Fluid Phase Behavior of the Licuri (Syagrus coronata) Fatty Acid Ethyl Ester + Glycerol + Ethanol Mixtures at Different Temperatures—Experimental and Thermodynamic Modeling

Abstract

This study provides experimental insights into the liquid–liquid equilibrium (LLE) of a system consisting of fatty acid ethyl ester (FAEE) derived from licuri oil, glycerol, and ethanol, evaluated at various temperatures and standard atmospheric pressures. FAEE was synthesized through transesterification of licuri oil using NaOH as a catalyst. The liquid phase compositions were assessed via titration, and the results were consistent with the solubility curves and overall compositions. Data reliability was confirmed using Hand and Othmer-Tobias correlations, with a determination coefficient (R²) of 1, validating the dependability of the results. The NRTL model was employed to correlate the LLE data, yielding a root-mean-square deviation (RMSD) of approximately 1.20%, signifying a strong correlation with experimental uncertainties. The selectivity (S) and distribution (D) parameters indicated the efficacy of glycerol in the system, with S values exceeding 1 under all conditions tested. This investigation is crucial for biodiesel production, highlighting the potential of licuri oil as a renewable feedstock and the importance of phase equilibrium studies in the separation processes of biodiesel production products.

1. Introduction

Biodiesel is a sustainable substitute for fossil fuels because of its renewable and biodegradable nature [1]. The quality of biodiesel is determined by the characteristics of the vegetable oil used as its precursor. Key parameters such as ash content, calorific value, viscosity, and density are vital for evaluating both the quality of the oil and the resultant biodiesel [1,2,3]. The ash content reflects the level of inorganic impurities in the oil, which may hinder combustion efficiency and lead to engine deposits [4]. The calorific value, which is indicative of the energy released upon combustion, is critical for determining the energy potential [5]. Viscosity and density are essential factors that influence the operational efficacy of biodiesel in engines, thereby affecting fuel atomization and combustion performance [6].

Various oilseeds exhibit distinct characteristics that affect biodiesel quality [7]. Soybean oil, with a density of approximately 0.903 g/cm³, is considered accessible and effective [8]. Canola oil, with a density of 0.914 g/cm³, is recognized for its advantageous properties and minimal saturated fatty acid content [9]. Palm oil, at a density of 0.89 g/cm³, is prized for its substantial yield and high energy content [7]. Sunflower oil, with a density of 0.920 g/cm³, has a well-balanced fatty acid profile [10]. Cottonseed oil, at a density of 0.908 g/cm³ [11], and peanut oil, with a density of 0.899 g/cm³ [12], are regarded as viable feedstocks because of their favorable physicochemical attributes. Coconut oil, which has a density of 0.886 g/cm³, is commonly utilized in tropical areas owing to its abundant supply and oxidative stability [11].

Licuri oil (Syagrus coronata) is a promising biodiesel feedstock owing to its advantageous physicochemical properties. With a density of 0.920 g/cm³, licuri oil presents similarities to soybean oil, a prevalent biodiesel source [13]. This similarity indicates that licuri oil is a feasible substitute for soybean oil because it possesses analogous combustion traits and oxidative stability. Salles et al. [13] underscored the potential of licuri oil and highlighted its appropriate physicochemical attributes for biodiesel production. Licuri is a predominant palm species in Brazil’s Caatinga ecosystem and covers extensive semiarid regions [14,15]. It has multiple applications, including culinary use, traditional medicine, and oil extraction. The literature indicates that licuri seeds contain an oil content of 39% to 50% by mass, primarily consisting of saturated fatty acids (86–90%), with lauric acid constituting 42–48% [13,16]. Licuri biodiesel exhibits excellent oxidative stability, low viscosity, and high density. Further investigations, such as those by Iha et al. [17], analyzed the properties of Syagrus coronata oil and its methyl esters for biodiesel applications, whereas Bezerra et al. [14] reviewed the energy potential of licuri.

