  Among the different contributions generating self-potential, the streaming
potential is of particular interest in hydrogeology for its sensitivity to
water flow. Estimating water flux in porous media using streaming potential
data relies on our capacity to understand, model, and upscale the
electrokinetic coupling at the mineral-solution interface. Different approaches
have been proposed to predict streaming potential generation in porous media.
One of these approaches is the flux averaging which is based on determining the
excess charge which is effectively dragged in the medium by water flow. In this
study, we develop a physically-based analytical model to predict the effective
excess charge in saturated porous media using a flux-averaging approach in a
bundle of capillary tubes with a fractal pore-size distribution. The proposed
model allows the determination of the effective excess charge as a function of
pore water ionic concentration and hydrogeological parameters like porosity,
permeability and tortuosity. The new model has been successfully tested against
different set of experimental data from the literature. One of the main
findings of this study is the mechanistic explanation to the empirical
dependence between the effective excess charge and the permeability that has
been found by several researchers. The proposed model also highlights the link
to other lithological properties and it is able to reproduce the evolution of
effective excess charge with electrolyte concentrations.
