2D multifractal analysis and porosity scaling estimation in Lower Cretaceous carbonates

The study of scaling porosity in carbonate rocks has great importance because (1) porosity measurements are usually made at scales that are different from the one of interest and (2) carbonate formations contain most of the hydrocarbon reservoirs and aquifers in the world. Despite these facts, scaling porosity in heterogeneous media, such as carbonate rocks, is still an open problem. The heterogeneity of carbonate rocks mainly resides in their complex texture. We have extended previous studies on carbonate multifractal behavior in pore space morphology at different scales, and we have developed a new equation based in fractal geometry that could be used to scale the porosity. In our methodology, we (1) perform a multifractal analysis in thin-section images of a set of complex carbonate rocks from the Lower Cretaceous, (2) review the effect of magnification in scanning-electronic-microscope and thin section images, (3) deduce a new scaling equation for porosity, and finally (4) evaluate this equation in the studied samples. We found that this new equation could be used under the approximation that the majority of the pores have a similar size, equivalent to the maximum pore size found in thin-section images. However, it must be applied carefully because the fractality/multifractality of pore spaces in carbonates could be present only in certain parts of the rocks and in a limited range that might not include the targeted scale. In fact, multifractality in the studied carbonate rocks seemed to be more complex than that found in previous studies. It was noticed that the proposed equation brought the benefit of fractal geometry formalism taking into account the physical scaling of pore space heterogeneities, and it indeed has the potential to estimate porosity at different spatial scales as an alternative method to find porosity when measurements are not available.