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

Abstract

The thermodynamic properties of sI clathrate hydrates involving methane and carbon dioxide guest moleculeshave been investigated using Monte Carlo (MC) simulations in the grand canonical ensemble, and analyticalcluster approximation (CA) theory. The CA approach is founded on the precise calculation of states within finitecells. Both the sI hydrate structure and the guest species were represented using a two-dimensional triangularlattice-gas model with single- and multiple-site occupancy. The investigation entailed monitoring the latticecoverage’s dependence on the chemical potential (adsorption isotherm) and examining quantities like Helmholtzfree energy, energy of the adsorbed phase, configurational entropy, and adsorption heat. Three distinct scenarioswere considered, each dependent on the intra- and interspecies interactions. First, the study was restricted to anideal clathrate hydrate, wherein lateral interactions were disregarded, and the system’s properties are governedby entropy alone. Second, lateral interactions between the guest species and water molecules were introducedby employing the well-established Lorentz-Berthelot mixing rules. Lastly, repulsive lateral interactions weretaken into account. In all cases, a remarkable agreement between the results obtained through CA and MC wasobserved, underscoring the significant potential of CA theory as a valuable tool for exploring cavity occupancyand selectivity in the sI clathrate hydrate formation process.