ML20054C537
| ML20054C537 | |
| Person / Time | |
|---|---|
| Site: | Big Rock Point File:Consumers Energy icon.png |
| Issue date: | 04/15/1982 |
| From: | CONSUMERS ENERGY CO. (FORMERLY CONSUMERS POWER CO.) |
| To: | |
| Shared Package | |
| ML20054C536 | List: |
| References | |
| NUDOCS 8204210271 | |
| Download: ML20054C537 (51) | |
Text
-.
s 1
BIG ROCK POINT PHYSICS METHODOLOGY REPORT l
REVISION 1 Consumers Power Company Jackson, Michigan April 15, 1982 e204210271 820415 PDR ADOCK 00000155 p
Page 1 i
i TABLE OF CONTENTS SECTION PAGE Abstract 2
1.0 Introduction 3
2.0 Lescription of the Big Rock Point Reactor 3
2.1 Physical Description 3-6 2.2 Operation and Surveillance 6-8 3.0 Physics Model 8
3.1 Overview 8 - 10 3.2 Assembly Physics Calculations 10 - 12 3.3 GROK Input Preparation 12 - 1h 3.h Description of the GROK Computer Program 14 - 2h 3.5 Peaking Factor Algorithm 2h - 27 3.6 Fluxwire Calculations 27 3.7 Thermal Hydraulic Limits 27 - 29 h.0 Uncertainty Analysis for the BRP Physics Model 29 h.1 Radial Power Distribution Uncertainty Factor 29 4.2 Axial Power Distribution Uncertainty Factor 29 - 31 h.3 Peak Heat Flux Uncertainty Factor 31 - 33 h.h MAPLHGR Uncertainty Factor 33 - 35 L.5 MCHFR Uncertainty Factor 35 - 37 h.6 Shutdown Margin 37 - 38 L.7 Void Coefficient Uncertainty Factor 39 - hh h.8 Method of Statistical Analysin kh - L8 5.0 Summary and Conclusions h8 - h9 References 50
s A
Page 2 AESTRACT The steady state calculational models used for fuel management and safety analysis of the Big Rock Point reactor are described. The application of the results to ' operation of the plant and verification of safety limits is discussed.
Error estimates are derived for the computed parameters.
i Page 3
1.0 INTRODUCTION
This report describes the steady state physics and thermal hydraulic computational models used by Consumers Power Company to support oper-ation of the Big Rock Point boiling water reactor. The methods des-cribed are employed in reload core design and safety analysis, and for periodic verification that the reactor is operating vithin prescribed limits.
The major component of the analytical model is GROK, a three-dimensional coase-mesh simulator code with thermal hydraulic feedback. This code, although undergoing many revisions, has been used for design and safety analysis of Big Rock Point since 1972.
2.0 DE3CRIPTION OF THE BIG ROCK POINT REACTOR 2.1 FHYSICAL DESCRIPTION Big Rock Point is a small commercial boiling water reactor located on the shore of Lake Michigan north of Charlevoix, Michigan. Big Rock Point (BRP) is the Country's oldest commercial BWR still in operation, having started up in 1962, and falls in that classification called BWR-1.
The plant is rated at 2LO MWt or about 72 MWe (gross), but generally runs at a lower power because of restrictive core thermal limits.
Although BRP is fundamentally similar to present day BWRs, there are some significant differences in design and mode of operation:
4 Page b l
2.1 PHYSICAL DESCRIPTION (CONT'D) 1.
The BRP reactor core is small, the active region being about six feet in height and six feet in diameter. An advantage of this is a very stable, leakage controlled power distribution as compared to modern plants whose core volume is about eight times larger. To compensate for the high leakage associated with the small core, reactivity (K-infinity) and hence fuel enrichment must be higher than for most later plants.
2.
Although shorter, ERP fuel assemblies, are vider than modern plants (7 " pitch versus "6"). The ERP 11 x 11 assembly is roughly the same in rod diameter and pitch to the modern 8 x 8 B'4R assembly. Because of the larger assembly, the ratio of control rods to interior assemblies is one to two rather than the typical one to four, i.e. a "D" lattice.
3 BRP has external recirculation loops with constant velocity pumps, therefore flow control is not employed, and maneuvering is done entirely with control rods. This is a disadvantage as far as plant flexability, but greatly simplifies predictive physics analysis and power distribution surveillance.
h.
BRP has only 32 control rods, as opposed to around 200 in the large modern plants. Since the reactivity inventory is about the same as a larger plant, individual control rod worths are generally larger for ERP.
During operation, banking the control rods in groups of greater than two rods would result in unacceptable
e i
Page 5 2.1 PHYSICAL DESCRIPTICU (CONT'D) h.
(Cont'd) axial power shapes, so that X - Y sy==etry is limited to half core rotational, rather than quadrant or octant.
5 LPRMs are present, but they are not part of the reactor pro-tective system. A high flux trip is provided by three excore detectors.
6.
In core power distribution =easurements are provided by the activation of flux wires, rather than a novable TIP detector.
There are only eight ceasurement locations arranged in four symmetrically located pairs. These are employed to verify calculated axial power shapes, but because of the small number of locations, they are not considered useful for radial power measurements.
~
7 The primary coolant system is pressurized to 1350 psi versus the typical 1000 pai. Maximum exit void fractions are about 55%, which is much lower than modern plants.
l l
8.
There is no on-line power distribution monitoring system comparable to later plants. The LPRMs are used to conitor changes in power distribution, but there is not an on-line thermal margin calculation.
l l
l l
J Page 6 2.1 PHYSICAL DESCRIPTION (CONT'D)
A diagram showing the core layout is shown in Figure 2-1.
The empty boxes are fuel assembly locations, the crosses are control rods labeled by bank, and the small circles are instrument stalk locations containing incore detectors and flux wire tubes. The four labeled boxes are neutron sources and empty core plugs. The 16 outer control rod blades, groups A and B, are strong (all poison tubes filled with B C) and are h
used only for shutdown. The 16 inner blades are weaker (40 inner poison tubes per blade are empty). Typically eight or ten of the weak blades are initially in the core at power and are used for long-term reactivity shim.
BRP fuel is similar to standard BWR fuel except that the assemblies are larger (11 x 11) and since all the interassembly water gaps are the same size, the assemblies are internally octant symmetric. Current BRP reload fuel has 113 fuel rods (composed of three Enrichment zones), four gadolinia bearing fuel rods, and four inert rods for improving LOCA performance. Approximately h of the core is refueled on annual cycles.
The plutonium recycle and cobalt-60 production programs previously engaged in at BRP have both terminated. No mixed oxide assemblies and only four cobalt bearing assemblies (to be discharged at the end-of-the-current-cycle) remain in the core.
2.2 OPERATION AND SURVEILLANCE Reload cores for BRP are designed, and a safety analysis is performed using the methods described in the following sections of this report.
