A group contribution equation of state for associating mixtures

RIIIDPMS[ EQUlUDRIA ELSEVIER

Fluid Phase Equilibria 116 (1996)537-544

A GROUP C O N T R I B U T I O N EQUATION OF STATE FOR ASSOCIATING MIXTURES

H. P. Gros, S. Bottini, E. A. Brignole* *PLAPIQUI, UNS-CONICET, 8000 Bahia Blanca, ARGENTINA. Abstract. In the present work a group contribution-associating-equation of state (GCA-EOS) is developed for the modeling of phase equilibria found in the near critical fluid extraction and dehydration of oxygenated compounds from aqueous solutions. The new equation of state is obtained by the inclusion of a 'group' contribution associating term to the GC-EOS model. The definition of a unique hydroxyl group to represent the association effect of hydrogen bonding in water and alcohols, greatly simplifies the extension of the model to multicomponent mixtures. This approach has been applied to determine the parameters for a common hydroxyl group for water, primary and secondary alcohols. On this basis, revised group and binary interaction dispersive parameters for water, primary and secondary alcohols, alkane groups, light hydrocarbons and CO 2 have been determined. Model predictions for binary and ternary data are presented. 1. Introduction. The potential of near critical fluid (NCF) extraction and high pressure distillation for separating oxychemicals from water has been discussed recently in several publications (Brignole et al., 1987; Zabaloy et al., 1992; Horizoe et al., 1993). The design and optimization of this process requires adequate thermodynamic models for predicting phase equilibria in mixtures of associating and non-polar components. There have been many attempts to model the effect of association on fluid phase equilibria. The best known concept is the chemical theory, which postulates the existence of distinct associating species (dimers, trimers, etc.) in solution (Anderko, 1989; Ikonomou and Donohue, 1988; Suresh and Elliot, 1991). A different approach has been based on the statistical theory of associating solutions (Wertheim ,1984a,b; 1986a-c). Wertheim's theory provides a relation between the residual Helmholtz function due to association and the monomer density. This monomer density is related to a A function characterizing the 'association strength'. Several authors (Chapman et al., 1990; Huang and Radosz, 1990,1991; Suresh and Elliot, 1992) have shown that Wertheim's expression for the Helmoltz function can be combined with attractive dispersion and repulsive interactions to generate equations of state able to represent thermodynamic properties of associating systems. The extension of these models to multicomponent associating mixtures is difficult. A group contribution approach, combining an associating term derived from Wertheim's statistical theory with the GC-EOS (Skjold-Jorgensen, 1984,1988), has been proposed to overcome this problem (Gros et al., 1994). In the present work this approach is further developed and applied to the phase equilibria modeling of binary and ternary mixtures containing alcohols, hydrocarbons, gases and water.

2. The Group Contribution Associating Equation of State (GCA-EOS). The residual Helmholtz function is obtained from the sum of three terms representing the contributions of different intermolecular forces: repulsive hard sphere (AhS), dispersive mean field (Adisp) and attractive specific (e.g. hydrogen bonding) (A assoc) interactions, A res = A m + A disp + A ~s°° . 0378-3812/96/$15.00 © 1996ElsevierScienceB.V. All rights reserved SSDI 0378-3812(95)02928-1

(1)

538

H.P. Gros et al. / Fluid Phase Equilibria 116 (1996) 537-544

2.1 Hard Sphere and Dispersive Terms.

The repulsive hard sphere and attractive dispersive terms are the same as in the original GC-EOS model (Skjold-Jorgensen, 1984,1988). The repulsive term is described by the Mansoori and Leland (1972) expression for hard spheres and requires only one pure component parameter, namely the hard sphere diameter (d). This is obtained from vapor pressure data and assumed temperature dependent following the generalized expression proposed by Fermeglia and Mollerup (1984) d = 1.06565dc(1.-. 12 exp(-2T c / 3T)).

