Permeability in fixed beds of spheres with size distributions and stochastically generated porous media analogs

We present a numerical study on the permeability in fixed beds of spheres with binary size distributions. The two particle species were randomly mixed and pressure gradients were applied to generate fluid flow through the particle assembly. The flow was resolved by a lattice Boltzmann method, and the drag forces on the particles were averaged and analyzed. In this study, the total volume fraction of the fixed bed was varied between 0.1 and 0.4, the volume fraction ratio from 1:1 to 1:6, and the particle size ratio from 1:1.5 to 1:4. A drag law for bidisperse fixed beds was established and extensions to fixed beds with polydisperse or continuous size distributions were proposed. If the size distribution is Gaussian, the permeability can be well approximated by that of a monodisperse fixed bed where the size of spheres equals the Sauter mean of the size distribution. If the size distribution is log-normal, an additional correction that is a function of the first, second and third order moments of the sphere size distribution may be needed. We constructed stochastic 2D and 3D porous media models using angular grains. While the permeability of 2D geometries is much smaller than the prediction of the drag law, the permeability of 3D geometries agrees very well with the prediction.