Quaternary liquid-liquid equilibria for (water + ethanol + diisopropyl ether + n-heptane) at 298.15 K

Chen Yao ^1,2, Dong Yanhui ^1,2, Zhang Shengli ^1,2
(¹ Department of Chemistry, Jinan University; ² Institute of Nanochemistry, Jinan University, 510632, China)

1. INTRODUCTION
In recent years there has been growing interest in the use of oxygenate additives to improve gasoline performance as anti-knocking agents and reduction air pollution. Reformulated gasoline includes certain oxygenated compounds such as alcohols and ethers. These are commonly methanol, ethanol, propanol, and butanol as well as methyl tert-butyl ether (MTBE), ethyl tert-butyl ether (ETBE), diisopropyl ether (DIPE) and tert-amyl methyl ether (TAME). DIPE is an ideal fuel additive to replace MTBE because of its high octane number and lower vapor pressure. To assess the solubility of DIPE in the alcohol aqueous with hydrocarbon, we continue to study the phase behavior of liquid alcohol aqueous mixtures of DIPE with gasoline-substitution hydrocarbons. Here we report liquid-liquid equilibrium (LLE) measurements on one quaternary system water + ethanol + DIPE + n-heptane at 298.15 K. The experimental LLE data were correlated by means of the modified UNIQUAC and extended UNIQUAC models ^[1,2] including both ternary and quaternary parameters coming from multicomponent intermolecular interactions, in addition to binary parameters. The constituent ternary systems of water + ethanol + n-heptane, water + ethanol + DIPE ^[3], water + DIPE + n-heptane ^[4], were used to obtain ternary parameters for accurate representation of the quaternary LLE system studied in this work. The binary parameters of miscible binary mixtures of constituents of the ternary and quaternary systems were obtained from vapor-liquid equilibrium data ^[5-8] and those of immiscible mixtures were obtained from mutual solubility data [3,9].

2. EXPERIMENTS
2.1 Materials
DIPE was provided by the Tianjin Kermel Chemical Reagents Development Center, with a mass fraction of 99.5 % at the fewest. Ethanol was supplied by Guangzhou Chemical Reagent Factory, with a minimum mass fraction of 99.5 %. n-Heptane was supplied by the Guangzhou Chemical Reagent Factory, with a minimum mass fractions of 99.7 %. All chemicals were used without further purification. For GC analysis, appreciable peaks have not been detected. Water was distilled twice.
2.2 Apparatus and Procedures
Ternary and quaternary LLE measurements were carried out at 298.15 ± 0.01 K. The quaternary mixtures were prepared by mixing stepwise the binary DIPE + n-heptane mixtures whose compositions are M₁, M₂, and M₃ with water, and then ethanol to cover the two-phase regions. The values of M₁, M₂, and M₃ are approximate 0.25, 0.50, and 0.75, respectively, indicating the mole fraction of DIPE in the binary DIPE + n-heptane mixtures. About 70 cm³ of each mixture was poured into the equilibrium glass cell placed in a thermostated water bath. The mixture was then stirred vigorously by magnetic stirrer for 3 h and then allowed to settle for 3 h, which was sufficient to separate into two liquid phases. Dry nitrogen gas was used to prevent contamination from moisture in the headspace of the equilibrium cell. Samples, withdrawn from upper and lower phases in the cell by a microsyringe, were analyzed by a gas chromatograph (GC-14C) equipped with a thermal conductivity detector. Each component of the ternary and quaternary mixtures was separated clearly, using a stainless steel column (2 m long, 3 mm i.d.) packed with Porapak QS. The temperatures of the injection system and detector system were all set at 513.15 K. The initial temperature and final temperature of the oven was kept at 483.15 K and 453.15 K, respectively. The hydrogen flow rates for both the separation and reference columns were set at 1.1 cm³ s^―1. The peak areas of the components, detected with a chromatopac (N2000), were calibrated with prepared known mixtures by mass. The mass of each component of the mixture was determined from the calibration and converted to mole fraction. Three analyses were done for each sample to obtain a mean value with a reproducibility of better than 0.1%. The accuracy of the measurements was estimated within ±0.001 in mole fraction.
2.3 Experimental results
Tables 1 and 2 show experimental LLE data for the water + ethanol + n-heptane and water + ethanol + DIPE + n-heptane mixtures.

3. CALCULATION PROCEDURE AND RESULTS
3.1 Calculation procedure
We have used the modified UNIQUAC^[1] and extended UNIQUAC^[2] models with binary and additional ternary and quaternary parameters for an accurate description of the experimental quaternary LLE data and constituent ternary data as well as binary VLE and mutual solubility data.
    The binary parameter defined by the binary energy parameter a_ji is expressed as
(1)
    where a_ji can be obtained from binary experimental phase equilibrium data, and C was set to 1 for the extended UNIQUAC and 0.65 for the modified UNIQUAC.
    The binary energy parameters for the miscible mixtures were obtained from the VLE data reduction using the following thermodynamic equations^[10]:

where P, x, y, and? are the total pressure, the liquid-phase mole fraction, the vapor-phase mole fraction, and the activity coefficient, respectively. The pure component vapor pressure, , was calculated by using the Antoine equation with coefficients taken from the literatures^[11,12]. The liquid molar volume, , was obtained by a modified Rackett equation^[13]. The fugacity coefficient, f, was calculated by the Eqn.(3). The pure and cross second virial coefficients, B, were estimated by the method of Hayden and O'Connell^[14]. The binary energy parameters for the partially miscible mixtures were obtained by solving the following thermodynamic equations simultaneously.

