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

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

Fluid Phase Equilibria 255 (2007) 17–23 Isobaric vapor–liquid equilibria for the quaternary reactive system: Ethanol + water + ethyl lactate + lactic...

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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, Mar´ıa Teresa Sanz ∗ , Sagrario Beltr´an Department of Chemical Engineering, University of Burgos, 09001 Burgos, Spain Received 5 January 2007; received in revised form 20 March 2007; accepted 22 March 2007 Available online 27 March 2007

Abstract Isobaric vapor–liquid equilibrium (VLE) data of the reactive quaternary system ethanol (1) + water (2) + ethyl lactate (3) + lactic acid (4) have been determined experimentally. Additionally, the reaction equilibrium constant was calculated for each VLE experimental data. The experimental VLE data were correlated using the UNIQUAC equation to describe the chemical and phase equilibria simultaneously. For some of the non-reactive binary systems, UNIQUAC binary interaction parameters were obtained from the literature. The rest of the binary UNIQUAC parameters were obtained by correlating the experimental quaternary VLE data obtained in this work. A maximum pressure azeotrope at high water concentration for the binary reactive system ethyl lactate + water has been calculated. © 2007 Elsevier B.V. All rights reserved. Keywords: Vapor–liquid equilibria; Chemical equilibrium; Esterification; Lactic acid; Ethyl lactate

1. Introduction Lactic acid esters are used as powerful high-boiling solvents. Ethyl lactate particularly is used as food and perfumery additive, flavor chemical and solvent [1]. Methyl, ethyl, isopropyl and n-butyl lactates are usually produced by conventional esterification of lactic acid with the corresponding alcohol. Esterification reactions are equilibrium-limited reactions and usually do not reach completion. Higher conversion can be obtained by shifting chemical equilibrium towards products formation by hybrid processes such as reactive distillation and pervaporation aided-reactors. By removing directly the products from the reactive section of the reactive distillation column, higher conversions can be obtained. Additionally, the integration of a pervaporation unit into conventional esterification processes is also attractive because pervaporation is based on the differences in solubility’s and transport rates in a dense membrane. The design of such hybrid processes requires the knowledge of phase equilibrium as well as of reaction kinetics. During the last years different studies on thermodynamic properties involv-



Corresponding author. Tel.: +34 947 258810; fax: +34 947 258831. E-mail address: [email protected] (M.T. Sanz).

0378-3812/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2007.03.022

ing lactic acid and its derivatives have been carried out in our work group. In a previous paper, VLE behavior for the quaternary reactive mixture methanol + water + methyl lactate + lactic acid was studied [2]. In this work, VLE measurements for the quaternary system involved in the esterification of lactic acid with ethanol at 101.33 kPa are presented: CH3 CHOHCOOH + CH3 CH2 OH  CH3 CHOHCOOCH2 CH3 + H2 O A previous kinetic study for the esterification of lactic acid with ethanol has already been performed in detail [3]. Quaternary experimental VLE data with simultaneous chemical equilibrium have been reported in the literature for different esterification systems. Hirata and Komatsu [4,5] studied the VLE of the systems involved in the esterification of acetic acid with butanol [4] and with ethanol [5] in a modified Othmer still. They reported the ratio of VLE composition establishing different correlations with temperature and composition. Lee and Kuo [6] presented VLE data for the esterification of acetic acid with isopropanol obtained in an Othmer type equilibrium cell. Similar procedure was followed by Kang et al. [7], Lee and Lin [8] and Lee and Liang [9] to determine the phase and reaction equilibria of the esterification of acetic acid with ethanol [7], isoamyl alcohol [8] and 1-pentanol [9], respectively. Recently, Teodorescu et

