Breeding Capability and Void Reactivity Analysis of Heavy-Water-Cooled Thorium Reactor

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Breeding Capability and Void Reactivity Analysis ofHeavy-Water-Cooled Thorium ReactorSidik PERMANA a , Naoyuki TAKAKI a & Hiroshi SEKIMOTO aa Research Laboratory for Nuclear Reactors , Tokyo Institute of Technology , 2-12-1-N1-17, O-okayama, Meguro-ku, Tokyo , 152-8550 , JapanPublished online: 05 Jan 2012.

To cite this article: Sidik PERMANA , Naoyuki TAKAKI & Hiroshi SEKIMOTO (2008) Breeding Capability and Void ReactivityAnalysis of Heavy-Water-Cooled Thorium Reactor, Journal of Nuclear Science and Technology, 45:7, 589-600

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Breeding Capability and Void Reactivity Analysis

of Heavy-Water-Cooled Thorium Reactor

Sidik PERMANA�, Naoyuki TAKAKI and Hiroshi SEKIMOTO

Research Laboratory for Nuclear Reactors, Tokyo Institute of Technology,2-12-1-N1-17, O-okayama, Meguro-ku, Tokyo 152-8550, Japan

(Received April 28, 2007 and accepted in revised form October 22, 2007)

The fuel breeding and void reactivity coefficient of thorium reactors have been investigated usingheavy water as coolant for several parametric surveys on moderator-to-fuel ratio (MFR) and burnup.The equilibrium fuel cycle burnup calculation has been performed, which is coupled with the cell calcu-lation for this evaluation. The � of 233U shows its superiority over other fissile nuclides in the surveyedMFR ranges and always stays higher than 2.1, which indicates that the reactor has a breeding conditionfor a wide range of MFR. A breeding condition with a burnup comparable to that of a standard PWRor higher can be achieved by adopting a larger pin gap (1–6mm), and a pin gap of about 2mm can beused to achieve a breeding ratio (BR) of 1.1. A feasible design region of the reactors, which fulfills thebreeding condition and negative void reactivity coefficient, has been found. A heavy-water-cooledPWR-type Th-233U fuel reactor can be designed as a breeder reactor with negative void coefficient.

KEYWORDS: fuel breeding, negative void coefficient, thorium reactor, heavy water, larger pin gap,burn up, breeding ratio

I. Introduction

Nuclear energy has contributed to fulfilling the world’senergy demand especially in relation to sustainable develop-ment without causing any greenhouse effect on the environ-ment for many years. A self-sustaining reactor system,which is related to breeding capability, is very essential toimprove the reactor capability for extending the sustainabil-ity of nuclear fuel resource. In the present stage, the water-cooled reactor, which is mainly a light water reactor, produc-es energy by consuming uranium fuel with a lower conver-sion ratio capability. The light water reactor requires en-riched uranium for maintaining its criticality, whose conver-sion ratio is about 0.6. A heavy-water-cooled reactor needsnatural uranium for its operation and obtains a conversionratio of about 0.8, as well as HTGR.1,2) Based on thewater-cooled-type reactors mentioned above, some research-ers have investigated some new reactor designs or modifiedwater-cooled reactor designs to obtain a better conversionratio capability. Some researchers have concentrated on thefast reactor designs to achieve a higher breeding condition,which can be achieved using harder spectrum. However, ithas some obstacles due to safety concerns associated witha positive void reactivity.1,3,4)

As a well-proven technology and commercial power plant,water-cooled reactors show a better safety characteristic with

regards to a negative void reactivity; however, it still hassome difficulties in achieving breeding condition. A harderspectrum is required in order to achieve a higher conversionratio and a high burn up.5–7) Research on reduced-modera-tion water reactor (RMWR) had been conducted by theJapan Atomic Energy Research Institute (JAERI) to analyzethe conversion capability.6–9) A modification reactor coredesign was based on the BWR tight lattice core to achievea hard spectrum. However, the tight lattice core is expectedto have a positive void coefficient.10,11) To reduce the posi-tive void coefficient and obtain a negative void coefficient,some core arrangement was done in order to enhance neu-tron leakage during coolant heat up. A pressurized waterreactor was proposed by using heavy water to replace thelight water coolant to obtain a harder neutron spectrumand a higher conversion ratio. This PWR with a heavy watercoolant obtained a higher moderator-to-fuel ratio (MFR) andreduced the difficulty of heat removal than the light watercoolant. Some previous works were done both in the US(EPRI) and in Europe (PSI) before the RMWR design wasproposed, which used Light Water Reactor (LWR) with ahard spectrum.11)

The impact of the moderator-to-fuel ratio was evaluatedbased on the light and heavy water coolant reactors withuranium fuel.2) Several fuel cycle options were employedto estimate the effect of recycled heavy metal (HM) on therequired enrichment and conversion ratio. This study showedthat a higher conversion ratio can be achieved by reducingthe moderator-to-fuel ratio (MFR) and increasing the recy-

�Atomic Energy Society of Japan

�Corresponding author, E-mail: [email protected]

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cled HM. A breeding condition can be achieved at a verytight lattice pitch (MFR � 0:3) for the recycled Pu system,which can be considered as U-Pu fuel, and at MFR � 0:4for the recycled TRU system (as U-TRU fuel). Heavy watercoolant was introduced to obtain a breeding condition for alarger lattice pitch. The result showed that at MFR � 0:8and MFR � 1:1, a breeding condition can be achieved forthe U-Pu and U-TRU fuel systems. It showed that the heavywater coolant obtains a larger MFR for breeding because itsneutron spectrum is harder than that of the light water cool-ant, which makes it easier for the heavy water coolant toobtain a breeding condition and to increase the heat removalcapability.

