Permeability in the thin section

We compute the porosity and specific surface area of a two-dimensional (2D) pore-scale segmented image of a natural rock sample, add existing relations linking tortuosity to porosity, and then use the Kozeny-Carman equation to obtain estimates of the absolute permeability of the three-dimensional (3D) host sample. These estimates are very close to the true permeability, measured or computed, of the host sample in rocks with well-connected pore space, including high-porosity sand, glass bead packs, low-to-medium porosity sandstones, and some carbonates. They are higher than the true permeability in carbonates with relatively large pores connected by constricted conduits. They fail in impermeable synthetically constructed samples with disconnected pores. Still, this extremely simple method proves to be viable for a large class of natural rocks. Moreover, it can be used to construct a permeability-porosity trend from a microscopic 2D image by selecting subsections of this image and computing their permeability-porosity pairs. Because the measured or computed permeability-porosity pair of the host 3D sample falls upon such a trend, we argue that this trend may be applicable at a spatial scale much coarser that of the pore-scale image.