74 I EA N. IN THE AT 100 MW OF THE AND

CALCULATION OF THE NEUTRON AND GAMMA-RAY DISTRIBUTION IN THE EBWR RADIAL SHIELD AT

100 M W OPERATION

WILMA SONIA HEHL

Publicação I E A N. 7 4

November — 1964

INSTITUTO DE E N E R G I A ATÔMICA Caixa Postal 11049 (Pinheiros)

C r o A D E UNIVERSITÁRIA " A R M A N D O DE S A L L E S OLIVEIRA"

S Ã O P A U L O - B R A S I L

IN THE EBWR RADIAL SHIELD AT 1 0 0 MW OPERATION (*)

by

Wilma Sonia Hehl

Reactor Engineering Di-vision Instituto de Energia Atómica

Sao Paulo, Brasil

Publicaçao lEA nß 7 4 November - 1 9 6 4

* Work done in I96I under the direction of Prof«M»Srotenhuis of the IINSE of the Argonne National Laboratory - USAEC - - Uo S. A.

Comissão Nacional de Energia Nuclear

Presidentes Prof» Luiz Cintra do Prado Universidade de SSo Paulo

Reitors Profo Luiz Antonio da Gama e Silva Instituto de Enex^gia Atômica

Diretors Prof» Romulo Ribeiro Pieroni Conselho Tecnico-Científico do lEA

Profo Jose Moura Gonçalves

; pela USP Profo Francisco João Humberto Maffei

Profo Rui Ribeiro Franco

' pela CNEN Profo Theodoreto Hol« de Arruda Souto )

Divisoes Didático-Científicass

DiVo de Física Nuclear? Prof» Marcello DoS» Santos

DiVo de Engenharia de Reatores; Prof» Paulo Saraiva de Toledo Div. de Ensino e Formaçãos Prof» Luiz Cintra do Prado

DiVo de Radioquímicas Prof, Fausto Walter de Lima DiVo de Radiobiologías Prof» Rômulo Ribeiro Pieroni

DiVo de Metalurgia Nuclear? Prof. Tharcisio D,Souza Santos DiVo de Engenharia Químicas Prof» Pawel Krumholz

c

Este estudo se refere ao cálculo da distribuição ra dial dos neutrons na blindagem do reator EB?/R operando a uma potência de 1 0 0 Mw»

O caroço do reator foi considerado como uma esfera de igual volume, pois esta aproximação mostrou ser a melhor.

Todos os cálculos foram feitos na direção radial, para uma blindagem constituida de água, boro, ferro, chumbo, concreto pesado e concreto comumo

Os fluxos rápido e térmico foram calculados por teoria de dois grupos, com um computador IBM-704<>

A determinação dos fluxos de raios gama e de gamas de captura também está apresentada neste trabalho»

O método de cálculo utilizado e explicado e os re- sultados obtidos são mostrados sob forma de tabelas e gráfi- cos o

RÉSUMÉ

Cette etude se x-efère au calcul de la distribution radiale des neutrons et des rayons gamma dans le blindage bio logiq.ue du réacteur EBY/R à la puissance de 1 0 0 Mw,

Le coeur du réacteur est assimilé à la sphère de même volume, de I 4 6 cm de diamètre et on démontre que ceci est la meilleure approximation de la géométrie réele. Tousles calculs ont été faits pour la direction radiale et pour un blindage constitué d'eau, de bore, de fer, de plomb, de bé=

ton lourd et de béton ordinaire.

Les flux neutroniques rapide et thermique ont été 'culés ejn. prennant une théorie à deux groupes? tous les ealculs .ont été faits avec un computateur IBM 7 0 4 «

Les déterminations de flux de rayonnement gamma du coeur même et de rayonnement gamma de capture sont aussi pré- seritéâ dans ce travail o

La méthode de calcul utilisée est expliquée et les résultats obtenus sont fournies sous forme de tableaux et de graphiques.

SUMMARY

The present study refers to the radial shield of the EBfR on an assumed operational level of 1 0 0 Mw,

The equal-volume sphere core, with a radius of 7 3 cm, was chosen for the study as indicated by calculations for the D best core geometry. Shielding in the radial direction, as made

up oí w a t e r , boron, steel, lead, heavy c o n c r e t e and light con

C r e t e , was analysed.

The fast an thermal neutron flux calculations were done by two-group analysis, with the aid of computer for the latter. Determination of the gamma flux from the core, as well as the capture gammas, comprise the rest of the calculations.

The procedures followed and the calculations made in connection with the study are explained, and the results are tabulated and plotted.

