A Strategy for Transition from a Uranium Fueled, Open
Cycle SFR to a Transuranic Fueled, Closed Cycle SFR
ARCHVES
by
MA SSACHUSETTS
INSHiUS
OF TECHNOLOGY
Joshua Richard
JUL 2 5 2012
B.S. Nuclear Engineering
University of Florida, 2010
u ?RARIES
Submitted to the Department of Nuclear Science and Engineering
in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE in NUCLEAR SCIENCE AND ENGINEERING
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2012
Copyright May 2012 Massachusetts Institute of Technology
All rights reserved
Author:
-
V
Certified by:
A
Joshua Richard
Department of Nuclear Science and Engineering
,
Michael Driscoll (thesis supervisor)
Professor Emeritus of Nuclear Science and Engineering
--7
Certified by:
ujid
TEPCO Professor of Nucl
Accepted by:
-
zimi (thesis reader)
ience and Engineering
-
Mujid Kazimi
TEPCO Professor f Nucle Science and Engineering
Chair, Department
ittee on Graduate Students
1
A Strategy for Transition from a Uranium Fueled, Open Cycle SFR to a
Transuranic Fueled, Closed Cycle SFR
by
Joshua Richard
Submitted to the Department of Nuclear Science and Engineering on May 11th, 2012, in partial
fulfillment of the requirements for the Degree of Master of Science in
Nuclear Science and Engineering
Abstract
Reactors utilizing a highly energetic neutron spectrum, often termed fast reactors, offer large fuel
utilization improvements over the thermal reactors currently used for nuclear energy generation.
Conventional fast reactor deployment has been hindered by the perceived need to use plutonium as fuel,
coupling the commercial introduction of fast reactors to the deployment of large-scale thermal reactor
used fuel reprocessing. However, the future of used fuel treatment in the United States is highly
uncertain, creating a bottleneck for the introduction of fast reactor technology. A strategy centered
around using uranium-fueled fast reactor cores in a once-through mode-a uranium startup fast reactor
(USFR)-decouples fast reactor commercialization from fuel reprocessing and enables transition to a
recycle mode once the technology becomes available and economic. The present work investigates the
optimal strategy for recycling spent fuel from once-through sodium cooled fast reactors (SFRs), by
analyzing the performance of various designs. A range of acceptable transitions are described and their
economic, breeding, nonproliferation, and safety performance are characterized.
A key finding is that the burnups of all cores were limited by the allowable fluence to the cladding rather
than by the core reactivity. The carbide cores achieve fluence-limited burnups 15-25% greater than the
comparable metal cores, though the metal cores can be optimized via decrementing the fuel volume
fraction to reach fluence-limited burnups within 10% of the carbide cores. The removal of minor
actinides from the recycled fuel has a minimal impact on the achievable burnups of both types of fuels,
decreasing the fluence-limited burnup by less than half a percent in all cases. Similarly, long-term storage
of the USFR fuel had minimal impact on the achievable burnups of all cores, decreasing the fluencelimited burnup by no more than 2% in all cases. Levelized fuel costs were in the range of 5.98 mills/kWh
to 7.27 mills/kWh for the carbide cores, and 6.81 mills/kWh to 7.57 mills/kWh for the optimized metal
cores, which is competitive with fuel costs of current LWRs and once-through SFRs. The metal and
carbide multicore cores, made using slightly more than one once-through SFR core, functioned as slight
fissile burners with fissile inventory ratios (FIRs) near 0.9. The uranium+ cores, made using one oncethrough SFR core plus natural uranium makeup, functioned in a fissile self-sustaining mode with FIRs
near unity. All cores discharged fuel that was less attractive for weapon use than that of an LWR. The
carbide cores had maximum sodium void worths in the range of $2.81-$2.86, approximately half the
worth of the metal cores, which were in the range of $4.97-$5.14. Carbide and metal multicore cores
possessed initial reactivities in the range of 15,000 pcm, requiring either multi-batch staggered reloading
or control system modifications to achieve acceptable shutdown margins. The uranium+ carbide and
metal cores achieved acceptable shutdown margin with the nominal control configuration and the singlebatch reloading scheme. The overall conclusion is that USFR spent fuel is readily usable for recycle.
Thesis Supervisor: Michael Driscoll
Title: Professor Emeritus of Nuclear Science and Engineering
2
Table of Contents
A b stra ct .........................................................................................................................................................
2
T a b le o f Co n te nts ..........................................................................................................................................
3
List of Fig u re s ................................................................................................................................................
6
List of T a b le s ...............................................................................................................................................-
9
1 In trod u ctio n .............................................................................................................................................
10
0
1.1 O bje ctive s..........................................................................................................................................1
10
1.2 Backg ro u nd .......................................................................................................................................
1.3 Organization of Thesis.......................................................................................................................14
15
2 M e th o d ....................................................................................................................................................
2 .1 In tro d u ctio n ......................................................................................................................................
15
2.2 Design Overview ...............................................................................................................................
15
2 .3 Ne u tro n ics .........................................................................................................................................
18
2 .3 .1 ERA NO S ......................................................................................................................................
18
2 .3 .2 M CNP .........................................................................................................................................
19
2.4 Fuel Cycle Econom ics........................................................................................................................21
2 .5 Sum m a ry ...........................................................................................................................................
3 Carbide Core Analysis...............................................................................................................................
3.1 Intro du ctio n .................................................................................................................................-
24
25
-.. 2 5
3.2 Radial Power Distribution .................................................................................................................
25
3.3 Transition Strategy ............................................................................................................................
27
3 .3 .1 O v e rvie w ....................................................................................................................................
27
3 .3 .2 M u ltico re....................................................................................................................................
28
3 .3 .3 Ura n iu m+. ...................................................................................................................................
31
3.4 Reactivity W orth of M inor Actinides ...........................................................................................
34
3.5 Storage Im pact ..................................................................................................................................
36
3.6 Econom ic Performance .....................................................................................................................
37
3.7 Fissile M aterial Ratios .......................................................................................................................
39
3.8 Nonproliferation M aterials Attractiveness ...................................................................................
42
3.9 Safety Characteristics........................................................................................................................
44
3.9.1 Sodium Void Coefficient.............................................................................................................
44
3.9.2 Shutdown M argin.......................................................................................................................
45
3
3.10 Sum m ary .........................................................................................................................................
4 M etal Core Analysis..................................................................................................................................
47
50
4.1 Introduction ......................................................................................................................................
50
4.2 Radial Power Distribution .................................................................................................................
50
4.3 Transition Strategy ............................................................................................................................
52
4.3.1 Overview ....................................................................................................................................
52
4.3.2 M ulticore....................................................................................................................................53
4.3.3 Uranium+. ...................................................................................................................................
55
4.3.4 Burnup Lim it Im provement Strategies...................................................................................
59
4.4 Reactivity W orth of M inor Actinides ...........................................................................................
79
4.5 Storage Im pact ..................................................................................................................................
81
4.6 Econom ic Performance .....................................................................................................................
83
4.7 Fissile M aterial Ratios .......................................................................................................................
86
4.8 Nonproliferation M aterials Attractiveness ...................................................................................
92
4.9 Safety Characteristics........................................................................................................................
93
4.9.1 Sodium Void Coefficient.............................................................................................................
93
4.9.2 Shutdow n M argin .......................................................................................................................
95
4.10 Sum m ary ......................................................................................-...................................................
96
5 Sum m ary and Conclusions .......................................................................................................................
99
5 .1 O v e rv iew ...........................................................................................................................................
99
5.2 Radial Power Distribution .................................................................................................................
99
5.3 Reactivity Profile and Burnup Perform ance of Carbide and M etal Cores ....................................
99
5.3.1 Nom inal Cases............................................................................................................................
99
5.3.2 M etallic Core Burnup Im provement M ethods.........................................................................100
5.4 Reactivity Impact of Minor Actinide Removal and Long Term Storage ...................
101
5.5 Econom ic Perform ance ...................................................................................................................
102
5.6 Fissile M aterial Ratios .....................................................................................................................
102
5.7 Nonproliferation M aterials Attractiveness .....................................................................................
103
5.8 Safety Characteristics......................................................................................................................103
5.8.1 Sodium Void Coefficients .........................................................................................................
103
5.8.2 Shutdow n M argin.....................................................................................................................104
5.9 Sum m ary .........................................................................................................................................
4
105
6 Recom m endations for Future W ork ......................................................................................................
107
6.1 Reactivity Control Im provem ents ...................................................................................................
107
6.2 Advanced Fuel M anagem ent Schem es ...........................................................................................
107
6.3 Conversion to a Conventional Breeder with Uranium Blankets .....................................................
108
Acknow ledgem ents...................................................................................................................................109
References ................................................................................................................................................
110
Appendix A: Sam ple ERANOS 3D-Variational Nodal Transport Input.......................................................112
Appendix B: Sam ple ERANOS RZ-Diffusion Input......................................................................................115
5
List of Figures
Figure 1. Axial USFR/TRU-SFR core layout, from (Fei, Innovative Design of SFR using
16
U ranium Startup (Ph.D . Thesis), 2012)........................................................................................
Figure 2. Radial configuration of the USFR/TRU-SFR core. Orange is fuel region 1, blue is fuel
region 2, green is fuel region 3, gray is the MgO reflector region, and black is the B4 C shield
17
assem b ly reg ion ............................................................................................................................
Figure 3. Reactivity vs. core residence time for the Pu-U-C reference case calculated using the
20
MCNP5/BGcore code and the ERANOS code package...........................................................
Figure 4. Distribution of combined unit cost for electrochemical reprocessing and remote
23
fabrication of fast reactor fuel, from (Shropshire, et al., 2009) .................................................
26
Figure 5. Radial flux profile for the carbide multicore core ......................................................
27
Figure 6. Radial flux profile for the carbide uranium+ core......................................................
the
reference
carbide
recycle
core
using
the
multicore
Figure 7. Reactivity vs. burnup for
30
tran sition strategy ..........................................................................................................................
Figure 8. Reactivity vs. burnup for the reloaded Pu-U-C fuel using the multicore strategy ........ 31
Figure 9. Reactivity vs. burnup for the reference carbide recycle core using the uranium+
33
tran sition strategy ..........................................................................................................................
Figure 10. Reactivity vs. burnup for the reloaded Pu-U-C fuel using the uranium+ strategy...... 34
Figure 11. Reactivity vs. burnup for the carbide core transitioned using the multicore strategy
35
displaying the reactivity worth of the minor actinides...............................................................
Figure 12. Reactivity vs. bumup for the carbide core transitioned using the uranium+ strategy
35
displaying the reactivity worth of the minor actinides...............................................................
Figure 13. Reactivity vs. burnup for the multicore carbide cores after cooling ....................... 36
Figure 14. Reactivity vs. burnup for the uranium+ carbide cores after cooling ....................... 37
Figure 15. Fissile material ratios as a function of burnup for the transition multicore carbide core
40
.......................................................................................................................................................
Figure 16. Fissile material ratios as a function of burnup for the transition uranium+ carbide core
41
.......................................................................................................................................................
Figure 17. Proliferation materials attractiveness of the multicore carbide TRU-SFR cores of
various reloads (diamonds), and the reference LWR attractiveness (triangle).......................... 42
Figure 18. Proliferation materials attractiveness of the uranium+ carbide TRU-SFR cores of
43
v ariou s relo ads ..............................................................................................................................
46
Figure 19. Shutdown margin of the equilibrium carbide multicore core..................................
47
Figure 20. Shutdown margin of the equilibrium carbide uranium+ core .................................
51
Figure 21. Radial flux profile for the metal multicore core......................................................
52
Figure 22. Radial flux profile for the metal uranium+ core......................................................
Figure 23. Reactivity vs. bumup for the reference metal recycle core using the multicore
53
tran sition strategy ..........................................................................................................................
Figure 24. Reactivity vs. bumup for the reloaded Pu-U metal fuel using the multicore strategy 55
6
Figure 25. Reactivity vs. burnup for the transition Pu-U metal core using the uranium+ strategy
57
.......................................................................................................................................................
Figure 26. Reactivity vs. burnup for the reloaded Pu-U metal fuel using the uranium+ strategy 59
Figure 27. Microscopic scattering and absorption cross sections of natural carbon, ENDF/B-VII
62
d ata ................................................................................................................................................
62
data........................
Figure 28. Scattering-to-absorption ratio of natural carbbn, ENDF/B-VII
Figure 29. Reactivity vs. burnup for the Pu-U metal fuel using the uranium+ strategy with 3%
63
vol. frac. of graphite moderator .................................................................................................
Figure 30. Reactivity vs. burnup for the Pu-U metal fuel using the uranium+ strategy with 5%
64
vol. frac. of graphite moderator .................................................................................................
Figure 31. Reactivity vs. burnup for the Pu-U metal fuel using the uranium+ strategy with 7%
64
vol. frac. of graphite moderator .................................................................................................
Figure 32. Microscopic scattering and absorption cross sections of Si-28, ENDF/B-VII data.... 65
66
Figure 33. Scattering-to-absorption ratio of Si-28, ENDF/B-VII data ......................................
Figure 34. Reactivity vs. burnup for the Pu-U metal fuel using the uranium+ strategy with 3%
67
vol. frac. of SiC m oderator ........................................................................................................
Figure 35. Reactivity vs. burnup for the Pu-U metal fuel using the uranium+ strategy with 5%
67
vol. frac. of SiC m oderator ........................................................................................................
Figure 36. Reactivity vs. burnup for the Pu-U metal fuel using the uranium+ strategy with 7%
68
vol. frac. of SiC m oderator ........................................................................................................
Figure 37. Microscopic scattering and absorption cross sections of Mg-24 and 0-16, ENDF/B69
V II data .........................................................................................................................................
Figure 38. Scattering-to-absorption ratio of Mg-24 and 0-16, ENDF/B-VII data.................... 69
Figure 39. Reactivity vs. burnup for the Pu-U metal fuel using the uranium+ strategy with 3%
70
vol. frac. of M gO m oderator ......................................................................................................
Figure 40. Reactivity vs. burnup for the Pu-U metal fuel using the uranium+ strategy with 5%
71
vol. frac. of M gO m oderator......................................................................................................
Figure 41. Reactivity vs. burnup for the Pu-U metal fuel using the uranium+ strategy with 7%
71
vol. frac. of M gO m oderator ......................................................................................................
Figure 42. Reactivity vs. burnup for the TRU-SFR metal core using the combined
pyroprocess/M N R cycle................................................................................................................73
Figure 43. Microscopic scattering and absorption cross sections of Na-23, ENDF/B-VII data... 75
Figure 44. Scattering-to-absorption ratio of Na-23, ENDF/B-VII data.................................... 75
Figure 45. Reactivity vs. burnup for the Pu-U metal fuel using the uranium+ strategy with a fuel
76
v o l. frac. o f 4 3% ............................................................................................................................
Figure 46. Reactivity vs. burnup for the Pu-U metal fuel using the uranium+ strategy with a fuel
77
v o l. frac. o f 37 %............................................................................................................................
Figure 47. Dependence of the fluence-limited and reactivity-limited average discharge burnup
for Pu-U-Zr metal fuel of various volume fractions, transitioned using the uranium+ strategy. . 78
7
Figure 48. Reactivity vs. burnup for the transition case and successive reloads of the uranium+
79
TRU-SFR metal core with a fuel volume percent of 30.85%....................................................
Figure 49. Reactivity vs. burnup for the metal core transitioned using the multicore strategy
80
displaying the reactivity worth of the minor actinides...............................................................
Figure 50. Reactivity vs. burnup for the metal core transitioned using the uranium+ strategy
80
displaying the reactivity worth of the minor actinides...............................................................
Figure 51. Reactivity vs. burnup for the uranium+ metal cores with 30.85% fuel volume fraction
82
after co o lin g ..................................................................................................................................
Figure 52. Fluence-limited burnup as a function of cycle for the uranium+ metal core with a fuel
83
volum e fraction of 30.85% .......................................................................................................
Figure 53. Fissile material ratios as a function of burnup for the transition multicore metal core87
Figure 54. Fissile material ratios as a function of burnup for the transition uranium+ metal core88
Figure 55. Fissile material ratios as a function of burnup for the first reload metal core after
89
MN R and pyroprocessing .............................................................................................................
Figure 56. Fissile material ratios as a function of burnup for the transition uranium+ metal core
90
w ith a fuel volum e fraction of 30.85% .....................................................................................
Figure 57. Fissile material ratios as a function of burnup for the first reload uranium+ metal core
91
w ith a fuel volum e fraction of 30.85% .....................................................................................
Figure 58. Fissile material ratios as a function of burnup for the second reload uranium+ metal
91
core with a fuel volum e fraction of 30.85% ..............................................................................
Figure 59. Proliferation materials attractiveness of the metal multicore TRU-SFR cores of
various reloads, recycled using the combined pyroprocessing/melt-and-recast strategy .......... 92
Figure 60. Proliferation materials attractiveness of the metal uranium+ TRU-SFR cores of
93
various reloads with the optimized fuel volume fraction of 30.85%........................................
95
Figure 61. Shutdown margin of the transition multicore metal core ........................................
96
Figure 62. Shutdown margin of the transition multicore metal core ........................................
8
List of Tables
Table 1. Core design specifications and operating parameters, from (Fei, Innovative Design of
15
SFR using Uranium Startup (Ph.D. Thesis), 2012) ...................................................................
Table 2. Reactivity comparison between the MCNP5/BGcore carbide case and the ERANOS
21
carb id e case ...................................................................................................................................
Table 3. Unit costs and lead times for front-end once-through fuel cycle steps used for
22
com parison to the recycle m ode ...............................................................................................
Table 4. Composition of reprocessed USFR spent fuel loaded into the carbide TRU-SFR core
28
using the multicore strategy with no cooling.............................................................................
28
Table 5. Plutonium vector for the reference multicore carbide core ........................................
Table 6. Composition of reprocessed USFR fuel loaded into the carbide TRU-SFR core using the
32
uranium + strategy w ith no cooling ..........................................................................................
Table 7. Levelized fuel costs for the carbide fueled SFR cores in recycle mode, with the
38
reference once-through LW R LFC ............................................................................................
Table 8. Sodium void coefficients of reactivity for the transition and equilibrium multicore
44
carb ide cores .................................................................................................................................
Table 9. Sodium void coefficients of reactivity for the transition and equilibrium uranium+
44
carb id e co res .................................................................................................................................
45
.....
Table 10. Control rod reactivity worths for several commercial sodium fast reactor designs
Table 11. Composition of fuel reloaded into the metal TRU-SFR core using the multicore
54
strategy w ith no cooling ................................................................................................................
Table 12. Plutonium vector for the reloaded TRU-SFR metal core using the multicore strategy 54
Table 13. Composition of reprocessed USFR fuel loaded into the metal TRU-SFR core using the
56
uranium+ strategy w ith no cooling ..........................................................................................
Table 14. Composition of reprocessed TRU-SFR fuel reloaded into the metal TRU-SFR core
58
using the uranium + strategy with no cooling.............................................................................
Table 15. Plutonium vector for the reloaded metal core using the uranium+ strategy.............. 58
Table 16. Levelized fuel costs for the metal fueled SFR cores in recycle mode, and the reference
84
once-through L WR LFC ...............................................................................................................
Table 17. Levelized fuel costs for the metal fueled SFR cores in mixed melt-andrecast/pyroprocessing recycle mode, and the reference once-through LWR LFC .................... 84
Table 18. Levelized fuel costs for the uranium+ metal cores with various moderating materials
85
added to reduce cladding fluence and enhance burnup ............................................................
Table 19. Levelized fuel costs of the uranium+ metal cores with a fuel volume fraction of
86
30.85% , including the effects of cooling ...................................................................................
Table 20. Sodium void coefficients of reactivity for the transition and equilibrium multicore
94
metal cores w ith melt-and-recast ...............................................................................................
Table 21. Sodium void coefficients of reactivity for the transition and equilibrium uranium+
94
metal cores with a fuel volume fraction of 30.85%.................................................................
9
1 Introduction
1.1 Objectives
The goal of the present work is to identify and characterize optimal strategies for transition from
a once-through, uranium-fueled SFR to a plutonium-fueled SFR in recycle mode. This transition
will seek to minimize the changes necessary to complete the process, aiming to simply replace
the uranium fuel with plutonium fuel recycled from the once-through mode of the SFR.
An important determination to make regarding the transition is the appropriate amount of fissile
material to be used in the creation of the recycle core. To provide insight into the core physics
resulting from such a determination, the power distribution, achievable discharge burnup, and
reactivity worth and burnup implications of excluding minor actinides from the recycled fuel, or
from long term cooling, will be evaluated. Using this information, estimates of the levelized fuel
costs will be developed, the production or destruction of fissile material will be characterized,
and the attractiveness of the spent fuel from a proliferation perspective will be addressed.
Finally, parameters describing the safety performance of the core will be estimated, including the
maximum sodium void worth and the shutdown margin achievable with the nominal control
assembly configuration. Taken together, these analyses will provide an overview of the potential
performance of the fast reactor in recycle mode, and will provide direction for further analysis of
the alternative fuel cycle strategy using uranium startup of fast reactors for transition to a recycle
mode for a fully closed fuel cycle.
1.2 Background
Fast spectrum reactors, also called fast reactors, are nuclear reactors in which the average energy
of neutrons present in the system is much greater than the thermal energies of neutrons in most
currently operating light water reactors. Historically, fast spectrum reactor development
progressed due to a perceived need for reactors that produced more fissile fuel than they
consumed. (Till & Chang, 2011) In the immediate postwar period, the potential of a fast reactor
to reach excellent breeding performance was recognized by both Enrico Fermi, creator of the
world's first man-made nuclear reactor CP-1, and Walter Zinn, the first director of Argonne
National Laboratory. In the years following the war, Zinn outlined the possible design
characteristics of a high-performance breeder reactor, and his work would become the basis for
the design of the Experimental Breeder Reactor-I (EBR-I). EBR-I was built at Argonne's
10
experimental facility in Idaho, and began operation in 1951 using metallic uranium fuel and
sodium-potassium (NaK) coolant. It was a small test reactor, meant to provide data and
experimental results for further fast reactor development. It also happened to be the first reactor
to generate electricity in the world, powering the building it was in and a nearby machine shop.
Later, in 1962, it was converted to operate using recycled plutonium, becoming the very first
reactor to operate on plutonium and also the first reactor to convert from a once-through uranium
cycle to a plutonium recycle mode.
However, EBR-I was subsequently decommissioned as a new, larger fast reactor design, the
EBR-II, took its place. EBR-II was designed from the beginning to be plutonium-fueled, and its
facility included not only the reactor and associated electricity generation equipment, but also an
on-site fuel processing facility, where the newly-discharged spent fuel was melted down and
recast for reuse in the EBR-II core. Even at this early juncture, the idea of a once-through,
uranium-fueled fast reactor had been discarded, with the emphasis on fuel breeding for fissile
resource maximization.
The concept of fuel reprocessing was not unique to the fast reactor concept. During the
Manhattan Project, Glenn Seaborg first separated microgram quantities of plutonium in 1942 via
co-precipitation with bismuth phosphate. (Forsberg, 2012) The process was scaled to kilogram
quantity and production began at the Hanford site in 1944, where spent fuel from the B-10
reactor was reprocessed for nuclear weapon plutonium production. In 1954, the solvent
extraction process PUREX finished development and was deployed for large scale reprocessing
of the low-burnup defense reactor spent fuel, with an eventual throughput of 5,000-7,000
MTHM/y.
Motivated by the progress the defense establishment had made with reprocessing technology, the
potential for commercial fuel reprocessing facilities was investigated, concomitant with the
expansion of commercial light water reactors for electricity generation. The first commercial
fuel reprocessing facility was opened in 1966 in West Valley, NY, owned and operated by the
The West Valley
Davison Chemical Company's Nuclear Fuels Services subsidiary.
Reprocessing Plant had a capacity of up to 300 MTHM/yr, substantially less than the DoD's
Hanford facility, yet still reasonable for the first attempt of medium-burnup commercial reactor
fuel. General Electric designed and constructed a plant in Morris, IL, which was completed in
1972. Finally, Allied General Services designed and constructed a large-scale (1500 MTHM/yr)
Commercial spent nuclear fuel
commercial fuel reprocessing facility from 1970-1977.
reprocessing was seen as an inevitable addition to the nuclear fuel cycle, given the scarcity of
uranium resources and the progress made in its technical development and deployment.
However, the commercial fuel reprocessing encountered significant obstacles during its lengthy
development and attempted deployment that ultimately precluded its inclusion as a permanent
component of the commercial nuclear fuel cycle. The West Valley plant ceased commercial
operation in 1972 to make process modifications in line with new regulatory requirements. After
11
four years of investment and attempted implementation, Nuclear Fuels Services decided that the
remaining modifications were too costly and complex to justify implementation and continued
operation, and so the decision was made not to restart fuel reprocessing operations and plant
ownership was transferred to the state of New York, together with the responsibility for waste
and environmental remediation. (U.S. Department of Energy, 2005) The GE plant in Morris, IL
was undergoing startup testing in 1975 when it was determined that it would not be able to meet
its fuel processing specifications, and so the facility never began commercial operation.
(National Research Council, 2006)
The Barnwell reprocessing plant experienced setbacks when environmental groups began
objecting to its operation in the early 1970's, and encountered further adversity when the Atomic
Energy Commission, which had been the regulatory authority the plant had been working with to
review and approve its design, was eliminated and the Nuclear Regulatory Commission assumed
the authority for regulating commercial nuclear facilities. (Norman, 1976) The NRC pursued
exhaustive public engagement during the licensing process, substantially hindering licensing
efforts. Furthermore, the detonation of a nuclear device by India in 1974 sparked fears of
nuclear materials proliferation to rogue states or terrorists, and reprocessing was seen as a key
avenue for such proliferation to occur. President Jimmy Carter sounded the death knell for
commercial fuel reprocessing in the United States in April of 1977, when he banned nuclear
reprocessing by the private sector based primarily on nonproliferation concerns. (Associated
Press, 1983) Though President Reagan would reverse this decision in 1982, additional uranium
resources had been located by that time, and coupled with the increased regulatory burden this
would prevent fuel reprocessing from being economically competitive with the once-through
cycle.
Today, fast reactors are again being considered for the next generation of commercial nuclear
power. A variety of factors have driven the renewed interest. The Generation-IV International
Forum (GIF), chartered in 2001 by 13 nations to carry out research and development on
advanced nuclear energy systems, set goals related to performance improvements for advanced
reactors in the areas of sustainability, economics, safety and reliability, and proliferation
resistance. (Generation-IV International Forum, 2002) GIF analyzed and recommended six broad
types of reactor configuration to meet these goals, one of which was the sodium-cooled fast
reactor.
The sodium-cooled fast reactor (SFR) is well positioned to meet the challenging goals of GIF.
