An adaptive Algebraic Multiscale Solver for Compressible (C-AMS) flow in heterogeneous oil reservoirs is developed. Based on the recently developed AMS [ ] for incompressible linear flows, the C-AMS extends the algebraic formulation of the multiscale methods for compressible (nonlinear) flows. Several types of basis functions (incompressible and compressible with and without accumulation) are considered to construct the prolongation operator. As for the restriction operator, C-AMS allows for both MSFV and MSFE methods. Furthermore, to resolve high-frequency errors, Correction Functions and ILU(0) are considered. The best C-AMS procedure is determined among these various strategies, on the basis of the CPU time for three-dimensional heterogeneous problems. The C-AMS is adaptive in all aspects of prolongation, restriction, and conservative reconstruction operators for time-dependent compressible flow problems. In addition, it is also adaptive in terms of linear-system update. Though the C-AMS is a conservative multiscale solver (i.e., only a few iterations are employed infrequently in order to maintain high-quality results), a benchmark study is performed to investigate its efficiency against an industrial-grade Algebraic Multigrid (AMG) solver, SAMG [ ]. This comparative study illustrates that the C-AMS is quite efficient for compressible flow simulations in large-scale heterogeneous 3D reservoirs.


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  1. Aziz, K. and Settari, A.
    [1979] Petroleum Reservoir Simulation. Blitzprint Ltd., Cagary, Alberta.
    [Google Scholar]
  2. Cortinovis, D. and Jenny, P.
    [2014] Iterative galerkin-enriched multiscale finite-volume method. J. Comp. Phys., under review.
    [Google Scholar]
  3. Efendiev, Y. and Hou, T.Y.
    [2009] Multiscale Finite Element Methods: Theory and Applications. Springer.
    [Google Scholar]
  4. Hajibeygi, H., Bonfigli, G., Hesse, M. and Jenny, P.
    [2008] Iterative multiscale finite-volume method. J. Comput. Phys., 227, 8621–.
    [Google Scholar]
  5. Hajibeygi, H. and Jenny, P.
    [2009] Multiscale finite-volume method for parabolic problems arising from compressible multiphase flow in porous media. J. Comput. Phys., 228, 5147–.
    [Google Scholar]
  6. Hajibeygi, H., Karvounis, D. and Jenny, P.
    [2011] A hierarchical fracture model for the iterative multiscale finite volume method. J. Comput. Phys., 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. Hou, T.Y. and Wu, X.H.
    [1997] A multiscale finite element method for elliptic problems in composite materials and porous media. J. Comput. Phys., 134, 189–.
    [Google Scholar]
  10. Jenny, P., Lee, S.H. and Tchelepi, H.A.
    [2003] Multi-scale finite-volume method for elliptic problems in subsurface flow simulation. J. Comput. Phys., 187, 67–.
    [Google Scholar]
  11. [2006] Adaptive fully implicit multi-scale finite-volume method for multiphase flow and transport in heterogeneous porous media. J. Comput. Phys., 217, 641–.
    [Google Scholar]
  12. Kunze, R., Lunati, I. and Lee, S.H.
    [2013] A multilevel multiscale finite-volume method. J. Comput. Phys., 225, 520–.
    [Google Scholar]
  13. 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]
  14. Lee, S., Zhou, H. and Techelpi, H.
    [2009] Adaptive multiscale finite-volume method for nonlinear multiphase transport in heterogeneous formations. J. Comput. Phys., 228(24), 9036–9058.
    [Google Scholar]
  15. Lunati, I. and Jenny, P.
    [2006] Multiscale finite-volume method for compressible multiphase flow in porous media. J. Comput. Phys., 216(2), 616–636.
    [Google Scholar]
  16. [2008] Multiscale finite-volume method for density-driven flow in porous media. Comput. Geosci., 12(3), 337–350.
    [Google Scholar]
  17. Lunati, I., Lee, S. and Tyagi, M.
    [2011] An iterative multiscale finite volume algorithm converging to exact solution. J. of Comp. Phys., 230(5), 1849–1864.
    [Google Scholar]
  18. Moyner, O. and Lie, K.A.
    [2014] The multiscale finite-volume method on stratigraphic grids. SPE Journal, in press, doi:10.2118/163649‑PA.
    https://doi.org/http://dx.doi.org/10.2118/163649-PA [Google Scholar]
  19. Stuben, K.
    [2010] SAMG User’s Manual. Fraunhofer Institute SCAI.
    [Google Scholar]
  20. Tomin, P. and Lunati, I.
    [2013] Hybrid multiscale finite volume method for two-phase flow in porous media. J. Comput. Phys., 250(13), 293–307.
    [Google Scholar]
  21. Trottenberg, U., Oosterlee, C. and Schueller, A.
    [2001] Multigrid. Elsevier Academic Press.
    [Google Scholar]
  22. Wang, Y., Hajibeygi, H. and Tchelepi, H.A.
    [2014] Algebraic multiscale linear solver for heterogeneous elliptic problems. Journal of Computational Physics, 259, 303–.
    [Google Scholar]
  23. 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]
  24. Zhou, H. and Tchelepi, H.A.
    [2008] Operator based multiscale method for compressible flow. SPE Journal, 13(2), 267–273, doi:10.2118/106254‑PA.
    https://doi.org/http://dx.doi.org/10.2118/106254-PA [Google Scholar]
  25. [2012] Two-stage algebraic multiscale linear solver for highly heterogeneous reservoir models. SPE J., SPE 141473-PA, 17(2), 523–539.
    [Google Scholar]

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