332
I n d . Eng. Chem. Res. 1995,34, 332-339
Calculations of the Solubilities of Solids in Supercritical Fluids Using the Peng-Robinson Equation of State and a Modified Mixing Model Ping-ChinChen, Moui Tang,?and Yan-PingChen' Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan, Republic of China
The Peng-Robinson equation of state is applied in this study to calculate the solubilities of solids in supercritical carbon dioxide and cosolvents. The mixture parameters of the equation of state are determined from a modified Huron-Vidal type mixing model with a volume correction term. The UNIFAC activity coefficient model is used in this work, and only a few group interaction parameters are needed in the determination of equation of state parameters for mixture calculations. The volume correction term is well-correlated in this research as a function of the molar volume of the solid molecule. Satisfactory results of the solubilities of solids in binary systems with supercritical carbon dioxide and in ternary mixtures with a n additional cosolvent are shown in this work. This model yields satisfactory solubility results which are superior to those from the traditional van der Waals mixing model with empirically fitted binary parameters.
Introduction Supercritical fluid extraction (SCFE) is a useful separation technology and is widely studied in many applications (e.g., Brennecke and Eckert, 1989; Johnston and Peck, 1989; Larsen and King, 1986). Carbon dioxide is usually used as a supercritical solvent because it is nontoxic and has a low critical temperature. It is also found that with a small amount of cosolvent there will be an enhanced solubility of the solid compound (e.g., Ekart et al., 1993; Lemert and Johnston, 1991, 1990). Correlation models for the supercritical fluid extraction process have been presented by many investigators, including the application of engineering equations of state (EOS). The key point of the EOS method is on the choice of a proper mixing model to determine the mixture parameters. Usually the simple van der Waals (VDW) mixing rules are used with empirically adjusted binary parameters. The binary parameters cannot be correlated, and even with the optimal parameters, appreciable errors s t i l l exist for various engineering equations (Haselow et al., 1986). Recently, a modified Huron-Vidal type mixing model (Huron and Vidal, 1979)has been applied in calculating the solubilities of aromatic solids in supercritical carbon dioxide (Sheng et al., 1992). In this model, a volume correction term has been used to evaluate the mixture parameters of the EOS. The constants of the volume correction term have been evaluated for some pure aromatic solids, and their values have been correlated by a simple function of the molar volume of the solid compound. Using the volume correction model, the calculations of solid solubilities can be generalized without individually adjusted parameters for each binary system. In this work, we extend our previous calculations to ternary mixtures including two solids or a cosolvent compound. The extension of the volume correction term to ternary mixtures is examined in this study, and the generalized correlation equations are
* Corresponding author. E-mail address:
[email protected]. edu.tw. + Present address: Department of Chemical Engineering, Chinese Culture University.
proposed for future predictive calculations. Calculation results from this modified mixing model are presented and compared with those from the traditional VDW mixing model with its best-fitted binary parameters.
Theory The solubility of a solid (component 2) in a supercritical fluid (component 1)is calculated by: y2 = (6 at42 sat exp(V,,,(P - p"z"t)~R~YC$~cFP> (1)
where the fugacity coefficient of the solid is computed from an EOS. In this study, we apply the PengRobinson EOS (Peng and Robinson, 1976) in our calculations:
p=-- RT V-b
U
V2+2bV-b2
For pure fluids, the EOS parameters a and b are determined from the characteristic critical constants and acentric factors. On mixture calculations, various mixing rules can be applied to evaluate the mixture parameters. For the simple VDW type mixing model, the mixture is taken as a pseudopure component, and the EOS parameters are calculated by:
(3) and (4)
where kij and lij are binary interaction parameters that are obtained from data regression of known experimental data. The binary parameters are very sensitive to solid solubility calculations, and no reliable correlation can be found for these empirical parameters. Despite using the binary parameters, a generalized calculation model has been proposed for phase equilibrium calculations by Huron and Vidal(l979). In their
0888-5885f95f2634-0332~09.Q~f00 1995 American Chemical Society
Ind. Eng. Chem. Res., Vol. 34,No. 1, 1995 333 Table 1. Correlation Results of Vapor-Liquid Equilibria of B h m Mixtures
no. of data pts 45 9 10 62 38 24 52 74 55 29 28 40 20 10 10 26
compounds n-pentane toluene n-hexane toluene n-heptane toluene acetone toluene C02 methanol methanol naphthalene C02 + benzene C02 toluene C02 m-xylene C02 naphthalene C02 l-methylnaphthalene benzene phenol C02 phenol C02 l-naphthol C02 2-naphthol methanol l-naphthol
+ + + + + +
+ + + + + + + + +
temp range (K) 293-313 343 313 308-328 298-313 521-579 298-393 311-542 303-543 373-423 353-703 343-353 348-423 393-453 413-473 520-579
press. range (MPa) 0.014-0.105 0.036-0.098 0.009-0.012 0.011-0.092 0.219-8.06 1.54- 11.74 0.912-13.27 0.304-15.2 0.303-17.23 1.42-10.44 0.811-14.39 0.024-0.099 1.01-5.07 1.01-5.07 1.01-5.07 1.11-13.48
this work
PT EOS 1.39 2.88 2.49 3.79 2.33 22.4 2.61 4.22 5.18 6.82 3.8 NA** NA NA NA NA
PR EOS 1.36 2.21 3.86 2.82 4.15 18.4 4.11 4.74 5.71 6.91 8.13 2.25 3.08 2.04 2 11.26
VDW* kijopt 0.95 2.93 8.77 3.48 7.52 4.23 55.9 4.14 6.28 13.8 3.83 2.7 3.01 4.81 1.01 4.21
data ref a b b b ;,d9e d,g, h
iJ,k j,1, m n i, o P9 9 r 5 S
f
* van der Waals mixing rule with optimal ku parameter. ** No EOS parameters available for these aromatic compounds.
