Stiff- and Compliant-porosity Based Model of Permeability - Theory and Experiments

Relation between porosity and permeability is not unique. We propose that comparison of functional dependencies of both, porosity and permeability, on stress provides useful constraints for their relation. Such a comparison shows which part of the void space in rocks controls the permeability, the compliant porosity or the stiff one. The compliant porosity (including very thin cracks and grain-contact vicinities) usually controls load dependencies of elastic moduli of rocks. This leads to exponentially-saturating functional dependencies of elastic properties on effective stress. Stiff pores (high-aspect-ratio pores) are less significant by loads from low to moderate ones (several tens of MPa). However, stiff pores can be of importance for the stress dependency of permeability. We propose a rather general model of permeability as a function of the stiff and compliant porosity. The model includes possibility, that in different rocks permeability can be controlled by stiff pores or, alternatively, by compliant pores or, finally by a combination of them. This model provides a powerlaw or an exponential differential-pressure dependency or a mixed behaviour of permeability in these situations, respectively. We show experimental results, on samples from a broad data basis of sedimentary rocks of Russian Perm region, indicating these types of behaviour.