Using elements of machine learning to solve the inverse problem of reconstructing the hydraulic conductivity field for a filtration problem

About the authors:

Vitaly P. Kosyakov, Cand. Sci. (Phys.-Math.), Senior Researcher, Tyumen Branch of the Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences; Associate Professor, Department of Oil and Gas Flow Metering, University of Tyumen; eLibrary AuthorID, Web of Science ResearcherID; lik.24@yandex.ru; ORCID: 0000-0002-2297-408X

Dmitry Yu. Legostaev, Junior Researcher, Tyumen Branch of the Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences; Senior Lecturer, Department of Applied and Technical Physics, University of Tyumen; eLibrary AuthorID, legostaevdy@yandex.ru; ORCID: 0000-0001-6371-7031

Abstract:

In the modern world, machine learning methods are widely used. In the oil industry, there is also a noticeable trend to use these methods in the context of digitalization and intellectualization of the entire production process.

The present work is devoted to the development of a technique for solving the inverse problem of restoring the permeability field of an oil reservoir with the combined use of machine learning elements and a filtration model. A computational algorithm has been implemented, which implies close mutual integration of the filtration part and the machine learning block, the results of which are used to parameterize the physically meaningful model. A network of radial basis functions is used as a machine learning model. The proposed solution search procedure includes the numerical solution of the direct and adjoint problems for the filtration model. Solving the adjoint problem allows one to apply gradient optimization methods widely used in machine learning methods.

The paper presents the results of a numerical experiment. On the example of a symmetrical two-dimensional development element, a solution was obtained for the problem of restoring the permeability field for a set of zonal-heterogeneous oil reservoirs. For the reconstructed fields, the characteristic sizes of inhomogeneities coincide with the initial ones with sufficient accuracy. The fundamental possibility of a qualitative restoration of the porosity-permeability characteristics of the interwell space is shown, which is impossible when using classical interpolation methods without involving additional data. The paper studies the influence of the choice of the type of control parameter on the behavior of the objective function and its derivative, which affects the process of solving the inverse problem. As a result of the study, the use of hydrodynamic resistance as an adaptable parameter in solving the inverse problem is proposed.

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