Quantification of Linear and Non-Linear Flow Behaviours in a Rock Fracture with Complex Void Geometry

Abstract

Understanding the process of fluid flow through fractured rock in subsurface engineering applications has been an active field of research for decades. Accurate modelling of the process is essential to providing guidance for the development of underground projects and reduction of associated risks. This work focuses on the study of flow behaviours in a single rock fracture with complex void geometry, which is fundamental to larger scale flow-related problems in fractured rocks. In this research, the effects of aperture variation, tortuosity and local roughness of fracture surfaces are quantified over segmented areas to develop a more accurate modified cubic law that improves flow prediction in rock fractures with rough walls. To account for the flow non-linearity when inertial effects become significant, new approximate analytical solutions of two-dimensional (2D) Navier-Stokes equations are derived under both the pressure boundary condition (PBC) and flow rate boundary condition (FBC) using the perturbation method. Considering the slowly varying feature of fracture apertures, the ratio of aperture variation to fracture length, instead of the commonly used ratio of mean aperture to fracture length, is used as the perturbation parameter in our solutions. The derived solutions are applied to 2D symmetric wedges and sinusoidal fractures, and it is found that the FBC solution provides more accurate flow estimations, due to a more precise quantification of inertial effects. The derived FBC solution is then extended to asymmetric geometries for more realistic representations of fracture voids at pore-scale. A non-linear Reynolds equation is then developed based on the derived FBC solution for rough rock fractures and results have shown a close agreement with both experiments and flow simulations in capturing the non-linear feature of flow through the fracture.