impact of different moderator ratios with light and heavy water cooled reactors in equilibrium...

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Annals of Nuclear Energy 33 (2006) 561–572

annals of

NUCLEAR ENERGY

Impact of different moderator ratios with light and heavy watercooled reactors in equilibrium states

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

Received 15 December 2005; received in revised form 27 February 2006; accepted 27 February 2006Available online 18 April 2006

Abstract

As an issue of sustainable development in the world, energy sustainability using nuclear energy may be possible using several differentways such as increasing breeding capability of the reactors and optimizing the fuel utilization using spent fuel after reprocessing as well asexploring additional nuclear resources from sea water. In this present study the characteristics of light and heavy water cooled reactorsfor different moderator ratios in equilibrium states have been investigated. The moderator to fuel ratio (MFR) is varied from 0.1 to 4.0.Four fuel cycle schemes are evaluated in order to investigate the effect of heavy metal (HM) recycling. A calculation method for deter-mining the required uranium enrichment for criticality of the systems has been developed by coupling the equilibrium fuel cycle burn-upcalculation and cell calculation of SRAC 2000 code using nuclear data library from the JENDL 3.2. The results show a thermal spectrumpeak appears for light water coolant and no thermal peak for heavy water coolant along the MFR (0.1 6MFR 6 4.0). The plutoniumquality can be reduced effectively by increasing the MFR and number of recycled HM. Considering the effect of increasing number ofrecycled HM; it is also effective to reduce the uranium utilization and to increase the conversion ratio. trans-Plutonium production suchas americium (Am) and curium (Cm) productions are smaller for heavy water coolant than light water coolant. The light water coolantshows the feasibility of breeding when HM is recycled with reducing the MFR. Wider feasible area of breeding has been obtained whenlight water coolant is replaced by heavy water coolant.� 2006 Elsevier Ltd. All rights reserved.

1. Introduction

Energy demand should become constant in a futureequilibrium society. Similar to sustainable development,the future equilibrium state needs an energy source whichcan maintain long-term sustainable supply without causingany environmental problems. Nuclear power can produceenough energy for long periods, even for a million yearsof mankind’s utilization by using FBR with the conversionratio (CR) of about unity and uranium from seawater(Sekimoto, 1994). In the equilibrium state, the rate ofenergy consumption remains constant. If the earth’s energysupply is secured by nuclear power generation, each pro-duced active nuclide density in the reactor may be also con-stant. This state is called ‘‘nuclear equilibrium state’’.

0306-4549/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.anucene.2006.02.013

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

The society in this condition is called the nuclear equilib-rium society. In the nuclear equilibrium state, the produc-tion rate of nuclear energy is constant, and the productionand disintegration rates of nuclear materials are constantas well. Therefore, the amount of each nuclide in a reactorbecomes constant if the refueling operation is continuous(Sekimoto and Takagi, 1991). We have called the nuclearfuel cycle at the nuclear equilibrium state ‘‘the equilibriumfuel cycle’’ (Sekimoto and Waris, 1999). In the futurenuclear equilibrium society, only natural uranium and/orthorium are employed as supplied fuel (Sekimoto and Tak-agi, 1991). This study showed that LWR could not achieveits criticality. Therefore, charged fuel should be enriched inLWR with conventional moderator to fuel ratio(MFR = 2) (Waris and Sekimoto, 2001a). In dealing withHM confining, it seems that in the case of uranium, it isnot recycled; the enrichment decreases considerably withincreasing number of confined nuclides in the reactor

mailto:[email protected]

Case 1: Once-through Case 2: Partial plutonium recycles Case 3: Full plutonium recycles Case 4: TRU confining fuel cycle.

Natural Uranium

EnrichedProcess Fabrication Reactor Separation

Disposal

NUCLEAR CENTER

Fig. 1. Fuel cycle scheme.

562 S. Permana et al. / Annals of Nuclear Energy 33 (2006) 561–572

(Waris and Sekimoto, 2001a,b, 2000). In the present study,we investigate several characteristics for different modera-tor to fuel ratios of light water and heavy water cooledreactors. Several fuel cycle schemes are performed in orderto analyze the effect of confined HMs to the reactorcharacteristics.

2. Reactor design parameters and fuel cycle options

2.1. Reactor design parameters

The basic reactor design parameters of investigatedsystems are tabulated in Table 1. The average power den-sity in fuel pellet is fixed to 280 W/cc, which correspondsto the cell-averaged power density of 100 W/cc. This cell-averaged power density is about the same as the core-averaged power density of the present standard PWR(Westinghouse) of 105 W/cc. In this study, the moderatorto fuel ratio (MFR) is varied from 0.1 to 4.0. ThoseMFR values are evaluated in order to cover the MFRranges such as the standard MFR of PWR (MFR =2.0), lower MFR cases until the MFR = 0.1 whichdenotes to near fast spectrum region and it higherMFR cases until MFR = 4.0.

2.2. Fuel cycle cases

The study employed discharge rate of 33% per year,which corresponds to the three batches with yearly refuel-ing, as a standard discharge constant. This reactor systemis loaded with enriched uranium. Spent fuel is separatedso that the stable nuclides go directly to the disposal facil-ity and radioactive nuclides are kept in the storage sys-tem. Whether the reprocessed heavy metals (HMs) willbe recycled into the reactor core or not depends uponthe fuel cycle to be investigated, and all fission products(FPs) go through to the disposal or storage as shown inFig. 1. Four fuel cycle cases are investigated in which ura-nium is discharged from the reactor with the standardrate for all fuel cycle cases:

Case 1: Once-through.Case 2: Partial plutonium recycles.Case 3: Full plutonium recycles.Case 4: TRU recycles.

