breeding and void reactivity analysis on heavy metal closed-cycle water cooled thorium reactor
TRANSCRIPT
Annals of Nuclear Energy 38 (2011) 337–347
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Annals of Nuclear Energy
journal homepage: www.elsevier .com/locate /anucene
Breeding and void reactivity analysis on heavy metal closed-cycle watercooled thorium reactor
Sidik Permana a,c,⇑, Naoyuki Takaki b, Hiroshi Sekimoto a
a Research Laboratory for Nuclear Reactors, Tokyo Institute of Technology, 2-12-1, O-okayama, Meguro-ku, Tokyo 152-8550, Japanb Tokai University, 1117 Kitakaneme, Hiratsuka, Kanagawa 259-1292, Japanc Nuclear and Biophysics Research Group, Department of Physics, Bandung Institute of Technology, Gedung Fisika, Jl. Ganesha 10, Bandung 40132, Indonesia
a r t i c l e i n f o a b s t r a c t
Article history:Received 9 March 2010Received in revised form 7 October 2010Accepted 13 October 2010Available online 9 November 2010
Keywords:Heavy waterThoriumBreederNegative voidHigher burnupClosed-cycle
0306-4549/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.anucene.2010.10.009
⇑ Corresponding author. Present address: Japan AtoNon-proliferation Science and Technology Center, 2mura, Ibaraki 319-1195, Japan. Tel.: +81 29 284 3446
E-mail address: [email protected] (S. Perm
Design parameters of heavy water (D2O) cooled thorium breeder reactors for actinides closed-cycle caseshave been investigated to find a design feasible area of breeding and negative void reactivity. Heavy met-als (HMs) closed-cycle shows narrower feasible area compared with feasible area of 233U closed-cycle. Inthorium fuel cycle, the breeding capability of the reactors becomes worse when all HMs are recycled. Theresult shows an opposite profile of breeding capability compared with uranium fuel cycle which obtainshigher breeding capability when more HMs are recycled. Feasible design area which has a breeding andnegative void reactivity can be estimated for higher burnup, even higher than 60 GW d/t for 233U closed-cycle; however, it is limited to 36 GW d/t for HM closed-cycle. Contribution of capture 235U is more sig-nificant to reduce breeding capability and contribution of 234U is also more effective to make the reactormore positive or less negative void coefficient for HM closed-cycle case in thorium fuel cycle system.
� 2010 Elsevier Ltd. All rights reserved.
1. Introduction
Recently, nuclear energy attracts many countries, which aremainly developing countries to build the nuclear reactor in orderto meet a national energy demand by using nuclear energy. Morethan 50 years, nuclear energy has contributed to fulfill the worldenergy demand especially in relation to the sustainable develop-ment of the world without any greenhouse effect to the environ-ment especially for developed countries. To perform thesustainable development of the world, one of the possible trend,is to pursue the fuel breeding capability of the reactor, which isvery essential for extending the sustainability of nuclear fuel re-source. The similar trend of the breeder reactors with the renew-able energies has been shown as a sustainable energy source(Zaleski, 2006). Thorium fuel technology has being developed wellnot only for conventional reactor but also provided the thoriumbreeder reactor programs to meet the global nuclear energy contri-bution as well as uranium fuel technology. Good breeding capabil-ity in thermal and epi-thermal neutron energy region, higher fuelstability, better proliferation resistance and so on, have beenshown by thorium cycle as the advantages compared with uranium
ll rights reserved.
mic Energy Agency, Nuclear-4 Shirane Shirakata, Tokai-; fax: +81 29 284 3678.ana).
cycle (Permana et al., 2007; Kim and Downar, 2002; Michael andOtto, 1998; Turan, 2000).
A low conversion ratio capability has been shown by presentlight water reactor of about 0.6 and for a heavy water cooled reac-tor of about 0.8 such as PHWR as well as high temperature gas-cooled reactor (HTGR) (Duderstadt and Hamilton, 1976; Permanaet al., 2006). To attain sufficient breeding condition of the reactors,some researchers try to develop some design feature based onwater-cooled technology and others more focused on fast reactortechnology. In case of fast reactor technology, it is easier to reachbreeding condition because of its harder spectrum capability (Per-mana et al., 2007; Iwamura et al., 1999; Hibi et al., 2001), however,due to the safety concern; fast reactor gives a positive void reactiv-ity (Duderstadt and Hamilton, 1976; Hibi and Sekimoto, 2005; Tak-aki, 2000). Some design modifications have been done to attainharder spectrum by tight lattice arrangement to achieve nearbreeding or breeding condition (Iwamura et al., 1999; Hibi et al.,2001; Iwamura et al., 2006, 2007), however, in such tight latticearrangement, a positive void occurs (Kim and Downar, 2002;Takahashi et al., 2000). Recycling options of HM have been studiedfor several moderator to fuel ratios (MFR) to estimate the breedingcan be achieved by uranium fuel cycle (Permana et al., 2006). Itshows that breeding condition is feasible for low MFR with moreHM are recycled and heavy water cooled gives better breedingcapability than light water coolant because of its harder spectrum.
Thorium fuel has been introduced for achieving better breedingcapability because of its better eta value at thermal energy and
Table 1Parameters.
