NMR T2 Response in Rough Pore Systems: Modeling and Analysis

Estimating pore size distribution from NMR T₂ responses typically assumes a smooth solid-pore interface. However, surface roughness accelerates NMR T₂ relaxation and thus leads to an underestimation of the pore size distribution. Until now, only a few studies investigated the surface roughness effect. This work systematically studies the influence of surface roughness on NMR T₂ responses and introduces a correction factor to bring incorrect T₂ values back to the correct values. This study includes three main sections: creating 3D pore structures with roughness, simulating NMR T₂ relaxation using the random walk method, and quantifying the roughness effect. Constrained Latin hypercube sampling is used to create representative examples in a space-filling manner, constrained by the fast diffusion limit. Then random walk simulations are implemented, and NMR T₂ responses in smooth and rough pores are calculated. To accurately estimate pore radius, a "value-to-value" model is developed to map the nonlinear relationship between a 3D roughness parameter and the proposed correction factor. The accuracy of the proposed model is validated by comparing the corrected NMR T₂ responses to the reference results obtained from smooth pore systems. Numerical results show that the proposed model can correctly evaluate pore sizes from decreased NMR T₂ responses caused by the surface roughness effect. Previous works incorporated this effect into surface relaxivity as they attempted to retain the pore radius and meanwhile reproduce the faster relaxation rate. However, this may break down the assumption of fast diffusion limit. Instead, this study mitigates this limitation by separating the roughness effect from surface relaxivity. The proposed correction factor offers an alternative approach to calculating the correct pore radius by accounting for the influence of surface roughness at the pore scale.