Stochastic 3D Navier-Stokes Flow in Self-Affine Fracture Geometries Controlled by Anisotropy and Channeling

This study presents a probabilistic analysis of 3D Navier-Stokes (NS) fluid flow through 30 randomly generated sheared fractures with equal roughness properties (Hurst exponent = 0.8). The results of numerous 3D NS realizations are compared with the highly simplified local cubic law (LCL) solutions regarding flow orientations and regimes. The transition between linear and nonlinear flow conditions cannot be described with a generally valid critical Reynolds number (Recrit), but rather depends on the individual fracture's void geometry. Over 10% reduction in flow is observed for increased global Re (>100) due to the increasing impact of nonlinear conditions. Furthermore, the fracture geometry promotes flow anisotropy and the formation of channels. Flow perpendicular to the shearing leads to increased channeling and fluid flow (similar to 40% higher) compared to flow parallel to the shearing. In the latter case, dispersed flow and irregular flow paths cause a reduction of LCL validity. Plain Language Summary The movement of fluid and heat through fractured rocks is massively affected by the void space of the contributing fractures and the velocity of the fluid. The opposing offset of the two fracture surfaces creates complex and variable void geometries. A calculation of the expected flow rates is very difficult. In most studies, simplifications are adopted neglecting these complex features by using a plane surface and assuming that the flow is taking place smoothly. We therefore simulate the real flow using the three-dimensional fracture void space and compare the results with simpler two-dimensional models. It can be demonstrated that the difference between the two types of simulations depends not only on the local simplification but also on the flow direction within the fractures and that the difference increases with higher flow velocities. If the fractures are not considered as a whole continuum but on the local scale, preferential fluid pathways or channels are formed in which most of the flow takes place. Depending on the flow direction, channels are more or less pronounced. We can show that in well-developed channels the differences between the calculation methods are much smaller than in the other parts of the domain. Key Points Shearing of fractures generates a directional flow anisotropy, with an increased flow rate perpendicular to the shearing Preferential channels are formed which localize the largest part of the volumetric flow in small parts of the entire fracture domain Spatial differences between the complex Navier-Stokes equations and the local cubic law can be explained by channeling processes