Introduction

Oilseeds are the primary source for the production of edible oils, an essential component of the human diet since it is the primary source of dietary lipids, the most concentrated source of metabolic energy (Vaisali et al. 2015). According to the United States Department of Agriculture (USDA), the annual global production of the major vegetable oils amounted to 203.84 Mt in 2018/19 (USDA 2019). These vegetable oils have been primarily produced in these large amounts for food purposes (O’Brien 2009). However, oils of vegetable origin are not only suitable for food purposes, but around 20% of the annually produced oils are also processed into biofuels and other chemical products (Biermann et al. 2011). In countries like Brazil, the use of vegetable oils in the energy sector is supported and encouraged by national programs and policies (Sampaio Neto et al. 2020).

Thus, given the high demand for vegetable oils, the oil industry’s attention has been brought to alternative matrices. Since the Brazilian Amazonian region presents several species with high oil content that have not been adequately studied yet, some groups have driven their research focus to the products typically cultivated in that region (Santos et al. 2013; Penha et al. 2015; Rosa et al. 2016; Vidoca et al. 2020).

In a previous publication of our group, physicochemical and nutraceutical properties of vegetable oils produced by Brazilian Amazonian oleaginous plant species have been identified (Pereira et al. 2019a). Such species as Pracaxi (Pentaclethra macroloba) and Patawa (Oenocarpus bataua), are of particular interest. The former produces fruits containing seeds from which is extracted oil with a high content of ω6 (from 12 to 13 wt% of linoleic acid) and ω9 (from 47 to 53 wt% of oleic acid) fatty acids and is considered a natural source of behenic acid (dos Santos Costa et al. 2014; Pereira et al. 2019a). In turn, the patawa oil, extracted from patawa fruit pulp, has a healthy FA content, presenting a ratio of 18.5/81.5 (w/w) saturated/unsaturated FA, in which the oleic acid represents more than 70 wt%. Although both of these oils are widely used in the cosmetic industry to prepare formulations of hair and skin products (Pereira Lima et al. 2017), their use might be further explored in the food industry.

The primary constituents of crude oils, such as patawa and pracaxi oils, are triacylglycerols (TAGs), partial acylglycerols, free fatty acids (FFAs), and variable amounts of non-glyceride compounds (such as phosphatides, fat-soluble vitamins, and pigments). The refining of edible oils makes seed oils obtained by extraction more palatable for human consumption, and usually refers to the operations of deacidification, bleaching, and deodorization (Dijkstra and Segers 2007). Because the presence of FFAs in vegetable oils is undesirable for biodiesel and edible oil production, the deacidification process determines its quality, having a significant economic impact on oil production (Manic et al. 2011).

The deacidification step is usually performed by chemical or physical refining. However, for oils with a high content of FFAs, the chemical refining may cause high losses of the neutral oil, while physical refining methods lead, in some cases, to undesirable alterations in color and oxidative stability reductions (Leibovitz and Ruckensteins 1983; Antoniassi et al. 1998). Considering the oils selected for this study, chemical or physical refining might affect the final product’s quality. Because of harvesting and oil extraction conditions, these oils can often present FFA contents higher than the maximum acid value of 4.00 mg KOH/g oil, recommended for cold-pressed and virgin oils (Codex Alimentarius 1999). In this context, the liquid–liquid extraction technique is an alternative to the traditional processes. This technique is based on the difference of solubility of FFAs and neutral TAGs in an appropriate solvent (Thomopoulos 1971).

The liquid–liquid deacidification can be conducted using short-chain alcohols, such as ethanol and isopropanol, as solvents (Bhattacharyya et al. 1987; Rodrigues et al. 2004; Casas et al. 2014). Moreover, study publications using this liquid–liquid or solvent extraction at room temperature and atmospheric pressure have shown that it reduces the energy consumption of oil refining, minimizes the losses of nutraceutical compounds, and avoids the formation of side products (Sengupta and Bhattacharyya 1992; Rodrigues et al. 2014).

