Stress-dependent permeability in sedimentary rocks: A fractal model based on poroelastic compressibilities

Stress variations in the subsurface can modify the permeability and the poroelastic compressibilities of rocks and soils. In general, stress-dependent permeability predictions are based on empirical models, which disregard the underlying connection between permeability and poroelastic compressibilites. In this work, we present a physically-based constitutive model to predict stress-induced permeability variations in sedimentary rocks accounting for the fact that drained pore compressibilities vary with the differential stress. The proposed model is based on a fractal conceptualization of the pore space and results in a closed analytical expression. We validate the proposed model with experimental measurements of pore compressibility and permeability in a series of sedimentary rocks by means of a fractal dimension parameter fitting. Results show that the corresponding fractal dimensions are in reasonable agreement with pore size distributions, obtained from thin section analysis, and capillary pressure saturation curves of the corresponding rocks, given by mercury intrusion tests. Finally, we compare the proposed model with alternative stress-dependent permeability models that are broadly used in the specific literature, such as, exponential and power law models, and attempt to provide these empirical models with a first order physical interpretation. The proposed approach and associated results may help estimating permeability from poroelastic compressibility measurements, which is, to date, widely regarded as a frontier in the overall fields of Geomechanics and Applied Geophysics.