Ind. Eng. Chem. Res. 1993,32, 2881-2887
2881
High-pressure Phase Equilibria for Carbon Dioxide-Methanol-Water System: Experimental Data and Critical Evaluation of Mixing Rules Ji-Ho Yoon, Moon-Kyoon Chun, Won-Hi Hong, a n d H u e n Lee' Department of Chemical Engineering, Korea Advanced Institute of Science and Technology, 373-1 Kusung-dong, Yusung-gu, Taejon, 305-701, South Korea
Equilibrium phase compositions for the carbon dioxide-methanol-water system were measured a t 313.2 K and pressures of 70, 100, and 120 bar. Three-phase equilibria for this system were also measured a t 305.15, 308.15, and 311.15 K, temperatures and pressures near the critical point of carbon dioxide. The two- and three-phase equilibrium data were correlated with the Soave-RedlichKwong and Patel-Teja equations of state incorporated with various types of the local composition and Huron-Vidal mixing rules. The Huron-Vidal mixing rules were found to be superior to the local composition models in predicting two-phase equilibria. Since the pressure range covering the three-phase region was very narrow, the Huron-Vidal mixing rules could not accurately predict the experimental three-phase equilibria. However, if there were a slight change of pressure in phase calculation, the Huron mixing models could correctly predict the experimental three-phase region and equilibrium compositions.
Introduction Supercritical fluid extraction of an aqueous solution containing several alcohols has been of interest due to the increasing energy costs of conventional processes such as atmospheric distillation. Particularly, supercritical fluid extraction of specific materials such as ethanol, lactic acid, and pharmaceuticals from bioproducta of fermentation has been approved as a powerful recovery process, since it has the ability to break the azeotropic limit of the solutions containing target materials and does not damage fermentation byproducts. Several studies on the phase behavior for a supercritical carbon dioxide system containing aqueous solution have been reported in the literature (Kuk and Montagna, 1983; Gilbertand Paulaitis, 1986;Radosz, 1986). Efremova and Shvartz (1969,1970)measured the liquid-liquid and gasliquid critical end points for carbon dioxide-ethanol (and methanol)-water systems. They also investigated the three-phase equilibria of those systemsand a higher-order critical end point at which the three-phase equilibrium behavior terminated. Takishima et al. (1986) measured the tie lines in the two-phase region and three-phase equilibrium compositions at temperatures near the critical point of carbon dioxide for the carbon dioxide-ethanolwater system. Panagiotopoulos and Reid (198613)reported that the carbon dioxide-n-butanol-water system exhibited extensive three-phase equilibria in the vicinity of a fourphase point. Di Andreth and Paulaitis (1987) and Di Andreth et al. (1987)suggested an experimentaltechnique for the accurate measurement of both the composition and the molar volume of individual phases in multiphase equilibria, and they measured the three- and four-phase equilibrium compositions and molar volumes for the carbon dioxide-2-propanol-water system. Cubic equations of state incorporated with various mixing rules have been not only applied in low-pressure vapor-liquid equilibrium (VLE)calculations,but used for estimating the high-pressure phase equilibria. Several authors (Panagiotopoulos and Reid, 1986a; Adachi and Sugie, 1986; Schwartzentruber et al., 1989) have proposed various local composition mixing rules to use binary interaction parameters. Although these local composition
* To whom correspondence should be addressed.
mixing rules have been successfully applied to both the low- and high-pressure VLE systems, these models could not be correctly applied to the multicomponent systems containing very similar components and the systems at low-densitylimit conditions (Michelsenand Kistenmacher, 1990). To overcome these problems Panagiotopoulos and Reid (1986b) suggested a density-dependent local composition model which could be correctly applied even to the systems at the low-density limit. This mixing rule is very similar to that proposed by Luedecke and Prausnitz (1985) except that b, mixture volume parameter, is used instead of p , molar density of mixtures. Huron and Vidal (1979) presented a new mixing rule by correlating the excess Gibbs free energy model at infinite pressure into cubic equations of state. An approach for matching the equations of state and the excess Gibbs energy model at zero pressure was originally performed by Mollerup (1986). Further, Michelsen (1990a,b)modified mixture parameters of the model into a density-independent and explicit form to increase computationalefficiency. Dahl and Michelsen (1990) confirmed that the model, the so-called modified Huron-Vidal second-order (MHV2)mixing rule, could be successfully applicable to the prediction of multicomponent VLE over a wide range of temperatures and pressures. Particularly, it has been illustrated that the MHV2 mixing rule is also able to correlate and predict high-pressure multiphase equilibria such as vapor-liquid-liquid equilibria (Dahl et al., 1992).
