Effect of shear-thinning rheology on transition of nonlinear flow behavior in rock fracture

Understanding the nonlinear flow of non-Newtonian fluids in rock fractures is critical for underground engineering (e.g., rock grouting). However, how to evaluate the effect of shear-thinning rheology on flow nonlinearity due to fracture heterogeneity is insufficiently understood. In this study, the Herschel-Bulkley-Papanastasiou (HBP) model is proposed to simulate grout flow in fracture with contact areas. The numerical result indicates that the alterations in contact zones of fracture due to the changes in aperture increase the nonlinear flow characteristics. The decrease of shear-thinning rheology reduces the development of eddy regions under constant boundary, which delays the occurrence of significant inertial effects. The local flow within the fracture is influenced by the change in spatial viscosity caused by the rheological properties of the fluid. A quantitative method is proposed to quantify the viscous dissipation of the shear-thinning fluid based on energy balance, and the results demonstrate that strong viscous dissipation is most important for suppressing the nonlinear flow. The predictive function of the critical Reynolds number for the transition from strong to weak inertial flow regime is established. The results can provide novel perspectives and concepts for evaluating the shear-thinning fluids flow in complex fractured media.