Ind. Eng. Chem. Res. 1992,31, 2769-2773
2769
Vapor-Liquid Equilibrium for Binary Systems Containing a Heavy Liquid and a Dense Fluid Wen-Lu Wengt and Ming-Jer Lee* Department of Chemical Engineering, National Taiwan Institute of Technology, Taipei, 106, Taiwan
Equilibrium phase compositions were measured for the binary systems of acetophenone plus carbon dioxide, ethane, or ethylene at temperatures from 313.15 to 348.15 K and pressures up to 190 bar or near the mixture critical pressures. The solubilities of three dense fluids in four heavy liquids were compared. Henry’s constants, partial molar volumes of the gas a t infinite dilution, and the Margules parameters of the Krichevsky-Ilinskaya equation were also determined. Moreover, the validity of the Soave, Patel-Teja, and Iwai-Margerum-Lu equations of state for such systems were tested by the measured data. In general, the Patel-Teja equation is better than the others.
Introduction Supercritical fluid extraction is an alternative method to separate a heavy compound or a heat-sensitive substance from a wide variety of mixtures. Although numerous efforts have been made in this field, few thermodynamic models can correlate satisfactorily the phase-equilibrium data of mixturea containing a supercriticalfluid over a wide range of pressure (Brennecke and Eckert, 1989; Johnston et al., 1989). Expansion of the experimental data for such systems could be fundamentally helpful in giving us better insight into the behavior of supercritical fluids and in model development. Recently, we made a series of vapol-liquid equilibrium measurements for the binary mixtures composed of a heavy liquid and a dense fluid by using a semiflow type apparatus. Those dense fluids include carbon dioxide, ethane, and ethylene. Meanwhile, four heavy liquidsoctane (a nonpolar fluid), 1-octanol and methyl benzoate (moderate polar fluids), and acetophenone (a strongly polar fluid)-were selected as the model compounds. The results of the binary systems containing octane, 1-octanol, or methyl benzoate have been published (Weng and Lee, 1992a-c) and those of the acetophenone-containing systems are reported in this article. The equilibrium phase compositions of acetophenonecontaining systems were measured at temperatures from 313.15 to 348.15 K and pressures up to 190 bar or near the mixture critical pressures. Together with our previous works, the gas solubilities in the four respective heavy liquids were compared. For practical uses, the saturated vapor compositions of acetophenone (yl) were correlated with the fluid density of the light component and the gas solubilities (zz)were fitted by the Krichevsky-Ilinskaya (KI) equation (Krichevsky and Ilinskaya, 1945). Henry’s constants, partial molar volumes of the gas at infinite dilution, and the Margules parameters of the KI equation were reported for 12 binary systems. Moreover, those phase-equilibrium data were used to test the applicability of the Soave (Soave, 1972), Patel-Teja (Pate1 and Teja, 1982), and Iwai-Margerum-Lu (Iwai et aL, 1988) equations of state with conventional mixing rules. The Patel-Teja equation is generally better than the others. However, the bubble pressures calculated from those three models appear unsatisfactory near the critical regions. Experimental Work Detailed illustration of the apparatus and operation was given elsewhere (Lee and Chao, 1988; Weng and Lee,
* To whom correspondence should be addressed. Present address: Department of Chemical Engineering, Ming-Hsin Engineering College, Hsinchu, 304, Taiwan.
