ML20008F291
| ML20008F291 | |
| Person / Time | |
|---|---|
| Site: | Quad Cities  |
| Issue date: | 06/30/1980 |
| From: | Cokinos D, Kohut P, Lai J BROOKHAVEN NATIONAL LABORATORY |
| To: | |
| References | |
| CON-FIN-A-3308 BNL-NUREG-29019, NUDOCS 8103120769 | |
| Download: ML20008F291 (61) | |
Text
--
BNL-NUREG-29019-INFORMAL REPORT LIMITED DISTRIBUTION
~
SIMULATION OF QUAD CITIES 1 CYCLE 1 OPERATION WITH THE ARMP CODE SYSTEM c.3 ~
r s D. Cokinos dj, (I P. Kohut - Y3 J. Lai t T I'IAR 1 0 1981 n L~
D. Diamond 684 ag. ,,
it Reactor Core Safety Analysis Group Brookhaven National Laboratory Upton, New York 11973 June 1980 \ C. esearch and Tecmbal l N Assistance Repor:
Prepared for U.S. Nuclear Regulatory Commission Washington, D. C. 20555 Under Interagency Agreement DE-AC02-76CH00016 NRC FIN No. A-3308 t Now at Southern Company Services l
9 /03/ A0 M 7
.\ RC Researca anc "ec1nica TABLE OF CONTENTS ,
\ kS$f$f8DC@ k@pQ{l PAGE ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . 11 LIST OF FIGURES ...................... iii L IS T OF TAB L E S . . . . . . . . . . . . . . . . . . . . . . . v ACKNOWLEDGMENTS ...................... vi
1.0 INTRODUCTION
..................... 1 2.0 CALCULATI0hML METHODOLOGY . . . . . . . . . . . . . . . 2 2.1 Fuel Assembly Calculations. CPM ......... 2 2.2 Reactor Core Calculations. N0DE-B ........ 2 2.3 Thermal Hydraulics Calculations. THERM-B . . . . . 4 3.0 DATA GENERATION . . . . . . . . . . . . . . . . . . . . 4 3.1 Fuel Assembly Design Data ............ 7 3.2 Reactor Core Data ................ 7 3.3 Operating Data . ................ 17 4.0 RESULTS AND COMPARISONS . . . . . . . . . . . . . . . . 17 4.1 In-Core Detectors ................ 21 4.2 N0DE-B No rmal i zati o n . . . . . . . . . . . . . . . 21
- 4. 3 Selection of Albedoes .............. 23 4.4 Cycl e 1 Eigenval ue . . . . . . . . . . . . . . . . 23 l 4.5 Power Distributions ............... 25 l 4.6 Modelling and Data Limitations . . . . . . . . . . 34 i
REFERENCES ........................ 40 l-
! DISTRIBUTION LIST ..................... 44 APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . .
A. . CPM, N0DE-B, TIP Outpus . . . . . . . . . . . . . . A-1 B. TIP Data Processing and Analysis . . . . . . . . . B-1 l
1
.y b[] fif )E}i
- t. ..
ABSTRACT The Advanced Recycle Methodology Program (ARMP) code systen has been used for the simulation of Cycle 1 operation of the Quad Cities 1 reactor. .
Two-dimensional void and exposure dependent data were generated for both controlled and uncontrolled states for each bundle type with the Collision Probability Module (CPM) code. The data were fed into N00E-B, a three- ,
dimensional core simulation code, which then calculated the incore power, void and exposure behavior throughout the first cycle. The results of the calculations are generally in good agreement with measured data.
l e
e 11 I
4
. - , . , , ., ,- y , w
LIST OF FIGURES Figure Title Page 2-1 Fl ow Di agram o f CPM . . . . . . . . . . . . . . . . . . 3 2-2 Flow Diagram of N0DE-B ................ 5 3.1 Block Diagram of Data Flow for Quad Cities 1 Simulation ...................... 6 3.2 Bundle Design for Type 1 Initial Fuel . . . . . . . . 12 3.3 Bundle Design for Type 2 Initial Fuel . . . . . . . . 13 3.4 Typical Quad Cities 1 Cycle 1 Control Cell . . . . . 14 3.5 Spatial Gd 023 Variation for Initial Fuel ....... 15 3.6 Quad Cities 1 Core Map with Fuel Assembly Type Loading for Cycle 1 . . . . . . . . . . . . . . . . 16 3.7 Typical Set of Operating Data . . . . . . . . . . . 18 4.1 Exposure Accumulation As a Function of Time For Actual Operation and Slope Showing Rate of Accumulation for Continuous Operation at Rated Conditions ...................20 l 4.2 Quad Cities 1 Core Map Showing the 18 Detector Pairs . 22 l
l 4.3 Cycle 1 Core Eigenvalue . . . . . . . . . . . . . . . 24 4.4 Notch Inventory Histogram and Eigenvalue . . . . . . 27 4.5 Power Histogram - Histogram and Eigenvalue . . . . . 28 4.6 Flow Histogram - Histogram and Eignevalue . . . . . 29 4.7 Measured and Calculated Axial Core Average Power Distribution at 247, 646, 800 and 1334 mwd /t . . . . 30 l
l l
l l iii
LIST OF FIGURES (Continued) 4.8 Measured and Calculated Axial Core Average Power Distribution at 2474, 3401, 3480 and 3696 mwd /t . . 31 4.9 Measured and Calculated Axial Core Average Power Distribution at 4297, 4809, 5471 and 5949 mwd /t . . 32 4.10 Measured and Calculated Axial Core Average Power -
Distribution at 6175, 6710 and 6948 mwd /t . . . . . 33 4.11 Measured and Calculated Axial Power Distribution for Individual Detectors at 247 mwd /t ......35 4.12 Measured and Calculate'd Axial Power Distribution for Individual Detectors at 800 mwd /t . . . . . . 36 4.13 Measured and Calculated Axial Power Distribution for Individual Detectors at 3401 mwd /t . . . . . . 37 4.14 Measured and Calculated Axial Power Distribution for Individual Detectors at 4809 mwd /t . . . . . . 38 4.15 Measured and Calculated Axial Power Distribution for Individual Detectors at 6710 mwd /t . . . . . . 39 4.16 Summaries of Operating Data for June and July 1973 . 41 4.17 Root-Mean-Squares of the Deviations Between Measured and calculated TIP Distributions ....42 iv
LIST OF TABLES Table Title Page i . 3.1 Initial Fuel Description . . . . . . . . . . . 8 3.2 Fuel Assembly Data . . . . . . . . . . . 9 3.3 B-Array Summary 10 3.4 Summary of Core Description . . . . . . . . . 11 4.1 Quad Cities 1 Burnup Stap Information for Cycle 1 . . . . . . . . . 19 4.2 Cycle 1 Statepoint Data and Calculated i keff ................... 26 i
l l
l l
l V
ACKNOWLEDGEMENTS We wish to thank Dr. R. N. Whitesel of EPRI for his valuable assistance in providing clarifications of, and corrections to, the operating data as well
- as for supplying us with the deck of cards containing the complete TIP set.
We have benefited from discussions on CPM with Dr. M. Edenius of Studsvik of America, Inc., and on NODE-B with Dr. R. Weader of NAI. Special thanks are due to Mr. W. Bornstein for his assistance in making CPM operational at BNL and to Ms. Penoyar for her efforts in maintaining current versions of the ARMP codes. The expert assistance generously offered by Mr. A. L. Aronson in the area of computer graphics is greatly appreciated. Mr. M. Dunenfeld was the NRC program monitor for this work and supplied guidance and encouragement.
O vi
1.0 INTRODUCTION
This project was undertaken by Brookhaven National Laboratory (BNL) with the dual objecti"as of: 1) developing an in-house capability for simulating-boiling water reacer (BWR) incore conditions; and 2) verifying parts of the ARMP code system. Being able to follow the fuel cycie history of a reactor allows neutronics data to be generated for static or dynamic safety calcu-lations at any point in time. This capability is necessary for BNL to pro-vide a wide range of technical assistance to the U.S. NL:.. ear Regulatory Com-
~
missicn. The ARMP code system is of interest because it represents state-of-the-art methodology and because it is widely used by utilities for fuel management and licensing. A previcus BNL reportl addresses these objec-tives for a pressurized water reactor.
Quad Cities 1, a.BWR-3 design, was chosen to study becausa careful documentation 2 of reactor design data, operating data for Cycles 1 and 2 and gamma scan measurements following Cycle 2 were available. The reporting was done for the Electric Power Research Institute by the reactor operator (Commonwealth Edison) and vendor (General Electric) with the intent of making available reference quality data for use in the qualification of core analysis methods.
In simulating BWR behavior, two basic calculational tools are used: 1) a two-jirensional lattice code which generates macroscopic cross section data for fuel bundle; and 2) a three dimensional reactor code which yields core reactivity, and power and exposure distributions. The ARMP code system 3 provides such a capability.
The two principal modules of APf4P whict were used for the Quad Cities 1 Cycle 1 simulation are the Collision Probabi ity Module (CPU) for the genera-1 t.1 of the fuel assembly data and EPRI-N0DE.1 for the calculation of the global core pcrameter. N0DE-B is primarily a neutronics code; detailed ther-mal hydraulics infonnation is evaluattd separately with THERM-B, another ARMP module. The channel flow data so generated are then introduced an input in N0DE-B.
The measured power as a function of axial position in each of 41 detec-i tors located throughout the interior of the core were compared with the I calculated detector' responses. The agreement between measured and simulated l data is generally good: very good agreement in the central and peripheral l locations in the first half of Cycle 1 and fair agreement in the second half.
l A description of the physics methodology employed in the codes is given in Chapter 2. Data generation and input information are presented in Chapter l 3. Results and comparisons with measured data are shown and discussed in
~
Chapter 4. Sample outputs of pin power distributions are given in Appendix A.
Appendix B describes a data processing, analysis and plotting code developed in order to facilitate the comparison between measuremants and calculations.
i i
l 1
2.0 CALCULATIONAL METHODOLOGY The medelling of the BWR core operation requires that the design and operatica of tre core be reasonably represented. A fuel assembly code, CPM, is first used to calculate few group parameters. The bundle power distribu-tion is obtained as a by-product of these calculations. The few group data is obtained as i function of exposure, void fraction, and moderator and fuel temperatures for both controlled and uncontrolled states, with and without xenon. These assembly data are then used as input into the three dimensional nodal con, N0DE-B, which calculates core wide power, exposure, and void dis-tribu' cions de well as reactivity for a given set of operating conditions.
2.1 Fuel Assert bly Cal cul ations. CPM.
The fuel assembly calculations were perfomed with the CPM code 4 This code, develcped by AB Energite(nik, Sweden, is a multigroup two-dimensional .
collision probtbility code which can be used for both PWR and BWR fuel as-semblies. The code can analyze a geometry consisting of an array of cyl-indrical fuel rods of varying compositions in a square pitch configuration. It treats gadolinia loaded fuel rods, crucifom control blades, incore detec-tors, water gaps and boron curtains. A flow diagram of the major calculation-al functions of the CPM code is shown in Figure 2-1. The code uses a 69 group microscopic cross section library which is based on ENDF/B-III.
A special mcJule is used for the treatment of the effective cross sections in the resonance region for important resonance absorbers and an equoralence expression relates the heterogeneous problem to an equivalent homogeneous problem. Effective absorption and fission cross sections are calculated from the resonance integrals which have been obtained from the equivalence expression. The code corrects for overlap effects in a mixture of resonance absorbers and for screening effects between different pins (Dan -
coff effect).
An auxiliary code, MICBURN, is used when the fuel rods contain gadolinia.
Effective gadolinia cross sections as a function of burnup are calculated by MICBURN and are entered as input in CPM for each fuel rod with a given gadolinium concentration.