Total power output MW t 3000Coolant material – D2OFuel cycle case – 233U and All HM recycledCladding material – Zircaloy-4Pellet diameter of fuel cm 1.31Outer diameter of fuel pin cm 1.45Pellet power density (average) W/cm3 140Moderator to fuel ratio (MFR) – 0.1–4.0Burnup GW d/t 6–50
338 S. Permana et al. / Annals of Nuclear Energy 38 (2011) 337–347
epi-thermal energy regions. This better conversion ratio of thoriumfuel is accompanied with a negative void coefficient (Permanaet al., 2007; Takahashi et al., 2000). It had been demonstrated someexperiment and prototype power reactors during the mid 1950s tothe mid 1970s using thorium fuel in HTGR, LWR and MSBR (IAEA,2005). Thorium as blanket material has been used in liquid metalcooled fast breeder reactor (LMFBR) and for neutron flux flatteningof the initial core of pressurized heavy water reactor (PHWR) dur-ing startup (IAEA, 2005). As demonstrated reactor to show itsbreeding capability, thorium fueled light water reactor (Shipping-port) showed its capability as well as MSBR project and a tight lat-tice BWR concept (Freeman et al., 1989; Nuttin et al., 2005; Akieet al., 1991; Michael and Otto, 1998; Turan, 2000). Advanced tho-rium breeder reactor (ATBR) has been proposed to evaluate thebreeding capability using plutonium and thorium fuel (Jaganna-than and Usha, 2006), with core-blanket fuel systems. PWR typereactors with light water and heavy water as coolants have beeninvestigated for their breeding capability using thorium fuel (Per-mana et al., 2007, 2008). It showed breeding and negative voidreactivity are possible can be achieved by thorium fuel for compa-rable discharged fuel burnup with conventional light water reac-tors. Therefore, it can be recognized that thorium has a potentialbreeding for both thermal and fast reactor types.
IAEA reported that some renewed and additional interest inthorium are based on (i) intrinsic feature of proliferation resistanceof thorium cycle, (ii) better thermo-physical properties and chem-ical stability of THO2 and more stable waste form, (iii) lesser longlived minor actinides, (iv) superior plutonium incineration, and (v)attractiveness feature of thorium related to accelerated driven sys-tem (ADS) and energy amplifier (IAEA, 2005). However, thoseadvantages of thorium fuel are accompanied by several challengesin the front and back end processes such as gamma radiation asso-ciated with U-232 for reprocessing U-233 and also some problemwith protactinium formed in thorium fuel.
Shippingport reactor loaded with Th–233U fuel is the only sys-tem that has been demonstrated to be capable of breeding withlight water coolant (Freeman et al., 1989) which has a heteroge-neous core that consists of four different regions with different fuellattice designs and fissile material concentrations. The attained to-tal averaged burnup was around of 15 GW d/t, it is unattractivelylow value as a competitive commercial reactor. However, there stillexist some incentives to pursue water cooled breeder reactor. Inrelation to fuel fabrications, handlings and reprocessing of U-233–thorium fuel type, LWBR (Shippingport) shows its technicalfeasibility up to 98% pure U-233 and less than 2% for other uraniumisotopes (Freeman et al., 1989). It also demonstrated burnup capa-bility up to maximum burnup of 50 GW d/t and average burnup of15 GW d/t. AECL has examined two mixed bundle strategies forburning thoria in existing CANDU six reactors and it containedsome thorium bundles which were designed to achieve burnupsof over 50 MW d/kg HE (IAEA, 2005).
The use of water-cooled technology is in common use through-out the world and it is shown by the current LWR plant technologyas well established technology through enormous operation expe-riences. This fact of water plant technology indicates that its tech-nology is reliable and acceptable for both public and utilities suchas transparent coolant is more convenient for maintenance espe-cially for utility company. In introducing phase of breeder reactors,by this water-cooled technology, there are fewer requirements fornew education for operators. One of the progressive programs forutilizing thorium fuel in PHWR type is India’s thorium breederreactor (Gupta et al., 2008). It combines fast reactor technologyand water-cooled technology by pursuing several stages of tho-rium utilization programs.
The study clarifies the design feasible area of breeding and neg-ative void reactivity coefficient for heavy water (D2O) cooled reac-
tor. The reactor system uses thorium fuel cycle with comparativeanalysis of 233U fuel closed-cycle and HM closed-cycle cases. Those233U and all HM fuels are produced from thorium fuel after attain-ing equilibrium nuclide density. Reactor criticality performance,breeding capability and void reactivity performance are evaluatedas main focus study in this present evaluation for various MFR(moderator to fuel volume ratio), burnup values and some voidedfractions.
2. Parameters and calculation methods
2.1. Equilibrium cell iterative calculation system (ECICS)
In this paper, we intend to evaluate the breeding capability andvoid reactivity coefficient based on thorium fuel cycle system,cooled by heavy water and to find its feasible region of breedingand negative void coefficients. An originally developed, very fastequilibrium burnup calculation code (Equilibrium Cell IterativeCalculation System: ECICS) is used for various fuel cell designsand burnup conditions (Sekimoto and Takaki, 1991; Permanaet al., 2007, 2006; Waris and Sekimoto, 2001a,b; Mizutani andSekimoto, 1998a,b,c, 1997; Seino and Sekimoto, 1998). The basicreactor design parameters are shown in Table 1. The key parame-ters such as MFR and burnup are employed. MFR is varied from0.1 to 4.0 by changing fuel pin configuration to cover some feasibledesign region for relatively higher or lower MFR than standardMFR of PWR (MFR = 2), which is selected also to cover a broaderneutron spectra investigation. In addition, the targeted burnupsare surveyed from 6 GW d/t to 50 GW d/t for evaluating the bur-nup effect. Several burnup values were investigated to cover sometypical burnup values of PWR (33 GW d/t), conventional CANDUreactor (7.5 GW d/t) (Duderstadt and Hamilton, 1976) and someother reactor types as comparable references.
The wide range of discharged fuel burnup is examined byadjusting fuel discharge rate in the equilibrium fuel compositioncalculation. This equilibrium burnup calculation code employed1238 fission products and 129 heavy nuclides and is coupled withthe PIJ cell calculation module of SRAC (Okumura et al., 1996). TheJENDL3.2 nuclear data library is used (Nakagawa et al., 1995). Afuel pin diameter of 1.452 was used in this study, which is 1.5times thicker than that of the standard PWR. This fuel pin diameterwas based on the fuel pin diameter of the Shippingport regularblanket (Freeman et al., 1989). There are two fuel cycle schemesin this evaluation; those are 233U closed-cycle and all heavy metals(HMs) closed-cycle schemes. The comparative analysis based onthis two different fuel cycle cases has been done to evaluate the ef-fect of recycled HM to the reactor in the thorium fuel cycle sys-tems. The reactor system is based on oxide fuel with Zircaloy-4as cladding and heavy water as coolant and moderator. In the firstcycle system, actinides except for 233U and fission products (FPs)are removed in the reprocessing process as waste to be disposedof. In the second fuel cycle system, only FPs are sent to final dis-posal stream.
