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Convergence of iterative coupling for coupled flow and geomechanics

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Abstract

In this paper, we study solving iteratively the coupling of flow and mechanics. We demonstrate the stability and convergence of two widely used schemes: the undrained split method and the fixed stress split method. To our knowledge, this is the first time that such results have been rigorously obtained and published in the scientific literature. In addition, we propose a new stress split method, with faster convergence rate than known schemes. These results are specially important today due to the interest in hydraulic fracturing (Dean and Schmidt SPE J. 14:707–714, 2009; Ji et al. SPE J. 14:423–430, 2009; Samier and De Gennaro 2007; Settari and Maurits SPE J. 3:219–226, 1998), in oil and gas shale reservoirs.

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References

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Authors and Affiliations

  1. Université de Lyon, CNRS UMR 5208, Université Lyon 1, Institut Camille Jordan, 43, blvd. du 11 novembre 1918, 69622, Villeurbanne Cedex, France

    Andro Mikelić

  2. Center for Subsurface Modeling, Institute for Computational Engineering and Sciences, The University of Texas, 201 East 24th Street, Austin, TX, 78712, USA

    Mary F. Wheeler

Authors
  1. Andro Mikelić
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  2. Mary F. Wheeler
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Correspondence to Andro Mikelić.

Additional information

This paper is dedicated to the 60th anniversary of C.J. van Duijn, because of his impact of applying rigorous mathematics to real world problems.

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Mikelić, A., Wheeler, M.F. Convergence of iterative coupling for coupled flow and geomechanics. Comput Geosci 17, 455–461 (2013). https://doi.org/10.1007/s10596-012-9318-y

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  • DOI: https://doi.org/10.1007/s10596-012-9318-y

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