Impact of local roughness gradients on laminar flow within granite fractures

Abstract Accurately predicting fluid dynamics in crystalline rock remains fundamental to deep geothermal reservoir management. In particular, within the wider pressure-stimulated zones of geothermal reservoirs, high fluid pressures drive low effective normal stress conditions, often resulting in normal opening or shear displacement with minimal abrasion. This study investigates the relationship between granitic fracture roughness and the resulting flow behavior under these conditions. While global surface statistics are frequently used to characterize fractures, this study investigates whether local topography fluctuations are a more critical factor. We conducted high-resolution topography measurements of granite fracture samples from three locations next to the geothermal anomaly of the Rhine Graben. Our analysis reveals that local fluctuations in the roughness height gradient dominate the evolution of the fracture aperture during shear. The resulting fracture voids exhibit mean apertures up to 2 mm larger than conventional models suggest, leading to a decreased normalized local aperture distribution, widening with shear distance. To quantify the fluid dynamic impact of these geometric shifts, we employed a dual-modeling approach applying laminar flow at low Reynolds numbers: a 1D model was used to isolate how the width of the aperture distribution affects the fracture hydraulics, while a 3D model investigated how the overall aperture increase governs the flow direction. Our results demonstrate that the local height gradients of natural fracture surfaces significantly increase hydraulic conductivity by expanding the mean aperture. However, an aperture distribution width of 18% (e.g. introduced by fracture shearing) leads to a pressure increase of above 25% compared to a parallel plate assumption. Furthermore, the increased aperture in sheared fractures was found to reduce spatial flow non-uniformity. These findings suggest that conventional models should be expanded beyond global statistics to integrate the geometrical effects of natural, extreme local height gradients by increasing the fracture mean aperture.