ML20135D243
| ML20135D243 | |
| Person / Time | |
|---|---|
| Site: | Arkansas Nuclear  |
| Issue date: | 10/16/1996 |
| From: | AFFILIATION NOT ASSIGNED |
| To: | |
| Shared Package | |
| ML20135D238 | List: |
| References | |
| TR-96-007(NP), TR-96-007(NP)-R01, TR-96-7(NP), TR-96-7(NP)-R1, NUDOCS 9703050149 | |
| Download: ML20135D243 (20) | |
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TR-96-007(NP) Revision 1 ANO Unit 2 Leak Rate Model For l l
Circumferential Cracks l In Steam Generator Tubes ;
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Prepared For Entergy Operations, Inc.
By Tetra Engineering Group, Inc.
October 16,1996 l
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. hDR DOCK 05 d368 P PDR l
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\ L Tetra Engineering Group, Inc.
USA: 110 Hopmeadow Street, Suite 800 Westogue CT, 06089 (1).860.651.4622 France:Immeuble Petra B. B.P. 272, 06905 SOPHIA ANTIPolls (33).92.96.92.54
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TLtra Engineenng Group, Inc. @ 1996 AllRights Reserved.
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I Non Proprietary {
This is a non proprietary version of a Tetra Engineering Group report. Proprietary information has been removed at locations indicated by a heavy vertical bar in the right margin. This report is '
submitted in confidence and is to be used solely for the purpose for which it is furnished. This report, parts thereof, or the information j contained within, may not be transmitted, disclosed, or reproduced in i any form without the written permission of !
Tetra Engineering Group,Inc. ;
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@ Copyright,1996 i Tetra Engineering Group,Inc. ,
Copyright under International Copyright Conventions ;
and under PAN AMERICAN Conveations.
ALL RIGilTS RESERVED 1
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ll TR 96407 ANO Unit 2 Leak Rate Model, Rev 1 Contents ) i i
1 Titra Engineering Group. Inc. C 1996 All Rights R: served.
Contents l
1 Introduction 1 .
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Leak Rate Model 2 j i
Crack Leakage Area 3 Tube Burst Pressure.. .. .. . . .3 Determination of Tube StifTness.. . 3 Normalized Burst Pressure . .4 Elastic Leakage Area. . . .5 Small Scale Yielding Correction . .. . . .7 Plastic Leakage Area.. .. .7 Flow Discharge Coefficient 8 Determination of Through Wall Extent 9 Calibration of Model 11 Sample Calculations . . . . .11 Insitu Leak Tests.. . .13 Monte Carlo Simulation 14 Conclusion 15 References 16 1R-96-007 ANO Unit 2 Laak Rate Model, Rev 1 Contents .lil
L w,a a,-s, an. mc. . ,,,. Yn. A Introduction l The alloy 600 steam generators at Arkansas Nuclear One Unit 2 have experienced significant numbers of OD-initiated circumferential cracks located in the expansion transition of the tubejust above the tubesheet. These cracks are of varying circumferential extent, sometimes occurring as a crack network in multiple axial planes, separated by remaining structural ligaments and may ;
possess arc segments which extend through-wall. Under postulated faulted load I conditions these cracks may leak. The amount ofleakage primarily depends on the effective differential pressure and the total crack opening area.
This report describes a leak rate model applicable to circumferential cracks at Arkansas Nuclear One Unit 2. The methodology is similar in approach to that described in Reference 1, with modifications to account for significant differences due to the circumferential orientation of the cracks.
This report supersedes the circumferential crack model proposed in Reference 2.
Changes from the approach described in Reference 2 include incorporating the !
percent degraded area and projected through wall are length as the contiolling !
variables, refinement of the flow discharge coefficient, and clarification and simplification of the methodology.
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TR-96-007 ANO Unit 2 Leak Rate Model, Rev 1 Introduction l1
Titra Engineering Group, Inc. C 1996 AllRights Reserved. ;
l Leak Rate Model l
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The leak rate from a circumferential crack is given by the same formula as for an ,
axial crack, References 1 and 2. !
Q = C K A )P,y Ip (1) where: ,
Q leak rate at operating temperature (GPM)
K flow discharge coefficient !
