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\caption{Isotopic Composition of Average Waste Streams}
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\label{fig:avg-isotope-comp}
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separation and trading with various facilities. This is done in a couple ways within Pyre, the first being various stream types such as waste or product,
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and the second being isotopic composition withing these streams. In Figure \ref{fig:avg-isotope-comp} the 3 waste streams shown in Figure \ref{fig:timeseries-waste}
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are compared isotopicaly. We do this comparison to further investigate the performance of each sub-process by identifying the appropriate separation of elements.
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We can see that the Electrowinner, shown in green, correctly contains heavier elements such as lanthanides while the Electroreductor, in red, is responsible for the lighter metals
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The Electrowinner, shown in green, correctly contains heavier elements such as lanthanides while the Electroreductor, in red, is responsible for the lighter metals
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as well as changing oxidation states which is not reflected in these streams.
\caption{Range of Isotopic Values for maximum potential diversion.}
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\label{fig:isotopic-range}
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\end{figure}
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is kept on the plot as a validation only appropriate processes are being affected.
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The other diversion scenario explored here is a theoretical maximum diversion scenario in which two scenarios are run: where parameters are set to their maximum and minimum values
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respectively.
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respectively. Although an unrealistic scenario since diversion is easily detected, the scenario shows us the worst case scenario and could be used to inform inspection intervals.
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Figure \ref{fig:isotopic-range} shows that after the 20 months scenario approximately a significant quantity of plutonium is unaccounted for. As such, inspections would need to occur
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at a similar interval, depending on the reported capacity.
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\section{US Fuel Cycle Transition}
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\section{US Fuel Cycle}
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After testing the capabilities of Pyre in a small scenario, we implement the archetype in the EG01-EG24 transition scenario described in the goals of this work.
Table \ref{tab:setup} shows the setup for a Sodium Fast Reactor transition. In addition to the above information, the scenario is initiated with 200 LWRs with another 200 being deployed
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in 2015 at the transition period. Two Pyre prototypes are deployed to handle the different fuel types seen in the above scenario. The PRIDE-based facility is configured to reprocess ceramic
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LWR waste while the INL-based facility handles metallic SFR fuel, and is deployed after the transition.
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Figure \ref{fig:net-cap} demonstrates the deployment and decommissioning of reactors in this scenario. In order to meet the average 1\% annual power growth, additional reactors are necessary
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while appropriate SFR fuel quantities are accumulated.
To verify functionality of the Pyre archetype, rather than the transition scenario itself, we take a look at the fuel production and utilization rather than facility deployment.
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Figures \ref{fig:TRU-util} and \ref{fig:u-util} demonstrate the appropriate reprocessing and fabrication of SFR fuel. Figure \ref{fig:TRU-util} shows around year 2125 the SFR pyroprocessing
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plants begin producing a sustainable amount of fuel. Since all SFRs are breeders in this scenario, we can see that as more reactors are deployed the TRU stock increases exponentially at year 2150. Similarly, the overall utilization of Uranium improves as reprocessing is heavily used.
Figure \ref{fig:fuel-mass} illustrates the complete transition from LWRs and UOX fuel to SFRs at year 2180. As seen in Figures \ref{fig:TRU-util} and \ref{fig:u-util}, TRU fuel
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production has increased enough to self-sustain the next generation of SFR reactors and decommission remaining LWRs.
The second aspect of this work is identifying potential places for diversion in a generic pyroprocessing facility. We took 2 primary approaches for this work, applying
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a cumulative sum detection algorithm and performing sensitivity analysis on key facility parameters.
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\section{Cumulative Sum}
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\subsection{Requirements of Diversion Detection}
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\paragraph{Online Diversion Detection}
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\paragraph{Ability to function without prior knowledge}
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The cumulative sum method (CUSUM) applied to Pyre was chosen to fit the following requirements: function with minimal prior information, have online diversion detection
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capabilities, and fit a modular approach. The CUSUM change detection algorithm relies on developing an expected mean value of a data stream as shown by the following equations \cite{basseville_detection_1993}.
