Multiscale characterization of pore spaces using multifractals analysis of scanning electronic microscopy images of carbonates

Pore spaces heterogeneity in carbonates rocks has long been identified as an important factor impacting reservoir productivity. In this paper, we study the heterogeneity of carbonate rocks pore spaces based on the image analysis of scanning electron microscopy (SEM) data acquired at various magnifications. Sixty images of twelve carbonate samples from a reservoir in the Middle East were analyzed. First, pore spaces were extracted from SEM images using a segmentation technique based on watershed algorithm. Pores geometries revealed a multifractal behavior at various magnifications from 800x to 12 000x. In addition, the singularity spectrum provided quantitative values that describe the degree of heterogeneity in the carbonates samples. Moreover, for the majority of the analyzed samples, we found low variations (around 5 %) in the multifractal dimensions for magnifications between 1700x and 12 000x. Finally, these results demonstrate that multifractal analysis could be an appropriate tool for characterizing quantitatively the heterogeneity of carbonate pore spaces geometries. However, our findings show that magnification has an impact on multifractal dimensions, revealing the limit of applicability of multifractal descriptions for these natural structures.