Liquid–liquid equilibrium of fatty systems: A new approach for adjusting UNIFAC interaction parameters

Fluid Phase Equilibria 360 (2013) 379–391

Contents lists available at ScienceDirect

Fluid Phase Equilibria journal homepage: www.elsevier.com/locate/fluid

Liquid–liquid equilibrium of fatty systems: A new approach for adjusting UNIFAC interaction parameters Gláucia F. Hirata a , Charlles R.A. Abreu b , Larissa C.B.A. Bessa a , Marcela C. Ferreira a , Eduardo A.C. Batista a , Antonio J.A. Meirelles a,∗ a b

EXTRAE, Department of Food Engineering (DEA), Faculty of Food Engineering (FEA), University of Campinas (UNICAMP), 13083-970 Campinas, SP, Brazil School of Chemistry, Federal University of Rio de Janeiro (UFRJ), 21941-909 Rio de Janeiro, RJ, Brazil

a r t i c l e

i n f o

Article history: Received 16 April 2013 Received in revised form 30 August 2013 Accepted 2 October 2013 Available online 12 October 2013 Keywords: Liquid–liquid equilibrium UNIFAC method Fatty acids Vegetable oils Deacidification

a b s t r a c t Along the refining process of vegetable oils the removal of free fatty acids is the most important purification step. The deacidification by liquid–liquid extraction using an alcoholic solvent has been shown to be a viable alternative from a technical point of view. In prior studies reported in the literature, the equilibrium data were determined and correlated for each different type of edible oil and they are most often represented in terms of mass fractions of pseudocomponents. However, to obtain a better predictive tool, it is necessary to consider the true compositions of these mixtures. In this work, several data for real multicomponent systems available in the literature were used to readjust group interaction parameters of the UNIFAC (Universal Quasi-Chemical Functional-group Activity Coefficients) method. A new group has also been proposed in order to simplify the description of the triacylglycerols. The deviations found using the original groups and parameters of UNIFAC were considerably higher than the deviations found in both alternative procedures, indicating that the correlation and prediction of this type of systems were significantly improved. The developed procedures were further tested using data measured for two validation systems, which confirmed the improvement in the predictive power of the UNIFAC method. © 2013 Elsevier B.V. All rights reserved.

1. Introduction The most important step of edible oil refining is the removal of free fatty acids (FFAs). Liquid–liquid extraction has been shown to be a viable route for deacidifying edible oils due to the fact that the corresponding losses of neutral oil in the extract stream could be considerably lower than the losses obtained in the traditional chemical refining as well as it could be performed at room temperature or close to it, a condition much milder than the temperature normally required for the alternative industrial process known as physical refining (220–270 ◦ C). Several studies suggested the use of short-chain alcohols as solvents for vegetable oil deacidification, especially ethanol because of its low toxicity, easy recovery, and good values of selectivity as well as appropriate distribution coefficients for FFAs. The addition of water to the alcoholic solvent reduces the

∗ Corresponding author. Tel.: +55 19 3521 4037; fax: +55 19 3521 4027. E-mail addresses: glaucia [email protected] (G.F. Hirata), [email protected] (C.R.A. Abreu), [email protected] (L.C.B.A. Bessa), [email protected] (M.C. Ferreira), [email protected] (E.A.C. Batista), [email protected] (A.J.A. Meirelles). 0378-3812/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.fluid.2013.10.004

distribution coefficients of FFAs, but enhances solvent selectivity and, in this way, decreases the losses of neutral oil [1–11]. Crude oils and fats contain mainly triacylglycerols (TAGs) and, to a lesser extent, FFAs. The physical–chemical properties of TAGs are determined mostly by the fatty acid moieties that are connected to the glycerol residue by ester bonds. These fatty acid moieties exhibit differences related to their carbon chain length and to the number, position, and type (cis or trans) of their double bonds. Their carbons chains vary from 4 to 24 carbon atoms and they may contain none, one or more double bonds [12]. The systems used for fat and oil deacidification are habitually treated as pseudoternary or pseudoquaternary ones, containing two pseudocomponents, oil and FFAs, and a pure or mixed solvent (alcohol + water). Such an approach assumes that the edible oil and the FFAs can be represented by a unique TAG and a single FFA, respectively. Based on this hypothesis, equilibrium data for a large variety of edible oils could be correlated using the UNIQUAC (Universal Quasi-Chemical) and the NRTL (Non-random, two liquid) models with very good results [3–6,13–16]. However, this approach does not take into account the differing partition behavior of specific TAGs and FFAs and does not allow a reliable prediction of equilibrium data for different fats and oils. If one considers the common variation in the composition of natural

[5]

[19]

1.18 0.04

0.04

[2] [7] [20] [19]

0.30 0.23

[2,3]

[8]

0.15

[9]

[21]

[7]

0.40

2.21 34.05 47.86 0.87 0.51 0.26 2.27 15.58 55.20 0.15 0.23 0.10 2.15 34.32 49.44 0.27 0.82 2.83 38.21 37.31 1.22 0.93 0.71

2.81 10.28 1.90

11.61 31.21 42.12

2.10 48.02 31.97 9.29 0.48

[23] [4]

[9]

0.37

0.75

[11]

0.20

[22]

0.57

0.23

0.92

1.40 75.28 9.95

3.73 23.36 63.79 0.60 0.25 0.19 3.81 25.83 51.37 6.39 3.98 23.67 53.61 5.45 4.19 25.07 51.15 5.87 0.39 0.29 1.50 37.66 35.08 2.65 1.57 0.15 3.39 26.69 39.65 4.29 0.63 0.44 4.66 39.56 8.86

3.51 61.25 2.06 0.14 2.90 2.80

2.41 4.96 5.06 7.17 0.10 12.39 12.54 0.17 12.38 0.12 1.16 19.57 0.66 14.65

0.06 7.38 0.19

0.02 12.85 0.13

0.90 24.39 1.01

14.24

0.06 7.21 0.11 0.05 0.05 3.84 14.58 73.45 0.30 0.18 0.09

0.81 8.73 17.80

0.65 1.10 44.69 0.08

0.90 0.69 8.03 2.50 11.60

References

Caproic (Cp) Capric (C) Lauric (L) Myristic (M) Palmitic (P) Palmitoleic (Po) Margaric (Mg) Margaroleico (Mo) Stearic (S) Oleic (O) Linoleic (Li) Linolenic (Le) Arachidic (A) Gadoleic (Ga) Arachidonic (Ao) Behenic (B) Erucic (E) Lignoceric (Lg)

C8:0 C10:0 C12:0 C14:0 C16:0 C16:1 C17:0 C17:1 C18:0 C18:1 C18:2 C18:3 C20:0 C20:1 C20:4 C22:0 C22:1 C24:0

2.21 0.81 15.77

Corn Canola Brazil nut Babassu (refined) Avocado seed

Table 1 Fatty acid composition of oils.

