Measurement and correlation of liquid-liquid equilibria for quaternary system of water + 2-propanol + dimethyl carbonate + octane

Chen Yao, Liu Xueen, Xiong Zihao
(Department of Chemistry, Jinan University, Guangzhou, 510632)

Abstract Experimental tie-line compositions for one quaternary system of water + 2-propanol + dimethyl carbonate + octane and one relevant ternary system of water + dimethyl carbonate + octane were measured at temperature of 298.15 K and ambient pressure. The experimental liquid-liquid equilibria results were correlated by using a modified UNIQUAC model with ternary and quaternary interaction parameters in addition to binary ones.

  1. INTRODUCTION
    Dimethyl carbonate (DMC) may be an ideal gasoline additive to replace 1,1-dimethylethyl methyl ether (MTBE) because of its excellent characteristics as a gasoline additive: high octane, low RVP, reduced CO and NOx emissions, and a very high density [1,2]. DMC has about 3 times the oxygen content of MTBE. It has both low toxicity and relatively quick biodegradability, and can be considered to be an option for meeting the oxygenate specification on gasoline and as a means of converting natural gas to a liquid transportation fuel [3]. To understand the mutual solubility of DMC with hydrocarbon in gasoline and assess the effect of DMC addition on hydrocarbon-water mutual solubility, we measured liquid-liquid equilibrium (LLE) data for quaternary mixtures of water + 2-propanol + DMC + octane, and relevant ternary mixtures of water + DMC + octane at 298.15 K. The experimental results were correlated by means of the modified UNIQUAC model [4] including ternary and quaternary parameters, in addition to binary parameters. The binary vapor-liquid equilibria (VLE), mutual solubility and ternary LLE relevant to the quaternaries have been available from the literatures: (2-propanol + octane) [5], (2-propanol + DMC) [6], (2-propanol+ water) [7], (DMC +octane) [8], (Octane +water) [9], (DMC +water) [10], (water +2-propanol + octane) [11], (water +2-propanol + DMC) [12], and (water + DMC + octane) measured in this work.
  2. EXPERIMENTS
    2.1 Materials
    2-Propanol was provided by Tianjin Chemical Reagent Factory with nominal minimum mass fraction of 0.997. Octane was supplied by the Guangzhou Chemical Reagent Factory with nominal minimum mass fractions of 0.997. The DMC was obtained from Tianjin Guangfu Chemical Reagents Factory with nominal minimum mass fraction of 0.992. The gas chromatograghy analysis gave mass fractions of 0.991 for DMC, 0.997 for 2-propanol and 0.998 for octane. Water was distilled twice and had a mass fraction of 0.999. All chemicals were used directly in this work.
    2.2 Apparatus and Procedures
    Ternary and quaternary LLE measurements were carried out at the temperature (298.15 ¡À 0.01) K. The experimental apparatus and procedures were described in detail previously [13]. The quaternary mixtures whose volume is about 80 cm3 were loaded in the equilibrium glass cell placed in a thermostated water bath, stirred for 3 h, and then left to equilibrate for 3 h. The liquid samples about 5 cm3, withdrawn from both upper and lower phases in the cell by using a milliliter syringe without changing the phase equilibria between two layers, were analyzed by a gas chromatograph (Shimadzu, GC-14C) equipped with a thermal conductivity detector. The accuracy of the experimental measurements was estimated to be within ¡À0.001.
    The quaternary mixtures were prepared by mixing binary mixtures of DMC + octane whose compositions are M1, M2, and M3 with water then 2-propanol stepwise to cover the two-phase region shown in Figure 1. The values of M1, M2, and M3 are approximate 0.25, 0.50, and 0.75, respectively, indicating the mole fraction of DMC in the binary mixtures of DMC + octane. Figure 1 shows schematically a tetrahedron to depict three planes of the quaternary mixtures of water + 2-propanol + DMC + octane. Experimental LLE data for the ternary mixtures of water + DMC + octane and quaternary mixtures of water + 2-propanol + DMC + octane are list in Tables 1 and 2.

