(Liquid + liquid) equilibrium of systems involved in the stepwise ethanolysis of vegetable oils

J. Chem. Thermodynamics 89 (2015) 148–158

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(Liquid + liquid) equilibrium of systems involved in the stepwise ethanolysis of vegetable oils Larissa C.B.A. Bessa, Marcela C. Ferreira, Simone Shiozawa, Eduardo A.C. Batista, Antonio J.A. Meirelles ⇑ Laboratory of Extraction, Applied Thermodynamics and Equilibrium, Department of Food Engineering, Faculty of Food Engineering, University of Campinas, Campinas, São Paulo 13083-862, Brazil

a r t i c l e

i n f o

Article history: Received 10 February 2015 Received in revised form 29 April 2015 Accepted 30 April 2015 Available online 21 May 2015 Keywords: (Liquid + liquid) equilibrium Monoacylglycerol Diacylglycerol Biodiesel Ethanol Modelling

a b s t r a c t Current concerns about adverse impacts to the environment and human health have encouraged the research and development of renewable fuels, such as biodiesel. The transesterification reaction is a three-stage reaction, which produces two intermediate products (diacylglycerols and monoacylglycerols). Accurate and proper knowledge of the phase equilibrium behaviour during the transesterification process is crucial for a better understanding of the reaction pathway, for the optimisation of reactors and the separation of the products. Thus, in order to thoroughly understand the entire transesterification system for biodiesel production, which consists of six different kinds of components, this study reports experimental results and the thermodynamic modelling of the (liquid + liquid) equilibrium (LLE) of two systems composed by {vegetable oils (sunflower or high oleic sunflower oils) + monoacylglycerols + diacylglycerols (+ethyl esters + fatty acids) + ethanol} at T = (303.15 and 318.15) K, at atmospheric pressure. The LLE experimental values were used to estimate NRTL parameters and to evaluate the UNIFAC model, using its original version with two different set of parameters. Results showed that, due to differences in the number of polar groups, mono- and diacylglycerols behave in opposite ways regarding phase distribution. Experimental data were well correlated using NRTL, in which the maximum deviation value was 0.434%. As for UNIFAC, the model predicted the experimental data with deviations varying within the range of (1.80 to 9.24)%. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Due to environmental adversities and the global concern about the conservation of non-renewable natural resources, combined with the growing sensitivity to the global warming, a search for environmentally friendly renewable energy sources, such as biodiesel, has gained recent significant attention [1]. Biodiesel, defined as mono-alkyl esters of fatty acids from vegetable oils or animal fats, is an environmentally attractive alternative to conventional petroleum diesel fuel. It presents many important technical advantages over petroleum diesel, including low toxicity, derivation from renewable feedstock, superior biodegradability, negligible sulfur content, higher flash point and lower exhaust emissions [2]. The process used most often for the biodiesel production is the transesterification (alcoholysis), a reaction between triacylglycerols (TAG) found in oils and fats and an alcohol in the presence ⇑ Corresponding author. Tel.: +55 19 3521 4037; fax: +55 19 3521 4027. E-mail addresses: [email protected] (L.C.B.A. Bessa), marcela.cravo@ gmail.com (M.C. Ferreira), [email protected] (S. Shiozawa), eacbat@fea. unicamp.br (E.A.C. Batista), [email protected] (A.J.A. Meirelles). http://dx.doi.org/10.1016/j.jct.2015.04.036 0021-9614/Ó 2015 Elsevier Ltd. All rights reserved.

of a catalyst (such as a base, an acid or an enzyme). Methanol is the most often used alcohol in biodiesel synthesis because of its suitable physical and chemical properties and low cost [3]. However, the advantages of using ethanol in biodiesel production include higher miscibility with vegetable oils that allows better contact in the reaction step and lower toxicity [4]. Transesterification produces methyl or ethyl esters, according to the selected alcohol. The reaction typically follows three steps, as shown in figure 1, where each fatty acid is sequentially taken out and converted to a molecule of fatty acid alkyl ester (biodiesel). The reaction (1) converts triacylglycerol (TAG) plus alcohol into diacylglycerol (DAG) plus a fatty acid alkyl ester. Subsequently, the reaction (2) generates monoacylglycerol (MAG) and another fatty acid alkyl ester. Finally, reaction (3) generates glycerol and a third fatty acid alkyl ester. Thus, complete conversion of one mole of TAG generates three moles of biodiesel [5]. This reaction is essentially biphasic from the beginning to the end under the reaction conditions usually employed in the industrial process [6]. Unconverted triacylglycerols, diacylglycerols, monoacylglycerols, glycerol, water and other undesirable components could

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(1)

O

H2C

O

C O

R1

HC

O

C O

R2

H2C

O

C

R3

TAG

O R

OH

R

O

C

H2C

O

C O

R1

HC

O

C

R2

R3

H2C

Alcohol

Ester

OH

DAG

O

(2)

H2C

O

C O

R1

HC

O

C

R2

H2C

(3)

HC H2C

R

OH

R

O

C

R1

OH

OH O

HC H2C

DAG

H2C

H2C

O

Alcohol

Ester

C

R2

R

OH

R

O

C

R2

OH MAG

Alcohol

O

O C

R2

OH MAG

O

O

OH

Ester

H2C

OH

HC

OH

H2C

OH

Glycerol

FIGURE 1. Generalized scheme of the transesterification steps for the production of biodiesel from triacylglycerols.

