isobaric vapor-liquid equilibria for methyl esters + butan-2-ol at different pressures

RlllM[ [OglUgRlil

ELSEVI E R Fluid Phase Equilibria 118 (1996) 249-270

Isobaric vapor-liquid equilibria for methyl esters + butan-2-ol at different pressures

Juan Or tega *, Pab lo H e r n a n d e z

Laboratorio de Termodindmica y Fisicoqufmica, Escuela Superior de lngenieros lndustriales, 3507 I-University of Las Palmas de G.C., Spain

Received 10 May 1995; accepted 5 July 1995

Abstract

Vapor-liquid measurements for the mixtures of three methyl esters (ethanoate, propanoate, butanoate) and butan-2-ol were obtained at 74.66, 101.32 and 127.99 kPa in a small capacity still. All systems were found to be thermodynamically consistent and the maximum likelihood principle was chosen as the regression technique to determine the parameters of different available equations. Only the mixture methyl butanoate + butan-2-ol presented a minimum azeotrope which shifted toward concentrations richer in alcohol as working pressure increased. Experimental results were compared with prediction by UNIFAC and ASOG methods.

Keywords: Experiments; VLE Data; Esters; Butan-2-ol

1. I n t r o d u c t i o n

There are a number of reasons for collecting VLE data at pressures other than atmospheric. Not only are such values of interest in engineering applications, there is also a need for observations on changes in mixture behavior with pressure, particularly the presence of singular points, which are relevant; for purification methods, and on effects of these intensive magnitudes in the theoretical analysis of solutions.

Therefore, this paper is part of an ongoing research project into the behavior of isobaric vapor- l iquid equilibria (VLE) in binary mixtures of alkyl esters and alcohols at our laboratory (Ortega et al., 1986; Ortega et al., 1987). Research analyzing the VLEs for the lowest methyl esters with normal and isomeric alcohols at different pressures have been undertaken with a view to systematizing that study (Ortega et al., 1990a; Ortega and Susial, 1990a; Ortega and Susial, 1993).

* Corresponding author.

0378-3812/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0378-3812(95)02821-8

250 J. Ortega, P. Hernandez / Fluid Phase Equilibria 118 (1996) 249-270

However, within the framework of the project, it has been considered both necessary and appropriate to report new values for systems containing isomeric alcohols, for which there are insufficient literature values at the present time. Thus, extending the range of working pressures contemplated in previous research, VLE values have now been determined experimentally for binary mixtures consisting of three methyl esters (ethanoate, propanoate, butanoate) and butan-2-ol at pressures of 74.66, 101.32, and 127.99 kPa. No VLE values for these systems have been found in the literature consulted. However, Horsley (1973) proposed an azeotrope for the mixture (methyl butanoate + butan-2-ol) at atmospheric pressure for the conditions Taz < 370.85 K and Xeste r > 0.335.

Besides reporting new experimental values, this paper also presents the results of correlations employed for those magnitudes measured by direct experimentation and those calculated indirectly from the experimental measurements. Furthermore, the experimental values have been compared with the predictions calculated using the ASOG model (Kojima and Tochigi, 1979) and two versions of the UNIFAC model, UNIFAC-1 (Fredenslund et al., 1975) and UNIFAC-2 (Larsen et al., 1987; Weidlich and Gmehling, 1987).

2. Experimental

2.1. Materials

The components used in the experiment were supplied by Fluka and were the highest commercial grade. The most relevant physical properties of the methyl esters used in this study, p, n(D, 298.15 K), and Tb, ~, did not differ greatly from the values reported earlier (Susial et al., 1989, Susial and Ortega, 1995; Ortega and Susial, 1991). The following experimental values were obtained for butan-2-ol at the temperature 298.15 K: p / ( k g m -3) = 802.29, 802.6 (Riddick et al., 1986), 802.3 (TRC, 1991); n(D) = 1.3949, 1.395 (Riddick et al., 1986), 1.3949 (TRC, 1991); Tb, 2 = 372.36 K, 372.65 (TRC, 1991), 372.66 K (Ambrose and Sprake, 1970), 372.7 (Reid et al., 1977; Riddick et al., 1986).

2.2. Apparatus and procedure

The experimental equilibrium still was a dynamic still in which both phases were refluxed. The still and the auxiliary fittings and equipment necessary for isobaric operation have been described in previous papers (Ortega et al., 1986; Ortega and Susial, 1993). The concentrations of the liquid and vapor phases were measured using an Anton Parr model DMA-55 vibrating-tube digital densimeter to a precision of +0.02 kg m -3, previously calibrated using water and n-nonane. Densities for the binary systems studied {x1CuH2u+jCOOCH3(u = 1, 2, 3)+xzCH3CH2CH(OH)CH~} at (298.15 ___ 0.01) K were validated by verifying the uniform distribution of excess volumes, V E, on methyl ester concentration. The resulting correlations, p = p(x~), were used to determine the equilibrium liquid and vapor concentrations, to a precision of ___ 0.002 units for the liquid phase and somewhat higher, +0.004, for the vapor phase. Comparing the concentrations of both phases calculated using V E = VE(xl) and p = p(xj) did not yield any significant differences.

J. Ortega. P. Hernandez/Fluid Phase Equilibria 118 (/9961249-270 251

3. Results

3.1. Densit ies and excess volumes

The densities, p, and excess volumes, V E, for each of the binary mixtures {x~ a methyl ester + x 2 butan-2-ol} were determined before calculating the equilibrium compositions, x~ and y~. The values

Table 1 Excess volumes for the binary mixtures methyl esters(I)+ butan-2-ol(2) at 298.15 K

xl P 109 V E x I P l0 ~) V E (kgm 3) (m 3 mo1-1) ( k g m - 3 ) (m 3 mol i)

xICH .~COOCH 3 + x2CH.~CH(OH)CH2CH 3 0.0000 802.29 0.0 0.6099 866.66 715.5 0.0238 804.11 74.6 0.6565 873.16 652.9 0.0984 810.63 260.0 0.7512 886.32 571.0 0.1532 815.24 423.9 0.8405 899.97 413.6 0.1890 818.66 490.0 0.8728 905.23 337.2 0.2704 826.90 599.3 0.8992 909.57 275.0 0.3426 834.40 691.5 0.9323 915.08 195.9 0.4259 843.57 762.4 0.9729 922.01 92.8 0.5249 855.58 760.7 1.0000 926.97 0.0 xIC2HsCOOCH 3 + x2CH3CH(OH)CH2CH 3 0.00(X) 802.29 0.0 0.4649 847.80 583.8 0.0433 806.18 92.2 0.5221 853.90 582. I 0.0782 809.38 169.9 0.5584 857.81 573.7 0. I 148 812.82 241.0 0.5944 861.65 569.4 0.1300 814.15 280.9 0.6065 867.48 530.2 0.2042 821.34 391.2 0.6828 871.50 505.0 0.2239 823.22 422.1 0.7266 876.50 457.0 0.2364 824.50 432.2 0.7668 881.00 422.0 0.2673 827.38 487.9 0.7913 883.86 386.7 0.3319 834.10 518.9 0.8545 891.01 317.8 0.3700 838.03 539.1 0.8930 895.73 234.7 0.3747 838.52 541.8 0.9392 901.33 140.7 (I.4117 842.24 569.4 0.9705 905.18 70.5 0.4560 846.84 585.2 1.0000 908.84 0.0 x iC 3 H v COOCH 3 + x2CH 3 CH(OH)CH 2 CH 3 0.0000 802.29 0.0 0.5001 847.79 522.5 0.0328 805.16 73.5 0.5458 852.00 502.8 0.0756 809.28 136.5 0.6414 860.42 480.1 0.0911 810.45 194.3 0.7072 866.31 429.5 0.1249 813.72 232.9 0.8309 877.21 304.3 0.1620 816.95 309.8 0.8624 879.94 268.6 0.2306 823.30 387.7 0.9015 883.41 206.9 0.3268 832.07 473.3 0.9636 889.07 79.5 0.3842 837.30 503.0 1.0000 892.35 0.0


