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The Fractal Dimension as a Petrophysical Parameter.
TEXAS UNIV AT AUSTIN
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The secondary electron emission from a Scanning Electron Microscope SEM was used to determine that the pore spaces of seven sandstones and four dolomites exhibited fractal behavior over certain length scales. Data from the SEM measurements produced log-log plots that not only verified the fractal nature of the rocks, but also allowed for the determination of their fractal dimensions. To model the transport properties of fractal lattices, a two dimensional model known as the Sierpinski Carpet was used as a starting point. Results developed for the petrophysical properties of such fractal lattices, such as porosity, permeability, capillary pressure, et. are presented here. Although the results cannot be directly compared with experiments, they demonstrate a methodology that can be applied to three dimensional lattices as well. A variation of a three dimensional fractal structure known as the Menger Sponge was used to model the pore spaces in rocks in an attempt to determine transport properties of rocks from fractal data. The fractal data on the rock samples obtained from the SEM was combined with corresponding core analysis data to test the model. It was determined that the simple Menger Sponge was an inadequate model for fractal pore space within rocks as it estimated porosity values much higher than those commonly encountered in rock samples. However, a modified version of this model showed potential for accurately representing the pore space of rocks as it produced porosity values that were in the same range as those of the rock samples.
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