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Fluid Phase Equilibria 259 (2007) 57–65

Isobaric vapor–liquid equilibria of 1,1-dimethylethoxy-butane + methanolor ethanol + water at 101.32 kPa

Alberto Arce ∗, Alberto Arce Jr., Jose Manuel Martınez-Ageitos, Ana SotoDepartment of Chemical Engineering, University of Santiago de Compostela, E-15782 Santiago de Compostela, Spain

Received 15 December 2006; received in revised form 29 January 2007; accepted 30 January 2007Available online 3 February 2007

bstract

Isobaric vapor–liquid equilibrium data (VLE) at 101.325 kPa have been determined in the miscible region for 1,1-dimethylethoxy-butaneBTBE) + methanol + water and 1,1-dimethylethoxy-butane (BTBE) + ethanol + water ternary systems, and for their constituent binary sys-ems, methanol + BTBE and ethanol + BTBE. Both binary systems show an azeotrope at the minimum boiling point. In the ternary systemTBE + methanol + water no azeotrope has been found, however, the system BTBE + ethanol + water might form a ternary azeotrope near the topf the binodal. Thermodynamically consistent VLE data have been satisfactorily correlated using the UNIQUAC, NRTL and Wilson equations for

he activity coefficient of the liquid phase. Temperature and vapor phase compositions have been compared with those calculated by the group-ontribution methods of prediction ASOG, and the original and modified UNIFAC. Predicted values are not in good agreement with experimentalalues.

2007 Elsevier B.V. All rights reserved.

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aci

eywords: VLE; BTBE; Alcohols; Water

. Introduction

The work presented in this paper continues the study on phasequilibria of alcohol and tertiary ether mixtures used as octane-nhancing components in gasoline [1,2]. The goal of this studys to know the behaviour of these systems when increasing the

olecular weight of the ether.Herein, thermodynamically consistent [3–6] vapor–liquid

quilibrium (VLE) data at 101.325 kPa are presented for the sys-ems 1,1-dimethylethoxy-butane (BTBE) + methanol + waternd (BTBE) + ethanol + water and for the two constituentinary systems alcohol + ether. The Wilson [7], NRTL [8]nd UNIQUAC [9] equations for the liquid phase activityoefficients are used to correlate experimental data. Group-ontribution methods ASOG [10,11], UNIFAC [3], and modifiedNIFAC-Dortmund [12,13] and UNIFAC-Lyngby [14] are

pplied to predict VLE data. No VLE data have been

ound in the open literature for the systems targeted in thisork.

∗ Corresponding author.E-mail address: eqaaarce@usc.es (A. Arce).

wtowLr

378-3812/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.fluid.2007.01.038

. Experimental

1,1-Dimethylethoxy-butane (butyl-tert-butyl ether or BTBE)as supplied by Yarsintez (Yaroslav, Russia) with nominalurity >99.9 mass%. Methanol and ethanol were supplied byerck (Madrid, Spain) and had a nominal purity >99.5 mass%.ater was purified using a Milli-Q Plus system. The water con-

ent of BTBE was 0.1 mass%, and for methanol and ethanol were.05 and 0.04 mass%, respectively, determined with a Metrohm37 KF coulometer. Table 1 gathers information about pure com-onents: experimental densities, refractive indices at 298.15 Knd boiling temperatures at 101.32 kPa, together with publishedalues for these parameters [15,16].

VLE data were obtained in a Labodest 602 Distillationpparatus that recycles both liquid and vapor phases (Fis-her Labor und Verfahrenstechnik, Germany). This apparatuss equipped with a Fischer digital manometer that measures toithin ±0.01 kPa and a ASL F250 Mk II Precision Thermome-

er, operating with a PT100 PRT, that provides the temperature

f the system with an overall precision of ±0.02 K. Distillationas carried out at 101.325 kPa under inert Argon atmosphere.iquid and vapor phase composition were determined indi-

ectly by densimetry and refractometry (see reference [17] for

58 A. Arce et al. / Fluid Phase Equilibria 259 (2007) 57–65

Table 1Densities (ρ), refractive indices (nD), and boiling points (Tb) of the pure compounds

Compound ρ (298.15 K) (g cm−3) nD (298.15 K) Tb (101.325 kPa) (K)

Exptl Lit Exptl Lit Exptl Lit

Water 0.99704 0.99704a 1.33250 1.33250a 373.15 373.15a

Methanol 0.78663 0.78664a 1.3264 1.32652a 337.50 337.696a

Ethanol 0.78522 0.78493a 1.35920 1.35941a 351.44 351.443a

BTBE 0.75757 0.7581b 1.39170 – 395.65 –

(

mda±Ratapf

3

vVT

TB

T

M

E

–) Not found.a Riddick et al.b Misako et al.

