Multiscale analysis of two fluid flow in porous media Seminar

Homogenization has been widely used as a tool to study fluid flow in porous media. This process allows macroscopic equations to be derived with effective parameters based on a set of representative cell problems. These cell problems are typically solved once on a representative sub-sample of the pore scale domain. For single fluid flow this process allows Darcy's law to be derived from Stokes' equations and parametrised through a single cell problem. In this talk we describe the use of homogenization to derive averaged equations for two fluid flow in porous media. The macroscopic equations form a coupled pair of non-linear PDEs for the fluid saturation and pressure. These are parametrised by a set of cell problems which are solved across a range of different saturation values. Under an appropriate set of assumptions these equations are shown to reduce to existing approximate models for two fluid flow. In addition we discuss the possible extension of this method to consider two fluid flow in deformable porous media.