The work considers the problem of gas hydrate dissociation in a porous medium under high-speed filtration conditions. A mathematical model of isotropic filtration using the two-term Forchheimer law is presented. The complete system of equations is splitted by physical processes into two blocks: convective transfer of saturation parameters (water, gas, and hydrate saturation) and the dissipative piezoconductivity equation taking into account heat and mass transfer. A numerical scheme based on the support operator method with a consistent approximation of the gradient and divergence is proposed to account for the flow between nodal domains of the grid, including nonlinear quadratic terms of the filtration law. The use of implicit schemes on irregular grids allows for the modeling of reservoirs with complex geometry and lithology. Calculations for various reservoir configurations are performed, and the results are consistent with the physics of the processes.

mathematical modeling, multiphase filtration, Forchheimer's law, support operator method, gas hydrates

Mathematical modelling in actual problems of science and technics