Nernst‐Planck‐based Description of Transport, Coulombic Interactions, and Geochemical Reactions in Porous Media: Modeling Approach and Benchmark Experiments

• Published in: Water resources research Vol. 54; no. 4; pp. 3176 - 3195
• Main Authors: Rolle, Massimo, Sprocati, Riccardo, Masi, Matteo, Jin, Biao, Muniruzzaman, Muhammad
• Format: Journal Article
• Language: English
• Published: Washington John Wiley & Sons, Inc 01-04-2018
• Subjects: Activity coefficients; Advection; Benchmarks; Computer simulation; COMSOL‐PHREEQC coupling; Coupling; Dispersion; Dye dispersion; Electromigration; electrostatic interactions; Electrostatic properties; flow‐through experiments; Fluxes; Geochemistry; Interactions; Ions; Mass transfer; Mathematical models; Modelling; multicomponent diffusion; Nernst‐Planck equations; Numerical simulations; Pore water; Porous media; reactive transport modeling; Thermodynamic activity; Transport
• ISSN: 0043-1397; 1944-7973
• DOI: 10.1002/2017WR022344

Transport of multicomponent electrolyte solutions in saturated porous media is affected by the electrostatic interactions between charged species. Such Coulombic interactions couple the displacement of the different ions in the pore water and remarkably impact mass transfer not only under diffusion, but also under advection‐dominated flow regimes. To accurately describe charge effects in flow‐through systems, we propose a multidimensional modeling approach based on the Nernst‐Planck formulation of diffusive/dispersive fluxes. The approach is implemented with a COMSOL‐PhreeqcRM coupling allowing us to solve multicomponent ionic conservative and reactive transport problems, in domains with different dimensionality (1‐D, 2‐D, and 3‐D), and in homogeneous and heterogeneous media. The Nernst‐Planck‐based coupling has been benchmarked with analytical solutions, numerical simulations with another code, and high‐resolution experimental data sets. The latter include flow‐through experiments that have been carried out in this study to explore the effects of electrostatic interactions in fully three‐dimensional setups. The results of the simulations show excellent agreement for all the benchmarks problems, which were selected to illustrate the capabilities and the distinct features of the Nernst‐Planck‐based reactive transport code. The outcomes of this study illustrate the importance of Coulombic interactions during conservative and reactive transport of charged species in porous media and allow the quantification and visualization of the specific contributions to the diffusive/dispersive Nernst‐Planck fluxes, including the Fickian component, the term arising from the activity coefficient gradients, and the contribution due to electromigration.
Key Points
Nernst‐Planck‐based approach to model multidimensional transport, charge interactions, and chemical reactions in flow‐through porous media
Computation and visualization of diffusive/dispersive, electromigration, and activity coefficients' gradient fluxes
Code validated with high‐resolution 2‐D experimental data and first fully 3‐D data set on multicomponent ionic transport