Hydraulic Diffusivity of a Partially Open Rough Fracture

We investigate the impact of closing a fracture with rough surfaces on the fracture hydraulic diffusivity, which controls the spatiotemporal evolution of pore-pressure perturbations in geological formations, particularly those composed of an impermeable matrix and highly permeable natural fractures. We build distributions of synthetic fracture apertures at a reservoir scale ( $$\sim$$ 500 m) from a self-affine model with isotropic Hurst exponents derived from field observations of fault surfaces. To quantify the hydraulic diffusivity of rough fractures, we conduct finite element simulations of transient fluid flow in a single fracture. We use a surface representation of the fracture aperture following the Reynolds lubrication approximation. We verify that our approximation is valid for a steady-state flow and a low Reynolds number (Re $$\ll$$ 1) from the comparison with a volume-represented fracture aperture model solved by the Navier–Stokes equations for incompressible fluids (INS). Subsequently, the effective hydraulic diffusivity of the rough fracture is estimated by fitting the computed pressure field with the solution of an equivalent parallel plate model. The results show that the long-range correlation aperture field (up to the fault scale) due to self-affinity significantly affects hydraulic pressure diffusion, which is manifested as a strong variability in the pressure distribution with the orientation of the imposed pressure drop. Based on a rigid-plastic rheology, when closing the fracture stepwise from the initial contact to the flow percolation threshold, a decrease in the hydraulic diffusivity over seven orders of magnitude in one direction along the fracture but over four orders of magnitude in the perpendicular direction is obtained. Our results have strong implications for the interpretation of some measured hydraulic diffusivity data as well as for the use of hydraulic diffusivity in interpreting the spatial distribution of fluid-induced seismic events in faulted reservoirs.