This document summarizes an economic model of nuclear reprocessing using the simulation software Vensim. The model evaluates the costs of the nuclear fuel cycle with and without reprocessing over the next 100 years. Preliminary results show that while reprocessing is currently expensive, it could help offset the large costs of constructing multiple nuclear waste repositories by reducing nuclear waste volumes. The model accounts for factors like the construction and decommissioning of nuclear power plants, mass flows within the fuel cycle, and the introduction of mixed-oxide fuel reactors over time.

1. Proceedings of the 17th International Conference on Nuclear Engineering
ICONE17
July 12-16, 2009, Brussels, Belgium
REVISION ICONE 17-75648
AN ECONOMIC MODEL OF NUCLEAR REPROCESSING USING VENSIM
Samuel Brinton Akira Tokuhiro
Mechanical and Nuclear Engineering Department Mechanical Engineering Department
Kansas State University University of Idaho
Manhattan, Kansas, USA Idaho Falls, Idaho, USA
ABSTRACT generation, with and without a fuel reprocessing. Preliminary
Even under the call for solutions to climate change and results demonstrate that the high cost of reprocessing can be
alternative energy sources to meet increasing energy demands, offset by the larger expense of having to construct ‘multiple’
the imminent “nuclear renaissance” is debated by those who Yucca Mountain-type repositories, under current NPP growth
want to know the final destination of spent nuclear fuel. One of forecasts and insistence of the once-through fuel cycle. Details
the alternatives to direct storage of spent fuel in a geological and results on various, sensible scenarios will be presented.
repository includes partial to full fuel reprocessing such that
fission products such as actinides can be removed, as well as INTRODUCTION
the recycling of plutonium and uranium into mixed oxide fuel In order to meet the increasing electricity demands, to
(MOX). With the anticipated construction of ‘new build’ address evidence of climate change, to curb greenhouse gases
nuclear power plants (NPPs), as well as the continued operation (GHG), and to reduce dependence on foreign oil, nuclear and
of the existing fleet, we anticipate that the inventory of spent alternative energies are receiving renewed interest. Lately there
fuel destined for storage in Yucca Mountain (or similar) will has been a focus on the ‘nuclear renaissance‘, which in effect is
continue to grow. Thus the U.S. DOE is promoting a sensible the anticipated large scale deployment of nuclear power plants
consideration of reprocessing, burning MOX in existing and (NPPs). This is due in part by the fact that by the year 2050 the
near-terms LWRs and continuing R&D on SFRs for its U.S. will have to replace most of the currently operating ‘fleet’
eventual commercial introduction. However, countries that of NPPs when they reach the end of their 60-year service life.
have chosen to reprocess are facing high costs and lingering Although U.S. national laboratories (INL) and the U.S. Nuclear
political opposition, while others who have chosen not to Regulatory Commission (NRC) are looking respectively at
reprocess equally face opposition to licensing and operating a ‘LWR sustainability’ and ‘Life beyond 60’, confidence in
adequate federal repository. material ‘durability’ with respect to safety is one of the major
This research continues ongoing research by the authors on concerns that presents itself as a technical challenge.
existing and planned realization of NPPs and the associated Separately, there is growing recognition that nuclear energy is
fuel cycle. That is, we have to date developed models of the the only energy source in the U.S. ‘energy mix’ that can supply
construction and decommissioning of NPPs in the U.S., a large fraction of the expected demand in base load power.
developed an associated model that includes construction of As such, after a 30-year lull in new NPP construction, next
reprocessing facilities, and finally, accounts for the mass flow generation NPP system design is underway. In fact, some 32
within the partially closed fuel cycle. From early on, we combined (construction) license (COL) applications have been
included the gradual introduction of MOX-burning LWRs and filed for the latest LWR designs; that is, the Gen’ III+ LWRs
SFRs into the existing and anticipated LWR fleet over the next (ABWR, US-APWR, EPR, AP-1000). Here, these LWRs are
100 years. All models were created using Vensim, a software considered ‘replacement’ LWRs from the current fleet. Also,
tool that facilitates development, analysis and under the U.S. Energy Act, 2005, the Department of Energy
compartmentalization of dynamic processes with feedback (DOE) and NRC are collaboratively developing the Next
models. Our model has been benchmarked against the MIT and Generation Nuclear Plant, a demonstration graphite-moderated,
U. Chicago reports on the future of nuclear energy. The current gas-cooled reactor that will also provide high-temperature
work presents cost estimates and uncertainties assigned to the process heat for partnering industries (oil, chemical etc.). These
mass flow model to evaluate the cost of NPP-based electricity
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2. NGNPs will have to be safe, economically competitive, Data on the percentage of reactors typically requesting
proliferation-proof and environmentally friendly. extensions was not available and thus a 100% extension rate
There is also interest in considering the availability and approval assumption was used. Using this assumption the first
accessibility of energy sources. Here in terms of uranium reactor to be decommissioned will be Oldbury 1 (United
resources, there is re-consideration of upgrading the nation’s Kingdom) in 2027 and the final reactor currently operating to
new and spent fuel reprocessing capability and integrating be decommissioned will be Kaiga 3 (India).