    Table 1 Equilibrium phase compositions in mole fraction (x) for the ternary mixtures of water + DMC + octane at 298.15 K

organic phase aqueous phase
x1 x2 1 ¨C x1 ¨C x2 x1 x2 1 ¨C x1 ¨C x2
0.0319 0.1181 0.8500 0.9920 0.0080 0.0000
0.0393 0.3586 0.6021 0.9550 0.0450 0.0000
0.0468 0.4836 0.4696 0.9391 0.0609 0.0000
0.0549 0.5505 0.3946 0.9362 0.0638 0.0000
0.0637 0.5627 0.3736 0.9576 0.0424 0.0000
0.0730 0.6108 0.3162 0.9585 0.0415 0.0000
0.0821 0.6609 0.2570 0.9688 0.0312 0.0000
0.0896 0.7540 0.1564 0.9505 0.0495 0.0000
0.0931 0.8086 0.0983 0.9675 0.0325 0.0000

Table 2 Equilibrium phase compositions in mole fraction x for the quaternary mixtures of water + 2-propanol + DMC + octane at 298.15 K

organic phase aqueous phase
x1 x2 x3 x1 x2 x3
{ x1water + x22-propanol + x3DMC + (1-x1–x2-x3) octane }
M1= 0.25
0.0000 0.0082 0.1240 0.8988 0.0582 0.0398
0.0000 0.0196 0.1108 0.8623 0.0962 0.0388
0.0000 0.0188 0.1040 0.8576 0.0993 0.0409
0.0000 0.0593 0.0858 0.8201 0.1288 0.0466
0.0000 0.0726 0.0696 0.8090 0.1426 0.0441
0.0000 0.0854 0.0572 0.7913 0.1543 0.0497
0.0230 0.0976 0.0575 0.7717 0.1755 0.0468
0.0281 0.1060 0.0520 0.7491 0.1938 0.0489
0.0213 0.1184 0.0404 0.7289 0.2050 0.0581
0.0228 0.1308 0.0330 0.6797 0.2414 0.0671
M2= 0.50
0.0009 0.0412 0.2675 0.8629 0.0836 0.0515
0.0009 0.0594 0.2107 0.8725 0.0829 0.0431
0.0139 0.0678 0.1527 0.8241 0.1167 0.0580
0.0195 0.0773 0.1007 0.7659 0.1795 0.0513
0.0196 0.0770 0.0877 0.6922 0.2544 0.0497
0.0196 0.0886 0.0700 0.7286 0.2306 0.0379
0.0101 0.1149 0.0773 0.7057 0.2257 0.0641
0.0194 0.1170 0.0650 0.6743 0.2530 0.0665
0.0169 0.1365 0.0584 0.6613 0.2720 0.0581
0.0250 0.1469 0.0509 0.6128 0.3034 0.0707
0.0352 0.1607 0.0900 0.5108 0.3390 0.1204
M3= 0.75
0.0392 0.0653 0.5794 0.8813 0.0570 0.0594
0.0437 0.1072 0.5946 0.8561 0.0798 0.0626
0.0411 0.1168 0.5150 0.8473 0.0836 0.0664
0.0142 0.0741 0.2950 0.7766 0.1118 0.1056
0.0102 0.0757 0.2052 0.7455 0.1423 0.1082
0.0131 0.0854 0.1914 0.7294 0.1562 0.1101
0.0116 0.0852 0.1692 0.7242 0.1630 0.1074
0.0117 0.0997 0.1596 0.6935 0.1899 0.1098
  1. CALCULATION PROCEDURE AND RESULTS
    3.1 Calculation procedure
    The modified UNIQUAC [4] model was used to correlate the experimental LLE data. The binary energy parameters,, for the completely miscible mixtures were obtained from the binary VLE data by using a computer program described by Prausnitz et al [14]. The binary energy parameters for the partially miscible mixtures were obtained by solving the following thermodynamic equations simultaneously.

and ( I, II = two liquid phases ) (2)

Ternary parameters t231, t312, and t123 and quaternary parameters t2341, t1342, t1243 and t1234 were determined from the experimental LLE data using a simplex method [15] by minimizing the objective function:

F= (3)

where min denotes minimum values, i = 1 to 3 for ternary mixtures or i = 1 to 4 for quaternary mixtures, j = 1, 2 (phases), k = 1, 2, …£¬M (number of tie lines), M = 2ni, and x is the liquid-phase mole fraction.

