Symbiotic systems consisting of large-FBR and small water-cooled thorium reactors (WTR

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Symbiotic systems consisting of large-FBR and small water-cooled thoriumreactors (WTR)

Ismail, Peng Hong Liem, Sidik Permana, Naoyuki Takaki, Hiroshi Sekimoto *

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

a r t i c l e i n f o

Article history:Received 11 September 2008Received in revised form 19 May 2009Accepted 24 May 2009Available online 26 June 2009

a b s t r a c t

Small long life water-cooled thorium reactors (WTR; 30–300 MWth) have been investigated. For realizingthorium cycle of the reactors, a uranium–thorium mixture core is introduced to fast breeder reactors(FBR; 3000 MWth) to be a 233U producer. In the present study, two distinct metallic fuel pins, with naturaluranium and thorium, are loaded into a large sodium-cooled FBR. The FBR itself is self-sustained by theplutonium produced in the uranium pins. Under the equilibrium burnup state, the FBR spent fuels areperiodically discharged with a certain discharge rate and then separated. Some actinides are returnedto the FBR core while 233U, which is discharged from the thorium pins, is utilized for the WTR fresh fuel.Fissile support capability is the main investigated parameter of the study. The system achieves highersupport capability at higher burnup and lower power of the WTR, and shows that larger number of ura-nium pins is better for the FBR criticality while larger number of thorium pins and lower burnup give bet-ter support factor capability. For a symbiotic system consisting 3000 MWth FBR and 100 MWth WTRs,where discharged fuel burnup is 96 and 60 GWd/t for the FBR and WTRs, one FBR can support 5 WTRs.

� 2009 Published by Elsevier Ltd.

1. Introduction

Nowadays, large scale light water reactors (LWR), by concur-rently utilizing uranium fuel cycle, have been intensively operatedfor generating electricity to meet the worldwide energy demand. Inmore optimistic scenario, some developed countries have intro-duced fast breeder reactors (FBR, in large scale) to be a good candi-date for nuclear energy in the future. But in other scenario, smallLWRs with long life core (by utilizing thorium fuel cycle) will alsocomplimentary be one of the candidate for the future scenario ofnuclear energy utilization (IAEA, 1985, 1995).

The needs for small sized and medium sized reactors (SMR),with power scale less than 300 MWe, have been identified bothby user countries and vendor countries (IAEA, 2004; Kuznetsov,2005). As for the user countries which are dominated by develop-ing countries facing a large growth of its domestic energy demand,there are many regions and applications where this increased de-mand will be best met by power plants in the above mentionedpower scale, due to a small grid system or for application in a re-mote area. As for the vendor countries in responding the needs,various reactor designs have been proposed including light waterreactors (LWR) type.

The needs of small sized reactors can be readily found, forexample, in the eastern region of Indonesia, where it consists of

a large number of dispersed less-developed small islands yet witha great potential to be developed as an industrial center based onmarine resources, as well as agro-business and agro-industry(APEC, 2006; Arbie et al., 1998). The design requirements of thesmall sized reactors for such region include:

1. Siting which determines the required reactor power level;rather high seismic condition of the eastern region of Indonesia(e.g. the horizontal ground acceleration is between 0.05 g and0.25 g) also favors for small sized or very small sized reactors.

2. Licensibility in the country of origin; the adoption of passivesafety concept, non-active safety mechanism, and otherimprovement of engineered safety features as well as verylow power level and power density should be taken intoaccount to simplify the licensing process.

3. Economic criteria; although small sized and very small sizedreactors tend to loose their economies of scale, the followingfactors must be considered in assessing the generation cost:(a) large social gain, (b) zero or the least government subsidy,and (c) smaller construction cost compared to the cost forupgrading the infrastructure and transportation in order toremove the ‘‘remoteness” qualification. In addition, simplifica-tion of design and licensing process, modularization etc. willlead to shorter construction times and savings in interest duringconstruction. The reduced capital requirements are also animportant factor for developing countries.

