Ind. Eng. Chem. Res. 1998, 37, 1619-1624
1619
Representation of Electrolyte Solution Properties by Means of the Peng-Robinson-Stryjek-Vera Equation of State Ensheng Zhao*,† and Benjamin C.-Y. Lu‡ Honeywell Hi-Spec Solutions, 343 Dundas Street, London, Ontario, Canada N6B 1V5, and Department of Chemical Engineering, University of Ottawa, Ottawa, Ontario, Canada K1N 6N5
The Peng-Robinson-Stryjek-Vera equation of state (Stryjek, R.; Vera, J. H. Can. J. Chem. Eng. 1986, 64, 334-340) was used with the Wong-Sandler mixing rule (1992) and the activity coefficient model of Chen et al. (AIChE J. 1982, 28, 588-596) to calculate osmotic coefficients and vapor-liquid equilibrium (VLE) values of electrolyte solutions. The osmotic coefficients calculated by this approach agree with those calculated from the original Chen model. The approach was also used to represent VLE for three ethanol-water-salt systems. The average absolute deviations of the calculated temperatures were around 1 K, and those of the calculated vapor-phase compositions were between 0.01 and 0.02 mole fraction. Introduction Thermodynamic properties of electrolyte solutions are needed in the design and simulation of chemical processes involving electrolyte solutions. Generally, the liquid-phase composition of an electrolyte system is represented by an activity coefficient model, which has the functional form
ln γi ) f(T,xi)
EOS approach, and the nonrandom-two-liquid (NRTL) model proposed by Chen et al. (1982) to represent electrolyte solution properties. Activity Coefficient Model for Electrolyte Solutions The expression for the excess Gibbs energy obtained by Chen et al. (1982, 1986) is given by
(1)
However, such a model is not recommended for representation of vapor-liquid equilibria (VLE) at high pressures. On the other hand, equations of state (EOS) are known to be useful in the representation of thermodynamic properties of nonelectrolyte solutions at high pressures and are capable of representing simultaneously phase equilibrium values including volumetric and energy properties. Among the EOS approach, Dahl and Macedo (1992) extended the Soave-RedlichKwong (SRK) cubic equation of state with a new approach for the MHV2 model for representing vaporliquid and liquid-liquid equilibria of mixtures with strong electrolytes. In their approach, they did not use a long-range Debye-Huckel term, nor did they report values of osmotic coefficients. Zuo and Guo (1991) applied the Patel-Teja cubic equation of state together with a long-range Debye-Huckel electrostatic contribution term to represent osmotic coefficients of electrolyte solutions for predicting the solubility of natural gas in formation water. However, the deviations of calculated osmotic coefficients are much larger than those obtained from activity coefficient models. In this work, an attempt was made to apply the cubic Peng-Robinson-Stryjek-Vera (PRSV) equation of state (Stryjek and Vera, 1986) with an extension of the Wong-Sandler mixing rules (1992), which was developed by combining the activity coefficient model and the * To whom correspondence is addressed. Telephone: (519)640-6610. Fax: (519)679-3977. E-mail: Ensheng.Zhao@ Ontario.Honeywell.Com. † Honeywell Hi-Spec Solutions. ‡ University of Ottawa.