ore details). Data for the composition dependence of theensities and refractive indices of studied systems have beenlready published [18]. Densities were measured to within0.00001 g cm−3 in an Anton Paar DMA 60/602 densimeter.efractive indices were measured to a precision of ±0.00001 inn ATAGO RX-5000 refractometer. The temperature was con-

rolled with a Hetoterm thermostat to maintain the temperaturet (298.15 ± 0.02) K. The maximum deviation found in com-osition analysis by using this method was ±0.003 in moleraction.

tadb

able 2oiling Temperatures (T), liquid an vapour mole fractions (xi, yi), activity coefficient

(K) x1 y1 γ1 γ2 GE/RT

ethanol (1) + BTBE (2)388.87 0.0096 0.1751 3.674 1.002 0.046377.92 0.0291 0.4577 4.228 0.924 −0.109371.36 0.0479 0.5887 3.986 0.879 −0.175362.06 0.0832 0.6940 3.603 0.923 0.100352.75 0.1519 0.7749 2.988 1.024 0.548

347.64 0.2116 0.8141 2.688 1.104 0.830344.54 0.2904 0.8421 2.260 1.178 1.011343.17 0.3449 0.8545 2.028 1.242 1.101342.47 0.3805 0.8609 1.900 1.292 1.147341.88 0.4168 0.8666 1.784 1.348 1.181

341.03 0.4807 0.8751 1.611 1.469 1.216340.60 0.5198 0.8798 1.522 1.556 1.219340.22 0.5587 0.8842 1.443 1.658 1.210340.00 0.5834 0.8870 1.397 1.729 1.197339.42 0.6542 0.8949 1.284 1.987 1.132

thanol (1) + BTBE (2)387.26 0.0444 0.2866 1.963 0.940 −0.095379.98 0.0897 0.4438 1.867 0.949 0.027370.67 0.1557 0.6109 1.989 0.955 0.210364.59 0.2186 0.7038 2.003 0.960 0.363360.54 0.2887 0.7545 1.874 1.004 0.551

357.74 0.3656 0.7936 1.721 1.045 0.673356.57 0.4229 0.8051 1.575 1.131 0.780355.68 0.4673 0.8139 1.489 1.208 0.847354.19 0.5804 0.8411 1.309 1.384 0.861353.33 0.6533 0.8564 1.222 1.563 0.840

352.83 0.7074 0.8646 1.161 1.780 0.805352.57 0.7358 0.8708 1.135 1.900 0.771352.28 0.7736 0.8792 1.102 2.097 0.712351.94 0.8229 0.8898 1.062 2.479 0.616351.78 0.8459 0.9025 1.054 2.539 0.551

. Results and discussion

For each binary system studied, Table 2 lists experimentalalues for x, y, T, γ , and GERT−1. For ternary systems, isobaricLE data were determined only for the homogeneous zones.able 3 lists the experimental liquid- and vapor-phase composi-

ions (x and y , respectively) and equilibrium temperatures (T),

i i

long with the corresponding activity coefficients (γ i). Fig. 1epicts the calculated isotherms of each ternary system. Theinodal curves were taken from previous work [19].

s (γ i), and GE/RT for the binary systems

T (K) x1 y1 γ1 γ2 GE/RT

339.09 0.6982 0.9001 1.225 2.195 1.068338.84 0.7344 0.9047 1.181 2.405 1.002338.61 0.7693 0.9096 1.144 2.654 0.925338.39 0.8035 0.915 1.110 2.960 0.837338.23 0.8284 0.9195 1.089 3.233 0.765

337.97 0.8739 0.9295 1.053 3.903 0.610337.78 0.9101 0.9401 1.030 4.698 0.467337.67 0.9372 0.951 1.016 5.539 0.344337.63 0.9485 0.9566 1.011 5.999 0.289337.61 0.9569 0.9614 1.008 6.387 0.246

337.60 0.9640 0.966 1.006 6.745 0.209337.60 0.9704 0.9705 1.004 7.124 0.174337.61 0.9829 0.981 1.001 7.957 0.104337.64 0.9909 0.9891 1.000 8.583 0.056

351.70 0.8533 0.9038 1.050 2.640 0.538351.55 0.8833 0.9148 1.032 2.959 0.452351.48 0.8949 0.9186 1.026 3.149 0.419351.43 0.9092 0.9246 1.018 3.385 0.371351.40 0.9174 0.9299 1.016 3.466 0.342

351.37 0.9268 0.9354 1.013 3.611 0.308351.35 0.9356 0.9391 1.008 3.874 0.276351.32 0.9442 0.9451 1.006 4.038 0.244351.32 0.9586 0.9561 1.002 4.358 0.185351.34 0.9653 0.9629 1.002 4.395 0.155

