ML20039B102

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Distribution Uncertainty Analysis
ML20039B102
Person / Time
Site: Big Rock Point File:Consumers Energy icon.png
Issue date: 12/15/1981
From:
CONSUMERS ENERGY CO. (FORMERLY CONSUMERS POWER CO.)
To:
Shared Package
ML20039B101 List:
References
NUDOCS 8112220290
Download: ML20039B102 (53)
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{{#Wiki_filter:'. BIG ROCK POINT POWER DISTRIBUTION UNCERTAINTY ANALYSIS nu1281-0015c142 8112220290 811215 PDR ADOCK 05000155 P PDR

Paga 1 of 52 BIG itOCK POINT POWER DISTRIBUTION UNCERTAINTY ANALYSIS Section Number Table of Contents Page Nu=ber I-Radial Pcver Distribution Uncertainty Analysis. L-7 II Axial Pcver Distribution Uncertainty Analysis. 33-36 III Local Power Distribution Uncertainty Analysic. . k5-h6 IV Su==ary 52 I~ o i f i i i

Paga 2 of 52 LIST OF FIGURES Firure No. Title Page No. 1 Assembly Enrichment and Cross Section Zones. 8 2 Various Core Loadings Analysed 9-10 3 PDQ and GROK Normalised Power and k @ Distributions.. 11-28 h Sn--ary of Radial Power Errors .... ~. 29-30 5 PDQ-GROK Radial Power Error Distribution.. 31 6 Void Dependent Albedos 32 7 GROK-Measured Flureire Error with no Corrections Applied. 37 8 GROK-Measured Flureire Error with Axial Shift Applied. 38 9 Spacer Grid Correction Factor 39 10 GROK-Measured Flureire Error with Spacer Grid Correction Applied. 40 1 GROK-Measured Flureire Error with In-Core Correction Applied bl li Percent Difference Between S= eared and Non-S= eared Distribution h2 13 GROK-Measured Flureire Error with Axial Snear Correction Applied h3 I 14 GRCK-Measured Flureire Error Distribution......... kh 15 Comparison of PDQ to CE Measured Data. hT-h9 16 PDQ-GROK Local Peaking Factor Error Distribution. 50 17 PDQ-CE Pin Power Error Distribution 51 4 4 + ,n,, ,n,

T Paga 3 of 52 REFERENCES 1. Mr David A Bixel, Nuclear Licensing Administrator, Consumers Power Company to Mr Dennis L Ziemann, Chief Operating Reactors Branch No 2 USNRC, October 30, ~1978, " Big Rock Point Physics Methodology Report." 2. Mr W D Meinert, Combustion Engineering to Mr B D Webb, Consumers Power Company, April 8, 1981, " Exchange of Experimental Data." 3 MEdenius, et.al. "CASMO-2 A Fuel Assembly Burnup Program", March, 1931

I. Radial Power Distribution Uncertainty Analysis nu1281-0015 c142

Page h of 52 RADIAL POWER DISTRIBUTICU UNCERTAIh"I'Y ANALYSIS Since the fluxvire system is inadequate for measuring a radial power distribution at Big Rock Point, a higher order calculation =ust be used to determine the accuracy of a radial power distribution as calculated by GROK. Therefore, a series of quarter core syc=etric, two dimensional fine mesh PDQ's were run to simulate the BRP reactor. The PDQ's are somewhat artificial in that all assemblies of any batch all have the sa=e exposure and only one void plane at a time is represented. The fuel used in the modeling process is designated as Exxon G3, an 11 x 11 bundle with.577 inch pitch and 3.lk", average enrichment. A diagram of a fuel bundle showing the enrich =ent and cross section zones used in the model is shovn on Figure 1. The inputs to the =odel that describe the fuel are realistic; that is, there is nothing artificial about the fuel. Ecvever, the description of the control blade was =odified somewhat so that the mesh lines in the blade vould line up with the =esh lines in the fuel rods. The vorth of the blade was then ad, justed back to its un-modified value by changing the radius of the B C absorber rods in the control blades. g It should be noted that all of the artificial aspects of the =odel should have no effect on the validity of the PDQ-GROK co=parisons, since GROK used inputs that are equivalent to the PDQ model.

Paga 5 of 52' The cross sections used by PDQ vere co=puted by CASMC2 (Reference 3), a transport theory code that does calculations on an asse=bly basis. _ Since PDQ is a diffusion theory code, the transport theory cross sections fro CASM02 =ust be adjusted for diffusion theory usage. This was done by a diffusion theory code called DIXY (equivalent to PDQ) that has been linked 'l to CASM02. DIXY vill iteratively adjust }j a and11E until the diffusion f theory reaction rates match the transport theory reaction rates. This process was perfor=ed only for =aterials with a high absorption cross section, such a gadolinia fuel and the control blade. The inputs to GRCK vere taken directly frc= CASM02. These include M, km kappa over nu, copper fluxvire reactica rate, one group flux and the infinite lattice local power distribution. Only the first three ite=s are required to calculate a power distribution. The others are needed to calculate fluxvire profiles and local peaking factors. Six different core loadings were analysed, each at voids of 0%, 25% and 50 ".. Three of the core loadings si=ulated BOC conditions and used control rods. The other three loadings simulated EOC conditions and did not use centrol rods. The various loadings, with the control rod positions, are shown in Figure 2. The power distributions as calculated by PDQ and GROK are shovn on Figure 3. Also, shown on Figure 3 is the PDQ calculated koo and the CASM02 infinite - lattice km (labeled as GROK k oo ). The asterisks en Figure 3 represent control blades that are in the core. Shown on Figure h is a sun =ary of - average percent errer by assembly location, percent error for all assembly locations and its standard deviation. This su-w/ is given for each void plane and for all of the void planes together.

Faga 6 of 52 ) For the GROK calculations, a different kernel was used than was given in the Physics Methodology Report (Reference 1). The transport kernel is nov defined as: y' = 0.60 x Mh + 0.h0 c M W A D a.,m Y'*4,m

  • K c0,4 2

where M 1, 33, mig,,g ic,,,,,,,,,,, y (33,,,,,,,,,,3,,,1,3,,,,3) and Y's,m is the node sise. The kernel rsported in Reference 1 was: W4,m = d M *jt A P.a.m Along with the change in the kernel, the radial albedos are nov void dependent. The albedos used are shown on Figure 6. One would expect the albedos to be dependent only on the physical properties of the reflector, ~ which don't change with in-channel voids. However, since the neutron transport =odel does not conserve neutrons, the albedos must vary to account for this. In preli=inarf comparison between PDQ and GROK, a bias was found in the calculated k effective between PDQ and GROK that varied with voids. Accordingly, all of the K cp's input to GROK vere adjusted by a void dependent multiplier, given below: % VOIDS k oo MULTIPLIER 0 1.002359 25 0 999330 50 0.991291 After these multipliers were applied, the observed average bias (fro = the final calculations) are: % VOIDS /k ( GacK ') 0 0.0000h2 25 -0.000004 i 50 -0.000205 I

4-Page_7 of 52 The final overall results, from Figure h, give an average percent error of 0.09995, with a standard deviation of 2.2893%. Since, the percent error was for=ulated as (GROK-PDQ) x 100/PDQ, an uncertainty statement for normalized I i power =sy be made as (1.0-(.0999+Fx2.2893)/100) PDQ ( GROK x ( vhere F is 1.6k5, the factor required for 95% confidence that, 95% of all GROK calculated assembly powers, after being multiplied by the uncertainty factor, vill be greater than the PDQ calculated assembly power. i Evaluating the uncertainty state =ent gives i PDQ ( GROK x 1.036660 or 3.6660%. Note that this is a one sided confi'dence level, not a two sided confidence. Implicit in this argn=ent is the assunption that the error dis %-ibution is no mal. The histogram given on Figure 5 shows that the error distribution .i is reasonably normal, so that the uncertainty statement is valid. i