On the other hand, the liquid–liquid extraction approach’s development demands a systematic study of the phase equilibrium involving fatty compounds and solvent. Thus, more experimental data relating to the equilibrium of systems composed by vegetable oils + fatty acids + solvents are necessary for designing industrial-scale equipment, expand the liquid–liquid equilibrium (LLE) databank for fatty systems containing vegetable oils, and to develop feasible liquid–liquid extraction oil refining processes.

Therefore, the present work aimed to investigate the LLE behavior of the following systems at 298.15 K and atmospheric pressure: patawa oil + oleic acid + anhydrous ethanol; pracaxi oil + oleic acid + anhydrous ethanol; pracaxi oil + oleic acid + azeotropic ethanol (6.02 wt% of water); pracaxi oil + oleic acid + azeotropic isopropanol (13.07 wt% of water). The reliability of the measured LLE data was tested using mass balance equations (Marcilla et al. 1995) and the Othmer–Tobias correlation (Othmer and Tobias 1942). Furthermore, the nonrandom two-liquid—NRTL (Renon and Prausnitz 1968) and universal quasi chemical—UNIQUAC (Abrams and Prausnitz 1975) models were used to correlate the experimental data and to obtain binary interaction parameters for the studied systems.

Material and methods

Materials

Crude patawa and pracaxi oils used in this study were kindly supplied by Amazon Oil Industry (Ananindeua, Brazil). Patawa and pracaxi oils presented initial acidity values of 0.49% and 1.62%, respectively, expressed as the mass fraction of oleic acid and determined according to the method Cd 3d-63 (AOCS 2009). Commercial oleic acid was acquired from Sigma-Aldrich (USA) with a purity of 90.76%. The solvents used in this work were anhydrous ethanol from Merck (Germany) with purity greater than 99.5%, and isopropanol from Merck (Germany) with purity greater than 99.8%. Purities provided by the manufacturer, no further purification methods were employed. The aqueous azeotropic solvents were gravimetrically prepared by the addition of deionized water (Milli-Q, Millipore) to the anhydrous ethanol (6.02 wt%) and isopropanol (13.07 wt%).

Fatty acid composition characterization

The fatty acid compositions of patawa and pracaxi oils were taken from the previous publication of this group about the physico-chemical characterization of these products (Pereira et al. 2019a). The commercial oleic acid was analyzed by gas chromatography (GC), according to the AOCS official method Ce 1–62 (AOCS 2009). The conversion of FA to fatty acid methyl esters (FAME) was conducted according to the method described by Hartman and Lago (1973). GC analyses were performed in a Clarus 600 gas chromatograph (PerkinElmer, USA) equipped with a flame ionization detector (FID) and a DB-WAX capillary column (length 30 m, internal diameter 0.25 mm, film thickness 0.25 μm; Agilent Technologies, USA), in the following operating conditions: Helium (carrier gas) at a flow rate of 1.78 mL min−1, FID temperature of 250 °C, injector at 250 °C, injection volume of 1 μL, column temperature ramp from 50 °C to 250 °C at 10 °C min−1. Individual FAME peaks were identified by comparing retention times to an external standard (FAME mix C8–C24; Sigma-Aldrich, USA). Retention times and peak areas were evaluated via Total Chrom software (version 6.3.2, PerkinElmer, USA). Results were expressed as relative percentages of the mass of total FA.

Triacylglycerol profile

In order to calculate the average molar mass of patawa and pracaxi oil TAGs, the procedure described by Antoniosi Filho et al. (1995) was used to obtain the probable TAG profile of the oils. This combinatorial analysis method uses the oils’ FA compositions, previously obtained by Pereira et al. (2019a), using the same analytical method described in the subtopic 2.1.2, as analytical input data to proceed the calculations based in a non-random model, which considers the preferences for FAs sterification positions.