Gex Gex,PDH Gex,lc ) + RT RT RT
(2)
where Gex is the excess Gibbs energy, PDH refers to the Pitzer-Debye-Hu¨ckel term used to describe the longrange interactions between ions, and lc is the local composition term used to account for the short-range interactions between all species. The Pitzer-DebyeHu¨ckel term is represented by
Gex,PDH RT
∑k
) -(
( )
Xk)
1000 Ms
1/2
(4AφIx/θ) ln(1 + θIx1/2) (3)
where k refers to all species, Ms is the molar mass of the solvent, and θ, set to be 14.9, is the closest approach parameter of the Pitzer-Debye-Hu¨ckel equation. The Debye-Hu¨ckel parameter, Aφ, is given by
Aφ ) (1/3)(2πNaσ/1000)1/2(e2/DkT)3/2
(4)
and the ionic strength, on a mole fraction basis, Ix, is given by
∑i Zi2xi
Ix ) (1/2)
(5)
where Zi is the charge number of ion i. Chen et al. (1982) proposed a temperature function of Aφ for aqueous solutions as follows:
Aφ ) 61.44534 exp[(T - 273.15)/273.15] + 2.864468{exp[(T - 273.15)/273.15]}2 + 183.5379 ln(T/273.15) - 0.6820223(T - 273.15) + 0.0007875695(T2 - 273.152) + 58.95788(273.15/T) (6)
S0888-5885(97)00649-0 CCC: $15.00 © 1998 American Chemical Society Published on Web 03/18/1998
1620 Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998
Equation 6 was adopted in this work for the VLE calculation of three ethanol-water-salt systems. The derivation of the Chen model (Chen et al., 1982; Chen and Evans, 1986) was based on two assumptions. As the repulsive forces between similarly charged ions are extremely large, the local composition of cations (anions) around cations (anions) was taken to be zero. The local electroneutrality was also assumed, supposing a zero net local ionic charge between cations and anions around a central solvent molecule. The resulting excess Gibbs free energy expression for a multicomponent electrolyte system given by Chen and Evans (1986) is as follows:
(14)
b ) 0.077796RTc/Pc
(15)
and
where R is given by
R ) [1 + k(1 - TR0.5)]2
k ) k0 + k1(1 + TR0.5)(0.7 - TR)
∑j XjGjmτjm ∑k XkGkm
Xa′ +
∑c Xc ∑ a′
∑j XjGjc,a′cτjc,a′c ∑j
∑a Xa ∑ c′
(17)
with
k0 ) 0.378893 + 1.4897153ω - 0.18137847ω2 +
+
Xa′′∑XkGkc,a′c ∑ a′′ k Xc′
(16)
The quantity k of eq 16 was modified by Stryjek and Vera (1986) to be
Gex,lc ) Xm ∑ m
a ) (0.457235R2Tc2/Pc)R
0.0196654ω3 (18)
XjGja,c′aτja,c′a
Xc′′∑XkGka,c′a ∑ c′′ k
(7)
Determination of Equation Parameters for Ionic Species
where X is the effective local mole fraction and the indexes under the summation sign, m, c, and a, denote molecule, cation, and anion, respectively. Furthermore,
Xi ) xiKi
The quantity k1 is an adjustable parameter characteristic of an individual pure compound. The modified form of the PR equation, the PRSV equation, was adopted in this work.
(8)
with Ki ) Zi for ions and Ki ) 1 for molecules. In eq 7 G and τ are parameters in the NRTL model, and
Gij ) exp(-Rijτij)
(9)
τij ) (gij - gjj)
(10)
where Rij is the nonrandomness factor, and gij and gjj are interaction energies between i-j and j-j species, respectively. The quantities Gji,ki and τji,ki are defined by
Gji,ki ) exp(-Rji,kiτji,ki)
(11)
τji,ki ) (gji - gki)/RT
(12)
As no critical properties are available for ionic species, the following methods are adopted to determine the two equation parameters (a and b) in eq 13. 1. Determination of Parameter b. In the work of Zuo and Guo (1991), the parameter b in the PR equation for an ionic species was treated the same as that in the Carnahan-Starling type equation:
b ) (2/3)πNaσ3
(19)
Equation 19 was adopted in this work. 2. Determination of Parameter a. In the determination of the parameter a, which is related to the attractive forces, the compressibility factor expression of the attraction portion of the square-well fluid proposed by Lee et al. (1985) was used:
Zatt ) -
ZMV0[exp(/2kT) - 1] V + V0[exp(/2kT) - 1]
(20)
V0 ) Naσ3/x2
(21)
In eq 20
As specified by Chen et al. (1982), the nonrandomness factor Rij was set equal to 0.2 throughout this work. This method was adopted in this work for two reasons: (1) The model is already normalized to the molar basis, thus making it easier to be incorporated with an equation of state. (2) The model was developed based on the NRTL model and can be conveniently used with the WongSandler mixing rule.