Fago 8 og 52 FIGURE 1 EURICHICiT MID CROSS SECTICN ZONES L L M L LOW ENRICHMENT M M H M MEDIUM ENRICEICIT M H H H H HIGH ENRICH! CIT M E H H I G - HIGH ENRICH! cit iiITH M H G H H H M H H H I H I I - SOLID ZIRCALOY INERT RODS M E E H H H H H M M H H H G H H H L M M E H H H H M M L L M M M M M M M LL DIAGONAL SUSETRY 16 l 17 l 15 l CROSS SECTION ZONES 12 12 11 10 1. Lov 1 2 1 2. Medium 17 12 3 h 3 1h 3. Medium 5 6 5 k. High 7 5 High 8 8 6. Gd 0 23 15 2 h 6 9 6 4 2 7. High 8 8 8. Zirealoy (solid) 7 9. High 5 6 5 10. I:mer Gap 12 3 h 3 11. Can 1 1 12-lh Water 13

15. S c Rods h

16. S.S. Cross Member 18 lb 1k

17. E=pty Tubes
18. Cu F1unire

Page 9 of 52 FIGUFI 2 VARIOUS CORE LOADINGS KEY: O Control Rod Out $ Control Rod in m ~ 17l 171,177127 assembly exposure in G'4D/MT. 7 a171717 IO 17;)0 O %7 7 g gs7 0 2] O 27 Core 1 at 0% voids _a 7 17 7" TM7 O ,e v 7a,!.7 17n,_ 7 0 ~ 7 17 o 0 27 g g ,7 0 27 0 27 Core 1 at 25% voids --C C ,l717k,,l77)@7 a, 7, lT l 17,s 7 0 %s ,a 7 0 27 g ' 17,)0 7 'O s 2 0 27 Core 1 at 50% voids 1O7k,.l7 17k,f-O 7 T U lbT 17,0 27 7 "7 0 o 27 g0 27 ,, 11 0 27 Core 2 at 0", voids . a n [ li 17g lim 7 17 j p 27 " 7(30'O 27 7 O l'30 27 0 27 Core 2 at 25% voids

Paga 10 of 52 FIGURE 2 a ~ ['T 7).lifLTMT 1h,,75.71,,0h7 7 76 27 c g0 27 17 0 2T core 2 at 50% voids a a I T ifT O - T flT v ,n 1 17 1 0 T T o 27 27 C g LT,o 27 LT 0 27 Core 3 at 0,25 & 50% voids e 25M5 "l*M 2g5 '25 15 7 _ g gy5 25 7 7 32 g 1 ,,15 7 32 T 22 core h at'o, 25 & 50% voids -- C sM,525k,32 25,15 25 7 32 g g g 15 T 'T 32 s 25 7 l 32 s 25l T l 32 Core 5 at 0, 25 & 50% voids d JJ 2_5h515g Mil1%I L g.5 lc )T 32!32 J 2=, 7 32 7 32 Core 6 at 0, 25 & 50% voids

FIGURE 3 BNP PCO CORE 1 AT BOC 0% VOIDS INPUTS FROM CASMC

  • E' 11 Of 32
ERP 1/4 CORE N0o1 00 VOID THIS CASE IhCLU0CC IN THE SUPPARY OF ALL C% VOID CASES P00 K EFFECTIVE 1.C315310 1

~ROK K EFFECTIVE 1.C30520 AVERAGE OF PERCENT ERRCR .2331 STANCARD DEVIATION OF PERCENT ERRCR 2.2389 1.36756 1 1c007 .83551 .76033 41427 P00 NORMALIZED POWE 1-32755 1 15853 -850?1 .81954 42265 GROK NORMALIZED POVE 01 -2.72 1 81 7.22 1,9c (GQOK - PDO)/GDCr*1C 1.23222 .96035 1.13807 1.11326 .65562 1 24273 .99590 1 12921 1 11267 66024 .65 2.59 .78 .05 -70 1 29538 1.04067 1.43242 1.C6193 .35670 1-29223 1.05965 1.4447e 1 03414 .35SJ4 .24 1.7c .96 -2.69 -38 1 53567 1.42511 1.17173 s 1,52262 1.41311 1.17126 .96 .25 .04 .69233 .82922 .43163 67725 .89294 43408 .75 -1.E4 -56 PDG AND GPCK ASSEVELY K-INrINITIES 1 072167 1.072312 .941c71 1 02e391 .964649 PCO V-INFINITY 1 074620 1.074620 .936050 1 035930 .972370 GROK K-INCINITY 002283 .00214P .006325 .006312 .007c40 (GROK - PDO)/GPOK 1 039339, .93C457 1.07239C 1.194134 1 001639 1 035930 .c3605C 1.074620 1.197230 1.209290 .003291 .005975 .002094 .002608 .C05496 1.041860 .936269 1.204976 1.201095 .958746 1 035c30 .c36050 1.209290 1.205280 .c72370 .005724 .C00233 .002734 .005946 .C14011 1 1944?6 1.184249 1.201361 1 197230 1.187230 1.208290 .00:379 .002511 .005706 964574 1 201567 .95Pc78 72370 1.209280 .972370 CG8017 .005556 .013772

FIGERE 3 eRP PCO CORE 2 AT ECC 0% VOIDS INPUTS FROM CASMO Page 12 of 52

9RP 1/4 CCRE NCa2 CO VOIO THIS CASE INCLUCEC IN THE SUPPARY OF ALL 0% VOID CASES DC0 K EFFECTIVE 1.0156390 1

CDOK K EFFECTIVE 1 015101 AVERAGE OF PERCENT ERROR .0721 STANDARD DEVIATION OF PERCENT ERRCR 2 8931 1,17681 1.14310 .88148 .61466 .34578 00Q NORMALIZED POWE 1 21062 1 17774 .86953 .6c855 .34474 GRJK NORMALIZED PCWE 2 79 2.c4 -1.37 6.66 .30 iGROK - PCQ)/GRCM*10 1.01996 1 25317 1.2a270 1.16106 40409 1-05510 1 27c10 1.24881 1 17104 .41198 3.33 2.C3 -3.52 .85 1.91 1 32840 1.37767 1.56797 1.03311 .33191 1-33639 1.4103C 1.54968 1.09379 .33819 .60 2.31 -1.19 .C6 1 89 1 36249 1.56011 .82063 1 31191 1 52983 .78319 -3.86 -1 98 -4.78 .88292 .c6750 41457 85501 .c6235 .40219 -3.26 .54 -3.08 PCG AND GRCK ASSEMBLY K-INFINITIES 1 035851 1.036000 .347524 .926151 .964583 PCQ K-INFINITY 1 035930 1.035930 .c36050 .?360c0 .?72370 GROK K-INFINITY .000C76 .000068 .012258 .010575 .009008 (GROK - PCO)/GROK 531576 1.C33678 1.072429 1.205657 .964848 c36050 1.C35930 1.074620 1.208290 .972370 204779 .002174 .002039 .002171 .C07736 1 038496 1.037011 1.205043 1 201210 .958685 1 035930 1 035930 1.209280 1 208280 .972370 .002477 .001044 .002679 .005851 .014074 1 072241 1.205719 .964153 1 074620 1 2C8280 .972370 .002214 .CC2120 .00840c 1 065500 1.201382 .958759 1 074620 1 208280 .972370 008487 .005709 .013998

FIGURE 3 WRP PCG CORE 3 AT BOC 0% VOIDS INPUTS FROM CASMO Page 13 of 52

0RP 1/4 CORE N0o3 00 VOIO THIS CASE INCLUCEC IN THE

SUMMARY

OF ALL 0% VOIO CASES POG K EFFECTIVE 1.0100660 1 G90K K EFFECTIVE 1.009543 AVERAGE OF PERCENT ERROR .0699 STANDARD DEVIATION OF PERCENT ERROR 2.4752 .99446 .89411 1 14563 1.08116 .75296 PDQ NORMALIZED POLS 1.02905 .90202 1 19630 1.13309 .75103 GROK NO RM AL I ZED PO*.'E 3.36 1.99 3.43 4.53 .26 (GROK - P00)/GROK.1C .88412 .95538 1.29926 1.38773 .26198 .91284 .96961 1.28427 1.38558 .87249 3-15 1.47 -1.16 .16 1.22 1.23110 1.26632 1.43554 .73070 .37268 1 22517 1 27590 1 42795 .72149 .37012 .48 .75 .54 -1.28 .69 1.30159 1.47877 .75483 1-24258 1.44211 .73794 -4.75 -2.54 -2.29 .85565 .93242 .39352 .82248 .92285 .38517 -4.06 -1.04 -2.17 P00 AND GROK ASSEMELY K-INFINITIES 1.037040 .939574 1.035361 1 031145 1.065973 POO K-INFINITY 1 035930 .936050 1.035930 1.035930 1.074620 GROK K-INFINITY .001072 .003765 .000549 .004619 .008047 (GROK - PDO)/GROM .930763 .924337 1.072516 1 205717 1.201367 .936050 .536050 1 074620 1 209280 1.208260 -005648 .001830 .001958 .002121 .005705 1.040785 1.03E879 1.205006 .964382 .958830 1,035930 1.035930 1.209260 .972370 .972370 .004687 .002847 .002710 .0C8215 .013925 1 072271 1.205715 .964499 1.074620 1.2C8280 .972370 002186 .CO2123 .008094 1.065503 1 201355 .958882 1 074620 1 208280 .972370 008484 .005731 .013871