The Antoniosi Filho et al. (1995) computational method takes into account that the most highly unsaturated FA preferentially acylates at the sn-2 position, taking the place of the radicals R2, as shown in Fig. 1. Subsequently, the remaining acids, including any unsaturated FA not requested at the sn-2 position, will be placed on the sn-1,3 positions of the glycerol backbone, replacing the R1 or R3 radicals (Fig. 1). Regarding sn-1,3 positions, the sn-3 position will contain the remaining FA with the highest degree of unsaturation and the sn-1 position the other. Finally, if sn-1,3 positions contain FAs with the same degree of unsaturation, then that one with the longer carbon chain length is preferentially acylated at the sn-3 position, thus replacing the R3 radical of Fig. 1. The probable TAG profiles of patawa and pracaxi oils can be found at Tables S1 and S2, respectively, in the Supporting information material. While the most representative TAG of patawa oil is the triolein (39.83 mol%) with a molecular mass of 885.45 g mol−1, the most abundant triglycerides of pracaxi oil are also triolein (14.02 mol%) and a TAG molecule comprised by two oleic acids e one behenic acid (14.92 mol%) with a molecular mass of 943.57 g mol−1.

Fig. 1
figure 1

Structure of the triacylglycerol molecule and sn stereospecific numbering positions

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Experimental procedure

Model fatty systems containing FAs and TAGs were prepared by adding known quantities of commercial oleic acid to patawa and pracaxi oils. While the liquid–liquid extraction using anhydrous ethanol solvent was performed for both oils, azeotropic ethanol and isopropanol were used only with the pracaxi oil.

The acidic oil was obtained by mixing the patawa and pracaxi oils with up to 10.98 and 15.02 wt% of commercial oleic acid, respectively, in the case of systems containing anhydrous ethanol. For the systems with ethanol and isopropanol plus water, the amounts of oleic acid dissolved in the pracaxi oil were up to 14.06 wt% and 18.03 wt%, respectively. The model fatty systems were mixed with the solvents, in the mass ratio oil:solvent 1:1 at 298.15 K, for determination of LLE data. It is worth noting that, aiming at better evaluate the performance of the liquid–liquid extraction technique, oleic acid concentrations selected for the evaluation of all model systems ranged from the initial free FA concentration of each oil to the maximum level where the addition of commercial oleic acid has not generated phase split.

The components were weighed using an analytical balance (model XT220A, Precisa, Switzerland) with an uncertainty of ± 2.10−4 g in the measurement. Weighted components were introduced in glass cells connected to a thermostatic circulating bath (Cole Parmer, USA) and vigorously stirred using a magnetic stirrer (Fisatom, Brazil) for at least 60 min at 298.15 K, to obtain good contact between both phases. Then all systems were left to rest for at least 24 h at a constant temperature in a thermostatic bath. Two clear layers and a well-defined interface were formed when the systems reached the equilibrium state. For the sake of this study, we prepared one equilibrium cell for each evaluated system, performing quantification analyses in triplicate.

Samples of both phases were collected for the quantification of the components. For the collection, we used syringes that were carefully inserted into side holes of the glass cells properly designed to collect both the bottom and top phases. First of all, the collection was performed in the top phase in order to cause the least perturbation in the system. Afterward, the bottom phase is collected, taking the same care to avoid the destabilization of the remaining system. It is worthy to note that the amounts of sample needed to immediately perform all measurements in triplicates were taken at once. This method was thoroughly tested and described in previous publications of this research group (Rodrigues and Meirelles 2008; Ferreira et al. 2018a, b).

The concentration of FFAs was determined by titration, according to the official AOCS method Cd 3d-63 (AOCS 2009) using an automatic titrator (model 848 Titrino plus, Methrom, Switzerland). The total solvent concentration, in oil and alcoholic phases, was determined by evaporation at 343.15 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 2e-84 (AOCS 2009) with a KF Titrino plus (model 870, Metrohm, Switzerland). The TAG concentration was determined by difference. In this study, all measurements were performed at least in triplicate, and standard deviations were used as the uncertainties of experimental phase compositions.