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al. [10] and Bernatov´a et al. [11] investigated the VLE behavior in a modified Dvorak and Boubl´ık still for the esterification of acetic with 2-propanol [10] and methanol [11], respectively. In all cases, activity coefficient models were used to correlate the VLE data of the quaternary reactive systems proving that the experimental chemical equilibrium data could be also satisfactorily predicted using conventional activity coefficient models with parameters calculated from vapor–liquid equilibrium data [12]. In this work, the experimental data were correlated by using the UNIQUAC equation to satisfy the phase as well as the chemical equilibrium of the mixture. The fitting procedure was similar to the one proposed by Teodorescu et al. [10] and Bernatov´a et al. [11]. For some of the non-reactive binary systems, interaction parameters were obtained from the literature and fixed in the fitting procedure. The rest of the UNIQUAC binary interaction parameters were obtained from the correlation of the experimental VLE data of the quaternary system obtained in this work.

and reactants by Eq. (4): Keq = Kx Kγ =

c c   (xi )νi (γi )νi i=1

(4)

i=1

3. Experimental 3.1. Materials Ethyl lactate was supplied by Aldrich with a reported purity of 99 wt%. It was purified by vacuum distillation, obtaining a final purity of 99.9%, as determined by gas chromatography (GC). Ethanol of 99.9 wt% purity was purchased from Lab-Scan. Water was nanopure. An aqueous lactic acid solution (20 wt%) was supplied by Acros. The amount of polymerized lactic acid was considered negligible after being determined by back titration. As an additional purity check, some physical properties of the pure components were measured and compared with values reported in the literature. Results were presented in a previous publication [14].

2. Thermodynamics of VLE with chemical reaction 3.2. Sample analysis Carvoli and Delogu [13] considered two different ways to study phase equilibrium of reacting systems: according to the first one, chemical and phase equilibrium must be reached simultaneously; in the second one, experimental conditions allow phase equilibrium to be reached in shorter time than chemical equilibrium. The second approach can be assumed for slow reaction systems. The general equation for VLE equilibrium at constant low pressure, p, and temperature, T, of a given mixture is given by, sat φi yi p = γi xi psat i φi

(1)

where γ i is the activity coefficient of component i, φi its fugacity coefficient and xi and yi the composition of the liquid and vapor phases respectively. φisat is the fugacity coefficient of pure saturated vapor i at temperature T and the corresponding saturation pressure psat i . When a reaction takes place in the liquid phase, an additional constraint for the chemical potential, μi has to be included, c 

ν i μi = 0

(2)

i=1

where c is the number of components, μi the chemical potential of component i and νi is the stoichiometric coefficient of component i in the reaction. The thermodynamic equilibrium constant, Keq is expressed in terms of the standard Gibbs energy change of reaction as:  Keq = exp

−G0 RT

 (3)

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

The samples were analyzed using a Hewlett Packard (6890) gas chromatograph (GC) equipped with series connected thermal conductivity (TCD) and flame ionization (FID) detectors. Helium, 99.999% pure, was used as carrier gas. The GC column was a 30 m × 0.25 mm bonded phase fused silica capillary column. The injector and detectors were at 523.15 and 533.15 K, respectively. The oven was operated at programmed temperature, from 363 to 473 K. 1,2-Propanediol was used as internal standard for analysis of the quaternary samples [15]. Quantitative analysis of monomer lactic acid was carried out by titration using phenolphthalein as indicator. Experimental concentration uncertainties were ±0.0005. 3.3. Apparatus and procedure VLE for the reactive quaternary system subject of this work was determined in an all-glass still of the Gillespie type with circulation of both the liquid and vapor phases. A detailed description of the apparatus has been previously reported [16]. The still was operated under a nitrogen atmosphere. The total pressure of the system was monitored with a digital manometer and controlled to the desired value (±0.09 kPa) by means of a pressure controller (Normastat 75). Temperature (±0.05 K) was measured with a digital thermometer (Ertco-Hart, Model 850). A kinetic study of the esterification reaction of lactic acid with ethanol is necessary to establish how the phase and chemical equilibria affect each other. As it was mentioned in Section 1, such study has already been performed in detail [3]. In that work, some experiments were carried out without the addition of external catalyst. Fig. 1 shows the experimental mole fraction of ethyl lactate at different reaction times obtained in the esterification of lactic acid with ethanol (T = 338.15 K, initial molar reactant ratio REtOH/HL = 3) without adding any

