Permeability of displaced fractures

Flow along fractures becomes increasingly important in the context of geo-engineering applications. Commonly, the permeability of fractures is approximated using the cubic law assumption. However, fracture flow is influenced by the surface roughness and the relative shear displacement. A numerical approach was used which calculates the flow pattern within a rough fracture. Therefore, fracture surfaces are generated using a power spectral density function and fracture flow is simulated under the incompressible Navier Stokes approximation. It is shown that the cubic law solution overestimates the permeability as modeled by the 3D numerical simulation of flow in fractures.