Thermodynamic Model All calculations are based on the Soave-Redlich-Kwong (Soave, 1972) equation of state (SRK-EOS) p=---RT v-b
a v(v+ b)
(1)
and the Patel-Teja (Pate1 and Teja, 1982) equation of state (PT-EOS)
p=--RT
v--b
a
v2
+ ( b + c)v-
bc
(2)
where the mixture parameters, b and c, for both equations are derived from the conventional mixing rules
0888-5885/93/2632-2881$04.00/00 1993 American Chemical Society
2882 Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993 n
b = zxibi
(3)
r=l
and n
c =p i c i
(4)
r=l
The corresponding equations for pure component parameters, bi and ci, are given in the literature (Soave, 1972; Pate1 and Teja, 1982). The most common method of obtaining mixture parameter a is to use the van der Waals one-fluid mixing rule a=
ggxixjui;
(5)
1=1J=1
with the combining rule (6) ai; = (aiaj)1/2(1- kij) While this mixing rule appropriately describes the phase behavior of mixtures such as hydrocarbons, it is in poor agreement with VLE results for mixtures containing polar components and other nonhydrocarbon chemicals. Much efforts in recent years have been made in developing alternative mixing rules. Panagiotopoulos and Reid (1986a) proposed a local composition model which uses an empirical modification of the combining rule to introduce two binary interaction parameters into mixture parameter a in phase equilibrium calculations. Their mixing rule uses eq 6 for a mixture parameter with a new combining rule ai; = (aia;)1'2[l
- ki;
+ (ki;- k;i)~i]
(7) Although this mixing rule has revealed several problems such as the "Michelsen-Kistenmacher syndrome" (Michelsen and Kistenmacher, 19901, it has been successfully applied to polar ternary mixtures, for example, carbon dioxide, water, and ethanol. This mixing rule is very similar to that proposed by Adachi and Sugie (1986),and in the case of binary systems, these two mixing rules are even practically identical. However, these mixing rules become different when applying to multicomponent systems. A different type of local composition model is the Wilson model (Wilson, 1964)proposed by Takishimaet al. (1986). According to this model, the local mole fraction, xji, is expressed by the following equations n
vji = exp[-(Aji - Aii)/RTI
(9) where A;i is the interaction energy between j and i molecules. Therefore, the following equation can be derived for the mixing rule (10) with the combining rule Yoon et al. (1993) successfully applied this mixing rule to the high-pressure binary and ternary systems of carbon dioxide, methanol, and ethanol. A detailed description of these local composition models including a procedure for
the calculation of fugacity coefficients is given elsewhere (Panagiotopoulos and Reid, 1986a;Takishima et al., 1986). Huron and Vidal (1979) originally developed a new method for deriving a mixing rule in connection with the excess Gibbs energy model, and thus they obtained an equation relating excess Gibbs energy at infinite pressure to the alb parameter of the SRK-EOS using the following equation n
g" = RT[ln cp -
ExiIn
cpi]
i=l
where cp and are the fugacity coefficients of the solution mixture and pure component i, respectively. The new model applied by Huron and Vidal was capable of correlating high-temperature and -pressure phase equilibria. Michelsen (1990a)proposed a modified formulation of the Huron-Vidal mixing rule which uses the SRK-EOS and a reference pressure of zero. The resulting equation could be obtained in the following explicit form
where a = 4 b R T and ai = ai/biRT. The recommended values of q1 and q2 for the modified Huron-Vidal first order (MHV1) mixing rule are -0.593 and 0, respectively, and those for the MHV2 mixingrule are -0.478 and -0.0047, respectively (Dahl and Michelsen, 1990). The fugacity coefficient for the MHVl and MHVP mixing rules is given by lnc~,=ln[-] R T P(v-6)
