Isothermal vapor–liquid equilibria for mixtures composed of 1,2-dimethoxybenzene, 2-methoxyphenol, and diphenylmethane

Fluid Phase Equilibria 178 (2001) 209–223

Isothermal vapor–liquid equilibria for mixtures composed of 1,2-dimethoxybenzene, 2-methoxyphenol, and diphenylmethane Shou-Ming Hwang, Ming-Jer Lee∗ , Ho-mu Lin Department of Chemical Engineering, National Taiwan University of Science and Technology, 43, Keelung Rd., Section 4, Taipei 106-07, Taiwan Received 17 August 2000; accepted 7 September 2000

Abstract Diphenylmethane was found to be a potential entrainer for separating the closely boiling mixtures of 2-methoxyphenol + 1,2-dimethoxybenzene via extractive distillation. To gain insight into the capability of this auxiliary agent, isothermal vapor–liquid equilibrium data were measured for the binary and the ternary mixtures containing 2-methoxyphenol, 1,2-dimethoxybenzene, and diphenylmethane at temperatures from 433.15 to 463.15 K. All the binary data passed thermodynamic consistency tests. However, there exhibits a large discrepancy between the experimental values and the predicted results from the UNIFAC model. The new data were correlated with the Wilson, the NRTL, and the UNIQUAC models, respectively. The model parameters determined from the binary data were applied to predict the phase equilibrium behavior of the ternary system. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Experiments; Data; Entrainer; Extractive distillation; 2-Methoxyphenol; 1,2-Dimethoxybenzene; Diphenylmethane

1. Introduction Phenol derivatives are widely used as intermediates for manufacturing a variety of speciality chemicals. Separation of such compounds from product mixtures is usually difficult but plays an important role in the process. The process of synthesis of 1,2-dimethoxybenzene requires to separate closely boiling mixtures of 2-methoxyphenol with 1,2-dimethoxybenzene. The boiling temperatures of these two compounds are within the range of 475–479 K. Conventional distillation can not be used economically. To explore other options for separating such mixtures, Lee et al. [1] studied the vapor–liquid equilibrium (VLE) behavior of binary systems of carbon dioxide with 1,2-methoxybenzene and 2-methoxyphenol at temperatures from 323.15 to 423.15 K and pressures up to 20 MPa. These VLE data provide a fundamental basis for the feasibility study on the separation of 1,2-methoxybenzene+2-methoxyphenol mixtures with supercritical carbon dioxide. ∗ Corresponding author. Tel.: +886-2-737-6626; fax: +886-2-737-6644. E-mail address: [email protected] (M.-J. Lee).

0378-3812/01/$20.00 © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 ( 0 0 ) 0 0 4 6 1 - 1

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Table 1 Selectivities at infinite dilution predicted from the UNIFAC model [3] for the mixtures of 2-methoxyphenol (1) and 1,2-dimethoxybenzene (2) with different solvents Solvent

γ1∞

γ2∞

∞ S12

1-Hexanol 1-Heptanol 1-Octanol 1-Nonanol 1-Decanol Benzene Phenol Butyl amine Pentyl amine Butyl methyl ether Propyl ethyl ether Butyl ethyl ether Dipropyl ether Propyl acetate Methyl propionate Ethyl propionate Propyl propionate Aniline Pyridine Diphenylmethane 1-Methylnaphthalene

0.77 0.79 0.82 0.85 0.87 2.88 0.39 1.50 1.74 1.94 2.69 3.06 3.06 1.57 1.62 1.83 2.02 0.79 0.22 3.90 4.00

2.43 2.34 2.27 2.20 2.15 1.08 0.36 1.36 1.52 1.64 2.04 2.25 2.25 1.31 1.31 1.45 1.58 0.52 0.88 1.41 1.58

0.32 0.34 0.36 0.38 0.41 2.66 1.06 1.10 1.14 1.19 1.32 1.36 1.36 1.20 1.24 1.26 1.28 1.53 0.25 2.77 1.58

Extractive distillation is another alternative method for separating these two closely boiling compounds. The choice of an appropriate entrainer is the key to success for development of the separation processes. The UNIFAC model [2] and its modifications [3–5], developed on the basis of group contribution concept, have been widely used in preliminary solvent screening (e.g. [6–8]). The selectivity at infinite dilution ∞ (S12 ) serves as an index for evaluating the solvent capability which is defined as ∞ = S12