IH THE EBWR RADIAL SHIELB AT 1 0 © MW OPERATION

b y

Wilma Sonia HeML

Reactor Engineering Division Instituto de Energia Atomiaa

São Paulo, Brasil INTRQEaGTIQl

The present study refers t o the radial shield of the EBWR on an assumed operational level of 1 0 0 Mw<,

The equal-voluKfô sphere c©re# with a radius ©f T 3 cm, w a s chosen for the study as indicated "by calemlations for the

b e s t core geometry. Shielding in the radial direction, as taade u p of water, boron, steel, lead, heavy concrete and light con»

C r e t e , was analysed.

The fast and thermal neutron flux calemlations were done by two-group analysis, with the aid o f c©Hij>uter for the latter. Determination o f the gamma flux from the core, as well as the capture gammas, eoinprise t á i e rest of the ealculations.

The procedures followed and the calculations m d e in connection with the study are explained, and the results are tabulated and plotted.

(if) Work done in 1 9 6 I under the direction of Prof.M.Grotenhuis o f the i m S E o f the Argonne National Laboratory - BSAEG - - U. S. A.

toy Jo75 inefees ia eross-B©@tloa and with m active tel^t Qf 4 ft. 4 i g » 2 t» * e l y 20 ^ of the asseHiblies are spiked [ML 5781 M d e M » ) . Ihe ealealatloas for the removal cr©es-TOeti<ms for

mm-W'2l6 - w a i o d s Of Caletilatlon for Use ia tte 'melm of Shields for Power Reaetors'®

= § R- 2 ^ - *lpplieatloa of F&al feutrm. Reffioml'

"Bieorf to thm Calculatim ftermal

Shields''

of Monographs In Niielear Ea©?Wj, Perga ffioa Press

CCHgO)^ 2.99 baWB - 5.6

- loi

<^(Mb) =^ 2.0065 CCCa) = 1.9719

^iW@} - 1.8614

Bemoval cross-sections for the frael elemeBts •mr^ thm.

dietSMinedi, using the data iadicated in Table 1^, #iich irteMeS TOl^s as follows I

V« 0.111 - 0.111

\fUEL ELEMENT

\ TyPE

material\

THIN £L£M£-MTS THICK ELEMENTS

SPIKES

\fUEL ELEMENT

\ TyPE

material\

ENRICHED NATURAL ENI?ICHED NATURAL

SPIKES

\fUEL ELEMENT

\ TyPE

material\

VOLUMS

FRACriOlf

ATOHiC DENSITV

VOLUME PRACTiaN

ATOMIC

oemiTv (»10^'^}

VOLUME

FmCTIOM DENSITY ^ATOMIC G lO^'^)

VOLUME FRACTION

ATOMIC

oemiry (xlO^'^i

FRACTION

ATOMIC

l>ENilTy («10^'^) .002f4 .000ff56 .Q0f276 .0000604. .00336 .00015^2 .00I73<^ .0000823 .0036 .O0Oi7o2 45^8 .00J56 .f6fO .0076)5 ,2230 .0/055 .2247^ .0fO63 .000262 .emo/24- u .oojijs .f6^3 .00767s .2264 .ZS6f .op7g .O03862 .oooiBse

.£68 .0223S .668 .02239 .588 .Sgg -omo S82

Ir . / 3 4 .oos&so . / 3 4 •H8 .006245 •m .00624s .250 .OfQS7

Nb 0OO3f51 .OOB73 .003 f 3 .OO0M31 .008)3 jOOOffSI

Ca .0365 jOOQBSn

0 in Spike M@€i.f ^.00757

Fe .0302 .00256 .0302 .OOS56 .0302 .00236 .0302 .0O2S6 .0302 .Q025i NOTES'. The rod follower has q volume fracHoitaf M3PS.;in Hne followerH(U^^^)=.Q0BIJ37xp^'^^ N(Fei= .0848J<i8^^

The conM nod has fhe sQmovoltt^S'fro.ction asih9 follower: irifhe rod NCFe)^.0760S%fO^^ M(8h.00073x U^^^ in Ui9 rod follower is imlud'tm ni*h U ^ * mtltec«ll.

Thick Elements

Enriched 0 , 1 1 5 Natural = 0 . 1 1 5

Spikes

Zl^=

The core was taien as divided luto four regions, each a sphericeuL shell with a thickness of

Region 1 - 3 ^ , 4 6 cm (radius of inner sphere) Region 2 - 1 3 . 2 0

Region 3 - 8 . 9 0

Region 4 - 1 6 . 4 4

Pig, 3 shows the core loading arrangement with the fuel elements distributed as follows;

Region No. of Elements

1 3 6 thin elements, enriched 2 2 8 spikes

5 1 6 thick elements, enriched 2 0 thim elements, enriched 4 4 0 thick elements, enriched

4 spikes

4 thick elements, natural The results of the calculations for the macroscopic removal cross-sections for each core region are listed below.

