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Procedure to Calculate TTW Initiation Time For the example trial, the following calculations were performed for Tube R92 C84: 1.0 Determination of N 1 1.1 At the start of a trial, the number of AVBs is selected by a random pick from the Poisson distribution developed from the number of affected AVBs observed in tubes without TTW. This CDF is given in Figure 2. Both Unit 3 steam generators have similar distributions and these data were combined to obtain the mean parameter for the Poisson distribution. | Procedure to Calculate TTW Initiation Time For the example trial, the following calculations were performed for Tube R92 C84: 1.0 Determination of N 1 1.1 At the start of a trial, the number of AVBs is selected by a random pick from the Poisson distribution developed from the number of affected AVBs observed in tubes without TTW. This CDF is given in Figure 2. Both Unit 3 steam generators have similar distributions and these data were combined to obtain the mean parameter for the Poisson distribution. | ||
1.2 For this trial for Tube R92 C84, a random pick from the CDF in Figure 2 gave four AVBs in the upper supports as having wear commencing at the start of Cycle 16.Therefore, N 1 = 4 which meets the criteria that 0 < N 1 < N 2.2.0 Determination of WIR, 2.1 The wear index growth rate before instability is calculated by summing the individual AVB wear rates from the upper supports using Eq. 2. The AVB wear rates are determined by N 1 random selections from the AVB wear rate distribution in Figure 3 (pre-initiation curve). For N, = 4, the growth in the wear index before tube instability (WIRj) is WIal 4 [Wi Pre WR E= [WAvBUS]i Page 4 of 10 Four random selections from the AVB wear rate CDF in Figure 3, pre-initiation curve gives, WIR 1 = 12.2 + 8.8 + 6.6 + 16.8 = 44.4% TW per years at power The equation for Line AC is WIAVB-US = 44.4 t.3.0 Determination of WIR 2 3.1 The wear index growth rate after instability is calculated by summing the individual AVB wear rates using Eq. 3. The AVB wear rates are determined by N 2 random selections from the AVB wear rate distribution in Figure 3 (post-initiation curve).3.2 Since N 2 = 7 for Tube R92 C84, the growth in the wear index after tube instability (WIR 2) is n7 DPost 1 WIR2 i=1 Ji Seven random selections from the AVB wear rate in Figure 3, post-initiation curve gives WIR 2 = 14.8 + 9.8 + 7.6 + 16.8 + 14.2 + 12.6 + 20.7 == 96.5 %TW per years at power 3.3 The intercept point (Figure 1 Point E) is calculated from the expression PointE ..AVB-us -WIR 2 tcYc = 82%TW -96.5 (0.926) = -7.36 %TW 3.4 Point E for this trial meets the criterion that the intercept is less than zero. This requirement ensures the slope for Line ED is always greater than or equal to the slope for Line AD (WIR 2 > WIRj). If Point E > 0, the AVB growth rates would be re-sampled and WIR 2 recalculated from Eq. 3 to satisfy this constraint. | 1.2 For this trial for Tube R92 C84, a random pick from the CDF in Figure 2 gave four AVBs in the upper supports as having wear commencing at the start of Cycle 16.Therefore, N 1 = 4 which meets the criteria that 0 < N 1 < N 2.2.0 Determination of WIR, 2.1 The wear index growth rate before instability is calculated by summing the individual AVB wear rates from the upper supports using Eq. 2. The AVB wear rates are determined by N 1 random selections from the AVB wear rate distribution in Figure 3 (pre-initiation curve). For N, = 4, the growth in the wear index before tube instability (WIRj) is WIal 4 [Wi Pre WR E= [WAvBUS]i Page 4 of 10 Four random selections from the AVB wear rate CDF in Figure 3, pre-initiation curve gives, WIR 1 = 12.2 + 8.8 + 6.6 + 16.8 = 44.4% TW per years at power The equation for Line AC is WIAVB-US = 44.4 t.3.0 Determination of WIR 2 3.1 The wear index growth rate after instability is calculated by summing the individual AVB wear rates using Eq. 3. The AVB wear rates are determined by N 2 random selections from the AVB wear rate distribution in Figure 3 (post-initiation curve).3.2 Since N 2 = 7 for