The reload design consists of selecting an assembly loading pattern and a control rod withdrawal sequence that meets the constraints on
9 5
Face 7 FIGURE 2-1 BIG ROCK FOINT CORE CONFNBURATION N
OOO A
O O
O O
O O
l 000
o i
Page 8 2.2 OPERATION AND SURVEILLAliCE (CCITT'D) shutdown margin, rod worth, notch worth, MAPLHGR, MCHFR, assembly power and heat flux while allowing operation at the highest possible power level. The safety analysis verifies that these limits will be met, and in addition verifies that other parameters: reactivity coefficients, beta / lambda, liquid poison worth and scram reactivity insertions times, are within the assumptions used in the plant accident and transient analyses.
The startup physics test program consists of verification of shutdown margin, comparison of the zero power critical control rod density with predictions, and comparison of measured flux vire shapes with predicted ones.
During operation power distribution calculations are periodically performed to evaluate cargin to thermal limits. Once a month cal-culated reactivity and flux wire activation shapes are compared with measurements to monitor the adequacy of the calculational model. The flux vire measurements are also used to calibrate the incore detectors and determine their alarm setpoints.
I 3.0 PHYSICS MODEL 3.1 OVERVIEW The calculational sequence for Big Rock Point physics is diagrammed in Figure 3-1.
The primary component of the sequence is the three i
dimensional reactor simulator program, GRCK. The remainder of the l
sequence primarily involves the generation of input for GRCK. The l-
. _ - - - _ ~ _ _ _ _..
. ~. - _.
._=
4 Page 9
]
i FIGURE 3-1 BRP PHYSICS 1
i CALCULATIONAL SEQUENCE i
i PHYSICAL PROPERTIES PELLET, ASSDOLY, CORE F
if CASMO J
l 9P INPUT PREPARATION CURVE, FITTING,ETC I
l 1V REACTOR OPERATING GROK STA E, PO M, ROD y
CORE SDIULATION POSITION,BURNUP l
4
-$ POWER DISTRIBUTION
-) MARGIN TO THERMAL LIMITS i
y ROD & HOTCH WORTHS y COEFFICIENTS l
4 INCREMENTAL BURNUP J REACTIVITY s
I
~
Page 10 31 OVERVIEW (CONT'D) input consists of: assembly neutronics parameters as a function of local operating conditions, physics features of each fuel type, hydraulic parameters, technical specification and other limits, and the reactor operating state. The assembly neutronics parameters are generated using the CASMO program.
The GROK program is run using the appropriate option to compute the desired core parameter. Reactivity, power distribution and margin to thermal limits are computed in a straightforward manner by modeling the reactor operating state being analyzed. Control rod worths and notch worths are computed by calculating reactivity at two different states (i.e., rod in sequence and rod inserted). Coefficients (void and doppler) are computed with a special option that allows one feedback mechanism to be varied while the vorth of the rest re=ain
- constant. Fuel burnup is incremented by inputting a core average exposure and allocating it based on the computed power distribution.
3.2 ASSFlGLY FHYSICS CALCULATIONS The purpose of assembly physics calculations in the calculational sequence is to determine the relationship between 'the physical state of the reactor and the neutronics parameters required in the GROK physics model. These calculations are typically performed for a horizontal slice of a single fuel assembly, for which the region of solution is the area bounded by the centerlines of the water gaps surrounding the bundle. They are two. dimensional with reflecting boundsry conditions, hence the term " infinite lattice".
4 Page 11 3.2 ASSD'BLY PHYSICS CALCULATIO!!S (CCIIT'D)
The inputs to the assembly physics calculations consist of the location, composition and temperature of all the important materials within the assembly, such as fuel, burnable poison and inert rods, flow channel, control rods and coolant. Dimensions and compositions of assembly components are acquired from the vendor drawings and design reports.
Structural materials are assumed to be at the coolant temperature, while the assembly average fuel and cladding temperatures are computed using a one dimensional heat transfer model of a fuel rod as in the program GAPEX. l The important outputs from the assembly physics calculations are: the infinite neutron multiplication factor, Kon ; the migration area, M ; the one-group flux; the ratio of kappa over nu; the fluxwire absorption
- factor, the local fuel pin power distribution,.and the de'ayed neutron fraction, Eeff.
Assembly physics calculations are performed with CASMO, which is a multigroup two dimensional transport theory code for static and burnup calculations of EWR and PWR fuel assemblies. The code handles a geo-metry consisting of cylindrical fuel rods of varying ec= position in a square pitch array, with allowance for gadolinium and other burnable poisons, in-core instrument channels, water gaps and cruciform control rods. CASMO incorporates libraries of multigroup neutron cross-sections and other nuclear parameters so that the calculation is a one-step process from the users standpoint. The program performs spectrum calculations on the various cc= positions within the assembly and generates few group cross-sections for each. These are then used in the two-dimensional neutronics calculation, which consists of a variation of
Page 12 3.2 ASSE'4BLY FHYSICS CALCULATIONS (CONT'D) transport theory called transmission-probabilities. Using the computed fluxes and few group microscopic cross-sections CASMO depletes the fuel isotopes stepwise out to the projected lifetime of the assembly. A complete description of the CASMO code, including verification data, has been submitted to the USNRC by Yankee Atomic Electric Company in connection with Vermont Yankee reload methodology.
3.3 GROK INPUT GENERATION In order to compute a three dimensional reactor power distribution, the physics algorithm in GROK requires three dimensional distributions of the basic physics parameters Km, M and the ratio '/p. These parameters in turn are dependent on the local operating state: power, steam voids, control rods and the burnup history of the fuel. These dependencies are computed separately from GRCK using assembly cell physics calculations simulating various local conditions, and the results are input to GECK in the form of coefficients to polynomial functions.
For instance, to compute the dependence of Kar on local steam void fractions, assembly physics calculations are performed at three dis-crete void fractions, usually 0%, 25% and 505 steam voids. The three values of K,resulting from these calculations are then fit to a simple polynomial in moderator density through the solution of 3 simultaneous equations resulting in:
Km = B (1 + B U + B 3
7 10 Where U is the moderator density relative to saturation, and E3, B7 and B10 "
E"
4 Page 13 3.3 GRCK INPUT GENERATIO:I (CONT'D)
Since K is also a function of control rods and the dependency on og control rods and steam voids are interrelated (non-separable), six more assembly physics calculations are performed resulting in two more equations similar to (1), one for one adjacent control rod, and for two adjacent control rods. For partially roded nodes, GROK inter-
.polates between the two appropriate evaluated equations.
The reactivity worth of other reactor operating parameters such as fuel burnup, burnable poison concentration., coppler and equilibrium xenon concentration is also computed with assembly physics calculations.
These worths are expressed in terms of AK/K vs nodal power, exposure or void weighted exposure, where AK/K = 1 ~
'2 (2)
K1 K is the " reference".value of Em and K is the " perturbed" value y
2 where the perturbation is due to changes in the operating parameter, i.e., doppler, xenon etc.
