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A simple correlation to evaluate binary interaction parameters of the Peng-Robinson equation of state: binary light hydrocarbon systems
Fluid Phase Equilibria, 74 (1992) 85-93
85
Elsevier Science Publishers B.V., Amsterdam
A simple,correlation to evaluate binary interaction parameters of the Peng-Robinson equation of state: binary light hydrocarbon systems Guanghua
Gao
Department of Chemical Engineering, Tsinghua University, 100084 Beijing (China)
Jean-Luc Daridon, Henri Saint-Guirons
and Pierre Xans *
Laboratoire de Physique des Matt%aux Industriels, Centre Universitaire de Recherche Scientifique, Universitk de Pau et des Pays de I’Adour, Avenue de Wniversite, 64000 Pau (France)
Frangois Monte1 &xi&
Nationale ELF-Aquitaine -C.S.T.C.S
Avenue Larribau, 64018 Pau Cedex (France)
(Received May 19, 1991; accepted in final form December 30, 1991)
ABSTRACT Gao, G., Daridon, J.-L., Saint-Guirons, H., Xans, P. and Montel, F., 1992. A simple correlation to evaluate binary interaction parameters of the Peng-Robinson equation of state: binary light hydrocarbon systems. Fluid Phase Equilibria, 74: 85-93 A simple correlation to evaluate binary interaction parameters kij of the Peng-Robinson equation of state for light hydrocarbons mixtures is proposed, as a function only of critical temperature and compressibility factor. The method yields results with an accuracy bordering on that obtained with methods requiring specific adjustments for each binary mixture coefficient kij.
INTRODUCTION
The Peng-Robinson equation of state (1976) is most frequently used in the petroleum industry and related fields. For the prediction of thermodyCorrespondence to: P. Xans, Laboratoire de Physique des MatCriaux Industriels, Centre Universitaire de Recherche Scientifique, Universitt de Pau et des Pays de l’Adour, Avenue de l’Universit6, 64000 Pau, France.
0378-3812/92/$05.00
0 1992 Elsevier Science Publishers B.V. All rights reserved
G. Gao et al. /Fluid Phase Equilibria 74 (1992) 85-93
86
namical properties of a pure component, it requires only the knowledge of the critical pressure, the critical temperature and the acentric factor. To improve performance of this equation when used in studies of binary mixtures, it is customary to introduce binary interaction parameters, k,,, in classical mixing rules. Values of kij for all possible binary pairs are determined by regressing vapour-ljquid equilibrium data for experimental mixtures, a procedure which removes the predictive power of this equation. The aim of this paper is to propose a simple correlation to calculate binary interaction parameters kij used with the Peng-Robinson equation of state for a certain number of hydrocarbon mixtures (C,-C,,). This procedure requires only the additional knowledge of the critical volume, V,, of each of the components.
BINARY INTERACTION
To calculate Peng-Robinson p=--
PARAMETERS
the vapour-liquid equilibria of the fluids studied, equation of state (1976) is used. a
RT v-b
(1)
v(v + b) + b(v -b)
The two parameters
a and b are expressed for pure components
a = 0.45724( R2T:/Pc)~
the
as
(2) (3)
b = 0.07780( RT,/P,) where (Y= [l + m(1 - T;/2)]2
(4)
m = 0.37464 + 1 S42260 - 0.26992d2
(5)
For the mixtures, a and b are replaced by a, and b, with the following mixing rules: a, = C Cxixj(aiaj)“*(l i
b, = &bi
- kij)
(6)
j
(7)
kij is an empirical binary parameter introduced to improve performance for the restitution of thermodynamic properties of mixtures, but its evaluation, from all possible binary pairs, is often a problem.
