CO₂–CH₄ Exchange Process in Structure I Clathrate Hydrates: Calculations of the Thermodynamic Functions Using a Flexible 2D Lattice-Gas Model and Monte Carlo Simulations

Abstract

A two-dimensional lattice-gas model, supplemented by Monte Carlo simulations in the grand canonical ensemble, is applied to study the CO 2 /CH 4 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 CH 4 by CO 2 . 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 CO 2 has an occupation of more than 80% of the cavities, and therefore displaces the CH 4 species. Only 13 to 15% of CH 4 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 CH 4 by CO 2 in sI clathrate hydrates.

Cluster approximation applied to multisite-occupancy adsorption: configurational entropy of the adsorbed phase for dimers and trimers on triangular lattices

“…In three recent papers from our group [56][57][58] we introduced a new 2D lattice-gas model to study the behavior of sI clathrate hydrates for different guest species such as CH 4 and CO 2 . The model was built by mapping the three-dimensional (3D) sI structure to a 2D lattice-gas model with triangular geometry (and periodic boundary conditions).…”

“…There are several motivations to study a lattice-gas of trimers adsorbed on a triangular substrate: (1) the trimer is the simplest case of a polyatomic adsorbate allowing for different adsorption states on a triangular lattice; (2) the obtained results can be compared with previous analytical and computational findings available in the literature; and (3) as discussed below, several experimental systems can be modeled using trimers of different shapes. [54][55][56][57][58] A triangular (2D parallelepiped) cluster composed by m = l 1 Â l 2 sites is used to obtain the grand canonical partition function of the system. The dependence on surface coverage of the chemical potential and the configurational entropy of the adsorbed phase are obtained for the five studied systems.…”

“…In three recent papers from our group, [56][57][58] a triangular lattice model was developed for the study of the stability and distortion of sI structure in methane, carbon dioxide and ehtylene clathrate hydrates. Based on calculations of the degree of deformation of the lattice and the free energy per site of the adsorbed phase, the stability of the sI structure was investigated.…”

Virtual Issue on Carbon Dioxide: Physical Chemistry That Impacts Its Capture, Sequestration, and Conversion

“…Methane is the second most abundant greenhouse gas after carbon dioxide and is the major component of natural gas. 22 They found that, in sI hydrates, CO 2 tends to displace CH 4 regardless of temperature, and this is an entropic not enthalpic effect. Finally, Paesani and co-workers used highly accurate first-principles calculations to develop many-body potential energy functions for neat methane and methane/water systems.…”

“…Longone at al. extended their two-dimensional lattice gas model to account for mixture adsorption, thus enabling the study of CO 2 for CH 4 exchange in clathrate hydrates . They found that, in sI hydrates, CO 2 tends to displace CH 4 regardless of temperature, and this is an entropic not enthalpic effect.…”