ML19211A502

Criticality Safety Benchmark Calculations for Low Enriched U Metal & U Oxide Rod-Water Lattices

ML19211A502
Person / Time
Site:	07106581
Issue date:	04/30/1979
From:	Charles Brown, Echodom W, Hansen L SIEMENS POWER CORP. (FORMERLY SIEMENS NUCLEAR POWER
To:
Shared Package
ML19211A494	List: ML19211A493 ML19211A495 ML19211A496 ML19211A498 ML19211A502
References
14897, XN-NF-499, NUDOCS 7912200029
Download: ML19211A502 (36)

Text

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CR;TICA!.lTY SAFETY BENCHMARK CALCEAT Oh8 i

FOR LOW-ENRICHED URAN UM METAL AND l b URAN UM DXIDE ROD-WATER LETTDES l

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CRITICALITY SAFETY BENCHMARK CALCULATIONS FOR LOW-ENRICHED URANIUM METAL

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AND URANIUM 0XIDE ROD-WATER LATTICES I

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O l1 MARCH 1979 EXgON NUCLEAR COMPANY,Inc.

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l CRITICALITY SAFETY BENCHMARK CALCULATIONS FOR LOW-ENRICHED URANIUM METAL AND URANIUM 0XIDE R0D-WATER LATTICES

. n, Prepared by:

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304tticf 77 g

Craig 0. Brown Date

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Licensing Engineer 2v h,

Ib Accepted cy: If C 1 M7f j.

L. E. 'Hansen, Senior

' Date Criticality Safety Specialist

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t Approved by: _

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/)/M!) /f W. S. Nechodom, Manager

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D$te Licensing and Compliance Approved by:

h3 '7 b R. Nilson, Manager Date Licensing Department 1

1631 246 I

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I'

I NUCLEAR REGUL ATORY COMMISSION DISCLAIMER h

qP IMPORTANT NOTICE REGARDING CONTENTS AND USE OF THIS DOCUMENT k,W

,PLEASE READ CAREFULLY O

This technical report was derived through research and development programs sponsored by Exxon Nuclear Com;:any, Inc. It is being sub.

mitted by Exxon Nuclear to the USNRC as part of a technical contri-bution to facilitate safety analyses by licensees of the USNRC which utilize Exxon Nuc! ear fabricatts reload fues or other technical services provided by Exxon Nuclear for licht water power reactors and it is true and correct to the best of Exxon Nuctear's knowledge, information, and belief. The information contained herein may be used by the USNRC g

in its review of this report, and by licensees or applicants before the

(

USNRC which are customers of Exxon Nuclear in their demonstration 3

of comoliance with the USNRC's regulations, j

^

Without derogating from the foregoing, neither Exxon Nuclear nor any person acting on its behalf; A.

Makes any warranty, express or impHed, with respect to the accuracy, completeness, or usefulness of the infor-mation contained in this document, or that the use of any information, epparatus, method, or process disclosed in this document will not infringe privately owned rights or fh.

B.

Assumes any liabilities with respect to the use of, or for e,

darrages resulting from the use of, any information, ap-g paratus, method, or process disclosed in this document.

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XN-NF-499 i

r TABLE OF CONTENTS

.U Section No.

Title Pace

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li i

List of Tables...................

ii

[

N List of Figures iii 1.0 Introduction....................

1 l

2.0 Description of Experimental Critical Data I

h 2.1 Yankee Critical Experiments..........

1 2.2 ORNL Critical Experiments...........

2 2.3 PNL Critical Experiments 2

1 3.0 Calculational Methods 3

3.1 Eighteen Energy Group Model..........

4 i

3.2 123 Energy Group Model 5

5 4.0 Calculational Results 6

5.0 Assessment of Results and Calculational Bias....

7 6.0 Conclusions 9

7.0 References.....................

27 bbl

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XN-NF-499 i

LIST OF TABLES l

L TABLE NO.

Pace I

Yankee Critical Experiments:

Fuel Rod Lattice Parameters..........

11 l

II Yankee Critical Experiment Results 12 3

III ORNL Critical Experiments:

Fuel Rod Lattice Parameters Depleted Uranium Block Neutron Absorber Plate 13 IV ORNL Critical Experiment Results 14 V

PNL Critical Experiments:

i Fuel Rod Lattice Parameters

}i Neutron Absorber Plates............

15 1

y VI PNL Critical Experiment Results.........

16 I

r VII Calculated K Values for Yankee Rod-Water $5ticalLattices..........

o 17 h

n L

VIII Calculated K Values for ORNL Critical EFF Lattices 18 IX Calculated K Values for PNL Cri tical Lkk5 ices...............

19 1631 249

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XN-NF-499 i

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I LIST OF FIGURES II.

it.

FIGURE NO.

Page s.*.;

ORNL Critical Assembly Arrangement h

I:

1 Case 1B Rods Only.....

20 QL 2

Case 2B Rods Only................

21 f

3 Case 3B Rods and Depleted Uranium........

22 P'

4 Case 4B Rods, Depleted Uranium, and BORAL....

23 5

Case SB Rods, Depleted Uranium, and BORAL....

24 7

5 6

PNL Critical Assembly Arrangement 25 l

c 3

7 Computer Code Calculational Models.........

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1 XN-NF-499 CRITICALITY SAFETY BENCHMARK CALCULATIONS FOR LOW-ENRICHED URANIUM METAL AND URANIUM 0XIDE ROD-WATER LATTICES

[-

b.

