Mechanical Stiffness and Permeability of a Reservoir‐Scale Rough Fracture During Closure

Abstract We study how the normal stiffness and the permeability of a realistic rough fracture at the field scale are linked and evolve during its closure up to the percolation threshold. We base our approach on a well‐established self‐affine geometric model for fracture roughness, which has proven to be a relevant proxy from laboratory to multi‐kilometer scales. We explore its implications for fracture apertures in reservoir‐scale open channels. We build our approach on a finite element model using the MOOSE/GOLEM framework and conduct numerical flow‐through experiments in a 256 granite reservoir hosting a single, partially sealed fracture under variable normal loading conditions and undrained conditions. Navier‐Stokes flow is solved in the embedded 3‐dimensional rough fracture, 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 including mechanisms that impact the contact surface geometry like asperity yield and deposit of fracture‐filling material in the open space of the rough fracture. The largely observed stiffness characteristic is shown to be related to the self‐affine property of the fracture surface. A strong anisotropy of the fracture permeability is evidenced when the fluid percolation thresholds are exceeded in two orthogonal directions of the imposed pressure gradient. We propose a unifying physically based law for the evolution of stiffness and permeability in the form of an exponential increase in stiffness as permeability decreases.