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

Yuliya O. Bobreneva (), Yury Poveshchenko, Viktoriia O. Podryga, Sergey V. Polyakov, Ravil M. Uzyanbaev (), Parvin I. Rahimly, Ainur A. Mazitov and Irek M. Gubaydullin ()
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Yuliya O. Bobreneva: Institute of Petrochemistry and Catalysis, Russian Academy of Sciences, Pr. Oktyabrya Street 141, Ufa 450075, Russia
Yury Poveshchenko: Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya Square 4, Moscow 125047, Russia
Viktoriia O. Podryga: Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya Square 4, Moscow 125047, Russia
Sergey V. Polyakov: Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya Square 4, Moscow 125047, Russia
Ravil M. Uzyanbaev: Institute of Petrochemistry and Catalysis, Russian Academy of Sciences, Pr. Oktyabrya Street 141, Ufa 450075, Russia
Parvin I. Rahimly: Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya Square 4, Moscow 125047, Russia
Ainur A. Mazitov: Institute of Petrochemistry and Catalysis, Russian Academy of Sciences, Pr. Oktyabrya Street 141, Ufa 450075, Russia
Irek M. Gubaydullin: Institute of Petrochemistry and Catalysis, Russian Academy of Sciences, Pr. Oktyabrya Street 141, Ufa 450075, Russia

Mathematics, 2023, vol. 11, issue 18, 1-16

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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