methods.tex

\section{Methodology}
We simulated the nuclear reactor operating history in the \gls{EU} beginning in 
1970 including \gls{MOX} production and use in France. 
The simulation captured all discrete regions, reactor facilities, and materials 
involved in \gls{EU} historical reactor operation
using \Cyclus fuel cycle simulation framework and \Cycamore agents.
In this simulation, the \gls{UNF} from \gls{EU} nations is stored for later use 
in French \glspl{SFR} and France begins production of fuel for \glspl{SFR}
in 2020 by recycling the stored \gls{UNF}.
The \glspl{SFR} are modeled after the \gls{ASTRID} breeder reactor \cite{varaine_pre-conceptual_2012}. All scripts and data used for the simulations in this article are available in 
\cite{bae_arfc/transition-scenarios:_2018}.


\subsection{\Cyclus}

\Cyclus is an agent-based fuel cycle simulation framework 
\cite{huff_fundamental_2016}, which means 
that each reactor, reprocessing plant, and fuel fabrication plant is modeled as an agent.
A \Cyclus simulation contains prototypes, which are fuel cycle facilities with
pre-defined parameters, that are deployed in the simulation as \texttt{facility} agents.
Encapsulating the \texttt{facility} agents are the \texttt{Institution} and \texttt{Region}.
A \texttt{Region} agent holds a set of \texttt{Institution}s. 
An \texttt{Institution} agent can deploy or decommission \texttt{facility} agents.
The \texttt{Institution} agent is part of a \texttt{Region} agent,
which can contain multiple \texttt{Institution} agents. Several versions of \texttt{Institution}
and \texttt{Region} exist, varying in complexity and functions \cite{huff_extensions_2014}.
 \texttt{DeployInst} is used as the institution archetype for this work, where the institution
deploys agents at user-defined timesteps. 

At each timestep (one month),
agents make requests for materials or bid to supply them and exchange
with one another. A market-like mechanism called the dynamic resource exchange
\cite{gidden_methodology_2016} governs the exchanges.
Each material resource has a quantity, composition, name, and a unique identifier
for output analysis. 

In this work, each nation is represented as a distinct \texttt{Region} agent,
that contains \texttt{Institution} agents, each deploying  \texttt{Facility} 
agents. The \texttt{Institution} agents then deploy agents according to 
a user-defined deployment scheme.


\subsection{Nuclear Deployment in the \gls{EU}}

The \gls{IAEA} \gls{PRIS} database \cite{iaea_nuclear_2017} contains worldwide reactor
operation history.
The computational workflow in this work, shown in Figure \ref{diag:comp}, automates data extraction from the 
\gls{PRIS} database. We import this database directly as a \texttt{csv} file to populate the simulation
with deployment information, listing the country, reactor unit, type, net capacity (\gls{MWe}), status,
operator, construction date, first criticality date, first grid date, commercial date, shutdown
date (if applicable), and unit capacity factor for 2013. Then only the \gls{EU} countries are extracted
from the \texttt{csv} file. We developed a python script to generate
a \Cyclus 
compatible input file accordingly, which lists the individual reactor units as agents. 


\begin{figure}
        \centering
\begin{tikzpicture}[node distance=1.5cm]
\node (database) [object] {Database (\texttt{.csv})};
\node (script) [process, below of=database] {Input Generation Script (\texttt{write\_input.py})};
\node (input) [object, below of=script] {\Cyclus Input File (\texttt{.xml})};
\node (cyclus) [process, below of=input]{\Cyclus};
\node (output) [object, below of=cyclus]{\texttt{Output File (\texttt{.Sqlite})}};
\node (script2) [process, below of=output]{Analysis Script (\texttt{analysis.py})};

\draw [arrow] (database) -- (script); 
\draw [arrow] (script) -- (input); 
\draw [arrow] (input) -- (cyclus);
\draw [arrow] (cyclus) -- (output);
\draw [arrow] (output) -- (script2);
\end{tikzpicture}
\caption{Green circles and blue boxes represent files and software 
processes, respectively, in the computational workflow.}
\label{diag:comp}
\end{figure}


Projections of future reactor deployment in this simulation are based on
assessment of analyses from references, for instance \gls{PRIS}, for reactors planned
for construction \cite{iaea_nuclear_2017}, the World Nuclear Association
\cite{world_nuclear_association_nuclear_2017}, and literature concerning the future of
nuclear power in a global \cite{joskow_future_2012} and European context
\cite{hatch_politics_2015}.  Existing projections extend to 2050.

