ML19312E212

Addendum to Basic Safety Rept Re Nuclear Uncertainties, Nonproprietary Version

ML19312E212
Person / Time
Site:	Millstone
Issue date:	05/31/1980
From:	NORTHEAST NUCLEAR ENERGY CO.
To:
Shared Package
ML19312E210	List: ML19312E209 ML19312E212
References
TAC-11348, TAC-11561, TAC-12505, TAC-42846, TAC-43380, NUDOCS 8006030476
Download: ML19312E212 (22)

Text

. .

. DOCKET NO. 50-336 ATTACIIMENT MILLSTONE NUCLEAR POWER STATION, UNIT NO. 2 BASIC SAFETY REPORT (BSR) ADDENDlH NUCLEAR UNCERTAINTIES NON-PROPRIETARY VERSION MAY, 1980 8006030

TABLE OF CONTENTS ,

Section Title Page 1.0 Nuclear Heat Flux Hot Channel Factor, 1 Fh(Z) .

1.1 Estimation of S2 .

3 1.2 Estimation of S,3, 5 1.3 Estimation of S pin

• 7 1.4 Estimation of S 3D 0 '

l.5 Corrhination of Variances 9 2.0 Enthalpy Rise Hot Channel Factor, F 10 r

3. 0 Radial Peaking Factor, F -

11 4.0 Surnnary 11 f

4 e

~

e i

4 l

6 1

LIST OF FIGURES Fi gure Title Page 1 Error in INCA reconstructed Axial Power Versus 12 INCA Axial Node 2 Standard Deviation of INCA Reconstructed Axial 13 Power Errors Versus INCA Axial Node 3 Cycle 1 Measured - Predicted 14 4 Cycle 2 'Fbasured - Predicted 14 5 Cycle 3 Measured - Predicted 14 6 Test Case of Cycle 1 ARO Pseudo Signals 15 7 Instrumented Assemblies - Deviations from Cal- 16 culated Assembly Powers 8 Non-Instrumented Assemblies - Deviations from 16 Calculated Assembly Powers 9 KENO-TURTLE Comparisons / Rods Adjacent to 17 ,

Waterholes 10 KENO-TURTLE Comparisons / Rods Away' from 17 Wate rholes 11 KENO-TURTLE Comparisons /All Rods 17 12 F Versus INCA Node 18 3D 13 Variation in S 3D vs. INCA Node 18 14 Fq Uncertainty vs. Elevation 19 t

POWER PEAKING FACTOR UNCERTAINTY ANALYSIS FOR MILLSTONE 2

. 1- ..

1.0 Nuclear Heat Flux Hot Channel Factor, F (Z) n The elevation dependent nuclear heat flux hot channel fae. tor, F (Z) is defined as the local fuel Tod linear power density divided by the average fuel rod linear power der.sity, assuming nominal fuel pellet and rod diaceters.

It is inferred in INCA from the following terms.

.l. F ,i , the ratio of assembly power to core average power for assembly 1, 1

2. F pin, the hot pin-to-assembly power ratio

3. Ff(Z), the variation in assembly power with elevation normalized to an average of 1.0.

4. F3D(Z), the axial variation in peak planar radial peaking factor a

as computed by three-dimensional relative to two-dimensional values.

For assembly 1, the elevation dependent F value can be constructed from:

Q - i i i i F(Z)l1 =F7 (Z) . Fasm

• pin

• 3D (}

l Equation 1 can be expanded in a Taylor series about nominal component values.

This expansion yields a linear statistic for the fractional deviation for F (Z).

Assuming no correlation between each component, the varience can be estimated

'from Equation 2.

~

l e

s S =' S +S +S +S (2)

Q Z asm pin 3D where 2

S = the estimated variance in fractional deviations in F ,

q 2

S = the estimated variance in fractional deviations of F g, S ,2,,= the estimated variance in fractional deviations in F, ,,

2 =

S the estimated variance in fractional deviations in F g p,

2 S

3D

=

the estimated variance in fractional deviations in F 39

~

2 2 2 2 In general, S , Sg and S may be elevation dependent; S ,2,,and S are

, q 3D elevation independent. Sources of error include instrumentation fluctuations and calibration error, INCA power synthesis modeling variabilities, and calculational errors. ',

For the purposes of determining a tolerance interval, the effective number of degrees of freedom can be estimated from Satterthwaite's formula.(1}

S Q . ,

= 4 4 4 (3)

"Q (S /v ) + (S4 , /v, ) + (S p /v ) + (S 3D 3D '

l i I (1) J. L. Jacch, " Statistical Methods in Nuclear Material Control", l

! TID-26298, 1973. '

1, h

i are the number of degrees of freedom associated with the where Ug, v ,,,, v33 axial, assembly pin and 3D components of Equation (1). The one-sided 95/95 N

is tolerance interval statement associated with Fq N ~" (4)

F q

= 3,F" (1 + g s) q whera l'. y (95/95) = the 95% probability, 95% confidence tolerance interval statistic. .

