Streaming Potential Coupling Coefficient Research Articles

Electrokinetic properties of NaCl solution via molecular dynamics simulations with scaled-charge electrolytes.

Scaling ionic charges has become an alternative to polarizable force fields for representing indirect charge transfer effects in molecular simulations. In our work, we apply molecular dynamics simulations to investigate the properties of NaCl aqueous solutions in homogeneous and confined media. We compare classical integer- and scaled-charge force fields for the ions. In the bulk, we validate the force fields by computing equilibrium and transport properties and comparing them with experimental data. Integer-charge ions overestimate dielectric saturation and ionic association. Both force fields present an excess in ion-ion correlation, which leads to a deviation in the ionic conductivity at higher ionic strengths. Negatively charged quartz is used to simulate the confinement effect. Electrostatic interactions dominate counter-ion adsorption. Full-charge ions have stronger and more defined adsorption planes. We obtain the electroosmotic mobility of the solution by combining the shear plane location from non-equilibrium simulations with the ionic distribution from equilibrium simulations. From the Helmholtz-Smoluchowski equation, the zeta potential and the streaming potential coupling coefficient are computed. From an atomic-scale perspective, our molecular dynamics simulations corroborate the hypothesis of maximum packing of the Stern layer, which results in a stable and non-zero zeta potential at high salinity. The scaled-charge model representation of both properties is in excellent qualitative and quantitative agreement with experimental data. With our work, we demonstrate how useful and precise simple scaled-charge models for electrolytes can be to represent complex systems, such as the electrical double layer.

Streaming Potential in Gas Phase Discrete Unsaturated Pore

The seismoelectric effect of porous media is the main basis for seismoelectric logging. At present, most of the studies on the seismoelectric effect in unsaturated porous media adopt the model of pores with continuous distribution of gas and liquid. There is a lack of theoretical research on the micro mechanism of the seismoelectric effect of unsaturated porous media with discrete gas phase, and the existing studies do not consider the effect of the electric double layer at the gas–liquid interface on the seismoelectric effect. Based on the capillary model, this work adopted the gas phase discrete model, combined the electric double layer theory and the seepage principle, considered the effect of electric double layer at the pore wall and the gas–liquid interface, and studied the micro principle of the seismoelectric effect of unsaturated porous media. Firstly, we studied the variation of gas–water two-phase flow pattern with saturation in unsaturated pores, then proposed the equivalent principle of series circuits, deduced the effective streaming current and conductance of a pore containing multiple bubbles, and then deduced the streaming potential coupling coefficient in the unsaturated pores. We also studied the effect of pore parameters such as saturation, pore size, bubble spacing, pore fluid viscosity, and salinity on the streaming potential coupling coefficient. The results show that the streaming potential coupling coefficient first increases and then decreases with the decrease in saturation, which is the same as the trend measured in Allègre’s experiment, and provide a theoretical explanation for the non-monotonic change in the coupling coefficient with saturation in unsaturated porous media.

A unified model for the permeability, electrical conductivity and streaming potential coupling coefficient in variably saturated fractured media

ABSTRACTWe present a new unified model for the permeability, electrical conductivity and streaming potential coupling coefficient in variably saturated fractured media. For those, we conceptualize the fractured medium as a partially saturated bundle of parallel capillary slits with varying sizes. We assume that the fracture size distribution of the corresponding medium follows a fractal scaling law, which allows us to establish a pressure head‐saturation relationship based on the Laplace equation. We first describe the flow rate, the conduction current and the electrokinetic streaming current within a single fracture. Then, we upscale these properties at the scale of an equivalent fractured media partially saturated in order to obtain the relative permeability, the electrical conductivity and the streaming potential coupling coefficient. The newly proposed model explicitly depends on pore water chemistry, interface properties, microstructural parameters of fractured media and water saturation. Model predictions are in good agreement with both experimental and simulated data and with another model from the literature. The results of this work constitute a useful framework to estimate hydraulic properties and monitor water flow in fractured media.