Even in a once-through mode, its exceptionally high burnups (-100 MWd/kgHM) lead to high
uranium utilization (ratio of heavy metal mass fissioned to the total mined uranium mass used for
making fuel), increasing the sustainability of the system. (Waltar, Todd, & Tsvetkov, 2012) Its
high power density (~600 kW/L) is almost six times greater than that of the typical pressurized
light water reactor (~104 kW/L), allowing for a smaller core and vessel for the same power
output. With the boiling point of the sodium coolant at 883 C (at STP), the primary vessel can
operate near atmospheric pressure while still reaching the high temperatures (300 C or greater)
12
required for efficient electricity operation. In fact, the sodium coolant is operated at an average
primary system temperature of ~550 C, much higher than the 300 C of the typical LWR, which
helps the SFR to achieve increased thermal efficiency (42% vs. 33.7% of thermal energy
converted to electricity). (Massachusetts Institute of Technology, 2011) Thus, the sodium fast
reactor is a desirable choice for meeting the next generation of energy challenges.
However, if fast reactors are to be started up using reprocessed plutonium from LWRs, the
availability of such material places an upper limit on the deployment rate of fast reactors,
keeping their share of total installed capacity less than 50% through the end of this century.
(Massachusetts Institute of Technology, 2011) This causes the impact on cumulative natural
uranium consumption of the introduction of TRU-initiated fast reactors to be smaller than
desired, at only 35% less than if fast reactors had not been introduced at all.
To obviate the bottleneck associated with fast reactor startup using TRU from LWRs and
enhance the market penetration of such reactors, it has been proposed to startup fast reactors
using a uranium-fueled, once-through mode. (Fei, Shwageraus, & Driscoll, A Cost Effective
Once-Through Startup Mode for SFRs, 2011) Employing enriched uranium to fuel fast reactors
allows for an early phase-out of light water reactors, such that once the LWRs currently in
service reach the end of their 60-year lifetime, they are retired and replaced with fast reactors
fueled with uranium. This has the long-term impact of reducing demand for natural uranium and
enables uranium savings to be realized in the century timeframe, as these fast reactors are
eventually converted to the recycle mode.
The key to successful startup of fast reactors using uranium is to ensure that they are able to
achieve uranium utilization and levelized fuel costs competitive with the current fleet of LWRs.
This was achieved primarily via the introduction of a high-albedo reflector as a replacement for
the traditional uranium blanket surrounding the reactor core. This reduces the leakage in the
uranium-fueled reactor to compensate for the reduced number of neutrons produced per
absorption in uranium as compared with plutonium. (Fei, et al., 2012) It also improves the
proliferation resistance of the core, as the plutonium bred in the uranium blankets of traditional
fast breeder reactors is typically weapon grade.
Once the economics become favorable or the waste management benefits are determined to be as
important as the economics, the once-through fast reactors will switch to a recycle mode to
greatly increase the natural uranium utilization of the cycle. The most straightforward and costeffective transition will require minimal changes to the core internals and heat extraction
systems, and would ideally include simply reprocessing the spent fuel generated by the oncethrough mode, using it to fabricate plutonium-uranium recycled fuel assemblies, and then
loading these assemblies back into the fast reactor. However, a range of performance and safety
analyses must be conducted to ensure a smooth and effective transition to a recycle mode. This
task is the principal focus of the present thesis.
13
1.3 Organization of Thesis
The thesis is organized into three sections, spanning six chapters. The first section provides a
broad overview of the project, including relevant background information and the methodology
behind the investigation. The second section presents the results and discussion of the research.
Chapter 2 describes the methodology behind the research performed, the computer codes used in
the analysis, and the economic models used to develop cost estimates. Chapter 3 presents
analysis of the reactivity, burnup, economics, breeding, proliferation materials attractiveness, and
safety characteristics of the carbide fast reactor cores. Chapter 4 provides this information for
the metal fast reactor cores. The third section concludes the thesis and provides a summary of
the main conclusions. Chapter 5 presents the most salient results obtained from the analysis, and
Chapter 6 provides recommendations for future work.
14
2 Method
2.1 Introduction
This chapter provides an overview of the design of the TRU-SFR, which is virtually identical to
that of the USFR proposed by MIT CANES researchers. (Fei, Innovative Design of SFR using
Uranium Startup (Ph.D. Thesis), 2012) The radial and axial layouts of the core are described, and
the relevant operating parameters of the system are presented. The computational codes used to
perform the core physics analysis are described, and a benchmark case is presented to enhance
confidence in the results obtained. The levelized fuel cycle cost model used for economics
calculations is presented, and the values used to obtain the cost estimates are provided.
2.2 Design Overview
The design of the TRU-SFR is identical to that of the USFR, save for the composition of the fuel
loaded into the core. As with many sodium-cooled fast reactors, the core consists of a series of
hexagonal assemblies, each with a triangular lattice of pins within a coolant duct. The design
specifications and operating parameters are shown in Table 1.
Table 1. Core design specifications and operating parameters, from (Fei, Innovative Design of SFR using Uranium
Startup (Ph.D. Thesis), 2012)
Parameters
Power (MWth/MWe)
Values
2400/1000
Active care height (cm)
102
Total height (cn)
Number of Fuel Assemblies
342
360
Number of Regulating Rods
Number of Shutdown Rods
Inlet temperatire (*C
13
Outlet temperature (*C
545
Assembly pitch (cm)
16.14
Assembly duct thickness (cm)
0.39
Assembly
14.92
(cm)
inner flat-flat distnce
Fuel Cladding thicimess (cm)
The reactor is a commercial-sized design
efficiency of 42%. The active core height
for a H/D ratio of 0.287. The core has
regulating assemblies and six shutdown
assembly.
6
395
0.05
producing 2400 MWth and 1000 MWe, for a thermal
is 102 cm, with a core diameter (fuel only) of 355 cm,
360 fuel assemblies with 19 control assemblies (13
assemblies), giving 19 fuel assemblies per control
15
Of particular note regarding the design of the USFR and the TRU-SFR cores is the lack of a
depleted uranium blanket for breeding plutonium. Instead, the core is surrounded by a highalbedo reflector to reduce neutron leakage and maximize the core's reactivity. The reflector
material was chosen to be magnesium oxide due to its reflective properties and excellent thermal
performance. (MacDonald & Driscoll, June, 2010) Both axial and radial reflectors are employed,
as shown in the axial core layout displayed in Figure 1.
*1-1
-
pe.ug
IWw~dd
"s Fk
I
I
kC.'.
Figure 1. Axial USFR/TRU-SFR core layout, from (Fei, Innovative Design of SFR using Uranium Startup (Ph.D. Thesis),
2012)
The upper and lower MgO reflectors are each 40 cm thick. The upper reflector occupies onethird of the gas plenum, which is 120 cm tall. The core has two radial rings of MgO reflector
assemblies and one radial ring of B4 C (with natural boron) shield assemblies, as displayed in
Figure 2.
16
Figure 2. Radial configuration of the USFR/TRU-SFR core. Orange is fuel region 1, blue is fuel region 2, green is fuel
region 3, gray is the MgO reflector region, and black is the B 4C shield assembly region
The reflector and shield assemblies are full-length, stretching the full 342 cm of core height. The
reflector assemblies are managed so as to spatially homogenize the fluence received throughout
their operating lifetime. In successive cycles, the assemblies are rotated 180', the inner and outer
rows are then swapped, the assemblies are rotated 180' again, and finally both rows are inverted
(flipped end-over-end). This sequence then continues until the assemblies are replaced.
The fuel assemblies are separated into three radial regions. The inner radial region, fuel region
1, is colored orange, the middle radial region, region 2, is colored blue, and the outer fuel region,
region 3, is colored green. 54 fuel assemblies are present in the inner fuel region, 156 in the
middle region, and 150 in the outer region. Control assemblies are present in all three fuel
regions and are colored purple. 7 control assemblies are present in the inner region (where flux
is peaked, due to uniform fissile loading), 6 control assemblies are located in the middle region,
and 6 control assemblies are located in the outer region, for a total of 19 control rods.
17
2.3 Neutronics
2.3.1 ERANOS
To perform the core physics and depletion calculations required for investigating the reactivity
and burnup performance of the plutonium core in recycle mode, the code suite European Reactor
ANalysis Optimized calculation System, version 2.1 (ERANOS-2. 1) was selected. (Ruggeri,
2006) Initially envisioned as a tool to develop and analyze SFR cores for construction in Europe,
particularly Super-Phenix, continued development of the code has well-positioned the code to
serve as the workhorse analysis tool for Generation-IV fast reactor designs.
ERANOS was written in ESOPE, a derivative of the FORTRAN-77 language developed by the
CEA, which can be compiled using most standard FORTRAN-77 compilers. A modular code
structure was employed, which can be used to create blocks of data (called SETs) for use in
calculations. External temporary storage and permanent storage are provided by the internal
GMAT and ARCHIVE functions, respectively. These functions are all part of the ALOS
workflow software used for development.
The main components of the ERANOS package are: nuclear data libraries (multigroup cross
sections from the JEF-3.1 evaluated nuclear data library), a cell and lattice flux code (ECCO),
core-wide reactor flux solvers (diffusion, Sn transport, and variational nodal transport), a
depletion calculation module, and various output processing modules. A brief overview of the
main components is presented below.
The data library used by ERANOS contains cross sections from the JEF-3.1 evaluated nuclear
data file. (Nuclear Energy Agency, 2009) JEF-3.1 was developed by the NEA for use in neutron
transport calculations, and has been benchmarked for use in fast reactor calculations. The JEF3.1 data was processed into several multigroup libraries within ERANOS using the NJOY
software. (McFarland & Muir, 1994) The main library is a 1968-group library with 41 principal
nuclides, mostly actinides and other important resonance absorbers. Probability tables are
included for the most important 37 of these 41 resonant absorbers. The remaining materials use
a 33-group library containing 246 nuclides, including pseudo (lumped) fission product data.
The 2-D lattice calculations are performed by the transport solver ECCO. ECCO uses the
subgroup method to perform resonance self-shielding of the 1968-group cross sections for the
materials present in the lattice. The geometry can be specified as either homogeneous or
heterogeneous. If a heterogeneous calculation is selected, the collision probability method is
used to perform flux calculations over the lattice. Specifying the homogeneous mode can greatly
expedite calculation. Since the mean free path of neutrons in a SFR is on the order of the size of
the lattice, the homogeneous approach is appropriate for the present analysis. The self-shielded
cross sections generated are then condensed and smeared to provide effective cross sections for
use in the core-wide coarse group flux calculation.
18
Three flux solvers are available for use in the ERANOS package: diffusion, Sn, and variational
nodal. The diffusion and variational nodal solvers can be performed in 1-,2-, or 3-D geometry.
The present analysis used the diffusion solver with an R-Z 2-D geometry to provide initial
scoping calculations and sodium void worth data, and the 3-D Cartesian geometry using the
variational nodal method for the core-wide depletion and dpa calculations.
The burnup module in ERANOS solves the Bateman equations for the actinides of interest, as
well as the lumped fission products. The material depletions are performed on the full-core
scale, as opposed to the lattice level. The material concentrations are then output for each
burnup step input by the user.
2.3.2 MCNP
To benchmark the use of ERANOS for plutonium-fueled SFR neutronic analysis, the MCNP5
Monte Carlo transport code was employed. (X-5 Monte Carlo Team, 2003) MCNP5 is frequently
employed as a benchmarking tool due to its highly accurate calculation method, which makes
very few assumptions in the solution of the neutron transport equation.
MCNP5 is written in ANSI-standard Fortran-90, making it suitable for most standard Fortran-90
compilers. The code shares data between various routines using Fortran modules. The code
operates in several default steps. The first step is IMCN, problem initiation, where the input file
is read and processed to prepare for calculation. The next step is cross section processing
(XACT), where the data libraries for the nuclides present in the problem are loaded into memory.
The calculational step MCRUN performs the stochastic solution and reports the specified results
to the user.
MCNP5 employs the Monte Carlo stochastic method of numerical solution to the problem of
neutron transport. The Monte Carlo method simulates the behavior of individual particles and
then estimates the mean values of user-specified parameters of particles in the physical system
based on the average behavior of the simulated histories. Unlike deterministic methods, which
provide near-complete system information (including the flux in every region of the geometry)
as a matter of course during their solution, stochastic methods require specific information to be
specified by the user for collection during the calculation. Though this requirement and the
method of individual particle simulation both result in relatively slower problem solution, their
use requires fewer assumptions to be made, chiefly the cross-section group collapsing necessary
for multi-group deterministic energy treatments. Monte Carlo methods are able to employ
continuous-energy cross section data libraries where the evaluated data can be used directly, with
no need for resonance self-shielding or other energy condensation. Thus, they are well-suited to
provide comparative neutronic analysis for method validation.
19
To eliminate differences based solely on the evaluated data, the JEF-2.2 library was also
employed for use with MCNP5 in continuous energy form. The problem geometry was kept
identical to that used in the ERANOS model. Since MCNP5 performs only steady-state
criticality analysis, the external depletion code suite BGcore was used to perform the burnup
calculation.
BGcore uses the MATLAB computing language to couple the steady-state flux calculation of
MCNP5 with a depletion solver for burnup analysis. (Fridman, Shwageraus, & Galperin, 2008)
The fluxes calculated by MCNP5 are read by BGcore using its MC2SAR module, which
provides the multigroup spectrum required for the SARAF depletion and decay module. SARAF
calculates the reaction rates necessary for solving the Bateman equations, and works via a direct
application of the matrix exponential method. The resulting fuel composition evolution for that
burnup step is then returned to MCNP5 using the SAR2MC module. MCNP5 then performs
another steady-state flux calculation using the updated material compositions, and the process
continues until the desired burnup is reached.
A comparison calculation was performed between ERANOS and MCNP5/BGcore to provide
confidence in the ERANOS results. (Fei, Innovative Design of SFR using Uranium Startup
(Ph.D. Thesis), 2012) The reference core was carbide with 15.2% plutonium, 75% of which was
Pu-239, for a total Pu-239 fissile loading of 11.4% of heavy metal. The resulting plot of
reactivity vs. core residence time (effective full power days, EFPD) is shown in Figure 3, and the
resulting reactivity disparities are presented in Table 2.
18500
18000
-+BGcore
S17500
E
--
ERANOS
0.
17000
16500
4)
16000
15500
15000
0
100
t FI
I - -T TT! T 1
200
300
1 ; -1 r
400
- T
500
600
Core residence time (EFPD)
Figure 3. Reactivity vs. core residence time for the Pu-U-C reference case calculated using the MCNP5/BGcore code and
the ERANOS code package
20
Table 2. Reactivity comparison between the MCNP5/BGcore carbide case and the ERANOS carbide case
Time
(Days)
BGcore ERANOS
reactivity Reactivity Ap (pcm)
0
100
200
300
400
500
(pcm)
(pcm)
18012.0
17525.8
17048.9
16545.0
16088.4
15621.1
18086.5
17518.1
17034.5
16545.9
16054.3
15558.9
74.55
-7.67
-14.43
0.94
-34.08
-62.17
The agreement between ERANOS and MCNP5/BGcore is well within acceptable limits. The
greatest disparity is actually encountered at BOC, where the ERANOS case has an initial
reactivity of 18086.5 pcm, while the BGcore reference case had an initial reactivity of 18012.0
pcm, for a reactivity difference of +74.55 pcm (0.4%). The disparity in the two calculations
ranges from this maximum of +74.55 pcm to a minimum of +0.94 pcm, fluctuating slightly
between the two extremes due to the stochastic nature of the BGcore solution. Ultimately, the
comparison establishes the ERANOS software as a reliable estimator of the reactivity of the SFR
core for use in performing core physics performance evaluations.
2.4 Fuel Cycle Economics
The levelized fuel cost is a measure of the costs associated with the production of a single unit of
energy. Commonly quoted in mills/kWh, it provides a meaningful way to compare the cost of
electricity generation between reactors and fuel cycles of different configurations. Two
important parameters are needed to compute the LFC: the cost of the fuel and the amount of
electricity generated. The formulations for these component parameters are given in Equation 1
and Equation 2. Equation 3 provides the formulation for the LFC itself.
Fuel Cycle Cost Net Present Value ($USD) = FCCNPV = ZC * (1 + id)n
(1)
where
Cn=cost for the nth fuel cycle component
id=discrete discount rate= 10% per year
tA=lead time from the date of fuel loading for the purchase of material from the nth fuel cycle
component
21
Levelized Cycle Energy (MWhe) = Eieve = Bd * M *
7th
*
24 *
* (1ec*Tcyc
ic *Tcyc
(2)
where
Bd=average discharge bumup (MWd/kgHM)
M=total heavy metal loading of the core (kgHM)
n1lh=thermal efficiency
ic=continuous discount rate=9.5% per year
Tcyc = cycle length (years) = P * 365
Lc=capacity factor--95%
P=Reactor thermal power rating (MWth)
Levelized Fuel Cost ($USD/MWh)
=
(mills/kWhe)
=
FCCNPV
Elevel
(3)
The cost of the fuel for a once-through cycle involves several front-end costs associated with
obtaining the uranium and making it into fuel for the reactor. These costs include mining, where
the ore is dug out of the ground and milled into the typical U3 0 8 yellowcake powder, conversion,
where the yellowcake is converted into UF 6 gas, enrichment, where the UF 6 gas is fed through
diffusion membranes or gaseous centrifuges to increase the concentration of U-235, and fuel
fabrication, where the enriched UF 6 gas is converted into U0 2 ceramic pellets and placed inside
the metallic fuel assembly structures. The unit cost ($/mass) of these steps can be obtained from
industry sources, and together the total cost of enriched fuel assemblies can be calculated by the
sum of the unit costs, adjusted for the lead times and the interest rate used by the utility. The
assumed costs for these fuel cycle steps are shown in Table 3. (Fei, Innovative Design of SFR
using Uranium Startup (Ph.D. Thesis), 2012)
Table 3. Unit costs and lead times for front-end once-through fuel cycle steps used for comparison to the recycle mode
Ore Purchase
Conversion
Enrichment
Fabrication
Unit Cost
Lead Time
100 $/kgNatU 2 years
10 $/kgNatU
2 years
1 year
100 $/SWU
0.5 years
250 $/kgU
22
The cost of the reprocessed fuel is driven by entirely different considerations. Since the recycled
fuel need not be mined, converted, or enriched, these costs are not included in the front-end fuel
cost of recycled fuel. Instead, the costs come from the processes used to dissolve the spent fuel
from the USFR, remove the fission products, and re-form the actinides into the desired fuel
composition (in this case, carbide) and fabricate it into a new assembly. Since the reprocessing
and fuel fabrication are usually performed in the same facility at the same time, these costs are
combined into a single parameter describing the total unit cost of creating new, recycled fuel
from spent fuel. Though this process has not been employed commercially in the United States,
several reports from U.S. government laboratories have sought to estimate the projected costs of
such a process. (Shropshire, et al., 2009) The projected unit cost of this recycle process, with
upper, lower, and median estimates, is shown in Figure 4. For the purposes of the present work,
the median estimate of $6000 per kg of reprocessed heavy metal was used, with the same lead
times for natural uranium purchase and fuel fabrication as the reference LWR case.
Low
NominalMean
High
Figure 4. Distribution of combined unit cost for electrochemical reprocessing and remote fabrication of fast reactor fuel,
from (Shropshire, et al., 2009)
Comparing the unit costs of the once-through LWR fuel cycle with the unit costs of the recycle
mode TRU-SFR fuel cycle, it is clear that on a per-mass basis, reprocessing is much more
expensive, hence no commercial reprocessing has been pursued in the United States. However,
this is much more of an issue for LWR fuel reprocessing, since much more fuel must be
reprocessed to obtain the necessary quantities of plutonium for new fuel fabrication.
Reprocessing the fuel from the USFR can be more economic because it has much more
plutonium as a fraction of total heavy metal, and that plutonium is "cleaner" because it has more
fissile plutonium as a fraction of total plutonium (see the discussion in Section 3.3.2.1 and
Section 3.3.3.1 on the increased worth of the USFR spent fuel for more details).
However, the need to reprocess fewer kg of spent fuel is only one factor in the effort to make the
recycle-mode TRU-SFR economically competitive with the once-through LWR fuel cycle.
Recall that the LFC depends on both the cost of the fuel and on the amount of electricity
generated from that fuel. To make a serious effort to achieve LFCs competitive with LWRs, the
SFR must produce more energy per kg of fuel since its fuel costs more per kg to make. This is
where the art and science of core physics analysis and design for burnup maximization enables
this strategy to be cost competitive. SFRs are able to achieve much higher burnups than LWRs
23
due to the breeding present in their fast spectrums, which greatly reduces the slope of their
reactivity vs. burnup curves. Thus, designing an economically competitive fast reactor recycle
mode centers around maximizing the achievable burnup of the recycle cores. This is
complicated in the present instance by the concurrent need to respect dpa limitations on cladding.
2.5 Summary
The core layout, design, and operating parameters of the recycle mode TRU-SFR were kept
identical to those of the once-through USFR. The core, designed for commercial operation,
operates at a nominal power level of 1000 MWe, with a thermal efficiency of 42%. The fuel in
the core is divided into three regions, with a uniform fissile loading for all regions. The key
design feature is the use of high-albedo MgO radial and axial reflectors in place of a depleted
uranium blanket, which reduces core leakage, maximizing reactivity.
The ERANOS code package was selected for core physics analysis. The 1968-group JEF-3.1
library, generated using NJOY, was used in the ECCO lattice calculation to perform the selfshielding resonance treatment and generate collapsed coarse-group cross sections for use in the
deterministic flux solvers present in the package. Both the RZ-diffusion solver and the XYZ
variational nodal transport method flux solvers were employed in the course of the analysis.
The ERANOS code package's appropriateness for the present analysis of a plutonium-fueled
SFR was benchmarked using the MCNP5/BGcore Monte Carlo linked depletion calculation
system. Maximum error was +74.55 pcm (0.4%) and occurred at BOC. Thus, the ERANOS
code was accepted for use as an effective and accurate reactor physics analysis tool.
The economics model employed was consistent in methodology and cost inputs to the work on
the once-through mode by Fei. (Fei, Innovative Design of SFR using Uranium Startup (Ph.D.
Thesis), 2012) The levelized fuel cost of a given SFR core was estimated by calculating the fuel
cycle cost of the recycled fuel and dividing it by the levelized amount of electricity produced
throughout the cycle.
24
3 Carbide Core Analysis
3.1 Introduction
The design of the recycle SFR core began by maintaining as many of the once-through core's
design features as possible. Of particular note is that the high albedo magnesium oxide (MgO)
reflector is retained in lieu of using a depleted uranium blanket typical of classical sodium fast
reactor designs. Since the reference once-through uranium-fueled core uses uranium-carbide
(UC) fuel, the initial design of the plutonium-fueled recycle core incorporated a plutoniumuranium-carbide (PUC) fuel form with a fuel volume fraction of 40%, as in the once-through
core.
In all cases examined, the burnup of the PUC core was fluence-limited. The fluence-limited
bumup was found to be acceptably high for achieving economic fuel cycle performance. The
target SFR fuel cycle cost was chosen as the reference LWR levelized fuel cost (LFC) of 7.11
mills/kWh. (Massachusetts Institute of Technology, 2011) The carbide cores consistently
approached this target, achieving varying degrees of success depending on the recycle strategy
employed.
The carbide fuel was found to have excellent neutronic characteristics in the recycle core, such
that the core's spectrum achieved a balance between reactivity performance (enabled by a fast
spectrum) and displacements-per-atom (dpa) damage in the cladding (lower dpa is associated
with a softer spectrum). The radial flux distribution in the core was found to remain nearly
constant with burnup (since a uniform initial enrichment was loaded).
3.2 Radial Power Distribution
The radial fast flux profile of the carbide-fueled TRU-SFR was characterized to provide an
overview of the power distribution present in the core, since power is roughly proportional to
power. The radial fast flux distribution was plotted at the beginning of the cycle, the middle of
the cycle, and the end of the cycle. The plot for the carbide core transitioned using the multicore
strategy is shown in Figure 5.
25
4.5E+15
4E+15
6
3.5E+15
E
3E+15
<-+BOC
-a-MOC
2.5E+15
-+EOC
X2E+15--
-
1.5E+15-U. 1E+15
5E+14
0
0
50
100
150
200
250
Radius (cm)
Figure 5. Radial flux profile for the carbide multicore core
As seen in Figure 5, the flux profile experiences only a minor change with bumup, with the
power shape flattening as the center zones are depleted more rapidly than the outer regions. The
peak fast flux (>0.1 MeV) is 3.87E+15 n/s/cm^2 at BOC, occurring at a radial position of 24.8
cm from the centerline. The peak fast flux at MOC is 3.37E+15 n/s/cm^2, and occurs on a
plateau from 26.6 cm to 33.85 cm from the centerline. The peak flux at EOC is 3.06E+15
n/s/cmA2, occurring from 81.5 cm to 86.0 cm. This outward movement of the power shape is due
to the core's uniform fissile loading, where all the fuel throughout the core contains the same
composition of fissile material. Since the outer regions experience more leakage than the center,
the center has a greater initial flux. However, this increased flux at BOC causes the fissile
material in this region to fission more rapidly than the outer regions, so its reactivity is depleted
more quickly than these outer regions. Thus, as the cycle progresses, the outer regions begins to
have more reactivity than the center zone despite their increased leakage, and the so the power
shape flattens. Complex fuel management schemes like those used for LWRs to flatten the
power profile at BOC are not employed since the core's bumup is fluence-limited, not reactivitylimited, so these schemes do not improve the average discharge burnup of the core.
26
5E+15
----
4.5E+ 15
4E1
E 3.5E+15
<
---BOC
-0---MOC
3E+15
EOC
2.5E+15
.2 2E+15* 1.5E+15
U.
-
1E+15
5E+14
0
0
50
100
150
200
250
Radius (cm)
Figure 6. Radial flux profile for the carbide uranium+ core
The radial flux profile for the carbide core displays more central peaking than the multicore case,
and experiences a larger swing with burnup. The peak flux at BOC is 4.52E+15 n/s/cm^2, 17%
greater than the peak BOC flux of the multicore carbide core. This higher flux level is due to the
decreased fissile loading present in the uranium+ transition core (6.92 HM% vs. 8.01 HM%
fissile plutonium) relative to the multicore core (see Section 3.3.3.1 for a more complete
description of the heavy metal loading of the uranium+ carbide core). The peak flux at MOC is
3.63 E+15 n/s/cmA2, at a radial location of 24.8 cm to 33.9 cm. The peak flux at EOC is
3.16E+15, occurring at 101.7 cm from the centerline. It is interesting to note that this EOC peak
flux for the uranium+ core is only 3.2% greater than that of the multicore case, indicating that the
two cores are neutronically similar.