Table \ref{tab:eu_deployment} lists the reactors that are currently  planned or
under construction in the \gls{EU}. In the simulation, all  planned constructions are completed 
without delay or failure and reach a lifetime of 60 years.  

\pagebreak
\begin{table}[h]
    \centering
    \caption {Power reactors under construction and planned. Replicated from \cite{world_nuclear_association_nuclear_2017}.}
    \label{tab:eu_deployment}
    \begin{tabular}{ccccr}
        \hline
        \textbf{Expected}&\textbf{Nation} &\textbf{Reactor} & \textbf{Type} & \textbf{Gross}\\
            \textbf{Operation}& & &  & \textbf{\gls{MWe}}\\
        \hline
        2018 & Slovakia  & Mochovce 3 & PWR & 440\\
        2018 & Slovakia & Mochovce 4 & PWR & 440 \\
        2018 & France & Flamanville 3 & PWR & 1600 \\
        2018 & Finland & Olkilouto 3 & PWR & 1720 \\
        2019 & Romania & Cernavoda 3 & PHWR & 720 \\
        2020 & Romania & Cernavoda 4 & PHWR & 720 \\
        2024 & Finland & Hanhikivi & VVER1200 & 1200 \\
        2024 & Hungary & Paks 5 & VVER1200 & 1200 \\
        2025 & Hungary & Paks 6 & VVER1200 & 1200 \\
        2025 & Bulgaria & Kozloduy 7 & \footnotemark AP1000 & 950 \\
        2026 & UK & Hinkley Point C1 & EPR & 1670 \\
        2027 & UK & Hinkley Point C2 & EPR & 1670 \\
        2029 & Poland & Choczewo & N/A & 3000 \\
        2035 & Poland & N/A & N/A & 3000 \\
        2035 & Czech Rep & Dukovany 5 & N/A & 1200 \\
        2035 & Czech Rep & Temelin 3 & AP1000 & 1200 \\
        2040 & Czech Rep & Temelin 4 & AP1000 & 1200 \\
        \hline
    \end{tabular}
\end{table}

    \footnotetext{The fate of many planned reactors is uncertain. The proposed reactor types
              are also unclear. The ones marked `N/A' for type are assumed to the \glspl{PWR}
              in the simulation.}
\FloatBarrier

For each \gls{EU} nation, we categorize the growth trajectory is categorized from
``Aggressive Growth'' to ``Aggressive Shutdown''. ``Aggressive growth'' is
characterized by a rigorous expansion of nuclear power, while
``Aggressive Shutdown'' is characterized as a transition to rapidly
de-nuclearize the nation's electric grid. We categorize each nation's growth 
trajectory into five degrees depending on G, the growth trajectory metric:

 \[
 G = \left\{\begin{array}{ll}
 \text{Aggressive Growth}, & \text{for } G \geq 2\\
 \text{Modest Growth}, & \text{for } 1.2 \leq G < 2\\
 \text{Maintenance}, & \text{for } 0.8 \leq G < 1.2 \\
 \text{Modest Reduction}, & \text{for } 0.5 \leq G< 0.8\\
 \text{Aggressive Reduction}, & \text{for } G \leq 0.5
 \end{array}\right\} = \frac{C_{2040}}{C_{2017}}\\\\
 \]
 \[
  G = \text{Growth Trajectory  } [-] 
 \]
 \[
 C_{i} = \text{Nuclear Capacity in Year i  } [\gls{MWe}].
 \]

The growth trajectory and specific plan of each nation in the \gls{EU} 
is listed in Table \ref{tab:eu_growth}.  

