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URTeC: 2163422

Complex Electrical Conductivity of Mudrocks and Source-Rock Formations Containing Disseminated Pyrite Siddharth Misra and Carlos Torres-Verdín, The University of Texas at Austin; Dean Homan and John Rasmus*, Schlumberger Copyright 2015, Unconventional Resources Technology Conference (URTeC) DOI 10.15530/urtec-2015-2163422 This paper was prepared for presentation at the Unconventional Resources Technology Conference held in San Antonio, Texas, USA, 20-22 July 2015. The URTeC Technical Program Committee accepted this presentation on the basis of information contained in an abstract submitted by the author(s). The contents of this paper have not been reviewed by URTeC and URTeC does not warrant the accuracy, reliability, or timeliness of any information herein. All information is the responsibility of, and, is subject to corrections by the author(s). Any person or entity that relies on any information obtained from this paper does so at their own risk. The information herein does not necessarily reflect any position of URTeC. Any reproduction, distribution, or storage of any part of this paper without the written consent of URTeC is prohibited.

Abstract Organic-rich mudrock and source-rock formations generally contain electrically conductive pyrite mineralization in the form of veins, laminations, and grains. When an external electromagnetic (EM) field is applied to geomaterials containing pyrite inclusions under redox inactive subsurface conditions, charge carriers in a brine-filled host (predominantly, ions in the pore-filling brine) and those in the electrically conductive mineral inclusions (electrons and holes) accumulate/deplete at impermeable host-inclusion interfaces giving rise to perfectly-polarized interfacial polarization (PPIP) phenomena. Such polarization phenomena influence the diffusion, accumulation, and migration of charge carriers in the mixture, thereby significantly altering the effective electrical conductivity and effective dielectric permittivity of the geomaterial. In addition, the relaxation process associated with polarization phenomena and the time required to develop field-induced polarization of inclusions contribute to the dispersive EM response of such geomaterials. This behavior causes the effective electrical conductivity (σeff) and dielectric permittivity (εeff) of mudrocks and source rocks containing pyrite inclusions to become frequency-dependent. Existing resistivity interpretation methods that neglect the effects of PPIP phenomena are inadequate for the study of organic-rich mudrock and source-rock formations. We constructed a laboratory whole core EM induction tool (WCEMIT), operating in the 10 kHz to 300 kHz frequency range, to investigate the effects of PPIP phenomena on directional multi-frequency inductive-complex conductivity measurements. Measurements were performed on 4-inch diameter, 2-ft long glass-bead packs containing disseminated pyrite inclusions. A semi-analytical numerical method was then implemented to estimate the effective conductivity and relative permittivity of pyrite-bearing glass-bead packs. We found significant frequency dispersion, large values of effective relative permittivity, drastic alteration in effective conductivity with respect to the conductivity of the uncontaminated host, and presence of effective anisotropy on conductivity and permittivity due to the effects of polarization of the disseminated pyrite inclusions. Estimated values of effective conductivity and relative permittivity of pyrite-bearing glass-bead packs were subsequently inverted using the PPIP model to estimate both the electrical conductivity of the uncontaminated host and the electrical properties of pyrite inclusions. Introduction The EM response of organic-rich mudrocks and source-rock formations exhibits frequency dispersion and high dielectric permittivity due to interfacial polarization (IP) of conductive mineral inclusions and that of surface chargebearing clay- and silt-sized grains. IP phenomena significantly influence charge-carrier migration, accumulation, and diffusion processes in geomaterials (Schmuck and Bazant, 2012; Wong, 1979). However, limited published laboratory and modeling work has been carried out to understand IP effects of electrically conductive inclusions on subsurface galvanic, EM induction, and EM propagation measurements (Anderson et al., 2006; Wang and Poppitt, 2013; Misra et al., 2015b). Existing resistivity interpretation techniques for the three above-mentioned subsurface EM measurements do not account for PPIP phenomena (Corley et al., 2010). As a result, conventional resistivity interpretation methods typically give rise to inaccurate results in pyrite-bearing sedimentary formations (Altman et al., 2008), pyrite-bearing mudrocks (Kethireddy et al., 2014), and pyrite-bearing source-rock formations (Anderson et

