Method Development for Calculating Minor Actinide Transmutation in a Fast Reactor

18 Pages·2014·0.42 MB·English

Chapter 17
Method Development for Calculating Minor
Actinide Transmutation in a Fast Reactor
ToshikazuTakeda,KojiFujimura,andRyotaYamada
Abstract Toeffectivelytransmuteminoractinides(MAs),whichhavelong-lived
radioactivity and high decay heat, fast reactors are very promising because many
minor actinides can be loaded and transmutation rates are high compared to light
water reactors. With the increase of loaded minor actinides, the neutron spectrum
becomes hard and core safety parameters will deteriorate. Especially, the sodium
voidreactivityincreaseswithMAadditiontocores.Toovercomethedifficulty,we
proposeMAtransmutationfastreactorsusingcoreconceptswithasodiumplenum
andinternalblanketregioninreactorcores.Therefore,coresbecomecomplex,and
calculationaccuracybecomespoor.Toaccuratelyevaluatetheneutronicproperties
suchasMAtransmutationrateandsodiumvoidreactivity,weimprovedcalculation
methods. Inthis chapter we show new methods for calculating MA transmutation
rates for each MA nuclide, for calculating the uncertainty of MA transmutation
usingsensitivities.Anewsensitivityisderivedthatisdefinedasarelativechange
of core parameters relative to infinite-dilution cross sections, not effective cross
sections.Toeliminatebiasfactorsinestimatingcoreparameteruncertainties,anew
method is proposed. This method is used to reduce the calculation uncertainty
throughtheuseofadjustedcrosssections.
Keywords Calculation methods • Fast reactors • Minor actinide • Sensitivity
•Sodiumvoidreactivity•Transmutation
17.1 Introduction
The importance of nuclear energy, as a realistic option to solve the issues of the
depletionofenergyresourcesandtheglobalenvironment,hasbeenacknowledged
worldwide. However, acceptance of large-scale contributions would depend on
satisfactionofkeydriverstoenhancesustainabilityintermsofeconomics,safety,
T.Takeda(*)•R.Yamada
ResearchInstituteofNuclearEngineering,UniversityofFukui,Fukui,Japan
e-mail:[email protected]
K.Fujimura
HitachiWorks,Hitachi-GENuclearEnergy,Ltd.,Ibaraki,Japan
©TheAuthor(s)2015 179
K.Nakajima(ed.),NuclearBack-endandTransmutationTechnologyforWaste
Disposal,DOI10.1007/978-4-431-55111-9_17
180 T.Takedaetal.
adequacyofnaturalresources,wastereduction,nonproliferation,andpublicaccep-
tance. Fast reactors with fuel recycle enhance the sustainability indices signifi-
cantly,leadingtothefocusonsodium-cooledfastreactors(SFR)intheGeneration
IV International Forum (GIF) and theInternational Project on Innovative Nuclear
Reactors and Fuel Cycles (INPRO) initiative of the International Atomic Energy
Agency(IAEA).
The necessary condition for successful fast reactor deployment is the under-
standingandassessmentofinnovativetechnologicalanddesignoptions,basedon
bothpastknowledgeandexperience,aswellasonongoingresearchandtechnology
development efforts. The severe accident at Tokyo Electric Power Company’s
FukushimaDai-IchiNuclearPowerStationcausedbytheGreatEastJapanEarth-
quakeandtsunamionMarch11,2011promptedallcountriestoredefinetheirfast
reactor programs. To achieve the successful deployment of fast reactors, drastic
safety enhancement is the most important issue to be established, especially in
Japan,wheretherestartofnuclearpowerplantsoncethesehavebeenstoppedisa
seriousmatterofargument.