1.0 INTRODUCTION

I i !

6 b

j This report summarizes the results of benchmark calculations performed k

to verify the accuracy, and provide an estimate of the calculational bias, of computer code models used to calculate effective multiplication factors for low enriched uranium metal (U) and uranium-dioxide (UO ) rod-water 2

lattices. Data from the Yankee critical experimentsII) as well as from experiments performed at Oak Ridge National Laboratory (2) (0RNL) and the Pacific Northwest Laboratories (PNL) of Battelle(3) were used in this benchmarking effort.

Descriptions of the critical and subcritical experi-i ments and results of the criticality calculations are provided in subsequent sections of this report. The analytical methods used in these evaluations are also discussed.

2.0

SUMMARY

DESCRIPTION OF BENCHMARK DATA 2.1 Yankee Critical Experiments 4

A number of critical experiments were performed for the " Yankee" 7

reactor in the late 1950's.

These experiments utilized stainless steel 235 ) in light water.(I) clad UO fuel rods (enriched to 2.70 wt.%

0 Table I 2

lists fuel assembly parameters used for one set of experiments where the q

critical number of rods in a cylindrical geometry was determined for various 1631 251 H

. q

y 1

XN-NF-499 j

i a

d lattic.e (rod-to-rod) pitches.

Table II summarizes the results of these critical experiments and gives critical cylinder radii for the respective lattice pitches.

(Lc' 1,l i

u 2.2 ORNL Critical Experiments

[

H l

s The results of a number of critical experiments conducted at ORNL l 'L i

employing unclad uranium metal rods (2) were obtained from E. B. Johnson 1

and G. E. Whitesides of ORNL. These experiments were performed for uniform l

235 lattices of 4.95 wt.%

U enriched rods, surrounded on all sides by an l

essentially infinite water reflector.

In conducting the actual experiments, q

the water height above the rods was varied to control the reactivity of the s

array.

Experiments were performed for rod-water lattices with and without I

the inclusion of such reflector and poison materials as depleted uranium, t

BORAL and stainless steel.

Table III lists fuel rod, neutron absorber i

plate, and reflector data which describe relevant physical characteristics g

of the experimental equipment.

Figures 1 through 5 depict graphically the arrangement of five selected experiments for which criticality calculations were performed. The experimental results of these five experiments are summarized in Table IV.

2.3 PNL Critical Experiments In 1976 experiments were initiated at the Pacific Northwest Laboratories l

of Battelle to provide criticality data on systems simulating LWR fuel assembly shipping packages and storage pools.(3) The initial experiments I

were conducted for aluminum clad UO rods in light water (enriched to 2.35 2

i 1631 252 XN-NF-499 235 ) arranged in lattices as depicted in Figure 6.

The effect of wt.%

U various fixed neutron absorbers (e.g., BORAL and stainless steel) on critical array dimensions was investigated.

Table V lists fuel rod and j(

poison plate parameters describing the material and dimensional make-up of the experimental core. Table VI summarizes the results of six experi-mental runs, noting critical separations, dimensions, etc.

3.0 CALCULATIONAL METHODS Methods used for criticality calculations are selected which permit accurate geometrical and neutronic modeling of the systems such that the effective multiplication factor (keff) can be computed with an acceptable degree of confidence. There are a number of Monte Carlo, transport and diffusion theory computer codes, and associated multigroup cross section j

data set preparation codes, which together are well suited to handle the

)

estimation of k for a variety of systems.

eff 1

i!

From the standpoint of applicability and flexibility, the multigrcup,

?

multiregion, three-dimensional KEN 0(4) Monte Carlo code is well suited to

't perform these calculations.

The KEN 0 code tracks individual neutrons in l t r'

the system and at each neutron collision point calculates the probability a';

of occurrence of various possible interactions (e.g., capture, fission, etc.).

The assigned neutron weight is reduced after each collision by the h

probability of absorption. When the weight is reduced below a pre-specified I

level for the particular region in which the collision occurs, " Russian Roulette" is played to determine if tracking of the neutron should be j

!1 1631 253 2 a 4A i

4 XN-NF-499 l1 1

0 terminated or continued with an increased weigh. Once a representative f

number of neutron histories have been compiled, fission rates, densities, h

,t, etc. are calculated. Benchmark calculations were performed using either the KENO-II(4) ccde with an 18 energy group calculational model or KENO-IV(5) p.

I with a 123 energy group model. Logical computer code input for the two g

models is depicted in Figure 7.

'a j H l 3.1 Eighteen Energy Group Model f

\\)

As discussed above, the KENO-IIf4) Monte Carlo code was used to calculate i

k values of the experimental benchmark data.

Eighteen energy group eff 4

cross section data input into KEN 0 were averaged using the CCELL(6),BRT-1(7)

j and GAMTEC-II(0) computer codes with either ENDF/B-III or GAM-1 cross

)

t is e

section library (9) data. Specifically, the cross sections for various material regions in the critical experiments were obtained as follows:

q j +

3

)',

FUEL REGION - The CCELL code was utilized to obtain cell-averaged o

multigroup (0<E<10 Mev) cross section data for the rod-water lattices, j

~~

(CCELL is a pin cell calculational code developed by Exxon Nuclear.

