equation.
J 00
-------
x (CH3SCH3)
Figure.36. x-y Diagram of Methanol-Dimethyl Sulfide Equilibria at
288.15 K.
101
-------
Effects of Reference Fugacitv
Three binary systems — methanol-carbon dioxide, methanoi-hydrogen sulfide, and
carbon dioxide-hydrogen sulfide — were studied using the Robinson-Chao (1971)
reduced state correlation for calculating the reference fugacities of carbon dioxide and
hydrogen sulfide. Table 22 lists the correlated results. The optimal model parameters
for the three activity coefficient equations are quite different from those using the Lee-
Erbar-Edmister (1973) reference fugacity model. The Robinson-Chao model gave better
results for the carbon dioxide-hydrogen sulfide system for all three activity coefficient
correlations (see Table 22). For the methanol-carbon dioxide and methanoi-hydrogen
sulfide systems, the use of the Robinson-Chao model improved the correlations slightly
for the Wilson and UNIQUAC equations, even though the model parameters could not
be properly optimized in the parameter evaluation process. However, the Robinson-
Chao model did a poorer job for the Margules equation than did the Lee-Erbar-
Ed mister model. An interesting comparison of the two methods of calculating reference
state fugacities is provided by the results obtained using the Margules equation to fit
data on the methanol-carbon dioxide. These results are presented in Figure 37 and
show local maxima and minima in bubble pressures when the correlation is developed
using the Robinson-Chao model. Maxima and minima indicate that liquid-phase
separation was predicted by the model calculation, even though the data do not sup-
port such predictions. The differences between carbon dioxide vapor pressures calcu-
lated from the Robinson-Chao and Lee-Erbar-Edmister models, and between experi-
mentally determined vapor pressures and those calculated from the two models should
also be noted.
MULTICOMPONENT VLE CALCULATIONS
As described earier. there are four types of VLE calculations: bubble point pressure
(BUBLP), bubble point temperature (RTJBLT), dew point pressure (DEWP) and dew
point temperature (DEWT). In principle, such calculations for a multicomponent sys-
tem are not different from those for a binary system. The BUBLP block diagram shown
in Figure 30 can be applied to the multicomponent bubble point pressure calculation by
substituting an arbitrary pressure as an initial guess.
The bubble point pressure calculation requires specifications of liquid composition
and system temperature, and it results in an estimation of the equilibrium vapor com-
position and system pressure. A computer program VLEBP (see Chang 1984) has been
developed to accomplish the above calculation, and it has been used in the previous sec-
tion to describe the behavior of binary systems. Success of this program should be
expected in calculations involving a multicomponent system comprised of subcritical
- 102-
-------
Table'22.. Activity Coefficient Correlations with Robinson-Chao
Reference Fugacity Model for CQ2 and H2S.
Margules
a12
A2i 021 RMSD%a EPb
; atui
Eyc
Me0H(l)-C02(2)
MeOB(l)-H2S(2)
C02(1)-H2S(2)
796.56/T
617.54/T
357.54/T
319.47/T 384.63/T 15.15 2-31
284.67/T 442.12/T 4.79 0.21
388.96/T 403.19/T 1.87 0.45
0.0149
Wilson
AAi2
AX21 RMSD# EPb
atm
Eyc
Me0H(l)-C02(2)
MeOH(l)-H2S(2)
C02(1)~H2S(2)
5794.9
208.25
11.370
6.1272 8.51 1.17
-1.4564 3.73 0.11
15.239 3.48 0.87
0.0180
UNIQUAC
Au\2
^21
Me0H(l)-C02(2)
HeOH(l)-H2S(2)
C02(1)-H2S(2)
1.2419 1159.3 10.36 1.54
-0.44861 1502.4 3.64 0.12
16.457 7.9126 3.41 0.86
0.0178
a RMSD % = { " C(Pe " PCal)/pe]2/nlI/2 x 100 % ,
1
where n = no. of data points.
b EP = [ " |Pe - PcalH/n.
