Modeling diffusion and adsorption in compacted bentonite: a critical review

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Abstract

The current way of describing diffusive transport through compacted clays is a simple diffusion model coupled to a linear adsorption coefficient (Kd). To fit the observed results of cation diffusion, this model is usually extended with an adjustable “surface diffusion” coefficient. Description of the negative adsorption of anions calls for a further adjustment through the use of an “effective porosity”. The final model thus includes many fitting parameters. This is inconvenient where predictive modeling is called for (e.g., for waste confinement using compacted clay liners).

The diffusion/adsorption models in current use have been derived from the common hydrogeological equation of advection/dispersion/adsorption. However, certain simplifications were also borrowed without questioning their applicability to the case of compacted clays. Among these simplifications, the assumption that the volume of the adsorbed phase is negligible should be discussed. We propose a modified diffusion/adsorption model that accounts for the volume of the adsorbed phase. It suggests that diffusion through highly compacted clay takes place through the interlayers (i.e., in the adsorbed phase). Quantitative prediction of the diffusive flux will necessitate more detailed descriptions of surface reactivity and of the mobility of interlayer species.

Introduction

Compacted clay engineered barriers are one of the serious options for the confinement of high-level toxic or radioactive waste (e.g., Nowak, 1980). The very low permeability of the clay barrier is expected to lengthen the lifetime of the waste packaging (canisters) and slow down the consequent release of contaminants. Low porosity, slow diffusive transport, high adsorption of cations, and plasticity/swelling (self-healing of fractures) are among the interesting properties of bentonite clays.

Any transport model to be used in performance assessment must be able to account for the results of small-scale diffusion experiments in the lab, but must also be grounded in the mechanisms of adsorption and diffusion so that the necessary extrapolation over time, distance (over 4 orders of magnitude in both), and environmental conditions (higher temperatures, near-saturation concentrations) can be meaningful. The following is a discussion on the modeling of diffusion through reactive pore networks, with the aim of devising a model better adapted to the particularities of highly compacted bentonite (at ca. 2 kg/l of bulk dry density).

Section snippets

State of the art diffusion through compacted bentonite

The current way of describing a diffusive flux F through a pore network is through Fick's law (with Dfree as the diffusion coefficient in pure water), with corrections for porosity ε and tortuosity τ:εCt=−Fxi=xiεDfreeτ2Cxi

If the diffusing species can be adsorb to the surface, a transient term ρbq/∂t (accumulation of adsorbed species) must be added to the left-hand side of the equation (ρb is the bulk dry density of the porous material). At low surface coverage, we can approximate q

Volume of the adsorbed phase

The porosity of compacted smectite is not as simple as that described by the classical diffusion/adsorption model. Smectite layers stack up to form particles (on the order of 10 layers per stack), where the interlayer space is available as porous volume (responsible for the swelling of smectites). Compacted smectite will then have two porosities: large pores between the clay particles, where diffusion can take place relatively unaffected by the surface, and very thin interlayer pores (two or

Conclusion

The free porosity must be correctly determined, not forgetting to subtract the interlayer porosity. This eliminates the need to use tortuosity as a fitting parameter to describe results of diffusion at different degrees of compaction. It also explains the semipermeable membrane behaviour of bentonite at higher degrees of compaction. But the rapid diffusion of hard acids vs. soft ones at equivalent values of Kd cannot yet be interpreted; interlayer diffusion may be fast enough that it is not

Acknowledgements

We thank ANDRA (Agence Nationale pour la Gestion des Déchêts Radioactifs, Châtenay-Malabry, France) for their funding under the form of a doctoral fellowship to ICB.

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