ABSTRACT

The dielectric permittivity of mudrocks cannot be determined from the mixing ratios of the constituent minerals and brine and their individual dielectric response. The high-frequency dielectric permittivity is linked (R2=0.77 correlation) to water content, but the relationship is complicated by mineral type and the hydration state. The cation exchange capacity (CEC) and specific surface area (SSA) determine the establishment of a polarizable electrical double layer and give rise to the long range diffusion of ions leading to Maxwell-Wagner polarization. This ultimately determines the dielectric response below 50 MHz. Procedures for SSA analysis based on sorption of 2-ethoxyethanol and CEC analysis based on methylene blue titration, were developed for investigating swelling clays. These were combined with a procedure for preparing remolded paste samples from pulverized rock and drill cuttings to form the basis of this investigation. In a case study of 123 drill cutting samples retrieved from an undisclosed well, dielectric analysis of the remolded samples exhibits R2=0.93 correlation with SSA, R2=0.86 correlation with CEC, and R2=0.81 correlation with clay content. A pseudodielectric log of the remolded drill cuttings exhibited a weak correlation with downhole resistivity, gamma ray, and compressional slowness logs measured by a service company in the shaly sections of the well, but no correlation in the sandy section of the well. This attributed to better preservation of shaly cuttings due to finer microstructure and therefore less alteration during uphole transport and sample preparation.

INTRODUCTION

Mudrocks constitute most of the deposits in sedimentary basins, forming the overburden and seals of many reservoirs, and knowledge of their electrical properties is important for geophysical exploration. Shales also form hydrocarbon source rocks and reservoirs, and although numerous methods exist to estimate reservoir properties in sandstones and limestones from electrical measurements (Zinszner and Pellerin, 2007); there are few validated approaches for using electrical measurements of clay-bearing rocks in a similar way (Myers, 1991, 1996, Fam and Dusseault, 1998a, 1998b; Seleznev et al., 2011; Revil, 2013). The principal aim of this investigation is to demonstrate how dielectric properties can be related to other petrophysical parameters and can contribute information that is not available from standard well logs. This is supported by a case to demonstrate how variations in mineralogy, specific surface area (SSA), and cation exchange capacity (CEC) affect the dielectric permittivity across a range of measured frequencies.

In the simplest electrical description of a composite material, the dielectric permittivity of the solids may be added volumetrically to the dielectric permittivity of the fluids (von Hipel, 1954). In porous rocks, this model is inadequate because fluids (e.g., brine) and solid surfaces interact and develop additional mobile charge carriers that can be polarized. In mudrocks, clay minerals exist as a compacted suspension of colloids with high SSA and their surfaces have a net negative charge with a high density of ionic attachment sites resulting from the exposed end of the silicate minerals from which the clay microstructure is assembled (Bergaya et al., 2006).

When immersed in brine, these ionic attachment sites strongly attract nearby counterions to neutralize the lattice charge excess, resulting in a strongly bound layer on the clay mineral surface known as the Stern layer, or inner Helmholtz plane (Gonçalvès and Trémosa, 2010). Additional layers of water molecules and ions are attracted in a more spread-out region beyond the Stern layer called the diffuse layer, but they remain relatively unrestricted and easily exchange with brine in the pore space. The combined Stern and diffuse layers are often referred to as the electrical double layer (EDL).

The amount of charge needed to saturate the available surface sites to balance the charge on the mineral surface (the CEC cmol/g) is loosely related to the SSA (Kellomäki et al., 1987). Kaolinite, illite, and chlorite group minerals form a relatively simple EDL when hydrated and a modest population of bound and diffuse counterions balance the surface charge. In swelling clays such as montmorillonite, there are interlayer planes containing cations of variable hydration states, with a very high SSA, and so clay minerals of this type have a high CEC (Tombácz and Szekeres, 2006). Although silicates with low SSA (1m2/g) such as quartz and feldspars still form an electrical double layer, the contribution to the overall CEC and, therefore, surface electric properties of these minerals is generally minor when clays are also present.

Ions in the EDL of silicate minerals have variable mobility associated with the strength of hydration and bonding to specific surface sites. The higher mobility of excess charges in the diffuse layer is considered to be the main contributor to surface conductivity in sandstones and mudrocks (Revil, 2012). The degree of surface charge and the charge partitioning in the electric double layer depends on variables such as the mineral type and the pore fluid characteristics, namely pH, ionic strength (“salinity”), and the cation species in the brine. The ability of partly hydrated cations to move tangentially around the silicate mineral grains leads to high electric polarizability, which is strongly dependent on frequency (Revil, 2013) and the orientation of the electric field to the bedding (leading to conductivity and dielectric anisotropy, Revil et al., 2013).

