Quaternary liquid-liquid equilibria for (water + 2-propanol + methyl tert-butyl ether + toluene) at 298.15 K

1. INTRODUCTION
Reformulated gasoline includes certain oxygenated compounds such as alcohols and ethers. These are commonly methanol, ethanol, propanols, and butanols as well as methyl tert-butyl ether (MTBE), ethyl tert-butyl ether (ETBE), and tert-amyl methyl ether (TAME). These oxygenated compounds are added to improve the octane rating and pollution-reducing capability of gasoline. MTBE is the primary oxygenated compound currently used in reformulated gasoline because of its low Reid vapor pressure (RVP) and the availability of the feedstock ethanol from renewable resources. In this sense, there has been an increasing interest in the thermodynamic behavior of liquid mixtures of MTBE with gasoline-substitution hydrocarbons. The multicomponent phase equilibria of the oxygenate ether and alcohol mixtures with water are useful and considerably focused not only on the process design for reformulated gasoline production but also on the problem of contamination of groundwater. Here we report liquid–liquid equilibrium (LLE) measurements on one quaternary system water + 2-propanol + MTBE + toluene 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 + 2-propanol + toluene ^[3], water + 2-propanol + MTBE, water + MTBE + toluene ^[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 [9,10].

2. EXPERIMENTS
2.1 Materials
MTBE was purchased from Tedia Company, Inc. with nominal minimum mass fraction of 99.8%. Toluene was supplied by the Guangzhou Chemical Reagent Factory with minimum mass fraction of 99.5%. 2-propanol was obtained from the Tianjin Chemical Reagent Institute with nominal minimum mass fractions 99.7%. All chemicals were used without further purification. GC analysis did not detect appreciable peaks. Water was distilled twice.
2.2 Apparatus and Procedures
Quaternary LLE measurements were carried out at (298.15±0.01)K. The experimental apparatus and procedure were described previously ^[11]. About 70 mL of each quaternary mixture was stirred by a magnetic stirrer for 3 hours and allowed to settle for 3 hours, which was sufficient for separation into two phases. The samples withdrawn from upper and lower phases were analyzed by a gas chromatography (Shanghai Analytical Apparatus Factory, GC-122). The accuracy of the measurements was estimated within ±0.001 in mole fraction.
2.3 Experimental results
Table 1 shows experimental LLE data for the water + 2-propanol + MTBE + toluene 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^[12]:
                  (2)
                 (3)
    where P, x, y, and g 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^[13,14]. The liquid molar volume, , was obtained by a modified Rackett equation^[15]. 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^[16]. The binary energy parameters for the partially miscible mixtures were obtained by solving the following thermodynamic equations simultaneously.

(4)
and ( I, II = two liquid phases )              (5)
    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^[17] 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).

Table 2 Calculated results of binary phase equilibrium data reduction

Table 3 Calculated results for ternary liquid-liquid equilibrium at 298.15 K

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

4. CONCLUSION
The quaternary LLE of the water + 2-propanol + MTBE + toluene 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 in better agreement with experimental results.

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水、 异丙醇、 甲基叔丁基醚、甲苯四元体系液液相平衡的研究
董艳辉 陈瑶
(暨南大学化学系 广东 广州 510632)
2005年8月8日收稿。国家教育部留学回国人员科研基金（No.2002247）, 广州暨南大学科研基金(No.640071) 和广东省科技计划基金(No.2003C33101)。
摘要 测定了水、异丙醇、甲基叔丁基醚和甲苯四元体系在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，四元混合物，Modified和extended UNIQUAC 热力学模型