\begin{table}[h]
    \centering
    \caption{Projected nuclear power strategies of \gls{EU} nations \cite{world_nuclear_association_nuclear_2017}}
        \begin{tabular}{lll}
            \hline 
                    \textbf{Nation} & \textbf{Growth Trajectory} & \textbf{Specific Plan }\\
                    \hline
                    UK & Aggressive Growth & {\small  13 units (17,900 \gls{MWe}) by 2030.}\\
                    Poland & Aggressive Growth &  {\small Additional 6,000 \gls{MWe} by 2035.}\\
                    Hungary & Aggressive Growth &  {\small Additional 2,400 \gls{MWe} by 2025.} \\ 
                    Finland & Modest Growth &  {\small Additional 2,920 \gls{MWe} by 2024.}\\
                    Slovakia & Modest Growth & {\small Additional 942 \gls{MWe} by 2025.}\\
                    Bulgaria & Modest Growth &  {\small Additional 1,000 \gls{MWe} by 2035.} \\
                    Romania & Modest Growth &  {\small Additional 1,440 \gls{MWe} by 2020.} \\
                    Czech Rep. & Modest Growth & {\small  Additional 2,400 \gls{MWe} by 2035.}\\
                    France & Modest Reduction & {\small No expansion or early shutdown.}\\
                    Slovenia & Modest Reduction & {\small No expansion or early shutdown.}\\
                    Netherlands & Modest Reduction & {\small No expansion or early shutdown.}\\
                    Lithuania & Modest Reduction & {\small No expansion or early shutdown.}\\
                    Spain & Modest Reduction &  {\small No expansion or early shutdown.} \\
                    Italy & Modest Reduction & {\small No expansion or early shutdown. }\\
                    Belgium & Aggressive Reduction & All shut down 2025.\\
                    Sweden & Aggressive Reduction & All shut down 2050.\\
                    Germany & Aggressive Reduction & All shut down by 2022.\\
                    \hline
        \end{tabular}

  \label{tab:eu_growth}
\end{table}
\FloatBarrier

Using this categorization to drive facility deployment, the simulation captures 
regional differences in reactor power capacity and \gls{UNF} production as a 
function of time. Accordingly, figure \ref{fig:eu_pow} shows the resulting simulated 
installed capacity in \gls{EU} nations.  Sudden capacity reductions seen near 2025 and in the 
2040s result from end-of-license reactor retirements and nuclear phaseout plans 
in nations such as Germany, Belgium and Sweden.
    
\begin{figure}[htbp!]
    \begin{center}
        \includegraphics[scale=0.6]{./images/eu_future/power_plot.png}
    \end{center}
    \caption{Installed nuclear capacity in the EU is distinguished by \texttt{Region}s in \Cyclus.
	    	 The large shift near 2025 is caused by total nuclear phaseout in Germany and Belgium.}
    \label{fig:eu_pow}
\end{figure}


\subsection{French \gls{SFR} Deployment Schedule}

Figure \ref{fig:sfr_num} shows
the French transition to \glspl{SFR} modeled in this simulation.
Historically aggressive growth of nuclear in the 1980s leads to a substantial 
shutdown of nuclear in the 2040s, which, in the simulation, are replaced by new 
\glspl{SFR}. The net capacity is kept constant at 64.7 GWe, which is the maximum predicted
installed capacity in France.

\begin{figure}[htbp!]
        \begin{center}
                \includegraphics[scale=0.6]{./images/french-transition/power_plot.png}
        \end{center}
        \caption{The potential French transition from \glspl{LWR} to 
                \glspl{SFR} when assisted by \gls{UNF} from other \gls{EU} 
        nations.}
        \label{fig:sfr_num}
\end{figure}

Figure \ref{fig:dep} shows the deployment required to support the transition in 
figure \ref{fig:sfr_num}. France must build 1.78 \glspl{ASTRID} per year, on average, to 
make up for the end-of-license decommissioning of power plants built in the 1980s and 1990s. 
The second period of aggressive building occurs when the first generation of \glspl{SFR} decommission
after 60 years. Starting in 2040, France deploys 600-\gls{MWe} \glspl{SFR} to make up for 
decommissioned French \gls{LWR} capacity. This results in an installed 
\gls{SFR} 
capacity of 64.7 GWe by 2078 when the final \gls{LWR} is 
decommissioned. 



\begin{figure}[htbp!]
    \begin{center}
        \includegraphics[scale=0.6]{./images/french-transition/sfr_deploy.png}
    \end{center}
    \caption{The deployment of \glspl{SFR} in France is characterized by a period of
    aggressive building.}
    \label{fig:dep}
\end{figure}


Finally, figure \ref{fig:tot_dep} shows the total deployment scheme we simulated.  
The French transition to \glspl{SFR} couples with the historical and projected 
operation of \gls{EU} reactors.  The steep transition from 2040 to 2060 
reflects the scheduled decommissioning of reactors built in the 1975-2000 era 
of aggressive nuclear growth in France.

\begin{figure}[htbp!]
    \begin{center}
        \includegraphics[scale=0.6]{./images/eu_future/onesim.png}
    \end{center}
    \caption{The total deployment scheme we simulated relies on \gls{UNF} 
    collaboration among nations.} 
    \label{fig:tot_dep}
\end{figure}

These figures reflect that, for the given assumptions, bursts of construction
are necessary to maintain capacity.  In reality, a construction rate of five 
reactors every year is ambitious, but might have the advantage of
larger scale production of components and more modular assembly and construction if major components can mostly be built off site.