MGROSCOPIC REMOVAL CROSS-SECTIONS

Regioia Z?,., (era"'^)

1 0 , 1 1 1 2 0 , 0 9 4 3 0 , 1 1 3 4 0 . 1 1 3

FAST ^JEITROM FLtK AT THE ESSE OF THE GORE

The fast neutron flux at the edge of the core was found by comparing the results derived from three methodss

KTHOD 1

1 . The flux at the first interface was determined, using a nula

cross-section X^.^ and the formula

/VI I {.A'/l S' /lie

i - ^ { 1 -

1

2 . Using the same formula and a cross-seetion -2, ^ for the entire region from the core center to the second interface, a corresponding value of flux at the latter point was calculated.

3 « Similarly, a flux ealc^ation was made again for the first interface, this time using a cross-section Z^,

4. The effect of the inner sphère, when treated' 'as h a v i n g a cross-section of Z^-^ on the flux at the second interface was

c î L l e u l a t e d ,

5 , The value found from Step 4 was subtracted from the vstlue

6 ,

obtained in Step 2 to give the correct value of flux at the se­

cond interface.

6 . For the other succeeding interfaces, a similar procedure was followed, whereby the effect on the flux at the outer face of a shell by the sphere within the shell is ta^ken into account,

7. The flux at the edge of the core was finally determined by summing up all the contributions of partial fluxes at the inter­

faces, considering the corresponding attenuations.

METHOD 2

1 , The flux at the first interface was determined using the formula

4j (e^l - 1 - I 4/M''X Ate,

2 . The eoBtribution of the flux found from Step 1 to the fltix at the edge of tl^ core, considering attentuation, was calcula­

ted using the formula 1?

hi

3 . The second region (spherical shell) was taken as a finite slab source and the flux at the second interface calculated from formula

2%

4 . The contribution from this region (second) to the flux at the edge of the eore was determined using the foiroula

§4

Power and soiurce strengths for the various core r e * gions were calculated from the curves of Figs. 1 and 2 , w h i c h

give values as follows;

TABLE 3

POWER AND SOURCE STRENGTHS FOR THE VARIOUS CORE REGIONS Region Power P^ (watts) Source Strength (n/cm^ x s e c )

1 0 . 2 8 1 X 1 0 ® 1 . 2 7 X lO-'-^

2 0.1^03 1 . 1 1 3 0 . 2 0 5 0 . 5 2

k 0 . 1 1 1 0 . 1 0

The results of the calculations based on the three methods are tabulated below.

5 « A aimilar proceehare was followed for the other regions, and the flux at the edge of the core was determined hy adding all the contributions of the partial fluxes from each region.

METHOD 3

1 . The core was treated as a homogenous sphere with an average removal cross-section Zr= 0 . 1 1 0 cm" and an average source strength § - 7 . 5 x 1 0 n/cm x see.

2 . Then the fliax at the edge of the core was determined from the formula

_ Q

8 .

TAILE 4

PAST NEUTRON PLUX AT THE EDGE OP THE CORE PROM EACH CORE REGION Region

1

2 3

Total

Method 1 Method 2

in n/cm x see )

7 o T 6 X 1 0 4 o 7 4 X 1 0 8 . 3 2 X 1 0 3 . 9 0 X 1 0 5 . 2 8 X 1 0 1 0 1 1 1 1 1 2 12

7 . 7 6 X 1 0 5 . 3 5 X

lo;

9.42 X 1 0

4.20 X 1 0 1 0 1 1

I

1 1 1 2 5 . 7 5 X 1 0 1 2

Method 3 (Homogenous

Cope )

3 . 2 0 X 1 0 .13

PAST NEUTRON F L M jI^fRIBOTIGN IN THE RAEiiAL SHIEED

The flux based on a homogenous core was ehosen for tríe- se calculations, with the flux distribution throughout the shield being determined from the formula

and the following datas

1

Q s= 7 . 5 X 1 0 ^ ^ fast neutrons/ cm^ x sec

0 . 1 1 0 cm"-^

R = 7 3 cm

= 0 . 1 2 1

CTj = 0.129

<s¡= 0 . 0 9 1

NAA-SR-238©

The resulting flux at the boundary of each shield is given in Table % and the distribution is plotted in Pig. 4.

