Isobaric Vapor-Liquid Equilibrium of Biomass-Derived Ethyl Levulinate and Ethanol at 40.0, 60.0 and 80.0 kPa

Abstract

Isobaric vapor-liquid equilibrium (VLE) data for binary mixtures of biomass–derived ethyl levulinate and ethanol were measured using an apparatus comprising a modified Rose-Williams still and a condensation system. Measurements were taken at temperatures ranging from 329.58 K to 470.00 K and pressures of 40.0, 60.0 and 80.0 kPa. The thermodynamic consistency of the VLE data was evaluated using the Redlich-Kister area test, the Fredenslund test and the Van Ness point-to-point test. The data was correlated using three activity coefficient models: Wilson, NRTL and UNIQUAC. The Gibbs energy of mixing of the VLE data was analyzed to verify the suitability of the binary interaction parameters of these models. The activity coefficients and excess Gibbs free energy, calculated from the VLE experimental data and model correlation results, were analyzed to evaluate the models’ fit and the non–ideality of the binary system. The accuracy of the regression results was also assessed based on the root mean square deviation (RMSD) and average absolute deviation (AAD) for both temperature and the vapor phase mole fraction of ethyl levulinate. The results indicate that the NRTL model provided the best fit to the experimental data. Notably, the experimental data showed strong correlation with the predictions of all three models, suggesting their reliability for practical application.

1. Introduction

As a potential renewable biomass–derived platform compound, ethyl levulinate (EL) contains a carbonyl group and an ester group, which has good reactivity and can be subject to a variety of chemical reactions, such as hydrolysis, reduction, condensation, addition, etc. [1]. Taking advantages of the above reaction, EL can be used not only as fragrances, oil additives [2,3] and plasticizers [4] but also as an important pharmaceutical [5] and chemical raw material [6,7]. In addition, EL and its derivative γ-valerolactone can be used as a new type of liquid fuel additive, which is widely used in the field of petroleum alternative energy [8]. It was reported that the addition of appropriate amounts of EL to diesel fuel can improve power, environmental performance, and lubrication [9].

Currently, there are three methods for the preparation of ethyl levulinate EL: (1) esterification of levulinic acid, (2) catalytic alcoholysis of furfural alcohol in an ethanol solvent, and (3) direct alcoholysis of cellulose. The esterification of levulinic acid involves its reaction with ethanol to produce EL [10]. The catalytic alcoholysis uses furfural alcohol as the feedstock and synthesizes EL under acidic conditions through heating [11]. Direct alcoholysis of cellulose refers to the acid-catalyzed alcoholysis of cellulose in an ethanol solvent to produce EL [12].

Regardless of the method, impurities such as ethanol will remain in the reaction system, and high–purity EL can be obtained through separation processes such as distillation and extractive distillation [13]. And vapor-liquid equilibrium (VLE) data is required to design the separation process for production of high-purity EL. However, only Alexander J. Resk et al. [14] presented isothermal vapor-liquid equilibrium (VLE) values for EL + ethanol at a temperature of 60 °C and the isobaric VLE data at different temperatures is still lacking. Besides, the boiling point of EL is about 480 K at atmospheric pressure, and distillation under a reduced pressures can improve equipment safety and reduce energy consumption. Moreover, the chemical engineering data bank needs to be updated and improved with new experimental data to fit the model parameters. In conclusion, measuring the isobaric vapor-liquid equilibrium (VLE) data of the ethyl levulinate and ethanol under depressurized conditions is essential.

This work focuses on the isobaric vapor-liquid equilibrium data of EL + Ethanol at 40.0, 60.0 and 80.0 kPa, with the aim of providing fundamental references and equilibrium data for industrial production. All VLE data were subjected to thermodynamic consistency tests, including the Redlich-Kister area test, the Fredenslund test and the Van Ness point-to-point test. Three activity coefficient models, Wilson, nonrandom two–liquid (NRTL), and universal quasichemical activity coefficient (UNIQUAC) were employed to correlate the experimental data of the binary system.

2. Experimental and/or Computational Methods

2.1. Chemicals

The chemicals of ethanol, cyclohexanone and ethyl levulinate were analytical grade and obtained from commercial sources. The relevant information is exhibited in

Table 1. Specification of Chemical Samples.

Chemicals	Formula	CAS Number	Mass Fraction	Source	Analysis Method	Tb (K)/101.3 kPa
						exp.	lit.
ethanol	C2H6O	64-17-5	0.998	Sinopharm Chemical Reagent Co., Ltd.	GC a	351.52	351.44 [15]
cyclohexanone	C6H10O	108-94-1	0.995	Meryer Technologies Co., Ltd.	GC a	428.73	428.80 [15]
ethyl levulinate	C7H12O3	539-88-8	0.99	Meryer Technologies Co., Ltd.	GC a	478.88	478.95 b

^a GC is gas chromatography, ^b T_b of EL was calculated with Aspen and the standard uncertainty u of T is u (T) = 0.04 K.

. The mass fractions of the chemicals were analyzed and confirmed using GC (gas chromatography), and no detectable impurity was observed. Therefore, all the reagents were utilized without any further purification. The boiling temperatures were measured with mercury thermometers, as presented in Table 1. The differences in boiling temperatures (${\mathrm{T}}_{\mathrm{b}}$) between the reference data and experimental data are all within 0.1 K.

2.2. Apparatus and Procedure

The isobaric vapor-liquid equilibrium experiments were carried out in a set of apparatus, as illustrated in Figure 1, which included a modified Rose-Williams still [16,17] and a condensation system. The still could ensure intimate and continuous contact of the vapor and liquid phases to establish phase equilibrium in a short time. The total volume of the still was about 160 cm³ with around 80 cm³ occupied by the liquid solution. The solutions were prepared gravimetrically by an Sartorius BCE224-1CCN electronic balance, with a precision of 0.1 mg. The energy supplied to the still is generated by a heating rod, with its voltage regulated by a transformer at a rate of (5~10 V)/(10~15 min). The coolant in the condensation system is composed of water and ethylene glycol in a mass ratio of 2:1, with the temperature set at 263 K to facilitate the rapid condensation of vapor into liquid, allowing it to return to the equilibrium chamber efficiently. All temperature measurements were obtained using a high-precision mercury thermometer, which had an uncertainty of 0.04 K. The pressure control of the set of apparatus was managed by a Liquid ring vacuum pump and a buffer tank with a capacity of 20 L. The Liquid ring vacuum pump operated continuously, while the amount of air entering the system was controlled by adjusting the valve connecting the buffer tank to the outside, which could regulate the pressure of the still to the set value of reduced pressure conditions and ensure the pressure of the entire system stable for a long time. A U-tube differential manometer was connected between the condenser and the buffer tank, with its uncertainty of 0.1 kPa to precisely measure the pressure. To ensure that all experiments reached phase equilibrium, the vapor and liquid samples were analyzed until the temperatures stabilized for more than 2 h. After equilibrium was attained, samples from both the vapor (chilled to liquid form) and liquid phases were extracted through the sampling ports. A micro-syringe was utilized to withdraw these samples, followed by three parallel tests of each sample using gas chromatography (GC).