It is 4

n a combination of the HRG(10) and THERMOS (11) codes, and is designed pri-D Es marily to produce broad group cell-averaged, resonance-corrected fuel 5)'

g, region cross section data.

Resonance energy cross section data are calcu-fI t'

lated using an adaptation of the Adler, Hinman, and Nordheim method (I2) to an intermediate resonance approximation.

The resonance integrals are allocated Y

to the various fine energy groups with provisions made for self-shielding.)

In addition CCELL was used to produce flux-weighted, epithermal multigroup I

cross section data (E > 0.683 ev) for fixed-poison material.

• L iI 163l 254 %

1, XN-NF-499

,i.

FIXED NEUTRON p0ISONS - The Battelle Revised Tnermos (BRT-1) code e

was utilized to produce thermal group (E < 0.683 ev) cross section data for any fixed neutron poisons associated with the critical experiments (e.g.,

i stainless steel, BORAL, etc.). BRT-1 performs a spatially-dependent trans-a6-port calculation to provide thermal group adjusted cross section data.

The 4

neutron energy spectrum of adjacent source regions is described using a N

30 x 30 scattering matrix calculated by the CCELL code.

p

[c.

5 REFLECTORS - The GAMTEC-II code was employed to calculate multi-e group cross section data for water and depleted uranium, both averaged over a neutron energy spectrum characteristic of an infinite medium.

GAMTEC-II is utilized primarily for averaging cross section data in essentially homo-geneous media.

Epithermal group constants are averaged over a 64-group slowing down spectrum computed using the B approximation to the Boltzmann y

equation. Thermal group constants are averaged over a Wigner-Wilkins flux spectrum (13), and resonance absorption cross sections are calculated usin the narrow-resonance and narrow-resonance infinite mass approxinaticns(12 3.2 123 Energy Group Model x

h The KEN 0 IV(5) computer code with 123 energy groups was used to calculate 1

the effective multiplication constants for the same critical experiments.

.2 Multigroup cross section data from the XSDRN 123 energy group data library were prepared for input into KENO IV using the NITAWL and XSDRNpM codes, both

'{

of which are a part of the AMPX Modular Code System (I4) 1 ;

i

)

NITAWL is an acronym for.Nordheim's I,ntegral Treatment A_nd Working

),

L_ibrary production. The code performs resonance self-shielding calculations

[

and combines the resonance and smooth cross sec: ion data into multi-tl group formats usable in other codes. Resonance calculations using the p

1631 255 :

L

XN-NF-499 Nordheim integral method were perfonned for the 238U associated with each of the critical experiments.

Dancoff correction factors and effective moderator cross section data necessary for the NITAWL calculations were f_

obtained using the DASQHE(15) subroutine of the CCELL code.

I

.4 The XSDRNPM code is a multiregion, multigroup, one-dimensional transport

{

theory code used to calculate reaction rates and eigenvalues as well as

{

produce cell-averaged fuel region cross section data.

(XSDRNPM is also f

part of the AMPX module and is a modified version of the XSDRNIIO) code.)

.f Specifically, the code performs a forward solution of the one-dimensional

\\

Jl Boltzmann transport equation in slab, cylindrical or spherical geometry.

j The solution may be performed in the multigroup discrete ordinates, dif-i fusion, or infinite medium approximation.

In addition, XSDRNPM computes multigroup constants averaged over both space and energy for use in other

{1 calculations. Hence, resonance-treated 2380 cross section data prepared by 1

NITAWL were input into XSDRNPM to produce cell-averaged multigroup con-I!y stants for input into KEN 0 IV.

This approach, wherein the fuel region is P

ie ik treated as a single homogeneous mixture (i.e., cell-averaged by XSDRNPM) 3 il not only simplifies the necessary KEN 0 input, but also enhances the flexi-l}

ii bility of the code in calculating reactivities of array designs which are jj geometrically more complex than the experimental criticals.

3h hm 4.0 CALCULATIONAL RESULTS Iu

)

J l

1 Results of k calculations are given in Tables VII, VIII and IX for eff the critical experiments summari ud m Section 2.

In each case the methods

]

4 1631 256

} A

y XN-NF-499 of analysis used were as discussed in Section 3.

Table VII summarizes the results of calculations performed for the Yankee critical experiment data.

It is noted that the KEN 0 calculated k values agree with previously L

eff performed DTF-IVII7) transport theory calculations within the statistical uncertainty of the Monte Ca !o calculations.

Table VIII tabulates calculational results for the ORNL uranium metal experimental data. For these results the eighteen group calculational model appears to do an adequate job in calculating the critical value for I

the first three cases which include rods in water only or rods in water reflected by depleted uranium.

For the cases employing the neutron absorber (BORAL) plate, however, results are conservatively high.

The 123 group calculational model gives results that remain consistent for all cases.

Calculated k values for the experiments performed at P"L are sum-df marized in Table IX. These experiments were performed to provide experi-mental criticality data on systems simulating the neutronic conditions of fuel element shipping packages and storage facilities.

As indicated in the table, calculated k values are in close agreement with the experimental eff data.

