Multiphase Flow in Porous Media

Abstract

We discuss in detail the observable consequences of percolation models of immiscible displacement in porous media, with emphasis on the critical behavior. At the microscopic level these 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 behaviors of the relative permeability and capillary pressure curves are obtained. Using these results we derive the shape of the saturation profiles in the presence of buoyancy or viscous pressure gradients.