Monte Carlo calculation of solubilities of aromatic compounds in supercritical carbon dioxide

Illlmll ELSEVIER

Fluid PhaseEquilibria 111 (1995)1-13

Monte Carlo calculation of solubilities of aromatic compounds in supercritical carbon dioxide Y o s h i o Iwai, Hirohisa Uchida, Y o s h i o Koga, Yasuhiko Mori, Y a s u h i k o Arai Department of Chemical Engineering, Faculty of Engineering, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-81, Japan Received 7 December 1994; accepted 27 March 1995

Abstract Monte Carlo method has been applied to calculate the solubilities (gas-solid equilibria) of naphthalene, dimethylnaphthalene isomers, and xylenol isomers in supercritical carbon dioxide. Carbon dioxide was treated as single-site molecule and naphthalene, dimethylnaphthalenes, and xylenols were treated as two-site (two benzene-ring groups), four-site (two benzene-ring and two methyl groups), four-site (one benzene-ring, one hydroxyl, and two methyl groups) molecules, respectively. The Lennard-Jones (12-6) potential was used as the site-site potential and the Lorentz-Berthelot mixing rules were adopted for unlike site pairs. A modified test particle method was used to calculate the residual chemical potentials of aromatic compounds in supercritical carbon dioxide based on the NVT canonical ensemble. The calculated results of solubilities show good agreement with the experimental values. The solubilities of isomers can be distinguished by the site model. The residual chemical potentials of xylenol isomers calculated by the site model are affected by the position of methyl group. This fact suggests the screen action of methyl group against hydroxyl group. The site model is very useful to explain the screen action. Keywords: Theory; Computer simulation; Monte Carlo; Solid-gas equilibria; Lennard-Jones; Supercritical fluid extraction; Aromatic compound

I. Introduction Recently, molecular simulation has been applied widely to calculate physical properties such as PVT relationship and vapor-liquid equilibria. In this work, Monte Carlo method was applied to calculate the solubilities of aromatic compounds in supercritical carbon dioxide. Supercritical fluid extraction method is used to separate certain valuable components from a condensed phase which may be a solid or liquid. In this work, the authors studied the case in which the condensed phase is a solid consisting of pure aromatic compound. Since the supercritical fluid can be assumed to be insoluble in the solid, the fugacity or chemical potential of aromatic compound in the solid phase can be obtained 0378-3812/95/$09.50 © 1995ElsevierScienceB.V. All rights reserved SSDI 0378-3812(95)02770-X

2

Y. lwai et al./Fluid PhaseEquilibria 111 (1995) 1-13

from the properties of pure component. Computer simulation is only necessary to calculate the fugacity or chemical potential of aromatic compound in the supercritical fluid phase. Furthermore, the simulation can be easily achieved because the solubility of solid component in supercritical fluid is usually very low and the composition of solid component can be assumed to be infinite dilution. In previous works (Eya et al., 1992 and Iwai et al., 1994), the authors calculated the solubilities of naphthalene, hexamethylbenzene and phenanthrene in supercritical carbon dioxide by Monte Carlo method and showed that the calculation results gave good agreement with the experimental data by introducing a binary interaction parameter between carbon dioxide and aromatic compound. The authors also calculated the effect of two binary interaction parameters k~2 (the deviation from geometric intermolecular attractions assumed for the unlike cohesive energy parameter) and 112 (the deviation from arithmetic intermolecular repulsions assumed for the unlike repulsive energy parameter) on the solubilities of naphthalene in supercritical carbon dioxide by Monte Carlo method (Iwai et al., 1995). In the calculations carbon dioxide and aromatic compound were treated as single site molecules. Furthermore, the solubilities of chain molecules in supercritical ethane were calculated by Monte Carlo simulation (Koga et al., 1994). Chain molecule and ethane were treated as a linear chain with many sites and single site molecules, respectively. In this work, the solubilities of naphthalene, dimethylnaphthalene isomers and xylenol isomers in supercritical carbon dioxide have been calculated by Monte Carlo method. Naphthalene was treated as two sites molecules, and dimethylnaphthalenes and xylenols were treated as four sites molecules to distinguish isomers.

