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A 1-D modelling of streaming potential dependence on water content during drainage experiment in sand

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 DV / DP 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. Key words: Electrical properties; Electromagnetic theory; Hydrogeophysics; Hydrology; Permeability and porosity; electrokinetic; streaming potential; self-potential; water content; water saturation; unsaturated condition; finite element modeling