γ1∞ γ2∞

(1)

∞ for where γi∞ is the activity coefficient of component i at infinite dilution. Table 1 lists the values of S12 the compounds of 2-methoxyphenol (1) and 1,2-dimethoxybenzene (2) with various solvents, in which the activity coefficients at infinite dilution were predicted from the UNIFAC model [3]. The prediction ∞ = 2.77) for promoting the separation. showed that diphenylmethane is potentially a good entrainer (S12 To understand the phase behavior of the related mixtures, VLE measurements were conducted for mixtures composed of 2-methoxyphenol, 1,2-dimethoxybenzene, and diphenylmethane at temperatures from 433.15 to 453.15 K. No VLE data were available in literature for such mixtures. The binary VLE data measured in the present study were correlated by the Wilson [9], the NRTL [10], and the UNIQUAC [11] models, respectively. The parameters determined from binary data were utilized directly to predict the phase behavior of the ternary system.

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Table 2 Properties of pure substances Compound

Tc (K)

Pc (kPa)

Vc (cm3 mol−1 )

Zc

ω

r

q

1,2-Dimethoxybenzene 2-Methoxyphenol Diphenylmethane

696.7a 698.9a 770.0b

3430a 4910a 2860b

411.5a 303.5a 547.5a

0.244 0.256 0.245

0.437b 0.556d 0.442b

5.146c 4.531c 6.715c

4.016c 3.488c 4.780c

a

Determined from the Joback group contribution model [14]. Taken from Reid et al. [14]. c Determined from the group-contribution method [3]. d Determined from the Lee–Kesler model [14]. b

Table 3 VLE data for 2-methoxyphenol (1) + 1,2-dimethoxybenzene (2) T (K)

P (kPa)

x1

y1

ln γ 1

ln γ 2

GE /(RTx1 x2 )

433.15

24.0 24.2 24.4 24.7 25.0 25.2 25.5 25.7 26.0 26.2 26.3

0.0 0.118 0.196 0.298 0.379 0.450 0.530 0.595 0.752 0.861 1.0

0.0 0.134 0.218 0.323 0.403 0.470 0.567 0.618 0.766 0.863 1.0

0.043 0.034 0.019 0.013 0.002 0.036 0.014 0.007 −0.001

−0.010 −0.012 −0.008 0.000 0.010 −0.021 0.010 0.020 0.072

−0.034 −0.018 0.000 0.021 0.027 0.037 0.053 0.056 0.073

38.9 39.2 39.6 40.1 40.9 41.4 41.7 42.3 42.7 42.8

0.0 0.119 0.203 0.295 0.425 0.517 0.592 0.752 0.860 1.0

0.0 0.138 0.224 0.313 0.442 0.525 0.617 0.765 0.861 1.0

0.062 0.024 −0.004 −0.004 −0.016 0.017 0.006 −0.001

−0.014 −0.010 0.004 0.018 0.043 0.003 0.028 0.082

−0.049 −0.017 0.007 0.036 0.050 0.047 0.060 0.090

61.4 62.0 62.5 62.9 63.8 64.4 64.7 65.3 65.6 65.8

0.0 0.130 0.208 0.299 0.420 0.532 0.586 0.748 0.860 1.0

0.0 0.143 0.224 0.318 0.453 0.552 0.605 0.765 0.866 1.0

0.041 0.025 0.017 0.045 0.016 0.017 0.015 0.004

−0.006 −0.003 −0.004 −0.021 0.003 0.002 −0.010 0.019

0.000 0.016 0.012 0.028 0.039 0.044 0.046 0.052

448.15

463.15

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Table 4 VLE data for 2-methoxyphenol (1) + diphenylmethane (2) T (K)

P (kPa)

x1

y1

ln γ 1

ln γ 2

GE /(RTx1 x2 )