s FIGQE 3 BRP PD0 CCRE 4 AT ECC 0% VOIDS INPUTS FROM CAEMC Paga lh of 52 =8RP 1/4 CCRE NO.C 00 VOIO THIS CASE INCLUDED IN THE SUPP ARY OF ALL 0% VOIO CASES P00 K EFFECTIVE .9983865 1 "ROK K EFFECTIVE .998897 AVEDAGE OF PERCENT ERRCR 0483 STANDARD DEVIATION OF PERCENT ERRCR 1.7342 1 05664 1.C8466 1.11635 1.15911 .52932 PCG NORMALIZED POWE 1 08033 1.0c922 1 12036 1 16998 .53473 GPOK NORMALIZED POWE 2.19 1.32 .36 .93 1 20 (OROK - P00)/ GROF.13 1.08364 1.13541 1.19760 1.20076 .78321 1 09922 1 13543 1 1914e 1.20102 .75856 1 42 .00 .33 .02 -3.25 1 11341 1 18635 1.55773 1 18155 .39334 1 12037 1.19149 1-554c6 1.14226 .39703 ,62 .43 .12 -3.44 .93 1 15465 1.19801 1 19043 1 16998 1 20102 1 14226 1-31 .25 -3.34 .52607 .79040 .30237 53473 .75856 .39703 1 62 -2.e8 1 17 POG AA0 GROK ASSEMBLY K-INFINITIES 989294 .989301 .989537 1.093245 .918343 PCG K-INFINITY .?92030 .cc2030 .99203C' 1.096370 .925660 Sc0K N-INFINITY .002758 .002751 .002513 .002850 .007904 (GROK - POO)/GROK 4992a7 .989336 .989878 1.093617 1.177794 -992030 .e92030 .992030 1.0c6370 1.187230 3002755 .002716 .002169 .002511 .007c48 .a89546 489873 1.183092 1.177500 .913278 902030 .cc2030 1.187230 1.187230 .925660 .002504 .002174 .003465 .00A196 013376 1 093215 1.093648 1.1774E2 1.096370 1.096370 1.187230 .002879 .002483 .008211 .o18339 1 177801 .913276 .925660 1.187230 .925660 007909 .007942 .01337c l . -. - ~

FIGGP2 3 SRP PCO CCRE 5 AT EOC Of VOIDS INPUTS FROM CASMO Page 15 of 52 9PP 1/4 CORE NO.E 00 VOID THIS CASE INCLUDED IN THE SUMPARY OF ALL 0% VOID CASES PCC K EFFECTIVE 1.C120270 1 GRCK K EFFECTIVE 14C12862 AVERAGE OF PERCENT ERRCP .5018 STANCARD DEVIATION OF PERCENT ERRCR 2.3317 1 22071 1 17678 1.00625 .72161 .32193 PDQ NORMALIZED POWEI 1 20750 1.18340 1 00168 .75361 .32820 GROK NCRMALIZED POWE8 -1.09 .56 .46 4.25 1.90 (CROK PCG)/GR0k+10: 1237667 1.57196 1 16903 1.076a4 .34493 1.35979 1.54651 1.17427 1.09895 .36206 -1.24 -1 65 .45 2.00 4.73 1.66770 1.64100 1.49359 .c6924 .273c0 1 63392 1 65199 1.49167 1 00134 .2c038 -2 07 .66 .13 3 20 5 68 1 12126 1 42419 .69995 1.10689 1.4C11e .68514 -1.30 -1.64 -2.15 .61906 .77750 .32666 61552 .78437 .32160 .41 .88 -1.64 PCG AND GROK ASSEMPLY K-INFINITIES .989226 .ccc427 .989264 .9ac406 .917932 PDG K-INFINITY .992020 .992030 .992030 .9c2030 .92c660 GROK K-INFINITY .002806 .CO2624 .002769 .002645 .009340 (GROK - DCC)/GROK .989697 1.C93057 .990069 1.la3620 .91a902 .o92030 1.C96370 .992C30 1 197230 .925660 .002352 .003022 .C01978 .003041 .007301 1.093252 1.093815 1.193019 1 177858 .913000 1 096370 1.J96370 1.187230 1 187230 .925660 .002844 .002330 .003547 .007894 .013676 .989797 1 193729 .918547 992030 1.187230 .925660 .0C2251 .0:2949 .007625 .983752 1 178026 .912994 S92030 1.187230 .925660 008345 .007752 .0136c4 l

FIGIBI 3 ' BRP P00 CORE 6 AT ECC 02 VOIDS INPUTS FR011 C ASMO Paga >16 of 52 =8RP 1/4 CORE NO.6 00 VOID THIS CASE INCLUCED IN THE SUPMARY OF ALL 0% VOID CASES PDG K EFFECTIVE 1.0280080 1 GROK K EFFECTIVE 1.028920 AVERAGE OF PERCENT ERROR 4782 STANDARD DEVIATION OF PERCENT ERROR 1.4249 1.66829 1.36502 1.57467 1.29502 .61274 PDG NORMALIZED POWE 1 65213 1.34869 1.55224 1.28419 .61581 GROK NORM ALIZE0 POWE .c2 -1.21 -1.45 .84 .50 (GROK - POG)/GROM*10 1 29517 1.28044 1.45756 1.29403 .71057 1 28403 1 25977 1.45254 1 25338 .71863 .87 -1.64 .35 .05 1 12 1 33634 1.32841 1.26492 .57815 .27823 1 33427 1.33454 1 27820 .5c574 .28149 .11 .46 1,05 2.95 1 12 .83489 1.06609 .52730 .84214 1.06711 .53931 86 13 2.23 44107 .55600 .235C8 44025 .57528 .23968 1 82 3.35 1.92 P00 AND GPOK ASSEMBLY K-INFINITIES 1 093133 .98c596 1 093339 1.0e3537 .984188 PDG K-INFINITY 1 0c6370 .9c2030 1 096370 1.096370 .992030 GROK K-INFINITY .002952 .002453 .002765 .002584 .007904 (CROK - PCQ)/CROK .989574 .989598 1.093476 1.183879 1 177c92 .9c2030 .ec2030 1.096370 1.187230 1.187230 002476 .002452 .002640 .002823 .007781 L 1 0c3110 1.0c3478 1 182850 .918922 .*13176 1.0c6370 1.096370 1 187230 .925660 .925660 002973 .002638 .003689 .007279 .013487 089702 1.183600 .918611 002030 1 187230 .925660 .0.02346 .003058 .007615 .983759 1.178029 .912988 .c92030 1.187230 .925660 .008337 .007750 .013689 d r

FIGERI: 3 'ORP PDQ CdPE.1 AT OCC 202 VOIOS IhPUTS FROM CASMO Pase 17 of 52 meRP 1/4 CORE N0 1 25 VOIO THIS CASE INCLUDED IN THE