The isobaric vapor-liquid equilibrium data for the cyclohexanone + ethanol binary system, which also contains ethanol, were measured at 101.3 kPa and compared with data from the literature to verify the reliability of the apparatus shown in Figure 2.

The results demonstrated that the isobaric VLE data for the binary system of Cyclohexanone + Ethanol at 101.3 kPa exhibited excellent agreement with reference data, thereby validating the reliability of the set of apparatus.

2.3. Analysis

The equilibrium compositions of the vapor (chilled to liquid form) and liquid phases were determined using a SHIMADZU GC-2014C equipped with a flame ionization detector (FID). A FFAP capillary column (30m × 0.32 mm × 0.25 μm) was used to effectively separate various components present in the sample, including ethanol. The carrier gas was high–purity nitrogen (≥99.999%) flowing at a rate of 30 mL·min⁻¹. The flow rates of hydrogen (≥99.999%) and air (≥99.99%) were 40 mL·min⁻¹ and 400 mL·min⁻¹, respectively. The temperatures of column, injector and detector were (363.15 K for 2 min then at 20 K/min rise to 483.15 K for 2 min, 513.15 K and 523.15 K). An injection volume of 0.8 μL was used for each sample in the GC analysis. The GC response peaks were analyzed in the LabSolutions chromatography station and the area correction normalization method was adopted for component quantitative analysis, obtaining the composition results of the vapor and liquid phase samples in the binary system. The GC was calibrated with standard solutions prepared gravimetrically by the electronic balance. For the binary system of ethyl levulinate + ethanol, five standard solutions with different mass ratios were prepared according to the gradient, and the corresponding peak area ratios were obtained by GC analysis (each standard solution was analyzed three times to ensure accuracy). The expressions of the calibration curves, the correlation coefficients R² and the relative mass correction factors were obtained by fitting the data points in Origin 2021 and are shown in Figure S1 provided in the Supplementary Materials. The uncertainties of the liquid–phase and vapor-phase mole fractions were both kept within 0.0003, ensuring the reliability of the results.

3. Results and Discussion

3.1. Vapor-Liquid Equilibrium Data

Isobaric vapor-liquid equilibrium (VLE) data for the binary system of EL (1) + Ethanol (2) at pressures of 40.0, 60.0 and 80.0 kPa were generated using the modified Rose-Williams still, and are presented in

Table 2. Isobaric VLE Data (T-x-y), Activity Coefficients (γ_i), ln(γ₁/γ₂), Dimensionless Excess Gibbs Free Energy (g^E) and Dimensionless Gibbs Energy of mixing functions (g^M,V and g^M,L) for the EL (1) + Ethanol (2) System at 40.0, 60.0 and 80.0 kPa ^a.

T(K)	x1	y1	γ1	γ2	ln(γ1/γ2)	gE	gM,V	gM,L
40.0 kPa
329.58	0.0000	0.0000		0.9998		0.0000	–0.0002
331.23	0.0748	0.0006	1.2477	1.0019	0.2194	0.0183	–0.0773	–0.2476
333.04	0.1551	0.0013	1.1653	1.0106	0.1424	0.0326	–0.1600	–0.3988
335.51	0.2586	0.0024	1.1096	1.0312	0.0733	0.0497	–0.2709	–0.5219
339.01	0.3742	0.0041	1.0625	1.0477	0.0140	0.0518	–0.4241	–0.6093
343.59	0.4983	0.0069	1.0286	1.0743	–0.0435	0.0500	–0.6185	–0.6431
349.78	0.6177	0.0119	1.0114	1.0906	–0.0754	0.0402	–0.8700	–0.6251
355.72	0.7041	0.0186	1.0073	1.1099	–0.0970	0.0360	–1.0992	–0.5714
362.54	0.7757	0.0291	1.0061	1.1223	–0.1093	0.0306	–1.3465	–0.5017
372.50	0.8476	0.0516	1.0036	1.1338	–0.1220	0.0222	–1.6734	–0.4047
381.70	0.8921	0.0828	1.0026	1.1397	–0.1282	0.0164	–1.9315	–0.3257
396.17	0.9371	0.1612	1.0019	1.1421	–0.1310	0.0101	–2.2190	–0.2247
411.69	0.9664	0.3043	1.0015	1.1427	–0.1319	0.0059	–2.2778	–0.1411
426.94	0.9848	0.5336	1.0012	1.1407	–0.1304	0.0032	–1.8987	–0.0756
435.46	0.9924	0.7136	1.0006	1.1396	–0.1301	0.0016	–1.3651	–0.0430
441.11	0.9967	0.8583	1.0002	1.1383	–0.1293	0.0006	–0.7940	–0.0215
445.93	1.0000	1.0000	0.9999			0.0000	–0.0001
60.0 kPa
338.72	0.0000	0.0000		0.9999		0.0000	–0.0001
340.57	0.0811	0.0008	1.3091	1.0048	0.2646	0.0262	–0.0815	–0.2552
343.27	0.1914	0.0020	1.1859	1.0182	0.1525	0.0472	–0.1970	–0.4410
346.72	0.3145	0.0037	1.0979	1.0404	0.0538	0.0565	–0.3407	–0.5662
351.86	0.4613	0.0069	1.0516	1.0747	–0.0217	0.0620	–0.5478	–0.6282
358.36	0.5945	0.0122	1.0223	1.1062	–0.0789	0.0540	–0.7980	–0.6211
367.72	0.7229	0.0234	1.0070	1.1377	–0.1220	0.0408	–1.1348	–0.5494
378.77	0.8174	0.0444	1.0043	1.1583	–0.1427	0.0303	–1.4933	–0.4450
388.92	0.8733	0.0740	1.0019	1.1695	–0.1547	0.0215	–1.7779	–0.3586
399.39	0.9126	0.1191	1.0010	1.1780	–0.1628	0.0152	–2.0134	–0.2812
414.73	0.9498	0.2229	1.0009	1.1812	–0.1656	0.0092	–2.2068	–0.1899
422.70	0.9633	0.3005	1.0008	1.1823	–0.1667	0.0069	–2.2057	–0.1504
433.86	0.9779	0.4449	1.0005	1.1836	–0.1681	0.0042	–2.0323	–0.1018
440.59	0.9849	0.5563	1.0003	1.1825	–0.1673	0.0028	–1.7944	–0.0755
447.21	0.9908	0.6871	1.0002	1.1784	–0.1640	0.0017	–1.4219	–0.0506
453.74	0.9959	0.8396	1.0000	1.1753	–0.1615	0.0007	–0.8592	–0.0259
459.64	1.0000	1.0000	0.9999			0.0000	–0.0001
80.0 kPa
345.58	0.0000	0.0000		0.9999		0.0000	–0.0001
347.63	0.0875	0.0010	1.3515	1.0071	0.2941	0.0328	–0.0866	–0.2639
349.88	0.1766	0.0021	1.2417	1.0187	0.1980	0.0535	–0.1786	–0.4127
352.52	0.2728	0.0035	1.1605	1.0379	0.1117	0.0677	–0.2844	–0.5184
355.84	0.3791	0.0055	1.0994	1.0671	0.0298	0.0762	–0.4142	–0.5874
359.61	0.4798	0.0081	1.0512	1.1018	–0.0470	0.0744	–0.5577	–0.6179
365.70	0.5976	0.0134	1.0271	1.1339	–0.0989	0.0665	–0.7806	–0.6074
374.62	0.7167	0.0243	1.0119	1.1675	–0.1430	0.0524	–1.0873	–0.5437
385.34	0.8101	0.0444	1.0084	1.2010	–0.1748	0.0416	–1.4215	–0.4445
398.15	0.8784	0.0821	1.0047	1.2197	–0.1939	0.0283	–1.7620	–0.3418
409.39	0.9168	0.1325	1.0021	1.2252	–0.2010	0.0188	–1.9921	–0.2677
424.44	0.9509	0.2364	1.0010	1.2309	–0.2067	0.0112	–2.1545	–0.1847
436.06	0.9687	0.3551	1.0006	1.2286	–0.2053	0.0070	–2.1123	–0.1323
448.49	0.9828	0.5315	1.0003	1.2231	–0.2011	0.0038	–1.8181	–0.0831
458.78	0.9919	0.7261	1.0002	1.2172	–0.1964	0.0018	–1.2710	–0.0452
466.02	0.9973	0.8947	1.0002	1.2099	–0.1903	0.0007	–0.6050	–0.0180
470.00	1.0000	1.0000	1.0001			0.0000	0.0001