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

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Table 1 Experimental VLE data corresponding to chemical equilibrium for the quaternary system ethanol (1) + water (2) + ethyl lactate (3) + lactic acid (4) at 101.33 kPa: liquid phase mole fraction xi , vapor phase mole fraction yi , temperature T and equilibrium reaction constant Keq

Fig. 1. Ethyl lactate mole fraction versus time for the auto-catalyzed esterification reaction of lactic acid with ethanol at 338.15 K, initial molar reactant ratio REtOH/HL = 3 (䊉 experimental data, — autocatalytic kinetic model [3]).

external catalyst. It can be observed that the reaction rate is not negligible, even without the addition of external catalyst. The VLE data for the reactive quaternary mixture have been obtained by using the Gillespie type still previously described where chemical and phase equilibria are expected to be reached. In order to avoid long operation times till chemical and phase equilibrium were reached, the still was filled with quaternary mixtures with a composition close to the chemical equilibrium. In addition, mixtures were kept in the still more than 4 h once temperature remains constant to ensure chemical and phase equilibrium. Subsequently, samples of liquid and condensed vapor were withdrawn for analysis. Some authors [6–11] add a heterogeneous catalyst to the system in order to shorten the operating time. 4. Results and discussion In this work, 115 experiments were carried out to determine the VLE behavior corresponding to chemical equilibrium at 101.33 kPa for this reactive quaternary mixture. The pressure, temperature and vapor and liquid composition were determined experimentally and are listed in Table 1. The concentration range of high monomer lactic acid concentration was not studied in order to avoid its polymerization. The vapor phase fugacity coefficients have been calculated using the virial equation of state truncated after the second term and the second virial coefficients were obtained from the Hayden and O’Connell [17] correlation. Because of the low vapor pressure of lactic acid, it was not necessary to use the “chemical” theory as was proved for the system water + lactic acid [2]. Activity coefficients were calculated from Eq. (1) by using the experimental VLE data from the quaternary system taking into account the non-ideality of the vapor phase. The vapor pressure of the pure components used in the vapor–liquid equilibrium calculations were obtained through the Antoine equation. Ai , Bi and Ci Antoine coefficients are given in Table 2 together with the van der Waals properties, ri and qi . According to Eq. (4), the equilibrium constant has been calculated for each experimental data. Similar to other esterification

T (K)

x1

x2

x3

y1

y2

y3

Keq

356.27 357.07 357.49 357.92 358.04 358.18 358.44 358.55 359.12 359.19 359.51 359.92 360.01 360.32 360.72 360.76 360.85 361.06 361.20 361.23 361.33 361.35 361.54 361.62 361.70 361.79 361.98 362.13 362.18 362.19 362.20 362.48 362.66 362.83 362.87 362.96 363.02 363.22 363.31 363.43 363.50 363.67 363.70 363.74 363.91 363.95 364.00 364.09 364.10 364.14 364.33 364.45 364.53 364.57 364.58 364.72 364.91 364.92 364.95 365.05 365.08

0.2622 0.2643 0.1956 0.1971 0.1942 0.2017 0.1541 0.1533 0.1581 0.1560 0.1248 0.1597 0.1155 0.1193 0.1072 0.1037 0.1361 0.1066 0.1309 0.1069 0.1197 0.1205 0.1237 0.1182 0.1067 0.0795 0.0881 0.0911 0.0863 0.0928 0.0756 0.0903 0.1006 0.0954 0.2923 0.0917 0.1411 0.1120 0.2851 0.0739 0.0739 0.1364 0.2339 0.1159 0.0797 0.0705 0.2424 0.1497 0.0848 0.2491 0.2369 0.0749 0.0615 0.1358 0.2317 0.0882 0.0550 0.0895 0.0553 0.1986 0.1489

