analysis of rod-by-rod fp inventory distributions in bwr 8 × 8 uo 2 ...

This article was downloaded by: [Washington State University Libraries ]On: 25 November 2014, At: 01:23Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: MortimerHouse, 37-41 Mortimer Street, London W1T 3JH, UK

Journal of Nuclear Science and TechnologyPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/tnst20

Analysis of Rod-by-Rod FP Inventory Distributionsin BWR 8 × 8 UO2 Assemblies Using Lattice PhysicsMethodToru YAMAMOTO a & Munenari YAMAMOTO ba Japan Nuclear Energy Safety Organization , TOKYU REIT Toranomon Bldg., 3-17-1Toranomon, Minato-ku, Tokyo , 105-0001 , Japanb Global Nuclear Fuel-Japan Co., Ltd. , 2-3-1 Uchikawa, Yokosuka-shi, Kanagawa ,239-0836 , JapanPublished online: 05 Jan 2012.

To cite this article: Toru YAMAMOTO & Munenari YAMAMOTO (2008) Analysis of Rod-by-Rod FP Inventory Distributions inBWR 8 × 8 UO2 Assemblies Using Lattice Physics Method, Journal of Nuclear Science and Technology, 45:1, 25-35, DOI:10.1080/18811248.2008.9711411

To link to this article: http://dx.doi.org/10.1080/18811248.2008.9711411

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) containedin the publications on our platform. However, Taylor & Francis, our agents, and our licensors make norepresentations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose ofthe Content. Any opinions and views expressed in this publication are the opinions and views of the authors,and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be reliedupon and should be independently verified with primary sources of information. Taylor and Francis shallnot be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and otherliabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to orarising out of the use of the Content.

This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in anyform to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

http://www.tandfonline.com/loi/tnst20

http://www.tandfonline.com/action/showCitFormats?doi=10.1080/18811248.2008.9711411

http://dx.doi.org/10.1080/18811248.2008.9711411

http://www.tandfonline.com/page/terms-and-conditions

http://www.tandfonline.com/page/terms-and-conditions

Analysis of Rod-by-Rod FP Inventory Distributions

in BWR 8� 8 UO2 Assemblies Using Lattice Physics Method

Toru YAMAMOTO1;� and Munenari YAMAMOTO2

1Japan Nuclear Energy Safety Organization, TOKYU REIT Toranomon Bldg.,3-17-1 Toranomon, Minato-ku, Tokyo 105-0001, Japan

2Global Nuclear Fuel-Japan Co., Ltd., 2-3-1 Uchikawa, Yokosuka-shi, Kanagawa 239-0836, Japan

(Received July 31, 2007 and accepted in revised form October 17, 2007)

Fuel rod gamma-ray spectrometry was performed for one-, two-, three-, and five-cycle irradiated BWR8� 8-4 fuel assembles, and relative rod-by-rod FP inventory distributions of 137Cs, 134Cs, 106Ru, and 95Zrwere obtained for the upper and lower axial height nodes of the assemblies. The measured data was cor-rected for the difference in gamma-ray transmission between UO2 and Gd2O3-UO2 rods. These distribu-tions were compared with those calculated using the collision probability method, Pij, of the SRAC codesystem with an infinite lattice model of the fuel assembly. The calculated results generally well reproducethe measured distributions, and the accuracy of the analysis method of the present study was evaluated tobe 1 to 2% for the inventory distributions of 137Cs, 2 to 3% for 134Cs, 2 to 3% for 106Ru, and 2 to 3% for95Zr, which represent the distributions of the burn-up, the thermal flux multiplied by the burn-up, thebuildup of 239Pu, and the fission rate at the end of the fuel discharge cycle, respectively. One of the notableresults of the analysis of this study is that the FP inventories for the Gd2O3-UO2 rods were underestimatedin most cases.

KEYWORDS: rod-by-rod FP inventory distribution, 137Cs, 134Cs, 106Ru, 95Zr, gamma-ray spectrom-etry, BWR, 8� 8-4 fuel, collision probability method, SRAC code system

I. Introduction

The Nuclear Safety Commission of Japan suggests in thereport ‘‘On fully loading of MOX fuel in the Advanced LightWater Reactors’’1) that current safety design and evaluationmethods for light water reactors should be improved by sys-tematic studies: (i) validation of burn-up calculation usingfuel postirradiation data, (ii) validation of nuclear design cal-culation by criticality experiments, and (iii) validation of nu-clear design calculation for burned fuel. Responding to thissuggestion, the Japan Nuclear Energy Safety Organization(JNES) has been working on and are planning research pro-jects, such as (a) the validation of burn-up calculation usingthe fuel postirradiation data of irradiated BWR 8� 8 and9� 9 UO2 fuels2) and, in the future, irradiated MOX fuelin one-third MOX-loading cores and a fully MOX-loadingcore of domestic plants, (b) the validation of nuclear designcalculation through BWR MOX core physics experiments,3)

and (c) the validation of nuclear design calculation thoughburned fuel critical experiments.4) The present study is partof the above (a) project and specifically related to the irradi-ated BWR 8� 8-4 UO2 fuel.

The rod-by-rod power distribution within fuel assembliesis one of essential parameters in core design and analysis es-pecially related to thermal margins such as maximum linear

heat generation and minimum critical power ratio for BWRcores. Verification work for these parameters has commonlybeen using measured data of power distributions of zero-power core physics experiments with fresh mock-up fuel as-semblies.5–7) However, studies using data of irradiated fuelassemblies are sparse because such measurements usuallyhave to be done in postirradiation facilities. Misu et al.8) re-ported experimental data of rod-by-rod distributions of 140Barepresenting fission rate distributions on irradiated BWR9� 9-1 UO2 and MOX assemblies using gamma scanningin the irradiated fuel storage pool of the GundremmingenBWR. Yamamoto et al.2) presented a study of rod-by-roddistributions of 137Cs, 134Cs, 106Ru, and 95Zr of irradiated8� 8-4 UO2 assemblies of unit 2 of Fukushima power sta-tion 2 obtained by rod-by-rod gamma spectrometry in a pos-tirradiation facility. The latter work showed a systematictrend for Gd2O3-UO2 rods that lattice calculations underes-timate relative values of those FP inventories, and furtherstudy was necessary to inquire the results by evaluatingthe effect of a difference in gamma-ray transmission throughfuel pellets.

