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Measurements of Liquid-Liquid Equilibria for a Methanol + Glycerol + Methyl Oleate System and Prediction Using Group Contribution Statistical Associating Fluid Theory A. Barreau,† I. Brunella,† J.-C. de Hemptinne,*,† V. Coupard,‡ X. Canet,§ and F. Rivollet§ IFP, 1-4 aVenue de Bois Pre´au, 92852 Rueil-Malmaison Cedex, France, IFP-Lyon, Rond-Point de l’e´changeur de Solaize, BP 3, 69360 Solaize, France, and Processium, 62 bouleVard Niels Bohr, BP 2132, 69603 Villeurbanne Cedex, France
A good understanding and prediction of the phase equilibrium of the fatty acid methyl ester (FAME) + glycerol + methanol ternary system is needed to design and optimize the separation unit of the biodiesel production process. In this work, new experimental vapor-liquid-liquid data on the ternary system have been measured at temperatures between 333.15 and 473.15 K. In addition, new data have been gathered on the methanol + glycerol [vapor-liquid equilibrium (VLE)] and methanol + methyl oleate (VLE and liquid-liquid equilibrium) binary systems. A group contribution method combined with a statistical associating fluid theory equation of state (GC-PPC-SAFT) proposed earlier by our group (Tamouza, S.; Passarello, J.-P.; Tobaly, P.; de Hemptinne, J.-C. Group contribution method with SAFT EOS applied to vapor liquid equilibria of various hydrocarbons series. Fluid Phase Equilib. 2004, 222-223, 67-76) and recently extended to predict VLE of heavy esters and their mixtures (Nguyen Huynh, D.; Falaix, A.; Passarello, J.-P.; Tobaly, P.; de Hemptinne, J.-C. Predicting VLE of heavy esters and their mixtures using GC-SAFT. Fluid Phase Equilib. 2008, 264, 184-200) is here applied to model vapor liquid-liquid equilibria of methanol + glycerol + methyl oleate. The SAFT parameters for the glycerol pure component have been regressed using two association schemes (4C and 3X2B). The dispersive binary interaction parameters kij have been regressed on the binary systems. The group contribution scheme was used for predicting the ester properties. 1. Introduction Biodiesel is produced by transesterification of triglycerides (TGs) from vegetable oils with an excess of methanol following the reaction: catalyst
TG + 3 methanol 798 3 fatty acid methyl ester + glycerol At the end of the reaction, there are two separate liquid phases, one rich in glycerol and the other rich in fatty acid ester. The simulation of the process requires the knowledge of the liquid-liquid equilibrium (LLE) of the ternary system fatty acid methyl ester (FAME) + glycerol + methanol in a large temperature domain. It is assumed at this stage that the small concentration of TGs that are left after reaction has no effect on the liquid-liquid separation. Data are needed to develop and/or validate any thermodynamic model. In the existing literature, a number of experimental work can be found on the FAME + glycerol + methanol mixture.3,4 Yet, in these cases, the considered esters are in fact mixtures of molecules with varying molecular masses. In this work, the purpose is to understand the phase equilibrium behavior in the presence of an ester that is representative of the industrial mix. The methyl oleate ester was chosen for this purpose [CH3(CH2)7CHdCH(CH2)7COOCH3]. Only two references have been found providing LLE data for the methyl oleate + methanol + glycerol mixture. Negi et al.5 have investigated the phase equilibria of this ternary system at 333.15 K, and * To whom correspondence should be addressed. Tel: +33 1 47 52 71 28. Fax: +33 1 47 52 70 25. E-mail:
[email protected]. † IFP. ‡ IFP-Lyon. § Processium.