A. Arce et al. / Fluid Phase Equilibria 259 (2007) 57–65 59

Table 3Boiling temperatures (T), liquid and vapour mole fractions (xi, yi), activity coefficients (γ i) and molar excess Gibbs free energies (GE/RT) for indicated the ternarysystems at 101.32 kPa

T (K) x1 x2 y1 y2 γ1 γ2 γ3 GE/RT

BTBE (2) + methanol (1) + water (3)337.65 0.0045 0.9877 0.0053 0.9925 8.415 1.003 1.149 0.039337.74 0.0457 0.9428 0.0393 0.9574 6.097 1.014 1.169 0.273337.75 0.0440 0.9262 0.0397 0.9495 6.325 1.013 1.458 0.293338.02 0.0094 0.9581 0.0121 0.9761 9.040 1.003 1.454 0.100338.12 0.0821 0.8770 0.0614 0.9196 5.143 1.023 1.840 0.503

338.38 0.0425 0.8975 0.0434 0.9328 7.017 1.009 1.563 0.331338.49 0.1096 0.8363 0.0723 0.8995 4.457 1.034 2.030 0.648338.76 0.1657 0.7970 0.0818 0.8953 3.317 1.077 2.382 0.817338.85 0.0898 0.8320 0.0704 0.8912 5.245 1.020 1.891 0.607339.01 0.0088 0.9035 0.0142 0.9532 10.918 1.004 1.430 0.158

339.02 0.0401 0.8557 0.0490 0.9072 8.161 1.004 1.607 0.387339.16 0.2227 0.7421 0.0893 0.8855 2.651 1.129 2.734 0.965339.21 0.1489 0.7776 0.0842 0.8725 3.726 1.057 2.238 0.841339.32 0.1112 0.7933 0.0806 0.8678 4.762 1.027 2.044 0.742339.41 0.3195 0.6458 0.0954 0.8808 1.929 1.264 2.557 1.112

339.76 0.0428 0.8126 0.0587 0.8792 8.911 1.001 1.597 0.458339.79 0.0109 0.8401 0.0219 0.9207 13.058 1.007 1.421 0.244339.97 0.0867 0.7622 0.0839 0.8409 6.186 1.011 1.828 0.727340.07 0.2159 0.6859 0.0988 0.8311 2.904 1.106 2.611 1.113340.18 0.3136 0.6250 0.0997 0.8512 2.014 1.241 2.921 1.189

340.22 0.1150 0.7370 0.0919 0.8273 5.068 1.022 1.992 0.863340.23 0.3755 0.5836 0.1009 0.8648 1.697 1.347 3.055 1.183340.29 0.0400 0.7717 0.0636 0.8561 10.083 1.005 1.546 0.504340.37 0.1482 0.7068 0.0989 0.8139 4.195 1.042 2.176 1.002340.42 0.2811 0.6268 0.1032 0.8244 2.300 1.187 2.838 1.239

340.48 0.2013 0.6599 0.1039 0.8024 3.206 1.089 2.414 1.171340.69 0.3237 0.5876 0.1068 0.8161 2.046 1.243 3.105 1.303340.72 0.1501 0.6716 0.1059 0.7876 4.341 1.042 2.114 1.081340.92 0.0371 0.7299 0.0732 0.8265 12.207 1.004 1.522 0.550340.94 0.1149 0.6853 0.1037 0.7880 5.547 1.020 1.915 0.964

340.96 0.4851 0.4851 0.1061 0.8676 1.343 1.585 3.122 1.136340.97 0.2969 0.5745 0.1101 0.7875 2.265 1.210 2.798 1.374341.09 0.0743 0.6914 0.1006 0.7850 8.277 1.001 1.714 0.806341.11 0.1994 0.6290 0.1114 0.7731 3.399 1.081 2.356 1.249341.18 0.1042 0.6708 0.1080 0.7748 6.297 1.014 1.819 0.953

341.23 0.3429 0.5400 0.1129 0.7821 1.995 1.270 3.125 1.416341.28 0.1292 0.6488 0.1114 0.7648 5.202 1.029 1.934 1.073341.39 0.1709 0.6267 0.1145 0.7601 4.035 1.058 2.146 1.216341.42 0.0572 0.6752 0.1012 0.7770 10.678 1.003 1.575 0.736341.43 0.0343 0.6901 0.0821 0.8016 14.481 1.011 1.458 0.577

341.46 0.0833 0.6551 0.1110 0.7588 7.999 1.007 1.716 0.905341.52 0.4762 0.4585 0.1148 0.8062 1.443 1.525 4.167 1.310341.57 0.5520 0.4137 0.1122 0.8473 1.209 1.765 4.038 1.101341.75 0.1691 0.6297 0.1190 0.7422 4.177 1.015 2.353 1.203341.77 0.0478 0.6414 0.1102 0.7642 13.673 1.024 1.375 0.679

