Fluid Phase Equilibria, 93 (1994) 285-295 Elsevier Science B.V.

285

Optimization of UNIQUAC structural parameters for individual mixtures: application to new experimental liquid-liquid equilibrium data for aqueous solutions of methanol and ethanol with isoamyl acetate

Albert0 Arce *, Antonio Blanco, Jose Martinez-Ageitos and Isabel Vidal

Chemical Engineering Department, University of Santiago de Compostela (Spain)

(Received January 19, 1993; accepted in final form June 1, 1993)

ABSTRACT

Arce, A., Blanco, A., Martinez-Ageitos, J. and Vidal, I., 1994. Optimization of UNIQUAC structural parameters for individual mixtures: application to new experimental liquid- liquid equilibrium data for aqueous solutions of methanol and ethanol with isoamyl acetate. Fluid Phase Equilibria, 93: 285-295.

Experimental liquid-liquid equilibrium data for the ternary mixtures water + methanol + isoamyl acetate and water + ethanol + isoamyl acetate at various temperatures are reported, together with the results of correlation by the original UNIQUAC equation using both structural parameters q and r from the literature and q’s and r’s optimized for each mixture as part of the overall correlation procedure. The improved fit obtained with the optimized parameters (which differed from the “universal” values only for the smaller molecules) may be viewed as being due to the active surface area and volume of a molecule being dependent upon its environment.

Keywords: experiments, LLE, correlation, UNIQUAC.

INTRODUCTION

Understanding the thermodynamics of phase equilibria is fundamental to the development of various kinds of industrial chemical process. In particu- lar, progress in the development of separation processes is hindered by unresolved problems in this field, and the construction of appropriate thermodynamic models on the basis of experimental data is an essential aspect of current research on separation (Zeck, 1991). Models such as the UNIQUAC and NRTL equations for the excess Gibbs free energy of

* Corresponding author.

0378-3812/94/$07.00 0 1994 - Elsevier Science B.V. All rights reserved SSDZ 0378-3812(93)02386-2

286 A. Arce et al. 1 Fluid Phase Equilibria 93 (1994) 285-295

mixtures are well suited to the correlation of multicomponent phase equi- librium data for application to the design of distillation and extraction units. The UNIQUAC equation in particular is widely used for this purpose.

The original UNIQUAC equation (Abrams and Prausnitz, 1975) has undergone several modifications. Anderson and Prausnitz (1978a, b) altered its structural parameters so as to improve its fit to vapour-liquid equi- librium data for binary and ternary mixtures containing alcohols; Maurer and Prausnitz (1978) multiplied the residual term by a constant C (C < 1) representing the reduction in molecular surface area; and a variety of other changes have been effected by Nagata and coworkers. Specifically, Nagata and Katoh ( 1981) likewise introduced an additional parameter in their “effective” UNIQUAC model; Nagata ( 1982) developed an “extended” UNIQUAC; Nagata and Ohtsubo (1986) applied an associated-solution UNIQUAC theory to alcohols; and Nagata (1989) further modified the extended UNIQUAC equation by introducing additional parameters for use with ternary systems. In spite of possessing different structural parameters, both the latter models have worked well for a test set of binary and ternary mixtures (Nagata, 1991), though Nagata et al. ( 1991) subsequently found the modified extended UNIQUAC to work better than the unextended form for a set of 81 binary systems. When Alessi et al. (1988) calculated q values for paraffins by applying group solution theory to dilute mixtures of isomers, they found that q values were markedly smaller for components involved in strong association phenomena.

In this paper we explore the possibility that the ultimate aim of the UNIQUAC, satisfactory overall correlation of phase equilibrium data, is best served if the structural parameters q and Y characterizing the compo- nents of liquid mixtures are optimized for each particular mixture. This procedure is perfectly compatible with the theoretical basis of the UNI- QUAC, amounting simply to treating the active surface and volume of a molecule as dependent upon its environment. We present here a comparison of the results of this approach with those of the original UNIQUAC equation (Abrams and Prausnitz, 1975) for ternary mixtures of methanol or ethanol with water and isoamyl acetate.

EXPERIMENTAL

Materials

Methanol and ethanol were supplied by Merck as 99.7% pure and isoamyl acetate by Aldrich as 99.1% pure. Measurements of physical characteristics (density, refractive index and boiling point) and chromatography confirmed their purity, and they were used without further purification.

