NEACRP - A - 567

Benchmark on Interactive Effects of Gadolinium

Poisoned Pins in BWRs

C, Maeder and P, Wydler

EIR, 5303 WLirenlingen, Switzerland

Status report prepared for the

26th meeting of NEACRP, Oak Ridge, USA, October 17 - 21, Kl83

In this report the results of the bumup calculations for a

simplified BWR fuel element with two adjacent gadolinium rods

are presented and discussed. Complete solutions were contri-

buted by FEZXX, Italy, ,Japan, Switzerland and the UK. Partial

results and additional calculations obtained from Denmark,

Italy, Poland and the US are included in the Appendices.

.

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contents

summary

;

.

1. Introduction

2. Problem Specification

3. Participants

4. Calculational Methods

5. Definitions and Method of Evaluation

6. Results

7. Discussion of the Results

8. Conclusions

9. References

Acknowledynent

Tables 1 - 30

Fiyures 1 - 26

l Appendix A:

Appendix B:

Appendix C:

Appendix D;

Appendix E:

Shadowiny Effect of Poisoned Pins

Influence of Calculation Models on Reactivity

Reaction Rates for the Reyular Lattice

Partial Solutions

Solutions Submitted after September 10, 1983

2

3

4

6

11

13

15

18

19

21

22

38

Al

A3

A5

A6

A9

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1. Introduction

From 1974 till 1977 the Nuclear Energy Agency Committee on Reactor Physics

(NEACRP) sponsored a BWR lattice benchmark exercise (L). Two of the con-

sidered lattices contained isolated.gadolinium fuel rods. In the meantime

fuel elements with adjacent poisoned fuel pins have been introduced in

BWRs to enhance the performance of the fuel. It has to be checked, whether

the calculational methods used in BWR core analysis can adequately predict

the resulting mutual shielding of the pins and, in particular, its effect

on the depletion of the burnable poison.

In view of this development, the Swiss Federal Institute for Reactor Re-

search (EIR) in 1980 proposed a naw gadolinium benchmark for a simplified

BWR fuel element with 14 unpoisoned and 2 adjacent poisoned fuel rods. The

intension was to investigate whether calculational methods used for iso-

lated Gd pins are capable of treating this nwre complex geometry with

sufficient accuracy. A preliminary calculation, in which an azimuthal

variation of the flux was taken into account in the Gd pin cells (cf.

Appendix A), indicated that the shadowing effect of neighbouring Gd rods

is small.

.’

.

‘.

First results for the benchmark problem with adjacent Gd rods, contributed

by EIR, EPRI and the Institute of Nuclear Research Swierk wera presented

at the European Nuclear Conference at Brussels in April 1982 CL). In

autumn 1981 the NEACRP provided an organisational basis for the new bench-

mark. In contrast to the earlier NEACRP lattice benchmarks (L), in which

6-group macroscopic cross sections "era prescribed, the participants wera

asked to use their own cross sections libraries and group structures and to per-

form burnup calculations up to 10 GWd/t. In addition, a reference solution

for the regular unpoisoned pin was requested, allowing checks on basic data

and calculational methods to be made (2).

The results obtained till sufmner 1982 were documented in a progress report

prepared for the 25th meeting of the NEACRP (4-j. Xn the meantime additio-

nal solutions have been obtained from Denmark, France, Italy and Japan bringing

the total number of solutions up to 11.

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‘.

.

:

!Co be able to present consistent standard deviations in th& tables of the

present report, the submitted results have been divided into 7 complete

solutions, which are discussed in the main part of the report, and 3 partial

solutions (from ENEA, EPRI and SWIERK), for which multiplication factors

only are given in Appendix D. The submitted ENEA- and RIS@-results are listed

in Appendix E.

2. Problem Specification

The simplified fuel element, as' shorn in Fig. 1, consists of 14 initially

identical unpoisoned fuel rods and 2 Gd rods. Taking the synnnetry into

account, the 16 pins can be reduced to 5 different unpoisoned pins (numbered

1 to 5 in Fig. 1) and a single Gd pin (number 6). Reflective boundary con-

ditions are prescribed on the four surf,aces. The material properties are as

follows:

Fuel:

ClS3d:

Material = UO 2, density = 10 g/cm3, temperature = 60V°C,

U-235 enrichment = 3 weight-%, diameter = 1 cm.

The Gd pin contains 3 weight-% of Gd203

(i.e. 0.3 g/cm3 Gd203 and 9.7 g/cm3 UO2).

Material = Zircaloy-2, density = 6.55 g/cm3,

temperature = 300 OC, inside diameter = 1 cn~,

outside diameter = 1.2 cm.

Moderator: Material = H20, void content = @A, state of saturation at

a temperature of 286 'C (pressure = 70.06 bar), lattice pitch = 1.6 cm.

The assembly average power density is 20 W per gram of the uranium metal

in the fresh fuel.

The following results are requested for assetily average exposure steps of

1 GWd per metric ton of loaded U metal up to 10 GWd/t:

- The multiplication factor km,

- the relative power of the 6 different rods normalised to an

assembly avarage value of 1,

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- the Gd pin avaraga densities of the isotopes Gd-155, Gd-157, U-235,

Pu-239 and ~~-240 in atoms/barn.cm,

- the spatial distribution of the Gd isotopes at 2 GWd/t. .’

A burnup calculation has also to be performed for a regular lattice without

burnable poison rods. The regular lattice is equivalent to a single un-

poisoned fuel pin with a IJO density of 10 g(cm3 and the associated cladding

and moderator. The infinite multiplication factor and the fuel pin awraga

densities of V-235, Pu-239 and Pu-240 are requested for the same burnup

intervals of 1 GWd/t.

In addition, the calculational method has to be briefly described.

3. Participants

The following organisations and authors participated in the benchmark

calculations:

AEEW:

AMN: -

CEA: -

CISE:

M.J. Halsall Atomic Energy Establishment Winfrith Dorchester, Dorset England

P. Neuhold AMN Ansaldo Impianti Via Gabriele D'Annunzio, 113 I-16121 Geneva Italy

P. Chaucheprat, G. Girieud and B. Nouveau Ddpartement des rgacteurs & eau Centre d'&udes nucl&ires de Cadarache B.P. No. 1 F-13115 Saint Paul l.ez Durance France

G. Pierini Centre ~nfomazioni Studi Esperienze P.O. BOX 12081 I-20134 Milan Ztaly

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C. Mae&x Eidg. Institut fiir Reaktorforschung CH-5303 W~renlingen Switzerland

NAIG: M. Yamanmto and H. Mimta Nippon Atomic Industry Group 4-l Ukishima-cho, Kawasaki-ku Kawasaki, 210 Japan

:

OSAKA: T. Take& a& H. Sat0 Osaka Vniversity Faculty of Engineering, Nuclear Engineering Yam&-oka 2-1, Suita Osaka

K. Shinhama and H. Kmmbata Jap~an Information Service, Tnc., Tosabori 2-2-7, Nishi-ku Osaka Japan

Partial solutions were provided by:

ENEA F. Casali Centre Nazionale Energia Nucleate e Energie Alternative Centm Ricerche Energie “Ezio Clem.stel” Via G. Mazzini, 2 I-40138 Bologna Italy

EPRI: B.A. Zolotar .Electr.ic Power Research Institute P.O. Box 10412 Pa10 Alto, CA 94303 USA

SWIERK: K. Kowalska Institute of Nuclear Research Swierk PL - 05400 Otwock Poland

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4. Calculational Methods

An overview of the adopted calculational methods is given in TAB 1.

The following descriptions are based on the summaries provided by the

participants.

4.1 AEEW

The solution is based on standard design calculation options normally used

in LWRWIMS (5). The exercise was taken as an opportunity to test the rela- - tively new CACTUS characteristics transport code in order to assess the

importance of a detailed spatial calculation.

A 28 group condensed WIMS library of cross-sections was used, with identi-

fiers 2235, 7238, 5239 for U-235, U-238 and Pu-239 and the pseudo-fission

product scheme as defined in Ref.(z).Cross-sections in 28 qroups were gs-

nerated using WIMS equivalence theory for the resonance qroups, and a

multicell collision probability calculation wag used to generate 28 group

fluxes for each region in the problem. For the design calculation there

wars nine regions: fuel, can and coolant for standard pins and 4 fuel zones

plus can and coolant for the Gd pins. Condensation to 6 qroups (with

boundaries at 821 keV, 9118.4, 0.625 and 0.140 eV) and pin-cell smearing wers followed by a straightforward diffusion theory solution in 4 x 4

meshes. For the re9ular lattice cass a simple pin-cell calculation was

made as above, and the smearing and diffusion calculations were omitted.

. .

Depletion is by numerical integration allowing only for the variation of

gadolinium through the fuel pin. Adjustments wars made by using the "FXNE"

option to radial reaction rates of gadolinium at 200 MWd/t intervals with

the full lattice calculation interval of 1000 MWd/t. The so-called

"DIFFERENTIAL" option was invoked to calculate the pin by pin isotopic

compositions for uss in evaluating the powsr distribution.

An alternative solution method which does not require pin cell smearing is

the CACTUS option in LWRWXMS. This method is based on explicit tracking

through the problem, integration of thetransport equation along each track

segment, and numerical integration of the scalar flux by means of tracks at

appropriate spaciny and angles. A detailed CACTUS calculation with 170

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spatial .zone.s was made for the poisoned lattice at start of life.

The results given in this report are based on a depletion calculation using

the diffusion theory method with "FINE" and "DIFFERENTIAL" options. How-

ever, the calculation was normalised to the detailed CACTUS eigenvalue by

adjusting the poison pin dimensions. To reduce the initial km from the

value of the adjusted desiqn calculation (1.0253) to the value of the de-

tailed CACTUS calculation (1.0093) it was found necessary to increase the

poison pin radius from 0.5 cm to 0.5775 cm. The fuel density was correspon-

dingly reduced and the clad density increased to preserve the total numba's

of atoms. This technique is currently used at Winfrith in PWR design cal-

culations to correct the initial worth of boron poison pins.(c).

