工程科学学报，第41卷，第4期：436-446,2019年4月 Chinese Journal of Engineering,Vol.41,No.4:436-446,April 2019 DOI:10.13374/j.issn2095-9389.2019.04.003:http://journals.ustb.edu.cn 基于最小应变能密度因子断裂准则的岩石裂纹水力压 裂研究 董卓12》，唐世斌2)区，郎颖娴2》 1)大连理工大学海岸和近海工程国家重点实验室，大连1160242)大连理工大学土木工程学院，大连116024 区通信作者，E-mail:tang shibine@dlut.eu.cn 摘要建立了考虑裂纹尖端非奇异项T应力的最小应变能密度因子断裂准则，研究了不同裂纹类型条件下T应力和泊松 比对起裂角的影响，结果表明裂纹起裂角不仅与奇异项应力强度因子有关，而且还需要考虑非奇异项T应力和泊松比的影响 作用.同时计算了含井筒对称双裂纹水力压裂模型的起裂角和临界水压，表明依据本文断裂准则计算得到理论解与实验结果 吻合良好.在此基础上，利用该准则从理论上分析了临界裂纹区尺寸、T应力、比奥系数、侧压系数、泊松比等因素对水力压裂 裂纹起裂特性的影响。参数分析表明：临界裂纹区尺寸、T应力和侧压系数对临界水压和临界起裂角有显著影响.临界水压随 着泊松比增大而减小，而临界起裂角呈现相反变化趋势.比奥系数对临界起裂角没有影响，但是在高水压条件下对起裂角具 有显著影响 关键词应变能密度因子：T应力：水力压裂：泊松比：比奥系数：起裂角：临界水压 分类号TG142.71 Hydraulic fracture prediction theory based on the minimumstrain energy density criterion DONG Zhuo),TANG Shi-bin,LANG Ying-xian!2) 1)State Key Laboratory of Coastal and Offshore Engineering,Dalian University of Technology,Dalian 116024,China 2)School of Civil Engineering,Dalian University of Technology,Dalian 116024,China Corresponding author,E-mail:tang_shibin@dlut.edu.cn ABSTRACT Hydraulic fracturing is a promising technique used in oil and gas reservoirs,enhanced geothermal systems,and coal gas production.Although its use is widespread,many aspects of hydraulic fracturing are still not well understood and need to be further in- vestigated to achieve increases in oil and gas production while mitigating the adverse aspects of hydraulic fracturing.Understanding how hydraulic pressure extends preexisting fractures and forms a complex fracture network is essential for the design and treatment of hydrau- lic fracturing.Critical water pressure and fracture initiation angle are two important parameters involved in the hydraulic fracture propa- gation process and production from a well.In the present study,a minimum strain energy density criterion,which considers the effects of Tstress and Poisson's ratio,was proposed to analyze fracture initiation during hydraulic fracturing.The fracture initiation angle for different crack types was investigated using the proposed theoretical method,and the results indicate that the fracture initiation angle is not only related to the stress intensity factor but also affected by the T-stress and Poisson's ratio.The critical water pressure and criti- cal initiation angle for two symmetric radial cracks emanating from a pressurized borehole were investigated,and the theoretical results were consistent with the experimental results.Through the proposed theoretical method,the influence of T-stress,radius of the fracture process zone,Biot's coefficient,lateral pressure coefficient and Poisson's ratio on the hydraulic fracturing behavior was analyzed.Pa- rameter analysis indicates that the radius of the fracture process zone,T-stress,and lateral pressure coefficient play an important role in the critical initiation angle and critical water pressure.The critical water pressure increases with the decrement of Poisson's ratio, 收稿日期：20180308 基金项目：国家自然科学基金面上项目(51874065)：国家自然科学基金资助项目(U1562103,51474046)工程科学学报，第 41 卷，第 4 期: 436--446，2019 年 4 月 Chinese Journal of Engineering，Vol． 