Lattice-gas model of methane and carbon dioxide sI clathrate hydrates: A comprehensive study using analytical cluster approximation and Monte Carlo simulations

The thermodynamic properties of sI clathrate hydrates involving methane and carbon dioxide guest molecules have been investigated using Monte Carlo (MC) simulations in the grand canonical ensemble, and analytical cluster approximation (CA) theory. The CA approach is founded on the precise calculation of states within finite cells. Both the sI hydrate structure and the guest species were represented using a two-dimensional triangular lattice-gas model with single- and multiple-site occupancy. The investigation entailed monitoring the lattice coverage's dependence on the chemical potential (adsorption isotherm) and examining quantities like Helmholtz free energy, energy of the adsorbed phase, configurational entropy, and adsorption heat. Three distinct scenarios were considered, each dependent on the intra- and interspecies interactions. First, the study was restricted to an ideal clathrate hydrate, wherein lateral interactions were disregarded, and the system's properties are governed by entropy alone. Second, lateral interactions between the guest species and water molecules were introduced by employing the well-established Lorentz-Berthelot mixing rules. Lastly, repulsive lateral interactions were taken into account. In all cases, a remarkable agreement between the results obtained through CA and MC was observed, underscoring the significant potential of CA theory as a valuable tool for exploring cavity occupancy and selectivity in the sI clathrate hydrate formation process.