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Mathematical notes of NEFU, 2018, Volume 25, Issue 4, Pages 84–101
DOI: https://doi.org/10.25587/SVFU.2018.100.20556
(Mi svfu236)
 

Mathematical modeling

Conservative difference scheme for filtering problems in fractured media

M. V. Vasil'eva, V. I. Vasiliev, A. A. Tyrylgin

M. K. Ammosov North-Eastern Federal University, Institute of Mathematics and Informatics, 42 Kulakovsky Street, Yakutsk 677000, Russia
Abstract: We consider filtration problems in the fractured media that are necessary when modeling the processes of extracting hydrocarbons from unconventional reservoirs, geothermal fields development, underground disposal of radioactive waste in aquifers, etc. Fracture networks in such oil pools can exist on different scales and differ in the nature of their occurrence. We discuss a mathematical model of fluid filtration in fractured porous media described by coupled equations of mixed dimension with assigning of a special flow function. The problem approximation is constructed through the finite difference method on structured grids using the embedded fracture model, which makes possible creating grids for the porous medium matrix independently of the fracture network grid. The construction of a conservative difference scheme is given for the matrix of porous medium with the use of an integro-interpolation method and generalized for coupled equations describing mathematical models of multicontinuum with hierarchical representation of fracture networks. The results of the numerical implementation of the two-dimensional model problem are presented.
Keywords: fractured porous medium, multicontinuum models, dual porosity model, mixed dimensional formulation, numerical simulation, filtration problem, embedded fracture model, convervative difference scheme.
Funding agency Grant number
Russian Foundation for Basic Research 17–01–00732
Received: 22.10.2018
Revised: 09.11.2018
Accepted: 13.11.2018
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: Russian
Citation: M. V. Vasil'eva, V. I. Vasiliev, A. A. Tyrylgin, “Conservative difference scheme for filtering problems in fractured media”, Mathematical notes of NEFU, 25:4 (2018), 84–101
Citation in format AMSBIB
\Bibitem{VasVasTyr18}
\by M.~V.~Vasil'eva, V.~I.~Vasiliev, A.~A.~Tyrylgin
\paper Conservative difference scheme for filtering problems in fractured media
\jour Mathematical notes of NEFU
\yr 2018
\vol 25
\issue 4
\pages 84--101
\mathnet{http://mi.mathnet.ru/svfu236}
\crossref{https://doi.org/10.25587/SVFU.2018.100.20556}
\elib{https://elibrary.ru/item.asp?id=36775154}
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