Fluid Phase Equilibria 233 (2005) 9–18

Isobaric vapor–liquid equilibria for systems composed by2-ethoxy-2-methylbutane, methanol or ethanol and

water at 101.32 kPa

Alberto Arce∗, Alberto Arce Jr., Eva Rodil, Ana SotoDepartment of Chemical Engineering, University of Santiago de Compostela, Av. Lope G´omez de Marzoa S/N, 15782 Santiago de Compostela, Spain

Received 16 February 2005; received in revised form 4 April 2005; accepted 11 April 2005Available online 11 May 2005

Abstract

Isobaric vapor–liquid equilibrium (VLE) data for 2-ethoxy-2-methylbutane (TAEE) + methanol + water and TAEE + ethanol + water ternarysystems, and for their binary subsystems alcohol + ether, have been determined experimentally at 101.32 kPa. Both binary systems form anazeotrope with a minimum boiling point. The ternary system TAEE + methanol + water does not form a ternary azeotrope, however, the ternarys surementsh originala©

K

1

ahftvtabs

ltwe

f

andlco-undm,

eper-

itherepu-lus, and, re-ter.

0d

ystem TAEE + ethanol + water shows a ternary azeotrope near the top of the binodal. Thermodynamically consistent VLE meaave been satisfactorily correlated with NRTL, and UNIQUAC equations for the liquid phase activity coefficient. The ASOG and thend modified UNIFAC group-contribution methods do not predict adequately the VLE data of this work.2005 Elsevier B.V. All rights reserved.

eywords: VLE; TAEE; Correlation; Prediction

. Introduction

Tertiary ethers of high molecular weights show good char-cteristics as oxygenated additives for unleaded gasoline. Itas been proved that their addition reduces harmful emissions

rom motor vehicles to the atmosphere, which contributes tohe global warming. Low volatility, high-octane value andery low solubility in water turns TAEE into a good alterna-ive to MTBE, which has raised issues about human healthfter the detection of the chemical in water resources, causedy the release of gasoline from leaking underground gasolinetorage.

VLE data are of prime importance in the design of distil-ation processes for predicting the vapor-phase compositionhat would be in equilibrium with a liquid mixture. In thisork, thermodynamically consistent[1–4] vapor–liquidquilibrium (VLE) data at 101.32 kPa are studied for systems

∗ Corresponding author. Tel.: +34 981 563100x16790;ax: +34 981 547140/528050.

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

2-ethoxy-2-methylbutane (TAEE) + methanol + waterTAEE + ethanol + water and for their two constituent ahol + ether systems. In the open literature we only have fothe vapor–liquid equilibrium of ethanol + TAEE systeisobaric at 87 kPa[5] and isothermal at 362.82 K[6]. TheWilson [7], NRTL [8] and UNIQUAC[9] equations for thliquid phase activity coefficients are used to correlate eximental data. Group-contribution methods ASOG[10,11],UNIFAC [1] and modified UNIFAC-Dortmund[12,13] andUNIFAC-Lyngby [14] are applied to predict VLE data.

2. Experimental

TAEE was supplied by Yarsintez (Yaroslav, Russia) wnominal purity >99.9 mass%. Methanol and ethanol wsupplied by Merck (Madrid, Spain) and had a nominalrity >99.5 mass%. Water was purified using a Milli-Q Psystem. The water contents of TAEE was 0.02 mass%for methanol and ethanol were 0.05 and 0.04 mass%spectively, determined with a Metrohm 737 KF coulome

378-3812/$ – see front matter © 2005 Elsevier B.V. All rights reserved.oi:10.1016/j.fluid.2005.04.003

10 A. Arce et al. / Fluid Phase Equilibria 233 (2005) 9–18

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

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

Experimental Literature Experimental Literature Experimental Literature

Water 0.99704 0.99704[15] 1.33250 1.33250[15] 373.15 373.15[15]Methanol 0.78663 0.78664[15] 1.3264 1.32652[15] 337.50 337.696[15]Ethanol 0.78522 0.78493[15] 1.35920 1.35941[15] 351.44 351.443[15]TAEE 0.76057 – 1.38857 – 374.57 374.7[16]

–: not found.

Table 1gathers information about pure components: exper-imental densities, refractive indices at 298.15 K and boilingtemperatures at 101.32 kPa, together with published valuesfor these parameters[15,16].

VLE data are determined in a Labodest 602 Distillationapparatus that recycles both liquid and vapor phases (Fis-cher Labor und Verfahrenstechnik, Germany). This still isequipped with a Fischer digital manometer that measured towithin ±0.01 kPa and an ASL F250 Mk II Precision Ther-mometer, operating with a wired PT100 PRT, that providesthe temperature of the system with an overall accuracy of±0.02 K. Distillation is carried out at 101.32 kPa under in-ert argon atmosphere. Liquid- and vapor-phase compositionwere determined indirectly by densimetry and refractome-try. Data for the composition dependence of the densitiesand refractive indices of studied systems have been alreadypublished by ourselves[17,18]. Densities were measured towithin ±0.00001 g cm−3 in an Anton Paar DMA 60/602 den-simeter. Refractive indices were measured to an accuracy of±0.00004 in an ATAGO RX-5000 refractometer. The temper-ature was controlled with a Hetoterm thermostat to maintainthe temperature at (298.15± 0.02) K. The maximum devia-tion in composition analysis was±0.003 mole fraction.

