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

ZENG Qing-dong; YAO Jun

doi:10.3879/j.issn.1000-0887.2014.11.007

Volume 35 Issue 11

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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

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

doi: 10.3879/j.issn.1000-0887.2014.11.007

School of Petroleum Engineering, China University of Petroleum(East China), Qingdao, Shandong 266580, P.R.China

Funds: The National Natural Science Foundation of China（51234007）

Received Date: 2014-01-06
Rev Recd Date: 2014-09-30
Publish Date: 2014-11-18

Abstract

Abstract

In view of fluid flow in cracks and rock deformation, the mathematical model for shale hydraulic crack propagation was established. The crack flow field 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 show that 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.
- hydraulic fracturing,
- crack propagation,
- natural crack,
- fluid-solid interaction,
- extended finite element method

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References(25)

References

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