Ind. Eng. Chem. Res. 1988,27,110-118
110
Pesthy, A. J.; Flagan, R. C.; Seinfeld, J. H. J. Colloid Interface Sci. 1983, 91, 525-545. Phanse, G. M.; Pratsinis, S. E., submitted for publication in Aerosol Sci. Technol. 1987. Pratsinis, S. E. Ph.D. Dissertation, University of California, Los Angeles, 1985. Pratsinis, S. E.; Kodas, T. T.; Dudukovic, M. P.; Friedlander, S. K. Ind. Eng. Chem. Process Des. Dev. 1986, 25, 634-642. Reiss, H. J . Chem. Phys. 1951, 19, 482-487. Sanders, J. H. Chem. Eng. News 1984, 62(28), 26-40. Springer, G. S. In Advances in Heat Transfer; Irvine, T. F., Hartnett, J . P., Eds.; Academic: New York, 1978; Vol. 14.
Ulrich, G. D. Chem. Eng. News 1984,62(32), 22-29. Villadsen J.; Michelsen, M. L. Solution of Differential Equation Models by Polynomial Approximation"; Prentice-Hall: Englewood Cliffs, NJ, 1978. Walker, K. L.; Homsy, G. M.; Geyling, F. T. J . Colloid Interface Sei. 1979, 69, 138-147. Weinberg, M. C. J . Am. Ceram. SOC.1983, 66, 439-443. Wilhoit, R. C. J . Phys. Chem. 1957, 61, 114-116.
Received for review January 28, 1987 Accepted July 20, 1987
SEPARATIONS Group Contribution Equation of State (GC-EOS): A Predictive Method for Phase Equilibrium Computations over Wide Ranges of Temperature and Pressures up to 30 MPa Steen Skjold-Jmgensen* Znstituttet for Kemiteknik, Technical University of Denmark, DK-2800 Lyngby, Denmark
The parameter tables for the group contribution equation of state, GC-EOS, have been revised and extended. T h e applicability of GC-EOS t o predictions of pure-component critical points, highpressure vapor-liquid equilibria, and liquid-liquid equilibria is demonstrated. Furthermore, GC-EOS is applied t o supercritical extraction calculations. Based on extensive testing, it is concluded that GC-EOS is a reliable method for phase equilibrium calculations for mixtures containing widely differing components. The method covers several hundred degrees kelvin and pressures up to about 30 MPa. Separation units such as distillation towers or extraction cascades are of great importance in almost any chemical plant. The maximum efficiency of such units is often limited by the thermodynamic equilibrium compositions in the phases contacted. Phase equilibrium information for a variety of mixtures over wide ranges of temperature and pressure is therefore of great importance. The number of mixtures of interest to, e.g., the petrochemical industry is enormous even when the scope is restricted to nonelectrolyte mixtures of components of low molar mass (e.g., a carbon number less than 25). Hence, it is desirable to be able to predict phase equilibria based on as little experimental information as possible or at best without any experimental input a t all. The introduction of the group contribution principle to phase equilibrium computations for liquid and gaseous mixtures marked a major breakthrough for the predictive capabilities. The ASOG and UNIFAC methods (Derr and Deal, 1969; Fredenslund et al., 1977) are classical examples of such methods for mixtures of nonelectrolyte intermediate boiling (273 K < TB< 423 K) components at low pressures. UNIFAC is the most general of the two, covering about 50 different functional groups. The method covers all kinds of phase equilibria between gases, liquids, and pure solids. *Present address: Novo Industri A/S, Novo Alle, DK-2880 Bagsvaerd, Denmark.
Application of the group contribution principle to high-pressure phase equilibrium computations has hitherto been limited to the PFGC equation (Cunningham, 1974) for which no comprehensive parameter tables have been published. A new group contribution equation of state, GC-EOS, especially designed to represent phase equilibria has been developed by Skjold-Jrargensen (1984). The original parameter tables developed for the method suffer from some obvious deficiencies. Only single-branched hydrocarbon chains are covered, and secondary and tertiary alcohols are completely missing. Furthermore, for some mixtures of polar and nonpolar components, the original parameters give rather odd results when extensive extrapolations relative to the database are performed.