2. Fundamental equations For a binary mixture consisting of supercritical carbon dioxide (1) and aromatic compound (2), the residual chemical potential is given as tz~ = - k T

In < exp( - ~b2/kT ) > N

(1)

where ~b2 is the potential energy experienced by component 2 placed at random locations in a fluid of N particles of carbon dioxide and < >N is a canonical ensemble average of the system of N particles. The Henry constant of component 2, /-/2, can be written as follows at infinite dilution condition H 2 = p , k T exp(Iz~/kT)

(2)

where Pl is the number density of supercritical carbon dioxide. The solubility of component 2, Y2, is usually very low. Therefore, Y2, can be calculated by (3)

y2=f~/H2

where f ~ is the fugacity of component 2 in gas phase. Since the fugacity of component 2 in the gas phase is equal to that in the solid phase (pure aromatic compound), the following equation is derived

fG=fS=ps2atexp( vS(p-ps2at) RT

}

(4)

Y. lwai et al. /Fluid PhaseEquilibria 111 (1995) 1-13 Table 1 The properties of aromatic compounds at 308.15 K Aromatic compound vs × 104 (m 3 mol- l)

pSat (Pa)

Naphthalene 2,3-Dimethylnaphthalene 2,6-Dimethylnaphthalene 2,7-Dimethylnaphthalene 2,5-Xylenol 3,4-Xylenol

29.173 b 1.274 d 1.222 d 1.690 d 12.15 h 5.686 h

1.119 a 1.547 c 1.368 ~ 1.368 f 1.257 g 1.243 g

Perry et al. (1984). b Fowler et al. (1968). c Ziger and Eckert (1983). d Osborn and Douslin (1975). ~ Richter (1946). f Assumed to be the same value of 2,6-dimethylnaphthalene. g Lide (1993). h Andon et al. (1960). a

where pSat is the saturation pressure, v is the molar volume, R is the gas constant, and superscript S means the solid state. From Eqs. (2)-(4), the solubility of component 2 is given as follows: sat

P2 exp Y2 = H2

(vS(p__p~at) RT

(5)

The properties for aromatic compounds, v s and pSat, are listed in Table 1.

3. Calculation procedure The authors considered a system of 108 real particles of carbon dioxide enclosed in a cube with periodic boundary conditions. The canonical (NVT) ensemble was used in the simulation. The standard Metropolis importance sampling method was used to obtain new configurations. After a large number of configurations were generated to reach equilibrium condition, a test particle was inserted according to the method proposed by Widom (1963). For every fifty configurations of the real particles of carbon dioxide, small test particle was tried to place at random location fifty times. When the test particle did not overlap with real particles of carbon dioxide, aromatic compound was placed on the position of the test particle and was rotated to sample the potential energies experienced for the purpose of sampling more effectively. On the other hand, when the test particle overlapped with real particles, the potential energy experienced by aromatic compound placed on the position should be infinite. So, it is not necessary to calculate the potential energy. The number of rotations against one insertion of test particle were two hundred for dimethylnaphthalene, and fifty for naphthalene and xylenol. The lengths of the calculation were 2.0 × 107 configurations of carbon dioxide for naphthalene, 1.5 × 10 6 configurations for dimethylnaphthalene, and 1.5 x 10 6 (low pressure) to 2.0 X 107 (high pressure) configurations for xylenol. The 95% confidence limits for the pressure and the residual chemical potential were calculated by using the overall average for the pressure and exp( - ~b2/kT) , and sub-averages for every 1.0 X 10 4 configurations.

