2182
Ind. Eng. Chem. Res. 1988,27, 2182-2187
the factors, the most important factor is temperature. Even with these advantages, it should be emphasized that factorial design is a tool, a means to an end. It will not replace sound technical judgement or creativity in experimental work. Nomenclature ai = coefficient of the estimated model CM = catalyst-molar ratio interaction d = unit of variation of x from f ei = residual of the ith experiment K = either C, (catalyst), M (molar ratio), or T (temperature) r = correlation coefficient xk = natural variable for element K and Zk,its mean xK = coded variable for element K Yci = estimated response for the ith experiment Yoi= response for the ith experiment T M = temperature-molar ratio interaction
TC = temperature-catalyst interaction TMC = temperature-molar ratio-catalyst interaction Registry No. CoCl,, 7646-79-9; oleic acid, 112-80-1; oleic alcohol, 143-28-2. Literature Cited Bhatia, V. H.; Gulati, I. B. “Chemistry and Utilization of Jojoba”. Chem. Era 1981, 137-144. Fisher, R. A. Design of Experiments, 8th ed.; Hafner: New York, 1965 (1st ed 1935). Miwa, T. K. “Jojoba Oil Wax Esters and Derived Fatty Acids and Alcohols. Gas Chromatographic Analyses”. J.Am. Oil Chem. SOC. 1971, 48, 259-264.
Urteaga, L. “Kinetic Analysis of EsterificationReaction using Alcohol and Acid of High Molecular Weight”. MS Thesis, Complutense University, Madrid, 1986.
Received for review February 3, 1988 Accepted July 19, 1988
Correlation of Liquid-Liquid Equilibria for Some Water-Organic Liquid Systems in the Region 20-250 “C H e r b e r t H. Hooper, S t e f a n Michel,+and John M. P r a u s n i t z * Materials and Chemical Sciences Division, Lawrence Berkeley Laboratory, and Chemical Engineering Department, University of California, Berkeley, California 94720
A group-contribution model of the UNIFAC type is used to correlate liquid-liquid equilibria for water-organic liquid systems over a wide temperature range. Good agreement with experiment is obtained using temperature-dependent water-organic interaction parameters. This correlation may be useful for engineering design for processing of fossil fuels. Mutual solubilities of hydrocarbons and water are of interest in the petroleum and related industries. Hydrocarbon-water systems are sometimes encountered at high temperatures; these systems may also contain a large number of hydrocarbon derivatives such as phenolics. For process design, the compositions of coexisting water and hydrocarbon phases must be known or estimated. Liquid-liquid equilibria (LLE) may be calculatd from an equation of state or from an excess-Gibbs-energymodel. In recent years, equations of state have been used to represent binary water-hydrocarbon equilibria (Tsonopoulos and Wilson, 1983; Kabadi and Danner, 1985; Ludecke and Prausnitz, 1985; Mollerup and Clark, 1988). However, only limited success was achieved when the same equation of state was used to represent the compositions of both liquid phases over a wide range of temperatures. Groupcontribution models are often used for correlating and estimating fluid-phase equilibria; the best known of these is UNIFAC (Fredenslund et al., 1975). In the original UNIFAC correlation, interaction parameters were fitted primarily to vapor-liquid equilibria (VLE); as a result, predictions of LLE were generally not quantitative. Magnussen and co-workers (1981) later published a set of UNIFAC interaction parameters fitted mostly to LLE data which gave significantly improved predictions of LLE. Further modifications to the UNIFAC model have focused on the combinatorial contribution to the excess Gibbs
* To whom correspondence should be addressed.
