Saturation-dependencies of three-phase relative permeabilities in mixed-wet and fractionally wet systems

The saturation-dependency behaviour of three-phase relative permeabilities is of central importance for modelling three-phase displacement processes in porous media. In this paper, and in related work, a method has been developed to determine the saturation-dependencies of three-phase relative permeabilities. This method is suitable for all types of mixed-wet and fractionally wet porous systems that contain clusters of oil-wet and water-wet pores with constant but different oil–water contact angles, reflecting weakly wetted conditions. Based on the classification of all allowed pore occupancies in a completely accessible porous medium, saturation-dependencies of the corresponding relative permeabilities are derived. Furthermore, three-phase relative permeabilities that appear to depend only on their own saturations are either linked to the corresponding two-phase relative permeabilities or it is shown that such a link cannot be established. A comparison has been made with existing relative permeability models with respect to their saturation-dependencies.