We apply an accurate numerical scheme to solve for Stokes flow directly on binarized three-dimensional rock images, such as those obtained by micro-CT imaging. The method imposes no-flow conditions exactly at the solid boundaries and employs an algebraic multigrid method to solve for the resultant set of linear equations. We compute the permeability of a range of consolidated and unconsolidated porous rocks; the results are comparable with those obtained using the lattice Boltzmann method and agree with experimental measurements on larger core samples. We show that the Kozeny-Carman equation can over-estimate permeability by a factor of 10 or more, particularly for the more heterogeneous systems studied. We study the existence and size of the representative elementary volume (REV) at lamina scale. We demonstrate that the REV for permeability is larger than for static properties-porosity and specific surface area-since it needs to account for the tortuosity and connectedness of the flow paths. For the carbonate samples, the REV appeared to be larger than the image size. We also study the anisotropy of permeability at the pore scale. We show that the permeability of sandpacks varies by less than 10 % in different directions. For sandstones, permeability changes by 25 % on average. However, the anisotropy of permeability in carbonates can be up to 50 %, indicating the existence of connected pores in one direction which are not connected in another.
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