Text

Criticality Safety Analysis of W Spent Fuel Storage Racks in Pool B of Crystal River Unit 3
	ML20212C112
Person / Time
Site:	Crystal River
Issue date:	09/16/1999
From:	Sarah Turner; HOLTEC INTERNATIONAL
To:	;
Shared Package
ML20138D882	List: 3F0999-07, Application for Amend to License DPR-72,to Change ITS Proposed in LAR 239,rev 0,increasing Licensed Capacity for Spent Fuel Assembly Storage in SFP & Revise Configuration for Storage of Fresh Fuel.Proprietary Encl Withheld; ML20212C096; ML20212C099; ML20212C112; ML20212C135; ML20212C150;
References
	HI-992128, NUDOCS 9909210142
	Download: ML20212C112 (39)
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O CRITICALITY SAFETY ANALYSIS 01 THE WESTINGHOUSE SPENT FUEL STORAGE RACKS IN POOL ~ B OF CRYSTAL RIVER UNIT 3 1

Prepared for the FLORIDA POWER CORPORATION by Stanley E. Turner, PhD, PE i

i Holtec Project No. 70695 Holtec Report HI-992128 230 Normandy Circle 555 Lincoln Dr. W Palm Harbor, FL 34683 Marlton,NJ 08053 9909210142 990916 .

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TABLE OF CONTENTS

1.0 INTRODUCTION

AND

SUMMARY

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 2.0 ANALYSIS CRITERIA AND ASSUMPTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.0 ACCEPTANCE CRITERIA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 4.0 DESIGN AND IN PUT DATA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 5.0 - M ETHO DOLOGY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 6.0 ANALY TICAL RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 7.0 FUEL CURRENTLY IN STORAG E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 8.0 REFERENC E S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 APPENDIX A- BENCHMARK CALCULATIONS (11 Pages Total)

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O tisrOFTAstes

- 4.1 ' l, SIGN BASIS FUEL ASSEMBLY SPECIFICATIONS . . . . . . . . . . . . . . . . . .

u 15-6.1 REACTIVITY UNCERTAINTIES DUE TO MANUFACTURING TOLERANCES (Limiting Reactivity Cases) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 6.2 UNCERTAINTIES IN FUEL ENRICHMENT AND U O2D EN S I TY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 6.3

SUMMARY

OF CRITICALITY CALCULATIONS REGION 2 POOL B UNRESTRICTED STORAGE . . . . . . . . . . . . . . . . . . . . . . . . 18 6.4

SUMMARY

OF CRITICALITY CA1.CULATIONS REGION 2 POOL B STORAGE IN PERIPHERAL CELLS . . . . . . . . . . . . . . . . . 19 6.5 EFFECT OF TEMPERATURE AND VOID ON CALCULATED REACTIVITY OF STORAG E RACKS ' . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 6.6 REACTIVITY EFFECTS OF ABNORMAL AND ACCIDENT CON DI TI ON S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 LIST OF FIGURES

' Fig. 1 1 MINIMUM BURNUP REQUIREMENTS FOR SPENT FUEL IN THE WESTINGHOUSE CR3 POOL B STORAGE RACKS Fig. 1 2 MINIMUM BURNUP REQUIREMENTS FOR SPENT FUEL IN THE WESTINGHOUSE CR3 POOL B STORAGE RACKS (WITH EXISTING FUEL SUPERIMPOSED)

Fig. 4 1 REGION 2 FUEL STORAGE CELL 4 O.

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1.0 INTRODUCTION

AND

SUMMARY

The purpose of the present evaluation of the new CR3 Pool B storage racks is to document the criticality safety of the Westinghouse-designed racks. These racks use Boral panels as the neutron absorber material in a classical Region 2 design (single panels between storage cells.) The analysis uses the KENO 5a Monte Carlo code with the 238-group cross-section library developed by the Oak Ridge National Laboratory. Check calculations were made with the MCNP code, a Monte Carlo code developed by the Los Alamos National Laboratory, to confirm the model geometry. CASMO4 was used for calculation of fuel depletion effects and manufacturing tolerances. As permitted in the USNRC guidelines, parametric evaluations were performed for each of the manufacturing tolerances and the associated reactivity uncertainties combined statistically. All calculations were made for an explicit modeling of the fuel and storage cell (infinite radial array) to define the enrichment-burnup combinations that assure a maximum effective multiplication factor (ka) of 0.95 including uncertainties under normal storage conditions, evaluated for 95% probability at the 95% confidence level.