Present address: Lehrstuhl f i u Thermodynamik,Universitat Dortmund, Dortmund, West Germany. 0888-5885/88/2627-2182$01.50/0
energy, and on the temperature dependence of the group-interaction parameters [for a review, see, e.g., Fredenslund and Rasmussen (1985) and Gmehling (198611. The most comprehensive and generally applicable groupcontribution model currently available is the Modified UNIFAC model of Larsen et al. (1987) intended primarily for predicting VLE and heats of mixing. UNIFAC predictions are necessarily most reliable for those thermodynamic data for which the interaction parameters are optimized (e.g., VLE, LLE, and heats of mixing) and for the temperature range over which the parameters are correlated. Further, since the UNIFAC model, in principle, applies to a large variety of mixtures, it is often not highly accurate for a limited class of mixtures. This paper presents a UNIFAC model suitable for LLE of systems containing water and hydrocarbons (and some hydrocarbon derivatives) over a wide range of temperatures. The scope here is much narrower than that of some previous correlations, for example, Larsen’s Modified UNIFAC and Magnussen’s UNIFAC-LLE. Only a single class of mixtures (water and hydrocarbons) and a single thermodynamic property (LLE) are considered. By sacraficing generality, quantitative predictions are obtained for the systems of interest at normal and advanced temperatures. We present here interaction parameters for water and seven common organic groups. Interaction parameters between water and organic groups are temperature dependent, while interactions not involving water are temperature independent. Inclusion of additional groups in 0 1988 American Chemical Society
Ind. Eng. Chem. Res., Vol. 27, No. 11, 1988 2183 Table I. Experimental Data Used for Determining Group-Interaction Parameters interaction binary data type no. of pts water-octane HZO-CHZ LLE 5 water-octane LLE 6 water-hexane LLE 3 LLE water-pentane 3 HZO-ACH LLE water-benzene 15 4 water-benzene LLE water-benzene LLE 8 HZO-ACCHZ LLE 4 water -to1u en e water-toluene LLE 6 water -m-xy1ene LLE 5 water-m-xylene LLE 6 1 water-1-methylnaphthalene LLE LLE water-1-methylnaphthalene 7 water-ethylbenzene LLE 4 HZO-ACOH water-m-cresol LLE 6 LLE water-p-cresol 6 LLE water-phenol 8 HZO-AN LLE water-quinoline 11 water-pyridine 11 VLE water-pyridine 17 VLE HZO-AS water-thiophene 4 LLE water-thianaphthene 9 LLE HZO-ACNHZ water-aniline 8 LLE CHZ-ACH hexane-benzene 7 VLE octane-benzene 6 VLE CHZ-ACCHZ heptane-toluene 6 VLE octane-p-xylene VLE 6 VLE octane-ethylbenzene 5 CHZ-ACOH octane-phenol 6 VLE octane-phenol VLE 8 octane-phenol 5 VLE octane-phenol 6 LLE CHZ-AN octane-pyridine VLE 13 octane-pyridine 17 VLE VLE nonane-pyridine 13 CHZ-AS heptane-thiophene 23 VLE CH2-ACNHZ hexane-aniline 5 LLE heptane-aniline 4 LLE ACH-ACCHZ VLE benzene-toluene 5 benzene-m-xylene 6 VLE ACH-ACOH 12 VLE benzene-phenol VLE benzene-phenol 28 ACH-AN benzene-pyridine VLE 7 benzene-pyridine VLE 6 ACH-AS benzene-thiophene 10 VLE ACH-ACNHZ benzene-aniline 11 VLE benzene-aniline 21 VLE ACCHZ-ACOH VLE toluene-phenol 9 ACCHZ-AN VLE toluene-pyridine 6 m-xylene-pyridine VLE 8 ACCHZ-AS toluene-thiophene 7 VLE toluene-thiophene VLE 7 ACCHZ-ACNHZ VLE toluene-aniline 10 VLE toluene-aniline 16 toluene-aniline 12 VLE ACOH-AN phenol-pyridine 12 VLE VLE p henol-4-methylpyridine 11 phenol-4-methylpyridine 10 VLE phenol-4-methylpyridine 11 VLE 11 VLE phenol-4-methylpyridine ACOH-AS VLE phenol-thiophene 10 ACOH-ACNHZ 3-methylphenol-2-methylaniline 8 VLE 3-methylphenol-3-methylaniline 7 VLE AN-AS pyridine-thiophene 14 VLE AN-ACNHZ VLE pyridine-aniline 9
