Microscale Simulations of NMR Relaxation in Porous Media Considering Internal Field Gradients

Abstract

Longitudinal and transverse nuclear magnetic resonance (NMR) relaxation signatures in porous rock were simulated on the microscale to examine and quantify how physical hydrologic parameters, such as rock‐surface properties and pore sizes, affect longitudinal and transverse NMR signals of real, complex media. Parameters studied were: magnetic field strength, rock susceptibility, pore coupling, and surface reactivity. Using the finite element method (FEM), simulations of the spatial‐ and time‐dependent magnetization evolution in arbitrary pore geometries, diffusion regimes, and heterogeneous distributions of rock surface properties, i.e., surface relaxivity, were compiled using an adapted generic diffusion model coupled with magnetic gradient field calculations. The numerical simulations were validated using analytical solutions that are available for simple pore geometries. We observed a pore‐size‐dependent ratio of transverse T2 and longitudinal T1 relaxation times, and thus a pore‐size‐related and rock‐susceptibility‐dependent effective transverse surface relaxivity was deduced. This can be used to improve estimates of pore sizes and thus of permeability from transverse NMR relaxometry measurements. Simulations of connected pore systems showed significant influences of interpore coupling at hydrologically relevant pore sizes, e.g., fine sands. Depending on the dominant diffusion regime, the typically heterogeneous distribution of surface relaxivities in rocks and sediments, i.e., geological noise, can lead to a significant underestimation of derived pore sizes and thus of permeability.