Data References: a Li et al. (1972); Gmehling et al.(1981); c Katayama et al. (1975); Ohgaki and Katayama (1976); e Suzuki and Sue (1990); f Thies and Paulaitis (1986);8 Gupta et al. (1982); Nagarajan and Robinson (1987); Morris and Donohue (1985);JSebastian et al. (1980b); Ng and Robinson (1978); Ng et al. (1982); * Vera and Orbey (1984); Barrick et al. (1987); Sebastian et al. (1980a);pMartin and George (1933); 4 Gmehling et al. (1982); Yau and Tsai (1992); Jan and Tsai (1991).
method, the excess Gibbs free energy of a mixture calculated from an EOS a t an infinite pressure limit is set equal to that from a group contribution activity coefficient model and the energy parameter of the EOS is determined from this equation. Their method has been applied to supercritical fluid extractions by Sheng et al. (1992) where the Helmholtz free energy was used instead of the Gibbs free energy in the original HuronVidal model. We employ the modified equation of Sheng et al. (1992) and apply the Peng-Robinson (PR) EOS (Peng and Robinson, 1976) in this calculation. The energy parameter of the PR EOS is determined from the following equations:
am&&,
xiaiQQi
(6)
QQ = ln[(4b- W 4 4 b + Wl
(7)
There is an extra degree of freedom for the determination of the volume parameter of the EOS from the method of Sheng et al. (1992). A volume correction term, bE, was introduced in additional to the simple pairwise summation of pure fluid properties:
+
In #cF = -ln(Zm - b,)
+ Vm6,- bm -
where
(5)
N = a b
bm = z x i b i bE
The fugacity coefficient of the solid component in the supercritical phase is then calculated by:
(8)
i
It is observed that with the volume correction term solid solubilities in the supercritical extraction process can be calculated with satisfactory accuracy (Sheng et al., 1992). Furthermore, the volume correction term can be correlated by a simple Margules type equation for binary system of a solid (component 2) and carbon dioxide (component 1):
(11)
26, + 2hibm/Nm 26, - 2hibm/Nm 2bm - Nm CR = A 2RTNm ( 2bm+Nm (13) The activity coefficient in eq 10 is calculated using the group contribution UNIFAC model (Larsen et al., 1987). In this study, we apply a modified form of the combinatorial part of the UNIFAC model proposed by Sheng et al. (1989). The residual part of the UNIFAC model requires group interaction parameters. Most group interaction parameters can be taken from Larsen et al. (1987). Some new group interaction parameters needed in our supercritical calculations are regressed from literature vapor-liquid equilibrium data. The group interaction parameters are written in a temperature-dependent form:
A, = a where K1 and KZ are two constants for each binary system.
+ /3(T - To)+ 6[Tl n ( 2 ) + T - To]
(14)
The three constants are obtained from optimal data regression of bubble point pressure calculations of
334 Ind. Eng. Chem. Res., Vol. 34,No.1, 1995 Table 2. Binary Group Interaction Parameters of the UNIFAC Model Regressed from This Work ~
group pairs (i-jp CH2-ACCH2 ACCHz-CHz CH2CO-ACCH2 ACCH2-CH2CO C02-CH30H CH30H-CO2 CHaOH-NAC NAC- CH30H ACH-ACOH ACOH-ACH C02-ACOH ACOH-C02 NAC-ACOH ACOH-NAC CH30H-ACOH ACOH-CH30H
a
B
-3.39 13.66 387.17 -100.11 740.5 - 111.85 4600 4600 1304.34 835.75 882.03 494.93 28.5 648.03 -870.16 -482.15
-0.75 4.14 -0.5 2.67 -2.32 2.2 0 0 -1.53 0.1 -0.03 -3.12 0.19 -0.55 4.55 -6.56
0.10
06
J
Expt. data at T=343K ooooo E x p t . data at T=353K - Thzs work *DO**
~~
6 1.1 47.86 12.55 13.25 0.96 0.82 0 0
0 0 0.51 0.67 -0.19 -0.01 -1.96 -15.74
a Abbreviations: NAC = naphthenic carbon; ACOH = aromatic OH; ACH = aromatic CH; ACCHz = aromatic CCH2.