.The cross sections in the data library are tabulated for different tem-peratures. Linear interpolation is used for any other temperature values in the tabulated range. Two fission spectra are in the library: one for U-235 and one for Pu-239. Hence an appropriate average fission spectrum is employed in the transport calculation.
2.2 Reactor Core Calculations; N0DE-B A complete global reactor analysis is perfomed by NODE-B6 whica simui-taneously solves for the core effective multiplication factor, and '1e three-
^
dimensional power, void, xenon and fuel exposure distributions. Bottom entry control rods and partial or full length gadalinia-loaded fuel rods are treated. The code handles up to 13 differeat fuel types constituting the core loading. Each fuel bundle used in the quarter or full core calculation is uniquely represented and diviaed into 12 axial segments or, nodes.
2
____q Input : Restart file g 4
Resonance : Data Library calculation
+ f I Macroscopic -7 c '
cross sections
{MICSURN 4
Micro group calculation 69 gr. max 5 regions
'r Condense to mac o groups (max 25 groups)
Homogenize to macro regions ,,
Condense to max 12 groups
- Macro group calculation in Calc. cross sectiors i
annular geometry for 2D-regions iP Condense to max 12 groups Cale. cross sections for 2D-regions
=
8
.s C- Control rod calc.
CROCOP
[
4
! 2-dimensional collision probability calculation 4
d Fundamental mode calc. I 4
Few group constants Reaction rates <
E
. Burnup corrector zero burnup
+
l Number densities l b
Burnup :
predictor ir l End I i
! Figure 2.1 Flow diagram of EPRI-CPM 3
1
NODE-B, a successor of the FLARE code, is based on a modification to the one-group diffusion theory in which the local infinite multiplication factor, k=, and migration area, M4, play an important role in estabishing local as well as core reactivities. The iterative interrelationship between power distribution and nuclear properties dich are functions of coolant flow and void behavior as well as of tenperature, xenon and burnup distributions, may be described by the flowchart cf Figure 2.2.
For an initial distribution of coolant voids, Doppler effect, xenon and fuel exposure, the source distribution and core eigenvalue are first con-verged. The power distributir,n is then calculated and new coolant voids, Doppler effect and xenon distributions are established. This power-void -
iteration is repeated until the nuclear properties and power-void distri-butions have converged to a value within input et . .e criteria. The power distribution which has converged in the above manner is used in the calcu-lation of the fuel exposure distribution over the entire exposure interval.
The sequence of source, power, void, Doppler and xenon convergence f e epeated at the new exposure level .
Operating conditions such as thermal reactor power, core pr sure, in-let subcooling, core flow and control rod positions are introduced as input and serve as the basis for the history of operation during the exposure intental characterized by these conditions.
2.3 Themal Hydraulics Calculations. THERM-B N0DE-B requires that flow data be input for each channel in the core (or quarter core) calculation. To obtain flow data the EPRI-THERM-B code7 ,
also a part of the ARMP code system, is used. This code evaluates core pressure drop, subcooling, and flow distribution within the core and deter-mines themal perfomance of the fuel . Inlet fluid velocities, axial void and quality distributions, critical heat flux ratios, pumphead requirements, fuel centerline and clad temperatures and average fluid densities are also calculated.
! Required input includes thermal reactor power, total recirculation flow, l nodal power distribution (obtainable from NODE-B), loss coefficients and in-let liquid velocity guesses. Because the power distribution is required input some iteration between THERN-B and N0DE-B is required.
3.0 DATA GENERATION l The principal source of information necessary for carrying out our
! calculations has been obtained from Reference 1. Fuel assembly data and ,
certain operating characteristics were the principal input for CPM. The MICBURN generated effective cross sections for gadolinia were also needed.
Core design and operating data along with data generated by CPM constituted the principal N0DE-B input. The core flow distribution as obtained from
[
THERM-B was also input. A simplified block diagram showing data flow among the various calculational modules is shown in Figure 3.1.
l 4
J TIME STEP t BEGINNING of STEP t B
POWER LEVEL ff.C POWER GUESS
- P , (t ~
E 1
CALCULATE MODERATCR DENSITY EURNUP EFFECT
) DISTRIBUTION U Exposure per Node E (t B
L 5 gy CALCULATE _ ijk ,
2 BU kaa1] . k (U) M. 13.k (U) 1 j, _
X:h0N EFFECT DOPPLER EFFECT Power per Node Fuel Temperature per Node Xenen & Iodine per Node li jk Doo k)BU 1 i
SOURCE CALCULATE TO POWER CCNVERSION
$ik ' ' #
NO POWER Tb SOURCL'
, COtNERSION J,
CALCULATE l DE M .
DENSIM 7Eg SOURCE h )
"NVERG COINERGED T ,Siik(t 9) and k YES E(t SOURCE E B
@ TO END OF STEP t E +
p . ijk E ijk B ijk COWERSION USE POWER: P (t B
PREDICT
~
S IN CORE SENSOR READINGS Figure.a.2 EPRI-NODE-B Flowchart 5
MICSURN FUEL DESIGN : ASSEMBLY "
DATA CONSTANTS f
CPM I
1 SUPERLINK REACTOR 8
~ CORE CONSTANTS (
OPER ATING DATA SUPPLEMENTAL CONSTANTS o , ,
THERM-B NODE-B t J ,
REACTIVITY POWER, VOIDS EXPOSURE TIP's ALSE00ES j NOT GOOD o
BOL NORMALIZED MEASURED :' TIP : CALCULATED DATA COMPARISON ! TIP's a GOOD ,.
o END -
l Figure 3.1. Data Flow in BWR Simulation
. Lwith the ARMP Code System i.
Li 16
3.1 Fuel Assembly Design Data The Quad Cities 1 Cycle 1 care contains 724 fuel assemblies. These bun-dies have a 7x7 rod array, an r.verage U235 enrichment of 2.12 w/o, and may be grouped in two main catessries based on the amount of gadolinium present.
Type 1 fuel has two fuel rods with gadolinium at 3 w/o each and one rod at 0.5
~
w/o. Type 2 fuel contains only two gadolinium rods at 3 w/o each. The gado-linium in the fuel rods is in the fom of Gd 23 0 . Each of these two types is composed of dished and undished bundles. Table 3.1 (Reference 1) sum-marizes fuel rod arrays, fuel rod pitch, rod-to-channel spacing, gap thick-nesses and control augmentation characteristics. Core loading information, assembly pitch, fuel pin pitch, average fuel compositions, fuel weights and other pertinent data are provided in Table 3.2 (Reference 1). Bundle design characteristics for types 1 and 2 initial fuel are shown in Figures 3.2 and 3.3 (Reference 1), respectively. A four bundle configuration with a cruciform control rod - a control cell - is shown in Figure 3.4.
The distribution of gadolinium along the vertical direction for the 0.5 w/o and 3.0 w/o concentrations is shown in Figure 3.5. In this Figure as well as in Figure 3.2 the 0.5 w/o concentration in the U02 is shown as " Type Z".
The 3.0 w/o gadolinium concentration in Figures 3.2, 3.3 and 3.5 is shown as
" Type Y". It can be seen that in the case of the 0.5 w/o concentration the gadolinium is spread only over a partial length of the fuel rod whereas in the 3.0 w/3 case it occupies almost the entire length of the rod.
It must be pointed out that Quad Cities 1 was among the first BWR's to be loaded with fuel containing burnable poison as a means for control augmen-tation, instead of boron curtains, provided for in the original Quad Cities design and which characterized the BWR-1 and BWR-2 reactors.
Assembly data are input in N0DE-B in the fom of the B-constants. B-constants are coefficients of polynomials derived by fitting void and/or exposure-dependent results of CPM calculations over appropriate void and/or exposure ranges. A list of the B-constants is given in Table 3.3.
3.2 Reactor Core Data As stated earlier, the Quad Cities 1 core contains 724 bundles. The rated power is 2511 Muth and the total core flow at rated power is 98.6 x 106 lb/hr. A summary of core design characteristics is given in Table 3.4.
A reactor core map showing the fuel loading configuration for Cycle 1, the locations of the 177 crucifom control rods and the 41 in-core instrument as-semblies, the latter indicated by solid dots, is shown in Figure 3.6. Most of these instrument assemblies, or monitors, are arranged so that they fom pairs With the whose members are located on both sides of the NE-SW core diagonal.
fuel loaded symmetrically with respect to this diagonal the pairing of the de-tectors provides a means for checking the consistency of the detectors when the reactor is operated with control rod patterns of similar degree of sym-me try. In-core detectors play a very important role since their responses es-tablish the standard which must be matched by the calculation.
7~
Table 3.1 INITIAL FUEL DESCRIPTION Type 1 Type 2 Undished Dished Undished Dished Fuel Assembly Number of Fuel Assemblies per Batch.. . 127 185 136 276 Fuel Rod Array- m . 7x7 7x7 Fuel Rod Pitch, in.. . 0.738 0.738 Penpheral-Rod-to-Channel Spacing, in... . 0.1435 1/2 Width of Wide Water Gap, in.-- 0.375 1/2 Width of Narrow Water Gap,irt 0.188 Cladding Length,in.. 156 Bundle Average Ennchment (wt % U-235 in Total U)- ..~. 2.12 2.12 Control Augmentation Type. Fuel Rods Fuel Rods Containing Gd,0, Containing Gd,0, Number ; . . . . 3 2 Control Length, in - . 138(2), 60(1) 138 Control Material-- 3.0 wt % Gd,0 3(2) 3.0 wt % Gd,0, 0.5 wt % Gd,0 3(1) locations in Fuel Lattice in Fuel Lattice Weight of U per Fuel Assembly Ib - ...- 433.4 423.8 433.4 423.9 kg- 196.6 192.2 196.6 192.3 Cha.nnel ~
Outside Dimensions,in.- 5.438 x 5.438 5.438 x 5.438 Thickness, in. . 0.080 0.080 inside Comer Radius,in. 0.40 0.40
, Material ... . . Zr.4 Zr-4
^
Water-UO, Volume Ratio (cold) -- 2.42 2.47 2.42 2.47 l
8
Table 3.2 INITIAL 7 X 7 FUEL ASSEMBLY DATA 3 Gd 2 Gd
. Dished Undished Dished Undished As sembly Type . . . . . . . la lb 2a 2b
~
No. of Assemblies, Ini tial Core. . . . . . . . 185 127 276 136 Assembly Pi tch, in. . 6.0 6.0 6.0 6.0 Fuel Rod Pi tch. . . . . . 0.738 0.738 0.738 0.738 Fuel Rods per Assembly. 49 49 49 49 Active Fuel Length, in. 144 144 144 144 Burnable Poison Positions. 3 3 2 2 No. of Spacer Grids.... 7 7 7 7 Inconel per Grid, lb... 0.102 0.102 0.102 .102 Zr-4 per Grid, Ib...... 0.537 0.537 0.537 0.537
- Spacer Width, i n. . . . . . . 1.625 1.625 1.625 1.625 Assembly Average Fuel Composition Gd23 0, gm.......... 269 269 260 260 00 2, kg.............. 218.05 222.97 218.07 222.98 To tal Fuel , kg . . . . . . . . . 218.32 223.24 218.33 223.24 e
e 9
Table 3.3 B-Array Summary B Constant Desc'ription B B B 2 3 M Unr@ded ,
B B B " "#
- 4 7 10 B B * # ~
- 3 8 11 B6 Bg B13 K= M ded B B y3 y4 B
41 a l Unrodded K E 15 16 axe B B g Byg ap M e4 an emperatwes 17 Dop B
20 21 23 B al Um ded K E,U B B 34 36 B
g E Adjustment B B * ## * ^
g 25 B
26 1,j,k .