The maximum k-effective values for unrestricted storage were determined with the KEN 05a code, assuming an infinite radial array of storage cells with a finite axial length, ;

water reflected. For each initial enrichment, minimum burnup values were determined that assure the maximum k-effective, including calculational and unufacturing l uncertainties, remains less than 0.95 for normal storage conditions under the assumed accident condition of the loss of all soluble boron. The upper cune in Figure 1-1 summarizes the results of the analyses, showing the minimum acceptable burnup for fuel of various initial enrichments. All points on the curve have the same maximum reactivity. Figure 1-2 shows the same burnup limit curves with currently existing spent fuel assemblies superimposed (plotted at 95% of the burnup determined from plant operating data).

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Parallel calculations were made to determine the minimum burnup required for fuel stored in the peripheral cells where radial neutron leakage reduces the reactivity in these cells. Figure 1-1 (lower curve) illustrates the minimum bumup required for fuel stored in the peripheral cells for fuel of various initial enrichments. All points on the curve represent the same maximum array reactivity (less than 0.95), and assumes all interior

)

cells are filled with fuel of the maximum allowable reactivity in accordance with the upper curve in Figure 1-1.

Evaluation of postulated accident conditions demonstrate that 360-ppm soluble boron is adequate to protect against the most serious fuel mis-loading accident, assuring that the maximum reactivity remains below the regulatory limit. Recent USNRC Guidelines allow partial credit for soluble boron, and this would be more than adequate to protect against the most serious fuel handling accident.

1 Results of the analyses confirm that the Westinghouse storage racks can safely accommodate fuel with initial enrichments up to 5.0%, with assurance that the maximum i reactivity, including calculational and manufacturing uncertainties, will be less than 0.95, with 95% probability at the 95% confidence level, provided the fuel conforms to the )

enrichment-burnup limits defimed in Figure 1-1.

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n U. 2.0 ANALYSIS CRITERIA AND ASSUMPTIONS To assure the true reactivity will always be less than the calculated reactivity, the following conservative analysis criteria or assumptions were used.

The racks contain the most reactive fuel authorized to be stored, without any control rods or burnable poison.

The moderator is pure, unborated water at a temperature within the design basis range corresponding to the highest reactivity.

Criticality safety analyses are based upon an infinite radial array of cells; i.e.,

no credit is taken for radial neutron leakage, except for storage in peripheral cells and for evaluating accident conditions where neutron leakage is inherent.

Neutron absorption in minor structural members is conservatively neglected; e.g., spacer grids are replaced by water.

The analyses assumed Mark B-10F and B-11 fuel, which were determined to be the most reactive.

r Mark B-10F and Mark B-11 fuel assemblies have axial blankets of low enriched fuel (2%), which precludes the existence of higher reactivity fuel of lower-than-average burnup at the ends of the assembly. The lower enrichment ends (oflow reactivity) avoid the penalty due to the axial distribution in burnup that might otherwise occur.

The remaining assumptions are defined in Section 4.0.

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n-b 3.0 ACCEPTANCE CRITERIA The limiting enrichment-burnup combinations are shown in Figure 1-1 and tabulated below, for acceptable storage of spent fuel in Region 2 of Pool B.

Unrestricted Peripheral Cells

Enrichment Burnup, Burnup,

% U-235 MWD /KnD MWD /KgU 2 6.41 -

2.5 13.26 1,42 3 19.56 6.33 1 1

3.5 25.47 11.16 -

4 31.94. 15.59 4.5 37.46 20.00 5.0 42.73 24.34 The primary acceptance criterion is that the maximum k, shall be less than 0.95, including calculation uncertainties and effects of mechanical tolerances. Applicable codes, standards, and regulations, or pertinent sections thereof, include the following:

General Design Criterion 62, Prevention of Criticality in Fuel Storage and l Handling. l USNRC Standard Review Plan, NUREG-0800, Section 9.1.2, Spent Fuel Storage. ;

USNRC letter of April 14,1978, to all Power Reactor Licensee.; - OT Position for Review and Acceptance of Spent Fuel Storage and Handling Applications, including modification letter dated January 18,1979.

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USNRC Regulatory Guide 1.13, Spent Fuel Storage Facility Design Basis,

. Rev. 2 (proposed), December,1981. ;

ANSI-8.17-1984, Criticality Safety Criteria for the Handling, Storage and Transportation of LWR Fuel Outside Reactors.

L. Kopp, " Guidance On The Regulatory Requirements For Criticality Analysis Of Fuel Storage At Light-Water- Reactor Power Plants", USNRC Internal Memorandum L. Kopp to Timothy Collins, August 19,1998.

