Dynamic permeability of porous media by the lattice Boltzmann method

•Dynamic permeability of porous media.•Limitations of the LBM method: High Knudsen numbers or high frequencies.•Confirmation of a universal scaling.

The lattice Boltzmann method (LBM) is applied to calculate the dynamic permeability K(ω)K(ω) 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(ω)K(ω). 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(ω)K(ω) 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 δAδA and the phase shift δBδB on K(ω)K(ω) shows that for high ωω even small errors in B   can cause drastic errors in ReK(ω). 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.

Graphical abstractThe lattice Boltzmann method (LBM) is applied to calculate the dimensionless dynamic permeability K′0(ω′c) of porous media for a dimensionless frequency ω′c. The real and imaginary parts of K′0(ω′c) are represented; the solid lines correspond to Poiseuille flows and the dots to various geometries.Figure optionsDownload full-size imageDownload as PowerPoint slide