and ZM ) 18 is the lattice coordination number for a square-well fluid. A comparison of eq 20 with eq 13 shows that the parameter a can be calculated from the equation
The PRSV Equation of State
Equation 22 was applied in the determination of the parameter a for ionic species. As far as the quantity /k was concerned, we adopted the Lennard-Jones energy parameter
The Peng and Robinson (1976) (PR) equation is
P) with
a RT V - b V(V + b) + b(V - b)
(13)
a ) ZMV0RT[exp(/2kT) - 1]
LJ/k ) 2.2789 × 10-8ZI1/2RI2/3σ-6
(22)
(23)
which was obtained by Shoor and Gubbins (1969),
Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 1621
Harvey and Prausnitz (1989), and Zuo and Guo (1991) by using the dispersion theory of Mavroyannis and Stephen (1962). In eq 23, ZI is the number of electrons on an ion, and RI is the ion polarizability. The numerical value of eq 23 has a unit of kelvin. Applying the Wong-Sandler Mixing Rules to Electrolyte Solutions In this work, the Wong-Sandler mixing rule (1992) was combined with the electrolyte NRTL model of Chen and applied to the representation of thermodynamic properties of electrolyte solutions. The Wong-Sandler mixing rule (1992) for the PR EOS is given by
∑∑xixj(b - RT)ij a
bmix )
Aex ∞ 1+ RT
and
(
amix ) bmix
∑
ai
( )
(24)
ai xi biRT
Aex ∞ x2
)
∑xibi - ln(x2 - 1)
(25)
where
(b - RTa )
) ij
(
bi -
) (
)
ai aj + bj RT RT (1 - kij) 2
(26)
In the above equations, Aex ∞ is the excess molar Helmholtz free energy at infinite pressure state and kij is the binary interaction parameter. By the assumption made by Wong and Sandler (1992), we have ex Aex ∞ ) G
(27)
In this work, the excess Gibbs free energy Gex is calculated from Chen’s electrolyte NRTL model. To reduce the number of parameters, we set the kij values for all ionic species-molecular species pairs equal to zero. The binary interaction parameters for ionic-ionic pairs were also set equal to zero because the forces between ions were accounted for by the PitzerDebye-Hu¨ckel term. Therefore, only two nontrivial binary interaction parameters are used for an electrolyte in its aqueous solution. Representation of Osmotic Coefficients in Aqueous Solutions with Single Electrolyte The definition of osmotic coefficient, φ, is given by (Robinson and Stokes, 1965)
ln aA ) -
νmWA φ 1000
(28)
where aA is the activity of the solvent, ν ()ν- + ν+) denotes the total number of moles of ions given by 1 mol of electrolyte, m is the molality of the solution, and WA is the molar mass of the solvent. In this study, water and ethanol are the solvents. The critical properties and equation parameters used in this study for water and ethanol are listed in Table 1.
Table 1. Critical Properties and PRSV Equation Parameters for Water and Ethanol property/parameter
water
ethanol
critical temperaturea (K) critical pressurea (bar) acentric factora k1b
647.3 221.2 0.344 -0.06635
513.9 61.4 0.644 -0.03374
a
From Reid et al. (1987). b From Stryjek and Vera (1986).
Table 2. Parameters Obtained by Chen et al. (1986) and from This Worka Chen et al.
this work
electrolyte
τca,w
τw,ca
τca,w
τw,ca
NaCl NaBr NaI NaF NaNO3 KCl KBr KI LiCl LiNO3 KNO3 RbCl RbBr RbI CsCl NH4Cl NH4NO3 HCl HBr HI HNO3 LiBr LiI HClO4 NaOH KOH CaCl2 CaBr2 CaI2 MgCl2 MgBr2 MgI2 SrCl2 BaCl2 Na2SO4 (NH4)2SO4 MgSO4 AlCl3
-4.5916 -4.6070 -4.6920 -3.7493 -3.6151 -4.1341 -4.1707 -4.1217 -5.1737 -4.6136 -3.2747 -4.1357 -4.0399 -4.0916 -4.3726 -4.0121 -3.3162 -5.2286 -5.2194 -5.2039 -4.3663 -5.3628 -5.0883 -5.4365 -4.7893 -5.0644 -5.2549 -5.4801 -5.1151 -5.3583 -5.5307 -5.7064 -4.9537 -4.2068 -3.8760 -3.7871 -4.1796 -5.2306
9.0234 8.9288 8.9820 7.4322 7.2886 8.1354 8.1699 7.9408 10.1242 8.7565 7.2728 8.2053 8.0151 8.1419 8.4238 7.8599 6.8739 10.1728 9.9746 9.7714 8.7223 10.5393 9.5925 10.7078 9.4200 9.2928 10.5126 11.0038 9.7214 10.6681 10.9725 11.3459 9.7230 7.9145 7.9756 7.7870 8.2533 10.0495
-4.0764 -4.1609 -4.3031 -4.1105 -2.8114 -3.5073 -3.5651 -3.5761 -4.7926 -4.1703 -2.5018 -3.5059 -3.3732 -3.4420 -3.5671 -3.3329 -2.4780 -4.8791 -4.9293 -4.9274 -4.1865 -5.0457 -4.7716 -5.1468 -4.3009 -4.6564 -4.8511 -5.1523 -4.7660 -4.9804 -5.2158 -5.4372 -4.4873 -3.6786 -2.9545 -2.7602 -3.4808 -4.8674
6.0293 6.0226 6.1184 6.4329 4.1064 5.0635 5.0875 4.9318 7.2473 5.8033 4.5270 5.1621 4.9148 5.0646 5.4552 4.7079 3.8257 7.3240 7.2094 6.9629 5.9383 7.7539 6.7379 7.9567 6.4286 6.9782 7.6630 8.2613 6.8817 7.8349 8.2081 8.6327 6.7793 5.0278 4.7436 4.3948 5.2854 7.2324
a
ca ) cation and anion in solution. w ) water.