Table 1Reactor design parameters of studied reactor

Power output (MW t) 3000Average power density of pellet (W/cc) 280Discharge constant (#/year) 0.33Fuel pellet diameter (mm) 8.0Pin diameter (mm) 9.6Moderator to fuel ratio (MFR) 0.1–4.0Fuel pellet OxideCladding Zircaloy-4Coolant Light water or heavy water

Case 1 is considered as once-through cycle case becauseof uranium and other HMs are discharged from the reactorwith the standard rate, on the other hand no HM is recy-cled. The other cases contain fresh fuel with some amountof HMs such as plutonium and MA from the spent fuelafter reprocessing. Additional amounts of half plutoniumfrom spent fuel with fresh fuel are loaded into the reactoris considered as partial plutonium recycles or Case 2. Fullplutonium mixed with fresh fuel is considered as full pluto-nium recycle or Case 3. The last case is considered as TRUrecycle or Case 4 because of additional spent fuel such asMAs is added to Case 3. These fuel cycle systems, Case1–Case 4, are evaluated in order to investigate the effectof increasing number of recycled HM.

3. Calculation method

3.1. Equilibrium state model

The nuclear fuel cycle is the central theme of the presentstudy. We called the nuclear fuel cycle at the nuclear equi-librium state the equilibrium fuel cycle. The nuclear equi-librium fuel cycle in the present study is considered tosatisfy the following conditions:

1. Number density of each nuclide in a reactor is constant.2. Refueling process is a continuous process.

In these conditions the number density of ith nuclide, ni,should satisfy the following equilibrium fuel cycle burn-upequation:

dni

dt¼ �ðki þ /ra;i þ riÞni þ

Xj

kj!inj þ /X

j

ra;j!inj þ si

ð1ÞIn strict nuclear equilibrium conditions nuclide numberdensities do not change in time

i:e:dni

dt¼ 0 ð2Þ

Therefore, equilibrium fuel cycle burnup equationbecomes:

�ðki þ /ra;i þ riÞni þX

j

kj!inj þ /X

j

ra;j!ini þ si ¼ 0

ð3Þ

S. Permana et al. / Annals of Nuclear Energy 33 (2006) 561–572 563

where / is the neutron flux, ki is the decay constant of ithnuclide, ri is the discharge constant of ith nuclide, kj!i isthe decay constant of jth nuclide to produce ith nuclide,rj!i is the microscopic transmutation cross-section of jthnuclide to produce ith nuclide, si is the supply rate of ithnuclide, ra,i is the microscopic absorption cross-section ofith nuclide.

Here, the absorption cross-section includes not only fis-sion and capture cross-sections but also (n, 2n) and othernuclear transmutation cross-section. The formation of fis-sion products can be estimated by using rj!i or kj!i givenby the following equation:

rj!i ¼ rf ;jcj!i ð4Þ

For neutron induced fission, where rf,j is the microscopicfission cross-section of jth nuclide, cj!i is the yield of ithnuclide from jth fissile nuclide and

kj!i ¼ kf;jcs;j!i ð5Þ

For spontaneous fission, where kf,j is the spontaneous fis-sion decay constant of jth nuclide, cs,j!i is the yield of ithnuclide from jth fissile nuclide spontaneous fission.

In the present study ni is not the total number of nuc-lides in the reactor core, but the number density of nuclidein the fuel pellet. When we consider ni as the number den-sity of nuclide in the fuel pellet, the upper limit of the fuelpellet density according to the fuel materials should betaken into account. Then we decided the total number den-sity of all nuclides in the fuel pellet should satisfy the fol-lowing equation:X

k2HMl2FP

nk þnl

2

� �¼ N total ð6Þ

In this Eq. (6) we take a half of the number density ofFP since each fission reaction produces two FPs. Thesmeared density of fuel pellet, Ntotal, depends upon the fuelmaterials, either oxide fuel, nitride fuel or metallic fuel.Since in this study we evaluate PWR with oxide fuel, thisvalue was chosen to be 93% of the theoretical density ofuranium oxide.

Fuel supply rate for the evaluated reactor core systemsatisfies the following equation:

si ¼ jiS ð7Þwhere si is the supply rate of ith nuclide, ji is the isotopicfraction of ith in supplied fuel (in atomic percent), S isthe supply rate of total fuel.

The neutron flux, /, in the fuel is determined from thefollowing equation:

P ¼ CX

i2HM

nirf ;i/ ð8Þ

where P is the average power density of fuel pellet, C is theenergy released per fission (200 MeV).

The equilibrium fuel cycle burnup equation is solved asbelow. First of all we solve Eq. (3) for HM only giving theinitial guess values for the supply rate of total fuel, S, and

the fraction of ith nuclide in supplied fuel, ji. Next, we cal-culate the number density of fission products employingEqs. (4) and (5), and the calculated number density ofHM into Eq. (3). This procedure is repeated until the totalnumber density of HM and FP satisfy the condition whichgiven by Eq. (6). Finally, the flux neutron in the fuel pelletis determined by normalization of number density of HMwith the average fuel pellet power density, P. These all pro-cedures are repeated so that the whole calculation resultssatisfy the two conditions given by Eqs. (6) and (8).

