1 Introduction

Levulinic acid (LA), a carboxylic acid with a keto-acid structure, is frequently referred to as a high-potential platform chemical generated from lignocellulosic sources [1]. LA is an organic acid, an important compound due to its applications in biofuels, medicines, food, agriculture, cosmetics, polymers, and chemical solvents [2]. Selection of the appropriate extraction method to maximize the extraction of carboxylic acids from water is crucial in obtaining extracts. The reactive extraction procedure has drawn more attention as a substitute and efficient method of carboxylic acid separation among many separation techniques [3]. This approach separates components based on their relative solubility in two immiscible liquids and their reversible reactivity with the extractant via the formation of a solute-extractant complex [4]. The acid–amine complex exhibits exothermic behavior. As a result, raising the temperature reduces the extraction of organic acids in the reactive extraction process [5].

For the reactive extraction of several carboxylic acids, including LA, the scientific literature provides a wide range of extraction investigations and modeling techniques. Kumar et al. [6] studied the reactive extraction of LA with trioctylamine amine (TOA) dissolved in different organic diluents. Maximum distribution coefficients (KD) on reactive extraction of LA were found when TOA is used with dichloromethane (DCM). The liquid− liquid equilibrium (LLE) for water + LA + dibasic esters systems was determined by Uslu et al. [7] and nonrandom two-liquid (NRTL) and universal quasi-chemical (UNIQUAC) models were used to correlate the LLE data for these ternary systems. Recent research by Datta et al. [8] examined the effects of two extractants on the recovery of LA by the reactive extraction method. LA reactive extraction utilizing trioctylamine in methyl isobutyl ketone was the main topic of study for Eda et al. [3]. They discovered that the three main variables influencing the reactive extraction process are LA, extractant concentration, and system temperature. Liquid–liquid extraction was examined by Brouwer et al. [1] in 2017 as a method of removing LA from complicated aqueous solutions. Furthermore, the extraction capability of the trioctylphosphine oxide (TOPO)-based deep eutectic solvent to remove levulinic, adipic, and succinic acids from water solutions was studied by Riveiro et al. [9]. In the following sequence, the efficacy of the investigated DESs in organic acid extraction was compared to TOPO as a reference solvent: TOPO-decanoic acid (DecAc) > TOPO-dodecanoic acid (DodecAc) [9]. In a similar study, Villar et al. [10] investigated the liquid–liquid extraction of LA from water utilizing ionic liquids (ILs) based on NTf2. They studied the extraction ability of NTf2-based ILs with imidazolium, pyridinium, and sulfonium cations for LA extraction from water. Experimental data indicated that there are no significant differences between different cations. Furthermore, the results showed that alkyl chain length has no major effect on these ILs’ extraction capabilities. The COSMO-RS results indicated that the distribution coefficients for all systems are relatively comparable. Marti et al. [11] recently investigated the selective separation of (LA), acetic (AA), and formic acids (FA) from aqueous mixed-acid solutions via reactive extraction with (TOA) to predict the antagonistic or synergistic effects on recoveries. The data reveal that the organic phase diluent, starting pH, and TOA concentration are all important parameters influencing extraction efficiency and selectivity. Furthermore, a recent study found that combining sunflower oil, a sustainable green solvent, with tri-n-butyl phosphate (TBP) and TOA reduced the toxicity and cost of the LA separation procedure. Based on the multistage results, TBP and TOA can achieve 97 and 94.20% extraction efficiency in three and five stages, respectively [4].

The present work aims to present experimental data on the liquid–liquid equilibria of ternary aqueous solutions of TOA and LA at T = (293.15, 313.15, and 333.15) K. For this purpose, the analytical and cloud point methods were used to determine tie line and binodal values. Although there are some reports about the physical extraction of levulinic acid using different chemical and natural solvents in ternary solutions [12], there are no experimental data on the chemical extraction and phase behavior of ternary aqueous systems containing LA and TOA in a wide concentration range of LA. Furthermore, to gain more information regarding the phase behavior of the studied system, infrared spectroscopy was carried out to provide experimental results about the possible interactions in the solutions. Finally, the measured data are modeled with NRTL and used as the activity coefficient model for the liquid phase. The data are modeled with available literature data on LLE [13, 14] followed by regression of the missing parameters. There are no prior works in the literature which had considered the above system.

