NUCLEAR ENERGY RESEARCH INITIATIVE (NERI)
SUMMARY REPORT
FEASIBILITY OF RECYCLING PLUTONIUM AND MINOR ACTINIDES
IN LIGHT WATER REACTORS USING HYDRIDE FUEL
Grant No. DE-FC07-06ID14736
NERI Project No. 2006-065
March 2006 through December 2008
Submitted by:
Lead Organization:
University of California, Berkeley
Ehud Greenspan
Collaborating Organizations:
Massachusetts Institute of Technology
Neil Todreas
Argonne National Laboratory
Temitope Taiwo
Submitted on:
March 10, 2009
Participating Organizations and Researchers
E. Greenspan (PI), F. Ganda, M. Fratoni, D. Olander, K. Terrani and M. Balooch
Department of Nuclear Engineering
University of California
Berkeley, CA 94720
gehud@nuc.berkeley.edu
N. Todreas (co-PI), P. Ferroni
Department of Nuclear Engineering
Massachusetts Institute of Technology
Cambridge, MA 02139
todreas@mit.edu
T. Taiwo(co-PI)
Argonne National Laboratory
9700 S. Cass Ave., Argonne, IL 60439
taiwo@anl.gov
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ACKNOWLEDGMENT
This report is based upon work supported by the U S. Department of Energy under Award
No. DE-FC07-06ID14736
DISCLAIMER
Any opinions, findings, and conclusions or recommendations expressed in this material are those
of the author(s) and do not necessarily reflect the views of the Department of Energy.
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Table of Contents
Executive summary
1
1. Introduction
7
1.1 About use of hydride fuels in LWR’s
7
1.2 Hydride fuels considered
7
1.3 Study objectives
9
1.4 Scope of work
10
1.5 References
10
2. Neutronic Analysis
13
2.1 Introduction
13
2.1 Benchmark our Fuel Assembly Computational Capability
15
2.3 Database establishment: identification of promising PWR fuel
assembly designs and comparison with equivalent hydrides
26
2.4 Identification of the most promising hydride fuels (fertile free, thoriumand uranium-based) for Pu multi-recycling
34
2.5 Pu+Np and “all TRu” multi-recycling in PWR using hydride fuels
54
2.6 Comparisons of hydride fueled systems
61
2.7 System analysis
64
2.8 Conclusion
72
2.9 References
75
3. Thermal hydraulic analysis
77
3.1: objectives of the thermal hydraulic analysis
77
3.2: reference plant
78
3.3: fuel physical property database
80
3.4: steady-state analysis
82
3.5: Large Break Loss Of Coolant Accident (LBLOCA) analysis
88
3.6: Main Steam Line Break (MSLB) analysis
100
3.7: Complete Loss Of Coolant Accident (CLOFA) analysis
120
3.8: conclusions
130
Appendix: the inverted core design
131
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4. Materials Analysis
140
4.1: Objectives of the materials analysis
140
4.2: Fabrication and characterization of uranium thorium zirconium hydrides 141
4.3: Transient hydride fuel behavior in LWRs
154
4.4: Kinetics of hydrogen desorption from zirconium hydride
171
4.5: Zircaloy cladding compatibility with hydride fuel
184
4.6: Oxidation behavior of hydride fuel in high temperature steam
185
4.7: Irradiation plans for liquid metal bonded hydride fuel rod
186
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Executive Summary
The objective of this DOE NERI program sponsored project was to assess the feasibility of
improving the plutonium (Pu) and minor actinide (MA) recycling capabilities of pressurized
water reactors (PWRs) by using hydride instead of oxide fuels. There are four general parts to
this assessment:
1) Identifying promising hydride fuel assembly designs for recycling Pu and MAs in PWRs
2) Performing a comprehensive systems analysis that compares the fuel cycle characteristics
of Pu and MA recycling in PWRs using the promising hydride fuel assembly designs
identified in Part 1 versus using oxide fuel assembly designs
3) Conducting a thermal-hydraulic and safety analysis to evaluate the power attainable from
hydride fuelled cores and assess the likelihood of licensing hydride fuel assembly designs
4) Assessing the compatibility of hydride fuel with cladding materials and water under
typical PWR operating conditions
Following is a summary of the work performed and of the results obtained
Neutronics
A Pu-containing hydride fuel (PuH2-U-ZrH1.6 with 45 weight % U) assembly design (referred to
as PUZH) was compared with two oxide fuel assembly designs that were proposed to overcome
the positive void coefficient of reactivity – CORAIL and MOX-UE. The CORAIL design offers
~30% natural uranium and Separating Working Unit (SWU) saving over conventional UO2
fuelled cores, but it provides for Pu stabilization rather than net destruction (a complete Pu
drawdown from the YMR would require ~300 CORAIL cores, three times the current LWR
fleet). It was found that a PWR loaded with these PUZH fuel assemblies will incinerate in the
first recycle twice as much TRU (primarily Pu) as it will do when loaded with MOX fuel
assemblies when both core designs are loaded with same amount of TRU and operate at the same
power level for the same time. This PUZH core will also be less expensive, since it uses depleted
uranium versus significantly larger quantities of enriched uranium required for the equivalent
MOX-UE core. Additionally, the PUZH fuel design has a lower power peaking factor than the
MOX-UE and, particularly, CORAIL fuel assemblies.
An assessment of the feasibility of enhancing the fractional plutonium destruction using hydride
fuels with varying amounts of thorium and uranium was undertaken as well. These fuels are of
the form ThH2-ZrH1.6-PuH2 and U-ZrH1.6-PuH2. It was found that the fertile free hydride fuel (of
the form PuH2-ZrH1.6), while offering the higher TRU destruction fraction of all the systems
analyzed, also allows multi-recycling of Pu in PWRs an unlimited number of times when
uniformly loaded in all fuel assemblies in the core. This unique feature of hydride fuels is due to
the incorporation of a significant fraction of the hydrogen moderator in the fuel, thereby reducing
the effect of spectrum hardening due to coolant voiding accidents; the large void reactivity
coefficient remains negative. The fractional transmutation of PuH2-ZrH1.6 was found 64% at the
first recycle and gradually decreases to about 20% towards the equilibrium recycle. The Fuel
Temperature Coefficient of Reactivity (FTC) was found positive in the third batch of the first
1
recycle of PuH2-ZrH1.6 fuel. However, addition of relatively small amount of either depleted U or
Th or using hydride fuel with D instead of H for the first recycle only can alleviate this problem.
An inert-matrix oxide fuel – PuO2-ZrO2, counterpart to the inert matrix hydride fuel PuH2-ZrH1.6
was investigated as well. Although the TRU destruction fraction at first recycle is almost as high
as that of PuH2-ZrH1.6 fuel, the maximum possible number of recycles of the oxide fuel is
limited, by positive reactivity effect of large core voiding, to 10 despite of the fact that the
leakage effect due to large core voiding was found significantly larger for oxide as compared to
hydride fueled cores.
The feasibility of recycling Pu+MA in hydride fuels was also assessed. It was found that hydride
fuels allow multi recycling of Pu+Np at least 6 times, before getting a positive large void
reactivity feedback. This corresponds to approximately 86 years of recycling campaign. A
number of approaches where investigated for making the large voiding reactivity coefficients of
NpH2-PuH2-ZrH1.6 fuelled cores negative beyond the 6th recycle. The most effective approach
identified is enlarging the fuel rod radius while conserving the lattice pitch. This approach might,
however, penalize the maximum attainable power unless an increase in the coolant pressure drop
across the core is allowed. It was also found that if it is desired to recycle all the TRU in PWRs
using hydride fuel, the number of possible recycles is limited to 3; the limit is imposed by a
positive large void reactivity feedback.
A preliminary system analysis was performed to compare the fuel cycle characteristics of Pu
multi-recycling in PWRs using the PuH2-ZrH1.6 hydride fuel assembly design versus Pu
recycling in PWRs using several of the promising oxide fuel assemblies. If desired to transmute
plutonium in a 2-tier system (i.e. recycle once in thermal reactors for Pu inventory reduction and
subsequently recycle all the leftover TRU in fast reactors), the number of cores required for
single recycling of the entire Pu inventory originally planned to be disposed of at the YMR
would be ~70 for conventional MOX fuel versus ~100 in case of inert matrix hydride or oxide
fuel. However, the inert matrixes would provide the greatest inventory reduction in one pass
leaving only 30% of the loaded plutonium inventory while the conventional MOX would leave
77% of the initial plutonium mass. Inert matrixes would also leave a substantially more
proliferation resistant discharged stream. Between oxide and hydride inert matrixes, it was found
that hydride leaves a more proliferation resistant discharged stream while no substantial
difference in other characteristics was observed. It is also noted that inert matrixes are most
likely the cheapest Pu recycling options, since they allow reaching the desirable cycle length in
PWRs with a smaller Pu loading, thereby providing the largest amount of electricity generated
per unit of reprocessed LWR spent fuel. Using CORAIL fuel assemblies is not a practical option
for the purpose of using all the Pu inventory originally planned for storage at the YMR; ~300
CORAIL cores would be required for this purpose.
Another system analysis performed is an evaluation of the repository impact of Pu multirecycling in different fuel types. The following characteristics, normalized per ton of Pu
transmuted and measured at the end of the transmutation campaign, were intercompared: (1) total
radioactivity of the TRU stream; (2) total neutron emission; (3) total decay heat; (4) total gamma
decay heat; (5) total toxicity in air; (6) total toxicity in water; and (7) total mass of 237Np and its
precursors (i.e. 241Am and 245Cm). It was found that all these measures of repository impact,
except for the mass of neptunium and its precursors, are slightly higher for PuO2-ZrO2 than for
PuH2-ZrH1.6 fuel. It was also observed that the radioactivity is higher for larger number of cores
2
operating in parallel for a smaller number of recycles, while all the other measures decrease with
the use of larger number of parallel cores.
The proliferation resistance was evaluated through the estimate of the following parameters
(normalized per ton of Pu transmuted) at the reprocessing plant: (1) total inventory of plutonium
to be handled at the reprocessing plant; (2) Pu fissile fraction; (3) neutron emission per gram of
plutonium and TRU; (4) specific decay heat for Pu and TRU. The total inventory of plutonium to
be handled in the reprocessing plant is quite similar in the case of PuO2-ZrO2 and PuH2-ZrH1.6.
However, the plutonium fissile fraction at the reprocessing facility, as well as the neutron
emission per gram of plutonium, shows that the PuH2-ZrH1.6 stream appears more proliferation
resistant than that of PuO2-ZrO2 for the first 9-10 recycles. The neutron emission per gram of
TRU and the specific decay heat are similar for the two fuel types. It is concluded that multirecycling in PuH2-ZrH1.6 is more resistant to proliferation than multi-recycling in PuO2-ZrO2.
Based on costs estimates for fuel fabrication, reprocessing and fuel and waste disposal, it was
found that the final cost of PuH2-ZrH1.6 would only be ~1.2% lower than that of PuO2-ZrO2, not
enough to justify the choice of this fuel based on this cost.
Another analysis performed compared a couple of systems at equilibrium: (1) A fleet of enriched
uranium fuelled PWRs operating in the once-through fuel cycle supported by a smaller fleet of
PWRs operating with Pu-recycling PuH2-ZrH1.6 fuelled cores so that the total TRU inventory in
the combined fleets is capped. (2) A fleet of PWRs designed to have CORAIL fuel assemblies. It
is assumed that the initial Pu feed comes from the LWR spent fuel that has been accumulated
already. It was found that, at equilibrium, the CORAIL system requires less natural uranium and
SWU and has a smaller repository impact than the coupled LWR+PUZH. This comparison did
not account for the amount of MA accumulated in the fuel discharged from the once-through
LWRs left over after the extraction of the Pu used for the initial loading into the CORAIL fuel
assemblies.
Thermal-hydraulics
The objective of the thermal hydraulic analysis was to compare the behavior of a PUZH-fueled
PWR core with that of geometrically identical cores, but loaded with different assemblies, both
during normal operation and during accident scenarios. These assemblies have the same
geometry, but differ either because of the type of fuel with which they are loaded or because of
the fuel arrangement in the lattice. The assemblies analyzed are the following: (1) an all-UO2assembly: the reference assembly; it uses UO2 fuel pins only; (2) a CONFU-assembly:
heterogeneous assembly made of standard UO2 fuel pins and pins made of recycled transuranics
in an inert matrix; (3) a CORAIL-assembly: heterogeneous assembly made of enriched UO2 pins
and MOX pins; and (4) a PUZH-assembly: homogeneous assembly containing U-Pu-Th-ZrH1.6
as fuel.
The steady state thermal-hydraulic analysis concluded that, under the constraint of the same
safety limits for all the core types, a PUZH-core can operate at the same power level as the
reference all-UO2 core while PWR cores loaded with either CONFU or CORAIL fuel assemblies
can only operate at about 80% of that power. This is due to the flatter pin-by-pin radial power
distribution characterizing the PUZH assembly.
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Transient analyses were performed for three accident scenarios: Large Break Loss Of Coolant
Accident (LBLOCA), Main Steam Line Break (MSLB) and Complete Loss Of Forced Flow
Accident (CLOFA). For all three scenarios, the PUZH-core was found to perform better than the
other two core types aimed at Pu/MA incineration, i.e. CONFU- and CORAIL-core. Particularly:
•
The peak cladding temperature for PUZH-core during LBLOCA was found to be about
300 K lower than that of all-UO2-, CONFU- and CORAIL-cores. This is mainly due to
the lower operating temperature characterizing the highly conductive PUZH fuel relative
to UO2-based fuels.
•
Unlike all-UO2-, CONFU- and CORAIL-cores, PUZH-core showed no return to
criticality in the event of a MSLB. This is due to the moderator temperature coefficient
(MTC) of PUZH-core, which was found to be the least negative among the cores
analyzed.
•
In the event of a CLOFA, the PUZH-core was found to reach a Minimum Critical Heat
Flux Ratio (MCHFR) larger than that of the CONFU- and CORAIL-cores, and similar to
that of the all-UO2-core. This is due both to a larger pre-accident MCHFR – resulting
from the flatter pin-by-pin power distribution characterizing the PUZH-assembly, than
CONFU and CORAIL, and to the larger (negative) value of the MTC/β ratio (which
controls the reactivity insertion upon coolant temperature variation) that caused a more
rapid reduction in power upon the accident.
Materials
The primary objective of the material analysis, as originally defined, was to investigate the
compatibility of hydride fuel with Zircaloy clad and with water under typical PWR operating
conditions. For this purpose we have located a damaged unused TRIGA fuel at the University of
California campuses at both Irvine and Davis and received DOE agreement to transfer the fuel
element from Davis to Berkeley. Unfortunately, we encountered numerous administrative
hurdles first by DOE and later by Davis and Berkeley and did not succeed getting the fuel to this
date. Consequently, we have modified the plan for the material analysis.
Two uranium-thorium-zirconium alloys were arc-melted and then hydrided to form fuels with the
nominal composition of (UTh4Zr10)H1.9 and (U4Th2Zr9)H1.5. Based on the analysis of these fuel
samples it appears that uranium-thorium-zirconium hydride fuels are superior to TRIGA fuel
(that does not have thorium) for power reactor use since the hydride matrix is more stable with
respect to dehydriding. Also, higher heavy metal densities can be achieved in fuels containing
thorium. Extensive study of the effects of irradiation on these fuels under typical light water
reactor conditions is necessary in order to adequately understand their performance compared to
TRIGA fuel and oxide fuels. An experiment intended for doing so at the ATR reactor an INL has
been planned.
Steady state and transient behavior of hydride fuel under PWR operating conditions were
investigated, taking into account the dependence of the fuel properties on the spatially varying
temperature and hydrogen concentration. The steady state temperature, hydrogen concentration,
and stress distributions across the hydride fuel were calculated for various linear heat generation
rates (LHGR). The extent of hydrogen radial redistribution across the fuel, driven by the
temperature gradient, is found more severe as the LHGR increases. Strains in the fuel occur from
4
thermal and hydrogen concentration gradients, with the latter being the dominant contributor.
Axial and azimuthal stresses are found both compressive at the fuel surface and tensile at the fuel
centerline. The fuel fracture criterion needs to be determined through finite element analysis.
The transient response of hydride fuel to a reactivity insertion accident scenario was studied by
artificially pulsing power in a square wave. The thermal response of the fuel to the changing
power level is found very rapid – on the order of few seconds. This is due to the small fuel rod
diameter and large thermal diffusivity of hydride fuel. There is no discernable alteration in the
hydrogen spatial distribution during the transient, since the characteristic hydrogen diffusion
time for these length scales is many orders of magnitude larger than the power transient
durations. Surprisingly, the stress across the fuel is actually reduced during the power pulse. The
temperature-induced stresses counteract the hydrogen-induced stresses, so the fuel is in its most
relaxed state during this stage of the transient. The fuel experiences maximum stress when the
temperature gradients diminish but the hydrogen displacement remains at the pre-transient
distribution.
In helium-bonded hydride fuel rods the flux of hydrogen atoms out of the fuel is found very
small during both steady state and transient operation. This is because the net rate of (desorption
– adsorption) quickly becomes zero when the equilibrium hydrogen partial pressure is
established in the gas plenum. The pressure buildup inside the cladding and the total fraction of
hydrogen lost from the solid fuel to the gas plenum are negligible even at very high fuel surface
temperatures. The extent of dehydriding is expected to be even less for liquid metal bonded
fuels. For the purpose of safety analyses assuming instantaneous equilibrium conditions is
judged to be a conservative and relatively accurate assumption.
Zirconium is an effective getter of hydrogen and can readily undergo hydriding. However the
fuel rod could be engineered such that the kinetics of hydrogen transfer from the fuel to the clad
is limited and effectively becomes insignificant during the lifetime of the fuel inside the reactor.
One such engineered approach we conceived is to substitute a liquid metal alloy for helium as
the fuel – clad bonding material. A ternary alloy of lead-tin-bismuth (Pb-33wt%Sn-33wt%Bi) is
proposed for this purpose. This alloy is chemically compatible with both the fuel and the clad.
Also hydrogen solubility in any of the components of the alloy is very limited at the fuel
operating temperatures. An investigation of the compatibility of the liquid metal bonded hydride
fuel with the cladding was initiated but has not been concluded by the time of the issuing of this
report.
An additional experimental study just recently initiated is to investigate the compatibility of
hydride fuel with high temperature steam that may occur in case of a severe accident that causes
the clad to rupture.
The experimental data available in the open literature on the swelling of hydride fuel and on the
fission gas released from hydride fuel is very limited. Moreover, there is no data available at all
on the feasibility of using liquid metal bonding instead of helium for hydride fuel. An irradiation
test of a liquid-metal bonded hydride fuel specimen in the ATR irradiation test reactor at the
Idaho National Laboratory was planned in order to improve the knowhow about hydride fuel
performance under power reactor irradiation conditions and investigate all the practicality and
effectiveness of the liquid metal bonding. We are now waiting for the ATR approval of this
irradiation test proposal.
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Recommendation for future work
The most important future undertaking is a study of the compatibility of hydride fuel with
Zircaloy clad and with high temperature and high pressure water and steam. Reliable
experimental data on the irradiation behavior of hydride fuel and, particularly, its irradiation
induced swelling and fission gas release need also be obtained. Establishing the feasibility of
using liquid metal instead of helium bonding is highly desirable along with an investigation of
the protection of the clad from hydriding such liquid metal bonding mayn provide. Estimation of
the commercial scale fabrication cost of hydride fuel is essential for evaluating the economic
viability of hydride fuel applications in LWR. Practical processes for recycling hydride fuel need
be developed as well.
More comprehensive system analyses that will address a number of promising scenarios,
including scenarios involving a combination of recycling campaign in LWR using hydride fuel
and recycling the leftover TRU – mostly MA, in fast spectrum reactors are also recommended. A
comprehensive comparison of the feasibility and performance of inert matrix hydride versus
oxide fuels is also desirable. Use of hydride fuel for recycling Pu and, possibly also MA in BWR
need also be explored; our previous study indicated that hydride fuels enable to eliminate water
rods and partial-length fuel rods and to reduce the water gaps between fuel bundles thus
providing a substantial increase – possibly close to 30%, in the core power density. Based on our
present study for PWR cores it is to be expected that, along with the power density increase,
hydride fuel will also enable improvement in the transmutation capability of BWRs.
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1. Introduction
1.1 About use of hydride fuels in LWRs
A comprehensive three-year feasibility study completed in 2006 under NERI Award No DEFG07-02SF22615 [1] has established that, based on neutronics, thermal-hydraulics, fuel
performance and safety analyses hydride fuel can safely operate in PWRs and BWRs without
restricting the linear heat generation rate of these reactors relative to that attainable with oxide
fuel. A detailed summary of the analysis performed and of the results obtained will be published
later this year as a special issue of Nuclear Engineering and Design [2-14]. Briefly, the study
identified a couple of particularly promising applications of hydride fuel in both PWRs and
BWRs:
(a) Eliminating dedicated water moderator volumes in BWR cores1 by loading hydride fuel rods
thus enabling to significantly increase the cooled fuel rods surface area as well as the coolant
flow cross section area in a given volume fuel bundle while significantly reducing the
heterogeneity of BWR fuel bundles thus achieving flatter pin-by-pin power distribution. The
net result is a possibility to significantly increase the core power density – on the order of
30% and, possibly, more, while greatly simplifying the fuel bundle design.
(b) Recycling plutonium in PWRs more effectively than is possible with oxide fuel by virtue of a
couple of unique features of hydride fuel – reduced inventory of 238U and increased inventory
of hydrogen. As a result of these features, the amount of Pu that needs to be loaded into the
hydride core to provide the reference cycle length is only 75% that is needed for MOX cores,
and the hydride core neutron spectrum is softer. Due to these characteristics, the hydride
fuelled core achieves nearly double the average discharge burnup – about 103 vs. 50
GWD/MTHM of MOX. The total Pu inventory in the discharged PUZH fuel is only 43% of
the initially loaded inventory versus 73 % in the discharged MOX fuel. The net amount of Pu
consumed per cycle is 60% larger with PUZH versus MOX fuel. The corresponding fissile
Pu to total Pu ratio is 44% versus 63%. The corresponding ratio of minor actinides (MA) to
Pu concentration at discharge is 13.25% versus 6.76%. The total neutron source strength at
discharge of PUZH fuel is 1250 n/s per gram of Pu and 5.25x105 n/s per gram of TRU
versus, respectively, 796 n/s and 2.23x105 n/s for MOX fuel. The decay heat levels are 2.35
w/gTRU for PUZH and 1.19 w/gTRU for MOX fuel. Nevertheless, the decay heat and
radiation levels per PUZH fuel assembly discharged are smaller than for MOX fuel
assembly.
1.2 Hydride fuels considered
The primary hydride fuel considering in this project is uranium-zirconium hydride similar to that
developed by General Atomics (GA) for TRIGA reactors [15]. The U-Zr hydride composition
used for the TRIGA fuel has, typically, 1.6 hydrogen atoms per Zr atom, i.e., it is U-ZrH1.6. The
Medium Enriched Uranium (MEU) fuel developed by General Atomics for TRIGA reactors
contains 45 w/o uranium of up to 20w/o 235U [15]. This corresponds to U/Zr atom ratio of 0.31.
The U-Zr hydride fuel considered throughout this project has the same elemental composition.
The uranium enrichment is a design variable. This fuel has been in use for more than 40 years in
1
Including water rods, possibly also replacing partial length by full length fuel rods, and minimizing the water gap
width in-between fuel bundles.
7
many reactors around the world both in constant power and pulsed power operating conditions. It
has an impressive record of safety.
The design limits set for the high power TRIGA core [16] are fuel temperatures of 750oC at
steady-state and 1050oC under transients. Although these temperatures are significantly lower
than the maximum permissible operating temperatures of UO2 fuel, the thermal conductivity of
hydride fuel is ~5 times higher than that of oxide fuel. Consequently, U-ZrH1.6 fuel can safely
operate at linear heat rates that even exceed those of commercial LWR. TRIGA fuel burnup also
significantly exceeds typical LWR oxide fuel burnup.
In high power TRIGA reactor [16] the fuel-average linear heat generation rate (LHGR) is
37kW/m while the peak LHR is 74 kW/m. The corresponding peak steady-state fuel temperature
is 550oC. For comparison, the average LHGR of oxide fueled PWR is 19 kW/m. The TRIGA fuel
discharge burnup is ~120 GWD/tHM versus <60 GWD/tHM of oxide fuel in PWR. The specific
power of the TRIGA fuel is 76 W/gHM versus ~36 W/gHM of the PWR. The water in TRIGA
reactors is at a significantly lower temperature than in LWR’s. Hence, the LHGR hydride fuel
could operate at in a PWR is significantly lower than in the TRIGA reactor. Nevertheless, the
detailed analyses performed in the previous study [1-14] established that U-ZrH1.6 fuel can safely
operate in both PWR and BWR cores at, at least, as high a LHGR as attainable with oxide fuel.
Relative to uranium dioxide fuel, U-ZrH1.6 fuel has a number of possible drawbacks:
(a) The nominal specific density of U-ZrH1.6 at room temperature is 8.256 g/cm3 and the
maximum practical U weight % is 45. This makes the atomic density of uranium in U-ZrH1.6
only about 40% that in UO2 fuel. For Pu and MA recycling, though, the relatively low U
loading is likely to be an asset rather than a disadvantage, as discussed in Section 2 of this
report – it reduces the inventory of Pu that needs to be loaded per core and increases the
fraction of the Pu that is consumed in one cycle. Moreover, the nominal density of a U-ThH2
fuel having 25 w/o U is 10.865 g/cm3 making the HM density in Th-hydride fuel nearly 12%
higher than the U density in UO2! This might enable increasing the PWR cycle length
beyond that attainable using oxide fuel using same loading of fissile material.
(b) Zircaloy may not be a compatible clad material for hydride fuel, as the hydrogen of the fuel
may hydride it. Nevertheless, half-a-dozen of approaches have been proposed for protecting
the Zy clad using a hydrogen permeation barrier [3] including the following: (i) Form a thin
oxide layer (~ 40 μm) over the hydride fuel pellets; it may retain the hydrogen up to 800oC
and will probably avoid fuel-cladding chemical reaction. (ii) Fill the fuel-clad gap with a
liquid metal. In addition to providing a hydrogen permeation barrier, the LM will
significantly reduce the gap-resistance to heat transfer and will enable to accommodate
significant pellet swelling with burnup without penalizing the fuel temperature. The
feasibility of using LM bonding for LWR UO2 fuel so as to improve the heat transfer from
the fuel to the clad and thus reduce the peak fuel temperature, delay onset of fission gas
release, avoids PCI and prevents Zy clad secondary hydriding due to clad failure has recently
been established by Olander et al. [3]. The LM is a low melting temperature (~120oC) alloy
of Pb, Sn and Bi at 33 weight % each.
The feasibility of such barriers needs to be carefully studied. The “default” approach is to use
SS clad. Experiments done at General Atomics with hydride fuel proved that [15] “hightemperature strength and ductility of the stainless steel or Alloy 800 fuel cladding provides
total clad integrity at temperatures as high as 950°C”. Whereas for low enrichment uranium
8
fuel use of SS clad will significantly penalize the neutron economy relative the Zy clad, the
penalty for Pu bearing fuel is smaller, due to the higher absorption cross section of Pu.
(c) If, due to a very severe accident, the hydride fuel temperature will significantly exceed
1000oC for a prolonged period of time, hydrogen could diffuse out from the fuel into the
fission gas plenum. If the gas pressure buildup will be excessive, it may pose a safety hazard.
Assessment of this hazard and its probability need yet to be performed.
(d) Hydride fuel may not be compatible with water coolant at PWR and/or BWR operating
conditions. Experiments performed at GA showed that there was no chemical reaction when
a very hot (1200oC) pellet of U-ZrH1.6 was dropped into a container of water. A safety
concern may be steam – fuel interaction in case of a breach in the clad. Based on the
experience with TRIGA fuel, steam – fuel interaction is not likely to be of safety concern.
Nevertheless, due to the higher operating temperatures and pressures of LWR’s, there may be
a compatibility issue.
Several types of hydride fuels have been considered for this study in addition to U-ZrH1.6; they
are members of a family of a composite hydride fuel that can be denoted as U-(ThnPumZrj)Hx;
the subscripts n, m, and j are the atomic proportions of the metals with respect to uranium
whereas the subscript x denotes the atomic ratio of H to the total metals excluding the U. The
uranium forms a separate metallic phase because its hydride (UH3) is unstable at the reactor
operating temperatures. The other constituents make a mixed-metal hydride (ThnPumZrj)Hx. The
hydrogen density in these fuels is comparable to that in the water of PWR. Even though the
experience with and data-base for thorium hydride and plutonium hydride fuels is small as
compared with that of zirconium hydride fuel, these fuels are expected perform comparably, if
not superior to ZrH1.6 fuel. According to Simnad [17], the developer of the U-ZrH1.6 TRIGA fuel,
U-ThH2 is even more stable than U-ZrH1.6 fuel and can operate at higher temperatures.
Plutonium also forms a very stable hydride; the equilibrium hydrogen pressure is 1 atm at 883oC
for ThH2, 810oC for ZrH1.6, and about 870oC for PuH2 [17]. Uranium-thorium-zirconium hydride
fuel was developed and characterized by Yamawaki et al. [18, 19].
1.3 Study objectives
The objective of this DOE NERI program sponsored project is to more thoroughly assess the
feasibility of improving the plutonium (Pu) and minor actinide (MA) recycling capabilities of
pressurized water reactors (PWRs) by using hydride instead of oxide fuels. There are four
general parts to this assessment:
(a) Identifying promising hydride fuel assembly designs for multi-recycling of Pu and MAs in
PWRs
(b) Performing a comprehensive systems analysis that compares the fuel cycle characteristics of
Pu and MA recycling in PWRs using the promising hydride fuel assembly designs identified
in Part 1 versus using promising assembly designs proposed for recycling in oxide fuel
(c) Conducting a safety analysis to assess the likelihood of licensing hydride fuel assembly
designs
(d) Assessing the compatibility of hydride fuel with cladding materials and water under typical
PWR operating conditions
9
1.4 Scope of work
Whereas the previous project [1, 2, 12] preliminary considered a single recycling of Pu in UZrH1.6 fuel, The present study considers multi-recycling of either Pu only, Pu and Np, or all the
TRU discharged from LWRs. Moreover, whereas the previous project [1, 2, 12] considered a
single, somewhat unrealistic MOX fuel recycling in a full core uniformly loaded with UO2 plus
PuO2, the present study examines three of the most promising assembly designs proposed for
recycling of oxide fuel – MOX-UE [20], CORAIL[20, 21] and CONFU [22, 23]; they enable full
core loading and multi-recycling of plutonium and possibly also minor actinides. The
transmutation characteristics of hydride fuel are also compared against those attainable using
plutonium in fertile-free, or “inert matrix”, oxide fuel [24]. Performance characteristics
considered include transmutation effectiveness, proliferation resistance of the discharged fuel
and fuel cycle economics.
There are three major parts to this study: neutronic and fuel cycle analyses, thermal-hydraulics
and safety analysis and evaluation of hydride fuel material properties. The work performed and
results obtained in these parts are described in, respectively, Chapters 2, 3 and 4 of this report.
1.5 References
1. E. Greenspan and the NERI project team, “Use of Solid Hydride Fuel for Improved LWR
Core Designs,” Final Summary Report for NERI Project # NE02-189, UCBNE Internal
Report UCB-NE-5105, April 30, 2006.
2. E. Greenspan, N. Todreas, B. Petrovic, P. Diller, P. Ferroni, M. Fratoni, F. Ganda, H.
Garkisch, F. Ginex, J. Malen, D. Olander, A. Romano, C. Shuffler and J. Trant, “Hydride
Fuel for LWR’s – Project Overview”, to be published in special issue of Nuclear Engineering
and Design, 2009.
3. D. Olander, H. Garkisch, B. Petrovic and E. Greenspan, “Hydride Fuel Materials
Performance and Design Constraints”, to be published in special issue of Nuclear
Engineering and Design, 2009.
4. F. Ganda, E. Greenspan and B. Petrovic, “Reactor Physics Analysis for PWR Cores”, to be
published in special issue of Nuclear Engineering and Design, 2009.
5. C. Shuffler, J. Trant, J. Malen, N. Todreas, ”Thermal Hydraulic Analysis for Grid Supported
Pressurized Water Reactor Cores”
6. P. Diller, N. Todreas and P. Hejzlar, “Thermal Hydraulic Analysis for Wire Wrapped PWR
Cores”, to be published in special issue of Nuclear Engineering and Design, 2009.
7. A. Romano, C. Shuffler, H. Garkisch, D. Olander and N Todreas, “Fuel Performance
Analysis for PWR Cores”, to be published in special issue of Nuclear Engineering and
Design, 2009.
8. C. Shuffler, J. Malen, P. Diller, F. Ganda, N. Todreas, E. Greenspan and B. Petrovic,
“Economic analysis for PWRs”, to be published in special issue of Nuclear Engineering and
Design, 2009.
9. M. Fratoni, F. Ginex, F. Ganda and E. Greenspan, “Reactor Physics Analysis for BWR
Cores”, to be published in special issue of Nuclear Engineering and Design, 2009.
10
10. P. Ferroni, C. Handwerk and N. Todreas, “Steady State Thermal-Hydraulic Analysis of
Hydride-fueled Grid-supported BWRs”, to be published in special issue of Nuclear
Engineering and Design, 2009.
11. F. Ganda, C. Shuffler and E. Greenspan, E., “Economic analysis for BWRs”, to be published
in special issue of Nuclear Engineering and Design, 2009.
12. F. Ganda and E. Greenspan, “Plutonium Recycling in Hydride Fueled PWR Cores”, to be
published in special issue of Nuclear Engineering and Design, 2009.
13. J. Malen, N. Todreas, P. Hejzlar, P. Ferroni and A. Bergles, “Thermal Hydraulic Design of a
Hydride-fueled Inverted PWR Core”, to be published in special issue of Nuclear Engineering
and Design, 2009.
14. F. Ganda and E. Greenspan, “Analysis of reactivity coefficients of hydride fueled PWR
cores,” to be published in Nuclear Science & Engineering, 2009.
15. M. T. Simnad, “The U-ZrHx Alloy: its Properties and Use in TRIGA Fuel”, Nucl. Eng.
Design, 64, p. 403-422, August 1981. Also General Atomic Report GA-A16029, 1980.
16. C. Iorgulis, M. Ciocanescu, M. Preda, and M. Mladin, “Neutronic Calculations Regarding the
New LEU 6x6 Fuel Bundle for 14 MW TRIGA-SSR, in order to Increase the Reactor Power
Up to 21 MW”, Int. Mtg. on Reduced Enrichment for Research and Test Reactors, Sao Paulo,
Brazil, October 1998.
17. M.T. Simnad, “An Assessment of Thorium Hydride or Deutride as a Reactor Fuel Matrix”,
Reprint from the archives of Prof. Mike Driscoll of MIT Nuclear Engineering Department.
1986. also M.T. Simnad, “Uranium Thorium Hydride Nuclear Fuel,” United States Patent No
4,493,809, May 27 1986.
18. T.Yamamoto, H. Suwarno, F. Ono, H. Kayano, and M. Yamawaki, “Preparation, Analysis
and Irradiation of Hydrided U-Th-Zr Alloy Samples For a New Fuel,” J. Alloys Compds.
271-273, 702-726, 1998.
19. M. Yamawaki, et al., “Development of U-Th-Zr Alloy Hydrides as Alternative ThoriumBase Fuel and MA Burning Target Fuel,” Proc. Int. Conf. on Future Nuclear Systems,
GLOBAL’99, Jackson Hole, Wy. 1999.
20. G. Youinou, and A.Vasile, “Plutonium Multirecycling in Standard PWRs Loaded with
Evolutionary Fuels”, Nuclear Science and Engineering: 151, 25-45, 2005.
21. G. Youinou, A. Zaetta, A. Vasile, M. Delpech, M. Rohart, and J.L. Guillet, “Heterogeneous
Assembly for Plutonium Multi-recycling in PWRs: The CORAIL Concept”, Proc. Global’
01, Paris, France, 2001.
22. E. Shwageraus, P. Hejzlar and M. Kazimi, “Feasibility of Multi-recycling of Pu and MA in
PWRs Using Combined Non-Fertile and UO2 (CONFU) Fuel”, Proc. GLOBAL’03, New
Orleans, LA, 2003.
23. E. Shwageraus, P. Hejzlar and M.S. Kazimi, “A Combined Nonfertile and UO2 PWR Fuel
Assembly for Actinide Waste Minimization Nuclear Technology”, Volume 149, Number 3,
Pages 281-303, 2005.
11
24. C. Degueldre, H. Akie, P. Boczar, N. Chauvin, M. Meyer and V. Troyanov, “Inert Matrix
Fuel Deployment for Reducing Plutonium Stockpile in Reactors,” Proc.GLOBAL’03, New
Orleans, LA. , 2003.
12
2 Neutronic Analysis
This section is organized as follows:
¾ Section 2.1: Introduction;
¾ Section 2.2: Benchmark our Fuel Assembly Computational Capability;
¾ Section 2.3: Database Establishment: Identification of Promising PWR Fuel Assembly
Designs and Comparison with Equivalent Hydrides;
¾ Section 2.4: Identification of the Most Promising Hydride Fuels (fertile free, thoriumand uranium-based) for Pu Multi-Recycling;
¾ Section 2.5: Pu+Np and “all TRu” Multi-Recycling in PWR Using Hydride Fuels;
¾ Section 2.6: Comparisons of Hydride Fueled Systems;
¾ Section 2.7: System Analysis;
¾ Section 2.8: Conclusions.
2.1 Introduction
The objective of the neutronic analysis is to assess the feasibility of multi-recycling plutonium
and TRU in PWR using hydride rather than oxide fuel and to quantify the resulting transmutation
effectiveness. The extra hydrogen in the fuel softens the neutron spectrum and thereby reduces
the critical Pu concentration [1,2]. The fuel hydrogen also mitigates the adverse effect of large
voiding on the core reactivity.
The study starts with the benchmarking our neutronic computational capabilities for
heterogeneous, plutonium-containing (CORAIL [3,4]) and TRU-containing (CONFU [14]), fuel
assemblies. Our verified computational capability is then applied to the comparison of the
performance of the reference Pu-hydride (PUZH) fuel assembly with two oxide fuel assembly
designs that were proposed to overcome the positive void coefficient of reactivity – CORAIL
and MOX-UE [3,4]. Both of these design approaches use enriched uranium, either segregated or
mixed with the Pu, to reduce the critical plutonium mass. These design approaches offer neither
substantial natural uranium nor Separating Working Unit (SWU) saving over conventional UO2
fuelled cores and they provide for Pu stabilization rather than net destruction. It will be shown
that the PUZH fuel offers a larger fractional transmutation than the equivalent MOX-UE oxide
fuel while using depleted uranium, because of its larger H/HM ratio.
A search for the hydride fuel composition that offers maximum fractional plutonium
transmutation is then undertaken; the design variables are amounts of thorium and uranium. The
three-constituent fuels examined are of the form ThH2-ZrH1.6-PuH2 and U-ZrH1.6-PuH2; the
volume fraction of the constituents vary. Also investigated is the possibility for multi-recycling
plutonium, inferring that the use of hydrides could allow for a larger number of recycles than
what would be possible with oxides. This is because the incorporation of a significant fraction of
the hydrogen moderator in the fuel (a unique feature of hydride fuels), would mitigate the effect
of spectrum hardening due to coolant voiding accidents, thereby allowing the large void
reactivity coefficient to remain negative for a larger number of recycles. Finally, the study
13
evaluates the possibility of recycling in hydride fuels neptunium together with plutonium and Pu
along with the entire MA stream.
The work is concluded with a system and economic analysis that compares the fuel cycle
characteristics of Pu and MA recycling in PWR using the promising hydride fuel assembly
designs identified in the previous part of the work versus Pu and MA recycling in PWRs using
oxide, including inert matrix fuel assemblies.
14
2.2
2.2.1
Benchmark our Fuel Assembly Computational Capability
Computer codes and data libraries
The calculations presented throughout this work were performed mostly with the
TRITON/NEWT sequence of SCALE 5.0 and 5.1 [5,6,7,8] applied to a single unit cell
configuration using the ENDF/B-V derived 238 energy group libraries generated using the
BONAMI and NITAWL modules for, respectively, the unresolved and resolved resonances. The
ability of NEWT/TRITON to correctly predict the performance of plutonium bearing fuel was
established by performing benchmark calculations with complex plutonium and TRU-bearing
assembly designs (such as the CORAIL and CONFU assemblies). A summary of the results of
those benchmarks are presented in this Section.
2.2.2
Benchmark of the CORAIL assembly
The CORAIL is a 17x17 PWR fuel assembly design having 264 fuel rods of which 84 are MOX
pins and the remaining 180 are UO2 pins using enriched uranium. The modeling of the CORAIL
assembly is particularly challenging, both because of the presence of degraded plutonium and
because of its strong heterogeneities, due to the positioning of MOX pins on the periphery and
UO2 pins in the center of the assembly, which in turn cause a strong flux gradient within the
assembly. For this reason a benchmarking effort was initiated between ANL and CEA of France,
using both deterministic and Monte Carlo codes [9]. In particular WIMS8 and MCNP4C where
used at ANL, and APOLLO2 and TRIPOLI4 where used at CEA. Initially large discrepancies
where found in the evaluated pin power distribution between WIMS8 and APOLLO2. These
discrepancies where later largely resolved by using the Pij + Sn model in APOLLO2 [9].
For the purpose of validating our computational tool - TRITON/NEWT code and associated
cross section libraries, part of SCALE 5.1 [8], against results of WIMS8 and APOLLO2, a
benchmark was performed for the CORAIL assembly.
First a static calculation was performed at BOL, mainly comparing k∞ and assembly pin power
distribution. Afterwards a depletion calculation was performed and several parameters were
compared including k∞, pin power distribution and most importantly the concentration evolution
of various actinides, averaged over the assembly. At this stage a significant disagreement was
found in the burnup-dependent concentrations of some of the minor actinides, particularly of
242m
Am. Therefore an effort was initiated to understand the reason of this discrepancy. The
afore-mentioned discrepancy was traced back to a difference in the branching ratio (BR) of the
(n,γ) reaction of 241Am. After changing the branching ratio in the SCALE libraries to the values
used by WIMS8, the agreement on 242mAm appeared satisfactory. Additionally the calculated
concentrations of several other minor actinides benefited from this change, particularly of 242Cm,
because it is formed by β- decay of 242Am. This demonstrated that the reason of the discrepancy
is not due to the cross section libraries, but to the branching ratio used by the codes.
For the most accurate results, the resolved resonance treatment should be done with CENTRM, a
continuous energy transport module. Unfortunately, at the time of this work, CENTRM was not
recommended by ORNL for reactor calculations at normal operating temperatures because of a
15
yet un-resolved issue with the absorption cross section of 238U [10]. Therefore the recommended
module for un-resolved resonance treatment remains NITAWL, based on the Nordheim method
and available with ENDF/B-V based cross sections. Nevertheless we will show some results
obtained with CENTRM before the cross section issue was found and made public.
The benchmark in [9] was performed for both 8 weight percent plutonium and 12 weight percent
plutonium. We performed both benchmarks, but for compactness and clarity in this report we
only show the results for the 8 weight percent plutonium design. The results accuracy for the 12
weight percent Pu design is similar.
2.2.3
CORAIL benchmark specification and computational methodology
The CORAIL benchmark geometric details are shown in Figure 2.1 and the atomic densities of
each of the constituents are given in Table I for the fuel, and in Table II and Table III for the
coolant densities in cold and hot conditions, respectively.
0.0779
MOX fuel
UO2 fuel
Guide tube
21.6098
Fuel Pin Configuration
1.262
R 0.47436
R 0.613012
R 0.41266
R 0.572945
1.262
Fuel Cell
Guide Tube cell
Figure 2.1 Geometric configuration of the CORAIL assembly (from [9])
16
The WIMS8 and APOLLO2 calculations used JEF2.2 derived cross section library whereas
TRITON for this analysis used ENDF/B-V derived 44 group library; only the BOL static
calculation was performed with the 238-groups library. The multi-group cross sections are
calculated using BONAMI for treating the unresolved resonances with the Bondarenko method,
and NITAWL to treat the resolved resonances using the Nordheim method. The depletion is
performed by ORIGEN-S.
Figure 2.2 shows the TRITON/NEWT model of the CORAIL assembly. The model employed
simulates the lower right quadrant of the assembly, with the water gap explicitly represented on
the side of the MOX pins as was done with the WIMS8 and the MCNP4C models.
2.2.4
CORAIL benchmark results: k∞ and pin power distribution evaluation at BOL
The BOL k∞ results of the benchmarks calculated at ANL and CEA are given in Table 2.1. To
adapt the calculations to the cross sections available in the Monte Carlo codes (MCNP and
TRIPOLI), all the results are at room temperature (294 K). Our results with TRITON are
therefore at 294 K as well; they are given in Table 2.2 together with the extent to which they
differ from MCNP4C results calculated using ENDF/B-V.
Table 2.1 Benchmark Results of the BOL k∞ from ANL and CEA
Methodology
Code
MCNP4C
Monte-Carlo
k∞
Library
ENDF/B-VI release 2
8% Pu
1.28861 ± 0.00031
12% Pu
1.29541 ± 0.00031
ENDF/B-VI release 5
1.28906 ± 0.00031
1.29609 ± 0.00031
ENDF/B-V
1.28937 ± 0.00032
1.29505 ± 0.00029
JEF-2.2
1.29409 ± 0.00031
1.29992 ± 0.00031
TRIPOLI 4
JEF-2.2
JEF-2.2 (6)
1.29637 ± 0.00038
1.28645
1.30187 ± 0.00039
1.29185
WIMS8
JEF-2.2 (28)
1.28633
1.29217
JEF-2.2 (172)
1.28706
1.29263
JEF-2.2
1.29649
1.30212
Deterministic
transport
APOLLO2
Table 2.2 Results of the TRITON/NEWT Simulations at BOL
XS library
Condition
BOL k∞
ENDF/B-V 44 groups
ENDF/B-V 238 groups
ENDF/B-V 44 groups
Nominal cold
Nominal cold
Nominal cold
1.289124
1.282912
1.289145
Difference (pcm) from MCNP4C
(ANL)
-19.0791
-500.865
-17.4504
(a)
ENDF/B-V 44 groups
Boron Branch cold 1.290805
N/A
Using 38 different zones to evaluate the power distribution and to allow for pin-dependent depletion.
(a)
17
Figure 2.2 TRITON model of the CORAIL assembly: bottom-right quarter of the assembly: in red the UO2
pins and in green the MOX pins. The water gap is modeled explicitly
The agreement with ANL MCNP on the multiplication factor is very satisfactory (less then 20
pcm and within a standard deviation) when the 44 group cross section library is used, but
becomes less satisfactory when the 238 groups library is used. This is likely due to fortuitous
compensation of errors.
Table 2.3 gives the normalized pin power distribution and the difference in percent between
TRITON with 44 groups and ANL-MCNP4C, with cross sections derived from ENDF/B-VI. The
agreement is satisfactory, showing a maximum discrepancy of 1.72 % and –1.48 %. The
agreement is worse between the reported results of ANL and CEA, being as high as 2.8%
between TRIPOLI and MCNP4C (using JEF2.2 and ENDF/B-VI respectively).
2.2.5
CORAIL benchmark results: k∞ evolution with burnup
Figure 2.3 shows a comparison of the differences in k∞ as a function of burnup for APOLLO2
and WIMS8 and for a number of cases to be presented in greater detail later. The difference
between APOLLO2 and WIMS8 (blue line) is larger than the difference between TRITON and
WIMS8; this is despite of the fact that both APOLLO2 and WIMS8 use JEF2.2 cross section
libraries while TRITON/NEWT uses ENDF/B-V. The difference becomes even smaller when
TRITON is compared with the average of WIMS and APOLLO. BR in the caption means
“Branching Ratio” and involves changes in the branching ratio of the (n,γ) reaction of 241Am, for
reasons to be explained later in Section 2.2.7. Changes in this parameter do not alter substantially
the calculated eigenvalues. The difference between TRITON and WIMS8 becomes larger than
the difference between APOLLO2 and WIMS8 at larger burnups if CENTRM is used to create
the multi-group cross sections (brown line with the circle marker).
18
Table 2.3 Normalized CORAIL pin power distribution at BOL: TRITON results and percent difference from
ANL MCNP with ENDF/B-VI. The maximum and minimum discrepancies are 1.72 % and –1.48 %
respectively (in red)
Triton
% diff MCNP
0.803
0.04%
0.809 0.796
0.82% 0.64%
0.767 0.901 0.825
-0.78% 1.72% 0.30%
0.911 1.024 0.888
0.75% 0.67% -0.32%
1.068 1.074 0.992 0.814 0.978
-1.02% 0.03% -0.73% 0.73% 1.13%
1.125 1.091
-0.87% -0.70%
0.901 1.033
-0.01% 1.51%
1.092 1.145 1.070 1.043 1.029 0.879 1.041
-1.10% -0.90% -1.05% 0.17% -0.27% 0.28% 0.78%
1.103 1.101 1.146 1.078 1.044 1.040 0.886 1.056
-0.70% -1.48%-0.58% -0.58% -0.24% -0.87% 0.48% 0.64%
1.161 1.153
0.23% -0.89%
1.128 1.099
-1.11% 0.37%
0.932 1.060
0.10% 0.88%
800.0
Apollo -WIMS
Difference in pcm
600.0
TRITON vs WIMS (BR 16.2%)
400.0
TRITON vs WIMS (BR 10%)
200.0
TRITON vs. average of Apollo and
WIMS (BR 10%)
TRITON vs. average of APOLLO
and WIMS (BR 16.2%)
0.0
-200.0
-400.0
0
10
20
30
40
50
Burnup (GWD/T)
Figure 2.3 Evolution with burnup of the differences in the k∞ (in pcm) between APOLLO and WIMS as
compared to TRITON versus WIMS and TRITON versus the average of WIMS and APOLLO. From top to
bottom: difference between APOLLO2 and WIMS8, between TRITON and WIMS8 with branching ratios of
16.2% and 10% in the (n,γ) reaction of 241Am, between the TRITON and the average of WIMS8 and
APOLLO2 and between TRITON and WIMS8 when CENTRM is used instead of NITAWL.
19
2.2.6
CORAIL benchmark results: Pin-wise power distribution and actinides evolution
with burnup
Pin-wise power distribution data are available in [9] at 0, 15, 30, 45 GWD/T for APOLLO2 and
WIMS8. The disagreement between these and TRITON’s is of the same order of magnitude
(always less than 3% and mostly less than 2%) as the disagreement between WIMS and
APOLLO − even though the latter two use the same cross sections; and is generally larger from
the results of APOLLO than of WIMS8; this maybe reflecting the fact that both WIMS and
TRITON model the water gap at the periphery of the assembly explicitly, while APOLLO does
not.
Similarly, assembly-wise average actinides concentration data are available in [9] at 15, 30, 45
GWD/T for APOLLO2 and WIMS8. These were compared to those of TRITON. The
discrepancy in concentration is reasonable for the major U isotopes, the Pu isotopes and 241Am.
The heavier minor actinides show less satisfactory agreement. Of particular concern is the
discrepancy – exceeding 60% – in the 242mAm concentration, which is even somewhat increased
when using the continuous-energy spectrum averaging module CENTRM instead of NITAWL to
generate the self-shielded cross sections. When CENTRM is used for cross section preprocessing, most of the actinides, with the exception of 238U, 238Pu, 241Am, 242mAm, 242Cm and
244
Cm show an increase in accuracy as compared to when NITAWL is used.