G. Gao et al. /Fluid Phase Equilibria 74 (1992) 85-93
87
For most authors the values of kij are back-calculated by trial and error from data available in the literature. These computations lead to the best results but remove the predictive character of the procedure used. For hydrocarbon pairs it should be noted that the binary interaction parameters are generally very close to zero, so they are usually taken as zero by many authors. Thus, they recover the predictive property of the Peng-Robinson equation as regards pure compounds, but this approach leads to less accurate results. To maintain the predictive character of this procedure, even in the case of a number of hydrocarbon mixtures (C,-C,,), we propose the following correlation: 1 -k,,
= [2(T,iT,j)1’2/(T,j
+ Tcj)]=“’
where ‘cij = (‘ci + zcj)/2
(9)
Zci and Zcj are the critical compressibility
factors of the two components. Consequently the Peng-Robinson equation should be used without any adjustable parameter, since the mixture law requires only knowledge of the critical parameters PC, V, and T, of each component.
PREDICTION
RESULTS AND DISCUSSION
We have estimated vapour-liquid equilibria (VLE) at high pressure using the binary interaction parameter of the Peng-Robinson equation of state calculated by eqn. (8) for a number of hydrocarbon systems which are made up of paraffins, cycloalkanes, alkenes and aromatic hydrocarbons CC,-C,,). A total of 252 isothermal VLE (P, T, x, y) data sets and 2320 VLE determinations (Knapp et al., 1982) are available and are listed in Table 1. The critical temperature, critical pressure, critical compressibility factor and acentric factor required to calculate vapour-liquid equilibria are given by Reid et al. (1977). The predicted results are summarized in Table 1 and compared with calculated values employing kij back-calculated by trial and error from experimental data which are compiled by Knapp et al. (1982). As indicated in Table 1, the agreement between estimated and experimental bubble point pressure as well as vapour phase composition in equilibrium is satisfactory. In other words, the deviation between experimental and predicted values using the binary interaction parameter kij calculated by eqn. (8) is not far from that employing optimized kij for individual isothermal VLE data.
7 106 124 66 16 104 56 131 156 41 95 17 26
84 74 7 62
Ethane -propane -n-pentane - n-hexane -n-heptane
Datum point
Methane - n-ethane -n-propane -n-butane - n-pentane - n-hexane - n-heptane -n-octane - n-nonane - n-decane -isobutane -cyclohexane -benzene -toluene
System
255-366 277-444 298-298 338-449
250-250 130-213 294-394 310-444 310-410 277-510 223-423 223-423 310-510 310-377 294-444 339-339 422-543
(K)
Temp. range
5.2 6.8 3.5 8.8
6.7 6.5 13.2 10.9 1.7 24.8 27.3 32.3 36.1 11.5 28.2 33.0 25.2 0.62 1.55 2.53 2.65
0.72 2.72 3.38 2.14 1.39 2.76 4.84 3.23 2.95 2.53 4.27 3.24 7.58 0.96 2.82 0.44 1.69
1.11 0.10 3.26 3.34 0.62 2.64 1.55 0.54 0.87 3.42 2.36 1.95 7.78
?A%,
AP
pressure (MPa) (AAD%)
Our mixing rule
0.0013 0.0063 0.0086 0.0109
0.0079 0.0152 0.0218 0.0267 0.0311 0.0352 0.0382 0.0413 0.0428 0.0200 0.0374 0.0383 0.0412
kl,
0.54 1.44 1.93 2.42
0.38 2.92 1.49 1.31 1.35 2.18 1.97 2.91 2.94 1.68 2.96 2.57 4.94
ZAD%,
0.88 1.10 0.40 1.13
0.29 0.05 1.47 0.80 0.33 0.57 0.23 0.41 0.22 0.79 0.35 0.89 2.23
$4D%,
0.0011 0.0078 0.0041 0.0033
0.0070 0.0119 0.0244 0.0241 0.0244 0.0300 0.0496 0.0474 0.0411 0.0256 0.0384 0.0304 0.0970
ki,
Original mixing rule with ki,-,
equilibria for the different mixing rules
Max.