0 4.2 AMN

:

a

Modules of the BLA code system were used to perform the following calcula-

tion steps:

1) Preparation of (one-group) thermal cross SectJons;

A transport theory method was used for averaging cross sections in the

pin cells. An additional supercell calculation provided the fluxes for

collap3inq the energy groups in the Gd pin cell.

2) Preparation of epithermal and fast cross sections (one broad qroup in

each enerqy ranqe). Epithermal cross sections were qenerated using a

GAM type ~??sonance calculation and a B-1 flux solution. In the top (fast)

broad qroup a discrete collision probability calculation was performed.

This allowed the fast fission effect to be treated appropriately. The.'

exposure dependence of the resonance cross sectionsincludes effects due

to isotope concentration, Dancoff factor and neutron spectrum.

3) 2-D lattice calculation:

Three-qroup diffusion theory was used, and each square fuel cell was

divided into a square fuel pin and a surrounding homoqenized clad-water

region (this procedure permits the modellinq of spatially varying void

contents).

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4) Effects of c?x&msure:

The thermal/epithermal cz'oss sections and 2-D fluxes were recalculated

after specified exposure steps.

4.3 CEA -

The calculations were performed with the APOLLO-NEPTUNE code which is beiny

developed by the CEA for light water reactor calculations CL). The APOLLO

code solves the transport equation in its integral form by the collision

probability method in the multigroup approximation. Tn the calculation 99

ane~'yy groups with 52 fast and 47 thermal groups were used (the thermal cut-

off is located at 2.8 eV).

The lattice calculations were performed with the ROT 4 option of the EVRYDICE a code (g), which is based on the following approximations:

- Four entering currents per cell.

- WIGNER cylindrization which respect to the tie11 Volume.

- The current anisotropy on the cell surfaces is neylected.

The calculations were carried out with a spatial mesh consistiny of 56 points

(22 independent points), these being distributed as follows:

- 7 points in each Gd pin cell. The fuel was divided into 5 spatial zones

ofequal volume to be able to calculate the fine spectrum flux in the

poisoned pin.

- 3 points in every UO2 cell. In the burnup calculations the depletion chain uranium + neptunium + plu-

tonium and the complete gadolinium chain from Gd-154 to Gd-160 were con-

sidered. The self-shieldiny of the resonance nuclei was recalculated for

each burnup step.

4.4 CISE

The calculations were performed with the NUOVO AUTOBUS code (z), which pro-

vides libraries of nuclear parameters for LWR fuel elements. The code is

capable of describiny several types of compositions (fuel, fuel with Gd

content, borosilicate, structural materials, cross control rods, Ay-Cd-In

rods) and solves two-dimensional finite difference diffusion equations in

five yroups with eneryy boundaries at 183 keV, 5.S keV, 0.625 .eV and 0.2 eV.

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Correlated group constants are used for the 'reiular cells. For the Gd pins

the transport-evaluated cross sections are properly modified to preserve the

correspondiny absorption rate.

4.5 EIR -

The solution is based on the code BOXER (c) and a 70-yroup library, with

resonance parameters, which. was derived from ENDF/B-4. The resonance ranye

is treated by a two-reyion collision probability method in,= few thousand

eneryy points. The cylindricalized fuel cells were calculated in the 70

energy yroups with en inteyral transport method assuming a first order spa-

tial polynomial approximation for the scatteriny source in each zone. The

Gd pin was divided into 4 annular zones of eq&l volume. The outgoiny sur-

face flux of the unpoisoned cell served as the boundary condition for the

Gd cell calculation. The pin cell homogenization was performed by flux-

volume-weiyhting with an energy dependent heterogeneity correction in the

Gd cell.

The lattice calculation in x-y yeometry used 11 eneryy yroups with upper

boundaries at 15 MeV, 0.821 MeV, 907, 76, 16, 4, 0.625, 0.32, 0.14, 0.058

and 0.025 eV. The calcul.ation is based on a transmission probability trans-

port method which approximates the anyular dependence of.the mesh surface

flux by a first order quadrupole spherical harmonics expansion and uses a

linear spatial representation of the volume source and of the mesh surface

flux.

The first two burnup step lengths were 0.1 and 0.4 GWd/t. These were

followed by steps of 0.5 GWd/t up to 5 GWd/t and +teps of 1 GWd/t beyond

5 GWd/t. After each step a cell calculation in the thermal energy ranye be-

low 4 eV and a twodimensional lattice calculation were perfortied. The time

dependence of the microscopic cross sections is taken into account by re-

calculating the burnup step usiny the one-yroup cross sections at the end

of the step (predictor - corrector method) end by a density dependent self-

shielding factor for the isotopes Pu-239 and Pu-240. Within .a burnup step the

neutron flux is expanded into .e second order Taylor series in the time

variable.

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4.6 NAIG

The data base used for the calculations is ENDF/B-5 for the main fertile

and fissile nuclides and ENDF/B-4 for the remaining isotopes. The cross

section library contains 68 enei-gy groups in the fast and epithermal range

(GAM type structure) and 30 groups in the thermal range (THERMOS structure).

The TGBLA model (11) uses a spatially dependent neutron energy spectrum to -

construct three-group (fast, epithermal and theimal) cross sections with

transport theory corrections for a diffusion theory calculation.

In the epithexmal energy range, the level-wise resonance integrals are cal-

culated by an improved intermediate resonance approximation with parameters

depending on the fuel temperature. The thermi neutron spectra in the fuel

cells are calculated using a method which is similar to the THERMOS forma-

lism. The major difference is that the neutron leakage from rod to rod is

taken into account. The leakage is determined by diffusion theory and fed

into the thermal spectrum calculation. Iterations between assembly diffusion

theory calculation and thermal spectrum calculation are carried out to de-

termine accurate, spatially dependent, thermal cross sections. The Gd rods

were subdivided into 10 regions of equal volume.

In the burnup calculations 100 isotopes are treated, including 25 fissile

and fertile isotopes and 48 fission products plus one pseudo fission pro-

duct. An improved burnup integration scheme is employed that avoids nu-

mez-ical problems associated with the stiff set of equations encountered in

poison burnup calculations. New flux spectra were calculated at 0, 0.2, 0.5,

1, 2, . . . . 10 GWd/t.

4.7 OSAKA

The solution was. obtained with the RESPLA code (g). RESPLA uses the 69

group WIMS cross section library for all nuclides except gadolinium and

69 group cross sections generated from ENDF/B-3 for the gadolinium iso-

topes.

The pin cell calculations were carried out in cylindrical approximation.

For the Gd pins a supercell, consisting of a Gd pin which is surrounded

by a mixture of the adjacent eight pin cells, was used to calculate the

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the flux fine structure. Each fuel pin including the Gd pin was divided into

six regions of equal volume. Based on these cell calculations the fine group

microscopic cross sections were condensed to 6,group cross sections with

energy boundaries at 0.821 MeV, 9.118 keV, 9.B77, 0.625 and 0.14 eV.

For the lattice calculation RESPLA utilises a transmission probability

method in which PO and Pl angular components of the neutron current a-e

considered. Each pin cell surface is divided into three subsurfaces to take

account of the spatial distribution of the neutron current. The heteroge-

neity within each pin cell is treated with response matrices obtained from

the pin cell calculations. The burnup calculation was performed using the

time steps 0.1 GWd/t, 0.4 GWd/t and 0.5 GWd/t thereafter. The flux and the

cross sections are assumed to be constant during e. time step.

5. Definitions and Method of Evaluation

In the evaluation of the results the following notation is used:

Varaibles and calculated quantities:

N = 7 = number of participants

E = exposure (GWd/t)

k = infinite neutron multiplication factor (-)

d = isotopic density (atoms/barn-cm)

Indices

lY?q = regular lattice

poi = poisoned lattice

25 = U-235

49 = Pu-239

40 = Pu-240

155 = Gd-155

157 = Gd-157

Gd = gadolinium

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From the submitted Xx?sult~ the following quantities an? derived:

Densities (dimensionless):

U-235 destruction: D25CEJ = L

d25COJ - d25(EJ 1 / d2$W Gd destruction: DGdW = dGdCO) - dGd(EJ 1 / aGdm , Total Gd density (atoms/barn.cm):

Reactivities (dimensionless):

Gadolinium reactivity worth:

Reactivity loss in the regular lattice:

Reactivity gain in the poisoned lattice:

P poi(EJ = kpoi(E) - kpoiCl) 1 / kpoiW In these formulae k(l) = k(E=l GWd/t) is chosen as the reference multipli-

cation factor in order to separate the xenon effect from the calculated

reactivity effects.

Standard deviations:

If yn(E) denotes any of the submitted or derived quantities of partici-

pant n (n = 1, 2, . . . . NJ, the rneaa value of all participants is defined

by

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The standard deviation (calkd STA.DEV. in the tables) is

and the coefficient of variation (called VARIATION in the tables) is

In TABS 2 - 26, in addition to the mean value, the standard deviation is

given for normalised quantities (relative power, reactivity and destruc-

tion) and the variation for the other quantities (multiplication factor and

densities).

In TABS 16 - 17 the reactivity deviation from the mean is calculated as

ApnCEl = kn(E, - r(E) 1 / FiE, .

6. Results

The submitted results ara listed in TABS 2 - 13 and represented graphi-

cally in FIGS 2 - 13 (figure numbers agree with the corresponding table

numbers,. If possible, corresponding results for the regular and the

poisoned lattice are shown on the same page.

The spatial distributions of the Gd isotopes at 2 GWd/t wera presented by

all participants as average values in annular zones. However, as can be

seen in TAB 1, the different participants chose different numbers of annuli

and different annular boundaries. To determine comparable quantities,

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quadratic interpolation functions ss s function of r2 (r = radius) were

fitted to the submitted radial distributions. From these functions average

values in 4 zones of equal volume (as. used in the EIR solutions) were de-

rived. The values sre listed in TABS 14 - 15 and plotted in the form of

histograms in FIGS 14 - 15.

