An Accurate Cubic Law for the Upscaling of Discrete Natural Fractures

Abstract Modeling fluid flow in fractured reservoirs requires an accurate evaluation of the hydraulic properties of discrete fractures. Full Navier-Stokes simulations provide an accurate approximation of the flow within fractures, including fracture upscaling. However, its excessive computational cost makes it impractical. The traditionally used cubic law (CL) is known to overshoot the fracture hydraulic properties significantly. In this work, we propose an alternative method based on the cubic law. We first develop geometric rules based on the fracture topography data, by which we subdivide the fracture into segments and local cells. We then modify the aperture field by incorporating the effects of flow direction, flow tortuosity, normal aperture, and local roughness. The approach is applicable for fractures in 2D and 3D spaces. This paper presented almost all existing CL-based models in the literature, which include more than twenty models. We benchmarked all these models, including our proposed model, for thousands of fracture cases. High-resolution simulations solving the full-physics Navier-Stokes (NS) equations were used to compute the reference solutions. We highlight the behavior of accuracy and limitations of all tested models as a function of fracture geometric characteristics, such as roughness. The obtained accuracy of the proposed model showed the highest for more than 2000 fracture cases with a wide range of tortuosity, roughness, and mechanical aperture variations. None of the existing methods in the literature provide this level of accuracy and applicability. The proposed model retains the simplicity and efficiency of the cubic law and can be easily implemented in workflows for reservoir characterization and modeling.