A fuel material that has a high capability of breeding inthe thermal or epithermal spectra region is required to over-come the lower conversion ratio of the water-cooled reactor.The thorium fuel with fissile 233U is the candidate that showsa better � in the thermal and epithermal regions than theother fissile nuclides, and it can provide the negative voidreactivity coefficient.5,10) The thorium cycle has been dem-onstrated in terms of breeding capability in the thermal neu-tron spectrum region such as in a Shippingport reactor, themolten salt breeder reactor (MSBR) project, and a BWRconcept with tight lattice fuels.12–16) This new BWR conceptaimed to achieve breeding target (BR over 1.0) and higherburnup. An advanced thorium breeder reactor (ATBR) wasproposed by Indian researchers. This reactor was based onan advanced CANDU reactor type.17) This study was con-ducted using the thorium and plutonium fuel system with acore blanket system. Those previous works show the feasi-bility of breeding in the thermal energy region fueled by233U-Th with some heterogeneous core for achieving breed-ing conditions. A feasible region of a homogenous core wasshown to satisfy the constrains of criticality, breeding andnegative void coefficient for several discharged fuel burn-ups.5) This study concluded that for a burnup of equal to30GWd/t or higher, MFR � 0:3 is needed for a breedingcondition and negative void coefficient.

The study on the feasible region of water-cooled breederreactors using 233U-Th fuel and heavy water as coolantwas carried out. In order to estimate the design configurationcriteria, the feasible region was determined based on thebreeding condition and negative void reactivity coefficientcriteria for each case. The study was carried out using thenuclear equilibrium state model.2,5,18) In the nuclear equilib-rium state, the production rate of nuclear energy is constant,and the reactions of nuclear materials are constant as well.Therefore, the amount of each nuclide in a reactor becomesconstant if the refueling operation is continuous. The breed-ing performance and feasible area of the heavy water thori-um reactor were investigated at different moderator-to-fuelratios (MFRs) and burnup. The required 233U enrichmentas initial fissile was employed to achieve the targeted dis-charge fuel burnup and it satisfied the criticality of thereactors. Some characteristics such as neutron spectrum, �value, and void reactivity were evaluated. The results showthe feasible design area of breeding and the negative voidreactivity coefficient.

II. Reactor Design Parameters and Fuel CycleOptions

The basic idea of this study is to evaluate the neutroniccharacteristics of heavy-water-cooled thorium thermal reac-tors. As mentioned in the introduction, previous studiesshowed the limited region of breeding for the light-water-cooled reactor, with U-Pu or Th-233U fuels, and it becomesa larger region of breeding when the light water coolant isreplaced with the heavy water coolant for U-Pu. For suchtight lattice pitches, a void reactivity of both light waterand heavy water coolants with U-Pu fuel tends to result ina positive void coefficient. However, the light-water-cooledreactor with Th-233U fuel showed a negative void reactivitycoefficient even for a conservative assumption since leakageis neglected. In addition, the light-water-cooled Th-233U fuelrequires lower fuel pellet power density (45W/cm3) toobtain a breeding condition for burn up � 30GWd/t, whichmakes the HM inventory larger. Employing heavy water canbe expected to result in a harder neutron spectrum than in thecase of the light water coolant as shown in Fig. 1, which isbased on the Th-233U fuel. The heavy water coolant causes areactor to more easily obtain a breeding condition at a rela-tively larger fuel pin pitch; therefore, wider MFR regionscan be evaluated. Based on the above condition, this studytried to enlarge the feasible region of breeding and thenegative void reactivity for a relatively higher burn up andlower HM inventory.

The basic reactor parameters of the investigated systemsare tabulated in Table 1. The power density in the fuel pelletis fixed at 140W/cm3, which is two times lower than thefuel pellet power density of the PWR standard. This fuelpellet power density was equal to about 19 kW/m of thelinear heat rate. The standard PWR has an average corepower density of about 100W/cm3; this average core powerdensity is based on the MFR of about 2 and it is equal to a

0.01

0.1

1

10

0.01 1 100 104 106

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eutr

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ectr

a p

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#/cm

2 s]

Energy [eV]

D2O

H2O

Fig. 1 Neutron spectra per unit lethargy of heavy and light watercoolant at MFR ¼ 2

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fuel pellet power density of 280W/cm3.1,19) In this paper,we intend to evaluate the breeding capability and void reac-tivity coefficient based on Th-233U fuel cooled by heavywater and to find its feasible region of breeding and negativevoid coefficients. The key parameters such as MFR andburnup are employed. The investigated MFR of the reactoris surveyed from 0.1 to 30.0 to cover a wider feasible region,which is selected to cover a broader neutron spectra investi-gation. In addition, the targeted burnups are surveyed from6GWd/t to 50GWd/t for evaluating the burnup effect.

The cell model was a one-dimensional cylindrical modelthat is divided into radius of fuel, cladding and coolant asshown in Fig. 2. The radius of fuel and cladding were fixed,and the radius of the coolant was varied to estimate the mod-eration ratio. The MFR calculation is divided into two differ-ent calculations based on the geometrical limit of MFR fortriangular lattice, which requires a 1mm pin gap (MFR ofabout 0.3). This 1mm pin gap is adopted as reference con-sidering the heat removal capacity.7) In general, either square

lattice or triangular lattice pitches are possible with thecylindrical model using the equivalence of coolant volume.This study focused on the triangular lattice pitch because itcan use a lower MFR for a 1mm pin gap. For MFR thathas pin gap � 1mm, we employed a volume ratio of moder-ator to fuel. This MFR can be called as geometrical MFR ormoderator-to-fuel volume ratio. For MFR in which the pingap is < 1mm, the geometrical MFR was fixed for a pingap of 1mm, and to calculate the MFR, the ratio of moder-ator number density is used. Those MFR can be called aseffective MFR or it can be categorized as the MFR withvoided condition. MFR ¼ 0:1 was calculated based on theeffective MFR, and for MFR ¼ 30:0, based on the geomet-rical MFR.