+(L-L) v-b ~ + In(
bi b
e) [y] T,nj
(14)
where the composition derivative of na can be calculated from each mixing rule. In order to apply the Huron-Vidal mixing rules to the PT-EOS, Sheng and Chen (1989) and Suen and Chen (1989) used the excess Gibbs energy model at infinite pressure as a reference pressure. Since the PTEOS possesses three parameters, the functional form of the PT-EOS derived by applying excess Gibbs energy at zero pressure becomes very complicated and implicit. However, the equation originally derived by Sheng and Chen (1989) is still expressed in more complicated form than the MHVl and MHV2 mixing rules. (15) where N = [bc
+ (b + ~ ) ~ / 4 ] ' / ~
Q = ln[(3b + c - 2N)/(3b + c + 2N)I
(16) (17)
The mixture parameters b and c are the same as in eqs 3 and 4. Applying these equations, the fugacity coefficients of components in a solution mixture can be expressed as
Ind. Eng. Chem. Res., Vol. 32, No. 11,1993 2883 A
11
pressure with carbon dioxide. Fine control of the system pressure could be obtained by using a pressure generator. A duplex recirculating pump was used to obtain rapid equilihrium,and each phase was recirculated througheach sampling valve under equilibrium conditions. The equilibrium compositions of each phase were determined by injecting the high-pressure sample into the gas chromatograph for on-line composition analysis. Each sample was analyzed at least three times, and the vapor- and liquidphase compositions were reproducible to within a mole fraction of 0.002 and 0.003, respectively. The cnrbon dioxide (purity of 99.9% ) used in this study was supplied by World Gas Co. The methanol (purity of 99.9%) was supplied by Merk, and HPLC grade distilled water supplied by Aldrich was used. These chemicals were used without further purification.
Results and Discussion
+-
i
9
'
A
Figure 1. Schematic diagram of the experimental apparStUS used in this work: (1) equilibriumcell,(2) high-pressure pump, (3) vapor sampling valve, (4) liquid sampling valve, (5) pressure generator, (6) pressure gauge, (7)rupture disk, (8) liquid reservoir, (9) metering valve, (10) COI cylinder, (11) He cylinder, (12) gas chromatography, and (13) vent line.
where
V, = v
R=
b,(b
+ (b + c)/2
+ 3c) + ci(c + 3b) 4N
+
4N(3bj c;) - &(3b = (3b
(19)
+ C)
+ c + W ( 3 b + e - 2N)
(20)
(21)
Any appropriate excess Gibbs energy model for VLE calculationscan he used for the Huron-Vidal mixing rules. In the present work, we use only the UNIQUAC model with the structural parameters R and Q given elsewhere (Gmehling et al., 1981; Sander et al., 1983). Experimental Section The phase equilibrium apparatus used in this work is shown in Figure 1. It is a circulation-type apparatus in which the coexisting phases are recirculated, on-line sampled, and analyzed. The apparatus and experimental procedures are almost the same as those given in the previous work (Yoon et al., 1993). The only difference is that the light liquid phase (middle phase) is recirculated through an extended tube over a vapor sampling valve for measuring multiphase equilibrium compositions. The experiment began hy charging the equilibrium cell with a mixture of liquid. After the cell was slightly pressurized hy carhondioxide, it was slowlyheatedto the experimental temprature. When the experimentaltemperature reached a steady state, the cell was pressurized to the desired