3.3 Transition Strategy
3.3.1 Overview
The transition from the once-through SFR (the USFR) to the recycle-mode SFR (the TRU-SFR)
incorporated two different strategies, selected to bracket the range of potential transition modes.
The uranium+ strategy sought to preserve the transuranic masses from the USFR core, which
created a lower bound on the plutonium enrichment of the TRU-SFR core. The multicore
strategy sought to preserve the composition (weight fractions) of the transuranics from the USFR
core, which created an upper bound on the plutonium enrichment of the TRU-SFR core. The
performance of the recycle core was then evaluated for these bracketing scenarios and the
optimal transition strategy was identified.
27
3.3.2 Multicore
3.3.2.1 Fuel Composition
The multicore strategy preserved the composition of spent fuel from the USFR in the transition
to the TRU-SFR. This principally consisted of maintaining the weight fractions of the transuranic
actinides in the spent fuel (shown in Table 4 below), and resulted in an upper bound on the
achievable maximum weight fraction of fissile plutonium of 8%.
Table 4. Composition of reprocessed USFR spent fuel loaded into the carbide TRU-SFR core using the multicore strategy
with no cooling.
Isotope
U-235
U-236
U-238
Pu-238
Pu-239
Pu-240
Pu-241
Pu-242
Np-237
Am-241
Am-242
Am-243
Cm-242
Cm-244
Cm-245
HM Weight %
3.09%
1.91%
85.26%
0.08%
7.91%
1.33%
0.10%
0.0088%
0.26%
0.004796%
0.000135%
0.000516%
0.000365%
0.000086%
0.000006%
The once-through USFR produces spent fuel with low minor actinide concentrations, with
americium and curium nuclides comprising less than 0.00 1%of the total heavy metal mass.
Since the fuel loaded into the TRU-SFR is obtained from a once-through uranium-fueled SFR, it
has a much higher quality plutonium vector, as shown in Table 5.
Table 5. Plutonium vector for the reference multicore carbide core
Isotope
Pu-238
Pu-239
Pu-240
Pu-241
Pu-242
% of Total Pu
0.90%
83.84%
14.05%
1.11%
0.09%
28
The high-quality plutonium reduces the total required plutonium mass in the recycle core. Since
the multicore strategy seeks to preserve the composition of the fuel extracted from the oncethrough SFR in the transition to the recycle mode, and the once-through core has lost mass due to
bumup during the cycle, it takes 1.16 spent fuel assemblies to make 1 recycled assembly.
3.3.2.2 Fuel Management Scheme
The TRU-SFR core is divided into three fuel regions, a reflector region, and a shield region, as
shown in Figure 1. The fuel management scheme necessarily differs from that of a typical LWR
because the fuel bumup is fluence-limited, not reactivity-limited. This unique characteristic led
to the development of an alternate fuel management strategy.
For the carbide core TRU-SFR, the fuel management seeks to achieve nearly the same discharge
burnup for all assemblies, regardless of fuel region. It accomplishes this by discharging the fuel
in the center zone (which has the highest flux, as shown in Figure 5 previously) after one cycle at
the fluence-limited burnup for that fuel. The fuel in the middle and outer zones is then shuffled,
such that the fuel in the outer zone is moved to the middle zone, and vice versa. Fresh fuel is
then loaded into the center zone and the reactor is restarted. During the next refueling outage, all
three zones are discharged and replaced with fresh fuel. The average discharge burnup of the fuel
is expected to be consistent across all three zones.
3.3.2.3 Reactivity Profile and Burnup Performance
The reference carbide core used with the multicore transition strategy has a fuel volume fraction
of 40% (consistent with the reference once-through carbide core). The reactivity over the cycle
is shown in Figure 7.
29
10000
Fluence Limit: 136 MWd/kgHM
5000
Reactivity Limit: 176 MWd/kgH
E
0S
50
100
250
150
300
350
400
U -5000-
-10000
-15000
- --
---
Average Burnup (MWd/kgHM)
Figure 7. Reactivity vs. burnup for the reference carbide recycle core using the multicore transition strategy
The multicore transition strategy using carbide fuel is characterized by an approximately linear
decrease in reactivity with increasing burnup. The initial reactivity (8441 pcm) and the shallow
slope (-62 pcm/(MWd/kgHM)) help to achieve a reactivity-limited bumup of 176 MWd/kgHM.
However, the radiation damage to the cladding must also be considered, as this is also a limiting
consideration in the maximum achievable bumup of fast reactors. The cladding radiation
damage metric used here is displacements-per-atom, or dpa, and the limit for the oxidedispersion steel (ODS) cladding employed is 200 dpa. Some aggressive estimates put the dpa
limit of ODS steel at 250 dpa, but this is a theoretical maximum achieved under ideal conditions,
and as such the more conservative 200 dpa limit was selected for the present work. (Kimura, et
al., 2011) If the ODS cladding can be shown to operate to greater than 200 dpa, the associated
fluence-limited bumups would necessarily be larger and would result in more favorable
economics, as long as the fluence remained the limiting factor on the achievable burnup. The
carbide reference core using the multicore transition strategy reaches the 200 dpa limit at a
burnup of 136 MWd/kgHM, which is 77% of the reactivity-limited burnup.
A reload simulation was also performed, taking the spent fuel from the plutonium-fueled core
and recycling it once to help predict the equilibrium behavior of the recycle mode. The resulting
reactivity curve is compared to that of the transition core in Figure 8. Since fluence is again the
limit on burnup, the reload core can achieve comparable bumup to the transition core.
30
20000
Transition Fluence Limit: 136 MWd/kgHM
Reload 1 Fluence Limit: 149 MWd/kgHM
Percent Change from Previous: 10%
15000
10000
-
E
Transition Reactivity Limit: 176 MWd/kgHM
Reload 1 reactivity Limit: 217 MWd/kgHM
Percent Change from Previous: 23%
5000
50
-5000
----
100
0
150
300
350
400
Transition
-*-Reload 1
-10000
-15000
Average Discharge Burnup (MWd/kgHM)
Figure 8. Reactivity vs. burnup for the reloaded Pu-U-C fuel using the multicore strategy
The reactivity curve for the reloaded carbide core has a similar slope as before (-73
pcm/(MWd/kgHM)), but begins with a higher initial reactivity, which results in a 23% larger
reactivity-limited burnup of 217 MWd/kgHM. However, the fluence-limited burnup only
increases 10%, from 136 MWd/kgHM to 149 MWd/kgHM. Thus, the fluence-limited burnup
decreases to only 69% of the reactivity-limited burnup, down 8% from 77%. Additionally, the
large excess reactivity at the beginning of the cycle (14430 pcm) makes it exceptionally difficult
to achieve shutdown without significant control modifications (see Section 3.9.2 for a more
detailed discussion).
The average discharge burnup of the multicore carbide core, while fluence-limited, still manages
to exceed that of a conventional SFR in a breeder configuration by 50% (since the reference SFR
breeder, GE's PRISM, is quoted as achieving an average discharge burnup of 100 MWd/kgHM).
(Waltar, Todd, & Tsvetkov, 2012) However, it falls 15% short of the average fuel burnup of a
typical SFR burner core, which reaches a burnup of 177 MWd/kgHM.
3.3.3 Uranium+
3.3.3.1 Fuel Composition
The uranium+ transition strategy seeks to preserve the actinide masses obtained from a single
once-through SFR core, supplementing the mass defect (mass lost to burnup) with natural
uranium. This strategy effectively places a lower bound on the effective fissile plutonium
enrichment loading achievable in recycle mode. The resulting fuel composition, after adding
883 kg of natural uranium to 41,657 kg of reprocessed USFR fuel, has the actinide vector shown
in Table 6.
31
Table 6. Composition of reprocessed USFR fuel loaded into the carbide TRU-SFR core using the uranium+ strategy with
no cooling
Isotope
U-235
U-236
U-238
Pu-238
Pu-239
Pu-240
Pu-241
Pu-242
Np-237
Am-241
Am-242
Am-243
Cm-242
Cm-244
Cm-245
HM Weight %
2.77%
1.65%
87.18%
0.07%
6.83%
1.14%
0.09%
0.0076%
0.23%
0.004140%
0.000117%
0.000446%
0.000315%
0.000074%
0.000005%
Since natural uranium (instead of reprocessed fuel from another assembly) was used to
supplement the mass defect from the once-through assembly, the heavy metal weight fraction of
uranium-238 (and uranium-235) increases relative to the weight fractions of the other actinides.
The heavy metal fraction of fissile plutonium (Pu-239 and Pu-241) decreases from 8.01 HM% to
6.92 HM% for the same reason, which decreases the reactivity of the core and increases the flux
required to attain the specified power level of 2400 MWth. The plutonium vector remains the
same as in the multicore strategy since only uranium is added.
3.3.3.2 Reactivity Profile and Burnup Performance
A depletion calculation of the uranium+ transition core in the recycle mode of the SFR was
performed to estimate the reactivity as a function of burnup. The results of this simulation are
shown in Figure 9.
32
A00
Fluence Limit: 118 MWd/kgHM
2000
Reactivity Limit: 138 MWd/kgH M
50
E
100
15
200
250
300
350
400
-2000
CL
-4000
l
-6000
M
-8000
-10000
-12000
-14000
-16000
Average Discharge Burnup (MWd/kgHM)
Figure 9. Reactivity vs. burnup for the reference carbide recycle core using the uranium+ transition strategy
The reactivity curve for the recycle core using the uranium+ strategy took a parabolic form, due
to the enhanced breeding relative to the multicore strategy (see Section 3.7 for a more detailed
explanation). The reactivity-limited burnup was 138 MWd/kgHM, a 21% decrease from the
multicore case. However, the fluence-limited burnup was 118 MWd/kgHM, a decrease of only
13%. The fluence-limited burnup was therefore 85% of the reactivity-limited burnup, which was
8% better than the multicore case. The initial reactivity was only 1133 pcm, with a maximum
reactivity of 2380 pcm at 65 MWd/kgHM, making for a more controllable system than with the
multicore strategy.
The Pu-U-C core using the uranium+ strategy for transition was recycled and a second reactivity
curve was generated for the reload cycle, as shown in Figure 10.
33
10000
Transition Fluence Limit: 118 MWd/kgHM
Reload 1 Fluence Limit: 124 MWd/kgHM
Percent Change from Previous: 5%
5000
Transition Reactivity Limit: 138 MWd/kgHM
Reload 1 Reactivity Limit: 173 MWd/kgHM
Percent Change from Previous: 25%
E
50
100
250
150
300
350
400
-5000
---
Transition
-u-Reload 1
-10000
-15000
Average Discharge Burnup (MWd/kgHM)
Figure 10. Reactivity vs. burnup for the reloaded Pu-U-C fuel using the uranium+ strategy
The reactivity curve for the reload plutonium core takes the same parabolic shape as the
transition core, but as was the case with the multicore recycle strategy, the uranium+ reload core
has a greater initial reactivity, 4590 pcm, than the transition core. The reload core's peak
reactivity is 5310 pcm at 43 MWd/kgHM. The reactivity peak occurs earlier for the reload core
than for the recycle core because the fissile plutonium loading has increased (due to slight
breeding) during the transition cycle, and as the amount of fissile plutonium increases the
conversion ratio decreases. The reactivity-limited burnup of the reload case is 173 MWd/kgHM,
an increase of 25% over the transition case. However, similar to the multicore strategy, the
fluence limit changes less, increasing only 5% to 124 MWd/kgHM for the reload case. Thus, the
fluence-limited burnup is only 71% of the reactivity-limited burnup for the reload case, a
decrease of 14% from the transition case.
3.4 Reactivity Worth of Minor Actinides
The reactivity worth of the minor actinides was investigated for the carbide cores for both the
multicore and uranium+ transition strategies. The reactivity curve for the transition multicore
case displaying the reactivity worth of the minor actinides is shown in Figure 11.
34
10000
NominalFluence Limit: 135.9 MWd/kgHM
MA Removed Fluence Limit: 136.3 MWd/kgH M
Percent Change from Previous: -0.3%
5000
U
0.
50
U
(U
a)
100
350
300
250
150
400
-+*-Nomninal
-5000
-
MA Remov ed
-10000
-15000
Average Discharge Burnup (MWd/kgHM)
Figure 11. Reactivity vs. burnup for the carbide core transitioned using the multicore strategy displaying the reactivity
worth of the minor actinides
Removing the minor actinides results in 4% greater initial reactivity (a reactivity worth of 352
pcm), but decreases the reactivity-limited burnup by 2%. This occurs because the removed MA
are replaced with additional plutonium and uranium to preserve mass, and the additional
plutonium raises the initial reactivity while slightly reducing the breeding and thus decreasing
the slope of the reactivity curve, resulting in a negligibly decreased reactivity-limited bumup.
The fluence-limited bumup increases negligibly (0.3%).
4000
Nominal Fluence Limit: 117.9 MWd/kgHM
MA Removed Fluence Limit: 118.1 MWd/kgH M Percent Change from Previous: -0.1%
2000
0
'
-
50
100
-
-
-
-
-
250
200
1
300
350
400
-2000
0.
-4000
C.IL
--
-6000.1-
-4-Nominal
-e-MA Removed
-8000
-10000
-12000
-14000
-
-16000
Average Discharge Burnup (MWd/kgHM)
Figure 12. Reactivity vs. burnup for the carbide core transitioned using the uranium+ strategy displaying the reactivity
worth of the minor actinides
35
The initial reactivity of the carbide core transitioned using the uranium+ strategy increased by
18% when the minor actinides were removed, giving a BOC reactivity worth of 203 pcm. The
reactivity-limited bumup decreases 2%, while the fluence-limited burnup increases negligibly by
0.1%.
Regardless of the transition strategy employed, the reactivity effect of the minor actinides is
minimal. It is therefore recommended to include them in the recycling strategy to reduce the
longevity of the radioactivity and amount of decay heat generated by the waste product of the
recycling process, as well as the total waste mass that must be disposed.
3.5 Storage Impact
The impact of storing the fuel for an extended period of time after discharge from the USFR was
evaluated for both the multicore and the uranium-+ carbide core cases. To simulate the effect of
cooling on the fuel, and to provide an upper limit on the reactivity lost to cooling, all of the Pu241 present in the fuel was assumed to have decayed into Am-241. The effect of this decay on
the initial reactivity and the achievable burnup of the core was then evaluated.
15000
Cooled Transition Fluence Limit: 134.1 MWd/kgHM (-1.29%)
Cooled Reload 1 Fluence Limit: 142.0 MWd/kgHM (-4.63%)
10000
5000
0
050
100
250
150
300
350
400
-5000
-*-Transition
-4-Reload 1
-10000
-15000
Average Discharge Burnup (MWd/kgHM)
Figure 13. Reactivity vs. burnup for the multicore carbide cores after cooling
As with the uncooled cores (Refer back to Section 3.3.2.3), the cooled cores do experience an
increase in reactivity after their first reprocessing/reload cycle, as the fluence-limited burnup
increases from 134 MWd/kgHM to 142 MWd/kgHM. However, relative to the uncooled fuel,
the loss of the Pu-241 does have a slight negative impact on the reactivity and thus the fluencelimited bumup. The reactivity of the cooled transition core decreases by 803 pcm (9.5%), and
36
the fluence-limited bumup decreases by 1.29%. However, these effects are small, making
storage a viable option in this case if fuel cycle pressures prevent rapid transition to the recycle
mode.
10000
_
Cooled Transition Fluence Limit: 116.1 MWd/kgH M (-1.59%)
Cooled Reload 1 Fluence Limit: 119.1 MWd/kgH M (-3.76%)
5000
E
Q.
-
--
--
0
50
100
0
150
250
300
350
400
U 5000
-*-Transition
--
Reload 1
-10000
-15000
Average Discharge Burnup (MWd/kgHM)
Figure 14. Reactivity vs. burnup for the uranium+ carbide cores after cooling
The results for the uranium+ cases were similar to those of the multicore cases. The initial
reactivity of the cooled fuel in the transition from the USFR to the TRU-SFR decreased 867 pcm
(77%), decreasing the fluence-limited burnup by 1.6% to 116.1 MWd/kgHM. The effect of
cooling was greater for the first reload of TRU-SFR fuel, where the initial reactivity of the
cooled fuel was 2270 pcm less than for the hot fuel. Accordingly, the fluence-limited bumup of
the cooled fuel decreased 3.8% to 119.1 MWd/kgHM, relative to the uncooled fuel. Again,
however, the loss of reactivity is not significant enough to preclude startup, and the initial
reactivity actually improves with successive reloads. Thus, while the cooling time of the fuel
must be accounted for in the design of the transition core, its impact is not significant enough to
drive the decision to reprocess fuel, which can then be decided based on economic, waste
management, or other factors.
3.6 Economic Performance
The fuel cycle costs of the TRU-SFR in the recycle mode are primarily dependent on the
achievable burnup of the fuel. Since this burnup is typically limited by the allowable fluence to
the cladding, maximizing the bumup means minimizing the cladding fluence. Since fuel that is
fluence-limited cannot be shuffled to overcome this limit, complicated fuel management schemes
are ineffective at improving the achievable burnup. Thus, the key to obtaining levelized fuel
37
costs (LFCs) on par with those of the current LWR once-through cycle is designing a transition
and recycle scheme that minimizes cladding fluence and maximizes the fluence-limited burnup
of the cycle.
For the carbide cores, two different transition and recycle strategies were investigated: the
multicore strategy, in which the composition (heavy metal weight fractions) of the spent fuel
from the USFR was preserved in the transition to the TRU-SFR, using slightly more than one
(- 1.12) once-through cores to satisfy the mass defect between the once-through mode and the
recycle mode, and the uranium+ strategy, in which the heavy metal masses of the USFR core
were preserved and supplemented with natural uranium to create the TRU-SFR recycle mode
core. The costs associated with these two strategies were similar from a reprocessing
perspective, but the resulting fluence-limited bumups varied, giving rise to differences in the
LFC achievable by each strategy.
As has been detailed in preceding sections, the achievable bumups of the transition and
equilibrium recycle mode carbide cores are exceptionally larger than those of the typical LWR.
The carbide core recycled using the multicore strategy achieved equilibrium average discharge
burnups of 149 MWd/kgHM (assuming no cooling), which is roughly three times that of the
typical LWR burnup of 50,000 MWd/kgHM. (Massachusetts Institute of Technology, 2011)
However, the multicore strategy suffers from issues with reactivity control (see Section 3.9.2)
and uses plutonium resources less efficiently. The recycle mode carbide core rectifies these
problems, and reaches a fluence-limited equilibrium average discharge burnup of 124
MWd/kgHM without any fuel cooling. The LFC computed using these achievable burnups is
shown in Table 7.
Table 7. Levelized fuel costs for the carbide fueled SFR cores in recycle mode, with the reference once-through LWR LFC
Fuel Type
LWR Oxide
SFR UC
SFR UC
SFR UC
SFR UC
SFR UC
SFR UC
SFR UC
SFR UC
Reprocessing Scenario
None (Once through)
Uranium+
Multicore
Uranium+
Multicore
Uranium+
Multicore
Uranium+
Multicore
Stage
Transition
Transition
1st reload
1st reload
Transition (cooled)
Transition (cooled)
1st reload (cooled)
1st reload (cooled)
Maximum Bumup
(Mwd/kgHM)
45
118
136
124
149
116
134
119
142
LFC (mills/kwh)
_______
7.00
7.17
6.41
6.89
5.98
7.27
6.49
7.12
6.20
As shown in Table 7, the LFCs of both the multicore and uranium+ transition strategies closely
approximate the LFC of the reference once-through LWR fuel cycle. The LFC of the transition
carbide core recycled using the uranium+ strategy is 7.17 mills/kWh, 2.4% greater than the 7.00
mills/kWh fuel cost of the reference LWR case. However, this slight disparity decreases once
the equilibrium cycle is reached (upon first reload of the TRU-SFR core), which obtains a LFC
of 6.89 mills/kWh, actually 1.5% less than the LWR case. This cost decrease is realized via the
38
increase in the fluence-limited bumup, which increases 5% from 118 MWd/kgHM to 124
MWd/kgHM. The enhanced efficiency of the SFR cores also helps them to approach lower
LFCs than the LWR reference case. A similar trend is experienced for carbide cores transitioned
using the multicore strategy, which for the first transition achieves a LFC of 6.41 mills/kWh,
8.4% less than the LWR reference case. The transition multicore case's LFC of 6.41 mills/kWh
is also 3.9% less than the LFC of 7.17 mills/kWh obtained for the uranium+ case. This is a
direct result of the enhanced fissile inventory present for the multicore case, which limits the
sustainability of the fuel cycle since it requires multiple USFR assemblies to create one TRUSFR assembly using this strategy.
Since cooling the fuel before reprocessing and reloading it into the core reduces the fissile
content which in turn reduces the fluence-limited bumup, the LFCs of the cooled core cases are
uniformly worse than those which were immediately reloaded. The LFC of the uranium+
transition core is 7.27 mills/kWh, 1.4% higher than if it had not been allowed to cool and 3.8%
higher than the reference LWR case. Similarly, the LFC of the transition multicore case also
increases, by 1.2% relative to the uncooled case, yet is still 7.3% less than the reference LWR
LFC. The cooled reload cases also have increased LFCs relative to the uncooled reloads, as the
uranium+ and multicore reload LFCs increase 3.3% and 3.7%, respectively. However, the
cooled uranium+ reload (equilibrium) case is only 1.7% more than the reference LWR LFC, and
the cooled multicore case is 11.4% less. Thus, the economic arguments for immediate
reprocessing are weak at best, and are expected to be outweighed by other fuel cycle
considerations, such as the capability to develop and deploy the reprocessing technology at an
acceptable cost or the desire to improve the waste management characteristics of the spent USFR
fuel.
3.7 Fissile Material Ratios
To characterize the creation or destruction of fissile material in the core as a function of burnup,
several fissile material ratios were identified and employed to provide additional insight into the
behavior of the core's reactivity as a function of bumup. Fissile material ratios consider a
particular element or set of elements and their fissile isotopes, and compare the amount present at
a particular bumup step to the initial quantity of the material present at the beginning of the
cycle. For the present analysis, three fissile material ratios were chosen to describe the core: the
fissile uranium ratio (FUR), which compares the quantity of U-233 and U-235, the fissile
plutonium ratio (FPR), which considers the quantity of Pu-239 and Pu-241, and the fissile
inventory ratio (FIR), which considers the sum of the fissile isotopes of these two elements. The
masses of these fissile isotopes are then weighted by their respective reactivity worths, as
calculated by the ERANOS code. Though typically these ratios are not weighted with the
reactivity worths of the fissile materials, it was decided that since this information was available
39
it should be used to provide a more complete picture of the gain or loss of reactivity due to fissile
isotope breeding (or burning). Ultimately, the unweighted values differed from the weighted
values by only 2-3%. The formulations of these expressions are shown in Equations 4-6 below.
Reactivity-Weighted Fissile Uranium Ratio (FUR)
Weighted mass of fissile uranium
(235
U
* W23s
+
2 33
U
*
W 233 ) at a given timestep
Initial reactivity-weighted mass of fissile uranium
(4)
Reactivity-Weighted Fissile Plutonium Ratio (FPR)
Weighted mass of fissile plutonium ( 239 Pu
*
W 239 and
24 1
Pu
* W241)
at a given timestep
Initial reactivity-weighted mass of fissile plutonium
(5)
Reactivity-Weighted Fissile Inventory Ratio (FIR)
Mass of fissile uranium and plutonium weighted by reactivity worth at a given timestep
Initial reactivity-weighted mass of fissile uranium and plutonium
(6)
These fissile material ratios were calculated as a function of burnup for the carbide cores
discussed in the preceding sections. Figure 15 shows the fissile ratios as a function of burnup for
the nominal multicore carbide transition core.
1.2
1
(a
0
M.
0.8
(U
Reactivity Limit
@ 176 MWd/kgHM
0.6
-+-#FIR
0.4
- -FPR
-r-*FUR
0.2
0
0
50
100
200
150
250
300
350
400
Average Discharge Efurnup (MWd/kgHM)
Figure 15. Fissile material ratios as a function of burnup for the transition multicore carbide core
For the transition multicore carbide core, the fissile inventory ratio is always less than 1,
meaning that the reactor is in a fissile-burning mode throughout the cycle. This is reflected in
the linearly decreasing reactivity as a function of burnup (recall Figure 7). However, note that
40
while the uranium is burned, plutonium is bred up until approximately 100 MWd/kgHM, at
which point there is a net burning of fissile plutonium. The fissile plutonium ratio peaks at 1.14
at 108 MWd/kgHM and equals approximately 1.13 when the core reaches its fluence-limited
burnup at 136 MWd/kgHM, such that when the fuel is removed and recycled again using the
multicore strategy (preserving weight percents), the reactivity of the reload core has improved
because the weight percent of fissile plutonium has increased. The fissile inventory ratio at the
fluence-limited burnup is 0.93, decreasing to 0.9 at the reactivity-limited burnup of 176
MWd/kgHM.
1.4
0
S12
EFluence Limit
@118 MWd/kgHM
0.8
Reactivity Limit
@ 138 MWd/kgHM
4)
0.6
g
) 0.4
LL
-+-
FIR
--
FPR
-*--FUR
0.2
0
0
50
100
150
200
250
300
350
400
Average Discharge Burnup (MWd/kgHM)
Figure 16. Fissile material ratios as a function of burnup for the transition uranium+ carbide core
Unlike the carbide core transitioned using the multicore strategy, the carbide core transitioned
using the uranium+ strategy serves as a net breeder of fissile material up until its fluence-limited
burnup is reached. The fissile inventory ratio remains above 1 until approximately 170
MWd/kgHM, which is after both the fluence-limited burnup is reached (at 118 MWd/kgHM) and
the reactivity-limited burnup is reached (at 138 MWd/kgHM). This is primarily due to the
enhanced plutonium breeding present in the system, which rises up to 1.29 at 108 MWd/kgHM
and remains so until the fluence-limited burnup is reached. The fissile inventory ratio rises to
approximately 1.06 at 65 MWd/kgHM before decreasing to 1.04 at the fluence-limited burnup.
This accounts for the slightly enhanced reactivity of the reload uranium+ carbide core relative to
the transition core as discussed in Section 3.3.3.2.