binary systems, and TOis taken as a constant reference temperature of 298.15 K. The two constants KIand KZin the volume correction, eq 9, are expressed as a function of a characteristic property of the solid. In this work, we use the solid molar volume as this property. This function of the volume correction term is determined from the supercritical extraction computations. Extension of eq 9 from binary mixtures to ternary systems with two solids in supercritical carbon dioxide, or with carbon dioxide and a cosolvent, is presented in this study. The constants in the volume correction term are generalized in this work, and this computation method can be used in a predictive manner with acceptable accuracy.
Results and Discussion To apply the EOS and UNIFAC activity coefficient model in phase equilibrium calculations, we need to have the group interaction parameters. Some of these are given by Larsen et al. (1987) and Sheng et al. (1992) when the Patel-Teja EOS (Patel and Teja, 1982) was used in supercritical calculations. We find in this research that although some group interaction parameters are regressed from vapor-liquid equilibrium calculations using the Patel-Teja EOS, these group interaction parameters are not limited by the specific type of EOS. Table 1 shows the vapor-liquid equilib-
0.08 ?
2%
0.06
{
L
4
0.04
1
0.00
0.20
0.40
0.60
0.80
1.00
Mole F r a c t i o n of B e n z e n e Figure 1. Pxy diagram of the benzene and phenol binary mixture from this work using the Peng-Robinson EOS (experimental data: Gmehling et al., 1982; Martin and George, 1933).
rium calculation results using the same group interaction parameters of the UNIFAC model and either the Patel-Teja or Peng-Robinson EOS.The group interaction parameters are taken from Larsen et al. (19871, Sheng et al. (1992), or regression of vapor-liquid equilibrium data in this research. It is observed that satisfactory results are obtained from both EOS. The combined GE and EOS model also yields better results than those from the traditional VDW mixing rules with its optimally fitted binary parameters. Since the group interaction parameters can be used in various EOS, we apply those parameters involving carbon dioxide and aromatic hydrocarbons presented in our previous research directly to our present calculations. Some new group interaction parameters of the UNIFAC model found in this study are reported in Table 2. A graphical presentation of those vapor-liquid equilibrium calculation results on the binary mixture of benzene and phenol using the Peng-Robinson EOS and the UNIFAC model is shown in Figure 1. It is observed that the calculated results match very well with the experimental data at different temperatures. We employ the volume correction term, eq 9, in these supercritical extraction calculations. The constants in
Table 3. Calculation Results of the Solid Solubilities in Supercritical Carbon Dioxide Using the Peng-Robinson EOS AADY2b (%) this work VDW" data no. of temp press. solid (comp 2) data pts range (K) range (MPa) opte KdK2 predd K1IK2 opte k12 optfk1dl12 ref naphthalene 44 308-333 8-29 8.45 8.48 36.41 9.75 g 15 308-328 10-28 5.46 6.68 9.51 7.71 h 2,6-dimethylnaphthalene anthracene 20 303-343 10-41 9.16 9.21 14.04 8.36 i 2,3-dimethylnaphthalene 14 308-328 10-28 5.42 6.92 14.35 8.41 h phenanthrene 15 318-338 12-28 8 8.04 15.4 6.14 h hexamethylbenzene 24 303-343 7-48 15.26 13.23 12.46 i 2,7-dimethylnaphthalene 10 308-328 8-24 10.76 14.15 8.4 j phenol 25 309 8-25 3.68 4.2 29.11 21.25 k 2-naphthol 25 308-343 10-36 12.96 13.91 31.46 14.01 1 3,4-xylenol 7 308 8-26 1.13 7.51 25.79 6.29 m 2,5-xylenol 8 308 7-27 4.48 6.95 34.56 6.5 n a van der Waals mixing rule. M Y 2 = (lOO/NP)Zil(v~,ica' - yz,iq)/yz,ieQ)I;NP = number of data points. Results using optimally fitted volume correction term parameters. Results using generalized correlated volume correction term parameters. e Results with a single Optimally fitted binary parameter. f Resulta with dual optimally fitted binary parameters. Data references: g McHugh and Paulaitis (1980); Kurnik et al. (1981); Johnston et al. (1982);J Iwai et al. (1993); Leer and Paulaitis (1980); Schmitt and Reid (1986); Mori et al. (1992); Iwai et al. (1990).