Very low MFR of approximately 0.1 has been studied forevaluating the hard spectrum characteristics that the spec-trum is nearly to the fast spectrum reactor characteristics.The tight lattice reactors (MFR � 1:0), PWR (MFR ¼ 2)and higher MFR condition (MFR > 10), which can be con-sidered as similar to the equivalent moderator or coolant-to-fuel ratio of CANDU or PTGR types,20) are included in thisinvestigated MFR range in order to obtain comparableresults. The study intends to evaluate the feasible area ofbreeding and negative void coefficient for the MFR regionof pin gap � 1mm; therefore, it focused on the higherMFR value. A much lower MFR (pin gap < 1mm) was usedfor evaluating the voided condition of MFR when the pingap is fixed. A fuel pin diameter of 1.452 was used in thisstudy, which is 1.5 times thicker than that of the standardPWR. This fuel pin diameter was based on the fuel pindiameter of the Shippingport regular blanket.12)

Several burnup values were investigated to cover sometypical burnup values of PWR (33GWd/t), conventionalCANDU reactor (7.5GWd/t)1) and some other reactor typesas comparable references. The reactor system was fueledusing 233U-Th oxide fuel with heavy water as coolant. Inthe burnup calculations, all heavy metals (HM) dischargedper year from the reactor together with fission products wereused for this study. The discharge fuel constants were usedto estimate the discharged fuel per year from the reactor,which can be considered in calculating the discharged fuelburnup. The fuel temperature, coolant temperature andheavy water density were 873K, 573K and 0.78 g/cc, re-spectively, with the core pressure of about 13MPa. In thisstudy, the reactor height was fixed at 370 cm and the reactorcore radius was varied depending on the MFR. For instance,MFRs of 0.5, 1.0, 2.0, 10.0 and 20.0 were equal to 150, 180,280, 450, and 622 cm of the core radius, respectively.

III. Calculation Method

1. Equilibrium Burn up and Cell CalculationIn the present study, the calculation model included two

different calculation methods. To calculate the equilibriumstate, the equilibrium burnup calculation model was usedand the cell calculation of the SRAC95 module was usedto generate the flux and microscopic cross section from thecell calculation. We have called this coupling calculationan equilibrium cell iterative calculation system (ECICS).21)

Table 1 Reactor design parameters

Parameter

Thermal power output [MWt] 3000Supply fuel 232Th-233U OxideCladding Zircaloy-4Coolant Heavy water

Fuel pellet average power density [W/cc] 140Linear heat rate [kW/m] 19

Fuel pellet diameter (inner) [cm] 1.31Fuel pin diameter (outer) [cm] 1.452Discharge fuel burnup [GWd/t] 6–50

Moderator-to-fuel ratio (MFR) [-]a 0.1–30Height of core [cm] 370

aWithout cladding

dp

Triangular LatticeTriangular Lattice

RfRcl

Rco

RfRcl

Rco

p : Pin pitch

d : Diameter of fuel pin

Rf : Radius of fuel pellet

Rcl : Radius of fuel cladding

Rco : Radius of coolant

Fig. 2 Fuel pin cell geometry

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The nuclear equilibrium-fuel cycle in the present study isconsidered to satisfy the following conditions:1) The number density of each nuclide in a reactor is

constant.2) The refueling process is continuous.The fuel composition in the core was directly calculated

under the equilibrium condition, and the fuel material flowssuch as natural uranium feed, thorium feed, spent fuel re-moval and actinides recycling were mathematically treatedas a continuous process. The discharge fuel constant wasexamined to determine how much fuel is discharged fromthe reactor per year to achieve the targeted discharge fuelburnup. In the equilibrium burnup calculation, 1,238 fissionproducts and 129 heavy nuclides are employed. This equi-librium burnup calculation is coupled with the PIJ cell calcu-lation module of SRAC9522) in order to estimate the critical-ity and cell configuration effect, and to obtain the neutronspectrum and 107 group microscopic cross sections, whichare condensed into one group microscopic cross section ofeach investigated case as shown in Fig. 3. The employednuclear data library was JENDL 3.2 and burnup chain ofTHCM66FP.23)

In the cell calculation, because of the limitation of theburnup nuclide library, we used 66 fission products, 26heavy metals, and 1 pseudo FP as representatives for evalu-ation. The data library from the cell calculation was used togenerate the nuclide data user for the equilibrium burnupcalculation. Thus, the main nuclides in the equilibrium burn-up calculation were updated iteratively based on the SRACdata library. The other evaluated nuclides in the equilibriumcalculation, which were not updated, come from some mixeddata library such as the JENDL and ENDF data libraries.Based on the consideration of the nuclear equilibrium-fuelcycle mentioned above, the conditions of the number densityof i-th nuclide, ni, in the core should satisfy the followingburnup equation:

dni

dt¼ �ð�i þ ��a;i þ riÞni þ

Xj

�j!inj

þ �Xj

�a; j!inj þ si ð1Þ

Under nuclear equilibrium conditions, the nuclide numberdensities do not change over time, that is,

dni

dt¼ 0 ð2Þ

Therefore, the equilibrium fuel cycle burnup equation be-comes

� ð�i þ ��a;i þ riÞniþ

Xj

�j!inj þ �Xj

�a; j!ini þ si ¼ 0 ð3Þ

where �: Neutron flux,�i: Decay constant of i-th nuclide,ri: Discharge constant of i-th nuclide,

�j!i: Decay constant of j-th nuclide to produce i-thnuclide,

�j!i: Microscopic transmutation cross section of j-thnuclide to produce i-th nuclide,

si: Supply rate of i-th nuclide,�a;i: Microscopic absorption cross section of i-th

nuclide.

