On the tensorial nature of the hydraulic aperture of rough fractures

Current fractured porous media models may account for the roughness and geometry of the fractures to upscale hydraulic apertures that represent the local aperture distributions. Still, such approaches do not discuss the tensorial nature of the hydraulic aperture, and by employing scalar representations, these models may fail to capture the anisotropy of the fluid flow in rough fractures. By mimicking natural fractures with walls of varying roughness and contact area, we derive hydraulic aperture tensors that preserve the anisotropic flow patterns enforced by local aperture distributions. This work underscores the critical need to represent hydraulic apertures as tensors to model anisotropic fluid flow in rough fractures and proposes a method for upscaling such tensors.