From the submitted multiplication factors and denskties the following

quantities ss defined in section 5 wers derived:

- R@activity deviations (TABS 16 - 17 and FIGS 16 - 17)

-~ gadolinium reactivity worth (TAB 18 and FIG 18)

- gadolinium destruction (TAB 19 and FIG 19)

- reactivity gain in the poisoned lattice ss a function of exposure

and of the Gd destruction (TABS 20 - 21 and FIGS 20 - 21)

- plutonium ratio (TABS 22 - 23 and FIGS 22 - 23)

- reactivity loss in the regular lattice ss s function of exposure,

u-235 destruction and Pu-239 density (TABS 24 - 26 and FIGS 24 - 26).

A quadratic interpolation was used to determine the reactivity gain (loss)

at given values of the Gd destruction, V-235 destruction and Pu-239 den-

sity (see TABS 21 and 25 - 26).

.’

l

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7. Discussion of the Results

To facilitate the subsequent discussion of exposuz'e dependent effects it is

useful to begin with an analysis of the influence of the Gd poisoning on the

neutron flux and the microscopic capture and absorption rates (uc$ and ~a$)

in the fresh lattice.

3-group flux spectra in the regular lattice and in the poisoned cell at zero

burnup are compared in TAB 27. Due to the large thermal cross sections of the

Gd isotopes the flux below 0.6 eV is reduced in the Gd cell, while, above this

energy limit, no appreciable effect on the flux spectrum can be detected.

however, because of the normalisation to the equal power density of 20 W/g

in both lattices, the energy integrated flux is larger in all cells of the

poisoned lattice.

The hard spectrum reduces the one-group cross sections of.a.11 nuclides in the

Gd cell (TAB 28). The largest reductions occur for the nuclides with impor-

tant resonances in the thermal energy range, i.e. for the Gd isotopes, U-235

and Pu-239. The cross sections of U-238 and Pu-240, whose resonances lie

above 0.6 eV, are only slightly affected.

The net effects of the flux and cross section changes on the reaction rates

are as follows:

- Capture and absorption rates of u-235 and Pu-239 are smaller in the

poisoned cell than in the regular lattice.

- The V-238 reactions remain practically unchanged.

- Pu-240 reaction rates become somewhat larger in the Gd cell (TAB 28).

The relative effects on the time variation of the nuclide densities in the

regular and the poisoned case can now be understood easily:

- The smaller absorption rate of U-235 in the poisoned cell causes a smaller

amount of v-235 destruction (TABS 4 and 5).

- The smaller Pu-239 absorption, together with only a negligible change in

U-238 capture increases the buildup of Pu-239 in the poisoned cell (TABS

6 and 7).

- The larger Pu-240 absorption and smaller Pu-239 capture in the Gd cell re-

duce the. buildup of Pu-240 (TABS 8 and 9) and the Pu-24O/Pu-239 - ratio (TABS 22 and 23).

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TAB 11 shows that the large cross section of Gd-157 causes a fast depletion

of this nuclide.

Let us now compare the results of the different solutions for the benchmark

problem.

The axposura dependent multiplication factors for the regular and the Gd

poisoned lattice are listed in TABS 2 and 3 and plotted in FIGS 2 and 3. The

corresponding deviations from the mean multiplication factor are shown in

TABS/FIGS 16 and 17.

By extrapolating the multiplication factors at 1 GWd/t and 2 GWd/t to zero

burnup the xenoQ effects shown in TAB 29 have been derived. It can be seen

that both for the regular and the poisoned lattice the standard deviation

of the xenon effect is considerably smaller than the standard deviation of

the multiplication factor at ze.ro burnup. Furthermore, the magnitude of the

xenon effect seems to be insensitive to the Gd poisoning. In the following

discussion of the deviations between the solutions it can therefore be

assumsd that effects related to xenon are negligible.

For the regular lattice good agreement between the CEA, CISE, EIR and NAIG

multiplication factors can be observed. Relative to the mean value AEEW and

AMN predict higher and OSAkX ~predicts consistently lower multiplication fac-

tors. The variation is 1% at the beginning of life and remains practically

constant during burnup.

TAB/FIG 24 shows the reactivity loss above 1 GWd/t for the regular lattice.

As can be seen in TAB/FIG 25 the reactivity loss is correlated with the

U-235 destruction. As one would expect only a week correlation between the

reactivity loss and the Pu-239 density can be identified.(TAB/FIG 26).

For the poisoned lattice similar variations of about 1% as in the regular

lattice can be observed both at zero burnup and at the highest exposure of

10 GWd/t. However, in this case the variation reaches a maximum of 1.4% at

intermediate exposurt? values where relatively large fluctuations in the

reactivity deviation curves (FIG 17) occur. These fluctuations can be asso-

ciated with different Gd destruction rates (TAB/FZG 19) and the resulting

sff& on the Gd reactivity worth (TAB/FIG 1~8). In particular, the troughs

and humps in the curves are caused respectively by low Gd destruction rates

- 17 -

(as predicted by CISE and OSAkYA) and high Gd destruction rates (as predicted

e.g. by AEEW).

A comparison of FIG 20 and FIG 21 shows that in the poisoned lattice the

reactivity gain above 1 GWd/t is more strongly correlated with the Gd de-

struction than with the burnup. A plot of the reactivity deviations as a

function of Gd destruction would therefore show smaller fluctuations than

are visible in FIG 17.

The densities of the heavy isotopes U-235 and Pu-240 (TABs/FZGS 4, 5, 8 and

9) as well as the Pu-24O/Pu-239 ratio (TABs/FZGS 22 and 23) show larger

variations in the poisoned than ln the regular lattice. The opposite is true

for the Pu-239 density (TABS/FIGS 6 and '7). Surprisinyly, in the regular

lattice the variation of the Pu-240 density is signifjcantly smaller than

that of the Pu-239 density. Such a systematic effect could be caused by

spectrum variations in the regular cell. For instance, from a simple two-

group model it can be estimated that at low burnup an increase in the epi-

thermal-to-thermal flux ratio enhances the Pu-239 and, to a lesser extent,

the ~~-240 concentration, the ratio of the enhancement factors being appro-

ximately 1.3. It is worth noticiny that at 2 GWd/t the variations of the

Pu-239 and Pu-240 densities are in a similar ratio (TABS 6 and 8).

The pin powers are compared in TABs/FXGs 12 and 13. For the pin with.the

hiyhest rating (pin 4) and the poisoned pin the maximum standard deviations

are respectively 0.008 and 0.035 (Relative to the averaye power of the

lattice this corresponds to pin power variations of 0.8 and 3.5%). Duriny

burnup the standard deviations are nearly constant.

Although for this benchmark exercise neither an "accurate" reference solution

nor experimental bias factors are known, it may be interesting to compare the

observed standard deviations with typical target accuracies for power reactors.

In TAB 30 variations of some important parameters are listed together with

target accuracies recommended by a 1971 ZAEA panel on reactor burnup physics

(l3J. More recently (in 1978)‘ the same taryet accuracies were adopted by

Crowther et al. (g).

TAB 30 shows that for the regular lattice the variations are laryer than the

taryet accuracies, except for U-235 depletion. This is true particularly for

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the Pu-239 concentration which exceeds the target accuracy by a factor of 3.

RX- parameters related to reactivity of the poisoned lattice no significant

increase of the variations can be observed which could be attributed to the

additional complexity of this lattice. Whereas the variations of the isoto-

pic concentrations in the poisoned lattice appear to be large, the pin power

variations are acceptable, especially in the case of pin number 4 with the

highest rating. It should be remembered however, that bias factors ar.e un-

knowm and definite conclu$ions concerning the accuracy of the solutions can

therefore not be drawn.

8. conclusions.

From the comparison of the results of the gadolinium benchmark the following 0 conclusions may be drawn:

- The uncertainties in the prediction of important parameters of simple pin

cells seem to be relatively large, A standard deviation of 6% for the Pu-

239 build-up is hardly acceptable. iY can be expected that the deviations

are caused predominantly by differences in the data base. To identify the

origin of the differences more precisely, a further investigation would be

desirable.

- For the geometrically more complicated~~adolinium poisoned lattice no

significant or only a small increase of the variations of the multiplica-

tion factor and the reactivity life-time can be identified. The variation

of the Pu-239 build-up is smaller and the variations for U-235 depletion

and Pu-240 build-up are considerably larger than the respective values for

the regular lattice. To be able to separate data from methods effects it

would be necessary to repeat the calculations starting from a connnon data

base.

- Both in the regular and the poisoned lattice the ~xenon effect does not con-

tribute significantly to the variations of the parameters. It is interesting

to notice that the magnitude of the xenon effect is rather insensitive to

the Gd poisoning,

- 19 -

- With the aim to identify particularly large parameter variations a compari-

son with target accuracies for power reactors has been made. Variations

exceeding the target accuracies by a factor of 2 or mre are observed for

the multiplication factors, the reactivity life-time in the poisoned

lattice and the Pu-239 build-up.

- If systematic biases are small compared with the variations it can be tenta-

tively deduced that pin powers in the poisoned lattice are predicted ade-

quately. For the Gd pin a somewhat larger pow& variation than for a nor-

mal fuel pin seems to be acceptable, since the rating is lower and the

number of Gd pins is small. Regarding the multiplication factor and the

reactivity life-time it can be said that, if the accuracy requirements ara

judged to be fulfilled for the simple pin cell, this can also be assumed

for the Gd poisoned lattice.

It should be mentioned that none of the solutions takes an azimuthal depen-

dence of the Gd depletion into account. Appendix A shows that the azimuthal

variation of the flux and the power is relatively small, indicating that in

normal design calculations azimuthal effects can be neglected.