2 A crack leakage area (in )
P,y effective differential pressure (psi) p fluid density (lb/in')
C Unit Conversion Constant (7.221)
The most important difference between the treatment of axial cracks in reference 1 and circumferential cracks covered in this report is the determination of the leakage area component, A. The circumferential crack leakage area will be modeled as a function of the percent degraded area (PDA) and through wall arc length. Lateral support of the tube will be considered in determining the crack leakage area (i.e. free bending is precluded). The supported condition is the only configuration of practical interest in a steam generator.
The flow discharge coefficient, K, is an empirical adjustment to account for surface roughness and the torturous flow path associated with stress corrosion cracks. The flow discharge coefficient, K, is determined in section 4 of this report.
The efTective differential pressure is the apparent pressure drop across the tube wall through the crack. This pressure drop is less than the full primary to secondary differential pressure because the primary water flashes to steam as the pressure decreases to the saturation pressure for the primary temperature. This flashing of the primary fluid effectively restricts the fluid flow to that which would occur if the secondary pressure were equivalent to the saturation pressure of the primary fluid at operating temperature.
TR-96-007 Al4O Unit 2 Leak Rate Model. dev 1 Leak Rate Model .l 2
T:tra Engineenng Group, Inc. @ 1996 All Rights R: served 1
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Crack Leakage Area The total leakage area, A, for circumferential cracks in the ANO-2 steam I generators is obtained by the summation of three terms, Reference 2:
A=Ana,aw + Aa,,,,,,,, + A na,uic (2) where:
Aami, elastic component Aco cu, correction component, to account for small scale yielding An ,, plastic component, accounting for gross yielding up to rupture I Theoretical formulations of the elastic and corrected components (Aci,3, and Acomcu.) are taken from Reference 3. This approach is often used in the relevant I literature and b' Seen advantageously compared to other methods by the German !
Reactor Safet) Authority GRS, Teference 4. The more empirical formulation of the plastic component (An,,,) is based mainly on an experimental program conducted by LABORELEC in Oelgium, Reference 5.
Tube Burst Pressure The degree that a circumferential crack will open at accident condition pressure is dependent on the ratio of the accident pressure to the overall burst pressure of the l tube with the circumferential flaw present. The methodology to determine the burst pressure of a tube with circumferential flaws is provided in Reference 6 for various tube conditions and flaw geometries. A simplified procedure using PDA and through wall are length as the controlling variables for the support conditions I pertinent to the ANO 2 steam generators is provided below. This methodology assumes a geometry of the crack as a single through wall segment with any additional degraded area uniformly distributed around the remaining tube circumference.
Determination of Tube Stiffness The eggerate support structure of the CE designed steam generators provides lateral restraint to the tube. This restraint increases the rotational stiffness of the tube and inhibits the opening of a circumferential crack located in a tube near the top of the tubesheet. The tube stiffness is calculated by the following, Reference 6:
TR-96-007 ANO Unit 2 Leak Rate Model, Rev 1 Crack Leakage Area l3
T tra Engineering Group, Inc. O 1996 AllRights Pcserved and >
where:
S Rotational Stiffness (in-') - ,
1 Supportl Distance from tubesheet to first support (in)
]
Support 2 Distance from first to second support (in) x Stiffness Index i ovia Tube Yield Strength o.n Tube Flow Stress Normalized Burst Pressure The normalized burst pressure ratio, P , and the neutral axis location, p, are determined by solving the following two equations simultaneously, Reference 6:
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l TR-96-007 ANO Unit 2 Leak Rate Model, Rev 1 Crack Leakage Area el4
i htra Engineenng Group, Inc. @ 1996 AllRights R served.
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l with terms are defined as follows:
P, Normalized Burst Pressure Ratio p Neutral Axis Location a Crack Half Angle 11 Adjustment for pressure on crack face R Tube Average Radius t Tube Wall Thickness tr Ratio of degraded tube outside through wall area Arc Arc length of through wall segment (degrees) '
PDA Percent Degraded Area of Crack K Stiffness Index The locations of a and p are shown in figure 1.
. ,- m c
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Nesend Asis .
