vvEPA
United States Industrial Environmental Research EPA-600/7-80-116
Environmental Protection Laboratory May 1980
Agency Research Triangle Park NC 27711
Solubilities of Acid Gases
and Nitrogen in Methanol
Interagency
Energy/Environment
R&D Program Report
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EPA-600/7-80-116
May 1980
Solubilities of Acid Gases
and Nitrogen in Methanol
by
J.K. Ferrell, R.W. Rousseau,
and J.N. Matange
North Carolina State University
Department of Chemical Engineering
Raleigh, North Carolina 27607
Grant No. R804811
Program Element No. INE825
EPA Project Officer: Robert A. McAllister
Industrial Environmental Research Laboratory
Office of Environmental Engineering and Technology
Research Triangle Park, NC 27711
Prepared for
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Research and Development
Washington, DC 20460
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CONTENTS
FIGURES
TABLES
INTRODUCTION - 1
STATEMENT OF OBJECTIVES 4
DEVELOPMENT OF THE THERMODYNAMIC MODEL 5
FUNDAMENTALS - 5
THERMODYNAMIC CORRELATIONS —13
Vapor Fugacity Coefficients 13
Activity Coefficients 18
Reference Fugacities 22
STRUCTURE OF THERMODYNAMIC MODEL 27
Model BUBLT— 28
Model DEWT 32
EVALUATION OF MARGULES PARAMETERS 33
Summary 56
EXPERIMENTAL EQUIPMENT AND PROCEDURE 57
REAGENTS 57
ANALYSIS 59
CALIBRATIONS 59
TEST DATA: METHANOL-C02 MIXTURES 60
MULTICOMPONENT PROCEDURE 61
MULTICOMPONENT MEASUREMENTS AND PREDICTIONS 61
CONCLUSIONS 73
LITERATURE CITED 75
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FIGURES
Number Page
1. Flow chart for BUBLT - 30
2. Flow chart for DEWT 31
3. Comparison of equilibrium experimental and predicted
pressures for methanol-carbon dioxide mixtures 40
4. Comparison of equilibrium experimental and predicted
pressures for methanol-nitrogen mixtures 43
5. Comparison of equilibrium experimental and predicted
pressures for methanol-hydrogen sulfide mixtures 46
6. Comparison of equilibrium experimental and predicted
pressures for carbon dioxide-nitrogen mixtures 49
7. Comparison of equilibrium experimental and predicted
pressures for carbon dioxide-hydrogen sulfide mixtures 52
8. Comparison of equilibrium experimental and predicted
pressures for nitrogen-hydrogen sulfide mixtures 54
9. Experimental apparatus 58
10. Comparison of experimentally determined equilibrium
pressures with those of Katayama et al (1975) for
methanol-C02 mixtures at 298.15 K 62
11. Comparison of predicted and measured equilibrium
pressures for four-component mixtures at 258.15 K 69
12. Comparison of predicted and measured equilibrium
pressures for four-component mixtures at 273.15 K 70
13. Comparison of predicted and measured equilibrium
vapor compositions for four-component mixtures at
258.15 K 71
14. Comparison of predicted and measured equilibrium
vapor compositions for four-component mixtures at
273.15 K 72
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TABLES
Number Page
1. Binary interaction constants for Soave modification of
Redlich-Kwong equations of state 17
2. Critical constants and Pitzer accentric factors 18
3. Constants used in Equation 21d for calculating
methanol liquid molar volume 24
4. Comparisons of experimental vapor-liquid equilibrium
data with model correlations for methanol (1) - car-
bon dioxide (2) mixtures 38, 39
5. Comparisons of interpolated experimental vapor-
liquid equilibrium data with mode] correlations
for methanol (1) - nitrogen (2) mixtures- 42
6. Comparisons of experimental vapor-liquid equilibrium
data with model correlations for methanol (1) -
hydrogen sulfide (2) mixtures 44, 45
7. Comparisons of interpolated experimental vapor-
liquid equilibrium data with model correlations
for carbon dioxide (1) - nitrogen (2) mixtures 48
8. Comparisons of experimental vapor-liquid equilibrium
data with model correlations for carbon dioxide (1) -
hydrogen sulfide (2) mixtures 50, 51
9. Comparisons of interpolated experimental vapor-liquid
equilibrium data with model correlations for nitrogen
(1) - hydrogen sulfide (2) mixtures 53
10. Margules parameters from parameter optimization
procedure GMAR --55
11. Comparisons of experimental vapor-liquid equilibrium
data with those of Katayama et al (1975) for methanol-
C02 mixtures at 298.15 K 63
12. Experimental vapor-liquid equilibrium data for methanol-
carbon dioxide-nitrogen-hydrogen sulfide mixtures at
258.15 K- 64
13. Experimental vapor-liquid equilibrium data for methanol-
carbon dioxide-nitrogen-hydroge'n sulfide mixtures at
273.15 K 65
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TABLES
(cont.)
Number Page
14. Comparison of model predictions with experimental
pressure and vapor composition for methanol-carbon
dioxide-nitrogen-hydrogen sulfide mixtures at 258.15 K 67
15. Comparison of model predictions with experimental
pressure and vapor composition for methanol-carbon
dioxide-nitrogen-hydrogen sulfide mixtures at 273.15 K 68
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INTRODUCTION
Considerable attention has been given recently to coal gasifica-
tion in the hope that a substitute for natural gas and crude oil can
be developed, thereby easing the prevailing energy shortage. For coal
gasification to be part of a solution to the energy shortage, prepara-
tion must be made to gasify literally millions of tons of coal.
Perhaps the most consistent feature of coal is its inconsistency.
Its molecular structure is undefined; its composition and character-
istics can vary widely depending upon the geographic area, the coal
seam, and even the location within the same seam, from which it is
mined. Thus when coal is gasified, the gas formed has a very complex
composition. Along with the desired products, H2, CO, hydrocarbons,
etc., there is a significant quantity of undesirables such as hLS,
C02, COS, benzene, phenol, etc. In this environmentally con-
scious era, coal gasification would be acceptable only if the environ-
mental impact of coal gasification can be accurately assessed and
then properly handled.
Recognizing this situation, the Environmental Protection Agency
in 1977 contracted for the design and construction of a coal gasifi-
cation-gas cleaning test facility at North Carolina State University,
to be operated by faculty and staff of the Department of Chemical
Engineering. Construction was begun in January 1978 and the plant
was completed and turned over to the University in the summer of 1978.
The principal components of the pilot plant are a continuous
fluidized bed gasifier, a cyclone separator and venturi scrubber for
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removing participates, condensables, and water-soluble species from
the raw synthesis gas, and absorption and stripping towers and a flash
tank for acid gas removal and solvent regeneration. The gasifier
operates at pressures up to 100 psig (791 kPa), has a capacity of 50
Ibs coal/hr (23 kg/hr), and runs with either steam-air or steam-02
feed mixtures. The acid gas removal system is modular in design, so
that alternative absorption processes may be evaluated. Associated
with the plant are facilities for direct digital control of all process
systems and for on-line data acquisition, logging, and graphical dis-
play. Facilities for sampling and exhaustive chemical analysis of all
solid, liquid, and gaseous feed and effluent streams are also available.
The overall objectives of the project are to characterize complete-
ly the gaseous and condensed phase emissions from the gasification-
gas cleaning process and to determine how emission rates of various
pollutants and methanation catalyst poisons depend on adjustable pro-
cess parameters.
The task of this study was to concentrate on the gas cleaning
portion of the project. Broadly speaking, gas cleanup systems can
be divided into three groups based on the absorbents used: amine
based systems, hot carbonate systems, and physical solvent systems.
In amine based systems the most common solvents are monoethanol-
amine (MEA) and diethanolamine (DEA). Acid gases, H2$ and C02> react
with the amine solution to form chemical complexes; the reactions may
be reversed by applying heat to the solution and stripping off the
H2S and CO^ in a regeneration tower. Amine systems are falling into
disfavor as they are both non-selective and suffer high vaporization
-------
losses. In addition, MEA forms stable compounds with COS and C$2
which cannot be regenerated by heat. Diglycolamine is increasingly
being employed in gas cleanup systems due to its lower volatility.
Another amine that is finding use is diisopropanol amine.
In hot carbonate processes, acid gases are absorbed in a counter-
current contactor by a carbonate solution. The gases are recovered
from the rich solution by flashing and steam-stripping in a low pres-
sure regenerator. Modern carbonate systems—such as the Benfield
Process, the Catacarb Process, and the Giemmarco-Vetrocoke Process-
have found many applications in today's gas, chemical and refinery
industries. These systems employ a 20 to 30 percent water solution
of potassium carbonate, operate at between 220° and 300°F, and uti-
lize various additives to increase the rate of gas absorption as well
as to catalyze the reactions.
The third general method for removing acid-gas from a raw-gas
stream is by physical absorption in an organic solvent without chemical
reaction. The solvent can be regenerated by heat, pressure reduction,
or gas stripping, producing a concentrated stream of the absorbed gas.
H2S and CO,, as well as minor components in the gas stream—including
COS, CS2 and mercaptans—are more soluble in many organic solvents
than fuel-gas species, especially at elevated pressure. In addition,
some of the physical solvents are highly selective for H2S over C02.
This aspect is important in applications where a H?S rich stream has to
be generated to be sent to a Claus Plant for sulfur recovery.
Refrigerated methanol is the solvent being used currently in the
NCSU facility. Methanol is also the solvent used in Lurgi's proprie-
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tary Rectisol process. After a careful search of the literature, it
was concluded that the data and correlations available to the techni-
cal public are not sufficient to analyze this system properly. Thus
the objective of this study was to generate part of the data and cor-
relations necessary for analysis of methanol-based acid gas removal
systems. The particular emphasis of this study was the multicomponent
vapor-liquid equilibrium behavior of selected constituents of crude
coal gas.
