Ionic Transport in Nano-Porous Clays with Consideration of Electrostatic Effects

Tournassat, Christophe; Steefel, Carl I.

doi:10.2138/rmg.2015.80.09

Cited by 55 publications

(69 citation statements)

References 127 publications

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“…A common assumption in groundwater applications is to neglect the electrostatic interactions between charged species in pore water and to describe solute displacement by Fickian diffusion. However, a number of contributions, mainly from the geochemistry literature, have focused on the importance of multicomponent ionic transport (Ben‐Yaakov, ; Boudreau et al, ; Gvirtzman & Gorelick, ; Lasaga, ; Steefel & Maher, ) and have shown the need of taking into account Coulombic interactions in practical applications in diffusion‐dominated low‐permeability matrices (Appelo & Wersin, ; Appelo et al, ; Alt‐Epping et al, ; Giambalvo et al, ; Liu, ; Liu et al, ; Tournassat & Appelo, ; Tournassat & Steefel, ). A few recent experimental studies (e.g., Muniruzzaman et al, ; Muniruzzaman & Rolle, ; Rolle et al, ) have shown the effects of electrostatic interactions between charged species during transport of strong electrolytes in porous media under advection‐dominated flow‐through conditions.…”

Section: Introductionmentioning

confidence: 99%

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

Rolle

Sprocati

Masi

et al. 2018

Water Resources Research

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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.

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Section: Introductionmentioning

confidence: 99%

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

Rolle

Sprocati

Masi

et al. 2018

Water Resources Research

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“…Tournassat and Steefel [12] reviewed the basics of the application of the Nernst-Planck equation applied to diffusive processes in the diffuse layer bordering charged surfaces in reactive transport codes. The fundamental hypothesis underlying such an application of the Nernst-Planck equation lies in the achievement of rapid equilibrium of the diffuse layer composition with the bulk water composition in a representative elementary volume (grid cell).…”

Section: Nernst-planck Equationmentioning

confidence: 99%

“…While their low permeability and high adsorption capacity are widely acknowledged, it is clear nonetheless that there is a need for an improved understanding of how the chemical and mineralogical properties of shales impact their macroscopic properties, especially transport [3][4][5][6][7]. It is at the pore scale that the chemical properties of clay minerals become important since their electrostatic properties can play a large role [8][9][10][11][12]. The negative electrostatic potential field at the clay mineral surfaces results in the presence of porosity domains where electroneutrality is not achieved in the aqueous solution: cations are attracted by the surfaces while anions are repulsed from them, resulting in the presence of a diffuse ion swarm, or diffuse layer, as opposed to the bulk porosity where electroneutrality prevails [13].…”

Section: Introductionmentioning

confidence: 99%

Modeling diffusion processes in the presence of a diffuse layer at charged mineral surfaces: a benchmark exercise

Tournassat

Steefel

2019

Comput Geosci

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The electrostatic properties of clay mineral surfaces play a significant role in their diffusion properties. The negative electrostatic potential field at clay mineral surfaces results in the presence of a diffuse layer that balances the mineral surface charge. The diffusion properties of the porosity fraction that is affected by this phenomenon are different from the diffusion properties of electroneutral bulk water. These properties have attracted growing interest from diverse communities in the past years, especially in the field of study of radioactive waste disposal. The influence of the diffuse layer can be described at the continuum scale by a set of equations that are formulated in terms of the Nernst-Planck equation. The number of codes that can handle the coupling between transport properties in clay affected by the presence of a diffuse layer in the porosity and chemical reactions is very limited, and no benchmark exercises have been published yet that make it possible to validate the numerical implementation of these equations in reactive transport codes. The present study proposes a set of benchmark exercises of increasing complexity that highlight caveats related to the finite difference (volume) treatment of the Nernst-Planck equation in the presence of a diffuse layer in heterogeneous systems. Once these problems are identified and solved, the codes PHREEQC, CrunchClay, and a new Fortran routine written for this study gave results in very good agreement for most of the benchmark exercises. When present, the differences in results were directly traceable to the differences in averaging methods at grid cell boundaries, and to the consideration or the omission of the activity gradient term in the Nernst-Planck equation.

