Fractal measurements of sandstones, shales, and carbonates

Abstract

Measurements were made of the fractal properties of sandstones, shales, and carbonates using a statistical analysis of structural features on fracture surfaces. Fractal behavior is associated with power law behavior for the number of features as a function of the feature size on the pore‐rock interface. Only one sedimentary rock, a novaculite, was found not to have a fractal structure. The fractal dimensions range from 2.27 to 2.89, and the long‐length limits to the fractal regime range from 2 μm to over 50 μm. In all cases, the fractal behavior extends to less than 0.2 μm which is the measurement resolution. The porosity associated with the fractal pore‐rock interface can be calculated from the fractal parameters. Some of the samples have additional porosity not associated with power law behavior. Photographs and other evidence are used to show that the fractal structures are the result of diagenesis. Fractal diagenetic structures include euhedral quartz overgrowths, druse quartz, calcite, dolomite, clays, and chert.