Best Fitted Data(Non-polar Aromatic)
***a*
Best Fitted Data(Non-polar AromaticJ
- ooooo Best Fitted Data(Po1ar Aromatic) - __ Correlated Curve
ooooo Best Fitted Data(Po1ar Aromatic) __ Correlated Curve
J
0.00
-
0.06
K'
0.04
1/
K2 -2.00
I
1
0.08
0.10
0.12
0.14
0.16
0.18
-4.00
1 -v 0.10 0.12 0.14
Vs( Z/mo 1)
the volume correction term are found to be dependent on the molar volumes of solids. Table 3 shows the aromatic binary systems which we examine in this study. We use the first five nonpolar systems to regress the constants of the volume correction term. For nonpolar aromatic solids, these constants are expressed as (V,in L/mol):
-
-6.00 0.08
0.20
Figure 2. Plot of the KI parameter against the solid molar volumes using the Peng-Robinson EOS.
:
0.16
0.18
0. 0
Vs(Z/mol) Figure 3. Plot of the KZ parameter against the solid molar volumes using the Peng-Robinson EOS.
u
1
Kl= 0.00156 + 0.O8417Vs+ 0.04838c (15) K2= -6.18029 + 135.566V8- 716.778c (16) We also use the last four systems to obtain the correlation equations for the polar aromatic systems. For polar aromatic solids, these constants are correlated by:
KI = 0.35855- 6.70852V8+ 34.61239c (17)
K2= 2.78488- 62.7384VS+ 154.467e (18) It is demonstrated in Table 3 that with either the optimally fitted volume correction parameters or the values calculated from the generalized equations (e.g., eqs 15-18),satisfactory solid solubilities are determined for both nonpolar and polar mixtures. The results are also superior to those from the traditional VDW mixing model with single or dual binary interaction parameters. We also apply these correlation equations to predict the volume correction term constants of hexamethylbenzene and 2,7-dimethylnaphthalene and to calculate their solubilities in supercritical carbon dioxide. For the predictive calculations on these two binary mixtures, satisfactory results are obtained. Our modified model with the volume correction term yields comparable results to those from the VDW mixing rules with dual best-fitted binary parameters. The correlation equations for the volume correction term are shown t o be useful for further predictive calculations. The correlations of the volume correction constants are shown graphically in Figures 2 and 3. The calculated solubilities of 2,6-dimethylnaphthalene in supercritical carbon dioxide at various temperatures are shown in Figure 4. Figure 5 presents another predicted solubility result of 2,7-dimethyInaphthalene in supercritical carbon dioxide. The calculations are again satisfactory with no
Figure 4. Calculated solubilities of 2,6-&methylnaphthalene in supercritical carbon dioxide using the Peng-Robinson EOS (experimental data: Kurnik et al., 1981).
empirically adjusted parameters. The predicted results are superior to those from the VDW mixing model if a nearly optimal binary parameter of 0.1is used. We extend the calculations to ternary mixtures with two solids (components 2 and 3) in supercritical carbon dioxide (component 1). In these cases, we use the following form for the volume correction term:
The K constants in eq 19 are determined from the generalized correlations of eqs 15-18 for each carbon dioxide-solid pair. In this way, the calculations of the ternary mixtures with two solids are totally predictive in nature, and the results are presented in Table 4. It is noticed that the solubilities of both solids are satisfactory. Our calculation results are also compared with those from the traditional VDW mixing rules with bestfitted binary parameters of K I Z and k13. It is the volume correction model which needs no empirical parameter
336 Ind. Eng. Chem. Res., Vol. 34, No. 1, 1995 Table 4. Calculation Results on Ternary Systems with T w o Solids in Supercritical Carbon Dioxide Using the Peng-Robinson EOS this work VDW" press. no. of temp M Y 2 AADY3 data ref solid (comp 3) solid (comp 2) data pts range (K) range (MPa) (%) (%I 15.44 20.47 d 4.68 2.43 12-28 phenanthrene naphthalene 18 308 11.56 11.68 d 12.7 16.22 12-28 2,6-dimethylnaphthalene phenanthrene 5 308 12.05 e 6.22 29.95 5.77 10-24 anthracene phenanthrene 10 308-318 23.67 15.14 d 10.52 21.82 12-28 2,3-dimethylnaphthalene naphthalene 5 308 14.46 d 11.19 12.33 5.92 12-28 2,3-dimethylnaphthalene 2,6-dimethylnaphthalene 18 308-318 22.6 15.93 17.18 13.96 9-24 24 308-328 2,6-dimethylnaphthalene 2.7-dimethylnaphthalene f 21.17 16.73 8.02 18.26 13-34 16 phenanthrene 2-naphthol 308-328 g 22.19 16.02 h 11.03 13.59 12-35 6 2-naphthol anthracene 308 d
a van der Waals mixing rule with dual best-fitted parameters. b c AADY = absolute average deviation of yz or y3. Data references: Kurnik and Reid (1982); e Kosal and Holder (1987); f Iwai et al. (1993); g Lemert and Johnston (1990); Dobbs and Johnston (1987).