The procedure developed by Marcilla et al. (1995), was used to test the validity of the experimental LLE data gathered. In this approach, the total mass used in the experiment (MOC) is compared with the sum of calculated oil and alcoholic phase masses (MOP and MAP, respectively). This procedure permits the calculation of the mass of each phase based on the experimental values by the least square fitting. Thus the relative deviation of the mass balance for each component is calculated, taking into account the mass fraction of each component of the system. The overall mass balance relative deviation (δ) is calculated by Eq. 1:

$$\delta (\%)=\frac{\left[\left({M}^{OP}+{M}^{AP}\right)-{M}^{OC}\right]}{{M}^{OC}}\times 100.$$
(1)

The reliability of the experimental tie-lines of the systems was also verified by applying the Othmer–Tobias correlation. The procedure described by Othmer and Tobias (1942) is an empirical method used to assure the consistency of the experimental data through the linearity of the graphic. This correlation is given by Eq. 2.

$$ln\left(\frac{100-{w}_{\mathit{ab}}}{{w}_{\mathit{ab}}}\right)=A+Bln\left(\frac{100-{w}_{ot}}{{w}_{ot}}\right),$$
(2)

where wab and wot stand for the mass percentages of alcohol in the bottom phase and the mass percentage of oil in the top phase, respectively. The values of A and B are dependent on individual systems.

Thermodynamic modeling

In this study, the experimental equilibrium data sets determined for the systems were used to adjust the interaction parameters of the NRTL (Renon and Prausnitz 1968) and UNIQUAC (Abrams and Prausnitz 1975) models. In both models, the mass fraction was used as the concentration unit because of the great contrast in the molecular mass of the components in the system. In liquid phases where the molecular weights of some compounds are much larger than that of solvent, the mole fraction may not be suitable for use as a unit of concentration (Batista et al. 1999). Therefore, toward applying the activity coefficient models, the equations had to be modified, as suggested by Oishi and Prausnitz (1978).

The adjustments were made by treating the patawa or pracaxi oil + oleic acid + anhydrous ethanol as pseudo-ternary systems and the pracaxi oil + oleic acid + ethanol or isopropanol + water as pseudo-quaternary systems. Therefore, systems were considered as composed by a single TAG having the patawa or pracaxi oil average molar mass, a representative FA with the molar mass of the commercial oleic acid, ethanol, or isopropanol, and water.

The values of UNIQUAC interaction (Eq. 3) and structural parameters (Eqs. 4, 5), and NRTL interaction parameters (Eqs. 6, 7) were calculated and adjusted by the following equations:

$${\psi }_{mn}=exp-\left(\frac{{a}_{mn}}{T}\right),$$
(3)
$${r}_{i}=\frac{1}{{M}_{i}}\sum_{j}^{C}{x}_{j}\sum_{k}^{G}{v}_{k}^{(j)}{R}_{k},$$
(4)
$${q}_{i}=\frac{1}{{M}_{i}}\sum_{j}^{C}{x}_{j}\sum_{k}^{G}{v}_{k}^{(j)}{Q}_{k},$$
(5)
$${\tau }_{ji}=\frac{\left({g}_{ji}-{g}_{ii}\right)}{RT},$$
(6)
$${G}_{ji}={\rho }_{ji}exp\left(-{\alpha }_{ji}{\tau }_{ji}\right),$$
(7)

where ri and qi are structural volume and area parameters, respectively, of the UNIQUAC activity coefficient model; xj is the mole fraction of the TAG of the pracaxi oil or commercial oleic acid; vk(j) is the number of groups k in molecule j; Mi is the average molar mass of the pracaxi oil or commercial oleic acid; C is the number of compounds in the oil or FA; G is the total number of groups; Rk and Qk are van der Waals parameters established in the literature (Magnussen et al. 1981) and more recently updated in the publication by Kang et al. (2015), where the authors present updates of the parameter matrix which reflects the information of a vast phase equilibrium data set.; τji is a coefficient defined by the ratio between the difference of energies of interactions between a j–i pair of molecules (gji); Gji is a coefficient defined by the constant ρji and the non-randomness constant for binary j–i interactions (αji).