GC-EOS The GC-EOS is derived by combination of four wellknown equations and principles in phase equilibrium thermodynamics: the van der Waals equation of state, the Carnahan-Starling expression for hard spheres, the NRTL equation, and the group contribution principle. The idea of combining equations of state with the local composition principle, which has been successfully applied in activity coefficients models, was proposed by Huron and Vidal (1979), Mollerup (1981), and others. The GC-EOS is a further development of this new generation of equations of state. The attractive energy interactions are considered
0888-5885/88/2627-0110$01.50/0 0 1988 American Chemical Society
Ind. Eng. Chem. Res., Vol. 27, No. 1, 1988 111
to take place through the surfaces of characteristic groups rather than through the surfaces of the parent molecules. The number of different interaction energies necessary to describe a large number of mixtures is thereby reduced by orders of magnitude. All quantities of interest to phase equilibrium computations can be derived from the expression for the residual Helmholtz function, AR,at specified temperature, volume, and composition. The residual Helmholtz function may be divided into an attractive term and a free volume term, (AR/RT)r,v,, = (AR/RT),tt
+ (AR/RT)fv
(1)
where the free volume part is described by the Mansoori and Leland (1972) expression for hard spheres, (AR/RT)fv= 3(X,X,/X3)(Y- 1) + (X$/Xi)(Y2 - Y - In Y)
+ n In Y (2)
with NC Xk
= CnJd? and
Y = (1- ~X3/6V)-l
J
n being the total number of moles, NC the number of components, V the total volume, and d the hard-sphere diameter per mole. The following temperature dependence is assumed for d: d = 1.065655dC(1- 0.12 exp(-2TC/3T))
(3)
where d, is the value of the hard-sphere diameter at the critical temperature T, for the pure component. As demonstrated in the following section, d, may be evaluated from an arbitrary vapor pressure data point for the component considered. The attractive part of AR is a group contribution version of a density-dependent NRTL-type expression,
where
&JL
= gJL - gLL
‘JL
= exp(aJL&JLq/RTV)
z is the number of nearest neighbors to any segment (set to lo), v: the number of group j in molecule i, ql the num-
ber of surface segments assigned to group j , ek the surface fraction of group k,4 the total number of surface segments, gllthe attractive energy parameter for interactions between segments of type j and i, and cyJ1 the corresponding nonrandomness parameter. For systems with no nonrandomness (e.g., alkane mixtures), a = 0 and the mixing rule in eq 4 reduces to the ordinary double summation type of mixing rule used in most simple equations of state. Furthermoe, eq 4 provides the theoretically correct double summation mixing rule for second virial coefficients regardless of the value of the nonrandomness parameters. As for the UNIFAC method (Fredenslund et al., 1977) the number of surface segments assigned to a specific group, ql, is in most cases based on the van der Waals surface areas calculated by Bondi. In a few cases, the q yalue has been determined by adjusting the model to experimental data. The interactions between unlike segments are defined by
where k,, is the binary interaction parameter. The following temperature dependences are assumed for the interaction parameters: g,, = g,,*[1 + g’,,(T/T,* - 1) + g”,, 1n (T/T,*)l and kij = kzj*[1 +
k’rj
In (T/TLJ*)I
(6)
where T,* = O.5(Tc*+ TJ*)
TI* is an arbitrary but fixed reference temperature for group i. For further information, see Skjold-Jerrgensen (1984). The Revised Parameter Tables The revised and extended group parameter tables are presented in Tables 1-111. The number of different alkane groups has been considerably increased when compared to the original parameter tables by Skjold-Jerrgensen (1984). In addition to the ordinary CH3, CH,, and CH groups (1-3), some special groups with slightly smaller surface areas have been defined (4-6). These alkane groups (B) are used when connected to a quaternary carbon (e.g., neopentane, four CH,(B); tert-butyl alcohol, one COH, three CH3(B)). The bulkiness around the quaternary carbon is thereby described by a smaller surface area exposed to interaction for the adjacent groups. The water-soluble (WS) alkane groups are used when the alkane groups are situated in a molecule containing water-soluble functional groups like alcohol and ketone groups (e.g., 2-butanol, two WS CH3, one WS CH, one CHOH). The use of the WS groups ensures a correct description of the mutual solubilities of these oxygenated compounds and water. The parameter tables have been extended to include secondary and tertiary alcohols. All kinds of alkanols are hereby covered by GC-EOS. The data base used for parameter estimation is virtually the same as the data base used for the original parameter tables. New data were introduced for branched alkanes (e.g., neopentane and 2,2,4-trimethylpentane) and for secondary and tertiary