2 Experimental

2.1 Materials

The chemicals tabulated in Table 1 obtained from Sigma-Aldrich were used without additional purification. The water content in LA was determined using the Karl-Fischer Titrator. The mass fraction of water for LA was less than 0.0090. Milli–Q ultrapure water (Type I, k: 0.05 μS cm−1 at 298 K) was obtained from the water purification system (Direct–Q 5 UV) and used to prepare the solutions. Densities were measured using a DMA HP density meter (Anton Paar GmbH, Graz, Austria). The apparatus was calibrated with water, and nitrogen 99.999 mol% at atmospheric pressure.

Table 1 Purity of the used chemicals
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2.2 Apparatus and Procedure

2.2.1 Determination of Binodal Curves

The binodal curves were determined using the cloud point method [15]. The binodal equilibrium values were collected using a glass vessel having a volume of 50 cm3. Water at a constant temperature was circulated using a thermostat around an external jacket placed on the glass vessel. The temperature was controlled using a thermostat (Model: Lauda E200, Germany) with an uncertainty of u(T) = 0.2 K. The creation of two liquid phases was indicated by the solution turning turbid after being titrated with TOA to a known concentration of an aqueous LA solution. A precision analytical balance (Model: Precisa 410AM-FR, Switzerland) with an uncertainty of u(m) = 0.002 g was used to compute the mass composition of the mixture for each point on the binodal curve by the amount of titrant added until turbidity was observed.

2.2.2 Determination of Tie Lines

The glass cell apparatus described by Männistö et al. [16] was used to perform the analytical LLE measurements at atmospheric pressure. The experimental apparatus used in the present work is like the one applied and described in detail in their previous study [15]. Feed samples were prepared to determine the tie lines by mixing required amounts of LA, TOA, and water in the glass cells at a constant temperature using the thermostat (Model: Lauda E200, Germany). The input and output water temperatures were monitored using calibrated Pt-100 probes and an ASL CTR-2000–24 thermometer with u(T) = 0.2 K uncertainty. The samples were mixed thoroughly and allowed to separate into two clear phases for at least 72 h. Equilibrium is reached when the difference in mass fractions between the two repeats is smaller than 0.01 percent. After separating into two clear phases, samples of the aqueous phase were taken using a Hamilton sample-lock syringe. The samples in the syringe were taken directly into the vials where the solvent (2-propanol) was placed before sampling. For each solution, after reaching equilibrium, the sampling and analysis were replicated at least three times. The concentration of each component in the bottom phase (aqueous phase) and top phase (organic phase) was determined using gas chromatography (GC) with an Agilent 7890B and mass balance calculations, respectively. The Agilent 7890B GC parameters are the same as presented in our previous work [17]. The known masses of 2-propanol with LA, TOA, and water were prepared for the calibration of GC. To calculate the relative response factor for each component, the known masses were used. As the average of several samples, the response factor Fi was computed using Eq. (1):

$${F}_{i}={F}_\text{std }.\frac{{A}_\text{std}}{{A}_{i}}.\frac{{m}_{i}}{{m}_\text{std}},$$
(1)

where Ai represents the peak area for component i, Astd denotes the peak area for 2-propanol which is employed as a solvent, and mi, and mstd are the masses for component i and the solvent respectively. Fstd, the response factor of 2-propanol, was set to 1. The relative response factor of the component and the solvent peak area in Eq. (1) was not considered while determining compositions during the sample phase analysis. An analytical balance (Model: Precisa 410AM-FR, Switzerland) with an uncertainty of u(m) = 0.002 g was used in the calculation of the weight fraction of each component in the mixture.