Here, the absorption cross section includes not only fissionand capture cross sections but also (n, 2n) and other nucleartransmutation cross sections. The formation of fission prod-ucts can be estimated using �j!i or �j!i given by the follow-ing equations:For neutron-induced fission,

�j!i ¼ �f ; j�j!i; ð4Þ

where�f ; j: Microscopic fission cross section of j-th nuclide,�j!i: Yield of i-th nuclide from j-th fissile nuclide,and for spontaneous fission,

�j!i ¼ �f ; j�s; j!i ð5Þ

where�f ; j: Spontaneous fission decay constant of j-th nuclide

�s; j!i: Yield of i-th nuclide from j-th fissile nuclide sponta-neous fission.

In the present study, ni is the number density of the nu-clide in the fuel pellet. When we consider ni as the numberdensity of the nuclide in the fuel pellet, the upper limit of thefuel pellet density according to the fuel materials should betaken into account. Then, we decided that the total numberdensity of all nuclides in the fuel pellet should satisfy the fol-lowing equation.

Xk2HMl2FP

nk þnl

2

� �¼ N total ð6Þ

Here, N total is the number density of heavy metal nuclide inthe fresh fuel (233U-232Th). The initial enrichment (233U) wasevaluated based on the targeted discharge fuel burnup underequilibrium condition. It was determined when the satisfieddischarged fuel burnup and neutron multiplication factorwere achieved. In this Eq. (6), we took half of the numberdensity of FP since each fission reaction can be consideredto produce two FPs. The smeared density of the fuel pellet,N total, depends on the fuel materials, either oxide fuel, nitridefuel or metallic fuel. Since in this study we evaluated PWR

Equilibrium fuelcycle burnupcalculation FP :1238, HM : 129

Nuclide density

Cell calculationThe PIJ SRAC 2002,JENDL-3.2 FP : 66, HM :26, and 1 pseudo FP

Flux, Microscopic XS

Collapsing into 1 group microscopic xsNormalization

Power density

Fig. 3 Flowchart of equilibrium cell iterative calculation systems(ECICSs)

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with thorium oxide fuel, this value was chosen to be 93% ofthe theoretical density of thorium oxide.

The fuel supply rate for the evaluated reactor core systemsatisfies the following equation:

si ¼ �iS ð7Þ

where si: supply rate of i-th nuclide,�i: isotopic fraction of i-th in supplied fuel (in

atomic percent)S: supply rate of total fuel

The neutron flux, �, in the fuel was determined from thefollowing equation:

P ¼ �Xi2HM

ni�f ;i� ð8Þ

where P: average power density of fuel pellet,�: energy released per fission (200MeV)

The flux level was determined from the heavy nuclidedensities and the designed power density level. Comparisonsof the fissile enrichments calculated using our model withthose of the typical PWR confirmed the applicability ofour calculation method.2,19,24) We compared the presentinvestigation result with the cell burnup of SRAC95 forcriticality and breeding. It showed small discrepancies forseveral burnup cases. The void reactivity coefficient discrep-ancy can be estimated using the discrepancy of the critical-ity. The results are tabulated in Table 2, which were basedon MFR ¼ 1:0 for several burnup values. It shows that thedifferences among k-eff and conversion ratios are about 1%.

2. Criticality and Breeding RatioTo evaluate the criticality of the system, we focused on

the infinite multiplication factor, kinf , and the effectivemultiplication factor, which was evaluated for a core heightof 370 cm. A different leakage factor was employed, whichdepends on the MFR and geometrical buckling. The extraneutrons can be used to convert fertile materials to fissilematerials such as a fertile material of 232Th that can betransmuted into 233U. This expression was actually referredto as the eta value (�). The breeding condition occurs when� > 2 since slightly more than one fission neutron is neededto maintain the chain reaction (some will leak out or beabsorbed in parasitic capture) while one neutron will beneeded to replace the consumed fissile nucleus by convertinga fertile material into a fissile nucleus. Thus, the extra neu-trons here are referred to as additional neutron that can beused to convert a fertile material into a fissile nucleus. Theconversion ratio here was calculated by using the equilib-rium atom compositions using this Eq. (9).

CR ¼capture rateðTh232þ U234Þ � capture rateðPa233Þ

Absorption rateðU233þ U235Þð9Þ

3. Void Reactivity CoefficientA void reactivity coefficient, �v, is calculated using the

following equation, where the voided conditions are investi-gated for different MFR and burnups. To evaluate the effectof void fraction, several voided conditions, from 5% to100% were evaluated. A voided condition was simulatedby decreasing the density of the coolant. A 5% void wasevaluated as the smallest voided condition and a 100% voidwas studied assuming that the total coolants in the core arevoided. Those voided conditions were evaluated in orderto determine the most conservative voided condition thatshows the least negative void coefficient. In this investiga-tion, we only considered the void reactivity coefficient basedon several coolant voided fractions.