41
3.8 Nonproliferation Materials Attractiveness
The composition of spent fuel generated by the USFR and the TRU-SFR was analyzed to
evaluate its attractiveness from the standpoint of potential proliferation for use in nuclear
weapons. The evaluation, proposed by Saito and Artisyuk, compares the fissile attractiveness of
a plutonium vector to the technical difficulties in constructing a weapon using that plutonium
vector, as described in Equation 7.
ao
Attractiveness =
(7)
DH a
SN
23 8
SN2
DH
a is the a-rossi function, defined by Saito as the ratio of the supercriticality (the amount of
reactivity above kinf=1) of the material in an infinite system to that material's prompt neutron
lifetime. DH is the decay heat and SN is the spontaneous fission neutron generation rate. The
attractiveness increases as the reactivity of the material increases, and decreases as the decay
heat increases and the number of spontaneous fission neutrons increases. The attractiveness is
plotted vs. the percent of plutonium that is Pu-238 and Pu-240, with various bands describing the
regions considered "weapons grade," "weapons usable," and "practically unusable."
The proliferation attractiveness of the plutonium generated by the multicore carbide core (with
melt and recast) through its various cycles (transition and equilibrium) was analyzed, and the
results are displayed in Figure 17.
2
102
....
...
...
.....
..
..
..........
..
..........
............
............
..
Un6i.061e...
10
......
...
.......
....
..
...
...
..............
..
...
------...........
......
.....
.. ..
. ..
..........
... ..
....
....
..
....
. ...
...
....
00
. ..........
.
.. . ... .
100
.....
.
. ..... .
....
....
... ..
.....
... . .... ...
.. ........
...................
.
................
W
*......
Grad4,
..
..
.......
...........
.....
..
...............
.... ..
.. . .... . .... ....
10
10 -
10-1
10
%Pu240
10
102
Figure 17. Proliferation materials attractiveness of the multicore carbide TRU-SFR cores of various reloads (diamonds),
and the reference LWR attractiveness (triangle)
42
The fuel transitioned into the TRU-SFR from the USFR is centrally located in the "weapons
usable" region of the attractiveness plot, yet still far from "weapon grade," with a Pu-238 fraction
of 0.90% and a Pu-240 fraction of 14.05%. After the first cycle in the TRU-SFR, the fuel's
plutonium vector moves toward the "practically unusable" region of the attractiveness diagram,
containing 2.20% Pu-238 and 24.61% Pu-240. After the first reloaded TRU-SFR cycle, the
equilibrium concentration is reached, with 2.81% Pu-238 and 29.73% Pu-240, placing the
plutonium vector just into the "practically unusable" region of the attractiveness diagram. The
reference LWR spent fuel contains 2.4% Pu-238 and 24% Pu-241, which makes it "weapons
usable." Thus, recycling the USFR fuel in the TRU-SFR serves an important nonproliferation
function, significantly reducing the plutonium's attractiveness to potential proliferators.
2
10.....,.
...............................
--..
...
- ....
--.
10
....
0~
10
10
10
10
%Pu240
10
10
Figure 18. Proliferation materials attractiveness of the uranium+ carbide TRU-SFR cores of various reloads
The materials attractiveness ofthe carbide cores transitioned using the uranium+ strategy was
also evaluated. These cores began with the same plutonium vector as the multicore cores, using
the same spent fuel from the USFR. The plutonium vector of the spent fuel discharged by the
transition cycle of the TRU-SFR contains 1.99% Pu-238 and 23.80% Pu-240. This is slightly
more attractive than the spent transition fuel generated by the multicore carbide case, primarily
because the multicore core reaches a higher average discharge bumup than the uranium+ core
(136 MWd/kgHM vs. 118 MWd/kgHM), so more Pu-240 is created via neutron capture of Pu239 and more Pu-238 is created primarily via alpha decay of Cm-242, which is itself created via
neutron capture and successive beta decay of Am-241. The composition of the spent fuel from
the equilibrium case has a plutonium vector with 2.33% Pu-238 and 28.60% Pu-240, placing it
just shy of the "practically unusable" region. However, the spent fuel from the equilibrium
TRU-SFR cycle is much less attractive from a proliferation perspective than that from the USFR,
encouraging a transition to the recycle mode if nonproliferation is a priority.
43
3.9 Safety Characteristics
3.9.1 Sodium Void Coefficient
A key characteristic of the dynamic response of a fast spectrum reactor core is the sodium void
coefficient of reactivity. This parameter describes the neutronic response to changes in the
density of the sodium coolant, often encountered in accident or overpower scenarios. This
coefficient is given in two forms, either as a percent of change in reactivity per percent of void
change, given in $/% void, or as an absolute reactivity worth of maximum coolant void, given in
$. Both forms of the sodium void worth were evaluated for the carbide cores, and the results for
the multicore melt-and-recast carbide core for its various cycles are shown in Table 8.
Table 8. Sodium void coefficients of reactivity for the transition and equilibrium multicore carbide cores
Transition Transition Equilibrium Equilibrium
Sodium void worth
BOC
0.0241
EOC
BOC
EOC
0.0235
0.0357
0.0304
1.6753
1.5608
2.8111
2.1848
($/%void)
Maximum void
worth ($)
1
The sodium void worth for the transition core is slightly positive at all points in the cycle, though
it begins at 0.0241 $/% void and decreases to 0.0235 $/% void at the end of the cycle. The
maximum void worth (with the sodium completely voided) is $1.67 at BOC, decreasing to $1.56
at EOC. Sodium void worths are slightly greater for the equilibrium core, beginning at 0.0357
$/% void and decreasing to 0.0304 $/% void at EOC. Similarly, the maximum void worths are
also increased, beginning at $2.81 and decreasing to $2.18 at EOC. The sodium void worths are
larger for the equilibrium core in part because the equilibrium core obtains a greater percentage
of its fissions from plutonium than the transition core. The transition core has heavy metal with
3.09% U-235, whereas the equilibrium core has only 0.64% U-235. This decrease in fissile
uranium loading impacts peff, which decreases from 426 pcm for the transition core to 348 pcm
for the equilibrium core.
Table 9. Sodium void coefficients of reactivity for the transition and equilibrium uranium+ carbide cores
Transition Transition Equilibrium Equilibrium
EOC
BOC
EOC
BOC
Sodium void worth
($/%void)
Maximum void
worth ($)
0.0244
0.0240
0.0371
0.0287
1.6693
1.4736
2.8590
1.9375
_
The sodium void worths for the carbide core transitioned using the uranium+ strategy are similar
to those of the carbide cores transitioned using the multicore strategy. The transition core has a
44
sodium void coefficient of reactivity of 0.0244 $/% void at BOC, which decreases to 0.0240 $/%
void at EOC. The maximum void worths of the transition core begin at $1.67 at BOC,
decreasing to $1.47 at EOC. The equilibrium uranium+ core begins with a sodium void
coefficient of 0.0371 $/% void, which decreases to 0.0287 $/% void at EOC. The equilibrium
core's maximum void worths are $2.86 at BOC and $1.94 at EOC.
Both carbide cores have sodium void worths significantly smaller (roughly half) than those of
other commercial-sized fast reactor designs. The oxide core of France's Super-Phenix I had a
maximum sodium void worth of $5.9, and the oxide core of the UK's CDFR had a maximum
void worth of $5.7. The oxide-fueled EFR had a maximum coolant void worth of $6.4. With a
maximum void worth of $1.67 for the transition cycle and $2.86 for the equilibrium cycle, the
TRU-SFR is well within standard practice for sodium void worth, with the choice of recycling
strategy (uranium+ or multicore) having little meaningful impact.
3.9.2 Shutdown Margin
Another important safety characteristic of the core is shutdown margin, which describes how
subcritical the system can be made using reactivity control methods. Shutdown margin ensures
that the nuclear chain reaction can be stopped so the reactor can be placed into a cold shutdown
condition, either for planned maintenance or refueling outages or in case of an accident. The
shutdown margin must also account for the reactivity gained as the fuel temperature decreases to
the cold condition, ensuring subcriticality for all conditions.
An important aspect of the criticality control of the core is the reactivity worth per control rod. If
the rod worth is too high, the system can be negatively impacted by a single failure.
Additionally, if the rod worth is large then the local flux shape experiences large fluctuations
with rod movement, which negatively impacts the cladding integrity. To provide an idea of the
acceptable range of rod worths, data for several commercial SFR designs is displayed in Table
10.
Table 10. Control rod reactivity worths for several commercial sodium fast reactor designs
Reactor
Nominal Full Electric
Power (Mwe)
Total Driver Fuel
Assemblies
# of Regulating
Rods
Regulating Rod
Worth (%Ak/k)
# of Shutdown
Rods
Super Phenix-1
BN-800
CDFR
SNR 2
ALMR
1242
870
1500
1497
303
364
409
349
414
92
21
16
18
25
9
0.40
0.42
0.278
0.34
0.76
3
12
12
0
3
Shutdown Rod
Worth (%Ak/k)
0.5
0.34
0.33
-
N/A
Fuel Assemblies/Control
Rod
15.17
14.61
11.63
16.56
7.67
The nominal USFR core has 19 control assembly positions. Each hexagonal assembly consists
of B 4C rods in a triangular lattice. The boron in the B 4 C is enriched to 60% B-10. This nominal
arrangement was kept in the transition to the recycle mode to facilitate low-cost, straightforward
implementation.
45
The shutdown margin and rod worths of the multicore carbide core for the equilibrium cycle
were evaluated, as the equilibrium cycle was found to have greater reactivity than the transition
cycle (recall Section 3.3.2.3). The results are shown in Figure 19.
20000
15000
-4--ARO
-r-ARI, Cool
10000
E
5000
01
50
100
200
150
300
350
400
-5000
-10000
-15000
-20000
-
BOC Shutdown Margin:+6979 pcm (+7371 w/o max rod)
ARho of -7453 pcm
Average rod worth:$1.13/rod (0.392% Ak/k)
-25000
Average Discharge Burnup (MWd/kgHM)
Figure 19. Shutdown margin of the equilibrium carbide multicore core
It is clear from Figure 19 that the standard configuration of control assemblies is not sufficient
for providing shutdown capability with some margin. With all rods in and the core at a cold
shutdown temperature of 200 C, the reactivity of the core drops 7453 pcm from 14432 pcm to
6979 pcm, which is still substantially supercritical. With the maximum-worth rod failed in an
ex-core position, the core's reactivity is supercritical by 7371 pcm. With 3-batch staggered batch
refueling similar to many LWRs, this initial reactivity could be halved to 7,216 pcm, but this
would still make the shutdown margin a slim -155 pcm. The average rod worth of 0.392% Ak/k
per rod is similar to that of the Super-Phenix I (0.40% Ak/k) and the BN-800 (0.42% Ak/k).
However, this is moot if it is not enough to drive the core subcritical. Thus, significant changes
to the control materials of the core and/or complex multi-batch fueling strategies must be
implemented if the multicore transition strategy were to be implemented.
46
10000
--5000
-g-h-+/-ARI,
ARO
Cool
0
E
0.
4..
100
50
250
150
300
35 0
400
-5000
-10000
-15000
-20000
BOC Shutdown Margin: -3913 pcm (-3466 pcm w/o max rod)
ARho of -8502 pcm
Average rod worth: $1.23/rod (0.447%Ak/k)
-30000
Average Discharge Burnup (MWd/kgHM)
Figure 20. Shutdown margin of the equilibrium carbide uranium+ core
The equilibrium carbide core transitioned using the uranium+ strategy can successfully be driven
subcritical with margin using the standard control configuration of the once-through USFR. The
shutdown margin with all rods inserted at a cold condition is -3913 pcm, which increases to 3466 pcm with the highest-worth rod removed, for a total change in reactivity from full power of
-8502 pcm. This makes the average rod worth 0.447% Ak/k, similar to that of Super-Phenix I
(0.40% Ak/k) and BN-800 (0.42% Ak/k). Thus, the uranium+ strategy is preferable to the
multicore strategy if minimal core control changes are desired.
3.10 Summary
The flux and reactivity performance of the carbide cores were characterized. Cores transitioned
from the USFR using both the multicore strategy and the uranium+ strategy were analyzed. The
multicore strategy preserved weight percents in the transition, while the uranium+ strategy
preserved masses, supplementing mass defects with natural uranium. The multicore strategy
resulted in a core with 8.01% fissile plutonium, while the uranium-+ strategy resulted in a core
with 6.92% fissile plutonium. The increased fissile loading of the multicore core resulted in a
peak fast flux at BOC of 3.87E+15 n/s/cm^2, 17% less than the peak fast flux at BOC of the
uranium+ core, which was 4.52E+15 n/s/cm^2. The power profiles of both cores began centerpeaked and flattened with burnup.
The transition multicore carbide core reached a fluence-limited burnup of 136 MWd/kgHM, with
an initial reactivity of 8441 pcm and a reactivity-limited burnup of 176 MWd/kgHM. This
fluence-limited burnup results in a levelized fuel cost of 6.41 mills/kWh, 8.4% less than the 7.00
47
mills/kWh levelized fuel cost of the LWR. The reactivity of the core increases after the first
reload (again using the multicore strategy), resulting in an initial reactivity of 14430 pcm, a
fluence-limited burnup of 149 MWd/kgHM, and a reactivity-limited burnup of 217 MWd/kgHM.
This reload case obtained a levelized fuel cost of 5.98 mills/kWh, 14.6% less than then reference
LWR cost. However, the multicore core experienced significant difficulties with reactivity
control due to its high initial reactivity. Inserting the 19 control assemblies (with B4 C enriched
to 60% 10B) decreased the initial reactivity to +6979 pcm (+7371 with the highest-worth rod
stuck out), meaning that the core was not able to go subcritical with the nominal configuration of
Significant design changes to the control system would need to be
control materials.
implemented to control the reactivity of this multicore carbide core, possibly including adding
additional control assemblies or reducing the amount of reflector material surrounding the core.
Another option would be to implement 3-batch staggered refueling. Both of these options will
make the transition from the once-through to the recycle mode more costly and complex, making
alternative transition strategies (such as uranium+) more desirable.
The transition uranium+ carbide core began with an initial reactivity of 1133 pcm and reached a
fluence-limited burnup of 124 MWd/kgHM, with a reactivity-limited burnup of 138
MWd/kgHM. This fluence-limited burnup was good for a levelized fuel cost of 7.17 mills/kWh,
only 2.4% more than the reference LWR LFC. The first reload of the TRU-SFR core achieved a
fluence-limited burnup of 124 MWd/kgHM, with an initial reactivity of 4590 pcm and a
reactivity-limited burnup of 173 MWd/kgHM. The reload core's burnup results in a LFC of 6.89
mills/kWh. The initial reactivity of the reloaded uranium+ carbide core can be controlled with
the nominal control assembly configuration from the once-through mode. With all rods inserted,
the initial reactivity of the core drops to -3910 pcm, or -3470 pcm without the highest-worth rod.
The average rod worth is 0.447% Ak/k, which is similar to that of the oxide-fueled Super-Phenix
I (0.40% Ak/k) and the oxide-fueled BN-800 (0.42% Ak/k). The maximum sodium void worth
of the multicore case is $2.81, and the maximum void worth of the uranium+ case is $2.86. Both
of these values are approximately half of the values for similar ceramic-fuel cores.
Removing minor actinides from the USFR fuel for recycle into the TRU-SFR carbide cores had
only a slight effect on their reactivity. The multicore transition core's initial reactivity increased
by 352 pcm (4.2%), but the fluence-limited burnup actually decreased by 0.2%. Likewise, for
the transition uranium+ carbide core, the initial reactivity increased by only 203 pcm, while the
fluence-limited burnup decreased by 0.1%.
Cooling the fuel (i.e. long term storage) before making the transition from the USFR to the TRUSFR also had a small impact on achievable burnup. The effects of cooling were approximated
by assuming all the Pu-241 had decayed into Am-24 1. For the multicore transition core, the
cooled fuel experienced a drop in reactivity of 803 pcm, which decreased the fluence-limited
burnup by 1.29%. The reloaded multicore core experienced a drop in reactivity of -2990 pcm,
which resulted in a fluence-limited burnup 4.63% less than the freshly reloaded fuel. For the
uranium+ transition core, the initial reactivity decreased by 867 pcm resulting in a 1.6% lower
48
fluence-limited burnup. The reloaded uranium+ carbide core lost 2270 pcm using cooled fuel,
which decreased the fluence-limited burnup by 3.76%. In both cases, however, the reactivity lost
due to fuel cooling is substantially less than the -7800 pcm reactivity loss with long-term cooling
for plutonium recycle in LWRs. (Arnold, 2011)
49
4 Metal Core Analysis
4.1 Introduction
While the carbide cores exhibit high fluence-limited burnups, economic fuel cycle costs,
proliferation resistance, and safe dynamic response, many fabrication and operational issues
associated with using a carbide fuel form remain unresolved. Additionally, the process used to
recycle the carbide fuel is unspecified, whether it should be through some form of aqueous
reprocessing or through alternate methods. (Plaue & Czerwinski, 2003)
Conversely, the United States has had extensive experience designing and operating sodiumcooled fast spectrum reactors using metallic fuel forms, including uranium metal, uraniumplutonium metal, and most recently uranium-plutonium-zirconium alloy.
Additionally,
reprocessing techniques to recycle fuel in these forms were developed and refined, resulting in
the pyrometallurgical process (pyroprocess) for recycling of metallic fuel. This experience in
both fuel design, in-core operation, and reprocessing makes metallic fuel desirable for a fast
spectrum reactor in recycle mode.
As with the carbide cores, the reactivity of the metal cores must be evaluated as a function of
burnup, and the resulting fluence-limited and reactivity-limited burnups must be identified. Both
the transition and equilibrium core reactivity profiles must be characterized. Additionally, the
effects of cooling time, the impact of removing minor actinides, and the safety characteristics of
the cores should be investigated. The fuel costs of the cores will be determined, and appropriate
strategies for improving the economics by increasing the achievable burnups will be evaluated.
The attractiveness of the TRU-SFR's spent fuel for potential proliferation will be characterized.
Ultimately, the most effective strategies for transitioning and operating metal cores in recycle
mode will be identified.
4.2 Radial Power Distribution
The radial flux profile of the metal cores transitioned using both the multicore and the uranium+
strategies were evaluated. The results for the multicore case are presented in Figure 21.
50
5E+15
S4E+15
--
O
E 3.5E+15
3E+15
2
--
MOO
E.
EOC
-aw ----
2E+15
+
1.5E+15
U
1E+15
5E+14
0
50
100
150
200
250
Radius (cm)
Figure 21. Radial flux profile for the metal multicore core
The peak fast flux for the metal transition multicore case at beginning of cycle (BOC) is
4.39E+15 n/s/cm^2, occurring at 23 cm from the core's centerline. The peak flattens and moves
outward with burnup, decreasing to 4.04E+15 n/s/cm^2 at 26.6 cm from centerline at the middleof-cycle (MOC) and to 3.76E+15 n/s/cm^2 at 28.42 at end-of-cycle (EOC). This peak fast flux
at BOC is 13% greater than the carbide multicore case, despite the greater fissile loading of the
metal core relative to the carbide core (see Section 4.3.2 for more detail). This is due to the
harder spectrum of the metallic fuel, which slows down neutrons less effectively than the carbide
core because the carbon in the carbide core is a low-A material, making it a more effective
neutron moderator.
51
6E+15
5E+15
-<BOC
E 4E+15
-----
-
3E+15
MOC
EOC
M 2E+15
UL
1E+15
0
0
50
100
150
200
250
Radius (cm)
Figure 22. Radial flux profile for the metal uranium+ core
The peak fast flux for the uranium+ transition metal core at BOC is 5.24E+15 n/s/cm^2 at a
radial position 23 cm from the centerline. This is 19.5% greater than the multicore metal core,
due to the decreased fissile loading of the uranium+ case relative to the multicore case (see
Section 4.3.3.1 for more details). It is also 16% greater than the carbide uranium+ case, due to
the metal fuel's harder spectrum. The peak fast flux decreases to 4.84E+15 n/s/cmA2 at a radial
position of 28.42 at MOC, and to 4.48E+15 n/s/cmA2 at a radial position of 28.42 at EOC. The
core at EOC attains a relatively flat profile out to ~100 cm from the centerline, where it begins to
decrease until reaching the edge of the core.
4.3 Transition Strategy
4.3.1 Overview
As with the carbide cores, two strategies were employed in determining the composition of
recycled fuel in metal form to transition to the TRU-SFR. The multicore strategy maintained the
weight percents of the heavy metals in the transition, and the uranium+ strategy maintained the
masses of the heavy metals, supplementing them with natural uranium to account for mass lost to
burnup or any differences in core mass between the nominal carbide once-through configuration
and the metal recycle mode configuration. The compositions these transition strategies created
are discussed in detail in the following sections.
52
4.3.2 Multicore
4.3.2.1 Fuel Composition
Since the multicore strategy seeks to preserve the fuel (actinide) composition generated by the
once-through USFR, the actinide vector is the same as shown in Table 4. However, due to the
change in the heavy metal volume fraction (90% for the metal fuel, and 95.2% for the carbide
fuel) and the fuel density (16.14 g/cc for the metal, 13.63 g/cc for the carbide), the heavy metal
mass loading increases from 42,540 kg to 47,620 kg. This increases the amount of once-through
carbide fuel (the nominal fuel form of the USFR) needed to fuel the TRU-SFR, requiring 1.19
spent assemblies to make 1 new, metal U-Pu assembly.
4.3.2.2 Reactivity Profile and Burnup Performance
The reference metal core used with the multicore transition strategy has a nominal volume
fraction of 40% (consistent with the once-through carbide core). The reactivity during the cycle
is shown in Figure 23.
20000
t
--
15000
Fluence Limit: 115 MWd/kgHM
E
10000
0.
cL
Reactivity Limit: 247 MWd/kgH M
5000
0
50
100
150
200
250
300
350
-5000
-10000
-
Average Discharge Burnup (MWd/kgHM)
Figure 23. Reactivity vs. burnup for the reference metal recycle core using the multicore transition strategy
The metal multicore transition strategy is characterized by a near-linearly decreasing reactivity
curve, with a large initial excess reactivity of 15478 pcm. The large initial reactivity and the
shallow slope (-66 pcm/(MWd/kg)) help the core to reach an exceptionally high reactivitylimited burnup of 247 MWd/kgHM. However, this is deceptive-the cladding damage due to
neutron fluence (measured here in displacements per atom, or dpa) must also be considered, to
53
ensure the cladding maintains its structural integrity with margin during operation. The
reference limit for the steel HT-9 cladding employed is 200 dpa. The multicore metal reference
core reaches this 200 dpa limit at a burnup of 115 MWd/kgHM, which is 48% of the reactivitylimited burnup.
The plutonium-uranium metal fuel discharged from this transition cycle was then reprocessed
and reloaded in the TRU-SFR, again using the multicore strategy to preserve the composition of
the spent fuel. The composition of the reloaded fuel is shown in Table 11.
Table 11. Composition of fuel reloaded into the metal TRU-SFR core using the multicore strategy with no cooling
Isotope
U-235
U-236
U-238
Pu-238
Pu-239
Pu-240
Pu-241
Pu-242
Np-237
Am-241
Am-242
Am-243
Cm-242
Cm-244
Cm-245
HM Weight %
0.98%
2.17%
83.80%
0.23%
9.43%
2.57%
0.26%
0.0480%
0.45%
0.031972%
0.001337%
0.004842%
0.002191%
0.001441%
0.000157%
The fissile plutonium loading (9.7% of heavy metal) of the reload core differs by 1.7% percent
from the transition core (8.0% of HM). The fissile uranium loading (0.98% of HM) is
approximately 2% less than in the transition case (2.77% of HM).
Table 12. Plutonium vector for the reloaded TRU-SFR metal core using the multicore strategy
Isotope
Pu-238
Pu-239
Pu-240
Pu-241
Pu-242
% of Total Pu
1.80%
75.23%
20.50%
2.09%
0.38%
54
The quality (percent of fissile) of the plutonium vector decreased for the reloaded fuel relative to
the transition fuel. The fissile plutonium fraction decreased from 84.95% to 77.32% of total
plutonium. However, more total fissile plutonium is present in the reload fuel, such that the
reactivity of the reload core is greater than the transition core, as shown in Figure 24.
20000
15000
-
Transition Fluence Limit: 115 MWd/kgHM
Reload 1 Fluence Limit: 119 MWd/kgHM
Percent Change from Previous: 3%
10000
Transition Reactivity Limit: 247 MWd/kgHM
--
Reload 1 Reactivity Limit: 253 MWd/kgHM
Percent Change from Previous: 2.6%
0.
.1
5000
0
-~
0
50
-5000
-
100
150
200
250
300
350
-u-Transition
-+-Reload 1
-10000
Average Discharge Burnup (MWd/kgHM)
Figure 24. Reactivity vs. burnup for the reloaded Pu-U metal fuel using the multicore strategy
The reactivity-limited burnup of the reloaded core (253 MWd/kgHM) is 2.6% more than for the
transition core (247 MWd/kgHM). Only a small increase is expected, given the small changes in
fuel heavy metal composition from the transition core to the reload core. The fluence-limited
burnup also increases slightly, up 3% from 115 MWd/kgHM to 119 MWd/kgHM. However, the
increase in fluence- and reactivity-limited burnup comes at the cost of increasing the initial
reactivity by 2190 pcm (15%), from 15,478 pcm to 17668 pcm. Greater initial reactivity leads to
control issues, as discussed in detail in Section 4.9.
4.3.3 Uranium+
4.3.3.1 Fuel Composition
Due to the mass differential between the reference once-though carbide core and the recycled
metal core, the fuel composition using the uranium+ recycle strategy with the metal core has a
much reduced plutonium fraction as compared to the recycled carbide core. This is displayed in
Table 13.
55
Table 13. Composition of reprocessed USFR fuel loaded into the metal TRU-SFR core using the uranium+ strategy with
no cooling
Isotope
U-235
U-236
U-238
Pu-238
Pu-239
Pu-240
Pu-241
Pu-242
Np-237
Am-241
Am-242
Am-243
Cm-242
Cm-244
Cm-245
HM Weight %
2.55%
1.47%
88.47%
0.07%
6.10%
1.02%
0.08%
0.0068%
0.20%
0.003698%
0.000104%
0.000398%
0.000281%
0.000066%
0.000004%
As compared to the carbide uranium+ transition core, the metal uranium+ transition core has a
11% lower fissile plutonium heavy metal fraction (6.92% of HM vs. 6.18% of HM). Using the
uranium+ strategy, only natural uranium is used to supplement the mass defect between the
once-through core at end-of-cycle and the recycled core. The mass defect is larger for the carbide
to metal transition (7716 kgHM) compared to the carbide-to-carbide transition (2636 kgHM,
which is the mass lost to burnup), so the fissile plutonium heavy metal fraction decreases. The
heavy metal fractions of all non-uranium nuclides also decrease. Note that the plutonium vector
for this transition core remains unchanged from that in Table 5.
4.3.3.2 Reactivity Profile and Burnup Performance
Since the uranium+ metal core has the lowest fissile plutonium enrichment (6.18% of heavy
metal), its fluence-limited bumup suffers accordingly. However, because it breeds plutonium at
a greater rate than the other cores, its reactivity-limited burnup remains high (see Section 4.7 for
a more detailed description of the breeding in the uranium+ metal core). The reactivity vs.
burnup curve for the uranium+ metal core is shown in Figure 25.