2.3 Fourier Transform Infrared Spectroscopy

At room temperature, FT-IR spectra were used to examine the interactions and bonding of the (trioctylamine + LA + water) system. PerkinElmer’s FT-IR with an ATR was used, and the wavenumber ranged from 4000 to 500 cm−1, resolution was 4 cm−1, and scan rate was 32. The interactions that underlie the extraction mechanism described in most of the earlier investigations are supported by the spectroscopic approach. The peak intensity shows the results related to bond formation between the involved species.

3 Results and Discussion

3.1 Experimental Binodal Curves and Tie Line Data

The binodal data and tie line compositions at T = (293.15, 313.15, and 333.15) K and atmospheric pressure for the trioctylamine + LA + water system are given in Tables 2 and 3, respectively, and phase diagrams are depicted in Fig. 1a–c, where the concentrations are expressed in weight fractions. Figure 1a–c also shows a comparison of the binodal curves for the examined system at T = (293.15, 313.15, and 333.15) K, demonstrating that as the temperature rises, the area of the two phases remains constant.

Table 2 Experimental binodal values for the TOA + LA + H2O system at T = (293.15, 313.15 ,and 333.15) K and 101 kPa pressure
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Table 3 Experimental tie lines for the TOA + LA + H2O system at T = (293.15, 313.15, and 333.15) K and 101 kPa pressure
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Fig. 1
figure 1

Phase diagram of TOA + LA + H2O system at a T = 293.15 K; b T = 313.15 K; and c T = 333.15 K: (■) experimental binodal, (—) calculated tie lines using binodal and mass balance at detectable water content area, (●) initial experimental points, (—) calculated tie lines using mass balance at very low water content area

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To determine the tie line compositions, the GC method and mass balance calculations were used to analyze both aqueous and organic phases, respectively. However, the GC method was also applied to examine the organic phases. It was found that the amount of acid measured in the organic phase was less than the initial amount used in the extraction. A similar phenomenon has been observed by Oliveira et al. [18]. This occurrence could be explained by the complex formation between extractant and acid. To circumvent this problem and following previous research [3, 6, 8], we computed the component concentrations in the organic phase using the mass balance (in the region where there was no water). Furthermore, the intersection of a binodal curve equation with linear equations derived from the initial points and the corresponding aqueous phase points were used to determine the coordinates of the organic phase in the LA-rich region. All the assumptions and calculations are provided in Section A of the Supporting Information. As shown in Fig. 1a–c, tie lines at high acid concentrations will allow for steeper tie lines and higher extraction efficiency [18]. Figure 1a–c depicts the effect of temperature on phase behavior, demonstrating that temperature has no substantial impact on phase separation in these systems.

From the composition data, the distribution coefficient (KD), for the studied system, is calculated using Eq. (2)

$${K}_\text{D}=\frac{{W}_{\text{LA}}^{\text{org}}}{{W}_{\text{LA}}^{\text{aq}}},$$
(2)

where \({w}_{\text{LA}}^{\text{org}}\) and \({w}_{\text{LA}}^{\text{aq}}\) are the LA weight fraction in the organic-rich and aqueous-rich phases, respectively. The distribution coefficient values (KD) were calculated and are reported in Table 3 and presented in Fig. 2 at T = (293.15, 313.15, and 333.15) K. This parameter gives an idea about the extraction capability of the TOA in this work. Comparing the distribution coefficient values (KD) for the studied system shows that KD values decrease by increasing the acid concentration in the aqueous phase. As seen in Table 3, the values of KD do not change much with temperature variations. As a result, selecting the appropriate diluent can increase the efficiency of the reactive extraction process. Proper diluent selection can improve the physical qualities of the extractant, such as density and viscosity, and facilitate extraction by enhancing the solvation of the acid-extractant complex. Most of the research on reactive extraction reveals that active diluents can participate in complex formation, e.g., by hydrogen bonding, and lead to high extraction efficiency when mixed with the extractant [3].

