Approximate models for bacteria leaching through porous media

To study leaching of bacteria through complex soils, the researcher has to employ numerical methods as the known theoretical methods available are too restricted. Direct simulation of diffusion faces the problem of absence of statistical stability as the diffusion times vary dramatically between different realisations and soil samples. We propose an approximation to the original leaching problem which is fast to simulate and is shown to give reliable approximation to the exit times in the whole range of parameter values including the problematic values that exhibit extreme behaviour. In addition, we have shown that a completely different type of pore structure, such as produced by tunnels through the soil, does not greatly affect diffusive properties when we are not close to the percolation threshold.