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

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[OglUgRlil

ELSEVIER

FluidPhase Equilibria 118 (1996) 249-270

Isobaric vapor-liquid equilibria for methyl esters + butan-2-ol at different pressures J u a n O r t e g a *, P a b l o 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-liquid 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 © 1996Elsevier ScienceB.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 Xester > 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.

251

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

3. Results 3.1. Densities 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 (kgm

3)

109 V E (m 3 mo1-1)

xICH .~COOCH 3 + x2CH.~CH(OH)CH2CH 3 0.0000 802.29 0.0 0.0238 804.11 74.6 0.0984 810.63 260.0 0.1532 815.24 423.9 0.1890 818.66 490.0 0.2704 826.90 599.3 0.3426 834.40 691.5 0.4259 843.57 762.4 0.5249 855.58 760.7 xIC2HsCOOCH 3 + x2CH3CH(OH)CH2CH 3 0.00(X) 802.29 0.0 0.0433 806.18 92.2 0.0782 809.38 169.9 0. I 148 812.82 241.0 0.1300 814.15 280.9 0.2042 821.34 391.2 0.2239 823.22 422.1 0.2364 824.50 432.2 0.2673 827.38 487.9 0.3319 834.10 518.9 0.3700 838.03 539.1 0.3747 838.52 541.8 (I.4117 842.24 569.4 0.4560 846.84 585.2 x iC 3H vCOOCH 3 + x2CH 3CH(OH)CH 2CH 3 0.0000 802.29 0.0 0.0328 805.16 73.5 0.0756 809.28 136.5 0.0911 810.45 194.3 0.1249 813.72 232.9 0.1620 816.95 309.8 0.2306 823.30 387.7 0.3268 832.07 473.3 0.3842 837.30 503.0

xI

P (kgm-3)

l0 ~) V E (m 3 mol i)

0.6099 0.6565 0.7512 0.8405 0.8728 0.8992 0.9323 0.9729 1.0000

866.66 873.16 886.32 899.97 905.23 909.57 915.08 922.01 926.97

715.5 652.9 571.0 413.6 337.2 275.0 195.9 92.8 0.0

0.4649 0.5221 0.5584 0.5944 0.6065 0.6828 0.7266 0.7668 0.7913 0.8545 0.8930 0.9392 0.9705 1.0000

847.80 853.90 857.81 861.65 867.48 871.50 876.50 881.00 883.86 891.01 895.73 901.33 905.18 908.84

583.8 582. I 573.7 569.4 530.2 505.0 457.0 422.0 386.7 317.8 234.7 140.7 70.5 0.0

0.5001 0.5458 0.6414 0.7072 0.8309 0.8624 0.9015 0.9636 1.0000

847.79 852.00 860.42 866.31 877.21 879.94 883.41 889.07 892.35

522.5 502.8 480.1 429.5 304.3 268.6 206.9 79.5 0.0

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

252

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

A0

At

A2

109 s(V z ) / ( m 3 m o l - 1)

x 2 butan-2-ol + x Methyl ethanoate Methyl propanoate Methyl butanoate

0.067 0.133 2.559

3620.2 2494.7 2278.5

- 595.1 - 161.9 - 1116.8

1467.7

8.8 9.6 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

where

Q=

VE/(m

3 mol-')

(1)

i

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• xlxffnethyl methetylhan°ate+xzbut1an-2-°l propanoate+xzbutan-2-ol v xlrnethyl butanoate+x2butan-2-ol o

0.2

0.4

xl

0.6

0.8

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)

348.12 350.18 352.41 354.03 355,73 358,25 359,84 361,38 362.62 363.93 364.12 365.58 366.45

38.24 41.94 46.21 49.50 53.18 59.02 62.97 66.99 70.29 74.02 74.53 78.94 81.65

367.52 368.57 369.28 370.80 371.73 372.36 372.44 373.08 373.69 374.20 374.92 375.54 376.24

85.07 88.53 90.94 96.27 99.70 101.32 102.30 104.67 107.03 109.7(I 111.98 114.52 117.38

376.98 377.60 378.26 378.56 378.89 379.46 380.03 380.63 381.19 381.26

120.58 123.19 126.14 127.99 129.00 131.54 134.22 136.96 139.66 140.07

(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

Methyl ethanoate Methyl propanoate Methyl butanoate

6.49340 6.58882 6.30360 6.31286 6.59921 6.32621 6.26852

1329.46 1469.36 1381.64 1159.84 1314.19 1159.00 1126.67

- 33.52 - 30.99 - 53.60 - 102.90 - 86.60 - 104.87 - 108.36

Butan-2-ol

s(p0) (kPa)

0.04

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

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

254

Boublick et aL (1973)

[•

--1 ¸

"-.-..~".£...

