Modelling solubility of solids in supercritical fluids using fusion properties

Fluid Phase Equilibria 158–160 Ž1999. 491–500

Modelling solubility of solids in supercritical fluids using fusion properties S. Garnier a , E. Neau a

a, )

, P. Alessi b , A. Cortesi b , I. Kikic

b

Laboratoire de Chimie Physique de Marseille, Faculte´ des Sciences de Luminy, case 901, 163 AÕenue de Luminy, 13288 Marseille Cedex 09, France b Dipartimento di Ingegneria Chimica, dell’Ambiente e delle Materie Prime (DICAMP), UniÕersita` di Trieste, Piazzale Europa 1, 34127 Trieste, Italy Received 31 March 1998; accepted 23 September 1998

Abstract The modelling of solid solubilities in supercritical fluids is usually performed by means of thermodynamic models based on cubic equations of state together with the use of correlations for estimating the solid properties. However, it was shown in the literature, that the error in sublimation pressure, which is very low for high molecular weight compounds, is in many cases responsible for large deviations between experimental and calculated solubilities. In this work, the sublimation pressure of solids is estimated by using experimental fusion data and liquid–vapour equilibrium properties obtained from an equation of state ŽEOS.. The results provided by this method are compared with those obtained using sublimation pressures from literature. It is shown that this method allows satisfactory solubility predictions when using a reliable EOS. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Equation of state; Solid–fluid equilibria; Supercritical fluids; Solubility data

1. Introduction The key property for processes using supercritical fluids is the solubility of low volatile components in supercritical gases. The optimisation of the processes can be performed only if the dependence of the solubility both on pressure and temperature can be accurately described. For this purpose, thermodynamic models based on cubic equations of state are usually considered together with the solid compound properties in the correlation of experimental data. However, for heavy components the sublimation pressure cannot be determined experimentally, so that this property is )

Corresponding author. Tel.: q33-4-91-829149; fax: q33-4-91-829152

0378-3812r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 Ž 9 9 . 0 0 1 5 1 - X

S. Garnier et al.r Fluid Phase Equilibria 158–160 (1999) 491–500

492

often estimated by empirical correlations. Neau et al. w1x showed that the sublimation pressure plays a dominant role in the correlation of solubility data and that, in many cases, the only way to obtain a reasonable calculation of these data is to consider the sublimation pressure as an adjustable parameter w2x, together with the binary interaction parameters k i j ; but, in these conditions, the fitted parameters are highly correlated and especially the k i j values cannot be correlated with respect to the molecular structure of the solid compound. In a previous work, Neau et al. w3x have shown that, in the case of high molecular weight compounds for which sublimation pressures cannot be measured, the most safe way to estimate them is to correlate experimental vapour pressure data through an analytical relation and to use normal fusion properties in order to settle the sublimation pressure equation with respect to temperature. When no experimental saturation pressures are available, which is the case for almost all heavy compounds, the authors proposed w3x to estimate them using an accurate equation of state ŽEOS. . The practical interest of this method is thus to require, besides the EOS, fusion property data which can be easily measured or found in the literature. In the case of compounds which may decompose before the melting point, fusion properties could always be estimated Ž as critical parameters. thanks to a group contribution method. In this paper, solubility data of solid compounds in supercritical fluids were correlated using sublimation pressures estimated by means of equations of state and fusion properties. Different EOS were considered for this purpose. Results yielded by this method are compared with those obtained using sublimation pressures from literature. Binary mixtures and ternary systems including two solid components in supercritical fluids were investigated.

2. Modelling of solubility data The solubility of a pure solid Žcomponent 2. in a supercritical fluid is estimated using the classical expression: y2 s

P2sub

Õ 2s

PF 2

RT

exp scf

Ž P y P2sub .

Ž1.

where, Õ 2s is the molar volume of the solid component Ž2. . In this work, the fugacity coefficient F 2scf is calculated by means of the Peng–Robinson EOS combined with different expressions for the attractive term aŽ T . and the covolume b; the sublimation pressure P2sub is estimated using the fusion properties of the solid component and the saturation curve derived from this EOS. 2.1. Equation of state The Peng–Robinson equations of state used in this work are the modified form ŽPRmr. proposed by Rauzy w10x and the one ŽPRmc. developed by Coniglio w6x. The general form is: Ps

RT y

aŽ T .