STATEMENT OF OBJECTIVES
The purpose of this study was to develop a thennodynamic model
for the system methanol-carbon dioxide-nitrogen-hydrogen sulfide.
To check the validity of the model predictions it was necessary to
have experimental vapor-liquid equilibrium data for the four compo-
nent system. As these data could not be found in the literature,
another objective of this research was to develop an experimental
apparatus to obtain multicomponent vapor-liquid equilibrium data for
mixtures of these components. The objective of the experimental pro-
gram was to obtain the multicomponent vapor-liquid equilibrium data
with the system pressure in the range of five to forty atmospheres
and system temperature in the range of 0°C to -20°C.
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DEVELOPMENT OF THE THERMODYNAMIC MODEL
FUNDAMENTALS
The main objective of this research was development of a thermo-
dynamic model for prediction of vapor-liquid equilibria for a multi-
component system containing the principal components in an acid gas
removal system. The multicomponent system chosen for study consisted
of mixtures of methanol, carbon dioxide, nitrogen and hydrogen sul-
fide. The structure of the thermodynamic model was made flexible to
facilitate future inclusion of additional components into the model.
This work was a continuation of that by Bass (19781. In the
interest of continuity, the next few paragraphs trace the thermody-
namic model development from its inception to its current
status.
Development of any phase equilibrium model begins with a considera-
tion of the fundamentals of phase equilibria. Since phase equilibria
is a vast subject, the intent here will be to discuss that segment
which applies to the thermodynamic model. Since the model
was based on one liquid phase in equilibrium with a vapor phase, the
phase equilibria discussion also focuses on this situation.
For liquid and vapor phases to be in equilibrium with each other
it is necessary that the system be in a state of equilibrium with
respect to the three processes of heat transfer, boundary displacement,
and mass transfer. Equality of temperature and of pressure between the
two phases assures equilibrium for heat transfer and boundary displace-
-------
merit processes. Unfortunately, the conditions necessary for establish-
ing mass transfer equilibrium cannot be expressed in a similar straight-
forward fashion. At a strictly mathematical level, Gibbs provided a
guide by defining the chemical potential function, v; for mass trans-
fer equilibrium, the chemical potential of each component must be in-
variant from phase to phase. Thus for a system comprised of N compo-
nents, equilibrium with respect to the processes mentioned earlier is
indicated by the following equalities:
TVap = TLiq (1)
(1 - 1 to N) (3)
To establish equilibrium between the two phases it is clear that
temperature and pressure of the two phases must be equal . However
what is necessary to obtain the equality of chemical potentials is
not clear. What is needed is an expression relating chemical potential
(an abstract quantity), to composition, temperature and pressure
(measurable quantities).
G. N. Lewis obtained the following expression for a pure ideal
gas at constant temperature:
v - n = RT In - (4)
P°
where
-------
u = chemical potential of the ideal gas at system temperature T
y° = chemical potential of the ideal gas at arbitrary reference
conditions
R = gas constant
T = temperature of the ideal gas
P = pressure of the ideal gas at system temperature, T
P° = pressure of the ideal gas at the arbitrary reference con-
ditions at which v is evaluated
Equation 4 represents an important simplification in it the
abstract chemical potential function is expressed in terms of a mea-
surable quantity, pressure. However, this is possible only under
pure ideal gas conditions. To remove this constraint, Lewis introduced
the function fugacity through the definition
f.
y. - v°. = RT In ~ (5)
f°
where
p. = chemical potential of component i at system temperature and
pressure
u? = chemical potential of component i at arbitrary reference
conditions
f • = fugacity of component i at system temperature T and pressure
f? = fugacity of component i at the arbitrary reference condition
at which \i. is evaluated
The concept of fugacity is akin to that of pressure; under ideal
gas conditions, fugacity and pressure are the same. Prausnitz (1969),
for example, refers to fugacity as a "corrected pressure." It should
-------
be noted that Equation 5 does not refer to a particular phase and,
therefore, applies to gases, liquids and solids.
It can be shown that equality of fugacity of each component in
every phase is equivalent to the corresponding equality of chemical
potentials. Thus the condition for mass transfer equilibrium can now
be written as
(6)
where
f. = fugacity of component i in the vapor phase
f- = fugacity of component i in the liquid phase
Equation 6 is a significant improvement on Equation 3 as the
abstract chemical potential term is replaced by fugacity, a term simi-
lar to pressure. Equation 6 is the fundamental thermodynamic rela-
tionship to be used. for phase equilibria. It now remains to develop
expressions relating fugacity to composition, temperature and pressure.
There are two basic methods for calculating the fugacities. The
first utilizes the exact relationship
• TIT l" «&•> , - "w -'» or
i ' »n n
where
R = gas constant
T = temperature
-------
P = total pressure
V = total volume
n^ = moles of component i
f.j = fugacity of component i
A single equation of state is used for both the vapor and the liquid
phase. This equation of state is used to solve the partial derivative
in Equation 7.
The use of Equation 7 to evaluate f.. requires utilization of a
pressure explicit equation of state that describes P-V-T properties
of the system over the limits of integration. While such calculations
are indeed possible for many single-component substances and for a limited
number of mixtures, it is not expected that the components encountered
in acid gas removal systems could be handled in this manner.
In the second method, liquid and vapor phases are treated inde-
pendently. To obtain fugacities in the vapor phase the following
expression is used:
(8)
i i i
where
. = fugacity coefficient of component i
y. = vapor phase mole fraction of component i
P = total pressure
The fugacity coefficient, ., is the measure of the deviation from
9
-------
ideal behavior of component i in the vapor phase.
Either of the following two equations can be used to calculate
the fugacity coefficient of component i, $ . :
In *. -JL/" [(|f-) -S!]dV - In z (9)
1 RT V 8ni T,V,n, V
J
i T,P,n.
O
z s pv/RT = compressibility factor
To obtain the fugacity coefficient from Equation 9 a pressure
explicit equation of state is necessary, while Equation 10 requires
a volume explicit equation of state. Since most equations of state
are in the pressure explicit form, Equation 9 is used more easily
than Equation 10.
Liquid fugacities are obtained from the definition
(11)
where
Y.: = activity coefficient of component i
x.. = liquid mole-fraction of component i
Ref
f? = reference state fugacity for component i
Although the choice of the reference state is arbitrary, the activity
10
-------
coefficient, which is a measure of deviation from ideal solution be-
havior, depends on the composition temperature and the choice of the
reference state. There are two choices for the reference fugacity:
one leading to an ideal solution in the sense of the Raoult's law and
the other to an ideal solution in the sense of the Henry's law.
For an ideal solution at constant temperature and pressure, the
fugacity of each component is proportional to its liquid mole frac-
tion. Thus for component i in an ideal solution,
= V- (12)
where C. is a proportionality constant dependent on temperature and
pressure but independent of the mole fraction of component i.
If Equation 12 holds over the entire range of composition, from
x- = 0 to x.j = 1, then the solution is ideal in the Raoult's law sense.
In this case, it is evident from the boundary condition at x- = 1 that
the proportionality constant, C.. , is equal to the fugacity of pure
liquid i at the temperature and pressure of the solution.
If on the other hand, Equation 12 holds over a small range of
x.., with x.. being close to zero, then the solution is ideal in the
Henry's law sense. In this case, the constant C.. is not equated to
the fugacity of pure liquid i, but to the fugacity of i in an infinite-
ly dilute solution.
A comparison of Equations 11 and 12 shows that activity coeffi-
cients of all the components are equal to unity in an Ideal solution.
In nonideal solutions, the term normalization of a component is often
11
-------
used. Normalization of a component refers to the conditions which
will lead to ideal behavior for that component. When the reference
state of component i is chosen in the Raoult's law sense, normaliza-
tion for component i implies
Y.J •> 1.0 as x.. ->• 1.0
On the other hand, if the reference state for component i is chosen
in the Henry's law sense, normalization for component i is
•y. -» 1.0 as x.j •* 0.0
If all components of a solution are normalized in the same way,
either in Raoult's law sense or in the Henry's law sense, normaliza-
tion is said to follow the symmetric convention. If some components
are normalized in the Raoult's law sense and others in the Henry's
law sense, the normalization follows the unsymmetric convention.
Using Equations 6, 8 and 11 to express equilibrium conditions
results in the relationship
(13)
As mentioned in the beginning of this section, the multicomponent
system being modelled consists of methanol -carbon dioxide-nitrogen-
hydrogen sulfide. Since methanol is a polar compound, and methanol
and carbon dioxide are known to associate in the vapor phase (Hemma-
12
-------
plardh and King, 1972), the thermodynamic model developed in this study
was based on the second method of calculating the fugacities; i.e.
Equation 13. The temperature and pressure range for which the thermo-
dynamic model was developed suggested the symmetric convention for
normalization. Furthermore, as pointed out by O'Connell (1977), severe
difficulties exist in using Henry's law for the reference state basis
when the solvent consists of more than one component. Since it was
believed that more flexibility would result from defining reference
liquid state conditions by the Raoult's law convention, particularly
in regard to adding components to the system model, this approach
was chosen.
THERMODYNAMIC CORRELATIONS
A foundation for the thermodynamic model was found in the final
form of the fundamental relationship of phase equilibria (Equation 13).
The next step was development of a structure for using the model. The
building blocks for this structure were thermodynamic correlations to
calculate fugacity coefficients, activity coefficients and reference
state fugacities for each component in the multicomponent system methanol-
carbon dioxide-nitrogen-hydrogen sulfide.
Vapor Fugacity Coefficients
To obtain the correlation for the fugacity coefficient, it was
decided to use Equation 9 with a pressure explicit equation of state.
13
-------
in *, = /[(-) -]dV - In z (9)
1 Kl V 8ni T,V,n. V
J
There are many equations of state, including Redlich-Kwong, the
Soave modification of the Redlich-Kwong , Benedict-Webb-Rubin and
virial.
