# Burnup Credit Evaluation for BWR Spent Fuel from Full Core Calculations
## 4 Full-Core Modelling  
### Cross-Section Preparation  
Nodal core simulators require homogenised cross-sections and diffusion data for each unique layer of the FA and the radial and axial reflectors at the different state points of the reactor operation. The diffusion data include homogenised multi-group or two-group cross-section sets, assembly discontinuity factors (ADFs), scattering tables, etc. [34]. For this purpose, a case matrix containing state points that comprehensively describe the FA and reflector design for the envisaged operational envelope was created [5]. It covers the possible range of depletion steps and changes in the operational parameters, such as moderator density, fuel temperature or the control rods' movements. Lattice codes produce the diffusion data by performing burnup and branch calculations in the form of a matrix. The nodal code then interpolates the unknown operational conditions lying between two branches or burnup steps or extrapolates them based on the available data if they are outside the set. The latter procedure can lead to incorrect results; thus, it is vital to cover the whole expected range of operating conditions while creating the case matrix [34]. Cross-section sets for the FA and reflector were prepared using the Polaris module of SCALE 6.2 [18]. The ENDF/B-VII.1 data library with 56 energy groups' structures was used in the calculations since it is optimised for LWR analysis [35] and significantly reduces the computational time in comparison with 252-energy group library. Cross-sections were homogenised for two energy groups as in a standard approach for nodal LWR modelling [5]. Post-processing was performed on Polaris lattice physics archive for use with DYN3D code. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Average heat flux & 430 kW/m\({}^{2}\) \\ Maximum heat flux & 1365 kW/m\({}^{2}\) \\ Peak fuel pellet temperature throughout the cycle & 1760 \({}^{\circ}\)C \\ Core average void fraction & 0.43 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Thermal hydraulic parameters at rated conditions [33]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Outlet reactor pressure, MPa & 7.171 \\ Inlet coolant temperature, \({}^{\circ}\)C & 278.3 \\ Core mass flow rate, kg/s & 14,502 \\ Thermal output, MWth & 3926 \\ Number of fuel assemblies & 872 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Design parameters for ABWR reactor core [32]. Figure 3 shows the computational models of dominant and vanished lattices in Polaris. The meshing is standard for the BWR fuel type provided by the code [18]. The fuel assemblies in the BWR reactor core are surrounded by the reflector, which can be water, a steam-water mixture or a mixture of water and structural material. The reflector model in the lattice code is typically developed by adding a reflector region to the east boundary of the typical FA configuration. This study considered three reflector types located at the bottom, side and top of the reactor core. The minimum size of the reflector is typically the width of the one FA [34]. For the current study, the bottom and top reflectors were modelled as two fuel assemblies in width, while the radial (side) reflector size was estimated by the equation from [34]:  
\[H=\frac{W^{3}}{6R^{2}\Big{(}2\text{arcsin}\Big{[}\frac{W}{2R}\Big{]}-\sin \Big{[}2\text{arcsin}\Big{[}\frac{W}{2R}\Big{]}\Big{]}\Big{)}} \tag{1}\]  
where  
\(H\) is the average distance from the FA bundle to the reactor pressure vessel (RPV);  
\(W\) is the width of the flat part of the FA bundle closed to the RPV;  
\(R\) is the RPV radius. The schematic reflector model is shown in Figure 4. The bottom reflector material is a mixture of stainless steel and water and the radial reflector consists of water, while the top, from the low-density water imitating the steam-water mixture. Figure 4: Reflector model for the cross-section preparation.