Effect of Porosity Gradient on the Permeability Tensor

ABSTRACTExperimental investigations often reveal that there is a correlation between porosity and permeability in rocks. The most commonly used model to predict the porosity–permeability relation is due to Kozeny–Carman or its many modifications. However, these models are problematic because they always involve an empirical constant and, in macroscopically heterogeneous porous media with non‐uniform porosity, more than one empirical constant would be required. Moreover, the tensor character of the permeability is not accounted for when the permeability is conceptualized as a plain function of the porosity. To overcome these limitations, we devise an approach by analysing the drag force in the volume averaging framework of poroelasticity. This allows us to deduce an expression for the inverse permeability tensor. It is the sum of the inverse of the permeability pertaining to a representative volume element and the second spatial derivative of porosity. Therefore, the gradient of porosity changes the permeability depending on the variations of macroscopic porosity variations. This result is thought to be relevant in applications where porosity maps are converted into permeability maps.