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\paragraph{Modular capability}
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\[ f_{t+1} = max(0, f_t + x_t - \mu - \delta) \]
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\subsection{Limitations of selected method}
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Where:
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\[ x_t = observed \hspace{2mm} data \]
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\[\mu = approximated \hspace{2mm} mean \]
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\[\delta = acceptable \hspace{2mm} change \]
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\paragraph{Startup time}
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This general function adds new observed values to the calculated mean. If the value is within region of error, typically 3$\sigma$, change is not reported.
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We favor this online diversion detection capability in an effort to achieve timely detection goals set by the IAEA \cite{international_atomic_energy_agency_implications_2004}.
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These intermittent inspections only have access to portions of the complete data stream, thus we aim to mimic reality as closely as possible. In addition, we need this
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algorithm to work on a variety of facilities with different sub-processes active, ruling out a nodal approach seen by \cite{Yilmaz_2016}.
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\paragraph{Material balance areas}
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\subsection{Limitations of selected method}
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\paragraph{Artificial noise}
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This approach is not without its drawbacks, since there is no prior data assumed we must generate a reasonable mean before being able to detect diversion. For this work
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we assume a startup time of approximately 6 months before an appropriate mean can be developed. The next limitation faced with this approach is observing one data stream at a time, while
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real inspections take a wide range of conditions into account. This concern is addressed by using sensitivity analysis, as seen later in this chapter, to inform on the most crucial
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sub-processes or settings.
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CUSUM relies on a variable mean and noise to obscure possible change points. When a simulator knows the exact value at each time step, without human reporting or measurement error, change
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detection becomes trivial. To combat this issue, noise is artificially created when the CUSUM class reads data. This way \Cyclus retains its constant operating value while the change point
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has potential to be obscured by measurement error. These detector uncertainties are assumed from common non-destructive and destructive assay practices used by the SEE LANL course \cite{}.
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\section{Verification}
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\subsection{Nefarious Diversion}
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\subsection{Operator Diversion}
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To test operator diversion capabilities, we ran the EG01-EG24 transition scenario shown in chapter 3 with inside operators. The scenario described in Table \ref{tab:setup} contains an LWR and SFR configurationg for Pyre. Each prototype siphoned material with different quantities and frequencies to demonstrate its reconfigurability. The LWR Pyre siphoned off 5\% every 10 timesteps while the SFR Pyre siphoned off 1\% excess every other timestep. Results for this scenario are shown in
\caption{A timeseries of diverted material from two Pyre facilities.}
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\label{fig:divertmat}
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\end{figure}
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\section{Test Cases}
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\subsection{PRIDE}
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\section{Sensitivity Analysis}
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\paragraph{An important aspect of safeguarding new facilities is to know the limits of monitoring}
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\paragraph{Key parameters were run over a range of values for diversion to verify the archetype's capabilities and identify operational ranges.}
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Sensitivity analysis is an important aspect of this work to know the limits of monitoring these facilities. In this work we use Dakota to alter \Cyclus input files, allowing us to easily
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run batches of scenarios. To properly use Dakota with \Cyclus, we must use DCWrapper, which uses python to interface between Dakota and \Cyclus' xml input files.
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Key parameters were run over a range of values for diversion to verify the archetype's capabilities and identify operational ranges. Parameters were selected from the most attractive
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sub-processes for diversion, the electrorefiner and electrowinner. These two processes are responsible for the production of Uranium and U/TRU ingots, therefore sensitivity analysis was run
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on each of their key parameters: Temperature, Current, Flowrate, Pressure, Stirrer Speed and Reprocessing Time.
This thesis was motivated by a lack of medium fidelity pyroprocessing plants in current fuel cycle simulators \cite{borrelli_approaches_2017}. Combined with
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the need for safeguards by design in next generation nuclear fuel cycle facilities, a pyroprocessing facility with diversion capabilities fills a technological gap.
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Pyre brings more detailed separations processes to nuclear fuel cycle simulators informed by more limited and specific electrochemical models such as SSPM and AMPYRE \cite{maggos_update_2015}.
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\Cyclus provides a modular interface to expand and test the capabilities of reprocessing and material diversion. We developed Pyre in the C++ \Cyclus environment to leverage this
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modular framework and test the facility in a key pyroprocessing transition-scenario. We ran a full US fuel cycle transitioning from LWRs to SFRs using only Pyre facilities to facilitate
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this transition. We verified Pyre's role in this transition-scenario by observing the simulation's uranium utilization, TRU production, and successful fueling and operation of SFRs to
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