A two-phase mathematical model to describe the dissolution of corium crust by molten steel

Abstract

This paper deals with the study of dissolution phenomena in corium crust, in a severe accident. In case of an In-Vessel Retention (IVR) strategy, it is expected that the corium pool will be surrounded by an oxide crust, which will be in contact with molten steel from the top, and along the sides. CORDEB experiments have shown that this crust becomes permeable, having an impact on the thickness of molten steel layer above it. A thin molten steel layer atop crust may lead to an excessive heat flux to the Reactor Pressure Vessel (RPV), resulting in a rupture or melt-through. Corium being a mixture of (U,Zr,O) atoms, undergoes a quaternary interaction with Fe atoms. Such an interaction plays an important role in the stability (or not) of the crust. A thermochemical study of this quaternary system shows that it can be reduced to a pseudo-binary in each phase: (U,Zr)+O in the oxide phase and (U,Zr)+Fe in the metal phase. Therefore, in this paper, dissolution of a binary two-phase porous region by liquid, is studied by means of an up-scaled mathematical model. The model is derived by volume averaging transport equations – Mass, Momentum and Specie – over a Representative Elementary Volume (REV). Final system of Partial Differential Equations (PDEs) is closed by deriving empirical relations for the effective diffusivities and for the mass transfer coefficients. Model is solved numerically to study the progress of dissolution, facilitating, molten steel filtration through the two-phase region. A qualitative comparison has also been made with CORDEB experiment. Results without convection show that the model is able to demonstrate the creation of liquid metal channels similar to the ones observed in the CORDEB findings. Further, the result with pressure gradient driven convection shows the possibility of complete crust dissolution, which is due to the convection enhanced dissolution in the corium crust.