Modeling electrokinetic transport and biogeochemical reactions in porous media: a multidimensional Nernst-Planck-Poisson approach with PHREEQC coupling

Electrokinetic techniques (EK) have been proposed and applied in different fields of science and engineering to enhance solute transport and species mobility in subsurface porous media. Modeling of EK requires a comprehensive approach allowing the description of the complex interplay between physical, chemical and biogeochemical processes occurring in EK applications. We propose a multidimensional modeling approach that allows the integrated description of fluid flow, solute transport (including electromigration and electroosmosis), Coulombic interactions between transported species, and a wide range of kinetic and equilibrium reactions. The proposed modeling tool, NP-Phreeqc-EK, is a coupling between COMSOL Multiphysics, which is used to solve fluid flow and solute transport in saturated porous media based on a Nernst-Planck-Poisson formulation, and PhreeqcRM, used to solve geochemical reactions. We illustrate the capabilities of NP-Phreeqc-EK with selected benchmarks in domains with different dimensions (1D, 2D and 3D). The results of the model are successfully compared with analytical solutions, numerical simulations with other software, and data from previously published EK-experiments. The outcomes of this study show the flexibility of the approach in simulating electrokinetic reactive transport processes in saturated porous media and highlight the importance of Coulombic interactions in EK applications. Such electrostatic interactions can strongly impact the performance of EK techniques since they affect the displacement velocities of charged species and can limit the maximum concentration of amendments that can be delivered through electromigration.