Table I. Phase Compositions and Equilibrium Ratios for the Acetophenone (l)/Carbon Dioxide (2) System TW)
313.15
328.15
348.15
P(ba) 20.0 35.0 50.0 65.0 75.0 81.0 25.0 40.0 60.0 80.0 95.0 110.0 115.0 25.0 45.0 70.0 100.0 130.0 155.0 165.0
YI
x2
Ki
K2
0.00017 O.OO0 18 0.00023 O.OO0 47 0.001 26 0.00186 0.00029 0.00031 0.00054 0.001 11 0.00360 0.0269 0.0347 0.00073 0.00067 O.OO0 97 0.00260 0.00874 0.0368 0.0864
0.190 0.308 0.437 0.574 0.694 0.803 0.181 0.290 0.411 0.558 0.654 0.763 0.806 0.145 0.251 0.389 0.527 0.656 0.777 0.888
0.00021 0.00026 0.00041 0.001 10 0.004 12 0.00947 0.00036 0.00044 0.00092 0.00251 0.0104 0.114 0.179 0.00085 0.00089 0.00159 0.00550 0.0254 0.165 0.771
5.27 3.25 2.29 1.74 1.44 1.24 5.51 3.44 2.43 1.79 1.52 1.28 1.20 6.91 3.99 2.57 1.89 1.51 1.24 1.03
Table 11. Phase Compositions and Equilibrium Ratios for the Acetophenone (l)/Ethane (2) . . System TW)
318.15
328.15
338.15
P(ba) 25.0 45.0 65.0 85.0 105.0 140.0 175.0 25.0 45.0 70.0 95.0 120.0 150.0 180.0 25.0 45.0 75.0 115.0 155.0 185.0
YI
x2
K1
K2
0.00011 0.00033 0.0108 0.0205 0.0258 0.0384 0.0477 0.00019 0.00040 0.005 13 0.019 8 0.031 1 0.043 5 0.055 3 0.00038 0.000 59 0.00496 0.0286 0.0420 0.0628
0.167 0.284 0.382 0.406 0.416 0.447 0.481 0.146 0.254 0.380 0.412 0.439 0.471 0.505 0.131 0.236 0.368 0.438 0.501 0.529
0.00014 0.00047 0.0174 0.0345 0.044 2 0.069 5 0.091 9 0.00023 0.00054 0.00827 0.0336 0.0555 0.0822 0.112 0.00044 0.00078 0.00785 0.0509 0.0842 0.133
5.98 3.52 2.59 2.41 2.34 2.15 1.98 6.87 3.93 2.62 2.38 2.21 2.03 1.87 7.62 4.24 2.70 2.22 1.91 1.77
1992a). Carbon dioxide (99.8%), ethane (99.0%), and ethylene (99.5%) were purchased from Matheson Gas Products, and acetophenone was supplied by Aldrich Chemicals with a purity of 99%. No further purification of those chemicals was made. The accuracy of measurements is better than f0.02 K for temperature and f0.1% for pressure. In general, the phase cornpositions were reproduced within *2%. However, the uncertainty is about 10-15% for the vapor compositions of acetophenone (yl) at low pressure, where y1 falls as low as
0888-588519212631-2769$03.00/00 1992 American Chemical Society
2770 Ind. Eng. Chem. Res., Vol. 31, No. 12, 1992 Table 111. Phase Compositions and Equilibrium Ratios for AcetoDhenone (l)/Ethylene (2) System T ( K ) P(bar) K1 K2 Y1 x2 5.04 0.000089 0.198 0.00011 318.15 30.0 0.000317 0.338 0.00048 2.97 55.0 0.002 19 0.441 0.00391 2.26 80.0 1.95 0.0103 0.508 0.0209 100.0 1.17 0.0208 0.554 0.0467 120.0 1.66 0.0296 0.585 0.0714 135.0 1.52 0.0462 0.627 0.124 160.0 0.00018 0.176 0.00022 5.68 328.15 30.0 0.00042 0.299 0.00061 3.34 55.0 2.41 0.00159 0.414 0.002 71 80.0 2.07 0.00604 0.481 0.0116 100.0 1.84 120.0 0.0144 0.536 0.031 1 0.0279 0.574 0.0656 1.69 140.0 1.51 170.0 0.0488 0.630 0.132 338.15 30.0 0.00038 0.166 0.00046 6.04 60.0 0.00076 0.301 0.00109 3.32 90.0 0.00299 0.418 0.00515 2.38 2.02 115.0 0.00929 0.490 0.0182 1.77 140.0 0.0217 0.554 0.0487 1.58 165.0 0.0403 0.608 0.103 1.41 190.0 0.0634 0.663 0.188
0
a
160-
-
-
0.0
0.2
0.4
0.6
0.8
\
1.0
x2 9 Y2 Figure 1. Pressure-composition diagram for acetophenone/ethane system.