-2-
-P
-S-
-3-
-4-
-6-
. -
- VDR model
0
with kr*=O.l
ooooo E q t d a t a a t 308K .*.a. Expt d a t a a t 318K -Predicted,thia w o r k - - VDR model with kfl and kfa=O.1
0 $
0
5
I I 1 I ~ I ' I 1 ( l I I I I 1 ( I ~ 1 l 1 I ' ' ' 1 1 ' (
10
20
25
I
P(MP:)
Figure 5. Calculated solubilities of 2,7-dimethylnaphthalene in supercritical carbon dioxide using the Peng-Robinson EOS (experimental data: Iwai et al., 1993).
and yields superior overall results to the VDW mixing model with dual fitted parameters. Figure 6 shows predicted results for the solubilities of 2,7-dimethylnaphthalene in the ternary mixture. It is demonstrated that predicted solubilities from the volume correction model are successful and agree well with experimental data. The solid (component 2) solubilities are then further examined on ternary mixtures with supercritical carbon dioxide (component 1) and a cosolvent (component 3). In these systems, the volume correction term is written as:
The constants K1 and KZ are determined from the generalized correlation equations (eqs 15-18) for each carbon dioxide-solid pair. The other constants, K3 and K4, due to the cosolvent molecules are determined from regression of experimental solubility data on ternary mixtures. The four ternary mixtures with cosolvents are listed in Table 5 where K3 is fixed for a specific solid and K4 varies with different cosolvents for the hexamethylbenzene system. It is also interesting to observe that K4 values follow approximately a linear relation with the carbon number of the cosolvent for the hexamethylbenzene system. A plot of the K4 values against
Figure 6. Calculated solubilities of 2,7-dimethylnaphthalene in the ternary mixture of 2,6-dimethylnaphthalene (2), 2,7-dimethylnaphthalene (3), and supercritical carbon dioxide (1)using the Peng-Robinson EOS (experimental data: Iwai et al., 1993). Table 5. Parameters of the Volume Correction Term for Ternary Mixtures with Cosolvents Using the Pen@-RobinsonEOS solute hexamethylbenzene hexamethylbenzene hexamethylbenzene hexamethylbenzene 2-naphthol
cosolvent acetone 3.5 mol % n-pentane 3.5 mol % n-octane 3.5 mol % n-undecane 3.5 mol % methanol 3.5-9 mol o/o
-158.13
K4 5.57
-158.13
8.04
-158.13
13.26
-158.13
19.58
K3
27.89
-0.16
the carbon number of the cosolvent is shown in Figure 7. Further correlations of this parameter for other solid systems can be made when an accurate EOS for the pure solute molecule and more experimental solid solubility data on ternary mixtures with cosolvents are available. Table 6 shows the comparison of the calculation results using the volume correction model to those from the VDW mixing rules with optimally fitted binary interaction parameters of k12, k13, and k23. The binary parameters of the VDW model have no regulation and can not be predicted in the calculations. The modified mixing model with the volume correction term includes an obvious correlation of its parameters with the
Ind. Eng. Chem. Res., Vol. 34, No. 1, 1995 337 Table 6. Calculation Results of the Solid Solubilitieson Ternary Systems with Supercritical Carbon Dioxide and Cosolventa Using the Peng-Robinson EOS AADYzb (%) cosolvent no. of data pts temp (K) press range (MPa) this work VOWa data ref acetone 10 308 10-35 9.47 2.89 c 3.5 mol % hexamethylbenzene n-pentane 6 308 10-35 4.76 6.12 d 3.5 mol % hexamethylbenzene n-octane 6 308 12-35 4.74 3.11 d 3.5 mol % hexamethylbenzene n-undecane 4 308 12-35 4.28 3.93 d 3.5 mol % 2-naphthol methanol 6 308 12-35 3.97 9.31 c 3.5 mol % 2-naphthol methanol 5 308 12-35 5.77 10.6 e 7 mol % 2-naphthol methanol 6 308 20-35 25.85 26.65 e 9 mol % a van der Waals mixing rule with three best-fitted binary parameters. AADYz = absolute average deviation of yz. Data references: Dobbs et al. (1987); Dobbs et al. (1986); e Dobbs and Johnston (1987). solid (comp 2) hexamethylbenzene
2oa Best Fitted Data
*a***
u
10 -2:
0
sc
16-
10 -3:
% I
4
K4
3
12:
a-
4
2
4
6
a
10
-4:
’c’
***am Ezpt. data(3.5% methanol)
0
AAAAA
‘u
00000
Ezpt. data(’/.&% methanol) Ezpt. d a t a ( 9 . a methanol)
- Thzs w o r k
10 -
...........................................................