Fig. 2
figure 2

Distribution coefficient versus wLA(aq) for TOA + LA + H2O at T = 293.15 K, (×); T = 313.15 K, (△) and T = 333.15 K, (□)

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3.2 Fourier Transform Infrared Spectroscopic Analysis

To obtain more information about the interactions, infrared spectroscopy analysis was carried out for the samples obtained from both phases in this region to study any potential interactions and complex formation (Fig. 1a–c). Some authors have already explained the formation of complexes between the organic acids and extractants such as trioctylamine by spectroscopy method [19,20,21]. To evaluate the mechanism of complex formation, it is crucial to be able to distinguish between the undissociated and dissociated forms of the carboxylic acids because of their pH-dependent species distribution (in the aqueous phase). Thus, FT-IR measurements of LA in water were performed at pH = 2 and 7 (pH adjustment using highly concentrated NaOH) at T = 293.15 K. According to the pKa value of LA (pKa = 4.64), the acid is largely in its undissociated form at pH 2 or lower, whereas it is nearly entirely dissociated at pH 7 or higher [19]. The FT-IR spectra of LA at various pH levels are shown in Fig. 3a. The 1300–1800 cm−1 area of the spectra showed the most significant variances. In Fig. 3a, there is a strong peak at 1710 cm−1, which is attributed to the carbonyl group’s stretching vibration in the undissociated acid at pH = 2. However, we can observe two peaks at 1554 and 1410 cm−1 at pH = 7 in Fig. 3a. According to the obtained results in [19, 20], these peaks can be attributed to the asymmetric and symmetric stretching vibrations of the carboxylate group of the dissociated form. In Fig. 3b, c, IR spectra bands are presented for the organic- and water-rich phases, respectively. Figure 3b displays the IR spectra of the organic-rich phase (pH = 4.55), revealing significant peaks in the 1300–2000 cm−1 region.

Fig. 3
figure 3

Infrared spectra: a Aqueous phase of levulinic acid solution at pH = 7 (red line) and pH = 2 (black line), adjusted by NaOH; b Organic-rich phases after equilibrium; c Water-rich phases after equilibrium

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The IR spectra of carboxylic acid were identified at 1727 cm−1, which is associated with a carbonyl group (undissociated form). It can be attributed to the C = O stretching of the carboxyl group that is hydrogen-bonded to TOA and/or other carboxyl groups (intermolecular) and/or to water. As can be seen from Fig. 3b, the peaks at 1466 cm−1, which were assigned to the carboxylate group (dissociated form), demonstrate the complex formation between the amine and the acidic proton of the carboxyl group. According to the spectrum of the aqueous-rich (pH = 2.65) in Fig. 3c, we can observe a band at 1707 cm−1, which indicates the existence of a hydrogen bonding between the carbonyl group (intermolecular) and/or water. However, carboxylate group peaks are absent in the aqueous phase. In the organic phase (Fig. 3b), the main band due to a carboxylate group (1466 cm−1) demonstrates strong interactions between the amine and the acidic proton of the carboxyl group. Furthermore, the carbonyl group at 1727 cm−1 indicates interaction between extractant and acid molecules through hydrogen bonding. Spectra of pure compounds can be found in the supporting information (Fig. S2).

4 Thermodynamic Framework

The LLE data of the ternary system of trioctylamine, water, and LA were correlated with the NRTL model at T = (293.15, 313.15, and 333.15) K.

The minimum objective function (OF) is used to calculate the binary interaction parameters of the NRTL model. The following expression is used for (OF):

$$OF=\sum_{k=1}^{M}\sum_{j=1}^{2}\sum_{i=1}^{3}({w}_{{ijk}}^{\text{exp}}-{w}_{{ijk}}^{\text{cal}}{)}^{2},$$
(3)

where the subscripts i, j, and k refer to the components, phases, and tie lines, respectively. M refers to the number of tie lines, whereas wexp and wcal denote the experimental and calculated data. Table 4 shows the interaction parameters obtained with this correlation.

