On the effect of flow regime and pore structure on the flow signatures in porous media

Abstract

In this study, lattice Boltzmann method (LBM) is utilized for three-dimensional simulation of fluid flow through two porous structures, consisting of grains with the same diameter: (i) a homogeneous porous domain, in which the grains are placed with a simple cubic packing configuration, and (ii) a randomly packed porous domain. An ultra-fine mesh size is considered to perform the simulations in three orders of magnitude of Reynolds number (Re), covering laminar to turbulent flow regimes, and capture different flow signatures. Pore velocity fields are derived, and their sample probability density functions (PDF) are analyzed vs time to investigate the dynamics of the flow. The analysis of the PDFs clearly shows that stagnant zones play a significant role in the formation of the pore flow fields, manifested by multimodal PDFs, and the distribution of the velocities in porous media at various Re cannot be characterized by a single PDF model regardless of the pore structure. While the velocities at the stagnant regions and in the vicinity of the solid boundaries are primarily affected by the viscous forces and exhibit a power-law PDF at different Re, the velocities in the main (preferential) flow pathways away from the boundaries are shown to be influenced by the inertial forces, hence having an exponential PDF when Re is low. At high Re, however, depending on the tortuosity of the porous structure, the velocities may exhibit an exponential or even Laplace PDF.