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Reactor physics ideas to design novel reactors with faster fissile growth

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Reactor physics ideas to design novel reactors with faster ﬁssile growth
q
V. Jagannathan
a,
*
, Usha Pal
a
, R. Karthikeyan
a
, Devesh Raj
a
, Argala Srivastava
a
, Suhail Ahmad Khan
b
a
Light Water Reactors Physics Section, Reactor Physics Design Division, Bhabha Atomic Research Centre, Mumbai 400 085, India
b
Reactor Project Division, Bhabha Atomic Research Centre, Mumbai 400 085, India
a r t i c l e i n f o
Article history:
Received 8 July 2007Accepted 25 February 2008Available online 14 April 2008
Keywords:
Fast reactorThorium breedersFissile growthTwo year cycle lengthMinimum control maneuvers
a b s t r a c t
There are several types of ﬁssion reactors operating in the world adopting generally the open fuel cyclewhich considers the naturally available ﬁssile nuclide, viz.,
235
U. The accumulated discharged fuel is con-sidered as waste in some countries. However the discharged fuel contains the precious man-made ﬁssileplutonium which would provide the sole means of harnessing the nuclear energy from either depleteduranium or the natural thorium in future. It must be emphasized that the present day power reactorsuse just about 0.5% of the mined uranium and it would be imprudent to discard the rest of the massas waste. It is therefore necessary to explore ways and means of exploiting the fertile mass which hasthe potential of providing the energy without the green house effects for millennia to come. This hasto be done by innovating means of large scale fertile to ﬁssile conversion and then using the man-madeﬁssile material for sustenance as well as growth of ﬁssion nuclear power. This paper attempts to give abroad picture of the available options and the challenges in realizing the theoretical possibilities.
2008 Elsevier Ltd. All rights reserved.
1. Introduction
The present day power reactors use mostly uranium basedfuel.
235
U is the only natural ﬁssile isotope serving as a match-stick to start the ﬁssion chain reaction process. It is necessaryto breed new ﬁssile material long before the
235
U would get ex-hausted. Nuclear reactors have the unique property of rejuvenat-ing themselves, i.e., when ﬁssile materials are consumed forpower generation, new ﬁssile materials can also be producedfrom neutron capture by fertile materials. When the latter processequals, or better, exceeds the former we can have continuousstock of ﬁssile material for several centuries or even millennia.The research on accelerator driven subcritical system (ADSS) arebeing pursued vigorously world over to use the spallation sourceof neutrons as a means of rapid ﬁssile growth. The acceleratortechnology, sustenance of high current ion beam, ion beam focus-ing, design of spallation target size and shape, effective heat re-moval in the surrounding blanket region near the intenseneutron source and maintenance of reasonably low and constantsubcriticality in the surrounding reactor medium are all chal-lenges still defying satisfactory solutions. It is therefore usefulto look into the principles of maximizing the ﬁssile conversionprocess in the existing or some innovative variant version of nu-clear reactors, which may also be suitable for ADS applicationeventually.The basic principles used in the physics design of power reac-tors so far is to minimize the quantum of fuel required for a givenpower generation. The design parameters gets more or less con-vergedtoanarrowrangeoncethechoiceoftypeofreactor,sayfastorthermalismadeandthechoiceofcoolant, moderator, structuralmaterials and control are made accordingly. In thermal powerreactors using natural uranium as fuel the minimum ﬁssile massis obtained by choosing optimum fuel assembly pitch or
V
m
/
V
f
for the fresh state of the fuel. In thermal reactors using enrichedfuel, a choice of
V
m
/
V
f
less than the optimum value is preferredto ensure negative coolant void or temperature coefﬁcient of reac-tivity. However there may not be any loss in the discharge burnupsince due to hardened neutron spectrum the ﬁssile conversion ra-tio gets improved and at the end of life, the reactivity may, in fact,behigherthanthat foranoptimum
V
m
/
V
f
. Thisadvantageisabsentinthereactorsusingnatural uranium. Infastreactorsall cross-sec-tionstendtobeoneortwoordersofmagnitudeloweranditisnec-essary to use nearly 5–10 times ﬁssile content even for criticality.The fuel cost of fast reactors is thus apparently dearer than that of thermal power reactors, and not surprisingly, therefore, there areveryfewoperatingfastreactors, perhapsmerelybywayofdemon-stration of technology. It must be however recognized that fastreactors have to wait for the accumulation of the necessary stock-pile of Pu from thermal power reactors.