The calculated value of Kay is then modified by a series of multipliers of the form (1 - AK/K) for each factor affecting reactivity. This procedure is repeated for each individual node in the calcul'ation resulting in. the three dimensional array of physics parameters required for the neutronics calculation.
Page lk 3.3 GROK IiPUT GE:iERATIO!! (CO:IT'D)
Table I is a compilation of the physics parameters evaluated for each fuel type in the Zeneration of GROK input. Column 1 is the desired physics parameter, columns 2 and 3 indicate what physical parameters are considered in the calculation of the physics parameter, columns h and 5 indicate the degree of polynomial used in GROK to describe the relationship, and column 6 shows the number of assembly physics calculations required to generate the coefficients. Many of the assembly calculations are used for more than one purpose, so the total number of calculations performed is less than the total indicated by adding column 6.
3.h DESCRIPTICII 0F THE GROK COMPUTER PROGRAM The following is a description of the calculations performed in the GROK computer program. GR0K incorporates the FLARE physics model along with a thermal-hydraulic feedback model, a local peaking factor calculation, and routines which evaluate margin to thermal limits.
3.h.1 GROK Physics Model GRCK calculates a nodal power density for a three dimensional core geometry. The code is based on modified one group diffusion theory using the infinite multiplication factor (Koo) and migration area (M )
as the basic physics inputs. An albedo at the core surface simulates the reflector so that only mesh points within the active fuel region are considered. Each assembly is represented by one horizontal and l
nine vertical mesh points (nodes).
l l
t
TABLE I Input for Power Operation Neutronics Parameter Functional Dependence Degree of Fit Minimum Number of A
B A
B Assembly Calculations M
Steam Voids 2
3 K
Control Rods Steam Voids 1
2 9
9 AK/K) Doppler Power Steam Voids 1
1 3
AK/K) Equilibrium Sm Power O
2 Xenon Cross Sections Burnup 2
3 AK/K) Xenon Xenon Concentration 2
3 AK/K) Initial Burnable Poison Control Rods Steam Voids 1
2 9
1 AK/K) Burnup Burnup Void-Weighted Burnup 2
2 30 2
6 Fraction of B.P. Remaining b.irnup K/v Burnup 2
10 Input for Zero Power M
Temperature 2
3 K
Control Rods Temperature 1
2 18 gg AK/K) Peak Samarium Burnup O
2 AK/K) Initial Burnable Poison Control Rods Temperature 1
2 18 5
Xenon, Burnup, Fraction of Burnable Poison remaining and K/v are the same as above, g
d i
Page 16 3.h.1 GROK Physics Model (Cont'd)
The complete iterative calculation consists of four levels:
1.
Source or Power Distribution, 2.
Void Distribution, 3
Control Rod Positioning snd Power Variation, and h.
Fuel Burnup or Thermal Limits Evaluation.
A description of each level follows. An explanation of the equations solved also appear.
3.h.1.a Source or Power Iteration The neutron source at each node is calculated as a function of:
1.
Kaa at that point, 2.
the neutron source at the six neighboring points, and 3
a transport kernel.
The transport kernel is a measure of the probability that a neutron born at node n is absorbed at node 4 and is a function of migration area and node spacing. Kan is calculated at each node and includes the following effects:
1.
Presence or absence of one or two adjacent control rods. These control rods can be strcng or weak in any combination.
2.
Local moderator density or coolant temperature.
3.
Power dependent xenon and Doppler reactivity.
h.
Local fuel expocure.
5 Presence of burnable poicons.
6.
Equilibrium or peak sanarium.
Page 17 a
3.4.1.a source or Power Iteration (Cont'd)
M i also calculated at each node as a function of local moderator 2
density or temperature. The initial values of Km and M are based on a flat power distribution and are updated thereafter following each void iteration.
3.h.l.a.1 Source Equations Source at node f is defined by:
(3-3)
Sg Key Af
=
absorption rate at f*
where Af
=
/
{SW
+
(3 h)
Sj Wff or Af
=
m where W
= probability that a neutron born in node m will be absorbed
-f in node { and the prime indicates summation over the six nearest neighbors.
Combining these equations and dividing Km by A (the eigenvalue) yields:
~
'g y-g g
Ny
/
=
mq (3-5)
's ey h6 "j) Wg, - 1]
A+K where A = eigenvalue og= albedo
- note: a single subscript or a will be used interchangeably with the subscript i
e fage 18 3.L.1.a.1 Source Equations (Cont'd) ay is non-zero at the boundaries of the core ( < 6 neighbors) only and is handled separately for the top reflector, bottom reflector, and for the sides of each peripheral fuel assenbly. Top and bottom albedoes are fixed, but horizontal albedoes are calculated as a function of nodal moderator density.
A is recalculated after each iteration based on a solution to the neutron balance summed over the entire core:
Source + Inleakage - Outleakage or, 3
Absorption
/
JI sy +)
SW -)
Sy Wf m (n 2 - 2)
( 3-6 )
,l A=
i m
q
)
1 8
i Kong where n j number of external nodes adjacent to node y, both ny and og
=
are zero for all internal nodes, and the sums are over all nodes in the reactor.
Equations 3-5 and 3-6 are the basic equesions solved during the source iteration. The transport kernel is defined as:
[A F.
2
+
(1-g) M (3-7)
W
=
g gm 2
2r -
Koe r X m 9
where M]
= migration area of node (
rj
= mesh spacing, and g.
= a kernal mixing factor A more detailed analysis of these equations are presented in Section 3 of reference L.
o a
Page 19 3.4.1.a.1 Source Equations (Cont'd)
Several source iterations are performed per void iteration. After each series of source iterations the nodal power distribution is computed from the neutron source by multiplying by the ratio of kappa (the effective energy released per fission) over nu (the average neutron yield per fission). A polynomial function of K/g versus burnup is included in GROK for each fuel type.
3.L.l.a.2 Physics Parameters - Km and M A three dimensional array of the quantities needed for the source calculation, K and M, is generated by the program using algebraic m
functions that describe the dependence of these quantities on local reactor conditions. The coefficients of these functions are input for each fuel type and are derived from the results of assembly physics calculations performed over the range of expected local operating conditions. The Km and M arrays are reevaluated after each void iteration and used as input for the next series of source iterations.
There are two reactor conditions normally simulated separately using GEOK sero power and power operation. For zero power calculations, M is calculated as a quadratic functica of isothermal reactor temper-l ature ranging from ambient conditions up to the operating saturation temperature. For power operation calculations, M is computed as a function of in-channel steam voids ranging from cero to core exit void fraction at full power. Kaa varies with void fraction, control rod configurstion, burnable poison concentration, fuel exposure, fuel temperature (nedal power) and xenon and samarium concentrations.
l
Page 20 3.L.l.a.2 Physics Parameters - K and M (Cont'd) og For sero power calculations Kag is required as a function of reactor temperature for the following combinations of control rods inserted into a node:
1.
no control rods, 2.
one weak control rod, 3
one strong control rod, k.
two veak control rods, 5
two strong control rods, and 6.
one weak and one strong control rod.
