Inertial Effects on Fluid Flow through Disordered Porous Media

We study the fluid flow through disordered porous media by numerically solving the complete set of the Navier-Stokes equations in a two dimensional lattice with a spatially random distribution of solid obstacles (plaquettes). We simulate viscous and non-viscous flow through these idealized pore spaces to determine the origin of the deviations from the classical Darcy's law behavior. Due to the non-linear contribution of inertia to the transport of momentum at the pore scale, we observe a typical departure from Darcy's law at sufficiently high Reynolds numbers. Moreover, we show that the classical Forchheimer equation provides a valid phenomenological model to correlate the variations of the friction factor of the porous media over a wide range of Reynolds conditions.