3. Results and discussion

f baric

VLE data are determined only for the homogeneous zones.The experimental liquid- and vapor-phase composition (xi

andyi , respectively) and equilibrium temperatures (T), alongwith the corresponding activity coefficients (γ i) are listedin Table 3. Fig. 1 shows the calculated isotherms of eachternary system for the homogeneous zones. Dashed lines inthe ternary diagrams of this figure are the binodal curves andwere taken from previous works[19,20].

At the equilibrium between the vapor and the liquid phasesat pressureP and temperatureT:

yiφiP = xiγiPsi φ

si exp

[V L

i (P − Psi )

RT

](1)

wherexi andyi are the mole fraction of componenti in theliquid and vapor phases, respectively;γ i its activity coeffi-cient;V L

i its molar volume in the liquid phase;φi andφsi its

fugacity coefficient and fugacity coefficient at saturation, re-spectively; andPs

i its saturated vapor pressure. In this work,V s

i was calculated from the Rackett’s equation,φi andφsi from

the second virial coefficient using the method of Hayden andO’Connell[21], andPs

i from Antoine’s equation:

log(Psi ) (kPa)= A − B

T (K) + C(2)

using the coefficientsA, B, andC reported inTable 4as takenf

wasc oint

F system bol (i

Table 2lists experimental values forx, y, T, γ, andGE/RTor each binary system studied. For ternary systems, iso

ig. 1. Calculated isotherms (T, K) for VLE at 101.32 kPa of the ternaryndicates binary azeotrope.

rom literature[6,15,22].Thermodynamic consistency of the binary systems

hecked out by means of two tests: (1) the point-to-p

s: (a) TAEE + methanol + water and (b) TAEE + ethanol + water. Sym♦)

A. Arce et al. / Fluid Phase Equilibria 233 (2005) 9–18 11

Table 2Boiling temperatures (T), liquid and vapor mole fractions (xi , yi ), activity coefficients (γ i ), andGE/RT for the binary Systems

T (K) x1 y1 γ1 γ2 GE/RT T(K) x1 y1 γ1 γ2 GE/RT

Methanol (1) + TAEE (2)367.80 0.0230 0.1945 3.116 1.002 0.028 336.89 0.7269 0.8228 1.170 2.249 0.335360.35 0.0618 0.3992 2.981 0.976 0.045 336.72 0.7668 0.8329 1.130 2.502 0.307351.58 0.1119 0.5753 3.155 0.971 0.102 336.60 0.8065 0.8442 1.093 2.828 0.273346.38 0.1849 0.6642 2.635 1.002 0.181 336.54 0.8273 0.8484 1.073 3.092 0.253344.79 0.2187 0.6831 2.423 1.044 0.227 336.52 0.8481 0.8572 1.058 3.318 0.230

343.22 0.2583 0.7052 2.240 1.082 0.267 336.47 0.8683 0.8642 1.044 3.649 0.208341.44 0.3137 0.7267 2.027 1.157 0.322 336.47 0.8864 0.8731 1.033 3.958 0.185338.67 0.4999 0.7712 1.493 1.476 0.395 336.49 0.9013 0.8811 1.024 4.269 0.165338.26 0.5406 0.7811 1.420 1.562 0.394 336.68 0.9509 0.9184 1.004 5.878 0.091337.13 0.6979 0.8100 1.189 2.157 0.353 337.28 0.9936 0.9765 0.999 12.807 0.015336.95 0.7337 0.8193 1.152 2.345 0.331 337.48 0.9989 0.9922 1.002 24.605 0.005

Ethanol (1) + TAEE (2)365.30 0.0592 0.3079 3.177 0.963 0.033 349.2 0.7631 0.7631 1.087 2.211 0.252361.28 0.0994 0.4159 2.932 0.960 0.070 349.22 0.7803 0.7700 1.072 2.314 0.238354.60 0.2234 0.5900 2.348 0.969 0.166 349.24 0.8039 0.7837 1.058 2.439 0.220353.58 0.2631 0.6064 2.128 1.013 0.208 349.3 0.8303 0.7972 1.039 2.639 0.196352.68 0.3079 0.6224 1.930 1.066 0.247 349.36 0.8531 0.8138 1.029 2.797 0.176

352.02 0.3427 0.6343 1.811 1.112 0.273 349.48 0.8757 0.8303 1.018 3.004 0.153351.52 0.3820 0.6421 1.676 1.177 0.298 349.64 0.8979 0.8499 1.010 3.223 0.128350.95 0.4301 0.6576 1.558 1.245 0.315 349.80 0.917 0.8692 1.005 3.441 0.107350.35 0.4950 0.6729 1.417 1.370 0.331 350.03 0.9319 0.8876 1.001 3.582 0.087349.91 0.5436 0.6916 1.348 1.452 0.332 350.17 0.9423 0.9011 0.999 3.706 0.075

349.70 0.5817 0.7026 1.290 1.540 0.328 350.45 0.9614 0.9233 0.992 4.264 0.049349.56 0.6144 0.7099 1.240 1.638 0.322 350.67 0.9741 0.9455 0.995 4.491 0.034349.40 0.6499 0.7208 1.197 1.746 0.312 350.85 0.9806 0.9582 0.994 4.576 0.024349.26 0.7026 0.7421 1.146 1.910 0.288 351.03 0.9903 0.9748 0.995 5.492 0.011349.22 0.7315 0.7527 1.118 2.033 0.272 351.17 0.9968 0.9827 0.991 11.384 −0.002

Fredenslund’s test, for which the condition�yi < 0.01 is metfor all data using a second-order polynomial of Legendre tofit the excess Gibbs energy (GE/RT), and (2) the Wisniak’sL–W test, for whichD < 2 is found.