CALCULATION OFTHE FAST NEUTRON DISTRIBUTION IH THE RADIAL SHIELD

thermal Shield (borcn xteel)

Dimensiones

1 -Diame-^sr 0i pteseuf£Vssx@l 81" or 2}3.4cm

2 - Innar oliomefer of PSflaclar B&'oir203,3 cm AHL -5601 3 - Ouier d¡amelar of cora 57,^'or H6f> cm colculaieel

4- Thermal Shield (boron s*sal) 1"or2.Bfcm AHL'S607 .S-Wafsr 1" or 2,S4cm AtiL-^iOl

thickness of reflector (H2O)

, radius cm (.H^O) 30S.Z

- 146.O diameter -» S7.Z

23 4 S € 7 10

I

• A. '

/I a ferial X¿ (cm)

C core 73

/ HzO 28.60

2 Boron SfeeJ 2 , 5 4

3 HzO _{2 . 5 4}

4 Steel 6.3s

S In s ula fion iS.20

6 Steel 1.91

7 lead 7.62

8 Boron ...

9 Heavy Concrete, M-a iS6 fo Lii^hf concrete J 03-a tb.4

\ calculated (assmbiy for Ps/ooMvi)

Colculaiion of the rieutron and gamrna-ray distribution it} Bß^R Radial Shield 6^ :

EC Hardik&

T, A . Laur'ifxen b. P. Moon apn'lj 20,1959

1 0 .

TABLE 5

FAST FLUX AT THE

BOmmET

Core H,0

Boron steel HgO

Steel

Insulation & He Steel

Lead Boron

Heavy concrete Light concrete

Thickness Removal Cross-section

0 Flux

(ens) ( m ) (n/cm^ X sec)

T 5 © . 1 1 0 3 . 2 0 X lO"^^

2 8 . 6 0 1 , 9 8 X l©""^

2 . 5 4 0 , 1 6 8 1 , 1 5 X 1 © " -

2 . 5 4 7 . 9 0 X l©-"^

6 . 3 5 0 . 1 6 8 2 , 0 3 X l©"''^

1 5 . 2 0 0 1 . 7 9 X 10-^" ^{1 0}

1 , 9 1 0 , 1 6 8 1.24 X 10-^®

7 . 6 2 0 , 1 1 6 4 . 1 9 X 1 0 ^

1 5 6 0 , 1 1 2 l o 5 3 X 1 © ^

8 6 . 4 0 . 0 8 6 6 1 , 4 © X 1 0 - 2

THERMAL liETOtQM FLUX AT THE EIQE ©F THE CORE By use of the fonuula

and an average thermal flux value of ^ ' 3- o * ) o h^u^-i ml and likewise values of <|>5 {ojitnUeay umIka)

from the reactor core calculations (refer t© Figs, 1 and 2 ) , the thermal neutron flux at the edge ©f the eore was calculated to be

JUlt

Material D K ^K2 L = DK' ³

A =

Water 0.246 0 , 2 2 4 , 8 X 1 0 ° ^ 1 . 1 8 0 8 X 1 0 ° • 2

0 . 7 3 8 0 . 5 2 4 0

Boron steel 0.345 1 . 3 6 1 , 8 7 6 . 4 5 1 5 X lO" =1

1 . 0 3 5 0 o 7 3 4 9

Water 0.246 0 . 2 2 4 , 8 X 1©°^ 1 , 1 8 0 8 X 10" • 2

0 , 7 3 8 0 . 5 2 4 ©

Steel 0 , 3 4 5 0,64 4,1 X l©"^ 1.4145 X 10" •1

1 . 0 3 5 0 . 7 3 4 9

Insulation 0o66l 4 X 10*^ 1 , 6 X 1 0 " ^ 1= 0 5 7 6 X 1 0 ° '7

1 . 9 8 3 1 . 4 0 8 ©

Steel ©6345 0.64 4. 1 X lO'"-'-1.4145 ^{X 1 0 ' •1} 1 . 0 3 5 © o 7 3 4 9

Lead 0 . 9 1 8 0 . 0 7 1 5.1 X 1 0 " ^ 4 . 6 8 1 8 X 10" ^•3 2 . 7 5 4 1 . 9 5 5 3

Heavy conCo 0 . 4 1 8 © ¿ 3 7 9 1,44 X l©"-*- 6 . 0 1 9 2 X 10" •2

1 , 2 5 4 0 . 8 9 0 3

Light cone. 1 , 0 0 0 . 0 7 4 4 5 . 5 X 1 © " - ^ 5 o 5 X 10" •3

3 o O 2 . 1 3

Above values were taken from "©aleulation of the

Neutron and aasHJ^ray Distribution in Radial Shield", P. C.

