Construction of an Analytical Solution of the Problem on the Formation of Gas Hydrate in a Porous Mine

In this paper, we propose the mathematical formulation of the problem on injection of a cold gas into a porous medium accompanied by the formation of gas hydrate. The mathematical formulation of the problem is an initial-boundary-value problem for a system of nonlinear partial differential equations expressing the laws of conservation of mass and energy supplemented by the conditions of mass and heat balance on the moving boundary of phase transitions. Within the framework of the rectilinear parallel approximation, we construct approximate analytical solutions with a temperature jump at the boundary where the gas hydrate appears. These solutions describe the relationship between the coordinate of the boundary of phase transition and the parameters of the injected gas and the porous medium.