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al., 2008). Passey et al. (2010) mentioned the challenges in resistivity interpretation due to presence of conductive pyrite inclusions in source-rock formations and shale gas reservoirs. Witkowsky et al. (2012) emphasized the need to correct resistivity measurements for the effect of pyrite content prior to using resistivity measurements in the delta logR method owing to a linear correlation of total organic content (TOC) and pyrite content, as observed in several shale gas formations. Recently, Chen and Heidari (2014) showed that directional dielectric permittivity estimation is strongly affected by presence and connectivity of mature organic matter and pyrite inclusions. Clavier et al. (1976) measured the effect of pyrite inclusions on various resistivity logging measurements. They observed a strong dependence of resistivity measurements on the distribution of pyrite inclusions and operating frequency of the logging tool; despite the absence of electrical connectivity of the pyrite phase, an increase in frequency of electrical measurements led to an increase in electrical conductivity of the mixture. Clavier et al. (1976) showed that the frequency dispersion response of a pyrite-bearing mixture depends on the operating frequency, pyrite volume fraction, and pore-filling brine salinity. Recently, Clennell et al. (2010) observed that disseminated pyrite inclusions in sandstones resulted in a drastic decrease in resistivity when pyrite content exceeded 5% volume fraction. They modeled the experimentally-measured conductivity and dielectric permittivity response of sandstones containing disseminated pyrite grains using the Hanai-Bruggeman equation in the 1 Hz to 100 kHz frequency range. In doing so, Clennell et al. (2010) neglected the effects of interfacial polarization of pyrite inclusions. More recently, Yu et al. (2014) showed that both laboratory and downhole measurements exhibited frequency dispersion in the 0.1 Hz to 10 kHz frequency range due to presence of pyrite inclusions (1-5 wt%) in high TOC marine shale cores. They suggested that the implementation of a complex resistivity method could improve resistivity interpretations in marine shale gas formations. Further, they used the empirical dual Cole-Cole model (instead of a mechanistic formulation) to analyze their data. In this paper, we use a Whole Core Electromagnetic Induction Tool (WCEMIT) to experimentally investigate the effects of interfacial polarization of pyrite inclusions on multi-frequency inductive-complex conductivity measurements in the frequency range 10 to 300 kHz. In order to avoid difficulties associated with galvanic methods (Kickhofel, 2010), WCEMIT is designed based on the physics of EM induction. Moreover, WCEMIT allows directional multi-frequency inductive-complex conductivity measurements of whole core samples. Being a tensor induction tool, WCEMIT measurements have both a resistive (R-signal) and a reactive component (X-signal). We analyze tool measurements (R- and X-signal) using a semi-analytical numerical method (Misra et al., 2015c), herein referred to as the semi-analytical WCEMIT response model, which simulates the multi-frequency WCEMIT response to 4-inch outer diameter, 2-ft long glass-bead packs placed symmetrically inside the tool conduit. Using this numerical method, we estimate effective permittivity and conductivity of the pyrite-bearing glass-bead packs. As the final step, the mechanistic multi-frequency PPIP model (Misra et al., 2015a) is used to estimate the conductivity and permittivity of the conductive inclusion phase and inclusion-free brine-filled host. The mechanistic basis of the PPIP model (Misra et al., 2015a) builds on the descriptions of interfacial polarization of conductive inclusions developed and validated by Wong (1979), Grosse and Barchini (1992), Revil and Florsch (2015), and Placencia-Gómez and Slater (2014). Method WCEMIT System. The system (Figure 1) is designed to perform multi-frequency inductive-complex conductivity tensor measurements, 𝛴̿ (Equation 2), on 4-inch diameter, 2-ft long geological whole core samples placed symmetrically inside the WCEMIT conduit (Figure 2). The measuring system generates data with a high signal-tonoise ratio at seven discrete frequencies: 19.6, 31.2, 41.5, 58.5, 87.6, 150, and 261 kHz. For frequencies below 10 kHz, the magnitude of induced receiver voltage decreases drastically and its phase becomes affected by environmental noise. At the other extreme, for frequencies above 300 kHz, the operating frequency approaches the resonant frequency of the transmitter coils; consequently, the coils exhibit capacitive properties that decrease the stability of the measurements. Figure 1 shows the laboratory setup of the system that comprises the tool and its peripheral electronics, specifically transmitter (Tx) resonance circuit, receiver amplifier (Rx), switch unit, transmitter pre-amplifier, and lockin amplifier. Figure 2 shows a 4-inch diameter, 2-ft long Berea sandstone whole core placed symmetrically inside the 4-inch inner diameter, 20-inch long tool conduit. The tool employs tri-axial EM induction physics to measure the complex-valued electrical trans-impedance, 𝑍𝑖𝑗 (Equation 3), tensor of samples placed in its conduit; 𝑍𝑖𝑗 is converted into apparent complex conductivity measurements using well-defined transmitter-receiver geometric constants (𝐾𝑖𝑗 ; Equation 3).

