The CPA EoS was presented by Kontogeorgis et al
The CPA EoS was presented by Kontogeorgis et al., in 1996 . The proposed equation is composed of two parts (SRK EOS + association term) such that it can well predict the thermodynamic behavior of hydrogen bonding materials as a result of considering the association term. Yakoumis et al. (1997) examined the ability of CPA EoS for VLE calculation of alcohol/hydrocarbon systems in comparison with the SRK equation of state. Their results indicated that the CPA EoS yields far better predictions for these systems . Kontogeorgis et al. (2000) used the sCPA EoS for pikfyve inhibitor solutions and they achieved very satisfactory results .
In addition to hydrogen bonding effects, the association term of CPA might be used to consider the effect of ions in calculating the activity coefficient of ionic liquids in liquid phase. This speculation has previously been applied to model the ionic liquids phase behavior through PC-SAFT EoS. Kamil et al. (2012) performed thermodynamic modeling of ionic liquids with PC-SAFT. They considered the effects of ions in the association term and achieved to the good results . Therefore, given the similarity of association terms in SAFT and CPA equation of states, ionic liquids might be modeled with CPA EoS, such that the effect of ions might be considered in the association term of CPA EoS. With regards to this speculation, as already mentioned, H. Soltani Panah (2017) used the CPA EoS to model prediction of the solubility of CO2 and H2S across various ionic liquids .
In 2013, Lan Ma et al. coupled the CPA EoS with two-step hydrate formation theory for predicting hydrate formation equilibrium conditions of hydrogen-containing systems. Their system included H2, CH4, C2H4, C2H6, C3H8 and tetrahydrofuran (THF). They substituted the SRK term of CPA with Patel-Teja EoS. Their results indicated a good agreement between the predicted results and the experimental data . In addition, ZarNezhad et al. (2013) coupled the CPA and two-step hydrate formation theory for predicting the equilibrium P-T conditions of H2S and CO2 containing sour gas hydrate. They revealed that their model was quite reliable over a wide range of temperatures as well as H2S and CO2 concentrations. The overall average absolute deviation between the predicted and measured values was calculated as about 3.32%, which was significantly lower than that of the other thermodynamic models .
In this study, the ability of CPA EoS coupled with the Chen-Guo method is examined for predicting the equilibrium conditions of methane gas hydrate formation and dissociation in the presence of six imidazolium-based ionic liquids. To perform this, the CPA parameters for six imidazolium-base ionic liquids including 1-ethyl-3-methylimidazolium hydrogen sulfate ([EMIM][HSO4]), 1-ethyl-3-methylimidazolium ethylsulfate ([EMIM][EtSO4]), 1-butyl-3-methylimidazolium tetrafluoroborate ([BMIM][BF4]), 1-(2-hydroxyethyl)-3-methylimidazolium tetrafluoroborate ([OH-EMIM][BF4]), 1-butyl-3-methylimidazolium chloride [BMIM][Cl], and 1-butyl-3-methylimidazolium bromide [BMIM][Br] are obtained using liquid density data. Moreover, the binary interaction parameters are tuned for ionic liquid-water and methane–ionic liquid systems using binary-mixtures data. Then, the flash calculation is performed for ternary mixtures of ionic liquids-water-methane systems using CPA EoS. Finally, the methane hydrate formation equilibrium conditions are predicted in the presence of the mentioned ionic liquids and the results are then compared with the experimental data.
Thermodynamic model As mentioned previously, according to Chen-Guo model, the gas hydrate formation is divided into two steps. The first step involves a basic hydrate formation which contains basic and linked cavities. The basic hydrate is stoichiometric and is formed by a quasi-chemical reaction. In this step, the linked cavities (small cavities) remain empty and the gas molecules occupy the basic cavities, (large cavities) . In the second step, gas molecules are adsorbed in the linked cavities (small cavities), with this step being described by Langmuir adsorption theory.