[1] Laboratory experiments are performed to understand the controlling parameters of the electrical field associated with the seepage of water through a porous material. We use seven glass bead packs with varying mean grain size in an effort to obtain a standard material for the investigation of these electrical potentials. The mean grain size of these samples is in the range 56-3000 mm. We use pure NaCl electrolytes with conductivity in the range 10 À4 to 10 À1 S m À1 at 25°C. The flow conditions cover viscous and inertial laminar flow conditions but not turbulent flow. In the relationship between the streaming potential coupling coefficient and the grain size, three distinct domains are defined by the values of two dimensionless numbers, the Dukhin and the Reynolds numbers. The Dukhin number represents the ratio between the surface conductivity of the grains (due to conduction in the electrical double layer coating the surface of the grains) and the pore water electrical conductivity. At high Dukhin numbers ()1) and low Reynolds numbers ((1), the magnitude of the streaming potential coupling coefficient decreases with the increase of the Dukhin number and depends on the mean grain diameter (and therefore permeability) of the medium. At low Dukhin and Reynolds numbers ((1), the streaming potential coupling coefficient becomes independent of the microstructure and is given by the well-known Helmholtz-Smoluchowski equation widely used in the literature. At high Reynolds numbers, the magnitude of the streaming potential coupling coefficient decreases with the increase of the Reynolds number in agreement with a new model developed in this paper. A numerical application is made illustrating the relation between the self-potential signal and the intensity of seepage through a leakage in an embankment.

Special Issue on Hydrogeophysics - Methods and ProcessesInternational audienceWe invert self-potential data in order to locate anomalous water flow pathways in dams and embankments and to estimate the seepage velocity. The inversion of the self-potential data is performed using the modified singular value decomposition for the inverse problem using a linear formulation of the forward problem. The kernel is solved numerically accounting for the topography of the system and the resistivity distribution, which is independently obtained through electrical resistance tomography. A prior constraint based on finite element modelling of ground water flow can also be used to provide a prior source current density model if needed. This self-potential tomography approach is first validated with a synthetic case study showing how the position of a preferential fluid flow pathway can be retrieved from self-potential and resistivity data and how the seepage velocity can be obtained inside one order of magnitude. This methodology is then applied to a test site corresponding to a portion of an embankment dam along the Rhône River in France. Two self-potential maps (with 1169 and 2076 measurements, respectively) and four resistivity tomograms are used to locate a leak. One self-potential profile and one resistivity profile are used together to perform the 2D inversion of the self-potential data to locate the anomalous leakage at depth and to estimate the flow rate. The depth at which the preferential fluid flow pathway is located, according to self-potential tomography, agrees with an independent geotechnical test using the Perméafor. This demonstrates the usefulness of this methodology to detect preferential water channels inside the body of a dam

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Abstract. The classical formulation of the coupled hydroelectrical flow in porous media is based on a linear formulation of two coupled constitutive equations for the electrical current density and the seepage velocity of the water phase and obeying Onsager's reciprocity. This formulation shows that the streaming current density is controlled by the gradient of the fluid pressure of the water phase and a streaming current coupling coefficient that depends on the so-called zeta potential. Recently a new formulation has been introduced in which the streaming current density is directly connected to the seepage velocity of the water phase and to the excess of electrical charge per unit pore volume in the porous material. The advantages of this formulation are numerous. First this new formulation is more intuitive not only in terms of establishing a constitutive equation for the generalized Ohm's law but also in specifying boundary conditions for the influence of the flow field upon the streaming potential. With the new formulation, the streaming potential coupling coefficient shows a decrease of its magnitude with permeability in agreement with published results. The new formulation has been extended in the inertial laminar flow regime and to unsaturated conditions with applications to the vadose zone. This formulation is suitable to model self-potential signals in the field. We investigate infiltration of water from an agricultural ditch, vertical infiltration of water into a sinkhole, and preferential horizontal flow of ground water in a paleochannel. For the three cases reported in the present study, a good match is obtained between finite element simulations performed and field observations. Thus, this formulation could be useful for the inverse mapping of the geometry of groundwater flow from self-potential field measurements.

Abstract. The classical formulation of the coupled hydroelectrical flow in porous media is based on a linear formulation of two coupled constitutive equations for the electrical current density and the seepage velocity of the water phase and obeying Onsager's reciprocity. This formulation shows that the streaming current density is controlled by the gradient of the fluid pressure of the water phase and a streaming current coupling coefficient that depends on the so-called zeta potential. Recently a new formulation has been introduced in which the streaming current density is directly connected to the seepage velocity of the water phase and to the excess of electrical charge per unit pore volume in the porous material. The advantages of this formulation are numerous. First this new formulation is more intuitive not only in terms of constitutive equation for the generalized Ohm's law but also in specifying boundary conditions for the influence of the flow field upon the streaming potential. With the new formulation, the streaming potential coupling coefficient shows a decrease of its magnitude with permeability in agreement with published results. The new formulation is also easily extendable to non-viscous laminar flow problems (high Reynolds number ground water flow in cracks for example) and to unsaturated conditions with applications to the vadose zone. We demonstrate here that this formulation is suitable to model self-potential signals in the field. We investigate infiltration of water from an agricultural ditch, vertical infiltration of water into a sinkhole, and preferential horizontal flow of ground water in a paleochannel. For the three cases reported in the present study, a good match is obtained between the finite element simulations performed with the finite element code Comsol Multiphysics 3.3 and field observations. Finally, this formulation seems also very promising for the inversion of the geometry of ground water flow from the monitoring of self-potential signals.