The estimation of interaction parameters of the NRTL model, as well as the calculus of the phase compositions, were based on the minimization of the objective function of composition (Eq. 8) developed by Stragevitch and D’Ávila (1997).

$$S=\sum_{m}^{D}\sum_{n}^{N}\sum_{i}^{C-1}\left[{\left(\frac{{\omega }_{inm}^{OP, exp}-{\omega }_{inm}^{OP, calc}}{{\sigma }_{{\omega }_{inm}^{OP}}}\right)}^{2}+{\left(\frac{{\omega }_{inm}^{AP, exp}-{\omega }_{inm}^{AP, calc}}{{\sigma }_{{\omega }_{inm}^{AP}}}\right)}^{2}\right],$$
(8)

where D is the total number of groups of data; N is the total number of tie lines; C is the total number of components or pseudo compounds in the group of data (m); w is the mass fraction; the subscripts i, n, and m are component, tie line, and group number, respectively; the superscripts OP and AP stand for oil and alcoholic phases, respectively; exp and calc refer to experimental and calculated concentrations, respectively; σωinmOP and σωinmAP are the standard deviations, or estimated experimental uncertainties, observed in the compositions of the oil and alcoholic liquid phases, respectively.

The estimation of the UNIQUAC interaction parameters was based on the minimization of the Rachford and Rice (1952) equation (Eq. 9), described by Walas (1985), and implemented using the MATLAB software (MathWorks, USA), as described in the literature (Pereira et al. 2019b).

$${f}_{(\beta )}=\sum \frac{{z}_{i}}{\beta +{K}_{i}\left(1-\beta \right)}-1,$$
(9)

where β is the fraction of the total material that is present in the first liquid phase, Ki is the distribution ratio between the activity coefficient of component i in the first liquid phase (I) by its activity coefficient in the second one (II) given by \({K}_{i}={\gamma }_{i}^{I}/{\gamma }_{i}^{II}\), and zi is the overall composition of component i provided by \({z}_{i}=\beta {x}_{i}^{I}+\left(1-\beta \right){x}_{i}^{II}\). The solution of Eq. 9 to obtain the phase fractions is carried out by Newton–Raphson iteration. Subsequently, the obtained phase fractions are used to calculate new compositions. Next, new values of distribution constants (Ki) are calculated with the appropriate phase equilibrium equation. Finally, these new Ki values are compared to the previous ones, and if the tolerance of 10–3 is not observed, the equation is solved again for phase fractions, using the new values. These calculations are repeated until the convergence is obtained. If the value of β is not between 0 and 1, it is considered that the calculation has not resulted in a phase split.

The deviations between experimental and calculated compositions in both phases (∆w), using UNIQUAC and NRTL models, were calculated according to Eq. 10:

$$\Delta w=100\sqrt{\frac{\sum_{n}^{N}\sum_{i}^{C}\left[{\left({\omega }_{inm}^{OP, exp}-{\omega }_{inm}^{OP, calc}\right)}^{2}+{\left({\omega }_{inm}^{AP, exp}-{\omega }_{inm}^{AP, calc}\right)}^{2}\right]}{2NC}},$$
(10)

where N is the total number of tie lines; C is the total number of components or pseudo compounds in the group of data.

Results and discussion

Table 1 shows that oleic and behenic acids are the most important FAs present in pracaxi oil. Meanwhile, as one may notice by Table 1, the oleic acid is the major FA of the patawa oil.