�v ¼��

� fvð10Þ

where

�� ¼ �void � �non-void ð11Þ

� ¼kinf � 1

kinfð12Þ

and fv and kinf are voided fraction of coolant and infi-nite multiplication factor, respectively. This is a con-servative evaluation, since the neutron leakage effect wasignored.5)

IV. Results and Discussion

1. Required Fissile Enrichment of 233UThe present study evaluated the required 233U enrichment

for different MFR and burnups. The evaluation of the re-quired enrichment was based on the initial enrichment thatis needed for criticality. The obtained results of the requiredenrichment are shown in Fig. 4 as a function of MFR fordifferent burnup cases. The required enrichment decreasesmonotonically with increasing MFR for all burnup cases.However, it shows a maximum enrichment at a certain lowerMFR for burnup of 36 and 50GWd/t, and for lower MFR, ahigher burnup requires a lower enrichment because of theharder spectrum and its higher breeding capability. A higherMFR makes a neutron spectrum become softer, which causesa reactor to require a lower enrichment. The required enrich-ment decreases rapidly with increasing MFR for MFR < 8,

Table 2 Equilibrium and cell burnup calculations

Burnup Enrichment Criticality (K-Eff) Conversion Ratio

[GWd/t] [%]Equilibri Cell Delta Equilibri Cell Deltaum [-] Burnup [-] (%) um [-] Burnup [-] (%)

10 6.16 1.003 1.001 �0:19 1.0998 1.101 0.1230 6.67 1.003 0.997 �0:58 1.0565 1.048 �0:77950 7.14 1.003 0.994 �0:93 1.0221 1.008 �1:389

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and in the case of MFR > 20, a reactor requires almost aconstant enrichment for higher MFR.

A heavy water coolant requires a higher fissile enrichmentthan a light water coolant to maintain its criticality becauseof the harder neutron spectrum2) as shown in Fig. 1 forTh-233U fuel at MFR ¼ 2. It shows that a light water coolantobtains a thermal peak in the thermal energy region at 0.1 eVand a small thermal peak appears for a heavy water coolantwhere the location of its peak shifts to higher energy (1 eV).In the case of the heavy water coolant, it does not have asufficient concentration of heavy water to thermalize theneutron spectrum for obtaining a high thermal peak as in

the case of the light water coolant. Therefore, a much heav-ier water coolant is required to thermalize the reactor25) asshown in Fig. 5. A heavy water coolant requires about twotimes higher enrichment of 235U than a light water coolantat MFR ¼ 2 for a U-Pu fuel system.2) The 233U enrichmentof heavy water coolant is also required, compared with alight water coolant,5) for the Th-233U fuel system. A Th-233U fuel system requires a lower enrichment than a U-Pufuel system for both heavy and light water coolants. A lowerfissile enrichment of 233U can be estimated from the � offissile 233U, which is superior to other fissile nuclides, alongthe MFR as shown in Fig. 6. Higher burnup requires ahigher enrichment of 233U forMFR > 0:3. This phenomenonis caused by the increase in the amount of fission product,which makes the neutron spectra become harder; therefore,to maintain a criticality condition for higher burnup, a higherenrichment is required.

Figure 7 shows the evaluation of required enrichment asa function of burnup for several MFRs. MFR ¼ 0:3 obtainsthe constant required enrichment along burnup and itsenrichment of MFR > 0:3 increases for higher burnup.For burnup of 6 to 50GWd/t, the required 233U enrichmentof the systems is lower than the 8% enrichment of 233U forall investigated cases. This condition shows that MFR ¼ 20

requires an enrichment of about 3 times lower thanMFR ¼ 2, and for tight pitch lattice case (MFR < 0:5), therequired enrichment of 233U is about two times higher thanthe enrichment at MFR ¼ 2.

2. Breeding CapabilityA better breeding capability of the heavy water coolant

was shown in several studies,2,7) because the heavy watercoolant has a harder spectrum than the light water coolant.Therefore, reducing the MFR is one option for making theneutron spectrum harder or for lowering the moderation ratio

3

4

5

6

7

8

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

6 GWd/t183650

En

rich

men

t[%

]

MFR[-]

6 GWd/t

Higher Burnup

1

2

3

4

5

6

7

8

0 5 10 15 20 25 30 35

6 GWd/t183650

En

rich

men

t[%

]

MFR[-]

Higher Burnup

(a)

(b)

Fig. 4 (a) Required 233U enrichment for MFR < 2 (b) Required233U enrichment as a function of MFR for different burnups.

0.01

0.1

1

10

100

0.01 1 100 104 106

MFR=0.10.52.08.020.0

Rel

ativ

e N

eutr

on

Sp

ectr

a p

er le

thar

gy[

#/cm

2 s]

Energy [eV]

MFR=20

0.1

0.5

28.0

MFR=20

8.0

Fig. 5 Neutron spectra per unit lethargy of heavy water coolantfor several MFRs

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capability of the reactors. A higher fuel breeding is alsotightly related to a higher � (� > 2) of the main fissile inthe core as shown in Fig. 6, which shows that the � of 233Uis always higher than 2.1 and it is superior to otherfissile nuclides along the MFR.5) A minimum conversionratio appears at a certain MFR (MFR ¼ 3 to 4) along theMFR as shown in Fig. 8. The MFR change is more signifi-cant to the change in the conversion ratio at MFR < 3,which shows that the conversion ratio increases rapidly withdecreasing MFR.

A breeding condition can be obtained along the MFR forlower burnup (6GWd/t) and its breeding value is reduced

for higher burnup. To achieve a breeding condition for burn-up of 30GWd/t or higher,MFR < 1:5 is needed. MFR ¼ 20

results in a better conversion ratio than MFR ¼ 2 at lowerburnup. However, its conversion ratio of MFR ¼ 20 isslightly lower for burnup > 36GWd/t. MFR ¼ 2 results ina breeding condition only for burnup < 30 as well asMFR ¼ 20. In the cases of the MFR of standard PWR(MFR ¼ 2) and conventional CANDU (CANDU6, MFR ¼20), a breeding condition of heavy-water-cooled Th-233Ufuel system was obtained in the relatively lower burnuprange compared with that of the conventional PWR. For atight lattice pitch case (MFR < 1:0) such as MFRs of 0.5and 0.3, the breeding ratio reaches higher than 1.1, but isstill lower than 1.2 in the surveyed burnup (6GWd/t to50GWd/t) ranges as shown in Fig. 9.

