Wideband directional complex electrical conductivity of geomaterials : a mechanistic description
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Subsurface electromagnetic (EM) measurements in shaly sands, sand-shale laminations, and organic-rich mudrocks, to name a few examples, exhibit directional and frequency dispersive characteristics primarily due to the effects of electrical conductivity anisotropy, dielectric permittivity anisotropy, and interfacial polarization phenomena. Conventional resistivity interpretation techniques for laboratory and subsurface EM measurements do not account for the effects of dielectric permittivity, dielectric loss factor, dielectric dispersion, and dielectric permittivity anisotropy arising from interfacial polarization phenomena. Furthermore, laboratory measurements on 1.5-inch-diameter, 2.5-inch-long core plugs acquired at discrete depths in wells are generally utilized to improve the estimation of petrophysical properties based on conventional resistivity interpretation of subsurface EM measurements. Electrical measurements performed on 4-inch-diameter, 2-feet-long whole core samples represent closer approximations to the electrical properties of subsurface formations compared to widely-used galvanic measurements of core plugs. The first objective of this dissertation is to develop a non-contact and non-invasive, laboratory-based EM induction apparatus, referred to as the WCEMIT, to measure the complex-valued electrical conductivity tensor of whole core samples at high resolution and at multiple frequencies for improved core-well log correlation. The tensor functionality of the WCEMIT is sensitive to the directional nature of electrical conductivity, dielectric permittivity, and dielectric loss factor, while its multi-frequency functionality is sensitive to the frequency-dispersive electrical properties of the samples. Finite-element and semi-analytic EM forward models of the WCEMIT are used to calibrate WCEMIT measurements and to estimate various effective electrical properties. WCEMIT measurements are successfully applied to the estimation of directional conductivity, dielectric permittivity, formation resistivity factor, Archie's porosity exponent, relative dip, azimuth, and anisotropy ratio. It is found that brine-saturated samples containing pyrite and graphite inclusions exhibit a negative X-signal response, large frequency dispersion in the R-signal response, large effective permittivity, and significant frequency dispersion of effective conductivity and permittivity in the frequency range of 10 kHz to 300 kHz. Further, graphite-bearing samples exhibit significantly different frequency dispersion properties compared to pyrite-bearing samples. Estimated values of effective relative permittivity of samples containing uniformly distributed 1.5-vol% of pyrite inclusions were in the range of 10³ to 10⁴, while those containing uniformly distributed 1.5-vol% of graphite inclusions were in the range of 10⁵ to 10⁶. At an operating frequency of 58.5 kHz, samples containing 1.5-vol% of graphite inclusions and those containing 1.5-vol% of pyrite inclusions exhibited effective conductivity values that were 200% and 95%, respectively, of the host conductivity. True conductivity and permittivity of hydrocarbon-bearing host media can be determined by processing the estimated effective conductivity and permittivity of conductive-mineral-bearing samples. Accordingly, the second objective of this dissertation is to develop a mechanistic electrochemical model, referred to as the PPIP-SCAIP model, that quantifies the directional complex electrical conductivity of geomaterials containing electrically conductive mineral inclusions, such as pyrite and magnetite, that are uniformly distributed in a fluid-filled, porous matrix made of non-conductive grains possessing surface conductance, such as silica, clay-sized particles, and clay minerals. PPIP-SCAIP model predictions successfully reproduce several laboratory measurements of multi-frequency complex electrical conductivity, relaxation time, and chargeability of mixtures containing electrically conductive inclusions in the frequency range of 100 Hz to 10 MHz. The mechanistic model predicts that the low-frequency effective electrical conductivity of geomaterials containing as low as 5% volume fraction of disseminated conductive inclusions will vary in the range of 70% to 200% of the host conductivity for operating frequencies between 100 Hz to 100 kHz, while its high-frequency effective relative permittivity will vary in the range of 190% to 90% of the host relative permittivity for operating frequencies between 100 kHz and 10 MHz. The model indicates high sensitivity of subsurface EM measurements to the electrical properties, shape, volumetric concentration, and size of the inclusion phase, and to the conductivity of pore-filling electrolyte.