Liquid–Liquid Phase Equilibria for Soybean Oil Methanolysis

Article pubs.acs.org/IECR

Liquid−Liquid Phase Equilibria for Soybean Oil Methanolysis: Experimental, Modeling, and Data Prediction Abraham Casas,† José Francisco Rodríguez,‡ Gonzalo L. del Peso,† Rosalía Rodríguez,† Gemma Vicente,†,* and Alicia Carrero† †

Department of Chemical and Energy Technology, ESCET, Universidad Rey Juan Carlos, c/Tulipán s/n, 28933 Móstoles, Madrid, Spain ‡ Repsol Technology Center, 28935 Móstoles, Madrid, Spain S Supporting Information *

ABSTRACT: Liquid−liquid equilibrium data of the system composed by soybean oil, fatty acid methyl esters (FAMEs), methanol, and glycerol were experimentally determined at temperatures of 25, 45, and 65 °C. Three binary systems (oil + methanol, oil + glycerol, and FAMEs + glycerol) and all the ternary combinations were evaluated. With these data, universal quasichemical (UNIQUAC) and non-random two-liquid (NRTL) binary interaction coefficients were calculated and validated. According to the results, the UNIQUAC model fitted the experimental data better than the NRTL one. In order to complete this study, UNIQUAC binary interaction coefficients for the mixtures of oil, FAMEs, methanol, and glycerol with monoglycerides and diglycerides were also predicted using a group contribution model (universal quasichemical functional-group activity coefficients) and checked using experimental data from the soybean oil transesterification reaction.

1. INTRODUCTION Nowadays, base-catalyzed transesterification of vegetable oils with methanol (also called methanolysis) is the most widely used technology to produce fatty acid methyl esters (FAMEs) as biodiesel on an industrial scale.1 This reaction is essentially biphasic from the beginning (methanol has a low solubility in triglycerides) to the end (glycerol is practically immiscible in FAMEs) under the reaction conditions usually employed in the industrial process (methanol:oil molar ratio of 6:1 and 60 °C).1,2 Therefore, the determination of the liquid−liquid equilibrium (LLE) data is crucial for a better understanding of the reaction pathway and the separation of the products. Furthermore, in the recent years there has been an increasing interest in the study of the transesterification reaction from the point of view of mass transfer between phases,3−6 which requires LLE data, thus complementing the large number of existing kinetic studies.7−10 Six major compounds coexist until the end of the triglyceride methanolysis reaction: triglycerides, FAMEs, methanol, glycerol, diglycerides, and monoglycerides. However, previous literature has focused mainly on the FAMEs−methanol− glycerol equilibrium, which represents the end of the reaction.11−16 The remaining binary and ternary systems formed by these six compounds have hardly been studied,12,17,18 with the exception of the oil−methanol binary mixture, which corresponds to the initial stage of the reaction.6,18−21 Given this situation, it is necessary to complete this information with new experimental data. It should be noted that mono-, di-, and triglycerides and FAMEs are actually groups of compounds whose composition varies according to the fatty acid profile. In this sense, only soybean oil and monoglycerides, diglycerides, and FAMEs derived from this oil were selected in this study as models for these compounds. © 2014 American Chemical Society

Moreover, high-purity mono- and diglycerides are difficult to purchase in sufficient quantities. Thus, their activity coefficients in mixtures of soybean oil, FAMEs, methanol, and glycerol were predicted with the UNIFAC (universal quasichemical functional-group activity coefficients) model. Therefore, the aim of this work is the measurement of the LLE data of all the binary and ternary systems among soybean oil, FAMEs, methanol, and glycerol at temperatures from 299.15 to 341.85 K. These new experimental data were used to estimate the binary interaction coefficients of the universal quasichemical (UNIQUAC) and non-random two-liquid (NRTL) models. New data from the quaternary system were acquired to test the validity of the estimated parameters. Finally, binary interaction coefficients including those of monoglycerides and diglycerides were predicted using the UNIFAC model and checked with experimental data from the soybean oil methanolysis reaction.