alcohols. The number of nonrandomness parameters and binary temperature dependence parameters ( k L J ’was ) kept as low as possible without serious loss of fitting capability. Furthermore, the parameters for certain families of interactions were kept constant, or it was ensured that they were of the same order of magnitude (e.g., water-alkane, alkane-alcohol interactions, etc.). Extrapolations should thereby result in a minimum of complications due to highly correlated parameters. The data base for gas-solvent group interactions has been extended with information about the solubility of solvents in compressed gases, when such information was available. Propane has been introduced as a new gas to provide optimum predictions of, e.g., supercritical extraction cycles using this gas. It should be noted that the gas-gas interactions are the same as in the original parameter tables. Range of Applicability The data base used to establish the GC-EOS parameter tables contains pure-component vapor pressures in the pressure range 2 kPa to the critical pressure, low- and high-pressure VLE information ( p < 30 MPa), Henry’s constants for gases in pure solvents, and a few data on
112 Ind. Eng. Chem. Res., Vol. 27, No. 1, 1988 Table I. Pure Grouo Parameters for GC-EOS group no. T*, K 1 600.0 CH, 2 CH, 600.0 3 CH 600.0 4 600.0 CHdB) 5 600.0 CHz(B) 6 600.0 CH(B) 7 600.0 WSCH, 600.0 8 WSCH, 9 600.0 WSCH 600.0 WSCH,(B) 10 600.0 11 WSCHz(B) 12 600.0 WSCH(B) 600.0 CYCHZ 13 CYCH 600.0 14 ACH 600.0 15 AC 600.0 16 17 ACCH, 600.0 18 600.0 ACCHZ CH30H 19 512.6 512.6 20 CHZOH 21 CHOH 512.6 22 COH 512.6 23 600.0 CH,CO 24 CHzCO 600.0 25 647.3 HZO 33.2 26 H2 126.2 27 NZ 132.9 co 28 154.6 29 0 2 190.6 30 CH, 282.4 31 C'H, 304.2 32 COZ 305.4 33 C'H, 369.8 34 propane 373.2 35 H'S
4 0.848 0.540 0.228 0.789 0.502 0.212 0.848 0.540 0.228 0.789 0.502 0.212 0.540 0.228 0.400 0.285 0.968 0.660 1.432 1.124 0.908 0.714 1.488 1.180 0.866 0.571 0.985 1.060 0.955 1.160 1.485 1.261 1.696 2.236 1.163
Pa 316 910.0 356 080.0 356 080.0 316910.0 356 080.0 356080.0 316 910.0 356 080.0 356080.0 316 910.0 356 080.0 356 080.0 466 550.0 466 550.0 723 210.0 723 210.0 506 290.0 506 290.0 1109 600.0 1207 500.0 1207 500.0 1207 500.0 888 410.0 888 410.0 1697 000.0 179 460.0 330 360.0 309 610.0 353 780.0 402 440.0 486 510.0 531 890.0 452 560.0 436 890.0 780 070.0
g' -0.9274 -0.8755 -0.8755 -0.9274 -0.8755 -0.8755 -0.9274 -0.8755 -0.8755 -0.9274 -0.8755 -0.8755 -0.6062 -0.6062 -0.6060 -0.6060 -0.8013 -0.8013 -0.9474 -0.6441 -0.6441 -0.6441 -0.7018 -0.7018 -0.6707 -0.0843 -0,1910 -0.1288 -0.27 50 -0.2762 -0.3724 -0.5780 -0.3758 -0.4630 -0.3946
g"
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1351 -0.0806 -0.1074 0.0000 0.0221 0.0000 0.0000 0.0000 0.0000 0.0000
In cm6.atm.mol/ (surface area segment)'.
mutual solubilities in binary systems with two liquid phases. The temperature range covered by this information varies from one group interaction to the other. In most cases, the interaction parameters are based on information covering more than 200 K. However, in some cases, the temperature range covered is on the order of 50
K. Table IV summarizes the general ranges of applicability and the deviations to be expected. It should be noted that K factors ( y l / x i ) of components in infinite dilution in mixtures containing water and/or alcohols may deviate considerably more than 15% from experimental values. The infinite dilution K factor for, e.g., an alkane in a water-alcohol mixture may be 4 0 4 0 % in error. For Henry's constants, the deviations are generally lower than 15% except for mixed solvents containing water and/or alcohols. As shown in the following section, the predictive capabilities of GC-EOS are very strong outside the abovementioned infinite dilution regions for some alcohol-water mixtures. GC-EOS is limited to mixtures with component size ratios less than 20 (e.g., in terms of critical volumes). This corresponds to the range of application of the CarnahanStarling equation for hard spheres, and it therefore excludes mixtures of, e.g., hydrogen and C3,,. How T o Use GC-EOS The application of GC-EOS to phase equilibrium computations requires user specified information shown in Table V. The information about group compositions is used to set up all the parameters necessary for the attractive part of AR. The vapor pressure information is used to calculate
the only missing parameter for each component, namely, the value of the hard-sphere diameter at the critical temperature, d,. The value of d, is found by matching the calculated and the experimental pure-component vapor pressures, a t Tsat. The critical pressure is only used to generate a good initial value of d, for this matching. An approximate value of p c may therefore be used. The d, value obtained is very close (in most cases within 5%) to the value obtained from the critical pressure. However, this difference is important as the vapor pressure is sensitive to the size of the molecule.
