Diffusion of Herschel–Bulkley slurry in fractures

Based on the continuity equation and the momentum equation in the cylinder coordinate, the motion equation of Herschel–Bulkley slurry front with radial flows in inclined, narrow smooth-walled fracture is theoretically derived. Then the impacts of grouting time, grouting pressure, rheological index and fracture aperture and dip angle on the slurry diffusing law are discussed in the analytical solution. The results show that a limited diffusion radius is reached for the case of constant grouting pressure. The grouting capacity decreases with the spreading of the diffusion range and the slurry becomes difficult to be injected. Furthermore, increasing the grouting pressure and decreasing the power law index are helpful to expand the spreading range. The greater the fracture dip angle, the greater the difference of diffusion radius between down-slope currents and inverse-slope currents, especially for the case of shear-thinning fluids. Because of the integration of spreading laws of fluids of Newton, Bingham plastic and Power law rheological model, this solution provides a reference for a better understanding of the flows of various non-Newtonian fluids in rock fractures, interfaces and cracks.