2. MATERIALS AND METHODS 2.1. Materials. Refined soybean oil was provided by Gustav Heess S.L. The fatty acid profile of this vegetable oil is shown in Table S1 in Supporting Information. Methanol (99%), glycerol (99%), acetic acid (99%), and 3A molecular sieves were supplied by Scharlab, S.L. Sodium methoxide (32 wt % in methanolic solution) was obtained from Merck. FAMEs were synthesized through soybean oil methanolysis using sodium methoxide as a catalyst and following the procedure described in a previous publication.22 Received: Revised: Accepted: Published: 3731

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xiIγi I = xiIIγi II

Gas chromatographic analysis required heptane (≥99.5%) and methyl heptadecanoate (≥99.7%) from Fluka and Nmethyl-N-(trimethylsilyl)trifluoroacetamide (MSTFA, synthesis grade), butanetriol (analytical standard), and tricaprin (analytical standard) from Sigma-Aldrich. 2.2. Equipment and Procedure. Liquid−liquid equilibrium experiments were performed in 100-mL sealed-cap glass vessels placed over a heating magnetic stirrer (JP Selecta AGIMATIC-ED). Temperature was measured using a Pt-100 probe (Heidolph EKT 3001) immersed in the 100-mL glass vessel and connected to the heater plate (error ±0.1 K). Feed mixtures comprised of different proportions of soybean oil, FAMEs, methanol, and glycerol were added to the vessel, heated to the chosen temperature, and stirred during 120 min. After reaction, the resulting layers were allowed to separate until both phases were clear. Samples of 5 mL were taken from both phases for further analysis, using a Transferpette pipet (Brand GmbH). Low-conversion soybean oil methanolysis was carried out in a 200-mL cylindrical reactor with a spherical bottom, immersed in a thermostated silicon bath. This reactor was initially filled with soybean oil and the mixture of methanol (6 mol/mol of oil) and sodium methoxide (0.2 mol/mol of oil) and preheated at 25 °C. The stirrer, located in the oil phase, was then turned on (100 rpm). After 4 h, samples were withdrawn from the nonpolar (oil/FAMEs) and polar (methanol/glycerol) phases and neutralized with a stoichiometric amount of acetic acid to stop the reaction. Finally, these samples were analyzed by gas chromatography. 2.3. Analytical Methods. FAME content was determined following EN 14103 standard in a Hewlett-Packard 6890 gas chromatograph with a column DB-WAX (30 m length, 0.25 μm thickness and 0.32 mm of internal diameter). Oven temperature was set at 200 °C and the pressure at 80 kPa, using He as carrier gas. Three analyses of a reference sample were carried out to calculate the experimental error, obtaining a value of ±0.6 wt % of FAMEs. Triglycerides, diglycerides, monoglycerides, and glycerol measurements were carried out in an Agilent 6890N gas chromatograph following the procedure shown in the EN 14105 standard. A special column for high temperatures (DB5ht, 15 m length, 0.10 μm thickness and 0.32 mm of internal diameter) and derivatization with MSTFA were used due to the high boiling points of these compounds. The column pressure was set at 24.1 kPa. The oven temperature was set at 120 °C for 5 min and was increased to 180 °C at a rate of 15 °C min−1 and then to 230 at 7 °C min−1 and finally to 370 at 10 °C min−1. This analysis was repeated twice, showing an error value of ±0.015 wt % for triglycerides and diglycerides, ±0.025 wt % for monoglycerides, and ±0.0015 wt % for glycerol. Methanol determination was performed by gravimetric analysis. The sample was weighed in a Sartorius TE214 S analytical scale with a precision of 0.0001 g. Then, the sample was placed in a vacuum rotary evaporator (60 °C) and after 30 min was weighed again. This procedure was repeated until the sample weight remained constant, and the weight difference corresponded to the methanol amount, due to its lower boiling point. This analysis showed an error value below 0.1 wt %.