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The tensor functionality of the tool is sensitive to the directional nature of electrical properties of the samples under investigation, while its multi-frequency functionality is sensitive to the dielectric-dispersive characteristic of those samples. A primary component of the tool is the tri-axial coil system constructed on its outer body. It comprises three separate coil systems, namely transmitter, bucking, and receiver coil system. Further, each coil system contains three collocated orthogonal coils: two saddle-type coils (X- and Y-coil) and one helical coil (Z-coil). Magnetic fields are generated by sequentially energizing the three orthogonal coils of the transmitter-coil system (Figure 3). To that purpose, an alternating current (𝐼𝑖 ) is driven sequentially through the three transmitter coils, where subscript i identifies the energized X-, Y-, or Z-coil. The transmitter current, 𝐼𝑖 , is measured within the resonance circuit using an Agilent 34401A 6.5 digit multimeter (Misra et al., 2015c). The i-th energized transmitter coil generates a magnetic field through the sample placed in the conduit. This in turn induces eddy currents in the sample volume. The magnitude and phase of the eddy currents depend on the electrical properties of the medium. Induced eddy currents subsequently induce a complex-valued voltage in each of the three orthogonal coils in the receiver (𝑉𝑟,𝑗 ) and bucking (𝑉𝑏,𝑗 ) coil system, where subscript j can be assigned a value of 1, 2, or 3 to differentiate between X-,Y-, and Z-coil, respectively, subscript r symbolizes the receiver coil system, and subscript b symbolizes the bucking coil system. Receiver and bucking coil systems are connected in series to remove complex-valued voltage contributions due to direct magnetic-field coupling between the transmitter and receiver coil systems. Complex-valued voltages induced across one of the three collocated orthogonal coils in the receiver coil system and those induced in the bucking coil system are simultaneously measured through the input channel of the lock-in amplifier driven by an Agilent E3630A dc power supply (Misra et al., 2015c) to remove the induced voltages between the corresponding transmitter and receiver coils. In doing so, 𝑉𝑟,𝑗 and 𝑉𝑏,𝑗 are added in accordance with the three-coil induction logging principle (Kickhofel et al., 2010) that removes the direct magnetic field coupling between transmitter and receiver coils, such that 𝑉𝑗 = 𝑉𝑟,𝑗 + 𝑉𝑏,𝑗 , (1) where 𝑉𝑗 is the complex-valued induced receiver voltage across the j-th coil that is free from contribution due to the direct magnetic-field coupling. Conventional rock formations have low dielectric permittivity and negligible frequency dispersion. Therefore, the induced receiver voltage response measured in such formations has negligible phase that results in an apparent conductivity (𝛴𝑖𝑗 ) measurement having negligible X-signal (reactive component). However, in our work, we measure samples exhibiting high dielectric permittivity and substantial frequency dispersion due to PPIP phenomena associated with disseminated conductive pyrite inclusions. Therefore, it is crucial to include negative-valued X-signal response for purposes of inverting the measured apparent complex conductivity tensor, 𝛴̿, to obtain the effective horizontal conductivity (σh,eff), horizontal permittivity (εh,eff), conductivity anisotropy (λc,eff), and permittivity anisotropy (λe,eff) of the sample placed symmetrically inside the tool conduit. The apparent complex conductivity tensor is expressed as 𝛴𝑥𝑥 𝛴𝑥𝑦 𝛴𝑥𝑧 ̿ 𝛴 𝛴 = ( 𝑦𝑥 𝛴𝑦𝑦 𝛴𝑦𝑧 ), (2) 𝛴𝑧𝑥 𝛴𝑧𝑦 𝛴𝑧𝑧 where 𝛴𝑖𝑗 is obtained by dividing the complex-valued induced receiver voltage in the j-th coil, 𝑉𝑗 , by the mathematical product of current in the i-th energized transmitter coil, 𝐼𝑖 , and the geometric factor of the i-th transmitter coil and j-th receiver coil coupling, 𝐾𝑖𝑗 . As explained earlier, 𝛴𝑖𝑗 has a resistive component, 𝑅𝑖𝑗 , and a reactive component 𝑋𝑖𝑗 . In other words, 𝛴𝑖𝑗 can be written as the ratio of trans-impedance (𝑍𝑖𝑗 ) and geometric factor of the transmitter-receiver coupling, which can be expressed as 𝑍𝑖𝑗 𝑉𝑗 𝛴𝑖𝑗 = 𝑅𝑖𝑗 + 𝑖𝑋𝑖𝑗 = − ( ) = − ( ), (3) 𝐾𝑖𝑗 𝐾𝑖𝑗 𝐼𝑖 where 𝑉𝑗 is the complex-valued induced receiver voltage, 𝑍𝑖𝑗 is the tans-impedance, which in tri-axial nomenclature is the ratio of complex-valued induced receiver voltage in the j-th coil and the current flowing in the i-th transmitter coil. 𝐾𝑖𝑗 used in Equation 3 is computed by modeling the induced receiver voltage as a function of sample conductivity using the COMSOL AC/DC module (Misra et al., 2015c). WCEMIT Measurements. 4-inch outer diameter, 3.8-inch inner diameter, 2-ft long cylindrical glass vases were used to prepare the glass-bead packs. All glass-bead packs were made of 575-µm radius glass beads fully-saturated with

