Dynamic permeability of porous media by the lattice Boltzmann method
Résumé
The lattice Boltzmann method (LBM) is applied to calculate the dynamic permeability K(omega) of porous media; an oscillating macroscopic pressure gradient is imposed in order to generate oscillating flows. The LBM simulation yields the time dependent seepage velocity of amplitude A and phase shift B which are used to calculate K(omega). The procedure is validated for plane Poiseuille flows where excellent agreement with the analytical solution is obtained. The limitations of the method are discussed. When the ratio between the kinematic viscosity and the characteristic size of the pores is high, the corresponding Knudsen number Kn is high and the numerical values of K(omega) are incorrect with a positive imaginary part; it is only when Kn is small enough that correct values are obtained. The influence of the time discretization of the oscillating body force is studied; simulation results are influenced by an insufficient discretization, i.e., it is necessary to avoid using too high frequencies. The influence of absolute errors in the seepage velocity amplitude delta A and the phase shift delta B on K(omega) shows that for high omega even small errors in B can cause drastic errors in Re[K(omega)]. The dynamic permeability of reconstructed and real (sandstone) porous media is calculated for a large range of frequencies and the universal scaling behavior is verified. Very good correspondences with the theoretical predictions are observed. (C) 2013 Elsevier Ltd. All rights reserved.