The equilibrium calculation is preformed to determinethe flux level. In this calculation, 1238 fission productsand 129 heavy nuclides are employed. This equilibriumburn-up calculation is coupled with the PIJ cell calculationmodule of SRAC 2002 in order to get the neutron spectrumand 107 group microscopic cross-sections which are con-densed into one-group microscopic cross-section of eachinvestigated case as shown in Fig. 2. We have called thiscoupling calculation an equilibrium cell iterative calcula-tion system (ECICS). In the cell, 26 heavy metals and 66fission products and 1 pseudo FP are employed.

3.2. Criticality

Eq. (1) can be written in a matrix form as follows:

Mn ¼ s; ð9Þwhere all coefficients in Eq. (1) compose the elements of M

matrix, and n and s are the vectors of ni and si, respectively.To evaluate the criticality of the system, h, defined by

h ¼P

i2HMvrf ;iniPj2HM;FPra;jnj

¼ ðvrf ; nÞðra; nÞ

ð10Þ

The h value is commonly used in the equilibrium stateanalyses (Waris and Sekimoto, 2001b); where v representsthe number of neutrons produced per one fission reaction.The h value is a ratio of the number of produced neutronsby fission and the number of absorbed neutrons in the sys-tem. In importance vector representation, Eq. (9) can bewritten as the following equation (Sekimoto and Nemoto,1997),

h ¼ ðf ; sÞða; sÞ ð11Þ

where importance vector f and a are calculated from thefollowing adjoint equations:

Mtf ¼ /mrf ð12ÞMta ¼ /mra ð13Þwhere Mt is the adjoint matrix of M. The vectors f and aare called fission neutron importance and absorbed neu-tron importance, respectively. The fission neutron impor-tance represents the number of neutrons produced fromfission of one nucleus of the studied nuclide and its familymembers (reaction products) during its existence in thereactor. While the absorbed neutron importance representsthe number of neutrons absorbed by one nucleus of the

Ntot=total Number density of nuclides in fuel pellet(93% of theoretical density of UO2)

THM = Total Number Density of HMs (cm-3) TFP = Total Number Density of FPs (cm-3) Si = Total supply rate (cm-3S-1) P = Average power density (Wcm-3) Γ = Energy released per fission (200 MeV)

ix,σ = Cross-section for the i-th HM of reaction x

jx,σ = Cross-section for the i-th FP of reaction x

gix ,,σ = Multi-group xs for the i-th HM of reaction x

gjx ,,σ = Multi-group xs for the i-th FP of reaction x

gφ = Multi-group neutron spectrum

START

S0, Ntot

Equilibrium Calculation for HM

HMi ∈ : 0=dt

dni And THMni

i =ΣEquilibrium Calculation for FP

FPj ∈ : 0=dt

dn j And TFPnj

j =Σ

TDEN=THM+TFP

TDEN

NSS

totii *1 =+

Normalized by Power Density

ΣΓ σ=HMi

ifinP ,

≤ ε– totNTDEN

CellCalculation

Collapse ofMulti-groupsCross-section

Inner Iteration

in jn

gφ

gix ,,σ gjx ,,σ

ix,σ

jx,σ

Outer Iteration

Fig. 2. Flowcharts of ECICS.


studied nuclide and its family members during its presencein the reactor (Sekimoto and Nemoto, 2000). These fissionneutron importance and absorbed neutron importance areused for other calculations and investigations.

By using this couple equilibrium burn-up calculationand cell calculation, we evaluated the relationship betweenh, which is defined by Eq. (5) and the infinite multiplicationfactor, k, which is defined by the following equation

k ¼P

j2HM;FPvrf;jnj/fpPj2HM;FPra;jnj/fpþ

Pk2claddingra;knk/cl þ

Pl2coolantra;lnl/co

ð14Þ

where /y is neutron flux, subscript y denotes the fuel cellregion (fp, cl, and co correspond to fuel pellet, cladding,and coolant, respectively.) and represents the number ofneutrons produced in each fission reaction. The actual cal-culation for k was performed by SRAC 2002 and h by theequilibrium burn-up code. We use nuclear data libraryfrom the JENDL 3.2 (Okumura et al., 2002).

3.3. Uranium enrichment

The uranium enrichment calculation is performed itera-tively until the one-group cross-sections and nuclide densi-ties are converged. The control parameter for this iterativecalculation is a, the ratio of h to k defined as the followingequation:

a ¼ hk¼ 1þ

Pk2claddingra;knk/cl þ

Pl2coolantra;lnl/coP

j2HM;FPra;jnj/fp

ð15Þ

In order to judge the criticality of the system, the neu-tron leakage from the system should be evaluated. For cur-rent PWR, the neutron leakage is estimated about 2% ofproduced neutrons. The following condition is employedfor the criticality condition in the present paper.

k ¼ 1:02 � kc ð16ÞFrom this coupling calculation procedure we evaluate

the value of the infinite multiplication factor, k. If k is equalto kc, then the calculation is finished and we choose the ini-tial enrichment input as the required uranium enrichmentfor the criticality of the investigated case. Finally, the ura-nium enrichment for criticality is determined by solving thefollowing three linear equations:

ðf24 � 1:02a24Þj24 þ ðf25 � 1:02a25Þj25

þ ðf28 � 1:02a28Þj28 ¼ 0; ð17Þj24 þ j25 þ j28 ¼ 100; ð18Þ100j24 � 0:09937j25 ¼ �0:1925; ð19Þ

where fx is a fission neutron importance, ax is an absorp-tion neutron importance and kx is an atomic percent ofuranium isotopes (234U, 235U and 238U) in the suppliedfuel. These calculations are repeated until the value of theinfinite multiplication factor, k is equal to kc.