Thesafetyaspectsoffastreactors(FRs)havebeenreviewed[1–4]inrepresen-
tative countries that have developed or have a plan to develop fast reactors in the
nearfuture,especiallyaftertheFukushimaaccident.Thesecountriesareimproving
thesafetyofSFRsbyconsideringtheDiD(defenseindepth).ThedesignsofSFRs
shouldhavetolerancetoDBA(designbasisaccidents)andBDBA(beyonddesign
basis accident) caused by internal and external events. The inherent safety and
passive safety should be effectively utilized for reactor shutdown and reactor
cooling. Forthecaseofsevereaccidents,itisindispensablefirsttoshutdown the
reactors.Furthermore,decayheatremovalisalsoindispensableeveninthecaseof
SBO (station black out). For SFRs, natural circulation can be expected in the
sodium heat transport systems and the decay heat can be removal to atmosphere
bytheaircoolingsystem.
In Japan, the Ministry of Education, Culture, Sports, Science and Technology
haslaunchedanationalprojectentitled“Technologydevelopmentfortheenviron-
mentalburdenreduction”in2013.Thepresentstudyisoneofthestudiesadoptedas
thenationalproject.Theobjectiveofthestudyistheefficientandsafetransmuta-
tion and volume reduction of MAs with long-lived radioactivity and high decay
heat containedin HLW insodium-cooled fast reactors. We are aimingto develop
MAtransmutationcoreconceptsharmonizingMAtransmutationperformancewith
coresafety.ThecoreconceptisshowninChap.2.Also,weareaimingtoimprove
design accuracy related to MA transmutation performance. To validate and
improve design accuracy of the high safety and high MA transmutation perfor-
manceofSFRcores,wedevelopedmethodsforcalculatingtransmutationratesof
individualMAnuclidesandestimatingtheuncertaintyofMAtransmutation.
AnewdefinitionoftransmutationratesofindividualMAnuclidesisderivedin
Chap. 3. Using the definition, one can understand the physical meanings of trans-
mutation for individual MA nuclides. Sensitivities are required to estimate the
uncertainty of MA transmutation rates from cross-section errors. In Chap. 4, sen-
sitivity calculation methods are derived. First, the sensitivity calculation method
17 MethodDevelopmentforCalculatingMinorActinideTransmutationinaFast... 181
relativetoinfinite-dilutioncrosssectionsisintroduced.TheMAtransmutationrates
areburn-upproperties.Thus,thesensitivitycalculationmethodforburn-up-depen-
dent properties is derived. Finally, we investigate how many energy groups are
requiredin sensitivity calculations. Calculated MA transmutation rates have large
uncertaintiesresultingfromthelargeuncertaintiesinMAcrosssections.Toreduce
theseuncertaintiesinMAtransmutationrates,weintroduceanewmethodtoreduce
predictionuncertaintiesofMAtransmutation rates inChap.5.Inthismethod, we
eliminate bias factors included in experiments and calculations by using ratios of
thecalculationtotheexperimentofcoreperformanceparameters.Afterremoving
thebiasfactors,thecrosssectionisadjustedusingmeasureddata.Theconclusions
areshowninChap.6.
17.2 MA Transmutation Core Concept
MAtransmutationcoreconceptsaredevelopedbyconsideringtheamountofMA
loadingandthesafety-relatedcoreparameters.IncreaseofMAloadinginthecore
ofaSFRmakestheamountofMAtransmutationlarge,whichmaydecreaselong-
termradiotoxicityanddecayheatofMA.Ontheotherhand,loadingalargeamount
of MA into the core of a SFR increases the sodium void reactivity. Therefore,
harmonization of MA transmutation and sodium void reactivity is a key issue in
designingthecoreconcepts.Asanexample,Fig.17.1showstherelationshipofMA
contentandsodiumvoidreactivity;whentheMAcontentisabout10%,thesodium
voidreactivityincreasesbyabout1$.
AhomogeneousMA-loadedcoreof750MWewasdesignedintheFaCTproject
[1, 2] (Fig. 17.2). The configuration of this core is a conventional homogeneous
core and homogeneous MA loading into the core fuel increases sodium void
reactivity.Therefore, MA content inthe corefuelassemblyislimitedtolessthan
about 5 wt%. On the other hand, the safety issue has become more and more
important sincetheFukushimaDaiichiNPPaccident.Further,lowvoidreactivity
SFR designing has been pursued in Russia and France [5]. In this study, the
coexistence of enhanced MA transmutation and zero void reactivity, that is, the
harmonizationofMAtransmutationandcoresafety,issetasanobjective.