A. Arce et ai. 1 F&id Phase E~~ilibria 93 (1994) 285-295 287

Liquid-liquid equilibrium (LLE) data were obtained in jacketed ceils as previously described (Correa et al., 1989). Phases in equilibrium were analysed by gas chromatography in a Hewlett-Packard 5890 Series II apparatus with thermal conductivity detection.

LLE data were obtained for the ternary systems water + methanol + isoamyl acetate and water + ethanol + isoamyl acetate at 25, 35 and 45°C (Tables 1 and 2).

CORRELATION

UNIQUAC correlations were performed using Sarrensen’s ( 1980) com- puter program. Values of q and Y for use without optimization in the original UNIQUAC equation (Abrams and Prausnitz, 1975) were obtained from Prausnitz et al. (1986) for water, methanol and ethanol; for isoamyl acetate they were calculated, using the UNIFAC group scheme, from published values of the parameters Qk and Rk (Magnussen et al., 1981). These values of q and r, shown in Table 3, were used as the initial values (q(O) and r(O)) in a one-at-a-time optimization procedure, as follows. In the tth iteration, q was first held fixed at the value obtained in the preceding iteration, q(‘- I), while the value of r = c@ ‘) giving the best fit to the experimental data was found, c being stepped from 0.6 to 1.2; this value of Y, rfrf, was then fixed while q@) was found analogously. Goodness of fit, for these purposes, was evaluated on the basis of two quantities: r.m.s. devia- tion in composition

k i J

1

l/2 F’= 100 E c c (xiik - $&2/6M

and the r.m.s. error in the solute distribution ratio

In cases of conflict between these criteria, the decision was based on the function showing the larger change with respect to the previous iteration.

The final values of q and r obtained at convergence for water and the alcohols are listed in Tables 4 and 5 (the values obtained for isoamyl acetate did not differ from the initial values) together with the values of F and Afl that were obtained with the optimized parameters and with the unoptimized parameters of Table 3. The corresponding values of the UNIQUAC parameters A, are listed in Tables 6 and 7.

288 A. Arce et al. 1 Fluid Phase Equilibria 93 (1994) 285-295

TABLE 1

LLE phase composition (mole fractions) of water( 1) + methanol( 2) + isoamyl acetate( 3)

Temperature Aqueous phase Organic phase

Xl x2 x3 Xi x2 x3

25°C 0.9996 0.0000 0.0004 0.0532 0.0000 0.9468 0.9233 0.0761 0.0006 0.0523 0.0364 0.9113 0.8935 0.1061 0.0003 0.0622 0.0556 0.8822 0.8337 0.1656 0.0007 0.0713 0.1003 0.8283 0.7724 0.2257 0.0019 0.0977 0.1510 0.7513 0.6986 0.2973 0.0041 0.1368 0.2272 0.6360 0.6509 0.3408 0.0083 0.1597 0.2620 0.5783 0.5801 0.4008 0.0191 0.2236 0.3524 0.4240 0.5712 0.4121 0.0168 0.2480 0.3765 0.3756

35°C 0.9998 0.0000 0.0002 0.0530 0.0000 0.9447 0.9145 0.0850 0.0005 0.0662 0.0492 0.8846 0.8605 0.1387 0.0008 0.0704 0.0827 0.8460 0.8442 0.1547 0.0011 0.0822 0.0951 0.8227 0.8133 0.1855 0.0012 0.0962 0.1234 0.7804 0.8054 0.1930 0.0016 0.1012 0.1382 0.7606 0.7572 0.2401 0.0027 0.1217 0.1762 0.7021 0.7160 0.2791 0.0049 0.1486 0.2216 0.6275 0.7057 0.2891 0.0052 0.1509 0.2271 0.6243 0.6523 0.3384 0.0093 0.1862 0.2877 0.5260 0.6363 0.3529 0.0108 0.1899 0.2940 0.5160 0.6002 0.3823 0.0175 0.2306 0.3445 0.4250

