Digital Subvolumes: Computational Approaches and Permeability-Porosity Transforms

The total porosity and absolute permeability of a large digital sample, a segmented 3D micro-CT-scan image of coarse aeolian sand, is computed using the Lattice-Boltzmann (LB) single-phase fluid flow simulation. An alternative and faster approach is to divide the large sample into subvolumes (elements), and use the LB method on each element. The permeability of the host sample is then obtained by Darcy's simulation on a synthetic volume comprised of the elemental permeabilities. The results of the first and the second method are practically identical in this example. Using subvolumes also helps produce a physically meaningful permeability-porosity trend from a single digital object. These results are likely to be valid only in samples with well-connected and homogeneous pore space. A counterexample comes from carbonate where appreciable part of the pore volume is located in vugs. Here the permeability-porosity trend formed by the majority of the subsamples exceeds the permeability of the host sample by about half of an order of magnitude due to the enhanced connectivity when dividing the host across the isolated vugs.