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Category Archives: Estimating Loss-of-Coolant Accident (LOCA) Frequencies Through the Elicitation Process
PWR Non-piping
The same three major non-piping components (RPV, valves, and pumps) as considered for BWRs are considered for PWRs, plus the steam generator and pressurizer are added. One of the operational experience databases showed an order of magnitude higher incident rate for PWR non-piping than BWR non-piping. This was partially attributed to the fact that there are more PWRs than BWRs. However, this comparison is also biased by the large number of steam generator tube failures reported in the databases. Steam generator tubes are subjected to a host of degradation mechanisms: fatigue, denting, external SCC, PWSCC, and overload failures. It was almost universally accepted that SGTRs would be the dominant contributor to the PWR Category 1 non-piping LOCA frequency. In fact the PWR steam generator tube failure frequency is the dominant contributor to the overall PWR small-break LOCA (Category 1 LOCAs) frequency when considering both the piping and non-piping contributions. Even so, it is the expectation of a number of the panel members that the steam generator tube contribution to the small-break LOCA frequency will decrease with time due to steam generator tube replacement programs and improvements made to the secondary side water chemistry.
In general, many of the same degradation mechanisms that are important for PWR piping are important for the non-piping components as well. PWSCC is an important degradation mechanism for many of the smaller Alloy 600 components such as the CRDMs, heater sleeves, steam generator tubes, and other penetrations. As was the case for piping, the likelihood of multiple cracks forming, and possibly coalescing, and the relatively fast propagation rates associated with this type of cracking makes this mechanism a major concern from a LOCA perspective. Also, since this mechanism is more severe at the higher temperatures associated with PWRs, it is considered to be a bigger threat for the PWRs than the BWRs, at least in the short term. As was the case for PWR piping, thermal fatigue is also a concern for PWR non-piping components. It is especially of concern at nozzle inlets and other locations where thermal stratification may exist. Furthermore, for all the reasons highlighted for piping, thermal fatigue is a mechanism that can lead to large leaks, i. e., fast propagation rates, attacks a wide area, and difficult to prioritize inspection protocols due to the fact that it can attack a variety of materials. Mechanical fatigue is another common degradation mechanism to both PWR piping and non-piping components.
Mechanical fatigue is most important for smaller components, such as heater sleeves and small penetrations that are subjected to vibratory stresses due to equipment operation.
Another mechanism of special concern to non-piping components is common cause bolting failures. This is especially relevant to manways and bolted valves. The common cause mechanism could be improper installation or maintenance of bolts, e. g., improper torque, external corrosion of multiple bolts, or possibly steam cutting of multiple bolts.
Also, boric acid corrosion of carbon steel components such as RPV and steam generators can be aggressive under certain conditions.
Figure L.31 shows the Category 1 LOCA frequencies for the major PWR non-piping components at 25 years. As expected, the expected failure frequencies are highest for the steam generator. The higher LOCA frequency for the steam generator is driven by the SGTR data.
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The other major contributors to the Category 1 LOCA frequencies for PWR non-piping were the RPV and the pressurizer. The main subcomponent contributing to the RPV frequency is the CRDMs while the main subcomponent contribution to the pressurizer frequency is the heater sleeves. For Category 2 LOCAs, a single SGTR cannot sustain such a leak. Thus, for the Category 2 LOCAs, the CRDM and pressurizer heater sleeves became the main contributors.
For Category 3 and 4 LOCAs there was no consistent agreement among the panelists as to the major contributors. As one can see in Figure L.32, all five major components contribute fairly equally to the Category 4 LOCA frequencies. As such, there is tremendous variability about the frequency associated with each component. This variability was also apparent for the Category 6 LOCAs. This variability reflects the inconsistent opinions and approaches followed by the panelists, as well as the difficulty of this type of assessment. As is to be expected, there was a wide array of possible failure modes for dissimilar components to be considered, and the panelists tended to gravitate towards a few of the failures that they personally thought were most credible. Given all of this, the level of variability was thought to be reasonable given the event frequencies. This was one reason for adopting the elicitation approach in the first place. The highest LOCA frequencies were for the pressurizer nozzle. In addition, many of the panelists considered manway or shell failures important, irrespective of the component type. Thus, they anticipated similar distributions for both the steam generator and pressurizer. There were also major differences of opinion among the panelists as to the most important failure modes.
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Figure L.33 shows the cumulative LOCA frequencies for the PWR non-piping components at 25 years of plant operations. The Category 1 LOCA frequencies for PWR non-piping are the highest frequencies estimated by the elicitation panel for piping or non-piping, BWR or PWR. The median frequency is almost 5×10-3. The variability among the panelists was very small. The difference between the minimum and maximum predictions was less than an order of magnitude. These high frequencies and low variability were driven by the SGTR data for which ample data exist in the operational experience databases; thus explaining both the high frequencies and excellent agreement between participants. For the Category 2 LOCAs, the agreement, at least on a minimum and maximum basis, is not nearly as good. However, the agreement on the basis of the spread in the IQR is nearly as good as it is for the Category 1 LOCAs. Again, for the Category 2 LOCAs, the major contributors are the CRDMs and the pressurizer heater sleeves. The much wider variability for the Category 3 through 6 LOCAs reflects differences in opinion among the panelists as to the important failure modes and their associated frequencies.
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1e-141e-13 1e-12 1e-11 1e-10 1e-9 1e-8 1e-7 1e-6 1e-5 1e-4 1e-3 1e-2 1e-1
Figure L.33 Cumulative PWR Non-Piping LOCA Frequencies at 25 Years of Plant Operations
Figure L.34 shows the effect of time on the PWR non-piping Category 1 LOCA frequencies. There is a very slight decrease in the frequency between 25 years (present day) and 40 years (end of plant license) due mostly to steam generator replacement programs and improved inspection and mitigation programs, e. g., improved eddy current inspection programs and improved secondary side water chemistry. There was also an expected decrease in the LOCA frequencies associated with CRDMs due to on-going head replacement programs and improved CRDM inspection programs that may go into effect over the next few years. However, there was some concern expressed that the maintenance and inspection programs for the larger component bodies (pressurizer, steam generator, RPV) may not be as rigorous as for the piping systems. Figure L.35 shows the effect of operating time on the PWR non-piping Category 6 LOCA frequencies. As can be seen in Figure L.35, the median values remain constant with time and the variability among the participants (at least on the basis of the IQR) also remains fairly constant. This tends to indicate that the participants did not foresee any significant aging effects to occur.