433.15

5.5 8.5 11.2 13.5 15.5 17.2 19.5 21.0 24.0 25.0 26.3

0.0 0.109 0.200 0.314 0.411 0.508 0.594 0.711 0.823 0.905 1.0

0.0 0.423 0.579 0.699 0.777 0.820 0.876 0.916 0.945 0.970 1.0

0.239 0.221 0.140 0.114 0.060 0.094 0.032 0.048 0.020

−0.005 0.060 0.062 0.052 0.113 0.059 0.076 0.276 0.321

0.225 0.576 0.403 0.321 0.345 0.329 0.219 0.607 0.566

9.7 14.2 17.8 22.5 25.6 28.6 32.6 34.5 38.2 40.4 42.8

0.0 0.095 0.194 0.310 0.408 0.495 0.597 0.699 0.813 0.902 1.0

0.0 0.376 0.542 0.693 0.750 0.807 0.858 0.905 0.942 0.964 1.0

0.288 0.162 0.172 0.105 0.094 0.097 0.047 0.035 0.009

0.013 0.041 0.025 0.097 0.104 0.149 0.100 0.179 0.410

0.459 0.415 0.329 0.415 0.397 0.489 0.299 0.410 0.549

15.2 22.0 27.8 33.9 38.5 44.3 49.8 54.3 59.0 62.0 65.8

0.0 0.094 0.197 0.316 0.414 0.496 0.602 0.701 0.808 0.897 1.0

0.0 0.351 0.540 0.654 0.743 0.804 0.857 0.900 0.941 0.964 1.0

0.250 0.165 0.080 0.061 0.099 0.081 0.063 0.046 0.015

0.024 0.027 0.093 0.073 0.083 0.120 0.129 0.125 0.288

0.537 0.341 0.413 0.281 0.363 0.404 0.395 0.394 0.466

448.15

463.15

2. Experimental work A static VLE apparatus was employed in the present study to measure the VLE data. The equipment is similar to that of Lee and Hu [12], but some modifications have been made by Hwang et al. [13]. The heart of the apparatus is a blind equilibrium cell, which was placed in a thermostatic bath (Model: HT-250, stability = ±0.03 K, Neslab, USA). The bath temperature was measured by a precision thermometer (Model: 1506, Hart Scientific, USA) with a platinum RTD probe to an accuracy of ± 0.02 K. A pressure transducer (Model: PDCR-330, Druck, UK) connected to digital readout (Model: DPI-262, Druck, UK) determined the equilibrium pressure to an accuracy of ± 0.1 kPa. While the vapor sample was taken with a

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Table 5 VLE data for 1,2-dimethoxybenzene (1) + diphenylmethane (2) T (K)

P (kPa)

x1

y1

ln γ 1

ln γ 2

GE /(RTx1 x2 )

433.15

5.5 6.8 7.5 9.5 11.5 13.8 16.5 18.0 19.8 21.6 24.0

0.0 0.059 0.107 0.223 0.323 0.460 0.567 0.663 0.777 0.891 1.0

0.0 0.240 0.357 0.560 0.674 0.787 0.852 0.890 0.936 0.969 1.0

0.151 0.059 0.003 0.008 −0.009 0.038 0.011 −0.003 −0.020

−0.003 −0.021 −0.025 0.002 −0.020 0.017 0.052 0.022 0.098

0.112 −0.135 0.108 0.020 −0.060 0.118 0.112 0.013 0.098

9.7 11.8 13.0 16.1 18.8 23.3 27.9 29.7 33.3 36.0 38.9

0.0 0.601 0.107 0.222 0.303 0.444 0.569 0.649 0.776 0.887 1.0

0.0 0.219 0.336 0.533 0.646 0.760 0.835 0.884 0.933 0.965 1.0

0.106 0.063 0.008 0.041 0.034 0.059 0.045 0.032 0.009

0.009 −0.006 −0.009 −0.022 0.027 0.082 −0.001 0.014 0.118

0.266 0.010 0.031 0.014 0.122 0.280 0.125 0.160 0.209

15.2 19.0 19.6 25.1 30.1 36.1 43.9 46.3 52.8 56.2 61.4

0.0 0.061 0.112 0.221 0.302 0.428 0.567 0.636 0.777 0.889 1.0

0.0 0.227 0.344 0.544 0.651 0.763 0.843 0.875 0.930 0.930 1.0

0.159 0.008 0.029 0.073 0.062 0.070 0.045 0.033 −0.004

0.027 −0.052 −0.042 −0.021 −0.031 0.028 0.022 0.065 0.126

0.607 −0.461 −0.152 0.037 0.037 0.211 0.160 0.232 0.108

448.15

463.15

six-way sampling valve (operable up to 573 K), the liquid sample was collected in a vial through a sampling port that was connected to the liquid circulation loop with a tee. Compositions of both vapor and liquid samples were analyzed by gas chromatography (Model: 8700, China Chromatography, Taiwan) with a thermal conductivity detector (TCD). A stainless steel column packed with 10% SP-2340 on Chromosorb 80/100 supelcopart (6 m × 1/8 in.) was used for sample analysis. The carrier gas, helium (99.99% purity), was heated up to 500 K before entering the vapor sampling valve to keep vapor sample from condensation. Four to five samples were replicated for individual phase at each experimental condition. The average area fraction was converted into mole fraction via calibration equations. The uncertainties of the reported mole fractions for liquid and vapor phases are within ± 0.002 and ± 0.005, respectively.

