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考虑任意压力分布的裂缝诱导应力场计算模型及其应用
彭瑀,李勇明,赵金洲
0
(西南石油大学油气藏地质及开发工程国家重点实验室,四川成都 610500)
摘要:
通过复分析和断裂力学Westergaard应力函数方法建立局部受均匀内压力作用下的诱导应力分布模型,并以此为基本单元结合数值积分复化矩形法的思路,叠加得到考虑任意压力分布情况的诱导应力计算模型。采用先计算再虚实分离的方法进行编程,验证单元模型的精度。模拟缝内压降、裂缝不对称延伸和净压力周期性波动对裂缝诱导应力的影响。结果表明:经典的裂缝诱导应力模型仅是局部受均匀内压力模型的特解;考虑缝内压降后,远井位置形成缝网的可能性大幅度下降,天然裂缝的稳定性显著提高;裂缝不对称延伸使裂缝附近的压应力区向短半缝偏移,但远离裂缝区域的诱导应力仍关于裂缝中垂线对称;缝内净压力周期性波动对诱导应力的影响范围在五分之一半缝长以内,求解远离裂缝区域的应力时,可以将平均压力直接带入经典公式计算。
关键词:  压裂  诱导应力  净压力  不对称延伸  数学模型
DOI:10.3969/j.issn.1673-5005.2017.03.011
投稿时间:2016-06-28
基金项目:国家自然科学基金重大项目(51490653);国家“973”重点基础研究发展计划(2013CB228004)
Modeling of fracture induced stress under arbitrary pressure distribution and its application in hydraulic fracturing
PENG Yu,LI Yongming,ZHAO Jinzhou
(State Key Laboratory of Oil & Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China)
Abstract:
A new fracture induced stress model was established that can calculate the stress distribution around a section of the fracture under local pressure, in which complex analysis and the Westergaard stress function in fracture mechanics were applied. Superposition of the above model to the whole hydraulic fracture, a novel model that can compute the induced stress around the fracture under arbitrary pressures was then developed. The simulation results show that the new model has high calculation accuracy, and the classical model can be as a special case of the new model. In the simulation of the influence of pressure drop, asymmetric propagation and net pressure undulate on the induced stress, the results show that, when the pressure drop is taken into consideration, the possibility for the formation of a fracture net is decreasing rapidly from wellbore to fracture tip, but the stability of natural fractures is increasing significantly. Asymmetric propagation can lead to a compressive stress section skewing to the short half fracture, while the stress distribution far from the fracture is still symmetrical to the mid-perpendicular. The affection of the net pressure undulate is within one fifth of the half fracture length. So in this case, the average pressure can be taken into the classical model to calculate the stress distribution far from the fracture face.
Key words:  hydraulic fracturing  induced stress  net pressure  asymmetric propagation  mathematical model