Analytical and Numerical Assessment of Hydraulic Properties of 3D Partially-Open Rock Fractures

Modeling fractured reservoirs requires an accurate assessment of the hydraulic properties of discrete fractures. High-resolution Navier-Stokes simulations provide an accurate description of the flow within the fractures, including fracture upscaling. However, its excessive computational requirements make it impractical. The traditionally used cubic law for fracture upscaling is known for its poor accuracy. This work introduces a new analytical model based on cubic law to estimate hydraulic properties of 3D rock fractures with the irregular contact-area distribution. We first briefly review the applicability of the existing models in the literature. Most of the current models exhibit major limitations related to prediction accuracy and practicality. For instance, most models neglect the effect of contact-area distribution. As a result, they fail to capture properly the heterogeneous and anisotropic flow behaviors caused by irregular contact-area distribution. In addition, some models work well only for idealized cases, such as parallel-smooth fractures with specific shapes of contact areas. Others are only valid for cases with fractional contact area and relative roughness less than certain values. Alternatively, we propose a dynamic indicator using a particle-percolation approach to quantify the effect of the contact-area distribution. We then introduce a more general modified cubic law, which accounts for different factors, including variable aperture, roughness, flow tortuosity, and contact-area distribution. The proposed model predictions are then compared with the solutions of the 3D high-resolution Navier-Stokes simulations and experimental measurements collected from public resources. We assess the predictability of our model and benchmark it with other existing models from the literature with dozens of fracture cases. We show significant superiority of our model compared with other existing models, especially for cases with pronounced fracture anisotropy where the impact of the fracture contact area is dominant. Moreover, results show that the hydraulic aperture decreases with the increase of frictional contact area almost linearly. The contact-area distribution shows a significant impact on hydraulic properties even with the same size of contact regions. We introduce a new analytical model to estimate the hydraulic properties of 3D partially-open rock fractures. Based on our benchmark that included dozens of fractures, our model is superior to commonly used models in the literature. The proposed model also retains the simplicity and efficiency of the cubic law, and can be easily implemented in workflows for reservoir characterization and modeling.