Bound water molecules in the EDL also contribute to the dielectric response (Gonçalvès and Trémosa, 2010), but their motion is constrained by surface attraction forces so that the net polarizability is likely to be somewhat lower than bulk water, occurring outside the diffuse layer (Fam and Dusseault, 1998a).

At submegahertz frequencies, the relative permittivity appears to diverge to enormous values, as does the dielectric loss. This is sometimes attributed to long-range diffusion of mobile ions in double layers and pore space (de Lima and Sharma, 1992) and the buildup of charge at rock internal interfaces where conductivity and permittivity of the neighboring (solid and fluid) components are different. This so-called Maxwell-Wagner (M-W) or space charge polarization contribution is always present in heterogeneous systems. Fuller and Ward (1970) demonstrate mathematically that the existence of imaginary conduction (a different phenomenon to M-W) could also drastically increase the submegahertz apparent dielectric permittivity, and later studies by Chelidze and Guegen (1999), Chelidze et al. (1999), Garrouch and Sharma (1995), and Revil (2013) provide a plausible physical model to support the mathematical derivations of Fuller and Ward (1970). However, low-frequency high-dielectric behaviors, such as M-W and imaginary conduction, are often obscured by electrode polarization of the metallic components of the measurement system when in contact with brine. Charge piling up on the electrode or sample boundary creates an effective series impedance (Malleo et al., 2010; Ishai et al., 2013), which disrupts measurement of conductivity at lower frequencies (subkilohertz) and permittivity at higher frequencies (up to 10 MHz), and its origin and possible solutions are explained in detail in the review by Ishai et al. (2013). For conductivity measurement, electrode polarization below 100 KHz can be bypassed using the four-electrode method; however, four-electrode geometries are inoperable at megahertz frequencies (Malleo et al., 2010), and so a data gap remains between approximately 100 KHz and 10 MHz for investigating rock electric behavior.

The best method for resolving the different electrodynamic processes occurring in mudrocks is by using a broad frequency of investigation. At high frequencies (several hundred MHz), the electric field oscillates sufficiently fast that the clay-surface polarization, M-W, and imaginary conduction cannot develop and the “background” dielectric permittivity of the minerals and fluid mixture can be measured. At lower frequencies (typically 1–50 MHz), M-W polarization and imaginary conduction become the dominant dielectric processes, but electrode polarization affects all measurements below 10 MHz and will not be investigated within the scope of this study.

Given that shales and mudrocks have electric behaviors that are strongly linked to SSA and CEC, has naturally led researchers to investigate the possible relationships that may exist between these electric properties and other petrophysical or geomechanical (Josh et al., 2014) characteristics. For instance, Fam and Dusseault (1998a, 1998b) investigate the dielectric permittivity of preserved shales to estimate SSA and Leung and Steiger (1992) develop a rapid wellsite method to evaluate SSA based on the dielectric analysis of reconstituted drill cuttings. Myers (1991) investigate shales in their original state (which requires carefully preserved samples) to provide a connection with CEC. Josh et al. (2012) and Josh (2014) were able to demonstrate a correlation between the dielectric permittivity and the P-wave velocity in a preserved shale sample.

The most widely accepted method for estimating the dielectric permittivity of mixtures is based on the equations of electromagnetic propagation and is known as the complex refractive index model (CRIM) (Birchak et al., 1974; Wharton et al., 1980; Seleznev et al., 2011). CRIM calculates the effective rock dielectric permittivity (εeff) following a simple mixing law between solid with dielectric permittivity of εma49, brine with dielectric permittivity of εrw80, and air or hydrocarbon with very low permittivity of εh1.0 if it is gas or air, and εh23 if it is oil:  
εeff=ϕSwεrw+ϕ(1Sw)εh+(1ϕ)εma,
(1)
where Sw and ϕ are the water saturation and porosity, respectively. However, M-W and EDL polarization are not factored into this equation, therefore, it is limited to frequencies above 50MHz. Knight and Endres (1990) and Knight and Abad (1995) attempt to integrate an additional term into the CRIM equation to account for the surficial polarization using the dielectric permittivity of the wetted matrix as a single mixture component in itself. In Myers’s (1991, 1996) model, the EDL polarization magnitude is related to the CEC.

At lower frequencies, the M-W phenomenon in brine-saturated rocks created by space charge separation can be large enough to make the rock permittivity significantly higher than the permittivity of any of the mixture’s constituents; i.e., it may appreciably exceed εrw=80 at MHz frequencies even when the water fraction (porosity×saturation) is modest. M-W processes are ultimately dependent on material contrasts, the geometry of the pore space, and the volume fraction of minerals and fluids. These can be accounted for using effective medium theory with simple pore/solid geometric elements based on ellipsoids (Asami, 2002). For the case of porous rocks, Sen et al. (1981) recognize a special class of effective medium models for systems relatively near percolation using a fractional exponent (close to 2) to describe the pore geometry. This is similar to the empirically derived model for rock conductivity familiar to petrophysicists as Archie’s law.

