Analytic implementation of the GRAAL model: Application to a R7T7-type glass package in a geological disposal environment

The Glass Reactivity with Allowance for the Alteration Layer Model (GRAAL) was proposed in 2008 to describe borosilicate nuclear glass alteration based on coupling an affinity law with the formation and dissolution of a passivating reactive interface. It is examined here in a simplified form in which only the affinity with respect to silicon is taken into account with a concentration at saturation Csat, and the precipitation of neoformed phases is described by an affine relation for silicon above a precipitation threshold Csat′. This simplified “analytical GRAAL” model is capable of predicting the quantities of altered glass and the silicon and boron concentration variations in analytical or semi-analytical form, and thereby identify the main characteristic quantities of the system. The model was tested against a series of laboratory experiments lasting from a few days to a few years; its sensitivity to the parameter values was examined, and the model was validated with respect to SON68 glass alteration in initially pure water. It was then applied to the alteration of a glass package in a repository over periods of up to a million years, by means of exploratory calculations comprising a sensitivity study of the internal model parameters and extrapolation to the temperatures expected in a geological repository in order to identify the parameters and mechanisms having the greatest impact on the residual alteration rate. Alteration is controlled by the precipitation of neoformed phases in every case. The transient conditions are of very limited duration with respect to either silicon or boron (no more than a 100 years, with less than 0.01% alteration of the package). In the precipitation law used in the model, the residual alteration rate and total package lifetime are determined primarily by two parameters: k′ (the precipitation kinetics) and σ′ (the precipitate surface area per unit volume in the geological barrier). The package lifetime is about 3 × 105 years at 30 °C assuming a reasonable value for σ′ (106 m−1), and would be increased by a factor 3–6 if precipitation in the barrier were disregarded. This cursory description of precipitation will be validated and refined through specific laboratory tests at 50 °C and lower temperatures, coordinated with the development of the “geochemical GRAAL” model and with integral tests in contact with clay and canister corrosion products.