^a Standard uncertainties u are u (T) = 0.04 K, u (P) = 0.1 kPa, u (x₁) = u (y₁) = 0.0003.

. The listed VLE data comprised: T (equilibrium temperature), x_i and y_i (mole fractions of the liquid and vapor phases, respectively), γ_i (activity coefficient), ln(γ₁/γ₂) (used for thermodynamic consistency test), g^E (dimensionless excess Gibbs free energy of the mixture), g^M,V and g^M,L (dimensionless Gibbs energy of mixing functions for the vapor and liquid phases, respectively).

For isobaric VLE data, the general expression is given in Equation (1) [19]:

$$\mathrm{P}{\mathrm{y}}_{\mathrm{i}}{\mathsf{\varphi }}_{\mathrm{i}}^{\mathrm{v}^}={\mathrm{P}}_{\mathrm{i}}^{\mathrm{s}}{\mathsf{\varphi }}_{\mathrm{i}}^{\mathrm{s}}{\mathsf{\gamma }}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{i}}\mathrm{e}\mathrm{x}\mathrm{p}\left[{\displaystyle \frac{{\mathrm{V}}_{\mathrm{i}}^{\mathrm{L}}(\mathrm{P}-{\mathrm{P}}_{\mathrm{i}}^{\mathrm{s}})}{\mathrm{R}\mathrm{T}}}\right]$$

(1)

where i represents the different components, P and ${\mathrm{P}}_{\mathrm{i}}^{\mathrm{s}}$ are the total system pressure and the saturated vapor pressure, respectively, ${\mathsf{\varphi }}_{\mathrm{i}}^{\mathrm{v}}$ and ${\mathsf{\varphi }}_{\mathrm{i}}^{\mathrm{s}}$ are the fugacity coefficient of the vapor phase and pure component i at pressure ${\mathrm{P}}_{\mathrm{i}}^{\mathrm{s}}$ and T, respectively, x_i, y_i and γ_i have the same meaning as above; ${\mathrm{V}}_{\mathrm{i}}^{\mathrm{L}}$ is the liquid mole volume. In addition, ${\mathrm{P}}_{\mathrm{i}}^{\mathrm{s}}$ refers to the saturated pressure at the equilibrium temperature, and is calculated using the extended Antoine equation, which is presented as [20]:

$$\ln ({\mathrm{P}}_{\mathrm{i}}^{\mathrm{s}},\mathrm{k}\mathrm{P}\mathrm{a})={\mathrm{C}}_{1\mathrm{i}}+{\displaystyle \frac{{\mathrm{C}}_{2\mathrm{i}}}{\mathrm{T}+{\mathrm{C}}_{3\mathrm{i}}}}+{\mathrm{C}}_{4\mathrm{i}}\mathrm{T}+{\mathrm{C}}_{5\mathrm{i}}\ln \mathrm{T}+{\mathrm{C}}_{6\mathrm{i}}{\mathrm{T}}^{{\mathrm{C}}_{7\mathrm{i}}}\hspace{1em}{\mathrm{C}}_{8\mathrm{i}}\le \mathrm{T}\le {\mathrm{C}}_{9\mathrm{i}}$$

(2)

Each component’s Antoine constants were given by Aspen Plus V11 and listed in

Table 3. Extended Antoine Equation Constants of the Pure Component ^a.

Components	${\mathbf{C}}_{1\mathbf{i}}$	${\mathbf{C}}_{2\mathbf{i}}$	${\mathbf{C}}_{3\mathbf{i}}$	${\mathbf{C}}_{4\mathbf{i}}$	${\mathbf{C}}_{5\mathbf{i}}$	${\mathbf{C}}_{6\mathbf{i}}$	${\mathbf{C}}_{7\mathbf{i}}$	${\mathbf{C}}_{8\mathbf{i}}(\mathbf{K}$)	${\mathbf{C}}_{9\mathbf{i}}\left(\mathbf{K}\right)$
ethanol	66.3962	−7122.3	0	0	−7.1424	2.8853 × 10−6	2	159.05	514.00
ethyl levulinate	68.4222	−9228.7	0	0	−7.2248	4.4062 × 10−18	6	240.40	666.10

^a The constants were taken from Aspen property databank.

.