First, the present paper gives a description about the meas-ured data of the rod-by-rod FP inventory distributions cor-rected by the difference in gamma-ray transmission betweenUO2 and Gd2O3-UO2 rods; then the comparisons of the datawith calculated results obtained by lattice analysis code anddiscussions are presented.

�Atomic Energy Society of Japan

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

Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol. 45, No. 1, p. 25–35 (2008)

25

ARTICLE

Dow

nloa

ded

by [

Was

hing

ton

Stat

e U

nive

rsity

Lib

rari

es ]

at 0

1:23

25

Nov

embe

r 20

14

II. Measured Data of Rod-by-Rod FP InventoryDistributions

1. BWR 8� 8-4 Fuel AssembliesThe major characteristics of the four BWR 8� 8-4

fuel assemblies under these measurements are shown inTable 1.9) Figure 110) shows an enrichment distributionamong the fuel rods, which has a one-eighth symmetry de-sign. Table 210) outlines the major parameters of unit 2 ofFukushima power station 2 (2F2) of Tokyo Electric PowerCompany (TEPCO) where the assemblies were irradiatedand discharged after one, two, three, and five cycles in1989 to 1997. The data of assembly average burn-ups and

other irradiation parameters of the four assemblies are shownin Table 3.9)

2. Gamma SpectrometryAs part of nondestructive measurements of fuel rods in a

postirradiation test facility, axial gamma spectrometry wasperformed after about one year from each end of the dis-charge cycle using a Ge(int) detector attached by a slit-typecollimator with a scanning speed of 0.5mm/s and the datawas averaged into 24 axial spans (nodes) with a 154.4mmlength.9) The measured gamma-rays are 137Cs-Ba (661.7keV, T1=2 ¼ 30:07 y), 134Cs-Ba (604.7 keV, T1=2 ¼ 2:062y), 106Ru-Rh (511.9 keV, T1=2 ¼ 373:59 d), and 95Zr-Nb(724.2 keV, T1=2 ¼ 64:02 d). The number of fuel rods is 16for the assemblies 2F2D1, 2F2D2, and 2F2D3, and 18 for2F2D8. Figure 2 shows the locations of measured fuel rodsin the assemblies. With necessary correction about measure-ment periods and decays, the intensities of those specificgamma-rays were normalized to obtain the rod-by-rod rela-tive intensity distributions within the fuel assembly. The rel-ative intensity of the gamma-rays is proportional to the rel-

Table 1 Major characteristics of the BWR 8� 8-4 fuel assem-blies9)

1. Fuel assemblyLattice 8� 8

Number of fuel rods 60Average enrichment 3.0wt%

2. Fuel rodOut diameter 12.3mmThickness of cladding 0.86mmCladding material Zry-2 (Zr lining)Pellet diameter 10.4mmPellet-cladding gap 0.20mmPellet density 97%TDHe pressure 0.5MPa

3. Water rodNumber of water rod 1 (Occupying four rods)Material Zry-2

A B C D E F G H1 4 3 3 3 3 4 52 2 G 2 2 G 2 43 G 1 4 4 1 G 34 2 4 45 2 4 4

22

33

6 G 1 4 4 1 G 37 2 G 2 2 G 2 48

54333345 4 3 3 3 3 4 5

1 to 5: order of enrichment (higher to lower)W: water rod

W

Fig. 1 Enrichment distribution among fuel rods of BWR 8� 8-4fuel assemblies10)

Table 2 Outline of unit 2 of Fukushima power station 2 (2F2)10)

Reactor thermal power 3,293MWCore flow 48:3� 103 t/hOutlet coolant temperature 286�CCoreNumber of fuel assemblies 764Effective fuel length 3.71mEquivalent core diameter 4.75m

Table 3 Irradiation histories of the BWR 8� 8-4 fuel assemblies9)

Assembly ID 2F2D1 2F2D2 2F2D3 2F2D8

Burn-up period 1989/1/14 1989/1/14 1989/1/14 1989/1/14–1990/3/8 –1991/8/14 –1992/11/14 –1997/1/30One cycle Two cycles Three cycles Five cycles

Assembly average 12.6 24.6 34.6 47.9burn-up (GWd/t)

Fuel rod average 9.6–14.1 21.4–27.1 30.5–38.0 43.2–51.0burn-up (GWd/t)

A B C D E F G H1 M O2 M M3 L M N4 M M M O5 O M M M6 N M L7 M M8 O M

2F2D1and 2F2D2: M and N (16 rods)2F2D3: M and L (16 rods)2F2D8: M and O (18 rods)

Fig. 2 Radial location of measured fuel rods of BWR 8� 8-4 fuelassemblies9)

26 T. YAMAMOTO and M. YAMAMOTO

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

Dow

nloa

ded

by [

Was

hing

ton

Stat

e U

nive

rsity

Lib

rari

es ]

at 0

1:23

25

Nov

embe

r 20

14

ative inventories of 137Cs, 134Cs, 106Ru, and 95Zr. These FPnuclides are directly produced by nuclear fission, except for134Cs, which is produced by absorbing a neutron of 133Cs.The inventories of 137Cs represent the burn-up of the fuelrod because of a long half life, 134Cs burn-up multipliedby thermal neutron flux since 133Cs is stable, 106Ru Pu build-up because it has an approximately ten times larger fissionyield for 239Pu than 235U and 95Zr power in the end of thedischarge cycle because of a shorter half-life.

3. Correction of Gamma-ray Transmission through aPelletAs will be mentioned later, burn-up calculations were per-

formed for two typical axial height nodes representing theupper and lower axial parts of the fuel assembly by usinga lattice physics code in an X-Y two-dimensional geometry.These calculations give the pellet average inventory (atoms/cm3) of the above-mentioned FP nuclides for each fuel rod.The intensity of the specific gamma-ray is proportional to thepellet average inventory of the specific FP nuclides as

I / �NNXi

nðriÞTðriÞVðriÞ: ð1Þ

Here,I is the intensity of the specific gamma-rays from the de-cays of the specific FP nuclide at the gamma-ray detector,�NN is the pellet average inventory of the specific FP,nðriÞ is a normalized relative inventory at a radial positionin the pellet ri, asX

i

nðriÞVðriÞ ¼ 1;

VðriÞ is the volume of the pellet at the radial position ri,TðriÞ is the transmission factor of the specific gamma-rayemitted at the radial position ri to the gamma-ray detector.

