Modelling effective diffusion for accurate NMR pore size analysis in nano- and microporous rocks

Low-field NMR (LF-NMR) is a widely applied technique for evaluating pore size distribution (PSD) in porous materials. Conventional approaches typically assume surface-controlled spin-spin relaxation and negligible diffusion contributions under the fast-diffusion regime, which introduces systematic errors when applied to nano- and microporous systems. In this work, we present the Effective Diffusion Cubic (EDC) model, a new framework for LF-NMR-based PSD estimation in tight rocks. The EDC method incorporates pore-size dependence of both the effective diffusion coefficient and the induced internal magnetic field gradient. Crucially, the effective diffusion coefficient, D(d), is parameterized by a logistic function that faithfully approximates the Padé form, enabling a precise quantification of diffusion-related effects on T₂ relaxation. Applied to nine siliciclastic core samples, the EDC approach produced PSDs corrected for diffusion-induced distortions and in closer agreement with independent reference data compared to conventional models. These results demonstrate that the EDC methodology provides a physically consistent and more accurate means of quantifying pore systems, thereby enhancing NMR-based petrophysical characterization of tight rock formations.