Mechanistic Two Stage Fission Gas Release Model

In this study, a mechanistic two stages model is developed which analytically simulates the two-step diffusion processes, grain lattice diffusion and grain boundary diffusion, coupled with the bubbles trap/resolution. Mathematical manipulation reveals that the release at high burn-up depend on the ratio of the diffusivities in the both processes, i.e., α ≅ D_v^eff/D_gb^eff where D_v^eff and D_gb^eff are effective volume and grain boundary diffusion coefficients, respectively. Thus, the ratio α is incorporated in the time-dependent third kind boundary condition at the equivalent grain surface. This model brings forth analytical solutions of the fractional release which are identical to that of either ANS5.4 or modified ANS5.4 model when α goes to the infinity. It turns out that this model describes the release behavior well in the high burn-up fuel and puts out a comparable prediction to the solution of FRAPCON-3 model under the same condition. It is also demonstrated that the new factor α not only ease the computational treatment for the high burn-up fuel performance evaluation, but also enables us to possibly separate the burn-up enhancement from the diffusion coefficients and to easily simulate the bubble-related phenomena in the grain boundary.