The osmotic coefficient data collected by Robinson and Stokes (1965) were used to determine the binary interaction parameters of aqueous electrolyte solutions. A comparison of the parameters obtained from this work with those obtained by Chen and Evans (1986) is presented in Table 2. The results indicate that the two sets of parameters are of the same order of magnitude. A comparison of the root-mean-square deviation (RMSD) of the calculated osmotic coefficients with those reported by Chen and Evans (1986) is presented in Table 3. It is observed that the results obtained from the equation of state approach are as accurate as those based on the original Chen model. The calculated results are also compared with those obtained by Zuo and Guo (1991) in Table 4, which shows that the results based on the proposed approach are much better than those obtained by Zuo and Guo (1991).
1622 Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 Table 3. Comparison of the Calculated Osmotic Coefficients with Those Reported by Chen et al. (1986) in Terms of Root-Mean-Square Deviation (RMSD) RMSD electrolyte NaCl NaBr NaI NaF NaNO3 KCl KBr KI LiCl LiNO3 KNO3 RbCl RbBr RbI CsCl NH4Cl NH4NO3 HCl HBr HI HNO3 LiBr LiI HClO4 NaOH KOH CaCl2 CaBr2 CaI2 MgCl2 MgBr2 MgI2 SrCl2 BaCl2 Na2SO4 (NH4)2SO4 MgSO4 AlCl3 overall average
max. molality 6 4 3.5 1 6 4.8 5.5 4.5 6 3.5 3.5 5 5 5 6 6 6 6 3 3 3 6 3 6 6 6 6 6 2 5 5 5 4 1.8 4 5.5 3 1.8
Chen et al. 1.2 0.6 0.7 0.02 0.2 0.2 0.3 0.2 2.4 0.4 0.6 0.2 0.2 0.1 0.4 0.07 0.5 1.9 0.8 1.0 0.5 2.8 1.5 3.3 2.3 1.5 9.0 13.0 2.4 9.0 9.0 11.0 5.0 1.2 2.2 0.8 5.0 6.0 2.57
Table 4. Comparison of the Calculated Osmotic Coefficients with Those Reported by Zuo and Guo (1991) in Terms of Absolute Average Percentage Deviation (AAPD) AAPD
this work 0.90 0.40 0.50 0.32 0.69 0.34 0.38 0.32 2.08 0.33 1.15 0.61 0.66 0.68 0.96 0.54 1.10 1.71 0.54 0.67 0.23 2.56 1.10 3.06 1.94 1.33 8.42 12.21 1.48 7.89 8.68 10.25 3.68 0.26 1.26 2.16 2.59 4.56 2.33
Representation of VLE Data for Ethanol-Water-Salt Systems When a salt is present in a mixed solvent, it is capable of altering the composition of the equilibrium vapor phase. Hence, the salt effect on vapor-liquid equilibrium provides an opportunity for enhanced separation. As there is an azeotrope in the ethanol-water system, the salt effect is important for the production of pure ethanol. In the application of the Chen model to multisolvent electrolyte solutions, one of the difficulties is the determination of the Debye-Hu¨ckel parameter Aφ. For simplicity, eq 4, which is the expression proposed by Chen et al. (1982) for aqueous solutions, was adopted. In this work, the VLE data reported by Dobroserdov and Il’yina (1965) for the ethanol-water system with sodium chloride, with calcium chloride, and with zinc chloride under isobaric conditions were used to evaluate the proposed procedure. The reason for considering the data for isobaric experiments is because separation processes are more often carried out under isobaric conditions than under isothermal conditions. Bubblepoint temperature calculations were carried out to represent the VLE of the above-noted systems. The binary interaction parameters for the ethanol-water system were determined from the VLE data for this system. The binary interaction parameters listed in
electrolyte
no.