Andreatta et al.6 have investigated the phase equilibria at 333.15 and 393.15 K. In this work, the experimental data range has been enlarged by performing both binary and ternary phase equilibrium measurements: The vapor-liquid equilibrium (VLE) has been measured for the glycerol + methanol and the methyl oleate + methanol systems (bubble temperatures) and LLE for the binary methanol + methyl oleate as well as for the ternary methanol + methyl oleate + glycerol systems have been conducted for temperatures from 333.15 to 473.15 K. Considering the lack of experimental data, most thermodynamic models that have been applied to the system of interest are based on group contributions. Negi et al.5 have investigated the UNIFAC and UNIFAC-Dortmund approaches. Although, according to their conclusion, the UNIFAC-Dortmund7 provides the best results, the model was not found to be adequate for representing this liquid-liquid phase split. Observing that the nonideality of this system is essentially due to the molecular associations, Andreatta et al.6,8 have investigated it using both the associating UNIFAC model9 and the GCA Equation of State (EoS).10 Considering that the three glycerol OH groups behave quite differently from the alcohol group, they have determined new parameters for the alcohol-glycerol interactions. Doing so, they obtained very good results for the methanol partitioning between the two liquid phases. Recently, Oliveira et al.11,12 have used the cubic-plusassociation EoS to describe this system. Evaluating several association schemes for the glycerol and several combining rules for glycerol-methanol cross-association, they conclude that glycerol should be described as a 3X2B association scheme (i.e., one electron donor and one electron acceptor site on each hydroxyl group). Their results are encouraging, although their
10.1021/ie901379x 2010 American Chemical Society Published on Web 05/13/2010
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Table 1. Bubble Point Temperature for the Methanol (1)-Glycerol (2) Binary System T (K) X(1)
P ) 30.0 kPa
P ) 50.0 kPa
P ) 70.0 kPa
P ) 90.0 kPa
P ) 101.3 kPa
0.3147 0.4640 0.5896 0.6061 0.7132 0.7512 0.8499 0.9505
330.2 321.2
344.6 333.4 329.1 329.0 326.6 325.3 322.4 321.3
354.2 342.3 337.9 337.3 334.7 333.5 330.4 329.2
362.7 349.3 344.9 344.2 341.2 339.9 336.7 335.3
366.0 352.8 347.9 347.6 344.3 343.1 339.9 338.4
317.1 315.0 313.8 311.0 310.1
Table 2. Bubble Point Temperature for the Methanol (1)-Methyl Oleate (2) Binary System T (K) X(1)
P ) 30.0 kPa
P ) 50.0 kPa
P ) 70.0 kPa
P ) 90.0 kPa
P ) 101.3 kPa
0.3582 0.4996 0.7497 0.8997
315.93 312.17 310.11 309.97
328.19 324.22 321.47 321.17
336.99 332.71 329.50 329.07
345.80 339.39 335.82 335.26
352.56 342.82 338.91 338.28
Figure 1. Ternary diagrams for methanol-glycerol-methyl oleate at (a) 333.15, (b) 403.15, and (c) 473.15 K. Black circle, experimental; gray circle, ref 6; and white circle, ref 5.
