ML20080R525
| ML20080R525 | |
| Person / Time | |
|---|---|
| Site: | Crane  |
| Issue date: | 01/23/1995 |
| From: | Bond G, Fu H, Luoma J GENERAL PUBLIC UTILITIES CORP. |
| To: | |
| Shared Package | |
| ML20080R516 | List: |
| References | |
| TR-091, TR-091-R00, TR-91, TR-91-R, NUDOCS 9503090347 | |
| Download: ML20080R525 (123) | |
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STEADY STATE REACTOR PHYSICS METHODOLOGY ,
1 - FOR TMI 1 TOPICAL REPORT 091 (REV. 0)
BA NO.: 135400 AUTHOR:
HUI-HSikFU ENGINEER, TMl FUEL PROJECTS January 23,1995 APPROVALS:
7AXX~
J.' D. LUOMA MANAGER, TMl FUEL PROJECTS G. R. BOND '
DIRECTOR, NUCLEAR ANALYSIS & FUEL
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TR 091 Rev.O Page1 ABSTRACT g
_ g This report describes the CASMO-3/ SIMULATE-3 code package for calculating TMI-1 nuclear physics data l by GPUN. The methodology has been verified against critical experiments and TMI-1 operating data. The .E :
results from these analyses demonstrate that the CASMO-3/ SIMULATE-3 methodology is accurate and E GPUN is capable of performing inhouse physics calculations. Nuclear reliabil!!y factors based on this methodology are determined. GPUN intends to use this methodology for performing nuclear design
- calculations for TMI-1.
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1 TR 091 Rev.O Page 2 !
1.0 - INTRODUCTION . . . . . . . . . . . . . .. .... .. .. ....... ....... ..... . . . 6 !
1 2.0 METHODOLOGY OVERVIEW . . . .. .... .. ..... .............. . ..... 8
- 2.1 CASMO-3 Description .............. ........... . .... . ... .. 8 i 2.2 TABLES-3 Description . . . . . . . . . ........... . . ....... ........ ... 9 j 2.3 SIMULATE-3 Description . . . . . . . .................... . ..... ..... 10 3.0 CASMO-3 VERIFICATION . . . . . .. ... . ...... .............. ....... .. 14 ,
3.1 Comparison with Uniform Pin Cell Criticals . . . . . . . . . . . . . . . . . . . . . . . .. . ' . . . 14 l 3.2 - Validation by Studsvik . . . . . . . . . . . . . . . . ............ ........ ....... 15 ,
4.0 ' SIMULATE-3 VERIFICATION . . . . . . . .... . . .......... ....... .. .... 30 f 4.1 Boron Letdown Results . . . . . . . . . . . . . . . . . . . . . . . . . . . ............... 30 4.2 Hot Full Power Comparisons . . . . . . . . . . . . . . . . . . . . . ........... ....... 31 !
, 4.3 Hot Zero Power Compensons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..... 32 !
4.3.1 All Rods Out Critical Boron Concentration . . . . . . . . . . . . . . . ......... 32 i L
4.3.2 Control Rod Worth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 ;
4.3.3 Isothermal Temperature Coefficient . . . . . . . . . . ..... .............. 33 !
4.4 TMI-1 Power Transient . . . . . . . . . . . . . . . . . .. ................. ....... 33 i 1 t 5.0 PIN POWER VALIDATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 ,
5.1 Comparison with Higher Order Numeric Calculation . . . . . . . . . . . . . . . . . . . . . . 77 5.1.1 Multiple Assembly Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 :
5.1.2 TMI.1 Cycle i and Cycle 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . ........ 78 !
5.2 Validation Versus B&W Crtical Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 :
- 6.0 RELI ABILITY FACTORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . 103 6.1 Method Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 I 6.2 HZP SOC ARO Crkical Boron . . . . . . . . . .. . . . . .............. .......... 106 )
6.3 .HZP BOC Control Rod Worth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 ;
)
6.4 HZP BOC loothermal Temperature Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . .. . 107 6.5 :HFP Cetical Boron . . . . . . . . . . . . . .... ...... .... . . . . . . . . . . . . 107 i 6.6 P eak Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 ;
6.6.1 Radial-Local Factor . . . . ................................ ... 108- i 6.6.2 Assembly Radial Power . . . . . . . . . . . . . . . . -. . . . . . . . . . . . . . . . . . . . . 108 j 6.6.3 Assembly Total Power . . . . ........................ ......... 109 )
6.6.4 Radial Pin Power . . . . . . . . . . . . . . ............ .... ......... 109 6.6.5 Total Pin Power . . . . ...... ............................... 110-J
7.0 CONCLUSION
. . . . . . . . . . . . . . . . . . . ......................... ....... 118 i
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8.0 REFERENCES
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 I
E-um TR 091 Rev.O Page 3 LIST OF TABLES Table 3.1 NS&E UO, Critical Experiments Table 3.2 KRITZ Pin Cell Critical Experiments
.. .. 17 18 I
Table 3.3 Pin Cell Critical Statistics . . . . ... .. . . . . . 19 g Table 3.4 K ,, for Pin Cell Criticals . .. . . . . . .. .. 20 g Table 3.5 Data for the KRITZ Series of Critical Cores . . . . .. .. . .. .. . 21 Table 3.6 Description of KRITZ Critical Cores .. . . . . ... . 22
- g' Table 3.7 Calculated K,,, for KRITZ Cores .. . . .. .... .. 23 E
Table 3.8 Summary of B&W Cores . . . .. . . . .. .. .... .. . . 24 Table 3.9 Summary of Data of the T6. B20 and ESADA Cores . ... . . 25 Table 3.10 K, Statistics for CASMO-3 .. . . ... . . ... .. . 26 l Table 4.1 HFP Letdown Boron Comparisons . ... . .. .... . .. ...... ... 35 W Table 4.2 HFP Radia! Power Distribution Comparisons . .... ....... . .. . ....... . 36 Table 4.3 HFP Axial Offset Comparisons . . ... . . ... .... . . . .. .. 37 3 Table 4.4 BOC HZP ARO Critical Boron . ... 38 Table 4.5 BOC HZP Control Rod Worth-Individual Groups E
. .. ........ ..... . . .. 39 Table 4.6 BOC HZP Control Rod Worth-Regulating Groups . . . . . . . .. .. . . . . .. ... 40 Table 4.7 BOC HZP isothermal Temperature Coefficients . . . . . . . . . . . . .. .. . 41 Table 5.1 Assembly Loadings for Multi-Assembly Problems . . . .... ... . ..... 80 Table 5.2 Multi Assembly Pin Power Comparison . . . .. .. .. .. .. .... . . . 81 Table 5.3 SIMULATE-3 and PDQ Power Comparisons . . . . . . . .
Table 5.4 B&W Critical Pin Power Results Summary . . . . . . . .......
82 83 El E! '
Table 6.1 Radial-Local Factor Statistical Results . . . . ....... .. ... ..... . 111 Table 6.2 Assembly Radial Power Statistical Results . . . . . . . . . . . . . . . . . .. ...... ... 112 gl Table 6.3 Assembly Total Peak Power Statistical Results . . . . ... . . ... ... ........ 113 g' Table 7.1 Summary of TMI-1 Applications ........ .... ... . ... ........... . 119 I
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TR 091 Rev.O Page 4 LIST OF FIGURES Figure 2.1 Flow Diagram of CASMO-3 . . . . . . . . . . . . . . . . . . . . . ......... . .... . 13 Figure 3.1 CASMO-3 Pin Cell Criticals K-EHective vs. Enrichment . .......... ...... .. 27 ;
Figure 3.2 CASMO-3 Pin Cell Criticals K-Effective vs. Lattice Pitch ....... ... .. ... .. 27 l l Figure 3.3 CASMO-3 Pin Cell Criticals K-Effective vs. H2 0/U Volume Ratio 28
{
- Figure 3.4 CASMO.3 Pin Cell Criticals K-Effective vs. Boron Concentration . ... ....... ... 28 ]
Figure 3.5 CASMO.3 Pin Cell Criticals K-Effective vs. Moderator Tempersture . . . . . . . . . . . . . . . 29 i Figure 3.6 CASMO-3 Pin Cell Criticals K-Effective vs. Measured Buciding . . . . ........... 29 Figure 4.1 Cycle 1 Boron Comparison . . . . . . . . . . . . . . ... .......... .......... 42 I
- Figure 4.2 Cycle 2 Boron Comparison .. .... .. ........ ... .. 43
.l Figure 4.3 Cycle 3 Boron Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . ............. . 44 Figure 4.4 Cycle 4 Boron Comparison . . . . . .. .......... .. .... . .. . 45 Figure 4.5 Cycle 5 Boron Comparison . . . . . . . . . . . . . . . . . . . . . ..................... 46 i Figure 4.6 Cycle 6 Boron Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
. Figure 4.7 Cycle 7 Boron Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . ............. 48 >
Figure 4.8 ' Cycle 8 Boron Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 !
Figure 4.9 Cycle 9 Boron Comparison . . . . . . . . . . . . . . . . . . . . . . . . ......... . 50 Figure 4.10 Letdown Baron Differences . . . .... . ............................. ... 51 1 Figure 4.11 BOC 6 Radial Power Distribution . .... .. ....... .......... .... ... 52 I Figure 4.12 MOC 6 Radial Power Distribution - . ................ ......... ..... . 53 Figure 4.13 EOC 6 Radial Power Distribution ... .. ............ .. . ............. 54 . ,
Figure 4.14 BOC 7 Radial Power Distribution ...... ........... ... . ............. 55 Figure 4.15 MOC 7 Radial Power Distribution . ................. . .. ........... 56 ,
Figure 4.16 EOC 7 Radial Power Distribution ........... ... .......... . ........ . 57 4 Figure 4.17 BOC 8 Radial Power Distribution . .......... ... ..................... 58 I Figure 4.18 MOC 8 Radial Power Distribution . . . . . . .... ....... .................. 59 Figure 4.19 EOC 8 Radial Power Distribution ........... ............ ........ ..... 60 Figure 4.20 BOC 9 Radial Power Distribution . ..................................,.. 61 j Figure 4.21 MOC 9 Radial Power Distribution ....... .. ........................... 62 i Figure 4.22 EOC 9 Radial Power Distribution ............. .......... ..... ........ 63 I Figure 4.23 BOC 6 Total Power Distribution ... ............................ ....... 64 Figure 4.24 MOC 6 Total Power Distribution .......... ................ . ......... 65 Figure 4.25 EOC 6 Total Power Distribution ...................... . ............... 66 Figure 4.26 BOC 7 Total Power Distribution .. ............ ................. .... 67 Figure 4.27 MOC 7 Total Power Distribution ... .... .............................. 68 Figure 4.28 EOC 7 Total Power Distribution ........................................ 69 Figure 4.29 ~ BOC 8 Total Power Distribution ........... ............... ......... 70 Figure 4.30 MOC 8 Total Power Distribution ......... ............. ............... 71 Figure 4.31 EOC 8 Total Power Distribution ......... ............................ 72 Figure 4.32 BOC 9 Total Power Distribution ........ .......................... .... 73 Figure 4.33 . MOC 9 Total Power Distribution ................... ................... 74 Figure 4.34 EOC 9 Total Power Distribution ............... ........................ 75 Figure 4.35 TMI Cycle 9100-50-100 Power Transient . . ...... ....................... 76 Figure 5.1 BOC 1 Radial Power Comparison Between SIMULATE-3 and PDQ . . . . . . . . . . . . 84 Figure 5.2 MOC 1 Radial Power Comparison Between SIMULATE-3 and PDQ . . . . . . . . . . . . . . . 85 i Figure 5.3 EOC 1 Radial Power Comparison Between SIMULATE-3 and PDQ . . . . . . . . . . . . . . . 86 !
Figure 5.4 BOC 2 Radial Power Comparison Between SIMULATE-3 and PDQ . . . . . . . . . . . . . 87 !
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TR 091 Rev.O Page 5 Figure 5.5 MOC 2 Radial Power Comparison Between SIMULATE-3 and PDO . . .. 88 Figure 5.6 EOC 2 Radial Power Comparison Between SIMULATE-3 and PDQ . 89 Figure 5.7 BOC 1 Peak Pin Power Comparison Between SIMUMTE-3 and PDQ . . . 90 Figure 5.8 MOC 1 Peak Pin Power Comparison Between SIMULATE-3 and PDO 91 Figure 5.9 EOC 1 Peak Pin Power Comparison Between SIMULATE-3 and PDO . . 92 Figure 5.10 BOC 2 Peak Pin Power Comparison Between SIMULATE-3 and PDQ .
. 93 lg Figure 5.11 MOC 2 Peak Pin Power Comparison Between SIMULATE-3 and PDO .. 94 ,
Figure 5.12 EOC 2 Peak Pin Power Comparison Between SIMULATE-3 and PDO . . . . . 95 g Figure 5.13 B&W Critical Experiment Geometry . . .. . . ... .. . . . . 96 g Figure 5.14 Core 1 Normalized Midplane Power Distribution . . .. . .. . .. 97 Figure 5.15 Core 5 Normalized Midplane Power Distribution .. .. .. . . . . 98 Figure 5.16 Core 12 Normalized Midplane Power Distribution . .. .. 99 Figure 5.17 Core 14 Normalized Midplane Power Distribution ..... ... . ..... . . . 100 Figure 5.18 Core 18 Normalized Midplane Power Distribution .. .. ... .. .. . . 101 Figure 5.19 Core 20 Normalized Midplane Power Distribution .. . . . . 102 g Figure 6.1 Frequency Distribution of B&W Criticals Comparisons .. .. . . . . 114 3 Figure 6.2 Frequency Distribution of Multi-Assembly Comparisons . . . . . . ... . . 115 Figure 6.3 Frequency Distribution of Assembly Radia! Power Comparisons . . . 116 Figure 6.4 Frequency Distribution of Assembly Total Power Comparisons .... . .. 117 1
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TR 091
'Rev.O Page 6
1.0 INTRODUCTION
This report describes the steady state physics method in use at GPUN for TMI-1. The method -
utHizes the incore fue' management computer codes CASMO-3, TABLES-3 and SIMULATE-3 (Refs.
1-3) developed by Studsvik. CASMO-3 is a multi-group two4imensional transport theory code for j
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the bumup calculation. TABLES-3 is a linkage code which reformats the two group cross sections ]
from CASMO-3 output fles according to the SIMULATE-3. format. SIMULATE-3 is a.three-l dimensional two group steady state reactor analysis code which predicts assembly power, control j l
rod worth, reactivity, boron concentrations, kinetics input, pin power, etc.
The CASMO 3/ SIMULATE-3 methodology has been thoroughly benchmarked by Studsvik, the
(. developer of the codes. CASMO-3 has been benchmarked against crtical experiments such as KRITZ experiments B&W crticals, BAPL and ESADA (Refs. 4-12). SIMULATE-3 has been benchmarked against B&W crticals, KWU reactors, and IAEA PWR problems (Refs.1315). These verify that CASMO-3/ SIMULATE 3 can accurately srnulate the reactor core during steady state operations. The methodology is now widely used by utilities for core analysis because it is accurate, easy to use and not CPU intensive. Since the computer codes have been extensively benchmarked by the vendor and other utilties (Refs.16-18), it is unnecessary to duplicate all of the .
I benchmark work. Therefore, the GPUN benchmark efforts are concentrated on how the CASMO-3/
SIMULATE 3 methodology can be accurately applied to TMI-1. The purpose is to demonstrate GPUN's understanding of the methodology and the capablity of using the codes. TMI 1 Cycles 1 to 10 (Refs.19-28) operations are modeled and the results are compared with the plant measurements _ in addition, pin coH crticals, B&W criticals and comparisons with PDQ (Ref. 29) results are also performed The results of ali the benchmarking establishes a basis of confidence for GPUN core analysis.
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TR 091 Rev.0 l Page 7 Section 2 of this report provides a brief overview of the computer codes. Section 3 gives the
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CASMO-3 verifications and Section 4 gives the SIMULATE 3 verifications. The accuracy of "
S:MULATE-3 pin power reconstruction is shown in Section 5. The determinations of the associated -
nuclear reliability factors are shown in Section 6. Section 7 summarizes the methodology and its ,
basis of confidence.
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TR 091 Rev.0 Page 8 2.0 METHODOLOGY OVERVIEW
. The steady state physics calculation uses CASMO-3 for fuel lattice cross section generation and
- SIMULATE-3 for throedimensional reactor simulation. . TABLES-3 is used to generate the SIMULATE-
, 3 cross section library from CASMO-3 cross section files. Brief descriptions of these three computer
. codes are given in this chapter.
2.1 . CASMO-3 Description CASMO-3 is a multi-group two-dimensonal transport theory code for burnup calculations on BWR and PWR assemblies or simple pin cells. It models cylindrical fuel rods in a square pitch array wth allowance for fuel rods loaded with gadolinium, burnable absorber rods, cluster control rods, instrument tube, water gaps, boron steel curtains, and cruciform control rods in the regions separating fuel assemblies. It can also be used to model fuel storage racks, asymmetric PWR fuel bundles, four BWR bundles, PWR colorset, and reflector data. -
l At GPUN CASMO-3 is used to generate group cross sections, discontinuity factors, fission products data, detector reaction rates, pin power data, and reflector cross sections required by SIMULATE-3. It is also used for automatic generation of effective cross sections for PDQ i
since it has a two4imensional diffusion theory routine. CASMO-3 has a 40 group and a 70 group nuclear data library Both libraries are based on ENDF/8-IV with some data taken from ENDF/B-V. The library contains absorption, fission, nufission, transport and Po scattering cross sections. Data is tabulated as functions of temperature if needed. The library also contrins yield values for fission products and decay constants. The 40 group j library is condensed from the 70 group library using typical light water reactor spectra for
[ m . _ es. 1 40 - ,, _ , - .t e P u N - p , _ _ s a - ,he i
TR 091 Rev.O Page 9 benchmark work performed at GPUN as recommended in Ref. 4. For fuel lattices ,
containing gadolinia pins. the computer code MICSURN-3 (Ref. 30), is used to generate =
effective Gd cross sections as a function of bumup.