4. Domestic participation and research and development coopera-tion for technology transfer.

0306-4549/$ - see front matter � 2009 Published by Elsevier Ltd.doi:10.1016/j.anucene.2009.05.009

* Corresponding author. Tel./fax: +81 3 5734 2955.E-mail address: [email protected] (H. Sekimoto).

Annals of Nuclear Energy 36 (2009) 1076–1085

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To provide such kind of energy supplies for the areas, the smallsized reactors, however, should provide simplicities due to the lim-ited infra-structures and nuclear engineers’ technical capabilities(Djokolelono et al., 1998). One of the simplicities to fulfill therequirements is long life core. The long life core can be achievedby enhancing internal conversion rate of fertile to fissile materials.For that purpose, we can use thorium and expect a high fissile pro-duction rate of 232Th to 233U. But any reactor is impossible to becritical if it is fueled by thorium only. It should be embodied bysome fissile enrichment. The best fissile option for such kind ofreactors is 233U. Unfortunately, 233U does not naturally exist andshould be produced in a kind of thorium fuel burning systems.Therefore, it should be designed a kind of systems to provide a fea-sibility for such a small long life reactors operation if it would bedesigned with thorium fuel.

To respond those requirements for the future, we propose asymbiotic system consisting of a large liquid metal cooled naturaluranium and thorium fueled fast breeder reactor (FBR,3000 MWth) and several small sized, long life, water-cooled tho-rium fueled, satellite-reactors (WTR, 30–300 MWth). We expectthat the FBR, which is likely to be operated in a developed (vendor)country, can provide surplus of 233U fissile material while produc-ing electricity because of its good neutron economy. The thoriumfuel cycle is chosen for the small sized WTR because it enablesus to design a long core life time, i.e. avoiding on-site refueling.The characteristic of long core life time is attributed to the highconversion ratio due to the high g-value of 233U. In addition, byusing thorium fuel, the WTR can be designed to have a negativemoderator temperature coefficient over the whole reactor life evenwith low moderator to fuel ratio (MFR). Although it is not dis-cussed in the paper, a high conversion ratio will lighten the burdenon the FBR to produce 233U fissile material if the WTR’s spent fuelsare reprocessed to recover the remaining 233U.

In this paper we report our results on the feasibility of the pro-posed symbiotic system, some parametrical results on the WTR de-signs and fissile support capability of the FBR. Our present researchpurpose is to get an optimum support factor (SF, i.e. how manyunits of small-WTR satellite-reactors can be supported by a singleFBR operation) of the symbiotic system.

The structure of the paper is as follows. The proposed symbioticsystem is described in Section 2. A detail description of calcula-tional methods is given in Section 3. Results and discussion arepresented in Section 4. And finally, conclusions of this study are gi-ven in Section 5.

2. Symbiotic system of a large-FBR and small-WTRs

The symbiotic system proposed in the present study is shown inFig. 1. Basically, it consists of:

(1) A large 3000 MWth FBR, for producing electricity and pro-viding surplus of fissile material, that is operated inside anuclear park, equipped with some accompanying nuclearfuel facilities for separation, storage and fabrication.

(2) Several small sized 30–300 MWth WTR satellite-reactors(fueled by 233U discharged from the FBR) deployed in a usercountry. No on-site refueling, reprocessing, etc. are expectedto be conducted in the deployed site.

where rU and rFP (in Fig. 1) are uranium and fission products dis-charge constants, respectively; which indicate discharge fractionsof the corresponding nuclides from the FBR core per year.

In a conventional FBR, it is common that its core consists of coreand blanket regions. Core is located in inner side and fueled by en-riched uranium/plutonium, while blanket is located in outer sideand usually fueled by natural uranium. In the present study, wepropose a uranium and thorium mixture core of the FBR. Uraniumand thorium fuel pins are arranged in the core without any blanketsurrounding it. There are some advantages of this mixture core de-sign such as: (i) it is more proliferation resistant than the conven-tional core, because blanket region (in conventional core) is easierto be taken out from the core, (ii) it has better (less negative one)void reactivity coefficient, and (iii) it provides higher flux level inthe thorium pins so that a higher fissile production can beachieved.

