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
Good constraints on hydrogeological properties are an important first step in any quantitative model of groundwater flow. Field estimation of permeability is difficult as it varies over orders of magnitude in natural systems and is scale-dependent. Here we directly compare permeabilities inferred from tidal responses with conventional large-scale, long-term pumping tests at the same site. Tidally induced water pressure changes recorded in wells are used to infer permeability at ten locations in a densely fractured sandstone unit. Each location is either an open-hole well or a port in a multilevel monitoring well. Tidal response is compared at each location to the results of two conventional, long-term and large scale pumping tests performed at the same site. We obtained consistent values between the methods for a range of site-specific permeabilities varying from 10 215 m 2 to 10 213 m 2 for both open wells with large open intervals and multilevel monitoring well. We conclude that the tidal analysis is able to capture passive and accurate estimates of permeability.
SUMMARY The understanding of electrokinetics for unsaturated conditions is crucial for numerous of geophysical data interpretation. Nevertheless, the behaviour of the streaming potential coefficient C as a function of the water saturation Sw is still discussed. We propose here to model both the Richards’ equation for hydrodynamics and the Poisson’s equation for electrical potential for unsaturated conditions using 1‐D finite element method. The equations are first presented and the numerical scheme is then detailed for the Poisson’s equation. Then, computed streaming potentials (SPs) are compared to recently published SP measurements carried out during drainage experiment in a sand column. We show that the apparent measurement of ΔV/ΔP for the dipoles can provide the SP coefficient in these conditions. Two tests have been performed using existing models for the SP coefficient and a third one using a new relation. The results show that existing models of unsaturated SP coefficients C(Sw) provide poor results in terms of SP magnitude and behaviour. We demonstrate that the unsaturated SP coefficient can be until one order of magnitude larger than Csat, its value at saturation. We finally prove that the SP coefficient follows a non‐monotonous behaviour with respect to water saturation.
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