A simplified flow diagram for CASMO-3 is shown in Figure 2.1. Effective resonance cross sections are calculated individually for each fuel pin. The cross sections are then used in a wies of micro group calculations to obtain detailed neutron energy spectra to be used El, for eneigy condensation and spatial homogenization of the pin cells. For PWR, the microgro ip spectra are directly used to obtain broad group cross sections for smeared pin J cells for the succeeding twodimensional transmission probability calculations. The eigenvalue and the flux distribution are obtained in the transport calculation and a fundamental buciding mode is used to include effects of leakage. The isotopic depletion ;
as a function of irradiation is calculated for each fuel pin and for each region containing a
- bumable absorber. A predictor-corrector approach is used for the bumup calculation.
Cross sections for PDQ (Ref. 29) are generated by comparing automaticrJiy within CASMO-3 a diffusion theory solution (DIXY) with the CASMO-3 transport theory solution.
I 2.2 TABLES-3 Description g TABLES-3 is a linkage code which reads the CASMO-3 output and generates a binary I' '
library to SIMULATE-3. The cross section library consists of 2-dimensional and/or 3 dimensional tables which may be interpolated to provide data at intermediate conditions. )
The allowed variables are exposure, void, history averaged void, fuel temperature, history l
averaged fuel temperature, moderator temperatute, history averaged moderator ;
temperature, boron concentration, history averaged boron concentrations, control rod, I
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, TR 091 Rev.O Page 10 history averaged control rod, and bumable absorber exposure.
1 The base cross section values are generated at nominal reactor conditions as a function of assembly exposure. Changes in cross sections from their base values are determined ,
by altering one variable from its base value at various exposures for modeling instantaneous change of operating conditions. For cumulative effects, the history data of cross sections . .,
I are obtained by comparing branch cases from the b3se depletion to depletions performed at the branch conditions. SIMULATE-3 will interpolate or extrapolate the tabulated delta cross sections based on the reactor conditions being modelled and add them to the base cross sections to obtain the appropriate total cross sections.
TABLES-3 also collects and functionalizes the CASMO-3 data required for pin power reconstruction and kinetics calculation in SIMULATE 3. This data consists of pin-by-pin 1
power distributions, comer-point flux ratios, detector flux peaking factors, detector microscopic cross sections, two-group neutron velocities, effective delayed neutron i
precursor yields, and precursor decay constants. The principal variations of these data are represented by a one dimensional table set in exposure. The additional dependencies of the data are represented by one-dimensional tables of the derivatives of the data as a function of exposure. SIMULATE-3 then reconstructs the pin power from these tables for the reactor conditions modeled.
2.3 SIMULATE-3 Description SIMULATE-3 is a three4imensional two group steady state reactor analysis code for performing incore fuel management studies, core design calculations, and calculations of safety parameters. It is an advanced nodal code which explicitly models the baffle and
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TR 091 Rev.O Page 11 reflector regions, thus eliminating the need for user adjustable parameters, or the need for ,
data normalization with higher order codes.
- A two group diffusion model, OPANDA, is used to determine the three dimensional ,
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distributions of neutron fluxes. The nodal equations are solved iteratively on nodal coupling coefficients and node-averaged fluxes. OPANDA is different from other advance nodal codes in that the intra-nodal flux shape in either the fast or thermal group is intimately coupled to the flux shape in the other group. It also constructs two-node problems for each nodal interface to obtain coupling relationships which involves only node-averaged fluxes and transverse leakages.
Conventional nodal codes have difficulty modeling the fluxes at assembly interfaces using the homogenized fluxes. SIMUL. ATE-3 overcomes this difficulty by coupling the homogenized fluxes with the assembly discontinuity factors from CASMO-3. When used in the OPANDA model, the assembly discontinuity factors change the neutron currents between assemblies and effectively eliminate the homogenization errors. The flux and leakage distributions at the fuelfsaffle interface as well as reaction rates in the baffle and reactor are generated using the CASMO-3 reflector option. The discontinuity factor concept is also used to treat the baffle / reflector homogenization in OPANDA. This provides accurate representation of the radial and axial reflector nodes, thus eliminating the use of albedos.
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All cross section data are generated from CASMO-3 assembly calculations and are tabulated as multklimensional tables by the TABLES-3 code. Instead of a direct calculation of nuclide concentrations, SIMULATE-3 uses macroscopic cross section data functionalized I
.I I TR 091 Rev. O I Page 12 versus exposure and history variables. A weighting variable is determined intemally for each fuel type and used in the history effects calculation. This is to account for the fact that cross sections are more sensitive to recent history values of state parameters and less sensitive to those of eariier history. Another characteristic of SIMULATE-3 depletion model ,
is the spatial representation used to model the radial cross section variation within an assembly. Therefore, the subdivision of each assembly is not required in order to model the influence of large exposure gradients within fuel assemblies.
l t The SIMULATE-3 pin power reconstruction method is based on the assumption of separability of the global flux (homogeneous intranodal flux) and local flux shapes j (heterogeneous " form functions"). The intranodal flux distributions are computed using biquadrate flux expansions and the form functions are computed from single assembly spectrum depletion calculations. Comer point fluxes are determined to preserve fluxes at nodal points assuming a biquadrate distribution. The spectral interactions between l
neighboring assemblies are explicitly modeled in the intranadal cross sections which allows l evaluation of pin-by-pin distribution of fission cross sections.
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TR 091 R:v. O
- Page 13 Figure 2.1 Flow Diagram of CASM0-3
~ ~1 rRestart
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Input -
- Tape 61 L.... . . .J !
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Resonance calculation < Data library
, < Tape 10
, g L. . . . ...J Macroscopic cross section I r -- - -
1
' Gd library -
- Tape 11/ Tape 13 .
Micro group calculation L---- - - J Condense to max 12 groups PWR Homogen1Ze to macro reg 1on 5
Macro group calculation in annular geometry Condense to max 12 groups Calc cross section for 2D. regions -
g
? g Pin cell Control rod calculation CROCOP
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Two. dimensional transport calculation. C0XY
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Fundamental mode calculation l!
W y
- "1 Two-dimensional l DiffusiontheoryDlXY~lFewgroupconstants r* Punch
- * * *fi le ii Reaction rates -
Tape 71 L . . . . . . .J Burnup corrector g
?
Number densities Zero burnup 9
Burnup predictor +---
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TR 091 Rev.O Page 14 -
3.0 CASMO-3 VERIFICATION CASMO-3 has been benchmarked by GPU Nuclear against selected pin cell critical experiments to verify the accuracy of the nuclear data library, neutron transport treatment and pin cell calculations. The GPUN benchmark used the options recommended by Studsvik and the results are described in Section 3.1.
I Other benchmarks are summarized in Section 3.2. Since the SIMULATE-3 cross section library is l
generated by CASMO-3 using the same vendor recommended options, the good agreement between th'e reactor operation data and CASMO-3/ SIMUL. ATE-3 results shown in Chapter 4 indirectly validate the CASMO-3 modeling accuracy. -
3.1 Comparison with Uniform Pin Cell Criticals The purpose of the pin cell critical comparisons is to provide an integral verification of the nuclear data library and the treatment of neutron transport and spectrum in pin cells. The NS&E criticals (Ref. 5) and the KRITZ criticals (Ref. 6) are modeled using CASMO-3. The pin cells are modeled as infinl3 uniform lattices. The measured buckling values are used for leakage corrections. The 40 group library is used in the criticality calculation.
The NS&E criticals are room temperature critical experiments with variations in fuel lattice pitch, fuel enrichment, and the soluble boron concentration. The critical experiments of interest are the -
ones with uranium oxide fuel and a light water moderator with key parameters given in Table 3-1.
The CASMO-3 calculated K-effectives are also listed in Table 3-1. The mean K-effective for the cases modeled is 0.99227 with a 0.00822 standard deviation.
t The KRITZ pin cell criticals are a series of critical experiments performed at various moderator temperatures and boron concentrations. Uranium oxide fuel rods of 1.35 w/o are used in the experiments and the lattice pitch is 1.8 cm. The moderator temperature, boron concentration, f
the measured buckling values and the calculated K-effectives are listed in Table 3.2 together with l
the CASMO-3 calculated K-effectives. The mean K-effective for the 24 KRITZ criticals modeled is 0.99574 with a 0.00201 standard deviation.
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[ S TR 091 l Rev.O Page 15 The calculated multiplication factors of both sets are all close to unity and show no specific trend.
The statistics of these pin cell comparisons are shown in Table 3.3. The average multiplication l factors for the 63 cases studied is 0.99359 with a standard deviation of 0.00677. The calculated K-effectives are plotted against fuel enrichment, moderating ratio, pellet diameter and buckling in Figures 3.1 to 3.6 which show no obvious trend in any parameter. Considering the 5, experimental uncertainty in the measured buckling and a lack of an asymptotic spectrum in smail ,
cores, the agreement is very good. The pin cell criticals benchmark the accuracy ' of CASMO-3 )
nuclear data library, treatment of neutron transport and spectrum in pin cells.
3.2 Validation by Studsvik CASMO-3 has been benchmarked extensively by Studsvik Energitenik, the developer of CASMO-3 (Ref. 4). The benchmarking covers pin cell lattices, BWR lattices with and without gadolinium and ;
cruciform control rod, PWR lattices with small and large water holes, Ag-in-Cd control rods and large B,C bumable poison rods, and fuel storage rack configurations. The cases are:
e Pin Cell C:iticals The BAPL, ESADA and TRX (Refs. 7,8, 9) critical experiments are analyzed using the CASMO-3 fundamental mode to determine K-effective. The BAPL fuel is uranium oxide and the TRX fuel is uranium metal. The ESADA cases consist of 0.7 w/o U-235 with 1.8 w/o enriched Pu-239. The experimental data and the calculated K-effective are shown ;
in Table 3.4.
e KRil2 Critical Experiments I, The KRITZ experiments (Ref.10) consist of several core types KRITZ-1 and KRITZ-2 are regular pin cell cores, KRITZ 3 contains PWR assemblies and KRITZ-4 contains BWR assemblies. The description of these critical cores are listed in Tables 3.5 and 3.6. The CASMO-3 calculated K-effectives are given in Table 3.7.
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Page 16 e B&W Critical Five B&W critical cores (Ref.11); one regular pin cell lattice and four 3x3 PWR type assemblies {14x14) are modeled. All five cores have a U-235 enrichmont of 2.46 percent.
The calculated K-effectives are summarized in Table 3.8.
P e Other Pin Cell Cores Four other pin cell cores, BAPL-UO2 TS, B&W B20 ESADA A-1 and C-18, and B&W 20 (Refs. 7, 8,12, respectively) are also analyzed. A!! the experiments are performed at I room tempe'rature.
L The BAPL-UO, T6 core has a 19 cm radius and 1.45 w/o enrichment. The B&W B20 l l
core has a 31 cm radius and 2.46 w/o enrichment. The ESADA A-1 core has a 22 cm radius and the C18 core has two annular regions of 15 cm and 22 cm radli. The ESADA f cores have natural UO2 fad containing 2% PuO2. The fraction of Pu239 in total Pu for the A-1 fuel and the outer region C-18 fuel is 92% while it is 72% in the inner region of C-18 fuel. The Pu240 fractions are 8% and 24%, respectively. Other experimental data and calculated K-effectives are listed in Table 3.9.
i L
The calculated K-effectke values are close to 1.000 as summarized in Tat %e 3.10. There is no observed trend in K-effectNe versus any parameter. These provide a verification of the CASMO-3 nuclear data library, the twodimensional transport theory calculation, and the absorber calculation.
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Table 3.1 NSEE UD, Critical Emperiments Case Enrichment Volume Ratio Fuel Pellet Lattice Boron Resoured (,
Number at 1 Density Diameter Pitch Camc. Buckling (CASRO-3)
Vyp: Vu (glcc) (ce) (ce) (@ M 1 1.328 3.02 7.53 1.5265 2.205 0 28.37 0.99370 2 1.328 3.95 7.53 1.5265 2.359 0 30.17 0.99638 3 1.328 4.95 7.53 1.5265 2.512 0 29.06 0.99702 4 1.328 3.93 7.52 0.9855 1.558 0 25.28 0.99455 5 1.328 4.89 7.52 0.9855 1.652 0 25.21 0.99453 6 1.328 2.88 10.53 0.9728 1.558 0 32.59 0.99783 7 1.328 3.58 10.53 0.9728 1.652 0 35.47 0.99653 8 1.328 4.83 10.53 0.9728 1.806 0 34.22 0.99710 9 2.734 2.18 10.18 0.7620 1.0287 0 40.75 1.00120 10 2.734 2.93 10.18 0.7620 1.1049 0 53.23 0.99905 11 2.734 3.86 10.18 0.7620 1.1938 0 63.26 0.99500 12 2.734 7.02 10.18 0.7620 1.4554 0 65.64 1.00161 13 2.734 8.49 10.18 0.7620 1.5621 0 60.07 1.00627 g 14 2.734 10.38 10.18 0.7620 1.6891 0 52.92 1.00554 g 15 2.734 2.50 10.18 0.7620 1.0617 0 47.5 0.99744 16 2.734 4.51 10.18 0.7620 1.2522 0 68.8 0.98847 17 3.745 2.50 10.37 0.7544 1.0617 0 68.3 0.99609 18 3.745 4.51 10.37 0.7544 1.2522 0 95.1 0.98869 19 3.745 4.51 10.37 0.7544 1.2522 0 95.68 0.98702 20 21 3.745 3.745 4.51 4.51 10.37 10.37 0.7544 0.7544 1.2522 462 74.64 0.98773 g 1.2522 718 63.66 0.98848 g 22 3.745 4.51 10.37 0.7544 1.2522 1277 40.99 0.99170 23 3.745 4.51 10.37 0.7544 1.2522 1349 38.39 0.99171 24 3.745 4.51 10.37 0.7544 1.2522 1493 33.38 0.99120 25 4.069 2.55 9.46 1.1278 1.5113 0 88 0.98042 26 4.069 2.55 9.46 1.1278 1.5113 3431 17.2 0.99937 34 4.069 2.14 9.46 1.1278 1.45 0 79 0.97844 37 2.49 2.84 10.24 1.0297 1.5113 0 70.1 1.00609 l
g, 42 3.037 2.64 9.28 1.1268 1.555 0 50.75 0.98582 43 3.037 8.16 9.28 1.1268 2.198 0 68.81 0.97672 44 4.069 2.59 9.45 1.1268 1.555 0 69.25 0.99003 ;
45 4.069 3.53 9.45 1.1268 1.684 0 85.52 0.98158 46 4.069 8.02 9.45 1.1268 2.198 0 92.84 0.99594 47 4.069 9.90 9.45 1.1268 2.381 0 91.79 0.98509 50 2.49 2.84 10.24 1.0297 1.5113 1694 20.2 1.00298 52 2.096 3.09 10.38 1.5240 2.4052 0 80.6 0.99489 53 2.096 4.12 10.38 1.5240 2.6162 0 85.7 0.98056 54 2.096 6.14 10.38 1.5240 2.9891 0 77 0.97805 55 2.096 8.20 10.38 1.5240 3.3255 0 61.6 0.97755 I
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^ =- Riv. 0 l Pzge 18 l I i Table 3.2 KRITZ Pin Cell Critical Experiments Case Core Boron Temperature Measured K, Number Type Conc. (* C) Buckling (CASMO-3)
(ppm) (M)
1 39(0)36 0.8 20 40 0.99615 3 0.8 90 37 0.99495 4 0.8 120 35 0.99426 5 0.8 140 34 0.99381 6 0.8 180 32 0.99314 '
- W 7 0.8 195 30 0.99299 8 0.8 205 30 0.99293 9 0.8 215 29 0.99295 ;
10 0.8 225 28 0.99299 i 11 46(0)36 47 90 35 0.99587 12 47 205 27 0.99464 l 13 47 225 26 0.99441 14 47 245 24 0.99454 15 46(0)36 175 20 30 0.99855
- 16 175 35 30 0.99832 17 175 50 29 0.99808 18 175 65 29 0.99788 !
