Electrokinetic Coupling Coefficient Research Articles

Seismoelectric Coupling Equations of Oil-Wetted Porous Medium Containing Oil and Water

For porous medium containing multiphase fluid, such as oil-wetted porous medium with oil–water dual phase fluid, its fluid interface will also produce electric double layer (EDL), which will play a role in the seismoelectric effects. At this time, the principle of seismoelectric effects is more complex. The existing theory for the seismoelectric effects is the Pride theory used in the water-saturated porous formation, which cannot meet the actual needs of the theoretical research of seismoelectric exploration in the porous formation with multiphase fluid. Carbonate porous formations are often oil-wetted; therefore, it is necessary to study the electrokinetic effects of oil-wetted porous medium containing multiphase fluid. In this paper, we treated the oil–water mixture as an effective fluid, and solved the effective elastic parameters and extended the Biot equations to the case of oil-wetted porous medium with oil–water dual phase fluid. We calculated the effective electromagnetic parameters and derived the macroscopic coupling equations of seismoelectric effects and electroseismic effects, and proposed the new electrokinetic coupling coefficients of the oil-wetted porous medium with dual phase fluid. We also deduced the coupling functions of electric and magnetic fields relative to the solid displacement in the homogeneous porous medium, and studied the polarization characteristics of the electric field. We use the derived coupling equations to simulate the seismoelectric logging while drilling in the model of oil-wetted porous formation with dual phase fluid under the excitation of multipole sources. The influence of drill collar wave on the acoustic field and electric field under the excitation of different sources was investigated, which has a certain guiding role in the selection of electrokinetic logging tools.

Study of the Seismoelectric Effect in Saturated Porous Media Using a Bundle of Capillary Tubes Model

The seismoelectric effect is the fundamental basis for seismoelectric logging. Most of the existing theories for the seismoelectric effect are based on the Pride theory, which adopts the assumption of a thin electric double layer and uses the volume-averaging method to derive the seismoelectric coupling equations; hence, the obtained electrokinetic coupling coefficient is not applicable to large-Debye-length cases. In addition, the Pride theory neglects the change in seepage velocity with the radial position of the pore when calculating the streaming current, which leads to an inaccurate reflection of the influence of pore size on the electrokinetic coupling coefficient. In this study, we proposed a flux-averaging method to solve the effective net residual charge density of porous media and further derived the electrokinetic coupling coefficient expressed by the effective net residual charge density. We also investigated the effect of formation parameters and compared the results with those calculated using the Pride theory. Since the proposed method is not limited by the thin electric double layer assumption, it is suitable for both small- and large-Debye-length cases. Moreover, we also carried out flume experiments to investigate the influence of salinity, where both thin and thick electric double layer cases were studied. The comparison between the results of the experiment and simulation verified the correctness of the proposed method. Furthermore, the proposed method took into account the variation in seepage velocity with pore location when solving for the streaming current; therefore, the influence of the pore size on the electrokinetic coefficient can be described more accurately.

Seismoelectric Effect of Oil-Wetted Porous Media Containing Two-Phase Flow

In oil reservoirs, if oil mainly has wettability in the solid phase, such as in carbonate reservoirs, the medium is oil-wetted. For oil-wetted porous media containing an oil and water two-phase flow, there are electric double layers at both the oil–solid interface and the oil–water interface, which can stimulate the seismoelectric effect. To date, most of the studies on the seismoelectric effects of porous media have mainly focused on water-wetted porous media, however, there are few reported studies on cases of oil-wetted porous media, especially on oil-wetted porous media containing an oil–water two-phase flow. In this paper, we adopted the oil-wetted pore model, in which oil and water are assumed to be immiscible, and each phase is continuous and distributed in parallel. We also considered the influence of the electric double layer at both the oil–solid interface and the oil–water interface on the seismoelectric effect. It was concluded that the seismoelectric effect of oil-wetted porous media containing a two-phase flow is mainly caused by the electric double layer at the oil–water interface, while the effect of the electric double layer at the oil–solid interface can be ignored. We regarded the two-phase flow as an equivalent fluid, and then we derived a governing equation of the seismoelectric effect and proposed the flux-averaging method to derive the electrokinetic coupling coefficients under the excitation of a steady acoustic field and a time-harmonic acoustic field. We also investigated the effects of formation parameters, namely, water saturation, pore size, water viscosity and porosity, on the seismoelectric effect, which can provide a theoretical reference for the study of seismoelectric logging in oil-wetted porous formations containing a two-phase flow.

