Derivation of Models of Compressible Miscible Displacement in Partially Fractured Reservoirs

We derive rigorously homogenized models for the displacement of one compressible miscible fluid by another in fractured porous media. We denote by the characteristic size of the heterogeneity in the medium. A parameter α ∈ [0, 1] characterizes the cracking degree of the rock. We carefully define an adapted microscopic model which is scaled by appropriate powers of . We then study its limit as → 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.