19 175 80 28 0.99770 20 175 90 28 0.99754 j e
22 175 170 24 0.99740 23 175 185 23 0.99754 24 175 205 22 0.99766 1
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Table 3.3 Pin Cell Critical Statistics I
CASMO-3 I;I1 Criticals Number of K-effective Standard Experiments Average Deviation NS&E 39 0.99227 0.00822 KRITZ 24 0.99574 0.00201 5
ALL 63 0.99359 0.00677 E ,
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TR 091 Rev.O Page 20 Table 3.4 K, for Pin Cell Criticals f Pin Cell Pin Radii Pitch Enr Boron B K, (cm) (cm) (w/o) Conc (M) (CASMO-3)
(ppm)
BAPL-UO, T1 0.76 2.1 1.3 0 28 0.99424 BAPL-UO 2 T2 0.76 2.2 1.3 0 30 0.99608 I
BAPL-UO, T3 0.76 2.3 1.3 0 29 0.99528 BAPL-UO, T4 0.49 1.4 1.3 0 25 0.99591 BAPL-UO 2 T5 0.49 1.5 1.3 0 25 0.99565 BAPL-UO 2 T6 0.49 1.4 1.3 0 33 0.99888 BAPL-UO, T7 0.49 1.5 1.3 0 35 0.99736 BAPL-UO 2 T8 0.49 1.7 1.3 0 34 0.99705 TRX 1 0.49 1.7 0 57 0.99228 1.3 TRX 2 0.49 2.0 0 55 0.99137 1.3 Us23 Pu ras ESADA A-1 0.64 1.8 0.7 1.8 0 69 0.98827 ESADA A-3 0.64 1.9 0.7 1.8 0 90 0.98295 ESADA A-4 0.64 2.5 0.7 1.8 0 105 0.99873 ESADA A-6 0.64 2.7 0.7 1.8 0 98 1.00044 ESADA A-7 0.64 3.5 0.7 1.8 0 50 0.99707 ESADA A4 0.64 1.8 0.7 1.8 260 63 0.99651 ESADA A-9 0.64 2.5 0.7 1.8 260 84 0.99490 ESADA A 10 0.64 1.8 0.7 1.8 530 58 0.99517 ESADA A-11 0.64 2.5 0.7 1.8 530 63 0.99571 ESADA A-12 0.64 2.5 0.7 1.4 0 80 0.99737 ESADA A-13 0.64 2.7 0.7 1.4 0 73 0.99763 l .
B.,
TR 091 .
E Rev.O E Page 21 Table 3.5 Data for the KRITZ Series of Critical Cores L I, i
Series Enrichment (w/o) Pitch (cm) Pin Radil (cm) i K1 1.35 1.80 0.62 K2 1.86 1.48 & 1.63 0.53 -
K3 3 1.4 0.5 )
K4 2.6 1.6 0.5
- For K2 2:1 and 2:13 respectively.
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![ . TR 091 3 Rev.O Page 22
!I Table 3.6 Description of KRITZ Critical Cores I K3 U-WH1 161x1 water holes, incl 0 ding guide tubes in the central assembly.
- g K3 U-CR1 Same as U-WH1 but with Ag-In-Cd control rods inserted in the guide tubes.
- 3 K3 U WH2 5 2x2 water holes in the central assembly and 3 in the peripheral ones.
K3 U-CR2 Same as U-WH2 but with boron-carbide control rods inserted in the central water holes.
{
K4 2:1 All assemblies >Jnpoisoned.
K4 2:2 Same as 2:1 but with a control rod cross in the central water gap.
K4 2:5 Same as 2:1 but with 7 Gd rods in each of the 4 central assemblies.
K4 3:1 All assemblies unpoisoned.
K4 3:2 Same as 3:1 but with 5 Gd rods in each of the 4 central assemblies.
K4 3:5 Same as 3:1 but with 3 Gd rods in each of the 4 central assemblies.
K4 4:1 Same as 3:1 but with 5 Gd rods in every second of the assemblies, in a checker board configuration.
K4 4:2 Same as 3:1 but with 3 Gd rods in every second of the assemblies, in a checker board configuration.
K4 5:1 Same as 3:1 but with 3 Gd rods in each assembly.
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Table 3.7 Calculated K, for KRITZ Cores Core Temp Boron Conc K, (K) (ppm) (CASMO-3)
K1 290 480 180 0.99869 j '
180 0.99878 5 K2 2:1 290 220 tM
- 520 30 1.00072 K2 2:13 290 450 0.99887 -
520 280 0.99895 K3 U-WH1 300 1100 0.99880 500 1000 0.99926 K3 U-CR1 300 700 1.00027 500 500 0.99876 l
=
K3 U-WH2 300 1100 1.00031 500 1000 1.00024 K3 UCR2 300 700 0.99970 500 500 0.99953 K4 2:1 300 300 1.00064 K4 2:2 300 100 1.00018 K4 2:5 300 50 1.00014 K4 3:1 300 300 1.00104 500 350 1.00155 K4 3:2 300 100 1.00164 K4 3:5 500 300 50 200 1.00147 g,
1.00180 5 500 200 1.00152 I
r K4 4:1 300 100 1.00067 500 50 1.00036 K4 4:2 300 200 1.00127 K4 5:1 300 50 1.00034 500 0 0.99932
- Benchmark results by Studsvik Energitenik AB (Ref. 4).
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- l Table 3.8 Summary of B&W Cores l 1
I Core Gap Boron Conc. K, (Pitch) (ppm) (CASMO-3) .
l -
0 1.00026 ll 0 1040 1.00145 i Ill 1 760 1.00291 IX 4 0 1.00037 +
X 3 140 1.00240 i
- Benchmark results by Studsvik Energitenik AB (Ref. 4). '
+ K, reduced by 0.00300 for comparison since the experimental K, was determined to be 1.00300.
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Page 25 Table 3.9 Summary of Data of the T6, B20 and ESADA Cores
- Core Pin Radil Pitch Boron Conc K, (cm) (cm) (ppm) (CASMO-3)
BAPL-UO2 T6 0.49 1.45 0 1.00132 !
B&W B20 0.52 1.51 1670 1.00082
- Benchmark results by Studsvik Energitenik AB (Ref. 4).
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l Table 3.10 K, Statistics for CASMO-3*
l K,
(CASMO-3)
Cold pin cells (9 cases) 1.00018 .00102 .
Hot pin cells (3 cases) 0.99948 i .00107 All pin cells (12 cases) 1.00001 .00103 Cold PWR cores (4 cases) 0.99977 2.00070 Hot PWR cores (4 cases) 0.99945 t .00062 All PWR cores (8 cases) 0.99961 t .t,M Cold BWR cores (9 cases) 1.00086 t.00062 Hot BWR cores (5 cases) 1.00084 2.00099 All BWR cores (14 cases) 1.00085 2 .00073
~
Cold B&W cores (5 cases) 1.00148 i .00118 All cold cores (25 cases) 1.00056 2 .00105 Cold cores which were also l measured hot (12 cases) 1.00018 2 .00104 All hot cores (12 cases) 1.00004 2 .00108 All cores (37 cases) 1.00039 2 .00107 B:nchrnark results by Studsvik Energttenik AB (Ref. 4).
TR 091 R2v. O Paga 27 Figure 3.1 CASMD 3 PIN CELL CRITICALS l't K EFFECTIVE VS. ENRICHMENT 1.03
! i ._c_ g.
. e I
C E
l g 1.00 t
, la . maam. j u e = =
! g i C~
i e i
. i : -
l 3.
s . I :
I 0.97 1 2 3 4 5
! muRIcmatuT(w/o)
Figure 3.2 ,
CASMO 3 PIN CELL CRITICALS K EFFECTIVE VS. LATTICE PITCH l
, i
- 1.03
! g': .
I . nsu o artz .
- - E
! e .
i.u
- ~
- 5. . ,
- _m
.. g .
wanme ll g
8 .
- g. .
0.97 I 2 3 4 IATTIca FITCI(CH)
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TR 091 ,
I R;v. O Page 28 , ;
I Figure 3.3 CASMD 3 PIN CELL CRITICALS ,
K EFFECTIVE VS. H201U VOLUME RATIO 1.03 l
. nsu a um '
?
" p $m _ _ _ _
u m . Joe w
E 1.00 - -
2e . -
g N ", E ,
i
.* . y I
' O.97 1 2 3 4 5 6 7 8 9 10 11 H20:U VOLUME RATIO Figure 3.4 ;
CASMD 3 PIN CELL CRITICALS K EFFECTIVE VS. BORON CONCENTRATION 1.03
. niu o em )
h 5=.",
g 4 Y .. .
i .
. l I
o,I O 500 1000 1500 2000 2500 3000 3500
, BORON CONCENTRATION (FFM) l
TR 091
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, Page 29 Figure 3.5 CASMD 3 PIN CELL CRITICALS l K EFFECTIVE VS. MODERATOR TEMPERATURE i -
1.03 i
g i -
l
,5 ,. . l, im , - - _
a
~
E g o a aoBoB s E l 34 0.97
- 250 300 350 400 450 500 550 MODERATOR'IEMPERATURE (DEGREES K) ,
l Figure 3.6 l' CASMO 3 PIN CELL CRITICALS K EFFECTIVE VS. MEASURED BUCKLING l g
._ c_
g .
g i. . _ . . - - - l,
.n. .. g
(
0 10 20 30 40 50 to 70 to to 100 .
MEASURED BUCKLING (M-2)
I
L TR 091 Rev.O Page 30 4.0 SIMULATE-3 VERIFICATION The SIMULATE-3 model is a ttwee4imensional model with a 2x2 radial node mesh per assembly and twenty-four axial nodes. The top, bottom and radial reflector regions are also explicitly modeled. Thermal hydraulic feedback and Doppler feedback are used. Fuel temperature is eg:::j as a function of power ary:1 exposure The boron history and moderator temperature history effect are included in the model. Close agreement between the modeling results and TMI 1 operating data (Refs.19-28) validates the applicability of SIMULATE-3 to the TMI-1 core.
4.1 Boron Letdown Resulta
- 1 Critical boron concentration is measured regularly during operation Hot full power depletions are j f performed to calculate the critical boron concentration for TMI 1 cycles The SIMULATE-3 calculated values are compared to the measured data at steady state operation statopoints and the results are plotted in Figures 4.1 - 4.9. The difference in the letdown boron comparison is usually small at the beginning and at the end of the cycle, with the maximum difference occurring at the middle of the
.)
j cycle. This phenomeru is W noticeable for Cycles 6,7,8, and 9 with longer cycle lengths as shown in Figure 4.10. The large dip in the middle of the cycle can be accounted for by the depletion of B 10 in the soluble boron Starting in Cyde 8, reactor coolant samples were taken regularly to measure the B-10 atomic %. The l
B-10 atomic % is close to 19.8% st the beginning of the cycle and it depistes to about 17% at the end of cycle assuming no replenishment of the coolant with fresh (natural) boron Since the cross sections are generated based on constant B-10 atomic % of 19.8, adjustments are made to the plant measured boron values to componente for the B-10 depletion ellect These are also plotted in Figures 4.8 and 4.9. With the B-10 depletion conection, the letdown boron comparison improves significantly as shown in Figure 4.10. Since future TMI 1 cycles will be two-year cycles with periode
B; TR 091 j Rev. 0 l Page 31 g,
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sampling of the B-10 atomic % as done in Cycles 8 and 9, the average difference of -9 ppm with a 9 ppm sti tard deviation is the model uncertainty for future cycles (see Table 4.1).
4.2 Hot Full Power Comparisons I'
The TMl 1 incore detector system consists of 52 detector strings with seven fixed rhodium detectors in each string. The detector strings are radially arranged to provide complete neutron flux information for one-quarter of a symmetric core. Symmetry can be applied to obtain full core neutron flux information. The detector signals are corrected for background, leakage, detector sensitivity and rhodium depletion.
The corrected signals from the rhodium detectors are connected to the assembly power by the plant I
process computer software (Ref. 31). The inferred measured assembly power distribution is ,
compared to SIMULATE-3 predicted assembly powe s at selected steady state points in the cycle. ;
Results from Cycles 1-5 are not included here because of the change of process computer software (Ref. 32) and the breakdown of detector insulation which resulted in a large uncertainty in the plant measured power.
1 The calculated radial power distribution compares well with the measured power distribution. The average % difference is 1.76% with a 0.71% standard deviation based on a total of 106 state points comparisons. Table 4.2 summarizes the radial power comparison results for Cycles 6-9. Figures 4.11
- 4.22 give the radial power distribution comparisons at the beginning, middle, and end of Cycles 6-9.
The axial offset which is defined as: .
A-O= P7 -P 8 Pr+P,x 100 I'
h TR 091 Rev.O I^ Page 32 where
[- Pr = power in the top haN of the core P. - power in the bottom half of the core h are also compared in Table 4.3. The average difference between the calculated and measured axial offset is 1.15% wth a 1.22% standard deviation. The agreement is very good considering that the measured axial offset varies by 2% during a day due to boron dilution and contrd rod movement.
Figures 4.23 - 4.34 provide the axial power distribution comparisons for Cycles 6-9. The overall agreement of the predictions with measurements for all four cycles is excellent
- f. 4.3 Hot Zero Power Comparisons The hot zero power (HZP) physics test is conducted at the beginning of the cycle to determine if the operating characteristics of the core are consistent with the design predictions and to assure that the core can be operated as designed The test condtion is 532*F and 2155 peig. This section compares the test results wth the SIMULATE-3 predicted values.
4.3.1 All Rods Out Critical Boron Concentration
(
The all rods out crtical boron concentration is determined by borating the core to an all rods out critical steady-state condklon. Calculated and measured data are compared in Table 4.4.
The average difference is -13 ppm with a 14 ppm standard deviation.
4.3.2 Control Rod Worth Thors are 61 fulllength contrd rods and 8 partiallength control rods at TMI. The contrd rods
nl
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TR 091 Rev.O i Page 33 gl l!
4 are grouped into eight groups with Group 8 consisting of eight partial length control rods.
Groups 1 through 4 are the safety rods while Groups 5 through 7 are the regulating control >
rods.
The control rod worth of Groups 5,6, and 7 are measured during the HZP physics test using the baron swap technique. This technique establishes a deboration rate of the reactor coolant system with compensation for the reactMty change through insertion of the control rod l group (s) of interest in incremented steps. The reactMty change is determined by a :
reactimeter. The control rod group worth is the sum of the reactMty changes for that group.
Table 4.5 shows the comparison between the calculated and measured control rod group worths. The mean of % differences is -2.78 with a standard deviation of 4.21 for an individual i regulating control rod group's worth. The mean of % difference is -2.93 with a standard deviation of 3.15 for the worth of all regulating control rod groups (See Table 4.6).
4 4.3.3 loothermalTemperature Coefficient The isothermal temperature coefficient at HZP is measured by first increasing the reactor l coolant's inlet temperature by 5'F, then decreasing it by 10* F and finally increasing it by 5'F.
The isothermal temperature coefficient is the change of reactMty dMded by the corresponding ;
temperature change. Table 4.7 compares the calculated and measured coefficient. The mean difference is 0.88 pcm/*F with a standard deviation of 0.34 pcm/*F.
l 4.4 TMI-1 Power Transient On November 20,1992, TMI-1 intentionally reduced power to 50% from 100% in order to clean Asist6c '
clams from the main condenser water boxes. After operating at 50% power for 3 days, the plant ,
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.g retumed to 100% power on November 23,1992. The 100-50-100 power transient was successfully simulated with SIMULATE-3. Figure 4.35 provides graphs of the core power, Group 7 control rod position, and axial imbalance versus time for the SIMULATE-3 model. The calculated imbalance swing agrees very well with the measured imbalance with slightly higher peaks. During the power ,
reduction, SIMULATE-3 estimated that the Group 7 control rod critical position was 27% withdrawn at 50% power which compares very well with the actual critical position of 34% withdrawn. In
. addition, SIMULATE-3 model predicted that 627 gallons of the Boric Acid Mix Tank (BAMT) borated water was needed in order to keep the reactor at 50% power while withdrawing Group 7 to 90%. This compares very well to the actual addition of 636 gallons. SIMULATE-3 estimates 5000 gallons of domineralized water would be required to deborate the core for the retum to 100% power. This is also close to the actual 4750 gallons of water added.
SIMULATE 4 successfully calculated the axial imbalance, critical control rod position, and critical boron concentrations during the power transient. These comparisons demonstrate that SIMULATE-3 can model tne xenon effects during a power transient.
