Lattice Boltzmann modelling of streaming potentials: Variations with salinity in monophasic conditions

Abstract

The streaming potential phenomenon is produced by the flow of an electrolyte in a porous medium and is used for geophysical prospecting. It is quantified through an electrokinetic (EK) coefficient. The dependence of the EK coefficient on the conductivity of the electrolyte is described by the Helmholtz-Smoluchowski (HS) equation. This equation provides successful forecasts of the EK coefficient in the standard range of concentration. However, experimental measurements show deviations to this equation at extreme low and extreme high salinities. The aim of this study is to model the EK coefficient using Lattice Boltzmann simulations in a 2-D capillary channel, with a view to understanding these deviations. The effect of the constitutive parameters of the HS equation such as the permittivity and the viscosity is discussed. The validity of the HS equation using strong ζ potentials is assessed. Finally, a model of bulk fluid conductivity is derived. This model allows to take into account the change of local ionic distribution in the vicinity of the mineral. It appears to have a significant impact on the derivation of ζ potentials at low salinities and in the presence of polyvalent counterions.