A feasibility study on the homogeneous core of a light-water-cooled reactor using the U-Pu fuel system that isbased on the PWR design showed that a breeding condition(CR � 1) can be achieved using a very tight lattice pitcharrangement (MFR � 0:3). A larger fuel pin pitch can beused (MFR � 0:8) to achieve a breeding condition2) for aheavy water coolant (U-Pu fuel system). Another study onthe light-water-cooled reactor using the Th-233U fuelsystem showed that a 1mm pin gap of triangular tightpitches obtains a breeding condition (CR � 1) for burnup� 30GWd/t or higher.5) It required a lower fuel pellet powerdensity (45W/cm3) and adopted a thicker fuel pin diameterthat is about 1.5 times thicker than that of a standard PWR.Therefore, a wider pin gap can be obtained for a larger fuelpin diameter at the same MFR. Those previous studiesadopted the tight lattice pitch arrangement of a triangular lat-tice to achieve a breeding condition. A larger ratio of pinpitch to fuel pin diameter (p/d) and a larger pin-to-pin gapare more preferable to increase the cooling ability and to im-prove the thermal hydraulic properties. In the present study,

1

2

3

4

5

6

7

8

0 10 20 40 60

En

rich

men

t[%

]

Burnup[GWd/t]

MFR=20

0.10.3

0.5

2.0

30 50

Fig. 7 Required 233U enrichment as a function of burnup for sev-eral MFRs

(a)

(b)

1.6

1.7

1.8

1.9

2

2.1

2.2

2.3

2.4

0

0.02

0.04

0.06

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0.1

0 2 3 4 5

Eta

[-]

Eta o

f 232Th

[-]

MFR[-]

6 GWd/t

Pu239

U233

Th232

U235

1.6

1.7

1.8

1.9

2

2.1

2.2

2.3

2.4

0

0.0225

0.045

0.0675

0.09

0 5 10 15 20 25 30

Eta

[-]

Eta o

f 232Th

[-]

MFR[-]

6 GWd/t

Pu239

U233

Th232

U235

1

Fig. 6 (a) � of several main nuclides forMFR < 5 (b) � of severalmain nuclides as a function of MFR for 6GWd/t

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a larger pin pitch can be used to achieve a breeding conditionfor a burnup comparable to that of a standard PWR with thepin gap from 1–6mm. For instance, to achieve a breeding ra-tio (BR) of 1.1, a pin gap of about 2mm (MFR ¼ 0:5) can beused. Therefore, better cooling ability and thermal hydraulicproperties can be expected from this study.

3. Void Reactivity CoefficientThe void reactivity coefficient was evaluated based on

the equilibrium condition. This equilibrium condition wasachieved based on the equilibrium burnup calculation, whichobtains the equilibrium nuclide densities in the reactors. A

conservative estimation was used for void evaluation, whenthe reactivity is based on the infinite neutron multiplicationfactor (k-infinity), since the neutron leakage effect was ig-nored. The void coefficient was evaluated for different MFRsand burnups. The obtained results of void reactivity coeffi-cient are shown in Figs. 10 and 11. In general, almost allthe regions showed a negative void coefficient except inthe case of lower MFR (MFR < 0:5). As a function ofMFR, the void reactivity coefficient has the most negativevalue at certain MFRs (MFR ¼ 2 to 3) depending on theburnup as shown in Fig. 10(b).

The void reactivity coefficient was less negative when theMFR was decreased until it reached the positive void reac-tivity. The minimum MFR as a limit region of negative voidcoefficient as shown in Fig. 10(a) for different burnup can beestimated. It shows that the void reactivity of burnup of6GWd/t obtains a positive value at MFR < 0:2. Therefore,MFR of about 0.2 can be expected as the minimum limit ofMFR for obtaining a negative void coefficient. For higherMFR, a negative value of void reactivity is always obtainedalong the investigated MFR; therefore, there is no maximumlimit of MFR for obtaining a negative void reactivity. Theminimum MFR for a negative void reactivity increased forhigher burnup. The void reactivity coefficient became morenegative with increasing void fraction, as shown in Fig. 11.This can be considered that the highest voided fraction(100%) is the most conservative void fraction, which showsthe least negative void coefficient. A higher burnup isconsidered to make the void reactivity coefficient becomeless negative because of the increase in the accumulationof fission products in the core.

Generally, the negative void coefficient can be estimatedusing the � profile of 233U as a main fissile, which can beconsidered to have a negative contribution.5) The analysisresult on a negative void reactivity or near-zero void reactiv-ity coefficients in the thorium-based fuel can be explained

(a)

(b)

0.85

0.9

0.95

1

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0 5 10 15 20 25 30 35

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nve

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n R

atio

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0.85

0.9

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1.15

1.2

0 1 2 4 6

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Co

nve

rsio

n R

atio

[-]

MFR[-]

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3 5

Fig. 8 (a) Conversion ratio forMFR < 6 (b) Conversion ratio as afunction of MFR for different burnups

0.9

0.95

1

1.05

1.1

1.15

1.2

0 10 20 50 60

Co

nve

rsio

n R

atio

[-]

Burnup[GWd/t]

20

MFR=0.10.30.5

2.0

30 40

Fig. 9 Conversion ratio as a function of burnup for several MFRs

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from the microscopic cross section characteristics of 233U inrelation to the change of spectrum. The MIT reported26) thata higher fission generates neutrons per thermal neutron ab-sorption in 233U, the lower value of its epithermal resonancecapture to fission ratio, and the value of � changing theleast among all fissile isotopes with the increase in neutronenergy at epithermal energy regions was shown in thethorium-based fuel cycle. This reduces the reactivity effectsof the changes in the neutron spectrum due to coolant tran-sients. Therefore, as mentioned above in the MIT report, a

Th-233U fuel is less affected by the spectrum hardening thatreduces its void and temperature coefficients.