The experimental results for the carhon dioxidemethanol-water system have rarely been reported except for those of Chang and Rousseau (1985). Moreover, they only measured the solubilities of carbon dioxide in methanol-water mixtures, but not the vapor-phase compositions. In the present work, the two- and three-phase equilibrium compositions for this system were measured at several temperatures and pressures and are listed in Table I. Prior to study of the ternary system, the high- and lowpressure VLE results for the three binary systems, carbon dioxide-methanol, methanol-water, and carbon dioxidewater, were closely examined and compared with the following models: SRK equation with the Panagiotopoulos-Reid mixingrule (SRK-P&REID), SRKequationwith theMHVl mixingrule (SRK-MHVl),SRKequation with the MHV2 mixing rule (SRK-MHV2), PT equation with the Wilson mixing rule (PT-WILSON),and PT equation with the Huron-Vidal mixing rule (PT-H&VIDAL). The average absolute deviations (AAD) of vapor and liquid mole fractions obtained from these models are summarized in Table 11. In general, the values estimated from these models revealed a similar magnitude of deviations from experimental VLE data. However the SRK-P&REID model waa in good agreement with experimental results and particularly for the carbon dioxide-water system. Nevertheless, it should be noted that the Huron-Vidal mixing rules (SRK-MHV1, SRK-MHV2, and PT-H& VIDAL models) were more robust than the local composition models (SRK-P&REID and PT-WILSON models) in that the calculated values by using the Huron-Vidal mixing rules were less sensitive to the variation of parameters in the fitting procedure. The binary interaction and UNIQUAC molecular interaction energy parameters calculated from the models treated in this study are listed in Table 111. For more accurate prediction, the UNIQUAC parameters for the methanol-water system werenewly calculated hya fitting procedurewithout using the previously determined values from low-pressure VLE data. The experimental and predicted results for the ternary system carbon dioxide-methanol-water a t 313.15 K and 70 bar are shown in Figure 2. As shown from this figure, the Huron-Vidal mixing rules were found to be superior to the localcomposition modelsfor equilibrium prediction in the two-phase region. It was also observed that the phase behaviors estimated from Huron-Vidal mixing rules were similar to each other. For two different local composition models, the SRK-P&REID model underestimated the concentration of carbon dioxide in the liquid
2884 Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993 Table 1. Two- and Three-Phase Equilibrium Compositions for Carbon Dioxide (1)-Methanol (2)-Water (3) System vapor liquid1 liquid2 (middle)
T,K 313.15
P,bar 70.0
100.0
120.0
305.15 308.15 311.15
72.0 73.7 75.0 76.5 77.6 81.0
Y1
YZ
YS
x1
x2
x3
Xl
x2
x3
0.994 0.993 0.991 0.990 0.989 0.989 0.983 0.976 0.923 0.894 0.983 0.971 0.954 0.882 0.975 0.989 0.991 0.988 0.985 0.983
0.005 0.006 0.007 0.008 0.010 0.010 0.014 0.021 0.069 0.093 0.013 0.024 0.038 0.101 0.022 0.009 0.005 0.011 0.013 0.016
0.001 0.001 0.002 0.002 0.001 0.001 0.003 0.003 0.008 0.013 0.004 0.005 0.008 0.017 0.003 0.002 0.004 0.001 0.002 0.001
0.039 0.069 0.143 0.233 0.298 0.325 0.042 0.069 0.171 0.421 0.039 0.074 0.157 0.421 0.396 0.101 0.031 0.468 0.180 0.416
0.220 0.354 0.485 0.548 0.574 0.572 0.222 0.314 0.451 0.461 0.189 0.309 0.439 0.445 0.485 0.367 0.162 0.448 0.468 0.475
0.741 0.577 0.372 0.219 0.128 0.103 0.736 0.617 0.378 0.118 0.772 0.617 0.404 0.134 0.119 0.532 0.807 0.064 0.352 0.109
0.895 0.907 0.917 0.903 0.930 0.917
0.091 0.048 0.020 0.064 0.047 0.072
0.014 0.045 0.063 0.013 0.023 0.011
Table 11. VLE Results for the Models Considered in This Work SRK-P&REID SRK-MHVl SRK-MHV2 PT-WILSON PT-H&VIDAL system T,K P,bar A A D x a AADp A A D x a AADp A A D x a AADp A A D x a AADp A A D x a AADp ref 4.33 0.07 4.42 0.07 8.64 0.08 8.75 0.13 8.37 0.06 c carbon dioxide (1)-methanol (2) 313.15 6-80 0.29 1.06 0.97 1.56 0.37 1.46 1.04 0.99 d 0.22 313.15 0.15-0.35 1.16 methanol (1)-water (2) 3.91 nab nab 3.81 nab e nab 3.61 0.51 nab 3.69 carbondioxide (1)-water (2) 313.15 50-610
*
a MX = (100/Np) (x? - x$')/x:'~'; where NP is the number of data points. na, not available. Suzuki et al., 1990. Gmehling et al., 1981. e Wiebe and Gaddy, 1940.