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- Cycle Number of Average Standard .g State Points Difference Deviation g (PPM) (PPM) 8 27 -13 9 9 -4 25 7 -l 1 8 & 9 combined 52 -9 9
- Difference = SIMULATE Measurement i
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]
l Cycle Number of Average Standard State Points Difference (%) Deviation (%)
E 6 30 1.00 0.20 )
7 24 1.35 0.15 8 27 2.61 0.13 9 25 2.15 0.51 6-9 combined 106 1.76 0.71' lg l % Difference - (SIMULATE 3 - Measurement)
- 100 / Measurement I
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E en TR 091 R6v. O Page 37 Table 4.3 HFP Axial Offset Comparisons * ,
Cycle Number of Averrge Standard State Points Difference (%) Deviation (%) ,g 6 30 1.46 1.14 5 7 24 0.73 1.05 8 27 1.51 1.49
- 9 23 0.77 1.03 6-9 combined 104 1.15 1.22 I'
% Difference = (SIMUI. ATE Measurement)
- 100 / Measurement
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L~. (PPM) (PPM) (PPM) 1 1617 1608 -9 2 1384 1379 -5
- 3 1249 1235 -14 4 1231 1213 -18 5 1182 1151 -31 6 1449 1444 -5 7 1891 1863 28 8 1846 1817 -29 9 2157 2172 15 10 2421 2418 -3 Avera9e -13 Standard Deviation 14 1
{
-: 1 TR 091 j Rev.O g, Page 39 3 Table 4.5 BOC HZP Control Rod Worth-Individual Groups Cycle CR Measured SIMULATE-3 Difference Group (PCM) (PCM) (%) l 1 5 1030 1132 9.90 1 1 6 1250 1188 -4.96 1 7 1100 1102 0.18 2 5 675 665 -1.48 2
2 6
7 1056 772 1038 779
-1.70 0.91 g'
W 3 5 1127 1058 -6.12 ;
3 6 1013 990 -2.27 3 7 789 742 -5.96 4 5 1420 1384 -2.54 4 6 1070 971 -9.25 4 7 1480 1381 -6.69 5 5 946 951 0.53 5 6 863 813 -5.79 5 7 1400 1311 -6.36 l
- 6 5 1531 1534 0.20 6 6 759 781 2.90 6 7 964 967 0.31 7 5 1220 1240 1.64 7 6 934 936 0.21 7 7 926 939 1.40 8 5 1214 1147 -5.52 '
8 6 927 852 -8.09 8 7 974 911 6.47 9 5 1134 1051 -7.32 ,
9 6 817 807 -1.22 9 7 889 833 -6.30 '
10 5 1400 1318 -5.86 10 6 713 708 -0.70 i 10 7 981 913 -6.93 Average -2.78 Standard Deviation 4.21
_l
k TR 091 Rev.O
(.- Page 40 L Table 4.6 BOC HZP Control Rod Worth-Regulating Groups r Cycle Regulating Measured SIMULATE-3 Difference
1 5-7 3380 3422 1.24 2 5-7 2503 2482 -0.84 !
[ 3 5-7 2929 2790 -4.75 l
4 5-7 3970 3736 -5.89 4 f 5 5-7 3209 3075 -4.18 6 5-7 3254 3282 0.86 7 5-7 3080 3115 1.14 8 5-7 3115 2910 -6.58 9 5-7 2840 2891 -5.25 10 5-7 3094 2939 -5.01 f Average -2.93 Standard Deviation 3.15
(
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l
TR 091 Rev.O Page 41 Table 4.7 BOC HZP loothermal Temperature Coefficients Cycle Boron Measured SIMULATE-3 Difference l
- (ppm) (PCM/*F) (PCM/*F) (PCM/* F) 1 1601 4.49 5.43 0.94 1 1461 3.04 3.89 0.85 1 1269 -5.27 -3.98 1.29 1 1245 -6.04 4.43 1.61 j 2 1366 0.94 1.70 0.76 2 1149 -5.31 -4.60 0.71 3 1248 0.30 0.41 0.71 3 992 -6.80 -6.07 0.73 4 1234 0.26 1.01 0.75 4 880 -10.80 -9.26 1.54 5 1178 -2.25 -1.34 0.91 5 C01 -12.96 -12.14 0.82 6 1445 0.57 1.04 0.47 7 1682 2.41 3.49 1.08 8 1840 1.50 2.00 0.50 9 2149 3.11 3.51 0.40 10 2417 2.13 3.00 0.87 Average 0.88 Standard Deviation 0.34 E
5 I :
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TR 091
{! Rsv. O Page 42 g
Figure 4.1 h CYCLE 1 BORON COMPARISON l
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TR 091 !
Rev.O g, Page 43 g Figure 4.2 CYCLE 2 BORON COMPARISON l! ^
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TR 091 l Rev.O Page 44 Figure 4.3 CYCLE 3 BORON COMPARISON 775 675 - -
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TR 091 Rev.O Page 45 i
Figure 4.4 ll .
l CYCLE 4 BORON COMPARISON a; i E+
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'3 TR 091 Rav. O Page 46 ll Figure 4.5 g CYCLE 5 BORON COMPARISON l 700 6,o _ _ N g \
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~ > SIMULATE 3 + PLANT I
i Ei TR 091 ~l Rav. O l
_ Page 47 l Figure 4.6 ll CYCLE 6 BORON COMPARISON g 1000 E
900 - - N% 5<
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TR 091 f'- Rav. O Page 48.
Figure 4.7 l
CYCLE 7 BORON COMPARISON r
i i 1200
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- > SIMULATE 3 + PLANT
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TR 091 R2v. O
. Page 49 Figure 4.8 l CYCLE 8 BORON COMPARISON g
1400 1300 - -
1200 - - N I
1100 - - N ~
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1000 - - N NN :
900 - - NN
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- * - - SIMULATE 3 ---o--- PLANT -
SIMULATE 3 ADJUSTED I'
I
TR 091.
. Rav. 0
,- . Page 50 Figure 4.9 CYCLE 9 BORON COMPARISON i
l 1700 t a- .,.
{. 1600 -
- 1500 - -
i 1400 - -
1300 - - N 1200 - -
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I EXPOSURE (GWDRWrU)
-> SIMULATE 3 ---C- PLANT -
S24ULATE 3 ADJUSTED 1
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TR 091 E
Rsv, O Page 51 g 5,
Figure 4.10 g
a LETDOWN BORON DIFFERENCES ai E,
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- CYCLE 6 3-- CYCLE 7 : : l CYCLE 8 CYCLE 9 CYCm..
,oso m o CYCu . .
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i l'
.l TR 091 I
Rev. 0 Page 52
[ .
')
l
'I Figure 4.11 g
BOC 6 Radial Power Distribution LI 8 9 10 11 12 13 14 15 I 0.992 1.142 1.026 1.179 1.103 1.219 0.836 0.416 i
H 0.989 1.140 0.993 1.190 1.094 1.226 0.838 0.420 i
I 0.324 0.175 3.335 - 0.903 0.764 - 0.596 - 0.170 -1.022
, 1.011 1.152 1.118 1.233 1.240 1.051 0.497 -
K 0.992 1.150 1.101 1.225 1.228 1.066 0.504 1.875 0.201 1.546 0.653 0.981 -1.342 -1.463 1.053 1.224 1.079 1.247 0.984 0.415
- l
\
L 1.058
-0.434 1.219 0.376 1.056 2.152 1.271
-1.849 -1.348 0.998 0.426
- 2.589 a
1.095 1.239 1.220 0.887
.M 1.059 1.253 1.221 0.905 l 3.481 -1.091 - 0.009 -1.992 lN 1.033 1.014 1.864 1.020 1.033
-1.312 -0.298 0.540 0.542 ,
0.582 PREDICTED IO AVERAGE % DIFFERENCE:
STANDARD DEVIATION -
9.
1.495 E 0.581 0.215 MEASURED s oirrsReuce 4
'I .
I
~ -t &-
TR og1.
5,,l Rav. O Page 53 -
Figure 4.12
- MOC 6 Radial Power Distribution 8 9 10 11 12 13
-g! '
14 15 1.099 1.308 1.106 1.286 1.103 1.221 0.813 0.427
)1 H 1.114 1.321 1.093 1.287 1.095 1.224 0.820 0.426 1
-1.288 - 0.917 1.250 - 0.140 0.726 - 0.245 - 0.797 .0.176 1.106 1.289 1.148 1.281 1.170 1.008 0.498 -
- K 1.108 1.289 1.142 1.283 1.168 1.015 0.497
- 0.212 - 0.051 0.583 - 0.201 0.203 - 0.664 0.119
, 1.108 1.299 1.063 1.216 0.916 0.414 L 1.120 1.205 1.051 1.229 0.927 0.419
.l l - 1.081 0.303 1.061 -1.048 -1.199 - 1.253 1.090 1.231 1.113 0.822 i M 1.073 1.227 1.112 0.817 1.565 0.285 0.104 0.639 l
N 0.971 0.953 1.869 0.954 0.956 0.514 0.519 l
- 0.214 - 0.981 0.558 pasocreo I i O AVERAGE % DIFFERENCE: -0.068 g 0.561 STANDARD DEVIATION 0.838E - 0.560 usAsunso s occaswes l1 I
I I
- l TR oss Rev. 0 - j
.;g Page 54 i
- u l i
,l Figure 4.13 ;
l EOC 6 Radial Power Distribution J
8 9 10 11 12 13 14 15
! 1.034 1.224 1.048 1.225 1.078 1.194 0.852 0.499 H 1.051 1.220 1.053 1.215 1.087 1.173 0.870 0.501 l
-1.579 0.310 - 0.439 0.845 - 0.866 1.797 - 2.034 - 0.411 1.044 1.218 1.099 1.246 1.140 1.028 0.569 l K 1.051 1.210 1.096 1.239 1.143 1.038 'O.564 :
- 0.603 0.649 0.240 0.573 - 0.197 - 0.953 0.905 )
l i
1.064 1.261 1.109 1.204 0.943 0.480 '
1.076 1.251 1.104 1.213 0.952 0.482 IL -1.188 0.756 0.384 - 0.737 -1.023 - 0.424 1.077 1.219 1.105 0.861 M 1.074 1.221 1.109 0.843 0.292 - 0.120 - 0.366 2.059 IN 0.994 0.999
- 0.575 0.980 0.981
- 0.020 0.570 0.576
- 0.984 I 0.617 PREDICTED IO AVERAGE % DIFFERENCE:
STANDARD DEVIATION
-0.157 g 0.917 I 0.622
- 0.839 MEASURED v.omvemswee I
j I ,
I I
E, TR 091 Rav. O
.Page 55 .
Figure 4.14 l !
BOC 7 Radial Power Distribution l l
8 9 10 11 12 13 14 15 1.122 1.259 1.239 1.249 1.128 1.238 0.830 0.385 H 1.104 1.267 1.219 1.234 1.124 1.230 0.832 0.388 !
1.576 - 0.568 1.600 1.234 0.292 0.696 --0.287 - 0.872 ,
1.186 1.287 1.266 1.248 1.252 1.250 1.052 1.046 1.057 1.053 0.399 0.408 E:
K 1.192 1.271 5)
- 0.510 1.260 1.457 0.176 0.526 0.379 - 2.104 1.225 1.284 1.104 1.222 0.806 0.309 L 1.230 1.295 1.130 1.233 0.833 0.315 i
- 0.412 - 0.810 - 2.269 -0.939 - 3.201 -1.878 1 1.242 1.286 1.029 0.867 <
M . 1.247 1.274 1.032 0.874 :
- 0.384 0.957 -0.254 -0.762 1.079 1.050 0.421 N 1.016 1.049 0.438 gl m
6.240 0.128 - 3.723 I O.484 PREDCTED I'
O AVERAGE % DIFFERENCE: -0.206 g 0.502 uEAsuREo-STANDAlW DEVIATION -
1.896 E -3.599 v.D M RENCE Il I,
(
l I
l Ii
TR 091 f.j Rev.O
~
Page 56
(
Figure 4.15 MOC 7 Radial Power Distribution
(
8 9 10 11 12 13 14 15
[. .
1.136 1.328 1.204 1.298 1.109 1.311 0.880 0.451 H 1.126 1.338 1.216 1.304 1.107 1.301 0.879 0.459 0.889 - 0.692 - 0.938 - 0.395 0.184 0.793 0.198 - 1.786 1.170 1.316 1.210 1.264 1.060 1.097 0.460 K 1.170 1.311 1.198 1.256 1.056 1.094 0.461
- 0.046 0.386 0.988 0.616 0.423 0.303 - 0.167 1.172 1.284 1.062 1.263 0.835 0.358
( L' 1.178 1.281 1.073 1.277 0.854 0.364
- 0.526 0.229 -1.037 -1.156 - 2.274 -1.487 1.141 1.198 0.984 0.865 M 1.135 1.197 0.983 0.847
. . 0.527 0.116 0.135 2.221 0.984 1.000 0.437 N- 0.973 1.004 0.448
.1.126 - 0.416 - 2.421 0.489 PREDICTED O AVERAGE % DIFFERENCE: - 0.239 0.503 usAsuRsD STANDARD DEVIATION -
1.121 -2.720 s DemERENCE I
E
~
TR 091
~
Rev.0 Page 57 ,
Figure 4.16 l EOC 7 Radial Power Distribution l
8 9 10 11 12 13 14 15 1.029 1.189 1.090 1.200 1.073 1.307 0.932 0.533 H 1.016 1.170 1.098 1.174 1.086 1.300 0.954 0.542 1.216 1.652 - 0.694 2.179 -1.146 0.506 - 2.321 -1.532 -
1.058 1.189 1.126 1.216 1.072 1.136 0.540 $,
K 1.058 1.161 1.115 1.206 1.083 1.141 0.541 m
- 0.012 2.435 1.024 0.872 -1.001 - 0.418 - 0.129 1.085 1.214 1.110 1.293 0.896 0.432 I l L 1.085 1.208 1.103 1.313 0.921 0.434 g!
- 0.005 0.531 0.659 -1.499 - 2.696 - 0.355 m, 1.107 1.186 1.020 0.934 M 1.105 1.184 1.031 0.916 0.175 0.192 -1.113 1.956 1.006 1.043 0.502 E N 1.003 1.056 0.501 5 0.341 -1.315 0.120 0.555 pasoctro I
O AVERAGE % DIFFERENCE: - 0.010 0.554 MEASUnso STANDARD DEMATION -
1.246 0.090 s oim mewes I
I I
I
TR 091 Rsv. O Page 58 Figure 4.17 BOC 8 Radial Power Distribution l r
L 8 9 10 11 12 13 14 15 E. -
1.052 1.265 1.060 1.146 1.031 1.251 1.002 0.377 r
L- H 1.187 1.263 1.052 1.142 0.985 1.211 1.002 0.388
-11.359 0.162 0.796 0.306 4.708 3.307 0.089 - 2.892
[ 1.220 1.285 1.025 1.223 1.195 1.117 0.378 1.296 1.014 1.211 1.169 1.130 0.393
[K 1.211 0.772 - 0.872 1.132 0.946 2.180 -1.182 - 3.630
[- 1.035 1.197 0.973 1.256 1.052 0.330 L 1.033 1.205 0.958 1.271 1.087 0.340 0.218 - 0.629 1.542 -1.165 - 3.198 - 2.790 1.018 1.248 1.157 0.941 M 0.982 1.245 1.180 0.945 3.724 0.166 -1.930 - 0.422 1.206 1.067 0.405 N 1.196 1.096 0.412 0.820 - 2.668 -1.814 4
[O AVERAGE % DIFFERENCE: - 0.428 0.596 0.588 ensoicTso ueAsunen STANDARD DEVIATION
- 2.886 1.276 v.D M EnEWcEll
[
____.-________.--___.____.m_______m___.____ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ _ . - _ _ _ _ _ . _ _ _ . _ _ _ _ _ _ _ _ _ . _ . _ _ _ _ _ _ _ . _ . _ . _ _ _ _ _ . _
E TR 091 =l Rsv.O Page 59 Figure 4.18 li i MOC 8 Radial Power Distribution gl l
8 9 10 11 12 13 14 15 0.940 1.131 1.019 1.186 1.042 1.296 0.988 0.405 H 0.999 1.098 0.980 1.173 1.000 1.273 0.975 0.422 '
- 5.913 3.026 3.990 1.083 4.158 1.784 1.376 -4.146 1.119 1.300 1.041 1.294 1.165 1.108 0.404 K 1.079 1.303 1.022 1.307 1.131 l,
1.120 0.416 !
3.717 - 0.271 1.884 - 1.013 2.971 -1.129 - 3.018 i 1.048 1.285 0.999 1.278 1.002 0.347 L 1.037 1.318 0.978 1.314 1.032 0.362 '
1.033 - 2.519 2.143 - 2.800 - 2.844 -4.099 1.046 1.292 1.100 0.891 M 1.008 1.310 1.119 0.888 3.803 -1.339 -1.736 0.284 '
l N
1.142 1.132 1.041 1.079 0.412 0.419 l 0.955 - 3.506 -1.747 O.593 PREDICTED '
O AVERAGE % DIFFERENCE: -0.083 g 0.585 MEASURED !
STANDARD DEVIATION -
2.759 g 1.463
- oirrenEucE I
I I'
I
y TR 091 q Rav. O i
[.' Page 60 u
Figure 4.19 n
EOC 8 Radial Power Distribution L
8 9 10 11 12 13 14 15 r .
0.934 1.092 0.999 1.145 1.029 1.278 1.001 0.473 H 0.979 1.055 0.962 1.111 0.997 1.256 0.999 0.491
-4.533 3.553 3.833 2.994 3.191 1.748 0.153 - 3.674
( 1.078 1.259 1.031 1.282 1.132 1.103 0.469 1.045 1.245 1.014 1.284 1.113 1.117 0.485
[K 3.134 1.076 1.705 - 0.228 1.728 -1.325 - 3.365 1.040 1.285 1.003 1.263 0.997 0.403
[L 1.028 1.093 1.306
-1.663 0.988 1.497 1.292
- 2.247 1.029
- 3.158 0.420
- 4.046 r
L 1.049 1.282 1.082 0.910 M . 1.022 1.294 1.101 0.913 2.617 - 0.938 -1.725 -0.394 1.110 1.040 0.461 N 1.097 1.000 0.475 1.189 - 3.691 -3.070 0.639 PREDICTED O AVERAGE % DIFFERENCE: -0.077 g 0.624 usAsunso
. STANDARD DEVIATION 2.571 g 2.317 s o nensuce i
[
Ei TR 091 .
Rav. O Page 61 .