41，No． 4: 436--446，April 2019 DOI: 10． 13374 /j． issn2095--9389． 2019． 04． 003; http: / /journals． ustb． edu． cn 基于最小应变能密度因子断裂准则的岩石裂纹水力压 裂研究 董 卓1，2) ，唐世斌1，2) ，郎颖娴1，2) 1) 大连理工大学海岸和近海工程国家重点实验室，大连 116024 2) 大连理工大学土木工程学院，大连 116024 通信作者，E-mail: tang_shibin@ dlut． edu． cn 摘 要 建立了考虑裂纹尖端非奇异项 T 应力的最小应变能密度因子断裂准则，研究了不同裂纹类型条件下 T 应力和泊松 比对起裂角的影响，结果表明裂纹起裂角不仅与奇异项应力强度因子有关，而且还需要考虑非奇异项 T 应力和泊松比的影响 作用． 同时计算了含井筒对称双裂纹水力压裂模型的起裂角和临界水压，表明依据本文断裂准则计算得到理论解与实验结果 吻合良好． 在此基础上，利用该准则从理论上分析了临界裂纹区尺寸、T 应力、比奥系数、侧压系数、泊松比等因素对水力压裂 裂纹起裂特性的影响． 参数分析表明: 临界裂纹区尺寸、T 应力和侧压系数对临界水压和临界起裂角有显著影响． 临界水压随 着泊松比增大而减小，而临界起裂角呈现相反变化趋势． 比奥系数对临界起裂角没有影响，但是在高水压条件下对起裂角具 有显著影响． 关键词 应变能密度因子; T 应力; 水力压裂; 泊松比; 比奥系数; 起裂角; 临界水压 分类号 TG142. 71 收稿日期: 2018--03--08 基金项目: 国家自然科学基金面上项目( 51874065) ; 国家自然科学基金资助项目( U1562103，51474046) Hydraulic fracture prediction theory based on the minimumstrain energy density criterion DONG Zhuo1，2) ，TANG Shi-bin1，2)  ，LANG Ying-xian1，2) 1) State Key Laboratory of Coastal and Offshore Engineering，Dalian University of Technology，Dalian 116024，China 2) School of Civil Engineering，Dalian University of Technology，Dalian 116024，China Corresponding author，E-mail: tang_shibin@ dlut． edu． cn ABSTＲACT Hydraulic fracturing is a promising technique used in oil and gas reservoirs，enhanced geothermal systems，and coal gas production． Although its use is widespread，many aspects of hydraulic fracturing are still not well understood and need to be further in￾vestigated to achieve increases in oil and gas production while mitigating the adverse aspects of hydraulic fracturing． Understanding how hydraulic pressure extends preexisting fractures and forms a complex fracture network is essential for the design and treatment of hydrau￾lic fracturing． Critical water pressure and fracture initiation angle are two important parameters involved in the hydraulic fracture propa￾gation process and production from a well． In the present study，a minimum strain energy density criterion，which considers the effects of T-stress and Poisson’s ratio，was proposed to analyze fracture initiation during hydraulic fracturing． The fracture initiation angle for different crack types was investigated using the proposed theoretical method，and the results indicate that the fracture initiation angle is not only related to the stress intensity factor but also affected by the T-stress and Poisson’s ratio． The critical water pressure and criti￾cal initiation angle for two symmetric radial cracks emanating from a pressurized borehole were investigated，and the theoretical results were consistent with the experimental results． Through the proposed theoretical method，the influence of T-stress，radius of the fracture process zone，Biot’s coefficient，lateral pressure coefficient and Poisson’s ratio on the hydraulic fracturing behavior was analyzed． Pa￾rameter analysis indicates that the radius of the fracture process zone，T-stress，and lateral pressure coefficient play an important role in the critical initiation angle and critical water pressure． The critical water pressure increases with the decrement of Poisson’s ratio