Flow stability and permeability in a nonrandom porous medium analog

The estimation of the permeability of porous media to fluids is of fundamental importance in fields as diverse as oil and gas industry, agriculture, hydrology, and medicine. Despite more than 150 years since the publication of Darcy's linear law for flow in porous media, several questions remain regarding the range of validity of this law, the constancy of the permeability coefficient, and how to define the transition from Darcy flow to other flow regimes. This study is a numerical investigation of the permeability and flow stability in a nonrandom quasi-tridimensional porous medium analog. The effect of increasing pressure gradient on the velocity field and on the estimation of Darcy and Darcy–Forchheimer coefficients is investigated for three different obstacles radius. The transition from Darcy flow to nonlinear behavior is associated with the formation of jets in the outlet of the porous medium and development of flow instabilities. Different representations of the Reynolds number proved adequate to detect deviation from the linear law. The instantaneous permeability calculated at each pressure gradient was sensitive to flow velocity, in agreement with previous studies stating that permeability cannot be conceptualized as a constant for real flows.