\documentclass{svmult} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage{amsfonts} %TCIDATA{OutputFilter=LATEX.DLL} %TCIDATA{Version=5.50.0.2960} %TCIDATA{} %TCIDATA{BibliographyScheme=BibTeX} %TCIDATA{Created=Monday, October 25, 2010 10:30:01} %TCIDATA{LastRevised=Thursday, October 28, 2010 02:41:45} %TCIDATA{} %TCIDATA{} %TCIDATA{CSTFile=svmult.cst} \makeindex \iffalse \newtheorem{theorem}{Theorem} \newtheorem{acknowledgement}[theorem]{Acknowledgement} \newtheorem{axiom}[theorem]{Axiom} \newtheorem{case}[theorem]{Case} \newtheorem{claim}[theorem]{Claim} \newtheorem{conjecture}[theorem]{Conjecture} \newtheorem{corollary}[theorem]{Corollary} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{exercise}[theorem]{Exercise} \newtheorem{lemma}[theorem]{Lemma} \newtheorem{problem}[theorem]{Problem} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{remark}[theorem]{Remark} \newtheorem{solution}[theorem]{Solution} \newenvironment{proof}[Proof]{\noindent\textbf{#1.} }{\ \rule{0.5em}{0.5em}} \fi \newtheorem{algorithm}[theorem]{Algorithm} \newtheorem{conclusion}[theorem]{Conclusion} \newtheorem{condition}[theorem]{Condition} \newtheorem{criterion}[theorem]{Criterion} \newtheorem{notation}[theorem]{Notation} \newtheorem{summary}[theorem]{Summary} \input{tcilatex} \begin{document} %TCIMACRO{\TeXButton{Title}{\title*{Modeling the Costs of Carbon Capture}}}% %BeginExpansion \title*{Modeling the Costs of Carbon Capture}% %EndExpansion %TCIMACRO{\TeXButton{Short Title}{\titlerunning{Short Title}}}% %BeginExpansion \titlerunning{Short Title}% %EndExpansion %TCIMACRO{% %\TeXButton{Author}{\author{Erin Baker\inst{1}\and %Gregory Nemet\inst{2}\and %Peter Rasmussen\inst{1}}}}% %BeginExpansion \author{Erin Baker\inst{1}\and Gregory Nemet\inst{2}\and Peter Rasmussen\inst{1}}% %EndExpansion %TCIMACRO{\TeXButton{Short Author}{\authorrunning{Short Author}}}% %BeginExpansion \authorrunning{Short Author}% %EndExpansion %TCIMACRO{% %\TeXButton{Institute}{\institute{Mechanical and Industrial Engineering Department, University of Massachusetts Amherst, Amherst, MA, 01003-1027 %\texttt{edbaker@ecs.umass.edu} %\and La Follette School of Public Affairs, University of Wisconsin - Madison, Madison, WI, 53706-1211 \texttt{nemet@wisc.edu}}}}% %BeginExpansion \institute{Mechanical and Industrial Engineering Department, University of Massachusetts Amherst, Amherst, MA, 01003-1027 \texttt{edbaker@ecs.umass.edu} \and La Follette School of Public Affairs, University of Wisconsin - Madison, Madison, WI, 53706-1211 \texttt{nemet@wisc.edu}}% %EndExpansion %TCIMACRO{\TeXButton{Make Title}{\maketitle}}% %BeginExpansion \maketitle% %EndExpansion %TCIMACRO{% %\TeXButton{Abstract}{\abstract{This paper explores the fundamental concepts required to model intertemporal carbon capture costs. %A technical overview of post-combustion, pre-combustion, and alternative combustion carbon capture %technologies is followed by a discussion of cost measures that allow for side-by-side comparison of one technology %to the next. Carbon capture cost measures include capital cost per unit output power, levelized electricity cost %(LEC) and CO$_{2}$ avoidance cost. The relationships between these cost measures is mathematically explored and %cost data for several carbon capture technologies obtained from a survey of the literature are provided. Carbon %capture technology cost data expressed in terms of the aforementioned cost measures are discussed before the %paper moves on to discuss the most significant drivers of intertemporal carbon capture cost reduction, which include %learning by doing (LBD), production returns to scale and research and development (R\&D). %\keywords{shell svmult}}}}% %BeginExpansion \abstract{This paper explores the fundamental concepts required to model intertemporal carbon capture costs. A technical overview of post-combustion, pre-combustion, and alternative combustion carbon capture technologies is followed by a discussion of cost measures that allow for side-by-side comparison of one technology to the next. Carbon capture cost measures include capital cost per unit output power, levelized electricity cost (LEC) and CO$_{2}$ avoidance cost. The relationships between these cost measures is mathematically explored and cost data for several carbon capture technologies obtained from a survey of the literature are provided. Carbon capture technology cost data expressed in terms of the aforementioned cost measures are discussed before the paper moves on to discuss the most significant drivers of intertemporal carbon capture cost reduction, which include learning by doing (LBD), production returns to scale and research and development (R\&D). \keywords{shell svmult}}% %EndExpansion \section{Introduction} In order to meet the challenge presented by climate change, low carbon energy technologies must supplant high carbon, fossil-based energy technologies. Uncontrolled carbon dioxide emissions from traditional fossil fuels such as coal and natural gas constitute about 60\% of the world's carbon dioxide emissions from fossil fuels and generate over 66\% of the world's electricity EIA\cite{EIA_IEO09} EIA\cite{EIA_06}. In the absence of climate policy, coal combustion is likely to increase in conjunction with global energy demands, especially in populous, coal-rich, developing countries such as China and India. This is true even under a wide range of climate change damage and policy scenarios Katzer et al. \cite% {Future_of_Coal07}. Accordingly, coal plants are likely to continue to play an integral role in providing the world's power but must do so emitting significantly less carbon dioxide than they do now. Incremental improvements to operating efficiencies alone are unlikely to be sufficient to meet carbon stabilization goals. In fact, it is suggested that emissions need to be reduced by 80-90\% in order to meet such goals. Given the continued reliance on combustible fuels along with anticipated climate change-induced carbon dioxide emissions reductions, carbon capture and storage (CCS) is likely to factor into any low carbon energy technology portfolio Katzer et al. \cite% {Future_of_Coal07}. There are a variety of CCS technologies in various stages of research, development, and demonstration (RD\&D), although none have been demonstrated on a commercial level yet. Carbon capture and storage describes two consecutive processes that control coal fired power plant carbon dioxide emissions -- the capture and compression of CO$_{2}$ followed by the transport and storage of it. This chapter focuses on carbon capture, which constitutes over 80\% of CCS costs Katzer et al. \cite{Future_of_Coal07}. The goal of this chapter is to highlight significant technical and economic aspects of carbon capture addressed by the literature and identify knowledge gaps in the field, with a focus on cost modeling. The rest of the chapter is organized as follows. In Section \ref{SecTech} we provide an overview of the key capture technologies. In Section \ref{SecCost} we review the current literature on cost estimates for capture technologies. In Section \ref{SecTechChange} we discuss the possibilities for technological improvement in CCS. We distinguish between technical change that results from increases in production, such as learning-by-doing and returns to scale, and technical change that results from focused investment in research and development (R\&D). We conclude in Section \ref% {SecConclusions}. \section{Overview of the Technology\label{SecTech}} CCS technologies involve removing carbon during the production of energy so that it can be stored rather than released into the atmosphere. There are three main categories of CCS corresponding to three points in the process: Pre-combustion carbon capture, alternative combustion (sometimes called oxy-firing), and Post-combustion removal Katzer et al. \cite% {Future_of_Coal07}. In this section we discuss each of these in turn. \#Initial investment costs for each technology will be discussed in Section % \ref{SecCost}. \subsection{Pre-combustion} Pre-combustion carbon capture technologies, which are used in conjunction with integrated gasification combined cycle (IGCC), separate carbon dioxide from the process stream prior to combustion. IGCC is a technology that is a modification of natural gas-fired combined cycle (NGCC). IGCC gasifies less expensive, otherwise \textquotedblleft dirty\textquotedblright\ fuels such coal and refinery residuals (e.g. petroleum coke) before