Figure 4.20 .5 BOC 9 Radial Power Distribution l-t 8 9 10 11 12 13 14 15 1.095 1.350 1.281 1.224 1.130 1.235 0.777 0.261 H- 1.097 1.346 1.248 1.208 1.113 1.238 0.788 0.274
-0.16% 0.30% 2.65 % 1.30 % 1.52 % -0.23% -1.38% -4.65%
l 1.335 1.349 1.186 1.299 1.080 0.973 0.282 K 1.318 1.354 1.164 1.287 1.076 0.980 0.294 1.24 % -0.38% 1.90% 1.00% 0.41 % -0.76% -3.90%
1.222 1.322 1.092 1.212 1.048 0.274 I
L 1.202 1.279 1.61 % 3.39%
1.085 0.63%
1.222
-0.80%
1.083
-3.28%
0.303
-9.67%
g*
1.155 1.245 1.042 0.886 M 1.143 1.237 1.043 0.905 1.09% 0.62% -0.12% -2.18% g h
1.083 1.045 0.385 N 1.091 1.042 0.401 g
-0.68% 0.28% -4.07%
0.488 I
ensocTso O AvEnAaE % DIFFERENCE: -0.nre g 0.498 usAsuneo -
STANDARD DEVIATION -
2.600 g -2.48% sappenewee I
I I
I
m TR O91 I
. Rev.O l
- Page 62 Figure 4.21 MOC 9 Radial Power Distribution 1
l 8 9 10 11 12 13 14 15 1 l
1.058 1.337 1.179 1.135 1.087 1.279 0.841 0.328 H 1.059 1.334 1.131 1.108 1.064 1.266 0.842 0.340
-0.06% 0.20 % 4.21 % 2.46 % 2.17% 1.02% -0.19% -3.33%
1.234 1.331 1.126 1.324 1.082 1.048 0.343 K 1.204 1.334 1.107 1.324 1.071 '1.036 0.349 I 2.43*A -0.26% 1.72% -0.05% 1.02% 1.14 % -1.71%
f.
1.165 1.353 1.085 1.263 1.038 0.318 L 1.159 1.350 1.082 1.287 1.054 0.342 0.57 % 0.19% 0.25 % -1.88% -1.45% -6.89%
l I 1.136 1.286 1.013 0.874 M 1.139 1.308 1.000 0.881 l
-0.24% -1.69% 0.58 % -0.84%
l 1.032 0.985 0.403 l N 1.031 0.990 0.414 0.13% -0.44% -2.62%
0.490 pasoicTso O AVERAGE % DIFFERENCE: - 0.163 0.496 usAsuaso sTANoAno DEvianon -
2.035 -1.17% v om m suce F
t
E-TR 091
~ Rav. O
- Page 63 -
Figure 4.22 .l EOC 9 Radial Power Distribution 8 9 10 11 12 13 14 15 0.995 .1.229 1.096 1.081 1.051 1.256 0.899 0.409 H 1.003 1.204 1.071 1.062 1.044 1.240 0.907 0.419
-0.73% 2.04 % 2.26 % 1.77% 0.66% 1.33 % -0.90% -2.30%
1.133 1.234 1.074 1.277 1.079 1.096 0.419 K 1.115 1.233 1.070 1.275 1.083 -1.080 ' O.425 1.62% 0.09% 0.34% 0.14% -0.43% 1.50 % - 1.25*A 1.100 1.298 1.065 1.274 1.073 I
0.387 L 1.103
-0.28%
1.286 0.89%
1.068
-0.25%
1.291
-1.33%
1.081
-0.77%
0.403
-4.17% l J
1.109 1.283 1.037 0.933 =
M 1.128 1.304 1.042 0.918
-1.69% -1.59% -0.48% 1.55 %
l N
1.043 1.051 1.023 1.018 0.470 0.474 l
-0.80% 0.51 % -0.82%
I '
l 0.557 enEmerun l O AVERAGE % DIFFERENCE: - 0.070 0.552 MEASUnED STANDARD DEVIATION -
1.429 1.07 % s ow e sucs I-I e
I
=
TR 091
~
e 64 Figure 4.23 I
BOC 6 Total Power Distribution
{.
- 8. 9- 10 11 12 -13 14 .15 r
t ,
g -N 5 . ,
(
) ) \
f-H '
r I
s r
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)' '
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< a a , 3 3
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. )
3 D
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3
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- )
,O PREDICTED --
( ,
TR 091 R3v. O Page 65 Figure 4.24 l
MOC 6 Total Power Distribution
, ,e ,, ,e s. I
) )
e ,, ,s H
l ' ) ) ' l Ti ' ll I t ,
k .
I
} 3. ] 3 1 J J J J > I
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I
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O PREDICTED --g i
_YfeBSED_3_E i
I!
l
I L IS2*o' Page 66 l
g Figure 4.25 EOC 6 Total Power Distribution I
L
) :) )
8 9 10 11 12 13 14 15 l
, m i
>) ij ;
H !
sl >
)
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I TR 091 ~
Rev.O Page 67 Figure 4.26 g BOC 7 Total Power Distribution
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Figure 4.27 ,
MOC 7 Total Power Distribution f
8 9 10 11 12 13 14 15 s
\ t,
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TR 091 E!
Ray. O Page 69 Figure 4.28 I EOC 7 Total Power Distribution l
8 9 10 11 12- 13 14 15 y
H t >
lt I
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TR 091 -
R:v. O -
. Page 70 '
Figure 4.29 BOC 8 Total Power Distribution 8 9 10 11 12 13 14 15 w y ..
( .
l ,l ,
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MEASURED + I
E; TR 091 -) '
Rsv. O Page 71 Figure 4.30 l MOC 8 Total Power Distribution l'
8 9 10 11 12 13 14 15 l-h [ ;* .
H + 6 ' '
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p_ .l TR 091 L' . RIV. 0 Page 72
[l Figure 4.31 )
EOC 8 Total Power Distribution 8 9 10 11 12 13 14 15
- j.
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- t
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BOC 9 Total Power Distribution l
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TR 091 i Rev.O 1 Page 74 f Figure 4.33 l l
{ MOC 9 Total Power Distribution 8 9 10 11 12 13 14 15 5 h 5, N, h *
- p N. S.
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Rev. 0 -
Page 75 Figure 4.34 I EOC 9 Total Power Distribution g
, , ,o ,, ,, ,e ,. ,,- I
, , , , , ., 1 g
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g= I g TR 091 ,
Rsv. O l Pags 76 FIGURE 4.35 TMl CYCLE 9 100-50-100 POWER TRANSIENT 100/; -- - ' 2 2 ' ~ 0 y ~2 ",
e: 3 i
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0 10 20 30 40 50 60 70 80 90 100 110 120 HOURS 100.
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( 0 10 20 30 40 50 SO 70 80 90 100 110 120 HOURS
+ MEASURED o SIM s !
TR 091 I Rev.O l Page 77 5.0 PIN POWER VAUDATION ,
SIMULATE-3 reconstructs the pin power from the calculated flux shapes and intranodal assembly powers.
Since no measured pin power data is available at TMI-1, higher oroer computer codes, namely, CASMO-3 and PDQ (Refs.1 and 29), are used for the pin power valdation. In addition, the B&W cold critical experiments (Ref. 33) are also used to benchmark the pin power reconstruction.
5.1 Comparison with Higher Order Numeric Calculation Two higher order computer codes, CASMO-3 and PDQ were used to benchmark SIMUI. ATE-3 pin power reconstruction accuracy. CASMO-3, a trant. port theory code, is considered the higher order benchmark for the multiple assembly configuration. PDO, a higher order diffusion code, is used to benchmark the pin power of a reactor core.
I 5.1.1 Multiple Assembly Configuration ,
A series of niuttiple assembly (2x2) configurations are setup to represent the possible combination of fuel enrichment, bumable poison rods, exposure, and control rod existence for typical TMI 1 core designs. The transport theory solution calculated by CASMO-3 is used as the higher order benchmark for SIMULATE-3.
The assembly fuel enrichment and bumable poison loading of the ten configurations studied are shown in Table 5.1. For each configuration, a 2x2 CASMO-3 run is submitted which directly calculates the spectral interaction between neighboring assemblies. This provdes the
" measured" value for the pin power comparison. Based on cross sections generated from single assembly CASMO-3 runs, SIMULATE-3 reconstructs the pin power of the assemblies using the surface discontinuity factors which account for the spectral interactions. Table 5.2 summarizes the comparison results.
l I
l
f
,c: .
. TR 091 Rev.O Page 78 The SIMULATE-3 calculated assembly powers and pin powers agree well with the CASMO values, with an average RMS error of 0.00874. There is no observed trend except that the RMS error for rodded configurations is slightly higher.
[ .
The multiessemblies pin power comparisons demonstrate that SIMULATE-3 pin power reconstruction is highly accurate.
5.1.2 TMi-1 Cycle 1 and Cycle 2 PDO, a fine mesh diffusion code, is also used as the benchmark for the SIMULATE-3 reconstructed pin power. Both PDQ and SIMULATE-3 cross sections are based on the same single assembly CASMO4 runs. The PDQ model has one mesh for each pin location. While the SIMULATE-3 model only hos 4 meshes per fuel assembly. -
i
-J The TMI-1 Cycle 1 core was depleted from 0 to 400 EFPD using PDQ and SIMULATE-3. The !
core was then shuffled for Cycle 2 and depleted to 250 EFPD using PDQ and SIMULATE-3.
The assembly powers and peak pin powers from both calculations were compared at selected exposures of the cycles. Results are shown in Table 5.3. The RMS error is about 1% in assembly power and 2% for peak pin power. This again demonstrates the accuracy of the SIMULATE-3 pin power reconstruction technique. The quarter core assembly power and peak pin power comparisons at BOC, MOC, and EOC are shown in Figures 5.1 to 5.12.
i 5.2 Validation Versus B&W Critical Experimenta The B&W critical experiments (Ref. 33) measured pin power distribution for various PWR latticer, consisting of different enrichments, large and small water holes, and po' son materials. CASMO-3/ SIMULATE-3 methodology was used to model these critical experiments. Cross section data were
a.l TR 091 .
Rev.O !
Page 79 generated based on single assembly CASMO-3 calculations. As shown in Figure 5.13, the critical j core geometry was slightly modified at the core boundary in the S'MULATE-3 model. This should not affect the pin power of the center assembly. -
SIMULATE-3 reconstructed pin powers were compared with the measured data. The pin by pin j comparisons are shown in Figures 5.14 - 5.19. The close agreement in pin power distribution. 0.8% !
RMS for lattices without gadolinia and 1.3% RMS for lattices with gadolinia, demonstrates the :
accu,ac,,,he S,Mumre.3.ma,ed pin -e, d,s1,,bution.1ae e 5.. aemma,izes tse senchma,e g;
results. !
l: .
Il Il l
I I
Il I
I I
I l I TR 091 Rev.0 1
Page 80 Table 5.1 Assembly Loadings for Multi-Assembly Problems I
Set Variation FA Type 1 initial FA Type 2 Initial
- I wt % U" BP Loading
- Burnup (GWD/MTU) wt % U" BP Loading" Burnup (GWD/MTU) .
1 Enrichment 4.00 0 4.65 0 I 2 Control Rod 4.65 0 4.65 Control Rod in 0
3 Enrichment 4.00 0 4.65 0 Control Rod Control Rod in i 4 Enrichment LBP 4.00 0 4.65 2.0 B C 0
t 5 LBP 4.65 0 4.65 2.0 B,C 0
Gd Pin I 2.0 Gd I 6 Enrichment Depletion 4.00 10 4.65 0 7 Enrichment 4.00 15 4.65 0 Depletion Control Rod in ,
Control Rod 8 Enrichment 4.00 0 4.65 15 Depletion APSRin APSR 9 Depletion 4.00 0 4.0 20 l BP Puli 1.7 B.C Pull (with BP)
Enrichment 10 Depletion 4.65 0 4.0 20
.I' BP Pull 1.7 B C Pull (with BP) wt %BC I ;
I TR 091 Rev.O Page 81 Table 5.2 Multi Assembly Pin Power Comparison
- Set Mean Std. Dev. RMS Peak Pin Worst Pin Rel. Diff Rel. Diff 1 0.00001 0.00209 0.00209 0.00097 0.00420 . ,
2 0.00146 0.01228 0.01237 -0.01363 0.02667 3 0.00080 0.01058 0.01061 -0.01146 0.02804 4 0.00008 0.00470 0.00470 -0.00564 0.00877 5 0.00053 0.00925 0.00926 -0.00877 0.01323 6 0.00068 0.00860 0.00863 0.00924 0.01310 7 -0.00008 0.00665 0.00664 -0.00645 0.01962 8 0.00079 0.00925 0.00928 -0.01038 0.01684 9 0.00103 0.01094 0.01099 -0.01096 0.01715 10 0.00159 0.01269 0.01278 0.01198 0.01957 Average 0.00069 0.00870 0.00874 -0.00691 0.01672 Rel. Difference = (SIMULATE CASMO-3) /CASMO-3 I
I E
I I
I I
I
l TR 091 Rev. O 1
{
{
Page 82 l Table 5.3 SIMUI. ATE-3 and PDQ Power Comparisons 8
A_gsombly Power Pin Power I EFPD RMS% % DIFF AT PEAK RMS % % DIFF AT ,
ASSEMBLY PEAK PIN 0.418 1.508 1.352 l I
O 1.282 4 0.980 0.357 1.485 1.503 25 0.758 -0.607 1.574 0.556 50 0.631 0.379 1.567 1.640 100 0.693 1.116 1.653 2.404 150 0.778 1.515 1.683 2.790 200 0.703 1.297 1.661 2.604 250 0.ES2 1.096 1.652 2.389 300 0.579 0.816 1.604 2.123 350 0.802 1.039 1.604 2.270 l
Cycle 2 j 0 1.3777 1.588 1.600 0.874 i
4 0.8436 1.725 1.519 1.365 25 0.7086 1.344 1.631 2.394 L 50 1.0576 1.355 1.605 2.501 100 0.7981 1.003 1.596 2.344 150 0.7120 l'
0.699 1.606 2.065 200 0.8735 0.554 1.661 1.826 250 1.1061 0.563 1.749 1.733 300 1.2721 0.483 1.831 1.751 350 1.5128 0.579 1.978 1.806
- % Difference = (SIMULATE PDO)
- 100/PDQ
E
- 8 TR 091 -
Rev.0 4 Page 83 Table 5.4 B&W Critical Pin Power Results Summary I~
l Core # 1 5 12 14 18 20
~
Fuel Assembly 2.46 % 2.46 % 4.02% 4.02% 4.02% 4.02% ,
Design 15x15 15x15 15x15 15x15 16x16 16x16 No Gd 12 Gd No Gd 12 Gd No Gd 16 Gd RMS Difference 0.60 % 1.40 % 0.90 % 1.10 % 0.90 % 1.30 % l (S3 - Meas) E Error in Peak Pin 0.27% 1.12 % 0.35 % 0.00 % 0.81 % -1.40%
h P
(S3 - Meas) 1 I
. I I
I E
II I
I.
I-I
m L TR 091
- Rev.O Page 84 l Figure 5.1 L BOC 1 Radial Power Comparison Between SIMULATE 3 and PDQ h
8 9 10 11 12 13 14 15
[. 1.385 1.149 1.057 1.098 1.101 1.242 1.542 1.043 .
H 1.420 1.188 1.073 1.123 '1.105 1.256 1.536 1.029 r 2.485 3.291 -1.451 2.213 4.391 1.078 0.418 1.332 b 1.149 1.083 1.078 1.051 1.122 1.149 1.179 0.942 I K 1.188 1.102 1.105 1.053 1.137 1.145 1.182 0.930 3.296 1.670 2.396 4.184 - 1.286 0.350 4.199 1.325
{ 1.057 1.078 1.037 1.000 1A31 1.005 1.220 0.674 L 1.073 1.105 1A34 1.070 1.019 1.100 1.217 0.688
( 1.473 2.412 0.324 0.ssa 1.189 4.472 0.25e 0.975 1.098 1.051 1.000 0.995 0.993 0.004 0.056 M 1.124 1.054 1.070 0.973 0.975 0.es2 0.e53
( 2.259 0.225 0.057 2.281 1.808 1.305 0.419 1.101 1.122 1A31 0.993 0.839 0.740 0.488 N 1.106 1.138 1.020 OJ76 0.823 0.749 0.484 4.467 1.356 1.133 1.778 2.000 OJ50 0.055 1J42 1.149 1.095 OJ04 0.748 0.400 O 1.257 ' 1.146 1.101 0.s92 0.749 0.448 1.178 0.254 4.556 1.333 0.027 0.753 1.542 1.179 1.220 0.856 0.488 - SEIULATE4 P 1.538 1.183 1.218 0.e53 0.484 - PD0 0.300 4.312 0.156 0.336 0.796 - 501FF
[ 1.043 0.942 0.674 R 1.031 0.931 0.888 1.206 1202 0.800 AVERAGE OlFFERENCE 4.000
( STANDAR0 DEVIATION 1.388 I
I TR 091 Rev.O Pa9e 85 Figure 5.2
-l MOC 1 Radial Power Comparison ,
Between SIMULATE-3 and PDQ i
I 8 9 10 11 12 13 14 15 -
1.378 1.281 1.159 1.227 1.123 1.184 1.199 0.785 H 1.380 1.267 1.147 1.220 1.117 1.181 1.197 0.781 1,297 1.088 1.087 0.610 0.586 0.229 0.212 0.535 1.281 1.176 1.234 1.137 1.196 1.079 1.036 0.738 i K 1.267 1.162 1.228 1.130 1.193 1.078 1.037 0.735 1.088 1.181 0.s51 0.807 0.233 0.298 4.127 0.431 1.159 1.234 1.143 1.211 1A86 1.008 1A25 0.555 .
