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Effective Properties for Flow Calculations

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Abstract

In this paper we discuss the background to the problems of finding effective flow properties when moving from a detailed representation of reservoir geology to a coarse gridded model required for reservoir performance simulation. In so doing we synthesize the pictures of permeability and transmissibility and show how they may be used to capture the effects of the boundary conditions on the upscaling. These same concepts are applied to the renormalization method of calculating permeability, to show its promise as an accurate, yet fast method.

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References

  1. Reservoir Characterisation,eds L. W. Lake and H. B. Carroll, Academic Press, 1986.

    Google Scholar 

  2. Reservoir Characterisation II,eds L. W. Lake, H. B. Carroll and T. C. Wesson, Academic Press, 1991.

    Google Scholar 

  3. Reservoir Characterisation III,ed B. Linville, Penn Well Publishing, 1993.

    Google Scholar 

  4. North Sea Oil and Gas Reservoirs I!,eds A. T. Buller, E. Berg, O. Hjelmeland, J. Kleppe, O. Torsæter and J. O. Aasen, Graham and Trotman, London, 1990.

    Google Scholar 

  5. North Sea Oil and Gas Reservoirs III,eds J. O. Aasen, E. Berg, A. T. Buller, O. Hjelmeland, R. M. Holt, J. Kleppe and O. Torsæter, Kluwer Academic, Dordrecht, 1994.

    Google Scholar 

  6. Mathematics in Oil Production,eds S. F. Edwards and P. R. King, Oxford University Press, 1988.

    Google Scholar 

  7. Mathematics of Oil Recovery,ed. P. R. King, Oxford University Press, 1992.

    Google Scholar 

  8. 2nd Conference on the Mathematics of Oil Recovery,eds D. Guerillot and O. Guillon, Editions Technip, Paris, 1988.

    Google Scholar 

  9. 3nd Conference on the Mathematics of Oil Recovery,eds M. A. Christie et al.,Delft University Press, 1992.

    Google Scholar 

  10. Fox. C.: Reservoir Characterisation using expert knowledge, data and statistics, Oil Field Review, Jan. 1992.

    Google Scholar 

  11. White, C. D., and Home, R. N.: Computing absolute transmissibility in the presence of fine-scale heterogeneity, paper SPE 16011, 9th SPE Symp. Reservoir Simulation, San Antonio, Texas (Feb. 1–4, 1987 ).

    Google Scholar 

  12. Indleman, P., and Dagan, G.: Upscaling of permeability of anisotropic heterogeneous formations, Parts 1–3, Water Resour. Res. 29 (1993), 917–943.

    Article  Google Scholar 

  13. Warren, J.E., and Price, H.S.: Flow in heterogeneous porous media, SPE J. Sept. 1961.

    Google Scholar 

  14. Begg, S. H., Carter, R. R. and Dranfield, P.: Assigning effective values to simulator gridblock parameters for heterogeneous reservoirs, SPE RE Nov. 1989.

    Google Scholar 

  15. Holden, L., Hoiberg, J. and Lia, O.: An Estimator for the Effective Permeability, Ref. [8].

    Google Scholar 

  16. Wilson, K. G.: The renormalisation group, Rev. Mod. Phys. 47 (1975), 773.

    Article  Google Scholar 

  17. Kirkpatrick, S.: Models of disordered materials, in Ill Condensed Matter, eds R. Balian, R. Maynard and G. Toulouse, North-Holland, Amsterdam, 1979.

    Google Scholar 

  18. King, P. R.: The use of renormalisation for calculating effective permeability, Transport in Porous Media 4 (1989), 37.

    Article  Google Scholar 

  19. King, P. R., Muggeridge, A. H. and Price, W. G.: Renormalisation calculations of immiscible flow, Transport in Porous Media 12 (1993), 237.

    Article  Google Scholar 

  20. Grindheim, A. O., and Aasen, J. O.: An evaluation of homogenisation techniques for absolute permeability, Lerkendal Petroleum Engineering Workshop, Trondheim, 1991.

    Google Scholar 

  21. Aharony, A, Hinrichsen, E. L., Hansen, A, Feder, J. Jpssang, T. and Hardy, H. H.: Effective renormalisation group algorithm for transport in oil reservoirs, Physica A 177 (1991), 260.

    Article  Google Scholar 

  22. Edwards, M. G., and Christie, M. A.: Dynamically Adaptice Godunov Schemes with Renormalisation in Reservoir Simulation, SPE 25268, 1993.

    Google Scholar 

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

    Article  Google Scholar 

  24. Durlofsky, L. J.: Modeling Fluid Flow Through Complex Reservoir Beds, SPE FE (Dec. 1992) 315–322.

    Google Scholar 

  25. Pickup, G. E., Jensen, J. L., Ringrose, P. S. and Sorbie, K. S.: A Method for Calculating Permeability Tensors using Perturbed Boundary Conditions, Ref. [9], 1992.

    Google Scholar 

  26. King, M. J.: Application and analysis of a new method for calculating tensor permeability, in New Developments in Improved Oil Recovery, ed De Haan, Geological Society Special Publication No. 84, 1975.

    Google Scholar 

  27. Ponting, D. K., in Ref. [7], p. 45, 1992.

    Google Scholar 

  28. Aziz, K. and Settari, A.: Petroleum Reservoir Simulation, Elsevier, Amsterdam, 1979.

    Google Scholar 

  29. Ripley, B. D.: Spatial Statistics,Wiley, New York, 1989, Ch 4.

    Google Scholar 

  30. Malick, K. M., and Hewett, T. A.: Boundary Effects in the Successive Renormalisation of Absolute Permeability, Stanford Center for Reservoir Forcasting (SCRF), Annual Report, May 1994.

    Google Scholar 

  31. King, P. R., and Williams, J. K.: Upscaling permeability: Mathematics of renormalization, in 4th Euro. Conf. Mathematics of Oil Recovery, 1994.

    Google Scholar 

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© 1995 Springer Science+Business Media Dordrecht

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King, M.J., King, P.R., McGill, C.A., Williams, J.K. (1995). Effective Properties for Flow Calculations. In: Adler, P.M. (eds) Multiphase Flow in Porous Media. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2372-5_7

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  • DOI: https://doi.org/10.1007/978-94-017-2372-5_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4645-1

  • Online ISBN: 978-94-017-2372-5

  • eBook Packages: Springer Book Archive

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