Transport in Porous Media

, Volume 68, Issue 2, pp 237–248 | Cite as

Analytical three-dimensional renormalization for calculating effective permeabilities

  • Christopher P. GreenEmail author
  • Lincoln Paterson
Original Paper


The ability to calculate an effective permeability of a heterogeneous reservoir based on knowledge of its small-scale permeability is fundamental to practical numerical reservoir characterization. One elegant technique that forms the basis of this process is renormalization (King, P.R.: Transport Porous Med. 4, 37–58 (1989)). In two dimensions, renormalization can be implemented using a simple analytical formula. In three dimensions, however, no such analytical result exists, and renormalization must be performed using a numerical implementation. In this article, we present a simple analytical approximation to the method of renormalization in three dimensions. A detailed comparison with numerical results demonstrates its accuracy and highlights the significant reduction in computational cost achieved.


Upscaling Renormalization Effective permeability Heterogeneous media 


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Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  1. 1.CSIRO PetroleumClayton SouthAustralia

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