341.83 0.0360 0.6494 0.0972 0.7694 16.026 1.016 1.440 0.639341.87 0.0263 0.6346 0.0906 0.7760 20.288 1.040 1.322 0.565342.10 0.0285 0.6231 0.1004 0.7560 20.571 1.026 1.375 0.606342.27 0.5574 0.3797 0.1184 0.7936 1.235 1.766 4.671 1.226342.29 0.6338 0.3257 0.1336 0.7966 1.172 1.987 5.498 1.123

343.37 0.6799 0.2987 0.1353 0.8587 1.066 2.257 0.860 0.811344.32 0.7182 0.2596 0.1430 0.8499 1.013 2.453 0.929 0.691345.63 0.7617 0.2152 0.1545 0.8376 0.966 2.746 0.925 0.546347.33 0.7915 0.1816 0.1701 0.8161 0.953 2.975 1.287 0.484349.16 0.8439 0.1371 0.2270 0.7444 0.916 2.824 2.844 0.262

356.27 0.8855 0.0985 0.3233 0.6272 0.925 2.528 4.254 0.139364.70 0.9193 0.0695 0.3465 0.5475 0.904 2.972 12.248 0.032

60 A. Arce et al. / Fluid Phase Equilibria 259 (2007) 57–65

Table 3 (Continued )

T (K) x1 x2 y1 y2 γ1 γ2 γ3 GE/RT

BTBE (2) + ethanol (1) + water (3)386.33 0.9354 0.0496 0.7051 0.2500 0.974 1.575 1.989 0.026388.38 0.9403 0.0484 0.7599 0.2042 0.986 1.244 1.983 0.016374.54 0.8904 0.0980 0.4530 0.4098 0.934 1.868 11.499 0.089377.84 0.9007 0.0826 0.5182 0.3681 0.954 1.795 5.929 0.111380.92 0.9043 0.0791 0.5741 0.3347 0.960 1.550 4.325 0.069

380.34 0.9043 0.0764 0.5685 0.3351 0.967 1.636 4.009 0.107371.07 0.8603 0.1179 0.3887 0.5025 0.926 2.130 5.468 0.184367.34 0.8550 0.1170 0.3396 0.5673 0.918 2.745 4.159 0.260363.35 0.7995 0.1682 0.3045 0.6272 1.004 2.423 3.061 0.569361.13 0.7651 0.2033 0.2574 0.7014 0.959 2.422 2.048 0.511

360.99 0.7679 0.1927 0.2524 0.6909 0.942 2.529 2.272 0.495359.70 0.7398 0.2237 0.2410 0.7159 0.976 2.364 1.958 0.594360.25 0.7456 0.2116 0.2469 0.7001 0.973 2.396 2.010 0.582359.33 0.7236 0.2347 0.2353 0.7242 0.987 2.310 1.633 0.619356.80 0.6277 0.3403 0.2074 0.7750 1.096 1.868 1.019 0.804

354.82 0.6241 0.3115 0.1927 0.6588 1.102 1.866 4.605 1.042353.92 0.6184 0.2965 0.1909 0.5890 1.139 1.812 5.347 1.176354.20 0.5586 0.3747 0.1836 0.6953 1.200 1.675 3.716 1.127352.91 0.5424 0.3572 0.1759 0.6082 1.243 1.613 4.625 1.299353.26 0.5230 0.3934 0.1751 0.6646 1.266 1.580 4.070 1.235

354.18 0.5574 0.3705 0.1842 0.6876 1.207 1.677 3.642 1.148354.77 0.5658 0.3678 0.1870 0.7146 1.182 1.717 2.967 1.078354.51 0.5028 0.4462 0.1791 0.7743 1.285 1.549 1.849 1.040355.57 0.5596 0.3917 0.1919 0.7773 1.190 1.703 1.228 0.934354.57 0.4846 0.4733 0.1778 0.8059 1.320 1.516 0.782 0.947

353.20 0.4597 0.4651 0.1671 0.7222 1.377 1.455 3.133 1.197352.59 0.4536 0.4455 0.1665 0.6679 1.423 1.438 3.577 1.320351.45 0.4268 0.4033 0.1653 0.5613 1.568 1.394 3.666 1.597351.44 0.3899 0.4585 0.1581 0.6091 1.643 1.331 3.501 1.503351.66 0.3476 0.5290 0.1507 0.6733 1.742 1.264 3.224 1.349

351.11 0.3335 0.4953 0.1523 0.6090 1.874 1.247 3.220 1.515350.77 0.3200 0.4512 0.1557 0.5454 2.023 1.242 3.057 1.689350.81 0.2978 0.4921 0.1503 0.5790 2.096 1.207 3.011 1.588350.96 0.2680 0.5577 0.1431 0.6336 2.205 1.159 2.976 1.413351.04 0.2462 0.6051 0.1356 0.6784 2.268 1.140 2.897 1.281