45°C 1 .OOoo 0.0000 0.0000 0.0548 0.0000 0.9452 0.9200 0.0794 0.0005 0.0572 0.0479 0.8948 0.8626 0.1358 0.0016 0.0763 0.0898 0.8339 0.8355 0.1631 0.0014 0.1035 0.1147 0.7818 0.8274 0.1709 0.0017 0.1038 0.1294 0.7668 0.8108 0.1867 0.0024 0.1146 0.1476 0.7378 0.7861 0.2116 0.0023 0.1138 0.1639 0.7223 0.7788 0.2185 0.0027 0.1287 0.1749 0.6964 0.7364 0.2598 0.0038 0.1439 0.2090 0.6471 0.6951 0.2977 0.0072 0.1797 0.2533 0.5670 0.6738 0.3182 0.0080 0.2009 0.2807 0.5184 0.6562 0.3364 0.0110 0.2121 0.3026 0.4853 0.6021 0.3829 0.0150 0.2337 0.3579 0.4084

For both mixtures and all temperatures, use of the optimized parameters improved Ap, in general very considerably (Tables 4 and 5). This improve- ment was generally accompanied by at least a slight improvement in F. At worst, F increased by about 0.02% in cases in which this increase allowed a very significant reduction in Afl.

A. Arce et al. / Fluid Phase Equilibria 93 (1994) 285-295 289

TABLE 2

LLE phase compositions (mole fractions) of water( 1) + ethanol( 2) + isoamyl acetate( 3)

Temperature Aqueous phase Organic phase

Xl x2 x3 XI x2 x3

25°C 0.9996 0.0000 0.0004 0.0532 0.0000 0.9468

0.9920 0.0078 0.0002 0.0765 0.0097 0.9138

0.9707 0.0290 0.0003 0.0700 0.0399 0.8901

0.9443 0.0554 0.0003 0.1146 0.0976 0.7878

0.9275 0.0720 0.0005 0.1425 0.1432 0.7143

0.9130 0.0862 0.0008 0.1574 0.1790 0.6636

0.8905 0.1085 0.0010 0.2363 0.2529 0.5108

0.8573 0.1400 0.0027 0.3271 0.3089 0.3640

35°C 0.9998 0.0000 0.0002 0.0553 0.0000 0.9447

0.9955 0.0039 0.0006 0.0570 0.0086 0.9344

0.9758 0.0235 0.0007 0.0785 0.0432 0.8783

0.9512 0.0480 0.0008 0.0902 0.0871 0.8227

0.9268 0.0723 0.0009 0.1191 0.1427 0.7382

0.9121 0.0869 0.0010 0.1512 0.1784 0.6704

0.8848 0.1128 0.0024 0.2300 0.2427 0.5273

0.8448 0.1510 0.0042 0.3339 0.3129 0.3532

45°C 1.0000 0.0000 0.0000 0.0548 0.0000 0.9452

0.9946 0.005 1 0.0003 0.0619 0.0127 0.9254

0.9736 0.0260 0.0004 0.0840 0.0530 0.8630

0.9554 0.0438 0.0008 0.1265 0.1080 0.7655

0.9256 0.0738 0.0006 0.1750 0.1926 0.6324

0.8995 0.0989 0.0016 0.2436 0.2883 0.468 1

0.8702 0.1266 0.0032 0.3636 0.3090 0.3274

TABLE 3

Universal values of q and r obtained from the literature or calculated by group contribution

methods

Substance 4 r

Methanol 1.432 1.431

Ethanol 1.97 2.11

Water 1.40 0.92

Isoamyl acetate 4.732 5.501

290 A. Axe et al. / FIuid Phase E~iii~r~ 93 f1994) 285-295

TABLE 4

UNIQUAC structural parameters q and r optimized for the mixture water( 1) + methanol(2) + isoamyl acetate(f) at various temperatures, together with values of the goodness-of-fit criteria F and A/I (see text) obtained with the optimized parameters and with the universal parameters (*) of Table 3 (for isoamyl acetate, the optimized and universal values coincide)

25°C 35°C 45°C

4 r 4 r 4 r

Water 1.40 0.552 1.40 1.104 1.12 0.552 Methanol 1.432 1.717 1.432 1.431 0.859 0.859