It is clear that the broadband dielectric permittivity of mudrocks is linked to petrophysical attributes of rock including the porosity, salinity, hydration state, and orientation of the bedding as well as CEC and SSA. In this study, a comprehensive investigation of these properties is presented in conjunction with dielectric analysis of the preserved rock and reconstituted pastes.

DIELECTRIC MEASUREMENT SYSTEMS

Several well-established methods (described in Josh et al., 2007, 2009) are used for determining the dielectric response of the samples investigated in this study (Figure 1).

For the end-loaded transmission line method, dielectric permittivity is determined using an inversion algorithm for the scattering parameters measured using a vector network analyzer (VNA, Agilent E5070A) for a section of coaxial transmission line terminated against the surface of the sample. Probes of this nature are described by Burdette et al. (1980) and Stuchly and Stuchly (1980) and are commercially available (e.g., Agilent 85070E high-temperature dielectric probe). The end-terminated probe suffers badly from high-frequency electrode polarization effects (Ishai et al., 2013), below 10 MHz for wet paste samples. It requires perfect gap-free contact with the sample, making it suitable for soft mudrocks, but it is inaccurate on rock surfaces with appreciable roughness. However, the end-loaded probe is a rapid measurement system, which makes it ideal for measuring large numbers of pulverized samples; e.g., it is ideal to measure permittivity of pastes made by remolding drill cutting samples (Leung and Steiger, 1992).

For the loaded coaxial transmission line method, dielectric permittivity can also be determined using an inversion algorithm for the VNA scattering parameters measured for a section of coaxial transmission line in which the annular space between the inner and outer conductors is filled with the sample under test (Nicholson and Ross, 1970; Weir, 1974; Baker-Jarvis et al., 1990). The radial electric field in the cell probes a sample volume that is substantially larger than investigated with an end-loaded probe. The loaded coaxial transmission line uses the reflection and transmission scattering parameters of the VNA, and this increases the accuracy and reliability of the measurements compared with the end-loaded probe. The sample requires specific dimensions (40 mm long, 16 mm diameter with a 7 mm hole [drilled] coaxially through the center), which are impractical to achieve for very soft mudrocks, fissile shales, and other friable rocks such as coal. The coaxial cell is therefore ideally used for “machinable” fine-grained rocks, powdered samples, and remolded pastes.

For the parallel plate method, dielectric permittivity is determined by measuring the capacitance and resistance of a three-terminal capacitor with the sample clamped between the electrodes (von Hipel, 1954). The cell used in this study is an Agilent 16451 dielectric test fixture, attached to an Agilent 4294A impedance analyzer. Parallel plate dielectric measurement is ideal for preserved samples prepared from core plugs between 20 and 40 mm in diameter sliced into disks approximately 10 mm thick with precision ground faces (tolerance of ±0.02mm from the average thickness). Instrumental measurements are converted into material dielectric parameters at each frequency of investigation using software.

Each of the three dielectric measurement systems provides the real and imaginary components of the relative dielectric permittivity (εr and εr, respectively). The apparent imaginary dielectric permittivity (or dielectric loss) is actually comprised the true relative dielectric permittivity (εr(true)) and an additional loss component resulting from ohmic conduction σ. Typically, dielectric instruments combine the loss processes (εr(true) and σ) into one “combined” dielectric loss or equivalent εr(combined) using 
εr(combined)=εr(true)+σ/ωεo,
(2)
where εo is the dielectric permittivity of free space and ω is the angular frequency.

PREPARATION AND COMPARISON OF POWDERS PASTES AND CUTTINGS

Petrophysical parameters are often best evaluated using preserved intact shale samples, hydrated with the original fluid content and composition. However, such shale cores are rare and they are often poorly preserved. Drill cuttings, however, are usually readily available, so establishing relationships between the cuttings’ properties and those of the intact rock are of great interest. It is also necessary to validate the context of powdered measurements by investigating pure minerals and rock powders in dry and hydrated states.

Measurements on powdered clay

Figure 2 shows the broadband dielectric responses of commercially available quartz, kaolinite, illite, and smectite powders measured in the air dry state. The samples were packed into the 16-mm coaxial transmission cell to a consistent density, using a shaped mandrel. The prevailing relative humidity in the lab was approximately 50±5%. There are many remarkable features in the data. For example, at the highest frequency, the kaolinite and smectite samples converge to relatively low relative dielectric permittivities of 3 and 6, respectively, which correspond to a solids permittivity of approximately 5 and 9, assuming the porosity is air filled. At 30 MHz, the smectite powder has three times the permittivity of kaolinite powder (εr=18 versus 5), and four times the permittivity of kaolinite powder at 1 MHz (εr=60 versus 15), indicating that smectite is much more dispersive than the kaolinite. At the same time, the total dielectric loss of the smectite is several times higher. Smectite is more hygroscopic than kaolinite and develops more partly mobilized ions, which are able to conduct and polarize, when allowed to stabilize with the laboratory atmosphere.