3.2 Calculation results
Table 3 presents the binary energy parameters of the modified UNIQUAC model for the constituent binary mixtures, along with the root mean square deviations between experimental and calculated values: dP for pressure, dT for temperature, dx for liquid-phase mole fraction, and dy for vapor-phase mole fraction. Table 4 shows the ternary parameters obtained in fitting the modified UNIQUAC model to the experimental ternary LLE data, and root-mean-square deviation of the mole fraction of tie lines between the experimental and calculated results. Figure 2 compares the experimental and correlated LLE of the ternary mixtures making up the quaternary mixtures of water + 2-propanol + DMC + octane at 298.15 K. The quaternary system exhibits type 2 quaternary LLE behavior, which is composed of two ternary LLE for the water + 2-propanol + DMC and water + 2-propanol + octane are classified as type 1, and one ternary LLE for the water + DMC + octane as type 2, are illustrated in Figure 2. Table 5 summarizes the correlated results for the quaternary mixtures obtained in fitting the modified UNIQUAC model with binary, ternary, and quaternary parameters to the experimental quaternary LLE data, together with the predicted results by the model with the binary and ternary parameters listed in Tables 3 and 4. The root-mean-square deviation between the experimental results and correlate results is 2.30 %. It seems that the modified UNIQUAC model is able to correlate the quaternary LLE successfully, and the model can give an accurate representation for the quaternary LLE by including the ternary and quaternary parameters in addition to the binary ones.

Table 3 The calculated results of fitting the model to the binary phase equilibria data

System(1+2) T/K a12/K a21/K dP/ kPa dT/K 103dx 103dy
2-propanol + octane 348.15 94.46 880.92 0.3 0.1 1.2 6.6
2-propanol + DMC 355.05¨C361.68 230.75 66.87 0.1 0.1 1.0 8.8
2-propanol + water 303.15 330.21 ¨C44.88 0.2 0.0 1.3 8.0
DMC + octane 361.73¨C395.56 64.24 279.30 0.2 0.1 1.2 6.8
Octane + water 298.15 3091.80 1305.90 ¡¡ ¡¡ ¡¡ ¡¡
DMC + water 298.15 702.87 269.81 ¡¡ ¡¡ ¡¡ ¡¡

Table 4 The calculated results of fitting the model to the ternary LLE data at 298.15 K

System(1+2+3) Na Ternary parameters Deviationb
water + 2-propanol + octane 8 t231 = ¨C0.1043 t132 = 0.2232
t123= 0.3844		 5.80c 4.10d
water + 2-propanol + DMC 12 t231 = ¨C0.4030 t132 = ¨C0. 2227
t123 = 2.4593		 6.53 0.87
water + DMC + octane 9 t231 = 0.0331 t132 = 0.0117 t123 = 0.0060 1.96 1.94

a Number of tie-lines.
b Root-mean-square deviations (mol %).
c Predicted results using binary parameters alone.
d Correlated results using binary and ternary parameters.

Table 5 The calculated results of fitting the model to the quaternary LLE data at 298.15 K

System(1+2+3+4) Na Quaternary parameters Deviationb
water + 2-propanol + DMC + octane 29 ¦Ó2341 = ¨C1.0287
¦Ó1342 = 1.1297
¦Ó1243 = ¨C61.0614
¦Ó1234 = 42.8804		 4.34c 2.30d

a Number of tie-lines.
b Root-mean-square deviations (mol %).
c Predicted results using binary and ternary parameters.
d Correlated results using binary, ternary and quaternary parameters.

Figure 1 Phase equilibria of (water + 2-propanol + DMC + octane). M1, M2 and M3 denote quaternary section planes

Figure 2 Experimental and calculated LLE of three ternary mixtures making up (water + 2-propanol + DMC + octane) at 298.15 K. ¡ñ, experimental tie-line data; ¡ª¡ª, correlated curve by the modified UNIQUAC model.

  1. CONCLUSION
    The experimental tie-line data were measured for the ternary mixtures of water + DMC + octane and quaternary mixtures of water + 2-propanol + DMC + octane at 298.15 K and atmospheric pressure. The modified UNIQUAC model is able to represent successfully the experimental liquid-liquid equilibrium results. The correlated results of ternary and quaternary LLE show a better agreement with the experimental results.