On the homogenization of some double-porosity models with periodic thin structures

Abstract

Models describing global behaviour of incompressible flow in fractured media are discussed. A fractured medium is regarded as a porous medium consisting of two superimposed continua, a connected fracture system and a system of disjoint matrix blocks. We derive global behaviour of fractured media versus different parameters such as the fracture thickness, the size of blocks and the ratio of the block permeability and the permeability of fissures. The homogenization results are obtained by means of the convergence in domains of asymptotically vanishing measure.

Keywords:

• double-porosity models
• fractured media
• thin fissures

AMS Subject Classifications::

• 35B27
• 74Q15
• 76M50
• 76S05

Acknowledgements

The authors would like to thank Prof. Alain Bourgeat for useful discussions. The work of B. Amaziane and L. Pankratov was partially supported by the GnR MoMaS 2439 CNRS ANDRA BRGM CEA EDF IRSN, whose support is gratefully acknowledged. This article was completed when L. Pankratov was visiting the Applied Mathematics Laboratory CNRS-UMR 5142 of the University of Pau. He is grateful for the invitation and hospitality.