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Fluid Phase Equilibria 255 (2007) 17–23

Isobaric vapor–liquid equilibria for the quaternary reactive system:Ethanol + water + ethyl lactate + lactic acid at 101.33 kPa

Patricia Delgado, Marıa Teresa Sanz ∗, Sagrario BeltranDepartment of Chemical Engineering, University of Burgos, 09001 Burgos, Spain

Received 5 January 2007; received in revised form 20 March 2007; accepted 22 March 2007Available online 27 March 2007

bstract

Isobaric vapor–liquid equilibrium (VLE) data of the reactive quaternary system ethanol (1) + water (2) + ethyl lactate (3) + lactic acid (4) haveeen determined experimentally. Additionally, the reaction equilibrium constant was calculated for each VLE experimental data. The experimentalLE data were correlated using the UNIQUAC equation to describe the chemical and phase equilibria simultaneously. For some of the non-reactive

inary systems, UNIQUAC binary interaction parameters were obtained from the literature. The rest of the binary UNIQUAC parameters werebtained by correlating the experimental quaternary VLE data obtained in this work. A maximum pressure azeotrope at high water concentrationor the binary reactive system ethyl lactate + water has been calculated.

2007 Elsevier B.V. All rights reserved.

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eywords: Vapor–liquid equilibria; Chemical equilibrium; Esterification; Lacti

. Introduction

Lactic acid esters are used as powerful high-boiling sol-ents. Ethyl lactate particularly is used as food and perfumerydditive, flavor chemical and solvent [1]. Methyl, ethyl, iso-ropyl and n-butyl lactates are usually produced by conventionalsterification of lactic acid with the corresponding alcohol.sterification reactions are equilibrium-limited reactions andsually do not reach completion. Higher conversion can bebtained by shifting chemical equilibrium towards products for-ation by hybrid processes such as reactive distillation and

ervaporation aided-reactors. By removing directly the prod-cts from the reactive section of the reactive distillation column,igher conversions can be obtained. Additionally, the integra-ion of a pervaporation unit into conventional esterificationrocesses is also attractive because pervaporation is based onhe differences in solubility’s and transport rates in a dense

embrane.

The design of such hybrid processes requires the knowledge

f phase equilibrium as well as of reaction kinetics. During theast years different studies on thermodynamic properties involv-

∗ Corresponding author. Tel.: +34 947 258810; fax: +34 947 258831.E-mail address: tersanz@ubu.es (M.T. Sanz).

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378-3812/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.fluid.2007.03.022

; Ethyl lactate

ng lactic acid and its derivatives have been carried out in ourork group. In a previous paper, VLE behavior for the quater-ary reactive mixture methanol + water + methyl lactate + lacticcid was studied [2]. In this work, VLE measurements for theuaternary system involved in the esterification of lactic acidith ethanol at 101.33 kPa are presented:

CH3CHOHCOOH + CH3CH2OH

� CH3CHOHCOOCH2CH3 + H2O

A previous kinetic study for the esterification of lactic acidith ethanol has already been performed in detail [3].Quaternary experimental VLE data with simultaneous chem-

cal equilibrium have been reported in the literature for differentsterification systems. Hirata and Komatsu [4,5] studied the VLEf the systems involved in the esterification of acetic acid withutanol [4] and with ethanol [5] in a modified Othmer still. Theyeported the ratio of VLE composition establishing different cor-elations with temperature and composition. Lee and Kuo [6]resented VLE data for the esterification of acetic acid with iso-ropanol obtained in an Othmer type equilibrium cell. Similar

rocedure was followed by Kang et al. [7], Lee and Lin [8] andee and Liang [9] to determine the phase and reaction equilibriaf the esterification of acetic acid with ethanol [7], isoamyl alco-ol [8] and 1-pentanol [9], respectively. Recently, Teodorescu et