Table 2 Coefficients A i and k obtained using Eq. (1) and standard deviations, s(V z), for the mixtures of methyl esters(I)+ butan-2- o1(2) Mixture k A 0 A t A 2 109 s(V z ) / ( m 3 mo l - 1 )

x 2 butan-2-ol + x Methyl ethanoate 0.067 3620.2 - 595.1 - 8.8 Methyl propanoate 0.133 2494.7 - 161.9 - 9.6 Methyl butanoate 2.559 2278.5 - 1116.8 1467.7 8.5

of these magnitudes are set out in Table 1. Table 2 presents the values for the coefficients k and A i in Eq. (1) used to correlate the (x~, V E) data for each system.

Q= XlX2 Y'.Ai[ x , / ( x, + k x 2 ) ] i w h e r e Q = V E / ( m 3 m o l - ' )

i

(1)

Fig. 1 plots the experimental values and the fitted curves for the three mixtures considered in this study. The V E values were positive in all cases, although the expansion effects decreased regularly with methyl ester chain length due to the weakening of the polar forces that occurs in this type of compound, as already reported in previous papers for similar mixtures. The regular distribution of the

800

600

Y

200

o

o xlmethyl ethan°ate+xzbutan-2-°l 1 • xffnethyl propanoate+xzbutan-2-ol v xlrnethyl butanoate+x2butan-2-ol

0.2 0.4 0.6 0.8 xl

Fig. 1. Excess molar volumes at 298.15 K for the mixtures (x~ methyl esters + x 2 butan-2-ol).

J. Ortega, P. Hernandez / Fluid Phase Equilibria 118 ~ 1996) 249-270 253

Table 3 Experimental vapor pressures for butan-2-ol

T (K) p0 (kPa) T (K) pi ° (kPa) 7" (K) p~) (kPa)

348.12 38.24 367.52 85.07 376.98 120.58 350.18 41.94 368.57 88.53 377.60 123.19 352.41 46.21 369.28 90.94 378.26 126.14 354.03 49.50 370.80 96.27 378.56 127.99 355,73 53.18 371.73 99.70 378.89 129.00 358,25 59.02 372.36 101.32 379.46 131.54 359,84 62.97 372.44 102.30 380.03 134.22 361,38 66.99 373.08 104.67 380.63 136.96 362.62 70.29 373.69 107.03 381.19 139.66 363.93 74.02 374.20 109.7(I 381.26 140.07 364.12 74.53 374.92 111.98 365.58 78.94 375.54 114.52 366.45 81.65 376.24 117.38

(x~, V >~) data points is indicative of good density values, and consequently, as stated above, there were no discrepancies between the estimates of the equilibrium concentrations calculated from the density values or those calculated from the excess volume values.

3.2. Vapor pressures

The influence of vapor pressures on the thermodynamic treatment of VLE data is well known. Therefore, new experimental (T, pO) values for butan-2-ol were obtained using the same equilibrium still for a range of temperatures approaching the boiling points of the pure components at the working pressures used. The values thus obtained were then correlated using a method of non-linear regression employing the classic Antoine equation. New values had already been published for methyl esters (Ortega and Susial, 1990b; Ortega and Susial, 1990a; Ortega et al., 1990b). Table 3 contains the

Table 4 Coefficients A, B, C used in this work along to the standard deviations, s(pi°), for butan-2-ol in the Antoine equation: log(pi°/kPa) = A - B / [ T / K + C]

Mixture A B C s(p0) Ref. (kPa)

Methyl ethanoate Methyl propanoate Methyl butanoate Butan-2-ol

6.49340 1329.46 - 33.52 6.58882 1469.36 - 30.99 6.30360 1381.64 - 53.60 6.31286 1159.84 - 102.90 6.59921 1314.19 - 86.60 6.32621 1159.00 - 104.87 6.26852 1126.67 - 108.36

0.04

Ortega and Susial (1990b) Ortega and Susial (1990a) Ortega et al. (1990b) This work TRC (1991) Boublik et al. (1973) Ambrose and Sprake (1970)


[ • - - 1 ¸

°#. I

~ 2 .

- 3 320

Boublick et aL (1973)

. 9 9 . "-.-..~".£...

2.5,¢" 7 " " . .

T/K

Fig. 2. Representation of differences, 6p~, between the curves obtained by Antoine equation using the parameters from literature o o The dashed line (- - .) corresponds to a difference of 2.5% with respect to Pi,lit and those determined by us, Pi,exp" the Antoine equation obtained with our experimental results.

experimental vapor pressures while Table 4 shows the constants A, B, and C used to correlate the data with the Antoine equation. Fig. 2 graphically represents the differences in the vapor pressure curves obtained using the Antoine equation for a given temperature range, along with the constants for butan-2-ol calculated in this study and the literature values (Ambrose and Sprake, 1970; Boublik et al., 1973; TRC, 1991). The figure shows that the differences in the curves plotted by Ambrose and Sprake (1970), Boublik et al. (1973), and TRC (1991) were small and though they increased slightly with temperature over a given range, they were in all cases less than 3%.

3.3. Equilibrium data and correlations

The p, T, x~, y~ values compiled by direct experimentation at the different working pressures (74.66, 101.32, 127.99) + 0.02 kPa and the corresponding values of y~ and "/2 for all three binary systems are listed in Table 5. Fig. 3(a)-3(c) shows the representation of (y~ - x Z) on xl and T on x~ and y~ for all cases. The activity coefficients for the mixtures characterized by { xlC ~H 2~ + 1COOCH 3( u = 1,2,3 ) + x2CH 3CH 2CH(OH)CH 3} were calculated using

"Yi = [fbiYiP/( xi 05i°P°)] exp[( pO_ p)viL/RT] (2)

taking the vapor phase to be non-ideal and calculating the fugacity coefficients, ~b~ and qSi ° by means of:

exp[(2 i yi j yiyj ij) JRT]

J. Ortega, P. Hernandez / Fluid Phase Equilibria 118 11996) 249-270 255

where the molar volumes, Vi L, for the pure components and their variations with temperature were assessed using a modified version of Rackett's equation (see Spencer and Danner, 1972). The values of the virial coefficients, B~j, in the equation of state, truncated at the second term, were calculated

Table 5 Experimental data for the mixtures (x t methyl esters + x 2 butan-2-ol) at different working pressures