The adjustment of interaction parameters for new UNIFAC groups as well as the eventual reevaluation of existing interaction parameters in order to improve the predictive capacity of this method is normally based on experimental equilibrium data obtained for systems containing few pure components. For instance, a series of works with sugar solutions has been based on the assignment of new groups and they also involved the adjustment or readjustment of interaction parameters using equilibrium data for binary and ternary systems containing pure carbohydrates [25–28]. Although a similar approach could also be of interest for fatty systems, only a limited set of research works has attempted to apply and/or to improve the UNIFAC method in this case [13,18,24,29,30]. The reason for this is probably related to the highly multicomponent character of real fatty systems and mainly to the very high prices of pure fatty compounds required for measuring equilibrium data in model systems. In fact, experimental equilibrium data for systems containing pure fatty compounds are very rare and do not provide a data basis sufficiently comprehensive for suggesting new groups and adjusting the corresponding interaction parameters or for readjusting parameters of existing groups in case of their specific use for this type of system. Taking into account the ever increasing importance of liquid–liquid equilibrium in the processing of fats and oils, including the two-phase liquid systems that occur during oil deacidification and biodiesel production, the present work developed two different procedures for improving the predictive capacity of the UNIFAC method when applied to fatty systems. The first one involving

Cotton (pretreated)

2. Modeling approach

8.06 6.46 47.42 15.47 7.60

Garlic

Grape (crude)

Macadamia nut

Palm (refined)

Peanut

Rice bran (refined)

Sesame

Soybean

Soybean 2

Sunflower

Triolein (comercial)

products, this prediction can be associated with somewhat high deviations even in the case of the same type of oil. For instance, the content of the major TAG found in olive oil, triolein, can vary from 40% to 45% of the total amount of triacylglycerols [17]. Considering that fats and oils are multicomponent mixtures containing mainly TAGs derived from a limited set of fatty acids (see Table 1), the use of group contribution methods for predicting equilibrium data seems particularly interesting. But the current methods and corresponding set of available parameters provide poor predictions of the experimental data reported in the literature [18]. The present work develops two procedures for improving the prediction capacity of the UNIFAC method when applied to liquid–liquid equilibrium of fatty systems. The first one is based only in the readjustment of the group interaction parameters. The second procedure is based on the designation of a new group specific for TAGs, aiming not only at a better prediction of liquid–liquid equilibrium but also at an easier way of linking the experimental procedures for analyzing fats, oils, and TAGs in general, to the calculation of equilibrium data by group contribution methods, as it will be explained later. As an additional aspect of the present work, an approach was used for adjusting and readjusting interaction parameters for the UNIFAC method based on experimental data for real multicomponent fatty systems, since equilibrium data for systems containing pure triacylglycerols are almost inexistent in the literature. Although the present work is mainly related to fats and oils deacidification by liquid–liquid extraction, almost the same type of system is of interest in the production of biodiesel. In fact the production of methylic or ethylic biodiesel involves the reaction of those alcohols with TAGs (transesterification) or with FFAs (esterification), generating fatty esters and glycerol or water, respectively. This means that the approach developed in the present work can also potentially help in the prediction of liquid–liquid equilibrium data required for some of the reactive and purification steps of the biodiesel production.

[24]

G.F. Hirata et al. / Fluid Phase Equilibria 360 (2013) 379–391

Fatty acids

380

G.F. Hirata et al. / Fluid Phase Equilibria 360 (2013) 379–391

381

Table 2 Summary of the data bank. Oil

System

Tie lines

Temperature

Avocado Babassu Brasil nut Canola (ethanol) Canola (methanol) Corn Corn 2 (ethanol) Corn 2 (methanol) Cotton (pretreated) Cotton (refined) Garlic Grape Grape (crude) Grape (refined) Macadamia Palm (bleached) Palm (oleic acid) Palm (palmitic acid) Peanut Rice bran Sesame Sunflower (linoleic acid) Sunflower (oleic acid) Sunflower 2 (ethanol) Sunflower 2 (methanol) Soybean Soybean 2 Tricaprylin (capric acid) Tricaprylin (lauric acid) Tricaprylin (linoleic acid) Tricaprylin (oleic acid) Triolein 1 Commercial triolein Triolein 2 Global

3 5 3 3 2 5 2 2 2 4 4 4 6 3 3 4 3 3 3 5 3 4 4 2 2 4 4 1 1 1 1 2 1 3 102

23 32 23 21 10 30 10 10 14 33 31 31 36 18 24 13 13 17 23 26 23 25 25 10 10 34 24 8 6 5 6 14 6 18 652

298.2 303.2 298.2 293.2, 303.2 293.2, 303.2 298.2 303.2, 313.2 303.2, 313.2 298.2 298.2 298.2 298.2 283.2, 290.7 298.2 298.2 318.2 318.2 318.2 298.2 298.2 298.2 298.2 298.2 303.2, 313.2 303.2, 313.2 323.2 303.2 298.2 298.2 298.2 298.2 293.2, 303.2 298.2 298.2 283.2–323.2

a

w (% by mass)a Original parameters

Recalculated parameters

New division

References

4.96 5.96 6.49 9.31 4.43 7.26 7.03 4.09 8.76 6.45 6.20 6.06 3.38 4.69 4.46 7.31 8.53 7.78 6.69 7.12 6.86 4.83 5.37 6.69 3.72 7.99 5.70 3.21 1.34 8.17 6.62 6.55 9.19 8.73 6.23

1.16 2.52 1.49 1.49 0.91 1.23 3.32 0.95 1.49 1.34 1.24 1.40 1.10 0.97 1.90 1.20 1.38 1.58 1.34 1.02 1.46 1.43 1.56 10.07 1.66 2.98 1.04 1.47 1.88 2.80 1.33 1.38 4.50 2.71 1.93

1.40 3.10 1.43 1.46 1.38 1.06 2.87 1.32 1.47 1.44 1.11 1.46 0.89 0.48 2.16 1.48 2.30 2.70 1.51 0.88 1.38 1.55 1.53 10.12 2.57 3.36 0.89 1.18 1.56 4.47 1.45 1.54 4.01 3.56 2.09

[19] [20] [7] [2] [2] [2,3] [37] [37] [8] [8] [9] [9] [21] [21] [7] [5] [5] [5] [19] [4] [9] [23] [23] [38] [38] [11] [22] [24] [24] [24] [24] [2] [24] [24]

Eq. (2).

only the readjustment of the set of interaction parameters of interest for this type of system and a second one that also includes the assignment of a new specific group. In both cases the adjustment of new interaction parameters was based on experimental data for real fatty systems already available in the literature. It is important to mention that all the modeling developed in this work was based on the original UNIFAC equations [31] using as initial estimates for the interaction parameters the liquid–liquid databank parameters obtained by Magnussen et al. [32]. Other UNIFAC versions seem to provide prediction of LLE of fatty systems as poor as the original UNIFAC. For instance, the following results were obtained for the system rice bran oil + free fatty acids + ethanol + water measured at 283, 308 and 333 K [33]: average deviations between predicted and experimental values equal to 2.77% in case of original UNIFAC and 3.20% for the modified UNIFAC (Dortmund) [34,35]. The software for adjusting the interaction parameters has been formulated in a way to allow the use of experimental data from real systems containing vegetable oils and commercial fatty acids. Each system was evaluated considering its main components (several TAGs and FFAs) in the calculation of phase equilibrium. However, to enable the comparison between the calculated values and the experimental ones, the objective function used for adjusting parameters was formulated in terms of the pseudocompounds, such as oil and aggregated FFAs, in the way the equilibrium data reported in the literature were measured. It should be noted that the software treats the systems as pseudoternary or as pseudoquaternary only in the calculation of the objective function. This means that phase equilibrium is evaluated taking into account all the main

components and then the sets of compositions of TAGs and FFAs are summed in each phase in order to obtain the compositions of both pseudocomponents, oil and aggregated FFAs, respectively. The liquid–liquid equilibrium calculations were performed by an isothermal flash, according to the Rachford-Rice equation. The adjustments of interaction parameters were carried out by minimizing the objective function expressed in Eq. (1) below, using the Simplex method [36]. S=

N P D   

OP,exp

[(Winm

2

AP,exp

OP,calc − Winm ) + (Winm

2

AP,calc − Winm ) ]

(1)

m−1 n=1 i=1

where D is the total number of data bank, N is the total number of tie lines in each group, P is the total number of pseudocomponents in each data bank; i, n, and m stand for pseudocomponent, tie line and data group, respectively; OP and AP refer to oil and alcoholic phases, respectively; exp and calc stand for experimental and calculated mass fractions (w), respectively. In the case of the original UNIFAC groups, the interaction parameters were taken from Magnussen et al. [32] and afterwards readjusted, but always using the pseudocomponent oil expressed in its TAG composition. Only TAGs belonging to an isomer set with composition higher than 0.5% by mass were considered, so that the number of components in the pseudocomponent oil varied from 10 to 40, according to the specific edible oil. In the case of the new suggested group, the pseudocomponent oil was treated as a collection of the hypothetical components indicated in Table 3 and the number of these hypothetical components varied from 6 to 15,

