Electron. J. Diff. Eqns., Vol. 2009(2009), No. 01, pp. 1-27.

Homogenized model for flow in partially fractured media

Catherine Choquet

We derive rigorously a homogenized model for the displacement of one compressible miscible fluid by another in a partially fractured porous reservoir. We denote by $\epsilon$ the characteristic size of the heterogeneity in the medium. A function $\alpha$ characterizes the cracking degree of the rock. Our starting point is an adapted microscopic model which is scaled by appropriate powers of $\epsilon$. We then study its limit as $\epsilon \to 0$. Because of the partially fractured character of the medium, the equation expressing the conservation of total mass in the flow is of degenerate parabolic type. The homogenization process for this equation is thus nonstandard. To overcome this difficulty, we adapt two-scale convergence techniques, convexity arguments and classical compactness tools. The homogenized model contains both single porosity and double porosity characteristics.

Submitted November 20, 2008. Published January 2, 2009.
Math Subject Classifications: 76S05, 35K55, 35B27, 76M50.
Key Words: Miscible compressible displacement; porous medium; partially fractured reservoir; double porosity; homogenization; two-scale limit of a degenerate parabolic equation.

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Catherine Choquet
Université P. Cézanne, LATP, CNRS UMR 6632
et Université de Savoie, LAMA, CNRS UMR 5127
FST, Case Cour A, 13397 Marseille Cedex 20, France
email: c.choquet@univ-cezanne.fr

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