1
c Ey = [ s lyie - yicaiI1/n.
1 ¦
103
-------
ID
4-a.xb Literature data
" - LEE model
RC model
!3
c
10
e o
_p ,
CO o
© o
k °
3 KS
CO
®
©
C_ o
p_ .
o
CO
o _
* r
0.0 0.2 0.4 0.6
hole Fraction x(C02)
0.8
1.0
Figure 37. Comparison of Using Lee-Erbar-Edmister and Robinson-Chao
Models in Margules Equation Activity Coefficient
Correlations for Methano1-C02 System.
104
-------
compounds (excluding components in Group I). However, there are no appropriate data
on systems containing methanol that can be used to test the accuracy of the multicom-
ponent calcualations. Satisfactory results should not be expected when the program is
used to perform VLE calculations on a multieomponent system that contains a super-
critical component. This is partly due to the difficulty of obtaining temperature-
independent parameter sets on binary mixtures involving supercritical components. It
is also due partly to inaccuracies in the measurement of the liquid mole fraction of the
supercritical component, which has an enormous effect on the pressure calculation.
-------
experimental
QUALITY ASSURANCE AND EXPERIMENTAL PROCEDURE
The research, work reported on here included, both the development of thermo-
dynamic models to predict vapor-liquid equilibria, and experimental data to use with
the models. The main emphasis of the quality assurance program for this portion of
the research was focused on the quality of the experimental data. As with other parts
of the overall research program, the responsibility for quality assurance was shared
among all personel responsible for the project. All costs associated with quality
assurance were included in the project' budget. Details of the experimental equipment
and procedures are described below.
Vapor-Liquid Equilibrium Apparatus
The experimental apparatus, shown in. Figure 38, included an equilibrium cell, a
constant-temperature' bath, temperature control devices, a pressure gauge, and a pump
for recirculating the gas. The stainless steel equilibrium cell had a volume of 1084 ml
and internal baffles. The entire cell was immersed in a 50% ethylene glycol-50% water
bath housed in an. industrial freezer. The bath temperature was maintained within
0.1°C of the set-point'temperature by a 300 watt immersion heater with an electronic
temperature controller and a precision mercury thermoregulator. A copper-constantan.
thermocouple and a calibrated digital temperature indicator were used to measure bath
temperature. A calibrated 16-inch Heise gauge was used to measure pressure in the
equilibrium cell. The gas phase in the cell was bubbled through the liquid phase using
a microflo diaphragm metering pump with a pumping capacity of 810 ml/hr.
- 106 -
-------
Figure 38. Vapor-L1qu1d Equilibrium Apparatus.
-------
Sampling Procedure
An experiment was started by evacuating the equilibrium, cell and drawing about
400 ml of solvent into the cell. Further evacuation was applied overnight for degassing
the solvent. When the bath temperature reached the desired value, the gas was intro-
duced to the cell. The diaphragm metering pump was started to bubble gas through the
liquid and assist in bringing the system to equilibrium. After 2 to 3 hours, the pressure
in the cell became constant; recirculation of the gas phase was continued for another 3
hours and then the solution was allowed to sit unagitated overnight. Approximately
0.5 ml of liquid was purged through a sampling line and collected in a glass graduated
cylinder, so that the flow rate of liquid sample was estimated before sampling. A 500-ml
teflon-coated steel bomb, wrapped with heating tape, was used to sample the equili-
brated liquid. A 0.5 to 3-ml liquid sample, obtained by timing the sampling period, was
allowed to expand through capillary tubing and a low dead-volume needle valve into
the evacuated sample bomb. The sample size was small enough that it could be com-
pletely vaporized, and yet it was large enough to insure accurate analysis by a gas
chromatograph. The sample was heated to 140°C for 3 hours and was pressurized with
helium to approximately 60 psig. The stainless steel tubing from the sampling bomb to
the gas chromatograph and the gas exit were also heated to 140°C by heating tape to
prevent methanol condensation during the sample analysis process.