.99.

°#. I

~2.

2.5,¢" 7 " " . .

-3

320

T/K

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

255

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

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

xI

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

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

256 Table 5 (continued)

321.90

0.9526

0.9867

1.013

321.12

1.0000

1.0000

1.000

1.906

372.36

0.0000

0.0000

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

p=101.32 kPa 1.000

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

378.56

0.0000

0.0000

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

p = 1 2 7 . 9 9 kPa 1.000

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

257

Table 5 (continued)

368.80

0.1300

0.3831

1,189

0.999

366.87

0.1585

0.4452

1,190

0,997

365.35

0.1824

0.4886

1.179

1,000

361.77

0.2365

0.5759

1.177

1.017 1.020

359.33

0.2834

0.6367

1.158

357.67

0.3145

0.6720

1.152

1.027

356.16

0.3442

0.7021

1 146

1.036

354.80

0.3734

0.7248

1 132

1.058

353.55

0.4014

0.7491

1 127

1.062

352.32

0.4303

0.7707

1 120

1.073

351.12

0.4581

0.7926

1 119

1.073

348.77

0.5224

0.8325

1 103

1.086

346.51

0.5879

0.8624

1.085

1.139

345.90

0.6048

0.8686

1.081

1,165

344.98

0.6337

0.8800

1.074

1.195

344.06

0.6640

0.8910

1.067

1.232

343.57

0.6899

0.9004

1.053

1.247

342.70

0.7249

0.9133

1.044

1.272

342.26

0.7597

0.9238

1.021

1.305

341.29

0.8002

0.9383

1.014

1.328

340.70

0.8302

0.9453

1.003

1.423

339.97

0.8671

0.9572

0.994

1.471

339.10

0.9037

0.9681

0.991

1.575

337.78

0.9528

0.9855

0.997

1.553

336.49

1.0000

1.0000

1.000

x C H COOCH +x CH CH(OH)CH CH 125

3

2

3

2

3

p=74.66 kPa 364.04

0.0000

363.50 362.73

0.0000

-

1.000

0.0133

0.0337

1.322

1.003

0.0300

0.0819

1.456

0.998

361.26

0.0620

0.1596

].433

1.000

359.78

0.0959

0.2347

1.423

1.001

359.20

0.1118

0.2606

1.379

1.007

358.00

0.1468

0.3202

1.338

1.010

357.50

0.1657

0.3497

].314

1.008

357.00

0.1835

0.3755

1.293

1.009

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

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

-

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

p=I01.32 kPa

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 (continued)

