DAG - diacylglycerol
FFA - free fatty acid
MAG - monoacylglycerol
nc - number of compounds in the system
nf - total number of phases
NP - total number of tie-lines
TAG - triacylglycerol
x_ijk^calc - calculated mass fraction of component i in phase j for the k tie-line
x_ijk^exp - experimental mass fraction of component i in phase j for the k tie-line
σ_j² - variance of the experimental phase j

Diets that are rich in fats and oils represent a risk factor for obesity and heart diseases so that physicians and other professionals related to health care area have recommended a reduction in such dietary habits. Since fats and oils are sources of essential fatty acids and liposoluble vitamins, the ingestion of this kind of food is recommended in a diary balanced diet [1]. However, low fat diets are usually not tolerated for long periods, due to the fact that the presence of fat increases the palatability of the food. An alternative to the reduction of the amount of fat consumed is the replacement of the conventional edible oil, which is rich in triacylglycerols molecules, by a diacylglycerol rich oil. Such enriched types of oil have been well accepted by consumers of fatty foods and studies have indicated that its consumption in replacement by the conventional oil can prevent health problems that are related to rich triacylglycerol oils consumption [2, 3].

Diacylglycerols can be produced by glycerol esterification processes, glycerolysis of triacylglycerols or from the partial hydrolysis of triacylglycerols [4]. Independently of the process used, the final product will contain a mixture of triacylglycerols, diacylglycerols, monoacylglycerols and free fatty acids (FFA), which are molecules with main polar groups, and so can be easily separated from glycerol and water present in the reactant medium. A further separation process is normally necessary to separate the diacylglycerols from the other molecules, and that can be achieved with distillation [5] or liquid-liquid extraction with polar solvents [6].

Distillation of oil molecules is a process related to high temperatures and high vacuum conditions (since are molecules with very high molecular weight and low volatility), different from liquid-liquid extraction that can be performed at ambient conditions. In fact, the temperature required for a liquid-liquid extraction process involving oil molecules should just be high enough to avoid the formation of a solid phase in the system.

For an appropriate process and equipment design, mathematical models are usually required. Voll et al. [6] obtained liquid-liquid UNIQUAC and NRTL interaction parameters for the system TAG + DAG + MAG + FFA + ethanol + water by correlating experimental data with the Gibbs free energy models, and verified the potential of DAG enrichment by liquid-liquid extraction strategy using ethanol and water as solvents. The water phase tends to have less TAG molecules, due to its higher hydrophobicity when compared to DAG, MAG and FFA. Since DAG presents higher hydrophobicity than MAG and FFA, simulations indicate that multiple equilibrium stages will ensure DAG enrichment in the oil.

Since a liquid-liquid system with 6 components demands 30 binary interaction parameters for Gibbs free energy models it is desirable that some of these parameters are previously known from smaller systems that contain the same components. In this context, the main subject of this work was to determine the binary interaction parameters between TAG, FFA (both from olive oil), ethanol and water from ternary systems comprising these 4 components. This procedure can reduce from 30 to 18 the number of unknown parameters to be determined in a 6 component liquid-liquid system.

Gonçalves and Meirreles [7] and Chiyoda et al. [8] presented experimental data and thermodynamic modeling of liquid-liquid equilibrium of palm oil + fatty acids (palmitic and/or oleic acid) + ethanol + water and soybean oil + linoleic acid + ethanol + water systems, respectively. The first study has shown that the behavior of the main free fatty acids of palm oil (palmitic and oleic) are quite similar in liquid-liquid equilibrium. However, for a high water content in the system (12.41 wt%), the thermodynamic model UNIQUAC overestimated or underestimated the different free fatty acids distribution coefficients depending on the acidity level. In the present work, it was an intention to use free fatty acids obtained from the own edible oil (by hydrolysis) used in the experiments. Olive oil is one of the edible oils with higher concentration in one particular fatty acid (in this case, the oleic acid)[9], and such fact probably improves the chances that the TAG and free fatty acids from this oil behave as pseudo-components for the modeling purposes. For that reason, olive oil was chosen as substrate in the present work.

