In Lan Ma et al coupled the CPA EoS with

In 2013, Lan Ma et al. coupled the CPA EoS with two-step hydrate formation S63845 australia 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 [27]. 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 [28]. 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) [1]. In the second step, gas molecules are adsorbed in the linked cavities (small cavities), with this step being described by Langmuir adsorption theory. According to this theory, the chemical potential of the basic hydrate in the equilibrium condition can be calculated as: , and denote the chemical potentials of the basic hydrate, water and gas, respectively. Also, is the number of gas molecules per water molecules in the basic hydrate. After substituting the relations for each of the chemical potentials and to simplify the equations, the following equation is obtained [14]:Where, denotes the number of linked cavities per water molecules and . In Equation (2), for gas hydrate with structure I and for structure II. is the fraction of linked cavities occupied by guest molecules which can be calculated using Langmuir theory, Further, f is the gas fugacity and denotes the product of three functions representing the contribution of temperature, pressure and activity of water (a) as