min T, K 273 310 373 311 273 313 374 273 372 273 373 298 310 368 293 298 273 293 343 362 398 332 293 342 355 371 399 384 383 399 383 293 353 381 386 328 298 298 357 359 343 353 298 355 328 343 355 384 383 389 359 359 353 363 373 391 376 397 411 419 357 475 476 357 390
max T, K 303 553 473 423 343 473 476 298 473 333 473 298 550 536 413 393 333 493 343 363 473 490 413 351 388 383 409 392 383 477 383 318 353 394 415 328 333 323 379 402 343 353 298 380 328 343 453 445 386 410 378 378 353 363 373 455 420 422 455 463 357 477 477 387 446
reP 1 2 2 2 1 3 4 1 4 1 4 1 2 2 1 1 1 5 6 6 4 7 1 6 6 6 6 6 6 6 6 1 6 6 6 6 1 1 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
OReferences for experimental data: 1,Sorensen and Arlt (1979); 2, Brady et al. (1982); 3, Tsonopoulos and Wilson (1983); 4, Anderson and Prausnitz (1986); 5, Zegalska (1968); 6, Gmehling and Onken (1977), 7, Leet et al. (1987). Table 11. Coefficients for Temperature-DependentWater( 1)-Organic Group(%)Interaction Parameters a 12 and a,,
av(0)
av(U 1OOOa ujp ajl(’)
CHZ -40.72 3.826 -4.110 3060.6 -5.374
ACH -39.04 3.928 -4.370 2026.5 -3.267
ACCH3 -50.19 3.673 -5.061 2143.9 -3.076
ACOH -39.10 2.694 -4.377 -199.25 -0.5287
AN -31.85 4.579 -3.565 -211.03 -2.515
AS -60.08 6.309 -6.724 3005.4 -5.630
ACNHZ -29.31 1.081 -3.286 -1553.4 6.178
2184
Ind. Eng. Chem. Res., Vol. 27, No. 11, 1988
Table 111. Temperature-Independent Interaction Parameters
aij
and a,i for Organic Groups j
CH2 0.0 -71.40 15.27 7094.0 6778.2 4633.5 5620.2
1
CH2 ACH ACCHB ACOH AN
AS ACNHz
ACH 131.30 0.0 47.31 2717.3 1936.2 1707.7 9859.0
ACCH, -1.613 -27.67 0.0 7857.3 21531.0 3424.7 5277.0
ACOH 8143.8 1208.5 816.21 0.0 -1748.2 828.80 -486.49
AN 6831.9 2905.8 7665.2 -350.53 0.0 2229.2 1831.2
AS 271.46 108.48 892.62 14518.0 -534.30 0.0
ACNHz 4472.8 763.60 599.20 4563.4 -1320.3
a
0.0
a
No data available for fitting AS-ACNH, interaction.
the model will require new mutual solubility data with water over a wide range of temperatures.
UNIFAC Model In UNIFAC, the activity coefficient is given as a sum of combinatorial and residual contributions: In yi = In yiC + In yiR
(1)
Originally, the Staverman-Guggenheim combinatorial expression (Staverman, 1950) was used. Alternative combinatorial expressions are used in several variations of UNIFAC as reviewed by Gmehling (1986). For this work, we choose the combinatorial expression used by Larsen and co-workers (1987) in their Modified UNIFAC model. Their expression is identical with that of Flory-Huggins, with the volume fractions replaced by surface fractions as suggested by Kikic et al. (1980). The modified Flory-Huggins combinatorial expression was shown to represent VLE of alkane mixtures significantly better than the Staverman-Guggenheim combinatorial expression (Larsen et al., 1987). For component i, we have In yic = In ( a i / x i ) + 1 - (ai/xi)
(2)
where the modified volume fraction (in effect, surface fraction) is (3) The molecular volume parameter, rr, is calculated by summing over (Bondi) group volumes as in UNIFAC. Our residual expression is the same as that in original UNIFAC; however, interaction parameters between water and hydrocarbon groups are now temperature dependent. For every pair of groups in a mixture, there are two binary interaction parameters uij - ujl
ai, = ___
R
(44
500
1 ACOH
Temperature,
"C
5IO0-
I
0,
Y
. I500
I
0
50
100
150
Temperature,
200
"C
Figure 1. Temperature dependence of water(l)-hydrocarbon(2) group-interaction parameters a I 2and a2,.
ently over a wide range of temperatures for several hydrocarbon groups. The parameters behave regularly for different hydrocarbon classes; however, the temperature dependence of aI2is different from that of aZ1. For the region 20-250 "C, the interaction parameters are given by
where T is in kelvin.
