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.

Automated summary

The study examines the validity of the commonly used Hagen-Poiseuille model of local resistance in porous media using direct numerical simulations, highlighting possible limitations and proposing a new constitutive model. Performance comparisons on three different artificial porous media show significant improvements in error reduction with the new model. The approach may have broad applications in network models of porous media built from intricate 3D images.