B g 28B 29 Unrodded F
I B B 30 31 32 "
- F _
B Not Used 33 B
35
- "~ ("88
- O* }
B B
- 37 38 0#at E B ad na a n de variation 39 40 10 L
Table 3.4
SUMMARY
OF CORE DESCRIPTION Rated Co re Thennal Powe r, MW. . . . . . . . . . . . . . 2511.0 l'
To tal Co re Fl ow a t Ra ted Powe r , i b/ hr . . . . . 98.6 x 106 Total Number of Fuel Assembli es. . . . . . . . . . . 724 Number of Fuel As sembly Type s. . . . . . . . . . . . . 4 Number of Fuel Assemblies of Each Type.... See Table 3.2 Total Number of Control El ements. . . . . . . . . . 177 Number of Control El ement Type s. . . . . . . . . . . 1 Number of Control Elements of Each Type... 177 Total Number of In-core Flux Monitors. . .. . 41 Heat Transfer Surface Area, f t . . 2. . . . . . . 62,747 Total Weight of U in Core, short tons..... 154.7 Core .
Core Lattice Pi tch , i n . . . . . . . . . . . . . . . . 12.0 Water /UO2 Vol ume Rati o ( col d) . . . . . . . 2.452-i 4
1' 11
l 2,12 wt% U-235 BUNDLE AVERAGE
~
WlOE-WIDE CORNER T T 3 3 2 2 2 2 3 d d d d d d d 3 2 2 1 1 1 2 g d d d l
T T 2 2 5Z 1 1 1 1 d d S
2 1 1 1 1 4Y 1 d d T T 2 1 1 1 1 1 1 l d d 1
2 1 1 4Y 1 1 1 d d d T T 3 2 1 1 1 1 2 d d d d d d d I
l - -
l ROD TYPE U-235 (wt%) Gd 02 3 (wt%) NO. OF ROOS l
1 2.47 0 27
! 2 1.70 0 14 l 3 1.20 0 5 1 4Y 2.47 3.0 2 '
5Z 2.47 0.5 1 S = SPACER CAPTURE ROD l T = TIE ROD d = OlSHED ROD IN A DISHED SUNOLE Figure 3.2 Bundle Design for Type 1 Initial Fuel 1
! 12 l
t.
y v 2.12 wt% L}235 BUNDLE AVER AGE l
WIDE-WIDE CORNER T T
~
3 3 2 2 2 2 3 d d d d d d d 3 2 2 1 1 1 2 l
d d d g
T T
~
2 2 1 1 1 1 1 d d S
2 1 1 1 1 4Y 1 d d T T 2 1 1 1 1 1 1 l d d 1
2 1 1 4Y 1 1 1 d d d T T 3 2 1 1 1 1 2 d d d d d d d s
RCD TYPE U-235 (wt%) l Gd 02 3 (wr%) NUMBER CF RODS 3
2.47 0 , 28 2 1.70 0 14 3 1.20 0 5 4Y 2.47 3.0 2 S = SPACER CAPTURE ROD T = TIE RO D d = DISHED ROD IN A DISHED BUNDLE Rgure 3.39 uncle Design tcr Type 2 initial Fuel 13
n!C e I A R '+
- @'@ @ @ @ @ $ 1 ,
{B 0 0 0 0 0 0' 'O 000O@EWO000OOU
~
@ ID D O O O O O G6 i G000000 O .
G OO@OOO 0000000 0
@ O0000.@ 00@O00,0 0 G, @OOOOO O O O O-O-OIO O
+@r@@@@ @O, p @o o-O-o,o,, p
( - ooo) .
'" =
LEGEND
< *V"'Oe;eeeeig"O g e o,SHeo e. i @ qpp@eeeee O SPACER CAPTURE ROD LOW Gd2 03 CONTENT - UO2 HIGH Gd 033 CONT ENT - UO2 LOW ENRICHMENT INTERMEDIATE ENRICHMENT HIGH ENRICHMENT j ,+ s, s@ @ @ @ @ @ @s,'s0 l
/ S (INSIDE RAD) y 4 A A B j C O I E F G H I I J l DIM. IDENTIFICATION l OlM. INCHES l 12.0 S.278 0.375 0.312 0.080 0.175 0.1435 0.738 l
l l l
OlM. IDENTIFICATION K ' L M l l l l R l S l OlM. INCH ES 4.875 0.187 1.562 l l l l 0.700 l 0.400 l l l l l I I I Figure 3.4 Typical Quad Cities 1 Cycle 1 Control Cell 14
t TOP OF ACTIVE FUEL TYPE Z TYPE Y 1 3 in.
i _ 1 36 in. 4 Y
V 60 in. 8 in.
2 n
/) N I
48 in.
N\
h
-] , 3 in.
a BOTTOM OF ACTIVE FUEL
- UO 2
- Ve ., 3.5 wt% Gd 023
- UO2 + 3.0 wt% Gd 023 Figure 3.5 Spanal Gd,0, Variation Initial Fuel 15
TOP PLAN VIEW CYCLE 1 6o d I I i I 58 I I I I 57 O O O +
55 54 53 gI E 52 ,, ; i i ;
50 t j i 48 8 9 O A 9 9 o lj 4a ,, I 8
46 45 i
'4 X I I X
I I -
l.L 42 ' '
'o 39 -
r.I f I. I
! 1 __
37 - 1 '
g g u"- j -
1 l 33 - 9 l0l e e- 0 e 32 I l l l9l i I 3o 3' ~
29 -
l l l l g l g l1 1 21 -2l1 2l1 2l1 2 i 2 g 900 28 2, _ I_ l 1 -
2 412 ,!2 , 2 if i 2 &p4
'6 24 25 -
23 _ n_
el le l el l1 2 e
12 , ;2 1 2l1
, 12 2
e l1 il2 2
i ,
1 2 1 e ,12 2
1 2 1 e k 2 %
g 22 gg _l L l l l l1 2l1 2 11 2l1 2 1 2l1 2 1 2 g 20 , I l 1l2 I
}2 n tl2 112 1 12 1 2 IS l l1 2 2l1 2[1 2 1 2 l e l 1 2l1 I7 16
'5
' ' ' ' ' 'I' L '1, L L- L i4 1 2 1 21 2 l1 2 1 a 1 2 13 l l E A A A 12 i I R I 12 i 2 1 2 5 2 i 2 11 2 io
- i i ; l O'
ji 2 i 2 i 2 i 9,,
2 i 2 08
- c. l l ! Ol l
., O , , ,: 2 ,12 06 l l l l 6 i i 2 i 2i1 2 g3 o4 l l 12 il2 0' :
l l l l 1 l 112 M ! l l l l l l l l l l ,
1 I i l il i l i l ) l l l l 1 1 1 00 02 04 06 08 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 01 03 05 07 09 11 13 15 17 19 *i 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 NUMBER OF FUEL ASSEMBLIES- 724 1 FUEL BUNDLES WITH 3 Gd20 3RODS AND Y NUMBER OF CONTROL RODS .177 2.262 in. ORIFICE DIAMETER - 312
$ NUMBER OF iN.CJRE INSTRUMENT ASSEMBLtES-41 1 NUMBER OF NEUTRON SOURCES- 7 2 FUEL BUNOLES WITH 2 Gd23 0 RODS AND
~
X STARTUP R ANGE IN*.8VMENTS-4 k INTERMEDIATE RANGE - BUS A -4 . FUEL BUNDLESWITH 2 Gd 023 RODS AND g INTERMEDIATE RANGE - BUS 8 4 1.424 in. ORIFICE DIAMETER - 84 NOTE: QUARTER CORE ROTATIONAL Af 40 MIRROR SYMMETRY Figure 3.6 Quad Cities 1 Core Map with Fuel Assembly Type Loading Arrangement for Cycle 1 ;
1 16
In any core follow calculational effort, in addition to the design data and the data generated from the assembly codes, one introduces albedoes, or leakage factors. In the case of BWR simulation with NODE-B there are three types of leakage factors: bottom leakage, top leakage and horizontal leakage factors. These leakage factors are selected within certain ranges and provide a means by which the difference between measured and calculated power distri-butions can be minimized.
A three-way sensitivity study was performed to determine the appropriate set of albedoes. This procedure is discussed in Section 4.3.
3.3 Operating Data Reactor operating data for the first two cycles of Quad Cities 1 have been compiled in Reference 1. There are 16 data sets which span the entire Cycle 1 operation of the reactor. These sets have been selected as repre-senting the plant's operating state during a given interval.
Each data set contains the following data:
Date Core Average Exposure Core Thermal Power Core Pressure Core Flow Inlet Subcooling Control Rod Configuration Complete Axial TIP Distribution for all 41 in-core Detectors A sample of a typical data set showing the axial TIP distribution for seven of the 41 detectors is shown in Figure 3.7. All data sets have been collected during steady state operation, and following a period of at least 48 hours5.555556e-4 days <br />0.0133 hours <br />7.936508e-5 weeks <br />1.8264e-5 months <br /> of operation under the same conditions. -
Core thermal power, inlet subcooling and recirculation flow rate have been taken directly from the process computer output. The detailed data which are input into the process computer and are necessary for the process computer evaluation ef 'the above " measured" parameters, have not been made available.
4.0 RESULTS AND DISCURION l
The flow of calculations performed using the codes described in Section 2
, was shown in Figure 3.1. The sixteen data sets collected during the Quad l Cities 1 Cycle 1 operation were used to simulate the operating history of the l core. Table 4.1 shows the exposure intervals during which the Quad Cities i l
~
core was operated with a control rod pattern in the A or B sequence and with reactor operating conditions compiled in the indicated data set. The exposure accumulation as a function of time during Cycle 1 is shown in Figure 4.1 along with the slope corresponding to operation at rated conditions.
k 17
OATASE7 C5. DECEMS ER 26,1972 Nactor Conditions Cee A<erage Ex;;csure. 2031.C M'.*.'c/t Cue Trecal Power. 2450.00 MW7 C::re Pressure. P,1C44.75 ::s:a C te F.cn. 97.37 Ut/hr det Se.~cang at P. 23.34 B:u/t Centrol Configuration Legend: 43, Fun Out; 0, Fu:! In.
43 48 48 48 43 43 43 43 48 48 43 48 43 43 48 48 43 43 48 43 48 04 48 24 43 43 43 43 43 46 43 48 45 32 43 0 43 0 43 0 43 32 43 43 43 45 43 36 48 14 43 36 43 36 48 14 43 35 43 43 43 48 43 0 48 0 43 0 49 0 43 0 43 43 43 49 43 22 43 48 48 24 43 24 48 48 43 22 43 48 43 0 48 8 48 3 43 0 48 8 43 3 43 0 43 43 48 24 48 28 43 43 '48 4@ 43 23 43 24 48 48 ~
43 0 43 5 43 8 43 0 48 8 43 8 43 0 43 43 43 22 43 43 48 24 4S 24 45 43 48 22 43 43 43 48 48 0 48 0 48 0 43 0 48 0 48 48 43 43 48 36 48 14 48 36 43 36 48 14 48 36 48 43 43 43 43 32 43 0 43 0 43 0 43 32 48 48 43 43 43 43 48 43 43 24 48 24 43 4; 43 43 43 48 43 48 48 48 43 48 48 48 48 43 45 48 48 48 48 Axial TIP Distribution 1609 36.3 58.5 75.2 -94.7 1C3.1 110.3 120.1 127.3 32.1 124.0 122.5 115.4 101.1 97.5 92.9 82.8 75.4 72.6 63.2 57.7 52.1 39.9 26.6 14.4 2403 24.2 58.9 80.1 1CO.9 117.0 126.2 133.2 134.7 130.6 121.3 122.1 127.4 126.6 122.4 119.7 113.5 99.7 95.7 65.7 71.0 60.7 47.9 32.9 21.8 32C9 34.6 55.7 73.5 59.S 99.1 108.6 110.6 114.8 110.2 100.1 104.1 103.5 1C6.8 106.0 102.7 97.4 85.2 80.4 73.1 58.9 51.4 38.7 26.0- 15.6
'-"* 46.5 75.1 93.9 111.9 122.4 124.7 122.8 124.9 119.4 106.3 109.2 107.0 100.1 94.6 S8.3 82.3 75.3 73.6 66.6 56.6 43.5 36.3 24.9 14.7
- :,. 9 16.5 29.1 40.0 51.1 61.1 70.3 79.3 94.3 107.2 111.7 110.9 100.9 e2.,
92.7 85.1 78.5 72.4 65.7 61.3 56.9 47.1 42.6 32.6 23.5 15.4 -
--*' 41.5 64.1 20.3 99.7 109.9 117.3 124.2 133.6 120.9 115.3 113.5 107.3 96.3 93.S 86.1 82.3 76.3 71.0 63.6 -54.6 47.0 35.9 24.0 13.4 1617 47.5 71.1 99.7 107.3 116.0 120.5 123.3 125.6 116.7 111.9 110.7 105.6 -
95.6 95.5 90.5 39.0 36.0 89.4 85.0 72.2 62.2 47.0 31.5 15.5 Figure 3.7 Typical set of operating data. Axial TIP distribution are shown here for seven of the /-1 detectors.