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l Figure 1 l
l The equations are valid over a specific range. p can not exceed x since the neutral axis can not be outside of the tube. Therefore p is set to n whenever the TR 96-007 ANO Unit 2 Leak Rate Model, Rev 1 Crack Leakage Area el5
Titra Engoneering Group, Inc. O 1996 All Rights Reserved.
calculated p is greater than n. In addition, for small circumferential cracks, failure of the tube would occur as an axial burst rather than burst of the circumferential l flaw. Therefore P, can not normally exceed the axial burst pressure ratio, P,,ia, of i (Reference 6): l t
i I (10)
However, for the purposes of determining the crack leakage area only, this limit is ignored and P, is allowed to exceed the axial burst ratio. To ensure that this burst pressure is not confused with the actual burst pressure of the tube a new term is defm' ed: ,
Pn,,m,,a = P,# f. (1I) :
For P, calculated from the circumferential crack procedure above and not limited to P,,i,,.
An alternate to the calculated P3 ,,,,ic,i pressure is the burst pressure regression correlation determined for ANO 2 steam generator tubes in reference 7. The burst pressure as a function of PDA is given by the following equation: ,
- 12) f Similar to Pn,,,,ica, Pc,,,,i, will exceed the axial burst pressure for small values i of PDA. Pc a.n values greater than P,,i, should only be used in determining the leakage and should not be used to determine the overall burst properties of the tube.
Elastic Leakage Area The elastic portion of the leakage area, Aa..iic, is calculated using the following equation, Reference 2:
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I TR-96-007 ANO Unit 2 Leak Rate Model, Rev 1 Crack Leakage Area el6 I .-- .
I T:tra Engineenng Group, Inc. C 1996 All Rights Reserved.
with the terms defined as follows:
P,,, Accident Pressure (psi) o Stress due to Accident Pressure (psi) a Through Wall Crack Segment Length (in) l R Tube Average Radius (in) t Tube Wall Thickness (in)
E Tube Elastic Modulus (psi)
Arc Arc length of through wall segment (degrees) 1 Small Scale Yielding Correction j The area correction for small scale yielding, A%e., is calculated using the l following equation, Reference 2:
Plastic Leakage Area The plastic portion of the leakage area, Ang,, is calculated using the following equation, Reference 2:
l Both k and 6 were empirically determined by laboratory testing of alloy 600 steam generator tubing, References 2 and 5. The equation for k is valid up to a calculated k of 7.5. The value for k is set to 7.5 if the calculated value of equation (20) exceeds 7.5.
TR-96-007 ANO Unit 2 Leak Rate Model, Rev 1 Crack Leakage Area el7
T:tro Engineering Group, Inc. C 1996 AllRights Reserved.
1 l Flow Discharge Coefficient l
! The flow discharge coefficient, K, is an empirical factor which accounts for the steface roughness and tortuous leak path associated with a stress corrosion crack.
Due to the lack of circumferential crack leak test data, leak tests of axial cracks, !
Reference 1, were used to determine K. The axial crack test data was fitted to a l best estimate exponential model using Marquart Levenberg non linear regression 1 analysis, Reference 8. The resulting formula for K, as a function of the crack l
- width, is as follows ,
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where the crack width, CW, is:
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l and A is the leakage area and a is the through wall crack length calculated in the l
previous section. The value of K as a function of crack width is shown in figure 2 below. Since K can not physically be a negative value, values from equation 22 less than lx10" are set to lx104 .
Figure 2 l
Flow Discharge Coefficient
! 0.6 0.5 0.4 g 0.3 0.2 0.1 j 0
l 0 2 4 6 8 10 12 14 16 18 20 22 24 i
4 l Crack Width (in ) !
TR-96-007 ANO Unit 2 Leak Rate Model, Rev 1 Flow Discharge Coefficient el 8
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Determination of Through Wall Extent The NDE inspection results for removed tubes from ANO 2 and other steam generators with similar circumferential cracks were examined to determine the l NDE response as a function of metallurgical indicated degraded area in reference l
- 11. The NDE depth profiles allow calculation of the PDA and through wall are length. For the case of the 0.115 rotating pancake coil, NDE depths greater than i are considered to represent a through wall condition on a best estimate basis. The !
plus point rotating coil probe has limited data but shows a bias toward indicating somewhat larger through wall depths than the 0.115 for equivalent metallurgical ;
conditions. Therefore, indicated depth by plus point rotating probe NDE will l be used as equivalent to through wall for the purposes of determining leakage.
