# Burnup Credit Evaluation for BWR Spent Fuel from Full Core Calculations
## 5 Results and Discussion
### Burnup Credit Analysis for the Realistic BWR FA Model
#### 5.2.1 Criticality Estimation for Single BWR FA
The given method assumes that the fuel in the considered system is at its peak reactivity burnup when loaded. This approach is less conservative than the fresh fuel approach which is the most conservative for criticality safety analysis [26]. As will be shown later, the dominant layer mainly contributes to the criticality of the current BWR assembly and, thus, it was chosen as the reference layer for the M1 and M2 models. The coolant density in lattice calculations was set as an average for the DOM layer (0.6 g/cm\({}^{3}\)). The estimation is based on the averaged coolant density profile for various BWR fuel assemblies described in [31]. For the 3D nodal model M3, DYN3D calculates coolant density distribution based on the channel model as well as other thermal-hydraulics and thermo-dynamics parameters of the fuel assembly at each burnup step. Figure 9 depicts the comparison of the depletion analysis for the three different models described above. The results show that the peak reactivity occurs earlier in the M3 case, when the fuel assembly is modelled under representative operational conditions, in comparison with the lattice approach M2. Furthermore, the assembly criticality at the peak is approximately 5% lower in the M3 case. A similar effect was observed in the study [16], where authors performed depletion analysis for 2D and 3D models of the BWR fuel assembly with uniform and non-uniform axial coolant density distributions. However, the investigation was limited to the peak reactivity area, while the current analysis covers the criticality evolution over the whole targeted burnups of the fuel assembly. The analysis of the M3 burnup curve beyond peak reactivity reveals a second increase in criticality near 30 GWd/tU burnup. Furthermore, after approximately 45 GWd/tU, the M3 curve has a steady negative bias with M1 and M2 cases. It occurs due to the leakage boundary conditions applied to the top and bottom. The power profile evaluation for the realistic FA model M3 at four different burnup stages is represented in Figure 10. The power distribution was normalised at the maximum power value observed at the 30 GWd/tU burnup step. It is seen that at the initial burnups steps, for example, 0 and 10 GWd/tU, the peak power is located at the bottom (dominant) FA layer. As the fissile material depletes and gadolinium burns in this layer, the power shifts towards the top (vanished) layer where the fuel is fresher and still has a higher fissile content, as seen from Figure 10 (30 GWd/tU burnup stage). This results in the formation of the second reactivity peak on the M3 burnup curve (Figure 9)since the fissile depletion and the gadolinium burning are now accelerated in the top part of the fuel assembly due to the increased power. Finally, when the burnable poison is completely depleted and the fissile content in the central parts of the fuel assembly is significantly reduced, the power distribution peaks at the least burnt parts of the fuel assembly, the very top and bottom (50 GWd/tU burnup stage). Overall, the dominant layer plays a significant role in power production, defining the reactivity of the whole FA. This is also seen from the comparison of the M3 and the dominant layer criticality curves (Figure 9). The curves mostly coincide on the whole range of the considered burnups, except in the interval between 35 to 45 GWd/tU where the vanished layer is prevalent; see the power curve in Figure 10.  
Figure 10: Power profile distribution for different burnups of the BWR assembly (M3 case). Figure 9: k\({}_{\text{eff}}\) as a function of burnup for the discussed 2D lattice models and 3D nodal code model of BWR assembly. Since the M3 approach showed a substantial decrease in criticality at the peak reactivity in comparison with M2, it can be considered as an alternative approach to evaluate the burnup credit.