The ternary and quaternary LLE calculations were carried out using the Eqns.(4) and (5). For the ternary systems of type 1 having a plait point, two-parameter UNIQUAC models predict generally larger solubility envelope than the experimental one. It is necessary to correlate ternary and quaternary LLE using ternary and quaternary parameters in addition to binary ones. The additional ternary parameter t_ijk was obtained by fitting the model to the ternary experimental LLE data and the quaternary parameter t_ijkl was determined from the quaternary experimental LLE data using a simplex method^[15] by minimizing the objective function:
F = (6)
where min means minimum values, i = 1 to 3 for ternary mixtures or i =1 to 4 for quaternary mixtures, j = phases I and II, k = 1,2,…,n (no. of tie lines), M = 2ni, and x = (the liquid-phase mole fraction).
3.2 Calculation results
Table 3 presents the constituent binary energy parameters of the modified and extended UNIQUAC models. Table 4 shows the ternary parameters obtained in fitting the modified and extended UNIQUAC models to the experimental ternary LLE systems, and root-mean-square deviation of the mole fraction of tie lines between the experimental and calculated results for the ternary LLE systems. It seems that the modified UNIQUAC model with the only binary parameters predicts the ternary LLEs more successfully than the extended UNIQUAC model, and these models can give a much more accurate representation for the ternary LLEs by including the ternary parameters in addition to the binary ones. Figure 1 compares the experimental and correlated liquid-liquid equilibrium results of three boundary ternary systems making up the quaternary system at T = 298.15 K. It shows good agreement between the experimental values and those correlated using additional ternary parameters in Figure 1. The quaternary system exhibits type 2 quaternary liquid-liquid behavior^[16], which are composed of two ternary liquid-liquid equilibrium for the mixtures (water + ethanol + DIPE) and (water + ethanol + n-heptane) classified as type 1, and one ternary liquid-liquid equilibrium for the mixtures (water + DIPE + n-heptane) as type 2.
    Table 4 summarizes the quaternary LLE results predicted by the modified UNIQUAC and extended UNIQUAC models with the binary and ternary parameters, together with root-mean-square deviations. The root-mean-square (r.m.s.) deviations predicted using the binary and ternary parameters are slightly large for the water + ethanol + DIPE + n-heptane system, but both models can describe accurately the quaternary experimental LLE data by the correlation involving the additional quaternary parameters, and the correlated r.m.s. is 1.88 mol% for the modified UNIQUAC model and 4.13 mol% for the extended UNIQUAC model.

Table 3 Calculated results of binary phase equilibrium data reduction

Table 4 Calculated results for ternary liquid-liquid equilibrium at 298.15 K

Table 5. Calculated Results for Quaternary Liquid-Liquid Equilibria at 298.15 K

a Number of data points. 
^b Modified UNIQUAC model.
^c Extended UNIQUAC model.
^d Predicted results using binary parameters alone. 
^e Correlated results using binary and quaternary parameters.
^f Root-mean-square deviation(mol%).

Figure 1 Experimental and calculated (liquid + liquid) equilibria of three ternary mixtures making up of (water + ethanol + DIPE + n-heptane) at T = 298.15 K. ●- - -●, Experimental tie line; ——, correlated by the modified UNIQUAC model with binary and ternary parameters taken from Tables 3 and 4.

4. CONCLUSION
The quaternary LLE of the water + ethanol + DIPE + n-heptane system were measured at 298.15 K in this work. The experimental quaternary liquid-liquid equilibrium data were successfully correlated by using both models including binary, ternary and quaternary parameters. The quaternary liquid-liquid equilibrium results calculated by the modified UNIQUAC model are more suitable agreement with the experimental results.

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水、乙醇、二异丙醚、正庚烷四元体系液液相平衡的研究
陈瑶^1,2 董艳辉^1,2, 张胜利^1,2
（¹ 暨南大学化学系；² 暨南大学纳米化学研究所，广州，510632）
摘要 测定了水、乙醇、二异丙醚和正庚烷四元体系以及相关的三元体系水、乙醇和正庚烷在298.15K和常压下的液液相平衡数据，含有二元、三元和四元参数的modified UNIQUAC 和 extended UNIQUAC 热力学模型成功地关联了这些实验数据。
关键词 液液平衡，含氧化合物，三元和四元混合物，Modified和extended UNIQUAC 热力学模型

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