introduction.tex

\section{Motivation}
In the US, the current fleet of nuclear reactors is comprised 
of two \gls{LWR} designs: \glspl{PWR} and \glspl{BWR}. 
Both designs use uranium dioxide pellets as fuel, with the uranium 
enriched to no more than 5\% $^{235}$U, and supply about 700-1000 MW of 
power. These types of reactors 
have commercially operated in the US since 1957. This fleet of 
reactors supplied about 19\% of all energy and over 50\%  
of all carbon-free energy in the US in 2021 
\cite{us_energy_information_administration_electricity_2022}, making nuclear 
energy the third largest producer of energy and the largest 
producer of carbon-free energy in the United States. Because of nuclear 
power's ability to produce large-scale carbon-free energy, it is 
expected to play a role in meeting carbon emission and climate change 
goals \cite{nea_meeting_2022}. The \glspl{LWR} 
currently deployed in the US have license expiration dates within 
the next 35 years, with the last license expiring in 2055 
\cite{nuclear_energy_institute_us_2021}. Therefore, if nuclear energy is 
to continue to produce energy in the US and assist in meeting carbon 
emission goals after 2050, we must extend current reactor licenses,  
build new reactors, or some combination of the two. 

Multiple countries around the world are building new \glspl{LWR}
\cite{world_nuclear_association_plans_2022} and developing
new reactor designs \cite{hussain_advances_2018}, often called 
advanced reactors, to 
replace or expand the current fleet of reactors. Advanced reactors 
cover a large swath of design space, with wider ranges in: energy output, 
fuel form, and cycle length. The variations in reactor designs allow 
advanced reactors to achieve higher fuel burnup, improved safety 
performance, and better economic competitiveness than the \gls{LWR} fleet. 
In the US, the \gls{DOE} established the \gls{ARDP} 
\cite{us_department_of_energy_office_of_nuclear_energy_advanced_nodate}
to ``speed the demonstration of advanced reactors'' 
\cite{us_department_of_energy_office_of_nuclear_energy_advanced_nodate}
by developing a cost-sharing program with private companies. The goal of 
\gls{ARDP} is to leverage this cost-sharing program to build 
first-of-a-kind advanced reactors, which will assist in their licensing and 
understanding challenges and opportunities in the construction process. 
The reactors built through this program are planned to be operational 
by the late 2020's.

One important question that has arisen from the \gls{ARDP} is how to
develop supply chains to support the nuclear fuel cycles of 
advanced reactors. One design parameter that is different from \glspl{LWR} 
and almost every advanced reactor is the fuel form. \glspl{LWR} use 
a ceramic uranium dioxide fuel, while advanced reactors typically use
fuel forms such as \gls{TRISO} fuel kernels with uranium oxycarbide, 
uranium dissolved in molten 
salts, and metallic alloy fuels \cite{hussain_advances_2018}.
Additionally, many advanced reactor designs require  
\acrfull{HALEU}, which is uranium enriched between 5\% and 20\% $^{235}$U,
compared with the 3-5\% $^{235}$U that is used in \gls{LWR} 
fuel. There is presently no commercial supply of \gls{HALEU} in the US that can 
provide fuel for the \gls{ARDP} projects or for a potential future fleet of 
advanced reactors. Recent international events limit the possibility of 
obtaining \gls{HALEU} from abroad. Therefore, the \gls{DOE} is investigating 
how to develop 
a supply chain and \gls{NFC} for uranium enriched to this 
increased level \cite{regalbuto_addressing_2020,dixon_estimated_2022}. 