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215

Fig. 1. Pressure-composition diagram for 2-methoxyphenol (1) + 1,2-dimethoxybenzene (2).

The purities of 1,2-dimethoxybenzene (TCI, Japan), 2-methoxyphenol (Merck, Germany), diphenylmethane (Aldrich, USA) are better than 99%. No impurity peaks were detected from chromatographic analysis. All the chemicals were used without further purification. The properties of these pure compounds are listed in Table 2. 3. Result and discussion The new isothermal VLE data are listed in Tables 3–5 for the binary systems of 2-methoxyphenol + 1,2-dimethoxybenzene, 2-methoxyphenol + diphenylmethane, and 1,2-dimethoxybenzene + diphenylmethane, respectively. The tabulated activity coefficients (γ i ) were calculated from the criteria of phase equilibria with assumption of ideal vapor phase, i.e. γi =

xi Pis

yi P exp[(P − Pis )ViL /(RT)]

(2)

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Fig. 2. Pressure-composition diagram for 2-methoxyphenol (1) + diphenylmethane (2).

where xi , yi , Pis are experimental liquid mole fraction, vapor mole fraction, and vapor pressure for component i, respectively. The liquid molar volume, ViL , was estimated from the modified Rackett model [15]. Table 6 gives the results of the thermodynamic consistency tests. All the binary VLE data passed both the point and the area tests. The methods of the consistency test have been detailed in [12]. Fig. 1 shows the phase diagram for 2-methoxyphenol + 1,2-dimethoxybenzene. It exhibits positive deviations from Raoult’s law. Although no azeotropes form in this system, the compositions of liquid and vapor phases are apparently too close to be separated efficiently by using conventional distillation. Figs. 2 and 3 illustrate the pressure-composition diagrams for 2-methoxyphenol + diphenylmethane and 1,2-dimethoxybenzene + diphenylmethane, respectively. These two systems are nearly ideal and have no azeotropes formation. The isobaric compositions are different significantly between liquid and vapor phases at any temperature for both systems so that the recovery of entrainer (diphenylmethane) from the residue of extractive distillation column is feasible with conventional distillation. The equilibrium phase-compositions were also measured for the ternary system of 2-methoxyphenol + 1, 2-dimethoxybenzene + diphenylmethane at temperatures from 433.15 to 463.15 K. Table 7 presents

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217

Fig. 3. Pressure-composition diagram for 1,2-dimethoxybenzene (1) + diphenylmethane (2).

the experimental results. Fig. 4 shows the experimental tie-lines of the coexisting phases at 463.15 K. No azeotropes were found at any of equilibrium temperatures in this ternary system. The relative volatilities of 2-methoxyphenol to 1,2-dimethoxybenzene (α 12 ), as listed in Table 7, increase with an increase of entrainer concentration. It is apparent that diphenylmethane is potent to facilitate the separation of the closely boiling mixtures of 2-methoxyphenol + 1,2-dimethoxybenzene.

4. Vapor–liquid equilibrium calculation 4.1. Prediction from the UNIFAC model The predicted results from two versions of the UNIFAC model [3,5] are compared with the experimental values in Figs. 1–3 and Table 8. Substantial deviations are shown in Fig. 1 for 2-methoxyphenol + 1, 2-dimethoxybenzene. While the UNIFAC model of 1982 version [3] underestimates the equilibrium

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Table 7 VLE data for ternary system of 2-methoxyphenol (1) + 1,2-dimethoxybenzene (2) + diphenylmethane (3) T (K)

