Abstract
Background The study of the reservoir structural heterogeneity in the geophysical prospecting of deep-seated minerals by electric exploring, by well and inter-well electric exploring on direct current, including the state of the inter-well profile, is of great scientific and technical importance. Bulk test of reservoir systems with complex geological parameters may be received by mathematical modeling based on the induced electromagnetic field. Aims and objectives A mathematical model describing electric fields created by point sources of current, with cylindrical inhomogeneities, electrodes and insulators has been developed; an algorithm for reducing the dimension of the problem is presented. The general solution of the given problem is accomplished on the base of the Fourier transform inversion formula, a two-dimensional boundary value problem is obtained, the second Green's formula is used for the solution of this problem. By means of transformations, the two-dimensional boundary value problem is transformed into a one-dimensional boundary value problem for which a particular solution is found by the method of constructing the Green's function. The integral equation is solved by the Krylov-Bogolyubov method. A universal algorithm for solving the problem is proposed for calculating the electric field of a point source at any point in the half-space. Results The method for solving the problem of well and inter-well electric exploring on direct current in a plane-parallel medium with cylindrical inclusions is described. Combined algorithms for the numerical analysis of electric fields developed by three-dimensional nonlinear self-consistent boundary value problems in a plane-parallel medium with cylindrical inhomogeneous inclusions, insulators and electrodes developed and tested on a computer are presented.
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