The problem of the combined use of filtration theory and machine learning elements for solving the inverse problem of restoring the hydraulic conductivity of an oil field

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

Emil N. Musakaev, Cand. Sci. (Tech.), Researcher, Tyumen Division of Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences; Specialist in Integrated Modeling of PITC Geofizika LLC; musakaev91@gmail.com

Abstract:

This article presents the methodology involving the combined use of machine learning elements and a physically meaningful filtration model. The authors propose using a network of radial basis functions for solving the problem of restoring hydraulic conductivity in the interwell space for an oil field. The advantage of the proposed approach in comparison with classical interpolation methods as applied to the problems of reconstructing the filtration-capacitive properties of the interwell space is shown. The paper considers an algorithm for the interaction of machine learning methods, a filtration model, a mechanism for separating input data, a form of a general objective function, which includes physical and expert constraints. The research was carried out on the example of a symmetrical element of an oil field. The proposed procedure for finding a solution includes solving a direct and an adjoint problem.

References:

1. Basniev K. S., Dmitriev N. M., Kanevskaya R. D., Maksimov V. M. 2006. Underground Hydromechanics. Moscow-Izhevsk: Institute of Computer Research. 488 pp. [In Russian]

2. Zakirov I. S. 2006. Development of the Theory and Practice of Oil Field Development. Moscow, Izhevsk: Institute of Computer Technologies. 356 pp. [In Russian]

3. Rozhenko A. I., 2018. Comparison of Radial Basis Functions. Sibirskiy zhurnal vychislitelnoy matematiki, vol. 21, no. 3, pp. 273-292. DOI: 10.15372/SJNM20180304 [In Russian]

4. Broomhead D. H., Lowe D. 1988. “Multivariable functional interpolation and adaptive networks”. Complex Systems: Journal, vol. 2, pp. 321-355.

5. Ertekin T., Sun Q. 2019. “Artificial intelligence applications in reservoir engineering: a status check”. Energies, vol. 12, art. 2897.

6. Glorot X., Bordes A., Bengio Y. 2011. “Deep sparse rectifier neural networks”. Proceedings of the 14^th International Conference on Artificial Intelligence and Statistics, vol. 15, pp. 315-323.

7. Kosyakov V. P. 2020. “Structural and parametric identification of an aquifer model for an oil reservoir”. Lobachevskii Journal of Mathematics, vol. 41, pp. 1242-1247. DOI: 10.1134/S1995080220070239

8. Misbahuddin M. 2020. “Estimating Petrophysical properties of shale rock using conventional neural networks CNN”. Society of Petroleum Engineers. DOI: 10.2118/204272-STU

9. Musakaev E. N., Rodionov S. P., Legostaev D. Yu., Kosyakov V. P. 2009. “Parameter identification for sector filtration model of an oil reservoir with complex structure”. AIP Conference Proceedings, vol. 2125, art. 030113. DOI: 10.1063/1.5117495

10. Otchere D. A., Arbi Ganat T. O., Gholami R., Ridha S. 2021. “Application of supervised machine learning paradigms in the prediction of petroleum reservoir properties: Comparative analysis of ANN and SVM models”. Journal of Petroleum Science and Engineering, vol. 200, art. 108182. DOI: 10.1016/j.petrol.2020.108182