the gasified stream is combusted in a gas turbine. Waste heat is partially recovered in an integrated steam turbine to maximize efficiency. \# CO$_{2}$, along with Criteria Pollutants, are removed prior to combustion from the gasified stream. At the beginning of the pre-combustrion process, slurry or dry-fed coal is fed along with an oxygen-rich stream to a gasifier where the two streams react to form syngas, a mixture of hydrogen and carbon monoxide: \begin{equation} C+H_{2}O\longrightarrow H_{2}+CO \end{equation} There are three broad categories of gasifiers: moving-bed gasifiers (Sasol-Lurgi dry ash), fluidized-bed gasifiers (GE and Shell), and entrained-flow gasifiers (i.e. ConocoPhillips E-Gas) Katzer et al. \cite% {Future_of_Coal07} Cormos et al. \cite{Cormos10}. In a conventional IGCC\ system the next step is sulphur removal. \ For a plant with capture, the syngas stream is then reacted with high-pressure steam, a process known as the water-gas shift (WGS) reaction, which converts CO into CO$_{2}$: \begin{equation} CO+H_{2}O\rightleftharpoons CO_{2}+H_{2} \end{equation} Research is being conducted on reducing the energy penalty incurred from the water-gas shift reaction through the use of improved WGS catalysts and advanced configurations of shift reactors in combination with various gasifier types (i.e. dry-feed versus slurry) Carbo \cite{Carbo09}. The hydrogen and carbon dioxide stream is then purified to remove sulfur dioxide before the carbon dioxide is separated from hydrogen. The CO$_{2}$ separation takes place via a physical or chemical absorption process. For example, EPRI has produced a design using Selexol, a physical solvent consisting of a proprietary mixture of glycols Esber \cite{Esber06}. Research is being performed on other physical solvents, such as chilled methanol, and on chemical solvents such as methyldiethanolamine (MDEA) Heintz et al. \cite{Heintz08}. The captured carbon dioxide is compressed to a supercritical fluid so that it can be transported for storage. The hydrogen product stream can be combusted to produce electric power or stored as chemical potential energy for later use. It has been noted that \textit{integrated} gasification and carbon dioxide separators could significantly increase IGCC energy efficiency Al-Juaied and Whitmore \cite{Al-Juaied09}. While few IGCC plants have been built at this point, they have multiple advantages over conventional Pulverized Coal (PC) plants, including higher efficiencies, lower pollutant emissions, excellent performance even when using less expensive, high ash coals Cormos et al. \cite{Cormos10}, and the ability to use biomass fuels. This last feature could result in lower carbon emissions since biomass is part of the carbon cycle. In addition, power plants equipped with pre-combustion technologies have hydrogen and electricity coproduction capabilities Cormos et al. \cite{Cormos10} Haines and Davison \cite{Haines09}, which allows for variable power output Haines and Davison \cite{Haines09}. Hydrogen and electricity coproduction performance is highest using entrained-flow gasifiers Cormos et al. \cite% {Cormos10}. Finally, IGCC plants are essentially \textquotedblleft capture ready." The main challenges of pre-combustion CCS are to make it energy efficient and reliable. The water-gas shift reaction consumes the largest amount of additional energy, followed by CO$_{2}$ compression and CO$_{2}$ recovery Katzer et al. \cite{Future_of_Coal07}. \subsection{Alternative combustion} Technologies that remove CO$_{2}$ during combustion are more varied and involve changing the environment in which combustion occurs so that carbon is not released. The most commonly discussed of these are versions of oxy-firing. The critical aspect of oxy-firing technologies is the use of an air separation unit (ASU) which produces an oxygen rich stream that is fed to boiler or superheater. Oxygen-rich combustion produces CO$_{2}$-rich flue gas that does not require any CO$_{2}$ separation, only purification of the CO$_{2}$ stream prior to compression. In addition, the oxygen-rich combustion reaction occurs at higher temperature, resulting in higher combustion efficiency than air-fed counterparts. On the other hand, the ASU creates an energy penalty. The oxy-firing chemical reactions for coal and gas are identical to the post-combustion reaction equations given below, except for the absence of nitrogen. Chemical looping, a promising oxy-firing technology, uses a metal oxygen carrier that removes oxygen from the air and transports the oxygen to be reacted with a hydrocarbon. One ongoing project that uses chemical looping to capture carbon dioxide is being demonstrated on a 10 MWe pilot plant Mattisson et al. \cite{Mattison09}. This technology faces the challenge of finding particles that are both effective and durable at high enough temperatures. \subsection{Post-Combustion} Unlike pre-combustion CCS, post-combustion technology builds on existing, industry-standard PC combustion technologies. Post-combustion is an \textquotedblleft end-of-the-pipe\textquotedblright\ pollution control which scrubs exhaust gas of CO$_{2}$ emissions. Air and fuel are fed to and combusted in a boiler or superheater. The PC combustion chemical reaction is (assuming complete combustion):% \begin{equation} C_{x}H_{y}+(x+\frac{y}{4})O_{2}\longrightarrow xCO_{2}+(\frac{y}{2})H_{2}O \end{equation} The resulting heat of combustion power is transferred via superheated steam to a steam turbine or generator to produce electric power. For coal-fired processes, combustion by-products consist of ash and wet solids bottoms and flue gas. The flue gas contains nitrogen in addition to a variety of air pollutants and particulates, including CO$_{2}$. Upon gravity-fed removal of the bottoms, the flue gas is treated to remove carbon monoxide (CO), particulate matter (PM), nitrogen oxides (NO$_{X}$) sulfur dioxide (SO$_{2}$% ), and mercury. A separation process captures CO$_{2}$ which is then compressed for transportation and storage. Post-combustion separation can be achieved via absorption (using amines), adsorption, membranes, or cryogenic processes, all of which are currently being researched. Amine-based CO$_{2}$ separation occurs via the following reaction: \begin{equation} 2RNH_{2}+CO_{2}+H_{2}O\rightleftharpoons (RHN_{3})_{2}CO_{3} \end{equation}% where $R$ represents a generalized organic group, in this case the rest of the amine compound involved in the chemical reaction. \ The double arrows indicate that the CO$_{2}$ separation reaction is reversible. PC combustion includes, in increasing order of efficiency, the following technologies: subcritical pulverized coal combustion (PC), supercritical pulverized coal combustion (SC), and ultra-supercritical pulverized coal combustion (USC). Overall plant efficiency increases as the temperature of the coal feed is increased from subcritical to supercritical to ultra-supercritical Katzer et al. \cite{Future_of_Coal07}. Post-combustion capture can also be used with Natural gas combined cycle (NGCC). NGCC is similar to IGCC except that natural gas is used instead of a solid coal or biomass feed. The combustion reaction for natural gas (represented here as pure methane) is: \begin{equation} CH_{4}+2O_{2}\longrightarrow CO_{2}+2H_{2}O \end{equation} An advantage of post-combustion capture technologies is that the majority of existing plants are PC and can be retrofitted with bolt-on carbon dioxide separation units and CO$_{2}$ compressors. However, retrofitting existing plants results in a significant drop in plant efficiency that is more pronounced for subcritical PC plants than for SC and USC plants Katzer et al. \cite{Future_of_Coal07}. \subsection{A Brief Comparison between Each Technology Branch} \#These three technology branches are at different levels are maturity, and are potentially useful in different cases. Table \ref{Tech_Comparison} was modified from \cite{Wall07} and compares each technology to the other. Post-combustion is the most technologically mature of the three technologies, and is most suitable for bolt-on retrofits of existing, uncontrolled plants. In addition, given post-combustion CO$_{2}$ capture is an end-of-the-pipe process and is does not affect upstream combustion, post-combustion could most suitably be applied for partial CO$_{2}$ capture, which could be desirable given incremental policy changes mandating CO$_{2}$ controls. Finally, post-combustion also does not require an oxygen