Computational Mechanics

, Volume 61, Issue 1–2, pp 137–155 | Cite as

Fully coupled simulation of multiple hydraulic fractures to propagate simultaneously from a perforated horizontal wellbore

  • Qinglei Zeng
  • Zhanli LiuEmail author
  • Tao Wang
  • Yue Gao
  • Zhuo ZhuangEmail author
Original Paper


In hydraulic fracturing process in shale rock, multiple fractures perpendicular to a horizontal wellbore are usually driven to propagate simultaneously by the pumping operation. In this paper, a numerical method is developed for the propagation of multiple hydraulic fractures (HFs) by fully coupling the deformation and fracturing of solid formation, fluid flow in fractures, fluid partitioning through a horizontal wellbore and perforation entry loss effect. The extended finite element method (XFEM) is adopted to model arbitrary growth of the fractures. Newton’s iteration is proposed to solve these fully coupled nonlinear equations, which is more efficient comparing to the widely adopted fixed-point iteration in the literatures and avoids the need to impose fluid pressure boundary condition when solving flow equations. A secant iterative method based on the stress intensity factor (SIF) is proposed to capture different propagation velocities of multiple fractures. The numerical results are compared with theoretical solutions in literatures to verify the accuracy of the method. The simultaneous propagation of multiple HFs is simulated by the newly proposed algorithm. The coupled influences of propagation regime, stress interaction, wellbore pressure loss and perforation entry loss on simultaneous propagation of multiple HFs are investigated.


Multiple hydraulic fractures Fluid partitioning XFEM Fully coupled simulation Perforation entry loss 



This work is supported by National Natural Science Foundation of China (Grant Nos. 11532008 and 11372157), the Special Research Grant for Doctor Discipline by Ministry of Education, China (Grant No. 20120002110075), the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 201326). Tsinghua University Initiative Scientific Research Program is also acknowledged.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Applied Mechanics Laboratory, School of Aerospace EngineeringTsinghua UniversityBeijingChina

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