(2)

The dispersive part is a group contribution version of a density dependent local composition expression (NRTL). The pure group parameters are the group surface qi and the dispersive energy between like groups *

,

8t

gii = gii(1.+gii(T/Ti - 1 . ) + g~i ln(T/Ti*)) -

(3)

Ti* is an arbitrary but fixed temperature for group i. The binary parameters are the asymmetric non randomness factor aij and the dispersive energy between unlike groups gij = k i j ~ f i gjj -

kij= k~

(1.+klj ln(T

(4)

/Ti;))

(5)

is a symmetric, temperature dependent, binary interaction parameter and

Ti~=(~*+T;)/2 .

(6)

2.2 Association Term.

The Helmholtz function due to association is calculated with a modified form of the expression used in the SAFT equation (Chapman et al., 1990; Huang and Radosz, 1990,1991). In the present work this expression is formulated in terms of associating groups. Therefore, A ass°¢ / R T = .

NGA ,V ( - (k,i) ~ nilk~__l[lnX i=l . .

.

X (k'i) 2 .

!M. +

2

1

(7) ~k

In this equation NGA represents the number of associating groups, n i the total number of moles of associating group i, X( k,0 the mole fraction of group i not bonded at site k and M i the number of association sites assigned to group i. The number of moles of the associating group i is

m=l

(8)

where yassoc(i,m) represents the number of associating group i in molecule m and n m the total number of moles of molecule m; the summation includes all NC components in the mixture. The mole fraction of group i not bonded at site k is determined by X (k'i)= 1 + 'j--~l ~--'~p; x(l'J)A(k'i'l'J) 1=1

' (9)

where the summation includes all associating groups and sites. X(k,i) depends on the molar density of the associating group j

539

H.P. Gros et al. / Fluid Phase Equilibria 116 (1996) 537-544

ej = n / V ,

(10)

and on the association strength between site k of group i and site 1 of group j A (k,i,l,j)= /l. (k,i,l,J)[exp(8 (k,i,i,j)/kT)-1].

(11)

The association strength is a function of the temperature T(K) and the characteristic association parameters 8 and 1<. These parameters have been proposed for a square well model of specific interactions between the two sites k and I (Chapman et al., 1990). The parameter 8 characterizes the association energy (well depth) and (cm3/mol) the associating volume (well width). The energy of association, and hence the association strength between two like-sites from the same or different associating groups (for example the interactions oxygenoxygen and hydrogen-hydrogen), are set equal to zero. Compared to other expressions proposed in the literature (Chapman et al., 1990; Huang and Radosz, 1990,1991; Suresh and Elliot, 1992) for the association strength, Eq.(11) does not include a radial distribution function. The simpler expression for A used in this work allows a straightforward group contribution formulation for the association term (Gros et al., 1994). The association contributions to the compressibility factor (Zass°c) and fugacity coefficients of component q in a mixture (¢qasSOC), are obtained from the partial derivatives of Aass°c with respect to volume V and number of moles of component q (nq). respectively =---

r~/~/

~

~,0 (12)

assoc

lnX(ka)

Mi]

*[Mif k=l 1.

i=l

L

1

1 ) ( OX(k'i)Onq T,V,n, eq

(13)

where n is the total number of moles. The final expressions for X(k, i) (Eq.(9)) and the partial derivates of X(k,i) (Eqs.(12) and (13)) depend on the number of associating groups and bonding sites assigned for each group. In the present work, we have considered that all association effects in single component, binary or multicomponent mixtures containing alcohols and water are due to the hydrogen bonding between the O(1) and I-1(2) sites of an unique associating OH group(i), the same for all alcohols and water. The energy and volume association parameters for the nonzero hydroxyl site-site interactions are 8(1,i,2,i)=-8(2,i , 1,i)=_si and r(1,i,2,i)=r(2,i , 1,i)=ri" Hence A(1,i,2,i)=- A (2,i,l,i)=A i represents the association strength between the unlike sites 1 and 2 in group i. Under the assumption of a solution with a unique associating group with two bonding sites (only self association is considered), Eq.(9) can be directly solved for the non-bonded molar fraction of group i

