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

Abstract

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.

Microscale Processes and Dynamics during CH4–CO2 Guest-Molecule Exchange in Gas Hydrates

“…Results from molecular dynamics simulations indicate a higher mobility of the guest molecules. Geng et al [68] reported diffusion coefficients in the range of 10 −10 to 10 −13 m 2 /s at 270 K and 10 −9 m 2 /s at 280 K, and Kondori et al [69] derived diffusion coefficients in the range of 10 −10 to 10 −12 m 2 /s at temperatures from 270 to 280 K. Graue et al [36] fitted isothermal phase-field simulations to guest-exchange data from magnetic resonance imaging experiments, and reported a diffusivity coefficient of 1.7 × 10 −9 m 2 /s The most sophisticated experimental data so far has been published by Salamantin et al [29]. The authors extrapolated guest-molecule diffusion coefficients from ice/gas-hydrate conversion experiments to their experimental conditions of T = 277 K and p = 3.8 MPa, and derived at D CH4 = 2.8 × 10 −14 m 2 /s and D CO2 = 8.1 × 10 −14 m 2 /s.…”

“…These steps can include, for example, lattice reorientations, lattice destruction, and reformation or defect hopping. Proposed mechanisms include a complete dissociation and reformation of the crystal lattice [26], the formation of a secondary CO 2 hydrate layer on top of the primary CH 4 hydrate grain with subsequent breaking and reformation of the underlying lattice structure [27], the dissolution and replacement of the outermost gas-hydrate shell of the primary grain with subsequent diffusion into a mostly intact crystal lattice [28], or the migration of guest molecules through holes in the cage walls after the outermost shell of the gas-hydrate grain had been dissolved and replaced by an amorphous CO 2 hydrate [29]. These mechanisms have mostly been derived from computer simulations.…”

Mathematical Model of Carbon Dioxide Injection into a Porous Reservoir Saturated with Methane and Its Gas Hydrate

“…The results of studies [25][26][27][28] successfully describe the features of the process kinetics but do not take into account the effect of heat and mass transfer in extended natural reservoirs. In addition, in [25][26][27][28] and other similar experimental studies, the results of studies of the replacement process in samples containing only the gas hydrate phase are described. However, a study of this process in porous media is also of great interest, since the high specific contact surfaces of gas, liquid and hydrate are realized in such media, which are necessary for the intensification of the replacement process.…”

Diffusion of gas mixtures in the sI hydrate structure

“…The exchange process can be divided into two parts 2,13,14 . The first part is the initial exchange at the surface of the hydrate, which occurs by a partial dissolution of the methane hydrate into the replacement fluid followed by an immediate enclathration of the surrounding fluid.…”