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Volume 11
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10.3390/math11183991
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Article

One Approach to Numerical Modeling of the Heat and Mass Transfers of Two-Phase Fluids in Fractured-Porous Reservoirs

by
Yuliya O. Bobreneva
1,*,
Yury Poveshchenko
2,
Viktoriia O. Podryga
2,
Sergey V. Polyakov
2,
Ravil M. Uzyanbaev
1,3,*,
Parvin I. Rahimly
2,
Ainur A. Mazitov
1 and
Irek M. Gubaydullin
1,3,*
1
Institute of Petrochemistry and Catalysis, Russian Academy of Sciences, Pr. Oktyabrya Street 141, Ufa 450075, Russia
2
Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya Square 4, Moscow 125047, Russia
3
Department of Digital Technologies and Modeling, Graduate School of Information and Social Technologies, Ufa State Petroleum Technological University, Kosmonavtov Street 1, Ufa 450062, Russia
*
Authors to whom correspondence should be addressed.
Mathematics 2023, 11(18), 3991; https://doi.org/10.3390/math11183991
Submission received: 3 August 2023 / Revised: 1 September 2023 / Accepted: 6 September 2023 / Published: 20 September 2023
(This article belongs to the Special Issue Parallel Computing and Applications)
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Abstract

The work is devoted to numerical modeling of the processes of heat and mass transfer of a two-phase fluid in the environment of a production well, which is necessary for monitoring the development of fractured-porous reservoirs. This work proposes an efficient approach to constructing a solution to the problem. To solve the problem, a model of the “double medium” type is used, where the pore part of the reservoir is considered as the first medium, and the system of natural fractures is considered as the second medium. For the resulting mathematical model, the difference schemes with time weights are constructed based on the algorithm of splitting by physical processes, which ensure the correctness and consistency of fluxes in the fracture system and the pore reservoir. In the numerical solution, the approximations of differential operators obtained in the framework of the finite difference method are used. For the parallel implementation of the developed numerical approach, the domain decomposition method and the matrix sweep algorithm are chosen. The program implementation is made using the MPI standard. Computational experiments are carried out, the results of which confirm the effectiveness of the developed numerical algorithm and its parallel implementation. In numerical experiments, the distributions of pressure and temperature near an operating production well are obtained, on the basis of which it is possible to adjust the operation of wells in order to increase production.
Keywords: mathematical modeling; two-phase filtration; fractured-porous reservoir; pressure; temperature; implicit finite difference schemes; matrix sweep method mathematical modeling; two-phase filtration; fractured-porous reservoir; pressure; temperature; implicit finite difference schemes; matrix sweep method
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MDPI and ACS Style

Bobreneva, Y.O.; Poveshchenko, Y.; Podryga, V.O.; Polyakov, S.V.; Uzyanbaev, R.M.; Rahimly, P.I.; Mazitov, A.A.; Gubaydullin, I.M. One Approach to Numerical Modeling of the Heat and Mass Transfers of Two-Phase Fluids in Fractured-Porous Reservoirs. Mathematics 2023, 11, 3991. https://doi.org/10.3390/math11183991

AMA Style

Bobreneva YO, Poveshchenko Y, Podryga VO, Polyakov SV, Uzyanbaev RM, Rahimly PI, Mazitov AA, Gubaydullin IM. One Approach to Numerical Modeling of the Heat and Mass Transfers of Two-Phase Fluids in Fractured-Porous Reservoirs. Mathematics. 2023; 11(18):3991. https://doi.org/10.3390/math11183991

Chicago/Turabian Style

Bobreneva, Yuliya O., Yury Poveshchenko, Viktoriia O. Podryga, Sergey V. Polyakov, Ravil M. Uzyanbaev, Parvin I. Rahimly, Ainur A. Mazitov, and Irek M. Gubaydullin. 2023. "One Approach to Numerical Modeling of the Heat and Mass Transfers of Two-Phase Fluids in Fractured-Porous Reservoirs" Mathematics 11, no. 18: 3991. https://doi.org/10.3390/math11183991

APA Style

Bobreneva, Y. O., Poveshchenko, Y., Podryga, V. O., Polyakov, S. V., Uzyanbaev, R. M., Rahimly, P. I., Mazitov, A. A., & Gubaydullin, I. M. (2023). One Approach to Numerical Modeling of the Heat and Mass Transfers of Two-Phase Fluids in Fractured-Porous Reservoirs. Mathematics, 11(18), 3991. https://doi.org/10.3390/math11183991

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