Damien Jougnot

A double layer model of the gas bubble/water interface

Zeta potential is a physico-chemical parameter of particular importance to describe sorption of contaminants at the surface of gas bubbles. Nevertheless, the interpretation of electrophoretic mobilities of gas bubbles is complex. This is due to the specific behavior of the gas at interface and to the excess of electrical charge at interface, which is responsible for surface conductivity. We developed a surface complexation model based on the presence of negative surface sites because the balance of accepting and donating hydrogen bonds is broken at interface. By considering protons adsorbed on these sites followed by a diffuse layer, the electrical potential at the head-end of the diffuse layer is computed and considered to be equal to the zeta potential. The predicted zeta potential values are in very good agreement with the experimental data of H(2) bubbles for a broad range of pH and NaCl concentrations. This implies that the shear plane is located at the head-end of the diffuse layer, contradicting the assumption of the presence of a stagnant diffuse layer at the gas/water interface. Our model also successfully predicts the surface tension of air bubbles in a KCl solution.

Monitoring of saline tracer movement with vertically distributed self-potential measurements at the HOBE agricultural test site, Voulund, Denmark

The self-potential (SP) method is sensitive to water fluxes in saturated and partially saturated porous media, such as those associated with rainwater infiltration and groundwater recharge. We present a field-based study at the Voulund agricultural test site, Denmark, that is, to the best of our knowledge, the first to focus on the vertical self-potential distribution prior to and during a saline tracer test. A coupled hydrogeophysical modeling framework is used to simulate the SP response to precipitation and saline tracer infiltration. A layered hydrological model is first obtained by inverting dielectric and matric potential data. The resulting model that compares favorably with electrical resistance tomography models is subsequently used to predict the SP response. The electrokinetic contribution (caused by water fluxes in a charged porous soil) is modeled by an effective excess charge approach that considers both water saturation and pore water salinity. Our results suggest that the effective excess charge evolution prior to the tracer injection is better described by a recent flux-averaged model based on soil water retention functions than by a previously proposed volume-averaging model. This is the first time that raw (i.e., without post-processing or data-correction) vertically distributed SP measurements have been explained by a physically based model. The electrokinetic contribution cannot alone reproduce the experimental SP data during the tracer test and an electro-diffusive contribution (caused by concentration gradients) is needed. The predicted amplitude of this contribution is too small to perfectly explain the data, but the shape is in accordance with the field data. This discrepancy is attributed to imperfect descriptions of electro-diffusive phenomena in partially saturated soils, unaccounted soil heterogeneity, and discrepancies between the measured and predicted electrical conductivities in the tracer infiltration area. This study opens the way for detailed long-term field-based investigations of the SP method in vadose zone hydrology.

Influence of surface conductivity on the apparent zeta potential of calcite

Zeta potential is a physicochemical parameter of particular importance in describing the surface electrical properties of charged porous media. However, the zeta potential of calcite is still poorly known because of the difficulty to interpret streaming potential experiments. The Helmholtz-Smoluchowski (HS) equation is widely used to estimate the apparent zeta potential from these experiments. However, this equation neglects the influence of surface conductivity on streaming potential. We present streaming potential and electrical conductivity measurements on a calcite powder in contact with an aqueous NaCl electrolyte. Our streaming potential model corrects the apparent zeta potential of calcite by accounting for the influence of surface conductivity and flow regime. We show that the HS equation seriously underestimates the zeta potential of calcite, particularly when the electrolyte is diluted (ionic strength ⩽ 0.01 M) because of calcite surface conductivity. The basic Stern model successfully predicted the corrected zeta potential by assuming that the zeta potential is located at the outer Helmholtz plane, i.e. without considering a stagnant diffuse layer at the calcite-water interface. The surface conductivity of calcite crystals was inferred from electrical conductivity measurements and computed using our basic Stern model. Surface conductivity was also successfully predicted by our surface complexation model.

Streaming potential modeling in fractured rock: Insights into the identification of hydraulically active fractures

Numerous field experiments suggest that the self-potential (SP) geophysical method may allow for the detection of hydraulically active fractures and provide information about fracture properties. However, a lack of suitable numerical tools for modeling streaming potentials in fractured media prevents quantitative interpretation and limits our understanding of how the SP method can be used in this regard. To address this issue, we present a highly efficient two-dimensional discrete-dual-porosity approach for solving the fluid flow and associated self-potential problems in fractured rock. Our approach is specifically designed for complex fracture networks that cannot be investigated using standard numerical methods. We then simulate SP signals associated with pumping conditions for a number of examples to show that (i) accounting for matrix fluid flow is essential for accurate SP modeling and (ii) the sensitivity of SP to hydraulically active fractures is intimately linked with fracture-matrix fluid interactions. This implies that fractures associated with strong SP amplitudes are likely to be hydraulically conductive, attracting fluid flow from the surrounding matrix.

An analytical study of seismoelectric signals produced by 1-D mesoscopic heterogeneities

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 center, 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 center. 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.