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2.

Ley V- '4.0 DESIGN AND INPUT DATA ,

l 4.1- Fuel Assembly Desien Soecifications i

t Two fuel assembly designs were used in the analyses; the B&W Mark B-10F fuel and the Mark B-11 fueli Other fuel designs, Mark B10 and Mark B 9/10 were also considered l but showed lower reactivity. Table 4.1 provides the pertinent design details for the Mark

( B-10, B-10F, and B-ll assembly types. Calculations showed that the Mark B-ll' fuel exhibits the highest reactivity at burnups from 0 to 30 MWD /KgU although the Ldifferences are minor. At burnups greater than 30 MWD /KgU, the Mark B-10F fuel u i

showed a slightly higher reactivity. Any burnable poison which may be in the fresh fuel ;

assemblies ~as Gd 2 3 0 or as ZrB 2 in IFBA rods, would reduce reactivity, but was not ;

included in the present analyses.

4.2 Pool B Recion 2 Rack Design

[ , _ In Region 2, the storage cells (see Reference 1) are composed of a single Boral absorber panel between the stainless steel walls of adjacent storage cells. These cells, shown in i

~

Figure 4.1, are located on a lattice spacing of 9.11

0.06 inches. The Boral absorber

_ panels have a thickness of 0.075 inch and a nominal B-10 areal density of 0.0216

0.0016 g/cm2 . The Boral panels are 7.5 0.06 inches in width.

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p 5.0 METHODOLOGY G

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The primary criticality analyses were performed with the three-dimensional NITAWL-KEN 05a Monte Carlo code package *. NITAWL was used with the 238-group SCALE-4.3 cross-section l library and the Nordheim integral treatment for U-238 resonance shielding effects. Benchmark

]

calculations, presented in Appendix A, indicate a bias of 0.0030

0.0012 (95%/95%)m, Verification calculations for selected cases were made with the MCNP code * (bias of 0.0009

0.0011, as shown in Appendix A). CASMO4, a two-dimensional deterministic codem using transmission probabilities, was used to evaluate the small (differential) reactivity effects of manufacturing tolerances. Validity of the CASMO4 code was established by comparison with KEN 05a and MCNP calculations for comparable rack cases.

l In the geometric model used in the calculations, each fuel rod and each fuel assembly were explicitly described. Reflecting boundary conditions effectively defined an infinite radial array ;

of storage cells. In the axial direction, a 30-cm water reflector was used to conservatively describe axial neutron leakage. Each stainless steel box and all associated Boral panels were also explicitly described in the calculational model. The fuel cladding material was I conservatively assumed to be zirconium; the actual Zircaloy, with a greater absorption cross- i section, would tend to slightly reduce reactivity although not significantly. In evaluating the use of peripheral cells for storage of lower burnup (higher reactivity fuel, with credit for radial neutron leakage) the KEN 05a code was used with 30 cm water reff ectors.

Monte Carlo (KEN 05a and MCNP) calculations inherently include a statistical uncertainty due to the random nature of neutron tracking. To minimize the statistical uncertainty of the KEN 05a calculated reactivities, a minimum of 4 million neutron histories were accumulated in each calculation, generally resulting in a statistical uncertainty of about 0.0003 Ak (Ic). A comparable number of neutron histories were accumulated in the MCNP verification calculations.

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O ' 6.o ANALYSIS RESULTS '

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6.1 Code Comoarison Calculations- CASMO4. KEN 05a and MCNP An independent method of analyses (MCNP) was used to verify the reference KEN 05a calculations. In addition, these calculations serve to verify the CASMO4 code, since -

CASMO4 is.'a two-dimensional code and cannot be directly validated against critical

{

' experiments. 'the USNRC guidelines, however, endorse CASMO4 and KEN 05a as ;

f acceptable methods of criticality analysis. Results of these code comparison calculations are listed below, corrected for bias.

1 These results are considered to be in good

- agreement, confirming the basic KEN 05a and MCNP ca!culations, and suggesting that the reference KENO 5a calculations may be slightly conservative.

4 COMPARISON OF CALCULATIONS

. CASE CASMO-4* KENO

MCNP*

1) 5% E fuel, w/0.0216 gB/cm 2 1.2166 1.2198 0.0014 1.2174

0.0014

2) 1.60% E w/ 0.'0216 gB/cm2 0.9144 0.9158

0.0013 0.9140

0.0014 j

, 3) 5% E fuel, w/0.0162 gB/cm2 1.2319 1.2358 0.0013 1.2343 0.0014 l

4) 1.60%E fuel w/0.0162 gB'"/cm2 0.9259 0.9278 0.0013 0.9262 + 0.0014

(1)- CASMO calculations are without U-234 for consistency with KENO 5a and MCNP. With U-234, the k, is 0.0009 to 0.0024 Ak tower, depending upon enrichment.

