Correlated Inversion of Complex Dielectric Dispersion and NMR Measurements in Conventional Carbonates

Combinations of dielectric and NMR measurements are frequently used to improve saturation modeling in complex situations, often incorporating the concept of wettability. Due to the two methods' distinct tools and physical mechanisms, the interplay of the electrical and magnetic fields and their constitutive equations are generally not addressed. This is directly counter to the situation with the medical imaging modalities, magnetic resonance electrical properties tomography (MREPT) and magnetic resonance electrical impedance tomography (MREIT), where field-specific polarizations and relaxations are used to enhance the contrast. Both electrical and magnetic (EM) fields at the frequencies typically encountered in laboratory and logging environments impart molecular motions impacted by pore structure. In both instances, restricted motions are reflected in their individual responses' time or frequency domain. Using time-domain relaxations and variations in both EM fields, this work focuses on the practicality of using NMR and dielectric relaxation comparisons originally proposed by Bloembergen, Purcell, and Pound (BPP). Similar to the dipolar relaxation equivalence in the BPP model, we develop a relaxation time correlation assuming representative Maxwell-Wagner relaxations for the key pore components demonstrated by Myers. The distributions of dielectric relaxation times evident in carbonate dispersion curves from 1 – 300 MHz were quantified using the Havriliak-Negami (HN) model. The quantifications are then used to evaluate characteristic dielectric dispersions curves generated from a dielectric model introducing multiple pore systems in carbonates. The modeled distributions are spectrally mapped to the NMR T2 distributions based on Debye shielding distances correlated with the conductivity. The interplay of pore connectivity and surface and bulk diffusivity are modeled using a "two-fraction fast exchange model" by Brownstein and Tarr. Using dielectric and NMR experiments along with a combination of micro-CT and SEM imaging techniques, the NMR-based spectral distribution of dielectric relaxation times demonstrates that variable-length scales and fractal dimensions accessed through the dielectric dispersion measurements are more extensive than that implied by the standard reference to the "texture" of a carbonate sample. We also show that the modeled distributions are closely correlated with the conductivity and provide improved petrophysical insight for the frequently used Archie exponent combination (MN) associated with the water tortuosity.