Quantification of Surface Roughness Effect on NMR T2 Relaxation Using a Novel 3D Pore Surface Roughness Characterization Workflow

Evaluation of pore size distributions in porous rocks using Nuclear Magnetic Resonance (NMR) T₂ relaxation time typically assumes spherical pores with smooth surfaces. This simplification leads to inaccuracies by neglecting the impact of surface roughness on NMR T₂ relaxation. Previous studies have attempted to incorporate the surface roughness effect into surface relaxivity to reduce these systematic errors in the estimation of pore size distribution, but these methods are often sample-specific, thereby limiting their broader applicability. To overcome these limitations, we propose a novel image-based surface sourghness characterization workflow and develop a correlation to correct the shortened T₂ relaxation times in rough spherical pores. Unlike previous approaches, our method decouples the geometric impact of surface roughness from surface relaxivity, preserving the fast diffusion limit and enhancing generalizability. The workflow simplifies roughness characterization by transforming each 3D volumetric pore structure into roughness profiles, deriving a dimensionless pore roughness coefficient (PRC). Random walk simulations are then employed to compute T₂ relaxation times for various pore configurations. The T₂ correction factor is defined as the ratio of the T₂ relaxation times in rough pores to those in the corresponding spherical pores of the same volume. A nonlinear mapping between PRC and T₂ correction factor is established to correct the NMR T₂ relaxation time. Numerical results demonstrate that the proposed method accurately predicts the intrinsic pore radius, making it a practical postprocessing tool for extracting representative pore sizes from NMR T₂ relaxation times while accounting for surface roughness effects.