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A three-dimensional network model of a porous medium is used to compute relative permeabilities and capillary pressures in drainage and imbibition. In contrast, the invasion-percolation model of drainage with trapping does not make a sensible prediction for the relative permeability of either the displaced or injected phases since it fails to represent the fluid connectivity correctly. We describe two realistic trapping mechanisms which overcome this difficulty by representing the flow of the wetting phase along irregularities in the pore-gain surface. In imbibition, we simulate the rate-dependent competition between bulk filling of pores and film flow and show how different displacement mechanisms affect relative permeability. We verify percolation-theory results for the effects of buoyancy forces on trapped saturation by simulation and derive an expression for the correlation length in displacements perturbed by viscous forces. We can then demonstrate how relative permeabilities measured in quasistatic systems at capillary equilibrium are still meaningful in larger-scale displacements where viscous forces predominate.
Blunt et al. (Tue,) studied this question.