Table 111. Binary Interaction and UNIQUAC Molecular Interaction Energy Parameters for the Models Considered in This Work
SRK-PLREID
SRK-MHVl
SRK-MHV2 PT-WILSON
system T,K P,bar k1z kz1 alz, K azl, K alz, K 021, K mz VZI 475 -87 1.0883 0.7432 0.0555 0.0814 495 -136 carbon dioxide (1)-methanol (2) 313.15 6-60 194 1.7773 0.5049 186 -116 313.15 0.15-0.35 -0.0918 -0.0693 -128 methanol (1)-water (2) -0.1256 0.3038 1206 -17 1226 102 0.4049 0.0871 313.15 50-510 carbon dioxide (1)-water (2) a
PT-H&VIDAL a12, K
540 -117 1394
a21, K ref -128 a 289 b 80 c
*
Suzuki et al., 1990. Gmehling et al., 1981. Wiebe and Gaddy, 1940.
CHjOH
CHjOH
\-
E X ~RguIt(Thl8 . Work) SRK-MHVZ SRK-PIREID SRK-MHVl PT-H&VIDAL PT-WILSON
HZO
cot
--
H2O
Exp. RguIt(Thh Work) SRK-YHV2 SRK-PIREID PT-HIVIDAL PT.WILSON
cot
Figure 2. Experimental and calculated results for the carbon dioxide-methanol-water system at 313.15 K and 70 bar.
Figure 3. Experimental and calculated resulte for the carbon dioxide-methanol-water system at 313.15 K and 100 bar.
phase and the PT-WILSON model overestimated it. Figures 3 and 4 show the equilibrium results measured and predicted a t 313.15 K and pressures of 100 and 120 bar, respectively. Since the predicted values from the SRK-MHV1 model were very similar to those from the SRK-MHVL model, the resulting line of values estimated from the SRK-MHV1model was deleted from these figures to avoid confusion. Like above 70-bar results, the agree-
ment between the experimental data and the predicted results from Huron-Vidal mixing rules was excellent, whereas large deviations from experimental results were observed for the local composition models. In particular, the SRK-PBEREID model still underestimated the concentration of carbon dioxide in the liquid phase. As pointed out by Michelsen and Kistenmacher (19901, the discrepancy arising in phase calculations of mixtures
Ind. Eng. Chem. Res., Vol. 32,No. 11,1993 2886 CH3OH
CHjOH
-
A
A
H2O
c02
Figure 4. Experimental and calculated resulta for the carbon dioxide-methanol-water system at 313.15 K and 120 bar.
Exp. Rrun(Thi8 Work)
nSRK-YHVZ
Exp. RIUlqTtll8 work) SRK-WV2 SRK-PIREID PTHIVIDAL PT-WILSON
PTHIVIDAL
H20
c02
Figure 6. Comparison of estimated and experimental three-phase equilibria for the carbon dioxidemethanol-water system at 305.15 K. CHjOH
' 6 Exp. Rrun(TM8 Work) I \SRK-MHV2 Exp. ReculqThia Work) SRK-MHV2 SRK-PLREID PT-HIVIDAL PT-WILSON
I
0.2
.
