The FuTure oF nuclear Fuel cycle - MIT Energy Initiative

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Figure 3a.3 relative uranium Cost vs. normalized Cumulative nuclear energy Generation 5 4 relative cost of uranium (year 2005 constant $) (c,$/kg)/100 3 2 1 rBI rBu 85% 50% 15% 0.5 G1 ▶ 1 2 3 4 5 6 7 8 9 10 20 30 40 50 G,cumulative GWe-yr of nuclear electricity @ 200 MT unat per Full Power GWe-yr (divided by 10 4 ) G5 ▶ G10 ▶ Figure Key lines Plot C, $/kgU G, GWe - yr ; E = ; 4 E 100 10 i θ = −0.10 for 15% cPdF Percentile, optimistic choice θ = 0.11 for 50% cPdF Percentile, Median case θ = 0.29 for 85% cPdF Percentile, conservative choice where G1 = 100 years at today’s rate of uranium consumption and electric generation G5 = 100 years at 5 × today’s rate (equivalent to 2.7%/yr exponential growth) G10 = 100 years at 10 × today’s rate (equivalent to 3.6%/yr exponential growth) also: rBI = 2007 red Book, Identified, < 130 $/kg rBu = rBI + undiscovered, < 130 $/kg BaSe year point @ [1,1] is 2005: 100 $/kg & 10 4 GWe-yr appendix to chapter 3: Formulation of cost/cumulative resource elasticity Model 147
Again, assuming that q = 0.29, the plot gives C ~ = 250 $/kg (vs. Eq. 2 @ 252.8), which would warrant serious consideration of timely development of alternatives to once-through LWRs. Again note that our estimates are in constant dollars: nominal dollars decades from now would be much higher. By introducing the further approximation that the reference condition is just the integral of the exponential scenario from - ∞ to 0, the following analytic relations can be derived (which obviates the need for the graphic method): Cost at time T: C(T) Cr = e icT Average cost, 0 to T: icT C = e - 1 Cr icT Thus for θ = 0.29, γ = 0.04/yr, T = 80 yrs as in our earlier example: C(80) = 2.53 ; C = 1.65 Cr Cr C(80)/Cr agrees within readable precision with the value given by the plot on Figure A.3. derivation oF CoSt/ConSumption relation The approach applied in the present work was to combine models for the ore grade elasticity of cumulative resources (% change in cumulative natural uranium divided by % change in cutoff ore grade, ppm natural uranium), with economy of scale and learning curve correlations to find a relation between cost, $/kg U NAT , and cumulative resources ≥ x ppm in grade, in metric tons of natural uranium. In turn, the required uranium can be expressed in terms of GWe-years of nuclear energy. The reader can then readily superimpose a demand growth scenario. Assume scale effects apply to the mass of ore excavated and processed to obtain a kilogram of natural uranium. Then for an ore grade of x ppm, the unit cost is just: n C Xr [3] ` = , $/kgU Cr X `j j where n = scale exponent, typically ~0.7 for many industrial chemical engineering processes and r refers to a reference case – e.g., the start of period. The ore grade ratio can be related to cumulative resources through the ore grade elasticity of cumulative resources inferred from, in the present instance, a log-normal model based on Deffeyes’ analysis. The model gives the slope (elasticity) as a function of the grade x; using a representative average value over the range of interest: 148 MIT STudy on The FuTure oF nuclear Fuel cycle
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Other Reports in This Series The Fu
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MIT Nuclear Fuel Cycle Study Adviso
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vi MIT STudy on The FuTure oF nucle
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viii MIT STudy on The FuTure oF nuc
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Study Findings and Recommendations
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Recommendation We recommend that a
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p Innovative nuclear energy applica
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p In line with many of our R&D reco
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The “once through” or open fuel
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have been implemented slowly. This
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Recommendation We recommend that th
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oped policies for specific wastes r
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nuClear Fuel CyCleS The united Stat
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- The primary differences were in t
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Recommendation Integrated system st
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Table 1.2 Summary of R&D Recommenda
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18 MIT STudy on The FuTure oF nucle
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the once-through Fuel Cycle for lig
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tricity costs. Waste management cos
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Figure 2.3 partial recycle of lWr S
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history of the nuclear Fuel Cycle B
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• What is the impact of timing of
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nuclear fuel cycles, the wastes (SN
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Because ore demand is closely coupl
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eStimatinG Future CoStS oF uranium
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Figure 3.3 relative uranium Cost vs
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Figure 3.4 100 year price trend for
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Stockpiling If supply interruption
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CitationS and noteS 1. Uranium 2007
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If SNF is to be shipped, typically
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a policy that maintains fuel cycle
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Dry cask storage is used for short
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For decommissioned sites, our econo
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with its attractiveness of jobs and
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2. The United States should create
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Table 5.1 United States Waste Class
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table 5.3 examples of operational G
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Waste Isolation Pilot Plant The uni
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Successful repository programs are
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designed with limited SNF storage c
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CitationS and noteS 1. A Handbook f
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energy spectrum centered at higher
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light Water reactor Fuel technical
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(fertile-free) to CR=1.0 (break-eve
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license. However, fuel reprocessing
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Figure 6.4 densification Factors as
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As expected, the breeder installed
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Figure 6.8 shows the development of
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Table 6.8 Uranium Cost in $/kg, Sta
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Figure 6.11 location of the tru inv
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SenSitivity analySiS: alternative a
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Fast reactor technical Characterist
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cooled fast reactor (SFR) fueled by
Page 113 and 114: Summary oF ConCluSionS Among the in
Page 115 and 116: [hoffman et al., 2006] e.a. hoffman
Page 117 and 118: This chapter reports the cost of th
Page 119 and 120: Table 7.1 Input Parameter Assumptio
Page 121 and 122: Twice-Through Cycle Table 7.3 shows
Page 123 and 124: Table 7.4 The LCOE for the Fast Rea
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Page 131 and 132: Figure 8.1 Weapons-usability Charac
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Page 139 and 140: Reprocessing choices Commercial rep
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Page 149 and 150: who are very concerned with global
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Page 161 and 162: Figure 3A.2 shows the results. As c
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Page 181 and 182: orehole diSpoSal There are three me
Page 185 and 186: table 7a.1 list of variables , 1 lc
Page 187 and 188: The Twice-Through Cycle The LCOE fo
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Page 191 and 192: In the Twice-Through Cycle, the pai
Page 193 and 194: table 7a.2 once-through Fuel Cycle
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Page 197 and 198: CitationS and noteS 1. The methodol
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Page 205 and 206: Figure a.3 Schematic view of Sbu an
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(~700°C) with higher thermal-to-el
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There are several unique consequenc
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performance goals can be achieved.
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is that it will be many decades bef
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system [1]. The nuclear power plant
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The HTRs can be used to provide hig
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[http://nextgenerationnuclearplant.
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CitationS and noteS Brinkmann, H. U
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The analysis is based on the assump
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considerations discussed above. We
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In our analysis we make the explici
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Figure d.4 transmutation Consequenc
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Figure d.5 breeder Consequences LWR
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facilities. These concerns are the
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Technological applicability Geologi
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It must be noted, that net risks an
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p Once-through fast reactor fuel. T
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Table E.1 Recycling Plant Functions
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Table E.3 Conventional Fuel Fabrica
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eactor. A summary of inputs from in
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