[

-1+

X (1,i) = X (2,i) = X i --

1÷ 2pi A i

(14)

and consequently

¢.×i/ t OV JT,n

=

X i' "P i A i V + 2n~AiX i

Oxi /

~ n q )T,V,_rlr~,q

=

, (i,q)

(15) X?Ai

--YaSSOOV + 2n*AiX i " (16)

540

H.P. Gros et al. / F l u i d Phase Equilibria 116 (1996) 537-544

TABLE 1. Energy r/k and Volume ~< Association Parameters for the common hydroxyl group. Associating Group OH

e,'k (K) 2700.

K (em3/mol) .8621

Type of Data Non bonded mole fraction of associating molecules at liquid like densities

Refermce Chapman et al. (1990)

TABLE 2. Pure Group Energy Parameters. Group

Ti*

qi

8*ii

8'ii

$"ii

CH3OH CH2OH

512.6 512.6

1.4320 1.1240

816116. 787954.

-0.3877 -0.3634

0.0

Pvap (1)

0.0

Pvap l-alcohols (1)-VLE 1-alcohols-alkm~es (2,3,4,5)

0.0 0.0

Pvap 2-alcdaols (1)-VLE 2-alcohols-alkmaes (6,7) Pvap (1)

o.o o.o

Pvap (1) I'vap (1)

0.0

Pvap (1)

0.0

Pv~p (1)

CHOH

512.6

0.9040

787954.

-0.3634

H20

647.3

0.8660

1383953.

-0.2493

CO2 Propane Prupylene Isobutane

304.2 369.8 364.8 408.1

1.2610 2.2360 2.024 3.0840

531890. 436890. 478300. 326400.

-0.5780 -0.4630 -0.4415 -0.4896

Type of Data mad Referaace

TABLE 3. Binary Interaction and Non randomness Parameters. Group i H20

CH3OH CH2OH

CHOH

Group j CH3 CH2 (WS)CH3 (WS)CH2 CH3OH CH2OH CHOH Propmae Propylaae CO2 CO2 Propmae CH3/(WS)CH3 CH2/(WS)CH2 Propane lsobtazme CO2 CH3/(WS)CH3 CH2/(WS)CH2 Propmae Isobutane

kij* 0.65 0,62 0.60 0.65 1.08 0.92 0.96 0.60 0.73 1.10 1.07 0.90 0.85 0.85 0.87 0.88 1.10 0.85 0.85 0.83 0.83

kij' 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

aij 15.00 16.50 1.20 1.20 -1.10 6.35 6.04 22.25 0.42 -1.98 -6.53 0.05 11.90 11.90 11.90 3.53 -7.5 5.6 5.6 5.6 5.3

c~ji 0.50 0.70 1.20 0.80 -1.50 0.70 1.10 0.49 0.42 -0.50 -4.12 1.60 1.62 1.62 1.89 1.77 -6.5 0.85 0.85 0.85 0.16

Type of Data mad Rd'erence Mutual Solubilities H20-n-alkmaes (8) Mutual Solubilities H20-n-alkmaes (8) Mutual Solub'tlities (8) / VLE (9,10A 1) H20-l-alcohols Mutual Solubilities (8) / VLE (9,10,11) H20-1-alcohols VLE H20-CH3OH (12) VLE H20-l-alcohols (9,10,11) VLE H20-2-alcohols (10,13,14) VLLE H20-Propmae (15) VLLE H20-Propylaae (16) VLLE H20-CO2 (17,18) HPVLE CH3OH.-CO2 (19,20) HPVLE CH3OH-Propme (21 ) Pvap 1-alcdaols (1)-VLE 1-alcohols-alk~aes (2,3,4,5) Pvap 1-alcohols (1)-VLE 1-aleohols-alkmaes (2,3,4,5) HPVLE 1-aleohols-Propmae (22,23) I-I]~VI,,E1-alcehols-Isobutmae (22) HPVLE l-alcoholsq202 (19,24) Pvap 2-alcohols (1)-VLE 2-aledaols-alkmaes (6,7) Pvap 2-alcohols (1)-VLE 2-alcohols-alkmaes (6,7) HPVLE 2-alcohols-Propmae (25,26) HPVLE 2-alcohols-Isobutane (27)

