Herschel–Bulkley浆液在裂隙中的扩散规律研究

Diffusion of Herschel-Bulkley slurry in fractures

基于柱坐标系下的流体连续性方程和动量方程,对Herschel-Bulkley浆液在光滑倾斜裂隙内做径向扩散流进行了理论推导,讨论了灌浆时间、灌浆压力、流变指数、裂隙开度及倾角对扩散规律的影响。研究结果表明:在注浆压力恒定的灌浆过程中,存在一极限扩散半径,且随着扩散范围的增大,进浆量逐渐降低,灌注难度逐渐增大;提高注浆压力以及降低浆液的流变指数有利于扩大浆液的扩散范围,且裂隙倾角越大,顺坡向与逆坡向的扩散半径差值也越大,特别是对于流变指数n小于1的剪切稀释浆液其差值尤为明显。该结果由于综合了牛顿、宾汉塑性和幂律型流变模式流体的扩散规律,从而为更好地认识各类非牛顿流体在岩体裂隙、界面、裂缝中的流动规律提供了理论参考。

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.