## 5 Results and Discussion
### GBC-68 Cask Criticality Analysis  
#### 5.2.1 The Impact of the Refuelling Scenario on Cask Criticality  
The first part of the research outlined the effect of the different shuffling procedures on final burnup distribution of the BWR fuel assemblies discharged from a reactor core [22]. This section investigates the shuffling procedure's impact on the cask reactivity. The full-core calculations were performed for five refuelling scenarios SP_A, SP_B, SP_C, SP_D and SP_E (see Section 4.1), four cycles of reactor operation and GE14 fuel assembly. The criticality analysis of the GBC-storage cask was carried out for two loads from the obtained burnup distributions:  
* 68 fuel assemblies from the centre (L\({}_{68}\));
* 5% least burnt fuel assemblies (L\({}_{5\%\text{L}}\)). L\({}_{68}\) and L\({}_{5\%\text{L}}\) cask loads are of interest for the criticality analysis since the first one represents the typical cask load since it contains FAs from the burnup distribution centre. The second is the worst-case load as it has the FAs with the lowest burnup and, thus, most critical. The different cooling times were introduced to estimate the effect of the fuel assemblies' storage time in the cooling pond on the later cask criticality. Five years is the minimum cooling time in the US before spent fuel can be moved to further transport or dry storage [33]. However, shorter times can be permitted in other countries such as Germany with a nine months minimum storage time before loading and an average storage time of approximately three years [34]. Here, five-year cooling time was considered a reference, with one- and ten-year lower and upper boundaries. Figure 7 represents the effective multiplication factor as a function of cooling time for the GBC-68 cask filled with BWR GE14 FA from L\({}_{68}\) and L\({}_{5\%\text{L}}\) loads from the five considered loading patterns. The average line provides with the averaged for the five refuelling scenarios k\({}_{\text{eff}}\) for the considered cask load. In the case of 68 typically burnt FAs (Figure 7a), the k\({}_{\text{eff}}\) deviates at a maximum of 0.7% at the highest cooling time ten years compared to the average for five distributions. This demonstrates that the average fuel burnup of the different refuelling scenarios exhibits limited variation, with slight advantages for the SP_A and a slight disadvantage for the SP_B which coincides with the conclusions from [22], where the maximum difference between average discharged burnups of different loading patterns were 1 GWd/tU. For the 5% least burnt FAs (Figure 7b) the difference is significantly higher, up to 3.7%. It means that the choice of shuffling procedure mainly affects the cask's criticality for the worst-case study (L\({}_{5\%\text{L}}\) load) compared to the typical fuel assemblies (L\({}_{68}\) load). These differences can be explained by the significantly lower than average burnups of the least burnt fuel assemblies in some of the refuelling patterns, for example, SP_C [22]. Another reason for the wider k\({}_{\text{eff}}\) spread for L\({}_{5\%\text{L}}\) load is that the FAs from L\({}_{68}\) load see closer axial coolant density profiles for different refuelling scenarios (Figure 8a). Hence, it does not affect the cask criticality as much as in the case of L\({}_{5\%\text{L}}\) load where the profiles are more spread (Figure 8b). Since fuel assemblies see different operational conditions under various refuelling scenarios, their final axial burnup profiles will also vary. The difference between coolant density profiles can also explain why some scenarios with higher burnup values (Table 3) have higher k\({}_{\text{eff}}\). The general trend is that fuel with higher burnup has lower criticality. Ref. [12] highlighted that the criticality at the upper layers of some BWR fuel assembly at their average discharge burnups increases with lowering the coolant density.