Table 1 Fatty acid composition of patawa and pracaxi oils, and commercial oleic acid
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Tables 2 and 3 present the experimental composition of the corresponding tie lines for the systems: pracaxi oil (1) + oleic acid (2) + anhydrous ethanol (3); patawa oil (4) + oleic acid (2) + anhydrous ethanol (3); pracaxi oil (1) + oleic acid (2) + ethanol (3) + water (5); pracaxi oil (1) + oleic acid (2) + isopropanol (4) + water (5). All concentrations are given as mass percentages. As one may notice by Table 3, while the water concentration, determined by Karl Fischer titration, in the alcoholic phase was found to be constant in both pracaxi oil + azeotropic alcohol systems, it was found to be negligible in the oil phase.

Table 2 Liquid–liquid equilibrium data for the system pracaxi oil (1) or patawa oil (4) + oleic acid (2) + anhydrous ethanol (3) at 298.15 ± 0.5 K and atmospheric pressure
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Table 3 Liquid–liquid equilibrium data for the system pracaxi oil (1) + oleic acid (2) + ethanol (3) or isopropanol (4) + water (5) at 298.15 K ± 0.5 K and atmospheric pressure
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In order to test the quality of the equilibrium data and evaluate the reliability of the results, the procedure developed by Marcilla et al. (1995), and already applied to fatty systems by several authors (Rodrigues et al. 2005a, 2006b; Reipert et al. 2011; Hirata et al. 2013) was used. The global mass balance deviations for all systems studied varied within the range from 0.01 to 0.53%, ensuring proper alignment between the experimental data relative to both overall and phase concentrations. The overall composition of the mixtures can be found on Tables S3 and S4 of the supporting information material.

The Othmer-Tobias, given in Eq. 2, was used to verify the consistencies of the tie-lines data. The constants (A and B) and the regression coefficients (R2) are given in Table 4. For the systems evaluated here, the values of the regression coefficients were superior to 0.97, indicating the high reliability of the experimental data.

Table 4 Othmer–Tobias constants and regression coefficients
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Commercial oleic acid, pracaxi, and patawa oils treated as pseudo components in this paper with average molar masses, as well as volume and area parameters values, shown in Table 5. The values found for UNIQUAC structural parameters in this work are in coherence with those found in the literature for water, ethanol, ispropanol, and commercial oleic acid molecules (Batista et al. 1999; Rodrigues et al. 2005b). It is worth noting that the representative TAGs considered for the modeling procedures are pseudo components with average molar masses calculated by pondering molar masses of the actual triglycerides found in pracaxi and patawa oils and their percentage mole fractions in the samples.

Table 5 Average molar masses (M) and structural parameters (ri and qi)
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The adjusted interactions parameters of the UNIQUAC and NRTL models for the systems evaluated here are presented in Table 6. The set of interaction parameters obtained in this study are coherent with those values reported in the publication by Rodrigues and Meirelles (2008), where the authors also employed the UNIQUAC and NRTL equations for modeling the LLE data of systems containing peanut and avocado seed oils + ethanol + water. Besides, UNIQUAC and NRTL interaction parameters of the same magnitude for studies evaluating de LLE behavior of systems composed by vegetable oils + free fatty acids + alcoholic solvents can be found elsewhere (Reipert et al. 2011; Homrich and Ceriani 2016).

Table 6 UNIQUAC and NRTL interaction parameters for the systems with Patawa* and Pracaxi Oils at 298.15 K
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Figure 2 shows the experimental points and the tie lines calculated using the NRTL model for the system patawa oil + oleic acid + anhydrous ethanol. Figures 3, 4, and 5 show the experimental points and the tie lines calculated using the NRTL and UNIQUAC models for the systems: pracaxi oil + oleic acid + anhydrous ethanol; pracaxi oil + oleic acid + ethanol + water; pracaxi oil + oleic acid + isopropanol + water, respectively. In the phase diagrams, ethanol + water and isopropanol + water were admitted as mixed solvents.

