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Two-phase flow equations with a dynamic capillary pressure

Published online by Cambridge University Press:  21 September 2012

JAN KOCH ,
ANDREAS RÄTZ  and
BEN SCHWEIZER
JAN KOCH
Affiliation:
Technische Universität Dortmund, Fakultät für Mathematik, Vogelpothsweg 87, D-44227 Dortmund, Germany emails: jan.koch@tu-dortmund.de, andreas.raetz@tu-dortmund.de, ben.schweizer@tu-dortmund.de
ANDREAS RÄTZ
Affiliation:
Technische Universität Dortmund, Fakultät für Mathematik, Vogelpothsweg 87, D-44227 Dortmund, Germany emails: jan.koch@tu-dortmund.de, andreas.raetz@tu-dortmund.de, ben.schweizer@tu-dortmund.de
BEN SCHWEIZER
Affiliation:
Technische Universität Dortmund, Fakultät für Mathematik, Vogelpothsweg 87, D-44227 Dortmund, Germany emails: jan.koch@tu-dortmund.de, andreas.raetz@tu-dortmund.de, ben.schweizer@tu-dortmund.de
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Abstract

We investigate the motion of two immiscible fluids in a porous medium described by a two-phase flow system. In the capillary pressure relation, we include static and dynamic hysteresis. The model is well established in the context of the Richards equation, which is obtained by assuming a constant pressure for one of the two phases. We derive an existence result for this hysteresis two-phase model for non-degenerate permeability and capillary pressure curves. A discretization scheme is introduced and numerical results for fingering experiments are obtained. The main analytical tool is a compactness result for two variables that are coupled by a hysteresis relation.

Keywords

Two-Phase flowCapillary hysteresisFinite-element scheme

Information

Type
Papers
Information
European Journal of Applied Mathematics , Volume 24 , Issue 1 , February 2013 , pp. 49 - 75
Copyright
Copyright © Cambridge University Press 2012

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