Wisniak–LW and Wisniak–Tamir’s modification ofMcDermott–Ellis tests have been used to eliminate thermo-dynamically inconsistent equilibrium points of the ternarysystems. In the first one, 0.96 <Li /Wi < 1 is fulfilled in

Fig. 2. (a) Experimental VLE data at 101.32 kPa (©) and corresponding UNIQUAC correlation (—) for the binary system methanol + TAEE. (b) ExperimentalVLE data at 101.32 kPa (©) and corresponding NTRLα = 0.1 correlation (—) for the binary system ethanol + TAEE.

12 A. Arce et al. / Fluid Phase Equilibria 233 (2005) 9–18

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

T (K) x1 x2 y1 y2 γ1 γ2 γ3 GE/RT

TAEE (2) + methanol (1) + water (3)336.94 0.8118 0.1537 0.8395 0.1470 1.065 3.140 1.620 0.244337.05 0.7822 0.1785 0.8259 0.1576 1.083 2.887 1.730 0.273337.16 0.8377 0.1131 0.8432 0.1340 1.028 3.859 1.901 0.207337.18 0.7600 0.1938 0.8138 0.1651 1.092 2.773 1.871 0.294337.23 0.7430 0.2112 0.8086 0.1700 1.108 2.615 1.909 0.309

337.30 0.7314 0.2179 0.8027 0.1727 1.115 2.568 1.977 0.320337.31 0.7988 0.1410 0.8187 0.1513 1.040 3.476 2.030 0.250337.36 0.8487 0.0889 0.8502 0.1226 1.015 4.460 1.773 0.181337.40 0.9220 0.0419 0.9148 0.0711 1.004 5.483 1.587 0.092337.46 0.8167 0.1085 0.8268 0.1387 1.022 4.119 1.867 0.218

337.47 0.9610 0.0206 0.9559 0.0374 1.003 5.854 1.476 0.046337.51 0.7801 0.1405 0.8092 0.1551 1.045 3.550 1.815 0.260337.55 0.9348 0.0298 0.9313 0.0551 1.002 5.943 1.551 0.070337.57 0.7648 0.1523 0.8000 0.1606 1.051 3.383 1.914 0.277337.58 0.8322 0.0872 0.8377 0.1267 1.011 4.661 1.779 0.190

337.59 0.6802 0.2596 0.7802 0.1868 1.152 2.307 2.204 0.361337.70 0.7358 0.1740 0.7849 0.1703 1.067 3.125 1.988 0.308337.71 0.8427 0.0717 0.8492 0.1145 1.007 5.100 1.698 0.168337.74 0.9745 0.0080 0.9772 0.0163 1.001 6.508 1.488 0.023337.74 0.9743 0.0078 0.9775 0.0159 1.002 6.511 1.477 0.024

337.76 0.9466 0.0182 0.9504 0.0364 1.002 6.381 1.501 0.050337.84 0.8101 0.0884 0.8205 0.1339 1.008 4.814 1.788 0.204337.96 0.6216 0.3094 0.7560 0.1999 1.205 2.044 2.528 0.401337.99 0.8017 0.0848 0.8147 0.1348 1.005 5.024 1.760 0.205338.11 0.7779 0.0959 0.7952 0.1472 1.007 4.830 1.795 0.230

338.30 0.8654 0.0360 0.8840 0.0766 0.998 6.655 1.560 0.110338.30 0.5879 0.3252 0.7296 0.2084 1.213 2.002 2.780 0.428338.34 0.7490 0.1000 0.7720 0.1580 1.006 4.930 1.805 0.253338.41 0.6763 0.1721 0.7334 0.1887 1.056 3.412 1.993 0.353338.43 0.5537 0.3656 0.7265 0.2135 1.277 1.816 2.881 0.439

338.56 0.5427 0.3701 0.7146 0.2172 1.275 1.816 3.013 0.449338.61 0.5297 0.3608 0.7061 0.2167 1.288 1.855 2.710 0.466338.62 0.7001 0.1218 0.7313 0.1821 1.009 4.617 1.869 0.304338.83 0.5143 0.3866 0.6936 0.2235 1.293 1.772 3.184 0.468338.83 0.6175 0.2049 0.6930 0.2081 1.076 3.112 2.120 0.411

338.86 0.6729 0.1242 0.7085 0.1926 1.008 4.747 1.854 0.324338.87 0.8095 0.0395 0.8441 0.0944 0.997 7.321 1.551 0.143338.89 0.4630 0.4901 0.7238 0.2290 1.495 1.430 3.821 0.424338.96 0.5071 0.3828 0.6833 0.2269 1.285 1.808 3.087 0.478338.99 0.4581 0.4889 0.7140 0.2301 1.485 1.435 3.987 0.431

