Permeability dependency on stiff and compliant porosities: a model and some experimental examples

The relation between porosity and permeability is not unique. We show that stress dependencies of both porosity and permeability can provide useful information clarifying this relation. We propose that comparison of the functional dependency of porosity and permeability on stress shows which part of the void space in rocks controls the permeability, the compliant porosity or the stiff porosity. The compliant porosity (including very thin cracks and grain-contact vicinities) usually controls the stress dependencies of elastic moduli of rocks. One then observes exponential-like dependencies of elastic properties on effective stress. Stress-induced deformation of stiff pores (equant pores) have less significance for stress dependencies of elastic properties on loadings of low to moderate magnitudes (several tens of MPa). However, such pores can play a significant role in 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 the possibility that, in different rocks, permeability can be controlled by stiff pores or, alternatively, by compliant pores, or, finally, by a combination of these. This model predicts a functional dependency of permeability on stress, ranging from power-law to exponential-law and to a mixed behavior of permeability in these situations, respectively. We show experimental results for four samples of sedimentary rocks from oil reservoirs of the Russian Perm region indicating these types of behavior.