and
Data Reduction
where uij characterizes the energy of interaction between group i and group j . When interaction parameters, aij,are obtained from water-hydrocarbon LLE data at several temperatures, we find that whenever i or j is water, aij shows a large temperature dependence. However, whenever i and j refer to organic groups, there is little temperature dependence. The form of the temperature dependence for waterorganic group interactions is determined empirically. Let 1 represent water and 2 represent an organic group. Interaction parameters a12and a21were adjusted independ-
One goal of this work is to develop a UNIFAC correlation suitable for multicomponent water-hydrocarbon LLE a t low and high temperatures. Unfortunately, very few high-temperature data are available for aqueous systems containing more than one hydrocarbon. Group-interaction parameters in the UNIFAC model were determined using binary data alone, and ternary data were used to test model predictions. Mutual solubility data and water-pyridine VLE data were used to determine interaction parameters a12and a21 where 1stands for water. Parameters for organic-organic group interactions were determined primarily from VLE data. Table I gives sources of experimental LLE and VLE data.
Ind. Eng. Chem. Res., Vol. 27, No. 11, 1988 2185
I
Experimbntal:
I
I
'
0 Anderson and Prausnitz b Sorensen and A r l t Calculated -Original UNIFAC with temperalureIndependent L L E paramelerr (Magnussrn et 01 1 Modified U N I F A C (Lorsen blOl ) This work
0
A 0
-
-----
-
Sorensen a n d A r l t
0 0 B r a d y , Cunningham a n d Wilson I
L e a t , L i n a n d Chao Anderson and Prausnitz
-
T h l s work
, W
10-1
E 5
m
._5 L
e
Y
-0 10-2
P
10-3
10-4L -25
I
25
I
I
I
75
125
175
"C
Temperature,
Figure 2. Experimental and calculated mutual solubilities of water and benzene.
I
-
10-6
110-4 225
I 0-7
Temperature, "C Figure 4. Experimental and calculated solubilities of some hydrocarbons in water.
t
-.-.-
_ _ _ _0_ _ _ _"_ -_ _.-.--. _ _ _ _ _ -- -.- - - --
0
5
E e
lo-l
1
0
e
Y
0
0
I
-,
Experimental: 0 Sorensen and A r l l Calculaled ~ r i g i n a UNIFAC l wilh temperatureIndependent L L E parameters (Mognussen el a1 ) -----Modified U N I F A C (Lorsen e t a 1 ) Thls work
IO' L
0
c
P
-
k// / I
I
naphthalene
c
.-
t
2
IO'
W
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ -- - - - - -
~ x I O - ~ -10
IO'
IO
30
Temperature,
50
70
"C
Figure 3. Experimental and calculated mutual solubilities of water and phenol.
The Redlich-Kwong equation of state was used for calculating vapor-phase fugacities. For nonpolar components, pure-component parameters in the equation of state were evaluated from critical properties (Chueh and Prausnitz, 1967). For water, the pure-component energetic parameter was correlated as a function of temperature. Cross parameters were determined according to the combining rules of de Santis et al. (1974). All parameters were fit by minimizing the sums of the squared differences between experimental and calculated VLE and LLE K factors. UNIFAC structural parameters Rk and Qk are those from the original work of Fredenslund et al. (1975). Table I1 presents coefficients for determining temperature-dependent interaction parameters u12 and uZ1for water with seven organic groups according to eq 5a and 5b. Figure 1 shows the temperature dependence of parameters ulz and u21for three representative organic groups
IO'
P
Experimental.
0
Sorensen and Arlt Brady. Cunningham and Wilroi L e e l , L i n and Chao Calculated: T h i s work
00
A
-
I,
I
0
50
I
100
I
150
I
I
200
250
Temperature, O C Figure 5. Experimental and calculated solubility of water in some hydrocarbons.
with water. Table I11 gives temperature-independent parameters for organic-organic group interactions. Because some of the parameters in Table 111are very large, we examined the Gibbs energy versus concentration curves for several binary and ternary systems. The curves did not show any peculiar behavior (e.g., multiple minima or maxima) which could lead to problems in flash calculations.
