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Title: Solving the Nernst‐Planck Equation in Heterogeneous Porous Media With Finite Volume Methods: Averaging Approaches at Interfaces

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [3]
  1. Lawrence Berkeley National Laboratory Berkeley CA USA, BRGM Orléans France, Université d'Orléans‐CNRS/INSU‐BRGM, Institut des Sciences de la Terre d'Orléans Orléans France
  2. Lawrence Berkeley National Laboratory Berkeley CA USA
  3. Rock‐Water Interaction, Institute of Geological SciencesUniversity of Bern Bern Switzerland, Laboratory for Waste Management, Nuclear Energy and SafetyPaul Scherrer Institute Villigen Switzerland
Publication Date:
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1604807
Alternate Identifier(s):
OSTI ID: 1604808
Resource Type:
Published Article
Journal Name:
Water Resources Research
Additional Journal Information:
Journal Name: Water Resources Research Journal Volume: 56 Journal Issue: 3; Journal ID: ISSN 0043-1397
Publisher:
American Geophysical Union (AGU)
Country of Publication:
United States
Language:
English

Citation Formats

Tournassat, Christophe, Steefel, Carl I., and Gimmi, Thomas. Solving the Nernst‐Planck Equation in Heterogeneous Porous Media With Finite Volume Methods: Averaging Approaches at Interfaces. United States: N. p., 2020. Web. doi:10.1029/2019WR026832.
Tournassat, Christophe, Steefel, Carl I., & Gimmi, Thomas. Solving the Nernst‐Planck Equation in Heterogeneous Porous Media With Finite Volume Methods: Averaging Approaches at Interfaces. United States. doi:10.1029/2019WR026832.
Tournassat, Christophe, Steefel, Carl I., and Gimmi, Thomas. Sun . "Solving the Nernst‐Planck Equation in Heterogeneous Porous Media With Finite Volume Methods: Averaging Approaches at Interfaces". United States. doi:10.1029/2019WR026832.
@article{osti_1604807,
title = {Solving the Nernst‐Planck Equation in Heterogeneous Porous Media With Finite Volume Methods: Averaging Approaches at Interfaces},
author = {Tournassat, Christophe and Steefel, Carl I. and Gimmi, Thomas},
abstractNote = {},
doi = {10.1029/2019WR026832},
journal = {Water Resources Research},
number = 3,
volume = 56,
place = {United States},
year = {2020},
month = {3}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1029/2019WR026832

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Works referenced in this record:

Anomalous kinetics in diffusion limited reactions linked to non-Gaussian concentration probability distribution function
journal, November 2011

  • de Anna, Pietro; Le Borgne, Tanguy; Dentz, Marco
  • The Journal of Chemical Physics, Vol. 135, Issue 17
  • DOI: 10.1063/1.3655895

Nernst-Planck-based Description of Transport, Coulombic Interactions, and Geochemical Reactions in Porous Media: Modeling Approach and Benchmark Experiments
journal, April 2018

  • Rolle, Massimo; Sprocati, Riccardo; Masi, Matteo
  • Water Resources Research, Vol. 54, Issue 4
  • DOI: 10.1002/2017WR022344

Dispersion and advection in unsaturated porous media enhanced by anion exclusion
journal, August 1991

  • Gvirtzman, H.; Gorelick, S. M.
  • Nature, Vol. 352, Issue 6338
  • DOI: 10.1038/352793a0

Calculation of multicomponent ionic diffusion from zero to high concentration: II. Inclusion of associated ion species
journal, January 1991


Evaluating the impacts of migration in the biofilm anode using the model PCBIOFILM
journal, September 2010


Mixing and Reaction Kinetics in Porous Media: An Experimental Pore Scale Quantification
journal, December 2013

  • Anna, Pietro de; Jimenez-Martinez, Joaquin; Tabuteau, Hervé
  • Environmental Science & Technology, Vol. 48, Issue 1
  • DOI: 10.1021/es403105b

The New Potential for Understanding Groundwater Contaminant Transport: P.W. Hadley and C. Newell
journal, November 2013