(1) T.E.Daubert, R.P.Dannex, Physical aad Thermodynamic Properties of Pure CTaemicals,Data Compilatioa, Taylor & Fraacis,Bristol, PA,1989. (2) H.Sugi, T.Katayama, J. Cheazz Eng. Japma, 11 (1978) 167. (3) M.D.Pena, D,R.Chaaa, An. Quire, 66 (1970) 747. (4) T.Hlakl, K.Yam~ao, K.Kojima, J. Chea~ Eng Data, 37 (1992) 203. (5) S.Govindasxvamy, A. Andiappma, S. Lak~hmanaa, J. Chem. Eng. Data, 21 (1976) 366. (6) H.C. V ~ Ness, C.A- Soczel, G.L Peloquin, R.L. Machado, J. Chem. Eng Data. 12 (1967) 217. (7) D.O.Hmasan, M.Van Winkle, J. Chem. Eng. Data, 12 (1967) 319. (8) J.M. Sorensea, W. Arlt, Dedaema Chemistu¢ Data Series, Vol V, Part 1, Schon & Wetzel, Frankfurt, F.R.Germ~y,1979. (9) H. Otatki, F.C. Williams, Chem. Eng. Prog. Syrup Set., 49 (1953) 55. (10) F.Barr-David, B.F. Dodge, J. Chem Eng. Data, 4 (1959) 107. (11) G.A. Ratcliff, K.C. Chao, C~m. J Chem. Eng., 47 (1969) 148. (12) V.O.Maripuri, G.A.Ratclif, J. Chea~ Eng. Data 17 (1972) 366. (13) A.Wilsoa, E.L.Simons, Ind. Eng. Chem., 44 (1952) 2214. (14) E.Sada, T.Morisue, J. Chem. Eng. Japan, 8 (1975) 191. (15) RKobayadai, D.L.Katz~ Ind. Eng. Chem,, 45 (1953) 440. (16) C.C.Li, J.McKetta, J. Chem. Eng. Data, 8 (1963) 271. (17) R.Wiebe, V.L.Gaddy, J. An1 Chem. Soc., 62 (1940) 815. (18) R.Wiebe, V.LGaddy, J. Am. Chem. Soc., 63 (1941) 475. (19) K.Suzafld , H.Sue,/vLItou, R.Smith, H.Inomata, K.Arai, S.Saito, J. Che~rz Eng. Data, 35 (1990) 63. (20) K.Ohgaki, T.Katayama, J. Cheal Eng. Data, 21 (1976) 53. (21) F. GalivelSola~iouk, S.Laugi~, D.Ridaoa, Fluid Phase Equilibria, 28 (1986) 73. (22) M.Zabaloy, H.Crros, S.Bottiui, E.Briguole, J. Chem. Eng. Data, 39 (1994) 214. (23) H.Horizoe, T.Taaimoto, I.Yamamoto, J. Chem. Frog Japma, 26 (1993) 482. (24) D.W.Jennlngs, R.Lee, A~T~a, J. Chea~ Eng. Data, 36 (1991) 303. (25) M.Zabaloy, G.Mabe, S.Bottini, E.A.Bri~aole, J. Chem. Eng. Data, 38 (1993) 40. (26) M~Zabaloy, H.Gros, S.Bottiui, E.A~Bri~aole, VII Congreso Argmtino Fco.Qca., Mar del Plata, Argentina, 1993. (27) Id_Zabaloy, G.Mabe, S.Bottini, E.A.Brignole, Fluid Phase Equilibria, 83 (1993) 159.