5.0 ASSESSMENT

OF RESULTS AND CALCULATIONAL BIAS The results of reactivity calculations for the Yankee critical experiments, using either the 18 group or the 123 group moiels, show a conservative bias of from +0.014 ak to +0.013 ak at the 95% confidence

! }63l/ i 1 e

-- ~ XN-fiF-499 } level. This conservative bias of approximately +1.0% in h is also in agreement with results of DTF IV calculations performed for the same lattices. , b For the ORNL critical lattices the results of the 123 group i) ,i i, calculations are consistently around the critical value (keff = 1.000). '[ The average resulting k for all cases (Cases 18-58) is 0.998 1 002. eff For the 18 group calculations, however, the results indicate a conservative bias for systems containing a BORAL poison plate. Cases 4B and SB indicate that the calculational results are conservatively high by not less than +0.025 Ak at the 95% confidence level. While these results are not suf-ficient to permit a clear definition of the calculational bias, the results strongly indicate that the BORAL cross section data averaging technique is conservative with respect to criticality safety. The critical experiments performed by Bierman, et al., at PNL most closely resemble Juel storage and transportation systems of the three sets of critical experiment data described in this report. i Hence, the results of these benchmark calculations are of particular interest. The average k for the 18 group calculations is 1.001 +.002 and for the 123 group eff calculations keff (average) is 0.998 +.002. Both values are within one ,) standard deviation of the critical value and results remain consistent for ' i various fuel rod arrays and absorber plate conditions. It should also j be noted that for the cases in which absorber plates were present, the .] attempt was made to choose several runs from many which had contrasting .i i i 1631 258 3 ' l il ua

_ _.u- ., m mm.- - -, S XN-NF-499 i critical parameters. For the BORAL cases the distance of the plates I from the fuel clusters was 0.645 1 006 cm and 4.442 1 060 cm, respectively. 9 T. These dimensions represent. maximum and minimum cluster-to-plate separation distances for the data reported. i

6.0 CONCLUSION

S .i '} In validating and assessing the accuracy of calculational models via a } benchmark calculations, it is important that a variety of experimental data i jj be utilized. This approach is of benefit not only in appraising the cal-i lt culational bias associated with the particular method, but also in establishing h o the region of validity of the calculational method. From the results b W of calculations summdrized in this report, both the 18 group and the d 123 group calculational models appear to adequately reproduce the critical 4j values. Where a significant calculational bias is indicated (i.e., ~1 the 18 energy group model calculations of the ORNL data, Cases 48 and E 5B), the bias is conservative with respect to criticality safety. m k This benchmarking effort was originally undertaken to determine the 't {f accuracy of the two described models which were primarily being used to calculate k values of spent fuel shipping containers and storage eff pools. Hence, the calculated results using the PNL critical experiment i data are especially encouraging as these results are, based on a cumulative ( T average, within one standard deviation of the critical value for both M calculational models. Although no effort has been made to firmly establish an actual h calculational bias for the two models, the theory-experiment correlations M ~'- 1631 259 1

i 1 Xti-fiF-499 show that the analytical methods used adequately reproduce the experimental i results. Nevertheless, since changes in poison materials, fissile enrichments, and other design parameters may influence the correlation M between theory and experiments, additional benchmark calculations will be made on a continuing basis to expand the region of validity of the analytical methods on an as-needed basis. d'o 1. J i l'i 1631 260 i s, 'li o M r !k ill.

9 3

1 1 x 1 1, ,9L !h l ! 1 i l 1 : I I E I L

l - 'Rh"t*99 l 3 TABLE I k T.'yy YANKEE CRITICAL EXPERIMENTS

[

(2.70 Wt.% 2350 Stainless Steel Clad UO RodsII)) 2 t 4 FUEL R0D LATTICE PARNIETERS o 4, 4? Enrichment, wt.% 235 U 2.70 Uranium Form Sintered UO Pellet Diameter, cm 2 0.762 3 Pellet Density, % pT 93 + 1 Clad Material } 304 SS Clad 00, cm i] 0.859 !.i,}} Clad Thickness, cm 0.041 Active Fuel Length, cm 121.9 Rod-to-Rod Pitch, cm

1 V

1.105 - 1.689* (square) m/V f 1.40 - 4.98* End Plugs k 304 SS 'j 1 l*

• The pitch was varied from experiment to experiment.

1631 261 g I i XN-NF-499 4 t TABLE II .E .2:- YANKEE CRITICAL EXPERIMENT RESULTS II 235 (2.70 Wt.% U Stainless Steel Clad UO Rods (I)) 2 a ji 1 Square Moderator-to-Critical l 235 Lattice Fuel Volume H/ U Number Critical Cylinder S Case Spacing, cm Ratio Ratio of Rods Radius, cm 1 , e f 1A l 1.105 (0.435 in.) 1.405 150 1851 26.820 2A 1.194 (0.470 in.) 1.853 198 1301 24.295 3 3A 1.455 (0.573 in.) 3.357 361 826 23.599 4A 1.562 (0.615 in.) 4.078 436 790 24.770 l 5A 1.689 (0.665 in.) 4.984 533 813 27.'473 i 1 aw t e A 4, 3 a 1631 262 39 b t s s a

fi

x,

m

XN-t;F-499 TABLE III ORNL CRITICAL EXPERIMENTS (4.95 Wt.% U Unclad Uranium Metal Rods ( )) 235 D'

L.

