Estimating irreducible water saturation and permeability of sandstones from nuclear magnetic resonance measurements by fractal analysis

Understanding the relationships between the pore structure and bulk properties such as irreducible water saturation (Swir) and permeability (k) of rocks is a crucial problem in geoscience. In this study, two types of fractal dimension were determined from nuclear magnetic resonance (NMR) T2 relaxation time distribution and models for estimating Swir and k using fractal theory were proposed. In view of the data of sandstone samples from upper Paleozoic formation in China, we found a good agreement between the predicted Swir values based on fractal analysis and the experimental measurements, and the estimated k values based on the proposed model are within one order of magnitude of measured k. Additionally, another four frequently used k estimation models were compared with our proposed model, and the result support that the proposed approach has great potential in investigating k while certain limitation still exists. This procedure was applied on another set of sandstone samples collected from a different location, and the predicted permeability values are reliable. Our study suggests that the proposed Swir estimation model using NMR T2 data and fractal dimensions provides useful insights into characterizing the pore space properties of sedimentary rocks. Our work demonstrates that we can use NMR data to infer Swir directly, and the estimated Swir value can be well integrated in permeability prediction model, which improves the applications of NMR in characterizing the properties related to rock pores.