Modeling the Piezoconductivity Process of a Two-Phase Fluid System in a Fractured-Porous Reservoir

Mass transfer in a carbonate reservoir of a fractured-porous type is considered. Such reservoirs have a natural system of destruction in the form of fractures and cavities. In this paper, a mathematical model of the fluid redistribution between a porous-type matrix and a network of natural fractures is proposed and studied. The resulting system of differential equations is quasi-linear and quite complex. A number of difficulties arise in its numerical solution. First, the system contains a large number of unknown functions. Second, the nature of the nonlinearity of the equations is such that the corresponding linearized system no longer has the property of the self-adjointness of the spatial differential operators. To solve this problem, the method of splitting by physical processes and the approximation of differential operators by the finite difference method are used. The resulting split mesh model is equivalent to the discrete original balance equations of the system (conservation of mass components of fluids and total energy of the system) written in the divergent form. This approach is based on a nonlinear approximation of mesh functions in time, which depends on the fraction of the volume occupied by fluids in the pores, and is simple to implement. This paper presents the results of numerical calculations and analyzes the space-time dynamics of pressure change processes.