0.7004 0.6914 0.7646 0.7687 0.7648 0.7656 0.8142 0.8057 0.8031 0.7985 0.8389 0.7958 0.8360 0.8323 0.8367 0.8535 0.7984 0.8428 0.8004 0.8520 0.8255 0.8273 0.8184 0.8263 0.8370 0.8787 0.8551 0.8504 0.8673 0.8471 0.8780 0.8498 0.8298 0.8574 0.4596 0.8481 0.7380 0.7965 0.4676 0.8637 0.8651 0.7243 0.5219 0.7728 0.8488 0.8674 0.4868 0.6823 0.8334 0.4917 0.5173 0.8440 0.8746 0.6852 0.4992 0.8060 0.8801 0.8003 0.8853 0.5449 0.6466

0.0161 0.0210 0.0180 0.0155 0.0189 0.0160 0.0136 0.0168 0.0152 0.0181 0.0136 0.0167 0.0164 0.0147 0.0163 0.0131 0.0200 0.0143 0.0186 0.0134 0.0155 0.0174 0.0190 0.0159 0.0171 0.0121 0.0155 0.0151 0.0120 0.0160 0.0116 0.0156 0.0232 0.0140 0.1453 0.0147 0.0452 0.0285 0.1429 0.0138 0.0141 0.0547 0.1380 0.0349 0.0181 0.0132 0.1472 0.0678 0.0215 0.1381 0.1313 0.0215 0.0119 0.0723 0.1380 0.0283 0.0112 0.0326 0.0114 0.1287 0.0850

0.5160 0.5285 0.4921 0.7038 0.5449 0.5699 0.5603 0.6962 0.5329 0.4423 0.4129 0.4703 0.5351 0.4078 0.4739 0.5528 0.4372 0.4890 0.7482 0.4458 0.5384 0.3672 0.4554 0.4427 0.4551 0.3141 0.3770 0.3700 0.4853 0.3722 0.4004 0.3429 0.3796 0.7079 0.7761 0.3454 0.3439 0.3597 0.5612 0.3003 0.3581 0.4292 0.3871 0.2751 0.3045 0.2820 0.4788 0.3353 0.3610 0.6496 0.4037 0.3781 0.2838 0.3406 0.4795 0.2459 0.2231 0.2889 0.2725 0.4154 0.3562

0.4815 0.4681 0.5041 0.2921 0.4505 0.4253 0.4357 0.2969 0.4624 0.5525 0.5829 0.5250 0.4587 0.5873 0.5196 0.4408 0.5556 0.5048 0.2434 0.5482 0.4531 0.6253 0.5377 0.5492 0.5376 0.6805 0.6156 0.6226 0.5070 0.6207 0.5932 0.6503 0.6111 0.2837 0.1967 0.6472 0.6444 0.6297 0.4160 0.6928 0.6345 0.5544 0.5928 0.7143 0.6868 0.7112 0.4976 0.6493 0.6287 0.3222 0.5760 0.6103 0.7090 0.6418 0.4949 0.7443 0.7707 0.6985 0.7201 0.5619 0.6238

0.0024 0.0033 0.0037 0.0041 0.0045 0.0047 0.0039 0.0068 0.0046 0.0051 0.0041 0.0046 0.0061 0.0048 0.0064 0.0063 0.0070 0.0060 0.0083 0.0058 0.0084 0.0072 0.0067 0.0079 0.0072 0.0051 0.0072 0.0072 0.0075 0.0069 0.0062 0.0066 0.0090 0.0083 0.0270 0.0072 0.0115 0.0103 0.0224 0.0068 0.0071 0.0161 0.0198 0.0104 0.0084 0.0066 0.0231 0.0149 0.0101 0.0278 0.0200 0.0114 0.0070 0.0172 0.0250 0.0095 0.0060 0.0122 0.0073 0.0223 0.0196