Application of critical path analysis to streaming potential coupling coefficient in porous media

Streaming potential is a passive hydrogeophysical method that can be used to monitor water flow in porous media. However, a quantitative use of this method requires a good understanding of the streaming potential generation in water saturated porous media. In this work, we used the Critical Path Analysis (CPA) method to propose a new model to estimate the streaming potential coupling coefficient (SPCC) in porous media. By comparing the proposed model with 109 experimental data points for both unconsolidated samples such as uniform glass bead and sand packs and consolidated samples such as sandstones, carbonates and with 36 simulated data points, we demonstrated that the CPA is applicable to model the SPCC for porous media with both narrow and broad pore size distributions. Additionally, from the obtained result for the uniform grain packings, we found the rc–d relationship between the critical pore radius rc and grain diameter d that was validated by using 70 experimental data points available in literature. The obtained rc–d relationship may be helpful for applications of CPA-based models for uniform grain packings. We believe that the CPA-based model is an useful alternative approach for modeling the streaming potential coupling coefficient in porous media along with two other models available in literature.

Understanding the Influence of Rock Content on Streaming Potential Phenomenon of Soil-Rock Mixture: An Experimental Study.

To applicate streaming potential phenomenon to study the seepage feature in the soil–rock mixture (SRM), research on the variation in the streaming potential phenomenon of SRM is the precondition. This paper deals, in assistance with the streaming potential test apparatus, with the streaming potential effect response of SRM subjected to different rock contents. The test results show that when the rock content increases from 10% to 30%, the streaming potential coupling coefficient increases with the increases in rock content at 85% compactness and 0.01 mol L−1 salinity. When the rock content is more than 30%, the streaming potential coupling coefficient decreases with the increases in rock content. As the rock content increases, the permeability coefficient has a negative correlation with the streaming potential coupling coefficient. The streaming potential increases first and then goes down with the increases in rock content, and the streaming potential decreases significantly when the rock content exceeds 50%. The findings indicate that the rock content is the key structural factor that restricts the streaming potential phenomenon of the SRM.

Dynamic streaming potential coupling coefficient in porous media with different pore size distributions

SUMMARY Seismoelectric signals are generated by electrokinetic coupling from seismic wave propagation in fluid-filled porous media. This process is directly related to the existence of an electrical double layer at the interface between the pore fluid and minerals composing the pore walls. The seismoelectric method attracts the interest of researchers in different areas, from oil and gas reservoir characterization to hydrogeophysics, due to the sensitivity of the seismoelectric signals to medium and fluid properties. In this work, we propose a physically based model for the dynamic streaming potential coupling coefficient (SPCC) by conceptualizing a porous medium as a bundle of tortuous capillaries characterized by presenting different pore size distributions (PSD). The results show that the dynamic streaming potential coupling coefficient is a complex function depending on the properties of pore fluid, mineral–pore fluid interfaces, microstructural parameters of porous media and frequency. Parameters influencing the dynamic SPCC are investigated and explained. In particular, we show that the PSD affects the transition frequency as well as the shape of the SPCC response as a function of frequency. The proposed model is then compared with published data and previous models. It is found that the approach using the lognormal distribution is in very good agreement with experimental data as well as with previous models. Conversely, the approach that uses the fractal distribution provides a good match with published data for sandstone samples but not for sand samples. This result implies that the fractal PSD may not be pertinent for the considered sand samples, which exhibit a relatively narrow distribution of pore sizes. Our proposed approach can work for any PSD, for example, including complex ones such as double porosity or inferred from direct measurements. This makes the proposed models more versatile than models available in literature.

Coupled inversion of hydraulic and self‐potential data from transient outflow experiments to estimate soil petrophysical properties

AbstractHydraulicproperties of soils could play an important role in affecting the partitioning of precipitation in the critical zone. In addition to traditional approaches, in the last two decades, many geophysical methods have been used to aid the hydrologic characterization and measurement of geological materials. In particular, the self‐potential (SP) method shows great potential in these hydrogeophysical applications. The objective of this study is to evaluate whether the addition of SP data can improve the estimation of hydraulic properties of soils in an outflow experiment. A stochastic, coupled hydrogeophysical inversion was developed, in which the governing equations were solved using the finite volume method and the parameter estimation was conducted using a Bayesian approach associated with the Markov chain Monte Carlo technique. The results show that the addition of SP data in the inversion could reduce the uncertainty related to the estimated hydraulic parameters of soils and the length of the associated 95% confidence interval can be shortened by ∼1/3. It is also shown that the electrical properties of soils at saturated and unsaturated conditions may also be estimated from the outflow experiment when SP data are available. Compared with hydraulic parameters, the accuracy of the estimated electrical properties is slightly lower. Among them, the saturated streaming potential coupling coefficientCsathas the highest accuracy and lowest uncertainty sinceCsatdirectly influences the magnitude of SP signals. The accuracy of other electrical parameters is lower than that ofCsat(and hydraulic parameters), and the associated uncertainty can be one order of magnitude larger.

