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

Abstract

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