The FuTure oF nuclear Fuel cycle - MIT Energy Initiative

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table 7a.1 list of variables (continued) , 3 lcoe for the Fast reactor recycle; FaSt reaCtor reCyCle , 3,L (p) lcoe for the light water reactor in the cycle; this is a function of the value attributed to the separated transuranics, p; , 3,L (p) = f 3,L + k 3,L + m 3,L + d 3,L (p) f 3,L front-end fuel cost for the light water reactor in the cycle, levelized in mill/kWh; f 3,L = u 3,LA + b 3,L k 3,L reactor capital cost for the light water reactor in the cycle, levelized in mill/kWh; m 3,L non-fuel operating and maintenance cost for the light water reactor in the cycle, levelized in mill/kWh; d 3,L (p) cost of disposal of spent fuel, including the cost of reprocessing, disposal of high level wastes and credits for the separated transuranics and uranium mix, levelized in mill/kWh; d 3,L (p) = s 3,L + w 3,L − u 3,LB − z 3,L (p) u 3,La cost of the raw uranium, levelized in mill/kWh; b 3,L enrichment, conversion and fabrication cost for uoX, levelized in mill/kWh; s 3,L reprocessing cost, levelized in mill/kWh; w 3,L high level waste disposal cost, levelized in mill/kWh; u 3,LB credit for the separated uranium, levelized in mill/kWh; z 3,L (p) credit for the separated transuranics, levelized in mill/kWh; , 3,F (p) lcoe for a fast reactor in the cycle; this is a function of the value attributed to the separated transuranics, p, used to fabricate the fuel; f 3,F (p) front-end fuel cost for a fast reactor in the cycle, levelized in mill/kWh; this is a function of the value attributed to the separated tranuranics, p, used to fabricate the fuel; k 3,F m 3,F d 3,F (p) u 3,FA z 3,F (p) b 3,F s 3,F w 3,F u 3,FB z 3,F (p) a p f 3,F (p) = u 3,FA + z 3,F (p) + b 3,F reactor capital cost for a fast reactor in the cycle, levelized in mill/kWh; non-fuel operating and maintenance cost for a fast reactor in the cycle, levelized in mill/kWh; cost of disposal of spent fuel, including the cost of reprocessing, disposal of high level wastes and credits for the separated transuranics and uranium mix, levelized in mill/kWh; d 3,F (p) = s 3,F + w 3,F − u 3,FB − a z 3,F (p) cost of purchasing depleted uranium used in fabricated the fast reactor fuel, levelized in mill/kWh; cost of purchasing the separated transuranics used for fabricating the fast reactor fuel, levelized in mill/kWh; cost of fabricating the fast reactor fuel, levelized in mill/kWh; reprocessing cost for fast reactor fuel, inclusive of interim storage for the separated streams and of low and intermediate-level waste disposal, levelized in mill/kWh; high level waste disposal cost, levelized in mill/kWh; credit for the separated uranium, levelized in mill/kWh; credit for the separated transuranics, levelized in mill/kWh; the Tru mass ratio (i.e. the ratio of the mass of Tru in fast reactor spent fuel to the mass of Tru in fresh fuel) adjusted for the present value difference between when the fuel is initially loaded and when it is next loaded; a = (q 2 /q 1 )e -R(B2−B1) , where q 2 /q 1 is the Tru mass ratio, B 1 is the date of loading of the fuel into the first fast reactor and B 2 is the date of loading of the recycled transuranics from the first fast reactor into a second fast reactor; R is the continuously compounded annual rate of interest; value attributed to the separated transuranics, $/kg; variable is solved for in deriving the two lcoes, , 3,L (p) and , 3,F (p); appendix to chapter 7: economics 169
The Twice-Through Cycle The LCOE for the Twice-Through Cycle is similar to equation (7A.1), except that we have to represent the costs incurred and electricity produced for both the first pass with fresh UOX fuel through a reactor and the second pass with the recycled, MOX fuel through a second reactor. So the numerator of our formula will show two profiles of costs, and the denominator will show two profiles of electricity production: (7A.2) The subscript 1 denotes the first pass with fresh UOX fuel, while the subscript 2 denotes the second pass with recycled, MOX fuel. The window of time [A 1 ,B 1 ] encompasses the electricity produced in the first reactor using the fresh UOX fuel, while the window of time [A 2 ,B 2 ] encompasses the electricity produced in the second reactor using the recycled, MOX fuel. Correspondingly, C 1t denotes the full set of realized costs related to the electricity produced in the first reactor, C 2t denotes the full set of realized costs related to the electricity produced in the second reactor, and Q 1t denotes the time profile of electricity produced in the first reactor, while Q 2t denotes the time