Correlation of Binary Mutual Solubilities We compare predictions of binary water-hydrocarbon mutual solubilities with experimental data. Because all binary solubility data spanning a wide temperature range
2186 Ind. Eng. Chem. Res., Vol. 27, No. 11, 1988 Phenol
Pyridine
0
limper, MICheI. and Prousnit2
A Anderson and Prausnitz CoIculoled Original UNlF4C milk tempaalurs-
40 50
i
. -.
fi90 ~iperimenta~
10
0 Hoop.,. Michel, and Prousnit2 A 4nderaon and Prausnitz Colculaled.
mdepend.nl LLE parameters (Maanussen e t 0 1 I UNIF4C (Lorsen # t o ! I -This Work
70 -----Modified
\
\
50
70
Figure 6. Liquid-liquid equilibria for the system water-toluenephenol at 200 "C (compositions in mole percent).
Figure 8. Liquid-liquid equilibria for the system waterthiophene-pyridine at 150 OC (compositions in mole percent).
10%Phenol E'perimentol 0 Hmper, Mtchel, ond Prausnitz A Anderson and Prausnttr
- -Original
UNlF4C milk temperoturaIndependent LLE poramelers IMognusssn et o l I Modifmd UNlF4C (Lorsen # t a l ) -This Work
94
1
97
k
water
Figure 7. Water-rich compositions for the system water-toluenephenol at 200 O C (compositions in mole percent).
were included in the parameter optimization, we cannot directly test the predictive capabilities of the model with binary data. However, we can determine the ability of the model to correlate simultaneously mutual solubilities for many hydrocarbons over a wide range of temperatures. In addition to comparison with experimental data, we also compare with predictions from Magnussen et al. (1981) and from Larsen et al. (1987). These comparisons are necessarily unfair because Magnussen et al.'s UNIFACLLE model was developed for the temperature range 25-40 "C using interaction parameters that are temperature independent. Magnussen et al.'s model is directed at a wide class of mixtures; thus, interaction parameters were not optimized to specific systems as in this work. Similarly, while Larsen et al.'s Modified UNIFAC model is intended for a wide range of temperatures, VLE and heat-of-mixing data were primarily used in parameter optimization. On the basis of these considerations, we do not expect quantitative predictions of water-hydrocarbon mutual solubilities at high temperatures from either the UNIFAC-LLE model or from Modified UNIFAC. However, we show results from these models because a specific correlation for water-hydrocarbon LLE is not available for comparison. As a first example, we consider the mutual solubilities of benzene and water in the range 0-200 "C. Figure 2 presents experimental data and predictions based on the three models. Magnussen et al.'s parameters accurately
predict mutual solubilities of benzene and water at 25 "C (the temperature at which the parameters were optimized), but extrapolations away from room temperature are poor. Predictions based on Modified UNIFAC are reasonably accurate between 0 and 100 "C, but errors as large as 100% are observed at higher temperatures. The model presented here gives reasonable predictions over the entire temperature range for which data are available. None of the models predicts the observed minimum in hydrocarbon solubility at room temperature. We next consider mutual solubilities of water and phenol; water is highly soluble in phenol at room temperature, and the two liquids are completely miscible above 65 "C. Figure 3 presents experimental data and model predictions. Again, solubility predictions based on Magnussen et al.'s parameters are accurate at room temperature but give large errors at higher (and lower) temperatures. An erroneous lower consolute point is predicted in this case. Modified UNIFAC predicts solubilities which are too low and are relatively temperature insensitive; the predicted upper consolute temperature is well above 200 OC. As expected from any classical model for the excess Gibbs energy, predictions of this work overshoot the upper critical solution temperature but give reasonable predictions well below that temperature. Magnussen et al.'s model is useful for predicting LLE at near-ambient temperatures; however, as expected, predictions of water-hydrocarbon LLE at temperatures remote from ambient are not satisfactory. Modified UNIFAC is useful for water-hydrocarbon LLE in cases where interaction parameters were fit to LLE data (e.g., H,O-ACH interactions in the water-benzene binary) but should not be