T x I Yl ~* ~2

xICH3COOCH3+x2CH3CH(OH)CH2CH3

p=74.66 kPa

364.04 0.0000 0.0000 - 1.000

362.19 0,0144 0.0787 1.553 1.007

361.16 0.0231 0.1213 1.533 1.008

358.52 0.0485 0.2344 1,514 0,999

355.40 0.0789 0.3464 1.498 0.999

353.80 0,0959 0.3971 1,477 1.002

352.56 0.1098 0.4369 1.468 1.000

351.13 0.1255 0.4778 1.464 1.002

350.12 0.1369 0.5049 1.460 1,005

349.06 0.1532 0.5341 1.423 1.008

347.43 0.1732 0.5740 1.419 1.013

346.10 0.1923 0.6055 1.402 1.018

344.55 0.2145 0.6397 1.391 1.024

343.30 0.2367 0.6697 1.370 1.021

341.00 0.2764 0.7157 1.345 1.029

339,22 0.3144 0.7500 1.310 1.037

337,34 0.3533 0.7800 1.286 1.057

336.26 0.3794 0.7977 1,267 1.066

335.37 0.4047 0.8118 1.244 1.079

334.50 0.4300 0.8257 1.225 1.088

332.80 0,4838 0.8517 1.187 1,111

331.00 0,5491 0.8765 1.142 1.158

329.63 0.5899 0.8934 1.134 1.178

328.37 0.6462 0.9090 1.099 1.242

326,97 0.7095 0.9236 1.067 1.365

325.49 0.7692 0.9407 1.054 1.441

324.23 0.8171 0.9546 1.052 1.488

323.38 0.8730 0.9668 1.027 1.639

322.53 0.9169 0.9776 1.019 1,770

256

Table 5 (continued)

J. Ortega, P. Hernandez / Fluid Phase Equilibria 118 (1996) 249-270

321.90 0.9526 0.9867 1.013 1.906

321.12 1.0000 1.0000 1.000

p=101.32 kPa

372.36 0.0000 0.0000 1.000

369.82 0.0203 0.0987 1.528 1.001

369.20 0.0260 0.1220 1.498 1.002

366.39 0.0561 0.2347 1.433 0.999

360 ,10 0 .1313 0 .4463 1.372 0 .997

358 .20 0 .1564 0 .4980 1.352 1 .003

356 .58 0 .1805 0 ,5437 1.337 1,001

355 .07 0 .2029 0 ,5813 1.326 1 .003

352 .40 0 .2444 0 .6405 1.307 1 .014

351.11 0 .2679 0 .6693 1.292 1 .016

349 .48 0 .2968 0.6991 1.277 1.031

348 .33 0 .3205 0 .7210 1.261 1 ,039

347 .28 0 .3430 0.7401 1.247 1 .047

346 .30 0 .3669 0 .7577 1.228 1 .057

344 .98 0 .4023 0 .7817 1.202 1,069

344 .35 0 .4232 0 .7918 1.179 1 .087

342 .95 0 .4623 0 .8149 1.159 1 .103

341 .53 0 .5129 0 .8375 1.121 1 .140

338 .52 0 .6119 0.8811 1,085 1 .202

337 .27 0 .6738 0 .8967 1.043 1 .318

335 .16 0 .7601 0 .9257 1.021 1 .425

333 .89 0 .8066 0 .9416 1.019 1 .477

332.81 0 .8573 0 .9563 1.009 1 .579

331.90 0.8988 0.9695 1.005 1.626

330.92 0.9423 0.9829 1.004 1.678

330.34 0.9699 0.9908 1.002 1.782

329.81 1 .0000 1.0000 1.000

p=127 .99 kPa

378 .56 0 .0000 0 .0000 1 .000

377 .19 0 .0152 0 .0670 1.452 0 .996

375 .95 0 .0304 0 .1135 1.266 1.002

374 .83 0.0461 0 .1615 1.220 1.001

371 ,83 0 .0863 0 .2763 1.199 1 .002

370 .42 0 .1066 0 .3294 1.198 0 .998

J. Ortega, P. Herna~lez / Fluid Phase Equilibria 118 ¢ 1996) 249-270 257

Table 5 (continued)

368.80 0.1300 0.3831

366.87 0.1585 0.4452

365.35 0.1824 0.4886

361.77 0.2365 0.5759

359.33 0 .2834 0 .6367

357 .67 0 .3145 0 .6720

356.16 0 .3442 0.7021

354.80 0.3734 0.7248

353.55 0.4014 0.7491

352.32 0.4303 0.7707

351.12 0.4581 0.7926

348.77 0.5224 0.8325

346.51 0.5879 0.8624

345.90 0.6048 0.8686

344.98 0.6337 0.8800

344.06 0.6640 0.8910

343.57 0.6899 0.9004

342.70 0.7249 0.9133

342.26 0.7597 0.9238

341.29 0.8002 0.9383

340.70 0.8302 0.9453

339.97 0.8671 0.9572

339.10 0.9037 0.9681

337.78 0.9528 0.9855

336.49 1.0000 1.0000

p=74.66

364.04

363.50

362.73

361.26

359.78

359.20

358.00

357 .50

357 .00

kPa

1 ,189

1,190

1.179

1.177

1.158

1.152

1 146

1 132

1 127

1 120

1 119

1 103

1.085

1.081

1 .074

1.067

1 .053

1.044

1.021

1.014

1.003

0.994

0.991

0.997

1 .000

x C H COOCH +x CH CH(OH)CH CH 1 2 5 3 2 3 2 3

0 .999

0 ,997

1,000

1.017

1.020

1.027

1.036

1.058

1.062

1.073

1.073

1.086

1.139

1,165

1.195

1.232

1.247

1.272

1.305

1.328

1.423

1.471

1.575

1.553

0 . 0 0 0 0 0 . 0 0 0 0 - 1 . 000

0.0133 0.0337 1.322 1.003

0.0300 0.0819 1.456 0.998

0.0620 0.1596 ].433 1.000

0.0959 0.2347 1.423 1.001

0.1118 0.2606 1.379 1.007

0.1468 0.3202 1.338 1.010

0.1657 0.3497 ].314 1.008

0.1835 0.3755 1.293 1.009

258

Table 5 (continued)


356.13 0.2103 0.4171 1.287 1.008

355.15 0.2418 0.4562 1.261 1.020

354.75 0.2605 0.4775 1.240 1.021

354.23 0.2807 0.5017 1.229 1.022

353.67 0.2982 0.5210 1.222 1.031

352.97 0.3213 0.5458 1.215 1.040

351.85 0.3679 0.5913 1.190 1.053

351.27 0.3941 0.6124 1.172 1.067

350.71 0.4209 0.6358 1.159 1.074

350.11 0.4493 0.6570 1.144 1.091

349.51 0 .4803 0 .6813 1.131 1.102

348 .82 0 .5146 0 .7056 1.118 1 .123

348 .23 0 .5484 0 .7264 1.100 1.150

347 .50 0 .5916 0 .7526 1.082 1.187

346.86 0.6319 0.7767 1.067 1.222

346.28 0.6699 0.7986 1.055 1.261

345.69 0.7098 0.8249 1.048 1.280

345.21 0.7554 0.8458 1.026 1.366

344.70 0.8015 0.8798 1.023 1.342

344.28 0.8395 0.9021 1.015 1.378

343.94 0.8733 0.9188 1.005 1.470

343.59 0.9070 0.9354 0.997 1.618

343.32 0.9340 0.9525 0.995 1.697

343.18 1.0000 1.0000 1.000 -

p=I01.32 kPa

372.36 0.0000 0.0000 - 1.000

370.68 0.0397 0.0941 1.355 0.995

369.80 0.0644 0.1443 1.312 0.995

368.82 0.0910 0.1953 1.292 0.998

366.96 0.1511 0.2951 1.238 1.002

366.34 0.1693 0.3233 1.232 1.006

365.40 0.1960 0.3638 1.229 1.011

364.14 0.2435 0.4289 1.209 1.012

363.61 0.2656 0.4564 1.198 1.012

363 .18 0 .2799 0.4701 1.185 1.022

362.77 0 .2940 0 .4873 1.184 1.025

362 .25 0 ,3138 0 .5084 1.175 1.031

J. Ortega, P. Hernandez/Fluid Phase Equilibria 118 (1996)249-270 259

Table 5 (cont inued)