mixed-oxide (MOX) burning NPPs, as well as fast reactors Decreasing the total reactors operating from the initial 436
(FRs) [eventually fast breeder reactors]. Thus, with respect to based on the beginning operation and subsequent
the ‘age’ of the U.S. current fleet of 104 LWRs, the state of decommissioning year gives the number of presently operating
nuclear technology, the projected increase in GHG-free reactors operating as a function of time for future beginning
electrical generating capacity and nuclear infrastructure and end fuel cycle calculations for the next 50 years, shown in
development, this research sought to define the bounding Figure 2.1. Figure 2.1 also includes the GWe capacity from
scenarios with respect to the costs associate with operating nuclear reactors as a function of time for the next 60
decommissioning and decontamination (D&D), deployment of years. An average of 853 MWe per reactor was calculated from
NPPs and front- and back-end (of the fuel cycle) processes, to the World Nuclear Association information paper [8] on
meet the nation’s energy requirements. Subsequently, an currently operating nuclear reactors which gives a current total
estimate of the cost and expenditures needed for new fuel of 436 reactors an electrical capacity of 371,927 MWe
reprocessing plants to meet the spent fuel generated by the (electrical as distinct from thermal). All data given in this report
fleet, as well as possibility of reducing the spent fuel inventory begins in 2008, the year in which this report was begun, and
currently intended for the Yucca Mountain repository was extends until 2068, the largest time period in which reasonable
sought. estimation can occur.
MODELING WITH VENSIM
Vensim [1] is a software tool that facilitates development,
analysis and compartmentalization of dynamic processes with
feedback models. Models are constructed graphically or in a
text editor and feature a good assortment of dynamic functions
such as arrays, Monte Carlo sensitivity analysis, optimization,
data handling, application interfaces and others. Although it has
some limitations, it is easy to use and a flexible initial tool in
processes characterized by number-scales (measurable
variables). Brinton and Tokuhiro have used Vensim for multiple
subsequent publications involving nuclear reactor development
and fuel cycle modeling [2, 3].
THE DECOMMISSIONING MODEL
The first step in the process of finding the global
reprocessing capacity was to find the rate at which the currently
operating reactors must be decommissioned due to license Figure 2.1 – Decommissioning of Currently Operating Reactors
terminations. The Nuclear Regulatory Commission of the
United States currently offers 40 year operation licenses with Using the STEP function in Vensim the model of
the ability to request a 20 year life extension [4]. There has also decommissioning the currently operating nuclear fleet was
been discussion of expansion of the operation life for yet created. Figure 2.2 shows the preliminary graphical model in
another 20 years bringing the total commercial operation to 80 Vensim with the Decommissioning Rate subtracting from the
years [5]. Operating Reactor Capacity. The graph of the decommissioning
The World Nuclear Association maintains a database of all rate in GWe/year is given in Appendix A.2.1.
operating and soon to be operating reactors in the world and the
current version of this report was used to find the initial
operation year of each of the reactors [6]. 60 years were added Operating
Reactor
to the initial operation years to give the probable years of Capacity Decommissioning
decommissioning. This assumes that all reactors request the Rate
license extensions or appropriate extensions in their respective Figure 2.2 – Vensim Model of Decommissioning Rate
countries. D. Klein, Chairman, NRC, has stated that
international regulatory licenses extend from 32 years in Italy
to a reactor based extension of up to 80 years in France [7].
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3. THE CONSTRUCTION MODEL
Operating Reactor Capacity
Although there are a plethora of possible nuclear growth
600
models currently being debated it was found that the World
Nuclear Association reference model in its 2005 report [9] most
closely resembled the earlier models created in previous 500
publications by Brinton and Tokuhiro [2][3][4]. The WNA
analysis provides three possible possibilities with a reference,
GWe
400
upper, and lower scenario. These scenarios are only applicable
to 2030. They were then expanded based on their constant rate
of increase from 2030 to 2068 to be applied to the fuel cycle 300
model of this paper. The reference model constant growth rate
of 6.92 GWe was used in the model of this paper though 200
inclusion of the upper and lower model is recommended in 2008 2014 2020 2026 2032 2038 2044 2050 2056 2062 2068
future publications. Figure 3.1 shows the growth of nuclear Time (Year)
capacity in GWe for the next 60 years in an expansion of the Operating Reactor Capacity : A
original WNA model.
