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

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 Ba 2+ , 85 Sr 2+ , Cs + / 137 Cs + , and 60 Co 2+ . 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.