1.8627 1.6150 2.2598 1.4724 2.4107 1.6720 2.1438 1.3454 3.1960 3.0813 4.7481 4.8014 2.5895 2.9171 2.2505 2.4631 2.1911 2.0376 1.8297 2.1266 3.0229 2.3110 2.4139 2.0240 2.7250 2.1879 2.5711 2.7446 2.1878 3.3287 2.1114 2.5006 2.5693 1.5579 1.4601 2.6470 5.8912 3.2127 2.0407 4.2311 2.5375 3.0356 4.4559 5.8547 3.7689 3.9534 2.5093 3.4909 4.1820 1.9399 4.4622 4.7655 3.7100 4.0611 2.2745 4.2227 4.8151 4.6689 5.3519 3.8292 4.6032

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

Table 1 (Continued ) T (K)

x1

x2

x3

y1

y2

y3

Keq

365.08 365.13 365.18 365.19 365.43 365.62 365.62 365.67 365.91 365.92 366.17 366.23 366.24 366.39 366.42 366.77 366.78 366.94 366.98 367.02 367.20 367.36 367.52 367.71 367.77 368.02 368.20 368.34 368.47 368.50 368.62 368.64 368.86 369.08 369.36 369.66 369.67 369.69 369.72 369.83 369.85 369.94 370.16 370.27 370.86 370.94 371.21 371.49 371.92 372.31 372.73 373.39 374.23 374.69

0.0553 0.1160 0.0853 0.0521 0.0532 0.0837 0.1484 0.1935 0.0987 0.1013 0.0455 0.1659 0.1038 0.0952 0.1387 0.1157 0.0388 0.1645 0.1052 0.1456 0.1134 0.0974 0.1501 0.1082 0.1376 0.1356 0.1172 0.1908 0.1247 0.1321 0.1203 0.1417 0.1568 0.1633 0.1197 0.1036 0.1419 0.1639 0.1467 0.1700 0.1681 0.1175 0.1864 0.1079 0.1172 0.1390 0.1393 0.1172 0.1459 0.1336 0.1794 0.1100 0.1132 0.1200

0.8791 0.7631 0.7995 0.8816 0.8809 0.7909 0.6320 0.5423 0.7467 0.7397 0.8915 0.5824 0.7360 0.7373 0.6297 0.6972 0.9019 0.5622 0.6989 0.5815 0.6822 0.7032 0.5933 0.6862 0.5668 0.6036 0.6386 0.4584 0.6211 0.6060 0.6171 0.5967 0.5272 0.4847 0.5953 0.6534 0.5495 0.4895 0.5162 0.4623 0.4271 0.5812 0.4028 0.6139 0.5641 0.5092 0.4850 0.5595 0.4627 0.5475 0.2583 0.5342 0.4940 0.4828

0.0110 0.0417 0.0344 0.0103 0.0105 0.0387 0.0953 0.1344 0.0521 0.0521 0.0092 0.1213 0.0584 0.0571 0.1041 0.0705 0.0081 0.1277 0.0699 0.1224 0.0770 0.0746 0.1178 0.0826 0.1332 0.1151 0.0985 0.1807 0.1102 0.1159 0.1095 0.1362 0.1584 0.1820 0.1245 0.0977 0.1618 0.1865 0.1823 0.1922 0.2067 0.1365 0.2290 0.1135 0.1474 0.1753 0.1953 0.1533 0.2133 0.1588 0.4107 0.1756 0.1984 0.2050

0.2999 0.3094 0.2735 0.2821 0.3037 0.2786 0.2980 0.4414 0.2935 0.2906 0.2432 0.3865 0.2864 0.2466 0.3021 0.2479 0.2406 0.3375 0.2665 0.3124 0.2457 0.2300 0.3272 0.3556 0.3111 0.2993 0.3495 0.3318 0.3227 0.3219 0.2989 0.2970 0.3502 0.3359 0.3013 0.2852 0.3720 0.2983 0.4157 0.3216 0.3413 0.3107 0.3362 0.2501 0.2867 0.3066 0.3488 0.2789 0.3359 0.2590 0.1948 0.2989 0.2828 0.3066

