Parallel Algorithm for Calculating Two-Phase Filtration Processes in a Carbonate Reservoir in Plane Geometry

The work considers the process of two-phase filtration in a carbonate fractured-porous reservoir. This process reflects the interaction of oil and water with the carbonate core of the well during oil extraction using the displacement method. For computer analysis, the filtration process in a plane perpendicular to the well axis is chosen. For this formulation, a mathematical model, a numerical method on a Cartesian grid, and a parallel algorithm for its implementation are proposed. The mathematical model of two-phase filtration of immiscible fluids in fractures and the matrix of a porous reservoir is based on the Buckley-Leverett approach, while there is no capillary pressure surge in both fractures and the matrix, the water and oil phases are weakly compressible, and the skeleton is non-deformable. During the filtration process in a fractured-pore type reservoir, the exchange of fluids between low-permeability pores and a network of natural fractures is taken into account within the Warren-Root model. The fluid flows in accordance with the classical Darcy law. The numerical method is based on the application of the finite difference method and the scheme of splitting by physical processes and spatial coordinates. The parallel algorithm involves decomposing the computational domain into a lattice of domains of equal cardinality and using block-parallel sweep method. The developed methodology is tested using the example of calculating the filtration process in a wide range of parameters. Numerical experiments have shown that the developed algorithm is highly efficient, and the numerical technique itself allows one to obtain results adequate to the modeled physical process.