Lattice Boltzmann modelling of intrinsic permeability

TL;DR

This paper examines how the Lattice Boltzmann method models intrinsic permeability in porous media, emphasizing the importance of low Knudsen numbers for accurate Navier-Stokes level simulations, especially in gas flows through ultra-tight media.

Contribution

It clarifies the conditions under which LBM accurately reproduces Navier-Stokes flow properties in porous media, highlighting the role of high-order moments and rarefaction effects.

Findings

High-order moments in LBM are significant for gas flows in ultra-tight media.

Low Knudsen number is essential for LBM to match Navier-Stokes predictions.

Neglecting high-order moments can lead to inaccuracies in permeability estimation.

Abstract

Lattice Boltzmann method (LBM) has been applied to predict flow properties of porous media including intrinsic permeability, where it is implicitly assumed that the LBM is equivalent to the incompressible (or near incompressible) Navier-Stokes equation. However, in LBM simulations, high-order moments, which are completely neglected in the Navier-Stokes equation, are still available through particle distribution functions. To ensure that the LBM simulation is correctly working at the Navier-Stokes hydrodynamic level, the high-order moments have to be negligible. This requires that the Knudsen number (Kn) is small so that rarefaction effect can be ignored. In this technical note, we elaborate this issue in LBM modelling of porous media flows, which is particularly important for gas flows in ultra-tight media.