A Simple Hysteretic Constitutive Model for Unsaturated Flow

In this paper, we present a constitutive model to describe unsaturated flow that considers the hysteresis phenomena. This constitutive model provides simple mathematical expressions for both saturation and hydraulic conductivity curves, and a relationship between permeability and porosity. The model is based on the assumption that the porous media can be represented by a bundle of capillary tubes with throats or “ink bottles” and a fractal pore size distribution. Under these hypotheses, hysteretic curves are obtained for saturation and relative hydraulic conductivity in terms of pressure head. However, a non-hysteretic relationship is obtained when relative hydraulic conductivity is expressed as a function of saturation. The proposed relationship between permeability and porosity is similar to the well-known Kozeny–Carman equation but depends on the fractal dimension. The performance of the constitutive model is tested against different sets of experimental data and previous models. In all of the cases, the proposed expressions fit fairly well the experimental data and predicts values of permeability and hydraulic conductivity better than others models.

Feature-preserving interpolation and filtering of environmental time series

We propose a method for filling gaps and removing interferences in time series for applications involving continuous monitoring of environmental variables. The approach is non-parametric and based on an iterative pattern-matching between the affected and the valid parts of the time series. It considers several variables jointly in the pattern matching process and allows preserving linear or non-linear dependences between variables. The uncertainty in the reconstructed time series is quantified through multiple realizations. The method is tested on self-potential data that are affected by strong interferences as well as data gaps, and the results show that our approach allows reproducing the spectral features of the original signal. Even in the presence of intense signal perturbations, it significantly improves the signal and corrects bias introduced by asymmetrical interferences. Potential applications are wide-ranging, including geophysics, meteorology and hydrology. A time series processing method that repairs both gaps and interferences.Preserves dependencies between multiple variables.Quantifies the uncertainty of the reconstructed signal.

Variations of petrophysical properties and spectral induced polarization in response to drainage and imbibition: a study on a correlated random tube network

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.

Geoelectrical Signatures of Reactive Mixing: A Theoretical Assessment

Characterizing the effects of subsurface fluid mixing on biogeochemical reactions is a key step toward monitoring and understanding a range of processes and applications in which fluids of different chemical compositions mix, such as aquifer remediation, CO2 sequestration, or groundwater‐surface water interactions. Yet the development of noninvasive methods to monitor mixing processes remains an outstanding challenge. Mixing processes are controlled by concentration gradients that develop at scales below the spatial resolution of hydrogeophysical imaging techniques. To overcome this difficulty, we propose to focus on the geoelectrical response of mixing‐driven chemical reactions, for which the products are electrically more conductive than the background solution. For such reactions, we investigate the impact of reactive mixing on the resulting effective electrical conductivity. The transport equations are solved using the Lamellar Mixing Theory for a range of velocity gradients representative of the stretching rates experienced by mixing fronts in heterogeneous porous media. Focusing on simple shear flows, we demonstrate that such reactions may result in substantial changes (several orders of magnitude) in the effective conductivity over time, thus providing geoelectrical signatures of reactive mixing dynamics. The temporal evolution of the effective conductivity depends on the relative orientations of the applied electrical potential gradient, mean flow, and velocity gradient, yielding different sensitivities to dispersion processes, stretching rates, and reaction kinetics. These results suggest that the use of chemical reactions with electrically conductive products could help to overcome present limitations of time‐lapse geophysical imaging in the monitoring of the spatiotemporal dynamics of subsurface reactive mixing processes.

An analytical effective excess charge density model to predict the streaming potential generated by unsaturated flow

The self-potential (SP) method is a passive geophysical method that relies on the measurement of naturally occurring electrical field. One of the contributions to the SP signal is the streaming potential, which is of particular interest in hydrogeophysics as it is directly related to both the water flow and porous medium properties. The streaming current is generated by the relative displacement of an excess of electrical charges located in the electrical double layer surrounding the minerals of the porous media. In this study, we develop a physically based analytical model to estimate the effective excess charge density dragged by the water flow under partially saturated conditions. The proposed model is based on the assumption that the porous media can be represented by a bundle of tortuous capillary tubes with a fractal pore size distribution. The excess charge that is effectively dragged by the water flow is estimated using a flux averaging approach. Under these hypotheses, this new model describes the effective excess charge density as a function of saturation and relative permeability while also depending on the chemical and interface properties, and on petrophysical parameters of the media. The expression of the model has an analytical single closed-form which is consistent with a previous model developed from a different approach. The performance of the proposed model is then tested against previous models and different sets of laboratory and field data from the literature. The predictions of the proposed model fits fairly well the experimental data and shows improvements to estimate the magnitude of the effective excess charge density over the previous models. A relationship between the effective excess charge density and permeability can also be derived from the proposed model, representing a generalization to unsaturated conditions of a widely used empirical relationship. This new model proposes a simple and efficient way to model the streaming current generation for partially saturated porous media.