The method of numerical simulation based on the splitting by physical processes of gas-hydrodynamic processes, which occur during the dissociation of gas hydrates in a porous medium, is described. In this paper, a coupled 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 thawed zone with absence of gas hydrates in thermodynamic equilibrium has been developed, by using the splitting by physical processes as a valid assumption. The obtained split model is differentially equivalent to the discrete initial balance equations of the system (conservation of the mass components of the fluids and the total energy of the system), written in divergent form. Such an approach to create completely conservative difference schemes in the studied fluid-hydrate medium requires the introduction of a special free-volume nonlinear approximation of grid functions over time, which depends on the volume fraction in the pores occupied by fluids, and is simple to implement. The direct unsplit use of the studied system for the purposes of determining the dynamics of variables and constructing the implicit difference scheme required for calculations of filtering processes with large time steps is difficult. The paper also presents the method of coupled solutions of systems of equations describing the processes in various fields, each of which is characterized by its own set of coexisting phases, and the coordination of computational schemes for them is not an automatic process. In the results of the calculations, the volumetric three-phase phase transitions were numerically investigated using a single calculation with a variable number of phases region of the entire plane of the P and T parameters. Using the example of the Messoyakha's gas hydrate deposit, the local processes of technogenic depressive impact directly near the wells on the dynamics of the gas distribution of gas hydrates thawing and formation of thawed two-phase zones were studied.