Significance of the dynamic stress perturbations induced by hydraulic fracturing

Hydraulic fracturing and microseismicity generation and radiation are dynamic processes. The associated dynamic stress perturbations could play a significant role in relevant studies, such as activation of weak planes including natural fractures, bedding planes, etc. We study how different the dynamic and static stress perturbations could be during hydraulic fracturing. Our work is based on a 2D plane-strain framework. A dynamic finite element method is applied to solve the equations of motion. The static stress perturbations are obtained when the models reach static equilibrium (i.e., after generated seismic waves die out). We compare the static and dynamic stress perturbations at a moment when a hydraulic fracture (HF) propagates to a certain length. Mohr circle analysis shows that around the HF the Mohr circle based on a dynamic stress tensor is closer to a failure line than that based on a static stress tensor. The peak static and dynamic stress perturbations during the process are also compared. We conclude that the absolute values of the peak dynamic stress perturbations are always greater than that of the peak static stress perturbations, especially in the area close to the HF and its tips. The effect of injection rates on the static and dynamic stress perturbations is also studied. The largest peak static and dynamic stress perturbations during the hydraulic fracturing process are measured. The absolute values of both the largest peak dynamic and static stress perturbations increase with injection rates. The absolute values of the difference between the largest peak dynamic and static stress perturbations also increase with injection rates due to more significant dynamic effects.

水力压裂以及微地震的产生和传播是动态过程。相关的动态应力扰动在诸如天然裂缝、层面等软弱面的激活等相关研究中可能起着重要作用。我们研究在水力压裂过程中动态和静态应力扰动可能存在的差异。我们的工作基于二维平面应变框架。采用动态有限元方法来求解运动方程。当模型达到静态平衡时（即产生的地震波消失后）获得静态应力扰动。我们在水力裂缝（HF）扩展到一定长度的时刻比较静态和动态应力扰动。莫尔圆分析表明，在水力裂缝周围，基于动态应力张量的莫尔圆比基于静态应力张量的莫尔圆更接近破坏线。还比较了过程中的静态和动态应力扰动峰值。我们得出结论，动态应力扰动峰值的绝对值总是大于静态应力扰动峰值的绝对值，尤其是在靠近水力裂缝及其尖端的区域。还研究了注入速率对静态和动态应力扰动的影响。测量了水力压裂过程中最大的静态和动态应力扰动峰值。最大动态和静态应力扰动峰值的绝对值都随注入速率的增加而增加。由于动态效应更显著，最大动态和静态应力扰动峰值之间差值的绝对值也随注入速率的增加而增加。