The tie lines measured at 328.2 K for the three ternary systems, which were used in the estimation of UNIQUAC parameters, are presented in Table 1. Tables 2 and 3 present the ternary system obtained at 298.2 K and the quaternary system at 328.2 K, respectively. The experimental data presented in Table 2 were not used for the parameters estimation of the excess Gibbs free energy model used in this work. These data were used to check the prediction capability of the thermodynamic model used.

The r_i and q_i values used for the UNIQUAC model are presented in Table 4, while the estimated interaction parameters A_ij e A_ji are presented in Table 5. It must be pointed out that only 10 parameters were adjusted in the present work, since the interaction parameters between ethanol and water were used as obtained by Kanda et al. [12], who studied the LLE of palmitic acid + ethanol + water/glycerol.

For the binary interaction parameters fitting a set with 9 experimental tie lines was used, which included 52 experimental mass fraction information of TAG, FFA, ethanol and water. The absolute deviation (AD) between the experimental and calculated data was 1.28 %, while the root mean square deviation (rmsd) was calculated as 2.10 % (considering all data, except that from Table 2). The low deviations values indicate that the UNIQUAC model was capable of correlate well the experimental data for the complex system presented in this work. Such conclusion can also be made by observing the comparison between experimental and calculated data in Fig. (1) (data from first to fourth lines of Table 1), Fig. (2), (data from Table 2, for Fig. (2-A) and data from fifth to eighth lines for Fig. (2-B)), Fig. (3) (data from eighth and ninth lines of Table 1) and Fig. (4) (data from Table 3). It is worth mentioning that the experimental data showed in Fig. (2-A) were not used in the interaction parameters estimation, which is indicating that the model can be used for liquid-liquid separation predictions in temperatures that are different from that used to obtain the model parameters.

Fig. (1). Ternary diagram for the system free fatty acid (FFA)(2) + ethanol(3) + water(4) at T = 328.2 K. Experimental ̶●̶, tie lines, □, overall composition) and UNIQUAC model -Δ-, tie lines; ―, binodal).

One can notice from Figs. (1) and (3) that ethanol and FFA from olive oil are completely miscible. On the other hand, olive oil TAG is only partially miscible in ethanol, as observed in Figs. (2) and (3). A small immiscibility region was observed for the ternary system TAG + FFA + ethanol (Fig. 3). This is expected because ethanol and TAG are partially miscible and, in addition, FFA has good miscibility with both ethanol and TAG due to its hydrophilic-hydrophobic balance.

Fig. (2). Ternary diagram for the system TAG(1) + ethanol(3) + water(4) at T = 298.15 K (A) and T = 328.2 K (B). Experimental ̶●̶, tie lines, □, overall composition), UNIQUAC model -Δ-, tie lines; ―, binodal).

The ternary system TAG + ethanol + water presented small miscibility regions. One occurs for high TAG concentration (above 75 wt%) associated to very small water concentration (below 0.5 wt%). The other miscibility region is obtained only for high ethanol concentrations (above 90 wt%).

Fig. (3). Ternary diagram for the system TAG(1) + FFA(2) + ethanol(3) at T = 328.2 K. Experimental ̶●̶ , tie lines), UNIQUAC model -Δ-, tie lines, □, overall composition; ―, binodal).

Fig. (4). Ternary diagram for the system TAG + FFA(1+2) + ethanol(3) + water(4) at T = 328.2 K. Experimental ̶●̶ , tie lines, □, overall composition), UNIQUAC model -Δ- , tie lines). (Experimental data from Table 3)

This work reports liquid-liquid equilibrium data for olive oil TAG, FFA, ethanol and water systems, comprising results for ternary and quaternary systems at 298.2 and 328.2 K. The UNIQUAC model provides a very satisfactory representation of the experimental liquid-liquid equilibrium values for the highly non-ideal mixtures investigated. Hydroalcoholic systems containing FFA presented wider miscibility regions when compared to TAG. This was attributed to the presence of the polar carboxylic acid group in FFA, what makes then more hydrophilic when compared to TAG molecules. Results obtained in the present work might be valuable for process development, phase separation and optimization related to DAG-enrichment oil processes.

The authors confirm that this article content has no conflict of interest.