Abstract

In models of porous media flows, for instance in hydrogeology, the porosity of the solid matrix is typically treated as a static quantity. However, under certain circumstances, such as in soft sedimentary rocks or in magma flows, the porosity of the solid material can evolve under the influence of fluid pressure. In particular, this can lead to the formation of solitary porosity waves and of higher-porosity channels. We consider a system of nonlinear PDEs for porosity and effective pressure, based on a poroviscoelastic model, which describes such phenomena. The focus of this talk is on the well-posedness of this PDE problem, which has been established in the literature only for initial porosities of high Sobolev smoothness. We discuss several preliminary results for porosities of low regularity, including cases with jump discontinuities that are of particular interest in geological applications. We then turn to some first results on a space-time adaptive numerical method based on a discontinuous Petrov-Galerkin approach for efficiently approximating the evolution of porosity channels. Finally, we discuss available measurement data and associated inverse problems.

This is joint work in progress with Simon Boisserée (Mainz), Lisa Maria Kreusser (Bath), and Evangelos Moulas (Mainz).