350.68 0.2283 0.5534 0.1411 0.6040 2.581 1.125 2.742 1.464350.57 0.2118 0.5050 0.1474 0.5512 2.918 1.130 2.510 1.601350.54 0.2002 0.4730 0.1528 0.5209 3.204 1.142 2.358 1.679350.51 0.1717 0.5516 0.1385 0.5785 3.393 1.088 2.418 1.459350.50 0.1519 0.6043 0.1270 0.6202 3.521 1.065 2.452 1.306

350.54 0.1352 0.6485 0.1167 0.6577 3.632 1.051 2.462 1.170350.45 0.1226 0.5956 0.1243 0.6043 4.280 1.055 2.281 1.290350.47 0.1087 0.5311 0.1362 0.5536 5.282 1.083 2.038 1.398350.55 0.0993 0.4818 0.1465 0.5217 6.196 1.122 1.869 1.453350.53 0.0870 0.5375 0.1294 0.5632 6.262 1.086 1.933 1.316

350.56 0.0786 0.5776 0.1166 0.5918 6.247 1.061 1.999 1.213350.59 0.0697 0.6212 0.1014 0.6299 6.129 1.049 2.046 1.099350.67 0.0617 0.6601 0.0889 0.6626 6.059 1.035 2.095 0.990350.71 0.0551 0.6936 0.0779 0.6944 5.943 1.030 2.122 0.898350.82 0.0465 0.6104 0.0879 0.6345 7.912 1.065 1.886 1.028

350.97 0.0395 0.5409 0.0980 0.5953 10.321 1.122 1.693 1.095351.09 0.0340 0.4806 0.1119 0.5593 13.613 1.181 1.562 1.124351.03 0.0360 0.4842 0.1122 0.5609 12.918 1.178 1.575 1.136351.63 0.2166 0.7318 0.1244 0.8145 2.313 1.106 2.681 0.896352.14 0.2957 0.6591 0.1414 0.7977 1.886 1.180 2.991 1.014

353.00 0.3929 0.5678 0.1594 0.7847 1.548 1.305 3.053 1.076352.37 0.3842 0.5528 0.1555 0.7363 1.582 1.288 3.777 1.171351.56 0.3416 0.5510 0.1514 0.6750 1.787 1.221 3.669 1.310

A. Arce et al. / Fluid Phase Equilibria 259 (2007) 57–65 61

Table 3 (Continued )

T (K) x1 x2 y1 y2 γ1 γ2 γ3 GE/RT

351.59 0.3178 0.5858 0.1470 0.7031 1.863 1.195 3.526 1.239351.26 0.2745 0.6175 0.1402 0.7007 2.084 1.144 3.384 1.216

350.87 0.2239 0.6318 0.1340 0.6767 2.481 1.096 3.059 1.233350.92 0.1908 0.6868 0.1239 0.7215 2.688 1.073 2.940 1.077350.98 0.1544 0.7479 0.1112 0.7673 2.978 1.045 2.887 0.890350.99 0.1226 0.7993 0.0962 0.8097 3.248 1.031 2.796 0.728351.01 0.1022 0.8345 0.0861 0.8396 3.488 1.024 2.721 0.614

351.06 0.0877 0.8588 0.0764 0.8628 3.603 1.020 2.629 0.529350.72 0.0784 0.7828 0.0808 0.7707 4.322 1.013 2.507 0.735350.66 0.0746 0.7571 0.0822 0.7446 4.632 1.014 2.417 0.797350.63 0.0703 0.7247 0.0844 0.7154 5.054 1.019 2.296 0.868350.59 0.0941 0.7056 0.0989 0.6960 4.423 1.020 2.412 0.962

350.57 0.1324 0.6760 0.1157 0.6738 3.672 1.032 2.591 1.095350.66 0.1170 0.7175 0.1056 0.7118 3.783 1.023 2.593 0.961350.53 0.1046 0.6551 0.1121 0.6487 4.515 1.026 2.350 1.108351.38 0.1440 0.8308 0.1010 0.8725 2.856 1.054 2.405 0.633351.31 0.1185 0.8605 0.0895 0.8864 3.088 1.036 2.631 0.539

351.18 0.0759 0.8995 0.0676 0.9041 3.670 1.016 2.649 0.399351.10 0.0565 0.9054 0.0555 0.9022 4.067 1.010 2.563 0.362351.01 0.0558 0.8861 0.0568 0.8784 4.229 1.008 2.584 0.417350.78 0.0491 0.7917 0.0616 0.7788 5.264 1.009 2.342 0.655350.75 0.0457 0.7501 0.0648 0.7395 5.958 1.013 2.241 0.746