supply, unlike pre-combustion and oxy-fueling. Post-combustion of course has drawbacks compared to pre-combustion and oxy-fueling: process integration for post-combustion lags behind the other two technologies, an attribute which has a direct impact on plant efficiency. Pre-combustion can only be used in conjuction with IGCC\ or NGCC\ plants, thus limiting its use. But, it allows for the creation? and storage of hydrogen (H$_{2}$), a capability that allows for better plant operational flexibility, especially given future increases in renewable energy sources that provide variable power over time (e.g. solar and wind). Oxy-fueling technologies are the least mature, but present opportunities for great efficiencies if development proceeds. \# %TCIMACRO{\TeXButton{B}{\begin{table}[tbp] \centering}}% %BeginExpansion \begin{table}[tbp] \centering% %EndExpansion \begin{tabular}{ccccc} \textbf{Technology} & \textbf{Retrofit} & \textbf{Partial Capture} & \textbf{% Requires} & \textbf{H}$_{\mathbf{2}}$\textbf{\ Production} \\ & \textbf{Capability} & \textbf{Capability} & \textbf{O}$_{\mathbf{2}}$% \textbf{\ Supply} & \textbf{Capability} \\ \hline Post-Combustion & Yes & Yes & No & No \\ Pre-Combustion & No & Unlikely & Yes & Yes \\ Oxy-Fueling & Yes & No & Yes & No \\ \hline \end{tabular}% \caption{Comparison between Post-Combustion, Pre-Combustion, and Oxy-Fueling Technologies}\label{Tech_Comparison}% %TCIMACRO{\TeXButton{E}{\end{table}}}% %BeginExpansion \end{table}% %EndExpansion \subsection{International Perspective} There are numerous overviews on the various strengths and weaknesses of carbon capture technologies in western countries Metz et al. \cite{IPCC_CCS} Katzer et al. \cite{Future_of_Coal07}), but there has also been a recent increase in the number of papers that discuss advanced, low-cost carbon capture technologies in China. For example, both the popular press and the literature report that Chinese companies are beginning to export advanced coal technologies to the United States, especially more efficient, less expensive gasifiers that are being produced in China Gallagher \cite% {Gallagher09}. \section{Cost Estimation of Capture Technology\label{SecCost}} In this section we will discuss the ways that the cost of carbon capture is measured, and present a range of estimates. There are three main ways that the costs of CCS technology options are compared: \begin{itemize} \item capital cost per unit of output power (\$/kW); \item levelized electricity cost (LEC) (\$/kWh); and \item unit CO$_{2}$ avoidance cost (\$/ton CO$_{2}$avoided). \end{itemize} \subsection{Capital Costs\label{SubSecCapital}} The capital cost per unit of output power refers to the cost of the additional capital required to capture carbon. It is measured in terms of the net power output of the host plant.\ For example, PC and NGCC\ post-combustion capture plants require CO$_{2}$capture and CO$_{2}$compression process units; pre-combustion plants require a WGS reactor, CO$% _{2}$capture, and CO$_{2}$compression process units; oxy-fuel capture plants require ASU, CO$_{2}$distillation, and CO$_{2}$compression process units Rubin et al. \cite{Rubi-Yeh_07}. \ It should be noted, however, that the failure to consider downstream, integrated carbon capture and storage processes neglects economic benefits that can be attained by holistic changes Rubin et al. \cite{Rubi-Yeh_07} Katzer et al. \cite{Future_of_Coal07}% . This conclusion serves as a reminder that carbon capture and carbon storage are interdependent processes. \ The IEA\ gives estimates of additional capital cost ranging from \$600 -- \$1700/kW Kerr \cite{IEA_CCS08}% . MIT estimates the additional capital cost for post combustion to be in the range of about \$700 -- \$1000/kW, pre-combustion and oxy-firing about \$450 - \$600/kW Katzer et al. \cite{Future_of_Coal07}. \subsection{Levelized Electricity Cost} \#Measuring additional capital cost is useful, particularly as capital costs are often a deciding factor in which new technologies get adopted. Moreover, it does not require an assumption about discount rates. However, it does not capture the full cost of CCS technologies, as it misses operating costs, and importantly, the \textit{parasitic energy loss} that is associated with most of the technologies. In order to account for both capital costs and energy loss, it is convenient to use the Levelized Electricity Cost (LEC). Additionally, this provides a metric that allows easy comparison across a wide variety of energy generation technologies that have very different cost structures. Here we start by describing measures for the energy less, and then discuss how this can be used to calculate the LEC. \subsection{Energy Penalty} Capture technology requires energy to work, thus the total energy output per unit of fuel will be reduced by any CCS system. Some of the systems have quite high energy losses. This loss is measured in a number of ways in the literature. Rubin et al. \cite{Rubin09a} define the fractional reduction in plant output per unit of energy input as \begin{equation} FR=1-\left( \frac{\eta _{CCS}}{\eta _{ref}}\right) \end{equation}% where$\eta _{CCS}$and$\eta _{ref}$measure net efficiency of a plant with and without CCS, respectively. This can also be interpreted as the fraction of energy produced which is devoted to capture rather than production of electricity. Another metric is the Energy Penalty -- the increase in plant energy input per unit of output -- defined as \begin{equation} EP=\left( \frac{\eta _{ref}}{\eta _{CCS}}\right) -1=\frac{FR}{1-FR} \end{equation} The estimated energy penalty varies considerably across the technologies. We have reported some estimates in Tables \ref{TabPre}--\ref{TabOxy} below. \bigskip \begin{table}[tbp] \begin{minipage}{6in} \centering \small\addtolength{\tabcolsep}{6pt} \begin{tabular}{c c c c c c c} \textbf{Citation\footnote{The key to the citations is as follows: Al-Juiaed ; EPRI from EPRI Report 1013355 as reported in ; SFA from SFA: Pacific study as reported in ; MIT ; IEA ; IPCC ; Rubin .}} & \textbf{Technology\footnote{The key to the technologies is as follows: CFB - circulating fluidized bed technology; PC - subcritical pulverized coal technology; SC - supercritical pulverized coal technology; USC - ultra-supercritical pulverized coal technology.}} & \textbf{Energy} & \textbf{LEC$_{base}$\footnote{LEC$_{base}$- levelized electricity cost of fossil fuel plant without capture.}} & \textbf{LEC$_{cap}$\footnote{LEC$_{cap}$- levelized electricity cost of fossil fuel plant with carbon capture.}} & \textbf{LEC$_{add}$\footnote{LEC$_{add}$- additional levelized electricity cost that results from equipping a fossil fuel plant with CO$_{2}$controls.}} & \textbf{C$_{a}$\footnote{C$_{a}$- CO$_{2}$avoidance cost.}} \\ & & \textbf{Penalty} & \textbf{c/kWh} & \textbf{c/kWh} & \textbf{c/kWh} & \textbf{\$/tonne} \\ \hline MIT & IGCC & 0.23 & 5.6 & 7.2 & 1.5 & 21 \\ Rubin & IGCC & 0.23 & 5.1 & 6.9 & 1.7 & 27 \\ IPCC & IGCC & 0.19 & 5.6 & 7.4 & 1.8 & 27 \\ SFA & GEQ & 0.19 & 6.7 & 8.8 & 2.1 & \textit{\textbf{30}} \\ EPRI & GEQ & - & 6.2 & 8.7 & 2.6 & 31 \\ EPRI & GERQ & - & 6.8 & 9.3 & 2.5 & 34 \\ EPRI & CoP & - & 6.2 & 9.2 & 3.0 & 43 \\ EPRI & Shell & - & 6.7 & 9.6 & 2.9 & 55 \\ IEA & IGCC & 0.15 & 4.2 & 8.4 & 4.2 & 57 \\ IEA & Biomass IGCC &0.50 & 7.1 & 12.4 & 5.3 & \textit{\textbf{82}} \\ Al-Juaied & IGCC & - & 8.0 & 18.2 & 10.2 & 148 \\ & & \textbf{Average} & \textbf{6.2} & \textbf{9.6} & \textbf{3.4} & \textbf{51} \\ \hline \end{tabular} \vspace{-7pt}\renewcommand{\footnoterule}{} \end{minipage} \caption{Pre-Combustion Capture Costs Surveyed in the Literature} \label{TabPre2} \end{table} \begin{table}[tbp] \begin{minipage}{6in} \centering \small\addtolength{\tabcolsep}{6pt} \begin{tabular}{c c c c c c c} \textbf{Citation\footnote{The key to the citations is as follows: EPRI from EPRI Report 1013355 as reported in ; SFA from SFA: Pacific study as reported in ; MIT ; IEA ; IPCC ; Rubin  and .}} & \textbf{Technology\footnote{The key to the technologies is as follows: CFB - circulating fluidized bed technology; PC - subcritical pulverized coal technology; SC - supercritical pulverized coal technology; USC - ultra-supercritical pulverized coal technology.}} & \textbf{Energy} & \textbf{LEC$_{base}$\footnote{LEC$_{base}$ - levelized electricity cost of fossil fuel plant without capture.}} & \textbf{LEC$_{cap}$\footnote{LEC$_{cap}$ - levelized electricity cost of fossil fuel plant with carbon capture.