Fluid Dynamics at Pore Scale

We discuss in detail simple statistical mechanical models of irmniscible displacement in porous media, with emphasis on the percolation and viscous fingering regimes where critical type behaviour is observed. The predictions of percolation models include the fractal nature of the non-wetting fluid configuration in drainage, and the size distribution of the residual non-wetting clusters in imbibition. At the macroscopic level it is suggested that percolation ideas are consistent with the usual multiphase darcy equations, and critical behaviours of the relative permeability and capillary pressure curves are obtained. In the case of viscous fingering, we focus on the effect of competition between anisotropy and disorder on the fingering process. The relation of viscous fingering to Diffusion Limited Aggregation is discussed.