In the present study, we assume that the system is in theequilibrium state. As for the FBR fresh fuel, natural uraniumand thorium fuels are loaded into the core in the correspondingfuel pins separately. Under the equilibrium state, both uraniumand thorium spent fuels are periodically discharged with a certaindischarge rate and then separated. After separation process, allactinides are recycled back to the FBR core while discharged-233Ufrom thorium pins is utilized as fresh fuel of small-WTR satellite-reactors mixed with natural thorium after fuel fabrication pro-cess. The fuel fabrication should be done inside the park toguarantee that the fuel will not be used for diverted purposes.All fission products (FPs) are removed from both fuel pin typesat the same rate with the 233U discharge rate and then kept instorage facility.

Fig. 1. Proposed symbiotic system of large-FBR and small-WTRs.

Ismail et al. / Annals of Nuclear Energy 36 (2009) 1076–1085 1077


Sodium coolant and metallic fuel had been adapted to the pres-ent FBR design (Mizutani and Sekimoto, 1998). Metallic fuel pro-vides the highest criticality capability of the sodium-cooled FBRwhile sodium is a good coolant material since it provides higherheat removal capability, in comparison with other liquid metals

(considering simple thermal characteristics such as the pumpingpower and the convective heat transfer coefficient).

The small-WTR, as the satellite-reactors, is based on the estab-lished pressurized water reactor technology. To some extent, thissmall-scale of the WTRs is derived from the large-scale of water

Fig. 2. Flowchart of ECICS calculation.

1078 Ismail et al. / Annals of Nuclear Energy 36 (2009) 1076–1085

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thorium breeder reactors (WTBR; 3000 MWth) (Permana et al.,2007). Once-through fuel cycle is employed to the reactor opera-tion. Some parametric investigations are also performed for theMFR and discharge fuel burnup to achieve an optimum design.

3. Calculation methods

Calculation for both types of reactors (large-FBR and small-WTR) in this study use the Equilibrium Cell Iterative CalculationSystem (Mizutani and Sekimoto, 1997) (ECICS) code that has beendeveloped and intensively used by our equilibrium fuel cycle re-search group. ECICS method employs an iterative procedure of cellcalculation to obtain the equilibrium fuel cycle as shown in Fig. 2.The calculation system provides basic advantages on equilibriumfuel cycle studies such as (i) fast and simple calculation mechanismto obtain equilibrium conditions without transient simulations,and (ii) provides comprehensive calculation results since it in-volves a large number of 1238 fission products and 129 heavy nuc-lides, available from evaluated nuclear data libraries. In the resultsand discussion section, some calculation results of both the ECICSmethod and cell-burnup (using SRAC code) (Okumura et al.,2005) will be compared to show the accountability this equilib-rium calculation method.

Nuclear fuel cycle at the nuclear equilibrium state is calledequilibrium fuel cycle and it satisfies the following conditions:

� Number density of each nuclide in reactor does not change.� Refueling process is a continuous process.

In these conditions, the number density of ith nuclide, ni, shouldsatisfy the following equilibrium fuel cycle burnup equation:

dni

dt¼ �ðki þ /ra;i þ riÞni þ

Xj

kj!inj þ /X

j

ra;j!inj þ si ¼ 0 ð1Þ

In strict nuclear equilibrium conditions nuclide number densitiesdo not change in time, where / is the neutron flux, ki the decay con-stant of ith nuclide, ri the discharge constant of ith nuclide, kj?i thedecay constant of jth nuclide to produce ith nuclide, ra,j?i themicroscopic absorption cross-section of jth nuclide to produce ithnuclide, si the supply rate of ith nuclide, and ra,i is the microscopicabsorption cross-section of ith nuclide.