(2) Uncertainty is the RMS of(1.7* 0.0004) and 0.0012 for KENO 5a.

-l (3) Uncertainty is the RMS of(1.7* 0.0004) and 0.0011 for MCNP. l

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4 O 6.2 Evaluation or uncertainties Calculations were made to determine the uncertainties in reactivity associated with manufacturing tolerances. . Tolerances that would increase reactivity were calculated; .

negative values are expected to be of equal magnitude but opposite in sign over the small tolerance variations. Results 'of these calculations are shown in Table 6.-l. The reactivity effects were separately evaluated, in a sensitivity study for each independent tolerance, and the results combined statistically.

Tolerances considered include the following.

6.2.1 Tolerance in Boron Loading in the Boral The standard manufacturing tolerance in B-10 loading is 8% of the nominal loading warranted. Composition and tolerances of the Boral are as follows:

i Nominal Tolerance ;

Thickness, inches 0.075

0.007 - '

B-10 loading, g/cm 2 Nominal 0.0216 0.0016 I Minimum 0.0200 -

)

l The reactivity uncertainty associated with the B-10 loading is shown in Table 6.1.

Thickness tolerance has no effect at given B-10 loading.

6.2.2 Tolerance in Boral Panel Width The tolerance in Boral panel width is 0.06 inch. Reactivity uncertainties for this tolerance are shown in Table 6.1.

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V 10 v 6.2.3 Tolerance in Box I.D. or Lattice Pitch In Region 2, there is no water gap and the tolerance in the lattice pitch reflects the tolerance in the Box I.D. The minimum cell pitch is 9.05, which, for a nominal pitch of 9.11 inches, corresponds to a tolerance of 0.06 inches. The reactivity uncertainty associated with this tolerance is given in Table 6.1.

6.2.4 Stainless Steel Thickness The nominal tolerance in steel thickness is 10% of the combined box wall and sheath.

For the nominal combined thickness of 0.09 inches, the reactivity uncertainty is given in Table 6.1.

6.2.5 Tolerances in Fuel Enrichment and Density For estimating the reactivity uncertainties associated with tolerances in fuel enrichment and density, conservative tolerances of 0.05% in enrichment and

0.200 g/cc in UO2 density were assumed. The reactivity uncertainty associated with the tolerance is summarized in Table 6.2. While the uncertainty due to UO2 density is not sensitive to enrichment, the uncertainty due to the enrichment tolerance varies substantially with enrichment, decreasing as the enrichment increases. The reactivity uncertainty associated with the tolerance in fuel enrichment and density were separately determined and the results are shown in Tables 6.2 and 6.4.

6.2.6 Uncertainty in Depletion Calculations The uncertainty in depletion calculations was taken as 5% of the reactivity decrement from beginning-of-life to the burnup of concern (see Reference 6). Results of the o depletion analyses, using this methodology are shown in Tables 6.3 and 6.4.

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U 6.3 Storace Rack Calculations 6.3.1 Region 2, Pool B - Unrestricted Storage !

Region 2 cf Pool B is designed for fuel of various enrichment-bumup combinations as illustrated in Figure 1-1. Calculations for the maximum reactivity for unrestricted storage, are itemized in Table 6.3. All cases (enrichments) in Figure 1-1 and Table 6.3 have the same maximum reactivity.

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6.3.2 Region 2, Pool B - Peripheral Storage Cells l

The capability of peripheral cells to safely accept fuel of lower burnup was also evaluated, based on 3-dimensional KENO 5a calculations. Results are shown in Figure 1-1 (lower curve) and itemized in Table 6.4. l In order to represent the geometry of the peripheral cells, calculations were made with KEN 05a in the dimensions representing the periphery of the rack with an infmitely thick radial water reflector (30-cm). The KEN 05a model assumed fuel of the maximum allowable reactivity in the internal cells (unrestricted storage) and determined the burnup of fuel in the peripheral cells that would yield a maximum reactivity below the regulatory l limit. The maximum reactivity is itemized in Table 6.4 and confirms that the peripheral cells can safely accommodate fuel of high reactivity (lower burnup) as illustrated in l

Figure 1.1. j l

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6.4 Abnormal and Accident Conditions 6.4.1 Temperature and Void Effects Temperature effects were also evaluated in the temperature range from 4 *C to 120 *C and the results are listed in Table 6.5. These results show that the temperature coefficient

.. of reactivity is negative and that 4 C (maximum water density) corresponds to the highest

) reactivity. Similarly, the void coefficient of reactivity (boiling conditions) was found to be negative.