Oxidative Uranium Release from Anoxic Sediments under Diffusion-Limited Conditions
journal, September 2017

  • Bone, Sharon E.; Cahill, Melanie R.; Jones, Morris E.
  • Environmental Science & Technology, Vol. 51, Issue 19
  • DOI: 10.1021/acs.est.7b02241

Internal Domains of Natural Porous Media Revealed: Critical Locations for Transport, Storage, and Chemical Reaction
journal, February 2016

  • Zachara, John; Brantley, Sue; Chorover, Jon
  • Environmental Science & Technology, Vol. 50, Issue 6
  • DOI: 10.1021/acs.est.5b05015

Cation diffusion in the electrical double layer enhances the mass transfer rates for Sr2+, Co2+ and Zn2+ in compacted illite
journal, September 2015


Ion adsorption and diffusion in smectite: Molecular, pore, and continuum scale views
journal, March 2016

  • Tinnacher, Ruth M.; Holmboe, Michael; Tournassat, Christophe
  • Geochimica et Cosmochimica Acta, Vol. 177
  • DOI: 10.1016/j.gca.2015.12.010

Multicomponent Diffusion Modeling in Clay Systems with Application to the Diffusion of Tritium, Iodide, and Sodium in Opalinus Clay
journal, July 2007

  • Appelo, C. Anthony J.; Wersin, Paul
  • Environmental Science & Technology, Vol. 41, Issue 14
  • DOI: 10.1021/es0629256

Molecular dynamics simulations of kinetic isotope fractionation during the diffusion of ionic species in liquid water
journal, December 2007


Impact of multicomponent ionic transport on pH fronts propagation in saturated porous media: MULTICOMPONENT IONIC TRANSPORT AND PH FRONTS
journal, August 2015

  • Muniruzzaman, Muhammad; Rolle, Massimo
  • Water Resources Research, Vol. 51, Issue 8
  • DOI: 10.1002/2015WR017134

Isotopic Fractionation by Transverse Dispersion: Flow-through Microcosms and Reactive Transport Modeling Study
journal, August 2010

  • Rolle, Massimo; Chiogna, Gabriele; Bauer, Robert
  • Environmental Science & Technology, Vol. 44, Issue 16
  • DOI: 10.1021/es101179f

Isotopic mass dependence of metal cation diffusion coefficients in liquid water
journal, April 2010

  • Bourg, Ian C.; Richter, Frank M.; Christensen, John N.
  • Geochimica et Cosmochimica Acta, Vol. 74, Issue 8
  • DOI: 10.1016/j.gca.2010.01.024

Simulating Donnan equilibria based on the Nernst-Planck equation
journal, July 2018


Benchmarks for multicomponent diffusion and electrochemical migration
journal, May 2015

  • Rasouli, Pejman; Steefel, Carl I.; Mayer, K. Ulrich
  • Computational Geosciences, Vol. 19, Issue 3
  • DOI: 10.1007/s10596-015-9481-z

Persistence of incomplete mixing: A key to anomalous transport
journal, July 2011


Reactive transport codes for subsurface environmental simulation
journal, September 2014


Fluid-Rock Interaction: A Reactive Transport Approach
journal, January 2009

  • Steefel, C. I.; Maher, K.
  • Reviews in Mineralogy and Geochemistry, Vol. 70, Issue 1
  • DOI: 10.2138/rmg.2009.70.11

Ionic Transport in Nano-Porous Clays with Consideration of Electrostatic Effects
journal, January 2015

  • Tournassat, Christophe; Steefel, Carl I.
  • Reviews in Mineralogy and Geochemistry, Vol. 80, Issue 1
  • DOI: 10.2138/rmg.2015.80.09

Modeling diffusion processes in the presence of a diffuse layer at charged mineral surfaces: a benchmark exercise
journal, September 2019


Obtaining the porewater composition of a clay rock by modeling the in- and out-diffusion of anions and cations from an in-situ experiment
journal, October 2008


Calculation of multicomponent ionic diffusion from zero to high concentration: I. The system Na-K-Ca-Mg-Cl-SO4-H2O at 25°C
journal, January 1991