cause significant engine damages and their loss of power. Therefore, high conversion and purification steps are of utmost importance for biodiesel production [7]. Some of the drawbacks of the industrial ethylic biodiesel production are associated with the lack of knowledge of the phase compositions during the reaction process. Thus, the measurement and modelling of equilibrium data, including the equilibrium involved in the steps of oil extraction, de-acidification, transesterification reaction and purification of the biodiesel, should be carried out in order to properly optimise operating conditions for economical and efficient ethylic biodiesel purification and alcohol recuperation processes. (Liquid + liquid) equilibrium involving alkyl esters, methanol, ethanol and glycerol systems, which correspond to the end of the transesterification reaction, have been extensively published in the literature in recent years [8–14], as well as the equilibrium involving vegetable oils, fatty acid and ethanol, which represents the initial stage of the reaction. [15–18]. However, phase equilibrium data taking into account the presence of partial acylglycerols are limited. Voll et al. [19] determined (liquid + liquid) equilibrium of hydrolysed palm oil, containing tri-, di- and monoacylglycerols and free fatty acids in its composition, with water and ethanol, in order to enrich the palm oil diacylglycerol content by (liquid + liquid) extraction. Oh et al. [20] and Casas et al. [6] discussed the (liquid + liquid) equilibrium results for the system triacylglycerol, fatty acid methyl esters, methanol, glycerol, diacylglycerol and monoacylglycerol involved in the methanolysis of crude palm oil and soybean oil, respectively. Even though, phase equilibrium data involving both partial acylglycerols and ethyl esters, required for some of the reactive and purification steps of the ethylic biodiesel production, are still scarce. In this context, the main objective of this study was to enhance the experimental data bank by providing information on the (liquid + liquid) equilibrium (LLE) related to systems that could be involved in biodiesel production and its purification processes, with special emphasis on phase equilibrium associated with the transesterification and esterification reactions. Thus, LLE values were determined using two different vegetable oils (sunflower and high oleic sunflower oils), two kinds of commercial mixtures of mono- and diacylglycerols from different sources (soybean and cottonseed oils) and two different ethyl esters (oleate and linoleate), so that each system consists of derivatives of different major fatty acid (oleic or linoleic). High oleic sunflower oil is derived from a high-oleic variety of the sunflower plant. It has an exceptional

oxidative stability due to the reduction in linoleic acid content [21]. The experimental results include the following kinds of systems: (vegetable oil + diacylglycerols + monoacylglycerols + ethanol), (vegetable oil + diacylglycerols + monoacylglycerols + ethyl ester + ethanol) and (vegetable oil + diacylglycerols + monoacylglycerols + fatty acid + ethyl ester + ethanol), so that the LLE was measured for multicomponent systems. In addition, these experimental values were used to adjust all binary interaction parameters of the NRTL model and to evaluate two different sets of parameters of the UNIFAC original model.

2. Experimental 2.1. Material The suppliers and the mass fraction purity of the solvents and fatty compounds used in this work are listed in table 1; none of them was subjected to further purification.

TABLE 1 Reagents and fatty compounds used in this work, its suppliers and mass fraction purity. Component

Supplier

Mass fraction puritya

Ethanol Toluene HPLC grade Acetic acid Sunflower oil HOSOb Mixture Ac

Merck Sigma Aldrich Merck Cargill Cargill SGS Agriculture and Industry Ltd. SGS Agriculture and Industry Ltd. Tecnosyn Sigma Aldrich

>0.995 >0.999 >0.998 >0.999e >0.999e >0.52f

Mixture Bd Commercial ethyl oleate Commercial ethyl linoleate a b c d e f

>0.52f >0.75 >0.65

As reported by the supplier. High oleic sunflower oil. Commercial mixtures of mono- and diacylglycerols from cottonseed oil. Commercial mixtures of mono- and diacylglycerols from soybean oil. Of fatty compounds. Of monoacylglycerols.

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2.2. Experimental procedure

TABLE 3 Probable triacylglycerol compositions of the vegetable oils.a

All fatty compounds used were converted to fatty acid methyl esters as reported by Hartman and Lago [22], and analysed by gas chromatography in order to determine the fatty acid composition according to the official method Ce 1f-96 of the American Oil Chemists’ Society (AOCS) [23]. The compositions of the commercial ethyl oleate and ethyl linoleate were also determined by gas chromatography. The analysis of fatty acid composition using the aforementioned method is a simple way to characterise oils and fats because it reduces the number of their constituents to no more than 18 to 20 fatty acids. On the other hand, their TAG composition includes much more than 100 components, if it is taken into account triacylglycerols with different fatty acid connected to the glycerol residue and the corresponding different types of isomerism. A detailed experimental analysis of oils and fats, in terms of TAGs, can be carried out by liquid or gas chromatography, but the identification of the chromatographic peaks, sometimes even for major components, requires a lot of knowledge and parallel information, since the required set of pure standards is often not available, attributing a relatively high uncertainty to these analyses. Owing to this difficulty in analysing these components experimentally, the probable triacylglycerol composition of the vegetable oils was calculated using the statistical algorithm suggested by Antoniosi Filho et al. [24]. These authors compared results acquired by the proposed method with those obtained by gas chromatography for several vegetable oils and observed high correlation between the gas chromatographic data and the statistical ones. The statistical method results in a very large number of TAGs and in order to reduce the number of components, all structural isomers were added up in a set of components with x carbons and y double bonds and named according to the major TAG in this isomer set. The groups with a total TAG concentration less than 0.5 wt.% were ignored. (Liquid + liquid) equilibrium results for the systems containing {sunflower oil + mixture A (+ethyl linoleate) + ethanol} and {HOSO + mixture B (+ethyl oleate + oleic acid) + ethanol} were determined at T = (303.15 and 318.15) K, at atmospheric pressure. These values were determined using a sealed headspace glass tubes (10 mL) (Perkin Elmer). Components were weighted on an analytical balance (Precisa, model XT220A, Sweden, ±0.0001 g). The tubes were vigorously stirred using a vortex (IKA, model Genius3) for 30 min. All systems were left to rest for at least 36 h with temperature controlled in a thermostatic bath Cole Parmer, model Polystat (T/K ± 0.01). Two clear layers and a well-defined

Group x:yb

Main TAG

M/g  mol1

50:2 52:2 52:3 52:4 54:2 54:3 54:4 54:5 54:6 56:2 56:3 58:2 58:3 58:4

PPLi OOP POLi LiLiP OOS OOO OOLi LiLiO LiLiLi OOA OOGa OOBe OLiBe LiLiBe

831.35 859.41 857.39 855.38 887.46 885.45 883.43 881.41 879.40 915.51 913.50 943.57 941.55 939.54

Sunflower oil

HOSO

% molar

% mass

% molar

% mass

0.84 2.85 7.54 6.96 1.29 6.95 20.87 31.93 19.53

0.80 2.79 7.36 6.78 1.31 7.01 21.00 32.04 19.57

8.95 2.51

8.70 2.44

6.09 55.27 21.09 3.36

6.12 55.42 21.10 3.35

0.61 0.60 1.52

0.63 0.62 1.62

0.65 0.59

0.70 0.64

a

Standard uncertainties u are u(x/%) = 0.5. x:y, x = number of carbons (except carbons of glycerol) and y = number of double bonds.