4

E lwai et al./FluidPhase Equilibria 111 (1995) 1-13

4. l n t e r m o l e c u l a r potential

The intermolecular potential energy between components a and b, ~bab, can be calculated by the Lennard-Jones potential n a nb (~ab = E

i

E4'ffij((o.ij/riy)12--(o.ij/rij) 6} j

(6)

where n is the number of sites in the molecule and, r~j is the distance between i and j sites, and and o. are the energy parameter and the size parameter, respectively. The authors adopted rcut = 4o-;j for the cut-off distances between every pair sites. The influence of the tail of the potential was estimated analytically, by assuming that the radial distribution functions of carbon dioxide molecules for each site were fixed to be 1 for distances greater than r~=. According to the Lorentz-Berthelot mixing rules, the potential parameters for unlike site pairs are expressed by o.ij = ( o.ii + o'//)/2

(7)

= ( ii jj)o

(8)

and

The corresponding state principle assures that all Lennard-Jones fluids for pure components obey the same reduced equation of state by using the reduced variables p* = No. 3 / V , T* = k T / e and p* = o. 3 p / e

(9)

where p is the number density, N is the number of particles, V is the volume, T is the absolute temperature, p is the pressure, k is the Boltzmann constant, and superscript * means the reduced property. Nicolas et al. (1979) proposed the reduced critical constant values of pc*, To* and Pc at critical point as 0.35, 1.35 and 0.1418, respectively. In this work, the parameters o. and e for carbon dioxide and o- for benzene-ring were calculated by using Tc and Pc of carbon dioxide and benzene (Reid et al., 1987), respectively. The parameters o. and e for methyl group were adopted from Jorgensen et al. (1984). The parameter o- for hydroxyl group was adopted from Jorgensen (1986). The structure of aromatic compounds and the positions of sites adopted in this work are shown in Figs. 1 and 2. The parameters e for benzene-rings and hydroxyl group were determined to give good 0 . 1 4 0 nm

0 . 2 4 2 nm

0 . 1 5 2 4 nm

6 Fig. 1. Structure of naphthalene and dimethylnaphthalene (DMN): ( Q ) site of benzene-ring; ( O ) site of CH 3.

Y. lwai et aL /Fluid Phase Equilibria 111 (1995) 1-13

0.1364

5

1

nn

~1

.1524

n|

Fig. 2. Structure of xylenol: ( 0 ) site of benzene-ring; (©) site of CH3;(/x) site of OH. representation of the solubilities of aromatic compounds in supercritical carbon dioxide as shown in Figs. 3 and 4. The potential parameters adopted in this work are listed in Table 2.

5. Results and discussion The calculated results of solubilities are listed in Tables 3 - 5 , and shown in Figs. 5 and 6. The calculated results are in good agreement with the experimental data and the solubilities of isomers are

10 -1

I

I

I

/0"" I

:~, 10-2 o" f

f

..... w,._~ ~

_31

10 200

,

, 51.o

220

240

260

e/k Fig. 3. Solubilities of naphthalene and 2,3-, 2,6-and 2,7-dimethylnaphthalene (DMN) in supercritical carbon dioxide at 308.15 K against energy parameters: horizontal lines, (---) naphthalene, Tsekhanskaya et al. (1964) experimental data at 12.9 MPa; (--) 2,3-DMN, Kumik et al. (1981); ( - - - - ) 2,6-DMN, Iwal et al. (1993); ( - - - --) 2,7-DMN, Iwai et al. (1993), experimental data at 12.4 MPa; plots and oblique lines, (©, ---) naphthalene, Monte Carlo calculation at 12.9 MPa; ( 0 , ---) 2,3-DMN; (A, ____) 2,6-DMN; (B, - - - - - ) 2,7-DMN, Monte Carlo calculation at 12.4 MPa.

6

E lwai et al./Fluid Phase Equilibria 111 (1995) 1-13 I

I

I

/~
10-2 I

/

/

101731.6 K

1200

1400

1600

1800

2000

e/k [K] Fig. 4. Solubilities of 2,5-and 3,4-xylenol in supercritical carbon dioxide at 308.15 K against energy parameters: horizontal lines, ( - - ) 2,5-xylenol, Iwai et al. (1990); ( - - - - ) 3,4-xylenol, Mori et al. (1992), experimental data at 12.7 MPa; plots and oblique lines, ( O , - - ) 2,5-xylenol; (rq, - - - ) 3,4-xylenol, Monte Carlo calculation at 12.7 MPa.

