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Matematicheskoe modelirovanie, 2020, Volume 32, Number 7, Pages 127–142
DOI: https://doi.org/10.20948/mm-2020-07-08
(Mi mm4201)
 

This article is cited in 2 scientific papers (total in 2 papers)

Study on the formation of Saffman–Taylor instability in oil reservoir in two-dimensional formulation

S. A. Bublik, M. A. Semin

Mining Institute of the Ural Branch of the Russian Academy of Sciences, Perm
References:
Abstract: The article is devoted to simulation of oil displacement by water and the formation of Saffman–Taylor instability. A circular domain with one injection well and 8 production wells located along the contour around the injection well is considered. To study the patterns of oil displacement by water, hydrostatic pressure, seepage velocity of oil and water, oil saturation are calculated. The graphical analysis of the solution considers mainly the oil saturation field. The calculation of the pressure field is done by means of solving the steady-state seepage equation. The oil-water seepage velocity is calculated using the linear Darcy's law. The oil saturation field is calculated by means of the solution of the advection transport equation. The two-phase nature of the flow lies in various relative phase permeabilities for oil and water. The Brooks–Corey model is used to calculate the relative phase permeabilities. The equations are solved numerically using the finite volume method. An irregular triangular grid is used to discretize the computational domain. As a result, it was established that the form of the Saffman–Taylor instability, by virtue of its randomness, strongly depends on the computational grid. After flooding of producing wells, the phase boundary stabilizes. Instability increases with increasing ratio of dynamic viscosities of oil and water.
Keywords: Saffman–Taylor instability, viscous fingering, seepage flow, porous media, finite volume method, Darcy's law, two-phase flow, Brooks–Corey model.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation МК-6244.2018.5
Received: 16.09.2019
Revised: 12.02.2020
Accepted: 02.03.2020
English version:
Mathematical Models and Computer Simulations, 2021, Volume 13, Issue 2, Pages 263–273
DOI: https://doi.org/10.1134/S2070048221020046
Document Type: Article
Language: Russian
Citation: S. A. Bublik, M. A. Semin, “Study on the formation of Saffman–Taylor instability in oil reservoir in two-dimensional formulation”, Matem. Mod., 32:7 (2020), 127–142; Math. Models Comput. Simul., 13:2 (2021), 263–273
Citation in format AMSBIB
\Bibitem{BubSem20}
\by S.~A.~Bublik, M.~A.~Semin
\paper Study on the formation of Saffman--Taylor instability in oil reservoir in two-dimensional formulation
\jour Matem. Mod.
\yr 2020
\vol 32
\issue 7
\pages 127--142
\mathnet{http://mi.mathnet.ru/mm4201}
\crossref{https://doi.org/10.20948/mm-2020-07-08}
\transl
\jour Math. Models Comput. Simul.
\yr 2021
\vol 13
\issue 2
\pages 263--273
\crossref{https://doi.org/10.1134/S2070048221020046}
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  • https://www.mathnet.ru/eng/mm/v32/i7/p127
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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