)
0.4
.
i 763 bar P U ~I70.2 bsr
~
0.6
1.o
0.8
CH3OH fraction in H 2 0 rich phase Figure 5. Comparison of estimated and experimental methanol concentration in vapor and liquid phases for the carbon dioxidemethanol-water system at 313.15 K and 120 bar.
containing very similar components, the so-called "Michelsen-Kistenmacher syndrome", may be responsible for inaccurate prediction of the Panagiotopoulos-Reid mixing rule. The PT-WILSON model could be very well applied to the carbon dioxide binary system containing polar components (Yoon et al., 1993), but this model was in poor agreement with several ternary systems containing carbon dioxide and water (Takishima et al., 1986). Figure 5 illustrates the experimental and estimated methanol concentrations in vapor and liquid phases on the basis of the carbon dioxidefree concentration a t 313.15 K and 120bar. Among the models considered,the PT-H&VIDAL model showed the best agreement with experimental data. However, from the viewpoint of process application, all models showed that a concentration of methanol of more than 98 mol % might be possible through supercritical fluid extraction. The experimental and estimated threephase equilibria at temperatures of 305.15, 308.15,and 311.15 K are depicted in Figures 6-8,respectively. Since the SRK-MHV2 and PT-H&VIDAL models exhibited better correlation with experimental two-phase equilibria than the other models, these two models were used to predict the three-phase equilibria. From these figures, the calculated results were a little different from the experimental data a t all temperatures studied, but if there were a slight change of pressure in the phase calculation,
H20
co2
Figure 7. Comparison of estimated and experimental three-phase equilibria for the carbon dioxide-methanol-water system at 308.15 K. CHjOH
A
Exp. R u n ( T M 8 Work)
nSRK-MHVZ
mw
=81.0 bar
?rd
I
7 L O bar
H20 c02 Figure 8. Comparison of estimated and experimental three-phase equilibria for the carbon dioxide-methanol-water system a t 311.15
K.
both models could also correctly predict the experimental three-phase equilibrium compositions. Moreover, it could be said that the experimental three-phase region was more sensitive to pressure change than the predicted results. Since the experimental three-phase equilibria for this system only existed at the narrow region near the critical
2886 Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993
point of pure carbon dioxide, it may be difficult to accurately predict with any thermodynamic model. In order to investigate the applicability of the Huron-Vidal mixing rules for the prediction of multiphase equilibria, the experimental three- or four-phase equilibrium data for a variety of systems must be provided and tested. Considering that the UNIQUAC parameters fitted by using the experimental binary data a t 313.15 K were used in the three-phase equilibrium calculations existing at different temperatures, it could be also estimated that the threephase behavior was comparatively well represented with the SRK-MHV2 and PT-H&VIDAL models.
Conclusions The two-phase equilibrium compositions for the carbon dioxide-methanol-water system were measured at 313.2 K and pressures of 70,100, and 120 bar. In particular, the three-phase equilibria appearing near the critical point of carbon dioxide were carefully measured because of their high sensitivityto small variations of pressure. These twoand three- phase equilibrium data were correlated with the original and modified versions of the local composition and Huron-Vidal mixing models. The agreement between the experimental and predicted results for two-phase equilibria was excellent for all Huron-Vidal mixing rules examined, whereas large deviations from experimental results were observed for the local composition models. For three-phase equilibria, the results calculated by using SRK-MHV2 and PT-H&VIDAL models were a little different from the experimental data a t all temperatures studied. It should be noted that, with a slight change of pressure, these two models could be well applied for the better prediction of three-phase equilibria. However, the Huron-Vidal mixing rules need to be tested and proven with a variety of systems including carbon dioxidealcohols-water for the more general application to the highpressure and multiphase equilibria. For this reason additional experimental and theoretical studies are in progress in our laboratory.
Acknowledgment This work was supported by the Korea Science and Engineering Foundation and University Awards Program of the Korea Advanced Institute of Science and Technology.
