Fluid Circulation in Coupled Free and Porous Domain: Implications of Porous Media Heterogeneity

Abstract

Fluid flow in coupled free and porous domain, particularly when the porous medium is heterogeneous, is encountered in many hydro-environmental conditions. These include, e.g., groundwater hydrology, conjunctive surface and subsurface flow, mud cake formation during drilling of oil wells and others. One of the most difficult problems in the study of coupled flow behaviour has been the development of a universally applicable modelling scheme for combining the flow regimes. This is because the free/porous interfacial properties (e.g., shear-stress; velocity slip) that determine the coupled flow behaviour are difficult to determine experimentally. On the other hand, the implications of various forms of heterogeneity in the porous media properties can be very different on the fluid flow behaviour. Difficulties may also arise in coupling the model equations (e.g., Navier-Stokes for free flow region and the Darcy Equation for the porous flow region) that govern the fluid flow in the individual regions. Consequently, models of coupled free and porous flow for hydro- environmental conditions are not very well developed at the moment. Our previous work suggests that fluid in the porous section may circulate because of complex (variable) pressure distributions in the domain. In this paper, we aim to analyse how porous media heterogeneity affects the flow circulation in the porous section of a coupled free and porous domain and subsequently the overall flow behaviour. For this purpose, we analyse flow patterns for several different domains made up of two porous layers with differing permeabilities. The governing model equations are discretised and solved using the standard finite volume method on a staggered (cell centred) mesh. The temporal discretisation is done using the implicit method. An in-house graphical user interface (GUI) has also been created specifically to aid in the visualisation of otherwise complex flow patterns. The GUI contains many plot (post processing) options that provide a comprehensive tool for the analysis of hydrodynamics and contaminant motion (not discussed in this paper) in coupled free and porous flow domains. The effects of altering the aspect ratio of the domain on the coupled flow pattern have also been analysed. This paper promises to bring a new dimension to the existing knowledge on coupled free and porous flow behaviour.