Comparison of predicted and calculated values of vapor-liquid
TABLE 1
Q 8
a
64 119 83 80
43 78 40 44 66 103 81
41 75
17 86 9
77 42
-n-octane - n-decane -cyclohexane -benzene
Propane -n-butane -n-pentane -n-hexane -n-heptane - n-decane -n-isopentane -benzene
n-Butane -n-heptane - n-decane
Ethylene -ethane - n-heptane -benzene
Propylene -n-propane -1-butene
310-344 277-410
263-293 216-516 348-348
355-538 310-510
323-423 344-460 333-493 333-533 277-510 273-453 310-477
273-373 277-510 233-533 273-553
3.1 4.7
4.8 9.7 9.1
4.0 4.9
4.1 4.5 4.8 4.8 7.1 4.6 5.9
5.3 11.8 9.0 8.2
1.25 0.55
0.65 1.62 5.48
0.87 1.52
0.37 3.00 1.13 1.62 2.73 2.15 4.41
2.10 3.10 3.81 5.10
1.13 0.54
3.49 0.80 0.77
0.99 0.71
1.83 2.66 1.25 3.59 0.62 2.47 2.15
0.50 1.36 1.78 0.42
0.0007
o.oooo
0.0002 0.0138 0.0158
0.0019 0.0045
0.0007 0.0019 0.0034 0.0048 0.0086 0.0017 0.0060
0.0129 0.0160 0.0121 0.0127
0.31 0.31
0.64 1.55 3.30
0.83 1.49
0.29 0.86 0.91 1.34 3.47 1.61 2.61
1.44 3.01 3.10 1.78
0.08 0.46
0.52 0.66 0.69
0.56 0.50
0.71 1.34 0.97 2.13 0.17 1.66 0.77
0.59 0.84 1.16 0.58
0.0063 0.0004
0.0089 0.0144 0.0311
0.0033 0.0078
0.0033 0.0267 0.0007 0.0056 0.0000 0.0111 0.0233
0.0185 0.0144 0.0178 0.0322
G. Gao et al. /Fluid Phase Equilibria 74 (I 992) 85-93
90
METHANE (1) - N-NONANE (2)
~
q-7x7-J
-9 4, diagram for methane-n-nonane: Fig. 1. Equilibrium pressure-composition calculated by eqn. (8); - - -, k,, = 0; o, experimental data (Shipman and Kohn, 1966).
METHANE (1) - CYCLOHEXANE (2)
T - 344.26
K
320
X(I), Y(I) Fig. 2. Equilibrium pressure-composition diagram for methane-cyclohexane: p, calculated by eqn. (8); - - -, k,, = 0; o, experimental data (Reamer et al., 1958).
kii
G. Gao et al. /Fluid Phase Equilibria 74 (1992) 85-93
METHANE
(1) - BENZENE
91
(2)
,tyxF
100
0
0.0
.2
.4 X(I),
.6
.6
1.0
Y(I)
Fig. 3. Equilibrium pressure-composition diagram for methane-benzene: -, ki, calculated by eqn. (8); ---, k,, = 0; o, experimental data (Elbishlawi and Spencer, 1951).
It is clear that, for mixtures made up of similar components, the coefficients kij are close to zero and our correlation gives results similar to those obtained with kij equal to zero. However, for asymmetric mixtures, e.g. methane-n-nonane, the improvement can reach 16% for bubble point pressures and 7% for the vapour phase composition. Figures l-3 compare VLE data for the methane-n-nonane, methanecyclohexane and methane-benzene systems with predicted values using the kij parameters calculated by eqn. (8). For comparison, results predicted by using zero values of kij are also shown in the same figures. The former procedure gives predicted values on better agreement with the experimental data. However, for the limited region in the vicinity of the critical point all these procedures show discrepancies between experimental and calculated results. Other studies have been carried out to solve this question on the basis of various kinds of equations of state. For example, Chueh and Prausnitz (1967) have estimated interaction parameters in mixture T, and V, calculations and used the Redlich-Kwong equation (1949) with certain alterations to calculate critical pressures; for any family of chemical components these parameters, upon suitable reduction, follow definite trends and thus can be used to generalize the process to multicomponent systems. These proce-
G. Gao et al. /Fluid Phase Equilibria 74 (1992) 85-93
92
dures involve much more elaborate calculations than ours, but we would nonetheless point out that they are particularly useful in the critical region.