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glycerol and methanol + methyl oleate were performed in an ebulliometer, which was described in a previous paper.18 2.2.2. LLE Measurements at Atmospheric Pressure. The liquid-liquid phase diagram boundary of the methanol + methyl oleate binary system was determined by turbidimetric analysis. At ambient temperature, methanol and methyl oleate are completely miscible. The mixtures were prepared by weighing and were introduced in the equilibrium cell. The cell was made of glass so that the liquid-liquid phase split could be observed visually. A thermostatic liquid was circulated through the jacket of the equilibrium cell to control its temperature to within (0.1 K. The equilibrium temperature was measured using a Hart Scientific model 1502A digital thermometer with a calibrated Pt 100Ω probe. A magnetic stirrer vigorously agitated the liquid mixture in the cell. The temperature was decreased very slowly until the cell content changed from transparent to turbid, indicating phase split. 2.2.3. VLLE Measurements. The liquid-liquid phase diagrams of the ternary mixture were determined using a static analytic technique, always in the presence of a vapor phase (i.e., at the system bubble pressure).19,20 The set up consisted of an equilibrium cell, which was composed of a sapphire tube pressed between two titanium pieces. The sealing was ensured by polymer O-rings. The inside volume was 15 mL. The pressure was measured by means of a pressure transducer with a hastelloy membrane connected to an Agilent switch data acquisition unit. The pressure transducer was maintained at constant temperature (higher than the highest temperature of the study). The uncertainty was estimated to (0.05 bar. The temperature of the equilibrium cell was regulated by means of an air convection oven. Two platinum resistance thermometers (Pt 100 Ω), previously calibrated using a Hart Scientific model 1502A digital thermometer with a Pt 100Ω probe, were inserted inside wells drilled in both top and bottom flanges of the equilibrium cell. They were also connected to the Agilent switch data acquisition unit. The uncertainty was estimated to be less than 0.02 °C. The cell was kept under vacuum for 1 h. The sample, whose composition was exactly known by weighing, was then introduced in the equilibrium cell through one of the two needle valves on the top flange. Equilibrium was reached by stirring the mixture for 15 min with a magnetic rod at 1500 rounds per minute at the study temperature. The mixture was then left for
Table 3. Liquid-Liquid Demixtion Temperature for the Methanol (1)-Methyl Oleate (2) Binary System x (methanol)
temperature (K)
0.9003 0.8514 0.7986 0.7506 0.693 0.6501 0.6178 0.5504 0.9497 0.965 0.9807
285.48 283.1 280.0 276.0 271.6 267.5 265.0 260.6 283.6 280.55 269.5
approach is more correlative than predictive (the methyl oleate parameters have been fitted13). In this work, we chose to test the group contribution method associated with the Perturbed chain-statistical associating fluid theory (SAFT) EoS (GC-PC-SAFT) developed by Tamouza et al.,1,14,15 as it is particularly well-adapted to predict phase equilibria in the presence of long molecules like the fatty acid esters. Nguyen Thi et al.16 and subsequently Nguyen Huynh et al.2,17 have improved GC-PC-SAFT EoS to predict the properties of mixtures containing heavy esters by adding a polar contribution, thus making a GC-PPC-SAFT EoS (the additional P stands for polar). This equation is here extended to predict the liquidliquid-vapor equilibrium of the ternary system methyl oleate + glycerol + methanol. The group contribution scheme is used for predicting the methyl oleate parameters. The glycerol and methanol parameters are determined individually. 