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synergistic_text.tex
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\section{Synergistic}\label{sec:synergistic}
The synergistic analysis in this work varied two parameters at a time to
investigate some of the combined effects of the input parameters. Synergistic
sensitivity analysis helps to identify if the combined effect of two parameters
has a greater impact on the metrics that when varying a single parameter.
It also helps to compare the effect of two different input parameters.
We ran synergistic
analysis on all combinations of two input parameters studied in the \gls{OAT}
analysis, except combinations of two reactor build shares to limit
the scope of this work. The
results presented here are only a subset of the analysis performed,
with the remaining results in Appendix \ref{app:s7_synergistic}.
\subsection{LWR lifetime and VOYGR build share}
When the percent of \glspl{LWR} operating for 80 years and the VOYGR build share
are varied, the results are consistent with the results from varying
each of the parameters by themselves. The effect on the \gls{HALEU} mass
(Figure \ref{fig:lwr_voygr_share_enr_u}) is fairly uniform across the
parameter space. As the VOYGR build share and percent of \gls{LWR} with
extended licenses increase, the \gls{HALEU} mass required decreases,
which is consistent with the results of the \gls{OAT} analysis for these
parameters. By combining these two parameters, there is a greater
decrease in the \gls{HALEU} mass than the decrease observed by just varying
a single parameter. However, the linear trend in the metric
are consistent with the results of the \gls{OAT} analysis for
each of these parameters, which suggests that these parameters do not
interact with each other to cause a greater effect on the metric.
The other \gls{HALEU} metrics, the \gls{HALEU} \gls{SWU}
and \gls{HALEU} feed, also decrease in a similar manner as the \gls{HALEU} mass.
\begin{figure}[h!]
\centering
\includegraphics[scale=0.7,trim=120 0 120 30, clip]{lwr_voygr_share_haleu.pdf}
\caption{Effect of the LWR lifetime and VOYGR build share on the HALEU mass.}
\label{fig:lwr_voygr_share_haleu}
\end{figure}
The total enriched uranium mass decreases with increasing \gls{LWR}
lifetimes, but increases with increasing VOYGR build share. There is a
greater decrease in the total fuel mass required as the \gls{LWR}
lifetime increases for greater values of VOYGR build share. This
suggests some interaction between these two parameters on this
output metric because the effects are not uniform across the parameter
space.
\begin{figure}[h!]
\centering
\includegraphics[scale=0.7,trim=120 0 120 30, clip]{lwr_voygr_share_enr_u.pdf}
\caption{Effect of the LWR lifetime and VOYGR build share on
the total enriched uranium mass.}
\label{fig:lwr_voygr_share_enr_u}
\end{figure}
\subsection{Xe-100 build share and Xe-100 burnup}
When the Xe-100 build share and discharge burnup are varied together,
there is a strong combined effect on the metrics. The \gls{HALEU}
mass required (Figure \ref{fig:xe100_share_xe100_burnup_haleu})
increases as the burnup decreases and as the Xe-100 share increases.
The combined effect of these parameters is pronounced, such that there
is a large increase in the \gls{HALEU} mass as the Xe-100 burnup
reaches its minimum and the Xe-100 build share reaches its maximum. This
effect stems from a larger portion of the advanced reactor fleet
using its fuel less efficiently as this corner of the input space is
reached. This result suggests that the discharge burnup of an advanced
reactor should be considered when determining the build share of an
advanced reactor, if this metric is important.
\begin{figure}[h!]
\centering
\includegraphics[scale=0.7, trim=120 0 120 30, clip]{xe100_share_xe100_burnup_haleu.pdf}
\caption{Effect of Xe-100 discharge burnup and Xe-100 build share
on HALEU mass.}
\label{fig:xe100_share_xe100_burnup_haleu}
\end{figure}
\begin{figure}[h!]
\centering
\includegraphics[scale=0.7, trim=120 0 120 30, clip]{xe100_share_xe100_burnup_enr_u.pdf}
\caption{Effect of Xe-100 discharge burnup and Xe-100 build share
on total fuel mass.}
\label{fig:xe100_share_xe100_burnup_enr_u}
\end{figure}
The total fuel mass (shown in Figure \ref{fig:xe100_share_xe100_burnup_enr_u})
reaches a minimum with a maximum Xe-100 build share
and Xe-100 discharge burnup, which matches the trends observed in the
\gls{OAT} analysis. A minimum is reached in this corner of the parameter
space because more of the advanced reactor fleet is getting more
energy out of the fuel used, so less fuel is required. Variations in the
Xe-100 burnup do not affect the results when there is a 0\% Xe-100 build
share because no Xe-100s are deployed. The Xe-100 build share does not
greatly affect the fuel mass required when the Xe-100 has a discharge
burnup of 28 MWd/kgU (the lowest value used in this work) because at this
burnup level, the Xe-100 requires a similar amount of enriched uranium as
the VOYGR for each 18 month period. Therefore, as the VOYGRs are replaced
with Xe-100s as a consequence of increasing the Xe-100 build share, the
cumulative total
fuel mass required does not change much.