CONCLUSION
This simple correlation to evaluate binary interaction parameters of the Peng-Robinson equation of state for light hydrocarbon mixtures was given in terms of critical temperature and compressibility factor of pure components. The proposed procedure yields slightly poorer results than those given by k,, back-calculated by trial and error from experimental data, but its accuracy is not far from that of the latter. On the other hand this correlation maintains the predictive character of the Peng-Robinson equation in the case of a number of light hydrocarbon mixtures.
LIST OF SYMBOLS
a, b kij
P
R T
T, V
x Y
Z
parameters in eqn. (1) binary interaction parameter pressure gas constant absolute temperature reduced temperature volume mole fraction of component mole fraction in vapor phase compressibility factor
Greek letter 0
acentric factor
Subscripts C
4 j lj m
critical property component cross-component mixture
G. Gao et al. /Fluid Phase Equilibria 74 (1992) 85-93
93
REFERENCES Chueh, P.L. and Prausnitz, J.M., 1967. Vapor-liquid equilibria at high pressures: calculation of critical temperatures, volumes and pressures of non polar mixtures. AIChE J., 13: 1107-1113. Elbishlawi, M. and Spencer, J.R., 1951. Equilibrium relations of two methane-aromatic binary systems at 150°F. Ind. Eng. Chem., 43: 1811-1815. Knapp, H., Doring, R., Gellrich, L., Pldcker, U. and Prausnitz, J.M., 1982. Vapor-liquid equilibria for mixtures of low boiling substances. Dechema, Frankfurt am Main, Germany. Peng, D.Y. and Robinson D.B., 1976. A new two-constant equation of state. Ind. Eng. Chem. Fundam., 15: 59-64. Reamer, H.H., Sage, B.H. and Lacey, W.N., 1958. Phase equilibriums in hydrocarbon systems - volumetric and phase behavior of the methane-cyclohexane system. Ind. Eng. Chem. Data Ser., 3: 240-245. Redlich, 0. and Kwong, J.N.S., 1949. On the thermodynamics of solutions. V - An equation of state. Fugacities of gaseous solutions. Chem. Rev., 44: 233-244. Reid, R.C., Prausnitz, J.M. and Sherwood, T.K., 1977. The properties of Gases and Liquids, 3rd edn. McGraw-Hill, New York. Shipman, L.M. and Kohn, J.P., 1966. Heterogeneous phase and volumetric equilibrium in the methane-n-nonane system. J. Chem. Eng. Data, 11: 176-180.
85
Elsevier Science Publishers B.V., Amsterdam
A simple,correlation to evaluate binary interaction parameters of the Peng-Robinson equation of state: binary light hydrocarbon systems Guanghua
Gao
Department of Chemical Engineering, Tsinghua University, 100084 Beijing (China)
Jean-Luc Daridon, Henri Saint-Guirons
and Pierre Xans *
Laboratoire de Physique des Matt%aux Industriels, Centre Universitaire de Recherche Scientifique, Universitk de Pau et des Pays de I’Adour, Avenue de Wniversite, 64000 Pau (France)
Frangois Monte1 &xi&
Nationale ELF-Aquitaine -C.S.T.C.S
Avenue Larribau, 64018 Pau Cedex (France)
(Received May 19, 1991; accepted in final form December 30, 1991)
ABSTRACT Gao, G., Daridon, J.-L., Saint-Guirons, H., Xans, P. and Montel, F., 1992. A simple correlation to evaluate binary interaction parameters of the Peng-Robinson equation of state: binary light hydrocarbon systems. Fluid Phase Equilibria, 74: 85-93 A simple correlation to evaluate binary interaction parameters kij of the Peng-Robinson equation of state for light hydrocarbons mixtures is proposed, as a function only of critical temperature and compressibility factor. The method yields results with an accuracy bordering on that obtained with methods requiring specific adjustments for each binary mixture coefficient kij.