3.4. Conversion ratio and breeding

In particular, 238U can be transmuted into 239Pu, while232Th can be transmuted into 233U. Hence if we load the

10

15

20

25

30

35D2 O Coolant

0.10.51234

Rel

ativ

e F

lux

per

Un

it L

eth

arg

y [#

.cm

-2s-1

]

MFR

No Thermal

Peak10

15

20

25

30

35O Coolant

0.10.51234

MFR

No Thermal

Peak


core of a reactor with such fertile material, we can use theextra neutrons to produce a new fissile fuel material. Thisprocess is frequently referred to as conversion, and nuclearreactors whose principal job is to produce 239Pu or 233U areknown as converter reactors (Duderstadt and Hamilton,1976). This is the essential idea behind the concept of abreeder reactor. To discuss this concept in more detail, itis useful to define the conversion ratio as

CR ¼ Average rate of fissile atom production

Average rate of fissile atom consumptionð20Þ

This quantity is also referred to as the breeding ratio(BR) if it is greater than unity. Consuming N atoms of fuelduring reactor operation will yield CR · N atoms of thenew fissile isotopes. The conversion ratio here is calculatedfrom the following equation:

CR ¼ Capture rate of ð238Uþ 240PuÞAbsorption rate of ð235Uþ 239Puþ 241PuÞ ð21Þ

0

5

0.001 0.1 10 1000 105 107

Neutron Energy [eV]

0

5

0.001 0.1 10 1000 105 107

Neutron Energy

Fig. 4. Relative neutron spectra per unit lethargy of heavy water coolantfor Case 1.

66

4. Results and discussion

4.1. Neutron spectra

The obtained neutron spectra are shown in Figs. 3–5.Figs. 3 and 4 describe the effect of MFR to the neutronspectra for Case 1. The thermal peak always appears forlight water coolant as shown in Fig. 3. However, atMFR = 0.1 there is still a thermal neutron component(with neutron energy <4 eV), even though there is almost

0

5

10

15

20

25

30

35

0.001 0.1 10 1000 105 107

O Coolant0.10.51234

Rel

ativ

e F

lux

per

Un

it L

eth

arg

y [#

.cm

-2.s

-1]

Neutron Energy [eV]

MFR

ThermalPeak

0

5

10

15

20

25

30

35

0.001 0.1 10 1000 105 107

H2 O Coolant0.10.51234

MFR

ThermalPeak

Fig. 3. Relative neutron spectra per unit lethargy of light water coolantfor Case 1.

0

1

2

3

4

5

0.001 0.1 10 1000 105 107

Case1Case2Case3Case4


Neutron Energy [eV]

D2O

0

1

2

3

4

5

0.001 0.1 10 1000 105 107



Neutron Energy

H2O

Rel

ativ

e F

lux

per

Un

it L

eth

arg

y [#

.cm

-2s-1

]

Fig. 5. Relative neutron spectra per unit lethargy of light water and heavywater coolants for different fuel cycles at MFR = 2.

no peak in that region. As expected, the neutron spectrabecome harder with decreasing MFR for all cases and forboth water coolants. In general, there is no thermal peak

Fig. 6. Number densities in the core of light water coolant for Case 1.

Fig. 7. Number densities in the core of heavy water coolant for Case 1.


for heavy water coolant along the MFR (0.1 6MFR 6 4),and its spectrum is harder than light water coolant asshown in Fig. 4. The neutron spectra trends for other casesshow the same profile as Case 1. Fig. 5 shows the relativeneutron spectra per unit lethargy of both coolants for dif-ferent fuel cycle cases at MFR = 2. This figure explains theHM confining effect to the neutron spectra for both cool-ants. Each fuel cycle has its own neutron spectrum, sinceneutron spectrum depends sensitively on its operating con-ditions (e.g., fuel loading, isotopic composition, tempera-ture, and coolant conditions) (Duderstadt and Hamilton,1976). The neutron spectrum becomes harder with increas-ing number of confined nuclides in the reactor core(Johansson, 1988). This change is attributed to the increas-ing number density of plutonium, especially fissile pluto-nium (239Pu, and 241Pu) in the recycled nuclides. Inthermal energy region microscopic absorption cross-sec-tion of fissile plutonium and trans-plutonium with an oddnumber of neutron like 242Am, 242mAm, 244Am, 243Cm,245Cm have absorption cross-section larger than 235U,therefore by recycling Pu and trans-plutonium of lightwater coolant, the flux depression occurs, and the neutronspectrum becomes harder (Waris and Sekimoto, 2001b).The neutron spectrum becomes harder gradually due tothe significant increase of the Pu isotope’s number densityin the core as shown in Cases 1–3. However, the effect ofincreasing number density of fissile plutonium to the fluxdepression in the heavy water coolant case is very smallalong the MFR (0.1 6MFR 6 4).