SUMMARY

OF ALL 25% VOID CASES PC0 K EFFECTIVE 1.0102340 '.1 GROK K EFFECTIVE 1.008484 AVERAGE OF PERCENT ERROR .3671 STANDARD DEVIATION OF PERCENT ERRCR 3 3438 s 1.46896 1.28519 .88545 .77317 46159 P00 NORMALIZE 0 POWE 1 35841 1.19938 .87669 .82783 46963 GROK NORMALIZE 0 POWE -8 14 -7.15 -1 00 6 60 1.71 (GROK P00)/GROK+10 1 25158 .99876 1.15858 1.09273 .67064 1 21499 .99509 1.14139 1.10753 .68047 -3.01 .37 -1 51 1.34 1 44 1 23049 1.01149 1 36721 1.04402 .3998? 1 22812 1.03745 1 41503 1.04752 .39833 .19 2.50' 3.38 .33 2 12 1.43165 1 32719 1 12538 s 1.44172 1 34992 1 16303 .70 1 69 3 24 .700C8 .87109 45486 .70614 .87221 .46916 66 .13 3.05 PCQ ANC GRCX ASSE."ELY K-INFINITIES 1.068999 1.069300 .923756 1.001074 .971025 P0Q K-INFINITY 1 064620 1.064620 .913430 1.005720 .972500 GROK K-INFINITY .004113 .004396 .011305 .004620 .301599 (GROK - P00)/GROK 1.014841 .913149 l.069149 1.175092 1 189207 1 005720 .913433 1 064620 1 170790 1 193490 .0C9069 .000308 .004254 .003674 .003589 1 013121 .915031 1 192519 1 189781 .965325 1 005720 .913430 1 193490 1 193490 .972560 .0C7359 .0C1753 .000914 .003946 .007460 1 175356 1.175139 1.188979 1,170790 1 170790 1.1934c0 .0C3900 .003715 .003780 970e33 1 189138 965493 .972580 1 193490 .*725d0 .001796 .003646 .007287 'I M ,e

FIGURE 3 BRP PCQ CCRE 2 AT BCC 29% VOIDS INPUTS FROM CASMO Pago 16 of 52

URP 1/4 CORE NO.2 29 VOIO THIS CASE INCLUDED IN THE

SUMMARY

OF ALL 25% VOIO CASES PCQ K EFFECTIVE 1.0067090 1 GRCK 4 EFFECTIVE 1 006038 AVERAGE OF PERCENT ERRCR .0608 STANDARD DEVIATION OF PERCENT ERROR 2.2441 1.09505 1.24244 1.42567 1 19301 .58146 P00 NORMALIZE 0 FOWE 1 10535 1 22745 1.36399 1.17641 .57429 GRCK NORM ALIZED POWE .e3 1.22 -4.54 .56 -1 25 (GFOK - PDQ)/G8.0M*1C .92116 1.21302 1.41250 1.36564 .54777 .?2879 1 10674 1 37031 1 30687 .54628 .P2 -1.36 -3 08 2 24 .27 + 1.06054 1.15077 1.42436 1.11008 .40227 1 07651 1.18789 1 45633 1 15658 41312 1.48 3.13 2 19 4.02 2.63 1 06096' 1.21743 .74331 1.c4450 1.22836 .71911 -1 58 .80 -3.36 .704c6 .76266 .37475 .69578 .7664 .36ac3 -1 32 40 -1.55 PDQ AND GPCK ASSEMELY K-INFINITIES 1.305150 1.013170 1.068985 1 069482 .971045 P00 K-INFINITY 1 005720 1.005720 1 064620 1.064620 .972590 GROK K-INFINITY .000567 .007408 .004100 .003628 .001578 (GROK - PDQ)/GROK .913358 1.016060 1.068702 1.193147 .?71091 913430 1.005720 1.064620 1.le3490 .9725ao 000079 .010281 .003e34 .000287 .001531 1.007867 1.0C7*34 1 192598 1 180084 .965614 1 005720 1.005720 1 193490 1.193490 .972580 .002135 .0C2201 .000747 .003692 .007162 1.068885 1.1c3400 .970373 1 064620 1 103490 .972580 .004006 .000069 .002269 1.062395 1.188975 .965304 1,064620 1 193490 .o725?0 .0020*C .0037e3 .007389

FIGEE 3 BRP POO CORE 3 AT BOC 2S% V01DS INPUTS FROM CASMO Paga 19 of "2

SRP 1/4 CORE NO.3 25 VOID THIS CASE INCLUCEC IN THE

SUMMARY

OF ALL 25% VOID CASES PCQ K EFFECTIVE .9864221 1 GROK K EFFECTIVE .985815 AVERAGE OF PERCENT ERRCR .1133 STANDARD DEVIATION OF PERCENT ERRCR 1 0017 1 00443 .90121 1.115R9 1.03125 .76740 PDQ NORMALIZED t<0WE 99736 .89269 1.13952 1 08812 .77146 GROK NORMALIZED POWE .71 .c5 2.07 5 23 .53 (GROK PDQ)/GR0M*10 .90417 .e6403 1.296C8 1.23103 .85977 .c0700 .c6328 1.26824 1.25183 .87074 31 .08 -1.41 1 54 1 26 1-20021 1.22356 1.40213 .77982 .41832 1.19013 1.23608 1.41590 .76937 41653 .85 1 01 .97 -1 36 .43 1 2a110 1 42872 .80577 1 25276 1.42650 .79327 -3.06 .16 -1.58 i 09396 94596 .44517 87107 .93906 43923 -2 63 .74 -1.35 PSQ AND GROK ASSEM8LY K-INFINITIES 1.010432 .51c818 1.009854 1 003617 1.062615 PCQ K-INFINITY 1 00572C .913430 1 005720 1.005720 1.064620 GROK K-INFINITY .0C4685 .006994 .004110 .002091 .001883 (GROK - PCO)/GROK .912213 .915406 1.069041 1.1c3335 1 198826 913430 .c13430 1.064620 1.193490 1 193490 001333 .002163 .004153 .000130 .003999 1.013883 1.011358 1.192602 .970655 .965460 11005720 1.005720 1.1934c0 .972580 .972500 .008117 .0C5606 .000744 .001980 .C07321 1.068854 1.193331 .970742 1 064620 1.193490 .972580 .003977 .000133 .001869 1 062293 1.188803 .965512 1.064620 1.1c3490 .972580 .002195 .003927 .007267

FIGURE 3 BRP P00 CCRE 4 AT ECC 25% VOIDS INPUTS FROM CASMO Paga 20 of 52 =BRP 1/4 CORE N0o4 20 VOIO f THIS CASE INCLUCED IN THE

SUMMARY

OF ALL 25% VOID CASES P30 K EFFECTIVE .9869335 i GRCM K EFFECTIVE ,989148 AVERAGE OF PERCENT ERROR .0190 STANDARD DEVIATION OF PERCENT ERRCR 1 7039 1.19226 1.18692 1.15637 1.12357 .55242 P00 NORMALIZED POWE 1 18245 1.17750 1.15404 1.14214 .56123 GRCK NORMALI2ED POWE .83 .80 .20 1.63 1.57 (GROK - PDO)/GROK.10 1 18617 1.19836 1 18296 1.12639 .75324 1 17750 1.18617 1 1Aa86 1.14539 .72825 .74 -1.03 .59 1.66 -3.43 1.15416 1 19195 1 43708 1.10456 .40741 1 15404 1.19986 1.45229 1.07939 41175 .01 .67 1 05 -2 33 1.05 1 12029 1.12431 1.10355 1 14214 1 14539 1.07939 1 91 1 84 -2 24 .55055 .75098 .40652 56123 .72825 41175 1.90 -3.12 1.27 t PDG AND GRCK ASSEMBLY K-INFINITIES .989318 .90a319 .989426 1.083652 .925260 PDQ K-INFINITY .?90060 .990060 .990060 1 084790 .931490 GROK K-INFINITY 000749 .000749 .000641 .001049 .006698 (GROK - DCO)/GROK .a89316 .989326 .989485 1.083661 1.169059 .990060 .99C060 .990060 1 084790 1 170990 0C0752 .0C0741 .000581 .001041 .001555 .989434 .989470 1 173971 1 168705 .919797 .99C060 .990060 1.170680 1.179880 .931490 .000633 .000596 .002640 .001858 .012563 1 083620 1.083689 1.168695 1 084740 1 084790 1 170880 .001079 .001015 .001866 .925259 1.16a067 .c19798 .931490 1 170880 .331490 .006689 .001548 .012562

