Inertial Effects on Fluid Flow through Disordered Porous Media

TL;DR

This study investigates how inertial effects influence fluid flow in disordered porous media by numerically solving Navier-Stokes equations, revealing deviations from Darcy's law at high Reynolds numbers and validating the Forchheimer equation as a model.

Contribution

It provides a detailed numerical analysis of inertial effects on flow in disordered media and confirms the applicability of the Forchheimer equation across various flow regimes.

Findings

Deviations from Darcy's law occur at high Reynolds numbers due to inertial effects.

The Forchheimer equation accurately models the flow behavior over a wide range of conditions.

Inertia significantly impacts fluid transport in disordered porous structures.

Abstract

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.