profile of electricity produced in the second reactor. The full set of realized costs will include the costs of reprocessing the fuel at the end of the first pass, including any storage costs, the costs of disposing of any separated waste stream that will not be passed along to the second reactor, the costs of fabricating the MOX fuel from the plutonium that is passed along from the first reactor to the second, and the cost of disposing of the spent MOX at the conclusion of the second pass. It is arbitrary whether the costs of reprocessing and MOX fuel fabrication are assigned to the first or to the second reactor, since the definition of the LCOE depends only upon the total costs for the complete pair of passes. We choose to assign the reprocessing costs to the first reactor, and the MOX fabrication costs to the second reactor. This allocation does not impact any of the results, only the form in which they are presented. Our definition of the LCOE looks at the whole cycle. Costs incurred at any point in the cycle—whether during the first pass of fresh UOX fuel, or in the reprocessing of the spent fuel and fabrication of the MOX fuel, or in the second pass with the MOX fuel—are levelized across the electricity produced throughout the full cycle, by both passes of the fuel. The Price of the Recycled Elements – Plutonium Equation (7A.2) does not include any explicit assessment of the value or price of the recovered plutonium passed from one reactor to another. The LCOE is defined independently of whatever price one might assign to the recovered plutonium, since the cost to one reactor would be exactly cancelled out in the equation as a credit to the other reactor. Of course, by attributing a price to the plutonium, p, one can decompose the LCOE of the cycle into two separate LCOEs, one for the electricity produced from the first pass reactor and one for the electricity produced from the second pass reactor: 170 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
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This chapter reports the cost of th
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Table 7.1 Input Parameter Assumptio
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Twice-Through Cycle Table 7.3 shows
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Table 7.4 The LCOE for the Fast Rea
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higher cost of disposal of the spen
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110 MIT STudy on The FuTure oF nucl
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power program might be used, as is
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Figure 8.1 Weapons-usability Charac
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inStitutional approaCheS to Fuel Cy
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Page 139 and 140: Reprocessing choices Commercial rep
Page 141 and 142: Table 8.2 Safeguard Technical Objec
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Page 145 and 146: port for nuclear power over the per
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Page 149 and 150: who are very concerned with global
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Page 157 and 158: There have been major changes in ou
Page 159 and 160: There are large financial and polic
Page 161 and 162: Figure 3A.2 shows the results. As c
Page 163 and 164: Figure A.3 plots Eq (2), where adva
Page 165 and 166: Again, assuming that q = 0.29, the
Page 167 and 168: Note that Eq. [7] suggests employin
Page 169 and 170: Figure 3b.1 Cumulative probability
Page 173 and 174: Figure 5a.1 decay of radioactivity
Page 175 and 176: and 241 Am. For the short term, hea
Page 177 and 178: Repository Engineering All reposito
Page 179 and 180: epreSentative repoSitory deSiGnS: u
Page 181 and 182: orehole diSpoSal There are three me
Page 185: table 7a.1 list of variables , 1 lc
Page 189 and 190: A proper representation of the chai
Page 191 and 192: In the Twice-Through Cycle, the pai
Page 193 and 194: table 7a.2 once-through Fuel Cycle
Page 195 and 196: above ground storage. However, the
Page 197 and 198: CitationS and noteS 1. The methodol
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Page 201 and 202: p Analogous to plutonium. Plutonium
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Page 223 and 224: system [1]. The nuclear power plant
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Page 229 and 230: CitationS and noteS Brinkmann, H. U
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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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