Abstract 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.

中文翻译：

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屈服幂律灌浆径向传播到饱和水均质裂缝中

摘要 本研究提出了均质裂缝（光滑平行板）之间屈服幂律流体单相径向流动的解析解，涵盖了屈服幂律流体的特殊情况，即 Herschel-Bulkley、Bingham 和 power定律流体，以及牛顿流体。首次给出了 Herschel-Bulkley 流体径向流动的解析解。推导出由屈服应力产生的活塞流区域的公式，表明它是恒定的，与屈服应力流体径向流动的半径无关，这也得到了数值模拟的验证。对于将屈服幂律灌浆注入饱和水裂缝的岩石灌浆过程建模，我们还使用雷诺方程建立了均质裂缝中两相（一个屈服幂律灌浆和一种牛顿流体）径向流的通用数学模型，该模型基于屈服幂单相径向流的导出解析解- 法律灌浆。通过求解两相径向流动问题，说明了压力分布和灌浆传播长度的演变。结果通常显示流变参数的高灵敏度以及水流和时间相关的流变特性对屈服幂律灌浆的径向传播的潜在重要影响。说明了压力分布和灌浆传播长度的演变。结果通常显示流变参数的高灵敏度以及水流和时间相关的流变特性对屈服幂律灌浆的径向传播的潜在重要影响。说明了压力分布和灌浆传播长度的演变。结果通常显示流变参数的高灵敏度以及水流和时间相关的流变特性对屈服幂律灌浆的径向传播的潜在重要影响。