Stationary electric fields in inhomogeneous media: towards the 90th anniversary of the Fok-Stefanescu problem solution

UDK: 550.832.7

DOI: 10.24887/0028-2448-2025-12-20-25

Key words: well logging, stationary electric field, lateral logging (LLS), apparent resistivity, mathematical modeling, direct problems of electrometry, logging curve, inverse problems of electrometry, academic tournament

Authors: O.B. Kuzmichev (RN-BashNIPIneft LLC, RF, Ufa); R.K. Gazizov (RN-TECHNOLOGIES LLC, RF, Moscow; Ufa University of Science and Technology, RF, Ufa); N.S. Belevtsov (RN-TECHNOLOGIES LLC, RF, Moscow; Ufa University of Science and Technology, RF, Ufa); S.Yu. Lukashchuk (RN-TECHNOLOGIES LLC, RF, Moscow; Ufa University of Science and Technology, RF, Ufa)

In the article, a brief historical overview and the current state of electrical logging problems are given, their relevance and practical significance are discussed, the formulation of the generalized Fok – Stefanescu problem is provided, and various approaches to its solution are discussed, including those which were obtained by the participants of the Academic Tournament. Academic Tournaments are held annually by Rosneft Oil Company with the aim of attracting young scientists to solve current physical and mathematical problems of the oil and gas industry. In 2024, the Academic Tournament was timed to coincide with the 90th anniversary of the publication of the fundamental monograph by academician V.A. Fok «Theory of determining the resistance of rocks by the logging method». V.A. Fok is a renowned specialist in the field of quantum mechanics and general relativity, who laid the foundations of the theory of electrical logging in our country. The problem proposed to the competition participants was aimed at assessing the possibility of constructing effective algorithms for identifying reservoir parameters. Multilayer reservoirs with a variable size of the invasion zone, which are close to practical conditions, were considered. The results of the tournament showed that the computational complexity of such a problem is significantly higher than the classic formulation. Despite the fact that the algorithms proposed by the tournament participants made it possible to solve the problem with accuracy acceptable for practice, an acceptable solution time is a task for the future.

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