3 6 1 . 7 6 0 . 3 3 3 4 0 .5301

3 6 1 . 2 7 0 . 3 5 3 8 0 . 5 5 0 4

3 6 0 , 8 2 0 . 3 7 5 4 0 , 5 6 9 5

3 6 0 . 3 2 0 . 3 9 7 8 0 . 5 9 0 3

3 5 9 . 8 6 0 . 4 2 0 9 0 . 6 1 0 2

3 5 9 . 3 4 0 . 4 4 6 9 0 , 6 3 2 7

3 5 8 . 7 0 0 . 4 7 9 8 0 . 6 5 9 6

3 5 8 . 1 2 0 . 5 1 3 7 0 . 6 8 4 6

3 5 7 . 2 2 0 . 5 6 0 5 0 . 7 1 7 5

3 5 6 , 6 0 0 , 6 0 0 3 0 , 7 4 4 3

3 5 5 . 9 0 0 . 6 4 8 9 0 . 7 7 3 0

3 5 5 . 3 2 0 . 6 9 0 1 0 .8001

3 5 5 . 0 2 0 . 7 1 7 2 0 . 8 1 5 2

3 5 4 . 4 9 0 , 7 6 2 9 0 . 8 4 6 2

3 5 3 . 8 1 0 . 8 1 9 9 0 . 8 7 8 0

3 5 3 . 6 4 0 . 8 3 5 5 0 . 8 9 0 3

3 5 3 . 5 0 0 . 8 5 3 0 0 . 9 0 0 3

3 5 3 . 0 4 0 . 8 9 3 0 0 .9211

352.84 0.9252 0.9427

352.74 0.9464 0.9571

352.66 1.0000 1.0000

p=127.99 kPa

378.56 0.0000 0.0000

377.76 0.0288 0.0632

376.92 0.0549 0.1159

375.86 0.0878 0.1748

375.30 0.1091 0.2101

374.92 0.1207 0.2287

374.01 0.1556 0.2816

372.90 0.1940 0.3405

372.12 0.2205 0.3755

371.42 0.2453 0.4092

370.36 0.2880 0.4630

369.87 0.3039 0.4785

368.83 0.3374 0.5174

368.23 0.3640 0.5421

367.00 0.4193 0.5959

1 .169

1 .161

1 .147

1 .138

1 .127

1 . 1 1 8

1 .106

1 .091

1 .077

1 . 0 6 3

1 . 0 4 3

1 . 0 3 3

1 .022

1 .014

1 ,000

1 .000

0 . 9 9 5

0 . 9 8 6

0.980

0.979

1 .000

1 598

1 276

1 237

1 215

1 207

1 181

1 180

1 .169

1 .167

1 .158

1 .149

1 .152

1 ,137

1 .123

1 . 0 3 4

1 , 0 4 0

1 . 0 4 8

1 . 0 5 5

1 . 0 6 3

1 . 0 7 0

1 .081

1 . 0 9 6

1 . 1 2 6

1 149

1 194

1 220

1 251

1 269

1 363

1 351

1 . 3 8 2

1 .531

1 . 6 0 4

1 . 6 9 0

1.000

0.995

0.992

0.995

0.994

0.996

0.997

0.997

1 . 0 0 3

1 . 0 0 4

1 . 0 0 5

1 .016

1 . 0 2 5

1 . 0 3 6

1 . 0 4 7

260

Table 5 (continued)


366 .16 0 .4563 0 .6293 1 .116 1.058

365 .58 0 .4870 0 .6545 1.106 1.068

365 .12 0 .5105 0 .6707 1.095 1.085

364 .48 0 .5498 0 .6989 1.079 1.105

363 .69 0 .6059 0 .7359 1.055 1.141

363 .30 0 .6387 0 .7577 1.042 1.158

362 .67 0 .6826 0 .7858 1 .029 1.194

362 .10 0 .7293 0 .8145 1 .015 1.239

361 .66 0 .7610 0 .8357 1.011 1.264

361 .26 0 .7949 0.8581 1 .006 1.292

360.85 0.8299 0.8792 0.999 1.348

360.44 0.8634 0.8985 0.993 1.433

360.20 0.8913 0.9145 0.986 1.531

359.91 0.9204 0.9369 0.986 1.561

359.76 0.9311 0.9435 0.986 1.624

359.67 1.0000 1.0000 1.000 -

xlC3HTCOOCH3+x2CH3CH(OH)CH2CH3

;)=74.66 kPa

364.04 0.0000 0.0000 - 1.000

363.93 0.0105 0.0175 1.751 1.001

363.69 0.0248 0.0359 1.532 1.005

363.53 0.0506 0.0707 1.486 1.002

363 .28 0 .0785 0 .1042 1 .423 1.004

363 .06 0 .1027 0 .1350 1.419 1.004

362 .85 0 .1265 0 .1635 1.405 1.006

362 .62 0 .1540 0 .1957 1.391 1.007

362 .44 0 .1840 0 .2252 1 .347 1 .013

362 .30 0 .2086 0 .2536 1 .344 1.011

362 .14 0 .2396 0 .2832 1.314 1.017

362 .00 0 .2737 0 .3116 1.271 1.028

361 .89 0 .3014 0.3391 1.260 1.031

361 .78 0 .3606 0 .3900 1.216 1.044

361 .76 0 .3849 0 .4076 1.191 1.054

361 .69 0 .4213 0 .4305 1 .152 1.080

361 .66 0 .4655 0 .4568 1 .107 1.117

361 .66 0 .4950 0.4731 1.078 1.147

J. Ortega, P. Hernandez / Fluid Phase Equilibria 118 (1996) 249-270 261

Table 5 (continued)

361.67 0.5322 0,5001

361,71 0.5681 0.5272

361.85 0.6240 0.5692

361.96 0.6718 0.6067

362.19 0.7162 0.6494

362,41 0.7684 0.6915

362,74 0.8084 0.7362

363.12 0.8532 0.7793

363.52 0.8891 0.8300

363.93 0.9174 0.8717

364.13 0.9461 0,9098

364.58 0.9729 0.9497

364.95 1.0000 1.0000

p=101 .32 kPa

372 .36 0 .0000 0 .0000

372 .26 0.0071 0 .0107

372 .13 0.0201 0 .0278

371 .95 0 .0333 0.0451

371 .66 0 .0645 0 .0842

371 .54 0 .0855 0 .1065

371 .39 0 .1097 0 .1342

371 .22 0 .1358 0 .1615

370.98 0.1799 0.2079

370.90 0.2034 0.2311

370.81 0.2331 0.2583

370.73 0.2615 0.2840

370.69 0.2880 0.3074

370.66 0.3135 0.3294

370.64 0.3449 0,3547

370.63 0,3728 0,3784

370.63 0.4005 0.4020

370.66 0.4307 0.4239

370.70 0.4620 0.4462

370.77 0.4938 0.4732

370.88 0.5428 0.5076

371.39 0.6316 0.5782

371.53 0.6605 0.5992

1.060

1.045

1.023

1.009

1.006

0.991

0 .992

0 .983

0.992

0.997

1.002

1 .003

1.000

1 640

1 511

1 488

1 446

1 385

I 366

1 335

1.306

1,287

1.259

1.237

1.217

1.199

1,174

1.159

1.146

1.123

i . I00

1.089

1.059

1.021

1.008

1 .174

1.201

1.250

1 .302

1.331

1 .423

1 .453

1 .564

1.571

1.567

1,676

1.828

I. 000

O. 994

O. 994

0.996

O. 997

O. 999

I. 000

I. 004

1. 008

1.010

1.015

1.021

1. 026

1. 031

1 . 0 4 1

1.047

1.054

I . 068

1.085

1.094

I . 128

1. 178

1. 209

262

Table 5 (continued)