Nomenclature a = parameter in the equations of state aij = interaction energy parameter of UNIQUAC model, K b = parameter in the equations of state c = parameter in the equations of state
g = Gibbs free energy k = binary interaction parameter in the Panagiotopoulos-
Reid mixing rule n = number of moles P = pressure, bar Q = structural parameter in UNIQUAC model q1, qz = mixing rule constants in eq 13 R = gas constant R = structural parameter in UNIQUAC model T = temperature v = molar volume x = mole fraction Greek Letters
equation of state parameter, a = a I b R T activity coefficient = binary interaction parameter in the Wilson mixing rule
a= y = 7
cp
= fugacity coefficient
A = interaction energy parameter in the Wilson mixing rule Superscripts
E = excess property E* = excess property at zero pressure Subscripts
i, j , k = molecular species m = mixture = infinite pressure state
Literature Cited Adachi, Y.; Sugie, H. A New Mixing Rule-Modified Conventional Mixing Rule. Fluid Phase Equilib. 1986,28, 103-116. Chang, T.; Rousseau,R. W. Solubilitiesof Carbon Dioxidein Methanol and Methanol-Water at High Pressures: Experimental Data and Modeling. Fluid Phase Equilib. 1985,23, 243-258. Dahl, S Michelaen,M. L. High-pressure Vapor-Liquid Equilibrium with a UNIFAC-Based Equation of State. AIChE J. 1990, 36, 1829-1836. Dahl, S.;Dunalewicz,A.; Fredenslund, A.; Rasmussen, P. The MHV2 Model: Prediction of Phase Equilibria at Sub- and Supercritical Conditions. J. Supercrit. Fluids 1992, 5 , 42-47. Di Andreth, J. R.; Paulaitis, M. E. An Experimental Study of Threeand Four-Phase Equilibria for Isopropanol-Water-Cabon Dioxide Mixtures at Elevated Pressures. Fluid Phase Equilib. 1987, 32, 261-271. Di Andreth, J. R.; Ritter, J. M.; Paulaitis, M. E. Experimental Technique for Determining Mixture Compositions and Molar Volumes of Three and More Equilibrium Phases at Elevated Pressures. Ind. Eng. Chem. Res. 1987, 26, 337-343. Efremova, G. D.; Shvartz, A. V. High-Order Critical Phenomena in Ternary System. Russ. J. Phys. Chem. 1969,43,968-970. Efremova, G. D.; Shvartz, A. V. High-Order Critical Phenomena in the System Ethanol-Water-Carbon Dioxide.Russ. J.Phys. Chem. 1970,44,614-615. Gilbert, M. L.; Paulaitis, M. E. Gas-Liquid Equilibrium for EthanolWater-Carbon Dioxide Mixtures at Elevated Pressures. J.Chem. Eng. Data 1986,31, 296-298. Gmehling, J.; Onken, U.; Arlt, W . Vapor-Liquid Equilibrium Data Collection: DECHEMA Chemistry Data Series; DECHEMA. FrankfurUMain, 1981; Vol. I, Part 1, pp 37-76. Huron, M.-J.; Vidal, J. New Mixing Rules in Simple Equations of State for Representing Vapow-Liquid Equilibria of Strongly NonIdeal Mixtures. Fluid Phase Equilib. 1979,3,265-271. Kuk, M. S.;Montagna, J. C. Solubility of Oxygenated Hydrocarbons in Supercritical Carbon Dioxide. In Chemical Engineering at Supercritical Fluid Conditions;Paulaitis, M. E., Penninger, J. M. L., Gray, R. D., Jr., Davidson, P., Eds.; Ann Arbor Science: Stoneham, MA, 1983; pp 101-111. Luedecke,D.; Prausnitz, J. M. Phase Equilibriafor Strongly Nonideal Mixtures from an Equation of State with Density-Dependent Mixing Rules. Fluid Phase Equilib. 