FIGURE 3 B P[P P00 CCRE S AT ECC 20% VOIDS INPUTS FROM CASMO Paga 21 of 52

8RP 1/4 CORE N0oS 20 VOID THIS CASE INCLUCED IN THE

SUMMARY

OF ALL 25% VOIC CASES PCQ K EFFECTIVE .9994864 4 GROK K EFFECTIVE 1 000401 AVERAGE OF PERCENT ERROR .2615 STANDARD DEVIATION OF PERCENT ERRCR 1.8129 1.32134 1 25832 1.07147 .77289 .37628 PDG NORMALI2ED POWEi 1.29076 1.24938 1 05909 .79810 .37959 GROK NORMALIZED POWEF -2 37 .80 -1.17 3.16 .87 (GROK - PCO)/GROK.10I 1.41183 1.55292 1.17129 1.05272 .38235 1.39168 1.52827 1.17883 1.07568 .39211 -1 45 -1.61 .64 2.13 2.49 1.59373 1.54168 1.39390 .94534 .30478 1 57412 1 56188 1 40627 .96861 .31766 -1.25 1.29 .89 2.40 4 06 1.08738 1.31310 .71044 1.09081 1.31117 .69867 .31 .15 -1.68 .63248 .75312 .35276 .63369 .74817 .34648 19 .66 -1 81 PDQ AND GROK ASSEMPLY K-INFINITIES .989325 .999399 .989334 .989280 .925362 PDG KeINFINITY .990060 .990060 .990060 .990060 .931490 GROK K-INFINITY .000743 .000668 .000733 .000788 .006579 (GR0K - PCO)/GROK .989532 1.083603 .989538 1.174923 .925832 .990060 1.084790 .9q0060 1 170880 .9314c0 000533 .001094 .003528 .003453 .006074 1 083690 1.083826 1.174123 1.168960 919878 1.08479C 1.084790 1 170880 1.170980 .931490 .001014 .000889 .002770 .001640 .012466 .989469 1.175027 .925454 790060 1.170880 .931490 000597 .0C3542 .006480 .903201 1.16*133 .919954 .990060 1.170880 .931490 .006928 .001492 .012394

FImmE 3 BRP PDG CORE 6 AT ECC 20% VOIDS INPUTS FROM CASMO Pag 2 22 of 52 C9RP 1/4 CORE NO.6 25 VOIO THIS CASE INCLUDED IN THE SUMPARY OF ALL 25% VOIO CASES P00 K EFFCCTIVE 1.C147500 4l GRCK K EFFECTIVE 1.315556 AVERAGE OF PERCENT ERROR .2397 STANDARD DEVIATION OF PERCENT ERROR 1.0976 1.69213 1.40072 1.51561 1.21774 .61950 PDQ NORM ALIZED POWE 1.66549 1.38201 1.50558 1.22867 .62799 GROK NORMALIZED POWE -1 60 -1.35 .67 .91 1 50 (GROK P00)/GROK.10 1.34c71 1.30796 1.40056 1.20685 .69310 1 33111 1.23789 1.40362 1.22140 .69192 -1 40 -1.56 .22 1.lc .17 1.34611 1.30952 1.21822 .60497 .30677 1 3?967 1.31457 1.235d5 .61953 .30819 .54 .38 1 43 2 35 .46 86429 1.04651 .56631 873C3 1.C5003 .57257 1 00 .34 1 09 49504 .57801 .27128 48*52 .52031 .27178 92 40 15 P00 AND GRCK ASSEMPLY K-INFINITIES 1.083701 .989533 1.083751 1.083813 -.983516 PDG K-INFINITY 1 084790 .990060 1.084790 1.084790 990060 GROK K-INFINITY .0C1C04 .C00533 .000930 .000901 .006609 (GROK - PCO)/GROK .989517 .989521 1.083701 1.175130 1.169203 .990060 .990060 1 084790 1.170880 1 170980 .000549 .CC0544 .0010C4 .003630 .001432 1 083664 1.083721 1.174215 .925828 .*20172 1 084790 1.084790 1 170860 .9314c0 .c314c0 .001038 .C00985 .002948 .006078 .012151 .989465 1.175031 .925604 .c90060 1.170880 .9314c0 .000601 .0C3545 .00631a .983295 1.169236 .920042 .990060 1 170880 .9314e0 .006033 .001404 .012290

BRP PCQ CORE 1 AT BCC 50% VOIDS INPUTS FROP CASMO =BRP 1/4 CCRE No.1 50 VOIC 23 of 52 THIS CASE INCLUDED IN THE SUPNARY OF ALL 50% VOID CASES P00 K EFFECTIVE 1.0158360 i GROK K EFFECTIVE 1.016518 AVERAGE OF PERCENT CRROR .0320 STANDARD DEVIATION OF PERCENT ERROR 3 0213 .84664 1 17346 1.20545 1.19110 .57344 PDG NORMALIZED POWE .80794 1.10942 1.17275 1 16300 .57702 GROK NORPALIZED POWE -4.79 -5.77 -2.79 1 89 .62 (CROK PDQ)/GROK.1C 1.11460 1.24141 1 20137 1.0c063 .685c2 1 07280 1 19130 1 19444 1 12736 .68728 -3.90 -4 21 .58 3.26 .20 1.50a60 1 27545 1.28134 .c6839 .40080 1 46e08 1.27335 1.35357 .e9596 .40502 -2.69 .17 5.34 2.77 1.04 1.29384' 1.18371 1.00318 1 31782 1.22139 1.03803 1 82 3.09 3.36 .63877 .74711 .42481 64453 .74817 42979 .89 .14 1.16 PDC AND GROM ASSEMBLY K-INFINITIES .887368 1 049354 1.049007 1.14c082 .961478 P00 K-INFINITY 878960 1.043630 1 043630 1.141860 .962490 GRCK K-INFINITY .C09566- .005485 .005152 .005449 .001052 (GROK - P00)/GRCK .990108 1.049210 1.048703 1.147602 1.171164 ,961720 1.043630 1.043630 1.141860 1.167140 .019120 .005347 .004861 .005029 .003448 1 149301 1.048599 1.174024 1 170958 .956213 1 141860 1.043630 1.167140 1.167140 .962490 .005641 .004761 .0058e8 .003271 .006521 1 147952 1.147611 1.171043 1 141860 1.141860 1 167140 .005335 .005037 .003344 .*61516 1.171168 .9562c3 ,962490 1.167140 .962490 .001012 .003451 .006438

BRP PCQ CORE 2 AT BCC 50% VOICS INPUTS FROM CASMO

PRP 1/4 CCRE NO.2 90 VOID ago 2h of 52 THIS CASE INCLUCCD IN THE SUPMARY OF ALL 50% VOID CASES P00 K EFFECTIVE

.9719231 i FROK K EFFECTIVE .971202 AVERAGE OF PERCENT ERROR .2767 STANDARD DEVIATION OF PERCENT ERROR 2.9439 1.08433 1.20559 1.39978 1 19026 .64895 000 NORMALIZED POWE 1.04263 1 16733 1 36021 1 20894 .65397 GROK NORMALIZED POWE -4.00 -3.29 -2.91 2.37 .75 (GROM - PCQ)/GROK*10 .93043 1.17269 1.37657 1.32097 .60466 90018 1 14149 1 35453 1.39670 .60199 -3.36 -2.73 -1.63 5.42 .44 1.03357 1.10589 1.37044 1 12344 46302 1-02973 1.13066 1.42702 1.17846 472o2 .37 2.19 3.96 4.67 2.09 1.04824 1.17761 .79443 1 04088 1.20448 .76406 .71 2.23 -3.97 740c9 .78632 .43183 -72968 .77580 .41347 -1.55 -1.36 -3.19 PDG AND GRCK ASSEMELY K-INFINITIES .969506 .976602 1 049026 1.049603 .961578 PDQ K-INFINITY .961720 .961720 1.043630 1.043630 .962490 GRCK K-INFINITY .008096' .C15474 .005170 .004765 .000948 (GROK - PCG)/GROK .886545 .979923 1.0484S7 1 174820 961441 479960 .961720 1.043630 1 167140 .962490 .008629 .018928 .004654 .006580 .001090 .971500 .971118 1.174009 1 170751 .956244 .961720 .961720 1 167140 1 167140 0624c0 .010169 .009772 .005855 .003094 .006499 1 048751 1.174987 .960887 1.043630 1.167140 .962490 .004007 .006723 .001665 1.042207 1.170558 .956096 1 043630 1.167140 .962490 001264 .002929 .006643 ' ' ~

