New Group-Interaction Parameters of the UNIFAC Model: Aromatic

Shou-Ming Hwang, Ming-Jer Lee*, and Ho-mu Lin. Department ... Denise Yaffe, Yoram Cohen, Gabriela Espinosa, Alex Arenas, and Francesc Giralt. Journal ...
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1740

Ind. Eng. Chem. Res. 2001, 40, 1740-1747

GENERAL RESEARCH New Group-Interaction Parameters of the UNIFAC Model: Aromatic Methoxyl Binaries Shou-Ming Hwang, Ming-Jer Lee,* and Ho-mu Lin Department of Chemical Engineering, National Taiwan University of Science and Technology, 43 Keelung Road, Sec. 4, Taipei 106-07, Taiwan

Isothermal vapor-liquid equilibrium (VLE) data were measured for binary systems of 1-octanol + 2-methoxyphenol and 1-octanol + 1,2-dimethoxybenzene and a ternary system of 1,2dimethoxybenzene + 2-methoxyphenol + 1-octanol at temperatures from 433 to 463 K. Maximum pressure azeotropes appeared in all three systems. Three correlative solution models were utilized in data reduction. Moreover, new group-interaction parameters of the UNIFAC model were determined from binary VLE data for several aromatic methoxyl (Ac-OCH3) binaries. The groupinteraction parameters were tested with VLE data of ternary systems. Introduction

Experiment Section

Phenol derivatives are crucial intermediates to synthesize a wide variety of specialty chemicals. Phase behavior of those product mixtures plays an important role in development of the manufacturing processes. Whenever phase equilibrium data are unavailable in the literature, a group-contribution model, such as UNIFAC,1-3 is usually adopted in a preliminary feasibility study to estimate the activity coefficients for liquid mixtures. Torres et al.,4 however, pointed out that the prediction was rather unsatisfactory for anisole-containing mixtures by using UNIFAC2 with group-interaction parameters of the methoxyl group (-OCH3) determined from aliphatic ethers (denoted as UNIFAC-1982-G). They thus defined a new aromatic methoxyl group (AcOCH3) and determined its group-interaction parameters with several other groups on the basis of vapor-liquid equilibrium (VLE) data of mixtures containing anisole (denoted as UNIFAC-1982-T). Hwang et al.5 used both the UNIFAC-1982-T and the most recent version of UNIFAC3 (denoted as UNIFAC-1998-G) to predict the VLE behavior of mixtures composed of 2-methoxyphenol, 1,2-dimethoxybenzene, and diphenylmethane. Poor results were obtained, suggesting that further modification on the group-interaction parameters was necessary. To expand the data sources for mixtures containing aromatic methoxyl groups, VLE data were measured in the present study for the mixtures composed of 2-methoxyphenol, 1,2-dimethoxybenzene, and 1-octanol. The new group-interaction parameters of AcOCH3 binaries for two versions of UNIFAC2,3 (denoted as UNIFAC-1982-H and UNIFAC-1998-H, respectively) were then redetermined by using VLE data of 12 binary systems. The validity of these parameters was tested with VLE data of three ternary systems, including 2-methoxyphenol + 1,2-dimethoxybenzene + 1-octanol, which was investigated experimentally in this work.

The purities of 1,2-dimethoxybenzene (TCI, Japan), 2-methoxyphenol (Merck, Germany), and 1-octanol (Aldrich, USA) are better than 99%. No impurities are detected by gas chromatographic analysis for these chemicals. The substances were used without further purification. Table 1 lists the critical constants, acentric factor, and the parameters of the UNIQUAC model for the pure compounds. These values are needed in the VLE calculations. A static-type VLE apparatus used in the present study is similar to that described by Hwang et al.7 A degassed solution was charged into the equilibrium cell, which was immersed in a thermostatic bath (model HT250, (0.03 K stability, Neslab, USA). The liquid-phase mixture was circulated by a liquid-pump to promote equilibration. The bath temperature was measured by a Microtherm (model 1560, Hart Scientific, USA) with a platinum RTD probe, accurate to (0.02 K. A pressure transducer (model PDCR-330, Druck, U.K.) connected to a digital readout (model DPI-262, Druck, U.K.) read the equilibrium pressure to an accuracy of (0.1 kPa. Vapor and liquid samples were analyzed by a thermal conductivity detector (TCD) gas chromatography (model 8700, China Chromatography, Taiwan) with a stainless steel column (10% SP-2340 Chromosorb 80/100 Supelcopart, 6 m × 1/8 in.) and using helium (99.99%, purity) as a carrier gas. Four to five samples were replicated for each phase at a given equilibrium condition. The accuracy of composition analysis is estimated to be better than (0.002 for the liquid phase and (0.005 for the vapor phase.

* Corresponding author. Fax: 886-2-2737-6644; E-mail: [email protected].

