Model of filtration in a hydrate-containing medium in the presence of saturation transfer with a non-classical law of motion

The spatial filtration problem in a three-phase (gas, hydrate, water) hydrate-equilibrium zone is considered. A mathematical model is presented that makes it possible to study two-dimensional fluid flows in the presence of a solid hydrate phase in areas with an irregular strata structure. To determine the velocity of fluids, a non-classical form of the law of motion is used (taking into account its nonlinearity), which is applicable, including under conditions of reduced permeability with low pressure drops. Based on the support operator method, effective computational algorithms are proposed that distinguish the hyperbolic (in the presence of saturation transfer) and dissipative subsystems of the problem. These algorithms are implemented in software on the meshes of irregular structure, which makes it possible to model spatially two-dimensional multiphase and multicomponent processes of gas hydrate dissociation in the porous medium of sedimentary basins. The developed program was tested using model calculations of piezoconductive processes in the presence of saturation transfer. The calculations showed that within spatial regions, when using nonlinear laws of motion, depression processes are less pronounced than in the case of the classical Darcy law. In this case, the processes of hydrate thawing accompany the depression gas extraction specified in the computational domain. Thus, the mathematical model and corresponding computational algorithms presented in this work make it possible to correctly describe the physics of low-permeability reservoirs.