Tube R92 C84, the growth in the wear index after tube instability (WIR 2) is n7 DPost 1 WIR2 i=1 Ji Seven random selections from the AVB wear rate in Figure 3, post-initiation curve gives WIR 2 = 14.8 + 9.8 + 7.6 + 16.8 + 14.2 + 12.6 + 20.7 == 96.5 %TW per years at power 3.3 The intercept point (Figure 1 Point E) is calculated from the expression PointE ..AVB-us -WIR 2 tcYc = 82%TW -96.5 (0.926) = -7.36 %TW 3.4 Point E for this trial meets the criterion that the intercept is less than zero. This requirement ensures the slope for Line ED is always greater than or equal to the slope for Line AD (WIR 2 > WIRj). If Point E > 0, the AVB growth rates would be re-sampled and WIR 2 recalculated from Eq. 3 to satisfy this constraint. | ||
The equation for Line ED is WIAVB-US = 96.5 t -7.36 Page 5 of 10 | The equation for Line ED is WIAVB-US = 96.5 t -7.36 Page 5 of 10 4.0 Calculation of Initiation Time From Eq. 1, the initiation time for this trial for Tube R92 C84 is tINIT 82-96.5(0.926) | ||
of Initiation Time From Eq. 1, the initiation time for this trial for Tube R92 C84 is tINIT 82-96.5(0.926) | |||
-7.36 =0.141 years at power 44.4-96.5 | -7.36 =0.141 years at power 44.4-96.5 | ||
-52.1 The above calculation is repeated 1000 times for 1000 trials per tube. The 1000 initiation times (tINIT) are ranked in ascending order and the median value (500th in ranking) is recorded.Page 6 of 10 Variable Initiation-Time Trial For Tube R92 C84 in 3E-088 140 ca 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Operation Time, t (Years at Power)Figure 1 -TTW Initiation-Time Calculation Example for One Trial Page 7 of 10 Unit 3 AVB Distribution for Tubes without TTW 1000 8 0 =Cumulative Distribution 800 700 600 C)500-0 400 300 200 100 00 0 1 2 3 4 5 6 7 8 9 10 11 12 Number of AVBs 1.0 0.9 0.8 U-0.7 0 CF 0.6 .2.0 0.4 0.5 0 0 0.4 >0.3 E 0.2 0.1 0.0 Figure 2 -Distribution of Affected AVBs in Unit 3 for Determining N, Page 8 of 10 Unit 3 AVB Wear Rates U-I.2 C U-C E..6Q°U E C., 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0 5 10 15 20 25 30 AVB Wear Rate, %TW per Years at Power 35 40 Figure 3 -Log-Normal AVB Upper Support Wear Rate Distributions for Unit 3 Page 9 of 10 Unit 3 AVB Wear Depths -Upper Supports L-a 0 dU.a 0 E UJ 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0 5 10 15 20 25 30 35 40 NDE Depth, (%TW)Figure 4 -Wear Depths for Tube/AVB Contacts at the Upper Supports after 0.926 Years at Power Page 10 of 10}} | -52.1 The above calculation is repeated 1000 times for 1000 trials per tube. The 1000 initiation times (tINIT) are ranked in ascending order and the median value (500th in ranking) is recorded.Page 6 of 10 Variable Initiation-Time Trial For Tube R92 C84 in 3E-088 140 ca 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Operation Time, t (Years at Power)Figure 1 -TTW Initiation-Time Calculation Example for One Trial Page 7 of 10 Unit 3 AVB Distribution for Tubes without TTW 1000 8 0 =Cumulative Distribution 800 700 600 C)500-0 400 300 200 100 00 0 1 2 3 4 5 6 7 8 9 10 11 12 Number of AVBs 1.0 0.9 0.8 U-0.7 0 CF 0.6 .2.0 0.4 0.5 0 0 0.4 >0.3 E 0.2 0.1 0.0 Figure 2 -Distribution of Affected AVBs in Unit 3 for Determining N, Page 8 of 10 Unit 3 AVB Wear Rates U-I.2 C U-C E..6Q°U E C., 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0 5 10 15 20 25 30 AVB Wear Rate, %TW per Years at Power 35 40 Figure 3 -Log-Normal AVB Upper Support Wear Rate Distributions for Unit 3 Page 9 of 10 Unit 3 AVB Wear Depths -Upper Supports L-a 0 dU.a 0 E UJ 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0 5 10 15 20 25 30 35 40 NDE Depth, (%TW)Figure 4 -Wear Depths for Tube/AVB Contacts at the Upper Supports after 0.926 Years at Power Page 10 of 10}} |
Revision as of 22:02, 11 May 2019
ML13142A032 | |
Person / Time | |
---|---|
Site: | San Onofre ![]() |
Issue date: | 05/20/2013 |
From: | St.Onge R J Southern California Edison Co |
To: | Document Control Desk, Office of Nuclear Reactor Regulation |
References | |
TAC ME9727 | |
Download: ML13142A032 (12) | |
Text