Furthermore, liquid–liquid equilibrium (LLE) in systems involving biodiesel has been studied to optimize separation and purification processes. Recent studies have investigated phase behavior in multicomponent systems, such as {biodiesel + glycerol + methanol}, for different plant matrices, highlighting the importance of understanding phase diagrams to optimize production processes [18,19,20,21].

Considering the potential of licuri as a viable energy matrix and the prevailing challenges associated with biodiesel production, particularly in relation to the purification process that necessitates substantial quantities of water [22], in addition to complications such as saponification, this research endeavor aims to ascertain the liquid–liquid equilibrium of compounds resulting from the transesterification process of licuri oil. The comprehension of phase diagrams pertaining to multicomponent mixtures is of paramount importance for the design, simulation, and optimization of various processes [23,24]. These considerations are particularly pertinent in biodiesel systems because of the intrinsic complexity of the mixture, which encompasses variations in the molecular asymmetry, chain length, and polarity [25]. Consequently, access to the phase diagrams of these constituents is essential to enhance the reaction, separation, and purification processes inherent in biodiesel production.

The objective of this research was to explore the liquid–liquid equilibrium, solubility curves, and tie-lines for the {FAEE licuri + glycerol + ethanol} system at temperatures of 303.15 K and 318.15 K under atmospheric pressure (~100 kPa, Maceió, Alagoas, Brazil). This system serves as a reaction mixture for synthesizing fatty acid ethyl esters (FAEE) from licuri oil (Syagrus coronata) through transesterification with sodium hydroxide as a catalyst. The NRTL model [26], which is recognized for its ability to correlate experimental activity coefficient data, was utilized. To verify the data reliability, Hand [27] and Othmer-Tobias [28] correlations were applied, which are essential for the determining tie lines.

2. Experimental Section

2.1. Materials

This study utilized licuri seeds sourced from the Federal University of Alagoas, located in Maceió, AL (Brazil). The licuri specimens underwent preliminary drying at 105 °C for 6 h to eliminate any residual moisture content. Following the initial drying phase, the specimens were stored in appropriate containers to maintain their integrity. In preparation for the subsequent oil extraction procedures, the specimens were subjected to a secondary drying treatment at 60 °C for 48 h to guarantee that any remaining moisture would not adversely affect the extraction yields. The oil was obtained through the application of a hydraulic press (TECNAL^®-TE098, Piracicaba, Brazil) operating at a pressure of 12 tons, subsequently undergoing filtration via a 2 μm porous medium and subsequent dehydration facilitated by magnesium sulfate (>97 wt%, procured from Nuclear, Rio de Janeiro, Brazil) at a temperature condition of 333.15 K [29]. Glycerol, anhydrous ethanol, and sodium hydroxide, with purities exceeding 99 wt% and 97 wt%, respectively, were obtained from Nuclear (Rio de Janeiro, Brazil) and used in their original form without any further purification.

2.2. Synthesis of Methyl and Ethyl Biofuels from Sesame (Sesamum indicum) Oil

The experimental procedure followed the protocols described in Toledo et al. [30], utilizing a 2 L jacketed glass reactor equipped with temperature control and mechanical stirring, maintained at 303.15 K. The reaction was carried out using NaOH (1 wt. %) and alcohol at an oil-to-alcohol molar ratio of 1:6 for 120 min. Subsequently, the reaction mixture was centrifuged to achieve a phase separation between the biodiesel- and glycerol-rich fractions.

The FAEE purification protocol consisted of sequential water washing procedures up to a pH of 10.0, initially employing a water-to-biodiesel ratio of 1:10 at 343.15 K to facilitate the removal of impurities. Following pH adjustment with sulfuric acid and continued washing until the pH reached 7.0, the biodiesel was desiccated using manganese sulfate, followed by filtration.