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3.75 S/m brine. In order to prepare a glass-bead pack, firstly, a mixture of glass beads and inclusions of desired sizes was poured into a cylindrical glass vase to make a 2-inch thick layer. Following that, brine is poured into the glass vase to fully saturate the 2-inch thick layer. Then, the vase was vibrated using a mechanical hand-held shaker to consolidate the mixture, remove trapped air bubbles, and uniformly distribute the pore-filling brine. The three abovementioned steps were repeated until the entire glass vase was tightly-filled with glass beads, inclusions, and brine. We consistently prepared 2-ft long samples inside the cylindrical vase with a brine-filled porosity of approximately 38%. Two sizes of nearly-spherical pyrite inclusions were used in this work, namely Pyrite Red (average diameter = 50 µm) and Pyrite Yellow (average diameter = 130 µm) grains manufactured by Washington Mills (http://www.washingtonmills.com/products/iron-pyrite/). The glass beads used in this work are 1.15-mm diameter Megalux beads manufactured by Swarco Company (http://www.swarco.com/en/Products-Services/TrafficMaterials/Glass-Beads). WCEMIT measurements on as-received whole core samples will require correction for the environmental and transport effects during core cutting and core surfacing (Misra et al., 2013). WCEMIT Response Model. A semi-analytical EM method was developed to perform WCEMIT response modeling (Misra et al., 2015c) that is significantly faster compared to the WCEMIT simulation performed with COMSOL-based EM finite elements. This numerical method computes the WCEMIT’s tri-axial EM sensor response in a medium with two concentric cylindrical regions that are in electrical communication with each other. We implemented this EM tool response model to estimate the σh,eff, εh,eff, λc,eff, and λe,eff of glass-bead packs (Figures 7, 8, 9, and 10). The method models helical and saddle-type coils in the induction (10-400 kHz) and propagation (0.4-2 MHz) frequency range. It allows for an infinitely-long electrically-anisotropic cylindrical volume surrounded by the helical and saddle-type coils (Figure 3) and a very low conductivity medium representing air. For modeling purposes, we simplified each turn of the helical coil as a circular coil, and each turn of the saddle-type coils as a single-turn coil described by an azimuthal aperture angle, height, and radius. First, Maxwell’s equations were solved in the infinitely-long medium, comprising the two electrically-connected anisotropic axially-symmetrical cylindrical layers, by expressing the solutions of Maxwell’s equations in terms of two scalar functions (Hansen potentials). A Green’s function solution of Maxwell’s equations was constructed with the Hansen potentials as the vector fields. Then, the electrical field induced in the cylindrical layers was solved analytically to obtain an integral function. Subsequently, we derived an expression of the induced receiver and bucking voltages in an integral form. A MATLAB-based adaptive Lobatto Quadrature method was implemented to solve the integral forms. We validated the semi-analytical tool response model by comparing its predictions with that of the COMSOL-based EM finite-element model. Figures 5 and 6 indicate good agreement between the two modeling schemes for R- and X-signal responses and for real- and imaginary-part of the induced voltage response, respectively. PPIP Model. We apply the PPIP model to estimate electrical properties of the inclusion-free host and disseminated inclusion phase by inverting the εeff and σeff of the samples. Assessment of electrical properties of the inclusion-free host leads to improved estimation of water saturation, TOC, and connate water salinity. In this paper, we generate PPIP model predictions that best fit the dispersive σeff and εeff values, which were estimated using the semi-analytical tool response model (Figures 11, 12, 13, and 14). Unlike empirical Cole-Cole-type models, the PPIP polarization model employs a mechanistic approach that incorporates all the key petrophysical parameters that govern the diffusion-charge dynamics inside and around the conductive spherical inclusions dispersed in the porous host medium in a redox-inactive condition (Misra et al., 2015a). The model assumes negligible EM coupling and dipole-dipole interaction among the inclusions and grains in the mixture. In this model, a linear approximation of Poisson-NernstPlanck’s (PNP) equations of dilute solution theory is first invoked to determine the induced dipole moment of a representative volume containing a single conductive inclusion completely surrounded by electrolyte or matrix. Next, the model invokes a consistent effective-medium formulation to determine the effective complex electrical conductivity of the mixture. Misra et al. (2015a) validated the PPIP model against laboratory measurements of frequency dispersion due to conductive inclusions disseminated in a brine-filled porous sand grains previously published in various peer-reviewed sources. Misra et al. (2015b) used this model to quantify the significant effect of a small volume fraction of pyrite and graphite inclusions on subsurface galvanic resistivity, EM induction, and EM propagation measurements. Results Using the WCEMIT system, we first measured the coplanar (Figure 7) and coaxial (Figure 8) apparent complex conductivity of glass-bead packs containing varied volume fractions (0.5%, 1.5%, 2.5%, or 5%) of uniformly distributed Pyrite Red inclusions. The real- and imaginary-part of an apparent complex conductivity measurement are

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also referred to as the R- and X-signal, respectively. In Figures 7 and 8, we observe frequency dispersions in the Rand X-signal responses. The magnitude of frequency dispersions in the R- and X-signal responses increase with an increase in volume fraction of Pyrite Red inclusions in glass-bead packs. As observed in many subsurface EM tool measurements (Anderson et al., 2006; Wang and Poppitt, 2013), we obtained large negative X-signal responses for pyrite-bearing glass-bead packs. This behavior indicates that presence of pyrite inclusions significantly influences the R- and X-signal responses. Interestingly, the R- and X-signal responses obtained in coaxial direction (Figure 8) are significantly different from that obtained in coplanar direction (Figure 7), implying that the glass-bead packs possess both conductivity and permittivity anisotropy. In order to estimate σeff and εeff values of glass-bead packs from the apparent complex conductivity measurements, the semi-analytical tool response model predictions, identified with dotted curves in Figures 7 and 8, were generated to fit the apparent complex conductivity measurements, identified with discrete points in Figures 7 and 8. Using the WCEMIT system, we also measured the coplanar (Figure 9) and coaxial (Figure 10) apparent complex conductivity of samples containing disseminated Pyrite Red (average radius = 25 µm) or Pyrite Yellow (average radius = 65 µm) inclusions at two different volume fraction (1.5% or 5% volume fraction). In Figures 9 and 10, we observe that frequency dispersions in R- and X-signal responses are significantly influenced by diameter of pyrite inclusions. Glass-bead packs containing larger-diameter Pyrite Yellow inclusions exhibit a peak in X-signal response. This peak is due to relaxation time associated with interfacial polarization phenomena, which depends on diameter of the homogeneously dispersed inclusions. We observe that the magnitude of frequency dispersions in R- and X-signal responses increase with an increase in the size of pyrite inclusions disseminated in the glass-bead packs. In order to obtain the σeff and εeff values of the glass-bead packs, semi-analytical tool response model predictions, identified with dotted curves in Figures 9 and 10, were generated to fit the apparent complex conductivity measurements, identified with discrete points in Figures 9 and 10. As described earlier, after measuring the R- and X-signal responses of glass-bead packs, the semi-analytical tool response model was implemented to find the best fit to the coplanar (Figures 7 and 9) and coaxial (Figures 8 and 10) apparent complex conductivity measurements. In doing so, we estimated horizontal (Figure 11) and vertical (Figure 12) (a) σeff and (b) εr,eff of the glass-bead packs. In Figures 11 and 12, we observe frequency dispersions in both the σeff and εr,eff of the glass-bead packs. Estimated values of εr,eff of the samples are in the order of 1e3 to 1e4, which are in agreement with observations made by Anderson et al. (2006) and Wang and Poppitt (2013). Further, we notice that the vertical values of σeff and εr,eff are less dispersive than the horizontal values. Interestingly, we made a counterintuitive observation that the σeff of glass-bead packs decreased with an increase in volume fraction at lower operating frequencies, whereas at higher operating frequencies, we observe a normal relationship, wherein pyrite inclusions act as conductive particles giving rise to an increase in the σeff with an increase in the pyrite content. The counter-intuitive behavior of the σeff of samples containing pyrite inclusions can be explained on the basis of perfectly-polarized interfacial polarization of pyrite inclusions (Misra et al., 2015a; Revil and Florsch, 2015) due to which inclusions behave as non-conductive particles at very low frequencies and as highly-conductive particles at high frequencies. Importantly, in order to obtain the true conductivity and permittivity values of the host and inclusion phase, PPIP model predictions, identified with dotted curves in Figures 11 and 12, were generated to fit the estimated σeff and εr,eff values of the glass-bead packs, identified with discrete points in Figures 11 and 12. Similar to Figures 11 and 12, we estimated horizontal (Figure 13) and vertical (Figure 14) (a) σeff and (b) εr,eff of the glass-bead packs containing disseminated Pyrite Red (average radius = 25 µm) or Pyrite Yellow (average radius = 65 µm) inclusions at two different volume fraction (1.5% or 5% volume fraction). In Figures 13 and 14, we observe that the frequency dispersions in σeff and εr,eff of samples is larger for packs containing Pyrite Yellow inclusions than that containing Pyrite Red inclusions because Pyrite Yellow inclusions are of larger particle size compared to Pyrite Red inclusions. In order to obtain conductivity and permittivity values of the inclusion-free host and the inclusion phase, PPIP model predictions, identified with dotted curves in Figures 13 and 14, were generated to fit the estimated values for glassbead packs, identified with discrete points in Figures 13 and 14. Based on excellent agreement of the PPIP model predictions with estimated values of σeff and εr,eff of the glass-bead packs, we estimated the following electrical properties for the pyrite inclusion phase and brine-saturated host that were unknown while performing the laboratory measurements: low-frequency horizontal conductivity of pyrite inclusions is 1000 S/m, low-frequency vertical conductivity of pyrite inclusions is 100 S/m, diffusion coefficient of pyrite inclusions is 3e-6 m2s-1, and diffusion coefficient of pore-filling brine is 2e-9 m2s-1. Importantly, estimated values of diffusion coefficient of charge carriers in pyrite and brine agree well with values mentioned in previously published peer-review sources (for e.g. Revil and Florsch, 2015). Estimation of the above-mentioned values was constrained by