18 u
Table 4.1 Quad Cities 1 Burn Step Information for Cycle 1 Exposure Interval Control Rod Reactor Data Sequence From Data Set No.
(mwd /t)
T 0 to 247 A 1 247 to 646 A 2 646 to 800 A 3 l
800 to 954 B 3 954 to 1,334 8 4 1,334 to 2,031 . B 5 2,031 to 2,474 8 5 2,474 to 2,8C4 A 6 2,891 to 3,401 A 6 3,401 to 3,480 8 7 3,480 to 3,696 B 8 3,696 ta 4,297 B 9 4,297 to 4,809 B 10 4,809 to 5,129 8 10 5,129 to 5,471 B 11 5,471 to 5,949 8 12 5,949 to 6,175 A 13 6,175 to 6,536 A 13 T
6,536 to 6,710 B 14 6,710 to 6,920 1 B 14 6,920 to 6,948 A 15 6,948 to 7.239 A 16 i
I e
19
9 I I I I I I I I I I I I
~
~
SLOPE
-7 -
CORRESPONDING -
- TO RATED /
- /
g6 -
POWER OPERATION /
3 /
o "5 -
/ -
/
E _
/ EXPOSURE g @4 j ACCUMULATION
@3 -
/ FOR CYCLE I -
x /
W l 2 -
l -
4 I I I I I i I i i i i I 6 8 10 12 2 4 6 8 :O 12 2 4 6 1972 1973 1974 -
DATE Figure 4.1 Exposure Accumulation as a Function of Time for Actual Operation and Slope Showing Rate of Accumulation for Continuous Operation at Rated Conditions f
i k $
,- s_
Af ter the release of Reference 1 there have been corrections to the oper-ating data. These corrections have already been incorporated in our calcula-tions. However, at a recent ARMP Users Festing cencern was expressed by var-ious workers about the consistency of certain data sets. Our approach to this problem has been to continue to regard the data reported in Reference 1 as correct, except for specific corrections communicated to us by EPRI, which as
. mentioned above are reflected in our work.
4.1 In-Core Detectors The locations of the 41 in-core detectors is shown in Figure 3.6. These detectors, also known as Traversing In-Core Probes (TIPS), are arranged so that 36 of them ,orm pairs. Each member of a pair is located on opposite sides of the NE-SW core diagonal. Five of the detectors are positioned on the diagonal itself. By virtue of their locations with respect to the control rods and to the Rymmetric loading of the fuel, the 36 (18 pairst TIPS in ad-dition to measuring the axial power distribution of the four-bundle groups, provide a basis for consistency in the TIP responses: the members of every pair located on opposite sides of the NE-SW diagonal are expected to yield reasonably similar distributions. This point is clarified below.
In the coordinate system of the Quad Cities core map a detector pair is represented by the coordinates (I,J) and (J-1, I+1). Figure 4-2 shows the core map with the detector locations.
Before measurements are made with the in-core detectors, the latter are cross cal ib rated. The calibration is acco,plished by bringing different TIP's into the same hole, called the Common Hole, and adjusting the gains of the respective amplifiers until the same power distribution is seen by each of the probes. This method ensures that the voltage output of the detectors will be consistent at the locations of the symmetric pairs. Any deviaton (beyond that expected statistically) in the power distributione, between the members of the pairs, therefore, will not be due to the detector itself. It may be due to differences in the way the detectors are positioned relative to the sur-rounding fuel bundles or to asymmetries in the core that have not been ac-counted for (fuel loading, control rods, local operating history).
4.2 N0DE-B tb rralization The Guad Cities 1 core is unique among commercial SWR's in the amount of operating data made available to interested workers. Cperating data, includ-ing axial power distributions sampled at 41 locations, were collected at 16 different exposure levels throughout Cycle 1.
We wish to emphasize that, having matched as closely as practically pos-sible the first available statepoint (247 mwd /t into Cycle 1), with the ex-
_ ception of the operating data, all input parameters have been kept constant for the entire cycle.
Since a considerable amount of measured data were available for each individual detector at narrowly spaced exposure points, a program called TIP was developed to evaluate, analyze, compare and plot the two distributions:
measured and calculated. Both individual detector and core average analyses 21
l l 1 l ll lIl 57 4 '
I I i iT iP i i Tt i i i ll l l l 1 i l l l l l 1 ii i i l i i l I i i i i l I I i i I i l i i/l 49 I '
. I1! l m Ii1l l l1lii 1A I ei, l i iTi i i Ti l I/T i t ,
i 11 1 Iii i lil i l l l s/l I I I I I i 1 1 I l i J l l I l i i i i i I/l i I I i i I
,, 1 i 1I ii ! 1 1I I I1I i i 1/i l i ! I I I i l l I ITi i i I fTl i iTI i 1/i i i i i i i ! i i
!! l l l l l l 4 l l l 1 I i (/i l 1 I I ! I i i i i l a
il l l l l l l 1 1 I I I I I/l i I l D I I i i i i I 33
$ 1I II I'OI I Il' ' ' 1' ' ' ' ' 1!
' II il Il l l?iI lAT2i3i415IsI71el9' iolie l'2! 3Italis
!I l l I i lI i i I/IT\j l Il i j i ! I i i I i I I i i i 'l I I I I I A 21 N ii i i i i I4 '
i i 23 II Iil I ili i I N1 1 31 i N 1 1ii I i i i i 1
ii i lIi i IM I i 41 I I NTI i l' I I i i i
l l l 1 M I/6 i i i si i l i IN I I I l i i I i i i I i t/l i i i I el i I I I IN l I I I I I i , i 1/l i i 1I 7 1i I i 1 IN l 11 I i
'7 i i I VIi l i i '
e_ [ lIIl IN i l l i i l/l '
i i I 9 I Ii l i IN l i i l t/l I i I
' r o' -1 Ii i i i l\1 i j 9 ^
' " ^ '
/ l l I i i 2' I i iIII IP \
l l I i i3 i i i i ii t
i I e4 I I I i l l l is! I l ! l g e is 24 32 4e 48 56 I-~
Figure 4.2 Quad Cities 1 Core Map showing Detector Locations.
Circles around detectors indicate locations at which -
comparisons in pcwer distributions are she,vn in this report.
22
were perfomed. A fitting index was developed which provides a basis for com-parison between measured and simulated power distributions. The index, based on the root-mean-squares (ms) of the deviations of the calculated from the measured nodal powers, is given by the following expression where i and j de-note the axial node and the detector, respectively.
~ -
41 12 h I
1 1 (Mij - C ij)2
=77 E j=1 I
i = 1 -
where i and j denote the axial node and the detector, respectively; M and C !
represent the measured and calculated TIP readings.
It was stated in an earlier section that N00E-B ca;culates the axial power distribution at 12 axial nodes. In the TIP measurements the four-bundle power is sampled at 24 nodes. Calculated core average axial as well as individual detector responses along with their corresponding measured dis-tributions are given and discussed in the following sections. A description of the TIP pr wram is given in Appendix B.
4.3 Selection of Albedoes The performance of N0DE-B, based on comparisons between calculated and measured TIP distributions, has been evaluated not at the beginning of the cy-cle but at the exposure level of 247 mwd /t, since the first measured power distribution was sampled at that level. An extensive series of calculations was made in which albedoes were varied over a broad range. Of the three types of albedoes required for the NODE-B input (top, bottom and horizontal), two were kept constant while the third was varied. Each type thus was allowed to vary so that the deviation between calculations and measurements could be minimized. An optimum set of albedoes was obtained in this manner at the ex-posure of 247 mwd /t. This set of albedoes along with all other assembly and core constants constituted the input set characteristic of the Cycle 1 core.
l l 4.4 Cycle 1 Eigenvalue Figure 4.3 shows the fluctuations of the core eigenvalue during Cycle 1.
This plot shows a decrease in the eigenvalue in the early part of the cycle from 1.011 to 1.004, a tendency towards stabilizing first around 1.0065, then around 1.0085 in its midpart, and, finally after an exposure of 5500 mwd /t it shows an upward trend for the remaining portion of the cycle. While errors in the data reported at the exposure levels of 247, 3480 and possibly 7239 mwd /t may not be ruled out, we note that the general behavior of the eigenvalue re-l sembles the trend obtained from the analysis of the initial cycle of 12 l
- BWR-4's 6 , for which instrument vibration problems led to the plugging of l holes at midcycle. Of course, in the case of Quad Cities 1, a BWR-3 plant, there have been no vibration problems, and, consequently, no changes in the design of the inlet channel flow systen.
23
t i
6 O
_ O O
co O
_ O O '
W e
, =
e E <
m a F- -
N o Oo O
e o
O S "
em
-O T5 -
C "u
h v
M w 4 e
O5 E
_ Oo a Oh c N w i
i l
}
l l
I I I l :
D O D O -
O O l O
- O -
O -
OO W 24
Table 4.2 lists the important Cycle i statepoint data along with calcu-lated eigenvalues, The notch inventory histogram during the course of Cycle 1 is shown in Figure 4.a along with the calculated eigenvalues. Periods of op-eration with control rod patterns in the A or B sequence are indicated in the upper part of the figure. One or more exposure steps, each corresponding to a specific set of operating conditions, have been evaluated for every interval of operation with a fixed control rod withdrawal sequence, indicated by the constant number of notches inserted.
. If the reactor were operated at the rated power level and flow and no
, other changes existed in the operating characteristics, the shape of the notch inventory curvd would translate directly to the shape of the excess reactivity available in the core. While the notch inventory histogram and the eigenvalue plot shown in Figure 4.4 reflect changes in operating characteristics inclu-ding powe*; and flows, general trends of the excess reactivity curve can still be discern d. In particuly, there may be a correlation between the increase in reactivity at end-of-cycle and the withdrawal of control rods. Figures 4.5 and 4.6 show the power and flow variations, respectively, along with the eigenvalue. The sharp drop in the calculated eigenvalue at Q. proximately 3500 mwd /t is noted. If the data are correct, the low eigen-value here, the result of the calculation of an exposure interval of only 79 mwd /t during a period when the power was reduced to 87% through the use of deep rods, may indicate that N0DE-B, as is the case with other BWR simulator codes, cannot produce consistent results unless cases where there are signi-ficant changes in the operating conditions are followed in great detail. It has not been possible to verify the validity of the operating data. On the basis of the infonnation given, it appears that the reactor had been operating under the stated conditions for a period of 5.5 days prior to the collection at operating data. The consistency of the data vis-a-vis the performance of ARfiP is dis-cussed in Section 4.5. 4.5 Power Distributions Having established the B-constants and core input parameters, relatively minor adjustments of the power distributions can be made by optimizing verti-cal and horizontal albedoes which primarily affect the power shape at the up-per and lower nodes, and, to some extent, the power in the peripheral buncles.
