A numerical study of the hydrodynamic conditions in coupled free and heterogeneous porous domains

Abstract

The existence of a free flow domain adjacent to a porous medium is a common occurrence in many environmental and petroleum engineering problems. The porous media may often contain various forms of heterogeneity, e.g., layers, fractures, micro-scale lenses, etc. These heterogeneities affect the pressure distribution within the porous domains. This, in turn, may influence the hydrodynamic conditions at the free/porous domain interface and, hence, the combined flow behaviour. Under steady-state conditions, the heterogeneities are known to have negligible effects on the combined flow behaviour. However, the significance of the heterogeneity effects on coupled free and porous flow under transient conditions is not certain. In this work, numerical simulations have been carried out to investigate the effects of heterogeneity in porous media on the hydrodynamics conditions on determining the behaviour of combined free and porous regimes. The coupling of the governing equations of motion in free and porous domains has been achieved through the well known Beavers and Joseph interfacial condition. Of special interests in this work are the porous domains with flow-through ends. They represent the general class of problems where large physical domains are truncated to smaller sections for ease of mathematical analysis. However, this causes a practical difficulty in modelling such systems. This is because the information on flow behaviour, i.e., boundary conditions at the truncated sections, is usually not available. Use of artificial boundary conditions to solve these problems effectively implies imposition of conditions, which do not necessarily match with the solutions required for the interior of the domain. This difficulty is resolved in this work by employing ‘stress free boundary conditions’ at the open end of the domains, which have been shown to provide accurate results by a number of previous authors. Heterogeneity in the porous media is introduced by defining a domain composed of two layers of porous media with different values of intrinsic permeability.