水力压裂中多裂缝间相互干扰力学分析

将复变函数理论与位错理论相结合 ,在考虑了裂缝表面有流体压力作用且裂缝间存在相互干扰的情况下 ,建立了无限大介质中裂尖应力强度因子的数学模型 ,利用该模型可对水力压裂中多裂缝间的相互干扰进行力学分析。假设裂缝沿着垂直于局部最大周向拉应力方向扩展 ,应用数值方法对所建立的数学模型求解 ,得到裂尖的应力强度因子及转角。数值计算结果表明 ,裂缝间存在相互干扰时所产生的剪切应力强度因子远远小于法向应力强度因子。当两个裂缝尖端垂向距离为零时 ,法向应力强度因子达到最大值。两个裂缝尖端没交叠之前裂缝基本沿着轴线扩展 ;当尖端交叠面积较小时 ,两裂尖偏离自己的轴线向避开对方的方向扩展 ;当尖端交叠面积较大时 ,两裂缝向靠拢对方的方向扩展 ,最终将贯通在一起

Mechanism of multi-fracture interaction in multi-layer hydraulic fracturing

Based on the theories of complex function and dislocation, a mathematical model for solving the stress strength of multiple cracks in infinite plate was developed, in consideration of the interactions between cracks and fluid pressure loaded on the surface of every fracture. The mechanism of multi crack interaction can be well explained with the mathematical model especially for hydraulic fracturing. It is assumed that the cracks propagate in the direction normal to the local maximum of tensile stress, both the intensity factors and the cracks propagation directions can be obtained using the solution of above model with numerical method. The calculated results show that the shear intensity factor is considerably smaller than the normal intensity factor, and the normal intensity factor has a maximum value when the vertical distance between two fractures is zero. The fractures tend to enhance propagation until the tips are overlapped. The two fractures pass over with each other when a small overlap appears, and they are approached when a large overlap exists. Finely, they are impeded with each other.