Dielectric Characterization of Surface Relaxivity

NMR and dielectric measurements provide unique petrophysical tools to probe the molecular dynamics of restricted geometries. Both techniques exhibit time-dependent relaxations sensitive to electromagnetic surface interactions and sensitivity to diffusion length scales in the case of NMR relaxation. However, diffusion rates typical for pore fluids limit the accessible length scales probed with NMR. Dielectric measurements provide additional length scale interactions and measurements that can be incorporated with conventional NMR. These clarify the relaxation time T1 and T2 size assignments typically represented by r1 and r2 surface relaxivity and define the lateral extent of the “fast diffusion limit.” Using protocols established with the coupled physics used in magnetic resonance electrical properties tomography (MREPT) for imaging dielectric properties of tissues, we adapt a dielectric permittivity differential length to area correlation based on Maxwell’s equations. An established staged differential effective medium model for matrix and vug dielectric dispersion and a dielectric-T2 mapping technique are used to evaluate the NMR relaxation, diffusion, and formation factors based on measured length scales from scanning electron microscope (SEM) images of the matrix and micro-CT images of the vug system. Correlated NMR and dielectric measurements during spontaneous brine imbibition provide an additional technique to address surface relaxivity by comparing changes in dielectric permittivity in parallel with characterized surface relaxation rates (T1S or T2S). Rates are compared with BPP model correlation times established through dry matrix high-frequency limit dielectric relaxation and T1 NMR dispersion based on comparative 2 MHz and 23 MHz T1 distributions. The dielectrically classified T2 distributions show good correlations with petrophysical properties and image-based size distributions. Modeled surface relaxivity in the matrix fraction falls within the expected range with vug values related to the overlap in the distributions. The technique uses the extensive dynamic mobile charge length scales from dielectric measurements (Maxwell-Wagner effect) to refine our interpretation of easily measured NMR multi-exponential response. Although based on carbonates with clay-free surface conductance, adaptation to scaled clastic dielectric dispersion measurements is proposed.