Harsitke, T, A, Lauritzen and D, P. Moon„ April 20» 1 9 5 9 .

1*5 2

, at the edge of thentore = 1 , 5 4 x 1 0 •"^ e/cm x sec.

The caletaations for -yiermal neutron flux were done by computer using ©ode R E- 3 4 . Because of the two black boundaries, the problem was divided into three parts^, as shorn by the pro- grams for the sphere and slab geometry.

THERMAL NEUTRON FLUK DISTRIBUTION IN THE RABIAL SHIEID Table 6 lists the constants used in the calculation of the thermal neutron flux distribution.

TABES 6

Tms OF CONSTAE^ FOR IHERMAL NEUTRON CMiG^TION

1 2 .

To check if the resxilts for attsnuatioB were reasonable, calculation was made for a ease in ^*i±eh Begion 4 of th© shield is water of infinite thickness. (See attached calculation sheets.)

Results are also plotted in Pig. 4 .

mmk mm. oBiQiimwG mom THE CORE

% using a treatment similar to that employed in the fast neutron flux ealeulationsj, the ^mima flux at four energy groups (l, 2 , 4 SBid 6 Ifev) were determined, taking into conside­

ration the prompt gammas from fission and delayed gammas from the decay produets. The calculations were made first on the basis of a four-region core^ then of a homogenous sphere with build­

up disregaMeds and finally of a homogenous sphere t^th build­

up taken into account.

The subsequent tables show the vju-ious data used for and the value resxilting from the different steps of the calcu - lations. These include linear absorption coeffieientsj gamma source strengths^, power and volume of each core region, and the totfid gamma fluxes at the edge of the core.

In the ealculationsj, the values used for the total gammas per fission originating from the core (prompt and de­

layed) were as follows, in accordance with A H L - 6 0 0 0 and AERB- R - 5 2 l 6 s

Energy (Mev) Total Gamma per Fission

1 1 0 . 3

2 3 . 8 5 4 0 . 4 6 5

6 0.G53

Tke gamma source strength Q was calculated using the data obtained and shown in Table 1 1 and the formula

In the four-region treatment of the core, a similar procedmre to that taken in the fast neutron flux calculations was followed, usiag the formulas indicated therein and referred

to previously as METHOD 2, For the treatment of the éo^e as a homogeneous sphere with build-up^ use was made of tléT' formula

2fi

2-

TABLE T

Ml tulla 4^ Br LfJlA.

LIHEAR ABSORPTION COEFFICIENT Energy ü( l 8. T )

(Mev)

1 2

k

£

8

,0,9013

0 . 6 0 5 9 0 . 6 5 8 2 0 . 7 3 6 8 0 . 8 2 8 4

H 2 0( 0 . 8 ) Z r( 6 . 4 4 ) F e( 7 . 8 5 ) N b( 8 . 4 ) C a ( l. 5 5 )

0.2488 0 , 5 7 2 2 0 . 2 0 5 1 0. 4 8 5 5 0 , 0 4 3 2 0 . 2 1 1 2 0 . 2 6 4 0 0 . 1 8 1 6 Q. . 3 4 7 7 0 . 0 5 7 8 0 . 0 1 7 0 0 . 2 1 9 6 0 . 1 7 6 1 0 , 2 9 0 6 0 . 0 5 4 9 0 , 0 1 5 0 0 , 2 1 7 0 Q, l 8 l 6 0 . 2 8 8 Í 0 , 0 3 4 6 0 . 1 3 8 4 0.2241 0 , 1 8 7 9 0 , 2 9 8 2 0 , 0 3 4 9

The above figures were taken from A N L- 6 0 0 © and the Handbook of Chemistry and Physics, 3 7 t h Edition.

TABIE 8

LINEAR ABSORPTIOK eOEFFICIEm F0R EACH F0EL ELEMENT

Energy Thin Elements Enriched Thick Elements Enriched Spikes (Mev) Thin Elements Natiiral Thick Elements Natural

|!l(em'^) fXicm'^) jUL(cffl'^)

1 0 . 5 T 1 4 G . i + 1 5 6 0,2k92

2 0 o 2 8 2 5 0 . 5 0 8 8 0 . 1 9 8 1 k ^ 0 . 1 5 4 6 0 . 1 9 9 2 0 , 0 7 3 9 6 0 . 1 6 5 9 0 , 2 1 5 5 0 . 0 7 2 6