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1e-8 1e-7 1e-6 1e-5 1e-4 1e-3 1e-2 1e-1 1e+0 |
LOCA Frequency (CY-1)
Figure L.34 Effect of Operating Time on the Cumulative Category 1 LOCA Frequencies for PWR
Non-Piping Components
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1e-14 1e-13 1e-12 1e-11 1e-10 1e-9 1e-8 1e-7 1e-6 1e-5 |
LOCA Frequency (CY-1)
Figure L.35 Effect of Operating Time on the Cumulative Category 6 LOCA Frequencies for PWR
Non-Piping Components
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Contrary to what was observed for the Category 1 and 6 LOCA frequencies, the median value of the Category 4 LOCA frequencies increases an order of magnitude between 25 and 40 years and then remains constant after that, see Figure L.36. As was the case for PWR piping, aging was thought to have the largest impact on LOCA Categories 3 and 4. It was thought by some that aging could accelerate near the end of the plant license faster than the effects of mitigation and inspection could become effective, especially if the plant operators do not see a return on their investment for such inspection and mitigation programs near the end of the plant’s license.
——- 1——— 1——— 1——— 1——— 1———- 1——— 1——— 1——— 1——-
1 e-11 1 e-10 1e-9 1 e-8 1 e-7 1 e-6 1 e-5 1 e-4 1 e-3 1 e-2 1 e-1
Figure L.36 Effect of Operating Time on the Cumulative Category 4 LOCA Frequencies for PWR
Non-Piping Components
Figures L.37 and L.38 show the cumulative MV estimates, along with the 5% and 95% bound values for the various participants for the PWR Category 1 and 4 non-piping LOCA frequency estimates, respectively, at 25 years of plant operating time. Of note from these figures is higher uncertainty among almost all of the participants for the Category 4 LOCAs when compared with the Category 1 LOCAs. A number of the panelists showed 3 to 4 orders of magnitude of uncertainty for the Category 4 LOCAs while all of the panelists had less than approximately 2 orders of magnitude of uncertainty in their Category 1 results. In addition, the variability in the panelist’s MV estimates was within 1 order of magnitude for their Category 1 results while the variability among their results spread over a range of almost five orders of magnitude for their Category 4 results. The fact that the agreement among the panelists was so good for the Category 1 predictions plus the low uncertainty of their individual predictions is a reflection that there was near consensus agreement that the single overwhelming dominant contributor to this class of LOCAs was SGTRs, for which ample field experience is available in the operational experience databases.
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Lh*h
——- 1——- 1—— 1——- 1——- 1——- 1—— 1——— 1——- 1——- 1——- 1—— 1——-
10-13 10-12 10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100
LOCA Frequency (CY-1)
Figure L.37 PWR Non-Piping Category 1 LOCA Frequencies Showing MVs, 5% LB, and 95% UB
Values for All Participants Who Responded to the PWR Non-Piping Questions
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10-13 10-12 10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 |
LOCA Frequency (CY-1)
Figure L.38 PWR Non-Piping Category 4 LOCA Frequencies Showing MVs, 5% LB, and 95% UB
Values for All Participants Who Responded to the PWR Non-Piping Questions
ATTACHMENT B TO APPENDIX D
BASIS FOR LOCA FREQUENCY MODELS
Attached as Tables D. B.1 (RR System Loop B) and D. B.2 (FW System Loop B) are the Excel spreadsheets on which the BWR LOCA frequency model is based. Attached as Tables D. B.3 (RC-HL), D. B.4 (RC Surge Line), and D. B.5 (HPI/NMU Line) are the spreadsheets on which the PWR LOCA frequency model is based.
The input to the calculation of a selection of posterior weld failure rates is summarized in Tables D. B.6 (BWR-1, NPS28), D. B.7 (BWR-2, NPS12), D. B.8 (PWR-1), D. B.9 (PWR-2), and D. B.10 (PWR-3).
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ASME XI Examination Category |
Component ID |
Description / Configuration |
NPS [inch] |
Wall Thk [inch] |
Weld Material |
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B-J |
1-4100A — 19BC |
14" Branch (CGE-1-4500) Connection to 29-inch pipe |
14.00 |
2.350 |
304N/SA182 |
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B-F |
1-4500A — 1(DM) |
Bimetal (INCONEL) weld; Pressurizer Surge Line Nozzle to Safe End |
14.00 |
1.406 |
SS |
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B-J |
1-4500A — 2 |
Bimetal (INCONEL) Weld: Safe End to Pipe |
14.00 |
1.406 |
SS |
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B-J |
1-4500A — 3 |
Pipe-to-Elbow |
14.00 |
1.406 |
SS |
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B-J |
1-4500A — 4 |
Pipe-to-Elbow |
14.00 |
1.406 |
SS |
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B-J |
1-4500A — 5 |
Pipe-to-Elbow |
14.00 |
1.406 |
SS |
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B-J |
1-4500A — 6 |
Pipe-to-Elbow |
14.00 |
1.406 |
SS |
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B-J |
1-4500A — 7 |
Pipe-to-Elbow |
14.00 |
1.406 |
SS |
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B-J |
1-4500A — 8 |
Pipe-to-Elbow |
14.00 |
1.406 |
SS |
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B-J |
1-4500A — 9 |
Pipe-to-Elbow |
14.00 |
1.406 |
SS |
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B-J |
1-4500A — 10 |
Pipe-to-Elbow |
14.00 |
1.406 |
SS |
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B-J |
1-4500A — 11 |
Pipe-to-Elbow |
14.00 |
1.406 |
SS |
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B-J |
1-4500A — 12 |
Pipe-to-Elbow |
14.00 |
1.406 |
SS |
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B-J |
1-4500A — 13 |
Pipe-to-Branch Connection |
14.00 |
1.406 |
SS |
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Table D. B.5 PWR-5 — HPI/NMU Line
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BWR Feedwater Nozzles
RPV nozzles constitute another potential non-piping LOCA concern. The example used to address this concern here is BWR feedwater nozzles, which have in the past been subject to thermal fatigue cracking [1.5]. The thermal fatigue problem was caused by mixing of hot reactor water and relatively cold feedwater (see Figure I.5) during reactor startups, shutdowns and other periods of low power operation, when feedwater heating is generally unavailable. Cracking of various depths, up to 1.5 inches (38 mm), was detected in a number of BWRs in the 1970s (see Figure I.6). At that time, the standard feedwater nozzle design incorporated a loose-fitting thermal sleeve/sparger configuration, as shown in Figure I.5. Since then, all U. S. BWRs have installed some type of fix, employing either welded-in spargers or multiple-sleeve designs with shrink fits and piston rings to protect the nozzle from the effects of the cold feedwater. No subsequent cracking has been discovered since the improved thermal sleeves were installed.
