Nuclear-magnetic-resonance (NMR) relaxation experimentation is an effective technique for nondestructively probing the dynamics of proton-bearing fluids in porous media. The frequency-dependent relaxation rate $T_1^{-1}$ can yield a wealth of information on the fluid dynamics within the pore provided data can be fit to a suitable spin diffusion model. A spin diffusion model yields the dipolar correlation function $G\left(t\right)$ describing the relative translational motion of pairs of ${}^1\mathrm{H}$ spins which then can be Fourier transformed to yield $T_1^{-1}$. $G\left(t\right)$ for spins confined to a quasi-two-dimensional (Q2D) pore of thickness $h$ is determined using theoretical and Monte Carlo techniques. $G\left(t\right)$ shows a transition from three- to two-dimensional motion with the transition time proportional to $h^2$. $T_1^{-1}$ is found to be independent of frequency over the range 0.01–100 MHz provided $h\gtrsim 5$ nm and increases with decreasing frequency and decreasing $h$ for pores of thickness $h<3$ nm. $T_1^{-1}$ increases linearly with the bulk water diffusion correlation time ${\tau }_b$ allowing a simple and direct estimate of the bulk water diffusion coefficient from the high-frequency limit of $T_1^{-1}$ dispersion measurements in systems where the influence of paramagnetic impurities is negligible. Monte Carlo simulations of hydrated Q2D pores are executed for a range of surface-to-bulk desorption rates for a thin pore. $G\left(t\right)$ is found to decorrelate when spins move from the surface to the bulk, display three-dimensional properties at intermediate times, and finally show a bulk-mediated surface diffusion (Lévy) mechanism at longer times. The results may be used to interpret NMR relaxation rates in hydrated porous systems in which the paramagnetic impurity density is negligible.

• Received 1 November 2016

DOI:https://doi.org/10.1103/PhysRevE.95.033116