Variable density flow in porous media. A study by means of pore level numerical simulations

This paper is devoted to the modelling of isothermal low Reynolds and Mach numbers transient compressible flow through porous media. Traditionally, th is type of flow at the macroscopic level is described by the classical Darc y's law combined with a mass balance that includes the transient term. This model is called the 'classic model'. The aim of this paper is to explore t he validity of this classic model. To this end, the flow of an ideal gas is considered within two-dimensional model porous media. The flow is due to t he imposed pressure variations at the outlet of the fluid domain. At the mi croscopic level, the flow is computed by solving the full compressible Navi er-Stokes equations in two dimensions. Special attention is given to the ou tlet boundary conditions. The analysis is based on the comparison between t he macroscopic data, obtained on the one hand by spatially averaging the mi croscopic results, and on the other hand by solving the problem directly at the macroscopic level. Situations for which a good agreement is found betw een the two series of data and situations for which discrepancies are obser ved are exhibited. These various behaviours are discussed in terms of the v arious time scales controlling the flow and are explained by analysing the flow structure at pore level. Copyright (C) 1999 John Wiley & Sons, Ltd.