TABLE 9

LINEAR ABSORPTION COEFFICIENT^ FOR EACH REGION OF THE CORE Energy Region 1 Region 2 Region 3 Region 4

(Mev) fa

(em-b

1 0 , 5 7 1 4 0 . 2 4 9 2 0 , 3 9 1 0 . 4 0 2 2 0 . 2 8 2 3 0 . 1 9 8 1 0 , 2 9 4 0 . 5 0 0

k 0 . 1 5 4 6 0 , 0 7 3 9 0 . 1 7 5 0 . 1 8 9

6 0 . 1 6 5 9 0 , 0 7 2 6 0 . 1 8 8 0,204

TABLE 1 0

AinSRAGE LINEAR ABSORPTION COEFFICIENT F0R EACH GAMMA ENERGFT GROUP PGR THE HOMOGENEOUS CORE

Energy (Mev) ^ (cm"''")

1 O o 3 7 1 2 0 , 2 8 0

4 0 . 1 6 5

6 0 , 1 7 4

T A M E 1 1

RegicMB

P^MER MM) ¥0. LWE OF EAGH GO Power (watts)

RE mGIQM

Volume (ciffiP)

1 2 , 8 1 X 10°^ 1 , 7 1 4 X 10^

2 4. 0 3 X 1©''' 2 . 8 1 2 X 10^

2.05 ^{X 1©"^} 3 . © 5 9 X i © ^

4 1.11 X 1©"^ 8 . 7 1 5 X 1 0 ^

TABLE 1 2 (mmk s G M C E STRENOTH FOR EACM mm^

RESIGNS

f ©ROUP IN T HE FOUR GORE

Energy Begion 1 Region 2 .2 Region 3 Region 4

(Mev) see)

1 4, 5 6 X 1®-^^ 2,14 X lO'''^ ⁴, 0 6 X 10-^^

2 l o 9 6 X

l©-'"^

8 . ® 1 X l©-*-^

4 2 , 3 6 X l®'^^ 2 . 0 6 X 1@^"^ 9 , 6 7 X lO"*"^ 1. 8 3 X l©^-*-

6 2 . 6 9 X l©-^-^ ^{2 o 4 8} X 1©-^"^ 1 . 1 © X lO-"--*-i. 2 , 0 9 X 10-^

TABLE 1 3

GAMMA. FLUXES AT THE E l ^ ©F THE CORE

Energy From From From From

(Mev) Region 1 legion 2 p Region 3 Region 4 f/cm X sec)

1 3 . 5 1 X 1 0 ^ 2 , 2 0 z 1 0 ® 3 . 8 © X 1 0 ^ 5.04 X l©-*-^

2 5.43 X

lo'^

1 . 3 0 X l©-""®

4 1. 7 6 X IG^ 1 . 3 © X 1 0 ^ ® 2 , 2 0 X 1 0 ^ ® 4 . 8 © X 10^^

6 1. 2 9 X 1 0 ® 1 , 0 3 X 1 0 ^ 1. 8 ® X 10^ 5 . 0 8 xl©"''®

1 6 .

TABLE 13 (Continued) TOTAL PLUX

Energy (Mev) IV( f/om^ x sec) 1 5.04 x lO-*-^

2 2 . 8 3 X 10-^^

4 5. 1 7 X 10^-^

6 , 5.49 X 10-^®

TABLE 1 4

GAMMA PLIX AT THE OF THE HMO^NEOUS SPHERICAL CORE, NO BUILI>.UP Energy (Mev) %{ 'Vera x sec)

1 4. 0 9 X 10-^^

2 2 . 0 2 X lO"*"-^

4 4. 0 8 X lO-*-^

6 4.48 X 10-'--'-

TABLE 15

GAMMA F L M AT THE EDGE OF Tm HCMOCENEOOS SPHERICAL CORE, WITH BUILD-UP

Energy (Mev) *| (//csa^ x see)

1 8 . 2 5 X 10-^^

2 4 . 0 9 X l©-*--^

4 8 . 3 4 X l©-"-^

6 9 . 1 4 X l©-"--*-

íEâBLE 1 6

Energf (Mev)

1

2

Core Divided lato Foijr Regions

6

5.04 ^X 10'

2 . 8 5 X 10- 5.17 ^X 10 5.49 X 10

,12 11

I

10

Homogeneoiis Spherical Core

Wo Bu^ld-up (f/cm X sec)

4, 0 9 X 1©1^

. 1 5 2 . 0 2 X 10"

4 , 0 8 X 1 0 4 , 4 8 X 1 0 1 2

11

Homogeneous Spherical Core With Build»up

8 . 2 5 X IQI-^

4 , 0 9 X lO""-^

8 . 5 4 X 10 9.14 X 10

1 2

I

1 1

FBOMPT GAMMA FLUX ATTEMTOATIOH IM THE RADIAL SHIELD

Taking the four gamsaa e a e r ^ gi'oups into account, cal»

culations were made for the gaissma flust distribution by the for­

mula

using values from Table l 6 for Q^, values from Table 1 0 for yj-s and taking jji^,-i.JUL- with values for JÜL^_ from AlíL-6000,

The resiilting pronrpt and fission product gamma flux attentuation is shown in Fig, 5 .