INTRODUCTION
The Peng-Robinson equation of state (1976) is most frequently used in the petroleum industry and related fields. For the prediction of thermodyCorrespondence to: P. Xans, Laboratoire de Physique des MatCriaux Industriels, Centre Universitaire de Recherche Scientifique, Universitt de Pau et des Pays de l’Adour, Avenue de l’Universit6, 64000 Pau, France.
0378-3812/92/$05.00
0 1992 Elsevier Science Publishers B.V. All rights reserved
G. Gao et al. /Fluid Phase Equilibria 74 (1992) 85-93
86
namical properties of a pure component, it requires only the knowledge of the critical pressure, the critical temperature and the acentric factor. To improve performance of this equation when used in studies of binary mixtures, it is customary to introduce binary interaction parameters, k,,, in classical mixing rules. Values of kij for all possible binary pairs are determined by regressing vapour-ljquid equilibrium data for experimental mixtures, a procedure which removes the predictive power of this equation. The aim of this paper is to propose a simple correlation to calculate binary interaction parameters kij used with the Peng-Robinson equation of state for a certain number of hydrocarbon mixtures (C,-C,,). This procedure requires only the additional knowledge of the critical volume, V,, of each of the components.
BINARY INTERACTION
To calculate Peng-Robinson p=--
PARAMETERS
the vapour-liquid equilibria of the fluids studied, equation of state (1976) is used. a
RT v-b
(1)
v(v + b) + b(v -b)
The two parameters
a and b are expressed for pure components
a = 0.45724( R2T:/Pc)~
the
as
(2) (3)
b = 0.07780( RT,/P,) where (Y= [l + m(1 - T;/2)]2
(4)
m = 0.37464 + 1 S42260 - 0.26992d2
(5)
For the mixtures, a and b are replaced by a, and b, with the following mixing rules: a, = C Cxixj(aiaj)“*(l i
b, = &bi
- kij)
(6)
j
(7)
kij is an empirical binary parameter introduced to improve performance for the restitution of thermodynamic properties of mixtures, but its evaluation, from all possible binary pairs, is often a problem.
G. Gao et al. /Fluid Phase Equilibria 74 (1992) 85-93
87
For most authors the values of kij are back-calculated by trial and error from data available in the literature. These computations lead to the best results but remove the predictive character of the procedure used. For hydrocarbon pairs it should be noted that the binary interaction parameters are generally very close to zero, so they are usually taken as zero by many authors. Thus, they recover the predictive property of the Peng-Robinson equation as regards pure compounds, but this approach leads to less accurate results. To maintain the predictive character of this procedure, even in the case of a number of hydrocarbon mixtures (C,-C,,), we propose the following correlation: 1 -k,,
= [2(T,iT,j)1’2/(T,j
+ Tcj)]=“’
where ‘cij = (‘ci + zcj)/2
(9)
Zci and Zcj are the critical compressibility
factors of the two components. Consequently the Peng-Robinson equation should be used without any adjustable parameter, since the mixture law requires only knowledge of the critical parameters PC, V, and T, of each component.
