Аннотация:
Diffusion is regarded as one of mechanisms, which leads to leakages through the fuel cladding during the long-term storage of spent nuclear fuel. The schematization of the diffusion process through a circular cylindrical cladding of fuel elements, where axial and circumferential diffusion flows are neglected, is considered. Fundamental properties of leakages through a cylindrical cladding of fuel elements associated with the effect of sorption, desorption, and diffusion are investigated; it is shown that the diffusion through the cladding material is the main limiting factor for leakages, whereas sorption and the effect of desorption are limited due to the saturation property. A mathematical model how to assess the maximum possible leakage of radioactive materials through the cladding of fuel elements due to diffusion processes during the long-term storage of spent nuclear fuel is proposed.
This model is presented in the form of a system of differential equations with initial and boundary conditions that make it possible to determine the concentration of radioactive materials inside the fuel cladding taking into account radioactive decay, the concentration of radioactive material in the fuel cladding material during diffusion, and the concentration of radioactive material in the volume outside the fuel cladding. The solution of differential equations, which represent a mathematical model of the leakage of radioactive materials through the cladding of a fuel element during the long-term dry storage of spent nuclear fuel, was performed using the straight line method. A qualitative analysis of the patterns of leakage of radioactive materials was carried out and the influence of the initial concentration and half-life of radioactive materials was established. A quantitative analysis of possible leakages of radioactive material through the cladding of a fuel element during the long-term storage of spent nuclear fuel has been carried out on the basis of computer modeling using specially developed original software.
