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 Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2017, Volume 159, Book 3, Pages 327–339 (Mi uzku1412)

Petroleum reservoir simulation using super-element method with local detalization of the solution

A. B. Mazo, K. A. Potashev

Kazan Federal University, Kazan, 420008 Russia

Abstract: In this paper, we propose a two-stage method for petroleum reservoir simulation. The method uses two models with different degrees of detailization to describe the hydrodynamic processes of different space-time scales. At the first stage, the global dynamics of the energy state of the deposit and reserves has been modeled (characteristic scale of such changes is km/year). The two-phase flow equations in the model of global dynamics operate with smooth averaged pressure and saturation fields, and they are solved numerically on a large computational grid of super-elements with a characteristic cell size of 200–500 m. The tensor coefficients of the super-element model have been calculated using special procedures of upscaling of absolute and relative phase permeabilities. At the second stage, a local refinement of the super-element model has been constructed for calculating small-scale processes (with a scale of m/day), which take place, for example, during various geological and technical measures aimed at increasing the oil recovery of a reservoir. Then we solve the two-phase flow problem in the selected area of the measure exposure on a detailed three-dimensional grid, which resolves the geological structure of the reservoir, and with a time step sufficient for describing fast-flowing processes. The initial and boundary conditions of the local problem have been formulated on the basis of the super-element solution. To demonstrate the proposed approach, we have provided an example of the two-stage modeling of the development of a layered reservoir with a local refinement of the model during the isolation of a water-saturated high-permeability interlayer. We have shown a good compliance between the locally refined solution of the super-element model.

Keywords: super-element method, numerical simulation, petroleum reservoir, local refinement, reservoir treatments simulation, two-phased flow, downscaling.

 Funding Agency Grant Number Russian Foundation for Basic Research 15-41-0269815-41-02699 The study was supported by the Russian Foundation for Basic Research and the Government of the Republic of Tatarstan (projects nos. 15-41-02698 and 15-41-02699).

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UDC: 519.63+532.546

Citation: A. B. Mazo, K. A. Potashev, “Petroleum reservoir simulation using super-element method with local detalization of the solution”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 159, no. 3, Kazan University, Kazan, 2017, 327–339

Citation in format AMSBIB
\Bibitem{MazPot17} \by A.~B.~Mazo, K.~A.~Potashev \paper Petroleum reservoir simulation using super-element method with local detalization of the solution \serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki \yr 2017 \vol 159 \issue 3 \pages 327--339 \publ Kazan University \publaddr Kazan \mathnet{http://mi.mathnet.ru/uzku1412} \elib{http://elibrary.ru/item.asp?id=32265840}