Mathematical model of the formation of a gas hydrate on the injection of gas into a stratum partially saturated with ice

The injection of a cold gas into a porous medium saturated with gas and ice that is accompanied by the formation of a gas hydrate is studied theoretically. Self-similar solutions describing the distribution of the basic parameters in the stratum are constructed for an axisymmetric problem with an extended region of phase transitions. The possible existence of four different types of solutions is indicated according to which, when cold gas is injected, it is possible that either a hydrate is formed from gas and ice on the front surface or there is hydrate formation from gas and ice in one extended region or hydrate formation both from gas and ice and gas and water in two extended regions or ice melts on the front surface and a hydrate is subsequently formed from gas and water on another front surface. Critical diagrams are constructed that distinguish the regions of existence of the different types of solutions.