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Transport in Porous Media

, Volume 93, Issue 3, pp 415–429 | Cite as

Inverse Estimation of the Effective Diffusion of the Filter in the In Situ Diffusion and Retention (DR) Experiment

  • Shuping Yi
  • Javier SamperEmail author
  • Acacia Naves
  • Josep M. Soler
Article

Abstract

Porous filters are often used in laboratory and in situ diffusion and retention experiments. The proper interpretation of these experiments requires knowing the effective diffusion, D e, of the filter which is commonly determined from laboratory diffusion experiments or estimated from the filter porosity. The D e of the filter in the in situ experiment may differ from the D e of the filter measured in the laboratory due to pore clogging. Here, we present an inverse method to estimate the D e of the filter of in situ diffusion experiments. The method has been tested for several sampling schemes, numbers of synthetic data, N, and standard deviations of the noise, σ. It has been applied to the following tracers used in the in situ diffusion and retention (DR) experiment performed in the Opalinus clay at Mont Terri underground research laboratory: HTO/HDO, Br,I, 22 Na+,133 Ba2+,85 Sr2+, Cs+/137Cs+, and 60Co2+. The estimation error increases with the standard deviation of the noise of the data and decreases with the number of data. It is smallest for sorbing tracers. The D e of the filter can be properly estimated from 12 data collected within the first 3 days for conservative tracers as long as σ ≤ 0.02 and for sorbing tracers as long as σ ≤ 0.05. The estimate of D e for conservative tracers is poor when data are collected from a 10-day experiment with daily sampling. The convergence of the estimation algorithm for conservative tracers improves by starting with a value of the D e smaller than the true value. The choice of the initial value of D e does not affect the convergence of the estimation algorithm for sorbing tracers. Filter clogging and vertical flow though the filter can influence the tracer transport through the filter. The use of the D e of the filter obtained from a laboratory test for the in situ experiment may result in large errors for strongly sorbing tracers. Such errors can be overcome by estimating the equivalent D e of the filter with the proposed inverse method which will be useful for the design of in situ diffusion experiments.