P (kPa)

x1

x2

y1

y2

α12 a

433.15

16.9 20.1 22.5 21.5 21.1 22.6 17.6 21.2 18.3 14.6

0.081 0.092 0.102 0.200 0.397 0.595 0.374 0.559 0.309 0.184

0.397 0.591 0.795 0.591 0.409 0.217 0.103 0.109 0.302 0.217

0.157 0.134 0.120 0.259 0.503 0.730 0.678 0.784 0.488 0.395

0.644 0.769 0.854 0.683 0.444 0.218 0.135 0.114 0.386 0.359

1.20 1.13 1.09 1.12 1.17 1.22 1.37 1.35 1.23 1.30

448.15

26.8 32.3 39.5 36.3 36.3 36.6 28.3 33.5 30.5 25.1

0.092 0.098 0.111 0.197 0.376 0.596 0.362 0.561 0.306 0.190

0.402 0.590 0.791 0.590 0.427 0.212 0.105 0.109 0.305 0.218

0.167 0.135 0.125 0.247 0.470 0.729 0.656 0.779 0.473 0.391

0.635 0.765 0.846 0.689 0.471 0.212 0.138 0.114 0.392 0.355

1.15 1.07 1.05 1.08 1.13 1.22 1.37 1.33 1.20 1.27

463.15

41.2 49.8 60.0 57.7 57.7 56.5 41.0 52.9 48.7 36.9

0.087 0.097 0.105 0.197 0.390 0.588 0.348 0.549 0.290 0.184

0.396 0.603 0.791 0.602 0.408 0.214 0.106 0.110 0.316 0.216

0.164 0.139 0.123 0.252 0.492 0.717 0.636 0.767 0.453 0.380

0.631 0.766 0.847 0.689 0.449 0.223 0.153 0.125 0.414 0.361

1.19 1.13 1.10 1.12 1.15 1.17 1.27 1.24 1.19 1.23

a

α 12 = (y1 /x1 )/(y2 /x2 ).

pressures, the results from the modified UNIFAC model of 1998 [5] are seen to be even worse that incorrectly predicted the existence of minimum pressure azeotropes. Large discrepancies also found in Fig. 2 for 2-methoxyphenol+diphenylmethane, regardless of the versions of the UNIFAC. The agreement is fair for 1,2-dimethoxybenzene + diphenylmethane as shown in Fig. 3. The modified UNIFAC model [5] that uses temperature-dependence interaction parameters yields slightly better results than those from the UNIFAC model of Gmehling et al. [3] for the binary systems containing diphenylmethane. The unsatisfactory predictions from the UNIFAC models could probably be attributed to the fact that the values of some interaction parameters of –OCH3 binaries are improper for those aromatics derivatives and/or the temperatures of the investigated systems are beyond the applicable range of the models. According to the molecular structures of those compounds of interest, the neighbors of –OCH3 in both 1,2-dimethoxybezene and 2-methoxyphenol are aromatic carbons. However, these interaction parameters in the UNIFAC models of Gmehling et al. [3,5] were determined from the experimental data of mixtures

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Fig. 4. Tie-lines for the ternary system of 2-methoxyphenol (1) + 1,2-dimethoxybenzene (2) + diphenylmethane (3) at 463.15 K.

Table 8 VLE prediction with three versions of the UNIFAC modela Mixture (1) + (2)

UNIFAC [3] T (K)

2-Methoxyphenol + 1,2-dimethoxybenzene

1P (kPa)

UNIFAC [5] 1y1

433.15 0.42 0.009 448.15 0.70 0.010 463.15 1.05 0.009 2-Methoxyphenol + diphenylmethane 433.15 3.64 0.085 448.15 5.69 0.088 463.15 8.88 0.093 1,2-Dimethoxybenzene + diphenylmethane 433.15 1.25 0.031 448.15 1.55 0.033 463.15 2.33 0.028 qP qP expt expt 2 n n calc calc a 1P = − Pk )2 /n; 1y1 = k=1 (Pk k=1 (y1,k − y1,k ) /n.

UNIFAC [16]

1P (kPa)

1y1

1P (kPa)

1y1

1.66 2.53 3.79 3.63 4.64 5.83 0.38 0.45 0.87

0.026 0.025 0.023 0.080 0.071 0.069 0.008 0.006 0.005

– – – – – – 1.30 1.64 2.60

– – – – – – 0.031 0.033 0.030

containing aliphatic ethers. It seems necessary to distinguish the groups of the aromatic –OCH3 interaction and the aliphatic –OCH3 interaction in order to improve the accuracy of predictions. Torres et al. [16] addressed this problem and defined a new aromatic methoxyl group (AC–OCH3 ). They determined the related interaction parameters from the VLE data of mixtures containing anisole. These new group parameters were applied in the present study to predict the VLE behavior for 1,2-dimethoxybezene + diphenylmethane. Unfortunately, the results become even worse as shown in Table 8. It appears that the group interaction parameters of AC–OCH3 binaries need further modification. An extensive study on the re-determination of the parameters is currently undergoing in our research laboratory.