9. References

(l-J M.J. Halsall, "Review of International Solutions to NEACRP Benchmark

BWR Lattice Cell Problems", AEEW-R 1052 ?1977)

(z) C. Maeder, K. Kowalska and B.A. Solotar, "A Computational Benchmark for adjacent poisoned fuel rods", Trans. Am. Nucl. Sot. c, 19& (1982)

CL) C. Maeder and P. Wydler, "Specifications for a BWR Benchmark Problem

with Adjacent Poisoned Fuel Rods", NEACRP-A-460 (1981).

(51 C. Naeder and P. Wydler, "Burnup Calculations for a BWR Lattice with

Adjacent Poisoned Fuel Rods", NEACRP-A-521 (1982)

(2) M.J. Halsall, "LWR-WXMS, A Computer Code for Light Water Reactor Lattice Calculations", AEEW-R 1498 (1982)

- 20 -

Cc) M.J. Halsall, "The Treatment of Burnable Poison Pins in LWRWZMS",

AEEW-M 1999 (1982)

(L) A. Hoffmann et al., "APOLLO, code multigroupe de r&solution de l'&qua-

tion du transport pour les neutrons thermiques et rapides",Note CEA-

N-1610 (1973)

(g) A.H&bert, "Development of the SPH method: cell homogenisation of a

zion-uniform lattice and reflector parameters calculation", Note CEA-

N-2209 (1981)

(2) P. Peroni and U. Ciarniello: Report CISE-1784 (1982)

(g) C. Maeder and J.M. Paratte, %.lculation of LWR Fuel Elements Con-

taining Burnable Poisons and Plutonium", Trans. Am. Nucl. Sot. z,

259 (1975)

(g) M. Yamamoto et al,, "Validation of the TGBLA BWR Bundle Design

Methods", Trans. Am. Nucl. Sot: e, 698 (1982)

(z) E. Saj, S. Sakurai and T. Takeda, "Application of the Response Matrix

Method to BWR Lattice Analysis", Annals of Nuclear Energy g, 155 (1981)

(2) "Reactor Burnup Physics", Proc. of an TAEA panel, 12-16 July 1971,

p. 278, Vienna (1973)

(E) R.L. Crowther et al., v*Feedback of Reactor Operating Data to Nuclear

Methods Developmentr', Proc. ANS Topical Meeting, Gatlinburg, p. 285 (1978)

(E) C. Maeder, internal EIR-report (August 1980)

(E) H. Neltrup, internal RISU-report (March 1983)

(g) T. Sate et al., internal report of the university of OSAm (1982)

(2) A. Ahlin and M. Edenius, "MICBm-CASMO/CPM for Analysis of Assemblies

with Gadolinium", Trans. Am. Nucl. Sot. 4& 590 (1~982)

- 21 -

'.

(El K. Kowalska, "The S-WIMS Code for the CYBER-72 Computer", INR-Report

No. 1509 (1975)

(g) J.R. Askew, F.J. Fayers and P.B. Kernshell, "A General Description of

the Lattice Code WIMS", 3. Brit. Nucl. En. Sot. !$ 564 (1966)

(2) E. Cupini et al., "KIM - A mo-Dimensional Monte Carlo Proyram for

Thermal Reactors”, CNEN-RT/FIMA(80)2 (1980)

Acknowledcjment

The authors are indebted to J.M. Paratte, El'R for valuable discussions

and suyyestions.

TAB. 1: a9unmzry of calc~~l.atio,,al methods

AEE!+Q

WINS (ENDF/B-4 for Gd)

RESPLA

69

6

Data 1ibw.y UIMS ENDF/B-4 ENDF/B-3 + MUFT-I V+TEMPEST ENDF/E-4 ENDF/B-4 + ENDF/B-4 (THERMOS for Cd) ENDF/B-5

Code &me LWR-WIMS BLA APOLLO NUOVO AUTOBUS EOXER TGBLA

Pin cell calculatb?l: nr. of groups 28 68 99 30 70 P8

nr.’ of zones in Gd-pin 4 4 3 16 4 10

Lattice calcu- klt?h

methodb D~/ch.m. D DPO D QPl D

m: of groups 6 3 99 3 11 3

nr. of zones 1 b-0 70 32 56 144 16 16

nr. of t&e pchte 11 14 16 14 17 13

horn: OF het.~ calculAt&t= hom/het het bet horn horn horn

a Fh’st/mmmd entry: Calcuk,t,k, bewee,, 1 and IO F / at ze,.o b,,z.,,up

-

b D : Diffusion cal.c,xlation DPO, DPl, QPl: Transport calculation with double Po, ch. m. : Characteristics transpoz.t method

double PI or quadmple PI approx<mation at cell boundaries

c horn : Fuel cell.6 (fuel p<n, clad and moderator) az.e homoge,,<zed het : .Yet&wgenous calculation withhat cell homogenizat<on

DPl

6

58

22

bet

CISE NAIG EIR os4.u

,

TAB. 2 K-INFINITY FOR REGULAR LATTICE *

------------------------------------------------------------------------------------------ EXPOSURE AEEW AMN CEA CISE EIR NAIG OSAKA MEAN VARIATION

(GWD/T)

OCNO XE) 1.3514 1.277'3 1.2926

1.3400 1.2681 1.2794

1.3298 1.2742

1.3278 1.27!+2 ; *;;z

1.3340 1.3060 1.3315 i 1.2767 1.2537 1.2752

1.2623 1.2613 I:2626 1.2646 1.2424 1.2627 008 z 1.2489. 1.2630 1.2445 1.2563 1.2495 1.2488 1.2501 1.2515 1.2301 I.2499 :008

1.2369 1.2357 1.2373 1.2381 1.2172 I.2369 008 5 1.2349 1.2329 1.2240 1.2238 1.2245 1.2246 1.2040 1.2241 :008 6 1.2213 1.2214 1.2111 1.2111 1.2119 1.2114 1.1908 1.2113 008 7 1.2080 1.2098 I.1987 .I.1993 I.1996 1.1985 I.1779 1.1988 :009 8 1.1951 1.1986 1.1865 1.1876 1.1875 1.1860 1.1652 1.1866 .009 9 'I.1825 1.1882 1.1747 1.1764 1.1758 1.1529 .009

10 1.1703 1.1781 1.1633 1.1652 XT 1.1645 . x;; 1.1410 . . 010 ------------------------------------------------------------------------------------------

TAB. 3 K-INFINITY FOR POISONED LATTICE ------ ------------------------------------------------------------------------------------------ EXPOSURE AEEW AMN CEA CISE EIR NAIG OSAKA MEAN VARIATION

(GWD/T) ------------------------------------------------------------------------------------------ OCNO XE) 1.0093 1.0140 .9970 1.0164 1.0110 1.0004

1 1.0024 1.0036 .9991 1.0058 I.0093 1.0044 : Z 1.0054 010 1.0020 :006

2 1.0295 1.0316 1.0?14 1.0286 1.0403 1.0368 1.0162 1.0306 .007

z I.0655 I.0631 1.0658 1.1042 1.1002 1.1035

5 1.1516 1.1412 1.1433 6 1.1866 1.1747 1.1731 7 1.1989 1.1895 1.1811

; I.1439 l.l8$i 1.1756 1.1832 I.1819 1.1654

10 1.1715 1.1727 1.1546

.0531

.0884 1196

:1501 1717

:I788

: E

.072? l.Oi9il 1.0439 I.0516 004

.I083 1.1051 1.0742 I. 0977 :011

: i;;; 1.1419 1.1714 1.1105 1.1465 1.1365 1.1683 .014 012

:I861 1895 1.1803 1.1834 1.1650 1.1651 1.1813 1.1827 :010 008

:I657 1765 1.1595 1.1707 1.1566 1.1466 1.1618 1.1724 :008 .008

TAB. 4 U-235 DENSITY FOR REGULAR LATTICE(l.O-4/BARN X CM)

--------------------------------------------------------------------------------- -~~~~--~~ EXPOSURE AEEW AMN CEA CISE EIR NAIG OSAKA MEAN VARIATION

(GWD/T) ------------------------------------------------------------------------------------------

0 2 ?Z

517f34 z;: 5:7a9

:z 6.777 6.775

Z~ 6.776 6.776 .ooo

517a9 6.253 6.257

5:770 6.243 6.254 .OOl

t2 5.769 5.780 5.757 5.777 .002

5.341 5.359 5.350 5.319 5.325 5.3Oi3 .003 a 4.927 4.959 4.940 4.898 4.911 4.a92 005

10 4.539 4.586 4.556 4.503 4.525 4.504 :006 ------------------------------------------------------------------------------------------

TAB. 5 U-235 DENSITY IN POISONED PIN(l.O-4/BARN X CM) ------

EXPOSURE AEEW AMN CEA CISE EIR NAIG OSAKA MEAN VARIATION (GWD/TJ

------------------------------------------------------------------------------------------ .O 6.573 6.572 6.571 6.574 6.572 6.572 6.572 6.572 000

2 6.353 6.352 6.340 6.374 6.33a 6.339 6.332 6.347 :002

i 6.059 6.077 6.036 6.115 6.032 6.038 6.041 6.057 .005 5.678 5.728 5.658 5.663 5.668 5.683 5.696 .009

a 5.256 5.342 5.248 x 5.249 5.269 5.291 10 4.a47 4.969 4.a53 5:003 ;* 2 4.861 . 4.860 4.894 ::;g

------------------------------------------------------------------------------------------

:

TAB. 6 PU-239 DENSITY FOR REGULAR LATTICE(l.O-5/BARN X CM) ------ ------------------------------------------------------------------------------------------ EXPOSURE AEEW AMN CEA CISE EIR NAIG OSAKA MEAN VARIATION

(GWD/T) , ------------------------------------------------------------------------------------------

2 2.075 2.529 2.233 2.137 2.225 2.215 2.393 2.258 068 4 3.808 4.557 4.020 3.848 4.011 4.048' 4.281 4.082 :064

TAB. 7 PU-239 DENSITY IN POISONED PIN(l.O-5/BARN X CM)