F(%) 0.350 0.336 0.387 AH%) 1.8 2.4 2.2 F*(%) 0.666 0.341 0.497 AB*(%) 6.2 3.2 4.2

TABLE 5

UNIQUAC structural parameters q and r optimized for the mixture water{ 1) + ethanol(2) + isoamyl acetate(3) at various temperatures, together with values of the good- ness-of-fit criteria F and A#I (see text) obtained with the optimized parameters and with the universal parameters (*) of Table 3 (for isoamyl acetate, the optimized and universal values coincide)

25°C 35°C 45°C

4 r 4 r 4 r

Water 1.68 0.736 1.40 0.736 0.84 0.92 Ethanol 1.97 2.11 1.97 2.11 1.97 2.53

F(%) 0.331 0.203 0.470 AS(%) 2.8 5.8 7.6 F*(%) 0.312 0.305 0.454 A/?*(%) 14.7 34.4 19.0

DISCUSSION

The salient features of our results are: (1) the considerable improvement in A/3 achieved with the optimized

values of q and r at the expense of, at most, a very slight increase in F; (2) the si~ificant degree of temperature dependence of the optimized

values; and

A. Arce et al. / Fluid Phase Equilibria 93 (1994) 285-295

TABLE 6

291

Adjustable binary UNIQUAC parameters A,, (K) obtained for the mixture wa- ter( 1) + methanol(2) + isoamyl acetate(3) at various temperatures using optimized and universal (*) values of the structural parameters q and r

A, A,, A,*, AJ:

25°C Water + methanol - 399.33 -473.07 959.9 1 - 449.03 Water + isoamyl acetate 50.32 272.91 239.47 534.45 Methanol + isoamyl acetate -112.20 183.66 -118.90 403.90

35°C Water + methanol - 1012.9 630.20 - 932.68 643.54 Water + isoamyl acetate 737.56 471.99 381.30 471.84 Methanol + isoamyl acetate - 195.39 -111.93 - 175.80 9.6605

45°C Water + methanol - 389.36 - 368.71 - 1092.9 856.71 Water + isoamyl acetate 2.6527 936.58 382.01 477.99 Methanol + isoamyl acetate 75.69 137.73 - 181.35 - 127.36

TABLE 7

Adjustable binary UNIQUAC parameters A,, (K) obtained for the mixture wa- ter( 1) + ethanol( 2) + isoamyl acetate( 3) at various temperatures using optimized and univer- sal (*) values of the structural parameters q and r

25°C Water + ethanol Water + isoamyl acetate Ethanol + isoamyl acetate

35°C Water + ethanol Water + isoamyl acetate Ethanol + isoamyl acetate

45°C Water + ethanol Water + isoamyl acetate Ethanol + isoamyl acetate

8.1089 - 397.56 127.44 - 116.71 349.17 294.71

496.06 -275.12 74.812

- 168.98 -27.551 49.577 -315.31 -21.655 594.53 216.94 537.10

- 189.97 435.72 180.86 - 385.97

69.324 683.45 54.615 1131.3 1814.4 278.12

- 197.63 456.59 266.97

- 357.97 454.82

- 338.45

- 332.93 504.74

-518.03

(3) the fact that in general only a minority of the optimized parameters differed from the “universal” values used as starting values.

In the latter respect, the results obtained at 35°C are especially striking (in particular, for the ethanol mixture a change in only one parameter - r for

292

TABLE 8

A. Arce et al. i Fluid Phuse Equilibria 93 (1994) 285-295

Values of the UNIQUAC structural parameters r and q for water, methanol and ethanol, as optimized for individual mixtures of water f (methanol or ethanol) + some third component

r 4 Mixtures KC) A/J A&t

Water 0.920 1.120 0.736 1.680 1.104 1.400 0.552 1.680 0.920 1.680 0.920 1.400 0.736 0.840 1.104 1.400 0.552 1.680 0.736 1.680 0.552 1.400 0.920 1.680 0.552 1.400 0.552 1.400 1.104 1.400 0.920 1.400 0.920 1.400 0.920 1.120 1.104 1,400 0.920 1.400 0.552 1.120 1.104 1.680 0.736 1.680 0.920 0.840 0.920 1.400 0.920 1.680 0.920 1.400 0.920 0.840 0.736 1.680 0.736 1.680 0.736 1.400 0.736 1.680 0.552 1.680 0.920 1.680 0.736 1.400