Õyb Õ 2 q 2 bÕ y b 2 where b is the covolume and aŽ T . the attractive term.

Ž2.

S. Garnier et al.r Fluid Phase Equilibria 158–160 (1999) 491–500

493

For the different equations, the expressions of b and aŽ T . for pure compounds are given by the following relations: . PRmr equation b s 0.07780

RTc Pc

,

a Ž T . s 0.45724 T

R 2 Tc2 Pc

C ŽT , v .

Ž3.

2

0.44507

ž ž / /

C ŽT , v . s 1 q m 1 y

Ž4.

Tc

m s 6.812553 Ž '1.12754 q 0.517252 v y 0.003737v 2 y 1 .

ž

2

Ž5.

/

. PRmc equation b s 1.56542V U ,

a Ž T . s a Ž T b . exp m1Ž 1 y TrT b .

0.4

y m 2 Ž 1 y TrT b .

0.5

Ž6.

where, aŽ T b . is the value of the attractive term aŽ T . at the normal boiling point T b , and: m1 s 1.8055m q 0.2189,

m 2 s y0.1111m q 0.0350

Ž7.

The Van der Waals volume V U ŽEq. Ž6.. is calculated using the group contribution volumes defined by Bondi w11x. The parameter m ŽEq. Ž 7.. is estimated with the group contribution method recently proposed by Trassy w7x for hydrocarbons, ethylenic and sulphured compounds. In this work the volume translation proposed by Peneloux et al. w12x, especially efficient for ´ correcting the liquid phase volume, was not used since it was shown previously w1x that, for the correlation of solid solubilities in supercritical fluids, this correction has a small influence. For mixtures, the classical Van der Waals mixing rules were used: as Ý

1r2 Ý yi y j Ž a i a j . Ž 1 y k i j . ,

i

b s Ý yi bi

j

Ž8.

i

2.2. Estimation of the sublimation pressure The sublimation pressure P sub of the solid was estimated, as described in a previous paper w3x, using the Clapeyron equation: ln

P sub

ž / Pt

D H sub sy R

ž

1

1 y

T

Tt

/

Ž9.

where Tt and Pt are the reference conditions chosen at the triple point of the pure component and D H sub is the sublimation enthalpy at this temperature, which can be expressed with respect to the fusion and vaporisation enthalpies as: D H sub s D H fus q D H vap

Ž 10.

Using the approximation that the triple point temperature Tt can be estimated by the normal fusion temperature, it is thus possible: to use experimental values of the normal fusion enthalpy in Eq. Ž 10.

S. Garnier et al.r Fluid Phase Equilibria 158–160 (1999) 491–500

494

and, from the EOS considered, to estimate the reference pressure Pt and the vaporisation enthalpy D H vap at this temperature. 3. Correlation of data As was shown previously w3x, the group contribution method used for estimating the EOS parameters is crucial for the prediction of sublimation pressures. Especially, the PRmc equation Ž Eqs. Ž6. and Ž7.. associated with the group contribution methods proposed by Avaullee ´ et al. w4,5x for the estimation of the normal boiling point and by Coniglio w6x and Trassy w7x for calculating m and b appeared to be superior to the PRmr equation ŽEqs. Ž3. – Ž5.. with the critical parameters obtained from the method of Constantinou and Gani w8,9x. Since the former group contribution methods w4–7x were only published for hydrocarbons, solubilities of solid hydrocarbon compounds in supercritical carbon dioxide and ethane were only considered in this work. The following schemes for correlating solubility data were considered: 1. the sublimation pressure P sub was taken from literature Žvalues are given in Table 1. ; 2. the sublimation pressure was estimated by means of an EOS using fusion properties given in Table 1. In each case, the equations of state used for the solid compound were: 1. the PRmr equation using the critical parameters from Constantinou and Gani w8,9x; 2. the PRmr equation with the critical parameters given by Avaullee ´ et al. w4x; 3. the PRmc equation with T b estimated by Avaullee ´ et al. w5x and with m and b values given by Trassy w7x. The values of the EOS parameters for solid compounds are given in Table 2. In all cases, the PRmr equation with literature EOS parameters was used for carbon dioxide and ethane.

