Electron. J. Diff. Eqns., Vol. 2007(2007), No. 97, pp. 1-29.

Derivation of models of compressible miscible displacement in partially fractured reservoirs

Catherine Choquet

We derive rigorously homogenized models for the displacement of one compressible miscible fluid by another in fractured porous media. We denote by $\epsilon$ the characteristic size of the heterogeneity in the medium. A parameter $\alpha \in [0,1]$ characterizes the cracking degree of the rock. We carefully define an adapted microscopic model which is scaled by appropriate powers of $\epsilon$. We then study its limit as $\epsilon \to 0$. Assuming a totally fractured or a partially fractured medium, we obtain two effective macroscopic limit models. The first one is a double porosity model. The second one is of single porosity type but it still contains some effects due to the partial storage in the matrix part. The convergence is shown using two-scale convergence techniques.

Submitted May 29, 2007. Published July 2, 2007.
Math Subject Classifications: 76S05, 35K55, 35B27, 76M50.
Key Words: Miscible compressible displacement; porous medium; partially fractured reservoir; double porosity; homogenization.

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Catherine Choquet
Laboratoire Analyse Topologie Probabilités, CNRS UMR 6632
Université P. Cézanne
Faculté des Sciences et Techniques de Saint-Jérôme, Case Cour A
13397 Marseille Cedex 20, France
email: c.choquet@univ-cezanne.fr

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