At low pressure, the vapor phase can be considered as an ideal gas, the Poynting factor $\mathrm{e}\mathrm{x}\mathrm{p}\left[{\mathrm{V}}_{\mathrm{i}}^{\mathrm{L}}(\mathrm{P}-{\mathrm{P}}_{\mathrm{i}}^{\mathrm{s}})/\mathrm{R}\mathrm{T}\right]$, ${\mathsf{\varphi }}_{\mathrm{i}}^{\mathrm{v}}$ and ${\mathsf{\varphi }}_{\mathrm{i}}^{\mathrm{s}}$ can be considered as 1, and then Equation (1) can be expressed as:

$$\mathrm{P}{\mathrm{y}}_{\mathrm{i}}^{^}={\mathrm{P}}_{\mathrm{i}}^{\mathrm{s}}{\mathsf{\gamma }}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{i}}$$

(3)

So, γ_i is calculable from Equation (3) and reported in Table 2. The experimental data indicates that the activity coefficients of EL and Ethanol in the vapor-liquid equilibrium system are greater than or equal to one at 40.0, 60.0 and 80.0 kPa. This suggests that the binary system exhibits significant positive deviation from ideal behavior, and that there may be strong interaction between the two components. Furthermore, as the molar fraction of EL increases in the liquid phase, the activity coefficient of EL decreases while the activity coefficient of Ethanol increases. However, at high concentrations of EL, the activity coefficient of Ethanol shows a decreasing trend. This behavior can be attributed to the intermolecular interactions between ethyl levulinate and ethanol.

The dimensionless excess Gibbs free energy g^E was calculated based on the experimental VLE data to reflect the difference between the actual solution and the ideal solution under identical conditions of temperature, pressure and composition. And g^E is given by Equation (4) [21]:

$${\mathrm{g}}^{\mathrm{E}}={\displaystyle \frac{{\mathrm{G}}^{\mathrm{E}}}{\mathrm{R}\mathrm{T}}}={\mathrm{x}}_1\ln \left({\mathsf{\gamma }}_1\right)+{\mathrm{x}}_2\ln \left({\mathsf{\gamma }}_2\right)$$

(4)

And g^E for the binary system of EL (1) + Ethanol (2) at pressures of 40.0, 60.0 and 80.0 kPa are listed in Table 2. It can be observed that g^E of the mixture deviates positively from ideal behavior at all three pressures, which is consistent with Raoult’s law. Additionally, as the mole fraction of EL in the liquid phase increases, g^E shows a trend of initially increasing and then decreasing.

3.2. Thermodynamic Consistency Tests

During the data measurement process, errors, both large and small, are inevitably introduced in the vapor-liquid equilibrium data. To evaluate the reliability of the experimental results, thermodynamic consistency tests are essential. As summarized by Jaime Wisniak et al. [22], the Redlich-Kister area test [23], the Fredenslund test [24] and the Van Ness point-to-point test [25] were used to assess the quality of the VLE data in this study.

For the Redlich-Kister area test, the underlying principle is the Gibbs-Duhem equation, which describes the thermodynamic relationship between activity coefficients and composition in binary mixtures:

$${\int }_{{\mathrm{x}}_1=0}^{{\mathrm{x}}_1=1}\ln {\displaystyle \frac{{\mathsf{\gamma }}_1}{{\mathsf{\gamma }}_2}}\mathrm{d}{\mathrm{x}}_1=-{\int }_{\mathrm{T}\left({\mathrm{x}}_1=0\right)}^{\mathrm{T}\left({\mathrm{x}}_1=1\right)}{\displaystyle \frac{{\mathrm{H}}^{\mathrm{E}}}{\mathrm{R}{\mathrm{T}}^2}}\mathrm{d}\mathrm{T}+{\int }_{\mathrm{P}\left({\mathrm{x}}_1=0\right)}^{\mathrm{P}\left({\mathrm{x}}_1=1\right)}{\displaystyle \frac{{\mathrm{V}}^{\mathrm{E}}}{\mathrm{R}\mathrm{T}}}\mathrm{d}\mathrm{P}$$

(5)

Under isobaric conditions, the second term on the right side of Equation (5) is equal to 0. And considering the enthalpy effects of mixing, the data set is regarded as thermodynamically consistent when the following condition is satisfied:

$$\mathrm{D}=100{\displaystyle \frac{\left|{\int }_0^1\ln \frac{{\mathsf{\gamma }}_1}{{\mathsf{\gamma }}_2}\mathrm{d}{\mathrm{x}}_1\right|}{{\int }_0^1\left|\ln \frac{{\mathsf{\gamma }}_1}{{\mathsf{\gamma }}_2}\right|\mathrm{d}{\mathrm{x}}_1}}=100{\displaystyle \frac{\left|\left|{\mathrm{A}}^{+}\right|-\left|{\mathrm{A}}^{-}\right|\right|}{\left|{\mathrm{A}}^{+}\right|+\left|{\mathrm{A}}^{-}\right|}}\le 2$$

(6)

Applying the Redlich-Kister area test to binary vapor-liquid equilibrium (VLE) data involves plotting ln(γ₁/γ₂) against the mole fraction x₁, resulting in a semi-logarithmic plot commonly referred to as the Redlich-Kister plot. In this plot, areas A⁺ and A^– represent the regions enclosed between the curve and axis above and below the x-axis, respectively. It is important to note that the Redlich-Kister test is applicable exclusively to binary mixtures.

In this work, the Redlich-Kister plots for the binary system of EL (1) + Ethanol (2) at all pressures are shown in Figure 3. And the values of D at 40.0, 60.0 and 80.0 kPa are 1.36, 1.04 and 0.33, respectively, all of which are less than 2. These results demonstrate that the experimental VLE data satisfy the thermodynamic consistency criteria according to the Redlich-Kister area test.

