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Numerical convergence study of iterative coupling for coupled flow and geomechanics

Abstract

In this paper, we consider algorithms for modeling complex processes in porous media that include fluid and structure interactions. Numerous field applications would benefit from a better understanding and integration of porous flow and solid deformation. Important applications in environmental and petroleum engineering include carbon sequestration, surface subsidence, pore collapse, cavity generation, hydraulic fracturing, thermal fracturing, wellbore collapse, sand production, fault activation, and waste disposal, while similar issues arise in biosciences and chemical sciences as well. Here, we consider solving iteratively the coupling of flow and mechanics. We employ mixed finite element method for flow and a continuous Galerkin method for elasticity. For single-phase flow, we demonstrate the convergence and convergence rates for two widely used schemes, the undrained split and the fixed stress split. We discuss the extension of the fixed stress iterative coupling scheme to an equation of state compositional flow model coupled with elasticity and a single-phase poroelasticity model on general hexahedral grids. Computational results are presented.

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Acknowledgments

A. Mikelić would like to thank the Institute for Computational Engineering and Science (ICES), UT Austin for hospitality in April 2009, 2010, 2011, and 2012. The research by M. F. Wheeler and B. Wang were partially supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences through the DOE Energy Frontier Research Center: The Center for Frontiers of Subsurface Energy Security (CFSES) under contract no. DE-SC0001114. The authors would also like to thank Dr. B. Ganis and Dr. R. Liu for their help in setting up the unstructured grid example.

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Correspondence to Andro Mikelić.

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Mikelić, A., Wang, B. & Wheeler, M.F. Numerical convergence study of iterative coupling for coupled flow and geomechanics. Comput Geosci 18, 325–341 (2014). https://doi.org/10.1007/s10596-013-9393-8

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  • DOI: https://doi.org/10.1007/s10596-013-9393-8

Keywords

  • Poroelasticity
  • Iterative coupling
  • Contraction mapping
  • Compositional flow
  • Multipoint flux mixed finite element method