Compositional analysis was conducted using a GC-2010/Shimadzu system equipped with an FID operating at 523.15 K, utilizing a ZB-WAX plus/Phenomenex column (30 m × 0.32 mm × 0.25 μm). The temperature program was initiated at 433.15 K and elevated to 498.15 K at predetermined heating rates. Fatty acid identification was accomplished through comparative analysis of retention times with standard mixtures, in accordance with the European Standard EN14103 protocols [31].

$$\%yield={\displaystyle \frac{m_{tricaprylin}{A}_B{f}_{tricaprylin}}{A_{tricaprylin}{m}_s}}·100$$

(1)

The variables m_tricaprylin, f_tricaprylin, and A_tricaprylin corresponded to the mass, response factor, and peak area of the internal standard, respectively. A_B is used to indicate the total FAEE peak areas, whereas ms refers to the mass of the sample.

According to the fatty acids detailed in

Table 1. The licuri oil used in this study contains primary fatty acids.

Compound	Fatty Acid	Cx:y a	Molar Mass(g·gmol–1)	Content wt%
				This Study b	Antoniassi et al. [15]	Araújo et al. [33]	La Salles et al. [13]
1	Caprylic acid	08:0—C8H16O2	144.21	13.3	9.2	8.8	9.0
2	Capric acid	10:0—C10H20O2	172.27	8.3	6.6	6.0	6.0
3	Lauric acid	12:0—C12H24O2	200.32	48.2	46.1	36.0	44.0
4	Myristic acid	14:0—C14H28O2	228.38	13.7	14	16.5	17.0
5	Palmitic acid	16:0—C16H32O2	256.43	5.4	6.5	8.9	8.0
6	Stearic acid	18:0—C18H36O2	284.48	2.2	3.5	5.7	4.0
7	Oleic acid	18:1—C18H34O2	282.46	7.0	10.3	14.2	14.0
8	Linoleic acid	18:2—C18H32O2	280.45	1.9	2.8	3.9	2.0

^a Cx:y, where x represents the carbon number, and y represents the number of double bonds. ^b Standard uncertainties u (wt%) are expressed as ±0.6 wt%.

, the computed average molar mass is 234.583 g/mol. To approximate the molar mass of the resultant esters, it was postulated that each fatty acid underwent a complete transformation into its respective ester throughout the transesterification procedure. Employing this premise, the approach articulated by Halvorsen et al. [32] was used to ascertain the molecular weights of the synthesized esters.

Table 1 highlights the fatty acid composition of licuri oil, with lauric acid accounting for 48% of the total, which is crucial for the oxidative stability of biodiesel and minimizes degradation during storage. Medium-chain fatty acids, such as caprylic (9%) and capric (6%), reduce the viscosity of biodiesel and enhance its atomization and combustion efficiency. Previous studies, such as those by La Salles et al. [13] and Antoniassi et al. [34], have confirmed the consistency of these values, reinforcing the viability of licuri as a raw material for biodiesel. Variations in the fatty acid content between studies can be attributed to differences in the cultivation and processing conditions of licuri.

2.3. Equipment and Methods for Liquid–Liquid Equilibrium

Liquid–Liquid Equilibrium Data

Previous studies [30] outlined a method for determining binodal and tie-line curves. To establish the phase boundaries, we conducted a turbidimetric study using isothermal titration. The experiment utilized a 50 mL jacketed equilibrium cell (illustrated in Figure 1) connected to a thermostatic bath (TECNAL, TE18, with ±0.5 K temperature uncertainty) set at 303.15 and 318.15 K. To ensure accurate experimental temperatures, we calibrated the thermostatic bath’s temperature controller, which was linked to the thermocouple, using a primary thermometer. A magnetic stirrer (PHOX, MS-HS2) was used to mix the solution.

To determine the tie lines, specific amounts of glycerol and biodiesel were introduced into the equilibrium cell while maintaining a consistent mass ratio across the experiments. Ethanol was then added to create various compositions, resulting in distinct tie lines. The mixture was then stirred for 12 h. This results in two distinct phases. Samples were taken from both phases for analysis. To assess the ethanol content, the samples were evaporated to a constant weight at 343.15 K for mass fraction calculations. Tie lines were drawn by interpolating the viscosity data obtained using an Ostwald viscometer operating at 300 cSt/s.

The composition of the mixture was determined using established binodal curves. Each sample and phase was measured independently three times, achieving an uncertainty of less than 1 wt%. The validation of the mass balance was executed by analyzing the comprehensive system mass and composition data.