1 ase Eq

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2

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p

φ

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c

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i

K

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8 P. Delgado et al. / Fluid Ph

l. [10] and Bernatova et al. [11] investigated the VLE behaviorn a modified Dvorak and Boublık still for the esterification ofcetic with 2-propanol [10] and methanol [11], respectively. Inll cases, activity coefficient models were used to correlate theLE data of the quaternary reactive systems proving that the

xperimental chemical equilibrium data could be also satisfac-orily predicted using conventional activity coefficient modelsith parameters calculated from vapor–liquid equilibrium data

12].In this work, the experimental data were correlated by using

he UNIQUAC equation to satisfy the phase as well as the chemi-al equilibrium of the mixture. The fitting procedure was similaro the one proposed by Teodorescu et al. [10] and Bernatova etl. [11]. For some of the non-reactive binary systems, interac-ion parameters were obtained from the literature and fixed inhe fitting procedure. The rest of the UNIQUAC binary inter-ction parameters were obtained from the correlation of thexperimental VLE data of the quaternary system obtained inhis work.

. Thermodynamics of VLE with chemical reaction

Carvoli and Delogu [13] considered two different ways totudy phase equilibrium of reacting systems: according to therst one, chemical and phase equilibrium must be reached simul-

aneously; in the second one, experimental conditions allowhase equilibrium to be reached in shorter time than chemi-al equilibrium. The second approach can be assumed for sloweaction systems.

The general equation for VLE equilibrium at constant lowressure, p, and temperature, T, of a given mixture is given by,

iyip = γixipsati φsat

i (1)

here γ i is the activity coefficient of component i, φi its fugacityoefficient and xi and yi the composition of the liquid and vaporhases respectively. φsat

i is the fugacity coefficient of pure satu-ated vapor i at temperature T and the corresponding saturationressure psat

i .When a reaction takes place in the liquid phase, an additional

onstraint for the chemical potential, μi has to be included,

c

i=1

νiμi = 0 (2)

here c is the number of components, μi the chemical poten-ial of component i and νi is the stoichiometric coefficient ofomponent i in the reaction.

The thermodynamic equilibrium constant, Keq is expressedn terms of the standard Gibbs energy change of reaction as:

(−�G0 )

eq = exp

RT(3)

This equilibrium constant is also expressed as a function ofhe mole fraction (xi) and the activity coefficients (γ i) of products

amii

uilibria 255 (2007) 17–23

nd reactants by Eq. (4):

eq = KxKγ =c∏

i=1

(xi)νi

c∏i=1

(γi)νi (4)

. Experimental

.1. Materials

Ethyl lactate was supplied by Aldrich with a reported purityf 99 wt%. It was purified by vacuum distillation, obtaining anal purity of 99.9%, as determined by gas chromatographyGC). Ethanol of 99.9 wt% purity was purchased from Lab-Scan.

ater was nanopure. An aqueous lactic acid solution (20 wt%)as supplied by Acros. The amount of polymerized lactic acidas considered negligible after being determined by back titra-

ion. As an additional purity check, some physical properties ofhe pure components were measured and compared with valueseported in the literature. Results were presented in a previousublication [14].

.2. Sample analysis

The samples were analyzed using a Hewlett Packard (6890)as chromatograph (GC) equipped with series connected ther-al conductivity (TCD) and flame ionization (FID) detectors.elium, 99.999% pure, was used as carrier gas. The GC columnas a 30 m × 0.25 mm bonded phase fused silica capillary col-mn. The injector and detectors were at 523.15 and 533.15 K,espectively. The oven was operated at programmed tempera-ure, from 363 to 473 K. 1,2-Propanediol was used as internaltandard for analysis of the quaternary samples [15]. Quantita-ive analysis of monomer lactic acid was carried out by titrationsing phenolphthalein as indicator. Experimental concentrationncertainties were ±0.0005.