2. Experimental Section 2.1. Materials. CHROMASOLV for high-performance liquid chromatography grade methanol (purity >99.9%, Sigma-Aldrich), technical grade methyl oleate (purity >70%, Aldrich), and normapur glycerol (VWR) was used without further purification. Because of the high price of the higher purity ester, we decided to use a technical grade to be representative of industrial fluid. It is noteworthy that the other measurements reported in the literature use a similar grade for methyl oleate.5,6 2.2. Apparatus and Procedure. 2.2.1. VLE Measurements. The isobaric vapor-liquid measurements of methanol +
Table 4. Experimental VLLE Data of the System Methanol (1)-Glycerol (2)-Methyl Oleate (3) overall composition 100 w1
100 w2
methyl oleate-rich phase 100 w3
100 w1
13.10 21.14 30.08 39.99 44.04 48.44 49.82 50.04
46.85 39.12 29.92 20.03 14.74 10.12 2.35 5.00
40.05 39.74 40.00 39.98 41.22 41.44 47.83 44.96
3.21 5.74 8.73 13.69 17.43 25.98
5.10 12.94 21.17 29.96 39.99 45.01 48.17
55.00 46.93 39.06 30.12 19.95 14.90 9.99
39.90 40.13 39.77 39.92 40.06 40.09 41.84
2.30 5.27 9.63 13.51 33.61
5.04 13.14 21.12 29.90
54.50 46.94 39.07 30.16
40.46 39.92 39.81 39.94
3.37 8.55 14.25
100 w2
glycerol-rich phase
100 w3
100 w1
100 w
T (K) ) 333.15 0.19 96.60 0.26 94.00 0.45 90.82 0.90 85.41 1.08 81.49 2.15 71.87
100 w3
P (MPa)
21.07 32.92 47.26 61.75 67.45 70.26
73.81 64.14 49.41 32.51 24.54 15.95
5.12 2.94 3.33 5.74 8.01 13.79
0.06 0.06 0.06 0.07 0.08 0.08 0.07 0.08
90.42 78.95 66.24 52.15 29.30
1.67 1.59 2.79 4.24 18.77
0.28 0.44 0.57 0.64 0.75
1.44 2.81 4.99
0.87 1.74 2.19 2.66
2
homogeneous liquid phase T (K) ) 403.15 0.68 97.02 1.04 93.69 2.10 88.27 1.92 84.57 11.18 55.21
7.91 19.46 30.97 43.61 51.93
homogeneous liquid phase T (K) ) 473.15 2.11 94.52 6.27 3.56 87.89 16.81 5.45 80.30 28.16 homogeneous liquid phase
92.29 80.38 66.85
Ind. Eng. Chem. Res., Vol. 49, No. 12, 2010 Table 5. Parameters for the PPC-SAFT Model, Including AADs on the Data Used methyl oleatea glycerol 4Cb glycerol 3X2Bb methanolc ε/k (K) σ (Å) m µ (D) xpµ m εAB/k (K) κAB AAD % virial coefficient vapor pressure liquid volume
259.51 3.8459 8.1407 1.8091 1.15 1355.78 0.0136
294.38 2.891 4.597 2.68 0.0049 1481.38 0.1485
261.34 2.5766 6.2025 2.68 0.043 501.87 0.602
199.8 2.6321 2.8271 1.7 0.35 2069.09 0.2373
15.7 3.7
14.6 1.45 2.64
16.5 1.16 0.8
1.38 2.58
a The methyl oleate parameters are calculated using the group contribution method. The AADs are therefore predicted. b The glycerol parameters have been fitted in this work. c The methanol parameters are taken from Mourah et al.28 Deviations are calculated based on the DIPPR correlation.
17 h to settle. Finally, two samples of each liquid phase were taken, diluted in ethanol, and analyzed by gas chromatography using a flame ionization detector. 2.3. Experimental Results. 2.3.1. Methanol + Glycerol. Bubble temperatures for the methanol + glycerol binary system were measured along five isobars: 30.00, 50.00, 70.00, 90.00, and 101.33 kPa. The results are presented in Table 1. 2.3.2. Methanol + Methyl Oleate. Bubble temperatures for the methanol + methyl oleate binary system were measured along five isobars: 30.00, 50.00, 70.00, 90.00, and 101.33 kPa. The results are presented in Table 2. The liquid-liquid phase boundary of this mixture at atmospheric pressure was determined between 283.5 and 260.6 K. The results are presented in Table 3. 2.3.3. Methanol + Glycerol + Methyl Oleate. The liquidliquid tie lines were measured at 333.15, 403.15, and 473.15 K. For each global composition, the glycerol phase and the fatty phase compositions at the equilibrium are reported. The equilibrium (bubble) pressures are also mentioned. Using the global compositions that remain in a single homogeneous liquid phase, the boundary of the liquid-liquid phase diagram can be estimated. All of the results are plotted in Figure 1. In this figure, the literature data5,6 at 333.15 K are also reported. Our experimental data are in good agreement with the data from Andreatta6 and with the data
