Scaling Up of an Underground Waste Disposal Model with Random Source Terms

In this paper, we study the global behavior of an underground waste disposal in order to obtain an accurate upscaled model suitable for the computations involved in safety assessment processes. The disposal is made of a high number of modules containing the waste material. One supposes that the modules or disposal units are periodicaly distributed and that each disposal unit leaks randomly. Recent theoretical works, by use of a combination of classical homogenization and probability theories, allow to derive a global model where only one deterministic leaking source is considered. We propose, using these theoretical results, to give a numerical approach for a such multiscale problem to obtain solutions of the deterministic problem and the first-order statistical moments.