Results and Discussion GC-EOS predictions for a number of mixtures were presented by Skjold-Jwgensen (1984). The revised parameter tables yield results for these mixtures which are virtually identical with the original predictions. The following results will therefore mainly focus on types of predictions which have not been covered previously. Critical pressures and temperatures predicted by GCEOS are exemplified in Table VI. As the parameters for the attractive part of the residual Helmholtz function are general group parameters and the hard-sphere diameter for each pure substance is fitted to, e.g., the normal boiling point, it should not be expected that the critical point is exactly reproduced. However, it appears from Table VI that in most cases, the predicted and experimental values correspond within 5% in pressure or 0.25 MPa and 1%in temperature or 5 K. As any other simple (two-constant-type) equation of state, only two properties can be correctly described at the critical point. The critical volume may be more than 30% wrong since 2, = 0.358 956 for the Carnahan-Starling/van der Waals
Ind. Eng. Chem. Res., Vol. 27, No. 1, 1988 113 6
LnK
-8
__
&1 L IO00
b..-
I
0
- 3 - 2 - t
%\\
500
\
20 0
100
2 3 4 CnP(MPo I
5 0
-1 j
I
2 0
-
10
-
0 5 -
- 3 - 2 - 1
0
I
2
3
4
5
InPlMPa 1
Figure 1. (a, top) C02-n-propylbenzene a t 313.1, 393.0, and 472.9 K. (b, bottom) N2-n-propylcyclohexane a t 313.6, 393.1, and 472.9 K. (-) GC-EOS. Experimental data by Laugier et al. (1984).
equation of state from which GC-EOS is derived. Rather large discrepancies for some of the oxygenated hydrocarbons are encountered. The pure-component vapor pressures are represented to within a few percent. Hence, a t the experimental critical temperature, the predicted vapor pressure is very close to the critical pressure. However, the GC-EOS does not predict these conditions to be critical (same density in both phases). No predictions are shown for long-chain heavy molecules. The critical point for such substances is of minor importance since the stability of the molecules is often very low a t the critical temperature. Figure 1 gives a comparison between GC-EOS predictions and experimental K values for two binary gas-aromat systems. As also demonstrated by Skjold-Jargensen (1984), the predicted K values are within 15% of the experimental values. At pressures above the recommended range of application (In P = 4 corresponds to 54.6 MPa), the deviations may increase somewhat. The experimental data by Yarborough (1972) offer an exceptional possibility for checking the predictive capabilities of GC-EOS for mixtures with up to 10 nonpolar components. As shown in Figure 2, the predictions are quite satisfactory. For the heavy components at low temperatures, the discrepancies are generally above the level indicated in Table IV. This is due to the very low vapor pressure of these components. The GC-EOS is not very reliable for predicting vapor pressures significantly below 2 kPa. Furthermore, the deviations increase as the critical point of the mixture is approached. Yarborough described the effect of variations in the aromaticity of the C7+ fraction. As shown in Figure 3, the effect of increasing the content of the aromat (toluene) in the C7+fraction is in most cases a slight rise in the K value of the light components. However, for hydrogen sulfide, the effect goes in the opposite direction, causing hydrogen sulfide to be less volatile than propane at toluene contents above 85% in the C7+fraction. All these trends are correctly predicted by GC-EOS. For alcohol-water and alkanewater mixtures, the model must describe the development of the nonidealities with
0.2
O2
,005
.
,
,
, 5
,
,
, 10
20
P(MPa)
"-C,
4
I
0002
'"": CH4
O
+2
5
IO
20
P(MPa)
Figure 2. Experimental and predicted K values for a nine-component mixture at 310.9 K. (- and - - -) GC-EOS. Experimental data by Yarborough (1972).