F = cc?culated or measured value of F 2

1.1 Estication of S g The v::riance estimate for the assembly power axial variation has several .

comper :.r.t s . These ir.clude detector reproducibility, depletion and dri.ft, and a::ial power shape reconstruction f rom integrated detector signals. The 2

cctic;ted value for S is obtained by Z

2 S (Z) = S (5 )

31 +SFIT(Z) 2 where S g = the estimated variance in the fractional measured value due to instrumentation errors ,

2 S

FIT (Z) = the estimated variance in the fractional value of Fg(Z) due to axial shape reconstruction as a function of elevation.

s i i-

. I.

e

, i 2

The two components of S g are independent. As shown in CENPD-153 Rev.1 (August 1974), the major component of g2S is S 2 CENPD-153 reports a KS FIT.

lue for the fitting procedure to be 2.41% and the KS value for the S Z

sum to be 2.45%. Therefore instrumentation error introduces a negligible 2

increase in S g.

Figure 1 shows the variation in Fq fitting error as a function of elevation.

These points span all Cycle 4 burnups and important power levels. Each axial

- - t oqC point represents or more reconstructions. There is a systematic error in reconstructed axial power shape. This systematic error represents higher harmonics of power shape which it is not possible to include in a model preserving only four integral quantities.

The invariance of the error profile with bur'nup or power level allows'a correction term to be developed as a function of elevation which eliminates the systematic errors.

INCA includes this correction function. The. .

standard deviation of residual errors can be computed from ,

._ + ct. 3c.

(6)

- 1

__ l l

I where Ff (Z) = reconstructed relative axial power at elevation Z l Xf (Z) = input relative axial power at elevation Z C(Z) =

correction function at elevation Z

_ i = shape index 1

l

Figure 2 shows the standard deviation of residual errors. These elevation dependent estimates of SFIT(Z) vill be used in the evaluation of height dependent Sq values. The number of degrees of freedom for these values 4 a , c.

is at each elevation.

1.2 Estimation of S,2 ,,

The variance estimate for the assembly ^ fractional power _ deviation has three components. Detector measurement error is one component; calculational error is the second component; extrapolation error is th'e third., The fractional

' errors will be combined as a root-mean square sum.

2 2 2 2 S =S asm m + Scale + Sint (7)

The measurement error vill manifest itself as an increased variance I'n '

(measur d-predicted) f ti al errors. Thus the sum S 2 ,g 2 vill be derived from comparisons of measured INCA inferred assembly powers.

Define this sum as S,2 . Plots of S mc f r cycles 1-3 in Millstone 2 are

+ ct s; shown in Figures 3-5. The largest obser ed value of S is Thus ac .

._ . + a y_ .

will be used as a value which bounds S . The number of degrees of me freedom associated with this statistic is the total nu=ber of measurements

- - + a p_

minus one, i.e. .

• A I

. r Non-instru=ented assemblics potentially can have higher measurement errors.

2 The additional term S he has been added to Equation 6 to account for this 1:4terpolation error. This error component is estimated by comparing INCA crrors with all normal input except that analytical detector signals renlace nor..lly measured values. The resultant INCA map displays assembly powers in in7tru.cated and non-instrumented locations. The difference between inpet assembly powers and INCA output assembly powers estimates INCA model'.ng and interpolation errors. Figure 6 shows a typical example of there errors. Figures 7 and 8 show histograms of deviations between input calculated ascerbly powers and INCA inf erred assembly powers. Because INCA modeling is r.ot perfect, instru=ented assemblics have a distribution of

. _ + 0.,C.

errore. Figarc 7 shows the deviations for cycles 1 and 2 L _

Cony:rlson of measured-to-calculated assembly powers include this modeling error. Figurc 8 shows the same deviations for non-instrumented assemblies.

Whilo Figure 7 and 8 have different skewnesses, their range is identical.

There in littic evidence that inferred non-instrumented assembly powers are significantly less accurate than nearured instrumented assembly powers. ,

o Since S~ has been chosen to be the maximum value from cycles 1-3, small oc 2

valung of S are implicitly included.

. + at,c, 2

Therefore S aSe =

1-4

I 1

2 1.3 Er.tication of S g F is. the factor relating local pin power to integrated assembly power.

I F is derived purely from calculation. ,

pin Errors in F are purely calculational errors.

g

}r:0 Monte Carlo calculations of F are compared with design

, codel (TURTLE) F values. In othervords KENO replaces experiment.

WCAP-9660 contains seven KENO-TUETLE pin power comparisons (Figures i .

4.1, 4.2,-4.4 and 4.5). Figures 9 and 10 show'the fractional errors for pins adjacent to water holes and those not adjacent to water holes. Figure 11 shows the total population of fractional errors.-

. + a. , c.