In order to perform a base case analysis of this problem, a modification to the software (VIPER-NOZ) was developed to estimate leakage and failure probabilities for BWR Reactor Vessel feedwater nozzles. The substantive changes to the VIPER software in VIPER-NOZ were the addition of thermal fatigue crack initiation and growth algorithms specific to the feedwater nozzle thermal cycling phenomenon, and zeroing out the effects of irradiation embrittlement, since feedwater nozzles are far enough from the reactor core region that neutron fluence effects are small. The VIPER-NOZ software was run for conditions representative of the original nozzle/sparger designs, to confirm that cracking probabilities consistent with early field experience (Figure I.3) are predicted. The boundary conditions were then modified to represent improved nozzle/sparger designs, which reduce the effects of thermal fatigue on the nozzle. The analyses were conducted for a 60 year operating lifetime, and included the effects of periodic ISI, which are performed for these nozzles on ten-year intervals. The results are given in the following table:
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Table I.3 Summary of BWR Feedwater Nozzle PFM Results
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The predicted leakage cases were treated as Category 0 breaks in this case, and since the nozzle is attached to a 12 inch diameter pipe, the maximum credible break size was assumed to correspond to single ended rupture of a 12 inch pipe, which corresponds to a Category 4 break. A total of 1 million simulations were run, and except for LBB type failures at 40 and 60 years, no other failures were predicted. Thus a failure frequency of less than 1E-6 is given for most entries in the above table.
Response: This comment duplicates Comment 3-3. See the response to Comment 3-3 for guidance on interpolation schemes
Submitted by Zouhair Elawar — Palo Verde Nuclear Generating Station Comment: The various LOCA frequency tables provided results for the past 25-year operating time period and for the 40-year average plant life. The more suitable value to select for use in PRA models may well be the expected LOCA frequencies applicable to the next 15 years. That particular selection allows for frequency penalties at aging plants as well as credits at plants with new steam generators and/or improved methods of inspections & leak detections. In order to extract the next 15-year LOCA frequencies from the existing tables, the user has to perform simple arithmetic calculations which may lead to human errors and inconsistent applications across the industry. Please provide frequency estimates for the next 15-year time period.
Response: As stated in the Executive Summary, the frequency estimates are not expected to change dramatically over the next fifteen years for any size LOCA, or even the next thirty-five years for LOCA Category 4 and smaller. Because of the predicted stability in these estimates over the near-term, it is recommended that the 25 year (i. e., current-day) results be used to estimate the average LOCA frequencies over the next 15 years of fleet operation. This last point was incorporated in both the Executive Summary and Section 7.4 of the revised NUREG.
Submitted by Zouhair Elawar — Palo Verde Nuclear Generating Station
Comment: There is insufficient description of small LOCA frequency’ “comparison results” relating to those in NUREG 5750 (which is most typically used in current PRA models). If one excludes the contribution of steam generator tube rupture frequency, the draft NUREG-1829 small LOCA value is ONE order of magnitude higher. Please add justifications for that large difference.
Response: This comment is very similar to Comment GC3. See the response to Comment GC3 for the comparison of NUREG-1829 with both NUREG/CR-5750 and operating experience estimates. More detailed information on these comparisons is available in Sections 7.9 and 7.10.
Submitted by Zouhair Elawar — Palo Verde Nuclear Generating Station
Comment: Provide a section on statistical validation of small LOCA frequency. By using the method of Jeffrey’s non-informative prior (over the past 1,500 reactor years with ZERO events excluding steam generator tube ruptures), the expected small LOCA frequency is at the 1E-04 level. This frequency is one order of magnitude lower than the frequency reported in the draft NUREG. Plant experiences of >1,500 reactor-years of operating history should be considered as valid predictor of small LOCAs. That consideration is further strengthened by improved methods and increased requirements for in-service — inspections & leak detections.
Response: A new section has been added to the NUREG (Section 7.10) to compare SB LOCA frequency estimates from the elicitation with operating experience. As discussed in this section, the elicitation estimates for BWR and PWR small break LOCA frequencies are generally consistent with operational experience estimates. The BWR and total PWR elicitation mean frequency estimates are only 20 percent and 100 percent higher, respectively, than operational experience estimates. Further the PWR SGTR frequencies are virtually identical to operating experience predictions. The biggest difference between the elicitation results and operating experience occurs for SB LOCA estimates that are determined without SGTR contributions. The elicitation mean frequency estimate is approximately 5 times higher than the operating experience estimate which accounts for nearly all of the 100% increase in the total PWR SB LOCA frequencies indicated above. Although the five-fold increase in the elicitation non-SGTR SB LOCA frequencies is not inconsistent with operating experience (Section 7.10), this difference is physically supported by the panelists’ qualitative and quantitative responses. The panelists indicated that medium and, to a lesser extent, small LOCAs in PWRs are most dramatically impacted by current PWSCC concerns (Section 6.3.2). This increase reflects this concern.
Surge Line
The surge line is one of the base case systems.
F.3.3.1 Dimensions and Welds — From the piping isometric available to the panel members, the surge line is a 14 inch line (14 inch outer diameter) with a thickness of 35.7 mm (1.406 inches). The material is SA376 Type 304, which is an austenitic stainless steel. There are some 13 welds in the line.
F.3.3.2 Stresses and Cycles — The stresses at the surge line elbow are provided in Reference F.5, which is evidently the highest stressed location in the line. These stresses include seismic events and are given in Table F.8. The stress amplitude is contained in this table, which is one-half the stress range (peak-to-peak value).
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Load Pair |
Amplitude |
Number/ |
Load Pair |
Amplitude |
Number/ |
|
(ksi) |
40 yr |
(ksi) |
40 yr |
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HYDRO-EXTREME |
190.17 |
6 |
9D-LEAK TEST |
52.20 |
50 |
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8A-OBE |
163.18 |
14 |
8G-LEAK TEST |
52.20 |
65 |
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9B-OBE |
162.06 |
14 |
8G-UPSET3 |
51.00 |
30 |
|
8B-HYDRO |
138.05 |
4 |
8G-12 |
50.96 |
90 |
|
8B-OBE |
127.94 |
10 |
8G-16 |
50.93 |
90 |
|
9A-OBE |
127.04 |
14 |
8E-8G |
50.92 |
13 |
|
8C-OBE |
64.76 |
68 |
8E-OBE |
43.38 |
77 |
|
9F-OBE |
64.17 |
68 |
9H-OBE |
42.79 |
500 |
|
8F-18 |
63.40 |
68 |
8H-13 |
39.82 |
90 |
|
9C-11 |
63.38 |
68 |
8H-OBE |
37.43 |
203 |
|
8D-OBE |
54.02 |
72 |
8H-UPSET4 |
35.42 |
40 |
|
9G-OBE |
53.42 |
400 |
8H-9E |
33.94 |
90 |
|
8G-18 |
52.38 |
22 |
2A-8H |
33.94 |
77 |
|
9D-11 |
52.35 |
22 |
3A-10A |
33.10 |
4120 |
|
8G-17 |
52.35 |
90 |
6-10A |
33.10 |
200 |
|
9D-LEAK TEST |
52.20 |
50 |
3B-10A |
33.10 |
4120 |
|
8G-LEAK TEST |
52.20 |
65 |
7-10A |
33.10 |
4580 |
|
8G-UPSET3 |
51.00 |
30 |
2B-SLUG1 |
32.87 |
100 |
|
8G-12 |
50.96 |
90 |
2B-SLUG2 |
32.87 |
500 |
|
4B-10A |
29.90 |
17040 |
To estimate the influence of seismic events, it is necessary to also have the stress history without such events. It is not possible to remove seismic events knowing only the information in the above table. This information was provided in Reference F.14 and is summarized in Table F.9.