This analysis establishes a multi-national material flow and demonstrates that, if such an aggressive deployment scheme 
took place, the \glspl{SFR} would have enough fuel.  Alternatively, the 
deployment of new \glspl{SFR} can be spread out by staggering scheduled 
decommissioning of \glspl{LWR} through lifetime extensions. For example,
we increased the original lifetime of French \glspl{LWR} (60 years) randomly 
by sampling from a uniform distribution of lifetime extension
magnitudes between 0 and 25 years. 
This results in a more gradual transition and \gls{ASTRID} construction
burden, as shown in figure \ref{fig:sfr_num_norm} and \ref{fig:sfr_dep_norm}.
The effect of \gls{LWR} lifetime extension is discussed in Section \ref{sec:life}.

\begin{figure}[htbp!]
    \begin{center}
        \includegraphics[scale=0.6]{./images/french-transition/unif_0_25.png}
    \end{center}
    \caption{The transition to \glspl{ASTRID}
             becomes more gradual if the
             French \glspl{LWR} lifetime extensions are sampled from a 
     uniform distribution $\in [0, 25]$ years.}
    \label{fig:sfr_num_norm}
\end{figure}

\begin{figure}[htbp!]
    \begin{center}
        \includegraphics[scale=0.6]{./images/french-transition/unif_0_25_dep.png}
    \end{center}
    \caption{The acute construction burden lessens if the
             French \glspl{LWR} lifetime extensions are sampled from a 
     uniform distribution $\in [0, 25]$ years.}
    \label{fig:sfr_dep_norm}
\end{figure}

\subsection{Material Flow}

The fuel cycle is represented by a series of facility agents whose material 
flow is illustrated in figure \ref{diag:fc}, along with
the \Cyclus archetypes that were used to model each facility.
In this diagram, \gls{MOX} Reactors include both French \glspl{PWR} and 
\glspl{SFR}.

% Define block styles
\tikzstyle{decision} = [diamond, draw, fill=blue!20, 
text width=4.5em, text badly centered, node distance=3cm, inner sep=0pt]
\tikzstyle{block} = [rectangle, draw, fill=blue!20, 
text width=5em, text centered, rounded corners, minimum height=4em]
\tikzstyle{line} = [draw, -latex']
\tikzstyle{cloud} = [draw, ellipse,fill=red!20, node distance=3cm,
minimum height=2em]


\begin{figure}
        \centering
        \scalebox{0.6}{
                \begin{tikzpicture}[align=center, node distance = 3cm and 3cm, auto]
                % Place nodes
                \node [block] (sr) {Mine (\texttt{SOURCE})};
                \node [cloud, below of=sr] (nu) {Nat U};
                \node [block, below of=nu] (enr) {Enrichment ({\footnotesize \texttt{ENRICHMENT}})};
                \node [cloud, below of=enr] (uox) {\acrshort{UOX}};
                \node [block, below of=uox] (lwr) {\gls{LWR} (\texttt{REACTOR})};
                \node [cloud, right of=lwr] (snf) {\gls{UNF}};
                \node [block, right of=snf] (pool) {Pool (\texttt{Storage})};
                \node [cloud, left of=lwr] (tl2) {Dep U};
                \node [cloud, right of=enr] (tl) {Dep U};
                \node [block, right of=tl] (sk) {Repository (\texttt{SINK})};
                \node [cloud, below of=sk] (cunf) {Cooled \gls{UNF}};
                \node [cloud, below of=pool] (cunf2) {Cooled \gls{UNF}};
                \node [block, below of=snf] (rep) {{\small Reprocessing ({\footnotesize \texttt{SEPARATIONS}})}};
                \node [cloud, below of=rep] (u) {Sep. U} ;
                \node [cloud, left of=rep] (pu) {Sep. Pu};
                \node [block, left of=pu] (mix) {Fabrication (\texttt{MIXER})};
                \node [cloud, below of=mix] (mox) {\gls{MOX}};
                \node [block, below of=mox] (mxr) {\gls{MOX} Reactors 
                (\texttt{REACTOR})};
                \node [cloud, right of= mxr] (snmox) {Spent \gls{MOX}};
                