6.4.2 - Mis-loaded Fuel Assembly The potential effects of abnormal and accident conditions were also considered, as indicated in Table 6.6. Only the case of a mis-loaded fuel assembly was found to have -

more than a negligible impact. The mis-loading of an unburned Mark B-11 assembly of l 5.0% enrichment into a Region 2 cell intended for spent fuel could potentially exc.eed the regulatory limit on k-effective, although criticality would not be reached. For this condition, calculations indicate that credit for 360 ppm soluble boron would maintain the maximum reactivity below the regulatory limit. j i

6.4.3 Eccentric Fuel Positioning i The fuel assembly is normally centered in the storage cell. Calculations made with the 1 assembly eccentrically positioned (4 assemblies at the point of closest approach) showed a lower reactivity, as expected, and confirmed that the centered position is the most conservative. l 11oltec Report 111-992128

m O 7.0 FUEL CURRENTLY IN STORAGE -

There are a number of spent fuel assemblies currently in storage. Figure 1-2 shows the i

' limiting burnups required (from Figure 1-1), with the enrichment-burnup values from the !

i fuel assemblies currently in storage superimposed. Burnup values for the spent fuel are shown at 95% of the reported burnups as an allowance for uncertainty in determining'the burnup.

Most fuel assemblies currently in storage may be safely accommodated in the unrestricted area of the storage racks, although a few (6 at the present time) will be administratively restricted to peripheral cells'.

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8.0 REFERENCES

1. Crystal River Unit 3' Rack Design Drawings (Westinghouse).

-l

2. ' R.M. Westfall, et. al., "NITAWL-S: Scale System Module for Performing ' l Resonance Shielding and Working Library Production" in SCALE: A Modular Code System for Performine Standardized Comnuter Analyses for Licensine Evaluation., NUREG/CR-0200,1979.

L.M. Petrie and N.F. Landers, " KENO Va. An improved Monte Carlo Criticality Program with Subgrouping" in SCALE: A Modular Code System for Performine Standardized Computer Analyses for Licensine Evaluation., NUREG/V-0200,1979.

3. M.G. Natrella, Exnerimental Statistics, National Bureau of Standards, l Handbook 91, August 1963.

)

4. J.F. Briesmeister, Ed., "MCNP - A General Monte Carlo N-Particle Transport Code, Version 4A", Los Alamos National Laboratory, LA-12625-M (1993).

5. A. Ahlin, M. Edenius, H. Haggblom, "CASMO- A Fuel Assembly Burnup.

Program," AE-RF-76-4158, Studsvik report (proprietary).

A. Ahlin and M. Edenius,"CASMO- A Fast Transport Theory Depletion Code for LWR Analysis," ANS Transactions, Vol. 26, p. 604,1977.

D. Knott, "CASMO4 Benchmark Against Critical Experiments",

Studsvik Report SOA-94/13 (Proprietary).

M. Edenius et al., "CASMO4, A Fuel Burnup Program, Users Manual" Studsvik Report SOA/95/1. l l

6. L. Kopp, " Guidance On' The Regulatory Requirements For ;

Criticality ' Analysis.Of Fuel Storage At Light-Water Reactor '

Power Plants", USNRC Internal Memorandum L. Kopp 'to l Timothy Collins, August 19,1998. '

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Table 4.1

' DESIGN BASIS FUEL ASSEMBLY SPECIFICATIONS FUEL ROD DATA' MARK B10 hfARK B10F MARK Bil Outside diameter, in. 0.430 0.428- 0.414 Cladding inside diameter, in. 0.377 0.382 0.370 Cladding material Zr-4 Zr-4 Zr-4 Stack density, gms UO2/cc 10.522 10.522 10.522 Pellet diameter, in. 0.370 0.3742 0.3622 Maximum enrichment, wt. % 5.0% 5.0% 5.0%

U-235 FUEL ASSEMBLY DATA Fuel rod array 15 x 15 15 x 15 15 x 15 Number of fuel rods 208 208 208 Fuel rod pitch, in. 0.568 0.568 0.568 Number of guide tubes 16 16 16 Guide tubes D.D., in. 0.5300. 0.5280 0.5280 Guide tubes I.D., in. 0.4980 0.5000 0.5000 Number ofinst. Tubes 1 1 1

)

Inst. tube O.D., in. 0.5441 0.4910 0.4910 Inst. tube I.D., in. 0.4410 0.4430 0.4430 O.