GAMMA FLUX DUE TO CAPTURE M THE RADIAL SHIELD MATERIAL Each shielding material was treated separately as a gamma ray source, with thermal flux distributed in a manner pre­

viously deteraiiaed furnishing the neutrons for the (n, ^)reaetions.

GAMMA FLUX AT TIE EBGE OF THE GOES AS CAKULATED BY THHEE METHODS

1 8 .

In calculating the gamma flux due to capture at the outer boundary of each shield material, the thermal neutron flux was approximated by exponential and constant sources, using the following formulass

For exponentlal Source

J

slope of the expon- ential source JUL - linear absoiption

^ coefficient

( 2 )

In the two preceding fortmilas

- i

Where 0 (O) is the thesrmal fltix at the outer boundary of the shield material ( under consideration

"ffis the number of gammas/fission Z.¿is the absorption cross-section For eonstantSource

J.

Where ^ Z^^H^i^

{o^

DATA USED FOR 0 CALCULATIONS

Material (Mev)

. O 0 I 7 3 6 2 , 2 5 1 ^{0 . 0 5 8}

Fe k 0 , 3 4 0 . 2 5 9

8 0 , 7 2 0 . 2 3 1

Pb 0 . 1 9 5 6

-

8 1 0 . 5 2 0

Heavy 0 , 1 2 6 k 0 . 6 3 6 0 . 1 0 1

concrete

8 0 . 7 2 3 0 , 0 7 8

Light 0 . 0 6 2 k ^{1 . 2 0 0 . 0 7 6} concrete

8 O o 5 5 0 , 0 5 8

0 . 0 2 2 0 . 1 9

0 . 0 0 5 0 . 0 6

0 . 0 0 9

= absorption cross-section i^ir = number of gammas/fission 0 (O) = the constant thermal flux Where several energies were involved, those below 4 Mev were taken as k Mev, while those between k and 8 Mev were Gonsldêréd as 8 Mev. Water generates only one gamma ray at

2 « 2 3 Mev, and this was taken into account.

Calling the gamma flux at the outer boundary of each shield material due to neutron capture its values were com- puted from data given in Table 1 7 . Results are tabulated in Table 18,

TABLE 17

2 0 .

T!ABLE 1 8

Material Energy (Mev) ( y/cm^ X sec) HgO

Fe

2 , 2 5

k

1 2 7 . 5 1 x 1 0 9 , 5 5 X 1 0 ° ^ °

8 2 . 1 8 X 10-^-^

Pb 8 2 . 1 5 X lo"^

Heavy concrete k 1 . 1 6 X 1 0 ^

8 2.42 X 1 0 ^

Light concrete k 9 . 9 3 X lO'l

8 2.44 ^X 1 0 * 1

CAPTURE RAYS A T T E H U A T I 0 K IN THE RADIAL SHIELD

formula

For these, calculations were performed using the

Z + Í t A l t e

and data given in Table 1 9 . Fig, 6 is a plot of the capture gamma ray attenuation in the radial shielding.

Material

H, 0

TABLE 1 9

DATA FOR COMPUTATION OF GAMMA RAY ATTENUATION (Mev) /cm^ x sec) ^ 5 (em"l)

2 . 2 3 4 . 0 8 , 0

7 . 5 1 X 1 0 1 2

0 . 0 5 8

GAMMA FLIX AT THE BOUHDARJ OF EACH SHIELD MATERIAL DUE TO MEDTRON CAPTURE

TABLE 1 9 (oontSBued)

Fe 2 . 2 3 - © « 3 1 5

4,© 9 . 5 5 X 1 © ! ® 0. 2 5 9

8.0 2 , 1 8 X 1 © ^ ^ 0. 2 3 1

Pb 2 , 2 3 - 0.488

4.0 - © . 4 7 5 8,® 2 . 1 3 X 10°^ 0 , 5 2 0

Heavy

concrete 2 . 2 3 - 0 . l 8

4. 0 1 . 1 6 X 1 0 ^ © , 1 © 1

8.0 2.42 X 10^ 0 . 0 7 8

Light

concrete 2 , 2 3 - 0,10

4.0 , 9 . 9 3 X 1 0 " ^ © . © 7 6

8.0 2.44 X l©"-*- 0, G 5 8

DOSE RATE EVALUATIOM AM3 CONCLUSIONS 1, Fast and Kiennal Neutron Fluxes

Both the fast and thermal fluxes calculated outside the radial shield of the reactor (light concrete) were found to be at safe biological levels,

2 . Gamma Rays

a. Prompt and Fissicgi Product Gaaimas

Tabtilated below are the dose rates calculated for the various gamma ray energy groups.