.3. Apparatus and procedure

VLE for the reactive quaternary system subject of this workas determined in an all-glass still of the Gillespie type with

irculation of both the liquid and vapor phases. A detailedescription of the apparatus has been previously reported [16].he still was operated under a nitrogen atmosphere. The totalressure of the system was monitored with a digital manometernd controlled to the desired value (±0.09 kPa) by means of aressure controller (Normastat 75). Temperature (±0.05 K) waseasured with a digital thermometer (Ertco-Hart, Model 850).A kinetic study of the esterification reaction of lactic acid

ith ethanol is necessary to establish how the phase andhemical equilibria affect each other. As it was mentioned inection 1, such study has already been performed in detail [3].n that work, some experiments were carried out without the

ddition of external catalyst. Fig. 1 shows the experimentalole fraction of ethyl lactate at different reaction times obtained

n the esterification of lactic acid with ethanol (T = 338.15 K,nitial molar reactant ratio REtOH/HL = 3) without adding any

P. Delgado et al. / Fluid Phase Equilibria 255 (2007) 17–23 19

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Table 1Experimental VLE data corresponding to chemical equilibrium for the qua-ternary system ethanol (1) + water (2) + ethyl lactate (3) + lactic acid (4) at101.33 kPa: liquid phase mole fraction xi, vapor phase mole fraction yi, tem-perature T and equilibrium reaction constant Keq

T (K) x1 x2 x3 y1 y2 y3 Keq

356.27 0.2622 0.7004 0.0161 0.5160 0.4815 0.0024 1.8627357.07 0.2643 0.6914 0.0210 0.5285 0.4681 0.0033 1.6150357.49 0.1956 0.7646 0.0180 0.4921 0.5041 0.0037 2.2598357.92 0.1971 0.7687 0.0155 0.7038 0.2921 0.0041 1.4724358.04 0.1942 0.7648 0.0189 0.5449 0.4505 0.0045 2.4107358.18 0.2017 0.7656 0.0160 0.5699 0.4253 0.0047 1.6720358.44 0.1541 0.8142 0.0136 0.5603 0.4357 0.0039 2.1438358.55 0.1533 0.8057 0.0168 0.6962 0.2969 0.0068 1.3454359.12 0.1581 0.8031 0.0152 0.5329 0.4624 0.0046 3.1960359.19 0.1560 0.7985 0.0181 0.4423 0.5525 0.0051 3.0813359.51 0.1248 0.8389 0.0136 0.4129 0.5829 0.0041 4.7481359.92 0.1597 0.7958 0.0167 0.4703 0.5250 0.0046 4.8014360.01 0.1155 0.8360 0.0164 0.5351 0.4587 0.0061 2.5895360.32 0.1193 0.8323 0.0147 0.4078 0.5873 0.0048 2.9171360.72 0.1072 0.8367 0.0163 0.4739 0.5196 0.0064 2.2505360.76 0.1037 0.8535 0.0131 0.5528 0.4408 0.0063 2.4631360.85 0.1361 0.7984 0.0200 0.4372 0.5556 0.0070 2.1911361.06 0.1066 0.8428 0.0143 0.4890 0.5048 0.0060 2.0376361.20 0.1309 0.8004 0.0186 0.7482 0.2434 0.0083 1.8297361.23 0.1069 0.8520 0.0134 0.4458 0.5482 0.0058 2.1266361.33 0.1197 0.8255 0.0155 0.5384 0.4531 0.0084 3.0229361.35 0.1205 0.8273 0.0174 0.3672 0.6253 0.0072 2.3110361.54 0.1237 0.8184 0.0190 0.4554 0.5377 0.0067 2.4139361.62 0.1182 0.8263 0.0159 0.4427 0.5492 0.0079 2.0240361.70 0.1067 0.8370 0.0171 0.4551 0.5376 0.0072 2.7250361.79 0.0795 0.8787 0.0121 0.3141 0.6805 0.0051 2.1879361.98 0.0881 0.8551 0.0155 0.3770 0.6156 0.0072 2.5711362.13 0.0911 0.8504 0.0151 0.3700 0.6226 0.0072 2.7446362.18 0.0863 0.8673 0.0120 0.4853 0.5070 0.0075 2.1878362.19 0.0928 0.8471 0.0160 0.3722 0.6207 0.0069 3.3287362.20 0.0756 0.8780 0.0116 0.4004 0.5932 0.0062 2.1114362.48 0.0903 0.8498 0.0156 0.3429 0.6503 0.0066 2.5006362.66 0.1006 0.8298 0.0232 0.3796 0.6111 0.0090 2.5693362.83 0.0954 0.8574 0.0140 0.7079 0.2837 0.0083 1.5579362.87 0.2923 0.4596 0.1453 0.7761 0.1967 0.0270 1.4601362.96 0.0917 0.8481 0.0147 0.3454 0.6472 0.0072 2.6470363.02 0.1411 0.7380 0.0452 0.3439 0.6444 0.0115 5.8912363.22 0.1120 0.7965 0.0285 0.3597 0.6297 0.0103 3.2127363.31 0.2851 0.4676 0.1429 0.5612 0.4160 0.0224 2.0407363.43 0.0739 0.8637 0.0138 0.3003 0.6928 0.0068 4.2311363.50 0.0739 0.8651 0.0141 0.3581 0.6345 0.0071 2.5375363.67 0.1364 0.7243 0.0547 0.4292 0.5544 0.0161 3.0356363.70 0.2339 0.5219 0.1380 0.3871 0.5928 0.0198 4.4559363.74 0.1159 0.7728 0.0349 0.2751 0.7143 0.0104 5.8547363.91 0.0797 0.8488 0.0181 0.3045 0.6868 0.0084 3.7689363.95 0.0705 0.8674 0.0132 0.2820 0.7112 0.0066 3.9534364.00 0.2424 0.4868 0.1472 0.4788 0.4976 0.0231 2.5093364.09 0.1497 0.6823 0.0678 0.3353 0.6493 0.0149 3.4909364.10 0.0848 0.8334 0.0215 0.3610 0.6287 0.0101 4.1820364.14 0.2491 0.4917 0.1381 0.6496 0.3222 0.0278 1.9399364.33 0.2369 0.5173 0.1313 0.4037 0.5760 0.0200 4.4622364.45 0.0749 0.8440 0.0215 0.3781 0.6103 0.0114 4.7655364.53 0.0615 0.8746 0.0119 0.2838 0.7090 0.0070 3.7100364.57 0.1358 0.6852 0.0723 0.3406 0.6418 0.0172 4.0611364.58 0.2317 0.4992 0.1380 0.4795 0.4949 0.0250 2.2745364.72 0.0882 0.8060 0.0283 0.2459 0.7443 0.0095 4.2227