SOUTHERN CALIFORNIA Richard 1. St. Onge EDISObNJ Director, Nuclear Regulatory Affairs and L.. ON Emergency Planning An EDISON INTERNATIONAL Company May 20, 2013 10 CFR 50.4 U.S. Nuclear Regulatory Commission ATTN: Document Control Desk Washington, DC 20555-0001
Subject:
Docket No. 50-361 Supplement to Response to Request for Additional Information (RAI 70)Regarding Confirmatory Action Letter Response (TAC No. ME 9727)San Onofre Nuclear Generating Station, Unit 2
References:
- 1. Letter from Mr. Elmo E. Collins (USNRC) to Mr. Peter T. Dietrich (SCE), dated March 27, 2012, Confirmatory Action Letter 4-12-001, San Onofre Nuclear Generating Station, Units 2 and 3, Commitments to Address Steam Generator Tube Degradation
- 2. Letter from Mr. Peter T. Dietrich (SCE) to Mr. Elmo E. Collins (USNRC), dated October 3, 2012, Confirmatory Action Letter -Actions to Address Steam Generator Tube Degradation, San Onofre Nuclear Generating Station, Unit 2 4. Email from Mr. James R. Hall (USNRC) to Mr. Ryan Treadway (SCE), dated March 15, 2013, Request for Additional Information (RAIs 68-72) Regarding Response to Confirmatory Action Letter, San Onofre Nuclear Generating Station, Unit 2 5. Letter from Mr. Richard J. St. Onge (SCE) to Document Control Desk (USNRC), dated April 1, 2013, Response to Request for Additional Information (RAIs 68, 69, 70 and RAI 2 Revision 1) Regarding Confirmatory Action Letter Response, San Onofre Nuclear Generating Station, Unit 2
Dear Sir or Madam,
On March 27, 2012, the Nuclear Regulatory Commission (NRC) issued a Confirmatory Action Letter (CAL) (Reference
- 1) to Southern California Edison (SCE) describing actions that the NRC and SCE agreed would be completed to address issues identified in the steam generator tubes of San Onofre Nuclear Generating Station (SONGS) Units 2 and 3. In a letter to the NRC dated October 3, 2012 (Reference 2), SCE reported completion of the Unit 2 CAL actions and included a Return to Service Report (RTSR) that provided details of their completion.
By e-mail dated March 15, 2013 (Reference 3), the NRC issued Requests for Additional Information (RAIs) regarding the CAL response.
SCE provided the response to RAIs 68, 69, 70, and RAI 2 Revision 1, in a letter dated April 1, 2013 (Reference 4). Enclosure 1 of this letter provides a supplement to the RAI 70 response.P.O. Box 128 San Clemente, CA 92672 Document Control Desk-2-May 20, 2013 There are no new regulatory commitments contained in this letter. If you have any questions or require additional information, please call me at (949) 368-6240.
Enclosure:
- 1. Supplement to RAI 70 response cc: A. T. Howell IIl, Regional Administrator, NRC Region IV J. R. Hall, NRC Project Manager, SONGS Units 2 and 3 G. G. Warnick, NRC Senior Resident Inspector, SONGS Units 2 and 3 R. E. Lantz, Branch Chief, Division of Reactor Projects, NRC Region IV ENCLOSURE 1 SOUTHERN CALIFORNIA EDISON SUPPLEMENT TO THE RESPONSE TO REQUEST FOR ADDITIONAL INFORMATION REGARDING RESPONSE TO CONFIRMATORY ACTION LETTER DOCKET NO. 50-361 TAC NO. ME 9727 Supplement to RAI 70 Response RAI 70 Reference 1, Response to RAI 2 -It is unclear to the staff how TTW initiation times were calculated (see description on pages 4 and 5 (of 18)). Describe each individual step, in sequential order, to calculating TTVV initiation time for a given tube, for a given trial. Provide (or reference) in figure form all distributions that were sampled.RESPONSE SUPPLEMENT Note: RAI Reference 1 is SCE's "Response to Request for Additional Information (RAIs 2, 3, and 4) Regarding Confirmatory Action Letter Response," dated February 25, 2013. SCE responded to RAI 70 via letter "Request for Additional Information (RAI 70) Regarding Confirmatory Action Letter Response," dated April 1, 2013. This response supplement demonstrates the process explained in the response to RAI 70.Single Trial Calculation of Initiation Time for Tube R92 C84 in 3E-088 The purpose of this discussion is to provide further details into how the initiation time is calculated using a bi-linear wear index model, which represents the tube conditions before and after in-plane instability.