For the Fredenslund test, the dimensionless excess Gibbs free energy g^E obtained from Equation (4) is correlated using a series of Legendre polynomials:

$${\mathrm{g}}^{\mathrm{E}}={\displaystyle \frac{{\mathrm{G}}^{\mathrm{E}}}{\mathrm{R}\mathrm{T}}}={\mathrm{x}}_1{\mathrm{x}}_2{\sum }_{\mathrm{k}=0}^{\mathrm{n}}{\mathrm{a}}_{\mathrm{k}}{\mathrm{L}}_{\mathrm{k}}\left({\mathrm{x}}_1\right)\hspace{1em}\mathrm{k}=0,1,\dots ,\mathrm{n}$$

(7)

where n is the degree of the polynomial used, and ${\mathrm{a}}_{\mathrm{k}}$ is the parameter of the Legendre orthogonal polynomial, which is shown in Equation (8):

$${\mathrm{L}}_{\mathrm{k}}\left({\mathrm{x}}_1\right)=\left[\left(2\mathrm{k}-1\right)\left(2{\mathrm{x}}_1-1\right){\mathrm{L}}_{\mathrm{k}-1}\left({\mathrm{x}}_1\right)-\left(\mathrm{k}-1\right){\mathrm{L}}_{\mathrm{k}-2}\left({\mathrm{x}}_1\right)\right]/\mathrm{k}$$

(8)

with ${\mathrm{L}}_0\left({\mathrm{x}}_1\right)=1$ and ${\mathrm{L}}_1\left({\mathrm{x}}_1\right)=2{\mathrm{x}}_1-1$ as the first two Legendre polynomials. The dimensionless excess Gibbs free energy g^E describes the relationship between the deviation of the components and the deviation of the solution:

$$\ln {\mathsf{\gamma }}_1={\mathrm{g}}^{\mathrm{E}}+{\mathrm{x}}_2{\displaystyle \frac{\mathrm{d}{\mathrm{g}}^{\mathrm{E}}}{\mathrm{d}{\mathrm{x}}_1}}$$

(9)

The pertinent activity coefficients (γ₁) can be calculated from Equation (9), and then the mole fraction of the vapor phase (y₁) can be determined based on the VLE expression (Equation (3)). As stated by Fredenslund, a set of P-T-x₁-y₁ data is considered consistent if the average absolute deviation between y₁ is below 0.01 units, which is

$$∆{\mathrm{y}}_1={\displaystyle \frac{1}{\mathrm{N}}}{\sum }_{\mathrm{i}=1}^{\mathrm{N}}\left|{\mathrm{y}}_{1,\mathrm{i}}^{\mathrm{e}\mathrm{x}\mathrm{p}}-{\mathrm{y}}_{1,\mathrm{i}}^{\mathrm{c}\mathrm{a}\mathrm{l}}\right|\le 0.01$$

(10)

where N is the number of data points at a specific pressure.

Typically, a Legendre series with three to five terms is sufficient to determine the accuracy of the data. In this work, g^E was correlated using a four-term Legendre polynomial, and the values of $∆$y₁ at 40.0, 60.0 and 80.0 kPa are 0.00014, 0.00005 and 0.00013, respectively, all of which are less than 0.01. Meanwhile, residuals of the equilibrium temperatures

$$∆\mathrm{T}={\mathrm{T}}_{\mathrm{i}}^{\mathrm{e}\mathrm{x}\mathrm{p}}-{\mathrm{T}}_{\mathrm{i}}^{\mathrm{c}\mathrm{a}\mathrm{l}}$$

(11)

obtained by correlating the activity coefficient model, are listed in

Table 4. Calculation of VLE Data (T-x-y), Activity Coefficients (γ_i), Dimensionless Excess Gibbs Free Energy (g^E), ΔT and Δln(γ₁/γ₂) Using the Wilson Model for the EL (1) + Ethanol (2) System at 40.0, 60.0 and 80.0 kPa ^a.

T (K)	ΔT (K)	x1	y1	γ1	γ2	gE	Δln(γ1/γ2)
40.0 kPa
329.58	0.00	0.0000	0.0000		1.0000	0.0000
331.19	0.04	0.0748	0.0006	1.2636	1.0036	0.0208	−0.0110
332.99	0.05	0.1551	0.0013	1.1755	1.0128	0.0358	−0.0065
335.56	−0.05	0.2586	0.0024	1.1055	1.0287	0.0469	0.0013
338.99	0.02	0.3742	0.0041	1.0597	1.0487	0.0514	0.0036
343.66	−0.07	0.4982	0.0069	1.0314	1.0707	0.0497	−0.0061
349.75	0.03	0.6177	0.0119	1.0156	1.0919	0.0432	−0.0030
355.77	−0.05	0.7040	0.0187	1.0087	1.1071	0.0362	−0.0039
362.59	−0.05	0.7757	0.0291	1.0048	1.1198	0.0291	−0.0009
372.53	−0.03	0.8476	0.0516	1.0022	1.1323	0.0208	0.0001
381.71	−0.01	0.8921	0.0827	1.0011	1.1395	0.0151	0.0013
396.12	0.05	0.9371	0.1606	1.0004	1.1451	0.0089	0.0041
411.66	0.03	0.9664	0.3035	1.0002	1.1453	0.0047	0.0036
426.95	−0.01	0.9848	0.5332	1.0001	1.1414	0.0021	0.0017
435.49	−0.03	0.9924	0.7139	1.0001	1.1378	0.0010	−0.0011
441.13	−0.02	0.9967	0.8587	1.0000	1.1350	0.0005	−0.0027
445.93	0.00	1.0000	1.0000	1.0001		0.0000
60.0 kPa
338.72	0.00	0.0000	0.0000		1.0000	0.0000
340.58	−0.01	0.0811	0.0008	1.3103	1.0043	0.0258	−0.0014
343.25	0.02	0.1914	0.0020	1.1872	1.0193	0.0483	0.0000
346.66	0.06	0.3145	0.0037	1.1069	1.0429	0.0607	−0.0058
351.85	0.01	0.4613	0.0069	1.0527	1.0752	0.0628	−0.0006
358.36	0.00	0.5945	0.0122	1.0254	1.1061	0.0558	−0.0031
367.75	−0.03	0.7229	0.0235	1.0105	1.1361	0.0429	−0.0048
378.78	−0.01	0.8174	0.0444	1.0043	1.1579	0.0303	−0.0003
388.91	0.01	0.8733	0.0740	1.0020	1.1700	0.0217	0.0003
399.40	−0.01	0.9126	0.1191	1.0010	1.1776	0.0152	−0.0003
414.71	0.02	0.9498	0.2226	1.0003	1.1825	0.0087	0.0017
422.69	0.01	0.9633	0.3002	1.0002	1.1831	0.0064	0.0013
433.88	−0.02	0.9779	0.4451	1.0001	1.1823	0.0038	−0.0007
440.61	−0.02	0.9849	0.5566	1.0001	1.1811	0.0026	−0.0009
447.20	0.01	0.9908	0.6869	1.0001	1.1794	0.0016	0.0010
453.73	0.01	0.9959	0.8393	1.0000	1.1774	0.0007	0.0018
459.64	0.00	1.0000	1.0000	1.0001		0.0000
80.0 kPa
345.58	0.00	0.0000	0.0000		1.0001	0.0000
347.66	0.02	0.0875	0.0010	1.3726	1.0059	0.0331	−0.0167
349.84	−0.04	0.1766	0.0021	1.2461	1.0203	0.0554	−0.0020
352.44	−0.08	0.2728	0.0035	1.1591	1.0413	0.0697	0.0044
355.81	−0.03	0.3791	0.0055	1.0979	1.0685	0.0765	0.0027
359.72	0.11	0.4796	0.0082	1.0603	1.0964	0.0759	−0.0136
365.75	0.05	0.5974	0.0135	1.0320	1.1310	0.0684	−0.0072
374.61	−0.01	0.7167	0.0243	1.0146	1.1679	0.0543	−0.0022
385.41	0.07	0.8101	0.0445	1.0063	1.1977	0.0394	−0.0007
398.18	0.03	0.8784	0.0820	1.0026	1.2185	0.0263	0.0012
409.34	−0.05	0.9168	0.1321	1.0012	1.2281	0.0182	0.0032
424.42	−0.02	0.9509	0.2361	1.0005	1.2320	0.0107	0.0014
436.05	−0.01	0.9687	0.3548	1.0002	1.2296	0.0067	0.0012
448.49	0.00	0.9828	0.5314	1.0001	1.2231	0.0036	0.0002
458.80	0.02	0.9919	0.7264	1.0000	1.2153	0.0016	−0.0014
466.03	0.01	0.9973	0.8948	1.0000	1.2086	0.0005	−0.0009
470.00	0.00	1.0000	1.0000	1.0000		0.0000

