Modeling diffusion processes in the presence of a diffuse layer at charged mineral surfaces: a benchmark exercise
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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.
KeywordsClay 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.
- 4.Grangeon, S., Vinsot, A., Tournassat, C., Lerouge, C., Giffaut, E., Heck, S., Groschopf, N., Denecke, M. A., Wechner, S., Schäfer, T.: The influence of natural trace element distribution on the mobility of radionuclides. The exemple of nickel in a clay-rock. Appl. Geochem. 52, 155–173 (2015)CrossRefGoogle Scholar
- 6.Robinet, J.-C., Sardini, P., Coelho, D., Parneix, J.-C., Prêt, D., Sammartino, S., Boller, E., Altmann, S.: Effects of mineral distribution at mesoscopic scale on solute diffusion in a clay-rich rock: example of the Callovo-Oxfordian mudstone (Bure, France). Water Resources Research, 48, W05554 (2012)Google Scholar
- 7.Tournassat, C., Gaboreau, S., Robinet, J. -C., Bourg, I. C., Steefel, C. I.: Impact of microstructure on anion exclusion in compacted clay media. CMS Workshop Lect Ser. 21, 137–149 (2016)Google Scholar
- 8.Appelo, C. A. J.: Multicomponent diffusion modeling in clay systems with application to the diffusion of tritium, iodide, and sodium in Opalinus clay. Supporting information (2007)Google Scholar
- 13.Tournassat, C., Bourg, I. C., Steefel, C. I., Bergaya, F.: Chapter 1 - surface properties of clay minerals. In: Tournassat, C., Steefel, C. I., Bourg, I. C., Bergaya, F. (eds.) Natural and Engineered Clay Barriers, vol. 6, pp 5–31. Developments in Clay Science; Elsevier (2015)Google Scholar
- 18.Parkhurst, D. L., Appelo, C. A. J.: Description of input and examples for PHREEQC Version 3– a computer program for speciation,batch-reaction, one-dimensional transport, and inverse geochemical calculations; U.S. Geological Survey Techniques and Methods, book 6, chap. A43, 497 p., available at http://pubs.usgs.gov/tm/06/a43/ (2013)
- 19.Steefel, C. I., Appelo, C. A. J., Arora, B., Jacques, D., Kalbacher, T., Kolditz, O., Lagneau, V., Lichtner, P. C., Mayer, K. U., Meeussen, J. C. L., Molins, S., Moulton, D., Shao, H., Šimunek, J., Spycher, N., Yabusaki, S. B., Yeh, G. T.: Reactive transport codes for subsurface environmental simulation. Comput. Geosci. 19, 445–478 (2015)CrossRefGoogle Scholar
- 24.Crank, J.: The Mathematics of Diffusion. Oxford University Press, Oxford (1975)Google Scholar
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