Experimental Results Tables 2 and 3 report the experimental results for 1-octanol + 2-methoxyphenol and 1-octanol + 1, 2-dimethoxybenzene, respectively. The tabulated activity coefficients were calculated from the equality of fugacity between coexistence phases for each constituent com-

10.1021/ie000795i CCC: $20.00 © 2001 American Chemical Society Published on Web 03/10/2001

Ind. Eng. Chem. Res., Vol. 40, No. 7, 2001 1741 Table 1. Properties of Pure Substances

d

compound

Tc (K)

Pc (kPa)

Vc (cm3 mol-1)

Zc

ω

r

q

1,2-dimethoxybenzene 2-methoxyphenol 1-octanol

696.7b

3427.8b

411.5b

0.244b

0.437c

5.1456d

698.9b 652.5a

4910.7b 2860.0a

303.5b 490a

0.256b 0.258a

0.556c 0.587a

4.5306d 6.6219d

4.016d 3.488d 5.828d

a Taken from Reid et al.6 b Determined from the Joback group contribution model.6 Determined from the group-contribution method.2

Table 2. VLE Data for 1-Octanol (1) + 2-Methoxyphenol (2) T (K)

P (kPa)

x1

y1

433.15

26.3 29.9 30.7 31.7 32.6 33.5 34.2 34.9 35.2 35.2 35.0 34.8 42.8 49.6 50.3 52.2 53.4 54.4 55.6 56.4 57.1 57.0 56.9 56.8 65.8 75.3 77.6 79.4 82.0 83.8 85.9 86.9 87.8 88.0 87.8 87.6

0.00 0.158 0.191 0.285 0.391 0.489 0.611 0.694 0.781 0.868 0.934 1.00 0.00 0.159 0.189 0.287 0.385 0.472 0.594 0.698 0.770 0.871 0.941 1.00 0.00 0.155 0.192 0.286 0.390 0.480 0.603 0.698 0.780 0.867 0.938 1.00

0.00 0.237 0.252 0.389 0.456 0.544 0.673 0.739 0.797 0.864 0.924 1.00 0.00 0.233 0.274 0.371 0.455 0.530 0.657 0.719 0.791 0.864 0.939 1.00 0.00 0.237 0.270 0.357 0.458 0.547 0.647 0.726 0.795 0.860 0.930 1.00

448.15

463.15

ln γ1

ln γ2

GE/(RTx1x2)

0.260 0.153 0.222 0.092 0.071 0.079 0.066 0.031 0.006 -0.006

0.027 0.074 0.026 0.097 0.122 0.085 0.117 0.212 0.319 0.431

0.481 0.577 0.400 0.398 0.388 0.343 0.384 0.412 0.412 0.370

0.254 0.256 0.177 0.108 0.075 0.082 0.023 0.033 -0.005 -0.001

0.049 0.044 0.065 0.092 0.113 0.081 0.194 0.179 0.329 0.319

0.611 0.550 0.474 0.414 0.383 0.337 0.353 0.374 0.341 0.319

0.284 0.224 0.129 0.100 0.908 0.053 0.032 0.022 -0.003 -0.007

0.027 0.058 0.076 0.093 0.093 0.140 0.170 0.205 0.329 0.409

0.514 0.579 0.447 0.401 0.368 0.362 0.349 0.362 0.353 0.320

yiP S

xiPi exp[(P - PiS)ViL/(RT)]

T (K)

P (kPa)

x1

y1

433.15

24.0 27.9 29.0 30.6 32.0 32.9 34.0 34.5 34.8 35.0 34.9 34.8 38.9 45.4 48.2 51.1 52.4 53.4 54.8 56.5 57.2 57.6 56.9 56.8 61.4 71.2 74.6 78.0 80.1 82.8 84.9 86.4 88.0 88.8 88.3 87.6

0.00 0.130 0.208 0.319 0.414 0.512 0.618 0.711 0.836 0.921 0.954 1.00 0.00 0.128 0.207 0.323 0.413 0.508 0.618 0.711 0.841 0.920 0.954 1.00 0.00 0.127 0.207 0.325 0.416 0.514 0.619 0.714 0.836 0.922 0.953 1.00

0.00 0.239 0.325 0.420 0.521 0.601 0.695 0.760 0.852 0.918 0.949 1.00 0.00 0.235 0.317 0.425 0.521 0.603 0.684 0.768 0.856 0.921 0.950 1.00 0.00 0.225 0.320 0.429 0.513 0.592 0.682 0.758 0.844 0.920 0.950 1.00

448.15

463.15

(1)

uc

xi ln γi ∑ i)1

ln γ1

ln γ2

GE/(RTx1x2)

0.394 0.271 0.151 0.148 0.106 0.094 0.059 0.019 0.003 -0.002

0.014 0.026 0.078 0.082 0.108 0.119 0.169 0.260 0.401 0.460

0.561 0.466 0.466 0.449 0.428 0.438 0.441 0.429 0.471 0.440

0.390 0.267 0.174 0.154 0.111 0.067 0.071 0.025 0.014 -0.002

0.018 0.058 0.099 0.084 0.091 0.140 0.141 0.270 0.369 0.439

0.592 0.614 0.563 0.466 0.406 0.402 0.446 0.477 0.579 0.418

0.377 0.286 0.169 0.127 0.089 0.067 0.047 0.014 0.011 -0.006

0.023 0.033 0.063 0.073 0.113 0.132 0.162 0.296 0.370 0.584

0.616 0.522 0.444 0.394 0.402 0.390 0.391 0.439 0.548 0.492

have to obey the following relations:

yi - xi ) 0

where xi , yi, PiS, and ViL are liquid mole fraction, vapor mole fraction, saturated vapor pressure, and liquid molar volume for component i, respectively. While the experimental vapor pressures were used in the calculation, the liquid molar volumes were estimated by the modified Rackett model.8 The excess Gibbs free energy (GE) was calculated from its definition