- As mentioned earlier the setting of the albedoes was made in an effort to match the calculated and measured powers. Because of the complexity of match-ing powers at each of the 41 monitors, the albedo optimization was made on the basis of the axial core average distribution. The selected albedo set yielded the lowest nns deviations - a measure of the goodness of fit - at the first available exposure point in the cycle.
It is recalled here that, once established, all NODE-B input parameters were kept constant during Cycle 1 and no further attempts were made to re-normalize the parameter set. The measured and calculated core average axial power distributions for each exposure level at which operating data sets were reported, are shown in Figures 4.7 through 4.10. In these plots, M and C de-note measured and calculated power respectively. The steady state exposure 25
TABLE 4.2 CYCLE 1 STATEPOINT DATA AND CALCULATED Keff Exposure Control k,g Interval Exposure Pcwer Ficw Pressure Rod (Wd/t) Step (%of (M1b/hr) (Psia) Sequence _Frem To (Wd/t) Rated) Notches in 0.0 247.0 247.0 87.017 84.39 1036.69 lb6 1.010997 247.0 646.0 399.0 89.735 99.61 1025.36 2b2 1.007526 g 646.0 800.0 154.0 89.214 94.65 1025.01 2016 1.c05188 800.0 1334.0 534.0 87.495 97.58 1039.41 2f92 1.004175 1334.0 2474.0 2x570.0 97.571 97.97 1044.75 2d56 1.006615 2474.0 3401.0 2x463.5 96.133 95.3 1039.04 2156 1.006291 3401.0 3480.0 79.0 87.495 94.84 , 1021.23 2[36 , 1.002678 B480.0 3696.0 216.0 , 92.393 94.72 1032.24 2fl0 1.008669 I 3696.0 4297.0 601.0 94.663 92.93 1030.52 2[90 1.008694 1 4297.0 1809.0 512.0 93.070 90.95 1020.02 2[54 1.008582 4809.0 5471.0 662.0 80.207 73.5 1010.17 2[04 1.006538 5471.0 5949.0 478.0 88.630 97.89 1029.82 2d64 l1.010284
^
5949.0 5175.0 226.0 88.013 94.14 1025.15 1892 1.012885 A&B 5175.0 5710.0 535.0 90.283 95.62 1027.61 1924 1.012521 36A 5710.0 5948.0 238.0 87.107 97.73 1016.16 1840 1.012543 A 5948.0 7239.0 291.0 87.750 95.94 1025.64 1688 1.015954 l _ __. _ . 26._ _ ._.
> +A+
2 00
+- A-+ < B > < --- A -> B B-A-1.015 - -
2200
~
2000 0 L N 1800 $ l.OIO - > p 9 NOTCHES - 1600 - INSERTED u;
% b t-l.OO5 -
N @ keff , A' CONTROL d ROD B
. SEQUENCE I.OOO >
2000 4000 6000 8000 ! EXPOSURE WD/T) Figure 4.4 flotch Inventory llistogram and Eigenvalue
n keff vs EXPOSURE n (keff AT END OF EXPOSURE STEP) - 10 0 a . 1.015 a , a - 90 POWER - 80
. I.OIO -
S 2 2 9 $ 3 o O_ 1.005 - keff b 1 1.000 ' ' ' ' ' > 2000 / 4000 6000 8000 ' EXPOSURE (MWD /T)) Figure 4.5 Power Histogram and Eigenvalue - t
(J4/4llAl) Mold O O o O O O O N a
# i i i i O
_ O O CD
, O -
_J _ O 8 O % W E E, G
?
P e
$ 6 Og O 3, sa J
1 '*" O3 f - -o WL 5 2 _ w e. _ 8 Ok E
- - _ Ow &
O E
~
(5 m I f I 4 C O o O O O O O O O
$$9 y 29
. =
g A
. . 4
. - . c ,
i1 f r j
- i! Ir f
//
=
<i a *
- v E // .g v E W
/ 8 W/
E n 1' s / g .
,i 2
~. /
//
- g ./ s .s.
/y ..:
</
, = , ; /
a ~=g /d ss # e s -
.s ,l //
,,- 2 - r .
- I j i h# -g a
=,
1
, .i -i- < m
.: e 3 - . n (e \
s' a , [ *5 o - , 1 34 - u
! . 5 -
; --)
9 \
.a 8
=
D
$. \,; ,o 3 .l . -
O
- 3 - 4 ,\ .., t
[ *Q , k
- , - . , 1 , .
u.
- : ' 5, g ** m
^\ y \ p.
_1 I A
. a.
i
\% a. u y
8
=. %s ,
2 o g 5
%6 - p N G k '
, a s cc
,.2 ,, ,.3 .. .. -, -- - - - -- -. .4 ,, , ; -- -- - =
G C a k
- g O 1
1 i
.s i.
U
., / -
. / t. ~
I! $ '
) //
** O" i
i i; C
/
f[
/
l, "E 1 y g gj
/4
//
-//
I, et h 45 t see G %T
' MM d
g g' t5 N' 8 ..g QM 2 / e4 H
] g
' *{ 5 b
e * ", 8 ,
- * ,/
j o "O -i $' = ;9 g 5 si a,, e-< C ~o .: . ** * ~- jf ; QQ e, j . g j Q
-i- 4
\. 5- ,d's ,
- ,. ,o O
. s. 1 9' C CO
*2
}'
i 5 :. t
; i e,;
ed 4 1 , [ c m 3 c' '8 w 4 $ #
,fg *O @ $ 1 *2]
{d g f' 2 T G 'o l
*. k a
- 2. - W ' T I
- l- l g
- $h .3
- Ik b !
r',
,. ,,* I %
- gg
- ' t at* 1 i ;
d t
- 4 ." i 3 Kf
, =
j, j x 'n Ii ;8- i l ,? 3 5!'.
? a! - S o
~;
*e l! W j s' :, i 3 *
's J 5 ,
a,, *. r Z i E
- Qu s E Il ,- G s t
~ M .
3 U t I- !
=- "h. . .
' , ;- ec m
=
3 g'st
! ,8 4 ~NN *.,
4g .- ;
- a l
5 I k E ,!8
- g ew m? #* * ** " * ' ' "'
[$ yd,T;, "" "" " aw ew xe: 2 e. i
.. . ,4',.*zse er.m w z--
30
f 8 C & E F e . . e * { e e' Y a ,W S s 5 ,f .tg
- s ( 8
. - 4 I e s w
-o f r +/
/)'
g 3 JW 8 Y C
*t y'
u E //a 8 E 9 i *
- l s'; 'n $ # 9 i, l jj .s A il 't 2 '
? .*
[ j Jk
's o /, a i
- j
$l s;
/ te t
3
//
4i
't 1- . .
n e 5i w 's r 8 e s [ y - *1 E g" l I
/s si ! + 1 u 1 8 9, 1 8 8v g
- a. a.
,r .e. ,
a
= -
a / e= 1
; .f; * /* c a
2 4 . e
.e
'a
**j i, (i 3 "
+/
f4 j 9 n w o
-) l u
[ /! ,
? (
- l Af y l $ i h I
- r. ( ..
., 5. : 2 / ~ .e w p
, j! s- !
g i 4\
- u a e 2, , o a' xs m y s' ;g 1 o a g
,3 c
. o ,.
. , ; x -
I i- E 4
*\
! "a
(\ y 3 !,
-g s c ss
- i N.
+ g,h, Ng .
3 g% I :- N*w\ A O I. s gN a
%.s -
*. g s = y aw e. ma
\
ae af
's m as aw a se sw ** **
\ *' t *f 8
4 G sw yw aa x w. a sia em pits ;e em DI.s w >
*C Q
ku CN s UT ~ s 2 g NN C
= y a wc i = W 8 i
- a m 3l ,[/ a 3g .a c 0
! e g 5 r 5 f 5 09
- l v r / s -
u r ,sa ug i ?' i cc H
? / s 3 e 3o 4 / '
' A -
t U Co y , 4 o < H4 i f f Cm 3 j, e a j g y l, s m l . ,a
..l L' #; y E t e-4 p 5 4,[ z
- 1 CC is E ~ s c4 I h I Oh ! O 1
j lW
- s
- 9 344 0
; 1i, "Tj $- .ft
+7] 3N me c
a {' y d
+s*
8% T - . o 5 g;
.r*
y CN o { - n i7 % 2 6 $? I
?E
, 3 C'
. .a
- 5. 2 a 4
..a M.
ss a e a o r ds\s=
$5, s 8, \ g Q
=
T E a t. l g
*\sa \
. u C
ec
, a l . A\ w C \ i,. E '\ g ..! 4 n } . ah
; ! 4 \, g ; ~1e
'= s l,
N,
]
t, l -x = = 2* 2 tse a ha 2 hi w we W #- #h au af F ute aw es est w he e or ee m& 9m r# a m P i .e 'id em Pl.v'3e 31 b
8 I a 8 8
's a g a
( = F /
/* 4
{ , iI
=
g
-!I. 5 i
/ 8 8
WE a u E / t
) #
1 -9 1 1 l /
/
s y
, 7, e
t 5$ r ::: *
// l 55 s
/t a
A
- 41 g 'b \
? 5 i e 4 s k
- O 4 , 41 -
1 1 s1 1 I*J h, a s 1
<t e
- \ m
=
o e E aa ,s* ; =E 2 *
'= ::
s* c O w
* * \
a W g - t : ~4 0 t I a v 4 g g a 8
* .c
; d +
" $ k $ 5* \ N 13 <\ , 4 ',R e
; , a s o\ s -
r j qg. -
$ r 3 c l- \\ =
s E N e
- - x\.
- 3 o a o 3 h *g -
8
\ ,
- 4 I
%w e eo 8 8
=# m
.w .w
. . . . 74 ,,, ,7; .. .. .e == ~~ ~ = s' .g g,i;, == ==
g cl 4 e Qu a e UN I s g T
, / s s MW+ E e . , ar . /w
- s. / ,
; )r
/
i f 44mcn s u E I 8 < [ s v t j 8 3 ) um.
- . ec 6
~
T i / s TC 2 y 5H . c . 3, r a z
~ r~ # $ / '
y [ *s 8 d#m 8 5 . 0
# T
- 5 s t . .: . 5 CO g ,
" s s.
CC t co T f s, j s/ a TV U l a [ I
)h $ )5 fI I
J,f s'
- 1 o
E si i ::
, ae
& = ~ ,' -$ <N
$ h h f
4 - W s d 3 + / l 5 -l i ; t. . 4 . o.
$.3
- i f d, 4 g a 9s -
e . e* j- 1
\
\ s
? !
\j ,8 G
w 4 h "N\ .s .N *
-8
-[ l h'
m i a
,,_u g -
Q
- N= 3 A N
N 8
= >a ew * * * * ** =*
mm sw *M 3* I *e?k mw m# a as aw ee s-4 ag gyj, ah ee I k_
4 8 A s
/ ,
!2! -}
e / j/
+=
- s 4 u E ) g
,?
2 5 ,,$ 4
} g S 4
$ i r : $
h5
- ; }9 .s, u C
)!
' 4 e C a I I 3% o 5 s s
- a w M
! T 3
I.\ 5 4 4 I g b 4 M
$ E \ .s y /p. a3
* . t 4 g M
- 3 3 $
+
\*l =
sr d f / t I 1 i , t ' u E .g g e % \ g / 6 # g E 8 4, 4
- \ e e /
A e / a o A ,i t e e,c
* =
$ "s N ; ! il .:
s l .a Is .i ,
. . . . e. . . .
,.2 g,v, ..
g~3g 5,, u o w
]*8 U T
[8i .f,
=
r =- 4/ =.