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the following properties of the inclusion phase and host that were known/assumed prior to performing the laboratory measurements: relative permittivity of pyrite inclusions is 12 (assumed), relative permittivity of pore-filling brine is 80 (assumed), conductivity of the brine is 3.75 S/m, conductivity of the brine-saturated host is 0.975 S/m (obtained from WCEMIT measurements on inclusion-free glass-bead packs), radius of glass beads is 575 µm, volume fraction of glass beads in the pack is 65.5%, surface conductivity of glass beads in brine is 1e-9 S (assumed), and the diameter and volume fraction of nearly-spherical pyrite inclusions that were homogeneously dispersed in the glass-bead packs was known for any given glass-bead pack. Based on the results shown in Figures 11 through 14, we find that samples containing uniformly distributed pyrite inclusions exhibit both effective conductivity and permittivity anisotropy. In Figure 15, effective conductivity anisotropy (λc,eff) of the glass-bead packs increases, while effective permittivity anisotropy (λe,eff) decreases with an increase in operating frequency. Also, λc,eff of such samples strongly depends on the volume fraction of pyrite inclusions. Further, we notice that the sensitivity of λe,eff to variations in volume fraction of pyrite inclusions is not as drastic as that of λc,eff. Figure 16 compares λc,eff and λe,eff of samples containing uniformly distributed Pyrite Red (25 µm) or Pyrite Yellow (65 µm) inclusions at two different volume fractions (1.5% or 5% volume fraction). We observe that an increase in size of pyrite inclusions increases conductivity anisotropy but decreases permittivity anisotropy. Interestingly, we observe a peak in the effective conductivity anisotropy for glass-bead pack containing Pyrite Yellow inclusions, which can be attributed to the peak of relaxation time of the perfectly-polarized interfacial polarization of those pyrite inclusions. Figure 16 shows that glass-bead packs containing pyrite inclusions exhibited λc,eff in the range of 1 to 1.2, and λe,eff in the range of 0.7 to 2.8. Conclusions Glass-bead packs containing uniformly distributed pyrite inclusions exhibited significant frequency dispersions in their R- and X-signal responses due to interfacial polarization of electrically conductive pyrite inclusions. Both R- and X-signal responses of pyrite-bearing glass-bead packs are significantly different from those of pyrite-free glass-bead packs. Consequently, accurate resistivity interpretation methods for pyrite-bearing formations must account for effects of interfacial polarization of pyrite inclusions. Large negative values of X-signal response were observed for glassbead packs containing more than 1% volume fraction of pyrite inclusions, confirming the dielectric (charge accumulation) behavior of such glass-bead packs. We successfully estimated σeff and εr,eff of inclusion-bearing glassbead packs using the semi-analytical tool response model. Estimated values of effective relative permittivity were in the range of 1e3 to 1e4 for pyrite-bearing glass-bead packs. Importantly, estimated values of effective conductivity for glass-bead packs containing pyrite inclusions decreased at low frequencies and increased at high frequencies with an increase in pyrite content. Effective electrical properties of inclusion-bearing samples are a function of size and volume fraction of the pyritic-inclusion phase. We showed that packs containing uniformly distributed inclusions exhibit both conductivity anisotropy, in the range of 1 to 1.2, and permittivity anisotropy, in the range of 0.7 to 2.8. Tensor resistivity modeling in formations containing uniformly dispersed pyrite inclusions must therefore account for presence of effective conductivity and permittivity anisotropy. We successfully estimated the true conductivity of the inclusion-free host and the diffusion coefficient of charge carriers in the pyrite inclusion phase and that in the porefilling brine by implementing the PPIP model. In summary, the σeff and εr,eff values obtained by inverting EM tool measurements were significantly influenced by interfacial polarization of pyrite inclusions. Conductivity and permittivity of the host medium can be derived from the estimated values of σeff and εr,eff by implementing a consistent electrochemical polarization model that quantifies the effects of various interfacial polarization phenomena occurring in the geomaterial. We strongly recommend that resistivity models used for resistivity interpretation of subsurface galvanic, EM induction, and EM propagation measurements in pyrite-rich sedimentary formations and pyrite-bearing organic-rich mudrock and source-rock formations account for perfectly-polarized interfacial polarization phenomena. Acknowledgements The work reported in this paper was funded by University of Texas at Austin’s Research Consortium on Formation Evaluation, jointly sponsored by Afren, Anadarko, Apache, Aramco, Baker-Hughes, BG, BHP Billiton, BP, Chevron, China Oilfield Services LTD., ConocoPhillips, Det Norske, ENI, ExxonMobil, Halliburton, Hess, Maersk, Mexican Institute for Petroleum, ONGC, OXY, Petrobras, PTT Exploration and Production, Repsol, RWE, Schlumberger, Shell, Southwestern Energy, Statoil, TOTAL, Weatherford, Wintershall and Woodside Petroleum Limited. We thank Schlumberger Reservoir Laboratories and Schlumberger Houston Formation Evaluation Center for providing laboratory facilities and technical support to our research work.