351.40 0.0010 0.9912 0.0018 0.9895 7.420 1.000 2.542 0.027351.32 0.0164 0.9761 0.0191 0.9727 4.804 1.001 2.501 0.099351.21 0.0150 0.9391 0.0183 0.9325 5.057 1.002 2.461 0.197

.9032

.8147

a

y

wamfi

P

fcP

Fb

351.13 0.0162 0.9121 0.0212 0350.86 0.0451 0.8308 0.0553 0

At the equilibrium between the vapor and the liquid phasest pressure P and temperature T,

iφiP = xiγiPsi φ

si exp

[V L

i (P − P si )

RT

](1)

here xi and yi are the mole fraction of component i in the liquidnd vapor phases, respectively, γ i its activity coefficient, V L

i itsolar volume in the liquid phase, φi and φs

i its fugacity coef-cient and fugacity coefficient at saturation, respectively, and

l

ul

ig. 1. Calculated isotherms (T (K)) for VLE at 101.32 kPa of the ternary systems (a) Binary azeotrope.

5.441 1.002 2.428 0.2725.131 1.003 2.440 0.546

si is its saturated vapor pressure. In this work, V L

i is calculatedrom the Rackett’s equation, φi and φs

i from the second virialoefficient using the method of Hayden and O’Connell [20] andsi from Antoine’s equation,

B

og(P s

i (kPa)) = A −(T (K)) + C

(2)

sing coefficients A, B, and C reported in Table 4 as taken fromiterature [15,21,22].

TBE + methanol + water and (b) BTBE + ethanol + water. Symbol (♦) indicates

62 A. Arce et al. / Fluid Phase Equ

Table 4Antoine Coefficients A, B, and C for Eq. (2)

Compound A B C

Watera 7.07405 1657.459 −46.130Methanolb 7.20519 1581.993 −33.439Ethanolb 7.23710 1592.864 −46.966BTBEc 5.82090 1212.51 −77.985

cdaef

DififcTd

prTc

TC(

M

M

E

TC(

B

B

a Reid et al.b Riddick et al.c Stephenson and Malanowski.

Thermodynamic consistency of the binary systems have beenhecked out by means of two tests: (1) the point-to-point Fre-

enslund’s test, for which the condition �yi < 0.01 is met forll data using a third-order polynomial of Legendre to fit thexcess Gibbs energy (GE/RT), and (2) the Wisniak’s L–W test,or which D < 2 is found.

nieD

able 5orrelation of VLE data of the indicated binary systems: model parameters (Wilson, N

T), liquid- and vapor-phase compositions (x, y) and pressure (P)

odel Parameters (J mol−1)

ethanol (1) + BTBE (2)Wilson �λ12 = 6361.1 �λ21 = 321.75NRTL (α = 0.3) �g12 = 4251.6 �g21 = 1423.8UNIQUAC �u12 = −655.44 �u21 = 7250.3

thanol (1) + BTBE (2)Wilson �λ12 = 3615 �λ21 = 1475.2NRTL (α = 0.1) �g12 = 10614 �g21 = −4963.4UNIQUAC �u12 = −1123.6 �u21 = 5516.2

able 6orrelation of VLE data of the indicated ternary systems: model parameters (Wilson

T), liquid- and vapor-phase compositions (xi, yi), and pressure (P)

TBE (2) + methanol (1) + water (3)

Parameters (J mol−1)Wilson �λ12 = 5761.6 �λ13 = 7369.8 �λ23 =

σ(T/K) σ(x1) σ(x2)0.00 0.0001 0.0001

NRTL (α = 0.3) �g12 = 5363.5 �g13 = 1345.1 �g23 =σ(T/K) σ(x1) σ(x2)0.26 0.0053 0.0037

UNIQUAC �u12 = −510.36 �u13 = −2148.1 �u23 =σ(T/K) σ(x1) σ(x2)0.28 0.0052 0.0034

TBE (2) + ethanol (1) + water (3)

Parameters (J mol−1)Wilson �λ12 = 3375.6 �λ13 = −956.16 �λ23 =

σ(T/K) σ(x1) σ(x2)0.02 0.0004 0.0004

NRTL (α = 0.3) �g12 = 5371.0 �g13 = −562.10 �g23 =σ(T/K) σ(x1) σ(x2)0.50 0.0114 0.0106

UNIQUAC �u12 = −1183.5 �u13 = −630.70 �u23 =σ(T/K) σ(x1) σ(x2)0.46 0.0109 0.0095

ilibria 259 (2007) 57–65

Wisniak-LW and Wisniak–Tamir’s modification of Macermot–Ellis tests have been used to drop thermodynamically

nconsistent equilibrium points of the ternary systems. In therst one, 0.96 < Li/Wi < 1 is fulfilled in all equilibrium points,or each system. In the modified Mac Dermot–Ellis test, theondition Di < Dmax is satisfied for all data of both systems.herefore, the thermodynamic consistency of the ternary VLEata reported in this work is confirmed.