S. Permana et al. / Annals of Nuclear Energy 38 (2011) 337–347 339
2.2. Conversion ratio
In this paper we only focused on thorium fuel, which related tothe process of 232Th nuclide, which can be transmuted into 233U.Breeding ratio as well as conversion ratio is evaluated by the fol-lowing equation;
CR ¼ capture rateðTh232þ U234Þ � capture rateðPa233ÞAbsorption rateðU233þ U235Þ ð1Þ
This conversion ratio definition is based on the reaction rate offissile and fertile nuclides and some contribution of intermediatenuclides. For parametric survey analysis, the obtained value ofthe conversion ratios is evaluated by using the equilibrium atomcomposition. This equation is employed based on the fertile andfissile nuclides with the contribution from intermediate nuclidessuch as 234U and 233Pa.
2.3. Void reactivity coefficient
The void reactivity coefficient, av, is calculated by the followingequation, where several conditions of voided are investigated fordifferent MFR and different burnups. Moderator to fuel ratio(MFR) evaluation is based on two different calculations in relationto geometrical limit of MFR for triangular lattice. This study fo-cused on the triangular lattice pitch because it can use a lowerMFR for a 1 mm pin gap (MFR of about 0.3) for considering the heatremoval capacity (Hibi et al., 2001). For MFR that has pin gap1 mm, we employed a volume ratio of moderator to fuel. ThisMFR can be called as geometrical MFR or moderator to fuel volumeratio. For MFR in which the MFR < 0.3, the geometrical MFR wasfixed for a pin gap of 1 mm, and to calculate the MFR, the ratioof moderator number density is used. This low MFR can be calledas effective moderator to fuel ratio. To evaluate the effect of voidfraction on void reactivity coefficient, several voided conditionhave been investigated from 5% to 100% voided. Decreasing thedensity of coolant simulates a voided condition. A 5% voided isevaluated for the smallest voided condition and a 100% voided isstudied assuming the total coolants in the core are voided. Thosevoided condition have been evaluated in order to know the mostconservative voided condition, which shows the least negative voidcoefficient or positive void coefficients.
av ¼DqDfv
ð2Þ
where
Dq ¼ qvoid � qnormal ð3Þ
q ¼ kx � 1kx
ð4Þ
kx is the effective or infinite multiplication factor (K-eff and K-inf,respectively) and fv and kx are void fraction and effective or infinitemultiplication factor, respectively. The infinite multiplication factorhas been used for this evaluation as the most conservative evalua-tion, since the neutron leakage effect is ignored. To evaluate theleakage effect on this void reactivity analysis, effective multiplica-tion factor has adopted. A comparative result of void reactivity coef-ficient profile will be shown and discussed in this paper based onthe leakage effect and the voided fraction effect evaluations.
2.4. Macroscopic XS and relative neutron production rate
The neutron reaction based evaluation of the system has beenused for analyzing some phenomena in which some nuclides con-tribute to the system whether individual or in total contributions.
This evaluation has been performed in order to analyze the profileof breeding capability and void reactivity coefficient. Isotopic mac-roscopic cross-section evaluation which is shown in followingequation has been used for estimating the contribution of somemain nuclides to breeding or conversion ratio capability which isbased on macroscopic capture cross-section and macroscopicabsorption cross-section values.
Ric ¼ Niri
c; for macroscopic capture cross-section ð5Þ
Ria ¼ Niri
a; for macroscopic absorption cross-section ð6Þ
i ¼ isotope
To evaluation the profile of void reactivity coefficient, the esti-mated analysis which based on the isotopic neutron productionrate has been used for several main nuclides. Individual contribu-tion or in total contribution of some nuclides to the void reactivitycoefficient can be estimated whether the contributions are nega-tive or positive values. Isotopic neutron production rate change Pi
as shown in the following equation will be used for the evaluation.
Pi ¼tRi
fP
i2fuelRia
�����void
�tRi
fP
i2fuelRia
�����normal
ð7Þ
tRif is the macroscopic neutron production cross-section of isotope i
and Ria is the macroscopic absorption cross-section of isotope i.
3. Breeding capability of heavy water cooled reactor
Breeding performance of heavy water cooled reactor for actini-des closed-cycle has been investigated for several key parameters.Breeding capability analysis is evaluated based on the capability ofconversion ratio for each case, which can be defined as a conver-sion ratio over than unity as a breeding condition. Those parame-ters will be shown and discussed at the following section such asconversion ratio profile of actinides cases and some comparativeanalyses.
3.1. Conversion ratio of 233U closed-cycle
Obtained conversion ratio of 233U closed-cycle case is shown inFig. 1. It shows conversion ratio profile as a function of MFR for dif-ferent burnup constants. As can be estimated, each burnup valuehas its own conversion ratio profile for different MFR. Higher bur-nup and higher MFR can reduce the conversion ratio capability ofthe reactors. The required MFR for obtaining a breeding conditionis varied for each case of investigated burnup. For instance,MFR < 1.3, MFR < 1.5 and MFR < 2.3 are required to have a breedingcondition for burnup of 50 GW d/t, 36 GW d/t and 18 GW d/t,respectively.
In case of the lowest investigated burnup (6 GW d/t), a breedingcondition can be achieved along the MFR (MFR = 0.1–4.0). Consid-ering the standard MFR value of PWR (MFR = 2) breeding conditioncan be obtained for burnup about 20 GW d/t or lower. When theMFR is reduced, for instance, a half MFR value (MFR = 1) of stan-dard PWR, it will reaches a breeding condition even for burnupof 50 GW d/t or higher. For obtaining a breeding value of 1.1, lowerMFR is required, such as MFR of about 0.4 or lower for burnup of50 GW d/t and it requires relatively higher MFR for lower burnupconstants as shown in Fig. 1.