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5
from Negi but only on the fatty phase composition. These last authors mention a negligible solubility of the ester in the glycerol, while it can in fact be measured. 3. Thermodynamic Modeling 3.1. GC-PPC-SAFT. The SAFT models have been extensively described in many papers. A number of important reviews are those of Mu¨ller and Gubbins,21 Economou,22 and Tan et al.23 The paper by de Hemptinne et al.24 summarizes the main equations and their use in the petroleum industry. It takes explicitly into account the molecular shape (as a chain of segments) and the pseudochemical bonds that may occur between electron donor or acceptor sites. In this work, we also include the specific contribution that results from the molecular polar character, which has been recommended by several authors.25-27 Nguyen Hunh et al.28 have extended the approach of Jog and Chapman25 incorporating, in the polar term, the chain character of the molecule. The basic equation is expressed as a perturbation expansion of the residual Helmholtz free energy: Ares ) Ahc + Adisp + Achain + Aassoc + Apolar
(1)
where Ahc and Adisp, respectively, account for chain and dispersive interactions, while Achain refers to the chain formation. Aassoc deals with associative interactions, and Apolar takes into account the molecular polarity as proposed by Nguyen Huynh et al.28 The GCPPC-SAFT model requires a number of pure component and binary interaction parameters, which are further discussed below. 3.2. Pure Compound Parameters. The model requires the following pure component parameters: - always at least three parameters: dispersive energy (εi), segment diameter (σi), and chain length (mi) - for polar molecules (using Apolar), its dipole moment (µi) and the fraction of dipolar segment (xp,iµ) (rather treated as a product of xp,iµmi because it is then independent of chain length) - for associating components, the association volume (κAiBi) and the association energy (εAiBi). In addition, the association scheme (number of electron donors and number of electron acceptors) must be stated. 3.2.1. Methyl Oleate. The ester molecule is described using the approach proposed by Nguyen Huynh et al.2 Segments
Figure 2. Results for the VLE of methanol + glycerol using the 3X2B and 4C association schemes for glycerol at 1 atm.
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Figure 3. Binary diagram of a methanol (1) + methyl oleate (2) mixture at 0.1013 MPa. Comparison between GC-SAFT with kij ) 0.0466 (solid lines) and experimental (b). Empty symbols are data from Oliveira.12
Figure 4. Binary LLE diagram of the methyl octadecanoate (1) + glycerol (2) mixture at 0.1013 MPa. GC-SAFT with kij ) 0.055 (solid lines) and experimental27 (b).
parameters (energy, ε; diameter, σ) and chain parameter m are calculated through the following group contribution relations:15
( ∏ )
14 CH2, 2 CHd, and 1 COO groups are given in refs 2, 15, and 17.
(4)
The dipole moment µi is calculated through the empirical relation proposed by Nguyen Huynh et al.2 The parameters of this relation as well as the fraction of dipolar segment xpµ are given in2 [µ ) µ0 - µ1(1 - 1/n) - µ2(1 - 1/n′) with n ) 17 and n′ ) 1]. The ester itself is not a self-associating molecule but with an associating molecule as methanol or glycerol, a cross-association energy εAB/k and a cross-association volume κAB must be taken into account. To keep the model as predictive as possible (avoid regressing too many parameters), Nguyen Huynh et al.17 propose that the cross-association parameters values be set to the 1-alkanols self-association parameters values.