GE ) RT

Determined from the Lee-Kesler model.6

Table 3. VLE Data for 1-Octanol (1) + 1,2-Dimethoxybenzene (2)

ponent by assuming an ideal vapor phase

γi )

c

(2)

Table 4 gives the results of thermodynamic consistency tests. All the binary isotherms passed the point and the area tests. Lee and Hu 9 detailed the methods of the consistency test. Figures 1 and 2 show the phase diagrams for 1-octanol + 2-methoxyphenol and 1-octanol + 1, 2-dimethoxybenzene, respectively. Each isotherm has a maximum pressure azeotrope and exhibits positive deviations from the ideality of Raoult’s law. The azeotropic conditions

∆Py P ) ∆Px P -

∑PiSyi ) 1 ∑PiSxi

(3) (4)

and

∂P/∂xi ) 0

(5)

Figure 3 shows ∆Px/∆Py and (x1 - y1) varying linearly with x1 around the azeotropic point of 1-octanol + 2-methoxyphenol at 433.15 K. Its azeotropic composition (x1az) was estimated to be about 0.845. The corresponding azeotropic pressure, as also shown in Figure 3, is about 35.2 kPa. Table 5 gives the azeotropic compositions and pressures for each isotherm. The equilibrium phase compositions were also measured for the ternary system of 1-octanol + 2-methoxyphenol + 1, 2-dimethoxybenzene. The experimental results are reported in Table 6. Figure 4 illustrates the tie-lines of the coexistence phases for this ternary

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Table 4. Results of Thermodynamic Consistency Tests consistency test indexa mixture (1) + (2) 1-octanol + 2-methoxyphenol 1-octanol + 1,2-dimethoxybenzene

GE/RT coefficientb

ln(γ1/γ2) coefficientc

T (K)

δ

A

C0

C1

C2

D0

D1

D2

D3

433.15 448.15 463.15 433.15 448.15 463.15

4.99 (+)d 4.41 (+) 4.29 (+) 3.62 (+) 3.76 (+) 4.87 (+)

1.76 (+) 1.47 (+) 2.58 (+) 2.88 (+) 2.78 (+) 1.05 (+)

0.382 0.380 0.381 0.436 0.450 0.387

-0.094 -0.182 -0.148 -0.059 -0.109 -0.089

0.145 0.167 0.126 0.094 0.183 0.270

-0.018 -0.015 -0.026 0.029 0.028 0.010

0.348 0.345 0.380 0.431 0.404 0.450

0.043 -0.016 -0.030 -0.045 -0.043 -0.013

0.214 0.090 0.197 0.242 0.226 0.232

n a Criteria for passing the thermodynamic consistency tests: δ < 5, where δ ) 100∑ E j-1 |δj*/n with δj* ) {[d(G /RT)/dx1] - ln(γ1/γ2)}j and A < 3, where A ) 100|A*| with A* ) ∫01 ln(γ1/γ2) dx. b GE/RT ) x1x2[C0 + C1(x1 - x2) + C2(x1 - x2)2]. c ln(γ1/γ2) ) D0 + D1(x2 - x1) + D2(6x1x2 - 1) + D3(x2 - x1)(1 - 8x1x2). d (+): passes the consistency test.

Figure 1. Pressure-composition diagram for 1-octanol (1) + 2-methoxyphenol (2).

Figure 3. Determination of the azeotropic conditions for 1-octanol (1) + 2-methoxyphenol at 433.15 K. Table 5. Azeotropic Points 1-octanol + 2-methoxyphenol

Figure 2. Pressure-composition diagram for 1-octanol (1) + 1,2-dimethoxybenzene (2).

system at 433.15 K, indicating that a ternary azeotrope with maximum pressure may exist in the vicinity of the corner of 1-octanol. The existence of the ternary azeotrope can be checked with the azeotropic rule, based on

1-octanol + 1,2-dimethoxybenzene

T (K)

x1az

Paz (kPa)

x1az

Paz (kPa)

433.15 448.15 463.15

0.845 0.838 0.828

35.2 57.2 88.0

0.899 0.894 0.891

35.0 57.8 88.9

the knowledge of the residue curve map (RCM). According to the experimental results, it is implied that the corners of 1-octanol and 1,2-dimethoxybenzene are nodes and that of 2-methoxyphenol is a saddle point (i.e., N1 ) 2 and S1 ) 1) in the triangular RCM. Furthermore, both binary azeotropes are saddle points (S2 ) 2 and N2 ) 0) and the ternary azeotrope is a node (N3 ) 1 and S3 ) 0). The results as mentioned above satisfy the azeotropic rule for ternary systems (Dorherty and Perkins10)

2(N3 - S3) + N2 - S2 + N1 ) 2

(6)

VLE Data Reduction The new binary VLE data were correlated with the φ-γ method. In the calculations, the vapor phase was

Ind. Eng. Chem. Res., Vol. 40, No. 7, 2001 1743 n

π1 )

∑

k)1

Figure 4. Tie lines for the ternary system of 1-octanol(1) + 2-methoxyphenol (2) + 1,2-dimethoxybenzene (3) at 433.15 K. Table 6. VLE Data for 1-Octanol (1) + 2-Methoxyphenol (2) + 1,2-Dimethoxybenzene (3) T (K)