Firstly, equilibrium calculation with a proper initial guess ofone-group constant set is performed. Then, material balance equa-tion in the fuel pellet with the fixed total number density of allheavy materials and fission products is solved. In the next step,one-group scalar neutron flux level, /, is normalized by the givenpower density, P, in the fuel pellet:

P ¼ CXi2HM

nirf ;i/ ð2Þ

where C is the energy released per fission (200 MeV), rf,i the micro-scopic fission cross-section of is nuclide, and HM stands for HeavyMetals.

And this iterative calculation is continued until flux level andnuclide number densities are converged. This iterative procedureis called an inner iteration.

After an inner iteration is performed, the next inner iteration isrepeated by employing freshly created one-group cross sections. Aset of both equilibrium calculation in the inner iteration and cellcalculation for preparing one-group cross section is repeated untilone-group scalar neutron flux and nuclides densities and one-group microscopic cross sections converge, satisfying correspond-ing convergence criterion. This iteration is called an outer iteration.

For evaluating the performance of the systems, a parameternamed support factor, SF, is proposed:

SF ¼ VFBR � rFBRP

ini;FBR

VWTR �P

ini;WTRtWTR

ð3Þ

where V is the volume of corresponding cores, ni the number den-

sity of the ith nuclide, rFBR the uranium discharge constant 1year

� �

of the large-FBR, and tWTR is the core life time of the small-WTR.As mentioned before, SF indicates how many units of small-

WTR satellite-reactors can be supported by a single FBR operation.Analysis of void reactivity coefficient will be presented and dis-

cussed with the assumption that changing the content of coolant

Table 1Basic design and its cell parameters of the large-FBRs.

Basic FBR design parametersTotal power output (MWth) 3000Power density (W/cc) 280Initial HM inventory (ton) 170Coolant SodiumFuel (U and Th) Zr10%

Cladding Ferritic-stainless

Cell parametersTheoretical density (g/cc) 15.90Fuel-pellet diameter, 2R1 (mm) 7.09Pin diameter, 2R2 (mm) 8.50Pin pitch, 2R3 (mm) 9.85Cladding thickness (mm) 0.48Effective fuel volume ratio 32.5%Smear density 75%Temperature (�C) 873

Cell geometry

Table 2Basic design and its cell parameters of small-WTRs.

Basic WTR design parametersTotal power (MWth) 30–300Power density (W/cc) 45Initial HM inventory (ton) 6.2–62Burnup (GWd/t) 20–60Core

Height (cm) 100–240Diameter (cm) 50–160

Coolant H2OFuel (233U,232Th) O2

Cladding Zircalloy-4

Cell parametersTheoretical density (g/cc) 10.0Fuel-pellet diameter, 2R1 (mm) 13.1Pin diameter, 2R2 (mm) 14.5Pin pitch, 2R3 (mm) 15.74Cladding thickness (mm) 0.7Moderator to fuel ratio (MFR) 0.3–2.0Smear density (%) 93Temperature (�C) 873

Cell geometry


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occurs which can be caused by boiling coolant in the bubble formor steam, or lost of coolant because the leakage. Void reactivitycoefficient is investigated for different MFR and fuel cycle systemsof both coolants based on the equilibrium nuclide condition. About100% voided fraction is chosen for this voided condition assumingall of coolant are voided which occurs in the core. The voided con-dition is calculated by decreasing density of coolant in unit cellcalculation.

4. Results and discussion

Basic reactor design including cell parameters of the FBR areshown in Table 1 while those of the small-WTRs are shown in Ta-ble 2. The FBR data are based on the conventional fast breeder reac-tors and the WTR data are taken from the Shippingport reactordesign (Freeman et al., 1989). The core volume of both reactorscan be determined by using its thermal power and power densitiesdata. The cross-sections data set for burnup calculations used inthis analysis are prepared by using SRAC-2002 code system(Okumura et al., 2005) with JENDL-3.2 library. In the cell calcula-tions, the collision probability (PIJ) and ultra-fine energy group(PEACO) options are selected.