Modeling the Frequency‐Dependent Effective Excess Charge Density in Partially Saturated Porous Media

AbstractIn the context of seismoelectric and self‐potential surveying, the effective excess charge density and the electrokinetic coupling coefficient are key parameters relating the measured electrical potential and the hydraulic characteristics of the explored porous media. In this work, we present a novel flux averaging approach that permits to estimate the frequency‐dependent effective excess charge density in partially saturated porous media. For this, we conceptualize the porous medium as a partially saturated bundle of capillary tubes under oscillatory flux conditions. We account for the pore size distribution (PSD) to determine the capillary‐pressure saturation relationship of the corresponding medium, which, in turn, permits to determine the pore scale saturation. We then solve the Navier‐Stokes equations within the saturated capillaries and, by means of a flux‐averaging procedure, obtain upscaled expressions for: (a) the effective excess charge density, (b) the effective permeability, and (c) the electrokinetic coupling coefficient, which are functions of the saturation and the probing frequency. We analyze and explain the characteristics of these functions for three different PSDs: fractal, lognormal, and double lognormal. It is shown that the PSD characteristics have a strong effect on the corresponding electrokinetic response. The proposed flux‐averaging approach has an excellent capability for reproducing experimental measurements and models in the literature, which are otherwise based on well‐known empirical relationships. The results of this work constitute a useful framework for the interpretation of electrokinetic signals in partially saturated media.

Influence of Pore Size Distribution on the Electrokinetic Coupling Coefficient in Two-Phase Flow Conditions

Streaming potential is a promising method for a variety of hydrogeophysical applications, including the characterisation of the critical zone, contaminant transport or saline intrusion. A simple bundle of capillary tubes model that accounts for realistic pore and pore throat size distribution of porous rocks is presented in this paper to simulate the electrokinetic coupling coefficient and compared with previously published models. In contrast to previous studies, the non-monotonic pore size distribution function used in our model relies on experimental data for Berea sandstone samples. In our approach, we combined this explicit capillary size distribution with the alternating radius of each capillary tube to mimic pores and pore throats of real rocks. The simulation results obtained with our model predicts water saturation dependence of the relative electrokinetic coupling coefficient more accurately compared with previous studies. Compared with previous studies, our simulation results demonstrate that the relative coupling coefficient remains stable at higher water saturations but vanishes to zero more rapidly as water saturation approaches the irreducible value. This prediction is consistent with the published experimental data. Moreover, our model was more accurate compared with previously published studies in computing the true irreducible water saturation relative to the value reported in an experimental study on a Berea sandstone sample saturated with tap water and liquid CO2. Further modifications, including explicit modelling of the capillary trapping of the non-wetting phase, are required to improve the accuracy of the model.

Pore-Scale Modeling of Electrokinetics in Geomaterials

Pore-scale finite-volume continuum models of electrokinetic processes are used to predict the Debye lengths, velocity, and potential profiles for two-dimensional arrays of circles, ellipses and squares with different orientations. The pore-scale continuum model solves the coupled Navier–Stokes, Poisson, and Nernst–Planck equations to characterize the electro-osmotic pressure and streaming potentials developed on the application of an external voltage and pressure difference, respectively. This model is used to predict the macroscale permeabilities of geomaterials via the widely used Carmen–Kozeny equation and through the electrokinetic coupling coefficients. The permeability results for a two-dimensional X-ray tomography-derived sand microstructure are within the same order of magnitude as the experimentally calculated values. The effect of the particle aspect ratio and orientation on the electrokinetic coupling coefficients and subsequently the electrical and hydraulic tortuosity of the porous media has been determined. These calculations suggest a highly tortuous geomaterial can be efficient for applications like decontamination and desalination.

