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Title: A model for discrete fracture-clay rock interaction incorporating electrostatic effects on transport

Abstract

Abstract A model based on the code CrunchClay is presented for a fracture-clay matrix system that takes electrostatic effects on transport into account. The electrostatic effects on transport include those associated with the development of a diffusion potential as captured by the Nernst-Planck equation, and the formation of a diffuse layer bordering negatively charged clay particles within which partial anion exclusion occurs. The model is based on a dual continuum formulation that accounts for diffuse layer and bulk water pore space, providing a more flexible framework than is found in the classical mean electrostatic potential models. The diffuse layer model is obtained by volume averaging ion concentrations in the Poisson-Boltzmann equation, but also includes the treatment of longitudinal transport within this continuum. The calculation of transport within the bulk and diffuse layer porosity is based on a new formulation for the Nernst-Planck equation that considers averaging of diffusion coefficients and accumulation factors at grid cell interfaces. Equations for function residuals and the associated Jacobian matrix are presented such that the system of nonlinear differential-algebraic equations can be solved with Newton’s method. As an example, we consider a 2D system with a single discrete fracture within which flow and advective transportmore » occurs that is coupled to diffusion in the clay-rich matrix. The simulation results demonstrate the lack of retardation for anions (e.g., 36 Cl ) of the contaminant plume within the fracture flow system because they are largely excluded from the charged clay rock, while the migration of cations (e.g., 90 Sr ++ ) is more strongly attenuated. The diffusive loss of divalent cations in particular from the fracture is accentuated by their accumulation in the diffuse layer within the clay-rich matrix.« less

Authors:
ORCiD logo;
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1712819
Alternate Identifier(s):
OSTI ID: 1763661
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Published Article
Journal Name:
Computational Geosciences
Additional Journal Information:
Journal Name: Computational Geosciences; Journal ID: ISSN 1420-0597
Publisher:
Springer
Country of Publication:
Netherlands
Language:
English
Subject:
58 GEOSCIENCES; Diffusion; clay-rich matrix; electrical double layer; fracture-matrix interaction

Citation Formats

Steefel, Carl I., and Tournassat, Christophe. A model for discrete fracture-clay rock interaction incorporating electrostatic effects on transport. Netherlands: N. p., 2020. Web. https://doi.org/10.1007/s10596-020-10012-3.
Steefel, Carl I., & Tournassat, Christophe. A model for discrete fracture-clay rock interaction incorporating electrostatic effects on transport. Netherlands. https://doi.org/10.1007/s10596-020-10012-3
Steefel, Carl I., and Tournassat, Christophe. Fri . "A model for discrete fracture-clay rock interaction incorporating electrostatic effects on transport". Netherlands. https://doi.org/10.1007/s10596-020-10012-3.
@article{osti_1712819,
title = {A model for discrete fracture-clay rock interaction incorporating electrostatic effects on transport},
author = {Steefel, Carl I. and Tournassat, Christophe},
abstractNote = {Abstract A model based on the code CrunchClay is presented for a fracture-clay matrix system that takes electrostatic effects on transport into account. The electrostatic effects on transport include those associated with the development of a diffusion potential as captured by the Nernst-Planck equation, and the formation of a diffuse layer bordering negatively charged clay particles within which partial anion exclusion occurs. The model is based on a dual continuum formulation that accounts for diffuse layer and bulk water pore space, providing a more flexible framework than is found in the classical mean electrostatic potential models. The diffuse layer model is obtained by volume averaging ion concentrations in the Poisson-Boltzmann equation, but also includes the treatment of longitudinal transport within this continuum. The calculation of transport within the bulk and diffuse layer porosity is based on a new formulation for the Nernst-Planck equation that considers averaging of diffusion coefficients and accumulation factors at grid cell interfaces. Equations for function residuals and the associated Jacobian matrix are presented such that the system of nonlinear differential-algebraic equations can be solved with Newton’s method. As an example, we consider a 2D system with a single discrete fracture within which flow and advective transport occurs that is coupled to diffusion in the clay-rich matrix. The simulation results demonstrate the lack of retardation for anions (e.g., 36 Cl − ) of the contaminant plume within the fracture flow system because they are largely excluded from the charged clay rock, while the migration of cations (e.g., 90 Sr ++ ) is more strongly attenuated. The diffusive loss of divalent cations in particular from the fracture is accentuated by their accumulation in the diffuse layer within the clay-rich matrix.},
doi = {10.1007/s10596-020-10012-3},
journal = {Computational Geosciences},
number = ,
volume = ,
place = {Netherlands},
year = {2020},
month = {11}
}

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https://doi.org/10.1007/s10596-020-10012-3

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Works referenced in this record:

An analogue of matrix diffusion enhanced by biogenic redox reaction in fractured sedimentary rock
journal, July 2006


An analytical solution for solute transport through fractured media with matrix diffusion
journal, June 1981


Development of approximate solutions for contaminant transport through fractured media
journal, January 2015


Coulombic effects in advection-dominated transport of electrolytes in porous media: Multicomponent ionic dispersion
journal, November 2013

  • Rolle, Massimo; Muniruzzaman, Muhammad; Haberer, Christina M.
  • Geochimica et Cosmochimica Acta, Vol. 120
  • DOI: 10.1016/j.gca.2013.06.031

Constitutive equations for ionic transport in porous shales
journal, January 2004