There are two methods to produce \gls{HALEU}: enrich natural uranium up to 
the required level
or downblend \acrfull{HEU} to the required enrichment level. The current US
nuclear commercial fuel cycle relies on enrichment of natural uranium 
to create fuel for \glspl{LWR}, but does not have the capability to enrich
natural uranium to produce \gls{HALEU} \cite{nuclear_energy_institute_addressing_2018}.  
\gls{HALEU} production through enrichment is limited by
the amount of available natural uranium and facility capacities, such 
as the material throughputs and \acrfull{SWU} capacity.
There are three potential sources of \gls{HEU} that can be downblended 
to produce \gls{HALEU}: the used \gls{EBR} fuel at \gls{INL} 
\cite{patterson_haleu_2019}, inventory at \gls{SRS} \cite{regalbuto_addressing_2020}, 
and inventory at Y-12 National Security Complex 
\cite{robinson_establishment_2020}. The size of each stockpile limits the amount 
of \gls{HALEU} produced through downblending, and the first two stockpiles 
are capable of producing no more than 20 MT of \gls{HALEU}
\cite{regalbuto_addressing_2020}.
Additionally, two of the potential stockpiles of \gls{HEU} to downblend  
contain impurities that potentially affect reactor performance 
\cite{vaden_isotopic_2018,nelson_foreign_2010}.
These impurities may limit the amount of downblended \gls{HEU} that a reactor 
a reactor can use at once. 
Currently, there is only one facility in the US commercially licensed to 
downblend \gls{HEU}, the BWXT Nuclear Fuel Services Inc. facility in 
Erwin, TN, which is expected to have the capacity to downblend 1-2 
MT of \gls{HEU}, producing up to 10 MT of \gls{HALEU} each year \cite{nagley_ha-leu_2020}.
Therefore, meeting \gls{HALEU} demand through downblending may require the 
development and licensing of additional facilities to downblend \gls{HEU} if 
the BWXT facility does not have enough capacity. 

The production of fuels needed for deploying advanced reactors 
is expected to have numerous impacts on the \gls{NFC}, stemming from 
the different materials and enrichment levels needed for advanced reactor
fuels. To assist in understanding the impacts 
from deploying \gls{HALEU}-fueled reactors, modeling the \gls{NFC} 
can provide the material requirements of potential transition scenarios. 
The technology employed in the \gls{NFC} often defines the fuel 
cycle type, and a transition in the nuclear fuel cycle occurs when 
introducing new fuel types or other fuel cycle technologies.  
Modeling  a \gls{NFC}, typically aided by a fuel cycle simulator, 
includes modeling the deployment and decommissioning of facilities in 
the \gls{NFC}, such as mines or reactors, and modeling the materials 
traded between facilities. 
\gls{NFC} simulators have been used to model a variety of \gls{NFC} 
transitions \cite{sunny_transition_2015,bae_fuel_2018,piet_dynamic_2011} 
and quantify the resource requirements of \glspl{NFC} transitions
\cite{bachmann_enrichment_2021}. Therefore, using \gls{NFC} simulators to 
model the transition from the US fleet of \glspl{LWR} to potential 
fleets of advanced reactors can inform \gls{DOE}, researchers, companies, 
and other key stakeholders of potential \gls{HALEU} needs for future 
advanced reactor deployment. Estimates on potential needs can then inform 
strategies to develop material supply chains to fuel advanced reactors. 