L 1.147 1.226 1.136 1.214 1.085 1.102 1.030 0.556 1.086 0.850 0.595 0.220 0.058 4.383 0.493 0.101 1.227 1.137 1.211 1A91 1.106 0.923 0.778 M 1.220 1.130 1.214 1.093 1.116 0.928 0.785 0.605 0.805 0.221 0.202 4.929 4.486 4.837 1.123 1.196 1.006 1.106 0.931 0.827 0.500 ,
N 1.117 1.193 1.006 1.117 0.937 0.840 0.505 0.581 0.228 0.054 4.931 1.184 0.647 1.491 1.049 g
1.079 1.098 0.923 0.827 0.544 5
O 1.182 1.076 1.102 0.928 0.840 0.552 0.221 0.292 0.389 4.490 1.493 1.520 1.199 1.036 1.025 0.778 0.500 - SIMULATE.3 P 1.197 1.038 1.030 0.785 0.505 - P00 0.205 0.136 0.499 0.843 1.054 - %DIFF 0.785 0.738 0.555 R 0.781 0.735 0.556 0.526 0.421 0.111 AVERAGE DIFFERENCE DA31 STANDARD DEVIATION 0.721 I
- I I
I 1
TR 091
{
Rev.O ]
Page 86
- g' Figure 5.3 EOC 1 Radial Power Comparison Between SIMUIATE-3 and PDQ i
l l 8 9 10 11 12 13 14 15 1.236 1.189 1.087 1.177 1.088 1.189 1.169 0.788
)
H 1.223 1.177 1.078 1.167 1.082 1.186 1.171 0.190 1.039 1.062 0.831 0.866 0.584 0.288 0.153 4.315 1.189 1.092 1.176 1.088 1.174 1.088 1.056 0.751 ,
K 1.177 1.082 1.185 1.081 1.167 1.0s7 1.080 0.755 1.062 0.893 0.965 0.674 0.589 0.142 4.334 4.584 1.087 1.176 1.088 1.178 1.077 1.121 1.033 0.578 i L 1.078 0.833 1.177 1.185 0.966 1.088 1.081 0.677 1.178 1.171 0.807 1.081 1.073 0.331 1.138 1.122 4.122 0.987 1.042 4.819 0.584 1.015 i
0.815 M 1.167 1.081 1.171 1.078 1.139 DJ72 0.825 0.869 0.676 0.609 0.3G4 0.105 0.512 1.216
,l 1.088 1.174 1.077 1.138 0.991 0.922 0.558 .
,F N 1.082 1.167 1.073 1.139 0.995 0.934 0.567 :
0.591 0.595 0.334 0.104 0.384 1.235 1.571 1.169 1.069 1.121 0.967 0.922 0.820 l
l O 1.166 ~ 1.067 1.122 OJ72 0.934 0.832 l
,g -
0.276 0.150 0.117 4.508 1.234 1.822 5 1.169 1.056 1.033 0.815 0.558 - SMULATE.3 P 1.171 1.059 1.041 0.825 0.567 - P00 0.144 4.328 0.812 1.211 1.569 - %DIFF l j 0.788 0.751 0.578
- R 0.790 0.755 0.584 0.307 4.577 1.010 STANDARD DEVIATION 0.796 il
- E
- i
._ ----------------_---------------J
E TR 091 -
Rsv.O Page 87 Figure 5.4 BOC 2 Radial Power Comparison I Between SIMUIATE-3 and PDQ t
8 9 10 11 12 13 14 15 0.767 0.837 0.921 1.042 1.271 1.028 0.875 0.581 .
H 0.767 0.839 0.919 1.039 1.288 1.029 0.882 0.584 4.052 0.190 0.209 0.297 0.218 4.080 4.798 4.482 0.840 0.990 1.025 1.113 1.395 1.036 0.800 0.559 g
K 0.841 0.988 1.017 1.109 1.378 1.038 0.810 0.5s3 5 4.006 0.189 0.748 0.329 1.259 4.218 1.245 0.764 0.934 1.034 1.020 1.126 1.348 1.068 0.961 0.455 L 0.930 1.025 1.014 1.122 1.341 1.104 0.966 0.483 0.448 0.834 0375 0.383 0.490 4.494 4318 1.739 g
1.078 1.140 1.138 1.417 1.371 1.254 0.835 5 M 1.070 1.132 1.132 1407 1.370 1.261 0.844 0.752 0.676 0.589 0.707 0.088 4545 1.083 1.359 1.444 1.372 1.300 1.109 1.043 0.556 N 1.350 0.676 1.420 1.380 1.377 1.117 1.055 0.586 g 1.725 0.856 0.195 0.738 1.171 1.771 4' 1.071 1.070 1.120 1.267 1.049 0.619 O 1.066 1.066 1.120 1.271 1.059 0.831 0.520 0.364 4.007 0.304 0.949 1.874 I P
0.901 0.903 0.821 0.827 0.980 0.980 0.846 0.852 0.561 0.569
- SNULATE 3
- PD0 g'
4 4.199 0.883 0.007 4.899 1.437 - %DIFF 0.596 0.573 0.464
)
R 0.595 0573 0.470 0.151 4.051 1.242 AVERAGE DIFFERENCE 4.119 STANDARD DEVIATION 0.793 I
I I
L f :
TR 091 Rev.O Figure 5.5 MOC 2 Radial Power Comparison Between SIMULATE-3 and FDQ U.
8 9 10 11 12 13 14 15 l
0.847 0.903 0.956 1.036 1.223 1.058 0.981 0.710 .
H 0.844 0.901 0.952 1.030 1.216 ' 1.055 0.sS3 0.711 0.320 0.216 0.486 0.592 0.583 0.310' 4.231 0.187 l
0.904 1.037 1.040 1.083 1.335 1.053 0.892 0.881
. K 0.901 1.031 1.032 1.077 1.325 1.051 0.898 0.884
'. 0.297 0.583 0.826 0.547 0.758 0.190 4.667 4.489 0.959 1.042 1.006 1.073 1.255 1.086 1.038 0.545 7
L 0.954 1.033 1.000 1.067 1.248 1.087 1.044 0.552 N 0.492 0.841 0.591 0.534 0.591 4.055 4.556 1.215 1.048 1.090 1.075 1.286 1.257 1.203 0.878 M
[ 1.041 0.629 1.084 0.590 1.088 0.547 1.278 0.824 1254 0.216 1.208 0.279 0.887 4.985 1.265 1.347 1.258 1.257 1.051 1.024 0.594 N 1.259 1.338 1.251 1.255 1.056 1.033 0.002 0.454 0.899 0.593 0.178 4.425 0.889 1.384 1.089 1.059 1.087 1.202 1.024 0.846 O 1.066 1.058 1.089 1.207 1.033 0.856 0.268 0.131 0.136 0.375 0.882 1.577 0.SS3 0.894 1.038 0.878 0.583 - SIMULATE 3
. P 0.987 0.900 1.045 0.887 0.002 - P00 4.355 -0.678 0.826 0.980 1.531 - %DIFF 0.710 0.882 0.545 R 0.712 0.885 0.552 0.322 0.447 1288 AVERAGE DIFFERENCE 0.054
{
STANDARD DEVIATION 0.679 i
l TR 091 Rev.O Page 89 Figure 5.6 EOC 2 Radial Power Comparison I' ,
Between SIMULATE-3 and PDQ 8 9 10 11 12 13 14 15 0.936 0.978 1.001 1.034 1.166 1.080 1.038 0.798 .
H 0.918 0.959 0.982 1.018 1.155 1.054 1.046 0.812 2.012 1.944 1.988 1.613 OJ72 0.567 0.748 1.774 0.977 1.091 1A67 1.065 1.254 1.047 0.946 0.767 g
K 0.959 1.071 1.046 1.050 1.247 1.043 0.954 0.783 3 1.877 1.889 IJ76 1.461 0.549 0.394 0.790 1.993 1.000 1.067 1.016 1.046 L181 1.082 1.059 0.614 L 0.982 1.046 0.998 1.031 1.171 1.061 1.075 0.629 1.879 2.004 1.783 1.423 0.843 0.000 1.523 2.397 g 1.038 1.066 1.045 1.203 1.179 1.152 0.891 5, M 1.022 1.051 1.031 1.193 1.175 1.161 0.910 1.602 1.467 1.366 0.808 0.327 .O.788 2.063 1.192 1.257 1.179 1.178 1.019 1.011 0.627 ,
N 1.182 1.250 1.170 1.174 1.023 1.027 0.s44 0.888 0.579 0.788 0.317 0.342 1.561 2.576 1.062. 1.047 1.060 1.150 1.011 0.678 O 1.056 1.043 1.059 1.180 1.026 0.8e4 0.526. 0.385 0.057 0.828 1.499 -2.342 1A36 0.943 1.056 0.890 0.826 - SitfulATE4 g P 1.044 0.952 1.073 0.908 0.s43 - POD g 0.746 4.901 1.588 2.006 -2.625 - %DIFF 0.796 0.785 0.612 R 0.810 0.781 0.628 1.757 1.983 -2.480 AVERAGE DIFFERENCE 0.019 ,
STANDARD DEVIATION 1.528 l
I i
I I
TR 091 Rev.O '
Page 90 l Figure 5.7 BOC 1 Peak Pin Power Comparison Between SIMULATE-3 and PDQ
- I 8 9 10 11 12 13 14 15 1.475 1.352 1.130 1.274 1.189 1.448 1.668 1.423
. H 1.497 1.370 1.138 1.272 1.181 1.430 1.645 1.406 .
)
1.443 1.321 0.738 0.141 0.643 1.280 1.411 1.209 1.352 1.181 1.270 1.125 1.343 1.264 1.444 1.371 K 1.370 1.194 1.283 1.119 1.336 1.249 1.425 1.353 1 i 1321 1.056 1.021 0.518 0.524 1.e' 25 1.340 1.330 1.130 1.270 1.103 1.246 1.117 1.316 1.423 1.188 L 1.139 1.283 1.098 1.230 1.099 1298 1.401 1.152 ;
-0.755 -1.036 0.483 1.326 1.856 1.348 1.549 1.389 1.274 1.125 1.246 1.076 1.192 1.016 1.229 1 M 1.273 1.120 1.230 1.045 1.180 0.983 1.216 0.086 0.473 1.276 2.99C 2.723 2.317 1.044
- 1.189 1.343 1.117 1.192 0.M6 1.077 0.878 N 1.182 1.337 1.099 1.161 0.918 . 1.054 0.889
! 0.558 0.434 1.592 2.897 3.239 2.192 1.092 1.448 1.264 1.316 1.016 1.077 0.820 O 1.431 1250 1.300 0.994 1.054 0.813
'g- 1.174 1.120 1.246 2.241 2.153 0.849 M 1.668 1.444 1.423 1.229 0.878 - SNULATE 3 i P 1.647 1.427 1.403 1.217 0.889 - P00 1.293 1.227 1.447 0.961 1.030 -%DIFF 1.423 1.371 1.168 R 1.408 1.355 1.153
!g 5 1.080 1.203 1.275 AVERAGE DIFFERENCE 0.956 f STANDARD DEVIATION 1.103 I
g .
!I .
l Bi ;
TR 091 1 Rev.O Page 91 Figure 5.8 MOC 1 Peak Pin Power Comparison Between SIMULATE-3 and PDQ l
8 9 10 11 12 - 13 14 15 1.454 1.367 1.228 1.311 1.191 1.268 1.323 1.059 .
H 1.417 1.333 1200 1.280 1.169 1.244 1.302 1.048 2.604 2.528 2.308 2.398 1.838 1.921 1.629 1.059 h;l 1.367 1.256 1.333 1.206 1.283 1.158 1.211 1.045 gi K 1.333 1.226 1.298 1.183 1.265 1.140 1.190 1.031 4 2.528 2.439 i.728 1.970 2.197 1.579 1.731 1.348 1.228 1.333 1.211 1.304 1.167 1.238 1.210 0.941 L 1.200 1.298 1.188 1.278 1.152 1.216 1.197 0.930 2.308 2.728 1.970 2.026 1.320 1.818 1.088 1.236 g; M
1.311 1.280 1.206 1.183 1.304 1.278 1.173 1.180 1.249 1.230 1.040 1.031 1.000 1.086 5l l
2.390 1.970 2.026 1.129 1.503 0.844 0.378 1.191 1.293 1.167 1.249 1.046 1.127 - 0.888 1 N 1.169 1.265 1.152 1.230 1.039 1.112 0.866 l
1.838 2.189 1.320 1.503 0.645 1.376 0.314 ,
1.268 1.158 1.238 1.040 1.127 0.898 ,
O 1.244 1.140 1.216 1.031 1.112 0.898 l
1.913. 1.570 1.818 0.834 1.367 0.002 1 P
1.323 1.302 1.211 1.190 1.210 1.197 1.090 1.086 0.869 0.866
- SIMULATE.3
- PD0 E'
5 1.621 1.722 1.061 0.368 0.309 -%DIFF 1.059 1.045 0.841 R 1.048 1.c31 0.s30 1.050 1.338 1.227 AVERAGE DIFFERENCE 1.594 STANDARD DEVIATION 0.675 l
I TR 091 I Figure 5.9 Rev.-O Page 92 EOC 1 Peak Pin Power Comparison
! Between SIMULATE-3 and FDQ I 8 1293 9
1.225 to 1.136 11 1.216 12 1.138 13 1.213 14 1.278 15 1.045 -
H 1.2 64 1.202 1.115 1.192 1.119 1.192 1.280 1.037 4 2.270 1.922 1.911 1.996 1.889 1.745 1.461 0.742 I
1.225 1.146 1.217 1.138 1.217 1.129 1.178 _ 1.041 K 1.202 1.124 1.191 1.119 1.193 1.114 1.183 1.027 IJ22 1.957 2.174 1.725 1.995 1.386 1255 1.383 1.136 1.217 1.138 1.218 1.135 la04 1.202 0.957 L 1.115 1.191 1.119 1.195 1.117 1.183 0.186 0.946 1J11 2.174 1.889 1.916 1.602 IJ18 1.383 1.167 1 1.216 1.138 1.218 1.137 1.213 1.089 1.105 M 1.192 1.119 1.195 1.120 1.190 1.058 1.098 1.996 1.725 1.916 1.536 1.933 1.030 0.674 1.138 1.217 1.135 1.213 1.005 1.174 0.940 N
i 1.119 1.193 1.117 1.190 1.073 1.151 0.929 1.698 1.995 1.602 1.941 1.071 2.025 1.132 1.213 1.129 1.204 1.069 1.174 0.996 i O 1.192 1.114 1.182 1.058 1.151 0.985 l 1.753 1.374 1.827 1.030 2.025 1.137 I
1.278 1.178 1.202 1.105 0.940 - SIMULATE 3 P 1260 1.163 1.186 1.098 0.929 - PDQ 1.469 ).264 1.383 0.674 1.!?S -%DIFF .
1.045 1.041 0.957 R 1.037 1.027 0.946 1 0.752 1.393 1.175 AVERAGE DIFFERENCE 1.574 I STANDARD DEVIATION 0.418 I
.I I
B: .
TR 091 Rev.O g Page 93 g Figure 5.10 BOC 2 Peak Pin Power Comparison Between SIMULATE-3 and PDQ 8 9 10 11 12 13 14 15 .