b

interface were formed when the systems reached the equilibrium state, the upper layer being the alcoholic phase (AP), and the lower layer the oil-rich phase (OP). At the end of the experiment, samples of both phases were carefully collected using syringes and diluted directly with toluene to guarantee an immediate dilution of the samples and avoid further separation into two liquid phases at ambient temperature. The compounds of each phase were identified and quantified. The quantification of ethyl esters, acylglycerols and ethanol was conducted in a HPLC (High-Performance Liquid Chromatography) Shimadzu, model 20AT, equipped with a single 10.0 nm Phenogel size exclusion column (300  7.8 mm ID, 5 lm) (Phenomenex, Torrance, CA, USA), a RI detector (RID-10A), a model CTO-10AS VP column oven set at 40 °C, a model CBM-20A system controller and a LC-Solution 2.1 software for data acquisition. Elution was carried out in isocratic mode using 0.25% (v/v) acetic acid in toluene at a flow rate of 1.0 mL  min1. An auto sampler and injector were used to inject 20 lL of the sample into the HPLC system [25,26]. This methodology was also used to qualitatively analyse all fatty reagents used in this study. The quantitative determination was carried out using calibration curves (external calibration) obtained by using solutions made with the same reagents used in the equilibrium systems. The compounds were diluted with toluene in the concentration range from (0.18 to 52) mg  mL1. The values obtained were fitted by linear

TABLE 2 Fatty acid composition of fatty reagents (% mass).a

a b c

Fatty acid/ethyl ester

Symbol

Cx:yb

Dodecanoic Tetradecanoic Hexadecanoic 9-Hexadecenoic Octadecanoic cis-9-Octadecenoic cis-9,cis-12-Octadecadienoic trans-9,trans-12-Octadecadienoic All-cis-9,12,15-octadecatrienoic All-trans-9,12,15-octadecatrienoic Icosanoic cis-9-Icosenoic Docosanoic 13-Docosenoic

L M P Po S O Li Li Tc Le Le Tc A Ga B E

C12:0 C14:0 C16:0 C16:1 C18:0 C18:1 C18:2 C18:2 Tc C18:3 C18:3 Tc C20:0 C20:1 C22:0 C22:1

Sunflower oil

HOSO

Mixture A

Mixture B

Ethyl oleate

0.07 6.15 0.09 3.38 31.68 57.32

0.05 3.86 0.09 2.90 80.94 10.44

0.02 0.72 22.08 0.47 2.33 16.45 57.02

2.54 0.29 4.62

0.16

0.31

0.28 0.16 0.71

0.29 0.25 0.87

0.04 0.09 11.38 0.08 5.52 23.38 52.21 2.57 3.53 0.20 0.41 0.14 0.45

Standard uncertainties u are u(w/%) = 0.02. Cx:y: x is the number of carbons and y is the number of double bonds. Trans isomers.

0.24 0.28 0.21 0.05 0.13

1.84 78.08 11.93

Ethyl linoleate 0.11 7.98 0.10 2.27 12.61 76.38 0.20

0.08 0.08 0.13 0.41

0.07 0.19 0.09

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L.C.B.A. Bessa et al. / J. Chem. Thermodynamics 89 (2015) 148–158 TABLE 4 Probable tri-, di- and monoacylglycerol compositions of the commercial mixture A.a

a

Main TAG

M/g  mol1

% molar

DAG

M/g  mol1

% molar

MAG

M/g  mol1

% molar

MLiP PPP PPO PPLi MLiO LiLiM POS OOP POLi LiLiP LiLiPo OOO OOLi LiLiO LiLiLi

803.30 807.33 833.37 831.35 829.34 827.32 861.42 859.41 857.39 855.38 853.36 885.45 883.43 881.41 879.40

0.71 1.39 2.80 9.89 0.98 0.84 0.54 3.71 13.13 23.16 0.91 1.70 6.58 15.46 18.19

MP MO MLi PP PoLi PS PO PLi SO OO OLi LiLi

540.85 566.89 564.88 568.91 590.91 596.96 594.95 592.93 623.00 620.98 618.97 616.95

0.24 0.33 1.13 5.62 15.44 0.18 8.90 11.82 0.18 5.13 19.40 31.65

M P Po S O Li

302.43 330.48 328.47 358.54 356.52 354.51

0.85 16.19 7.72 0.18 19.53 55.54

Standard uncertainties u are u(x/%) = 0.5.

TABLE 5 Probable tri-, di- and monoacylglycerol compositions of the commercial mixture B.a

a

Main TAG

M/g  mol1

% molar

DAG

M/g  mol1

% molar

MAG

M/g  mol1

% molar

PPO PPLi LiLiP PLeLi POS OOP POLi OOS SOLi OOLi LiLiO LiLiLi LiLiLe

833.37 831.35 855.38 853.36 861.42 859.41 857.39 887.46 885.45 883.43 881.41 879.40 877.38

1.03 2.46 13.01 1.76 0.90 4.30 10.54 1.59 5.86 14.35 21.84 18.97 3.41

PP OS PO PLi PLe SO SLi OO OLi LiLi LiLe

568.91 596.96 594.95 592.93 590.91 623.00 620.98 620.98 618.97 616.95 614.94

1.16 0.30 7.36 14.41 0.59 3.31 1.95 6.74 29.59 31.73 2.86

P S O Li Le

330.48 358.54 356.52 354.51 352.49

12.49 2.78 26.87 56.13 1.72

Standard uncertainties u are u(x/%) = 0.5.

TABLE 6 Composition of the vegetable oils and commercial mixtures A and B (% mass).a

TABLE 7 Probable diacylglycerol compositions of the vegetable oils.a

Mass fraction

TAG DAG MAG a

Mole per cent

Sunflower oil

HOSO

Mixture A

Mixture B

DAG

M/g  mol1

Sunflower oil

99.33 0.67

99.00 1.00

6.49 32.35 61.16

5.26 34.86 59.89

PP PO PLi SO OO OLi LiLi AO OGa OBe LiBe

568.91 594.95 592.93 623.00 620.98 618.97 616.95 651.05 649.04 679.11 677.09

0.28 4.41 7.72 0.86 15.29 37.92 32.69

Standard uncertainties u are u(w/%) = 0.46.