In this formulation, the distribution in the FP inventory is as-sumed to depend only on the radial direction. In order to de-rive the pellet average inventory distribution from the specif-ic gamma-ray intensity distribution, the gamma-ray trans-mission factor F ¼

Pi nðriÞTðriÞVðriÞ should be considered.

For this purpose, first nðriÞ and then F were evaluated.The pellet radial inventory distributions nðriÞ of the FP nu-

clides were calculated by using MVP-BURN,11) a continuous

energy Monte Carlo code coupled with a burn-up calculationmodule. The calculation was performed in a two-dimension-al geometry, and material conditions representing the irradi-ated BWR 8� 8-4 UO2 fuel assembly are shown in Table 1.Using the predictor corrector option, the burn-up step was setto be 0.5GWd/t from 0 to 15GWd/t and 5GWd/t after that.At each burn-up step, 50 batches with neutron histories perbatch of 10,000 were calculated and the initial 10 batcheswere excluded from statistical analysis. This makes the stat-istical error of infinite multiplication factors around 0.1%dk.A typical statistical error of the radial inventory distributionis around 0.5% for major FP nuclides. Other conditions areshown in Table 4. Figure 3 shows comparisons of the ob-tained pellet radial inventory distributions of 137Cs, 106Ru,and 95Zr between F6 (UO2) and B3 (Gd2O3-UO2) for anin-channel void fraction of 0% at 0.25GWd/t. Due to a larg-er absorption of thermal neutrons in the peripheral region ofthe Gd2O3-UO2 pellet, the FP inventory is relatively largerin the peripheral region of the pellet than that of the UO2 pel-let. Figure 4 shows comparisons of those distributions at50GWd/t. As the burn-up increases, both of the UO2 andthe Gd2O3-UO2 pellets pile Pu in the peripheral region ofthe pellet and the fission rate increases in the peripheral partof the pellet. This makes a steep increase in the FP invento-ries at the outer parts of the pellets. On the other hand, thedifference in the distribution between the UO2 and Gd2O3-UO2 pellets is smaller than that at 0.25GWd/t.

By using these pellet radial inventory distributions, F wasanalyzed by an analytical method (see Appendix) and thecomparison was made between the values for F6 (UO2)and B3 (Gd2O3-UO2). Table 5 summarizes ðFðB3Þ=FðF6Þ �1Þ � 100. Figure 5 shows an example of a 0% void fraction.The difference of the gamma-ray transmission factor of B3(Gd2O3-UO2) and that of F6 (UO2) is 1 to 3% and changeswith the FP nuclides and the exposures. These trends are re-lated to the above-mentioned difference in pellet radial dis-tributions of the FP inventory and also the difference of thefuel pellet densities between the UO2 and Gd2O3-UO2 rods.The density of B3 (Gd2O3-UO2) is about 2% smaller than F6(UO2) and so the gamma-ray transmission in the pellet of B3(Gd2O3-UO2) is larger than that of F6 (UO2).

The set of values of Table 5 was applied to obtain the rel-ative FP inventory distributions based on the conditions that

Table 4 Calculation of pellet radial inventory distribution of BWR 8� 8-4 UO2 fuel assembly

Rods for radial inventory F6 for representing UO2 rodsdistribution B3 for representing Gd2O3-UO2 rods

Radial region of pellet 10 regions (equal volume) for F6 and B3

FP nuclides 137Cs (661.7 keV)106Ru (511.9 keV)95Zr (724.2 keV)

In-channel void fraction (%) 70% for representing core upper hight0% for representing core lower height

Exposure (GWd/t) 0.25 for beginning of exposure15 for end of one-cycle exposure50 for discharge exposure

Analysis of Rod-by-Rod FP Inventory Distributions in BWR 8� 8 UO2 Assemblies Using Lattice Physics Method 27

VOL. 45, NO. 1, JANUARY 2008

Dow

nloa

ded

by [

Was

hing

ton

Stat

e U

nive

rsity

Lib

rari

es ]

at 0

1:23

25

Nov

embe

r 20

14

(1) the F6 rod and the B3 rod are representing all the UO2

rods and all the Gd2O3-UO2 rods respectively in the assem-bly, (2) the values can be interpolated to the different nodeaverage exposures, and (3) the values of 134Cs (604.7 keV)can be interpolated from the values of 137Cs (661.7 keV)and 106Ru (511.9 keV) because the gamma-ray energy of134Cs is close to those of 137Cs and 106Ru and in between,and the values of ðFðB3Þ=FðF6Þ � 1Þ � 100 change almostlinearly in this small gamma-ray energy range.

4. Rod-by-Rod FP Inventory DistributionsThe gamma-ray measurements were conducted for the

fuel rods in symmetrical two or four positions as shown inFig. 2. In order to reduce the statistical error of the gam-ma-ray counting measurements, the average values of thesymmetrical positions were obtained. The middle rows ofthe rod locations of Tables 6 to 9 show the obtained rod-by-rod relative FP inventory distributions of 137Cs, 134Cs,106Ru, and 95Zr for the assemblies 2F2D1 (one-cycle irradi-ation), 2F2D2 (two-cycle irradiation), 2F2D3 (three-cycle ir-radiation), and 2F2D8 (five-cycle irradiation). The averagevalue of the inventories of all the rod positions is normalizedto 1.0.

The measurement error derived by the counting statisticsof the gamma-ray measurements is 0.5 to 0.6% for 137Csand 134Cs, 0.6 to 1.0% for 106Ru, and 0.7 to 2.1% for 95Zras 1 standard deviation. One of the other possible errorswould be the azimuthal distributions of the FP inventory inthe pellet that depend on the locations of the fuel rods inthe assembly. According to the measurement of another typeof BWR fuel of five-cycle irradiation, the gross gamma-raystrength varies by �2 to 3% from the average values for thefuel rods in the peripheral location of the fuel assembly andby less for the fuel rods inside the fuel assembly. In order toavoid this effect, the gamma-ray measurement system wasadjusted to see the surface of the fuel rod that correspondsto the average gross gamma-ray strength in the azimuthal di-rection. This adjustment could cause a systematic error of atmost 1 to 2% for the relative distribution of the FP inventory.Therefore, the experimental error was evaluated to be 1 to2% for 137Cs, 134Cs, and 106Ru, and 1 to 3% for 95Zr.