Table 1 Literature data for the solid molar volume, the sublimation pressure, the molar fusion enthalpy and the fusion temperature Compounds

Õs Žcm3 moly1 .

P sub Žbar.

Ref.

D H fus ŽJ moly1 .

Tf ŽK.

Ref.

n-octacosane n-triacontane n-dotriacontane naphtalene 2,3-m-naphtalene 2,6-m-naptalene 2,7-m-naphtalene fluorene anthracene phenanthrene pyrene hexamethylbenzene triphenylmethane biphenyl perylene

489.40 522.20 555.00 110.00 154.70 139.23 136.80 139.30 142.60 151.00 158.50 152.70 240.90 131.00 340.40

eŽ67.83708y29 552.37r T . eŽ72.30058y31 811.83r T . eŽ76.76408y34 071.29r T . 10 Ž8.583y3733.9r T . 10 Ž9.0646y4302.5r T . 10 Ž9.4286y4419.5r T . eŽ21.80118y10 105.69r T . 10 Ž9.4286y4419.5r T . 10 Ž7.1464y4397.6r T . 10 Ž9.6310y4873.4r T . 10 Ž8.3946y4904.0r T . 10 Ž8.1336y3855.0rŽTy21.0.. 10 Ž9.7858y5228.0r T . 10 Ž9.4068y4262.0r T .

w23x w23x w23x w24x w25x w25x w19x w25x w25x w25x w25x w25x w25x w25x w26x

64 945.1 70 168.9 75 392.7 19 060.0 25 101.0 25 055.0 23 349.0 19 580.0 28 830.0 16 460.0 17 110.0 20 640.0 20 920.0 18 800.0 32 580.0

337.65 338.48 342.34 353.50 377.95 383.32 368.81 387.95 489.70 373.70 424.35 438.70 365.60 344.15 551.29

w27x w27x w27x w28x w28x w28x w28x w28x w28x w28x w28x w29x w30x w31x w32x

S. Garnier et al.r Fluid Phase Equilibria 158–160 (1999) 491–500

495

Table 2 EOS parameters for the heavy component, to be used with: Ž1. the PRmr equation ŽEqs. Ž4. – Ž6.. using the method of Constantinou and Gani; Ž2. the PRmr equation ŽEqs. Ž4. – Ž6.. using the method of Avaullee ´ et al.; Ž3. the PRmc equation ŽEqs. Ž7. – Ž9.. using the method of Avaullee ´ et al. for T b and Trassy for m and b Compounds n-octacosane n-triacontane n-dotriacontane hexamethylbenzene naphtalene 2,3-m-naphtalene 2,6-m-naphtalene 2,7-m-naphtalene phenanthrene anthracene pyrene triphenylmethane biphenyl fluorene perylene

Ž1.

Ž2.

Tc ŽK.

Pc Žbar.

823.2 836.2 848.3 705.9 739.0 769.0 769.0 769.0 826.5 826.5 879.6 841.2 760.5 813.4 921.4

7.19 6.64 6.64 22.73 38.18 28.22 28.22 28.22 30.85 30.85 27.01 21.83 32.26 33.27 24.53

Ž3.

v

Tc ŽK.

Pc Žbar.

v

T b ŽK.

m

b Žcm3 .

1.190 1.262 1.332 0.538 0.320 0.410 0.410 0.410 0.426 0.426 0.406 0.621 0.410 0.365 0.548

823.3 846.9 859.5 729.3 767.0 785.1 785.1 785.1 899.3 880.7 950.5 860.5 752.5 809.0 1053.8

5.81 5.31 4.93 23.58 41.82 30.77 30.77 30.77 29.10 27.95 27.73 18.46 32.41 29.65 24.19

1.117 1.168 1.217 0.442 0.296 0.393 0.393 0.393 0.501 0.476 0.547 0.714 0.395 0.420 0.696

704.9 723.1 739.9 520.7 501.7 542.9 542.9 542.9 629.1 621.2 669.3 646.6 513.1 553.0 760.8

1.2415 1.2842 1.3201 0.7806 0.5688 0.6646 0.6646 0.6646 0.6079 0.6079 0.6416 0.8396 0.6636 0.7211 0.6671