regression and the corresponding equations were generated for quantification. To verify the quality of the results, the procedure developed by Marcilla et al. [27] and previously applied to fatty systems by Rodrigues et al. [28] was utilised. According to Marcilla et al. [27], values of global mass balance deviation less than 0.5% ensure the good quality of the experimental data. The global mass balance deviation corresponds to the difference between the sums of the calculated mass in both liquid phases and the actual value for total mass used in the experiment, divided by the total mass. 2.3. Thermodynamic modelling 2.3.1. NRTL modelling approach The experimental values determined were used to adjust all binary interaction parameters of the NRTL model. Parameters adjustments were made by considering the systems as if they were composed by a single triacylglycerol, representatives of diacylglycerol and monoacylglycerol, ethyl linoleate or ethyl oleate, ethanol

a

HOSO 6.80 0.84 4.06 68.22 17.14 1.12 0.41 0.40 1.01

0.22 0.61

Standard uncertainties u are u(x/%) = 0.5.

and oleic acid, when applied, so that the systems studied are composed by up to 6 components. The molar masses Mi of the representative tri-, di- and monoacylglycerol and ethyl esters were, respectively, determined from the molar composition of the vegetable oils, commercial mixtures of mono- and diacylglycerols and the commercial ethyl esters. The binary parameters were obtained according to the procedure developed by Stragevitch and d’Ávila [29], using the modified simplex method by the minimisation of the composition objective function defined as:

2 ! ! 3 FI;exp FII;exp FI;calc 2 FII;calc 2 D X N X P1 X w  w w  w inm inm inm inm 4 5; S¼ þ m¼1 n¼1 i¼1

rwFIinm

rwFIIinm

ð1Þ

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where D is the total number of data sets, N is the total number of tie lines, P is the total number of components in each data set; i, n, and m stand for component, tie line and data group, respectively; FI and FII refer to phases I and II, respectively; exp and calc stand for experimental and calculated mass fractions (w), respectively, rwOP and

systems were ‘‘CH3’’, ‘‘CH2’’, ‘‘CH’’, ‘‘CH = CH’’, ‘‘CH2COO’’, ‘‘COOH’’ and ‘‘OH’’. Two sets of interaction parameters were used to test the prediction capability of LLE data. In both cases, the model used was that presented by Fredenslund et al. [30], and the set of binary interaction parameters denoted as UNIFAC-LLE is that updated by Magnussen et al. [31]. The set of parameters here referred to as UNIFAC-HIR was presented by Hirata et al. [32], wherein the authors used several data for real multicomponent oil de-acidification systems to readjust group interaction parameters. Those systems were composed by several triacylglycerols and fatty acids, ethanol and water. All individual components – tri-, di- and monoacylglycerols, and ethyl esters – were considered for UNIFAC modelling calculations.

inm

rwAPinm are the standard deviations observed in the composition of the two liquid phases. The deviations between experimental and calculated compositions in both phases were calculated using the root mean square deviation (Dw/%), which is given by the following equation:

0

N X P  X

B B n¼1 i¼1 Dw ¼ 100B B @

 2 11=2 FII;calc þ wFII;exp  w C i;n i;n C C : C 2NP A

wFI;exp  wFI;calc i;n i;n

2

3. Results

ð2Þ Through the size exclusion chromatography (HPSEC) it was possible to identify the classes of compounds present in each fatty reagent used in this study. Thus, it was observed that the commercial mixtures of mono- and diacylglycerols, besides these components, also contain a small amount of triacylglycerols. In addition, it was identified the presence of a very small amount of diacylglycerols in the vegetable oils and the presence of fatty acids in the commercial ethyl oleate. The quantification of these compounds will be discussed later. The fatty acid composition of the vegetable oils and the commercial mixtures of mono- and diacylglycerols are presented in table 2, as well as the ethyl ester composition of the commercial ethyl oleate and ethyl linoleate. Table 3 shows the probable TAG compositions of the sunflower and high oleic sunflower oils. The names given to the main TAG in table 3 are related to the symbols used for each fatty acid in table 2, i.e., the TAG named POLi, for instance, is a triacylglycerol composed by palmitic acid (P), oleic acid (O) and linoleic acid (Li). The same applies to all the other TAGs.

2.3.2. UNIFAC modelling approach The UNIFAC thermodynamic model was used to predict the LLE of the system. Structural groups selected to represent the studied

TABLE 8 Average molar masses of each pseudocomponent. Pseudocomponent

M/g  mol1

TAG_sunflower oil TAG_HOSO DAG_mixture A DAG_mixture B MAG_mixture A MAG_mixture B Ethyl oleate Ethyl linoleate Oleic acid Ethanol

877.86 883.21 605.08 612.19 348.57 352.12 306.33 306.79 282.46 46.07

TABLE 9 (Liquid + liquid) equilibrium values for the system {sunflower oil (1)a + DAG1 (3) + MAG1 (5) (+ethyl linoleate (7)) + ethanol (10)} at T = (303.15 and 318.15) K, and P = 93.8 kPa.b T/K

a b c

Overall Composition

Alcoholic phase

d/%c

Oil phase

w1

w3

w5

w7

w10

w1

w3

w5

w7

w10

w1

w3

w5

w7

w10

303.15

0.4969 0.4415 0.4041 0.3863 0.3658 0.3516 0.4740 0.4518 0.4332 0.4040 0.3849 0.3632

0.0034 0.0223 0.0346 0.0413 0.0480 0.0524 0.0111 0.0114 0.0113 0.0105 0.0108 0.0109

0.0000 0.0367 0.0603 0.0732 0.0862 0.0947 0.0150 0.0157 0.0159 0.0148 0.0156 0.0159

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0208 0.0406 0.0703 0.0887 0.1096

0.4997 0.4995 0.5010 0.4992 0.5000 0.5013 0.4999 0.5003 0.4990 0.5004 0.5000 0.5004

0.0578 0.0997 0.1340 0.1643 0.2081 0.2498 0.0810 0.0873 0.0952 0.1094 0.1355 0.1429

0.0026 0.0187 0.0293 0.0364 0.0439 0.0490 0.0092 0.0094 0.0092 0.0086 0.0095 0.0093

0.0000 0.0550 0.0825 0.0960 0.1038 0.1070 0.0234 0.0235 0.0229 0.0205 0.0210 0.0199

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0149 0.0294 0.0523 0.0731 0.0900

0.9396 0.8266 0.7542 0.7033 0.6442 0.5942 0.8864 0.8649 0.8433 0.8092 0.7609 0.7379

0.8630 0.7762 0.7095 0.6641 0.6142 0.5648 0.8123 0.7806 0.7391 0.6796 0.6453 0.5947

