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When pH and alkalinity increase, calcite frequently precipitates and hence modifies the petrophysical properties of porous media. The complex conductivity method can be used to directly monitor calcite precipitation in porous media because it is sensitive to the evolution of the mineralogy, pore structure and its connectivity. We have developed a mechanistic grain polarization model considering the electrochemical polarization of the Stern and diffuse layers surrounding calcite particles. Our complex conductivity model depends on the surface charge density of the Stern layer and on the electrical potential at the onset of the diffuse layer, which are computed using a basic Stern model of the calcite/water interface. The complex conductivity measurements of Wu et al. on a column packed with glass beads where calcite precipitation occurs are reproduced by our surface complexation and complex conductivity models. The evolution of the size and shape of calcite particles during the calcite precipitation experiment is estimated by our complex conductivity model. At the early stage of the calcite precipitation experiment, modelled particles sizes increase and calcite particles flatten with time because calcite crystals nucleate at the surface of glass beads and grow into larger calcite grains. At the later stage of the calcite precipitation experiment, modelled sizes and cementation exponents of calcite particles decrease with time because large calcite grains aggregate over multiple glass beads and only small calcite crystals polarize.

In this work, we revisit the seminal concept of Johnson–Koplik–Schwartz (JKS) length Λ, that is a characteristic length representing an effective pore size which controls various transport-related properties of porous media, such as, the permeability and the electrical conductivity. We present a novel closed-form equation that predicts the behaviour of Λ in partially saturated media, for different saturation states. Using previous models in the literature that predict the intrinsic and relative electrical conductivities under partially saturated conditions, we infer the JKS length Λ and the electrical formation factor F as functions of water saturation and properties associated with the pore-size distribution of the probed porous medium. The proposed method permits to estimate the effective permeability and the relative permeability directly from electrical conductivity measurements, thus opening new-avenues for the remote characterization of partially saturated media. We believe that this new model will prove useful for various characterization and modelling applications from reservoir (CO2 or hydrogen storage) to vadose zone studies. [ABSTRACT FROM AUTHOR]

In reservoir and environmental studies, the geological material characterization is often done by measuring its electrical conductivity. Its main interest is due to its sensitivity to physical properties of porous media (i.e. structure, water content, or fluid composition). Its quantitative use therefore depends on the efficiency of the theoretical models to link them. In this study, we develop a new physically based model that takes into account the surface conductivity for estimating electrical conductivity of porous media under partially saturated conditions. The proposed model is expressed in terms of electrical conductivity of the pore fluid, water saturation, critical water saturation and microstructural parameters such as the minimum and maximum pore/capillary radii, the pore fractal dimension, the tortuosity fractal dimension and the porosity. Factors influencing the electrical conductivity in porous media are also analysed. From the proposed model, we obtain an expression for the relative electrical conductivity that is consistent with other models in literature. The model predictions are successfully compared with published experimental data for different types of porous media. The new physically based model for electrical conductivity opens up new possibilities to characterize porous media under partially saturated conditions with geoelectrical and electromagnetic techniques. [ABSTRACT FROM AUTHOR]

Electrical conductivity is one of the most commonly used geophysical method for reservoir and environmental studies. Its main interest lies in its sensitivity to key properties of storage and transport in porous media. Its quantitative use therefore depends on the efficiency of the petrophysical relationship to link them. In this work, we develop a new physically based model for estimating electrical conductivity of saturated porous media. The model is derived assuming that the porous media is represented by a bundle of tortuous capillary tubes with a fractal pore-size distribution. The model is expressed in terms of the porosity, electrical conductivity of the pore liquid and the microstructural parameters of porous media. It takes into account the interface properties between minerals and pore water by introducing a surface conductivity. Expressions for the formation factor and hydraulic tortuosity are also obtained from the model derivation. The model is then successfully compared with published data and performs better than previous models. The proposed approach also permits to relate the electrical conductivity to other transport properties such as the hydraulic conductivity. [ABSTRACT FROM AUTHOR]

We implement a procedure to simulate the drainage and imbibition in random, 2-D, square networks. We compute the resistivity index, the relative permeability and the characteristic lengths of a correlated network at various saturation states, under the assumption that the surface conductivity can be neglected. These parameters exhibit a hysteretic behaviour. Then, we calculate the spectral induced polarization (SIP) response of the medium, under the assumption that the electrical impedance of each tube follows a local Warburg conductivity model, with identical DC conductivity and chargeability for all the tubes. We evidence that the shape of the SIP spectra depends on the saturation state. The analysis of the evolution of the macroscopic Cole-Cole parameters of the spectra in function of the saturation also behaves hysteretically, except for the Cole-Cole exponent. We also observe a power-law relationship between the macroscopic DC conductivity and time constant and the relative permeability. We also show that the frequency peak of the phase spectra is directly related to the characteristic length and to the relative permeability, underlining the potential interest of SIP measurements for the estimation of the permeability of unsaturated media. [ABSTRACT FROM AUTHOR]

The presence of mesoscopic heterogeneities in fluid-saturated porous rocks can produce measurable seismoelectric signals due to wave-induced fluid flow between regions of differing compressibility. The dependence of these signals on the petrophysical and structural characteristics of the probed rock mass remains largely unexplored. In this work, we derive an analytical solution to describe the seismoelectric response of a rock sample, containing a horizontal layer at its centre, that is subjected to an oscillatory compressibility test. We then adapt this general solution to compute the seismoelectric signature of a particular case related to a sample that is permeated by a horizontal fracture located at its centre. Analyses of the general and particular solutions are performed to study the impact of different petrophysical and structural parameters on the seismoelectric response. We find that the amplitude of the seismoelectric signal is directly proportional to the applied stress, to the Skempton coefficient contrast between the host rock and the layer, and to a weighted average of the effective excess charge of the two materials. Our results also demonstrate that the frequency at which the maximum electrical potential amplitude prevails does not depend on the applied stress or the Skempton coefficient contrast. In presence of strong permeability variations, this frequency is rather controlled by the permeability and thickness of the less permeable material. The results of this study thus indicate that seismoelectric measurements can potentially be used to estimate key mechanical and hydraulic rock properties of mesoscopic heterogeneities, such as compressibility, permeability and fracture compliance. [ABSTRACT FROM AUTHOR]