FIGtEE 3 BRP PDG CCRE 3 AT 90C 90% VOIDS INPUTS FROM CASMO Page 25 of 52 BRP 1/4 CCRC NO.3 50 VOIO THIS CASE INCLUDED IN THE SUwPARY OF ALL 50% VOIO CASES PCC K EFFECTIVE .9506812 q GROK K EFFECTIVE .949614 AVERAGE OF PERCENT ERROR .3451 S.TANDARD DEVIATION OF PERCENT ERROR 2.6417 1 02457 .92462 1.09180 99039 .79790 P00 NORMALIZED POWE .96805 .88355 1.09343 1 04422 .79293 GROK NORFALIZED POWE -5 84 -4.65 .15 5.16 .63 (GROK - PCQ)/GR0K+1f .92783 .97197 1.27134 1.20041 .87597 .90030 .95477 1.25024 1.31997 .87109 -3 06 -1.80 -1.69 3.00 .56 1 15525 1.17427 1.360E2 .83680 .47956 1.15171 1 19326 1-40342 .81985 .46982 .31 1.59 3 05 -2 07 -2 07 1.24652 1.35901 .e5831 1.25562 1.40745 .95063 .73 3.44 .90 .91485 .95292 .50507 .91613 .95331 .50026 .14 .04 .96 PDQ AND GROK ASSEP9LY K-INFINITIES .974331 .891322 .974659 .966569 1 042160 PDG K-INFINITY 961720 .878960 .961720 .961720 1.043630 GROK K-INFINITY .013113 .014064 .013454 .005042 .001409 (GROK - PDG)/GROK .885821 .8P8143 1.048720 1.17486E 1 170340 .878o60 .878960 1.C43630 1 167140 1.167140 .3078C5 .010448 .004877 .006619 .002742 .976674 .974284 1.174103 .961073 .956037 .961720 .961720 1.167140 .962490 .?62490 .015549 .013064 .005966 .001472 .006704 l 1.048647 1.174852 .961118 1.043630 1.1 7140 .962490 .004907 .'10660S .001425 1.042010 1 170333 .956076 1.043630 1.167140 .962450 001552 .002736 .006664 l

ffg BRP P00 CORL 0 AT ECC $0% VOIDS INPUTS FROH CASMO 26 of 52 9RP 1/4 CORT N0o4 50 VOID THIS CASE IdCLUDED IN THE SUPMARY OF ALL 50% VOID CASES PCO K EFFECTIVE .o658255 q GROK K EFFECTIVE .966367 AVERAGE OF PERCENT ERROR .0805 STANDARD DEVIATION OF PERCENT ERROR 2.5539 1 32534 1 28464 1 192a2 1.08985 .58212 PDG NORMALIZED POWE 1 26881 1.24232 1.17970 1.11589 .58975 GROK NORMALIZED POWE -4.46 -3.41 -1.12 2.33 1.29 (GROK PCO)/GROK*1C 1.28434 1.25532 1.17407 1.05449 .72544 1 24232 1.22656 1.18520 1.09610 .70441 -3.38 -2 34 .94 3 83 -2 99 1.19190 1.173d0 1.31334 1.C2741 42521 1 17970 1.18520 1.36259 1.02705 43061 -1 03 .96 3 61 .04 1 25 1.08840 1.05377 1.02716 1 11589 1.09610 1.02705 2 46 3.86 .01 .58124 .72445 .42480 .58975 .70441 .43061 1.44 -2 85 1 35 P00 AND GRCK ASSEM5LY K-INFINITIES .982604 .962601 .982555 1.067170 .926126 PDG K-INFINITY .977660 977660 .977660 1.061820 .927260 GRCK K-INFINITY .005057 .005054 .005048 .005039 .001223 (GROK - P001/GROK .9825a8 .982595 .982525 1.067011 1.141817 977660 .977660 .977660 1.061820 1.141860 .005051 .005048 .004977 .004889 .000038 .982603 .982499 1.146664 1.141671 .921119 .a77660 .977660 1 141360 1 141860 .a27260 .005056 .004950 .0042C7 .000166 .006622 1.067139 1.067032 1.141661 1,061820 1 061820 1.141860 .005009 .004909 .000174 .926125 1 141823 021121 .927260 1.141860 027260 .001224 .000C32 .006621

BRP PCQ CCRE U AT EOC 50% VOIDS INPUTS FROM CASMO E3

8RP 1/4 CCRE NO.S $0 VOID age 7 of 52 THIS CASE INCLUCED IN THE

SUMMARY

O'- ALL 50% VOID CASES P00 K EFFECTIVE .9767649 i GROK K EFFECTIVE .976707 AVERAGE OF PERCENT ERROR .1555 STANDARD DEVIATION OF PERCENT ERROR 2.4032 1.42101 1.33711 1 12929 .81708 .43774 PCQ NORMALIZED POWE 1 35844 1.30080 1 10850 .84150 .43712 GROK NORM ALIZED POWE -4.61 -2.79 -1 88 2.90 .14 (GROK PCO)/GROK*1C 1.45046 1.53566 1 16695 1.01462 42367 1 41128 1.50304 1 17929 1 05561 .42572 -2.78 -2.17 1 05 3 88 .48 1 52a87 1.45049 1.28843 .91538 .34111 1 51216 1.47662 1 32992 .94292 .35054 -1 17 1.77 3.12 2.92 2.69 1.05364 1.20184 .72150 1.07267 1.23115 .71477 1 77 2.36 .94 .65098 .72921 .383c3 .65299 .71905 .376C1 29 -1.41 -2.11 PDG AND GPOK ASSEMBLY K-IhFINITIES .982648 .992629 .982642 .982524 .926504 PCQ K-INFINITY 977660 .97766C .977660 .977660 .927260 GROK K-INFINITY .005102~ .005082 .005096 .004975 .000815 (GROK - PCO)/GROK .982640 1.067221 .9825C6 1.147997 .926657 977660 1.C61820 .977660 1.141860 .927260 t .005094 .005087 .004957 .005375 .000651 l 1 367213 1.067129 1.146896 1.141874 .921394 1.061R20 1.061820 1.141860 1.141860 .927260 l .005079 .C05000 .004402 .000012 .006337 .982516 1.147972 .926523 .977660 1.141960 .927260 l .004967 .005353 .000795 .976616 1 141855 .9214P7 .977660 1.141860 .927260 001068 .000004 .006226 l [ i

i E3 BRP P00 CCRE 6 AT ECC 50% VOIDS INPUTS FROM CASMO Page 28 of 52 =BRP 1/4 CCRE NO.6 50 VOIO THIS CASE INCLUDED IN THE

SUMMARY

OF ALL 50% VOID CASES l P00 K EFFECTIVE .9911712 4 3ROK K EFFECTIVE .990536 AVERAGE OF PERCENT ERROR .1752 STANDARD DEVIATION OF PERCENT ERRCR 1 9827 1.71896 1.43838 1.46602 1.14952 .63140 PDG NORMALIZED POWE 1 66103 1.40312 1.458C4 1.17958 .64359 GROK NOPMALIZED POWE -3 49 -2 51 .55 2.55 1 89 (GROK - PDQ)/GROK.1C 1 40252 1.33331 1 34546 1.11957 .67731 1.36478 1.30684 1 35675 1 15999 .67300 -2 77 -2.03 .83 3.48 .64 1.34979 1.28388 1.16272 .63489 .34190 1 33531 1.29211 1.19871 .64756 .34094 -1.08 .64 3 00 1.96 .28 .88561 1.01188 .60670 ,90147 1.C3494 .60985 1 76 2 23 .52 .53112 .50525 .31381 53313 .59902 .31023 .38 -1.06 -1.15 P00 AND GRCK ASSEMELY K-INFINITIES 1.067299 .982695 1.067285 1.067236 .976800 P00 K-INFINITY 1.061820 .977660 1 061820 1.061820 .977660 GROK K-INFINITY .005160 .005150 .005147 .005101 .000880 (GROK - PCO)/GROK .982685 .982684 1.067157 1.148057 1.141972 .977660 .977660 1 06182G 1 141860 1.141860 .005139 .005139 .005026 .005427 .000098 1.067267 1.067191 1.147065 .926823 .921695 1 061820 1.061820 1.141860 .927260 .927260 .005130 .005058 .004558 .000471 .006002 .982572 1.14802A .926690 .977660 1 141860 .927260 .005024 .005402 .000614 .976756 1.142001 .921614 .977660 1.141860 .927260 .000925 .000123 .006089

