Hydrodynamic Porosity: A New Perspective on Flow through Porous Media, Part II

Abstract

In this work, we build upon our previous finding that hydrodynamic porosity is an exponential function of pore-scale flow velocity (or interstitial Reynolds number). We previously discovered this relationship for media with a square cavity geometry—a highly idealized case of the dead-ended pore spaces in a porous medium. Thus, we demonstrate the applicability of this relationship to media with other cavity geometries. We do so by applying our previous analysis to rectangular and non-rectangular cavity geometries (i.e., circular, and triangular). We also study periodic flow geometries to determine the effect of upstream cavities on those downstream. We show that not only does our exponential relationship hold for media with a variety of cavity geometries, but it does so almost perfectly with a coefficient of determination (R2) of approximately one for each new set of simulation data. Given this high fit quality, it is evident that the exponential relationship we previously discovered is applicable to most, if not all, unwashed media.