Theory and numerics of erosion processes in fluid-saturated porous media

摘要

In the current contribution we present a continuum-based erosion model for fluid-saturated porous materials. We focus on the hydro-mechanical aspect of erosion, e.g. the sand production problem in petroleum wells. As a consequence, the model is restricted to a set of mass balance equations assuming that the solid skeleton is rigid. Phenomenologically, it is assumed that the erosion process is mainly driven by the discharge of the pore fluid (Vardoulakis et al. 1996; Stavropoulou et al. 1998). These assumptions can also be manifested thermodynamically (Steeb and Diebels 2003b; Steeb et al. 2004) and experimantally (Skjeerstein et al. 1997). Thus several constitutive equations are presented taking the effects of internal erosion into account. The paper is closed with several one- and two-dimensional numerical experiments based on Galerkin finite elements.