232
Th and depleted uranium (
238
U) are equal candidates forbreeding of ﬁssile material since they produce, respectively,
233
U
0196-8904/$ - see front matter
2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.enconman.2008.02.019
q
Paper Submitted to: ICENES 2007 13th International Conference on EmergingNuclear Energy Systems, 3–8 June, 2007, Istanbul, Turkey.
*
Corresponding author. Tel.: +91 22 2559 3739/3768 (O), +91 22 65219051 (R);fax: +9 1 22 2550 5151.
E-mail addresses:
vjagan@barc.gov.in, v_jagan1952@rediffmail.com (V. Jagan-
nathan).Energy Conversion and Management 49 (2008) 2032–2046
Contents lists available at ScienceDirect
Energy Conversion and Management
journal homepage: www.elsevier.com/locate/enconman
and
239
Pu on neutron capture and subsequent two ‘
b
’ decays. The
233
U isotope has an excellent neutronic characteristic. It has theleast capture to ﬁssion ratio and hence the ‘
g
’ value, which is thenumber of ﬁssion neutrons produced per neutron absorbed inthe ﬁssioningatom, remains close to or above 2.3, in the entire en-ergy range, except near 2eV. Fig. 1 gives a comparison of the ‘
g
’valuesforthethreenuclides
235
U,
239
Puand
233
U. Itisthispropertyof
233
U which opens the possibility of a thermal breeder. Howeverin the fast energy range, the ‘
g
’ value of
239
Pu is much higher andhence is a preferred nuclide for fast breeder reactors (FBR).Fastreactorsarebelievedtobenaturalbreederssincetheyhavethe best rejuvenating potential, i.e., they can produce more ﬁssilematerial than what they consume over a period of time. This isfacilitated by two distinguishing features in a fast reactor. One islarge scale loading of pure fertile mass in what is called the ‘blan-ket’ regions and the second is, despite using highly enriched fuel,the level of neutron ﬂux is higher by at least one order of magni-tude due to low cross-sections compared to thermal reactors of comparable power levels. In this context, it must be noted thatthereisanetﬁssilemateriallossinthecoreregionwhichissoughtto be made up by the production of ﬁssile atoms in the blanket re-gionbycapturingofneutronsleakingoutofthecore. Sincetheﬂuxlevel in the blanket region is usually lower by 3–6 times and theaveragecapturecross-sectionoffertileatomlike
238
Uislowerthantheabsorptioncross-sectionofﬁssileatomlike
239
Pubysimilaror-der, the replenishment of ﬁssile loss may be feasible only by usingmuch larger fertile mass. The fertile mass in blanket region is typ-ically more than twice that of the core mass in fast reactors. Theblanket region surrounds the core both radially and axially. Butfor the blanket regions, even the fast reactors cannot have thebreeding potential, in spite of the fact that the value of ‘
g
’ is aboutthree in the fast energy range.Beforewediscussthemeansof enhancingtheﬁssileconversionrateinsomehypotheticalreactor,weshall attempttoqualitativelyinter-compare the conversion rates in different types of thermalpower reactors and fast reactors which are already designed andoperational.Among the thermal power reactors, pressurized heavy waterreactors (PHWR) have the highest ﬁssile conversion rate sincethe ﬂux level is high and there is least competition for absorptionof neutrons from the small and depleting seed content of 0.71% orlessof
235
U.InLightWaterReactors(LWR)usingenricheduraniumtheconversionrateislowerforsimilarreasoning.Howeverthefuelresidence time in LWR is much longer, which is important for pro-longingthe durationof cumulativefertile capture. InPHWR, undernominal conditions, the fuel is discharged after 6–12 months of residence time. In LWR the residence time can be 3–4 years. Inall reactors the conversion rate is the highest at the time of dis-charge since the competition of absorption of neutrons from theseed content is the least. The energy extracted from unit mass iscalledthedischargeburnupandcompares as7MWD/kgfor PHWR using natural uranium and 35 or 43MWD/kg in LWRs using 3.3%(western pressurized water reactors – PWR) or 4% (Russian VVER)enriched fuel, respectively. The discharge Pu content in PHWR isunder 3.5g/kg, while in LWR it is 10–11g/kg. For the same quan-tumof energy generation, the PHWRs canproduce more thandou-ble the quantity of Pu compared to LWRs. However, this Pu wouldbe contained in 6–8 times larger discharged fuel mass. Hence dueto lower speciﬁc Pu content the reprocessing loss of Pu in case of PHWR would be higher. The residual non-depleted
235
U in the dis-charged fuel of PHWR is around 2–3g/kg while in LWR it is about10g/kg.In fast reactor the initial ﬁssile feed in the core region is typi-cally 20–30% of reactor grade Pu with 74% ﬁssile. After extractionof energy of the order of 100MWD/kg the initial ﬁssile seed con-tent would have decreased by 10% and would have been partiallyreplenished by ﬁssile conversion in the core region to the tune of 4–5%. Thus the discharge fuel would still contain 15–24% of seedmaterial with somewhat degraded ﬁssile fraction. As will be seeninthe ensuingdiscussions, the asymptoticﬁssile accumulationpo-tential infertileblanket regionis 90–100g/kgina typical fast neu-tron spectrum with peak near 100keV. In practice, however, theblanket fuel may be discharged much earlier due to provision of less coolant ﬂow compared to core region and the blanket
1E-3 1E-2 1E-1 1E+0 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7
Energy in eV
012345
E t a v a l u e
U-233U-235Pu-239
Fig. 1.