0.0048 0.0265 0.0397 0.0468 0.0532 0.0573 0.0137 0.0136 0.0129 0.0118 0.0122 0.0118

0.0000 0.0194 0.0373 0.0467 0.0598 0.0702 0.0073 0.0080 0.0087 0.0088 0.0089 0.0107

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0247 0.0483 0.0832 0.1064 0.1271

0.1322 0.1779 0.2135 0.2424 0.2728 0.3077 0.1667 0.1731 0.1910 0.2166 0.2272 0.2557

0.05 0.07 0.06 0.06 0.01 0.02 0.02 0.08 0.18 0.25 0.01 0.21

318.15

0.4970 0.4738 0.4599 0.4410 0.4133 0.3858 0.4636 0.4429 0.4243 0.3945 0.3730

0.0034 0.0113 0.0160 0.0225 0.0321 0.0411 0.0116 0.0113 0.0111 0.0107 0.0106

0.0000 0.0153 0.0244 0.0369 0.0555 0.0730 0.0160 0.0157 0.0155 0.0151 0.0154

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0096 0.0306 0.0497 0.0796 0.1015

0.4996 0.4996 0.4997 0.4996 0.4991 0.5001 0.4992 0.4995 0.4994 0.5001 0.4995

0.0774 0.0908 0.1007 0.1140 0.1385 0.1754 0.0979 0.1054 0.1184 0.1392 0.1445

0.0025 0.0084 0.0122 0.0176 0.0268 0.0367 0.0099 0.0089 0.0090 0.0095 0.0085

0.0000 0.0233 0.0368 0.0528 0.0764 0.0935 0.0213 0.0238 0.0230 0.0222 0.0203

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0074 0.0227 0.0386 0.0669 0.0844

0.9201 0.8775 0.8503 0.8156 0.7583 0.6944 0.8635 0.8392 0.8110 0.7622 0.7423

0.8557 0.8234 0.8001 0.7656 0.7190 0.6455 0.7885 0.7451 0.7001 0.6371 0.5869

0.0044 0.0143 0.0189 0.0259 0.0363 0.0450 0.0132 0.0125 0.0122 0.0115 0.0112

0.0000 0.0076 0.0129 0.0202 0.0322 0.0481 0.0089 0.0091 0.0094 0.0099 0.0108

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0108 0.0349 0.0573 0.0907 0.1150

0.1399 0.1547 0.1681 0.1883 0.2125 0.2614 0.1786 0.1984 0.2210 0.2508 0.2761

0.02 0.00 0.02 0.12 0.09 0.05 0.16 0.17 0.12 0.02 0.18

Includes only TAG. Standard uncertainties u are u(T/K) = 0.1, u(P/kPa) = 0.3, u(w) = 0.0022. Overall mass balance deviation [27].

TABLE 10 (Liquid + liquid) equilibrium values for the system {HOSO (2)a + DAG2 (4) + MAG2 (6) (+ethyl oleate (8) + oleic acid (9)) + ethanol (10)} at T = (303.15 and 318.15) K, and P = 94.1 kPa.b T/K

b c

Alcoholic phase

d/%c

Oil phase

w4

w6

w8

w9

w10

w2

w4

w6

w8

w9

w10

w2

w4

w6

w8

w9

w10

303.15

0.4947 0.4388 0.4003 0.3818 0.3637 0.3443 0.4701 0.4504 0.4304 0.4025 0.3821 0.3603

0.0050 0.0251 0.0392 0.0455 0.0520 0.0590 0.0144 0.0141 0.0136 0.0135 0.0133 0.0131

0.0000 0.0355 0.0605 0.0716 0.0831 0.0955 0.0165 0.0164 0.0159 0.0162 0.0163 0.0163

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0184 0.0379 0.0651 0.0819 0.1032

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0017 0.0035 0.0060 0.0075 0.0095

0.5003 0.5006 0.5000 0.5011 0.5012 0.5012 0.4990 0.4990 0.4987 0.4967 0.4989 0.4976

0.0541 0.0858 0.1301 0.1353 0.1682 0.2089 0.0645 0.0709 0.0755 0.0882 0.0956 0.1103

0.0046 0.0207 0.0346 0.0406 0.0469 0.0552 0.0117 0.0117 0.0112 0.0116 0.0117 0.0117

0.0000 0.0537 0.0834 0.0948 0.1044 0.1105 0.0263 0.0261 0.0241 0.0232 0.0225 0.0221

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0128 0.0264 0.0479 0.0619 0.0811

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0020 0.0041 0.0070 0.0086 0.0107

0.9413 0.8398 0.7519 0.7293 0.6805 0.6254 0.8975 0.8765 0.8587 0.8221 0.7997 0.7641

0.8544 0.7813 0.7173 0.6844 0.6376 0.5912 0.8380 0.8030 0.7544 0.7006 0.6635 0.6186

0.0068 0.0294 0.0435 0.0507 0.0573 0.0653 0.0179 0.0169 0.0165 0.0158 0.0159 0.0152

0.0000 0.0177 0.0343 0.0445 0.0560 0.0672 0.0069 0.0081 0.0081 0.0083 0.0101 0.0095

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0236 0.0483 0.0806 0.1008 0.1252

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0014 0.0028 0.0050 0.0065 0.0083

0.1388 0.1716 0.2049 0.2204 0.2491 0.2763 0.1372 0.1470 0.1699 0.1897 0.2032 0.2232

0.09 0.01 0.02 0.04 0.03 0.04 0.01 0.08 0.01 0.09 0.01 0.05

318.15

0.4958 0.4723 0.4571 0.4395 0.4146 0.3828 0.4615 0.4399 0.4225 0.3935 0.3665

0.0050 0.0136 0.0190 0.0256 0.0354 0.0458 0.0138 0.0137 0.0123 0.0124 0.0121

0.0000 0.0152 0.0247 0.0364 0.0537 0.0722 0.0157 0.0159 0.0138 0.0144 0.0144

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0090 0.0291 0.0450 0.0728 0.0905

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0008 0.0027 0.0041 0.0067 0.0083

0.4992 0.4989 0.4992 0.4985 0.4963 0.4992 0.4992 0.4987 0.5023 0.5002 0.5082

0.0749 0.0853 0.0904 0.1006 0.1202 0.1574 0.0846 0.0976 0.1025 0.1240 0.1214

0.0046 0.0116 0.0155 0.0212 0.0307 0.0412 0.0119 0.0122 0.0115 0.0114 0.0110

0.0000 0.0247 0.0376 0.0545 0.0738 0.0941 0.0251 0.0249 0.0217 0.0200 0.0194

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0066 0.0225 0.0362 0.0595 0.0758