0.6921 0.6783 0.7146 0.7102 0.6884 0.7073 0.6820 0.5316 0.6899 0.6934 0.7497 0.5878 0.6970 0.7372 0.6754 0.7341 0.7529 0.6376 0.7149 0.6623 0.7348 0.7511 0.6475 0.6177 0.6607 0.6755 0.6240 0.6375 0.6501 0.6514 0.6739 0.6740 0.6164 0.6295 0.6679 0.6875 0.5918 0.6673 0.5434 0.6430 0.6193 0.6561 0.6235 0.7221 0.6775 0.6557 0.6061 0.6840 0.6187 0.6999 0.7360 0.6525 0.6665 0.6385

0.0077 0.0120 0.0116 0.0075 0.0077 0.0137 0.0193 0.0262 0.0161 0.0156 0.0068 0.0252 0.0163 0.0157 0.0219 0.0175 0.0062 0.0242 0.0180 0.0247 0.0190 0.0184 0.0245 0.0260 0.0275 0.0245 0.0258 0.0299 0.0267 0.0260 0.0265 0.0284 0.0328 0.0339 0.0300 0.0266 0.0356 0.0336 0.0400 0.0341 0.0383 0.0323 0.0391 0.0266 0.0347 0.0369 0.0438 0.0357 0.0442 0.0397 0.0664 0.0463 0.0486 0.0529

3.2282 4.8424 5.5521 3.8682 3.4710 4.5285 3.6764 2.2175 3.8474 5.2200 3.8997 4.4764 5.9182 4.7338 4.0730 5.6465 2.9516 3.4282 4.0890 4.7324 6.1031 5.9360 3.2474 3.4521 4.7025 4.0901 3.7611 3.5898 6.0058 4.0961 4.8147 5.8757 5.2353 4.8087 4.6300 5.1095 4.8949 5.4114 3.1378 3.0433 3.4887 4.4716 3.6044 3.7076 4.4206 5.6410 3.4285 3.8025 3.8223 4.6487 5.4682 2.7115 3.3047 3.3265

reactions, the equilibrium constant shows a slight dependence on temperature in the range considered in this work. Experimental VLE data for this reactive quaternary system were correlated by using the UNIQUAC equation to satisfy the chemical equilibrium condition as well as the vapor–liquid equilibrium condition. In the fitting procedure some of the nonreactive binary UNIQUAC interaction parameters were fixed in

Fig. 2. VLE for the binary reactive system water (2) + ethyl lactate (3) at 40 (, ) and 60 ◦ C (, ). The continuous lines represent the VLE calculated by using parameters from Table 3. The points correspond to experimental data of Vu et al. [20].

the values obtained from the literature, i.e.: ethanol + water [19], ethanol + ethyl lactate [14] and water + lactic acid [2,3]. The rest of the binary interaction parameters were obtained directly from the quaternary VLE data correlation. These UNIQUAC binary interaction parameters were obtained by minimizing the following objective function through the Simplex-Nelder-Mead method: O.F. =

n  c 

(γexp,ij − γcalc,ij )2

(5)

j=1 i=1

where n is the number of experimental VLE data, c the number of components, and γ exp , and γ calc the experimental and calculated activity coefficients, respectively. All the binary UNIQUAC parameters are listed in Table 3. By using the binary UNIQUAC interaction parameters listed in Table 3, it is possible to calculate the binary reactive systems that could not be experimentally determined in the circulation still used in this work. Fig. 2 shows the VLE calculated for the binary reactive system water (2) + ethyl lactate (3) with the UNIQUAC parameters presented in Table 3 at 40 and 60 ◦ C. In this graph, experimental results obtained by Vu et al. [20] for this binary reactive system are also shown. As can be observed not big differences exist between the VLE behavior predicted by UNIQUAC equation with binary interaction parameters obtained from correlation of the quaternary VLE data and VLE experimental data obtained directly in the study of the VLE behavior for this binary reactive system. A maximum pressure azeotrope is formed at high water concentration. Vu et al. [20] reported a predicted azeotropic composition at 6.5–6.7 mol% ethyl lactate based on their UNIQUAC fit. In this work, azeotropic compositions at 6.4–6.6 and 6.8–7.0 mol% ethyl lactate have been predicted by using the binary interaction parameters listed in Table 3 at 40 and 60 ◦ C, respectively.

