Two-phase Lattice Boltzmann modelling of streaming potentials: influence of the air–water interface on the electrokinetic coupling

Abstract

The streaming potential phenomenon is an electrokinetic effect that occurs in porous media. It is characterized by an electrokinetic (EK) coefficient. The aim of this paper is to simulate the EK coefficient in unsaturated conditions using the Lattice Boltzmann method in a 2-D capillary channel. The multiphase flow is simulated with the model of Shan & Chen. The Poisson–Boltzmann equation is solved by implementing the model of Chai & Shi. The streaming potential response shows a non-monotonous behaviour due to the combination of the increase of charge density and decrease of flow velocity with decreasing water saturation. Using a ζ potential of −20 mV at the air–water interface, an enhancement of a factor 5–30 of the EK coefficient, compared to the saturated state, can be observed due to the positive charge excess at this interface which is magnified by the fluid velocity away from the rock surface. This enhancement is correlated to the fractioning of the bubbles, and to the dynamic state of these bubbles, moving or entrapped in the crevices of the channel.