Modelling of silica diffusion experiments with 32Si in Boom Clay

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Abstract

A mathematical model describing the dissolution of nuclear glass directly disposed in clay combines a first-order dissolution rate law with the diffusion of dissolved silica in clay. According to this model, the main parameters describing the long-term dissolution of the glass are ηR, the product of the diffusion accessible porosity η and the retardation factor R, and the apparent diffusion coefficient Dapp of dissolved silica in clay.

For determining the migration parameters needed for long-term predictions, four Through-Diffusion (T-D) experiments and one percolation test have been performed on undisturbed clay cores. In the Through-Diffusion experiments, the concentration decrease after injection of 32Si (radioactive labelled silica) was measured in the inlet compartment. At the end of the T-D experiments, the clay cores were cut in thin slices and the activity of labelled silica in each slice was determined. The measured activity profiles for these four clay cores are well reproducible.

Since no labelled silica could be detected in the outlet compartments, the Through-Diffusion experiments are fitted by two In-Diffusion models: one model assuming linear and reversible sorption equilibrium and a second model taking into account sorption kinetics. Although the kinetic model provides better fits, due to the sufficiently long duration of the experiments, both models give approximately similar values for the fit parameters. The single percolation test leads to an apparent diffusion coefficient value about two to three times lower than those of the Through-Diffusion tests.

Therefore, dissolved silica appears to be strongly retarded in Boom Clay. A retardation factor R between 100 and 300 was determined. The corresponding in situ distribution coefficient Kd is in the range 25–75 cm3 g−1. The apparent diffusion coefficient of dissolved silica in Boom Clay is estimated between 2×10−13 and 7×10−13 m2 s−1. The pore diffusion coefficient is in the range from 6×10−11 to 1×10−10 m2 s−1.

Introduction

A way to immobilise high-level waste issuing from the reprocessing of spent nuclear fuel is to encapsulate it in glass and to dispose this vitrified waste in deep geological layers such as Boom Clay. For a safety analysis, it is important to know the rate of dissolution of glass in argillaceous environments. For this purpose, Pescatore (1994) developed a model where the dissolution of glass (assumed to occur according to a first-order rate law; Grambow, 1987) is coupled with the diffusion of dissolved silica in the clay. To estimate the long-term (up to thousands of years) glass dissolution rate with this model (e.g. Aertsens and Van Iseghem, 1999, Maillard and Iracane, 1998), one needs to know the product ηR (with η the diffusion accessible porosity and R the retardation factor) and the apparent diffusion coefficient Dapp of dissolved silica in clay. To determine these parameters, four Through-Diffusion experiments and a percolation experiment have been performed with Boom Clay cores using 32Si as radioactive tracer.

Section snippets

Through-Diffusion experiments

Only a brief description of the Through-Diffusion experiments is given here. More detailed information has been published previously (De Cannière et al., 1998). To avoid a possible confusion with the terminology used in the previous article (De Cannière et al., 1998), the denominations “Through-Diffusion” and “Flow-Through” tests refer to the same experimental concept: purely diffusive experiments without any water movement (i.e., absence of any hydraulic gradient in the experiment).

At the

Description of the models

The traditional Through-Diffusion model assumes a constant concentration at the inlet and a zero concentration at the outlet. With these assumptions, one derives as a function of time an expression for the percolated quantity at the outlet. Due to an unexpected and significant depletion of 32Si at the inlet, and the fact that no labelled silica could ever be detected at the outlet, this model was not suitable for the 32Si Through-Diffusion experiments. Because no labelled silica could be

In-Diffusion model with sorption equilibrium

Because two data sets are available (the decrease of 32Si concentration at the inlet as a function of time and the 32Si profile in the clay core), it is evident that we try to fit both data sets with the same values for the fit parameters.

However, the value of the parameter C0 is different for both data sets. The 32Si concentrations in the water of the inlet compartment were measured by liquid scintillation counting. Here, appropriate calibration for 32Si was possible, allowing to express 32Si

Conclusion

Considering sorption kinetics for describing the in-diffusion experiments of silica in Boom Clay cores provides a better fit than assuming sorption equilibrium. Because the duration of the experiments is sufficiently long (about 3 years), sorption equilibrium is approximately reached at the end of the experiments. Therefore, the values of the fit parameters provided by the two models do not differ remarkably. For short durations, when the sorption equilibrium might not be reached, only the

Acknowledgements

This research was financially supported by the European Commission under contract FI4W-CT95-0001 and by NIRAS/ONDRAF under contract CCH090-123. The authors thank Karel Lemmens, Martin Put, and Pierre Van Iseghem for their support. The authors also thank Yves Minet and Enzo Curti for their help in tracing the origin of the values mentioned in Table 3.

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