The Redlich-Kwong equation is commonly considered one of the best
two parameter equations of state and was the first equation of state
used in the present therinodynamic model. Subsequently, it was deter-
mined that the Soave modification of the Redlich-Kwong equation of state
provided a significant improvement in accuracy; it was used in the
remainder of this work. The Soave modification of the Redlich-Kwong
equation of state is given by
aa
where
v = vapor molar volume
a,b = constants in the Soave modification of the Redlich-Kwong
equation of state
a - function of temperature and acentric factor, u
For any pure component, constants a, b and a are obtained from
a = 0.42747 R2 T2 / P (14a)
\f \t
14
-------
b = 0.08664 R T / Pr (14b)
c c
a = [1 + (0.48508 + 1.55171u> - 0.15613to2} {1 - (-)}]2 (14c)
where
T = critical temperature
P = critical pressure
0) = Pitzer acentric factor
For a mixture, constants a and b are obtained by the mixing rules
N
b - I y.b. (14d)
N N
«a " I I y
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Equation 14 can also be expressed as
Pv3 - RTv2 + (a - RTb - Pb2)v - ab = 0 (15)
The largest root of Equation 15 is the vapor phase molar volume.
Substitution of Equation 14 into Equation 9 yields the following
equation for fugacity coefficient of component i
bi
In * = (z-1) - In (z-B)
where
A = 2f» (16a)
irr
(16b)
Fugacity coefficients were calculated for the component of interest
from Equation 16. Binary interaction constants, K.., are presented in
Table 1. Of the six binary interaction constants required by the model,
three were found in the literature, while the other three were cal-
culated using experimental binary x-P-T data. The criterion used to
obtain these constants was the minimization of the bubble point pressure
variance. Generally the binary interaction constants are small and
on the order of 0.00 to 0.25 (Graboski and Daubert, 1978). The sum of
16
-------
the squares of the deviations between pressure predicted by the model
and experimental pressure was calculated for several values of K-. in
' ' J
the range 0.00 to 0.25. Using quadratic interpolation the optimum
value of K.. was taken as that minimizing the sum of the square of the
' 0
deviations for each of the three binaries for which literature values
were unavailable. Critical constants and Pitzer acentric factors
used in the model are given in Table 2.
TABLE 1
Binary Interaction Constants for Soave Modification
of Redlich-Kwong Equation of State.
System K.. Source
lethanol - C02 0.0628 a
lethanol - N2 0.080 b
lethanol - H2S -4.000 c
02 - N2 -0.022 Graboski and Daubert (1978)
:02 - H2S 0.102 Graboski and Daubert (1978)
- H~S 0.140 Graboski and Daubert (1978)
Calculated from x-P-T data found in literature (Yorizane et al.,
1969; Katayama et al., 1975).
Calculated from x-P-T data found by Weber and Knapp (unpublished
data, Dechnische Universitat, Berlin, Fachdereich 10, Berfahrenseechink,
Institut fiir Thermodynarnik and Anlagentechm'k, 1978).
Calculated from x-P-T data found in literature (Yorizane et al.,
1969).
17
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TABLE 2
Critical Constants and Pitzer Acentric
Factors (Reid et al., 1977).
Component
Methanol
co2
N2
H2S
]c
512.6
304.2
126.2
373.2
Pc
(atm)
79.9
72.8
33.5
88.2
vc
(cc/mole)
118.0
94.0
87.5
98.5
00
0.559
0.225
0.040
0.100
Activity Coefficients
A number of correlations are available for activity coefficients.
Prominent among them are the Wohl equation, the Wilson equation, and
the UNIQUAC equation. Adler et al (1966) have recommended a special
case of the Wohl equation, the four-suffix Margules equation, as the
best choice for calculating activity coefficients in systems of the
type under study here. Based on this recommendation, the four-suffix
Margules equation was selected to calculate activity coefficients in
the model. It should also be mentioned that the Wilson equation was
examined, but convergence problems associated with estimation of model
parameters reinforced the decision to use the Margules equation.
Truncating the original Wohl polynomial (1953) to include only
the terms up to the fourth power and assuming equal molal volumes
for the components, the following expression for the activity coef-
18
-------
ficient of component i in a mu Hi component solution can be obtained:
N N N
log Y. = 4 I I I x.x.x 8..
1 j=l k=l £=1 J k * 1J
N N N N
(17)
where B. ,.,, are related to binary Wohl constants, A.., A., and D..
i J j i i j »
and a ternary constant C* (to be discussed in subsequent paragraphs).
Depending on the values of the integers i, j, k, and £,
is determined by the following rules:
If i = j = k = £,
If i = j = k ^ i,
A
Pijk£= Biii£=
If 1 = j f k = i,
.
+ Ak. - D1|£) (17c)
If i = j t k j« £,
6ijk£ = eiik£ = 6ik£i = •
19
-------
1/12 [(Ak. + A£. + A.k£) - CVik£] (17dconfd)
If 1 t j ? k
Aik£
where
Aik + \i + AU + A*i * \£ + A£k,
C*. .. = ternary constant for component i in the ik
ternary mixture.
Adler et al. (1966) studied the effect of C* on the deviation
of the predicted vapor composition from the experimental vapor com-
position for a number of ternary systems. Their study indicated that
for all systems the value of C* can be expected to be very near zero.
This implies that the term in the series expansion of the excess
free energy owing to clusters of three molecules, all different, is
not exceptionally important. In fact, the expected population of
such clusters seems to be about equal to the average of the popula-
tions expected for triple clusters from the binary data. Based on
this the value of C* was taken as zero in the model.
To calculate values for B-JJ^. it is necessary to know the con-
stants A.., A., and D.. for all binary mixtures that can be formed
' J J I IJ
by the system components. Unfortunately, solution theory 1s not
at a point where these constants can be calculated a priori from pure
20
-------
component properties; they must be estimated from binary experimental
vapor-liquid equilibrium data.
A total of six binaries result from the combinations of the com-
ponents of the multicomponent system, methanol-carbon dioxide-nitro-
gen-hydrogen sulfide. They are methanol-carbon dioxide, methanol-
nitrogen, methanol-hydrogen sulfide, carbon dioxide-nitrogen, carbon
dioxide-hydrogen sulfide, and nitrogen-hydrogen sulfide. For each of
these binaries, extensive equilibrium data were collected from the
literature.
For a binary system, the four-suffix Margules equation simplifies
to
log YI - xj [A.. + 2(A.. - AIJ - D.-Jx. + 30.^] (18)
The binary constants A..., A., and D.. were evaluated from the binary
experimental x-P-T data using a number of techniques. The constants
which were finally used in the model were evaluated by the technique
which resulted in the smallest deviation between the predicted pressure
and the experimental pressure. The details of this technique will be
discussed in the section dealing with parameter evaluation.
It should be noted that the binary constants, A.., A., and D..,
I J J » IJ
are evaluated for a fixed temperature and pressure. The effect of
pressure on the liquid phase is usually small and the pressure depend-
ence of the constants was neglected. For the temperature dependence,
a simple inverse relationship with respect to temperature has been sug-
gested (Adler et a!., 1966). Assumptions of A.., A... and D.. to be
1J J 1 IJ
21
-------
inversely proportional to absolute temperature were used in the para-
meter evaluation techniques. For the binary mixtures involving nitrogen,
use of the inverse temperature dependence for the constants was found
to give unsatisfactory results. A number of alternatives were tested
to obtain the constants for these binaries. The one which was most
successful involved the interpolation of experimental binary x-P-T
data. System pressure P was evaluated for a number of values of the
liquid mole fraction x at the temperatures of interest using linear
interpolation of the experimental system pressure with respect to the
temperature. These interpolated x-P-T data then were used to obtain
the binary constants at the temperatures of interest.
Reference Fugacitles
Reference states for all the components were chosen as the pure
liquid at the temperature and pressure of the system.
Methanol. The reference state fugacity for methanol was obtained
from the following exact thermodynanric relationship:
jf viiq* = vapor phase fugacity coefficient of saturated i
22
-------
v-10' = liquid molar volume
The vapor pressure for methane! was calculated from the Antoine equa-
tion:
log1Q P*(mmHg) = 7.87862 - |(k)-43.247 {20)
Antoine constants were determined from experimental vapor pressure data
of Eubank (1970) for temperatures from -40°C to +30°C. Molar volumes
of methanol were calculated from a corresponding states correlation of
Chueh and Prausnitz (Reid et al, 1977)
(2D
Ny = (1.0 - 0.89w) [exp(6.9547 - 76.2853 Tr + 191.3060
- 203.5472 ij + 82.7631 ij)] (21a)
bjTr + CjTr + djTr + ej/Tr
(21b)
PC = 1/VC (21c)
ln(l-Tr) (21d)
23
-------
where
z = critical compressibility factor
u = Pitzer acentric factor
T = reduced temperature = T/T
VG = critical volume
Constants for Equation 21d are given in Table 3. Using the above
correlation for the liquid molar volume and evaluating the integral
in Equation 19, the following expression is obtained for the reference
fugacity of methanol:
(22)
-) -1]}
. .
TABLE 3
Constants Used in Equation 21d for
Calculating Methanol Liquid Molar Volume
Cj
0
1
2
0.
0.
-0.
11917
98465
55314
0
-1
-0
.009513
.60378
.15793
0
1
-1
.21091
.82484
.01601
-0.
-0.
0.