The peakings of 137Cs and 95Zr are smaller since enrich-ment distribution design aims at flatter power and then flatterexposure distributions. On the other hand, those of 134Cs and106Ru both have a steep rise toward water gaps and especial-ly fuel channel corners between the assemblies, which is

0.60.81.01.21.41.61.82.02.22.4

0.0 0.2 0.4 0.6 0.8 1.0r/Ro

Nor

mal

ized

Rel

ativ

e V

alue

Cs137/F6

Cs137/B3

0.60.81.01.21.41.61.82.02.22.4

0.0 0.2 0.4 0.6 0.8 1.0r/Ro

Nor

mal

ized

Rel

ativ

e V

alue

Ru106/F6

Ru106/B3

0.60.81.01.21.41.61.82.02.22.4

0.0 0.2 0.4 0.6 0.8 1.0r/Ro

Nor

mal

ized

Rel

ativ

e V

alue

Zr95/F6

Zr95/B3

Fig. 4 Pellet radial FP inventory distributions for in-channel voidfraction of 0% at 50GWd/t

0.60.81.01.21.41.61.82.02.22.4

0.0 0.2 0.4 0.6 0.8 1.0r/Ro

Nor

mal

ized

Rel

ativ

e V

alue

Cs137/F6Cs137/B3

0.60.81.01.21.41.61.82.02.22.4

0.0 0.2 0.4 0.6 0.8 1.0r/Ro

Nor

mal

ized

Rel

ativ

e V

alue

Ru106/F6

Ru106/B3

0.60.81.01.21.41.61.82.02.22.4

0.0 0.2 0.4 0.6 0.8 1.0r/Ro

Nor

mal

ized

Rel

ativ

e V

alue

Zr95/F6Zr95/B3

Fig. 3 Pellet radial FP inventory distributions for in-channel voidfraction of 0% at 0.25GWd/t



Dow

nloa

ded

by [

Was

hing

ton

Stat

e U

nive

rsity

Lib

rari

es ]

at 0

1:23

25

Nov

embe

r 20

14

caused by the effect that thermal and epithermal neutrondensities are larger around the water gaps than inside the as-semblies. These peakings are larger in the upper nodes thanin the lower nodes because the relative difference in waterdensity between the water gaps and the inside of the assem-blies is larger for the upper nodes than for the lower nodesdue to an axial distribution of in-channel void fraction.

III. Calculation Method for Rod-by-Rod FP Inven-tory Distribution

The rod-by-rod distributions of the FP inventories were

calculated with an infinite lattice model of the fuel assemblyin an XY two-dimensional geometry. This analysis is basedon the condition that the assemblies for which the rod-by-rodFP inventories measured were irradiated in the cores withoutbeing significantly influenced by adjacent conditions such asthe fuel assemblies of very different neutron spectra, a con-trol blade, and reflectors. Actually, the three fuel assembliesof one-, two-, and three-cycle irradiations in this study havenot experienced adjoining to the assemblies of largely differ-ent enrichments and the control blade. On the other hand, theassembly, 2F2D8, of the five-cycle irradiation faced the re-flector in one of the four sides in the fifth cycle. Discussionwill be made on this effect later in this paper.

The burn-up calculations were carried out using a collisionprobability module (Pij) of 107 neuron energy groups of theSRAC code system12) for the upper and lower axial nodes ofthe assemblies 2F2D1, 2F2D2, 2F2D3, and 2F2D8. The irra-diation histories of the in-channel void fractions and thepowers of the specific nodes of these fuel assemblies wereprovided by the plant operator and taken into account in anapproximate way explained later in this section.

A burn-up time step is 0.25GWd/t until burnable poison(Gd2O3) is burned out, that is, a node average exposure,15GWd/t, and 1.0GWd/t after this exposure.

Resonance cross sections were obtained by a hyperfine en-ergy group calculation module, PEACO,12) from 961.12 eVto the thermal cutoff energy, 1.86 eV,13) and a nuclear datalibrary, JENDL-3.2,14) was used.

Table 5 Comparison of gamma-ray transmission factors between B3(Gd2O3-UO2 rod) and F6(UO2 rod)

FPGamma-rayEnergy (keV)

In-channel void (%)Node average

exposure (GWd/t)(F(B3)/F(F6)-1) � 100

137Cs 661.7 0 0.25 2.8

15 2.3

50 1.5

70 0.25 2.4

15 2.2

50 1.5

106Ru 511.9 0 0.25 3.2

15 2.8

50 1.8

70 0.25 2.9

15 2.7

50 1.7

95Zr 724.2 0 0.25 2.5

15 1.2

50 1.3

70 0.25 2.2

15 1.3

50 1.2

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 10 20 30 40 50 60Node average burn–up(GWd/t)

(F(B

3)/F

(F6)

–1)x

100

Cs137(0%V)Ru106(0%V)Zr95(0%V)

Fig. 5 Comparison of gamma-ray transmission factor betweenB3(Gd2O3-UO2 rod) and F6(UO2 rod) for in-channel void frac-tion of 0%



Dow

nloa

ded

by [

Was

hing

ton

Stat

e U

nive

rsity

Lib

rari

es ]

at 0

1:23

25

Nov

embe

r 20

14

A geometrical calculation option, IGT ¼ 16, was selectedin the Pij calculations. This option is dedicated to light waterfuel assemblies characterized by a square pitch lattice withpin rods. It also permits placements of the pin rods on anygrid point of an x-y division of a rectangular lattice, which

allow us to divide a moderator region of a pin rod cell intofour regions, and every pin rod has its own annular subdivi-sions. A geometrical model and burn-up region (M-region)numbers of the SRAC-Pij calculations are shown inFigure 6. Geometrical dimensions and atomic number den-

Table 6 Comparison between measured rod-by-rod FP inventory distributions and calculated ones for 2F2D1 (one-cycle irradiation)