Figure 3.3 – Vensim Model of Operating Reactor Capacity for
Modeling Period
FUEL CYCLE MODEL ELEMENTS
The nuclear fuel cycle was first broken down into ‘pre-
reactor’ (front end) and ‘post-reactor’ )back end) sections for
analysis. The pre-reactor elements of the cycle include mining
and milling, conversion, enrichment, and fabrication. The post-
reactor elements of the cycle include interim storage of spent
fuel and final storage of high level waste (HLW). Other
elements added to the model included nuclear reprocessing and
mixed oxide (MOX) fabrication. Using multiple sources
including the WISE Uranium Project [10], MIT ‘Future of
Nuclear Power’ Report [11], and Lamarsh and Baratta [12] the
authors found the quantitative uranium and total heavy metal
Figure 3.1 – Construction Scenarios of Nuclear Capacity
requirements to produce 1 GWe in a modern nuclear reactor.
Assumptions used in the calculation of the fuel cycle values are
Using the constant rate function in Vensim the model of
given in Table 4.1.
capacity growth for the next 60 years was created. Figure 3.2
shows the preliminary graphical model in Vensim with the
Table 4.1 – Assumptions Used in Fuel Cycle Calculations
Decommissioning Rate subtracted from and the Construction Ore Grade:
Rate addedto the Operating Reactor Capacity. The Operating Mining Waste/Ore Ratio: 5
0.2 % U
Reactor Capacity in GWe can be seen as a function of time in Extraction Losses:
Figure 3.3 incorporating both the construction and Milling
4.2399%
decommissioing rates. Conversion Losses: 0.5%
Product Assay: Tails Assay:
Enrichment
Operating 3.6 % U-235 0.3 % U-235
Reactor
Capacity Fuel
Construction Rate Decommissioning Losses: 0.5%
Rate Fabrication
Power Plant
Fuel Burnup: 50 GWd/t U Efficiency: 33%
Figure 3.2 – Vensim Model of Construction and (LOW)
Decommissioning Rates Power Plant
Fuel Burnup: 100 GWd/t U Efficiency: 45%
(HIGH)
Notice that there are two assumption scenarios for the
power plant section of the fuel cycle. It is likely that the other
elements will not change significantly during the modeled
period but an increase in burnup and thermal efficiency is being
considered in Generation IV reactors which are likely to be
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4. built in the next sixty years. The two model systems used given in reports by MIT [11] and the OECD [13]. These reports
throughout this paper will refer to these differences as LOW were chosen due to the relative significance of the reports and
(50 GWd/t U, 33%) and HIGH (100 GWd/t U, 45%). their wide range in cost variation. The variation between
Using the above assumptions, the required values at each these(what costs?) costs is due to the estimates applied by each
of the steps in the fuel cycle were calculated and are provided institution. We noted that there is a general lack of available
in Table 4.2 (LOW) and Table 4.3 (HIGH). The values given data on the economics of nuclear reprocessing; further, there
are in metric tonnes. The Vensim model including all the fuel are differences in perspective. That is, in brief, Europe
cycle elements is shown in the Appendix in A.4.1. The (France) currently engages in reprocessing while the United
equations of each of the elements include the values of Table States continues to function under past President Carter’s
4.2 and 4.3 multiplied by the Operating Reactor Capacity to legacy to not reprocess spent fuel. The costs based on these
relate each value to the power production. It should be noted reports are given in Table 5.1.
that the fabrication of uranium oxide (UOX) in the original fuel
assemblies is separated from the fabrication of reprocessed Table 5.1 – Cost Estimations of Fuel Cycle Processes
mixed oxide (MOX) fuel assemblies and these are equal in MIT OECD
value to create one GWe from the UOX and another GWe from
Mining and Milling 30 50 $/kg U3O8
the MOX.