382

G.F. Hirata et al. / Fluid Phase Equilibria 360 (2013) 379–391

Table 3 Hypothetical oil components in terms of FA-TAGs and the new division of groups. Hypothetical component

Ma (g/mol)

Co-TAG Cp-TAG C-TAG L-TAG M-TAG P-TAG Po-TAG Mg-TAG Mo-TAG S-TAG O-TAG Li-TAG Le-TAG A-TAG Ga-TAG Ge-TAG Ao-TAG Be-TAG E-TAG Lg-TAG

128.85 156.90 184.95 213.01 241.06 269.11 267.10 283.13 281.11 297.17 295.15 293.14 291.12 325.22 323.20 321.19 317.15 353.27 351.26 381.33

a

UNIFAC Groups CH3

CH2

CH CH

CH5/3 OCO

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

4 6 8 10 12 14 12 15 13 16 14 12 10 18 16 14 10 20 18 22

0 0 0 0 0 0 1 0 1 0 1 2 3 0 1 2 4 0 1 0

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

M is the molar mass.

according to the specific edible oil. The average deviations between the experimental and calculated equilibrium values were evaluated in each data bank according to Eq. (2). Although the equilibrium calculations take into account the diversity of components present in every pseudocomponent, oil or commercial fatty acid, it should be noted that the objective function (Eq. (1) above) and the deviation estimations (Eq. (2)) were based on the composition of the whole pseudocomponents because the experimental information is available only in this form.

  P  N  OP,exp AP,exp OP,calc 2 AP,calc 2  [(wi,n − wi,n ) + (wi,n − wi,n ) ]  w = 100

n=1 i=1

2NP (2)

The denominator 2NP in the above equation refers to the total number of data in the system, where N and P were already mentioned before and the factor 2 is related to the number of phases in the system (alcoholic and oil phases). Besides, in order to evaluate the individual behavior of the phases, the deviations in each one were calculated separately in a similar way. This kind of calculation was performed for the validation systems and in this case, the factor 2 is replaced to 1 and only the difference between the experimental and calculated values in the respective phase was considered in the numerator. A comprehensive data bank was collected, containing 102 systems and a total of 652 tie lines at temperatures ranging from 283.2 to 323.2 K. Table 2 shows a summary of the equilibrium systems used. For each group of data Table 2 gives the oil type, the number of systems, the number of tie lines, the temperature range, the corresponding reference and the calculated deviations (w) for the three approaches. A variety of oils was considered: those rich in linoleic acid (corn, cotton, grape seed, sesame, soybean and sunflower), some rich in oleic acid (commercial triolein and macadamia), others rich in palmitic and oleic acids or in linoleic and oleic acids (palm, avocado, Brazil nut, canola, garlic, peanut, and rice bran) and at last one oil rich in lauric acid (babassu). Furthermore, a limited set of systems containing pure TAGs, triolein or tricaprylin, was also used. The composition in terms of fatty acids of each fatty pseudocomponent, whether it is an oil or a commercial fatty acid, is available

in the selected references. In case of some oils the corresponding compositions are reported in Table 1. Some references also contain the composition expressed in terms of TAGs and, in this case, the TAG composition was used for the equilibrium calculations and the re-estimation of the interaction parameters between the UNIFAC original groups. For the references that do not contain this last information, the probable TAG composition was estimated using the statistical algorithm suggested by Antoniosi Filho et al. [39]. These authors compared values obtained 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. Furthermore, this approach allowed the use of experimental values even in the case of equilibrium data without explicit TAG composition. One must consider that the most common analysis of oils and fats is carried out by gas chromatography after their derivatization, i.e. after their transformation into fatty acid methyl esters (FAMEs). This simplifies, in a very significant way, the effort for characterizing oils and fats, because it increases the volatility of the components to be analyzed and mainly because it reduces the number of their constituents to no more than the corresponding 18–20 fatty acids (see Table 1). In contrast, their TAG composition includes much more than 100 components, if one takes into account triacylglycerols with different fatty acid residues connected to the glycerol residue and the corresponding different types of isomerism, such as structural and cis-trans isomers. A detailed analysis of oils and fats, in terms of TAGs, can be performed by liquid chromatography or even by gas chromatography, but the identification of the chromatographic peaks, sometimes even for major components, demands a lot of expertise and parallel information, since the required set of pure standards is often not available. A new group division was proposed with the aim of simplifying the description of the pseudocomponent oil. The new division was so defined that the pseudocomponent oil could be described in terms of the fatty acids constituting the TAG molecules. Each fatty acid residue along with a third of the glycerol residue was assumed to be an independent hypothetical component, named as FA-TAG, so that every TAG molecule was then composed of three unities of these hypothetical components. An additional group was created (CH5/3 OCO) that corresponds to one third of the glycerol residue. It should be noted that the central residue of glycerol (CH) and the two lateral residues (CH2 ) were not differentiated, therefore

G.F. Hirata et al. / Fluid Phase Equilibria 360 (2013) 379–391

383

of COO to obtain the parameters for CH5/3 OCO, according to Bondi [43]. 3. Experimental

Fig. 1. Scheme of the new division of TAGs in hypothetical components.

generating the group CH5/3 OCO. A scheme of how the triacylglycerol molecules were considered can be seen in Fig. 1. In this way, vegetable oils were assumed to be mixtures of such hypothetical components independent of the actual connectivity between the residues of fatty acids and glycerol. At first sight this proposition can be considered rather arbitrary but, on the other hand, it reduces the number of different hypothetical components of the pseudocomponent oil to the number of its constituent fatty acids and circumvents the problem of estimating its probable TAG composition based on statistical methodologies, as it was aforementioned. Note that defining the entire glycerol residue as a new group does not add any simplification to the characterization of the pseudocomponent oil, since such a definition would require the specification of the real connectivity between that residue and three fatty acid residues, an information that could only be directly obtained by chromatographic analysis without the above mentioned derivatization or by a statistical procedure. Assuming that the pseudocomponent oil is composed of fatty acid residues connected to one third of the glycerol residue allows the direct use of the most common chromatographic results available for characterizing oils and fats; it also preserves the real molar mass of the pseudocomponent oil and does not impede to take into account the partition behavior of the different oil components. In fact, the pseudocomponent oil in each equilibrium phase would be usually characterized by gas chromatography of the corresponding FAMEs, so that the differences in the partition behavior of its constituent TAGs are directly expressed in the fatty acid composition of the pseudocomponent oil present in each phase. A procedure similar to the one proposed in the present work was already used in investigations on the trans-isomerization of vegetable oils. Although the actual reactions involve the double bonds of the unsaturated TAG molecules, their experimental rate constants were directly associated with the fatty acids present in their chemical structure [40–42]. This simplification could be assumed because the trans-isomerization occurs in the fatty acid residues and the glycerol residue is a molecular part common to all TAGs. In the present case this hypothesis was moved forward an additional step by considering that the differences in the partitioning of the TAG molecules in the LLE-system are reflected in their fatty acid residues. Table 3 shows the hypothetical components (fatty acid residues plus one third of the glycerol residue) that could be contained in any pseudocomponent oil and also their division into UNIFAC groups, including the new group CH5/3 OCO. The hypothetical component Cp-TAG, for instance, includes the CH5/3 OCO group and the original UNIFAC groups corresponding to the carbon chain of the caprylic acid residue. The values of volume (Vw ) and surface area (Aw ) of van der Waals for the new group are given in Table 4 and they were obtained by linear interpolation of the corresponding values for groups CH, CH2 , CH3 e CH4 and added to the values of Vw and Aw Table 4 Values of Vw , Aw , Rk , Qk for CH5/3 and CH5/3 OCO. Group