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0010 0.0033 0.0051 0.0078 0.0097

0.9205 0.8784 0.8565 0.8237 0.7753 0.7073 0.8708 0.8395 0.8230 0.7773 0.7627

0.8418 0.8184 0.7936 0.7638 0.7096 0.6737 0.8032 0.7609 0.7241 0.6593 0.6230

0.0065 0.0158 0.0218 0.0297 0.0394 0.0507 0.0149 0.0152 0.0139 0.0134 0.0139

0.0000 0.0073 0.0128 0.0197 0.0338 0.0430 0.0082 0.0081 0.0078 0.0091 0.0086

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0109 0.0358 0.0548 0.0871 0.1085

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0007 0.0021 0.0033 0.0056 0.0072

0.1517 0.1585 0.1718 0.1868 0.2172 0.2326 0.1621 0.1779 0.1961 0.2255 0.2388

0.06 0.05 0.03 0.03 0.01 0.08 0.01 0.07 0.20 0.08 0.13

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a

Overall Composition w2

Includes only TAG. Standard uncertainties u are u(T/K) = 0.1, u(P/kPa) = 0.5, u(w) = 0.0014. Overall mass balance deviation [27].

153

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TABLE 11 Deviations for the global mass balance of the phase compositions.

a

System

d/%a

Sunflower oil/DAG1/MAG1/ethyl linoleate/ethanol, T = 303.15 K Sunflower oil/DAG1/MAG1/ethyl linoleate/ethanol, T = 318.15 K HOSO/DAG2/MAG2/ethyl oleate/oleic acid/ethanol, T = 303.15 K HOSO/DAG2/MAG2/ethyl oleate/oleic acid/ethanol, T = 318.15 K

0.085 0.087 0.039 0.068

Overall mass balance deviation according to Marcilla et al. [27].

For the commercial mixtures of mono- and diacylglycerols, the probable TAG compositions were determined using the same procedure and, from these compositions, the compositions in monoand diacylglycerols were estimated considering the probability of the partial rupture of the triacylglycerols without preference for specific ester bonds. Tables 4 and 5 present the probable TAG, DAG and MAG compositions of the commercial mixtures A and B, respectively, where the symbols given to DAGs follow the same reasoning aforementioned for the TAGs. Note that the compositions of each class of components, viz. TAG, DAG and MAG, presented in tables 4 and 5, sum to 100%. The concentration of fatty acids in the commercial ethyl oleate was determined by titration according to the official method 2201 of the IUPAC [33] with an automatic buret (Metrohm, Model Dosimat 715). The analysis was replicated three times and the average value is 8.43 wt.%, expressed in oleic acid. As for the commercial mixtures A and B, the quantification of mono-, di- and triacylglycerols was performed by gas chromatography with flame ionisation detector, according to the official method ASTM D 6585 [34]. This analysis was carried out at the Analytical Center of the Institute of Chemistry at the University of Campinas (IQ/UNICAMP), and the results are presented in table 6. Having these compositions, calibration curves were made with the commercial mixtures A and B and the angular coefficients obtained for the diacylglycerols were used to determine the DAG compositions in the vegetable oils, which are also presented in table 6. The correct and detailed characterisation of input materials allowed the construction of calibration curves in order to thoroughly describe the equilibrium phases obtained in the experiments in terms of their various classes of components. Despite being very small, the composition of DAG in the vegetable oils was taken into account in both the experimental data

and in the thermodynamic calculations. However, in the case of the NRTL model, the molar masses Mi of the representative DAG were calculated considering only the molar composition of the commercial mixtures of mono- and diacylglycerols. The average molar masses of diacylglycerols from mixture A and mixture B were calculated according to tables 4 and 5, and the values obtained were M = (605.08 and 612.19) g  mol1 for DAGs from mixtures A and B, respectively. It is worth mentioning that the error introduced by considering only the compositions of the commercial mixtures in the DAGs molar masses calculation is fairly small, since the amount of DAGs in the vegetable oils are quite low, as already mentioned, and because the average molar masses of DAGs from vegetable oils (M = (615.93 and 614.10) g  mol1 for DAGs from sunflower oil and HOSO, respectively) do not differ significantly from those calculated for the commercial mixtures. These average molar masses were calculated according to the diacylglycerols compositions of the vegetable oils, presented in table 7, which were estimated in the same way as for the mixtures A and B. Similarly, the TAG content in the commercial mixtures of monoand diacylglycerols was also taken into account, but, due to the same reasons presented above, the average molar masses were calculated considering only the molar composition of the vegetable oils. According to table 3, the obtained values were M = (877.86 and 883.21) g  mol1 for sunflower and high oleic sunflower oils, respectively. The average molar masses of monoacylglycerols from mixtures A and B were calculated according to tables 4 and 5, obtaining the values of M = (348.57 and 352.12) g  mol1 for MAGs from mixture A and B, respectively. Average molar masses of the commercial ethyl oleate and ethyl linoleate were determined from their ethyl ester composition presented in table 2. The obtained values were M = (306.33 and 306.79) g  mol1, respectively. The average molar masses of each pseudo component considered in the NRTL modelling is summarised in table 8. Regarding the UNIFAC model, all different components were considered in the calculation, i.e., all tri- and diacylglycerols from vegetable oils, all tri-, di- and monoacylglycerols from mixtures A and B, and all ethyl esters from commercial oleate and linoleate, so that the compositions of the input materials were employed as precisely as possible. This means that, in total, 62 different components were considered.

4.5

4.0

3.5

3.0

Ki

2.5

2.0

1.5

1.0

0.5

0.0

303.15

318.15 Temperature/K

FIGURE 2. Average distribution coefficient of: e, DAG1; h, MAG1; s, ethyl linoleate; D, DAG2; , MAG2; +, ethyl oleate; d, oleic acid.

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FIGURE 3. (Liquid + liquid) equilibrium for the systems: d, sunflower oil (1) + DAG1 (3) + MAG1 (5) + ethanol (10), and , HOSO (2) + DAG2 (4) + MAG2 (6) + ethanol (10) at T = 303.15 K.