------------------------------------------------------------------------------------------ EXPOSURE AEEW AMN CEA CISE EIR NAIG OSAKA MEAN VARIATION

(GWD/T) ------------------------------------------------------------------------------------------

z 4.210 2.268 2.227 4.207 2.241 4.097 2.136 3.964 2.408 4.385 2.185 4.052 2.410 4.401 2.268 4.188 :039 046

6 5.671 5.891 5.542 5.427 5.856 5.498 5.975 5.694 .038 8 6.765 7.289 6.943 6.624 7.185 6.859

10 7.639 8.440 7.815 7.537 8.145 7.792 :%i ------------------------------------------------------------------------------------------

TAB. 8 PU-240 DENSITY FOR REGULAR LATTICE(l.O-6/BARN X CM) ------ ------------------------------------------------------------------------------------------ EXPOSURE AEEW AMN CEA CISE EIR NAIG OSAKA MEAN VARIATION

(GWD/T) ------------------------------------------------------------------------------------------

TAB. 9 PU-240 DENSITY IN POISONED PIN(l.O-6/BARN X CM) -*---- ------------------------------------------------------------------------------------------ EXPOSURE AEEW AMN CEA CISE EIR NAIG OSAKA MEAN VARIATION

(GWD/T) ------------------------------------------------------------------------------------------

2 .605 .521 .625 .520 ,676 .612 .750 .616 133

: 2.492 2.102 2.438

e;;; ;- 2% ;* ;;i 2.799

;%z :I08

5.. 506 4.643 5.194 8 9.127 7.745 8.479 71725 9: 193 81870

5.813 094 9.479 a:660 :081

10 12.919 11.073 11.928 11.340 12.750 12.540 13.410 12.280 .070 ------------------------------------------------------------------------------------------

.’ , l

TAB. 10 GD-155 DENSITY IN POISONED PIN(l.O-4/BARN X CM) --e--v- ------------------------------------------------------------------------------------------ EXPOSURE AEEW AMN CEA CISE EIR NAIG OSAKA MEAN VARIATION

(GWD/T) ------------------------------------------------------------------------------------------

0 1.47E+OO 1.47E+OO 1.47E+OO 1.47E+OO l.47E+OO'l.47E+OO 1.47E+OO 1.47E+OO 9.94E-01 9.88E-01 9.34E-01 l..O4E+OO 9.67E-01 9.53E-01 l.OlE+OO 9.84E-01 6.95E-01 7.OlE-01 6.39E-01 7.8lE-01 6.79E-01 6.72E-01 7.47E-01 7.02E-01 .068

4 4.19E-01 4.43E-01 3.85E-01 5.3lE-01 4.2lE-01 4.2lE-01 4.89E-01 4.44E-01 .112 1.97E-01 2.3lE-01 1.88E-01 3.12E-01 2.lOE-01 2.17E-01 2.6lE-01 2.3lE-01

------------------------------------------------------------------------------------~~~~--

6.56E-02 9.15E-02 6.24E-02'1.47E-01 8.12E-02 8.23E-02 9.95E-02 8.99E-02 7 1.59E-02 2.82E-02 1.65E-02 5.05E-02 1.93E-02 2.32E-02 2.65E-02 2.57E-02

TAB. 11 GD-157 DENSITY IN POISONED PIN(l.O-4/BARN X CM) ------- ------------------------------------------------------------------------------------------ EXPOSURE AEEW AMN CEA CISE EIR NAIG OSAKA MEAN VARIATION

(GWD/T) ------------------------------------------------------------------------------------------

0 1.56E+OO 1.56E+OO 1.56E+OO 1.56E+OO 1.56E+OO 1.56E+OO 1.56E+OO 1.56EtOO 000 2 5.OOE-01 5.43E-01 5.lOE-01 6.06E-01 5.45E-01 5.37E-01 5.45E-01 5.4lE-01 :063

z 2.18E-01 2.66E-01 2.39E-01 3.2lE-01 2.56E-01 2.58E-01 2.55E-01 2.59E-01 122 5.95E-02 9.27E-02 6.99E-02 1.32E-01 8.29E-02 8.93E-02 8.63E-02 8.75E-02 :260 5.8OE-03 1,59E-02 8.7lE-03 3.96E-02 9.42E-03 1.53E-02 1.29E-02 1.54E-02 .735

7 9.48E-05 1.23E-03 1.65E-03 4.94E-03 2.56E-04 l.gOE-03 3.7OE-04 1.49E-03 ;.;;; 2.75E-07 7.lOE-04 4.04E-05 1.2l,E-04 9.32E-07 1.26E-03 1.82E-06 3.04E-04 .

------------------------------------------------------------------------------------------

TAB. 12 POWER IN PIN 4 (-) -------

EXPOSURE AEEW AMN CEA CISE EIR NAIG OSAKA MEAN STA. DEV. (GWD/T)

0 1.163 1.165 1.159 I.153 1.159 1.166 1.178 1.163 008 2 1.118 I.123 1.111 1.116 1.113 1.113 1.126 1.117 :006 4 1.060 1.074 1.057 1.070 1.062 1.060 1.071 1.065 .007

i 1.004 1.027 I.009 1.023 1.014 1.012 1.014 1.015 008

1.010 .996 .997 .996 .996 :007 10 % . 1.008 .995 :E -996 .995 :;;: .gg5 .006

------------------------------------------------------------------------------------------

TAB. 13 POWER IN POISONED PIN c-j ---v--e ------------------------------------------------------------------------------------------ EXPOSURE AEEW AMN CEA CISE EIR NAIG OSAKA MEAN STA. DEV.

(GwD/T) ------------------------------------------------------------------------------------------

0 .462 .384 .355 .391 411 .394 035 2 :;2 .592 .563 .507 :;i; .566 :559 .553 :026 4 .771 .755 .769 .674 .736 .757 .731 .742 .034

: 985

1:045 :;2! .956 870 936 .935 .932 .035

1.007 1:022 :;;A 1:003 1.018 1.010 021 10 1.047 .990 1.010 1.041 .gg4 1.008 I,. 022 1.016 :022

------------------------------------------------------------------------------------------

.

l ,

TAB.14 RAD. GD-155 DISTRIBUTION AT 2 GWD/T ------ --ee--- ---------------------------------------------------------------------------------

R;;&- AEEW AMN CEA CISE EIR NAIG OSAKA MEAN VARIATION

------------------------------------------------------------------------------------------

:;2 1.273 1.264 1.278 I.363

zz 1.279 1.264 1.289 027

1.176 1.188 1.174 1.276 1.187 1.167 1.198 I032 .39 .947 .952 .879 1.004 :946 .914 .969 .945 .042

----~~~-----:~~~-----~~~~-----:~~~-----~~~~-----~~~~-----:~~~-----~~~~-----~~~~-----:~~~--

a At the centre of the annular region

TAB.15 RAD. GD-157 DISTRIBUTION AT 2 GWD/T w-mm-- ------------------------------------------------------------------------------------------

RADIUS AEEW AMN CEA CISE EIR NAIG OSAKA MEAN VARIATION (CM)

------------------------------------------------------------------------------------------

:;i 1.027 1.088 1.038 1.157 1.081 1.074 1.041 1.072 041

.705 .797 .715 .8a5 -812 .780 .744 .777 :080 .39 .335 .396 .277 .276 .335~ ,,~ .314 180 .47 .ooo .ooo .008 .018 .062 .025 I:027

------------------------------------------------------------------------------------------

TAB.16 REACTIVITY DEVIATION FROM MEAN FOR REGULAR LATTICE(-) ------ ---------------------------------------------------------------------------------- -------- EXPOSURE AEEW AMN CEA CISE EIR NAIG OSAKA MEAN STA. DEV.

(GWD/T) ------------------------------------------------------------------------------------------ OCNO XE) .015 .006 -. 001 -.003 000 .002 -. 019 000 010

1 014 :012

-003 -. 001 .ooo -:001 .OOl -.017 : 000 : 009 2 .004 -. 000 -.OOl -. 000 -.016 .ooo 008

z 010

:010 005

:006 -. 000 -. 001 000

: 000 :E -.016 000 :008

-.ooo -. 001 .OOl -.016 : 000 .008 5 .oog 007 -. 000 -. 000 .ooo .ooo -.016 .ooo .008 6 008

ii :008

:008 -. 000 -. 000 .OOl .ooo ,-.017 000 .008 009

:010 -.ooo .ooo 001

:001 -. 000 -.017 : 000

.007 -. 000 .OOl -.OOl -.018 000 :::; 9 .006 .Oll -. 000 .OOl -. 001 -. 019 : 000 009

10 . 006 .013 -. 000 -001 ::i; -.OOl -.019 .ooo :010 ------------------------------------------------------------------------------------------

TAB.17 REACTIVITY DEVIATION FROM MEAN FOR POISONED LATTICE(-)

------------------------------------------------------------------------------------------ EXPOSURE AEEW AMN CEA CISE EIR NAIG OSAKA MEAN STA. DEV.

(GWD/T) ----------------------------------------------------------------~------------------------- OCNO XE) .004 009

:002 -.008 .Oll .006 -.005 -.015 000 010

1 .ooo -.003 .004 .007 .002 -.012 : 000 :006 2 -.OOl -001 .OOl -.002 .006 -.014 000 007

i 001

:006 .OOl .004 -.008 :% 008 -.017 : 000 :009 .002 .005 -.008 010 :007 -.021 000 011

2 .013 004

:006 .006 -.015 :010 -.023 : 000 :014

.016 .004 -.016 .006

.

. . .

TAB.18 GD-REACTIVITY WORTH(-)

------------------------------------------------------------------------------------------ EXPOSURE AEEW AMN CEA CISE EIR NAIG OSAKA MEAN STA. DEV.

