A Poroelasticity Model Using a Network-Inspired Porosity-Permeability Relation

Abstract

Compressing a porous material or injecting fluid into a porous material can induce changes in the pore space, leading to a change in porosity and permeability. In a continuum scale PDE model, such as Biot’s theory of linear poroelasticity, the Kozeny–Carman equation is commonly used to determine the permeability of the porous medium from the porosity. The Kozeny–Carman relation assumes that there will be flow through the porous medium at a certain location as long as the porosity is larger than zero at this location. In contrast, from discrete network models it is known that percolation thresholds larger than zero exist, indicating that the fluid will stop flowing if the average porosity becomes smaller than a certain value dictated by these thresholds. In this study, the difference between the Kozeny–Carman equation and the equation based on the percolation theory, is investigated.