In the present study, the following notations were given to the components: DAG1 for the DAGs of (sunflower oil + mixture A), DAG2 for the DAGs of (HOSO + mixture B), and MAG1 and MAG2 for the MAGs of mixtures A and B, respectively. Tables 9 and 10 contain the values of the overall composition and the corresponding tie lines for the systems composed by {sunflower oil (1) + DAG1 (3) + MAG1 (5) (+ethyl linoleate (7)) + ethanol (10)} and {HOSO (2) + DAG2 (4) + MAG2 (6) (+ethyl oleate (8) + oleic acid (9)) + ethanol (10)} at T = (303.15 and 318.15) K. All concentrations are expressed in mass fraction. The mass balances were checked and the average results obtained for each set of experimental values are shown in table 11. In all cases, the average values were lower than 0.09%, which indicates the good quality of the experimental data. Note that the mass balance deviations for every tie line are also given in tables 9 and 10 and that the highest value obtained (0.25%) is still much lower than the maximum deviation suggested by Marcilla et al. [27] for checking the quality of the experimental data. The ratio between the content of the component i in the alcoholic phase and the content of this component in the oil phase in each tie line is called distribution coefficient. The average distribution coefficients of the components, with the corresponding error bars, are shown in figure 2. It can be observed that for all systems studied, the distribution coefficients of DAGs and esters were smaller than unity, indicating their preference for the oil phase. On the

other hand, for MAGs and fatty acids, the distribution coefficients were greater than unity, showing a clear preference for the alcoholic phase. The miscibility of a vegetable oil in ethanol is affected mainly by the unsaturation and chain length of its fatty acids constituents [35]. Figure 3 presents the experimental ELL values for both systems studied at T = 303.15 K. It can be observed that the two-phase region for the system {HOSO (2) + DAG2 (4) + MAG2 (6) + ethanol (10)} is larger than the biphasic region of the system {sunflower oil (1) + DAG1 (3) + MAG1 (5) + ethanol (10)}, indicating a greater miscibility in the case of the last system. In fact, sunflower oil is rich in linoleic acid, a fatty acid more unsaturated than oleic acid, which is the major fatty acid present in HOSO. For any given temperature, the more unsaturated the vegetable oil, the greater is its miscibility in ethanol and, consequently, the smaller the two-phase region. Tables 12 and 13 contain values of the parameters of the NRTL model adjusted to the experimental values for the two systems studied. The deviations between the experimental and calculated values are shown in table 14. Figures 4 and 5 present the experimental and calculated tie lines for the system (sunflower oil + mixture A + ethanol) at T = 303.15 K, indicating the DAG1 and MAG1 distribution, respectively. These figures confirm that those components show opposite behaviour. This occurs because monoacylglycerols contain higher number of polar groups (hydroxyl groups) than diacylglycerols, increasing their solubility in ethanol. The same behaviour is observed for DAG2 and MAG2, at both temperatures. Figure 6 shows experimental and calculated tie lines for the system (sunflower oil + mixture A + ethyl linoleate + ethanol) at T = (303.15 and 318.15) K. In order to have a better interpretation of the five-component phase equilibrium, the experimental and calculated results are represented in a simplified form, showing only the ethyl ester (w7) and ethanol (w10) compositions in a explicit way and grouping the acylglycerols as a third pseudo component, which consists of TAG-DAG-MAG. From that figure, it is noted that an increase in temperature from T = (303.15 to 318.15) K causes a small decrease in the two-phase region, indicating an improvement in the mutual solubility of acylglycerols (TAG, DAG and MAG) and ethanol. This behaviour is observed for both systems studied and has already been reported in literature [10,12,36,37]. From figures 4–6 and table 14, it can be seen that the NRTL model accurately described the LLE behaviour of the systems. Tie lines calculated by the NRTL model and the experimental data almost overlap, indicating an accurate description of the LLE and confirming the low deviations between experimental values and calculated compositions. Concerning the UNIFAC, this model did not provide the same precision, as indicated in table 14. According to figure 7, which

TABLE 12 NRTL parameters for the system {sunflower oil (1) + DAG1 (3) + MAG1 (5) (+ethyl linoleate (7)) + ethanol (10)}. T = 303.15 K

T = 318.15 K

Pair i-j

Aij/K

Aji/K

aij

Aij/K

Aji/K

aij

1-3 1-5 1-7 1-10 3-5 3-7 3-10 5-7 5-10 7-10

992.88 118.46 533.19 70.866 40.941 56.945 140.8 3247.3 121.58 15.523

434.45 347.69 19.786 1444.7 29.715 306.98 2056 656.37 671.29 166.97

0.56984 0.10296 0.5319 0.49292 0.37757 0.56977 0.1 0.13493 0.37836 0.57

731.47 142.52 793.26 54.153 90.781 47.73 118.31 2938.2 135.01 45.658

447.06 321.03 21.109 1464.7 28.25 298.3 1652.9 1033.4 686.43 201.97

0.46997 0.12137 0.57 0.50555 0.31806 0.37065 0.10777 0.14639 0.49335 0.56979

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TABLE 13 NRTL Parameters for the system {HOSO (2) + DAG2 (4) + MAG2 (6) (+ethyl oleate (8) + oleic acid (9)) + ethanol (10)}. T = 303.15 K Pair i-j 2-4 2-6 2-8 2-9 2-10 4-6 4-8 4-9 4-10 6-8 6-9 6-10 8-9 8-10 9-10

Aij/K 355.85 89.708 433.71 7206.5 253.21 1407.8 110.07 3741.4 2759.3 160.15 1855.5 327.15 59.733 35.525 474.94

T = 318.15 K Aji/K 237.48 63.743 175.41 546.15 1757.2 256.19 3165.9 39.494 38.441 13.354 631.23 940.35 803.63 83.099 339.78

aij

Aij/K 428.74 94.895 464.9 7621.4 268.53 1262.7 102.26 3112.2 2425 132.18 2142.3 334.06 92.819 44.798 223.97

0.56925 0.21735 0.14045 0.10614 0.36497 0.1 0.20321 0.14479 0.4131 0.13943 0.10585 0.44749 0.44596 0.13313 0.48174

Aji/K 239.34 49.48 190.16 246.39 1739.3 343.43 2775.4 42.715 37.322 13.578 793.5 955.19 782.9 84.608 437.6

aij 0.55624 0.21395 0.12222 0.12729 0.38638 0.10001 0.1978 0.22118 0.56989 0.15407 0.10002 0.45553 0.34846 0.11002 0.41941