The sampling device for the gas phase was similar to that for liquid phase. Gas
sampling was done quickly, within 10 seconds, and the pressure in the equilibrium cell
was not upset by more than 10 psig. The gas sampling bomb was then heated and pres-
surized with helium, as was done with the liquid sampling bomb.
Sample Analysis
The sample was analyzed by a Tracor 550 gas chromatograph using a 10-in x 1/8-in
Porapak QS packed column and a thermal conductivity detector. The flow rate of the
carrier gas (helium) was 2o ml/min, and the column temperature was set at 110°C.
Each sample analysis was repeated five times at 5 psig. The component peaks were
integrated by a digital integrator and recorded on a strip chart recorder. Calibration
curves were prepared for the carbon dioxide-methanol, nifcrogen.-meth.anol, and water-
methanol mixtures by plotting peak ratio vs. mole ratio. They are shown in Figures 39,
40, and'41. The thermal response factors (the slopes of the plots) were 1.075, 0.935, and
0.709 for carbon dioxide-to-methanol, nitrogen-to-methanol, and water-to-methanol,
respectively. These calibration curves were made by analyzing samples with known
compositions in a sampling bomb with a septum. The calibrated samples of carbon
dioxide in methanol were prepared by first filling the 500 ml bomb with carbon dioxide.
- 108-
-------
The pressure of the carbon dioxide was adjusted by a vacuum pump and measured by a
mercury manometer. Then a fixed amount of methanol between 0.5 and 2.0 ml was
injected by a syringe into the bomb. The bomb was heated and pressurized with helium
as usual. The calibration of nitrogen in methanol was similar to that of carbon dioxide.
The thermal response factor for nitrogen-to-carbon dioxide was obtained by dividing
the factor for nitrogen-to-methanol by the factor for carbon dioxide-to-methanol. The
factor of 0.870 was used in this work, which is very close to 0.875 reported by Diet/
(1967).
Mole Ratio, x(CQ2)/x(MeGH)
Figure 39. GC Calibration Curve for Methanol-Carbon Dioxide System.
109
-------
Hole Ratio, x(N2)/xCrieOH)
Figure 40. GC Calibration Curve for Methanol-Nitrogen System.
no
-------
Hole Ratio, x(H20)/x(rieOH)
Figure 41. GC Calibration Curve for Methanol-Water System.
m
-------
Chemicals
Carbon dioxide with a purity of 99.99% and nitrogen with a purity of 99,999%
were used in the experiment. These gases were supplied by the Aireo Company.
Certified A.C.S. grade methanol with a purity of 99.9% was obtained from the Fisher
Scientific Company. Distilled water was obtained from the laboratory.
EXPERIMENTAL RESULTS AND DISCUSSION
Vapor-liquid equilibrium data for the methanol-carbon dioxide, methanol-carbon
dioxide-nitrogen, and methanol-earbon dioxide-water systems obtained in this work are
presented in Tables 23, 24, and 25, respectively. The comparison of these data to the
literature data and/or the calculated results from the extended SRK equation of state
are discussed in the following sections.
TABLE 23
EXPERIMENTAL VAPOR-LIQUID EQLTLEBRUM p-T—x DATA FOR
THE METHANOL(l)-CO (2) SYSTEM
243.15 K
258.15 K
273.15 K
298.15 K
P atm
x2
P atm
x2
P atm
x2
P atm
¦ 'x2
2.03
0.0588
2.19
0.0398
1.91
0.0228
2.57
0.0180
4.75
0.1500
5.50
0.1056
5.15
0.0643
5.50
0.0391
7.11
0.2307 .