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

21

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

Water Ethanol Ethyl lactate Lactic acid a

ri

qi

0.9200 2.1055 4.4555 3.1648

Antoine constants

1.4000 1.9720 3.9280 2.8800

Literature for the Antoine constants

A

B

C

7.0436 7.1688 7.8269 7.2471

1636.91 1552.60 2489.7 1968.21

224.92 222.42 273.15 158.94

[18] [18] [18] [19]

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

No azeotrope was found for the other two calculated VLE systems: ethanol (1) + lactic acid (4) and ethyl lactate (3) + lactic acid (4). To evaluate the quality of the correlation, the experimental variables have been recalculated by taking into account phase and chemical equilibrium. To solve the phase and chemical reaction equilibrium simultaneously, an algorithm similar to the one proposed by Barbosa and Doherty [12] has been used in this work. In this study, the following empirical expression for the reaction equilibrium constant was used: ln Keq = 7.8927 −

2431.2 T (K)

phase was about 30 wt%. Although the presence of lactoyllactic acid is not very important at this concentration (about 1 wt%), oligomers formation and esterification could take place in some extent. Barbosa and Doherty [22] pointed out the need for having accurate thermochemical data to correctly describe the phase and chemical equilibrium of reactive mixtures. The deviations obtained in the value of the reaction equilibrium constant could be also responsible for the differences between experimental and calculated variables. 4.1. Reactive phase diagrams

(6)

For a graphical representation of a quaternary system Barbosa and Doherty [23] introduced a set of transformed composition variables. In this work, the calculation of these transformed composition variables was done by taking ethanol (reactive) as the reference component:

This expression for the reaction equilibrium constant was obtained by using the experimental data obtained in this work as well as the data obtained in the previous kinetic study [3], where Kγ was evaluated by using the new UNIQUAC interaction parameters obtained in this work. The average absolute percent deviations between experimental and calculated variables were the following: x2 /% = 2.67, x4 /% = 15.54, T/% = 0.18, y1 /% = 13.60, y2 /% = 11.79; y3 /% = 9.64, and y4 /% = 27.89. Deviations between experimental data and the calculated variables are slightly high. The highest errors were obtained for lactic acid, specially its vapor composition due to the low vapor pressure of lactic acid. Lactic acid can suffer self-esterification reactions at concentration higher than 20 wt% in water [21]. In this work, the presence of lactic acid oligomers was avoided by using commercial dilute aqueous solutions of lactic acid. The highest superficial lactic acid concentration in the liquid

X2 = −(x2 + x1 );

X3 = −(x3 + x1 );

X4 = (x4 − x1 )

(7)

Y2 = −(y2 + y1 );

Y3 = −(y3 + y1 );

Y4 = (y4 − y1 )

(8)

There are two constraints for these new composition variables: X2 + X3 − X4 = −1

(9)

Y2 + Y3 − Y4 = −1

(10)

Table 3 UNIQUAC binary interaction parameters for the quaternary system ethanol (1) + water (2) + ethyl lactate (3) + lactic acid (4) at 103.33 kPa, τ ij = exp[−(aij + bij T)/T] Component 1

Component 2

i

j

aij /K

Ethanol

Lactic acid

1 2

2 1

Ethanol

Ethyl lactate

1 2

Ethanol

Water

Water

bij

Reference

191.28 −43.32

– –

This work This work

2 1

−148.67 341.77

– –

[14] [14]

1 2

2 1

728.97 −756.95

Lactic acid

1 2

2 1

−39.61 155.18

– –

[3] [3]