Conversion 8 8 $/kg U
Table 4.2 – Calculated Fuel Cycle Requirements (1 GWe UOX, Enrichment 100 110 $/kg SWU
1GWe MOX) for LOW (50 GWd/t U, 33%)
UOX Fabrication 275 275 $/kg U
Mining and Milling 212.22 t U3O8 212.22 t U3O8
Interim Storage 400 570 $/kg U
Conversion 264.83 t UF6 179.062 t U
Reprocessing 1000 620 $/kg HM
Enrichment 32.90 t UF6 100798 SWU
MOX Fabrication 1500 1100 $/kg HM
UOX Fabrication 25.11 t UO2 22.14 t U
HLW Storage 300 60 $/kg HM
Interim 25.11 t Spent Fuel 22.14 t U
Reprocessing 25.11 t Spent Fuel 22.14 t U
MOX Fabrication 25.11 t MOX Fuel 22.14 t MOX Fuel DISCUSSION OF RESULTS
Final Storage of The results for the models in terms of average fuel cycle
25.11 t HLW cost and comparative fuel cycle costs with and without
HLW 25.11 t HLW
reprocessing were the primary focus of the research. Using the
Table 4.3 – Calculated Fuel Cycle Requirements (1 GWe UOX, LOW total fuel cycle element values and the OECD cost values
1 GWe MOX) for LOW (100 GWd/t U, 45%) without reprocessing it was found that the average total fuel
Mining and Milling cycle cost per GWe was $43.59 million and with reprocessing
77.82 t U3O8 77.82 t U3O8
the average total fuel cycle cost per GWe was $89.98 million.
Conversion 97.10 t UF6 65.66 t U The comparison of these two alternatives demonstrates a ratio
Enrichment 12.06 t UF6 36959 SWU of 2.0642 meaning the cost of the additional GWe from
UOX Fabrication reprocessing cost 6.42% greater than the original GWe
9.21 t UO2 8.12 t U
produced from UOX. This additional cost percentage translates
Interim/Final Storage 9.21 t Spent Fuel 8.12 t U to $2.78 million per GWe.
Reprocessing 9.21 t Spent Fuel 8.12 t U The HIGH OECD model had a larger reprocessing
MOX Fabrication 9.21 t MOX Fuel comparative cost due to the lower initial cost of the UOX
8.12 t MOX Fuel
Final Storage of
produced GWe. Without reprocessing the average total fuel
9.21 t HLW cycle cost was found to be $30.09 million per GWe which is
HLW 9.21 t HLW
$13.5 million less than the LOW model. The average total fuel
cycle cost with reprocessing for the HIGH model was $23.78
FUEL CYCLE COST MODEL million less than the LOW model cost at $66.19 million. This
Once the fuel cycle elements of the model were added the ratio of MOX GWe cost to UOX GWe cost is 1.2000 or 20%
final step was to add cost elements in relation to the fuel cycle more at a cost of roughly $6.02 million. As was stated before,
values and tabulate the individual costs into a total fuel cycle the lower UOX GWe cost due to less material input
cost. The Total Fuel Cycle Cost was given in terms of requirements leads to this being a higher additional cost for the
$/Operating GWe in order to relate the cost to the production of reprocessing.
electricity which will be covering the cost of the fuel cycle. The same models were created with the MIT cost values
There are multiple different costs which have been estimated and the values of the total fuel cycle costs and ratios are given
for the fuel cycle elements and the authors compared the costs Table 6.1. Further research may expand the rates and include
4 Copyright © 20xx by ASME

5. factors including reprocessing capacity and long term storage reduce the amount of high-level waste destined for Yucca
capacity. Inserting the above costs into the model it was then Mountain-like facilities, the choice to pursue reprocessing is
observed that the model was variable based on the input costs. would be attractive. It is also plausible that even at $34 million
The comparison of these costs is provided in the conclusions. per GWe, relative to the cost of a federal site well in excess of
$1 billion, that reprocessing is indeed a ‘sensible’ option.
Table 6.1 – Cost Results for MIT Cost Values for LOW and However, to be fully confident of the parameters that impact
HIGH Models bottom dollar costs and associated metrics, we need to further
Average Total Ratio
Average quantify the uncertainties in the modeled elements. We hope
Difference that this will aid policy makers and stakeholders.
Cost (million) MOX/UOX
(million) Finally, as our model is based on assumptions that may
LOW-Without introduce additional uncertainties, we plan next to study the
$ 34.18 NA NA
Reprocessing
propagated sensitivity of these assumptions with respect to the
LOW-With
$ 106.51 3.116 $ 38.15 outcome. For example, the production of a second GWe from
Reprocessing
HIGH-Without the original fuel from the MOX cycle section requires
$ 23.65 NA NA significant assumptions since depleted and separated uranium
Reprocessing
HIGH-With costs and storage are not explicitly included but rather included
$ 76.51 3.235 $ 29.21 into the overall MOX fabrication cost. This and related
Reprocessing
compilation of contributing factors will be considered when
such detailed data become available. The model development
CONCLUSIONS thus continues.
