Impact of Internal Magnetic Field Gradients on the NMR Relaxation Time Distribution

We explore the impact of internal magnetic field gradients, which arise due to the presence of a magnetic susceptibility contrast between grains and the pore fluid, on the relaxation time distribution. Relaxation times provide powerful insight into the pore geometry. This link to pore geometry relies on the fast-diffusion assumption, where relaxation is controlled by the pore surface and each pore is treated as isolated and is described by a single relaxation time. This allows the relaxation time distribution to be interpreted as a pore size distribution. However, internal gradients can complicate this interpretation by providing an additional relaxation mechanism impacting the decay.

We present both synthetic and laboratory studies investigating the impact of internal gradients on the relaxation time distribution. A COMSOL multiphysics package is employed to determine the magnetic field’s spatial distribution across the pore space, and to simulate the pore’s NMR relaxation. The NMR simulation accounts for both surface relaxation, and relaxation related to internal gradients. We observe that as the influence of internal gradients increases, through either greater magnetic susceptibility contrasts or the use of longer echo times, the shape of the relaxation time distribution is altered. In these cases, relaxation within a single pore is no longer described by a single characteristic relaxation time, instead requiring multiple relaxation times to capture the time-dependent behavior. As a result, the relaxation time distribution is broadened and shifted to faster relaxation times. Laboratory results, performed for several samples sieved to ensure narrow grain size distributions and with varying magnitudes of magnetic susceptibility contrasts, exhibit similar trends to those observed in the synthetic studies. These results have significant implications for the interpretation of relaxation data to obtain pore size distributions, and the derived estimates of hydraulic conductivity for materials containing magnetic components.