06922
61432
34095
0
-0
0
.07480
.34546
.46795
-0.084476
0.087037
-0.239938
24
-------
Carbon Dioxide and Hydrogen Sulfide. Fugacities for pure carbon dioxide
and hydrogen sulfide were determined from a three-parameter reduced
states correlation (Robinson and Chao, 1979).
fo
log -J- = log v + ulog v (23)
log v(0) = B0 + B1 Pr + B2 P^ - log Pp (23a)
BQ = -20.651608 + 84.517272 Tr - 15.376424
+ 152.65216 Tj| - 84.899391 ij + 24.84688
- 2.9786581 T (23b)
If 0.8 > Tr ^0.3 B1 = (j>* 3QJJ T ) ' (23c)
* r
If 0.9 > Tr >_ 0.8 B1 = 0.321895 Tr - 0.184316 (23d)
If 1.8 > T > 0.9 B, = 58.16962 - 326.54444 T
~ r —~ i r
+ 775.11716 T^ - 1006.8122 T^
+ 773.32667 tj - 351.56938 T^
+ 87.677429 T*j - 9.2617986 T^ (23e)
25
-------
If 0.8 > Tr ^0.3 B2 = 0 (23f)
If 0.9 > T > 0.8 B, = 0.0549369 (0.8 - T ) (23g)
r — £ i
If 1.0 > Tr >_ 0.9 B2 = 0.673344 x TO"3 - 0.685226 x 10"2 Tr (23h)
If Tr >_ 1.0 B£ = 0.72203901 - 2.7182597 Tr
+ 3.984423 T2 - 2.8712448 T3
+ 1.0202739 lAr - 0.14314712 TJJ (231)
log v
-------
Nitrogen. The Chao-Seader equation with adjusted parameters was used
to obtain the reference fuqacity of nitrogen.
log -± = 2.7365534 - 1.9818310/Tr
- 0.51487289 Tr + 0.042470988 T*
- 0.002814385 TJJ + (-0.029474696
+ 0.021495843 Tf) Pf - log Pr + ^ (24)
STRUCTURE OF THERMODYNAMIC MODEL
Starting from the fundamental thermodynamic relationship of phase
equilibria (Equation 13), two routes are available for phase equili-
bria calculations. One is the bubble point calculational procedure
and the other is the dew point calculational procedure.
Input data for the bubble point calculations are the pure com-
ponent constants, T , P , V , and u, the Margules constants for all
c c c
the binaries in the system and the liquid mole fractions of all the
components in the system. One more piece of information is necessary
and that could be either the system temperature or the system pres-
sure. Thus within the bubble point calculational procedure itself
there are two options. In the first, the system temperature 1s chosen
as the last input variable. In this case the output of the calcula-
tional procedure is the system pressure and the vapor mole fraction
of the system components. In the second, it is the system pressure
27
-------
that is the last input variable and the output variables are the sys-
tem temperature and the vapor mole fractions of the system components.
Also, for the dew point calculational procedure either the sys-
tem temperature or the system pressure can be made an input variable.
The other data necessary for this procedure are the pure component
constants, the Margules constants for all the binaries in the system,
and the vapor mole fractions for all the components in the system.
The output from this procedure includes the liquid mole fractions and
either the system pressure (if temperature was the input variable) or
the system temperature (if the pressure was the input variable).
Of the four calculational procedures the isothermal bubble point
calculational procedure (temperature is an input variable) is the sim-
plest and models based on this procedure require the least amount of
computer time to yield a solution. With this in mind the thermodynamic
model developed was based on the isothermal bubble point calculational
procedure and was called BUBLT. Figure 1 shows the flow chart for model
BUBLT. Later, another model was developed to perform the isothermal
dewpoint calculations and was called DEWT. The flow chart for model
DEWT is shown in Figure 2. Complete listings of programs for BUBLT
and DEWT are given by Matange (1980).
Model BUBLT
The flow chart for model BUBLT is shown in Figure 1. The program
starts by reading critical constants and Pitzer acentric factors
(Tc, PC, Vc, and to) for all system components. Margules constants
(A.-, A.., and D. .) for all binary combinations are read next, fol-
' J J ' ' J
lowed by an input of system temperature and liquid mole fractions for
28
-------
all components. In the first iteration an initial guess of the sys-
tem pressure is made. Convergence is not significantly affected by
the initial value of the pressure, but an initial guess of zero or
some very high pressure (supercritical) is unacceptable. Arbitrarily,
two atmospheres was chosen as the initial guess.
Since the system temperature and liquid mole fractions are known,
the activity coefficients, y.j» of all system components are calculated
next using the Margules equation in subroutine WOHL. The iterative
procedure begins with the next step.
Subroutine REFSTS is called to calculate reference fugacities,
Ref
f? , of all components using expressions developed in the previous section.
The vapor mole fraction of each component is then calculated using
the relationship
,
v -
yi ~
SUMY is set equal to the sum of all yj and system pressure is obtained
from the expression
(26)
+1
The pressure calculated by Equation 26 is compared to the previous
value, which on the first iteration is 2.0 atmospheres. If the dif-
ference between these two values is greater than 0.01 atmosphere,
values of vapor mole fractions, y^, are normalized and vapor fugacity
29
-------
Subroutine VFUGCS
y^SUMY
BUBLT
Read TC,PC,VC,o>
Read Margules Consts
Read T, all x.
P = 2 atm
*- = 1.0
Subroutine WOHL
Subroutine
y, -
SUMY =
= IYI-XI
Subroutine VFUGCS
Figure 1 Flow Chart for BUBLT
30
-------
c
DEWT
Read TC, PC, VC, u>
Read Margules Consts
Read T, all y
P = 1.0
« 1.0
1
Subroutine REFSTS
^(T,
SUMX
,y)
e VFUGCS
/ViRef
1
MX^-^^
St?^^>
TYes
•^^^
latiort^^^
ging7x^>
TNO
J">-^No
Change P
Figure 2 Flow Chart for DEWT
31
-------
coefficients, ., are calculated by calling subroutine VFUGCS. The
reference state fugacity is recalculated in the next iteration using
the pressure calculated from Equation 26 and the next iteration is
begun.
When an unchanging value of pressure is achieved (tolerance being
0.01 atmosphere) the stoichiometric check SUMY = 1.0 is made (tolerance
being 0.0001). If SUMY is not equal to unity, vapor composition is
normalized, the vapor fugacity coefficients are recalculated and the
program loops back to the step where the reference fugacities were
calculated.
If SUMY is equal to unity convergence has been achieved and
system pressure and vapor composition are printed.
Model DEWT
Figure 2 shows the information flow chart for the computer model
DEWT. As mentioned earlier, this model performs the isothermal dew
point calculation.
Model DEWT begins by reading in critical constants and Pitzer
acentric factors for all system components. This is followed by
reading in Margules constants, A.., A.., and D..t for all binaries
in the system, system temperature and vapor compositions.
Calculations begin by initializing the system pressure and the
Rpf
activity coefficients to unity. Next the reference fugacities, fv ,
and the vapor fugacity coefficients, <*., are calculated. The liquid
mole fractions, x^, are calculated and SUMX is set equal to the sum
of all x..
32
-------
If SUMX is not constant (tolerance 0.0001), the program loops
back. Subroutine WOHL is called and the activity coefficients are
recalculated and the control is transferred back to the point where
x- is calculated. When SUMX is a constant, the program moves ahead.
In the next step, a check is made to see if the calculations are
diverging. This is necessary because it is possible to specify a
vapor composition and a temperature for which no equilibrium solution
exists and which would give rise to diverging behavior. If diverging
behavior is encountered, the best results obtained so far are normal-
ized and output; otherwise, normal calculations continue. Next,
a check is made to verify is SUMX is equal to unity (tolerance being
0.0001). If not, system pressure is adjusted using a Newtonian inter-
polation method, working from successive values of SUMX. If SUMX is
equal to unity, convergence has been achieved and the system pressure
and the liquid composition are output.
EVALUATION OF MARGULES PARAMETERS
Earlier work with the thermodynamic model made it quite clear
that the success of the model hinges heavily on the accuracy of the
Margules constants. This has been the impetus to investigate thorough-
ly the process of obtaining these constants.
As mentioned earlier, the four-suffix Margules equation was used
to calculate activity coefficients for binary mixtures. Three Mar-
gules constants, A.., A.., and D.., are required for each binary mix-
1 J J 1 I J
ture. The four components of interest are methanol, carbon dioxide,
nitrogen, and hydrogen sulfide. They can be combined to give a total
33
-------
of six binary systems: methanol -carbon dioxide, methanol-nitrogen,
methanol -hydrogen sulfide, carbon dioxide-nitrogen, carbon dioxide-
hydrogen sulfide and nitrogen-hydrogen sulfide. Thus, a total of
eighteen Margules constants had to be evaluated.
A number of parameter estimation techniques were investigated.
With few exceptions, the basis of these techniques was a program called
GMAR, which is a nonlinear parameter search program written by G. W.
Westley of the Computing Technology Center of Union Carbide Corpora-
tion in Oak Ridge, Tennessee. This program was modified by Dr. R. M.
Felder of the Chemical Engineering Department, North Carolina State
University. Typically, input data to program GMAR consist of m data
points for any given function f (x1 , x2> .... x^; b1 , b^ ..... b ) =
f(x_, b_), where x, , . .., x are the variables and b, , ...» b are the
parameters. Program GMAR calculates the values of the parameters b, ,
..., b which minimize the weighted sum of squares of the residual,
where
m *
Residual = I (WE^-Cdata point - ffx^.bj], (27)
where (WE)., is a weighting factor assigned to the 1 data point.
Also necessary to run program GMAR are the derivatives of the function
f(x,b) with respect to the parameter b, , .... b - These derivatives
-- i p
were provided to GMAR by writing a subroutine called FUNC. Listings
of program GMAR and all necessary subroutines are given by Matange,
(1980).
34
-------
The original approach to evaluation of Margules parameters used
the Margules expression for activity coefficients as the function
f(x_,b) in the program GMAR. Experimental values of the activity co-
efficients were obtained using binary x-y-P-T data and the following
equation:
i
The fugacity coefficient, 4.^, was obtained from subroutine VFUGCS
Ref
and the reference fugacity, f . , from subroutine REFSTS. The Mar-
gules parameters were thus obtained for all six binaries. The Mar-
gules parameters of each binary were then used in the model BUBLT
to predict the pressure and the vapor composition for that binary.