339.02 0.8182 0.0317 0.8591 0.0805 0.999 7.739 1.523 0.127339.02 0.5948 0.2141 0.6724 0.2176 1.076 3.093 2.173 0.434339.05 0.6696 0.1190 0.7051 0.1928 1.001 4.926 1.822 0.317339.13 0.4487 0.4902 0.6973 0.2341 1.473 1.448 4.218 0.443339.19 0.6420 0.1203 0.6814 0.2045 1.004 5.142 1.799 0.339

339.27 0.6340 0.1123 0.6730 0.2059 1.001 5.530 1.783 0.339339.29 0.5635 0.2254 0.6519 0.2255 1.090 3.015 2.167 0.461339.35 0.4804 0.3782 0.6465 0.2344 1.265 1.864 3.134 0.510339.35 0.4573 0.4234 0.6541 0.2363 1.344 1.679 3.418 0.501339.39 0.4134 0.5359 0.7008 0.2387 1.591 1.339 4.432 0.424

339.49 0.7671 0.0348 0.8204 0.0999 0.999 8.601 1.491 0.153339.52 0.6047 0.1116 0.6489 0.2181 1.002 5.841 1.732 0.354339.52 0.4662 0.3785 0.6301 0.2394 1.262 1.890 3.104 0.525339.53 0.4025 0.5391 0.6839 0.2419 1.586 1.342 4.691 0.434339.55 0.5355 0.2339 0.6295 0.2341 1.097 2.988 2.182 0.486

A. Arce et al. / Fluid Phase Equilibria 233 (2005) 9–18 13

Table 3 (Continued)

T (K) x1 x2 y1 y2 γ1 γ2 γ3 GE/RT

339.56 0.4572 0.3951 0.6286 0.2407 1.282 1.818 3.263 0.524339.58 0.5221 0.2594 0.6266 0.2360 1.118 2.713 2.317 0.501339.61 0.8268 0.0158 0.8932 0.0464 1.005 8.767 1.416 0.093339.65 0.4393 0.4252 0.6288 0.2427 1.330 1.698 3.483 0.520339.67 0.5018 0.2815 0.6174 0.2400 1.143 2.534 2.415 0.520

339.75 0.3873 0.5446 0.6615 0.2454 1.581 1.337 4.999 0.445339.75 0.5038 0.2635 0.6116 0.2416 1.124 2.718 2.307 0.517339.77 0.5697 0.1124 0.6175 0.2340 1.003 6.166 1.707 0.376339.85 0.5976 0.0736 0.6496 0.2128 1.003 8.542 1.524 0.298339.88 0.7190 0.0368 0.7820 0.1198 1.002 9.617 1.465 0.178

339.90 0.5457 0.1234 0.5982 0.2450 1.009 5.853 1.722 0.403339.91 0.5665 0.0885 0.6185 0.2314 1.005 7.707 1.580 0.341339.92 0.3953 0.4758 0.6125 0.2498 1.426 1.547 3.877 0.523339.95 0.3575 0.6082 0.6991 0.2502 1.797 1.212 5.358 0.384339.99 0.5507 0.0863 0.6054 0.2397 1.009 8.163 1.544 0.344

340.04 0.5460 0.0780 0.6023 0.2414 1.010 9.079 1.501 0.330340.14 0.3430 0.6133 0.6744 0.2528 1.794 1.206 5.989 0.394340.20 0.5952 0.0517 0.6618 0.1990 1.012 11.233 1.415 0.255340.36 0.6847 0.0320 0.7641 0.1243 1.009 11.281 1.405 0.180340.39 0.3121 0.6195 0.6205 0.2627 1.797 1.229 6.072 0.434

340.44 0.5359 0.0449 0.6152 0.2275 1.036 14.658 1.332 0.260340.45 0.5833 0.0435 0.6605 0.1966 1.021 13.074 1.359 0.238340.50 0.3188 0.6270 0.6323 0.2618 1.785 1.206 6.915 0.407340.62 0.3085 0.6314 0.6154 0.2640 1.788 1.202 7.066 0.413340.79 0.5254 0.0349 0.6212 0.2189 1.053 17.924 1.272 0.234

340.80 0.6305 0.0301 0.7243 0.1452 1.022 13.790 1.346 0.194340.84 0.5434 0.0350 0.6395 0.2056 1.046 16.760 1.282 0.228340.92 0.5951 0.0317 0.6932 0.1653 1.032 14.841 1.320 0.208340.93 0.2801 0.6554 0.5952 0.2715 1.883 1.178 7.180 0.412340.94 0.7427 0.0119 0.8531 0.0519 1.016 12.420 1.349 0.115

341.03 0.5680 0.0294 0.6765 0.1782 1.051 17.183 1.250 0.202341.05 0.2864 0.6749 0.6542 0.2685 2.014 1.128 6.904 0.357341.11 0.6634 0.0219 0.7731 0.1059 1.025 13.679 1.329 0.163341.15 0.5332 0.0282 0.6427 0.2008 1.059 20.097 1.229 0.206341.28 0.2624 0.6884 0.6133 0.2751 2.044 1.123 7.763 0.368

341.36 0.5399 0.0260 0.6574 0.1851 1.061 19.948 1.239 0.203341.49 0.6688 0.0160 0.7943 0.0849 1.030 14.815 1.303 0.146341.73 0.2293 0.7076 0.5571 0.2853 2.090 1.115 8.384 0.380341.88 0.6014 0.0176 0.7388 0.1179 1.050 18.443 1.257 0.168341.96 0.6750 0.0102 0.8204 0.0581 1.036 15.649 1.287 0.131