Data from the removed tubes were then examined to determine the proportion of the degraded region which would be considered through wall by NDE as a j function of the indicated degraded area. This is shown in figure 3 below.
Figure 3 ECT Indicated Through Wall Extent vs. Indicated PDA (Pulled Tubes) 1 e Proportion of ECT indicated PDA=> %l l 0.9 Predicted 95% UL F .-- - ' - -Linear Regression , . ,
j I 0.8 - - - - - -
j- -J 5 g 0.7 es r
- N +p'
-j -
- y s
Q 0.6 4- 2 Se ? 0.5 !
-y
/;
-s~
z n y y 0.4 -]- 4 W- -----
j EI 2 0.3 -
-d .- /* d c
0.2
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/- i 4 --
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^ ' ^ ^ - - -
O 0 20 40 60 80 100 Indicated PDA TR-96-007 ANO Unit 2 Leak Rate Model, Rev 1 Determination of Through Wall Extent l 9
T:tra Engineenng Group, Inc. C 1996 AIIRights Reserved.
i Figure 3 indicates that flaws with small degraded areas will have proportionally smaller through wall arc lengths. This makes physical sense in terms of circumferential crack geometry and the way stress corrosion progresses in a steam generator tube. The 95% upper bound on the regression provides reasonable, conservative, values for estimating the through wall extent as a function of the indicated PDA.
- An alternate and more conservative approach would be to assume that the entire l
degraded area forms one through wall are length. This can be used to simplify calculations when the overall numbers of flaws are small and the resulting leakage is also small.
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l TR-96-007 ANO Unit 2 Leak Rate Model, Rev 1 Determination of Through Wall Extent . h0
TLtta Engineering Group, Inc. C 1996 AllRights R: served.
1 Calibration of Model Sample Calculations !
Sample calculations were performed for a range of PDA using ANO 2 steam l generator conditions and tube mechanical properties, References 7 and 9. In the first case, the geometry of the flaw was assumed to be a single throughwall crack ,
equivalent to the PDA. Table 1 shows the calculated leakage values using both l the theoretical and correlation values for the tube burst properties. Normal !
operating and postulated accident condition differential pressures used in the calculations are 1350 psi and 2500 psi respectively.
Table 1 Sample Leakage Calculation i Through Wall Extent Equivalent to PDA l PDA Leakage (GPM) Theoretical Leakage (GPM) Correlation Normal Operation Accident Condition Normal Operation Accident Condition 5 4.57E-06 1.04E-05 4.55 E-06 1.0lE-05 10 1.99E-05 4.42E-05 , 1.98E-05 4.26E-05 15 5.06E-05 0.000112 5.02E-05 0.000107 20 0.000103 0.000229 0.000102 0.000216 25 0.000183 0.000416 0.000181 0.000385 30 0.0003 0.000699 0.000295 0.00063 35 0.000462 0.001118 0.000452 0.00097 40 0.000679 0.07354 0.000658 0.02012 45 0.000965 0.2542 0.000922 0.09976 50 0.001335 0.6578 0.001253 0.2521 55 0.02907 1.515 0.007467 0.5337 60 0.1089 2.963 0.06276 1.034 65 0.2294 4.704 0.1547 1.881 70 0.4033 6.866 0.3068 3.55 75 0.6364 9.274 0.576 7.4 80 1.277 20.77 1.17 18.09 85 3.921 64.47 3.318 54.44 90 24.21 353.9 19.51 284.1 TR 96-007 ANO Unit 2 Leak Rate Model, Rev 1 Calibration of Model e h1
Tetra Engineering Group. Inc. O 1996 AllRights Reserved.
l The calculated leakages in table 1 are conservative compared to the actual steam generator leakages expected. The conservatism is due to the assumed geometry and use of 95/95 lower bound material properties. No consideration is given to NDE uncertainty in the sample calculation.
Table 2 shows the calculated leakage values using figure 3 to estimate the through wall extent as a function of PDA. Both the theoretical and correlation values for i
, the tube burst properties are provided. Normal operating and postulated accident l condition differential pressures used in the calculations are 1350 psi and 2500 psi respectively.