2.4. Quality Test of the Experimental Data

To assess the quality of the tie-line data, the Hand [27] (Equation (2)) and Othmer-Tobias [28] (Equation (3)) correlations were applied.

$$\ln \left({\displaystyle \frac{w_3^I}{w_1^I}}\right)=A+B·ln\left({\displaystyle \frac{w_3^{II}}{w_2^{II}}}\right)$$

(2)

$$\ln \left({\displaystyle \frac{{1-w}_1^I}{w_1^I}}\right)=A^{\prime }+B^{\prime }·ln\left({\displaystyle \frac{1-w_2^{II}}{w_2^{II}}}\right)$$

(3)

In these equations, specific symbols denote mass fractions: ω₁^I represents biodiesel in the biodiesel-rich phase, ω₃^I signifies alcohol in the biodiesel-rich phase, ω₃^II indicates alcohol in the glycerol-rich phase, and ω₂^II stands for glycerol in the glycerol-rich phase. The Hand and Othmer-Tobias correlations utilize different parameters: A and B for the former and A′ and B′ for the latter. The correlation coefficient (R²) was used to evaluate the reliability of the experimental data. Notably, the absolute deviations were less than 1.3%, suggesting high-quality data.

2.5. Distribution Coefficient and Selectivity

Two parameters were derived from the LLE data of the ternary systems: the distribution coefficient (D₂) and separation factor (S). These parameters are described by Equations (4) and (5), as follows:

$$D_2={\displaystyle \frac{w_2^{II}}{w_2^I}},$$

(4)

$$S={\displaystyle \frac{\left(w_2^{II}/w_2^I\right)}{\left(w_1^{II}/w_1^I\right)}}.$$

(5)

In these equations, $w_2^I$ and $w_2^{II}$ denote the mass fractions of glycerol in the FAEE-rich and ethanol-rich phases, respectively. Similarly, $w_1^I$ and $w_1^{II}$ represent the mass fractions of FAEE in the ethanol-rich and glycerol-rich phases.

3. Thermodynamic Modeling

Ferrari et al. [35] proposed a method for the LLE computation and parameter estimation. A multiphase liquid–liquid flash method was utilized to ascertain the liquid–liquid equilibrium along with a phase stability test. A non-random two-liquid (NRTL) model was employed to correlate the liquid–liquid equilibrium (LLE) data obtained from the tie line, and calculations were performed to determine the activity coefficients [26]. Specifically, the NRTL model, outlined in Equation (6), was employed to determine the activity coefficient.

$$ln{\gamma }_1=\left({\displaystyle \frac{{\sum }_{j=1}^n{\tau }_{ji}{x}_j{G}_{ji}}{\sum _{k=1}^n{x}_k{G}_{ki}}}\right)+{\sum }_{j=1}^n\left({\displaystyle \frac{x_j{G}_{ij}}{\sum _{k=1}^n{x}_k{G}_{kj}}}\right)\left({\tau }_{ij}-{\displaystyle \frac{\sum _{m=1}^n{\tau }_{mi}{x}_m{G}_{mi}}{\sum _{k=1}^n{x}_k{G}_{kj}}}\right)$$

(6)

In these equations, x_i signifies the mole fraction of component i, and γ_i denotes the activity coefficient. The experimental temperature is represented by T. These formulations rely heavily on the interaction parameters described in Equation (7).

$${\tau }_{ij}={\displaystyle \frac{g_{ji}-g_{ii}}{RT}}={\displaystyle \frac{∆g_{ji}}{T}} G_{ij}=exp\left(-{\propto }_{ij}{\tau }_{ij}\right),$$

(7)

where g_ij represents the binary interaction parameter, while α_ij serves as a coefficient for non-randomness.

