Controlled ion transport in the subsurface: A coupled advection–diffusion–electromigration system

Abstract

Ion transport within saturated porous media is an intricate process in which efficient ion delivery is desired in many engineering problems. However, controlling the behavior of ion transport proves challenging, as ion transport is influenced by a variety of driving mechanisms, which requires a systematic understanding. Herein, we study a coupled advection–diffusion–electromigration system for controlled ion transport within porous media using the scaling analysis. Using the Lattice–Boltzmann–Poisson method, we establish a transport regime classification based on an Advection Diffusion Index (ADI) and a novel Electrodiffusivity Index (EDI) for a two-dimensional (2D) microchannel model under various electric potentials, pressure gradients, and concentration conditions. The resulting transport regimes can be well controlled by changing the applied electric potential, the pressure field, and the injected ions concentration. Furthermore, we conduct numerical simulations in a synthetic 2D porous media and an x-ray microcomputed tomography sandstone image to validate the prevailing transport regime. The simulation results highlight that the defined transport regime observed in our simple micromodel domain is also observed in the synthetic two- and three-dimensional domains, but the boundary between each transport regime differs depending on the variation of the pore size within a given domain. Consequently, the proposed ADI and EDI emerge as dimensionless indicators for controlled ion transport. Overall, our proof-of-concept for ion transport control in porous media is demonstrated under advection–diffusion–electromigration transport, demonstrating the richness of transport regimes that can develop and provide future research directions for subsurface engineering applications.