(1)

where xIi and xIIi are the molar fractions of the component i in phases I and II, respectively, whereas γIi and γIIi are the activity coefficients of the component i in phases I and II, respectively. Thereby, the determination of equilibrium data requires the calculation of γIi and γIIi , which can be accomplished by estimating parameters of activity coefficient models (such as UNIQUAC or NRTL) with LLE experimental data or by the prediction of these coefficients (e.g., determination by group contribution models such as UNIFAC). UNIQUAC23 and NRTL24 have been selected for the modeling of activity coefficients in this work. In the UNIQUAC model, activity coefficients (γi) are calculated by taking into account the contribution of the combinatorial contribution, γCi , due to the size and shape of the molecules and the residual contribution, γiR, caused mainly by interaction energy as expressed in eq 2:

ln γi = ln γiC + ln γi R

(2)

The first term is calculated with the eq 3 ln γiC = (1 − Vi + ln Vi ) −

V V⎞ z ⎛ qi⎜1 − i + ln i ⎟ 2 ⎝ Fi Fi ⎠

(3)

where z has a usual value of 10. ri and qi are the van der Waals molecular volume and molecular superficial area, respectively, which were calculated using the UNIFAC model25,26 (Table S2 in Supporting Information). Finally, Vi and Fi are calculated with eqs 4 and 5, xj being the molar fraction of j compound: ri Vi = ∑j rjxj (4)

Fi =

qi ∑j qjxj

(5)

The residual contribution term was calculated with the eq 6 ⎛ ∑j qjxjτji ln γi R = qi⎜⎜1 − ln − ∑j qjxj ⎝

∑ j

⎞ ⎟ ∑k qk xkτkj ⎟⎠ qjxjτij

(6)

where τij is calculated with the following equation: ⎛ −Uij ⎞ τij = exp⎜ ⎟ ⎝ T ⎠

(7)

In this equation, parameter coefficient between compounds in K. Note that for each pair coefficients (Uij ≠ Uji; Uii = 0). In the NRTL model, activity using this expression ln γi =

∑j xjτjiGji ∑k xkGki

+

∑ j

Uij is the binary interaction i and j and T the temperature of compounds there are two coefficients (γi) are calculated

⎛ ∑ x τ G ⎞ ⎜⎜τij − m m mj mj ⎟⎟ ∑k xkGkj ⎠ ∑k xkGkj ⎝ xjGij

(8)

3. MODELING OF LIQUID−LIQUID EQUILIBRIUM DATA 3.1. Activity Coefficient Models. In LLE, the following condition must be satisfied

where x is the molar fraction. The value of Gij is obtained with the eq 9: Gij = exp( −αijτij) 3732

(9)

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αij values were considered 0.3 if compounds i and j were completely miscible and 0.2 when they were immiscible (Table S3 in Supporting Information).24 τij is calculated with the equation ⎛ Aij ⎞ τij = exp⎜ ⎟ ⎝T ⎠

Table 1. Experimental Equilibrium Compositions (wt %) for the Binary Systems Oil (1)−Methanol (3), Oil (1)−Glycerol (4), and FAMEs (2)−Glycerol (4) phase I

(10)

where Aij is the binary interaction coefficient between compounds i and j in NRTL model (Aij ≠ Aji; Aii = 0) and T the temperature in K. Finally, LLE of binary mixtures with diglycerides and monoglycerides has been predicted using the last revision25 of the original UNIFAC method developed by Fredenslund et al.26 3.2. Liquid−Liquid Equilibrium Calculation. LLE calculation has been performed through the minimization of Gibbs free energy (ΔGT) ΔGT =

(11)

methanol (3)

oil (1)