\subsection{MMR build share and Xe-100 burnup}
When the \gls{MMR} build share and Xe-100 burnup are varied together,
the effect on the metrics is not as consistent as the results from varying
other pairs of parameters, as Figure \ref{fig:mmr_share_xe100_burnup_enr_u}
shows. As the Xe-100 burnup increases, the fuel mass required by
all of the advanced reactors
decreases. However, the effect of increasing the \gls{MMR} build share
is dependent on the Xe-100 discharge burnup. At smaller Xe-100 discharge
burnup values, the fuel mass decreases with increasing \gls{MMR} build share.
But at larger Xe-100 discharge burnup values, the fuel mass increases
with increasing \gls{MMR} build share. The different trends result from
changes in how much fuel the Xe-100 requires at each refueling and
the difference between that and the amount of fuel required by the \gls{MMR}.
At the lowest burnup values, the Xe-100 requires more fuel than the
\gls{MMR}. Therefore, as the Xe-100s are replaced with \glspl{MMR} from
increasing the \gls{MMR} share, the
total mass of fuel required in the transition decreases. However, as
the Xe-100 burnup increases, the Xe-100 requires less fuel than the
\gls{MMR}. Therefore, requiring more of the advanced reactor fleet to be
\glspl{MMR} increases the total fuel mass required by advanced reactors in
the transition. These results identify how these two input parameters
interact to affect the output metrics. We observe the at small Xe-100
burnup values increasing the \gls{MMR} build share decreases the metric, but at high Xe-100 burnup
values increasing the \gls{MMR} build share increases the metric in
all six metrics considered in this work (see Appendix
\ref{app:s7_synergistic}).
\begin{figure}[h!]
\centering
\includegraphics[scale=0.7, trim=120 0 120 30, clip]{mmr_share_xe100_burnup_enr_u.pdf}
\caption{Effect of Xe-100 discharge burnup and MMR build share
on total fuel mass.}
\label{fig:mmr_share_xe100_burnup_enr_u}
\end{figure}
\subsection{Transition start and Xe-100 build share}
\begin{figure}[h!]
\centering
\includegraphics[scale=0.7, trim=120 0 120 0, clip]{ts_xe100_share_enr_u.pdf}
\caption{Effect of transition start time and Xe-100 build share
on total fuel mass.}
\label{fig:ts_xe100_share_enr_u}
\end{figure}
\begin{figure}[h!]
\centering
\includegraphics[scale=0.7, trim=120 0 120 0, clip]{ts_xe100_share_swu.pdf}
\caption{Effect of transition start time and Xe-100 build share
on total fuel mass.}
\label{fig:ts_xe100_share_swu}
\end{figure}
As Figure \ref{fig:ts_xe100_share_enr_u} shows, as the Xe-100 build
share increases, the total fuel mass decreases. However, there is little
effect in the total fuel mass as the transition start time is delayed.
The magnitude of the effect on the fuel mass
from varying the Xe-100 build share is greater than the magnitude of
the effect from varying the transition start time. This is consistent
with the results from the \gls{OAT} analysis, and is observed for five
of the metrics considered in this work. This result suggests that the
transition start time is not as important as the other parameters when
trying to minimize or maximize certain metrics.
The effect of varying these two parameters is the opposite when the total
\gls{SWU} capacity is considered: varying the transition start time has
a greater impact on the metric than varying the Xe-100 build share
as shown in Figure \ref{fig:ts_xe100_share_swu}. This
result stems from the similar \gls{SWU} capacities needed for the Xe-100
and VOYGR and the replacement of VOYGRs with Xe-100s with
increasing Xe-100 build share, leading to little change in the total
\gls{SWU} capacity required when
varying the Xe-100 build share. Therefore, the transition start time has
more impact on this metric than the Xe-100 build share, and there is little
of a combined effect observed because of the small impact from each parameter
on this metric.