The correlation of the experimental (P, T, x, y) results iserformed with a computer program that runs a non-linearegression method based on the maximum likelihood principle.he models used to calculate the liquid-phase activity coeffi-ients are Wilson’s equation, the NRTL equation, setting the

on-randomness parameter, α, to different values and select-ng the value giving the best correlation, and the UNIQUACquation using the structural parameters r and q taken fromauber and Danner [23] and with the parameter q′ set to 1.00

RTL and UNIQUAC) and root mean deviations (σ) in equilibrium temperature

σ (T (K)) σ(x) σ(y) σ(P (kPa))

0.37 0.0016 0.0099 0.030.42 0.0024 0.0103 0.030.37 0.0014 0.0099 0.03

0.44 0.0047 0.0093 0.040.43 0.0043 0.0087 0.040.43 0.0045 0.0092 0.04

, NRTL and UNIQUAC) and root mean deviations in equilibrium temperature

24949 �λ21 = 1073.3 �λ31 = 1469.4 �λ32 = 7282.3σ(y1) σ(y2) σ(P/kPa)0.0283 0.0258 2.280

3165.4 �g21 = 597.66 �g31 = 301.43 �g32 = 17479σ(y1) σ(y2) σ(P/kPa)0.0185 0.0141 0.730

4363.5 �u21 = 6599.1 �u31 = 3772.7 �u32 = 877.373σ(y1) σ(y2) σ(P/kPa)0.0167 0.0119 0.830

24981 �λ21 = 2702.8 �λ31 = 5320.3 �λ32 = 8501.5σ(y1) σ(y2) σ(P/kPa)0.0534 0.0310 4.853

4924.0 �g21 = −46.836 �g31 = 6006.5 �g32 = 14917σ(y1) σ(y2) σ(P/kPa)0.0045 0.0105 0.081

5107.5 �u21 = 6349.4 �u31 = 3157 �u32 = 1160.6σ(y1) σ(y2) σ(P/kPa)0.004 0.0106 0.040

A. Arce et al. / Fluid Phase Equilibria 259 (2007) 57–65 63

Fig. 2. (a) Experimental VLE data at 101.32 kPa (©) and corresponding NTRL � = 0.3 correlation (—) for the binary system methanol + BTBE. (b) ExperimentalVLE data at 101.32 kPa (©) and corresponding NTRL α = 0.1 correlation (—) for the binary system ethanol + BTBE.

F QUAC(

ftbfclccmsQs

uttiU

TeFries methanol + BTBE and ethanol + BTBE, with the predictionof the UNIFAC-Dortmund model. In Table 8 are listed the rootmean standard deviations between the experimental VLE data

Table 7Root mean square deviations (σ) between the experimental boiling temperatures(Tb) and vapour-phase compositions (y) and those calculated by the ASOG,UNIFAC, and modified UNIFAC methods for the indicated binary systems

Methods Methanol (1) + BTBE (2) Ethanol (1) + BTBE (2)

σ(Tb (K)) σ(y1) σ(Tb (K)) σ(y1)

ig. 3. Experimental VLE data at 101.32 kPa (arrows), and corresponding UNIb) BTBE + ethanol + water. Symbol (♦) indicates binary azeotrope.

or water and to 0.96 and 0.92 for methanol and ethanol, respec-ively, taken from Anderson and Prausnitz [24]. The values of theinary interaction parameters are summarised in Tables 5 and 6or binary and ternary systems, respectively, along with theorresponding mean standard deviations (σ) in temperature,iquid- and vapor-phase compositions, and in pressure. Fig. 2ompares the NTRL α = 0.3, and the NRTL α = 0.1 temperature-omposition curves with the experimental results for the systemsethanol + BTBE and ethanol + BTBE, respectively. In Fig. 3 is

hown the comparison of the calculated values using the UNI-UAC equation with the experimental VLE data for the ternary

ystems.VLE data for the binary and ternary systems are predicted

sing the following group-contribution methods to calculate

he liquid-phase activity coefficients: the ASOG-KT method,he original UNIFAC method, with the structural and group-nteraction parameters recommended by Gmehling et al. [25] theNIFAC-Dortmund method; and the UNIFAC-Lyngby method.

AUUU

correlation (- - - �) for the ternary systems (a) BTBE + methanol + water and

able 7 lists the root mean standard deviations between thexperimental VLE data for binary systems and those predicted.ig. 4 compares the experimental VLE compositions of the bina-

SOG 0.93 0.018 3.69 0.038NIFAC 0.40 0.014 3.00 0.034NIFAC-Dortmund 0.31 0.014 2.15 0.024NIFAC-Lyngby 1.59 0.014 2.37 0.023

64 A. Arce et al. / Fluid Phase Equilibria 259 (2007) 57–65

Fig. 4. Experimental VLE data at 101.32 kPa of the binary systems (a) methanol + BTBE (©) and (b) ethanol + BTBE, and the data predicted using the UNIFAC-Dortmund method (—).

