Spatial filtration model of hydrate-containing media with a non-classical law of motion

The work provides a description of the spatial filtration problem in a three-phase hydrate equilibrium zone. A mathematical model is presented for studying two-dimensional fluid flows taking into account the solid hydrate phase and the irregular structure of formations. A non-classical form of the motion law is used, applicable at low permeability and low pressure drops. Efficient computational algorithms based on the support operator method are proposed that make it possible to separate the hyperbolic and dissipative subsystems of the problem. The algorithms are implemented on meshes of irregular structure to model the two-dimensional multiphase processes of gas hydrate dissociation. Testing is carried out on model piezoconductive processes with saturation transfer, where it is shown that depression processes are less expressed when using a nonlinear law of motion.