The problem of hydrate formation in the layer of snow at the injection of cold gas

Over the recent years, the technology of underground gas storage is one of the most pressing tasks. It is known that the world geological reserves contain large volumes of gas in the composition of natural hydrates, amounting to $2\cdot1016$ m$^3$. So, in natural conditions, for example, in underground deposits, it is possible to create gas hydrate repositories with gas conserved in them. Thus, gas in gas-hydrate storage facilities will take much less volume, since 1 m$^3$ of gas hydrate contains up to 180 m$^3$ of gas. In this regard, the study of the hydrate formation process in the so-called ice-cold reservoirs representing gas storage facilities located in permafrost is of great interest. The technology of underground gas conservation in the conditions of gas hydrate stability will ensure a high level of safety of gas storage and transportation without requiring large economic costs.
The paper presents a mathematical model of the methane hydrate formation process when a cold gas is injected into a snow layer in the initial state saturated with the same gas. Some limiting diffusion scheme of hydrate formation, is considered, according to which the intensity of hydrate formation is limited by the diffusion of gas through the hydrate crust formed between snow and gas upon their contact. The equilibrium regime is formally implemented in the case when the diffusion coefficient tends to infinity. The obtained system of equations with initial and boundary conditions is solved by finite difference method using explicit scheme.
As a result of the numerical study, the dynamics of pressure, temperature, hydration and snow saturation in cases of diffusion and equilibrium schemes have been obtained. It is shown that the initial values of snow saturation, pressure, gas permeability and reduced diffusion coefficient have a significant influence on the intensity of the process of complete hydrate formation. It was found that with the increase of the reduced diffusion coefficient, the process of hydrate formation taking into account diffusion kinetics tends to an equilibrium regime. It is established that a more intensive growth of hydration saturation is implemented in the equilibrium regime.