FUEL R0D LATTICE PARAMETERS j 235 Enrichment, wt.% U 4.95 Uranium Form Metal Uranium Density, %pT 99 Rod 00, cm 0.762 (unciad) Rod Length, cm 30.0

t u

Rod-to-Rod Pitch, cm 2.05 (square) [f m/V Ratio 8.22 f ) DEPLETED URANIUM BLOCK N

1 Material Uranium Metal U(0.185) jj 3

I Uranium Density, g/cm 19.04 t length, cm 60.4 ,j Width, cm 21.7 [{ Height, cm 25.9 (centered) b NEUTRON ABSORBER PLATE g Material BORAL (Brooks and Perkins) l1 Core Material B C and Al a 4 Wt.% B C in Core 38.9 (CRNL measurement) 4 3 Core Density, g/cm 2.63 Core Thickness, cm 0.429 A Clad Material 1100 Aluminum Clad Thickness, cm 0.104 T Width, cm 47.114 Height, cm 25.876 (centered) N 7 Total Width, cm 0.637 f 1631 263 . tv h :.

• G

XN-NF-499 j c. TABLE IV E s DT ORNL CRITICAL EXPERIMENT RESULTS } 235 (4.95 Wt.% U Unclad Uranium Metal Rods (2)) h i b ! !j o Lattice Number Critical Water Reactivity at 1 Case Number of Rods Height Above Lattice, cm Given Water Heicht, c F{ } Rod-Water Lattice Only 4 IB 22 203 7.1 +12.1 y 0 28 23 195 15.24 0.0 J 1 ,:q J. Rod-Water Lattice + U(0.185) Block 3B 104 (Run) 245 9.5 +4.3 l} Rod-Water Lattice + U(0.185) Block + BORAL Sheet ij 4B 105 (Run) 324 15.24 0.0 j 5B 359 11.94 +0.6 33 s i 3it 1631 264 it a s d bn 1: D Id 1 .a

n XN-NF-499 TABLE V PNL CRITICAL EXPERIMENTS 235 (2.35 Wt.% U Aluminum Clad UO R ds ) = 2 l} C:. FUEL R0D LATTICE PARAMETERS g

.y Enrichment, wt.%

U 2.35 i.05 f 35 Uranium Fonn U0 5-Uranium Loading, gm/ rod U0 82 2 235U Axial Loading, gm/cm 0.187 Fuel Diameter, cm 1.118 U0 Density, % pT 84 2 Clad Material 6061 Aluminum Clad OD, cm 1.27 ( h Clad Thickness, cm 0.076 j Active Fuel Length, cm 91.44 Rod-to-Rod Pitch, cm 2.032 (square) { Vm/V 2.92 j f End Plugs Aluminum j 5

f NEUTRON ABSORBER PLATES g

3 Composition g 304-L Steel BORAL $.g w 3 Density, g/cm 7.93 2.49 Element, wt., y At 62.39 + 2.80 B 28.70 + 0.25 C 7.97[0.41 j Fe 68.24 + 0.34 0.33 + 0.04 Cr 18.56 7 0.10 1 Mn 1.58 T 0.05 1 1 Ni 11.09[0.06 h Plate Width, cm 35.6 35.6 Plate Height, cm 91.5 91.5 Plate Thickness, cm 3.02 + 0.13 7.13 1 0.11 (includes d 4.85 + 0.15 0.102 cm Aluminum on @i' either side of core) 1631 265 it w

~ h i I TABLE VI PNL CRITICAL EXPERIMENT RESULis (2.35 Wt.% U Aluminum Clad U0 Rods (3)) 235 2 Fuel Clusters Absorber Plates Critical Separation Experiment No. in Lattice Size, Thickness (t ), Distance to Fuel Between fuel Clusters P Cluster (G), mm (Xc), m Case Number Array Fuel Rods mm Rod-Water Lattice Only 1C 002 1 20 x 18.0810.02 2C 014 3 20 x 16 84.1 1 0.5 Tn Rod-Water Lattice + 304L Steel 3C 028 3 20 x 16 4.85 1 0.15 6.45 1 0.06 68.8 1 0.2 4C 035 3 20 x 17 3.02 + 0.13 40.42 + 0.70 114.7 + 0.3 Rod-Water Lattice + BORAL SC 020 3 20 x 17 7.13 + 0.11 6.45 4 0.06 63.4 + 0.2 6C 016 3 20 x 17 7.13 + 0.11 44.42 1 0.60 90.3 1 0.5 Ea78 m m U Cb Ch Tf5,TE j i #' ' " " ~ ~ ' '*'**** N JMMl(OUS*rdiYMYFivNMNMM*A4

• • 'WO'***"

...... _.. ~.... - -.. - - TABLE VII CALCULATED K VALUES FOR YANKEE R00-WATER CRITICAL LATTICES EFF (2.70Wt.% 0 Stainless Steel Clad U0 Rods (I}) 235 2 CCELL-KEN 0 II NITAWL-XSDRNPM-KEN 0 IV CCELL-DTF-IV (18-group) (123-group) Cri!icaj Calculated Calculated Calculated Ex 'tl Moderator-Reactivity Reactivity Reactivity Square to-Fuel eff i ") lattice Volume Cylinder (keff) (keff + o) (k Case Spacing, in. Ratio Radius, cm 1A 0.435 1.405 26.820 1.016 1.006 i.006 1.007 i.005 i 2A 0.470 1.853 24.294 1.015 1.014 +.005 1.013 +.005 3A 0.573 3.357 23.600 1.011 1.003 +.005 1.008 +.004 4A 0.615 4.078 24.771 1.009 1.010 +.005 1.002 +.004 5A 0.665 4.984 27.172 1.005 1.005 +.005 1.013 +.004 Average: 1.008 +.002 1.009 +.002 Ea os T w e e N C7 N h&lhhhh$$ WD55{=!b%YOS'**NY? 4 NMk% T:- ~ ' "" :T:"~ ~"% - -M:- . x mw n-- w-