Table 2 Sample Leakage Calculation Through Wall Extent per Figure 3 PDA Leakage (GPM) Theoretical Leakage (GPM) Correlation Normal Operation Accident Condition horNal Operation Accident Condition 5 0 0 0 0 10 0 0 0 0 15 0 0 0 0 20 0 0 0 0 25 0 0 0 0 30 0 0 0 0 35 8.90E-10 1.39E-08 S.07E-10 7.34 E-09 40 5.47E-09 6.63E-08 4.54 E-09 5.0$E-08 l l
45 1.58E-08 1.49E-07 1.65E-08 1.62E-07 50 3.39E-08 2.60C 97 4.26E-08 4.07E-07 55 5.94E-08 3.88E-07 ? 06E-08 8.99E-07 60 1.45E-07 1.29E-06 1.fSE-07 2.03E-06 65 2.88E-07 2.92E-06 3.9 3 E-07 0.00093 70 5.95E-07 0.002064 8 s0E-07 0.007932 75 1.34E-06 0.01789 2.07E-06 0.05331 80 3.76E-06 0.1486 0.000518 0.3755 85 0.007396 1.26 0.02648 2.427 90 0.3258 9.946 0.7967 17.56 i
The calculated leakages in table 2 are more realistic, yet still conservative, l compared to the actual steam generator leakages expected. The conservatism j comes from the use of the 95/95 upper bound on the proportion through wall t geometry and 95/95 lower bound material properties. As expected and confirmed i by operation, negligible leakage would be expected from small circumferential !
cracks (PDA <50%).
j TR 96-007 ANO Unit 2 Leak Rate Model, Rev 1 Calibration of Model e h2
Titra Engineering Group. Inc. 01996 AllRights Reserved.
insitu Leak Tests Insitu pressure test have been performed on a number of tubes with circumferential stress corrosion cracks in CE designed steam generators,
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Reference 10. A few of these tubes leaked during pressure tests allowing a J measurement of the leakage at elevated pressures.
l Three tubes tested in the ANO Unit 2 steam generators had leakage measurements and NDE determined depth profiles of the cracks. The 0.115 rotating pancake '
coil probe was used to provide the NDE depth profiles. Therefore, NDE depths greater than are considered to represent a through wall condition. l Mechanical properties for the tubes in the ANO Unit 2 steam generators are given on a row and heat basis, with a number of different heats present in each row. i Mechanical Properties for the leak tested tubes were estimated by taking the average of the mechanical properties of the two most likely heats for the row of the tubes tested. Mechanical Properties of the Millstone Unit 2 tune was based on the destructive exam results. Mechanical properties of the Maine Yankee tubes was estimated.
A comparison with the calculated and measured leakages is provided in table 3.
Table 3 Insitu Leak Test 3 Comparison of Calculated and Measured Leakages (GPM)
Tube PDA Through wall Measured Theoretical Correlation
(%) Arc Length (GPM) (GPM) (GPM)
(degrees) 1 ANO R24 L132 20.7 30 0.05 <0.01 <0.0 I l ANO R32 L126 51.6 90 0.15 0.10 0.07 ANO R48 L50 34.7 80 0.04 0.19 0.09 MP2 R19 L25 73 197 0.1 0.08 0.07 MY R49 L122 63.1 109 0.2 0.25 0.25 MY R88 L45 81.7 105.4 0.28 0.32 0.44 The measured leakage values from the insitu tests are in good agreement with the calculated values using the best estimate flow discharge coefficient and both the theoretical and the conelation methods.
TR.96-007 ANO Unit 2 Leak Rate Model, Rev 1 Calibration of Model e h3
Titra Engineering Group. Inc. C 1996 AIIRights Reserved.
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l Monte Carlo Simulation Monte Carlo simulation techniques can be used to account for uncertainty and variability of the inputs to the leakage model. Inputs to be model are:
- 1. Burst Correlation as a function of PDA
- 2. Proportion of Flaw Through Wall as a function of PDA
- 3. Tube Mechanical Properties
- 4. Flow Discharge Coefficient as a function of crack opening An distribution is used to model the variation about the burst correlation, reference 12. The through wall extent of a circumferential crack is assumed to vary as a function of PDA with a used to model the scatter about the l regression correlation. Mechanical properties are sampled based on the distribution of properties present in the ANO Unit 2 steam generator tubes. A distribution is used to model scatter about the flow discharge correlation.
TR-96-007 ANO Unit 2 Leak Rate Model, Rev 1 Monte Carlo Simulation e h4
Tsfra Engineenng Groqq. Inc. C 1996 AllRehts R: served.