applied for cases where VLE data were used in data reduction (e.g., H,O-ACOH interactions in water-phenol systems). Figures 4 and 5 present experimental data and predictions of this work for some additional binary aqueous systems. Figure 4 shows solubilities of organic liquids in water, while Figure 5 presents the solubility of water in organic liquids. The solubility of water in unsubstituted aliphatic and aromatic hydrocarbons does not vary substantially for different hydrocarbons. Thus, for clarity, solubility data for water in toluene are omitted from Figure 5. The results presented here indicate that binary waterhydrocarbon mutual solubilities are correlated well with our UNIFAC model. Reasonable agreement with experimental data is obtained over a wide temperature range
Ind. Eng. Chem. Res., Vol. 27, No. 11, 1988 2187
and for liquids exhibiting a wide range of mutual solubilities with water. Predictions are least accurate for systems near a liquid-liquid critical point. For the critical region, it is necessary to apply a nonclassical correction as discussed b y de Pablo and Prausnitz (1988). Prediction of Ternary Mutual Solubilities Very few t e r n a r y data are available for water-hydrocarbon mixtures at temperatures exceeding 100 O C . Because only binary data were used in determining the UNIFAC parameters, we can use the limited ternary data to test model predictions. We again refer to the correlations of Magnussen et al. and Larsen et al., keeping in mind the differences between their works and ours. Figure 6 presents measured and predicted mutual solubilities for the system water-toluene-phenol at 200 "C. As expected, predictions based on Magnussen et al.'s temperature-independent parameters are poor at this elevated temperature. Modified UNIFAC incorrectly predicts an immiscibility region for the water-phenol binary system and overestimates the solubility of water in toluene by a factor of 2. The predicted two-phase region is thus in poor agreement with experiment. Predictions of this work correctly match the binary water-toluene boundary and give semiquantitative agreement with experiment along the binodal curve. Figure 7 shows results for the water-rich region of the water-toluene-phenol t e r n a r y system at 200 "C. The UNIFAC model presented here predicts the binodal curve almost within experimental error. As a final example, Figure 8 presents measured and predicted LLE at 150 "C for the system waterthiophene-pyridine. Predictions are again in semiquantitative agreement with experiment.
Conclusions This work presents a UNIFAC correlation for LLE in water-hydrocarbon systems for the temperature region 20-250 "C. This correlation m a y be useful for engineering design for petroleum, coal-gasification, or coal-liquefication processes. Computer programs are available upon request.
Acknowledgment This work was supported b y the Director, Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences Division of the US Department of E n e r g y under Contract DE-AC03-76SF00098. Additional support was provided b y the Donors of the Petroleum Research Fund, administered b y the American Chemical Society. S.M. gratefully acknowledges the Henrich-Hertz-Foundation (West Germany) for the g r a n t of a fellowship.
Nomenclature a;, = interaction parameter for i-j interaction ~ ~ $= 0 )empirical coefficient ~ ~ $ 1= ) empirical coefficient a;.(2)= empirical coefficient LLE = liquid-liquid equilibria Qk = surface area parameter for group k R = gas constant Rk = volume parameter for group k r; = molecular volume parameter for component i T = temperature u;'= interaction parameter for i-j interaction VLE = vapor-liquid equilibria xi = mole fraction of component i in liquid
Greek Symbols yi = activity coefficient for component i
y$ = activity coefficient, combinatorial part yi = activity coefficient, residual part 0;= modified volume fraction of component i in the mixture
Registry No. Octane, 111-65-9; hexane, 110-54-3; pentane, 109-66-0; benzene, 71-43-2; toluene, 10888-3; m-xylene, 108-38-3; 1-methylnaphthalene, 90-12-0; ethylbenzene, 100-41-4; m-cresol, 108-39-4;p-cresol, 106-44-5; phenol, 108-95-2;quinoline, 91-22-5; pyridine, 110-86-1; thiophene, 110-02-1; thianaphthene, 95-15-8; aniline, 62-53-3; heptane, 142-82-5; p-xylene, 106-42-3; 4methylpyidine, 108-89-4; 3-methylphenol, 108-39-4; 2-methylaniline, 95-53-4.