Table 2 The potential parameters Site

o- (nm)

e/k

(K)

CO 2 Benzene-ring(Naphthalene) Benzene-ring(Dimethylnaphthalene) Benzene-ring(Xylenol) CH 3 OH

0.3910 0.5501 0.5501 0.5501 0.3775 a 0.307 b

225.3 251.0 215.5 50.94 104.2 a 1731.6

a Jorgensen et al. (1984). b Jorgensen (1986).

Table 3 The calculated results for naphthalene p (MPa)

/x~ X 1020 (J)

9.4+0.1 10.4+0.2 12.7 + 0.2 14.9 + 0.2

-3.69 -3.81 - 3.92 - 3.98

< < < <

-3.68 -3.80 - 3.91 - 3.96

Y2 x 103 (-) < < < <

-3.67 -3.78 - 3.89 - 3.94

7.87+0.18 10.1+0.3 13.5 _+0.5 16.2 + 0.9

--4.38 < --4.33 < --4.27

--4.52 < --4.48 < --4.43 --4.59 < --4.54 < --4.48

11.0+0.6 12.4-t-0.7

2.63-t-0.27 3.14+0.38

1.87-t-0.24

4 . 4 3 < -- 4 . 3 6 < -- 4 . 2 9 4 . 5 3 < -- 4 . 4 8 < -- 4 . 4 2

-- 4 . 5 9 < -- 4 . 5 3 < -- 4 . 4 7

- -

- -

/z~ X 10 20 (J)

//,~ X 10 20 (J)

Y2 X 10 3 (-)

2,6-DMN

2,3-DMN

9.7-t-0.5

p (MPa)

Table 4 T h e c a l c u l a t e d r e s u l t s for d i m e t h y l n a p h t h a l e n e i s o m e r s

4 . 5 5 < -- 4 . 5 0 < -- 4.45 -- 4 . 5 8 < -- 4 . 5 3 < -- 4 . 4 7

2.36 + 0.30 2.74 _ 0.37

3.79 + 0.49

2.42 + 0.29 3.42 + 0.38 -- 4 . 3 9 < -- 4 . 3 5 < -- 4 . 2 9

1.83 + 0 . 3 0

- -

Y2 X 10 3 (-)

/x~ X 10 2° (J)

Y2 X 10 3 (-)

2,7-DMN

2.

r.z

a~

ga

t-,

8

Y. lwai et al. / Fluid Phase Equilibria 111 (1995) 1-13

Table 5 T h e calculated results for xylenol isomers p (MPa)

2,5-Xylenol

3,4-Xylenol

/x[ × 102° (J) 7.9___0.2 8.0 -1-0.2 8.6+0.4 9.6 -t- 0.6 12.7+0.4 16.7-t-0.4 24.9+0.3

-2.65 < - 3.06 < -3.65 < - 3.89 < -4.07 < -4.14 < -4.14<

-2.64 < - 3.04 < -3.63 < - 3.86 < -4.05 < -4.11 < -4.10<

-2.62 - 3.03 -3.60 - 3.82 -4.03 -4.07 -4.06

Y2 × 103 ( ' )

P'~ × 102° (J)

0.516+0.014 1.07 -t- 0.04 3.29+0.21 5.30 + 0.44 8.47+0.46 10.9+0.9 14.8+1.4

- 2.73 -3.17 - 3.77 - 4.06 - 4.26 - 4.36 - 4.38

< < < < < < <

- 2.72 -3.14 - 3.75 - 4.02 - 4.24 - 4.32 - 4.34

Y2 × 103 ( ' ) < < < < < < <

- 2.70 -3.12 - 3.73 - 3.98 - 4.21 - 4.28 - 4.29

0.291 -t- 0.009 0.635 + 0.034 2.06+0.11 3.63 -t- 0.30 6.14+0.35 8.51 + 0.78 12.1 + 1.2

distinguished by the site model. Fig. 7 shows the calculated residual chemical potential of xylenol isomers in supercritical carbon dioxide. As shown in this figure, the residual chemical potentials are affected by the positions of methyl groups. When two methyl groups exist near hydroxyl group (2,6-xylenol), the chemical potentials are high. On the other hand, when no methyl group exists near hydroxyl group (3,4- and 3,5-xylenol) the chemical potentials are low. When one methyl group exists near hydroxyl group (2,3-, 2,4- and 2,5-xylenol), the chemical potentials are moderate. The difference of the residual chemical potential suggests the screen action of methyl group against hydroxyl group.