2.2.7
Branching ratio of 241Am
The large discrepancy observed in 242mAm prompted us to investigate the effect of the branching
ratio of the (n,γ) reaction of 241Am. The branching ratio is energy dependent, therefore it needs to
be evaluated by spectrum-weighting the energy-dependent branching ratio using Equation 2.1
(where fγ1(E) is the energy dependent branching ratio).
∞
∫ f γ1(E)σc (E)φ(E)dE
f γ1 = 0
(2.1)
∞
∫ σc (E)φ(E)dE
0
We obtained from [11] the data in Figure 2.4, showing the branching ratio of the (n,γ) reaction of
241
Am to generate 242Am (and 242mAm) as a function of energy. All the most recent nuclear data
files are in good agreement in the thermal region and, with the exception of JENDL-3.3, exhibit
a similar behavior also in the epithermal region. The default SCALE 5.1 libraries of the depletion
module ORIGEN-S have a branching ratio of 16.2% for the creation of 242mAm from the (n,γ)
reaction of 241Am.
20
1.0
Branching ratio of
241
Am
0.9
0.8
0.7
ENDF/B-VII.b2
ENDF/B-VI.8
ENDF/B-V.2
JEFF-3.1
JENDL-3.3
0.6
0.5
0.4
-5
10
-4
10
-3
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
8
10
Energy [eV]
Figure 2.4 Branching ratio of 241Am (n,γ) reaction
To estimate how accurate this number is with respect to the more recent evaluations, we
performed a spectrum weighting on the typical spectra for few representative fuel types. Starting
from the energy-dependence of the branching ratio shown in Figure 2.4 for the ENDF/B-VI (red
line), we weighted it over the fluxes of a typical PWR with 5% enriched UO2 and with MOX.
Additionally we integrated over the CORAIL average fuel spectrum and over the average
spectrum of PUZH fuel1, which is softer than that of MOX fuel because of its larger hydrogento-Pu ratio in the fuel assembly.
The resulting evaluated branching ratios are compared in Table 2.4. All the resulting branching
ratios are of the order of 10% to 11%, making the SCALE 5.1 default value of 16.2% clearly
inadequate. Recently presented measurements at the CEA labs of Saclay and Cadarache of a
branching ratio of 10.5% ±0.1% at 0.025 eV [12] further confirm our spectrum averaged results.
Table 2.4. Resulting evaluated branching ratios for different typical fuel types spectra
PWR MOX PUZH CORAIL
BR 242Am 0.884 0.893 0.889 0.893
BR 242mAm 0.116 0.107 0.111 0.107
2.2.8
Re-evaluation of the CORAIL benchmark with the modified branching ratio
WIMS8 in use at ANL uses a branching ratio of 10%, while APOLLO2 uses 11.5% for (n,γ)
capture reaction of 241Am. To test the importance of the branching ratio on the observed
discrepancy of 242mAm, we changed the branching ratio in the scale binary libraries to 10%, and
re-performed the benchmark calculation.
Table 2.5 compares the calculated nuclei evolutions using the new libraries with a 10%
branching ratio (on the right side) to the nuclei evolution in case of 16.2% branching ratio (on the
1
PUZH is an acronym for a hydride fuel of the type U-PuH2-ZrH1.6, which has been studied extensively at UCB as
an alternative for the disposition of plutonium in PWR.
21
left side). The disagreement on the 242mAm evolution virtually disappears, confirming our
assumption that the discrepancy found initially was mainly due to the difference in the branching
ratio. The other differences are roughly similar, with the exception of 242Cm, which is formed
mainly by β- decay of 242Am. Large discrepancies in the number densities of heavier actinides,
especially the curium isotopes are well known and documented in the literature: for example the
reported uncertainties in the number densities of curium isotopes in the OECD-proposed
benchmark A for Pu recycling in PWR, [10] are: 17%, 26%, 11% and 19% for respectively
242
Cm, 243Cm, 244Cm, 245Cm. Except for 245Cm these values exceed the discrepancies found
between TRITON/NEWT and WIMS8.
Table 2.5. Percent difference in the assembly-average concentrations in TRITON as compared to WIMS for
the case of NITAWL with 10% 241Am branching ratio
TRITON BR 16.2% versus WIMS8
2.2.9
45 GWD/T
TRITON BR 10% BR versus WIMS8
15 GWD/T
30 GWD/T
15 GWD/T
30 GWD/T
45 GWD/T
U-234
-2.50%
-8.60%
-4.00%
-5.40%
-5.70%
-5.70%
U-235
-2.10%
1.00%
-7.80%
-0.70%
-1.80%
-2.90%
U-236
7.80%
2.00%
4.80%
4.60%
4.20%
3.20%
U-238
0.00%
0.10%
-0.10%
0.00%
0.00%
0.00%
Pu-238
-0.50%
-1.50%
0.40%
-0.10%
0.00%
0.90%
Pu-239
0.50%
-2.20%
-4.10%
0.50%
-2.60%
-3.20%
Pu-240
-0.50%
-1.10%
-2.70%
-0.60%
-1.30%
-2.20%
Pu-241
1.10%
-1.10%
-1.50%
0.60%
-0.50%
-1.50%
Pu-242
1.80%
1.80%
5.00%
1.50%
2.60%
3.80%
Am-241
2.30%
1.50%
1.10%
2.10%
1.60%
1.60%
Am-242m
42.40%
61.20%
61.40%
-13.10%
-0.30%
0.30%
Am-243
4.00%
6.00%
16.70%
0.20%
9.10%
12.30%
Cm-242
-8.60%
-10.10%
-6.90%
-3.90%
-1.90%
-1.70%
Cm-243
18.20%
8.10%
14.00%
20.10%
20.80%
18.40%
Cm-244
-7.30%
-10.80%
5.80%
-13.90%
-5.00%
-1.50%
Cm-245
-26.60%
-35.40%
-23.20%
-34.20%
-29.40%
-29.50%
Benchmark of the reactivity coefficients of first recycle plutonium in CORAIL
To validate the accuracy of our reactivity coefficients calculations, we benchmarked our
calculated Beginning-Of-Life (BOL) reactivity coefficients with those reported in reference [3]
for the CORAIL fuel assembly. In the absence of enough details in reference [3], the fuel
assembly geometry and material composition, density and temperature as specified for the
CORAIL benchmark [9, 7] were used. The BOL soluble boron concentration assumed is 1700
ppm [3]. The BOL coolant temperature coefficient of reactivity, calculated for the temperature
range from 583 K to 593 K, is -14 pcm/K. This value is in reasonable agreement with the -20
pcm/K reported in reference [3].
2.2.10 Benchmark of the CONFU fuel assembly
The CONFU assembly [14,15,16], has been proposed for multi-recycling of TRU in PWR. The
TRITON/NEWT benchmark results, presented in this section, are compared against the
22
CASMO-4 results obtained at MIT. The characteristics compared are the evolution with burnup
of k∞, pin power distribution and the concentrations of the most important actinides.
The TRITON/NEWT model of the lower right quadrant of the CONFU fuel assembly is very
similar to that of the CORAIL fuel assembly (Figure 2.2): the 84 peripheral pins are fertile free
fuel containing minor actinides, while the 180 central pins are made of 4.2% enriched UO2. The
composition, in atoms/b-cm, of the two fuel types is given in Table 2.6. The density of the fertile
free fuel is 5.526 g/cm3, the density of the UO2 fuel is 10.34 g/cm3. The temperature of both fuel
types is 900 K, that of the water is 580 K. The dimensions of the UO2 and fertile free fuel rods
are the same: the fuel radius is 0.4095 cm, the clad inner radius is 0.4178 cm and the clad outer
radius is 0.475 cm. Control rod guide tubes’ inner and outer radius are 0.5715 cm and 0.612 cm
respectively. The assembly average power density is 104.5 kW/liter. The pitch is 1.26 cm while
the assembly pitch is 21.5 cm.
Figure 2.5 shows the evolution of k∞ with burnup as calculated with TRITON/NEWT and
CASMO-4. The two curves are indistinguishable. The maximum discrepancies between the two
codes prediction of the pin-wise power distribution are in the corner pin, which is showing a
maximum discrepancy of 3.83%. The CONFU assembly-averaged isotopic evolution with
burnup were compared for the most important actinides: 235U, 236U, 238U, 238Pu, 239Pu, 240Pu,
241
Pu, 242Pu, 241Am, 242mAm and 244Cm. The agreement between the TRITON and CASMO
predictions is excellent for all the evaluated actinides with the exception of 242mAm which shows
a discrepancy of about 20%: CASMO predicts a higher concentration. As in the case of
CORAIL, this is likely due to differences in the branching ratio of the (n,γ) reaction of 241Am
between TRITON and CASMO.
1.4
CASMO-4
TRITON/NEWT
1.3
k-inf
1.2
1.1
1
0.9
0.8
0
20
40
60
80
100
Burnup (GWD/MTiHM)
Figure 2.5 CONFU assembly k∞ evolution with burnup as predicted by CASMO-4 and TRITON/NEWT
23
Table 2.6. Nuclei Density of the CONFU Fuel Assembly in atoms/b-cm
Fertile free
UO2
U-235
5.6835E-08
0.000981
U-238
7.797E-06
0.022086
Pu-239
0.00116425
Pu-242
0.00011912
Am-243
3.4713E-05
Cm-244
1.1654E-05
Y-89
0.00070454
Zr
0.03332603
U-234
1.7066E-09
7.88E-06
Np-237
0.0001601
Pu-240
0.00054789
Am-241
0.00011056
Cm-242
0
Cm-245
8.8965E-07
Mg
0.01871896
U-236
4.6944E-08
Pu-238
6.6027E-05
Pu-241
0.00016453
Am-242
4.497E-07
Cm-243
1.1791E-07
Cm-246
1.3997E-07
O-16
0.05447767
0.046117
2.2.11 Comparison of k∞ estimated with an equivalent pin cell and an assembly calculation
Doing depletion analysis for a full fuel assembly and 238 energy groups is not practical with our
TRITON/NEWT system due to excessive memory requirements. However, since the reference
TRU-hydride fuel assembly features a uniform configuration, reactor physics characteristics,
such as achievable burnup, actinide concentration evolution and reactivity coefficients can be
estimated using a unit cell analysis, even at a high energy resolution through the use of the 238
energy group library. Other characteristics, such as the assembly power peaking factors and
control rods worth, require a full 2-D assembly calculation. A unit cell model that will properly
represent a fuel assembly has to account for the extra water present in the assembly in the control
rods channels and the inter-assembly gap.
The pitch-to-diameter ratio (P/D) of the fuel pins in the reference assembly is 1.3261. When the
extra water present in the control rod thimbles and in the inter-assembly gap is taken into
account, the equivalent unit cell P/D is 1.393. All the unit cell results presented in this report
were obtained from calculations performed with the 238-groups library of SCALE-5.1. Figure
2.6 shows on the left the evolution of k∞ of the effective unit cell model loaded with plutonium
hydride (PUZH) in comparison with that of the fuel assembly, and on the right the percent
difference between the two lines.
24
0.20%
1.2
assembly
1.15
0.15%
% difference on k-inf
single pin
k-inf
1.1
1.05
1
0.95
0.10%
0.05%
0.00%
0
0.9
0
500
1000
1500
2000
EFPD
500
1000
1500
2000
-0.05%
EFPD
Figure 2.6 k∞ evolution of the assembly and the equivalent unit cell for PUZH fuel with plutonium from first
recycling (left) and Percent difference in the k∞ evolutions (right)
2.2.12 Conclusions
The TRITON/NEWT sequence and associated cross section libraries of the SCALE 5.1 code
package were found of satisfactory accuracy for modeling complex TRU-containing PWR fuel
assemblies like the CORAIL and CONFU, provided that the ORIGEN default branching ratio for
production of 242mAm is changed to approximately 10-11%. A value of 10% for the branching
ratio was found to provide good agreement with the calculated results of both APOLLO2 and
WIMS8 in the case of CORAIL. In case of CONFU, the agreement between the TRITON and
CASMO predictions is good for all the evaluated actinides with the exception of 242mAm which
shows a discrepancy of about 20%: CASMO, which likely uses a slightly different value for the
branching ratio of 241Am, predicts a higher concentration of 242mAm.
Since the reference TRU-hydride fuel assembly features a uniform composition, integral reactor
physics characteristics, such as achievable burnup, actinide concentration evolution and
reactivity coefficients can be estimated using a unit cell analysis, even at a high energy resolution
through the use of the 238 energy group library. Other characteristics, such as the assembly
power peaking factors and control rods worth, require a full 2-D assembly calculation.
25
2.3 Database Establishment: Identification of Promising PWR Fuel
Assembly Designs and Comparison with Equivalent Hydrides
In this section the Pu bearing oxide fueled PWR designs to be used as the reference are
identified. CORAIL, MOX-UE [3] and CONFU [13,14,15] are the most promising among a
number of oxide fuel assembly designs that were proposed to overcome the positive void
coefficient that arises when the total plutonium inventory in PWR reaches ~12w/o (i.e. after 2 to 3
recyclings). All three design approaches use enriched uranium, either segregated or mixed with
the Pu (or TRU), to reduce the required TRU mass.
These designs offer neither substantial natural uranium nor Separating Working Unit (SWU)
saving over conventional UO2 fuelled cores as they offer Pu (or TRU) stabilization rather than
net destruction. The heterogeneous configurations (CORAIL and CONFU) feature relatively
large pin-wise power peaking factor.
2.3.1
CORAIL characterization and comparison with PuH2-U-ZrH2 (PUZH) for
first-recycle plutonium
The main purpose of the CORAIL assembly (described in detail in Section 2.2.3) is to safely
allow for multi-recycling of plutonium in PWR [3]. The resulting heterogeneous system has been
shown to be capable of stabilizing the plutonium inventory without requiring any modification to
the control system of the core and without the insurgence of positive void reactivity feedback at
the onset of a large core voiding [3]. Its drawbacks are the requirement of enriched uranium and
a relatively high power peaking factor due to the heterogeneous configuration.
The CORAIL design is a rather effective plutonium burner, destroying about 40% of the initial
plutonium loaded in the peripheral rods – thanks to the UO2 rods surrounding the plutonium
loaded ones [3]. However, because plutonium is loaded only in the peripheral rods – which are
only 84/264 or less than a third – and the UO2 rods create about the same amount of plutonium
that is consumed in the peripheral ones, the assembly design ends up being a plutonium
stabilizer. A proper comparison of the CORAIL assembly with a hydride fuel design can be done
assuming an identical geometry and linear heat rate, but changing the fuel type. The performance
of the two systems (CORAIL and homogeneous hydride) is compared with plutonium from the
first recycling, called Pu-V1 in [3] and given in Table 2.72.
Table 2.7 The Plutonium Isotopic Composition for the First Recycling (from (Youinou, 2005))
238
Pu 239Pu 240Pu 241Pu 242Pu 241Am Pu-fissile
Pu-V1 2.7% 56% 25.9% 7.4% 7.3% 0.7% 63.7%
For the first recycling the CORAIL assembly is loaded with 8 weight percent Pu-V1 in the
peripheral 84 fuel rods and with 5.4% enriched UO2 in the central 180 fuel rods. Table 2.8 gives
the assembly average densities and the total amount of plutonium, 235U and 238U per assembly at
BOL.
2
Expected to be the average composition from LWR available in France around 2015.
26
Table 2.8. BOL Assembly-Average Densities (g/cc) and Masses (kg/assembly) of Plutonium, of 235U and 238U in
the CORAIL Assembly
g/cc kg/assembly
Pu 0.2551
13.15
235
U 0.3276
16.89
238
U 8.2481
425.27
The first hydride fuel considered for this comparison is of the type U-PuH2-ZrH1.6, also known as
PUZH; it has been studied extensively at UCB in a previous project [1, 17, 18 and 2]. The PUZH
fuel used in this analysis has the same plutonium vector (Pu-V1) loaded in each rod, mixed with
uranium depleted to 0.3% 235U. The uranium atomic density is chosen identical to the one loaded
as a maximum in TRIGA reactors (of 9.4137·10-3 at/barn-cm, corresponding to 3.72 g/cc of
metallic uranium). The amount of plutonium is then adjusted to match the CORAIL fuel cycle
length of 1255 days, resulting in a density of 0.86 g/cc of plutonium. Zirconium hydride fills the
remaining volume fraction of 72%. The overall fuel density is 8.6278 g/cc. Table 2.9 gives the
assembly average densities and volume fractions of the fuel constituents. Table 2.10 gives the
assembly average densities and total mass per assembly. The total content of plutonium is about
3.3 times higher than in the case of CORAIL, but the uranium total amount is about half.
Moreover the CORAIL contains uranium with an average enrichment of 3.8%, while the PUZH
assembly contains depleted uranium. Figure 2.7 shows the evolution of kinf for the two fuel
types: the PUZH fuel shows a flatter behavior.
Table 2.9. Assembly-Average Densities and Volume Fractions of the Fuel Constituents of the PUZH
PuH2
U
ZrH1.6
g/cc
0.8678
3.7211
4.0388
Volume fraction
8.34%
19.53%
72.12%
Table 2.10. Assembly-Average Densities of the U and Pu in the PUZH Assembly
g/cc kg/assembly
Pu 0.8606
44.37
235
U 0.0110
0.57
238
U 3.7092 191.25
A useful measure of the transmutation capability of these fuel types is the residual inventory at
discharge of plutonium plus minor actinides (or total TRU) as compared to the mass loaded. The
CORAIL fuel at discharge contains 107.77% of the loaded TRU, while the PUZH fuel contains
68.24% of the originally loaded TRU. In other words the CORAIL stabilizes the plutonium
inventory while the PUZH consumes 31.76% of the loaded TRU in one pass through the core.
27
1.3
1.25
1.2
kinf
1.15
CORAIL
1.1
PUZH
1.05
1
0.95
0.9
0
500
1000
1500
EFPD
Figure 2.7: k∞ evolution with fuel life (in EFPD) for CORAIL and PUZH first recycle
Table 2.11 and Table 2.12 give the detailed mass balances for, respectively, the CORAIL and
PUZH at BOL and EOL. The amount of americium and curium in the discharged PUZH
assembly is about three times higher than in the case of CORAIL. Additionally the residual
plutonium in the PUZH is still about twice as much, reflecting the higher loading, despite the
higher destruction fraction. The downloaded plutonium is more degraded in the PUZH assembly,
having only 49.8% of fissile fraction, while in the CORAIL the fissile fraction is 58.68%.
Table 2.11. Nuclide Balance for the CORAIL Assembly with First Recycle Plutonium
TOT U
TOT Np
TOT Pu
Fiss Pu/Pu
TOT Am
TOT Cm
BOL (g/assembly) EOL (g/assembly)
442164
419309
0.00
248.95
13057
13260
63.75%
58.68%
92.04
487.84
0.00
193.87
Table 2.12. Nuclide Balance for the PUZH Assembly with First Recycle Plutonium
TOT U
TOT Np
TOT Pu
Fiss Pu/Pu
TOT Am
TOT Cm
BOL (g/assembly) EOL (g/assembly)
191820
184298
0.00
34.78
44052
28257
63.75%
49.80%
312.34
1507.19
0.00
553.69
28
2.3.2
MOX-UE characterization and comparison with PuH2-U-ZrH1.6 (PUZH) for
first-recycle plutonium
The MOX-UE [3] (MOX with Enriched Uranium) design is a standard 17x17 fuel assembly
containing 264 fuel rods and 25 guide tubes (24 control rods and 1 central instrumentation
channel). Four assembly designs were analyzed, as in [3]; their plutonium content is 0% (or
conventional UO2 fuel), 4%, 8% and 12%. The uranium enrichment is consequently varied to
achieve an assembly burnup of 60 GWd/t. The uranium enrichment, from [3] is 4.9% for the
reference UO2 core (no plutonium), 3.7% for 4% Pu, 2.3% for 8% Pu and 0.3% for 12% Pu. The
geometry of the system, not described in [3], is assumed for consistency and ease of comparison
to be the standard 17x17 PWR assembly design used for the PUZH and CORAIL assemblies. All
fuel assemblies were designed to have the same cycle length at the same power level.
The mass balance for the different MOX-UE assembly designs is reported in Table 2.13 to Table
2.16 for, respectively, 0%, 4%, 8% and 12% plutonium. The TRU transmutation effectiveness is
summarized in the last column of Table 2.17. The MOX-UE-4 assembly, that containing only
plutonium and depleted uranium, has the best transmutation performance. The mass of loaded
TRU (Pu and Am only) is 54 kg/assembly, and the total remaining TRU at EOL is 48 kg, giving
a fractional TRU destruction of 16.35%. Smaller plutonium loading, and correspondingly larger
235
U loading, decrease the transmutation effectiveness.
The PUZH fuel assembly achieves the largest TRU fractional destruction of 31.6%. For
comparison, a MOX-UE fuel assembly initially loaded with same amount of TRU gives a
fractional transmutation of 15.6%. Design and performance data for this equivalent MOX-UE
fuel assembly are given in the last line of Table 2.17; the data given was obtained by interpolated
between the corresponding values of the MOX-UE-3 and MOX-UE-4 designs. The required
plutonium weight fraction is 9.3, and the uranium enrichment need be 1.7%.
Table 2.13. Nuclide Balance for the MOX-UE-1 Assembly with 0% First Recycle Plutonium
TOT U
TOT Np
TOT Pu
Fiss Pu/Pu
TOT Am
TOT Cm
BOL
(g/assembly)
475607
0.00
0.00
N/A
0.00
0.00
EOL
(g/assembly)
447107
324
5654
70.58%
100.9
35.2
Table 2.14. Nuclide Balance for the MOX-UE-2 Assembly with 4% First Recycle Plutonium
TOT U
TOT Np
TOT Pu
Fiss Pu/Pu
TOT Am
TOT Cm
BOL
(g/assembly)
457500
0.00
18944
63.75%
134.32
0.00
29
EOL
(g/assembly)
438777
215.20
16198
59.67%
748.25
336.97
Table 2.15. Nuclide Balance for the MOX-UE-3 Assembly with 8% First Recycle Plutonium
TOT U
TOT Np
TOT Pu
Fiss Pu/Pu
TOT Am
TOT Cm
BOL
(g/assembly)
439300
0.00
37963
63.75%
269.18
0.00
EOL
(g/assembly)
424061
159.36
30607
58.04%
1253.15
459.41
Table 2.16. Nuclide Balance for the MOX-UE-4 Assembly with 12% First Recycle Plutonium
TOT U
TOT Np
TOT Pu
Fiss Pu/Pu
TOT Am
TOT Cm
BOL
(g/assembly)
421046
0.00
57055
63.75%
404.5
0.00
EOL
(g/assembly)
408444
83.15
45681
57.54%
1734.2
564.25
Table 2.17. Summary of the MOX-UE Fuel Assemblies Performance, as compared to PUZH and CORAIL;
included also a MOX-UE with the same initial TRU mass as PUZH
Pu (weight%)
Uranium
enrichment (%)
Cycle length
(EFPD)
TRU @ BOL
(g/assembly)
TRU @ EOL
(g/assembly)
TRU fractional
destruction
MOX-UE 1
0
4.9
1226
0.0
6114
N/A
MOX-UE 2
4
3.7
1122
19078
174989
8.28%
MOX-UE 3
8
2.3
1164
38232
32479
15.05%
MOX-UE 4
12
0.3
1222
57459
48062
16.35%
CORAIL
N/A
N/A
1256
13149
141901
-7.92%
PUZH
18.78
0.3
1246
44365
30353
31.58%
MOX-UE eq*
*
9.3
1.7
N/A
44365
37449
15.59%
Equivalent to PUZH in terms of amount of Pu loaded; data obtained by interpolating designs MOX-UE 3 and
MOX-UE 4
It is concluded that the PUZH fuel offers twice as large fractional transmutation as the equivalent
MOX-UE oxide fuel. That is, a PWR loaded with PUZH fuel assemblies will incinerate in the
first recycle twice as much TRU (primarily Pu) as it will do when loaded with MOX-UE fuel
assemblies when both core designs are loaded with same amount of TRU and operate at the same
power level for the same time. The PUZH core is likely to be less expensive as it uses depleted
uranium versus significantly larger quantities of 1.7% enriched uranium required for the
equivalent MOX-UE core.
2.3.3
Power peaking factor of CORAIL, PUZH and MOX-UE
A drawback of the CORAIL design is a higher power peaking factor than in uniformcomposition fuel assemblies. The CORAIL parameters for first recycling – fuel rod position,
30
number, uranium enrichment and plutonium weight fraction – were chosen to avoid a peaking
factor higher than 1.2 at any point along the fuel life. This was in fact verified by our
calculations.
Figure 2.8 shows the burnup-dependent pin-wise power peaking of the CORAIL, MOX-UE and
PUZH fuel assemblies. It is observed that the PUZH fuel design has a lower power peaking
factor than all the plutonium-bearing fuel assemblies analyzed along the entire fuel life (it is
always less than 1.09). The MOX-UE-1 design, that is essentially a conventional UO2 fuel
assembly design, has a lower peaking factor. However, this fuel does not contain plutonium at
BOL. The higher initial plutonium content in the MOX-UE fuel assemblies the higher becomes
the peaking factor. For the equivalent amount of Pu as in the PUZH fuel assembly, the peaking
factor of the MOX-UE fuel assembly is more than 1% point larger – approximately 1.096 versus
1.058 for the PUZH design at BOL.
The maximum peaking factor for the MOX-UE-1, MOX-UE-3 and PUZH fuel assembly designs
– respectively 1.058, 1.096 and 1.083 – is in the same location; in the vicinity of a number of
water-filled guide tubes. The lower peaking factor of the PUZH design is due to its enhanced
moderation resulting from having hydrogen in the fuel, making it less sensitive to the extra
moderation provided by the guide tubes water.
CORAIL
MOX-UE-4
MOX-UE-3
MOX-UE-2
PUZH
MOX-UE-1
1.2
1.18
1.16
Power peaking factor
1.14
1.12
1.1
1.08
1.06
1.04
1.02
1
0
200
400
600
800
1000
1200
1400
EFPD
Figure 2.8 Pin-wise power peaking factor for the various fuel assemblies analyzed
2.3.4
Reactivity coefficients of CORAIL, MOX-UE and PUZH with 1st recycle Pu
This section summarizes the three-batch core average characteristics for the MOX-UE and
PUZH, estimated from the results calculated for the equivalent unit cell using the methodology
described in [19]. The results of the calculation of the reactivity coefficients of the CORAIL fuel
assembly were presented in Section 2.2.9 in connection with the benchmarking.
31
The coefficients of reactivity – especially CTC and SVRC, are strongly dependent on the amount
of soluble boron. An approach typically used at the level of unit cell and fuel assembly analysis
is to assume a cycle average boron concentration. This assumption underestimates the necessary
amount of soluble boron at BOC, leading to non-conservative estimates of the CTC and SVRC.
Hence, time-dependent soluble boron concentration is calculated for our analysis.
For the PUZH fueled unit cell, the BOC needed amount of boron is 2758 ppm while at EOC no
boron is left in the core (0 ppm). The EOC core average k∞ is assumed 1.05, allowing for 5%
neutron leakage probability from the finite core. All the reactivity coefficients of the PUZH
fueled unit cell with plutonium from first recycling were found substantially negative, offering a
margin of safety even without the use of burnable poisons to reduce the critical soluble boron.
Next consider the MOX-UE fueled unit cells. First their exact boron let-down curve has been
estimated. It was found that the BOC required boron concentration is quite similar for the MOXUE fuel types, as evidenced in the last column of Table 2.18; this is despite of the substantially
different isotopic concentration.
Table 2.18. Summary of the MOX-UE Fuel Assemblies Performance, as Compared to PUZH; Included also a
MOX-UE with the Same Initial TRU Mass as PUZH
Pu w/o
MOX -UE 1
MOX -UE 2
MOX -UE 3
MOX -UE 4
MOX-UE eq
PUZH
0
4
8
12
9.3
10
U
enrichment (%)
4.9
3.7
2.3
0.3
1.7
0.3
Cycle length
(EFPD)
1494.8
1389.6
1393.4
1431.6
N/A
1433.2
Fractional Pu
destruction
N/A
10.58%
17.69%
18.71%
18.32%
35.69%
Sol Bor at
BOC (ppm)
2513.7
2167.1
2395.9
2604.6
N/A
2758.3
Figure 2.9 shows on the left the cycle-by-cycle LVRC for the MOX-UE fueled unit cells (MOXUE-1 to MOX-UE-4) and on the right the corresponding core-average burnup-dependent LVRC.
All other coefficients of reactivity were found negative). It is observed that only the MOX-UE-1
and MOX-UE-3 are acceptable over the entire desired burnup range without use of burnable
poisons. MOX-UE-4 has a positive LVRC at BOC that is only slightly negative at EOC. From
the trends in Figure 2.9 it appears that an increase in the fractional content of plutonium beyond
the 12 w/o value of MOX-UE-4 will results in positive values of core-averaged LVRC even at the
EOC when there is no boron – an un-acceptable situation from the safety viewpoint. This result
is consistent with the values reported in the literature [3], for which 12w/o plutonium loading (as
in the case of MOX-UE-4) is the limit for a negative LVRC. For comparison, using PUZH fuel
with depleted uranium as in the case of MOX-UE-4 enables attaining the same cycle length of
the MOX-UE fueled systems while maintaining all the coefficients of reactivity, including the
LVRC (in Figure 2.10), substantially negative. In addition, the fractional destruction of TRU in
the PUZH fueled system is about twice that of the largest fractional transmutation attainable
using MOX-UE fuel (Table 2.17 and Table 2.18).
32
100.00
200.00
0.00
0.00
LVRC (pcm/% void)
LVRC (pcm/% void)
-100.00
-200.00
-400.00
-600.00
MOXUE-1
MOXUE-2
-300.00
-400.00
MOXUE-1
MOXUE-2
-500.00
MOXUE-3
-600.00
MOXUE-3
-800.00
-200.00
MOXUE-4
-700.00
MOXUE-4
-1000.00
-800.00
0
200
400
600
800
1000
1200
1400
1600
0
100
200
EFPD
300
400
500
600
EFPD
Figure 2.9 Large void coefficient of reactivity (LVRC) of MOX-UE fueled unit cell (left); core average (right)
0.00
0.00
-50.00
LVRC (pcm/% void)
LVRC (pcm/% void)
-50.00
-100.00
-150.00
-200.00
-100.00
-150.00
-200.00
-250.00
-300.00
-250.00
0
200
400
600
800
1000
1200
1400
1600
0
EFPD
100
200
300
400
500
600
EFPD
Figure 2.10 Large void coefficient of reactivity of PUZH fueled unit cell (left); core average (right)
33
2.4 Identification of the Most Promising Hydride Fuels (fertile free, thoriumand uranium-based) for Pu Multi-Recycling
2.4.1
Depletion performance for 1st Pu recycle of fertile-free hydride fuels and of hydride
fuels with variable amounts of thorium
An assessment was undertaken of the feasibility of enhancing the fractional plutonium
transmutation using thorium-based and fertile-free hydride fuels. These fuels are of the form
ThH2-ZrH1.6-PuH2, with Pu from first recycling. All the results pertain to the reference PWR unit
cell dimensions (Table 2.19), and were obtained from effective unit cell analysis accounting for a
3-batch fuel management strategy using the methodology described in [19].
Table 2.19. Unit Cell Geometry and Specific Power
Clad outside diameter
P/D
Fuel diameter
Clad inside diameter
Pitch
Specific power
Hydride Fuels
0.95 cm
1.3261
0.8192 cm
0.8357 cm
1.26 cm
76.715 W/giHM
Oxide Fuels
0.95 cm
1.3261
0.8205 cm
0.8357 cm
1.26 cm
36.138 W/giHM
The fuel composition is determined using the following procedure: Initially a plutonium amount
is guessed with the intent of matching the fuel cycle length of about 1430 EFPD3. A certain
fraction of the remaining fuel volume is assigned to ThH2 and the balance to zirconium hydride
(ZrH1.6). Once the cycle length obtained in this way is known, the plutonium amount is increased
or decreased to reach the desired cycle length and the remaining volume is split between the two
hydrides (ThH2 and ZrH1.6) in the same ratio as before. This is repeated until convergence. This
parametric study covered the entire ThH2 to (ThH2 + ZrH1.6) volume fraction range from 0 v/o to
100 v/o. The case having 0 v/o ThH2 is a fertile-free based hydride fuel. Table 2.20 gives the
resulting composition of the unit cells examined, all featuring the same cycle length in EFPD.
The required plutonium amount increases with the thorium content, going from 0.772 g/cm3 for
the case without thorium (PuH2-ZrH1.6) to 1.098 g/cm3 for the case with no zirconium (ThH2PuH2). Correspondingly, the density of the fuel increases from 5.956 g/cm3 for the fertile free
case to 9.595 g/cm3 for the case without zirconium. Because of the strongly varying amount of
heavy metal, the fuel burnup is highly varying – from 624.0 GWD/MTiHM for the fertile free
case to 50.5 GWD/MTiHM for the case without zirconium.
3
1430 EFPD is the cycle length of the CORAIL, MOX-UE and PUZH fueled assemblies that use first recycle
plutonium
34
Table 2.20: Properties of ThH2 and Fertile-Free Hydride Fueled Unit Cells
ThH2 v/o of ZrH1.6
Pu density (g/cm3)
Fuel density (g/cm3)
HM density (g/cm3)
Th density (g/cm3)
Burnup (EFPD)
Burnup
(GWD/MTiHM)
0%
0.772
5.956
0.766
0.0
1427
20%
0.783
6.683
2.519
1.742
1425
30%
0.808
7.052
3.407
2.606
1428
40%
0.839
7.422
4.296
3.463
1430
50%
0.876
7.790
5.181
4.312
1433
60%
0.917
8.157
6.062
5.153
1435
70%
0.960
8.521
6.936
5.984
1436
80%
1.005
8.882
7.803
6.806
1436
100%
1.098
9.595
9.513
8.424
1434
624.0
189.4
140.3
111.5
92.6
79.3
69.3
61.6
50.5
Figure 2.11 shows that, for the same three batch cycle length, the burnup reactivity swing is
reduced with an increase in the ThH2 content. This is because the conversion ratio increases with
the thorium volume fraction.
1.4
0% v/o ThH2
20% v/o ThH2
1.3
70% v/o ThH2
1.2
100% v/o ThH2
kinf
1.1
1
0.9
0.8
0.7
0.6
0.5
0
200
400
600
800
1000
1200
1400
EFPD
Figure 2.11 k∞ evolution dependence on the ThH2 volume fraction
The transmutation performance of the analyzed fuels is quantified by means of the TRU
destruction fraction, defined as the ratio between the mass of TRU at discharge and the mass of
the loaded TRU. Also of interest for proliferation concerns is the plutonium fissile fraction at
discharge, defined as the ratio between the mass of 239Pu and 241Pu and the total mass of
plutonium.
Figure 2.12 gives the TRU destruction fraction and the plutonium fissile fraction at discharge as
a function of the ThH2 volume fraction. The TRU destruction fraction decreases with the ThH2
volume fraction, from a value of 63.89% for fertile free fuels to 35.85 % for ThH2-PuH2. This
latter performance is similar to the one of PUZH (35.69%) and about double that of the highest
performing MOX-UE (18.71%). Fertile free fuels (FFF), or almost fertile free fuels (AFFF) (i.e.
those with a little amount of ThH2) feature a TRU destruction fraction that is slightly less than
double that of PUZH. The plutonium fissile fraction increases with the thorium content, from a
low of 22.38% for the fertile free fuel to a maximum of 45.25% for ThH2-PuH2 fuel.
35
70%
TRU destr frac
60%
Fiss fraction
50%
40%
30%
20%
10%
0%
0%
20%
40%
60%
80%
100%
ThH2 volume fraction
Figure 2.12. TRU destruction fraction and fissile fraction at discharge versus the ThH2 v/o
2.4.2
TRU destruction fraction for 1st Pu recycle of PUZH and MOX with partial
uranium loading
Both MOX and PUZH fuelled cores with Pu from first recycle (Table 2.7) and different fractions
of uranium loading are analyzed in this section. The MOX fuel examined is of a more general
composition than the “conventional” MOX – it may contain a certain amount of ZrO2 to make up
for the volume fraction of the fuel that is not fully loaded with uranium. The inert matrix oxide
fuel PuO2-ZrO2 is evaluated as well to provide a fair comparison with the inert matrix hydride
fuel PuH2-ZrH1.6.
Among the evaluated parameters are the attainable burnup, the mass balance of actinides
throughout the recycling, the TRU destruction fraction, the plutonium fissile fraction, the initial
conversion ratio (ICR), and the reactivity coefficients as a function of the fuel life, for the last
recycle. Additionally, for both fuel types, a multi-recycling analysis was performed. As for the
Th-containing hydrides described in the previous section, all the results pertain to the reference
PWR unit cell dimensions and were obtained from effective unit cell analysis (Table 2.19).
The uranium used is depleted to 0.3% and the plutonium vector taken from the UO2 fuelled LWR
spent fuel (also referred to here as “from the repository”) is that of Table 2.7. For both fuel types
(i.e. PUZH and MOX) the fuel composition is determined in the following way: the uranium
amount is given as a fixed parameter, indicated in the following as a fraction of the maximum
uranium loadable in the specific fuel type, as explained in the next paragraph. For each fuel type
the plutonium amount is guessed and the amount of zirconium (hydride or oxides) is calculated
by filling the space not taken by either the uranium or the plutonium, each in the appropriate
chemical form. The cycle length is calculated for this composition, and eventually the plutonium
amount is adjusted to give the desired cycle length of 1430 Effective Full Power Days (EFPD).
The PUZH fuel analyzed in this study comprises of 5 different uranium loadings, referred to as
percent of the maximum loading allowable in zirconium hydrides: U 0%, 25%, 50%, 75% and
100% of the maximum: 3.72 g/cm3 – corresponding to the reference U-ZrH1.6 fuel. The resulting
fuel compositions for the various uranium amounts in case of PUZH for the first irradiation are
given in Table 2.21.
36
Table 2.21. Properties of PUZH Fuels with Partially-Loaded Uranium
Characteristic
3
U density (g/cm )
Pu density (g/cm3)
HM density (g/cm3)
fuel density (g/cm3)
H/HM
Burnup (GWD/MTiHM)
EFPD
0%
0
0.7337
0.7338
5.9415
82.04
628.4
1376.0
Fraction of uranium
25%
50%
75%
0.9301
1.8601
2.7902
0.7564
0.7791
0.8018
1.6865
2.6392
3.592
6.6087
7.2759
7.9432
34.89
21.85
15.73
284.2
182.1
132.6
1430.1
1434.3
1420.9
100%
3.7203
0.8245
4.5448
8.6104
12.18
102.9
1395.8
The amount of uranium in the MOX fuel is specified in g/cm3 to match the amount present in the
PUZH fuel with variable uranium concentration; these correspond to 0%, 11%, 22%, 34% and
45% of the maximum heavy-metal (HM) loadable in Pu-U-O24. Three additional cases are
investigated, corresponding to 64%, 84% and 100% of the maximum loadable uranium, since the
maximum amount of uranium that can be loaded in the PUZH fuel is a fraction of the mass that
can be loaded in MOX.
MOX fuel, as opposed to PUZH, present the additional issue that, after the desired amount of
uranium is specified and the required plutonium amount is calculated to reach the desired cycle
length of 1430 EFPD, the sum of the desired uranium and of the required plutonium may exceed
the available volume. If this is the case, the uranium amount is reduced to, together with the
plutonium, fill the available space. The resulting mass of ZrO2 would then obviously be zero.
This particular situation is happening only for uranium loading close to the maximum possible.
Practically, in our analysis, also along the multi-recycling, it happens only for the case labeled as
MOX 100% uranium. The densities of the MOX fuels for the first recycling are shown in Table
2.22.
In the following each case for either PUZH or MOX is identified based on the percentage of
uranium loaded, or by the first row of, respectively, Table 2.21 and Table 2.22. During multirecycling, as the plutonium quality degrades, the Pu amount that is necessary to re-load
increases. Additionally, if the uranium becomes, as a result of transmutation, non proliferation
resistant (i.e. the 235U content becomes greater than 20%), it is necessary to add some depleted
uranium, effectively increasing the reloaded amount of uranium. All this can result in a slight
deviation from the previous percentage value. Nevertheless, for sake of consistency, the cases
will still be referred to by the initial uranium fractional loading.
4
The exact mass depends on the maximum possible density of plutonium and uranium –10.96 g/cm3 for 100% UO2
or to 11.5 g/cm3 for100% PuO2. For the purpose of labeling the percentages of uranium are related to the density of
11.15 g/cm3 corresponding to the case with 0% zirconium oxide and with enough plutonium from 1st recycling to
match a cycle length of 1430 EFPD.
37
Table 2.22 MOX Fuel Composition for Each of the Cases Analyzed5
Density
0% 11.2%
U (g/cm )
0
0.930
Pu (g/cm3)
0.767 0.798
HM (g/cm3)
0.767 1.729
3
HM-O2 (g/cm ) 0.870 1.961
UPUZH (g/cm3)
0
0.930
3
Zr (g/cm )
2.738 2.429
ZrO2 (g/cm3) 3.698 3.281
Fuel (g/cm3)
4.569 5.241
3
U percent of maximum
22.4% 33.7% 44.9% 64.2% 83.6% 100.0%
1.860 2.790 3.720 5.322 6.924 8.286
0.838 0.878 0.920 0.990 1.057 1.105
2.698 3.669 4.640 6.312 7.981 9.391
3.061 4.162 5.264 7.161 9.054 10.654
1.860 2.790 3.720
N/A
N/A
N/A
2.117 1.805 1.492 0.954 0.418
0
2.859 2.438 2.016 1.289 0.564
0
5.920 6.600 7.280 8.450 9.618 10.654
The depletion properties of PUZH and MOX fuel at the first recycle are summarized in Table
2.23. The TRU destruction fraction is defined as the fraction of TRU remaining at the reactor
shutdown as a fraction of the plutonium loaded before irradiation.
Table 2.23 PUZH and MOX TRU Destruction Fraction and Pu Fissile Fraction at Discharge
U % of total in PUZH
PUZH TRU destruction fraction
MOX TRU destruction fraction
PUZH fissile fraction at EOL
MOX fissile fraction at EOL
0%
64.36%
63.65%
21.63%
24.50%
25%
54.13%
49.76%
32.87%
38.05%
50%
47.83%
42.65%
38.52%
43.39%
75%
42.39%
37.11%
42.74%
46.99%
100%
37.48%
32.56%
46.13%
49.65%
Figure 2.13 through Figure 2.15 compare the results obtained for variable uranium with those
obtained with variable thorium concentration, presented in the previous section. Figure 2.13
shows a comparison of the TRU destruction fraction for the variable uranium and variable
thorium bearing fuels, defined as a fraction of the maximum loadable6. It is found that the
transmutation performance of MOX fuels is slightly worse than that of hydride-based fuels (both
PUZH and TPZH, or Thorium-based PUZH), for each uranium loading except 0%, for which it
is similar. The performance of uranium bearing hydride fuels appears similar but slightly worse
than that of thorium bearing hydride fuels. The similarity of the 0% case of PUZH and TPZH is
not coincidental, since they are the same fuel type (PuH2-ZrH1.6). On the other hand, the strong
similarity of the 0% MOX could not have been expected as it pertains to a very different system
– MOX with 0% U, that is, PuO2-ZrO2.
The picture is slightly different when comparing, in Figure 2.14, the TRU destruction
performance as a function of H/HM for the three fuel types. For the same H/HM, the TPZH fuels
outperform the uranium bearing PUZH fuels. MOX-based fuels have a lower fractional
transmutation than TPZH but slightly higher than PUZH for the same H/HM, except for the
largest H/HM, corresponding to the 0% U case.
5
The MOX fuel is smeared to 95.5% of the theoretical density.
The percent in the abscissa indicates the fraction of the maximum loadable amount of thorium in PuH2-ThH2ZrH1.6 for the case indicated as “TPZH”, and of the maximum amount of uranium in U-ZrH1.6-PuH2 for the case
indicated as “PUZH”. For the case indicated as MOX, the percentage in the abscissa refers to the maximum amount
loadable in U-ZrH1.6-PuH2, not to the maximum loadable in MOX, which is substantially higher. The cases with
heavier loadings of uranium are omitted from these graphs, which have the purpose of comparing the TRU
destruction fraction for the same amount of uranium in case of MOX and PUZH.
6
38
Figure 2.15 provides, yet, another comparison – as a function of the amount of plutonium
initially loaded in the fuel, It is observed that for the same fractional destruction, PUZH fuels
require a substantially lower amount of plutonium than either MOX or thorium bearing PUZH
fuels.
TRU destruction fraction
80.00%
PUZH
70.00%
TPZH
60.00%
MOX
50.00%
40.00%
30.00%
20.00%
0%
20%
40%
60%
80%
100%
Volume percent of the maximum loadable
Figure 2.13 TRU fractional transmutation at discharge for variable uranium and variable thorium cases;
First recycle
70.00%
TRU destruction fraction
60.00%
50.00%
40.00%
PUZH
30.00%
TPZH
20.00%
MOX
10.00%
0.00%
0
20
40
60
80
100
H/HM
Figure 2.14 TRU fractional transmutation at discharge as a function of H/HM; First recycle
39
70.00%
PUZH
TRU destruction fraction
60.00%
TPZH
50.00%
MOX
40.00%
30.00%
20.00%
10.00%
0.00%
0.7000
0.8000
0.9000
1.0000
1.1000
1.2000
Initial Pu fuel density (g/cc)
Figure 2.15. TRU fractional transmutation at discharge for the as a function of the initial plutonium loading
in g/cm3; First recycle
2.4.3
Reactivity coefficients for 1st Pu recycle in PUZH and MOX fuel with variable
uranium loading
In this section the reactivity coefficients of PuH2-ZrH1.6(-ThH2)-U and UO2-PuO2-ZrO2 fuels
with variable uranium loading are evaluated for the first recycle. The reactivity coefficients
calculations start with an estimation of the required soluble boron, followed by
burnup-dependent calculations of the reactivity coefficients with soluble boron.
For PUZH fuel with variable uranium loading the core average CTC with soluble boron is found
positive since BOC for uranium loadings up to about 50% of the maximum possible. At EOC the
core-average CTC are negative for all uranium loadings, indicating that without soluble boron all
the geometries might be feasible. Similar findings apply to the SVRC. The LVRC is less
restrictive – it is negative through the cycle for all the uranium loadings greater than or equal to
25%. Only the case of 0% U features positive LVRC through about the first 1/3 of the cycle.
When the soluble boron concentration becomes sufficiently small, though, the LVRC becomes
negative indicating that without soluble boron the LVRC is likely to be negative throughout the
cycle. The core average FTC is found negative for the first recycle for a fractional uranium
loading greater or equal to 25% of the maximum loadable in PUZH. However, with 0% uranium
loading the FTC is found positive along the entire third batch, making the core-average FTC
positive as well. Therefore this case will be practically feasible only up to a burnup level reached
after the second batch. As an alternative approach, it was inferred, based on fuel hydrogen
induced spectrum hardening considerations, that the substitution of D for H would eliminate the
positive FTC that was found due to up-scattering by the fuel hydrogen atoms that shifts the
thermal neutron peak to better overlap the 0.3 eV resonance of 239Pu.
Figure 2.16 shows the burnup-dependent (left) and the core-average (right) FTC for H and D
based Pu-Zr fuels. The cycle length is exactly the same in both cases (1430 EFPD). It is observed
that the FTC is negative and slightly decreasing in the case of D-based fuel, and increasing in the
case of H-based fuel. In this latter case the FTC starts more negative than in the D-based fuel at
BOL and eventually becomes larger and substantially positive towards EOL; the core average is
also positive.
40
4
4
2
FTC with H
FTC with D
S i 3
3
FTC with H
2
FTC with D
FTC (pcm/K)
FTC (pcm/K)
3
1
0
1
0
-1
-1
-2
-2
-3
-3
0
500
1000
1500
0
EPFD
100
200
300
400
500
EPFD
Figure 2.16 Burnup dependent FTC (pcm/K) for ZrH1.6-PuH2 and ZrD1.6-PuD2 fueled unit cells (left); core
average (right)
Since the neutronic performances of the two fuels are similar (See Table 2.32), it is concluded
that the use of deuterium-based fuel is a satisfactory approach for Pu first recycling in fertile-free
hydride fuel. There is no need for D in the second and following recycles. An alternative design
approach for the first recycle is to add approximately 25% uranium for the first recycle; there is
no need of uranium for the following recycles.
The first recycle FTC of MOX fuel with variable uranium loading is negative and decreasing
with time for all the cases. It becomes more negative as the uranium fraction increases from 0%
to 33.7% after which it becomes insensitive to further increase in the uranium loading. The core
averaged CTC and SVRC are negative throughout the first recycle for all cases except the 0%
case, indicating that the first depletion cycle may have to be started with some uranium (at least
11.2% of the maximum) if soluble boron alone is used for reactivity compensation. More
problematic for MOX fuels is the core average LVRC: it is positive with soluble boron at BOC
for each of the cases analyzed. Cases with lower initial uranium loading have more positive BOC
LVRC, but they also feature more negative values towards the end of the cycle.
Without soluble boron, all the CTC SVRC and LVRC are negative for all the uranium loadings,
including the 0% case. Therefore it is concluded that, if a means of control other than soluble
boron were to be used, also the case with 0% uranium can safely be used for the first recycle.
Hopefully, use of burnable poisons will provide an acceptable solution.
2.4.4
Multi-recycling logic of PUZH and MOX fuel with variable uranium loading
Both the uranium and the plutonium are recycled during multi-recycles of PUZH and MOX
fuels. The minimum amount of uranium to be loaded is decided beforehand. The first irradiation
starts with depleted uranium (0.3%). All the uranium remaining after irradiation is re-cycled into
the next cycle (minus the reprocessing losses of 0.1% [20]). If the recycled uranium is not
enough to match the amount required, the balance is added using depleted uranium. If, on the
other hand, the amount of downloaded uranium is larger than at the beginning of the irradiation –
in other words if there was a net production of uranium, the entire amount is re-fabricated in the
new fuel, after accounting for the processing losses. This latter situation happens only in the case
41
of 0% uranium, for both MOX and PUZH, where a small net production occurs during the
multiple recycles.
As in the case of uranium, the entire amount of plutonium remaining after irradiation, minus the
reprocessing losses of 0.1%, is recycled in the newly fabricated fuel. The total amount of
plutonium is adjusted to meet the required cycle length of 1430 EFPD, for each of the cases and
for each irradiation step, by adding fresh plutonium coming from the LWR spent fuel, the
isotopic composition of which is shown in Table 2.7.
2.4.5
Uranium and plutonium mass balance along the recycling for PUZH fuel with
variable uranium loading
The uranium loaded in each recycle for each of the 5 cases remains constant at the original value
for all the cases except for the 0% uranium, which shows a slight increase. Additionally, the
enrichment of the uranium has to remain below the limits imposed by proliferation concerns.
Again, this is an issue only for the case of 0% uranium: the formation of relatively large
quantities of 234U in the first few re-cycles (see Figure 2.17 for the isotopic evolution of the
uranium present in the fuel for the case of 0% uranium), leads to a formation of growing amounts
of 235U in the following re-cycles7. Therefore it is necessary to add a minimum amount of
depleted uranium, determined re-cycle by re-cycle, to denature the mixture below the enrichment
limit for proliferation purposes (20%).
