## 4 Model Application
Gas atoms are not generated during LWR transient operation. The gas atoms begin to release when they reach the grain boundaries. The release of gas atoms lasts for 40,000 h. Figure 9 reflects that the FGR fraction drops with increasing linear heat generation rates, and the relationship is same as the above models between the FGR fraction and grain size. A small difference exists between this model and [PERSON]'s model, but the greatest error was restricted within 5%, and thus, the results are convincing. Most of the error was within 5%, indicating that our model can provide reasonable results. Figure 6: Gas release fraction versus time for constant gas production with different grain sizes in this model and [PERSON]’s model [49] ([PERSON] et al., 2008). Figure 8: Gas release fraction versus time without gas production under different temperature conditions in this model, [PERSON]’s model, and experiments [50]. Figure 7: Gas release fraction versus time for constant gas production with different grain sizes in this model and [PERSON]’s model [5]. Figure 9: Gas release fraction versus time without gas production with different grain sizes and liner heat rates in this model and [PERSON]’s model [51]. In order to investigate the sensitivity of fission gas release for diffusion coefficient, all parameters and conditions in [PERSON]'s model were held constant except for the variation in the diffusion coefficient. Figure 10 demonstrates that the FGR fraction increases with a rising diffusion coefficient. The results of \(a=10\) um, \(P^{\prime}=70\) kW/m under one diffusion coefficient and 30 MWd/kgU, \(a=20\) um, \(P^{\prime}=60\) kW/m under half of diffusion coefficient and 30 MWd/kgU, and \(a=20\) um under all diffusion coefficients and liner heat rates in this model are close to [PERSON]'s model. While some differences exist between this model and [PERSON]'s model, the overall trend is consistent. Therefore, the outcomes are effective. The isothermal fission gas release was modeled using the following parameters [3]: \(T=1300^{\circ}\)C, \(P^{\prime}=38\) kW/m, \(D=1.6173\times 10^{-18}\) m\({}^{2}\)/s, and \(t=5\) h, and the irradiation range was approximately 10 GWd/tUO\({}_{2}\). There were three radiuses for fission gas release, 5 um, 7.5 um, and 11.5 um. The second case is applied in this situation. The initial concentration of gas atoms is zero on the grain boundary and remains finite in the grain center. Gas atoms are not generated during LWR transient operation. The gas atoms begin to release when they reach the grain boundaries. The release of gas atoms lasts for 3000 h. As shown in Figure 11, aside from the 5 um case, the results in both of these two models are similar. The effect of grain size on the FGR fraction also corresponds to above models' results. Figure 11: Gas release fraction versus time without constant gas production under different grain sizes in this model and [PERSON]’s model [3]. Figure 10: Gas release fraction versus time without gas production under different diffusion coefficients with unique grain sizes in this model and [PERSON]’s model [51]. Fission gas release in oxide fuel was analyzed using BISON and TRANSURANUS with the following parameters [14]: \(T=1673\) K, \(P^{\prime}=41.3\) kW/m, \(D=7.5595\times 10^{-18}\) m\({}^{2}\)/s, \(t=10\) h, and the irradiation range was approximately 46 GWd/tU. The radius was 4.68 \(\upmu\)m. This condition suits in the second case. The initial concentration of gas atoms is zero on the grain boundary and remains finite on the grain center. Gas atoms are not generated during LWR transient operation. The gas atoms begin to release when they reach the grain boundaries. The release of gas atoms lasts for 80 h. As shown in Figure 12, the time in [PERSON]'s experiments is 80 h, but in this model, the time 10 h. The final values of the FGR fraction are close in these two models.