A weighted least-squares objective function was used to optimize the binary interaction parameter in the thermodynamic model, as shown in Equation (8).

$$\min FO={\sum }_{k=1}^{NP}{\sum }_{j=1}^{nf}{\sum }_{i=1}^{nc}{\displaystyle \frac{{(x_{ijk}^{calc}-x_{ijk}^{exp})}^2}{{\sigma }_j^2}}$$

(8)

In the NRTL model, molar fractions of component i in phase j for the k tie-line are denoted as $x_{ijk}^{calc}$ and $x_{ijk}^{exp}$, with NP indicating total tie lines, nf for phases, nc for compounds, and ${\sigma }_j^2$ representing experimental phase variance. The optimization process involved two main steps. First, the particle swarm optimization algorithm [35] was employed for parameter estimation, followed by refinement using a modified simplex method [36]. The alignment of the NRTL model with the experimental data was evaluated using Equations (9) and (10), which calculated the root-mean-square deviation (rmsd%) and absolute deviation (AD%), respectively.

$$\mathrm{rmsd}=100·\sqrt{{\displaystyle \frac{\sum _{k=1}^{NP}\sum _{j=1}^{nf}\sum _{i=1}^{nc}\frac{{(x_{ijk}^{calc}-x_{ijk}^{exp})}^2}{{\sigma }_j^2}}{Np\times nf\times nc}}}$$

(9)

$$\mathrm{AD}=100·{\displaystyle \frac{\sum _{k=1}^{NP}\sum _{j=1}^{nf}\sum _{i=1}^{nc}|x_{ijk}^{calc}-x_{ijk}^{exp}|}{Np\times nf\times nc}}$$

(10)

The tie lines obtained experimentally facilitated the correlation of the binary parameters within the NRTL model, accounting for the interactions among licuri oil, FAEE, glycerol, and ethanol. The analysis of these component interactions was enhanced by correlating them with the binary parameters of the NRTL model and employing the established tie lines as a foundational reference.

4. Results and Discussion

4.1. Experimental Data

The experimental liquid–liquid equilibrium data for the {FAEE + glycerol + ethanol} systems at specified temperatures and atmospheric pressures are presented in

Table 2. Data for the two-phase equilibrium curve of the licuri FAEE–glycerol–ethanol mixture at temperatures of 303.15 K and 318.15 K, measured at normal atmospheric pressure (101.3 kPa), expressed as mass fractions (w) ^a.

T = 303.15 K			T = 318.15 K
100.w1	100.w2	100.w3	100.w1	100.w2	100.w3
83.82	6.31	9.87	86.81	3.56	9.62
74.09	6.93	18.98	76.75	4.82	18.42
64.59	7.84	27.57	62.61	8.19	29.19
53.85	10.18	35.97	53.24	11.26	35.49
42.81	14.77	42.42	41.88	16.23	41.88
31.81	20.73	47.46	30.51	22.56	46.92
22.94	25.91	51.15	21.5	28.17	50.32
13.61	32.93	53.47	13.21	34.37	52.41
6.87	41.91	51.22	5.72	46.04	48.26
2.62	53.55	43.83	1.66	69.04	29.29
2.33	63.78	33.89	1.47	78.57	19.96
1.08	73.68	25.22	1.26	88.12	10.61
0.99	89.1	9.91

Standard error estimate: 1%. ^a Standard uncertainties: u(T) = 0.5 K; u(P) = 1 kPa; u(w) ≤ 1.0 wt%. Mass fractions: w₁ (FAEE); w₂ (glycerol); w₃ (ethanol).

and

Table 3. Data on liquid–liquid phase equilibrium for FAEE licuri (1), glycerol (2), and ethanol (3) at temperatures of 303.15 K and 318.15 K measured under normal atmospheric pressure (101.3 kPa), with weight fraction represented by w ^a.