A striking feature of the data (Figure 2) is the similarity of the high-frequency readings, which indicate a common solid or matrix response at moderate dry density. This is consistent with the observations of Myers (1991), who reasons that beyond 1 GHz, there is no surface polarization contribution, and one sees a simple mineral-water mixture. The air-dry clay can be differentiated at lower frequency, in which the mobility (conductivity curves) and polarization (permittivity curves) of the surface bound charges occur.

Measurements on plastic clay (remolded paste)

In vacuum-oven-dried conditions, most silicate minerals including clays have flat dielectric responses, with values of the permittivity in the range of εr=36 at all frequencies. Although clay minerals contain excess surface charges, these are not available to contribute to electric polarization processes appreciably until the ions are hydrated. When mixed with enough water to form an electric double layer (using procedures outlined in Josh et al., 2009), clay powders form a thick paste, which can be remolded plastically into the geometry required for each of the three dielectric measurement instruments. All three methods give similar permittivity and loss curves at higher frequencies (Josh et al., 2009), whereas the end-loaded probe data suffer from more noticeable electrode polarization effects at frequencies below approximately 10 MHz, leading to an overestimation of the true permittivity of the clay. The permittivity values for the plastic clay (Figure 3) are uniformly higher than for the clay in the dry state, but the results are consistent. At a high frequency, one sees a mixture of kaolinite solid (dielectric constant of εr=4.5) and water (dielectric constant of εr=80), whereas at low frequency, one sees the additional polarization contributions of the fully hydrated clay surfaces. The imaginary permittivity shows a straight line with a slope of 1 on a log-log plot against frequency, which is characteristic of ohmic loss caused by conduction (see equation 2). For air-dry powders (Figure 2), the gradient (εr versus frequency on log-log scales) was significantly lower than 1, demonstrating that the conduction occurs as a result of hydration (comparing Figures 2 and 3). Furthermore, the samples are each affected differently by the water. For example, kaolinite and illite, which were significantly different across the frequency range when they were air dried, show almost identical dielectric curves when hydrated to pastes. The kaolinite paste has a lower SSA/CEC (kaolinite SSA=40m2/g and illite SSA=52m2/g), but an increased water content (kaolinite=48.0wt% and illite=42.1wt%) (Table 1), and the two physical attributes are canceling one another out.

Preparation and measurement of remolded pastes from drill cuttings

Drill cuttings come in various states, either “washed and dried” from archive material, or they may still be fresh and wet with mud (i.e., ditch cuttings at the well site). From the “as-received” gently washed and dried cuttings, approximately 20 g of the largest solid fragments were selected. Any apparent drilling mud was removed, and the fragments were ground in a ring mill head for approximately 1 min to produce a uniform powder. A known mass (20 g) of the powder was mixed with a known mass (50 g) of deionized water, in a centrifuge tube, and then centrifuged for 1 h at 5000 rpm. The water was then decanted into a separate jar, and its electric conductivity was measured with an electric conductivity meter (Orion). The cuttings paste at the end of the tube was extruded into a small acrylic jar, kneaded gently to ensure uniformity (without expressing water or trapping air bubbles), and was then pressed against the end-loaded coaxial transmission line for the dielectric measurement, made on freshly remolded material. Four readings were taken per sample and averaged. The sample was then weighed, oven dried at 104°C, and weighed again to determine the bulk density, grain density, and water content of the paste (Table 1).

Note that the same pastes are suitable for measurement in the 16-mm coaxial cell, which is more accurate, but slower and so not really practical for hundreds of samples. In the case study below, the coaxial cell was used for verification and quality control of each batch of end-probe measurements.

CASE STUDY FROM A DEEPWATER WELL

A total of 123 drill cuttings samples spaced regularly at 6.08-m (20-ft) intervals and covering several different rock formations were provided from a single well (the location and well name are proprietary information, so they are referred to here as the undisclosed location [UDL]). The upper section of the sampled interval in the well is substantially homogeneous and dominated by mudrocks, whereas the lower section contains sand, marls, and an additional thin shale sequence with a similar gamma ray response to the upper shale (Figure 4). In addition to the cuttings, two preserved whole round cores were retrieved from the upper section at approximately Y+256m and Y+362m (the depths are marked as red bars on the depth track), and each of these produced four plugs (38 mm diameter). The preservation process used for this study involved plugging the core samples soon after recovery, then wrapping them in cling film followed by foil, then dipping them in wax. Preservation was maintained in the laboratory by machining the samples as required, then immediately storing them under Shell Ondina 60 preserving oil and refrigeration prior to measurement.