343.82 0.1828 0.7895 0.5836 0.3144 2.542 1.025 11.308 0.257344.59 0.1760 0.8110 0.6137 0.3268 2.699 1.011 13.606 0.217345.82 0.1505 0.8354 0.5962 0.3461 2.933 0.997 11.554 0.194347.69 0.1281 0.8636 0.5751 0.3771 3.108 0.987 15.047 0.156

TAEE (2) + ethanol (1) + water (3)347.03 0.4307 0.2687 0.4074 0.3031 1.124 2.602 2.588 0.593347.11 0.4483 0.2363 0.4143 0.2984 1.095 2.905 2.440 0.574347.16 0.3966 0.3383 0.4105 0.3059 1.224 2.077 2.859 0.606347.17 0.4663 0.2057 0.4250 0.2910 1.077 3.248 2.313 0.552347.18 0.4777 0.2485 0.4364 0.2908 1.079 2.686 2.661 0.550

347.18 0.3700 0.3872 0.4033 0.3122 1.288 1.851 3.129 0.609347.19 0.4428 0.1625 0.4115 0.2943 1.098 4.155 1.990 0.544347.25 0.4582 0.1672 0.4190 0.2906 1.077 3.979 2.064 0.536347.27 0.4933 0.2521 0.4508 0.2871 1.076 2.606 2.739 0.534347.30 0.4852 0.1741 0.4369 0.2817 1.059 3.699 2.195 0.523

347.31 0.5014 0.1881 0.4515 0.2770 1.058 3.365 2.323 0.518347.39 0.4984 0.1649 0.4472 0.2754 1.051 3.806 2.181 0.508347.43 0.4300 0.1048 0.4188 0.2837 1.139 6.161 1.691 0.491

14 A. Arce et al. / Fluid Phase Equilibria 233 (2005) 9–18

Table 3 (Continued)

T (K) x1 x2 y1 y2 γ1 γ2 γ3 GE/RT

347.43 0.4508 0.3369 0.4602 0.2952 1.194 1.995 3.045 0.549347.45 0.4341 0.3625 0.4550 0.2997 1.225 1.881 3.184 0.553

347.47 0.4108 0.3983 0.4459 0.3063 1.268 1.748 3.425 0.555347.48 0.5534 0.2213 0.4964 0.2683 1.047 2.756 2.755 0.478347.49 0.4652 0.1187 0.4371 0.2730 1.097 5.224 1.837 0.492347.55 0.4950 0.1261 0.4528 0.2646 1.065 4.757 1.962 0.483347.57 0.3874 0.4414 0.4411 0.3135 1.325 1.609 3.766 0.546

347.58 0.4707 0.1099 0.4408 0.2695 1.089 5.553 1.815 0.479347.59 0.5765 0.2297 0.5218 0.2639 1.052 2.602 2.904 0.455347.65 0.5344 0.1318 0.4787 0.2531 1.039 4.339 2.105 0.462347.72 0.3882 0.0606 0.4157 0.2769 1.238 10.298 1.457 0.432347.72 0.5992 0.1948 0.5385 0.2500 1.039 2.894 2.682 0.433

347.81 0.3765 0.0514 0.4149 0.2763 1.270 12.079 1.405 0.413347.81 0.3268 0.5249 0.4231 0.3266 1.492 1.399 4.391 0.526347.84 0.5618 0.1226 0.4989 0.2405 1.022 4.405 2.147 0.435347.86 0.6277 0.2015 0.5652 0.2462 1.035 2.743 2.868 0.405347.90 0.4867 0.3691 0.5186 0.2936 1.223 1.784 3.375 0.487

348.00 0.6060 0.1218 0.5392 0.2234 1.017 4.098 2.253 0.403348.06 0.5301 0.3401 0.5524 0.2846 1.189 1.867 3.233 0.456348.09 0.6700 0.1777 0.6051 0.2290 1.029 2.872 2.803 0.364348.11 0.4342 0.4430 0.5064 0.3102 1.328 1.559 3.837 0.485348.13 0.5450 0.3291 0.5640 0.2813 1.177 1.903 3.155 0.445

348.17 0.6437 0.1186 0.5745 0.2096 1.014 3.927 2.330 0.372348.35 0.3830 0.0391 0.4402 0.2507 1.297 14.152 1.362 0.382348.38 0.6138 0.2822 0.6199 0.2617 1.138 2.048 2.893 0.392348.39 0.3986 0.4918 0.5002 0.3217 1.413 1.443 4.127 0.474348.41 0.7173 0.1686 0.6550 0.2156 1.027 2.821 2.880 0.315

348.42 0.7163 0.1808 0.6603 0.2200 1.037 2.683 2.953 0.316348.43 0.7172 0.1508 0.6483 0.2079 1.016 3.039 2.764 0.313348.44 0.7106 0.1239 0.6357 0.1961 1.005 3.487 2.578 0.315348.54 0.4898 0.4141 0.5661 0.3024 1.294 1.604 3.454 0.441348.60 0.3687 0.0308 0.4414 0.2470 1.338 17.554 1.308 0.357