T (K)	Overall Composition (Sol)			Experimental (Tie-Lines)
				Biodiesel Rich-Phase (FAEE)			Glycerol Rich-Phase (Gly)
	100.w1	100.w2	100.w3	100.w1	100.w2	100.w3	100.w1	100.w2	100.w3
303.15	32.01	23.41	44.58	54.64	10.24	35.12	10.18	36.41	53.41
	32.68	26.45	40.87	59.13	9.24	31.63	8.55	42.74	48.71
	33.49	31.02	35.49	67.33	7.75	24.92	4.46	49.54	46.00
	34.39	34.56	31.05	70.97	7.12	21.91	2.67	58.11	39.22
	38.97	38.51	22.52	79.34	6.23	14.43	1.37	67.64	30.99
	41.91	42.03	16.06	83.62	6.07	10.31	0.82	76.66	22.52
	44.04	44.21	11.75	87.53	5.93	6.54	1.22	82.49	16.29
	47.45	46.52	6.03	91.17	5.71	3.12	1.20	90.35	8.45
318.15	39.41	21.06	39.53	54.61	10.82	34.57	7.20	42.33	50.47
	37.43	25.01	37.56	61.73	8.23	30.04	5.25	47.57	47.18
	34.87	31.05	34.08	66.74	7.33	25.93	3.66	54.13	42.21
	33.52	35.21	31.27	70.14	6.65	23.21	2.89	59.88	37.23
	32.01	40.86	27.13	74.59	6.13	19.28	2.43	65.48	32.09
	31.04	46.63	22.33	80.71	5.22	14.07	1.41	71.85	26.74
	30.19	52.64	17.17	85.34	5.04	9.62	1.39	78.16	20.45
	30.72	58.22	11.06	90.48	4.26	5.26	0.80	85.42	14.18

Standard error estimate: 1%. ^a Standard uncertainties: u(T) = 0.5 K; u(P) = 1 kPa; u(w) ≤ 1.0 wt%. Mass fractions: w₁ (FAEE); w₂ (glycerol); w₃ (ethanol).

. In Table 2, the binodal curve data are presented for both the temperatures. From these data, it can be deduced that the ternary system has type I fluid behavior (one binodal curve). From the binodal curve, it is possible to deduce that the binodal curve is composed of the biodiesel rich phase (FAEE) and the glycerol-rich phase (Gly). Table 3 shows the overall composition of the solutions that gave rise to tie lines. The experimental accuracy was assessed using type-A uncertainty derived from analytical measurement standard deviations [37]. The mass composition uncertainties in equilibrium for fatty acid esters were between 0.04% and 0.7%, for alcohols between 0.08% and 0.9%, and for glycerol between 0.06% and 0.7%.

The analysis of the data indicates that with an increase in temperature, there is a general trend of increased phase separation, although this trend is not uniform across all points of the binodal curve. In some cases, the mass fraction of FAEE in the biodiesel-rich phase increased from 83.82% to 86.81%, indicating that higher temperatures favor the separation of FAEE from glycerol. However, at other points, a decrease in the mass fraction of FAEE was observed, suggesting that the miscibility may be affected by specific interactions between the components. These variations indicate that although temperature generally favors phase separation, specific molecular interactions can influence miscibility in different regions of the binodal curve. This reflects the complexity of the system and the need for detailed analysis to optimize the separation conditions.

The data suggest that a higher temperature of 318.15 K favors phase separation, with the FAEE-rich phase showing an increase in the mass fraction of FAEE and the glycerol-rich phase exhibiting an increase in glycerol content. This behavior suggests that an increase in the temperature improves the separation efficiency, resulting in more distinct phase compositions. Higher temperature facilitates separation due to more effective molecular interactions and reduced solubility of glycerol in the FAEE-rich phase, which is consistent with the binodal curve data.

4.2. Quality Test of the LLE Data

Prior to thermodynamic modeling of the liquid–liquid extraction (LLE) experimental data, a thorough quality assessment was performed to ensure the thermodynamic consistency of the equilibrium experimental data. The experimental data were analyzed through Othmer-Tobias and Hand correlation methodologies.

Table 4. Evaluation of the LLE experimental data quality for the three-component system: licuri FAEE (1); glycerol (2); and ethanol (3).

