Slow immiscible displacement flow in disordered porous media

The immiscible displacement of a wetting fluid by a non-wetting fluid in a disordered porous medium is studied in the capillary region, i.e. when capillary forces are dominant, by using the invasion percolation model to describe the displacement mechanism. The porous medium is represented by a two-dimensional network of interconnected capillaries whose radii follow a uniform size distribution. Disorder is assigned to the medium by considering the probabilities of occurrence of inaccessible pores, p_s, and non-conductive capillaries, p_b. It is found that the dynamic behaviour of the displacing fluid and the fraction of invaded pores depend on the degree of disorder of the medium. The results can provide an interpretation of the effects of the dead-end pore volume on the oil recovery and the displacement behaviour.