Modeling the processes of joint filtration in melted zone and piezocunductive medium with gas hydrate inclusions

In the paper the thermodynamically equilibrium joint discrete model of a two-component (H$_2$O, CH$_4$) three-phase (water, methane, hydrate) filtration fluid dynamics and two-phase processes in a melted zone with absence of gas hydrates is considered, for which the splitting by physical processes is performed. The aim of the study is to construct a joint family of two-layer fully conservative difference schemes of the support operators method with space-time temporal scales in accordance with the proposed algorithm for splitting the equilibrium model in terms of physical processes, both in the melted zone and in the gas hydrate inclusions medium. The direct unsplit utilization of the studying system for the purposes of determining the dynamics of variables and constructing the implicit difference scheme required for calculations of filtering processes with large steps in time is difficult.