Vw

Aw

Rk

Qk

CH5/3 CH5/3 OCO

9.08 24.28

1.09 3.29

0.5985 1.6005

0.436 1.316

In order to validate the results of the proposed modeling procedures two systems were selected and investigated in terms of their equilibrium data as well as in terms of the partition behavior of the most important oil components. The first one was the system palm oil + pure palmitic acid + solvent (93.87% ethanol and 6.13% water), and the second one was composed of an oil mixture containing babassu, palm and soybean oils in the ratio 43:27:30, respectively, mixed with pure oleic acid and anhydrous ethanol. Palm oil is nowadays the vegetable oil with the largest production in a worldwide scale, used for edible purposes as well as for the biodiesel production. On the other hand, the selected mixed oil involves oils rich in lauric, palmitic, oleic and linoleic acids. This means that it exhibits a distribution of different TAGs higher than in normal oils and can be considered a test particularly difficult for the suggested LLE calculation procedures. 3.1. Material Refined palm and babassu oils were obtained from Campestre Ind. e Com. de Óleos Vegetais Ltda. (Brazil), and refined soybean oil from Cargill (Brazil). Palmitic and oleic acids were acquired from Sigma, both with a minimal purity of 98% by mass. The solvents used were anhydrous ethanol from Merck (purity >99.5% by mass) and the hydro-alcoholic mixture prepared by the addition of deionized water (Milli-Q, Millipore) to anhydrous ethanol. The fatty reagents (babassu, palm and soybean oils, oleic and palmitic acids) were analyzed by gas chromatography of FAMEs, according to the official method (1–62) of the AOCS [44]. The samples preparation in the form of FAMEs was carried out according to the official method (2–66) of the AOCS [45]. The fatty samples were analyzed on a capillary gas chromatograph Agilent 6850 Series GPC System GC equipped with a flame ionization detector and a DB-23 Agilent capillary column (50% cyanopropyl – methylpolysiloxane), 0.25 ␮m, 60 m × 0.25 mm i.d.; column flow 1.00 mL min−1 , linear velocity 24 cm s−1 , detector temperature 553.2 K, injector temperature of 523.2 K, oven temperature 383.2 K for 5 min, 383.2–488.2 K (5 K min−1 ), 488.2 K for 24 min; the carrier gas used was helium and the injection volume was 1.0 ␮L. FAMEs were identified by comparison with retention times of standards purchased from Nu Check Inc. (Elysian, IL). The quantification was performed by internal normalization. Fatty acid compositions of the fatty reagents are shown in Table 5. The probable TAG composition of the edible oils was determined using the algorithm suggested by Antoniosi Filho et al. [39]. This 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 (see Table 6). Note that the UNIFAC division of groups does not distinguish the types of isomerism that are common among the TAG molecules, so that this simplification is fully justified. Moreover, groups with a total TAG composition less than 0.5% are ignored. Thus, certain fatty acids which appear in Table 5 (Po and Ga for palm oil and Co, Po, A, Ga, B and Lg for the mixed oil) do not appear in Table 6, either because the TAG with these fatty acids was contained in a group named by other main TAG or because its composition is below the minimum level indicated above. The oils were also characterized by their residual free fatty acid content. Palm oil had 0.099 ± 0.003% by mass of FFAs and the mixed oil had 0.097 ± 0.002% by mass of FFAs.

384

G.F. Hirata et al. / Fluid Phase Equilibria 360 (2013) 379–391

Table 5 Fatty acid composition of fatty reagents (% by mass). Fatty acid

Symbol

Cx:ya

M (g/mol)

Babassu oil

Caproic Caprilic Capric Lauric Myristic Palmitic Palmitoleic Margaric Margaroleic Stearic Oleic Linoleic Linolenic Arachidic Gadoleic Behenic Lignoceric

Co Cp C L M P Po Mg Mo S O Li Le A Ga B Lg

C6:0 C8:0 C10:0 C12:0 C14:0 C16:0 C16:1 C17:0 C17:1 C18:0 C18:1 C18:2 C18:3 C20:0 C20:1 C22:0 C24:0

116.16 144.22 172.27 200.32 228.38 256.43 254.42 270.45 268.43 284.49 282.47 280.45 278.44 312.54 310.52 340.59 368.65

0.21 3.33 3.26 45.87 15.47 8.53

a

2.32 16.57 4.04 0.17 0.13 0.11

Palm oil

0.30 0.80 41.43 0.14

Soybean oil

10.85

4.67 42.63 9.26 0.22 0.38 0.16

3.72 23.55 53.94 6.90 0.37 0.21 0.47

Mixed oil 0.25 1.44 1.41 19.91 6.91 17.87 0.07

3.33 25.43 20.44 2.23 0.27 0.14 0.18 0.10

Oleic acid

0.07

0.10 99.43 0.07 0.25 0.08

Palmitic acid

0.23 98.44 0.06 0.05 0.55 0.30 0.34 0.03

Cx:y, x is the number of carbons and y is the number of double bonds.

Table 6 Probable composition of triacylglycerols of the vegetable oils. Group x:ya

32:0 34:0 36:0 38:0 38:1 38:2 40:0 40:1 40:2 42:0 42:1 42:2 42:3 44:0 44:1 44:2 44:3 46:0 46:1 46:2 46:3 48:0 48:1 48:2 48:3 48:4 48:5 50:0 50:1 50:2 50:3 50:4 52:1 52:2 52:3 52:4 54:1 54:2 54:3 54:4 54:5 54:6

Main triacylglycerol

CpLL LLC LLL LLM CpLO CpLLi LLP CLO CLLi LMP LOL LLiL LLeL PPL LOM LLiM CpOLi MPP LOP LLiP COLi PPP MOP OOL LOLi LLiLi LLiLe PPS POP OOMm /PLiPp MOLi MLiLi POS POO POLi PLiLi POA SOO OOO OOLi OLiLi LiLiLi

M (g/mol)

582.91 610.97 639.01 667.07 665.06 663.04 695.12 693.11 691.09 723.18 721.17 719.15 717.13 751.24 749.22 747.21 745.19 779.29 777.28 775.26 773.24 807.35 805.33 803.31 801.3 799.28 797.27 835.4 833.38 831.37 829.35 827.31 861.44 859.42 857.41 855.39 889.49 887.48 885.46 883.44 881.43 879.42

‘m,p’ represent which is the main triacylglycerol for mixed and palm oils, respectively. a x:y, x = number of carbons (except carbons of glycerol) and y = number of double bonds.

Mixed oil

Palm oil

% Molar

% Mass

0.60 0.85 2.46 2.26 0.95 0.76 4.05 1.12 0.89 2.76 5.13 4.22 0.59 2.91 3.25 2.97 0.90 1.51 6.51 5.59 1.11 0.89 2.89 6.12 6.42 3.17 0.55

0.45 0.67 2.02 1.93 0.81 0.65 3.61 0.99 0.79 2.56 4.74 3.90 0.54 2.81 3.12 2.85 0.86 1.51 6.49 5.56 1.10 0.92 2.98 6.31 6.60 3.25 0.56