94.38 92.72 89.98

5.62 7.28 10.02

0.25 0.55 0.84

99.75 99.45 99.16 phase II

oil (1) 0.10 0.17 0.84

glycerol (4) 99.90 99.83 99.16 phase II

oil (1) 99.93 99.87 99.85

glycerol (4) 0.07 0.13 0.15 phase I

methanol (3)

T (°C)

FAMEs (2)

glycerol (4)

FAMEs (2)

glycerol (4)

26 46.2 68.7

99.96 99.93 99.88

0.04 0.07 0.12

0.66 0.83 1.34

99.34 99.17 98.66

Table 2. RMSD Values for All the Systems Studied in This Work

where R is the ideal gas constant, T is the temperature (in K), nT is the total number of moles, nI is the number of moles in the phase I, nII is the number of moles in the phase II, and GE (excess Gibbs free energy in each phase) is calculated as (12)

This condition must be satisfied with the following equation: ni = niI + niII

oil (1)

28 47.7 63.7 T (°C) 27 46.2 68.7

nT

i

T (°C)

phase I

n I (RT ∑i xiI ln xiI + GE(I )) + n II (RT ∑i xiII ln xiII + GE(II ))

GE = RT ∑ xi ln γi

phase II

(13)

system

UNIQUAC

NRTL

oil (1)−methanol (3) oil (1)−glycerol (4) FAMEs (2)−glycerol (4) oil (1)−FAMEs (2)−methanol (3) oil (1)−FAMEs (2)−glycerol (4) oil (1)−methanol (3)−glycerol (4) FAMEs (2)−methanol (3)−glycerol (4) all systems

0.0118 0.0022 0.0022 0.0139 0.0056 0.0492 0.0248 0.0249

0.0511 0.0025 0.0019 0.0556 0.0058 0.0443 0.0385 0.0412

3.3. Parameters Estimation. The binary interaction coefficients of UNIQUAC (Uij) and NRTL (Aij) models were estimated by minimizing the objective function, in this case the residual squares sum, RSS: NTL

RSS =

NP

NC

∑ ∑ ∑ (xiIexp − xiIcalc)2 N =1 I=1 i=1

(14)

where xIiexp and xIicalc were the experimental and calculated molar fraction of the compound i in the phase I, respectively. NTL are the number of tie lines, NP the number of phases in equilibrium, and NC the number of compounds. Minimization was carried out with the MATLAB software using a direct search function such as pattern search and default options (patternsearch) to find a proper first assumption of the global minimum, followed by a local minimum solver (f minsearch with “Algorithm” and “Interior point” options activated) to converge to the optimized answer. The computer codes for NRTL and UNICUAC models have been included as Supporting Information.

Figure 1. Liquid−liquid equilibrium for methanol (1)−FAMEs (2)− soybean oil (3) at 47.7 °C. Composition in mass fractions. Empty symbols, experimental data; blue solid lines, equilibrium curve and tie lines calculated with UNIQUAC; red dashed lines, calculated with NRTL.

4. RESULTS AND DISCUSSION Experimental equilibrium compositions of the binary mixtures are shown in Table 1 (in wt %) and in Table S4 of the Supporting Information (in molar fractions). Methanol solubility in the soybean oil phase ranged between 5.62 and 10.02 wt % with temperatures from 28 to 63.7 °C. These values corresponded to methanol:oil molar ratios from 1.6:1 to 3:1 (stoichiometric ratio of transesterification reaction) and were consistent with previous values shown in the literature (5.03 and 7.30 wt % at 25 °C).6,20 Furthermore, the concentration of

oil in the methanol phase did not exceed the value of 0.84 wt % in the temperature range studied. Table 1 also shows high immiscibility of the soybean oil and FAMEs with glycerol binary mixtures. In all cases, glycerol solubility in oil and FAMEs was below 0.15 wt %. The values reported previously 3733

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Figure 2. Liquid−liquid equilibrium for FAMEs (1)−methanol (2)− glycerol (3) at 45.7 °C. Composition in mass fractions. Empty symbols, experimental data; blue solid lines, equilibrium curve and tie lines calculated with UNIQUAC; red dashed lines, calculated with NRTL.