^a Standard uncertainties u are u (T) = 0.04 K, u (P) = 0.1 kPa, u (x₁) = u (y₁) = 0.0003.

, Tables S2 and S3, with the distribution plots shown in Figure 4, Figure 5 and Figure 6. The residuals in these plots exhibit random behavior, indicating that the isobaric VLE data satisfy the Fredenslund test.

For the Van Ness point-to-point test, the work of Van Ness in 1995 demonstrated that the application of the Van Ness point-to-point test involves calculating the value of ln(γ₁/γ₂) for each data point, comparing them with the calculated values obtained by fitting the activity coefficient model, and analyzing the residual distribution of ln(γ₁/γ₂):

$$∆\ln \left({\mathsf{\gamma }}_1/{\mathsf{\gamma }}_2\right)=\left[\ln \left({\mathsf{\gamma }}_1^{\mathrm{e}\mathrm{x}\mathrm{p}}/{\mathsf{\gamma }}_2^{\mathrm{e}\mathrm{x}\mathrm{p}}\right)-\ln \left({\mathsf{\gamma }}_1^{\mathrm{c}\mathrm{a}\mathrm{l}}/{\mathsf{\gamma }}_2^{\mathrm{c}\mathrm{a}\mathrm{l}}\right)\right]$$

(12)

If the residuals are randomly distributed, the set of data is considered consistent.

In this work, the residuals of ln(γ₁/γ₂) are listed in Table 4, Tables S2 and S3, with the distributions shown in Figure 4, Figure 5 and Figure 6, which exhibit distinct random behavior, indicating that the isobaric VLE data satisfy the Van Ness point-to-point test.

Given that both the Fredenslund and Van Ness point-to-point tests rely on comparing experimental data with model-predicted values, a certain level of model dependency is inevitably introduced into the assessment.

3.3. Data Correlation

The experimental VLE data for the binary system of EL (1) + Ethanol (2) at 40.0, 60.0 and 80.0kPa was fitted by the Wilson [26], NRTL [27] and UNIQUAC [28] models, which was carried out using Aspen Plus V11.0. A. Marcilla et al. [29] suggested that the necessity of considering the temperature dependence of the model parameters can be detected prior to the correlation process by analyzing the Gibbs energy of mixing of the experimental VLE data. For a binary isobaric vapor-liquid equilibrium system, when the vapor phase is treated as an ideal gas, the dimensionless Gibbs energy of mixing of the vapor and liquid phases (g^M,V and g^M,L) can be expressed as follows:

$${\mathrm{g}}^{\mathrm{M},\mathrm{V}}={\displaystyle \frac{{\mathrm{G}}^{\mathrm{M},\mathrm{V}}}{\mathrm{R}\mathrm{T}}}={\mathrm{y}}_1\ln \left({\displaystyle \frac{{\mathrm{y}}_1\mathrm{P}}{{\mathrm{P}}_1^{\mathrm{s}}}}\right)+{\mathrm{y}}_2\ln \left({\displaystyle \frac{{\mathrm{y}}_2\mathrm{P}}{{\mathrm{P}}_2^{\mathrm{s}}}}\right)$$

(13)

$${\mathrm{g}}^{\mathrm{M},\mathrm{L}}=\left({\mathrm{x}}_1-{\mathrm{y}}_1\right)\left[\ln \left({\displaystyle \frac{{\mathrm{y}}_1{\mathrm{P}}_2^{\mathrm{s}}}{{\mathrm{y}}_2{\mathrm{P}}_1^{\mathrm{s}}}}\right)\right]+{\mathrm{g}}^{\mathrm{M},\mathrm{V}}$$

(14)

where P and ${\mathrm{P}}_{\mathrm{i}}^{\mathrm{s}}$ are the total system pressure and the saturated vapor pressure of the pure component i, respectively.

The calculated g^M,V and g^M,L are listed in Table 2, with the corresponding vapor and liquid g^M curves shown in Figure 7 and Figure S2. The horizontal axis is represented by the mole fraction of the light component (x₂, y₂) to ensure consistency. The tie-lines connecting the Gibbs energy of mixing of the conjugated vapor and liquid phases are close to being tangent to the smooth g^M,L curve, which connects all g^M,L at different temperatures. Therefore, consistent and good (near the experimental data) fitting results can be achieved without any temperature dependence in the model according to A. Marcilla.

However, the temperature range for the binary VLE system of EL + Ethanol is quite large. To ensure the accuracy of fitting, temperature dependence is appropriately introduced into the relevant model parameters. The corresponding equations are presented in

Table 5. Binary Forms of the Wilson, NRTL, and UNIQUAC Equations Used in This Study.