100
U-232
U-233
U-234
U-235
U-236
U-237
U-238
90
80
70
atom %
60
50
40
30
20
10
0
0
5
10
15
20
Cycle Number
25
30
35
Figure 2.17 Uranium isotopic evolution, in atom percent, as a function of the recycle number for the case with
0% initial uranium loading; PUZH fuel
The total mass of plutonium loaded in the fuel, shown in Figure 2.18 (left), increases with the
recycle number, reflecting degradation of its isotopic quality. Since the energy produced in each
recycle is the same, the total mass of recycled plutonium (shown in Figure 2.18, right) increases
7
The first recycle, indicated as step zero in the abscissa, has a nominal composition of the standard depleted
uranium. This is somewhat arbitrary: the intention is to have 0 g/cm3 of uranium. Nevertheless, in order for
ORIGEN to properly update the isotopes, it is necessary to initialize the composition with negligible amounts of
each isotope that is to be traced. The initialization values are set somewhat arbitrarily at the standard depleted
uranium isotopic.
42
3
2.5
2.5
2
2
Pu recycled (g/cc)
Rho Pu (g/cc)
as well. It is observed that fuels with higher uranium loading require also a higher amount of
plutonium loading, and discharge a higher amount of plutonium for recycling. On the other hand,
the plutonium that is withdrawn from the repository, or the difference between the total loading
and the recycled mass, decreases with the recycle number for each of the five cases examined. It
can also be observed that the cases with lower uranium loading feature a smaller decrease in the
withdrawal mass, maintaining their plutonium destruction capability more effectively with
multiple recycles. This reflects the fact that the conversion ratio becomes smaller with lower
uranium loading.
U 0%
U 25%
U 50%
U 75%
U 100%
1.5
1
0.5
1.5
U 0%
U 25%
U 50%
U 75%
U 100%
1
0.5
0
5
10
15
20
Cycle Number
25
30
0
35
0
5
10
15
20
Cycle Number
25
30
35
Figure 2.18 Plutonium loading (left) and recycled (right), in g/cm3, as a function of the recycle number;
PUZH fuel
2.4.6
Uranium and plutonium mass balances along the recycling for MOX fuel with
variable uranium loading
In this section the MOX fuel with variable uranium loading is analyzed along the first 10
recycles. Even though an equilibrium composition is not completely reached, the recycling is
stopped at the 10th recycle because the LVRC becomes positive for each of the MOX fuel types,
both with and without soluble boron (see Section 2.4.12), even when accounting for the
increased leakage due to large core voiding (See Section 2.4.13). Therefore, for safety concerns,
no further recycling can be made. The total uranium loaded in each recycle for each of the 8
cases of MOX fuel remains constant at the original value for all the cases except for the 0% and
100% uranium, which show respectively a slight increase and a decrease. The decrease in the
case of 100% uranium reflects the increase in the amount of plutonium required along the multirecycling; since, by definition of 100% uranium, no spare volume is left, every increase in the
plutonium has to be compensated by a reduced volume of uranium. Additionally, the enrichment
of the uranium has to remain below the limits imposed by proliferation concerns. As in the case
of PUZH, this is an issue only for the case of 0% uranium: the formation of relatively large
quantities of 234U in the first few recycles leads to a formation of growing amounts of 235U in the
following recycles. Therefore it is necessary to add a minimum amount of depleted uranium,
determined recycle by recycle, to denature the mixture below the enrichment limit for
proliferation purposes (20% 235U).
43
The total mass of plutonium loaded in the fuel, shown in Figure 2.19 (left), increases with the
recycle number, reflecting its degradation in isotopic quality. Since the energy produced in each
recycle is the same, the total mass of recycled plutonium (shown in Figure 2.19, right) increases
as well. It is observed that fuels with larger uranium loading require also a larger amount of
plutonium loading and discharge a larger amount of plutonium for recycling. The plutonium that
is withdrawn from the repository, or the difference between the total loading and the recycled
mass, decreases with the recycle numbers for each of the five cases. It is also observed that the
cases with lower uranium loading feature a smaller decrease in the withdrawal mass, maintaining
their destruction properties more effectively than cases with larger uranium loadings with
multiple recycles.
1.8
2.2
1.6
2
1.4
Pu recycled (g/cc)
Rho Pu (g/cc)
1.8
1.6
1.4
U 0%
U 11.2%
U 22.4%
U 33.7%
U 44.9%
U 64.2%
U 83.6%
U 100.0%
1.2
1
0.8
0.6
1.2
1
0.6
0.4
0.2
0
1
2
3
4
5
6
Cycle Number
7
8
9
U 0%
U 11.2%
U 22.4%
U 33.7%
U 44.9%
U 64.2%
U 83.6%
U 100.0%
0.8
10
1
2
3
4
5
6
Cycle Number
7
8
9
10
Figure 2.19 Plutonium loaded (left) and recycled (right), in g/cm3, as a function of the recycle number; MOX
fuel
2.4.7
TRU destruction fraction and plutonium fissile fraction at discharge for PUZH and
MOX fuels with variable uranium loading
Figure 2.20 shows the TRU destruction fraction for PUZH and MOX fuels – both with variable
uranium – as a function of the recycle number. The TRU destruction fraction is defined here to
be one minus the ratio of the number of TRU atoms discharged to the number of plutonium
atoms loaded. It is observed that, as expected, the TRU destruction fraction decreases with the
uranium loadings because of an increase in the conversion ratio. A similar trend is observed for
MOX and PUZH fuels.
44
0.8
0.8
U 0%
U 25%
U 50%
U 75%
U 100%
0.7
0.6
TRU destruction fraction
TRU destruction fraction
0.7
0.5
0.4
0.3
0.2
0.1
U 0%
U 11.2%
U 22.4%
U 33.7%
U 44.9%
U 64.2%
U 83.6%
U 100.0%
0.6
0.5
0.4
0.3
0.2
0
5
10
15
20
Cycle Number
25
30
0.1
35
0
1
2
3
4
5
6
Cycle Number
7
8
9
10
Figure 2.20 TRU destruction fraction as a function of the recycle number; PUZH fuel (left) and MOX fuel
(right)
The TRU destruction fraction for low uranium content fuels compares favorably with critical fast
reactor systems envisioned in [9] for multi-recycling of TRU - 18.6% TRU destruction fraction
for fast critical systems and 29.2% for ATW, both at equilibrium. This is not quite a fair
comparison as only Pu is recycled in the above considered PWR cores.
Figure 2.21 shows the plutonium fissile fraction at discharge for PUZH and MOX fuels as a
function of the recycles. A different behavior is observed for different uranium loading -decreasing for heavier uranium loading and increasing (or remaining flat in case of MOX) for the
case with 0% initial uranium loading. Intermediate uranium loadings have mixed behavior in
PUZH: for example the case of 25% uranium loading increases for the first three recycles and
decreases thereafter.
0.5
0.65
U 0%
U 25%
U 50%
U 75%
U 100%
0.45
0.55
0.4
0.5
Pu fissile fraction
Pu fissile fraction
U 0%
U 11.2%
U 22.4%
U 33.7%
U 44.9%
U 64.2%
U 83.6%
U 100.0%
0.6
0.35
0.3
0.45
0.4
0.35
0.3
0.25
0.25
0.2
0
5
10
15
20
Cycle Number
25
30
35
0.2
0
1
2
3
4
5
6
Cycle Number
7
8
9
10
Figure 2.21 Plutonium fissile fraction at discharge as a function of the recycle number; PUZH fuel (left) and
MOX fuel (right)
This peaking is a reflection of a similarly-peaking behavior in the concentration of 241Pu at
discharge, shown for PUZH in Figure 2.22. The inventories of the recharged 240Pu and 241Pu at
each recycle in PUZH are shown in Figure 2.23.
45
10
U 0%
U 25%
U 50%
U 75%
U 100%
9.5
Pu-241 atom %
9
8.5
8
7.5
7
Figure 2.22
0
5
10
15
Cycle Number
20
25
241
Pu concentration at discharge as a function of the recycle number; PUZH fuel
0.250
0.900
0.800
0.200
0.600
Inventory (g/cc)
Inventory (g/cc)
0.700
0.500
0.400
inventory of Pu240 U 0%
0.300
0.150
0.100
inventory of Pu241 U 0%
inventory of Pu241 U 25%
inventory of Pu240 U 25%
0.200
0.050
inventory of Pu240 U 50%
0.100
inventory of Pu241 U 50%
0.000
0.000
0
5
10
15
0
20
5
10
15
20
Cycle Num ber
Cycle Number
Figure 2.23 Inventory of 240Pu (left) and 241Pu (right) in the re-charged plutonium at each recycle; PUZH fuel
2.4.8
Initial conversion ratio of PUZH and MOX fuels with variable uranium loading
The Initial Conversion Ratio (ICR), calculated as:
ICR =
ΦΣ Un,γ− 238 + ΦΣ Un,γ− 234 + ΦΣ nPu,γ− 238 + ΦΣ nPu,γ− 240 + ΦΣ nPu,γ− 242
ΦΣ nPu,a− 239 + ΦΣ nPu,a− 241 + ΦΣ Un ,−a 235 + ΦΣ Un ,−a 233 + ΦΣ nPu,a− 243 + λ Pu − 243 N Pu − 243 + λ Pu − 241 N Pu − 241
is plotted in Figure 2.24 for PUZH and MOX fuels as a function of recycles. 234U, normally not
accounted for in the calculation of ICR, is included here because of its relatively large
importance in the case of 0% uranium loading (see Figure 2.17). For both PUZH and MOX the
ICR increases with the recycles and is higher the higher is the uranium loading.
46
0.75
0.8
0.7
0.75
0.65
0.7
0.6
0.65
0.6
ICR
ICR
0.55
0.5
0.45
0.4
U 0%
U 11.2%
U 22.4%
U 33.7%
U 44.9%
U 64.2%
U 83.6%
U 100.0%
0.45
0.4
0.35
0.3
0.55
0.5
U 0%
U 25%
U 50%
U 75%
U 100%
0.35
0
5
10
15
20
Cycle Number
25
30
35
0.3
0
1
2
3
4
5
6
Cycle Number
7
8
9
10
Figure 2.24 ICR as a function of recycle number, for different uranium loading; PUZH fuel (left) and MOX
fuel (right)
2.4.9
One-group cross sections of fertile-free PUZH fuel at equilibrium (33rd recycle)
The BOL effective one-group cross sections and related neutronic characteristics of PUZH fuel
at the beginning and end of the equilibrium recycle are summarized in, respectively, Table 2.24
and Table 2.25.The nuclei present in the system are ranked by the fractional absorption per
fission neutron. The dominant role is played by the plutonium isotopes. The uranium isotopes
have only a minor role because of their low concentration in this fuel. The average η value for
this fuel is 1.21453 at BOC and 1.11067 at EOC.
Table 2.24 Total, Absorption, Fission Cross Sections, ν and η of PUZH at Beginning of Equilibrium Cycle
Total XS
(b)
41.704
31.178
47.531
16.630
20.906
28.025
Absorption XS
(b)
33.015
19.896
38.392
5.687
9.347
16.409
Fission XS
(b)
20.960
0.700
28.673
0.555
1.899
0.633
ν
η
Pu
Pu
241
Pu
242
Pu
238
Pu
234
U
Fraction of neutron absorbed
per fission neutron(%)
42.12%
27.94%
15.03%
8.78%
1.74%
0.76%
2.895
3.135
2.959
3.182
3.065
2.655
1.838
0.110
2.210
0.310
0.623
0.102
H in H2O
Zr in ZrH1.6
235
U
238
U
0.75%
0.72%
0.56%
0.55%
11.983
6.917
25.635
21.378
0.010
0.032
16.934
6.973
0
0
12.261
0.139
N/A
N/A
2.448
2.826
0
0
1.772
0.056
Zr in Clad
H in ZrH1.6
236
U
16
O in H2O
0.34%
0.27%
0.23%
0.20%
6.999
11.051
22.208
3.432
0.035
0.006
9.183
0.005
0
0
0.386
0
N/A
N/A
2.588
N/A
0
0
0.109
0
239
240
47
Table 2.25 Total, Absorption, Fission Cross Sections, ν and η of PUZH at End of Equilibrium Cycle
240
Pu
239
Fraction of neutron absorbed
per fission neutron(%)
25.79%
34.590
Absorption XS
(b)
23.062
Total XS (b)
Pu
Pu
242
Pu
243
Am
241
Am
238
Pu
24.73%
23.38%
9.10%
4.40%
2.37%
1.84%
54.394
56.160
16.873
39.171
49.481
22.803
45.613
46.981
5.846
29.676
40.246
11.093
H in H2O
Zr in ZrH1.6
103
Rh
0.90%
0.79%
0.74%
12.227
6.928
19.899
0.011
0.033
13.002
0.74%
0.70%
0.69%
0.61%
0.61%
0.58%
0.57%
0.49%
0.49%
0.47%
26.128
43916.1
28.246
68.256
1247.8
27.092
17.380
41.666
21.551
202.257
13.468
36718.7
19.504
23.241
1216.9
15.548
9.295
32.162
7.001
68.263
241
244
Cm
Xe
235
U
131
Xe
149
Sm
234
U
133
Cs
109
Ag
238
U
152
Sm
135
Fission XS (b)
ν
η
0.689
3.134
0.094
28.761
34.844
0.544
0.555
0.877
1.939
2.892
2.958
3.182
3.771
3.413
3.058
1.823
2.194
0.296
0.070
0.074
0.534
1.035
3.787
0.291
14.423
2.446
1.809
0.623
2.653
0.106
0.135
2.828
0.055
2.4.10 Shutdown margin at equilibrium (33rd recycle) for fertile-free PUZH fuel
The control rods shutdown margin is evaluated for the equilibrium PUZH core (33rd recycle).
The evaluation is done at BOL – when the reactivity of the fuel is maximal, both with and
without soluble boron and with all the core constituents at cold (300 K) shutdown condition; the
water density is correspondingly 1 g/cm3. Conservatively, the concentrations of both Xe and Sm
are set to zero; no credits are assumed for partially burned fuel batches. The calculations are
done for a 2-D quarter assembly model using TRITON and 238 energy groups. Two types of
control rods are investigated: B4C and standard Ag-In-Cd (AIC).
The results are summarized in Table 2.26 where they are compared to those obtained for the
reference UO2 fueled core. It is found that the AIC control rods are not capable of keeping the
cold shut-down PUZH fuelled core below the desired value of 0.95. However, with B4C control
rods k∞ becomes 0.97038 and the corresponding keff is expected to be smaller than 0.95 even
without any soluble boron in the coolant. The shutdown margin of a PUZH core that uses B4C
control rods (0.97038) is comparable to that of the reference UO2 core that uses the reference
AIC control rods (0.97419). If a larger shutdown margin is needed, the B4C could be enriched
with 10B.
48
Table 2.26 BOL Control Rod Shutdown Margin With and Without Critical Soluble Boron; Equilibrium
Recycle
no CR
AIC
B4C
PUZH fuel
k∞ with
k∞ without
soluble boron soluble boron
1.09981
1.22860
0.97097
1.05076
0.89777
0.97038
UO2 fuel (reference)
k∞ with soluble
k∞ without
boron
soluble boron
1.12866
1.35481
0.85074
0.97419
0.75451
0.85589
2.4.11 Reactivity coefficients at equilibrium (33rd recycle) for PUZH fuel with variable
uranium loading
At the 33rd recycle for PUZH fuel, the FTC are negative and flat for all the cases, more negative
for higher uranium–containing systems. The CTC and SVRC, on the other hand, are positive at
the beginning of each batch, making the core-averaged values positive as well. However, when
the CTC and SVRC are evaluated without soluble boron, they remain negative throughout the
entire cycle. All the systems feature a similar behavior, with a slight deviation only in case of 0%
uranium.
A very different behavior is observed for LVRC. It is known [3] that the LVRC becomes
positive in MOX systems for Pu loading higher than about 12 w/o (corresponding to about 1.2
g/cm3 of plutonium). This is also shown in Section 2.4.12 (Figure 2.27). This limits the number
of feasible multi-recycles in MOX. In case of PUZH fuel, towards equilibrium, the lowest
amount of plutonium is in 0% uranium and is about 2.4 g/cm3. Nevertheless, it is observed in
Figure 2.25 that its LVRC has negative values at the end of each of the batches and of the
core-average as well. This suggests that the case with 0% uranium and little or no soluble boron
will feature negative LVRC throughout the fuel life, making this fuel feasible.
100
100
U 0%
U 25%
U 50%
U 75%
U 100%
U 0%
U 25%
U 50%
U 75%
U 100%
80
LVRC (pcm/% void)
LVRC (pcm/% void)
60
50
0
40
20
0
-20
-50
0
500
1000
1500
EFPD
-40
0
50
100
150
200
250
EFPD
300
350
400
450
500
Figure 2.25 LVRC with soluble boron, as a function of burnup (left), core average value along the
equilibrium recycle (right); PUZH fuel
Without soluble boron, the CTC and SVRC are both negative, as expected, and decreasing with
burnup. The core average LVRC (in Figure 2.26) is positive for all the heavier uranium loading
(25% to 100%), but is negative throughout the cycle for the case with 0% uranium. Therefore, if
a method was devised to reduce enough the soluble boron necessary for controlling the excess
49
reactivity, such as the use of burnable poisons [2,25], the case with 0% uranium could be
successfully and safely used to infinitely recycle plutonium in PWR.
60
60
50
40
20
LVRC (pcm/% void)
LVRC (pcm/% void)
40
0
-20
U 0%
U 25%
U 50%
U 75%
U 100%
-40
-60
0
30
20
U 0%
U 25%
U 50%
U 75%
U 100%
10
0
-10
-20
500
1000
-30
1500
EFPD
0
50
100
150
200
250
EFPD
300
350
400
450
500
Figure 2.26 LVRC without soluble boron, as a function of burnup (left) and core average value along the
equilibrium cycle (right); PUZH fuel
2.4.12 Reactivity coefficients at the 13th step for MOX fuel with variable uranium loading
Even though equilibrium cannot be reached in Pu multi-recycling in MOX, in this section the
reactivity coefficients for MOX fuel with variable uranium loading at the 10th recycle to prove
that this is, indeed, the maximum feasible recycle of MOX fuel.
The FTC are found negative and decreasing with burnup for all the cases. A slight uranium
increase from the 0% to the 33.7% case causes a decrease in the value of the FTC along the
cycle; a further increase in the uranium loading has significantly smaller effect on the coreaverage FTC.
The CTC and SVRC are positive at BOC but negative at EOC for all the cases, implying that
without soluble boron they will both be negative throughout the cycle, which in fact has been
verified.
On the other hand, the burnup-dependent and cycle-average LVRC, shown in Figure 2.27, are
positive for all the cases examined at both BOC and EOC even when the soluble boron
concentration is zero. It is concluded that recycle 10 with MOX fuel is not feasible based on
spectral effect alone. It is shown in Section 2.4.13 that the 10th recycle in MOX is the last
feasible recycle when accounting for the negative reactivity effect of the core leakage.
50
260
190
U 0%
U 11.2%
U 22.4%
U 33.7%
U 44.9%
U 64.2%
U 83.6%
U 100.0%
LVRC (pcm/% void)
220
U 0%
U 11.2%
U 22.4%
U 33.7%
U 44.9%
U 64.2%
U 83.6%
U 100.0%
180
LVRC (pcm/% void)
240
200
180
170
160
150
160
140
140
120
0
50
100
150
200
250
EFPD
300
350
400
450
130
500
0
50
100
150
200
250
EFPD
300
350
400
450
500
Figure 2.27 Core-average LVRC (pcm/%void) with soluble boron (left) and without soluble boron (right) at
13th recycle; MOX fuel
2.4.13 Reactivity of PuO2-ZrO2 fuel accounting for the leakage effect of core voiding
All the void reactivity effects reported above did not account for the voiding effect on the core
leakage probability. Figure 2.28 shows the burnup-dependent, core-average void reactivity effect
for an infinite lattice of unit cells fuelled with PuO2-ZrO2 (calculated using TRITON/NEWT)
compared to the leakage effect (negative) of core voiding (also in pcm) as calculated with
MCNP. It is observed that (1) the void reactivity becomes more negative with burnup, reflecting
the lower inventory of plutonium; (2) the LVRC increases after about 60% void for all the
burnups, and becomes positive at every burnup after around 90% void; this is due to spectrum
hardening effects; (3) the negative leakage effect of voiding is substantially larger than the
positive spectral effect, resulting in substantially negative reactivity coefficients.
40000
0 EFPD
67.99 EFPD
30000
203.97 EFPD
475.93 EFPD
20000
(pcm)
Core average void Reactivity
339.95 EFPD
Effect of leakage (pcm), sign inverted
10000
0
0%
20%
40%
60%
80%
100%
-10000
-20000
Coolant Void Fraction
Figure 2.28 Core average void reactivity effect (LVRC) expressed in pcm, and compared to the leakage effect
of core voiding (displayed as positive) as calculated by MCNP
51
Figure 2.29 shows the evolution of the BOL large void reactivity coefficients, for both 90% and
100% voiding, as a function of the recycle number for PuO2-ZrO2 fuel. The discrete points
represent spectral effects as calculated by NEWT; they are all positive. The straight lines are the
leakage effect of voiding the core as calculated with MCNP; they are all negative. It is found that
for 100% void the spectral effects are overcompensated by the large leakage effect; it is larger
than -30000 pcm while the spectral effect gets to slightly above +20000 pcm. On the other hand,
at 90% voiding the spectral effect exceeds the leakage effect after about the 10th recycle. It is
concluded that the maximum number of plutonium recycling in MOX is certainly less or equal to
10.
spectral and leakage effect (pcm)
40000
35000
Leakage effect (pcm) (100% void)
30000
100% void RC
25000
20000
Leakage effect (pcm) (90% void)
15000
90% void RC
10000
5000
0
0
2
4
6
8
10
12
Recycle number
Figure 2.29 BOL LVRC for 90% and 100% void as a function of recycle. Discrete points are spectral effect
(positive) while straight lines are leakage effect (negative)
2.4.14 Summary table for fertile-free PUZH fuel along the multi-recycling
Table 2.27 gives a summary, recycle by recycle, of selected characteristics of the fertile-free
PUZH cores (i.e. PuH2-ZrH1.6) obtained from the plutonium multi-recycling calculations
described in this chapter. It is observed that the amount of plutonium consumed per cycle (9th
column) increases with the recycles although the fractional plutonium consumption per recycle
decreases. Because of the increased plutonium loading with recycling, the specific power and
discharge burnup keep decreasing. However, the TRU consumed per recycle or per unit of
energy generated is practically constant at about 0.364 kg of TRU/MWt-yr.
52
Table 2.27 Summary Table for PUZH with Pu Recycling
kgPu/
MWt-yr
kgTRU/
MWt-yr
Pu
recycled
(g/cc)
Pu
consume
d (g/cc)
0.539
0.410
0.359
0.001
0.195
0.585
0.446
0.375
1.083
0.004
0.346
0.590
0.450
0.371
1.209
0.006
0.492
0.605
0.462
0.373
24.39%
1.327
0.010
0.604
0.613
0.468
0.372
34.08%
24.81%
1.430
0.016
0.714
0.626
0.477
0.372
32.07%
25.02%
1.520
0.018
0.805
0.634
0.484
0.370
293.2
30.28%
25.34%
1.602
0.027
0.886
0.640
0.489
0.371
196.5
281.0
29.01%
25.44%
1.675
0.028
0.962
0.647
0.493
0.369
187.8
268.5
27.75%
25.71%
1.745
0.038
1.028
0.651
0.497
0.369
10
181.8
259.9
26.85%
25.75%
1.803
0.038
1.093
0.657
0.501
0.368
11
175.3
250.7
25.94%
25.96%
1.861
0.047
1.147
0.660
0.503
0.368
12
171.0
244.5
25.28%
25.98%
1.910
0.047
1.202
0.664
0.506
0.364
13
166.7
236.5
24.47%
26.10%
1.951
0.056
1.246
0.666
0.508
0.367
14
163.1
233.2
24.12%
26.12%
1.996
0.056
1.285
0.665
0.507
0.367
15
160.1
228.5
23.63%
26.25%
2.034
0.056
1.331
0.672
0.513
0.366
16
156.4
223.6
23.15%
26.29%
2.073
0.066
1.362
0.672
0.513
0.366
17
154.2
220.4
22.80%
26.29%
2.104
0.066
1.400
0.676
0.515
0.366
18
152.2
217.6
22.51%
26.28%
2.132
0.066
1.428
0.678
0.517
0.366
19
150.5
215.1
22.25%
26.26%
2.158
0.066
1.455
0.680
0.519
0.365
20
147.8
211.3
21.87%
26.42%
2.187
0.077
1.478
0.680
0.519
0.365
21
146.4
209.3
21.66%
26.41%
2.209
0.077
1.507
0.682
0.520
0.367
22
144.8
208.2
21.54%
26.42%
2.234
0.077
1.528
0.683
0.521
0.365
23
143.9
205.7
21.28%
26.39%
2.249
0.077
1.551
0.688
0.525
0.368
24
142.5
205.5
21.26%
26.40%
2.272
0.077
1.561
0.686
0.523
0.365
25
141.9
202.9
20.98%
26.37%
2.282
0.077
1.585
0.692
0.528
0.364
26
140.2
200.4
20.74%
26.49%
2.300
0.088
1.590
0.686
0.524
0.362
27
139.3
198.4
20.54%
26.54%
2.314
0.088
1.613
0.687
0.524
0.362
28
138.6
197.5
20.43%
26.52%
2.326
0.088
1.626
0.687
0.524
0.364
29
138.0
197.3
20.41%
26.52%
2.338
0.088
1.639
0.687
0.524
0.364
30
137.4
196.6
20.33%
26.50%
2.348
0.088
1.651
0.690
0.526
0.364
31
136.9
195.8
20.25%
26.48%
2.356
0.088
1.658
0.691
0.527
0.364
32
136.5
195.1
20.18%
26.46%
2.364
0.088
1.665
0.691
0.527
0.364
33
136.1
194.6
20.12%
26.45%
2.372
0.088
1.673
Burnup
(GWD/
MT)
TRU
destruction
fraction
Fissile
fraction
Pu
loaded
(g/cc)
U
loaded
(g/cc)
0
Specific
power
(W/gHM
)
456.7
628.4
64.36%
21.63%
0.734
0.000
1
359.1
508.2
50.69%
23.75%
0.931
2
308.1
442.1
45.39%
23.36%
3
275.3
391.4
40.23%
23.95%
4
250.3
357.9
36.83%
5
231.3
330.6
6
217.5
311.0
7
205.3
8
9
Cycle
#
53
2.5 Pu+Np and “all TRu” Multi-Recycling in PWR Using Hydride Fuels
2.5.1
Pu and Np multi-recycling in hydride fuel with variable uranium loading: mass
balances of U, Pu and Np
Due to proliferation concerns the AFCI program is considering co-recycling of neptunium with
plutonium. This will greatly increase the 238Pu concentration and make the Pu more proliferation
resistant. The feasibility of multi-recycling Pu together with Np is investigated in this section.
The fuel cycle scheme examined is shown in Figure 2.30. The Pu+Np composition fed to the
system as makeup fuel is assumed that given in [20] – Table 1 col. b, based on “extended PWR
benchmark with 10y cooling”. In absence of more accurate information, it is assumed that Np
forms a hydride of the type NpH2; that it is stable at reactor operating conditions; and that it has
the same density as PuH2 (10.4 g/cm3).
The amount of make-up Pu+Np that is loaded at each recycle is adjusted so as to achieve the
desired cycle length (i.e. 1430 EFPD). As for the “Pu only systems”, several cases were studied
with a varying amount of uranium, from zero to the maximum loadable (i.e. 3.72 g/cm3). The
remaining fuel volume is taken by ZrH1.6. The detailed fuel composition at first recycling is
given in Table 2.28. It is observed that the required plutonium amount increases with the
uranium amount, going from 0.7986 g/cm3 for 0 g/cm3 of U to 1.108 g/cm3 for 3.72 g/cm3 of U.
Correspondingly, the neptunium amount increases from 0.061 g/cm3 to 0.085 g/cm3. The
hydrogen density decreases with the increasing uranium amount.
The re-cycling has been done 13 times (corresponding to 14.3*13=186 years): even though
equilibrium has not been reached, the recycling was stopped because the large void reactivity
coefficient (also accounting for the leakage effect) becomes positive.
Table 2.28 Fuel Composition at First Recycle for the 6 Cases Analyzed with Varying Uranium Loading
Case #
Fuel density (g/cc)
U density (g/cc)
Pu density (g/cc)
Np density (g/cc)
Zr density (g/cc)
H density (g/cc)
1
6.0004
0
0.7986
0.0614
5.0438
0.0964
2
6.3421
0.465
0.8255
0.0635
4.8940
0.0940
3
6.6868
0.93
0.8583
0.0660
4.7409
0.0916
4
7.3804
1.86
0.9320
0.0717
4.4298
0.0868
5
8.0799
2.79
1.0175
0.0783
4.1121
0.0819
6
8.7821
3.72
1.1084
0.0853
3.7912
0.0771
The total amount of reloaded Pu is comprised of the amount of plutonium recycled and of the
makeup plutonium (plutonium from LWR spent fuel), both given in Figure 2.31. Figure 2.32
gives similar information on the neptunium inventory. It is observed that cases with low uranium
content require less plutonium and neptunium makeup for the first few recycles but larger
amount of makeup after the 3rd to 4th recycle. This is due to the low conversion ratio of the low
U-content cores.
54
Figure 2.30 Fuel cycle scheme with plutonium and neptunium recycle
3
1
U 0.00 g/cm3
U 0.46 g/cm3
0.95
U 0.93 g/cm3
Pu from LWR spent fuel (g/cm3)
Pu recycled (g/cc)
2.5
2
1.5
U 0.00 g/cm
3
U 0.46 g/cm3
1
U 0.93 g/cm
3
U 1.86 g/cm3
U 2.79 g/cm
3
U 1.86 g/cm3
0.9
U 2.79 g/cm3
0.85
U 3.72 g/cm3
0.8
0.75
0.7
0.65
U 3.72 g/cm3
0.5
0.6
0
0
2
4
6
8
Cycle Number
10
12
0.55
14
0
2
4
6
8
Cycle Number
10
12
14
Figure 2.31 Required plutonium recycled density (g/cm3) (left) and makeup plutonium density (g/cm3) (right)
as a function of the re-cycle number for NpH2-U-PuH2-ZrH1.6
55
0.08
0.12
U 0.00 g/cm3
0.11
U 0.46 g/cm3
0.075
U 0.93 g/cm3
Np from LWR spent fuel (g/cm3)
0.1
Np recycled (g/cc)
0.09
0.08
0.07
U 0.00 g/cm3
U 0.46 g/cm3
0.06
U 0.93 g/cm3
U 1.86 g/cm3
0.05
U 2.79 g/cm3
0.04
U 2.79 g/cm3
U 3.72 g/cm3
0.065
0.06
0.055
0.05
U 3.72 g/cm3
0.045
0.03
0.02
U 1.86 g/cm3
0.07
0
2
4
6
8
Cycle Number
10
12
0.04
14
0
2
4
6
8
Cycle Number
10
12
14
Figure 2.32 Required neptunium recycled density (g/cm3) (left) and makeup plutonium density (g/cm3)
(right) as a function of the re-cycle number for NpH2-U-PuH2-ZrH1.6
2.5.2
TRU destruction fraction of Pu+Np recycling in hydride fuel
The achievable burnup, the corresponding fuel residence time in the core, the TRU fractional
destruction and the plutonium fissile fraction at discharge are given in Table 2.29 for the first
recycle for NpH2-U-PuH2-ZrH1.6 fuel. It is observed that the achievable burnup is the highest in
the case without uranium – 556 GWD/MT. The corresponding TRU destruction fraction is 57%.
In the second recycle these values drop to, respectively, 395.5 GWD/MT and 31.3%. These
values are somewhat smaller than those obtained when recycling only plutonium (Section 2.4.2).
Table 2.29 Properties of NpH2 U PuH2 ZrH1.6 Fuel at First Recycling
Case #
Burnup (GWD/MTiHM)
Fuel residence time (EFPD)
TRU destruction fraction
Pu fissile fraction at discharge
1
556.0
1430.7
56.91%
27.42%
2
353.2
1430.7
49.03%
34.91%
3
258.0
1431.1
44.35%
38.87%
4
167.0
1430.5
37.31%
44.23%
5
123.0
1430.3
31.77%
47.97%
6
97.3
1430.3
27.32%
50.69%
Figure 2.33 shows the evolution with recycling of the TRU destruction fraction and of the fissile
Pu fraction at discharge. The latter is decreasing with the recycles for heavier uranium loaded
cores but initially increases for low uranium loaded cores. Both effects are due to the increasing
amount of makeup Pu that needs to be loaded as the recycling proceeds.
56
0.6
0.6
U 0.00 g/cm3
0.55
U 0.46 g/cm3
0.55
U 0.93 g/cm3
0.5
U 0.93 g/cm3
U 1.86 g/cm3
U 1.86 g/cm3
U 2.79 g/cm3
0.45
U 2.79 g/cm3
0.5
U 3.72 g/cm3
Pu fissile fraction
TRU destruction fraction
U 0.00 g/cm3
U 0.46 g/cm3
0.4
0.35
0.3
0.25
U 3.72 g/cm3
0.45
0.4
0.35
0.2
0.3
0.15
0.1
0
2
4
6
8
Cycle Number
10
12
0.25
14
0
2
4
6
8
Cycle Number
10
12
14
Figure 2.33 TRU destruction fraction (left) and Pu fissile fraction (right) as a function of the re-cycle number
for NpH2-U-PuH2-ZrH1.6 fuel
2.5.3
Reactivity coefficients of Pu+Np recycling in hydride fuel
For NpH2-U-PuH2-ZrH1.6 at the 1st recycle, the core averaged FTC increases throughout the
cycle for all uranium loadings, and is higher (i.e. less negative) for smaller uranium loading. The
case with no initial uranium loading has a positive FTC after about 400 EFPD, corresponding to
a fuel life of 1200 EFPD, or about 84% of the theoretically achievable life (1430 EFPD).
However, the addition of about 0.25 g/cm3 of U would be sufficient to reduce the FTC to
negative values throughout the first cycle. Alternatively, the use of deuterium would have a
similar effect as in the case of Pu only (see Section 2.4.3). All the other reactivity coefficients
(i.e. CTC, SVRC and LVRC for either 90% voiding or 100% voiding (not corrected for leakage
effect of voiding)) are negative and are decreasing throughout the cycle, for each of the uranium
loadings.
The core averaged FTC and LVRC (90% and 100% void) for NpH2-U-PuH2-ZrH1.6 at the 13th
recycle have a quite different behavior than at the 1st recycle; the FTC is mostly flat throughout
the cycle and substantially negative for each of the uranium loadings, including the case with no
uranium. The case with no initial uranium features the smallest spectral effect for both 90% and
100% void; their value is +4050 pcm for 90% void and +7200 pcm for 100% void. Both values
are larger than the negative effect of leakage. It is concluded that the 13th recycle is non feasible
because of positive LVRC. All the other core-averaged reactivity coefficients are negative for
each of the uranium loadings.
Consequently, a 3-D MCNP calculations were performed to estimate the neutron leakage
probability from the PuH2-NpH2-ZrH1.6 fuelled cores at recyclings <13. Figure 2.34 shows the
evolution of the maximum core-average burnup-dependent large void spectral effect of the
reactivity coefficient (positive) as a function of the recycle numbers as well as the leakage effect
of voiding (negative) as calculated by MNCP.
It is found that the number of maximum recycling is limited to 6. It is imposed by the 100%
voiding that is more constraining for this fuel than the 90% voiding.
57
8000
Max RC for 100% void
Leakage effect for 100% void
Max RC for 90% void
Leakage effect for 90% void
Reactivity effect (pcm)
6000
4000
2000
0
0
2
4
6
8
10
12
14
-2000
-4000
-6000
Recycle number
Figure 2.34 Evolution of the maximum core-average, burnup-dependent spectral component of the reactivity
coefficient (positive) as a function of recycle at BOL, compared to the leakage effect (negative) of voiding as
calculated by MCNP; NpH2-PuH2-ZrH1.6 fuel
2.5.4
Ways to increase the number of acceptable recycles for NpH2-PuH2-ZrH1.6 fuel
A number of approaches where investigated for making negative the large voiding reactivity
coefficients beyond the 6th recycle for NpH2-PuH2-ZrH1.6 fuel:
1. Add slightly enriched uranium;
2. Add burnup poisons (erbium);
3. Enlarge the fuel rod radius while keeping the same pitch.
Of these, only the latter was found effective in substantially extending the range of feasible
number of recycles. The rationale for enlarging the fuel radius, while keeping the pitch at the
original level, is that more of the moderation would be performed by the hydrogen in the fuel
instead of the hydrogen in the water. This would not change substantially the neutronic behavior
during normal operation, while it would allow for more hydrogen to remain in the system during
large voiding.
It was found that an enlargement of the clad outside diameter from 0.95 cm to 1.03 cm would be
sufficient to extend the feasible range to the 13th recycle. On the down side, this would penalize
the maximum attainable power by up to 14% because of the larger friction losses associated with
the reduction in the hydraulic diameter, unless an increase in the pressure drop is allowed.
2.5.5
Recycling of all the TRU in hydride fuel
The rationale of the fuel cycle scheme examined for the multi-recycling all the TRU in hydride
fuel is similar to the one for recycling Pu only, described in Section 2.5.1. As for the Np+Pu
evaluation, the TRU vector (shown in Table 2.30) used for the initial loading and for the makeup
is taken from [20], Table 1 col. b, based on “extended PWR benchmark with 10y cooling”. As
for the case of recycling Np+Pu, because of the limited information on the physical properties of
the hydrides, two assumptions were made:
58
1) The MA form hydrides of the form AmH2, CmH2 etc. that are stable at reactor operating
conditions;
2) The MA-hydrides have a density equal to that of PuH2 – 10.4 g/cm3.
The fuel composition at BOL of the first recycles is shown in Table 2.31 for the six cases
analyzed; they differ in the amount of uranium loading (from 0 to 3.72 g/cm3). The TRU amount
is adjusted to match the desired cycle length of 1430 EFPD; it increases from 0.894 g/cm3 for no
uranium to 1.754 g/cm3 for the maximum uranium amount. Np, Am and Cm are all in amount
proportional to the plutonium amount according to the values in Table 2.30.
Table 2.30 TRU Vector, from [20], Table 1 col. b, Based on “Extended PWR Benchmark with 10y Cooling”
Isotope
Fraction
U-235
0.002
U-236
0.002
U-238
0.325
NP-237
6.641
PU-238
2.749
PU-239
48.652
PU-240
22.98
PU-241
6.926
PU-242
5.033
AM-241
4.654
AM-242M
0.019
AM-243
1.472
CM-242
0.000
CM-243
0.005
CM-244
0.496
CM-245
0.038
CM-246
0.006
Table 2.31 Fuel Composition at First Recycles for the 6 Cases Analyzed with Varying Uranium Loading (all
TRU-Recycling Hydrides)
Case #
U density (g/cc)
Fuel density (g/cc)
Pu density (g/cc)
Np density (g/cc)
Am density (g/cc)
Cm density (g/cc)
Zr density (g/cc)
H density (g/cc)
1
0.0
6.0808
0.8946
0.0688
0.0637
0.0056
4.9516
0.0962
2
0.465
6.4886
1.0427
0.0802
0.0742
0.0066
4.7261
0.0937
3
0.93
6.8939
1.1860
0.0912
0.0844
0.0075
4.5035
0.0911
4
1.86
7.6850
1.4363
0.1105
0.1022
0.0091
4.0807
0.0861
5
2.79
8.4402
1.6199
0.1246
0.1153
0.0102
3.6990
0.0811
6
3.72
9.1689
1.7540
0.1349
0.1248
0.0111
3.3477
0.0762
The TRU destruction fraction and the plutonium fissile fraction at discharge are shown in Figure
2.35 as a function of the recycle number for the MAH2-U-PuH2-ZrH1.6 fuel. Although as high as
47% of the TRU loaded are fissioned in the first recycle when no uranium is added, the TRU
fractional destruction reaches 10-15% for all the initial uranium loadings by the 3rd recycle. It is
also observed that while the plutonium fissile fraction at discharge decreases steadily for the
heavier uranium loadings, it has a peak similar to that of Pu only for the smaller U loadings.
59
0.5
0.55
0.45
U 0.00 g/cm3
0.5
U 0.46 g/cm3
0.35
U 0.93 g/cm3
0.3
U 2.79 g/cm3
U 1.86 g/cm3
Pu fissile fraction
TRU destruction fraction
0.4
U 3.72 g/cm3
0.25
0.2
0.45
U 0.00 g/cm3
0.4
U 0.46 g/cm3
U 0.93 g/cm3
0.15
U 1.86 g/cm3
0.35
U 2.79 g/cm3
U 3.72 g/cm3
0.1
0.05
0
1
2
0.3
3
Cycle Number
0
1
2
3
Cycle Number
Figure 2.35 TRU destruction fraction (left) and Pu fissile fraction (right) as a function of the re-cycle
number; MAH2-U-PuH2-ZrH1.6 fuel
The reactivity coefficients for MAH2-U-PuH2-ZrH1.6 fuel were evaluated at each recycle with
and without soluble boron. At the 3rd recycle (the limit), only the FTC is negative and flat
throughout the cycle, with the larger uranium loadings featuring a more negative FTC. All the
other reactivity coefficients are positive and increasing throughout the cycle.
60
2.6 Comparisons of Hydride Fueled Systems
The purpose of this section is to directly compare the properties of hydride fuels (Pu only, Pu +
Np, all TRU) at first recycle with variable uranium amounts, in terms of achievable burnup
(Figure 2.36), maximum core average FTC (Figure 2.37), TRU destruction fraction and fissile
fraction at discharge (Figure 2.38). It is observed that the maximum achievable burnup, as high
as 628 GWD/MTiHM in case of recycling plutonium only, features a positive FTC before
reaching EOL. Therefore, practically, the uranium content should be increased to about 0.5
g/cm3, which would decrease the feasible burnup to less than 500 GWD/MTiHM. The addition
of Np, on the other hand, would reduce the FTC to negative with just 0.2 g/cm3 of U, while the
feasible burnup would be reduced to about 500 GWD/MTiHM, making the addition of Np for
the first few recyclings probably a preferred approach. The addition of the entire TRU vector
makes the FTC negative throughout the entire cycle without the addition of uranium, even
though the achievable burnup and the TRU destruction fractions are penalized. It will be
interesting, therefore, to analyze the possibility of recycling Pu+Np+Am, which may feature a
negative FTC without a need for uranium.
3-batches achievable burnup (GWD/MTiHM)
700
Pu only
Pu Np
All TRU
600
500
400
300
200
100
0
0
1
2
3
4
U content (g/cc)
Figure 2.36 First recycle, three-batch achievable burnup (GWD/MTiHM) as a function of uranium loading,
for recycling Pu only, Pu + Np or all TRU in hydride fuels
Table 2.32 provides a summary of selected neutronic properties of the TRU-bearing fuels studied
at the 1st recycle. “MOX reference” is the standard MOX with 0% ZrH1.6; “Pu D-hydride no U”
and “Pu hydride 25% Umax” are added because they are possible approaches to make the sign of
the FTC negative at the first recycle (as discussed in Section 2.4.3). All the presented fuels
feature the same cycle length. Characteristics compared include burnup, U, Pu and MA amounts
(for the elements and for the most important isotopes) at BOL and EOL; and incineration
capability. Also compared are measures of repository impact ((Np and its precursors, total TRU
inventory at discharge, decay and gamma heat) and measures of proliferation resistance
(Fissile/total Pu, MA/Pu, neutron emission per g of Pu and of HM, and likewise for heat
61
emission). It is observed that fertile free, Pu-loaded MOX, hydride and deuteride, have similar
characteristics in all the measures examined.
1
Max core average FTC (pcm/K)
0.5
Pu only
Pu Np
All TRU
0
-0.5
-1
-1.5
-2
-2.5
-3
-3.5
-4
0
1
2
3
4
U content (g/cc)
Figure 2.37 First recycle, maximum core-average FTC (pcm/K) as a function of uranium loading, for
recycling Pu only, Pu + Np or all TRU in hydride fuels
70.00%
60.00%
Pu only
Pu Np
All TRU
50.00%
Pu fissile fraction at discharge
TRU destruction fraction
60.00%
50.00%
40.00%
30.00%
20.00%
40.00%
30.00%
Pu only
Pu Np
All TRU
20.00%
10.00%
10.00%
0.00%
0.00%
0
1
2
3
4
0
U content (g/cc)
1
2
3
U content (g/cc)
Figure 2.38 First recycle, TRU destruction fraction (left) and Pu fissile fraction at discharge (right) as a
function of uranium loading, for recycling Pu only, Pu + Np, or all TRU in hydride fuels
62
4
Table 2.32 Summary of neutronic properties of selected TRU-bearing fuels at 1st recycle
MOX
MOX no
Pu hydride
Pu deutride
Pu+Np
TRU
Property
reference
U
no U
no U
hydride
hydride
Burnup (GWD/MtiHM)
51.4
622.1
627.9
620.1
555.9
462.4
Residence time (EFPD)
1426.4
1427.8
1429.0
1429.2
1430.7
1428.8
Initial Pu loading (g/cc)
1.0977
0.7617
0.7562
0.7658
0.7986
0.8945
Initial Pu loading (Pu w/o)
10.43
16.68
12.70
12.73
13.30
14.71
Initial U loading (g/cc)
8.1740
0
0
0
0
0
Initial Np loading (g/cc)
0
0
0
0
0.0614
0.0688
Initial Am loading (g/cc)
0
0
0
0
0
0.0637
Initial Cm loading (g/cc)
0
0
0
0
0
0.0057
At discharge
U inventory (g/cc)
7.8894
235
U
1.4E-02
0.0006
1.1E-04
0.0006
9.7E-05
0.0006
1.1E-04
0.0011
2.0E-04
0.0016
2.7E-04
236
2.6E-03
7.1E-05
7.1E-05
7.2E-05
8.3E-05
9.4E-05
238
7.9E+00
7.0E-05
7.8E-05
7.1E-05
7.8E-05
7.9E-05
U
U
Pu inventory (g/cc)
0.85
0.23
0.23
0.24
0.31
0.44
77.36%
0.842
30.65%
0.577
30.31%
0.574
31.00%
0.590
38.42%
1.549
49.35%
2.322
239
0.572
0.029
0.022
0.028
0.055
0.118
240
0.910
0.404
0.382
0.401
0.475
0.601
241
1.537
0.787
0.719
0.794
0.922
1.215
242
1.027
1.484
1.635
1.535
1.754
1.621
% Pu incinerated/cycle
22.6%
69.4%
69.7%
69.0%
61.6%
50.7%
Fissile Pu/ Tot Pu
56.5%
24.5%
21.9%
24.3%
27.4%
33.3%
Pu inventory/ initial Pu
238
Pu
Pu
Pu
Pu
Pu
MA inventory (g/cc)
4.86E-02
4.57E-02
4.27E-02
4.47E-02
6.57E-02
1.04E-01
Th:
3.17E-09
1.51E-09
1.77E-09
1.56E-09
9.12E-05
9.16E-05
Pa:
6.89E-10
4.17E-10
3.73E-10
4.22E-10
3.33E-07
2.86E-07
Np:
1.75E-03
2.26E-05
2.22E-05
2.29E-05
2.47E-02
3.13E-02
Am:
3.30E-02
2.38E-02
2.47E-02
2.35E-02
2.48E-02
4.11E-02
Cm:
1.39E-02
2.19E-02
1.80E-02
2.12E-02
1.61E-02
3.17E-02
Bk:
1.02E-09
1.65E-08
4.14E-09
1.40E-08
2.92E-09
3.17E-08
1.53E-02
4.31E-03
3.72E-03
4.31E-03
3.02E-02
4.87E-02
% TRU incinerated/cycle
0.90
18.2%
0.28
63.4%
0.27
64.0%
0.28
63.2%
0.37
56.7%
0.55
47.2%
MA/Pu at discharge (%)
5.7%
19.6%
18.6%
18.8%
21.4%
23.6%
Neutron source (n/s/cc)
1.38E+05
40.06
2.23E+05
59.33
1.89E+05
57.74
2.17E+05
58.26
1.70E+05
50.97
3.43E+05
60.71
237
Np+
241
Am+
245
Cm
Total TRU inventory
Activity (Ci/cc)
Decay heat (w/cc)
Gamma Decay heat (w/cc)
0.27
0.37
0.37
0.37
0.38
0.82
3.07E-03
635.81
6.92E-03
1251.60
6.73E-03
1314.42
6.73E-03
1260.57
5.39E-03
1280.53
4.73E-03
1190.36
1.57E+04
8.00E+05
6.95E+05
7.69E+05
4.55E+05
6.28E+05
Specific heat (w/g Pu)
0.05
0.26
0.26
0.25
0.21
0.17
Specific heat (w/g HM)
0.03
1.32
1.37
1.32
1.01
1.50
Neutrons per g Pu (n/s)
Neutrons per g HM (n/s)
63
2.7 System Analysis
2.7.1
System analysis performance for reduction of accumulated Pu inventory
Plutonium stabilizing fuel assemblies, such as the CORAIL and MOX-UE, do not offer Pu
inventory draw-down after the first recycle: for this reason we decided to compare the following
two energy systems:
(1) A system comprised of conventional once-through UO2 fuelled PWRs and PUZH fuelled
PWRs; the ratio of the number of cores of the two types are adjusted so as to stabilize the
amount of Pu in the combined system.
(2) A system consisting of PWRs having CORAIL cores only.
The most promising hydride fuel was identified to be PuH2-ZrH1.6 (called “PUZH” in the present
Section) for its highest TRU transmutation performance and for its physical characteristics that
allow for unlimited number of plutonium recycling in PWR. The best performing oxide fuel, in
terms of TRU destruction fraction, was identified as PuO2-ZrO2 (called “MOX” in the present
Section), which is the inert-matrix counterpart of the optimal hydride fuel. This latter does not
allow indefinite multi-recycling (see Section 2.4.12); it nevertheless offers the fastest destruction
of the accumulated plutonium inventory among the analyzed oxide fuels. These two optimal
hydride and oxide fuel systems are compared in Sections 2.7.3, 2.7.4, 2.7.5 and 2.7.6 for their
performance with respect to the reduction of the accumulated plutonium inventory in the Yucca
Mountain Repository.
2.7.2
System analysis: comparison with CORAIL
The PUZH fuel core does not require any natural uranium (i.e. it can use depleted uranium as
feed) and no SWU, while the CORAIL cores requires 7 kg of natural uranium and 5.4 SWU per
kg of uranium used as fuel (because of the required enrichment). Since the PUZH fuel is a net
plutonium destroyer, at equilibrium the PUZH core will be supported for its plutonium feed by
6.7 standard UO2 LWR8. This is compared with 7.7 self-sufficient CORAIL assemblies: they
will need 26% less natural uranium and SWU as compared to 6.7 PWR + 1 PUZH, and produce
50% less minor actinides.
It is therefore concluded that at equilibrium the CORAIL system requires less natural resources
and has a smaller repository impact than the coupled LWR+PUZH. It is also noted that the
CORAIL system would not be practical for a substantial Pu draw-down from the YMR, since the
number of cores required to load the entire YMR Pu inventory would be ~300, three times larger
than the current US operating fleet of commercial reactors.
2.7.3
Material balance
The 63,000 MTiHM of LWR spent fuel that is planned to be stored at the Yucca Mountain
Repository (YMR) will contain about 750 MT of Pu and 61 MT of minor actinides. The present
section estimates the level of reduction in TRU inventory that can be obtained by multi-recycling
8
The resource consumptions of the typical UO2 PWR (using 5% enriched uranium) are 10.3 kg of natural uranium
and 7.92 SWU per kg of enriched uranium.