}yd wU e
s s
\. ~
,/. s -,I e i e2 o
; e e w
/ =
- 51. - \, ,
. a co
-! f f I 4 Q<
r v
/ # s q e* a \ se u g [8 2
\ "s* 3@
/ U l W t ^r r ;
I g *k, -t c ,/ / 4 ' s h
=i
\* g dCec t
Y 3 / ~
- o /
's 0
; W e g 1.. m 7
., e/ -
- c5 5 fr s .
a o ~ s[ $ . @
!$ I a
\- \, laum s v ,
~f / zw e .e a eis a me zg aw .
=s ae e d' ?
, 4 e e@
a j i
Tl $
A 5 Y , 4 r
- 4 \ Y I C
, I .
~
1 g J / <
- e a
* }
- "t- i .
E {t 2 3- 8 e j 3 9 7. j f ' s' 4
, r a *
.i
*\ e t '\. ".
't N I f \
-
- x *a=
I ?
\\
- 8 a , s9 ** ** *#
x m .a sea a-w 33 i
interval at the endpoint of which the data apply is also given. One notes in these plots the 24 measured points as opposed to the calculated 12 points. These figures show that in the first half of the cycle the agreement be-tween measurements and calculations is, in general, very good. In the last third of the cycle there is a tendency for the calculation to overpredict the power in the central nodes by an amount ranging from 12%, first, to 25%, towards the end of the cycle. Comparisons between measured and calculated individual TIP traces are giver. in figures 4.11 through 4.15 for five different exposure levels. The - agreement in the power distributions shown in these figures is considered to be typical throughout the cycle and throughout the core. The best as well as worst agreements between measurements and calculations are represented in this set. The four detectors for which results are shown are the two central detectors 24-25 and 24-33 and two peripheral detectors 48-49 and 32-57 (see Figure 4.2). The five exposure points are as follows: 247, 800, 3401, 4809 and 6710 mwd /t. Very good agreement is obtained in both the central and peripheral detectors in the first half of th'. cycle. As exposure is increased there is a tendency for the calculations to overpredict the central nodes of the central detectors, but this overprediction is limited to below 25%. While it is difficult to account for the apparent disagreements between ARMP and the measured data observed in specific regions of the core, or.c must keep in mind the limitations of the modelling inherent in the codes used as well as the limitations associated with the available data. Some of these limitations are discussed in the following section. 4.6 Modelling and Data Limitations The methods used in the ARMP codes are ' established and accepted by the roactor canmunity as standard calculationa mols. Large volumes of data are generated at various stages of the calculat... 1 process so that nuclear
- and thermal hydraulic effects may be represented a'. 'aithfully as possible.
Core eigenvalue, power-moderator density convergence, 'ower, exposure and void distributions result from a set of input operatin3 'nd physical conditions. To assess the qual!ty of the results presented in this .. apter, one must consider the adequacy of the representation, in the codes, of the many complex phenomena characterizing the steady state operation of a power reactor. The nuclear characteristics of the fuel are represented as a function of
- the relative moderator density at each node in the core. Correct determina-l tion of the moderator density rests on the correct evaluation of the nodal power, channel flow rates and void generation. -
While every effort is made to accurately represent the fuel assemDly core topography as well as physical conditions, accurate prediction of the local power in the vicinity of a control blade remains a difficult task when thermal hydraulic feedback is to be accurately modelled. l 34
8 9 t t 4 s
- e
- I
- g r . ye a
' I '
5 v W
,- *t i "s {t e
,, *t
- / e s w/ l ,
e s I . . l
'e C y at . y g et Ig
+y .,
4 l g I E I l l e i
; -
- 1 - 4 i
- ~ e e g a e
* / ?* e *s
- l
. -a * ! e
- e 4 I y' 's et I e /
es a y l '
- u ,. ,
i y l s a
- i s a
.'t,. e 4
!l .
,,8
,/ cm s si ,
.' .s. ,
.g 5 3 ! d I t l 4 w a u. l ;gj 3 f, l' ,j ' g ,- >
e- : . '
.g 2 w
?t
= \ ./ T
* -; l w 6 w C
, 1 4
4 ! i 4 g j ./ :. L 9 ; y c' t4 i , o 7
*l ai $
5 ..5 ag- -g 4.
;- Y- s s '. =
T y +. a\ g - a C I -l G .h I I 2 [ o E "h 13 s aN , w
-E 9 7 I .x .. M
- I
'h -
[. ,t - k I It C Sh g f *. 3 .x .. k u a - i a l l
= >% L1
* ., = .,
a :ss w ees eaa a s. mz a w- ea a- a af o ne ww m .ps a s. ee as aa a? eMe' M:.s le .e *Me le 4 s 'ie W Q 3 o 1 't 4 s i s W Iaf a I= s Y
/ !s
*t M U l
s I ( )~ F7 e tN g- E / E // GT l V t w E / t .E
*t M3 CA Ls E / a p l M af
/' /4 f Ch U4 r 3 -
d/ 9
~" .1 ~
J*
/ /'
I > f
~*
//
s/ t' I
!s bUc 4 s ' s te T o / s ~o !
C Li
'2 5
cj S 10 f g 9 O l
? !/ s I
.I s J ef Tu
// 3 8 G U y' ,
p c (- ,
~
4 3, c. s, f 4' .;$ e
^
j$ e 2M w @
- r I d.
I QM I i s; Y I 3g J \ a *r
,g; A
(g e o as +3 y - . t* g - 4 m S q M 0 $ g\ L $ w . d
!k i\
! kc ft. -
.e 4
e i e s, , ..x ,. e % Q l l 8,
'h 3 ' s, y j o,
?,
g y I s q . I st ec . r a m r aj s. s x i = 4,. r A
- V a
t ,. i
-3 I
! 'a'.s i
s 1 fx-n [ s 3 n f ! l = - 3 i a, 3 . l i
. w\ 1 '
\ l 1 8 .g 3 )q l ew a vae va o.a =h) ** se as eu a# aw n we se o a aw x ., aa w4 es a m .*
ene' I4 f e9I k si"',e , ta i st ' ie l 35 l
8 I t t 5 8 s e e * { s y g = , s 3 s {n /. *t l t . at j sa = l C
- r s ! e
- s E/ 9 8 9
. C at
. = *1
- s. t 4 /J i , 4 1 e e g ,i e e
; s
*3 *t e
- e 8 o
- e , e
~
s 3 a g
$ / *g f i *f *
- e
_. m 2 I # . s /
,4
,e
( F ' s J s f 2 3 5
- / *1 ( 8 c
- y s
/
- g? .
2 . a e o m
* . .a n .
t* 5 ! g ,
/
"a Y, !
t
*: 3 I i .
E 5 -3. 's I e
= w,
= e-
*a og . e,
/ *t eg =
{.
- t {
-{
a p.
; f :. w ,
; (i 4/ w I E-5 8
2 t.a f ?* f , s C g,
.- ;. o.
, ;_i ._,
.. .> : + ' c e a - a g s
= at
- a c.
N *. _r ,.
!. r_ a e .
- s a ,
r a- a. e
.s
^
- s
- a .5
.a .
*s , w
- *N : : -
a a
\=N-. *.,
; *. m z
S ,-
.x = =
, i a w sw aw su em af mw sw asa m m. rw am mm of U m e4
.m *~ pe..r;. as
.s w3% w i. 3. 3 o
t
.C
.' , y
't 8 l ,s ,,,
. .I ,
-s -
. v e ; ; . e 0%
! ; s /s' *= i ; ; *e
- . </ i - , E "c a-"=!!
=
! r V ; 1 r ,o O W/ 'S t gj S *
. C
(/
// *t I
t w c E
/j *t Uh
.g j ; //
..3 j i U
M G />/ 3 I 1 ! s ., g
- Q t '8 ./ 3
- 8/ 6 2 , s' g 2
? ', C C3
// *s i +e b i
- 1
/,s , a o mC g + j y CI s i GW
- , .s ' .e, :. ,
( ,a,
. e. b. u i <
i za
/*-
i * .. ! cQ e- 4-a
** l 4 ej g aB.. / 8 9, a .. as-o 2 g
.;N 2 h, s
Yg N I i ~ < i I il ' n
= ci a ,5g s 5q s e,i m 4 -' s a :
s I. e \ d. 4, f ; ' se a r
- :: s s g .
- e. . *. e. NN * .a ,
.- 7' s e
~, & ,,,
A A n 4 A
~, !
-i Ca.o h I I $ ,
g T *e 7 , * .O 2 I. a f a: a s ; , a ir . t a g , a , s a
- 4 E 4 N sE g ; a .,
; N - *. 3* y\ \ *.
- xa , N a M \
E g a 'g s as aw an av ss um m. s? rw sw saa em x *-
- s- m- m zu af
.x - .W. } t' .se e s-:4 D .; ae 36
e 4 1 s I s '4 s # I i * '* s 9 {
- s 8 J, 8 *t s 3 *a
}. $r
~
J j e e _ e ., , E 9 s 't g
. . *t -
w E et 2 a s; e i e i 5 le I
. e- .a e ;g
~g *t I et 8 e s/
2 y s
- s
. p a 2 s' lg
~
; -s K 's .e s' '
E ; E *{ .J i d , 9 2 l 8 [8 5 / *t - r *r
- I '
. g g 4 l 4 $\ )
s g* ! d i s a 3, (. a
.~
's S, 5:
t a f n: u
& I, J T & il W f e e. 4 o e' s:
r - l
.i 9 j
- = - , 8{
*
- s j
! je :
! (i w. [ ! s i k
e : . -e
* : s- .*
I' ls .iI* O
- _i*91 C
8
- _i 2 E j .i 81 l
w i Cj 4 58 7 I e y 0a e 1 g
! i s ;# C E I; * *
'a 5 E W H
s 1 e d,- i n g! !w I a C i a i C e\ ! 4 W i
\s(
*5 ; *. w A
I ag . Edw W { v j a
- t. *a. %* .m
.a 3 x f 8 5 -
A, ; 5 %
'a i Q l *N
{ a
! (8 % 8 54 %
ae ae m mr aw 3 s.: a se r* wp 3m au a ses ~w n oia e s. aw aw as ea ot em 3* t.s k em M ' .s'h 3g
,o P-8 A
e 4 'D C3
" .D 8 A M 8
4 I g < w I s t C l, !a s 3 // s$'
*e I
s l
; s y
[ !g 3 c2 uu t i
- EI 8'
l - E e - CO
! i r j,- Mw
. =' CU i - e . +t . m c ,t .i s
- i. ua y . e- i 2 -u l w i ] !
Co I w
- s . I, OC
, .'/ ] ., I e l' e ' M&
~
4 * '
^.
- s. C C 8 l
- 43 3
, t
/p .' s,
~ ; < te ~- -a g 'i f I j 3 a e. l J'e, ' . "o >4 j- ;
s 's i f, 1 3 k ar4
/: ?! .
l / 3T
's j ,/
.t, j - e ;a c J/ , >=4
'S w f
f s w
- e. g+
-? *:= m *-
.i93 m
~
s' ** ,f 5 f ,' *2 3 u *5
=
1,
- e. y l t t ( = ):
,8 I
1,e= cm I -I o 5 g I a > -a +1 r - /
.s 3 2, .s. i
. ,e. ' : 4
- q
,i,
- / ,
=
, J ji ,t Y /e .' g
*. y
;- .j !* ; g 3/ 9
; :4 ! a e s ,* !
i 3' 4 e a d '
- L i r! >
, d $ ( 3 "4
f
.- i jl \\x*. ! E I a
> t u I b 1-i g l
- Ahv. !g e *\ !
O i , 5 1 e
\ 's d * '
%'4sN 8
?. .*
~ 3 i A S f
- i I
I ,g 2* $s w m ra a s.