Wilson
$\begin{array}{c}\ln {\gamma }_1=-\ln \left(x_1+A_{12}{x}_2\right)+x_2\left({\displaystyle \frac{A_{12}}{x_1+A_{12}{x}_2}}-{\displaystyle \frac{A_{21}}{x_2+A_{21}{x}_1}}\right)\\ \ln {\gamma }_2=-\ln \left(x_2+A_{21}{x}_1\right)-x_1\left({\displaystyle \frac{A_{12}}{x_1+A_{12}{x}_2}}-{\displaystyle \frac{A_{21}}{x_2+A_{21}{x}_1}}\right)\end{array}$
$A_{12}=a_{12}+{\displaystyle \frac{b_{12}}{T}}$$A_{21}=a_{21}+{\displaystyle \frac{b_{21}}{T}}$
NRTL
$\begin{array}{l}\ln {\gamma }_1=x_2\left[{\displaystyle \frac{{\tau }_{12}{G}_{12}^2}{{(x_1+x_2{G}_{12})}^2}}+{\displaystyle \frac{{\tau }_{21}{G}_{21}^2}{{(x_1+x_2{G}_{21})}^2}}\right]\\ \ln {\gamma }_2=x_1\left[{\displaystyle \frac{{\tau }_{12}{G}_{12}^2}{{(x_2+x_1{G}_{12})}^2}}+{\displaystyle \frac{{\tau }_{21}{G}_{21}^2}{{(x_2+x_1{G}_{21})}^2}}\right]\end{array}$
$G_{12}=\exp (-{\alpha }_{12}{\tau }_{12})$$G_{21}=\exp (-{\alpha }_{21}{\tau }_{21})$${\tau }_{12}=a_{12}+{\displaystyle \frac{b_{12}}{T}}$${\tau }_{21}=a_{21}+{\displaystyle \frac{b_{21}}{T}}$
UNIQUAC
$\ln {\gamma }_1=\ln \left({\displaystyle \frac{{\phi }_1}{x_1}}\right)+{\displaystyle \frac{Z}{2}}{q}_1\ln \left({\displaystyle \frac{{\theta }_1}{{\phi }_1}}\right)+{\phi }_2\left(l_1-{\displaystyle \frac{r_1}{r_2}}{l}_2\right)-q_1\ln \left({\theta }_1+{\theta }_2{\tau }_{21}\right)+{\theta }_2{q}_1\left({\displaystyle \frac{{\tau }_{21}}{{\theta }_1+{\theta }_2{\tau }_{21}}}-{\displaystyle \frac{{\tau }_{12}}{{\theta }_2+{\theta }_1{\tau }_{12}}}\right)$
$\ln {\gamma }_2=\ln \left({\displaystyle \frac{{\phi }_2}{x_2}}\right)+{\displaystyle \frac{Z}{2}}{q}_2\ln \left({\displaystyle \frac{{\theta }_2}{{\phi }_2}}\right)+{\phi }_1\left(l_2-{\displaystyle \frac{r_2}{r_1}}{l}_1\right)-q_2\ln \left({\theta }_2+{\theta }_1{\tau }_{12}\right)-{\theta }_1{q}_2\left({\displaystyle \frac{{\tau }_{21}}{{\theta }_1+{\theta }_2{\tau }_{21}}}-{\displaystyle \frac{{\tau }_{12}}{{\theta }_2+{\theta }_1{\tau }_{12}}}\right)$
${\tau }_{12}=\exp \left({\displaystyle \frac{a_{12}+b_{12}}{T}}\right)$$\hspace{1em}{\tau }_{21}=\exp \left({\displaystyle \frac{a_{21}+b_{21}}{T}}\right)$

. For the NRTL model, the nonrandomness parameter (αij) was fixed at 0.3, as recommended in Aspen Plus.

The interaction parameters for the thermodynamic models were determined using the maximum likelihood principle. The objective function is expressed as follows:

$$\mathrm{O}\mathrm{F}=\sum _{\mathrm{i}=1}^{\mathrm{N}}\left[{\left({\displaystyle \frac{{\mathrm{T}}_{\mathrm{i}}^{\mathrm{e}\mathrm{x}\mathrm{p}}-{\mathrm{T}}_{\mathrm{i}}^{\mathrm{c}\mathrm{a}\mathrm{l}}}{{\mathsf{\sigma }}_{\mathrm{T}}}}\right)}^2+{\left({\displaystyle \frac{{\mathrm{P}}_{\mathrm{i}}^{\mathrm{e}\mathrm{x}\mathrm{p}}-{\mathrm{P}}_{\mathrm{i}}^{\mathrm{c}\mathrm{a}\mathrm{l}}}{{\mathsf{\sigma }}_{\mathrm{P}}}}\right)}^2+{\left({\displaystyle \frac{{\mathrm{x}}_{\mathrm{i}}^{\mathrm{e}\mathrm{x}\mathrm{p}}-{\mathrm{x}}_{\mathrm{i}}^{\mathrm{c}\mathrm{a}\mathrm{l}}}{{\mathsf{\sigma }}_{\mathrm{x}}}}\right)}^2+{\left({\displaystyle \frac{{\mathrm{y}}_{\mathrm{i}}^{\mathrm{e}\mathrm{x}\mathrm{p}}-{\mathrm{y}}_{\mathrm{i}}^{\mathrm{c}\mathrm{a}\mathrm{l}}}{{\mathsf{\sigma }}_{\mathrm{y}}}}\right)}^2\right]$$

(15)

The objective function is to minimize the differences of experimental (exp) and calculated (cal) values of T, P, x_i, and y_i. $\mathsf{\sigma }$ denotes standard deviation, and N denotes the experimental data number.

The correlation results of each activity coefficient model, including the calculated VLE data, residual analysis, activity coefficients, and dimensionless excess Gibbs free energy, are listed in Table 4 (Wilson), Table S2 (NRTL) and Table S3 (UNIQUAC).

The T-x-y diagrams for the binary system of EL (1) + Ethanol (2) at 40.0, 60.0, and 80.0 kPa are presented in Figure 8, with the y-x diagrams shown in Figure 9. As shown in the figures, no azeotrope is observed for the EL and ethanol system at 40.0, 60.0, and 80.0 kPa. For the binary system, the fitting deviations of all three models are quite small. The curves of all three models smoothly pass through the experimental points at all pressures, and the curves nearly coincide, indicating that all three models exhibit a good correlation with the experimental vapor-liquid equilibrium data.

The inset in Figure 9 shows that as the pressure decreases, the y-x curve deviates further from the main diagonal. This suggests that lowering the equilibrium pressure is beneficial for the separation of ethyl levulinate and ethanol. Overall, the effect of this improvement is not significant.

The γ_i-x₁ and g^E-x₁ diagrams for the binary system are shown in Figure 10 and Figure 11, respectively. All the activity coefficients and the dimensionless excess Gibbs free energy were calculated from the correlation results of the Wilson model using Equation (3) and (4). The calculated results are generally consistent with the experimental measurements, further confirming the applicability of the activity coefficient model. Moreover, at lower pressures, the activity coefficients of EL and ET are smaller, and the dimensionless excess Gibbs free energy is also smaller, indicating that the binary system deviates less from the ideal state. This behavior may be attributed to the polarity difference between EL and ethanol.

