\documentclass{beamer}
\usepackage[style=apa,natbib=true]{biblatex}
\usepackage{cleveref}

\bibliography{Supporting/Beamer.bib}
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%Information to be included in the title page:
\title{Should We Always Aim for Higher Quality?}
\subtitle{The Impact of the Groundwater Restoration Framework in In-Situ Uranium Recovery in Wyoming}
\author{Alexander Gebben}
\institute{Center for Business and Economic Analysis, University of Wyoming}
\date{2024}

\begin{document}
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\frame{\titlepage}
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\begin{frame}
	\huge
	\centering
What is In Situ Mining?
\end{frame}

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\begin{frame}
\frametitle{Ranger Open Pit Uranium Mine, Australia}
\includegraphics[width=\textwidth]{Images/Ranger_Uranium_Mine_01.jpg}
\end{frame}
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\begin{frame}
\frametitle{Smith Ranch-Highland ISL Uranium Mine, Wyoming}
\includegraphics[width=\textwidth]{Images/Smith-Ranch-Highland.jpg}\footnote{\tiny Image used with permission from Cameco Corporation}
\end{frame}
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\begin{frame}
\frametitle{In Situ Operation}
\includegraphics[width=\textwidth]{Images/Process_Facility.png}
\end{frame}
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\begin{frame}
\frametitle{Uranium Extraction Wells}
\includegraphics[width=\textwidth]{Images/Recovery_Well.png}
\end{frame}
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\begin{frame}
\frametitle{In Situ Site Boundaries}
\includegraphics[width=\textwidth]{Images/Boundry.png}
\end{frame}
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\setbeamercovered{transparent}%still covered={\opaqueness<1->{0}},again covered={\opaqueness<1->{10}}}
\begin{frame}
\frametitle{Regulation of In Situ Mines: Aquifer Exemption}
\only<1>{\onslide<1>\begin{quote}``Any underground injection, except into a well authorized by rule or except as authorized by permit issued under the UIC program, is prohibited.'' \tiny-- 40 CFR \(\textsection\) 144.11
	\end{quote}}
	\only<2->{\onslide<2->\textbf{To start a in situ mine the aquifer must be exempt by the EPA}\footnote{\tiny \citep{cheung2014,usepa2015a}}
		\begin{enumerate}
				\onslide<3->\item{Must not currently serve as a source of drinking water}
				\onslide<3->\item{Will not serve as a source of drinking water in the future}
				\begin{itemize}
				\onslide<4->\item{Already highly contaminated (TDS above 10,000 \(\frac{mg}{L}\))}
				\onslide<4->\item{Low population: unlikely to use the groundwater in the foreseeable future.}
		\end{itemize}
		\end{enumerate}
	}
	
\end{frame}

\begin{frame}
\frametitle{Regulation of In Situ Mines: Aquifer Restoration}
\only<1>{\begin{quote}``The primary goal of a restoration program is to return the water quality within the exploited production zone and any affected aquifers to pre-operational (baseline) water quality conditionsd''\tiny--NRC Licensing Standards \citep{luthiger2003}\end{quote}}

\only<2->{\textbf{Aquifers must be restored to a pre-mining state}
		\begin{enumerate}
			\onslide<2->\item{Show all constituents (uranium, selenium, TDS ect.) are returned to original levels}
			\onslide<3->\item{Sample groundwater before starting}
		\onslide<4->\item{Sweep the aquifer after completion}
				\begin{itemize}
					\onslide<4->\item{Filter the water and use for irrigation}
					\onslide<4->\item{Inject the water into deeper formation}
					\end{itemize}
			\onslide<5->\item{Filter the water that flows in to replace the mined water}
			\onslide<6->\item{Monitor acidity and constituent in water}
			\end{enumerate}
		%	\onslide<7->\textbf{Once exempt a aquifer can never be used as a public drinking water source.}
		}
\end{frame}

\begin{frame}
\frametitle{Regulation of In Situ Mines: Economic Consequences}
\only<1>{Mines are required to spend more resources to clean aquifers with a low economic value}

\onslide<2-3>\textbf{Aquifer Exemption Rule}
		\begin{enumerate}
			\onslide<2-3>\item{Removes reservoirs from uranium production}
			\onslide<2-3>\item{Uranium can only be extracted from low value aquifers}
			\onslide<2-3>\item{Removes reservoirs from use as a drinking water source (even after restoration)}
			\onslide<2-3>\item{Does not consider opportunity costs}
				\begin{itemize}
					\onslide<3>\item{Is the aquifer best used as a mine or for drinking water?}
					\onslide<3>\item{Are there substitute sources of drinking water?}
					\onslide<3>\item{What is the expected value of the groundwater?}
				\end{itemize}
		\end{enumerate}
	