P (kPa)

x1

x2

x3

y1

y2

y3

433.15

27.7 26.6 27.3 28.3 31.2 31.4 30.6 33.4 34.6 34.1 34.8 33.0 34.4 34.4 43.3 43.5 44.0 45.0 49.7 49.9 50.3 53.4 55.6 55.4 56.2 53.3 55.4 56.6 51.6 68.4 68.1 68.8 70.0 76.2 77.5 78.1 82.9 84.7 86.0 86.9 82.4 85.5 86.2 78.9

0.082 0.100 0.105 0.107 0.338 0.322 0.325 0.501 0.529 0.715 0.733 0.456 0.613 0.800 0.079 0.100 0.102 0.107 0.328 0.322 0.321 0.503 0.531 0.710 0.725 0.443 0.620 0.800 0.344 0.079 0.098 0.106 0.105 0.328 0.323 0.324 0.501 0.549 0.713 0.717 0.443 0.616 0.806 0.347

0.061 0.224 0.445 0.680 0.543 0.388 0.180 0.099 0.340 0.187 0.090 0.249 0.189 0.104 0.062 0.218 0.452 0.676 0.553 0.390 0.194 0.101 0.336 0.188 0.103 0.266 0.181 0.104 0.089 0.063 0.229 0.441 0.679 0.554 0.383 0.183 0.106 0.316 0.188 0.112 0.259 0.194 0.095 0.077

0.857 0.676 0.450 0.213 0.119 0.290 0.495 0.400 0.131 0.098 0.177 0.295 0.198 0.096 0.859 0.683 0.446 0.217 0.119 0.289 0.485 0.396 0.134 0.102 0.172 0.291 0.199 0.096 0.567 0.858 0.673 0.454 0.216 0.119 0.295 0.494 0.393 0.135 0.099 0.172 0.298 0.190 0.099 0.577

0.173 0.193 0.187 0.180 0.446 0.438 0.451 0.584 0.608 0.750 0.765 0.546 0.665 0.826 0.166 0.193 0.187 0.186 0.414 0.418 0.431 0.579 0.585 0.732 0.748 0.523 0.662 0.810 0.457 0.157 0.180 0.186 0.180 0.415 0.416 0.426 0.572 0.601 0.735 0.740 0.520 0.657 0.816 0.451

0.057 0.209 0.417 0.640 0.474 0.323 0.145 0.078 0.301 0.170 0.076 0.212 0.166 0.092 0.062 0.211 0.431 0.629 0.488 0.345 0.171 0.088 0.301 0.175 0.095 0.235 0.164 0.099 0.078 0.062 0.222 0.416 0.630 0.485 0.337 0.161 0.093 0.283 0.175 0.104 0.228 0.176 0.090 0.067

0.770 0.598 0.396 0.180 0.080 0.239 0.404 0.338 0.091 0.080 0.159 0.242 0.169 0.082 0.772 0.596 0.382 0.185 0.098 0.237 0.398 0.333 0.114 0.093 0.158 0.243 0.175 0.091 0.466 0.781 0.598 0.398 0.190 0.100 0.246 0.413 0.335 0.116 0.091 0.156 0.251 0.167 0.094 0.482

448.15

463.15

assumed to be ideal and three correlative solution models, including the Wilson,11 the NRTL,12 and the UNIQUAC,13 were employed, respectively, to calculate the activity coefficients. The values of binary parameters were determined, on the basis of the maximum likelihood principle (Prausnitz et al.14), by minimization of the following objective function (π1)

{[

] [

(pkcalc - pkexpt) σP

2

+

]}

(y1,kcalc - y1,kexpt) σy1

2

(7)

where σ is standard deviation. The values of σP and σy1 were taken to be 0.1 kPa and 0.005, respectively. Table 7 presents the results of data reduction for the binary systems. The smooth curves in Figures 1 and 2 represent the correlated results from the NRTL model. With these determined binary parameters, each solution model was applied to predict the bubble points of 1-octanol + 2-methoxyphenol + 1,2-dimethoxybenzene. The results of predictions are compared with the experimental values in Table 8. In general, the average deviations from these three activity coefficient models are almost in the same order of magnitudes. Determination of New Group-Interaction Parameters for UNIFAC An aromatic methoxyl group (Ac-OCH3) was treated as an aromatic carbon group (Ac) plus an (aliphatic) methoxyl group (OCH3) in the conventional UNIFAC.2,3 Torres et al.4 found that this treatment was unsatisfactory for anisole-containing systems. They thus defined an individual aromatic methoxyl group, Ac-OCH3, and reported several group-interaction parameters of the AcOCH3 binaries for the UNIFAC of 1982 version.2 However, the VLE data used in their parameter determination were limited to the mixtures containing anisole. In some instances, those determined values are not as suitable for the mixtures containing compounds other than anisole.5 Moreover, their method neglects neighboring group effects. In the present study, two types of aromatic methoxyl groups were specified and the interaction parameters were obtained on the basis of VLE data of 12 binary systems, in which the mixtures contain at least one of the following compounds: anisole, 1,2dimethoxybenzene, 2-methoxyphenol, and 4-methoxyphenol. To distinguish the positions of methoxyl group attached on the benzene ring, we defined two types of aromatic methoxyl groups: Ac-OCH3 (ortho) and Ac-OCH3 (para). The first one refers to either a single aromatic methoxyl group on the ring or the group at the ortho position, while the second one represents the group at the para position. Two versions of UNIFAC2,3 are investigated in this study. The first one2 is in the same form as the original version of 1977,1 in which the interaction energy difference between dissimilar and similar pairs of groups, amn, was considered as a temperature-independent parameter, i.e.