Modeling multi-component transport and enhanced anaerobic dechlorination processes in a single fracture–clay matrix system
journal, March 2010

  • Chambon, Julie C.; Broholm, Mette M.; Binning, Philip J.
  • Journal of Contaminant Hydrology, Vol. 112, Issue 1-4
  • DOI: 10.1016/j.jconhyd.2009.10.008

Double-porosity modelling of oscillatory gas motion and contaminant transport in a fractured porous medium
journal, November 1990

  • Nilson, R. H.; Lie, K. H.
  • International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 14, Issue 8
  • DOI: 10.1002/nag.1610140804

Reciprocal Relations in Irreversible Processes. I.
journal, February 1931


Ion equilibrium between montmorillonite interlayer space and an external solution—Consequences for diffusional transport
journal, April 2009


Contaminant transport in fractured porous media: Analytical solution for a single fracture
journal, June 1981

  • Tang, D. H.; Frind, E. O.; Sudicky, E. A.
  • Water Resources Research, Vol. 17, Issue 3
  • DOI: 10.1029/WR017i003p00555

Development of a discontinuous approach for modeling fluid flow in heterogeneous media using the numerical manifold method: A Discontinuous Approach for Flow in Heterogeneous Media with NMM
journal, June 2015

  • Hu, Mengsu; Wang, Yuan; Rutqvist, Jonny
  • International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 39, Issue 17
  • DOI: 10.1002/nag.2390

Characterizing flow and transport in fractured geological media: A review
journal, August 2002


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

Reactive transport modeling in fractured rock: A state-of-the-science review
journal, October 2005


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

Matrix Diffusion Effects on Contaminant Migration from an Injection Well in Fractured Sandstone
journal, May 1984


Multicomponent diffusion in a 280 m thick argillaceous rock sequence
journal, August 2018


Solving the Nernst‐Planck Equation in Heterogeneous Porous Media With Finite Volume Methods: Averaging Approaches at Interfaces
journal, March 2020

  • Tournassat, Christophe; Steefel, Carl I.; Gimmi, Thomas
  • Water Resources Research, Vol. 56, Issue 3
  • DOI: 10.1029/2019WR026832

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

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


Reactive transport codes for subsurface environmental simulation
journal, September 2014


Comparison of the Nernst–Planck model and the Poisson–Boltzmann model for electroosmotic flows in microchannels
journal, November 2007


Multicomponent reactive transport in discrete fractures: I. Controls on reaction front geometry
journal, August 1998


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


Reciprocal Relations in Irreversible Processes. II.
journal, December 1931


Application of nonequilibrium fracture matrix model in simulating reactive contaminant transport through fractured porous media
journal, January 2015

  • Joshi, Nitin; Ojha, C. S. P.; Sharma, P. K.
  • Water Resources Research, Vol. 51, Issue 1
  • DOI: 10.1002/2014WR016500

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


Comparing Discrete Fracture and Continuum Models to Predict Contaminant Transport in Fractured Porous Media: D. Blessent et al. Groundwater xx, no. x: xx-xx
journal, March 2013

  • Blessent, Daniela; Jørgensen, Peter R.; Therrien, René
  • Groundwater, Vol. 52, Issue 1
  • DOI: 10.1111/gwat.12032

Discretizing the Fracture-Matrix Interface to Simulate Solute Transport
journal, July 2008


Tracer Penetration into Welded Tuff Matrix from Flowing Fractures
journal, August 2002

  • Hu, Qinhong; Kneafsey, Timothy J.; Trautz, Robert C.
  • Vadose Zone Journal, Vol. 1, Issue 1
  • DOI: 10.2136/vzj2002.1020

Field tracer-transport tests in unsaturated fractured tuff
journal, September 2001


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


Fracture/matrix interaction in a fracture of finite extent: FLOW IN FINITE FRACTURES
journal, August 2010


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

Diffusion and reaction in rock matrix bordering a hyperalkaline fluid-filled fracture
journal, September 1994


Molecular dynamics simulations of the electrical double layer on smectite surfaces contacting concentrated mixed electrolyte (NaCl–CaCl2) solutions
journal, August 2011


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

Modeling the Ionic Strength Effect on Diffusion in Clay. The DR-A Experiment at Mont Terri
journal, January 2019


Multicomponent Ionic Transport Modeling in Physically and Electrostatically Heterogeneous Porous Media With PhreeqcRM Coupling for Geochemical Reactions
journal, December 2019

  • Muniruzzaman, Muhammad; Rolle, Massimo
  • Water Resources Research, Vol. 55, Issue 12
  • DOI: 10.1029/2019WR026373

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

Modelling approaches for anion-exclusion in compacted Na-bentonite
journal, July 2011


Contaminant transport in sets of parallel finite fractures with fracture skins
journal, May 1998


A Green's function method for two-dimensional reactive solute transport in a parallel fracture-matrix system
journal, June 2018


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

A physically based approach for modeling multiphase fracture–matrix interaction in fractured porous media
journal, September 2004


An embedded boundary method for the Navier–Stokes equations on a time-dependent domain
journal, January 2012

  • Miller, Gregory; Trebotich, David
  • Communications in Applied Mathematics and Computational Science, Vol. 7, Issue 1
  • DOI: 10.2140/camcos.2012.7.1

Numerical analysis of contaminant removal from fractured rock during boiling
journal, June 2012