To understand the mechanism of conversion ratio profile basedon the neutron reaction profile, the analysis of macroscopic cross-section condition for several main nuclides will be discussed inthis paper. Those breeding conditions can be estimated by the pro-file of macroscopic cross-section of several main nuclides, which
0.8
0.9
1
1.1
1.2
1.3
0 0.5 1 1.5 2 2.5 3 3.5 4
Con
vers
ion
Rat
io [-
]
Burnupdecreases
6 GWd/t 18 GWd/t
36 GWd/t 50 GWd/t
Breeding
MFR [-]
Fig. 1. Conversion ratio of 233U closed-cycle reactor.
340 S. Permana et al. / Annals of Nuclear Energy 38 (2011) 337–347
contributes to the fuel cycle system as shown in Fig. 2 for 233Uclosed-cycle case and burnup of 36 GW d/t. The breeding ratio willalways higher than unity when the macroscopic capture cross-section of 232Th is higher than the macroscopic absorption cross-section of 233U. In principle, based on Eq. (1) of conversion ratiocalculation, the numerator is based on the capture of fertilenuclides and some intermediate nuclides. And for the denominatoris based on absorption rate of some fissile nuclides. In case of 233Uclosed-cycle, some contributions of other nuclides such as macro-scopic capture cross-section of 234U and macroscopic absorptioncross-section of 235U are also can be estimated, however, the con-tribution is not so significant as shown in Fig. 2. Therefore, becausethe main contribution comes from the reaction rate of main fertilenuclide (232Th) and main fissile nuclide (233U), the estimation canbe understood easily based on the ir contribution. As shown in
0
0.005
0.01
0.015
0.02
0 0.5 1 1.5 2 2.5 3 3.5 4
Mac
ro x
s [1
/cm
]
Moderator to Fuel Ratio [-]
Absorb
233U
Capture 232 Th
Capture 234UAbsorb 235U
Capture 233Pa
Fig. 2. Macroscopic cross-section profile of several nuclides for 233U closed-cycle.
Fig. 2, macroscopic capture cross-section of 232Th is alwayssuperior to macroscopic absorption cross-section rate of 233U forMFR < 1.5 and it becomes inferior when MFR > 1.5. This estimationcan explain the breeding capability of the reactor, in which thebreeding condition can be achieved at MFR < 1.5 for burnup of36 GW d/t. The same analysis of reaction rate for several mainnuclides can be adopted for other burnup constant cases.
3.2. Conversion ratio of HM closed-cycle
This analysis is based on the fuel cycle option for all heavy met-als (HMs) or all actinides are recycled into the reactor, namely, HMclosed-cycle case. The MFR change has more significant impact tothe conversion ratio in the range of MFR < 2, which shows the ob-tained conversion ratio decreases rapidly with increasing MFR.Fig. 3 shows the conversion ratio of HM closed-cycle case as a func-tion of MFR for different burnup constants. The required MFR forobtaining breeding is varied for each burnup case. For instance,MFR < 0.9, MFR < 1.2, MFR < 1.5 and MFR < 1.7 are estimated tohave a breeding condition for burnup of 50 GW d/t, 36 GW d/t,18 GW d/t and 6 GW d/t, respectively. At MFR > 1.8, breeding can-not be achieved by HM closed-cycle case, even for the lowest bur-nup (6 GW d/t). Considering the breeding condition for allinvestigated burnup (6–50 GW d/t) of HM closed-cycle case, it isdifficult to design a breeder reactor for standard MFR value ofPWR (MFR = 2), even for the lowest investigated burnup (6 GW d/t). For a half MFR value (MFR = 1) than standard PWR, it is difficultto reach a breeding for burnup of 50 GW d/t or higher, however, itis still possible for burnup of about 40 GW d/t or lower.
Adopting the same way as mentioned before in the previoussection by estimating the profile of macroscopic cross-section ofseveral main nuclides, the profile of breeding conditions for HMclosed-cycle case also can be estimated as shown in Fig. 4 forburnup of 36 GW d/t. Fig. 4 shows that macroscopic capturecross-section of 232Th is always higher than macroscopic absorp-tion cross-section of 233U at MFR < 1.3. Based on this estimation,which is based on the profile of macroscopic capture cross-sectionof 232Th and macroscopic absorption cross-section of 233U, breed-ing can be obtained by MFR < 1.3. However, the obtained resultshows the breeding can be achieved for MFR < 1.2. In case of HM
0.8
0.9
1
1.1
1.2
1.3
0 0.5 1 1.5 2 2.5 3 3.5 4
Con
vers
ion
Rat
io [-
]
MFR [-]
Burnupdecreases
6 GWd/t
18 GWd/t
36 GWd/t
50 GWd/t
Breeding
Fig. 3. Conversion ratio of HM closed-cycle.
0
0.005
0.01
0.015
0.02
0 0.5 1 1.5 2 2.5 3 3.5 4
Mac
ro x
s [1
/cm
]
Moderator to Fuel Ratio [-]
Absorb233 U
Capture232 Th
Capture 234U
Absorb 235U
Capture 233Pa
Fig. 4. Macroscopic cross-section profile of several nuclides for HM closed-cycle.
0.8
0.9
1
1.1
1.2
1.3
0 0.5 1 1.5 2 2.5 3 3.5 4
36 GWd/t
Con
vers
ion
Rat
io [-
]
MFR [-]
U-233 Closed
HM Closed
Fig. 5. Conversion ratio of 233U and HM closed-cycle cases as a function of MFR.
0 100
5 10-4
1 10-3
1.5 10-3
2 10-3
2.5 10-3
0 0.5 1 1.5 2 2.5 3 3.5 4
Mac
ro x
s [1
/cm
]
Moderator to Fuel Ratio [-]
Capture 234U
Absorption 235U
U-233 Closed
HM C
lose
d
Fig. 6. Macroscopic cross-section profiles of capture 234U and absorption 235U for233U and HM closed-cycle cases.
