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Calculation of permeability from 3D tomographic rock images was performed by combining renormalization group approaches (RGA) and lattice Boltzmann method (LBM). Images of sandstone rock samples (i.e., Fontainebleau, Berea, and Sumatera sandstones) with block size of 2563 voxels were used in this study. LBM was applied to calculate permeability of each smallest block (i.e., 64 and 128 voxels) as sub-blocks of the larger block (2563 voxels). The calculated permeability will form analogue to hydraulic conductance networks. RGA were then applied to the networks for all three perpendicular directions using several RGA schemes, i.e., King, Karim–Krabbenhoft, Green–Paterson, and their combinations. It was shown that as the number of renormalizations increases, the average permeability decreases. The effective permeability calculated by combining RGA and LBM were lower than permeability of the single largest block. Karim and Krabbenhoft’s scheme produced mostly higher estimation than the others and closest to the true permeability. Degree of anisotropy is influenced by the initial block size prior to RGA scheme.

Calculation of anisotropy permeability from 3D tomographic images using renormalization group approaches and lattice Boltzmann method