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References Altman, R., Anderson, B., Rasmus, J., and Luling, M., 2008, Dielectric effects and resistivity dispersion on induction and propagation-resistivity logs in complex volcanic lithologies: A case study, SPWLA 49th Annual Logging Symposium, Austin, Texas, May 25-28. Anderson, B., Barber, T., and Luling, M., 2006, Observations of large dielectric effects on induction logs, or can source rocks be detected with induction measurements, SPWLA 47th Annual Logging Symposium, Veracruz, Mexico, June 4-7. Anderson, B., Barber, T., Lüling, M., Sen, P., Taherian, R., and J. Klein, 2008, Identifying potential gas-producing shales from large dielectric permittivities measured by induction quadrature signals, SPWLA 49th Annual Logging Symposium, Austin, Texas, May 25-28. Chen, H., and Heidari, Z., 2014, Pore-scale evaluation of dielectric measurements in formations with complex pore and grain structures, SPWLA 55th Annual Logging Symposium, Abu Dhabi, U.A.E., May 18-22. Clavier, C., Heim, A., and Scala, C., 1976, Effect of pyrite on resistivity and other logging measurements, SPWLA 17th Annual Logging Symposium, Denver, Colorado, June 9-12. Clennell, M. B., Josh, M., Esteban, L., Piane, C. D., Schmid, S., Verrall, M., and McMullan, B., 2010, The influence of pyrite on rock electrical properties: A case study from Nw Australian gas reservoirs, SPWLA 51st Annual Logging Symposium, Perth, Australia, June 19-23. Corley, B., Garcia, A., Maurer, H.M., Rabinovich, M. B., Zhou, Z., DuBois, P., and Shaw, N., 2010, Study of unusual responses from multiple resistivity tools in the Bossier formation of the Haynesville shale play, SPE Annual Technical Conference and Exhibition, Florence, Italy, September 12-22. doi:10.2118/134494-MS. Grosse, C. and Barchini, R., 1992, The influence of diffusion on the dielectric properties of suspensions of conductive spherical particles in an electrolyte, Journal of Physics D, 25(3), 508-515. doi:10.1088/0022-3727/25/3/026. Kethireddy, N., Chen, H., and Heidari, Z., 2014, Quantifying the effect of kerogen on resistivity measurements in organic-rich mudrocks, Petrophysics, 55(02), 136-146. Kickhofel, J. L., Mohamide, A., Jalfin, J., Gibson, J., Thomas, P., Minerbo, G., and Homan, D. M., 2010, Inductive conductivity tensor measurement for flowline or material samples, Review of Scientific Instruments, 81(7), 075102. Misra, S., Torres-Verdín, C., and Sepehrnoori, K., 2013, Environmental and transport effects on core measurements of water saturation, salinity, and wettability, SPE Annual Technical Conference and Exhibition. Misra, S., Torres-Verdín, C., Revil, A., Homan, D., and Rasmus, J., 2015a, Interfacial polarization of disseminated conductive minerals in absence of redox-active species: Mechanistic model and validation, Submitted to the Geophysics Journal. Misra, S., Torres-Verdín, C., Revil, A., Homan, D., and Rasmus, J., 2015b, Interfacial polarization of disseminated conductive minerals in absence of redox-active species: Effective electrical conductivity and dielectric permittivity, Submitted to the Geophysics Journal. Misra, S., Torres-Verdín, C., Homan, D., Rasmus, J., and Minerbo, G., 2015c, Laboratory investigation of petrophysical applications of multi-frequency inductive-complex conductivity tensor measurements, SPWLA 56th Annual Logging Symposium. Passey, Q. R., Bohacs, K., Esch, W. L., Klimentidis, R., and Sinha, S., 2010, From oil-prone source rock to gasproducing shale reservoir - geologic and petrophysical characterization of unconventional shale gas reservoirs, CPS/SPE International Oil & Gas Conference and Exhibition, Beijing, China, June 8-10. doi:10.2118/131350-MS.