0
IO
07
/
12
30
io
0
P(EPa) Figure 9. Calculated solubilities of 2-naphthol in supercritical carbon dioxide with various amounts of methanol cosolvent using the Peng-Robinson EOS (experimental data: Dobbs and Johnston, 1987).
3
with multiple binary parameters. Graphical illustrations of our calculation results for the ternary mixtures with cosolvents are shown in Figures 8 and 9. It is again demonstrated that our modified mixing model gives good agreement to the experimental data. This mixing model can be applied to various EOS with the same type of correlations for the volume correction constants (Chen et al., 1994). With this mixing model, solid solubilities in supercritical fluids can be predicted with acceptable accuracy.
3 li
Expt. data(acetone) data( sntane) 00000 Ezpt. data6ctane) *e*** Ezpt. data(undecane) - Thzs w o r k **e**
Conclusion
A A A A ~Expt.
0 u
t 0
0
io
30
40
Figure 8. Calculated solubilities of hexamethylbenzene in supercritical carbon dioxide with various cosolventa using the PengRobinson EOS (experimental data: Dobbs et al., 1986, 1987).
properties of the solid or the cosolvent compounds and yields comparably good results to the VDW mixing rules
A modified mixing model is proposed in this study to calculate the solid solubilities in supercritical extraction with cosolvents. This modified method uses the PengRobinson equation of state and the UNIFAC group contribution activity coefficient model. A volume correction term is included in this mixing model where its parameters are expressed as functions of the characteristic properties of the solids or the cosolvents. Generalized correlations are presented in this study. Our calculation results also show superior accuracy to those of the traditional van der Waals mixing rules with multiple binary parameters. The mixing model sug-
338 Ind. Eng. Chem. Res., Vol. 34,No. 1, 1995 gested in this research is useful in predicting engineering calculations.
Acknowledgment The authors are grateful to the National Science Council, Republic of China, for supporting this research (NSC82-0402-E002-067). Nomenclature A = Helmholtz free energy, or the group interaction parameter of the UNIFAC model a, b = parameters of the Peng-Robinson equation of state K = constant in the volume correction term k, 1 = binary interaction parameters N = p a r a m e t e r defined in e q 6 n = number of moles P = pressure Qv = p a r a m e t e r defined in e q 12 QQ = p a r a m e t e r defined in e q 7 R = gas constant T = temperature x = mole fraction y = solubility of solid in the supercritical phase V = volume Greek Letters a,B, 6 = constants of the group interaction parameter of
the UNIFAC model y = activity coefficient I$ = fugacity coefficient Superscripts E = excess property, or the volume correction term sat = saturated property SCF = supercritical phase
Subscripts i , j = component i or j m = mixture property s = solid phase 1, 2, 3 = component 1,2, or 3
Literature Cited Barrick, N. W.; Anderson, J. M.; Robinson, R. L. Solubilities of Carbon Dioxide in Naphthalene, Phenanthrene, and F'yrene at Pressures to 1.6MPa and Temperatures from 373 to 433K. J . Chem. Eng. Data 1987,32,372-374. Brennecke, J. F.; Eckert, C. A. Phase Equilibria for Supercritical Fluid Process Design. AIChE J . 1989, 35, 1409-1427. Chen, P. C.; Tang, M.; Chen, Y. P. A Mixing Model for the Calculation of the Solid Solubilities of Solids and Their Mixtures in Supercritical Fluids. Separation Technology; Elsevier: Amsterdam, 1994; pp 49-58. Dobbs, J. M.; Johnston, K. P. Selectivities in Pure and Mixed Supercritical Fluid Solvents. Znd. Eng. Chem.Res. 1987, 26, 1476-1482. Dobbs, J. M.; Wong, J. M.; Johnston, K. P. Nonpolar Co-Solvents for Solubility Enhancement in Supercritical Fluid Carbon Dioxide. J . Chem. Eng. Data 1966,31,303-308. Dobbs, J. M.; Wong, J. M.; Lahiere, R. J.; Johnston, K. P. Modification of Supercritical Fluid Phase Behavior Using Polar Cosolvents. Z n d . Eng. Chem. Res. 1987,26, 56-65. Ekart, M. P.; Bennett, K. L.; Ekart, S. M.; Gurdial, G. S.; Liotta, C. L.; Eckert, C. A. Cosolvent Interactions in Supercritical Fluid Solutions. AZChE J . 1993,39,235-248. Gmehling, J. Phase Equilibria in Binary Systems Formed by Phenol with Benzene. n-Octane, and n-Decane. J . Chem. Enp. Data 1982,27, 371-373. Gmehlinz. J.: Onken. U.: Arlt. W. Vawr-LwuidEauilibrium Data Collectlibn;' DECHEIhl Chemistry Data Senes: Frankfurt, 1981. Gupta, M. K.; Li, Y. H.; Hulsey, B. L.; Robinson, R. L. Phase Equilibria for Carbon Dioxide-Benzene at 313.2, 353.2 and 393.2K. J . Chem. Eng. Data 1982,27, 55-57.