Conclusion This report provides a leak rate model applicable to circumferential cracks at Arkansas Nuclear One Unit 2. The methodology is similar in approach to that described in Reference 1, with modifications to account for significant differences due to the circumferential orientation of the cracks. The model uses NDE measured percent degraded area and projected through wall are length as the controlling variables in determining the leakage under postulated accident conditions.
Two methods are suggested fa determining the burst properties of the tube for use within the leakage model. The theoretical method relies on a analytic determination of the bending moments and neutral axis location in determining the burst pressure of the flawed tube. The correlation method uses a regression of empirical test results. Both methods give reasonable results.
A best estimate of the flow discharge coefficient was developed from laboratory test data of axial stress corrosion cracks. The flow discharge coefficient should be reevaluated as laboratory leak tests of circumferential stress corrosion cracks become available.
Through wall extent of the circumferential crack was determined as a function of the NDE indicated degraded area. The 95% upper bound on the regression of pulled tube data provides a reasonable, yet conservative, value for use in leakage calculations. As a more conservative alternative, the entire degraded area can be assumed to be represented by a single through wall segment.
The measured leakage values from the insitu tests and in-service measurement are in good agreement with the calculated values using the best estimate flow discharge coefficient and both the theoretical and the correlation methods.
Monte Carlo simulation techniques can be used to model uncertainty and variability in the inputs to the leakage model. This technique is recommended as the best means to obtain the best estimate and 95%/95% upper bound leakage values for a postulated distribution of flaws.
TR-96-007 ANO Unit 2 Leak Rate Model, Rev 1 Conclusion
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T tra Engineering Group. Inc. C 1996 AllRights Reserved.
References i
- 1. "PWR Steam Generator Tube Repair Limits: Technical Support Document for ;
Expansion Zone PWSCC in Roll Transitions", EPRI Report NP-6864-L - ;
Rev.2, August 1993. I 1
- 2. " Leak Rate Model For ANO 2 Circumferential Cracks", Tetra Engineering Group Report TR-95-023, August 2,1995.
- 3. C. Wuthrich (Brown Boveri)," Crack Opening Areas in Pressure Vessels and Piping", Engineering Fracture Mechanics, Vol 18, No. 5,1983.
- 4. H. Grebner and A. Hofler (Gesellschaft fur Reaktorsicherheit)," Crack ,
Opening and Leak Rate Evaluation for Piping Components and Through l Cracks", Nuclear Engineering and Design 135,1992.
- 5. " Belgian Approach to Steam Generator Tube Plugging for Primary Water l Stress Corrosion Cracking", EPRI Report NP-6626-SD and its Addendum 1 titled " Experimental Work"(March 1990).
- 6. "Circumferential Cracks in Steam Generator Tubes: Structural Analysis l Model and Integrated Burst Pressure Database", Tetra Engineering Group l Report TR-95-030, Revision 2, November 15,1995.
- 7. "ANO Unit 2 Steam Generator Tubes: Evaluation of Burst Pressures with Circumferential Flaws Present", Tetra Engineering Group Report TR-95-024, April 11,1996.
- 8. P. S. Jackson," Flow Discharge Coefficient Correlation for Axial EZ-PWSCC in Alloy 600 Steam generator Tubes", Tetra Engineering Calculation 96PSJ027, Rev. O, April 12,1996.
- 9. "ANO Unit 2 Steam Generator Tubes: 95/95 Mechanical Properties", Tetra Engineering Group Report TR-95-025, March 31,1996. ,
- 10. "CEOG Support of Utility Responses to NRC Generic Letter 95-03:
Circumferential Cracking of Steam Generator Tubes", CEOG Task 888, October 1995. j
- 11. "ANO Unit 2 Determination of Plugging Limits For Steam Generator Tubes With Circumferential Cracks", Tetra Engineering Group Report TR-95-026, l April 29,1996.
- 12. " Probability of Burst Model for ANO-2 TTS Circumferential Cracks", Tetra Engineering Group Report TR-96-005, Revision 1, October 16,1996.
TR-96-007 ANO Unit 2 Leak Rate Model, Rev 1 References . hS
ATTACHMENT 4 TR-96-005, REV.1 NON-PROPRIETARY l
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