}} & \textbf{LEC$_{add}$\footnote{LEC$_{add}$ - additional levelized electricity cost that results from equipping a fossil fuel plant with CO$_{2}$ controls.}} & \textbf{C$_{a}$\footnote{C$_{a}$ - CO$_{2}$ avoidance cost.}} \\ & & \textbf{Penalty} & \textbf{c/kWh} & \textbf{c/kWh} & \textbf{c/kWh} & \textbf{\$/tonne} \\ \hline MIT & CFB & 0.36 & 5.1 & 8.5 & 3.4 & 44 \\ MIT & SC & 0.23 & 5.3 & 8.4 & 3.2 & 44 \\ MIT & USC & 0.27 & 5.2 & 8.1 & 2.9 & 45 \\ MIT & PC & 0.37 & 5.3 & 9.0 & 3.6 & 45 \\ SFA & SC & 0.27 & 3.7 & 9.8 & 6.2 & 47 \\ Rubin & SC & - & 4.9 & 8.1 & 3.1 & 49 \\ IPCC & SC & 0.31 & 5.5 & 8.7 & 3.2 & 49 \\ EPRI & SC & - & 5.7 & 9.9 & 4.2 & 59 \\ IEA & SC & 0.24 & 4.0 & 8.1 & 4.1 & \textit{\textbf{69}} \\ & & \textbf{Average} & \textbf{5.0} & \textbf{8.7} & \textbf{3.8} & \textbf{50} \\ \hline \end{tabular} \vspace{-7pt}\renewcommand{\footnoterule}{} \end{minipage} \caption{Post-Combustion Capture Costs Surveyed in the Literature} \label{TabPost} \end{table} \begin{table}[tbp] \begin{minipage}{6in} \centering \small\addtolength{\tabcolsep}{6pt} \begin{tabular}{c c c c c c c c} \textbf{Category} & \textbf{Citation\footnote{The key to the citations is as follows: EPRI from EPRI Report 1013355 as reported in ; SFA from SFA: Pacific study as reported in ; SFA from a study by SFA: Pacific as reported in ; MIT ; IEA ; IPCC ; Rubin  and .}} & \textbf{Technology\footnote{The key to the technologyies is as follows: NGCC - natural gas combined cycle technology; NGCC OXY - oxy-fueled natural gas combined cycle technology SC - supercritical technology.}} & \textbf{Energy} & \textbf{LEC$_{base}$\footnote{LEC$_{base}$- levelized electricity cost of fossil fuel plant without capture.}} & \textbf{LEC$_{cap}$\footnote{LEC$_{cap}$- levelized electricity cost of fossil fuel plant with carbon capture.}} & \textbf{LEC$_{add}$\footnote{LEC$_{add}$- additional levelized electricity cost that results from equipping a fossil fuel plant with CO$_{2}$controls.}} & \textbf{C$_{a}$\footnote{C$_{a}$- CO$_{2}$avoidance cost.}} \\ & & & \textbf{Penalty} & \textbf{c/kWh} & \textbf{c/kWh} & \textbf{c/kWh} & \textbf{\$/tonne} \\ \hline Post-Combustion & IPCC & NGCC & 0.16 & 4.4 & 6.4 & 2.0 & 63 \\ and & Rubin & NGCC & - & 4.1 & 5.9 & 1.9 & 63 \\ Oxy-Fueling & EPRI & NGCC & - & 6.0 & 8.4 & 2.4 & \textit{\textbf{71}} \\ Natural Gas & SFA & NGCC & 0.13 & 6.5 & 8.9 & 2.3 & 78 \\ & IEA & NGCC & 0.09 & 4.8 & 7.6 & 2.8 & \textit{\textbf{93}} \\ & IEA & NGCC OXY & 0.28 & 4.3 & 6.7 & 2.4 & \textit{\textbf{68}} \\ & & & \textbf{Average} & \textbf{5.0} & \textbf{7.3} & \textbf{2.3} & \textbf{73} \\ \hline Oxy-Fueling & MIT & SC & - & 5.6 & 7.7 & 2.0 & 33 \\ & SFA & SC & - & 6.7 & 10.2 & 3.4 & 49 \\ & Rubin & SC & - & 4.9 & 8.7 & 3.7 & \textit{\textbf{59}} \\ & IEA & SC & 0.24 & 4.4 & 8.5 & 4.1 & \textit{\textbf{59}} \\ & & & \textbf{Average} & \textbf{5.4} & \textbf{8.7} & \textbf{3.3} & \textbf{50} \\ \hline \end{tabular} \vspace{-7pt}\renewcommand{\footnoterule}{} \end{minipage} \caption{Oxy-Fueling Combustion Capture Costs Surveyed in the Literature} \end{table} \subsection{Calculating the LEC} The LEC is the total cost of generating electricity amortized over the total amount of electricity produced by the plant. For fossil fuel plants the LEC\ is made up of the levelized cost of capital, the fuel cost, and Operating and Maintenance (O\&M) costs. The levelized capital cost amortizes the initial capital cost over the total energy output. Specifically, we amortize the capital cost of a kW of power, $K_{p}$, at a discount rate $\delta$ over a lifetime $L$, and divide the result by the energy produced in a year: the capacity factor, $CF$ multiplied by the number of hours in a year ($h$), 8760 . Let the amortization factor be represented by $f\left( \delta ,L\right) \equiv \frac{\delta }{\left( 1-\left( 1+\delta \right) ^{-L}\right) }$. Then \begin{equation} LEC_{CAP}=\frac{K_{p}}{CF\cdot h}\cdot f\left( \delta ,L\right) \label{CkWh} \end{equation}% To get the total LEC we add the $LEC_{CAP}$ with the fuel and O\&M costs per kWh. The LEC$_{fuel}$ will depend on the cost of the fuel C$_{fuel}$ and the efficiency of the plant $\eta$, as follows:% \begin{equation} LEC_{fuel}=\frac{0.003412\cdot C_{fuel}}{\eta } \end{equation}% where $C_{fuel}$ is the fuel price in dollars per MMBtu in terms of High Heating Value (HHV), the constant $0.003412$ converts from MMBtu to kWh, and $\eta$ is the efficiency of the plant. \#Thus, the total $% LEC_{capture}=LEC_{CAP}+LEC_{fuel}$ \textbf{is there also an LEC o\&M --we shoud maybe discuss this. This should be consistent with how we calculated it in the tables\#} We can calculate the \textit{additional} LEC from CCS, from the additional capital cost, $K_{add}$, the energy penalty $EP$, the baseline efficiency of the plant $\eta _{ref}$, the fuel price $C_{fuel}$, and any additional O\&M cost $OM_{add}$, as follows:% \begin{equation} LEC_{add}=\frac{K_{add}}{CF\ast h}f\left( \delta ,L\right) +\frac{% 0.003412\cdot C_{fuel}\cdot EP}{\eta _{ref}}+OM_{add} \end{equation}% This assumes there is no reduction in the capacity factor with CCS. We are most interested in the total LEC with capture (since this is what will drive the market share of fossil generation with CCS versus other low- or no-carbon options), and the additional LEC due to CCS. \# Tables \ref{TabPre} %--\ref{TabOxy} below present a range of estimates for the impact of CCS on LEC. \subsection{CO$_{2}$ Avoidance Cost} Finally, the third category of cost metrics is the cost of CO$_{2}$ avoidance. This is useful, since it gives an idea of how high a carbon price would have to be before CCS is adopted. The cost of CO$_{2}$ avoidance can be calculated from the LEC as follows:% \begin{equation} C_{a}=\frac{LEC_{CCS}-LEC_{ref}}{Q_{ref}-Q_{CCS}} \end{equation}% Where LEC$_{i}$ $i=CCS,ref$ refers to the LEC for plants with and without CCS, respectively, and $Q_{i}$ refers to the carbon emissions per unit of electricity (i.e. kWh or MWh depending on how the LEC is measured). $\,$\ Tables \ref{TabPre}--\ref{TabOxy} below show\ a range of estimates for the cost of CO$_{2}$ avoidance. Tables \ref{TabPre}--\ref{TabOxy} summarize CCS capture costs for pre-combustion, coal post-combustion, and\ natural gas and oxy-firing methods as reported in the literature. Cost estimates within each category are presented in order of lowest to highest cost of CO$_{2}$ avoidance. We present the energy penalty, the LEC for no capture, the additional LEC, and the total LEC with capture, and the CO$_{2}$ avoidance cost, as well as averages across all references. Some papers did not explicitly report the cost of CO$_{2}$ avoidance, so we have calculated it. These numbers are in bold italic in the table. If emissions rates were not explicitly given we assumed pre-capture rates of $1700$ and $836$ lbs/MWH for coal and gas respectively, and a capture rate of 90\%. All monetary amounts are presented in 2009 dollars. Note that the additional LEC and the cost of CO$_{2}$ avoidance are not perfectly correlated \#across the different studies\#. For example, in Table % \ref{TabPost} the MIT CFB and SPC technologies have higher additional LEC than MIT USC, but lower cost of CO$_{2}$ avoidance. This is due to differences in the baseline rate of emissions for the technologies, as well as to actual capture rate. The USC technology has a lower baseline emissions rate, therefore fewer emissions are captured with the technology. We see a similar issue with the natural gas technologies in Table \ref{TabOxy}. They have the lowest additional LECs, but higher cost of avoidance, since gas has lower emissions in the baseline. Pre-combustion and post-combustion have about the same average cost of avoidance, but pre-combustion has much more variance between the estimates, largely due to two outliers -- Al-Juaied and IEA IGCC with biomass. Without those outliers the average cost of CO$_{2}$ avoidance is only \$36/tonne (close to the median of \$34), much lower than the averages for the other technologies, and in fact lower than any individual estimate of post-combustion. The least robust are the estimates for oxy-fueling, with the fewest papers that have attempted this, and a lower amount of data reported in these papers. A very important issue to consider is that the additional LEC and the cost of CO$_{2}$ avoidance are in each case comparing the given technology with and without CCS. To get a better estimate, we would want to compare the actual technology