I

I

I

.....

10 -2

.........

I

........

I

10-3

10-4

I

8

I

I

10

12

I

14

16

p [MPa] Fig. 5. Solubilities of naphthalene and 2,3-, 2,6-and 2 , 7 - d i m e t h y l n a p h t h a l e n e ( D M N ) in supercritical carbon dioxide at 308.15 K: ( - - - ) naphthalene, T s e k h a n s k a y a et al. (1964); ( - - ) 2 , 3 - D M N , K u r n i k et al. (1981); ( - - - ) 2 , 6 - D M N , Iwai et al. (1993); ( . . . . ) 2 , 7 - D M N , Iwai et al. (1993), e x p e r i m e n t a l data; ( O ) naphthalene; ( 0 ) 2 , 3 - D M N ; ( • ) 2 , 6 - D M N ; (11) 2 , 7 - D M N , M o n t e Carlo calculation; vertical a n d horizontal lines for naphthalene and 2,7-DMN represent fluctuations in

calculation results of solubilities and pressures, respectively.

}I. lwai et al. / F l u i d Phase Equilibria 111 (1995) 1-13

9

10 -,~

I O4

~t

10-3

I 3= El:

1 0-40

'

I

,

10

I

20

,

30

p [MPa] Fig. 6. Solubilities of 2,5-and 3,4-xylenol in supercritical carbon dioxide at 308.15 K: ( - - ) 2,5-xylenol, lwai et al. (1990); ( - - - - ) 3,4-xylenol, Mori et al. (1992), experimental data; ( O ) 2,5-xylenol; ([3) 3,4-xylenol, Monte Carlo calculation; vertical lines represent fluctuations in calculation results of solubilities.

-3

-4

,

0

I

10

,

p [iPa]

I

20

30

Fig. 7. Residual chemical potentials of xylenols in supercritical carbon dioxide; (O) 2,3-xylenol; ( D ) 2,4-xylenol; (~) 2,5-xylenol; (zx) 2,6-xylenol; (X7) 3,4-xylenol; ( ® ) 3,5-xylenol; lines, smoothed lines.

10

Y. lwai et aL /Fluid Phase Equilibria 111 (1995) 1-13

II

2

II

v

0

0.6 r [nm]

.2

Fig. 8. Radial distribution functions for hydroxyl group in carbon dioxide at 308.15 K and 13 MPa; ( - - ) 2,5-xylenol; (---) 2,6-xylenol; ( - - - - - ) 3,4-xylenol.

Fig. 8 shows the radial distribution functions for hydroxyl group in carbon dioxide. For the calculation one xylenol and 256 panicles of carbon dioxide were enclosed in a cube. The length of calculations were 5.0 X 10 6. When two methyl groups exist on the position of 3 and 4, carbon dioxide can easily come around hydroxyl group and the peak is highest. When methyl groups exist on the position of 2 and 6, carbon dioxide cannot easily come around hydroxyl group because of the screen effect of methyl groups and the peak is lowest. In the case of 2,5-xylenol the screen effect is moderate and the peak is moderate. Fig. 9 shows the radial distribution functions for methyl groups of 2,5-xylenol in carbon dioxide. The first peak of second position of methyl group is higher than that of fifth position of methyl group, because the density of carbon dioxide near hydroxyl group is high and the second position of methyl

I

-c-1 v

t2~

i

0

I

0.6 r [nm]

i

i

.2

Fig. 9. Radial distribution functions for methyl group of 2,5-xylenol in carbon dioxide at 308.15 K and 13 MPa; ( - - ) second position; (---) fifth position.