                \draw[->, thick] (sr) -- (nu);
                \draw[->, thick] (nu) -- (enr);
                \draw[->, thick] (enr) -- (tl);
                \draw[->, thick] (enr) -- (tl2);
                \draw[->, thick] (tl) -- (sk);
                \draw[->, thick] (tl2) -- (mix);
                \draw[->, thick] (enr) -- (uox);
                \draw[->, thick] (uox) -- (lwr);
                \draw[->, thick] (lwr) -- (snf);
                
                \draw[->, thick] (lwr) -- (snf);
                \draw[->, thick] (snf) -- (pool);
                \draw[->, thick] (pool) -- (cunf);
                \draw[->, thick] (pool) -- (cunf2);
                \draw[->, thick] (cunf) -- (sk);
                \draw[->, thick] (cunf2) -- (rep);
                
                \draw[->, thick] (rep) -- (u);
                \draw[->, thick] (rep) -- (pu);
                \draw[->, thick] (pu) -- (mix);
                \draw[->, thick] (mix) -- (mox);
                \draw[->, thick] (mox) -- (mxr);
                \draw[->, thick] (mxr) -- (snmox);
                \draw[->, thick] (snmox) -- (rep);
                
                \end{tikzpicture}
        
                }
                \caption{Fuel cycle facilities (blue boxes) represented by 
                        \Cyclus archetypes (in parentheses) pass materials (red 
                ovals) around the simulation.} 
                \label{diag:fc}
\end{figure}

A mine facility provides natural uranium, which is enriched by an enrichment
facility to produce \gls{UOX}. Enrichment wastes (tails) are disposed of to a 
sink facility representing ultimate disposal. The enriched \gls{UOX} fuels
the \glspl{LWR} which in turn produce spent \gls{UOX}. The used fuel
is sent to a wet storage facility for a minimum of 72 months. \cite{carre_overview_2009}.

The cooled fuel is then reprocessed to separate plutonium and uranium,
or sent to the repository.
The plutonium mixed with depleted uranium (tails) makes \gls{MOX} (Both for
French \glspl{LWR} and \glspl{ASTRID}).
Reprocessed uranium is unused and stockpiled. Uranium is reprocessed
in order to separate the raffinate (minor actinides and fission products)
from usable material. Though neglected in this work, reprocessed
uranium may substitute depleted uranium for \gls{MOX} production. In the
simulations, sufficient depleted uranium existed that the complication of
preparing reprocessed uranium for incorporation into reactor fuel
was not included. However, further in the future where the depleted
uranium inventory drains, reprocessed uranium (or, natural uranium) will need to be utilized. 

\FloatBarrier

\section{Scenario Specifications}
Table \ref{tab:gen} lists the scenario specifications defining the
simulations presented in this work.
The reprocessing and \gls{MOX} fabrication capacity in France
prior to 2020 is modeled after the 
French La Hague and MELOX sites \cite{schneider_spent_2008, hugelmann_melox_1999}.


\begin{table}[h]
    \centering
    \caption{Simulation Specifications}
    \begin{tabularx}{\linewidth}{bsx}
        \hline
        \textbf{Specification} &\textbf{ Value} & \textbf{Units}\\
        \hline
        Simulation Starts & 1970 & year\\
        Simulation Ends & 2160 & year\\ 
        Production of \gls{ASTRID} fuel begins & 2020 & year\\
        \glspl{SFR} become available & 2040 & year\\
        Reprocessed uranium usage &  Not used anywhere & -\\
        Minimum \gls{LWR} \gls{UNF} cooling time & 72 & months \\
        Minimum \gls{ASTRID} \gls{UNF} cooling time  & 36  & months\\
        Separation efficiency of U and Pu & 99.8 & \% \\
        Reprocessing streams & Pu and U & - \\
        Reprocessing capacity before 2020 & 91.6 \cite{schneider_spent_2008} & $\frac{\text{metric tons of \gls{UNF}}}{month}$  \\
        Reprocessing capacity after 2020 & 183.2 & $\frac{\text{metric tons of \gls{UNF}}}{month}$\\
        \gls{LWR} \gls{MOX} fabrication throughput & 16.25 \cite{hugelmann_melox_1999} & $\frac{\text{metric tons of \gls{MOX}}}{month}$\\
        \gls{ASTRID} \gls{MOX} fabrication throughput & No limit ($\infty$) & $\frac{\text{metric tons of \gls{MOX}}}{month}$ \\
        \gls{LWR} \gls{MOX} recycling  &  Not reprocessed & - \\
        \gls{ASTRID} \gls{MOX} recycling & $\infty$-pass & - \\  
        \hline
    \end{tabularx}
    \label{tab:gen}
\end{table}


\pagebreak

\section{Reactor Specifications}
Three major reactors are used in the simulation, \gls{PWR}, \gls{BWR}, and ASTRID-type \gls{SFR} reactors.