The equilibrium phase compositions as well as the equilibrium vaporization ratios (K, = y ; / x i )for the acetophenonejcarbon dioxide, acetophenone/ethane, and acetophenone/ethylene systems are listed in Tables I, 11, and 111, respectively. Figure 1 illustrates the variation of pressure with saturated compositions for the ethane-containing system at 318.15, 328.15, and 338.15 K. A remarkable change of ethane solubility shows on the 318.15 K isotherm around 65 bar, and the ethane solubility isotherms have an obvious crossover within the investigated pressure range. This phenomenon could result from the condition that is very close to the upper end point of the vapor-liquid-liquid coexistence as indicated in our previous report for the l-octanol/C02 system (Weng and Lee, 1992b). Due to blind cells being used in this work, we cannot observe the phase behavior directly. Further experimental evidence is needed. Figure 2 presents the pressure-composition diagram for the acetophenone/ carbon dioxide system. Unlike the ethane-containing system, there is no crossover for the isotherms being investigated. Similar behavior was observed for the acetophenonelethylene system. Figure 3 shows the variation of saturated vapor composition of acetophenone Cyl) with the reduced pressure (Pr,2= P/PC,Jat 328.15 K. The acetophenone solubilities are very sparing and vary not much over the reduced pressurea lower than unity,whereas they increase markedly
200
1 1'
00
160-
0
n -
120 ,
a
80; 40 1
I
o i . , . , . . . , . , . , , . , , . . . r 0.0
0.2
0.6 0.8 1.0 x2 9 Y2 Figure 2. Pressure-composition diagram for acetophenone/carbon dioxide system. 0.06
,
0.04
4
0.4
I7
ii
c
x 0.02
0.0
1 .o
2.0
3.0
4
Figure 3. Variations of saturated vapor composition of acetophenone with reduced pressure at 328.15 K.
0.8
~
0.6
E
ljf!?
01 d LU3.3 d3 d0 o0 d 0Acetophenone Methyl 1 -0ctanol Benzoate
0.2
0.0
I
0
50
100
P
/
150
2
bar
Figure 4. Solubilities of ethane in the liquids a t 338.15 K.
as Pr,2> 1. The ethane- and carbon dioxide-containing isotherms are at about the same reduced temperature (Tr2 = 1.07), but these two isotherms do not superpose in the high-pressure range. A slightly higher reduced temperature for the ethylene-containing isotherm (Tr2= 1.16) leads the vapor composition of acetophenone to become much less sensitive to the pressure. The ethane and ethylene solubilities in the four heavy liquids octane, 1-octanol, methyl benzoate, and aceto-
Ind. Eng. Chem. Res., Vol. 31, No. 12,1992 2771
10
-' 0 0 0
no0
Methyl Benzoate Meeo Acetophenone AUA
0.0 -
0
50
100
P
/
150
A A A
200
0.01 5
0.01 0
0.005
bar
cm
Figure 5. Solubilities of ethylene in the liquids a t 338.15 K.
-3
Figure 7. Correlation between saturated vapor composition of acetophenone and carbon dioxide density (curves represent the best-fitted results from eq 1).
0.8
0.6 X
jI
P
P I
dense fluid COZ
4
0.4
0.2
Table IV. Empirical Correlation for Saturated Vapor Composition of Acetophenone
CzHs
4
0.0 i 0
Octane 1 -0ctanol Methyl Benzoate Mees Acetophenone 00000
C2H4
00[100
A-A
50
100
P
/
150
1 200
bar
Figure 6. Solubilities of carbon dioxide in the liquids at 348.15 K.
phenone are compared as illustrated in Figures 4 and 5, respectively. It is shown that the solubilities of the nonpolar gases in the nonpolar liquid (octane) are much larger than those in the polar liquids. The dipole moments of methyl benzoate (1.9D) and l-octanol(2.0 D) are almost the same, but the polar interactions among methyl benzoate molecules could be stronger h e to ita smaller molecular size. On the basis of the intermolecular force concept, that may lead the gas solubilities in methyl benzoate to be less than those in l-octanol. Since acetophenone has the highest dipole moment and the smallest molecular size among those four liquids, the intermolecular forces between acetophenone molecules may be the strongest that could result in the lowest gas solubilities in acetophenone. However, as given in Figure 6, the solubilities of carbon dioxide in methyl benzoate and in acetophenone are enhanced which could be attributed to weak Lewis acid-base interactions between acidic carbon dioxide and the basic aromatics (Le. charge-transfer effects).
