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The paper presents a physical and mathematical model of quasi-three-dimensional non-stationary filtration of a water-oil mixture in a system of horizontal wells and the corresponding numerical calculation method. Based on them, a computer program was created, designed to solve a number of scientific and production problems. The developed model and program are aimed at theoretical and numerical study of the processes of mass transfer of the oil-water mixture in the field of analysis, maintenance and development of natural formations with high-viscosity oil deposits. The results of numerical experiments for calculating the two-phase flow of an incompressible fluid in a reservoir are given as an example of a real field, located in the north of Western Siberia. The paper proposes an approach to discretization of the computational domain, based on the construction of a dynamic computational grid in a natural semi-fixed coordinate system. For the first time, the problem of calculating two-phase mass transfer using a semi-fixed natural grid and an analytical expression for the flow rates of phases in current streams of a found shape has been solved. Based on the proposed model, calculation and parametric studies of various modes of field development with a system of parallel horizontal wells were performed.

Non-stationary mass transfer of oil-water mixture in reservoirs with a system of horizontal wells