Node 18137Cs 134Cs 106Ru 95Zr

A CB D A CB DA CB DA CB D

3

4

1

2

W

1.281.280.11.241.240.3

1.131.11 W1.5

1.061.07

-0.40.540.58

-4.20.920.93

-0.7

0.970.961.30.860.842.0

1.401.41

-1.71.191.19

-0.6

1.061.024.0

0.961.01

-4.70.720.74

-2.10.870.89

-1.6

0.880.852.70.930.893.9

0.950.950.01.051.050.0

1.051.014.5

1.091.080.70.880.94

-5.51.000.990.5

1.101.090.60.880.88

-0.6W W

Node 5

1

2

3

4

Top: Calculated valuesMiddle: Measured valuesBottom: (Calculated - Measured)/Measured 100

1.061.050.51.121.13

-1.2

1.101.11

-1.30.680.73

-4.80.990.990.7

1.071.042.10.890.890.0

1.091.054.0

1.041.040.01.151.141.5

1.161.14 W2.0

0.950.940.90.700.78

-8.20.890.90

-0.4

1.151.123.00.960.951.2

1.241.24

-0.11.271.242.2

1.211.22 W

-0.8

0.910.93

-1.80.520.58

-6.20.840.830.8

1.051.023.20.960.932.8

1.301.31

-1.11.161.151.8

1.081.05 W2.6

0.950.931.90.720.77

-4.40.890.90

-1.1

0.930.920.60.970.97

-0.3

0.910.93

-2.41.061.07

-0.9

1.101.09 W0.8

0.950.931.60.970.98

-0.60.890.89

-0.1

1.191.154.20.930.95

-2.5

Table 7 Comparison between measured rod-by-rod FP inventory distributions and calculated ones for 2F2D2 (two-cycle irradiation)



3

4

1

2

W

1.221.183.41.181.180.7

1.101.07 W3.2

1.051.031.30.690.73

-4.10.920.93

-1.5

0.981.00

-2.20.870.88

-1.0

1.351.304.71.161.115.2

1.051.041.1

0.950.98

-2.50.800.84

-3.90.870.88

-1.2

0.880.90

-1.30.940.96

-2.2

0.920.94

-2.10.991.04

-4.1

1.031.002.6

1.071.061.30.960.98

-2.61.021.010.2

1.111.082.90.910.891.7

W W

Node 4

1

2

3

4


1.031.011.51.081.09

-0.7

1.071.052.20.800.83

-2.90.991.00

-0.9

1.061.09

-2.80.900.900.1

1.071.033.6

0.980.970.41.091.063.0

1.121.12 W0.3

0.950.923.00.840.87

-3.40.900.92

-1.8

1.161.16

-0.20.950.950.3

1.141.095.01.191.127.1

1.171.18 W

-1.1

0.920.911.20.700.76

-5.80.860.91

-5.2

1.081.070.30.950.97

-1.6

1.241.240.71.121.084.0

1.051.05 W

-0.3

0.960.941.30.820.84

-1.20.910.92

-1.2

0.930.920.30.971.00

-3.4

0.840.87

-3.20.990.971.2

1.061.08 W

-1.7

0.960.97

-1.41.051.050.40.930.93

-0.1

1.231.212.00.940.922.8



Dow

nloa

ded

by [

Was

hing

ton

Stat

e U

nive

rsity

Lib

rari

es ]

at 0

1:23

25

Nov

embe

r 20

14

sities of the material regions were taken from the design basespecifications of the fuel vender of the BWR 8� 8-4 assem-bly. Corners of a fuel channel box were modeled by a rectan-gular form, and a large water rod was simulated by foursmall water rods while conserving the amount of water

and cladding material. Burnable fuel rods, Gd2O3-UO2, have10 radial regions of equal volume. The temperatures of thepellets and the moderator were postulated to be 900 and559K.

The rod-by-rod FP inventory distributions in the fuel as-

Table 9 Comparison between measured rod-by-rod FP inventory distributions and calculated ones for 2F2D8 (five-cycle irradiation)



3

4

1

2

W

1.121.110.5

1.061.051.2

1.091.071.9

1.061.05 W1.2

1.021.03

-1.10.810.82

-1.20.940.96

-1.9

0.900.91

-0.5

1.231.193.2

1.021.011.1

1.091.053.8

1.021.011.1

0.941.02

-7.60.840.87

-2.80.890.880.9

0.960.950.2

1.020.974.7

1.021.06

-4.00.990.917.8

1.021.06

-4.0

1.011.13

-11.60.950.941.61.021.010.7

0.980.934.9

W W

Node 6

1

2

3

4


1.021.020.1

1.041.031.6

1.041.021.8

1.051.05

-0.60.880.90

-2.31.001.02

-2.1

0.930.930.0

1.041.031.6

0.990.971.6

1.081.09

-1.11.051.032.1

1.081.09 W

-1.1

0.970.97

-0.30.930.94

-1.60.940.940.0 0.2

0.970.97

1.061.050.3

1.101.082.8

1.101.072.5

1.101.08 W2.8

0.940.94

-1.00.860.89

-3.30.890.92

-3.6

0.960.96

-0.6

1.171.170.3

1.021.02

-0.31.071.051.8

1.021.02 W

-0.3

0.960.98

-2.40.860.87

-0.10.920.920.3

0.970.960.8

0.980.934.7

1.031.05

-2.20.981.01

-2.5

1.031.05 W

-2.2

0.981.10

-12.51.010.964.60.990.954.0

1.000.946.2

Table 8 Comparison between measured rod-by-rod FP inventory distributions and calculated ones for 2F2D3 (three-cycle irradiation)