The plug samples were visually homogeneous, but most had weak bedding laminations visible with X-ray CT. Plugs were cut in pairs in the horizontal and vertical directions so that anisotropy in the permittivity and conductivity could be investigated in the same shale horizons. Disks approximately 10 mm thick were trimmed off the ends of each plug (Table 2) for measurement in the parallel plate capacitance cell.

Mineralogy, cation exchange capacity, and specific surface area

A subset of 21 samples was selected from the complete 123 drill cuttings spanning the depth and lithological variations. These underwent additional mineralogical analysis to investigate the physicochemical mechanisms giving rise to the dielectric response. The SSA was determined using sorption of 2-ethoxyethanol (EGME) (Kellomäki et al., 1987; Cerato and Lutenegger, 2002) (see Appendix A), which is chosen because of its suitability for investigating interlayer surfaces in swelling clays (Table 1). The CEC was determined using methylene blue (MB) and the tetrasodium pyrophosphate method of Wang et al. (1996) (see Appendix A). The mineralogy was determined using X-ray diffraction (XRD). XRD patterns were recorded with a PANalytical X’Pert Pro Multipurpose Diffractometer (see Appendix A). The sum of the clay mineral contents (kaolinite, illite, chlorite, and smectite) determined by XRD provided the clay content of the cuttings.

Typically the SSA of the UDL shales ranges from approximately 120300m2/g, which is consistent with the major contributors to SSA in particular being smectite (SSA=700m2/g), which typically accounts for 20%–45% by dry mass; kaolinite (SSA=40m2/g), which typically accounts for 15%–30%; and illite (SSA=60m2/g), which typically accounts for 4%–8%.

The correlation between the measured SSA and analytical SSA determined from XRD mineral composition is better than R2=0.97, but the analytical SSA overpredicts the measured SSA by approximately 20% (see Appendix A for the procedure). A possible explanation for this is that the crystal structure and elemental composition of smectite for instance can vary between samples (e.g., Mitchell and Soga, 2005), and this may affect the analytical SSA calculation. Likewise, some of the illite could in fact be muscovite or another lower surface area polytype.

SSA and CEC correlate very strongly (Figure 5) because the exchange of cations with the nearby fluid can only occur at the mineral-water interface. Either the charge density is always the same (Woodruff and Revil, 2011), or it increases in a consistent way as the mineralogy changes. The latter is suggested by the good fit to data for the standard minerals kaolinite, Ward Illite, and smectite, and also Pierre shale (Table 1). That is to say, electric charge density trends for this population of shale cuttings suggest that variation in smectite is the main driver of the CEC and SSA changes.

Dielectric analysis of remolded drill cuttings

In Figure 4, the 30 MHz, 100 MHz, and 1 GHz dielectric permittivities (track 4) of the cuttings pastes (all 123) with depth are presented in the well to create a pseudodownhole log.

Mudrocks contain appreciable amounts of nonclay minerals, mainly quartz, feldspars, and carbonates, which are relatively electrically inert compared with the phyllosilicates and make a minor contribution to dielectric dispersion. It is likely that the dominant factor in driving the dielectric response of shales is in fact the hydrated ions associated with the clay minerals present. Clay content is also one of the common parameters of interest in petrophysical log interpretation, and it can be estimated from gamma ray and from the separation of the neutron porosity and density porosity logs.

Variations in cuttings permittivity (track 4) generally vary with the gamma ray curve (track 1), but there are several excursions that do not correspond to gamma ray or neutron-density indicators. Moreover, the dielectric dispersion index (track 3), obtained by subtracting the 1 GHz permittivity from the 30 MHz permittivity, shows very different values in the upper and lower shale sections, even though the gamma ray response is essentially the same. Therefore, the dielectric curves from cuttings provide pointers to possible changes in the mudrock type that are not seen in conventional wireline log responses, and which could be important for drilling stability and or/reservoir development.

There are moderately strong correlations between dielectric response (real and imaginary permittivity) and clay content (Figure 6), suggesting that the clay content can be determined from dielectric logs existing in the petroleum industry (Hizem et al., 2008). Following the reasoning of Myers (1991), the low-frequency dielectric response is driven by surface interactions and, therefore, clay content, whereas the high-frequency dielectric response is more related to the moisture content and relatively insensitive to mineralogy and CEC/SSA. Results presented in Figure 6 demonstrate that at least the real component of dielectric permittivity correlates with the clay content, and the correlation is slightly better at 10 MHz than at 1 GHz, which is consistent with Myers’ (1991) claim.