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Placencia-Gómez, E., and Slater, L. D., 2014, Electrochemical spectral induced polarization modeling of artificial sulfide-sand mixtures, Geophysics, 79, 6, 91-106. Revil, A., and Florsch, N., 2015, The complex conductivity response of porous media with metallic particles. 1. A theory for disseminated semi-conductors. Intended for publication in Geophysics. Schmuck, M., and Bazant, M. Z., 2012, Homogenization of the Poisson-Nernst-Planck equations for ion transport in charged porous media, preprint available http://arxiv.org/abs/1202.1916. Wang, H., and Poppitt, A., 2013, The broadband electromagnetic dispersion logging data in a gas shale formation: A Case Study, SPWLA 54th Annual Logging Symposium, New Orleans, Louisiana, June 22-26. Witkowsky, J. M., Galford, J. E., Quirein, J. A., and Truax, J. A., 2012, Predicting pyrite and total organic carbon from well logs for enhanced shale reservoir interpretation. SPE Eastern Regional Meeting, Lexington, Kentucky, October 3-5. doi:10.2118/161097-MS. Wong, J., 1979, An electrochemical model of the induced-polarization phenomenon in disseminated sulfide ores, Geophysics, 44, no. 7, 1245-1265. Yu, G., Hu, W., He, Z., Xiang, K., Hu, H., He, L., and Li, P., 2014, Complex resistivity characteristics of high TOC marine shale core samples and its applications, SEG Annual Meeting, Denver, Colorado, October 26-31. Figures

Figure 1. Photograph of the WCEMIT system comprising a 4-inch inner diameter, 20-inch long WCEMIT and peripheral electronics. The WCEMIT system is designed to perform multi-frequency inductive-complex conductivity tensor measurements on 4-inch diameter, 2-ft long cylindrical samples.

Figure 2. Photograph of a 4-inch diameter, 2-ft long Berea sandstone whole core placed in the tool conduit of the 4inch inner diameter, 20-inch long WCEMIT for measuring multi-frequency complex conductivity tensor of whole core.

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Figure 3. Display of the orthogonal collocated coils in the transmitter-, bucking-, and receiver-coil system of the WCEMIT. Helical coil in the figure is a simplified representation of the Z-coil in WCEMIT coil systems. Rectangular planar coils in the figure are a simplified representation of the X- and Y-saddle-type coils in WCEMIT coil systems.

(a) (b) (c) (d) Figure 4. Photographs of the 4-inch outer diameter, 2-ft long cylindrical glass-bead packs made of 1.15-mm diameter glass beads filled with 3.75 S/m brine (a) without inclusions, (b) with 2.5% volume fraction of dispersed pyrite, (c) with 5% volume fraction of dispersed pyrite, (d) with 0% (light) and 5% (dark) volume fraction of dispersed pyrite layers. (a)

(b)

1.15

0

X-signal (S/m)

COMSOL EM model

R-signal (S/m)

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1.1

1.05

1 1 10

2

10

Frequency (KHz)

Figure 5. Comparison of multi-frequency WCEMIT tool response modeling results obtained using finiteelement COMSOL AC/DC simulation (circles) to that obtained using the semi-analytical EM code (triangles) for the (a) R- and (b) X-signal response to a cylindrical volume that has an effective conductivity of 1 S/m, conductivity and permittivity anisotropy of 1, effective relative permittivity of 10000, and dielectric loss factor of 0.1.

-0.5

-1

-1.5 1 10

2

10

Frequency (KHz)

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(a)

-2

(b) Imag. induced voltage (V)

Real induced voltage (V)

-3

10

-4

10

-5

10

-6

10

1 S/m (COMSOL) 10 S/m (COMSOL) 1 S/m (EM model) 10 S/m (EM model)

-4

10

-6

10

-8

10

-10

1

10

2

10

10

1

Figure 6. Comparison of multi-frequency WCEMIT tool response modeling results using the finiteelement COMSOL AC/DC simulation (circles) to that obtained using the semi-analytical EM code (triangles) for the (a) real part and (b) imaginary part of the induced receiver voltage response to two cylindrical volumes of effective conductivity of 1 and 10 S/m, respectively, conductivity and permittivity anisotropy of 1, effective relative permittivity of 1, and dielectric loss factor of 0.

2

10

Frequency (KHz)

10

Frequency (KHz)

(a)

(b) 0

1

Figure 7. Coplanar multi-frequency (a) R-signal and (b) X-signal response, identified with discrete points, of glass-bead packs containing varied volume fractions (0.5%, 1.5%, 2.5%, or 5%) of Pyrite Red inclusions. Dotted curves identify semi-analytical tool response model predictions that best fit the tool response.

X-Signal (S/m)

R-Signal (S/m)

-0.05 0.95

0.9

0.85

-0.1

-0.15 0% 0.5% 1.5% 2.5% 5%

-0.2

0.8 1 10

-0.25 1 10

2

10

2

10

Frequency (kHz)

Frequency (kHz)

(a)

(b)

1

0

Figure 8. Coaxial multi-frequency (a) R-signal and (b) X-signal measurements, identified with discrete points, of glass-bead packs containing varied volume fractions (0.5%, 1.5%, 2.5%, or 5%) of Pyrite Red inclusions. Dotted curves identify semi-analytical tool response model predictions that best fit the tool response.