The core locations of the strong versus weak rods do not change and therefore have been built into the program. Since the strong control rods are withdrawn before significant power levels are achieved, Kay 's for power operation are computed as a function of steam voids for the following fractions of control only:
1.
no control rods, 2.
one weak control rod, and 3.
two weak control rods.
l If the fuel type in question contains burnable poisons, coefficients to polynomials are input that describe AKoo /Kon due to the burnable l
poison as a function of control density and moderator condition in the l
l same manner as K Since the burnable poison typically does not cover og the entire active length of the assembly, parameters are input that describe the axial position of the poison.
e Page 21
- 3. !.. l. a. 2 Physics Parameters - Kan and M (Cont'd)
Functions are also provided that describe the reactivity defect due to xenon as a function of nodal power. The equilibrium xenon-135 and iodine-135 concentrations are calculated for each node according to:
(c I+e X) db P S
f 1
(3-8)
X
=
'94 X
A y+
da a
c I f
2 (3-9)
I
=
egg A I Where P is the reactor power and A is a decay constant. The quantities 6 E y 7, the iodine yield at rated power in an average node; 1 [ f 7,
e 7
0 the xenon yield; and 4
, the xenon absorption rate, are calculated as a function of fuel burnup based on input coefficients for h fuel type. Transient xenon after shutdown is calculated from the following:
I
- A Xt
- A It
- A Xt+ ^
'9A *
~*
(3-10)
X
=X e
/t eqp A
-A 7
y Where t is the time after shutdown. The reactivity worth in a K/K of xenon is then computed as a function of the calculated xenon concentration using input coefficients.
f The program also accounts for the reactivity defect due to samarium.
For power operation calculations an equilibrium value is used, while for zero power calculations either the peak samarium defect is used or zero defect depending on whether the assembly has been previously burned or is fresh fuel.
Page 22 3.L.1.a.2 Physics Parameters - K and M (Cont'd) an The reactivity defect due to doppler is comp 6ted as a function of local power and steam voids. The two basic relationships used to calculate this function are:
1.
the variation of effective fuel temperature with LHGR, and 2.
the reactivity defect from doppler as a functicn of fuel temperature at different void conditions.
GROK calculates the doppler defect as a linear function of power multiplied by a linear function of steam voids as specified by input coefficients for each fuel type.
The Kaa vs exposure and void-weighted exposure equation is of the following form:
(3,11) ofE' 2h f )
23 j (1.0 - B 21 g (1.0 - B Ef)-B Y
V E
AK
=
B 22 B
+
Burnup 25 vhere E
= exposure at nodey g
Vg = void history at node f (product of exposure and voids)
The coefficients for equation 3-11 are calculated by a two dimensional least squares fit of computed Kaa versus burnup out to at least 1.5 times the expected average discharge exposure for three different void conditions (usually 0, 25 and 505). For burnable poison fuel, a polynomial function is provided that describes the burnup-dependent behavior of the reactivity worth of the poison.
o Page 23, 1
3.h.2 void Iteration i
The void modal in FLARE has been entirely replaced by a more sop-chiticated thermal hydraulics model. It requres the core active coolant flow, coolant inlet enthalpy, reactor vessel outlet pressure, total reactor power, and the nodal relative power distribution calculated in the source loop. Spacer loss coefficients, core inlet friction factorc, hydraulic diameters, wetted perimeters and thermal hydraulic model celect'ons are required user input data. These parameters are obtained from analyses and test data from both the vendor and Consumers Power. The reactor core is hydraulically modeled with closed flow channels each containin6 one fuel accembly.
An iterative solution technique is used where the total core active coolant flow ic uci formly apportioned to each flow channel in the reactor core. The total prescure gradient, made up of components due to friction, momentum, elevation, and local losses, through each flow channel is then calculated using this estimate.
The average pressure gradient for the reactor core is then calculated and each channel flow rate is modified as follows:
Wnew (',J) = Wold (I,J)
Pave (3-12)
P(1,J )
where:
Wnew (I,J) s New ectimate of flow rate in flow channel (I,J).
Wold (I,J) = Previous estimate of flow rate in flow channel (I,J).
Pave = Avera6e precoure gradient for the reactor core.
P(I,J) = Pressure gradient of flow channel (I,J).
4
Page 2h 3.h.2 Void Iteration (Cont'd)
After the channel flow rates are modified they are su=ced and normalized to the known total core active coolant flow. This new estimate of channel flov rates is then used to recompute the flow channel pressure gradients. The procedure is repeated for each power / flow iteration.
Nodal steam void fraction is calculated from nodal quality, pressure and fuel geometry using the EPRI void fraction model as described in reference 3, and conterted to relative moderator density. This is a
needed to calculate Kog, M" a d horizontal abbedoes for the next series of source iterations. The void and source iterations are continued until a converged power and void distribution is attained.
3.h.3 control Rod Positioning and Power Variation GROK has a control loop which will automatically adjust control rod groaps one notch at a time in any given input sequence until the core reactivity equals a pre-set value. An automatic search for the reactor power required for criticality at any given control rod position is also available.
- 3. h. h ' Fuel Burnup GROK updates nodal fuel burnups using the computed power distribution, the assembly wei hts as input by fuel type, and the core average C
exposure increment for the burnup step.
3.5 PEAFING FACTOR ALGORITHM The peaking factor correlation's function in GRCK is to find peak pin powers for each assembly, which are necesct y inputs to the MCliFR, MCPR
+
Page 25 3.5 PEAKING FACTOR ALGORITHM (Cont'd) and heat flux calculations. The code first takes the coarse global power shape and finds a polynomial function describing the axial power shape in each node via a SPLINE curve fit.
These functions are evaluated at four points per node. This method describes in finer detail the axial power variations that occur over the length of the assembly and results in a ec=puted power for every two inches of core height. These vill be referred to as expanded or sub-nodal powers.
The local fuel pin powers by a local peaking factor. These local peaking factors are calculated by combining the gross horizontal power tilt across an assembly at each axial sub-node with the beginning of life (BOL) assembly infinite lattice local power df.stribution.
The infinite lattice local power distributions are derived by means of two dimensional assembly physics calculations for each fuel type, and are input for thee assembly control conditions:
1.
uncontrolled, 2.
singly weak contro'lled, and 3
doubly weak controlled.
The program will orient the local power distributions for controlled assemblies based on which corners of the assembly are adjacent to control rods. If a sub-node contains a control rod tip, the controlled power distribution is chosen. For the sub-node immediately above the
Page 26 3.5 PEAKING FACTOR ALGORITHM (Cont 'd) control rod tip, the following equation is used to calculate the pin powers:
PP = 0.47 x PP + 0 53 x PP (3-13) u c
where PP = pin power u = uncontrolled c = controlled This equation is conservatively based on a three dimensional physics calculation of the power peaking at the tip of a control rod.