371.81

372.39

372.64

372.97

373.35

373.73

374.23

374.77

375.07

375.17

375.35

p=127.99

378.56

378.47

378.29

378.19

378.06

377.95

377.82

377.69

377.62

377.60

377.59

377.58

377.59

377.60

377.64

377.71

377.77

377.87

377.97

378.09

378.13

378.33

378.41

378.88

379.12

kPa

0.7025 0.6392 1.002 1.230

0.7746 0.7064 0.987 1.294

0.8031 0.7349 0.983 1.326

0.8349 0.7684 0.979 1.366

0.8666 0.8060 0.978 1.398

0.8992 0.8458 0.978 1.451

0.9299 0.8904 0.981 1.458

0.9618 0.9406 0.987 1.423

0.9806 0.9696 0.989 1.420

0.9917 0.9864 0.992 1.480

1.0000 1.0000 1.000 -

0 . 0 0 0 0 0 . 0 0 0 0 - 1 . 0 0 0

0.0142 0.0183 1.460 1.003

0.0434 0.0552 1.448 1.001

0.0640 0.0775 1.383 1.002

0.0891 0.1065 1.370 1.001

0.1191 0.1375 1.327 1.003

0.1559 0.1744 1.290 1.007

0 .2075 0 .2229 1.243 1 .014

0 .2336 0 .2468 1.225 1.018

0 .2593 0 .2710 1 .213 1.021

0 .2818 0 .2927 1.206 1 .022

0 ,3083 0 .3146 1.185 1 .028

0.3327 0.3371 1.176 1.031

0.3510 0.3518 1.163 1.036

0.3846 0.3760 1.133 1.050

0 .4118 0.4009 1.126 1 .052

0 .4450 0 .4237 1.099 1.071

0 .4724 0 .4468 1.088 1 .078

0 .5010 0 .4702 1.077 1.088

0 .5331 0 .4947 1.061 1 .104

0 .5532 0 .5183 1.070 1.099

0 .5821 0 .5392 1.052 1.116

0 .6195 0.5591 1.022 1.170

0 .6856 0 .6178 1.007 1.209

0 .7196 0 .6490 1.001 1.235

J. Ortega, P. Hernandez / Fluid Phase Equilibria 118 ~ 1996) 249-270 263

Table 5 (continued)

379.34 0.7458 0.6768 1.001 1.245

379.64 0.7809 0.7082 0,992 1.292

379.71 0.7965 0.7277 0.997 1,295

379.95 0.8220 0.7559 0.997 1.317

380.55 0.8540 0.7939 0.991 1.329

380.83 0.8894 0.8404 0.999 1.346

381.66 0.9471 0.9205 1.004 1.365

381.93 0.9692 0.9522 1.008 1.398

382.24 0.9862 0.9780 1.008 1.422

382.54 1.0000 1.0000 1.000 -

using the empirical correlations of Tsonopoulos (1974). These calculations for V~ t and Bij were also included in the consistency test put forward by Fredenslund et al. (1977). Applying this test, all the mixtures proved to be thermodynamically consistent. All the systems studied displayed a positive shift

o.5 1 (a)

0.4

0.3

0.1

0.0

-0 .1 o o'.2 o'.4 o'.6 o'.8

Xf

370 (a)

360 -

3 3 0 -

320 I I o o'.2 o'.. o'.8 1

x l

Fig. 3. Plots of Y l - x] vs. x 1 and T vs. x~ or y] for the mixtures xt methyl esters+ x 2 butan-2-ol for (O) , methyl ethanoate, (O), methyl propanoate, and ( v ) , methyl butanoate at different working pressures: (a), 74.66 kPa, (b), 101.32 kPa: (c), 127.99 kPa.

264 J. Ortega, P, Hernandez / Fluid Phase Equilibria 118 (1996) 249-270

0.5 380 .

(b)

0.4

0.3

0.1

0.0

- 0 . 1 330 0 0.2 0.4 0.6 0.8 I 0

Xl

370"

3 4 0 "

0 . 5 , 390"

I

0.4

-,,.,

(c)

0.3

0 .1 -

380"

0 .0 m.,, . . . ~,~_ "~] 3 4 0

- 0 . 1 0 0'.2 0'.4 0'.8 0'.8 I 330 1 0 Xl

Fig. 3 (continued).

(b)

0.2 0.4 0.6 0.8 1 XI

(c)

ole o14 o16 ot8 x!

J. Ortega, P. Hernandez / Fluid Phase Equilibria 118 ! 19961249-270 265

away from ideality, with the values of Yi decreasing slightly as the working pressure increased. The values of Y2 were also recalculated using Eq. (2) with the values of pO calculated by means of the Antoine equation and the constants A, B and C for butan-2-ol reported by other workers. However,

T a b l e 6

P a r a m e t e r s o b t a i n e d in t he d i f f e r e n t e q u a t i o n s u s e d f o r the b i n a r y m i x t u r e s x ~ m e t h y l e s t e r s + x 2 b u t a n - 2 - o l a t t he d i f f e r e n t