It was found that the predicted variables compared well with the ex-
perimental data for all the binaries.
The Margules expression for the activity coefficients was not
the only available choice for the function f(x.,b.) used in program
2
GMAR. The expression for log(y.j/Yj) was also tried and was found to
improve the accuracy of the Margules constants. Even further improve-
ment was achieved when the Margules constants were obtained using a
Fletcher Powell search procedure in the program FPOW which minimizes
the residual given by
Residual = I E^ic^lD*2 + (Y2C-Y2D)2] (29)
35
-------
where
Y1C'Y2C = ca^culatecl values of y^ and y2> from Equation 18,
Y1D'Y2D = va^ues of "h and Y2 obtai'ned from experimental data
Although these efforts were rewarded by improvement in the fit
to experimental data, there is a scarcity of reliable data in the
x-y-P-T form. However, several sets of data were found of the form
x-P-T; i.e. vapor compositions were not measured in the reported
experimental programs. Data in this form were found for all six of
the binary combinations.
A program for evaluating Margules parameters from x-P-T equili-
brium data was developed. This program, called GMAIN, used bubble
point calculation procedures in conjunction with GMAR to calculate
the Margules constants. Values of Margules parameters are adjusted
until the difference between the system pressure calculated by the
model and the experimental pressure was minimized.
Another advantage of the above technique was the flexibility it
allowed in using data at different temperatures. For the methanol-
carbon dioxide, the methanol-hydrogen sulfide and the carbon dioxide-
hydrogen sulfide systems, it was found that assuming the Margules
parameters to be inversely proportional to the absolute temperature
was quite satisfactory. For these binaries, a simple modification
of program GMAR made it possible to obtain the optimum Margules para-
meters using data at all temperatures. This significantly improved
the accuracy of the constants. For binary mixtures involving nitro-
gen, the inverse temperature relationship for the Margules parameters
36
-------
was unacceptable. For these systems Margules parameters at each tem-
perature of interest were obtained.
Methanol-COo. The optimum values of the Margules parameters for the
methanol-carbon dioxide system were obtained by using data by Katayama
et al. (1975) at 298.15 K and data by Yorizane et al. (1969) at 258.15
K and 243.15 K. Margules parameters were evaluated using the three
data sets and assuming the parameters to be inversely proportional to
temperature. Table 4 compares model predictions to experimental data
for methanol-carbon dioxide mixtures. Since vapor compositions were
available for the data at 298.15 K, both system pressures and vapor
compositions have been compared in Table 4 for this data set. Vapor
composition data were not available at 258.15 K and 243.15 K and hence
only the system pressures are compared at these temperatures. Figure
3 compares the predicted pressures with the experimental pressures
at 298.15 K, 258.15 K and 243.15 K. Excellent agreement was obtained
between predicted and experimental values of the vapor mole fractions
of carbon dioxide at 298.15 K. Good agreement was obtained between
the predicted and experimental system pressures for all three tempera-
tures.
Methanol-No. Data provided by Knapp and Weber were used to evaluate
Margules parameters for methanol-nitrogen mixtures. As indicated
1H. Knapp and W. Weber. Unpublished data. Dechnische Unlversitat,
Berlin. Fachdereich 10. Berfahrenseechink. Institut ftir Thermody-
namik and Anlagentechnlk. (1978).
37
-------
Table 4
Comparisons of Experimental Vapor-Liquid Equilibrium
Data with Model Correlations for Methanol (l)-Carbon Dioxide (2)-Mixtures
x2
0.015
0.041
0.070
0.131
0.256
0.361
0.450
0.610
0.662
exp
(atm)
2.16
5.58
9.39
17.08
29.62
40.80
46.97
53.88
55.77
Pcalc
(atm)
2.17
5.46
8.90
15.66
28.66
39.12
46.94
54.60
54.79
298.15
DP
(atm)
0.01
-0.12
-0.49
-1.42
-0.96
-1.68
-0.03
0.72
-0.98
K
y2
exp
0.9202
0.9685
0.9797
0.9878
0.9917
0.9928
0.9930
0.9929
0.9922
calc
0.9221
0.9679
0.9796
0.9875
0.9920
0.9931
0.9934
0.9931
0.9931
Dy
0.0019
-0.0006
-0.0001
-0.0003
0.0003
0.0003
0.0004
0.0002
0.0009
DP - P P • nv = v - v
'calc exptl' u ^.calc •/2,exptl
Average percent deviation for pressure = 3.0
Average percent deviation for y~ = 0*06
Experimental data by Katayama et al. (1975)
258.15 K
X2
0.072
0.145
0.219
0.333
0.471
exp
(atm)
4.0
8.0
12.0
16.0
20.0
Pcalc
(atm)
4.95
8.96
12.49
17.11
20.81
DP
(atm)
0.95
0.96
0.49
1.11
0.81
DP = Pcalc - Pexptl
Average percent deviation for pressure = 10.2
Experimental data by Yorizane et al. (1969)
(continued)
38
-------
Table 4
(continued)
243.15°K
xz
0.048
0.107
0.172
0.240
0.327
0.426
0.550
0.789
exp
(atm)
2.0
4.0
6.0
8.0
10.0
12.0
13.0
13.7
Pcalc
(atm)
2.54
5.05
7.35
9.41
11.60
13.35
14.21
12.86
DP
(atm)
0.54
1.05
1.35
1.41
1.60
1.35
1.21
-0.84
DP = Pcalc - Pexptl
Average percent deviation for pressure = 17.0
Experimental data by Yorizane et al. (1969)
39
-------
60
50 -
40 —
30 —
20 —
10 —
O : MIA OF KATAYAMA
A Q : DATA OF YORIZANE
.•MODEL PREDICTION
00
0.2
0.4
0.6
0.8
MOl FRACTION C02 IN LIQUID, X
1.0
Figure 3. Comparison of Equilibrium Experimental Predicted Pressures
for Methanol - Carbon Dioxide Mixtures.
-------
earlier the inverse temperature relationship for the Margules para-
meters does not work and values were obtained at each temperature.
Since the multicomponent model was to be tested at 273.15 K and 258.15 K
equilibrium pressure and liquid compositions for methanol-nitrogen
mixtures at 273.15 K and 258.15 K were obtained by linear interpo-
lation of experimental pressure with respect to temperature at a num-
ber of values of the liquid mole fraction. Data at each temperature
(273.15 K and 258.15 K were used separately in GMAR to obtain optimum
values of the Margules parameters at specific temperatures. Table 5
and Figure 4 compare the system pressure predicted by the model and
the experimental pressure for the methanol-nitrogen system. Excellent
agreement between the predicted and experiment pressure was obtained.
Methanol-I^S. Optimal Margules parameters for the methanol-hydrogen
sulfide system were obtained using data by Yorizane et al. (1969) at
273.15 K, 258.15 K and 248.15 K. The Margules parameters for this sys-
tem were found to be inversely proportional to temperature so that
the optimal parameters were based on data at all three temperatures.
As shown in Table 6 and Figure 5, good agreement was found between
the system pressure predicted by the model and the experimental pres-
sure.
CCL^Ng.- The carbon dioxide-nitrogen system followed the pattern set
by the methanol-nitrogen system: Margules parameters were not in-
versely proportional to temperature. Data of Zenner and Dana (1969)
and Kaminishi et al. (1966) were interpolated to obtain x-P values at
41
-------
Table 5 Comparisons of Interpolated Experimental Vapor-Liquid
Equilibrium Data with Model Correlations for Methanol
(1) - Nitrogen (2) Mixtures
273.15 K
X2
0.0000
0.0025
0.0050
0.0058
0.0118
0.0165
Pexptl
(atm)
0.00
10.00
20.00
24.20
50.30
74.00
Pcalc
(atm)
0.04
9.91
20.25
23.66
50.90
74.47
DP
(atm)
0.04
-0.09
0.25
-0.54
0.60
0.47
DP = Pcalc " Pexptl
Average percent deviation for pressure = 1.2
Experimental data obtained by interpolation of data by Knapp and Weber3
258.15 K
x2
0.0000
0.0025
0.0050
0.0075
0.0100
0.0125
0.0150
0.0175
Pexptl
(atm)
0.00
10.00
20.00
31.30
42.50
53.00
66.20
78.00
Pcalc
(atm)
0.01
10.09
20.49
31.25
42.38
53.93
65.92
78.39
DP
(atm)
0.01
0.09
0.49
-0.05
-0.12
0.93
-0.28
0.39
np = P - P
UK calc exptl
Average percent deviation for pressure = 0.9
Experimental data obtained by interpolation of data by Knapp and Weber3
aKnapp and Weber. Unpublished data. Dechnische Uniyersitat,
Berlin. Fachdereich 10. Berfahrenseechink. Institut fiir Thermody-
namik and Anlagentechnik (1978).
42
-------
80
70
60
50 -
40
I I
Q: INTERPOLATED DATA (273.15 K) FROM
DATA OF KNAPP
INTERPOLATED DATA (258.15 K) FROM
DATA OF KNAPP
MODEL PREDICTION
273.15 K
30 5
00
SCALE CHANGED
258.15 K
I
I
0.005
0.010
0.015
MOL FRACTION N2 IN LIQUID, X
OJ020
Figure 4. Comparison of Equilibrium Experimental and Predicted Pressures
for Methanol-Nitrogen Mixtures.
43
-------
Table 6 Comparisons of Experimental Vapor-Liquid Equilibrium
Data with Model Correlations for Methanol (1) -
Hydrogen Sulfide (2) Mixtures.
xz
0.092
0.199
0.329
0.453
0.484
0.608
0.7*3
0.840
273.1
Pexptl
(atm)
2.0
4.0
6.0
7.5
8.0
9.1
9.8
10.0
5 K
Pcalc
(atm)
2.16
3.83
5.72
7.45
7.83
8.98
9.44
9.48
DP
(atm)
0.16
-0.17
-0.28
-0.05
-0.17
-0.1?