56
8000
"
"
6000
"'1
4000
00.
Reactivity Limit: 212 MWd/kgHM
-
2000--
3
50
100
150
200
-
250
300
350
-2000
-4000
-6000
-8000
Average Discharge Burnup (MWd/kgHM)
Figure 25. Reactivity vs. burnup for the transition Pu-U metal core using the uranium+ strategy
The reactivity curve takes a parabolic form, due to the enhanced breeding present with the
reduced fissile/fertile ratio. The reactivity-limited burnup occurs at 212 MWd/kgHM, 54%
greater than for the carbide uranium+ core. However, the fluence-limited burnup occurs at 90
MWd/kgHM, which is 24% less than the carbide core's 118 MWd/kgHM. This marked decrease
in fluence-limited bumup is driven by the higher fast flux in the fuel, which arises due to the
lower fissile fraction and the harder spectrum. The reactivity-limited burnup is reduced by 21%
relative to the multicore case, entirely due to the reduced fissile fraction.
The spent fuel discharged from this transition case was then recycled and reloaded into the TRUSFR using the uranium+ strategy. Since the fissile inventory ratio of this transition cycle is above
1, the discharged spent fuel had a greater fissile heavy metal fraction, as shown in Table 14.
57
Table 14. Composition of reprocessed TRU-SFR fuel reloaded into the metal TRU-SFR core using the uranium+ strategy
with no cooling
Isotope
U-235
U-236
U-238
Pu-238
Pu-239
Pu-240
Pu-241
Pu-242
Np-237
Am-241
Am-242
Am-243
Cm-242
Cm-244
Cm-245
HM Weight %
0.73%
1.47%
87.08%
0.16%
7.94%
2.00%
0.20%
0.0366%
0.32%
0.019486%
0.000836%
0.003737%
0.001620%
0.001155%
0.000129%
The weight fraction of fissile material in the reloaded fuel increases approximately 2% from the
transition core. However, the plutonium quality decreases, with a 7.1% drop in fissile plutonium
fraction, as shown in Table 15.
Table 15. Plutonium vector for the reloaded metal core using the uranium+ strategy
Isotope
Pu-238
Pu-239
Pu-240
Pu-241
Pu-242
% of Total Pu
1.58%
76.72%
19.37%
1.98%
0.35%
58
10000
Transition Fluence Limit: 90 MWd/kgHM
Reload 1 Fluence Limit: 98 MWd/kgHM
Percent Change from Previous: 9%
8000
6000
E
-Transition
Reactivity Limit: 212 MWd/kgHM
Reload 1 Reactivity Limit: 227 MWd/kgHM
Percent Change from Previous: 7%
4000
2000S
-
0
50
100
150
200
50
300
350
-2000
-4000
-+-Transition
-*-Reload 1
-6000
-8000
Average Discharge Burnup (MWd/kgHM)
Figure 26. Reactivity vs. burnup for the reloaded Pu-U metal fuel using the uranium+ strategy
The 2% increase in fissile plutonium loading is reflected by increases in both the reactivity- and
fluence-limited burnups. The reloaded core's reactivity-limited bumup increased 7% from 212
MWd/kgHM to 227 MWd/kgHM, and the fluence-limited burnup increased 9% from 90
MWd/kgHM to 98 MWd/kgHM. However, the increase in the fissile plutonium fraction has the
detrimental effect of increasing the initial reactivity by the significant amount of 5490 pcm,
which leads to issues in reactivity control and safety performance during transients.
Additionally, as the fissile loading increases, the breeding decreases, such that the parabolic
shape encountered for the transition core begins to approach the linearly decreasing shape of the
multicore strategy.
4.3.4 Burnup Limit Improvement Strategies
Using metallic fuel, achievable bumups were found to be limited by the cladding damage (dpa),
rather than a lack of reactivity. The magnitude of the disparity between the fluence-limited and
reactivity-limited bumups for the metallic fuel stands in contrast to that of the carbide fuel.
Where the metallic fuel had fluence-reactivity burnup limit disparities of 134 MWd/kgHM (for
the multicore strategy) and 129 MWd/kgHM (for the uranium+ strategy) on the equilibrium
cycle, the carbide fuel had disparities of 68 MWd/kgHM (for the multicore strategy) and 49
MWd/kgHM (for the uranium+ strategy). Since it is desirable to maximize the bumup of the
fuel to minimize the levelized fuel cost, converging these two burnup limits is a priority for the
metal cores, whose fluence-limited burnups are 20% (multicore) and 21% (uranium+) lower than
for the carbide cores.
59
The determining factors for cladding dpa are fissile loading and spectrum hardness. With greater
fissile loadings, the flux required to reach a given power drops, as shown in Equation 8:
P=
K
*
ff
p(E, r)Efiss (E, r)dEdV
(8)
where K is the recoverable energy released per fission. As the flux drops, fewer lattice
displacements occur and the clad is damaged less. Thus, increasing the enrichment is one
method of reducing the cladding dpa.
Several problems arise with simply increasing the fissile loading to reduce the dpa. As will be
discussed in Section 4.9.2, increasing the enrichment leads to issues with reactivity control.
Additionally, it increases the number of feed assemblies required for reprocessing and
fabrication of a new product assembly, driving up costs. However, increasing the fissile loading
is not the only method of reducing the cladding dpa.
Embedded in the above equation is the dependence of the fission cross section on energy. The
cladding total cross section also depends on energy, and so the neutron energy spectrum present
in the reactor can have a significant impact on the cladding dpa. Beyond the probability of
interaction as described by the cross section's energy dependence, the neutron's energy also
affects the amount of damage inflicted per collision. Thus, reducing the average energy of the
neutrons in the reactor can help to alleviate damage issues.
But there is no free lunch when it comes to simply softening the spectrum. Fast reactors are
designed, after all, to run on more energetic neutrons than thermal reactors for a host of reasons,
and softening the spectrum can. be counterproductive for accomplishing these tasks. The
breeding ratio of fissile creation to fissile destruction decreases as the spectrum slows into the
epithermal region, where resonances severely decrease the actinide cross sections'
characteristically large fission to capture ratio present at high energies. Decreased breeding
significantly decreases the reactivity-limited burnup, essentially replicating the issue of a
reactivity/fluence burnup limit gap except that the reactivity becomes the deciding factor.
Additionally, the absorption cross sections of neutron poisons, such as xenon and samarium,
become significantly larger at lower energies, further hindering the core's reactivity.
Thus, it is important to strike a balance between a spectrum soft enough to keep dpa low so that
the fluence-limited burnup is acceptably high, and a spectrum hard enough to enable sufficient
breeding such that the reactivity-limited burnup is acceptably high. Ideally, in the present
situation, the fluence/reactivity limit gap would be closed via a softening of the spectrum such
that the fluence-limited burnup increases and the reactivity-limited burnup decreases until they
converge to the same value. Several strategies are presented which attempt to achieve this goal.
60
4.3.4.1 Addition of Moderating Materials
One possible method for slightly softening the spectrum is the addition of moderating materials
to the fuel assembly. One possible method of introducing these materials consists of sleeves
placed in the sodium bond gap between the fuel pin and the cladding, though this method
reduces the thermal conductivity of the pin leading to higher fuel temperatures. Other possible
methods include homogeneous mixing in the fuel pin itself, or introducing separate pins of the
material into each assembly. Whatever the method used to introduce these moderating materials,
they can serve to slow down neutrons based on their reasonably high scattering cross section.
4.3.4.1.1 Graphite
Graphite is an excellent moderating material, and is commonly used in thermal reactors such as
the Advanced Gas Reactor (AGR) in the United Kingdom to moderate neutrons to thermal
energies. When applied to a fast reactor, far less graphite would be employed than in a thermal
reactor to maintain an acceptably fast spectrum. However, reactor physics analysis must be
performed to determine what amount, if any, should be incorporated.
Carbon is a particularly effective moderator because it is a light element (A=12) with a high
scattering-to-absorption cross section ratio. The low-A increases the energy lost per collision, as
described by the average logarithmic energy decrement, 4. The high scattering-to-absorption
cross section ratio minimizes parasitic absorption as the neutrons are slowed down. The product
of 4 and the scattering-to-absorption ratio is called the moderating ratio, and is used to describe
the effectiveness of a material at slowing down neutrons; the greater the moderating ratio, the
more effective the moderator. (Rinard, 1991) Though this parameter is typically calculated as a
thermal-averaged single value, this approach has limited usefulness for characterizing its
performance in a fast spectrum reactor. Instead, the continuous energy scattering and capture
cross sections can be inspected visually to gain a qualitative sense of their relative disparity, and
their ratio can be plotted to give a quantitative description of their moderating effectiveness.
61
Incident neutron data I ENDFIB-Vil.0 I CNat II Cross section
0.1
0
a
h
ao0
incident energy (MeV)
Figure 27. Microscopic scattering and absorption cross sections of natural carbon, ENDF/B-VII data
Incident neutron data i ENDFB-Vl.O I CNat I MT=102:
(zg) radiative capture I Scattering-to-absorption ratio
10000000
1000000
r
C
100000-
W
C.
E
0
1E-10 1E-2
E-
IE-7
1E-
1E-5
1E4
0.,01
an1
0.1
I
10
100
Incident energy (MCV)
Figure 28. Scattering-to-absorption ratio of natural carbon, ENDF/B-VII data
As shown in Figure 27, carbon has a large disparity in its scattering and absorption cross sections
at thermal energies, and this disparity increases monotonically until about 1 MeV, upon which
the first scattering resonances are encountered. Figure 28 helps provide a quantitative
description of this disparity: the microscopic scattering cross section is roughly 500 times larger
than the capture cross section at thermal energies (-0.0025 eV). The ratio increases throughout
62
the epithermal spectrum, peaking at a scattering-to-absorption ratio of approximately 5 million
from 10 keV to 100 keV, and then decreasing to approximately 1 million at 1 MeV before
dropping sharply thereafter. From these visual inspections, it is expected that carbon is likely to
be a very effective moderating agent in the hard spectrum present in the uranium-plutonium
metal core.
ERANOS simulations were performed to evaluate the reactivity profile and burnup performance
of the graphite-added metal core TRU-SFR transitioned using the uranium+ strategy. Cases with
3% volume fraction, 5% volume fraction, and 7% volume fraction of graphite were modeled,
with the graphite replacing fuel volume in each case.
8000
->Reference Fluence Limit: 90 MWd/kgH M
3% Graphite Fluence Limit: 101 MWd/kgH M
Percent Change from Previous: 12.1%
6000
4000
2000-+*-Reference
E
-0-3% Graphite
CL 0
50
100
150
200
250
300
350
-6000
-2000
-4000
-6000
...........
-8000
-10000
-12000
Average Discharge Burnup (MWd/kgHM)
Figure 29. Reactivity vs. burnup for the Pu-U metal fuel using the uranium+ strategy with 3% vol. frac. of graphite
moderator
As was expected, graphite serves as an excellent moderator, softening the spectrum such that the
fluence-limited bumup increases 12%, from 90 MWd/kgHM to 101 MWd/kgHM. However, it
does so at significant cost to the initial reactivity of the system: the system is subcritical by 1600
pcm at BOC. However, if this initial reactivity deficit can be compensated for and the system is
allowed to breed with burnup, the ultimate reactivity-limited burnup could be as high as 150
MWd/kgHM. However, this would mean that the achievable burnup is still significantly
fluence-limited, with a difference of 49 MWd/kgHM between the reactivity and the fluencelimited burnups. As shown in Figure 29, the addition of graphite essential serves only to
vertically shift the reactivity vs. burnup curve downward, which reduces the reactivity-limited
burnup by 30% to 150 MWd/kgHM (assuming the initial reactivity deficit could be overcome).
One possible method of overcoming the reactivity limitations at BOC includes the introduction
of staggered batch (multi-batch) refueling, which would have no effect on the fluence-limited
63
burnup but can compensate for reactivity deficits at BOC. However, since the fluence-limited
burnup increases by only 12%, the fuel cycle cost is still not likely to become more competitive.
10000
Reference Fluence Limit: 90 MWd/kgHM
5% Graphite Fluence Limit: 110 MWd/kgH M
Percent Change from Previous: 22.7%
5000
--E
0.
CL
Reference
-m-5% Graphite
050
-50
50
100
150
200
250
300
350
-5000
(U
-10000
-15000
Average Discharge Burnup (MWd/kgHM)
Figure 30. Reactivity vs. burnup for the Pu-U metal fuel using the uranium+ strategy with 5% vol. frac. of graphite
moderator
10000
5000
0
U
0.
350
-5000
U
(U
0
-10000
-15000
-20000
Average Discharge Burnup (MWd/kgHM)
Figure 31. Reactivity vs. burnup for the Pu-U metal fuel using the uranium+ strategy with 7% vol. frac. of graphite
moderator
As shown in Figure 30 and Figure 31, adding larger amounts of graphite (5% and 7% of the total
core volume fraction, respectively) softens the spectrum such that the reactivity of the core is
significantly subcritical. This renders the cores impractical for operation. Graphite appears to be
too effective as a moderating material, such that it slows enough neutrons into the resonance
64
region such that the product of nu (the average number of neutrons released in fission) and the
macroscopic fission cross section no longer exceeds the absorption cross section, driving kinf
below unity.
4.3.4.1.2 Silicon Carbide
Silicon carbide presents an interesting choice as a potential moderating material. Able to
withstand exceptionally high temperatures, it is a credible candidate for fast reactor service.
Since it contains carbon, it has similarly desirable moderating characteristics, but with a lower
carbon density. Silicon also has excellent moderating properties, though slightly less so than
carbon. Since the issue encountered when using graphite as the spectrum softening material
arose from carbon's over-moderation of neutrons, silicon carbide had promise as a potential
upgrade.
Incident neutron data I ENDFB-Vil.0 I Si28 11 Cross section
n
E
0
S
0
C)
Incident energy (MeV)
Figure 32. Microscopic scattering and absorption cross sections of Si-28, ENDF/B-VII data
65
Incident neutron data I ENDFB-Vil.0 I Si28 I MT=102:
(z,g) radiative capture I Scattering-to-capture ratio
10e000
-
-
1000_10
CL
tooE
0
to-
IE-10
1E.9
IE4
IE7
IE
1E-5
IE4
0.001
01
0.1
to
1
too
incident energy (MeV)
Figure 33. Scattering-to-absorption ratio of Si-28, ENDF/B-VII data
Silicon, similar to carbon, is a light material (A=28) and has a high scattering-to-capture cross
section ratio in the thermal and low epithermal region, increasing monotonically from
approximately 5 at 1 meV to nearly 10,000 at 10 keV. However, unlike carbon, silicon-28
(which comprises 92.2% of natural silicon) has significant resonances in both its scattering and
absorption cross sections beginning at approximately 20 keV, which causes significant
fluctuations (from 10,000 to less than 1) in the scattering-to-capture cross section ratio above this
energy. The complex resonance structure in the fast region of the spectrum makes the
moderating performance of SiC very difficult to predict, making direct simulation crucial for
evaluating the fluence reduction benefit. However, note that the scattering-to-capture ratio for
Si-28 remains below that of carbon at all energies, suggesting improved performance relative to
the graphite inserts.
66
8000
Reference Fluence Limit: 90 MWd/kgHM
SiC Fluence Limit: 97 MWd/kgHM
Percent Change from Previous: 7.7%
-3%
6000
4000RIeIf..e-rn.cIe
2000
--
-+-
Reference
---
3% SiC
.
50
o
100
250
150
300
350
-2000
-4000
-6000
-8000
-10000
Average Discharge Burnup (MWd/kgHM)
Figure 34. Reactivity vs. burnup for the Pu-U metal fuel using the uranium+ strategy with 3% vol. frac. of SiC moderator
Adding the equivalent of 3% volume fraction of SiC to the core successfully softened the
spectrum such that the fluence-limited burnup was increased, by 7.7% from 90 MWd/kgHM to
97 MWd/kgHM. The reactivity remained positive, beginning at 771 pcm and peaking at 3900
pcm at 60 MWd/kgHM. The core is still fluence-limited, as the reactivity-limited burnup occurs
at 181 MWd/kgHM, which is 84 MWd/kgHM greater than the fluence-limited burnup.
8000
Reference Fluence Limit: 90 MWd/kgH M
5% SiC Fl uence Limit: 102 MWd/kgH M
Percent Change from Previous: 13.7%
6000
4000
Reference
-.2000
ECL
2
5% Si C
0
-2000
9
50
100
150
200
250
300
350
-4000
-6000
-8000
-10000
-12000
Average Discharge Burnup (MWd/kgHM)
Figure 35. Reactivity vs. burnup for the Pu-U metal fuel using the uranium+ strategy with 5% vol. frac. of SiC moderator
The case with 5% volume fraction of SiC follows the trend established by the 3% vol. frac. case.
The reactivity vs. burnup curve is shifted vertically downward, reducing the reactivity
67
throughout the cycle while also reducing the fluence to the cladding. This causes a 13.7%
increase in the bumup achievable before reaching the 200 dpa cladding fluence limit, rising from
90 MWd/kgHM to 102 MWd/kgHM. However, the initial reactivity is slightly subcritical,
standing at -375 pcm. This can be rectified by slightly decreasing the amount of SiC added to
the system, reducing the SiC volume percent to less than 5%.
10000
Reference Fluence Limit: 90 MWd/kgHM
7% SiC Fluence Limit: 109 MWd/kgHM
Percent Change from Previous: 20.6%
5000
-+.-
Reference
-a-7% SiC
0
50
E.
200
100
250
300
350
-5000
N
-10000
-15000
Average Discharge Burnup (MWd/kgHM)
Figure 36. Reactivity vs. burnup for the Pu-U metal fuel using the uranium+ strategy with 7% vol. frac. of SiC moderator
As was expected, the case with 7% added SiC had too soft a spectrum, decreasing the initial
reactivity to -1330 pcm, far too subcritical for startup. However, it is interesting to note the
magnitude of the percent increase in the fluence-limited burnup seems to be consistent for
various increases in the amount of SiC added. Adding 3% SiC to the core increased the fluencelimited burnup by 7.7%, so the fluence-limited burnup increased 2.6% per percent increase in the
SiC content. Adding 5% SiC to the core increased the fluence-limited burnup by 14%, a 2.7%
burnup increase per percent SiC added. Adding 7% SiC to the core increased the fluence limited
burnup by 21%, resulting in a 2.9% bumup increase per percent SiC added. It seems that not
only is SiC effective at increasing burnup, but also that it becomes slightly more effective as
more is added.
4.3.4.1.3 Magnesium Oxide
Magnesium oxide has been utilized in the USFR as a high-albedo reflector to minimize leakage.
Thus, it holds promise as a moderating material for use in softening the core's spectrum. An
evaluation of the cross sections of magnesium and oxygen will provide insight into the potential
68
effectiveness of MgO. Since natural magnesium consists of 79.0% Mg-24 and natural oxygen
consists of 99.7% 0-16, these isotopes will be examined.
Incident neutron data I ENDFB-VII.0 I II Cross section
ICi
I10.1-
-0.01-
0
oI
M-4
1E-5
IE4
E-7-
IE-)
IE-I
IE-10
IE-9
1E-6
0-7
1ES
1E-5
IE-4
0001
0.01
10
0L
100
Incident energy (MeV)
Figure 37. Microscopic scattering and absorption cross sections of Mg-24 and 0-16, ENDF/B-VII data
Incident neutron data I ENDFIB-Vil.0 II MT=2 : (z,zO) elastic scattering I
IF$
016
ScaiCapture Ratio
018
Mg24 Mg24SeatfCaptureRate
--
1000000-
C
C
9
10000-
E
00
0
1E-10
I
1E-9
SEO
ON
IE7
E-
1E-5
IE-4
0,001
C0I
0.1
1
10
100
incident energy (MSV)
Figure 38. Scattering-to-absorption ratio of Mg-24 and 0-16, ENDF/B-VII data
Mg-24 and 0-16 share similar scattering cross sections, ranging from 5-50 barns in the thermal
region and remaining roughly 5 barns up until approximately 50 keV. Here, Mg-24 has a large,
narrow capture resonance, which drives down its scattering/capture microscopic cross section
ratio to 5. 0-16 experiences its first scattering resonances around 0.5 keV, and has no significant
69
capture resonances. Mg-24's scattering-to-capture cross section ratio ranges from 15 to 500 in
the thermal region, and fluctuates around an average value of 10,000 in the range of 0.1 to 12
MeV. This suggests its moderating performance will be similar to that of silicon, but slightly
improved because its resonances begin at higher energies. 0-16's scattering-to-capture cross
section ratio ranges from 5,000 to 100,000 in the thermal region and, due to the relatively
constant (in lethargy space) scattering cross section and the 1/v capture cross section, goes as 1/v
from 1E-8 MeV to 0.2 MeV, ranging from 5,000 to 1E8. The ratio then fluctuates around an
average value of 1E8 until 50 MeV. These cross sections suggest that MgO will be somewhat
similar to SiC in moderating effectiveness, though slightly less so, since Mg-24 has cross section
characteristics similar to Si-28 and 0-16 is slightly less effective a moderator than C-12.
8000
Reference Fluence Limit: 90 MWd/kgHM
MgO Fluence Limit: 96.5 MWd/kgHM
Percent Change from Previous: 7.2%
-3%
6000
4000
E
2000
-4-
Reference
---
3% MgO
0.
50
100
150
250
300
350
S-2000
S-4000
-6000
-8000
-10000
Average Discharge Burnup (MWd/kgHM)
Figure 39. Reactivity vs. burnup for the Pu-U metal fuel using the uranium+ strategy with 3% vol. frac. of MgO
moderator
As was expected, adding 3% MgO to the assembly had a similar fluence reduction to the SiC
additive, increasing the fluence-limited bumup by 7.2%, from 90 MWd/kgHM to 96.5
MWd/kgHM. This is 0.5% less than the 3% SiC case, making MgO a slightly less effective
spectrum softener than SiC. The initial reactivity of the core was reduced from 2920 to 436 pcm
with MgO, while the SiC was reduced to 771, a difference of 335 pcm. Thus, the MgO increased
the fluence-limited bumup less and reduced the reactivity of the core more than the SiC,
indicating that the SiC is desirable from a purely neutronic perspective.
70
8000
Reference Fluence Limit: 90 MWdI/kgH M
5% MgO Fluen ce Limit: 101 MWd/kgH M
Percent Change from Previous: 12.7%
6000
4000
E
-- Reference
2000
-. s-5%MgO
50
100
150
200
250
300
350
-2000
-4000
-6000
-8000
-10000
-12000
Average Discharge Burnup (MWd/kgHM)
Figure 40. Reactivity vs. burnup for the Pu-U metal fuel using the uranium+ strategy with 5% vol. frac. of MgO
moderator
10000
->
Reference Fluence Limit: 90 MWd/kgH M
7% MgO Fluence Limit: 107 MWd/kgHM
Percent Change from Previous: 19.4%
5000
-- Reference
E
--m-7% MgO
50
100
1
200
250
300
350
-5000
-10000
-15000
Discharge Burnup (MWd/kgHM)
Figure 41. Reactivity vs. burnup for the Pu-U metal fuel using the uranium+ strategy with 7% vol. frac. of MgO
moderator
Adding 5% MgO increased the fluence-limited burnup 12.7%, from 90 MWd/kgHM to 101
MWd/kgHM. This is comparable to, though less effective than, the 13.7% increase gained by
adding 5% SiC.
Adding 7% MgO increased the fluence-limited burnup by 19.4%, to 107
MWd/kgHM, also less than the 20.9% increase gained when adding 7% SiC. Adding 3% MgO
resulted in a 2.4% fluence-limited burnup increase per percent MgO added, while adding 5% and
7% MgO resulted in 2.6% and 2.8% increases in fluence-limited burnup per percent MgO added,
respectively. Adding 3%, 5%, and 7% SiC increased the fluence limited burnup by 2.6%, 2.7%,
71
2.9% per percent SiC added, respectively. Though SiC is more effective as a spectrum softener
from a purely neutronic perspective, MgO is already in widespread use in the USFR and TRUSFR as a high-albedo axial and radial reflector, which might make it desirable to utilize MgO in
the pins for purposes of consistency. MgO has also been successfully tested as an inert matrix
for minor actinide burnup in SFRs, providing enhanced confidence in its suitability for the
present system.
4.3.4.2 Melt-and-Recast
Another option to increase the fuel burnup between full reprocessing steps is to incorporate the
melt-and-recast (MNR) system of spent fuel recycling. As used early in EBR-II operation and
recently proposed by Ehud Greenspan, MNR is a simple, cheap alternative to full pyroprocessing
wherein the spent fuel is melted down, the gaseous and volatile fission products are collected,
and the remaining materials (actinides and solid fission products) are recast into the metal fuel
form. (Greenspan & Heidet, 2010) Though this methodology cannot be used indefinitely, it can
be used in conjunction with full pyroprocessing to reduce fuel recycling costs over the long term.
Melt-and-recast functions by capitalizing on the large difference in the fluence-limited burnup
and the reactivity-limited burnup instead of seeking to eliminate it. MNR is applied to
essentially replace the fuel cladding without trying to make major changes to the fuel
composition, since the reactivity of the fuel is not the limiting factor. By replacing the cladding,
the fuel recycled using the MNR process would then be able to achieve the reactivity limit on
burnup, at which time it could be recycled using a full pyroprocess.
The fuel cycle using MNR would begin as outlined previously, with the USFR spent fuel
recycled using the full pyroprocess and loaded into the TRU-SFR. However, once the fuel in the
TRU-SFR reaches its fluence limit, it would be removed from the core and not pyroprocessed,
but fed into the MNR process. This would replace the cladding while having very little impact
on the fuel's composition, such that the reactivity-limited burnup of the fuel would be only
slightly impacted. The fuel from the MNR process would then be reloaded into the reactor and
burned until it reached its reactivity-limited bumup, at which time it would be recycled using the
full pyroprocess, and the cycle would begin again. Essentially, the MNR process would replace
every other pyroprocess step, and since MNR is expected to cost less than the full pyroprocess,
this would result in cost savings.
Since the combined MNR/pyroprocessing recycle strategy depends on maximizing both the
fluence-limited burnup per cycle and the difference between the fluence-limited and reactivitylimited burnups, the multicore transition strategy was identified as the ideal means of beginning
the recycle mode. After the first USFR-to-TRU-SFR transition is completed using the multicore
strategy (where the composition of spent fuel is maintained), subsequent reloads can be
72
performed using the uranium+ strategy (where natural uranium can be used to supplement mass
differences between discharged and reloaded assemblies). The bumup vs. reactivity results of
such a system are displayed in Figure 42.