p r e s s u r e s

x ICH 3 C O O C H 3 + x 2 C H 3 C H ( O H ) C H 2 C H 3

p = 7 4 . 6 6 k P a

M a r g i i l e s A12 = 0 . 4 4 4 A21 = 0 . 2 1 3

V a n L a a r A I 2 = 0 . 4 3 5 A21 = 0 . 7 5 1

W i l s o n Ai2 = 6 7 . 8 "~ A21 = 2 0 1 4 . 6 a

N R T L , cr = 0 . 4 7 A g l 2 = 2 3 5 7 . 3 a Age1 = 3 3 2 . 1 a

U N I Q U A C , z = 10 Aul2 = 5 2 3 3 a Au21 = - 1921 a

R e d l i c h - K i s t e r A o = 0 , 5 5 5 A~ = 0 . 1 3 1 A 2 = 0 . 0 8 5

E q , ( 1 ), k = 0 . 5 0 A o = 0 , 6 6 9 A ~ = - 0 . 5 4 2 A 2 = 0 . 5 9 1

p = 1 0 1 . 3 2 k P a

M a r g i i l e s Al2 = 0 , 4 0 4 Ae l = 0 . 2 8 3

V a n L a a r A l z = 0 , 4 1 9 A2t = 0 . 5 2 9

W i l s o n A12 = 6 9 3 . 7 a A21 = 8 0 0 . 7 a

N R T L , a = 0 . 4 7 Agl2 = 1 2 5 5 . 4 a Ag?l = 2 3 3 . 3 '~

U N I Q U A C , z = 10 A U t 2 = 4 3 4 4 . 5 a Au2j = - 1777.1 "~

R e d l i c h - K i s t e r A o = 0 . 4 6 3 A~ = 0 . 0 7 0 A 2 = - 0 . 0 4 6

Eq . ( I ) , k = 0 . 3 7 Ao = 0 . 4 2 3 A t = - 0 . 0 6 1 A 2 = 0 . 1 6 7

p = 1 2 7 . 9 9 k P a

M a r g t i l e s A ~ 2 = 0 . 1 1 6 A 21 = - 0 . 2 6 2

V a n L a a r A le = 0 . 2 2 7 A21 = 0 . 4 9 2

W i l s o n A12 = - 6 5 5 . 4 a A21 = 2 2 8 7 . 2 a

N R T L , o~ = 0 . 4 7 A g l 2 = 2 7 6 0 . 9 a Ag21 = -- 1 1 4 6 . 8 a

U N I Q U A C , z = 10 AUl2 = 5 1 4 8 . 7 ~ Au21 = - - 2 2 6 3 . 9 a

R e d l i c h - K i s t e r A o = 0 . 3 0 7 A~ = 0 . 1 4 8 A 2 = 0 . 0 0 8

E q . (1) , k = 0 .41 Ao = 0 . 2 9 3 A l = - - 0 . 4 0 0 A2 = 0 , 5 2 5

x iC 2 H s C O O C H 3 + x 2 C H 3 C H ( O H ) C H 2 C H 3

p = 7 4 . 6 6 k P a

M a r g i i l e s A 12 = 0 . 4 5 7 A 21 = 0 , 4 9 2

V a n L a a r AI2 = 0 . 3 5 3 A21 = 0 . 5 2 9

W i l s o n AI2 = - 4 0 4 , 5 a A21 = 1938 .5 a

N R T L , a = 0 , 4 7 A g l 2 = 1 8 5 0 . 6 a Agel = - - 3 2 9 . 7 a

U N I Q U A C , z = 10 Au12 = 4 7 4 8 . 9 a z~U21 = - - 2 1 1 4 . 6 a

R e d l i c h - K i s t e r A o = 0 . 4 2 3 A I = 0 . 0 8 2

E q . ( I ) , k = 0 , 4 5 A o = 0 . 4 8 8 A~ = - 0 . 3 4 5

p = 1 0 1 . 3 2 k P a

Marg i~ les AL2 = 0 . 3 1 3 A?I = 0 , 2 4 6

V a n L a a r A12 = 0 . 3 1 2 A2 t = 0 . 3 7 5

W i l s o n A I 2 = 4 0 . 5 a A2~ = 1060.1 "~

N R T L , a = 0 . 4 7 Agl2 = 9 9 9 . 7 a Ag21 = 100.5 a

U N 1 Q U A C , z = 10 Au12 = 4 1 5 0 . 2 a Au21 = - 2 0 3 4 . 8 a

R e d l i c h - K i s t e r A o = 0 . 3 4 5 A~ = 0 . 0 5 9

Eq . ( 1 ), k = 0 , 3 8 A o = 0 . 2 4 7 A I = - 0 . 0 4 8

A 2 = 0 . 0 3 3

A 2 = 0 , 3 3 8

A 2 = - 0 . 0 8 5

A 2 = 0 . 1 6 1

6 (T /K) ~( y~) s(GE/RT) 0 . 0 3 0 . 0 0 5 0 . 0 2 5

0 . 0 2 0 . 0 0 2 0 . 0 0 8

0 . 0 2 0 . 0 0 2 0 . 0 0 7

0 . 0 2 0 . 0 0 2 0 . 0 0 8

0 . 0 2 0 . ( /03 0 . 0 t 0

0 . 0 2 0 . 0 0 2 0 . 0 0 7

0 . 0 2 0 . 0 0 3 0 . 0 0 9

0 .01 0 . 0 0 5 0 . 0 1 5

0 .01 0.(X)3 0 . 0 0 7

0 .01 0 . 0 0 3 0 . 0 0 6

0 .01 0 .0( /3 0 . 0 0 6

0 .01 0 . 0 0 4 0 . 0 0 7

0 .01 0 . 0 0 4 0 . 0 0 8

0 .01 0 . 0 0 4 0 . 0 1 1

0 . 0 2 0 . 0 1 0 0 . 0 3 7

0 . 0 2 0 . 0 0 5 0 . 0 1 4

0 . 0 2 0 . 0 0 5 0 . 0 1 4

0 . 0 2 0 . 0 0 5 0 . 0 1 4

0 . 0 2 0 . 0 0 6 0 . 0 1 8

0 . 0 2 0 . 0 0 5 0 . 0 1 5

0 .01 0 . 0 0 4 0 . 0 0 9

0 . 0 4 0 . 0 0 6 0 . 0 0 7

0 . 0 2 0 . 0 0 5 0 . 0 0 5

0 . 0 2 0 . 0 0 4 0 . 0 0 5

0 . 0 2 0 . 0 0 4 0 . 0 0 5

0 . 0 2 0 . 0 0 6 0 . 0 0 6

0 . 0 2 0 . 0 0 4 0 . 0 0 6

0 .01 0 . 0 0 3 0 . 0 0 3

0 . 0 4 0 . 0 0 8 0 . 0 0 8

0 . 0 4 0 . 0 0 5 0 . 0 0 6

0 . 0 4 0 . 0 0 5 0 . 0 0 6

0 . 0 4 0 . 0 0 5 0 . 0 0 6

0 . 0 3 0 . 0 0 5 0 . 0 0 6

0 . 0 3 0 . 0 0 5 0 . 0 0 6

0 . 0 2 0 . 0 0 6 0 . 0 0 5

266

Table 6 (continued)


p = 127.99 kPa

Margi~les A I 2 = 0.292 A 2 1 = 0.253 Van Laar At2 = 0.237 A2~ = 0.384 Wilson /112 = - 795.4 ~ /12~ = 2033.9 a NRTL, a ~ 0.47 Agt2 = 2007.2 a /1g21 = - 760.8 a

UNIQUAC, z = 10 /1ux2 = 4693 a /1U21 = - -2295.9 a Red l i ch -K i s t e r A o = 0.304 A t = 0.110

Eq. (1), k ~ 0.29 A o = 0.267 A 1 = - 0 . 3 4 7

x IC 3HvCOOCH3 -I- x 2CH3CH(OH)CH2CH 3

A 2 = - 0 . 1 0 5

A 2 = 0.432

p = 74,66 kPa

Margi~les A t 2 = 0 . 4 5 5 A21 = 0.506 Van Laar At2 = 0.421 A21 = 0.459 Wilson A I 2 = - - 172.5 a /121 = 1589.6 a NRTL, a = 0 . 4 7 /1gtz = 998.1 a /1gzt = 413 a

UNIQUAC, z = 10 /1ut2 = 4208.9 a /1/,121 = - 1990.3 a

Red l i ch -K i s t e r A o = 0.439 A t = 0.018

Eq. (1), k = 0.51 A o = 0.487 A t = - 0 . 0 7 6 A 2 = - 0 . 0 6 0 p = 101.32 kPa

MargiJles A~2 = 0.318 A21 = 0.237 Van Laar A I 2 = 0.411 A 2 1 = 0.291 Wilson At2 = 1096.2 a /121 = 198.2 ~ NRTL, a = 0.47 Ag12 = - -438.6 a Ag21 = 1731.1 ~

UNIQUAC, z = 10 Aut2 = 3159.9 a /1u21 = - 1676.8 a Red l i ch -K i s t e r A 0 = 0.351 A i = - 0.069 A 2 = - 0.079 Eq. (1), k = 0.40 A 0 = 0.255 A~ = 0.262 A 2 = - 0 . 2 3 3 p = 127.99 kPa

Margiiles A I 2 = 0.328 A2t = 0.330 Van Laar A 12 = 0.349 A2t = 0.307 Wilson Al2 = 326.4 a A2j = 770.1 a NRTL, cr = 0.47 / 1 g 1 2 = 147.4 a /1g2t = 946.3 a UNIQUAC, z = 10 Aut2 = 3489.7 a Au2t = - 1858.1 a Red l i ch -K i s t e r A o = 0.323 A 1 = - 0.020 Eq. (1), k = 0.34 Ao = 0.344 A 1 = 0 . 1 0 2 A 2 = - 0 . 1 4 6