4.2. Nuclide densities

The compositions of nuclide densities in the core areshown in Figs. 6 and 7. These Figs. 6 and 7 contain selectedimportant nuclides of Case 1 for light water coolant andheavy water coolant, respectively, in equilibrium states.In case of light water coolant as shown in Fig. 6, the num-ber density of fissile materials decreases when the MFR isincreased, however the number density of 241Pu has a max-imum value. For fertile materials, the number density 238Uincreases and the number density 240Pu decreases when theMFR is increased. Number density of trans-plutonium hasa maximum value with increasing the MFR. All fertilematerial as well as fissile 239Pu decreases when the MFRis increased for heavy water coolant. However, for otherfissile materials as well as trans-plutonium, it increaseswhen the MFR is increased. In general, the trans-pluto-nium (243Am and 244Cm) number densities of the heavywater coolant case increase with MFR and its number den-sities of heavy water coolant case are smaller than lightwater coolant. Fig. 6 shows also that light water coolanthas better sensitivity to a change in the nuclide densitiescaused by a change in the MFR. The number density of235U for heavy water coolant decreases when the MFR isincreased; this is the opposite trend to the light water cool-ant. Those phenomena related to the capability of lightwater coolant to thermalize the neutron in the core, there-

fore the 235U nuclide density as fissile material decreaseswhen the MFR is increased. For heavy water coolant, itis not enough to thermalize the core, along the MFR(0.1 6MFR 6 4). In order to keep reactor critical, morefissile material of 235U is needed which means fissile 235U

Fig. 9. Number densities in the core of heavy water coolant for differentfuel cycle cases at MFR = 2.


increases when the MFR is increased. For the plutoniumnumber density change which is related to the MFRchange, the light water coolant has better ability todecrease the plutonium than the heavy water coolant.

Figs. 8 and 9 explain the selected number densities ofCase 1–Case 4 at MFR = 2 in equilibrium states. On theother hand, its show the effect of confined HM to the mate-rial number densities in the core. These figures show thattrans-neptunium number densities increase with increasingnumber of confined HM for both coolants. Number densi-ties of 243Am and 244Cm for heavy water coolant are lowerthan light water coolant for all fuel cycle cases. The numberdensity of plutonium for heavy water coolant is higher thanlight water coolant because of harder spectrum of heavywater. The plutonium discharging cases (Cases 1 and 2)have similar patterns in the actinides number density, butthe number density of trans-neptunium for Case 2 is higherthan Case 1. The plutonium recycling cases (Cases 3 and 4)have the same trends in the actinides number density; how-ever the number density of trans-neptunium for Case 4 islarger than that of Case 3.

4.3. One group microscopic cross-sections

The obtained results of one group microscopic fissionand absorption cross-sections are tabulated in Tables 2and 3. The one-group microscopic fission and absorptioncross-section of fissile materials increase with increasingthe MFR for light water coolant as shown in Table 2.

Fig. 8. Number densities in the core of light water coolant for differentfuel cycle cases at MFR = 2.

The fertile materials such as 238U and 240Pu have a peakof one group microscopic fission cross-section along theMFR, where the peak position is located at MFR valuesof around 2.0 and 1.0, respectively. In the heavy watercoolant as shown in Table 3, its one group microscopic fis-sion and absorption cross-section of fissile and fertile mate-rials increase with increasing MFR except 240Pu. The onegroup microscopic fission cross-section of 240Pu has a peakwhich is located at MFR value of around 2.0.

In general, the values of one group microscopic fissionand absorption cross-sections for light water coolant havehigher value than heavy water coolant. This is because thelight water coolant is more effective to thermalize the corethan heavy water coolant along the MFR (0.1 6MFR 6 4).

4.4. Plutonium quality

The change of MFR results in the change of the pluto-nium isotopes composition, i.e., a plutonium vector. Figs.10 and 11 demonstrate the plutonium vector for differentMFR of Case 1. The plutonium quality is defined as the fis-sile plutonium percentage. The value of plutonium qualitydecreases monotonically when the MFR is increased. Inshort, the plutonium quality effectively is reduced byincreasing the MFR. This condition occurs because themoderation effect increases when the MFR is increased.The moderation capability is effective to reduce the mainfissile plutonium (239Pu) as shown in Figs. 10 and 11.

Table 2One group microscopic cross-section of fission and absorption for light water coolant in Case 1 [barn]

Cross-section MFR 234U 235U 236U 238U 237Np 238Pu 239Pu 240Pu 241Pu 242Pu 243Am 244Cm

Fission 0.1 0.384 2.96 0.137 0.056 0.401 1.387 2.843 0.439 4.276 0.313 0.251 0.5220.3 0.456 4.707 0.192 0.076 0.484 1.617 5.643 0.517 8.149 0.382 0.333 0.6480.5 0.487 6.586 0.225 0.087 0.522 1.714 10.03 0.552 12.906 0.413 0.378 0.7151 0.508 15.357 0.275 0.098 0.548 1.909 34.139 0.58 36.416 0.436 0.429 0.792 0.481 51.436 0.291 0.099 0.521 2.677 121.23 0.557 129.576 0.416 0.435 0.823 0.448 81.102 0.279 0.095 0.487 3.341 185.98 0.525 203.495 0.39 0.418 0.824 0.425 101.1 0.267 0.092 0.462 3.793 228.22 0.5 252.774 0.371 0.404 0.817