[ ]

ψmn ) exp -

amn T

(8)

The second one was developed by Gmehling et al. in 1998,3 in which they reformulated both the combinatorial and the residual terms with a temperature-dependent Ψmn, i.e.

[

]

amn + bmnT + cmnT2 ψmn ) exp T

(9)

Gmehling et al.3 also revised the group area parameter (Qk) and volume parameter (Rk) by data correlation, rather than estimation from the Bondi method.15 In this

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Table 7. VLE Data Reduction with the Wilson, the NRTL, and the UNIQUAC Models Wilson

NRTL

UNIQUAC

RMSDc

RMSDc

RMSDc

mix ida

T (K)

(λ12 - λ11)/ R (K)

(λ21 - λ22)/ R (K)

∆P (kPa)

∆y1

(g12 - g22)/ R (K)

(g21 - g11)/ R (K)

R

∆P (kPa)

∆y1

(u12 - u22)/ R (K)

(u21 - u11)/ R (K)

∆P (kPa)

∆y1

M1 M2 M3b

433-463 433-463 433-463

159.31 246.43 -85.48

111.10 3.49 246.89

0.3 0.5 0.1

0.013 0.010 0.006

-114.49 251.65 -289.78

373.30 -6.07 423.06

0.440 0.546 0.410

0.3 0.5 0.1

0.014 0.010 0.006

-15.15 43.26 232.08

45.77 -11.90 -180.16

0.3 0.5 0.1

0.013 0.010 0.006

a M1, 1-octanol (1) + 2-methoxyphenol (2); M2, 1-octanol (1) + 1,2-dimethoxybenzene (2); M3, 2-methoxyphenol (1) + 1,2dimethoxybenzene (2). b Data source: Hwang et al.5 c RMSD: root-mean-square deviation, defined as RMSD ∆P ) [∑m)1n(Pmcalc - Pmexpt)2/ n]1/2; RMSD ∆y1 ) [∑m)1n(y1,mcalc - y1,mexpt)2/n]1/2.

Table 8. Predicted Results for the Ternary System of 1-Octanol (1) + 2-Methoxyphenol (2) + 1,2-Dimethoxybenzene (3)

Table 10. Group-Interaction Parameters of Aromatic Methoxyl Binaries for the UNIFAC

RMSDa T (K)

model

∆P (kPa)

∆y1

∆y2

∆y3

433.15

Wilson NRTL UNIQUAC

1.3 1.4 1.3

0.008 0.008 0.007

0.005 0.005 0.005

0.005 0.005 0.005

463.15 a

RMSD as defined in Table 7.

Table 9. List of Constituent Groups UNIFACa substance

1982-G 1998-G

AcCH × 5 Ac × 1 OCH3 × 1 1,2-dimethoxyAcCH × 4 benzene Ac × 2 OCH3 × 2 2-methoxyphenol AcCH × 5 Ac × 1 OCH3 × 1 4-methoxyphenol AcCH × 5 Ac × 1 OCH3 × 1

anisole

1982-T

1982-H 1998-H

AcCH × 5 Ac × 1 AcOCH3 × 1 AcCH × 4 AcOCH3 × 2

AcCH × 5 Ac × 1 AcOCH3(ortho) × 1 AcCH × 4 AcOCH3(ortho) × 2

AcCH × 5 AcCH × 5 AcOCH3 × 1 AcOCH3(ortho) × 1 AcCH × 5 AcCH × 5 AcOCH3 × 1 AcOCH3(para) × 1

a

UNIFAC-1982-G: both equation and group parameters were given as in Gmehling et al.2 (1982). UNIFAC-1982-T: equation was defined as in Gmehling et al.2 (1982), and the group parameters of AcOCH3 binaries were given in Torres et al.4 (1992). UNIFAC-1982-H: equation was defined as in Gmehling et al.2 (1982), and the group parameters of AcOCH3 binaries are given in this study. UNIFAC-1998-G: both equation and group parameters were given as in Gmehling et al.3 (1998). UNIFAC-1998-H: equation was defined as in Gmehling et al.3 (1998) and the group parameters of AcOCH3 binaries are given in this study.

study, QAc-OCH3 ) 1.208 and RAc-OCH3 ) 1.5102 are used, which were obtained from the Bondi method by Torres et al.4 The constituent groups of anisole, 1,2-dimethoxybenzene, 2-methoxyphenol, and 4-methoxylphenol are given in Table 9 for each version of the UNIFAC. The optimal group-interaction parameters of the Ac-OCH3 binaries are determined by minimization of the following objective function (π2) np

π2 )

nc

∑ ∑ (ln γi,kcalc - ln γi,kexpt)2

(10)

k)1 i)1

where nc and np refer to the number of components and the number of data points, respectively. The experimental activity coefficients, γi,kexpt, in the above equation were obtained by introducing experimental VLE data into eq 1. The algorithm used in the parameter determination is similar to that of Fredenslund et al.1 Table

a

aCH3,Wa aAc,W aAcCH,W aOH,W aAcOH,W

UNIFAC-1982-T 181.74 aW,CH3 35.484 aW,Ac 705.24 aW,AcCH 246.3 aW,OH 4291.74 aW,AcOH