Hitachi proposed an axially heterogeneous core (AHC) concept with sodium
plenum[6,7].Itwasclarifiedthatanincreaseoffluxlevelatthetopofthecorefuel
causedbythepresenceoftheinternalblanketanddecreaseoftheheightoftheinner
corefuelgreatlydecreasedsodiumvoidreactivity.Inthecoreconcept,sodiumvoid
reactivity can be extremely reduced without disrupting core performance for
normaloperation.ThedifferenceincoreconfigurationsbetweentheHitachiAHC
withsodiumplenumproposedinFR‘91[6]andtheASTRIDACV[5],whichhas
been recently studied in France, is that absorber material is loaded in the upper
shieldfortheASTRIDACV.
We are going to optimize the specifications of the core shown in Fig. 17.3 to
realize the high MA transmutation and zero sodium void reactivity. Figure 17.4
182 T.Takedaetal.
Fig.17.1 Dependencyofsodiumvoidreactivityonminoractinide(MA)content
Fig.17.2 CoreconfigurationofthehomogeneousMA-loadedcore
shows the axial distribution of coolant density and the density coefficient of that
core.Thesodiumdensitycoefficient(%Δk/kk0/Δρ)inthesodiumplenumbecomes
positive. On the other hand, sodium density change (Δρ) in the sodium plenum
becomes negative because of the increase of coolant temperature for an accident
such as ULOF (unprotected loss of flow accident). Therefore, net sodium void
reactivitybecomesnegative.
Themechanismforreducingsodiumvoidreactivityofthecoreisthattheaxial
neutronleakageislargelyenhancedwithcoolantvoidinginthesodiumplenum.It
is known that the evaluated leakage component of sodium void reactivity with
diffusion theory might be overestimated by about 50 %. Therefore, calculation
17 MethodDevelopmentforCalculatingMinorActinideTransmutationinaFast... 183
Fig.17.3 Verticalviewof
axiallyheterogeneouscore
withsodiumplenum
Fig.17.4 Axialdistributionofcoolantdensityanddensitycoefficient
accuracy for sodium void reactivity of the core with a sodium plenum might be
poor. Thus, we should consider change of the neutron spectrum in the heteroge-
neousMAloadedcore.Figure17.5showstheneutronspectraforMOXdriverfuel
without MA and 10 % MA-mixed fuels in transmutation target with and without
Zr-Hx.Thespectrumof10%MA-mixedfuelintransmutationtargetwithoutZr-Hx
is slightly softer than that of the MOX driver fuel withoutMA, becausethe 10 %
MA-mixed fuel in the transmutation target has no fissile plutonium but the MOX
driver fuel includes 239Pu and 241Pu. The neutron spectrum of the moderator
mixturetargetfuelisclearlysofterthanotherfuels.
184 T.Takedaetal.
Fig.17.5 NeutronspectraforMOXfuelandMAtransmutationtargetfuels
17.3 MA Transmutation Rate
LetusfirstintroduceadefinitionoftransmutationratesofindividualMAnuclides
fueledinareactorcore.Thecalculationmethodofthetransmutationraterelativeto
the nuclides is as follows. First, conventional burn-up calculations are carried out
andburn-up-dependentfluxineachregioniscalculated,whichisusedinthesecond
step calculation. In the second step, we consider only the relevant MA in each
regionandperformburn-upcalculationsusingthefluxobtainedinthefirststep.