3

4

1

2

W

1.161.133.91.131.102.4

1.071.08 W

-1.3

1.021.03

-0.80.740.79

-4.8

1.111.12

-0.90.910.92

-1.0

0.870.842.6

1.281.216.91.111.101.3

1.021.07

-4.7

0.930.930.10.810.84

-2.9

1.051.08

-3.10.860.851.0

0.930.921.4

0.950.99

-3.10.991.02

-3.5

1.031.011.7

1.051.005.30.971.00

-3.8

1.041.003.3

1.031.04

-0.7

0.950.940.8

W W

Node 3

1

2

3

4


1.021.03

-0.11.061.041.3

1.061.07

-1.00.840.822.3

1.081.09

-1.60.991.00

-1.4

0.910.891.4

1.051.06

-0.9

0.960.960.51.081.09

-1.7

1.111.11 W0.5

0.960.950.40.880.92

-3.4

1.131.120.6

0.920.910.3

0.960.942.6

1.091.10

-0.71.151.131.6

1.141.14 W

-0.5

0.910.95

-3.50.750.80

-5.2

1.161.123.8

0.860.851.0

0.940.913.5

1.201.146.11.091.10

-1.2

1.031.06 W

-3.6

0.940.99

-4.50.830.84

-0.8

1.051.050.0

0.900.900.2

0.960.923.8

0.860.833.60.970.961.6

1.061.10 W

-3.9

0.990.99

-0.51.081.071.5

1.071.12

-5.00.980.961.9

0.990.980.8



Dow

nloa

ded

by [

Was

hing

ton

Stat

e U

nive

rsity

Lib

rari

es ]

at 0

1:23

25

Nov

embe

r 20

14

semblies depend on the irradiation history of the power den-sity and the in-channel void fraction. In order to take into ac-count these parameters, the following process was adopted:(1) implementing burn-up calculations at a constant powerdensity corresponding to the rated power of the plant andconstant void histories, 0, 40, and 70% in-channel void frac-tions, (2) compiling a table of rod-by-rod FP nuclide inven-tory distributions as a function of two variables, node aver-age exposures, and in-channel void fractions, and (3) inter-polating the values of the table to obtain the rod-by-rod FPnuclide inventory distributions at the node average exposureand the historical void (exposure-average value of in-chan-nel void fraction) for the specific nodes of the assemblyfor which the measured rod-by-rod FP inventory distribu-tions are given in Tables 6 to 9.

IV. Comparison between Calculated and MeasuredRod-by-Rod FP Inventory Distributions

The values of the top rows of the rod locations in Tables 6to 9 show the calculated relative rod-by-rod FP inventorydistributions. The average value of each rod position is nor-malized to 1.0. The bottom rows show the difference definedas (calculated value � measured value)/measured value �

100. Table 10 shows the root mean square (RMS) of the dif-ference of the eight fuel rod locations as ‘‘RMS’’ and also thedifferences for the B3 rod as ‘‘Gd.’’

Table 6 shows that the differences for the one-cycle irra-diation assembly are in the range of 0 to 2% for almost allthe fuel rods in nodes 18 and 5, except the A4 and B3 rods.The table indicates the general good accuracy of the calcula-tions of the rod-by-rod FP inventory distributions includingthose for 134Cs and 106Ru that show larger peakings, 1.3 to1.4, around the corners of the assemblies. Even after the cor-rection of the gamma-ray transmission factors, the calcula-tions are systematically underestimated from 1 to 8% forthe B3 rod. This trend of the B3 rod commonly appears inthe two-, three-, and five-cycle irradiation assemblies,though the difference gets smaller with irradiation cycles.The differences larger than 4% are seen in 137Cs, 106Ru,and 95Zr for the A4 and 106Ru for the B2 of node 18, butnot seen in node 5. This is possibly due to a larger experi-mental error for node 18.

Table 7 shows that the differences for the two-cycle irra-diation assembly are in the range of 0 to 3% for almost allthe fuel rods in nodes 17 and 4 with some exceptions ofthe A1, A2, and B3 rods. It is noticed that the A1 and A2rods are located in the peripheral region of the assembly,

1 2

WR

1 1 133

2 2 2

3 33

3 33

3

3

3

4

1 1 1 1 1 1

5

1

2

3

3

2

2

2

2

2

2

2

2

2

2

2

2

2 2 2 2 2

1

2

1 1

1

1

1

1

1

1

1

1

1

33 31 13 3

2

13

3

3

3

3

3

6

3

3

7

3

3

3

3

8

3

3

9

3

3

3

3

10

3

3

3 3

4

3

3

3

3

3

3

3

3

13

3 3

3

3

3

33

13

3

5

17

29

1 1

17 13 7

18

30

8

9

10

1

1

3

3

33 3

3 3

3

3 3

1

1

1 1

3 3 3 3 3 3

3 3 3 3

33

3

3

3

3 3

3

3

3

3 3 3 3

3 3

3 3 3

3

3 33 3 3 3 3

3 3 3

3

3 3

3

33

33

33 3 3 3

3 3 3 33 3

3 33

3

16

3 3

3

3

33

33

3

3

33

3

12

1

1 1

20

29

1

1

1

20

19

1

40 40

41

1

30

39

11

1

6

1 1

1

39

41

1 1

1

3

1

3 3

33

18

14 15

14

12

1

2

2

2

2

2

2

2

2

2

2

2

1

1

1

1

1

1

1

1

1 1 1

333 3 3

1

3

1

3 3

3

3

3

3

3

3

3

3

333

33

5

3333

1

6

1

291

20

291

20

33

3

33 333

7

1 33

33

13

1 33

33

17

1 3 333

3

3

40

413

3

3

3

40

413

16

3

3 3

13

17

3

3 3

13

18

3

3 3

13391

30

391

30

19

3

3 3

13

14

3

3

13

18

3

3

13

8

3

3 3 33

13

9

3

3 3

13

10

3

3 3

13

15

3

3 3

13

14

3

3 3

13

13

3

3 3

13

3

3

3

3 3 3

11

3

3 3

13

2 2 2 2

11

2 22

1

3

1

2 2 2

10

3

3 3

13

9

3

3 3

13

8

3

3 3

13

7

3

3 3

13

6

3

3 3

13

5

3 3

3 3

13

3

3 3

3

3

3 3

3

1: fuel channel and fuel cladding, 2: out-channel water, 3: in-channel water, 4 to 19: UO2

pellet, 20 to 29, and 30 to 39: UO2-Gd2O3 rod, 40: water inside water rods, and 41: claddingof water channel

Fig. 6 Geometrical model and M-region number of SRAC-Pij calculation



Dow

nloa

ded

by [

Was

hing

ton

Stat

e U

nive

rsity

Lib

rari

es ]

at 0

1:23

25

Nov

embe

r 20

14

and the effect from adjoining assemblies for these rods islarger than for those in the inner location of the assembly.