361.76

0.3334

0.5301

1.169

1.034

361.27

0.3538

0.5504

1.161

1,040

360,82

0.3754

0,5695

1.147

1.048

360.32

0.3978

0.5903

1.138

1.055

359.86

0.4209

0.6102

1.127

1.063

359.34

0.4469

0,6327

1.118

1.070

358.70

0.4798

0.6596

1.106

1.081

358.12

0.5137

0.6846

1.091

1.096

357.22

0.5605

0.7175

1.077

1.126

356,60

0,6003

0,7443

1.063

1 149

355.90

0.6489

0.7730

1.043

1 194

355.32

0.6901

0.8001

1.033

1 220

355.02

0.7172

0.8152

1.022

1 251

354.49

0,7629

0.8462

1.014

1 269

353.81

0.8199

0.8780

1,000

1 363

353.64

0.8355

0.8903

1.000

1 351

353.50

0.8530

0.9003

0.995

1.382

353.04

0.8930

0.9211

0.986

1.531

352.84

0.9252

0.9427

0.980

1.604

352.74

0.9464

0.9571

0.979

1.690

352.66

1.0000

1.0000

1.000

378.56

0.0000

0.0000

377.76

0.0288

0.0632

1 598

376.92

0.0549

0.1159

1 276

0.992

375.86

0.0878

0.1748

1 237

0.995

375.30

0.1091

0.2101

1 215

0.994

374.92

0.1207

0.2287

1 207

0.996

374.01

0.1556

0.2816

1 181

0.997

372.90

0.1940

0.3405

1 180

0.997

372.12

0.2205

0.3755

1.169

1.003

371.42

0.2453

0.4092

1.167

1.004

370.36

0.2880

0.4630

1.158

1.005

369.87

0.3039

0.4785

1.149

1.016

368.83

0.3374

0.5174

1.152

1.025

368.23

0.3640

0.5421

1,137

1.036

367.00

0.4193

0.5959

1.123

1.047

p=127.99 kPa 1.000 0.995

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

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

1.060

1.174

361,71

0.5681

0.5272

1.045

1.201

361.85

0.6240

0.5692

1.023

1.250

361.96

0.6718

0.6067

1.009

1.302

362.19

0.7162

0.6494

1.006

1.331

362,41

0.7684

0.6915

0.991

1.423

362,74

0.8084

0.7362

0.992

1.453

363.12

0.8532

0.7793

0.983

1.564

363.52

0.8891

0.8300

0.992

1.571

363.93

0.9174

0.8717

0.997

1.567

364.13

0.9461

0,9098

1.002

1,676

364.58

0.9729

0.9497

1.003

1.828

364.95

1.0000

1.0000

1.000

p = 1 0 1 . 3 2 kPa 372.36

0.0000

0.0000

372.26

0.0071

0.0107

1 640

O. 994

372.13

0.0201

0.0278

1 511

O. 994

371.95

0.0333

0.0451

1 488

0.996

371.66

0.0645

0.0842

1 446

O. 997

371.54

0.0855

0.1065

1 385

O. 999

371.39

0.1097

0.1342

I 366

I. 000

371.22

0.1358

0.1615

1 335

I. 004

370.98

0.1799

0.2079

1.306

1. 008

370.90

0.2034

0.2311

1,287

1.010

370.81

0.2331

0.2583

1.259

1.015

370.73

0.2615

0.2840

1.237

1.021

370.69

0.2880

0.3074

1.217

1. 026

370.66

0.3135

0.3294

1.199

1. 031

370.64

0.3449

0,3547

1,174

1.041

370.63

0,3728

0,3784

1.159

1.047

I. 000

370.63

0.4005

0.4020

1.146

1.054

370.66

0.4307

0.4239

1.123

I . 068

370.70

0.4620

0.4462

i . I00

1.085

370.77

0.4938

0.4732

1.089

1.094

370.88

0.5428

0.5076

1.059

I . 128

371.39

0.6316

0.5782

1.021

1. 178

371.53

0.6605

0.5992

1.008

1. 209

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

262 Table 5 (continued)

371.81

0.7025

0.6392

1.002

1.230

372.39

0.7746

0.7064

0.987

1.294

372.64

0.8031

0.7349

0.983

1.326

372.97

0.8349

0.7684

0.979

1.366

373.35

0.8666

0.8060

0.978

1.398

373.73

0.8992

0.8458

0.978

1.451

374.23

0.9299

0.8904

0.981

1.458

374.77

0.9618

0.9406

0.987

1.423

375.07

0.9806

0.9696

0.989

1.420

375.17

0.9917

0.9864

0.992

1.480

375.35

1.0000

1.0000

1.000

-

378.56

0.0000

0.0000

-

1.000

378.47

0.0142

0.0183

1.460

1.003

378.29

0.0434

0.0552

1.448

1.001

378.19

0.0640

0.0775

1.383

1.002

p=127.99 kPa

378.06

0.0891

0.1065

1.370

1.001

377.95

0.1191

0.1375

1.327

1.003

377.82

0.1559

0.1744

1.290

1.007

377.69

0.2075

0.2229

1.243

1.014

377.62

0.2336

0.2468

1.225

1.018

377.60

0.2593

0.2710

1.213

1.021

377.59

0.2818

0.2927

1.206

1.022

377.58

0,3083

0.3146

1.185

1.028

377.59

0.3327

0.3371

1.176

1.031

377.60

0.3510

0.3518

1.163

1.036

377.64

0.3846

0.3760

1.133

1.050

377.71

0.4118

0.4009

1.126

1.052

377.77

0.4450

0.4237

1.099

1.071

377.87

0.4724

0.4468

1.088

1.078

377.97

0.5010

0.4702

1.077

1.088

378.09

0.5331

0.4947

1.061

1.104

378.13

0.5532

0.5183

1.070

1.099

378.33

0.5821

0.5392

1.052

1.116

378.41

0.6195

0.5591

1.022

1.170

378.88

0.6856

0.6178

1.007

1.209

379.12

0.7196

0.6490

1.001

1.235

263

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

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)