Methanol 1.431 1.718 1.431 1.432 1.717 1.432 0.859 1.146 1.717 1.718 0.859 1.718 1.717 0.859

Water + methanol + trichloroethene 27.5 13.9 6.5 Water + methanol + 1,2-dichloroethane 25.0 23.6 1.2 I-Nitropropane + methanol + water 25.0 5.5 4.6 Water + methanol + 2,3-dichloro- 1,3-butadiene 20.0 21.3 4.2 Water + methanol + acetic acid, ethenyl ester 20.0 4.0 3.6 Acetic acid, ethyl ester + methanol + water 20.0 9.7 8.2 I-Butanol -t methanol + water 30.0 3.9 2.3 Acetic acid, butyl ester + methanol + water 30.0 5.7 2.7 Butanoic acid, ethyl ester + methanol + water 30.0 16.5 1.2 1-Hexanol + methanol + water 20.0 3.6 2.1 Water + methanol + toluene 25.0 89.3 16.3 Water + methanol + acetic acid, pentyl ester 30.0 5.3 4.1 I-Heptanol + methanol + water 20.0 3.3 2.0 I-Octanol + methanol + water 20.0 2.8 2.4 Water + methanol + diphenyl ether 25.0 13.4 12.3 Acetic acid, ethyl ester + ethanol + water 20.0 7.2 4.5 I-Butanol + ethanol + water 25.0 10.4 7.0 Diethyl ether + ethanol + water 25.0 8.6 6.9 I-Pentanol -t ethanol + water 25.5 6.4 5.4 Water + ethanol + benzene 25.0 3.4 3.4 Water + ethanol + cyclohexene 25.0 28.9 6.0 Water + ethanol + cyclohexane 25.0 4.3 1.5 Water + ethanol + hexane 25.0 9.1 4.4 4-Methyl-2-pentanol + ethanol f water 30.0 3.6 2.1 Water + ethanol + 2-chlorotoluene 25.0 7.7 7.7 Water + ethanol + toluene 25.0 18.1 2.9 4-Heptanone + ethanol + water 25.5 19.3 10.7 3-Methylbutanoic acid ethyl ester-t ethanol + w rater 25.0 5.1 3.3 Water + ethanol + heptane 25.0 3.8 2.1 Water + ethanol + 1,3_dimethylbenzene 25.0 2.8 2.2 Water + ethanol + 1,4-dimethyibe~ene 25.0 37.7 4.4 Water + ethanol + 1-octene 25.0 6.6 5.6 Water + ethanol + 2,2,~t~methyl~ntane 25.0 5.3 2.2 Water + ethanol + diphenyl ether 25.0 9.8 7.4 1 -Heptadecanol + ethanol + water 25.0 3.2 1.7

Water + methanol + trichloroethene 27.5 13.9 6.5 Water + methanol + 1,2-dichloroethane 25.0 23.6 1.2 I-Nitropropane + methanol -t water 25.0 5.5 4.6 Water + methanol + 2,3-dichloro-1,3-butadiene 20.0 21.3 4.3 Water + methanol + acetic acid, ethenyl ester 20.0 4.0 3.6 Acetic acid, ethyl ester + methanol + water 20.0 9.7 8.2 1 -Butanol + methanol + water 30.0 3.9 2.3

A. Arce et al. / Fluid Phase Equilibria 93 (1994) 285-295 293

TABLE 8 (continued)

r 9 Mixtures t(“c) AB A&t

1.145 1.718 Acetic acid, butyl ester + methanol + water 30.0 5.7 2.7 1.717 1.146 Butanoic acid, ethyl ester + methanol + water 30.0 16.5 1.2 1.145 1.718 1 -Hexanol + methanol + water 20.0 3.6 2.1 0.859 1.432 Water + methanol + toluene 25.0 89.3 16.3 1.431 1.718 Water + methanol + acetic acid, pentyl ester 30.0 5.3 4.1 1.717 1.432 I-Heptanol + methanol + water 20.0 3.3 2.0 1.717 1.146 I-Octanol + methanol + water 20.0 2.8 2.4 1.145 1.432 Water + methanol + diphenyl ether 25.0 13.4 12.3