The gross horizontal power tilt across each assembly at each sub-node is calculated by fitting the one group neutron flux in the assembly with the flux in the accembly on either side to a quadratic equation. This equation is solved at the center line of each row of fuel pins in both the X and Y directions and the result is multiplied by the infinite lattice localc to yield total local peaking factors. For assemblies on the edge of the core a atraight line interpolation in performed with the one adjacent acsembly.
The flux is calculated from the sub-nodal power and polynomial equationc tat deceribe the variation of the flux to power ratio 1
( g(- ) as a function of steam voids, control and fuel exposure.
The coefficients for these equations are derived from the assembly phy ics calculationc and are input to GEOK.
After the nodal local pin powers are calculated, the program celectc the highest one.
The maximum total local power including tilt is then chosen as the local peaking factor for that cut-node and ic later
Page 27 35 PEAKING FACTOR ALGORITHM (Cont'd) used in the calculation of peak heat flux.
3.6 FLUXWIRE CALCULATIONS GROK includes a fluxwire activation computation for comparison of the calculated core power shape with fluxwire measurements. Coefficients to functions that describe the ratio of the neutron activation in a copper fluxwire located in the corner of an assembly to the assembly power as a function of steam voids, control rod position, and assembly exposure are input for each fuel type. This data is obtained from two dimensional assembly physics calculatons. The results from the four assemblies adjacent to the fluxwire position are averaged and the axial shape is printed out.
The total activations for the eight fluxwires are normalfzed and printed out also. The fluxvire positions can be scen in Figure 2-1.
37 THERMAL HYDRAULIC LIMITS A thermal limit calculation to determine the peak heat flux and the minimum critical heat flux ratio (MCHFR) in the core is performed by GROK.
Local peak heat fluxes for each sub-node are calculated based on total core power, normalized power shape, local peaking factors and the heat transfer area for each fuel type. Hot channel flow reduction and enthalpy rise factors are included in this calculation. The synthesized Hench-Levy correlation is then applied to yield critical heat flux and MCHFR. Another thermal limit found is the minimum critical power ratie (MCPR) as calculated by the Exxon Nuclear XU2 correlation. 7 MCPR is expected to replace MCHFR as a technical specifi-cation limit in the future, and at that time MCHFR will no longer be calculated.
Page 28 e
o 3.7 THERMAL HYDRAULIC LIMITS (Cont'd)
The ratio of calculated to allowable maximum averace planar linear heat generation rate (MAPLHGR) for each sub-node of every assembly is found based on total core power, normalized power shape and the limits for MPLHGR input by fuel type as a function of exposure. The maximum fraction of MAPLHGR limit for each assembly and fuel type is then determined as shown by equations 3-lh and 3-15 2=
(X)(F)(B)
(3-14) 137 1441 (PTH) where Z = maximum allowable radial times axial for each quarter node F = active fuel length B = number of fuel rods per assembly X = MAPLHGR limit at each node based on exposure of that node and a linear interpolation between input MAPLHGR limit PTH = core thermal power 12 f{f 3
96
- 10 5
137.14hl =
8h assemblies where.96 = ECCS gamma smearing factor.
Fraction of MAPLEGR limit = P, (3-15)
Z where P = actual radial times axial.
MAPLHGR limits are from the Technical Specifications as derived from LOCA analyses.
1
Page 29 h.0 UNCERTAINTY ANALYSIS FOR THE BRP PHYSICS MODEL The results of the Physics Model are compared to either measured data or higher order calculations and uncertainty factors for the safety limits are derived from the comparisons.
h.1 RADIAL POWER DISTRIBUTION UNCERTAINTY FACTOR A series of fine mesh quarter core symmetric diffusion theory power distributions were calculated with the PDQT program.
The cross sections input to PDQT computed by CASMO for a typical BRP reload fuel, designated as Exxon G3 This fuel type is similar or identical to almost all of the fuel currently used at 3RP. Six different core loadings were simulated at full power, three at BOC that used various control rod patterns and
.three at EOC that did not use any control rods. Each of the six loadings had a power distribution calculated by PDQT for 0%, 25% and 50% average voids.
The same core loadings and conditions were then analysed with GROK. The inputs to GROK are exactly equivalent to the PDQT inpr.ts.
The results of the comparison between GROK and PDQT is a standard deviation of 2.289h%. For a 95/95 one-sided confidence band, the standard deviation should be multiplied by 1.6h5, resulting in an uncertainty factor of 3.7661%. In other words, for 95% confidence that 95% of the GROK j
calculated assembly radial powers will be greater than their PDQT l
counterparts, the GROK power should be multiplied by 1.037661.
i h.2 AXIAL PCWER DISTRIBUTION UNCERTAINTY FACTOR This uncertainty factor is based on comparisons of GROK computed flux-wire profiles to actual measured fluxwire profiles for the past five I
cycles. The ecmparison includes three corrections to the GROK computed data and one correction to the measured data.
Page 30 h.2 AXIAL PO'ER DISTRIBUTION UNCERTAINTY FACTOR (CONT'D)
The correction to the measured data is an axial shift that re-positions the data relative to the core boundaries. This is necessary because it is difficult to judge the core boundries by geometry because of wire slippage when the wire is inserted into the reactor.
The first correction to the calculated data is a sub-nodal power multiplier that accounts for power depressions caused by spacer grids. This multiplier is also applied to the peak heat flux calculation. Because of normalization, most regions of the core have slightly elevated powers while a small region around the spacer grids have a moderately reduced power.
The second correction to the calculated axial fluxvire profiles is applied to the data in a similar fashion as the spacer grid correction. This correction accounts for flux depressions caused by the fission chamber in-core detectors. This correction is not applied to the peak heat flux because the' in-cores should have very little effect on the fuel.
The last correction to the calculated fluxvire profiles is an axial power dictribution smearing factor. This correction accounts for the finite amount of time (10 to 15 seconds) that is takes both to insert the wire into the reactor and to then withdraw the wire. The correction assumes that the GRCK computed axial distribution is in equilibrium with the neutron flux. The correction then computes the amount of activation any particular wire segment would receive as it transnits the
Page 31 h.2 AXIAL POWER DISTRIBUTION UNCERTAINTY FACTOR (CONT'D) core on insertion; the anount it would receive during the 30 minute irradiation time and the amount it would receive as the wire segment is withdrawn from the core. The three seperate amounts of activation received are decayed up to the point in time that the wire tip just leaves the reactor and then they are added together to form a new axial fluxvire profile.
The fluxwire is measured in 28 segments of 2 inches each. GROK computes fluxwire activation in 28 nodes from the 36 sub-node power distribution. Due to a slight inadequacy in the boundry conditions of the spline fit that computed the 36 sub-node power distribution, the top and bottom two fluxvire points are ignored in the axial power distribution uncertainty factor. This should not be a problem since the top and bottom 5 inches of core should never be thermal-limiting.