Seismoelectric surface-wave analysis for characterization of formation properties, using dispersive relative spectral amplitudes

We have studied seismoelectric (SE) surface-wave signals and found that they can be used to infer changes in the SE coupling properties at depth. SE surface-wave signals have much higher amplitudes than SE body-wave signals. We measured the seismic and the electrical potential or electromagnetic (EM) field along the surface of the earth. We used dispersive relative spectral amplitudes (DRSAs) that measure the frequency-dependent relative strength of electrical signals versus seismic signals associated with SE surface-wave signals. We find that DRSAs have sensitivity to contrasts in the electrokinetic coupling coefficient and other relevant petrophysical properties at depth. Our discovery can mitigate the major limitation that plagues body-wave-based SE methods: the relative weakness of the converted EM signals from seismic body waves. We envision applications to characterize subsurface rock, fluid, and fluid-flow properties (e.g., porosity, permeability, and dynamic fluid viscosity, salinity) in the near surface, for aquifers, and shallow geothermal reservoirs.

Streaming Potential Measurements on the Binary Mixture Triethylamine-Water Near the Demixing Phase Transition

Large density fluctuations developing near the phase transition point of the binary mixture affect physical parameters directly related to the electrokinetic coupling coefficient. Here the first electrokinetic measurements for a porous rock sample are carried out with a critical binary mixture of triethylamine-water, especially around the phase transition point. From the measured streaming potential coefficient, the zeta potential is obtained for the critical composition. The results show that there is no anomaly in the streaming potential coefficient as the temperature approaches the demixing temperature. It is also seen that the streaming potential coefficient and the zeta potential in magnitude decreases with increasing temperature. This observation is opposite to what has been observed in literature. It means that the properties of the electric double layer for the mixtures are different from those for aqueous electrolytes. Additionally, the zeta potential for the critical composition is predicted to fluctuate around the critical point.

Dependence of Dynamic Electrokinetic-Coupling-Coefficient on the Electric Double Layer Thickness of fluid-filled porous formations

Electrokinetic coupling between pore-fluid flow and electric field arising from the electrical double layer (EDL) has many applications in geoscience. In this study, we extended the formulas for the dynamic electrokinetic coupling coefficient (ECC) to arbitrary scaled capillaries. These two ECC formulas for the cylindrical and slit apertures, respectively, were derived without the thin or thick EDL assumption used in previous studies, relating to the normalized radius (the ratio of capillary radius to Debye length). By the identical ECC formulas for streaming current and electroosmosis effects, it is confirmed that Onsager’s reciprocity is generally satisfied for arbitrary scaled and shaped apertures. This ECC tends to the results using the thick and the thin EDL assumptions respectively with the decrease and increase of the normalized radius. It is shown that the relative error is less than 10.0% if the normalized radius is less than 0.8 and is larger than 20, respectively. Otherwise, the thick and the thin EDL assumptions are inapplicable. The high-frequency limit phase of this ECC increases from 45 o to 90 o with the decrease of the normalized radius, rather than that remains at 45 o under the thin EDL assumption. The linear approximation for solving the Poisson-Boltzmann equation influences the electric potential in the EDL and the ECC, which increases with the decrease of the normalized radius. If the normalized radius is larger than 7, the error is within 5.0% even though the linear approximation has been mathematically invalid when the salinity is 0.001 mol/L and zeta potential is -150 mV.