Y. lwai et al. / F l u i d Phase Equilibria 111 (1995) 1-13

11

group exist near hydroxyl group. The locations of second peaks for two methyl groups are different. It is the results of the high density of carbon dioxide behind hydroxyl group. In spite of using the same potential parameters for isomers, the radial distribution functions for hydroxyl group of xylenol isomers in carbon dioxide are different. Furthermore, the radial distribution functions for methyl groups of 2,5-xylenol in carbon dioxide are different. This means that the site model will be adopted to distinguish isomers. The group contribution methods such as UNIFAC (Fredenslund et al., 1977) and ASOG (Tochigi et al., 1990) are widely used. However, they cannot distinguish isomers, because the group contribution methods give the same parameters for the same group and the position of groups is not considered. If the information of molecular simulation such as solubilities and radial distribution functions for the site model is accumulated, the group contributions may be revised. In this work, the author treated the parameters e for benzene-rings and hydroxyl group as fitting parameters. The value of e for hydroxyl group is much larger than that of Jorgensen for liquid alcohols. The parameters e for benzene-ring listed in Table 2 are disparate. Specially the value for benzene-ring (xylenol) is very small. Furthermore, the authors calculated the values of o" and e for carbon dioxide and tr for benzene-ring by using the critical constants proposed by Nicolas et al. (1979) because the authors continuously used those constants from the previous works (Eya et al., 1992, Iwai et al., 1994, Koga et al., 1994). Recently, Smit (1992) and Johnson et al. (1993) proposed new critical constants for Lennard-Jones fluids. If those values are used for calculation of tr and e, the calculated solubilities may slightly changed and optimum values of e for benzene-rings and hydroxyl group may be changed. Re-examination of parameter values is necessary in the future work. However, the main purpose of this paper is to show that the site model is useful to distinguish isomers. The results will not be changed even if the values of parameters are slightly changed.

6. Conclusion The solubilities of naphthalene, dimethylnaphthalene isomers and xylenol isomers in supercritical carbon dioxide have been calculated by Monte Carlo method. Naphthalene was treated as two-site molecules and dimethylnaphthalenes and xylenols are treated as four-site molecules. It is shown that the site model is very useful to distinguish isomers and the calculated results are in good agreement with the experimental data.

7. List of symbols

f H k k12 and /12 n a and n b N P F

fugacity Henry's constant Boltzmann constant binary interaction parameters number of sites in molecules a and b, respectively number of particles in a cube pressure distance between particles

12

R rcut

T u

V Y <

Y. lwai et al. /Fluid Phase Equilibria 111 (1995) 1-13

gas constant cut-off distance absolute temperature molar volume volume of a cube mole fraction in supercritical fluid phase (solubility) canonical ensemble average for N particles system

Greek letters E

/zr P or

6ab

energy parameter residual chemical potential number density size parameter intermolecular potential between molecules a and b potential energy experienced by aromatic compound

Superscripts gas phase (supercritical fluid phase) G solid phase S saturation sat reduced value

Subscripts C i,j 1

2

critical property sites i and j supercritical carbon dioxide aromatic compound

Acknowledgements We gratefully acknowledge the financial support provided by the Grant-in-Aid for Scientific Research on Priority Areas (Supercritical Fluid 224, 1994, 06214219), The Ministry of Education, Science and Culture, Japan.

References Andon, R.J.L., Biddiscombe, D.P., Cox, J.D., Handley, R., Harrop, D., Herington, E.F.G. and Martin, J.F., 1960. Thermodynamic properties of organic oxygen compounds. Part 1. Preparation and physical properties of pure phenol, cresols, and xylenols. J. Chem. Soc.: 5246-5254. Eya, H., Iwai, Y., Fukuda, T. and Arai, Y., 1992. Monte Carlo calculation of solubilities of high-boiling component in supercritical carbon dioxide. Fluid Phase Equilibria, 77: 39-51. Fredenslund, Aa., Gmehling, J. and Rasmussen, P., 1977. Vapor-liquid equilibria using UNIFAC, Elsevier, New York. Fowler, L., Trump, W.N. and Vogler, C.E., 1968. Vapor pressure of naphthalene. J. Chem. Eng. Data, 13: 209-210.

