Liquid-liquid equilibria for two ternary systems of (water+dimethoxymethane+diisopropyl ether or 2,2,4-trimethylpentane) at 298.15K

Chen Yao ^1,2 , Zhang Shengli ^1,2, Li Renqiang³
(¹ Department of Chemistry, Jinan University, Guangzhou 510632; ² Institute of Nanochemistry, Jinan University, Guangzhou 510632; ³Department of Biotechnology, Jinan University, Guangzhou 510632, China)

Abstract Liquid–liquid equilibrium tie line data were determined for two ternary systems of water + dimethoxymethane + diisopropyl ether or 2,2,4-trimethylpentane at 298.15 K and ambient pressure. The experimental liquid–liquid equilibrium results have been successfully correlated by a modified and an extended UNIQUAC models both with binary and ternary parameters.
Keywords Liquid–liquid equilibria, Octane boosters, Ternary mixtures, Modified and extended UNIQUAC models

1. INTRODUCTION
Recently several fuel oxygenates have been added to gasoline to enhance the octane number and reducing air pollution. So, these reformulated gasolines contain a large amount of octane boosters such as methyl tert-butyl ether (MTBE), diisopropyl ether (DIPE) and dimethoxymethane (DMM). 2,2,4-Trimethylpentane (TMP) is an essential component in gasoline. As a part of our research work on thermodynamic properties of octane boosters ^[1,2], this paper reports liquid–liquid equilibrium (LLE) measurements on two ternary systems water + DMM + DIPE or TPM at 298.15 K. The experimental LLE data were correlated by means of the modified UNIQUAC and extended UNIQUAC models ^[3,4] including both binary and ternary parameters. The binary parameters of miscible binary mixtures of constituents of the ternary systems were obtained from vapor–liquid equilibrium (VLE) data ^[5,6] and those of immiscible mixtures were obtained from mutual solubility data ^[7,8].

2. EXPERIMENTS
2.1 Materials
TMP was supplied by the Tianjin Damao Chemical Reagents Factory, with minimum mass fraction of 0.990. DIPE was provided by the Tianjin Kermel Chemical Reagents Development Center, with a mass fraction of 0.995 at the fewest. DMM was provided by the Shanghai Chemical Reagents Company, Inc., with minimum mass fraction of 0.995. 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 LLE measurements were carried out at 298.15 ± 0.01 K. About 70 cm³ of ternary mixtures were 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 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 less than 0.1% deviation. 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 + DMM + DIPE and water + DMM +TMP mixtures.

3. CALCULATION PROCEDURE AND RESULTS
3.1 Calculation procedure
We have used the modified UNIQUAC^[3] and extended UNIQUAC^[4] models with binary and ternary parameters for an accurate description of the experimental ternary LLE 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^[9]:
(2)
(3)
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^[10,11]. The liquid molar volume, , was obtained by a modified Rackett equation^[12]. 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^[13]. 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 LLE calculations were carried out using the Eqns.(4) and (5). The additional ternary parameter τ_ijk was obtained by fitting the model to the ternary experimental LLE data and the ternary parameterτ_ijk was determined from the ternary experimental LLE data using a simplex method^[14] by minimizing the objective function:
= (6)
where min means minimum values, i = 1 to 3 for ternary 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 extended UNIQUAC model with the only binary parameters predicts the ternary LLEs more successfully than the modified 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. Figures 1 and 2 give the comparison of the experimental and correlated liquid–liquid equilibrium results of two ternary systems of (water + DMM + DIPE or TMP) as show type 2 at T = 298.15 K. DMM can dissolve in TMP with any proportion. So addition of DMM will not bring separation in gasoline. Figures 1 and 2 show good agreement between the experimental values and those correlated using additional ternary parameters. Both models can describe accurately the ternary experimental LLE data by the correlation involving the additional ternary parameters.

Table 3 Calculated results of binary phase equilibrium data reduction

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

a Number of tie lines.
^b Modified UNIQUAC model
^c Extended UNIQUAC model.
^d Predicted results using only binary parameters.
^e Correlated results using binary and ternary parameters.
^f Root-mean-square deviation (mol%).

Figure 1 Experimental and calculated (liquid + liquid) equilibria of the ternary mixtures of (water + DMM + DIPE) at T = 298.15 K. ●- - -●, Experimental tie line; ——, correlated by the extended UNIQUAC model with binary and ternary parameters taken from Table 4.

Figure 2 Experimental and calculated (liquid + liquid) equilibria of the ternary mixtures of (water + DMM + TMP) at T = 298.15 K. ●- - -●, Experimental tie line; ——, correlated by the extended UNIQUAC model with binary and ternary parameters taken from Table 4.

4. CONCLUSION
The ternary liquid–liquid equilibrium of the water + DMM + DIPE and water + DMM + TMP systems were measured at 298.15 K in this work. The experimental ternary liquid–liquid equilibrium data were successfully correlated by using both models including binary and ternary parameters. The ternary liquid–liquid equilibrium results calculated by the extended UNIQUAC model are more suitable agreement with the experimental results.

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三元体系(水 + 二甲氧基甲烷 + 二异丙醚或异辛烷)液液相平衡的研究
陈瑶^1,2*, 张胜利^1,2，李任强³
（¹ 暨南大学化学系；² 暨南大学纳米化学研究所，³ 暨南大学生物工程系，广州 510632）
2007年3月12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 测定了两个三元体系水、二甲氧基甲烷、二异丙醚和水、二甲氧基甲烷、异辛烷在298.15K和常压下的液液相平衡数据，并用含有二元和三元参数的modified UNIQUAC 和 extended UNIQUAC 热力学模型关联了这些实验数据，两个模型的计算结果均和实验结果较吻合。
关键词 液液平衡，含氧化合物，三元混合物，Modified和extended UNIQUAC 热力学模型

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