Figure 4. Liquid−liquid equilibrium for soybean oil (1)−glycerol (2)− methanol (3) at 46.2 °C. Composition in mass fractions. Empty symbols, experimental data; blue solid lines, tie lines calculated with UNIQUAC; red dashed lines, calculated with NRTL.

Table 3. UNIQUAC Parameters (Uij) Estimated for the System Soybean Oil (1)−FAMEs (2)−Methanol (3)− Glycerol (4) Uij

soybean oil (1)

FAMEs (2)

methanol (3)

glycerol (4)

soybean oil (1) FAMEs (2) methanol (3) glycerol (4)

0 585.00 13.49 544.44

−331.21 0 −56.06 83.94

520.74 579.24 0 65.03

69.75 315.25 28.00 0

fractions) and they are also collected in Tables S5−S8 of the Supporting Information (in molar fractions) at each temperature. Figure 1 shows the LLE for the methanol (1)−FAMEs (2)−soybean oil (3) mixture. As can be observed, the presence of FAMEs increased the solubility of methanol in the oil phase, while the equilibrium content of soybean oil remained low in the methanol phase. These data add to the limited literature information for this mixture, which is crucial for understanding the behavior in the initial stage of the methanolysis reaction.6,17 This could contribute to an enhanced design of the agitation− mixing system in biodiesel industrial production. LLE of the FAMEs (1)−methanol (2)−glycerol (3) mixture is shown in Figure 2. In this case, the substitution of soybean oil by glycerol led to a system with a higher biphasic region. It is well-known that the low solubility of glycerol in the FAME phase represents an advantage in the production of biodiesel through triglyceride methanolysis. The glycerol byproduct formed in this reaction is released from the FAME phase and the reaction equilibrium is shifted toward product formation. This situation is less favored when the methanol to oil ratio is high, because the glycerol solubility in the FAME phase increases. For this reason, methanol to oil ratios higher than 6 are not usually used in the industrial production of biodiesel. As commented before, glycerol is hardly miscible in soybean oil and FAMEs; thus, the glycerol (1)−soybean oil (2)− FAMEs (3) data plot in Figure 3 represents a practically immiscible system for almost the whole concentration range. The same situation was found for mixtures of soybean oil (1),

Figure 3. Liquid−liquid equilibrium for glycerol (1)−soybean oil (2)− FAMEs (3) at 46.2 °C. Composition in mass fractions. Empty symbols, experimental data; blue solid lines, tie lines calculated with UNIQUAC; red dashed lines, calculated with NRTL.

were only slightly higher (0.25 and 0.33 wt % at 25 and 45 °C, respectively).15 These experimental data from binary mixtures were used to obtain a first approximation of their binary interaction coefficients in the UNIQUAC and NRTL models. Rootmean-square deviations (RMSD) between calculated and experimental values in these binary mixtures are shown in Table 2. The results showed that UNIQUAC and NRTL accurately fitted the data from soybean oil and FAMEs with glycerol. However, only the UNIQUAC model achieved an acceptable fit for the experimental data in the soybean oil− methanol mixture. The UNIQUAC method has also shown an adequate fit of LLE data for these mixtures in previous publications.15−17 The next step of this work was to evaluate the LLE of all the possible ternary mixtures in the soybean oil−FAMEs− methanol−glycerol system. LLE experimental data for these ternary mixtures are represented in Figures 1 −4 (in mass 3734

