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

摘要

This paper is devoted to the modelling of isothermal low Reynolds and Mach numbers transient compressible flow through porous media. Traditionally, this type of flow at the macroscopic level is described by the classical Darcy's law combined witha mass balance that includes the transient term. This model is called the 'classic model'. The aim of this paper is to explore the validity of this classic model. To this end, the flow of an ideal gas is considered within two-dimensional model porousmedia. The flow is due to the imposed pressure variations at the outlet of the fluid domain. At the microscopic level, the flow is computed by solving the full compressible Navier-Stokes equations in two dimensions. Special attention is given to theoutlet boundary conditions. The analysis is based on the comparison between the macroscopic data, obtained on the one hand by spatially averaging the microscopic results, and on the other hand by solving the problem directly at the macroscopic level.Situations for which a good agreement is found between the two series of data and situations for which discrepancies are observed are exhibited. These various behaviours are discussed in terms of the various time scales controlling the flow and areexplained by analysing the flow structure at pore level.