Velocity Magnitude Distribution for Flow in Porous Media

Transport in porous media is dominated not only by the average fluid velocity but also by the local fluid velocities. In this study, a computational approach was used to investigate the statistical distribution of the velocity magnitude for flow through different types of porous media including sphere packings and scaffolds. The sphere packings were both ordered media, such as simple cubic, body-centered cubic, and face-centered cubic, as well as randomly packed media with monodisperse sphere packing, bidisperse sphere packing, and tridisperse sphere packing. The scaffolds were anisotropic nonwoven fibers and isotropic foam scaffolds. The main objective was to discover whether the fluid velocity follows a common statistical distribution for all types of examined porous media. The fluid flow was simulated by the Lattice Boltzmann method (LBM), and each velocity field was normalized by the mean pore velocity magnitude. Kolmogorov–Smirnov (KS) goodness-of-fit tests were used to test the hypothesis that the velocity distributions followed specific statistical probability density functions. It was found that the Weibull distribution fitted the velocity distributions in all examined porous media. Velocity distributions in the randomly packed spheres and scaffolds were represented by a single Weibull distribution, while those in ordered sphere packings followed Weibull distributions with different characteristic values. The pore size distribution for each type of porous medium configuration appeared to be important for the form of the velocity distribution.