541

H.P. Gros et al. / Fluid Phase Equilibria 116 (1996) 537-544

3. Model Parameters. We have defined a unique hydroxyl group OH to represent the effect of hydrogen bonding in water and alcohol molecules. The values for the energy ~ and volume ~: association parameters corresponding to the hydroxyl group are shown in Table 1. These were fitted in such a way that similar values to the ones reported by Chapman et al. (1990) were obtained for the molar fraction of non-bonded associating group as a function of temperature. Water and methanol at liquid like densities were the hydrogen bonding molecules considered. On the basis of the associating parameters, new dispersive pure energy parameters (gii) have been obtained for the associating groups (CH2OH, H20, etc.) and revised binary interaction parameters (k.jl and CX.lj.) have been estimated for pairs of groups in which one or both depict associating, behavior. We have kept the original definition of groups and the values for the reference temperature T i and group surface area qi proposed by Skjold-Jorgensen (1988). The determination of the dispersive pure group energy parameters for water, methanol, carbon dioxide, propane and isobutane (all considered as single groups in the dispersive contribution) was based on pure component vapor pressure information. For primary and secondary alcohols, alcohol (CH2OH, CHOH) and alkane (CH3, CH2) groups are present in a given molecule. Therefore, pure component vapor pressure information of alcohols and binary vapor-liquid equilibrium data of alcohols with n-alkanes were used to determine simultaneously the dispersive pure energy for the alcohol group, and the binary interaction and non randomness parameters between alcohol and alkane groups. Binary parameters H20-Alcohol groups were obtained from the fitting of low and high pressure VLE data for binary alcohol-water mixtures. The 'water soluble' (WS) alkane groups are used for alkane groups present in a water soluble organic molecule (e.g. alcohols). The use of these groups ensures a correct description of liquid-liquid mutual solubilities between water and alcohols. This additional experimental information was used to obtain H20-(WS)Alkane binary parameters. Binary liquid-liquid mutual solubilities between water and n-alkanes were used to adjust the interaction parameters H20-Alkane. H20-propane/propylene/CO2 binary parameters were obtained fitting binary VLL experimental data. Those for Alcohol-propane/ isobutane/CO 2 were obtained from recent high pressure VLE data. The original parameter values were used for all non associating groups and the interactions between them. The pure group energy parameters are shown in Table 2. The binary interaction and non randomness parameters are given in Table 3 together with the references to experimental information. 4. Results and Discussion.

4.1 Correlation of Binary Phase Equilibria. The GCA-EOS model has been used to correlate VLE data of binary systems alcohol-hydrocarbon/gas. Average deviations in pressure and composition vapor phase are reported in Table 4 for each system. The experimental data are correlated with acceptable accuracy. TABLE 4. GCA-EOS binary VLE correlation.

BinarySystezn

Press.(bar)

Temp.(K)

Azectrope

% AADa Press.

% AAD y(1).

Ref~rmce b

CO2( 1)-MOdamaol(2) Prop~me( 1)-Methanol(2 ) Prop ~me(1)-Ethanol( 2 ) Prop~me(1 )-2-Butanol Isobutane( 1)-Fahmaol(2 ) Isobutane( 1)-Prop~mol(2 ) Isobutane(1 )-2-Prop~mol(2 ) Hex~me(1)-Ethmaol(2 ) Hexmae(1)-2-Btaanol(2) HepUme(1)-Prop~aol(2) Heptmae( l~)-2-Propanol(~2~)

7.-80. 3.-45. 13.-40. 10.-40. 4.-16.5 4.-16.5 4.-27.5 0.2-0.5 0.4--0.8 0.3-0.4 0.2-0.3