64
the accumulated mass of Pu in a given number of PWR cores, using either one of the systems
defined in Section 2.7.1.
The analysis is performed by assuming a given number of hydride cores operating in parallel,
and making the assumption that this number will not be varied during the recycling campaign.
This determines the number of recycles necessary to consume the entire accumulated inventory
of plutonium, and therefore the duration of the recycling campaign9.
The number of cores that can be used for recycling the total Pu inventory vary from 1 (requiring
a large number of recyclings) to 101 for PUZH and from 10 to 98 for MOX. In MOX the number
of parallel cores used for recycling cannot be less than 10, since a smaller number of cores would
require a larger number of recyclings than the 10 that are allowed in this fuel type before the
large void coefficient of reactivity becomes positive (see Section 2.4.12). On the contrary, PUZH
fuel can multi-recycle plutonium an un-limited number of times, allowing the entire recycling
campaign to be operated even with as low as one core.
At the end of the recycling campaign, the leftover TRU stream will compose of:
1) The MA discharged from the PuH2-ZrH1.6 core at each multi-recycling step;
2) The plutonium left over after the PuH2-ZrH1.6 irradiation campaign will be ended.
There could be a further reduction in the plutonium leftover after the entire YMR inventory will
have been drawn-down, by concentrating the plutonium leftover in different hydrides cores into
fewer cores, to reach the inventory necessary for the desired cycle length. However, this option
has not been studied in the present work.
Figure 2.39 shows the plutonium loaded and consumed at each recycle in PuH2-ZrH1.6 fuelled
PWR core. It is observed that the amount of plutonium consumed at each recycle slightly
increases with recycling while the amount of plutonium loaded at each recycle increases
significantly with the recycling; this reflects the significant decrease in the fractional
transmutation of Pu with the recycle number reported in Figure 2.20. The net result is a
substantial increase in the amount of plutonium that accumulates in the system with increased
number of recyclings. The amount of MA keeps accumulating as well.10
Figure 2.40 shows the TRU mixture remaining after the recycling campaign for the PUZH and
for the optimal MOX as a function of the number of cores, expressed as a fraction of the initial
mass of plutonium. It is observed that a larger number of cores (i.e. smaller number of required
plutonium recycles) results in a smaller accumulation of MA, but also in a larger residual
inventory of plutonium at discharge. The net effect, somewhat surprisingly, is that the total TRU
mass after the recycles is relatively constant with the number of parallel cores; slightly smaller
for smaller number of cores (and more recycles), at about 30-35% of the initial inventory. It is
also observed that the residual TRU inventory is slightly higher for MOX cores than for PUZH
cores.
9
The total YMR plutonium inventory may not be an exact multiple of the consumption per cycle of a given hydride
fleet (actually, in general it will not). For this reason, after the recycling campaign will be over, there will be a “leftover” plutonium amount stemming only from the simplifying assumption that the hydride fleet size will not be
varied during the recycling campaign. This would make a comparison between different fleet sizes difficult. To
obviate this problem, it is chosen to normalize all the results presented in this and following Sections per ton of TRU
fissioned. It is also noted that the target amount of plutonium to be transmuted is likely not constant, because of the
continued accumulation of plutonium from operating LWR, isotopic decay etc… Also for this reason, the
normalization approach makes the presented results of more general validity.
10
The number of fissions per recycle is constant, though.
65
140
Pu kg/assembly Loaded
Pu kg/assembly Consum.
MA kg/assembly at EOL
120
100
kg
80
60
40
20
0
0
5
10
15
20
25
30
35
Cycle #
Figure 2.39 Plutonium (in kg/assembly) loaded and consumed at each recycle in PuH2-ZrH1.6, and MA (in
kg/assembly) discharged at the end of each recycle
MOX Residual TRU after campaign
PUZH Residual TRU after campaign
MOX MA discharged during campaign
PUZH MA discharged during campaign
MOX Residual Pu after campaign
PUZH Residual Pu after campaign
TRU remaining after recycling campaign
60.00%
50.00%
40.00%
30.00%
20.00%
10.00%
0.00%
0
20
40
60
80
100
120
Number of parallel cores
Figure 2.40 TRU mixture remaining after the recycling campaign for the optimal PUZH and for the optimal
MOX, expressed as a fraction of the initial mass of Pu inventory, as a function of a variable number of
cores11.
11
There could be a further reduction in the plutonium leftover after the entire YMR inventory will have been drawndown, by concentrating the plutonium leftover in different hydrides cores into fewer cores, to reach the inventory
necessary for the desired cycle length. However, this option has not been studied in the present work.
66
2.7.4
Repository impact
The repository impact12 is evaluated through the estimate of the following normalized parameters
at the end of the campaign, as a function of the total number of PUZH and MOX cores:
1) total radioactivity of the TRU stream (Ci/ton of initial Pu), in Figure 2.41 (left);
2) total neutron emission (n/s/ton of initial Pu), in Figure 2.41 (right);
3) total decay heat (W/ton of initial Pu), in Figure 2.42 (left);
4) total gamma decay heat (W/ton of initial Pu), in Figure 2.42 (right);
5) total toxicity in air (m3of Air/ton of initial Pu), in Figure 2.43 (left);
6) total toxicity in water (m3of H2O/ton of initial Pu), in Figure 2.43 (right).
7) total mass of 237Np and its precursors (i.e. 241Am and 245Cm) (ton/ton of initial Pu), in
Figure 2.44.
It is observed that all these measures of repository impact, except for the mass of neptunium and
its precursors as a fraction of total Pu transmuted, are slightly higher for MOX than for PUZH,
more so for larger number of cores. It is also observed that the radioactivity is higher for larger
number of cores, while all the other measures decrease with the use of higher number of parallel
cores (i.e. with a smaller number of recyclings).
3.00E+11
n/sec at YMR per MT of Pu transm uted
Ci at YM R per M T of Pu transmuted
6.00E+06
5.00E+06
4.00E+06
MOX Tot Ci at YMR
3.00E+06
PUZH Tot Ci at YMR
2.00E+06
1.00E+06
MOX Tot neutr/sec at YMR
2.50E+11
PUZH Tot neutr/sec at YMR
2.00E+11
1.50E+11
1.00E+11
5.00E+10
0.00E+00
0.00E+00
0
20
40
60
80
100
0
120
20
40
60
80
100
120
Number of parallel cores
Number of parallel cores
Figure 2.41 Total radioactivity (Ci/ton of initial Pu) (left) and neutron emission (n/s/ton of initial Pu) (right)
sent to YMR after the end of the recycling campaign as a function of the number of parallel PUZH and MOX
cores.
Table 2.33 shows the repository impact related characteristics of the residual stream after
transmutation in either PUZH or MOX fuelled cores (in a selected number of parallel cores) as
compared to those in the original LWR-derived Pu disposed at YMR (in column 1). All the
values are normalized per ton of Pu transmuted13. It is observed that the total radioactivity
decreases after transmutation, while all the other parameters increase.
12
The measured parameters for the repository impact are evaluated at 10 years after discharge. Longer recycling
campaigns allow more time for the TRU to decay before the end of the recycling campaign, resulting in smaller
repository impact if measured at the end of the campaign itself. No account is taken for possibly longer
reprocessing/disposal times.
13
For LWR the values are normalized “per ton of Pu to be transmuted”, or the total inventory of 750 MT
67
While this implies a heavier heat and toxicity load on the YMR after the transmutation
campaign, it also shows a much greater proliferation resistance of the transmuted stream as
compared to the original one, since the residual stream would has a small amount of highly
degraded plutonium and a high neutron, gamma ray and heat emission would make the diversion
and handling of the residual stream difficult (more information of this in Section 2.7.5).
1.40E+02
MOX Tot decay heat at YMR
1.00E+05
Gamma h eat YM R p er M T o f Pu
tran smu ted
Decay heat YMR per MT of Pu transm uted
1.20E+05
PUZH Tot decay heat at YMR
8.00E+04
6.00E+04
4.00E+04
2.00E+04
MOX Tot gamma heat at YMR
1.20E+02
PUZH Tot gamma heat at YMR
1.00E+02
8.00E+01
6.00E+01
4.00E+01
2.00E+01
0.00E+00
0.00E+00
0
20
40
60
80
100
120
0
20
Number of parallel cores
40
60
80
100
120
Number of parallel cores
2.50E+13
1.20E+20
MOX TOT toxicity m3Air YMR
1.00E+20
Toxicity (m 3H2O) to YM R per M T of P u
transm uted
T oxicity (m3Air) to YM R per M T of Pu
transmu ted
Figure 2.42 Total decay heat (W/ton of initial Pu) (left) and gamma decay heat (W/ton of initial Pu) (right)
sent to YMR after the end of the recycling campaign as a function of the number of parallel PUZH and MOX
cores
PUZH TOT toxicity m3Air YMR
8.00E+19
6.00E+19
4.00E+19
2.00E+19
MOX TOT toxicity m3H2O YMR
PUZH TOT toxicity m3H2O YMR
2.00E+13
1.50E+13
1.00E+13
5.00E+12
0.00E+00
0.00E+00
0
20
40
60
80
100
0
120
20
40
60
80
100
120
Number of parallel cores
Number of parallel cores
Figure 2.43 Total toxicity (m3of Air/ton of initial Pu) (left) and (m3of H2O/ton of initial Pu) (right) and sent to
YMR after the end of the recycling campaign as a function of the number of parallel PUZH and MOX cores
68
Tot Mass of Np and Precursors (% of Pu
transmuted)
MOX Np and precursors to TMR
(MT)
18.00%
16.00%
PUZH TOT Np and Prec to YMR
14.00%
12.00%
10.00%
8.00%
6.00%
4.00%
2.00%
0.00%
0
20
40
60
80
100
120
Number of parallel cores
Figure 2.44 Total mass of 237Np and its precursors (i.e. 241Am and 245Cm) (ton/ton of initial Pu) sent to YMR
after the end of the recycling campaign as a function of the number of parallel PUZH and MOX cores
Table 2.33 Repository Impact of the Pu Stored at YMR Before the Recycling Campaign and of the TRU
Stream After a Multi-Recycling Campaign in MOX and PUZH Fuels, for Selected Number of Parallel Cores
LWR Pu
PUZH
MOX
PUZH
MOX
PUZH
MOX
at YMR
1 core
1 core
6 cores**
6 cores
80 cores
80 cores
n/s
5.393E+08
2.658E+11
N/A
2.445E+11
N/A
1.414E+11
1.600E+11
Ci
1.057E+07
2.955E+06
N/A
3.533E+06
N/A
4.272E+06
5.374E+06
decay heat
21463
95395
N/A
85397
N/A
51841
58688
gamma heat
7.05
125.06
N/A
90.85
N/A
32.21
38.40
m3 of Air
5.660E+19
1.079E+20
N/A
9.738E+19
N/A
6.586E+19
7.549E+19
1.068E+13
2.042E+13
N/A
1.843E+13
N/A
1.246E+13
1.429E+13
3
m of H2O
* All values are normalized per MT of LWR Pu transmuted; ** Recycling campaign with PUZH ~66 years.
2.7.5
Proliferation resistance
The total inventory of plutonium to be handled in the reprocessing plant is quite similar in the
case of MOX and PUZH. However, the fissile fraction at the reprocessing facility (i.e. 10 years
after download) − shown in Figure 2.45 as a function of the recycling number − shows that the
PUZH stream is more proliferation resistant than that of MOX for the first 9-10 recycles.
Similarly, the neutron emission per gram of plutonium at the reprocessing plant − shown in
Figure 2.46 as a function of the recycle number − is higher for PUZH than for MOX. Other
important measures of proliferation resistance: 1) the neutron emission per gram of TRU at the
reprocessing plant − shown in Figure 2.47 as a function of the recycle number − as well as the
specific decay heat, are similar for the two fuel types.
It is concluded that multi-recycling in PuH2-ZrH1.6 appears more resistant to proliferation than
multi-recycling in PuO2-ZrO2.
69
Pu Fissile (% of total Pu)
25%
20%
PUZH Fiss Frac after 10 years cooling
15%
MOX Fiss Frac after 10 years cooling
10%
5%
0%
1
3
5
7
9
11
13
Recycle #
Figure 2.45 Plutonium fissile fraction for the first 13 recycles at the reprocessing plant (after 10 years of
cooling), for PUZH and MOX fuelled system as a function of the recycle number
1500
1480
1460
PUZH n/sec/gPu
MOX n/sec/gPu
n/sec/gPu
1440
1420
1400
1380
1360
1340
1320
1300
1
3
5
7
9
11
13
Recycle #
Figure 2.46 Neutron emission per gram of Pu at the reprocessing plant (after 10 years of cooling), for PUZH
and MOX fuelled system as a function of the recycle number
500000
450000
400000
PUZH n/s/gTRU
MOX n/s/gTRU
n/sec/gPu
350000
300000
250000
200000
150000
100000
50000
0
1
3
5
7
9
11
13
Recycle #
Figure 2.47 Neutron emission per gram of TRU at the at the reprocessing plant (after 10 years of cooling), for
PUZH and MOX as a function of the recycle number
70
2.7.6
Fuel cycle costs
Since the mass of plutonium loaded in PuH2-ZrH1.6 and PuO2-ZrO2 is very similar (4.5% higher
in case of PuO2-ZrO2), and the cost of reprocessing is mainly a factor of the total plutonium to be
processed, it is expected that the cost of the two fuels will be similar, only slightly higher for
MOX. However, hydrides have a slightly higher fabrication costs due to the cost of hydrating.
Absent industry data, in previous studies on uranium-based hydrides [21, 22] it was assumed that
the fabrication cost of hydrides is the same as oxide on a “per volume base”, which would
effectively double the cost on a “per heavy metal” base. The fabrication cost for a typical PWR
assembly (for a fabrication cost of 275 $/kgHM, [23]) is about 130,000$. From industry estimate,
it is known that the typical fabrication cost of a MOX assembly is ~550,000$ [24]. The inert
matrix MOX and PUZH load ~10% less plutonium than standard MOX (i.e. PuO2-UO2).
Conservatively, it is assumed here that the cost of fabrication of inert matrix MOX will be the
same as of standard MOX, and that the cost of fabrication of PuH2-ZrH1.6 will be higher by
130,000$, effectively doubling the part of the cost not related to plutonium handling, for a total
fabrication cost per assembly of 680,000$ for PuH2-ZrH1.6.
However, the main part of the recycling cost comes from the reprocessing of spent fuel, that
were estimated in [24] at 1800 $/kgHM for the reprocessing, plus the cost of disposing the high
level waste (253 $/kg) minus the cost of disposing the unprocessed spent fuel (500+200$/kg),
resulting in a total cost of 0.63 million$ for a standard UO2 PWR assembly. Considering that it is
necessary to recycle 6.7 and 6.9 spent LWR assemblies to obtain the plutonium respectively for a
PuH2-ZrH1.6 assembly and for a PuO2-ZrO2 assembly, the reprocessing part of the cost amounts
respectively to 4.2 and 4.4 million$/assembly. Summing the respective fabrication costs of 0.55
and 0.68 million$/assembly, the final cost of PuH2-ZrH1.6 would only be ~1.2% lower than that
of PuO2-ZrO2, not enough to justify the choice of this fuel based on this cost estimation.
2.7.7
System analysis: conclusions
It was found that, at equilibrium, the CORAIL system requires less natural resources and has a
smaller repository impact than the coupled LWR+PUZH. For the purpose of Pu inventory
reduction, PuH2-ZrH1.6, offers only a slightly smaller repository impact than PuO2-ZrO2 on most
of the analyzed parameters, but is the preferred choice from the perspective of proliferation
resistance, featuring a smaller fissile fraction and a higher plutonium specific neutron emission
rate. The cost difference is likely not significant enough to justify the choice of one fuel type
over the other.
71
2.8 Conclusions
The neutronic part of this project assessed the feasibility of multi-recycling plutonium and TRU
in PWR using hydride rather than oxide fuel. The extra hydrogen in the fuel softens the neutron
spectrum and thereby reduces the critical Pu concentration. First our neutronic computational
capabilities have been benchmarked against heterogeneous, plutonium-containing (CORAIL
[3,4]) and TRU-containing (CONFU [14]), fuel assemblies. The TRITON/NEWT sequence and
associated cross section libraries of the SCALE 5.1 code package were found of satisfactory
accuracy for modeling complex TRU-containing PWR fuel assemblies like the CORAIL and
CONFU, provided that the ORIGEN default branching ratio for production of 242mAm is changed
to approximately 10-11%. A value of 10% for the branching ratio was found to provide good
agreement with the calculated results of both APOLLO2 and WIMS8 in the case of CORAIL. In
case of CONFU, the agreement between the TRITON and CASMO predictions is good for all
the evaluated actinides with the exception of 242mAm which shows a discrepancy of about 20%:
CASMO, which likely uses a slightly different value for the branching ratio of 241Am, predicts a
higher concentration of 242mAm. Since the TRU-containing hydride fuel assemblies analyzed
feature a uniform composition, integral reactor physics characteristics, such as achievable
burnup, actinide concentration evolution and reactivity coefficients can be estimated using an
equivalent unit cell analysis. Modeling an equivalent unit cell enables using the 238 energy
group cross-section library. Other characteristics, such as the assembly power peaking factors
and control rods worth, were calculated using a full 2-D fuel assembly model using the 44 group
library.
An equivalent Pu-hydride (PUZH) fuel assembly was compared with two oxide fuel assembly
designs that were proposed to overcome the positive void coefficient of reactivity – CORAIL
and MOX-UE. The CORAIL design offers ~30% natural uranium and Separating Working Unit
(SWU) saving over conventional UO2 fuelled cores, but it provides for Pu stabilization rather
than net destruction (a complete Pu drawdown from the YMR would require ~300 CORAIL
cores, three times the current LWR fleet).It was found that the equivalent PUZH fuel (i.e. with
45% uranium loading) offers twice as large a fractional transmutation as the equivalent MOXUE oxide fuel. That is, a PWR loaded with these PUZH fuel assemblies will incinerate in the
first recycle twice as much TRU (primarily Pu) as it will do when loaded with MOX fuel
assemblies when both core designs are loaded with same amount of TRU and operate at the same
power level for the same time. This equivalent PUZH core (i.e. with 45% uranium loading) will
also be less expensive, since it uses depleted uranium versus significantly larger quantities of
enriched uranium required for the equivalent MOX-UE core. Additionally, the equivalent PUZH
fuel design has a lower power peaking factor than both MOX-UE and CORAIL fuel assemblies.
The PUZH fuel with heavy plutonium loading (as in the case of MOX-UE-4) enables attaining
the same cycle length of the MOX-UE fueled systems while the LVRC substantially more
negative, which is an important safety feature.
An assessment of the feasibility of enhancing the fractional plutonium transmutation using
hydride fuels with varying amounts of thorium and uranium was undertaken as well. These fuels
are of the form ThH2-ZrH1.6-PuH2 and U-ZrH1.6-PuH2 respectively. It was found that the fertile
free hydride fuel (of the form PuH2-ZrH1.6), while offering the higher TRU destruction fraction
of all the systems analyzed, also allows multi-recycling of Pu in PWR an unlimited number of
times when uniformly loaded in all fuel assemblies in the core. This unique feature of hydride
72
fuels is due to the incorporation of a significant fraction of the hydrogen moderator in the fuel,
thereby reducing the effect of spectrum hardening due to coolant voiding accidents; the large
void reactivity coefficient remains negative. The fractional transmutation of PuH2-ZrH1.6 was
found to be about 64% at the first recycle and gradually decreases to about 20% towards the
equilibrium recycle. The FTC of this promising fuel was found positive in the third batch,
thereby potentially limiting the practically achievable burnup, and therefore the transmutation
effectiveness. The use of deuterium instead of hydrogen in PuH2-ZrH1.6 fuel was found an
effective approach for obtaining a negative fuel temperature coefficient of reactivity during the
first recycle, practically without penalizing the achievable burnup or TRU transmutation
effectiveness. Addition of relatively small amount of either depleted U or Th offer two
alternative approaches for providing a negative FTC over the entire first recycle, but slightly
penalize the attainable fractional transmutation. An inert-matrix oxide fuel counterpart -- PuO2ZrO2, was investigated as well. Although the TRU destruction fraction at first recycle is almost
as high as that of PuH2-ZrH1.6 fuel, the practical applicability of this fuel for multi-recycling is
limited − due to a positive reactivity effect introduced by large voiding the maximum possible
number of recycles is limited to 10 despite of the fact that the leakage effect due to large core
voiding was found significantly larger for oxide as compared to hydride fueled cores.
The feasibility of recycling Pu+MA in hydride fuels was also assessed: it was found that hydride
fuels allow multi recycling of Pu+Np at least 6 times, before getting a positive large void
reactivity feedback. This corresponds to approximately 86 years of recycling campaign. A
number of approaches where investigated for making negative the large voiding reactivity
coefficients beyond the 6th recycle for NpH2-PuH2-ZrH1.6 fuel14. Enlarging the fuel rod radius
while conserving the pitch was found effective for substantial extension of the feasible number
of recycles. This approach does not substantially change the neutronic behavior during normal
operation, while it would result in a larger amount of hydrogen to remain in the core during large
voiding. On the down side, this would penalize the maximum attainable power because of the
larger friction losses associated with the reduction in the hydraulic diameter, unless an increase
in the pressure drop is allowed. It was also found that if it is desired to recycle all the TRU in
PWR using hydride fuel, the number of possible recycle would be limited to 3; the limit is
imposed by a positive large void reactivity feedback.
Finally, a system analysis was performed to compare the fuel cycle characteristics of Pu multirecycling in PWR using the promising hydride fuel assembly designs identified before versus Pu
recycling in PWRs using the most promising oxide fuel assemblies. It was found that, at
equilibrium, the CORAIL system requires less natural uranium and SWU and has a smaller
repository impact than the coupled LWR+PUZH.
The investigation of the reduction in TRU inventory attainable by multi-recycling Pu in a given
number of PWR cores using either the optimal hydride or the optimal oxide fuels found that a
larger number of cores (i.e. smaller number of required plutonium recycles) results in a smaller
accumulation of MA, but also in a larger residual inventory of plutonium at discharge. The net
effect, somewhat surprisingly, is that the total TRU mass after the recycles is relatively constant
with the number of parallel cores; slightly smaller for smaller number of cores (and more
14
Based on physics considerations, it is expected that a similar concept would apply successfully also to the “all
TRU” hydride fuel, but not to oxide fuels.
73
recycles), at about 30-35% of the initial inventory. It was also found that the residual TRU
inventory is slightly higher for MOX cores than for PUZH cores.
The repository impact was evaluated through the estimate of the following parameters
(normalized per ton of Pu transmuted) at the end of the campaign, as a function of the total
number of best-performing PUZH and MOX cores: 1) total radioactivity of the TRU stream; 2)
total neutron emission; 3) total decay heat; 4) total gamma decay heat; 5) total toxicity in air;
6)total toxicity in water; and 7) total mass of 237Np and its precursors (i.e. 241Am and 245Cm). It
was found that all these measures of repository impact, except for the mass of neptunium and its
precursors, are slightly higher for MOX than for PUZH, more so for larger number of cores. It
was also observed that the radioactivity is higher for larger number of cores, while all the other
measures decrease with the use of higher number of parallel cores (i.e. with a smaller number of
recyclings).
The proliferation resistance was evaluated through the estimate of the following parameters
(normalized per ton of Pu transmuted) at the reprocessing plant: 1) total inventory of plutonium
to be handled at the reprocessing plant; 2) Pu fissile fraction; 3) neutron emission per gram of
plutonium and TRU; 4) specific decay heat for Pu and TRU. The total inventory of plutonium to
be handled in the reprocessing plant is quite similar in the case of MOX and PUZH. However,
the plutonium fissile fraction at the reprocessing facility, as well as the neutron emission per
gram of plutonium, shows that the PUZH stream appears more proliferation resistant than that of
MOX for the first 9-10 recycles. The neutron emission per gram of TRU and the specific decay
heat are similar for the two fuel types. It is concluded that multi-recycling in PuH2-ZrH1.6 is more
resistant to proliferation than multi-recycling in PuO2-ZrO2.
Based on costs estimates for fuel fabrication, reprocessing and fuel and waste disposal, it was
found that the final cost of PuH2-ZrH1.6 would only be ~1.2% lower than that of PuO2-ZrO2, not
enough to justify the choice of this fuel based on this cost.
It is concluded that PuH2-ZrH1.6, while offering an only slightly smaller repository impact than
PuO2-ZrO2 on most of the analyzed parameters, is the preferred choice from the perspective of
proliferation resistance, featuring a smaller fissile fraction after 10 years of cooling and a higher
plutonium specific neutron emission. The cost difference is likely not significant enough to
justify the choice of one fuel type over the other.
If desired to transmute plutonium in a 2-tier system (i.e. recycle once in thermal reactors for Pu
inventory reduction and subsequently recycle all the leftover TRU in fast reactors), the number
of core-passes (i.e. total parallel cores or equivalently fewer cores used in series) required to
eliminate the entire Pu inventory originally planned to be disposed of at the YMR would be ~300
in case of using CORAIL fuel assemblies, ~70 for conventional MOX and ~100 in case of inert
matrix hydrides or oxides. This implies that CORAIL would not be a practical option for that
purpose with the current LWR fleet. Inert matrixes would provide the greatest inventory
reduction in one pass (see Table 2.32), leaving only 30% of the initial plutonium after the
campaign, while the conventional MOX would leave 77% of the initial plutonium mass. Inert
matrixes would also leave a substantially more proliferation resistant discharged stream.
Between oxide and hydride inert matrixes, it was found that hydride leaves a more proliferation
resistant discharged stream (Section 2.7.5), while no substantial difference on other parameters
was observed. It is also noted that inert matrixes are most likely the cheapest Pu recycling
options, since they allow reaching the typical cycle length in PWR with a smaller Pu loading,
74
thereby providing the largest amount of electricity generated per unit of reprocessed LWR spent
fuel.
2.9
References
[1]
F. Ganda and E. Greenspan, “Plutonium Incineration Capability of Hydride Versus MOX
Fuel in PWR”, Proceedings of GLOBAL’05, Tsukuba, Japan, 2005.
[2]
F. Ganda and E. Greenspan, “Physics Analysis of Hydride Fuel in PWR Cores,” Submitted
to Nuclear Science and Engineering, 2009.
[3]
G. Youinou and A. Vasile, “Plutonium Multirecycling in Standard PWRs Loaded with
Evolutionary Fuels”, Nuclear Science and Engineering: 151, 25-45, 2005.
[4]
F. Ganda, M. Milosevic, T. Taiwo and E. Greenspan, “TRITON/NEWT Calculation of the
CORAIL Assembly for Plutonium Recycling in PWR”, Joint International Topical Meeting
on Mathematics & Computation and Supercomputing in Nuclear Applications MC2007,
Monterey, California, 2007.
[5]
M.D. DeHart, “TRITON: A Two Dimensional Depletion Sequence for Characterization of
Spent Nuclear Fuel”, Nuclear science and technology division (94), Oak Ridge National
Laboratory, 2005.
[6]
M.D. DeHart, “NEWT: a New Transport Algorithm for Two-Dimensional Discrete
Ordinates Analysis in Non-Orthogonal Geometries”, Nuclear science and technology
division (94), Oak Ridge National Laboratory, 2005.
[7]
D. Hamrin et al., “SCALE-5: A Modular Code System for Performing Standardized
Computer Analyses for Licensing Evaluation”, Oak Ridge National Laboratory Radiation
Safety Information Computational Center Computer Code Package COO725, 2004.
[8]
O.W. Hermann, and C.V. Parks, “SAS2H: A Coupled One-Dimensional Depletion and
Shielding Analysis Module”, NUREG-CR-0200, Rev. 6, Vol. 1, Section 2, Oak Ridge
National Laboratory, 1998.
[9]
T.K. Kim et al., ”Benchmark Comparisons of Deterministic and Monte Carlo Codes for a
PWR Heterogeneous Assembly Design”, PHYSOR, Chicago, Ill, April 25-29, 2004.
[10] SCALE Newsletter, Number 35, January2007.
[11] CORAIL benchmark specifications-03, internal communication, Nov 2003.
[12] O. Bringer et al., ”Detailed studies of Minor Actinide Transmutation-Incineration in HighIntensity Neutron Fluxes”, PHYSOR-2006, Vancouver, BC, Canada, September 10-14,
2006.
75
[13] Nuclear Energy Agency, “Physics of Plutonium Recycling,” Vol. II, OECD, Paris, 1995.
[14] E. Shwageraus, P. Hejzlar and M.S. Kazimi, “Feasibility of Multirecycling of Pu and MA
in PWRs Using Combined Non-Fertile and UO2 (CONFU) Fuel. Proc. GLOBAL’03, New
Orleans, LA, 2003.
[15] E. Shwageraus, P. Hejzlar and M.S. Kazimi, “Use of Thorium for Transmutation of
Plutonium and Minor Actinides in PWRs”, Nuclear Technology, 147, 2004.
[16] E. Shwageraus, P. Hejzlar and M.S. Kazimi, “A Combined Non-fertile and UO2 PWR Fuel
Assembly for Actinide Waste Minimization,” Nuclear Technology, Volume 149, Number
3, Pages 281-303, 2005.
[17] F. Ganda, D. Barnes and E. Greenspan, “OECD Benchmark A & B of MOX Fueled PWR
Unit Cells using SAS2H,” Proc. Int. Mtg. Mathematics and Computation – MC2005,
Avignon, France, 2005.
[18] F. Ganda and E. Greenspan, “Plutonium Recycling in Hydride Fueled PWR Cores.
Accepted for publication in Nuclear Engineering and Design, 2009.
[19] F. Ganda and E. Greenspan, “A Simplified Method for Multi-Batch PWR Core Analysis
based on SAS2H Unit Cell Calculations,” Proc. Int. Mtg. Mathematics and Computation –
MC2005, Avignon, France, 2005.
[20] R.N. Hill et al., “Multiple Tier Fuel Cycle Studies for Waste Transmutation”, ICONE-1022575, Arlington, VA, April 14-18, 2002.
[21] C. Shuffler, J. Malen, P. Diller, F. Ganda, N. Todreas, E. Greenspan and B. Petrovic,
“Economic analysis for PWRs” Accepted for publication in Nuclear Engineering and
Design, 2009.
[22] F. Ganda and E. Greenspan, “Economic Analysis of Hydride-Fuelled BWR,” Accepted for
publication in Nuclear Engineering and Design, 2009.
[23] DOE RW 0533, 2001. Analysis of the total system life cycle cost of the civilian radioactive
waste management program.
[24] M. Bunn, J.P. Holdren, S. Fetter and B. Van Der Zwaan, ”The Economics of Reprocessing
versus Direct Disposal of Spent Nuclear Fuel,” Nuclear Technology, Vol. 150, June 2005.
[25] F. Ganda and E. Greenspan, “Neutronic Analysis of Hydride Fuelled PWR Cores”.
Accepted for publication in Nuclear Engineering and Design, 2009.
76
3. Thermal hydraulic analysis
This section is organized as follows:
¾ Section 3.1: objectives of the thermal hydraulic analysis;
¾ Section 3.2: reference plant;
¾ Section 3.3: fuel physical property database;
¾ Section 3.4: steady-state analysis;
¾ Section 3.5: Large Break Loss Of Coolant Accident (LBLOCA) analysis;
¾ Section 3.6: Main Steam Line Break (MSLB) analysis;
¾ Section 3.7: Complete Loss Of Coolant Accident (CLOFA) analysis;
¾ Section 3.8: conclusions;
¾ Appendix: the inverted core design.
While the first eight sections were part of the original project proposal, the appendix describes an
innovative core design that was developed in parallel. Such design consists of hexagonal blocks
of hydride fuel perforated with cooling channels. Although the investigation of this design was
not part of the project scope requirement, a brief summary of the inverted core project is
presented for completeness.
3.1 Objectives
The thermal hydraulic analysis was aimed at comparing the behavior of a PUZH-fueled PWR
core with that of geometrically identical cores, but loaded with different assemblies, both during
normal operation and during accident scenarios. These assemblies have the same geometry, but
differ either because of the type of fuel with which they are loaded or because of the fuel
arrangement in the lattice. The assemblies analyzed are the following:
-
all-UO2-assembly: the reference assembly; it uses UO2 fuel pins only.
-
CONFU-assembly: heterogeneous assembly made of standard UO2 fuel pins and pins
made of recycled transuranics in an inert matrix.
-
CORAIL-assembly: heterogeneous assembly made of enriched UO2 pins and MOX pins.
-
PUZH-assembly: homogeneous assembly containing U-Pu-Th-ZrH1.6 as fuel.
The corresponding cores are referred to as all-UO2-, CONFU-, CORAIL- and PUZH-core. Their
geometry is identical to that of the PWR core of Seabrook, which is the plant used as reference in
the project. Key plant parameters are summarized in Table 3.1.
CONFU- and CORAIL- cores were analyzed since, like PUZH-core, are capable of recycling
plutonium and Minor Actinides (MA). The all-UO2-core, instead, cannot be used for that purpose
but it was analyzed anyway for two reasons:
-
the all-UO2-core is the only core for which the behavior during normal operation and
during accident scenarios is known. Plant response data found in [1] could therefore be
used to benchmark the plant modeling technique used in this project;
77
-
the safety margins characterizing the all-UO2-core during various accident scenarios are
known. They were used as metric of comparison of the core performance, in the sense
that they were used to “rank” the core types examined against a core type, i.e. the
Seabrook core, which has been licensed and is currently in operation.
3.2 Reference plant
The Seabrook plant, a Westinghouse 4-loop PWR, was used as reference plant for this project.
Key plant parameters, referred to nominal operating conditions, are summarized in Table 3.1.
While the geometry of the plant was kept fixed throughout the project, in some cases thermal
hydraulic parameters used in the analyses deviated from those shown in the table, due to
conservative margins, accident-specific, that were added in the modeling of steady-state and
transient conditions. The new values are presented in the following sections whenever such
margins are added.
Table 3.1 – Nominal parameters for the reference core1
Parameter
Vessel
Vessel inner diameter
Unit
Value
m
4.394
Steam Generators
m
m
Westinghouse
model F
5109.7
20.62 ([2])
5626
17.47
15.44
24.89 ([3])
8.73 ([3])
1.44 ([3])
7.06 ([2])
0.539 ([3])
3.59 ([2])
3.10 ([2])
4.28 ([2])
16
3.13 ([2])
~0.51 ([2])
m
~0.70 ([2])
m
m
m2
m
kg/s
0.407
0.703
0.183
71
476.28
Steam generator type
Heat transfer area per SG
Overall height
Number of tubes per SG
Tube outer diameter
Tube inner diameter
Tube pitch
Height of bundle
Largest curvature radius for U-tubes
Height of straight part of tubes (tubesheet excluded)
Tubesheet thickness
Inner diameter of SG main body (downcomer included)
Inner diameter of SG secondary pool (downcomer excluded)
Inner diameter of SG upper head
Number of moisture separators per SG
Moisture separator height
Moisture separator inner diameter (lower part)
Moisture separator inner diameter (upper part, inclusive of liquid
return path)
Steam flow restrictor diameter at SG outlet nozzle
Main steam line inner diameter
Main Steam Line Isolation Valve (MSLIV) flow area
Length of main steam line between SG outlet nozzle and MSLIV
Steam flow per SG
1
All data are from [1] except otherwise specified.
78
m2
m
mm
mm
mm
m
m
m
m
m
m
m
Primary inlet temperature
Primary outlet temperature
Steam outlet temperature
Steam pressure
Feedwater temperature
Mass of each SG (dry)
Volume available for primary coolant in each SG
Volume available for secondary coolant in each SG
Weight of secondary coolant in each SG at HZP
Pressurizer
Volume
Inner diameter
Core
Active height
Equivalent core diameter
Pressure
Total primary flow rate
Effective flow rate for heat transfer
Core average mass flux
Vessel inlet temperature
Vessel outlet temperature
Average void fraction in the hot subchannel
Maximum void fraction in the hot subchannel
UO2 weight
Power
Core thermal power
Average core power density
Average Linear Heat Generation Rate (LHGR)
Peak LHGR for normal operation
Nuclear Enthalpy Rise Hot Channel Factor used in safety analyses
Total heat flux hot channel factor used in safety analyses
Assemblies
Number of assemblies
Lattice type
Rods per assembly
Guide thimbles per assembly
Guide thimble inner/outer diameter (mm)
Instrumentation tubes per assembly
Instrumentation tube inner/outer diameter (mm)
Grids per assembly
Assembly side width
Assembly pitch
Total assembly length (nozzles included)
ºC
ºC
ºC
MPa
ºC
kg
m3
m3
kg
325.7
292.6
284.8
6.89
226.67
316154
~27.3
~167.1
76205
m3
m
50.97
2.13
m
m
MPa
kg/s
kg/s
kg/s m2
ºC
ºC
%
%
kg
3.6576
3.3706
15.513
18358
17476
3675.4
293.1
325.7
6
20.6
101034
MW
W/cm3
W/cm
W/cm
3411
104
178.6
446.2
1.65
2.50
mm
mm
cm
cm
m
Fuel Rods
79
193
17× 17
264
24
11.430 / 12.243
1
11.379 / 12.294
8
21.40
21.50
4.063
Number of fuel rods in the core
Active length
Total rod length
Fission gas plenum length
Clad outer diameter
Clad inner diameter
Rod pitch
Cladding thickness
Cladding material
Fuel-clad gap thickness
Pellet diameter
Pellet height
m
m
mm
mm
mm
mm
mm
mm
mm
mm
Form loss coefficients
Bottom fuel nozzle
Bottom grid spacer
Intermediate grid spacers
Upper grid spacer
Intermediate Flow Mixers
Top fuel nozzle
50952
3.6576
3.8760
188.7
9.500
8.357
12.6
0.571
Zr alloy
0.0825
8.19
9.83
1.6992
0.389
0.4822
0.3834
0.4154
0.5519
3.3 Fuel physical property database
Physical properties for PUZH fuel are not available in the literature. However, studies on similar
fuels were performed by Prof. Yamawaki and Prof. Konashi and their colleagues, who measured
the properties of Ux-Thy-Zrz-Ht fuels as a function of temperature. Even though these fuels do not
contain plutonium, their physical properties can be considered reasonable estimates of PUZH
properties. Among the fuels examined, UTh4Zr10H27 was chosen to represent PUZH because, at
the initial stage of the project:
-
the optimized composition of PUZH was not known, and motivations based on chemical
similarity could not be formulated;
-
UTh4Zr10H27 was the most documented fuel type within the Ux-Thy-Zrz-Ht family.
Density, thermal conductivity, specific heat and linear thermal expansion data are presented
below.
3.3.1 Density
The correlation presented by Tsuchiya ([5]) for hydrogenated UTh4Zr10 was used to get the
density of UTh4Zr10H27:
ρ = 8440 − 29.9 × t
where t is the ratio of H to U-Th4-Zr10. When applied to UTh4Zr10H27, the formula gives a value
of 7592.7 kg/m3.
3.3.2 Thermal conductivity
Thermal conductivity of UTh4Zr10H27 is shown in Figure 3.1.
80
60
U-Th4-Zr10-H27
UO2
50
k (W/m K)
40
30
20
10
0
300
500
700
900
1100
1300
T (K)
Figure 3.1 – UTh4Zr10H27 thermal conductivity vs temperature ([5])
3.3.3 Specific heat
Specific heat of UTh4Zr10H27 is shown in Figure 3.2.
650
Specific heat (J/kg K)
600
U-Th4-Zr10-H27 (from [3])
UO2 (from [4])
550
500
450
400
350
300
250
200
200
300
400
500
600
700
800
900
T (K)
Figure 3.2 – UTh4Zr10H27 specific heat vs temperature ([5], [6])
3.3.4 Linear thermal expansion coefficient
Linear thermal expansion coefficient of UTh4Zr10H27 is shown in Figure 3.3.
81
12.5
12
U-Th4-Zr10-H27
UO2
CTE*10^-6 (1/K)
11.5
11
10.5
10
9.5
9
300
400
500
600
700
800
900
T (K)
Figure 3.3 – UTh4Zr10H27 coefficient of thermal exp. vs temperature ([4])
The discontinuity experienced by thermal conductivity of UTh4Zr10H27 at about 900 K (Figure
3.1) is due to hydrogen release. In this regard it is important to note that after comparing ternary
alloys (U-Th-Zr) to binary alloys (U-Zr, e.g. TRIGA fuel), Yamamoto stated: “the ternary alloy
can hold more hydrogen than U-Zr alloy at the same temperature. In other words, it can hold a
certain amount of hydrogen at a higher temperature than the U-Zr alloy. This fact gives an
attractive advantage if it is used as a nuclear fuel” ([7]). From this observation, it can be
concluded that PUZH fuel can operate at higher temperatures than the most well know hydride
fuel, i.e. U0.31ZrH1.6, the latter being a binary hydride.
3.4 Steady-state analysis
3.4.1 Objectives of the analysis
The steady-state analysis was aimed at calculating the maximum steady-state power that a core
can attain without breaching some thermal hydraulic constraints. The analysis was performed for
each of the core types listed in Section 3.1, assumed to be at Beginning Of Life (BOL).
3.4.2 Code used and modeling approach
The steady-state analysis was performed using the VIPRE code ([8]). The main features of the
code input file are:
¾ 1/8th of the core was modeled, shown in Figure 3.4;
¾ the hot assembly was assumed to be located at the centre of the core (in red in Figure
3.4);
¾ the 1/8th of core was modeled as composed by 6 pseudo-assemblies2, identified with
letters “a” to “f” in Figure 3.4:
- 1/8th of the hot assembly (“a” in Figure 3.4);
- two halves of the two adjacent assemblies (“b” and “c” in Figure 3.4);
2
The term “pseudo-assembly” is used to identify fractions of assemblies or multiple assemblies lumped together.
82
- a pseudo-assembly equivalent3 to two assemblies (“d” in Figure 3.4);
- a pseudo-assembly equivalent to 7 assemblies (“e” in Figure 3.4);
- a pseudo-assembly equivalent to 14 assemblies (“f” in Figure 3.4);
The 1/8th fraction of the hot assembly was modeled in detail, i.e. by specifying geometry of each
pin and subchannel, as well as the radial peaking factor of each pin. Pseudo-assemblies “b”
through “f” were modeled using a lumping approach. The dashed lines shown in Figure 3.4,
which do not have any correspondent meaning in the VIPRE model (because of lumping),
indicate the location of the assemblies.
Figure 3.4 – Assembly lumping and radial peaking factors used in the steady-state analysis
The radial peaking factors corresponding to each pseudo-assembly are shown in Figure 3.4 and
described in Section 3.4.4.
3.4.3 Thermal hydraulic constraints
The maximum attainable core power is defined as the maximum power that does not cause any
of the thermal hydraulic constraints to be breached. These constraints are summarized in Table
3.2, and a brief description of each follows the table. The search for the maximum attainable
3
Pseudo-assembly “d” is formed by 1 whole assembly and two halves of two separate assemblies. “Equivalent to two
assemblies” means that the number of fuel rods, flow area etc. are equal to those characterizing two assemblies lumped
together.
83
power is performed, for each core type, by increasing core power and coolant flow rate starting
from low values, but maintaining their ratio fixed, till one4 of the constraints is matched and none
of the others is exceeded.
Table 3.2 – Thermal hydraulic constraints used in the steady-state analysis
Core type
all-UO2, CONFU
and CORAIL
PUZH
MCHFR
Core
pressure
drop5
(kPa)
Max. fuel
T (ºC)
Max. fuel
average T
(ºC)
Max
cladding
surface T
(ºC)
Core
enthalpy rise
(kJ/kg)
2.11
150
2805
1400
349
195
2.11
150
850
Not applied
349
195
MCHFR (Minimum Critical Heat Flux Ratio): the limit value for this parameter was chosen
using a reverse engineering approach, i.e. it is equal to the MCHFR calculated for the all-UO2core. The MCHFR limit ensures a margin from the critical heat transfer conditions.
Core pressure drop: again, a reverse engineering approach was used to fix the maximum allowed
core pressure drop. The decision of not allowing the pressure drop to exceed the reference core
value was made to avoid pump system upgrading. Should a higher pressure drop be allowed, a
larger core power could be achieved, not only for PUZH but also for the other core designs.
Fuel temperature: for all-UO2-, CONFU- and CORAIL-core, 2805°C and 1400°C are used to
prevent fuel melting (2805ºC is the melting point of UO2) and exceeding approximately 5%
fission gas release ([9]). For PUZH, the temperature is limited to prevent excessive hydrogen
release. The value of 850ºC was chosen as the temperature corresponding to the same hydrogen
pressure as that characterizing U-ZrH1.6 at 750ºC (~0.3 atm, [10]), which was the maximum
allowed temperature fixed for U-ZrH1.6 in the previous NERI project ([11]). Consistent with this
data comparison, while comparing ternary alloys (U-Th-Zr, i.e. PUZH type) to binary alloys (UZr, i.e. TRIGA type) Yamamoto states: “the ternary alloys can hold more hydrogen than U-Zr
alloy at the same temperature. In other words, it can hold a certain amount of hydrogen at a
higher temperature than the U-Zr alloy. This fact gives an attractive advantage if it is used as a
nuclear fuel” ([7]). The choice of the maximum allowed fuel temperature should account also
for fission gas release. However, detailed investigations of this phenomenon for ternary hydrides
have not been found in the public literature. So far, the only available source dealing with this
phenomenon ([12]) discusses experiments performed on UTh4Zr10H20 irradiated at low linear
power (14 kW/m) and burnup of 1.1% FIMA (equivalent to about 17 GWD/ton), and states that:
“Released fission gas was not observed because of low burnup of pellet”. For PUZH, the limit of
850ºC on maximum centerline temperature clearly prevents fuel melting.
Cladding surface temperature. 349°C was chosen to assure sufficient margin between the oxide
corrosion layer thickness that unavoidably forms during steady state operation and the maximum
oxide thickness allowed during LOCA severe accidents. According to the NRC Regulation 10
CFR 50.46, the maximum thickness shall nowhere exceed 17% of the total cladding thickness
before oxidation.
4
Actually, the status of the constraints when the maximum attainable power is reached is that two are matched: one among
MCHFR, core pressure drop, maximum fuel temperature, maximum fuel average temperature and maximum cladding surface
temperature, plus the core enthalpy rise. The latter, in fact, is kept constant throughout the analysis regardless of whether the
core power is the maximum or a lower value.
5
Core lower and upper plates excluded.
84
Core enthalpy rise. The value chosen is the core enthalpy rise for the reference core, under
licensing conditions. This parameter is typically constrained to limit the temperature at the exit
of the core, so that steam generator tube corrosion can be maintained within acceptable limits.
3.4.4 Analysis assumptions
The core types analyzed, i.e. all-UO2-, CONFU-, CORAIL- and PUZH-core, have the same
geometry, operating pressure, core inlet temperature, core enthalpy rise and coolant flow rate,
which are fixed at the licensing values of the Seabrook Power Station ([1]). Table 3.3
summarizes the key assumptions that are common to all the core types analyzed. The geometric
parameters, also common to all the core types, are shown in Table 3.1. Particularly, Table 3.3
highlights the difference between the nominal values (from Table 3.1) and the licensing values
actually used in the steady-state analysis. Consistent with practice in Safety Analyses (Chapter
15 of [1]), the thermal hydraulic conditions of the analyzed cores are obtained by applying a
conservative margin to the normal operation values.
Table 3.3 – Licensing values used for steady-state analysis (common to all the
core types)
Parameter
Operating conditions
Pressure (MPa)
Core inlet temperature (ºC)
Power and flow rates
Core thermal power (MW)
Coolant enthalpy rise across the core (kJ/kg)
Coolant flow rate through the core (flow between peripheral
assemblies and baffle not included) (kg/s)
Percentage of coolant flowing through guide thimbles
Nominal
values
Licensing
values
15.513
293.1
15.513
296.3
3411
191
3479
195
17843
17843
2
2
Important parameters missing from Table 3.3 are those related to the power distribution inside
the core. In fact, while it was reasonable to fix the parameters of Table 3.3 to the same values
regardless of the core type under examination, parameters related to the power distribution
should be core-specific. These parameters are:
- pin radial peaking factor Fpin – ratio between the power of the hottest pin and that of the
average pin in the same assembly;
- assembly radial peaking factor Fassembly – ratio between the power of the hottest assembly
and that of the average assembly;
- pin axial peaking factor Faxial – ratio between the maximum linear power along the hottest
pin and the average linear power in the same pin.
Actually, only Fpin was set to core-specific values. This is because for CONFU- and PUZH-core
only 2D neutronic analyses, at assembly-level, have been performed, and neither whole core data
nor axial data were available. Therefore, it was decided to fix Fassembly and Faxial for all the core
types to the licensing values typically used for UO2-cores. Table 3.4 summarizes the values used
for Fassembly, Fpin and Faxial in the steady-state analysis of the cores analyzed. Values of the
enthalpy rise hot channel factor (FΔH = Fassembly × Fpin) and of the total peaking factor (FQ = FΔH
× Faxial) are also shown.
85
Table 3.4 – Power peaking factors used in the steady-state
analysis
Fassembly
F pin
All-UO2
1.515
1.089
CONFU
1.515
1.241
CORAIL
1.515
1.152
PUZH
1.515
1.083
Faxial
1.515
(chopped cosine)
1.515
(chopped cosine)
1.515
(chopped cosine)
1.515
(chopped cosine)
FΔH
FQ
1.650
2.500
1.880
2.848
1.745
2.644
1.641
2.486
Besides that for the hot assembly, the radial peaking factors used for the pseudo-assemblies
shown in Figure 3.4 were arbitrarily chosen6, with the constraint of power normalization across
the whole core. The intra-assembly radial power distributions used for the hot assembly in the
steady-state analysis are instead shown in Figures 3.5 through 3.8. Together with the radial
peaking factor corresponding to the hottest pin, Fpin, these figures also show the pin location at
which the MCHFR is detected.
0
1.035
0.992
0
0.999
1.050
0
0.999
1.003
0.972
1.012
1.002
1.018
0.985
1.059
1.028
1.007
0.978
1.054
0.986
1.022
1.008
1.019
1.003
0
1.064
1.018
0
0.992
0.995
1.008
*+1.089
1.012
1.001
0.987
*Hot Pin
0
1.034
0.935
0.971
0.940
0.916
0.962
0.960
0.960
+ MCHFR
0.918
Figure 3.5 – Intra-assembly pin peaking factors for all-UO2, Fresh Assembly, BOL,
w/IFBA ([1])
0
0.980
1.071
0
1.179
1.144
0
0.434
1.141
UO2 Pins
0.460
0.985
1.136
1.145
1.112
1.031
0.802
1.170
0.471
1.116
1.141
1.111
1.020
0.431
1.151
Gd Pins
FFF Pins
0
+1.187
1.146
0
0.824
1.168
1.160
1.134
0.997
0.423
1.086
*Hot Pin
0
0.931
*1.241
1.021
0.808
1.137
0.985
1.003
0.958
+ MCHFR
0.965
Figure 3.6 – Intra-assembly pin peaking factors for CONFU, Recycle 01, BOL, w/Gd2O3
([13])
6
It was demonstrated that the radial peaking factors assumed for the assemblies surrounding the hot assembly do not appreciably
affect the MCHFR of the core.