Table 4 Summary of regressed NRTL parameters in this work, τij = aij + bij/T(K) at T = 333.15 K
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Also, the root-mean-square deviation (RMSD) method is used to assess the consistency in the difference between the experimental and calculated values. The RMSD is calculated using the following equation:

$$RMSD={\left\{\sum_{k=1}^{M}\sum_{j=1}^{2}\sum_{i=1}^{3}\frac{\left({w}_{{ijk}}^{\text{exp}}-{w}_{{ijk}}^{\text{cal}}{)}^{2}\right)}{6M}\right\}}^{1/2}$$
(4)

Prior work carried out on phase equilibria of systems containing LA [13] provided binary interaction parameters for the LA + water system at 333.15 K. These same parameters were used at 293.15 and 313.15 K. For the binary system of trioctylamine and water, the binary interaction parameters were obtained via regression of a single data point from an earlier work carried out on trioctylamine containing systems [14]. There was no available phase equilibria modeling work in the literature with respect to the binary system of LA and TOA. As a result, regression of the parameters was carried out using Aspen V11. The parameters of the other two subsystems, water-LA and water-trioctylamine, were fixed to the values obtained in the earlier work [13, 14]. The parameters were validated using the decanter model in Aspen. The initial points of the experiment were used as the mass fraction of the feed in the decanter and the resulting stream split was merged into the experimental results to observe the deviation and closeness between the experimental and model results.

By correlating the experimental data with the NRTL model, four regressed parameters were used to obtain the calculated tie line values. The default value of α at 0.3 could not describe the system. Then, the α was changed to 0.2. As can be observed in Fig. 4a–c, the obtained tie lines at high concentrations of LA are in good agreement with respect to the experimental data at the studied temperatures. At dilute concentrations of LA, the slope of the tie lines slightly deviates in the opposite direction. This deviation in the experimental data is also observed, which is not assumed in the NRTL model in its full physical significance. The observed gap between the tie lines at high and low concentrations of LA could be attributed to the formation of the complex described earlier. In the organic phase, the measured concentrations deviate from the model as a complex is formed between LA and TOA via ion-pair and hydrogen bonding. The model is therefore more suited for describing this system where a high concentration of LA is present.

Fig. 4
figure 4

Phase diagram of TOA + LA + H2O system at a T = 293.15 K; b T = 313.15 K and c T = 333.15 K: (■) experimental binodal, (—○—) experimental tie lines, (▲) initial experimental points, (★) calculated tie lines

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The calculated RMSD values were 0.057, 0.102, and 0.219 for the three measured temperatures of 293.15, 313.15, and 333.15 K, respectively. The calculated RMSD values show that all the predicted distribution coefficients agree relatively well with the experimental results. The lowest RMSD value was when the system is at 293.15 K and highest was when the temperature is at 333.15 K. Additionally, the agreements between predictions and measurements are acceptable considering the experimental uncertainty. Furthermore, the results of the calculated LLE data and the experimental LLE data shown in Figs. 1 and 4 also support the above conclusion.

The coherence of the NRTL parameters to fulfill the LLE phase split was checked according to Marcilla et al. [22] using the Graphical User Interface (GUI) in MATLAB code. The NRTL miscibility boundaries at α = 0.2 for the different subsystems of the ternary system of LA-TOA-H2O indicate that the parameters can be used to describe the system. The plait point location and the binary GM(L) curves for each subsystem are also provided in the supporting information. The former and latter graphs are presented in the Supporting Information as Figs. S3 and S4, respectively.

5 Conclusion

For the TOA + LA + H2O system, the experimental binodal data and the tie line compositions at T = (293.15, 313.15, and 333.15) K were obtained using cloud point and analytical methods at atmospheric pressure. Temperature dependency was negligible for the obtained binodal values. Additionally, higher extraction efficiencies are feasible with higher acid concentrations, as shown by the slope of the determined tie lines. Furthermore, our infrared spectroscopy (FT-IR) confirmed the complex formation between LA and TOA through hydrogen bonding and ion-pair formation. Moreover, the NRTL model was used to correlate the experimental binodal and tie line data. It was found that the studied model is satisfactory in representing the liquid–liquid equilibrium data of LA + TOA + water system at all temperatures.