that would be used in the absence of climate change policy with the given technology with CCS. For example, we may want to use the lowest baseline LEC for each coal study. In this case the pre-combustion additional LEC increases to 4.4 cents/kWh and the cost of CO$_{2}$ avoidance is \$64/tonne. This gives an estimate of reducing CO$_{2}$below the otherwise lowest cost technology. Which cost is appropriate depends on assumptions about the technology that will be otherwise most competitive. If IGCC turns out to be competitive because of other pollution emissions, for example, then the costs given in the table above are appropriate. But, if IGCC is being used primarily to reduce CO$_{2}$emissions, then the higher cost is more appropriate. Note that while the cost of CO$_{2}$avoidance is greater, the total LEC with capture is much lower for post-combustion than for pre-combustion. \section{Technical Change and CCS\label{SecTechChange}} In this section we discuss how technical change can be modeled for CCS. We consider two large categories of technical change. The first is technical change that is related to the quantity of production. These production-related changes include learning-by-doing (LBD) and scale effects. Knowledge acquired from production and economies of scale drives the resulting cost reductions. Ultimately they are spurred by increases in demand. The second category is non-incremental technical change that results from investments in research and development (R\&D). Understanding the potential improvements from both of these avenues is very important for policy design. \subsection{Production Effects\label{SecProductionEffects}} Increased production has been noted to decrease production costs through two channels--- LBD and returns to scale. Experience effects have been noted empirically in manufacturing since Wright \cite{Wright_36} and in services since Bryan and Harter \cite{Will-Hart_1899}. First, it was qualitatively observed that workers became more efficient as they produce more units. Second, it was observed that unit costs decrease with accumulated production experience. Arrow \cite{Arrow62} went on to formalize the concept of LBD in his seminal paper, focusing mainly on labor costs. In Section \ref{SubSecLBD} we will discuss how the concepts of LBD\ can be applied to CCS. Several studies, however, have criticized the attribution of cost reductions to LBD (see for example Dutton and Thomas \cite{Dutt-Thom_84}). Argote and Epple \cite{Argo-Eppl_90} proposed four alternative hypotheses for the observed technical improvements: economies of scale, knowledge spillovers, organizational forgetting, and employee turnover. In Section \ref{SubSecRTS} we will focus on the first of these, returns to scale.\footnote{% Knowledge spillovers are especially important in firm-level analyses of technical change. The latter two categories are typically addressed by depreciating the value of experience over time Thompson \cite{Thompson_07}.} In particular, it has been argued that capital costs respond more to returns to scale, while O\&M costs respond more to LBD Arrow \cite{Arrow62a}. Finally, in Section \ref{SubSecProdEff} we discuss some applications of production effects and provide an illustrative example of combining LBD and returns to scale to estimate future costs. Although there are gains that result from increasing the size of individual CCS plants, we ignore this increasing unit scale effect by assuming that: (1) optimal scale is similar to that of current coal plants, (2) this optimal scale is achieved quickly, and (3) that it is uniform so that every future CCS plant operates at this optimal scale. Other work modeling the cost of CCS generally assumes plants are built at steady scale and that the main returns to unit scale are in the development of the infrastructure Bielicki \cite{Bielicki_08}. \subsubsection{LBD\label{SubSecLBD}} LBD has most commonly been represented as a power function, for its simplicity and generally very good fit to observations. Measures of fit for energy technologies are often well above 0.90 McDonald and Schrattenholzer \cite{McDo-Schr_01}. Let total O\&M costs at time$t$be represented by$% N_{t}$and O\&M costs for the$m$individual components \#(see the top of Section \ref{SubSecCapital} for a discussion of the different units)\# be represented by$n_{i,t}$. Then the learning curve can be represented as follows: \begin{equation} {N}_{t}=\sum_{i=1}^{m}{n}_{i,t-1}\cdot \left( \frac{{E}_{t}}{{E}_{t-1}}% \right) ^{-b_{i}} \label{EqLBD} \end{equation}% where experience ($E$) in operating CCS plants is the sum of the CCS electricity output since$t=0$. Studies of learning rates for O\&M costs have been calculated for an array of similar technologies Taylor et al., Taylor and Nemet, Nemet \cite{Tayl-Rubi_05,Tayl-Neme_06, Nemet_07}. Estimates of O\&M learning rates for CCS in particular also exist Rubin et al., Yeh and Rubin, van den Broek et al. \cite{Rubi-Yeh_07,Yeh-Rubi_07, Broe-Hoef_09}. Based on these studies, Table \ref{Tablrates} provides the results of a survey of learning rates for technologies relevant to carbon capture and sequestration. The median value from these studies, 0.11, is slightly below the value from a survey of a broad set of learning rates in the energy sector Nemet \cite{Nemet_09a}, suggesting that CCS may improve at a slower rate than smaller scale technologies which may involve many more, albeit smaller, units.% %TCIMACRO{\TeXButton{B}{\begin{table}[tbp] \centering}}% %BeginExpansion \begin{table}[tbp] \centering% %EndExpansion \begin{tabular}{lcc} \hline \textbf{Analogous} & \textbf{Capital} & \textbf{Operations \&} \\ \textbf{Technology} & \textbf{Cost} & \textbf{Maintenance} \\ \hline Flue Gas Desulferization (FGD) & 0.110 & 0.220 \\ Hydrogen Steam Methane Reforming & 0.270 & 0.270 \\ Coal IGCC & 0.000 & 0.000 \\ & 0.100 & 0.050 \\ & 0.100 & 0.060 \\ & 0.110 & 0.220 \\ & 0.120 & 0.220 \\ & 0.140 & 0.120 \\ Liquified Natural Gas (LNG) & 0.140 & 0.120 \\ & 0.000 & 0.000 \\ & 0.100 & 0.060 \\ & 0.100 & 0.060 \\ & 0.110 & 0.220 \\ Oxygen Production & 0.100 & 0.050 \\ Pulverized Coal & 0.000 & 0.000 \\ & 0.050 & 0.180 \\ & 0.060 & 0.150 \\ & 0.110 & 0.220 \\ & 0.120 & 0.220 \\ Selective Catalytic Reduction (SCR) & 0.120 & 0.130 \\ & 0.168 & 0.269 \\ & & \\ & & \\ \textbf{Summary Statistics} & & \\ \hline Mean & 0.101 & 0.135 \\ Median & 0.110 & 0.130 \\ Standard Deviation & 0.060 & 0.092 \\ n & 21 & 21 \\ Maximum & 0.270 & 0.270 \\ Minimum & 0.000 & 0.000 \\ \hline \end{tabular}% \caption{Estimates of Learning Rates for Technologies Related to Carbon Capture}\label{Tablrates}% %TCIMACRO{\TeXButton{E}{\end{table}}}% %BeginExpansion \end{table}% %EndExpansion \subsubsection{Returns to Scale\label{SubSecRTS}} Increases in demand for CCS will lead to increases in manufacturing capacity for the individual components, which enable the manufacturing firms to reduce costs through economies of scale. Specifically, as demand for power plants with CCS increases, manufacturing of the components---gasifiers, air separation units, etc.---will increase so that production will grow to a more efficient scale. Manufacturers of these components take advantage of the resulting opportunities for cost reductions through, for example, spreading fixes costs, investing in automated processes, and developing specialized equipment. These changes reduce the cost of components for power plants. The general relationship is that costs of components fall as demand for CCS increases. Specifically, the total capital costs of CCS$M_{t}$will respond to scale in the following way, \#where$m_{i,t}$is the capital cost of technology component$i$at time$t$\#,$n$is the total number of components,$k_{t}$and$k_{t-1}$are the levels of demand for CCS plants in period$t$and the previous period$t-1$, respectively; and$a_{i}$is the component-specific scaling factor appropriate for the particular component. \begin{equation} {M}_{t}=\sum_{i=1}^{n}{m}_{i,t-1}\cdot \left( \frac{{k}_{t}}{{k}_{t-1}}% \right) ^{a_{i}} \label{scalecost} \end{equation}% This gives the total cost, unlike in the learning curve above, which gives the per-unit cost. Total cost increases as demand increases, but less than proportionally. To get the per-unit cost, we divide$M_{t}$by$k_{t}$. Since CCS components are not being manufactured at any large scale currently, we suggest using empirical estimates from other industries about the effects on unit cost of increases in manufacturing scale. One way to address this is to use estimates of cost reductions that result from up-scaling in the chemical and related industries, which probably includes the largest set of empirical estimates on scale Sinclair et al. \cite% {Sinc-Klep_00}. Moreover, the processes in the chemical industry are rather similar to those in a CCS plant. We use estimates of scaling parameters from many studies surveyed by Remer and Chai \cite{Reme-Chai_90}. Figure \ref% {FigRTS} below shows scaling factors for 570 manufacturing processes cited in their study. These include chemical processes, oil refineries, power plants, pollution controls. For the 570 scaling factors, we calculated the following descriptive statistics: mean$=0.68;$median$=0.68;$standard deviation$=0.13;$minimum$=0.23;$maximum$=1.07$.