10.32
0.2070
10.74
0.1388
10.29
0.0733
9.91
0.3505
15.85
0.3475
20.62
0.2834
17.38
0.1300
12.40
0.5339
19.13
0.4845
28.14
0.4451
29.79
0.2238
13.28
0.7154
21.28
0.7179
31.92
0.6462
39.85
0.3334
47.64
' 0.4354
53.82
0-5683
- 112 -
-------
Methanol-Carbon. Dioxide Binary System.
The experimental apparatus and procedure described in the preceding section were
tested by comparing the experimental equilibrium data on the methanol-carbon dioxide
system with literature data. The gas-phase compositions were not determined because
the concentrations of methanol were too small to be measured.
TABLE 24
¦EXPERIMENTAL VAPOR-LIQUID EQUILIBRIUM P-T-x DATA FOR
THE METITAN0L(1]-C0 (2)-N (3) SYSTEM
10.25
20.16
30.15
40.13
39,79
30.40
20.40
10.54
0.9322
0.7379
0.7388
0.7355
0.7823
0.8133
0.8413
0.8817
0.0849
0.2585
0.2517
0.2508
0.2074
0.1804
0.1551
0.1173
243.15 K
0.0029
0.0057
0.0098
0.0137
273.15 K
0.0103
0.0083
0.0036
0.0010
0.1881
0.4385
0.3195
0.2590
0.4501
0.5112
0.6269
0.8343
0.8119
0.5635
0.6805
0.7410
0.5499
0.4888
0.3731
0.1657
As shown in Figure 16, the experimental data are in good agreement with the calcu-
lated results from the extended SRK equation of state at all four temperatures of 243,
258, 273, and 298 K. The root mean square deviation of bubble pressures from calcu-
lated values is 4.18% for a total of 26 data points. The root mean square deviation of
bubble pressures is 4.88% for the data of Katavama et al. (1975), and Ohgaki and
Katayama (1976) at 298 K, while the deviation is 1.24% for the data of this work at
that temperature. This comparison indicates a favorable correspondence of the experi-
mental data of this work and the two sets of literature data.
-------
Methanol-Carbon Dioxide-Water System
The vapor-liquid equilibrium P-T-x data of this ternary system were taken at tem-
peratures of 243, 258, 273, and 298 K. These data show that carbon dioxide is less solu-
ble in the methanol-water mixture than in pure methanol at low pressures, and the
equilibrium pressures level off near the carbon dioxide Taper pressure.
The use of the fitted binary parameter sets listed in Table 6 to predict ternary
methanol-carbon dioxide-water bubble point pressures by the extended SRK equation
of state gave results that compared favorably with experimental data. The use of both
the K{j and Ci}- parameter sets gave better results than use of Kl} only; this is reflected
by root mean square deviations between calculated and measured bubble pressures of
8.46% for use of a full parameter set and 12.45% for use of a reduced parameter set.
Calculated results at the water-to-methanol mole ratio of 0.2 are also plotted with
experimental data in Figure 42. Although a local maximum was noted in each calcu-
lated isotherm, none was found in the experimental data. It should be recognized that
calculation of equilibrium conditions for the ternary mixture requires use of binary
parameters evaluated from data on mixtures of methanol-carbon dioxide and of water-
carbon dioxide. Parameters for water-carbon dioxide mixtures were evaluated from
data in a Henry's law region, while parameters for methanol-carbon dioxide were
evaluated from data covering the entire composition range. The simple quadratic mix-
ing rules used in the SRK calculations may be inappropriate for these systems, and give
the metastable state solutions of local maxima and minima, which imply existance of
LLG equilibria. At the temperature of 298 K, which is near the critical temperature of
carbon dioxide, the equation failed to calculate bubble pressures of the ternary system
having carbon dioxide mole fractions over 0.39.
Figure 43 presents a plot of bubble point pressure vs. carbon dioxide mole fraction
in the liquid from r = 0 to r = 00 at 273.15 K, as calculated by the extended SRK
equation. Similar calculations can be performed at other temperatures, and the calcu-
lated results are believed to have good reliability as the results fit the experimantal data
well at r = 0.2.