Water

Ethyl lactate

1 2

2 1

64.53 99.80

– –

This work This work

Ethyl lactate

Lactic acid

1 2

2 1

52.64 125.29

– –

This work This work

−2.0046 2.4936

[19] [19]

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

List of symbols standard Gibbs energy (J/mol) G0 reaction equilibrium constant Keq reaction equilibrium constant based on concentration Kx n number of experimental VLE data O.F. objective function p pressure (kPa) R gas constant (J mol−1 K−1 ) T absolute temperature (K) x liquid mole fraction y vapor mole fraction

Fig. 3. The bubble and dew point temperature surfaces at 101.325 kPa for the quaternary reactive system ethanol (1) + water (2) + ethyl lactate (3) + lactic acid (4) at chemical equilibrium: X3 /Y3 , X2 /Y2 , versus temperature, T.

By using the transformed composition variables the condition for a reactive azeotrope can be expressed as [23]: Xi = Yi

(11)

Greek symbols γ activity coefficient φ fugacity coefficient μ chemical potential in the liquid phase ν stoichiometric coefficient Subscripts calc calculated value eq equilibrium exp experimental value i component 1 ethanol 2 water 3 ethyl lactate 4 lactic acid

Fig. 3 represents the reactive vapor and liquid surfaces calculated by using the transformed molar fractions. The binary mixtures formed by one reactant and one product do not react. Any other mixture will react obtaining a quaternary mixture in chemical and phase equilibrium represented by a point inside the temperature-composition diagram. As can be observed, the two surfaces do not have a common tangent plane, which means that reactive azeotropy does not occur for this particular system. Different equilibrium conditions would be achieved by using higher concentration of lactic acid aqueous solutions instead of dilute aqueous solution (20 wt%). A 50 superficial wt% lactic acid solution contains already 46 and 3 true wt% of lactic acid monomer and dimmer respectively [24]. For aqueous lactic acid solutions higher than 20 wt% the role of oligomers should be taken into account.

Financial support of “Junta de Castilla y Le´on” through Grant BU019A/05 and “Consejer´ıa de Educaci´on y Fondo Social Europeo” through predoctoral Grant EDU/1490/2003 (P. Delgado) is gratefully acknowledged.

5. Conclusions

References

The VLE for the quaternary reactive system ethanol + water + ethyl lactate + lactic acid has been experimentally determined. The UNIQUAC activity coefficient model has been used to correlate experimental VLE data and it has been proved to be a good model for description of phase and chemical equilibrium. Some of the non-reactive binary interaction parameters were taken from the literature and fixed in the fitting procedure. The rest of the UNIQUAC binary interaction parameters were obtained directly from the correlation of the quaternary VLE data obtained in this work. These binary interaction parameters allowed us to calculate the VLE behavior of the binary reactive mixtures. It was found a maximum pressure azeotrope for the binary reactive system water + ethyl lactate at high water concentrations. Further thermodynamic studies should be done, including higher order polymers of lactic acid, in order to achieve a global understanding of the real system.

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Superscripts c number of components sat saturation Acknowledgments

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[19] Aspen Plus 11.1, Aspen Technologies. Cambridge, MA 02141-2201, USA. [20] D.T. Vu, C.T. Lira, N.S. Asthana, A.K. Kolah, D.J. Miller, J. Chem. Eng. Data 51 (2006) 1220–1225. [21] C.H. Holten, Lactic acid: Properties and Chemistry of Lactic Acid and Derivatives, Verlag Chemie, Weinheim, 1971. [22] D. Barbosa, M.F. Doherty, Chem. Eng. Sci. 43 (1988) 541–550. [23] D. Barbosa, M.F. Doherty, Proc. R. Soc. London A 413 (1987) 459–464. [24] D.T. Vu, A.K. Kolah, N.S. Asthana, L. Peereboom, C.T. Lira, D.J. Miller, Fluid Phase Equilib. 236 (2005) 125–135.