348.63 0.7477 0.1332 0.6805 0.1916 1.015 3.150 2.703 0.282348.64 0.6511 0.2708 0.6611 0.2547 1.132 2.060 2.711 0.354348.69 0.6124 0.3153 0.6461 0.2707 1.174 1.877 2.887 0.373348.71 0.6997 0.2209 0.6856 0.2326 1.089 2.301 2.584 0.319348.78 0.6200 0.0666 0.5752 0.1785 1.029 5.835 1.967 0.347

348.81 0.4468 0.4660 0.5584 0.3151 1.385 1.472 3.621 0.438348.84 0.5179 0.4065 0.6032 0.2987 1.289 1.598 3.235 0.411348.84 0.5618 0.3700 0.6305 0.2883 1.242 1.695 2.969 0.391348.88 0.5428 0.0539 0.5335 0.1907 1.086 7.675 1.705 0.370348.89 0.4676 0.0373 0.4879 0.2110 1.152 12.265 1.515 0.365

348.92 0.5926 0.0577 0.5632 0.1766 1.048 6.632 1.852 0.352348.93 0.4047 0.0337 0.4690 0.2221 1.278 14.270 1.368 0.365348.93 0.3654 0.5480 0.5078 0.3340 1.533 1.321 4.538 0.440349.05 0.5673 0.0501 0.5542 0.1745 1.072 7.514 1.756 0.356349.09 0.4761 0.0349 0.5055 0.1990 1.164 12.283 1.493 0.356

349.11 0.6304 0.0539 0.5951 0.1587 1.034 6.341 1.926 0.327349.17 0.8280 0.1346 0.7770 0.1790 1.025 2.863 2.897 0.202349.24 0.7167 0.0583 0.6647 0.1377 1.010 5.067 2.158 0.275349.24 0.2346 0.6739 0.4139 0.3632 1.923 1.156 5.976 0.415349.26 0.5548 0.0438 0.5548 0.1700 1.089 8.315 1.683 0.349

349.28 0.4813 0.4627 0.6099 0.3150 1.378 1.460 3.284 0.396349.35 0.3466 0.5766 0.5153 0.3423 1.613 1.269 4.528 0.419349.37 0.2986 0.6224 0.4742 0.3530 1.722 1.212 5.337 0.414349.38 0.6813 0.0478 0.6419 0.1341 1.021 5.989 2.020 0.290349.51 0.8654 0.0951 0.8118 0.1443 1.011 3.231 2.700 0.993

A. Arce et al. / Fluid Phase Equilibria 233 (2005) 9–18 15

Table 3 (Continued)

T (K) x1 x2 y1 y2 γ1 γ2 γ3 GE/RT

349.52 0.6386 0.0417 0.6199 0.1343 1.046 6.843 1.868 0.309349.52 0.3392 0.5881 0.5156 0.3469 1.638 1.254 4.586 0.411349.63 0.7284 0.0433 0.6919 0.1141 1.019 5.581 2.055 0.253349.66 0.8046 0.0519 0.7523 0.1091 1.002 4.450 2.333 0.201349.66 0.4347 0.5136 0.5987 0.3301 1.476 1.361 3.320 1.200

349.76 0.8859 0.0744 0.8343 0.1223 1.005 3.471 2.629 0.135349.77 0.3287 0.6050 0.5227 0.3516 1.697 1.226 4.551 0.398349.94 0.8123 0.0386 0.7601 0.0943 0.992 5.125 2.333 0.183350.09 0.8090 0.0341 0.7716 0.0803 1.005 4.915 2.241 0.185350.14 0.8511 0.0327 0.8134 0.0720 1.005 4.590 2.337 0.849

350.18 0.8757 0.0462 0.8479 0.0758 1.017 3.417 2.311 0.137350.56 0.8924 0.0283 0.8799 0.0438 1.020 3.184 2.242 0.114350.57 0.2574 0.6831 0.4871 0.3768 1.959 1.133 5.315 0.358350.77 0.9004 0.0191 0.8720 0.0437 0.994 4.674 2.420 0.095351.21 0.9553 0.0052 0.9467 0.0113 1.000 4.379 2.415 0.882

351.81 0.2267 0.7317 0.4956 0.4027 2.157 1.087 5.404 0.305353.08 0.1809 0.7796 0.4764 0.4314 2.476 1.049 4.905 0.264354.82 0.1392 0.8238 0.4559 0.4673 2.885 1.017 4.072 0.213355.37 0.1424 0.8348 0.4575 0.4830 2.772 1.020 5.010 0.198355.66 0.1347 0.8395 0.4502 0.4876 2.853 1.015 4.576 1.521

356.75 0.1077 0.8583 0.4361 0.5094 3.320 1.002 2.916 0.167357.91 0.0838 0.8759 0.4199 0.5341 3.937 0.993 1.986 0.136360.00 0.0474 0.9214 0.3128 0.5944 4.808 0.985 4.778 0.109372.40 0.0022 0.9889 0.0547 0.9384 11.815 1.010 0.792 0.013

Table 4Antoine coefficientsA, B, andC for Eq.(2)

Compound A B C

Water 7.07405 1657.459 −46.130[22]Methanol 7.20519 1581.993 −33.439[15]Ethanol 7.23710 1592.864 −46.966[6]TAEE 5.92454 1216.99 −64.119[6]

all equilibrium points, for each system. In the modifiedMcDermott–Ellis test, the conditionDi < Dmax is satisfiedfor all data of both systems. Therefore, the thermodynamicconsistency of the ternary VLE data reported in this work isconfirmed.

