1887

Abstract

Summary

Simulation of multiphase flow in fractured reservoir is a computational challenge. A key issue is the effective coupling between flow in the porous matrix and in the fracture network. It requires computational grids honouring as much as possible the fracture geometry without degenerated/distorted elements. Standard techniques may degrade efficiency and are not a foolproof solution. Moreover, two point flux approximation (TPFA) demands a good quality of the mesh to mitigate discretization error.

In this work compare two different approaches. The first one has been proposed by . The second method we consider is the one originally proposed by .

We evaluate the two techniques by means of 2D synthetic problems based on realistic discrete fracture networks. Steady state and unsteady state simulations are performed using TPFA. We also present results obtained with computational methods based on coupling the fracture network with mimetic finite differences or extended mixed finite elements. The latter two approaches, even though more complex, are more robust with respect to mesh geometry and can be beneficial for the problem at hand.

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2014-09-08
2020-04-04
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References

  1. Adler, P., Thovert, J.F. and Mourzenko, V.
    [2012] Fractured porous media. Oxford University Press.
    [Google Scholar]
  2. Alpak, F.
    [2010] A mimetic finite volume discretization method for reservoir simulation. SPE Journal, 15(2), 436–453.
    [Google Scholar]
  3. Arbogast, T., Douglas, J.Jr., and Hornung, U.
    [1990] Derivation of the double porosity model of single phase flow via homogenization theory. SIAM J. Math. Anal., 21(4), 823–836.
    [Google Scholar]
  4. Barenblatt, G. and Zheltov, Y.
    [1960] Fundamental equations of filtration of homogeneous liquids in fissured rocks. Dokl. Akad. Nauk SSSR, 13, 548–.
    [Google Scholar]
  5. Becker, R., Hansbo, P. and Stenberg, R.
    [2003] A finite element method for domain decomposition with non-matching grids. M2AN Math. Model. Numer. Anal., 37(2), 209–225.
    [Google Scholar]
  6. Becker, R., Burman, E. and Hansbo, P.
    [2009] A Nitsche extended finite element method for incompressible elasticity with discontinuous modulus of elasticity. Comput. Methods Appl. Mech. Engrg., 198(41–44), 3352–3360.
    [Google Scholar]
  7. Brezzi, F., Lipnikov, K. and Shashkov, M.
    [2005a] Convergence of the mimetic finite difference method for diffusion problems on polyhedral meshes. SIAM J. Numer. Anal., 43(5), 1872–1896 (electronic).
    [Google Scholar]
  8. Brezzi, F., Lipnikov, K. and Simoncini, V.
    [2005b] A family of mimetic finite difference methods on polygonal and polyhedral meshes. Math. Models Methods Appl. Sci., 15(10), 1533–1551.
    [Google Scholar]
  9. Brezzi, F., Lipnikov, K. and Shashkov, M.
    [2006] Convergence of mimetic finite difference method for diffusion problems on polyhedral meshes with curved faces. Math. Models Methods Appl. Sci., 16(2), 275–297.
    [Google Scholar]
  10. Brooks, R.H. and Corey, A.T.
    [1964] Hydraulic properties of porous media. Civil Engineering Dept., Colorado State Univ., Fort Collins, CO.
    [Google Scholar]
  11. Cheng, S.W., Dey, T. and Shewchuk, J.
    [2012] Delaunay mesh generation. CRC Press.
    [Google Scholar]
  12. Choi, E., Cheema, T. and Islam, M.
    [1997] A new dual-porosity/dual-permeability model with non-Darcian flow through fractures. Journal of Petroleum Science and Engineering, 17(3), 331–344.
    [Google Scholar]
  13. D’Angelo, C. and Scotti, A.
    [2012] A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. ESAIM: Mathematical Modelling and Numerical Analysis, 46(02), 465–489.
    [Google Scholar]
  14. Durlofsky, L.
    [2003] Upscaling of geocellular models for reservoir flow simulation: A review of recent progress. 7th International Forum on Reservoir Simulation Bühl/Baden-Baden, Germany, 23–27.
    [Google Scholar]
  15. Fumagalli, A. and Scotti, A.
    [2013] A numerical method for two-phase flow in fractured porous media with non-matching grids. Advances in Water Resources, 62, 464–.
    [Google Scholar]
  16. Gong, B. and Durlofsky, L.
