Refined Thermal Modelling of a SNF Shipping-Cask Drying Process Analytical and Statistical Approaches

Before being back-filled with an inert gas and as preparation for shipment, a spent-nuclear-fuel shipping cask must usually be vacuum-dried. This process results in an increase in the spent fuel temperature, due to the degradation of heat transport by the cover gas. The drying process is typically modelled by a thermal conduction set to zero in all the shipping-cask free spaces. However, this approach does not take into account heat transfers that occur in a rarefied medium and, therefore, may be extremely conservative. A first analysis was performed in order to spot the cask areas whose thermal behaviour is modified by the drying process. This analysis involved the calculation of the Knudsen number, defined as the molecular mean-free-path to a representative length scale, for all the free spaces. The only area impacted by the drying process appeared to be the mechanical gap between the fuel basket and the shielding materials. During the drying process, the Knudsen number is actually large enough within the gap to consider the gas as a non-continuous medium. Results and methods coming from the microfluidics area were therefore used to develop a modelling, which is based on a double approach. First, an analytical approach was used. This approach consists in adding to the Fourier equation a new equation accounting for the thermodynamical non-equilibrium within the gap (MaxwellSmoluchowski temperature jump). A thermal model, suitable to calculate heat transfers at pressures as low as 1 mbar, was developed. A second model, based on a statistical approach, was then developed. This model involves the Direct Simulation Monte Carlo method, a reference method used for microfluidics calculations. Computer simulations were performed and led to a good agreement with the results obtained by the analytical approach.