Laboratory and subsurface electromagnetic (EM) measurements on mudrocks are acquired at various operating frequencies. In the presence of an external EM field, clay- and conductive-mineral-rich mudrocks exhibit directional and frequency dispersive effective electrical conductivity and dielectric permittivity due to interfacial polarization (IP) phenomena. Conventional EM interpretation methods do not account for the IP effects clays and conductive minerals, and they process the effective conductivity and permittivity obtained at various frequencies separately using frequency-independent empirical models. Therefore, these interpretation methods generate inaccurate estimates of water saturation and total organic carbon in mudrock formations. We coupled an inversion algorithm with an electrochemical model, referred to as the PS model, to estimate water saturation, brine conductivity, surface conductance of clays, average grain size of clays, and average grain size of pyrite inclusions from multi-frequency conductivity and permittivity measurements.
The PS model predicts that the low-frequency effective conductivity of a mudrock containing 5% volume fraction of disseminated pyrite grains will vary from 70% to 200% of pyrite-free host conductivity with change in the operating frequency of EM measurements from 100 Hz to 100 kHz. Further, the high-frequency effective relative permittivity of that mixture will vary from 190% to +90% of the pyrite-free host relative permittivity with change in the operating frequency from 100 kHz and 10 MHz. The PS model predicts that, in contrast to EM induction and EM propagation logging measurements, galvanic resistivity measurements will be highly sensitive to laminations and non-sensitive to disseminated inclusions of clays and conductive minerals. Dielectric dispersion measurements at operating frequencies close to or higher than 100 MHz are shown to be unsusceptible to the IP effects of clays and pyrite grains.
The inversion algorithm coupled with the PS model jointly processes the multi-frequency electrical conductivity and dielectric permittivity of geological formations computed from the galvanic resistivity, EM induction, EM propagation, and dielectric dispersion logs. The inverted parameters exhibit low sensitivity to initial guesses and converge for initial guesses that are one to two orders of magnitude different from the true parameter values. The inversion algorithm was applied to two distinct synthetic cases of clay- and pyrite-bearing formations. Further, the inversion scheme was successfully applied to jointly interpret recently published multi-frequency effective conductivity and permittivity logs in a clay- and pyrite-bearing shale formation. Estimates of water saturation, brine conductivity, and surface conductance of clays in that formation are 0.84, 17.7 S/m, and 3.8×10−6 S, respectively.