Fractal dimension from the box counting method for REV permeability estimation

Resumo

Thomeer-based methods, widely used for permeability estimation of rock samples, rely on the
determination of pore throat distributions from mercury injection capillary pressure, for both sandstones and
carbonates. These methods comprise three different approaches for permeability calculation, all of them based on
concepts related to the Thomeer hyperbola. In this work, for the sake of permeability evaluation, we review and
adapt the expansion of the tubular bundle model of Purcell to a fractal tubular bundle for permeability calculation.
Our study is motivated by the assumption that fractal theory can be used to improve upscaling procedures, since it
provides the ideal mathematical tool to deal with the commonly observed self-similarity properties of complex
natural media. Furthermore, fractal concepts have been introduced and presented as a well-suited approach for
flow modeling because of their simple description of highly ramified spaces. Adding up to mercury injection data,
the box-counting method is applied to the analysis of thin-sections of thirty limestone samples as a way to obtain
their fractal dimension and hence permeability at the representative elementary volume (REV). It turns out that
the fractal approach proves to be not only of straightforward application but also to improve estimates of
permeability carried along the lines of Thomeer methodological principles.