268.99 287.75 306.52 105.70 67.83 88.28 88.28 88.28 91.03 91.03 99.99 132.33 84.08 88.83 123.47

For binary mixtures, the interaction parameter Ž Eq. Ž8.. between the SCF and the solid compound was tuned to experimental solubility data at different temperatures, assuming for simplicity that k 12 is independent on temperature. For ternary mixtures, the solubilities y 2 and y 3 of the two solids in the supercritical fluid were calculated with Eq. Ž1., assuming that the two solids are not miscible, as described in the literature w18,19,22x. The fugacity coefficients of the two solids F 2scf and F 3scf in the supercritical phase were estimated with the EOS using the binary interaction parameters k SCFrsolid previously determined; the interaction parameters k 23 between the two solids were set equal to zero.

4. Results 4.1. Binary mixtures The results obtained with the different methods for the modelling of solubility data in supercritical fluids Žcarbon dioxide or ethane. are reported in Table 3. For each SCF, the global deviation, taking into account the total number of experimental data for each binary system, is also indicated. Concerning the use of sublimation pressures giÕen in the literature Žmethod I. , the following can be noted. . In the case of the solid aromatic compounds considered herewith Žwhich have less than twenty carbon number. similar deviations between experimental and calculated solubilities can be obtained with the three methods, whatever the supercritical fluid.

496

P sub from literature ŽI. Ž1.

Ž2. D y2 Ž%.

k 12 CO2 r solid (2) n-octacosane hexamethylbenzene naphtalene

biphenyl 2,3-m-naphtalene 2,6-m-naphtalene 2,7-m-naphtalene fluorene anthracene

P sub from EOS and fusion ŽII.

0.0516 0.0663 0.0985 0.0995 0.1001 0.0816 0.0906 0.0917 0.0772 0.0908 0.0624 0.0650 0.0669 0.0731

64.28 14.12 7.83 22.46 1.85 15.73 15.37 6.96 40.74 13.44 15.10 17.61 19.67 6.80

k 12

0.0377 0.0617 0.1122 0.1131 0.1128 0.0647 0.0968 0.0973 0.0775 0.0962 0.0843 0.1407 0.1419 0.1413

Ž3. D y2 Ž%. 84.78 14.27 12.63 25.71 3.93 14.51 17.34 7.17 41.37 17.11 24.49 30.32 35.64 13.88

Ž1. D y2 Ž%.

k 12

0.0855 0.0812 0.1157 0.1166 0.1157 0.0622 0.1055 0.1053 0.0755 0.1040 0.0859 0.1096 0.1073 0.1167

21.30 12.55 14.54 27.29 4.87 17.15 21.05 10.70 42.84 23.61 18.73 20.18 16.95 8.54

k 12

Ref. NT NP

Ž2. D y2 Ž%.

k 12

Ž3. D y2 Ž%.

0.0763 0.1547 0.1036 0.1046 0.1052

69.19 44.45 7.20 21.13 1.68

0.0657 0.1617 0.0926 0.0936 0.0931

86.35 49.19 14.81 29.97 4.65

0.1044 0.1017 0.0897 0.1027 0.1348 0.2241 0.1985 0.1878

16.18 7.33 39.30 11.19 23.57 52.51 53.68 21.85

0.1006 0.0972 0.0769 0.0979 0.1209 0.1374 0.1440 0.1410

18.14 7.48 41.65 17.14 18.02 31.84 36.72 16.47

k 12

0.1057 0.1342 0.0893 0.0904 0.0891 0.1110 0.0938 0.0899 0.0551 0.0897 0.1171 0.1337 0.1366 0.1415

D y2 Ž%. 24.62 20.08 17.33 33.02 5.84 17.21 22.95 14.01 45.65 27.20 11.35 20.59 20.62 8.82

w13x w14x w15x w16x w17x w16x w18x w18x w19x w19x w14x w14x w22x w20x

4 2 1 1 1 2 3 3 2 2 3 2 2 3

45 20 9 9 9 13 15 15 8 10 23 19 11 88

S. Garnier et al.r Fluid Phase Equilibria 158–160 (1999) 491–500

Table 3 Binary mixtures: correlation of solubility data of solids in a supercritical fluid. Comparison of the k 12 fitted values and the mean deviation on the solubility D y 2 Ž%. using the sublimation pressure from literature ŽI. or estimated from the EOS and fusion properties ŽII., and different equations of state: Ž1. PRmr equation with critical values of Constantinou and Gani, Ž2. PRmr equation with the critical values of Avaullee ´ et al., Ž3. PRmc equation with the normal boiling point of Avaullee ´ et al. and m and b values from Trassy