Experimental Study on the Streaming Potential Phenomenon Response to Compactness and Salinity in Soil–Rock Mixture

The study on the effect of material structure and solution properties on the streaming potential of the soil–rock mixture (SRM) will be beneficial for improving the reliability of the measurement results for self-potential monitoring in embankment dams. We design two experimental groups and investigate the changes of potential and pressure during seepage of SRM (slightly clay materials) with different compactness and different concentration. The effects of the compaction degree and solution concentration on the streaming potential coupling coefficient and streaming potential were analyzed. The test results demonstrate that when the clay content in soil matrix is slight, the potential has a linear relationship with the hydraulic head difference, and seepage obeys Darcy’s law. The surface conductivity is negligible at 0.01 M (1 M corresponds to a concentration of 58.4 g L−1) salinity, the compactness of the SRM decreases (the permeability coefficient increases), the apparent streaming potential coupling coefficient and pressure difference decrease is the reason streaming potential decreases. The permeability coefficient of the SRM is not affected by the change in salinity (0.0001–1 M) at 85% compactness, and its seepage characteristics are related to the mineral composition, morphology and the thickness of the bound water layer (electric double layer). This study lays a foundation for further research on the self-potential method to monitor the structure of embankment dams.

Predicting Electrokinetic Coupling and Electrical Conductivity in Fractured Media Using a Fractal Distribution of Tortuous Capillary Fractures

Electrokinetics methods have attracted increasing interest to characterize hydrogeological processes in geological media, especially in complex hydrosystems such as fractured formations. In this work, we conceptualize fractured media as a bunch of parallel capillary fractures following the fractal size distribution. This conceptualization permits to obtain analytical models for both the electrical conductivity and the electrokinetic coupling in water saturated fractured media. We explore two different approaches to express the electrokinetic coupling. First, we express the streaming potential coupling coefficient as a function of the zeta potential and then we obtain the effective charge density in terms of macroscopic hydraulic and electrokinetic parameters of porous media. We show that when the surface electrical conductivity is negligible, the proposed models reduces to the previously proposed one based on a bundle of cylindrical capillaries. This model opens up a wide range of applications to monitor the water flow in fractured media.

A Physically Based Model for the Streaming Potential Coupling Coefficient in Partially Saturated Porous Media

The electrokinetics methods have great potential to characterize hydrogeological processes in porous media, especially in complex partially saturated hydrosystems (e.g., the vadose zone). The dependence of the streaming coupling coefficient on water saturation remains highly debated in both theoretical and experimental works. In this work, we propose a physically based model for the streaming potential coupling coefficient in porous media during the flow of water and air under partially saturated conditions. The proposed model is linked to fluid electrical conductivity, water saturation, irreducible water saturation, and microstructural parameters of porous materials. In particular, the surface conductivity of porous media has been taken into account in the model. In addition, we also obtain an expression for the characteristic length scale at full saturation in this work. The proposed model is successfully validated using experimental data from literature. A relationship between the streaming potential coupling coefficient and the effective excess charge density is also obtained in this work and the result is the same as those proposed in literature using different approaches. The model proposes a simple and efficient way to model the streaming potential generation for partially saturated porous media and can be useful for hydrogeophysical studies in the critical zone.