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4 O Tahie6.i REACTIVITY UNCERTAINTIES DUE TO MANUFACTURING TOLERANCES (Limiting Reactivity Cases)

Ouantity Nominal Value Tolerance Ak Boron-10 loading 0.0216 g/cm 2 A 0.0016 g/cm 2

0.0041 Boral width 7.500 inchea

0.06 inch i 0.0012 Cell box I.D.- 9.11 inches 0.06 inch

0.0026 SS thickness 0.075/0.020 *10% 0.0008 Statistical combination of 0.0052 tolerance uncertainties 10 Holtec Report Hi-992128

.O Tesi 6.2 UNCERTAINTIES IN FUEL ENRICHMENT AND UO2 DENSITY Enrichment Ak for 0.05% AE% Burnuo. MWD /KnU Ak for 0.200 n/cc 2

0.0075 0 0.0012 2.5 -

0.0056 10 0.0009 3.0. *0.0043 20- 0.0010 3.5

0.0034 30 0.0014 4.0

0.0029 40 0.0020 4.5 0.0024 45 0.0023' 5.0 .

0.0018 8

Highest most conservative value used Holtec Report Hi-992128 -

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p V

APPENDIX A: BENCHMARK CALCULATIONS A.1 INTRODUCTION AND

SUMMARY

Benchmark calculations have been made on selected critical experiments, chosen, in so far as possible, to bound the range of variables in the rack designs. Two independent methods of analysis were used, differing in cross section libraries and in the treatment of the cross sections. MCNP4a [A.1] is a continuous energy Monte Carlo code and KEN 05a [A.2]

uses group-dependent cross sections. For the KEN 05a analyses reported here, the 238-group library was chosen, processed through the NITAWL-II [A.2] program to create a working library and to account for resonance self-shielding in uranium-23S (Nordheim integral treatment). The 238 group library was chosen to avoid or minimize tlie errors t (trends) that have been reported (e.g., [A.3 through A.5]) for calculations with collapsed cross section sets.

In rack designs, the three most significant parameters affecting criticality are (1) the fuel enrichment, (2) the 3 B loading in the neutron absorber, and (3) the lattice spacing (or water-gap thickness if a flux-trap design is used). Other parameters, within the normal range of rack and fuel designs, have a smaller effect, but are also included in the analyses.

Table A.1 summarizes results of the benchmark calculations for all cases selected and I analyzed, as referenced in the table. It is important to note that there is obviously considerable overlap in parameters since it is not possible to vary a single parameter and maintain criticality; some other parameter or parameters must be concurrently varied to maintain criticality.

One possible way of representing the data is through a spectrum index that incorporates all I of the variations in parameters. KEN 05a computes and prints the " energy of the average l lethargy causing fission" (EALF). In MCNP4a. by utilizing the tally option with the identical 238-group energy structure as in KENO 5a, the number of fissions in each group may be collected and the EALF determined (post-processing).

t Small but observable trends (errors) have been reported for cai, ilations with the 27-goup and 44-group collapsed libraries. These errors are probably due to the o

V use of a single collapsing spectrum when the spectrum should be different for the various cases analyzed as evidenced by the spectrum indices.

Appendix A, Page 1

i l

O Figures A.1 and A.2 show the calculated k,y for the benchmark critical experiments as a function of the EALF for MCNP4a and KEN 05a, respectively. The scatter in the data f(even for comparatively minor variation in critical parameters) represents experimental error' in performing the critical experiments within each laboratory, as well as between the various testing laboratories. The B&W critical experiments show a larger experimental error than the PNL criticals. This would be expected since the B&W criticals encompass a greater range of critical parameters than the PNL criticals.

Linear regression analysis of the data in Figures A.1 and A.2 show that there are no trends, as evidenced by very low values of the correlation coefficient (0.13 for MCNP4a and 0.21 for KENO 5a). The total bias (systematic error, or mean of the deviation from a k,y of exactly 1.000) for the two methods of analysis are shown in the table below.

Calculational Bias of MCNP4a and KENO 5a MCNP4a 0.0009 0.0011 KEN 05a 0.0030 0.0012 The bias and standard error of the bias were derived directly from the calculated k,3 values in Table A.1 using the following equations", with the standard error multiplied by the one-sided K-factor for 957c probability at the 95 % confidence level from NBS Handbook 91

[A.18] (for the number of cases analyzed, the K-factor is -2.05 or slightly more than 2).