33.314 74.764 -184.04 251.5 -459.64

aCH3,Xb aAc,X aAcCH,X aOH,X aAcOH,X aAc,Yc aAcCH,Y aAcOH,Y

UNIFAC-1982-H 179.5 aX,CH3 268.3 aX,Ac 837.4 aX,AcCH 465.1 aX,OH 1233.4 aX,AcOH 351.2 aY,Ac -252.2 aY,AcCH -558.7 aY,AcOH

4.9 -101.2 -639.2 168.1 -791.6 -330.2 620.6 296.6

aCH3,Xb aAc,X aAcCH,X aOH,X aAcOH,X aOH,Yb aAcCH,Y aAcOH,Y

UNIFAC-1998-H 110.8 aX,CH3 -123.8 aX,Ac 623.6 aX,AcCH 517.6 aX,OH 563.1 aX,AcOH 167.2 aY,OH 413.3 aY,AcCH 1162 aY,AcOH

58.6 6321.6 -728.7 734.6 -315.6 74.8 -96.7 -315.6

W: Ac-OCH3. b X: Ac-OCH3 (ortho). c Y: Ac-OCH3 (para).

10 lists the new values of the group-interaction parameters for the Ac-OCH3 binaries. In the UNIFAC-1998H, bmn and cmn were assigned as zero to reduce the number of adjustable parameters. The parameters of Ac-OCH3 (ortho) binaries in the UNIFAC-1982-H and the UNIFAC-1998-H were determined from the VLE data of M1 to M10, and those of Ac-OCH3 (para) binaries were from those of M11 and M12 of Table 11. Since amn values of Ac-OCH3/OH binaries are unavailable for the UNIFAC-1982-T,4 they were also determined in this study from the VLE data of M1 and M2. Table 11 shows the calculated results of the binary systems with several versions of the UNIFAC, including the UNIFAC-1982G,2 1982-T,4 1982-H (new), 1998-G,3 and 1998-H (new). With the newly determined group-interaction parameters, both the UNIFAC-1982-H and the UNIFAC1998-H apparently improve the accuracy of VLE calculations for the majority of binary mixtures. Table 12 compares the predictions from four versions of the UNIFAC with experimental values of three ternary systems. In general, the UNIFAC-1998-H gives the best prediction. Figure 5 compares the predicted results from five versions of the UNIFAC with the experimental values for ethanol (1) + anisole (2) at 101.3 kPa.16 This system was not included in the data bank for determination of group-interaction parameters. While all the models underestimate the equilibrium temperatures at x1 ) 0.1 and 0.2, the UNIFAC-1982-H gives the best prediction over the rest of the composition range.

Ind. Eng. Chem. Res., Vol. 40, No. 7, 2001 1745 Table 11. Results of VLE Calculations from the UNIFAC for Binary Systems RMSDb 1982-G mix ida M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 grand RMSD M11 M12

1982-T

1982-H

1998-G

1998-H

T (K)

n

∆Pb

∆y1b

∆P

∆y1

∆P

∆y1

∆P

∆y1

∆P

∆y1

433.15 448.15 463.15 433.15 448.15 463.15 433.15 448.15 463.15 433.15 448.15 463.15 433.15 448.15 463.15 343.15 353.15 333.15 343.15 358.15 368.15 358.15 368.15 353.15

10 10 10 10 10 10 9 8 8 9 9 9 9 9 9 12 11 22 15 9 9 17 19 20

3.8 5.3 8.3 1.2 3.7 7.3 0.4 0.7 1.1 1.2 1.5 2.3 3.7 5.8 9.0 0.7 1.0 2.6 4.4 4.6 6.3 0.8 1.0 0.3 3.9

0.054 0.051 0.045 0.027 0.028 0.022 0.009 0.010 0.009 0.030 0.032 0.028 0.086 0.090 0.095 0.014 0.029 0.045 0.048 0.039 0.043 0.012 0.016 0.006 0.041

2.2 2.8 4.6 1.0 2.9 6.3 0.8 1.2 1.8 1.3 1.6 2.6 2.4 3.9 6.2 0.6 1.0 1.2 0.2 0.4 0.8 0.6 1.0 0.4 2.5

0.039 0.037 0.031 0.030 0.031 0.027 0.009 0.009 0.008 0.032 0.024 0.030 0.068 0.038 0.052 0.014 0.030 0.008 0.008 0.013 0.007 0.015 0.019 0.007 0.029

1.1 1.1 2.1 1.5 1.4 4.2 1.1 1.8 2.7 0.4 0.6 0.9 2.8 1.9 3.4 0.9 1.7 1.7 1.4 1.0 1.1 0.9 0.7 0.7 1.7

0.023 0.021 0.015 0.022 0.010 0.019 0.019 0.018 0.018 0.033 0.026 0.022 0.072 0.043 0.056 0.014 0.030 0.021 0.013 0.021 0.012 0.009 0.014 0.015 0.026

1.3 3.0 7.6 1.2 1.4 3.5 1.7 2.5 3.8 0.4 0.5 0.9 3.6 4.6 5.8 1.3 1.4 1.3 0.7 0.9 1.3 3.5 4.8 1.4 3.0