Equilibrium Data Treatment Empirically, the saturated vapor composition of those supercritical fluid-containing systems can be correlated well with the density of the dense fluids (p) (Lee and Weng, 1992b,c). Similarly, it is valid for the acetophenone-containing systems. As an example, Figure 7 shows the relation for acetophenone/C02 system. It appears a quadratic correlation exists between ln(yl) and p for each isotherm; that is, (1) I d y l ) = C, + Clp + C2p2
T (K) n 313.15 328.15 343.15 318.15 328.15 338.15 318.15 328.15 338.15
6 7 7 7 7 6 7 7 7
C, -8.9846 -8.4895 -7.4221 -10.3512 -9.5717 -8.7624 -12.2828 -11.0277 -9.4664
c1 201.560 227.157 66.216 1051.604 867.465 740.624 2533.857 1988.315 1287.791
m (106) 0.34328 0.33006 0.34023 -0.38023 -0.26075 -0.18758 -1.70871 -1.15485 -0.49986 c 2
(10-2) 0.0029 0.1862 0.2083 0.2041 0.0598 0.0702 0.1616 0.3600 0.2259
"AAD= (loo/n)~;ll~ldc - ylexPtlk. where p was calculated from the Patel-Teja equation of state at the same T and P as the corresponding mixture. This empirical equation is practically of interest because it is capable of interpolating the saturated vapor composition over a wide range of pressures that a conventional equation of state may fail. The best-fitted values of coefficients C,, C1,and Cz as well as the average absolute deviations (AAD) of Ayl are reported in Table IV for those three acetophenone-containing systems. The gas solubility data were correlated by the KI equation, W 2 / X 2 ) = In Hz,l+ [A(xlZ- l)/RT] + Vzm(P- P l o ) / R T (2) where represents Henry's constant of a gas (component 2) in a solvent (component 1) at the saturated pressure of the solvent (Pl"),A is the Margules constant, and V2- stands for the partial molar volume of the gae at infinite dilution. In this study, the fugacity of carbon dioxide was calculated from the equation reported by Huang et aL (1985)and those of ethane and ethylene were calculated from the Lee-Kesler equation (Lee and Kesler, 1975). Mathmetically the values of Hz,l,A, and ?2m for each isotherm can be obtained by fitting the solubility data to the KI equation, but the resulting values of A and could be unreasonable. h a consequence, the partial molar volumes of the solute at infinite dilution were calculated fmt from the generalized equation proposed by Brelvi and O'Connell (1972) accompanying the modified Rackett model (Spencer and Danner, 1972) for liquid densities. Then the values of H2,1 and the Margules constant were determined by a least-squares algorithm. The results are given in Table V, which show that the KI equation cor-
v2-
2772 Ind. Eng. Chem. Res., Vol. 31, No. 12, 1992
'"I