(GWD/T) ------------------------------------------------------------------------------------------ OCNO XE) .253 243

:216 .250 -235 .241 250 242 .245 007

1 .225 216 :I83

211 2 194

:;W$ .186 :184

208 :I76

:213 :211 .214 :005 180 182 184 006

3 4

:067 :Ki

147 :I08

157 :119

142 :104

:145 :151 :151 :006 107

2 .074 066 .085 .063 :068 :A;; 2;:

.006 008

028 :008

038 :017

:031 .050 .030 .033 .037 .036 :007

; 015

: 009 .023 008

:001 .013' .Oll

.OOl .008 007 .ooo :iE 005

:004 9 -. 001 005

:005 008 :003 -. 001 ::g -.003 .004

10 -. 001 :007 .003 -.OOl .002 -.005 :K .004 ------------------------------------------------------------------------------------------

TAB.19 GD-DESTRUCTION IN POISONED PIN (-) ------ ----------------------------------------------------------------~------------------------- EXPOSURE AEEW AMN CEA CISE EIR NAIG OSAKA MEAN STA. DEV.

(GWD/T) ------------------------------------------------------------------------------------------

2 .507 .495 .524 .456 .501 .509 .486 .497 .021

i .699 .681 .7lO .636 .691 .fj!u .669 .683 .024 .842 .823 .850 .781 ,834 .832 .810 .825 023

2 .933 .918 .935 .884 .928 - 923 .910 .919 :018 .978 .969 .979 .950 .973 .972 .967 .970 .OlO

TAB.20 REACTIVITY GAIN FOR POISONED LATTICE(-) ------ ------------------------------------------------------------------------------------------ EXPOSURE AEEW AMN CEA CISE EIR NAIG OSAKA MEAN STA. DEV.

(GWD/T) ------------------------------------------------------------------------------------------

; .027 028 032 023 032 .027 029 .003

060 :102

1059 :067 :047 22; :065 055 :086

:059 .007 4 .096 .104 .082 .098 .I00 .095 .008

TAB.21 REACTIVITY GAIN(-) AND GD-DESTRUCTION(-) m-e-e-

GD-DEST. AEEW AMN CEA CISE EIR NAIG OSAKA MEAN STA. DEV. ------------------------------------------------------------------------------------------

.50 .026 .029 .029 .027 .031 .031 .029 ,029 002 .60 .040 043

:064 044

:064 .040 045

:065 .047 043

:059 043

:063 :002

2: .060 .061 .067 .003

085 .Q88 .086 .087 .090 .083 087 .002 .90 :I28 127 :Z 119 123 117 :I24 .004

1.00 .200 :I92 .185 :177 :I83 2; :I85 .I86 .007 -------~----------------------------------------------------------------------------------

:

TAB.22 PU-24O/PU-239 DENSITY FOR REGULAR LATTICE t-) ------ ------------------------------------------------------------------------------------------ EXPOSURE AEEW AMN CEA CISE EIR NAIG OSAKA MEAN VARIATION

(GWD/T) ------------------------------------------------------------------------------------------

TAB.23 PIJ-24O/PU-239 DENSITY IN POISONED PIN (-) -e-w-w ------------------------------------------------------------------------------------------ EXPOSURE AEEW AMN CEA CISE EIR NAIG OSAKA MEAN VARIATION

(GWD/T) ------------------------------------------------------------------------------------------

2 .027 .023 .028 024 028 .028 031 027 W6

: .059 .050 060 :052 :060 .061 :064 :058 :085

097 :135

.079 : 094 084 ,097 .098 .097 .084 8 106

:131 .I27 :I18

3; 134

:I66 132 :!Zi

:165 .I58 084

10 . 169 .I57 .I54 :082 ------------------------------------------------------------------------------------------

TAB.24 REACTIVITY LOSS FROM 1 GWD/T FOR REGULAR LATTICE (-) ------ ------------------------------------------------------------------------------------ ------ EXPOSURE AEEW AMN CEA CISE EIR NAIG OSAKA MEAN STA. DEV.

(GwD/T) ------------------------------------------------------------------------------------- -m--m

2 012 009 .009 011 .oog 009 .009 .Ol 0 .OOl

z :034 :027 .029 :031 .029 :030 029 .055 045

:063 050

:069 -050 049

:06a 051

:071 :050

:030 050

a .075 .069 071 : 069 :g

10 .095 -079 .oa7 .oa6 .oa6 .090 1090 .oaa .004 .005

------------------------------------------------------------------------------------------

TAB.25 REACTIVITY LOSS(-) AND U-235 DESTRUCTION(-) FOR REGULAR LATTICE v-e-e- ------------------------------------------------------------------------------------------ U235 DES AEEW AMN CEA CISE EIR NAIG OSAKA MEAN STA. DEV. ------------------------------------------------------------------------------------------

.oa :i;;

.OlO .Oll .012 .OlO .OlO .009 011 .OOl .I4 026 .02a 02a .027 02a .026 102a 002

:2 .051 :043 .046 :046 .045 :047 .045 .046 :003

071 . 32 :091

061 107a

.065 064 1oa2

064 .066 .065 .oa5 1oa3 .oa6 .oa5

065 1oa4

003 :004

------------------------------------------------------------------------------------------

TAB.26 REACTIVITY LOSS(-) AND PU-239 DENSITYlIE-5/BARN X CM) FOR REGULAR LATTICE ------ ------------------------------------------------------------------------------------------

PU-239 AEEW AMN CEA CISE EIR NAIG OSAKA MEAN STA. DEV. ------------------------------------------------------------------------------------------

2.ao 020 :035

011 :021

.015 ola 015 015 3.90 .02a I032 102a 102a

.013 015 003

.024 102a :005 5.00 052

:071 032

:044 .043. 047

:063 2;; .043 .039 042

:059 .006

6.10 .059 .060 .055 ooa 7.20 .093 .059 .079 .oa5 .07a .oao .074 .07a :011

------------------------------------------------------------------------------------------

,

- 35 -

TAB. 27 Average fluxes in the regular and in the poisoned pin cell

(EIR results at 0 GWd/t)

Energy range Flux $I (1013/cm2sec)

cew Regular lattice Poisoned cell

1.5.lo7 - 900 8.95 11.52

900 - 0.6 2.86 3.69

0.6 -0 2.53 2.04

1.5*107 - 0 '14.34 17.25 ,

4 poi ' 'reg

1.29

1.29

0.81

1.20

l'AB. 28 cell-average, microscopic, one-group cross sections and

reaction rates (EIR-results at 0 GWd/t)

Quantity Nuclide Regular lattict? Poisoned cell

0 Gd-155 2500 200 a (barn) Gd-157 10800 770

U-235 65 20

V-238 1.01 0.84

Pll-239 208 91

Pu-240 242 221

'c ' 'a U-235 0.18 0.25

L-j U-238 0.89 0.87

Pll-239 0.36 0.39

~~-240 1.00 1.00

Oa @ U-235 93 35

-10 -1 (10 set ) V-238 1.45 1.45

Pu-239 298 157

Pu-240 347 381

- 36 -

TAB. 29 Xenon reactivity worth at 0 GWd/t in mk (1 mk = 0.001)

solution Regular latt&?

AEEW 32.2

AMN 36.8

CEA 32.9

USE 29.1

EIR 34.1

NAIG 33.9

OSAKA 31.4

Mean 32.9

%a.dev. 2.4

Poisoned lattice Reg.-poi.

33.7 - 1.5

37.9 - 1.1

30.3 2.6

32:9 - 3.8

32.3 1.8

28.4 5.5

27.4 4.0

31.8

3.5

1.1

2.3

- 37 -

TAB. 30 Target accuracy and variation of resuk?

ParY7mete~ Target variation C%) am2.uwey C%) - from Ref.(E) Reg.kttice Pois.lattice

MultipIication f?actor 0,25-0.5 0 GWd/t 1.0 1.0 5 GWd/t 0.8 1.4

10 GWd/t 1.0 0.8

Reactivity life-time 2-5 5.@ 7. la

Changes in isotope eomp: ~235. depletion 2 1.2 3.7 h23g build-up 2 6.0 4.8 Pu240 build-up 1.8 7.0

Pin power rekxtive to LattSce 2 Pin no. 4 (max. rating) 0.8

Gd pin 3*5

a) From standard deviations of reactivity Losses between 1 and 10 GWd/t

(0,005 and 0.0064 respectively for the regdar and the poisoned lattice)

assuming a reactivit$ swing of 1% pep GWd/t at the end of life.

- 38 -

1.30

1.25

1.20

1.15

1.10

FIG. 2 K-INFINITY FOR REGULRR LRTTICE 1.20

1.15

1.05

---- WIN w.-.m.vCER -~-..- CISE -...-...- EIFI . . . . . . . . . . . . NFIIG

X OSRKR , I , I

0. 2. A. 6. 0. 10.