Comparison of
g
-values of
233
U,
235
U and
239
Pu.
V. Jagannathan et al./Energy Conversion and Management 49 (2008) 2032–2046
2033
discharge criteria is based on the maximum power allowable asper the ﬂow provided in the respective region.From the above discussion, it is possible to identify the param-eterswhichwouldhelpinmaximizingtheconversionrateoffertiletoﬁssileandalsoenableaccumulationofaslargeanamountofﬁs-sile material after a given quantum of ﬁssion energy generation.The fertile capture is proportional to the volume or mass of fertilematerial loading, prevalent ﬂux level, the spectrum averaged cap-ture cross-section of fertile nuclide and the duration of the fuel cy-cle campaign. One must attempt to maximize each of theseparameters individually.Depleted uraniumand pure thoriumare the best fertile materi-als to allow high conversion rates. PHWR using natural uraniumhas very small excess reactivity and hence can ill-afford any fertilemassloading,exceptinitsinitialcore. Theyhavetheleastparasiticabsorption in D
2
O coolant/moderator. However it considers largemass of zirconium as structural material, which may somewhatoff-set the above advantage. Boiling water reactors (BWR) havehigher conversion rate compared to PWR due to harder neutronspectrum. High conversion PWR with tight lattice pitch was seri-ously considered in nineties, but was found to have positive cool-ant temperature coefﬁcient. The conversion ratios of PHWR andPWR compare as
0.7 and
0.6, respectively.In the fast reactor the blanket region is usually beyond the ac-tive core. The blanket region receives the neutrons leaking out of core. Also due to leakage at the outer boundary of blanket, the ﬂuxlevel would continuously diminish radially and axially outward.Hence ﬁssile formation rate per unit mass in blanket region wouldbe a fraction of ﬁssile destructionrate per unit mass inthe corere-gion. The seed refueling schedule and the blanket refueling sche-dule may not match. In view of this mismatch in ﬁssile depletionand formation rates, the fast reactors may sometimes reduce tomere converters rather than breeders or may have unacceptablelarge doubling time for the ﬁssile material hold ups both in pileand out of pile.Infastspectrum,ﬁssioncross-sectionof
232
Thislowerthanthatof
238
U by about four times. The absorption and ﬁssion cross-sec-tions of
233
U are lower by factor of two in thermal energy rangecompared to those of
239
Pu, while they are higher for
233
U in fastenergy range. When thorium or depleted uranium is irradiated inthermal, intermediate or fast neutron spectra, the formation of Uor Pu would monotonically increase and ﬁnally saturate to anasymptotic value. This asymptotic ﬁssile accumulation potentialinanyenergyrangecanbe approximately inferredfromthecondi-tion that:
r
232c
N
232
¼
r
233a
N
233
r
238c
N
238
¼
r
239a
N
239
which gives,N
233
=
N
232
¼
r
232c
=
r
233a
N
239
=
N
238
¼
r
238c
=
r
239a
Here N
233
, N
232
are the nuclide concentrations of
233
U and
232
Th,
r
232c
;
r
233a
are the effective microscopic capture and absorptioncross-sections of
232
Th and
233
U, respectively in a given spectrum.N
239
, N
238
are the nuclide concentrations of
239
Pu and
238
U,
r
238c
;
r
239a
are the effective microscopic capture and absorptioncross-sections of
238
U and
239
Pu, respectively, in a given spectrum.Fig. 2 gives plot of these ratios in the entire energy range. It is seenthat the
233
U can accumulate up to 1.3% (13g/kg), while
239