increasing carbon chain length. The data base for the corresponding group interactions therefore includes LLE data. Figures 4 and 5 give a comparison between experimental and GC-EOS values of the mutual solubilities of water with n-alkanes and primary n-alcohols. The qualitative trends are correctly represented by GC-EOS for these systems for which the activity coefficients may amount to millions. However, systematic deviations occur with a carbon chain length above 8. The revised parameter tables cover secondary as well as tertiary alcohols. Figure 6 shows a predicted isotherm
114
Ind. Eng. Chem. Res., Vol. 27, No. 1, 1988
Table 11. Binary Parameters k,,*(above the Diagonal) and 4,'(below the Diagonal) --_______ no. 1 2 3 4
5 6 I
8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
I
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.094 0.094 0.000 0.000 0.000 0.000 0.000 0.000 0.084 0.084 0.000 0.000 0.000 0.252 0.154 0.061
0.000 0.000 0.000 0.000 o.00n
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
1.000
1.000 1.000
1.000 1.000 1.000
1.000 1.000 1.000 1.000
1.000 1.000 1.000 1.000 1.000
1.000 1.000 1.000 1.000 1.000 1.000
1.000
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.oao
1.000 1.000 1.000 1,000 1.000 1.000 1.000 1.000 1.000
1.000 1.000 1.000 1,000 1.000 1.000 1.000 1.000 1.000 1.000
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
1.000 1.000 1,000 1.000 1.000 1,000 1.000 1.000 1.000 1.000 1.000 1.000
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
1.041 1.041 1.041 1.041 1.041 1.041 1.041 1.041 1.041 1.041 1.041 1.041 0.980 0.980
1.041 1.041 1.041 1.041 1.041 1.041 1.041 1.041 1.041 1.041 1.041 1.041 0.980 0.980 1.000
0.975 0.975 0.975 0.975 0.975 0.975 0.975 0.975 0.975 0.975 0.975 0.975 0.994 0.994 1.007 1.001
1.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.084 0.084 0.084 0.084 0.084 0.084 0.084 0.084 0.084 0.084 0.084 0.084 0.084 0.084 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -0.250 -0.250 -0.250 0.000 0.000 0.252 -0.252 -0.252 --0.252 -0.252 -0.252 --0,252 0.154 0.154 0.154 0.154 0.154 0.154 0.154 0.056 0.056 0.056 -0.061 0.056 0.056 -0.061 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0 000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Table 111. Binary Nonrandomness Parameters, a,, no.
1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.391 0.391 0.000 0.000 2.335 10.220 10.220 10.220 5.146 5.146 0.495 -1.000 -2.889 -2.890 0.000 0.000 0,000 3.369 0.000 0.000 0.528
2
3
4
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.391 0.391 0.391 0.391 0.391 0.391 0.000 0.000 0.000 0.000 0.000 0.000 2.158 2.335 2.158 10.220 10.220 10.220 10.220 10.220 10.220 10.220 10.220 10.220 5.146 5.146 5.146 5.146 5.146 5,146 0.495 0.495 0.495 -1.000 -1.000 -1.000 -2.889 -2.889 -2.889 -2.890 '. 2.890 -2.890 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 3.369 3.369 3.369 0.000 0.000 0.000 O.Oo0 0.000 0.000 0528 0.528 0.628
5
6
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0,000 0.000 0.000 0.391 0.391 0.000 0.000 2.158 10.220 10.220 10.220 5.146 5.146 0.495 -1.000 -2.889 -2.890 0.000 0.000 0.000 3.369 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.391 0.391 0.000 0.000 2.158 10.220 10.220 10.220 5.146 5.146 0.495 -1.000 -2.889 -2.890 0.000 0.000 0.000 3.369 0.000 0.000 0.528
o.oO0
0.528
__ 7
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.391 0.391 0.000 0.000 2.335 10.220 10.220 10.220 5.146 5.146 1.229 -1.000 -2.889 -2.890 0.000 0.000 0.000 3.369 0.000 0.000 0,528
0.000 0.000 0.000 0.000 0.000 0.094 0.094 0.000 0.000 0.000 0.000 0.000 0.000 0.084 0.084 0.000 0.000 0.000 -0.252 0.154 0.056 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.094 0.094 0.094 0.094 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.084 0.084 0.084 0.084 0.00 0.000 0.000 0.000 0.250 -0.250 0.252 -0.252 0.154 0.154 0.061 0.056 0.000 0.000 0.000 o.noo 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.094 0.094 0.000 0.000 0.000 0.000 0.000 0.000 0.084 0.084 0.00 0.000 -0.250 -0.252 0.154 0.056 0.000 0.000 0.000 0.000 0.000
0.000 0,000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.097 0.097 0.000 0.000 0.000 0.097 0.097 0.000 0.000 0.000 0.000 0.000 -0.086 -0.086 0.000 0.583 0.583 0.605 0.317 0.317 0.357 0.357 0.367 0.000 0.000 0.086 0.086 0.086 -0.252 -0.252 0.154 0.154 0.284 0.284 0.000 0.115 0.115 0.000 0.146 0.146 0.065 0.000 0.000 0.065 0.065 0,210 0.210 0.000 0.000 0.000 0.111 0.111 0.000 0.000 0.000 0.000 0.000 0.080 0.080 0.000 o.noo 0.000 0.047 0.047 -0.141
____ 8
9
0.000 0.000 0.000 0.000 0.000 0.000 0.000 n.ooo 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.391 0.391 0.391 0.391 0.000 0.000 0.000 0.000 2.158 2.158 10.220 10.220 10.220 10.220 10.220 10.220 5.146 5.146 5.146 5.146 0.637 0.637 -1.000 -1.000 -2.889 -2.889 -2.890 -2.890 0.000 0.000 0.000 0.000 0.000 0.000 3.369 3.369 0.000 0.000 0.000 0.000 0.528 0.~28
for the system n-heptane-2-butanol. GC-EOS represents the data very well. Also for the ketone-water interactions, some information about mutual solubilities were included in the data base. Figure 7 shows the results for the system 2-butanone-water. GC-EOS correctly predicts the existence of a liquid-liquid immiscibility although the phase split is somewhat shifted. The performance of GC-EOS is of the same quality as well-known activity coefficient models (UNIQ'CJAC, NRTL, UNIFAC).
