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The paper deals with some typical problems of gas hydrates dissociation in a porous medium, which in the first approximation can be reduced to one-dimensional. The research aims to study the mutual effects of underground gas hydrates and climate change, as well as some important technological and ecological problems of the flow in the well or fault area in the presence of hydrate-containing formations. New conservative difference schemes were developed for this class of problems. They are based on the splitting of gas-hydrodynamic processes. The advantage of these schemes is the phased solution of parabolic and hyperbolic equations. This approach greatly simplifies the solution procedure and at the same time increases its stability. Notably, within the framework of the approach, an algorithm was proposed to jointly solve the systems of equations describing the processes in various fields characterized by their own set of coexisting phases. The coordination of computational schemes for them is not a trivial and automatic process. Numerical calculations using mathematical modeling for the joint description of the gas hydrate zone and the zone with no gas hydrates were carried out. The results of calculations showed the applicability of the developed methods for solving the problems under study.

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The paper presents an algorithm for solving the problem of the process of mass transfer of a two-phase fluid in a fractured-porous reservoir in a one-dimensional formulation. The presence of natural fractures in such reservoirs impedes various types of exploration and field development. Fractured-porous reservoirs are characterized by intense exchange fluid flow between fractures and porous blocks. Each system has its own individual set of filtration-capacity parameters, and this fact complicates the problem under consideration. To study the mass transfer of a two-phase fluid in a medium with double porosity, a four-block mathematical model with splitting by physical processes is proposed. The model is described by a system of partial differential equations. The splitting method forms two functional blocks on the water saturation and the piezoconductivity. For the numerical solution of this system, an absolutely stable implicit finite-difference scheme is constructed in the one-dimensional case. On the basis of the proposed difference scheme, pressures and saturations in the fracture system and matrix are obtained.