2.51 3.23 2.14 0.97 0.79 3.31 4.41 2.24

2.68 3.44 2.28 1.03 0.87 3.65 4.85 2.46

0.60 1.84 3.00 2.47 1.04

0.68 2.09 3.39 2.80 1.17

% Molar

% Mass

0.43

0.39

5.25 1.38

4.99 1.30

1.59 28.37 6.87

1.56 27.83 6.73

5.85 24.51 10.26 1.39 0.74 2.68 6.29 3.57 0.84

5.93 24.80 10.35 1.39 0.77 2.80 6.56 3.71 0.87

G.F. Hirata et al. / Fluid Phase Equilibria 360 (2013) 379–391

3.2. Experimental procedure The equilibrium cells used are similar to those described by Silva et al. [46]. The cell was jacketed and has connection to a thermostatic bath (Cole Parmer – Model 12101-55, accurate to 0.1 K) to control the cell temperature. Thermometers (Cole-Parmer Instrument Co) with subdivisions of 0.1 K were used for monitoring the cell temperature. The component quantity was determined by weighing on an analytical balance (Precisa instruments, XT220A, accurate to 0.0001 g). The mixture was stirred vigorously with a magnetic stirrer (Fisatom, Model 752A) for 30 min and left to rest for 24 h, in order to obtain complete phase separation and achieve thermodynamic equilibrium, with two clear phases and a welldefined interface. The concentration of FFAs was determined by titration according to official method 2201 of the IUPAC [47] with an automatic buret (Metrohm, Model Dosimat 715). The solvent concentration (ethanol + water), in oil and alcoholic phases, was determined by evaporation at 373.2 K in an oven with air circulation and renewal (Marconi, model MA 035/3, Brazil) until constant mass. The water concentration was determined by Karl Fischer titration, according to AOCS method Ca 23–55 [48], with a KF Titrino (Metrohm, Model 701), so that the ethanol content could be determined by the difference between these last two analyses. The oil (total TAG) composition was obtained by difference. The measurements were carried out at least in triplicate. The uncertainties of the compositions varied within the following ranges: for the system with palm oil (0.02–0.36)% by mass for oil, (0.01–0.08)% by mass for palmitic acid, (0.02–0.37)% by mass for ethanol, and (0.01–0.25)% by mass for water; for the system with the mixed oil (0.04–0.30)% by mass for oil, (0.01–0.10)% by mass for oleic acid and (0.04–0.28)% by mass for ethanol. In order to test the quality of the equilibrium data the procedure developed by Marcilla et al. [49], and already applied to fatty systems by Rodrigues et al. [8], was used. Such procedure consists of calculating the masses of the two liquid phases (MOP and MAP ) from the experimental composition values in terms of the pseudocomponents (wiOP and wiAP ), by a least-squares fitting. The deviations between the sum (MOP + MAP ) and MOC (the total amount of the initial mixture), calculated according to (|(M OP + M AP ) − M OC |/M OC ) × 100, were always less than 0.5%, indicating the good quality of the experimental data [49]. Additional samples were taken from each equilibrium phase and the solvent evaporated according to the procedure already described. The residual fatty components of each phase were derivatized to fatty acid methyl esters and analyzed by gas chromatography according to the methodology indicated before. Considering that the free acidity used in the validation systems is almost totally composed of pure fatty acids, either palmitic or oleic acids (see Table 5), the acidity value determined by titration can be subtracted, in a solvent free basis, from the fatty acid composition determined by gas chromatography in order to obtain the fatty acid composition of the TAGs present in each equilibrium phase. Furthermore, from this fatty acid composition it can be obtained either directly the oil composition in terms of the hypothetical components shown in Table 3 or, by the algorithm of Antoniosi Filho et al. [39], its TAG composition.

4. Results and discussion Table 2 shows the deviations between calculated and experimental compositions for every literature system. The deviations were estimated according to Eq. (2) for the three procedures used for the equilibrium calculations, original UNIFAC groups with literature interaction parameters, original groups with readjusted

385

parameters, and the hypothetical oil components with a new group division and new adjusted parameters. As expected, the original parameters could not describe well this kind of system and for most systems the correlation of the equilibrium data was significantly improved, either by using the readjusted parameters or the parameters adjusted with the new division of groups. Tables 7 and 8 give the values of the interaction parameters in cases of original UNIFAC groups with re-estimated parameters and of the new division of groups. Fig. 2 shows the obtained results for canola oil using ethanol as solvent at 293.2 K [2]. It can be noted that the values calculated with the original parameters are far from the experimental points, both for the alcoholic and oil phases, especially for the region with high free acidity. The readjusted parameters and the adjusted ones for the new division of groups generate values much closer to the experimental ones, and binodal curves in good agreement with the experimental biphasic region. One can also observe that the tieline inclinations obtained using the original UNIFAC parameters exhibit an inverse behavior in comparison to the experimental one, estimating the pseudocomponents partition coefficients wrongly. The set of readjusted parameters and the adjusted parameters for the new division improve, in a very significant way, the description of the experimental tie-lines. The global deviations for the entire set of equilibrium data shown in Table 2 are 6.23% in case of the original parameters, 1.93% for the readjusted parameters, and 2.09% in case of the adjusted parameters with the new division of groups. The last two procedures were able to significantly decrease deviation values between experimental and calculated results. Note that Fig. 2 seems to reveal a prediction of the equilibrium data with the original parameters worse than that indicated by the deviation value. In fact, Eq. (2) estimates the deviations based on the experimental region of phase splitting, while the original set of UNIFAC parameters predicts a much larger region of two-phase coexistence, meaning that a significant part of the predicted region is not included in the evaluation of those deviations. Tables 9 and 10 give the equilibrium data measured in this work for the validation systems. In addition, the concentrations of TAGs expressed in fatty acids in the phases, determined by gas chromatography, are shown in Tables 11 and 12. It should be observed that these concentrations are in a (solvent + free fatty acids) free basis, i.e., they represent only the fatty acid composition belonging to the pseudocomponent oil in each phase. As one can see in Figs. 3 and 4, the new interaction parameters readjusted for the UNIFAC original groups and the set of adjusted parameters for the new division of groups improved the equilibrium prediction for both validation systems. The deviations between experimental and calculated values are given in Table 13 in terms of pseudocomponents. In the case of both validation systems, the calculated deviations are lower for the original division of groups with readjusted parameters, but even for the approach based on the new group division the improvement was noteworthy. In this latter case, in order to evaluate the influence of the designation of an arbitrary group in the equilibrium prediction, an investigation was carried out. The equilibrium was calculated in two ways: the first one using the new division proposed in this work (CH5/3 OCO), and the other one considering the differentiation between the central group (CHOCO) and the lateral groups (CH2 OCO) in the equilibrium calculation, both using the interaction parameters readjusted based on the new division approach. It was considered a mixture containing the triacylglycerol POP (43.41 wt%), stearic acid (2.48 wt%) and ethanol (54.11 wt%) at 30 ◦ C. The same test was done with the triacylglycerol OPP, instead of POP, in order to evaluate the influence of the connectivity of the fatty acids in the glycerol molecule. The deviations between the results of two different prediction ways

386

G.F. Hirata et al. / Fluid Phase Equilibria 360 (2013) 379–391

Table 7 Matrix of re-estimated UNIFAC interaction parameters for the original groups.

CH2 C C OH H2 O COOH COOC

CH2

C C

OH

H2 O

COOH

COOC

0.00 267.19 −27.03 26,526.91 −418.37 −500.77

−323.03 0.00 76.26 −199.06 −790.67 66.66

927.60 798.95 0.00 −292.63 −391.64 271.05

1888.63 1458.48 358.76 0.00 −435.16 871.55

17.35 1634.71 −301.27 6.88 0.00 209.16

14,726.95 300.39 181.89 −20.15 −175.89 0.00

Table 8 Matrix of UNIFAC interaction parameters for the new division of groups.

CH2 C C OH H2 O COOH CH5/3 OCO

CH2

C C

OH

H2 O

COOH

CH5/3 OCO

0.00 −226.57 2600.97 4679.84 417.07 −84.67

−12.44 0.00 −419.69 −279.73 −1285.66 −1074.73

660.85 1357.64 0.00 −393.09 −416.83 73.53

2740.89 512.67 283.28 0.00 −393.18 104.42

289.33 400.85 −496.58 −657.13 0.00 980.50

156.86 −639.22 710.64 3434.78 −777.08 0.00

Fig. 2. Canola oil + oleic acid + ethanol at 293.2 K, () experimental, (· · ·) original UNIFAC, (- - -) reestimated parameters of UNIFAC, (—) new division of groups.

Table 9 Liquid–liquid equilibrium data for the system palm oil (1) + palmitic acid (3) + solvent [ethanol (5) and water (6)] at 318.2 K.a Line

1 2 3 4 5 6 a

Overall composition

Alcoholic phase

Oil phase

100w1

100w3

100w5

100w6

100w1

100w3

100w5

100w6

100w1

100w3

100w5

100w6

49.71 47.88 45.89 43.73 41.76 39.83

0.05 1.99 3.98 6.00 8.12 10.03

47.16 47.05 47.06 47.19 47.05 47.07

3.08 3.08 3.07 3.08 3.07 3.07

2.74 2.57 2.81 2.72 3.75 5.92

0.07 2.00 4.24 6.18 8.41 10.34

90.15 88.53 86.65 84.68 81.50 78.04

7.04 6.90 6.30 6.42 6.34 5.70

87.73 84.60 80.31 76.08 71.34 66.98

0.07 1.97 4.15 6.04 8.24 10.06

11.75 12.81 14.77 16.98 19.39 21.80

0.45 0.62 0.77 0.90 1.03 1.16

Standard uncertainties (u) for mass fraction (w) and temperature (T) are u(w) ≤ 0.0037 (see details on uncertainties range in Section 3.2) and u(T) = 0.1 K.