ig. 1. Ethyl lactate mole fraction versus time for the auto-catalyzed esterifica-ion reaction of lactic acid with ethanol at 338.15 K, initial molar reactant ratio

EtOH/HL = 3 (� experimental data, — autocatalytic kinetic model [3]).

xternal catalyst. It can be observed that the reaction rate is notegligible, even without the addition of external catalyst.

The VLE data for the reactive quaternary mixture have beenbtained by using the Gillespie type still previously describedhere chemical and phase equilibria are expected to be reached.

n order to avoid long operation times till chemical and phasequilibrium were reached, the still was filled with quaternaryixtures with a composition close to the chemical equilibrium.

n addition, mixtures were kept in the still more than 4 h onceemperature remains constant to ensure chemical and phase equi-ibrium. Subsequently, samples of liquid and condensed vaporere withdrawn for analysis. Some authors [6–11] add a hetero-eneous catalyst to the system in order to shorten the operatingime.

. Results and discussion

In this work, 115 experiments were carried out to determinehe VLE behavior corresponding to chemical equilibrium at01.33 kPa for this reactive quaternary mixture. The pressure,emperature and vapor and liquid composition were determinedxperimentally and are listed in Table 1. The concentration rangef high monomer lactic acid concentration was not studied inrder to avoid its polymerization.