The root mean square deviation (RMSD) and average absolute deviation (AAD) of the VLE data for the three models were computed to assess the correlation. The expressions for RMSD and AAD are given as follows:

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{D}\left(\mathrm{T}\right)={\left[{\displaystyle \frac{{\sum }_{\mathrm{i}=1}^{\mathrm{N}}{\left({\mathrm{T}}_{\mathrm{i}}^{\mathrm{e}\mathrm{x}\mathrm{p}}-{\mathrm{T}}_{\mathrm{i}}^{\mathrm{c}\mathrm{a}\mathrm{l}}\right)}^2}{\mathrm{N}}}\right]}^{0.5}$$

(16)

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{D}\left({\mathrm{y}}_1\right)={\left[{\displaystyle \frac{{\sum }_{\mathrm{i}=1}^{\mathrm{N}}{\left({\mathrm{y}}_{1\mathrm{i}}^{\mathrm{e}\mathrm{x}\mathrm{p}}-{\mathrm{y}}_{1\mathrm{i}}^{\mathrm{c}\mathrm{a}\mathrm{l}}\right)}^2}{\mathrm{N}}}\right]}^{0.5}$$

(17)

$$\mathrm{A}\mathrm{A}\mathrm{D}\left(\mathrm{T}\right)={\displaystyle \frac{1}{\mathrm{N}}}\sum _{\mathrm{i}=1}^{\mathrm{N}}\left|{\mathrm{T}}_{\mathrm{i}}^{\mathrm{e}\mathrm{x}\mathrm{p}}-{\mathrm{T}}_{\mathrm{i}}^{\mathrm{c}\mathrm{a}\mathrm{l}}\right|$$

(18)

$${\mathrm{g}}^{\mathrm{E}}={\displaystyle \frac{{\mathrm{G}}^{\mathrm{E}}}{\mathrm{R}\mathrm{T}}}={\mathrm{x}}_1\ln \left({\mathsf{\gamma }}_1\right)+{\mathrm{x}}_2\ln \left({\mathsf{\gamma }}_2\right)$$

(19)

$$\mathrm{A}\mathrm{A}\mathrm{D}\left({\mathrm{y}}_1\right)={\displaystyle \frac{1}{\mathrm{N}}}\sum _{\mathrm{i}=1}^{\mathrm{N}}\left|{\mathrm{y}}_{1\mathrm{i}}^{\mathrm{e}\mathrm{x}\mathrm{p}}-{\mathrm{y}}_{1\mathrm{i}}^{\mathrm{c}\mathrm{a}\mathrm{l}}\right|$$

(20)

Table 6. Interaction Parameters, RMSD (T), RMSD (y₁), AAD (T), and AAD (y₁) for the System of EL (1) + Ethanol (2) with Three Models.

Model	${\mathbf{a}}_{\mathbf{i}\mathbf{j}}$	${\mathbf{a}}_{\mathbf{j}\mathbf{i}}$	${\mathbf{b}}_{\mathbf{i}\mathbf{j}}\left(\mathbf{K}\right)$	${\mathbf{b}}_{\mathbf{j}\mathbf{i}}\left(\mathbf{K}\right)$	α	RMSDs		AADs
						T(K)	y1	T(K)	y1
40.0 kPa
Wilson	1.214	−0.614	−712.28	360.39	−	0.04	0.0003	0.03	0.0002
NRTL	0.914	−1.581	−544.98	928.90	0.3	0.04	0.0003	0.03	0.0002
UNIQUAC	−1.665	1.186	456.12	−373.90	−	0.04	0.0003	0.03	0.0002
60.0 kPa
Wilson	0.819	−0.419	−567.91	274.83	−	0.02	0.0002	0.02	0.0001
NRTL	0.672	−1.155	−445.86	778.85	0.3	0.02	0.0002	0.01	0.0001
UNIQUAC	−1.479	1.025	380.68	−314.53	−	0.02	0.0002	0.02	0.0001
80.0 kPa
Wilson	1.650	−0.962	−886.16	463.07	−	0.04	0.0002	0.03	0.0001
NRTL	1.307	−2.070	−673.95	1136.03	0.3	0.04	0.0002	0.03	0.0001
UNIQUAC	−2.095	1.454	602.82	−475.74	−	0.05	0.0002	0.04	0.0001

presents the correlated parameters for the three models, along with the RMSDs and AADs for the equilibrium temperature and vapor mole fraction. For the binary system of EL (1) + Ethanol (2) at 40.0, 60.0 and 80.0kPa, the RMSD_max (y₁) = 0.0003, the AAD_max (y₁) = 0.0002, the RMSD_max (T) = 0.05 K and the AAD_max (T) = 0.04 K. The RMSD (y₁) and AAD (y₁) < 0.001. RMSD (T) and AAD (T) < 0.1 K. The deviations were relatively small and fell within the acceptable error range. Based on the results, the Wilson, NRTL and UNIQUAC models provided accurate correlations of the experimental data, exhibiting similar levels of accuracy.

4. Conclusions

The isobaric VLE data of EL + Ethanol was measured using an apparatus that included a modified Rose-Williams still and a condensation system, operating at pressures of 40.0, 60.0 and 80.0 kPa. The VLE data passed the Redlich-Kister area test, the Fredenslund test and the Van Ness point-to-point test, confirming its thermodynamic consistency. For the systems of EL + Ethanol at all pressures, the Wilson, NRTL and UNIQUAC activity coefficient models were all successfully correlated with the VLE data. The curves of all three models on the T-x-y plot smoothly pass through the experimental points and are almost coincided. The analysis of the Gibbs energy of mixing for the VLE data shows that the binary interaction parameters have weak temperature dependence. The RMSD (y₁) and AAD (y₁) values were less than 0.001, while the RMSD (T) and AAD (T) values were less than 0.1 K. These results indicated that the experimental data is reliable. The generated VLE data can be used to design the separation processes for ethyl levulinate and ethanol in the material product system. The binary interaction parameters obtained from the regression using three local composition activity coefficient models—Wilson, NRTL, and UNIQUAC—are not only applicable to binary systems, but can also be extended to multicomponent systems containing ethyl levulinate and ethanol. Moreover, the VLE data obtained in this study may serve as a useful reference for similar binary systems, such as methyl levulinate and methanol. In addition, the variations of the activity coefficients and excess Gibbs free energy for the EL + Ethanol system reveal the interaction between ethyl levulinate and ethanol, as well as the system’s positive deviation characteristics. In future studies, it is recommended to conduct additional vapor-liquid equilibrium experiments over a wider range of pressures and with other levulinate ester−alcohol systems, in order to further validate the applicability of thermodynamic models and to improve the thermodynamic database for levulinate ester compounds.