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Table 4. Experimental (exp) and Calculated (calc) Equilibrium Compositions (wt %) soybean oil phase T (°C) 23 45.7 65.7 a

methanol phase

data

oil

FAMEs

methanol

glycerol

oil

FAMEs

methanol

glycerol

exp calca exp calca exp calca

49.14 47.46 47.82 48.25 47.97 45.75

45.34 46.20 44.14 44.75 44.24 45.26

5.30 6.29 7.47 6.93 7.40 8.89

0.22 0.04 0.57 0.07 0.39 0.11

0.63 0.01 0.13 0.01 0.04 0.01

2.67 0.82 1.86 0.65 2.37 1.18

67.25 66.92 58.93 60.10 58.32 62.22

29.45 32.26 39.08 39.24 39.27 36.59

LLE data were calculated using the UNIQUAC model and parameters from Table 3.

Table 5. Experimental (exp) and Calculated (calc) Compositions (wt %) after Soybean Oil Methanolysisa soybean oil phase

methanol phase

data

oil

FAMEs

methanol

glycerol

diglycerides

monoglycerides

oil

FAMEs

methanol

glycerol

diglycerides

monoglycerides

expb calcc

69.5 72.0

12.0 10.09

6.6 6.8

0.1 0.01

11.5 10.9

0.3 0.2

0.1 0.2

0.8 0.7

84.2 81.5

1.7 1.6

8.7 10.5

4.5 5.5

Reaction conditions: T = 25 °C; Methanol:oil molar ratio = 6:1; Catalyst (CH3OK):oil molar ratio = 0.2:1; N = 100 rpm; time =240 min. Experimental content values were normalized excluding catalyst concentration. cLLE data were calculated using the UNIQUAC model and parameters from Table 3 and Table S10 (Supporting Information). a b

reaction. In this case, the diglycerides and monoglycerides are distributed between the oil phase and the methanol phase. These compounds possess fatty acid chains and OH groups that favor the solubility in both phases. In a recent study,28 contents higher than 10 wt % of these compounds were also found after low-conversion palm oil methanolysis. UNIQUAC calculated values were similar to the experimental ones, thus proving the validity of the model and parameters estimated in this work. Future studies focusing on the effect of the concentration of catalyst (in each phase) on the activity coefficients would be convenient to have a thorough knowledge of the phase equilibrium during the reaction.

glycerol (2), and methanol (3), the ternary diagram of which is shown in Figure 4. Each ternary mixture was used to calculate initial values of the binary coefficients (Uij or Aij) for the UNIQUAC and NRTL models (starting with estimations from binary mixtures). RMSD values (from Table 2) reveal a proper fit for both models except for the soybean oil (1)−FAMEs (2)−methanol (3) system with NRTL. Having estimated the initial values of all binary coefficients, these were re-estimated taking into account all the experimental data (binary and ternary mixtures) simultaneously. The final estimated values for UNIQUAC and NRTL are collected in Tables 3 and S9 (Supporting Information), respectively. The RMSD value for this overall estimation was much lower for the UNIQUAC model than for the NRTL one. Moreover, comparing the LLE calculated with experimental values (Figures 1−4), it can also be seen that UNIQUAC was more suitable for the LLE modeling of these four compounds, as previously observed in the literature.15−17,19,27 Next, a new set of experimental data obtained from a quaternary mixture (at three different temperatures) was evaluated to check the validity of the estimated parameters with UNIQUAC. The initial mixture chosen for this purpose was 0.5 mol of soybean oil, 4.5 mol of methanol, 0.5 mol of glycerol, and 1.5 mol of FAMEs. Results are shown in Table 4. As can be seen, UNIQUAC adequately reproduced the LLE for this quaternary mixture in the temperature range studied. Finally, the set of binary interaction coefficients (Uij) was completed, including values of mixtures with diglycerides and monoglycerides. For this purpose, these UNIQUAC binary interaction parameters were estimated using the activity coefficient data (γi) predicted by UNIFAC for binary mixtures that included these compounds. Estimated parameters are shown in Table S10 in the Supporting Information. The validity of the whole set of Uij parameters for UNIQUAC was tested by comparing calculated LLE with experimental data from the soybean oil methanolysis. Both sets of data are collected in Table 5. Experimental data corresponded to a reaction with a conversion below 15%. This low-conversion profile concentration was chosen because the reaction mixture contained significant amounts of all of the components involved in the