The carbon dioxide solubilities in a methanol-water mixture at a molar ratio of 0.2
were calculated by the extended SRK equation of state from system temperature, pres-
sure, and assuming that the vapor-phase contained only carbon dioxide (see the section
Gas Solubility Calculation Using an Equation of State). The calculated and measured
carbon dioxide solubilities are listed in Table 26. For a total of 35 data points, the aver-
age error for the carbon dioxide solubilities was 12.73%. The average error could be
reduced to 8.71% if the comparison between calculated and experimental values was
restricted to the 29 data points having a mole fraction of carbon dioxide in the liquid of
0.4. Additionally, the solubility calculations became inaccurate as the system pressure
- 114-
-------
Hole Fraction x(C02)
Figure 42. Methanol-Carbon Dioxide-Water Equilibria at r = 0.2.
115
-------
Hole Fraction x(C02)
Figure 4-3. Methanol-Carbon Dioxide-Hater Equilibria at 273.15 K.
116
-------
approached an aaymtote near the vapor pressure of carbon dioxide at the system tcm-
perature.
TABLE 25
EXPERIMENTAL VAPOR-LIQUID EQULIBRIUM P^T-x DATA FOR
THE METHAN0L(1)-C02(2)-H20{3) SYSTEM AT r = 0,2
P atm
xi
x3
T =
243.15 K
1.61
0.8082
0.0323
0.1615
3.31
0.7777
0.0688
0.1537
5.53
0.7306
0.1160
0-1534
7.02
0.7092
0.1548
0.1360
9.31
0.8469
0.2198
0.1333
12.17
0.5604
0.3308
0.1088
13.61
0.4083
0.5092
0.0823
T —
258.15 K
2.35
0.8108
0.0292
0.1600
5.10
0.7782
0.0680
0.1558
11.15
0.7099
0.1476
0.1425
18.48
0.5752
0.3153
0.1095
21.67
0.3800
0.5743
0.0857
21.85
0.2972
0.6458
0.0570
T =
273.15 K
2.44
0.82 L8
0.0193
0.1589
5.73
0.7971
0.0474
0.1555
8.99
0.7742
0.0766
0.1492
13.58
0.7378
0.1197
0.1427
18.79
0.6869
0.1802
0.1329
24.87
0.6318
0.2504
0.1178
29.97
0.5444
0.3522
0.1034
33.04
0.3570
0.5730
0.0700
33.14
0.3003
0.6403
0.0594
=
Xi
- 117-
-------
TABLE 25 (CONTINUED)
EXPERIMENTAL VAPOR-LIQUID EQULIBRIUM P-T — x DATA FOR
THE METHAN0L(1)-C02(2)-H20(3) SYSTEM AT r = 0.2
P atm
X1
x2
x3
T =
298.15 K
2.91
' 0.8213
0.0145
0.1836
5.14
0.8051
0.0279
0.1670
8.20
0.7949
0.0489
0.1582
12.57
0.7848
0.0870
0.1484
16.20
0.7700
0.0830
0.1470
20.49
0.7487
0.1070
0.1443
25.70
0.7205
0.1427
0.1388
30.79
0.8879
0.1775
0.1348
35.11
0.6859
0.2073
0.1288
40.22
0.6351
0.2432
0.1217
45.01
0.5991
0.2914
0.1085
49.91
0.5569
0.3397
0.1034
54.04
0.5124
0.3928
0.0948
Methanol-Carbon Dioxide-Nitrogen System
Vapor-liquid equilibrium data were taken for methanol-carbon. dioxide-nitrogen
mixtures at 243.15 and 273.15 K. These eight data points are given in Table 24. The
mole fractions in the vapor were determined for carbon dioxide and nitrogen; the
methanol content of the vapor phase was neglected.