The correlation of the experimental (P, T, x, y) results isperformed with a computer program that runs a non-linearregression method based on the maximum likelihood prin-ciple. The models used to calculate the liquid-phase activity

coefficients are Wilson’s equation, the NRTL equation,setting the non-randomness parameter,α, to different valuesand selecting the value giving the best correlation, and theUNIQUAC equation using the structural parametersr andqtaken from Daubert and Danner[23] and with the parameterq′ set to 1.00 for water and to 0.96 and 0.92 for methanol andethanol, respectively, taken from Anderson and Prausnitz[24]. The values of the binary interaction parameters are sum-marised inTables 5 and 6for the binary and ternary systems,respectively, along with the corresponding mean standard de-viations (σ) in temperature, liquid- and vapor-phase compo-sitions, and in pressure.Fig. 2compares the UNIQUAC, andthe NRTL (α = 0.1) temperature–composition curves with theexperimental results for the systems methanol + TAEE andethanol + TAEE, respectively.Fig. 3 shows the comparisonof the calculated values using the UNIQUAC equation withthe experimental VLE data for the ternary systems.

Table 5Correlation of VLE data of the indicated binary systems: model parameters (Wilson, NRTL and UNIQUAC) and root mean deviations (σ) in equilibriumtemperature (T), liquid- and vapor-phase compositions (x, y) and pressure (P)

Model Parameters (J mol−1) σ(T) (K) σ(x) σ(y) σ(P) (kPa)

Methanol (1) + TAEE (2)Wilson �λ12 = 1615.1,�λ21 = 4357.5 0.26 0.0037 0.0076 0.16NRTL (α = 0.3) �g12 = 4059.8,�g21 = 1190.0 0.27 0.0039 0.0073 0.16UNIQUAC �u12 =−656.48,�u21 = 6587.1 0

Ethanol (1) + TAEE (2)Wilson �λ12 = 4610.4,�λ21 = 438.61 0NRTL (α = 0.1) �g12 = 5071.3,�g21 =−713.11 0UNIQUAC �u12 =−1541.4, 2�u21 = 6727.4 0

.25 0.0035 0.0076 0.15

.24 0.0041 0.0085 0.16

.22 0.0041 0.0075 0.14

.25 0.004 0.0084 0.16

16 A. Arce et al. / Fluid Phase Equilibria 233 (2005) 9–18

Table 6Correlation of VLE data of the indicated ternary systems: model parameters (Wilson, NRTL and UNIQUAC) and root mean deviations in equilibrium temperature(T), liquid- and vapor-phase compositions (xi , yi ) and pressure (P)

Model Parameters (J mol−1) σ(T) (K) σ(x1) σ(x2) σ(y1) σ(y2) σ(P) (kPa)

TAEE (2) + methanol (1) + water (3)Wilson �λ12 = 2400.0,�λ13 =−5029.3,�λ23 = 24911,

�λ21 = 3651.92,�λ31 = 7702.8,�λ32 = 9187.80.16 0.0024 0.0052 0.0448 0.0415 1.52

NRTL 0.2 �g12 = 5117.6,�g13 =−550.71,�g23 = 7319.7,�g21 = 220.13,�g31 = 2437.8,�g32 = 38410

0.17 0.0036 0.0037 0.0028 0.0046 0.01

UNIQUAC �u12 =−680.29,�u13 = 856.43,�u23 = 8592.5,�u21 = 6994.7,�u31 =−631.57,�u32 = 817.86

0.08 0.0021 0.0014 0.0026 0.0021 0.18

TAEE (2) + ethanol (1) + water (3)Wilson �λ12 = 5374.3,�λ13 = 6065.1,�λ23 = 24984,

�λ21 =−357.18,�λ31 = 4183.5,�λ32 = 109400.02 0.0005 0.0004 0.0407 0.0499 1.9

NRTL 0.2 �g12 = 2563.0,�g13 =−1014.1,�g23 = 2388.6,�g21 = 1946.5,�g31 = 5432.7,�g32 = 20991

0.17 0.0063 0.0043 0.0038 0.0043 0.01

UNIQUAC �u12 =−1447.1,�u13 =−465.96,�u23 = 7375.8,�u21 = 7666.9,�u31 = 2695.6,�u32 = 613.47

0.17 0.006 0.0037 0.0035 0.0039 0.01

Fig. 3. Experimental VLE data at 101.32 kPa (→), and corresponding UNIQUAC correlation (�) for the ternary systems: (a) TAEE + methanol + water and(b) TAEE + ethanol + water. Symbol (♦) indicates binary azeotrope.

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

A. Arce et al. / Fluid Phase Equilibria 233 (2005) 9–18 17

Fig. 5. (a) Experimental VLE data at 101.32 kPa of the system TAEE + methanol + water (→), and the data predicted using the UNIFAC method (). (b)Experimental VLE data at 101.32 kPa of the system TAEE + ethanol + water (→), and the data predicted using the UNIFAC-Dortmund method (). Symbol(♦) indicates binary azeotrope.

