Simulation of isothermal fission gas release An analytical solution

Abstract An analytical version of a previous diffusion model representing fission gas release during isothermal irradiation of UO 2 nuclear fuel is presented. The previous numerical version was successfully applied to a variety of experiments. The present model, although based on more restrictive assumptions, gives a quick but sufficiently accurate estimation, useful to predict experiments or more detailed calculations. The main new hypotheses are: constant fuel grain radius, constant gas generation rate and constant grain boundary gas content. The latter is met at the final stage of fuel irradiation, after grain boundary saturation, and partially met at the beginning of irradiation, when the grain boundary is nearly empty. Two analytical solutions are obtained and conveniently matched, yielding a unique solution representing the whole process. The difference between the analytical and numerical results for the fractional release is appreciable only near the matching. It is lower than 1% over 93% of the process duration for all the temperatures tested, ranging from 1250 to 2000 K and has no significant effect on the results at the end of life.