The previous study that was based on a homogeneous coreand light- and heavy-water-cooled U-Pu fuel systems2) ob-tained a positive void coefficient that can be estimated fromthe required enrichment profile as a function of MFR. Thevoid coefficient becomes positive at MFR < 1:0 for the lightwater coolant and at MFR � 4:0 for the heavy water cool-ant.2) In the case of MFR < 1 for the light water coolant,a lower MFR requires a lower enrichment, which meansthat if the enrichment is the same as the enrichment atMFR ¼ 1:0, the criticality of the lower MFR (MFR < 1:0)becomes higher. This condition causes the reactor to havea positive void reactivity for light water coolant. A similarinterpretation on void reactivity analyses as mentioned forlight water coolant can be applied for the heavy water cool-ant core at MFR < 4:0 as mentioned for the light-water-coolant core case. Those void coefficient reactivity analysesabove were based on the conservative assumption (no leak-age effect) for homogeneous core. In comparison with thelight-water-cooled Th-233U fuel system,5) even for lowerMFR (MFR � 0:3), a negative void coefficient can still beattained. Therefore, it can be concluded that light- andheavy-water-cooled U-Pu systems can obtain a positive voidcoefficient, while for the Th-233U fuel system, a negativevoid coefficient can be obtained for a tight lattice pitcharrangement. However, the MFR region of the Th-233U fuelsystem for obtaining a negative void coefficient was limitedto certain MFRs. Therefore, from the present study of theheavy-water-cooled Th-233U fuel system, a wider MFR forobtaining negative void coefficient can be achieved.

4. Feasible Area of Breeding and Negative Void Reactiv-ity CoefficientThe feasibility study of breeding has been conducted for

(a)

(b)

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

0 1 2

6 GWd/t183650

Vo

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oef

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e-3[

dk/

k/%

vol]

MFR[-]

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-3

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0.5

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6 GWd/t183650

Vo

id R

eact

ivit

y C

oef

. x10

e-3[

dk/

k/%

vol]

MFR[-]

5% void

0.5 1.5

Higher

Higher

Burnup

Burnup

Fig. 10 (a) Void reactivity coefficient of 5% void for MFR < 2

(b) Void reactivity coefficient of 5% void as a function ofMFR for different burnups

-2

-1.5

-1

-0.5

0

0.5

0 20 100

6 GWd/t

18

36

50

Vo

id r

eact

ivit

y co

ef. x

1e-3

[d

k/k/

%vo

l]

Void fraction [%]

MFR=1.0

40 60 80

Fig. 11 Void reactivity coefficient as a function of voided fractionat MFR ¼ 1:0

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several parametric surveys and evaluations, which can besummarized to show a feasible design region of breeding.In addition, the feasible design region can be used to evalu-ate the void reactivity in order to estimate a feasible regionof negative void reactivity. A feasible region of breeding isobtained by estimating the maximum achievable burnupwhen the conversion ratio is equal to unity for each MFRvalue. The limit of MFR for obtaining a negative void reac-tivity is obtained only in the lower limit of MFR and there isno higher MFR limit, because a higher MFR always obtainsa negative void reactivity. The obtained results of a feasibleregion of breeding and negative void coefficient were esti-mated and shown in Fig. 12.

The solid line indicates the investigated result and thedashed line shows the extrapolation result based on theinvestigated result. The range of investigated MFR was 0.1to 30 and the investigated burnup was 6 to 50GWd/t. Alimit of the negative void reactivity coefficient line indicatesthe lower limit of MFR for obtaining the negative void reac-tivity coefficient, and in this case, a 5% voided condition wasused for this analysis. A breeding condition limit denotes themaximum achievable burnup when the conversion ratio isequal to unity. It shows that the feasible area of breedingcan be achieved for all investigated values; however, theburnup capability is different for each MFR condition. Re-garding this feasible area of breeding, we can estimate theburnup capability of the breeding condition for certainMFRs. Therefore, it is easier to estimate the design specifi-cation for a breeder reactor with a negative void coefficientusing this feasible region.

A breeding condition and negative void reactivity coeffi-cient for higher burnup (burnup > 30GWd/t) can be achiev-ed at 0:3 < MFR � 1:5, as shown in Fig. 11(a). A higherMFR (MFR > 10) can achieve the breeding condition andnegative void coefficient, which requires a lower enrichmentfor the systems. However, the burnup capability is limited toabout 25GWD/t, for instance, at MFR ¼ 20 or higher. Alower MFR (0:3 < MFR < 2) is preferable for achieving abreeding condition with higher burnup capability; however,it needs more enrichment (about 3 times) than higher MFR(MFR ¼ 20).

Regarding achievable burnup evaluation, a higher MFRcan achieve a breeding condition with an achievable burnupthat is relatively lower than that of the standard PWR andrelatively higher than that of the conventional CANDU-typereactors. A higher MFR requires a large amount of heavywater in the reactor core; therefore, a larger reactor corediameter is required. For a lower MFR, it can be used toimprove the breeding condition under the relatively higherburnup as the standard PWR or even higher. In addition,the reactor core can be estimated to have a comparable coresize with the standard PWR core.

