## 4 Model Application  
By comparing the results of the above cases between this model and [PERSON]'s model, we have shown that our model can predict well the above the cases. In this section, the parameters of other models will be incorporated into this model. The validated scenarios in the model primarily consist aforementioned two cases. Then, the results will be compared and analyzed between this study and other models' processing to validate its effectiveness. Fission gas release for uranium dioxide fuel was modeled using a new mechanistic and engineering approach [49]. The parameters \(T\) = 1050 \({}^{\circ}\)C, \(P^{\prime}\) = 18 kW/m, \(D\) = 5.8510 \(\times\) 10\({}^{-20}\) m\({}^{2}\)/s, and \(t\) = 3000 h were selected, and the irradiation range was approximately 70 GWd/tU. This situation is close to the first case. Namely, the initial concentration of gas atoms both on the grain center and boundary are zero. The gas atoms are generated constantly and then diffuse towards the grain boundaries during LWR steady-state operation. The gas atoms begin to release when they reach the grain boundaries. The release of gas atoms lasts for 3000 h. There are three radiuses for fission gas release: 10 \(\upmu\)m, 20 \(\upmu\)m and 40 \(\upmu\)m. Figure 6 shows that the results are similar in these  
Figure 4: Gas release fraction versus time without gas production [44]. Figure 5: Gas release fraction versus time for constant gas production [44]. two models. Furthermore, this figure demonstrates that the FGR fraction decreases with increasing grain size. Coupling with the FALCON code, fission gas release was modeled using uranium dioxide fuel [5]. The conditions were as follows: \(T\) = 500 \({}^{\circ}\)C, \(P^{\prime}\) = 20 kW/m, \(D\) = 4.0312 \(\times\) 10\({}^{-21}\) m\({}^{2}\)/s, and \(t\) = 40,000 h, the irradiation range was approximately 75 GWd/tU. The first case is chosen here. The initial concentration of gas atoms both on the grain center and the boundary are zero. Gas atoms are generated constantly and then diffuse towards the grain boundaries during LWR steady-state operation. The gas atoms begin to release when they reach the grain boundaries. The release of gas atoms lasts 40,000 h. There are two radiuses for fission gas release: 9 \(\upmu\)m and 51 \(\upmu\)m. As shown in Figure 7, the results of this model and [PERSON]'s model are not fitted as well. This may be related to the fact that the FGR fraction is sensitive to the grain size. Another case of the FGR was reported in oxide fuels for sodium fast reactors [50]. Its parameters were \(T\) = 1250 K, \(P^{\prime}\) = 42 kW/m, \(D\) = 5.0283 \(\times\) 10\({}^{-20}\) m\({}^{2}\)/s, and \(t\) = 40,000 h, and the burnup was approximately 12 GWd/tU. The radius was 10 \(\upmu\)m for fission gas release. This situation is similar to 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 the reach grain boundaries. The release of gas atoms lasts for 40,000 h. Figure 8 indicates that the FGR fraction rises with increasing temperature. The results are slightly different between this model and [PERSON]'s model, and the difference of results is within 15%. Fission product gas release with microstructure dependence has been modeled for UO\({}_{2}\) fuel [51]. The main parameters were as follows: \(T\) = 675 K, \(P^{\prime}\) = 50 kW/m for \(D\) = 6.3283 \(\times\) 10\({}^{-21}\) m\({}^{2}\)/s, \(P^{\prime}\) = 60 kW/m for \(D\) = 6.9323 \(\times\) 10\({}^{-21}\) m\({}^{2}\)/s, \(P^{\prime}\) = 70 kW/m for \(D\) = 7.4877 \(\times\) 10\({}^{-21}\) m\({}^{2}\)/s, and \(t\) = 40,000 h, and the burnup was approximately 30 MWd/kgU. There were three radiuses for fission gas release: 10 \(\upmu\)m, 20 \(\upmu\)m and 50 \(\upmu\)m,. This situation corresponds to the second case. The initial concentration of gas atoms is zero on the grain boundary and remains finite on the grain center.