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

  • Christophe TournassatEmail author
  • Carl I. Steefel
Open Access
Original Paper


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.


Clay Diffusion Diffuse layer Nernst-Planck equation Poisson-Boltzmann CrunchClay PHREEQC 



This work was supported by the Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy (BES-DOE) under Contract No. DE-AC02-05CH11231; the French National Radioactive Waste Management Agency (Andra, project CTEC, P.I. J-C. Robinet and Mélanie Lundy) (Andra, project CTEC, P.I. J-C. Robinet); and the CNRS Défi NEEDS (project MIPOR-TRANSREAC). Carl I. Steefel acknowledges funding from L’Institut Carnot for his visit to the BRGM.

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Authors and Affiliations

  1. 1.Lawrence Berkeley National LaboratoryBerkeleyUSA
  2. 2.BRGMOrléansFrance
  3. 3.Université d’Orléans – CNRS/INSU – BRGMUMR 7327 Institut des Sciences de la Terre d’OrléansOrléansFrance

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