86
0
+*1.152
1.147
0
1.116
1.076
0
0.898
1.120
UO2 Pins
1.117
1.111
1.133
1.081
1.044
1.012
0.869
1.111
1.104
1.130
1.075
1.038
1.004
0.861
1.098
MOX Pins
0
1.104
1.064
0
0.867
1.081
1.066
1.045
0.962
0.793
1.014
*Hot Pin
0
0.876
1.062
0.911
0.747
0.927
0.839
+ MCHFR
0.825
0.803
0.811
Figure 3.7 – Intra-assembly pin peaking factors for CORAIL, Recycle 01, BOL, 8% Pu,
600 ppm B ([14])
0
1.041
1.039
0
1.040
1.042
0
1.030
0.968
0.987
0.985
1.046
0.985
0.988
1.040
0.978
0.970
0.982
1.045
0.985
0.988
1.041
0.976
0.966
0
1.056
1.062
0
1.035
0.972
1.026
*+1.083
1.066
0.975
0.964
*Hot Pin
0
1.040
0.949
0.956
0.958
0.930
0.949
+ MCHFR
0.926
0.955
0.987
Figure 3.8 – Intra-assembly pin peaking factors for PUZH, Fresh Assembly, BOL, Recycle
01 (calculated in this project)
3.4.5 Results
The core configurations (core type plus operating conditions) characterized by the maximum
attainable power are summarized in Table 3.5, together with the relevant results derived from the
steady-state analysis. The cells containing the thermal hydraulic constraints are highlighted in
grey.
Table 3.5 – Maximum attainable power comparison
ºC
ºC
ºC
ºC
ºC
ºC
AllUO2core
2.5
1.515
1.089
1.515
2.11
2070
1321
685
402
374
348.5
kPa
149.8
Units
Total peaking factor (FQ)
Assembly radial peaking factor
Max. intra-assembly pin peaking factor
Axial peaking factor
MCHFR
Max. fuel temperature
Max. average fuel temperature
Max. pellet surface temperature
Max. cladding inside temperature
Max. average cladding temperature
Max. cladding outside temperature
Core pressure drop (Core plates
excluded)
87
CONFUcore
CORAILcore
PUZHcore
2.848
1.515
1.241
1.515
2.11
1799
1161
653
397
372
348.4
2.644
1.515
1.152
1.515
2.11
1772
1145
635
394
370
348
2.486
1.515
1.083
1.515
2.11
805
751
684
402
374
348
105.7
107.9
150.3
Max. subchannel exit quality
Hot assembly exit quality (subch.
averaged)
Max. subchannel exit void fraction
Hot assembly exit void fraction (subch.
averaged)
Core thermal power
Core power difference percentage with
respect to all-UO2-core
%
0.3
1.1
4.0
0.4
%
0.09
0.19
0.74
0.10
%
1.88
6.27
19.66
2.56
%
0.51
1.12
4.24
0.59
MW
3479
2761
2801
3487
0
-20.6
-19.5
+0.2
3.4.6 Conclusions
The most important conclusions arising from the steady-state analysis are:
-
while CONFU and CORAIL can reach only about 80% of the power attainable by the allUO2-core, PUZH-core can operate at 100% of that power without exceeding any thermal
hydraulic limit. This is due to the homogeneity of the fuel lattice, which yields a flatter
intra-assembly power distribution.
-
The weakness of PUZH, i.e. the inability to operate safely above 850ºC, is not the
limiting constraint since the thermal conductivity assumed for this fuel, which is about
80% higher than that of UO2 ([5]), prevents the fuel centerline temperature from reaching
the 850ºC limit.
-
The MCHFR is the limiting parameter for all the core configurations.
It must be pointed out that the first conclusion above is a consequence of having imposed, to all
the core types, the same MCHFR limit. However, the licensing of reactors different from typical
all-UO2 reactors, aimed at plutonium-MA recycling other than electricity generation, may be
performed using different safety limits than those applied to all-UO2 reactors. If, for example, the
MCHFR limit was reduced, CONFU- and CORAIL-core would be able to reach higher power
levels than those shown in Table 3.5.
3.5 Large Break LOCA analysis
3.5.1 General event description
A Loss Of Coolant Accident (LOCA) is defined as a condition IV event, i.e. an event whose
occurrence is not expected during the life of a plant, but that is however postulated since it may
yield the release of significant amount of radioactive material. It is the result of a pipe rupture of
the Reactor Coolant System (RCS) pressure boundary: if the rupture total cross-sectional area is
equal or greater than 1 ft2 the scenario is typically referred to as LBLOCA.
The LBLOCA analyzed here consists of a double-ended guillotine break of a cold leg, located
between the RCS pump and the vessel inlet nozzle. The transient following the break occurrence
can be divided in three consecutive phases:
- blowdown: it is the phase immediately after the break, characterized by a rapid
depressurization of the RCS. Lasting about 10-30 seconds, this phase can be further
divided in two subphases: an ultra-rapid cooling of the fuel rods, through forced
convection caused by coolant flowing upward in the core and being released from the
break, followed by a fuel rod isolation phase, during which fuel rods are practically
88
thermally isolated since only steam is left in the vessel. Core power is at decay power
levels because of the large negative reactivity insertion due to coolant loss and
vaporization.
- Refill: the Emergency Core Cooling System (ECCS) injects borated water into the RCS
causing the vessel lower head and core lower plenum to be progressively filled with
water. Fuel rod temperature in this phase increases monotonically.
- Reflood: the continuous water injection by the ECCS causes the liquid level to reach the
bottom of the fuel rods which, because of their temperature higher than the Leidenfrost
temperature, cause water to boil. Heat removal through boiling causes fuel rod
temperature at the bottom of the core to progressively reduce, until it falls below the
Leidenfrost value so that the rods, locally, can be quenched. The quenching front moves
progressively upward both because of the cooling effect due to the steam released from
lower axial locations and because of axial heat conduction, inside the rods, across the
quenching front. During the reflood phase, cladding temperature at any axial location
tends to increase and then, once the rod is quenched locally, decrease.
The maximum cladding temperature during the transient, typically reached during reflood, is
referred to as Peak Cladding Temperature (PCT).
While that discussed above is the description of a general LBLOCA event, the description of the
event actually analyzed requires specifying several assumptions made, both boundary conditions
(mainly from the specifications dictated by Chapter 15 of any PWR Safety Analysis Report) and
simplifying assumptions made to reasonably model the event accounting for the available
computational tools. Such assumptions are presented in Section 3.5.4 and 3.5.5.
3.5.2 Objectives of the analysis
The analysis modeled the occurrence of a Large Break Loss Of Coolant Accident (LBLOCA) at
the Seabrook plant, in which the core was assumed to be, alternatively, of all-UO2-, CONFU-,
CORAIL- or PUZH-type. The objectives of the analysis were:
- verify whether a steady-state core power of 3479 MWt yields a PCT above the limit value
established by 10CFR50.46, i.e. 2200ºF (1478 K), at any time during the LBLOCA;
- compare the PCT of the different core types during the LBLOCA.
As done in the steady-state analysis, the characteristics of the plant used for the LBLOCA
analysis reflect those of Seabrook Power Station ([1]). Geometry of the plant (core included) and
out-of-core thermal hydraulic parameters are summarized in Table 3.1. Table 3.6 shows instead
the thermal hydraulic parameters used for the core.
3.5.3 Code used and modeling approach
The LBLOCA analysis was entirely performed using RELAP-3D version 2.3.6 ([15]).
The RELAP analysis consisted of two runs for each core type: a steady-state run aimed at finding
the thermal hydraulic conditions characterizing the plant in the pre-accident state, and a transient
run which actually modeled the LBLOCA starting from the state obtained through the steadystate run.
The plant nodalization implemented in the RELAP files is shown in Figure 3.9. It is worth noting
that:
89
a) the break assumed was a double ended guillotine break located in the cold leg between
the primary pump discharge and the vessel inlet nozzle;
b) the three intact loops are lumped together, while the broken loop is modeled separately;
c) the axial modeling of the core was performed using 16 axial zones: the bottom and the
top zones are 45.3 cm long each, while the remaining 14 zones are 22.6 cm long each.
The heated part of the core includes all the 14 central zones plus a fraction of the two
outermost ones;
d) the radial modeling of the core consisted of three channels:
-
channel 335 represents the hot channel (hot assembly). Its flow area does not
include the flow area of the guide thimbles, which however contribute in terms of
wetted perimeter;
-
channel 333 represents the remaining 192 channels lumped together (193 are the
assemblies contained in the core). Again, its flow area does not include the guide
thimble flow area, while the region between the peripheral assemblies and the
core baffle is included;
-
channel 320 contains the fraction of coolant that, after flowing down through the
downcomer, bypasses the core by going through the guide thimbles and between
the core baffle and the barrel;
e) other than the 2.5% of total primary flow bypassing the core through channel 320, about
2% of the same flow bypasses the core by flowing directly from the vessel inlet to the
vessel outlet nozzle, and by going from the vessel inlet nozzle to the vessel head to cool
it;
f) two heat structures are embedded in channel 335: the hottest pin and a dummy rod
representing the remaining 263 rods contained in the hot assembly. Therefore, even
though the subchannel-level modeling performed with VIPRE for the steady-state
analysis (see Sections 3.4.2 and 3.4.4) was undoubtedly more detailed than the lumping
approach used in RELAP, an hot pin is however modeled7. Mixing is allowed between
channel 333 and channel 335.
7
The good accuracy of the core thermal hydraulic model was proved by the MCHFR calculated by RELAP, which was only 10%
larger than that predicted by VIPRE.
90
Figure 3.9 – RELAP plant nodalization used for LBLOCA analysis
3.5.4 RELAP model for steady-state
Table 3.6 shows the thermal hydraulic parameters characterizing the steady-state for the cores
analyzed. Contrary to the methodology followed in the steady-state analysis, where a crucial
parameter like the coolant flow rate through the core was input explicitly in the VIPRE input file,
the more extended plant modeling performed with RELAP does not allow directly entering this
flow rate, which is instead a consequence of the input primary pump characteristics and of the
input form losses that are encountered by the coolant while flowing from the inlet to the outlet
vessel nozzle. For this reason, for some of the key thermal hydraulic parameters used for
transient initialization, Table 3.6 shows both the desired value (from [1]) and the simulated
value. The agreement is quite good. Parameters for which the desired value is not displayed are
input directly, and therefore it is understood that the simulated value coincides with the desired
one. In order to highlight the conservatism implemented in the analysis, the nominal value of
each variable is also shown.
Table 3.6 – Steady-state key thermal hydraulic parameters used for LBLOCA initialization,
common to all core types
Units
Nominal
MPa
15.513
ºC
293.1
ºC
326.2
Simulated
Operating conditions
Core pressure
Coolant temperature at core inlet
Average coolant temperature at core
outlet
Power and flow rates
91
15.513 (desired)
15.709 (simulated)
296.3 (desired)
296.4 (simulated)
329.3 (desired)
328.2 (simulated)
Core thermal power
MW
Axial peaking factor
3411
~1.40
Total primary circuit coolant flow rate
Active flow rate through the core (guide
thimble flow is not included, but flow
between peripheral assemblies and baffle
is included)
Core bypass flow, contribution 1 (guide
thimble flow + flow between baffle and
barrel)
Core bypass flow, contribution 2 (flow
from vessel inlet nozzle to outlet nozzle +
flow from the inlet nozzle to the vessel
head)
3479
1.515 (chopped cosine) and
1.515 (peaked at ~2.8 m)
18358 (desired)
18363 (simulated)
kg/s
18358
kg/s
17568
17568 (desired)
17558 (simulated)
kg/s
448
448 (desired)
465 (simulated)
kg/s
342
342 (desired)
340 (simulated)
See Table
3.1
See Table 3.1
Plant geometry
As indicated in Table 3.6, the LBLOCA analysis considers two possible steady states to initialize
the transient: one characterized by a typical chopped cosine axial power shape, which makes the
power distribution in the core identical to that assumed in the steady-state analysis (Section 3.4),
and one characterized by a top-skewed axial power shape. The choice of adding this last case
was consistent with the LBLOCA analysis methodology described in Chapter 15 of [1], which
states that the most limiting axial power profile for LBLOCA transient initialization is an 8.5foot top-skewed profile. However, since reference [1] does not provide any graphic
representation of this profile, the profile adopted in this analysis derives from [16]; it is peaked at
about 9.2 feet (2.80 m) (see Figure 3.10). Although such a power profile is unusual for a PWR at
steady-state, its adoption has been found to be very frequent in LBLOCA analyses. However, as
mentioned in [17], “this shape corresponds to a transient power condition that would not be
sustained long enough for decay heat to assume this shape following trip”.
1.8
1.6
Power peaking
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0
2
4
6
8
Axial coordinate (ft)
10
12
Figure 3.10 – Top-skewed axial power shape used, in addition to chopped-cosine, for
LBLOCA transient initialization
92
The pin radial peaking factor Fpin and the assembly radial peaking factor Fassembly entered in the
REALP steady-state file were those assumed for the VIPRE steady-state analysis, which are
shown in Table 3.4. These peaking factors, as well as the axial peaking factor, are assumed to
remain constant during the whole transient scenario.
3.5.5 RELAP model for transient
The plant response to the LBLOCA event consists of a series of actions actuated with a certain
delay time with respect to the first of the following two signals being detected:
-
S1 (low pressurizer pressure): PRZ pressure drops below 1935 psia (13.34 MPa);
-
S2 (low core flow): coolant flow rate at core inlet drops below 87% of the nominal value,
i.e. below 15674 kg/s.
The protective actions are summarized in Table 3.7, together with the corresponding delay times
which are consistent with those used in Chapter 15 of [1] for the LBLOCA analysis.
Table 3.7: Sequence of events following the occurrence of the break
Main Steam Line Isolation Valves
start closing
RCP trip. Coastdown starts
Delay with respect to S-signals (s),
or actuation setpoint
2 s after S1
1 s after S2
2 s after S1
Main Feedwater Isolation Valve
start closing
2 s after S1
Auxiliary Feedwater Pumps start
injecting
75 s after S1
PRZ Power Operated Valves open
Safety injection signal
Accumulators start injecting
PRZ pressure > 2425 psia
31 s after PRZ pressure has dropped
below 1867 psia
Notes
5 s are needed for
complete closure
10 s are needed
for complete
closure
They close after
PRZ pressure has
decreased below
2330 psia
CCP, SIP and
RHRP flow rates
vary based on
RCS pressure
Cold leg pressure < 600 psia
Conservative assumptions that are also made to reduce the ECCS capability to mitigate the event
are consistent with those used in Chapter 15 of [1]. They can be summarized as follows:
a) Reactor trip is not credited, i.e. control rods are assumed completely withdrawn during
the whole transient.
b) Boron contained in ECCS water is not credited.
c) 1 out of 4 accumulators is not credited.
d) 1 out of 2 ECCS trains is assumed not available, i.e. 1 Centrifugal Charging Pump, 1
Safety Injection Pump and 1 Residual Heat Removal Pump are not credited. The capacity
of the remaining train is 10% degraded.
93
In addition, the containment pressure variation assumed8 during the LBLOCA corresponds to
that of a transient in which the containment atmosphere cooling system is perfectly working. In
this way, the backpressure is maintained quite low and the flow through the break, after the
period when it is chocked, is higher. Figure 3.11 compares the containment pressure evolution
assumed in the LBLOCA analysis to that used in [1] for containment design purposes. In spite of
being different, they are both conservative since the ECCS cooling capability is challenged by a
low backpressure, while the containment isolation is challenged by a high backpressure.
4
3.5
Pressure (bar)
3
LOCA analysis
Containment analysis
2.5
2
1.5
1
0.5
0
0
100
200
300
Time (s)
400
500
600
Figure 3.11 – Containment pressure evolution used for LOCA analysis compared to that
used for containment design purposes
Technical specifications regarding the LBLOCA mitigation capability are shown in Table 3.8
and derive from [1].
8
Since the containment atmosphere is not modeled explicitly but simply plays the role of a fixed boundary condition for the
primary circuit after the break, the evolution of the containment backpressure is entered as input data.
94
Table 3.8 – Nominal and simulated ECCS capability to mitigate LOCA event ([1])
Units
Nominal
Simulated
Accumulators
Number of units
Water volume in each unit
Nitrogen volume in each unit
Accumulator water temperature
Boron concentration
Injection pressure setpoint
m3
m3
ºC
ppm
MPa
4
24.07
14.16
38-65
2600-2900
4.83
3 (one is not credited)
24.07
14.16
52
0 (boron not credited)
4.14
Centrifugal Charging Pumps (CCPs)
Number of units
Discharge head at shutoff
Discharge head at max flow rate
Max flow rate
MPa
MPa
m3/s
2
18.54
4.18
0.03470
1 (one is not credited)
18.54
4.18
0.0312 (10% degraded)
High pressure Safety Injection Pumps (SIPs)
Number of units
Discharge head at shutoff
MPa
Discharge head at max flow rate
MPa
Max flow rate
m3/s
2
10.60
5.08
0.04164
1 (one is not credited)
10.60
5.08
0.03748 (10% degraded)
Residual Heat Removal Pumps (RHRPs)
Number of units
Discharge head at shutoff
Discharge head at max flow rate
Max flow rate
2
1.37
0.822
0.2965
1 (one is not credited)
1.37
0.822
0.2668 (10% degraded)
MPa
MPa
m3/s
3.5.6 Results
The output of the LOCA analysis consists of the time evolution of all the plant thermal hydraulic
variables during the transient. In this section only the key parameters are shown, starting with
“generic” plant variables like pressure, break flow, injected flow etc., and then focusing on the
limiting variable for LBLOCA transients, i.e. the Peak Cladding Temperature (PCT). While the
time evolution of the “generic” parameters is the same regardless of the type of fuel and of the
axial power profile, PCT evolution depends both on the fuel and on the axial power profile
assumed for the analysis.
In all the plots the break occurs at time t0= 5 seconds.
3.5.6.1 Time evolution of “generic” plant parameters
The following plots show the time variation of several thermal hydraulic plant variables, most of
which are referred to the primary system. Since they are very well known in the context of
LOCA analysis and do not contain any atypical feature, they are not discussed further.
95
Figure 3.12 – Evolution of some plant parameters during LBLOCA (same for all core
types)
96
3.5.6.2 PCT time evolution
The PCT has been found to depend on the assumed axial power profile (chopped cosine vs top
skewed) only in terms of the shape of the curve PCT-vs-time and in terms of the axial location at
which the maximum PCT is reached. The difference in numerical values between the axial
power shapes investigated is instead quite small. Likewise, the fuel composition similarities
between all-UO2-, CONFU- and CORAIL-assembly cause the corresponding PCT profiles to be
substantially the same, with only small differences of the order of 20ºC. For these reasons,
regarding these assemblies, only for all-UO2 and CONFU the PCT-vs-time plots are shown
below (Figures 3.13 and 3.14). Figure 3.15 presents PUZH results.
Figure 3.13 – Peak cladding temperature behavior for all-UO2-core, for alternate axial
power shapes. Steady-state core power: 3479 MWt
97
Figure 3.14 – Peak cladding temperature behavior for CONFU-core, for alternate axial
power shapes. Steady-state core power: 3479 MWt
98
Figure 3.15 – Peak cladding temperature behavior for PUZH-core, for alternate axial
power shapes. Steady-state core power: 3479 MWt
Table 3.9 summarizes the maximum PCTs reached during blowdown and reflood phases by the
assemblies investigated.
99
Table 3.9 – Summary of the maximum PCTs reached during LBLOCA (K)
Phase
Blowdown
Refill-reflood
All-UO2-core
TopCosine
skewed
1067
1068
1026
1066
CONFU-core
TopCosine
skewed
1084
1081
1029
1104
CORAIL-core
TopCosine
skewed
1096
1135
1052
1117
PUZH-core
TopCosine
skewed
906
759
854
872
3.5.7 Conclusions
The most important conclusions arising from the LBLOCA analysis are:
a) the 1478 K cladding temperature limit established by 10CFR50.46 is never reached by
any of the assemblies investigated;
b) the maximum PCT for PUZH-core is much lower than those of the reference fuels. The
reference fuels yield maximum PCTs between 1068 and 1135 K for both the axial power
profile assumed for the core; after blowdown, the maximum PCT for PUZH-core is 759
K and 872 K for chopped cosine and top-skewed power profile respectively. The lower
temperatures for PUZH-core are due to its higher thermal conductivity, which causes the
maximum steady-state fuel centerline temperature to be about 1000 K lower than that of
the other core types.
3.6 Main Steam Line Break analysis
3.6.1 General event description
A major Main Steam Line Break (MSLB) is defined as a condition IV event, i.e. an event whose
occurrence is not expected during the life of a plant, but that is however postulated since it may
yield the release of significant amount of radioactive material. In fact, the break causes a rapid
depressurization of the secondary side and an increase in steam flow rate through the Steam
Generator (SG) nozzles with a consequent overcooling of the RCS. Because of the negative
moderator temperature reactivity coefficient, the reduction in primary coolant temperature results
in reactivity insertion and, depending on the initial conditions, an increase in core power or, if
the reactor was in shutdown at the time of break occurrence, in a possible return to criticality. In
both cases Departure from Nucleate Boiling (DNB) may occur locally, with consequent fuel pin
failure. The overcooling caused by the break is not radially uniform in the core, but is more
significant in the sector which receives water mostly from the loop affected by the break. Control
rod insertion and borated water injection by the Emergency Core Cooling System (ECCS) are
aimed at preventing/limiting the power excursion.
While that discussed above is the description of a general MSLB event, the description of the
MSLB event analyzed in this project requires specifying several assumptions made, which are
both boundary conditions (mainly from the specifications dictated by Chapter 15 of any PWR
Safety Analysis Report) and simplifying assumptions made to reasonably model the event
accounting for the available computational tools. These assumptions are presented in Section
3.6.4.
3.6.2 Objectives of the analysis
100
The MSLB analysis was performed for the Seabrook plant ([1]) in which, alternatively, the core
was assumed to be loaded with all-UO2-, CONFU-, CORAIL- and PUZH-assemblies. The case
of the all-UO2-core was mainly used to validate the plant modeling technique, by comparing the
results obtained with those given in [1]. The analysis of the other three core types was aimed at
comparing their thermal hydraulic behavior during a MSLB, particularly the Minimum Critical
Heat Flux Ratio (MCHFR) reached during the transient.
3.6.3 Code used and modeling approach
The analysis was performed using RELAP-3D ([15]) and VIPRE ([8]). RELAP was used to
model the plant (primary and secondary circuits) response upon MSLB. Output data from
RELAP were then used as input in VIPRE for a more detailed analysis of the core. This was
done to better capture the core thermal hydraulics since the core model in the VIPRE input file
was much more detailed than that in the RELAP input file.
The plant nodalization contained in the RELAP input file is shown in Figure 3.16. Important
observations about such nodalization are as follows:
-
the three intact loops are lumped together while the faulted loop is modeled individually.
-
The secondary side is modeled up to the Main Steam Line Isolation Valves (MSLIVs,
components 186 and 286 in Figure 3.16), i.e. all the components downstream the
MSLIVs (common steam header, turbine etc.) are not modeled.
-
The active core (in yellow in Figure 3.16) is modeled as composed of two channels and
three Heat Structures (HS, not shown in Figure 3.16). Channel 333 lumps the
subchannels contained in the 3/4th core fraction fed mainly by the three intact SGs, while
channel 335 lumps the subchannels contained in the 1/4th core fraction mainly fed by the
faulted SG. The three HSs are: HS1 represents the hot assembly (assumed to face channel
335), which is modeled by lumping all its rods; HS2 represents 47 assemblies lumped
together, facing channel 335; HS3 represents 145 assemblies lumped together and facing
channel 333.
-
The valves marked in black (906 and 908) are used to model the break occurrence.
During Hot Zero Power (HZP)-steady-state9 they are fully closed and the path that would
be followed by steam, in case it was produced in the SGs, is that through the MSLIVs
186 and 286. At time t = 5 s the break occurs and it is modeled by instantly opening
valves 905 and 908. Starting from this time, the faulted SG blows down completely while
the intact SGs depressurize only slightly since valve 906 closes upon MSL low-low
pressure signal detection10.
9
The MSLB is assumed to occur when the plant is in HZP conditions: see Section 3.6.4 for details.
For ease of programming, the modeling of the partial depressurization of the intact SGs upon MSLB is performed by using
valve 906, which replaces the function of MSLIV 186 after break occurrence, i.e. at t≥5s. In fact, in spite of being open, during
HZP-steady-state valve 906 does not affect the pre-accident scenario since valve 908 is closed and volume 907 is very small.
Thus, the steam free path in the lumped loops is through MSL 185 and MSLIV 186. However, starting from t=5s:
valve 905 and 908 open instantly (break occurs);
valve 186 and 286 close instantly;
2 seconds after the low-low pressure signal in MSL 285 is generated, valve 906 starts to close, and take 6 seconds to
complete closure. The closure of valve 906 stops the depressurization of the intact loops.
10
101
-
Complete coolant mixing is assumed to occur both in the vessel lower plenum and in the
vessel upper plenum11.
-
For ease of visualization, the nodalization of the SG boiling regions (components 170 and
270) and of the SG U-tubes (components 108 and 204) are shown with fewer subvolumes
than those actually used in the RELAP plant model. Volumes 170 and 270 are divided in
13 axial subvolumes (instead of the six shown), while volumes 108 and 240 are divided
in 22 subvolumes (from U-tube inlet to U-tube outlet).
After running RELAP, the time evolution of:
-
total core power;
-
coolant temperature and half flow rate at the inlet of channel 335;
-
pressure at the inlet of channel 335;
are used as input for a detailed modeling, performed with the VIPRE code, of 1/8th of the core.
This core fraction was modeled in the same way as in the steady-state analysis discussed in
Section 3.4. In particular, the core modeling (except for the peaking factors) was the same as that
shown in Figure 3.4, which therefore reproduces half of channel 335 of the RELAP model,
including half of HS2 and 1/8th of HS1. As shown in Figure 3.4, the red region, which represents
1/8th of HS1 plus the corresponding subchannels, was analyzed via subchannel mode, i.e. single
rods and subchannels are modeled explicitly. In this way it was possible to accurately monitor
the thermal-hydraulics of the hot assembly and particularly to predict the Minimum Critical Heat
Flux Ratio (MCHFR).
11
The importance of this assumption for the present analysis is not significant since coupling between neutronics and thermal
hydraulic is not performed (see Section 3.6.4.5). It is instead a key assumption in any MSLB analysis modeling spatial
coupling since the coolant mixing in the vessel lower plenum significantly influences the power distribution among the
different sectors of the core. If no mixing is assumed to occur, the temperature at the inlet of the fourth of the core fed mostly
by the faulted loop will be the same as that of the coolant entering the vessel through the “faulted” cold leg, which is the lowest
temperature in the RCS during a MSLB. As a consequence, the power peaking corresponding to that fraction of the core will
be very high. The prediction of whether this is the most conservative scenario is however not easy. In fact, while on one hand
the power peaking corresponding to that sector of the core is overestimated, on the other the coolant temperature at the inlet of
that sector is underestimated. In terms of MCHFR these two factors act in opposite directions since the high power has a
detrimental effect while the low coolant temperature is beneficial. For the present analysis, since the power spatial distribution
in the core was simply assumed (see Section 3.6.3.5), the choice of a complete mixing in the lower plenum can be considered
conservative: in fact, the coolant at the inlet of the sector of the core generating more power is relatively hotter than that
obtainable by assuming an incomplete coolant mixing. It is worth mentioning that none of the Seabrook reference documents
consulted describes the assumptions made for the coolant mixing in the vessel lower and upper plenum.
102
Figure 3.16 – RELAP-3D plant nodalization used for MSLB analysis
103
3.6.4 Detailed MSLB scenario description
The MSLB modeled in this study consists of a double-ended guillotine break of the Main Steam
Line (MSL) that connects one of the four steam generators to the common steam header. The
modeling of the whole scenario required several assumptions to be made, regarding both the
status of the plant just before the accident occurrence (pre-accident assumptions) and the
performance and timing of the various plant components that change their operational status
upon MSLB (post-accident assumptions). Some assumptions are common to both the preaccident and the post-accident condition (whole-scenario assumptions). Consistent with the
common practice in safety analyses, conservative assumptions are made, i.e. they tend to
overestimate the reactivity insertion and to underestimate the performance of the control and
shutdown systems. Pre-accident, whole-scenario and post-accident assumptions are qualitatively
described below. Assumptions on the reactivity coefficients and on the power distribution in the
core are exceptions to this grouping: in spite of being post-scenario assumptions they are
discussed in separate sections for clarity.
Table 3.11 summarizes the quantitative aspects of the assumptions made. Unless otherwise
specified, the assumptions are from Section 15.1.5 of [1].
3.6.4.1 Pre-accident assumptions
1) The core pre-accident condition is Hot Zero Power (HZP) at End Of Cycle (EOC). All the
control rods are fully inserted, except for the most reactive bank which is conservatively
assumed to be stuck in its fully withdrawn position during the whole transient. The preaccident shutdown margin is -1.3 % Δk/k for all the cores analyzed ([19]). The combination
HZP+EOC+stuck control bank is the worst scenario for the MSLB accident since RCS
overcooling is maximized. In fact:
- at HZP the secondary coolant inventory in each SG is maximum (~55% larger than
that during Hot Full Power (HFP));
- at HZP the RCS and the fuel contain less stored energy than that characterizing the
system at reactor shutdown following operation at full power. If the pre-accident
condition was HFP, the reactor would be tripped by overpower protection system and
the additional stored energy characterizing this shutdown condition (with respect to
that, lower, at HZP) would be removed via the cooldown caused by the MSLB before
the no-load RCS temperature assumed in the present analysis is reached;
- at EOC the delayed neutron fraction is the smallest, i.e. 0.0044 vs 0.0075 ([19])
characteristic of Beginning of Cycle (BOC); this clearly yields maximum neutronic
feedback upon MSLB;
- at EOC no boron is contained in the RCS;
- because of the harder neutron spectrum characterizing the core at EOC, the injection
of borated water into the RCS is less effective than at BOC.
2) The whole RCS is at a uniform temperature of 291.7 ºC.
3) The percentage of RCS flow not going through the core is assumed to be the same as that at
HFP, i.e. ~5%. Reference [1], which refers this percentage to HFP, does not give the
correspondent value at HZP.
104
4) Main Feedwater (MFW) flow to the SGs is zero, and no steam flows from the SG outlet
nozzles12.
3.6.4.2 Whole-scenario assumptions
1) RCS cooldown is maximized by neglecting decay heat and assuming offsite electric power
available. Continued operation of the Reactor Coolant Pumps (RCPs) allows heat stored in
the primary coolant to be removed through the secondary side.
2) Heat generated by RCPs is neglected. This assumption, in spite of not being mentioned in
any of the literature sources consulted, was made for ease of plant modeling and to increase
the extent of RCS cooling.
3) Containment pressure is 0.1 MPa ([20]). This is a conservative assumption since the actual
containment pressure resulting from MSLB at HZP is much higher13: steam flow through the
break is therefore maximized.
4) No SG tube plugging is assumed to maximize SG heat removal capability.
3.6.4.3 Post-accident assumptions
1) The break location is assumed to be just upstream the Main Steam Line Isolation Valve
(MSLIV), so that MSLIV closure cannot prevent the faulted SG to blow down completely.
2) Spurious activation of the Auxiliary Feedwater (AFW) to the faulted SG is assumed to occur
coincident with the postulated break and to be terminated by the operator after 30 minutes
from the onset of the accident. AFW water is at a temperature of 10ºC and a flow rate of 145
kg/s.
3) Safety Injection Signal (SIS) is generated upon low-low pressure detection (3 MPa) in the
affected Main Steam Line (MSL) ([19]).
4) A 2-second delay is assumed between SIS generation and actual SIS receipt by the plant
control system. Upon SIS receipt:
- MSLIV in the broken MSL starts closing; it takes 6 sec. to complete closure;
- MSLIVs in the intact MSLs start closing and take 50 seconds to complete closure. In
spite of the fact that [1] seems to assume same closure time for all the MSLIVs (6 s),
the present analysis uses a longer time to artificially reproduce the partial blowdown of
the unaffected SGs. The depressurization of the unaffected SGs resulting from using a
closure time of 6 s was in fact found to be much less pronounced than that shown in
[1].
- Main Feedwater Isolation Valves (MFIVs) start closing and take 12 seconds to
complete closure. Because of the depressurization of the secondary system, during the
time interval between break occurrence and closure of the main feedwater lines MFW
flow rate to all the SGs instantly increases from zero to 108% of the nominal value.
12
In a real plant at HZP, MFW and steam flow rates are not zero. A small flow rate is in fact required in order to remove, from the
primary coolant, the heat produced by fission product decay and by Reactor Coolant Pump (RCP) operation. In this analysis,
however, these two heat sources are neglected and therefore pre-accident MFW and steam flow are both zero.
13
Safety analysis of the containment assumes unavailability of one containment spray train. Under this assumption, a MSLB at
HZP yields a containment peak pressure of about 0.35 MPa (chapter 6 of [1]).
105
- ECCS starts pumping borated water from the Refueling Water Storage Tank (RWST)
into the RCS. Due to equipment delay and travel time through ECCS lines, 25 seconds
are required for the borated water to actually reach the RCS.
5) ECCS performance is conservatively reduced by assuming the most restrictive single active
failure, i.e. the unavailability of one of the two ECCS trains (one charging pump, one safety
injection pump and one residual heat removal pump are assumed not working). The
pumped14 flow rate, as a function of the RCS pressure, is shown in Figure 3.17.
30
Pumped flow rate (kg/s)
25
20
15
10
5
0
0
3
6
9
12
15
18
RCS pressure (MPa)
Figure 3.17 – ECCS flow performance assumed during MSLB ([21])
6) RWST water is assumed to be at 10ºC and to contain 2700 ppm of boron.
7) Accumulators are set to passively start injecting 2600 ppm borated water into the RCS when
its pressure drops below 4.14 MPa ([1]). Water is injected at 0ºC ([19]).
3.6.3.4 Post-accident assumptions: reactivity coefficients
Common practice of safety analyses is to use conservative values of thermal hydraulic,
neutronics and general plant parameters. As an example concerning reactivity coefficients, Table
4.3.2 of [1] provides two upper bounds for the rodded Moderator Density Coefficient (MDC)
during the core life:
MDC≤ 28 pcm/(kg/m3) (best estimate)
MDC≤ 50 pcm/(kg/m3) (design limit)
For transients like the MSLB which requires, for conservatism, the use of the most positive
MDC, reference [19] suggests using 54 pcm/(kg/m3): a value much higher than the best estimate
upper bound and even slightly higher than the design limit. Likewise, the delayed neutron
fraction used for MSLB analysis of a typical UO2-fueled PWR is 0.0044 ([1], [24]), which is
more typical of discharged fuel than of core average EOC fuel (~0.0052, [25]). The present
14
The term “pumped” is intentionally used to exclude the flow injected by accumulators.
106
analysis uses this conservative approach for all the input data not specifically associated with the
type of fuel: valve closure times, safety injection flow rate, set-points for safety system actuation
are examples of these parameters. Instead, the values chosen for reactivity coefficients and
delayed neutron fractions are the best estimates calculated as part of this project or found in the
open literature. This is because of two reasons:
-
in spite of the well known temperature dependence of the reactivity coefficients, the
reference documents (e.g. [1]) do not specify the dependence actually used in MSLB
analysis. For example, reference [19] suggests using a MDC of 54 pcm/(kg/m3) without
however saying whether this coefficient is kept constant regardless of the coolant
temperature or if a temperature dependence is instead implemented;
-
a complete list of conservative estimates of plant parameters is available only for all-UO2
cores; conversely, only best estimates are available for CONFU, CORAIL and PUZH
assemblies.
Table 3.10 summarizes the reactivity coefficients, delayed neutron fraction (β) and boron worth
(BW) used for the assembly types under consideration. All these values are referred to EOC
conditions which correspond, in terms of core average burnup, to the value shown in the first to
last row. Numerical values for which reference is not shown have been calculated in this project.
The table is then followed by important considerations regarding the methodology used to
determine the reactivity coefficients.
Table 3.10 – Neutronic parameters used in MSLB analysis
FTC
(pcm/ºC)
Rodded MTC
(pcm/ºC)
BW
(pcm/ppm)
β
Rodded MDC
(pcm/(kg/m3))
All-UO2
-3.08
(Fig. 4.3-27 of [1])
-36.2
(Fig. 5-1 and 5-12
of [26])
-9.2
(Fig. 5-20 of [26],
consistent with Fig.
6.4.6 of [25])
0.0052
(Fig. 5.4.1 of [25])
24.2
(from MTC)
CONFU
CORAIL
PUZH
-4.21
-5.17
-2.80
-26.7
-31.0
-13.9
-6.4
(Fig. 6.4.6 of [25])
-4.5
(Table VIII of [27]
-3.6
0.0048
(Fig. 5.4.1 of [25])
17.9
(from MTC)
0.0041
(Table 4.3.I of [25])
20.8
(from MTC)
0.0036
9.3
(from MTC)
Fuel Temperature Coefficient (FTC) and Moderator Temperature Coefficient (MTC): although
the FTC and MTC vary with temperature, a single temperature-independent value was used for
each of these coefficients and for each core type. The selection of these values was based on a
common principle, regardless of the core type: the value selected is the one that, when assumed
over the temperature ranges:
-
292-392ºC for the core average fuel temperature, for FTC;
-
292-230ºC for the coolant, for MTC;
gives approximately the same reactivity insertion as that actually due to temperature-dependent
reactivity coefficients when coolant and/or fuel average temperature vary over the same
temperature intervals15. The “sources” of data used to calculate what numerical value causes this
15
The coolant temperature range used for MTC calculation, i.e. 292-230ºC, is a reasonable approximation of the RCS
107
condition to be met depends on whether the core is an all-UO2-core or one of the remaining
three. In fact, for the all-UO2-core no neutronic analysis were performed, and the references
shown in parentheses in Table 3.10 were used to calculate FTC and MTC. These references are
in fact plots showing the reactivity coefficient variation with temperature, an example of which
is shown in Figure 3.18. These plots were used to first calculate the reactivity insertion due to the
mentioned temperature perturbations (from the HZP value of 292ºC) using the reactivity
coefficient temperature dependence shown by the plot itself, and then the average FTC and MTC
by dividing such reactivity insertions by the amplitude of the temperature perturbations. These
average FTC and MTC are those shown in Table 3.10.
Figure 3.18 – Typical low leakage core design FTC vs fuel temperature ([1])
For the other core types, i.e. CONFU, CORAIL and PUZH, plots analogous to that shown in
Figure 3.18 are not available. Therefore, the numerical values shown in Table 3.10 were obtained
by running, for each assembly type a single assembly depletion analysis in which:
1) fuel and coolant temperature are separately perturbed by the amount previously
mentioned (from 292 to 392ºC for the fuel, from 292 to 232ºC for the coolant) at three
burnup values, corresponding to once burned, twice burned and discharged fuel;
2) the reactivity variations caused by the fuel temperature perturbation at the three burnup
levels are calculated and averaged, thus obtaining a single reactivity variation ΔρF; the
overcooling occurring during MSLB, as shown in [1]. The choice of the fuel temperature perturbation, instead, was not based
on data contained in the reference documents since they do not describe the core averaged fuel temperature variation occurring
during MSLB. Therefore, since:
FTC becomes less and less negative as the fuel temperature increases;
MSLB safety analysis practice recommends using the most negative FTC and MTC ([19], [1]);
the temperature interval chosen is only 100ºC for conservativism. In this way, other than starting at a relatively low
temperature (292ºC) the perturbed fuel temperature is itself quite low, guaranteeing a more negative FTC.
108
same is done for the reactivity variations due to coolant temperature perturbation, thus
obtaining ΔρC;
3) the EOC equilibrium core FTC is calculated as ΔρF/100, while the EOC equilibrium core
MTC is calculated as ΔρC/60; these are the values shown in Table 3.10.
The methodology summarized by means of points 1) through 3) was actually performed twice:
one time for an assembly not having control rods inserted and a second time for an assembly in
which control rods are inserted. In fact, an important consideration concerns the meaning of the
word “Rodded”, which is used in Table 3.10 both for MTC and for MDC. This term is important
since the pre-accident steady state condition assumed for the MSLB analysis is HZP. For the
present analysis the term “Rodded” is intended to refer to a situation in which Control Rod
Banks C and D are fully inserted, while both Control Rod Banks A and B, as well as the
Shutdown Banks, are withdrawn. This consideration is important since MTC becomes more and
more negative as the number of control rods inserted increases (and consequently MDC becomes
more and more positive). In fact, the insertion of control rods causes H/HM to decrease since
they displace coolant. As a consequence, the operating point on the keff vs H/HM curve shifts to
smaller H/HM, which is where the curve has a larger slope (negative). A larger (negative) slope
means a more negative MTC. Unfortunately, reference documents ([19], [1]) do not specify how
the EOC-HZP condition is achieved, i.e. how many control rods are actually inserted. Therefore,
since graphs of Rodded MTC for the reference all-UO2 core are available only for the cases:
-
Control Rod Bank D inserted;
-
Control Rod Banks C and D inserted;
it was decided to associate the Rodded MTC (and MDC) used to a situation in which Control
Rod Banks C and D are inserted, while all the other banks are withdrawn. This assumption was
extended to the other types of core, i.e. CONFU-, CORAIL- and PUZH-core, for which however
average core Rodded MTC values can not be found in the public literature. Therefore, to account
for control rod insertion, the depletion analyses mentioned above were performed not only for an
assembly in which control rods are not inserted (leading to MTCout) but also for an assembly in
which control rods are inserted (leading to MTCin). The EOC-HZP average core Rodded MTC
was then determined by weighing MTCin with the number of assemblies that are assumed to
actually have control rods inserted (Nin), and MTCout with the number of assemblies that do not
(Nout). Since Control Rod Banks C and D have 8 and 5 control rods respectively ([1]), the EOCHZP average core MTC shown in Table 3.10 was calculated as:
Rodded MTC =
N in × MTC in + N out × MTC out 13 × MTC in + (193 − 13) × MTC out
=
193
193
At equilibrium EOC, MTCin was found to be about 1.4 times MTCout, while FTCin was found to
be about 0.7 times FTCout.
Moderator Density Coefficient (MDC): the MDC shown in Table 3.10 is calculated by dividing
the reactivity insertion due to the coolant temperature perturbation (obtained through the MTC)
by the coolant density variation caused by the perturbation itself, calculated at a constant
pressure of 15.513 MPa.
109
Boron Worth (BW) and delayed neutron fraction (β): BW and β are simply extracted from the
references indicated in parentheses in Table 3.10.
3.6.4.5 Post-accident assumptions: power distribution
Although the total core power excursion upon MSLB is calculated by RELAP as a function of
the RCS overcooling caused by the break, the power distribution among the four core sectors
(corresponding to the four loops) is:
-
uniform in the RELAP analysis, in order to be consistent with the 100% coolant mixing
assumed in the vessel lower plenum;
-
non-uniform in the VIPRE analysis, in order to account for the different degrees of
overcooling affecting the four RCS loops. From the quantitative viewpoint, the radial
power distribution used in the VIPRE analysis was assumed based on data found in the
literature ([18]). In particular, the fourth of the core fed mostly by the faulted loop is
assumed to generate half of the total core power, at any time during the transient. The hot
assembly, which is assumed to be located in this sector of the core, is assumed to have a
radial peaking factor of 4.25 (with respect to the core average assembly). For the VIPRE
analysis, the radial power distribution in the core can therefore be expressed by means of
the following assembly radial peaking factors:
¾
hot assembly: 4.25;
¾
8 assemblies surrounding hot assembly: 3.8;
¾
each of the remaining 47 assemblies located in the “affected” fourth of the
core: 1.9095;
¾
each of the 145 assemblies located in the “unaffected” sector of the core:
0.4731.
Both in the RELAP and in the VIPRE analysis:
16
-
the pin-by-pin power distribution is uniform in all the assemblies16. This is consistent
with a typical EOC power distribution;
-
the axial power distribution, shown in Figure 3.19, is assumed to be top-peaked with a
maximum peaking factor of 1.85. It has a peak of 1.85 and coincides with the mean of
several core-averaged axial profiles obtained in the extensive benchmark analysis
described in [18]. Consequence of this assumption is that the hot spot modeled in the
final VIPRE analysis generates a linear power 4.25×1.85×1.0 = 7.86 times higher than
the core average linear power.
Because of the lumping approach used in the RELAP model, i.e. single rods are lumped together, the uniform pin-by-pin power
distribution was an input of the VIPRE model only.
110
2
1.8
Axial peaking factor
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
0.5
1
1.5
2
2.5
3
3.5
4
Axial location (m)
Figure 3.19 – Axial power profile assumed during the MSLB transient ([18])
Quantitative assumptions used for MSLB analysis are summarized in Table 3.11.
Table 3.11 – Quantitative assumptions made for MSLB scenario modeling
Parameter
Value17
Reference
Core and RCS
Pressure in the vessel (MPa)
Primary coolant temperature (ºC)
15.513
291.7
17999
(17946)
Total coolant flow rate through RCS (kg/s)
Active coolant flow rate through the core as % of RCS
flow rate, at HFP (guide thimble flow not included)
Coolant flow rate through the core (kg/s)
Delayed neutron fraction
Shutdown margin
Reactivity coefficients
Pin-by-pin power distribution
1/4th core sector power multiplier (ratio between power
produced by the “affected” fourth of the core and the
power that it would produce if power distribution was
uniform through the core)
Hot assembly radial peaking factor
Axial peaking factor
17
95
[1]
17087
See Table 3.10
-1.3 % Δk/k
See Table 3.10
[1]
111
[1]
uniform
Assumed in this
analysis
1 (RELAP)
2 (VIPRE)
Assumed in this
analysis
1.0 (RELAP)
4.25 (VIPRE)
Assumed in this
analysis
Assumed in this
analysis
1.85
At EOC-HZP, unless otherwise specified.
[1]
[1]
Using volumetric
flow from [19]
and [28]
Coolant mixing in vessel lower and upper plenum
100%
Secondary side
Steam pressure in the SG dome (at HFP) (MPa)
6.895
Steam pressure in the SG dome (at HZP) (MPa)
7.543
Secondary coolant inventory per SG (kg)
SG tube plugging
AFW flow to faulted SG (kg/s)
76194 (76205)
0%
144.8
At break
occurrence
Time of AFW actuation
ECCS
Steam line low-low pressure setpoint used for Safety
Injection Signal (SIS) (MPa)
Delay between SIS and SIS reception (s)
Actions at SIS reception
MSLIV closure time (s)
Main feedwater valve closure time (s)
Delay between SIS reception and ECCS actuation (s)
RWST boron concentration (ppm)
RWST water temperature (ºC)
Accumulator boron concentration
Accumulator setpoint pressure (MPa)
Accumulator water temperature (ºC)
ECCS injection flow rate
Miscellaneous
Decay power (MWt)
[1]
Calculated to
satisfy RCS
temperature of
292ºC
[1], [21]
[19]
[19]
[19]
3
[19]
2
MSLIVs and
MFIVs start
closing
6
12
25
2700
10
2600
4.14
0
Minimum flow
(see Figure 3.17)
[19]
0
0.1 for the whole
transient
Containment pressure (MPa)
Assumed in this
analysis
[19]
[19]
[19]
[19]
[1]
[19]
[1]
[1]
[19]
[21]
[1]
[20]
3.6.5 Validation of the plant modeling technique
This section compares the results obtained for the reference all-UO2-core with those presented,
for the same core, in the reference documents ([1] and [19]). Even though the reactivity
coefficients used are probably not the same as those used in the reference documents, the
comparison is useful to verify the accuracy of the analysis and the correctness of the RELAP
plant model. This comparison is made by means of plots showing the time variation of key plant
parameters during the transient. In each figure, the plot on the left is that obtained here while that
on the right derives from the reference documents (mainly [1] and [19]). It needs to be stated that
while the present analysis assumes the MSLB to occur instantaneously at t = 5 s, the reference
documents model the break as an instantaneous event occurring at t = 0 s. This does not affect
the results, but only the way the two time scales need to be compared: a generic time instant t’ on
112
the present analysis time-axis corresponds to the time instant t’+5 s on the reference document
time-axis.
The first two sets of plots, presented in Figure 3.20, show the reactivity and power excursions
resulting from the RCS overcooling occurring after MSLB. Even though the general trend is the
same, some differences can be noted:
1) In spite of starting with approximately the same shutdown margin, i.e. -1.3% Δk/k
equivalent to -2.5 $ in this analysis and -2.95 $ in the reference documents18, the
reactivity insertion calculated here is slower, with a consequent delay in return to
criticality (after about 90 s here, after 20 s in the reference documents). This is probably
due to two reasons:
-
the smaller MDC used: by assuming that the reactivity coefficients mentioned in
the reference documents have been used as temperature independent parameters,
the comparison of the MDCs would be: 24.2 pcm/(kg/m3) in this analysis versus
54 pcm/(kg/m3) in reference document [19]. The lower MDC assumed here
resulted in a slower return to criticality.
-
The significant liquid carryover through the break, which is predicted here but not
in the reference documents19. Such carryover causes the faulted SG to
depressurize more slowly, resulting in a milder RCS overcooling.
2) The peak power predicted in this analysis is about 858 MWt, with a plateau at about 700
MWt. The reference documents instead show a peak power of about 520 MWt. This is
due, among others minor reasons, to the different FTC used. Assuming again that the
reactivity coefficients mentioned in the reference documents have been used as
temperature-independent parameters, the comparison would be: -3.08 pcm/K in this
analysis versus -5.76 pcm/K used in reference document [19].
18
19
The difference in dollars is due to the delayed neutron fraction assumed in the two analyses: 0.0044 in the reference
documents, 0.0052 here.
The tendency of RELAP to predict an excessive liquid carryover through the faulted steam line during SG blowdown is a
problem frequently encountered by RELAP users, and detailed investigations have been performed to understand the reasons
([29]). Reference [29] states: “In the past, a tendency to over-predict liquid entrainment to the break in steam line break
transients have been attributed to shortcoming in interphase drag modeling. Recent studies however, have indicated that this is
not the case, and the most likely explanation is the failure to model the accumulation of liquid on structures in the upper SG”.
In the present RELAP model, in fact, the liquid-steam separation is performed by a single component located above the riser of
the U-tube boiling region, which reproduces the effect of steam separators and steam dryers combined. The liquid-steam
separation performed by this component is not modeled mechanicistically, i.e. by means of hydraulic laws governing the
separation process actually occurring in the swirl vane zone of the separators and in the corrugated plates of the dryers, but
simply by entering, as input, the component inlet flow steam quality above which the outlet flow must have a certain steam
quality, the latter to be specified as well. MSLB tests performed on a 1/125 scale model reproducing a SG of the Seabrook type
showed little liquid carryover through the faulted steam line. In this regard, Reference [29] authors state: “Although the present
authors and their colleagues do not believe that the dryers themselves could have such a significant effect, it is suggested that
liquid carryover to the break in the experiment may have been reduced by the accumulation of liquid on other structures in the
upper part of the SG, as a result of eddies in the local vapor flow”. It is likely that the break flow rate plots shown in the
reference documents have been obtained by forcing the code to use a break flow rate table, rather than to let it calculate the
break flow as a function of the upstream pressure. Alternatively, an artificial distortion of the SG dome geometry, coupled with
the addition of components/flow paths not existing in the actual SG, might have been used to prevent liquid carryover through
the faulted steam line. These tricks have been tried, however without success. The liquid carryover was therefore maintained as
part of the MSLB transient.
113
6.9e8
Figure 3.20 – Reactivity and core power during MSLB (left: this analysis; right: [1] and
[19])
The role played by the MDC in determining the time at which criticality is achieved was also
verified by running a MSLB analysis with the same MDC, FTC and β presumably used in the
reference documents. As it can be seen from Figure B.6, the time of return to criticality coincides
with that shown on the top right plot of Figure 3.21, i.e. about 20 s. However, the power peak is
still overestimated, i.e. 850 MWt vs 520 MWt, which means that factors other than reactivity
coefficients differ in the two analyses.