|
Load Pair |
Amplitude |
Number/ |
Load Pair |
Amplitude |
Number/ |
|
(ksi) |
40 yr |
(ksi) |
40 yr |
||
|
HYDRO-EXTREME |
190.17 |
6 |
8G-16 |
50.93 |
90 |
|
9B-HYDRO |
149.86 |
4 |
8G-9H |
50.92 |
128 |
|
8A-UPSET 4 |
140.42 |
14 |
2A-8E |
40.10 |
90 |
|
9B-UPSET4 |
139.43 |
10 |
8H-9H |
40.09 |
100 |
|
8B-UPSET4 |
105.89 |
14 |
9H-10A |
40.09 |
272 |
|
9A-UPSET4 |
105.13 |
2 |
9E-13 |
39.82 |
90 |
|
9A-LEAK |
103.86 |
12 |
3A-10A |
33.10 |
4120 |
|
8F-18 |
63.40 |
68 |
6-10A |
33.10 |
200 |
|
9C-11 |
63.38 |
68 |
3B-10A |
33.10 |
4120 |
|
9F-LEAK |
63.37 |
68 |
7-10A |
33.10 |
4580 |
|
8C-LEAK |
63.37 |
35 |
2B-SLUG1 |
32.87 |
100 |
|
2A-8C |
62.30 |
33 |
2B-SLUG2 |
32.87 |
500 |
|
8G-18 |
52.38 |
22 |
5-10A |
29.90 |
9400 |
|
8G-17 |
52.35 |
90 |
4A-10A |
29.90 |
17040 |
|
9D-11 |
52.35 |
22 |
4B-10A |
29.90 |
17040 |
|
2A-8D |
51.20 |
72 |
2B-10A |
20.60 |
14400 |
|
8H-9G |
51.18 |
400 |
2A-10A |
20.60 |
14805 |
|
8G-UPSET3 |
51.00 |
30 |
10A-UPSET1 |
20.59 |
70 |
|
9D-12 |
50.96 |
50 |
10A-UPSET5 |
20.59 |
30 |
|
8G-12 |
50.96 |
40 |
10A-UPSET6 |
20.59 |
5 |
|
10A-UPSET2 |
20.59 |
95 |
|||
|
1B-10A |
20.59 |
1533 |
|||
|
1B-10B |
20.00 |
87710 |
The cyclic stress amplitudes of Tables F.8 and F.9 provide the information for the initiation analysis, but additional information is required for the growth portion of the analysis. The spatial gradient (primarily radial) is required. Also, when analyzing the stability of a through-wall crack, the steady normal operating stress is needed. This stress is considered to be the sum of the pressure, deadweight and restraint of thermal expansion stresses. The values of these latter two are given in Reference F.5 as
Cdw = 0 Ote = 102.6 MP (14.88 ksi).
Many of the high stress contributors in Tables F.8 and F.9 are from rapid excursions of the coolant temperature. The largest stress amplitude (half the peak-to-peak) is 1,310 MPa (190 ksi), so the stresses are large (but localized). These are the stresses at the peak stress location, which is not at weld. The spatial stress gradients (both along the surface and into the pipe wall) are required for a thorough analysis. The radial gradient (into the pipe wall) can be estimated by the procedure given in Section 5.3 of Reference F.5, i. e.,
The following specific rules were applied to assign stress to the uniform and gradient categories:
• Cyclic stresses associated with seismic loads were treated as 100 percent uniform stress.
• Cyclic stresses greater than 310 MPa (45 ksi) were treated as having a uniform component of 310 MPa (45 ksi), and the remainder were assigned to the gradient category.
• For those transients with more than 1000 cycles over a 40 year life, it was assumed that 50% of the stress was uniform stress and 50% a through-wall gradient stress. In addition, for these transients, the uniform stress component was not permitted to exceed 69 MPa (10 ksi).
The gradient stress mentioned above is assumed to vary through the thickness as
= &o — 3£ + 3 £2 j [F.6]
In this equation, co is the stress at the inner wall of the pipe, £ = x / h, x is the distance into the pipe wall from the inner surface, and h is the wall thickness. The stresses and cycles are high enough that fatigue crack initiation is important, which has been considered in Reference F.5, which shows a probability of 0.981 of a leak in 40 years for this component. The LOCA probabilities will be less. The use of the gradient along the surface will reduce this.
A refined stress analysis was available as part of the efforts reported in Reference F.6. These stresses included details of the variation of the stress in the circumferential direction, and are referred to as the “refined stresses”. The stresses used in the surge line evaluation were based on the actual stress analysis for a CE-designed plant in response to NRC Bulletin 88-11 dealing with surge line stratification. The loadings were based on the methods approved by the NRC staff in the CE Owner Group Report CEN 387-NP, "Pressurizer Surge Line Flow Stratification Evaluation," Rev. 1-NP, December 1991. Additional evaluations of the local stress distributions in the elbow were conducted to get the detailed stress distribution around the circumference of the elbow. The critically stressed location that produced the highest probability of cracking was the circumferential stresses in the side of the elbow due to stratification bending. Detailed stresses are not provided, because they belong to the plant that allowed us to use them.
F.3.3.3 Results — PRAISE runs were made using the versions that can treat fatigue crack initiation. No inspections were considered. Since crack initiation is considered, there will be no effect of a pre-service inspection. The results are summarized in Table F. 10.
|
Table F.10 Cumulative PRAISE Results for the Surge Line Elbow
|
It is seen that the seismic stresses do not have a large effect, roughly a factor of 3. The use of the refined stresses greatly reduces the calculated failure probabilities. The computer run for 380 lpm (100 gpm) took about 20 hours and resulted in no failures in 107 trials. The runs for > 5,700 lpm (1,500 gpm) with the stresses from Tables F.8 and F.9 had 2 and 1 failures in 107 trials, respectively, and these runs each took many hours. Hence, it is evident that the Monte Carlo simulation with multiple fatigue crack initiation sites does not allow definition of the small probabilities of large leaks in the surge line elbow, and an alternate procedure was developed. Stratified sampling is not used for fatigue crack initiation.