5. CONCLUSIONS Methanol solubility in soybean oil was much higher (5.62− 10.02 wt %) than that of this oil in methanol (0.25−0.84 wt %), whereas the solubility of soybean oil and FAMEs with glycerol was very low in the temperature range studied (25−65 °C). Ternary mixtures with soybean oil and glycerol were practically immiscible in all of the concentration ranges. Diglyceride and monoglyceride solubility in methanol was higher than that of soybean oil. The liquid−liquid equilibrium of all the compounds involved in soybean oil methanolysis was adequately determined using UNIQUAC instead of NRTL. Finally, UNIQUAC binary interaction coefficients for the mixtures with diglycerides and monoglycerides were correctly estimated with coefficient activities predicted with UNIFAC. However, further experiments should be carried out with pure diglycerides and monoglycerides to complete the estimation of UNIQUAC parameters.

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ASSOCIATED CONTENT

S Supporting Information *

Tables S1−S10 and computer codes for calculating activity coefficients for NRTL and UNIQUAC models. This material is available free of charge via the Internet at http://pubs.acs.org. 3735

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(19) Batista, E.; Monnerat, S.; Kato, K.; Stragevitch, L.; Meirelles, A. J. A. Liquid−liquid equilibrium for systems of canola oil, oleic acid, and short-chain alcohols. J. Chem. Eng. Data 1999, 44, 1360. (20) Yaginuma, R.; Moriya, S.; Yoshikazu, S.; Kodama, D.; Tanaka, H.; Kato, M. Homogenizing effect of ethers added to immiscible methanol/oil binary mixtures. Sekiyu Gakkaishi 2001, 44, 401. (21) Mohsen-Nia, M.; Dargahi, M. Liquid−liquid equilibrium for systems of (corn oil + oleic acid + methanol or ethanol) at (303.15 and 313.15) K. J. Chem. Eng. Data 2007, 52, 910. (22) Casas, A.; Ruiz, J. R.; Ramos, M. J.; Pérez, Á . Effects of triacetin on biodiesel quality. Energy Fuels 2010, 24, 4481. (23) Abrams, D. S.; Prausnitz, J. M. Statistical thermodynamics of liquid mixtures: A new expression for the excess Gibbs energy of partly or completely miscible systems. AIChE J. 1975, 21, 116. (24) Renon, H.; Prausnitz, J. M. Local compositions in thermodynamic excess functions for liquid mixtures. AIChE J. 1968, 14, 135. (25) Fredenslund, A.; Jones, R. L.; Prausnitz, J. M. Groupcontribution estimation of activity coefficients in nonideal liquid mixtures. AIChE J. 1975, 21, 1086. (26) Wittig, R.; Lohmann, J.; Gmehling, J. Vapor−liquid equilibria by UNIFAC group contribution. 6. Revision and extension. Ind. Eng. Chem. Res. 2003, 42, 183. (27) Lee, M. J.; Lo, Y. C.; Lin, H. M. Liquid−liquid equilibria for mixtures containing water, methanol, fatty acid methyl esters, and glycerol. Fluid Phase Equilib. 2010, 299, 180. (28) Oh, P. P.; Chong, M. F.; Lau, H. L. N.; Chen, J.; Choo, Y. M. Liquid−liquid equilibrium (LLE) study for six-component transesterification system. Clean Technol. Environ. Policy 2013, 15, 817.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone:+34 91 4888531. Fax: +34 91 4887068. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

Financial support from REPSOL, S.A. is gratefully acknowledged.

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dx.doi.org/10.1021/ie403927c | Ind. Eng. Chem. Res. 2014, 53, 3731−3736