PREDICTION
RESULTS AND DISCUSSION
We have estimated vapour-liquid equilibria (VLE) at high pressure using the binary interaction parameter of the Peng-Robinson equation of state calculated by eqn. (8) for a number of hydrocarbon systems which are made up of paraffins, cycloalkanes, alkenes and aromatic hydrocarbons CC,-C,,). A total of 252 isothermal VLE (P, T, x, y) data sets and 2320 VLE determinations (Knapp et al., 1982) are available and are listed in Table 1. The critical temperature, critical pressure, critical compressibility factor and acentric factor required to calculate vapour-liquid equilibria are given by Reid et al. (1977). The predicted results are summarized in Table 1 and compared with calculated values employing kij back-calculated by trial and error from experimental data which are compiled by Knapp et al. (1982). As indicated in Table 1, the agreement between estimated and experimental bubble point pressure as well as vapour phase composition in equilibrium is satisfactory. In other words, the deviation between experimental and predicted values using the binary interaction parameter kij calculated by eqn. (8) is not far from that employing optimized kij for individual isothermal VLE data.
7 106 124 66 16 104 56 131 156 41 95 17 26
84 74 7 62
Ethane -propane -n-pentane - n-hexane -n-heptane
Datum point
Methane - n-ethane -n-propane -n-butane - n-pentane - n-hexane - n-heptane -n-octane - n-nonane - n-decane -isobutane -cyclohexane -benzene -toluene
System
255-366 277-444 298-298 338-449
250-250 130-213 294-394 310-444 310-410 277-510 223-423 223-423 310-510 310-377 294-444 339-339 422-543
(K)
Temp. range
5.2 6.8 3.5 8.8
6.7 6.5 13.2 10.9 1.7 24.8 27.3 32.3 36.1 11.5 28.2 33.0 25.2 0.62 1.55 2.53 2.65
0.72 2.72 3.38 2.14 1.39 2.76 4.84 3.23 2.95 2.53 4.27 3.24 7.58 0.96 2.82 0.44 1.69
1.11 0.10 3.26 3.34 0.62 2.64 1.55 0.54 0.87 3.42 2.36 1.95 7.78
?A%,
AP
pressure (MPa) (AAD%)
Our mixing rule
0.0013 0.0063 0.0086 0.0109
0.0079 0.0152 0.0218 0.0267 0.0311 0.0352 0.0382 0.0413 0.0428 0.0200 0.0374 0.0383 0.0412
kl,
0.54 1.44 1.93 2.42
0.38 2.92 1.49 1.31 1.35 2.18 1.97 2.91 2.94 1.68 2.96 2.57 4.94
ZAD%,
0.88 1.10 0.40 1.13
0.29 0.05 1.47 0.80 0.33 0.57 0.23 0.41 0.22 0.79 0.35 0.89 2.23
$4D%,
0.0011 0.0078 0.0041 0.0033
0.0070 0.0119 0.0244 0.0241 0.0244 0.0300 0.0496 0.0474 0.0411 0.0256 0.0384 0.0304 0.0970
ki,
Original mixing rule with ki,-,
equilibria for the different mixing rules
Max.
Comparison of predicted and calculated values of vapor-liquid
TABLE 1
Q 8
a
64 119 83 80
43 78 40 44 66 103 81
41 75
17 86 9
77 42
-n-octane - n-decane -cyclohexane -benzene
Propane -n-butane -n-pentane -n-hexane -n-heptane - n-decane -n-isopentane -benzene
n-Butane -n-heptane - n-decane
Ethylene -ethane - n-heptane -benzene
Propylene -n-propane -1-butene
310-344 277-410
263-293 216-516 348-348
355-538 310-510
323-423 344-460 333-493 333-533 277-510 273-453 310-477
273-373 277-510 233-533 273-553
3.1 4.7
4.8 9.7 9.1
4.0 4.9
4.1 4.5 4.8 4.8 7.1 4.6 5.9
5.3 11.8 9.0 8.2
1.25 0.55
0.65 1.62 5.48
0.87 1.52
0.37 3.00 1.13 1.62 2.73 2.15 4.41
2.10 3.10 3.81 5.10
1.13 0.54
3.49 0.80 0.77
0.99 0.71
1.83 2.66 1.25 3.59 0.62 2.47 2.15
0.50 1.36 1.78 0.42
0.0007
o.oooo
0.0002 0.0138 0.0158
0.0019 0.0045
0.0007 0.0019 0.0034 0.0048 0.0086 0.0017 0.0060
0.0129 0.0160 0.0121 0.0127
0.31 0.31
0.64 1.55 3.30
0.83 1.49
0.29 0.86 0.91 1.34 3.47 1.61 2.61
1.44 3.01 3.10 1.78
0.08 0.46
0.52 0.66 0.69
0.56 0.50
0.71 1.34 0.97 2.13 0.17 1.66 0.77
0.59 0.84 1.16 0.58
0.0063 0.0004
0.0089 0.0144 0.0311
0.0033 0.0078
0.0033 0.0267 0.0007 0.0056 0.0000 0.0111 0.0233
0.0185 0.0144 0.0178 0.0322
G. Gao et al. /Fluid Phase Equilibria 74 (I 992) 85-93
90
METHANE (1) - N-NONANE (2)
~
q-7x7-J
-9 4, diagram for methane-n-nonane: Fig. 1. Equilibrium pressure-composition calculated by eqn. (8); - - -, k,, = 0; o, experimental data (Shipman and Kohn, 1966).