After all of the corrections are applied to the fluxwire measurements and to the calculated data, the standard deviation of the error between calculated and measured data is 3.22h6%. For 95/95 one sided confidence, the error band is 1.6h5 times this value, or 5.30h5%.
h.3 PEAK HEAT FLUX UNCERTAINTY FACTOR There are several components that makeup the peak heat flux error:
the accuracy of the CASMO infinite lattice local power distribution, the accuracy of GROK's method of calculating the local peaking factor, the accuracy of GECK's nodal power distribution and the 2% heat balance error.
Page 32 h.3 PEAK HEAT FLUX UNCERTAINTY FACTOR (CONT'D)
The accuracy of GROK's local peaking factor calculation was determined by comparing loca1' peaking factors from GROK to local peaking factors from PDQT.
The PDQ7 power distributions refered to in section 4.1, above, were also edited for partition power. Since the problem mesh was laid out with one mesh line per pin, the partition power is the same as pin power.
The GROK runs were also edited to print the local power distributions.
The infinite lattice local power distributions that were input to GROK were taken from the CASMO calculations that were made for the PDQ7 cross sections. On an assembly by assembly basis, the highest pin power calculated by PDQ7 is compared to the highest pin power calculated by GROK for the same assembly. Note that the pin location does not have to be the same.
The results of the pin power comparison is an average difference of 2.17h7% (GROK high) with a standard deviation of h.7561%.
The 95/95 one sided confidence error band is then 1.6h5 times the standard deviation minus the average difference. The average difference is subtracted because GROK typically over-predicts the assembly local power peaking factor. The resulting local power peaking factor uncertainty factor is 5.6h91%.
Page 33 L.3 PEA'{ HEAT FLUX UNCERTAINTY FACTOR (CONT'D)
Another component to the local power peaking factor uncertainty is from the accuracy of the CASMO-PDQT system. A comparison was made to a set of three local power distribution measurements. The comparison resulted in a standard deviation of 1.9153h%. For 92 degrees of freedom (93 symmetrically collapsed measurements), the 95/95 confidence level error band is 1.66h x 1.9153h% = 3.18713%.
Statistically combining these two uncertainty factors along with the 2% heat balance error and the radial and axial uncertainty factors results in a peak heat' flux uncertainty factor of 9.h017%.
h.h MAPLHGR UNCERTAINTY FACTOR The limi'; is expressed as the ratio of the calculated average planar LHGR to the maximum average planar LEGR. Ideally, the ratio should be less than unity to protect the safety limit. However, the ratio chould be less than 1-U, where U is large enough to ensure that with 95/95 confidence, the safety limit is not violated because of power distribution errors.
Since the limit is calculated as:
l L = APLHGR MAPLHGR statistical propagation of errors gives U as:
U =S/ dL
+
dL dAPLHGR TPLHGR dMAPLHGR
' MAPLHGR
Page 3h 4.4 MAPMGR UNCERTAINTY FACTOR (CONT'D)
Substituting in the partial derivatives, the equation becomes:
f fAPLHGR OYAPMGR \\
U=
APMGR
+
V MAPMGR /
\\ (MAPMGR)2
/
The value of CAPMGR is determined by multiplying APMGR by the nodal power uncertainty factor, which is the statistical combination of the radial, axial and heat balance errors. The nodal power uncertainty, with 95/95 confidence, is 6.5055%. To make U large, APMGR should be as large as possible, which is the value of MAPMGR.
No erro: is assumed in the value of MAPMGR, however there is an error -
in the exposure value that is used in the table of MAP M GR versus exposure. The uncertainty in MAP MGR becomes:
CIGPMGR = d MAPMGR L
- CE The error in exposure is assumed to be the nodal power uncertainty factor times the nodal exposure.
If there is negative feedback in the calculational methods, which seems likely, this vill be a conservative. assumption.'or nodal exposure error. Substituting values in for TE and TMAPMGR becomes:
@ %P MGR = dMAPMGR x E x OTiodal dE The table of IGPMGR versus exposure for Exxon G3 fuel was used to find the maximum absolute value of dMAPMGR x E.
The maximum value found dE was 3.8283 Currently, all but h non-limiting assemblies at ERP have IGP EGR tables identical or similar to G3, so the value of 3.8283 is acceptable.
P
Page 35 h.h
!MPLHGR UNCERTAINTY FACTOR (CONT'D)
The value of U becomes large for small values of MAPLHGR, so the smallest value on the table of 6.69 is used. The equation for U may now be simplified to:
1 x
x E x Giodal)
U=
(TNodal)2 (MAPLHGR dE
+
Using the values discussed above, U may be evaluated as.078h2, which means that the ratio must be less than.92158 to protect the safety limit.
4.5 MCHFR UNCERTAINTY FACTOR The limit is expressed as the ratio of critical heat flux (CHF) to axtual heat flux (AHF), which is not allowed to be less than 3.0.
This CHF may be formulated as L =
2 3.0.
Usin's statistical propagation AHF of errors, the uncertainty factor for L is:
U=
6L
+
aL aCHF
@ HF OAHF 7AHF Ey evaluating the partial derivatives, the equation becomes:
+ [(CHF j
U=
/1 AHF EHF
\\ A.HFI TAHF /
For larger values of AHF, U will become smaller. Thus AHF will be chosen as the largest allowed, that is 1/3 CHF, minus allowance for the uncertainty factor.
In terms of percentage, CAHF is the same as the peak heat flux uncertainty factor. However, to get the correct units, it must be multiplied by the value of AHF.
From references 13 and 14, the critical heat flux correlation is given in three seperate functions. The function used is dependent on the flow and quality conditions. The functions are:
Page 36 h.5 MCHIH U:ICERTAINTY FACTOR (CCUT'D)
CHF = 1.0h5
.06G +.000kh(1000-P) for X < X.
CHF = 3.3h5
.155G -3.26X +.000hh(1000-P) for X. < X < X2 CHF =.h99
.626X +.000hh(1000-P) for X > X2 where X = nodal quality, G = assembly flow per unit area, g and X2 are break points that depend on the assembly flow. The uncertainty in the breakpoints may be ignored by chosing the largest uncertainty of the three functions.
To evaluate 7~CHF, the uncertainties in assembly flow and nodal quality must be known. Assembly flow is assumed to be a function of inlet subcooling, the radial power distribution.and core flow. Assuming linear independence of these parameters, the statistical propagation of the errors results in a standard deviation of assembly flow of.025639
- 10 2
lbm/hr 'ft Nodal quality is assumed to be a function of inlet subcooling, the nodal power distribution, core flow and the reactor pressure. Once again, linear independence is assumed, so the statistical propagation of the errors in these parameters results in a standard deviation of nodal, quality of.00h728h.
Using the standard. deviations of flow and quality and statistical propagation of errors, TCHF may be determined. The largest value of TCHF comes from the second function given above:
6 (3.26 Cx)2. (3gg,1g gp)2 =.01597h G CHF = (.155 FIG)
+
The error on reactor pressure is taken from the ERP Technical Specifications, asetion 6.1.2 (9/16/1980) as the tolerance of the high pressure trip (5 psi). The tolerance is acsumed to be at 90% two sided confidence, so it is divided by 1.65 to get a standard deviation.
