[1] The understanding of the streaming potential in partial water saturation conditions in porous media is of great interest for the interpretation of spontaneous polarization observations. We built a device which allows us to quantify the streaming potential at various saturation conditions using a sand column of 1-m height and 8-cm diameter. This is the first time that such a quantification has been performed. Different gases such as argon, nitrogen, and carbon dioxide are injected into the sand to decrease its water saturation, and to make the fluid flow within the sand. The measured electrokinetic coupling coefficient in partial saturation is either constant or decreases by a factor $3 with decreasing water saturation from 100 to 40%, whereas the sand electrical resistivity is enhanced by a factor of $5.

The final version is available on www.blackwell-synergy.comInternational audienceThe electrokinetic potential results from the coupling between the water flow and the electrical current because of the presence of ions within water. The electrokinetic coupling is well described in fluid-saturated media, however its behaviour under unsaturated flow conditions is still discussed. We propose here an experimental approach to investigate streaming potential variations in sand at unsaturated conditions. We present for the first time continuous records of the electrokinetic coefficient as a function of water content. Two drainage experiments have been performed within a column filled with a clean sand. Streaming potential measurements are combined with water pressure and water content measurements every 10 centimeters along the column. In order to model hydrodymanics during the experiments, we solve Richards equation coupled with an inverse problem to estimate the hydraulic parameters of the constitutive relations between hydraulic conductivity, water pressure and water content. The electrokinetic coefficient $C$ shows a more complex behaviour for unsaturated conditions than it was previously reported and cannot be fitted by the existing models. The electrokinetic coefficient increases first when water saturation decreases from 100\% to about 65\% - 80\%, and then decreases as the water saturation decreases, whereas all previous works described a monotone decrease of the normalized electrokinetic coupling as water saturation decreases. We delimited two water saturation domains, and deduced two different empirical laws describing the evolution of the electrokinetic coupling for unsaturated conditions. Moreover we introduce the concept of the electrokinetic residual saturation $S_w^{r,ek}$, which allows us to propose a new model derived from the approach of the relative permeability used in hydrodynamics

The streaming potential, due to fluid circulation in rock, was measured on saturated sediments (Fontainebleau sandstones). The electrokinetic coupling coefficient, which is the ratio of the streaming potential and the excess pore pressure, is proportional to the fluid resistivity. Additionally, for a fluid conductivity of 10−3 S/m, the electrokinetic coupling coefficient varies from 10 to 6642 mV/0.1 MPa for sample permeability in the range of permeabilities from 0.15 × 10−15 to 1220 × 10−15 m2. The different values of the electrokinetic coupling coefficient have been explained by the effect of increasing surface conductivity which becomes nonnegligible compared to fluid conductivity for low permeability. When the sample is deformed under triaxial stress up to failure, the vertical permeability (along the principal stress) drops by about 0.20%/0.1 MPa when failure occurs. The typical variation of the electrokinetic coupling coefficient is a large increase beginning with the onset of the localization of the shear band at about 75% of the yield stress and stopping at the failure. This increase of the electrokinetic coupling coefficient is due to an increase of ζ potential in the shear zone when new surfaces are created and connected. Possible consequences of our results are given concerning the electrical fields which could appear during the preparation of an earthquake. It is shown that in some cases, self‐potential anomalies reported in the deformed zone preceding an earthquake occurrence could be due to an increase of the electrokinetic coupling coefficient from 75% of the yield stress to rupture in the vicinity of one of the electrodes. Any variation of fluid resistivity or permeability in the vicinity of one electrode could change the electrokinetic coupling coefficient, inducing a surface electrokinetic potential anomaly. In regard to the interpretation of the electrokinetic effect which occurs at large distance from the epicenter, a larger electrokinetic potential anomaly could be measured between electrodes situated along a vertical fluid flow, for instance, in a shallow borehole. An electrokinetic potential anomaly up to 30 mV, for a fluid conductivity of 0.01 S/m and a rock permeability of 10−12 m2, could be observed with a change of the underground water table level as slight as 50 cm (50 mbar). Moreover, if the permeability between the electrodes is increased by a factor of 8 × 103, the electrokinetic coupling coefficient could be enhanced by a factor up to 650.

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To better understand and interpret seismoelectric measurements acquired over vadose environments, both the existing theory and the wave propagation modelling programmes, available for saturated materials, should be extended to partial saturation conditions. We propose here an extension of Pride's equations aiming to take into account partially saturated materials, in the case of a water-air mixture. This new set of equations was incorporated into an existing seismoelectric wave propagation modelling code, originally designed for stratified saturated media. This extension concerns both the mechanical part, using a generalization of the Biot-Gassmann theory, and the electromagnetic part, for which dielectric permittivity and electrical conductivity were expressed against water saturation. The dynamic seismoelectric coupling was written as a function of the streaming potential coefficient, which depends on saturation, using four different relations derived from recent laboratory or theoretical studies. In a second part, this extended programme was used to synthesize the seismoelectric response for a layered medium consisting of a partially saturated sand overburden on top of a saturated sandstone half-space. Subsequent analysis of the modelled amplitudes suggests that the typically very weak interface response (IR) may be best recovered when the shallow layer exhibits low saturation. We also use our programme to compute the seismoelectric response of a capillary fringe between a vadose sand overburden and a saturated sand half-space. Our first modelling results suggest that the study of the seismoelectric IR may help to detect a sharp saturation contrast better than a smooth saturation transition. In our example, a saturation contrast of 50 per cent between a fully saturated sand half-space and a partially saturated shallow sand layer yields a stronger IR than a stepwise decrease in saturation.

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We describe in this paper the theoretical background for the electrokinetics in rocks and in porous media, to be included in the special issue “Electrokinetics in Earth Sciences” of International Journal of Geophysics. We describe the methodology used for self-potential (SP) and for seismoelectromagnetic measurements, for both field and laboratory experiments and for modelling. We give a large bibliography on the studies performed in hydrology to detect at distance the water flow, to deduce the thickness of the aquifer and to predict the hydraulic conductivity. The observation of SP has also been proposed to detect fractures in boreholes, to follow the hydraulic fracturing, and to predict the earthquakes. Moreover, we detail the studies on geothermal applications.