On one method of numerical modeling of piezoconductive processes of a two-phase fluid system in a fractured-porous reservoir

A method of numerical modeling based on splitting by physical processes of two-phase fluid transfer in a formation with fractured-porous reservoirs is described. Reservoirs of this type have a natural fracture system and are described by the dual porosity model. A four-block mathematical model of the fluid redistribution between a pore-type matrix and a natural fracturing pattern is proposed and studied. The resulting system is complex and entails a number of difficulties associated with a large number of variables and the absence of important properties of a linearized system of equations, such as self-adjointness and symmetry, which are present in the description of piezoconductive processes. The complete splitting by physical processes is carried out to solve this problem. The resulting 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. This approach is associated with a nonlinear approximation of the grid functions in time, which depends on the fraction of the volume occupied by the fluids in the pores, and is easy to implement.