Abstract. 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.

We conducted laboratory measurements of Vp (compressional waves), Vs (shear waves), porosity and permeability on forty nine dry carbonate core plug samples at ambient pressure and temperature. We also, performed an initial lithological description, based on Dunham's carbonate rock classification to fully characterize the samples. The study results were analyzed to search for potential correlations between the different rock properties and lithological characteristics. We used cross plots of porosity-permeability, Vp - porosity, Vs - porosity, Vp - permeability, Vs – permeability, and Vp-Vs, for all samples and each rock type. The preliminary results from our analysis suggest that the acoustic velocities are highly affected by heterogeneity. The study also confirms an inverse relation between porosity and acoustic velocities, where pore size and pore type can be the main factors controlling the acoustic response at a given porosity. In addition, a general inverse tendency between permeability and acoustic velocities is found. The results also show that carbonate mudstones follow consistent trends of porosity-permeability, Vp - porosity, Vs - porosity, Vp - permeability, and Vs - permeability. This result can probably be attributed to the relativlely more uniform internal structure of carbonate mudstones compared with the other carbonate rock types. Wackestones and packestones present relationships that are less consistent and more dispersed than the ones found for mudstones for instance. The rest of the rock types display a great scatter and non apparent relationships. Finally, we find an empirical correlation between Vp and Vs that can be used to identify gas zones. This study has a great significance in the process of a better understanding of how acoustic velocities from different types of carbonate rocks relate to each other and to their rock properties. This knowledge can potentially be used to diagnose gas zones, predict Vs values, identify different types of carbonate rocks using well log data, and improve seismic interpretation and inversion.

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