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Table 10 VLE prediction for 2-methoxyphenol (1) + 1,2-dimethoxybenzene (2) + diphenylmethane (3) with the determined binary parameters of Table 9 T (K)

433.15

448.15

463.15

433.15–463.15

a

Model

Wilson NRTL UNIQUAC Wilson NRTL UNIQUAC Wilson NRTL UNIQUAC Wilson NRTL UNIQUAC

RMSDa 1P (kPa)

1y1

1y2

1y3

1.18 1.18 1.09 1.65 1.41 1.62 1.98 2.04 1.75 1.67 1.55 1.93

0.000 0.003 0.004 0.000 0.007 0.008 0.003 0.005 0.005 0.004 0.004 0.007

0.001 0.003 0.004 0.001 0.010 0.009 0.003 0.004 0.006 0.004 0.005 0.007

0.001 0.001 0.002 0.001 0.004 0.002 0.001 0.002 0.003 0.003 0.003 0.003

As defined in Table 9.

4.2. Data correlation for binary systems The φ–γ method was used in the present study to correlate the new binary VLE data. While correlative solution models, including the Wilson, the NRTL, and the UNIQUAC, were employed to represent the non-ideality of liquid mixtures, the vapor mixtures were assumed as ideal due to low equilibrium pressures. The optimal values of the temperature-specific binary parameters were determined by the minimization of the following objective function π : " #2 " #2  expt n  expt calc  calc X (y − y ) (Pk − Pk ) 1,k 1,k + π= (3)   σp σy1 k=1 where σ i is the standard deviation of the measured variable i. In the correlations, the values of σ were set to 0.1 kPa for pressure and 0.005 for vapor composition, respectively. The optimization algorithm is similar to that of Prausnitz et al. [17]. Table 9 lists the correlated results, showing that the root mean square deviations (RMSD) are comparable among these three solution models. The solid curves in Figs. 1–3 represent the calculated results from the NRTL model. The parameters determined from the binary data were utilized directly to predict the bubble pressures and vapor compositions for the ternary system of 2-methoxyphenol + 1,2-dimethoxybenzene + diphenylmethane. The predicted results are given in Table 10, indicating that the estimations are reasonably well.

5. Conclusion Isothermal VLE data have been determined experimentally with a static apparatus for the binary and the ternary mixtures composed of 2-methoxyphenol, 1,2-dimethoxybenzene, and diphenylmethane over

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a temperature range of 433.15 to 463.15 K. No binary and ternary azeotropes were found in these investigated systems. The experimental results revealed that the presence of diphenylmethane could increase the relative volatilities of 2-methoxyphenol to 1,2-dimethoxybenzene. Various versions of the UNIFAC model were unable to quantitatively predict the phase behavior of 2-methoxyphenol + 1,2-dimethoxybenzene and 2-methoxyphenol + diphenylmethane, suggesting that the interaction parameters of AC–OCH3 binaries need to be re-determined. The Wilson, the NRTL, and the UNIQUAC models were capable of accurately correlating all the three binary systems and yielded reasonable predictions for the ternary system. List of symbols A G (gij −gjj )/R N P q r R ∞ S12 T (uij −ujj )/R V x y Z

index of area consistency test Gibbs free energy (J mol−1 ) parameter of the NRTL model (K) number of data points pressure (kPa) surface area parameter of the UNIQUAC model volume parameter of the UNIQUAC model gas constant (kPa cm3 mol−1 K−1 or J mol−1 K−1 ) selectivity at infinite dilution temperature (K) parameter of the UNIQUAC model (K) molar volume (cm3 mol−1 ) mole fraction of liquid phase mole fraction of vapor phase compressibility factor

Greek letters α α 12 γ δ (λij −λii )/R π σ φ ω

parameter of the NRTL model relative volatility activity coefficient index of point consistency test parameter of the Wilson model (K) objective function standard deviation Fugacity coefficient acentric factor

Subscripts c critical property i component i ij i–j pair interaction p pressure y1 vapor composition of component 1

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Superscripts calccalculated E excess property exptexperimental L liquid phase s saturation

Acknowledgements Financial support from the National Science Council, ROC, through Grant no. NSC88-2214-E011-018 is gratefully acknowledged. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]

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