S. Permana et al. / Annals of Nuclear Energy 38 (2011) 337–347 341
closed-cycle, some contributions of other nuclides such as macro-scopic capture cross-section of 234U and macroscopic absorptioncross-section of 235U are significant as shown in Fig. 4. The contri-bution of 234U capture and 235U absorption has same value alongthe MFR. The denominator of 235U absorption is expected to havemore impact to reduce the breeding than 234U capture for addi-tional contribution for increasing breeding. Therefore, breedingcan be achieved lower than that estimation of capture 232Th andabsorption of 233U only, because the contribution of 235U absorp-tion is also effective to reduce breeding capability.
3.3. Comparative result of 233U and HM closed-cycles
Breeding capability analysis will be discussed in this section forcomparison purpose between both cases of 233U and HM closed-cycle. Comparison result of obtained breeding for two fuel cyclecases is shown in Fig. 5, which shows the conversion ratio profileof both cases as a function of MFR for burnup of 36 GW d/t. Fig. 5shows that to achieve a breeding condition for burnup of36 GW d/t, it requires a design region of MFR < 1.2 and MFR < 1.5for HM closed-cycle and 233U closed-cycle, respectively. For obtain-ing a breeding condition of 1.1, the feasible design region is atMFR = 0.5 for both cases and its breeding value becomes higherwhen MFR is reduced. Conversion ratio of HM closed-cycle has ahigher value at MFR < 0.5 than 233U closed-cycle; however, it valuebecomes less at MFR > 0.5. Breeding condition for the standardMFR value of PWR (MFR = 2), can be achieved by 233U closed-cycle,although the burnup is relatively lower than conventional PWRburnup. However, for HM closed-cycle case, even for the lowestburnup, a breeding condition cannot be obtained.
As mentioned at the previous section that the contribution ofcapture 234U and absorption 235U are also can be involved for eval-uating breeding capability based on the profile of macroscopiccross-section for both fuel cycle cases. More significant contribu-tion of capture 234U and absorption 235U is shown in HM closed-cy-cle comparing to 233U closed-cycle case because of highermacroscopic value as shown in Fig. 6. Higher contribution of cap-ture 234U and absorption 235U can be involved for higher MFR. Incase of HM closed-cycle, at small MFR there is so small differentmacroscopic cross-section values between capture 234U and
absorption 235U, and at higher MFR, it obtains a similar value foreach other. The biggest different value for both cases is shownfor macroscopic absorption cross-section value of 235U which isabout 5 times bigger value for HM closed-cycled compared with233U closed-cycle. The contribution of macroscopic absorptioncross-section of 235U has more significant value for reducing thebreeding capability of HM closed-cycle at MFR > 0.5 comparedwith 233U closed-cycle case. The additional contribution of capture234U, to increase the breeding capability is also can be added, how-ever, its contribution is not dominant than the contribution of 235Uas the denominator based on the concept of conversion ratio,which is shown in Eq. (1). This higher accumulated 234U and 235U
342 S. Permana et al. / Annals of Nuclear Energy 38 (2011) 337–347
and some others nuclides come from the recycled nuclides in HMclosed-cycle case.
4. Void reactivity profile of heavy water cooled reactor
The evaluation of void reactivity coefficient will be discussed inthis section. A comparative analysis based on the void reactivityprofile of 233U and heavy metal closed-cycle cases will be shownas well as the evaluation for several voided fraction cases andthe effect of leakage on void reactivity. Those parameters will beshown and discussed at the following section such as leakage effecton void reactivity; voided fraction effect on reactivity and compar-ative analysis of void reactivity based on two fuel cycle cases.
4.1. Leakage effect on void reactivity
The Leakage effect has been evaluated to analyze the compari-son profile of void coefficient with leakage and no leakage condi-tions. This evaluation also is conducted to know the conservativecondition where the reactivity changes are based on the infinitemultiplication factors which means no leakage is involved. In addi-tion, the evaluation of leakage effect has been employed to showsthe contribution of leakage to void reactivity as a function of MFR.The multiplication factor value for evaluating its reactivity changeshas been adopted for leakage effect evaluation. The difference ofvoid reactivity coefficient for no leakage and with leakage is rela-tively small for lower MFR as shown in Fig. 7, which shows voidreactivity of leakage and no leakage cases as a function of MFRfor burnup 36 GW d/t and 233U closed-cycle case. This conditionshows that the contribution of leakage to reduce the positive voidor to make more negative void is less for lower MFR than higherMFR. The contribution of leakage is more effective for higherMFR than lower MFR because the reactor is more thermalized.
Almost all MFR regions show negative void reactivity for bothconditions, except for small MFR (MFR < 0.4), it becomes positivevoid reactivity. Higher MFR is more preferable for obtaining morenegative void reactivity. Therefore, it can be estimated a lower lim-it of MFR for obtaining negative void reactivity as well as the esti-mation of higher limit of MFR for breeding as mentioned in the
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0 0.5 1 1.5 2 2.5 3 3.5 4
Void
Rea
ctiv
ity C
oef.
x10e
-2 [d
k/k/
%vo
l]
MFR [-]
Void Fraction = 50 %
No Leakage
With Leakage
(36 GWd/t)
Fig. 7. Leakage effect on void coefficient as a function of MFR for 233U closed-cycle.
previous sections. In case of burnup of 36 GW d/t, the lower limitof MFR can be estimated at around MFR = 0.35 and MFR = 0.25for no leakage condition and leakage condition cases, respectively.Higher burnup contributes to make the reactor less negative voidreactivity, therefore, lower limit of MFR for negative void reactivitybecomes relatively shift to lower MFR. In case of lower burnup, thereactor becomes more negative or less positive void reactivity coef-ficient than higher burnup which causes the lower limit of MFR forobtaining negative void reactivity shift to relatively higher MFR.
