MATHEMATICAL MODEL WITH NON-LOCAL BOUNDARY CONDITION OF INCOMPRESSIBLE FLUID FILTRATION

Abstract

This work is devoted to an actual problem today – the creation of cost-effective technology of combined development of several reservoirs. Joint development of oil reservoirs combining two or more oil reservoirs into one production facility by simultaneous extraction of reservoir fluids from them by a single network of wells [1, 2]. Oil fields, as a rule, are multilayer, and the productive formations are heterogeneous, first of all, by reservoir properties: first of all, they have different permeability and thickness. It is economically unprofitable to drill a different production grid for each of the productive formations. One of the primary tasks of putting an oil field into commercial development is to combine productive formations into single production facilities and to carry out joint development of these formations. After the reservoirs are combined into a single production facility, they are drilled using a single grid of production and injection wells [3, 4]. This paper considers a two-layer reservoir with different permeability and thickness. Numerical solution of the model is proposed to determine the pressure field of incompressible fluid at known total flow rate. The technology of combined development of several reservoirs isolated from each other is used. We construct special difference equations in the neighbourhood of internal boundaries that allow us to apply the integro-interpolation method in a two-connected domain. Special differences equations in the vicinity of internal borders, allowing overcome the difficulties arising from the borders of the domain are constructed. The necessity of combined development in order to reduce the economic costs is revealed and justified. Based on the numerical investigations of the problem, obtained numerical results in programming language Fortran, and graphics in Tecplot for double-layer reservoirs. The article also found an analytical solution of this problem for the two reservoirs and made a comparative analysis of the results. Given conclusions about the quality and accuracy of used iterative method. The scientific novelty of this work is to research several layers by simultaneous selection of the reservoir fluids single well.The method of solving and analysis of the results will be of interest to those skilled in the development the oil fields.