Dynamic Capillarity and Hysteretic Effects in Two­Phase Flow in Porous Media: Modeling, Upscaling and Simulation

Abstract

Flow and transport processes in porous media are relevant for a huge variety of applications covering all areas of modern society. To describe and predict the relevant processes, it is crucial to understand the complicated underlying phenomena. The mathematical models are based on fundamental balance equations, which are complemented by constitutive equations describing the specific material behavior. These relations must be expressed using effective parameters, which should combine all pore­scale effects. However, these parameters are simply postulated in many state-of-the-art models and not derived from a pore-scale model. In particular, the interface dynamics between the fluids are typically neglected or incorporated on an empirical basis. In the first part of this work, we consider these effects for simple pore geometries and apply upscaling techniques to derive effective two-phase flow equations. The upscaled models at the Darcy scale are coupled, nonlinear partial differential equations, which may even degenerate and can involve strong heterogeneities or even discontinuous physical properties. These issues raise analytical and numerical challenges. Besides appropriate discretization methods, linearization schemes must be applied. By domain decomposition methods, essentially different regions are decoupled to parallelize computations and reach a reasonable performance. These numerical aspects are considered in the second part of this work.