EXPOSURE (GWO/TJ

FIG. 3 K-INFINITY FOR POISONEO LRTTICE I I I

---- RNN -.-.-.-CER -..-..- CISE

2. A. 6. a. EXPOSURE lGWO/T)

FIG. 4 U-235 FOR REGULFIR LRTTICE 1 , 1 ,

flEE!A ---- RMN -.-.-.-CER -..- ..- CISE -...-...- EIR

. . . NRIG x USRKR

EXPOSURE (Gi.D/TJ

6.5

5.0

FIG. 5 U-235 IN POISONED PIN

---- l=iMN -.-.-.-CEfl -..- ..- CISE -...-...- EIIT . . ..- . . NRIG

d.5 na 2. b. 6. 8. I

EXPOSURE fGWU/Tl

. . :

.,

FIG. 6 PU-239 FOR REGULRR LRTTICE

8. &

REEW ---- FlilN -.-.-.-CEB -..-..- CISE - .- - EIR . . . NRIG

X OSRKR , 1 ,

A. 6. 8. EXPOSURE cGWD/Tl

FIG. 7 PU-239 IN POISONED PlN I 1 1 1

,

---- RHN -.-.-.-cm -..- ..- CISE -...-...- EIR . . .-.. . . . .-. . NFIIG

X OSRKR 1 , I I

2. 4. 6. 8. 10. EXPOSURE cGWD/Tl

, : 4 p’

