A finite element approach to forward modeling of nuclear magnetic resonance measurements in coupled pore systems

Abstract

Porous media characterized by a hierarchy of length scales are ubiquitous in industry and nature, and include carbonate rocks, cements, heterogeneous catalysts, and biological cells. Nuclear magnetic resonance (NMR) is a popular tool for studying liquid-saturated porous materials, where the spin relaxation rate is generally considered proportional to pore size. However, in porous granular media, the relaxation rate is modified by diffusion between the intraparticle and interparticle pores. The observed relaxation rates do not reflect the pore size under such conditions. Deconvolving the various contributions of surface relaxation, geometry, and diffusion is nontrivial, and forward models are a powerful technique for elucidating the underlying pore structure. Various forward models have been proposed previously, including analytic solutions and random walk simulations. Here, a finite element method is adopted to simulate the diffusion of nuclear magnetization in a coupled pore geometry. We validate our model against existing solutions and use the simulations to determine the surface relaxivity of powdered silica by matching experimental results. The finite element approach is more versatile than other modeling methods, allowing direct visualization of the diffusing magnetization and being trivially extensible to multidimensional NMR exchange experiments.