0.06 0.013 0.010 0.05 0.008 0.007

0.05 0.008 0.007 0.04 0.008 0.007 0.03 0.007 0.006

0.02 0.006 0.005 0.01 0.007 0.004

0.02 0.008 0.003

0.04 0.009 0.004 0.04 0.009 0.004

0.04 0.009 0.004

0.05 0.008 0.003 0.04 0.009 0.004 0.02 0.007 0.003

0.04 0.009 0.005 0.05 0.010 0.005 0.05 0.010 0.005 0.05 0.010 0.004

0.04 0.009 0.004 0.04 0.007 0.003 0.03 0.009 0.004

0.06 0.006 0.003 0.04 0.005 0.003 0.04 0.005 0.003 0.04 0.005 0.003 0.05 0.005 0.002 0.04 0.005 0.003 0.03 0.005 0.003

a All parameters in J mol 1.

t h e d i f f e r e n c e s w e r e n o t v e r y a p p r e c i a b l e , r e a c h i n g o n l y 4 % in t h e w o r s t c a s e s . U s i n g t h e c o n s t a n t

v a l u e s f o r t h e m e t h y l e s t e r s p u b l i s h e d in t h e l i t e r a t u r e , n a m e l y , b y T R C ( 1 9 9 1 ) , B o u b l i k e t a l . ( 1 9 7 3 ) ,

a n d A m b r o s e e t a l . ( 1 9 8 1 ) f o r e t h a n o a t e ; b y T R C ( 1 9 9 1 ) a n d B o u b l i k e t a l . ( 1 9 7 3 ) f o r p r o p a n o a t e ;

a n d b y T R C ( 1 9 9 1 ) f o r b u t a n o a t e , t h e d i f f e r e n c e s in t h e Yi v a l u e s w e r e c o m p a r a b l e t o t h e p r e c e d i n g

c a s e , t h a t i s , < 4 % . T h e s e r e s u l t s p r o v e d v a l i d a t i o n o f t h e v a p o r p r e s s u r e s a n d c o r r e l a t i o n s c o m p u t e d

a t o u r l a b o r a t o r y f o r t h e t e m p e r a t u r e r a n g e s e t o u t in T a b l e 3.

T h e t r e a t m e n t o f t h e e x p e r i m e n t a l d a t a i n v o l v e d f i t t i n g t h e a c t i v i t y c o e f f i c i e n t s u s i n g t h e m a x i m u m

l i k e l i h o o d p r i n c i p l e , m i n i m i z i n g t h e o b j e c t i v e f u n c t i o n

4

O . F . = E [Mi ,ca l - 2 2 Mi,exp. ] / S M i ( M i = P , T , x , y ) ( 4 ) i = l

J. Ortega, P. Hernandez / Fluid Phase Equilibria 118 ¢ 1996) 249-270 267

A series of changes previously effected by our laboratory were made in the original program of Prausnitz et al. (1980), as reported earlier. The data were correlated using various now classic equations for the treatment of VLE data, such as the van Laar, Margi~les, Wilson, NRTL and UNIQUAC equations and other polynomial equations, such as the Redlich-Kister equation and an equation analogous to Eq. (1) above, which were also used in the data reduction procedure. The values of the standard deviations, SMi, for each of the magnitudes in Eq. (4) used in the simultaneous regression procedure were 0.02 kPa for p, 0.01 K for T, 0.002 for x~, and 0.004 for Yl-

Table 6 gives the constant values calculated for each of the correlations. Generally, they all appeared to be suitable for correlating the data for the mixtures considered here. Fig. 3 plots the experimental values and the curves obtained by setting Q = Y l - x l and Q = T-~,VXITb, i in an expression analogous to Eq. (1). The figures clearly reveal the variation in the magnitudes considered with ester type and, in particular, the presence of an azeotrope in the mixture (methyl butanoate + butan-2-ol), which shifted toward the fractions less rich in the methyl ester as working pressure increased. The exact location of the singular point, a minimum azeotrope, was calculated using the relations referred to above and Eq. (1), which yielded the following contour conditions for determin- ing the location of the azeotrope:

y, = x l ( O T / O x , ) p = ( O T / O y l ) p = O (s)

If Q = Yl - X l in Eq. (1), then:

0 = ]~_~Aiz i where z = x , / [ x I + kx2] (6)

Table 7 Error percentage obtained in prediction of activity coefficients using different models on the mixtures methyl esters + butan- 2-ol at various working pressures

ASOG UNIFAC-2 UNIFAC- 1

O H / C O O a O H / C O O C b O H / C O O C c O H / C O O C d C O H / C O O e C C O H / C O O C f O H / C O O ~

Butanol-2-ol + 74.66 kPa Methyl ethanoate 7.9 2.9 2.5 7.6 2.4 3.6 1.8 Methyl propanoate 7.8 4.0 5.2 8.2 3.9 5.5 3.6 Methyl butanoate 5.3 3.5 3.5 9.0 3.1 6.0 3.8 101.32 kPa Methyl ethanoate 9.6 2.8 3.1 8.8 2.8 4.7 1.5 Methyl propanoate 9.2 4.5 6.5 9.8 5.3 7.3 5.1 Methyl butanoate 7.7 4.4 3.6 12.4 3.7 9.5 6.1 127.99 kPa Methyl ethanoate 14.5 5.4 5.4 12.9 7'.0 9.1 4.5 Methyl propanoate 10.7 4.6 6.9 10.9 (:~.5 8.7 6.2 Methyl butanoate 8.0 3.9 3.5 12.5 4.3 9.9 6.6

:' Kojima and Tochigi (1979). b Larsen et al. (1987). c Gmehling et al. (1993). cl Gmehling et al. (1982). " Fredenslund et al. (1975). t Fredenslund et al. (1977). g Macedo et al. (1983).


but if instead Q = T - XlTb, l -- X2Tb. 2 for condition (5), then:

0 = - rb ,2 + (1 - 2xl), ( 7 )

where a = E A i zi and /3= (dcr /dz) .

The coefficients A~ in cr correlated the temperature values and hence differed from the coefficients in expression (6), where they were correlations for yl - x~. Solving these equations yielded numerical values for the azeotropes at the different working pressures:

p = 74.66 kPa T = 361.7 K p = 101.32 kPa T = 370.6 K p = 127.99 kPa T = 377.6 K

Yl = xl = 0.451 y~ = x~ = 0.399 yj = x I : 0.351

which agrees with the proposal by Horsley (1973) at atmospheric pressure.

4. Theoretical prediction of VLE using group-contribution models

Isobaric VLE values for the systems considered in this study were predicted using the ASOG model (Kojima and Tochigi, 1979) and two versions of the UNIFAC model, here designated by UNIFAC-1 (Fredenslund et al., 1975) and the more recent, UNIFAC-2 (Larsen et al., 1987; Weidlich and Gmehling, 1987). The accuracy of the predictions was assessed in all cases by comparing the values of the activity coefficients, Yi, derived implicitly from Eqs. (2) and (3). Table 7 presents the percentage errors in the estimates of the % values.