    [2008] Upscaling discrete fracture characterizations to Dual-Porosity, Dual-Permeability models for efficient simulation of flow with strong gravitational effects. SPE Journal, 13(1), 58–67.
    [Google Scholar]
  17. Guevara-Jordan, J.M. and Arteaga-Arispe, J.
    [2007] A second-order mimetic approach for tracer flow in oil reservoirs. Latin American & Caribbean Petroleum Engineering Conference.
    [Google Scholar]
  18. Hansbo, A. and Hansbo, P.
    [2002] An unfitted finite element method, based on Nitsche’s method, for elliptic interface problems. Comput. Methods Appl. Mech. Engrg., 191(47–48), 5537–5552.
    [Google Scholar]
  19. Karimi-Fard, M., Durlofsky, L. and Aziz, K.
    [2004] An efficient discrete-fracture model applicable for general-purpose reservoir simulators. SPE Journal, 9(2), 227–236.
    [Google Scholar]
  20. Karimi-Fard, M., Gong, B. and Durlofsky, L.
    [2006] Generation of coarse-scale continuum flow models from detailed fracture characterizations. Water Resources Research, 42(10), 1–13.
    [Google Scholar]
  21. Kuznetsov, Y., Lipnikov, K. and Shashkov, M.
    [2004] The mimetic finite difference method on polygonal meshes for diffusion-type problems. Comput. Geosci., 8(4), 301–324 (2005).
    [Google Scholar]
  22. Lim, K., Hui, M. and Mallison, B.
    [2009] A next-generation reservoir simulator as an enabling technology for a complex discrete fracture modeling workflow. SPE Paper 124980.
    [Google Scholar]
  23. Lipnikov, K., Moulton, J.D. and Svyatskiy, D.
    [2008] A multilevel multiscale mimetic (M3) method for two-phase flows in porous media. J. Comput. Phys., 227(14), 6727–6753.
    [Google Scholar]
  24. Mallison, B., Hui, M. and Narr, W.
    [2010] Practical Gridding Algorithms for Discrete Fracture Modeling Workflows. ECMOR XII, 12th European Conference on the Mathematics of Oil Recovery, September 2010, 1–11.
    [Google Scholar]
  25. Martin, V., Jaffré, J. and Roberts, J.E.
    [2005] Modeling fractures and barriers as interfaces for flow in porous media. SIAM J. Sci. Comput., 26(5), 1667–1691 (electronic).
    [Google Scholar]
  26. Moës, N., Dolbow, J. and Belytschko, T.
    [1999] A finite element method for crack growth without remeshing. Int. J. for Numerical Methods in Eng., 46(1), 131–150.
    [Google Scholar]
  27. Mustapha, H. and Dimitrakopoulos, R.
    [2011] Discretizing two-dimensional complex fractured fields for incompressible two-phase flow. International Journal for Numerical Methods in Fluids, 65(7), 764–780.
    [Google Scholar]
  28. Mustapha, H., Dimitrakopoulos, R., Graf, T. and Firoozabadi, A.
    [2011] An efficient method for discretizing 3D fractured media for subsurface flow and transport simulations. International Journal for Numerical Methods in Fluids, 67(5), 651–670.
    [Google Scholar]
  29. Mustapha, H.
    [2012] A Gabriel-Delaunay triangulation of complex fractured media for multiphase flow simulations. ECMOR XIII-13th European Conference on the Mathematics of Oil Recovery, 1–18.
    [Google Scholar]
  30. [2014] An efficient hybrid local nonmatching method for multiphase flow simulations in heterogeneous fractured media. Engineering with Computers, 1–14, doi:10.1007/s00366‑014‑0355‑0, (on line).
    https://doi.org/10.1007/s00366-014-0355-0 [Google Scholar]
  31. Nielsen, H.M., Natvig, J.R. and Lie, K.T.
    [2012] Accurate modeling of faults by multipoint, mimetic and mixed methods. SPE Journal, 17(2), 568–579.
    [Google Scholar]
  32. Persson, P.O. and Strang, G.
    [2004] A simple mesh generator in Matlab. SIAM Rev., 46(2), 329–345 (electronic).
    [Google Scholar]
  33. Saas, L., Faille, I., Nataf, F. and Willien, F.
    [2005] Finite volume methods for domain decomposition on non-matching grids with arbitrary interface conditions. SIAM journal on numerical analysis, 43(2), 860–890.
    [Google Scholar]
  34. Sahimi, M.
    [2012] Flow and Transport in Porous Media and Fractured Rock: From Classical Methods to Modern Approaches. J. Wiley and Sons.
    [Google Scholar]
  35. Warren, J. and Root, P.
    [1963] The behaviour of naturally fractured reservoirs. SPE J., 3(3), 245–255.
    [Google Scholar]
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