0.025 0.034 0.042 0.023 0.018 0.019 0.026 0.025 0.023 0.008 0.006 0.015 0.080 0.071 0.069 0.018 0.030 0.018 0.013 0.026 0.019 0.028 0.023 0.033 0.032

1.8 2.8 5.8 1.0 2.7 5.5 1.1 2.0 3.5 0.5 0.4 0.7 1.9 2.6 3.8 1.1 2.0 1.1 0.3 1.0 1.5 1.1 1.5 0.7 2.3

0.034 0.037 0.037 0.022 0.018 0.017 0.018 0.020 0.021 0.032 0.023 0.016 0.049 0.046 0.054 0.017 0.033 0.010 0.007 0.022 0.016 0.015 0.013 0.012 0.026

423.15 438.15 453.15 438.15 453.15

9 9 9 9 9

0.6 0.7 1.1 0.8 0.8 0.7

0.024 0.016 0.013 0.017 0.012 0.015

0.5 0.4 0.6 0.1 0.4 0.4

0.019 0.010 0.008 0.015 0.019 0.015

1.4 2.0 3.0 0.3 0.1 1.7

0.051 0.041 0.037 0.008 0.013 0.034

1.2 1.4 2.0 1.9 0.1 1.2

0.041 0.028 0.022 0.011 0.011 0.025

grand RMSD

a M1: 1-octanol + 1,2-dimethoxybenzene (this work). M2: 1-octanol + 2-methoxyphenol (this work). M3: 2-methoxyphenol + 1,2dimethoxybenzene.5 M4: 1,2-dimethoxybenzene + diphenylmethane.5 M5: 2-methoxyphenol + diphenylmethane.5 M6: benzene + anisole.4 M7: hexane + anisole.4 M8: heptane + anisole.4 M9: propanol + anisole.4 M10: butanol + anisole.4 M11: p-cresol + 4-methoxyphenol.7 M12: p-cresol + catechol.7 b RMSD as defined in Table 7.

Table 12. Results of VLE Predictions from the UNIFAC for Ternary Systems RMSDb UNIFAC-1982-G mix ida T1 T2 T3 grand RMSD

UNIFAC-1982-H

T (K)

n

∆P (kPa)

∆y1

∆y2

∆y3

∆P (kPa)

∆y1

∆y2

∆y3

433.15 448.15 463.15 433.15 448.15 463.15 453.15

10 10 10 15 15 15 15 90

1.3 2.3 3.8 2.8 2.6 4.0 1.2 2.4

0.032 0.034 0.032 0.031 0.022 0.023 0.029 0.029

0.033 0.039 0.036 0.031 0.028 0.027 0.011 0.029

0.023 0.023 0.023 0.037 0.022 0.028 0.029 0.027

1.0 1.8 2.8 1.5 0.9 2.9 1.0 1.8

0.022 0.022 0.022 0.032 0.017 0.025 0.025 0.024

0.022 0.025 0.027 0.039 0.024 0.032 0.022 0.028

0.010 0.010 0.012 0.021 0.020 0.025 0.024 0.019

RMSDb UNIFAC-1998-G mix ida T1 T2 T3 grand RMSD

UNIFAC-1998-H

T (K)

n

∆P (kPa)

∆y1

∆y2

∆y3

∆P (kPa)

∆y1

∆y2

∆y3

433.15 448.15 463.15 433.15 448.15 463.15 453.15

10 10 10 15 15 15 15 90

1.2 2.0 3.3 1.7 1.3 4.8 0.7 2.5

0.040 0.032 0.028 0.028 0.022 0.026 0.021 0.030

0.043 0.038 0.035 0.021 0.022 0.026 0.021 0.029

0.021 0.023 0.017 0.015 0.013 0.021 0.033 0.021

1.0 1.8 2.7 1.6 1.1 2.2 0.6 1.7

0.035 0.033 0.023 0.022 0.020 0.024 0.025 0.026

0.030 0.030 0.023 0.024 0.025 0.025 0.016 0.025

0.012 0.010 0.012 0.014 0.013 0.017 0.028 0.017

a T1: 2-methoxyphenol (1) + 1,2-dimethoxybenzene (2) + diphenylmethane (3). T2: 1-octanol (1) + 2-methoxyphenol (2) + 1,2-dimethoxybenzene (3). T3: p-cresol (1) + 4-methoxyphenol (2) + catechol (3). b RMSD as defined in Table 7.

Conclusions Isothermal VLE data have been determined experimentally by using a static apparatus for the binary and the ternary mixtures composed of 1-octanol, 2-methoxy-

phenol, and 1,2-dimethoxybenzene over a temperature range of 433-463 K. Maximum pressure binary azeotropes were found in 1-octanol + 2-methoxyphenol and 1-octanol + 1,2-dimethoxybenzene, and one ternary

1746

Ind. Eng. Chem. Res., Vol. 40, No. 7, 2001 (uij - uij)/R ) parameter of UNIQUAC model, K V ) molar volume, cm3 mol-1 x ) mole fraction of liquid phase y ) mole fraction of vapor phase Z ) compressibility factor Greek Symbols R ) parameter of the NRTL model δ ) index of point consistency test γ ) activity coefficient (λij - λii)/R ) parameter of the Wilson model, K π ) objective function σ ) standard deviation φ ) fugacity coefficient. ω ) acentric factor Subscripts