4.1. Small water-cooled thorium-fueled reactors (WTRs)

WTRs with a power range of 30–300 MWth, a burnup range of20–60 GWd/t and an MFR range of 0.3–2.0 (2.0 is the presentLWR design), have been investigated and; burnup and safety per-formances of the reactors will be discussed. In this WTR case, bur-nup is calculated in open cycle where HM and FPs are removedfrom the reactor core with a fixed discharge constant value peryear, while thorium and 233U are constantly supplied in its freshfuel.

The burnup performance is indicated by the required enrich-ment, fissile inventory ratio (FIR; which is defined as a ratio of dis-charge to initial fissile inventory) and core life time while thesafety performance is indicated by the coolant void reactivity coef-

ficient. In the cases of power and MFR change of this study, thepower density in pellet is fixed; therefore, different cases of powerand MFR have different core volume on calculation.

Fig. 3 shows the required enrichment and FIR of the reactors forthree discharge fuel burnup (BU) cases, i.e. 20, 40, and 60 GWd/t. Inthe calculation, the core height is fixed (Hcore = 140 cm) while thecore radius is changed within a range (Rcore = 75–123 cm). Therange of core radius is used because a different MFR implementsa different core volume which is a consequence of a cell dimensionchange due to MFR change. A higher discharge fuel burnup pro-vides more efficient fuel utilization and partly reduces fuel cost.A longer core life time can be also achieved by higher dischargefuel burnup. On the other hand, a higher discharged fuel burnuprequires a higher 233U fissile enrichment and it increases the initialfuel cost. In other words (will be shown in Fig. 5 later), a higher fuelcost for higher enrichment is compensated by a longer core lifetime which will provide simplicity since the reactors can be oper-ated without on-site refueling. The simple operation turns to be-come a requirement for realizing small nuclear power plant inremote and less developed areas.

FIR decreases as the discharged fuel burnup increases because ahigher burnup level needs a higher initial fissile enrichment and itreduces the fertile to fissile conversion rate. So far, in WTRs side,we assume the reactor is operated in once-through cycle. The FIRwould be a significant parameter if in the future we introduce aclosed-cycle of the WTR satellite-reactors. In the closed-cycle, weinclude a reprocessing activity of the WTR spent fuel inside the nu-clear park where the 233U fissile from the spent fuel goes to fabri-cation facility and is re-used for fresh fuel of the WTR in thesubsequent operation. In that case, a higher FIR reduces the needof 233U from the FBR, so that the system achieves more efficientfuel utilization, though it takes more cost for reprocessing.

Fig. 3 also shows that the initial fissile enrichment does not sig-nificantly change in MFR range of 1.0–2.0. But within the MFRrange of 0.3–1.0, the lower MFR achieves a higher FIR which repre-sent higher conversion rate of 232Th into 233U. Another fact, asmentioned before, decreasing MFR will reduce core volume eventhough it should be designed in a tighter lattice. At this point, we

0

2

4

6

8

10

12

14

0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1

MFR [ - ]

233

U E

nric

hmen

t [ %

]

0.0

0.2

0.4

0.6

0.8

1.0

FIR

[ - ]

Enrichment [ BU = 20 GWd/t ]Enrichment [ BU = 40 GWd/t ]Enrichment [ BU = 60 Gwd/t ]FIR [ BU = 20 GWd/t ]FIR [ BU = 40 GWd/t ]FIR [ BU = 60 GWd/t ]

Hcore = 140 cm

Rcore = 75~123

Fig. 3. Required enrichment and fissile inventory ratio (FIR) of the WTR-100 MWth.



choose MFR = 1.0 for the symbiotic system because it is a moderateof MFR design and far from the geometrical limit of MFR = 0.3which has minimum fuel pin gap 1.0 mm of the tri-angular latticedesign.

For a range of power scale 30–300 MWth, it is shown in Fig. 4that as the power increases, the required enrichment decreasesand FIR increases, so that the design becomes neutronically andeconomically better. In addition, within the range, it can be shownthat it is better to choose a power level as high as possible, becauseby increasing power the WTR achieves a higher FIR but simulta-neously needs a lower enrichment.

