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Finite volume approximation for an immiscible two-phase flow in porous media with discontinuous capillary pressure

Abstract : We consider an immiscible incompressible two-phase flow in a porous medium composed of two different rocks so that the capillary pressure field is discontinuous at the interface between the rocks. This leads us to apply a concept of multi-valued phase pressures and a notion of weak solution for the flow which have been introduced in [Cancés \& Pierre, {\em SIAM J. Math. Anal}, 44(2):966--992, 2012]. We discretize the problem by means of a numerical algorithm which reduces to a standard finite volume scheme in each rock and prove the convergence of the approximate solution to a weak solution of the two-phase flow problem. The numerical experiments show in particular that this scheme permits to reproduce the oil trapping phenomenon.
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https://hal.archives-ouvertes.fr/hal-00675681
Contributor : Konstantin Brenner <>
Submitted on : Thursday, February 21, 2013 - 11:21:27 AM
Last modification on : Wednesday, September 16, 2020 - 4:05:25 PM
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  • HAL Id : hal-00675681, version 2

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Konstantin Brenner, Clément Cancès, Danielle Hilhorst. Finite volume approximation for an immiscible two-phase flow in porous media with discontinuous capillary pressure. Computational Geosciences, Springer Verlag, 2013. ⟨hal-00675681v2⟩

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