Computational Geosciences

, Volume 22, Issue 1, pp 423–437 | Cite as

On the numerical simulation of crack interaction in hydraulic fracturing

  • E. W. Remij
  • J. J. C. Remmers
  • J. M. Huyghe
  • D. M. J. Smeulders
Open Access
Original Paper


In this paper, we apply the enhanced local pressure (ELP) model to study crack interaction in hydraulic fracturing. The method is based on the extended finite element method (X-FEM) where the pressure and the displacement fields are assumed to be discontinuous over the fracture exploiting the partition of unity property of finite element shape functions. The material is fully saturated and Darcy’s law describes the fluid flow in the material. The fracture process is described by a cohesive traction-separation law, whereas the pressure in the fracture is included by an additional degree of freedom. Interaction of a hydraulic fracture with a natural fracture is considered by assuming multiple discontinuities in the domain. The model is able to capture several processes, such as fracture arrest on the natural fracture, or hydraulic fractures that cross the natural fracture. Fluid is able to flow from the hydraulic fracture into the natural fracture. Two numerical criteria are implemented to determine whether or not the fracture is crossing or if fluid diversion occurs. Computational results showing the performance of the model and the effectiveness of the two criteria are presented. The influence of the angle between a hydraulic fracture and a natural fracture on the interaction behaviour is compared with experimental results and theoretical data.


Extended finite element method Enhanced local pressure model Hydraulic fracturing Crack interaction 



This research was sponsored by the Dutch TKI Gas foundation, under grant number TKIG01025 with financial support from Baker Hughes, EBN, GDF Suez, Total and Wintershall.


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© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • E. W. Remij
    • 1
  • J. J. C. Remmers
    • 1
  • J. M. Huyghe
    • 1
  • D. M. J. Smeulders
    • 1
  1. 1.Department of Mechanical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands

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