The solubility calculation with the extended SRK equation of state was used to
predict the solubility of the nitrogen-carbon dioxide mixture in methanol. Table 27 lists
the calculated and measured solubilities. Figure 44 shows excellent agreement between
calculated carbon dioxide solubilities and experimental data; the average error is
8.25%. However, the calculated nitrogen solubilities are lower than the measured
values; the average error is 39.5% for the eight data points.
- 118 -
-------
Measured x
Figure 44, Calculated and Measured Solubilities of Carbon Dioxide
and Nitrogen in Methanol.
119
-------
TABLE 26
CALCULATED AND EXPERIMENTAL CARBON DIOXIDE SOLUBILITIES, x(COA
IN THE MIXTURE OF METHANOL AND WATER AT r = 0.2
fji
P atcn
Experimental
Calculated
243.15
1.61
0.0323
0.0368
3.31
0.0686
0.0755
5.53
0.1160
0.1287
7.02
0.1548
0.1624
9.31
0.2198
0.2212
12.17
0.3308
0.3098
13.61
0.5G92
0.3718
258.15
2.35
0.0292
0.0338
5.10
0.0660
0.0733
11.15
0.1476
0.1627
18.46
0.3153
0.2906
21.6
0.5743
0.3719
21.85
0.6458
0.3778
273.15
2.44
0.0193
0.0238
5.73
0.04/ 4
0.0557
8.99
0.0766
0.0874
13.58
0.1197
0.1328
18.79
0.1802
0.1865
24.87
0.2504
0.2553
29.97
0.3522
0,3248
33.04
0.5730
0,3795
33.14
0.6403
0.3818
298.15
2.91
0.0145
0.0169
5.14
0.0279
0.0298
8,20
0.0469
0.0475
12.57
0.0870
0.0727
16.20
0.0830
0.0938
20.49
0.1070
0.1185
25.70
0.1427
0.1490
30.79
0.1775
0.1792
35.11
0.2073
0.2055
40.22
0.2432
0.2375
45.01
0.2914
0.2688
49.91
0.3397
0-3028
54,04
0.3928
0.3332
- 120-
-------
Avg Error —
xa2o
Efe - XcdVZe
1
100
35
v /
= 12.73%
r =
xMeOH
TABLE 27
CALCULATED AND EXPERIMENTAL SOLUBILITY RESULTS FOR
METHANOL(l)-CO -(2)-N (3) SYSTEM
P aim
y(Exp.)
x(C02)
x(N2)
eo2
N2
Exp
Cal
Exp
Cal '
T
= 243.15 K
10.25
0.1881
0.8119
0.0649
0.0493
0.0029
0.0021
20.16
0.4385.
0.5835
0.2585
0.2352
0.0057
0.0032
30.13
0.3195
0.6805
0.2517
0.2368
0.0098
0.0058
40.13
0.2590
0.7410
0.2508
0.2340
0.0137
0.0080
T
= 273.15 K
39.78
0.4501
0.5499
0.2074
0.1929
0.0103
0.0084
30.40
0.5112
0.4888
0.1804
0.1754
0-0083
0.0043
20.40
0.8269
0.3731
0.1551
0.1511
0.0038
0.0022
10.54
0.8343
0.1857
0.1173
0.1071
0.0010
0.0005
Avg Error
8.25%
39.47%
' ioo%'
,, 8 J
The discrepancies between experimental and calculated nitrogen mole fractions may
be due to experimental errors. Specifically, nitrogen may migrate faster than methanol
in transferring a sample through the capillary tube to the sampling bomb and/or from
the sample bomb (where all of the sample has been vaporized) to the gas chromato-
graph sampling loop. Such occurrences would result in high measured nitrogen
Avg Error —
Efx, - xcd)/i
- 121 -
-------
solubility. Additionally, the relative insensitivity of the thermal conductivity detector
to a low concentration of nitrogen, which exists in a liquid phase sample, may contri-
bute some deviations to the experimental data. The binary data on hydrogen solubili-
ties in methanol reported by Yorizane et a!. (1989), which were obtained using a tech-
nique and apparatus similar to the present work, were found higher than' the values
shown by Landolt-Bornstein et al. (1976). Zeck and Knapp (1983) have used an
apparatus similar to that used here to measure gas solubilities in methanol in a range of
0.1 to 1.0 mole fraction of gas in liquid: they, however, used another type of apparatus
(volume measurement) to measure gas solubilities in a mole fraction range of 0.0002 to
0,04. These data indicate that the sampling and analytical methods used in the experi-
ments of the present work may not be suitable for a sparsely soluble gas. However, they
appear to be very reliable in obtaining data on a very soluble gas such as carbon diox-
ide.
