Lattice-Boltzmann computation of hydraulic pore-to-pore conductance in packed beds of uniform spheres

This paper presents a study on pore conductance in packed beds of uniform spheres. Fluid flow through the packed beds is simulated by a parallel Lattice-Boltzmann (LB) model. To facilitate a pore-level analysis, the void spaces within beds are divided into interconnected pore elements, and the flow fields in each pore element are reconstructed from the LB-simulated results. By this way, the flow structures are effectively identified in pores regardless of their complicated shapes. The reconstructed pore-flow data are employed to determine the hydraulic pore-to-pore conductance, which is used in pore network model to calculate bulk permeability. Results show that as bed porosity increases, the hydraulic pore-to-pore conductance presents a transition from one-peak distribution to wide distribution. Furthermore, a new model based on the LB reconstructed pore radius is proposed, which provides predictions of permeability much closer to the Carman-Kozeny predictions compared to the previous literature predictions based on the use of hydraulic and equivalent radii and/or geometric correction functions employed in the Hagen-Poiseuille expression for fluid flow in cylindrical tubes.