,4 p, y 4s s. =r g ,_ ,,, g ,,, , ,, , . , ,f ers4 P L.s .s 3I
8 9
-1 1 i e .
,= :g 1 I
a; r e i t
# / le ! g 't I ' e ) *
]
e
,s j 'd
,I
- s E si :n
= s E 't 4
I' er l } t i e 'l j e f
,, i e '. 4
.< $ t a
-j 4
a f , 9,3
-e .. ./ -.
. =,, ! .
*r l Y f ,
4 .g i t * * { ; **
.. /
g . e +
- t. . 4 v J f
.k *l 8
<r 4 rt b* 4 i
a 's.
-ai] ei d
\
j' !
- s
[ r !I,
.8)
O g! / < *t= ? 4 ;-
~2
- s >
g 2 g 5 2s )' J l
=
,f e
O 5t. ,8 i4% a
, q' g*
.g I
{ "I t .
+3 8 8
j
~3 $ ;I 4 f 0 i
5 t Es
- ; g, e I
( S :a ' t 4 7
- 4:
, gi
?
g
$ !* T '
> b e C' * [ k.
- I C
$ $ 5' n l %
F *t 8'
.f i ,
,, ei s + s. T a g =
j { '! *\ E 3 6
'd g O
- s a "
g : g
-k i .*
6, . . 4 g g e.d.
. g - . .
1 _ '4
-; .a 4- .T.
m
==
- t a s. a'-
( i 3 g I ' "g
"\ .l s
O 5 i
*J NN. 4
'!, w 2
E '. g O e= = we " *~ * ** ** *
=n am,
.e =N p :.re'so. ea ee m? .d je[v";e L **,
b *% 35
.O E S 8 -O s
.g .t CO
, s == CO
+
a / je !' s / == M *@
* ,8 / fB * * *C i
I s j $ I F/
// +E a
l s j I I 6 p/ +3 i e MC M
.l - r . s' I - F / ( c s/ to y ls *
's C // *t u E C b 1 '.
l
.= / t l' l ft
- o y Ja o C ed 4
i #i }S 8/ l9
, U T.)
I / *f // *t -Q
? l' < ? E! $ C ed sr J l t.; o -R < 'e 's -R
k I, g I, N
.\ **= **
l *T= 0 "O T, $$ r g 6 2 f Y, .$ -> 1 g 2 ce **
~= ==
& E-I 4 1f E ,t 4 if G P"*
.= g ! 4 !5 s e f
,f 8 9.
-i f *t y ,3; .g z
; e * ,
? e i
- a, . .
l' : s ; . . t e ' ri A - './ 1
. 43 i= !.
$ El 8
$ kk 8 i 4
- 1-: 4 n ft * '
i S ; a 'g j o3 3 ,, G 2 y I
. f. T y !* k*
a' f -i s '. I 3 . s - ,4 I al 4 g a a == S I ' ', .
-y
- v. 4.
3 : 1 , E. % .g - E, $g
? V *. 9 -', *.
$ % f $ i N. w
- i k~'s 1 E :,
-as e anc = we a sa ar m.
.=A.
= ee ea we er w as a see ae e e- *9 aa ea af b ; .s in o m s.a. .e se 38
e s
& 2 B B
! /h Ih
! r #
/ S bh 3 r 6ll/ $
m = j l e m e f e 3 9 o / 2 4
- a e 3 a
f/ w/ e g'/ ' w // c ds g 8 3 \,'a 3 8/ s
.s
//
I: r l' . f.- \ -
- 1 ,
)4 ,
// e e. ,
a g e
/ g s a . eg s a
- s .,1 g :. J , =e y
? ? / d
\ .s*i ? 5
- si s
a, / e a w s 4
'!e\
4; m 6 4 i
\ ! ) -8 i' i N% ~
i 1 u o s a 14
- s i ;
a
) ! w j y \\
w 2 $ r a 51 , E 1- *jg\ ei
.,e $u a .
p w : u
\ 'I !
"
- W e .
w as as a we a s.a a mi e ,, e e, m e6 ea er em m ws m ois en si sem a e, ,g ,, ,p A om Phsus e m pi.eue ku Q% 3m cEO A a a
! Mc C .-4 -
. / wm Ia e
!f M j l 5r / yNg
- r ,
e s - a c g am
- m r s }o cw l MO 2 4 a a
s
- g ..
3 "o o i e e e s-g Q 2 r e p
\.
* . ,s Oa C
p. i e
- p
'3 I 's t <! t e' a A j C e4 e
- d E, w g cc
\e 3 a - .
tt N
/ QH
** * ..g" b >
8 a ' 3 'r1 h W O g /\ Tf x < c 'Oc
; - W e
. a 4 a; OM
= 3 d s' %
's8i 2
a 5 s, 4
\
a 8 v 4 i s 4 1 a : 4 m I
'l e I
.$ .\
! H.
f h_
. s j v T 2 b -
7o e
- o
?a i !
I f e y a 7 I j " r - / / r *
- I 3 9 I s N
- CO i \ "s a
\\ C s *s :
ks sa
= x o a a M
. 9 6 k ! k ' 3 I l
==
N. == a eN PI's is "" #" "# aw m ass a su a si e4 4 t l l 39
In the case of Quad Cities 1 Cycle 1 operation the performance of the ARMP modules can only be judged on the basis of the measured TIP data. Thus, CPM, THERM-B and NODE-B, the primary ARMP modules used in the BWR simulation, are collectively judged in tems of the proximity of the 24 measured nodal powers (for each of the 41 detectors spread throughout the core) to the 12 calculated axial TIP readings these codes will produce. The correctness of certain wide-ranging input paramaters can only be established from the com-parison of the measured with the calculated power. . A typical set of such input parameters includes the energy structure and size of pin mesh of the fuel bundle in CPM, loss coefficients in THERM-B and ~ the monitor response coefficients for certain control rod configurations in NODE-B. Accurate simulation of the operating history of a BWR requires the sam-pling of a large volume of operating data at as many representative exposure levels (or times) as could be effectively utilized by the code. Inspection of the daily charts showing power, flow, control rod notches and other operating data indicate frequent changes in these data. The operating data collt.cted imply that tne reactor was operating at steady state conditions far at least 48 hours before the data were taken - a good practice. However, based on the charts shown in Reference 2 it appears that operating periods characterized by varying parameters, were lumped into " steady state statepoints". The effect of such lumping has not been quantitatively evaluated. Figure 4.16 shows summaries of operating data for June and July 1973. These data are represented in the calculations by Dataset 9, collected on July 19, 1973. The inset in the above figure gives the constant reactor conditions which must be assumed in carrying out the nodal calculations. We note in this figure that in the 43 calendar days there was one shutdown which lasted for a period of less than five days. Of the remaining 38-day interval there were 5 days during which no data are available. Thus, in the 43-day period (June 6 to July 19) during which the set of constant conditions, summarized in the l figure as well as in Table 4.2, were used in NODE-8, data exist for only 33 l days . Of these 33 days, the operating conditions were constant during a peri-l od of only 18 days. It is to be noted that during 16 of the 38 days (42% of ! the time) the reactor was operated with variable conditions. The assump-tion that the reactor is operated at steady state conditions for 100% of the time, introduces a discrepancy in the c;iculations which results in a signi- ! ficant increase in the ms deviations of the calculated from the abserved power distributions. l Many of the Cycle 1 operating intervals are characterized by such incon-sistencies in the operating data. Figure 4.17 shows the variati'an of the rms l deviations of the calculated from the measured power data. The similarity be-tween this curve and the eigenvalue curve, shown in Figure 43 is noticed. REFERENCE 3 .
- 1. J. W. Herczeg, J. Lai, M. Todosow, and D. J. Diamond, " Simulation of a l
PWR First Cycle with the ARMP System," BNL-NUREG-25607, January 1979. 1 I 40
i ! L; l E 9tY3 *
. = .
e 2 , . y=,$ go%*
- - - , .. : *8t e
se
=
. g . a .
, , .e . = ,
, g
- ~ _ - - - - - _ - - _ _ g , .
g , . . g , . g , ,
" g , ,
- *" g , .
- ~ - g , .
9
- - g , .
- ,, g , .
, g , .
- h' g , .
. - - g , . .a g4a Oe g , , ,
, ~
g g , . _
- 5"
.t g
- . 'e =- *
"~ g , .
8
- - g . .
< (<,- '
~ g g
a pg s .
. n-e- '
" g . . t
- l - "
v g . , a a
' . , D
. d i -- '"
- n-e f g . . g3 r-r -
o-4>g oe g g n7 i9 t1 t ca -- g . a
= .
ry
, P. g el pu t
t n
. _ paa / g s
. OJ s f i_ . . fd
- n . { .
- C o
N.
.s 2 - on
- 9 iu l
a _ g . s 3 -
.. ee
_ l' l- - - - -
- - __ l- _i . .
i n ru i . . aJ m
"t di
/
J /l-b w-i i mr uo I t- Sf
'b W al S i . .
'F, a ps 8-i , .
5 e x 6 t.2 3- - i 1 b,73 0h5.,r2-7 4D8 oe i
~r e21 0b/ P- i , . 4
'u. a r.1l .M.- t _
i , . e
- pwF3 g - I a i , . r
- it Po 9. ni '
I
' os , .
u
,l i
, g i s92u t-I e y
, . i
_ n ~ d4 a s w .0 s.,I a. =o =w1- 4-WA 3 i i , . , F vh alS i . . ,
' e e ,, e e -
ITyf t r rl i . .
. a. 5: a( ,( u( n-i . .
~,
~ I- .
i . . , ,
. _ " i . . , ,
" i . .
1 _ 4D8 oz 7
. i . .
9 . _ g ~ i . . 4_ 7 i n
~
- o. +, i . .
t . ,
. )
. i . .
7
- . i . .
6 c i . . .aa
.. i . o
=
(
. .a i
' . I 1 n
., ;1 i i
4 . . Mi .L
*' u e. .
' mtrv i .
se _l Ni .
. ~":. .
- i
,*<o z .
'v - .f/ sw1 .- - - _ - . _ . [s i
.= .
s . , _ m , 4 y, , p a
. u m ,a 3 n . .
,5na .i"y. B 3
- i , L e
--i - u-O O
I' I I I O CO O 5 O , o - O E N 5 0 O
- - O 5 O ~
s W e= O Eo O 38 O #3 c ii
- 8'C 1
OO O> 5ga% O h %c e sv :A Ei O ~~ na O gg O . v to 5% e
= :E, "
O O
- O k e l O w N ~
~.
T C f O 5-o Q { I I l I O D O D# m - _ SW8 d2
1 REFERENCES (cont.)
- 2. N. H. Larsen, G. R. Parkos and O. Raza, " Core Design and Operating Data for Cycles 1 and 2 of Quad Cities 1," Electric Power Research Institute NP-240, November 1976.
- 3. " ARMP: Advanced Recycle Methodology Program," System Documentation, CCM-3 Part I.1, Electric Power Research Institute,1977.
- 4. A. Ahlin and M. Edenius, "The Collision Probability Module EPRI-CPM,"
ARMP: System Documentation, CCM-3 Part II.2, Electric Power Research Institute, 1977.
- 5. A. Ahlin and M. Edenius, MICBURN, ARMP System Documentation, Part II.3, i Electric Power Research Institute,1977.
- 6. "EPRI-NODE-B," ARMP System Documentation, Part II.4, Chapter 15, Electric Power Research Institute,1977.
- 7. "EPRI-THERM-B Code Description," ARMP System Documentation, Part II.4, Chapter 17, Electric Power Research Institute,1977.
- 8. R. L. Crowther, C. M. Kang, G. R. Parkos and R. A. Wolters, " Feedback of Reactor Operating Data to Nuclear Methods Development," Adva..ces in Reactor Physics, Gatlinburg, Tennessee, April 1978.