METHANE (1) - CYCLOHEXANE (2)
T - 344.26
K
320
X(I), Y(I) Fig. 2. Equilibrium pressure-composition diagram for methane-cyclohexane: p, calculated by eqn. (8); - - -, k,, = 0; o, experimental data (Reamer et al., 1958).
kii
G. Gao et al. /Fluid Phase Equilibria 74 (1992) 85-93
METHANE
(1) - BENZENE
91
(2)
,tyxF
100
0
0.0
.2
.4 X(I),
.6
.6
1.0
Y(I)
Fig. 3. Equilibrium pressure-composition diagram for methane-benzene: -, ki, calculated by eqn. (8); ---, k,, = 0; o, experimental data (Elbishlawi and Spencer, 1951).
It is clear that, for mixtures made up of similar components, the coefficients kij are close to zero and our correlation gives results similar to those obtained with kij equal to zero. However, for asymmetric mixtures, e.g. methane-n-nonane, the improvement can reach 16% for bubble point pressures and 7% for the vapour phase composition. Figures l-3 compare VLE data for the methane-n-nonane, methanecyclohexane and methane-benzene systems with predicted values using the kij parameters calculated by eqn. (8). For comparison, results predicted by using zero values of kij are also shown in the same figures. The former procedure gives predicted values on better agreement with the experimental data. However, for the limited region in the vicinity of the critical point all these procedures show discrepancies between experimental and calculated results. Other studies have been carried out to solve this question on the basis of various kinds of equations of state. For example, Chueh and Prausnitz (1967) have estimated interaction parameters in mixture T, and V, calculations and used the Redlich-Kwong equation (1949) with certain alterations to calculate critical pressures; for any family of chemical components these parameters, upon suitable reduction, follow definite trends and thus can be used to generalize the process to multicomponent systems. These proce-
G. Gao et al. /Fluid Phase Equilibria 74 (1992) 85-93
92
dures involve much more elaborate calculations than ours, but we would nonetheless point out that they are particularly useful in the critical region.
CONCLUSION
This simple correlation to evaluate binary interaction parameters of the Peng-Robinson equation of state for light hydrocarbon mixtures was given in terms of critical temperature and compressibility factor of pure components. The proposed procedure yields slightly poorer results than those given by k,, back-calculated by trial and error from experimental data, but its accuracy is not far from that of the latter. On the other hand this correlation maintains the predictive character of the Peng-Robinson equation in the case of a number of light hydrocarbon mixtures.
LIST OF SYMBOLS
a, b kij
P
R T
T, V
x Y
Z
parameters in eqn. (1) binary interaction parameter pressure gas constant absolute temperature reduced temperature volume mole fraction of component mole fraction in vapor phase compressibility factor
Greek letter 0
acentric factor
Subscripts C
4 j lj m
critical property component cross-component mixture
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93
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