370

(a)

0.4 360

-

0.3

0.1

330 -

0.0

-0.1

o

o'.2

o'.4

o'.6 Xf

o'.8

320 I

o

o'.2

o'..

o'.8

I

1

xl

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)

(b)

0.4 370"

0.3

0.1

340"

0.0

-0.1

330 0

0.2

0.4

0.6

0.8

I

0

0.2

0.4

Xl

0.5,

XI

0.6

0.8

390"

(c)

(c) 0.4

380"

0.3

I

-,,.,

0.1-

0 . 0 m.,,.

-0.1

1

0

. . ~,~_

0'.2

"~]

0'.4

0'.8 Xl

0'.8

I1

340

330

0

Fig. 3 (continued).

ole

o14

x!

o16

ot8

J. Ortega, P. Hernandez/ FluidPhase 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,

Table 6 P a r a m e t e r s o b t a i n e d in t h e 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 at t h e d i f f e r e n t pressures x ICH 3COOCH 3 + x 2CH 3CH(OH)CH

2CH 3

6(T/K)

~( y~)

s(GE/RT)

Margiiles

A12 = 0 . 4 4 4

A21 = 0 . 2 1 3

0.03

0.005

0.025

Van Laar

AI2 = 0.435

A21 = 0 . 7 5 1

0.02

0.002

0.008

"~

A21 = 2 0 1 4 . 6 a

0.02

0.002

0.007

Agl2 = 2357.3 a

Age1 = 332.1 a

0.02

0.002

0.008

p = 74.66 kPa

Wilson NRTL,

Ai2 = 67.8 cr = 0 . 4 7

UNIQUAC,

z = 10

Aul2 =

Au21 =

0.02

0.(/03

0.0 t 0

Redlich-Kister

A o = 0,555

5233 a

- 1921 a A~ = 0 . 1 3 1

A 2 = 0.085

0.02

0.002

0.007

E q , ( 1), k = 0 . 5 0

A o = 0,669

A ~= - 0.542

A 2 = 0.591

0.02

0.003

0.009

Margiiles

Al2 = 0,404

Ael = 0.283

0.01

0.005

0.015

Van Laar

Alz = 0,419

A2t = 0 . 5 2 9

0.01

0.(X)3

0.007

A12 = 6 9 3 . 7 a

A21 = 8 0 0 . 7 a

0.01

0.003

0.006

0.01

0.0(/3

0.006 0.007

p = 101.32 kPa

Wilson NRTL,

Agl2 =

a = 0.47

UNIQUAC,

z = 10

Ag?l = 2 3 3 . 3 Au2j = - 1777.1

1255.4 a

AUt2 = 4344.5 a

'~ "~

0.01

0.004

A 2 = - 0.046

0.01

0.004

0.008

A 2 =0.167

0.01

0.004

0.011

A 21 = - 0 . 2 6 2

0.02

0.010

0.037

A21 = 0 . 4 9 2

0.02

0.005

0.014

A21 = 2 2 8 7 . 2 a

0.02

0.005

0.014

a

0.02

0.005

0.014

a

0.02

0.006

0.018

Redlich-Kister

A o = 0.463

A~ = 0 . 0 7 0

Eq. (I), k = 0.37

Ao = 0.423

A t = -0.061

Margtiles

A ~2 = 0 . 1 1 6

Van Laar

Ale = 0.227 A12 = - 6 5 5 . 4 a

p = 127.99 kPa

Wilson NRTL,

o~ = 0 . 4 7

UNIQUAC,

Ag21 = -- 1 1 4 6 . 8 Au21 = - - 2 2 6 3 . 9

Agl2 = 2760.9 a

z = 10

AUl2 =

5148.7 ~

Redlich-Kister

A o = 0.307

A~ = 0 . 1 4 8

A 2 = 0.008

0.02

0.005

0.015

E q . (1), k = 0 . 4 1

Ao = 0.293

Al = --0.400

A2 = 0 , 5 2 5

0.01

0.004

0.009

x iC 2 H s C O O C H 3

+ x 2CH3CH(OH)CH2CH

3

p = 74.66 kPa Margiiles

A 12 = 0 . 4 5 7

A 21 = 0 , 4 9 2

0.04

0.006

0.007

Van Laar

AI2 = 0 . 3 5 3

A21 = 0 . 5 2 9

0.02

0.005

0.005

A21 = 1 9 3 8 . 5 a

0.02

0.004

0.005

= --329.7 a

0.02

0.004

0.005

4748.9 a

z~U21 = - - 2 1 1 4 . 6 a

0.02