The vapor phase fugacity coefficients have been calculatedsing the virial equation of state truncated after the second termnd the second virial coefficients were obtained from the Hay-en and O’Connell [17] correlation. Because of the low vaporressure of lactic acid, it was not necessary to use the “chemi-al” theory as was proved for the system water + lactic acid [2].ctivity coefficients were calculated from Eq. (1) by using the

xperimental VLE data from the quaternary system taking intoccount the non-ideality of the vapor phase. The vapor pressuref the pure components used in the vapor–liquid equilibriumalculations were obtained through the Antoine equation. Ai, Bi

nd Ci Antoine coefficients are given in Table 2 together withhe van der Waals properties, ri and qi.

According to Eq. (4), the equilibrium constant has been cal-ulated for each experimental data. Similar to other esterification

364.91 0.0550 0.8801 0.0112 0.2231 0.7707 0.0060 4.8151364.92 0.0895 0.8003 0.0326 0.2889 0.6985 0.0122 4.6689364.95 0.0553 0.8853 0.0114 0.2725 0.7201 0.0073 5.3519365.05 0.1986 0.5449 0.1287 0.4154 0.5619 0.0223 3.8292365.08 0.1489 0.6466 0.0850 0.3562 0.6238 0.0196 4.6032

20 P. Delgado et al. / Fluid Phase Equilibria 255 (2007) 17–23

Table 1 (Continued )

T (K) x1 x2 x3 y1 y2 y3 Keq

365.08 0.0553 0.8791 0.0110 0.2999 0.6921 0.0077 3.2282365.13 0.1160 0.7631 0.0417 0.3094 0.6783 0.0120 4.8424365.18 0.0853 0.7995 0.0344 0.2735 0.7146 0.0116 5.5521365.19 0.0521 0.8816 0.0103 0.2821 0.7102 0.0075 3.8682365.43 0.0532 0.8809 0.0105 0.3037 0.6884 0.0077 3.4710365.62 0.0837 0.7909 0.0387 0.2786 0.7073 0.0137 4.5285365.62 0.1484 0.6320 0.0953 0.2980 0.6820 0.0193 3.6764365.67 0.1935 0.5423 0.1344 0.4414 0.5316 0.0262 2.2175365.91 0.0987 0.7467 0.0521 0.2935 0.6899 0.0161 3.8474365.92 0.1013 0.7397 0.0521 0.2906 0.6934 0.0156 5.2200366.17 0.0455 0.8915 0.0092 0.2432 0.7497 0.0068 3.8997366.23 0.1659 0.5824 0.1213 0.3865 0.5878 0.0252 4.4764366.24 0.1038 0.7360 0.0584 0.2864 0.6970 0.0163 5.9182366.39 0.0952 0.7373 0.0571 0.2466 0.7372 0.0157 4.7338366.42 0.1387 0.6297 0.1041 0.3021 0.6754 0.0219 4.0730366.77 0.1157 0.6972 0.0705 0.2479 0.7341 0.0175 5.6465366.78 0.0388 0.9019 0.0081 0.2406 0.7529 0.0062 2.9516366.94 0.1645 0.5622 0.1277 0.3375 0.6376 0.0242 3.4282366.98 0.1052 0.6989 0.0699 0.2665 0.7149 0.0180 4.0890367.02 0.1456 0.5815 0.1224 0.3124 0.6623 0.0247 4.7324367.20 0.1134 0.6822 0.0770 0.2457 0.7348 0.0190 6.1031367.36 0.0974 0.7032 0.0746 0.2300 0.7511 0.0184 5.9360367.52 0.1501 0.5933 0.1178 0.3272 0.6475 0.0245 3.2474367.71 0.1082 0.6862 0.0826 0.3556 0.6177 0.0260 3.4521367.77 0.1376 0.5668 0.1332 0.3111 0.6607 0.0275 4.7025368.02 0.1356 0.6036 0.1151 0.2993 0.6755 0.0245 4.0901368.20 0.1172 0.6386 0.0985 0.3495 0.6240 0.0258 3.7611368.34 0.1908 0.4584 0.1807 0.3318 0.6375 0.0299 3.5898368.47 0.1247 0.6211 0.1102 0.3227 0.6501 0.0267 6.0058368.50 0.1321 0.6060 0.1159 0.3219 0.6514 0.0260 4.0961368.62 0.1203 0.6171 0.1095 0.2989 0.6739 0.0265 4.8147368.64 0.1417 0.5967 0.1362 0.2970 0.6740 0.0284 5.8757368.86 0.1568 0.5272 0.1584 0.3502 0.6164 0.0328 5.2353369.08 0.1633 0.4847 0.1820 0.3359 0.6295 0.0339 4.8087369.36 0.1197 0.5953 0.1245 0.3013 0.6679 0.0300 4.6300369.66 0.1036 0.6534 0.0977 0.2852 0.6875 0.0266 5.1095369.67 0.1419 0.5495 0.1618 0.3720 0.5918 0.0356 4.8949369.69 0.1639 0.4895 0.1865 0.2983 0.6673 0.0336 5.4114369.72 0.1467 0.5162 0.1823 0.4157 0.5434 0.0400 3.1378369.83 0.1700 0.4623 0.1922 0.3216 0.6430 0.0341 3.0433369.85 0.1681 0.4271 0.2067 0.3413 0.6193 0.0383 3.4887369.94 0.1175 0.5812 0.1365 0.3107 0.6561 0.0323 4.4716370.16 0.1864 0.4028 0.2290 0.3362 0.6235 0.0391 3.6044370.27 0.1079 0.6139 0.1135 0.2501 0.7221 0.0266 3.7076370.86 0.1172 0.5641 0.1474 0.2867 0.6775 0.0347 4.4206370.94 0.1390 0.5092 0.1753 0.3066 0.6557 0.0369 5.6410371.21 0.1393 0.4850 0.1953 0.3488 0.6061 0.0438 3.4285371.49 0.1172 0.5595 0.1533 0.2789 0.6840 0.0357 3.8025371.92 0.1459 0.4627 0.2133 0.3359 0.6187 0.0442 3.8223372.31 0.1336 0.5475 0.1588 0.2590 0.6999 0.0397 4.6487372.73 0.1794 0.2583 0.4107 0.1948 0.7360 0.0664 5.4682373.39 0.1100 0.5342 0.1756 0.2989 0.6525 0.0463 2.711533