The original UNIFAC-1 model was used with various alcohol/ester interaction pairs existing in the literature, including the interaction pair O H / C O O , not recommended for alkyl esters (Macedo et al., 1983). Unexpectedly, this interaction pair yielded the best prediction results, whereas the interaction pair originally proposed, O H / C O O C , produced the highest errors, of around 10%. Both the version of the Lyngby group (Larsen et al., 1987) and the version of the Dortmund group (Weidlich and Gmehling, 1987) yielded excellent results for all the mixtures under all the experimental conditions, with mean errors of around 5%. Finally, in the ASOG model estimation errors increased progressively with working pressure; conversely, the predictions improved with methyl ester chain length. This latter finding is significant, because the ASOG model uses the more flexible C O 0 group for all alkyl esters instead of the COOC group employed in UNIFAC-1, which uses different areas depending upon whether or not the esters are an alkyl ethanoates.

Summing up, even though this study used an isomer of an alcohol, which usually results in poorer predictions, the overall results were positive, with mean errors in the range of 5 -10% for all the mixtures under all the experimental considered.

J. Ortega, P. Hernandez / Fluid Phase Equilibria I 18 (1996) 249-270 269

5. List of symbols

A,B,C n(D)

P po R T Th.~ V L

x~

Yi

coefficients of Antoine equation refractive index at D-sodium line working pressure vapor pressure of species i gases universal constant absolute temperature normal boiling temperature of species i liquid molar volume liquid mole fraction of species i vapor mole fraction of species i

Greek letters 7~ activity coefficient of species i p density ~b i fugacity coefficient of species i

Acknowledgements

We are thankful (PB92-0559).

to the DGICYT (MEC) frem Spain for financial support for this project

References

Ambrose, D., Ellender, J.H., Gundry, H.A., Lee, D.A. and Townsend, R., 1981. Thermodynamic properties of organic oxygen compounds. LI. The vapour pressures of some esters and fatty acids. J. Chem. Thermodyn., 13: 795-802.

Ambrose, D. and Sprake, C.H.S., 1970. Thermodynamic properties of organic oxygen compounds. XXV. Vapor pressures and normal boiling temperatures of aliphatic alcohols. J. Chem. Thermodyn., 2: 631-645.

Boublik, T., Fried, V. and H~la, H., 1973. The Vapour Pressures of Pure Substances. Elsevier, Amsterdam. Fredenstund, Aa., Jones, R.L. and Prausnitz, J.M., 1975. Group contribution estimation of activity coefficients in nonideal

liquid mixtures. AIChE J., 21: 1086-1099. Fredenslund, Aa, Gmehling, J. and Rasmussen, P, 1977. Vapor-Liquid Equilibria Using UNIFAC. A Group Contribution

Method. Elsevier, Amsterdam. Gmehling, J., Li, J. and Schiller, M., 1993. A modified UNIFAC model. 2. Present parameter matrix and results for different

thermodynamic properties. Ind. Chem. Eng. Res., 32: 178-193. Gmehling, J., Rasmussen, P. and Fredenslund, Aa., 1982. Vapor-liquid equilibria by UNIFAC group contribution. Revision

and extension. 2 lnd. Eng. Chem. Process Des. Dev., 21:118-127. Horsley, L.H., 1973. Azeotropic Data--I l l . Advances in Chemistry Series 116, A.C.S. Washington DC. Kojima, K. and Tochigi, K., 1979. Prediction of Vapor-Liquid Equilibria by the ASOG Method. Kodansha Ltd.. Tokyo. Larsen, B.L., Rasmussen, P. and Fredenslund, Aa., 1987. A modified UNIFAC group contribution model for prediction of

phase equilibria and heats of mixing. Ind. Eng. Chem. Res., 26: 2274-2286. Macedo, E.A., Weidlich, U., Gmehling, J. and Rasmussen, P., 1983. Vapor-liquid equilibria by UNIFAC group contribution

Revision and extension 3. Ind. Eng. Chem. Process Des. Dev.. 22: 676-678.


Ortega, J., Pefia, J.A. and de Alfonso, C., 1986. Isobaric vapor-liquid equilibria of ethyl acetate+ethanol mixtures at 760_+0.5 mmHg. J. Chem. Eng. Data, 31: 339-342.

Ortega, J., Oc6n, J., Pefia, J.A., de Alfonso, C., PazAndrade, M.I. and Fern~indez, J., 1987. Vapor-liquid equilibrium of the binary mixtures CnH2n + I(OH) (n = 2, 3, 4)+ propyl ethanoate and ethyl ethanoate. Can. J. Chem. Eng., 65: 982-990.

Ortega, J. and Susial, P., 1990a. Measurements and prediction of VLE of methyl propanoate/ethanol/propan-l-ol at 114.66 and 127.66 kPa. J. Chem. Eng. Jpn., 23: 349-353.

Ortega, J. and Susial, P., 1990b. VLE at 114.66 and 127.99 kPa for the systems methyl acetate+ethanol and methyl acetate +propan-l-ol. Measurements and prediction. J. Chem. Eng. Jpn., 23: 621-626.

Ortega, J. and Susial, P., 1993. Vapor-liquid equilibria behavior of methyl esters and propa-2-ol at 74.66, 101.32, and 127.99 kPa. J. Chem. Eng. Jpn., 26: 259-265.

Ortega, J., Susial, P. and de Alfonso, C., 1990a. Vapor-liquid equilibrium measurements at 101.32 kPa for binary mixtures of methyl acetate+ethanol or propan-l-ol. J. Chem. Eng. Data, 35: 350-352.

Ortega, J., Susial, P. and de Alfonso, C., 1990b. Isobaric vapor-liquid equilibrium of methyl butanoate with ethanol and 1-propanol binary systems. J. Chem. Eng. Data, 35: 216-219.

Ortega, J. and Susial, P., 1991. Vapor-liquid equilibria of mixtures of methyl butanoate +propan-2-ol at 74.66, 101.32, and 127.99 kPa. Ber. Bunsenges Phys. Chem., 95: 1214-1219.

Prausnitz, J.M., Anderson, T.F., Greens, E.A., Eckert, C.A., Hsieh, R. and O'Connell, J.P., 1980. Computer calculations for multicomponent V-L and L-L equilibria. Prentice-Hall, Inc., Englewood Cliffs, NJ.

Reid, R.C., Prausnitz, J.M. and Sherwood, T.K., 1977. The Properties of Gases and Liquids, 3rd edn., MacGraw-Hill, New York.

Riddick, J.A., Bunger, W.B. and Sakano, T.K., 1986. Organic Solvents. Techniques of Chemistry, Vol. II, 4th edn., Wiley-Interscience, New York.

Spencer, C.F. and Danner, R.P.J., 1972. Improved equation for predicting of saturated liquid density. J. Chem. Eng. Data, 17: 236-241.

Susial, P., Ortega, J., de Alfonso, C. and Alonso, C., 1989. Vapor-liquid equilibrium measurements for methyl propanoate-ethanol and methyl propanoate-propan-l-ol at 101.32 kPa. J. Chem. Eng. Data, 34: 247-250.

Susial, P. and Ortega, J., 1995. Vapor-liquid equilibria of methyl ethanoate with n-butyl and iso-butyl alcohol at 74.66 and 127.99 kPa. J. Chem. Eng. Jpn., 28: 66-70.

TRC, 1991. Thermodynamic Tables of Non-hydrocarbons, Texas A and M University, College Station, TX. Tsonopoulos, C., 1974. An empirical correlation of second virial coefficients. AIChE J., 20: 263-272. Weidlich, U. and Gmehling, J., 1987. A modified UNIFAC model. 1. Prediction of VLE, and H E. Ind. Eng. Chem. Res.,

26: 1372-1381.

isobaric vapor-liquid equilibria for methyl esters + butan-2-ol at different pressures

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