10
11
12
0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.391 0.391 0.000 0.000 2.158 10.220 10.220 10.220 5.146 5.146 0.637 -1.000 --2.889 -2.890 0.000 0.000 0.000 3.369 0.000 0.000 0.528
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.391 0.391 0.000 0.000 2.158 10.220 10.220 10.220 5.146 5.146 0.637 -1.000 -2.889 -2.890 0.000 0.000 0.000 3.369 0.000 0.000 0.528
o.noo 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
n.ooo
0.000 0.391 0.391 0.000 0.000 2.335 10.220 10.220 10.220 5.146 5.146 1.229 -1.000 -2.889 -2.890 0.000 0.000 0.000 3.369 0.000 0.000 n.528
13
14
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 4.048 4.048 10.220 10.220 10.220 10.220 10.220 10.220 5.146 5.146 5.146 5.146 0.522 0.522 0.000 0.000 -0.977 -0.977 -0.977 -0.977 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 6.920 6.920
15
16
17
0.391 0.391 0.391 0.391 0.391 0.391 0.391 0.391 0.391 0.391 0.391 0.391 0.000 0.000 0.000 0.000 0.000 0.000 1.416 15.000 15.000 20.740 15.000 15.000 0.846 0.000 -0.312 0.000 0.000
0.391 0.391 0.391 0.391 0.391 0.391 0.391 0.391 0.391 0.391 0.391 0.391 0.000 0.000 0.000 0.000 0.000 0.000 1.416 15.000 15.000 20.740 15.000 15.000 0.846 0.000 -0.312 0.000 0.000 0.000 0.000 -4.772 0.391 0.391 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.416 15.000 15.000 20.740 15.000 15.000 0.846 0.000 -0.312 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000
-4.772 0.391 0.391 0.000
Paulaitis et al. (1981) reported some tie lines for the system water-ethanol-carbon dioxide under supercritical extraction conditions. Table VI1 gives a comparison between these data and GC-EOS predictions. A t 308 K the ratio between the vapor pressures of water and ethanol is about 0.38, and the deviations from ideality in the liquid water-ethanol mixture are modest. As indicated in Table VII, the ratio between the corresponding K values ranges between 0.03
Ind. Eng. Chem. Res., Vol. 27, No. 1, 1988 115 18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
0.975 0.975 0.975 0.975 0.975 0.975 0.975 0.975 0.975 0.975 0.975 0.975 0.994 0.994 1.007 1.007 1.000
0.811
0.715 0.682 0.682 0.715 0.682 0.682 0.715 0.682 0.682 0.715 0.682 0.682 0.735 0.735 0.826 0.826 0.774 0.774 1.016
0.715 0.682 0.682 0.715 0.682 0.682 0.715 0.682 0.682 0.715 0.682 0.682 0.722 0.722 0.826 0.826 0.774 0.774 1.016 1.000
0.715 0.682 0.682 0.715 0.682 0.682 0.715 0.682 0.682 0.715 0.682 0.682 0.719 0.719 0.826 0.826 0.774 0.774 1.085 1.000 1.000
0.834 0.834 0.834 0.834 0.834 0.834 0.834 0.834 0.834 0.834 0.834 0.834 0.870 0.870 0.925 0.925 0.888
0.834 0.834 0.834 0.834 0.834 0.834 0.834 0.834 0.834 0.834 0.834 0.834 0.870 0.870 0.925 0.925