Surface Probing with Streaming Potential: The Polymer Flooding Scenario

The first experimental evidence of polymer adsorption in natural carbonates obtained from streaming potential measurements is presented. The surface probing of the Estaillades core was realized in a highly saline environment with I ~ 3 M similar to formation water naturally found in some oil reservoirs, which are typical target for enhanced oil recovery (EOR) by Smart Water Injection Methods (SWIM) and Hybrid SWIM. A highly sensitive setup with an exceptional signal-to-noise ratio even at high salinity, allowing to discriminate voltage fluctuations below 0.1 mV, was used to probe the streaming potential coupling coefficient. The injection of partially hydrolyzed polyacrylamide Flopaam 3130S was followed by chase flooding with formation water for several pore volumes, to assure that any changes measured after the polymer flooding are due to the retained polymer. We show that the streaming potential coupling coefficient changes sign after polymer adsorption. This result not only is an unambiguous evidence for polymer adsorption but has implications on chemical EOR scenarios that need to consider wettability changes due to inversion of surface charge.

Frequency-Dependent Streaming Potential in a Porous Transducer-Based Angular Accelerometer.

This paper presents a transient model of streaming potential generated when fluid flows through a porous transducer, which is sintered by glass microspheres and embedded in the circular tube of a liquid circular angular accelerometer (LCAA). The streaming potential coupling coefficient (SPC) is used to characterize this proposed transient model by combining a capillary bundle model of a porous transducer with a modified Packard’s model. The modified Packard’s model is developed with the consideration of surface conductance. The frequency-dependent streaming potential is investigated to analyze the effect of structure parameters of porous media and the properties of the fluid, including particle size distribution, zeta potential, surface conductance, pH, and solution conductivity. The results show that the diameter of microspheres not only affects bandwidth and transient response, but also influences the low-frequency gain. In addition, the properties of the fluid can influence the low-frequency gain. Experiments are actualized to measure the steady-state value of permeability and SPC for seven types of porous transducers. Experimental results possess high consistency, which verify that the proposed model can be utilized to optimize the transient and steady-state performance of the system effectively.

Streaming Potential Coupling Coefficient and Transport Properties of Unsaturated Carbonate Rocks

Core Ideas Streaming potential coupling coefficient is dependent on saturation in carbonate rocks. Salinity influences the streaming potential coupling coefficient. Water relative permeability can be estimated from streaming potential measurements. Transport properties of carbonate rocks can be modeled using the van Genuchten approach. We measured the streaming potential coupling coefficient of natural saturated and unsaturated carbonate rocks. Saturation was achieved with NaCl brines with salinities ranging from 2 × 10−3 to 2.0 mol L−1. The magnitude of the coupling coefficient increased with decreasing salinity, similarly to the trend observed for sandstones. The permeability had a low impact on the values of the streaming potential coupling coefficient at high and low salinity. The zeta potential was calculated at full saturation using a modified version of the Helmholtz–Smoluchowski equation that accounts for surface electrical conductivity. Under atmospheric conditions, the magnitude of the zeta potential decreased with the increase in salinity. We also explored the relationships between the streaming potential coupling coefficient and water saturation in three partially saturated limestones using a steady‐state flow experiment. We found good agreement between the van Genuchten approach and experimental data, and fitted both the relative permeability and capillary pressure curves with the same value of the van Genuchten exponent mv. We validated the predictive water relative permeability model described by Revil in water‐wet rocks when the second fluid phase is non‐polar.

Seismoelectric coupling in unsaturated porous media: theory, petrophysics, and saturation front localization using an electroacoustic approach

The seismoelectric method is based on the interpretation of the electrical field associated with the conversion of mechanical to electromagnetic energy during the propagation of seismic waves in heterogeneous porous media. We propose an extension of a poroacoustic model that takes into account fluid flow and the effect of saturation. This model is coupled with an electrokinetic model accounting for the effect of saturation and in agreement with available experimental data in sands and carbonate rocks. We also developed new scaling laws for the permeability, the streaming potential coupling coefficient and the capillary entry pressure of porous media. The theory is developed for frequencies much below the critical frequency at which inertial effects starts to dominate in the Navier–Stokes equation (>10 kHz). The equations used to compute the propagation of the P waves and the seismoelectric effect in unsaturated condition are solved with finite elements using triangular meshing. We demonstrate the usefulness of a recently developed technique, seismoelectric beamforming, to localize saturation fronts by focusing seismic waves and looking at the resulting seismoelectric conversions. This method is applied to a cross-hole problem showing how a saturation front characterized by a drop in the electrical conductivity and compressibility is responsible for seismoelectric conversions. These conversions can be used, in turn, to determine the position of the front over time.