Fig. 5 shows core life time for both the ECICS equilibrium andcell-burnup calculation cases. Core life time increases as the dis-

charge fuel burnup increases for power level of 100 MWth. As dis-cussed in Section 3, a higher fuel burnup can be achieved by asmaller discharge constant (ri). The figure shows that, for both cal-culation methods, the WTRs can achieve around 30 years core lifetime for the discharge fuel burnup of 60 GWd/t with small discrep-ancies (about 4.5%) between the two methods. The discrepancyshows that our equilibrium calculation method is acceptable forthis investigation. And since the core life time is independent tothe WTR’s thermal power level, then the same core life times arealso achieved by 30 and 300 MWth WTR cases.

An additional comparison result between ECICS equilibriumand cell-burnup calculation is shown in Fig. 6. In the figure, it isshown that the criticality of equilibrium calculation is slightly

WTR [ 30; 100; 300 MWth & MFR = 1.0 ]

0

2

4

6

8

10

12

14

0 50 100 150 200 250 300 350 400Power [ MWth ]

Enric

hmen

t [ %

]

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

FIR

[ - ]

Enrich. [ 20 GWd/t ]Enrich. [ 40 GWd/t ]Enrich. [ 60 Gwd/t ]FIR [ 20 GWd/t ]FIR [ 40 GWd/t ]FIR [ 60 GWd/t ]

Fig. 4. Enrichment and FIR vs. WTR’s power.

0

5

10

15

20

25

30

35

40

0 10 20 30 40 50 60 70Burnup [ GWd/t ]

Cor

e Li

fetim

e [ y

ear ]

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

4.5%

5.0%

Dis

crep

ancy

[ %

]Cell-Burnup

Equilibirum

Discrepancy

Fig. 5. Core life time of WTR-100 MWth under equilibrium and cell-burnup calculation.



higher than that of cell-burnup calculation and the criticality ofcell-burnup calculation case decreases as increasing both MFRand WTR’s fuel burnup level. Therefore, the discrepancy betweenthe two calculation increases as increasing both MFR and fuel bur-nup level. But in these MFR and burnup range, all discrepancies arelower than 7% and show acceptability of the ECICS equilibrium cal-culation method.

Fig. 7 shows coolant void reactivity coefficient that is related tosafety characteristic. The figure shows less negative values forhigher discharged fuel burnup. In other words, when the WTR isdesigned to achieve a higher discharged fuel burnup, the safety

performance decreases. Furthermore, the coefficient becomes lessnegative for higher MFR. However, since the present design hasnegative values for all discharged fuel burnup and MFR ranges,the safety aspect for the WTR operation is confirmed.

4.2. Sodium cooled, natural uranium and thorium-fueled fast breederreactors

From the early stage of our study on nuclear equilibrium state,equilibrium analysis of liquid metal fast reactors had beenperformed to achieve an optimized design in fuel and coolant

0.930

0.940

0.950

0.960

0.970

0.980

0.990

1.000

1.010

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6MFR [ - ]

k eff

[ - ]

0%

1%

2%

3%

4%

5%

6%

7%

8%

Dis

crep

ancy

[ %

]

Equi. [ 20 or 60 GWd/t ]

Cell [ 20 GWd/t ]

Cell [ 60 GWd/t ]

Discrepancy [ 20 Gwd/t ]

Discrepancy [ 60 GWd/t ]

Fig. 6. keff of WTR-100 MWth for 20 and 60 GWd/t cases under equilibrium and cell-burnup calculation.

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0 10 20 30 40 50 60 70WTR Discharge Fuel Burnup [ GWd/t ]

Void

Coe

ffici

ent x

10-3

[ dk/

k/%

void

]

MFR = 0.5MFR = 1.0MFR = 2.0

Fig. 7. Coolant void reactivity coefficient of 100 MWth WTR with 5% void fraction.



materials composition of the reactor (Sekimoto and Takaki, 1991;Takaki and Sekimoto, 1992; Takaki et al., 1993). It was assumedthat in a nuclear equilibrium state, the production and annihilationof each nuclide are balanced in the system for a long time period.Actinides confining and fission products discharging strategieswere investigated to reduce radioactive wastes.

