Numerical Modeling of Two-Phase Fluid Filtration for Carbonate Reservoir in Two-Dimensional Formulation

Ravil M. Uzyanbaev (), Yuliya O. Bobreneva, Yury A. Poveshchenko, Viktoriia O. Podryga, Sergey V. Polyakov, Parvin I. Rahimly and Irek M. Gubaydullin
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Ravil M. Uzyanbaev: Department of Digital Technologies and Modeling, Graduate School of Information and Social Technologies, Ufa State Petroleum Technological University, Kosmonavtov Street 1, 450062 Ufa, Russia
Yuliya O. Bobreneva: Institute of Petrochemistry and Catalysis, Russian Academy of Sciences, Pr. Oktyabrya Street 141, 450075 Ufa, Russia
Yury A. Poveshchenko: Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya Square 4, 125047 Moscow, Russia
Viktoriia O. Podryga: Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya Square 4, 125047 Moscow, Russia
Sergey V. Polyakov: Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya Square 4, 125047 Moscow, Russia
Parvin I. Rahimly: Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya Square 4, 125047 Moscow, Russia
Irek M. Gubaydullin: Institute of Petrochemistry and Catalysis, Russian Academy of Sciences, Pr. Oktyabrya Street 141, 450075 Ufa, Russia

Mathematics, 2024, vol. 12, issue 21, 1-22

Abstract: This work considers the isothermal process of incompressible viscous fluid filtration in an oil-saturated, fractured-porous reservoir. A study of the pressure and water saturation distribution process is carried out for a case in which a production well is put into operation. For this problem, i.e., a mathematical model in a two-dimensional formulation, a numerical method and a parallel algorithm are proposed. The mathematical model of two-phase filtration is written in accordance with the classical laws of continuum mechanics and Darcy’s law and also includes a function of fluid exchange between low-permeability pores and high-permeability natural fractures within the framework of the Warren–Root model. The numerical solution is based on the finite-difference method and a splitting scheme of physical processes and spatial coordinates. For a split system with respect to piezoconductivity, an implicit finite-difference scheme with fixed saturations is constructed, and with respect to saturation transfer, explicit and implicit difference schemes are constructed. For parallel implementation of the developed numerical approach, a method based on geometric parallelism is selected. Testing of the developed method is performed using the example of calculating liquid mass transfer for a wide range of parameters. To verify the model, the obtained calculated pressure curves are compared with field data recorded by a deep-well measuring device. The results allow for estimation of the distribution of reservoir pressure and water saturation depending on the permeability of the fracture set and the pore part. The obtained results allow for monitoring of well operations, reducing unexpected accident risks and optimizing the development system in order to increase oil production in fractured-porous reservoirs. Computational experiments confirm the efficiency of the developed numerical algorithm and its parallel implementation.

Keywords: mathematical modeling; two-phase filtration; fracture system; pressure; saturation; implicit finite-difference schemes; geometric parallelism (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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