-0.36
-0.52
DP = P - P
UK "calc Hexptl
Average percent deviation for pressure =3.7
Experimental data by Yorizane et al. (1969)
x2
0.165
0.231
0.298
0.367
0.403
0.490
0.585
0.662
258,15
Pexptl
(atm)
2.0
3.0
3.4
4.2
4.4
5.0
5.4
5.8
K
Pcalc
(atm)
2.26
2.90
3.54
4.19
4.52
5.23
5.79
6.04
DP
(atm)
0.26
-0.10
0.14
-0.01
0.12
0.23
0.39
0.23
DP = Pcalc - PexPtl
Average percent deviation for pressure = 4.9
Experimental data by Yorizane et al. (1969)
(continued)
44
-------
Table 6 (continued)
248.15 K
x2
0.203
0.290
0.3?7
0.465
0.582
0.733
_..
exptl
(atm)
2.0
2.5
3.0
' 3.4
4.0
4.3
Pcalc
(atm)
1.96
2.57
2.8?
3.71
4.22
4.43
DP
(atm)
-0.04
0.07
-0.18
0.31
0.22
0.13
DP = Pcalc - Pexptl
Average percent deviation for pressure = 4.7
Experimental data by Yorizane et al. (1969)
45
-------
10
I I T
O A El •" DATA OF YORIZANE
8
r 6
£
4 —
2 —
0.0
MODEL PREDICTION
0.2
0.4
^ o
248.15 K
0.6
0.8
TO
MOL FRACTION H2S IN LIQUID, X
Figure 5. Comparison of Equilibrium Experimental and Predicted Pressures
for the Methanol-Hydrogen Sulfide Mixtures.
46
-------
273.15 K and 258.15 K. Optimal values of the Margules parameter were
obtained for the two temperatures using the interpolated data in GMAR.
Model predictions based on optimal Margules parameters are compared
to experimental values in Table 7 and Figure 6. The comparison between
predicted pressure and experimental pressure is excellent.
C_0_o - H?S. Sobocinski and Kurata (1969) have reported data for carbon
dioxide-hydrogen sulfide mixtures at 288.71 K, 266.48 K and 244.26 K.
Since the inverse temperature relationship was found to be acceptable
for this system, optimal values of Margules constants were obtained
using data at all three temperatures. Table 8 compares system
pressure and vapor composition with the corresponding experimental
data for carbon dioxide-hydrogen sulfide mixtures. Comparisons be-
tween predicted pressure and experimental pressure for this system
is shown graphically in Figure 7.
NplUgS.* Data °f Robinson and Besserer (1972) were interpolated as
described earlier to obtain equilibrium x-P values at 273.15 K and
258.15 K. Interpolated data were used to evaluate optimal Margules
parameters at 273.15 K and 258.15 K using GMAR. Comparisons between
experimental and model-predicted equilibrium pressures are shown in
Table 9 and Figure 8; Agreement is excellent.
47
-------
Table 7 Comparisons of Interpolated Experimental Vapor-Liquid
Equilibrium Data with Model Correlations for Carbon
Dioxide (1) - Nitrogen (2) Mixtures
x2
0.000
0.025
0.050
0.075
0.100
273.15
Pexptl
(atm)
34.20
47.20
60.00
71.40
82.40
K
Pcalc
(atm)
31.19
46.79
59.20
70.07
80.53
DP
(atm)
-3.01
-0.41
-0.80
-1.33
-1.87
DP = Pcalc " Pexptl
Average percent deviation for pressure = 3.0
Experimental data obtained by interpolation of data by Zenner and Dana
(1963) and Kaminishi et al. (1966).
258.15 K
X2
0.000
0.025
0.050
0.075
0.100
Pexptl
(atm)
21.50
35.80
49.00
62.00
74.60
Pcalc
(atm)
20.69
35.33
48.72
61.25
73.26
DP
(atm)
-0.81
-0.47
-0.28
-0.75
-1.34
DP = P - P
UK Kcalc pexptl
Average percent deviation for pressure = 1.7
Experimental data obtained by interpolation of data by Zenner and
Dana (1963) and Kaminishi et al. (1966).
48
-------
95
80
GO
GO
65
50
35
20
T
I
I
INTERPOLATED FROM DATA OF ZENNER ET AL
& TORIUMI ET AL
MODEL PREDICTION
0.0
273.15 K
0.2
0.4
0.6
0.8
MOL FRACTION N? IN LIQUID, X
1.0
Figure 6. Comparison of Equilibrium Experimental and Predicted Pressures
for the Carbon Dioxide-Nitrogen Mixtures.
49
-------
Table 8 Comparisons of Experimental Vapor-Liquid Equilibrium
Data with Model Correlations for Carbon Dioxide (1) -
Hydrogen Sulfide (2) Mixtures
288.71°K
x2
0.948
0.815
0.640
0.419
Pexptl
(atm)
20.41
27.22
34.02
40.83
Pcalc
(atm)
19.99
27.46
34.00
41.69
DP
(atm)
-0.42
0.24
-0.02
0.86
y2,exptl
0.770
0.540
0.395
0.272
y2,calc
0.748
0.531
0.395
0.261
Dy
-0.022
-0.009
0.000
-0.011
DP = Pcalc - Pexptl
Dy = y2,calc - y2,exptl
Average percent deviation for pressure = 1,3
Average percent deviation for y^ = 2.1
Experimental data of Sobocinski and Kurata (1969)
266.48°K
0.887
0.630
0.164
13.61
20.41
27.22
14.19
19.97
26.47
0.58
-0.44
-0.75
0.590
0.340
0.095
0.573
0.356
0.128
-0.017
0.016
0.033
= p . p
Kcalc pexptl
Dy = y2,calc " y2,exptl
Average percent deviation for pressure = 3.1
Average percent deviation for y2 = 14.1
Experimental data of Sobocinski and Kurata (1969)
(continued)
50
-------
Table 8 (continued)
244.26°K
x2
0.915
0.235
Pexptl
(atm)
6.80
13.61
Pcalc
(atm)
6.95
13.52
DP
(atm)
0.15
-0.09
y2,exptl
0.572
0.120
y2,calc
0.563
0.144
Dy
-0.009
0.024
np = P - p
UP calc exptl
Dy = y2,calc " y2,exptl
Average percent deviation for pressure = 1.4
Average percent deviation for y^ - 10.8
Experimental data of Sobocinski and Kurata (1969)
51
-------
60
50
40
ae 30
§
LU
£
20
10
I I T
O A EH : DATA OFSOBOCINSKI
: MODEL PREDICTION
0.0
I
I
I
I
0.2 0.4 0.6 0.8
MOL FRACTION C02 IN LIQUID, X
1.0
Figure 7. Comparison of Equilibrium Experimental and Predicted Pressures
for Carbon Dioxide-Hydrogen Sulfide Mixtures.
52
-------
Table 9 Comparisons of Interpolated Experimental Vapor-Liquid
Equilibrium Data with Model Correlations for Nitrogen
(1) - Hydrogen Sulfide (2) Mixtures
xl
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
0.018
0.020
0.022
0.024
273.1
Pexptl
(atm)
10.7
14.0
18.5
23.0
28.0
33.5
39.0
44.4
50.0
55.7
61.4
66.8
72.3
5°K
Pcalc
(atm)
10.05
14.11
18.54
23.30
28.36
33.68
39.21
44.89
50.67
56.47
62.22
67.87
73.32
DP
(atm)
-0.65
0.11
0.04
0.30
0.36
0.18
0.21
0.49
0.67
0.77
0.82
1.07
1.02
DP = Pcalc * PexPtl
Average percent deviation for pressure =1.5
Experimental data interpolated from data of Robinson and Besserer (1972)
0.000
0.004
0.008
0.012
0.016
0.020
0.024
258.1
6.2
16.4
29.4
43.8
58.3
72.8
85.7
5CK
6.47
16.85
29.54
43.93
59.10
73.85
86.88
0.27
0.45
0.14
0.13
0.80
1.05
1.18
DP = Pcalc * Pexptl
Average percent deviation for pressure - 1.7
Experimental data interpolated from data of Robinson and Besserer (1972)
53
-------
100
80
60
CO
e/5
£ 40
20
I I I
O A : INTERPOLATED FROM DATA OF ROBINSON
: MODEL PREDICTION
258.15 K
I
I
I
OO 0.005
0.010
0.015
273.15 K
I
0.020 0.025
MOL FRACTION N2 IN LIQUID, X
Figure 8. Comparison of Equilibrium Experimental and Predicted
Pressures for Nitrogen-Hydrogen Sulfide Mixtures.
54
-------
Summary
Margules parameters for six binary mixtures have been determined
from vapor-liquid equilibrium data found in the literature. Consti-
tuents of these mixtures are taken from the group methanol, hydrogen
sulfide, carbon dioxide and nitrogen. Parameters for the three nitro-
gen-free binary mixtures were found to be inversely proportioned to
temperature, while parameters for the three nitrogen containing mix-
tures did not follow such a relationship. Since the model is to be
tested against multicomponent equilibrium data taken at 273.15 K and
258.15 K. Margules parameters for each of the six binary mixtures
were evaluated at these temperatures and are given in Table 10. The
fits of binary equilibrium data to that predicted using these para-
meters are excellent.
