\section{Comparison of fuel assembly model with respect to equilibrium core output}
This section is devoted to compare the nuclide inventory obtained in the fuel assembly simulations with the output of the equilibrium core. The models investigated are those presented in this chapter, the comparison is carried out between the nuclide vector after the first irradiation cycle (at higher power) in the FA model and the fuel irradiated in position 101 (central position) in the core.
\subsection{2D fuel assembly model}
The deviations of the 2D fuel assembly with full reflective boundary conditions are presented in Fig. \ref{fig:discr_core2d}. 
\begin{figure}[h]
\centering
\includegraphics[width=0.85\textwidth]{images/plots/FA/2D_fa/discr.png}
\caption{Comparison of the \acrshort{EoC} concentration in a 2D fuel assembly model with full reflective boundaries to the results obtained from a core simulation.}
\label{fig:discr_core2d}
\end{figure}
The models show good agreement for most the fission products of interest and plutonium isotopes. Discrepancies arise in minor actinides and some specific FPs, such as $^{91}$Kr ( $t_{\frac{1}{2}} = $ 8.57 s), $^{129m}$Te ( $t_{\frac{1}{2}} = $ 33.6 d), $^{134}$Cs.
The production of all minor actinides is overestimated in the fuel assembly as a consequence of the spectral shift discussed in Sect. \ref{sp_shift}. They all comes from successive captures from plutonium and the capture reactions rate are enhanced as a consequence of softer spectrum. This phenomenon brings to an overestimation up to 40\% in $^{246}$Cm.\\
As indicated in the previous section, one of the main limitations resides in the difference of the neutron spectrum obtained in the FA model respect to the fuel assembly irradiated in the core. A possible solution was investigated, i.e. varying the boundary conditions to modulate the spectrum. Fig. \ref{fig:discr_alb} shows the comparison among the FA model with partial reflective boundary conditions and the core on the nuclide inventory at \acrshort{EoC}. An opposite behaviour is encountered with respect to the previous case, showing that the nuclide vector is strongly affected by the partially reflective boundary condition in this case study.
\begin{figure}[h]
\centering
\includegraphics[width=0.85\textwidth]{images/plots/FA/2D_fa/discr_albedo.png}
\caption{Comparison of the EoC concentration in a 2D fuel assembly model with partial reflective boundary conditions to the results obtained from a core simulation.}
\label{fig:discr_alb}
\end{figure}
The albedo parameter used for the simulation was the same discussed before, the one that guarantees to obtain the same $k_{eff}$ of the equilibrium core.
This choice is arbitrary and does not reflect the real neutron leakage from the fuel assembly analysed but it points out where the discrepancy comes from.\\

As previously stated, the purpose of the fuel assembly model is not to be fully representative of the fuel assembly irradiated in the core in the best estimate results but to provide a surrogate model to perform uncertainty quantification. The scope of this work in this regard is limited to assess and try to explain the discrepancies obtained.

\subsection{3D fuel assembly model}
The analysis of nuclide vector obtained in the 3D fuel assembly simulation is carried out in this section. The comparison with the results of the 2D model are presented in Fig. \ref{fig:discr3d}.  
\begin{figure}[h]
  \centering
    \begin{minipage}{0.9\textwidth}
        \includegraphics[width=\linewidth]{images/plots/FA/3D_fa/discr_2D_90.png} 
    \end{minipage}
\caption{Comparison of EoC nuclides concentration in 3D FA model with respect to the results of the  2D fuel assembly model. Bright and dull bars are referred to the model with and without axial depletion respectively.}
\label{fig:discr3d}
\end{figure}

$^{134}$Cs shows the largest discrepancy around 6\% among all the nuclides investigated. Other concerning fission products show discrepancies lower than 1\%. 
Minor actinides are in agreement with 2D model if the axial division of the fuel material is not taken into account, as highlighted by the dull bars in the plot.
% \\
% The discrepancies of the 3D FA with respect to the core are basically the same of the 2D one, Fig. \ref{fig:discr_core2d} for the nuclides considered (those showing non-negligible deviations among the observables). The only deviation increase is seen for $^{134}$Cs, from 4\% to 10\%. 