13. FIG. 8 PU-240 FOR REGULRR LRTTICE

\ , , I

FIEEW ---- RMN -.-.-.- CER -..-..- CISE -...- . ..- EIR

~~~ NTG 1

6. 8. 10.

FIG. 9 PU-240 IN POISONED PIN

13. cjg

--. -

11. -

10. -

9. -

a. -

7. -

REEW ---- FlMN -.-.e.-CEfl -..-..- CISE -...-...- ElR . . . . . . . . . . . . . . NRIG

X OSRKR 0. , ,

0. 2. A. 6. 8. 10. EXPOSURE cGWO/Tl EXPOSURE lGWO/TJ

.’ ,

‘, *

l

1.6 FIG. 10 GO-155 IN POISONEO PIN 1.6

FIG. 11 GO-157 IN POISONEO PIN 1 1 I I I ,

0.4

REEW ---- RMN w.-.-.-CER -..-..- CISE

. NRIG X OSRKR

2. 4. EXPOSURE cGWO/Tl

6.

l .

1.4

Ii

\ 1.2

"\

REEW ---- FINN -.-.-.-CEI? -..-..- CISE -...-...- EIR . NfiIG

X OSRKR

0.4 1

0. 2. 4. 6.

1.10

E :

1.05

FIG. 12 POWER IN PIN 4 , I 1 I

REEW ---- RMN m.-.v.-CER -~-~- CISE -...-...- EIR . . . . . . . . . . . NRIG

X OSRKR

I I , ,

2. 4. 6. 8. EXPOSURE (GWD/Tl

1.1

0.8

0.7

0.6

0.5

0.4

FIG. 13 POWER IN POISONEO PIN 1 I I 1

J

REEM ---- FNIN v.-.-.-CER -..- ..- CISE -...-... - EIR . . . . . . . . . . . . NRIG

t X OSRKR 0.3 1 1 , , 1

0. 2. 4. 6. 8. 10. EXPOSURE tGWD/T)

: ,

. . . a 1 4 FIG.14 FiRD. GO-155 DISTRIBUTION RT 2 GWO/T

r , I , 1

0.3 - REEW

---- WIN -.-.-.-CER -..-..- CISE -...-...- EIR . . . . . . . . . . . . . NRIG

X OSRKR 0.0 I 1 I I I

0. 0.1 0.2 0.3 0.4 RRDIUS(Ctll

-

0.5

1 4 FIG.15 RRD. GO-157 CIISTRI8UTION RT 2 GWD/T

I I I , I

1.3

1.2

1.1

1.0

0.2

0.1

0.0

L----- --- . lzz .---.

f?EEW ---- RHN -.-.-.-CER -..-..- CISE -...-...- EIR . . NRIG

X OSFIKR

7

-

-..-~. .-.-

0. 0.1 0.2 0.3 0.4 RRCIIUS~CN~

zl -.. 0.5

0.04 FIG.16 RERCTIVITY IJEV. FOR REGULFIR LRTTICE

1 I L I

REEW ---- RMN

0.03 -.-.-.-CER - CISE

-...-...- EIR . . . . . . . . . . NRIG

X OSRKR 0.02

-0.03 < 0. 2. A. 6. a. 10.

EXPOSURE cGuwT1

0,04 FIG.17 REQCTIVITY DEV. FOR POISONED LRTTICE

, I 1 I

REEW ---- RNN

0.03 - e.-.-.-CER -~-..- CISE -...-...- EIR . . . . . . . . . . . . NFIIG

X OSRKR 0.02 -

----...-.

-0.01 -

X

-0.02 -

-0.03 > 0. 2. A. 6. 0. 10.

EXPOSURE lGlJL'/TJ

.’ ,

. . .

0.00

FIG.18 GO-REFICTIVITY WORTH

FIEEW ---- RNN -.-.-.vCER -..-..- CISE -...-...- EIR

-....-.....

NFIIG X OSRKR

-0.05 7 0. 2. A. 6. 0. 10.

EXPOSURE ~G!-dD/Tl

. .

l

1.0 , FIG.19 GD-DESTRUCTION IN POISONED PIN

0.9 -

0.8 -

0.7 -

0.6 -

7

5 p 0.5 -

2 E 2 0.A-

0.3 -

FIEEW ---- ITIN -.-.-.-CEfl -..-..- CISE -...-...- EIR

. NRIG X OSFIKFI

EXPOSURE tGWD/Tl .,.

0.20

0.15

0.05

0.00

FIG.20 RERCTIVITY GRIN FOR POISONED LRTTICE I I

REEW ---- RMN -.-.-.-CC4 -~-..- CISE -...-...- EIR . . . . . . . . . . . . NFIIG

X OSFiKFi

EikOSURE cGWD/TJ

0 20 FIG.21 RERCTIVITY GRIN RN0 GO-DESTRUCTION I',"'.,',,'.","'."""

0.05

0.00 e

FlEEW ---- WIN -.-.-.-El? -~-..- CISE -...-...- EIR

NRIG X OSflKfl

I . . . . I. I . 1..

, 0.6 0.7 0.8 0.9 GO-OESTRUCTIONI-I

.,

0.00

.

l . . . .

FIG.22 PU-240/PU-239 DENSITY FOR REGULRR LRl .TIl CE , , 1 I

/

/.

Iin

I’

---- RNN e.e.-.-CER

1'

-..-..- CISE -...-...- EIR . . NR:

X OSRKR 1 1 I 1 2. 4. 6. 0. 10.

EXPOSURE cGWD/Tl

:IG.23 PU-240/PU-239 DENSITY IN POISONED PIP I 1 1 I

,

---- RHN v.m.-.-CER -..-..- CISE -...-...- EIR . . . . . . . . . . ...'. NRIG

y OSRKR 1 I I 1 2. A. 6. 0. 10.

EXPOSURE IGWCVTI

0.10

0.09

0.08

0.07

7 0.06

Tl g J 0.05 z 2 ’ 0.04 E &

0.03

0.02

0.01

0.00

FIG.24 RERCTIVITY LOSS FOR REGULFIR LRTTICE 1 , I ,

4

REEW ---- FINN e.-.-.-CER -~-..- CISE -...-...- EIR . . . . . . . . . NFIIG

X OSRKR

EXPOSURE ~G'AO/Tl

0.10

0.08

0.07

0.03

FIG.25 REXTIVITY LOSS RN0 U-235 FOR REG. LFITTICE , 1 1 1 1

---- WIN -.-.-.-CCR -~-..- CISE -...-...- EIR . . . . . . . . . . . . . NRIG

0.00 1 , , 1 i , 0.08 0.12 0.16 0.20 0.24 0.28 0.32

U-235 OESTRUCTION(-1

.~ . .

0 l0 FIG.26 REQCT. LOSS RN0 IV-239 FOR REG. LRTTICE , '. , " , " x , " ,

0.08 -

0.07 -

7 0.06 -

ci z J 0.05 - z 2 2 c-j 0.04 -

i2

0.03 -

0.00-,.,,,,,,,,,,,,,,.,.,,. 2.8 3.6 4.4 5.2 6.0 6.8

PU-239 DENSITY(l.0-S/BRRN X CM1

- Al -

APPENDIX A Shadowing Effect of Poisoned Pins

At EIR, c. Maeden pesfomned a burnup calculation up to 5 GWd/t with a sub-

division of the Gd cell into 2x2 meshes for the few-group lattice calcula-

tion (E). The subdivision is illustrated in FIG Al, Case A. During burnup

the isotope densities in the Gd pin were tracked in 16 regions, 12 of which

az-e different from each other. These regions were obtained by subdiving each

annulus of the standard case (Case S in FIG Al) into 4 azimuthal regions

(e.g. annulus 64 was divided into the regions 74, 84, 84 and 94). For the

fine-group cell calculation, which was performed in cylindrical geometry as

in the standard case, the regions lying in the same annulus wez'e homogenised,

thus neglecting the azimuthal flux dependence in the Gd pin. The superposi-

tion of the flux values obtained in the cell and in the lattice calculations

provided the flux spectra which were used to determine the one-group reac-

tion rates for the burnup calculation.

FIG Al shows that the effects of the azimuthal subdivision of the Gd pin ase

small. The associated reactivity difference is less than 0.2%, and the largest

difference in the average power of the Gd pin (at 2 GWd/t) amounts to 0.6%.

An azimuthal power variation of 4% can be observed in the four sectors of

the pin.

By means of the response matrix pnogi-am REPRO-FLUS0 H. Neltrup, Ri.5'6 National

Laboratory, Denmark, determined detailed flux distributions in a lattice with

an isolated Gd pin and in a poisoned lattice with adjacent Gd pins as shown

in FIG 1 (l6). For this calculation the cell geometry and 6-group macnosco-

pit cross sections were taken from Ref. (A). Each Gd pin was subdived into

16 azimuthal sectors and 7 annuli, thus considering a total number of 112

subregions pen pin. Within the four azimuthal sectors shown in FIG Al, case A

a flux tilt of 11% was predicted for the most absorbing energy group. The

total absorption in the two poisoned pins corresponds to twice the absorption

in the isolated pin minus a correction of 4%. The EIR and Risb investigations

indicate that the usual BWR reactor physics design methods, which are based on

one-dimensional cylindrical cell calculations, axe adequate for adjacent Gd pins.

Cenire

- A2 -

Case A (azimuthal subdivision 1

l

.523 .54i.

.54i .545

Case S (standard case j

.lzl : .540

Relative power in Gd pin at 2 GWd/t

- 2

1.001

.

2 1

Exposure (GWd/t 1

0.999 0 4 2 3 4 5

Fig. Ai Effect of Gd pin subdivision ( El R- results I

- A3 -

APPENDIX B Influence of Calculation Models on Reactivity

Par the poisoned lattice three participants (AEEW, EIR and OSAKA) performed

additional calculations in which they varied different parameters of the

calculaCiona1 models. The resulting reactivity changes (Ap = Ak/k) are listed

in TAB Bl.

The diffusion and transport calculations perform&d by AEEW at zero burnup are

described in Section 4.1. The EIR multiplication factors for the 70- and 8-

group lattice calculations are respectively 1.0118 and 1.0096.

OSAKA performed a burnup calculation using burnup steps of 1 GWd/t between

1 and 10 GWd/t instead of the standard steps.of 0.5 GWd/t ~(lJ. It should be

kept in mind that the necessary number of time steps depends on how the burn-

up models account for the time variation of the microscopic cross sections

and the flux during a time step. Alsoassessedby 0SA.U were the influence of

the angular flux approximation on the cell surface (DPO of DPl) and the num-

ber of annular zones in the Gd pin.

TAB Bl indicates that the angular approximation of the cell surface flux and

(above a certain minimum) the number of groups for the lattice calculation

have a small influence on the results. More important mdel parameters are

the lattice calculation method (diffusion versus transport theory), the num-

ber of time points during burnup end the spatial subdivision in the Gd pin.

- A4 -

TdB. Bl Reactivity influence of calculation models for the

poisoned lattice

Calculation

by

Calculational parameter Exposure Reactivity

tQ.'d/tJ change (%)

AEEW Diffusion instead of transport calculation

0 1.6

EIR

OSdkYd

OSdKd

OSAm

70 instead of 1 11 groups for lattice 8 instead of talc. 11 groups

13 instead of 22 time points

DPO- instead of DPl-approxi- mation for lattice calculation

1 instead of 6 annular zones in Gd pin

0 0.1

0 - 0.2

6 - 2.1

0 0.3 5 - 0.2

2 - 1.1 6 2.0

- A5 -

'.

APPENDIX C Reaction Rates for the Regular Lattice

!FAB Cl contains macroscopic absorption and production reaction rates, norm-

lized to 100% for each reaction, as a function of burnup. These values, which

were provided by G. Pierini, CISE, are useful for assessinq the contribution

of different isotopes to the multiplication f&to=,

TAB. Cl Reaction Rates (%) in the Regular Lattice (CISE-Results)

Exposure (GWd/t) 0 2 4 7 10

Absorptions in U-235 63 54 49 43 37

Absorptions in U-238 30 29 29 28 28

Absorptions in Pu-239 0 6 10 14 18

Other absorptions 7 11 12 15 17

Productions by U-235 94 86 79 73. 64

Productions by U-238 6 6 6 6 6

Productions by Pu-239 0 8 15 22 28

Other productions 0 0 0 1 2

- A6 -

APPENDIX D Partial Solutions

B. Zolotar, EPRI, performed a calculation f& the poisoned lattice using the

CASMO code (g), and K. Kowalska, SWIERK, provided results for both lattices

up to 7 GWd/t obtained with S-WIMS (E), the latter code being an adapted

version of the British WIMS-D code'(g). The calculation methods and the de-

tailed results of the EPRI and SWIERK solutions are described in Refs. (2) -

and (5).

.’

Calculations for both lattices were also performed by F. Casali, ENEA Bologna,

using the Monte Carlo code KIM (gj. The data base for KIM was obtained from

the UKNDL and ENDF/B-4, with the exception of the Gd isotopes for which the

evaluation of the Joint European File was used. The energy range above 5 eV

was divided into 70 groups, and a scheme corresponding to a practically in- *

finite number of groups was used in the thermal range, For the calculation of

the time dependence of the microscopic cross sections and the nuclide densi-

ties the Gd pin was divided into 3 annular sonas, The flux and microscopic

reaction rates were determined at 14 time points between 0 and 10 GWd/t. The '*

computing time was about 1.5 hours per time point for the poisoned case. So

far, the poisoned lattice has only been calculated.up to 4 GWd/t.

The multiplication factors obtained by ENEA, EPRI and SWIERK and the respec-

tive deviations from the mean values (cf..TABs 2-3) are listed in TABS Dl

and D2.

- 27 -

TAB. Dl Additional Multiplication Factors for the Regular Latt$ce

Exposme CGWd/tJ

0 (No Xe,

1

2

3

4

5

6

7

8

9

10

1.3390 .006

1.2869 ..009

2.2692 . 005

1.2618 .OlO

1.2449 .006

1.2354 .009

1.2226 .009

1.2067 .OO?

1.2000 .Oll

1.1844 .008

1.1740 .009

1.3360 .003

1.2794 .003

1.2673 .004

1.2543 .004

1.2401 .003

1.2277 .003

1.2146 .003

1.2019 ,.003

SWIERK 1

a Statistical ewe? C 1 sta. dev.) between 0.0018 and 0.0028

b AP = Reactivity deviation from mean value of TAB 2

- A8 -

TAB. DZ Additional Multiplication Factors for the Poisoned Lattice

Exposure CGWd/t)

0 (No Xe)

1

2

3

4

5

6

7

8

9

10 -

ka HAP '

7.9965 - .009

7.9883 - .014

1.0187 - .012

z.0504 - .Oll

2.0846 - .012

EPRl SWIERK

k AP

1.0279 .022

1.0240 .022

1.0512 .020

1.0834 .021

1.1208 .021

1.1618 .O22

1.1955 .026

1.2109 .024

1.2110 .025

1.2020 .025

1.1885 .023

a Stat-istieal e?po? between 0.0019 and 0.0040

k AP

1.0035 - .002

1.0013 - .OOl

1.;230 - .007

1.0440 - .017

1.0654 - .029

1.0880 - .043

1.1127 - .048

1.1389 - .037

b Ap = Reactivity deyiation from the mean value of TAB 3

- A9 -

,

.

APPENDIX E Solutions Submitted after September 10, 1983

ENEA:

RI@:

cf. p. 5

H. Neltmp Risb National Laboratory Postbox 49 DK-4000 Roskilde

Denmark

TAB. E2 K-INFINITY FOR REGULAR LATTICE ------- --------------------------- EXPOSURE' ENEA RI@

(GWD/T)

O(N0 XE) I.3390 1.3180 1 1.2869 1.2637 2 I. 2692 1.2358 z 1.2618 1.2449 1.2427

1.2310 5 1.2354 1.2192 6 1.2ii6 I.2074

; 1.2067 1.1958 1.2000 1.1845

9 1.1844 1.1734 10 1.1740 1.1625

---------------------------

TAB. E3 K-INFINITY FOR POISONED LATTICES

EXPOSURE ENEA RI@ (GWD/T)

--------------------------- OCNO XE) .9965 .9815

1 9883 .9798 2 I:0187 1.0093

z 1.0504 1.0435 1.0846 1.0855

5 1.1379 6 I.1739 7 1.1866

; 1.1837

10 X~~ . ---------------------------

- Al0 -

TAB. E4 U-235 DENSITY FOR REGULAR LATTICE(l.O-4/BARN X CM)

EXPOSURE ENEA RI@ (GWD/T)

0 6.777 t5.777 2 6.25a 6.261

: 5.77a 5.7a7 5.330 5.347

1: 4.911 4.937 4.517 4.553

---------------------------

TAB. E5 U-235 DENSITY IN POISONED PIN(l.O-4/BARN v--e--- --------------------------- EXPOSURE ENEA RI@

(GWD/T) ---------------------------

0 6.574 6.573 c 6.083 6.352 6.106 6.37a

i 5.747 5.341

10 4.941

X CM)

TAB. E6 PU-239 DENSITY FOR REGULAR LATTICE(l.O-5/BARN X CM)

---------------------------

EXPOSURE ENEA RISfj (GWD/T)

--------------------------- 2 2.061 2.133

3.714 3.902 5.062 5.330

4

i 6.151 6.484 IO 7.025 7.430

---------------------------

TAB. E7 PU-239 DENSITY IN POISONED PIN(l.O-5/BARN X CM) ------- --------------------------- EXPOSURE ENEA

(GWD/T) RI+

--------------------------- 2 2.140 2.217 4 3.943 4.174 6 5.664 8 6.758

10 7.615 ---------------------------

. .

.

- All -

‘.

.

TAB. E8 PU-240 DENSITY FOR REGULAR LATTICE(l.O-6/BARN X CM)

EXPOSURE ENEA RIS# (GWD/T)

--------------------------- 2 .954 .884 4 3.187 3.083 i 6.083 9.437 9.409 6.027

10 13.030 13.052

TAB. E9 PU-240 DENSITY IN POISONED PIN(l.O-6/BARN X CM) ------- -----------~--------------- EXPOSURE ENEA RIS$

(GWD/T)

2 ".657 471 4 2.423 2:067 6 4.864 8 a.428

10 12.250

.

TAB.ElO GD-155 DENSITY IN POISONED PIN(l.O-4/liiAiN X CM) ,

--------------------------- EXPOSURE ENEA RI@

(GWD/T) ---------------------------

0 1.47E+OO 1.47E+OO 2 9.4OE-01 9.6lE-01 3 6.72E-01

z 4.42E-01 4.29E-02

6 6.76E-02 7 1.82E-02

---------------------------

TAB.Ell GD-157 DENSITY IN POISONED PIN(l.O-4/BARN X CM) -------

‘

.

EXPOSURE ENEA RIS$ (GWD/T)

--------------------------- 0 1.56E+OO 1.56E+OO 2 4.&3E-01 5.29E-01 3 2.35E-01 4 9.88E-02 6.46E-02 5 6 7

- Al2 -

,

.’

TAB.El2 POWER IN PIN 4 C-j ------- --------------------------- EXPOSURE ENEA RIS$

CGWD/TJ ---------------------------

; 1.154 '1.174 I.137 1.126

4 1,055 1.066

i 1.007

.992 10 .991

---------------------------

TAB.Elj POWER IN POISONED PIN ---v-n- --------------------------- EXPOSURE ENEA

CGWD/T) RIS$

--------------------------- 0 .36a .32Q 2 i33 4 :716 6 a 1.026

10 1.02a ---------------------------