2 2 .

TABLE 2 0

(r/hr)

1 . 6 2 X ^{l© - 7} 5 , 7 5 X l©-^^

9 . 7 2 X 1 0 - ^ 5 . 1 5 X 1 © - * ^ 2 , 5 6 X 1 0 ' ^

2.84 X 1 © - 1

5 . 1 5 X 1 © - * ^ 2 , 5 6 X 1 0 ' ^ 2 . 8 5 X ^{l© - 2} 2 . 5 7 X lO"*^

7 . 7 4 X 1 0 " ^

1.46 X 1 0 ®

2 . 5 7 X lO"*^

7 . 7 4 X 1 0 " ^ 1 . 4 4 X ^{1 © 2} 1 . 3 0 X 1 © - ^ 9 . 9 3 X ^{1 © - ^ 5 , 2 6} X 1 © - ^

>-

2 . 4 4 X 1 0 - 1 2 . 2 0 X 1 0

PROMPT AND FISSION PRODUCT SAMMA RAYS DOSE RATES

Energy (Mev) Flux {i/cx^ x sec) Dose Rate (r/hr)

1 . 0 SM X 1 0 " ^ ^ 1 . 2 8 X 1 0 " l ®

2 . 0 3 . 0 5 X 1 © " ^ 9 . 7 0 X lO'-'-®

4. 0 2 . 5 2 X 1 0 ° ^ 1.34 X 1 0 " ^

6.© 5 . 0 8 X lO"*-'" 3.66 X 1 0 ' ^ b. Thermal Neutron Capture GaBsnas

Tabulated below are the dose rates calculated for the thermal neutron capture gammas.

TABLE 2 1

THERMAL NEUTRON CAPTURE GAM5A RAYS DOSE RAOES

f 2

Source Energy (Itev) ' ' % - H^® 2.23

Steel 4

8

Lead 8

Heavy concrete 4

8

Light concrete 4

8

The dose rate calculated at the outer boundary of the EBWR radial shield is less than 2 mr/hy, and so will not exceed the maximum permissible levels established in the last report of the ICRP, (International Commission on Eadiological Protection).

1 . M . Grotesahmis, "Lectm-e Notes on Reactor Shielding", M L - 6000

2« E. A O Wifflunc, J . M O Harrer, "Hazards Evaluation Report Associated with the Operation of ESm at 100 m, ANL-

»5781, Addendum

5. F, C O Hardtke, T» A. Lauxltzen, D,P, Moon, "Calculation of the Neutron and Gamma-Ray Distribution in EBWR Radial Shield 4. A« F, Avezy, D , E . Bendall, J» Butler, K.T» Spinney, "Methods

of Calculation for use in the Design of Shields for Power Reactors", AERE-'R52l6

5 . B,T. Price, C C , Horton, K O L \ Spinney, "Radiation Shielding"

International Series of Monografs on Nuclear Energy, Pergamon Press

6. D O S O Duncan, H.O. Iffliittum, Jr., "Application of Fast Neutron Removal Theory to the Calculation of Tberiml Neutron Flux Distributions in Reactor Shields", MA-SR"2580

7 . M , K , Butler, J.M. Cook, "RE-J^, AÎ^Î TM-^JOk Reactor Shielding Program", ANL-5859

8. Handbook of Chemistry and Physics, 37th Edition ACKNOWLEDGEMENTS

The study and corresponding calculations were made during the 1961 Spring Term of the International Institute of Nuclear Science and Engineering of the Argonne National Laboratory, in connection with ray appointm.ent as Participant in that Term.

I wish to thank Prof. E.G. Taeeker, Director of the IINSE for the arrangements made to me to allow the furtherance of ny train­

ing in the field of reactor shielding. Allow me to thank Professor M O• Grotenhuis, Professor of Reactor Shielding, in particular for his most understanding help and guidance, and the IINSE for making available the meeessary facilities and also the assistance by many members of the Staff of the Argonne National Laboratory.

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