Figure 5. Comparison of the predicted results from five versions of the UNIFAC model with the experimental values of ethanol (1) + anisole (2) at 101.3 kPa. Experimental data were taken from Gmehling et al.16

azeotrope likely was formed in 1-octanol + 2-methoxyphenol + 1,2-dimethoxybenzene. The Wilson, the NRTL, and the UNIQUAC models correlated well the binary VLE data and predict satisfactorily the VLE behavior for the ternary system. Group-interaction parameters of aromatic methoxyl binaries in the UNIFAC have been determined in the present study. The results showed that the UNIFAC-1998-H with the new parameters generally yielded the best prediction for the ternary systems. These new group-interaction parameters extend the applicability of the UNIFAC to the mixtures containing aromatic methoxyl substitutes.

c ) critical property i ) component i ij ) i-j pair interaction P ) pressure y1 ) vapor composition of component 1 Superscripts az ) azeotrope calc ) calculated E ) excess property expt ) experimental L ) liquid phase s ) saturation

Acknowledgment

Literature Cited

Financial support from the National Science Council, ROC, through Grant No. NSC88-2214-E011-018 is gratefully acknowledged.

(1) Fredenslund, Aa.; Gmehling, J.; Rasmussen, P. VaporLiquid Equilibria Using UNIFAC: A Group-Contribution Method; Elsevier: Amsterdam, 1977.

Nomenclature A ) index of area consistency test G ) Gibbs free energy, J mol-1 (gij - gjj)/R ) parameter of the NRTL model, K n ) number of data points Ni ) number of nodes in the system containing i components P ) pressure, kPa q ) surface area parameter of the UNIQUAC model Qi ) surface area parameter of group i r ) volume parameter of UNIQUAC model Ri ) surface area parameter of group i R ) gas constant, J mol-1 K-1 Si ) number of saddle points in the system containing i components T ) temperature, K

(2) Gmehling, J.; Rasmussen, P.; Fredenslund, Aa. VaporLiquid Equilibria by UNIFAC Group Contribution. Revision and Extension. 2. Ind. Eng. Chem. Process Des. Dev. 1982, 21, 118. (3) Gmehling, J.; Lohmann. J.; Jakob, A.; Li, J.; Joh. R. A Modified UNIFAC (Dortmund) Model. 3. Revision and Extension. Ind. Eng. Chem. Res. 1998, 37, 4876. (4) Torres, M. A. Y.; Bottini, S. B.; Brignole, E. A. Vapor-Liquid Equilibria for Binary Mixtures with Anisole. Fluid Phase Equilib. 1992, 71, 85. (5) Hwang, S. M.; Lee, M. J.; Lin, H. M. Isothermal VaporLiquid Equilibria for Mixtures Composed of 1,2-Dimethoxybenzene, 2-Methoxyphenol, and Diphenylmethane. Fluid Phase Equilib., in press. (6) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill: New York, 1987. (7) Hwang, S. M.; Lee, M. J.; Lin, H. M. Isothermal VaporLiquid Equilibria for Mixtures of 4-Methoxyphenol, Catechol, and p-Cresol. Fluid Phase Equilib. 2000, 172, 183. (8) Spencer, C. F.; Danner, R. P. Improved Equation for Predication of Saturated Liquid Density. J. Chem. Eng. Data 1972, 17, 236. (9) Lee, M. J.; Hu, C. H. Isothermal Vapor-Liquid Equilibria for Mixture of Ethanol, Acetone, and Diisopropyl Ether. Fluid Phase Equilib. 1995, 109, 83.

Ind. Eng. Chem. Res., Vol. 40, No. 7, 2001 1747 (10) Doherty, M. F.; Perkins, J. D. On the Dynamics of Distillation Processes-III. The Topological Structure of Ternary Residue Curve Map. Chem. Eng. Sci. 1979, 34, 1401. (11) Wilson, G. M. Vapor-Liquid Equilibrium XI: A New Expression for the Excess Free Energy of Mixture. J. Am. Chem. Soc. 1964, 86, 127. (12) Renon, H.; Prausnitz, J. M. Local Composition in Thermodynamic Excess Function for Liquid Mixture. AIChE J. 1968, 14, 135. (13) Abrams, D. S.; Prausnitz, J. M. Statistical Thermodynamics of Liquid Mixtures: A New Expression for the Excess Gibbs Energy of Partly or Completely Miscible Systems. AIChE J. 1975, 21, 116. (14) Prausnitz, J. M.; Anderson, T. F.; Grens, E. A.; Eckert, C. A.; Hsieh, R.; O’Connell, J. P. Computer Calculations for Multicomponent Vapor-Liquid and Liquid-Liquid Equilibria; PrenticeHall: New York, 1980.

(15) Bondi, A. Physical Properties of Molecular Crystals, Liquids and Glasses; Wiley: New York, 1968. (16) Gmehling, J.; Onken, U.; Arlt, W. Vapor-Liquid Equilibrium Data CollectionsOrganic Hydroxy Compounds: Alcohols (Supplement 1); Chemical Data Series, Vol. 1, Part 2c; DECHEMA, Frankfurt/Main, 1982.

Received for review September 1, 2000 Revised manuscript received January 15, 2001 Accepted January 25, 2001

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