When modeling the \gls{NFC} to assist in answering questions about 
\gls{HALEU} demand and other resources required to meet the demand, 
there is a large array of input parameters that must be considered, 
such as when to start a transition, the speed of the 
transition, and the advanced reactors to deploy. Many times, modelers make 
assumptions about transition parameters 
\cite{sunny_transition_2015, djokic_application_2015}
and others use energy projections to determine the parameters 
\cite{dixon_estimated_2022}. Both are valid methods to determine 
transition parameters, but only considering a select set of parameters may 
not capture all of the possible material demands of a transition. 
Therefore, fuel cycle modelers often perform sensitivity analysis on 
the transition to understand the potential range of material 
requirements and how their assumptions affect demand. 
Sensitivity analysis involves 
modeling a fuel cycle with small perturbations in various input 
parameters and analyzing the variance or spread of select output metrics. 
Sensitivity analysis has been used in multiple \gls{NFC} analyses 
\cite{chee_sensitivity_2019,feng_sensitivity_2020,thiolliere_methodology_2018,passerini_sensitivity_2012}
to identify the model parameter or parameters that have the greatest 
impact on specific model outputs or material requirements. Sensitivity 
analysis can also reveal underlying information about a system that is not 
necessarily intuitive, such as how much the modeling methodology 
affects the results. Understanding the 
material requirements of a \gls{NFC} coupled with sensitivity analysis 
aids in understanding key model parameters and optimizing the 
\gls{NFC} based on given criteria, such as 
minimizing the amount of \gls{HALEU} required. Various 
optimization schemes have been applied to \glspl{NFC} to optimize the fuel 
cycle based on minimizing certain criteria: fuel requirements \cite{kim_selection_1999},
waste production \cite{shwageraus_optimization_2003}, and combinations 
of these metrics in multi-objective 
problems \cite{passerini_systematic_2014}. By combining \gls{NFC} transition 
analysis with sensitivity analysis and optimization, one obtains
a deep understanding of potential \gls{HALEU} demand, potential supply 
chain requirements, and how to alter reactor deployment to aid in developing 
the supply chain. 

\section{Research Goals}
The goal of this work is to investigate the impacts of deploying reactors 
fueled 
by \gls{HALEU} in the United States, including the impacts that the reactors 
have on the \gls{NFC} and the impacts the \gls{NFC} has on the reactors. 
The results of this work are intended to
aid and guide policy makers and key stakeholders on how to best establish a 
fuel cycle to support the deployment of \gls{HALEU}-fueled reactors. 
Within this primary goal, there are three specific objectives:
\vspace{0.2cm} 
\noindent
\begin{enumerate}
\item \textbf{Quantify potential material requirements for the transition 
from \glspl{LWR} to advanced reactors in open and closed 
fuel cycles.} This objective aims 
at understanding how large-scale decisions in fuel cycle 
modeling (e.g., the reactors deployed and the type of fuel cycle)
impact the material requirements. 
Material requirements considered for this objective include  
the mass of \gls{HALEU}, the feed uranium and \gls{SWU} capacity 
required to produce enriched uranium for advanced reactors, and 
the amount of \gls{UNF} that requires disposal. 

\item \textbf{Understand the impacts of fuel cycle parameters on the material 
requirements and design optimized transition scenarios.} 
This objective 
aims at understanding the effects of small-scale decisions in 
fuel cycle modeling (e.g., reactor burnup and transition start time)
on material requirements, and how this information can be used by 
decision makers to develop optimal fuel cycle transitions. Fuel cycle 
parameters of interest include the transition start time, the 
build share of different advanced reactors, and the discharge 
bunrup of advanced reactors. Optimized transitions scenarios are 
scenarios in which one or multiple material requirements are minimized, 
which would make it simpler to establish the fuel cycle. 

\item \textbf{Identify potential limitations in using downblended \gls{HEU} 
on reactor performance.}  This objective aims at understanding 
how this \gls{HALEU} production method may affect reactor operation 
and limit the use of this method in supporting the transition to 
\gls{HALEU}-fueled reactors. The performance of the reactor is based on 
reactor physics parameters. Potential limitations include 
the impact of residual uranium isotopes from the downblending 
process impacting reactor physics performance. 


\end{enumerate}
These goals will be met by completing the following steps:
\vspace{0.2cm} 
\noindent
\begin{enumerate}
\item \textbf{Model the transition from \glspl{LWR} to advanced reactors.} 
Example transition scenarios to multiple fuel cycles with \gls{HALEU}-fueled 
reactors will 
be modeled using the \gls{NFC} simulator \Cyclus \cite{huff_fundamental_2016}. 
Multiple transitions will be modeled, with each one varying based on the type
of advanced reactors deployed, energy demand, and fuel cycle option 
(open or closed). This 
step will quantify and compare the material requirements of each transition 
scenario to understand how the reactors deployed, energy demand, and fuel cycle
options affect material requirements. This step also includes the 
development of OpenMCyclus, a coupling between \Cyclus and OpenMC, to 
provide dynamic modeling of fuel depletion within a fuel cycle model. 