V. Design Feasible Area of Water-Cooled BreederReactor with Uranium and Thorium Cycle

To determine the breeding capability of a water-cooledreactor, previous studies were conducted based on theU-Pu fuel system for both coolants and light-water-cooled

Th-233U fuel system.2,5) Those studies showed the limitedregion of breeding for the light-water-cooled U-Pu orTh-233U fuels, and the region becomes wider when the lightwater coolant is replaced with the heavy water coolantfor U-Pu as shown in Table 3. Table 3 shows the feasiblebreeding region for light- and heavy-water-cooled reactorsusing the uranium and thorium fuel system for burnup of33GWd/t. In the case of the light-water-cooled U-Pu fuelsystem, a pin gap of about 0.5mm for a triangular latticeof MFR ¼ 0:3 (fuel pin diameter equal to 9.6mm) isrequired. Therefore, to achieve a breeding condition for afixed pin gap of 1mm (MFR ¼ 0:5), a 40% voided condition

(a)

(b)

0

10

20

30

40

50

60

0 1 4

Bu

rnu

p[G

Wd

/t]

Moderator to Fuel Ratio [-]3

Limit of negativevoid reactivity

Limit of breeding

Feasible area of breedingand negative void reactivity

0

10

20

30

40

50

60

0 10 15 20 25 30

Bu

rnu

p[G

Wd

/t]

Moderator to Fuel Ratio [-]

Limit of negativevoid reactivity

Limit of breeding

Feasible area of breedingand negative void reactivity

5

2 5

Fig. 12 (a) Feasible area of breeding and negative void reactivityfor MFR ¼ 0:0 to 5.0 (b) Feasible area of breeding and negativevoid reactivity for MFR ¼ 0:0 to 30

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is needed for realizing the effective MFR of 0.3. This condi-tion can be obtained by adopting a BWR type. A wider pingap of heavy-water-cooled U-Pu fuel system can be used forobtaining a breeding condition (pin gap = 1.8mm); there-fore, a PWR type can be used for this system. A light-water-cooled Th-233U fuel system has a larger pin gap thana light-water-cooled U-Pu fuel system, which shows that apin gap of about 1mm can be used for breeding.

In relation to the void reactivity, the light water and heavywater coolants with U-Pu fuel show a positive void reactivitycoefficient for conservative assumption (leakage is neglect-ed) for such tight lattice and voided condition. Only thelight-water-cooled Th-233U fuel system shows a negativevoid reactivity coefficient even for a lower pin gap. There-fore, it is easier to estimate the feasible area that fulfills abreeding condition and a negative void coefficient for aTh-233U system than for a U-Pu fuel system. A limited areaof breeding and a negative void coefficient were shown inthe case of the light-water-cooled Th-233U fuel system5)

and by changing the coolant from light water to heavy water,the feasible area becomes wider as shown in this study. Asmentioned above, the light-water-cooled Th-233U fuel sys-tem requires a tight lattice pitch with about �1mm pingap to obtain a breeding condition and a negative voidcoefficient for a burnup comparable to that of a standardPWR. In comparison with the heavy-water-cooled Th-233Ufuel system, because of its wider feasible area of breedingas shown in Fig. 12, a larger pin pitch (pin gap) can be used.Therefore, it is easier for a heavy-water-cooled Th-233Ufuel system to obtain both conditions of breeding and nega-tive void coefficient, which can be considered to have bettercooling ability and thermal hydraulic properties. For in-stance, to obtain a breeding condition and negative voidcoefficient for a burnup comparable to that of PWR, it isfeasible for 0:3 < MFR � 1:5, which is equal to a pin gapof 1–6mm (ratio of pitch to pin diameter (p/d) equal to1.07–1.4) of triangular pin pitch arrangement. As expected,a better breeding condition and a negative void reactivitycoefficient can be achieved using the Th-233U fuel systemfor the water-cooled reactor system. The heavy-water-cooledTh-233U fuel system can be used to fulfill the requirements

of breeding, negative void coefficient, higher burnup andlarge pin gap.

VI. Conclusions

The breeding capability and void reactivity of a Th-233Ufuel reactor were investigated using heavy water as coolant.The enrichment of 233U for the systems requires lower than8% for all investigated cases. The results have confirmedthat the � of 233U always stays higher than 2.1 and is superiorover other fissile nuclides along the investigated MFR,which causes the reactor to have a breeding condition for awide range of MFR. A larger pin gap (1–6mm) can be usedto achieve a breeding condition for a burnup comparable tothat of a standard PWR or higher, and to achieve a breedingratio (BR) of 1.1, a pin gap of about 2mm can be used.A feasible design region of the reactors, which fulfills thebreeding condition and negative void reactivity coefficient,has been found. A heavy-water-cooled PWR-type Th-233Ufuel reactor can be designed as a breeder reactor withnegative void coefficient.

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Table 3 Feasible design region of breeding (burnup 33GWd/t)

Coolant H2O H2O D2O D2O

Fuel (U-Pu) Oxide (Th-233U) oxide (U-Pu) Oxide (Th-233U) oxide

Triangular Lattice: 9.6 14.5 9.6 14.5Pin diameter (mm)selected in the study

Effective Pin Gap 5�0:5a),b) 5�1:0a),b) 51:8a),b) ¼1:4{6:0a)

(mm) to meet breeding 50:7 (U-TRU oxide 52:5 (U-TRU oxiderequirements fuel)a),b) fuel)a),b)

Void Reactivity under Positive Negative Positive Negativethe above effective pingap situations

a)Under triangular lattice geometry, the minimum gap distance was selected to be 1.0mm.b)When the effective pin gap is less than 1.0, the coolant void conditions are included in the determination of the above values.

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