114
Figure 3.21 – Reactivity and core power during MSLB (obtained by using conservative
reactivity coefficients probably used in the reference documents)
Figure 3.22 compares the SG dome pressure evolution predicted in this analysis to that shown in
[1]. It can be noticed that the present analysis predicts a slightly slower SG depressurization
during the first seconds of the transient: about 35-40 s are needed for the faulted SG to
depressurize to 400 psia, while about 20 s are needed according to the reference documents. This
phenomenon, together with the higher pressure at which the depressurization curve tends to
change slope, are due to the liquid carryover previously discussed. Since liquid is lost through
the break instead of steam, the rate of depressurization is lower. Another notable difference is the
faulted SG pressure evolution at t > 100 s. While the plot on the right shows a very regular
reduction in pressure, this analysis delivered an irregular behavior characterized by a pressure
plateau in the time interval 100-180 s and a pressure constancy from 220 s to the end of the
transient. The first anomaly is probably a consequence of the overestimation of the core power,
which instead of causing the depressurization curve to simply bend at t~50 s (see right plot of
Figure 3.22), causes the SG pressure to even stall. The constancy of the faulted SG pressure is
instead due to an equilibrium between the AFW flow injected into the faulted SG and the break
flow.
Figure 3.22 – SG dome pressure during MSLB
(left: this analysis; right: from [19])
115
Figure 3.23 shows on the right the break flow rate evolution according to the reference
documents, throughout the whole transient duration, while on the left the flow rate evolution
predicted by the present analysis, but only up to 100 s20. It can be noticed that, while the
reference document shows a regular steam-only break flow rate, the present analysis predicts a
liquid carryover spike in the time interval, from the MSLB occurrence, 2-20 s. Besides such
liquid spike, however, the steam flow rate predicted by the present analysis (see first 2 postMSLB seconds as well as at t > 25 s) reproduces exactly that shown by the reference document.
Unfortunately, as discussed earlier, the liquid carryover could not be eliminated or reduced.
Figure 3.23 – Break flow rate evolution after MSLB (left: detail from this analysis; right:
from [1])
Figure 3.24 shows the time evolution of the core average coolant temperature, which regulates
the core power evolution by means of the MDC. The time profile in the first 50 s is similar in the
two analyses. In the time interval 50-90 s the present analysis predicts a more rapid RCS cooling
than that shown by the reference documents. This is because of the late return to criticality
predicted by the present analysis, which implies that the core power is zero up to about 90 s,
versus 25 s of the reference documents. During the interval 105-200 s the coolant temperature
evolution predicted by the present analysis shows a plateau, due to the overestimation of the peak
core power. This is a common feature with Figure 3.222, where also the SG pressure remains
constant. The overestimation of the coolant temperature during the rest of the transient is both
due to the difficulty to accurately model the heat transfer coefficient in the U-tube region21, and
20
The interruption at 100 s was only made to more clearly show the liquid carryover phenomenon.
21
Reference [30] states: “It often is difficult to obtain a satisfactory agreement with steam generator full-power
conditions. The difficulty arises because the heat transfer coefficient calculated on the outside surface of the
steam generator tubes is based on general vertical-pipe correlations rather than correlations that account for the
swirling flows present within the tube bundle region. (…) resulting in excessively high calculated primary coolant
temperatures”. It can be inferred that such difficulty characterizes even more the operation during a transient like
a MSLB. Even though the suggestion given in the RELAP manual to solve this problem, i.e. instead of using the
U-tube region hydraulic diameter as the heated diameter that the minimum tube-to-tube spacing be used, a
satisfactory reproduction of the temperature evolution predicted by the reference documents was not achieved.
116
C o o la n t a v e ra g e te m p e ra tu re in th e c o re (K )
to the higher RCS pressure predicted by the present analysis, as shown in Figure 3.25. In fact, the
lower RCS pressure estimated in the reference documents allows the accumulators to inject cold
water in the primary system. The accumulator pressure injection setpoint is 600 psia, which is
never reached in the present analysis, whereas it is reached at about 140 s in the reference
documents.
590
570
550
530
510
490
470
450
0
100
200
300
400
500
600
Time (s)
Figure 3.24 – Average coolant temperature in the core after MSLB (left: this analysis;
right: from [1])
Figure 3.25 – RCS pressure evolution during MSLB (left: this analysis; right: from [1])
The limiting parameter typically calculated in MSLB analyses is, as mentioned in Section 3.6.2,
the MCHFR. Figure 3.26 shows the time evolution of this parameter, up to t = 400 s, predicted
by the present analysis using the Westinghouse W-3L correlation implemented in the VIPRE
code ([8]). The minimum value reached, i.e. 2.3, should be compared to that mentioned in
reference document [19], i.e. 1.79. However, this comparison is not particularly useful since the
MCHFR is very sensitive to power level, core pressure, coolant flow rate and temperature, i.e.
parameters whose time evolution was not found to be always in agreement with that shown by
the reference documents [1] and [19]. This is not only because of a non optimal plant modeling,
117
but also because of different assumptions, driven both by lack of data and by judgment.
Although MCHFR is the “final” output parameter upon which designers base their judgment of
the plant capability to safely respond to a MSLB, its comparison with the value 1.79 can not be
used to establish the accuracy of the analysis presented here. In fact, if this was the case, the hot
assembly peaking factor assumed here, 4.25, could have been increased until the minimum
MCHFR matched 1.79. The accuracy of the analysis should instead be judged based on the plant
parameter comparison performed by means of Figure 3.20 through Figure 3.25. Conversely, the
minimum MCHFR must be used as comparative parameter of the different core types analyzed,
i.e. all-UO2-, CONFU-, CORAIL- and PUZH-core.
11
10
9
MCHFR
8
7
6
5
4
3
2
0
100
200
300
400
500
Time (s)
Figure 3.26 – MCHFR evolution for all-UO2 core during the first 400 seconds of MSLB
transient
3.6.6 Results
CONFU-, CORAIL- and PUZH- cores were analyzed in the same way as the all-UO2-core. The
only differences concern the fuel thermo-physical properties and the neutronic parameters listed
in Table 3.10. Figure 3.27 shows the power excursion of each core, whereas Table 3.12
compares the minimum MCHFRs obtained.
118
UO2
CONFU
CORAIL
PUZH
Figure 3.27: core power evolution during MSLB
Table 3.12 – Peak power and MCHFR during MSLB
Peak core power (MWt)
MCHFR
All-UO2
CONFU
CORAIL
PUZH
858
2.3
643
2.9
656
3.3
0
>10
3.6.7 Conclusions
A MSLB event occurring at HZP-EOC conditions was modeled. Four core types, loaded with
all-UO2-, CONFU-, CORAIL- and PUZH- assemblies respectively were analyzed. RELAP-3D
and VIPRE were used for this purpose. The analysis did not model a spatial coupling between
thermal hydraulics and neutronics, i.e. the total core power excursion is calculated by RELAP as
a function of the global RCS overcooling caused by the break, but the non-uniform power
distribution in the core was assumed based on data found in the literature. Such power
distribution was used as input for the thermal hydraulic analysis performed with the VIPRE
code. The quality of the RELAP plant model was assessed by comparing the time evolution of
RELAP output parameters referred to the all-UO2-core with those shown in the reference
119
documents analyzing MSLB ([1], [19]). Conclusions arising from the MSLB analysis are the
following:
1) the accuracy of the RELAP plant modeling was found to be satisfactory. This is true in
spite of some discrepancies between the time evolution of the plant parameters used to
assess the adequateness of the plant model and that shown in the reference documents.
These discrepancies are due to two reasons:
-
the use of different assumptions (due to lack of information or because of
particular needs characterizing the present analysis);
-
the overestimation of the break flow rate during the first 20 s after the event
initiation. This problem, related to the erroneous prediction of liquid carryover
through the faulted main steam line, is due to the present inability to model the
SG so that liquid from the inside the SG is prevented from flowing to the break.
2) PUZH-core was found to have better post-MSLB performance with respect to the other
core types analyzed since it does not reach criticality after MSLB. The other core types,
instead, do. This is because the reactivity excursion before criticality is more significant
for high values of the Moderator Density Coefficient (MDC) which was found to be, for
PUZH-assemblies in the HZP-EOC conditions, about half that of all-UO2-, CONFU- and
CORAIL- assemblies.
3) Like the other assembly types analyzed, PUZH-assemblies were found to have a negative
Fuel Temperature Coefficient (FTC). This is beneficial, in terms of safety, for any event
leading to the reaching of criticality and subsequent increase in power. However, in terms
of comparison between the various core types, PUZH-assemblies were found to have a
FTC less negative than the other assembly types, i.e. about 33 and 46% lower than that of
CONFU and CORAIL respectively, and about 9% lower than that of all-UO2 assemblies.
For the MSLB analysis performed here, however, such less negative FTC does not affect
the PUZH-core performance since criticality is not reached.
3.7 Complete Loss of Flow Accident analysis
3.7.1 General event description
CLOFA is defined as a Condition III incident ([1]) consisting of the complete loss of forced
reactor coolant flow, which may result from a simultaneous loss of electrical supplies to all
Reactor Coolant Pumps (RCPs). Following this loss, RCPs start coastdown causing the coolant
flow rate through the core to decrease, with consequent reduction of its own heat removal
capabilities. In case this event was not followed by immediate reactor scram, the increasing
incapability of the coolant to remove heat would yield fuel pin failure and thus core damage.
Protection against CLOFA is however provided by reactor scram, which initiates upon reception
of one of the following two signals:
-
RCP power supply undervoltage/underfrequency signal (not used in this analysis);
-
low reactor coolant loop flow signal.
As a consequence of reactor scram, core power rapidly decreases to decay power level, and this
terminates the accident scenario.
120
3.7.2 Objectives
The objective of the analysis was to compare the response, and in particular the Minimum
Critical Heat Flux Ratio (MCHFR), of a PUZH-core with that characterizing other core types
aimed at Pu/Minor Actinides incineration, i.e. CONFU- and CORAIL-core, during a CLOFA
scenario. In spite of not being aimed at Pu/Minor Actinides recycling, the all-UO2-core is
analyzed in order to validate the plant modeling technique.
3.7.3 Code used and modeling approach
The CLOFA analysis was performed using two codes: RELAP 3D© ([15]) and VIPRE ([8]).
RELAP was used to model the time evolution of the plant parameters during the accident (both
in the primary and secondary system), focusing in particular on core power, core pressure,
coolant flow rate through the core and coolant temperature at core inlet. These parameters were
then entered as input in the VIPRE code which, relative to RELAP, models the core more in
detail. The strategy of using two codes is motivated by the fact that the RELAP input file used in
this analysis does not model the core with a sufficiently high spatial resolution: the active22 core
is in fact modeled by means of only two channels, as done for the MSLB analysis (the plant
nodalization is in fact the same as that shown in Figure 3.16):
-
channel 333: a single channel formed by the subchannels of 145 assemblies lumped
together;
-
channel 335: a single channel formed by the subchannels of 48 assemblies lumped
together;
and three heat structures:
-
heat structure 1: a single rod formed by the fuel rods of 145 assemblies lumped together,
facing channel 333;
-
heat structure 2: a single rod formed by the fuel rods of 47 assemblies lumped together,
facing channel 335;
-
heat structure 3: a single rods formed by the fuel rods of the hot assembly lumped
together, facing channel 335.
The VIPRE input file used for the CLOFA analysis is again the same as that used for the steady
state analysis (see Section 3.4): it models 1/8th sector of the core, in which all the subchannels
contained in the hot assembly are modeled individually. This allows performing a more detailed
thermal hydraulic analysis than that obtainable using RELAP only.
3.7.4 Detailed event description and assumptions made
The assumptions made to model CLOFA are grouped in four categories:
22
-
pre-accident thermal hydraulic condition assumptions;
-
scenario evolution assumptions;
-
reactivity coefficient assumptions;
-
power distribution assumptions;
The term “active” is used to identify the thermal hydraulic structures actually involved in the heat generation and removal. A
core bypass channel, which is not “active”, is modeled separately.
121
and are described as follows.
3.7.4.1 Pre-accident thermal hydraulic condition assumptions
The main plant thermal hydraulic parameters characterizing the reactor before the accident
occurrence are summarized in Table 3.12. Since some parameters, e.g. primary coolant flow rate,
can not be entered into RELAP as input but are calculated by the code based on specified
boundary conditions, e.g. pump performance, the value actually used is shown together with the
target value (in parenthesis), i.e. with the value prescribed by the literature source used as
reference. In case no target value is shown, the two coincide.
Table 3.12 – Pre-accident thermal hydraulic operating conditions used for CLOFA
analysis (all from [1])
Parameter
Value
Notes
Core thermal power (MWt)
3479
102% of nominal reactor power
RCS pressure (MPa)
15.51
Nominal pressure
18336
RCS coolant flow rate (kg/s)
Nominal flow rate
(18358)
Core active coolant flow rate
17388
(kg/s)
(17476)
+3.2ºC with respect to nominal
Core inlet temperature (ºC)
296.3
value
3.7.4.2 Scenario evolution assumptions
In the present analysis electrical equipment is not modeled and thus the low flow signal is the
only signal used to initiate reactor scram. In particular, the reactor scram is assumed to start one
second after the coolant flow rate has dropped below 87% of the nominal value in any of the
primary circuit loops ([1]).
3.7.4.3 Reactivity coefficient assumptions
Two assumptions were made about reactivity coefficients: the pre-accident values, i.e. the
steady-state normal operation values, and their evolution with temperature during the transient.
They are discussed as follows.
Steady-state: Since, for a fixed coolant flow rate, the severity of core overheating due to RCP
coastdown increases with core power, CLOFA is assumed to occur when the reactor is at
Beginning Of Cycle (BOC) ([1]). This is because of the need of minimizing the moderator
negative feedback upon temperature increase. In fact, the Moderator Temperature Coefficient of
Reactivity (MTC) has its least negative value at BOC, when the concentration of soluble boron
in the primary circuit is maximum (~1400 ppm for a typical PWR [1]). Although the best
estimate of the core average MTC at Hot Full Power (HFP)-BOC is -19.6 pcm/K (Figure 4.3-33
of [1]), reference [1] analyzes CLOFA assuming conservatively a very large MTC, i.e. +9
pcm/K. This value is even larger than that corresponding to Hot Zero Power-BOC (~-1 pcm/K)
and may be close to that characterizing HFP operation at a boron concentration around 2700
ppm. In fact, reference [31] shows that at HFP-BOC the AP1000 design would reach a MTC of
about 5 pcm/K if the boron concentration was 2500 ppm.
Although the practice of using conservative estimates of reactivity coefficients is a feature
common to all the safety analyses, the present analysis uses best-estimate values for the
122
reactivity coefficients. This is because the achievement of the same level of conservativism, in
terms of reactivity coefficients, as that used in [1] for an all-UO2 core, is difficult to preserve
when analyzing reactors different than an all-UO2 type. In other words, the level of
conservativism resulting from increasing, for an all-UO2 core, the moderator temperature
coefficient from -19.6 pcm/K (best-estimate) to +9 pcm/K (conservative value) is difficult to
translate to another type of core, for which the increase of MTC by 28.6 units (9+19.6) from its
best-estimate HFP-BOC value may yield an overconservative/unreasonable value.
Consistent with the choice of the MTC, the values used for Fuel Temperature Coefficient (FTC),
Boron Worth (BW) and delayed neutron fraction (β) are also best-estimate values for each type
of core. They are summarized in Table 3.13. Numerical values for which reference is not shown
have been calculated in this project and do not derive from external sources.
Transient evolution: Among the parameters shown in Table 3.13, FTC, BW and β were assumed
to remain fixed during the transient and equal to their pre-accident values23. The MTC
dependence on coolant temperature is instead accounted for, and it is shown in Figure 3.28. The
polynomial function used to plot the curves allows reproducing, for the all-UO2 core, the MTC
variation with temperature shown in [1] whereas, for the other core types, it yields an MTC vs
temperature curve having the same shape as that for the all-UO2 core but translated to lower or
higher values of MTC to allow matching the pre-accident values shown in Table 3.13.
Table 3.13 – Reactivity coefficients and neutronic parameters used in pre-CLOFA
operation (core-average values referred to HZP-BOC conditions)
CORAIL
CONFU
PUZH
All-UO2
-2.5
FTC
-3.4
(Fig. 4.3-27 in
-2.5
-2.1
(pcm/ºC)
(Fig. A.9 of [32])
[1])
-19.6
-1324
MTC
(Fig. 4.3-33 in
-6.1
-8.4
(Fig. A.10 in
(pcm/ºC)
[1])
[32])
-6.3
BW
(Fig. 5-18 in
-4.9
-5.1
-2.8
(pcm/ppm)
[26])
0.0075
0.006
0.006
β
(Table 4.3-2 in
(Fig. 5.4.1 of
(Table 4.3.III of
0.00342
[1])
[33])
[13])
This assumption is reasonable since: β depends only on the fuel composition (which does not change appreciably during the
transient); FTC varies only slightly as the average fuel temperature decreases (e.g. from -2.5 pcm/K at 630ºC to -2.9 pcm/K at
292ºC for an all-all-UO2 core); BW is not supposed to play any role since the high pressure of the RCS during the transient
prevents injection of borated water.
24
The MTC value used for PUZH-core refers to a burnable poison-free design: from the MTC viewpoint this is a conservative
assumption since the presence of burnable poisons, needed to reduce the critical boron concentration, would make MTC more
negative thus yielding a milder core power reduction soon after CLOFA occurrence. The detrimental effect caused by burnable
poison addition on thermal hydraulics, i.e. the increase in pin-by-pin power distribution non-uniformity, was accounted for by
analyzing the power distribution shown in Figure 3.5 other than that shown in Figure 3.8.
23
123
20
10
MTC (pcm/C)
0
-10
-20
CORAIL
-30
CONFU
PUZH
-40
UO2
-50
260
270
280
290
300
310
320
330
Coolant temperature (C)
Figure 3.28 – MTC variation with coolant temperature assumed in this analysis
Power distribution assumptions: the axial power distribution in the core as well as the radial
power distribution among the assemblies are the same for all the core types. The former is a
chopped-cosine power profile having a maximum peaking factor of 1.515. The latter features a
hot assembly peaking factor25 of 1.515. These are conservative values typically used in the safety
analyses of all-UO2 PWRs ([1]).
The pin-by-pin power distribution is instead different depending on the assembly type under
consideration, as shown in Figures 3.5 through 3.8. It is important to note that, while for the allUO2-, CONFU- and CORAIL-type assemblies only one power distribution was considered, two
pin-by-pin power distributions were analyzed for the PUZH-type assembly. The first, shown in
Figure 3.8, refers to a burnable poison-free assembly which was proved to yield a negative core
average MTC at BOC in spite of being characterized by a very high Critical Boron
Concentration (2750 ppm ([32])). Because of the need to prevent boron-assisted corrosion
phenomena, this concentration must be reduced, and therefore burnable poisons (BP) need to be
loaded in the fresh assemblies. The BP loading, which significantly affects CBC and less
significantly the pin-by-pin power distribution, has not been fixed yet and it is therefore a design
variable. For the CLOFA analysis it is assumed that the addition of a reasonable amount of BP
would cause the PUZH-assembly power distribution to resemble that of the IFBA-containing allUO2 assembly shown in Figure 3.5, which is therefore the second pin-by-pin power distribution
analyzed for PUZH-type assemblies.
It is important to note that all the power distributions used are assumed to be fixed during the
accident, i.e. while the core power varies, its axial and radial profiles remain constant.
3.7.5 Validation of the plant modeling technique
This section compares the results obtained for the all-UO2-core with those presented, for the
same core, in [1]. Even though the reactivity coefficients used here are not the same as those
used in [1]26, the comparison is useful to verify the accuracy of the analysis and the correctness
25
The assembly peaking factor is defined as the ratio between the power of the assembly to which it is referred and the power of
the average assembly.
26
Except for MTC, reference [1] does not specify the numerical values of the reactivity coefficients actually used to perform the
124
of the RELAP plant model. This comparison is made by means of plots showing the time
variation of key plant parameters during the transient. In each figure, the plot on the left is that
obtained here while that on the right derives from [1].
Figure 3.29 shows the variation of core power during CLOFA. The trend predicted in this
analysis is very similar to that shown in the reference document ([1]). Reactor scram occurs after
about 3 seconds from the accident initiation, causing the core power to drop to about 15% of
nominal power in less than 2 seconds. Subsequently, core power slowly decreases.
4.0E+09
C o re th e rm a l p o w e r (W )
3.5E+09
3.0E+09
2.5E+09
2.0E+09
1.5E+09
1.0E+09
5.0E+08
0.0E+00
0
2
4
6
8
10
Time (s)
Figure 3.29 – Core power evolution during CLOFA for all-UO2 core (left: this analysis;
right: [1])
The core power profiles in the pre-scram period, i.e. the first 3 seconds after the accident
initiation, do exhibit a slight difference: while [1] does not show any power variation, a power
reduction from 3479 MWt to about 3080 MWt is obtained in the present analysis. This is due to
the large negative MTC which, as the coolant average temperature in the core increases from
about 315ºC to about 318ºC (see Figure 3.3027), causes an insertion of negative reactivity which
adds to that due to FTC. It has been separately verified that the use of a positive MTC equal to
that used in [1], i.e. +9 pcm/K, would have caused the core power to decrease of only 100 MWt
instead of the 400 MWt reduction (3479-3080) shown in the left plot of Figure 3.29. Therefore,
while in the present analysis the negative feedback due to MTC is coupled with that due to the
FTC, causing a significant (400 MWt) reduction in core power, in reference document [1] the
positive feedback due to MTC overwhelms the negative feedback due to FTC, resulting in a
substantially flat pre-scram power profile.
27
CLOFA analysis.
Reference document [1] does not show the variation of the coolant average temperature during CLOFA. For this reason, Figure
3.30 does not have a plot with which being compared.
125
Figure 3.30 – Coolant average temperature in the core during CLOFA for all-UO2 core
Figure 3.31 shows the variation of the coolant flow rate through the core during CLOFA. It can
be seen that the present analysis well reproduces the flow rate profile shown in [1], with a slight
overestimation (3-5%) over the whole transient.
Figure 3.31 – Evolution of coolant flow rate through the core for all-UO2 core (left: this
analysis; right: [1])
Figure 3.32 shows the variation of the Minimum Critical Heat Flux Ratio (MCHFR) during
CLOFA. Both the present analysis and reference [1] predict a reduction of MCHFR followed by
a sharp increase after reactor scram. However, two main differences can be noticed:
-
the present analysis underestimates the MCHFR with respect to that calculated in [1]
(2.073 vs 2.17);
-
in the first 3 seconds after the accident initiation, the present analysis predicts a very
small reduction in MCHFR, i.e. from 2.138 to 2.073, while reference [1] shows a
MCHFR reduction from 2.7 to 2.17.
The use of a different correlation might be the main reason for these differences. In fact, the
present analysis computes the critical heat flux (CHF) by means of the W-3L correlation
available in the VIPRE code. Reference [1], instead, does not explicitly state what CHF
126
correlation was used in CLOFA analysis. However, in a chapter not dedicated to safety analysis,
i.e. Chapter 4 “Reactor” of [1], it is stated that: “For conditions outside the range of applicability
of WRB-1 or WRB-2, the W-3 correlation is used” ([1]). Because of the mildness characterizing
CLOFA scenario it is likely that one of the two WRB correlations were actually used. These two
correlations are specific for Westinghouse-design assemblies provided (WRB-2) or not provided
(WRB-1) with Intermediate Flow Mixers ([33])28.
3.4
This analysis
From [1]
3.2
MCHFR
3
2.8
2.6
2.4
2.2
2
0
1
2
3
4
5
6
Time (s)
Figure 3.32 – Evolution of MCHFR during CLOFA for all-UO2 core
It must be pointed out, however, that the scarcity of information given in [1] about the modeling
of the CLOFA scenario does not allow the exclusion of other factors, like a different time
variation of the core inlet coolant temperature, as causes of the differences between the two
MCHFR profiles shown in Figure 3.32.
3.7.6 Results
Figure 3.33 shows the time variation of the core power for the four core types analyzed. Only the
pre-scram evolution is shown since it is the most critical for CLOFA scenario. Because of the
negative MTC characterizing all core types at normal operating conditions, they all experience a
reduction in power soon after the accident initiation, i.e. when the operating conditions do not
differ substantially from the nominal ones. In particular, the power reduction is maximum for the
PUZH-core while it is minimum for the CORAIL-core. This is because the ratio MTC/β, which
controls the reactivity insertion upon coolant temperature variation, is maximum (in absolute
value) for PUZH (-0.038 $/ºC) while it minimum for CORAIL (-0.010 $/ºC).
28
The WRB correlations are more accurate than the W-3L correlation. As a consequence, their use allows less margin from the
failure limit, i.e. from CHFR=1: the minimum CHFR typically allowed in safety analyses is in fact 1.3 if the W-3 correlation is
used, while it is 1.17 if one of the two WRB is used ([34]).
127
3500
3400
Core power (MWt)
3300
3200
3100
3000
CORAIL
2900
CONFU
2800
UO2
2700
PUZH
2600
2500
0
0.5
1
1.5
2
2.5
3
Time (s)
Figure 3.33 – Evolution of core power during CLOFA
Figure 3.34 shows the MCHFR time variation during CLOFA for the four core types analyzed.
While two cases for the PUZH-core29 were evaluated, only that referred to a burnable poisonfree pin-by-pin power distribution is shown: this is because the MCHFR time variation obtained
in the other case, i.e. using the all-UO2 assembly power distribution to the PUZH-assembly, does
not differ appreciably from that shown in Figure 3.34. The minimum MCHFR reached by each
core type during CLOFA is shown in Table 3.14.
29
The two cases analyzed differ only for the pin-by-pin power distribution assumed for the assemblies. Since the RELAP input
file models the hot assembly by lumping all its subchannels and rods, the pin-by-pin power distribution does not affect the
output parameters (e.g the core power evolution) obtained by running the RELAP plant model. For this reason, no mention to
two PUZH-core cases was done while commenting Figure 3.33. Conversely, the VIPRE output parameters (e.g. the MCHFR)
depends on the pin-by-pin power distribution since the VIPRE file models individually each rod and subchannel contained in
the hot assembly.
128
3
PUZH (BP-free power distribution)
MCHFR (W-3L)
2.8
UO2
CONFU
2.6
CORAIL
2.4
2.2
2
1.8
1.6
0
0.5
1
1.5
2
2.5
3
3.5
Time (s)
Figure 3.34 – Evolution of MCHFR during CLOFA
Table 3.14 – MCHFR during CLOFA scenario
MCHFR (W-3l
correlation)
Core type
Minimum
At steadyduring
state
CLOFA
All-UO2
2.138
2.073
CONFU
1.866
1.791
CORAIL
1.870
1.788
PUZH (BP-free pin-by-pin power distribution)
2.146
2.110
PUZH (all-UO2 pin-by-pin power distribution)
2.143
2.106
MCHFR
variation % with
respect to steady
state value
-3.0
-4.0
-4.4
-1.7
-1.7
From the results shown in Figure 3.34 and Table 3.14 it can be concluded that CLOFA causes all
core types to experience a slight reduction in MCHFR with respect to their steady state values.
However, while the absolute value of the minimum MCHFR during the CLOFA scenario of each
core type mainly depends on the starting MCHFR, i.e. the steady state MCHFR, the severity of
MCHFR reduction depends on the extent by which core power decreases soon after the accident
initiation30. Since CONFU- and CORAIL-cores have not only the most non-uniform pin-by-pin
power distribution but also the least negative MTC/β ratio, they experience the smallest MCHFR
during the transient (1.791 and 1.788 respectively) and the largest MCHFR reduction from the
30
Since 1) all core types are geometrically identical and 2) they have same steady-state coolant flow rate, the coolant flow rate
reduction experienced by the four core types is the same. Thus, the differences in average coolant temperature in the core
depend on the core power only.
129
pre-accident value (-4% and -4.4% respectively). Conversely, the homogeneity of the pin-by-pin
power distribution characterizing PUZH-type assembly together with the large negative value of
the MTC/β ratio cause the MCHFR to start from a relatively high MCHFR (~2.14) and to
experience a small MCHFR reduction during the transient (-1.7%).
3.7.7 Conclusions
The following conclusions arise from the CLOFA analysis:
-
the level of accuracy of the modeling of the CLOFA plant response can be considered
acceptable for the preliminary stage characterizing this project. For the all-UO2-core
used for the model validation, the time evolution of the main plant parameters was found
to be consistent with that shown in the reference document ([1]), with only small
differences due to the scarcity of input data specifications in [1] and to simplifying
assumptions made in this analysis.
-
CLOFA was found to be a mild accident scenario for all the core types analyzed, during
which the core experiences a slight reduction in MCHFR with respect to the steady-state
value. This reduction was found to be smaller for the PUZH-core compared to the other
core types aimed at Pu/Minor Actinides incineration, i.e. CONFU- and CORAIL-core.
The reason lies in the more negative MTC/β ratio characterizing the PUZH-core, which
causes the core power to decrease more significantly after CLOFA initiation for the
PUZH-core than for the CONFU- or CORAIL-core.
-
Given the mildness charactering the CLOFA scenario and the short time interval to reach
the most limiting conditions (<5 seconds), the thermal hydraulic margin of safety of a
core during CLOFA, i.e. the minimum value reached by the MCHFR, does not depend
much on the post-accident evolution of the plant parameters, but on the MCHFR
characterizing the core before the accident initiation. From this viewpoint, the
homogeneity of the PUZH-assembly lattice allows the PUZH-core to perform better than
the CONFU- and CORAIL-cores, and to resemble the performance of an all-UO2 core.
Even though a preliminary estimate of the PUZH-core safety margin during CLOFA was
done in this analysis, a more accurate evaluation can be done once the pin-by-pin power
distribution of a PUZH-type fresh assembly is finalized, i.e. when the burnable poison
loading, so far still a design variable, is fixed.
3.8 Conclusions of the thermal hydraulic analysis
Steady state and transient analyses were performed for a PWR plant having the same geometry
as that of Seabrook power station ([1]). The reactor core was alternatively assumed to be loaded
with four types of assembly, having identical geometry but different fuel and/or fuel
arrangement:
-
all-UO2-assembly: homogeneous assembly containing UO2 fuel pins only.
-
CONFU-assembly: heterogeneous assembly made of standard UO2 fuel pins and pins
made of recycled transuranics in an inert matrix.
-
CORAIL-assembly: heterogeneous assembly made of enriched UO2 pins and MOX pins.
-
PUZH-assembly: homogeneous assembly containing U-Pu-Th-ZrH1.6 as fuel.
130
The steady state analysis demonstrated that, under the constraint of the same safety limits for all
the core types, a PUZH-core can operate at the same power level as the all-UO2-core while
CONFU- and CORAIL-core can only operate at about 80% of that power. This is due to the flat
pin-by-pin radial power distribution characterizing the PUZH-assembly.
The transient analyses performed were: Large Break Loss Of Coolant Accident (LBLOCA),
Main Steam Line Break (MSLB) and Complete Loss Of Forced Flow Accident. (CLOFA). For
all three scenarios, the PUZH-core was demonstrated to perform better than the other two core
types aimed at Pu/MA incineration, i.e. CONFU- and CORAIL-core. Particularly:
-
the peak cladding temperature for PUZH-core during LBLOCA was found to be about
300 K lower than that of all-UO2-, CONFU- and CORAIL-cores. This is mainly due to
the lower operating temperature characterizing the highly conductive PUZH fuel relative
to UO2-based fuels;
-
unlike all-UO2-, CONFU- and CORAIL-cores, PUZH-core showed no return to criticality
in the event of a MSLB. This is due to the moderator temperature coefficient of PUZHcore, which was found to be the least negative among the core analyzed;
-
in the event of a CLOFA, the PUZH-core was found to reach a MCHFR larger than that
of the CONFU- and CORAIL-cores, and similar to that of the all-UO2-core. This is due
both to a larger pre-accident MCHFR (due to the flat pin-by-pin power distribution
characterizing the PUZH-assembly) than CONFU and CORAIL, and to the larger
(negative) value of the MTC/β ratio (which controls the reactivity insertion upon coolant
temperature variation) which caused a more rapid reduction in power upon the accident.
Appendix A: inverted core design
A.1 Description of the design
Although the idea of an inverted fuel design is not new (see Pope [35] for Gas Cooled Fast
Reactors), Malen was the first to propose a variation of such a design for PWR applications
([36]). Malen’s design consisted of vertically-oriented hexagonal blocks of hydride (U-ZrH1.6)
fuel (referred as “assemblies”), perforated by coolant channels arranged in a triangular lattice. A
cylindrical Zircaloy clad forms the walls of each coolant channel, and a certain gap separates the
outer clad surface from the inner surface of the fuel. Each channel is provided with multiple
short-length twisted tapes (TTs) aimed at critical heat flux (CHF) enhancement. The TT pitch,
which strongly affects the CHF performance, is designated as y and is defined as the axial
distance, in units of coolant channel diameter, traveled by the tape to complete a 180º rotation
around the coolant channel axis.
Although the fuel contained in each assembly is a single block, it can be imagined as composed
of a number of smaller hexagonal units, called fuel subprisms, each having a coolant channel at
the centre (see Figure A.1). The combination: coolant channel + channel clad + fuel-clad gap +
fuel subprisms is referred as “unit cell”. Figure A.1 shows a subchannel view of the inverted
design (left) and of the typical rodded design (right). The latter is referred to as “standard
design”, and the corresponding core as “standard core” (SC).
131
Figure A.1 – Inverted (left) vs standard (right) unit cell design ([36])
The innovative nature of the inverted design is twofold: hydride is used in place of UO2 and an
inverted configuration is used instead of the more common standard configuration. The inverted
configuration is made possible by the more favorable workability properties of hydrides with
respect to those of UO2: hexagonal U-Zr blocks can be easily drilled to create cooling channels
and then hydrated to obtain the final fuel composition (e.g. U-ZrH1.6).
A.2 Motivations
Two factors motivated interest in the inverted design:
- in his preliminary study, Malen ([36]) found the inverted design to have the potential to
allow an increase in power density, with a consequent reduction in the cost of nucleargenerated electricity;
- based on the findings of the plutonium incineration project, the inherent hydrogen content
of hydride fuel makes it an advantageous alternative fuel for Plutonium and Minor
Actinides burning.
It was therefore decided to investigate further this novel design.
A.3 Objectives
The inverted design project is aimed at determining the economic competitiveness of an inverted
PWR with respect to other PWR core designs referred to as “competitor designs” and presented
in Section A.6. To achieve this objective, the calculation of the maximum power density
attainable by an inverted PWR, together with cost estimates for the new design, need to be
performed.
A.4 Project status
The tasks performed in the period April 2007-August 2008 mainly concerned:
- the establishment of the design constraints;
- the estimate of the maximum power attainable by a “point design” core configuration, i.e.
by a single inverted core geometry, which is shown in Figure A.2.
The objectives presented in Section A.3, which have not been reached yet, will require switching
from a point design methodology to a spectrum design methodology, meaning that the
132
computation of the maximum attainable power density will need to be performed over a wide
range of inverted core geometries, and not only for a single geometry as done with the point
design core configuration.
Figure A.2 – Point design investigated for the inverted core (TTs not whosn)
A.5 Analysis methodology
The analysis methodology planned for this project is the same as that used by Malen in his
preliminary investigation ([36]), i.e. power-limiting constraints need to be fixed and used to
compute the maximum power density attainable by an inverted PWR core. What actually differs
from Malen’s approach is the level of detail with which such constraints are chosen and
examined. Because of the preliminary nature of his work, Malen did not account for all the
possible design constraints, and some of them were neglected:
-
constraints related to the manufacturability of the inverted assembly;
-
constraints related to the structural integrity of the inverted assembly during operation;
-
constraints related to the physical separation between adjacent fuel assemblies (Malen
assumed an infinite array of unit cells);
-
coolant pressure drop across the core;
-
fuel performance constraints (sizing of gaps to accommodate fuel swelling);
-
neutronic constraints (void reactivity coefficient);
133
-
enrichment and cycle length.
A.5 Competitor core designs
Competitor core designs are PWR core designs with which the inverted design will need to be
finally compared, in order to have a complete understanding of the potentials that such design
has for future deployment. Competitor core designs, which have been investigated in previous
research project at MIT and UCB, are summarized in Table A.1 together with the inverted point
design discussed in Section A.4. In this table, the core designs are grouped according to the type
of fuel and according to their geometric configuration (standard, annular, inverted). The table
shows, for each competitor design, its main geometric characteristics and, most importantly:
-
the attainable power uprate relative to the reference UO2 core described in [1];
-
the type of analysis performed to compute the power uprate (point design analysis or
spectrum analysis).
Configuration →
Type of analysis
Power uprate
relative to reference
pin oxide (%)
D31 (mm)
P/D
Neutronic
constraints?
Cycle length
(months)
Enrichment
Tabel A.1 – PWR competitor designs
UO2
HYDRIDE (U-Th-Zr-hydride)
Standard
Annular
Standard
Inverted
Point
design Spectrum Spectrum
Point
Spectrum design
(from
design
design
design
[1])
+24%
+50%
(estimate
up to
0
+26%
+50%
(w/o
accounting for
+55%
neutronics)
neutronics)
8.63(i);
9.5
6.5
5.9
8
10
15.37(o)
1.33
1.39
1.07
1.4
1.3-1.4
1.46
Met
Met
Met
Not applied
Met
Met
18
~14
18
~10
~12
18
5%
5%
8-9%
12.5%
12.5%
17.5%
A.6 Design constraints
Design constraints used for the inverted point design shown in Figure A.2 are summarized in
Table A.2. Some of them were used in the estimate of the maximum attainable power of the
inverted point design, while others are still under investigation and will be added next.
31
Diameter and pitch are defined as follows:
- D: fuel rod diameter for standard and annular geometries (for annular geometry an inner and an outer
diameter are presented); cooling channel diameter for inverted geometry;
- P: fuel rod pitch for standard and annular geometries; cooling channel pitch for inverted geometry;
134
Table A.2 – Design constraints used for inverted point design
Already in use
Will be added
Geometric
Non-geometric
Duct thickness, 9 mm
Peak fuel T, 650ºC
CHF
Duct-fuel gap thickness, 3 mm
Peak clad T, 350°C
Core pressure drop
PCT during LOCA,
Maximum coolant
Clad thickness, 0.6 mm
1204°C
velocity
Cladding-fuel gap thickness, 0.2
Void react coefficient ,<0
mm
Fuel web thickness, 2 and 3 mm
Cycle length, 18 months
Fuel block height, 20 cm
The main reason why some constraints have not been used in the computation of the maximum
attainable power is that the TT design has not been finalized yet. The geometry of the TTs,
particularly the twist ratio and the spacing between successive TTs, strongly affect the CHF and
pressure drop performance of the inverted core. Likewise, the maximum coolant velocity limit,
which is imposed to protect the TTs from excessive mechanical stresses, will be fixed once the
investigation on TTs design is performed.
A.7 Preliminary result
Figure A.3 shows the variation of the peak fuel temperature with the cooling channel pitch, for
different core power levels. Besides the main x-axis, a secondary x-axis is shown: it contains the
fuel web thickness which, being defined as the thickness of fuel comprised between two adjacent
cooling channels, is function of the cooling channel pitch (main x-axis), cooling channel
diameter (fixed to 10 mm), cladding wall thickness (fixed to 0.6 mm per Table A.2) and fuelclad gap width (fixed to 0.2 mm per Table A.2).
135
Positive
VRC
Figure A.3 – Graphic representation of maximum core power attainable by the inverted
point design of Figure A.2
It can be seen that the maximum power attainable by a core fueled with inverted assemblies
having the point design geometry shown in Figure A.2 is about 5300 MWt. This value is
however a preliminary result since the constraints shown in the last column of Table A.2 are still
to be applied and they may reduce such power.
The big arrows in Figure A.3 define the allowed design space for the point design investigated:
such design space is delimited by a minimum allowed pitch and a maximum allowed fuel
temperature. The minimum pitch, equal to 13.8 mm, prevents the inverted design under
investigation to have a positive void reactivity coefficient (VRC), which affects designs having
high H/HM ratios32. In fact, for a fixed cooling channel diameter, when the pitch becomes too
small the amount of heavy metal per unit cell is insufficient to guarantee a small H/HM ratio,
resulting in a positive void reactivity coefficient.
32
H and HM are the hydrogen and heavy metal atom density respectively.
136
Beside the VRC, also the fuel web thickness imposes a lower limit to the cooling channel pitch.
In fact, if the fuel web thickness is too small, the strength of the resulting fuel block may be
insufficient to sustain the mechanical stresses arising during manufacture, transport and
assembly. For this reason, based on structural strength considerations, the fuel web thickness was
limited to 3 mm (conservative limit) and 2 mm (optimistic limit). As explained above, however,
the VRC constraint was found to be more limiting than the fuel web thickness constraint.
A.8 Work being performed
The inverted core design effort is currently focused on the following tasks:
-
elaboration of pressure drop and CHF calculation techniques in order to use these
parameters as power limiting constraints;
-
TT design optimization;
-
development of a code able to automatically perform the calculation of the maximum
attainable power for multiple inverted geometries.
References
[1]
Seabrook Power Station Updated Safety Analysis Report, Revision 8, 2002.
[2]
Personal communication: R.E. White (FPL) to P. Ferroni (MIT). September 2006.
[3] B. Corder, "Westinghouse Model F Steam Generator General Information", Attachment 1 of
"Callaway Plant, Engineering Technical Procedure, ETP-BB-01309 Steam Generator Eddy
Current Testing Acquisition and Analysis Guidelines". January 2003. Available at NRC
electronic library. ADAMS No. ML032320341.
[4] M. Yamawaki et al., Development of U-Th-Zr Alloy Hydrides as Alternative Thorium-base
Fuel and MA Burning Target Fuel. Proc. Of the Int. Conference on Future Nuclear
Systems, GLOBAL’99, Jackson Hole, WY, August 29-September 3, 1999.
[5] B. Tsuchiya et al., Thermal Diffusivity Measurements of Uranium-Thorium-Zirconium
Hydride. Journal of Alloys and Compounds 312 (2000), 104-110.
[6] NUREG/CR-6150, SCDAP/RELAP5/MOD3.1 Code Manual Volume IV: MATPRO - A
Library of Materials Properties for Light Water Reactor Accident Analysis. Idaho National
Engineering Laboratory, November 1993.
[7] T. Yamamoto et al., Development of new reactor fuel materials: hydrogenation properties of
U-Th-Zr alloys and neutron irradiation effects on their hydrides. Journal of Nuclear
Materials 247 (1997) 339-344.
[8]
C. Stewart, VIPRE-01: A Thermal Hydraulic Code for Reactor Cores. Vol.2: User’s
Manual. 1989.
[9]
M.S. Kazimi, N.E. Todreas, “Nuclear Systems I, Thermal Hydraulic Fundamentals”,
Taylor & Francis, third printing, 1993.
137
[10] K. Konashi et al., “Thermodynamic Stability of ThZr2Hx at High Temperature”, Journal of
Physics and Chemistry of Solids 66 (2005) 625-628.
[11] P. Ferroni, N.E. Todreas, “Steady State Thermal Hydraulic Analysis of Hydride Fueled
BWRs”. Center of Advanced Nuclear Engineering Systems (CANES), MIT-NFC-PR-079.
2006.
[12] K. Konashi, M. Yamawaki, “The Development of Thorium Hydride Fuel”,
Characterization and Quality Control of Nuclear Fuels, edited by C. Ganguly and R.N.
Jayaraj, (Allied Publishers Pvt. Ltd. 2004) 92-106.
[13] M. Visosky, M. S. Kazimi, P. Hejzlar, “Actinide Minimization Using Pressurized Water
Reactors”, Center of Advanced Nuclear Engineering Systems (CANES), MIT-NFC-PR085, June 2006.
[14] T. K. Kim et al. “Benchmark Comparisons of Deterministic and Monte Carlo Codes for a
PWR Heterogeneous Assembly Design”, PHYSOR 2004, Chicago, IL, April 25-29, 2004.
[15] RELAP 3D© Code Manual. Volume 1: Code Structure, System Models, and Solution
Methods. Idaho National Laboratory. Revision 2.3. Idaho Falls, ID, 2003.
[16] L. Heins, Framatome ANP GmbH, “Core Damage Extent Analysis to Fulfill an Additional
LOCA Requirement”, SEG FSM Topical Meeting on LOCA Issues, Argonne National
Laboratory, May 25-26, 2004.
[17] NUREG-1793, “Final Safety Evaluation Report Related to Certification of the AP1000
Standard Design”, September 2004.
[18] N. Todorova, K. Ivanov, B. Taylor, “Pressurised Water Reactor Main Steam Line Break
(MSLB) Benchmark”. Nuclear Engineering Program, Pennsylvania State University.
NEA/NSC/DOC(2003)21.
[19] Seabrook Station Facility Operating License NPF-86 License Amendment Request 04-03,
Application for Stretch Power Uprate. March 17, 2004. Available at NRC electronic
library. ADAMS No. ML040860307.
[20] Personal communication: G. Myers (FPL) to P. Ferroni (MIT). July 2007.
[21] Seabrook Station Response to Request for Additional Information Regarding License
Amendment Request 04-03, Application for Stretch Power Uprate. October 12, 2004.
Available at NRC electronic library. ADAMS No. ML042890281.
[22] Seabrook Power Station Updated Final Safety Analysis Report. Revision 7, 2001.
Available at NRC electronic library. ADAMS No. ML012180289.
[23] Personal communication: P.A. Bergeron (AREVA) to P. Ferroni (MIT). July 2007.
[24] Attachment 1 of "Callaway Plant, Engineering Technical Procedure, ETP-BB-01309 Steam
Generator Eddy Current Testing Acquisition and Analysis Guidelines". Attachment titled:
138
"Westinghouse Model F Steam Generator General Information", by Brad Corder, January
2003. Available at NRC electronic library, ADAMS No. ML032320341.
[25] E. Shwageraus, “Rethinking the Light Water Reactors Fuel Cycle”, PhD thesis,
Massachusetts Institute of Technology. September 2003.
[26] M.A. Tremblay, J.P. Gorski, “Seabrook Station Cycle 5 Nuclear Design Report”, YAEC1927, Yankee Atomic Electric Company, Auburn, MA, November 1995.
[27] G. Youinou, A. Vasile, “Plutonium Multirecycling in Standard PWRs Loaded with
Evolutionary Fuels”, Nuclear Science and Engineering 151 (2005) 25-45.
[28] FPL Energy-NRC meeting, “Seabrook Station Stretch Power Uprate”, March 3, 2004.
Available at NRC electronic library. ADAMS No. ML040630431.
[29] NUREG/IA-0106 TEC/L/0471/R91, “Assessment of PWR Steam Generator Modelling in
RELAP5/MOD2. Prepared by J.M. Putney, R.J. Preece, national Power Technology and
Environmental Centre, United Kingdom. Published by US NRC. June 1993.
[30] RELAP 3D© Code Manual. Volume 5: User’s Guidelines. Idaho National Laboratory.
Revision 2.3. Idaho Falls, ID, 2003.
[31] AP1000 Design Control Document, Revision 14, 2004. Available at NRC electronic
library, ADAMS No. ML050750282.
[32] E. Greenspan et al., “Feasibility of Recycling Plutonium and Minor Actinides in Light
Water Reactors Using Hydride Fuel”. NERI-Project No. 2006-065. Quarter 4 Report. April
30, 2007.
[33] Fuel safety Criteria in NEA Member Countries, Compilation of Responses Received from
Member Countries. Nuclear Energy Agency. NEA/CSNI/R(2003)10. March 2003.
Available online at: http://www.nea.fr/html/nsd/docs/2003/csni-r2003-10.pdf
[34] P. Hejzlar, N. Todreas, “Response to Letter to the Editor on the round table discussion on
reactor power margins published in Nuclear Engineering and Design 163 (1–2) 1996”.
Nuclear Engineering and Design 201 (2000) 347-352.
[35] Pope, M.A., Yarsky P.J., Driscoll M.J., Hejzlar P. and Saha P., “An Advanced Vented Fuel
Assembly Design for GFR Application,” ANS Trans., Vol. 92, p. 211, San Diego, USA,
June 5-9, 2005.
[36] J. Malen, N. Todreas, P. Hejzlar, P. Ferroni, A. Bergles, “Thermal Hydraulic Design of a
Hydride-fueled Inverted PWR Core”, accepted for publication in Nuclear Engineering and
Design, 2009.
139
4. Materials Analysis
This section is organized as follows:
¾ Section 4.1: Objectives of the materials analysis;
¾ Section 4.2: Fabrication and characterization of uranium thorium zirconium hydrides;
¾ Section 4.3: Transient hydride fuel behavior in LWRs;
¾ Section 4.4: Kinetics of hydrogen desorption from zirconium hydride;
¾ Section 4.5: Zircaloy cladding compatibility with hydride fuel;
¾ Section 4.6: Oxidation behavior of hydride fuel in high temperature steam;
¾ Section 4.7: Irradiation plans for liquid metal bonded hydride fuel rod.
Each of these sections is self-contained – has its own equations, figures, tables and references
numbering.
4.1 Introduction
The primary objective of the material analysis, as originally defined, was to investigate the
compatibility of hydride fuel with Zircaloy clad and with water under typical PWR operating
conditions. For this purpose we have located a damaged unused TRIGA fuel at the University of
California campuses at both Irvine and Davis and received DOE agreement to transfer the fuel
element from Davis to Berkeley. Unfortunately, we encountered numerous administrative
hurdles first by DOE and later by Davis and Berkeley and did not succeed getting the fuel to this
date. Consequently, we have modified the plan for the material analysis as reported below.
Initially two uranium-thorium-zirconium hydride fuel samples were fabricated in our lab based
on recommendations from the neutronics study. The fabricated fuels were further characterized
through multiple techniques to develop a deep understanding of the material systems and extract
parameters and information that would govern its behavior during reactor operation.
Also a coupled transient heat transfer and hydrogen diffusion study was performed at the fuel
level in order to characterize the behavior of the material under power transients. The analysis
maps the temperature, hydrogen concentration and stress across the fuel during the power
transient. The major differences between the oxide and hydride type fuels and the advantages of
the latter are pointed out.
Another set of experiments was aimed at determining the kinetics of hydrogen desorption from
the hydride fuel. This is an important phenomenon that needs to be understood in order to be able
to predict the fuel behavior and cladding pressure buildup during transient scenarios.
Compatibility of liquid metal bonded hydride fuel with Zircaloy cladding is an essential
component of this feasibility study. Zirconium getters hydrogen very aggressively and current
LWR cladding failures are related to hydrogen pickup of cladding from the hydrogen produced
during the waterside corrosion. Therefore an alloy of lead-tin-bismuth (Pb-33wt%Sn-33wt%Bi)
was proposed as the gap filling material in order to retard the kinetics of hydrogen transfer from
hydride fuel to the cladding. An experimental setup is built to test the effectiveness of this
approach.
140
An investigation of the kinetics of oxidation of the hydride fuel exposed to high temperature
steam in case of severe accident has been initiated but not completed. A plan for irradiation and
post irradiation examination of the liquid metal bonded hydride fuel was also developed.
4.2 Fabrication and Characterization of Uranium Thorium Zirconium
Hydrides
3.2.1
Introduction
Hydride nuclear fuels consist of metallic uranium particles dispersed in a hydride matrix. In the
case of TRIGA fuel, the matrix consists solely of the δ-zirconium hydride (ZrH1.6) phase.