4 l l i l i-l. t l 43 i
DISTRIBUTION LIST U. S. Nuclear Regulatory Ccmmission H. Denton D. Ross M. Dunenfeld (2) L. Rubenstein - S. Fabic L. Lois 0..Fieno (7) W. Johnston Public Docurent Room - R. Minogue Bethesda Technical Library i Advisory Comittee Reactor Safeguards (16) Director, Office of Standards Cevelopment Technical Assistant, Executive Director's Office Brookhaven National Laboratory Core and Systems Code Development Group Core Performance Group t';E Associate & Deputy Chairmen Nuclear Safety Group Leaders External A. Ancona, Ancona Assoc. T. Anderson W. , D. Bel 1, EPSC M. Edenius, Studsvik W. Eich, EPRI S. Hartzell, UCC E. Lanning, NPPD R. Lee, EPRI G. Lellouche, J.PRI R. Mills , C-E R. Mosteller, S. Levy Assoc. C. Owsl ey, ENC G.. Sherwood,-GE J. Taylor, B & W e y -- ,, n , _ .y~s _ -. -- m-..Mr '-' - * '
APPEtIDIX A Pin power distributions for the Quad Cities 1 Type 1A bundle obtained from CPf! is given in Figure Al for 0, 5000, 7000,10,000 and 20,000 !!Wd/t. The burnup and isoi.opics for this bundle are given in Figure A2. m 9 O 4 9 A-1
P_03GR 1.143 Disl 33.B.UJ.I.0!Lv.Lcini
.. S.8 2. 1. 1.2 0 1.183 963 _0 t"fd/t.
405 1.1.0.9 1 2.0.4_. 1.098 . . 9. 8.5 .. 8L9 1 181 .944 .791 .789 1.15.4 1 212a . 9.6.3
.954 ..312 E.4.9- _L 0.0 2.
1 037 1.163 1.011 1.054 1.175 1.008 POWER D I S TRIBUTIOf4( W/C. o , 1;090
.965 1.C20 5,000!Gd/t
- 8 1.075 918 911 1.031 1.051 944 se79 1.031 1.075 932 .860 862 1 075 1.101 964 766 902 f.306 1.121 1,051 922 1.005 1.061 1.12o. 1.021 POWER DISTRIBUTICtf(W/CM3) 1 057
. 943 994 7,000_ fwd /t 1.044 905 960 1.009 .1.056 _.935 . 884 1.011 1.056 927 887 890 1 051 1.02G 998 .E95
.974 996 1.114 .$949.1.006 1.066 1.066 1.119* 1.019 POWE9 GIS T 4,I-3UTION ( W/CM3 ) .
.1.039 - 10.000iMd/t
. 9 -- t .982 1 027 . 9 10 .971 1.000 1 046 .933 .89L .
1.003 1 0 h.9 .945,
,903 .906 1.037 1.066 1.005 .934 .963 1.011
. 97 3 .993 1.103 1. 066 1.0.65 1. i lM
- 1.021 POWEk 0: ST2.13UT' ON ( W/ CM3) 1.033
. 962 .973 *
.99S .933 .973 20,000 igd /t
.987 1.029 .965. .934 -
.991 1.03h .972% .942 .966 '
1.009 1.030 1.014 .9,60 .368 1.020
.999 .988 1.067 1.092 1.052 1.0745 1.022 Figure A1 -
Pin Power Distributions from 0 to 20,000 lu!d/t A-2 L
'~
90 Cp ti 00 F U(L 'A S SE HOL Y B URN UP' ~CODY WilIiS'I O N' 'h 0'0"2 "C'P.E AT I0lT~0 ATE"= 4i'iC 2'0 I19 76 'EX EC'UTION" 'Oh T E h OUAD CITIIS DISHER I NITI AL DUNOL E 000 TYPE 1A 'o 702122G3040% FP OPLS BU.'Rt10P = 2 0 0 0 0. 0 0 @ B ut< !JU P IN MWO/KG , HEIGHT PER CENT OF U35 X 1. t. + 0 0 21.67 .14
... . 19. 5 7.. 19. 6 9.. 20,000 mwd /t
_ . _ . _ . . . _ _ . . . ... . 19 42 _ . . _ . 21.37 18.09 17.70 .36 .61 1. 07 _..20.72. 20.d9 16.63 17.53 . . . . . . , . . . . . . . . . , . . _ . , . . . . . ._ . . . . . . . . . 3 8 . . . . 8 4. 1. 0 1 1. 0 9 . . , , . 20.73 20.85 16.56 17.39 17.45 .33 .05 1.02 1.11 1.11
. .21.44.22.01 19. E0 to.39 16.51.19.75. . . . . . . . . . . ._ . 35 .77 . 9 5' 1. 16 1.03 ..%
20.03 20.37 22.50 21.45 21.58 22.65 20.50 .19 .40 .76 .23 .62 7 WEIGHT PEF. CENT OF U36 X 1. E + C 1 WEIGHT PER CENT OF U36 X 1.1+00 1.62 96.78
. . 1. 5 7.. 2.07 . . . , . _ . . , . . _.... _, _ _ ,_ . . . _.. _ ... _... 9 6. 9 5 96.67._ _
2.15 1.97 2.46 96.SL 96.75 56.17 2.11 2.7e 2 54 2.44 2.11 2. 7*- 2.53 2.A3 2,43 96.5.7. 96.04 96.10 96.13 2.15 2.8' 2.62 2.35 96.56 96.03 96.10 96.13 96.13 2.53 2.64 9.6. 53,,. 95. Era. 90. 0 7, 9 6. 2 0 96.09 96.D' 3* 1.57 2.09 2.86 2.77 2.78 2.67 2.10 96.88 96.58 95.'31 95.94 95,94 95.9 w -
~ ' ~ '
W .I GHT PEP. CENT OF PU39 X 1.E+C1 " HEIGHT PER CENT OF PU40 X 1.E+01
-3,12.. . . . . _ . . .
2.26
.. 3. 3 3 .. 3. 6 2 '
2 15 1.85 3.E6 3.91 L.35 ' 2.03 1. 77 1.52 3.69 4.11 4. 50 4.70 . . 2.00 1,63 1.J2 1.85 3.69 4.12 4.51 4.71 4.72 2.00 1.63 1.52 1.46 1.46
..... 3. 5 3 .3.96 4 34 .4 57..4 53 4.36 -
2.03 1.73 1.57 1. 96 1. t,2 1.5 3.43 4.30 4.'15 3.77 4 12 4 30 3.91 2.20 1.98 1.81 1.77 1. P7 1.8-WiIGHT PER CENT OF PU41 X 1.d+02 , WEIGHT PER CENT OF DU42 X 1.i+02 7 95 S.08 7.77 7.38 . ,
. . . . . , 3.98 2.73 7.81 7.22 6.26 3.39 2.24 1.30
. . . . 7.61 7 23 6.83 6.71 .
. . . . . . . _ . , . _ . . . . . . . . . . . . , , . . . . . . . , . . 3.14. 1.96 1.48, 1.29 7.64 7.25 6.9.0 6.70 6.75 , 3.15 1 9.; 1.4/ 1 27 1.26 7.91 7.33 7.11 o.13 7.02 7.29 3.43 2.20 1.Ga 1.12 1. L 9 1. 7b 9.15 7.S9 7.52 7.74 7.80 7.9E e.34 A.21 3.03 P.39 2. i'. 2.17 2.
Figure A2
'Burnup and Isotopics of Quad Cities Type 1A bundle at 20 GUd/t
APPENDIX B The TIP Program
SUMMARY
A program has been written which evaluates and analyzes the measured data _ frm TIP traces of operating BWR's and compares those data with calculations of the three-dimensional code NODE-B. The program called TIP performs the specific functions outlined in the following sections. The comparisons be-tween measurements and calculations are made only after the N0DE-B results have been run using a.nonnalization factor such that the total calculated counts is set equal to the total measured counts. The program also plots the combined as well as individual detector responses of both measured and calculated distributions. Allowance is made for the rejection of detectors that do not yield symmetric readings. A simplified block diagram of TIP's main functions is shown in Figure 81. I. MEASURED DATA The following calculations are performed with the measured data: (a) Summation of all measured nodal values of TIP traces; core aver-age reading. (b) Summation of each detector's nodal values; detector average reading. (c) Summation of all horizontal nodes yielding core axial average di stribution .
'd) Comparison of node-by-node and total detector response for those pairs of detectors (18 pairs) symmetrically located with respect to the NE-SW diagonal axis (absolute and percent).
(e) Application of a symmetry test, identification of those pairs which have yielded unsymmetric data and option for elimination from the comparison and analysis pi ocess of the " bad" pairs. The limit of acceptance is at user's option. ( f) All detectors are arranged to occupy positions in the lower right quadrant. This arrangement is made possible by the sym-metric fuel loading of the core. Those detectors which in real-ity are located throughout the upper right, left, and lower left quadrants are now " reflected" on the lower right quadrant. Thus the entire core with all 41 detectors are exactly represented. The program provides the detector coordinates in both core wide and quarter core designations. Transposition between core wide and quarter core . identification of detector pairs is also provided. B-1
II. MEASURED AND CALCULATED DATA Combined as well as individual detector comparisons are made in both absolute and relative terms. The following functions are performed with the calculated data. (a) Summation of the calculated values for each of the simulated de-tector's responses; core average reading.
. (b) Summation of each datector's nodal values; detector average reading (c) Summation of all nodes by horizontal plane yielding core axial average distribution.
Comparison between measurements and calculation are done for the fol-lowing conditions. (c) All 41 Detectors
- 1. Single detector, node by node
- 2. Single detector, integrated counts
- 3. Combined detectors responses yielding core average axial distribution.
(d) Only " Good" Detectors (Pairs failing symmetry tests are ignored)
- 1. Single detector, integrated counts
- 2. Combined good detectors responses yielding core average ax-tal distribution A fitting index, based on the square of the differences between measured and calculated values of the core average axial distribution, provides a measure of comparison between measurement and calculations.
Plots A core axial average of normalized, simulated detector response is plot-ted together with the corresponding measured distribution. These plots are made on-line and can also be put on a microfiche or 35mm film. The user has the option to request the plots of all calculated individual TIP data along [ with the corresponding measured distributions, on-line and/or fiche. l Data Handling , Measured data have been available to us in punched cards. There are 24 l axial points for each of the 41 detectors of Quad Cities 1. A complete data ! . set is available for every set of operating conditions in Cycles 1 and 2. The calculated detector responses obtained from NODE-B are catalogued on I a file ~which can be readily accessed. Selected edits from a sample job for BOL conditions of' Quad Cities 1 as well as a plot of the core axial average distribution of the measured and calculated detector responses are given in the following pages. l l l B-2 l
APPLICATIONS While developed primarily for the purpose of analyzing the measured TIP data from the Quad Cities-1 reactor and comparing these data with calculations obtained from N00E-8, the program described here, can be easily applied to any BWR and .it can be used with any of the 3-D nodal codes available at BHL. Many other functions could be added to the program to suit particular needs. e B-
~
i
~ f[
t B-3 [:-
MEASURED NODE-D NORMAll2ED ,
#
- SIMUL ATED TIP DATA CALCULATION TIP DATA I
PRO RAM ,
- i. ;
U y o y u u CORE AVERAGE. HELATIVE ME ASURED- CALCULATED CHECK OF FULL CORE TO DETECTOR AVERAGE, FITTING INDEX PAIR PLOTS OF CORE DETECTOR I/4 CORE NODE-BY- NODE PERCENT DEVIATIONS AXIAL AVERAGES PAIR SYMMETRY REDUCTION AND INDIVIDUAL COMPARISONS RMS RESPONSES figure Ill Block Otagram of TIP Program's Major functions 1 _. _ . _ ~ -
- .- -__ _. , - - - - , - - , - _ , _ _ _ ,}}