A Matter of Geometry: Predicting Single Fracture Permeability by Evaluating Imaging Methods and Persistent Homology Analysis  

Fractures play a significant role in various geoscientific applications, such as nuclear waste disposal, geothermal energy, and hydrocarbon extraction. Understanding the governing hydraulic characteristics of fractures and their impact on flow processes is crucial for the success of these applications. Among the many parameters that affect fracture behavior, permeability stands out as one of the most critical. Several methods have been developed to investigate fracture permeability, including flow-through experiments and numerical hydraulic simulations. However, it is important to note that the geometry of a fracture greatly influences its permeability. This study focuses on examining different workflows to directly estimate the permeability of a single fracture based on its geometry. In the first step to achieve this, we apply and evaluate three fracture surface imaging methods: (1) handheld laser scanner (HLS), (2) mounted laser scanner (MLS), and (3) Structure from Motion (SfM). We conducted our study using a bedding joint in Flechtinger sandstone as the fracture sample. After capturing the fracture geometries using these imaging methods, we perform numerical flow simulations to estimate hydraulic apertures. Our findings reveal that due to limited resolution and accuracy, the HLS is not suitable for use in numerical flow simulations. However, MLS and SfM result in hydraulic apertures that exceed experimental air permeameter measurements (81 ± 1 µm). The hydraulic apertures obtained using MLS and SfM are 163 µm and 207 µm, respectively. To bridge the discrepancy between simulations and measurements, we stepwise increase the contact area, resulting in hydraulic apertures of 85 µm at 5 % contact area and 83 µm at 7 % contact area for MLS and SfM, respectively. In the second step, we utilize the topological persistent homology (PH) method to calculate permeability directly from the fracture geometry derived from MLS, eliminating the need for laboratory experiments or numerical simulations. We create three different datasets of the same fracture, varying in spatial resolution (200 µm, 100 µm, and 50 µm). The results from the PH analysis demonstrate hydraulic apertures ranging from 73 µm to 92 µm, which align closely with the air permeameter measurements. Notably, the accuracy of fracture permeability prediction improves with higher resolution. In summary, this study presents an effective workflow that enables the direct estimation of fracture permeability based on the geometry of a sandstone fracture. By utilizing different imaging methods and topological analysis, we provide valuable insights into understanding and predicting fracture permeability.