# 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  
Lattice codes simulate fuel assembly in an infinite 2D geometry, typically with one reference water density, an estimation of the average fuel temperature and the use of a constant power approximation over burnup. However, in a real reactor core, the assembly has a limited size, surrounded by fuel assemblies from other cycles and by a reflector at the top and bottom of the fuel assembly. At the same time, the FA power varies due to burnup processes as only the reactor power is kept constant. Thus, the peak assembly power changes axially during the burnup, which is opposite to the constant power approach of the lattice calculations. At the same time, the fuel assembly power is balanced \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Case** & \(\Delta_{\text{AVRG}}\) & \(\Delta_{5\%\text{L}}\) & \(\Delta_{5\%\text{H}}\) & \(\Delta_{68}\) & \(\Delta_{\text{BR}}\) \\ \hline SP\_A\_new & 0 & 0 & 0 & 0 & 0 \\ SP\_A\_old & 0.07 & \(-\)0.2 & 0.9 & 0.08 & 3 \\ SP\_C\_new & \(-\)1 & \(-\)8.9 & 4.1 & \(-\)0.3 & 15.3 \\ SP\_C\_old & \(-\)1 & \(-\)8.6 & 5 & \(-\)0.5 & 16.4 \\ SP\_B & \(-\)0.4 & 0.1 & 0.9 & \(-\)0.6 & 3.1 \\ SP\_D & \(-\)0.7 & \(-\)1.2 & 2.4 & \(-\)0.8 & 5.5 \\ SP\_E & \(-\)0.3 & 0.4 & 0.5 & \(-\)0.4 & 3.1 \\ \hline \hline \end{tabular}  
* \(\Delta_{j}=B_{ij}-B_{SP\_A\_new;j}\), where \(j\) is the index of the burnup distribution parameter (B\({}_{\text{AVRG}}\), B\({}_{5\%\text{L}}\), B\({}_{5\%\text{H}}\), B\({}_{68}\) or BR); \(i\) is one of the considered cases; \(B_{RP\_A\_new;j}\) is the value of the burnup distribution parameter with index \(j\) for the SP_A_new case; \(j\) is the value of the burnup distribution parameter with index \(j\) for the case \(i\).  
\end{table} 
Table 6: Analysis of the differences in the burnup distribution parameters in comparison with the SP_A_new case as a reference (\(\Delta_{j}\) *, GWd/tU). with the other FAs through the core power. In the current section, the authors aim to determine how the transition from the lattice computations (radial infinite medium approach) to a more realistic assembly model in a core simulator--a 3D approach with realistic water density distribution and fuel temperatures, but still employing reflective boundary conditions in the radial direction--affects the function of k\({}_{\text{eff}}\) over burnup and to estimate the impact of the given 3D approach on the burnup credit. For this purpose, the following models based on the BWR GE14 assembly design (Figure 1) were analysed:  
* A 2D lattice model of the dominant layer (DOM) without burnable poison or in terms of the burnup credit, the so-called \"fresh fuel\" approach, which is referred to as Model 1 (M1). * A 2D lattice model of the DOM layer with burnable poison, or the \"peak reactivity\" approach (M2). * A 3D nodal model of the realistic FA with DOM and vanished layers (VAN), natural uranium blankets, non-uniform axial coolant density distribution and the reflectors on the fuel assembly ends (M3). The boundary conditions are set to reflective in the radial direction and vacuum in the axial. In addition, two separate 3D nodal models of the FA, containing DOM and VAN layers only, were created to estimate the contribution of each layer to the total criticality of the FA. The \"fresh fuel\" approach is considered as the most traditional method of criticality safety analysis with respect to analysing spent fuel storage systems, which implies that the system is loaded with unirradiated fuel without burnable poison. Due to today's widespread use of fuel assemblies containing burnable poisons, the \"peak reactivity\" approach has been adopted by the nuclear community [12]. As burnable absorber depletes faster than uranium during fuel irradiation, this leads to a reduction in the initial excess reactivity at the beginning of assembly life, with further rise of the fuel assembly criticality up to a maximum level referred to as the peak reactivity, followed by a further decline.