Page 37 h.5 MCHFR UNCERTAINTY FACTOR (CONT'D)
Given that the fractional derate from full power is 1 - U/3, the largest allowed heat flux is 1/3 CHF (1-U/3). From the functions for CHF, the largest allowed value of CHF is 1.3h5 Thus the equation for U may be reduced to:
f
.015974 2
+
1.3h5 U=
2 x 1/3 x 1.3h5(1-U/3) 1/3 x 1.345(1-U/3) 11/3 x 1.3h5(1-U/3)1 b
x.09h0lT)2 This equation has U on both sides and may be solved iteratively. The solution is U =.373h, which means that MCHFR must be greater than 3.3734.
h.6 SHUTDOWN MARGIN The error in rod worths for a shutdown margin test was derived by comparing GROK calculated rod worths to a two dimensional, fine mesh, quarter core symmetric PDQT calculated rod worths. Three different core loadings were analysed at ambient conditions by first calculating an eigenvalue with all rods in and then calculating an eigenvalue for each control rod in the quarter withdrawn. Since quarter core symmetry was used, this was in reality the same as pulling groups of two or four rods at a time.
In order to compensate for this, GROK was used to calculate the worth of one rod relative to its group of rods, and the error in rod worth from the quarter core comparison is then multiplied by this fraction to get a single rod worth error. The results of the comparison show GROK under predicts rod worths by.001320 AK with a standard K
deviation of.001950 AK. Since the slight under prediction of rod K
worth by GROK may be taken advantage of the 95/95 confidence level error band for rod worths is 1.699 times the standard deviation minus 0
the averaSe error, which is.002
/K. The value of 1.699 is used
Page 38 h.6 SHUTDOWII MARGIII (COIIT'D) because there were 30 comparisons, or 29 degrees of freedom.
Ilo error is assumed in the critical eigenvalue because the lowest measured / calculated eigenvalue in the past 5 cycles is used. The table below gives critical eigenvalue data by cycle.
CYCLE TEGERATURE IIOTCHES OUT EIGEIVALUE 15 100 F 81 985870 16 190 F 99 99063h 17 6h F 104 9858h2 18 74 F 99 988013 s
Page 39 L.7 VOID COEFFICIE iT UNCERTAIIITY The void coefficient is calculated with GROK by runninc a case at nominal conditions and then running a case at higher power and a case at lower power with all feedback mechanisms except moderator density unchanged from the first case. The void coefficient is then calculated as:
VC = AK AV where aK and AV are differences in K effective and core average void fraction from the two perturbed GROK cases.
Using statistical propagation of errors, the standard deviation of the void coefficient may be formulated as:
a. %K 0V TaV With the partial derivatives substituted in,7/C becomes:
[ AV
\\
TAV =
[ aK j
1
+
aK )
(( AV)2 Q7 j I
\\
The values of AK and AV are taken from the void coefficient calculation, described above.
A value of Ta K was derived from an end of cycle coastdown. The end of cycle ik was used because it had an extended coastdown, which lasted approximately two =cnths.
Following a coastdown with GROK should give a good indication of the model's ability to calculate a void coefficient since the problem is a fairly simple reactivity balance where decreasing negative feedbacks of voids, xenon and doppler (where voids are predominate) are balanced against the increasing negative feedback of fuel exposure.
Page 40 h.7 VOID COEFFICIENT UNCERTAINTY (CONT'D)
Figure h-1 gives plots of calculated K-effective versus cycle average exposure. The plots show a slight trend of K-effective to decrease with cycle exposure, which may or may not be due to a bias in fuel exposure feedback. Assuming the trend is due to fuel exposure, it was subtracted out of the cycle lh coastdown data, which made the bias of K-effective versus core average voids slightly larger. The altered coastdown data is shown on Figure h-2.
More coastdown points are showr on Figure L-2 than Figure h-l.
The value of CIhK is taken as the vertical scatter of the data about a linear least squares fit line through the data. The slope of the line indicates the calculational bias of the void coefficient and will be accounted for later.
The standard deviation of the calculate change in void fraction ( AV) cannot be derived in such a straight-forward manner.
Instead, AV is assumed to be a function of core flow (F), inlet subcooling (S), core pressure (P) and the void model (V). Using statistical propagation of errors, the error of AV can be calculated as :
2 2
2 2
daV
+
daV
+
daV
+ daV 7
0F CF dS CS OP TP BV TV Values for the partial derivatives daV and daV were computed by doing 0F BS a void coefficient calculation with GROK, using perturbed values of flow and subcooling and comparing the calculated change in average void fraction to the calculated change in average void fract ion when nominal values were used.
The partial derivative with respect to the void model was done in much the same fashion, only an artificial void fraction multiplier was used to perturb the void model. The partial derivative with respect to pressure was not evaluated directly but used the chain rule of derivatives, the partial derivative with respect to voids and an
~
^
I i
l 3
I i
i l-ycle 16 Cycle 17 1.000, l
?
999.
a.
h 998.
o 1
p h'
.997 E
j 5
- 996, ra e
p.
i H
E+
P; O
L4 995-aw
%H rzl
%o f
ti E
.994_
8m
- 1 c+ o a
Q 0
1 2
3 4
5 6
0 1
2 3
4 5
6 7N G
M Ea m
4o e
i G H l
l D
M ta H
o d
1.000.
y "3 un o
Cycle 13 Cycle lh Cycle 15 o
M 999 e
- 998, e
m x
o 997.
Ei 4
m 996.
'l
-995-m m
m 994 g
0 1
2 3
4 5
6 0
1 2
3 4
5 6
0 1
2 3
4 5
6 CYCLE EXPOSURE i
I FIGURE h-2 Pagn 42 BRP Cycle 14 Coastdown LPRIME 0.9990--
0.9985-'
4 1
0.9980-1 0.9975--
+
+
+
+
+
l 0.9970-
+
4 w
+
0.9965-0.9960 ~
0.9955 ~
i 0.9950-i i
i i
i i
i a
O.18 0.19 0.20 0 21 0.22 0.23 0.24 i
Core Average Void Fraction I
Page h3 h.7 VOID COEFFICIENT UNCERTAINTY (COUT'D) estimate of DV, or the partial derivative of void fraction with respect dP to pressure. This was estimated by assuming the enthalpy of the water is constant, the quality is then pressure dependent and all of the volume change will take place in the steam bubbles. Thus the partial derivative BaV is the product of daV and aaV.
dP OV dP In order to evaluate "iEV, values for the standard deviations of pressure, core flow, inlet subcooling and the void model must also be known. A value for Ei'S of.6L8 Btu /lbm was estimated by a statistical propagation of the instrument errors of all of the instruments used to calculate inlet subcooling. A value for (TF of 285000 lbm/hr was estimated for core flow due to instrument error and an assumed 250000 lbm/hr error in core bypass flow. The error for reactor pressure is described in section k.5, above. Reference 3 gives the standard deviation of the error in the void mod 51 as.051.