The correlation between εr and SSA (Figure 7a and 7b) is very strong at 10 MHz, but becomes poorer as the frequency is increased from 10 MHz to 1 GHz. The reverse is true for εr (Figure 7c and 7d) where the correlation with SSA improves as the frequency is increased. Much weaker correlations may also exist between dry powder dielectric measurements and SSA for single mineral standards (e.g., Figure 2), but it is likely that consistent correlation between permittivity and SSA is aided by stable and elevated levels of hydration, so that all the surface active ions are mobilized for conduction and for polarization. The polarization is only developed fully at low frequencies, so the correlation with permittivity and SSA is higher at 10 MHz. Equivalent imaginary relative permittivity (εr(combined)) is comprised of dissipation from polarization (εr(true)) and from ohmic conduction (σ). However, the conduction component becomes relatively less important with increasing frequency so that at 1 GHz, the true polarization loss εr(true) is dominant. This is a possible reason why the εr correlation with SSA improves as the frequency is increased.

The correlation between εr and CEC (Figure 8a and 8b) also worsens with an increase in frequency, but the correlation of CEC with εr (Figure 8c and 8d) improves with frequency. CEC also correlates strongly with the real dielectric permittivity of wet pastes, and this is attributable to water facilitating the exchange of cations and the associated dielectric polarization processes at mineral surfaces and in interlayer regions.

The water content of the paste is a strong determinant of the dielectric permittivity at all frequencies and in particular at frequencies above 100 MHz (Figure 9), but it is not the same for every paste sample. The percentage of hydratable clay minerals in the cuttings controls the plasticity of the paste and the eventual amount of water retained during consolidation by centrifugation. Therefore, the high-water-content, high-dielectric-permittivity pastes come from the cuttings with more clay minerals and/or a greater proportion of surface-active clay minerals (the so-called plasticity index; Mitchell and Soga, 2005). Given that surface-active clay minerals influence shale strength (Olsen, 1974; Leung and Steiger, 1992), the dielectric response of a paste below 100 MHz is a predictor of the physical properties of the rock forming the cuttings (Josh et al., 2012).

The water content of the paste samples is also strongly related to the SSA (at least when investigating paste samples at ambient laboratory conditions, R2=0.80, for data in Table 1), which is consistent with the affinity of water to high-surface-area hydrophilic clays. If more surface area is available and the water has an affinity for the clay minerals (e.g., Josh et al., 2012), then one will observe more retained water in a prepared paste. Ultimately, the correlation between εr and water content (Figure 9) improves slightly at a very high frequency.

Cuttings dielectric logs versus wireline petrophysical logs

Cuttings measurements were plotted against the smoothed wireline log responses from the depths at which the cuttings were taken (Figure 4). A 6.08-m (20-ft) running window smoothing was applied to the logs to approximate mixing during uphole transport and give the wireline data a similar sampling depth range as the cuttings.

Despite the fact that lithological units could not be matched exactly owing to the smoothing procedure, there is mild correlation in some instances. For example, the high-frequency conductivity measured on the drill cuttings is directly comparable with conventional resistivity and conductivity logs. In the example provided in Figure 10, the conductivity from an array induction log is calculated and then compared to the 30 MHz and 1 GHz conductivity of the drill cuttings calculated from εr using equation 2.

It is immediately apparent that the drill cuttings dielectric analysis is significantly more successful in the upper shaly section of the well than in the lower sandy section of the well. Several possible causes include disaggregation of the sandy units and clumping of the clayey units during uphole transport leading to better representativeness of the clayey cuttings upon retrieval. The in situ resistivity of the porous sandy units (Figure 10b) is dominated by the pore fluid, which is flushed away during drilling and cuttings sampling. Furthermore, the porosity of the coarser grained sandy units is completely destroyed during paste preparation. There may also be hydrocarbon effects in the sands that increase the resistivity. This explains why the broad spread in log-based conductivity (from approximately σ=0.1 to 5S/m is not reflected in the conductivity determined from cuttings and no cuttings to log correlation is seen (R20.01). Within shales, however, significant dielectric processes arising from CEC and SSA are occurring at a scale of microns and this is not completely destroyed during cuttings sampling at the well site or during paste preparation. The paste preparation procedure is likely to enhance the surface effects from constituent hydratable minerals. In the upper section of the well (Figure 10a), the cuttings-based conductivity is typically similar in value to the log values, despite an apparently very mild correlation (R2=0.480.50).

For samples from the more shale-rich upper section of the well, the correlation between real dielectric permittivity of the drilling cuttings remolded paste and the gamma ray log is moderate (Figure 11), and it is stronger at 30 MHz than it is at 1 GHz. No correlation exists for the lower section of the well, which has lower clay contents. The inference is that samples with increased swelling clay content in the upper part of the well produce a wetter paste, with more CEC and surface charge (Table 1). There is a thick upper shale and a thinner lower shale, both with gamma ray responses of around 100 API units. However, the lower shale in Figure 4 has a lower and more variable dielectric constant than the upper shale. The lower shale has a distinctly lower value of the dielectric dispersion parameter (30 MHz εr to 1 GHz εr) than the upper shale.

