Optical analog of the permeability of sandstones

We demonstrate a correlation between the transmissivity of sandstones to visible light and their fluid permeability. By means of experiments carried out on sandstone and sand packs, we show that the light transmission increases when the contrast between the indices of refraction of the matrix material and pore-filling fluid is reduced, and that, for a given fluid, it is greatest for rocks with the largest grains. We present qualitative and analytical arguments, and results of a numerical simulation, which account for these correlations. The simulations also yield the space and time distribution of the transmitted light. Finally, we show that light transmission provides a method of mapping the permeability of sandstone without fluid flow, and at high spatial resolutions. Extension of these findings to rocks other than sandstones is discussed.