ro

wter

Fig. 2. VLE for the binary reactive system water (2) + ethyl lactate (3) at 40(uV

terfbfm

O

wbcQ

itstUIfoipdomV

74.23 0.1132 0.4940 0.1984 0.2828 0.6665 0.0486 3.304774.69 0.1200 0.4828 0.2050 0.3066 0.6385 0.0529 3.3265

eactions, the equilibrium constant shows a slight dependencen temperature in the range considered in this work.

Experimental VLE data for this reactive quaternary system

ere correlated by using the UNIQUAC equation to satisfy

he chemical equilibrium condition as well as the vapor–liquidquilibrium condition. In the fitting procedure some of the non-eactive binary UNIQUAC interaction parameters were fixed in

6tep

�, �) and 60 ◦C (�, �). The continuous lines represent the VLE calculated bysing parameters from Table 3. The points correspond to experimental data ofu et al. [20].

he values obtained from the literature, i.e.: ethanol + water [19],thanol + ethyl lactate [14] and water + lactic acid [2,3]. Theest of the binary interaction parameters were obtained directlyrom the quaternary VLE data correlation. These UNIQUACinary interaction parameters were obtained by minimizing theollowing objective function through the Simplex-Nelder-Meadethod:

.F. =n∑

j=1

c∑i=1

(γexp,ij − γcalc,ij)2 (5)

here n is the number of experimental VLE data, c the num-er of components, and γexp, and γcalc the experimental andalculated activity coefficients, respectively. All the binary UNI-UAC parameters are listed in Table 3.By using the binary UNIQUAC interaction parameters listed

n Table 3, it is possible to calculate the binary reactive systemshat could not be experimentally determined in the circulationtill used in this work. Fig. 2 shows the VLE calculated forhe binary reactive system water (2) + ethyl lactate (3) with theNIQUAC parameters presented in Table 3 at 40 and 60 ◦C.

