We compare leading models for permeability evolution as a function of changing effective stress for various lithologies. In particular, the permeability compliance model as given in the literature is analyzed and compared to the cubic law, where changing pore aperture is cast in terms of pore spacing, bulk modulus, and changing pore pressure. Using equivalence relationships, it is shown that empirically derived values of permeability compliance for various lithologies can be used to determine the average spacing between pores used in the cubic law and related to the material strength of the rock (Bulk modulus). We derive equations for different rock types to calculate the pore network for each rock. In addition, we use values from the literature for bulk modulus for each lithology to calculate the permeability compliance and find excellent agreement with values for permeability evolution with changing stress found in the literature.
The cubic law predicts permeability loss under the same conditions based on the density of pores (number and size per unit volume). If a rock has a denser pore network (small s/b) it will have more pores available to accommodate a given deformation, leading to smaller permeability loss. We find that the term (s/b*1/K) found in the cubic law is proportional to the permeability compliance, where s is the average spacing between pores, b is the average pore diameter, and K is the bulk modulus. Therefore, permeability compliance can be viewed as a description of a rock’s ability to resist permeability loss due to the pore network’s compression during pressure-driven deformation.