Electric potential anomaly induced by humid air convection within Piton de La Fournaise volcano, La Réunion Island

Self potential (SP) anomalies over Piton de La Fournaise volcano (La Réunion Island) are generally interpreted as resulting from meteoritic water porous flow. However, there is no clear evidence that the subsurface is permanently saturated. Recently, a convective subsurface airflow has been evidenced within a quiescent cone at Piton de La Fournaise (Formica Leo). SP and thermal anomalies are reported on the unsaturated edifice and are seen to be correlated. It is proposed that the SP signal is generated by the movement of water films present on the porous matrix, induced by the intense humid airflow within Formica Leo. The structure of the cone, determined from electrical resistivity tomography (ERT), ground penetrating radar (GPR), microgravimetric and kinematic GPS data, is used to constrain a 3D numerical model of the air convection. The calculated temperature is then used to derive the related SP signal, the electrokinetic coupling coefficient being estimated from direct observations of the electrical resistivity of the soil. Extrapolating these results to the scale of the volcano, it is thus proposed that a cold humid airflow enters the flanks of the 400m-high terminal dome, flows up along the sloped and stratified volcanic layers before exiting through the vertical fractures around the Dolomieu collapse. It is demonstrated that the SP anomalies catches the main features recovered over the entire volcano. This result strongly suggests that humid airflow may play a major role on the generation of SP anomalies at Piton de la Fournaise volcano, and perhaps in other unsaturated volcanic edifices.

Detection of non-aqueous phase liquid contamination by SH-TE seismoelectrics: A computational feasibility study

In this work we propose a one dimensional numerical study of the seismoelectric signals produced in a fresh water aquifer contaminated by either light or dense non-aqueous phase liquids ((L/D)NAPLs), considering a pure SH-wave seismic source. We investigate the nature of the electromagnetic response generated at media interfaces, the so called Interface Response (IR), by comparing it with the electromagnetic field generated by a current sheet; wherefrom we are able to interpret that the source of the IR behaves as an electric current flowing along the interface, differently to what happens when the IR is originated by the action of a P-wave, where electric charge accumulation generates an electric dipole. We perform a parametric study to analyze how the presence of contaminants affects the IR, resorting to an effective media approach to compute mechanical and electromagnetic properties, and considering three different effective fluid-saturation dependent electrokinetic coupling coefficient models. We observe, as expected, that porosity plays an important role in the amplitude of the IRs. When considering different NAPL saturations, significant effects on the IRs are only seen when the thickness of the contaminated layer is above a threshold value, which depends on the present contaminant and the considered effective electrokinetic coupling coefficient model.

Theory of transient streaming potentials in coupled unconfined aquifer‐unsaturated zone flow to a well

AbstractA semianalytical solution is presented for transient streaming potentials associated with flow to a pumping well in an unconfined aquifer, taking into account the effect of flow in the unsaturated zone above the water table. Flow in the unsaturated zone is modeled with a linearized form of Richards' equation using an exponential model for soil moisture retention and unsaturated hydraulic conductivity. Archie's law is invoked for unsaturated electrical conductivity. The unsaturated electrokinetic coupling coefficient is modeled with a decaying exponential, where the maximum value is at and below the water table. The coupled flow and electrokinetic problem is solved using Laplace and Hankel transforms. The results of the model predicted behavior are presented and compared to that observed in laboratory simulations of pumping tests. The early time polarity reversal predicted the model is observable in the experiments. Other nonmonotonic streaming potential behaviors predicted by the model are also evident in experimental measurements. The model is used to estimate hydraulic parameters from SP data and these compare well to those obtained from drawdown data. For example, a hydraulic conductivity of 3.6 × 10−4 m/s is obtained from SP data compared to 3.4 × 10−4 m/s from drawdown data.

Force and flux relations for flows of ionic solutions between parallel plates with porous and charged layers

We derive coefficients of the electrokinetic coupling matrix (χ(11), χ(12), and χ(21)) for the flow of an ionic solution through a parallel-plate geometry having porous and charged layers grafted onto a solid surface with a known potential and demonstrate Onsager reciprocity for the cross terms (i.e., χ(12)=χ(21)). Our results enable the prediction of system outputs in the solid-porous-fluid system from parameters that are either known or may be measured and inferred. These electrokinetic coupling coefficients are in terms of the potential, ϕ, and fixed charge, ρ(f), only, removing dependence on field gradients and fluid velocity. Additionally, we present simplified expressions of these coupling coefficients in limiting regions of the parameter space. Away from these limits, we present numerical results demonstrating the facility of our functional form for facile numerical approximation and report the utility and accuracy of our analytical approximations.