. f TABLE VIII CALCULATED K VALUES FOR ORNL CRITICAL LATTCES EFF (4.95 Wt.% U Unclad Uranium Metal Rods (2)) 235 CCELL-KEN 0 II NITAWL-XSDRNPM-KEN 0 IV (18-group) (123-group) Calculated Calculated Reactivity Reactivity Lattice Number of Critical Water (keff + a) (keff + ") Case Number Rods Height Above Lattice, cm Rod-Water Lattice Only 1B 22 203 7.1 0.988 i.006 0.997 i.005 G 2B 23 195 15.24 0.998 +.006 0.999 +.006 Rod-Water Lattice + U(0.185) Block 3B 104(Run) 245 9.5 1.001 i.006 0.993 i.006 Rod-Water Lattice + U(0.185) Block + BORAL Sheet 4B 105 (Run) 324 15.24 1.038 i.005 1.000 i.005 SB 359 11.94 1.037 +.006 0.999 _+.005 x? Average: 1.012 +.003 0.998 +.002 ER 1 u 8 Os CO ... = ~ ~ ~ ~ .___.,=- = y [6h$1.Q%%MlittNIMf4!!$le6Y WA*EASN4%MWGNJMO3MNWE 7? S= MLym+--N=

TABLE IX 9 CALCULATE 0 K VALUES FOR PNL CRITICAL LATTICES EFF (2.35 Wt.% 2350 Aluminum Clad UO Rods (3)) 2 CCELL-KENO II NITAWL-XSORNPM-KEN 0 IV (18-group) (123-group) Calculated Calculated Experiment Number of Fuel Separa lo tween Reactivity Reactivity Case Number Clusters in Array Fuel Clusters, cm (keff + o) (keff 1 ") Rod-Water Lattice Only IC 002 1 1.008 1 005 1.004 1 005 2C 014 3 8.41 1.007 1 005 0.991 1 005 Rod-Water Lattice + 304L Steel 3C 028 3 6.88 0.994 i.004 0.997 i.004 4C 035 3 11.47 0.997 +.005 1.000 +.005 Rod-Water Lattice + BORAL SC 020 3 6.34* 0.995 +.005 0.999 +.005 EC 016 ch 3 9.03 1.007 +.005 0.999 +.004 .L xx u ~

• ii 1.

Average: 1.001 +.002 0.998 +.002 8 N

• 6.33 cm assumed in reactivity calculation

__ -n ~ N " m W m ' = " ~ ~ ~ ~ ~ ~ ~ ~ ~p. pgtveR595%wnmMwwnvMvWm

j. XN-NF-499 T-l [-. 4 I-t I, h-i l. h [. E d t., Water I j kA Is L. oooooooooooO oO l-b,' oooooooooooCoo e oooooooooooccc ? { t-oooooooooooccc ( oooooooooooccc Water i ).: oooeoooooeoeoc Water [ s' ooooooooooccoo j (. oooooooooooooe t oooooooooooooe [ oooooooooc.cc e - 1; 4 i oooooooooooC o-oooooooooooeo. (. oooooooooooooo -r 1 7 ooooooooooccoc i ooooooo ](( t TOP VIEW l l l.4 k{? i ~. Reflector: 7.1 cm water above fuel 15.24 cm water in all other directions [.[# l l,. : ! II, !!b i 3 'l tr FIGURE 1 76 ORNL Critical Assembly Arrangement jf3l }g {. Case 18 - LATTICE #22 (203 Rods)

p. -

4 h:. t.

{ XN-NF-499 L k'. t i f i I l-1 [, Water r l I OO OOO O OO O 1 O OO OO O O OO OO [' OO OO OO O O OO OOO c OO 00 00 0 0 00 000 OO OO OO O O OO OOO O i OOO OO OO O O O O OOO O ( Water OOO OOOOO O O O OOO O Water E ih 000 00 00 0 0 0 0 00 0 0 0 00 0000 0 0 00 000 0 iI!f OOO OOOO O OOOO OO O OOO OO OO O O O OOO O O t : } O OO OO OO oO oO OO O J OO O O OO O OOOOOO iI t O OOOO O OOOOO ij OOO O O OO ] I i i4 ~ i' TOP VIEW g-g- i Reflector: 15.24 cm water in all directions {? Lh i [ l .i:P FIGURE 2 . lI' i,L 1 it ORNL Critical Assembly Arrangement ' f; Case 28 - LATTICE #23 (195 Rods) ! i [L i I-i i : 1631 271 l [.~- hb

} l. XN-NF-499 3, l DEPLETED URANIUM SLCCK Lt (See Table III) h I i l.r-t v i b j oooooooo oooooooo a oooooooo oooooooo l r; oooooooo oooooooo I 0.627 cm [ oooooooo oooooooo ihI oooooooo oooooooo i[ oooooooo oooooooo oooooooo oooooooo i [ oooooooo oooooooo i Typ. oooooooo oooooooo .g oooooooo oooooooo i ; oooooooo oooooooo j !i, j oooooooo oooooooo oooooooo oooooooo [ oooooooo oooooooo jj,' ; oooooooo oooooooo l l ooo oo ( h-E lji f!! r t j' I-I r 's n[t TOP VIEW !iI Reflector: 9.5 cm water above fuel N L 15.24 cm water in all other directions r FIGURE 3 ORNL Critical Assembly Arrangement p Case 38 RUN #104 (245 Rods) I i t,. 1631 272 , = b.

