Fractal sandstone pores: Automated measurements using scanning-electron-microscope images

Abstract
An automatic technique has been developed to measure precisely the fractal dimension of the microstructure of sandstones from scanning-electron-microscope (SEM) images of fracture surfaces. The technique involves digitizing the images, filtering, counting geometrical features as a function of feature size, and fitting feature histograms. The magnification of the SEM is changed to cover 2.5 orders of magnitude in feature sizes. A power-law model, which includes the resolution of the digital filter, accounts for the feature size distributions for all magnifications and the scaling from magnification to magnification. Results have been obtained for a dozen sandstones, and the fractal dimension is observed to range from 2.55 to 2.85. The precision for averaged images is ±0.01. In addition, a long-length limit to the fractal regime is defined and measured.

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