Y. lwai et al. / Fluid Phase Equilibria 111 (1995) 1-13

13

Iwai, Y., Koga, Y., Hata, Y., Uchida, H. and Arai, Y., 1995. Monte Carlo simulation of solubilities of naphthalene in supercritical carbon dioxide. Fluid Phase Equilibria, 104: 403-412. Iwai, Y., Mori, Y., Hosotani, N., Higashi, H., Furuya, T., Arai, Y., Yamamoto, K. and Mito, Y., 1993. Solubilities of 2,6-and 2,7-dimethylnaphthalene in supercritical carbon dioxide. J. Chem. Eng. Data, 38: 509-511. Iwai, Y., Mori, Y., Koga, Y., Arai, Y. and Eya, H., 1994. Monte Carlo calculation of solubilities of high-boiling component in supercritical carbon dioxide and solubility enhancements by entrainer. J. Chem. Eng. Japan, 27: 334-339. Iwai, Y., Yamamoto, H., Tanaka, Y. and Arai, Y., 1990. Solubilities of 2,5-and 2,6-xylenols in supercritical carbon dioxide. J. Chem. Eng. Data, 35: 174-176. Johnson, K.J., Zollweg, J.A. and Gubbins, K.E., 1993. The Lennard-Jones equation of state revisited. Mol. Phys., 78: 591-618. Jorgensen, W.L., 1986. Optimized intermolecular potential functions for liquid alcohols. J. Phys. Chem., 90: 1276-1284. Jorgensen, W.L., Madura, J.D. and Swenson, C.J., 1984. Optimized intermolecular potential functions for liquid hydrocarbons. J. Am. Chem. Soc., 106: 6638-6646. Koga, Y., Iwai, Y. and Arai, Y., 1994. Monte Carlo simulation for chain molecules in supercritical ethane. J. Chem. Phys., 101: 2283-2288. Kurnik, R.T., Holla, S.J. and Reid, R.C., 1981. Solubility of solids in supercritical carbon dioxide and ethylene. J. Chem. Eng. Data, 26: 47-51. Lide, D.R., 1993. CRC Handbook of Chemistry and Physics 74th edn., CRC Press, New York. Mori, Y., Shimizu, T., Iwai, Y. and Arai, Y., 1992. Solubilities of 3,4-xylenol and naphthalene + 2,5-xylenol in supercritical carbon dioxide at 35 °C. J. Chem. Eng. Data, 37: 317-319. Nicolas, J.J., Gubbins, K.E., Streett, W.B. and Tildesley, D.J., 1979. Equation of state for the Lennard-Jones fluid. Mol. Phys., 37: 1429-1454. Osborn, A.G. and Douslin, D.R., 1975. Vapor pressures and derived enthalpies of vaporization for some condensed-ring hydrocarbons. J. Chem. Eng. Data, 20: 229-231. Perry, R.H., Green, D.W. and Maloney, J.O. (Eds.), 1984. Perry's Chemical Engineering's Handbook, 6th edn., McGraw-Hill, New York. Reid, B.C., Prausnitz, J.M. and Poling, B.E., 1987. The Properties of Gases and Liquids, 4th edn., McGraw-Hill, New York. Richter, F., 1946. Beilstein Handbuch der Organishen Chemie, 4th edn., Springer-Verlag, Berlin. Smit, B., 1992. Phase diagrams of Lennard-Jones fluids. J. Chem. Phys., 96: 8639-8640. Tochigi, K., Tiegs, D., Gmehling, J. and Kojima, K., 1990. Determination of new ASOG parameters. J. Chem. Eng. Japan, 23: 453-463. Tsekhanskaya, Y.L., Iomtev, M.B. and Mushkina, E.V., 1964. Solubility of naphthalene in ethylene and carbon dioxide under pressure. Russ. J. Phys. Chem., 38: 1173-1176. Widom, B., 1963. Some topics in the theory of fluids. J. Chem. Phys., 39: 2808-2812. Ziger, D.H. and Eckert, C.A., 1983. Correlation and prediction of solid-supercritical fluid phase. Ind. Eng. Chem. Proc. Des. Dev., 22: 582-588.