( i XN-NF-499 i t i l 3 DEPLETED URANIUM BLOCK i (See Table III) i i l i. t i ti [_ e O O O OOO O O O OO C O O OOO O b lr, OO oO O OO O OoOoO O O O O O h 0.627 cm i ~- O OO O OOO OO OO O O O OO O O P-00 0 0 0 0 O'O O O O O O O O O O O {(( OOOOO O O O O O O C OO O OO O OO OO O O OOO OO O OO O O O O b OOO OO O O O OOO O O O O O O O k l. O O OOO O OO O OO O OO O O O O ' ( O O O O OO O O OO OC O O O OO O I t O OO O OOO O OO OO O O O O O O [ j' 0 00 0 OOOO oO O O O O O O O O 5.10 cm " l 0 0 0 O O O O O O OO O OO O O O O y O O O O OO O' O OO O O O OO O OO 0.637 cm I t' OO O OO OO O O OO O O OO O OO "i Boral Sheet O OO O O OO O O O O O O O O cO O OO O OOO O O O OccOOO O O O (See Table III) jI O O O OO O O O O OO OO OO C O O [.. O OO OOO O O O O O O O O O O O O P t. TOP VIEW 5:F ., - P t w. Reflector: 15.24 cm water in all directions 'E l NW i i i 7 FIGURE 4 b ORNL Critical Assembly Arrangement Ih Case 4B - RUN #105 (324 Rods) 1631 273 f? a , V. t*1

XN-NF-499 [ n I } DEPLETED URANIUM SLOCK i i (See Table III) I r .I i o O OO OO OO O OO O O O ; C c0 0O n O OOOO OO O O O O O O C c cO OO i O OO OO OO O OO O cO oeoO OO 0.627 cm 1 O O O O O OO O OO OC C 0 C O O OC 6 I I I O O O OO OO O OO O C D 0 C ': O OO l ^ O OO OO OO O OO O O O O O O O OC O OC 0 0O O O O O OC O O C oO OO i O OO O OO O O OO OC OO C C O OO O OO O O OO OOO OC OC O C O OO 5.10 cm O OOO O O O O OO OO O O C 0 0 OO g O OOO OOO O OO Occ0 C : oO c 0.637 cm O OO O OO O O OO OO ooc O O OC O O O O OO O O OO Oc0eccoOO Boral Sr.ca: O O OO O O O O OO O cO cC coOo (See Table III) O OO O O O O O OO OC O O C O OO l O OOO O OOO OO OO OeOO O OC O OO O O OOO OO OO OO C C O OC I~ ] OO OO OO O O OO OO O DOoO OO OO O OOOO OO OoCOcc0 O rr TOP VIEW Reflector: 11.94 cm water above fuel i 15.24 cm water in all other directions i l FIGURE 5 l ORNL Critical Assembly Arrange. ment Case 5B (359 Rods) Jg}j }74

XN-NF-499 4 1 FIGURE 6 t f PNL CRITICAL EXPERIMENTS t GRAPHICAL ARRANGEMENT OF SIMULATED SHIPPING PACKAGE CRITICAL i g i 50.5 51! < - 3 n l l t 1 - T6 4 A*.C ~33 -n 4: in, 3g3,,,,n,g, g Y Y _e I I! I e d i 'I l fx l l;xlC00 I C 3 oo CARION STII. *A*.<

i

\\ e f O 'l i 5 0 E h 3 x 00000 x 3 - U U y l if x, z'- I . = 1 = e t I P Cl 5 C *. d'. A *I l 5 b t gi i b l E-x 00000 x E f fy t 0 6 l 152 - i imins I o g 7 i 2 o o 3 5 8 t ICP C* P L I i ooe oo G 3 j li M3 x518th.35 mm l j E x oooo00g x E 3 W - 76 M oiGLE j S S l i j Pc/ 8 4 E tb C4 E l fl '~' f 4 i l

o i POISON 9 tall l [

'f j -[ j lt y Ij $ 12.7 9m :131 mm y f i g - - -#000 0 8 l - e s. eCel ~6 Al RCOS I l s s ll l jj 12.7 mm SICK lf/ { E E{ j j g g 'j ACRYt!C 7'.A'E5 a j y i I li E l 153:513 6.35 cm t l l E

j

,' 6061 76 Al I l 0 i C00 } G i x 00000 x i i f CHANNEL f l t q t v a Q ll 50T701.1 C r,,gi, j ny i l fC SPACER RODS k v i 23.4 mm E-IC.< g] S ,_r. ACRYllC PLA,c 3C5 im tmins I l .t31.3 mm- -.- END Vf D't i i PLAN VIEW h D** 3 1631 275 ie P aw w c 2 l F

V f e

~ 2

f XN-NF-499 L.