Saline pulse test monitoring with the self‐potential method to nonintrusively determine the velocity of the pore water in leaking areas of earth dams and embankments

A method is proposed to localize preferential fluid flow pathways in porous media on the basis of time‐lapse self‐potential measurements associated with salt tracer injection upstream. This method is first tested using laboratory data. A network of nonpolarizing electrodes located is connected to a highly sensitive voltmeter used to record the resulting electrical field fluctuations occurring over time at the surface of the tank. The transport of the conductive salt plume through the permeable porous materials changes the localized streaming potential coupling coefficient associated with the advective drag of the excess charge of the pore water and is also responsible for a diffusion current associated with the salinity gradient. Monitoring of the electrical potential distribution at the ground surface can be used to localize the pulse of saline water over time and to determine its velocity. This method applies in real time and can be used to track highly localized flow pathways characterized by high permeability. Our sandbox experiment demonstrates the applicability of this new method under well‐controlled conditions with a coarse‐sand channel embedded between fine‐sand banks. A finite element model allows us to reproduce the time‐lapse electrical potential distribution over the channel, but some discrepancies were observed on the banks. Finally, we performed a numerical simulation for a synthetic case study inspired by a recently published field case study. A Markov chain Monte Carlo sampler is used to determine the permeability and the porosity of the preferential fluid flow pathway of this synthetic case study.

Constitutive equations for coupled flows in clay materials

We first upscale the local transport (Stokes and Nernst‐Planck) equations to the scale of a single capillary saturated by a binary 1:1 electrolyte. These equations are then upscaled to the scale of a network of tortuous capillaries embedded in a homogeneous and continuous mineral matrix, including the influence of the distribution of pore sizes but excluding the effect of connectivity between the pores. One of the features of our theory is to account for transport along the mineral surface in the so‐called Stern layer because of recent evidence that this mechanism is effective in describing frequency‐dependent electrical conductivity. Real clay materials are, however, not described by a set of capillaries, so we have to modify the model to include the effect of transversal dispersivity, for example. We found no evidence for transport in the Stern layer because of the discontinuity of the solid phase at the scale of a representative elementary volume in clay materials. The effect of the diffuse layer is accounted for through the use of a Donnan equilibrium approach to determine the effective concentrations of the ions in the pore space, which are different from the ionic concentrations of an ionic reservoir in local equilibrium with the porous material. We found that the diffuse layer controls various transport properties, including, for example, the DC electrical conductivity, the osmotic efficiency coefficient, the streaming potential coupling coefficient, and the macroscopic Hittorf numbers. Comparison to a large data set of experimental data, mainly on clay materials, confirms the validity of the derived relationships used to describe the material properties entering into the constitutive equations.

Streaming potential coupling coefficient of quartz glass bead packs: Dependence on grain diameter, pore size, and pore throat radius

The Helmholtz-Smoluchowski (HS) equation is commonly used to relate the streaming potential coupling coefficient of rocks to their zeta potential, pore fluid dielectric permittivity, conductivity, and viscosity despite it being known for almost [Formula: see text] that it does not work well for porous media. One of the problems is that the HS equation contains no implicit dependence on grain size, pore size, or pore throat size. Another has been the lack of high-quality data relating the streaming potential coupling coefficient to rock microstructural parameters. In this, predominantly experimental work, we have measured the streaming potential coupling coefficient for 12 sizes of quartz glass beads and two fluid salinities. A comparison of the new data and the existing data with the conventional HS equation and Revil’s grain size-dependent HS model shows the grain size-dependent model to be far superior in describing the data. Recognizing their utility in reservoir characterization, we have developed new equations that describe how the streaming potential coupling coefficient varies with pore diameter and pore throat diameter. We have compared experimental determinations as a function of pore throat diameter with these new relationships and found them to work very well if the ratio of the mean pore diameter to the pore throat diameter is 1.662, which is valid for random arrangement of monodisperse spheres. The zeta potential has also been calculated from the grain size-dependent HS equations and are found to be approximately constant and in agreement with the theoretically predicted values. The equations presented in this paper allow the streaming potential coupling coefficient of a reservoir rock to be calculated as a function of grain size, pore size, and pore throat size.

