Percolation effects in immiscible displacement

The observable consequences of percolation models of immiscible displacement in porous media are discussed, with emphasis on the critical behavior. At the microscopic level, these include the fractal nature of the nonwetting fluid configuration at breakthrough in drainage, and the size distribution of the residual nonwetting clusters in imbibition. At the macroscopic level, it is suggested that percolation ideas are consistent with the usual multiphase Darcy equations, and critical behaviors of the relative permeability and capillary pressure curves are obtained. By using these results, predictions are made for the shape of the fluid saturation profiles near the percolation thresholds in the presence of buoyancy or viscous pressure gradients. Finally, it is pointed out that very close to the percolation thresholds, the diverging correlation length requires these macroscopic ideas to be modified. A simple way of doing this is suggested.