Haselow, J. S.; Han, S. J.; Greenkorn, R. A.; Chao, K. C. Equation of State for Supercritical Extraction; ACS Symposium Series 300; American Chemical Society: Washington, DC, 1986; pp 156-178. Huron, M. J.; Vidal, J. New Mixing Rules in Simple Equations of State for Representing Vapor-Liquid Equilibria of Strongly Nonideal Mixtures. Fluid Phase Equilib. 1979, 3, 255-271. Iwai, Y.; Yamamoto, H.; Tanaka, Y.; Arai, Y. Solubilities of 2,5and 2,6-Xylenols in Supercritical Carbon Dioxide. J. Chem.Eng. Data ISSO, 35, 174-176. Iwai, Y.; Mori, Y.; Hosotani, N.; Higashi, H.; Furuya, T.; Arai, Y. Solubilities of 2,6- and 2,7-Dimethylnaphthalene in Supercritical Carbon Dioxide. J . Chem. Eng. Data 1993,38,509-511. Jan, D. S.;Tsai, F. N. Modeling Phase Behavior of Carbon Dioxide with Aromatic Solvents. Znd. Eng. Chem. Res. 1991,30, 19651970. Johnston, K. P.; Peck, D. G. Modeling Supercritical Mixtures: How Predictive Is It? Znd. Eng. Chem. Res. 1989,28, 1115-1125. Johnston, K. P.; Ziger, D. H.; Eckert, C. A. Solubilities of Hydrocarbon Solids in Supercritical Fluids. The Augmented van der Waals Treatment. Znd. Eng. Chem.Fundam. 1982,21,191197. Katayama, T.; Ohgaki, K.; Maekawa, G.; Goto, M.; Nagano, T. Isothermal Vapor-Liquid Equilibria of Acetone-Carbon Dioxide and Methanol-Carbon Dioxide Systems at High Pressures. J . Chem. Eng. Jpn. 1975,8,89-92. Kosal, E.; Holder, G. D. Solubility of Anthracene and Phenanthrene Mixtures in Supercritical Carbon Dioxide. J . Chem.Eng. Data 1987,32, 148-150. Kurnik,R. T.; Reid, R. C. Solubility of Solid Mixtures in Supercritical Fluids. Fluid Phase Equilib. 1982, 8, 93-105. Kurnik, R. T.; Holla, S. J.; Reid, R. C. Solubilities of Solids in Supercritical Carbon Dioxide and Ethylene. J. Chem. Eng. Data 1981,26,47-51. 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, 22742286. Larson, K. A.; King, M. L. Evaluation of Supercritical Fluid Extraction in the Pharmaceutical Industry. Biotechnol. Prog. 1986,2,73-82. Leer, R. A. V.; Paulaitis, M. E. Solubilities of Phenol and Chlorinated Phenols in Supercritical Carbon Dioxide. J . Chem. Eng. Data 1980,25, 257-259. Lemert, R. M.; Johnston, K P. Solubilities and Selectivities in Supercritical Fluid Mixtures Near Critical End Points. Fluid Phase Equilib. 1990, 59, 31-55. Lemert, R. M.; Johnston, K. P. Chemical Complexing Agents for Enhanced Solubilities in Supercritical Fluid Carbon Dioxide. Znd. Eng. Chem. Res. 1991,30, 1222-1231. Li, I. P. C.; Wong, Y. W.; Chang, S. D.; Lu, B. C. Y. Vapor-Liquid Equilibria in Systems n-Hexane-Benzene and n-PentaneToluene. J . Chem. Eng. Data 1972,17,492-498. Martin, A. R.; George, C. M. Partial Vapour Pressures and Refractivities of Mixtures of Benzene with Nitrobenzene, Phenol, Benzyl Alcohol, or p-Dichlorobenzene. J . Chem. Soc., Part ZZ 1933,1413-1416. McHugh, M. A.; Paulaitis, M. E. Solid Solubilities of Naphthalene and Biphenyl in Supercritical Carbon Dioxide. J . Chem. Eng. Data 1980,25, 326-329. Mori, Y.; Shimizu, T.; Iwai, Y.; Arai, Y. Solubilities of 3,4-Xylenol and Naphthalene 2,5-Xylenol in Supercritical Carbon