Modeling Transient Streaming Potentials in Falling‐Head Permeameter Tests

We present transient streaming potential data collected during falling-head permeameter tests performed on samples of two sands with different physical and chemical properties. The objective of the work is to estimate hydraulic conductivity (K) and the electrokinetic coupling coefficient (Cl ) of the sand samples. A semi-empirical model based on the falling-head permeameter flow model and electrokinetic coupling is used to analyze the streaming potential data and to estimate K and Cl . The values of K estimated from head data are used to validate the streaming potential method. Estimates of K from streaming potential data closely match those obtained from the associated head data, with less than 10% deviation. The electrokinetic coupling coefficient was estimated from streaming potential vs. (1) time and (2) head data for both sands. The results indicate that, within limits of experimental error, the values of Cl estimated by the two methods are essentially the same. The results of this work demonstrate that a temporal record of the streaming potential response in falling-head permeameter tests can be used to estimate both K and Cl . They further indicate the potential for using transient streaming potential data as a proxy for hydraulic head in hydrogeology applications.

The Determination of Electrokinetic Coupling-Coefficient and Zeta Potential of Rock Samples by Electrokinetic Measurements

The electrokinetic effects are important in the understanding of electric properties in porous medium. In this study, the streaming potential and streaming current of saturated samples are measured at different concentrations, then three methods are applied to obtain the zeta-potential and electrokinetic coupling coefficient. The study shows that the results obtained from streaming potential and streaming current methods agree well with each other, but the results obtained from simplified streaming potential method become seriously inaccurate at low concentrations due to the influence of surface conductance. This experimental study also provides a reliable estimate of the surface conductivity and its contribution to zeta-potential at given concentrations.

Changes in Electrokinetic Coupling Coefficients of Granite under Triaxial Deformation

Electrokinetic phenomena are believed to be the most likely origin of electromagnetic signals preceding or accompanying earthquakes. The intensity of the source current due to the electrokinetic phenomena is determined by the fluid flux and the electrokinetic coupling coefficient called streaming current coefficient; therefore, how the coefficient changes before rupture is essential. Here, we show how the electrokinetic coefficients change during the rock deformation experiment up to failure. The streaming current coefficient did not increase before failure, but continued to decrease up to failure, which is explained in terms of the elastic closure of capillary. On the other hand, the streaming potential coefficient, which is the product of the streaming current coefficient and bulk resistivity of the rock, increased at the onset of dilatancy. It may be due to change in bulk resistivity. Our result indicates that the zeta potential of the newly created surface does not change so much from that of the preexisting fluid rock interface.

Estimation of hydraulic conductivity and water table map in a large‐scale laboratory model by means of the self‐potential method

The goal of this paper is to estimate the position of the water table and hydraulic conductivity of a homogeneous porous medium by means of the self‐potential method. The hydrogeophysical experiments were carried out at the Hydrogeosite Laboratory of the Istituto di Metodologie per l'Analisi Ambientale, Consiglio Nazionale delle Ricerche (Marsico Nuovo, Italy); the laboratory is a large‐scale model sized 10 × 7 × 3 m3that is filled with a homogeneous medium made up of quartz‐rich sand with a medium‐high hydraulic conductivity in the order of 10−5m s−1. Self‐potential signals generated by the groundwater flow, during a pumping test, were measured on the ground surface, on both the pumping and the recovery phases. A novel methodology to estimate the hydraulic conductivity from self‐potential measurements is proposed. Hydraulic conductivity very close to that calculated from hydraulic data, by means of Neuman‐type curves, has been obtained by solving the electrical flow equation through a linear least squares method. Moreover, a kriging with external drift geostatistical methodology has been proposed to estimate the hydraulic head distribution. The advantages given by this geostatistical method are that (1) hydraulic head distribution can be estimated without any previous electrokinetic coupling coefficient calculation and (2) the method is valid for either linear or nonlinear relationships between self‐potential and hydraulic head gradients. An original finding of this work is that the relationship between self‐potential signals and drawdown, around a pumping well, is not always linear: linearity applies only when the groundwater velocity is low, but high nonlinearity occurs when hydraulic head gradient rises up. Kriging with the external drift method could be used for the inversion of the hydraulic conductivity distribution, in a real heterogeneous aquifer, by means of an appropriate conditioning technique.