T (K)	Hand			Othmer-Tobias
	R2	A	B	R2	A′	B′
303.15	0.9969	−0.8265	1.0724	0.9912	−0.6702	0.7881
318.15	0.9894	−0.6232	1.1856	0.9967	−0.5088	0.9758

lists the fitting parameters, along with the regression coefficients corresponding to each temperature. All datasets exhibited regression coefficients exceeding 0.98, thereby substantiating the dependability of the liquid–liquid equilibrium experimental data obtained in this investigation.

The Othmer-Tobias and Hand equation parameters reflect the linearity of the graphical representation, with the regression coefficient R² near unity. This linear relationship serves as an indicator of the credibility of the liquid–liquid experimental data. These high R² values indicate that the experimental data fit well with the theoretical correlations, which reinforces the accuracy of the measurements and the robustness of the data presented in Table 2 and Table 3. Validation of the data is crucial, as it confirms that the trends observed in the binodal curves and tie lines are representative of the actual behavior of the system.

4.3. Separation Factor and Distribution Coefficient

The experimentally determined distribution coefficients and separation factors for the FAEE licuri + glycerol + ethanol system are presented in

Table 5. Distribution coefficients of ethanol (D2) and separation factors (S) for ternary system {FAEE licuri (1) + glycerol (2) + ethanol (3)}.

T (K)	S	D1	D2	T (K)	S	D1	D2
303.15	1254.85	0.01	15.83	318.15	2257.22	0.01	19.96
	999.12	0.01	13.93		952.12	0.02	15.51
	778.90	0.02	12.57		787.89	0.02	13.76
	628.76	0.02	10.86		327.89	0.03	10.68
	216.91	0.04	8.16		218.54	0.04	9.00
	96.50	0.07	6.39		134.66	0.05	7.38
	31.99	0.14	4.63		67.96	0.09	5.78
	19.08	0.19	3.56		29.67	0.13	3.91

. A separation factor exceeding 1 (S > 1) at both the temperatures examined indicates that glycerol (the solvent) can efficiently extract alcohol (the solute) from FAEE solutions (the diluents).

At both temperatures (303.15 K and 318.15 K), the values of S were significantly greater than 1, demonstrating the ability of glycerol to efficiently separate ethanol from FAEE. Notably, the values of S increase with rising temperature, from 1254.85 at 303.15 K to 2257.22 at 318.15 K, suggesting that higher temperatures intensify the interactions between glycerol and ethanol, enhancing the selectivity of glycerol.

The D2 values, which were also above 1, indicated the greater solubility of ethanol in the glycerol-rich phase compared to the FAEE-rich phase. An increasing trend of D2 values was observed as the temperature increased, suggesting that higher temperatures promoted ethanol solubility in the glycerol-rich phase. This is consistent with the more pronounced phase separation observed in Table 2 and Table 3, where the glycerol-rich phase became more distinct from the FAEE-rich phase at elevated temperatures.

Figure 2 illustrates the separation factor (S) and distribution coefficient (D2) parameters pertaining to the FAEE licuri + glycerol + ethanol system in relation to the mass fraction of glycerol in the biodiesel phase. The observed values of S and D2, all exceeding 1.0, indicated the feasibility of extracting glycerol from the FAEE + glycerol solution using glycerol as the extraction agent.

The reason for the high separation factor values can also be interpreted in another way. In terms of molecular forces, at a given temperature, the interactions between the ethanol and glycerol molecules (attractive forces) are stronger than the interactions between ethanol and FAEE licuri.

4.4. Thermodynamic Modeling Results

The tie lines for the systems at specified temperatures displayed a unique behavior influenced by the ethanol distribution. A slight increase in the immiscibility region was noted, indicating a favorable phase separation for the production of licuri FAEE. Tie-line construction was enabled through quantitative analysis of the equilibrium phase products. Coexisting phase points beneath the equilibrium curve were used, with each phase representing the tie-line’s extremities, as depicted in Figure 3.