There is a moderate positive correlation between the real relative dielectric permittivity at 30 MHz and 1 GHz from cuttings and the compressional sonic slowness log (DTCO, Figure 12), indicating that some factors that lead to higher velocity are picked up in the dielectric properties of the cuttings paste; namely, rocks with less clay (i.e., lower in SSA and real dielectric permittivity) are faster. This “dielectric indicator” of elastic properties from cuttings at first sight compares unfavorably with the strong correlation between the dielectric constant and sonic velocity seen for preserved shales (Josh et al., 2012; Josh, 2014). However, shales are rarely cored and the extra electrochemical qualification of shale type from cuttings dielectrics can provide a useful constraint on elastic properties in addition to mechanical properties and swelling behavior.

The correlations between paste measurement and logs are generally weak (Figures 10–12), but it is remarkable that they exist between the dielectric permittivity of a paste and the elastic properties logs (Josh et al., 2012).

Dielectric analysis of preserved samples

At 10 MHz, the real dielectric permittivity (Figure 13) of the samples parallel-to-bedding is approximately 50% higher than it is normal-to-bedding. Similarly, the conductivity of the samples when the electric field is parallel-to-bedding is approximately four times higher than when it is normal-to-bedding. The well logs in Figure 4 show anisotropy ratios of around 5 in the upper and lower shales, between Rh and Rv (track 2). For comparison, Clavaud (2008) reveals that the shales from many worldwide locations also show substantial anisotropy in their electric resistivity (i.e., compacted shales with porosity of 18% displayed electric anisotropy of about 6, whereas less compacted shales with around 35% porosity have anisotropy in conductivity of about 2) and Revil et al. (2013) demonstrate anisotropy of 8 for conductivity in the Bakken shale. Therefore, the shales, in this study, have anisotropy at the higher end of the range typically encountered. It is, therefore, clearly important to retain consistency in the orientation of samples for other dielectric analysis on preserved samples.

Measurements of normal-to-bedding are also more consistent than measurements of parallel-to-bedding (Figure 13) because they are less affected by microcracking (vertical plugs are also more easy to obtain from the available preserved whole-round core materials from many wells). Vertical samples (1, 2, 3 and 4) show moderate levels of dielectric dispersion over the frequency range of 10–100 MHz, and the similarity in the shapes of the four curves demonstrates common structural and mineralogical characteristics. The ordering of sample 3<1<4<2 at 100 MHz most likely indicates an increase in water content and porosity in that order because at 100 MHz, the effect of water content exerts a strong influence on rock dielectric properties. Samples 2 and 4 have similar 10-MHz permittivity that distinguishes them from samples 1 and 3. The contribution of low-frequency interfacial polarization processes is, therefore, presumably greater in the former two samples, and that could be explained if these samples had greater content of high-surface-area clays.

The variation of dielectric properties observed in plugs from just two short whole-core sections in one well significantly demonstrates that remolded cuttings paste measurements tend to average out a range of rock subtypes sampled in any particular 6-m interval.

CONCLUSION

The use of high-frequency dielectric and conductivity analysis on mudrocks is complicated by the existence of significant quantities of diverse clay mineralogy. Unlike many other common minerals such as quartz and carbonate, clays are transformed during hydration into a suspension of colloids leading to a few additional dielectric and conduction phenomena. Long-range diffusion leads to Maxwell-Wagner polarization, the establishment of a polarizable electric double layer, and ions moving in the pore space create apparent high dielectric behavior and imaginary conduction may also contribute. For this reason, hydrated clays do not conform to the simplest mixture models, but necessitate the addition of new phenomenon after hydration that do not exist in the dry constituents and are not present in many mixture models.

From an experimental viewpoint, the arguments in support of the best dielectric analysis practice are in fact based on what the study is hoping to reveal about the sample. Different methods are used to determine the formation of dielectric permittivity from those that are best suited for rock strength, wellbore stability, porosity, saturation, and hydrocarbon content. For example, an investigation of anisotropy necessitates the preparation of orthogonal sample pairs of preserved material measured using a parallel plate cell. In a case study at an undisclosed location, the parallel-to-bedding dielectric permittivity was approximately six times greater than the orthogonal-to-bedding measurement and nearly perfectly matched the service company resistivity logs for the same section of well. Likewise, where only the drill cuttings are available, it is still possible to recover mineral and textural properties of the formation by using the known hydration behavior of clays. Two different methods of sample hydration have been presented. First, a dry powdered sample was allowed to stabilize in a controlled humidity environment and second, a paste was made by adding water to the powder using centrifugation to drive out the excess. Both methods have the ability to resolve differences in shale component mineralogy (quartz, kaolinite, illite, and smectite, each respond quite differently) and do not require substantial chemical pretreatments. Other rock textural properties such as SSA, CEC, and XRD mineralogy were also determined for the purposes of comparison using procedures developed specifically for shale mineralogy and swelling clays.