Inthissecondstepofcalculation,nuclidekisproducedfromtheoriginalnuclide
l.Therearemanypassesofreactionsoftransmutationoftheinitialnuclide(shown
by N) and the production of N as is shown in Fig. 17.6. We can calculate the
productionrateofnuclidekattimeTfromtheinitialnuclidelas
P ¼Ne ðTÞ=Ne ð0Þ ð17:1Þ
lk k l
whereNe ð0Þisnumberdensityofnuclidelattime0andNe ðTÞisnumberdensityof
l k
nuclide k at time T, assuming nuclide lis present aloneat t¼0.Using Ne ðTÞ, the
k
overallfission(seeFig.17.6)relativetotheinitialnuclideliscalculatedas
XZT
OFl ¼ σkðtÞNe ðtÞϕðtÞdt ð17:2Þ
f k
k
0
whereσk(t)isfissioncrosssectionofnuclidekattimet,ϕ(t)isneutronfluxattime
f
t, and Σ is summation over all nuclides k resulting from initial nuclide l; this
17 MethodDevelopmentforCalculatingMinorActinideTransmutationinaFast... 185
Fig.17.6 TransmutationofinitialMAnuclidesandproductionoftheMAnuclide
includes all the fissions from the initial nuclide l. Furthermore, the production of
otherMAnuclidesexcepttheinitialnuclidelcanbecalculatedby
X
OMAl ¼Ne ð0Þ P ð17:3Þ
l lk
k∈MA,k6¼l
ThePuandUproductionfromnuclidelisgivenby
X
PUl ¼Ne ð0Þ P ð17:4Þ
l lk
k∈U,Pu
TheproductionofMAnuclidelfromPuandUisgivenby
X
PUMl ¼ Ne ð0ÞP ð17:5Þ
k kl
k∈U,Pu
TheproductionofMAnuclidelfromotherMAisgivenby
X
MAMl ¼ Ne ð0ÞP ð17:6Þ
k kl
k∈MA,k6¼l
UsingEqs.(17.2),(17.3),(17.4),(17.5),and(17.6),thenettransmutationofnuclide
liscalculatedby
186 T.Takedaetal.
TRl ¼OFlþOMAlþPUl(cid:2)PUMl(cid:2)MAMl ð17:7Þ
In Fig. 17.6, the individual parameters OMAl, PUl, PUMl, MAMl, and OFl are
shown.PUMlandMAMldenotetheproductionsoftherelevantMAnuclidefrom
fuel (Pu, U) and other MA nuclides, respectively. Thus, there are minus signs in
these parameters in Eq. (17.7), whereas other parameters show the elimination of
therelevantMAnuclide,sothesignsarepositive.
When weconsider thetotalMA transmutation forallMAnuclides,thesecond
andthefifthtermscanceleachother,sothewholetransmutationisgivenby
X X (cid:2) (cid:3)
TR¼ TRl ¼ OFlþPUl(cid:2)PUMl ð17:8Þ
l∈MA l∈MA
Therefore,wecandefinetheMAtransmutationofMAnuclidelby
TRl ¼OFlþPUl(cid:2)PUMl ð17:9Þ
Thus, the transmutation rate is composed of two terms: the first is the amount of
incineration rate by fission and the second is the net transmutation rate to fuel
(UandPu).Thefirstfissionratesofindividualnuclidescontainthedirectfissionof
the relevant nuclide plus the fission of other nuclides transmuted by decays or
neutron reactions as “overall fission” [OFl in Eq. (17.9)] (Fig. 17.7). It was found
that the indirect fission contribution by 238Pu and 239Pu is remarkably large for
nuclides239Npand241Am.ThenetproductionratesofUandPuarecalculatedfrom
the difference between the production rates of U and Pu from the relevant MA
nuclide and the MA production from the initial U and Pu. Figure 17.7 shows the
overall fission rate of 237Np in a thermal advanced pressurized water reactor
(APWR) and two fast reactors, a MOX-fueled sodium-cooled fast reactor and a
metal-fueledlead-cooledfastreactor[8].Inthethermalreactor,theoverallfission
rateisabout5%inonecycleandisverysmallcomparedwiththefastreactors.In
fast reactors, the direct fission of 237Np is rather large, and the 238Pu fission
contributionisalsolarge.The239Pufissioncontributionissmallforfastreactors.
Wearedevelopingacalculationcodesystembasedontheforegoingmethodand
are planning to apply the system to MA transmutation core design. In the core
design we consider a homogeneous MA loading core, and a heterogeneous MA
loadingcore,inwhichMAisloadedinspecialassemblieswithmoderators.
