Flow of yield stress and Carreau fluids through rough-walled rock fractures: Prediction and experiments

Many natural phenomena in geophysics and hydrogeology involve the flow of non-Newtonian fluids through natural rough-walled fractures. Therefore, there is considerable interest in predicting the pressure drop generated by complex flow in these media under a given set of boundary conditions. However, this task is markedly more challenging than the Newtonian case given the coupling of geometrical and rheological parameters in the flow law. The main contribution of this paper is to propose a simple method to predict the flow of commonly used Carreau and yield stress fluids through fractures. To do so, an expression relating the "in situ'' shear viscosity of the fluid to the bulk shear-viscosity parameters is obtained. Then, this "in situ'' viscosity is entered in the macroscopic laws to predict the flow rate-pressure gradient relations. Experiments with yield stress and Carreau fluids in two replicas of natural fractures covering a wide range of injection flow rates are presented and compared to the predictions of the proposed method. Our results show that the use of a constant shift parameter to relate "in situ'' and bulk shear viscosity is no longer valid in the presence of a yield stress or a plateau viscosity. Consequently, properly representing the dependence of the shift parameter on the flow rate is crucial to obtain accurate predictions. The proposed method predicts the pressure drop in a rough-walled fracture at a given injection flow rate by only using the shear rheology of the fluid, the hydraulic aperture of the fracture, and the inertial coefficients as inputs.