Ahmad Ghorbani

Source rocks for oil and gas are often associated with shales that are rich in pyrite and kerogen. Induced polarization is a suitable tool to characterize these formations. We develop a new experimental database of 43 laboratory experiments using mixtures of clay and pyrite under fully or partially water-saturated conditions. The liquid water saturation is in the range of 20%–100%, whereas the pyrite content is in the range of 0%–17%. Spectral-induced polarization measurements are performed in the frequency range of 0.1 Hz to 45 kHz at room temperature (approximately 25°C ± 1°C). The complex conductivity spectra are fitted with a Cole-Cole model, and the Cole-Cole parameters are determined using a stochastic procedure based on a Markov chain Monte Carlo sampler. The Cole-Cole parameters associated with low-frequency dispersion are then plotted as a function of the (water) saturation and pyrite content (volume fractions). Four predictions of the model are tested against the experimental data. We find that the model is able to explain the results, including (1) the chargeability depends on the pyrite content in a predictable way, (2) the (instantaneous) conductivity depends on the saturation according to Archie’s law, (3) the Cole-Cole exponent does not depend on the saturation and pyrite content (except at very small pyrite content of <1 vol%), and (4) the relaxation time is inversely proportional to the instantaneous conductivity. We also develop a more advanced petrophysical model using a double Cole-Cole distribution, in which one distribution is associated with the clay minerals and the other is associated with the pyrite.

The anisotropy in the complex conductivity of a clay-rock formation is investigated through laboratory and in situ measurements. Laboratory measurements have been conducted on four samples from two cores of the Callovo-Oxfordian Formation from the Paris Basin (France). This clay-rock formation is anisotropic with a well-defined bedding plane. Two of the cylindrical core samples are taken in the transverse direction with respect to the bedding plane, whereas two other core samples are taken in the in-plane direction. The complex conductivity spectra are performed in the frequency range of 20 mHz to 45 kHz and in a broad pore water saturation range from near saturation to a residual saturation of approximately 25%. The complex conductivity spectra are fitted with a double Cole-Cole model, whereas the low-frequency contribution corresponding to the induced polarization effect and the high-frequency contribution is related to the Maxwell-Wagner polarization. The six Cole-Cole parameters are investigated as a function of saturation, and we evaluate their degree of anisotropy versus the effect of saturation. The low-frequency instantaneous conductivity and normalized chargeability indicate a consistent degree of anisotropy with an anisotropy ratio equal to 3.8 ± 0.5 for one core sample and 6.5 ± 0.9 for the second core sample. These values represent a substantial level of anisotropy. The low-frequency Cole-Cole exponent and relaxation time do not indicate substantial amount of anisotropy. The monitoring of the evolution of the weight in the controlled humidity chamber seems to indicate that their relative permeabilities do not indicate a strong anisotropic behavior. Finally, the laboratory data are discussed in the context of field data obtained with an azimuthal array of 12 electrodes.

A petrophysical model describing spectral induced polarization (IP) has been developed for clay rocks accounting for the Maxwell-Wagner polarization. It is also used to connect the complex conductivity to the relative permeability of the material. This model is applied to the Callovo-Oxfordian clay rock of the Paris Basin (France) where the Meuse/Haute-Marne Underground Research Laboratory is located. Laboratory experiments are performed using eight clay-rock cores to study the effect of desiccation on their spectral-IP response. The measurements are performed along the foliation plane. Complex conductivity spectra are measured over a frequency range of 1 mHz to 45 kHz. These spectra are fitted with a double Cole-Cole model to extract the evolution of the Cole-Cole parameters with the saturation during the desiccation process. The low-frequency Cole-Cole model corresponds to IP phenomena, whereas the high-frequency Cole-Cole model corresponds to the Maxwell-Wagner contribution. We obtain the value of the first and second Archie’s exponents and we check the relationship between the surface conductivity and the cation exchange capacity of the clay rocks. We are also able to connect the relative permeability curve to the second (saturation) Archie’s exponent. The monitoring of the complex conductivity can be used to predict how the permeability of the clay-rock formation changes with the water content.

Spectral induced polarization spectra were carried out on three graphitic schists and two graphitic sandstones. The microstructural arrangement of graphite of two graphitic schists was studied with thin sections using transmitted and reflected light optical and electron microscopic methods. Chemical maps of selected areas confirm the presence of carbon. The complex conductivity spectra were measured in the frequency range 10 mHz to 45 kHz and in the temperature range +20 °C down to −15 °C. The measured spectra are fitted with a double Cole‐Cole complex conductivity model with one component associated with the polarization of graphite and the second component associated with the Maxwell‐Wagner polarization. The Cole‐Cole exponent and the chargeability are observed to be almost independent of temperature including in freezing conditions. The conductivity and relaxation time are dependent on the temperature in a predictable way. As long as the temperature decreases, the electrical conductivity decreases and the relaxation time increases. A finite element model is able to reproduce the observed results. In this model, we consider an intragrain polarization mechanism for the graphite and a change of the conductivity of the background material modeled with an exponential freezing curve. One of the core sample (a black schist), very rich in graphite, appears to be characterized by a very high conductivity (approximately 30 S/m). Two induced polarization profiles are discussed in the area of Thorens. The model is applied to the chargeability data to map the volumetric content of graphite.

