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

Unconventional Reservoir simulations involve several challenges not only arising from geological heterogeneities, but also from strong nonlinear physical coupling terms. All exiting upscaling and multiscale methods rely on a classical sequential formulation to treat the coupling between the nonlinear flow-transport equations. Unfortunately, the sequential strategies become severely inefficient when the flow and transport equations are strongly coupled. Examples of these cases include compositional displacements, and processes with strong capillarity effects. To extend the applicability of the multiscale methods for these challenging cases, in this paper, we propose a Constrained Pressure Residual Multiscale (CPR-MS) method. In the CPR-MS method, the CPR strategy is used to formulate the pressure equation, the approximate conservative solution of which is obtained by employing a few iterations of the iterative multiscale procedure. Several local- (ILU(k), BILU(k), etc.) and global-stage (Multiscale Finite Volume, MSFV, and Multiscale Finite Element, MSFE) solvers with different localization conditions (Linear BC, Reduced Problem BC, etc.) are employed in order to find an optimum strategy for the highly nonlinear compositional displacements. Numerical results for a wide range of test cases are presented, discussed and future studies are outlined.

© EAGE Publications BV
Loading

Article metrics loading...

/content/papers/10.3997/2214-4609.20141778
2014-09-08
2024-04-26

  • From This Site

    /content/papers/10.3997/2214-4609.20141778
    dcterms_title,dcterms_subject,pub_keyword
    -contentType:Journal -contentType:Contributor -contentType:Concept -contentType:Institution
    10
    5
Loading full text...

Full text loading...

References

  1. Appleyard, J.R.
    [1983] Nested factorization. SPE Reservoir Simulation Symposium, San Francisco, California.
     [Google Scholar]
  2. Aziz, K., Durlofsky, L. and Tchelepi, H.
    [2005] Notes on Petroleum Reservoir Simulation. Department of Petroleum Engineering, School of Earth Sciences, Stanford University, California, USA.
     [Google Scholar]
  3. Cao, H.
    [2002] Development of Techniques for General Purpose Simulation. Phd thesis, Stanford University, USA.
     [Google Scholar]
  4. Cao, H., Tchelepi, H.A., Wallis, J.R. and Yardumian, H.
    [2005] Constrained residual acceleration of conjugate residual methods. SPE paper 96809, SPE Annual Technical Conference and Exhibition, Dallas, Texas, USA, doi: doi:10.2118/96809‑MS.
     https://doi.org/10.2118/96809-MS [Google Scholar]
  5. Coats, K., Chu, W.G.C. and Marcum, B.
    [1974] Three-dimensional simulation of steamflooding. SPE J., 14(6), 573–592.
     [Google Scholar]
  6. Cortinovis, D. and Jenny, P.
    [2014] Iterative galerkin-enriched multiscale finite-volume method. J. Comp. Phys., under review.
     [Google Scholar]
  7. Efendiev, Y. and Hou, T.Y.
    [2009] Multiscale Finite Element Methods: Theory and Applications. Springer.
     [Google Scholar]
  8. Fung, L.S.K. and Dogru, A.H.
    [2007] Parallel unstructered solver methods for complex giant reservoir simulation. SPE paper 106237, SPE Reservoir Simulation Symposium, Houston, Texas, USA.
     [Google Scholar]
  9. Hajibeygi, H., Bonfigli, G., Hesse, M. and Jenny, P.
    [2008] Iterative multiscale finite-volume method. J. Comput. Phys., 227, 8621–.
     [Google Scholar]
  10. 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]
  11. [2011] Adaptive iterative multiscale finite volume method. J. Comput. Phys., 230(3), 628–643.
     [Google Scholar]
  12. 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]
  13. 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]
  14. Hajibeygi, H. and Tchelepi, H.A.
    [2014] Compositional multiscale finite-volume formulation. SPE Journal, 19(2), 316–326.
     [Google Scholar]
  15. 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]
  16. 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]
  17. [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]
  18. Jenny, P. and Lunati, I.
    [2009] Modeling complex wells with the multi-scale finite volume method. J. Comput. Phys., 228, 702–.
     [Google Scholar]
  19. Kunze, R., Lunati, I. and Lee, S.H.
    [2013] A multilevel multiscale finite-volume method. J. Comput. Phys., 225, 520–.
     [Google Scholar]
  20. 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]
  21. Lukyanov, A.A.
    [2010] Meshless upscaling method and its application to a fluid flow in porous media. ECMOR XII. Oxford. UK.
     [Google Scholar]
  22. [2012] Adaptive fully implicit multi-scale meshless multi-point flux method for fluid flow in heterogeneous porous media. ECMOR XIII. Biarritz. France.
     [Google Scholar]
  23. Lunati, I. and Jenny, P.
    [2008] Multiscale finite-volume method for density-driven flow in porous media. Comput. Geosci., 12(3), 337–350.
     [Google Scholar]
  24. 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]
  25. 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]
  26. Saad, Y. and Schultz, M.
    [1986] Gmres: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., 7(3), 856–869.
     [Google Scholar]
  27. Spillette, A.G., Hillestad, J.G. and Stone, H.L.
    [1973] A high-stability sequential solution approach to reservoir simulation. SPE J., sPE 4542.
     [Google Scholar]
  28. Wallis, J.R., Kendall, R.P., Little, T.E. and Nolen, J.S.
    [1985] Constrained residual acceleration of conjugate residual methods. SPE Reservoir Simulation Symposium, doi:10.2118/13536‑MS.
     https://doi.org/10.2118/13536-MS [Google Scholar]
  29. Wallis, J.
    [1983] Incomplete gaussian elimination as a preconditioning for generalized conjugate gradient acceleration. SPE Reservoir Simulation Symposium, doi:doi:10.2118/12265‑MS.
     https://doi.org/10.2118/12265-MS [Google Scholar]
  30. Wang, Y., Hajibeygi, H. and Tchelepi, H.A.
    [2014] Algebraic multiscale linear solver for heterogeneous elliptic problems. Journal ofComputational Physics, 259, 303–.
     [Google Scholar]
  31. Watts, J.W.
    [1999] A total velocity sequential preconditioner for solving implicit reservoir simulation matrix equations. SPE paper 51909, SPE Reservoir Simulation Symposium, Houston, Texas, USA.
     [Google Scholar]
  32. 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]
  33. Younis, R.
    [2009] Advances in Modern Computational Methods for Nonlinear Problems; A Generic Efficient Automatic Differentiation Framework, and Nonlinear Solvers That Converge All The Time. Phd thesis, Stanford University, USA.
     [Google Scholar]
  34. Zhou, H., Lee, S. and Tchelepi, H.
    [2011] Multiscale finite-volume formulation for saturation equations. SPE J., 17(1), 198–211.
     [Google Scholar]
  35. Zhou, H. and Tchelepi, H.A.
    [2007] Operator based multiscale method for compressible flow. SPE 106254 presented at the SPE Reservoir Simulation Symposium, Houston, TX, USA.
     [Google Scholar]
  36. [2012] Two-stage algebraic multiscale linear solver for highly heterogeneous reservoir models. SPE J., SPE 141473-PA, 17(2), 523–539.
     [Google Scholar]
http://instance.metastore.ingenta.com/content/papers/10.3997/2214-4609.20141778
Loading
A Constrained Pressure Residual Multiscale (CPR-MS) Compositional Solver
Conference Proceedings 2014, 1 (2014); https://doi.org/10.3997/2214-4609.20141778
/content/papers/10.3997/2214-4609.20141778
/content/papers/10.3997/2214-4609.20141778
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