Table 8 shows that the differences for the three-cycle irra-diation assembly are in the range of 0 to 3% with some ex-ceptions of A1, A3, B2, and B3.

Table 9 shows that the differences for the five-cycle irra-diation assembly are in the range of 0 to 3% except those of95Zr. For 95Zr, the B3 and B4 rods of node 15, and the A2,A4, and D1 rods of node 6 show differences in the range of 0to 3%. These exceptions are mainly due to the assembly2F2D8, which was irradiated in the peripheral location ofthe core and has a large gradient of the neutron flux fromthe inner core region to the reflector region. Table 11 sche-matically shows an assembly configuration and also themeasured rod-by-rod 95Zr inventory distribution in node15. In this case, the simple averaging of the symmetricalrod positions would not give accurate inventory distribu-tions. This effect also has some influence on the 106Ru distri-butions. The largest difference of 95Zr is seen in the B2 rod.This is possibly due to a larger experimental error for thisrod added to the error caused by the special location of thefuel assembly.

V. Discussion

The RMS values in Table 10 represent the general differ-ence between the measured rod-by-rod FP inventory distri-butions and the analysis results, and indicate that the analysismethod of the present study is evaluated to have an accuracyof 1 to 2% for the rod-by-rod burn-up distribution, 2 to 3%for the thermal flux � burn-up, 2 to 3% for the 239Pu build-up, and 2 to 3% for the fission rate at the end of the cycle ofthe irradiation, which are represented by the inventories of137Cs, 134Cs, 106Ru, and 95Zr, respectively.

It was also observed that the lattice analysis of this studyshows an underestimation of the FP inventories for theGd2O3-UO2 rods (the B3 rods) especially in the first and sec-ond cycles even after the gamma-ray transmission correc-tions were applied to the measurement results. Misu etal.8) show the C/E of a 140Ba distribution of a MOX9� 9-1 fuel assembly after one-cycle irradiation and nineof 12 Gd2O3-UO2 rods show underestimations up to 3%;however, the degree of underestimation is not significantcompared with that in this study.

Ikehara et al.15) studied the effect of void distributions in

Table 11 Measured rod-by-rod 95Zr inventory distribution of node 15 for 2F2D8 (five-cycle irradiation)

A C E GB D F H

1 0.74 1.07

2 0.68 0.92

3 0.74

4 0.82 0.85 0.91 W W

5 WW 0.94 1.18 1.22

6 1.13

7 1.33 1.15

8 1.11 1.20

Reflector Region

Fuel AssemblyFuel Assembly

Fuel Assembly

Fuel Assembly

Table 10 Summary of comparison between measured rod-by-rod FP inventory distributions and calculated ones

Assembly Irradiation Axial 137Cs 134Cs 106Ru 95Zr

Cycles Node RMS Gd RMS Gd RMS Gd RMS Gd

2F2D1 1 18 2.4 �4:8 1.8 �4:2 3.0 �2:1 2.5 �5:5

5 3.3 �8:2 2.9 �6:2 2.1 �4:4 2.0 �0:6

2F2D2 2 17 2.2 �2:9 2.5 �4:1 3.2 �3:9 2.4 �2:6

4 2.0 �3:4 4.2 �5:8 2.0 �1:2 1.9 0.4

2F2D3 3 18 1.4 2.3 2.6 �4:8 3.4 �2:9 3.2 �3:8

3 1.7 �3:4 3.0 �5:2 3.3 �0:8 2.8 1.5

2F2D8 5 15 1.5 �2:3 1.3 �1:2 3.4 �2:8 5.9 1.6

6 1.2 �1:6 2.4 �3:3 1.1 �0:1 5.8 4.6



Dow

nloa

ded

by [

Was

hing

ton

Stat

e U

nive

rsity

Lib

rari

es ]

at 0

1:23

25

Nov

embe

r 20

14

radial planes on nuclear characteristics in a BWR UO2 as-sembly by using a coupled code system of a lattice physicsanalysis code and a subchannel analysis code and showedthat smaller void fractions of subchannels of Gd2O3-UO2

rods cause a larger negative Gd effect and burn Gd fasterthan the analysis based on homogeneous void fractions. Thisindicates the possibility that the burn-up of Gd2O3-UO2 rodsis larger in actual depletion conditions than in the burn-upcalculation based on the homogeneous void fractions. Thiswould be partly related to the results of the present study.Anyway, further study is necessary to investigate the causes.

On the other hand, the underestimation of the analysis ofthe FP inventories of Gd2O3-UO2 rods does not have a sig-nificant effect on the maximum local power peaking factorof the fuel assembly (LPF, the maximum value of the rod-by-rod relative power distribution in the assembly), becausethe fuel rods showing the LPF are usually UO2 rods with thetypical BWR fuel enrichment design and the influence on theLPF is smeared by the limited number of Gd2O3-UO2 rods inthe total fuel rod number of the assembly.

VI. Conclusion

The relative rod-by-rod FP inventory distributions of137Cs, 134Cs, 106Ru, and 95Zr for the upper and lower axialheight nodes were obtained from the rod-by-rod gamma-ray spectrometry for the one-, two-, three-, and five-cycle ir-radiated BWR 8� 8-4 fuel assembles. The measured distri-butions were corrected for the difference in the gamma-raytransmission between the UO2 and Gd2O3-UO2 rods. Thedistributions were compared with those calculated usingthe collision probability method, Pij, of the SRAC code sys-tem with the infinite lattice model of the fuel assembly. Thecalculated results generally well reproduce the measured dis-tributions, and the accuracy of the analysis method of thepresent study was evaluated to be 1 to 2% for the inventorydistributions of 137Cs, 2 to 3% for 134Cs, 2 to 3% for 106Ru,and 2 to 3% for 95Zr, which represent the distributions of theburn-up, the thermal flux multiplied by the burn-up, thebuildup of 239Pu, and the fission rate at the end of the fueldischarge cycle, respectively. One of the notable results ofthe analysis in this study is that the FP inventories of theGd2O3-UO2 rods were underestimated in most cases.

References

1) On Fully Loading MOX Fuel in the Advanced Light Water Re-actors, Nuclear Safety Commission of Japan, Jun. 28, 1999(1999), [in Japanese].