1985,22,1-19. Michelsen, M. L. A Modified Huron-Vidal Mixing Rule for Cubic Equations of State. Fluid Phase Equilib. 1990a, 60, 213-219. Michelsen, M. L. A Method for Incorporating Excess Gibbs Energy Models in Equations of State. Fluid Phase Equilib. 1990b, 60, 47-58. Michelsen, M. L.; Kistenmacher, H. On Compwition-Dependent Interaction Coefficients. Fluid Phase Equilib. 1990,58,229-230. Mollerup, J. A Note on the Derivation of Mixing Rules from Excess Gibbs Energy Models. Fluid Phase Equilib. 1986, 25, 323-327. Panagiotopoulos, A. Z.; Reid, R. C. New Mixing Rule for Cubic Equation of State for Highly Polar,Asymmetric Systems. ACS Symp. Ser. 1986a, No. 300, 571-582. Panagiotopoulos, A. Z.; Reid, R. C. Multiphase High Pressure Equilibria in Ternary Aqueous Systems. Fluid Phase Equilib. 1986b, 29, 525-534. Patel, N. C.; Teja, A. S. A New Cubic Equation of State for Fluids and Fluid Mixtures. Chem. Eng. Sci. 1982, 37, 463-473. Radosz,M. Multiphase Equilibria in High-pressure Ternary Systems Containing Secondary Alcohols and Water. Fluid Phase Equilib. 1986,29, 515-523. Sander, B; Skjold-Jargeneen, S.; Rasmussen, P. Gas Solubility Calculations. I. UNIFAC. FluidPhase Equilib. 1983,11,105-126.
Ind. Eng. Chem. Res,, Vol. 32,No. 11,1993 2887 Schwartzentruber, J.; Renon, H.; Wantanasiri, S. Development of a New Cubic Equation of Statefor Phase Equilibrium Calculations. Fluid Phase Equilib. 1989,52, 127-134. Sheng, Y.-J.; Chen, Y.-P. A Cubic Equation of State for Predicting Vapor-Liquid Equilibria of Hydrocarbon Mixtures Using a Group Contribution Mixing Rule. Fluid Phase Equilib. 1989, 46, 197210. Soave, G. Equilibrium Constants from a Modified Redlich-Kwong Equation of State. Chem. Eng. Sci. 1972,27, 1197-1203. Suen, S.-Y.;Chen, Y.-P. Calculation of Multiphaee Equilibria by a Group Contribution Equation of State.Fluid Phase Equilib. 1989, 52, 75-82. Suzuki, K.; Sue, H.; Itou, M.; Smith, R. L.; Inomata, H.; Arai, K.; Saito,S.Isothermal Vapor-Liquid Equilibrium Data for Binary Systems at High Pressures: Carbon Dioxide-Methanol, Carbon Dioxide-Ethanol, Carbon Dioxide-1-Propanol, MethaneEthanol, Methane-1-Propanol, Ethane-Ethanol, and Ethane-1-Propanol Systems. J. Chem. Eng. Data 1990,35,63-66. Takishima, S.; Saito, K.; Arai, K.; Saito, S.Phase Equilibria for COT CaHsOH-HzO System. J. Chem. Eng. Jpn. 1986,19,48-56.
Wiebe, R.; Gaddy, V. L. The Solubility of Carbon Dioxide in Water at Various Temperatures from 12 to 40 "C and at Preseures to 500 Atmospheres. J. Am. Chem. SOC.1940,62,815-817. Wileon, G. M. Vapor-Liquid Equilibrium. XI. A New Expression for the Excess Free Energy of Miring. J. Am. Chem. SOC.1964,86, 127-130. Yoon, J.-H.; Lee, H A . ; Lee, H. High-pressure Vapor-Liquid Equilibria for Carbon Dioxide + Methanol, Carbon Dioxide Ethanol, and Carbon Dioxide + Methanol Ethanol. J. Chem. Eng. Data 1993,38,53-55.
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Received for review April 22, 1993 Revised manuscript received July 7, 1993 Accepted July 19, 1993. Abstract published in Advance ACS Abstracts, October 1, 1993.
