Reactivation of Fractures in Subsurface Reservoirs—A Numerical Approach Using a Static-Dynamic Friction Model

  • Runar L. BergeEmail author
  • Inga Berre
  • Eirik Keilegavlen
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)


Fluid-induced slip of fractures is characterized by strong multiphysics couplings. Three physical processes are considered: Flow, rock deformation and fracture deformation. The fractures are represented as lower-dimensional objects embedded in a three-dimensional domain. Fluid is modeled as slightly compressible, and flow in both fractures and matrix is accounted for. The deformation of rock is inherently different from the deformation of fractures; thus, two different models are needed to describe the mechanical deformation of the rock. The medium surrounding the fractures is modeled as a linear elastic material, while the slip of fractures is modeled as a contact problem, governed by a static-dynamic friction model. We present an iterative scheme for solving the non-linear set of equations that arise from the models, and suggest how the step parameter in this scheme should depend on the shear modulus and mesh size.



This work was partially funded by the Research Council of Norway, TheMSES project, grant no. 250223, and travel support funded by Statoil, through the Akademia agreement.


  1. 1.
    B.T. Aagaard, M.G. Knepley, C.A. Williams, A domain decomposition approach to implementing fault slip in finite element models of quasi-static and dynamic crustal deformation. J. Geophys. Res. Solid Earth 118(6), 3059–3079 (2013)CrossRefGoogle Scholar
  2. 2.
    W.M. Boon, J.M. Nordbotten, I. Yotov, Robust discretization of flow in fractured porous media (2016), ArXiv e-printsGoogle Scholar
  3. 3.
    P. Dietrich, R. Helmig, M. Sauter, H. Hötzl, J. Köngeter, G. Teutsch, Flow and Transport in Fractured Porous Media, vol. 1 (Springer, Berlin, 2005)CrossRefGoogle Scholar
  4. 4.
    G.R. Foulger, M.P. Wilson, J.G. Gluyas, B.R. Julian, R.J. Davies, Global review of human-induced earthquakes. Earth Sci. Rev. 178, 438–514 (2017)CrossRefGoogle Scholar
  5. 5.
    E. Keilegavlen, J.M. Nordbotten, Finite volume methods for elasticity with weak symmetry. Int. J. Numer. Methods Eng. 112(8), 939–962 (2017)MathSciNetCrossRefGoogle Scholar
  6. 6.
    E. Keilegavlen, A. Fumagalli, R. Berge, I. Stefansson, I. Berre, PorePy: an open-source simulation tool for flow and transport in deformable fractured rocks (2017), ArXiv e-printsGoogle Scholar
  7. 7.
    N. Kikuchi, J. Oden, Contact Problems in Elasticity (Society for Industrial and Applied Mathematics, Philadelphia, 1988)CrossRefGoogle Scholar
  8. 8.
    M.W. McClure, R.N. Horne, Investigation of injection-induced seismicity using a coupled fluid flow and rate/state friction model. Geophysics 76(6), WC181–WC198 (2011)CrossRefGoogle Scholar
  9. 9.
    J.R. Rice, Spatiotemporal complexity of slip on a fault. J. Geophys. Res. Solid Earth 98(B6), 9885–9907 (1993)CrossRefGoogle Scholar
  10. 10.
    E. Ucar, E. Keilegavlen, I. Berre, J.M. Nordbotten, A finite-volume discretization for deformation of fractured media (2016), ArXiv e-printsGoogle Scholar
  11. 11.
    E. Ucar, I. Berre, E. Keilegavlen, Three-dimensional numerical modeling of shear stimulation of naturally fractured rock formations (2017), ArXiv e-printsGoogle Scholar
  12. 12.
    A. Zang, V. Oye, P. Jousset, N. Deichmann, R. Gritto, A. McGarr, E. Majer, D. Bruhn, Analysis of induced seismicity in geothermal reservoirs an overview. Geothermics 52(Supplement C), 6–21 (2014); Analysis of Induced Seismicity in Geothermal OperationsGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Runar L. Berge
    • 1
    Email author
  • Inga Berre
    • 1
  • Eirik Keilegavlen
    • 1
  1. 1.University of BergenDepartment of MathematicsBergenNorway

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