Laboratory diffusion testing for waste disposal — A review
journal, February 1991


Effect of fluid-sediment reaction on hydrothermal fluxes of major elements, eastern flank of the Juan de Fuca Ridge
journal, May 2002


Seeming Steady-State Uphill Diffusion of 22 Na + in Compacted Montmorillonite
journal, September 2013

  • Glaus, Martin A.; Birgersson, Martin; Karnland, Ola
  • Environmental Science & Technology, Vol. 47, Issue 20
  • DOI: 10.1021/es401968c

Reactive Transport Modeling of Coupled Processes in Nanoporous Media
journal, September 2019

  • Tournassat, Christophe; Steefel, Carl I.
  • Reviews in Mineralogy and Geochemistry, Vol. 85, Issue 1
  • DOI: 10.2138/rmg.2019.85.4

Non-Fickian dispersion in porous media explained by heterogeneous microscale matrix diffusion: NON-FICKIAN DISPERSION AND HETEROGENEOUS DIFFUSION
journal, November 2008

  • Gouze, Philippe; Melean, Yasmin; Le Borgne, Tanguy
  • Water Resources Research, Vol. 44, Issue 11
  • DOI: 10.1029/2007WR006690

Multicomponent ionic diffusion in porewaters: Coulombic effects revisited
journal, May 2004

  • Boudreau, Bernard P.; Meysman, Filip J. R.; Middelburg, Jack J.
  • Earth and Planetary Science Letters, Vol. 222, Issue 2
  • DOI: 10.1016/j.epsl.2004.02.034

Improving noble gas based paleoclimate reconstruction and groundwater dating using 20Ne/22Ne ratios
journal, February 2003


Multicomponent ionic dispersion during transport of electrolytes in heterogeneous porous media: Experiments and model-based interpretation
journal, September 2014

  • Muniruzzaman, Muhammad; Haberer, Christina M.; Grathwohl, Peter
  • Geochimica et Cosmochimica Acta, Vol. 141
  • DOI: 10.1016/j.gca.2014.06.020

Multispecies diffusion models: A study of uranyl species diffusion: MULTISPECIES DIFFUSION MODELS
journal, December 2011

  • Liu, Chongxuan; Shang, Jianying; Zachara, John M.
  • Water Resources Research, Vol. 47, Issue 12
  • DOI: 10.1029/2011WR010575

Diffusion of sea water ions—I. Diffusion of sea water into a dilute solution
journal, December 1972


The treatment of multi-component diffusion and ion pairs in diagenetic fluxes
journal, March 1979


Multicomponent diffusion of a suite of tracers (HTO, Cl, Br, I, Na, Sr, Cs) in a single sample of Opalinus Clay
journal, February 2010

  • Appelo, C. A. J.; Van Loon, L. R.; Wersin, P.
  • Geochimica et Cosmochimica Acta, Vol. 74, Issue 4
  • DOI: 10.1016/j.gca.2009.11.013

Stretching, Coalescence, and Mixing in Porous Media
journal, May 2013


Relevance of local compound-specific transverse dispersion for conservative and reactive mixing in heterogeneous porous media: COMPOUND-SPECIFIC TRANSVERSE DISPERSION
journal, July 2011

  • Chiogna, Gabriele; Cirpka, Olaf A.; Grathwohl, Peter
  • Water Resources Research, Vol. 47, Issue 7
  • DOI: 10.1029/2010WR010270

Microscopic reactive diffusion of uranium in the contaminated sediments at Hanford, United States: MICROSCOPIC REACTIVE DIFFUSION
journal, December 2006

  • Liu, Chongxuan; Zachara, John M.; Yantasee, Wassana
  • Water Resources Research, Vol. 42, Issue 12
  • DOI: 10.1029/2006WR005031

Evaporation rates across a convective air boundary layer are dominated by diffusion: DIFFUSION-DOMINANT EVAPORATION RATES
journal, March 2013

  • Haghighi, E.; Shahraeeni, E.; Lehmann, P.
  • Water Resources Research, Vol. 49, Issue 3
  • DOI: 10.1002/wrcr.20166