To this is added additional components of error due to pressure, inlet subcooling and core flow, resulting in a value for CIV of.0576.
How tr V may be evaluated as.0022.
Note that this is significantly a
smaller than the error in the void model itself, because the char.ge in void fraction is of primary interest, not the magnitude of the void fraction.
- Also, C3'VC may now be evaluated as.01525 To get a 95/95 two sided confidence level error band for the calculated void coefficient, this
e
~
Page kh k.7 VOID COEFFICIENT UNCERTAINTY (CONT'D) should be multiplied by the factor of 196 and added to the absolute value of the slope of the linear least squares fit line refered to above.
The slope is
.0052, resulting in an error band of.0351.
h.8 FETHOD OF STATISTICAL ANALYSIS In all cases the standard deviation of a calculated variable that is dependent on several parameters is found by the statistical propagation of errors. That is, for a function of several variables, f(X,Y,Z,... ),
the standard deviation of the function is given by the formula:
TTf af
+
df
+
df
+.
= k E TX di TY dZ TZ An implicit assumption to this method is that the error distribution of each parameter is normal and that the various parameters are independent of one another. Figures 4-3 through h-5 show the error distributions for radic1, axial and local errors. The radial error was found by comparing GROK r.ormalized assembly powers to PDQ. The axial error was found by comparing GROK computed axial fluxvire profiles to measured fluxwire axial profiles. The local error was found by comparing peak pin per assembly from GROK to PDQ. Instrument errors, such as stea= flow or recirculation flow, were also assumed to be normal. Also, the manufacturer's stated tolerance was assumed to be at 90% two sided confidence, so they were divided by a factor o'r 1.6k5 to get a standard deviation.
1
Pap 43 FIGURE k-3 Radial Error Distribution FREQUENCY 130 -
120 110 100 -
i 90 80 -
70 -
60 -
50 -
40 -
30 -
20 10
~
N-l nn, nn
-8
-6
-4
-2 0
2 4
6 8
j Radial Percent Erroc j
__J
~
FIGURE h-h Paga 46 Axial Error Distribution FREQUENCY 3900 --
3600 3300 3
i 2700f 2400 2l00 1800 1500 '
1200 ~
900 600 ~
300 2 M
m_
_m
-12
-9
-6
-3 0
3 6
9
~
Axial Percent Er r o,
FIGURE h-5 Paga 47 Local Error Distribution FREQUENCY 80 -
70 60 50 i 40 b
30i 20 '
10 f two t^asu
-8
-6
-4
-2 0
2 4
6 l
Local Dercent Error l
r-
Page 48 4.8 IETHOD OF STATISTICAL ANALYSIS (CONT'D)
The assumption of independence is not exactly true, but the second order effects should be small enough to ignore. For example, an error in i
the radial power distribution will cause a change in the axial power distribution, but the difference in the axial should be small enough to ignore. Another aspect of the independence assunption in that the point in the core that has the largest deviation of calculated to actual in one parameter does not also contain a large deviation in one or all of the other parameters.
5.0 SUISIARY AND CONCLUSIONS The reactor physics methods employed at Consumers Power Company are very similar to methods used elsewhere in the industry. The computer models are or are derived from widely accepted codes which are well tested and documented.
Agreement with measured data and higher order calculations has demon-strated the accuracy and applicability of the methodology. Reactivity is consistently predicted at both cold and hot operating conditions, and power distributions agree well with the measurements, and higher order calculations indicating that the various neutronic effects are being properly modeled. The table below symnarizes the various uncertainty factors at a 95/95 ene or two sided confidence level.
-++m
Page h9 5.0 SIRCIARY A!!D CO!ICLUSIO!IS (COIIT'D)
Parameter Tyce Uncertainty Factor Bundle Power one sided 3 7661%
Axial Power one sided 5 30h5%
Local Peaking one sided 5.6h91%
Peak Heat Flux
- one sided 9.4017%
MAPLHGR*
one sided s.92158 MCHFR*
one sided 23.373h Void Coefficient two sided
.0351 s
- the uncertainty factor includes the effects of the 2% heat balance error.
}
Page 50 REFERENCES 1.
A. Ahlin and M. Edenius, "CASMO - The Fuel Assembly Burnup Program", AE-RF-76 h158, AB ATOMENERGI, Sweden (1976).
2.
E.E. Pilat et al, " Methods for the Analysis of Boiling Water Reactors Lattice Physics", YAEC-1232, Yankee Atomic Electric Co. (December 1980).
3 G.S. Lellouche, " Mechanistic Model for Predicting Two-Phase Void Fraction for Water in Vertical Tubes, Channels and Rod Eundles", EPRI NP-22h6-SR (February 1982).
4.
D.L. Delp, et al, " FLARE - A Three Dimensional Boiling Water Reactor Simulator", GEAP-4598 (July 1964).
5 B.D. Webb, " Power Peaking at the Tip of a Cruciform Control Rod", Consumers Power Company, (January 6, 1972).
6.
" Jersey Nuclear Company Development Fuel Assemblies for Loading in the Consumers Power Company Big Rock Point Reactor Cycle 9", JN-70-1, Jersey Nuclear Company, (Nove=ber 15, 1970), pp. 100-105, corrected via conversation between SVanVolkinburg and GFPratt, Consumers Power Company, (August 29, 1977).
7 K. Galbraith and J. Jaech, "The XN-2 Critical Power Correlation", XN-75-3h, Exxon Nuclear Company, (August 1, 1975).
8.
A.A. Armand, "The Resistance During the Movement of a Two-Phase System in Horizontal Pipes", Translated by V. Beak, AERE Trans 828. Izvestiya Vsesojuznogo Teplotekhnicheskogo Instituta (1), pp 16-23, (19h6).
9
" General Electric Company Analytical Model for Loss-of-Coolant Analysis in Accordance with 10CFR50 Appendix K", NEDO-20566, (January, 1976).
10.
W.J. Eich et al, " Advanced Recycle Methodology Program System Documentation",
EPRI-RP118-1, (October,1976).
11.
K.P. Galbraith, "GAPEX, A Computer Program for Predicting Pellet to Cladding Heat Transfer Coefficients", XN-73-25, Exxon Nuclear Company (August 13, 1973).
12.
W.R. Cadwell, "PDQ-7 Reference Manual", WAPD-TM-676 (1967).
13.
" Jersey Nuclear Company Development Fuel' Ascemblies for loading in the Consumers Power Company Big Rock Point Reactor Cycle 9", JN-70-1, (November 15, 1970).
lb.
" Jersey Nuclear Company Puo -UO Development Fuel Assemblies for loading 2
y in the Consumers Power Company hig Rock Point Reactor Cycle 10", JN-71-6, (September 1, 1971).
-