where nk is the number of groups k in the molecule i made of ngroups different groups. The εk, σk, and Rk values for the 2 CH3,
All of the parameters values for methyl oleate are given in Table 5. The results of the vapor pressure and liquid volume predictions are compared with the accepted experimental values
ngroups
ngroups
εi )
∑ k)1
ni
nk
εk
(2)
k)1
ngroups
∑nσ
k k
σi )
k)1 ngroups
(3)
∑n
k
k)1
ngroups
mi )
∑nR k
k
k)1
Ind. Eng. Chem. Res., Vol. 49, No. 12, 2010 Table 6. PPC-SAFT kij Values binary system
kij
methanol + methyl oleate methanol + glycerol glycerol + methyl oleate
0.0466 -0.020 0.055
taken from DIPPR29 and the absolute average deviations (AADs) are provided in the same table. 3.2.2. Methanol. Mourah et al.30 have shown that the 2B association scheme (one electron donor and one electron acceptor) for methanol gave better results on the computed VLE and LLE of the methanol + n-alkane binary systems. The authors have regressed all of the PPC-SAFT parameters (energy, εi; diameter, σi; chain parameter, mi; the association parameters, κAiBi and εAiBi; and the fraction of dipolar segment, xp,iµ; the dipole moment, µi, was fixed to its experimental value). All of the values are reported in Table 5. 3.2.3. Glycerol. For glycerol, the usual approach6,8,11,12 is to consider that each of the three hydroxyl groups contains an electron
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donor and an electron acceptor site, leading to the so-called 3X2B association scheme. Yet, there is some evidence from both spectroscopy and ab initio calculations31 that intramolecular OH-OH interactions in fact deactivate a number of these potential association sites. This would lead to a 4C association scheme (2X2B) with only 2 OH groups forming hydrogen bonds. The PPCSAFT parameters (energy, εi; diameter, σi; chain parameter, mi; the association parameters, κAiBi and εAiBi; and the fraction of dipolar segment, xp,iµ) have been regressed, using these two different association schemes by a regression of vapor pressure, saturated liquid density, and second virial coefficient data from the DIPPR database.29 The experimental dipole moment was taken from DIPPR. Global average deviations are, respectively, 1.4, 0.9, and 23.0% with the 3X2B association scheme and 1.9, 2.8, and 23.6% with the 4C association scheme. The parameter values are reported in Table 5. 3.3. Correlation of the Binary Systems. For extending the GC-PPC-SAFT to mixtures, the van der Waals one-fluid model and modified Lorentz-Berthelot mixing rules are used.
Figure 5. Comparison between GC-PPC-SAFT predicted (solid) and experimental (dashed) tie lines of the ternary system methanol-glycerol-methyl oleate in mass percent at (a) 333.15, (b) 403.15, and (c) 473.15 K.
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εij ) (1 - kij)√εii εjj σij )
(
σii + σjj 2
)
(5) (6)
The combining rules used for the cross-association energy εAiBj and the cross-association volume κAiBj are the following (CR1), as recommended by Derawi et al.:32 εAiBj )
εAiBi + εAjBj AiBj , κ ) √κAiBiκAjBj 2
(7)
3.3.1. Glycerol + Methanol. The 3X2B association scheme to calculate the pure component properties of glycerol seems better than the 4C association scheme. Yet, as shown in Figure 2, the 4C association scheme yields a better VLE description of the glycerol + methanol binary system without kij. This is why we continued with the 4C association scheme and the kij were regressed on the data presented in Table 1. 3.3.2. Methanol + Methyl Oleate. The kij parameter was regressed on the VLE data of Table 2. Figure 3 shows that the use of this same parameter provides a prediction of a liquid-liquid phase split in the same range of temperature and compositions as experimentally observed. With kij ) 0, no liquid-liquid phase split is observed at all. The data are also compared with the recently published data of Oliveira et al.,33 with very good results. 3.3.3. Glycerol + Methyl Oleate. VLE or LLE data are not available in the literature for this binary system, but Korgitzsh34 has investigated LLE of the glycerol + n-alkyl-methyl-ester (RCOOCH3) with R ) 6, 8, 10, 12, and 18 carbon atoms. For methyl oleate, R also has 18 carbon atoms with two double bonds. So, kij was regressed on the LLE experimental data of the glycerol + methyl octadecanoate (Figure 4) and applied for the glycerol + methyl oleate binary system. Here again, using kij = 0, no liquid-liquid phase split is observed. The methyl octadecanoate PPC-SAFT parameters were calculated using the same group contribution scheme. Unfortunately, only data for the ester rich phase have been found. 3.4. Prediction of the LLE Ternary System. The GC-PPCSAFT was used to predict the LLE of the methanol + glycerol + methyl oleate ternary system with the kij regressed on the binary system and is summarized in Tables 5 and 6. The LLE calculated with GC-PPC-SAFT are plotted in Figure 5 and compared with our experimental data. Presented in weight percent, the comparison between calculated and experimental values is much more severe than if presented in mole percent (Figure 6). Using the molar scale, the experimental or calculated diagram boundaries are very close to the axes; while using the mass scale, we can better appreciate the difference between calculated and experimental values. Figure 5 shows that the methanol + glycerol + methyl oleate ternary diagram is well-predicted with GC-PPC-SAFT in a very large temperature domain. Nevertheless, we can notice that the ester solubility in the glycerol phase is underestimated and that the calculated liquid-liquid diagram is larger than the experimental diagram. It must be stressed that in determining binary parameters between ester and glycerol, only solubility data in the ester-rich phase have been used (no binary solubility data of glycerol in ester have been found). As a result, it cannot be expected that the glycerol phase be predicted with great accuracy.