Table 10 Liquid–liquid equilibrium data for the system mixed oil (2) + oleic acid (4) + anhydrous ethanol (5) at 308.2 K.a Line

1 2 3 4 5 6 a

Overall composition

Alcoholic phase

Oil phase

100w2

100w4

100w5

100w2

100w4

100w5

100w2

100w4

100w5

49.04 48.24 47.59 46.50 45.71 44.94

0.05 0.86 1.63 2.44 3.24 4.03

50.91 50.90 50.78 51.06 51.05 51.03

15.77 16.77 18.63 20.45 23.35 27.51

0.10 0.98 1.76 2.69 3.47 4.25

84.13 82.25 79.61 76.86 73.18 68.24

75.12 72.66 70.70 66.36 63.25 58.25

0.09 0.86 1.51 2.40 3.12 4.01

24.79 26.48 27.79 31.24 33.63 37.74

Standard uncertainties (u) for mass fraction (w) and temperature (T) are u(w) ≤ 0.0030 (see details on uncertainties range in Section 3.2) and u(T) = 0.1 K.

G.F. Hirata et al. / Fluid Phase Equilibria 360 (2013) 379–391

387

Table 11 Experimental values of the palm oil components expressed in fatty acids (% by mass).a Fatty acid

Lauric Myristic Palmitic Palmitoleic Stearic Oleic Linoleic Linolenic Arachidic Gadoleic a b c

Line 1

Line 2

Line 3

Line 4

Line 5

Line 6

OPb

APc

OP

AP

OP

AP

OP

AP

OP

AP

OP

AP

0.28 0.78 41.48 0.13 4.70 42.78 9.08 0.22 0.39 0.16

0.77 1.02 38.44 0.18 3.40 43.99 11.40 0.47 0.22 0.11

0.28 0.78 41.55 0.17 4.72 42.70 9.03 0.22 0.39 0.16

0.78 3.31 31.19 0.16 4.05 44.70 14.64 0.82 0.23 0.12

0.28 0.78 41.52 0.17 4.72 42.72 9.05 0.21 0.39 0.16

0.96 1.50 30.30 0.28 4.59 49.20 12.39 0.39 0.25 0.14

0.28 0.79 41.56 0.13 4.75 42.68 9.04 0.22 0.39 0.16

0.92 1.80 17.56 0.36 5.88 58.16 14.33 0.51 0.33 0.15

0.28 0.80 41.46 0.13 4.80 42.71 9.06 0.21 0.39 0.16

0.85 1.73 19.72 0.19 6.00 57.06 13.46 0.43 0.37 0.19

0.29 0.81 41.41 0.14 4.81 42.65 9.11 0.23 0.39 0.16

0.63 1.39 37.34 0.32 4.80 44.42 10.39 0.30 0.27 0.14

Standard uncertainties (u) for mass fraction (w) and temperature (T) are u(w) = 0.0001 and u(T) = 0.1 K. Oil phase. Alcoholic phase.

Table 12 Experimental values of the mixed oil components expressed in fatty acids (% by mass)a . Fatty acid

Caproic Caprilic Capric Lauric Myristic Palmitic Palmitoleic Stearic Oleic Linoleic Linolenic Arachidic Gadoleic Behenic Lignoceric a b c

Line 1

Line 2

Line 3

Line 4

Line 5

Line 6

OPb

APc

OP

AP

OP

AP

OP

AP

OP

AP

OP

AP

0.08 1.25 1.27 18.56 6.64 18.33 0.07 3.46 26.25 21.06 2.28 0.28 0.16 0.19 0.12

0.17 2.32 2.13 27.85 8.44 15.37 0.06 2.65 21.80 16.90 1.86 0.18 0.11 0.10 0.06

0.08 1.22 1.24 18.36 6.62 18.37 0.07 3.47 26.58 20.98 2.27 0.28 0.16 0.19 0.11

0.14 2.08 1.95 25.90 7.98 14.80 0.06 2.55 25.69 16.59 1.83 0.17 0.11 0.10 0.05

0.08 1.25 1.26 18.37 6.56 18.22 0.07 3.46 26.87 20.88 2.25 0.28 0.15 0.19 0.11

0.14 1.92 1.80 24.22 7.59 14.59 0.06 2.53 28.52 16.38 1.79 0.17 0.11 0.11 0.07

0.08 1.27 1.27 18.34 6.50 18.06 0.07 3.43 27.16 20.83 2.24 0.28 0.15 0.19 0.13

0.12 1.74 1.66 22.59 7.23 14.71 0.06 2.63 30.33 16.58 1.82 0.19 0.12 0.12 0.10

0.09 1.27 1.27 18.35 6.49 17.95 0.06 3.38 27.66 20.56 2.21 0.28 0.15 0.18 0.10

0.12 1.66 1.58 21.58 6.96 14.76 0.06 2.63 31.62 16.69 1.81 0.20 0.12 0.12 0.09

0.09 1.29 1.29 18.44 6.45 17.71 0.07 3.33 28.12 20.39 2.11 0.27 0.15 0.19 0.10

0.10 1.53 1.48 20.45 6.75 15.28 0.06 2.83 31.83 17.25 1.86 0.22 0.13 0.14 0.09

Standard uncertainties (u) for mass fraction (w) and temperature (T) are u(w) = 0.0001 and u(T) = 0.1 K. Oil phase. Alcoholic phase.

Fig. 3. Palm oil + palmitic acid + (ethanol + water) at 318.2 K, () experimental, (· · ·) original UNIFAC, (- - -) reestimated parameters of UNIFAC, (—) new division of groups. Table 13 Absolute average deviations for the validation systems expressed in terms of pseudocomponents. System

w (%) Original parameters a

Palm oil + palmitic acid + ethanol + water Mixed oil + oleic acid + ethanol a b c

Oil phase. Alcoholic phase. Both liquid phases.

b

c

Re-estimated parameters

New division

OP

AP

GLOBAL

OP

AP

GLOBAL

OP

AP

GLOBAL

6.16 14.15

3.03 15.89

4.85 15.04

1.94 3.73

0.55 1.61

1.43 2.87

3.10 6.55

1.31 4.12

2.38 5.47

388

G.F. Hirata et al. / Fluid Phase Equilibria 360 (2013) 379–391

Fig. 4. Mixed oil + oleic acid + ethanol at 308.2 K, () experimental, (· · ·) original UNIFAC, (- - -) reestimated parameters of UNIFAC, (—) new division of groups.

