Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 97, pp. 1-29.

Title: Derivation of models of compressible miscible displacement
       in partially fractured reservoirs

Author: Catherine Choquet (Univ., P. Cezanne, Cedex, France)

Abstract:
 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.