0.006

0.006

Redlich-Kister

A o = 0.423

A I = 0.082

A 2 = 0.033

0.02

0.004

0.006

Eq. (I), k = 0,45

A o = 0.488

A 2 = 0,338

0.01

0.003

0.003

Wilson NRTL,

AI2 = - 4 0 4 , 5 a = 0,47

UNIQUAC,

z = 10

a

Agl2 = 1850.6 a

Au12 =

Agel

A~ = - 0 . 3 4 5

p = 101.32 kPa Margi~les

AL2 = 0 . 3 1 3

A?I = 0 , 2 4 6

0.04

0.008

0.008

Van Laar

A12 = 0 . 3 1 2

A2t = 0.375

0.04

0.005

0.006

A2~ = 1060.1 "~

Wilson NRTL,

AI2 = 40.5 a

a = 0.47

UN1QUAC,

z = 10

Agl2 = 9 9 9 . 7 Au12 = 4 1 5 0 . 2

a a

Ag21 = 1 0 0 . 5 Au21 = - 2 0 3 4 . 8

0.04

0.005

0.006

a

0.04

0.005

0.006

a

0.03

0.005

0.006

Redlich-Kister

A o = 0.345

A~ = 0 . 0 5 9

A 2 = - 0.085

0.03

0.005

0.006

E q . ( 1 ), k = 0 , 3 8

A o = 0.247

A I = - 0.048

A 2 = 0.161

0.02

0.006

0.005

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

266 Table 6 (continued) p = 127.99 kPa

Margi~les A I 2 = 0.292 Van Laar At2 = 0.237 Wilson /112 = - 795.4 ~ NRTL, a ~ 0.47 Agt2 = 2007.2 a U N I Q U A C , z = 10 /1ux2 = 4693 a Redlich-Kister A o = 0.304 Eq. (1), k ~ 0.29 A o = 0.267 x IC 3 H v C O O C H 3 -I- x 2 C H 3 C H ( O H ) C H 2 C H 3 p = 74,66 kPa Margi~les Van Laar Wilson NRTL, a = 0 . 4 7 U N I Q U A C , z = 10 Redlich-Kister Eq. (1), k = 0.51 p = 101.32 kPa MargiJles Van Laar Wilson NRTL, a = 0.47 U N I Q U A C , z = 10 Redlich-Kister Eq. (1), k = 0.40 p = 127.99 kPa Margiiles Van Laar Wilson NRTL, cr = 0.47 U N I Q U A C , z = 10 Redlich-Kister Eq. (1), k = 0.34

A21 = 0.506 A21 = 0.459 /121 = 1589.6 a /1gzt = 413 a /1/,121 = - 1990.3 a A t = 0.018 A t = -0.076

A~2 = 0.318 A I 2 = 0.411 At2 = 1096.2 a Ag12 = --438.6 a Aut2 = 3159.9 a A 0 = 0.351 A 0 = 0.255

and by TRC

A21 = 0.237 0.291 /121 = 198.2 ~ Ag21 = 1731.1 ~ /1u21 = - 1676.8 a A i = - 0.069 A~ = 0.262

not very

likelihood

appreciable,

reaching

0.003 0.004 0.004 0.004 0.003 0.004 0.003

- 0.079 A2 = -0.233

0.04 0.05 0.05 0.05 0.04 0.04 0.03

0.009 0.010 0.010 0.010 0.009 0.007 0.009

0.005 0.005 0.005 0.004 0.004 0.003 0.004

A2 = -0.146

0.06 0.04 0.04 0.04 0.05 0.04 0.03

0.006 0.005 0.005 0.005 0.005 0.005 0.005

0.003 0.003 0.003 0.003 0.002 0.003 0.003

for butanoate,

by TRC

the differences

results proved

validation

for the temperature

range

data involved

minimizing

only

4%

in the literature, namely,

for ethanoate;

of the experimental

principle,

0.008 0.009 0.009 0.009 0.008 0.009 0.007

A 2 =

0.330 A2t = 0.307 A2j = 770.1 a /1g2t = 946.3 a Au2t = - 1858.1 a A 1 = - 0.020 A 1= 0 . 1 0 2

esters published

c a s e , t h a t is, < 4 % . T h e s e The treatment

A2 = -0.060

0.02 0.04 0.04 0.04 0.05 0.04 0.02

1.