Absorption 0.1 2.035 3.957 1.202 0.419 3.978 2.916 4.174 2.754 5.319 2.749 4.511 2.4740.3 4.999 6.483 2.401 0.574 8.155 4.427 8.799 12.304 10.555 8.928 13.291 6.230.5 7.881 9.041 3.482 0.686 12.205 5.758 15.857 27.853 17.033 14.301 22.219 9.651 14.256 19.915 5.924 0.877 21.981 12.016 53.922 71.968 48.957 22.854 39.621 15.4662 22.39 62.276 7.484 1.075 36.041 41.22 187.97 126.37 174.28 26.299 51.233 17.9493 26.814 96.821 7.352 1.171 43.85 66.147 286.29 149.45 273.287 26.083 53.492 17.6714 29.496 120.08 7.076 1.224 48.609 83.094 350.15 161.17 339.197 25.544 54.056 17.195

Table 3Microscopic cross-section of fission and absorption for heavy water coolant in Case 1 [barn]

Cross-section MFR 234U 235U 236U 238U 237Np 238Pu 239Pu 240Pu 241Pu 242Pu 243Am 244Cm

Fission 0.1 0.304 2.072 0.099 0.043 0.317 1.129 1.882 0.361 2.762 0.247 0.191 0.410.3 0.309 2.506 0.111 0.048 0.325 1.225 2.206 0.373 3.349 0.255 0.206 0.4270.5 0.311 2.881 0.119 0.051 0.328 1.305 2.533 0.379 3.896 0.259 0.215 0.4381 0.314 3.647 0.132 0.055 0.333 1.45 3.326 0.385 5.161 0.263 0.228 0.4562 0.314 4.785 0.148 0.058 0.336 1.607 4.862 0.387 7.478 0.264 0.241 0.4823 0.313 5.728 0.159 0.059 0.337 1.691 6.548 0.386 9.738 0.263 0.25 0.5014 0.311 6.644 0.169 0.06 0.336 1.746 8.565 0.384 12.123 0.261 0.256 0.517

Absorption 0.1 0.907 2.678 0.621 0.346 2.257 1.933 2.517 1.064 3.311 0.825 1.996 1.2190.3 1.206 3.287 0.845 0.408 2.935 2.368 3.146 1.404 4.077 1.06 2.61 1.5460.5 1.518 3.823 1.054 0.458 3.553 2.752 3.757 1.777 4.793 1.345 3.214 1.8871 2.322 4.932 1.526 0.559 4.956 3.525 5.187 3.019 6.464 2.372 4.899 2.9052 3.963 6.606 2.337 0.722 7.489 4.602 7.852 7.867 9.572 5.379 9.151 5.4263 5.625 7.983 3.07 0.858 9.917 5.408 10.686 16.497 12.638 8.945 14.157 8.1084 7.307 9.291 3.773 0.975 12.356 6.119 14.015 28.491 15.893 12.717 19.579 10.731


Generally, reducing the plutonium quality is more effectiveby light water coolant in comparison to heavy water cool-ant when the MFR is increased. The plutonium quality fordifferent fuel cycles are summarized in Figs. 12 and 13. Theresults show that plutonium quality decreases with increas-ing number of recycled HM for both coolant cases. On theother hand, it is worsened by increasing number of recycledHM (Case 1–Case 4). In the case of heavy water coolant, ithas higher plutonium quality than light water coolant forall fuel cycle cases (Cases 1–4).

4.5. Required uranium enrichment and conversion ratio

The obtained required uranium enrichment and conver-sion ratio are shown in Figs. 14 and 15. The requiredenrichment decreases considerably with increasing numberof confined HM in the reactor for the light water coolant.Considering MFR values of 1.0 and above, the requiredenrichment of light water coolant becomes minimum atMFR = 2.0 for all investigated fuel cycles. The minimumenrichment at MFR = 2 can be explained by Table 4.The table shows the macroscopic production rate of Case1 with different MFR for light water coolant. The macro-

scopic production rate for each material is defined as themacroscopic production for that material divided by mac-roscopic absorption of fuel for all materials. This estima-tion is based on the criticality value which corresponds tothe production rate to the absorption rate in the reactorcore. At MFR = 2, the production rate of fissile plutonium(239Pu and 241Pu) gives the highest value. The contributionof fissile plutonium to maintain the criticality condition ofthe reactors becomes considerably effective; therefore pro-duction rate of 235U shows the lowest value. Because of this235U enrichment reaches its lowest level when MFR is 2.

In dealing with the tight lattice, i.e., MFR values of lessthan 1.0, the investigated fuel cycles can be separated intoplutonium discharging cases (Cases 1 and 2) and plutoniumrecycling cases (Cases 3 and 4). The plutonium dischargingcases means all or half of plutonium is discharged or notrecycled. The required uranium enrichment of the pluto-nium discharging cases (Cases 1 and 2) increase withdecreasing MFR for light water coolant in the range of0.3 < MFR < 1.0. However, in the range of MFR < 0.3,it decreases with decreasing MFR. Therefore, the maxi-mum enrichment is obtained at MFR = 0.3 for dischargingcases. The production rate of fissile plutonium (239Pu and

0

20

40

60

80

100

0.1 0.5 1 2 3 4

Pu238

Pu239

Pu240

Pu241

Pu242

Plu

ton

ium

Vec

tor

[%]

Moderator to Fuel Ratio [ - ]

Fig. 11. Plutonium vector of heavy water coolant for Case 1.

