Skip to main content
SpringerLink
Log in

Modified adaptive local–global upscaling method for discontinuous permeability distribution

  • Original Paper
  • Published:
Computational Geosciences Aims and scope Submit manuscript

Abstract

The paper is devoted to the upscaling method appropriate for single-phase flow in media with discontinuous permeability distribution. The suggested algorithm is a modification of the iterative adaptive local–global upscaling developed by Chen and coauthors. The key feature of this method is a consistency between local and coarse global calculated characteristics. In this work, we apply a modified procedure to determine the boundary conditions used in the local fine-scale computation. To increase the accuracy of these boundary conditions on each iteration, we involve an additional preliminary step based on the results of coarse scale calculations from the previous iteration. Numerical tests show an essential improvement of the accuracy of upscaled flow rates for most of the realizations of statistical permeability distribution. Although the developed method is universal, its efficiency increases with increasing of permeability contrast.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Aavatsmark, I.: Multipoint flux approximation methods for quadrilateral grids. In: The 9th International Forum on Reservoir Simulation, Abu Dhabi, 9–13 December 2007

  2. Ababou, R., McLaughlin, D., Gelhar, L.W., Tompson, A.F.B.: Numerical simulation of three-dimensional saturated flow in randomly heterogeneous porous media. Transp. Porous Media, 4, 549–565 (1989)

    Article  Google Scholar 

  3. Boe, O.: Analysis of the upscaling method based on conservation of dissipation. Transp. Porous Media, 17, 77–86 (1994)

    Article  Google Scholar 

  4. Chen, Y., and Durlofsky, L.J.: Adaptative local–global upscaling for general flow scenarios in heterogeneous formations. Transp. Porous Media, 62, 157–185 (2006)

    Article  MathSciNet  Google Scholar 

  5. Chen, Y., Durlofsky, L.J., Gerritsen, M., Wen, X.H.: A coupled local-global upscaling approach for simulating flow in highly heterogeneous formations. Adv. Water Resour. 26, 1041–1060 (2003)

    Article  Google Scholar 

  6. Durlofsky, L.J.: Numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media. Water Resour. Res. 27, 699–708 (1991)

    Article  Google Scholar 

  7. Durlofsky, L.J.: Upscaling and griding of fine scale geological models for flow simulation. In: The 8th International Forum on Reservoir Simulation, Iles Borromees, Stresa, Italy, 20–24 June 2005

  8. Gelhar, L.W.: Stochastic Subsurface Hydrology. Prentice Hall, Englewood Cliffs (1992)

    Google Scholar 

  9. Fossen, H., Schultz, R.A., Shipton, Z.K., Mair, K.: Deformation bands in sandstone: a review. J. Geol. Soc. 164, 755–769 (2007)

    Article  Google Scholar 

  10. Holden, L., and Nielsen, B.F.: Global upscaling of permeability in heterogeneous reservoirs: the Output Least Square (LOS) method. Transp. Porous Media, 40, 115–143 (2000)

    Article  MathSciNet  Google Scholar 

  11. Kolyukhin, D., Schueller, S., Espedal, M., Fossen, H.: Deformation band populations in fault damage zone—impact on fluid flow. Comput. Geosci. 14, 231–248 (2010). doi:10.1007/s10596-009-9148-8

    Article  MATH  Google Scholar 

  12. Kumar, A., Farmer, C.L., Jerauld, G.R., Li, D.: Efficient upscaling from cores to simulation models. In: SPE 38744 Annual Technical Conference and Exhibition, San Antonio, TX, 5–8 October (1997)

  13. Marchuk, G.I.: Methods of Numerical Mathematics, p. 510. Springer, New York (1982)

    MATH  Google Scholar 

  14. Odling, N.E., Harris, S.D., Knipe, R.J.: Permeability scaling properties of fault damage zones in siliclastic rocks. J. Struct. Geol. 26(9), 1727–1747 (2004)

    Article  Google Scholar 

  15. Pickup, G.E., Ringrose, P.S., Corbett, P.W.M., Jensen, J.L., Sorbie, K.S.: Geology, geometry and effective flow. Pet. Geosci. 1, 37–42 (1995)

    Google Scholar 

  16. Renard, P., de Marsily, G.: Calculating effective permeability: a review. Adv. Water Resour. 20, 253–278 (1997)

    Article  Google Scholar 

  17. Sabelfeld, K.K.: Monte Carlo Methods in Boundary Value Problems. Springer, New York (1991)

    MATH  Google Scholar 

  18. Sanchez-Vila, X., Grirardi, J., Carrera, J.: A synthesis of approaches to upscaling of hydraulic conductivities. Water Resour. Res. 31(4), 867–882 (1995)

    Article  Google Scholar 

  19. Sternlof, K.R., Karimi-Fard, M., Pollard, D.D., Durlofsky, L.J.: Flow and transport effects of compaction bands in sandstone at scales relevant to aquifer and reservoir management. Water Resour. Res. 42, W07425 (2006). doi:10.1029/2005WR004664

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre for Integrated Petroleum Research, University of Bergen, Allégaten 41, 5007, Bergen, Norway

    Dmitry Kolyukhin & Magne Espedal

Authors
  1. Dmitry Kolyukhin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Magne Espedal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dmitry Kolyukhin.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kolyukhin, D., Espedal, M. Modified adaptive local–global upscaling method for discontinuous permeability distribution. Comput Geosci 14, 675–689 (2010). https://doi.org/10.1007/s10596-010-9180-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10596-010-9180-8

Keywords

Search

Navigation