Abstract:
This paper presents a new method of local upscaling of absolute permeability for super element simulation of oil reservoir. Upscaling performed for each block of super element unstructured grid. To do this, the set of problems of steady state one phase flow solved on a fine computational grid with the initial scalar field of absolute permeability with various boundary conditions that reflect the specific variants of filtrational flow through the super element and take into account the presence or absence of boreholes in the coarse block. The resulting components of the effective permeability tensor in each super element found from the solution of the problem of minimizing the deviations of averaged on a detailed computational grid from approximated on a coarse super element grid normal flows through the super element faces. The results of using the method are demonstrated for reservoirs with periodic and non-periodic structure of absolute permeability field. The comparison with the traditional methods of local upscaling is performed.
Keywords:
upscaling, absolute permeability, porous media, petroleum reservoir simulation, super element method.
Citation:
A. B. Mazo, K. A. Potashev, “Absolute permeability upscaling for super element model of petroleum reservoir”, Mat. Model., 29:6 (2017), 89–102; Math. Models Comput. Simul., 10:1 (2018), 26–35
\Bibitem{MazPot17}
\by A.~B.~Mazo, K.~A.~Potashev
\paper Absolute permeability upscaling for super element model of petroleum reservoir
\jour Mat. Model.
\yr 2017
\vol 29
\issue 6
\pages 89--102
\mathnet{http://mi.mathnet.ru/mm3859}
\elib{https://elibrary.ru/item.asp?id=29207729}
\transl
\jour Math. Models Comput. Simul.
\yr 2018
\vol 10
\issue 1
\pages 26--35
\crossref{https://doi.org/10.1134/S207004821801009X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85042566971}
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https://www.mathnet.ru/eng/mm3859
https://www.mathnet.ru/eng/mm/v29/i6/p89
This publication is cited in the following 6 articles:
F. Mazlumi, M. Mosharaf-Dehkordi, M. Dejam, “Simulation of two-phase incompressible fluid flow in highly heterogeneous porous media by considering localization assumption in multiscale finite volume method”, Appl. Math. Comput., 390 (2021), 125649
T. F. Kireev, G. T. Bulgakova, “Near-well upscaling for simulation of wells with hydraulic fractures”, Math. Models Comput. Simul., 11:6 (2019), 877–883
A. Mazo, K. Potashev, M. Khamidullin, “Simplified model to estimate productivity of horizontal well with multistage hydraulic fracturing”, Lobachevskii J. Math., 40:8, SI (2019), 1186–1193
Alexandr Mazo, Konstantin Potashev, “Scaling in Super Element Model of Petroleum Reservoirs”, J. Phys.: Conf. Ser., 1392:1 (2019), 012072
Mazo A.B., Potashev K.A., “Local Refinement of the Super Element Model of Oil Reservoir”, Georesury, 19:4 (2017), 323–330
A. B. Mazo, K. A. Potashev, “Modelirovanie razrabotki neftyanogo plasta metodom superelementov s lokalnoi detalizatsiei resheniya”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 159, no. 3, Izd-vo Kazanskogo un-ta, Kazan, 2017, 327–339
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