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A super-convergent staggered algorithm for the simulation of hydraulic fracturing treatments

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Abstract

In this paper, a super-convergent algorithm is presented for the simulation of hydraulic fracturing process in impervious domains using the extended finite element framework. The hydro-fracture inflow is modeled based on the Darcy law, in which the fracture permeability is incorporated by taking advantages from the well-known cubic law. The hydro-mechanical coupling between the fracturing fluid flow and the surrounding bulk is carried out by employing a sequential iterative procedure known as the staggered Newton algorithm. The convergence rate of the existing staggered solutions in the literature is examined, and an alternative super-convergent approach is proposed. Finally, through several numerical simulations the sanity of the developed framework is demonstrated.

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Notes

  1. The medium mesh was formerly used in the first example.

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Acknowledgements

The authors wish to appreciate Professor Amir R Khoei (Sharif University of Technology), and Dr. Mohammad R Hirmand (University of Waterloo) for their valuable communications regarding the partitioned solutions.

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  1. School of Civil and Environmental Engineering, UNSW Australia, Sydney, 2052, Australia

    M. Vahab & N. Khalili

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  1. M. Vahab
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  2. N. Khalili
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Correspondence to M. Vahab.

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Vahab, M., Khalili, N. A super-convergent staggered algorithm for the simulation of hydraulic fracturing treatments. Int J Fract 217, 49–64 (2019). https://doi.org/10.1007/s10704-019-00362-0

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