It presents an example calculation in the context of the analytical procedure given in RAI 70 response.
Also discussed is the determination of the anti-vibration bar (AVB) wear rates at tube contact locations.
Figure 1 shows the calculation of tINIT for a single trial. Tube R92 C84 in 3E-088 was chosen to show the calculation procedure.
The analysis variables are shown to aid in the description of the probabilistic solution for TTW initiation time and the numerical calculations.
The important points on the wear index lines are labeled A through E.Governing Equations The equation that defines the initiation time is MP-U -WIR 2 tcYc WIR 1 -WIR 2 Where: EOP is the end of the operating period for Unit 3, and tINIT is the initiation time (Figure 1 Point B)MOP-US is the wear index at EOP from AVB wear in the upper supports (Figure 1 Point D)WIR 1 is the growth rate in the WIAVB-US prior to initiation (slope of Line AB in Figure 1)Page 2 of 10 WIR 2 is the growth rate in the WIAvE-us after initiation (slope of Line BD in Figure 1)tcyc is the length of the operating period (0.926 years at power)Equation 1 is the solution for the intersection of the two lines (AC and ED) and defines the time in the operating period when the change in the upper support wear index slope due to in-plane instability occurs. Point B in Figure 1 represents the calculated initiation time as determined by the model.The growth in the wear indices in the AVB upper supports before in-plane instability (WIR 1) and after in-plane instability (WIR 2) are calculated from the following:
... [WRAB-us]i (2)WIR2 E=1 AN=N r' AIRPOst WIR 2... AVB-[us]i (3)AIPr e adI~s where ....AB-US and rAVBus are the cumulative distribution functions (CDF) for the AVB wear rates derived from wear depth data for tubes without TTW and with TTW. The variable N 1 is the number of AVB upper-support locations in the tube before in-plane instability.
The parameter N 2 is the number of AVB upper-support locations with detected wear in the tube after 0.926 years at power.Analysis Input For Tube R92 C84 in 3E-088, the following input data are known from the Cycle 16 inspection results and used in the simulation to determine Line ED in Figure 1.1) Total number of AVB upper support locations having detected wear after 0.926 years at power is seven, N 2 = 7.2) Wear index due to AVB wear in upper supports after 0.926 years at power, WEOPUS = 82% TW (Figure 1 Point D).The following variables that are treated statistically and used to determine Line AC: 1) Number of AVB upper support locations before in-plane instability (N 1) is randomly picked from Poisson distribution in Figure 2 based on tubes with no TTW.2) AVB wear rates before and after in-plane instability are randomly selected from the distributions in Figure 3.AVB Wear Rates The AVB wear rates for the upper supports (B03 through B10) were determined by dividing the AVB wear depths by the 0.926 years at power. The technical basis for using the full operating interval of 0.926 years at power to establish the AVB wear rates was discussed in the response to RAI 2 with supporting data given in RAI 68. As shown in Figure 4, the AVB upper support Page 3 of 10 wear depths in tubes are not significantly dependent on whether in-plane instability had occurred or not. Final AVB wear depths for tubes with TTW are similar to the final wear depths for tubes without TTW including the upper extreme values. The average wear depth for tubes with TTW is 10.1% TW with a maximum depth of 37% TW. For tubes without TTW, the average depth is 8.9% TW and the maximum is 36% TW. This indicates that the wear rates at individual tube/AVB contact points before in-plane instability are not significantly elevated after TTW has initiated.
It is appropriate to use 0.926 years at power to develop AVB wear rates for conditions prior to in-plane instability (tubes without TTW) since it is reasonable to assume that AVB wear in these tubes began at the start of Cycle 16. Since the AVB depths in tubes with TTW include AVB locations that existed before in-stability, it is also reasonable to assume that these locations make up the upper tail for the distribution of wear rates shown in Figure 4. Given the depth distribution comparison shown in Figure 4, the interval 0.926 years at power was used to determine the CDF for AVB wear rates for conditions following in-plane instability.
The post-initiation curve was used to calculate the wear index rate WIR 2 since this will result in a steeper slope for Line BD and a longer initiation time to be calculated in the simulation.
