# Burnup Credit Evaluation for BWR Spent Fuel from Full Core Calculations
## 5 Results and Discussion
### Burnup Credit Analysis for the Realistic BWR FA Model
#### 5.2.2 The Burnup Credit of the Core  
In this section, the authors aim to estimate the possible credit from the reactivity reduction of the irradiated BWR fuel assembly based on the realistic FA model M3 combined with the number of fuel assemblies discharged at the burnups of the least and most optimal burnup distributions SP_C_new and SP_A_new, respectively. This approach will be called \"burnup credit of the core\". It should be noted that the criticality estimation of the FA based on M3 model does not reflect on its position in the reactor core (see description given above) since M3 simulates a single FA in the reflective radial boundary conditions. The here suggested approach for BUC analysis is based on full core modelling and, hence, is significantly more time-consuming and requires more computational power than the lattice approach or the M3 approach. However, it is crucial to create an understating about the gain which could be harvested in the case of a higher investment into the modelling or maybe just the use of fuel management data which would be available for most of the operating nuclear power plants nowadays. For this purpose, the authors developed the concept of the normalised reactivity gain from applying the BUC approach, based on the discharged burnup distributions SP_C_new and SP_A_new, to the M3 FA model in comparison with the existing BUC approaches. The normalised reactivity gain was estimated as:  
\[\rho_{i}^{j}=\frac{\left(k_{j}-k_{i}\right)}{k_{j}k_{i}}.\frac{n_{i}}{N}\cdot 1 0^{5} \tag{2}\]  
where  
\(i\) is the burnup bin number from the discharged burnup distribution;  
\(j\) is one of the approaches, fresh fuel, peak reactivity or peak reactivity, of the realistic FA model;  
\(\rho_{i}^{j}\) is the normalised reactivity gain between the FA criticality at the bin \(i\) and the FA criticality at the approach \(j\);  
\(k_{j}\) is the FA k\({}_{\text{eff}}\) at the approach \(j\);  
\(k_{i}\) is the FA k\({}_{\text{eff}}\) at the bin \(i\) of the considered discharged fuel burnup distribution;  
\(n_{i}\) is the number of FAs in the bin \(i\);  
\(N\) is full number of FAs in the distribution. The normalised reactivity gain shows how much reactivity (in the form of the delta to the more approximate method) is gained by the fuel assemblies from a specific burnup bin of the considered burnup distribution. Thus, the introduced parameter correlates the gain from the optimisation of the loading pattern (achieving higher FA burnup) with the optimisation of the modelling and simulation (return on the investment in the modelling). The results of the analysis are summarised in Figure 11. At the SP_C_new distribution, the 35 GWd/tU and 40 GWd/tU bins have the same number of the FAs as at 60 GWd/tU. However, the normalised reactivity gain from the last bin is higher. Thus, the high burnup bin at 60 GWd/tU contributes over proportionally. In the case of the SP_A_new distribution, the gain from the first two bins is close to the gain from the last bin (the number of the FAs are equal for both sets of bins). For both cases, the reactivity gain is almost negligible for 5% of the least burnt fuel assemblies in comparison to the FAs with burnups close to average and 5% of the highest burnt FAs. Here, the value could even change the sign in the case the fuel assemblies have not achieved the estimated peak value. Furthermore, the normalised reactivity gain for the optimal shuffling procedure (SP_A_new) is approximately three times higher than for the least optimal (SP_C_new) near the averaged discharged burnups. Table 7 represents the reactivity gain over the whole reactor core for the BUC of the core approach in comparison with the fresh fuel, the peak reactivity and the peak reactivity of the realistic FA model approaches. It is seen that the reactivity gain is approximately 1120 pcm higher for the SP_A_new burnup distribution than for the SP_C_new one.