Nuclear magnetic resonance surface relaxivity and its advanced application in calculating pore size distributions

Both laboratory and downhole nuclear magnetic resonance (NMR) measurements are commonly used to calculate the pore size distribution (PSD) that is important in determining the reservoir storage capacity and evaluating producibility, etc. The surface relaxivity is a key parameter to calculate the PSD using NMR transversal relaxation time (T-2) distributions. Accurate surface relaxivity value would result in a reasonable PSD. In order to comprehensively study surface relaxivity, the conventional sandstone, tight sandstone, and shale samples are selected to perform experiments including porosity, permeability, NMR, mercury injection capillary pressure (MICP) and low temperature nitrogen adsorption (LTNA), etc. Three approaches, including LTNA, MICP, and Kozeny's equation, are used to determine the surface relaxivity. We find that for all samples, the surface relaxivity determined with Kozeny's equation is greater than that using LTNA and MICP data, indicating that surface relaxivity of smaller pores is less than that of bigger pores. It is also observed that the surface relaxivity of conventional sandstone is greater than that of tight sandstone and shales. The surface relaxivity of sandstone and shale samples are both affected by clay content. For shale samples, the surface relaxivity ranges from 3.41 mu m/s to 9.79 mu m/s and is influenced by organic matter contents as well. An equation for predicting surface relaxivity of shale is established. Finally, we propose an advanced method for calculating reasonable PSDs of sandstone and shale formation by the combination of two surface relaxivities, which could be applied to laboratory and field wells.