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“…In addition to the diffuse layer, ions may also adsorb directly onto the Stern layer of the surface or to the interlayer (IL) space between individual TOT (tetrahedral‐octahedral‐tetrahedral) layers enabling ion‐exchange like processes (e.g., Appelo et al, ; Bourg et al, ; Glaus et al, ; Leroy et al, ; Leroy & Revil, ; Tertre et al, ). Mass flux of a charged solute in such clayey media is not just dependent on its own properties or concentration gradient, but it is a function of the physicochemical properties of clay, as well as the composition and charge of other dissolved species in the porewater solution (e.g., Alt‐Epping et al, ; Appelo & Wersin, ; Tournassat & Appelo, ; Tournassat & Steefel, ). Thus, a formulation based on multiple continua, incorporating the charge‐driven processes in the diffuse layer, interlayer, Stern layer and free water, is required to rigorously and accurately describe mass transport (e.g., Appelo et al, , ; Birgersson & Karnland, ; Jougnot et al, ; Steefel et al, ; Gimmi & Alt‐Epping, ).…”

Section: Introductionmentioning

confidence: 99%

“…Only a few modeling frameworks can simulate coupled anion and cation transport influenced by charge induced electrostatic interactions (Meeussen, ; Parkhurst & Appelo, ; Rasouli et al, ; Steefel et al, ). When considering clay systems in continuum‐scale reactive transport models, a multiporosity approach is typically adopted where the total pore space of a clay rock is assumed to be composed of (i) a charge‐free (or free, or bulk, or macro) porosity, (ii) a diffuse layer (or micro) porosity, and (iii) an interlayer porosity (e.g., Appelo et al, ; Tournassat & Steefel, ). The diffusive/dispersive fluxes in each of these porosities are described by the Nernst‐Planck equation, and the equilibrium between the free water and diffuse layer is calculated by Donnan equilibrium.…”

Section: Introductionmentioning

confidence: 99%

Multicomponent Ionic Transport Modeling in Physically and Electrostatically Heterogeneous Porous Media With PhreeqcRM Coupling for Geochemical Reactions

Muniruzzaman

Rolle

2019

Water Resources Research

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Low-permeability aquitards, such as clay layers and inclusions, are of utmost importance for contaminant transport in groundwater systems. Although most dissolved species, contaminants, and clay surfaces are charged, the role of electrostatic interactions in subsurface flow-through systems has not been extensively investigated. This study presents a two-dimensional multicomponent reactive transport investigation of diffusive/dispersive and electrostatic processes in homogeneous and heterogeneous clay systems. The proposed approach is based on multiple continua and is capable to accurately describe charge interactions during ionic transport in the free water, diffuse layer, and interlayer water of charged porous media. The diffuse layer composition is simulated by considering a mean electrostatic potential following Donnan approach, whereas the interlayer composition is calculated by adopting the Gaines-Thomas convention. Diffusive/dispersive fluxes within each subcontinuum (free water, diffuse layer, and interlayer) are calculated solving the Nernst-Planck equation while maintaining a net zero-charge flux. Furthermore, the multidimensional flow and transport model is coupled with the geochemical code PHREEQC, by utilizing the PhreeqcRM module, thus enabling great flexibility to access all PHREEQC's reaction capabilities. The code is benchmarked in 1-D systems against other software and previously published experimental data. Successively, reactive transport simulations are performed in 2-D clayey-sandy flowthrough domains with spatially variable physical and electrostatic properties at both laboratory and field scales. The results reveal that different properties of surface charge, diffuse layer, and Coulombic interactions impact the transport of charged species and lead to distinct spatial distribution of the ions in the different subcontinua and to significantly different breakthrough curves.

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Ionic Transport in Nano-Porous Clays with Consideration of Electrostatic Effects

Cited by 55 publications

References 127 publications

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

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

Modeling diffusion processes in the presence of a diffuse layer at charged mineral surfaces: a benchmark exercise

Multicomponent Ionic Transport Modeling in Physically and Electrostatically Heterogeneous Porous Media With PhreeqcRM Coupling for Geochemical Reactions

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