\FRAME{ftbpFU}{5.1463in}{% 2.4498in}{0pt}{\Qcb{Histogram of Scaling Factors Relevant to CCS (n=570)}}{% \Qlb{FigRTS}}{figrvalhist.eps}{\special{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio TRUE;display "USEDEF";valid_file "F";width 5.1463in;height 2.4498in;depth 0pt;original-width 5.2155in;original-height 2.4676in;cropleft "0";croptop "1";cropright "1";cropbottom "0";filename 'FigRvalHist.eps';file-properties "XNPEU";}} \subsubsection{Production Effects on Future Costs\label{SubSecProdEff}} The production effects on future costs depends on the future demand for CCS, which in turn depends on costs, as well as carbon policies, the broader economy, and the characteristics of competing technologies. Thus, estimating the size of production effects on future costs requires a sophisticated dynamic model. Here we discuss two papers -- one on applying learning curves, the other on returns to scale. We go on to provide a very simple illustration of how to combine these two effects in order to estimate the impact that increases in demand can have on the cost of CCS. Rubin et al. \cite{Rubi-Yeh_07} provides an example of applying learning curves to CCS. In this paper they first develop a set of experience curves for seven technologies relevant to CCS. They then decompose CCS plant designs into sub-systems, and apply a learning rate from the related technologies to each of the sub-systems based on judgement of similarity. These learning rates ranged from$0.05$to$0.27$, with a median of$0.12$. From this, they estimated the overall learning rate for CCS plants, and found that this was only between$0.03-0.05$, much lower than most of the component learning rates. The reason for this is that many of the subsystems are very similar to current technologies, and thus are starting from a much higher experience base, leading to less cost reduction over time. Nemet and Baker \cite{NemetBaker08} provide an example of applying returns to scale to a pre-commercial energy technology, in this case purely organic solar cells. In this paper they modeled returns to scale in a way quite analogous to LBD. The key difference is that the scale of the cost reduction is related to new installed capacity in a particular period, rather than to cumulative installed capacity. Thus, they apply equation (\ref{scalecost}), but used a scaling factor of$-0.18$. They considered both R\&D with uncertain non-incremental impacts and returns to scale. They found that R\&D had a much larger potential for technical change, but that subsidies to induce demand could play the role of a hedge against uncertainty in the outcomes of the R\&D program. Since CCS will probably have both LBD and returns to scale, the ideal model would incorporate both. Here we present a simplistic example of exogenous technical change through both LBD and returns to scale. It is exogenous because we are taking the demand for CCS as given. In reality, production effects have positive feedbacks -- the lower the price, the higher the demand, the lower the price in the next period. We will apply LBD to O\&M and returns to scale to capital costs. In general, the dynamics of O\&M costs respond to different influences than do the capital cost components. There is much more evidence that O\&M costs change as a function of learning-by-doing than there is for capital costs, which tend to respond to economies of manufacturing scale Rosenberg \cite% {Rosenber_82}. As in many other industrial facilities, plant operators find ways to improve the operation of their plants as they gain experience. For example, we might expect improvements in capacity factor because less maintenance is needed as operators make better decisions. We have taken the demand from the CCTP scenario called \textquotedblleft CCS Stabilization" Clarke et al. \cite{CCTP08}. The demand for energy generated using coal with CCS is approximately 10 EJ in 2035, 100 EJ in 2050, and 250 EJ in 2100. We assume that the demand increases linearly between these points, and model 5 year periods. We translate EJ into kWh, and then translate that into installed capacity measured in kW. \ We then calculate the demand for new capacity, as the difference between installed capacity in successive periods.% %TCIMACRO{\TeXButton{B}{\begin{table}[tbp] \centering}}% %BeginExpansion \begin{table}[tbp] \centering% %EndExpansion \begin{tabular}{llllllllll} \textbf{Year} & \textbf{2020} & \textbf{2030} & \textbf{2040} & \textbf{2050} & \textbf{2060} & \textbf{2070} & \textbf{2080} & \textbf{2090} & \textbf{% 2100} \\ \hline Demand (EJ) & 1.7 & 6.7 & 40.0 & 100.0 & 130.0 & 160.0 & 190.0 & 220.0 & 250.0 \\ Demand (TWh) & 463 & 1852 & 11111 & 27778 & 36111 & 44444 & 52778 & 61111 & 69444 \\ Total Installed (GW) & 67 & 267 & 1667 & 4267 & 6867 & 10667 & 14468 & 19468 & 24468 \\ New Installations (GW) & 67 & 133 & 1267 & 1333 & 1867 & 1933 & 2467 & 2533 & 3067% \end{tabular}% \caption{Summary of Assessment Results for Pre-Combustion}\label{TabDemand}% %TCIMACRO{\TeXButton{E}{\end{table}} }% %BeginExpansion \end{table} %EndExpansion Table \ref{TabDemand} shows the values we used up to 2060. It can be seen from this table that the demand for new installations increases dramatically in 2040, and then decreases in 2055. For illustration, we will use the average CO$_{2}$avoidance cost of$\$51$% /tonne from Table \ref{TabPre} above. This is equivalent to an additional LEC of $3.54$ cents per kWh. We assume that this LEC can be apportioned into capital costs, O\&M costs, and fuel costs in the ratio 69:22:09. We have taken this ratio from David and Herzog \cite{DavidHerzog01}, Table 2, using the values for IGCC 2000. We apply equation (\ref{EqLBD}) to the O\&M costs, using a learning ratio of $0.13$ and total installed capacity as representing the total experience. We apply returns to scale to the total capital cost of the new capacity, using a scaling factor of $0.68$, and then divide total capital cost by the new capacity, to get a per-unit cost. We assume that the energy penalty will not be affected by learning or scale, and so the fuel cost remains the same throughout the simulation. Figure \ref% {FigProdEffects} shows the results of this exercise, with the cost of CO$% _{2}$ avoidance measured on the left axis and cumulative installed capacity measured on the right axis. The cost of CO$_{2}$ avoidance moves downward through time, but not smoothly. The large decreases are due to large increases in the scale of production. In particular, as we point out above, there is a very large increase in scale between 2035 and 2040 in order to meet the large demand in 2050. We also note that the cost \textit{increases} in some periods. This is due to the decrease in scale when demand starts to increase at a slower pace. In particular, given the data above, the pace of new plants decreases after 2050, thus, there is a bump up in costs. The learning effects are much smoother, but not as pronounced. The LEC due to capital costs decreases from $2.45$ cents in 2020 to $0.64$ cents in 2050; while the LEC due to O\&M decreases from $0.78$ to $0.31$ during the same period.