Dioxide at 35 "C. J . Chem. Eng. Data 1992,37, 317-319. Moms, W. 0.;Donohue, M. D. Vapor-Liquid Equilibria in Mixtures Containing Carbon Dioxide, Toluene, and 1-Methylnaphthalene. J . Chem. Eng. Data 1986,30, 259-263. Nagarajan, N.; Robinson, R. L. Equilibrium Phase Compositions, Phase Densities, and Interfacial Tensions for COz Benzene. J . Chem. Eng. Data 1987,32,369-371. Ng, H. J.; Robinson, D. B. Equilibrium Phase Properties of the Toluene-Carbon Dioxide Systems. J . Chem. Eng. Data 1978, 23,325-327. Ng, H. J.; Huang, S. S. S.; Robinson, D. B. Equilibrium Phase Properties of Selected m-Xylene Binary Systems, m-XyleneMethane and m-Xylene-Carbon Dioxide. J . Chem. Eng. Data 1982,27,119-122. Ohgaki, K.; Katayama, T. Isothermal Vapor-Liquid Equilibrium Data for Binary Systems Containing Carbon Dioxide at High Pressures: Methanol-Carbon Dioxide, n-Hexane-Carbon Diox-
+
+
Ind. Eng. Chem. Res., Vol. 34,No. 1, 1995 539 ide, and Benzene-Carbon Dioxide Systems. J . Chem.Eng. Data 1978,21,53-55. Patel, N. C.; Teja, A. S. A New Cubic Equation of State for Fluids and Fluid Mixtures. Chem.Eng. Sci. 1982,37,463-473. Peng, D. Y.; Robinson, D. B. A New Two-Constant Equation of State. Znd. Eng. C k m . Fundam. 1976,15,59-64. Schmitt, W. J.; Reid, R. C. Solubility of Monofunctional Organic Solids in Chemically Diverse SupercriticalFluids. J. Chem.Eng. Data 1986,31,204-212. Sebastian, H. M.; Nageehwar, G. D.; Lin, H. M.; Chao, K C. VaporLiquid Equilibrium in Binary Mixtures of Carbon Dioxide+Diphenylmethaneand Carbon Dioxide+l-Methylnaphthalene. J. Chem.Eng. Data 1980a,25, 145-147. Sebastian, H. M.; Simnick,J. J.;Lin,H. M.; Chao, K C. Gas-Liquid Equilibrium in Mixtures of Carbon Dioxide+Toluene and Carbon Dioxide+m-Xylene. J. Chem. Eng. Data 198Ob, 25, 246-248. Sheng, Y. J.; Chen, Y. P.; Wong, D. S. H. A Cubic Equation of State for Predicting Vapor-Liquid Equilibria of Hydrocarbon Mixtures Using a Group Contribution Mixing Rule. FZuid Phase Equilib. 1989,46, 197-210. Sheng, Y. J.; Chen, P. C.; Chen, Y. P.; Wong, D. S. H. Calculation of Solubilities of Aromatic Compounds in Supercritical Carbon Dioxide. Znd. Eng. Chem.Res. 1@92,31,967-973.
Suzuki, K.; Sue, H. Isothermal Vapor-Liquid Equilibrium Data for Binary System a t High Pressures: Carbon DioxideMethanol, Carbon Dioxide-Ethanol, Carbon Dioxide-1-Propanol, Methane-Ethanol, Methane-1-Propanol, Ethane-Ethanol, and Ethane-1-Propanol Systems. J. Chem.Eng. Datu 1990,35,6366. "hies, M. C.; Paulaitis, M. E. Vapor-Liquid Equilibrium for 1-NaphthoVMethanoland NaphthaleneMethanol Mixtures a t Elevated Temperatures and Pressures. J . Chem. Eng. Data 1986,31 23-25. Vera, J. H.; Orbey, H. Binary Vapor-Liquid Equilibria of Carbon Dioxide with 2-Methyl-1-Pentene, 1-Hexene, 1-Heptene and m-Xylene a t 303.15,323.15 and 343.15K J. C k m . Eng. Data 1@84,29,269-272. Yau, J. S.; Tsai, F. N. Correlation of Solubilitiesof Carbon Dioxide in Aromatic Compounds. FZuid Phase Equilib. lW2, 73,l-25.
Received for review March 11,1994 Accepted August 4, 1994" e Abstract published in Advance ACS Abstracts, October 1, 1994.