F nol +E rows)b

aewtm

TR(t

M

B

B

4

ig. 5. (a) Experimental VLE data at 101.32 kPa of the system BTBE + methaxperimental VLE data at 101.32 kPa of the system BTBE + ethanol + water (arinary azeotrope.

nd those predicted for the ternary systems. Fig. 5 compares thexperimental VLE data for the system BTBE + methanol + water

ith the prediction of UNIFAC model and for the sys-

em BTBE + ethanol + water with the prediction of the ASOGodel.

able 8oot mean square deviations (σ) between the experimental boiling temperatures

Tb) and vapour phase compositions (yi) for the indicated ternary systems andhose calculated by the ASOG, UNIFAC, and modified UNIFAC methods

ethods σ(Tb (K)) σ(y1) σ(y2) σ(y3)

TBE (1) + methanol (2) + water (3)ASOG 1.22 0.0093 0.0181 0.0143UNIFAC 1.09 0.0084 0.0162 0.0134UNIFAC-Dortmund 1.33 0.0272 0.0475 0.0333UNIFAC-Lyngby 2.69 0.0347 0.0450 0.0314

TBE (1) + ethanol (2) + water (3)ASOG 2.25 0.0322 0.0406 0.0265UNIFAC 3.04 0.0441 0.0479 0.0278UNIFAC-Dortmund 2.97 0.0368 0.0466 0.0354UNIFAC-Lyngby 4.35 0.0659 0.0533 0.0610

tsasbctM

i3ftctmta

water (arrows), and the data predicted using the UNIFAC method (- - - �). (b), and the data predicted using the ASOG method (- - - �). Symbol (♦) indicates

. Conclusions

Experimental VLE data were determined for the binary sys-ems methanol + BTBE and ethanol + BTBE and for the ternaryystems BTBE + methanol + water and BTBE + ethanol + watert the constant pressure of 101.32 kPa. Thermodynamical con-istency of the experimental VLE data reported in this work haseen checked out by means of the point-to-point Fredenslund’sonsistency test and the Wisniak’s L–W test, for the binary sys-ems, and the Wisniak-LW and Wisniak–Tamir’s modification of

ac Dermot–Ellis tests, for the ternary systems.Both binary systems form azeotrope at the minimum boil-

ng point. For the binary methanol + BTBE has been found at37.60 K, corresponding to a composition near to 0.97 in molarraction of methanol, and for ethanol + BTBE at 351.32 K nearo 0.95, in molar fraction of ethanol. Arrowheads in Fig. 3b,orresponding to the ternary system BTBE + ethanol + water,

end to close in on a single point near the binodal curve which

ight be a ternary azeotrope. However, for the ternary sys-em BTBE + methanol + water arrowheads tend to the binaryzeotrope as shown in Fig. 3a.

e Equ

gtewts

tiswps

LA�

nPqrT�

Vxy

Gα

φ

γ

�

ρ

Si1

SLs

A

T0

R

[

[

[[[

[

[

[

[[[

[

[

[

Publication Data, Hemisphere Publishing Corp., New York, 1989.

A. Arce et al. / Fluid Phas

The equations of Wilson, NRTL, and UNIQUAC are, ineneral, a good correlation of the experimental VLE data ofhese systems. For the binary system ethanol + BTBE, the NRTLquation, with α set to 0.1 gives the slightly better results,hereas the UNIQUAC equation gives the small deviations for

he binary system methanol + BTBE and for the two ternaryystems.

The group-contributions methods used for the prediction ofhe VLE of these systems do not accurately represent the exper-mental results. The UNIFAC-Dortmund model for the binaryystems, and the UNIFAC and ASOG for BTBE + methanol +ater and BTBE + ethanol + water, respectively, give the bestredictions, however deviations from experimental results aretill high.

ist of symbols, B, C Antoine coefficients (Eq. (2))g NRTL binary interaction parameter

D refractive indexpressureUNIQAC area parameterUNIQUAC volume parametertemperature

u UNIQUAC binary interaction parametermolar volumemole fraction in the liquid phasemole fraction in the vapor phase

reek lettersNRTL non-randomness parameterfugacity coefficientactivity coefficient

λ Wilson binary interaction parameterdensity

ubscriptsith component

, 2, 3 components 1, 2, 3

uperscriptsliquidsaturation

[

[

ilibria 259 (2007) 57–65 65

cknowledgment

The authors are grateful to the Ministerio de Ciencia yecnologıa (Spain) for financial support under project PPQ2003-1236.

eferences

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