- 122 -
-------
SUMMARY OF CONCLUSIONS
The objective of the research reported here was to develop a thermodynamic frame-
work that could be used to describe the equilibrium behavior of methanol with com-
pounds found in the gas produced from coal. The approach that was taken divided the
constituents into three groups: Group I consisted of supercritical components, Group H
consisted of compounds that are normally gases at the conditions of interest, and
Group EH contained compounds that are liquids at the conditions of interest. This divi-
sion was used to select either an equation of state or an activity coefficient formulation
of the equilibrium criteria. Once this selection was made, appropriate' parameters in
the formulation were evaluated from binary data obtained from the literature and
experiments that were part of this study. With the parameters evaluated in this way, it
is possible to predict the behavior of systems containing any number of the components
from Group T, Group II, and/or Group III. A more specific discussion of the accom-
plishments of the work described in this report follows.
A vapor-liquid equilibrium apparatus was developed along with a sampling tech-
nique and analytical method to obtain equilibrium data on systems having high gas
solubilities. Good data were obtained from this apparatus for carbon dioxide solubilities
in methanol with and without an inert gas (nitrogen), and in mixtures of methanol and
water. However, low solubilities of nitrogen in methanol cannot be measured accu-
rately.
Bubble point pressure variance provided a useful objective function in the parame-
ter search procedure for both equation-of-state and activity coefficient methods. This
search procedure, which Includes a bubble point pressure calculation, does not require
measurement of vapor-phase composition.
Mathias' polar' correction factor improved the calculation of vapor pressures with
the SRK equation of state for polar compounds of methanol and water, but this factor
may not necessary for ethyl mercaptan and dimethyl sulfide.
¦ Temperature-dependent binary interaction parameters in the extended SRK equa-
tion of state have greatly improved the accuracy of correlations of methanoi-containing
binary VLE systems comprised of constituents from coal gasification. Ternperature-
- 123-
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independent binary interaction parameters are satisfactory for gas-gas mixtures. These
parameters are applicable in a broad range of temperatures.
Phase equilibrium calculations using the extended SRK equation of state were satis-
factory for mixtures of methanol-gas systems as long as the gas component had a mole
fraction in the liquid less than 0.6. They did not provide satisfactory predictions for
those systems at high gas concentrations in the liquid phase. However, absorption-
stripping processes that condition synthetic gas mixtures operate at liquid circulation
rates that maintain the levels of dissolved gases below those at which the equation of
state loses its accuracy.
The extended SRK equation of state tends to predict false LLG three-phase equili-
bria in methanol-light hydrocarbon and methanol-acid gas systems. This is believed to
be caused by the quadratic mixing rules for interaction parameters.
The use of the optimized parameter sets enables the equation of state to predict the
behavior of a methanol-containing multicomponent system; comparisons between
experimental data and bubble point pressure calculations for methanol-H2-N2j
methanol-CO-Ng, and methanol C02-H20 systems mixtures were good.
A simple gas solubility calculation using the extended SRK equation of state was
effective in calculating mixed-gas solubilities in a pure solvent and pure gas solubilities
in a mixed solvent.