phenanthrene

triphenylmethane pyrene

0.0773 0.0629 0.0692 0.0717 0.1066 0.0685 0.0690

perylene Global

triphenylmethane Global

0.1685 0.1559 0.1607 0.1595 0.1528 0.1724 0.1705

16.45 y0.0220 y0.0186 y0.0189 0.0262 0.0439 0.0093 0.0422 0.0164 0.0629

44.58 24.19 39.12 18.22 21.50 9.53 34.59 17.76 18.04 24.09

32.62 7.98 15.07 11.46 36.66 34.06 14.73

0.1339 0.1173 0.1232 0.1258 0.1420 0.1257 0.1273

23.67 y0.0272 y0.0271

66.94 64.10

0.0060 0.0558 0.0867 0.1457 0.1191 0.1244

16.33 26.69 13.01 41.29 16.28 17.34 27.28

30.83 19.26 9.38 15.26 25.75 26.52 10.74

0.2785 0.1460 0.1536 0.1508 0.1222 0.3986 0.1961 0.2967

91.77 6.46 20.64 12.33 16.96 95.27 41.22 19.85 35.07

0.0975 0.0877 0.0935 0.1000 0.0939 0.1084 0.1123 0.18512

20.76 22.66 14.18 9.07 24.30 29.10 11.77 14.01 24.08

0.1114 0.0937 0.1013 0.1096 0.1117 0.1253 0.1269 0.2389

30.14 25.80 16.28 17.88 34.73 26.63 10.89 18.66 17.5

w14x w18x w20x w21x w14x w14x w20x w20x

3 3 3 1 2 3 2 2

21 15 86 7 13 22 96 19

0.0222 0.0299 0.0285

50.91 33.12 42.36

0.0225 0.0344 0.0362

74.18 74.86 78.19

0.0193 0.0285 0.0276

35.62 40.84 42.13

0.0498 0.1280 0.1412 0.1042 0.0803

20.63 15.65 45.37 9.74 13.76 25.42

0.0329 0.0857 0.0619 0.0455 0.0600

29.64 16.74 28.52 19.80 20.05 36.08

0.0274 0.0781 0.0571 0.0471 0.0522

32.32 13.93 22.79 28.64 30.15 26.18

w23x w23x w23x w24x w14x w14x w18x w14x w14x

1 2 3 2 1 3 3 2 2

6 10 16 10 6 21 15 11 12

15.27 y0.0222 y0.0196 y0.0230 0.0014 0.0584 0.0526 0.0873 0.0731 0.0897

29.46 40.69 46.64 20.24 28.49 13.57 28.09 26.99 25.13 28.11

cal . exp x 2 41r2 The objective function used for this purpose was: D y 2 Ž%. s Ž10 2 r NP .Ý i wŽ y 2exp . i y y2 i r y2 i

S. Garnier et al.r Fluid Phase Equilibria 158–160 (1999) 491–500

C2 r solid (2) n-octacosane n-triacontane n-dotriacontane biphenyl naphtalene anthracene phenanthrene

25.92 13.34 6.12 6.77 17.24 29.49 10.04

497

S. Garnier et al.r Fluid Phase Equilibria 158–160 (1999) 491–500

498

Table 4 Ternary mixtures: prediction of solubility data of two solids in a supercritical fluid using method ŽII-3.; the sublimation pressure is estimated from the EOS and fusion properties, and the PRmc equation is used with the normal boiling points of Avaullee ´ et al. and m and b values from Trassy SCF CO 2 CO 2 CO 2 CO 2 CO 2 CO 2

Solid Ž2. 2,6-m-naphthalene 2,3-m-naphthalene phenanthrene phenanthrene phenanthrene phenanthrene

Solid Ž3. 2,7-m-naphthalene 2,6-m-naphthalene naphthalene 2,3-m-naphthalene 2,6-m-naphthalene anthracene

k 12 0.0899 0.0938 0.1114 0.1114 0.1114 0.1114

k 13 0.0897 0.0899 0.0904 0.0938 0.0899 0.1337

D y 2 Ž%. 34.00 15.14 20.04 20.20 20.12 28.94

D y 3 Ž%.

