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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. 

AbstractElectrokinetic in-situ recovery is an alternative to conventional mining, relying on the application of an electric potential to enhance the subsurface flow of ions. Understanding the pore-scale flow and ion transport under electric potential is essential for petrophysical properties estimation and flow behavior characterization. The governing physics of electrokinetic transport is electromigration and electroosmotic flow, which depend on the electric potential gradient, mineral occurrence, domain morphology (tortuosity and porosity, grain size and distribution, etc.), and electrolyte properties (local pH distribution and lixiviant type and concentration, etc.). Herein, mineral occurrence and its associated zeta potential are investigated for EK transport. The new Ek model which is designed to solve the EK flow in complex porous media in a highly parallelizable manner includes three coupled equations: (1) Poisson equation, (2) Nernst–Planck equation, and (3) Navier–Stokes equation. These equations were solved using the lattice Boltzmann method within X-ray computed microtomography images. The proposed model is validated against COMSOL multiphysics in a two-dimensional microchannel in terms of fluid flow behavior when the electrical double layer is both resolvable and unresolvable. A more complex chalcopyrite-silica system is then obtained by micro-CT scanning to evaluate the model performance. The effects of mineral occurrence, zeta potential, and electric potential on the three-dimensional chalcopyrite-silica system were evaluated. Although the positive zeta potential of chalcopyrite can induce a flow of ferric ion counter to the direction of electromigration, the net effect is dependent on the occurrence of chalcopyrite. However, the ion flux induced by electromigration was the dominant transport mechanism, whereas advection induced by electroosmosis made a lower contribution. Overall, a pore-scale EK model is proposed for direct simulation on pore-scale images. The proposed model can be coupled with other geochemical models for full physicochemical transport simulations. Meanwhile, electrokinetic transport shows promise as a human-controllable technique because the electromigration of ions and the applied electric potential can be easily controlled externally. Graphical abstract