were calculated (using Eq. (2)), and the values varied from 0.072% to 0.230%. If these values are compared with the global deviations shown in Table 13, it can be seen that considering the differentiation between the lateral CH2 OCO and the central CHOCO does not affect significantly the equilibrium prediction. In fact, the highest deviation between the different approaches (0.23%) is ten times lower that the lowest deviation between predicted and experimental results (2.38%) reported for the new division of groups (Table 13). Back to the analysis of Table 13, it can be seen that the deviations are higher in the case of the mixed oil for all the three procedures, indicating that a higher scattering of TAGs seems to represent a more stringent test for the different procedures used in the equilibrium prediction. It should be noted that the mixed oil contains a significant amount of an oil rich in lauric acid, babassu oil, and the data used for adjusting the sets of parameters contained a relatively lower quantity of experimental results obtained for oils with TAGs of low molecular weight. Figs. 5 and 6 compare the calculated and experimental compositions of the oil components in both equilibrium phases. Fig. 5 shows the results for the mixed oil, in which the oil components are expressed in terms of TAGs and, for this reason, only the results obtained for the original division of groups are shown. In the case of Fig. 6 the oil components of the palm oil are expressed in terms of the hypothetical oil components (see Table 3) and, for this reason, the results obtained for the new division of groups are also shown. For the construction of Fig. 6, some modifications in the way the data are expressed were required. Firstly, the experimental composition expressed in fatty acids (Tables 11 and 12) were converted into hypothetical compounds (FA-TAGs), taking into account that the oil composition in fatty acids is the same that in FA-TAGs in terms of molar fractions, and their different molar masses were used in this conversion. Secondly, since for the UNIFAC original groups the calculated results are obtained in terms of TAGs, it was also necessary to transform them into FA-TAGs. Thus, the TAGs molecules were broken so that the fatty compositions in the phases become represented in terms of hypothetical components. This procedure was not necessary for the new division of groups since the oil compounds composition is already calculated in FA-TAGs. Unfortunately a complete comparison of both procedures (TAG and FA-TAG) was not always possible, since in the case of the hypothetical components, the specific connection between each fatty acid residue and the glycerol moiety was not taken into account and assuming a specific connection only for comparison purposes may be rather arbitrary. On the other hand, in the case of the original division of groups some of the fatty acids detected in the vegetable oil analysis were not expressed in its TAG composition because

each set of TAG was represented by its major component, as it was explained before. Fortunately, this occurs for hypothetical components with very low concentration, such as Po-TAG in both palm and mixed oils. Anyway, all these figures show the significant improvement in the partition of oil components caused by the new set of UNIFAC parameters with the original division of groups. In fact, it was observed a very important decrease in the deviation values between the experimental and calculated mass fractions of the components, calculated in a way similar to Eq. (2), where P can assume different values as indicated hereafter. These deviations were calculated in six different ways for each system: three of them representing the pseudocomponent oil in its respective TAGs and the other three, in its hypothetical components, and the results are shown in Table 14. In the first case (comparison in terms of TAGs), only the deviations calculated for the original division of groups are presented, due to the reasons already mentioned. In the first line of each system in Table 14, the calculations were done taking into account only the fatty compounds within the pseudocomponent oil. Note that, in this case, P is equal to 15 (palm oil) or 40 (mixed oil) (see Table 6). When the deviations were calculated considering the components TAG + fatty acid + solvent, P becomes 18 (palm oil) or 42 (mixed oil). In order to compare the results shown in Table 13 (which consider the mixtures as pseudo-ternary or -quaternary systems) with those of Table 14, the same procedure was done for the third line of each system, but assuming P equal to the number of pseudocomponents (P = 4 for palm oil and P = 3 for mixed oil), since part of the reduction in the deviation values is due to the higher value in the denominator. If the oil is expressed in terms of hypothetical components, the same calculation procedure was used, considering the three different components groups in a way similar to the first case. In this approach, P decreases to 10 (palm oil) or 15 (mixed oil), when only the hypothetical components are considered, summing 13 (palm oil) or 17 (mixed oil) when the solvent components were included. The comparison between the experimental and calculated data was done using the same data expressed in terms of FA-TAGs, as was done in Fig. 6. In the case of the original UNIFAC parameters the deviations between experimental and calculated results are much larger than the values for the new set of parameters and for the new division of groups, suggesting a much better performance in partition prediction (see Table 14). As one can see, both procedures, the new division of groups and the re-estimated parameters for the original division, improve considerably the performance of the UNIFAC method for predicting the partitioning of the components. It should

G.F. Hirata et al. / Fluid Phase Equilibria 360 (2013) 379–391

389

Fig. 5. Comparison of experimental and calculated mass fractions wTAG of mixed oil components (expressed in terms of TAGs) in the oil phases: UNIFAC with original parameters () and readjusted ones (+), and in the alcoholic phase: UNIFAC with original parameters () and readjusted ones (×).

Fig. 6. Comparison of experimental and calculated mass fractions wFA-TAG of palm oil components (expressed in terms of hypothetical components) in the oil phases: UNIFAC with original parameters (), readjusted ones (+) and with the new division of groups (); and in the alcoholic phase: UNIFAC with original parameters (), readjusted ones (×) and with the new division of groups ().

Table 14 Absolute average deviations for the validation systems with the oil components explicitly considered. System

Components involved

w (%) Original parameters a

OP

Palm oil + palmitic acid + ethanol + water

Mixed oil + oleic acid + ethanol

a b c d

TAG TAG + palmitic acid + ethanol + water (TAG + palmitic acid + ethanol + water)d FA-TAG FA-TAG + palmitic acid + ethanol + water (FA-TAG + palmitic acid + ethanol + water) d TAG TAG + oleic acid + ethanol (TAG + oleic acid + ethanol) d FA-TAG FA-TAG + oleic acid + ethanol (FA-TAG + oleic acid + ethanol) d

Oil phase. Alcoholic phase. Both liquid phases. P (Eq. (2)) is equal to the number of pseudocomponents.

b

AP

c

GLOBAL

Re-estimated parameters

New division

OP

AP

GLOBAL

OP

AP

GLOBAL

0.70 1.84

0.33 0.93

0.54 1.46

0.25 0.50

0.18 0.25

0.22 0.39

– –

– –

– –

3.90

1.97

3.09

1.05

0.54

0.84

–

–

–

1.90 2.62

0.63 1.17

1.41 2.03

1.10 1.10

0.23 0.30

0.80 0.81

0.89 1.16

0.51 0.64

0.72 0.94

4.73

2.11

3.66

1.98

0.55

1.45

2.09

1.15

1.69

0.52 2.81 10.53 2.83 5.10 12.15

0.58 3.15 11.80 2.17 5.28 12.58

0.55 2.99 11.18 2.53 5.19 12.36

0.15 0.72 2.69 1.50 1.80 4.29

0.09 1.18 1.18 0.43 0.63 1.51

0.12 0.55 2.08 1.11 1.35 3.21

– – – 1.15 2.24 5.33

– – – 0.79 1.44 3.43

– – – 0.99 1.88 4.48

390

G.F. Hirata et al. / Fluid Phase Equilibria 360 (2013) 379–391

be noted that this significant improvement in the prediction of the partition behavior of oil components was obtained despite the fact that no partition data of oil components were directly used in the procedure of adjustment/readjustment of parameters. Naturally, the composition of pseudocomponents in terms of TAGs or hypothetical compounds was taken into account and this consideration was sufficient for significantly improving the group contribution approach. In fact, the behavior of the experimental equilibrium data in terms of pseudocomponents reflects the differences in compositions of the various vegetable oils, making possible the strategy used for adjusting/readjusting interaction parameters. This might mean that, in the case of equilibrium data of systems containing natural products composed of a set of similar compounds, a reliable characterization of these products can act as a good proxy for improving the correlative and predictive capacity of calculation methodologies without requiring a comprehensive data characterization of the phases in equilibrium. 5. Conclusions This work suggests a new approach to adjust/readjust interaction parameters of the UNIFAC method based on experimental data from real systems, provided the detailed composition of each pseudocomponent used in the equilibrium system is available. On the basis of a large experimental data bank for LLE of fatty systems, this approach was tested to readjust interaction parameters associated with the UNIFAC original groups and to adjust parameters associated with a new division of groups. Both alternatives improved significantly the capacity of the UNIFAC method for describing LLE of fatty systems, an improvement further tested in the case of two validation systems and taking into account the distribution of different fatty compounds between the two liquid phases. Although the new division of groups simplifies the representation of the pseudocomponent oil and shortens the path that goes from their analytical characterization to its chemical description, the improvement of the UNIFAC method obtained by adjusting/readjusting the interaction parameters was more impressive in the case of the original division of groups. List of symbols

Aw D FAME FA-TAG FFA LLE N P Qk Rk TAG Vw w

van der Waals surface area total number of data groups (Eq. (1)) fatty acid methyl ester hypothetical component free fatty acid liquid–liquid equilibrium total number of tie lines in each group (Eq. (1)) total number of components/pseudocomponents in every data group (Eq. (1)) van der Waals surface area of group k van der Waals volume of group k triacylglycerol van der Waals volume mass fraction

Subscripts i pseudocomponent (Eq. (1)) data group (Eq. (1)) m n tie line (Eq. (1)) Superscripts alcoholic phase AP calc calculated

exp OC OP

experimental overall composition oil phase

Acknowledgements The authors wish to acknowledge CAPES for the scholarship and FAPESP (08/56258-8 and 09/54137-1), CNPq (304495/2010-7 and 483340/2012-0) and FAEPEX/UNICAMP for the financial support.