In the present study, sodium cooled and metallic fueled FBR isinvestigated and its kinf and SF are evaluated. The FBR kinf is shownin Fig. 8 as a function of both thorium fraction in the FBR core anddischarge fuel burnup. The figure shows that the criticality de-creases with increasing thorium fraction due to smaller numberof the uranium pins in the core. The criticality increases withincreasing the discharge fuel burnup because a higher fuel burnupgives a higher 239Pu production in the uranium pins.

The criticality threshold kinf = 1.05 is chosen for the metal fuelFBR employed in the present study with an assumption of 5% neu-tron leakage in the reactor core. In order to satisfy the criticalitycondition, the thorium fraction in the FBR core is adjusted. Pro-

duced uranium in the FBR’s thorium pins is discharged as muchas possible while the reactor operation should be kept under thecritical condition. Fig. 8 also shows the maximum thorium fractionfor several burnup cases under the criticality constraint. A higherburnup requires smaller number of uranium pin fraction in thecore for keeping criticality.

Discharge rate of 233U as a function of both the FBR thoriumfraction and discharge fuel burnup is shown in Fig. 9. The figureshows that the rate increases proportionally with increasing FBRthorium fuel fraction for fixed discharged fuel burnup. The dis-charge rate also increases with decreasing fuel burnup for fixedthorium fraction, since a lower burnup means greater dischargeconstant (ri). Any effort to increase the 233U discharge rate simulta-neously reduces the FBR criticality performance, since the dis-charge rate is inversely proportional to the FBR criticality.

Fig. 9 also presents the relation between discharge rate of 233Uand thorium fraction in the FBR core, at critical condition. The lineshows the boundary of feasible region of the system to be operated

1.00

1.05

1.10

1.15

1.20

0 10 20 30 40 50

Thorium Fraction in the FBR Core [ % ]

kin

fo

f th

e F

BR

[ -

] 96 [ GWd/t ]

53 [ GWd/t ]

32 [ GWd/t ]

21 [ Gwd/t ]

11 [ GWd/t ]

5 [ GWd/t ]

Fig. 8. FBR criticality profile.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 10 20 30 40Thorium Fraction in the FBR Core [ % ]

Dis

char

ged

233

U [

ton/

year

]

( at kinf = 1.05 )

( 96 GWd/t )

( 53 GWd/t )

( 32 GWd/t )

( 21 GWd/t )

( 11 GWd/ t )

( 5 GWd/t )

k inf > 1.05

k inf < 1.05

Fig. 9. Mass of discharged 233U from FBR core.



under the condition of kinf P 1.05. Under this criticality condition(kinf = 1.05), the discharge rate of 233U can be consistently increasedby decreasing FBR discharge fuel burnup or by decreasing FBR tho-rium fuel fraction; the 233U discharge rate increases asymptoticallyto infinity by reducing discharged fuel burnup at FBR thorium fuelfraction of about 11%. However, the FBR burnup level can not besignificantly decreased, since it would not be practical and increasethe fuel cost.

4.3. System of symbiotic large-FBR and small-WTRs

Fissile support capability, expressed by SF as defined in Eq. (3),of the FBR to the small-WTR satellite-reactors is linearly propor-

tional to the discharge rate of 233U from the FBR but inversely pro-portional to the required uranium amount for the WTR satellite-reactor fresh fuel.

Fig. 10 shows SF and the corresponding thorium fraction in theFBR core for three different cases of WTRs discharge fuel burnup ata fixed 300 MWth power of WTRs, where the WTRs’ MFR = 1.0 andthe FBRs’ criticality condition of kinf = 1.05. The figure indicates thatfor a fixed FBR burnup, the system achieves a higher SF when theWTRs burnup level is increased. Although initial fissile inventoryincreases by increasing the WTRs burnup level, the higher SF in-creases is due to the longer core life time.