Table V. Parameters of the KI Equation for Heavy Liquid (l)/Dense Fluid (2) Mixtures
8
. ,, . octane/COZ
313.15 328.15 348.15 318.15 Mtane/CzHs 328.15 338.15 318.15 octane/CzH4 328.15 338.15 313.15 1-octanol/CO, 328.15 348.15 318.15 l-octanol/CzHs 328.15 338.15 318.15 l-octanol/CzH, 328.15 338.15 methyl benzoate/COz 313.15 328.15 348.15 methyl benzoate/CzH6 318.15 328.15 338.15 methyl benzoate/CzH4 318.15 328.15 338.15 313.15 acetophenone/COz 328.15 348.15 318.15 acetophenone/CzH6 328.15 338.15 318.15 acetophenone/C2H4 328.15 338.15
'AAD
125.72 141.34 162.41 52.95 54.32 61.58 74.68 83.63 89.69 197.67 217.09 240.21 103.56 111.34 123.22 136.80 152.27 159.61 120.30 156.72 175.56 119.04 139.92 160.14 146.97 162.85 170.51 131.24 164.30 193.09 135.30 163.33 184.01 165.37 185.89 196.95
2310.56 2263.73 2226.92 848.14 614.15 690.52 1045.93 1142.32 1119.72 3104.06 3038.75 2949.74 1947.18 1613.32 1651.39 1973.70 2068.41 2024.88 2262.32 2320.84 2008.32 1432.89 1778.35 2034.00 2134.57 2112.68 2019.91 2056.81 2268.99 2334.58 753.06 1232.77 1542.13 1964.83 2067.81 2018.02
52.48 55.74 61.33 69.91 72.76 76.05 64.81 67.48 70.55 48.27 50.18 53.41 63.98 65.65 67.56 59.34 60.90 62.68 41.50 43.30 45.69 56.43 57.44 58.61 52.23 53.18 54.27 40.46 41.22 42.62 53.59 54.26 55.05
49.23 50.20 50.95
4.89 5.42 4.00 4.41 1.44 1.58 2.58 2.78 2.80 1.13 3.07 3.53 1.35 1.82 1.63 3.02 3.35 4.13 4.44 4.16 4.05 1.56 0.93 1.43 3.09 3.15 2.98 5.39 3.73 5.04 2.22 1.89 1.38 1.79 1.74 2.46
j
C C
0
0 D
0.4
0.5
O
0
0.6
7
L l
Figure 8. Variations of the reduced Henry's constant with reduced temperature.
Iwai-Margerum-Lu (IML). Quadratic mixing rules with a single adjustable binary interaction constant, k,,,, were used in the phase-equilibrium calculations, Le.,
with (4)
and (5)
= (loO/n)~.;-~([l(f~/x~)~' - (fZ/~~~"'Pt~]/(f~/~Z~expt~k~ 2
relates the gas solubility data acceptably well. As seen from Figure 8, Henry's constant increases with temperature for those binary systems within the observed temperature ranges, and the reduced Henry's constants (Hz,l/Pc,l) appear to have a generalized correlation with except for the the reduced temperature Tr,l (=T/TC,,) l-octanol/COz, octane/ethane, and octane/ethylene systems.
where ci = -biui for the IML equation of state. The optimal interaction parameter (kalZ)for each system was determined from the bubble-point calculations by minimization of the following objective function, T , with a modified Levenberg-Marquardt algorithm:
Cubic Equations of State The equilibrium data of the 12 binary systems were also employed to test the applicability of three representative cubic equations of state: Soave, Petel-Teja (PT), and
The results of data reduction are compiled in Table VI.