0.793 DJ18 1.007 1.164 1.360 1.179 0.951 0.786 H 0.782 0.906 0.992 1.144 1.34s 1.14e 0.937 0.'780 1.456 1.308 1.556 1.757 1.025 2.838 1.545 0.723 0.923 1.120 1.122 1.289 1.529 1.202 0.923 0.782 K 0.910 1.109 1.128 1.288 1.493 1.187 0J22 0.757 1.452 1.001 0.541 0.079 2.425 1.255 0.097 0.630 _
1.025 1.134 1.125 1.263 1.451 1.243 1.157 0.764 L 1.007 1.138 1.105 4.307 1.242 1.435 1.228 1.147 0.780 g
1.828 1.856 1.707 1.122 1.100 0.M5 0.472 g 1.211 1.305 1.275 1.582 1.486 1.386 1.140 M 1.185 1.298 1.252 1.581 1.45s 1.345 1.132 ,
2.220 0.501 1.841s 1.385 0.700 1.531 0.080 1.459 IJ73 1.473 1.481 1.263 N
1.254 0.900 g
1.437 1.529 1.452 1.467 1.'25 1 1.217 0.985 g' 1.510 2.884 1.467 0.982 0.S92 3.057 0.526 1.237 1.239 1.264 1.382 1.261 0.984 O 1.199 1.220 1.245 1.354 1.222 OJ75 3.204 1.599 1.559 2.075 3.191 0J21 O.982 0.946 1.178 1.156 1.000 - SIMULATE 3 E'
5' P 0.961 0.939 1.162 1.143 0.991 - PDQ 2.205 0.898 1.342 1.111 0.900 -%DFF 0.808 0.781 0.781 R 0.796 0.771 0.773 i 1.515 1.237 1.088
{
AVERAGE DIFFERENCE 1.345 STANDARD DEVIATION OJ14 1
I I
l
.g TR 091 I Figure 5.11 Rev.O ,
-I '
MOC 2 Peak Pin Power Comparison Between SIMULATE-3 and PDQ ;
1 S 9 10 11 12 13 14 15 ,
I H 0.873 0.e59 0.976 0.958 1.028 1.007 1.135 1.111 1.306 1.285 1.150 1.118 1.041 1.021 0.943 0.930 1.599 1.843 2.045 2.197 1.642 2.853 1.969 1.434
_ 0.977 1.146 1.112 1.202 1.434 1.172 0.996 0.915 K 0.959 1.129 1.107 1.182 1.405 1.151 0.985 0 903
'I 1.893 1.032 1.50S 1.115 0.497 1.085 1.726 1.175 2.071 1.338 1.889 1.191 1.140 1.206 1.299 0.891 s L 1.012 1.109 1.061 1.151 1.322 1.170 1.183 0.885 2.027 0.559 2.223 2.067 1.210 1.777 1.124 0.660 1.151 1.209 1.177 1.408 1.342 1.286 1.168 I M 1.126 2.211 1.353 1.188 1.725 1.153 2.099 1.389 1.331 1.329 0.948 1.260 2.063 1.154 1.178 1.443 1.340 1.342 1.168 1.180 1.017 N 1.333 1.414 1.324 1.330 1.150 1.155 1.007 1.485 2.065 1.201 0.902 1.565 2.147 0.953 1.167 1.179 1.192 1.286 1.180 1.003 O 1.135 1.157 1.172 1.260 1.155 0.994 2.801 1.866 1.733 2.055 2.156 0.944
. 1.045 0.998 1.206 1.168 1.016 - SIMULATE 4
{
P 1.025 0.987 1.193 1.154 1.007 - PDQ l I R 1.921 0.S44 0.931 1.098 0J15 1.073 0.891 1.187 0.874 -%DIFF 0.904 0.886 1.390 1.171 0.580 I AVERAGE DIFFERENCE STANDARD DEVIATION 1.576 0.553 I
i I
I ,
El TR 091 Rev.O l Page 95 E Figure 5.12 l EOC 2 Peak Pin Power Comparison Between SIMULATE-3 and PDQ ,
I l
1 Ii '
8 9 10 11 12 13 14 15 .
O.963 1.042 1.056 1.109 1.234 1.112 1.084 1.034 H 0.931 1.004 1.020 1.072 1.207 1.084 1A81 1.029 ,
3.481 3.826 3.580 3.471 2.203 2.583 0.268 0.525 l 1.041 1.176 1.120 1.148 1.322 1.133 1A32 1.006 K 1.003 1.145 1.092 1.118 1.300 1.105 1.017 1.003 3.778 2.707 2.555 2.647 1.731 2.571 1.455 0.279 1.056 1.120 1.073 1.120 1.246 1.139 1.196 0.989 L 1.020 .092 1A36 1.087 1.230 1.114 1.190 0.967 3.570 1583 3.531 3.083 1.309 2.226 0.496 0.175 ,
1.114 1.148 1.119 1.291 1.246 1.212 1.146 M 1.078 1.119 1.086 1.272 1.234 1.200 1.141 ,
3.378 2.801 3.058 1.486 1.013 0.986 0.456 1.261 1.325 1.245 1.245 1.109 1.137 1.025 N 1.237 1.302 1.228 1.232 1.086 1.119 1.018 1.907 1.806 1.380 1.039 2.108 1.581 0.898 1.116 1.132 1.137 1.210 1.136 1A21 O 1.089 1.104 1.113 1.198 1.119 1.014 2.451 2.499 2.202 0.980 1.585 0.641 l 1.082 1.030 1.183 1.144 1A23 - SitIULATE.3 P 1.079 1.015 1.188 1.139 1.017 - P00 0.325 1.458 0.463 0.457 0.630 -%DrF 1E31 1.003 0.966 R 1.026 1.001 0.985 0.497 0.240 0.111 AVERAGE DIFFERENCE 1.781 ;
STANDAR0 0EAAT10N 1.149 Ii i
I
I I -
I TR 091 Rev.O Page 96 Figure 5.13 B & W CRITICAL EXPERIMENT GEOMETRY Duter FuelRegion inner Fuel Region ;
x i i
/
/ -
i i l
'x /
/
I ' -
I ,
l I
I
,8 , ,
1 g
/
urow cor soona.y i xs=uan.3 c.. soon .,
I E
I
E, TR 091 I Rev.O g ,
Page 97 5
Figure 5.14 CORE 1 I
Normallud Midplane Power Distribution i
i 1.02s 0.999 0.9ss 0.9s5 0.9st 0.9s3 0.942 g;
RH DET 1.018 1A11 0.987 0.981 0.907 0.906 0.945 g 0.007 4.012 Om1 0.004 0.015 4.003 4.003 i 1.023 1.067 1.014 1.010 1.051 0.984 0.946 l
1.019 1.067 1.012 1.009 1.058 f.999 0.945 0.004 0.000 0.002 0m1 4.007 4.015 O.001 1.005 1.006 1.041 0.952 ,
WATER 1.001 1.000 WATER 1.032 0.953 0.004 0.004 0.000 4.001 1.000 1.187 1.008 0.981 0.945 1.054 Om6 1.1H s.9s3 1.086 0.002
,,5.
0.988 Om2 O,.,
0.945 Omo 0,3, ll 1 WATER 1.059 0.95 0334 0.000 4.002 0.001 l DJ83 0.943 0.925 g
0.908 0J38 0.823 E' 0.005 0A05 OA02 .
0227 0218 0225 CJ14 0.002 OA02 OJ07 - 83 0J03 - MEAS DA04 - DIFF AVERAGE DIFFERENCE 0.000 STANDARD DEVIATION OA06 Ii I!
I
L TR 091 Rev.0
- Page 98 l L
Figure 5.15 CORE 5 y Nonnalized Midplane Power Distribution L
F-w
_ 1.020 0.898 % "li - 0.917 1.050 1.081 1.092.
0.932 1.036 1.063 1.072 !
RH OET 1.005 0.913
.ff[
0.015 -0.015 MF . -0.015 0.014 0.018 0.020 1.013 1.023 0.905 1.003 1.131 1.106 1.098 0.999 1.017 0.931 1.007 1.125 1.094 1.089 0.014 0.006 0.026 4.004 0.006 0.012 0.009 L 0.985 1.079 1.171 1.104 !
WATER 0.988 1.087 WATER 1.158 1.100 4.023 0.008 8.813 0.004
[
l* ] 1.028 1.149 1.101 1.092 u S..
f 1.050 4.022 1.131 0.018 1.018 1.088 0.013 1.031 1.086 0.006 1.071 WATER 1.048 1.035 1.070
{
0.030 -0.004 0.001 r 5,, P.942 1.058 I h 0.963 1.054
' 5- -
4.021 0.004 1.019 1.067 IYT wu .
1.018 ' 1.000
.I 1
- 4. , .
0.001 0.007 l ~;di. . 1.078 - S3 1.070 - MEAS 0.008 - DIFF AVERAGE DIFFERENCE 0.001 STANDARD DEVIATION 0.014 I
I I
O O
TR 091 Rev.0 Page 99 Figure 5.16 CORE 12 Normalized Midplane Power Distribution 1.081 1.029 1.010 0.998 0.986 O.954 0.919 RH DET 1.075 1.041 1.006 1.019 1.000 0.960 0.923 0.006 0.012 0.004 0.021 -0.014 0.006 4.004 '
1.067 1.125 1.040 1.028 1.081 U.978 0.922 1.067 1.125 1.044 1.034 1.075 0.987 0.927 0.000 0.000 -0.004 -0.006 0.006 4.009 0.005 1.131 1.122 1.053 0.924 WATER 1.114 1.118 WATER 1.034 0.942 0.017 0.004 0.019 -0.018 1.080 1.142 1.112 0.976 0.912 1.083 1.137 1.102 0.979 0.908 l 0.003 0.005 0.010 0.003 0.004 1.069 0.937 0.896
. WATER 1.071 0.939 0.895 .
4.002 4.002 0.001 1 0.983 0.909 0.878 0.958 0.900 0.883 0.005 0.009 -0.005 0.883 0.859 0.884 0.856
-0.001 0.003 0.837 - S3 0.845 - MEA 0 4.008 - OlFF AVERAGE DIFFERENCE -0.001 STANDARD DEVIATION 0.009 I
a
=
TR 091 Rev.O Pago 100 -
{
Figure 5.17 CORE 14 Normalized Midplane Power Distribution
{
[- l
[ 1.095 0.972 0.966 1.050 1.049 1.032 RH OET 1.091 0.992 jjj%){s.
, T 0.976 1.057 1.038 1.028 l
[ 0.004 4.020 ? .. .
-0.010 0.007 0.011 0.004 1.078 1.117 0.980 1.045 1.158 1.078 1.037 1.080 1.118 1.000 1.054 1.158 1.091 1.028 4.002 -0.001 0.020 -0.009 8.888 0.013 0.009 1.067 1.145 1.163 1.039 WATER 1.072 1.138 WATER 1.140 1.038
-0.005 0.007 0.023 0.001 W^T e;;2uw 1.110 1.183 1.071 1.026
[ %1..-.y 1.114 1.151 1.059 1.013 ff"] 4.004 8.832 0.012 0.013
( 1.067 1.005 1.004 WATER 1.080 1.011 1.003 0.013 0.006 0.001 1 O.925 0.984 2
0.942 0.976 ,
1 1 4.017 0.008 O.985 0.974 0.985 0.978 0.000 0.004 l 0.962 - S3 f I 0.959 - MEAS L Om3 - Ou :
AVERAGE DIFFERENCE 4.001 STANDARD DEVIATION 0.011
E a
TR 091 Rev.O Page 101 gi mi Figure 5.18 l
CORE 18 l Normalized Midplane Power Distribution ,
1.216 1.034 1.001 0.986 0.968 0.946 0.921 I ;
RH DET 1.205 1.033 0.997 0.977 0.959 0.941 0.909 0.011 0.001 0.004 0.009 0.009 0.005 0.012 1.081 1.032 1.027 1.013 0.981 0.949 0.920 1.076 1.021 1.012 1.010 0.982 0.946 0.912 0.005 0.011 0.015 0.003 4.001 0.003 0.008 -
1.080 1.218 1.204 1.039 0.957 0.917 1.065 1.228 1.203 1.043 0.957 O.928 0.015 8.818 0.001 0.004 0.000 -0.011 1.175 0.964 0.912 1.183 0.974 0.924 LARGE WATER 0.008 0.010 0.012 HDLE 1.160 0.952 0.900 1.170 0.970 0.909
-0.010 -0.018 4/)09 1.001 0.921 0.882 0.995 0.924 0.886 0.006 4.003 -0.004 0.889 0.861 0.893 0.866
-0.004 -0.005 0.837 - S3 0.833 - MEAS 0.004 - OlFF AVERAGE DIFFERENCE 0.000 STANDAR0 DEVIATl0N 0.009 e
- t. ,
l [ r
{'
s TR 091
, . Rev.0
, Page 104
- t. ,
" i
{(D "2
- D) 2 3
o, = y,1 where N is the total number of values. j
~
. j b l The difference distribution is tested for normalty using other the W test (N s 50) or the D' test (N
> 50) of Ref. 34. If the difference distribution is normal, the one-sided 95/95 tolerance limit is used l
( to determine the reliabilty factor. The one-sided upper tolerance limit, D , is defined by: j
[
, l,
[l .
I D,,,,, = D + K,,,,, x ay f
q; I
where the first term is the modeling bias and the second term is the 95/95 uncertainty %ctor which is the sampling standard deviation multiplied by the K value for a 95/95 upper tolerance limit. The value for K can be obtained from Table A-7 in Ref. 35 which accounts for the fact that sample uncertainty is used. If the difference distribution is not a normal distribution, the non-parametric i
tolerance method from Ref. 36 is used to obtain the one-sided 95/95 upper tolerance limit for j_ sample size greater than 50. The D, value is then applied to the calculated parameters 60 that modeling bias and uncertainty are included, thus assunng conservative safety analysis results.
l l t:
In summary, the reliabulty factor is applied to the calculated physics parameters to obtain Om values to be used in reload analysis. For physics parameters which are based on the absolute difference between the calculated and measured values, one has Parameter,,wy = Parameter e,3, + Reliability Factor i
E_
TR 091 -
Rev, 0 =
Page 105 which can be rewritten as I
I Parame ter,,,,,, ' Parame tere,1, + Bias + UF,,,,,, .
or ,
Parame ter,,,,ey = Parameter ca lc + Bias - UF,,,,,,
where I
Bias = -T),
and UF 333i s the 95/95 one sided uncertainty factor which is always applied in the direction so that I
the reload analysis results wRI be more conservative.
The same method cdn be applied when relative difference, i.e.,
I i i
-I, D =1-1{ C -M j
1 ,
is used. For physics parameters which are based on the relative difference between the calculated and measured values, one has Parameter,,g,ey = Parametercalc x (1 + Reliability Factor) ,
The above equation can be rewritten in terms of bias and UF,w, i.e.,
Parameterestety = Parametercalc x (1 + Bias + UF,,,,s) o, I
(E TR 091 1 Rev. 0 Page 106 h
Parametersa,n = Parameterca, x (1 + Bias - UF,,,,,)
l
.j Again, the 95/95 uncertainty factor, UF ,3m, is applied in the direction so that the reload analysis I
. results wHI be conservative. .
i 8.2 HZP BOC ARO Critical Boron
=
The reliablit/ factor for HZP ARO critical boron is determmed based on the TMI-1 Cycles 1 to 10 start-up physics test results shown in Table 4.4. The differences between calculated and measured critical boron concentration range from -31 ppm to 15 ppm with a sample mean and standard deviation of 13 ppm and 14 ppm respectively. The difference distribution is found to be a normal distribution using the W test of Ref. 34. For a sample size of 10, the K factor for 95/95 upper tolerance limit is 2.911 and the reliability factor is 54 ppm.
6.3 HZP BOC Control Rod Worth The control rod worth for the individual control rod Groups 5,6 and 7 are measured using the boron dRution technique during the hot zero power start-up test. The reliabBity factor for control rod worth is determined based on the TMI 1 Cycles 1 to 10 siart-up physics test results -
shown in Table 4.5. The % differences between calculated and measured control rod worth range from -9.25% to 9.90% with a sample mean and standard deviation of -2.78% and '4.21%.
respectively. The difference distribution fated the W normality test of Reference 34 for 95%
confidence Based on the difference distribution range, the reliabatty factor for individual control rod worth is chosen to be -15%. This is a conservative wtimate cerh' sg the mean and standard distribution of the difference distribution (See Table 4.5).
The reliabilty factor for the regulating control rod Grotes 5,6 and 7 combined, can be determined ll
E_
TR 091 Rev.O l.
eE Page 107 ba. tad on the TMI-1 Cycles 1 to 10 start-up physics test results shown in Table 4.6. The percent I
differences between calculated and measured control rod worth range from -6.58% to 1.24% with a sample mean and standatd deviation of -2.93% and 3.15%, respectivoly. The difference distribution faued the W normality test of Reference 34 for 95% confidence. Because of the difference range. the reliabuity factor for the combined regulating control rod worth is chosen to be -10%. This is a conservative estimate considering the mean and standard deviation of the - I difference distribution.
6.4 HZP BOC loothermal Temperature Coefficient The reliabHity factor for the isothermal temperature coefficient is determined based on the TMI-1 Cycles 1 to 10 start-up physics test results shown in Table 4.7. The difference betweei, calculated and measured isothermal temperature coefficient ranges from 0.4 PCM/*F to 1.61 PCM/*F with a sample mean and standard deviation of 0.88 and 0.34 PCM/*F respectively. The difference distribution is found to be a normal distribution using the W test. For a sample size of 17, the K ,
factor for 95/95 upper tolerance limit is 2.486. With a bias of -0.88 PCM/*F, the reliability factor is -0.036 PCM/*F ur overheating accidents and -1.722 PCM/*F for overcooling accidents.
6.5 HFP Critical Boron I
The reliablity factor for the hot full power critical boron is determined based on the Cycles 8 and 9 comparisons shown in Table 4.1. The difference distribution ranges from -36 ppm to 8 ppm with a mean of -9 ppm and a standard deviation of 9 ppm. The difference distribution is normal based on the D' test (Ref. 34) results with a 95% significance level. For a sample size of 52, the K factor for 95/95 upper tolerance limit is 2.049 and the reliabilty factor is 28 ppm.
6.6 Peak Power I
The nuclear reliabilty factors for predictions of the peak radial and total (maximum axial segment)
I
r I
s TR 091 Rev.O Page 102 Figure 5.19 CORE 20 L Nonnalized Midplano Power Distribution l
l l
I 1.388 1.092 1.065 1.060 1.048 1.033 1.026 RH OET 1.277 1.082 1.059 1.043 1.043 1.017 1.010 0.023 0.010 0.006 0.017 0.005 0.016 0.016 1.120 1.003 1.064 1.080 1.036 0.957 0.997 1.110 1.011 1.0F7 1.075 1.034 0.973 0.979 0.010 -0.008 0.00b 0.005 0.002 -0.016 0.018
~
? 1.214 1.290 1.046 0.935 1.238 1.268 1.073 0.954 ke i -0.024 0.022 0.027 l. 4.019 1.288 0.982 0.992 1.284 0.972 0.999 )
LARGE WATER 4A18 0.010 4.007 l HOLE 1.279 1.043 1.005 j 1.280 1.045 0.999 l
-0.001 -0.002 0.006 !