20000
--Transition (multicore) Fluence Limit: 115 MWd/kgHM
1st Reload (uranium+) Fluence Limit: 94.2 MWd/kgHM
-2nd Reload (uranium+) Fluence Limit: 97.1 MWd/kgHM
15000
10000
Transition (multicore) Reactivity Limit: 249 MWd/kgHM
1st Reload (uranium+) Reactivity Limit: 232 MWd/kgHM
2nd Reload (uranium+) Reactivity Limit: 240 MWd/kgHM
0
5000>
0
50
-5000
100
150
2
200
300
350
---
Transition MNR
-+-1st Reload MNR
--- 2nd Reload MNR
---
-10000
Average Discharge Burnup (MWd/kgHM)
Figure 42. Reactivity vs. burnup for the TRU-SFR metal core using the combined pyroprocess/MNR cycle
The transition case using the multicore cycle remains unchanged from the previous analysis. Its
large (134 MWd/kgHM) difference between the fluence- and reactivity-limited burnups allows
the core to run until reaching the fluence limit at 115 MWd/kgHM, melt and recast the fuel, and
then run until the reactivity limit is reached (249 MWd/kgHM), such that the fuel is
pyroprocessed only when the fuel has reached a bumup of almost 250 MWd/kgHM. The impact
of this recycled high-burnup spent fuel on the reactivity profile of successive reloads was
investigated, to characterize the equilibrium bumup behavior of this MNR/pyroprocess cycle.
After the first pyroprocess recycle step from the TRU-SFR ("1st Reload" in Figure 42), the
reactivity vs. burnup profile shifts downward such that the initial reactivity decreases from 15500
pcm to 6820 pcm, and the reactivity-limited bumup decreases from 249 MWd/kgHM to 232
MWd/kgHM. The fluence-limited bumup also decreases, from 115 MWd/kgHM to 94.2
MWd/kgHM. However, after another successive MNR/pyroprocess cycle, the equilibrium
(approximated by the "2nd Reload") achieves better burnup performance. The 2nd Reload case
reaches a fluence-limited bumup of 97.1 MWd/kgHM and a reactivity-limited burnup of 240
MWd/kgHM, which is acceptably high for economic performance as discussed in Section 3.6.
73
4.3.4.3 Varying the Fuel Volume Fraction
The final method of improving the achievable bumup of the metallic core was to vary its fuel
volume fraction. Varying the fuel volume fraction had several effects on the composition of the
fuel and also on the neutron moderating environment. Varying the fuel volume fraction is
perhaps the most simple method of adjusting the spectrum, and as such it holds much promise as
a viable strategy for maximizing fuel burnup.
Varying the fuel volume fraction also means adjusting the coolant (or sodium bond) volume
fraction to account for the changes in fuel volume. As the fuel volume fraction decreases, the
coolant volume fraction increases, and vice versa. These alterations can come either via an
increase/decrease of the coolant outside the cladding (altering the diameter of both the fuel and
the clad) or via an increase/decrease in the size of the sodium bond within the pin (altering the
fuel diameter while keeping the cladding diameter constant). The second option allows for the
thermal-hydraulic characteristics of the plant to remain the same, while also improving on the
void coefficient in the case of shrinking the fuel (since the sodium in the bond will not
experience the voiding that occurs in the coolant). Thus, the fuel volume fraction was varied by
altering the fuel diameter while keeping the cladding diameter intact.
Varying the fuel volume fraction is similar to the previous discussion of adding moderator
materials since it is essentially equivalent to adding or removing sodium, which can slow
neutrons slightly (though it cannot be counted a true moderator-if it was, fast reactors wouldn't
use it as a coolant!). The scattering and capture cross sections of Na-23 (100% of natural
sodium) are shown in Figure 43, and their ratio is shown in Figure 44.
74
Incident neutron data I ENDFIB-VII.0 I Na23 I i Cross section
n
C
0
V
S
'ii
0
C)
incident energy (Mev)
Figure 43. Microscopic scattering and absorption cross sections of Na-23, ENDF/B-VII data
Incident neutron data! ENDFB-VII.0
i Na23 i IMT=2
: (z,zO)
elastic scattering I Na24 scattering-to-capture ratio
CL
E
1E-10
IE.2
1E4
E-7
IE-6
IE-
IE-4
O001
0.01
0.1
10
Incident energy (MeV)
Figure 44. Scattering-to-absorption ratio of Na-23, ENDF/B-VII data
Sodium has a higher average thermal capture cross section (0.5 barns) than both Si-28 (0.2
barns) and Mg-24 (0.05) but a nearly equivalent scattering cross section (thermal average of 5
barns). This causes Na-24's scattering-to-absorption ratio to range from 2 to 50 in the thermal
region, which is substantially less than Mg-24's range of 15-500 but similar to Si-28's range of 4
to 75. However, the epithermal and fast regions are of more interest for this application, and
here the resonance structure of sodium differentiates its neutronic behavior from that of Mg-24
75
and Si-28. Na-23 experiences its first capture resonance near 0.01 MeV, while Si-28 and Mg-24
both experience their first capture resonance near 0.05 MeV. Na-24's average scattering cross
section in the range 1 keV to 1 MeV is approximately 5 barns, similar to that of Mg-24 and
greater than that of Si-28 (2.5 barns). However, Na-23 has wider, greater-amplitude capture
resonances in this range, making it more of an absorber of neutrons in the fast spectrum. It's
scattering-to-capture ration in this range averages 5,000, which is similar to that of Mg-24 and
Si-28, but the precise resonance behavior varies significantly and is expected to impact the effect
of the sodium as a spectrum softener.
Since the uranium+ strategy has much more of a need to improve the fluence-limited burnup,
efforts focused on this strategy rather than the multicore approach. With the nominal fuel
volume fraction at 40%, the fuel volume fraction was increased to 43% and decreased to 37% to
gain insight into the neutronic response.
8000
Reference Fluence Limit: 90 MWd/kgH M
43% vol. frac Fluence Limit: 81 MWd/kgH M
Percent Change from Previous: -9.8%
--
6000
4000-
-+Reference
0
---
43 Vol. Frac.
0
0
50
100
150
200
300
350
-2000
-4000
-6000
-8000
Average Discharge Burnup (MWd/kgHM)
Figure 45. Reactivity vs. burnup for the Pu-U metal fuel using the uranium+ strategy with a fuel vol. frac. of 43%
As seen in Figure 45, increasing the fuel volume fraction has the effect of hardening the
spectrum, as less moderator is present to collide with and slow the neutrons in the system before
they interact with the fuel. Hardening the spectrum enhances the conversion ratio of the system,
which causes the reactivity swing to increase; the initial reactivity of the system drops from 2920
pcm to 1220 pcm, while the peak reactivity increases from 5780 pcm to 6240 pcm. The fluencelimited burnup decreases 9.8% from 90 MWd/kgHM to 81 MWd/kgHM. Since the goal is to
increase the fluence-limited burnup via spectrum softening, it is apparent that the fuel volume
fraction must be decreased to accomplish this objective.
76
8000
---- Reference Fluence Limit: 90 MWd/kgHM
37% vol. frac Fluence Limit: 100 MWd/kgHM
Percent Change from Previous: 10.8%
6000
4000-
E
0
-20
Reference
---
37 Vol. Frac.
50
100
250
20
150
300
350
400
-2000
lu -4000
-6000
------
-8000
-
-10000
-12000
Average Discharge Burnup (MWd/kgHM)
Figure 46. Reactivity vs. burnup for the Pu-U metal fuel using the uranium+ strategy with a fuel vol. frac. of 37%
Decreasing the fuel volume fraction 3%, from 40% to 37%, softens the spectrum and reverses
the reactivity and fluence trends encountered for the 43% fuel volume fraction case. The initial
reactivity increases from 2920 pcm to 4680 pcm, and the peak reactivity remains nearly constant,
dropping slightly from 5780 to 5660 pcm. However, the peak reactivity occurs 16 MWd/kgHM
earlier in the cycle, occurring at 41.7 MWd/kgHM instead of 57.8 MWd/kgHM. This alteration
of the reactivity vs. burnup curve stands in contrast to the changes incurred when adding
moderator materials such as SiC or MgO. In those cases, the fuel volume fraction was unaltered
and the coolant (sodium bond) volume fraction was adjusted to account for the addition of the
moderator. This strategy had the effect of shifting the reactivity curve downward with negligible
change in the slope of the curve. However, when altering the fuel volume fraction, the
conversion ratio is more significantly impacted via two phenomena. First, the reduction in fuel
volume fraction under the uranium+ strategy means that less natural uranium must be added to
the discharged USFR fuel during the pyrometallurgical recycling process. This effectively
increases the fissile loading as a percent of heavy metal, which reduces the breeding in the
system and alters the shape of the reactivity curve, flattening it somewhat. Additionally, sodium
serves as a better spectrum softener, not because it is a better moderator, but because it captures
or preferentially absorbs enough neutrons to soften the spectrum enough that the dpa is limited
but reactivity is not as significantly impacted.
This effective spectrum softening improves the fluence-limited burnup, which increases 10.8%
from 90 MWd/kgHM to 100 MWd/kgHM. This indicates improved performance relative to the
addition of 3% SiC or 3% MgO, which increased the fluence-limited bumup 7.7% and 7.2%,
respectively. Importantly, the initial reactivity remains positive and actually increases due to the
higher concentration of fissile plutonium in the fuel (though the total plutonium mass loading
remains constant). The reactivity-limited burnup begins to converge toward the fluence-limited
77
However, a 92
burnup, decreasing 9.7% from 212 MWd/kgHM to 192 MWd/kgHM.
MWd/kgHM gap still exists between the reactivity-limited and the fluence-limited burnups,
indicating that further reductions in the fuel volume fraction can be pursued.
Accordingly, a sensitivity analysis was performed to determine the optimal fuel volume fraction
at which the fluence-limited burnup would be maximized. The fuel volume fraction was
decreased to a lower limit of 30.85%, at which point the mass discharged from the USFR
equaled the mass recycled into the TRU-SFR, such that no natural uranium was necessary to
compensate for a mass defect from the UC fuel to the Pu-U-Zr metal fuel. The results of this
investigation are presented in Figure 47.
180
170
c
160
150
MC
140
-4- Fluence-limited
130
--
Reactivity-limited
120
L.
0
110
---
-
-------
100
90
30%
31%
32%
33%
34%
35%
36%
37%
Fuel Volume Fraction
Figure 47. Dependence of the fluence-limited and reactivity-limited average discharge burnup for Pu-U-Zr metal fuel of
various volume fractions, transitioned using the uranium+ strategy.
As the fuel volume fraction decreases, the fluence-limited and reactivity-limited burnups
converge toward each other. At the specified minimum of 30.85% fuel volume fraction, the
fluence-limited burnup is 122 MWd/kgHM, only 19 MWd/kgHM less than the reactivity-limited
burnup of 141 MWd/kgHM. If the fuel cycle choice was made to create multiple TRU-SFR
plutonium-fueled assemblies from a single USFR assembly, this disparity could be eliminated by
reducing the fuel volume fraction until the reactivity-limited burnup converged with the fluencelimited burnup, which is likely to occur around 29.2% fuel volume fraction (using linear
extrapolation).
The impact of successive fuel recycles was investigated to determine the equilibrium cycle
behavior of the uranium+ metal core with a fuel volume fraction of 30.85%. The reactivity as a
function of burnup for two successive reloads is displayed in Figure 48.
78
10000
-+-Transition
--A- Reload 1
-4- Reload 2
5000
E
50
100
1
200
250
300
350
400
450
-5000
-10000
-15000
-20000
Transition Fluence Limit: 121.5 MWd/kgHM
Reload 1 Fluence Limit: 112.1 MWd/kgHM
Percent Change from Transition: -7.7%
Reload 2 Fluence Limit: 112.0 MWd/kgH M
Percent Change from Reload 1: -0.15%
-25000
Average Discharge Burnup (MWd/kgHM)
Figure 48. Reactivity vs. burnup for the transition case and successive reloads of the uranium+ TRU-SFR metal core with
a fuel volume percent of 30.85%
The initial reactivity of the first reload cycle decreases 53% from 7806 pcm to 3703 pcm. This is
primarily due to the loss of fissile material throughout the transition cycle, since the fissile
inventory ratio is approximately 0.9 during this time (See Section 4.7 for a more detailed
analysis of the breeding in the system). The fluence-limited burnup decreases accordingly,
decreasing 7.7% from 121.5 MWd/kgHM to 112.1 MWD/kgHM. The reactivity-limited bumup
remains mostly unchanged, since the breeding of the system increases once the fissile content is
decreased relative to the fertile content.
However, the fuel converges to the equilibrium cycle essentially after one reload. The initial
reactivity of the second reload core is only 254 pcm less than the first reload core. This is
because the fissile inventory ratio of the second core is 0.98, keeping the fissile content between
loading and discharge essentially unchanged. This is also reflected in the fluence-limited bumup
change, which is only 0.15% less for the second reload core than for the first reload core.
Equilibrium behavior can be assumed to be reached after the 2nd reload, as the fissile inventory
ratio of this cycle is 1.01.
4.4 Reactivity Worth of Minor Actinides
As with the carbide cores, the reactivity worth of the minor actinides was evaluated for the metal
cores. Reactivity worths were evaluated for cores transitioned from the USFR using both the
multicore and the uranium+ recycling strategies, at a nominal fuel volume fraction of 40%.
79
20000
Nominal Fluence Limit: 115.3 MWd/kgHM
MA Removed Fluence Limit: 115.4 MWd/kgH M
Percent Change from Previous: 0.1%
15000
iC.)
-u-Nominal
0.
-+-MA Removed
.1.~
5000
C.,
0
0
-
50
100
150
200
250
300
350
-5000
-10000
---
Average Discharge Burnup (MWd/kgHM)
Figure 49. Reactivity vs. burnup for the metal core transitioned using the multicore strategy displaying the reactivity
worth of the minor actinides
The initial reactivity of the fuel with the minor actinides removed is increased by 1.6% (240
pcm) relative to the case with all minor actinides left intact. However, the reactivity-limited
burnup decreases 1.1% from 247 MWd/kgHM to 244 MWd/kgHM. As in the carbide core, this
is because the removal of the minor actinides must be compensated via the addition of additional
plutonium and uranium content, such that the initial reactivity is slightly increased but the
breeding is slightly decreased. The fluence-limited bumup increases negligibly (0.1%) due to
the slight addition of uranium and plutonium.
8000
Nominal Fluence Limit: 89.99 MWd/kgHM
MA Removed Fluence Limit: 89.89 MWd/kgHM
Percent Change from Previous: -0.1%
6000
4000
E.
0.
2000
C)
%0
0
-+-Nominal
-e-MA Remove d_
50
100
150
200
250
300
350
-2000
-4000
-6000
-8000
Average Discharge Burnup (MWd/kgHM)
Figure 50. Reactivity vs. burnup for the metal core transitioned using the uranium+ strategy displaying the reactivity
worth of the minor actinides
80
Similar to the multicore case, removing the minor actinides from the fuel loaded into the TRUSFR impacts the fluence- and reactivity-limited burnups only slightly. The initial reactivity
increases 2.7% (80 pcm), while the reactivity-limited burnup decreases 1.3%. The fluencelimited burnup decreases 0.1%, primarily due to the reactivity worth of the minor actinides being
replaced with natural uranium. This stands in contrast to the multicore case, where both uranium
and plutonium are added which slightly increases the fluence-limited burnup because the
reactivity of the uranium-plutonium mix is greater than that of the minor actinides (throughout
the cycle), whereas the natural uranium added in the uranium+ case has a reduced reactivity
(throughout the cycle) than the minor actinides.
For both the multicore and the uranium+ strategies, minor actinides have minimal impact on
reactivity, reactivity-limited burnup, and fluence-limited burnup. Since destroying minor
actinides via irradiation is a major benefit to waste storage and disposal, it is recommended to
include the minor actinides in the fuel recycling process.
4.5 Storage Impact
Since the timetable for transitioning once-through USFR reactors to TRU-SFR reactors in a
plutonium recycle mode is uncertain, the impact of cooling was evaluated for the optimal metal
fuel recycle core, with a fuel volume fraction of 30.85%, transitioned using the uranium+
strategy. To simulate the impact of cooling the fuel, all of the Pu-241 was assumed to have
decayed into Am-241. This provides a conservative baseline estimate of the reactivity loss
associated with cooling the fuel; Pu-241 has a 14.4 year half-life, so if the fuel is recycled on the
order of this time frame, it will retain significant quantities of the Pu-241.
The effect of cooling was investigated for both the initial transition, and for the successive
reloads. In each case, all of the Pu-241 was assumed to have decayed away into Am-241, and
the subsequent reactivity penalty was evaluated, first for the transition case and then for the first
and second reloads. The reactivity vs. burnup profiles for the cooled uranium+ metal cores are
shown in Figure 51, and the reactivity penalty associated with fuel cooling is further highlighted
in Figure 52.
81
10000
-_-_-_-_-_-_Cooled Transition Fluence Limit: 120.3 MWd/kgHM (-0.98%)
Cooled Reload 1 Fluence Limit: 108.9 MWd/kgHM (-2.89%)
Cooled Reload 2 Fluence Limit: 107.2 MWd/kgHM (-4.29%)
5000
E
50
100
1
200
250
300
350
400
450
5000
+
-10000
0)
-+-Transition
- -Reload 1
-4-Reload 2
-15000
-20000
-25000
Average Discharge Burnup (MWd/kgHM)
Figure 51. Reactivity vs. burnup for the uranium+ metal cores with 30.85% fuel volume fraction after cooling
The reactivity vs. burnup trend of the transition core of cooled fuel remains largely unchanged
from those of the fuel that was reprocessed with minimal cooling (compare with Figure 48). The
initial reactivity of the transition case has decreased by 775 pcm (9.9%), which decreases the
reactivity-limited burnup by 0.7%. Only slight changes in reactivity are encountered for the fuel
cooled before the transition from the USFR to the TRU-SFR, since this fuel has only small
amounts of Pu-241 (0.08% of HM, see Table 15).
Larger variations in reactivity and reactivity profiles are encountered for the TRU-SFR reload
cases. For the first core of cooled reloaded fuel, the initial reactivity is 2173 pcm (59%) less than
fuel reloaded without significant cooling. This leads to a reactivity-limited burnup decrease of
12%. For the second reload of cooled fuel, the initial reactivity is 3170 pcm (80%) less than for
the hot fuel. However, the breeding in the system is enhanced in this case and so the reactivitylimited burnup of the cooled fuel core is surprisingly close to that of the hot fuel core, differing
by only 0.8%.
82
124
-- Immediately Reloaded
20-U-Cooled then Reloaded
-0.98% difference
122
120
:
118
I
-
- --
116
-2.89% difference
114
112
110
4.29% difference]
---
108
106
2
1
3
Cycle
Figure 52. Fluence-limited burnup as a function of cycle for the uranium+ metal core with a fuel volume fraction of
30.85%
Similar to the reactivity-limited burnup change, the fluence-limited bumup of the transition core
is only minimally impacted by the effect of cooling, decreasing only 0.98% from that of the hot
core. Again, however, the reload cores experience greater decreases in achievable burnups. The
first reload core using cooled fuel achieves a fluence-limited bumup of 108.9 MWd/kgHM, 2.9%
less than for the hot reloaded core. The second cooled reload core experiences a greater drop,
reaching a fluence-limited burnup of 107.2 MWd/kgHM, 4.3% less than for the second hot
reloaded core. The fluence-limited burnup of the cooled second reload core is 1.5% less than for
the cooled first reload core. This stands in contrast to the near-identical fluence-limited burnups
of the uncooled first and second reload cores, which differ by only 0.15%. This suggests that the
cooled cores may take an additional cycle to reach equilibrium compared to the uncooled cores.
4.6 Economic Performance
The economic performance of the metal TRU-SFR cores was evaluated to determine the most
effective strategy for transition from the USFR to the TRU-SFR. The achievable burnups of the
metal core cases were used together with the front-end fuel cycle costs discussed in Section 3.6
to develop levelized fuel cost estimates for each metal core iteration.
83
Table 16. Levelized fuel costs for the metal fueled SFR cores in recycle mode, and the reference once-through LWR LFC
Fuel Type
Reprocessing Scenario
_________
Stage
__________________ _________________
Maximum Burnup
(MWd/kgHM)
LFC (mills/kwh)
________
LWR Oxide
None (Once through)
Metal
Uranium+
Transition
90
9.18
Metal
Metal
Metal
Multicore
Uranium+
Multicore
Transition
1st reload
1st reload
115
98
119
7.49
8.56
7.30
-_45
7.00
Table 16 displays the levelized fuel costs for the metal cores at a nominal fuel volume fraction of
40%.
It is clear that the achievable bumups for these cases are too low, resulting in
uncompetitive fuel cycle costs. The multicore metal core achieves a maximum discharge burnup
of 115 MWd/kgHM, resulting in a LFC of 7.49 mills/kWh, 7% larger than the LWR reference
LFC of 7.00 mills/kWh. The uranium+ metal core fares even worse, achieving a maximum
burnup of only 90 MWd/kgHM, which gives a LFC of 9.18 mills/kWh, a staggering 31%
increase over the nominal LWR LFC.
It is clear from these results that simply transitioning the USFR carbide core to the TRU-SFR
with a metal fuel form, keeping all else constant, is not an economically attractive strategy.
Hence, several strategies were investigated to identify possible means of improving the fluencelimited burnups of the metal cores, as discussed in Section 4.3.4. One possible means of
improving the fuel burnup before full reprocessing was the melt-and-recast strategy, in which the
fuel and cladding were melted down and re-casted using a simple process once the fluence limit
of the cladding was reached, and the recast fuel was then reloaded into the core and allowed to
run until its excess reactivity was exhausted (or the fluence limit was again exceeded). This
allowed for every other recycle step to be the cheaper melt-and-recast (MNR) process, which
was assumed to cost half of what full pyroprocessing would cost, making its unit cost
$3,000/kgHM. The economic impacts of incorporating this strategy are displayed in Table 17.
Table 17. Levelized fuel costs for the metal fueled SFR cores in mixed melt-and-recast/pyroprocessing recycle mode, and
the reference once-through LWR LFC
Fuel Type
Reprocessing Scenario
_________
_________________
LWR Oxide
None (Once through)
SFR Metal
SFR Metal
SFR Metal
Multicore & Melt and Recast
Uranium+ & MNR
Uranium+ & MNR
Stage
_________________
Maximum Burnup
(MWd/kgHM)
-_45
Transition
1st reload
2nd reload
LFC (mills/kwh)
_______
7.00
115 (230)
94(188)
97 (194)
6.90
7.85
7.68
With the MNR strategy, the large gap between the fluence-limited and reactivity-limited
bumups is exploited to allow for the incorporation of the melt-and-recast step between full
pyroprocessing steps. Thus, the transition core utilized the multicore strategy, which has a larger
gap between the fluence- and reactivity-limited burnups. Subsequent reloads are completed
preserving fissile masses using the uranium+ strategy. In Table 17, the maximum burnups listed
are the initial first-run burnups (the fluence-limited burnups) reached before the melt-and-recast
84
process is performed. The core is then reloaded and burned until it reaches the reactivity-limited
burnup, shown in parentheses in the table. The resulting levelized fuel cost for each cycle
(between full pyroprocessing steps) is then computed and displayed. The transition case
achieves a competitive LFC of 6.90 mills/kWh, 1.4% less than the nominal LWR LFC of 7.00
mills/kWh. However, the LFC increases as the TRU-SFR fuel is pyroprocessed and reloaded
using the uranium+ strategy, increasing to 7.85 mills/kWh (12% higher than the nominal LWR
case) for the first reload and then decreasing slightly to 7.68 mills/kWh (9.7% higher than the
LWR case) for the second reload, which approaches equilibrium behavior. This increase in the
LFC from the transition case to successive reloads occurs because the transition cycle has a
fissile inventory ratio of approximately 0.8 upon reaching its reactivity-limited bumup, and since
the reload cases use the uranium+ strategy, little fissile material is added in the pyroprocess
recycle. However, once reloaded, the fuel has a fissile inventory ratio of slightly more than 1, as
equilibrium behavior is attained, resulting in little change in the LFCs of the reload cores (See
Section 86 for a more detailed discussion of the FIR of the various metallic cores).
Table 18. Levelized fuel costs for the uranium+ metal cores with various moderating materials added to reduce cladding
fluence and enhance burnup
LFC
Additive
Heavy Metal Mass (kg)
Fluence-Limited Bumup
(MWd/kgHM)
(mills/kwh)
None
3%SiC
5%SiC*
7%SiC*
3%Graphite*
3%MgO
5%MgO*
7%MgO*
47620
46192
45239
44287
46192
46192
45239
44287
90.0
96.9
102.3
108.6
100.9
96.5
101.5
107.5
9.18
8.59
8.18
7.76
8.31
8.62
8.24
7.83
In an effort to improve the fluence-limited burnup of the metal core transitioned using the
uranium+ strategy, moderating materials were introduced as a means of softening the spectrum
and reducing the cladding dpa. The achievable fluence-limited burnups of these cases are
displayed in Table 18, with the cores that are subcritical (absent any specialized fuel
management strategy) marked with an asterisk. As discussed in Section 4.3.4.1, the addition of
various moderating materials was only mildly successful in enhancing the fluence-limited
burnup of the core. However, all moderating materials were able to improve on the fluencelimited burnup of the uranium+ reference case, which was 9.18 mills/kWh, which is 31% greater
than the reference LWR LFC of 7.00 mills/kWh. The greatest improvement in the fluencelimited burnup was encountered for the case with 7% SiC additive, which achieved a fluencelimited burnup of 108.6 MWd/kgHM, and was able to obtain a LFC of 7.76 mills/kWh, only
11% greater than the reference case. The 7% MgO case reached a fluence-limited burnup of
107.5 MWd/kgHM, resulting in a LFC of 7.83 mills/kWh. Still, though, these LFCs are greater
85
than desired, especially since the effects of fuel cooling and successive reloads were not taken
into account.