Fig. 11 shows SF and the corresponding thorium fraction of theFBR core for three different WTRs’ thermal power cases and a fixed

0

2

4

6

8

10

0 20 40 60 80 100 120 140 160 180 200FBR Burnup [ GWd/t ]

Supp

ort F

acto

r [ -

]

12

16

20

24

28

32Th-Fraction in FB

R C

ore [ % ]

SF [ WTR ; 20 GWd/t ]SF [ WTR ; 40 GWd/t ]SF [ WTR ; 60 GWd/t ]Thorium Fraction

Fig. 10. Support factor and thorium fraction of the 300 MWth WTRs (fixed power).

0

4

8

12

16

20

0 20 40 60 80 100 120 140 160 180 200

FBR Burnup [ GWd/t ]

Su

pp

ort

Fac

tor

[ -

]

12

16

20

24

28

32

Th

-Fractio

n in

FB

R C

ore [ %

]

SF [ WTR ; 30 MWth ]



Thorium Fraction

Fig. 11. Support factor and thorium fraction of the 60 GWd/t WTRs (fixed burnup).



60 GWd/t burnup. The figure shows that, for a fixed FBR burnup,the system achieves a lower SF when the WTRs power level is in-creased due to higher initial fissile inventory for starting up.

From the latest two figures, it can be seen that SF increases asthe thorium fraction decreases, because to increase SF (or dis-charge rate of 233U) we should keep FBR criticality by increasinguranium fraction in the FBR core. On the other hand, the effort ofincreasing SF will decrease simultaneously FBR discharge fuel bur-nup and it consistently implies on decreasing thorium fraction.From the two trends shown in Figs. 9 and 10, we can choose thebest SF from the combination of the desired discharge fuel burnupof FBR and WTR for a certain power scale of the WTR.

For an example, if we choose the power of WTRs to be100 MWth and the system is operated with fixed discharge fuelburnup of both FBR and WTRs at 96 (based on the current FBR bur-nup achievement, i.e. about 100 GWd/t) and 60 GWd/t, respec-tively, then the symbiotic system achieves SF = 5. It means that asingle FBR operation can support 5 WTRs operation and the powerproduction ratio of small-WTR to large-FBR and is around 0.17.

5. Conclusions

The performances of a symbiotic system consisting of a largefast breeder reactor (FBR, 3000 MWth) centralized in a nuclearpark and small water-cooled thorium fueled (WTR, 30–300 MWth)satellite-reactors outside the park were investigated. As for theFBR, the reactor is supplied by natural uranium and thorium intwo different metallic fuel pin types. The thorium fuel pins arededicated for producing 233U fissile while the uranium fuel pinsare for keeping the FBR criticality with produced plutonium. Asfor satellite-reactors, a long life (high burnup) WTR suitable forsmall remote and less developed areas is designed. The WTR dis-charged fuel burnup is feasible up to 60 GWd/t with about 31 yearsof core life time within the power scale of 30–300 MWth.

A feasible area to establish the proposed symbiotic system isfound with the following characteristics:

(1) SF increases with decreasing FBR discharge fuel burnup.(2) SF increases with increasing WTR discharge fuel burnup and

with decreasing WTR thermal power.(3) A higher SF requires a smaller thorium fraction in the FBR

core.

Within the feasible area, a symbiotic system can be designedwith the best SF from the combination of the desired dischargeburnup of FBR and WTR for a certain power scale of the WTR.

If we design the symbiotic system consisting of 3000 MWth FBRand 100 MWth WTRs, where discharge fuel burnup is 96 and60 GWd/t for the FBR and WTRs, respectively; then one FBR cansupport 5 WTRs and the power production ratio of small-WTR tolarge-FBR is about 0.17.

Acknowledgements

This study was supported partly by the Center of Excellence:‘‘Innovative Nuclear Energy System” (COE-INES) Program of Re-search Laboratory for Nuclear Reactors, Tokyo Institute ofTechnology.

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Symbiotic systems consisting of large-FBR and small water-cooled thorium reactors (WTR

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