TABLE 14 Average deviations in phase composition. System

Sunflower oil/DAG1/MAG1/ethyl linoleate/ethanol, T = 303.15 K Sunflower oil/DAG1/MAG1/ethyl linoleate/ethanol, T = 318.15 K HOSO/DAG2/MAG2/ethyl oleate/oleic acid/ethanol, T = 303.15 K HOSO/DAG2/MAG2/ethyl oleate/oleic acid/ethanol, T = 318.15 K a b

Dw/% NRTL

UNIFAC-LLEa

UNIFAC-HIRb

0.434 0.388 0.348 0.332

9.237 7.844 6.305 5.690

5.070 2.511 2.781 1.804

Original parameters [31]. Parameters from Hirata et al. [32].

contain experimental and calculated tie lines for the system (HOSO + mixture B + ethanol) at T = 303.15 K, using both sets of parameters, the ethanol mass fraction was underestimated in the oil phase and overestimated in the alcoholic phase, particularly in the case of UNIFAC-LLE parameters. In both cases, the slope of the calculated tie lines was more accentuated than the slope of the experimental ones. This effect was greater when using the UNIFAC-LLE parameters, resulting in higher deviations values.

However, using the UNIFAC-HIR set of parameters, the model predicted a different behaviour for diacylglycerols, indicating a preference for the alcoholic phase, which is not consistent with experimental results. These deviations can be somehow justified by the fact that neither Magnussen et al. [31] nor Hirata et al. [32] used experimental values involving partial acylglycerols in their data set when adjusting the parameters. Similar improperly description in LLE modelling of systems containing vegetable oils,

FIGURE 4. (Liquid + liquid) equilibrium for the system {sunflower oil (1) + DAG1 (3) + MAG1 (5) + ethanol (10)} at T = 303.15 K, DAG1 distribution: d, experimental data; - -, calculated values using NRTL.

FIGURE 5. (Liquid + liquid) equilibrium for the system {sunflower oil (1) + DAG1 (3) + MAG1 (5) + ethanol (10)} at T = 303.15 K, MAG1 distribution: d, experimental data; - -, calculated values using NRTL.

L.C.B.A. Bessa et al. / J. Chem. Thermodynamics 89 (2015) 148–158

FIGURE 6. (Liquid + liquid) equilibrium for the system {sunflower oil (1) + DAG1 (3) + MAG1 (5) + ethyl linoleate (7) + ethanol (10)}: j, experimental data at T = 303.15 K; h, experimental values at T = 318.15 K; - - -, calculated values using NRTL at T = 303.15 K; , calculated values using NRTL at T = 318.15 K.

157

FIGURE 8. (Liquid + liquid) equilibrium for the system {HOSO (2) + DAG2 (4) + MAG2 (6) + ethyl oleate (8) + oleic acid (9) + ethanol (10)} at T = 303.15 K: d, experimental values; - - -, calculated values using UNIFAC-LLE; , calculated values using UNIFAC-HIR.

biodiesel production due to the deviations in the prediction of LLE for this type of system. 4. Conclusions

FIGURE 7. (Liquid + liquid) equilibrium for the system {HOSO (2) + DAG2 (4) + MAG2 (6) + ethanol (10)} at T = 303.15 K: d, experimental values; - - -, calculated values using UNIFAC-LLE;     , calculated values using UNIFAC-HIR.

partial acylglycerols, free fatty acids, ethanol and/or biodiesel, using UNIFAC, has already been reported in the literature [4,19,38,39]. On the other hand, according to values in table 14, using the UNIFAC-HIR set of parameters, it can be observed there is an improvement in the LLE description, and this is especially significant taking into account the ethyl esters behaviour. Figure 8 shows the tie lines for the system (HOSO + mixture B + ethyl oleate + oleic acid + ethanol) at T = 303.15 K, in which similar components were grouped up into the x-axis. The improvement in the description using the UNIFAC-HIR set of parameters is fairly evident. Although Hirata et al. [32] have advanced significantly in the LLE description of systems containing vegetable oils, it can be observed that further enhancement is still needed. The results presented in figures 7 and 8 show that despite the availability of group interaction parameters and their practical use, UNIFAC models must be used cautiously in design analysis and process simulation of

The results presented in this study confirm that it is indeed important to consider the partial acylglycerols when studying the phase equilibrium in biodiesel systems, mainly in the transesterification step. In addition, the information acquired in this study may also be useful for the downstream processes in cases of incomplete conversion. It was observed that monoacylglycerols, which has a higher number of polar groups (hydroxyl groups), have a higher affinity with the alcoholic phase when compared to diacylglycerols. The NRTL model was applied to the equilibrium results and the binary interaction parameters were optimised for each system. Good agreement was observed between experimental values and the correlations, indicating the applicability of this model for such systems. In contrast, the UNIFAC model, using two sets of parameters from the literature, yielded higher deviations values, which motivates future work to improve further the model by adjusting a specific set of parameters. The results obtained in the present study may allow a more accurate description of the real behaviour of the transesterification system involved in biodiesel production process and, consequently, its optimization. Acknowledgements The authors wish to acknowledge CAPES for the scholarship and FAPESP (08/56258-8 and 09/54137-1) and CNPq (304495/2010-7 and 406856/2013-3) for the financial support. References [1] J.G. Veneral, D.L.R. Junior, M.A. Mazutti, F.A.P. Voll, L. Cardozo-Filho, M.L. Corazza, E.A. Silva, J.V. Oliveira, J. Chem. Thermodyn. 64 (2013) 65–70. [2] B.R. Moser, In Vitro Cell. Dev. Biol. Plant 45 (2009) 229–266. [3] A.V. Marjanovic, O.S. Stamenkovic, Z.B. Todorovic, M.L. Lazic, V.B. Veljkovic, Fuel 89 (2010) 665–671. [4] R.C. Basso, C.A.S.D. Silva, C.D.O. Sousa, A.J.D.A. Meirelles, E.A.C. Batista, Bioresour. Technol. 131 (2013) 468–475. [5] K. Bozbas, Renew. Sustainable Energy Rev. 12 (2008) 542–552. [6] A. Casas, J.F. Rodríguez, G.L. del Peso, R. Rodríguez, G. Vicente, A. Carrero, Ind. Eng. Chem. Res. 53 (2014) 3731–3736.

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JCT 15-86