F.3.3.4 Alternate Procedure — In cases where the dominant degradation mechanism is fatigue crack initiation with subsequent growth, PRAISE currently has no way of generating low probability results other than conventional Monte Carlo simulation. This is the dominant mechanism for three of the base line components; the surge line elbow, the HPI make up nozzle and the BWR feedwater line elbow. Excessive computer time is needed to generate probabilities of various size leaks for these components, with some runs taking 4 days on a 3 GHz pc, with no leaks of even 380 lpm (100 gpm). An alternate procedure is needed to estimate leak probabilities for the large leaks of interest, and such a procedure is described below.
As part of a standard analysis, the PRAISE software computes the crack opening area and leak rate as functions of the length of through-wall cracks. Hence, this information is readily available, and can be used to determine the length of a through-wall crack needed to produce a given leak rate, such as 380 lpm (100 gpm), 5,700 lpm (1,500 gpm), etc. The probability of having a leak of a given magnitude is then the probability of having a through-wall crack exceeding that length. The half-crack length, b, is considered, which is a function of the desired leak rate, q. Hence, b(q) can be considered as known.
The probability of a double-ended-pipe-break (DEPB) is also of interest. In the cases of interest here, the critical net section stress failure criterion is used. For a through-wall crack, the value of b for a DEPB is given by the expression
 |
![Подпись: [F.7]](/img/1183/image130.png "image130"){kind=small} |
where R[ is the inside radius, aflo is the flow stress (average of yield and ultimate) and aLC is the load controlled stress, which is equal to the pressure plus deadweight stress.
The version of PRAISE that performs Monte Carlo simulation of fatigue crack initiation and growth commonly provides information on the probability of having any leak and a leak exceeding a given magnitude. In order to have a nonzero number for the latter, a leak exceeding that magnitude must occur during the simulation. The problem is that this often does not occur within a number of trials that can be reasonably performed. In order to overcome this, PRAISE was modified to print out the length of any crack resulting in a leak and the time at which it first became through-wall. This was then used to estimate the size distribution of through-wall cracks as a function of time. The complementary cumulative distribution, denoted as Pb(>b), is concentrated upon. Then the probability of a leak greater than q is given by
PlK (> q) = Pb [> b(q)] [F.8]
Table F.11 summarizes the information from a PRAISE run using the stresses from Table F.9 for the crack opening area (A) and leak rate (q) for a given half-length of a through-wall crack (b).
Table F.11 Half Crack Lengths and Areas for a Given Leak Rate
(Surge Line Elbow, Table F.9 Stresses)
|
Q, gpm |
b, inches |
b nRi |
A, in2 |
A A • Apipe |
|
100 |
5.981 |
0.445 |
0.936 |
0.010 |
|
1500 |
10.379 |
0.591 |
10.028 |
0.143 |
|
5000 |
11.791 |
0.671 |
46.762 |
0.476 |
|
DEPB |
15.95 |
0.907 |
— |
— |
A table of lengths of through-wall cracks was generated from the modified version of PRAISE using 104 trials using the stresses of Table F.9 (no seismic). In this run, there were 2,162 leaks within 25 years, 5,932 within 40 years and 8,890 within 60 years. Dividing these numbers by 104 provides leak probabilities that are nearly the same as obtained from the Monte Carlo simulation with 107 trials. Figure F.2 is the complementary cumulative distribution of leaking crack sizes for the three times of interest.
The upper curve is for 60 years, because there is a higher probability of encountering a longer crack at this longer time. The lines in this figure are least squares curve fits, which are discussed later.
6.0
 |
Figure F.2 shows changes in slope, and the “lumpiness” of the distribution is readily apparent. This “lumpiness” is representative of a multi-modal probability density function of crack length, which is most likely due to the fatigue crack initiation sites being taken as 50 mm (2 inches) in length. That is, each two-inch segment around the circumference is taken as an independent initiation site. The surface length of an initiated crack is also a random variable. Once a crack initiates, it grows, and can link with neighboring cracks. This growth and linking can lead to sudden increases in crack length (by linking) and evidently is responsible for the multi-modal nature of the probability density function of crack length.
 |
The multi-modal nature of the probability density function is clearly shown in Figure F.3.
Figure F.3 Histogram of the Half-Length of Through-Wall Cracks at 60 Years for the Surge Line
Pleasing curve fits to the lines in Figure F.2 are not possible. A good fit could perhaps be obtained by assuming that the histogram of Figure F.3 consists of a sum of lognormals with medians to match the
location of the modes and relative weights adjusted to match the relative heights of their modes. This is believed to be unwarranted, since the multi-modal nature of the density function is an artifact of the modeling assumption of a 50 mm (2 inch) long initiation site. It is better to just smooth out the cumulative distribution, and this was accomplished by a linear least squares curve fit to the cumulatives on log-linear scales. Since it is desired to represent the curve at long cracks, the fit was performed only for cracks corresponding to a probability less than 0.2. This eliminates the numerous cracks at higher probabilities that would skew the curve fit if included in the least squares calculations. The lines in Figure F.2 are the curve fits obtained in this manner.
The assumed functional form was
P(> b) = 0.2e“c(b"b°-2) [F.9]
The values of C and b0.2 depend on the time. Once they are evaluated, the leak probabilities of a given size are obtained using the crack sizes in Table F.11. Table F.12 summarizes the results.
Table F.12 Summary of Results for Surge Line Elbow (Table F.9 Stresses)
|
Time, years |
25 |
40 |
60 |
|
Number of cracks |
2162 |
5932 |
8890 |
|
Cracks above 0.2 |
1730 |
4744 |
7109 |
|
b0.2 |
2.072 |
2.089 |
2.108 |
|
C |
1.876 |
1.597 |
1.425 |
|
P(>5.981) |
1.31×10-4 |
4.00×10-4 |
8.02×10-4 |
|
P(>10.379) |
3.41×10-8 |
3.56×10-7 |
1.52×10-6 |
|
P(>11.791) |
2.42×10-9 |
3.73×10-8 |
2.04×10-7 |
|
P(>15.95) |
9.86×10-13 |
4.86×10-11 |
5.43×10-10 |
Table F.13 summarizes the results along with corresponding ones obtained directly from the Monte Carlo simulation. The conventional Monte Carlo simulation used 106 trials for 380 lpm (100 gpm) and 107 trials for 5,700 lpm (1,500 gpm).