55
-------
Table 10 Margules parameters from Parameter Optimization
Procedure GMAR
Binary
A12
A21
D12
273.15°K
Methanol
Methanol
Methanol
co2(i) -
co2(i) -
N2(l) -
(1) - C02(2)
(1) - N2(2)
(1) - H2S(2)
N2(2)
H2S(2)
H2S(2)
1.3395
5.2000
1.0758
2.1228
0.5705
0.8115
0.6427
1.1446
0.5374
0.3023
0.5777
-66.5928
0.6940
2.2000
0.9891
3.1223
0.5793
-72.8469
258.15°K
Methanol
Methanol
Methanol
co2(i) -
co2(i) -
N2(D -
(1) - C02(2)
(1) - N2(2)
(1) - H2S(2)
N2(2)
H2S(2)
H2S(2)
1.4174
11.0000
1.1383
0.6328
0.6037
0.8990
0.6800
1.1657
0.5686
0.2849
0.6113
-114.3787
0.7342
8.7000
1.0466
0.7872
0.6130
-123.1370
56
-------
EXPERIMENTAL EQUIPMENT AND PROCEDURE
The experimental apparatus used to obtain multicomponent vapor
liquid equilibrium data was a modification of the system used by
Bass (1978). A schematic diagram of the apparatus is shown in Figure
9. The stainless steel cell had a volume of 1084 ml and was equipped
with internal baffles. Valves used in the recycle line as well as
those used for sampling and gas charging were teflon packed and rated
for use at high pressure. Liquid in the cell was recirculated using
a microflo pulsafeeder metering pump, model L20-S-3, manufactured by
the Interpace Corporation. The diaphragm used in this pump eliminated
any possibility of contamination. Pressure in the equilibrium cell
was measured using a 16-inch Heise gauge graduated in 0.5 psi incre-
ments up to 1250 psia. The gauge had a guaranteed accuracy of 0.1
percent of the full scale. An Ashcroft type 1327 portable dead weight
tester was used to confirm calibration of the gauge. Temperatures
were measured using a copper-constantan thermocouple and a digital
temperature indicator calibrated against known temperatures. The
entire high pressure apparatus was housed in a Harris industrial
freezer which provided the refrigeration. A Thermistemp temperature
controller, a fan and a heater controlled the temperature in the cell
within 0.1°C.
REAGENTS
Methanol was Fisher Spectranalyzed(R)with a stated purity of
99.95 percent. Carbon dioxide and nitrogen used in the research had
57
-------
en
CO
CO,
- way valve
/
temperature
controller
digital
thermocouple
pressure gauge
N2
' \
H2S
Mix
heater
capillary
tubing
equilibrium cell
magnetic stirrer
Figure 9, Experimental Apparatus.
-------
a stated purity of 99.99 percent and 99.999 percent, respectively.
These gases were supplied by Airco Inc. A mixture of 15.1 percent
hydrogen sulfide in nitrogen, supplied by Air Products, was used.
ANALYSIS
Analyses of liquid and vapor samples taken during a run were done
on a Tracer model 550 gas chromatograph equipped with a thermal con-
ductivity detector, a temperature programmer and a heated gas sampling
valve. Component separation was achieved in a stainless steel column,
3 meters in length and 3.2 mm in diameter, packed with Porapak QS.
The signal from the gas chromatograph was analyzed using Southern
Analytical's Supergrator-3 digital integrator and a Leeds and North-
rup strip chart recorder.
CALIBRATIONS
Calibration of the gas chromatograph-supergrator combination
was done by injecting known amounts of components into the gas chroma-
tograph and noting the corresponding areas integrated by the super-
grator. For each amount of every component the corresponding area
was obtained for at least five replicate injections. The mean and
the standard deviation were calculated for the replicate areas. The
mean area was the response of the gas chromatograph-supergrator for
the amount of the particular component under consideration and became
part of the calibration data for that component. The percent stan-
dard deviations of the replicate areas provided a measure of the pre-
cision of the replicate areas obtained. The percent standard devia-
59
-------
tion of the replicate areas was calculated at each calibration point
for all four components. The average of these values is reported as
the average percent standard deviation for area for each component
in the following paragraphs. Calibration data in the form of g-moles
of a component and the corresponding area integrated by the gas chroma-
tograph-supergrator combination were fit with linear equations for
all four components. Determination of unknown compositions were
performed using these linear equations for the four components.
For methanol calibration, different concentrations of methanol
in distilled, deionized water were prepared. Varying amounts of
samples at each concentration were injected into the gas chromatograph.
Sample injections were done using a Hamilton microliter syringe.
All injections involved a sample volume greater than 2 microliters.
The smallest graduation on the syringe was 0.1 microliter. It was
observed that for methanol the average percent standard deviation
for the area was less than 0.6. For the calibration of carbon di-
oxide, nitrogen and hydrogen sulfide, gaseous injections at various
pressures were made using the gas sampling valve. The pressure gauge
used for this purpose had a least count of 0.034 atm. The average
percent standard deviations for the area for carbon dioxide, nitrogen
and hydrogen sulfide were 0.49, 0.53 and 1.79, respectively.
TEST DATA: METHANOL - C02 MIXTURES
For the purpose of verifying the proposed experimental procedure,
vapor-liquid equilibrium data were taken for methanol-carbon dioxide
mixtures at 298.15 K. On the basis of excellent comparison of these
60
-------
data with those of Katayama et al. (1975), the experimental apparatus
and procedure were judged sound. The comparison is shown in Figure
10 and Table 11. The average deviation of COg mole fraction of car-
bon dioxide between the two sets of data was 5.4%.
MULTICOMPONENT PROCEDURE
The first step in taking multicomponent vapor-liquid equilibrium
data was to fill the equilibrium cell with about 390 ml of methanol.
The refrigeration system was turned on to achieve the desired tempera-
ture in the cell, and the three gases were added to generate the de-
sired overall composition and pressure. Liquid in the cell was re-
circulated for six hours and then allowed to sit unagitated for at
least twelve hours prior to sampling. Samples were allowed to ex-
pand through the capillary tubing into the evacuated sample containers.
Sampling was done quickly and the cell pressure was seldom disturbed
by more than 0.48 atm. The vapor sample container was pressurized to
approximately 1.36 atm with helium and then both containers were
monitored to insure that the methanol in the samples did not approach
the point of condensation. The contents of each container were analyzed
a minimum of five times using the gas chromatograph.
MULTICOMPONENT MEASUREMENTS AND PREDICTIONS
Multicomponent vapor-liquid equilibrium data were taken for
methanol-carbon dioxide-nitrogen-hydrogen sulfide mixtures at 258.15 K
and 273.15 K. Data are given in Tables 12 and 13. Four data points
were taken at 258.15 K and four more were obtained at 273.15 K. At
61
-------
UJ
OC
D
UJ
OC
Q.
60
SO
40
30
20
10
• DATA OF KATAYAMA
• THIS STUDY
O.O O.2
0.4
0.6
0.8
1.0
MOL FRACTION CO - IN LIQUID
2
Figure 10. Comparison of Experimentally Determined Equilibrium
Pressures with Those of Katayama et al. (1975) for
Methanol-C02 Mixtures at 298.15 K.
62
-------
Table 11 Comparison of Experimental Vapor-Liquid Equilibrium
Data with Those of Katayama et al. (1975) for Methanol-
C02 mixtures at 298.15 K.
p
(atm)
9.39
29.62
46.97
*2
0.070
0.256
0.450
*2b
0.065
0.250
0.420
Note: Average percent deviation for x« = 5.4.
aData of Katayama et al. (1975).
Data from this investigation.
each data point, vapor and liquid compositions were determined by gas
chromatographic analysis; five repetitions were conducted on each of
the vapor and liquid samples. The gas chromatographic analysis pro-
vided the absolute amounts for the four components in the system.
Since it was the composition that was being sought, replicates of every
analysis were normalized so that each replicate indicated the same
amount of carbon dioxide. Carbon dioxide was chosen for this role
because, over the entire data set, it was the component that was most
significant in both the liquid and the vapor phases. After normali-
zation, percent deviations for all the other components were calculated.
For liquid sample analysis over the entire data set, the average
percent standard deviation for methanol, nitrogen and hydrogen sul-
63
-------
Table 12 Experimental Vapor-Liquid Equilibrium Data for Methanol-
Carbon Dioxide-Nitrogen-Hydrogen Sulfide Mixtures at 258.15 K
P.atm
9.34
20.75
29.64
40. 1C
XCH3OH
0.9081
0.7680
0.6462
0.7419
Xco2
0.0736
0.2100
0.3312
0.2346
xw
N2
0.0029
0.0031
0.0052
0.0078
XH2S
0.0153
0.0189
0.0209
0.0157
yCH3OH
N.D.a
N.D.a
N.D.a
N.D.a
yco2
0.5400
o.em
0.5892
0.4580
yN
N2
0.4000
0.3654
0.4004
0.5420
yH2S
0.052
0.0235
0.0104
N.D.a
aN.D. = not detected.
-------
en
Table 13 Experimental Vapor Liquid Equilibrium Data for
Methanol-Carbon Dioxide-Nitrogen-Hydrogen Sul-
fide Mixtures at 273.15 K
P.atm
9.2
21.2
29.0
39.8
XCH3OH
0.8997
0.7433
0.6961
0.6872
Xco2
0.0850
0.2339
0.2832
0.2849
xw
N2
0.0019
0.0018
0.0033
0.0074
XH2S
0.0134
0.0211
0.0175
0.0204
yCH3OH
N.D.a
N.D.a
N.D.a
N.D.a
yco2
0.6853
0.8007
0.7720
0.5847
y»2
0.2839
0.1648
0.2026
0.3760
yH2S
0.0308
0.0345
0.0218
0.0393
aN.D. = not detected
-------
fide was 0.8, 5.1 and 3.0, respectively. In the vapor samples, the
amount of methanol present was too small to be detected. In the
vapor sample analysis, the average percent standard deviation for
nitrogen and hydrogen sulfide was 0.7 and 5.1, respectively.
The experimental temperature and liquid phase composition were
used in program BUBLT to predict equilibrium system pressure and
vapor composition. Comparisons of predicted and experimental results
at 258.15 K and 273.15 K are given in Tables 14 and 15, respectively.
Over the entire data set, the average deviation of pressure was 7.9%
and the average deviations for mole fractions in the vapor were 7.1%
for carbon dioxide, 11.7% for nitrogen and 24.8% for hydrogen sulfide.