X-Signal (S/m)

0.96

R-Signal (S/m)

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10

0.92

0.88

-0.04

-0.08 0% 0.5% 1.5% 2.5% 5%

0.84 -0.12 0.8 1 10

2

10

Frequency (kHz)

1

10

2

10

Frequency (kHz)

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(a)

(b) 0

0% 1.5%, 25  m 1.5%, 65  m 5%, 25  m 5%, 65  m

Figure 9. Coplanar multi-frequency (a) R-signal and (b) X-signal response, identified with discrete points, of glass-bead packs containing Pyrite Red (25 µm) or Pyrite Yellow (65 µm) inclusions at two different volume fractions (1.5% or 5%). Dotted curves identify semi-analytical tool response model predictions that best fit the tool response.

-0.05

X-Signal (S/m)

R-Signal (S/m)

1.1

1

-0.1

-0.15

0.9 -0.2

0.8 1 10

-0.25 1 10

2

10

Frequency (kHz)

(a)

(b) 0

X-Signal (S/m)

R-Signal (S/m)

0.92

0.88

-0.08 -0.12 -0.16

0.84

-0.2

0.8 1 10

2

10

0% 1.5%,25  m 1.5%,65  m 5%,25  m 5%, 65  m

-0.24 1 10

Frequency (kHz)

2

10

Frequency (kHz)

(a)

5

1.05

(b)

10

Effective relative permittivity

0.5% 1.5% 2.5% 5%

0.95

0.9

0.85

0.8 1 10

Figure 10. Coaxial multi-frequency (a) R-signal and (b) X-signal response, identified with discrete points, of glass-bead packs containing Pyrite Red (25 µm) or Pyrite Yellow (65 µm) inclusions at two different volume fractions (1.5% or 5%). Dotted curves identify the semi-analytical tool response model predictions that best fit the tool response.

-0.04

0.96

1

2

10

Frequency (kHz)

1

Effective conductivity (S/m)

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1.2

Figure 11. Estimated values of horizontal (a) effective conductivity and (b) effective relative permittivity, identified with discrete points, of glassbead packs containing varied volume fractions (0.5%, 1.5%, 2.5%, or 5%) of Pyrite Red inclusions. Dotted curves identify PPIP model predictions that best fit the estimated values of effective conductivity and effective relative permittivity.

4

10

3

2

10

Frequency (kHz)

10 1 10

2

10

Frequency (kHz)

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(a) Effective relative permittivity

Effective conductivity (S/m)

0.9

0.85

3

Effective relative permittivity

Effective conductivity (S/m)

5

0.9

Figure 13. Estimated values of horizontal (a) effective conductivity and (b) effective relative permittivity, identified with discrete points, of glassbead packs containing Pyrite Red (25 µm) or Pyrite Yellow (65 µm) inclusions at two different volume fractions (1.5% or 5%). Dotted curves represent PPIP model predictions that best fit the estimated values of effective conductivity and effective relative permittivity.

4

10

3

0.8 1 10

10 1 10

2

10

Frequency (kHz)

2

10

Frequency (kHz)

(a)

5

(b)

10

Effective relative permittivity

1.5%, 25  m 1.5%, 65  m 5%, 25  m 5%, 65  m

0.9

0.85

0.8 1 10

(b)

10

1.5%, 25  m 1.5%, 65  m 5%, 25  m 5%, 65  m

1

0.95

2

10

Frequency (kHz)

(a)

1

0.5% 1.5% 2.5% 5%

10 1 10

2

10

Frequency (kHz)

1.1

Figure 12. Estimated values of vertical (a) effective conductivity and (b) effective relative permittivity, identified with discrete points, of glass-bead packs containing varied volume fractions (0.5%, 1.5%, 2.5%, or 5%) of Pyrite Red inclusions. Dotted curves identify PPIP model predictions that best fit the estimated values of effective conductivity and effective relative permittivity.

10

2

0.8 1 10

Effective conductivity (S/m)

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10

0.95

1.2

(b)

4

1

Figure 14. Estimated values of vertical (a) effective conductivity and (b) effective relative permittivity, identified with discrete points, of glass-bead packs containing Pyrite Red (25 µm) or Pyrite Yellow (65 µm) inclusions at two different volume fractions (1.5% or 5%). Dotted curves identify PPIP model predictions that best fit the estimated values of effective conductivity and effective relative permittivity.

4

10

3

2

10

Frequency (kHz)

10 1 10

2

10

Frequency (kHz)

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(b) Effective permittivity anisotropy

Effective conductivity anisotropy

1.15

1.1

1.05

1 1 10

2

10

3

2.6 2.4 2.2 2 1.8

(b)

1.5%, 25  m 1.5%, 65  m 5%, 25  m 5%, 65  m

1.15

1.1

1.05

1 1 10

2

10

Frequency (kHz)

Effective permittivity anisotropy

1.2

0.5% 1.5% 2.5% 5%

1.6 1 10

(a) 1.25

Figure 15. Estimated values of (a) effective conductivity anisotropy and (b) effective permittivity anisotropy, identified with discrete points, of glass-bead packs containing varied volume fraction (0.5%, 1.5%, 2.5%, or 5%) of Pyrite Red inclusions. Dotted curves connect the discrete points to provide better visualization of dispersion trends.

2.8

Frequency (kHz)

Effective conductivity anisotropy

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(a) 1.2

2

10

Frequency (kHz)

3

Figure 16. Estimated values of (a) effective conductivity anisotropy and (b) effective permittivity anisotropy, identified with discrete points, of the glass-bead packs containing Pyrite Red (25 µm) or Pyrite Yellow (65 µm) inclusions at two different volume fractions (1.5% or 5%). Dotted curves connect the discrete points to provide better visualization of dispersion trends.

2.5

2

1.5

1

0.5 1 10

2

10

Frequency (kHz)

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