Pu canaccumulateupto0.35%(3.5g/kg) inthermal energyrange. Ininter-mediate energy range, these ratios show several spikes reaching upto 20% corresponding to the sharp resonances of the capturing nu-clide. The ratio is seen to be higher for thorium capture in the en-ergy range 100eV to 10KeV. The actual asymptotic ﬁssile contentcan be obtained from the spectrum average cross-section valuesin a given reactor application.A hypothetical study was done to observe the ﬁssile accumula-tion in fertile fuel rods irradiated in a typical thermal or fast ﬂuxambience at different ﬂux and ﬂuence values. Fig. 3a shows theplot of ﬁssile formation in thorium and natural uranium fuel rodsexposed to a constant one group ﬂux level of 10
14
n/cm
2
/s in athermal reactor ambience. It is seen that the U
total
in Th accumu-lates up to 17g/kg with 85% ﬁssile in a typical thermal spectrum,while the Pu
total
accumulation in U is seen to be under 7g/kg with60–65% ﬁssile, after irradiation time of 1500 days. Fig. 3b showssimilar plot for thorium and depleted uranium fuel rods irradiatedatconstantonegroupﬂuxlevelof1
10
15
and4
10
15
n/cm
2
/sinafastreactorambience.AsseeninFig.3b,infastneutronspectrum
1.0E-21.0E-11.0E+01.0E+11.0E+21.0E+31.0E+41.0E+51.0E+61.0E+7
Energy in eV
0.000.050.100.150.20
C a p . i n F e r t i l e / A b s . i n f i s s i l e
Cap. Th-232 / Abs. U-233Cap. U-238 / Abs. Pu-239
Fig. 2.
Asymptotic ﬁssile accumulation potential in each energy group.2034
V. Jagannathan et al./Energy Conversion and Management 49 (2008) 2032–2046
bothUin Thand Puin Uaccumulate to about
100g/kg, the valuebeing slightly larger for Pu in U, albeit with lesser ﬁssile content.Unlike in thermal spectrum, the ﬁssile fraction remains above90% for verylarge ﬂuence levels up to 1000 days or so at the aboveﬂux levels.One of the major characteristics of fast reactors is relativelyhigh power density which results in high neutron ﬂux level, rapidfuel depletion and short refueling intervals. However, a low neu-tronﬂuxwouldenableindecreasingthedepletionrateofseedfueland hence a longer fuel cycle duration for a given reactivity inven-tory. Since fertile zones reach nearly the same asymptotic ﬁssilecontent, albeit at different times, a lower ﬂux ambience is prefera-ble from the following considerations. A core design with seed tofertile fuel mass ratio of 50:50, with somewhat larger ﬁssile con-tent in the seed and a considerable power share from fertile blan-ket zones would decrease the mean power density and hence theambient ﬂux level. This would help in conserving the ﬁssile con-tent in seed zone for longer duration and allow the fertile zonesto reach the asymptotic ﬁssile content.Twoother key parameterswhichinﬂuencethedesignconsider-ationare
k
1
and burnup variation of fertile zone after a given neu-tron ﬂuence. It was seen that the
k
1
of fertile zone rises fromnearly zero to about unity after an irradiation time of about 3000daysataﬂuxlevelof2
10
15
n/cm
2
/s.Inviewofthischaracteristicof fertile zones, it should be possible by judicious mix of seed andfertile zones to obtain a core design with a small and ﬂat core
040080012001600
Irradiation Time (Days)
048121620
U i n T h o r P u i n U ( g / k g )
Irradiation at Constant One Group Flux Level of 2.0E14 n/cm
2
/sec
U-Tot in Th (g/kg)U-Fis in Th (g/kg)Pu-Tot in U (g/kg)Pu-Fis in U (g/kg)
Fig. 3a.
Production of U from Th or Pu from U in A thermal spectrum.
050010001500200025003000
Irradiation Time in Days
04080120160
U i n T h o r P u i n U ( g / k g )
Pu in U - Flux = 1.0E+15 n/cm
2
/secU in Th - Flux = 4.0E+15 n/cm
2
/secU in Th - Flux = 1.0E+15 n/cm
2
/secPu in U - Flux = 4.0E+15 n/cm
2
/sec
Fig. 3b.
Production of U from Th or Pu from U in a fast spectrum. (
Note.
