UPSCALING OF MULTIPHASE FLOW PROCESSES IN HETEROGENEOUS POROUS MEDIA

The present article gives a mathematical model describing flow of two fluid phases in a heterogeneous porous medium. The medium contains disconnected inclusions embedded in the background material. This background material is characterized by higher value of the non-wetting phase entry pressure than the inclusions that causes non-standard behavior of medium at the macroscopic scale. During which the displacement of the non-wetting fluid by the wetting fluid, some portions of the non-wetting fluid become trapped in the inclusions. Secondly, if the medium is initially saturated with the wetting phase then it starts to drain only after the capillary pressure exceeds the entry pressure of the background material. These effects cannot be shown by standard upscaling approaches based on the assumption of local equilibrium of the capillary pressure. So, we can propose a relevant modification of the upscaled model obtained by asymptotic homogenization. The modification relates the type of flow equations and the calculation of the effective hydraulic functions. The heterogeneities of the porous media are typically well represented in the global fine-scale solutions. In particular, the connectivity of the media is properly embedded into the global fine-scale solution. Thus, for the porous media with channelized features, where there are high or low permeability regions have long-range connectivity. Hence this type of approach is expected to work better.