E .1 f k, (3A.1) n o A classical example of experimental error is the corrected enrichment in the PNL experiments. first as an addendum to the initial report and secondly, by revised values in subsequent reports for the same fuel rods.

These equations may be found in any standard text on statisties, for example, reference p - [A.6] (or the MCNP4a manual) and is the same methodology used in MCNP4a and in KEN 05a.

Appendix A, Page 2

. - ~

F

!O v

[ k,' - ({ k,)2 /n 4,. i (3A.2) n (n-1) i Blas - (1- k )

K or (3A.3) .

l where k, are the calculated reactivities of n critical experiments; o, is the unbiased

. estimator of the standard deviation of the mean (also called the standard error of the bias 4 (mean)); K is the one-sided multiplier for 95% probability at the 95% confidence level (NBS Handbook 91 [A.18]).

Formula A.3 is based on the methodology of the National Bureau of Standards (now NIST) '

and is used to calculate the values presented on page A-2. The first portion of the equation,

( l- R ), is the actual bias which is added to the MCNP4a and KENO 5a results. The second j term, Ko;, is the uncertainty or standard error associated with the bias. The K values used were obtained from the National Bureau of Standards Handbook 91 and are for one-sided statistical tolerance limits for 95 % probability at the 95% confidence level. The actual K i values for the 56 critical experiments evaluated with MCNP4a and the 53 critical I experiments evaluated with KEN 05a are 2.04 and 2.05, respectively. I The bias values are used to evaluate the maximum karvalues for the rack designs. j KEN 05a has a slightly larger systematic error than MCNP4a, but both result in greater precision than published data [A.3 through A.5] would indicate for collapsed cross section sets in KEN 05a (SCALE) calculations.

The benchmark critical experiments include those with enrichments ranging from 2.46 w/o l to 5.74 w/o and therefore span the enrichment range for rack designs. Linear regression analyses for the data of various enrichtnents confirms that there are no trends, as indicated '

by low values c' ae cerrelation coefficients (0.03 for MCNP4a and 0.35 for KENO 5a).

Thus, there are no corrections to the bias for the various enrichments.

The cross-comparison of calculations with codes of comparable sophistication is suggested l in Reg. Guide 3.41. Results of this comparison, shown in Table A.1, confirm no significant difference in the calculated values of k ar for the independent codes. Since it is ;

very unlikely that two independent methods of analysis would be subject to the same error,

this comparison is considered confirmation of the absence of an enrichment effect (trend) in the bias.

O LJ Appendix A. Page 3

. ~

O Several laboratories have performed critical experiments with a variety of thin absorber panels similar to the Boral panels in the rack designs. Of these critical experiments, those performed by B&W are the most representative of the rack designs. PNL has also made some measurements with absorber plates, but, with one exception (a flux-trap experimen'i the reactivity worth of the absorbers in the PNL tests is very low and any significant errr that might exist in the treatment of strong thin absorbers could not be revealed.

No trends with reactivity worth of the absorber was found, although based on the calculations, at least two of the B&W critical experiments seem to have unusually large experimental errors. B&W made an effort to report some of their experimental errors.

Other laboratories did not evaluate their experimental errors. These data substantiate the absence of any error (trend) in either of the two codes for the conditions analyzed, (data points fall on a 45' line, within an expected 95 % probability limit).

The critical experiments selected for analysis cover a range of fuel pellet diameters from 0.311 to 0.444 inches, and lattice spacings from 0.476 to 1.00 inches. In the rack designs, f

I the fuel pellet diameters range from 0.303 to 0.3805 inches O.D. (0.496 to 0.580 inch lattice spacing) for PWR fuel and from 0.3224 to 0.494 inches O.D. (0.488 to 0.740 inch lattice spacing) for BWR fuel. Thus, the critical experiments analyzed provide a reasonable representation of power reactor fuel. Based on the data in Table A.1, there does not appear to be any observable trend with either fuel pellet diameter or lattice pitch, at least over the range of the critical experiments applicable to rack designs.

Various soluble boron concentrations were used in the B&W series of critical experiments and in one PNL experiment, with boron concentrations ranging up to 2550 ppm. Analyses of the very high boron concentration experiments (> 1300 ppm) show a tendency to slightly overpredict reactivity for the three experiments exceeding 1300 ppm. In turn, this would suggest that the evaluati on of the racks with higher soluble boron concentrations could be slightly conservative.