max. molality
Zuo and Guo
this work
NaCl KCl LiCl LiBr LiI LiNO3 HCl HBr HI HNO3 NaOH NaBr NaI NaNO3 KBr KOH KI KNO3 K2SO4 Na2SO4 MgCl2 MgSO4 MgBr2 Mg(NO3)2 CaBr2 CaCl2 Ca(NO3)2 overall average
35 29 23 23 17 23 23 10 17 17 23 19 17 19 17 23 20 18 7 19 19 17 17 17 17 19 23 528
6.0 4.8 6.0 6.0 3.0 6.0 6.0 1.0 3.0 3.0 6.0 4.0 3.0 4.0 3.0 6.0 4.5 3.5 0.7 4.0 4.0 3.0 3.0 3.0 3.0 4.0 6.0
3.48 1.72 4.91 6.94 2.18 3.24 4.54 0.37 2.33 1.44 1.94 2.17 1.74 1.05 1.03 2.50 1.59 1.29 1.18 5.28 7.42 4.91 5.90 3.88 5.70 7.22 5.93 3.53
0.82 0.21 1.70 2.07 0.89 0.44 1.39 0.22 0.55 0.21 1.62 0.32 0.31 0.58 0.35 1.05 0.23 0.98 0.87 1.03 4.36 2.11 2.63 1.51 2.44 3.67 1.99 1.58
Table 5. Results and Binary Interaction Parameters of the Ethanol-Water System system
k12
R12
∆g12
∆g21
ethanol (1)- 0.12694 0.48459 1776.6 5359.4 water (2)
∆T (K)
∆y × 100
1.62
0.50
Table 6. Results and Binary Interaction Parameters of Three Ethanol-Water-Salt Systems system ethanol-watersodium chloride ethanol-watercalcium chloride ethanol-waterzinc chloride
c (mol/L)
∆ge,caa
∆gca,ea
∆T (K)
∆y × 100
1.0
100 630
21 333
0.64
1.77
0.9
11 255
27 465
1.26
1.20
1.0
67 139
25 613
1.14
1.18
a ∆g e,ca and ∆gca,e are binary interaction parameters, where e denotes ethanol and ca denotes cation and anion.
Table 2 for selected salt-water binaries were determined from the regressions of the osmotic coefficients for these systems, whereas those for the different salt-ethanol systems were obtained from regressions of the VLE data for the ternary systems. The correlation results and interaction parameters obtained for the ethanol-water system without the presence of salt are listed in Table 5. A comparison of the calculated equilibrium compositions with the experimental data is shown in Figure 1. The results and parameters obtained for the three salt-containing systems are listed in Table 6and are also depicted in Figures 2-4. The average absolute deviations of the temperature were around 1 K, and those of the calculated vapor-phase composition were between 0.01 and 0.02 mole fraction.
Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 1623
Figure 1. Ethanol (1)-water (2) system at 760 mmHg.
Figure 3. Ethanol (1)-water (2)-CaCl2 system at 760 mmHg.
Figure 2. Ethanol (1)-water (2)-NaCl system at 760 mmHg.
Figure 4. Ethanol (1)-water (2)-ZnCl2 system at 760 mmHg.
Conclusion The PRSV equation of state was used with the WongSandler mixing rule and the electrolyte local composition model of Chen to represent the osmotic coefficients and VLE values for electrolyte solutions. The proposed approach reproduces osmotic coefficients of the original activity coefficient model of Chen for aqueous electrolyte solutions without increasing the number of binary interaction parameters. The calculated osmotic coefficients are more accurate than those obtained by Zuo and Guo. In addition, the VLE of the ethanol-water-sodium chloride, the ethanol-water-calcium chloride, and the ethanol-water-zinc chloride systems are represented by the proposed approach. It is observed that this approach can represent the VLE of these systems very well. The azeotropic point was removed in the ethanolwater-calcium chloride and ethanol-water-zinc chloride systems, with the salt effect more evident in the case of the presence of calcium chloride as depicted in Figures 3 and 4.