Table 19. Levelized fuel costs of the uranium+ metal cores with a fuel volume fraction of 30.85%, including the effects of
cooling
Reprocessing Scenario
Fluence-Limited Burnup
(MWd/kgHM)
Reactivity-Limited
Burnup (MWd/kgHM)
LEG (mills/kwh)
Transition
Transition (cooled)
Reload 1
Reload 1 (cooled)
Reload 2
Reload 2 (cooled)
121.5
120.3
112.1
108.9
112
107.2
140.5
139.5
127.9
125.7
138.3
137.1
6.81
6.87
7.29
7.47
7.29
7.57
As discussed in Section 0, varying the fuel volume fraction was found to be an effective method
for improving the fluence-limited burnup of the uranium+ metal core. The transition case
reached a fluence-limited burnup of 121.5 MWd/kgHM, resulting in a LFC of 6.81 mills/kWh,
2.7% less than the reference LWR LFC. The LFC decreases slightly if the fuel is cooled before
the transition from the USFR to the TRU-SFR is made, resulting in a LFC of 6.87 mills/kWh,
1.8% less than the reference LWR LFC. Upon reloading of the TRU-SFR fuel, the LFC increases
to 7.29 mills/kWh, 4.1% greater than the reference case. If this first reload fuel is cooled, it
results in a LFC of 7.47, which is 6.7% greater than the reference. The second reload
approximates that of the first, obtaining an identical LFC of 7.29 mills/kWh if the fuel is not
cooled. If the fuel is cooled, the LFC is 7.57 mills/kWh, 8.1% greater than the reference. The
fluence-limited burnup of the cooled reload cases keeps rising because the reload cases contain a
higher proportion of Pu-241 due to the extended burnups, such that the loss of this Pu-241
increases in reactivity worth with successive reloads. The most important conclusion in this
economic analysis is that the LFCs for the range of cases investigated are generally within 10%
of the LWR reference LFC. Since significant uncertainty exists in many parameters used to
estimate these costs (reprocessing cost, tolerable dpa, etc), and also considering that the LFC is
only ~10% of the busbar cost, then the differences in the LFCs of the various cases should not
prejudice the selection of most of the systems studied, but rather other factors such as ease of
transition, safety, and nonproliferation should be considered.
4.7 Fissile Material Ratios
The fissile material ratios applied to the carbide cores (recall Section 3.7) were also applied to
the various metal cores. The fissile material ratios of the metal core transitioned using the
multicore strategy with a nominal fuel volume fraction of 40% are shown in Figure 53.
86
1.2
1
0
Fluen ce Limit
115 MWd/kgHM
6
S@
Reactivity Limit
@ 245 MWd/kgHM
-+-FIR
E.I
-FPR
0.2
0
0
50
100
200
150
250
300
350
Average Discharge Burnup (MWd/kgHM)
Figure 53. Fissile material ratios as a function of burnup for the transition multicore metal core
Similar to the carbide-fueled configuration, the metal multicore transition case functions as a
fissile burner throughout the cycle, with the fissile inventory ratio remaining below one at all
times. The fissile inventory ratio at the fluence-limited burnup of 115 MWd/kgHM is 0.9, and it
decreases to 0.8 by the time the reactivity-limited burnup of 245 MWd/kgHM is reached. The
carbide multicore case experienced enhanced breeding, as it discharged with a fissile inventory
ratio of 0.93 at its fluence-limited burnup of 136 MWd/kgHM. This is reflected in the shape of
the fissile plutonium ratio curve, which for the metal core peaks at 1.06 at 77 MWd/kgHM and
decreases to 1.05 at the fluence-limited burnup of 115 MWd/kgHM. The multicore carbide
core's fissile plutonium ratio peaked at 1.14 at 108 MWd/kgHM and discharged at 1.13, which
drives the carbide core's higher fissile inventory ratio.
87
1.4
(0
0 .8
T
Fluence Limit
@ 90 MWd/kgH M
Reactivity Limit
@ 210 MWd/kgHM
0.6
4)
-
) 0.4-
-+-F-R
--
U)
0.2
-
-
FUR
-
0
0
50
100
150
200
250
300
350
Average Discharge Burnup (MWd/kgHM)
Figure 54. Fissile material ratios as a function of burnup for the transition uranium+ metal core
The metal uranium+ transition core functions as breeder, similar to the uranium+ carbide core.
However, the metal core is more effective a breeder than the carbide, as the fissile inventory ratio
of the metal core peaks at 1.1 at 77 MWd/kgHM and is 1.09 at the fluence-limited burnup of 90
MWd/kgHM. The carbide core, for comparison, peaks at 1.06 at 65 MWd/kgHM and 1.04 at the
fluence-limited burnup of 118 MWd/kgHM. The fissile plutonium ratio of the uranium+ metal
core peaks at 1.32 at 96 MWd/kgHM, and is 1.3 at the fluence-limited burnup of 90
MWd/kgHM. This is the driving force behind the enhanced reactivity of the reloaded uranium+
TRU-SFR metal core, which is able to reach a fluence-limited burnup of 98 MWd/kgHM, as
discussed in Section 4.3.3.2.
The fissile material ratios were also investigated for the metal cores incorporating the melt-andrecast strategy. Since these cores ran to greater burnups before full pyroprocessing was
undertaken, they generally functioned as fissile material burners. The fissile material ratios of
the first core that was pyroprocessed and reloaded after the transition burn-MNR-burn cycle is
shown in Figure 55.
88
1.2
Fluence Limit
@ 94.2 MWd/kgH M
0.8
0 .6
-
0.4
----
Reactivity Limit
@ 232 MWd/kgHM
---
----Melt and Recast Limit
--
@@188 MWd/kgHM
-- m-FPR
FUR
0.2
-
0
0
50
100
150
200
250
300
350
Average Discharge Burnup (MWd/kgHM)
Figure 55. Fissile material ratios as a function of burnup for the first reload metal core after MNR and pyroprocessing
When the fluence limit of this reload core is reached at 94.2 MWd/kgHM, the fissile inventory
ratio is 1.07, nearly equal to the fissile plutonium ratio of 1.1. This is because the transition
cycle has fissioned most of the fissile uranium left in the recycled USFR fuel, so little is left for
the first reload of TRU-SFR fuel. Note, though, that the fissile inventory ratio is only slightly
greater than 1 (1.01) at the maximum bumup of the recast fuel, though the fissile plutonium ratio
is 1.05 at this point. Ultimately, this results in slightly enhanced reactivity for the second TRUSFR reload cycle, as discussed in Section 4.3.4.2.
The fissile material ratios were also investigated for the uranium+ metal cores with the fuel
volume fraction of 30.85%, optimized to maximize their fluence-limited bumups. The fissile
material ratios of the uranium+ transition metal core with a fuel volume fraction of 30.85% are
shown in Figure 56.
89
1.2
(A
0
0.8
Reactivity Limit
@ 140.5 MWd/kgHM
Cm
0.6
-
Fluence Limit
@ 121.5 MWd/kgHM
0.4
--
FIR
U)-e
U)
FU R
0.2
0
0
50
100
150
200
250
300
350
400
450
Average Discharge Burnup (MWd/kgHM)
Figure 56. Fissile material ratios as a function of burnup for the transition uranium+ metal core with a fuel volume
fraction of 30.85%
This uranium+ transition core functions as a net fissile burner, with a linearly decreasing fissile
inventory ratio as a function of bumup. The fissile inventory ratio at the fluence-limited burnup
is 0.91, whereas the fissile inventory ratio of the transition uranium+ metal core with a fuel
volume fraction of 40% was 1.09 at its fluence-limited bumup of 90 MWd/kgHM. This occurs
because less plutonium breeding occurs, as the fissile plutonium ratio peaks at 1.085 at 100
MWd/kgHM and is 1.08 at the fluence-limited burnup of 121.5 MWd/kgHM. This conversion
behavior is the underlying cause of the reactivity loss of the first reload of the TRU-SFR when
using this 30.85% metal fuel and the uranium+ recycling strategy, as described in Section 0.
90
1.2
W)
0
0.8
4'
*0
Reactivity Limit
@ 127.9 MWd/kgHM
0.6
-.-
0
4)
FIR
- - -FPR
0.4
-*-
FUR
0.2
0
0
50
100
150
200
250
300
350
400
450
Maximum Burnup (MWd/kgHM)
Figure 57. Fissile material ratios as a function of burnup for the first reload uranium+ metal core with a fuel volume
fraction of 30.85%
The burner behavior is lessened for the first reload of this 30.85% metal uranium+ core, as the
fissile inventory ratio now increases with burnup until 50 MWd/kgHM and thereafter decreasing
to 0.99 at the fluence-limited burnup of 112 MWd/kgHM. This indicates that the first reload
core is close to reaching equilibrium, yet still needing to converge further. The general flatness
of the fissile inventory ratio and the fissile plutonium ratio suggests that the equilibrium cycle for
this SFR will have a conversion ratio of unity, such that by the end of cycle approximately the
same fissile material will be present as at the beginning.
1.2
U)
0
0.86
.0-
Reactivity Limit
@138.3 MWd/kgHM
0.6
---
0.4
(I)
LL
FIR
- --
FPR
-*
FUR
0.2
0
0
50
100
150
200
250
300
350
400
450
Maximum Burnup (MWd/kgHM)
Figure 58. Fissile material ratios as a function of burnup for the second reload uranium+ metal core with a fuel volume
fraction of 30.85%
91
This steady-state converter behavior of the equilibrium cycle is confirmed by analyzing the
fissile material ratios of the second TRU-SFR metal fuel uranium+ reload, as shown in Figure
58. The fissile inventory ratio peaks at 1.03 at 50 MWd/kgHM, and then equals unity at the
fluence-limited bumup of 112 MWd/kgHM. The fissile plutonium ratio is 1.02 at the fluencelimited burnup, which is just enough to compensate for the burned fissile uranium. The fissile
material ratios of this case corroborate the conclusion of the reactivity vs. burnup analysis
conducted in Section 0, that the maximum fluence-limited bumup achieved by the equilibrium
cycle is 112 MWd/kgHM.
4.8 Nonproliferation Materials Attractiveness
. ...
.....
........
.........
.
.....
...
....
....
...
. .....
......
..
.....
..
..
......
..
..........
..
......
..
....
...........
. ...
....
.....
...
10
... ....
. ..
U
00
0-)
D110
.........
..
..........
.. .....
... ..... .... 7
............. ....
100
.............
.... ......
.
I .....
W 1 .......
...............
Gr6dor
10
10
2
. .....
. ..... ..
.
...............
...........
........
......
....
.....
...
...
.......
10-I
100
%Pu240
.......
.....
...
...
....
....
..
10
10
Figure 59. Proliferation materials attractiveness of the metal multicore TRU-SFR cores of various reloads, recycled using
the combined pyroprocessing/melt-and-recast strategy
The initial transition core, pyroprocessed from the USFR spent fuel, contains a plutonium vector
with 0.9% Pu-238 and 14.05% Pu-240, placing it in the middle of the "weapons usable" band of
the attractiveness function. After the first cycle in the TRU-SFR, the spent fuel contains 2.48%
Pu-238 and 24.95% Pu-240, placing it on the boundary of the "weapons usable" band. After the
first and second reloads, the fuel converges to an equilibrium plutonium vector with 2.20% Pu238 and 29.3% Pu-240, slightly more attractive than the transition case yet still almost
"practically unusable." In all cases, the spent fuel from the TRU-SFR is significantly less
attractive from a proliferation perspective than the spent fuel from the USFR. Thus, transitioning
from the once-through USFR mode to the recycle TRU-SFR mode serves an important
nonproliferation function, providing additional justification for moving to the recycle mode
rapidly.
92
~
Pradc
.
.. ........
0
10
10
10
10
%Pu240
10
10
Figure 60. Proliferation materials attractiveness of the metal uranium+ TRU-SFR cores of various reloads with the
optimized fuel volume fraction of 30.85%
The materials attractiveness of the uranium± cores more closely resembles that of the carbide
cores than the multicore metal cores. The plutonium vector after the transition cycle consists of
1.88% Pu-238 and 21.43% Pu-240. The vector then converges to its equilibrium values of
2.44% Pu-238 and 28.03% Pu-240 after the second reload. Compare this to the equilibrium
values of the uranium+ carbide core, which has 2.33% Pu-238 and 28.60% Pu-240, making these
two core configurations roughly equivalent in terms of proliferation materials attractiveness.
These values are also equivalently attractive as those of the multicore metal core, which has less
Pu-238 (2.20% vs. 2.33%) but more Pu-240 (29.33% vs. 28.60%). Ultimately, the choice of fuel
type (carbide vs. metal) and reprocessing strategy (multicore vs. uranium+) has little impact on
the degree of proliferation attractiveness of the TRU-SFR spent fuel. All configurations make
the plutonium vector significantly less attractive than the USFR spent fuel, serving as additional
motivation for moving to the fuel recycle mode sooner rather than later.
4.9 Safety Characteristics
4.9.1 Sodium Void Coefficient
The sodium void coefficients of reactivity were evaluated for the metal cores transitioned using
the multicore and the uranium+ strategies. The results for the metal multicore core using the
melt-and-recast strategy are displayed in Table 20.
93
Table 20. Sodium void coefficients of reactivity for the transition and equilibrium multicore metal cores with melt-and-
recast
Transition
BOC
Sodium void
Transition @ Transition Equilibrium
BOC
EOC
MNR
Equilibrium
@ MNR
Equilibrium
EOC
0.0369
0.0220
0.0175
0.0615
0.0276
0.0221
1.2596
0.7235
0.5571
5.1389
1.5688
0.9877
worth ($/%void)
Maximum void
worth ($)
The sodium void coefficient of reactivity begins at 0.0369 $/% void, decreasing to 0.022 $/%
void at the fluence-limited burnup of 115 MWd/kgHM. After the fuel is melted and recast, the
sodium void coefficient of reactivity decreases to 0.0175 $/% void at the reactivity-limited
burnup. The maximum void worths decrease accordingly with burnup, beginning at $1.26 and
decreasing to $0.724 at the melt-and-recast point and even to $0.557 at the reactivity-limited
burnup (EOC). The equilibrium core has a greatly increased void coefficient of reactivity at
BOC, beginning at 0.0615 $/% void, almost double that of the
transition core, decreasing to
0.0276 $/% void at the melt-and-recast limit, and further decreasing to 0.0221 at the reactivitylimited burnup. The maximum void worths follow a corresponding trend, beginning at $5.14
and decreasing to $1.57 at the MNR point and to $0.988 at the reactivity-limited burnup.
Table 21. Sodium void coefficients of reactivity for the transition and equilibrium uranium+ metal cores with a fuel
volume fraction of 30.85%
Transition Transition Equilibrium Equilibrium
Sodium void worth
BOC
EOC
BOC
EOC
0.0371
0.0203
0.0607
0.0260
($/%void)
Maximum void
worth ($)
2.7272
I
0.8078
I
4.9732
I
1.1168
I
The uranium+ metal cores behave similarly to those of the multicore metal cores. The sodium
void coefficient of reactivity begins at 0.0371 $/% void and decreases to 0.0203 $/% void for the
transition case. The equilibrium case, due to the increased plutonium content, has more positive
sodium void coefficients, beginning at 0.0607 $/% void and decreasing to 0.026 $/% void at
EOC. The maximum void worths of the transition core begin at $2.73 and decrease to $0.808 at
EOC. The maximum void worths of the equilibrium cycle begin at nearly double that of the
transition cycle, starting at $4.97 and decreasing to $1.12 at EOC.
While the maximum sodium void worths of the metal cores ($5.14 for the multicore case and
$4.97 for the uranium+ case) are greater than those of the carbide cores ($2.81 for the multicore
case and $2.86 for the uranium+ case), they are still similar to those of other commercial-sized
metal fuel fast spectrum reactors. The ALMR, which was similar to the design of the IFR and
the S-PRISM fast reactors, had a maximum void worth of $6.5. Thus, though the carbide cores
have less positive sodium void worths, the metal cores are still within acceptable limits.
94
4.9.2 Shutdown Margin
The shutdown margin of the metal cores was investigated for both the multicore (with melt-andrecast) and uranium+ transition strategies. The multicore case with the greatest reactivity was
the transition cycle, so this cycle was the focus of the shutdown analysis. The results for the
transition multicore case are presented in Figure 61.
20000
15000
10000
0
-o-ARO
-
-- w-ARI, Cool
----
-
5000
0.
50
-
100
150
200
250
300
350
-5000
-10000
-15000
BOC Shutdown Margin: +6370 pcm (+6830 pcm w/o max rod)
ARho of 8,740 pcm
Average rod worth: $1.10/rod (0.460 %Ak/k)
-20000
Average Discharge Burnup (MWd/kgHM)
Figure 61. Shutdown margin of the transition multicore metal core
Similar to the multicore carbide core, the multicore metal core is unable to go subcritical with the
standard control assembly configuration. The reactivity of the core with all rods in is 6370 pcm,
which increases to 6870 pcm with the highest-worth rod out. The total change in reactivity with
all rods inserted is 8,740 pcm, for an average rod worth of 0.460% Ak/k. This rod worth is
similar to that of the oxide-fueled BN-800 (0.42% Ak/k) and less than that of the metal-fueled
ALMR (0.76% Ak/k). However, the positive shutdown reactivity is an issue which must be
resolved, and so the multicore case is not desirable unless other motivations deem acceptable the
added cost of modifying the control assembly system or implementing a multi-batch refueling
strategy.
95
10000
5000
-
-
50
E
-
-1-AR ICool
- - - - - - - - - - -- - - - -
100
150
0
250
300
350
400
450
-5000
CL-10000
-15000
-20000
-25000
-30000
-35000
BOC Shutdown Margin: -3569 pcm (-2970 w/o max rod)
ARho of -11,375 pcm
Average rod worth: $1.43/rod (0.599%Ak/k)
-40000
Average Discharge Burnup (MWd/kgHM)
Figure 62. Shutdown margin of the transition multicore metal core
The shutdown margin of the transition uranium-+ metal core with a fuel volume fraction of
30.85% was identified as the limiting scenario. With all rods inserted, the uranium+ metal core
successfully reached a shutdown condition with negative reactivity, achieving a shutdown
margin of -3569 pcm (-2970 pcm without the highest-worth rod). The total change in reactivity
with all rods inserted was -11,375 pcm, for an average rod worth of 0.599% Ak/k. This rod
worth is more than that of the uranium+ carbide core (0.447% Ak/k), but still less than that of the
ALMR metal core, which has an average rod worth of 0.76% Ak/k. Thus, the uranium+
transition strategy is preferable to the multicore strategy if minimizing changes to the core
configuration is a priority, regardless of whether carbide or metal fuel is employed.
4.10 Summary
The reactivity and burnup performance of the multicore and uranium+ metal cores was
evaluated. The multicore metal transition core achieved a fluence-limited burnup of 115
MWd/kgHM, with a reactivity-limited burnup of 247 MWd/kgHM, for a LFC of 7.49
mills/kWh. The reactivity-limited bumup of the metal multicore transition case is 41% greater
than that of the corresponding carbide multicore transition case, yet its fluence-limited burnup is
15% less. The harder spectrum of the metal fuel increases the cladding dpa per unit bumup,
resulting in poorer bumup performance and higher LFCs. The uranium+ metal transition core
reached a fluence-limited bumup of 90.0 MWd/kgHM, with a reactivity-limited bumup of 212
MWd/kgHM, for a LFC of 9.18 mills/kWh. The carbide uranium+ transition core's reactivitylimited burnup was 54% less, but its fluence-limited burnup was 24% greater.
The large
disparities in the metal cores' fluence-limited and reactivity-limited burnups, which resulted in
96
high LFCs, indicated that additional methods of softening the spectrum to increase the fluencelimited burnup and improve the economic performance were needed.
The first method of improving the fluence-limited burnup of the metal cores involved adding
various moderating materials to soften the spectrum and reduce the dpa per unit burnup. Adding
3% graphite to the system improved the fluence-limited burnup by 12%, but dropped the initial
reactivity of the core below zero, though this could possibly be overcome using some sort of
multi-batch fuel management scheme. Adding 5% SiC increased the fluence-limited burnup by
14%, with the initial reactivity dropping to approximately zero, and adding 5% MgO increased
the fluence-limited burnup by 13% but dropped the initial reactivity to less than that of the SiC.
The second method for improving the achievable burnup between full pyroprocessing reloads
was to run the transition core until the fluence limit was reached, at which point the fuel was not
reprocessed but rather simply melted down and recast with new cladding. This "melt-and-recast"
approach saved on recycling costs since melting the fuel was assumed to be half as expensive as
full pyroprocessing, which improves the fuel cycle cost. The LFC for this strategy came to 6.90
mills/kWh, 1.4% less than the nominal LWR LFC. However, issues with reactivity control limit
the cost effectiveness of this transition strategy.
The final means of improving the fluence-limited burnup was to reduce the metal fuel volume
fraction. By reducing the fuel volume fraction from the nominal 40% to 30.85% (at which point
the heavy metal mass of the metal core equaled that of the carbide core), more sodium was
introduced to the system which had an important spectrum softening effect. Additionally, fewer
kg of HM needed to be reprocessed for fabrication of the recycled assemblies, lowering fuel
cycle costs. The resulting fluence-limited burnup of the uranium-+ metal core with a fuel volume
fraction of 30.85% was 6.81 mills/kWh, 2.7% less than the nominal LWR LFC.
The impact of minor actinides on the initial reactivity and the fluence-limited burnups of the
metal cores was found to be minimal, similar to that of the carbide cores. Removing the minor
actinides from the nominal multicore metal transition core increased the initial reactivity by 240
pcm, and increased the fluence-limited burnup by only 0.1%. Removing the minor actinides
from the uranium+ transition metal core increased the initial reactivity by only 80 pcm and
decreased the fluence-limited burnup by 0.1%. Cooling the fuel before loading it, using the
uranium+ strategy with a fuel volume fraction of 30.85%, reduced the fluence-limited burnup by
only 0.98% in the transition cycle, and by only 4.29% for the equilibrium cycle.
The metal cores achieved acceptable nonproliferation performance, while safety results were
mixed. Transitioning from the once-through USFR mode to the recycle TRU-SFR mode reduced
the attractiveness of the plutonium in the fuel from "weapons usable" to "practically unusable."
The multicore metal core had issues with reactivity control for shutdown, being unable to reach a
subcritical configuration using the nominal control arrangement of the USFR with single-batch
refueling. The uranium+ metal core achieved a shutdown margin of -3570 pcm (-2970 without
97
the max-worth rod), with an average rod worth of 0.599% Ak/k. This compares favorably to the
average rod worth of the metal-fueled ALMR, whose rods were worth 0.88% Ak/k. The
uranium+ metal core has a maximum sodium void worth of $4.97, still less than the ALMR's
$6.5 total void worth.
Ultimately, the uranium+ metal core with a fuel volume fraction of 30.85% was identified as the
optimal metal-fuel transition strategy from the nominal carbide USFR core. It achieved
economic burnups with safe dynamic characteristics and adequate control.
98
5 Summary and Conclusions
5.1 Overview
Possible strategies for transition from a once-through, uranium-fueled sodium-cooled fast reactor
(the USFR) to a plutonium-fueled SFR in recycle mode (the TRU-SFR) were examined.
Strategies for transition from the nominal carbide USFR core to both carbide and metal TRUSFR cores were investigated. The general features of the USFR were preserved, in particular use
of a high-albedo reflector in place of a breeding blanket. The power distributions, reactivity
profiles, reactivity impacts of minor actinide removal and long term storage, economic
performances, breeding behavior, nonproliferation and safety characteristics were characterized.
This chapter presents a summary of the results obtained from these efforts.
5.2 Radial Power Distribution
The radial power distribution of the carbide and metal cores were both center-peaked, since the
nominal recycling scenario used only a single-batch reloading scheme with a uniform fissile
loading. The radial power profiles flattened with burnup as the fissile material in the center was
depleted more rapidly than on the outer regions. The metal cores experienced greater peak fast
fluxes (4.39E+15 n/s/cmA2 for the multicore case and 5.24E+15 n/s/cmA2 for the uranium+ case
at BOC) than the carbide cores (3.87E+15 n/s/cmA2 for the multicore and 4.52E+15 n/s/cmA2 for
the uranium+), since these metal cores have a harder spectrum. The uranium+ cores have higher
peak fluxes than the multicore cores due to decreased fissile loadings.
5.3 Reactivity Profile and Burnup Performance of Carbide and Metal
Cores
5.3.1 Nominal Cases
The nominal carbide and metal cores both had a fuel volume fraction of 40%. The carbide cores
had fuel with a density of 13.63 g/cc, with a heavy metal fraction (of fuel) of 0.952. The metal
cores had fuel with a density of 16.14 g/cc, with a heavy metal fraction of 0.9 (the rest of the fuel
alloy consisted of zirconium). Thus, for a fixed fuel volume fraction, the metal cores had a
higher total fissile loading.
The transition multicore carbide core reached a fluence-limited burnup of 136 MWd/kgHM, with
an initial reactivity of 8441 pcm and a reactivity-limited burnup of 176 MWd/kgHM. The
99
reactivity of the core increased after the first reload (again using the multicore strategy), resulting
in an initial reactivity of 14430 pcm, a fluence-limited bumup of 149 MWd/kgHM, and a
reactivity-limited burnup of 217 MWd/kgHM. The transition uranium+ carbide core began with
an initial reactivity of 1133 pcm and reached a fluence-limited burnup of 124 MWd/kgHM, with
a reactivity-limited burnup of 138 MWd/kgHM. The first reload of the TRU-SFR core achieved
a fluence-limited burnup of 124 MWd/kgHM, with an initial reactivity of 4590 pcm and a
reactivity-limited burnup of 173 MWd/kgHM.
The nominal metal cores generally experienced greater differences between their fluence-limited
and reactivity-limited values. The multicore metal transition core achieved a fluence-limited
burnup of 115 MWd/kgHM, with a reactivity-limited burnup of 247 MWd/kgHM, a significant
difference of 132 MWd/kgHM. The reactivity-limited burnup of the metal multicore transition
case (247 MWd/kgHM) is 41% greater than that of the corresponding carbide multicore
transition case (176 MWd/kgHM), yet its fluence-limited bumup is 15% less. The harder
spectrum of the metal fuel increases the cladding dpa per unit burnup, resulting in poorer
fluence-limited burnup performance. The uranium+ metal transition core reached a fluencelimited burnup of 90.0 MWd/kgHM with a reactivity-limited bumup of 212 MWd/kgHM, for a
difference of 122 MWd/kgHM. The carbide uranium+ transition core's reactivity-limited burnup
(138 MWd/kgHM) was 54% less, but its fluence-limited burnup (124 MWd/kgHM) was 24%
greater. The large disparities in the metal cores' fluence-limited and reactivity-limited burnups,
despite their greater fissile loading as compared to the carbide cores, indicate that additional
methods of softening the spectrum to increase the fluence-limited bumup are needed.
5.3.2 Metallic Core Burnup Improvement Methods
The first method of improving the fluence-limited bumup of the metal cores involved adding
various moderating materials to soften the spectrum and reduce the dpa per unit burnup. Adding
3% graphite to the system improved the fluence-limited burnup by 12%, but dropped the initial
reactivity of the core below zero, though this could possibly be overcome using some sort of
multi-batch fuel management scheme. Adding 5% SiC increased the fluence-limited burnup by
14%, with the initial reactivity dropping to approximately zero, and adding 5% MgO increased
the fluence-limited bumup by 13% but dropped the initial reactivity to less than that of the SiC.