\item \textbf{Perform sensitivity analysis and optimize select transition scenarios.}
Sensitivity analysis will be performed on one of the transition scenarios
modeled by coupling \Cyclus with Dakota \cite{adams_dakota_2021}, a program 
for uncertainty quantification and sensitivity analysis. This step 
will identify the most impactful model parameters on 
the material requirements of the transition. These results will then be 
used to determine optimized transition scenarios to minimize specific 
material requirements, thereby demonstrating an effective application of 
this methodology. 

\item \textbf{Neutronics analysis of \gls{HALEU} created from impure \gls{HEU}.}
The neutronics of the \gls{HALEU}-fueled reactors in the transition scenarios 
will be modeled to identify potential effects of using \gls{HALEU} produced 
from downblended \gls{HEU} with known impurities. This step will investigate 
potential limitations in using this \gls{HALEU} production method and 
how different \gls{HALEU} production methods affect reactor operation and 
key safety parameters, such as neutron multiplication, delayed neutron 
fractions, and reactivity coefficients.
\end{enumerate}


The subsequent chapters of this dissertation present the work done to 
complete each of 
these steps and accomplish each objective. Chapter 2 
provides necessary 
background information and a literature review on the nuclear fuel cycle,
nuclear fuel cycle 
modeling efforts, and the use of \gls{HALEU} in reactors.
Chapter 3 discusses the methodology for modeling the transition to advanced 
reactors in once-through and closed fuel cycles. This chapter includes 
descriptions of
the scenarios modeled, information on the reactors included in the 
transitions, and the flow of 
material in each scenario. The scenarios modeled vary based on the 
advanced reactors deployed, the energy demand of the scenario, and the 
type of fuel cycle (open or closed). This chapter also includes discussion 
of the development of OpenMCyclus, a code that couples \Cyclus with OpenMC 
\cite{romano_openmc:_2015}
to provide fuel depletion during a fuel cycle simulation.

Chapter 4 presents and discusses the results of the 
once-through fuel cycle transition scenarios. Chapter 5 presents 
and discusses the 
results of the closed fuel cycle transitions. For each of the transition 
scenarios modeled, we compared them based on the number of reactors 
deployed and material requirements, such as the total mass of enriched 
uranium, mass of \gls{HALEU}, 
feed mass to enrich uranium, the \gls{SWU} capacity required to enrich 
uranium, and the mass of \gls{UNF} discharged from the reactors. 

Chapter 6 provides results 
and analysis of the sensitivity analysis performed for select once-through 
and closed fuel cycle transition scenarios. Model parameters considered 
for the sensitivity analysis include the transition start time, 
the percent of \glspl{LWR} that receive license extensions, the build share 
of each advanced reactor, and the discharge fuel burnup of the 
\gls{HALEU}-fueled advanced reactors. The analysis considers each model 
parameters effect and their combined effects from varying multiple 
parameters on the same material requirements considered in Chapters 4 and 5.

Chapter 7 provides 
results and discussion of the optimization of select once-through and 
closed fuel cycle transitions. The fuel cycles are optimized for minimizing 
the \gls{SWU} capacity required to produce \gls{HALEU}, minimize the 
mass of \gls{UNF} disposed, and both in a multi-objective problem. This 
portion of the work is done by coupling \Cyclus with Dakota, 
and the discussion includes analysis of the results 
and the performance of this methodology for optimizing \glspl{NFC}. 

Chapter 8 provides the methodology and 
results of evaluating the performance of downblended \gls{HEU} in 
the \gls{HALEU}-fueled advanced reactors. Metrics considered for the 
reactor performance include the \keff, \betaEff, energy- and 
spatially-dependent neutron flux, and the fuel, coolant, moderator, and
total reactivity temperature feedback coefficients. 
Finally, Chapter 9 concludes this dissertation by summarizing 
the main results of the work, identifying gaps in the work, and 
proposing future work to address the gaps and 
build upon this work.