2) T. Yamamoto, K. Kawashima, ‘‘Verification of lattice analysismethod through BWR UO2 PIE data analysis,’’ Proc. Int.Conf. on PHYSOR 2004, Chicago, Illinois, USA, Apr. 25–29, 2004 (2004).

3) T. Yamamoto, S. Kikuchi, K. Kawashima, K. Kamimura, ‘‘Ex-perimental results and analysis of core physics experiments,FUBILA, for high burn-up BWR full MOX cores,’’ Proc.Int. Conf. on PHYSOR 2006, Vancouver, Canada, Sept. 10–14, 2006 (2006).

4) K. Kawashima, T. Yamamoto, K. Kamimura, ‘‘Analysis of re-

actor physics experiment for the irradiated LWR MOX fuels,’’Proc. Int. Conf. on ICAPP ’06, Reno, NV, USA, Jun. 4–8,2006, Paper 6077 (2006).

5) E. Saji, H. Shirayanagi, ‘‘Analysis of boiling water reactormixed-oxide critical experiments with CASMO-4/SIMU-LATE-3,’’ Nucl. Sci. Eng., 121, 52 (1995).

6) K. Ishii, Y. Ando, N. Takada et al., ‘‘Analysis of high moder-ation full MOX BWR core physics experiments BASALA,’’Trans. At. Energy Soc. Jpn., 4[1], 45 (2005), [in Japanese].

7) M. F. Murphy, M. Plaschy, F. Jatuff et al., ‘‘Fission and cap-ture rate measurements in a SVEA-96 Optima2 BWR assem-bly compared with MCNPX predictions,’’ Proc. Int. Conf. onPHYSOR 2006, Vancouver, Canada, Sept. 10–14, 2006(2006).

8) S. Misu, H. Spieling, H. Moon, A. Koschel, ‘‘Pin-by-pin gam-ma scan measurement on MOX and UO2 fuel assemblies andevaluation,’’ Proc. Int. Conf. on the PHYSOR 2000, Pittsburgh,Pennsylvania, USA, May 7–12, 2000 (2000).

9) Safety Experiments of High Burn-up Fuel (BWR High Burn-upFuel, Comprehensive Evaluation), Nuclear Power EngineeringCorporation, Mar. 2002 (2002), [in Japanese].

10) Application for Establishment Permit of Modification of Unit 2of Fukushima Power Station 2, Tokyo Electric Power Compa-ny, Sept. 29, 1986 (1986), [in Japanese].

11) K. Okumura, T. Mori, M. Nakagawa et al., ‘‘Validation of acontinuous-energy Monte Carlo burn-up code MVP-BURNand its application to analysis of post irradiation experiment,’’J. Nucl. Sci. Technol., 37[2], 128 (2000).

12) K. Okumura, K. Kaneko, K. Tsuchihashi, SRAC95: GeneralPurpose Neutronics Code System, JAERI-Data/Code 96-015(JAERI), (1996), [in Japanese].

13) K. Kanda, T. Yamamoto, H. Matuura et al., ‘‘MOX fuel corephysics experiments and analysis—aiming for plutonium ef-fective use—,’’ Nihon-Genshiryoku-Gakkai Shi (J. At. EnergySoc. Jpn., 40[11], 834 (1998), [in Japanese].

14) T. Nakagawa, K. Shibata, S. Chiba et al., ‘‘Japanese evaluatednuclear data library version 3 revision-2,’’ J. Nucl. Sci. Tech-nol., 32, 1259 (1995).

15) T. Ikehara, Y. Kudo, M. Yamamoto, T. Tamitani, ‘‘A study onthe effect of detailed void fraction distribution on the nucleardepletion characteristics for BWR fuel bundles using coupledTGBLA-COBLAG system,’’ Trans. 2004 Annual Meeting ofthe Atomic Energy Society of Japan, Kyoto University,Sept. 15–17, B34 (2004), [in Japanese].

Appendix

When there are gamma-ray sources (a linear density of q)on a line of length L, as shown in Fig. 7, the number of pho-tons being transmitted through point a is given by integratingthe contribution of the sources on the length L.Z L

0

qe��xdx ¼q

�ð1� e��LÞ

a L

gamma-rayx

Fig. 7 Transmission of gamma-ray



Dow

nloa

ded

by [

Was

hing

ton

Stat

e U

nive

rsity

Lib

rari

es ]

at 0

1:23

25

Nov

embe

r 20

14

For the example shown in Fig. 8, the gamma-rays that are generated on the line of the angle u with a linear density q and aretransmitted through a pellet and a fuel cladding toward a detector surface at a distance Xd without collisions are expressed as

DR1ðuÞ ¼X4k¼2

qk

�k

exp �X5i¼kþ1

�iLi

!� ½1� expð��kLkÞ�

þ exp �X5i¼2

�iLi þXk�1

i¼2

�iLi

!( )� ½1� expð��kLkÞ�

266664

377775� cos udS:

The gamma-rays that are transmitted toward the detector surface when there are no materials to collide with the gamma-raysare expressed as

DR0ðuÞ ¼X4k¼2

2qkLk � cos udS:

The gamma-rays from all gamma-ray sources in the pellet are shown as

DR1 ¼ 2

Z sin�1ðRf =XdÞ

0

DR1ðuÞdu;

DR0 ¼ 2

Z sin�1ðRf =XdÞ

0

DR0ðuÞdu:

Then the gamma-ray transmission factor is defined as

T ¼DR1

DR0

:

L5 L4 L3L2 L2

L3 L4 L5

u

1Xd

2

3

4

5

Regions 1 to 4: fuel pellet, Region 5: fuel claddingXd: distance between center of fuel pellet and gamma-ray detector surfaceLn (n=2 to 5): line segment pass through regions 1 to 5q: gamma-ray strength for regions 1 to 4

gamma-raydetector surface

Fig. 8 Schematic diagram of calculation model of gamma-ray transmission through a pellet and a cladding toward to agamma-ray detector surface



Dow

nloa

ded

by [

Was

hing

ton

Stat

e U

nive

rsity

Lib

rari

es ]

at 0

1:23

25

Nov

embe

r 20

14

analysis of rod-by-rod fp inventory distributions in bwr 8 × 8 uo 2 ...

Documents