## 留言板

 引用本文: 曾青冬, 姚军. 基于扩展有限元的页岩水力压裂数值模拟[J]. 应用数学和力学, 2014, 35(11): 1239-1248.
ZENG Qing-dong, YAO Jun. Numerical Simulation of Shale Hydraulic Fracturing Based on the Extended Finite Element Method[J]. Applied Mathematics and Mechanics, 2014, 35(11): 1239-1248. doi: 10.3879/j.issn.1000-0887.2014.11.007
 Citation: ZENG Qing-dong, YAO Jun. Numerical Simulation of Shale Hydraulic Fracturing Based on the Extended Finite Element Method[J]. Applied Mathematics and Mechanics, 2014, 35(11): 1239-1248.

## 基于扩展有限元的页岩水力压裂数值模拟

##### doi: 10.3879/j.issn.1000-0887.2014.11.007

###### 作者简介:曾青冬（1987—），男，江西赣州人，博士生（E-mail: upc.zengqd@163.com）;姚军(1964—),男,山东平邑人,教授,博士生导师(通讯作者. E-mail: rcogfr_upc@126.com).
• 中图分类号: O346.1;O242.21

## Numerical Simulation of Shale Hydraulic Fracturing Based on the Extended Finite Element Method

Funds: The National Natural Science Foundation of China（51234007）
• 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.
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##### 出版历程
• 收稿日期:  2014-01-06
• 修回日期:  2014-09-30
• 刊出日期:  2014-11-18

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