For \glspl{LWR}, we used a linear core size model to capture
varying reactor capacity. For example, a 
1,200 \gls{MWe} PWR has $193*\frac{1,200}{1,000} = 232$ \gls{UOX} assemblies, each
weighing 446 kg.
After each 18 month cycle, one-third of the 
core (77 assemblies) discharges. Refueling
is assumed to take two months to complete, during which the reactor
is shut down. The specifications are defined in table \ref{tab:reactor-specs} 
which details the reactor specifications in this simulation. \gls{LWR} 
specifications are modified linearly for varying power capacity.
The \gls{ASTRID} design targets a 60 year lifetime, which this 
simulation assumes for all \glspl{ASTRID} \cite{gauche_generation_2012}.


\begin{table}[h]
    \centering
    \caption{Baseline \gls{LWR} and \gls{ASTRID} simulation specifications.}
    \begin{tabular}{lrrr}
        \hline
        \textbf{Specification} & \textbf{\gls{PWR} \cite{sutharshan_ap1000tm_2011}} & \textbf{\gls{BWR} \cite{hinds_next-generation_2006}} & \textbf{\gls{SFR}} \cite{varaine_pre-conceptual_2012}\\
        \hline
                Lifetime [y] \tablefootnote{The simulated reactor lifetime reaches the licensed lifetime unless 
        the reactor is shut down prematurely.} & 60 & 60 & 60 \\
                Cycle Time [mos.]& 18 & 18 & 12\\ 
                Refueling Outage [mos.]& 2 & 2  & 2\\
                Rated Power [\gls{MWe}] & 1000 & 1000 & 600\\
                Assembly mass [kg] & 446 & 180 & -- \\
                Batch mass [kg] & -- & -- & 5,568\\
                Discharge Burnup [GWd/tHM] & 51 & 51 & 105 \\
                Assemblies per core \tablefootnote{Number of assemblies and corresponding \gls{LWR} core 
        masses are reported for a 1000-\gls{MWe} core. Reactors with different core  
        powers are modeled with a linear mass assumption.} & 193  & 764 & -- \\

                Batches per core & 3 & 3 & 4\\
        Initial Fissile Loading [t] & 4.3  $^{235}$U & 5.8  $^{235}$U & 4.9 Pu \\
                Fuel & \gls{UOX} or \gls{MOX} & \gls{UOX} & \gls{MOX} \\
        \hline
    \end{tabular}
        
    \label{tab:reactor-specs}

    \end{table}


\subsection{Material Definitions}
Reactor transmutation of the nuclear fuel was modeled using isotopic `recipes',
such that fresh and spent fuel recipes were defined for each reactor type (see
tables \ref{tab:comp_fresh} and \ref{tab:comp}).

This work relied on reference \gls{LWR} \gls{UOX} and \gls{LWR} \gls{MOX}
compositions retrieved from \gls{AFCI} analyses in Appendix C of
\cite{piet_fuel_2006}.
The \gls{LWR} \gls{UOX} depletion calculations were conducted using ORIGEN2
with the \gls{PWR} one group cross sections provided by default. Meanwhile,
the \gls{LWR} \gls{MOX} depletion calculations relied on WIMS8
\cite{wims8_wims_1999} to provide accurate cross sections to ORIGEN. For this
purpose, WIMS8 calculations used the 172-group, JEF2.2-based cross section
library.

Finally, the \gls{ASTRID} compostions were retrieved from the \gls{ASTRID}
design as published in \cite{varaine_pre-conceptual_2012}. 

\begin{table}[h]
    \centering
    \caption{Fresh fuel compositions in the simulation \cite{piet_fuel_2006, varaine_pre-conceptual_2012}.}
%   \scalebox{0.86}{
        \begin{tabular}{lrrr}
            \hline
             & \multicolumn{3}{c}{ Composition [\%]} \\
            Recipe & U-235  & U-238  & Pu \\ 
            \hline
            Fresh \gls{UOX} Fuel & 4.29 & 95.71 & -   \\ 
            Fresh \gls{LWR} \gls{MOX} Fuel & 0.2 & 90.7 & 9.1 \\ 
            Fresh \gls{ASTRID} Fuel & 0.3 & 77.7 & 22 \\
            \hline
        \end{tabular}
        
        \label{tab:comp_fresh}
\end {table}