CO₂-CH₄ Exchange Process in Structure I Clathrate Hydrates: Calculations of the Thermodynamic Functions Using a...

A two-dimensional lattice-gas model, supplemented by Monte Carlo simulations in the grand canonical ensemble, is applied to study the CO₂/CH₄ exchange process in sI clathrate hydrates. The coverage dependence of the Helmholtz free energy, chemical potential, entropy, and degree of deformation of the sI structure is given. Two different situations are considered according to the value of the intra- and inter-species' interactions. First, lateral interactions between the guest species and water molecules are introduced by following the well-known Lorentz-Berthelot mixing rules. Second, the study is restricted to an ideal clathrate hydrate, where the lateral interactions are neglected and entropy governs the exchange of CH₄ by CO₂. In the case of real clathrate hydrates (non-zero lateral interactions), the displacement phenomenon is clearly observed from the behavior of the chemical potential and Helmholtz free energy as functions of coverage. The guest species CO₂ has an occupation of more than 80% of the cavities, and therefore displaces the CH₄ species. Only 13 to 15% of CH₄ remains stagnant in the sI structure. With respect to the degree of deformation, a direct relationship between cell distortion and cell occupancy is observed. Finally, the detailed analysis carried out for the ideal clathrate hydrate allows us to interpret the physical mechanism underlying the exchange process: it is entropy, not energy, that drives the displacement of CH₄ by CO₂ in sI clathrate hydrates.