Interface Stability Criteria for Ex-Vessel Corium Solidification

In case of a severe accident at a nuclear power plant (NPP) involving the reactor core melt-down and the subsequent reactor pressure vessel (RPV) melt-through, confident solidification of ex-vessel corium is considered to be the imperative condition of safe retention of corium within the plant containment in the long term. The rate-determining process for solidification of ex-vessel coriums in the long-term is the chemical diffusion in the liquid phase at the solid-liquid interface. The process of chemical diffusion in the diffusive boundary layer can evolve and take on different rates, depending on the boundary conditions and the melt composition. The chemical diffusion coefficient models presented to date in the literature resort to correlations of the former to the self-diffusion coefficients among other intrinsic properties. The general feature of such models is that they predict in the tracer limit that the main diagonal coefficients tend towards the self-diffusion coefficients whereas the cross-over terms cancel out. It is revealed in this study that this particular feature is characteristic of prototypic corium melts, mixtures of several major as well as minor components. Following the corium-concrete interaction, the multicomponent ex-vessel corium melts would contain certain fractions of silica. Accordingly, they are considered in this paper as silicate oxide melts. As a first contribution, this paper comes up with a development of interface stability criteria for its application to solidification of silicate oxide melts. For ex-vessel corium melts, not far removed from equilibrium solidification conditions (long-term retention), the extension of the FICK’s law due to ONSAGER can be applied to description of the diffusive mass transfer. This formalism implies that the diffusive fluxes are linear combinations of the products of the phenomenological diffusion coefficients and the driving forces (gradients). In this regard, the near equilibrium solidification of corium containing N components is determined by a (N−1)(N−1) chemical diffusion matrix comprising the proper and cross-over coefficients. On the other hand, by comparison to the constitutional super cooling criterion of the interface stability in the course of solidification, a relationship between the macroscopic solidification conditions and the phenomenological coefficients can be established. This analysis, earlier developed for liquid metal solidification, has received attention in this study in view of its extension onto the solidification of multicomponent oxide melts. The important conclusion whatsoever is that the crossover terms can’t be neglected as easily as in the case of liquid metal alloys, particularly for silicate melts. As in prototypic corium compositions certain tracer diffusion coefficients can be relatively easily obtained from an experiment, this paper suggests an empirical method for determination of corium constituents’ self-diffusivities from controlled solidification tests.