Streaming current generation in two‐phase flow conditions

Linde, Niklas; Jougnot, Damien; Revil, A.; Matthäi, Stephan; Arora, Tanvi; Renard, Didier; Doussan, Claude

doi:10.1029/2006gl028878

Cited by 124 publications

(278 citation statements)

References 19 publications

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“…(in units of C m -3 ) is defined as the excess of charge per unit pore volume at full water saturation [9,10,11]. We neglect the charge density that is associated with the interface between the wetting and the non-wetting phases, since it is small in comparison with the charge density associated with the pore water-solid interface [9].…”

Section: The Reference Statementioning

confidence: 99%

“…We neglect the charge density that is associated with the interface between the wetting and the non-wetting phases, since it is small in comparison with the charge density associated with the pore water-solid interface [9]. The charge density …”

Section: The Reference Statementioning

confidence: 99%

“…We assume that the surface charge density at the interface between water and the non-wetting phase is negligible (see [9]), and therefore 0 0 = n Q and 0 = n j .…”

Section: Ampère's Lawmentioning

confidence: 99%

“…The material properties of the material are taken to be relatively similar to the sand used for the experiment reported by [9]. The intrinsic permeability, k, is set to 8 × 10 -12 m 2 and the porosity, φ, is 0.34.…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…To the best of our knowledge, our model is the first rigorous attempt to derive the governing equations that describe the effect of water saturation upon streaming potential and electro-osmosis. A less rigorous derivation of the governing equation for streaming potentials in unsaturated media was recently presented by Linde et al [9] who also compared laboratory experiments from a primary drainage experiment of a saturated sand column to new theory. This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

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Electrokinetic coupling in unsaturated porous media

Revil

Linde

Cérepi

et al. 2007

Journal of Colloid and Interface Science

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216

337

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Abstract. We consider a charged porous material that is saturated by two fluid phases that are immiscible and continuous at the scale of a representative elementary volume. The wetting phase for the grains is water and the non-wetting phase is assumed to be an electrically insulating viscous fluid. We use a volume averaging approach to derive the linear constitutive equations for the electrical current density as well as and the seepage velocities of the wetting and non-wetting phases at the scale of a representative elementary volume. These macroscopic constitutive equations are obtained by volume-averaging Ampère's law together with the Nernst-Planck equation and the Stokes equations. The material properties entering the macroscopic constitutive equations are explicitly described as a function of the saturation of the water phase, the electrical formation factor, and parameters that describe the capillary pressure function, the relative permeability function, and the variation of electrical conductivity with saturation. New equations are derived for the streaming potential and electro-osmosis coupling coefficients. A primary drainage and imbibition experiment is simulated numerically to demonstrate that the relative streaming potential coupling coefficient depends not only on the water saturation, but also on the material properties of the sample as well as the saturation history. We also compare the predicted streaming potential coupling coefficients with experimental data from four dolomite core samples. Measurements on these samples include electrical conductivity, capillary pressure, the streaming potential coupling coefficient at various level of saturation, and the permeability at saturation of the rock samples. We found a very good agreement between these experimental data and the model predictions.

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Section: The Reference Statementioning

confidence: 99%

Section: The Reference Statementioning

confidence: 99%

“…We assume that the surface charge density at the interface between water and the non-wetting phase is negligible (see [9]), and therefore 0 0 = n Q and 0 = n j .…”

Section: Ampère's Lawmentioning

confidence: 99%

Section: Numerical Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Electrokinetic coupling in unsaturated porous media

Revil

Linde

Cérepi

et al. 2007

Journal of Colloid and Interface Science

Self Cite

216

337

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Hydraulic conductivity field characterization from the joint inversion of hydraulic heads and self‐potential data

Ahmed

Jardani

Revil

et al. 2014

Water Resources Research

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Pumping tests can be used to estimate the hydraulic conductivity field from the inversion of hydraulic head data taken intrusively in a set of piezometers. Nevertheless, the inverse problem is strongly underdetermined. We propose to add more information by adding self-potential data taken at the ground surface during pumping tests. These self-potential data correspond to perturbations of the electrical field caused directly by the flow of the groundwater. The coupling is electrokinetic in nature that is due to the drag of the excess of electrical charges existing in the pore water. These self-potential signals can be easily measured in field conditions with a set of the nonpolarizing electrodes installed at the ground surface. We used the adjoint-state method for the estimation of the hydraulic conductivity field from measurements of both hydraulic heads and self potential during pumping tests. In addition, we use a recently developed petrophysical formulation of the streaming potential problem using an effective charge density of the pore water derived directly from the hydraulic conductivity. The geostatistical inverse framework is applied to five synthetic case studies with different number of wells and electrodes and thickness of the confining unit. To evaluate the benefits of incorporating the self-potential data in the inverse problem, we compare the cases in which the data are combined or not. Incorporating the self-potential information improves the estimate of hydraulic conductivity field in the case where the number of piezometers is limited. However, the uncertainty of the characterization of the hydraulic conductivity from the inversion of the self-potential data is dependent on the quality of the distribution of the electrical conductivity used to solve the Poisson equation. Consequently, the approach discussed in this paper requires a precise estimate of the electrical conductivity distribution of the subsurface and requires therefore new strategies to be developed for the joint inversion of the hydraulic and electrical conductivity distributions.

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

Malama

2014

Water Resources Research

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A 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 3 10

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Streaming current generation in two‐phase flow conditions

Cited by 124 publications

References 19 publications

Electrokinetic coupling in unsaturated porous media

Electrokinetic coupling in unsaturated porous media

Hydraulic conductivity field characterization from the joint inversion of hydraulic heads and self‐potential data

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

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