Analytical three-dimensional renormalization for calculating effective permeabilities |
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Authors: | Christopher P Green Lincoln Paterson |
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Institution: | (1) CSIRO Petroleum, Private Bag 10, Clayton South, Vic., 3169, Australia |
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Abstract: | 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. |
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Keywords: | Upscaling Renormalization Effective permeability Heterogeneous media |
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