E er 1: CALCULATIONAL METHODS KENO H (18 Gp.) MODEL i CCELL n. i. GAMTEC H DRT-1 l=- z KENO H { u t. ? KENO IV (123 Gp.) MODEL NITAWL t 3 XSDRNPM R[ -lh,. : t .E KENO N j"f 1 i in et d. F FIGURE 7 1631 276 C COMPUTER CODE CALCULATONAL MODELS I i

_. _. __ _ Qc,. it XN-NF-499 4 A 4

7.0 REFERENCES

3y sp (1) V. E. Grob, et al, " Multi-Region Reactor Lattice Studies Results of p Critical Experiments in Loose Lattices of U0 Rods in H 0," WCAP-1412, f 2 2 Westinghouse Electric Corporation (1960). s}- (2) Information obtained via persc,nal communication with E. B. Johnson and G. E. Whitesides, Oak Ridge National Laboratory, Oak Ridge, i i Tennessee (September 1976). j (3) S. R. Bierman, E. D. Clayton and B. M. Durst, " Critical Separation Between Subcritical Clusters of 2.35 Wt.". U-235 Enriched 00 Rods in 4 7 Water with Fixed Neutron Poisons," PNL-2438, Pacific Northwest 4 Laboratories (October 1977). j k p (4) G. E. Whitesides and N. F. Cross, " KEN 0 - A Multigroup Monte Carlo j. Criticality Program," CTC-5, Union Carbide Corporation Nuclear W Division (September 1969). $e (5) L. M. Petrie and N. F. Cross, " KEN 0 IV: An Improved Monte Carlo j Criticality Program," 0RNL-4938, Oak Ridge National Laboratory 4 (November 1975). h.x (6) W. W. Porath, "CCELL Users Guide," BNW/JN-86, Pacific Northwest j Laboratories (February 1972). T,. (7) C. L. Bennett and W. L. Purcell, "BRT-1: Battelle Revised THERMOS," BNWL-1434, Pacific Northwest Laboratories (June 1970). i l (8) L. L. Carter, C. R. Richey and L. E. Hushey, "GAMTEC-II: A Code for i Generating Consistent Multigroup Constants Utilized in Diffusion and Transport Theory Calculations," BNWL-35, Pacific Northwest Laboratories W, - (March 1965). Q (9) G. D. Joanou, J. S. Dudek, and E. J. Lashan, " GAM-I: A Consistent P d Multi-Group for Calculation of East Neutron Spectra and Multi-GroupI i Constants," GA-1850, General Atomic Division, General Dynamics f>t Corporation,1961. j l (10) J. L. Carter, Jr., "HRG-3: A Code for Calculating the Slowing-Down 7! Spectrum in the P or B, Approximation," BNWL-1432, Pacific Northwest 3 Laboratories (June 19707 J f, !$.k Y (11) D. R. Skeen and L. J. Page, " THERMOS /BATTELLE: The Battelle Version of L the THERMOS Code," BNWL-516, Pacific Northwest Laboratories (September T 1967). I 1 m (12) F. T. Adler, G. W. Hinman and L. W. Nordheim, "The Quantitative h? Evaluation of Resonance Integrals," Proc. Intern. Conf. Peaceful i/* Uses of Atomic Energy, Geneva,16, p.1988,1958. I N 1631 277 ! k I a: '. 1 E h,'

h A XN-NF-499 j,

1i G o",'

7.0 REFERENCES

(Continued) l-4 >-2 (13) H. Amster and R. Suarez, "The Calculation of Thermal Constants b'.' Averaged Over a Wigner-Wilkings Flux Spectrum," WAPD-TM-39, Bettis Atomic Power Laboratory, 1957. [< (14) N. M. Greene, et al, "AMPX - A Modular Code System for Generating Coupled Multigroup Neutron-Gamma Libraries from ENDF/B," 0RNL-TM-3706, Oak Ridge National Laboratory (March 1976). i 2lji (15) T. M. Traver, " Users Manual for DASQHE," BNWL-CC-2274, Pacific Northwest Laboratories (September 1969). l tf (16) N. M. Greene and C. W. Craven, Jr., "XSDRN: A Discrete Ordinates Spectral Averaging Cod 0," ORNL-TM-2500, Oak Ridge National Laboratory l [( (July 1969). 9 (17) K. D. Lathrop, "DTF-IV - A FORTRAN-IV Program for Solving the Multi-group Transport Equation with Anisotropic Scattering," LA-3373, Los Alamos Scientific Laboratory (July 1965). r.j 1631 278 w'& il N a r.. 5" m Le v::. u; C-7 1 u ' 10837 t;e

I .g ..f=, XN-NF-499 Issue Date: 4/16/79 O i tr l T ri. L8 CRITICALITY SAFETY '3 BENCHMARK CALCULATIONS FOR LOW-ENRICHED URANIUM METAL )l. ,$:.' F AND URANIUM OXIDE ROD-WATER LATTICES J EIb 5[j'e ?$ Distribution mW C. O. Brown (5) T. G. Eckhart (3) L. E. Hansen (2) W. S. Nechodom V R. Nilson [k J. H. Nordahl .R L. C. O'Malley

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