298.-313 313.-373. 325.-375. 330.-370. 310.-365. 320.-365. 320.-390. 313. 333. 333. 320.

no no no no yes no no yes yes yes yes

8.0 7.5 7.1 3.6 2.9 11.0 4.0 1.8 3.4 1.0 3.5

0.24 1.8 0.7 0.2 0.9 1.5 2.3 2.0 4.6 1.0 4.0

(20) (21) (22) (26) (22) (22) (27) (2) (7) (3) (6)

a % AAD = average absolute deviation b From Tables 2 and 3

Simultaneous correlation of VLE and LLE is a difficult test for the GCA-EOS. Figures 1 and 2 show HPVLE correlation for ethanol-water and predicted mutual solubilities of n-alcohols-water compared with

H.P. Gros et al. / F l u i d Phase Equilibria 116 (1996) 537-544

542

experimental data, respectively. The agreement is quite good considering the wide range of pressure, temperature and alcohol molecular weights covered with a single set of association and dispersive binary interaction parameters. 1.00E+00 100 T = 523 K o

i[

=

1.OOE-O1

j

~

1.00E-02

N

1.00E-03

J

O

0

l

10 ~r~£


T = 423 K I

i

1.00E-04

~

1.00E-05

I i

: 1

0

0.5

1

3

,

i

I

*

I

4

5

6

7

8

Number of Carbon Atoms

x (1) - y (1) F i g l . I-IPVLE Ethanol (1)-Water (2); - David and Dodge (1959).

\\

GCA-EOS; (o) Barr-

Fig,2. Binary Mutual Solubilities Watex(1)-,n-Alcohols(2); T = 2 9 8 K ; - GCA-EOS; Expeximc:ntal Data: • (1) in (2),0 (2) in (1), Sorms~n and Arlt (1979).

4.2. Predictions of Ternary Phase Equilibria l~ulautis et al. (1981) have reported tie lines for the system water-ethanol-carbon dioxide under supercritical extraction conditions. Table 5 gives a comparison between these data, GC-EOS and GCA-EOS predictions. A better description of K values for water and ethanol is achieved with the association model. T A B L E 5. Experimental and calculated K values for water(1)-ethanol(2)-CO2(3 ) at 308 K. Data by Paulaitis et al. (1981) Aqueous phase

102 K 1

x (1)

exp.

GC-EOS

GCA-EOS

exp.

GC-EOS

GCA-EOS

exp.

GC-EOS

GCA-EOS

P=103 bar 0.944 0.032 0.852 0.118 0.677 0.249

0.42 0.82 1.7

0.40 0.48 0.60

0.53 1.20 2.00

0.16 0.18 0.18

0.23 0,19 0.13

0.16 0.17 0.12

0.41 0.32 0.13

0.45 0.36 0.20

0.36 0.24 0.12

P=138 bar 0.943 0,032 0.851 0.118 0.691 0.238

0,42 0.71 2.2

0,50 0.56 0.72

0.70 1.70 3.50

0.16 0.17 0.23

0.33 0.24 0.16

0.18 0.25 0.23

0.40 0.32 0.13

0.41 0.35 0.19

0.35 0.25 0.12

x (2)

K2

10"~K3

The near critical fluid solvents are to some extent soluble in the liquid phase. In Fig. 3 the experimental CO 2 solubilities reported by Kuk and Montagna (1983) and Horizoe et al. (1993) are compared with predicted values using the GCA-EOS model. The predictions are in good agreement with the experimental data over the entire composition range. Brignole et al. (1987) have proposed the use of light hydrocarbons (propane, isobutane) at near critical conditions as extraction solvents for the recovery of alcohols from aqueous solutions. Based on that, Horizoe et al. (1993) have reported experimental liquid-near critical fluid data for the system water-ethanol-propane. The experimental distribution coefficients for ethanol mad water are compared with predicted values using the GCAEOS in Figs. 4 and 5. It can be seen that both coefficients are predicted with acceptable accuracy. The GC-EOS model has failed to give accurate predictions of water relative volatilities in alcoholwater-light hydrocarbon ternary mixtures. In Fig. 6 the experimental data reported by Zabaloy et al. (1992) for the system water-2-propanol-propane are compared with predicted values using the GC-EOS and GCA-EOS models. The comparison indicates that the values predicted by the associating model are in better agreement with the experimental data.