0.560 0.560 0.560 0.560 0.560 0.560 0.560 0.560 0.560 0.560 0.560 0.560 0.605 0.605 0.692 0.692 0.696 0.696 1.042 0.949 0.949 0.949 0.989 0.989
1.063 1.216 1.216 1.063 1.216 1.216 1.063 1.216 1.216 1.063 1.216 1.216 1.200 1.200 1.243 1.243 1.169 1.169 1.435 2.600 2.600 2.600 1.343 1.343 1.172
1.040 1.040 1.040 0.900 0.900 0.900 1.040 1.040 1.040 0.900 0.900 0.900 1.021 1.021 1.071 1.071 1.071 1.071 1.011 1.175 1.175 1.175 0.815 0.815 0.778 0.999
0.958 0.958 0.958 0.958 0.958 0.958 0.958 0.958 0.958 0.958 0.958 0.958 0.958 0.958 0.953 0.953 0.953 0.953 0.973 1.135 1.135 1.135 n.a. n.a. 0.660 1.013 1.000
0.907 0.907 0.907 0.907 0.907 0.907 0.907 0.907 0.907 0.907 0.907 0.907 0.907 0.907 0.941 0.941 0.823 0.823 0.955 1.172 1.172 1.172 0.688 0.688 0.769 n.a. 1.019 n.a.
0.998 0.940 0.940 0.998 0.940 0.940 0.998 0.940 0.940 0.998 0.940 0.940 1.020 1.020 1.008 1.008 0.942 0.942 0.892 1.137 1.137 1.137 0.741 0.741 0.612 1.071 0.978 0.959 n.a.
0.977 0.977 0.977 0.977 0.977 0.977 0.977 0.977 0.977 0.977 0.977 0.977 0.981 0.981 1.019 1.019 1.019 1.019 0.955 0.955 0.955 0.955 0.931 0.931 0.560 1.085 0.962 n.a. n.a. 0.977
0.892 0.814 0.814 0.892 0.814 0.814 0.892 0.814 0.814 0.892 0.814 0.914 0.928 0.928 1.074 1.074 0.891 0.891 0.945 0.985 0.985 0.985 1.025 1.025 0.923 1.196 1.045 1.025 0.967 0.932 0.950
0.987 0.987 0.987 0.987 0.987 0.987 0.987 0.987 0.987 0.987 0.987 0.987 0.987 0.987 0.994 0.994 0.905 0.905 0.883 0.739 0.739 0.739 0.782 0.782 0.632 1.127 0.994 0.991 n.a. 1.009 0.994 0.880
1.Oo0 1.000 1.000 1.000 1.000
0.920 0.920 0.920 0.920 0.920 0.920 0.920 0.920 0.920 0.920 0.920 0.920 0.872 0.872 1.005 1.005 0.915 0.915 0.910 1.014 1.014 1.014 n.8. ma. 0.952 ma. 0.865 0.943 n.a. 0.953 n.a. 0.928 0.917 0.915
O.Oo0 O.Oo0 O.Oo0 0.000 0.000 0.000
0.000 0.605 0.357 0.086
0.000 0.000 0.065 0.000 0.000
0.000 -0.141
0.811 0.811 0.811 0.811 0.811 0.811 0.811 0.811 0.811 0.811 0.811 0.777 0.777 0.861 0.861 0.794 0.794
0.000 0.000 0.000
0.000 0.000 -0.035 0.471 0.350 0.168 0.000 0.342 0.108 0,009 0.150 -0.093 0.018
0.000 0.000 0.000
0.000
0.000 0.000 0.000 -0.191 -0.191 0.000 0.000 0.350 0.350 0.285 0.285 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.231 0.231 o.Oo0 0.000
0.888 0.959 1.004 1.004 1.004
0.000 0.000
0.888 0.888 0.959 0.953 0.953 0.953 1.000
0.000 -0.191 -0.214 -0.214 0.000 0.000 0.000 0.000 0.000 0.350 n.a. n.a. 0.285 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.108 0.108 0.000 0.000 0.000 0.000 0.231 0.000 0.000 n.a. 0.000 n.a.
0.000 0.270 0.141 -0.061 0.197 0.277 0.122 0.209 0.000 -0.122
-0.100 -0.086 n.a. -0.067 0.030 0.037 0.086 0.000 ma.
0.000 0.020 n.a. 0.009 -0.048 0.042 n.a. -0.002 0.000 0.052 0.000 0.000 -0.098 0.258 0.021
n.a. n.a. -0.100 n.a. n.a. n.a.