Ethanol 1.263 1.183 1.684 1.578 2.527 1.972 2.106 1.972 2.106 1.972 2.527 1.972 2.106 1.972 2.106 1.972 2.106 2.366 2.106 1.972 2.527 1.578 2.527 1.972 1.684 1.972 1.684 1.972 2.106 1.972 2.527 1.972 2.106 1.972 2.106 1.578 2.527 1.578 2.106 1.183

Acetic acid, ethyl ester + ethanol + water 20.0 7.2 4.5 1-Butanol + ethanol + water 25.0 10.4 7.0 Diethyl ether + ethanol + water 25.0 8.6 6.9 1-Pentanol + ethanol + water 25.5 6.4 5.4 Water + ethanol + benzene 25.0 3.4 3.4 Water + ethanol + cyclohexene 25.0 28.9 6.0 Water + ethanol + cyclohexane 25.0 4.3 1.5 Water + ethanol + hexane 25.0 9.1 4.4 4-Methyl-2-pentanol f ethanol + water 30.0 3.6 2.1 Water + ethanol + 2-chlorotoluene 25.0 7.7 7.7 Water + ethanol + toluene 25.0 18.1 2.9 4-Heptanone + ethanol + water 25.5 19.3 10.7 3-Methylbutanoic acid, ethyl ester + ethanol + water 25.0 5.1 3.3 Water + ethanol + heptane 25.0 3.8 2.1 Water + ethanol + 1,3_dimethylbenzene 25.0 2.8 2.2 Water + ethanol + 1 ,Cdimethylbenzene 25.0 37.7 4.4 Water + ethanol + 1 -octene 25.0 6.6 5.6 Water + ethanol + 2,2,4_trimethylpentane 25.0 5.3 2.2 Water + ethanol + diphenyl ether 25.0 9.9 7.4 I-Heptadecanol + ethanol + water 25.0 3.2 1.7

water - results in a reduction in A/? from 34% to 6%), as is the fact that optimization of r and q for isoamyl acetate resulted in no change in their values.

Table 8 shows the results of optimizing q and r in the same way for all other mixtures of water + (methanol or ethanol) + some third component for which data have been published in the DECHEMA Chemistry Data Series, Vol. V, Part 2 (Sorensen and Arlt, 1980) (in view of the finding that the optimized values of q and r for bulky third components differed little from their universal values, these parameters were in fact only optimized for water and methanol or ethanol in the calculations whose results are listed in Table 8). In all cases, A&, the value of A/? obtained using the optimized values of q and r, is at least as small as Apuniv, the value obtained using the

294 A. Arce et al. /Fluid Phase Equilibria 93 (1994) 285-295

universal values of these parameters (the goodness-of-fit criterion used is A/? because it is more sensitive than F to changes in q and r; see Tables 3 and 4). The greatest deviations of optimal q and r values from the universal values are shown by water, and the smallest by ethanol.

The above behaviour was of course to be expected: given enough data for a given system, optimizing q and r as well as the usual adjustable UNIQUAC parameters naturally improves goodness of fit by any chosen criterion. The question of theoretical interest is whether this procedure is simply a compu- tational stratagem to improve UNIQUAC results, or whether the suggestion made in the Introduction - that the active volume and surface area of molecules should be treated as environment-dependent - is supported by observation of coherent trends in optimized q and r values in analogous series of systems. However, a satisfactory answer to this question - and to the similar question of the coherence of the temperature dependence of q and r - will require examination of a very large number of systems, and is beyond the scope of this article.

CONCLUSIONS

For the correlation of LLE data via the UNIQUAC equation, it is advantageous to treat the components of the mixture as though the active surface areas and volumes of their molecules depend on their environment, i.e. on the other components of the mixture.

ACKNOWLEDGEMENT

This work was partly supported by the DGICYT (Spain) under Project PB92-0365.

LIST OF SYMBOLS

A, F

M

4 Qk

x,

&,k

h

xilk

binary adjustable UNIQUAC parameter for components i and j r.m.s. deviation in composition number of conjugate phase pairs molecular volume fraction group volume parameter molecular surface area fraction group surface area parameter experimental mole fraction of component i in phase j of conjugate phase pair k calculated Xi,k

A. Arce et al. / Fl~~ Phase E~~ilibri~ 93 (1994) 285-295 295

Greek letters

solute distribution ratio calculated idem

A> r.m.s. error in the solute distribution ratio

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