Figure 6. Comparison between GC-PPC-SAFT predicted (solid) and experimental(dashed)tielinesoftheternarysystemmethanol-glycerol-methyl oleate at 333.15 K plotted in mole percent.
4. Conclusion New experimental VLE data of glycerol + methanol and methanol + methyl oleate systems were performed, and the liquid-liquid diagram of the methanol + glycerol + methyl oleate ternary system was described in a large temperature domain from 333.15 to 473.15 K. A group contribution method was used to calculate the PPCSAFT parameters of the methyl oleate. Glycerol was represented with a 4C association scheme, and the SAFT parameters were regressed. Binary kij on the methanol + glycerol, methanol + methyl oleate, and glycerol + methyl oleate binary systems were defined. Thus, we have shown that the GC-PPC-SAFT model so defined was able to predict with good quality the liquid-liquid diagram of the methanol + glycerol + methyl oleate ternary system. This result is encouraging for further work on the description of the LLE of the FAME + glycerol + methanol systems present in biodiesel production. Literature Cited (1) Tamouza, S.; Passarello, J.-P.; Tobaly, P.; de Hemptinne, J.-C. Group contribution method with SAFT EOS applied to vapor liquid equilibria of various hydrocarbons series. Fluid Phase Equilib. 2004, 222-223, 67–76. (2) Nguyen Huynh, D.; Falaix, A.; Passarello, J.-P.; Tobaly, P.; de Hemptinne, J.-C. Predicting VLE of heavy esters and their mixtures using GC-SAFT. Fluid Phase Equilib. 2008, 264, 184–200. (3) Zhou, H.; Lu, H.; Liang, B. Solubility of multicomponent systems in the biodiesel production by transesterification of Jatropha curcas L. oil with methanol. J. Chem. Eng. Data 2006, 51, 1130–1135. (4) Di Felize, R.; De Faveri, D.; De Andreis, P.; Ottonello, P. Component distribution between light and heavy phases in biodiesel processes. Ind. Eng. Chem. Res. 2008, 47, 7862–7867. (5) Negi, D. S.; Sobotka, F.; Kimmel, T.; Wozny, G.; Schoma¨cker, R. Liquid-liquid phase equilibrium in glycerol-methanol-methyl oleate and glycerol-monoolein-methyl oleate ternary systems. Ind. Eng. Chem. Res. 2006, 45, 3693–3696. (6) Andreatta, A. E.; Casa, L. M.; Hegel, P.; Bottini, S. B.; Brignole, E. A. Phase equilibria in ternary mixtures of methyl oleate, glycerol, and methanol. Ind. Eng. Chem. Res. 2008, 47, 5157–5164. (7) Weidlich, U.; Gmehling, J. A modified UNIFAC model. 1. Prediction of VLE, hE, and γ∞. Ind. Eng. Chem. Res. 1987, 26, 1372–1381. (8) Andreatta, A. E.; Lugo, R.; de Hemptinne, J.-C.; Brignole, E. A.; Bottini, S. B. Phase equilibria modeling of biodiesel related mixtures using the GCA-EoS model. Fluid Phase Equilib. 2010, in press.
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ReceiVed for reView September 2, 2009 ReVised manuscript receiVed April 23, 2010 Accepted April 28, 2010 IE901379X
