Inverse Estimation of the Effective Diffusion of the Filter in the In Situ Diffusion and Retention (DR) Experiment
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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.
KeywordsIn situ diffusion experiment Filter Inverse method Parameter identifiability
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- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Van Loon, L.R., Glaus, M. A.: Effective diffusion coefficient of several tracers in Teflon filters. PSI Technical Note, Switzerland (2008)Google Scholar
- 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
- 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