c, = c x i c i
(6)
i=l
Table VI. Bubble-Point Calculations from the Soave, Patel-Teja (PT), and Iwai-Margerum-Lu (IML) Equations of State" SRK PT IML AAD AAD AAD n Ay,' (lo-') mixture (1)/(2) AP/P ("lo) AP/P (010) AYI (IO-') P (bar) P I P (%) AYI (lo-*) kQ12 k w kin, octane/COz octane/C& octane/CzH4 l-octanol/COz 1-octanol/CzH6 l-octanol/CzH4 methyl benzoate/COz methyl benzoate/Cz& methyl benzoate/CzH4 acetophenone/COZ acetophenone/c&s acetophenone/C2H4
total data points grand av ( % )
20 15-113.5 18 25-68 20 15-95 20 40-190 18 20-110 19 30-180 19 30-145 21 20-130 19 25-150 20 20-165 20 25-185 21 30-190
0.1326 -0.0038 0.0170 0.1044 0.0519 0.0429 0.0434 0.0524 0.0065 0.0369 0.0661 0.0128
4.0 3.0 1.5 11.8 5.6 1.3 5.1 8.6 8.4 5.7 2.7
0.111 0.486 0.093 0.487 0.485 0.191 0.128 1.384 0.952 0.402 0.710 0.745
5.3
0.514
5.5
0.1115 -0.0084 -0.0050 0.0908d 0.035Id 0.0228d 0.0320 0.0409 0.0011 0.0292 0.0551 0.0011
3.7
1.1
1.2 12.0 5.6 1.4 4.8 8.7 7.2 8.3 6.1 2.8
0.206 0.450 0.109
0.505
0.408 0.169 0.094 1.098 0.494 0.327 0.554 0.549
0.0882 -0.0011 0.0036 0.1103 0.0685 0.0657 0.0143 0.0373 0.0011 0.0260 0.0567 0.0223
14.6 8.4 4.2 6.9 10.1 7.5 10.0 6.9 13.7
0.598 0.485 0.311 0.498 0.587 0.306 0.107 1.140 0.576 0.296 0.583 0.120
7.4
0.467
3.8 ~. 1.2
1.2
235 5.2
0.421
"Temperature ranges: 313.15-348.15 K (for C02-containing systems); 318.15-338.15 K (for C & , -and CzH4-containingsystems). * AP/PAAD = (100/n)zi-,[(lP"1' - p"'p'I)/p"'pt]k. 'Ay, AAD = (lOO/n)~~.,lyld'- ylaxPtJh.d F = 1.270267 and E, = 0.308 for 1-octanol (Georgeton et al., 1986).
Ind. Eng. Chem. Res., Vol. 31, No. 12, 1992 2773 In general, the Patel-Teja equation is better than the others. The smooth curves shown in Figures 1and 2 are the calculated values from the Patel-Teja equation. It appears that the accuracy is acceptable except near the critical regions. More sophisticated mixing rules may be required to improve the validity of the equations of state for the supercritical fluid-containing systems over a wide range of pressures. Conclusion The phase-equilibrium data of three binary systems composed of acetophenone plus carbon dioxide, ethane, or ethylene were reported at temperatures between 313.15 and 348.15 K and pressures up to 190 bar or near the mixture critical pressures. A comparison being made in this work shows that the solubilitiesof ethane and ethylene in the following respective heavy liquids decrease in the sequence of octane, 1-octanol, methyl benzoate, and acetophenone, whereas those of carbon dioxide decrease in the sequence of octane, methyl benzoate, acetophenone, and 1-octanolbecause the weak charge-transfer complexes may form between acidic carbon dioxide and the basic aromatics. Each acetophenone solubility isotherm (yJ correlates well with the dense-fluid density and the gas solubility data can be correlated by the KI equation with acceptable accuracy. Moreover, the values of Henry's constant, partial molar volume of the light component at infinite dilution, and Margules parameter in the KI equation were reported for each isotherm, which may be of interest for practical uses. We also found that the Patel-Teja equation is generally better than the Soave and the Iwai-MargerumLu equations of state for the supercritical fluid-containing systems. However, the results of the bubble-point calculations from the three models are not so satisfactory where the conditions are near the critical regions. More complex mixing rules may be needed to improve the validity of the equations of state for such systems over a wide range of pressures. Acknowledgment Financial support from the National Science Council, ROC, through Grant No. NSC81-0402-EOll-06is gratefully acknowledged. Nomenclature A = Margules parameter of the KI equation (J mol-') a, b, c = parameters in the equations of state Co-C2 = coefficients in eq 1 f = fugacity (bar) H2,1 = Henry's constant at the saturated pressure of the heavy