! Figure 9 shows a small in pin power near

~

~i -

-+a.E vater holes while a slight of pin powers away from water holes is shown in Figure 10. The bias for underestimated pins is handled as a separate cultiplying factor in the evaluation of F

, Q and Fr. With this bias removed direct comparisons of standard deviation can be made. As can be seen in Figures 9,10 and 11 the pins adjacent to water holes have a standard deviation less than the population as a whole and less than pins not adjacent to water holes.

(2) L. Pct -le and N. F. Cross, "KENOIV - An Icproved Monte Carlo Critica #1ty Pr6 gram", ORNL-4938, Nov.1975.

_ + a. , c.

S is chosen to be which is the largest variance shown in pin _ _

Figures 9-11. Experimental (KENO statistical) error which amounts to

_- > a ,c has not been removed, thus this evaluation is conservative. The

~ ~

2 number of degrees of freedom for S is , from the entire population.

pin _ _

2 1.4 Estimation of S 3D A

F is a factor correcting planar radial peaking factors computed in 3D

! a two-dimensional TURILE for three-dimensional effects. F 3D is defined by Equation 8.

_ . -t- CL3 C.

(8) a .

2D where F xy = TURTLE two-dimensional estimate of radial peaking factor F

xy(Z) = cstimated three-dimensional radial peaking factor F

xy(Z) is obtained from coarse mesh three-dimensional TURTLE calculations by methods described in WCAP-8403.

F3D(Z) has been evaluated at several times in core life, several power levels

_ t cLi c between of core rated power and for rod depletion histories

- _ + a ,c .

spanning and unrodded insertions. Figures 12 and 13 give the mean values of F 3D and the standard deviation at each of the INCA axial nodes. Each

_ +ctci mean value of F3D( has observations. The number of degrees of freedom for

- _ + o.ic.

l S3D( ) is _,

at each elevation. .,

+ -

INCA includes the height dependent correction for F 3D' 'E"#* ' "" "

multiplier on the computed Fq (Z). Figure 13 is then the height dependent value of S3D(Z) to be combined with the other uncertainties.

1.5 Combination of Variances Direct application of Equation 2 is first used to compute Sq (g).

i

)

/

+ a c.

3 _ ,_ + o. , c.,

Figure 14 supports a uncertainty value for .

- ~

.~+ a ,c _ + a ic.

all elevations between - -

and of core height. Thus it is expected

. . + Q C. 3 that INCA inferred FQ (Z) values wiP b.: within ,,

of actual values with 95%

probability and 95% confidence. The remaining planes, at the top and ,

bottom of the core, are not limiting planes during normal operation, j ,

Detailed investigation of three (3) cycles of operating data are l

cupportive of this conclusion.

t

i

}

2.0 Enthalpy Rise llot Channel Factor, Fr The enthalpy rise hot channel factor F is defined as h li (9)

I'Ir =

o F (Z)

Q li dZ where h = core height N

The uncertainty in F has been evaluated by integrating the Fq (Z) lg Monte Carlo simulation values obtained in Section 1.5. The uncertainty of F is sensitive to axial shape because S and g S are height dependent.

r 3D Therefore the F uncertainty value has been evaluated with

1. ~

i

.? "_iC

]+ The et c.maximum value of S for Fr obtained is - ._ .

+o n c The resultant one-sided 95/95 tolerance interval is

_ _+ai.t l+ a ,t.Thus an uncertainty of in F is supported. Thus it is expected

~ ' ~ ~ '

_ _ + 0. , t I that INCA inferred values of rF will be within _ ,

of actual values with 95%

probability and 95% confidence. ... t , J. .

e 5

e i s

- I

. F

e L

3.0 Radial Peaking Factor, F xy The radial peaking factor F is the ratio of the peak pin power density to the planar average power density. There exist only three component errors to Fxy, i.e., F and F and F The error in F should be less than asm pin 3D. xy that obtained for F . The F q fractional error is conservatively assumed equal to the F (Z) error. Thus F q (Z) 1 (1+KS)lg. q M llstone 2 ,

Technical Specifications require verification of F only over the middle

• Y . . ._ + 0. , c.

70% of core height. Over this axial interval KS Q<, This maximum statistic will be assumed to conservatively bound all applicable core heights. It is therefore expected that INCA inferred F 's will be within

_ + a c. X7 of actual values with 95% probability and 95% confidence over the interval 0.15 5 Z 1 85.

4.0 Summary

. + C 8- __ + a C. ._ _ + a ,c.

Uncertainty factors of and F on F and on F Q _ _ r . xy have been shown to be adequate. These 95/95 tolerance intervals apply independent of core e

power level, burnup and radial location within the core. The F Q

uncertainty is valid for core elevation between seven and 87% of core and applies to the peak Fq value in each axial plane. The F uncertainty factor applies to the middle 70% of core height.

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