Table F.13 Cumulative PRAISE Results for the Surge Line Elbow as Obtained from the Alternate
Procedure and Directly from Monte Carlo Simulation
(Table F.9 Stresses)
|
Direct Monte Carlo |
Alternate Procedure |
||
|
25 |
0.233 |
0.216 |
|
|
О A |
40 |
0.587 |
0.593 |
|
60 |
0.882 |
0.889 |
|
|
>100 |
25 |
7.5×10-6 |
1.31×10-4 |
|
40 |
7.1×10-5 |
4.00×10-4 |
|
|
60 |
2.51×10-4 |
8.02×10-4 |
|
|
О |
25 |
<10-7 |
3.41×10-8 |
|
m |
40 |
<Ю7 |
3.56×10-7 |
|
A |
60 |
1.0X10-7 |
1.52×10-6 |
|
о |
25 |
— |
2.42×10-9 |
|
о о |
40 |
— |
3.73×10-8 |
|
л |
60 |
— |
2.04×10-7 |
|
DEPB |
25 |
— |
9.86×10-13 |
|
40 |
— |
4.86×10-11 |
|
|
60 |
— |
5.43×10"1U |
Table F.13 shows that the alternate procedure is able to greatly extend the leak rates whose probabilities can be estimated. In cases where direct comparisons are possible, the alternate procedure gives higher leak probabilities. The direct Monte Carlo for 5,700 lpm (1,500 gpm) employed 107 trials and took 36 hours of computer time. The alternate procedure used 104 trials, so took about 2 minutes. Even in this era of fast cheap computer time, it would still be prohibitive to use direct Monte Carlo to generate the results obtained by the alternate procedure. It would take 1010 trials to produce the DEPB results in the above table. This translates to 36,000 hours of computer time, or about 4 years.
BENGT LYDELL
The approach is documented in “Base Case Report No. 2.” For systems other than the five Base Case Systems, the base case results established anchor distributions for BWR and PWR Code Class 1 reference piping systems. As an example, the base case results for PWR hot legs were applied to PWR cold legs but adjusted to account for insights about the service conditions and degradation susceptibility specific to cold legs. For the other BWR and PWR piping systems not covered by the base case study, the base case results were adjusted downwards or upwards as appropriate by accounting for unique piping design features (e. g., size, material, and weld population), service conditions and field experience. For nonpiping passive components the base case report again was used as the main reference (or source of calibration parameters) in combination with reviews of relevant operating experience. In summary, this Panel Member’s response to the elicitation questions is based on insights from degradation mechanism analyses in combination with reviews and statistical evaluations of operating experience.
Defect Distribution and Leak Rate at Failure — With Leak Detection
In the previous section it was assumed that the defect would instantaneously snap open to the full COD associated with its length at the moment the pressure boundary was breached. In reality this will probably not happen. Instead, the very large defects, which are those of interest, will probably grow to different through wall depths at different points around the length. Thus, much smaller surface defects would begin to breach the boundary at different points around the defect. The COD of these small defects would then remain elastic until the whole defect progressed to the surface. In this scenario, the leak from the defect would start very small and grow, slowly at first and then probably very quickly before snapping open to the fully plastic COD.
During this time of surface crack combination, the leak rate may exceed the value at which the operators shut the reactor down to a safe state in order to investigate the leak. Provided this occurs before the crack reaches a critical size, i. e., before the leak rate moves very quickly to the final leak state. Whilst the high leak rate may still occur, the plant would be in a safe condition. This can be seen as leak detection.
This probability of leak detection is almost certainly associated with the length of the defect that is itself related to the rate of leakage in the previous section. Thus, expert judgement was again used to introduce a factor, based on the leak rate, which would represent this probability of leak detection. Figure G.6 shows this plot as a function of leak rate.
From this plot it can be seen that the reduction factor for Category 1 (380 lpm [100 gpm]) is about five, rising to a factor of about fifty at Category 6 (1,900,000 lpm [500,000 gpm]).
PUBLIC COMMENT RESPONSES
APPENDIX M — PUBLIC COMMENT RESPONSES
Submitted by: Bill Galyean — Idaho National Laboratory
Comment: [Note: The footnote indications below do not appear in the submitted comment; they were added as reference points for the response.] Aside from the fact that I was a contributing panel member in the elicitation process, I want to express my compliments on the effort made by the NRC management and staff to produce realistic and useful results. I believe with the significant research performed in recent years coupled with the accumulated operating experience, reasonable estimates of LOCA frequencies can be made. NRC has recognized these facts and acted accordingly and appropriately. That said, I also wish to express my opinion on the some of the details of the elicitations process and portions of the subsequent analyses about which I disagree, but with the acknowledgement that had they been done differently, the results would not change significantly (i. e., the reported results would probably be reduced by less than an order of magnitude). The first issue relates to the interpretation of the LOCA frequencies and associated uncertainties. The instructions given to the panel members stated that we were to make a best-estimate1 of the “single ‘true’ value”2 for the industry-wide (or more accurately BWR-wide and PWR-wide) LOCA frequency. This is an issue because I do not believe a “single true value” exists for the LOCA frequency. Specifically, I believe each plant has differences in design, construction, operations, age, and maintenance such that in reality the plant-to-plant variation in LOCA frequencies will be quite large. These two interpretations can be made consistent however, if the “single true value” is viewed as an average or mean value of the population of frequencies. While on the surface this might seem to be a question of semantics and appears to have little significance, the implication of the interpretation on the uncertainty characterization is significant. If the “single true value” interpretation is employed, the question becomes, what does the uncertainty associated with this value represent. Since the implicit assumption is that plant-to-plant variability does not exist (otherwise how can there be a single frequency appropriate for the entire industry?), then there is no stochastic or aleatory uncertainty associated with the estimate. That is, the presence of outliers (or event plant-to-plant variability) in the population of nuclear power plants (NPP) is ignored. The uncertainty therefore represents the level of confidence of each panel member’s estimate of this single true frequency.3 Given that the uncertainty represents an individual’s confidence in their own estimate, what is the basis for automatically assuming the probability distribution associated with this confidence uncertainty is not symmetrical?4 Or to ask more specifically, with this interpretation of the point estimate value and associated interpretation of the uncertainty, why do the authors assume that the uncertainty surrounding each panel member’s estimate should be a lognormal distribution that is weighted toward higher (conservative) values? While I agree that the uncertainty associated with LOCA frequencies should be asymmetrically weighted toward higher values; this is based on the observation that not all plants are identical, and that if a LOCA occurs at a plant, that plant will likely be shown to be a poor performer, not representative of the fleet as a whole.5 This is not the same as assuming the confidence uncertainty surrounding the estimates provided by the panel members, of a “single true value” should be represented with a lognormal (which was done in the elicitation).6 [Note: the use of the lognormal distribution became entrenched in PRA with its use in WASH-1400 (1975). However, the model employed then was motivated by the sparse data available from the commercial nuclear power industry at that time. Data used in that study were collected from many different industries and sources. These data were used to develop a probability distribution of the population of possible values, effectively capturing the random component of the uncertainty. Specifically, the