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中文摘要：
考虑裂缝内流体流动和周围岩石应力变形,建立了页岩人工裂缝扩展的数学模型,分别采用有限元和扩展有限元求解裂缝流场和岩石应力场,并通过Picard迭代方法耦合求解,计算结果与经典模型结果吻合,验证了模型正确性.在此基础上,分析了岩石弹性模量、Poisson（泊松）比和注入速度对裂缝几何形态的影响以及水力裂缝任意角度逼近天然裂缝扩展动态.结果表明：弹性模量和注入速度对裂缝形态具有重要影响,而Poisson比对裂缝形态影响较小;随着页岩脆性增高,压裂裂缝趋于＂长窄型＂扩展;地应力差和逼近角越大,水力裂缝越易贯穿天然裂缝;水力裂缝与天然裂缝相交处裂缝宽度存在相对较大的降低;扩展有限元方法避免了计算过程中的网格重构与网格加密,减少了计算量,该模型可以为页岩压裂设计提供理论指导.
英文摘要：
In viewof fluid flowin cracks and rock deformation,the mathematical model for shale hydraulic crack propagation was established.The crack flowfield and the rock stress field were solved with the finite element method and the extended finite element method respectively,and the two fields were coupled through the Picard iteration.The presented model gave results consistent with those of the classic model,which verified correctness of the former.Based on the model,the effects of the rock elasticity modulus,Poisson＇s ratio and injection rate on the crack geometry,and the dynamic process of a hydraulic crack approaching a natural crack at an arbitrary angle,were simulated.The numerical results showthat the elasticity modulus and injection rate have significant influence on the crack geometry,while the Poisson＇s ratio has little effect：the more brittle the shale is,the longer and narrower the hydraulic crack will grow：the greater the principal stress difference and the approaching angle are,the easier the hydraulic crack crosses the natural crack：there is a relatively large decrease in the crack width at the intersection between a hydraulic crack and a natural crack：the extended finite element method avoids mesh reconstruction and refinement during computation,and reduces the computing time.The presented model provides an effective theoretical tool for the shale fracturing design.
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