0

20

40

60

80

100

0.1 0.5 1 2 3 4

Pu238Pu239Pu240Pu241Pu242

Plu

ton

ium

Vec

tor

[%]


Fig. 10. Plutonium vector of light water coolant for Case 1.

0

20

40

60

80

100

Pu-238Pu-239Pu-240Pu-241Pu-242

Plu

ton

ium

Vec

tor

[%]

Case 1 Case 2 Case 3 Case 4

Fig. 12. Plutonium vector of light water coolant for different fuel cycles atMFR = 2.

0

20

40

60

80

100

Pu-238Pu-239Pu-240Pu-241Pu-242

Plu

ton

ium

Vec

tor

[ %

]

Case 1 Case 2 Case 3 Case 4

Fig. 13. Plutonium vector of heavy water coolant for different fuel cyclesat MFR = 2.


241Pu) gives the lowest value at MFR = 0.3. The contribu-tion of fissile plutonium is not effective to maintain the crit-icality condition of the reactors; therefore production rateof 235U becomes the highest value as shown in Table 4.On the other hand, the 235U enrichment requires highest

value at MFR = 0.3. The required enrichment alsodecreases significantly as MFR decreases in the range ofMFR < 1.0 for the plutonium recycling cases (Cases 3

0

2

4

6

8

10

12

14

16

0.4

0.6

0.8

1

0.2

00 0.5 1 1.5 2 2.5 3 3.5 4

H2O Coolant

Case 1Case 2Case 3Case 4


En

rich

men

t [%

]

Co

nversio

n R

atio [ - ]


Enrichment

Conversion RatioBreeding

. .5



Fig. 14. Enrichment (%) and conversion ratio for light water coolant.

0

2

4

6

8

10

12

14

16

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2 2.5 3 3.5 4



En

rich

men

t [

% ]

Co

nversio

n R

atio [ - ]


Enrichment

Conversion ratio

D2O Coolant



Breeding

Fig. 15. Enrichment (%) and conversion ratio for heavy water coolant.

Table 4Macroscopic production rate of nuclides for light water coolant in Case 1(–)

Relative macroscopic production

Nuclide Moderator to fuel ratio (MFR), in Case 1

0.1 0.3 0.5 1 2 3 4

235U 0.6344 0.6678 0.6491 0.5460 0.5236 0.6076 0.7071239Pu 0.2915 0.2854 0.3154 0.4202 0.4886 0.4770 0.4508241Pu 0.0094 0.0256 0.0422 0.0898 0.1321 0.1303 0.1205238U 0.1812 0.1571 0.1404 0.1158 0.0879 0.0718 0.0617240Pu 0.0061 0.0036 0.0025 0.0016 0.0010 0.0008 0.0006

Table 5Macroscopic production rate of nuclides at MFR = 2 for light watercoolant (–)


Nuclide Fuel cycle cases, at MFR = 2

1 2 3 4

235U 0.5236 0.4687 0.3959 0.3968239Pu 0.4886 0.5089 0.5277 0.5274241Pu 0.1321 0.1630 0.2158 0.2157238U 0.0879 0.0878 0.0878 0.0878240Pu 0.0010 0.0013 0.0021 0.0021

Table 6Macroscopic production rate of nuclides for heavy water coolant in Case 1(–)


Nuclide Moderator to fuel ratio (MFR), in Case 1

0.1 0.3 0.5 1 2 3 4

235U 0.6071 0.6771 0.7192 0.7784 0.8271 0.8380 0.8282239Pu 0.3080 0.2687 0.2492 0.2262 0.2123 0.2168 0.2334241Pu 0.0033 0.0041 0.0048 0.0069 0.0125 0.0189 0.0260238U 0.1793 0.1558 0.1382 0.1086 0.0772 0.0609 0.0511240Pu 0.0061 0.0053 0.0046 0.0033 0.0019 0.0012 0.0009


and 4). The depleted uranium is more than enough forloaded fuel at MFR = 0.4 and at MFR = 0.3 for Case 3and Case 4, respectively. This is why the author did notcontinue to evaluate at MFR < 0.3 and at MFR < 0.4 forplutonium recycling cases.

In case of heavy water coolant in the MFR range(0.1 6MFR 6 4.0,) the required uranium enrichmentincreases as the MFR is increased and it reaches the max-imum value at MFR = 3 for plutonium discharging cases.As shown in Table 6, the relative macroscopic productionrate of 235U shows the highest value at MFR = 3.0. Forplutonium recycling cases, the required enrichmentincreases when the MFR is increased, and it’s minimumat MFR = 0.8 and at MFR = 1.2 for Case 3 and Case 4.The depleted uranium is more than enough for loaded fuel.This is the reason why in case of heavy water coolant, theinvestigation is not extended to MFR < 0.8 and toMFR < 1.2 for recycled HM cases.