authors of WASH-1400 did not know which value in the population of values collected, was the most appropriate value to use. Therefore the entire population of values was characterized in the probability distribution. The data were not combined, or averaged to estimate a single value, and the uncertainty modeled with the lognormal distribution was not meant to describe a statistical confidence on a single true value, but used to describe the variability in possible values. Quoting directly from WASH-1400: “Because of the large spread, the failure rate data were treated as random variables, incorporating both the physical variability and the uncertainty associated with the rates. Moreover, since the study’s results were to apply to a population of approximately 100 nuclear plants, it was important to show the possible variability and uncertainty in this population.” The consequences of employing the lognormal distribution to characterize each individual panel member’s uncertainty, manifests itself in how the estimates were interpreted and processed (by the authors) and in the effects of the overconfidence adjustment made to the base case results. Specifically, the best-estimates solicited by the authors of this “single true value” were interpreted as median values of the lognormal distribution, allowing for the derivation (by the authors) of a higher mean value. [Note that for any probability distribution skewed toward higher values, the lognormal being one example, the mean will always be greater than the median.] This calculated mean value was then used to represent the panel member’s input to the aggregation process used for generating the LOCA frequency results. Additionally, this assumption of a lognormal for the uncertainty on each panel member’s estimate, has the additional impact of calculating an even higher (compared to the non-adjusted calculated mean) mean value after the widening of the uncertainty in the overconfidence adjustment. My concerns are twofold. First, the opinions of the panel members were solicited, and then modified (increased) by the authors.7 Irrespective of the instructions and discussions during the elicitation process, this point was viewed with dismay by more than one panel member. Second, the processes and analyses employed have introduced a conservative bias into the final base case results, with additional conservative bias8 inserted in the various sensitivity studies.9 This “creeping conservatism” is not necessarily undesirable given the significant uncertainties and the uses to which the results will be employed; however, it should be explicitly acknowledged and clearly stated rather than obscured in the details of the analyses.10
Response: The authors have identified ten separate issues in this comment, as indicated by the inserted footnotes. The responses to these issues are provided below.
Issue 1: The instructions given to the panel members stated that we were to make a best-estimate1 of the “single ‘true’ value”2 for the industry-wide (or more accurately BWR-wide and PWR-wide) LOCA frequency.
1. Issue 1 Response: The panel members were not asked to provide a ”best-estimate“ of any quantity. Rather, they were asked to provide a MV and LB and UB values for each question. The MV was defined such that, in the panel member’s opinion, the unknown true value for that particular question has a 50% chance of falling above or below the MV, with similar definitions for the LB and UB values (Section 3.8.5).
Issue 2: The instructions given to the panel members stated that we were to make a best-estimate1 of the “single ‘true’ value”2 for the industry-wide (or more accurately BWR-wide and PWR-wide) LOCA frequency.
2. Issue 2 Response: Additionally, the panel members were not asked to estimate a ’’single ’true‘ value“ of any quantity. Rather, the elicitation focused on estimating generic, or average, LOCA frequencies for the commercial fleet by combining the contributions from individual component failures. As stated in Section 2 of NUREG-1829, the generic BWR and PWR estimates were determined by first estimating the separate LOCA frequency contributions associated with specific BWR piping, BWR non-piping, PWR piping, and PWR non-piping failures for each panelist. These individual piping and non-piping component failure frequencies were then combined to estimate parameters of the total passive system LOCA frequency distributions for BWR and PWR plants at each distinct LOCA category and time period. Panelists were specifically instructed to consider broad plant differences in estimating these component failure frequencies and their uncertainties (Section 3). More information related to the instructions given to the panel can be found in Sections 2 and 3 of NUREG-1829.
Issue 3: If the “single true value” interpretation is employed, the question becomes, what does the uncertainty associated with this value represent. Since the implicit assumption is that plant-to-plant variability does not exist (otherwise how can there be a single frequency appropriate for the entire industry?), then there is no stochastic or aleatory uncertainty associated with the estimate. That is, the presence of outliers (or event plant-to-plant variability) in the population of nuclear power plants (NPP) is ignored. The uncertainty therefore represents the level of confidence of each panel member’s estimate of this single true frequency.3
3. Issue 3 Response: More precisely, as stated in Section 3.8.5, the elicited quantities for each question (MV, LB and UB) are percentiles of each panel member’s subjective distribution. As stated above, this subjective distribution should consider broad plant difference related to plant design that can affect the LOCA frequency. Also, except for the base case frequencies used to anchor the results, panel members were never asked about absolute frequencies, only about relative frequencies of specific components, subsystems or systems. Their responses were then combined to form estimates of LOCA frequencies.
Issue 4: Given that the uncertainty represents an individual’s confidence in their own estimate, what is the basis for automatically assuming the probability distribution associated with this confidence uncertainty is not symmetrical?4
4. Issue 4 Response: The distribution associated with the response to any question was assumed to be asymmetrical only if the stated LBs and UBs were not symmetrical about the MV.
Issue 5: While I agree that the uncertainty associated with LOCA frequencies should be asymmetrically weighted toward higher values; this is based on the observation that not all plants are identical, and that if a LOCA occurs at a plant, that plant will likely be shown to be a poor performer, not representative of the fleet as a whole.5
5. Issue 5 Response: As noted above and in NUREG-1829, the estimated LOCA frequencies are industry-wide or “generic, or average, estimates for the commercial fleet” (Section 2). Consequently, the uncertainties associated with the estimates pertain to these generic estimates and not to any individual plants whose LOCA frequencies may differ from the generic estimates. As stated in Section 2 of the NUREG, the panelists were instructed to account for broad plant-specific factors which influence the generic LOCA frequencies in providing uncertainty bounds, but not consider factors specific to any individual plants. Thus, the uncertainty bounds should include both contributions related to the uncertainty of the generic estimates as well as uncertainty due to broad plant-specific fleet differences.
Issue 6: This is not the same as assuming the confidence uncertainty surrounding the estimates provided by the panel members, of a “single true value” should be represented with a lognormal (which was done in the elicitation).6
6. Issue 6 Response: The lognormal, or split lognormal when the responses are asymmetrical, is a reasonable distribution for representing the responses to the various questions so that the responses can be combined to estimate LOCA frequencies. Based on the sensitivity analyses conducted in Section 7, the authors expect that the log-normal distribution assumption has an inconsequential impact on the bottom line parameter estimates, especially in light of the large uncertainties observed in the final results. Note that the report does not estimate the distributions of LOCA frequencies, but only the four bottom-line parameters (mean, median, 5th and 95th percentiles) of these distributions.