\FRAME{ftbpFU}{5.0194in}{3.3155in}{0pt}{\Qcb{Cost of CO$_{2}$ Avoidance and Total Installed Capacity}}{\Qlb{FigProdEffects}}{% figprodeffects.bmp}{\special{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio TRUE;display "USEDEF";valid_file "F";width 5.0194in;height 3.3155in;depth 0pt;original-width 5.0868in;original-height 3.3501in;cropleft "0";croptop "1";cropright "1";cropbottom "0";filename 'FigProdEffects.bmp';file-properties "XNPEU";}} The results are quite sensitive to assumptions about the quantity of the initial stock. \#In Figure \ref{FigProdEffects}, we have assumed that the initial cost of CO$_{2}$ avoidance is for demand equal to $1.7$ EJ, as shown in Table \#. To investigate the importance of this assumption, we vary this inital stock between $0$ and $10$ \textbf{[Peter check what the lower value is, I don't think it is zero]. } Figure \ref{FigInitialCost} shows how the reduction in the cost is related to the assumption about the initial stock. This is the point that Rubin et al. \cite{Rubi-Yeh_07} make in their paper, and indicates that care must be taken to correctly assess the initial experience and level of production when modeling cost reductions through production effects. \FRAME{ftbpFU}{4.1307in}{2.7683in}{0pt}{\Qcb{Impact of the Initial Capacity Stock on Cost Reductions}}{\Qlb{FigInitialCost}}{% figperredcost.wmf}{\special{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio TRUE;display "USEDEF";valid_file "F";width 4.1307in;height 2.7683in;depth 0pt;original-width 4.1812in;original-height 2.7922in;cropleft "0";croptop "1";cropright "1";cropbottom "0";filename 'FigPerRedCost.wmf';file-properties "XNPEU";}} The calculations are somewhat less sensitive to the values of the learning ratio and scale factor, but still impacted. Figure \ref{FigImpactParams} shows the percentage reduction in cost under different combinations of the learning ratio and scale factor. In the worst case, the learning ratio is lower by one standard deviation and the scale factor is higher by one standard deviation; in the best case these are reversed. A change in the scale factor by one standard deviation has a larger impact than a change in the learning ratio.\FRAME{ftbpFU}{7.7398in}{5.2971in}{0pt}{\Qcb{Impact of the Initial Capacity Stock on Cost Reductions}}{\Qlb{FigImpactParams}}{% figimpactparams.wmf}{\special{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio TRUE;display "USEDEF";valid_file "F";width 7.7398in;height 5.2971in;depth 0pt;original-width 10.2562in;original-height 7.0089in;cropleft "0";croptop "1";cropright "1";cropbottom "0";filename 'FigImpactParams.wmf';file-properties "XNPEU";}} These calculations are meant to be illustrative only, showing the impact of various assumptions on the potential for cost reduction through production impacts. Carefully combining these two avenues of production impacts is open to future work. \subsection{Research and Development\label{SecRD}} A second avenue for technical change is through R\&D, sometimes called learning through searching. This refers to a focused investment into finding new technological solutions to a problem. It is possible to have non-incremental technical change through this avenue. The relationship between R\&D investments and technical change is inherently uncertain. For more mature technologies, historical data and historical comparisons, e.g., Moore's law from the semiconductor industry, may exist and be useful. With highly innovative technologies, however, history provides only sketchy guidance. In such cases, common to R\&D management, decision analytic techniques are often used to obtain the necessarily subjective judgment of experts who are most familiar with the specific technologies Clemen and Kwit, Peerenboom et al., Sharpe and Keetin \cite{Clemen01}\cite% {PeerenboomBuehringJoseph89}\cite{Sharpe:98}. Here we review three papers that report on the results of expert elicitations into CCS\ technology. Baker et. al. \cite{BakerChonKeisler08} elicited probabilities of technical success conditional on US funding trajectories, for three categories of CCS: pre-combustion, chemical looping, and post-combustion. They defined technological endpoints in terms of a number of factors, and assessed the probability of achieving these endpoints conditional on US government funding (See Table \ref{TabFund} for funding trajectories). Table \ref% {TabBaker} summarizes the technological endpoints using the metrics discussed in Section \ref{SecCost} above. The numbers in bold are based directly on data from the paper. All other data used for calculations are from David and Herzog \cite{DavidHerzog01}. Baker et al. \cite% {BakerChonKeisler08} found (1) that the collection of more information appears to be of high value, especially on chemical looping (an oxy-firing technique), but on the other two categories as well; and (2) a significant amount of disagreement between experts, even over the most mature technology, that was most pronounced in regards to cost estimates. The goal of the study was to determine the impact on the entire marginal abatement cost curve, and so the elicitations were specifically NOT conditioned on a carbon tax. Thus the study did not get at the possible impact of demand-pull instruments. \begin{table}[tbp] \begin{minipage}{6in} \centering \small\addtolength{\tabcolsep}{6pt} \begin{tabular}{c c c c c} \textbf{Technology} & \textbf{Years} & \textbf{Low} & \textbf{Medium} & \textbf{High} \\ & & & & \\ \hline %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Pre-Combustion & 10 & 5 & 20 & 50 \\ Pre-Combustion & 10 & 0.5/5 & 1/10 & 5/10 \\ Oxy-Fueling\footnote{With chemical looping.} & 15 & 5 & 15/30 & 50 \\ \hline \end{tabular} \vspace{-7pt}\renewcommand{\footnoterule}{} \end{minipage} \caption{Funding Trajectories from Baker et al. } \label{TabFund} \end{table} \begin{table}[tbp] \begin{minipage}{6in} \centering \small\addtolength{\tabcolsep}{6pt} \begin{tabular}{c c c c c c c} \textbf{Technology} & \textbf{Energy} & \textbf{LEC$_{base}$\footnote{LEC$_{base}$ - levelized electricity cost of fossil fuel plant without capture.}} & \textbf{LEC$_{add}$\footnote{LEC$_{add}$ - additional levelized electricity cost that results from equipping a fossil fuel plant with CO$_{2}$ controls.}} & \textbf{LEC$_{cap}$\footnote{LEC$_{cap}$ - levelized electricity cost of fossil fuel plant with carbon capture.}} & \textbf{C$_{a}$\footnote{C$_{a}$ - CO$_{2}$ avoidance cost.}} & \textbf{LEC$_{capture}$ Percent Cost Increase} \\ & \textbf{Penalty} & \textbf{c/kWh} & \textbf{c/kWh} & \textbf{c/kWh} & \textbf{\$/tonne} & \\ \hline %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Pre-Combustion & 0.11 & 5.0 & \textit{\textbf{0.8}} & 5.8 & 13.4 & 16\% \\ Pre-Combustion & 0.30 & 4.4 & 1.7 & 6.1 & 25.0 \textbf{c/kWh} & 39\% \\ Oxy-Fueling\footnote{With chemical looping.} & - & 4.4 & 0.6 & 5.0 & 8.9 & 14\% \\ \hline \end{tabular} \vspace{-7pt}\renewcommand{\footnoterule}{} \end{minipage} \caption{Technological Endpoints from Baker et al. } \label{TabBaker} \end{table} \bigskip An NAS study focused on implementation of CCS technologies by 2025 \cite% {NRCouncil07}. They compare a no-DOE funding scenario with the DOE program as currently projected to be funded. The DOE projected spending an average of about \$220M a year over a 20 year period starting in 2001, on the CCS program. This program, however, includes six research streams: CO$_{2}$ capture; carbon storage; monitoring, mitigation and verification; breakthrough concepts; non-CO$_{2}$ greenhouse gases; and infrastructure development. The first research stream is most similar to the technologies assessed in Baker et al. and discussed in this review. The research stream on \textquotedblleft breakthrough technologies" also considers CO$_{2}$ capture technologies and so is relevant. The NAS, rather than defining endpoints in terms of specific technology, considered the overall success in terms of increase in the LEC. Four possible choices of increases in LEC were given to the expert panel: less than 10\%; between 10-20\%; between 20-30\%; or greater than 30\%. The mean increase in LEC from the panel assessments was about 15-18\% with the DOE program and about 16-20\% without it, depending on the level of carbon tax \cite{NRCouncil07}\footnote{% The carbon tax is assumed to impact the private sector incentive to innovate; but does not impact the increase in LEC\ directly.} \footnote{% \label{FootnoteCOE}These estimates of LEC only include additional cost of capture and compression, but exclude the cost of geologic storage. They are presented only for comparison purposes. The actual LEC may vary by fuel type, sequestration method and distance, and changes in carbon price and demand for fuel. The estimates presented here assumes zero carbon price and a baseline coal price of \$1.7/GJ of primary energy. The detailed assumptions and calculations are presented in the following section.}. Figure \ref{FigNAS} compares the average probabilities in the NAS study with Baker et al.