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Transport in Porous Media

, Volume 26, Issue 3, pp 229–260 | Cite as

Effective Relative Permeabilities and Capillary Pressure for One-Dimensional Heterogeneous Media

  • Magnar Dale
  • Steinar Ekrann
  • Johannes Mykkeltveit
  • George Virnovsky
Article

Abstract

The paper presents an analytical construction of effective two-phase parameters for one-dimensional heterogeneous porous media, and studies their properties. We base the computation of effective parameters on analytical solutions for steady-state saturation distributions. Special care has to be taken with respect to saturation and pressure discontinuities at the interface between different rocks. The ensuing effective relative permeabilities and effective capillary pressure will be functions of rate, flow direction, fluid viscosities, and spatial scale of the heterogeneities.

The applicability of the effective parameters in dynamic displacement situations is studied by comparing fine-gridded simulations in heterogeneous media with simulations in their homogeneous (effective) counterparts. Performance is quite satisfactory, even with strong fronts present. Also, we report computations studying the applicability of capillary limit parameters outside the strict limit.

heterogeneous porous media effective relative permeabilities effective capillary pressure. 

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References

  1. 1.
    Abdin, A., et al.: 1995, Stochastic analysis of flow in porous media II: Comparison between perturbation and Monte-Carlo results, Transport in Porous Media 19, 261–80.Google Scholar
  2. 2.
    Amaziane, B., Bourgeat, A. and Koebbe, J.: 1991, numerical simulation and homogenization of two-phase flow in heterogeneous porous media, Transport in Porous Media 6, 519–47.Google Scholar
  3. 3.
    Amaziane, B. and Bourgeat, A.: 1988, Effective behavior of two-phase flow in heterogeneous reservoirs, in: M. F. Wheeler (ed.), Numerical Simulation in Oil Recovery, IMA Vol. Math. Appl. 11, Springer-Verlag, New York, pp. 1–22.Google Scholar
  4. 4.
    Bourgeat, A.: 1984, Nonlinear homogenization of two-phase flows in naturally fractured reservoirs with uniform fracture distribution, Comput. Methods Appl. Mech. Engrg. 47, 205–16.Google Scholar
  5. 5.
    Chang, J. and Yortsos, Y. C.: 1992, Effect of capillary heterogeneity on Buckley- Leverett displacement, Sphere, May, 285–293.Google Scholar
  6. 6.
    Chang, C-M. et al.: 1995, Stochastic analysis of two-phase flow in porous media: I. Spectral/ perturbation approach, Transport in Porous Media 19, 233–259.Google Scholar
  7. 7.
    Dale, M.: 1991, Effective relative permeabilities for a one-dimensional heterogeneous reservoir, in L.W. Lake, H. B. Carroll jr. and T. C. Wesson (eds), Reservoir Characterization II, Academic Press, pp. 652–655.Google Scholar
  8. 8.
    Dale, M.: 1995, Preprint, Rogaland University Center.Google Scholar
  9. 9.
    van Duijn, C. J., Molenaar, J. and de Neef, M. J.: 1995, The effect of capillary forces on immiscible two-phase flow in heterogeneous porous media, Transport in Porous Media 21, 71–93.Google Scholar
  10. 10.
    ECLIPSE 100 Reference Manual 92A, Appendices, Intera, 1992.Google Scholar
  11. 11.
    Ekrann, S. and Dale, M.: 1992, Averaging of relative permeability in heterogeneous reservoirs, in: P. R. King (ed.), The Mathematics of Oil Recovery, Clarendon Press, Oxford, pp. 173–199.Google Scholar
  12. 12.
    Ekrann, S., Dale, M., Langaas, K. and Mykkeltveit, J.: 1996, Capillary limit effective two-phase properties for three-dimensional media, SPE Paper 35493.Google Scholar
  13. 13.
    Ekrann, S.: 1992, Effective properties, in: S. M. Skjæveland and J. Kleppe (eds), SPOR Monograph Recent Advances in Improved Oil Recovery Methods for North Sea Sandstones Reservoirs, Norwegian Petroleum Directorate, StavangerGoogle Scholar
  14. 14.
    Hinderaker, L., Skjæveland, S. M. and Nystrand, B. V.: 1992, Key parameters for Norwegian Sandstone reservoirs, In: S. M. Skjæveland and J. Kleppe (eds), SPOR Monograph Recent Advances in Improved Oil Recovery Methods for North Sea Sandstones Reservoirs, Norwegian Petroleum Directorate, Stavanger.Google Scholar
  15. 15.
    Marle, M. G.: 1981, Multiphase Flow in Porous Media, Editions Technip.Google Scholar
  16. 16.
    Mykkeltveit, J.: 1993, A proof of the capillary limit algorithm in EFFECT, Preprint, Rogaland Research Institute.Google Scholar
  17. 17.
    Quintard, M. and Whitaker, S.: 1988, Two-phase flow in heterogeneous porous media: The method of large-scale averaging, Transport in Porous Media 3, 357–413.Google Scholar
  18. 18.
    Quintard, M. and Whitaker, S.: 1990, Two-phase flow in heterogeneous porous media I: The influence of large spatial and temporal gradients, Transport in Porous Media 5, 341–79.Google Scholar
  19. 19.
    Quintard, M. and Whitaker, S.: 1990, Two-phase flow in heterogeneous porous media II: Numerical experiments for flow perpendicular to a stratified system, Transport in Porous Media 5, 429–72.Google Scholar
  20. 20.
    Saez, A. E., Otero, C. J. and Rusinek, I.: 1989, The effective homogeneous behavior of heterogeneous porous media, Transport in Porous Media 4, 213–38.Google Scholar
  21. 21.
    Shvidler, M. I.: 1989, Average description of immiscible fluid transport in porous media with small-scale inhomogeneity, Translated from Izvestiya Akad. Nauk SSSR, Mekh. Zhidkosti i Gaza 6, 92–99.Google Scholar
  22. 22.
    Smith, E.H.: 1991, The influence of correlation between capillary pressur and permeability on the average relative permeability of reservoirs containing small scale heterogeneity, in: L. W. Lake, H. B. Carroll jr. and T. C. Wesson (eds), Reservoir Characterization II, Academic Press, New York, pp. 52–76.Google Scholar
  23. 23.
    Yortsos, Y. C. and Chang, J.: 1990, Capillary effects in steady-state flow in heterogeneous cores, Transport in Porous Media 5, 399–420.Google Scholar
  24. 24.
    Yortsos, Y. C., Satik, C., Bacri, J.-C. and Salin, D.: 1993, Large-scale percolation theory of drainage, Transport in Porous Media 10, 171–195.Google Scholar

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Magnar Dale
    • 1
  • Steinar Ekrann
    • 2
  • Johannes Mykkeltveit
    • 2
  • George Virnovsky
    • 2
  1. 1.Rogaland University CenterStavangerNorway
  2. 2.RF –Rogaland ResearchStavangerNorway

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