Numerical study of inertial effects on permeability of porous media utilizing the Lattice Boltzmann Method

Abstract

The Darcy law provides the basic linear equation for single-phase fluid flow in porous media in ideally simplified conditions. The Darcy equation has been shown to be valid in flow processes happening in sufficiently low Reynolds number regimes. At higher Reynolds numbers, inertial effects cause extra hydrodynamic head loss and Darcy's law becomes invalid. The Forchheimer equation is a semi-empirical relationship which accounts for the effect of the inertial effects on apparent permeability reduction.In this research, the apparent permeability reduction due to inertial effects is studied in simple and complex porous structures. For this purpose a Lattice Boltzmann based simulator was developed to model single-phase fluid flow in porous media. The simulator was verified by experimental and analytical solution tests and then was implemented to study high Reynolds number flow processes in three dimensional regular and irregular shaped porous structures. The effects of inertial on the onset and extent of non-Darcy flow in different geometries was studied. It was also shown that the Forchheimer equation does not accurately fit the high Reynolds number flow in simple and complex porous media. It was observed that a quadratic relationship exists between the introduced “scaled permeability” and the mass flow rate in the range of moderate Reynolds numbers. A new empirical correlation was proposed that fits the scaled permeability and mass flow rate relationship results very well. The proposed correlation predicts the scaled permeability change due to inertial effects more accurate than the Forchheimer equation.