A finite-volume discretization for deformation of fractured media
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Simulating the deformation of fractured media requires the coupling of different models for the deformation of fractures and the formation surrounding them. We consider a cell-centered finite-volume approach, termed the multi-point stress approximation (MPSA) method, which is developed in order to discretize coupled flow and mechanical deformation in the subsurface. Within the MPSA framework, we consider fractures as co-dimension one inclusions in the domain, with the fracture surfaces represented as line pairs in 2D (face pairs in 3D) that displace relative to each other. Fracture deformation is coupled to that of the surrounding domain through internal boundary conditions. This approach is natural within the finite-volume framework, where tractions are defined on surfaces of the grid. The MPSA method is capable of modeling deformation, considering open and closed fractures with complex and nonlinear relationships governing the displacements and tractions at the fracture surfaces. We validate our proposed approach using both problems, for which analytical solutions are available, and more complex benchmark problems, including comparison with a finite-element discretization.
KeywordsDeformation Fracture mechanics Geomechanics Finite-volume method
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The work was funded by the Research Council of Norway through grants no. 228832/E20, 267908/E20 and 250223 and Statoil ASA through the Akademia agreement.
- 1.Jaeger, J.C., Cook, N.G., Zimmerman, R.: Fundamentals of Rock Mechanics. Wiley, New York (2009)Google Scholar
- 7.Anderson, T.L.: Fracture Mechanics: Fundamentals and Applications. CRC, Boca Raton (2005)Google Scholar
- 12.Crouch, S.L., Starfield, A.: Boundary Element Methods in Solid Mechanics: With Applications in Rock Mechanics and Geological Engineering. Allen & Unwin, London (1982)Google Scholar
- 20.Kim, J., Tchelepi, H.A., Juanes, R.: Stability, accuracy and efficiency of sequential methods for coupled flow and geomechanics. In: SPE Reservoir Simulation Symposium. Society of Petroleum Engineers (2009)Google Scholar
- 28.Andrews, D.: Test of two methods for faulting in finite-difference calculations. Bull. Seismol. Soc. Am. 89(4), 931–937 (1999)Google Scholar
- 34.Shewchuck, J.: Engineering a 2D quality mesh generator and Delaunay triangulator. In: Lin MC, Manocha D (eds.) Applied computational geometry: towards geometric engineering. Lecture notes in computer science, vol. 1148. From the First ACM Workshop on Applied Computational Geometry, pp 203–222. Springer, New York (1996)Google Scholar
- 35.Zehnder, A.T.: Fracture mechanics. (Lecture notes in applied and computational mechanics, vol. 62). Springer, Netherlands (2012)Google Scholar
- 38.Sneddon, I.N.: Fourier Transforms. McGraw Hill Book Co, Inc., New York (1951)Google Scholar
- 40.Lie, K.A.: An introduction to reservoir simulation using MATLAB user guide for the MATLAB reservoir simulation toolbox (MRST). SINTEF ICT, Department of Applied Mathematics (2014)Google Scholar
- 41.Aagaard, B., Knepley, M., Williams, C., Strand, L., Kientz, S.: PyLith user manual, version 2.1.0. Computational Infrastructure for Geodynamics (CIG), University of California, Davis (2015)Google Scholar