\footnote{% Reprinted from Baker et al. \cite{BakerChonKeisler08}} The left panel compares the NAS assessments assuming no DOE funding, with the Baker assessments assuming a low funding trajectory for each technology, a total of about \$15M per year. The right panel compares the NAS assessments assuming DOE funding (\$220M over six categories), with the Baker assessment assuming a high funding trajectory for each technology, a total of about \$110M per year. The mid-points of each range is used for the NAS figures; that is, \textquotedblleft less than 10\%" is represented by 5\%, etc. The figures show the probability of achieving the additional cost to LEC on the horizontal axis, or better. So, for example, in the left panel with no or low funding, the NAS has a probability of achieving an additional cost of 15\% or less of about 55\%; Baker et al. has about 7.5\%. \FRAME{ftbpFU}{% 7.0843in}{1.9913in}{0pt}{\Qcb{The cumulative probability over the additional COE needed to achieve CCS.}}{\Qlb{FigNAS}}{Figure}{\special{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio TRUE;display "USEDEF";valid_file "T";width 7.0843in;height 1.9913in;depth 0pt;original-width 9.7999in;original-height 2.7356in;cropleft "0";croptop "1";cropright "1";cropbottom "0";tempfilename 'FigCumProbCOE.wmf';tempfile-properties "XNPR";}}Note that the estimates without breakthrough technical change given in Tables \ref{TabPre}--\ref% {TabOxy}\ above report an additional LEC ranging from 27\% to over 100\%. with the averages for each technology ranging between 50\% - 80\%. The NAS panel, even in the absence of DOE\ funding find that additional LEC will be \textit{no more} than 35\% whereas only 7 of the studies find an increase in LEC of 40\% or less. NAS finds a 50-50 chance that the additional LEC will be no more than 15\%. This corresponds to a cost of CO$_{2}$ avoidance of about \$10/ton CO$_{2}$avoided.\footnote{% Assuming$0.081$tons of carbon per kWh.} Thus the NAS\ panel appears quite optimistic next to Tables \ref{TabPre}--\ref{TabOxy}. Rao et al.\cite{Rao-Rubi_06} elicits technological parameters and then extrapolates the cost impacts of those parameters using a model. They consider one sub-technology of Post-combustion -- amine-based capture -- focus on the near term (2015), and condition only on the current US funding trajectory (\textquotedblleft with modest increases"). The results suggest that the cost of CO$_{2}$avoidance and the additional LEC will be reduced by about$18\%$on average, from baseline values of$\$47$/tonne and $3.8$ cents/kWh to $\$39$and$3.1$cents. The most optimistic outcomes, with probabilities of well under$5\%$, were$\$30$ and $2.5$ cents, respectively. If we assume a baseline LEC of $6.8$ cents/kWh, then the mean and most optimistic estimates are equivalent to increases in the LEC of $% 46\%$ and $37\%$, respectively. If we compare this with the two studies above, this implies either that this technology is much less promising than the other CCS technologies considered in the studies above, or that this group of experts is much more pessimistic. These values imply a small improvement over the values given in Table \ref{TabPre}--\ref{TabOxy}. \section{Conclusions\label{SecConclusions}} In this paper we have briefly reviewed the three categories of Carbon Capture technologies -- pre-combustion, oxy-firing methods, and post-combustion. We have defined and discussed key metrics for evaluating the costs of these technologies, namely, capital cost, energy penalty, the levelized cost of electricity, and the cost of CO$_{2}$ avoidance. In Section \ref{SecCost} we provide a summary of the cost estimates from the literature and tie together these various metrics. We then go on to discuss the avenues of technical change for CCS, distinguishing between production effects and R\&D. We provide an overview of two key production effects, LBD and returns to scale. In Section \ref{SubSecProdEff} we provide an illustrative example of combining these two effects. In Section \ref{SecRD} we reviewed three papers that provide estimates for the efficacy of R\&D into carbon capture technologies. We find that there is a wide range in the current estimates of the cost of the technology, both between different groups of researchers, and between different technologies for given groups of researchers. Pre-combustion generally has a lower cost of CO$_{2}$ avoidance, but a higher total LEC. The MIT group consistently has the lowest estimates, and the IEA consistently has the highest. One challenge is to pin down exactly what assumptions about the state of the technology have been made for these baseline estimates so that they can be used appropriately with LBD and returns to scale models. We saw that production effects can appear to lead to dramatic cost reductions, potentially reducing the costs by a factor of 4 or 5. However, great care must be taken when attempting to model cost reductions through these avenues. First, it seems likely that both LBD and scale will play a role, but it is less clear how these different effects should be applied, and to which components and aspects of cost. Second, it is crucial to very carefully align initial costs with an associated initial production level and experience level. In particular, it can sometimes be difficult to determine how much experience is assumed in the cost estimates provided in Tables \ref{TabPre} - \ref{TabOxy}. Moreover, the components of CCS vary considerably in the amount of experience that has been accrued in their manufacture, with some being very similar to mature technologies. Finally, there is always a question about how far costs can really decrease given physical limitations. In this paper we have focused on \textit{modeling} future costs, but if these models are to be used to analyze polices, then further care must be taken. In particular, LBD does not necessarily justify policy intervention on its own; only if there are spillovers is policy justified. Similarly, returns to scale have existed in many industries and has not always proven a problem. However, if the firms likely to produce CCS components have a history of being particularly myopic; or are likely to have trouble raising the required capital (perhaps because the demand for CCS\ will be entirely policy-driven), then policies aimed at increasing the scale may be justified. Of course, in the absence of a direct climate policy, such as a carbon tax or cap and trade, it may be argued that directed technology policy is a second-best response. In reviewing the three R\&D studies, we see that as the study becomes more technologically detailed, the predictions become less optimistic. Moving from Rao et al., to Baker et al., to NAS, we move from a very detailed study of a particular technology, to a broad study of three technological categories, to a general characterization of all carbon capture technology. The best guesses (means or medians) of these three studies for the percent increase in LEC due to capture given minimal government funding are about 46\%, 30\%, and 15\% respectively. On the one hand, the chance of success must increase when considering a wider range of technologies, and so this progression is logical. On the other hand, it is possible that when the technological detail is suppressed, some of the barriers to achieving success become less obvious. It would be ideal to combine a set of technologically detailed elicitations with a broad overview of the potential for change across all technologies. Finally, in order to craft the most efficient and effective policies, there is a need to model a combination of production effects and non-incremental technical change resulting from R\&D. An understanding of how these effects are likely to interact will help provide support to the design of an optimal, coherent portfolio of policies to address climate change in the presence of technical change. \begin{acknowledgement} The research leading to these results was completed while Baker was visiting the Precourt Energy Efficiency Center at Stanford University; and was partially supported by funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement n% %TCIMACRO{\U{b0} }% %BeginExpansion ${{}^\circ}$ %EndExpansion 240895 -- project ICARUS \textquotedblleft Innovation for Climate Change Mitigation: a Study of energy R\&D, its Uncertain Effectiveness and Spillovers\textquotedblright . \end{acknowledgement} \bigskip \bigskip \bibliographystyle{plain} \bibliography{acompat,ccshandbook_10} \end{document}