Ref.

NT

NP

32.92 21.48 15.52 26.71 17.39 11.70

w19x w18x w18x w18x w18x w22x

2 2 1 2 1 2

12 18 9 10 5 10

. For the n-paraffins Ž n-C 28 in CO 2 or n-C 28 , n-C 30 and n-C 32 in n-C 2 . larger deviations are observed, especially when using the PRmr equation both with models Ž 1. and Ž2.. This result may be explained by the doubtful extrapolations proposed by the authors w23x for the sublimation pressure of heavy n-paraffins. Method II proposed for estimating sublimation pressure from EOS and fusion properties should be considered as an alternative for correlating solubility data of solids in SCF when no experimental data are available Žas in the case of perylene.. Results reported in Table 3 show the following. . With the PRmc model Ž3. and for all components results are comparable to the one obtained when using P sub from literature. This is not the case of the PRmr equation Ž models 1 or 2. which can lead to deviations greatly increased Žlike for phenanthrene or pyrene in CO 2 .. This result is due to the fact, already mentioned, that the PRmr equation leads to less satisfactory predictions of sublimation pressures than the PRmc model; it can also be noted that this effect is enhanced for hydrocarbon mixtures with CO 2 which are always more difficult to represent with a very simple k i j model. . The solubility of perylene in SCF carbon dioxide can be predicted with a precision comparable to the one obtained for the other solids in the same fluid.

Fig. 1. Solubility of solids in supercritical CO 2 at T s 308.15 K: Ža. phenanthrene, Žb. naphthalene. Experimental data: q s pure component in CO 2 . I s component in the mixture CO 2 –phenanthrene–naphthalene. Calculated data using PRmc with P sub from fusion properties and EOS Žmethod II-3.: pure component in CO 2 . P P P component in the mixture CO 2 –phenanthrene–naphthalene.

S. Garnier et al.r Fluid Phase Equilibria 158–160 (1999) 491–500

499

4.2. Ternary mixtures For ternary mixtures including two heavy solids in a supercritical fluid a crucial point is to know whether or not a predictive method should be able to reproduce the enhancement effect of the solubilities observed when mixing given solid components. In many cases one of a compound is more dissolved in the supercritical phase and reacts as an entrainer for the other solid component. Results obtained with the PRmc model ŽII-3. are given in Table 4. It can be shown that the predictions of the solubilities for ternary mixtures are satisfactory and in agreement with the results obtained for the corresponding binary systems with CO 2 . Furthermore, the modelling is able Ž Fig. 1. to predict the increased solubility of phenanthrene with naphthalene in CO 2 with respect to the one of the pure solid in CO 2 . It must be noted that the evolution of the solubilities with respect to pressure was more satisfactory predicted when using the PRmr equation Žmodel I-1. ; but results could always be improved by using quadratic mixing rules for the covolume.

5. Conclusion The study of heavy hydrocarbon solids in supercritical fluids has shown that, in the case where no experimental sublimation pressure data are available, solubilities can be predicted with a satisfactory precision using fusion properties and an appropriate EOS ŽPRmc. based on the group contribution methods developed by Avaullee ´ et al. w5x and Trassy w7x. The prediction of ternary mixtures including two solids in a SCF was also able to reproduce the enhancement effect of solubilities observed in some cases when mixing given solids. The method proposed herewith, in particular the group contributions methods proposed for heavy hydrocarbons w5–7x, should be extended to other organic compounds in order to be used for the supercritical extraction of natural products.

