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132 The Open Thermodynamics Journal, 2010, Volume 4 Ding-Yu Peng Table 1. Critical Constants and the Size Parameters Calculated by Means of Equation (24) Substance T c/K P c/kPa b/(cm 3 /mol) n-Pentane 469.70 3369.02 90.175 n-Hexane 507.30 3012.36 108.92 n-Heptane 540.10 2735.75 127.69 n-Octane 568.76 2486.49 147.95 Cyclohexane 553.64 4075.00 87.875 Methylcyclohexane 572.12 3471.00 106.61 Benzene 562.16 4898.00 74.235 Toluene 591.80 4106.00 93.223 Water 647.29 22089.75 18.953 Methanol 512.58 8095.79 40.952 Chloroform 536.55 5472.00 63.421 Tetrahydrofuran 540.10 5190.00 67.309 Table 2. Correlation of Vapor-Liquid Equilibrium Data Measured under Isobaric Conditions Component 1 Component 2 P/kPa NP 10 2 12 T / °C y Reference n-Hexane Benzene 101.33 24 0.4909 0.20 0.0045 [18] n-Hexane Benzene 101.33 12 0.4732 0.11 0.0076 [19] n-Heptane Benzene 24.0 9 0.6038 0.16 0.0043 [20] n-Heptane Benzene 53.33 9 0.4962 0.11 0.0015 [20] Cyclohexane Benzene 101.19 20 0.4534 0.10 0.0057 [21] Cyclohexane Benzene 101.33 20 0.4166 0.06 0.0020 [22] Cyclohexane Benzene 101.33 30 0.4283 0.07 0.0188 [18] Cyclohexane n-Hexane 101.33 16 0.0265 0.07 0.0056 [18] Cyclohexane n-Heptane 101.33 19 -0.0013 0.08 0.0071 [22] Cyclohexane n-Heptane 101.33 25 0.0294 0.07 0.0069 [23] Cyclohexane Toluene 101.33 20 0.2859 0.13 0.0071 [22] Cyclohexane Toluene 101.33 21 0.2973 0.10 0.0071 [24] Methylcyclohexane Benzene 101.33 23 0.2847 0.20 0.0094 [22] Methylcyclohexane n-Heptane 101.33 11 0.0059 0.04 0.0010 [22] Methylcyclohexane n-Heptane 101.33 12 0.0125 0.02 0.0020 [24] Benzene Toluene 101.33 12 -0.0174 0.05 0.0046 [19] n-Hexane Toluene 101.33 25 0.3158 0.41 0.0110 [22] n-Heptane Toluene 101.33 22 0.2346 0.23 0.0048 [22] n-Heptane Toluene 101.33 17 0.2623 0.04 0.0029 [25] noted that for a binary system, if necessary, the value of one of the size parameters can be arbitrarily set and the values of the other size parameter and the interaction parameter can then be determined by regression on the VLE data. This is so because the three parameters in the reformulated van Laar equation for a binary system are related to the coefficients in the Carlson and Colburn [13] forms by the following simultaneous equations: b 1 b 2 = A B (25) b 1 12 = A (26) The reformulated van Laar model was tested by correlating the VLE data of a number of hydrocarbon systems. The optimal values of the binary interaction parameters for all the binary systems were determined by means of Barker’s method [17]. For each of the binary mixtures tested, the correlation of the VLE data was essentially a one-parameter regression process because the size parameters have already been calculated by means of Equation (24). The optimal interaction parameters determined from VLE data measured under isobaric conditions are presented in Table 2 whereas those determined from data measured under isothermal conditions are presented in Table 3. As shown in Figs. (2 to 19), the VLE values of the hydrocarbon systems as well as the
Extending the Van Laar Model to Multicomponent Systems The Open Thermodynamics Journal, 2010, Volume 4 133 Table 3. Correlation of Vapor-Liquid Equilibrium Data Measured under Isothermal Conditions Component 1 Component 2 t / °C NP 10 2 12 P /kPa y Reference n-Pentane Benzene -17.78 16 1.2286 0.05 0.0036 [26] n-Pentane Benzene 16 24 0.8490 0.54 0.0401 [26] n-Pentane Benzene 35 12 0.7572 0.29 0.0029 [27] n-Pentane Benzene 40 14 0.7010 0.31 0.0050 [27] n-Pentane Benzene 45 14 0.6533 0.40 0.0065 [27] n-Pentane Benzene 50 14 0.6141 0.84 0.0074 [27] n-Hexane Benzene 25 10 0.7079 0.01 0.0017 [28] n-Hexane Benzene 25 30 0.7066 0.02 0.0019 [29] n-Hexane Benzene 25 21 0.7077 0.01 0.0013 [29] n-Heptane Benzene 25 12 0.6081 0.01 0.0014 [28] n-Heptane Benzene 45 15 0.5326 0.10 0.0034 [30] n-Heptane Benzene 60 14 0.4508 0.06 0.0086 [31] n-Heptane Benzene 75 11 0.3795 0.38 0.0079 [32] n-Heptane Benzene 80 15 0.3811 0.09 0.0122 [31] n-Octane Benzene 55 27 0.3622 0.26 0.0061 [33] n-Octane Benzene 65 26 0.3311 0.39 0.0072 [33] n-Octane Benzene 75 13 0.2996 0.36 0.0109 [33] Cyclohexane Benzene 8 12 0.7513 0.00 0.0011 [34] Cyclohexane Benzene 14 12 0.7142 0.00 0.0006 [34] Cyclohexane Benzene 20 12 0.6791 0.00 0.0010 [34] Cyclohexane Benzene 25 11 0.6009 0.01 0.0021 [35] Cyclohexane Benzene 40 7 0.5765 0.02 0.0039 [36] Cyclohexane Benzene 40 7 0.5705 0.03 0.0040 [37] Cyclohexane Benzene 40 6 0.5809 0.08 0.0037 [38] Cyclohexane Benzene 70 7 0.4618 0.05 0.0032 [36] Cyclohexane n-Hexane 25 29 0.1221 0.03 0.0026 [39] Cyclohexane n-Heptane 25 11 0.1002 0.06 0.0018 [40] Cyclohexane Toluene 25 11 0.5304 0.11 0.0056 [40] Methylcyclohexane Benzene 40 18 0.5220 0.02 0.0018 [41] Methylcyclohexane Benzene 75 29 0.4208 0.42 0.0082 [42] Methylcyclohexane Toluene 40 18 0.3641 0.01 0.0006 [41] Methylcyclohexane Toluene 75 27 0.2903 0.05 0.0017 [42] Methylcyclohexane Ethylbenzene 40 17 0.2800 0.02 0.0011 [41] n-Hexane Toluene 70 9 0.2966 2.68 0.0192 [43] n-Heptane Toluene 25 11 0.4150 0.13 0.0032 [40] Chloroform Tetrahydrofuran 30 19 -2.4610 0.10 0.0029 [44, 45] Methanol Water 24.99 13 1.9906 0.13 0.0150 [46] Methanol Water 35 12 2.2029 0.35 0.0257 [47] Methanol Water 39.9 10 2.3674 0.19 0.0069 [48] Methanol Water 50 10 2.1812 0.47 0.0178 [47] Methanol Water 50 14 2.4223 0.17 0.0150 [49] Methanol Water 55 20 2.3820 0.31 0.0120 [49] Methanol Water 60 18 2.3433 0.47 0.0070 [49] Methanol Water 65 10 2.2793 0.73 0.0132 [47]
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