n this graph, experimental results obtained by Vu et al. [20]or this binary reactive system are also shown. As can bebserved not big differences exist between the VLE behav-or predicted by UNIQUAC equation with binary interactionarameters obtained from correlation of the quaternary VLEata and VLE experimental data obtained directly in the studyf the VLE behavior for this binary reactive system. A maxi-um pressure azeotrope is formed at high water concentration.u et al. [20] reported a predicted azeotropic composition at

.5–6.7 mol% ethyl lactate based on their UNIQUAC fit. Inhis work, azeotropic compositions at 6.4–6.6 and 6.8–7.0 mol%thyl lactate have been predicted by using the binary interactionarameters listed in Table 3 at 40 and 60 ◦C, respectively.

P. Delgado et al. / Fluid Phase Equilibria 255 (2007) 17–23 21

Table 2Pure components parameters: van der Waals properites, ri and qi, and Antoine equationa coefficients Ai, Bi and Ci

Compound ri qi Antoine constants Literature for theAntoine constants

A B C

Water 0.9200 1.4000 7.0436 1636.91 224.92 [18]Ethanol 2.1055 1.9720 7.1688 1552.60 222.42 [18]E 9L 1

sa

vatpwr

l

oawapayDalprtbT

paoeiaobc

4

avpr

X

Y

a

TU

C

E

E

E

W

W

E

thyl lactate 4.4555 3.9280 7.826actic acid 3.1648 2.8800 7.247

a Antoine equation: log(p(kPa)) = A − B/[(T(◦C)) + C].

No azeotrope was found for the other two calculated VLEystems: ethanol (1) + lactic acid (4) and ethyl lactate (3) + lacticcid (4).

To evaluate the quality of the correlation, the experimentalariables have been recalculated by taking into account phasend chemical equilibrium. To solve the phase and chemical reac-ion equilibrium simultaneously, an algorithm similar to the oneroposed by Barbosa and Doherty [12] has been used in thisork. In this study, the following empirical expression for the

eaction equilibrium constant was used:

n Keq = 7.8927 − 2431.2

T (K)(6)

This expression for the reaction equilibrium constant wasbtained by using the experimental data obtained in this works well as the data obtained in the previous kinetic study [3],here Kγ was evaluated by using the new UNIQUAC inter-

ction parameters obtained in this work. The average absoluteercent deviations between experimental and calculated vari-bles were the following: x2/% = 2.67, x4/% = 15.54, T/% = 0.18,1/% = 13.60, y2/% = 11.79; y3/% = 9.64, and y4/% = 27.89.eviations between experimental data and the calculated vari-

bles are slightly high. The highest errors were obtained foractic acid, specially its vapor composition due to the low vaporressure of lactic acid. Lactic acid can suffer self-esterification

eactions at concentration higher than 20 wt% in water [21]. Inhis work, the presence of lactic acid oligomers was avoidedy using commercial dilute aqueous solutions of lactic acid.he highest superficial lactic acid concentration in the liquid

X

Y

able 3NIQUAC binary interaction parameters for the quaternary system ethanol (1) + wate

omponent 1 Component 2 i j

thanol Lactic acid 1 22 1

thanol Ethyl lactate 1 22 1

thanol Water 1 22 1

ater Lactic acid 1 22 1

ater Ethyl lactate 1 22 1

thyl lactate Lactic acid 1 22 1

2489.7 273.15 [18]1968.21 158.94 [19]

hase was about 30 wt%. Although the presence of lactoyllacticcid is not very important at this concentration (about 1 wt%),ligomers formation and esterification could take place in somextent. Barbosa and Doherty [22] pointed out the need for hav-ng accurate thermochemical data to correctly describe the phasend chemical equilibrium of reactive mixtures. The deviationsbtained in the value of the reaction equilibrium constant coulde also responsible for the differences between experimental andalculated variables.