17 MethodDevelopmentforCalculatingMinorActinideTransmutationinaFast... 187
Fig.17.7 Calculationexampleofoverallfissionrateof237Npbydevelopedcalculation.APWR
advancedpressurizedwaterreactor
17.4 Sensitivity Calculation Method
17.4.1 Sensitivity to Infinite-Dilution Cross Section
Core characteristics such as k , power distribution, and control rod worth are
eff
calculated by using effective cross section in deterministic methods. Sensitivities
are usually calculated by using sensitivity calculation codes such as SAGEP [9],
SAGEP-T[10],andSAINT[11].However,thesensitivitiesareforrelativechanges
of effective cross sections. Here we derive a calculation method of sensitivities
relative to infinite-dilution cross sections for fast reactor analysis. Usually the
effective cross sections are calculated by using the Bondarenko self-shielding
factor method, the subgroup method. In that method the effective cross sections
areexpressedbytheinfinite-dilutioncrosssectionandtheself-shieldingfactorsf
σe¼f (cid:3)σ ð17:10Þ
Theself-shieldingfactorsdependonthebackgroundcrosssectionandtemperature.
Thebackgroundcrosssectionfornuclidei0inahomogeneousmediumiscalculated
bytheformula
X
1
σbi0 ¼Ni0k6¼i0 Nk(cid:3)σtk ð17:11Þ
whereN istheatomicnumberdensityoflightnuclidekandσk isthemicroscopic
k t
totalcrosssection.Thesensitivitycoefficientisdefinedbytherelativechangesof
thecorecharacteristicscausedbytherelativechangesofthecrosssections.Herewe
188 T.Takedaetal.
consider the following two sensitivities, the sensitivity S, which results from the
relative change of the infinite-dilution cross sections, and the approximate sensi-
e
tivity S, which is the result of the relative change of the effective cross sections.
FromEq.(17.10),thechangeoftheeffectivecrosssectioncanbeexpressedby
dσe df dσ
¼ þ ð17:12Þ
σe f σ
Therefore, the improved sensitivity is expressed by using the approximate sensi-
tivityasfollows:
(cid:4) (cid:5)
dR=R dR=R df=f
S(cid:4) ¼ (cid:3) 1þ ð17:13Þ
dσ=σ dσe=σe dσ=σ
Sensitivitiesand cross sectionsare dependent on nuclides,reactiontypes(suchas
fission, capture, and scattering), and energy groups. Here we consider the case
where there is a perturbation in σ of nuclide i, reaction type j, in energy group g.
Thisperturbationcausesachangeintheself-shieldingfactorfofnuclidei0,reaction
j0,inenergygroupg0.Thesecondtermoftheright-handsideofEq.(17.14)hasto
cover the contributions for all nuclides i0, reaction types j0, in energy groups g0;
therefore,wehavetotakethesummationoveri0,j0,andg0.Thesensitivityforthe
nuclidei,reactiontypej,inenergygroupgisgivenby
XX dfi0=fi0
Si,j,g ¼eSi,j,gþ eSi0,j0,g0 (cid:3)dσji0=σj0i ð17:14Þ
0 0 j j
i j
The first term is the direct contribution to S; it can be calculated using the
conventional tools evaluating sensitivity coefficients such as SAGEP, SAGEP-T,
and SAINT. The second term represents the indirect contribution through the
change of self-shielding factor. These coefficients can be calculated as follows:
hereweapplytheresonanceapproximationforheavynuclides,whichissuitablefor
treatingfastreactorswithhardneutronspectraratherthanlightwaterreactors.The
self-shieldingeffectdependsontheneutronspectrum;wheretheneutronspectrum
fortheheavynuclidei0 iswrittenas
1 1
ϕðEÞ/ (cid:3) ð17:15Þ
σi0ðEÞþσi0 E
t b
Equation(17.15)indicatesthatwhenσi0(E)andσi0 changebythesamefactor,the
t b
neutronspectrumremainsthesame;thisshowsthattheratiohhasaneffectonthe
neutronspectrum,andalsoontheself-shieldingfactor.Followingasimilarmethod
[12],thecoefficientinthesecondtermoftheright-handsideofEq.(17.14)iscalled
TERMandcanbewrittenas