FIGURE h SUMPARY OF ALL 2SX VOID CASES Pago 29 of 52

6. CASES IN THE SET 126. TOTAL POINTS IN THE STATISTICS AVERACE OF PERCENT ERROR

.1189 ST AND ARD DEVI ATION OF PERCENT ERROR 2 0808 4 -2 12 -2 05 .92 2 83 .82 .91 -1 00 .76 1 68 .22 .23 1.50 1.65 .90 1.65 .12 .74 .76 .01 .58 .04 SUMM ARY OF ALL 0% VOID CASES

6. CASES IN THE SET 126. TOTAL P,0INTS IN THE STATISTICS AVERAGE OF PERCENT ERRCR

.2106 STANDARD DEVIATION OF PEPCENT ERROR 2.2011 .55 .48 .39 3.80 .84 1.11 47 .84 .44 1.07 .28 1.07 .02 .20 1.55 -1 43 -1 11 -1.73 .64 .34 .54

SUMMARY

OF ALL 50% VOID CASES '6. CASES IN THE SET 126. TOTAL PCINTS IN THE STATISTICS AVERAGE OF PERCENT ERRCR .0298 STANDARD DEVIATION OF DERCENT ERPOR 2.3696 -4.53 -3.73 -1.52 2 87 .63 -3.21 -2 55 .18 3 81 .66 -1.11 1 16 3 68 1.70 .79 1.31 2.87 .33 .27 -1 08 .82

FIGtJRE k Pago 30 of 52 SunRARY CF THE LAST 18e CASES ( 378. TOTAL POINTS IN THE STATISTICS) AVERAGE OF PERCENT ERROR .0999 STANDARD DEVIATION OF PERCENT ER8tCR 2.2993 5 -2.03 -1.77 .68 3.16 .76 -1 00 -1.03 .59 1.?8 .21 -.54 1.24 1 77 .80 1,33 .08 .e3 . 94 .20 .67 .47 o =.

FIGURE 5 Pya 31 of 52 PDQ-GROK Normalized Power Error Distribution PERCENTAGE 36j i 33y 30-}- 27 24 21

s -]

15 - 12 i 9 i 3-t wm tww -8 -6 -4 -2 0 2 4 6 8 ERROR MIDPOINT t

Paga 32 of 52 FIGURE 6 VOID EEPENDE'IT ALBEECS 0% VOIDS 0 0 0 0 0.15 0 0 0 0 0.10 0 0 0 0.30 0.20 0 0 0.30 0.15 0.10 0.20 25". VOIDS 0 0 0 0 0.25 0 0 0 0 0.125 0 0 0 0.h0 0.40 0 0 0.L0 0.25 0.125 0.ho 50% VOIDS 0 0 0 0 0.35 0 0 0 0 0.15 0 0 0 0.60 0.50 0 0 0.60 0.35 0.15 0 50

II. Axial Power Distribution Uncertainty Analysis I i nu1281-0015c142

Paga 33 of 52 AXIAL POWER DISTRIBUTION UNCERTAINTY ANALYSIS By examining four cycles of operating data in the for= of fluxvire profiles, an axial uncertainty factor =ay be derived. This is done by comparing the =easured profiles to a set of GROK calculated fluxwire profiles, after various corrections are applied to either set of data. The co=parisons include h7 sets of =easure- =ents, with 8 fluxwire holes per =easure=ent. Of the 376 possible nu=ber of holes, 20 were not =easured for various reasons. Also, only 33 sets of =easure-ments were made with a sy==etric rod pattern. Several corrections were made to either the =easured or the calculated data to account for various observed phenomena. The first correction is made to the =easured data, while three othe:s are =ade to the calculated data. The first is an axial shift of the ceasured data to account for the fact that the fluxvire's position cannot be accurately determined with respect to the fuel colu=n. The wire is counted in 28 equal segments of 2 inches each. These 28 measurements are evapared to a comparable set of calculated data, a percent difference generated and~a su= of the squared percent difference accumulated. The =easured data is then shifted up to 8 inches.in either direction, with a final resolution of 1/8 inch, until the su= of the percent error is minimized. The shifted =easured data is found by linearly interpolating between the actual =easured data at the shifted coordinates. For a measured data point that is significantly away fro = its neighbors-(an outlier) this process will cause so=e s=oothing of that point, unless the shift is an integral number of-fluxwire positions. Percent error is used instead of a si=ple difference because percent error vill weight the lower power edges of the core where a shift would be more visible.

Paga 3h of 52 The average percent error and the average error plus and minus 1.6k5 standard deviations of the average (by fluxvire position) for the uncorrected data is shown on Figure 7 The sa=e data corrected for the axial shift is shown en Figure 8. The 1.6h5 factor is required to give 95% confidence that 95% of the data falls belov (or above) that point. Note that this is a one-sided, not a two-sided confidence level. The seccnd correction factor is used to account for the power depression caused by spacer grids. The correction factor was deter =ined g$aphicly by plotting the Lanthinu=-lk0 activity (averaged over 5 rods from a single bundle), estimating what the axial power distribution would have been without the spacer grids and deter =ining the correction factor. The axial distributions and the correction factor are shown en Figure 9. This correctica factor should also be applied to the three dimensional power distribution so that the thermal li=its calculation may account for the increase or decrease in local powers. The average percent error after the spacer grid correction is applied is shown on Figure 10. The next correction applied is to account for the flux depression around the in-core fission chanbers. Since this is in the channel, away frc= the fuel, this correction should not be applied to the three dimensional power distribution. This c'orrection factor was determined graphicly by plotting the average error distribution (after the spacer grid correctica), correlating the re=aining dips in the graph to in-core loce.ticas, and deter =ining a correction factor that would correct for the dips. The in-core correction contains three small spikes to accoant for an over-correction in'the spacer grid facter. This over-correction =ay have occured because the flux dip between the channels is not as deep as the flux dip in the fuel because neutron diffusion vould tend to smear the dip out between the channels. The average error after the in-core r r . - -. ~

Page 35 of 52 correction applied is shown en Figure 11. Se final correction is used to account for the smearing effects that occurs when the wire is moved through the active ccre region. The wire is assu=ed to take 10 seconds to transit the core at a constant velocity. The residence time in the core is 30 =inutes. The basic process is governed by the following differential equation: 6h A 6h U63 E3 U dt Assuming copper-6h (N6h) does n t capture another neutron, that copper-63 (N63) d " * 'iE"ifiC**t1Y d'P *** **d th"t U l ,6h=0 when t=0 (initial conditions), then equation h has the following solution: 63 763 (1 -

  • Agg = N where A6h is the activity of copper-6h, O'63 is the absorption cross section of copper-63, ) is the neutron flux and 1 6h is the decay constant of copper-6k.

The profile that GRCK calculates is taken as N On wire insertica, the 63 U~b top vire seg=ent is inserted to the bottc= seg=ent of the core and it is irradiated for a certain amount of time and accu =ulates an snount of activity as governed by equation h. The time is 1/28th of the total insertion time. Then the wire is =oved into the second seg=ent, the top segment accumulates. ore activity frc= the next seg=ent up frc= the bottom of the core while the previous activity is decayed by the sa=e amount of time. At the sa e time the second segment starts to accu =ulate activity frc= the bottc= segment of the -core. And so the wire = oves to the top of the core. Pulling the wire out of the core is,just the opposite of pushing the wire into the core. The smeared distribution is the addition of the activation accumulated during insertion, withdrawal and the steady state operation, all decayed to the point

Page 36 of 52 where the wire just leaves the core. The percent difference between a s= eared and non-smeared typical axial distribution is shown en Figure 12. The average difference fer the fluxvire data after the s= earing correction is shown on Figure 12. The overall average (all 26 points of all the measured holes, 9963 points) is .k19% + h.057%. Since the percent error was formulated as M-G x 100 G where M is the =easured data and G is the GRCK calculated data, then an uncertainty statement may be for=ulated as: M < G (1 + A + PT ) where A is the average error (.h19%), F is the standard deviation of the average error (h.057%) and F is. 6h5, the factor required for 95% confidence that 95% of the measured date will fall below the GROK calculated data. This occurs at 6.255%. This uncertainty argu=ent assu=es that the error distributien is normal. Figure ik shows that the error distribution is approxi=ately normal, so the uncertainty statement is valid.