Thorium rods are pre-irradiated for a ﬂuence of 2
10
14
n/cm
2
/s for 700 days).
V. Jagannathan et al./Energy Conversion and Management 49 (2008) 2032–2046
2035
excess reactivity for as long a duration as possible. The burnupaccumulated in fertile zone compare as 75–85MWD/kg at theabove ﬂuence while the seed zone attains burnup of
100MWD/kg for the above ﬂux level in about 2200 days. These features sug-gest that one canconsider athreebatchfuelingwitha cyclelengthof about 720 days where the seed fuel shouldreside in the core forthree fuel cycles and the fertile rods should reside for at least fourfuelcycles.Theprevalentﬂuxlevelinseedandfertilezonesshouldbe comparable.It is necessary to consider as high a seed content and a fairlyhigh discharge burnup so that the blanket regions are capable of accumulating ﬁssile content close to the asymptotic value. In nor-mal FBR, after accounting for leakagefromcore, one would still re-quire appropriate control maneuvers for compensating the burnupreactivity swing. Here we would like to mention that the parasiticabsorption in structural material, coolant and net leakage out of core/blanket regions are normally inevitable. They all cut into theavailability of neutrons for fertile to ﬁssile conversion. It musthowever be possible to minimize at least the control absorberinventory by suitably devising means of loading equivalent fertile
Table 1
Core design parameters of the conceptual fast thorium breeder reactor (FTBR)
Core parameters Units ValuesThermal power MWt 2500Electric power MWe 1000Coolant SodiumCycle length Days 720Cycle energy MWD 1,800,000Mean discharge burnup MWD/T100,000Discharge mass T 18Fuel batch size 1/3rd coreNumber of assemblies per batch 120Number of Seed assemblies in core 360Number of seedless blanket assemblies 120Number of seedless blanket/control assemblies 25Additional ThO
2
+Ni reﬂector assemblies 120Hexagonal assembly lattice pitch mm 184Effective diameter of core+radial blanket regions mm 4830Number of steel reﬂector assemblies 96Number of B
4
C assemblies for shielding –Active core height inclusive of 200mm internalblanketmm 1500Top axial blanket thickness mm 300Bottom axial blanket thickness mm 300Average linear heat rating w/cm 150.8
Description of seeded fuel assemblies (360)
Inner region of the seeded fuel assemblyNumber of seed fuel rods 217Seed pellet diameter mm 5.7Steel clad OD mm 6.6PuO
2
seed content in Dep. UO
2
% 45Fuel density (oxide) g/cm
3
10Hexagonal pin pitch mm 8.3Inner steel channel inner/outer dimension mm 126/132Number of fuel cycles 3Outer region of the seeded assemblyNumber of irradiated fertile Dep. U fuel rods 90PuO
2
Seed content % In situ (4–5%)Pellet diameter mm 8.8Steel clad OD mm 9.8Hexagonal pin pitch mm 12Fuel density (oxide) g/cm
3
10Outer steel channel inner/outer dimension mm 176/182Number of fuel cycles (1+3)
Description of seedless fertile blanket assemblies (120 + 25)
Inner region of the blanket assemblyNumber of seedless ThO
2
rods 127Pellet diameter mm 8.8Steel clad OD mm 9.8Hexagonal pin pitch mm 10.85Fuel density (oxide) g/cm
3
9Inner steel channel inner/outer dimension mm 126/132Number of cycles in this location 1–3Outer region of the blanket assemblyNumber of Dep. U blanket fuel rods 90Pellet diameter mm 8.8Steel clad OD mm 9.8Hexagonal pin pitch mm 12Fuel density (oxide) g/cm
3
10Outer steel channel inner/outer dimension mm 176/182Number of cycles in this location 1
Description of seedless ThO
2
+ steel rods assemblies
Number of such assemblies in the core 120Location of ThO
2
rods in the assembly Inner 127locationsDescription of ThO
2
rods Same as aboveLocation of steel rods in the assembly Outer 90locationsLocation in the core of these assemblies Outermost layerNumber of cycles in this location for ThO
2
rods One
Seed Fuel Rods (217) Irradiated Fertile Rods (90)
Fig. 4a.
Two region – PuO
2
seeded MOX+one cycle irradiated Dep. UO
2
.
Seedless ThO
2
Rods (127)Depleted UO
2
Rods (90)
Fig. 4b.
Two region seedless ThO
2
+Dep. UO
2
fuel assembly.2036
V. Jagannathan et al./Energy Conversion and Management 49 (2008) 2032–2046

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