Hydride matrices have higher hydrogen atomic densities when compared to PWR or BWR
coolants, and act as effective moderators to enhance the thermalization of neutrons in fission
reactors. This allows more compact core designs with high power density, since a considerable
fraction of the water moderator can be replaced with hydrogen within the fuel. In addition to
higher thermal conductivity compared to the oxide fuels, hydride fuels also exhibit thermallyinduced hydrogen up-scattering that accompanies Doppler feedback, which in turn provides a
negative prompt temperature coefficient of reactivity [1].
Uranium-thorium-zirconium hydride fuel has been proposed as an optimized matrix for the deep
burn of plutonium and minor actinides [2-5]. The proposed fuel could achieve TRU (transuranic
elements) destruction fractions as high as twice those realized with MOX (mixed oxide) fuel.
Unlike MOX fuel, it is also possible to realize infinite cycles of partitioning and transmutation
with the hydride fuel without the risk of large positive reactivity coefficients as the cycles
progress [6].
3.2.2
Fuel fabrication
Two uranium-thorium-zirconium hydride fuels of the overall chemical formulae (UTh4Zr10)H1.9
and (U4Th2Zr9)H1.5 have been fabricated in order to investigate and characterize the
microstructure and the corresponding phases forming the material. Fuel fabrication was
performed in Idaho National Laboratory’s (INL) Materials and Fuels Complex (MFC). All the
fabrication activities were performed either inside fume hoods with continuous air monitoring or
in negative-pressure gloveboxes.
Two alloys of uranium-thorium-zirconium were prepared by arc melting of high-purity metal
feedstock (>99%) in an argon glovebox under 4 ppm oxygen. The metals were initially acid
treated so that any impurities and scaling on the surface were removed. Arc melting was done
through the arc-lift process where the solidified buttons were turned 5 times and re-melted to
achieve good homogeneity. Between each melting step, the surface of the button was abraded to
remove impurities agglomerated at the surface. Arc melting resulted in melt temperatures in
excess of 4000 °C. The melt was then quickly solidified in a copper hearth, resulting in a
quenched microstructure with dendrite formation. According to the ternary phase diagram of the
U-Th-Zr system [7], both of the alloys at equilibrium are in the γ(U+Zr) + α-Th two phase
region. The γ phase is a solid solution of uranium and zirconium with a body-centered cubic unit
cell, whereas the α-thorium phase has a face-centered cubic unit cell.
The arc-melted alloys were cut into disks of 2 mm thickness prior to hydriding in order to reduce
the diffusion path length of hydrogen atom (diffusion-limited hydriding kinetics are assumed).
141
The metal disks underwent hydriding in a conventional tube furnace under 1 atm of hydrogen
gas for 4 hours. Furnace temperature was initially set at 900 °C and was gradually reduced to 500
°C over the hydriding period. Since the hydriding process is diffusion-limited high temperatures
were advantageous. Also, the material was able to better withstand the increase in volume at
higher temperatures while maintaining its physical integrity. On the other hand, the furnace
temperature had to be reduced eventually in order to increase the activity of hydrogen in the solid
phase, and thus achieve higher hydrogen-to-metal (H/M) ratios. Figure 1 illustrates two of the
hydride discs thus fabricated.
Figure 1. (UTh4Zr10)H1.9 fuel disks fabricated at INL. The disk to the left has experienced
cracking due to severe volume expansion.
The detailed composition of the fuels is presented in Table 1. Actual H/M ratios were determined
by weighing the samples prior to and after the hydriding process. The theoretical H/M ratios are
calculated based on the assumption that the two hydride phases forming the fuels are δ-ZrH1.6+x
and ThZr2H7-x while uranium remains metallic (α-U). Volume fractions of each phase and the
fuel density are all calculated based on the crystal structure of the aforementioned three different
phases in the fuel. The theoretical density of the (UTh4Zr10)H1.9 is in good agreement with the
experimental value of 7.55 gr/cm3 determined by Tsuchiya et al. [8].
Table 1. Detailed Composition and Calculated Densities for (UTh4Zr10)H1.9 and (U4Th2Zr9)H1.5
Fuels.
(UTh4Zr10)H1.9 (U4Th2Zr9)H1.5
Theoretical H/M† ratio
2.08
1.47
Theoretical H/(Zr+Th) ratio
2.23
2.00
Actual H/M ratio
1.93
1.55
Actual H/(Zr+Th) ratio
2.07
2.11
Vol% α-U
4.49
20.14
Vol% δ-ZrH1.6
11.75
32.92
83.76
46.93
7.57
9.10
Vol% ThZr2H7-x
3
Fuel Density [gr/cm ]
† M=U+Th+Zr
142
3.2.3
Characterization
3.2.3.1 X-ray diffractometry
XRD samples were prepared by depositing fuel powder on a low background silicon singlecrystal sample holder using slurry of powder and ethanol. Samples were also mixed with
lanthanum hexaboride (LaB6 SRM 660a) powder to be used as internal standard during pattern
refinement. High-resolution diffraction patterns were obtained using a Phillips PANalytical
X’Pert Pro instrument with a Cu Kα source.
Rietveld refinement was performed on the experimental patterns for the two fuels. Formation of
ThZr2H7-x, δ-ZrH1.6+x, α-U, and minute amounts of ε-UH3 was confirmed. Detailed results are
presented in Table 2. The lattice parameter of α-U and ε-UH3 phases could not be accurately
determined for the (UTh4Zr10)H1.9 fuel due to the small volume fraction of these phases in this
fuel. None of the following phases (accompanied by the corresponding space group) were
detected in either of the fuels: ε-ZrH1.8-x (I4/mmm); δ-UH3 (Pm-3n); δ-UZr2 (P6/mmm); ZrH
(P42/n); ThH2 (I4/mmm); Th4H15 (I-43d).
Table 2. Lattice Parameter of Phases Present in the (UTh4Zr10)H1.9 and (U4Th2Zr9)H1.5 Fuels
Determined through Rietveld Refinement.
Space
(UTh4Zr10)H1.9 (U4Th2Zr9)H1.5
Group
Phase
ThZr2H7-x Fd-3m
δ-ZrH1.6
Fm-3m
α-U
Cmcm
ε-UH3
Pm-3n
a = 9.186(2) Å
a = 4.783(1) Å
N/A
N/A
N/A
N/A
a = 9.184(4) Å
a = 4.762(2) Å
a = 2.855(4) Å
b = 5.862(4) Å
c = 4.956(7) Å
a = 6.655(1) Å
Reference
a = 9.154 Å 9
a = 4.777 Å 10
a = 2.854 Å 11
b = 5.869 Å
a = 4.955 Å
a = 6.627 Å 12
The experimental powder patterns along with the results of the refinement fit are shown in
Figure 2 for both fuels. Structure factor calculation (SFC) could be performed to match the
experimental XRD intensities from different phases to the calculated volume fractions presented
in Table 1. SFC was done specifically comparing the 022 type reflection from the ThZr2H7-x
phase and the 021 and 110 reflections from the α-U phase in the (U4Th2Zr9)H1.5 fuel. Scattering
from hydrogen atoms was neglected in this calculation since the atomic scattering factor from
this element is negligible compared to that of the other species. The resulting normalized
intensities agree well with the experimental values (Table 3).
Table 3. Comparison of Peak Intensities between Experimental Results and Structure Factor
Calculations.
Phase
ThZr2H7-x
α-U
Reflection
Experimental
SFC
022
021
110
1
0.75
0.32
1
0.79
0.27
143
(UTh4Zr10)H1.9
LaB6
ThZr2H7-x
δ-ZrH1.6+x
α-U
ε-UH3
UO2
Counts
2000
1000
0
25
30
35
40
45
50
2θ
(U4Th2Zr9)H1.5
LaB6
ThZr2H7-x
δ-ZrH1.6+x
α-U
ε-UH3
UO2
Counts
1000
500
0
25
30
35
40
45
50
2θ
Figure 2. Powder x-ray diffraction patterns for (UTh4Zr10)H1.9 and (U4Th2Zr9)H1.5 fuels along
with Rietveld refinement fit.
144
3.2.3.2 Scanning electron microscopy
Scanning electron microscopy was performed on a JEOL instrument model JSM-5610 equipped
with secondary and backscatter electron detectors and an Oxford ISIS EDS (energy dispersive xray spectroscopy) system. The accelerating potential during operation was 15 kV. Figure 3
shows the backscattered electron image of the two fuels. The morphology of both fuels showed
three distinct phases present. Each region corresponds to the one of the structures identified in
the previous section, where the phases from brightest to darkest are α-U, ThZr2H7-x, and δZrH1.6+x respectively. This is the case since the intensity of the backscattered image is
proportional to the average atomic number in each phase. This is also in agreement with the
corresponding EDS spectra.
Severe microcracking is observed in the microstructure of the (UTh4Zr10)H1.9 fuel, a result of
volume expansion during processing. The cracks are both transgranular and intergranular,
forming a network that expands across the microstructure. However, no sign of cracking is
observed in the microstructure of (U4Th2Zr9)H1.5. This is in agreement with the calculated
percent volume expansions of 22.4% and 17.7% upon hydriding for (UTh4Zr10)H1.9 and
(U4Th2Zr9)H1.5 fuels, respectively. Solubility of thorium in the γ(U+Zr) phase and zirconium and
uranium in the α-Th phase are assumed to be zero in this analysis. The volume expansion is then
calculated based on the change in the molar volume of the phase prior to and after hydriding. The
extent of cracking for (UTh4Zr10)H1.9 fuel significantly worsened over time after hydriding when
the material was stored at room temperature. This is due to residual stresses in the material.
However no such behavior was observed in case of the (U4Th2Zr9)H1.5 fuel.
The morphology of both fuels shows elongated grains, but this feature is much more noticeable
in the (U4Th2Zr9)H1.5 fuel. This morphology is due to the formation of dendrites during the
solidification of metal alloys. Uranium particles are evenly dispersed in small scale in
(UTh4Zr10)H1.9 fuel (≤1 μm in diameter) while in (U4Th2Zr9)H1.5 fuel the uranium particle
distribution is random with large particle size. Similar characteristics can be seen for δ-ZrH1.6+x
grains of different sizes with an average diameter in the range of a few micrometers. These
micrographs further show that the ternary ThZr2H7-x phase is the dominant phase in both fuels.
This major chemical phase resides approximately 85 vol% of the (UTh4Zr10)H1.9 sample where it
is continuous. On the other hand only ~46 vol% of the (U4Th2Zr9)H1.5 sample constitutes this
phase.
145
Figure 3. Backscattered electron image of (UTh4Zr10)H1.9 and (U4Th2Zr9)H1.5 fuels.
3.2.3.3 Transmission electron microscopy
Transmission electron microscopy was performed using a TECNAI-G2-F30 microscope with a
300 keV field emission gun. TEM images were recorded using a low scan CCD camera attached
to a Gatan GIF 2000 image filter. Four TEM specimens were prepared through microtome
cutting at thicknesses of 25 and 50 nm for each fuel. Thin samples are essential because of the
significant electron beam attenuation by samples consisting of high atomic number elements.
Powderized fuel was initially embedded in spur-resin in a micro-vial, which was then solidified
146
at 60 °C overnight. The microtome specimens were cut using the diamond blade of a Leica EM
UC6rt instrument and were then placed on a 3mm copper grid supported by thin carbon film.
A bright field image of (U4Th2Zr9)H1.5 is presented in Figure 4. This image lacks any
morphological information since the specimens were prepared starting from fine powder, and
during microtomy further cracking occurred. Dislocation-free grains of ThZr2H7-x and δ-ZrH1.6+x
phase are shown with good coherence at the grain boundary. EDS was performed by the TEM in
scanning mode, confirming the composition of the grains shown in the image.
ThZr2H7-x
α-U
δ-ZrH1.6+x
0.5μm
Figure 4. Bright field image of (U4Th2Zr9)H1.5 fuel.
High-resolution (HRTEM) images of ThZr2H7-x, δ-ZrH1.6+x, and α-U phases were generated
through phase contrast imaging. The microscope’s spherical and chromatic aberration
coefficients were reported as 1.2 mm and 1.4 mm by the manufacturer. Figure 5 shows the phase
contrast image of the three phases forming the fuels along with the fast Fourier transformation of
each image into reciprocal space. The extent of defocus for the ThZr2H7-x phase contrast image is
determined through analysis of contrast transfer function contours based on scattering from an
amorphous region of the sample. No amorphous region was present during imaging of the δZrH1.6+x or α-U phase, and Bloch wave computer simulation [13] was used instead to estimate
the defocus value. This approach is shown in the middle section of Figure 5 where the phase
contrast image of δ-ZrH1.6+x is matched by computer simulation at 25 nm sample thickness and 40 nm defocus.
147
{131}
{202}
FFT
-331
-202
-1-33
-13-1
1-31
13-3
3-31
20-2
323 zone axis
{111}
{220}
{200}
t
-111
-20
15
-220
FFT
Δf 0
-11-1
002
20
00-2
1-11
25
1-1-1
2-20
30
110 zone axis
FFT
148
220
-40
-60
FFT
-1-14
{112}
-112
0-44
-130
0-22
-15-2
1-52
02-2
{114}
1-30
04-4
1-1-2
311 zone axis
{022}
11-4
Figure 5. Phase contrast imaging on (U4Th2Zr9)H1.5 fuel. Top: 323 zone axis of ThZr2H7-x phase
(Δf=-100nm). Middle: 110 zone axis of δ-ZrH1.6+x along with Bloch wave computer simulation
(Δf=-40nm). Bottom: 311 zone axis of α-U (Δf=-60nm).
The observations from HRTEM are in agreement with the XRD results, confirming the
formation of ThZr2H7-x and δ-ZrH1.6+x. No sign of formation of tetragonal ε-ZrH1.8 phase is
observed. The FFT of the image corresponding to the uranium phase is representative of
diffraction from an orthorhombic phase. This result rules out formation of significant amounts of
cubic ε-UH3.
3.2.3.4 Nanoscale dynamic stiffness mapping (DSM)
DSM (TriboScope nanoindenter, Hysitron, Minneapolis, MN) coupled with an atomic force
microscopy controller (NanoScope IIIa, Veeco, Santa Barbara, CA) was used to determine the
elastic modulus of the phases forming the uranium-thorium-zirconium hydride fuels. The
technique provides topography as well as viscoelastic properties through storage and loss moduli
mapping across the fuel microstructure at nanometer length scales. This was done by applying a
sinusoidal electrostatic force acting on the spring-suspended center of the force-displacement
transducer of the nanoindenter while contact mode imaging was conducted. A cube-corner
diamond tip was attached to this transducer. The amplitude and the phase of the resulting
transducer displacement signal were measured with a dual-channel lock-in amplifier, and this
information was used to determine the local indentation moduli of the sample at each pixel of the
imaging process. In the present case only the storage modulus (designated as elastic modulus) is
reported due to negligible magnitudes of loss modulus found for the samples studied. The
diamond tip radius used for imaging was calibrated by a standard quartz sample with an elastic
modulus of 69.7 GPa. Balooch et al [14] provide detailed description of the instrument and the
technique.
Two areal regions of 3.5x3.5 μm2 and 10x10 μm2 in size were investigated in the (U4Th2Zr9)H1.5
fuel, and the results are presented in Figure 6. The elastic modulus values are represented by the
false color in the images. The variation of the elastic modulus (black spots) along the black
149
horizontal lines superimposed on the images is also shown for further clarification. Three distinct
regions, corresponding to α-U, ThZr2H7-x, and δ-ZrH1.6+x, are apparent from brightest to darkest,
respectively. The microstructure in this set of images is directly comparable to what was
previously characterized during backscattered scanning electron microscopy.
The elastic moduli of α-U and δ-ZrH1.6+x are reported as 202 GPa [15] and 130 GPa [16],
respectively. The results of this study are in good agreement with the values reported previously
for these two phases. The elastic modulus of the ternary ThZr2H7-x phase has not been reported
previously and the mean value is determined here as 172 GPa.
Elastic Modulus (GPa)
240
200
150
100
220
220
200
200
180
180
160
160
140
140
120
120
100
100
0
0.5
1
1.5
2
2.5
3
Position (μm)
3.5
0
2
4
6
8
Position (μm)
Figure 6. Elastic modulus mapping across the microstructure of (U4Th2Zr9)H1.5 fuel.
3.2.4
Discussion
Fuel fabrication could be improved by homogenization of the arc-melted metal alloys prior to
hydriding in order to remove the dendritic structure. The hydriding process could also be greatly
improved if the desired H/M ratio is initially established at high temperature and then maintained
during the cool down. The diffusion-limited process takes place relatively quickly at high
temperature under high pressure of hydrogen gas while the material is ductile enough to
accommodate the large volume expansion. During the cool-down step, the hydrogen partial
pressure should be continuously reduced to correspond to the desired H/M ratio. This inhibits
formation of hydrogen concentration gradients that would in turn induce stress across the
material. The equilibrium partial pressure of hydrogen with zirconium hydride and thoriumzirconium hydride is known [17, 18] as a function of temperature. At equilibrium, the activity of
hydrogen in the gas and the two hydride phases is identical; therefore the exact H/M ratio in each
phase could be determined. However, the equilibrium partial pressure of hydrogen changes by
four orders of magnitude over the processing temperatures of these hydrides. Therefore,
sophisticated instrumentation and control systems are necessary to execute this procedure.
The thermodynamic stability of the possible metal hydrides in this system increases as follows:
UH3, ThH2, δ-ZrH1.6+x, ThZr2H7-x [19,20,21,22,23]. However, the thermodynamic stability
changes as a function of H/M ratio. This result is in agreement with the characterization
150
observations, where only the latter two hydrides were observed. Uranium hydride is unstable
above 420 °C (under 1 atm of H2 gas). The residual uranium hydride formation, as detected by
XRD analysis, is due to the presence of hydrogen in the furnace during the cool-down.
The actual H/M ratio in the ThZr2H7-x phase is unknown. Bartscher et al. [9] have studied the
ThZr2Dx system using neutron scattering and report the lattice parameter for the cubic unit cell as
a function of different deuterium to metal ratios up to x = 6.3. Linear extrapolation of these
results matches the determined lattice parameter of this phase to hydrogen stoichiometry of 7 (as
in ThZr2H7) in both fuels.
The density of hydrogen in hydride nuclear fuels is of great importance since it replaces a part of
the moderator and thus significantly affects the neutronic properties. Figure 7 shows the
hydrogen and uranium atomic densities in different hydride fuels as a function of atomic percent
uranium dispersed in the hydride matrix. Uranium-thorium-zirconium hydride fuels are superior
to uranium-zirconium hydride fuels since similar uranium atomic densities could be achieved
with higher hydrogen atomic densities.
8E+22
Atomic Density [cm-3]
7E+22
6E+22
HHDensity
[cm‐3]
in UxZrH1.6
in UxZrH
1.6 Fuel
5E+22
UUDensity
[cm‐3]
in UxZrH
1.6 Fuel
4E+22
Series3
H in UxThZr2H7 Fuel
3E+22
Series4
U in UxThZr2H7 Fuel
2E+22
U and H in (UTh 4Zr10)H1.9 Fuel
U and H in TRIGA Fuel (U0.31ZrH1.6)
U and H in (U4Th 2Zr9)H1.5 Fuel
1E+22
0
0
2
4
6
8
10
12
at% U
Figure 7. Hydrogen and uranium atomic density as a function of at% uranium metal in different
hydride matrices.
3.2.5
Conclusions
Two uranium-thorium-zirconium alloys were arc-melted and then hydrided to form fuels with the
nominal compositions of (UTh4Zr10)H1.9 and (U4Th2Zr9)H1.5. Powder XRD analysis showed both
these fuels consisted of the α-U, δ-ZrH1.6+x, and ThZr2H7-x chemical phases with the last being
the dominant in both. SEM and TEM (in bright-field and high-resolution mode) imaging
confirmed the presence of these three phases. Atomic force microscopy along with nanoscale
dynamic stiffness analysis performed on fuel specimens to map the Young’s modulus across the
microstructure revealed the elastic modulus of ThZr2H7-x to be 172 GPa.
Uranium-thorium-zirconium hydride fuels appear to be superior to TRIGA fuel for power reactor
151
use since the hydride matrix is more stable with respect to dehydriding. Also, high uranium and
hydrogen atomic densities are achieved in fuels containing thorium. Extensive study of the
effects of irradiation on these fuels under typical light water reactor conditions is necessary in
order to adequately understand their performance compared to TRIGA fuel and oxide fuels.
3.2.6
Acknowledgement
The aid and valuable technical insight of Dr. Mitchell Meyer and all the Fuels and Applied
Science Building personnel at the Materials and Fuels Complex of Idaho National Laboratory is
gratefully acknowledged.
3.2.7
References
1. F. Ganda, E. Greenspan, “Physics analysis of hydride fuel in PWR cores,” submitted to
Nuclear Science and Engineering, (2008).
2. F. Ganda, E. Greenspan, “Plutonium Incineration Capability of Hydride Versus MOX Fuel in
PWR,” Procd. Global ’05, Tsukuba, Japan (Oct. 2005).
3. F. Ganda and E. Greenspan, “Incineration of Plutonium in PWR Using Hydride Fuel,” Proc.
2005 International Conference on Advances in Nuclear Power Plants ICAPP–2005, Seoul,
Korea (May 2005).
4. F. Ganda, E. Greenspan, “Plutonium Recycling in Hydride Fueled PWR Cores,” accepted for
publication in Nuclear Engineering and Design, (2008).
5. F. Ganda, E. Greenspan, “Neutronic Analysis of Hydride Fuelled PWR Cores,” accepted for
publication in Nuclear Engineering and Design, (2008).
6. F. Ganda, E. Greenspan, “Plutonium and Neptunium multi-recycling in PWR using hydride
fuels,” Physor 2008, Interlachen, CH. (2008).
7. T.A. Badaeva, G.K. Alekseenko, “Structure of Alloys of the Thorium-Uranium-Zirconium
System,” Struct. Alloys Certain Systems Cont. Uranium Thorium, pp.376-394, (1963).
8. B. Tsuchiya, J. Huang, K. Konashi, W. Saiki, T. Onoue, M. Yamawaki., “Thermal Diffusivity
Measurement of Uranium-Thorium-Zirconium Hydride,” J. Alloy and Compounds, 312,
pp.104-110, (2000).
9. W. Bartscher, J. Rebizant, A. Boeuf, R. Caciuffo, F. Rustichelli, J. Fournier, W. Kuhs,
“Distribution of Deuterium in the Cubic Laves Phase ThZr2Dx,” Journal of Less Common
Metals, 121, pp.455-460 (1986).
10. R. Beck, “Zirconium-Hydrogen Phase System,” Trans. Am. Soc. Metals, 55, pp.542-555
(1962).
11. Sturken, Post., Acta Crystallogr., 13, 852, (1960).
12. W. Bartscher, A. Boeuf, R. Caciuffo, J. Fournier, W. Kuhs, J. Rebizant, F. Rustichelli,
“Neutron Diffraction Study of Beta-UD3 and Beta-UH3,” Solid State Communications, 53
(4), pp.423-426, (1985).
152
13. J.M. Zuo and J.C. Mabon, Web-based Electron Microscopy Application Software: WebEMAPS, Microsc Microanal 10(Suppl 2), 2004; URL: http://emaps.mrl.uiuc.edu/.
14. G. Balooch, G. Marshall, S. Marshall, O. Warren, S. Asif, M. Balooch, “Evaluation of a New
Modulus Mapping Technique to Investigate Microstructural Features of Human Teeth,”
Journal of Biomechanics, 37, pp.1223-1232, (2004).
15. ASM Handbooks, Vol 2., Properties and Selection: Nonferrous Alloys and Special-Purpose
Materials.
16. S. Yamanaka, K. Yoshioka, M. Uno, M. Katsura, H. Anada, T. Matsuda, S. Kobayashi,
“Thermal and Mechanical Properties of Zirconium Hydride,” J. Alloys and Compounds, 293295, pp.23-29, (1999).
17. M. Simnad, ”The U-ZrHx Alloy: Its Properties and Use in TRIGA Fuel,” Nuclear Eng.
Design, 64, pp.403-422 (1981).
18. K. Konashi, B. Pudjanto, T. Terai, M. Yamawaki, “Thermodynamic stability of ThZr2Hx at
high temperature,” Journal of Physics and Chemistry of Solids, 66, pp.625-628, (2005).
19. C.J.M. Northrup, Jr., “The Hydrogen-Uranium System,” Journal of Physical Chemistry, 79,
pp.726-731 (1975).
20. E. Wicke, K. Otto, “The Uranium Hydrogen System and the Kinetics of Hydride Formation,”
Z. Phys. Chem., Neue Folge, 31, pp.222-248 (1962)
21. M. W. Mallett, I. E. Campbell, “The Dissociation Pressure of Thorium Dihydride in the
Thorium-Thorium Dihydride System,” Journal of the American Chemical Society, 73,
pp.4850-52, (1951).
22. ‘W. Wang, D.R. Olander, “Thermodynamics of the Zr-H System,” Journal of American
Ceramic Society, 78 [12], pp.3323-28 (1995).
23. W. Bartscher, J. Rebizant, “Equilibrium and Thermodynamics Properties of The ThZr2-H
System,” Journal of the Less Common Metals, 136, pp.385-394, (1988).
153
4.3 Transient Hydride Fuel Behavior in LWRs
3.3.1
Introduction
Hydride nuclear fuels (uranium-zirconium hydride) have been successfully utilized in many
research and test reactors as well as space programs. The added presence of hydrogen in the fuel
provides neutron moderation within the fuel in addition to the traditional moderator. This allows
displacement of moderator with fuel, effectively increasing power density. Hydride fuels also
have a higher thermal conductivity than oxide fuels and feature a fuel-temperature-driven
reactivity feedback due to fuel hydrogen neutron scattering; the latter effect accompanies
Doppler feedback. Hydride fuel has also been proposed as an optimized matrix for the deep burn
of plutonium and minor actinides. The proposed fuel could achieve TRU (transuranic elements)
destruction fractions as high as twice that realized within MOX (mixed oxide) fuels [1].
Uranium - zirconium hydride fuel consists of metallic α-U phase dispersed in a δ-ZrH1.6 matrix.
The fuel is typically fabricated by massive hydriding of uranium zirconium alloys formed by arc
melting of the metal components. Uranium inside the fuel remains metallic since the equilibrium
partial pressure of the UH3 phase at fuel processing temperatures is very high (pH2 = 1atm for
UH3 at ~700K, where hydriding temperatures range from 800K – 1200K). Maximum heavy
metal loading inside the fuel is limited to 45 vol% uranium which corresponds to the fuel
composition of U0.31ZrH1.6. During operation of the reactor, the temperature gradient across the
fuel drives the hydrogen to the cooler regions due to the large heat of transport of hydrogen in
the δ-ZrH1.6 phase (TQ = 640K) [2]. Thermal conductivity of the fuel is a function of both
temperature and hydrogen concentration, with a stronger dependence on the latter. The
volumetric heat capacity has the same dependencies; however its dependence on the temperature
is more marked. Hydrogen diffusivity is an exponential function of temperature with a small
dependence on hydrogen concentration (site blocking by other hydrogen atoms during stochastic
jumps).
It is therefore necessary to couple the heat conduction to the hydrogen diffusion in order to
achieve accurate results in predicting the temperature and hydrogen concentration profiles both
under steady state and transient operating conditions. Accurate modeling of the coupled transient
behavior will provide detailed information of the stress across the fuel as well as the necessary
information for predicting the possibility of excessive hydrogen release from the fuel during
accidents.
3.3.2
Methodology
3.3.2.1 Hydride fuel properties
3.3.2.1.1
Thermal conductivity and volumetric heat capacity
The fuel is a composite structure of metallic α-uranium dispersed in a δ-zirconium hydride
matrix. The thermal conductivity of the fuel can be calculated as the product of thermal
diffusivity, density, and specific heat capacity of the composite material. These properties can
be estimated using the rule of mixtures where thermal diffusivity and density are estimated on
volume fraction basis and heat capacity on mass fraction basis, respectively. Therefore the
overall thermal conductivity of the fuel can be estimated using the thermal properties of uranium
as a function of temperature and zirconium hydride as a function of both temperature and H/Zr
154
ratio [3,4,5,6] as shown in Equation 11 (Fig. 1a). A similar approach can be used to determine the
volumetric heat capacity of the fuel as function of temperature and H/Zr ratio in the composite
fuel (Fig. 1b). The influence of burnup on these properties is unknown and therefore this analysis
is applicable only to fresh fuel. Thermal conductivity is however expected to decrease as
function of burnup since hydride fuel experiences large swelling rates, especially at low burnups.
Hydride fuel also has good fission gas retention properties indicating that voids containing noble
gases are form during operation. This is related to swelling and will further deteriorate the
thermal conductivity.
⎞
κ ZrH1.6
ρ
C
⎛
⎞⎛
⎞⎛
k Fuel = kU ⎜ vU +
(1 − vU ) ⎟⎜ vU + ZrH1.6 (1 − vU ) ⎟ ⎜⎜ wU + p ,ZrH1.6 (1 − wU ) ⎟⎟
κU
ρU
C p ,U
⎝
⎠⎝
⎠⎝
⎠
(1)
Thermal Conductivity [W/cm.K]
1.8 0. 0.2
1.75
1.65
0.23
0.22
0.2
0. 22
0.21
0.19
0. 2
5
0.1
0.
16
0.18
0.1
7
14
0.
1.5
0.23
0.21
0.
18
1.6
1.55
0.25
0.24
17
0.
H/Zr Ratio []
1.7
0.25
23 4
0.2
2
0.
21
0.
2
0.
19
3
0.1 12
0
0.1
6
1.45
1.4
300
500
0.1
8
0.1
7
0.1
5
400
0.1
9
600 700 800
Temperature [K]
1
900
1000
Refer to the Table of notations in Section 6 for a description and respective units of all the variables
discussed in the Equations throughout this paper.
155
3
Volumetric Heat Capacity [J/cm .K]
1.8
4
4.2
1.75
1.7
3.6
3.8
3.2
3.4
3.6
1.6
4
H/Zr Ratio []
3.4
3
3
3.2
2.8
2.6
2.4
2.2
2
1.65
1.55
1.5
500
600 700 800
Temperature [K]
900
3.8
2.8
400
2.6
2.4
2
1.4
300
2.2
1.45
1000
Figure 1. Thermal conductivity and volumetric heat capacity of the U0.31ZrHx fuel as functions of
temperature and H/Zr ratio.
3.3.2.1.2
Hydrogen diffusivity
The diffusivity of hydrogen in zirconium hydride has been measured over a relatively large range
of temperatures and hydrogen concentrations by Majer et al. [7]. The only set of data
corresponding to δ phase zirconium hydride (H/Zr ratio = 1.58) yields the diffusion coefficient
as:
⎛ -58.8 ⎞
D = 1.53 × 10 −3 exp ⎜
⎟
⎝ RT ⎠
(2)
The Einstein diffusion model describes the diffusion coefficient as the following:
D=
1 λ2
6 τ
(3)
where λ is the jump distance of the diffusing species and τ is the mean residence time in each site
before a jump. The mean residence time is inversely proportional to the product of the number
of available adjacent jump sites (η) and the jump frequency. The jump frequency is the product
of vibration frequency of the species in that site (υ) with an Arrhenius factor that determines the
probability of each vibration leading to a successful jump. Therefore, the pre-exponential factor
in the diffusion coefficient can be expressed as:
1
Do = λ 2ηυ
6
(4)
η is the product of the number of adjacent jump sites (6, since hydrogen is on a simple cubic
lattice inside the face centered cubic Zr unit cell where the overall structure corresponds to a Fd3m space group) with the probability that the site is not currently occupied by another hydrogen
atom. This probability can be determined from the stoichiometry and structure of the system; the
pre-exponential term can therefore be estimated as:
156
1
⎛ C⎞
Do = λ 2 6 ⎜ 1 − ⎟υ
6
2⎠
⎝
(5)
Activation energy for diffusion is essentially independent of hydrogen concentration, assuming
the mechanism of diffusion doesn’t change in the range of interest (H/Zr ratio from 1.5 to 1.7).
The final expression that is used for the diffusion coefficient of hydrogen in δ-ZrHx is the
following:
⎛ C⎞
⎛ -58.8 ⎞
D = 7.29 ×10−3 ⎜1 − ⎟ exp ⎜
⎟
2⎠
⎝
⎝ RT ⎠
(6)
3.3.2.2 Heat conduction model
The transient radial heat equation for an axial slice of fuel with internal heat generation and
variable properties is shown below:
∂
( ρC pT ) = 1r ∂∂r ⎜⎝⎛ kr ∂∂Tr ⎟⎠⎞ + q&′′′
∂t
(7)
All terms are treated as radially and temporally variant except for the internal heat generation
which is approximated as spatially uniform. The validity of this assumption is addressed in
detail in the discussion section 4.3. The steady-state solution defines the initial condition and the
time-dependant heat generation drives the model. The two necessary boundary conditions are
zero heat flux at the fuel centerline and a fuel surface temperature that depends on the coolant
temperature and the conductance between. This second relation is shown below.
TR f ( t ) = −
kR f ( t ) ⎛ ∂T ⎞
+ T∞
⎜
⎟
h ⎝ ∂r ⎠ R f ,t
(8)
where the heat conductance, h, is defined as:
⎛ δ
ln ⎜ 1 + gap
⎜
Rf
1
= Rf ⎝
h
k gap
⎞
⎛
δ clad
ln ⎜ 1 +
⎟⎟
⎜ R +δ
⎠ + R +δ
( f gap ) ⎝ k f gap
clad
⎞
⎟⎟
⎠+ 1
hhyd
(9)
A semi-implicit Crank-Nicolson scheme is used for discretization [8] whereby time is discretized
with the trapezoid rule and space with the central difference formula, obtaining inherent stability
and second order accuracy. At first glance, the solution might require an iterative predictorcorrector algorithm since the unknown iterate is not known explicitly. However, if the extra
effort is made to form the relation into a linear system, the problem is transformed into solving a
sparse linear system of equations at each time-step. Fortunately, MATLAB® contains LAPACK,
a library of linear algebra subroutines that solves linear systems such as these quickly and
accurately. The full discretization of the heat equation can be found in Appendix A.
3.3.2.3 Hydrogen diffusion model
The driving force for flux of hydrogen atoms across the fuel exists due to temperature and
concentration gradients across the pellet. The radial flux is equal to:
⎛ dC TQC dT ⎞
J r = − DN Zr ⎜
+ 2
⎟
⎝ dr T dr ⎠
157
(10)
After relating the flux and concentration in a conservation equation such as in Huang et al. [9],
an explicit time-discretization scheme is used since the rate of change of the concentration is
small and linearization introduces only small errors. Flux at the surface of the fuel is
approximated to be zero; the accuracy of this simplification is addressed in section 4. In the
conservation equation, the fluxes are multiplied by a ratio of surface area and volume which
correspond to the surface through which the flux is passing and the volume of fuel in which
hydrogen resides. Since hydrogen exists only in the δ-ZrHx phase (the flux of hydrogen atoms in
the α-U phase is negligible [9]), this area to volume ratio is weighted by the fraction of this phase
(~0.9). The fully-expanded discretized diffusion equation and its derivation can be found in
Appendix B.
3.3.2.4 Coupling Algorithm
As mentioned earlier, there is a high degree of interdependency of the pertinent variables. The
heat equation for temperature depends on thermal conductivity and volumetric heat capacity.
The hydrogen diffusion equation depends on temperature, hydrogen concentration, and
diffusivity. The diffusivity, thermal conductivity, and volumetric heat capacity all depend on
temperature and hydrogen concentration.
The following operator splitting algorithm is used for each time-step. The heat equation is semiimplicitly solved for the current temperature using properties from the previous time-step and
extrapolated properties for the current time step (see Appendix A). Next, the hydrogen
concentration is explicitly calculated for the current time-step using parameters only at the
previous time-step (see Appendix B). Third, the diffusivity, thermal conductivity, and
volumetric heat capacity are updated with the current temperature and hydrogen concentration.
This process is shown in Figure 2 where arrows denote inputs, circles are variables (dashed lines
denote the previous time step), rectangles are equations, pentagons are boundary conditions, and
the hexagon is power density (assumed independent of other variables).
Before the transient solution algorithm is run, the steady-state equations are solved using a
similar process with a relative error tolerance for convergence of 103 times machine precision.
q& ''' ( t )
T
Heat
Equation
k
ρCp
C
D
T
=0
TTRSf ((tt))
∇C r = 0 = 0
DR =0
∇T
r =0
Diffusion
Equation
Eqn. 1
k
Eqn. 1
ρCp
Eqn. 6
D
f
C
T
Figure 2. A single time-step in the solution algorithm.
158
3.3.2.5 Stress Calculation
The two sources of strain in the material arise from temperature and hydrogen concentration
gradients across the fuel. Olander [10] reported the linear coefficient of expansion of hydrogen
as β=0.027 per unit change of H/Zr ratio in ZrHx. The temperature dependent coefficient of
thermal expansion of the zirconium hydride has been reported as α = 3.36 ×10−6 ⎡⎣1 + 4.40 ×10−3 T ⎤⎦ per
unit change of temperature in Kelvin [11]. The elastic modulus of zirconium hydride is
approximately 130 GPa in the temperature range of interest [12]. The elastic modulus of the
composite fuel is obtained using the rule of mixtures as 145GPa (vol% α-U = 19.4). With a
similar analysis, the Poisson ratio for the composite is 0.3 (να-U = 0.23, νZrH1.6 = 0.32 [12]). Total
strain in the fuel is the sum of elastic, thermal and hydrogen strains. The constitutive equations
in the axi-symmetric cylindrical coordinates are then presented as:
εr =
1
⎡σ r −ν (σ θ + σ z ) ⎤⎦ + α ( ΔT ) + β ( ΔC )
E⎣
(11)
εθ =
1
⎡σ θ −ν (σ r + σ z ) ⎦⎤ + α ( ΔT ) + β ( ΔC )
E⎣
(12)
εz =
1
⎡σ z −ν (σ θ + σ r ) ⎤⎦ + α ( ΔT ) + β ( ΔC )
E⎣
(13)
Eliminating the displacement vectors in the definition of cylindrical strains, the relationship in
Equation 14 is obtained. Using the constitutive equations coupled with this condition and also
assuming a plane strain scenario in the axial direction, a differential equation governing the
radial stress across the fuel is determined (Eqn. 15). The fuel is assumed initially restrained in the
axial direction (the plain strain assumption); later by application of Saint Venant’s principle the
unrestrained axial stress is determined [13]. The two necessary boundary conditions are a zero
stress gradient at the fuel centerline and zero radial stress at the fuel surface.
d εθ εθ − ε r
+
=0
dr
r
1 d ⎛ 3 dσ r
⎜r
r 2 dr ⎝
dr
(14)
dC
⎞ −E ⎡ d
(α T ) + β ⎤⎥
⎟=
dr ⎦
⎠ 1 −ν ⎢⎣ dr
(15)
The radial equilibrium condition in cylindrical coordinates (Eqn. 16) is used to calculate the
azimuthal stress across the fuel based on the radial stress.
σθ =
∂
( rσ r )
∂r
(16)
To determine the distribution of axial stress across the fuel, the axial stress is first calculated
assuming complete restraint in the axial direction (εz = 0). Then the difference from the average
of this quantity across the fuel is denoted as the actual magnitude of axial stress (Saint Venant’s
principle). For complete set of calculations showing the derivation of different stress components
please refer to Appendix C.
Simpson and Cann [14] report the mode I fracture toughness of δ-zirconium hydride as 3
MPa.m½ at 573 K. Ductile phase toughening in the fuel due to the presence of uranium particles
is expected by crack bridging and process zone toughening mechanisms. By conservatively
ignoring such effects, linear elastic fracture mechanics can be applied. However finite element
methods are necessary to predict the evolution of flaw size in the material due to the complex
state and distribution of stress and are beyond the scope of this work. An adequate scheme would
159
be to artificially assign cracks to different regions of the material that would in turn correspond
to dissimilar states of stress. The progression in flaw size and geometry that correspondingly
depends on the evolution of the changing stress state can then be studied.
3.3.2.6 Model physical parameters
The model was composed of a fuel element 1 cm in diameter, housed inside a Zircaloy cladding
of 0.9 mm in thickness, with a 70 μm molten lead-tin-bismuth (Pb-33.3wt%Sn-33.3wt%Bi) gap
in between. The gap and cladding were not modeled explicitly but instead were introduced as
the outer boundary condition along with the hydraulic conditions. The conductivities used for
the liquid-metal (LM) gap and clad were 0.20 W/cm.K [15] and 0.16 W/cm.K [16], respectively.
The thermal-hydraulic heat transfer coefficient was estimated using the Presser correlation for
the Nusselt number with the typical geometry and operating parameters of a PWR, resulting in
an approximate value of 1 W/cm2.K. The bulk coolant temperature was 575 K and the pitch to
diameter ratio was 1.2. The fuel-averaged H/Zr ratio was 1.6.
3.3.3
Results
3.3.3.1 Steady state results
The steady-state calculations were conducted with 500 spatial nodes at linear heat rates (LHR) of
100, 200, and 300 W/cm. The results of the steady state temperatures, H/Zr ratios, and axial
stress distributions are shown in Figures 3a, 3b, and 3c respectively.
Steady-State Distribution: Temperature
840
100
200
300
820
800
Temperature [K]
780
760
740
720
700
680
660
Linear Heat
Rate
640
0
0.1
0.2
0.3
Radius [cm]
160
0.4
0.5
Steady-State Distribution: H/Zr Ratio
1.7
1.68
1.66
H/Zr Ratio []
1.64
1.62
1.6
1.58
Linear Heat
Rate
1.56
100
200
300
1.54
1.52
0
0.1
0.2
0.3
Radius [cm]
0.4
0.5
Steady-State Distribution: Axial Stress
100
200
300
Axial Stress [MPa]
200
100
0
Linear Heat
Rate
-100
-200
-300
0
0.1
0.2
0.3
Radius [cm]
0.4
Figure 3. Top to Bottom: steady-state temperature, H/Zr ratio, and axial stress distributions at
LHRs of 100, 200, and 300 W/cm.
As expected, the fuel temperature gradient and outer fuel temperature increase with LHR. The
hydrogen concentration gradients are also steeper with increasing LHR. With a LM bonded fuel,
even though the average temperature is lower when compared to the conventional He gap fuel,
the extent of hydrogen redistribution is more severe (as reported by Olander [10]). This has been
confirmed by the model but is not shown in this paper. This trend is justified by inspection of the
flux governing equation where the T-2 dependence of the temperature gradient term enhances its
impact at lower temperatures.
The largest component of stress is the axial stress, whose value is influenced by the temperature
and hydrogen concentration gradients in an opposing manner. However, hydrogen-induced
stresses are the dominant component, as is evident from the steady state results. Generally, the
fuel surface experiences severe compression from axial and azimuthal components of stress,
while all three components of stress are tensile at the central region of the fuel. Even though the
161
hydrogen redistribution is larger with increasing LHR, the magnitude of stress might not increase
due to larger thermally induced strains.
3.3.3.2 Transient results
A parametric transient case study was completed with a nominal LHR and coolant temperature
of 300 W/cm and 575K, respectively. The power was pulsed to twice the nominal value for 2.5s
and then dropped to 5% while the coolant temperature and fuel-to-coolant conductance remained
constant. This represents a simplified and exaggerated reactivity insertion accident (RIA) with a
large pulse height, a long pulse width, and a subsequent SCRAM. The hydrogen redistribution,
although present, is miniscule since the hydrogen diffusivity is orders of magnitude smaller than
the thermal diffusivity (~2x10-8 cm2/s compared to ~6x10-2 cm2/s). Consequently, only the
resultant spatial fuel temperature and axial stress distributions are shown in Figure 4a and 4b
respectively.
RIA: Temperature [K]
0.45
0
80
0
77
0.4
770
0
86
83
0
0
80
0
83
800
0.25
71 0
Radius [cm]
0
74
0.35
0.3
0
68
0
71
0
77
740
0.2
89 0
86 0
830
92 0
1
2
3
800
920
0.05
74 0
86 0
0.1
77 0
89 0
0.15 830
4
5
Time (s)
RIA: Axial Stress [MPa]
-3 00
0.45
-2 25
-2 25
-1 50
-150
Radius [cm]
0.3
-3 75
-7 5
0.4 -75
0.35
-3 00
-1 50
-75
0
0
0
75
75
75
15 0
0.25 150
22 5
0.2
0
15
15 0
0.15 225
1
2
3
4
37 5
30 0
22 5
0.05
225
0.1
5
Time (s)
Figure 4. Fuel temperature and axial stress response to RIA
162
The fuel temperature directly follows the power pulse, rapidly peaking as the power jumps and
then relaxing down after the SCRAM. The stress response of the fuel is interesting in that the
axial stress is actually lowered and flattened during the power pulse. This is caused by the
increased thermal stresses that counteract the dominating stresses created by the hydrogen
concentration gradient. As the fuel cools during the SCRAM portion, the hydrogen-induced
stresses remain unopposed and the overall stress increases. Figure 5 shows the maximum fuel
temperature for various pulse heights and durations induced on a fuel operating with nominal
linear heat rate of 300 W/cm.
Maximum Fuel Temperature [K]
91
5
1.7
1.6
1.5
1.4
86
5
84 5
87
5
88
5
1.3
1.2
86 5
1.1
1
89
5
5
85
Pulse Magnitude [X Full Power]
5
92
5
90
5
89
5
88
85 5
1.8
87 5
86 5
1.9
845
2
85 5
1
84 5
2
3
Pulse Duration [s]
4
5
Figure 5. Maximum fuel temperature during power pulse.
3.3.4
Discussion
3.3.4.1 Comparison of constant to variable properties
Table 1 summarizes the relative percent error one would accrue by using material properties that
are independent of temperature and hydrogen concentration for a steady-state solution. The
constant values used for thermal conductivity and volumetric heat capacity were 0.16 W/cm.K
and 2.3 J/cm3.K. Results are shown for LHRs of 100, 200, and 300 W/cm.
Although the relative percent errors may seem small, a 3% relative difference amounts to 30 K at
a temperature of 1000 K. Also, at 100 W/cm, the overshoot in temperature and undershoot in
H/Zr ratio at the fuel centerline would bring about a significant error in the axial stress. A
moderate discrepancy in any of these terms may have a significant effect on the overall fuel
behavior.
3.3.4.2 Extent and effect of hydrogen desorption
The extent of hydrogen release from the LM bonded fuel is unknown. However, it is believed to
be smaller when compared to the case of fuel gap filled with helium (He), since the hydrogen is
readily released from the surface into a much larger volume and the gas phase solubility is
infinite. For perspective, it is appropriate to study fuel with a He filled gap. The extent of release
can then be estimated by the equilibrium partial pressure of hydrogen inside the cladding, which
163
can be expressed as a function of temperature and fuel surface hydrogen concentration according
to Wang et al. [17] as:
⎛ Ceq
P [atm] = ⎜
⎜ 2−C
eq
⎝
2
⎞
⎛
2.07 × 104 ⎞
⎟⎟ exp ⎜⎜ 8.01 + 5.21Ceq −
⎟
T [ K ] ⎟⎠
⎝
⎠
(17)
The free volume inside the cladding due to the plenum volume and gap is approximately 40 cm3.
Assuming a pre-pressurization to 1 MPa of He, the total pressure in the cladding can be
calculated as the sum of partial pressures of hydrogen and helium that in turn obey the ideal gas
law. Therefore equilibrium pressure inside the cladding as function of temperature and H/Zr
ratio at the fuel surface could be estimated as shown in Figure 6a. The plenum and gap are
conservatively assumed to be at the fuel surface temperature. The amount of hydrogen within
each fuel rod is approximately 25 moles. The equilibrium fractional loss of this amount as
function of fuel surface temperature and H/Zr ratio at the fuel surface is also shown in Figure 6b.
Adsorption of hydrogen on the inner surface of cladding and its subsequent diffusion into the
cladding is ignored. Over time however, this will result in a larger fractional release of hydrogen
into the cladding.
3.3.4.3 Magnitude and effect of power depression
A pin cell model was built in MCNP (Monte Carlo N-Particle Transport Code) to determine the
steady state power profile during the reactor operation so the accuracy of the uniform power
approximation could be addressed. The steady state temperature and hydrogen concentration
results with the uniform power LHR of 300 W/cm were used as input for the cross-sections and
number densities of the MCNP model. The power was tallied in 10 radial shells of the fuel. The
resultant power profile was used to update the heat and Hydrogen diffusion model and the
process was iterated until convergence.
Equilibrium Internal Cladding Pressure [MPa]
1. 1
1.01
1.001
1.000 1
1.78
16
1.8
2
4
1.76
1.72
1.1
1.01
2
4
1.68
1.001
1.7
1.000 1
H/Zr Ratio []
8
1.74
1.66
1.64
1.1
900
1000
1100
Temperature [K]
164
2
800
1.01
1.6
700
1.001
1.62
1200
Fraction of Hydrogen Released from Fuel
1.8
1.76
01
0.0
00 1
0. 0
05
1e -0
06
1e -0
7
1e -00
1.78
1e -008
1.72
1
1.68
0
0.00
1.7
05
1e -0
6
1e -00
7
1e -00
H/Zr Ratio []
1.74
1e -008
1.66
1.64
900
1000
1100
Temperature [K]
1
800
0
0. 00
1.6
700
05
1e -0
6
1e -00
1.62
1200
Figure 6. Top: equilibrium total pressure inside the cladding [MPa]. Bottom: total fraction of
hydrogen inside the fuel lost to the gaseous phase inside the cladding in equilibrium.
The normalized power profile for the first iteration is shown in Figure 70. The maximum
difference between the uniform and depressed power profiles is around 2% and it changes the
centerline temperature by 2.25 K, or ~0.8% of the fuel centerline to coolant temperature drop.
Its effects on the Hydrogen concentration and stresses are even smaller, leaving one to conclude
that the uniform power profile is a good assumption.
Normalized Power Profile at 300 W/cm
1.03
Normalized Power
1.02
1.01
1
0.99
0.98
Average
Quadratic Fit
MCNP
0.97
0
0.1
0.2
0.3
Radius [cm]
0.4
0.5
Figure 7. Distribution of the power profile across the fuel operated at 300 W/cm linear heat
rate
165
3.3.5
Conclusions
Steady state and transient behavior of several aspects of the fuel operating performance have
been investigated, taking into account the temperature and hydrogen concentration dependence
of the fuel properties.
Steady state temperature, hydrogen concentration, and stress profiles of the hydride fuel operated
at various linear heat rates have been calculated. The extent of hydrogen redistribution, driven
by the gradient in temperature, becomes more severe as the power increases. Strains in the fuel
occur from thermal and hydrogen concentration gradients, with the latter being the dominant
contributor. Axial and azimuthal stresses are both compressive at the surface and tensile at the
fuel centerline. These results are in agreement with what was previously shown by Olander,
where the dependence of fuel properties (except the coefficient of thermal expansion) on
temperature and hydrogen concentration were ignored [10]. The fuel fracture criterion is
unknown and needs be determined through finite element methods.
The transient response of hydride fuel to a reactivity insertion accident scenario was studied by
artificially pulsing power in a square wave. The thermal response of the fuel to the changing
boundary conditions is very rapid (on order of few seconds) due to the small fuel rod and large
thermal diffusivity. There is no discernable alteration in the transient hydrogen profile, since the
characteristic diffusion time for these length scales is many orders of magnitude larger than the
transient durations. However, it is necessary to model the hydrogen diffusion since it is important
to know the steady-state distribution for the initial conditions. Surprisingly, the stress across the
fuel is actually reduced during the power pulse. The temperature-induced stresses counteract the
hydrogen-induced stresses, so the fuel is in its most relaxed state during this stage of the
transient. The fuel experiences maximum stress when temperature gradients diminish but the
hydrogen displacement remains at the pre-transient distribution.