Nomenclature a ) cohesion parameter in equations of state (Pa‚m6/mol2) Aex ) excess Helmholtz free energy (J/mol) Aφ ) Debye-Hu¨ckel parameter b ) covolume parameter in the PR equation (m3/mol) c ) molarity of the solution (mol/L) D ) dielectric constant e ) charge of an electron (4.802 × 10-10 esu) E ) configurational internal energy (J/mol) gij ) binary interaction parameters in the NRTL model (J/ mol) Gex ) excess Gibbs energy (J/mol) Ix ) ionic strength on a mole basis k ) Boltzmann’s constant (1.3805 × 10-16 erg/K) m ) molality of the solution (mol/kg) Ms ) molar mass of solvent (g/mol) Na ) Avogadro’s constant (6.023 × 1023 mol-1) P ) pressure (Pa) R ) universal gas constant (8.314 J/mol‚K) T ) temperature (K) V ) molar volume (m3/mol) WA ) molar mass of water (g/mol) xi ) mole fraction of component i Xi ) effective local mole fraction
1624 Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 Zi ) absolute charge number of ion i Zm ) lattice coordination number for the square-well fluid Greek Letters R ) parameter in equations of state Rij ) nonrandomness factor in the NRTL model RI ) polarizability of ionic species (mL) γi ) activity coefficient of component i ) energy parameter in potential functions (J/mol) θ ) closest approach parameter in the Pitzer-DebyeHu¨ckel equation ν ) the total number of moles of ions given by 1 mol of electrolyte σ ) diameter of molecule or ion (m) τij ) binary interaction parameter in the NRTL model φ ) osmotic coefficient ω ) acentric factor Superscripts ex ) excess properties lc ) local composition term PDH ) Pitzer-Debye-Hu¨ckel term Subscripts c ) critical properties ca ) cation and anion e ) ethanol i, j ) components i and j, respectively ij ) binary interaction term or parameters of components i and j m ) any molecular species mix ) mixture R ) reduced properties w ) water ∞ ) infinite pressure state
Part I: Single solvent, single completely dissociated electrolyte system. AIChE J. 1982, 28, 588-596. Dahl, S.; Macedo, E. A. The MHV2 model: A UNIFAC-based equation of state model for vapor-liquid and liquid-liquid equilibria of mixtures with strong eletrolytes. Ind. Eng. Chem. Res. 1992, 31, 1195-1201. Dobroserdov, L. L.; Il’yina, V. P. Liquid-vapor phase equilibrium of alcohol-water mixtures in the presence of certain salts, at atmospheric pressure. T 422R, Directorate of Scientific Information Services, Canada, Nov 1965. Translated by E. R. Hope from Tr. Leningradskogo Tecknologicheskogo Instituta Pishchevoi Promyshlennosti 1956, 13, 92-100, and 1958, 14, 139154. Harvey, A. H.; Prausnitz, J. M. Thermodynamics of high-pressure aqueous systems containing gases and salts. AIChE J. 1989, 35, 635-644. Lee, K. H.; Lombardo, M.; Sandler, S. I. The generalized van der Waals partition function. II. Application to the square-well fluid. Fluid Phase Equilib. 1985, 21, 177-196. Mavroyannis, C.; Stephen, M. J. Dispersion forces. Mol. Phys. 1962, 5, 629-638. Peng, D.-Y.; Robinson, D. B. A new two-constant equation of state. Ind. Eng. Chem. Fundam. 1976, 15, 59-64. Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The properties of gases and liquids; 4th ed.; McGraw-Hill: New York, 1987. Robinson, R. A.; Stokes, R. H. Electrolyte solutions, 2nd ed.; Butterworths Scientific Publications: London, 1965. Shoor, S. K.; Gubbins, K. E. Solubility of nonpolar gases in concentrated electrolyte solutions. J. Phys. Chem. 1969, 73, 498-505. Stryjek, R.; Vera, J. H. PRSVsAn improved Peng-Robinson equation of state with new mixing rules for strongly nonideal mixtures. Can. J. Chem. Eng., 1986, 64, 334-340. Wong, D. S. H.; Sandler, S. I. A theoretically correct mixing rule for cubic equations of state. AIChE J. 1992, 38, 671-680. Zuo, Y.-X.; Guo, T.-M. Extension of the Patel-Teja equation of state to the prediction of the solubility of natural gas in formation water. Chem. Eng. Sci. 1991, 46, 3251-3258.
Literature Cited Chen, C.-C.; Evans, L. B. A local composition model for the excess Gibbs energy of aqueous electrolyte systems. AIChE J. 1986, 32, 444-454. Chen, C.-C.; Britt, H. I.; Boston, J. F.; Evans, L. B. Local composition model for excess Gibbs energy of electrolyte system.
Received for review September 10, 1997 Revised manuscript received December 11, 1997 Accepted December 11, 1997 IE970649L
