Upscaling unsaturated flow in binary porous media with air entry pressure effects

We consider flow in a porous medium containing coarse-textured inclusions with a low value of air entry pressure, embedded in a fine-textured background material having high entry pressure. During imbibition some air remains trapped in the inclusions, while during drainage the inclusions become drained only after the capillary entry pressure exceeds the pressure of the background material. These effects can only be reproduced by a two-phase flow model, and not by the Richards' equation. However, if an upscaled form of the Richards' equation with appropriately modified capillary and permeability functions is used, the results are in a reasonable agreement with the two-phase flow model.