We next determined the permeability of several microtomography-based images of Fontainebleau sandstone. Figure 3 depicts portions of two of these sandstone images. The resolution was 5.72 µm per lattice spacing and data sets were 5103 voxels in size. A mirror image boundary condition was applied along directions perpendicular to the applied force. The porous medium was made periodic in the flow direction by creating its mirror image at the inlet. The numerical calculations were carried out on a 1020 x 510 x 510 system for all but the lowest porosity system. We found that at the lowest porosity (7.5%) there were not enough nodes across the pores to produce a reliable flow field. So for this case the permeability was determined from a 256(3 piece of the sandstone image that was mapped to a 5123 image, and calculations were performed on a 1024 x 512 x 512 system. In addition to requiring sufficient resolution, another potential source of error is not having precise knowledge of the location of the pore/solid interface. For example, an error of half a lattice spacing could be significant when modeling flow in narrow channels like that in the low porosity system. Figure 4 shows the computed permeability compared to experimental data [13]. Clearly there is good agreement, especially at the higher porosities.
Figure 3: 64 x 64 portions of the Fontainebleau sandstone media. On the left is the 7.5% porosity medium, on the right is the 22% porosity medium. The solid matrix is made transparent to reveal the pore space (grey shaded region).
Figure 4: Measured (line) and modeled (diamonds) permeabilities of Fontainebleau sandstone medium.