Fig. 2
figure 2

System of patawa oil (1) + oleic acid (2) + anhydrous ethanol (3) at 298.15 K: (triangle) represents experimental feed compositions; (circle) represents phase compositions experimental points, green dashed lines represent calculated tie lines with NRTL model

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Fig. 3
figure 3

System of pracaxi oil (1) + oleic acid (2) + anhydrous ethanol (3) at 298.15 K: (triangle) represents experimental feed compositions; (circle) represents phase compositions experimental points, solid red lines and green dashed lines represent calculated tie lines with UNIQUAC and NRTL models, respectively

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Fig. 4
figure 4

System of pracaxi oil (1) + oleic acid (2) + aqueous solvent [ethanol (3) + water (5)] at 298.15 K: (triangle) represents experimental feed compositions; (circle) represents phase compositions experimental points, solid red lines and green dashed lines represent calculated tie lines with UNIQUAC and NRTL models, respectively

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Fig. 5
figure 5

System of pracaxi oil (1) + oleic acid (2) + aqueous solvent [isopropanol (4) + water (5)] at 298.15 K: (triangle) represents experimental feed compositions; (circle) represents phase compositions experimental points, solid red lines and green dashed lines represent calculated tie lines with UNIQUAC and NRTL models, respectively

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As can be observed from Fig. 3, the deviations of the mass balance tend to increase with the oleic acid concentration. However, as shown by the Othmer–Tobias correlation (Table 4), the obtained regression coefficient for this ternary system was higher than 0.97, which ascertains the consistency of the tie-lines data. One may also notice that the use of mixed solvents such as ethanol + water (Fig. 4) and isopropanol + water (Fig. 5), resulted in slighter tie-lines inclinations. These inclination reductions indicate that by adding water to the alcoholic solvent, the ability for extracting free FA is also reduced, as observed by Rodrigues et al. (2005a).

Figures 2, 3, 4 and 5 show that both thermodynamic models studied described the phase compositions of the systems investigated with accuracy. The calculated tie lines using the structural and interaction parameters obtained here for UNIQUAC and NRTL models were compared with experimental data. Mean deviations in phase compositions, calculated according to Eq. 10, are shown in Table 7. Furthermore, it can be observed by Figs. 1, 2, 3 and 4 that the tie lines calculated for FFA concentrations almost overlapped experimental data, which indicates a good representation of LLE in the range of composition evaluated.

Table 7 Mean Deviations in Phase Compositions
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One may also notice by Figs. 3, 4 and 5 that the water content of ethanol expanded the heterogeneous region, in which alcoholic and oil phases are immiscible. The widening of this region has a beneficial effect on the oil refining process, while it allows the deacidification of highly acidic oils. The broadest phase splitting region is observed in Fig. 5 in which the mixed solvent [isopropanol + water] is used. This positive effect of water on the performance of solvents has been observed in various publications in the literature (Gonçalves and Meirelles 2004; Dalmolin et al. 2009; Ansolin et al. 2013). It can also be observed that while the UNIQUAC model more closely captured the correct slope of the curves, the NRTL model presented higher deviations between the experimental and calculated values near the plait point of the systems, which is where the overall systems’ oleic acid concentrations varied up to 14, 11, 14, and 18 wt% in Figs. 2, 3, 4 and 5, respectively. Likewise, deviations values were also found to be higher near the plait point in publications regarding the LLE of ternary systems containing fatty compounds and alcoholic solvents (Follegatti-Romero et al. 2010).

Losses of neutral oil to the alcoholic phase and of the solvent to the oil phase were also minimized. This result can be explained by the decrease of mutual solubility between oil and solvent by the presence of water in the system. The reduction in neutral oil and solvent losses can be seen in the baseline of the figures and the data shown in Tables 2 and 3. On the other hand, Fig. 6 shows that the addition of water reduces the solvent capacity of extracting FFAs from the oil phase. It is also worth noting in this figure, the excellent performance of the UNIQUAC model to describe the distribution of fatty compounds between the liquid phases.