.1. Reactive phase diagrams

For a graphical representation of a quaternary system Barbosand Doherty [23] introduced a set of transformed compositionariables. In this work, the calculation of these transformed com-osition variables was done by taking ethanol (reactive) as theeference component:

2 = −(x2 + x1); X3 = −(x3+ x1); X4 = (x4 − x1) (7)

2 = −(y2 + y1); Y3 = −(y3 + y1); Y4 = (y4 − y1) (8)

There are two constraints for these new composition vari-bles:

2 + X3 − X4 = −1 (9)

2 + Y3 − Y4 = −1 (10)

r (2) + ethyl lactate (3) + lactic acid (4) at 103.33 kPa, τij = exp[−(aij + bijT)/T]

aij/K bij Reference

191.28 – This work−43.32 – This work

−148.67 – [14]341.77 – [14]

728.97 −2.0046 [19]−756.95 2.4936 [19]

−39.61 – [3]155.18 – [3]

64.53 – This work99.80 – This work

52.64 – This work125.29 – This work

22 P. Delgado et al. / Fluid Phase Eq

Fig. 3. The bubble and dew point temperature surfaces at 101.325 kPa for theq(

f

X

cmActttDhdamst

5

eTrarwTodattcia

L�

KKnOpRTxy

Gγ

φ

μ

ν

Sceei1234

Scs

A

GEg

R

[

uaternary reactive system ethanol (1) + water (2) + ethyl lactate (3) + lactic acid4) at chemical equilibrium: X3/Y3, X2/Y2, versus temperature, T.

By using the transformed composition variables the conditionor a reactive azeotrope can be expressed as [23]:

i = Yi (11)

Fig. 3 represents the reactive vapor and liquid surfaces cal-ulated by using the transformed molar fractions. The binaryixtures formed by one reactant and one product do not react.ny other mixture will react obtaining a quaternary mixture in

hemical and phase equilibrium represented by a point insidehe temperature-composition diagram. As can be observed, thewo surfaces do not have a common tangent plane, which meanshat reactive azeotropy does not occur for this particular system.ifferent equilibrium conditions would be achieved by usingigher concentration of lactic acid aqueous solutions instead ofilute aqueous solution (20 wt%). A 50 superficial wt% lacticcid solution contains already 46 and 3 true wt% of lactic acidonomer and dimmer respectively [24]. For aqueous lactic acid

olutions higher than 20 wt% the role of oligomers should beaken into account.

. Conclusions

The VLE for the quaternary reactive system ethanol + water +thyl lactate + lactic acid has been experimentally determined.he UNIQUAC activity coefficient model has been used to cor-

elate experimental VLE data and it has been proved to begood model for description of phase and chemical equilib-

ium. Some of the non-reactive binary interaction parametersere taken from the literature and fixed in the fitting procedure.he rest of the UNIQUAC binary interaction parameters werebtained directly from the correlation of the quaternary VLEata obtained in this work. These binary interaction parametersllowed us to calculate the VLE behavior of the binary reac-ive mixtures. It was found a maximum pressure azeotrope for

he binary reactive system water + ethyl lactate at high wateroncentrations. Further thermodynamic studies should be done,ncluding higher order polymers of lactic acid, in order to achieveglobal understanding of the real system.

[[[[

uilibria 255 (2007) 17–23

ist of symbolsG0 standard Gibbs energy (J/mol)eq reaction equilibrium constantx reaction equilibrium constant based on concentration

number of experimental VLE data.F. objective function

pressure (kPa)gas constant (J mol−1 K−1)absolute temperature (K)liquid mole fractionvapor mole fraction

reek symbolsactivity coefficientfugacity coefficientchemical potential in the liquid phasestoichiometric coefficient

ubscriptsalc calculated valueq equilibriumxp experimental value

componentethanolwaterethyl lactatelactic acid

uperscriptsnumber of components

at saturation

cknowledgments

Financial support of “Junta de Castilla y Leon” throughrant BU019A/05 and “Consejerıa de Educacion y Fondo Socialuropeo” through predoctoral Grant EDU/1490/2003 (P. Del-ado) is gratefully acknowledged.

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ase Eq

[

[

[

[

[[

[

P. Delgado et al. / Fluid Ph

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[[[

uilibria 255 (2007) 17–23 23

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