The activity coefficient models using the four-suffix Margules, Wilson, and UNI-
QUAC equation are excellent for binary systems that contain condensable components
(those from Groups II and III). They are especially useful in describing the vapor-liquid
equilibrium behavior of systems containing volatile liquids, such as methanol, mercap-
tans and sulfides. The determined parameters in these models may be used to describe
the multicomponent system without further adjustment, but there is no guarantee for
describing the behavior of a system containing a supercritical component.
The Wilson and UNIQUAC equations are superior to the four-suffix Margules equa-
tion for most of the systems studied. The former two equations have a good built-in
temperature-dependent relationship and do not predict false phase separations for
methanol-acid gas and methanol-light hydrocarbon systems.
Recently developed equations of state—which include density dependent mixing
rules (Mat hi as and Copeman, 1983; Won, 1983) based on the two-fluid, local composi-
tion theories—should be useful in future applications describing the vapor-liquid equili-
brium behavior of systems having components covering a broad range of densities or
with polar or hydrogen-bonding components. Coal-produced gas that is • conditioned
with a physical solvent is an example of such a system.
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The use of the bubble point pressure criterion for evaluation of the binary parame-
ters in an equation of state should be maintained. However, a phase envelope calcula-
tion or a VLE flash calculation summarized by Van Ness and Abbott (1982) may be
appropriate to describe the phase behavior of a system at fixed temperature and pres-
sure.
A direct sampling and analysis method for high pressure liquid sample needs to be
developed to simplify the currently-used method and to obtain reliable data for gases of
low solubility. The design and construction of an apparatus to be able to measure iiroi-
tieomponent solubilities at constant temperature and pressure are essential in future
work.
-------
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LIST OF SYMBOLS
a — energy constant in extended SRK equation
A - aP/RzT2
A:}, A y,-, Dl} — binary Margules parameters
Af, Bt, Ct — Antoine equation constants
b — Tolnme constant in extended SRK equation
B - bP/RT
Cvy — interaction parameter of b in extended SRK equation
/,¦ — fugacity of i
// — fugacity of i at reference state
¦ ----- excess Gibbs free energy
lft j — Henry's law constant for solute i in solvent j
Ktj — interaction parameter of a in extended SRK equation
m - parameter used to correlate a in the SRK equation
n — number of data points
ni — moles of i in mixture
N — number of components in mixture
ps — saturated vapor pressure
p* — yapor pressure
p — Mathias' polar correction factor
P — pressure
Pc — critical pressure
Pca! — calculated pressure
Pe — experimental pressure
P ref ~~ reference pressure
q — structure area parameter in UNIQUAC equation
q' — modified structure area parameter in UNIQUAC equation
r — structure size parameter in UNIQUAC equation
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r — water to methanol mole ratio
R — gaa constant
T — temperature
Tc — critical temperature
Tr — reduced temperature, T/Tc
Au12, A«2i temperature-independent binary UNIQUAC parameters
v — specific volume
v[ — liquid molar volume of i
£>/° — partial molar volume of solute i at infinite dilution
V — volume
Vc — critical molar volume .
— mole fraction i
— mole fraction i in liquid phase of two-phase mixture
j/,- — mole fraction I in vapor phase of two-phase mixture
z — compressibility factor = Pv/RT
zc — critical compressibility factor
Greek
a j- — temperature-dependent function in extended SRK equation
— constant in Margules equation
7, - activity coefficient of i
8j — solubility parameter of i
A\12, A\2i temperature-independent binary Wilson parameters
A,y, Ak;: Akj- — temperature-dependent binary Wilson parameters
pc critical liquid molar density
cr2 — bubble point pressure variance
Tt-y, t,,. Tkj — temperature-dependent binary UNIQUAC parameters
t * — fugacity coefficient of saturated i
4s£ — fugacity coefficient of liquid
t>)t- — Pitzer acentric factor
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