Procedure to Calculate TTW Initiation Time For the example trial, the following calculations were performed for Tube R92 C84: 1.0 Determination of N 1 1.1 At the start of a trial, the number of AVBs is selected by a random pick from the Poisson distribution developed from the number of affected AVBs observed in tubes without TTW. This CDF is given in Figure 2. Both Unit 3 steam generators have similar distributions and these data were combined to obtain the mean parameter for the Poisson distribution.
1.2 For this trial for Tube R92 C84, a random pick from the CDF in Figure 2 gave four AVBs in the upper supports as having wear commencing at the start of Cycle 16.Therefore, N 1 = 4 which meets the criteria that 0 < N 1 < N 2.2.0 Determination of WIR, 2.1 The wear index growth rate before instability is calculated by summing the individual AVB wear rates from the upper supports using Eq. 2. The AVB wear rates are determined by N 1 random selections from the AVB wear rate distribution in Figure 3 (pre-initiation curve). For N, = 4, the growth in the wear index before tube instability (WIRj) is WIal 4 [Wi Pre WR E= [WAvBUS]i Page 4 of 10 Four random selections from the AVB wear rate CDF in Figure 3, pre-initiation curve gives, WIR 1 = 12.2 + 8.8 + 6.6 + 16.8 = 44.4% TW per years at power The equation for Line AC is WIAVB-US = 44.4 t.3.0 Determination of WIR 2 3.1 The wear index growth rate after instability is calculated by summing the individual AVB wear rates using Eq. 3. The AVB wear rates are determined by N 2 random selections from the AVB wear rate distribution in Figure 3 (post-initiation curve).3.2 Since N 2 = 7 for Tube R92 C84, the growth in the wear index after tube instability (WIR 2) is n7 DPost 1 WIR2 i=1 Ji Seven random selections from the AVB wear rate in Figure 3, post-initiation curve gives WIR 2 = 14.8 + 9.8 + 7.6 + 16.8 + 14.2 + 12.6 + 20.7 == 96.5 %TW per years at power 3.3 The intercept point (Figure 1 Point E) is calculated from the expression PointE ..AVB-us -WIR 2 tcYc = 82%TW -96.5 (0.926) = -7.36 %TW 3.4 Point E for this trial meets the criterion that the intercept is less than zero. This requirement ensures the slope for Line ED is always greater than or equal to the slope for Line AD (WIR 2 > WIRj). If Point E > 0, the AVB growth rates would be re-sampled and WIR 2 recalculated from Eq. 3 to satisfy this constraint.
The equation for Line ED is WIAVB-US = 96.5 t -7.36 Page 5 of 10 4.0 Calculation of Initiation Time From Eq. 1, the initiation time for this trial for Tube R92 C84 is tINIT 82-96.5(0.926)
-7.36 =0.141 years at power 44.4-96.5
-52.1 The above calculation is repeated 1000 times for 1000 trials per tube. The 1000 initiation times (tINIT) are ranked in ascending order and the median value (500th in ranking) is recorded.Page 6 of 10 Variable Initiation-Time Trial For Tube R92 C84 in 3E-088 140 ca 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Operation Time, t (Years at Power)Figure 1 -TTW Initiation-Time Calculation Example for One Trial Page 7 of 10 Unit 3 AVB Distribution for Tubes without TTW 1000 8 0 =Cumulative Distribution 800 700 600 C)500-0 400 300 200 100 00 0 1 2 3 4 5 6 7 8 9 10 11 12 Number of AVBs 1.0 0.9 0.8 U-0.7 0 CF 0.6 .2.0 0.4 0.5 0 0 0.4 >0.3 E 0.2 0.1 0.0 Figure 2 -Distribution of Affected AVBs in Unit 3 for Determining N, Page 8 of 10 Unit 3 AVB Wear Rates U-I.2 C U-C E..6Q°U E C., 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0 5 10 15 20 25 30 AVB Wear Rate, %TW per Years at Power 35 40 Figure 3 -Log-Normal AVB Upper Support Wear Rate Distributions for Unit 3 Page 9 of 10 Unit 3 AVB Wear Depths -Upper Supports L-a 0 dU.a 0 E UJ 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0 5 10 15 20 25 30 35 40 NDE Depth, (%TW)Figure 4 -Wear Depths for Tube/AVB Contacts at the Upper Supports after 0.926 Years at Power Page 10 of 10