Literature Cited Anderson, F. E.; Prausnitz, J. M. "Mutual Solubilities and Vapor Pressures for Binary and Ternary Aqueous Systems Containing Benzene, Toluene, m-Xylene, Thiophene and Pyridine in the Region 100-200 OC". Fluid Phase Equilib. 1986, 32, 63. Brady, C. J.; Cunningham, J. R.; Wilson, G. M. "Water-Hydrocarbon Liquid-Liquid-Vapor Equilibrium Measurements to 530 OF". GPA/API Research Report RR-62,1982; Gas Processors Association, Tulsa, OK Chueh, P. L.; Prausnitz, J. M. "Vapor-Liquid Equilibria at High Pressures. Vapor-Phase Fugacity Coefficients in Nonpolar and Quantum Gas Mixtures". Znd. Eng. Chem. Fundam. 1967,4(6), 492. de Pablo, J. J.; Prausnitz, J. M. "Thermodynamics of Liquid-Liquid Equilibria Including the Critical Region". AZChE J. 1988, in press. de Santis, R.; Breedveld, G. J. F.; Prausnitz, J. M. "Thermodynamic Properties of Aqueous Gas Mixtures at Advanced Pressures". Znd. Eng. Chem. Process Des. Dev. 1974, 13, 374. Fredenslund, A.; Rasmuasen, P. "From UNIFAC to SUPERFAC-and back?". Fluid Phase Equilib. 1985,24, 115. Fredenslund, A.; Jones, R. L.; Prausnitz, J. M. "Group-Contribution Estimation of Activity Coefficients in Nonideal Liquid Mixtures". AIChE J. 1975, 21(6), 1086. Gmehling, J. "Group Contribution Methods for the Estimation of Activity Coefficients". Fluid Phase Equilib. 1986, 30, 119. Gmehling, J.; Onken, U. "Vapor-Liquid Equilibrium Data Collection". DECHEMA Chemistry Data Series; Deutsche Gesellschaft fiir Chemisches Apparatewesen: Frankfurt/Main West Germany, 1977; Vol I, Parts 1-8. Hooper, H. H.; Michel, S.; Prausnitz, J. M. "High-Temperature Mutual Solubilities for Some Binary and Ternary Aqueous Mixtures Containing Aromatic and Chlorinated Hydrocarbons". J . Chem. Eng. Data 1988, in press. Kabadi, V. N.; Danner, R. P. "A Modified Soave-Redlich-Kwong Equation of State for Water-Hydrocarbon Phase Equilibria". Znd Eng. Chem. Process Des. Dev. 1985,24, 537. Kikic, I. Alessi, P.; Rasmussen, P.; Fredenslund, A. "On the Combinatorial Part of the UNIFAC and UNIQUAC Models". Can. J. Chem. Eng. 1980,58, 253. Larsen, B. L.; Rasmussen, P.; Fredenslund, A. "A Modified UNIFAC Group-Contribution Model for Prediction of Phase Equilibria and Heats of Mixing". Znd. Eng. Chem. Res. 1987, 26, 2274. Leet, W. A.; Lin, H. M.; Chao, K. C. "Mutual Solubilities in Six Binary Mixtures of Water + a Heavy Hydrocarbon or a Derivative". J. Chem. Eng. Data 1987, 32, 37. Ludecke, D.; Prausnitz, J. M. "Phase Equilibria for Strongly Nonideal Mixtures from an Equation of State with Density-Dependent Mixing Rules". Fluid Phase Equilib. 1985, 22, 1. Magnussen, T.; Rasmussen, P.; Fredenslund, A. "UNIFAC Parameter Table for Prediction of Liquid-Liquid Equilibria". Znd. Eng. Chem. Process Des. Deu. 1981, 20, 331. Mollerup, J. M.; Clark, W. M. "Correlation of Solubilities of Gases and Hydrocarbons in Water". Presented at the AIChE Spring National Meeting, New Orleans, LA, 1988, paper 12e. Sorensen, J. M.; Arlt, W. "Liquid-Liquid Equilibrium Data Collection". DECHEMA Chemistry Data Series; Deutsche Gesellschaft fiir Chemisches Apparatewesen: Frankfurt/Main West Germany, 1979; Vol. V, Part 1. Staverman, A. J. Recl. Trav. Chim. Pays-Bas 1950, 69, 163. Tsonopoulos, C.; Wilson, W. "High-Temperature Mutual Solubilities of Hydrocarbons and Water". AIChE J. 1983,29(11), 990. Zegalska, B. Bull. Acad. Polon. Sci., Ser. Sci. Chim. 1968, 16, 357. Received for review March 23, 1988 Accepted July 11, 1988
