sensitivity.tex

Sensitivity analysis identifies how and the extent to which variations 
in model input parameters affect select performance 
metrics of the fuel cycle. Additionally, it reveals the combined effect 
of varying multiple parameters on 
an output metric. This information can then be used to design 
an optimized transition scenario by identifying which input parameters 
will affect the results the most, and how these parameters should be 
changed to obtain desired results (e.g., minimizing \gls{HALEU} requirements
of a transition). 

\section{Methodology}
We performed sensitivity analysis on Scenario 7 (once-through fuel cycle 
transition to Xe-100, VOYGR, and \gls{MMR} with a no growth energy demand) 
using a coupling between \Cyclus with Dakota \cite{adams_dakota_2021}, an 
open-source code developed by \acrfull{SNL} for uncertainty quantification, 
sensitivity analysis, and optimization. This coupling mirrors  
the scripts in the \texttt{dcwrapper} GitHub repository 
\cite{chee_arfcdcwrapper_2019}. We performed three different types 
of sensitivity analysis: \acrfull{OAT}, synergistic, 
and global. \gls{OAT} analysis varies a single input parameter to 
investigate the effect of each parameter individually. In the context of 
this work, synergistic 
analysis varies two input parameters at once to investigate how the 
interaction of the two parameters affects the results. Finally, the global 
sensitivity
analysis varies more than two input parameters to provide a holistic 
view of how multiple parameters interact and affect the output metrics. 
For this work, we considered variations in the transition 
start time, the build share of each type of advanced reactor, 
the \gls{LWR} lifetimes, and the discharge burnup of fuel from the 
\gls{HALEU}-fueled reactors. 

The transition start time ranges from January 
2025 to January 2040 in three-month intervals, but the same energy demand 
is specified for all perturbations (87.20 GWe-yr). We consider this parameter 
to provide a relaxation of the aggressive 2025 transition start date 
used in the transition analysis of Chapters \ref{ch:once_through_results} and
\ref{ch:recycle_results}.

We consider three 
iterations of the build share, once for each advanced reactor, with 
build share percentages ranging from 0-50\% 
in increments of 5\%. To account for the build share of an advanced reactor,
we adjusted the deployment scheme described in Section \ref{sec:once-through-methods}.
Instead of the reactor type with the largest power output 
deployed first, the reactor with the specified build share is deployed first 
until the build share is met. Then the remaining two advanced reactor types are 
deployed in the manner described in Section \ref{sec:once-through-methods},
with the larger of the two remaining reactors preferentially deployed and 
the smaller reactor deployed last to meet or exceed the power demand. Figure 
\ref{fig:build-share-deploy} illustrates how we applied this deployment 
scheme to meet a fictional demand of 530 MWe and a VOYGR build share of 
50\%. We vary this parameter of the transition because of the large effect 
of the advanced reactors deployed in each of the transition scenarios. 
Unless an advanced reactor build share is specified, this analysis 
applies the same advanced reactor deployment schedule as Scenario 7
(see Section \ref{sec:nogrowth_reactors}).

\begin{figure}
    \centering 
    \includegraphics[scale=0.5, trim=50 100 100 0,clip]{VOYGR_build_share.pdf}
    \caption{Demonstration of the adjusted advanced reactor deployment 
    scheme to meet a demand of 530 MWe and a VOYGR build share of 
    50\%.}
    \label{fig:build-share-deploy}
\end{figure}

The \gls{LWR} lifetimes are varied based 
on the percent of the fleet that operate for 80 years. This 
variable varies between 0-50\%, in increments of 5\%, of the \gls{LWR} 
fleet operating for 80 
years, while the other \glspl{LWR} operate for 60 years. This input 
parameter reflects the effects of different numbers of \glspl{LWR} 
receiving license extensions to 80 years. Various utilities are exploring 
and pursuing license extensions for \glspl{LWR}, so including this parameter 
reflects this occurrence. The 
\glspl{LWR} do not all start operation at the same time, so the 
selection of the \glspl{LWR} that operate for 80 years affects the results, 
even if the number is the same. Therefore, reactors are prioritized based 
on their power outputs for the lifetime extensions, reflecting the greater likelihood of 
larger units receiving a license extension. Previous sensitivity analysis of 
fuel cycle transitions considered the impact of the transition start time 
and the \gls{LWR} lifetimes \cite{chee_sensitivity_2019,feng_sensitivity_2020},
which provides some basis for why these input parameters were selected for this 
work.

Finally, we varied the discharge burnup of the two \gls{HALEU}-fueled 
reactors in this work (the Xe-100 and \gls{MMR}) because these two reactors 
are reaching burnup levels larger than the \gls{NRC}-approved 62 MWd/kgHM 
\cite{noauthor_higher_2023}. Therefore, it is possible that these 
reactors would need to be operated under different conditions until
higher burnups are approved by the \gls{NRC}.
Therefore, inclusion of this variable explores the impact 
on resource needs if these reactors are prohibited from achieving 
their 
reported burnup values. This analysis is not performed for the VOYGR because this 
design aims to achieve a burnup that is within the \gls{NRC} limit. 

To vary the burnup of the Xe-100, we considered two difference approaches. The 
first approach was to vary the number of passes through the core for each pebble 
while keeping the length of each pass and the total mass of uranium 
in the core constant (i.e., reducing the number of batches). Varying the 
number of passes between one and six 
results in discharge burnup values of 28, 56, 84, 112, 140, and 168 MWd/kgU, 
using Eq. \ref{eq:fuel_mass}. This approach provides a coarse grid 
for the burnup values that reflects possible changes to meet current 
\gls{NRC} regulations. The second approach varies the length 
of each pass by one month, while keeping the number of passes and the 
total mass of uranium 
constant. This approach provides a more fine grid around the declared 
burnup value, reflecting potential small variations in reactor operation. 
The second approach results in burnup values of 151 and 185 MWd/kgU, 
which are about $\pm$10\% of the stated discharge burnup of 168 MWd/kgU. 

To vary the \gls{MMR} burnup, we varied the cycle time (and thus lifetime) of 
the reactor while the total mass of uranium was held constant. 
Cycle times of 10, 15, and 20 years were considered, resulting in burnup 
values of 41, 62, and 82 MWd/kgU. Additionally, the lifetime was varied to 
result in burnup values $\pm$10\% and $\pm$5\% around the stated burnup of 
82 MWd/kg, resulting in burnup values of 74, 78, 86, and 90 MWd/kgU. 

The sensitivity analysis focuses on the effects of these input parameters 
on the following metrics: the amount of waste generated that 
must be sent to a repository (\gls{UNF} mass), the mass of enriched uranium, 
the mass of \gls{HALEU},
the amount of \gls{SWU} capacity required to produce all enriched uranium, the 
\gls{SWU} capacity required to produce \gls{HALEU}, and the feed uranium 
required to produce \gls{HALEU}. We considered each of these metrics 
within the transition analysis, allowing for comparison between Chapters 
\ref{ch:once_through_results}, \ref{ch:recycle_results}, and this chapter. 
We compare each metric based on the cumulative sum required, starting 
at the transition start time. 

\input{oat.tex}

\input{synergistic_text.tex}

\input{global.tex}