Analysis of hydrodynamic conditions in adjacent free and heterogeneous porous flow domains

Abstract

The existence of a free-flow domain (e.g. a liquid layer) 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 domain. This 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 coupled flow behaviour. However, the significance of the heterogeneity effects on coupled free and porous flow under transient conditions is not certain. In this study, numerical simulations have been carried out to investigate the effects of heterogeneous (layered) porous media on the hydrodynamics conditions in determining the behaviour of combined free and porous regimes. Heterogeneity in the porous media is introduced by defining a domain composed of two layers of porous media with different values of intrinsic permeability. 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 interest in this work are 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 the imposition of conditions that do not necessarily match with the solutions required for the interior of the domain. This difficulty is resolved in this study by employing ‘stress-free boundary conditions’ at the open ends of the domains, which have been shown to provide accurate results by a number of previous workers. Copyright © 2005 John Wiley & Sons, Ltd.