Mechanical stiffness and permeability of a reservoir-scale rough fracture during closure

Natural or artificial fluid flow in deep fractured reservoirs, such as Enhanced Geothermal Systems (EGS), is primarily controlled by open fractures and faults, and is considered a key element for hydraulic performance. Flow along these fractures is strongly affected by channeling between fracture asperities and by deposits sealing the open fracture space due to mineral precipitation. Fracture asperities and fracture sealing also impact the mechanical behavior of fractures, especially their mechanical stiffness. Here, we study both the permeability and the stiffness of a rough fracture at the field scale during its closure.We base our approach on a well established self-affine geometrical model for fracture roughness. We develop a finite element model based on the MOOSE/GOLEM framework and conduct numerical flow experiments in a 256 × 256 × 256 m^3 granite reservoir hosting a single, partially sealed fracture under variable normal loading conditions. Navier-Stokes flow is solved in the embedded 3-dimensional rough aperture, and Darcy flow is solved in the surrounding poroelastic matrix. We study the evolution of the mechanical stiffness and fluid permeability of the fracture-rock system during fracture closure by considering the asperity yield and the depositing of fracture-filling material in the open space of the rough fracture. The evolution of the fault volume, fracture normal stiffness and permeability are monitored until fluid percolation thresholds are exceeded in two orthogonal directions of the imposed pressure gradient. Finally, we propose a physically based law for the stiffness and permeability evolution as a function of the fault volume. It is demonstrated that during closure, stiffness increases exponentially as the fault volume decreases. A strong anisotropy of the fracture permeability is also evidenced when reaching percolation thresholds.