Radial propagation of yield-power-law grouts into water-saturated homogeneous fractures

This study presents analytical solutions for single-phase radial flow of yield-power-law fluids between homogeneous fractures (smooth parallel plates), which covers the special cases of yield-power-law fluids, i.e., Herschel-Bulkley, Bingham and power-law fluids, as well as Newtonian fluids. The analytical solution for radial flow of Herschel-Bulkley fluids is given for the first time. A formula for the plug flow region created by the yield stress is deduced, showing that this is constant and independent of the radius for radial flow of yield-stress fluids, which is also verified by numerical simulations. For modeling of the rock grouting process where the yield-power-law grouts are injected into water-saturated fractures, we also established a general mathematical model for the two-phase (one yield-power-law grout and one Newtonian fluid) radial flow in homogeneous fractures using the Reynolds equation based on the derived analytical solutions for single-phase radial flow of yield-power-law grouts. By solving the two-phase radial flow problem, the evolution of pressure distribution and grout propagation length is illustrated. The results generally show the high sensitivity of the rheological parameters and the potentially important impact of water flow and time-dependent rheological properties on the radial propagation of yield power-law grouts.