A Process-Based Approach for Three-Phase Capillary Pressure and Relative Permeability Relationships in Mixed-Wet Systems

In the reservoir simulation of three-phase displacement processes, the saturation dependency of three-phase relative permeabilities is of central importance. However, little is known a priori about these saturation dependencies in nonstrongly water-wet systems. This behavior is intimately connected with the pore-scale physics of these displacements for the specific wettability state of the system. We refer to a model, which connects the macroscopic properties with the underlying pore-scale physics as a process-based model. In this paper, and in related work, such a model has been developed to determine the saturation-dependency regions of three-phase relative permeabilities. This processes-based model applies to both non-spreading and spreading oils for all types of mixed-wet and fractionally-wet porous systems that contain clusters of oil-wet and water-wet pores. Based on a classification of all allowed pore occupancies in a completely accessible porous medium, saturation-dependencies of the corresponding relative permeabilities are derived. The variation of regions in saturation space where the three-phase relations depend on either one or two phase saturations is determined and analysed in terms of the basic parameters of the model, i.e. range of pore size distribution, fraction of water-wet pores and the interfacial tensions (σgw, σgo, σow ).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.