The interaction dynamics between glycerol and ethanol was significantly influenced by a temperature increase of 15 K (from 303.15 to 318.15 K). Enhanced phase separation was observed at 318.15 K, which improved the purification efficiency of licuri oil FAEE owing to increased pair affinity. In the FAEE/glycerol/alcohol systems, the tie lines demonstrated favorable slopes, effectively representing complete composition coordinates. The ternary diagrams of the biodiesel/glycerol/alcohol systems exhibited minimal changes in the tie-line slopes when the temperature increased from 303.15 to 318.15 K. As shown in Figure 3, the calculated tie-line values of the NRTL model closely matched the experimental data across all conditions. The accuracy of the model was confirmed by a root-mean-square deviation (rmsd)of approximately 1% for binary interaction parameters (

Table 6. The fitted binary interaction parameters for the NRTL model (with αij = 0.2) were applied to the studied systems.

System: FAEE licuri (1) + glycerol (2) + ethanol (3)
Temperature (K)	Pair i-j	Δgij (K) a	Δgji (K) a	rmsd × 100
				Phase FAEE	Phase Glyc
303.15–318.15	1-2	348.53	3766.41	1.18	0.71
	1-3	−336.62	1146.82
	2-3	−291.87	1029.74

^a Fitted parameters were $∆g_{ij}=\left(g_{ij}-g_{ii}\right)/R$.

). The absolute deviations (AD) recorded at 303.15 K and 318.15 K were 1.3% and 1.00%, respectively.

The difference in attractiveness between pairs of compounds was reflected in the signs and magnitudes of the ∆gij and ∆gji values. Negative values imply the presence of appealing interactions, whereas positive values denote repulsive or less-advantageous interactions. For FAEE and ethanol, the attractiveness was more pronounced on the side of FAEE, whereas for glycerol and ethanol, the attractiveness was more pronounced on the side of glycerol. This explains why glycerol is effective in extracting ethanol, as the attractive interactions between glycerol and ethanol outweigh the less favorable interactions between ethanol and FAEE.

The separation factor indicates that glycerol is a more effective solvent than biodiesel for the extraction of methanol and ethanol. Ethanol exhibits higher solubility in glycerol compared to biodiesel, with glycerol being immiscible in biodiesel. This phenomenon was consistent with the theoretical mechanism proposed by Zhang and Wu [38]. The insolubility of glycerol in biodiesel, devoid of alcohol, results from its propensity to self-associate rather than disperse. This behavior is attributed to the entangled glycerol structure and network configuration of the biodiesel. Strong hydrogen bonding and elongated glycerol molecules lead to entanglement, hindering dispersion unless sufficient compounds with similar intermolecular strengths are present. Although some biodiesel constituents, such as water, may dissolve in glycerol, their availability is restricted by the heavy compound network in biodiesel. Ethanol, which is amphiphilic, aids in the dispersion of glycerol. Thus, a uniform mixture can be obtained by adding appropriate quantities of ethanol. The FAEE licuri (1) + glycerol (2) + ethanol (3) system exhibits type I fluid phase behavior, which is a crucial characteristic to consider.

5. Conclusions

This study produced notable results concerning the liquid–liquid equilibrium (LLE) of a mixture containing licuri fatty acid ethyl ester (FAEE), glycerol, and ethanol. The experiments were conducted at temperatures of 303.15 K and 318.15 K under a pressure of 101.3 kPa. The successful production of FAEE from licuri oil underscores the viability of this raw material as a biodiesel source. The solubility or binodal curves (Type I) and tie-lines were consistent and validated by Hand and Othmer-Tobias correlations, with determination coefficients (R²) close to 1, indicating the high precision of the experimental data. The NRTL model demonstrated its efficacy in correlating data for highly non-ideal mixtures, yielding a root mean square deviation of 1.20%, thus providing a reliable representation of the system. The selectivity (S) and distribution (D) parameters indicated that glycerol was an effective separation agent, with S values greater than 1 under all the tested conditions, facilitating the purification of licuri FAEE. The increase in temperature favored phase separation, confirming the efficiency of glycerol in extracting the system components. These findings are fundamental for the optimization and efficiency of industrial biodiesel production processes, promoting the sustainable use of renewable resources and strengthening the viability of licuri as a promising source of biofuels. The importance of phase equilibrium studies has been highlighted for separation processes involving the products of biodiesel production reactions.