A homogenized model of an underground waste repository including a disturbed zone

The mathematical model describing the leaking of an underground waste repository should include the multiscale geometry and the large variation of the geological coefficients. Numerical simulations for performance assessments using such a local and detailed model are unrealistic, and there is a need to replace this local model ( mesoscopic model) by a global one ( macroscopic model). After introducing a small parameter epsilon, linking the relative size of the waste packages to the repository module size and to geological parameters, a first-order accurate macroscopic model of a repository module is obtained by studying the asymptotic behavior of the mesoscopic model when epsilon tends to 0. The mathematical homogenization method that we use herein leads to an accurate macroscopic model which could be used as a global repository model for far field numerical simulations in performance assessment.