6. List of symbols a b D H sub, D H fus , D H vap F scf ki j NP , NT P, Pc , Pt , P sub T, T b , Tc , Tf , Tt Õ, Õ s y v

attractive term of the Peng–Robinson EOS covolume sublimation, fusion and vaporisation enthalpies fugacity coefficient for solid in the supercritical phase binary interaction parameter between species i and j number of data points and number of temperatures pressure, critical pressure, triple point pressure and sublimation pressure temperature, normal boiling temperature, critical temperature, fusion temperature, triple point temperature molar volume, solid molar volume mole fraction in the supercritical phase acentric factor

500

S. Garnier et al.r Fluid Phase Equilibria 158–160 (1999) 491–500

References w1x E. Neau, S. Garnier, P. Alessi, A. Cortesi, I. Kikic, in: Ph. Rudolf von Rohr, Ch. Trepp ŽEds.., High Pressure Chemical Engineering, Elsevier, Amsterdam, 1996, pp. 265–270. w2x E. Reverchon, G. Della Porta, R. Taddeo, P. Pallado, A. Stassi, Ind. Eng. Chem. Res. 34 Ž1995. 4087–4091. w3x E. Neau, S. Garnier, L. Avaullee, ´ Fluid Phase Equilibria Žto be published.. w4x L. Avaullee, ´ L. Trassy, E. Neau, J.-N. Jaubert, Fluid Phase Equilibria 139 Ž1997. 155–170. w5x L. Avaullee, ´ E. Neau, G. Zaborowski, Entropie 202 Ž1997. 36–40. w6x L. Coniglio, Thesis, Universite´ d’Aix-Marseille III, 1993. w7x L. Trassy, Thesis, Universite´ de la Mediterranee, ´ ´ 1998. w8x L. Constantinou, R. Gani, AIChE J. 40 Ž10. Ž1994. 1697–1710. w9x L. Constantinou, R. Gani, J.P. O’Connel, Fluid Phase Equilibria 103 Ž1995. 11–22. w10x E. Rauzy, Thesis, Universite´ d’Aix-Marseille II, 1982. w11x A. Bondi, J. Phys. Chem. 68 Ž3. Ž1964. 441–451. w12x A. Peneloux, E. Rauzy, R. Freze, ´ ´ Fluid Phase Equilibria 8 Ž1982. 7–23. w13x M. Mc Hugh, A.J. Seckner, T.J. Yogan, Ind. Eng. Chem. Fundam. 23 Ž1984. 493–499. w14x K.P. Johnston, D.H. Ziger, D.H. Eckert, Ind. Eng. Chem. Fundam. 21 Ž1982. 191–197. w15x M. Mc Hugh, M.E. Paulaitis, J. Chem. Eng. Data 25 Ž1980. 326–329. w16x S.T. Chung, K.S. Shing, Fluid Phase Equilibria 81 Ž1992. 321–341. w17x S. Sako, K. Ohgaki, T. Katayama, J. Sup. Fl. 1 Ž1988. 1–6. w18x R.T. Kurnik, S.J. Holla, R.C. Reid, J. Chem. Eng. Data 26 Ž1981. 47. w19x Y. Iwai, Y. Mori, N. Hosotani, H. Hogashi, T. Furuya, Y. Arai, J. Chem. Eng. Data 38 Ž1993. 509–511. w20x G. Anitescu, L.L. Tavlaridesn, J. Sup. Fl. 10 Ž1997. 175–189. w21x J.M. Dobbs, K.P. Johnston, Ind. Eng. Chem. Res. 26 Ž1987. 1476–1482. w22x E. Kosal, G.D. Holder, J. Chem. Eng. Data 32 Ž1987. 148–150. w23x I. Moradinia, A.S. Teja, Fluid Phase Equilibria 28 Ž1986. 199–209. w24x W.J. Schmitt, R.C. Reid, J. Chem. Eng. Data 31 Ž1986. 204–212. w25x D.H. Ziger, C.A. Eckert, Ind. Eng. Chem. Process Des. Dev. 22 Ž1983. 582–588. w26x W.J. Lyman, W.F.R., D.H. Rosenblatt, Handbook of Chemical Property Estimation Methods, 1990. w27x S. Calange, Thesis, Universite´ de Pau et du Pays de l’Adour, 1996. w28x CRC Press, Handbook of Chemistry and Physics, 77th edn., 1996. w29x M.E. Spaght, S.B. Thomas, G.S. Parks, J. Phys. Chem. 36 Ž1932. 882–888. w30x J. Eibert, Thesis, Washington University, St. Louis, 1944. w31x G.W. Smith, Mol. Cryst. Liq. Cryst. 49 Ž1979. 207–209. w32x R. Sabbah, L. ElWatik, J. Therm. Anal. 38 Ž4. Ž1992. 855–863.