We consider a mixture made of dispersed metallic particles immersed into a background material saturated by an electrolyte. Below the freezing temperature (typically 0°C to −4°C), a fraction of the liquid water in the pore space is transformed into ice, whereas the salt remains segregated into the liquid-pore water solution. Our goal is to understand how freezing affects the complex conductivity (induced polarization) of such mixtures. Complex conductivity measurements (96 spectra) are performed in a temperature-controlled bath equipped with a high-precision impedance meter. We cover the temperature range from +20°C to −15°C to −18°C and the frequency range from 10−2 Hz to 45 kHz. The spectra are fitted with a double Cole-Cole complex conductivity model. A finite-element model is used to further analyze the mechanisms of polarization by considering an intragrain polarization mechanism for the metallic particles and a change of the conductivity of the background material modeled with an exponential freezing curve. This curve is used to relate the liquid water content to the temperature. In the context of freezing, we test all the aspects of the intragrain polarization model developed in the previous papers of this series, at least for a weakly polarizable background material. The Cole-Cole exponent and the chargeability are observed to be essentially independent of temperature including in freezing conditions. This means that all the relaxation times of the system follow the same temperature dependence and that the chargeability is controlled by the volume fraction of metal. The instantaneous conductivity (high-frequency conductivity) and the relaxation times depend on the temperature in a predictable way, and their product can be considered to be essentially temperature independent. The analytical and numerical models can reproduce the inverse relationship between the relaxation time and the instantaneous conductivity.

Desiccation influences the complex conductivity of porous media with disseminated metallic particles. We expand the mechanistic model developed in the previous papers of this series to include the effect of saturation upon the complex conductivity of mixtures of mineral grains, pyrite, and pore water. During desiccation, the salt is assumed to be segregated in the liquid pore water; therefore, the conductivity of the pore water increases when saturation decreases. We have performed 14 experiments corresponding to 91 complex conductivity spectra. In these experiments, the saturation of the water phase is changed over time by desiccation. The resulting spectra are fitted by a double Cole-Cole model used as the fitting model. We also developed a mechanistic model in which the chargeability and the relaxation time of the low-frequency polarization are expected to change with saturation in a predictable way. We first characterized the properties of the background material made by an illitic clay material. We determine how the Cole-Cole parameters depend on saturation. The Cole-Cole exponent is essentially independent on saturation. When the chargeability of the mixture is dominated by the presence of pyrite, it becomes independent of the saturation but a small effect on the chargeability is observed at low pyrite contents. The instantaneous conductivity of the background decreases with the saturation in a predictable way. The relaxation time depends on the inverse of the instantaneous conductivity and therefore on saturation. This dependence is well-explained through numerical simulations made with the finite-element method. Finally, we analyze the complex conductivity spectra of two clay-rock core samples from the Callovo-Oxfordian formation in the Paris Basin (France). The spectra are shown as a function of their desiccation and explained thanks to the newly developed model.

We investigate the influence of temperature and salinity upon the spectral induced polarization of 10 samples including rocks with their mineralization (galena, chalcopyrite) plus sand mixed with semi-conductors such as magnetite grains, graphite, and pyrite cubes of two different sizes. Measurements are made in a temperature-controlled bath with a high-precision impedance meter and using NaCl solutions. We cover the temperature range 5-50°C and the frequency range 10^-2 Hz to 45 kHz. For one large pyrite cube, we also investigated 6 salinities from 0.1 to 10 S m^-1 (at 25°C, NaCl) and three salinities for graphite. The spectra are fitted with a Cole Cole complex parametric conductivity model for which we provide a physical meaning to the four Cole Cole parameters. As expected, the Cole Cole exponent and the chargeability are both independent of the temperature and salinity. The instantaneous and steady state (DC, Direct Current) conductivities depend on both salinity and temperature. This temperature dependence can be fitted with an Arrhenius’ law (combining the Stokes-Einstein and Vogel-Fulcher-Tammann equations) with an activation energy in the range 15±1 kJ Mol^-1. This activation energy is the same than for the bulk pore water conductivity demonstrating the control by the background electrolyte of these quantities, as expected. The instantaneous and DC conductivities depend on the salinity in a predictable way. The Cole Cole relaxation time decreases with the temperature and decreases with the salinity. This behavior can be modeled with an Arrhenius law with an apparent activation energy of 7±3 kJ mol^-1. A finite element model is used to analyze further the mechanisms of polarization and can reproduce the temperature and salinity dependencies observed in the laboratory.