1887
  1. Home
  2. Conferences
  3. Conference Proceedings
  4. ECMOR XIV - 14th European Conference on the Mathematics of Oil Recovery
  5. Conference paper

Abstract

Summary

The MultiScale Finite-Volume (MSFV) method is known to produce non-monotone solutions. The causes of the non-monotone solutions are identified and connected to the local flux across the boundaries of primal coarse cells induced by the basis functions. We propose a monotone MSFV (m-MSFV) method based on a local stencil-fix that guarantees monotonicity of the coarse-scale operator, and thus the resulting approximate fine-scale solution. Detection of non-physical transmissibility coefficients that lead to non-monotone solutions is achieved using local information only and is performed algebraically. For these ‘critical’ primal coarse-grid interfaces, a monotone local flux approximation, specifically, a Two-Point Flux Approximation (TPFA), is employed. Alternatively, a local linear boundary condition is used for the basis functions to reduce the degree of non-monotonicity. The local nature of the two strategies allows for ensuring monotonicity in local sub-regions, where the non-physical transmissibility occurs. For practical applications, an adaptive approach based on normalized positive off-diagonal coarse-scale transmissibility coefficients is developed. Based on the histogram of these normalized coefficients, one can remove the large peaks by applying the proposed modifications only for a small fraction of the primal coarse grids. Though the m-MSFV approach can guarantee monotonicity of the solutions to any desired level, numerical results illustrate that employing the m-MSFV modifications only for a small fraction of the domain can significantly reduce the non-monotonicity of the conservative MSFV solutions.

© EAGE Publications BV
Loading

Article metrics loading...

/content/papers/10.3997/2214-4609.20141777
2014-09-08
2024-04-18

  • From This Site

    /content/papers/10.3997/2214-4609.20141777
    dcterms_title,dcterms_subject,pub_keyword
    -contentType:Journal -contentType:Contributor -contentType:Concept -contentType:Institution
    10
    5
Loading full text...

Full text loading...

References

  1. Aziz, K. and Settari, A.
    [2002] Petroleum Reservoir Simulation. Blitzprint Ltd., Cagary, Alberta.
     [Google Scholar]
  2. Christie, M.A. and Blunt, M.J.
    [2001] Tenth SPE comparative solution project: A comparision of upscaling techniques. SPE Reservoir Evaluation and Engineering, 4, 317–.
     [Google Scholar]
  3. Hajibeygi, H., Bonfigli, G., Hesse, M.A. and Jenny, P.
    [2008] Iterative multiscale finite volume method. Journal of Computational Physics, 227, 8621–.
     [Google Scholar]
  4. Hajibeygi, H. and Jenny, P.
    [2009] Multiscale finite-volume method for parabolic problems arising from compressible multiphase flow in porous media. Journal of Computational Physics, 228, 5147–.
     [Google Scholar]
  5. [2011] Adaptive iterative multiscale finite volume method. Journal of Computational Physics, 230, 643–.
     [Google Scholar]
  6. Hajibeygi, H., Karvounis, D. and Jenny, P.
    [2011] A hierarchical fracture model for the iterative multiscale finite volume method. Journal of Computational Physics, 230(24), 8729–8743.
     [Google Scholar]
  7. Hajibeygi, H., Lee, S.H. and Lunati, I.
    [2012] Accurate and efficient simulation of multiphase flow in a heterogeneous reservoir by using error estimate and control in the multiscale finite-volume framework. SPE Journal, 17(4), 1071–1083.
     [Google Scholar]
  8. Hajibeygi, H. and Tchelepi, H.A.
    [2014] Compositional multiscale finite-volume formulation. SPE Journal, 19(2), 316–326.
     [Google Scholar]
  9. Hesse, M.A., Mallison, B.T. and Tchelepi, H.A.
    [2008] Compact multiscale finite volume method for heterogeneous anisotropic elliptic equations. SIAM Multiscale Model. Simul., 7, 962–.
     [Google Scholar]
  10. Hou, T. and Wu, X.H.
    [1997] A multiscale finite element method for elliptic problems in composite matrials and porous meida. Journal of Computational Physics, 134, 189–.
     [Google Scholar]
  11. Jenny, P., Lee, S.H. and Tchelepi, H.A.
    [2003] Multi-scale finite-volume method for elliptic problems in subsurface flow simulation. Journal of Computational Physics, 187, 67–.
     [Google Scholar]
  12. [2006] Adaptive fully implicit multi-scale finite-volume method for multiphase flow and transport in heterogeneous porous media. Journal of Computational Physics, 217, 641–.
     [Google Scholar]
  13. Jenny, P. and Lunati, I.
    [2009] Modeling complex wells with the multi-scale finite volume method. Journal of Computational Physics, 228, 702–.
     [Google Scholar]
  14. Lee, S.H., Wolfsteiner, C. and Tchelepi, H.A.
    [2008] Multiscale finite-volume formulation for multiphase flow in porous media: black oil formulation of compressible, three-phase flow with gravity. Comput. Geosci., 12(3), 351–366.
     [Google Scholar]
  15. Lee, S.H., Zhou, H. and Tchelepi, H.A.
    [2009] Adaptive multiscale finite-volume method for nonlinear multiphase transport in heterogeneous formations. Journal of Computational Physics, 228(24), 9036–9058.
     [Google Scholar]
  16. Lunati, I. and Jenny, P.
    [2007] Treating highly anisotropic subsurface flow with the multiscale finite-volume method. SIAM Multiscale Model. Simul., 6(1), 308–318.
     [Google Scholar]
  17. Wang, Y., Hajibeygi, H. and Tchelepi, H.A.
    [2014] Algebraic multiscale solver for flow in heterogeneous porous media. Journal of Computational Physics, 259, 303–.
     [Google Scholar]
  18. Wolfsteiner, C., Lee, S.H. and Tchelepi, H.A.
    [2006] Well modeling in the multiscale finite volume method for subsurface flow simulation. SIAM Multiscale Model. Simul., 5(3), 900–917.
     [Google Scholar]
  19. Zhou, H., Lee, S.H. and Tchelepi, H.A.
    [2011] Multiscale finite-volume formulation for saturation equations. SPE Journal, 17(1), 198–211.
     [Google Scholar]
  20. Zhou, H. and Tchelepi, H.A.
    [2008] Operator-based multiscale method for compressible flow. SPE Journal, 13, 273–.
     [Google Scholar]
  21. [2012] Two-stage algebraic multiscale linear solver for highly heterogeneous reservoir models. SPE Journal, 17(2), 523–539.
     [Google Scholar]
http://instance.metastore.ingenta.com/content/papers/10.3997/2214-4609.20141777
Loading
Monotone Multiscale Finite Volume Method for Flow in Heterogeneous Porous Media
Conference Proceedings 2014, 1 (2014); https://doi.org/10.3997/2214-4609.20141777
/content/papers/10.3997/2214-4609.20141777
/content/papers/10.3997/2214-4609.20141777
Loading

Data & Media loading...

Most Cited This Month Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error