VLE data for the ternary and binary systems are pre-dicted using the following group-contribution methodsto calculate the liquid-phase activity coefficients: theASOG-KT method, the original UNIFAC method, withthe structural and group-interaction parameters recom-mended by Gmehling et al.[25], the UNIFAC-Dortmundmethod, and the UNIFAC-Lyngby method.Table 7lists theroot mean standard deviations between the experimentalVLE data for binary systems and those predicted.Fig. 4

Table 7Root mean square deviations (σ) between the experimental equilibrium tem-peratures (T) and vapor-phase compositions (y) and those calculated by theASOG, UNIFAC, and modified UNIFAC methods for the indicated binarysystems

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

σ(T) (K) σ(y1) σ(T) (K) σ(y1)

ASOG 3.22 0.0496 2.24 0.0351UNIFAC 1.21 0.0140 0.75 0.0109UNIFAC-Dortmund 1.13 0.0144 0.25 0.0153UNIFAC-Lyngby 1.88 0.0197 0.75 0.0107

Table 8Root mean square deviations (σ) between the experimental equilibrium tem-peratures (T) and vapor phase compositions (yi ) for the Indicated ternary sys-tems and those calculated by the ASOG, UNIFAC, and modified UNIFACm

M

T0799535

T359

compares the experimental VLE compositions of thebinaries methanol + TAEE and ethanol + TAEE, with theprediction of the UNIFAC-Dortmund model.Table 8 liststhe root mean standard deviations between the experimentalVLE data and those predicted for the ternary systems.Fig. 5 compares the experimental VLE data for the systemTAEE + methanol + water with the prediction of the UNIFACmodel and for the system TAEE + ethanol + water with theprediction of the UNIFAC-Dortmund model.

4. Conclusions

Experimental VLE data are determined for the binary sys-tems methanol + TAEE and ethanol + TAEE at the constantpressure of 101.32 kPa. At the same pressure, experimen-tal isobaric VLE data are determined for the ternary sys-tems TAEE + methanol + water and TAEE + ethanol + water.Thermodynamical consistency of the experimental VLE datareported in this work has been checked out by means ofdifferent tests, the point-to-point Fredeslund’s consistencytest and the Wisniak’sL–W test for the binary systems,and the Wisniak–LW and Wisniak–Tamir’s modification ofMcDermott–Ellis tests for the ternary systems.

Both binary systems form a minimum boiling pointazeotrope, the binary methanol + TAEE at 336.47 K to a com-p ande tiono t withvc ater,t urvew sys-t narya

or-

ethods

ethods σ(T) (K) σ(y1) σ(y2) σ(y3)

AEE (1) + methanol (2) + water (3)ASOG 1.85 0.0437 0.0376 0.02UNIFAC 1.94 0.0439 0.0468 0.032UNIFAC-Dortmund 2.47 0.0353 0.0143 0.02UNIFAC-Lyngby 2.71 0.0546 0.0611 0.05

AEE (1) + ethanol (2) + water (3)ASOG 0.40 0.0346 0.0156 0.02UNIFAC 0.35 0.0197 0.0111 0.016

UNIFAC-Dortmund 1.77 0.0501 0.0515 0.0264UNIFAC-Lyngby 2.25 0.0494 0.0525 0.0160

r sultst . For

osition near to 0.87, in molar fraction of methanolthanol + TAEE at 349.20 K near to 0.76, in molar fracf ethanol. These last values are in excellent agreemenalues found in the bibliography[26]. Arrowheads inFig. 3b,orresponding to the ternary system TAEE + ethanol + wend to close in on a single point near the binodal chich is a ternary azeotrope. However, for the ternary

em TAEE + methanol + water arrowheads tend to the bizeotrope as can be seen inFig. 3a.

The Wilson, NRTL, and UNIQUAC equations used to celate experimental VLE data of these systems turn in rehat are in good agreement with the experimental results

18 A. Arce et al. / Fluid Phase Equilibria 233 (2005) 9–18

the binary system ethanol + TAEE the NRTL equation, withα set to 0.1, gives the slightly better results whereas the UNI-QUAC equation gives the smallest deviations for the binarysystem methanol + TAEE and for the two ternary systems.

The group-contributions methods used for the predictionof the VLE of these systems do not show a good agree-ment with the experimental results. The UNIFAC-Dortmundmodel gives the best predictions for binary and ternary sys-tems, however deviations from experimental results are stillhigh.

List of symbolsA, B, C Antoine coefficients (Eq.(2))�g NRTL binary interaction parameternD refractive indexP pressureq UNIQUAC area parameterr UNIQUAC volume parameterT temperature�u UNIQUAC binary interaction parameterV molar volumex mole fraction in the liquid phasey mole fraction in the vapor phase

Greek lettersα NRTL non-randomness parameterγ

�

ρ

φ

Si1

SLs

A

Tec-n 03-0

References

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[ 45

[ 46

[ g.

[ r-

[ ev. 14

[ s and

[ oper-ressNew

[ . Dev.

[ . Pro-

[ uilib.

activity coefficientλ Wilson binary interaction parameter

densityfugacity coefficient

ubscriptsi th component

, 2, 3 components 1, 2, 3

uperscriptsliquidsaturation

cknowledgement

The authors are grateful to the Ministerio de Ciencia yologıa (Spain) for financial support under project PPQ201236.

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