The FuTure oF nuclear Fuel cycle - MIT Energy Initiative

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Probabilistic Approach Given the present state of knowledge, the parameters n, s, and f were each assumed uniformly distributed over a range suggested by a review of the applicable literature: 0.5 ≤ n ≤ 1.0 1.5 ≤ s ≤ 3 70% ≤ f ≤ 100% The ranges were selected as follows: (a) Economy of scale exponent, n Reference (7) reports n values for a total of 28 plants and processes. The mean is 0.63 and the range 0.40 to 0.83. Simon suggests a data-based exponent of 0.5 based on the scale of an industry as opposed to that of an individual production unit (8). Finally, several of the cruder models for uranium costs surveyed by Schneider (9) take no credit for scale economies, hence, in effect, n = 1.0. To encompass this information a uniform range between 0.5 and 1.0 was assumed. (b) Resource vs. grade elasticity, s Determination of this parameter based on Deffeyes’ model has been described in the main text of this chapter. The results were plotted in Figure A.2. The range selected spans ore grades between 200 and 10,000 ppm. This allows for not only evolution over time, but for the fact that grade varies within a given mine and between different mines, and exploitation is not necessarily in descending rank order of grade. (c) Learning, f Reference (10) reviews learning curve studies, and reports a range consistent with other findings of approximately 70 to 100%. The upper limit also accommodates most earlier uranium production cost studies, which apparently take no credit for learning. Results of Analysis Figure 3A.4 plots the results generated by 10 4 trials, sorted into Dq bins, together with a smoothed polynomial curve fit. The results were used to identify q values corresponding to ≤ 15%, ≤ 50%, ≤ 85%, namely q = -0.10, 0.11, 0.29. These are the values used in Figure A.3 to provide “optimistic,” “median case,” and “conservative” cost lines. Note in Figure A4 that some values of q are negative, which shows that the approach could accommodate the historical records of falling metal costs over the course of the 20 th century if appropriate values of n, s, and f were specified. appendix to chapter 3: Formulation of cost/cumulative resource elasticity Model 151
Figure 3b.1 Cumulative probability distribution Function for θ cumulative PdF 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.2 –0.1 0 0.1 0.2 0.3 0.4 0.5 theta Discussion The overall model in its present form is admittedly crude. However, it provides a framework for incorporation of future improvements. In particular, better (than uniform) frequency distribution functions for n, s, and f could be specified, given greater insight into uranium geochemistry and mining experience. Allowing n = 1 and f = 100% merely to accommodate past oversimplification is open to question. Following the practice adopted in the recent AFCI review (3), a triangular PDF, zero at the low and high values of the range, and peaked at the nominal value, may be warranted. Separative WorK (SWu) requirementS This subject is of interest because SWU can be traded off for natural uranium feed requirements, by reducing the enrichment facility tails composition. Per kg of product, P, at enrichment X p , given in weight percent (w/o), F, the U NAT feed required is: where X N = 0.711 w/o, natural uranium enrichment X W = specified tails enrichment Curve fits to data from the exact expression for kg of SWU per kg of product (S/P) in the range of interest (2.5 < X P < 7 w/o) give the following linear approximations: x W , W/o S/p ~ 0.10 3.00 X P – 3.03 0.15 2.57 X P – 2.72 0.20 2.27 X P – 2.51 0.25 2.06 X P – 2.36 0.30 1.89 X P – 2.24 0.35 1.75 X P – 2.14 152 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
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Summary oF ConCluSionS Among the in
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[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
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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
Page 163 and 164: Figure A.3 plots Eq (2), where adva
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Page 181 and 182: orehole diSpoSal There are three me
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Page 187 and 188: The Twice-Through Cycle The LCOE fo
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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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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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