To analyze the void reactivity profile in this study, the estima-tion which based on the relative production rate concept, can beused to understand the phenomena from the neutron reactionpoint of view. The relative production rate profile as a function ofMFR for 233U closed-cycle case is shown in Fig. 8, which based onthe main nuclides contribution. This estimation concept of relativeproduction rate is calculated based on Eq. (7). Fig. 8 shows the neg-ative contribution for void reactivity, mainly comes from fissilenuclides of 233U and 235U. Positive contribution comes from fertilenuclide of 232Th, some small contribution from 234U and very smallcontribution from 233Pa and plutonium isotopes.
The net contribution of all nuclides is obtained as a negativealong the MFR regions except for lower MFR. The net contributionis similar to the profile of 233U contribution. Therefore, in case of233U closed-cycle, the negative contribution of void reactivity canbe estimated from the negative contribution of 233U. Based on thisevaluation, the negative contribution can be obtained mainlycomes from fissile nuclides and the positive contribution mainlycomes from fertile nuclide. Some additional contributions alsocome from other intermediate nuclides whether, its contributionis positive or negative value, and however, their contribution is rel-atively small for 233U closed-cycle case.
Leakage effect of void reactivity is also evaluated for HM closed-cycle case as well as 233U closed-cycle case, which is shown inFig. 9. The similar profile to 233U closed-cycle is shown by HMclosed-cycle case for no leakage and with leakage conditions ofvoid reactivity coefficient. Mainly, MFR regions show negative voidreactivity for conditions, except for small MFR (MFR < 0.7), it be-comes positive void reactivity. In case of burnup of 36 GW d/t,the estimated lower limit of MFR are about MFR = 0.65 andMFR = 0.45 for no leakage and leakage conditions, respectively.
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0 0.5 1 1.5 2 2.5 3 3.5 4
Rel
ativ
e Pr
oduc
tion
Rat
e [-]
MFR [-]
233U
232Th234U
235U233Pa and Pu
Total
Fig. 8. Macroscopic cross-section profile of several nuclides for 233U closed-cycle asa function of MFR.
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0 0.5 1 1.5 2 2.5 3 3.5 4
Void
Rea
ctiv
ity C
oef.
x10e
-2 [d
k/k/
%vo
l]
MFR [-]
Void Fraction = 50 %
No Leakage
With Leakage
(36 GWd/t)
Fig. 9. Leakage effect on void coefficient as a function of MFR for HM closed-cycle.
S. Permana et al. / Annals of Nuclear Energy 38 (2011) 337–347 343
Relatively higher MFR for negative void limit of MFR is expectedbecause of higher burnup contribution and the relatively lowerMFR of the negative limit of MFR for lower burnup contribution.
The evaluation of void reactivity which based on the estimationconcept of relative production rate is also adopted for HM closed-cycle. The relative production rate profile for HM closed-cycle caseis shown in Fig. 10, which based on the main nuclides contributionas a function of MFR. It shows the negative contribution, mainlycomes from the contribution of 233U and 235U. On the other side,the positive contribution comes from fertile nuclide of 232Th,234U, and some small contribution from 233Pa and plutonium iso-topes. The net contribution of all nuclides mainly based on the big-gest negative contribution of 233U and for positive contribution of
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0 0.5 1 1.5 2
Rel
ativ
e Pr
oduc
tion
Rat
e [-]
MFR [-]
233U
232Th
234U
235U
233Pa
Total
Pu
Fig. 10. Macroscopic cross-section profile of several nuclides for HM closed-cycle asa function of MFR.
234U and 232Th. The profile of net contribution to void reactivityis similar to the profile of 233U contribution; however, its value be-comes less negative or more positive because of higher positivecontribution of 234U and 232Th.
4.2. Voided fraction effect on void reactivity
The evaluation of voided fraction effect on void reactivity hasbeen employed for some voided fractions of 5–100% voided. Thosevoided fractions are studied to evaluate the dependence of voidreactivity condition to the change of voided fraction condition. Inaddition, to understand the most conservative condition of voidreactivity coefficient where those voided fraction change will givesthe less negative void coefficient or more positive void coefficient.The obtained results of void reactivity are shown in Fig. 11 for sev-eral voided fraction of burnup 36 GW d/t with no leakage evalua-tion. The result shows each voided fraction gives the differentprofile of void reactivity coefficient as a function of MFR.
Voided fractions of 5–100% give negative void coefficients ex-cept for MFR < 0.8, it obtains positive void coefficient depends onvoided fraction case. Regarding to the MFR limit for obtaining anegative void reactivity, the obtained MFR limits shifts to higherMFR for higher voided fraction. Fig. 11 shows that there are twoareas which show the conservative condition which based on thevoided fraction 5% and 100%. Voided fraction of 5% obtains alwaysless negative void coefficient than other voided fraction along theMFR except at MFR < 0.8. At those lower MFR (MFR < 0.8), 100%voided fraction shows less negative void or even more positivevoid reactivity. In this regards, it can be estimated that smallestvoided fraction (5%) can be used for void reactivity analysis as acondition of conservative assumption at MFR > 0.8 and on theother side, at MFR < 0.8, highest voided fraction (100%) can beadopted as a condition of conservative condition.
As mentioned at previous section, several voided fractions havebeen studied in order to evaluate the change of voided fractionwhich affects to the change of void reactivity coefficient profile.Those studies have been used also for analyzing the void coefficientprofile for HM closed-cycle case as shown in Fig. 12. It shows the
-0.4
-0.3
-0.2
-0.1
0
0.1
0 0.5 1 1.5 2 2.5 3 3.5 4
Void
Rea
ctiv
ity C
oef.
x10e
-2 [d
k/k/
%vo
l]
MFR [-]
no Leakage cases (36 GWd/t)
5 % voided
50 % voided
100 % voided
Fig. 11. Voided fraction effect on void coefficient as a function of MFR for 233Uclosed-cycle reactor.
-0.4
-0.3
-0.2
-0.1
0
0.1
0 0.5 1 1.5 2 2.5 3 3.5 4
Void
Rea
ctiv
ity C
oef.
x10e
-3 [d
k/k/
%vo
l]
MFR [-]
no Leakage cases (36 GWd/t)
5 % voided50 % voided
100 % voided
Fig. 12. Voided fraction effect on void coefficient as a function of MFR for HMclosed-cycle reactor.
