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

In this work, the authors propose an algorithm for solving the problem of the process of mass transfer of a two-phase fluid in a fractured-porous reservoir in a one-dimensional formulation. The presence of natural fractures in such reservoirs impedes various types of exploration during field development. Fractured porous reservoirs are characterized by intense exchange fluid flow between fractures and porous blocks. Each system under consideration has its own individual set of filtration-capacity parameters that complicates the problem. To study the mass transfer of a two-phase liquid in a medium with double porosity, a four-block mathematical model with splitting by physical processes is proposed. The model is described by a system of partial differential equations. The method of splitting by physical processes forms two functional blocks: by water saturation and piezoconductivity. For the numerical solution of this system, an absolutely stable implicit finite-difference scheme is made in the spatially one-dimensional case. On the basis of the proposed difference scheme, pressures and saturations in the matrix and fracture system are calculated.