component (bar) k,, = binary interaction constant in the combining rule of a12 K = equilibrium ratio n = number of data points P = pressure (bar) Pl0= vapor pressure of the heavy component (bar) P,,z = reduced pressure (=P/P,,2) R = gas constant (J mol-' K-*) T = t e m p e r a t u r e (K) Tr,l= reduced temperature (=T/T,,,) Tr,2= reduced temperature (= T / TC,J E = parameter in the Iwai-Margerum-Lu equation of state V2- = partial molar volume of a gas at infinite dilution (cm3 mol-')
r = mole fraction of liquid phase y = mole fraction of vapor phase Greek Symbols = objective function (eq 7) p = density of the light component (mol ~ m - ~ ) @ = fugacity coefficient A
Superscripts calc = calculated value expt = experimental data Subscripts 1 = for component 1 (heavy component) 12 = for 1-2 pair interaction 2 = for component 2 (light component) c = critical property i = for component i i j = for i-j pair interaction j = for component j m = for mixture r = reduced property Registry No. Acetophenone,98-&%2; carbon dioxide, 124-389;
ethane, 74-84-0; ethylene, 74-85-1. Literature Cited Brelvi, S. W.; OConnell, J. P. Corresponding States Correlations for Liquid Compressibility and Partial Molal Volumes of Gases at Infinte Dilution in Liquids. AZChE J . 1972, 18, 1239-1243. Brennecke, J. F.; Eckert, A. A. Phase Equilibria for Supercritical Fluid Process Design. AZChE J . 1989,35, 1409-1427. Georgeton, G. K.; Smith Jr., R. L.; Teja, A. S. Application of Cubic Equations of State to Polar Fluids and Fluid Mixtures. In Equations of State Theories and Applications; Chao, K. C., Robinson Jr., Eds.;ACS Symposium Series 300; American Chemical Society: Washington, DC, 1986, pp 434-451. Huang, F. H.; Li, M. H.; Lee, L. L.; Starling, K. E.; Chung, F. T. H. An Accurate Equation of State for Carbon Dioxide. J . Chem. Eng. Jpn. 1985,18,490-495. Iwai, Y.; Margerum, M. R.; Lu, B. C.-Y. A New Three-Parameter Cubic Equation of State for Polar Fluids and Fluid Mixtures. Fluid Phase Equilib. 1988, 42, 21-41. Johnston, K. P.; Peck, D. G.; Kim, S. Modeling Supercritical Mixtures: How Predictive Is It? Znd. Eng. Chem. Res. 1989, 28, 1115-1125. Krichevsky, I. R.; Ilinskaya, A. A. Partial Molal Volumes of Gases Dissolved in Liquids (the Thermodynamics of Dilute Solutions of Nonelectrolytes). Acta Physicochim. USSR 1945, 20, 327-348. Lee, B. I.; Kesler, M. G. A Generalized Thermodynamic Correlation Based on Three-Parameter corresponding States. AlChE J. 1975, 21, 510-527. Lee, R. J.; Chao, K. C. Extraction of 1-Methylnaphthalene and mCresol with Supercritical Carbon Dioxide and Ethane. Fluid Phase Equilib. 1988,43, 329-340. Patel, N. C.; Teja, A. S. A New Cubic Equation of State for Fluids and Fluid Mixtures. Chem. Eng. Sci. 1982, 37, 463-473. Soave, G. Equilibrium Constants from a Modified Redlich-Kwong Equation of State. Chem. Eng. Sci. 1972,27, 1197-1203. Spencer, C. F.; Danner, R. P. Improved Equation for Prediction of Saturated Liquid Density. J. Chem. Eng. Data 1972,17,236241. Weng, W. L.; Lee, M. J. Vapor-Liquid Equilibrium of the Octane/ Carbon Dioxide, Octane/Ethane, and Octane/Ethylene Systems. J. Chem. Eng. Data 1992a, 37, 213-215. Weng, W. L.; Lee, M. J. Phase Equilibrium Measuremenb for the Binary Mixtures of 1-Octanol Plus COz, CzHe and C2H4. Fluid Phase Equilib. 199213, 73, 117-127. Weng, W. L.; Lee, M. J. Phase Equilibrium Measurements for Binary Mixtures of Methyl Benzoate Plus COz, CzHe and C2Hl. J . Chem. Eng. Jpn. 1992c, 25, 211-215.
Received for reuiew May 25, 1992 Accepted September 4, 1992