Numerical Simulation of Shear-Horizontal-Wave-Induced Electromagnetic Field in Borehole Surrounded by Porous Formation

Seismoelectric field excited by purely torsional loading applied directly to the borehole wall is considered. A brief formulation and some computed waveforms show the advantage of using shear-horizontal (SH) transverse-electric (TE) seismoelectric waves logging to measure shear velocity in a fluid-saturated porous formation. By assuming that the acoustic field is not influenced by its induced electromagnetic field due to seismoelectric effect, the coupling governing equations for electromagnetic field are reduced to Maxwell equations with a propagation current source. It is shown that this simplification is valid and the borehole seismoelectric conversion efficient is mainly dependent on the electrokinetic coupling coefficient. The receivers to detect the conversion electromagnetic field and to obtain shear velocity can be set in the borehole fluid in the SH-TE seismoelectric wave log.

Tensorial Electrokinetics in Articular Cartilage

Electrokinetic phenomena contribute to biomechanical functions of articular cartilage and underlie promising methods for early detection of osteoarthritic lesions. Although some transport properties, such as hydraulic permeability, are known to become anisotropic with compression, the direction-dependence of cartilage electrokinetic properties remains unknown. Electroosmosis experiments were therefore performed on adult bovine articular cartilage samples, whereby fluid flows were driven by electric currents in directions parallel and perpendicular to the articular surface of statically compressed explants. Magnitudes of electrokinetic coefficients decreased slightly with compression (from ∼−7.5 μL/As in the range of 0–20% compression to −6.0 μL/As in the 35–50% range) consistent with predictions of microstructure-based models of cartilage material properties. However, no significant dependence on direction of the electrokinetic coupling coefficient was detected, even for conditions where the hydraulic permeability tensor is known to be anisotropic. This contrast may also be interpreted using microstructure-based models, and provides insights into structure-function relationships in cartilage extracellular matrix and physical mediators of cell responses to tissue compression. Findings support the use of relatively simple isotropic modeling approaches for electrokinetic phenomena in cartilage and related materials, and indicate that measurement of electrokinetic properties may provide particularly robust means for clinical evaluation of cartilage matrix integrity.

Detection of advected concentration and pH fronts from self‐potential measurements

In this paper, we report on a series of experiments aimed at testing the possibility of detecting concentration or pH fronts advected through a well‐controlled, laboratory‐scale, artificial aquifer system, using self‐potential monitoring. A rectangular Plexiglas tank was filled up with water‐saturated sand, inside of which an array of unpolarizable electrodes was installed. After a nearly uniform, steady state flow was established by tilting the tank and controlling the water level at both ends, we abruptly changed the salt concentration or pH of the upstream fluid. During the subsequent motion of the concentration or pH front thus generated, the electrical potential differences between each electrode and a reference were recorded. We observed systematic, sharp variations successively occurring at increasing distances in the flow direction. These signals precisely corresponded to the calculated arrival times of the front at the various electrodes. Additional experiments were performed, in which the lateral motion of a transverse concentration or pH front was monitored. In the case of a NaCl front, the self‐potential signal can be modeled as the sum of two terms, (1) a junction potential term produced by the difference in ionic mobility of Na+ and Cl− and (2) an electrokinetic term corresponding to the variations of the electrokinetic coupling coefficient caused by changes in concentration. In the case of a pH front, only the electrokinetic term appears to be present.