-0.017 0.024 0.007 0.000 0.000
25
26
27
28
29
30
-2.889 -2.889 -2.889 -2.889 -2.889 -2.889 -2.889 -2.889 -2.889 -2.889 -2.889 -2.889 -0.977 -0.977 -0.312 -0.312 -0.312 -0.312 1.301 1.301 1.301 1.301 0.352 0.352 0.371 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -2.890 0.220
-2.889 -2.889 -2.889 -2.889 -2.889 -2.889 -2.889 -2.889 -2.889 -2.889 -2.889 -2.889 -0.977 -0.977 0,000 0.000 0.000 0.000 1.301 1.301 1.301 1.301 n.a. n.a. 0.371
0.000
-0.029 0.025 0.000 n.a.
0.000 0.000 0.032
0.000 0.000
1.000 1.000 1.000 1.ooo 1.000 1.000 1.000 0.991 0.991 0.990 0.990 0.973 0.973 0.850
0.800 0.800 0.800 0.784 0.784 0.560 1.243 1.058 1.050 n.a. 0.994 0.985 0.875 0.997 0.000
I_____
18
19
20
21
22
23
24
0,000 0.000 0.000 O.Oo0 0.000 0.000 0.000 0.000
0.836 0.532 0.532 0.836 0.532 0.532 0.836 0.532 0.532 0.836 0.532 0.532 0.787 0.787 1.416 1.416 1.416 1.416 0.000 0.000 0.000
1.471 1.471 1.471 1.471 1.471 1.471 1.471 1.471 1.471 1.471 1.47 1 1.471 1.471 1.471 3.500 3.500 2.728 2.728
1.471 1.471 1.471 1.471 1.471 1.471 1.471 1.471 1.471 1.471 1.471 1.471 1.471 1.471 3.500 3.500 2.728 2.728 0.000 0.000
0.854 0.854 0.854 0.854 0.854 0.854 0.854 0.854 0.854 0.854 0.854 0.854 0.854 0.854 4.581 4.581 1.871 1.871 0.576
0.854 0.854 0.854 0.854 0.854 0.854 0.854 0.854 0.854 0.854 0.854 0.854 0.854 0.854 4.581 4.581 1.871 1.871 0.576
0.000
0.000 0.000
0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 1.416 15.000 15.000 20.740 15.00 15.000 0.846 0.000 -0.312 0.004 0.000
0.000 0.000 0.000 0.000 0.000
0.000
0.000 0.576 0.576 0.000 0.300 0.267 0.267 0.115 0.423 0.304 0.130 0.378 0.302 0.553
0.000 0.000 0.000 0.000 0.000 0.000
0.000
1.471 1.471 1.471 1.471 1.471 1.471 1.471 1.471 1.471 1.471 1.471 1.471 1.471 1.471 4.091 4.091 0.784 0.784 0.000 0.000 0.000 0.000
0.000 0.000
0.000 0.000
-1.370 0.695 0.376 0.376 0.115 0.185 0.724 0.468 0.941 1.051 0.553
-1.933 0.695 0.376 0.376 0.115 0.185 0.724 0.468 0.941 1.051 0.553
0.000
0.000 0.000 0.000 0.000
-2.210 -0.466 0.000 0.695 0.352 0.376 n.a. 0.376 0.473 0.115 0.721 0.185 0.399 0.724 0.170 0.468 0.599 0.941 1.051 0.691 0.553 n.a.
0.000 0.000 0.000 -0.466
0.000 0.352 ma. 0.473 0.721 0.399 0.170 0.599 0.691
ma.
0.495 -1,000 0.495 -1,000 0.495 -1.000 0.495 -1,000 0.495 -1.000 0.495 -1.000 1.229 -1.000 0.637 -1,000 0.637 -1,000 1.229 -1.000 0.637 -1.000 0.637 -1.000 0.522 0.000 0.522 0.000 0.846 0.000 0.846 0.000 0.846 0.000 0.846 0.000 0.000 -1.052 -1.370 -1.052 -1.933 -1.052 -2.210 -1.052 -0.175 0.000 -0.175 0.000 0.000 0.579 0.579 0.000 0.371 0.000 0.371 0.000 0.239 n.a. 0.399 0.000 0.556 0.000 0.236 0.000 0.400 0.000 0.435 -1.000 0.000 n.a.
Table IV. General Ranges of Applicability and Typical Expected Deviations of the Predictions Performed by GC-EOS ranges of applicability typical dev 15% 100 K < T < 700 K 2 kF'a < P < 30 MPa JMJ < 15% IApsatl < 5% 0.05 < V C i / V
