We consider a model of diffusion in a random media originated from the nuclear waste management industry. In each site of the cubic lattice $Z^{d}$ there is an obstacle with a positive integer valued random capacity. On the other hand, on the origin and independently of the distribution of the obstacles, independent random walks are introduced so that at time $t$, $N(t)$ random walks have been born, and so that they survive until touching an obstacle. When this happens the capacity of the touched obstacle decreases by one. An obstacle of 0 capacity disappears. For low values of $N(t)$ we prove that with probability 1, the saturated obstacles correspond to a sphere of volume $N(t)$. With the help of this fact, and using the second version of the method of enlargement of obstacles of Sznitman, we prove that there are three injection regimes, depending on $N(t)$ and the dimension. In particular estimates on the asymptotic behaviour of the principal Dirichlet eigenvalue of the discrete Laplacian operator on a box of side $t$ with sites removed with positive probability, each one independent of the others, is required. This is a joint work with Gerard Ben Arous.