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Beamer/In_Situ_Presentation.nav
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Beamer/In_Situ_Presentation.snm
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\beamer@slide {EQPROFITALL}{28} \beamer@slide {EQPROFITALL}{31}

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Beamer/In_Situ_Presentation.tex
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\documentclass{beamer} \documentclass{beamer}
\usepackage[style=apa,natbib=true]{biblatex} \usepackage[style=apa,natbib=true]{biblatex}
\usepackage{cleveref}
\bibliography{Supporting/Beamer.bib} \bibliography{Supporting/Beamer.bib}
\setbeamercovered{transparent=25} \setbeamercovered{transparent=25}
%Information to be included in the title page: %Information to be included in the title page:
@ -12,6 +14,13 @@
\begin{document} \begin{document}
%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%
\frame{\titlepage} \frame{\titlepage}
%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\huge
\centering
What is In Situ Mining?
\end{frame}
%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%
\begin{frame} \begin{frame}
\frametitle{Ranger Open Pit Uranium Mine, Australia} \frametitle{Ranger Open Pit Uranium Mine, Australia}
@ -38,27 +47,6 @@
\frametitle{In Situ Site Boundaries} \frametitle{In Situ Site Boundaries}
\includegraphics[width=\textwidth]{Images/Boundry.png} \includegraphics[width=\textwidth]{Images/Boundry.png}
\end{frame} \end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Do In Situ Operations Create 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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\setbeamercovered{transparent}%still covered={\opaqueness<1->{0}},again covered={\opaqueness<1->{10}}} \setbeamercovered{transparent}%still covered={\opaqueness<1->{0}},again covered={\opaqueness<1->{10}}}
\begin{frame} \begin{frame}
@ -121,6 +109,34 @@
\onslide<4->\item{Marginal abatement costs higher than marginal benefits } \onslide<4->\item{Marginal abatement costs higher than marginal benefits }
\end{enumerate} \end{enumerate}
\end{frame} \end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\huge
\centering
Are current restoration rules efficient?
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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} \begin{frame}
\frametitle{Comparing Restoration Benefits and Costs} \frametitle{Comparing Restoration Benefits and Costs}
@ -135,7 +151,6 @@
\includegraphics[width=0.6\textwidth]{Images/Price_Histogram.png}} \includegraphics[width=0.6\textwidth]{Images/Price_Histogram.png}}
\only<3-4>{ \only<3-4>{
\textbf{Results} \textbf{Results}
\onslide<3>{Operating plans of five mines were reviewed. \onslide<3>{Operating plans of five mines were reviewed.
\begin{itemize} \begin{itemize}
\item{Adds \$4.3 dollar's per pound produced.} \item{Adds \$4.3 dollar's per pound produced.}
@ -175,13 +190,19 @@ Hedonic models predict land value changes between 0.3\% and 15\% of total value\
} }
\end{frame} \end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} \begin{frame}
\frametitle{Mining Model } \huge
\centering
What are the market dynamics of uranium production?
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Mining Model}
\only<1>{ \only<1>{
\tiny
\begin{equation} \begin{equation}
\label{EQPROFITALL} \label{EQPROFITALL}
\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} \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} \end{equation}
Subject to: \(\beta\cdot C_{Facility}\ge W_{t}^{\alpha}-W_{t-1}^{\alpha}\), and \(\gamma_{Drill}\ge W_{t}^{\alpha}-W_{t-1}^{\alpha}\) 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 \newline
@ -189,13 +210,22 @@ Subject to: \(\beta\cdot C_{Facility}\ge W_{t}^{\alpha}-W_{t-1}^{\alpha}\), and
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. 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>{ \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} \begin{equation}
\label{EQPROFIT} \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} \ \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} \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: 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<3>{ \only<4>{
\begin{equation} \begin{equation}
\label{EQINFWELL} \label{EQINFWELL}
T^{\star}=\frac{\ln(P_{ur})+\ln(q_{i})-\ln(C_{op}-r C_{Res})}{D} T^{\star}=\frac{\ln(P_{ur})+\ln(q_{i})-\ln(C_{op}-r C_{Res})}{D}
@ -205,8 +235,63 @@ Where \emph{D} is the decline rate of the well, and r is the instantaneous priva
\Delta T^{\star}=\frac{\ln(C_{op}-r C_{Res})-\ln(C_{op})}{D} \Delta T^{\star}=\frac{\ln(C_{op}-r C_{Res})-\ln(C_{op})}{D}
\end{equation} \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}
%%%%%%%%%%%%%%%%%%%%%%
\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}
%%%%%%%%%%%
\section{Reference}
\begin{frame}
\frametitle{Reference}
\tiny
\printbibliography
\end{frame} \end{frame}

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Beamer/Supporting/Beamer.bib
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@book{mccain2017, @book{mccain2017,
title = {Properties of {{Petroleum Fluids}} (3rd {{Edition}})}, title = {Properties of {{Petroleum Fluids}} (3rd {{Edition}})},
author = {{McCain William D Jr}}, author = {McCain, William},
date = {2017}, date = {2017},
publisher = {PennWell}, publisher = {PennWell},
abstract = {Petroleum can exist as either a liquid or a gas, either in the reservoir or on the trip to the surface. These properties are the basis for the chemistry of petroleum. This long-awaited new edition to author acclaimed text expands on the various compounds of this essential hydrocarbon. It includes new chapters on petroleum gas condensates and volatile oils, while the discussion on oilfield waters is extended. A vital resource for petroleum engineering students, this book is equally useful as a reference for practicing engineers. New Features: Two new chapters on gas condensates; A new chapter on volatile oils; A simplified explanation of phase behavior and an extended discussion of oilfield waters; An expanded review of the components of petroleum and the methods of determining its composition.}, abstract = {Petroleum can exist as either a liquid or a gas, either in the reservoir or on the trip to the surface. These properties are the basis for the chemistry of petroleum. This long-awaited new edition to author acclaimed text expands on the various compounds of this essential hydrocarbon. It includes new chapters on petroleum gas condensates and volatile oils, while the discussion on oilfield waters is extended. A vital resource for petroleum engineering students, this book is equally useful as a reference for practicing engineers. New Features: Two new chapters on gas condensates; A new chapter on volatile oils; A simplified explanation of phase behavior and an extended discussion of oilfield waters; An expanded review of the components of petroleum and the methods of determining its composition.},