基于互补算法的水力裂缝与天然裂缝相互作用边界元模型

Boundary element model for mechanical interaction between hydraulic fracture and natural fracture based on complementary algorithm

水力裂缝与天然裂缝的相互作用力学机制是确定水力压裂裂缝扩展形态的关键。基于天然裂缝变形与受力状态,推导天然裂缝变形的互补约束条件,并结合间断边界元,建立水力裂缝与天然裂缝相互作用的力学分析模型。通过压剪裂缝理论解和求解天然裂缝力学响应的试算法验证模型可靠性。以页岩气多段压裂水平井为例进行实例分析,并探讨水力裂缝与天然裂缝力学响应特征和变化规律,结果表明:基于互补算法的边界元模型计算结果与实例井微地震结果一致;水力裂缝靠近或接触天然裂缝时,水力裂缝尖端会发生钝化,天然裂缝面会发生张开或剪切,并以剪切为主;逼近角大于60°时,天然裂缝面很难发生张开;逼近角不等于90°时,水力裂缝和天然裂缝接触点与天然裂缝破裂点存在偏移;逼近角、净压力和天然裂缝摩擦因数越大,水力裂缝穿过天然裂缝可能性越大。

Mechanical interaction between a hydraulic fracture anda natural fracture is a crucial issue for analyzing hydraulic fracture growth. The complementary constraints of natural fractureswere derived from the deformation and stress state of natural fractures,then the mechanical model for solving interaction betweena hydraulic fracture and a natural fracture was established based on boundary element method. The model was validated by the analytical solution of frictional cracksand the trial method for solving mechanical response of natural fractures. A case study was conducted based on a multi-staged fractured horizontal well of shale gas,and mechanical response characteristics were investigated by the new model. Results show that results calculated by the model are consistent with the microseismic measurement result. When a hydraulic fracture contacts with a natural fracture,the hydraulic fracture tip can be blunted. The natural fracture can be opened and slipped near the contact location,and slipping zone is larger than opening zone.When the approaching angle is larger than 60°,opening of thenatural fracture is difficult to occur. The initiation location of a natural fracture is not coinciding with the contact location. The hydraulic fracture has more chances to penetrate the natural fracture under the condition of large approaching angle,net pressure and friction coefficient.