A Multiscale Microstructural Model of Permeability in Fractured Solids

We discuss a microstructural model of permeability in fractured solids, where fractures are modeled as recursive families of parallel, equidistant faults. Faults are originated by the attainment of a resistance threshold under the action of a confinement pressure over an initially undamaged, fully elastic matrix, not necessarily isotropic. The initially undamaged matrix might possess a natural permeability, which is modified by the progressive damage of the rock. The particular organization of the micro-faults considered in the model allows to define analytically the equivalent permeability of the solid. The model is particularly appealing to describe the permeability of rock undergoing the process of fracking, in a form that has great computational advantages, since the approach does not track explicitly the formation of individual macro-faults.