e t al. ( 1 9 8 1 )

at our laboratory

0.010 0.007 0.007 0.007 0.006 0.005 0.004

A2t =

= 0.328 A 12 = 0.349 Al2 = 326.4 a / 1 g 1 2 = 147.4 a Aut2 = 3489.7 a A o = 0.323 Ao = 0.344

(1991)

0.013 0.008 0.008 0.008 0.007 0.006 0.007

A21 =

AI2

values for the methyl and Ambrose

/12~ = 2033.9 a /1g21 = - 760.8 a /1U21 = --2295.9 a A t = 0.110 A 1= - 0 . 3 4 7

At2 = 0.455

were

A2 = -0.105 A 2 = 0.432

0.06 0.05 0.05 0.04 0.03 0.02 0.01

A2~ = 0.384

At2 = 0.421 A I 2 = - - 172.5 a /1gtz = 998.1 a /1ut2 = 4208.9 a A o = 0.439 A o = 0.487

a All parameters in J mol

the differences

0.253

A21 =

(1991)

by TRC

and Boublik

i n t h e Yi v a l u e s

cases.

(1991),

Using

Boublik

e t al. ( 1 9 7 3 )

were comparable

of the vapor pressures

s e t o u t in T a b l e

the objective

in the worst

the constant e t al. ( 1 9 7 3 ) ,

for propanoate; to the preceding

and correlations

computed

3.

fitting the activity coefficients

using the maximum

function

4

O.F.=

E [ M i , c a l - Mi,exp. ] 2/ S M2i i=l

(Mi=P,T,x,y)

(4)

267

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

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 YlTable 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 determining the location of the azeotrope:

y, = x l

(s)

(OT/Ox,)p=(OT/Oyl)p=O

If Q = Yl - X l in Eq. (1), then: 0=

(6)

]~_~Aiz i where z = x , / [ x I + kx2]

Table 7 Error percentage obtained in prediction of activity coefficients using different models on the mixtures methyl esters + butan2-ol at various working pressures ASOG

UNIFAC-2

OH/COO a OH/COOC Butanol-2-ol + 74.66 kPa Methyl ethanoate 7.9 Methyl propanoate 7.8 Methyl butanoate 5.3 101.32 kPa Methyl ethanoate 9.6 Methyl propanoate 9.2 Methyl butanoate 7.7 127.99 kPa Methyl ethanoate 14.5 Methyl propanoate 10.7 Methyl butanoate 8.0

UNIFAC- 1 b OH/COOC

c

OH/COOC

d

COH/COO e CCOH/COOC f OH/COO ~

2.9 4.0 3.5

2.5 5.2 3.5

7.6 8.2 9.0

2.4 3.9 3.1

3.6 5.5 6.0

1.8 3.6 3.8

2.8 4.5 4.4

3.1 6.5 3.6

8.8 9.8 12.4

2.8 5.3 3.7

4.7 7.3 9.5

1.5 5.1 6.1

5.4 4.6 3.9

5.4 6.9 3.5

12.9 10.9 12.5

7'.0 (:~.5 4.3

9.1 8.7 9.9

4.5 6.2 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).

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

268

but if instead Q = T - XlTb,l -0 =

where

X2Tb.2 for condition (5), then:

- rb,2 + (1 - 2xl), a=

(7)

E A i zi and /3= ( d c r / d z ) .

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 p = 101.32 kPa p = 127.99 kPa

T = 361.7 K T = 370.6 K 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 - 1 0 % 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 coefficients of Antoine equation refractive index at D-sodium line working pressure po vapor pressure of species i gases universal constant R T absolute temperature Th.~ normal boiling temperature of species i VL liquid molar volume liquid mole fraction of species i x~ vapor mole fraction of species i Yi Greek letters 7~ activity coefficient of species i p density ~bi fugacity coefficient of species i

A,B,C n(D) P

Acknowledgements We are thankful to the DGICYT (MEC) frem Spain for financial support for this project (PB92-0559).

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