		\onslide<4->\textbf{Aquifer Restoration Rules}
		\begin{enumerate}
			\onslide<4->\item{Resources must be spent to restore aquifers not used for drinking water}
			\onslide<4->\item{Marginal abatement costs higher than marginal benefits }
		\end{enumerate}
\end{frame}
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\begin{frame}
	\huge
	\centering
Are current restoration rules efficient?
\end{frame}
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\begin{frame}
\frametitle{In Situ Operations Externalities}
\begin{itemize}
	\item{\footnotesize If a mine is \emph{not restored}, pollutants move \(\approx\) 500 feet in 100 years.}
\end{itemize}
\begin{columns}
\begin{column}{0.5\textwidth}
\begin{figure}[ht]
\includegraphics[width=\textwidth]{Images/Pollution1.png}
	\caption{\footnotesize Intial TDS (\(\frac{650 mg}{L}\))}
\end{figure}
\end{column}
\begin{column}{0.478\textwidth}
\begin{figure}[ht]
	\includegraphics[width=\textwidth]{Images/Pollution2.png}
	\caption{\footnotesize 100 Years later:TDS \(\frac{400 mg}{L}\)}
\end{figure}
\end{column}
\end{columns}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
	\frametitle{Comparing Restoration Benefits and Costs}
	\only<1>{
		Areas with high TDS (in red) have a \emph{low cost} of restoration.
	\includegraphics[width=0.9\textwidth]{Images/TDS_Wyoming.jpeg}\footnote{\tiny Data used comes from  \citep{eia2020a,wyomingstategeologicalsurvey2024}. TDS is interpolated with regional smoothing.}
}
\only<2>{
	Uranium resources are typically in rural parts of the State. 
	Low land prices in these areas suggest mining is the highest values use.
	\centering
	\includegraphics[width=0.6\textwidth]{Images/Price_Histogram.png}}
\only<3-4>{
\textbf{Results}
\onslide<3>{Operating plans of five mines were reviewed. 
	\begin{itemize}
		\item{Adds \$4.3 dollar's per pound produced.}
			\begin{itemize}
				\item{Cost vary by geology. \$1.6-\$10.84 per pound}
			\end{itemize}
		\item{Average of \$15 million per project}
		\item{A discount of 10\% was assumed which reduces industry estimates of cost}
\end{itemize}}
\onslide<4>{
	Wyoming land values over a uranium resource.
	\begin{itemize}
		\item{Weighted average price of \$239 per acre}
		\item{Average mine lease area of 13,750 acres}
		\item{Total expected value of land of \$3.29 million dollars}
	\end{itemize}
}

}
\only<5>{Average restoration costs are \emph{4.5 times larger} than the value of land for a typical in situ mine.
\newline

Even under the strongest assumptions it is not plausible that the restoration costs are efficient. 
\newline

Hedonic models predict land value changes between 0.3\% and 15\% of total value\footnote{\tiny\citep{guignet2015,mukherjee2014}}.
}
\only<6>{
	Other factors suggest the actual cost is nearly zero.
	\begin{itemize}
		\item{Most mines are on ranches, not farms or urban areas}
		\item{High groundwater quality provides alternative sources}
		\item{Water is restored naturally over time}
		\item{Home filtration may be more cost effective}
	\end{itemize}