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0 0.5 1 1.5 2 2.5 3 3.5 4
36 GWd/t
Void
Rea
ctiv
ity [d
k/k/
%vo
l]
MFR [-]
U-233 Closed
HM Closed
no Leakage case (50% voided)
Fig. 13. Void reactivity coefficient of 233U and HM closed-cycle cases as a functionof MFR.
344 S. Permana et al. / Annals of Nuclear Energy 38 (2011) 337–347
void reactivity profile for several voided fraction of 36 GW d/t withno leakage condition. The results show that each voided fractiongives the different profile of void reactivity coefficient as a functionof MFR as shown also in 233U closed-cycle case. Voided fractions of5–100% give negative void coefficients except for MFR < 2, it ob-tains positive void coefficient depends on voided fraction condi-tions. Two areas of MFR can be adopted for conservativecondition of voided fraction which based on the voided fraction5% and 100%. At MFR > 2, voided fraction of 5% can be estimatedas a conservative condition of voided fraction in which gives al-ways less negative void coefficient along the MFR. Meanwhile, atMFR < 2 100% voided fraction can be used as a voided fraction con-dition for a conservative assumption.
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0 0.5 1 1.5 2
Rel
ativ
e M
acro
Pro
duct
ion
rate
[-]
MFR [-]
233U(a)
232Th(b)
234U(a)
233U(b)
234U(b)
232Th(a)
Fig. 14. Isotopic macroscopic production rate of 233U and HM closed-cycle cases forseveral nuclides as a function of MFR. (a) 233U closed-cycle and (b) HM closed-cycle.
4.3. Comparative analysis on void reactivity
Void reactivity profile is also evaluated and will be presented inthis section for comparative analysis purpose of 233U and HMclosed-cycle cases. The obtained void reactivity profile of both fuelcycle cases as a function of MFR is shown in Fig. 13. It shows that toobtain negative void reactivity for burnup of 36 GW d/t, it requiresa design region of MFR > 0.35 and MFR > 0.65 for 233U closed-cycleand HM closed-cycle, respectively. By recycling all HM, void reac-tivity becomes worse than only recycling 233U. Void reactivity pro-file of HM closed-cycle is more positive or less negative valuescompared with 233U closed-cycle. Therefore, the MFR limits forobtaining a negative void coefficient shift to higher MFR when allHM are recycled.
Some main nuclides contribute to void reactivity, whether itscontribution is negative or positive values. Those contributionsfrom several main nuclides is illustrated in Fig. 14, which showsrelative macro production rate as a function of MFR. Contributionof 233U for both fuel cycle cases has similar profile and its contribu-tion of HM closed-cycle case has less negative value. Positive con-tribution of 232Th has relatively similar value, however, it slightlydifferent for higher MFR and it has higher positive contributionfor 233U fuel cycle case. A big different value of 234U contributionis shown for positive contribution of void reactivity for both fuelcycle cases. It can be seen from Fig. 14, when all HMs are recycled,
the positive contribution of 234U has higher value, which about 3 to7 times higher contribution compared with the positive 234U con-tribution for 233U closed-cycle case.
Negative contribution mainly comes from fissile nuclide of 233Uand its profile has similar trend with void reactivity trend for bothfuel cycle cases as shown in Figs. 8 and 10. Therefore, the profile ofvoid reactivity also can be easily estimated by evaluating the con-tribution of 233U, whether its contribution is positive or negative.The contribution of 232Th gives a positive contribution to the voidreactivity coefficient along the MFR for both 233U and HM closed-cycles. As additional contribution which makes the reactor morepositive or less negative void reactivity comes from nuclide 234Ufor both fuel cycle cases. More significant contribution of 234U is
0 10 20 30 40 50 600
0.5
1
1.5
2
2.5
3
3.5
4
Burnup [GWd/t]
Mod
erat
or to
Fue
l Rat
io(M
FR) [
-]
233U Closed
Negative Void Limit
Breeding Limit
100% voided, with leakage
Fig. 15. Feasible design area for 233U closed-cycle reactor.
S. Permana et al. / Annals of Nuclear Energy 38 (2011) 337–347 345
shown for HM closed-cycle case, which the contribution of 234U ishigher than that contribution of 234U for 233U closed-cycle, or evenhigher than its contribution of 232Th for HM closed-cycle case atMFR < 2 as shown in Fig. 15. Therefore, it can be understood, thatwhen all HMs are recycled, accumulated 234U amount becomeshigher and it affects to more positive or less negative value of voidreactivity coefficient.
3
3.5
4
(MFR
) [-]
HM Closed
100% voided, with leakage
5. Feasibility design area of breeding and negative voidreactivity
The present study intends to estimate a design feasible areawhich fulfills breeding and negative void reactivity coefficientbased on the evaluation of various moderator to fuel volume ratio(MFR), burnup values and some voided fractions. This section clas-sifies a feasible design area of breeding and negative void coeffi-cient for 233U fuel closed-cycle and HM closed-cycle cases.Design feasible area will be presented as a map, which is shownas function of moderator to fuel ratio (MFR) parameter versus bur-nup. A voided fraction of 100% voided is chosen for a conservativeassumption, in which assuming no water exist as coolant and mod-erator. The leakage effect is still involved in this evaluation for100% voided condition.
0 10 20 30 40 50 600
0.5
1
1.5
2
2.5
Burnup [GWd/t]
Mod
erat
or to
Fue
l Rat
io
Negative Void Limit
Breeding Limit
Fig. 16. Feasible design area for HM closed-cycle reactor.