The paste dielectric routine was applied to a series of cuttings samples retrieved from the case study well to produce a “pseudolog.” The well contained a dominantly “shaly” upper section and a dominantly “sandy” lower section. Cuttings paste real dielectric permittivity exhibited up to R2=0.93 correlation with SSA, up to R2=0.86 correlation with CEC, and up to R2=0.81 correlation with the clay content. More significantly, a very weak but noticeable correlation appears to exist in the shaly units between the cuttings paste dielectric permittivity and the service company logs (R2=0.50 for resistivity log, R2=0.54 with gamma ray, and R2=0.41 with DTCO). But the correlation does not exist in the sandy units, probably because they are more friable and become disaggregated and nonrepresentative during uphole transport.

ACKNOWLEDGMENTS

The authors would like to thank those involved with providing the samples and the framework for the case study who wish to remain anonymous, R. Banks and T. Siggins for instrumentation development, and D. Dewhurst for editorial advice. We would also like to thank M. Raven for his expertise in clay mineralogy and L. Esteban for assistance in data collection.

OTHER PETROPHYSICAL ANALYSIS

Specific surface area

The SSA was determined using sorption of EGME (Kellomäki et al., 1987; Cerato and Lutenegger, 2002), which is chosen because of its suitability for investigating interlayer surfaces in swelling clays. A sample of 1–2 g of powder is dried at 110°C to drive off as much water as possible. The sample is then quickly weighed and immersed in EGME, and then placed in an evacuated drying atmosphere. After the samples have fully dried (determined by monitoring the change in mass), they are weighed again and the increase in weight from the dry samples provides the mass of the monolayer of EGME coating the internal surface area.

Published values of SSA for smectite are typically 700m2/g and illite ranges from 10to100m2/g (Kellomäki et al., 1987; Tiller and Smith, 1990; Cerato and Lutenegger, 2002). In this study, values of SSA for illite of 60m2/g based on measurements of Ward illite (68% illite and 28% quartz from XRD).

An analytical determination of SSA has been provided to verify the quality of the estimates made from XRD mineralogy using an equation which sums the typical published values of SSA for the constitutive minerals and their percentage contents as follows:  
analyticalSSA=700×content(smectite)+60×content(mica-illite)+40×content(kaolinite).
(A-1)
All other mineral grains within the samples (quartz, feldspars, carbonates, etc.) have negligible SSA based on experience with source minerals.
Cation exchange capacity

The CEC was determined using MB and the tetrasodium pyrophosphate method of Wang et al. (1996). Each clay sample was oven dried at 105°C for several hours before carefully weighing 0.5 g of the clay into 70 ml plastic containers. About 50 ml of 2% sodium pyrophosphate solution was added to the containers and vigorously shaken for 10 min in a Spex shaker mill. The dispersed clay was transferred with 150 ml of deionized water into a 250-ml conical flask and placed on a heating magnetic stirrer. The samples were gently boiled for 10 min and then allowed to cool to room temperature. A fresh MB solution was made by accurately weighing the equivalent of 3.74 g MB (gravimetrically determined to be 3H2O) into a 1000-ml volumetric flask and making up to volume with deionized water. The MB solution was transferred into a 25-ml burette placed above the clay suspension. While the clay suspension was being stirred, 0.5 ml of the MB solution was added. Stirring was continued for a minute before a drop of the liquid was deposited onto a filter paper using a small glass rod. A dark-blue spot appeared on the filter paper surrounded by a clear liquid halo. Additional 0.5 ml amounts of the MB were added to the constantly stirred clay suspension before the spot test was repeated. This was done until the clear halo turned blue, after which another spot test was performed after stirring a further 2 min. If the blue halo disappeared, then a further 0.5 ml of MB solution was added to the suspension and the spot test was repeated. The end point was obtained when a blue halo remained after stirring for 2 min.

X-ray diffraction mineralogy

The mineralogy was determined using XRD. XRD patterns were recorded with a PANalytical X’Pert Pro Multipurpose Diffractometer using Fe-filtered Co-Ka radiation, variable divergence slit, 1° antiscatter slit, and fast X’Celerator Si strip detector. The diffraction patterns were recorded in steps of 0.017° 2θ with a 0.5-s counting time per step and logged to data files for analysis. Quantitative analysis was performed on the XRD measurements from all bulk samples using the commercial package SIROQUANT from Sietronics Pty Ltd. The results are normalized to 100%, and hence they do not include estimates of unidentified or amorphous materials. The subset contained 21 samples, some of which were selected as being extremes in the dielectric response and others to give an approximately even spatial distribution throughout the borehole length. Standard commercial clays and widely studied outcrop shales are included for comparison (Table 1).

Freely available online through the SEG open-access option.