References [1] S. Monnerat, A.J.A. Meirelles, 9th World Congress of Food Science and Technology, Budapeste, Hungria, 1995, p. 52. [2] E. Batista, S. Monnerat, K. Kato, L. Stragevitch, A.J.A. Meirelles, J. Chem. Eng. Data 44 (1999) 1360–1364. [3] C.B. Gonc¸alves, E. Batista, A.J.A. Meirelles, J. Chem. Eng. Data 47 (2002) 416–420. [4] C.E.C. Rodrigues, R. Antoniassi, A.J.A. Meirelles, J. Chem. Eng. Data 48 (2003) 367–373. [5] C.B. Gonc¸alves, A.J.A. Meirelles, Fluid Phase Equilib. 221 (2004) 139–150. [6] C.E.C. Rodrigues, P.A. Pessôa Filho, A.J.A. Meirelles, Fluid Phase Equilib. 216 (2) (2004) 271–283. [7] C.E.C. Rodrigues, F.A. Silva, A. Marsaioli Jr., A.J.A. Meirelles, J. Chem. Eng. Data 50 (2005) 517–523. [8] C.E.C. Rodrigues, E.C.C.D. Reipert, A.F. Souza, P.A. Pessôa Filho, A.J.A. Meirelles, Fluid Phase Equilib. 238 (2005) 193–203. [9] C.E.C. Rodrigues, A. Filipini, A.J.A. Meirelles, J. Chem. Eng. Data 51 (2006) 15–21. [10] C.B. Gonc¸alves, P.A. Pessôa Filho, A.J.A. Meirelles, J. Food Eng. 81 (2007) 21–26. [11] C.E.C. Rodrigues, E.C.D. Peixoto, A.J.A. Meirelles, Fluid Phase Equilib. 261 (2007) 122–128. [12] R.D. O’Brien, Fats and Oils: Formulating and Processing for Applications, Technomic Publishing Company, Pennsylvania, 1998. [13] R.C. Basso, A.J.A. Meirelles, E.A.C. Batista, Fluid Phase Equilib. 333 (2012) 55–62. [14] C.A.S. da Silva, G. Sanaiotti, M. Lanza, A.J.A. Meirelles, E.A.C. Batista, J. Chem. Eng. Data 55 (2010) 2416–2423. [15] W.L. Priamo, M. Lanza, A.J.A. Meirelles, E.A.C. Batista, J. Chem. Eng. Data 54 (2009) 2174–2181. [16] E.C.D. Reipert, C.E.C. Rodrigues, A.J.A. Meirelles, J. Chem. Thermodyn. 43 (2011) 1784–1790. [17] S. Heron, A. Tchapla, J. Ital. Food Sci. 4 (1990) 262–263. [18] E. Batista, S. Monnerat, L. Stragevitch, A.J.A. Meirelles, J. Chem. Eng. Data 44 (1999) 1365–1369. [19] C.E.C. Rodrigues, A.J.A. Meirelles, J. Chem. Eng. Data 53 (2008) 1698–1704. [20] E.C.D. Reipert, Food Engineering Faculty, M.Sc. Thesis, University of Campinas, 2005 (in Portuguese). [21] G. Sanaiotti, J.S.R. Coimbra, J.C. Gomes, L.A. Minim, J. Chem. Eng. Data 53 (2008) 1492–1497. [22] M. Mohsen-Nia, H. Modarress, H.R. Nabavi, J. Am. Oil Chem. Soc. 85 (2008) 973–978. [23] G.B. Gomes, C.E.C. Rodrigues, A.J.A. Meirelles, XII Congresso Interno de Iniciac¸ão Científica–UNICAMP, Campinas, Brazil, 22–24 September, 2004, p. 205 (in Portuguese). [24] A. Krip, M.Sc. Thesis, Food Engineering Faculty, University of Campinas, 2002 (in Portuguese). [25] M. Catté, C.G. Dussap, J.B. Gros, Fluid Phase Equilib. 105 (1995) 1–25. [26] O. Ferreira, E.A. Brignole, E.A. Macedo, Ind. Eng. Chem. Res. 42 (2003) 6212–6222. [27] N. Spiliotis, D. Tassios, Fluid Phase Equilib. 173 (2000) 39–55. [28] H. Kurarnochi, H. Noritomi, D. Hoshino, K. Nagahama, Fluid Phase Equilib. 130 (1997) 117–132. [29] Z. Tang, Z. Du, E. Min, L. Gao, T. Jiang, B. Han, Fluid Phase Equilib. 239 (2006) 8–11. [30] D.S. Negi, F. Sobotka, T. Kimmel, G. Wozny, R. Schomäcker, Ind. Eng. Chem. Res. 45 (10) (2006) 3693–3696. [31] A. Fredenslund, R.L. Jones, J.M. Prausnitz, AIChE J. 21 (1975) 1086–1099. [32] T. Magnussen, P. Rasmussen, A. Fredenslund, Ind. Eng. Chem. Process Des. Dev. 20 (1981) 331–339. [33] C.M. Oliveira, B.R. Garavazo, C.E.C. Rodrigues, J. Food Eng. 110 (3) (2012) 418–427. [34] U. Weidlich, J. Gmehling, Ind. Eng. Chem. Res. 26 (7) (1987) 1372–1381. [35] J. Gmehling, J. Li, M. Schiller, Ind. Eng. Chem. Res. 32 (1) (1993) 178–193. [36] J.A. Nelder, R.A. Mead, Comput. J. 7 (4) (1965) 308–313. [37] M. Mohsen-Nia, M. Dargahi, J. Chem. Eng. Data 52 (3) (2007) 910–914. [38] M. Mohsen-Nia, A. Khodayari, J. Chem. Thermodyn. 40 (2008) 1325–1329. [39] N.R. Antoniosi Filho, O.L. Mendes, F.M. Lanc¸as, Chromatographia 40 (1995) 557–562. [40] R. Ceriani, A.M. Costa, A.J.A. Meirelles, Ind. Eng. Chem. Res. 47 (2008) 681–692. [41] M. León Camacho, M.V. Ruiz Méndez, E. Graciani Constante, Grasas Aceites 54 (2003) 138–144. [42] G. Hénon, Z. Zemény, K. Recseg, F. Zwobada, K. Kövári, J. Am. Oil Chem. Soc. 76 (1999) 73–81.

G.F. Hirata et al. / Fluid Phase Equilibria 360 (2013) 379–391 [43] A. Bondi, Physical Properties of Molecular Crystals Liquids and Glasses, John Wiley, New York, 1968. [44] A.O.C.S. Official Methods and Recommended Practices of the American Oil Chemists’ Society, vol. 1–2, third ed., A.O.C.S. Press, Champaign, 1988. [45] A.O.C.S. Official Methods and Recommended Practices of the American Oil Chemists’ Society, fifth ed., A.O.C.S. Press, Champaign, 1998.

391

[46] L.H.M. Silva, J.S. Coimbra, A.J.A. Meirelles, J. Chem. Eng. Data 42 (1997) 398–401. [47] IUPAC Standard Methods for the Analysis of Oils, Fats and Derivatives, sixth ed., Pergamon Press, New York, 1979. [48] D. Firestone (Ed.), AOCS Official Methods and Recommended Practices of the American Oil Chemists’ Society, A.O.C.S. Press, Champaign, 1989. [49] A. Marcilla, F. Ruiz, A.N. García, Fluid Phase Equilib. 112 (1995) 273–289.