Local Hydraulic Resistance in Heterogeneous Porous Media

We examine the validity of the commonly used Hagen-Poiseuille model of local resistance of porous media using direct numerical simulations. We provide theoretical arguments that highlight possible limitations of this model and formulate a new constitutive model that is based on the circularity of iso-pressure surfaces. We compare the performance of both models on three different three-dimensional artificial porous media. We show that the new model improves the root-mean-squared-relative error from 59%, 48% and 32% for the HP model to 12%, 14% and 18% for the three porous media respectively. We anticipate that our approach may find broad application in network models of porous media that are typically build from 3D images with intricate pore geometries.