The number of critical experiments with PuO2 bearing fuel (MOX) is mere limited than for UO fuel. However, a number of MOX cri:ical experiments were analyzed and the results are shown in Table A.1. Results of these analyses are generally slightly above a k, of 1.00, indicating that when Pu is present, both MCNP4a and KEN 05a tend to over7tedict the reactivity, and indicate that calculations for spent fuel may be slightly conservative.

O Appendix A. Page 4

^

i s v

A.2 References

[A.1] J.F. Briesmeister, Ed., "MCNP4a - A General Monte Carlo N-Particle Transport Code, Version 4A; Los Alamos National ;

Laboratory, LA-12625-M (1993).

[A.2] SCALE 4.3, "A Modular Code System for Performing Standardized Computer Analyses for Licensing Evaluation", NUREG-0200 '

(ORNL-NUREG-CSD-2/U2/R5, Revision 5, Oak Ridge National Laboratory, September 1995.

l

[A.3] M.D. DeHart and S.M. Bowman, " Validation of the SCALE Broad l Structure 44-G Group ENDF/B-Y Cross-Section Library for Use in Criticality Safety Analyses", NUREG/CR-6102 (ORNL/TM-12460)

Oak Ridge National Laboratory, September 199,.

l 1

[A.4] W.C. Jordan et al., " Validation of KENOV.a", CSD/TM-238, Martin Marietta Energy Systems, Inc., Oak Ridge National Laboratory, December 1986.

[A.5] O.W. Hermann et al., " Validation of the Scale System for PWR Spent Fuel Isotopic Composition Analysis", ORNL-TM-12667. Oak Ridge National Laboratory, undated, j

[A.6] R.J. Larsen and M.L. Marx, An Introduction to Mathematical Statistics and its Anolications, Prentice-Hall,1986.

[A.7] M.N. Baldwin et al., Critical Experiments Supporting Close Proximity Water Storage of Power Reactor Fuel, BAW-1484-7, Babcock and Wilcox Company, July 1979.

[A 8] G.S. Hoovier et al., Critical Experiments Supperting Underwater Storage of Tightly Packed Configurations of Spent Fuel Pins, BAW-1645-4, Babcock & Wilcox Company, November 1991.

! [A.9] L.W. Newman et al., Urania Gadolinia: Nuclear Model l Development and Critical Experiment Benchmark. BAW-1810,

} Babcock and Wilcox Company, April 1984.

O v

l Appendix A. Page 5

.O-

[A.10] J.C. Manaranche et al., " Dissolution and Storage Experimental Program with 4.75 w/o Enriched Uranium-Oxide Rods," Trans.

Am. Nucl. Soc. 33: 362-364 (1979).

[A.11] S.R. 3.errnan and E.D. Clayton, Criticality Experiments with Subcritical Clusters of 2.35 w/o and 4.31 w/o :"U Enriched UO 2 Rods in Water with Steel Reflecting Walls, PNL-3602, Battelle Pacific Northwest Laooratory, April 1981.

[A.12] S.R. 3ierman et al., Criticality Experiments with Suberitical Clusters of 2.35 w/o and 4.31 w/o "U Enriched UO2Rods in Water with Uranium or Lead Reflecting Walls, PNL-3926, Battelle Pacific Northwest Laboratory, December,1981.

[A.13] S.R. Bierman et al., Critical Separation Between Suberitical 2

Clusters of 4.31 w/o "U Enriched UO 2Rods in Water with Fixed Neutron Poisons, PNL-2615, Battelle Pacific Northwest Laboratory, October 1977.

[A.14] S.R. Bierman, Criticality Experiments with Neutron Flux Traps Containing Voids, PNL-7167, Battelle Pacific Northwest Laboratory, April 1990.

[A.15] B.M. Durst et al., Critical Experiments with 4.31 wt %2 "U Enriched UO: Rods in Highly Borated' Water Lattices, PNL-4267, Battelle Pacific Northwest Laboratory, August 1982.

[A.16] S.R. Bierman, Criticality Experiments with Fast Test Reactor Fuel Pins in Organic Moderator, PNL-5803, Battelle Pacific Northwest Laboratory, December 1981.

[A.17] E.G. Taylor et al., Saxton Plutonium Program Critical Experiments for the Saxton Partial Plutonium Core, WCAP-3385-54, Westinghouse Electric Corp., Atomic Power Division, December 1965.

[A.18] M.G. Natrella, Experimental Statistics, National Bureau of Standards, Handbook 91,- August 1963.

O Appendix A. Page 6

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ML20212C112

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ML20212C112

Text

1.0 INTRODUCTION

SUMMARY

SUMMARY

SUMMARY

1.0 INTRODUCTION

SUMMARY

8.0 REFERENCES

SUMMARY

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