5.1. Feasible design area of 233U closed-cycle
The feasible design area of D2O reactor which satisfies bothbreeding capability and negative void coefficient is indicated inFig. 15 for 233U closed-cycle. The limit line of negative void reactiv-ity coefficient describes the lower limit of MFR for obtaining nega-tive void reactivity coefficient. The breeding limit line denotes themaximum achievable burnup while keeping the conversion ratioequal to unity. Breeding capability is preferable for lower MFRand it capability can be achieved even for relatively higher burnupthan 50 GW d/t. Increasing MFR makes the breeding capability be-comes worse and it reduces the feasible obtained burnup region forbreeding. Therefore, for higher investigated MFR (MFR > 3), thebreeding capability in relation to achievable burnup for breedingcondition is limited to burnup of about 10 GW d/t.
Negative void reactivity is more effective for lower burnupwhich requires lower MFR limit, however, it MFR limit requireshigher MFR when burnup is increased. This map of feasibility de-sign area of breeding and negative void reactivity can be adoptedas reference design area for designing the reactor which has abreeding capability and at the same time it obtains negative voidreactivity in thorium fuel cycle system. Based on the area whichis shown in Fig. 15, the expected area of breeding and negative voidreactivity can be extended even for more than 60 GW d/t, however,its possible area becomes narrow because of the limitation ofbreeding capability line and negative void reactivity limit.
The estimated map can be used to choose a desirable regionsuch as desirable higher MFR or higher burnup values for thoriumfuel cycle system when the reactor only recycling 233U. Higher MFRis preferable for obtaining higher cooling ability, better thermalhydraulic values and some better safety points of view. In addition,higher burnup is also more acceptable in relation to fuel utilization,long life core and some economic points of view. The optimizationregion can be estimated to cover all merits of higher MFR as well ashigher burnup. The MFR of around MFR = 1 can be adopted as anoptimum reference for intermediate lower MFR and can be usedfor obtaining higher burnup (>50 GW d/t).
5.2. Feasible design area of HM closed-cycle
Feasible area of breeding and negative void coefficient of HMclosed-cycle will be presented and discussed in this section, whichis shown in Fig. 16. As can be expected, by increasing HM closed-cycles, the reactor can have a higher breeding capability in ura-nium fuel cycle system (Permana et al., 2006; Waris and Sekimoto,2001a). In this regard, the same estimation of HM closed-cycle willbe adopted for this thorium fuel cycle system. The feasible area ofbreeding and negative void reactivity for HM closed-cycle showsthat it’s breeding area is limited to MFR = 2, otherwise, it becomesnot breeding for MFR > 2. In addition, the area shows the designfeasible area is limited to burnup of 36 GW d/t, because the breed-ing limit and negative void reactivity limit reach at the same pointat around burnup of 36 GW d/t and MFR of 1.1. This feasible areacan be used for evaluating the reactors with HM closed-cycle inthorium fuel cycle system.
Negative Void Limit
Breeding Limit
0 10 20 30 40 50 600
0.5
1
1.5
2
2.5
3
3.5
4
Burnup [GWd/t]
Mod
erat
or to
Fue
l Rat
io(M
FR) [
-]
100% voided, with leakage
Fig. 17. Feasible design area of 233U and HM closed-cycle cases as a function of MFRand burnup.
346 S. Permana et al. / Annals of Nuclear Energy 38 (2011) 337–347
5.3. Comparative analysis on feasible design area
The comparative results of 233U and HM closed-cycle cases onfeasible areas of breeding and negative void coefficient are shownin Fig. 17. Regarding the feasible area of breeding, only 233U closed-cycle case shows its breeding area along the MFR and a feasiblearea of HM closed-cycle is limited to MFR < 2. The feasible areaof HM closed-cycle is smaller than 233U closed-cycle as a functionof MFR and burnup value.
The optimize region can be adopted at around of MFR = 1 forboth 233U and HM closed-cycle cases. This optimum MFR is rela-tively not so small MFR (a half than standard MFR of PWR) and itshows better burnup values can be used for breeding and negativevoid reactivity coefficient. Higher burnup value can be used forthat optimum MFR even for burnup >50 GW d/t when the reactorsystem uses only recycled 233U and its burnup value is limited toburnup <36 GW d/t when the system uses recycled all heavy met-als (HMs).
Based on the overall investigated results, the feasible area of233U closed-cycle is wider than HM closed-cycle. This condition ex-plains that only if 233U is recycled, the area becomes wider andwhen all HM are recycled, the area become worst. In addition,the opposite result of breeding capability has been shown in tho-rium fuel cycle that recycled more HM reduces the breeding capa-bility compared with uranium fuel cycle which obtains higherbreeding capability when more HM is recycled. The importantfinding from the results, that the contribution of capture 235U inHM closed-cycle case is more significant to reduce the breedingcondition. In addition, the contribution of accumulated 234U inHM closed-cycle case is also more significant to make a reactor ob-tains more positive or less negative void reactivity coefficient.Therefore, the feasible area to fulfill a breeding and negative voidcoefficient becomes worse for HM closed-cycle.
6. Conclusion
Design feasible area of breeding and negative void reactivity hasbeen investigated for various and wide range of design parametersof heavy water (D2O) cooled thorium breeder reactors for two dif-
ferent fuel cycle systems of 233U and HM closed-cycles. As the fea-sible area of breeding and negative void reactivity coefficient, thearea of 233U closed-cycle has wider than HM closed-cycle. This con-dition explains that only 233U is recycled, the area becomes widerand when all HM are recycled, the area becomes worse. In addition,the opposite result of breeding capability has been shown in tho-rium fuel cycle that more recycled HM reduces the breeding capa-bility, compare to uranium fuel cycle which obtains higherbreeding capability when more HM is recycled. The feasible designarea which has a breeding and negative void reactivity for 233Uclosed-cycle can be estimated for higher burnup even higher than60 GW d/t, however, its feasible area for HM closed-cycle is limitedto 36 GW d/t. The important finding from the results, that the con-tribution of 235U is more significant to reduce the breeding capabil-ity and the contribution of 234U is also more effective to make thereactor more positive or less negative void coefficient for HMclosed-cycle case in thorium fuel cycle system. Therefore, the fea-sible area to fulfill breeding and negative void coefficient becomesworst for HM closed-cycle.
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