Simulation of flow through a single fracture calibrated with air permeameter measurements Marco Fuchs, Sina Hale, Gabriel C. Rau, Kathrin Menberg, Philipp Blum

Determining fluid flow through natural fractures is an important task in many geoscience-related fields, such as geothermics. In order to estimate crucial parameters of single fractures controlling the flow and flow distribution, for example hydraulic apertures, hydro-mechanical numerical models have been established in recent years in addition to experimental methods. Although models enable a greater variety of analyses, they still require time-consuming processing before and after the simulation. This study presents a novel workflow for hydro-mechanical modeling of a single fracture, with a particular focus on simplifying and shortening data preparation and calibration. First, a Python code matches laser scans of two fracture surfaces by enabling translation in the x-y-direction, minimizing the average mechanical aperture between the fracture surfaces, and automatically generating an input file for numerical modeling in MOOSE. Hydraulic simulations are conducted representing the fracture as a 2D-domain in a 3D-environment and computing Darcy velocities based on the cubic law. The additional use of an external mechanical contact model enables theoretical deformation of the fracture due to normal stress and thus estimation of flow under different lithostatic pressures representative of depths between 50-5,000 m. Subsequently, a mobile air permeameter is used to obtain calibration data. The entire workflow was tested on a bedding joint in a sandstone block sample (Flechtinger Sandstone, North German Basin). Initial hydraulic simulations without mechanical stress result in hydraulic apertures between 509 µm and 604 µm depending on the matching type, whereas the measured aperture is 82.2 µm. Consequently, the surfaces are matched by preconditioning of the initial contact area. The best consistency between measured and modelled hydraulic aperture is achieved when the contact area is equivalent to 33.5 % of the fracture surface. In addition, the velocity distribution in the fracture indicates that the flow generally occurs along few preferential pathways that are structurally predetermined by smaller fissures or mineralogically distinct veins characterized by higher mechanical apertures or smoother mineral surfaces. Due to the high proportion of contact area, the flow through the fractures is highly localized. The results of the mechanically deformed fractures illustrate an exponential reduction of the hydraulic apertures with depth. The hydraulic aperture converges at approximately 50 µm which is representative of depths that are significantly larger than 5,000 m. The change of the pathway distribution and the exponential reduction of hydraulic apertures at increasing contact area seem realistic and are comparable to results of other studies. Although the preconditioned contact area of 33.5 % appears to be very high, initial contact areas of up to 20 % were also found in other studies of the Flechtinger Sandstone. In conclusion, this study displays a less time-consuming workflow compared to conventional methods. In future work, a further adaptation could be achieved by creating the surface scans using the dense image matching (DIM) method, which is more flexible and less cost-expensive as laser scanners.