}
\end{frame}

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\begin{frame}
	\huge
	\centering
What are the market dynamics of uranium production?
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Mining Model}
\only<1>{
\begin{equation}
	\label{EQPROFITALL}
\tiny	\pi=\sum_{t=0}^{T}\left[\left(P_{ur} \cdot \left(W_{t}^{\alpha}-W_{t-1}^{\alpha}\right)-\left(C_{Drill}+C_{Res}\right)\cdot\left(W_{t}-W_{t-1}\right)\right)\frac{1}{(1+r)^t}\right]-C_{Facility}
	\end{equation}
Subject to: \(\beta\cdot C_{Facility}\ge W_{t}^{\alpha}-W_{t-1}^{\alpha}\), and \(\gamma_{Drill}\ge W_{t}^{\alpha}-W_{t-1}^{\alpha}\)
\newline
\normalsize
Where \(P_{ur}\) is the price of uranium, \(W_{t}\) is the total number of wells drilled in a aquifer at time \emph{t}, \(\alpha\) is a constant between zero and one representing the decline in ore grade across the reservoir, \(C_{Drill}\) is the cost to drill a well, \(C_{Res}\) is the cost to restore the water affected by a well, \emph{r} is the yearly discount rate of the firm, \(C_{Facility}\) is the investment cost in the uranium processing facility, \(\beta\) is a factor that converts the dollars spent to construct a uranium processing facility to output capacity, and \(\gamma_{Drill}\) is the maximum available drilling capacity in the region. 
}
\only<2>{
	\textbf{Arp's exponential Decline Curve}
		\begin{equation*}q=q_{i}\cdot e^{-D\cdot T}\end{equation*}
			Where \emph{q} is the production at time \emph{t}, \(q_{i}\) is starting production rate, and \emph{D} is some constant between zero and one.\citep{mccain2017}
			\begin{itemize}
				\item{Production choices of a well are fixed after they are drilled.\citep{anderson2018}.}
			\end{itemize}
	}

\only<3>{
\begin{equation}
	\label{EQPROFIT}
	\pi_{w}=\int_{t=0}^{T}\left[ \left(P_{ur}\cdot q_{i}\cdot e^{-Dt}-C_{op}\right)e^{-rt}\right] \,dt-C_{Drill}-C_{Res}\cdot e^{-rT} 
\end{equation}
Where \emph{D} is the decline rate of the well, and r is the instantaneous private discount rate. Since the terminal time \emph{T} is a choice variable the optimal time to operate the well can be found with:
}
\only<4>{
\begin{equation}
	\label{EQINFWELL}
	T^{\star}=\frac{\ln(P_{ur})+\ln(q_{i})-\ln(C_{op}-r C_{Res})}{D}
\end{equation}
\begin{equation}
	\label{TIMEDIFF}
	\Delta T^{\star}=\frac{\ln(C_{op}-r C_{Res})-\ln(C_{op})}{D}
\end{equation}
}
\end{frame}

\begin{frame}
\frametitle{Other Inefficiencies}
\begin{equation}
	\Delta T^{\star}=\frac{\ln(C_{op}-r C_{Res})-\ln(C_{op})}{D}
\end{equation}
	\begin{itemize}
		\item{As \(r C_{Res}\) increases wells are operated longer to avoid retirements costs.}
		\item{If \(r C_{Res}> C_{op}\) the well is never shut down.}
		\item{Unintended consequence of increasing well operating time.}
	\end{itemize}
\end{frame}


\begin{frame}
\frametitle{Uranium Supply}
	\begin{figure}
	\includegraphics[width=\textwidth]{Images/SUPPLY_PLOT.jpeg}
	\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%
\section{Econometric Model}
\begin{frame}
\frametitle{Econometric Model}
	From \cref{EQPROFITALL} expansion of production is defined by a exponential conststant. 
	\begin{itemize}
		\item{A log-log form is used.}
	\end{itemize}

	From eq. (2) there is a time delay in production, and capital is sunk when prices decrease
	\begin{itemize}
		\item{Production lags are used}
	\end{itemize}
	Additional control included for inventories of uranium at power plants. Capturing future price expectations.\footnote{Data source of \citep{eia1993,eia1994,eia1995,eia1996,eia1997,eia1998,eia1999,eia2000,eia2001,eia2002,eia2003,eia2004,eia2005a,eia2006a,eia2007a,eia2008a,eia2009a,eia2010b,eia2011a,eia2012a,eia2013,eia2014a,eia2015b,eia2016a,eia2017c,eia2018a,eia2019a,eia2020b,eia2021a,eia2022b,eia2023b,eia2024}}

	A time trend is included to acount for average ore grade decline.
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Results}
\centering
	\includegraphics[width=0.8\textwidth]{Images/UR_Supply_Reg_Table.png}
\end{frame}
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\begin{frame}
\frametitle{Price Shock Over Time}
	\includegraphics[width=\textwidth]{Images/Price_Shock.jpeg}
\onslide<2>{A 0.66 elasticity translates to a 3.1\% reduction in uranium production, if the regulation add \$4.3 dollars per poind of uranium. }
\end{frame}
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\section{Reference} 
\begin{frame} 
\frametitle{Reference}
\tiny
\printbibliography 
\end{frame}



\end{document}