Diffusion Model for Gas Replacement in an Isostructural CH4–CO2 Hydrate System

Guest exchange in clathrates is a complex activated phenomenon of the guest–host cage interaction on the molecular-scale level. To model this process, we develop a mathematical description for the nonequilibrium binary permeation of guest molecules during gas replacement based on the microscopic “hole-in-cage-wall” diffusive mechanism. The transport of gas molecules is envisaged as a series of jumps between occupied and empty neighboring cages without any significant lattice restructuring in the bulk. The gas exchange itself is seen as two-stage swapping initiated by almost instantaneous formation of a mixed hydrate layer on the hydrate surface followed by a much slower permeation-controlled process. The model is constrained by and validated with available time-resolved neutron diffraction data of the isostructural CH4 guest replacement by CO2 in methane hydrate, a process of possible importance for the sequestration of CO2 with concomitant recovery of CH4 in marine gas hydrates.