Fig. 6
figure 6

Distribution diagram at 298.15 K for systems: filled square, pracaxi oil (1) + oleic acid (2) + anhydrous ethanol (3); open square, pracaxi oil (1) + oleic acid (2) + ethanol (3) + water (5); triangle, pracaxi oil (1) + oleic acid (2) + isopropanol (4) + water (5); black symbols represent experimental points and red symbols represent UNIQUAC model calculations

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Figure 7 shows experimental and model estimated distribution coefficients (k2) and selectivity (S1/2) for the pracaxi systems evaluated here as a function of acidity level in the oil (w2), which is the mass fraction of oleic acid dissolved in the oil to obtain model fatty systems containing FAs and TAGs. Distribution coefficients and selectivity values were calculated according to Eqs. 11 and 12, respectively, where the subscript i represents oleic FA, and j is the pracaxi oil.

Fig. 7
figure 7

Experimental fatty acid distribution coefficients (filled circle) and selectivity (○) for the systems: (A) pracaxi oil (1) + oleic acid (2) + anhydrous ethanol (3); (B) pracaxi oil (1) + oleic acid (2) + ethanol (3) + water (5); (C) pracaxi oil (1) + oleic acid (2) + isopropanol (4) + water (5); solid red lines and green dashed lines represent calculated tie lines with UNIQUAC and NRTL models, respectively

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$${k}_{i}=\frac{{\omega }_{i}^{AP}}{{\omega }_{i}^{OP}}$$
(11)
$${S}_{i/j}=\frac{{k}_{i}}{{k}_{j}}$$
(12)

It can be observed from data showed in Fig. 7 that azeotropic ethanol and isopropanol provided higher selectivity values than anhydrous solvent. The addition of water could decrease the neutral oil loss. On the other hand, anhydrous ethanol showed the highest distribution coefficients of up to 1.47. Therefore, despite the addition of water increase the selectivity, decreasing the neutral oil loss, the FA distribution coefficient was found to be lower in the presence of water.

The azeotropic isopropanol system showed the lowest FFA distribution coefficients. This result implies that, since free FA showed a preference for the oil phase, this mixed solvent [isopropanol + water] may not be effective in removing free FA from pracaxi oil. As observed by Rodrigues et al. (2006a), low FA distribution coefficients demand a higher number of theoretical stages to deacidify the oil in an industrial operation totally.

Results also indicated that the UNIQUAC model presents a better description of the selectivity values. NRTL model provides reasonable descriptions of selectivity for the system represented in Fig. 7a. However, the NRTL model description fails mainly for the experimental points of systems described in Fig. 7b, c. Possibly, the higher experimental uncertainties recorded in these systems affected the performance of the NRTL model. Regarding the oleic acid distribution coefficients, both models provided good calculations.

Conclusions

In this paper, phase equilibrium data for liquid–liquid systems containing patawa or pracaxi oil + oleic acid + solvent (anhydrous ethanol, azeotropic ethanol [ethanol + 6.02 wt% of water], and azeotropic isopropanol [ispropanol + 13.07 wt% of water]) were measured at 298.15 K. Results obtained here showed that the addition of water to the solvent phase resulted in a substantial increase of selectivity values and broader phase splitting regions for both azeotropic alcohols evaluated here, which allow the use of these solvents to deacidify highly acidic vegetable oils. However, in the case of azeotropic isopropanol, the low values of FFA distribution coefficients suggested that this solvent may not be effective in removing this compound from the oil phase. On the other hand, despite azeotropic ethanol showed slightly lower FFA distribution coefficients when compared to anhydrous ethanol, its high selectivity values suggested that it could be a good solvent for deacidification of either patawa or pracaxi oils.

The NRTL and UNIQUAC models were used to describe the LLE behavior of systems, exhibiting mean deviations of 0.68% and 0.66%, respectively. Accordingly, the results shown in this paper corroborate to the expansion of the use of deacidification technique by liquid–liquid extraction of vegetable oils. This paper shows the feasibility of using ethanol as an FFA extractant and confirms previous evidence of the superiority of this solvent above other short-chain alcohols in the liquid–liquid extraction. Finally, we showed a positive perspective of using the liquid–liquid extraction technique for pracaxi oil refining.