The complete model graphic in Vensim includes the
Construction and Decommissioning Rates, Currently Operating
Capacity, Fuel Cycle Elements (Mining and Milling, ACKNOWLEDGMENTS
Conversion, Enrichment, UOX Fabrication, Interim Storage, The authors would like to thank Dr. M. Hosni, Professor
Reprocessing, and Repository), Fuel Cycle Element Costs and Head of the Mechanical and Nuclear Engineering
(Mining and Milling Cost, Conversion Cost, etc.), and Total Department at Kansas State University, for his continued
Fuel Cycle Cost. The complete model is shown in the Appendix support.
as A.4.1.
Using the final model and applying the costs of Table 5.1 REFERENCES
the OECD and MIT reports give very distinct total fuel cycle [1] Vensim Program, Version 5, Ventana Systems, Inc.
costs. The non-recycling options (excluding the reprocessing,
MOX fabrication, and final storage of spent MOX fuel) give an [2] Brinton, S. and A. Tokuhiro, An Initial Study on
average total cost (LOW-HIGH)/2 of $36.84 million (OECD) Modeling the U.S. Thermal and Fast Reactor Fuel Cycle and
and $28.91 million (MIT) per GWe. The recycling elements of Deployment Model Using Vensim, ICONE-16, Orlando, FL,
the two estimates are significantly different with totals of USA, may 11-15, 2008.
$78.08 million (OECD) and $91.51 million (MIT). Since the
recycling elements create an additional GWe capable fuel total [3] Brinton, S. and A. Tokuhiro. An Initial Study on
the difference in cost for this additional GWe is an important Modeling the Existing and Anticipated Fleet of Thermal and
factor in deciding to pursue reprocessing. However, the ratio of Fast Reactors using VENSIM, ICONE-15, Nagoya, Japan,
the MIT model shows a 111 to 123% additional cost for the April 22-26, 2007
MOX produced GWe. This is significantly higher than the
OECD model ratios of an additional 6 to 20%. The MIT cost [4] Nuclear Regulatory Commission, As of 1/15/09 at
values for reprocessing are not reprocessing supportive and URL: http://www.nrc.gov/reactors/operating/licensing/renewal/
their high level l require further study as their results are nearly process.html
identical to the OECD values without reprocessing. It is likely
that the source of the 100% increase in values is caused by the [5] Nuclear Regulatory Commission, As of 1/15/09 at
fact that each of the cost values of the MIT report is several URL: http://www.nrc.gov/reading-rm/doc-collections/
hundred dollars higher per kg than the OECD report. The commission speeches/2007/s-07-008.html
OECD costs are labeled as nominal and the MIT values are
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addition of roughly $4 million per GWe could significantly
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6. [8] World Nuclear Association, As of 1/15/09 at URL:
http://www.world-nuclear.org/info/reactors.html
[9] World Nuclear Association, As of 1/15/09 at URL:
http://www.world-nuclear.org/reference/pdf/economics.pdf
[10] WISE Uranium Project, As of 1/15/09 at URL:
http://www.wise-uranium.org/nfcm.html
[11] Massachusetts Institute of Technology, The Future of
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Nuclear Engineering, 3rd Ed., Prentice Hall, ISBN-10:
0201924981, 2001.
[13] OECD/NEA, “The Economics of the Nuclear Fuel
Cycle”, 1994
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7. ANNEX A
OVERSIZE GRAPHICS
40
30
20
10
0
2008 2011 2014 2017 2020 2023 2026 2029 2032 2035 2038 2041 2044 2047 2050 2053 2056 2059 2062 2065 2068
Time (Year)
Decommissioning Rate: A GWe/Yea
Figure A.2.1 Decommissioning Rate Based on Beginning Operation Dates and a 60 Year License
Mining and UOX Spent Fuel UOX MOX
Conversion Enrichment Interim Repository
Milling Fabrication Reprocessing Fabrication
Storage
Operating
Reactor
Construction Rate Capacity Decommissioning
Rate
UOX Spent Fuel UOX MOX Repository
Mining and Conversion Enrichment Fabrication Interim Reprocessing Fabrication
Milling Cost Cost Cost Cost Storage Cost Cost Cost Storage Cost
Fuel Cycle
Total Cost
Figure A.4.1 – Complete Vensim Model for Fuel Cycle Total Cost Calculation
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