Keywords

In situ diffusion experiment Filter Inverse method Parameter identifiability 

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References

  1. Appelo, C.A.J.: Modeling of Cs-data from diffusion experiments in the laboratory and in-situ DI-A experiments (phase 12) in Opalinus clay. Part 2: Modeling DI-A1 experiment. Technical report for Nagra. March 2008Google Scholar
  2. Bourke, P.J., Gilling, D., Jefferies, N.L., Lever, D.A. Lineham, T.R.: Mass transfer through clay by diffusion and advection: description of INTRAVAL Test Case 1a. Safety Studies. Nirex Radioactive Waste Disposal NSS/R159, 1990Google Scholar
  3. Dai Z., Samper J.: Inverse problem of multicomponent reactive chemical transport in porous media: formulation and applications. Water Resour. Res 40, W07407 (2004). doi: 10.1029/2004WR003248 CrossRefGoogle Scholar
  4. Dewonck, S., Blin, V., Radwan, J., Filippi, M., Landesman, C., Ribet, S.: Long term in situ tracer diffusion tests in the Callovo-Oxfordian clay: Results and modeling. In: Clays in Natural & Engineered Barriers for Radioactive Waste Confinement 4th International Meeting in March 2010, Nantes, France, 2010Google Scholar
  5. Glaus M.A., Rosse R., van Loon L.R., Yaroshchuk A.E.: Tracer diffusion in sintered stainless steel filters: Measurement of effective diffusion and implications for diffusion studies with compacted clays. Clays Clay Min. 56, 677–685 (2008)CrossRefGoogle Scholar
  6. Leupin, O.X., Wersin, P., Gimmi, Th., Soler, J.M., Dewonck, S., Wittebroodt, C.,Van Loon, L., Eikenberg, J., Baeyens, B., Samper, J., Yi, S., Naves, A.: Diffusion and retention experiment at Mont Terri underground rock laboratory in St. Ursanne. In: Clays In Natural & Engineered Barriers for Radioactive Waste Confinement 4th International Meeting in March 2010, Nantes, France, 2010Google Scholar
  7. Li Y.H., Gregory S.: Diffusion of ions in sea water and in deep-sea sediments. Geochim. Cosmochim. Acta 38, 703–714 (1974)CrossRefGoogle Scholar
  8. Molera M., Eriksen T.: Diffusion of 22Na+,85Sr2+, 134Cs+ and 57Co2+ in bentonite clay compacted to different densities: experiments and modeling. Radiochim. Acta 90, 753–760 (2002)CrossRefGoogle Scholar
  9. Oscarson D.: Surface diffusion: is it an important transport mechanism in compacted clays?. Clays Clay Min. 42, 534–543 (1994)CrossRefGoogle Scholar
  10. Palut J.M., Montarnal P., Gautschi A., Tevissen E., Mouche E.: Characterisation of HTO diffusion properties by an in situ tracer experiment in Opalinus clay at Mont Terri. J. Contam. Hydrol. 61(1), 203–218 (2003)CrossRefGoogle Scholar
  11. Radwan, J., Tevissen, E., Descostes, M., Blin, V.: Premiers éléments d’interprétation et de modélisation des expériences de diffusion de traceurs inertes et réactifs en laboratoire souterrain de Meuse/Haute-Marne. Note technique CEA NTDPC/SECR 05-046/A, 2005Google Scholar
  12. Samper J., Dai Z., Molinero J., García-Gutiérrez M., Missana T., Mingarro M.: Interpretation of solute transport experiments in compacted Ca-bentonites using inverse modelling. Phys. Chem. Earth 31, 640–648 (2006)CrossRefGoogle Scholar
  13. Samper J., Dewonck S., Zheng L., Yang Q., Naves A.: Normalized sensitivities and parameter identifiability of in situ diffusion experiments on Callovo–Oxfordian clay at Bure site. Phys. Chem. Earth 33, 1000–1008 (2008)CrossRefGoogle Scholar
  14. Samper, J., Yang, Q., Yi, S., García-Gutiérrez, M., Missana, T., Mingarro, M., Alonso, Ú., Cormenzana, J.L.: Numerical modelling of large-scale solid-source diffusion experiment in Callovo–Oxfordian clay. Phys. Chem. Earth 33(Supplement 1), S208–S215 (2008b)Google Scholar
  15. Samper J., Yi S., Naves A.: Analysis of the parameter identifiability of the in situ diffusion and retention (DR) experiment. Phys. Chem. Earth 35, 207–216 (2010)CrossRefGoogle Scholar
  16. Soler, J.M, Samper, J., Yllera, A., Hernández, A., Quejido, A., Fernández, M., Yang, C., Naves, A., Hernán, P., Wersin, P.: The DI-B in-situ diffusion experiment at Mont Terri: results and modelling. Phys. Chem. Earth. 33(Supplement 1), S196–S207 (2008)Google Scholar
  17. Takeda M., Hiratsuka T., Finsterle S.: An axisymmetric diffusion experiments for the determination of diffusion and sorption coefficients of rock samples. J. Contam. Hydrol. 123, 114–129 (2011)CrossRefGoogle Scholar
  18. Tevissen E., Soler J.M., Montarnal Ph., Gautschi A., Van Loon L.R.: Comparison between in situ laboratory characterization of HTO and halides diffusion in Opalinus clay at the Mont Terri URL. Radiochim. Acta 92, 781–786 (2004)CrossRefGoogle Scholar
  19. Van Loon, L.R., Glaus, M. A.: Effective diffusion coefficient of several tracers in Teflon filters. PSI Technical Note, Switzerland (2008)Google Scholar
  20. Van Loon L.R., Wersin P., Soler J.M., Eikenberg J., Gimmi Th., Hernán P., Dewonck S., Savoye S.: In-situ diffusion of HTO, 22Na+, Cs+ and I in Opalinus clay at the Mont Terri underground rock laboratory. Radiochim. Acta 92, 757–763 (2004)CrossRefGoogle Scholar
  21. Van Loon L.R., Baeyens B., Bradbury M.H.: Diffusion and retention of sodium and strontium in Opalinus clay: Comparison of sorption data from diffusion and batch sorption measurements, and geochemical calculations. Appl. Geochem. 20, 2351–2363 (2005)CrossRefGoogle Scholar
  22. Wersin, P., van Dorp, F.: Diffusion and retention (DR) experiment in borehole BDR-1 Phase 11 (1 July 2005–30 June 2006): radiation protection and working plan. Mont Terri Technical Note 2005-2047 (2005)Google Scholar
  23. Wersin P., Van Loon L.R., Soler J., Yllera A., Eikenberg J., Gimmi T., Hernan P., Boisson J.Y.: Long-term diffusion experiment at Mont Terri: first results from field and laboratory data. Appl. Clay Sci. 26, 123–135 (2004)CrossRefGoogle Scholar
  24. Wersin P., Soler J.M., Van Loon L., Eikenberg J., Baeyens B., Grolimund D., Gimmi T.h., Dewonck S.: Diffusion of HTO, Br,I−, Cs+, 85Sr2+ and 60Co2+ in a clay formation: results and modeling from an in situ experiment in Opalinus clay. Appl. Geochem. 23, 678–691 (2008)CrossRefGoogle Scholar
  25. Yi, S., Samper, J., Naves, A., Soler, J.M.: A preliminary reactive transport model of Cs+ for the in situ diffusion and retention (DR) experiment. Appl. Geochem. (under review) (2012)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Shuping Yi
    • 1
    • 2
    • 3
  • Javier Samper
    • 1
    Email author
  • Acacia Naves
    • 1
  • Josep M. Soler
    • 4
  1. 1.ETS Ingenieros de Caminos, Canales y PuertosUniversidad de A CoruñaA CoruñaSpain
  2. 2.Electric Power Design InstituteGuangzhouChina
  3. 3.PKU Center for Water ResearchPeking UniversityBeijingChina
  4. 4.Institute of Environmental Assessment and Water Research (IDAEA-CSIC)BarcelonaSpain

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