H.P. Gros et al. / F l u i d Phase Equilibria 116 (1996) 537-544

0.2

1.2

/

P, O

=

0.15

/ ,

I.L

/

0

/

/

/

[

~-.

T = 403 K

/

08 -;~--

/

/ // ~1~I¸ /

0.1

0

/

543

~5

0.6 0.4

/

/ []

0.05

[]

'~'

0

' c - - ~-!:~-. . . . . _ J ..... : ~ -- -

I

U-I

-_

T. 4K ,

0 0

0 0

0.2

0.4

0.6

0.2

0.4

0.6

Ethanol Mole Fraction in Aqueous Phase (Propane Free Basis)

Ethanol Mole Fraction Fig, 3. Solubility of CO2 in ethanol-water mixtures; - - GCA-EOS; (-) Kuk and Montagna (1983) at 333 K and 200 bar, ( n ) Horizoe et al. (1993) at 383 K mad 100 bar.

0.3

Fig, 4. Ethanol Distribution Coefficient between Water and Propane; - - GCA-EOS; (o I-I) Hofizx~ et al. (1993); Pressure = 99 bar.

._>

.o

,° I

.~ ~ 0.2

f3 • (~

13¸.¸

T = 403 K

6>

~ u ~ 0.1

0

~:_:-i.-.~:; 0

0.2

-

I

T =384 K 0.4

0.1 0.6

Ethanol Mole Fraction in Aqueous Phase (Propane Free Basis)

Fig,

0.8

5. Water-ethanol-propane ternary, system at near critical conditions, Water Distribution Coefficient; --K}CA-EOS; (o, ra) Horizoe et al. (1993); Pressure = 99 bar.

[]

...................... 0.5 0.6 0.7 0.8

0.9

1

Propane Mole Fraction in Liquid Phase Fig 6. Water(1)/Propane(3) relative volatility in mixtures with 2propanol(2) at 353 K mad x2/xl = 10; - - GCA-EOS predictions;-GC-EOS predictions; (r'l) Experimental Ternary Data by Zabaloy et al. (1992); (*) Experimental Binary Data by Kobayashi and Katz (1953).

References

A. Anderko, Fluid Phase Equilibria, 50 (1989) 21. F. Barr-David, B. F. Dodge, J. Chem. Eng. Data, 4 (1959) 107. E. A. Brignole, S. Skjold-Jorgensen, Aa. Fredenslund, Ind. Eng. Chem. Res., 26 (1987) 254. W. G. Chapman, K. E. Gubbins, G. Jackson, M. Radosz, Ind. Eng. Chem. Res., 29 (1990) 1709. M. Ferme~ia, J. Mollerup, Paper D14, CHISA, Prague, 1984. H. P. Gros, M. S. Zabaloy, S. B. Bottini, E. A. Brignole, 3rd. International Symposium on Supercritical Fluids, Strasbourg, France, 1994. H. Horizoe, T. Tanimoto, I. Yamamoto, Y. Kano, Fluid Phase Equilibria, 84 (1993) 297. S. H. Huang, M. Radosz, Ind. Eng. Chem. Res., 29 (1990) 2284. S. H. Huang:, M. Radosz, Ind. Eng. Chem. Res., 30 (1991) 1994. G. D. Ikonomou, M. D. Donohue, Fluid Phase Equilibria, 39 (1988) 129. R. Kobayashi, D. L. Katz, Ind. Eng. Chem., 45 (1953) 440.

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