A Directed Percolation Model for Clogging in a Porous Medium with Small Inhomogeneities

We propose a microscopic model based on directed percolation for the process of mechanical clogging of a porous medium by particles suspended in a fluid flow. Under appropriate conditions the deposited particles may form fractal clusters. A criterion for the occurrence of fractal clogging is presented. It links together the particle size and the pore size distribution. The effect of microscopic inhomogeneities is studied inside and outside the critical region using Monte Carlo calculations in two dimensions. The critical exponents remain unchanged because the perturbation induced by these inhomogeneities is irrelevant. The percolation threshold is found to shift to higher values almost linearly with increasing size of obstacles. For size distributed obstacles the arithmetic mean of the distribution is the only significant parameter which determines the shift. Type and broadness of the distribution have no influence. Also the percolation probability depends only on the mean even outside the critical region for all values of the occupation probability. Occupying the same fraction of the porous matrix, large obstacles cause more particles to deposit than small ones.