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FIGUR3 10 Paga 40 of 52 GROK-MEASURED FLUXWIRE ERROR SPACER GRID CCRRECTION APPLIED AVERAGE PLUS/MINUS 1.545 STANDARD DEVIATION 8 - a.__.........i......__....i......___.. 4.. __.......i.....__.. 4............i.........__.i.. v _.

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FIGURE 11 Page !.1 of 52 GROK-MEASURED FLUXWIRE ERROR IN-CCRE DETECr0R CORRECTION APPLIED AVERAGE PLUS/MINUS 1.645 STANDARD DEVIATION - _42............i.......................i............i...........

4.......................i.

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6 3 4 FIGURE 13 Page h3 of 52 ~. E . GROK-MEASURED FLUXWIRE ERROR ~ c AXIAL fMEAR CORRECTION APPLIED AVERAGE PLUS/MINUS 1.S45 STANDARD DEVIATIGN . 2c.q...........j......._..t...........9............t............t...........9............j j. 4 3 1 1 + 2 r u............i........... 6...........,6...........,6.......... 6.......... 6.......... 6 ~

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?!OURE 1% Paga 4k of 52 ~ MEASURED-GROK ERROR DISTRIBUTION FREQUENCY 2200 -- r 2000 - 1E00 g L^~ iS00 5 f (. i400 - y y 9 u, o f000 - L L 800 x S00 - ( 400 - r200 - J mm t/ x' M _.-_ m b6 h0 2 4 6 8 0 2 6 2 4 ERROR MIDP0lNT r, ) 2 .( e._.,-, --.n. ~ ~ -

up III. Local Power Distribution Uncertainty Analysis nu1281-0015c142

Paga h5 of 52 LOCAL PO'RR DISTRIBUTION UNCERTAINTY ANALYSIS 4 The infinite lattice local power distributions are input to GROK for each control state at beginning of life, 25% voids, with gadolinia. Once the three di=ensional power distribution is calculated, GROK vill tilt the local power distribution according to the one group flux in adjacent nodes in relation to the one group flux in the node under consideration. GROK vill then pick the maxi =u= of the tilted local power distribution as the =aximu= local power for the asse=bly. The current =ethod then compares the =axi=um of the tilted local power distribution to the maximum of the infinit'e lattice local power distribution and uses the larger of the two values as the asse=bly peak local power. However, the co=parisons between PDQ and GROK show this to be unnecessary, since GROK already overpredicts the asse=bly local peak by an average of 2.lThT% vith a stancard deviation of h.7562%. If the infinite lattice local peak is also included in the co=parison, the average overprediction - increase slightly to 2.2282% while the standard deviation goes up nearly one percent to 5.7352%. Thus, the method of using the infinite lattice locals in the co=parisons is not necessary since the tilted local power distribution already overpredicts the local peak power. Since GROK was co= pared to PDQ for local power peaking, the uncertainty of the PDQ =ust also be accounted for. This was done by cc= paring the results of a PDQ calculation that used CASM02 cross sections to a set of Co=bustion Engineering critical experi=ents. Three sets of geometry were analysed i e er -rwwwra-

Paga h6 of 52 The percent errors and the geometries are shown on Figure 15. Combining the three experiments, there was a total of 93 pin co=parisons. More pins I i vere measured by CE, but the sy==etric measurements were averaged, leaving 93 symmetricaly unique 1ceations. The percent error was ec=puted as (CE-PDQ) x 100/PDQ, so the uncert:dnty factor would be co=puted as the average error plus 1.664 times the standard deviation, where 1.66h is the required factor for 95% confidence that 95". of the errors vill be less than the stated number, for 92 degrees of freedom (93 data pointa). With an average error of.32566% and a standard deviation of 1.9153h", the 95/95 (one sided) confidence level is at 3.51277%. 5 The 95/95 confidence level for the GROK co=puted local peaking factors is then the statistical combination of the 95/95 confidence levels of the CE-PDQ cc=parisons and the PDQ-GROK comparisons. Thus, with 95% confidence, 95% of the errors in local peaking vill be less than 6.6523%. This uncertainty analysis assu=es that the error distributions for both the PDQ-GROK co=parison and the PDQ-CE co=parisons are normal. Figure 16 shows the error distribution for the PDQ-GROK local peaking factor comparison and Figure 17 shows the error distribution for the PDQ-CE pin power comparison'. Both distributions are reasonably normal, so the uncertainty analysis is valid. l 4 J

3 6 6 1 90 1 0 8 9 2 2 8 5 0 7 f o 7 4 e 2 6 g 0 2 4 2 a P 2 1 4 0 5 7 1 1 s 23 9 79 1 22 3 6 2 8 A 3 T 1 AD DE 2 R 3 6 U 3 6 9 SA 2 E M l EC 5 D 5 1 N 8 A 5 8 5 D

  • 1 Q

R 1 P ET E N 0 A m E t E s 8 8 W 0 N 2 6 G IF E B ECNE 5 R 3 5 7 EF 2 0 F I D TN 3 E 8 3 C 8 2 8 REP 1 8 2 4 k 3 6 L. 3 3 2 3 3 1 = 4 5 5 C 7 5 2 3 6 8 1 0 1 99 8 2 k 1 6 3 6 = 1 EVA 67 5 ga l

._m. s ? e Page 48 of 52 FIGURE 15 \\ -1.938 -3.183 l 4.087 i e l 2.392 4.675 .517 i 3.566 4 i .131 1.053 1 -2.97a .292 -1.k69 2.275 .220 ~1.528 1.269 3.591 2.Lin 4'.839 465 474 -4.610 -2.050 -1.469 1 .313 -1.841 -1.065 -1.604 { -3 518 -2.374 -1.130 . BOO -1,069 .210 -1.196 .662 .480 1.224 -3.o33 WATEll .305 1.k75 3.272 996 3.241 3.145 3.720 3.982 2.206 .338 i ccH'J/PI4 COMPAltED TO C.E. Em111M12nB ( C8-I14 )

  • 1" PIA 4 AJS =.44240 G =2.35521

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B g o-o ee b Cm1

  • C 43 A

e W Va y am M e e e o O. M C.-e N. + G3m a e M GJ.V5 h e 7-y,, ,_y.__-_ .-__,...e,#g m a r - -

~ FIGURE 16 Paga 50 of 52 IPDQ-GROK Local Peaking Factor Error Dristribution

LCUENCY i10 y 3

130 i l 90d 3 1 EGj 3 'o 3 SCj 1 J. 50 d i i

o f

/ f - - ~ f 'f . k 30 ^ 20 ,g) x 9 tW M k 3< 2 . <b3 -12 -3 -6 -3 0 3 6 9 12 i E:'iGR MIDFGINT p. e-,,- -y 9 g g y 7~s. w w---- c--

5E"ide 52 PDQ-CE Pin Power Error Distribution FEGUENCY 20 7 !?h t id 17 IS y II t i i H. 13 12 4 .1 i 10 xz ?4 W 0 ? x b . 4 3 h_ -5 -4 -3 -2 -1 0 1 2 3 4 5 ER9GR MIJPCI.NT

~ IV. Suma ry nu1281-0015c142

Paga 52 of 52 SIDAARY By cc= paring GROK to higher order calculations and to measured data, uncertainty ^ factors were determined for axial, radial and local power distributions. The uncertainty factors for 95/95 confidence are: -Radial 3.666% .bcial 6.255% Local 6.652% Statistically cc=bining the radial and axial uncertainty factors gives a nodal uncertainty factor: 2 2 Nodal Uncertainty = 3.666.+ 6.255 7 250% = Statistically combining the nodal and local uncertainty factors gives a peak pin power uncertainty factor: Peak Pin Uncertainty = .250 + 6.652 9.8h0%. = t _m._- ,y r , -, - -,}}

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