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72 Y. Xie et al. / Applied Energy 175 (2016) 69–81 Fig. 2. Heat capacity of [hmim][Tf2N] and [bmim][PF6] from different sources. Table 3 Equations and parameters for temperature-dependent property. Property Density Viscosity Surface tension Heat capacity Equation (1) q 1⁄4 C1 þ C2T (2) ln g 1⁄4 C1 þ C2=T þ C3 ln T (3) r1⁄4 C1ð1T=TcÞðC2þC3T=TcÞ (4) Cp 1⁄4 C1 þ C2T þ C3T2 Unit q/kg m3, T/K g/Pa s, T/K r/N m1, T/K Cp/J mol1 K1, T/K IL [hmim][Tf2N] [bmim][Tf2N] [bmim][PF6] [hmim][Tf2N] [bmim][Tf2N] [bmim][PF6] [hmim][Tf2N] [bmim][Tf2N] [bmim][PF6] [hmim][Tf2N] [bmim][Tf2N] [bmim][PF6] Parameters C1 C2 1636.5 0.8915 1718.3 0.9456 1614.0 0.8306 223.1 13542.1 57.55 5330.4 304.4 18135.4 0.0131 8.617 0.0127 8.639 0.0111 6.073 472.1 0.3581 499.1 0.0549 464.0 4.780 C3 – – – 30.71 6.433 42.51 22.69 21.53 8.531 0.00060 0.00093 0.0063 The critical temperatures (Tc) and pressures (Pc) of CO2 and CH4 are (304.2 K, 73.8 bar) and (190.6 K, 46.1 bar), respectively. The non-random two-liquid (NRTL) model was used to calculate the activity coefficient of gas in the liquid phase. In this work, firstly, h1 and h2 were extrapolated from the measured gas solubility data with the method described in the Ref. [68]. Secondly, t1 and t2 were fitted by setting the binary inter- action parameters of NRTL to be zero basing on the experimental data of gas solubility at low pressures. Thirdly, the NRTL parame- ters were further fitted with the fixed t and t basing on the 12 experimental data of gas solubility in the whole investigated pres- sure range. The available experimental data of CO2 solubility in [hmim] [Tf2N], [bmim][Tf2N] and [bmim][PF6] has been evaluated in our previous work [15], and the model parameters (h1, h2, t1, t2, mij, mji, nij and nji) for CO2–IL system were obtained basing on the con- sistent experimental data. For CH4, the experimental solubility data in [hmim][Tf2N], [bmim][Tf2N] and [bmim][PF6] at different temperatures and pressures was only measured in three literatures [68–70]. Therefore, all the available experimental data of CH4 sol- ubility was used without evaluation. The method used for param- eter fitting is the same as that for CO2. The fitting results for CO2–IL and CH4–IL systems are listed in Tables 4 and 5. The comparisons of experimental and modeling results are illustrated in Figs. 5–7. In general, the modeling results agree well with the experimental data. For [hmim][Tf2N], the calculated CO2 solubility at the pressures higher than 20 bar is slightly higher than the experimental data. For [bmim][PF6], the experimental CH4 solubility at 333 K is irregular, and the modeling results show dif- ferences from the experimental data at 333 K. As no other experi- mental data is available, further verification of either modeling results or experimental data is impossible. For gas mixture, the interaction of CO2 and CH4 in the vapor phase was neglected, while the binary interaction parameters j1⁄41 lnci 1⁄4 Pm þ j1⁄41 j ij Pm r1⁄41 r rj rj sij Pm PmsjiGjixjXm xGPmxsG l1⁄41 Gli xl Gij 1⁄4 expðcijsijÞ; l1⁄41 Glj xl Gji 1⁄4 expðcjisjiÞ; cij 1⁄4 cji ð8Þ cij was assumed to be 0.2 in this work, Gij, Gji, sij and sji are binary interaction parameters. sij and sji are temperature-dependent, i.e.: equations: HiðT;PÞ1⁄4HiðTÞexp Vi P : lnHiðTÞ1⁄4h1 þh2: T V1i 1⁄4v1þv2T sij 1⁄4mij þnij=T sji 1⁄4mji þnji=T ð9Þ The Henry’s constant was calculated by the following 1 RT ð10Þ ð11Þ ð12Þ where HiðT;PÞ is the Henry’s constant of gas at system temperature and pressure, HiðTÞ is the Henry’s constant of gas at zero pressure, V1i is the infinite dilution partial volume of gas in solvent, and h1, h2, t1 and t2 are the correlation parameters. l1⁄41 Glj xlPDF Image | CO2 Separation with Ionic Liquids
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