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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Green, C.P., Paterson, L. Analytical three-dimensional renormalization for calculating effective permeabilities. Transp Porous Med 68, 237–248 (2007). https://doi.org/10.1007/s11242-006-9042-y
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DOI: https://doi.org/10.1007/s11242-006-9042-y