Transport properties of the Callovo‐Oxfordian clay rock under partially saturated conditions

A series of experiments were performed to characterize the permeability, the specific storage, the capillary pressure, the streaming potential coupling coefficient, and the electrical conductivity of a very low permeability Callovo‐Oxfordian clay rock at different water saturations. The Callovo‐Oxfordian formation is presently investigated as a potential host to store nuclear wastes because of its very low permeability (typically 10 nd at saturation) and high specific surface area. We first present the constitutive transport equations including an electrokinetic cross‐coupling term in the generalized Darcy and Ohm constitutive equations. Then we present new experimental results using measurements of transient weight losses of samples submitted to a change in the relative humidity imposed by an automated humidity system in a hermetic chamber. These experiments are interpreted with a 1‐D analytical model of the coupled hydromechanical and transport equations. The hydromechanical transport properties (relative permeability and specific storage) of this clay rock are investigated in the relative saturation range from 0.23 to 0.70. We demonstrate that below 30% in relative humidity, the flux of the vapor phase with respect to the flux of the liquid water phase cannot be neglected. The relative apparent permeability can be described by a simple power law relationship with the saturation. In addition, we measure the electrical conductivity and the streaming potential coupling coefficient at various saturations. The electrical conductivity is described by a model accounting for electrical double‐layer contributions to surface conductivity. The measurement of the streaming potential coupling coefficient agrees with a power law model for the coupling coefficient versus the relative water saturation. A relationship between the exponent used to characterize the relative permeability and the second Archie's exponent used to describe the dependence of the electrical conductivity of the material with respect to the saturation is discussed.

Diffusion of ionic tracers in the Callovo-Oxfordian clay-rock using the Donnan equilibrium model and the formation factor

The transient diffusion of cationic and anionic tracers through clay-rocks is usually modeled with parameters like porosity, tortuosity (and/or constrictivity), sorption coefficients, and anionic exclusion. Recently, a new pore scale model has been developed by Revil and Linde [Revil A. and Linde N. (2006) Chemico-electromechanical coupling in microporous media. J. Colloid Interface Sci. 302, 682–694]. This model is based on a volume-averaging approach of the Nernst–Planck equation. The influence of the electrical diffuse layer is accounted for by a generalized Donnan equilibrium model through the whole connected pore space that is valid for a multicomponent electrolyte. This new model can be used to determine the composition of the pore water of the Callovo-Oxfordian clay-rock, the osmotic efficiency of bentonite as a function of salinity, the osmotic pressure, and the streaming potential coupling coefficient of clay-rocks. This pore scale model is used here to model the transient diffusion of ionic tracers ( 22Na +, 36Cl −, and 35 SO 4 2 - ) through the Callovo-Oxfordian clay-rock. Speciation of SO 4 2 - shows that ∼1/3 of the SO 4 is tied-up in different complexes. Some of these complexes are neutral and are therefore only influence by the tortuosity of the pore space. Using experimental data from the literature, we show that all the parameters required to model the flux of ionic tracers (especially the mean electrical potential of the pore space and the formation factor) are in agreement with independent evaluations of these parameters using the osmotic pressure determined from in situ pressure measurements and HTO diffusion experiments.

Hysteresis of the self-potential response associated with harmonic pumping tests

Harmonic pumping tests performed in an unconfined aquifer are responsible for a non-linear and phase shifted behavior of the self-potential response recorded at the ground surface with respect to the change in the pressure heads of the aquifer. The observed non-linearity of the transfer function can be reproduced with a petrophysical model in which the permeability, the capillary pressure curve, and the streaming potential coupling coefficient are modelled inside a unified framework approach based on the van Genuchten parametrization including a hysteretic behaviour with the water saturation. The field equations for the hydraulic heads and the self-potential signals are solved with a finite-element code, which is used to compute the time variation of the self-potential variations over time for two numerical experiments accounting or not for hysteresis. Only the model with hysteresis can reproduce the field observations.