The flux of hydrogen atoms, in a fuel assembly with a He filled gap, out of the fuel during steady
state and transient operation of the fuel is very small since the net rate (desorption – adsorption)
quickly becomes zero when the equilibrium hydrogen partial pressure is established. The
pressure buildup inside the cladding and the total fraction of hydrogen lost from the solid state to
the cladding volume are negligible even at very high fuel surface temperatures. The extent of
dehydriding is expected to be even less for LM bonded fuels.
3.3.6
Acknowledgements
The authors wish to thank Professor Per Peterson for helpful discussions and comments.
3.3.7
Notation
Symbol
k
v
w
κ
ρ
Cp
T
&
q′′′
Quantity (Units)
Thermal conductivity (W/cm.K)
Volume fraction
Mass fraction
Thermal diffusivity (cm2/s)
Mass density (kg/cm3)
Specific heat capacity (J/gr.K)
Temperature (K)
Volumetric heat generation rate (W/cm3)
166
TRf
h
T∞
δ
J
D
λ
τ
η
υ
NZr
C
TQ
S
β
α
εr, εθ, εz
σr, σθ, σz
E
ν
R
kDH
Fuel surface temperature (K)
Heat transfer coefficient (W/cm2.K)
Coolant temperature (K)
Cladding/gap thickness (cm)
Radial flux (cm-2/s)
Macroscopic diffusion coefficient (cm2/s)
Jump distance during diffusion (cm)
mean residence time in each lattice site(s)
number of available adjacent jump sites
Vibrational frequency inside lattice (s-1)
Zirconium number density in δ-ZrH1.6
Phase (atoms/cm3)
H/Zr ratio in ZrHx
Heat of transport of H in δ-ZrH1.6 (K)
surface area/volume of shell (cm-1)
coefficient of expansion of hydrogen
coefficient of thermal expansion (K-1)
radial, azimuthal, and axial strain
radial, azimuthal, and axial stress (MPa)
Elastic (Young’s) modulus (GPa)
Poisson’s ratio
Gas constant (kJ/mole.K)
Dehydriding rate (mole/cm2.s)
4.3.8 APPENDIX A
The radial heat equation with variable properties is a non-linear partial differential equation
(Eqn. 7), so discretization must be done carefully. A well known procedure is that of Crank and
Nicolson [8], in which time is discretized with the trapezoid rule and space with central
difference. This first step is shown below:
1
Δt
( ( ρC T )
p
j +1
i
− ( ρ C pT )
j
i
) = 12 ( q&′′′
i
j +1
+ q&i′′′ j ) +
j +1
j +1
j
j
⎡
⎤
1 1 ⎢⎛ ∂T ⎞
⎛ ∂T ⎞
⎛ ∂T ⎞
⎛ ∂T ⎞ ⎥
⎜ rk
⎟ − ⎜ rk
⎟ + ⎜ rk
⎟ − ⎜ rk
⎟
2 ri Δr ⎢⎝ ∂r ⎠ri+ 1 ⎝ ∂r ⎠ ri− 1 ⎝ ∂r ⎠ ri+ 1 ⎝ ∂r ⎠ ri− 1 ⎥
2
2
2
2 ⎦
⎣
(A1)
where i and j indicate the radial node and time step, respectively. All terms are considered as
node-centered. The equation is expanded and shuffled more:
(( ρC )
j +1
p i
ri − 1
ri + 1
ri − 1
⎡ ri + 1
⎤
j
2
Ti j +1 − ( ρ C p ) Ti j = QΔt + ω ⎢ 2 ki +j +11 (Ti +j1+1 − Ti j +1 ) − 2 ki −j +11 (Ti j +1 − Ti −j1+1 ) +
ki +j 1 (Ti +j1 − Ti j ) − 2 ki −j 1 (Ti j − Ti −j1 ) ⎥
i
2
2
2
2
ri
ri
ri
⎢⎣ ri
⎥⎦
)
(A2)
where the following terms and notations are defined and used for convenience:
Q=
1
( q&i′′′ j +1 + q&i′′′ j )
2
ω=
ki ± 1 =
2
Δt
2Δr 2
(A3)
(A4)
1
( ki ±1 + ki )
2
(A5)
Since a marching procedure is performed with time, solving for the j+1st iterate from the known
jth iterate, the thermal conductivity and volumetric heat capacity at the j+1st time step are not
known as they depend on both temperature and hydrogen concentration. Further, the functional
dependencies are highly non-linear. Initially, predictor-corrector iterations were performed at
each time step, requiring substantial increases in run-time. Newton-Raphson methods were also
167
considered but were deemed too laborious. A final, simpler method that produces results with
essentially no difference is a first-order Taylor extrapolation of the material properties using the
jth and j-1st values. This procedure is outlined below:
∂k j
k j − k j −1
≈ k j + Δt
= 2k j − k j −1
∂t
Δt
k j +1 ≈ k j + Δt
( ρc )
j +1
p
≈ 2 ( ρcp ) − ( ρcp )
j
j −1
(A6)
(A7)
The node-centered radius terms are also expanded accordingly:
(
ri = Δr i − 1
ri ± 1
2
ri
2
ri ± Δr
) (A8)
Δr
2 = 1 ± Δr = 1 ±
2ri
ri
2 Δr i − 1
=
(
2
)
= 1±
1
2i − 1
(A9)
Utilizing these enhancements, the final form of the semi-implicitly discretized heat equation is
acquired:
⎧
⎡ ρ c j +1
⎤ ⎫ ⎧ ⎡ ρc j
⎤⎫
⎪T j +1 ⎢ ( p )i + ⎛ 1 + 1 ⎞ k j +1 + ⎛1 − 1 ⎞ k j +1 ⎥ ⎪ ⎪T j ⎢ ( p )i − ⎛ 1 + 1 ⎞ k j − ⎛ 1 − 1 ⎞ k j ⎥ ⎪
i −1/ 2
i
i +1/ 2
i −1/ 2
i
i +1/ 2
⎜
⎟
⎜
⎟
⎜
⎟
⎜
⎟
⎪⎪
⎥ ⎪⎪ QΔt
⎢ ω
⎥ ⎪⎪ ⎪⎪ ⎢ ω
⎝ 2i − 1 ⎠
⎝ 2i − 1 ⎠
⎝ 2i − 1 ⎠
⎝ 2i − 1 ⎠
⎦⎬ +
⎣
⎦ ⎬=⎨ ⎣
⎨
ω
⎪
1 ⎞ j +1 ⎤
1 ⎞ j +1 ⎤ ⎪ ⎪ j ⎡⎛
1 ⎞ j ⎤
1 ⎞ j ⎤ ⎪
j ⎡⎛
j +1 ⎡ ⎛
j +1 ⎡ ⎛
⎪
⎪
⎪+Ti +1 ⎢ − ⎜1 +
⎪
T
k
T
k
1
1
k
T
k
1
+
+
+
−
+
−
−
i +1 ⎢⎜
⎟ i +1/ 2 ⎥ i −1 ⎢⎜
⎟ i −1/ 2 ⎥
⎟ i +1/ 2 ⎥ i −1 ⎢ ⎜
⎟ i −1/ 2 ⎥
⎪⎩
⎣⎝ 2i − 1 ⎠
⎦
⎣⎝ 2i − 1 ⎠
⎦ ⎭⎪
⎣ ⎝ 2i − 1 ⎠
⎦
⎣ ⎝ 2i − 1 ⎠
⎦ ⎪⎭ ⎩⎪
(A10)
4.3.9 APPENDIX B
The hydrogen mass balance equation can be written for a differential radial shell in terms of the
flux within the fuel as the following:
cij +1 = cij + ⎡ J i −j 1 Si − 1 − J i +j 1 Si + 1 ⎤ Δt
⎢⎣
⎦
2
2
2
2⎥
(B1)
where c is the molar concentration of hydrogen in mole H/cm3; J is the hydrogen atom flux
specified earlier in equation 10. S is the ratio of inner/outer surface of each radial shell to its
volume with units of cm-1:
Si ± 1 =
2
(
2π ri ± 1 l
2
π r2 − r2
i+ 1
i− 1
2
2
)l
=
(
2 ri ± Δr
2
)
(B2)
⎛
⎞
⎜ ⎡ ri + Δr 2 ⎤⎦ − ⎡⎣ ri − Δr 2 ⎤⎦ ⎟
⎝⎣
⎠
2
2
After substituting Eqn. A9 and simplifying, B2 becomes:
Si ± 1 =
2
(
2 ri ± Δr
)
2 =
( 2ri Δr )
⎧
⎪− →
Δr
⎪
ri =Δr ( i − 1 )
2 ⎯⎯⎯⎯→
2
⎨
ri Δr
⎪+ →
⎪
Δr
⎩
ri ± Δr
i −1
(i − 12 ) (B3)
i
( i − 12 )
The atomic ratio of hydrogen to zirconium is:
Ci j =
M Zr
ρ Zr
cij
(B4)
Substituting for Equations B3, B4, and 10, Equation B1 generates the following result:
168
Ci j +1
ρ Zr
M Zr
= Ci j
ρ Zr
M Zr
⎡
ρ
+ ⎢ − Di −j 1 Zr
⎢
2 M
Zr
⎣
j
⎧ j
⎫
j
i −1
ρ
⎪ Ci − Ci −1 TQ Ci − 12 Ti − Ti −1 ⎪
+
+ Di +j 1 Zr
.
⎨
⎬
2
2
1
−
−
r
r
T
r
r
M
Δ
−
i
i −1 ⎪ r i
Zr
⎪⎩ i i −1
i− 1
⎭
2
2
(
)
j
⎤
⎧ j
⎫
j
i
⎪ Ci +1 − Ci TQ Ci + 1 2 Ti +1 − Ti ⎪
⎥ Δt
+
.
⎨
⎬
2
Ti + 1
ri +1 − ri ⎪ i + 1 Δr ⎥
⎪⎩ ri +1 − ri
⎭
2
2
⎦
(
)
(B5)
Further simplification of the above results in the fully explicit discretization for H/Zr ratio as:
⎡
⎧
⎫⎤
j
j
⎢
Δt j
i
⎪⎪ TQ (Ti +1 − Ti ) ⎪⎪⎥
−
1
⎢1 − 0.9 2 Di + 1
⎨
⎬⎥
2
2 i+ 1
Δr
⎡
⎢
⎪
⎪⎥
2 Ti +j 1
2
⎢
⎪⎭⎥
2
Δt j
i
⎩⎪
j +1
j ⎢
j
Ci = Ci ⎢
⎥ + Ci +1 ⎢ 0.9 2 Di + 12
1
Δr
⎧
⎫
+
i
⎢
⎢
⎥
j
j
2
⎢⎣
Δt j
i − 1 ⎪⎪ TQ (Ti − Ti −1 ) ⎪⎪ ⎥
⎢
⎨1 +
⎬ ⎥
2
⎢ −0.9 Δr 2 Di − 12
i− 1 ⎪
⎪ ⎥
2 Ti −j 1
⎢
2 ⎪
2
⎩
⎭⎪ ⎦
⎣
(
)
(
⎡
⎢
Δt
i −1
+C ⎢0.9 2 Di −j 1
2 i− 1
⎢ Δr
2
⎢⎣
j
i −1
(
( )
)
)
(
( )
)
⎧
⎫⎤
j
j
⎪⎪ TQ (Ti +1 − Ti ) ⎪⎪⎥
⎨1 +
⎬⎥
2
⎪
⎪⎥
2 Ti +j 1
2
⎩⎪
⎭⎪⎥⎦
( )
(B6)
⎧
⎫⎤
⎪⎪ TQ (Ti j − Ti −j1 ) ⎪⎪⎥
⎨1 −
⎬⎥
2
⎪
⎪⎥
2 Ti −j 1
⎪⎩
⎪⎭⎥⎦
2
( )
4.3.10 APPENDIX C
Equation 15 for the radial stress is first discretized with central difference:
⎛
1 1 ⎜ 3 dσ r
r
2
ri Δr ⎜⎜
dr
⎝
− r3
r
i+ 1
dσ r
dr
2
r
i− 1
2
⎞
⎟ = −E
⎟⎟ 1 −ν
⎠
⎡1 ⎛
⎢ ⎜αT
⎢⎣ Δr ⎝
− αT
r
i+ 1
2
r
i− 1
2
Ci + 1 − Ci − 1 ⎤
⎞
2
2
⎥
⎟+β
Δr
⎥⎦
⎠
(C1)
Utilizing Eqn. A8 and Eqn. A9 and taking into account the linearly temperature dependant
coefficient of thermal expansion Equation C1 becomes:
⎛
⎜
⎝
−E
=
1 −ν
2
2
⎞
⎛ ⎡
⎛
1 ⎤ ⎞
1 ⎤ ⎞
⎡
1
1
i
σ
+
−
−
(
)
⎟⎟ + σ r ,i +1 ⎜⎜ i ⎢1 +
⎟
⎜
r
i
,
1
−
⎥ ⎟
⎢⎣ 2i − 1 ⎥⎦ ⎟⎟
⎜
⎠
⎝ ⎣ 2i − 1⎦ ⎠
⎝
⎠
β
⎡ ⎛⎡
⎤
2
2 ⎤⎞
⎤
⎡
α o ⎜ T 1 − T 1 + a Ti + 1 − Ti − 1 ⎟ + ( Ci +1 − Ci −1 ) ⎥
⎢⎣ 2
2⎥
⎦⎠ 2
⎣⎢ ⎝ ⎢⎣ i + 2 i − 2 ⎥⎦
⎦
⎡
⎣
σ r ,i ⎜ −i ⎢1 +
2
1 ⎤
1 ⎤
⎡
− ( i − 1) ⎢1 −
2i − 1 ⎥⎦
⎣ 2i − 1 ⎥⎦
2
(C2)
With the boundary conditions described in section 2.5, Equation C2 can be solved in the matrix
form, obtaining the radial stress across the fuel. The azimuthal stress across the fuel is then
determined through Equation 16 as the following, where the condition of radially symmetric
stress is again applied:
σ θ ,i =
(
1
i (σ r ,i +1 + σ r ,i ) − ( i − 1) (σ r ,i + σ r ,i −1 )
2
)
(C3)
As discussed in section 2.5 the axial stress is defined as the difference between the actual to the
mean of the restrained axial stress (such that εz = 0), as shown in Equation C4.
σ z ,i = σ zR,i − σ zR,i
(C4)
The actual and mean of the restrained axial stress are found as shown in Equations C5 and C6.
The reference temperature was taken as 750K, corresponding to the typical fuel processing
temperatures, during which the material is assumed to be free of residual stresses. The reference
value of H/Zr ratio is 1.6.
(
)
σ zR,i = ν (σ θ ,i + σ r ,i ) − E ⎡ α o ⎡⎣Ti + aTi 2 ⎤⎦ − α o ⎡⎣Tref + aTref2 ⎤⎦ + β ( Ci − Cref ) ⎤
⎣
⎦
169
(C5)
σ zR,i =
2
R2
∫
R
0
rσ zR, r dr =
2
R2
∑ ( i − 1 2 )σ
m
i =1
R
z ,i
Δr 2
(C6)
4.3.11 References
1. F. Ganda, E. Greenspan, “Plutonium Incineration Capability of Hydride Versus MOX Fuel in
PWR,” Procd. Global ’05, Tsukuba, Japan (Oct. 2005).
2. A. Sommer, W. Dennison, NAA-SR-5066, (1960).
3. S. Yamanaka, K. Yamada, K. Kurosaki, M. Uno, K. Takeda, H. Anada, T. Matsuda, S.
Kobayashi, “Thermal Properties of Zirconium Hydride,” J. Nuclear Materials, 294, pp.94-98
(2001).
4. Y. Takahashi, M. Yamawaki, K. Yamamoto, “Thermophysical Properties of UraniumZirconium Alloy,” J. Nuclear Materials, 154, pp.141-144 (1988).
5. I. Grenthe, J. Fuger, R. Konings, R. Lemire, A. Muller, C. Nguyen-Trung, H. Wanner,
Chemical Thermodynamics of Uranium, OECD Publications, Paris, France (2004).
6. B. Tsuchiya, J. Huang, K. Konashi, M. Teshigawara, M. Yamawaki, “Thermophysical
Properties of Zirconium Hydride and Uranium-Zirconium Hydride,” J. Nuclear Materials,
289, pp.329-333 (2001).
7. G. Majer, W. Renz, R. Barnes, “The Mechanism of Hydrogen Diffusion in Zirconium
Dihydrides,” J.Phys.: Condens. Matter, 6, pp.2935-2942 (1994).
8. J. Crank, P. Nicolson, "A Practical Method for Numerical Evaluation of Solutions of Partial
Differential Equations of the Heat Conduction Type," Proceedings of the Cambridge
Philosophical Society, 43, pp.50–64. (1947).
9. J. Huang, B. Tsuchiya, K. Konashi, M. Yamawaki, “Estimation of Hydrogen Redistribution
in Zirconium Hydride under Temperature Gradient,” J. Nuclear Sci. and Tech., 37, No. 10, pp
887-892 (2000).
10. D. Olander, M. Ng, “Hydride Fuel Behavior in LWRs,” J. Nuclear Materials, 346, pp.98-108
(2005).
11. M. Simnad, ”The U-ZrHx Alloy: Its Properties and Use in TRIGA Fuel,” Nuclear Eng.
Design, 64, pp.403-422 (1981).
12. S. Yamanaka, K. Yoshioka, M. Uno, M. Katsura, H. Anada, T. Matsuda, S. Kobayashi,
“Thermal and Mechanical Properties of Zirconium Hydride,” J. Alloys. Comp., 293-295,
pp.23-29 (1999).
13. H. Rust, Nuclear Power Plant Eng., (1979), 393.
14. L. Simpson, C. Cann, “Fracture Toughness of Zirconium Hydride and Its Influence on The
Crack Resistance of Zirconium Alloys,” J. Nuclear Materials, 87, pp.303-316 (1979).
15. Y. Kim, D. Olander, S. Yagnik, “Liquid-Metal-Bonded Gap for Light Water Reactor Fuel
Rods,” Nuclear Tech., 128, pp. 300-312 (1999).
16. J. Fink, “Zircaloy Thermal Conductivity: Preliminary Recommendation,” International
Nuclear Safety Center, Argonne National Laboratory: Available from: http://www.insc.anl
.gov/matprop/zircaloy/zirck.pdf, (2000).
17. W. Wang, D. Olander, “Thermodynamics of the Zr-H System,” J. Am. Ceram. Soc., 78 [12],
pp.3323-28 (1995).
170
4.4 Kinetics of Hydrogen Desorption from Zirconium Hydride
4.4.1 Introduction
Hydride nuclear fuels conventionally consist of metallic uranium particles dispersed in a matrix
of zirconium hydride as demonstrated by fuels utilized in the SNAP program and currently used
in GA’s TRIGA reactors. Hydride fuels offer much superior thermal conductivity and fission gas
retention while suffering from larger extent of swelling. Hydrogen is bound to the fuel that acts
as the moderator and could effectively replace the coolant for this purpose resulting in more
compact core designs with higher power density. Thermally-induced hydrogen up-scattering that
accompanies Doppler feedback provides a negative prompt temperature coefficient of reactivity
that makes the fuel very attractive.
Hydride fuels are processed through bulk hydriding of the uranium-zirconium alloys where the
uranium-zirconium alloy is exposed to hydrogen gas at high temperatures. The stoichiometry of
the hydride matrix is customized by controlling the pressure and temperature during the process.
During the early stages of the hydriding process the kinetics are surface reaction limited (soon to
become limited by diffusion) and are controlled through the hydrogen adsorption and desorption
rates. However more importantly the kinetics of the surface reaction are of concern during
reactor operation where dehydring from the fuel causes hydrogen buildup and permeation
through the cladding.
3.4.2
Thermodynamics
Hydrogen dissolves in zirconium metal and undergoes reaction to form two distinct hydrides of
zirconium, the cubic δ-ZrHx (Fm-3m) [1] and tetragonal ε-ZrHx (I4/mmm) [2] at lower and
higher hydrogen to metal ratios, respectively. Both of the hydrides span a large range of
hydrogen stoichiometries as depicted in Figure 1 [3].
The pressure-temperature-composition relationship for the hydrogen gas in equilibrium with δZrHx has been developed by Wang et al. [4] and is presented in Equation 1, where C is the H/Zr
ratio.
2
⎛
172 [ kJ ] ⎞
⎛ C ⎞
P [atm] = ⎜
⎟
⎟ exp ⎜⎜ 8.01 + 5.21C −
RT [ K ] ⎟⎠
⎝ 2−C ⎠
⎝
3.4.3
(1)
Kinetics
In a closed system the net rate of desorption of hydrogen from the surface of the hydride is the
difference between the rates of desorption and adsorption. The adsorption process involves two
steps where initially a hydrogen molecule from the gas (H2) dissociates on the surface to
hydrogen atoms (HS). The surface hydrogen atom then diffuses to the bulk into the hydrogen
sublattice (HI). The first step of the desorption process involves the interstitial hydrogen atom
(HI) diffusing to the surface, leaving behind a vacancy in the hydrogen sublattice (VI). The next
step involves reaction of two hydrogen atoms on the surface of the hydride to from a hydrogen
molecule which immediately desorbs. All the above reactions are summarized in Table 1.
171
1000
k= 2
900
k= 1
β+δ
Temperature [ C]
800
k= 0
k = -1
δ
700
k = -2
600
k = -3
500
k = -4
α+δ
400
ε
k = -5
k = -6
δ+ε
k = -7
300
k = -8
k = -9
200
1.3
1.4
1.5
1.6
1.7
1.8
1.9
H/Zr Ratio
Figure 1. Phase Diagram for Zirconium-Hydrogen System [3] with equilibrium H2 isobars
labeled as PH2=10k atm.
Table 1. Reaction Steps Involving the Desorption and Adsorption of Hydrogen form Hydride
Surface.
Description
Reaction
1) Adsorption – Gas to Surface
H 2 ( g ) + 2V S → 2 H S
2) Adsorption – Surface to Bulk
H S +V I → H I
3) Desorption – Bulk To Surface
H I → H S +V I
4) Desorption – Surface to Gas
2 H S → H 2( g ) + 2V S
For the gas to surface adsorption reaction (reaction 1), the overall rate is the product of the rate at
which the hydrogen molecules collide with the hydride surface (derived from kinetic theory of
gases), the probability that the collision site is unoccupied, the probably that the adjacent site to
the collision site is also unoccupied, and the sticking probability. Therefore rate of the first
reaction is presented in Equation 2 as:
R1 = ( 2π mkT )
−1/ 2
pH 2 β (1 − ys ) η0 e
2
− Ha
kT
(2)
pH2 is the pressure of the hydrogen gas. ys is the fraction of occupied sites by hydrogen atoms on
the surface. β is the 2-D coordination number of the surface sites for the hydrogen atoms and is
dependent on the specific crystallographic plane exposed to the gas.
172
For the reaction of hydrogen atom going from the surface to bulk (reaction 2), the overall rate is
proportional to the product of the fraction of sites occupied with hydrogen atoms on the surface
with the fraction of vacancies on the hydrogen sublattice in the bulk (Equation 3).
R2 = k2 ys (1 − ξ s )
(3)
ξs is the fraction of occupied hydrogen sublattice sites by hydrogen atoms in the bulk. k2 is a rate
constants with an Arrhenius dependence on temperature.
The rate for the first step involving desorption (reaction 3) is proportional to the hydrogen atom
concentration in the bulk adjacent to the surface and the portion of vacant site at the surface
(Equation 4). k3 is a rate constants with an Arrhenius dependence on temperature.
R3 = k3ξ s (1 − ys )
(4)
The rate of the surface to gas desorption reaction (reaction 4), is proportional to the hydrogen
atom concentration at the surface and the probability of another surface hydrogen atom jumping
into and adjacent site of a particular hydrogen atom on the surface. The later is the product of
jumping frequency (I), hydrogen atom concentration and a combinatorial number (depending on
the positioning and coordination number of the surface atoms). Einstein equation predicts the 2D (surface) diffusion coefficient proportional to the product of the square of jumping distance (λ)
and jumping frequency as:
DS =
1 2
λ I
4
(5)
Substituting for jumping frequency using Equation 5, it is possible to determine the surface to
gas desorption rate as:
R4 =
zNDS
λ
2
ys 2
(6)
Where z is the combinatorial number and N is the aerial density of the total surface sites.
3.4.4
Experimental setup
An experiment has been set up to determine the rates of hydrogen desorption and adsorption on
hydride samples. The experimental setup is shown in Figure 2. The sample is placed in a 316
stainless steel vessel that is enclosed in a furnace. The gas pressure is continuously monitored
through a high pressure transducer connected to the vessel. The volume of the vessel and the
connecting pipes up to the V1 valve and the interior of the pressure transducer is 19.5 cm3. The
system has been designed with minimal volume in order to record changes in molar gas content
with higher accuracy through measuring pressure changes.
The sample is placed inside the stainless steel vessel through an opening in the bottom and the
cavity is then welded with a stainless steel cap. Utilization of conventional flange and gasket was
not possible since the copper gasket was unable to withstand the experimental temperatures
inside the furnace.
173
High Pressure
Transducer
Vacuum Gauge
V2
V1
Furnace
V3
V4
He
H2
SS316
Vessel
V5
Vacuum
Pump
Fig 2. Experimental setup
3.4.5
Hydriding and diffusion
The hydride samples are processed with control over stoichiometry of the hydride by control of
temperature and hydrogen pressure required by Equation 1. The samples start out as thin disks of
zirconium at 1mm thickness and 1.35 cm in diameter. Upon hydriding however significant
volume expansion takes place (~16%) that would increase the dimensions of the specimen
accordingly. The hydrogen diffusion path to establish uniform concentration across the hydride
is the half thickness of the specimen (l) and the characteristic diffusion time (l2/D) for this
process is relatively short. The diffusion coefficient of hydrogen in the δ-zirconium hydride has
been reported by Majer et al. [5] as:
⎛ -58.8 [ kJ ]
D ⎣⎡cm 2s-1 ⎦⎤ = 1.53 ×10−3 exp ⎜
⎜ RT [ K ]
⎝
⎞
⎟⎟
⎠
(7)
Therefore for instance at 900 °C and 800 °C the characteristic diffusion time for this process is
11 and 20 minutes respectively. These times were used to process hydrides of uniform hydrogen
concentration at each experimental temperature.
3.4.6
Hydrogen loss through the vessel wall
The hydriding and dehydriding processes do not take place in a closed system because of the
permeability of stainless steel vessel to hydrogen. The leakage rate of hydrogen from the vessel
(flux) could be written in terms of the parameters shown in Equation 8, where Φo, δ, and HΦ are
the pre-exponential term in permeability, thickness of the vessel, and the activation energy
associated with the permeation process respectively.
Rleakage = Φ o
1
δ
⎛ −HΦ ⎞
p exp ⎜
⎟
⎝ RT ⎠
(8)
Permeation of hydrogen through stainless steel has been extensively studied [6] and the
activation energy is reported as 60 KJ/mole. Measuring the rate of pressure drop, using an empty
vessel filled with hydrogen gas at different temperatures, the permeation rate of the vessel has
174
been calculated. The pre-exponential term and activation energy were determined as 1.14x10-4
mole H2/m.s.MPa½ and 53.2 KJ/mole respectively that are in great agreement with literature. The
leakage rate as a function of temperature is shown in Figure 4.
‐14.4
ln(Ф [mole H2/m/sec/MPa½ ])
‐14.5
‐14.6
‐14.7
‐14.8
‐14.9
‐15
‐15.1
⎡ mole H 2 ⎤
⎛ −53.2[kJ] ⎞
−4
Φ⎢
⎟
⎥ = 1.2 ×10 exp ⎜
m.s.
MPa
⎝ RT [K] ⎠
⎣
⎦
‐15.2
‐15.3
‐15.4
0.82
0.84
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
1000/T [K-1]
Fig 3. Leakage rate of hydrogen (permeation) from the stainless steel vessel as function of
temperature.
3.4.7
Experimental method and results
After the uniform hydriding is achieved across the sample, the system is quickly pumped down
to vacuum, isolated and the rise in pressure due to dehydriding is monitored. The hydriding and
dehydrding are done in sequence at constant temperature. This allows pinpointing the hydrogen
concentration at the hydride surface at the beginning of the dehydriding process based on the
equilibrium condition during the hydriding.
A typical graph showing the rise in pressure as a function of time during dehydriding is
presented in Figure 4. The rise in pressure is very fast and equilibrium conditions are quickly
established. The zirconium hydride disk used for the dehydriding experiments was 14.04 mm in
diameter and 1.04 mm in thickness. The dehydridng experiment was performed at 14 different
temperatures and starting H/Zr ratios (Table 2).
175
1.75
T= 881°C H/Zr Ratio=1.6
T = 881 C
H/Zr Ratio (t=0) = 1.603
1.50
pressure [atm]
1.25
1.00
0.75
0.50
0.25
0.00
0
100
200
300
400
500
time [sec]
Fig 4. Typical rise in pressure as function of time during dehydriding from zirconium hydride
disk.
3.4.8
Interpretation of pressure rise
The rate of change in the hydrogen gas pressure accumulated in the vessel is due to rates of
hydrogen gas adsorption and desorption from the hydride and the rate at which the hydrogen
leaks from the vessel. Conservation of mass can be applied at the surface of the hydride disk and
the vessel boundary as shown in Figure 5 (Equations 9 and 10).
l
Rdesorption
Rdesorption
Rdiffusion
Rleakage
Radsorption
Radsorption
p
x=l/2
x=0
(a)
(b)
Fig 5. (a) Conservation of hydrogen mass at the hydride surface. (b) Conservation of hydrogen
gas inside the vessel.
176
1
Rdiffusion
2
x= l
= Rdesorption − Radsorption
(9)
2
V dp
1
= ( Rdesorption − Radsorption ) Sd − Rleakage Sv
RT dt
2
(10)
The rate of diffusion and leakage are divided by a factor of 2 since they correspond to flux of
hydrogen atoms and the rates of adsorption and desorption correspond to that of hydrogen gas. V,
R, T, Sd, and Sv are vessel volume (19.5 cm3), gas constant, temperature, disk surface area (3.561
cm2), and vessel surface area respectively. By applying Fick’s first law the rate of diffusion into
the surface of the hydride is determined as:
Rdiffusion = −2 DN Zr
∂ξ
∂x
(11)
x= l
2
where Nzr is the zirconium number density in δ-zirconium hydride (the number density of
hydrogen lattice sites is twice that of zirconium atoms, hence Nzr is multiplied by 2). Substituting
for the difference between rates of desorption and adsorption from Equations 9 and 11 into 10,
the following is formulated:
∂ξ
V dp Sv
+
Rleakage = − DN Zr
∂x
RTSd dt 2Sd
(12)
x= l
2
Equation 12, employing the experimental results, could serve as the boundary condition in order
to solve the transient diffusion equation (Fick’s second law) across the hydride disk.
3.4.9
Solution to the diffusion equation
The disks are assumed to have uniform hydrogen concentration across the thickness at the
beginning of the dehydriding process that is determined by the pressure at which the disks were
processed (initial condition). The boundary condition at the surface of the disk is provided using
the experimental results using Equations 8 and 12. Diffusion equation is solved (for details of the
semi-implicit numerical solution refer to appendix A) for a disk of zirconium hydride with halfthickness of 0.52 mm and starting uniform H/Zr ratio of 1.603 at 881°C (the dehydriding results
are shown in Figure 4) and the evolution in the hydrogen concentration is shown in Figures 6 and
7.
The details of the different dehydriding experiments are summarized in Table 2. Steady state
surface H/Zr ratio is calculated by plugging the steady state hydrogen pressure (the constant
pressure reached at the end of the dehydriding experiment) into Equation 1. The calculated
surface and average H/Zr ratios are generated through the results of the solution of diffusion
equation.
177
H/Zr ratio
500
1.53
450
400
4
1.5
1.55
350
55
1.
time [sec]
300
1.56
53
1.
250
1.
56
1.54
200
1.58
1.51
1.53
150
1.52
1.5
7
100
1.5
55
1.
1. 5
8
1.59
49
1.
1. 5
7
50
48 7
1.
4
1.
1.5
6
1.5
2
1.59
1.6
1.54
1.58
1.6
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
1.4
6
1.6
1.5
1
1.55 1.53
1.56
1.59 1.57
0.45
0.5
x [mm]
Figure 6. Evolution in the hydrogen concentration profile as a result of dehydriding
1.62
1.60
1.58
H/Zr Ratio
1.56
1.54
1.52
1.50
t=5sec
t=10sec
t=25sec
t=50sec
t=100sec
t=200sec
t=300sec
t=500sec
1.48
1.46
1.44
1.42
0.0
0.1
0.2
0.3
0.4
0.5
x [mm]
Figure 7. Evolution in the hydrogen concentration profile as a result of dehydriding
178
Table 2. Complete Set of Experimental Conditions and Details
Steady state Steady state Calculated Calculated Percent loss
Processing As
Temperature
H2 pressure processed H2 pressure surface
of hydrogen
average
surface
[°C]
H/Zr ratio [atm]
H/Zr ratio H/Zr ratio H/Zr ratio from hydride
[atm]
743
0.41
1.632
0.16
1.546
1.616
1.621
0.6
770
0.91
1.654
0.38
1.579
1.622
1.630
1.5
798
2.90
1.704
0.65
1.581
1.664
1.674
1.8
800
4.58
1.735
0.74
1.589
1.682
1.696
2.3
829
2.19
1.639
0.82
1.553
1.591
1.600
2.4
830
4.48
1.694
0.90
1.560
1.637
1.649
2.7
852
4.07
1.658
1.16
1.550
1.562
1.573
5.1
859
1.45
1.560
0.88
1.512
1.506
1.517
2.8
861
2.33
1.599
1.19
1.538
1.538
1.552
2.9
863
4.27
1.648
1.22
1.538
1.582
1.590
3.5
880
4.51
1.630
1.35
1.522
1.555
1.566
3.9
881
3.37
1.603
1.40
1.524
1.528
1.544
3.7
902
4.41
1.599
1.64
1.508
1.517
1.533
4.1
920
4.51
1.578
2.14
1.508
1.469
1.480
6.2
4.4.10 Determination of the reaction order
In order to determine the dependence of the flux on the surface hydrogen concentration (and
therefore test the applicability of the second order kinetics earlier discussed), the surface
hydrogen flux is plotted against hydrogen gas pressure in Figure 8.
0.06
1016K
1043K
1071K
1073K
1102K
1103K
1125K
1132K
1136K
1153K
1154K
1175K
1193K
0.04
2
Flux [mole H/cm .sec]
0.05
0.03
0.02
0.01
0.00
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
Pressure [atm]
Figure 8. Dependence of surface hydrogen flux on hydrogen gas pressure inside the chamber
179
As appears on the figure, the flux is linearly dependent on the hydrogen gas pressure and no
correlation with the evolving hydrogen surface concentration is observed. At the beginning of the
desorption process, the hydrogen gas pressure inside the chamber is zero. Therefore the
adsorption rate, that is directly dependent on the gas pressure, is also zero, and the intercept of
the flux curve with the y axis is the absolute desorption rate. The slope of the flux curve then
corresponds to the absolute rate of desorption per unit of hydrogen gas pressure. This
relationship is mathematically developed as the following:
f ( t ) = kd − ka pH 2 ( t ) (13)
This relationship suggests zero order kinetics similar to what has been discussed by Venables et
al. [7]. Assuming zero order kinetics the absolute rates of hydrogen adsorption and desorption
are plotted as a function of temperature, to determine the Arrhenius dependence. Desorption data
also include thermogravimetry data from set of experiments performed under vacuum.
‐2
Pressure Experiments
‐3
Thermogravimetry
ln(kd [mole H.cm-2 .s-1 ]
‐4
‐5
‐6
‐7
‐8
‐9
‐10
0.8
0.85
0.9
0.95
1
1.05
1.1
1000/T [K-1 ]
Figure 9. Arrhenius dependence of the hydrogen desorption rate from zirconium hydride
180
‐3
Pressure Experiments
ln(ka [mole H.cm-2 .s-1.atm-1 ]
‐3.5
‐4
‐4.5
‐5
‐5.5
0.8
0.85
0.9
0.95
1
1000/T [K -1 ]
Figure 10. Arrhenius dependence of the hydrogen adsorption rate from zirconium hydride
The zero order rate equations for hydrogen desorption and adsorption processes are presented in
Equations 14 and 15 respectively. The reproducibility of the pressure buildup curves through
utilization of the below equations is examined in Figure 11, where somewhat poor results are
shown.
⎛ −215 [ kJ ] ⎞
⎡ mole H ⎤
kd ⎢ 2 2 ⎥ = 1.73 ×108 exp ⎜
⎟
⎣ cm .sec ⎦
⎝ RT
⎠
(14)
⎛ −86 [ kJ ] ⎞
⎡ mole H 2 ⎤
ka ⎢ 2
= 1.75 × 102 exp ⎜
⎟
⎥
⎣ cm .sec.atm ⎦
⎝ RT ⎠
(15)
181
2.5
2
Pressure [atm]
1.5
1
0.5
0
0
50
100
150
200
250
Time [sec]
300
350
400
450
500
Figure 11. Reproduction of pressure buildup curves through utilization of the zero order kinetics
parameters. The smooth lines represent the model
3.4.10 Discussion and conclusion
Although zero order kinetics is apparent, it does not agree with the thermodynamics governing
the binary system. The mismatch between the model and experimental pressure buildup curves is
precisely due to this reason, since the equilibrium hydrogen pressure at large times that coexists
with the hydride after the desorption process stops, corresponds to the relationship discussed in
Equation 1. Therefore the relationships developed above are missing some component of surface
hydrogen concentration dependence and further scrutiny and analysis of the results is required to
determine the mechanism governing the kinetics.
With respect to the applicability of the above study to the overall applicability of hydride nuclear
fuels in LWRs the following could be concluded. The rates of hydrogen desorption and
adsorption are sufficiently fast at high temperatures (i.e. during power transients) such that
thermodynamic equilibrium is quickly established. Therefore for the purpose of safety analyses
assuming instantaneous equilibrium conditions is a conservative and relatively accurate
assumption.
182
4.2.17 References
1. R. Beck, “Zirconium-Hydrogen Phase System,” Trans. Am. Soc. Metals, 55, pp.542-555
(1962).
2. S. Sidhu, N. Satya Murthy, F. Campos, D. Zauberis, “Neutron and X-ray Diffraction
Studies of Nonstoichiometric Metal Hydrides,” Advances in Chemistry Series,
Washington D.C., 39, pp.87-98, (1963).
3. K. Moore, W. Young, “Phase Studies of Zr-H System at High Hydrogen Concentrations,” J.
Nuc. Mat., 27, pp.316-324 (1968).
4. W. Wang, D. Olander, “Thermodynamics of the Zr-H System,” J. Am. Ceram. Soc., 78 [12],
pp.3323-28 (1995).
5. G. Majer, W. Renz, R. Barnes, “The Mechanism of Hydrogen Diffusion in Zirconium
Dihydrides,” J.Phys.: Condens. Matter, 6, pp.2935-2942 (1994).
6. C. San Marchi, B. Somerday, S. Robinson, ”Permeability, solubility and diffusivity of
hydrogen isotopes in stainless steels at high gas pressures,” International Journal of
Hydrogen Energy, 32, pp.100-116 (2007).
7. J.A. Venables, M. Bienfait, Surf. Sci., 61, (1970) 667.
183
3.5 Zircaloy Cladding Compatibility with Hydride Fuel
Compatibility of Zircaoly, conventionally used as the fuel cladding for LWR fuels, with hydride
fuel has significant impact on the outcome of the feasibility study. Currently the oxide fuel cycle
length inside the reactor is limited by the cladding performance. Zirconium is an effective getter
of hydrogen and readily undergoes hydriding. Therefore the susceptibility of Zircaoly cladding
to hydride formation and damage is obvious from the thermodynamic standpoint. However the
fuel could be engineered such that the kinetics of hydrogen transfer from the fuel to cladding is
limited and effectively becomes insignificant during the lifetime of the fuel inside the reactor.
The proposed design for such fuel rod is to substitute helium as the gap filling material between
the cladding and the fuel, with a liquid metal alloy. A ternary alloy of lead-tin-bismuth (Pb33wt%Sn-33wt%Bi) is proposed to be used for this purpose. The alloy is chemically compatible
with both the fuel and the cladding. Also hydrogen solubility in any of the components of the
alloy is very limited at the operating temperatures of the fuel assembly.
To further investigate the compatibility of the liquid metal bonded hydride fuel with the cladding
a set of experiments are currently being conducted where the fuel is exposed to the cladding,
submerged in liquid metal, at different times, temperatures, and contact pressures. Figure 1
shows the setup of the experiment, were the contact is made inside an open stainless steel
pressure cell. The contact pressure between the fuel and the cladding is controlled through the
application of torque over the screw that pushes the fuel and cladding together. In case that a
certain thickness of a gap is top be maintained between the fuel and the cladding, platinum wires
are used. The stainless steel pressure cells are heated inside an argon environment.
Torque Screw
τ
Stainless steel sheet
Zircaloy
Pt wires
F
Hydride fuel
Submerged in Liquid Metal
(Sn‐33wt%Pb‐33wt%Bi)
Figure 1. Experimental setup for the liquid metal bonded fuel – Zircaoly cladding compatibility
test.
The temperatures of the experiment are in the range of what is expected for steady state LWR
operation (i.e. 450°C and 500°C). After the fuel is exposed to the cladding, the cladding is
mounted and metallography followed by optical and scanning electron microscopy will be
performed in order to investigate formation of any hydride in the cladding. The work is done
with Zircaloy 4 cladding, and (U4Th2Zr9)H1.5 hydride fuel. Originally the experiment was
expected to be conducted using commercial TRIGA fuel, however such fuel could not be
obtained due to multiple administrative hurdles from different organizations involved in the
process.
184
4.6 Oxidation Behavior of Hydride Fuel in High Temperature Steam
During sever accident conditions the fuel cladding could burst and result in introduction of water
into the cladding. The water in turn evaporates into high temperature steam that could react with
the fuel and the inner wall of the cladding. To determine the susceptibility of hydride type fuels
an experiment was performed using a thermogravimetry (TGA) setup. The goal was to determine
the kinetics of steam reaction with the fuel based on the mass gain as a function of time.
Typically such analysis yields rate information that then could be analyzed in order to determine
the mechanism of the phenomenon examined. A very preliminary experiment has been
performed. The sample used was a small piece of (U4Th2Zr9)H1.5 hydride fuel exposed to a
mixture of steam and helium at 900 °C. The oxide scale forming on the surface of the fuel
however was not adherent and quickly spalled and fractured away from the surface. Therefore
due to the severe reaction rates no kinetic data could be deduced from the steam reaction with the
hydride fuel. This result appears to be in some contradiction with that reported by Dr. Simnad,[1]
— the developer of TRIGA fuel, that exposing small and large samples of TRIGA fuel heated to
900oC to water caused no damage except surface discoloration [1].
The exposition of hydride fuel samples to steam experiments need be continued. It should be
noted that the steam temperature expected in operating LWR will be on the order of only 400oC
rather than 900oC used in this single experiment. Moreover, the outcome of the oxidation
reaction could significantly change based on the composition of the fuel – in case of TRIGA fuel
an outer oxide layer could be protective where no thorium is present. Therefore further
investigation is required before sound conclusions could be drawn.
Reference
1. M.T. Simnad, “The U-ZrHx Alloy: Its Properties and Use in TRIGA Fuel,” General Atomics
publication GA-A16029, August 1980.
185
4.7 Irradiation Plans for Liquid Metal Bonded Hydride Fuel
4.7.1 Introduction
The experimental data available in the open literature on the swelling of hydride fuel and on the
fission gas released from hydride fuel is very limited [1-6]. Moreover, there is no data available
at all on the feasibility of using liquid metal bonding instead of helium for hydride fuel. The
liquid-metal bonding will enable to provide a sufficiently large gap between the initially loaded
hydride fuel and the clad to accommodate the relatively large swelling of hydride fuel without
increasing the fuel temperature. The liquid metal bonding will also eliminate a large temperature
gradient between the fuel surface and the cladding ID and, possibly, will protect the Zircaloy
clad from the fuel hydrogen. An irradiation test of a hydride fuel specimen in the ATR
irradiation test reactor at the Idaho National Laboratory was planned in order to investigate all
the above mentioned issues. A brief description of the proposed experiment follows.
4.7.2 Brief description of the proposed ATR experiment
The objective of ATR experiment is to perform a realistic irradiation test of combined innovative
uranium hydride fuel with a low-melting liquid metal (Sn,Bi,Pb) as the gap filler [7]. The test
will utilize a Zircaloy-clad mini-fuel element instrumented for continuous recording of fuelcenterline and cladding outside temperatures and evolved-gas composition. The mini-fuel
fabrication steps and assembly into ATR capsule are shown in Figure 1.
Figure 1. Mini-fuel fabrication steps
Since TRIGA Uranium/Zr hydride fuel has yet to be delivered to Berkeley campus, a mock up of
mini-fuel has been assembled with Cu pellets instead of the actual fuel. From large ingot, Cu
pellets have been drilled out using the diamond core drilling technique to an approximate size
followed by an in-house designed centerless grinder to the precise diameter equal to the LWR
UO2 pellets. The actual U-Zr hydride pellets production for mini-fuel will be accomplished in a
186
glove box. The partially assembled mini fuel rod consisting of Cu pellets, Zircaloy clad and
liquid metal filled gap in between is shown in Figure 2.
Figure. 2 Mini-fuel cladding with Cu pellets, Zircaloy cladding and LM filled gap
The initial thickness of the fuel-cladding gap is chosen so as to achieve closure prior to the end
of irradiation at ATR. During irradiation, fuel-centerline and outside cladding as well as
composition of gaseous fission products are monitored at the ATR facilities. The post-irradiation
examination at UC Berkeley include: possible fuel cracking, gas bubbles formation in the frozen
alloy, hydrogen distribution in fuel, hydride precipitation in cladding, void around uranium
particles, dimensional changes of cladding and second-phase particles generation in the fuel.
The mini-fuel rodt will be instrumented for continuous recording of fuel- centerline and
cladding-OD temperatures as well as of gas composition. A constant fuel-centerline temperature
is maintained for an irradiation period of one year, which corresponds to ~50% burnup of the U235. The initial thickness of the fuel-cladding gap is chosen to achieve closure prior to the end of
irradiation.
The mini-fuel rod (“rodlet”) will be inserted into an ATR capsule equipped for gas flow in the
annulus between the specimen and the capsule wall. Varying the He/Ne ratio of the flowing gas
controls the fuel-centerline temperature. The upper end-cap of the rodlet contains a space to
allow fission gases to escape. The He/Ne gas, containing any released fission gases, will enter an
instrument that will measure the gas composition.
The Post-Irradiation-Experiments (PIE) planned include the determination of:
•
the state of fission gases: remaining in the fuel, or collected as bubbles in the liquid-metal
in the gap
•
behavior of hydrogen: redistribution in the fuel; hydriding of the cladding
•
morphology of the fuel: cracking; second-phase particles; voids around uranium particles
•
diametral expansion of the cladding
•
pellet-cladding mechanical interaction.
Information such as the above will help determine whether this fuel concept is suitable for
commercial use. A list of specific experiments planned is given in Table 1.
187
Table 1. Post-Irradiation-Experiments Planned
Phenomenon
Instrumentation
Fuel cracking
Xe in the plenum gas
Gas bubbles in the frozen alloy
Hydride precipitates in cladding
Uranium particles
Voids around U Particles
Diametral expansion of the cladding
Second-phase particles in the fuel
OM, SEM
On-line
OM
OM, SEM
SEM
TEM
micrometer
SEM
4.7.3 Irradiation conditions
Three requirements must be met by the irradiation regime:
• For the entire irradiation time the fuel-centerline temperature remains at ~ 650oC2.
• A burnup of ~50% of the U-235 should be achieved in ~1 year of irradiation
• The fuel-cladding gap should close before the end of irradiation
The most desirable irradiation condition would be to maintain constant both the fuel-centerline
and cladding OD temperatures. However, in the ATR, the neutron flux and the coolant
temperature are fixed. These conditions do not result in constant fuel-centerline and cladding OD
temperatures because of the burnup of U-235, which continually reduces the fission rate and
hence the linear heat rate. The compromise condition for the proposed test is to maintain the
fuel-centerline temperature (To) constant by allowing the cladding OD temperature (TCO) to rise
during irradiation. These two temperatures are related by:
To = Tcoolant + ΔThyd + ΔTCap + ΔTgap2 + ΔTC + ΔTgap1 + ΔTf
(1)
where Tcoolant = ATR coolant temperature, ~ 60oC
To = fuel centerline temperature = 650 - 700oC
the intervening temperature drops are across:
ΔThyd = hydraulic boundary layer
ΔTcap = ATR capsule wall
ΔTgap2 = helium/neon flush gas
ΔTC = Zircaloy cladding
ΔTgap1 = liquid metal gap filler
ΔTf = fuel
Dimensions of the specimen are given in Table 2 and thermal conductivities are given in Table 3.
2
This centerline-temperature is higher than required of the hydride fuel in commercial LWRs, but it tests the
performance limits of the fuel.
188
Table 2. Specimen & Capsule Radial Dimensions
COMPONENT
Fuel-pellet radius
Cladding ID/2
Cladding OD/2
Capsule ID/2
Capsule OD/2
SYMBOL
Rf
RCI
RCO
RcapI
RcapO
CM
0.467
0.487
0.557
0.571
0.730*
* assumes a 1/16 “ wall thickness
Table 3 Thermal Conductivities (W/cm-K)
MATERIAL SYMBOL W/CM-K
Zr hydride
kf
0.18*
Zircaloy
kC
0.17*
Liquid metal
kgap1
0.3*
Helium/neon
kgap2
Table B1
Capsule wall
kcap
0.17#
#
* temperature-independent
depends on alloy; stainless steel assumed
4.7.4 Summary
Design and performance of a mini fuel element consisting of a 5-pellet stack of (U,Zr) hydride
fuel, Zircaloy cladding and a Bi-Sn-Pb liquid metal alloy in the fuel-cladding gap were analyzed
with the objective of an irradiation test in the ATR. A thermal-neutron flux of ~ 3x1013 n/cm2-s
is estimated required in order that the fuel-centerline temperature remains constant at ~ 650oC.
At this flux, 50% burnup of the U-235 is attained in 1 year of irradiation. An initial gap thickness
of ~100 μm is required for gap closure at the end of the irradiation. The specialized machining
and welding techniques required for fabrication of the mini-fuel element have been developed.
4.7.5 References
1. J. D. Gylfe et al, “Evaluation of Zirconium Hydride as Moderator in Integral Boiling –Water
Superheat Reactors”, NAA-SR-5943 (1960)
2. A. Lillie et al, “Zirconium Hydride Fuel Element Performance Characteristics”, Atomics
International/USAEC Rept. AI-AEC-13084 (1973)
3. M. T. Simnad, “The U-ZrHx alloy: its properties and use in TRIGA fuel”, Nucl. Engin. &
Design 64 (1981) 403
6. D. Olander and O. Ng, “Hydride Fuel Behavior in LWRs” J. Nucl. Mater, 346 (2005) 98
7. D. Olander & D. Wongsawaeng “A Liquid-metal bond for improved LWR fuel
performance”, Nucl. Technol., 159 (2007) 279
189