Mathematical Modelling of an Array of Nuclear Waste Containers

The goal of this paper is to give a mathematical model describing the global behaviour of the nuclear waste disposal process. The physical situation can be described as an array made of high number of alveoles inside of a low permeable layer (e.g. clay) included between two layers with slightly higher permeability (e.g. limestone). Radioactive elements are leaking from their containers over a period of time ]0, tm[ . In a porous media (clay) there is a dilution effect (similar to diffusion) and convection due to some underground water flow. The real physical situation is simplified by replacing 5 alveoles by one macro alveole and by considering the convection velocity as a given field. These simplifications seam to be unimportant for understanding the global effects. The typical size of such macro alveole is of order : 100 m width, 1000 m length, 5 m hight. The distance between two alveoles is also of order 100 m. The size of law permeable layer is of order 150 m hight, and 3000 length. Since alveoles are small compared to the size of layer and their number is large direct numerical simulations using the microscopic model is unrealistic. On the other hand the ratio between domain length and the length of one alveole is small, of order 1/30, and allows an asymptotic study with respect to that small parameter, denoted by ε, using the method of homogenization and boundary layers.