Ultimately, adding moderator materials showed some promise for improving fluence-limited
burnups of the metal cores and reducing the gap between the fluence-limited and the reactivitylimited bumups. However, the optimal method of incorporating these materials into the
assemblies must be further investigated.
The second method for improving the achievable burnup between full pyroprocessing reloads
was to run the transition core until the fluence limit was reached, at which point the fuel was not
100
reprocessed but rather simply melted down and recast with new cladding. This "melt-and-recast"
approach saved on recycling costs since melting the fuel was assumed to be half as expensive as
full pyroprocessing, which improves the fuel cycle cost. However, issues with reactivity control
complicate this transition strategy, making multi-batch staggered reloads or modifications to the
control systems necessary.
The final means of improving the fluence-limited burnup was to reduce the metal fuel volume
fraction. By reducing the fuel volume fraction from the nominal 40% to 30.85% (at which point
the heavy metal mass of the metal core equaled that of the carbide core), more sodium was
introduced to the system which had an important spectrum softening effect. Additionally, fewer
kg of HM needed to be reprocessed for fabrication of the recycled assemblies, lowering fuel
cycle costs. The fluence-limited burnup of the equilibrium uranium+ metal core with the
optimized fuel volume fraction was only 10% less than that of the equilibrium carbide uranium+
core. Reducing the fuel volume fraction is the most straightforward method of improving the
fluence-limited burnup of the metal cores.
5.4 Reactivity Impact of Minor Actinide Removal and Long Term Storage
The impact on initial reactivity and fluence-limited burnup of removing minor actinides from the
recycled fuel during the reprocessing step was investigated. The initial reactivity of the
multicore carbide core increased by 4% but the fluence-limited burnup increased by only 0.3%.
The initial reactivity of the uranium+ carbide core increased 18% yet this translated into only a
0.1% increase in the fluence-limited burnup. The metal cores experienced similarly small
impacts when the minor actinides were removed during recycling. The metal multicore case's
initial reactivity increased only 1.6%, and the fluence-limited burnup increased negligibly
(0.1%). The metal uranium+ case experienced a 18% increase, yet the fluence-limited burnup
actually decreases negligibly (-0.1%). In all cases, it is clear that removing the minor actinides
during the reload process has minimal impact on the achievable reactivity of the reloaded core.
Thus, it is recommended to leave the minor actinides in the heavy metal so as to alleviate waste
management issues associated with their disposal, such as the long-lived nature of their decay
heat and dose from radioactive decay.
The impact of cooling the fuel in long-term storage was also investigated. To simulate the effect
of long-term cooling, all the Pu-241 (til/2=14. 4 years) present in the fuel discharged by the USFR
was assumed to have decayed into Am-241. The carbide multicore core experienced a drop in
initial reactivity of 9.5%, with a corresponding decrease in fluence-limited burnup of 1.3%. The
carbide uranium+ core experienced a decrease in initial reactivity of 77%, though the fluencelimited burnup decreased only 1.6%. The metal uranium+ core lost 59% of its initial reactivity,
though the fluence-limited burnup decreased only 1%. Ultimately, the total effect of long-term
101
storage on achievable bumup was minimal, and so the decision to move to the recycle mode
need not be driven by a desire to maintain the reactivity worth of the spent fuel generated by the
once-through USFR.
5.5 Economic Performance
In all cases, the levelized fuel cost of the recycle cores relative to each other was driven by the
achievable fluence-limited bumup of each. Their cost-competitiveness relative to the nominal
LWR once-through fuel cycle was driven by the balance of their increased front-end fuel costs
against their increased bumups and higher thermal efficiencies (42% vs. 33.7% for the LWR).
The multicore transition carbide core results in a levelized fuel cost of 6.41 mills/kWh, 8.4% less
than the 7.00 mills/kWh levelized fuel cost of the LWR. The reload multicore carbide case
obtained a levelized fuel cost of 5.98 mills/kWh, 14.6% less than the reference LWR cost. The
uranium+ transition carbide core achieved a levelized fuel cost of 7.17 mills/kWh, only 2.4%
more than the reference LWR LFC. The uranium+ carbide reload core's burnup results in a LFC
of 6.89 mills/kWh. The metal multicore transition core generates a LFC of 7.49 mills/kWh, and
its reload (with melt-and-recast) develops a LFC of 7.85 mills/kWh. The metal uranium+
transition core with an optimized fuel volume fraction of 30.85% obtains a LFC of 6.81
mills/kWh, with a LFC of 7.29 mills/kWh for the reload case.
Most of these cores managed to obtain LFCs within +10% of the reference LWR case,
suggesting that the optimal recycle strategy may not be driven by the fuel cycle economics but
by other factors, such as the cost of converting from the once-through mode to such a recycle
strategy, the safety performance of the recycle mode core, or the proliferation attractiveness of
the spent fuel generated by the recycle mode.
5.6 Fissile Material Ratios
The ratio of fissile material, at a given burnup, to the fissile material present at BOC was
calculated for the carbide and metal cores. Fissile material included U-233, U-235, Pu-239, and
Pu-241. The ratios were weighted by the reactivity worth of each fissile isotope, so that the
actual impact on the core's reactivity could be more accurately judged. This reactivity weighting
only impacted the final results by 2-3% compared to mass-only comparisons. The reactivityweighted fissile inventory ratio (FIR) of the carbide transition multicore core was 0.93 at EOC,
meaning that the core functioned as a slight burner of fissile material during this cycle. The
uranium+ carbide transition core had a FIR of 1.04 at EOC, so it functioned as a slight breeder
during this cycle. The metal multicore transition core had an EOC FIR of 0.90, and the
uranium+ metal transition core (with a fuel volume fraction of 30.85%) had an EOC FIR of 0.91.
102
The equilibrium cycle of this uranium+ case possessed a FIR of 1.0, meaning that it reached
steady-state conversion behavior. Generally, the multicore cores functioned as slight fissile
burners, and the uranium+ cores functioned in a fissile steady-state, with FIR's barely above or
approximately equal to one.
5.7 Nonproliferation Materials Attractiveness
The quality of plutonium generated by the TRU-SFR is of keen interest to the nonproliferation
community, as the quality of plutonium generated by fast reactors in the past has been assumed
to be very attractive to potential proliferators. The plutonium discharged by the USFR and
transitioned into the TRU-SFR was classified as "weapons usable" using Saito's methodology,
though it was still far from "weapon grade." It contained 0.9% Pu-238 and 14.05% Pu-240,
making it slightly more attractive than the plutonium generated by LWRs, which typically has
2.4% Pu-238 and 14.05% Pu-240. However, after a few cycles in the TRU-SFR, the plutonium
vector becomes significantly less attractive regardless of whether carbide or metal fuel was used,
or which transition strategy was employed. The equilibrium carbide multicore core had
plutonium with 2.81% Pu-238 and 29.73% Pu-240, making it "weapons unusable." The
equilibrium uranium+ carbide core had plutonium with 2.33% Pu-238 and 28.60% Pu-240,
placing it just inside the "weapons usable" band. The metal cores fared similarly, as the
plutonium in the equilibrium multicore metal core had 2.81% Pu-238 and 29.73% Pu-241,
placing it on the edge of the "weapons usable" band. The metal uranium+ equilibrium core had
2.44% Pu-238 and 28.03% Pu-240, making it also just inside the "weapons usable" region. In all
cases, the SFR spent fuel was the same or less attractive than LWR spent fuel.
5.8 Safety Characteristics
5.8.1 Sodium Void Coefficients
The sodium void coefficient of reactivity and the maximum sodium void worth were evaluated
for the carbide and metal cores to provide insight into their kinetic safety behavior. The carbide
cores performed significantly better than other ceramic (oxide) cores and the metal cores. The
multicore carbide transition core had a peak sodium void coefficient of reactivity of 0.0241 $/%
void, with a maximum void worth of $1.68, both at BOC. These values increased to 0.0357 $/%
void with a maximum worth of $2.81 for the equilibrium cycle at BOC. For the uranium+
multicore carbide transition core, the sodium void coefficient of reactivity was 0.0244 $/% void
with a maximum void worth of $1.67, both at BOC. These values increased to 0.0371 $/% void
and $2.86 for the equilibrium case, both at BOC. The maximum worth values obtained for the
103
carbide multicore and uranium+ cores were similar, and were improved relative to those of
commercial oxide-fueled SFR designs. France's Super-Phenix I had a maximum sodium void
worth of $5.9, and the UK's CDFR had a maximum worth of $5.7.
The metal cores performed more consistently with previous commercial fast reactor designs,
with higher sodium void coefficients and void worths than the carbide cores. The multicore
transition metal core had a sodium void coefficient of reactivity of 0.0369 $/% void, with a
maximum worth of $1.26. These values increased to 0.0615 $/% void and $5.14 for the
equilibrium cycle (using melt-and-recast). The uranium+ metal transition core obtained values
of 0.0371 $/% void and $2.73, which increased to 0.0607 $/% void and $4.97 for the equilibrium
cycle. Both the multicore and uranium+ cores compare favorably to the other large metal-fueled
commercial SFR, the US's ALMR, which has a maximum void worth of $6.5. Though the
carbide cores have approximately half the sodium void worth of other oxide and metal cores, the
metal cores analyzed here still achieve acceptable performance consistent with previous SFR
designs.
5.8.2 Shutdown Margin
The single-batch-loaded multicore cores, both carbide and metal, have significantly greater
initial reactivity than do the uranium+ cores, which leads to complications with reactivity
control. The carbide multicore equilibrium core (the limiting case) cannot reach a subcritical
configuration with the nominal control configuration inherited from the USFR (19 control rods,
60% enriched B-10) and single batch reloading, as its initial reactivity is 14432 pcm and the
reactivity change with all rods inserted is -7453 pcm, for a shutdown reactivity of +6973 pcm.
The average rod worth of the carbide core was slightly above $1 ($1.13 per rod, 0.392% Ak/k),
but was similar to that of the oxide-fueled Super-Phenix I (0.40% Ak/k) and BN-800 (0.42%
Ak/k). The multicore metal core had an initial reactivity of 15110 pcm, and inserting all the
control rods decreased the reactivity by 8,740 pcm to +6370 pcm. The average rod worth of the
metal multicore core was $1.10 (0.460% Ak/k) per rod, greater than that of the carbide core
(0.392% Ak/k) but similar to that of the BN-800 (0.42% Ak/k). Though these shutdown margin
issues could be alleviated via the addition of control assemblies to the core or by employing a
multi-batch reloading scheme, these strategies would add to the complexity of the transition
process and would require additional analysis.
The uranium+ cores, on the other hand, experienced no such issue with reactivity control using
the nominal control configuration and single-batch refueling. The carbide equilibrium core (the
limiting case) began with a reactivity of 4590 pem, dropping 8502 pcm to -3913 pcm with all
rods inserted (-3466 pcm without the maximum-worth rod inserted). The average rod worth of
the carbide uranium+ core was $1.23 per rod (0.447% Ak/k), which was comparable to that of
104
the carbide multicore core (0.392% Ak/k) and to the Super-Phenix I (0.40% Ak/k) and BN-800
(0.42% Ak/k). The metal transition core began with a reactivity of 7806 pcm, which decreased
by 11,375 pcm to -3570 pcm with all rods inserted (-2970 pcm without the maximum-worth
rod). Its average rod worth was $1.43 (0.460% Ak/k) per rod, still less than the comparable
metal-fueled ALMR, which has an average rod worth of 0.76% Ak/k. These cores are more
straightforward to transition from the once-through USFR mode than are the multicore cores,
requiring no changes to the nominal reactivity control systems and possessing the capacity to do
single-batch refueling.
5.9 Summary
A range of options for transitioning the once-through, uranium-fueled USFR to the plutoniumfueled, recycle mode TRU-SFR were identified. The carbide cores achieved higher fluencelimited burnups than the metal cores, and had smaller deficits between these fluence-limited
burnups and their reactivity-limited burnups. The metal cores were able to approach the burnups
of the carbide cores via the introduction of moderating materials, the use of the melt-and-recast
strategy, and decreasing the fuel volume fraction. Decreasing the fuel volume fraction was
found to be the most effective, straightforward method. The fluence-limited burnup of all the
cores experienced little perturbation from the removal of minor actinides during fuel
reprocessing, so it is recommended that they remain in the recycled fuel for improved waste
management. Similarly, long-term storage of the fuel had little effect on the achievable fluencelimited burnup of any core, such that the decision to reprocess need not be driven by a desire to
maximize the reactivity of the spent fuel stockpile.
The multicore cores (both carbide and metal) functioned as slight burners of fissile material, and
the uranium+ cores functioned essentially at a fissile steady-state. All TRU-SFR cores generated
plutonium that was less attractive than that discharged by the USFR, and was comparable to that
of current LWRs. The carbide cores had sodium void worths that were roughly half that of the
metal cores, which had worths consistent with those of previous SFR designs. Shutdown
margins of the multicore cores (carbide and metal) were positive, absent the addition of
additional control assemblies or the introduction of multi-batch staggered reloading. The
uranium+ cores had comfortable shutdown margins. The average rod worths were acceptable for
all cases. In short, all cores achieved varying degrees of success at transitioning from the oncethrough mode to the recycle mode.
Future focus should be on the uranium+ metal core with an optimized fuel volume fraction
(30.85% in this case). Metal is preferable to carbide because the knowledge base and
development level is significantly higher. Uranium+ is preferable to the multicore strategy
because it allows for a self-sustaining equilibrium cycle (with a small amount of natural uranium
105
added), the excess reactivity is more easily manageable, and its fuel cycle cost is still comparable
to that of the reference LWR. If, in the future, the motivation exists to move to a conventional
uranium-blanket breeder, the multicore strategy may be employed at that time to increase the
initial reactivity to compensate for the increased leakage.
106
6 Recommendations for Future Work
6.1 Reactivity Control Improvements
Safe and effective reactivity control is essential for any nuclear reactor. This study of the TRUSFR has characterized the control capabilities possible using the nominal configuration of
control assemblies inherited from the USFR, which has 19 B4 C control assemblies at 60% B-10
enrichment. However, this control system is not capable of attaining acceptable shutdown
margin if the multicore recycle strategy is employed with single-batch refueling. Concurrent
with investigation into multi-batch reloading, investigations into adding control assemblies or rearranging the assemblies is recommended. The creation of two separate banks of control
assemblies, one for reactivity adjustments during normal operation and another for ultimate
shutdown capability, should be explored.
To prevent reactivity insertion accidents, it is desired to limit the average control assembly worth
to less than $1, such that the system can avoid going prompt critical if one rod is removed.
Limiting the control assembly worth is also desirable for minimizing local peaking and
preventing excessively large flux variations with control assembly movement. Though the
present analysis achieved average rod worths similar to those of previous commercial fast reactor
designs, it may be desirable to improve the resiliency further than has previously been achieved.
Thus, when investigating methods to improve the shutdown margin of the TRU-SFR, effort
should be made to reduce the average rod worth below $1. In view of the underdeveloped status
of UC fuel, it is recommended that future work focus on metal fueling, e.g. of the IFR type.
6.2 Advanced Fuel Management Schemes
Loading the core in multiple batches with staggered reloading is an effective way to reduce the
initial reactivity of the core and increase the reactivity-limited burnup. However, this reloading
system adds complexity to the refueling schedule and the refueling process. Core design should
be performed to evaluate the optimal loading pattern of fresh and burned assemblies, and the
optimal number of batches should be evaluated to balance a high capacity factor with the desired
decrease in initial reactivity. The impact of multi-batch refueling on cladding dpa and fluence
should be evaluated to determine whether these still limit the achievable discharge burnup.
107
6.3 Conversion to a Conventional Breeder with Uranium Blankets
The current USFR and TRU-SFR operate with fissile inventory ratios near unity, allowing for a
steady-state equilibrium cycle to be maintained but no additional fissile inventory to be
generated. If it becomes necessary or desirable to increase the fissile production of the system, a
switch to a more conventional breeder reactor with a uranium blanket in place of the high-albedo
reflector will need to be made. The reactivity and burnup performance of this transitional core
configuration must then be evaluated, including the required increase in fissile loading to account
for the additional leakage to the blanket. The resulting equilibrium cycle should be
characterized, including the desired recycle strategy, whether uranium+ or multicore. Fissile
material ratios should be calculated for both the core and the surrounding blanket. The safety
parameters such as sodium void worth and shutdown margin should be reevaluated. At present
there appears to be no obvious difficulties in transforming the cores evaluated in this thesis into
conventional breeder mode-e.g. as discussed by Till and Chang.
108
Acknowledgements
The author is thankful for the financial support provided for this research by the multi-sponsored
MIT study on "The Future of the Nuclear Fuel Cycle." The author also wishes to thank the
National Nuclear Security Administration's Office of Nonproliferation and International Security
for the financial support provided for this research as part of the Next Generation Safeguards
Initiative's Nuclear Nonproliferation and International Safeguards Graduate Fellowship Program.
The author is thankful for the patient and understanding support of the project provided by his
advisor, Professor Emeritus Michael Driscoll, and his thesis reader and mentor, Professor Mujid
Kazimi. Their kindness in helping the author to obtain and understand the results of the research
were greatly appreciated, and their expeditious yet thorough and constructive review of his thesis
was greatly valued.
The author also wishes to thank his father, Jonathan Richard, and mother, Marietta Richard, for
their unwavering love and support as he worked to complete the research and write the thesis.
His brother, William Richard, is greatly appreciated for the brotherly love and encouragement he
provided throughout the project. The author would like to thank his friends Dave Chauncey,
Aaron Shoemaker, Mark Mayleben, and Erik Yeary for their steadfast friendship and his friends
from his community groups at CoaH who supported him as he worked to complete his Master's
degree. The author also wishes to extend the deepest thanks and praise to the Author of all, his
Savior, Jesus Christ, for his redeeming grace and mercy in all of life, and especially for the
successful completion of this degree. To Him be the glory, forever and ever. Amen!
109
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111
Appendix A: Sample ERANOS 3D-Variational Nodal Transport Input
# include "BUcalculation.proc"
# include "fluxcalculation.proc"
# include "outputananlysis.proc"
# include "core_description.proc"
!# include "core_descriptionNaplenum.proc"
# include "ecco cellsdescription.proc"
!# include "NAKeccocells description.proc"
!# include "ecco_cellsdescriptionGPN.proc" ! reference calculation with Gas plenum
!# include "eccocellsdescriptionNaplenum.proc"
!# include "NAKeccocells descriptionNaplenum.proc"
!*******************STEEL WHILE LINA WORKS ON IT***********
->TESTEDREFLECTORMATERIALS
MATERIAUSIMPLE 'RADREFLTEST' STRUCTURE
FORMULEMOLECULAIRE 3.581 ! 3.581 (Theoretical density without porocity)
ELEMENT CIA 1.00
'Mg24' 78.99
'Mg25' 10.00
'Mg26' 11.01
ELEMENT CIA 1.0
'016' 100.00
DILATATION (EXPSTRU)
MATERIAUSIMPLE 'AXREFLTEST' STRUCTURE
FORMULEMOLECULAIRE 3.581
ELEMENT CIA 1.00
'Mg24' 78.99
'Mg25' 10.00
'Mg26' 11.01
ELEMENT CIA 1.0
'016' 100.00
DILATATION (EXPSTRU)
will be modified only in Na plenum calculations
112
SIMPLEMATERIAL 'PLNCOMP' ABSORBER
MOLECULARFORMULA 2.51981
ELEMENT CIA 4.00 ! CIA: Atomic porcentage for each isotopes
'B1O' 20.0
'BIl' 80.0
CORPS 'CO' 1.0
EXPANSION (EXPSTRU)
I*******************STEEL
WHILE LINA WORKS ON IT********
!*******************TO MODIFY***************************
->NAINFRACTION 11.4;! in the bound (won't be voided)
->FUELFRACTION 40.0; ! Use of Inverted Fuel (Ting)
->HT9_FRACTION 25.7;
->NAOUTFRACTION 22.9; ! in the coolant (will be voided)
->MEANENRICHMENT 11.6199;
->FUELUSED 'U235'; ! 'UPU' or 'U235'
!*******************TO MODIFY***************************
->PASSE (300);
->ITER 16.;
->NG 33 ;
->TYPE GEO '3D'; ! for fluence calculation need to be 3D
->TRANSPORT 'YES';
->PTH 2.4E9 ;
->EXPENSIONCORE 'NO';
->ADJOINT 'NO' ;
->ZINT 1 150 40 80;
->MASS 40335; ! totale mass of HM in the REFERENCE core (used for BU calculation)
!->MASS 45600; ! totale mass of HM in the TID core (used for BU calculation)
!->MASS 53010.1 ; !total mass of HM for 9.9% enriched TID core with corrected El input
->PERT _NB 1 ; ! number of the perturbation, for the archives
->PERTITER 9 ; !nb of iteration of PASSE efpd before PERT calc
->DNAPERT 0.85 ; ! sodium density g/cm3
113
->TFUELPERT 1030; ! Tfuel celcius
!PERTURBATIONCALCULATION ; ! if we do this, then we can't do
! the first ECCOSTDCALCULATION
->T3MEDITION 'YES';
COREEVOLUTIONCALCULATION;
MATERIALRESULTSEVOLUTION;
->RADTRZR 0.5 ;
->RAD_T_3DXYMIN 30 30;
->RAD_T_3DXYMAX 30 16;
->RADTZ 151 ;
->AX_T_3DXY 33 23;
->RADTRZRMIN 0.0;
->RAD_T_RZRMAX 210.0;
->AX_T_Z_MIN 100.0;
->AX_T_Z_MAX 202.0;
-> ITER 3 ;
TRAVERSEXY;
-> ITER 6 ;
TRAVERSEXY;
-> ITER 9 ;
TRAVERSEXY;
* DAY;
*MBUP;
*
'Mean BU in MWd/HMKg';
*RHOV;
*DPAC;
Fin;
114
Appendix B: Sample ERANOS RZ-Diffusion Input
# include "BUcalculation.proc"
# include "flux calculation.proc"
# include "output ananlysis.proc"
# include "core_description.proc"
!# include "core_descriptionNaplenum.proc"
# include "ecco cellsdescription.proc"
!# include "NAKeccocells description.proc"
!# include "ecco_cellsdescriptionGPN.proc" ! reference calculation with Gas plenum
! include "eccocellsdescriptionNaplenum.proc"
!# include "NAKeccocells descriptionNaplenum.proc"
!*******************STEEL WHILE LINA WORKS ON IT***********
->TESTEDREFLECTORMATERIALS
MATERIAUSIMPLE 'RADREFLTEST' STRUCTURE
FORMULEMOLECULAIRE 3.581 ! 3.581 (Theoretical density without porocity)
ELEMENT CIP 1.00
'Mg24' 78.99
'Mg25' 10.00
'Mg26' 11.01
ELEMENT CIP 1.0
'016' 100.00
DILATATION (EXPSTRU)
MATERIAU_SIMPLE 'AXREFLTEST' STRUCTURE
FORMULEMOLECULAIRE 3.581
ELEMENT CIP 1.00
'Mg24' 78.99
'Mg25' 10.00
'Mg26' 11.01
ELEMENT CIP 1.0
'016' 100.00
DILATATION (EXPSTRU)
will be modified only in Na plenum calculations
115
SIMPLEMATERIAL 'PLNCOMP' ABSORBER
MOLECULARFORMULA 2.51981
ELEMENT CIA 4.00 ! CIA: Atomic porcentage for each isotopes
'B10' 20.0
'B11' 80.0
CORPS 'CO' 1.0
EXPANSION (EXPSTRU)
!*******************STEEL
WHILE LINA WORKS ON IT********
!*******************T0 MODIFY***************************
->NAINFRACTION 11.4;! in the bound (won't be voided)
->FUELFRACTION 40.0; ! Use of Inverted Fuel (Ting)
->HT9_FRACTION 25.7;
->NAOUTFRACTION 22.9; ! in the coolant (will be voided)
->MEANENRICHMENT 11.6199;
->FUELUSED 'U235'; ! 'UPU' or 'U235' ***Modified fuel composition in e-c_d.proc (JOSH)
!*******************T0 MODIFY***************************
->PASSE (300);
->ITER 16;
->NG 33 ;
->TYPEGEO 'RZ'; ! for fluence calculation need to be 3D
->TRANSPORT 'NO';
->PTH 2.4E9 ;
->EXPENSIONCORE 'NO';
->ADJOINT 'NO' ;
->ZINT 1 150 40 80;
->MASS
(Changed
!->MASS
!->MASS
40335 ; ! totale mass of HM in the REFERENCE core (used for BU calculation)
from 37025) (JOSH)
45600 ; ! totale mass of HM in the TID core (used for BU calculation)
53010.1 ; !total mass of HM for 9.9% enriched TID core with corrected El input
->PERTNB 1 ; ! number of the perturbation, for the archives
->PERTITER 9 ; !nb of iteration of PASSE efpd before PERT calc
116
->DNAPERT 0.75 ; ! sodium density g/cm3
->TFUELPERT 1030; ! Tfuel celcius
!PERTURBATIONCALCULATION; if we do this, then we can't do
! the first ECCOSTDCALCULATION
->T3MEDITION 'YES';
COREEVOLUTIONCALCULATION;
MATERIALRESULTSEVOLUTION;
->RAD_T_RZR 0.5;
->RAD_T_3D_XYMIN 30 30;
->RADT_3DXYMAX 30 16;
->RADTZ 151 ;
->AX_T_3DXY 33 23;
->RAD_T_RZRMIN 0.0;
->RAD_T_RZRMAX 210.0;
->AXTZ MIN 100.0;
->AX_T_Z_MAX 202.0;
ARCHIVE 'ARCHDON' ->EDLMEDIUM MEDIUM STANDARD;
ARCHIVE 'ARCHDON' ->PDLMICRO MICRO STANDARD;
ARCHIVE 'ARCHDON' ->EDLCHAINE CHAINE EVOLUTION;
ARCHIVE 'ARCH3DEVOL' -> EDLCORE EDLCORE;
ARCHIVE 'ARCH3DEVOL' -> EDLGEOMETRY EDLGEOMETRY;
->VAR 0;
->SUFFD ('FLXD'/CAR(VAR));
->SUFFC ('CONC'/CAR(VAR));
ARCHIVE 'ARCH3DEVOL' ->EDLCONCENTRATION ('STD_'/SUFFC);
ARCHIVE 'ARCH3DEVOL' -> EDLFLUX
-> BEFFITER (VAR);
(SUFFD);
BEFFCALCULATION;
->ITER3;
TRAVERSEXY;
117
-> ITER 6 ;
TRAVERSEXY;
-> ITER 9 ;
TRAVERSEXY;
* DAY;
*MBUP;
*
'Mean BU in MWd/HMKg';
*RHOV;
Fin;
118