All percent deviations used experimental values as a basis. The high
percent deviation obtained for hydrogen sulfide was partly due to
the relative insensitivity of the thermal conductivity detector in
the gas chromatograph to hydrogen sulfide, especially at low concen-
tration.
Figures 11 and 12 compare the system pressure predicted by the
model and the experimental pressure at 258.15 K and 273.15 K, respec-
tively. Figures 13 and 14 compare the predicted vapor composition
and the experimental vapor composition at 258.15 K and 273.15 K,
respectively. These figures show excellent agreement between model
predictions and experimental data.
Clearly, the model satisfies many of the objectives of this
research project. Namely, it is now possible to predict equilibrium
behavior for mixtures of CC^-^S-N,, and methanol over a limited
temperature range. Additional research 1s needed to expand
the range of the model, to adapt it to general bubble
66
-------
Table 14 Comparison of Model Predictions with Experimental
Pressure and Vapor Compositions for Methanol
Carbon Dioxide-Nitrogen-Hydrogen Sulfide Mixtures
at 258.15 K
en
P
-------
Table 15 Comparison of Model Predictions with Experimental
Pressure and Vapor Compositions for Methane!-Carbon
Dioxide-Nitrogen-Hydrogen Sulfide Mixtures at
273.15 K
P(atm) yCH.OH yC0
n
exptl model DPa exptl model Dy exptl model Dy exptl model Dy exptl model Dy
9.2 12.05 2.85 N.D.C 0.0037 - 0.6853 0.6414 -0.0439 0.2839 0.3227 0.0388 0.0308 0.0322 0.0014
21.2 22.14 0.94 N.D.C 0.0023 - 0.8007 0.8284 0.0277 0.1648 0.1385 -0.0263 0.0345 0.0308 -0.0037
» 29.0 30.77 1.77 N.D.C 0.0019 - 0.7720 0.7357 -0.0363 0.2026 0.2442 0.0416 0.0218 0.0183 -0.0035
39.8 39.11 -0.69 N.D.C 0.0017 - 0.5847 0.6286 0.0*39 0.3760 0.3561 -0.0199 0.0393 0.0136 -0.0257
DP " Pmodel " Pexptl
Dy = ymodel " yexptl
CN.D. = not detected
-------
50
I I
T= 258.15 K
40
30
20
i
10
10
o>
20
30
40 50
PRESSURE, EXPTl, ATM
Figure 11. Comparison of Predicted and Measured Four-Component Mixtures
at 258.15 K.
69
-------
50
4O —
30
20 —
10
PRESSURE, EXPTL, ATM
Figure 12. Comparison of Predicted and Measured Pressures for
Four-Component Mixtures at 273.15 K.
70
-------
10
08
0.6
0.4
01
0.08
006
Qj04
O02
001
I- ?5B 15 K
0: co2
A- N2
Q: H2s
I
I I
001 002 004 006 008 0.1 O2
VAPOR COMPOSITION, EXPTL
CM 06 0.8 10
Figure 13. Comparison of Predicted and Experimental Vapor Compositions for
Four-Component Mixtures at 258.15 K.
71
-------
1.0
0.8
0.6
0.4
B 02
01
0.08
0.06
004
0.02
O.O1
I I
I =273.15 K
O: co2
A: N2
D : HZS
I
I I
OO2 004 006 OO8 0.1 O2
VAPOR COMPOSITION, EXPTL
04 0.6 0.8 1.0
Figure 14. Comparison of Predicted and Experimental Vapor Compositions
for Four-Component Mixtures at 273.15 K.
72
-------
point, dewpoint and flash calculations, and to include additional key
constituents of crude coal gas.
CONCLUSIONS
1. A thermodynamic model was developed which successfully correlated
vapor-liquid equilibrium data for the six binary mixtures that can be
formed from carbon dioxide, hydrogen sulfide, nitrogen and methanol.
The model uses the Soave modification of the Redlich-Kwong equation
of state to describe the gas phase, the four-suffix Kargules equation
to express activity coefficients, and pure liquids at the temperature
and pressure of the system as reference states. Margules parameters
were evaluated from a parameter search procedure known as GMAR. These
parameters were found to be functions of temperature, with the func-
tionality varying according to the binary mixture.
2. An experimental equilibrium cell, complete with sampling devices and
gas chromatographic analysis capabilities, was constructed. The
apparatus was checked by a favorable comparison of experimentally
measured equilibrium data to literature data.
3. Experimental vapor-liquid equilibrium data were obtained for methanol-
carbon dioxide-nitrogen-hydrogen sulfide mixtures at 258.15 K and
273.15 K. Pressures in these experiments ranged from 6 to 40 atm.
4. A multicomponent version of the vapor-liquid equilibrium model was
used to predict vapor compositions and equilibrium pressures based
on measured liquid compositions and system temperature. There was
excellent agreement between experimental and predicted pressures and
carbon dioxide and nitrogen vapor mole fractions. There was fair
73
-------
agreement between experimental and predicted hydrogen sulfide mole
fractions; this was believed due to poor chromatograph sensitivity to
low hydrogen sulfide concentrations.
74
-------
LITERATURE CITED
Adler, S. B.; Friend, Z.; and Pigford, R. L. "Application of the
Wohl Equation to Ternary Liquid-Vapor Equilibria." American
Institute of Chemical Engineering Journal 12 (1966):629-637.
Adler, S. B.: Ozkardesh, H.; and Schreiner, W. C. "These Equations
Predict Equilibria." Hydrocarbon Processing 47 (1968): 145-153.
Adler, Stanley B.; Spencer, Calvin E.; Ozkardesh, Hal; and Kuo, Chia-
Ming. "Industrial Uses of Equations of State: A State-of-the
Art Review." Phase Equilibria and Fluid Properties in the Chemi-
cal Industry, ACS Symposium Series 60, 1977.
Arai, Yasuhiko; Kaminishi, Gen-Ichi; and Saito, Shozaburo. "The
Experimental Determination of the P-V-T-X Relations for the
Carbon Dioxide-Nitrogen and the Carbon Dioxide-Methane Systems."
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Bass, D. G. "The Solubility of Acid Gases in Methanol." M.S.
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Besserer, George J., and Robinson, Donald B. "Equilibrium Phase
Properties of Nitrogen-Hydrogen Sulfide System." Journal of
Chemical and Engineering Data 20 (1975): 157-161.
Bezdel, L. S., and Teodorovich, V. P. "The Solubilities of Carbon
Dioxide, Hydrogen Sulfide, Methane, and Ethylene in Methanol
at Low Temperatures." Gazovaia Promshlenmost (Moscow) 8 (1958):
38-43.
Bierlein, James A., and Kay, Webster B. "Phase Equilibrium Properties
of System Carbon Dioxide-Hydrogen Sulfide." Industrial and
Engineering Chemistry 45 (1953): 618-624.
Chao, K. C., and Seader, J. D. "A General Correlation of Vapor-Liquid
Equilibria in Hydrocarbon Mixtures." American Institute of
Chemical Engineering Journal 7 (1961):598-605.
Cubank, P. T. "A Review of Volumetric, Thermodynamic, and Other
Physical Properties for Methanol." Chemical Engineering Progress
Symposium Series-Methanol Technology and Economics 98 (1970);
16-23.
Erbar, John H., and Edmister, Wayne C. "New Constants for Chao-Seader
Correlation for N«, HpS, and CO,,." Oklahoma State University,
Stillwater, Oklahoma (1978).
75
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Graboski, M. S., and Daubert, T. E. "A Modified Soave Equation for
Phase Equilibrium Calculations. 2. Systems Containing C02, H^S,
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TECHNICAL REPORT DATA
(Please read {nUructions on the reverse before completing)
1. REPORT NO.
-6PP/7-8(bll6_
IZ
4. TITLE AND SUBTITLE
Solubilities of Acid Gases and Nitrogen in Methanol
7 AUTHOFUS)
J.K. Ferrell, R. W.Rousseau, and J. N. Matange
3. RECIPIENT'S ACCESSION NO.
5. REPORT DATE
May 1980
6. PERFORMING ORGANIZATION CODE
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
North Carolina State University
Department of Chemical Engineering
Raleigh, North Carolina 27607
1O. PROGRAM ELEMENT NO.
INE825
11, CONTRACT/GRANT NO.
Grant R804811
12. SPONSORING AGENCY NAME AND ADDRESS
EPA, Office of Research and Development
Industrial Environmental Research Laboratory
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
Final; 9/79-4/80
14. SPONSORING AGENCY CODE
EPA/600/13
15 SUPPLEMENTARY NOTES jERL-RTP project officer is Robert A. McAllister, Mail Drop
61, 919/541-2160.
16. ABSTRACT
The report describes a thermodynamic model, developed to predict the
equilibrium behavior of carbon dioxide, hydrogen sulfide, nitrogen, and methanol
mixtures. The model uses the four-suffix Margules equation to describe liquid-phase
nonidealities and the Soave modification of the Redlich-Kwong equation of state to
describe the gas phase. Model parameters were obtained from previously published
binary vapor/liquid equilibrium data. Vapor/liquid equilibrium data were obtained
experimentally for CO2/H2S/N2/methanol mixtures at temperatures of 258.15 K and
273.15 K and pressures of 6-40 atm. Model predictions of equilibrium pressure and
vapor compositions from specifications of temperature and liquid compositions com-
pared favorably with experimentally measured values.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
Pollution
Carbinols
Solubility
Gases
Nitrogen
Thermodynamics
Mathematical Models
Carbon Dioxide
Hydrogen Sulfide
b.IDENTIFIERS/OPEN ENDED TERMS
c. COS AT I field/Group
Pollution Control
Stationary Sources
Acid Gases
13B
07C
07D
07B
20M
12A
3. DISTRIBUTION STATEMENT
Release to Public
19. SECURITY CLASS (This Report),
Unclassified
21. NO. OF PAGES
83
20. SECURITY CLASS (This page)
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
79
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