On quasistationary solution of the equation of gas diffusion in hydrate layer

In this paper, the problem of hydrate layer formation in a spherical particle whose core consists of the water (or ice) phase in a diffusion mode that involves the mobile gas diffusion in the bed of methane hydrate formed at the interface between gas and ice (or water) is solved. A quasistationary solution of the gas diffusion equation is obtained. The time of total water (or ice) transition in the hydrate state is determined. Distributions of diffusing gas concentration fields by coordinate passing through the hydrate layer, which arises on the gas–water (or ice) interface, are obtained. The growth dynamics of the hydrate layer in a spherical particle in relation to the saturation density of mobile gas is revealed. It is established that an increase in saturation density of the diffusing gas by four times leads to a decrease in dimensionless time of total water (or ice) transition in the hydrate state by three times. It is shown that in rather wide limits of the solubility of gas as a part of hydrate depending on the pressure, the numerical solution of the diffusion equation coincides well with its analytical solution.