1.083 0.947 0.968 l l 1.077 0.982 0.978 !
, 0.006 0.015 0.010 !
E.
0.892 0.900 ;
.??l{l$, 4.008 l
kg g {g 0.925 - S3 i Edin 0.931 - MEAS
-0.006 - OlFF AVERAGE DIFFERENCE 0.000 I STANDARD DEVIATION 0.013
i um TR 091 Rev.O Page 103 6.0 RELIABILITY FACTORS TMI-1 reload analysis requires physics parameters input from physics calculations. Reliability factors are used to ensure that the calculated parameters such as the temperature coefficient, hot pin power, etc.,
to be used for determination of operating limits and setpoints, include the model uncertainties and the sampling uncertainties. The reliability factors determined in this report are based on TMI-1 Cycles 1 through 10 operation data. These values are typical of the values used in reload analysis, but they will be evaluated, and revised tf rieeded, as more operation data is available.
6.1 Method Description The reliability factor can be determined by first determining the difference between calculated and I measured values, i.e.,
D3=C3 -M 3 where D, = lth difference, C, = lth calculated value.
M, = lth measured value.
This difference distribution is then tested for normality using the method described in ANSI N15.15 (Ref. 34). The sample mean and standard deviation of the difference distribution are calculated as:
N N p ,
[D 2=1 2
[(C -M) 2*1 3 3 N N and
TR 091 ;
Rev.0 j Page 108 ;
1 powere are determined by statistically combining the corresponding global reliabuity factor with the local reliability fac:or. The former is based on the assembly nodal power distribution, and the latter is based on the radial-local factor. This section describes the calculation of individual component's reliabuity factor and those of the combined peaking factors.
6.6.1 Radial-Local Factor The radial-local factor is defined as the ratio of the pin power to the assembly radial power The SIMULATE-3 reconstructed pin powers have been benchmarked against B&W critical experiments and multi-assambly analyses in Section 5. The statistical results of the radial-local factor comparisons are shown in Table 6.1 and the frequency plots are shown in Figures 6.1 - 6.2. Although the relative difference distributions appear to be normal, the D' test indicates that the combined relative difference distribution is not a normal distribution for a 95% significance level. The 95/95 nuclear reliabilty factor is determined to be 1.007 using the non-parametric upper tolerance limit which is very close to the 1.008 value calculated assuming normal distribution. For conservatism, the radial-local nuclear reliabuity factor is 1.008.
6.6.2 Assembly Radial Power L
{
The reliabilty factor for the assembly radial power has been determined by comparisons against the TMI 1 Cycles C
- plant data at selected state points (Section 4). All of the eighth core locations are used in determining the uncertainty. The statistical results of the assembly radial power comparisons are shown in Table 6.2 and the frequency plot is shown in Figure 6.3. The sample mean and standard deviation of the relative dillerence distribution is 0.00191 and 0.01814, respectively. The combined relative dliterance distribution is slightly skewed as shown in the frequency plot and it is not a normal distribution based on the D' test criteria for a 95% significance level. Using the non-parametric method, the 95/95
)
o
B TR 091 Rev.O "
Page 109 nuclear reliability factor is determined to be 1.033 which happens to be the same value if I
calculated assuming normal distribution.
I a
6.6.3 Assembly Total Power E The nuclear reliability factor for the assembly total power (maximum axial segment power)'
has been determined by comparisons against TMl-1 Cycles 6-9 plant data at selected state points (Section 4). For the peak power statistics, the three highest measured segments are used. The statistical results are shown in Table 6.3 and the frequency plot is shown in Figure 6.4. The sample mean and standard deviation of all data is -0.015 and 0.02266. ;
respectively. The frequency plot shows that the distribution is skewed and the D' test l
indicates that the distribution is not a normal distribution for a %% significance level. The I
95/95 nuclear reilability factor is 1.051 using the non-parametric method which is slightly less than the 1.053 value determined assuming normal distribution. For conservatism, the assembly total power nuclear reliability factor is 1.053.
6.6.4 Radial Pin Power The nuclear reliability factor for the radial pin power is obtained by using a Monte Carlo method to combne the uncertainties of assembly radial power factors and radial-local factors. The Monte C,arlo simulation randomly sampled the data from the assembly values and the radial-local components. The predicted values were multiplied to simulate calculated radial pin power factors. The corresponding measured values from Cycles 6-9 were also multiplied to give the " measured
- factors. The relative difference distribution is I
then obtained and Satterthwaite's approximation (Ref. 37) was used to determine the equtvalent degrees of freedom. The difference distribution is not a normal distribution based on the D' test for a 95% significance level. The 95/95 nuclear reliablity factor determined from the non-parametric method is 1.033 which is slightly less than the 1.035 value obtained I
l c - -------- _ --- _ _
r L
TR 091 r Rev. 0 Page 110
[-
assuming normal distribution. For conservatism, the radial peak pin power nuclear reliability
(
factor is 1.035.
I L
y 6.6.5 Total Pin Power The nuclear reliabulty factor for the total pin peer is obtained by using the Monte Cario' method described in Section 6.6.4 to combine the uncertainties of assembly total power factors and radiallocal factors. The difference distribution obtained is not a normal distribution based on the D' test for a 95% significance level. The 95/95 nuclear reliabuity factor determined from non-parametric method is 1.054 which is slightly less than the 1.055 value obtained assuming normal distribution. The total peak pin power nuclear reliability factor is 1.055.
- - - - - - - - - - m___.-~ _ m____. ____ _______ ___ ___ _,,____ ___ _ __ _ _ _ _ _ _ _
TR 091 -
Rev.O Page 111 l
Table 6.1 Radial-Local Factor Statistical Results
- I I I
- of Mean Standard Normality . )
Points Difference Deviation l B&W Critical Experiment 192 -0.00073 0.01143 Yes ,
Multi-Assembly Problems 15930 0.00003 0.00449 No Combined 16122 0.00003 0.00464 , No
- Difference = SIMULATE Measurement I
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- TR 091 Rev.O I Page 112
[
Table 6.2 Assembly Radial Power Statistical Results L
f Cycle Number Mean Standard Normality of % Difference Deviation
- Points 6 522 -0.00053 0.01031 No L -
t.
7 667 + 0.00001 0.01048 No 8 406 -0.00140 0.02739 No
[
i 9 667 -0.00400 0.02077 No r
All 2262 -0.00191 0.01814 No
(
- % Difference = (SIMULATE-3 Measurement)
- 100/ Measurement i
(
\
L
l E.
TR 091 l Rev.O E Page 113 Table 6.3 Assembly Total Peak Power Statistical Results Cycle Number Mean Standard Normality I
of % Difference Deviation ~
Points l
6 1566 0.01840 0.0146 No 7 2001 -0.01553 0.01843 No j I
8 1218 -0.0146 0.03367 No i
9 2001 -0.01202 0.02294 No All 6786 -0.015 0.02266 No
- % Difference = (SIMULATE Measurement)
- 100/ Measurement i l
I, I1 I l I
I I;
I_l
p RvO L Page 114 Figure 6.1
[
Frequency Distribution of B&W Criticals Comparisons f
< .5 l 7
[ .
40
}
35 -
30 -
25 r lg
[ ! l i'2af.
( 15 -
I io -
t ,
'~
l O klii: u : :
4.035 4.030 4.025 4.020 4.015 4.010 4.005 0 l
u i1i 0.00b 0.010 0.015 0.020 0.025 0.030 0.035 DIFFERENCE MIDPOINT I
Ta o91 Rev.O Page 115 Figure 6. 2 Frequency Distribution of Multi Assembly Comparisons l
9000 !
l l 8000f l
I 4
l 70 T '
I i ,
6000 i I
l l
,000 -
, $i! '
E .
E
- 4000 -- g l
3
- 3000 -
i i 20 . 1 I I; l
20m f l; o , : -- m R i : M -- i i I
-, m ,0 m,, e ,. . . ,, ,,,, ,,,, ,,,, g DIFFERENCE MIDPOINT 1
I I
TR 091 e Rov. O Page 116
[ Figure 6.3 Frequency Distribution of Assembly Radial Power Comparisons F
- u. ,
" 700 -
[
i l !
. 600 i
u 500 - -
I L , 400 - ;
h c f u F 300 --
i i
i I !
u !
200 h !
F l i
L l
t
( 3oo __ l
' n:!,
c 0 -: - , , , , .1 : : , ,
,h ,
1 1 ,
4.12-0.11-0.10 0.09 4.08 0.07 0.06 0.05 0.04 4.03 4.02 4.01 0.00 041 0.02 0.03 0.04 0.05 0.06 DIFFERENCE M10PONT
[
TR 091 Rev.O l Page 117 Figure 6.4 I
Frequency Distribution of Assembly Total Power Comparisons l
I l l \
I 2500 - ,
i i :
i l 2000 -
I ;
l E !
y 1500 -- l' l .
j i -
1000 l 7 i
I l l '
I 500 -
0
-0.14 i -- : - i -
-0.12 k
4.10 4.08 4.06 4.04 4.02 0.00
- : i 0.02
- E -:---i 0.04 i
0.06 0.08 0.10 i ,
I' DIFFERENCE MIDPONT ,
I
- I
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L TR 091 Rev.0
[ Page 118 L
f
7.0 CONCLUSION
L -
This report justifies GPUN's use of CASMO-3 and SIMULATE-3 for reload design of TMI-1, a B&W 177 fuel assembly plant. CASMO-3 and SIMULATE-3 are widely used computer codes in the industry and have I
L been extensively benchmarked by the developer, Studsvik. This report emphasizes the application of CASMO-3 and SIMULATE-3 in modeling TMI-1 cores and compares the results to actual plant operations p data; thus, demonstrating GPUN's capability to use these models in performing in-house physics analysis.
l The in-house benchmark includes a comparison of calculated and measured data from various beginning-(
of-cycle hot zero power startup tests, as well as steady-state and plant power maneuvering operations.
All the comparisons show very good agreement between calculated and measured data. The benchmark -
results and corresponding reliability factors are summarized in Table 7.1. These reliability factors are based on TMI-1 Cycles 1 through 10 operation data and they will be reevaluated each cycle to ensure that 95/95 tolerance / confidence is satisfied.
( It is concluded that CASMO-3 and SIMUL. ATE-3 accurately model the TMI-1 core and that GPUN has the capability to use these models in performing reload physics analysis in support of licensing TMI-1 cores.
l D
an TR 091 l Rev.O u Page 119 Table 7.1 Summary of TMI-1 Applications I
Number Degrees Mean* Standard 95/95 of of Deviation Reliability Cycles Freedom Factor HZP BOC ARO Critical 10 9 -13 ppm 14 ppm 54 ppm I
Baron HZP BOC IndMdual CR 10 29 -2.78% 4.21 % -15%
Group Worth HZP BOC Regulating CR 10 9 -2.93% 3.15 % -10%
Group Worth HZP BOC isothermal 10 16 0.88 PCM/*F 0.34 PCM/*F Temp. Coefficient
-0.036 PCM/*F+
or l
3
-1.722 PCM/*F HFP Critical Boron 2 51 -9 ppm 9 ppm 28 ppm Radial-Local Factor '
18121 0.00003 0.00464 1.008 Assembly Radial Power 4 2261 -0.19% 1.81 % 1.033 Assembly Total Power 4 6785 -1.50% 2.27% 1.053 Radial Pin Peak 4 2746 -0.22% 1.94 % 1.035 Total Pin Peak. 4 2468 -1.56% 2.30 % 1.055
- Difference = SIMULATE Measurement
% Difference = (SIMULATE Measurement)
- 100/ Measurement
- 4.036 PCM/*F for overheating accidents and -1.722 PCM/*F for overcooling accidents.
l I
I Il !
I:
I V
TR 091 -
Rev.O Page 120 h
.8.0. REFERENCES
{
- 1. M. Edenius and B. H. Forssen, "CASMO-3 A Fuel Assembly Burnup Program V4.7," Studsvik/NFA.
89/03, Rev. 3, June 1993, Studsvik Energitenik.
[
L-
- 2. J. A. Umbarger," TABLES-3, Library Preparation Code for SIMULATE-3," Studsvik/SOA-92/03, Rev.
D April 1992.
[ 3. K S. Smith, J. A. Umbarger and A. S. DiGiovine, ' SIMULATE-3, Advanced Three-Dimensional Two-Group Reactor Analysis Code V4.02,* Studsvik/SOA-92/01, Rev. O, April 1992. l
- 4. P. Jernberg, "CASMO-3 Benchmark Against Critical Experiments," Studsvik/NFA-86/11, August 1986. -
.l
(' 5. L E. Strawberry and R. F. Bany " Criticality Calculations for Uniform Water-Moderated Lattices,"
Nuclear Science and Engineering,23,58-73 (1965).
- 6. E. Blomsjo, M. Edenium, and R. Persson, " Critical Experiments up to 245'C with H2 0-Moderated
[ UO,-Rod Lattices in KRITZ,".AE-RF 71-267, Studsvik, AB Atomenergi, Sweden.
- 7. J. R. Brown et. al., " Kinetics and Buckling Measurements on Lattices of Slightly Enriched Uranium
( of UO, Rods in Light Water," Bettis Plant WAPD-176,1958.
- 8. R. D. Leamer et. al., "PuO2 -UO, Fueled Critical Experiments," WCAP-3726-1, Westinghouse 1967.
{. 9. " Listing of Thermal Benchmark Experiments". U.S. Atomic Energy Commission RRD: TP:043 (1974).
- 10. E. Johansson, "The Reactivity from CASMO/DIXY Calculations with the Libraries E3Ll80C and E3Lfl0GB for Various Experimental Coros," Studsvik/NR-85/73,1985,
- 11. M. N. Baldwin; G. S. Hooveler; R. L Eng; and F. G. Welfare, " Critical Experiments Supporting Close
[ Proximity Water Storage of Power Reactor Fuel," BAW 1484 7, Babcock & Wilcox,1979.
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{.. P25-1 EPRI, NP-2855,1983.
j 13. K S. Smith, " Pin Power Reconstruction: Benchmarking Against the B&W Critical Experiments,"
t Trana Am. Nuc. Soc., 56,531,1988.
- 14. K S. Smith and D. M. VerPlanck, "KWU-PWR SIMULATE 3P Solution to the KWU PWR Depletion
[ Benchmark Fivb;e,T.," Studsvik/SDA-89/06,1989.
- 15. K S. Smith and K R. Rompe," Testing and Applications of the QPANDA Nodal Model,"Intemational Topical Meeting on Advances in Reactor Physics, Mathematics, and Computations," 11, 861, Paris,
(~ Aptf1987.
l
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- _ - - . _ - - - - _ . _ _ . - _ _ - _ _ . _ . - . _ - _ - _ . - _ _ _ - _ - - - _ . . - _ _ . . - . _ _ _ _ . _ - ._. . - _ . _ .._b
== i TR 091 l EE Rev. O ,
Page 121 ;
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- I l
- 16. A. S. D5Giovine et. al.,'CASMO-3G Validation," YAEC-1363, Yankee Atomic Electric Company, April, 1988.
- 17. A. S. CiGiovine et. al.,
- SIMULATE-3 Validation and Ver* cation,* YAEC-1659, Yankee Atomic Electric Company, September 1988.
- 18. " Nuclear Design Methodology Using CASMO-3/ SIMULATE-3P,* DPC-NE-1004, Duke Power ,
Company, January 1tXy]. .
- 19. " Core Operation Recort Three M8e island Unit 1 Cycle 1 Operation, September 2,1974 - February 21,1976." En u3. October 1976.
- 20. " Core Operanon Pep: Three Mle Island Unit 1, Cycle 2 Operation May 24,1976 - March 18, 1977,* BAW-1459 'cf '977.
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- 22.
- Core Operation Report Three Mile Island Unit 1. Cyde 4 Operation, AprB 28,1978 - February 17, 1979," BAW-1579, September 1979.
- 23.
- Core Operation Report Three MRe Island Unit 1, Cyde 5 Operation, October 3,1985 - October 31, 1986," BAW 1987, AprR 1967. .
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2110, July 1990.
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27,1991," August 1992.
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B&W Fuel Company, January 1994.
- 28. 'TMI 1 Cyde 10 Startup Report" GPU Nuclear I.etter C311-94-2003, from T. G. Broughton, Vice President, TMI-1, to the NRC, dated January 13,1994.
- 29. *ARMP-02: PDQ7-E/ HARMONY User's Manual,' EPRI NP-4574-CCM,11,9, V2, AprR 1987.
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Studsvik/NFA-89/11, November 1989.
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- 32.
- Metropolitan Edison NSS On-Une Computer Programs for the 855 System," NPGD-TM-308.
Babcock & WBcox, Dec.1974.
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DOE /ET/34212-41, BAW 1810, AprH 1984.
I
I
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- 34. " Assessment of the Assumption of Normality Employing individual Observed Values,* ANSI N15.15-1974.
- 35. Mary Gibbons Natrella. " Experimental Statistics." John Wiley & Sons (1966).
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' ~
- 37. C. A. Bennett and F. L Frankin,' Stat;stical Analysis in Chemistry and the Chemical Indu'stry," John Wiley & Sons, New York, NY, (1961).
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