The average value (on the neutron spectrum) of g of239Pu is higher than that of 235U. Therefore, 239Pu is a bet-ter fissile isotope than 235U for tight-lattice PWR systems(Ronen and Leibson, 1988). This fact may explain the pat-tern of the required uranium enrichment as a function ofMFR and the fuel cycle for MFR < 1.0. Therefore, therequired enrichment of the light water coolant decreases

Fig. 16. Feasible area of breeding for light water and heavy watercoolants.


with decreasing MFR, at MFR < 0.3 (Cases 1 and 2) andMFR < 1.0 (Cases 3 and 4). In case of heavy water coolant,the required uranium enrichment increases with increasingMFR for all fuel cycle cases, except for plutonium dis-charging cases (Cases 1 and 2) at MFR > 3, where itdecreases. Considering the effect of increasing number ofrecycled HM, it is considerably effective to reduce the ura-nium utilization. As shown in Figs. 14 and 15, the requireduranium enrichment decreases when the number of recy-cled HM is increased. It can be explained by Tables 5and 7 for both coolants that relative macroscopic produc-tion rate of 235U decreases and simultaneously, the relativemacroscopic production rate of fissile plutonium increasesas the number of recycled HM increases. By increasingnumber of recycled HM, the contribution of fissile pluto-nium is more effective to maintain the criticality condition.Based on the contribution of fissile plutonium, the requiredenrichment of 235U decreases significantly especially atlower MFR.

As expected, for both coolants, the conversion ratio(CR) increases as the MFR decreases, though there is asmall negligible local optimum at MFR = 1.0 of Case 1for light water coolant. Therefore, in order to obtain theCR value higher than unity, the MFR should be reduced.The value of CR for heavy water coolant is higher thanlight water coolant. Simultaneously, the CR also increaseswith increasing number of recycled HM in the reactor.

4.6. Feasible area of breeding

The breeding condition can be achieved when the CR ishigher than unity. The light water coolant shows the feasi-bility of breeding for plutonium recycling cases. Fig. 14shows its feasibility at MFR 6 0.3 and at MFR 6 0.4 forCase 3 and Case 4, respectively. On the other hand, thebreeding can be achieved for light water coolant by reduc-ing the MFR using recycled HM especially plutonium anddepleted uranium as fuel. In case of the heavy water cool-ant, the CR becomes more than unity for all fuel cases(Cases 1–4).

The feasibility of breeding is shown in Fig. 15 for heavywater coolant which can be seen at MFR 6 0.15, atMFR 6 0.2, at MFR 6 0.8 and at MFR 6 1.2 of Cases1–4, respectively. Because of the CR value for heavy water

Table 7Macroscopic production rate of nuclides at MFR = 2 for heavy watercoolant (–)


Nuclide Fuel cycle cases, at MFR = 2

1 2 3 4

235U 0.8271 0.7101 0.2406 0.1643239Pu 0.2123 0.3064 0.5760 0.6039241Pu 0.0125 0.0301 0.1953 0.2129238U 0.0772 0.0776 0.0742 0.0768240Pu 0.0019 0.0048 0.0429 0.0490

coolant is higher than light water coolant for all fuel cycles,it seems that the feasibility of breeding for heavy water ishigher than light water coolant. Fig. 16 shows the feasiblearea of breeding for both coolants. The x-axis denotes themoderator to fuel ratio (MFR) and y-axis shows the fuelcycle cases which can be defined as increasing the numberof recycled HM (Cases 1–4). The line shows the maximumMFR of each fuel cycle case for getting breeding condition.The graph shows the maximum MFR increases as the num-ber of recycled HM increases for both coolants. The max-imum MFR for breeding for light water coolant is lowerthan heavy water coolant. On the other hand, the heavywater coolant has wider feasible area of breeding thanthe light water coolant. Simultaneously, wider feasible areaof breeding can be obtained by increasing the number ofrecycled HM.

5. Conclusion

The effect of different moderator to fuel ratios (MFR)and different fuel cycle cases of light water and heavywater cooled reactor in equilibrium states have beenexamined. The key properties such as neutron spectra,plutonium quality, and required uranium enrichment havebeen studied. The criticality and conversion ratio havebeen investigated in order to show the feasible area ofbreeding. A thermal spectrum peak appears for lightwater coolant and no thermal peak for heavy watercoolant along the MFR (0.1 6MFR 6 4). Because the


spectrum of heavy water coolant is harder than lightwater, the nuclide density of 235U and 239Pu is higherfor heavy water coolant. The production of trans-pluto-nium such as Am and Cm for heavy water coolant aresmaller than light water coolant. The plutonium qualityof heavy water coolant is higher than light water coolantfor all different MFR and fuel cycle cases. By increasingthe MFR and number of recycled HM, the plutoniumquality can be reduced effectively. The heavy water cool-ant requires higher uranium enrichment and gives higherconversion ratio than light water coolant. By increasingthe number of recycled HM, the uranium utilization canbe reduced and the conversion ratio can be increased,effectively. The feasibility of breeding can be obtainedfor light water coolant when HM is recycled with reduc-ing the MFR. Better conversion ratio of heavy watercoolant gives wider feasible area of breeding when lightwater coolant is replaced by heavy water coolant.

Acknowledgements

The authors acknowledge the support given by the Cen-ter of Excellent Innovative Nuclear Energy System (COE-INES) Tokyo Institute of Technology and Dr. A. Waris forhis support, ideas and discussions.

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