Issue 7: First, the opinions of the panel members were solicited, and then modified (increased) by the authors.7
7. Issue 7 Response: It is misleading to state that “.. .the opinions of the panel members [were] modified (increased) by the authors”. Rather, an overconfidence adjustment was applied to increase only the uncertainties for those panelists whose responses indicated more confidence than the group average. The panelists’ median estimates were not modified. The justification for the overconfidence adjustment is provided in Section 5.6.2. Responses were not modified in any other manner.
Issue 8: Second, the processes and analyses employed have introduced a conservative bias into the final base case results, with additional conservative bias8 inserted in the various sensitivity studies.9
8. Issue 8 Response: The only “conservative bias” that may have been introduced in the summary estimates was through the use of the overconfidence adjustment. However, as discussed in Section 5.6.2 and by reviewing the wide range of uncertainty estimates provided by the panelists, there is good reason to believe that at least some of the panelists may have been overconfident. Only those panelists that were more confident than the group median were adjusted. Furthermore, sensitivity studies indicated that the error factor adjustment used was a reasonable adjustment scheme. This method was not the most conservative adjustment scheme which could have been used.
Issue 9: Second, the processes and analyses employed have introduced a conservative bias into the final base case results, with additional conservative bias8 inserted in the various sensitivity studies.9
9. Issue 9 Response: Sensitivity analyses were conducted to examine the impact of the assumptions used to process the results. The assumptions and methods used to calculate the “baseline” LOCA estimates are clearly stated in Sections 5 and 7. Additionally, the methods used to conduct each sensitivity analysis are clearly explained in Sections 5 and 7 and comparisons are made to the baseline results so that the effects on the LOCA frequency estimates are readily apparent. Those sensitivity analyses resulting in the largest differences from the baseline estimates are clearly discussed in the report.
Issue 10: This “creeping conservatism” is not necessarily undesirable given the significant uncertainties and the uses to which the results will be employed; however, it should be explicitly acknowledged and clearly stated rather than obscured in the details of the analyses.10
10. Issue 10 Response: The NUREG report systematically documents the assumptions and analysis used to calculate the LOCA frequency estimates. The NUREG also discusses the effects of alternative assumptions and analysis methods using sensitivity studies. The analysis procedures utilized in the elicitation process were fully discussed with the panelists at several times throughout the process: during the base case review, prior to conducting the individual elicitations, during the presentation of the preliminary results, and during the preparation of the draft NUREG. Each panelist was also provided numerous opportunities to modify their results, including changes if they believed the initial instructions were unclear, or if the processing of their results did not actually reflect their solicited opinion. None of the panelists elected to provide wholesale changes to their estimates based on these issues. General feedback from the panelists about the elicitation process in general, and the processing of the results in particular, was favorable.
Submitted by Joseph Conen of the BWR Owners Group
Comment: Another issue is the inclusion of thermal fatigue as a degradation mechanism for the BWR feedwater line. We are not aware of any thermal fatigue issue other than the feedwater nozzles; that issue was resolved in the early 1980s through several mitigation measures including the installation of GE — designed triple thermal sleeve. A rigorous inspection program per NUREG-0619 is currently in place. Not a single one of hundreds of these inspections have turned up any evidence of cracking. Thus, thermal fatigue is not an issue in the NSSS portion of the BWR feedwater line. In addition, please refer to the letter from T. Essig (U. S.NRC) to T. J. Rausch (BWROG), dated June 5, 1998, subject: BWROG-Safety Evaluation of Proposed Alternative to BWR Feedwater Nozzle Inspections (TAC M94090). This letter provides evidence that the thermal fatigue of the FW nozzles is effectively managed at BWRs and provides the basis for revising the examination frequencies.
Response: The NUREG report acknowledges the improvements that have been implemented in BWRs as a result of the NUREG-0619 inspection requirements. As stated in Section 6.3.2, "There was a rash of feedwater nozzle cracks reported in the 1970 to early 1980 time period in BWRs. Plant and system modifications were implemented after a detailed study of the problem and augmented inspections are being conducted based on NUREG-0619 requirements. These mitigation measures have proven effective as no new thermal fatigue cracks have been discovered in these BWR feedwater nozzles over the last 20 years." However, as stated in Section L.2 when discussing the relative contributions for various BWR piping systems, "There was wide variability expressed for the feedwater system. Several participants thought that its susceptibility was similar to that of the recirculation system while others thought that it would make an inconsequential contribution.” This latter group generally thought that the mitigation programs in place for the feedwater system were generally effective and additional thermal fatigue locations within the feedwater system were not significant LOCA contributors.
However, rationale provided by some of the panelists who believe that thermal fatigue is a significant contributor to the LOCA frequency estimates is summarized in Section L.2 and Section 6.3.2. As stated in Section 6.3.2, “The BWR plants are expected to be more prone to thermal fatigue problems compared with the primary side of PWR plants because they experience greater temperature fluctuations during the normal operating cycle. In BWR plants, thermal fatigue remains an important contributor for the feedwater lines and the RHR system.” Additionally, “…thermal fatigue is an aging mechanism that could lead to a large LOCA because it does not manifest itself as a single crack, but as a family of cracks over a wide area. Thermal fatigue cracks also tend to propagate rapidly, and since it is not material sensitive (i. e., it can attack a number of materials), it is difficult to prioritize critical areas for inspections.” These reasons explain why thermal fatigue is still regarded as an important LOCA contributor by many panelists.
The general variability in opinion expressed by the elicitation panelists for feedwater, main steam, and RHR systems is summarized in the box and whisker plots in Figures L.6 through L.8. Some of the differences associated with the illustrated variability in these figures results from the diversity in opinion about the significance for thermal fatigue in BWR plants.
ATTACHMENT C TO APPENDIX D
BASIS FOR LOCA FREQUENCY MODELS
Attached as Table D. C.1 is an Excel spreadsheet used to calculate time-dependent LOCA frequencies. Table D. C.1 includes the parameters input to the BWR-1 Cat1 LOCA frequency calculation.
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Combined LOCA Frequencies due to Reactor Vessel Failures
Tables I.4 and I.5 summarize and combine the above RPV LOCA frequency results for BWRs and PWRs, respectively. For BWRs, three RPV LOCA contributors are addressed: RPV vessel beltline region, large nozzles (6 through 28 inch diameter), and small penetrations (partial penetration welded nozzles, 4 inch in diameter or less, such as CRDs). The individual LOCA probability contributions for each of these are provided in the top three sections of Table I.4, and they are summed in the bottom section of the table. These address all LOCA categories as well as the three time periods under consideration (0-25 yrs, 25-40 yrs, and 40-60 yrs). Note, in Table 4.4 in Section 4 of the main body of this report, only the results for the BWR beltline region and the large feedwater nozzles are presented. The results for the BWR CRDs and other small penetrations listed in Table I.4 of this appendix were not included in Table 4.4 since the estimates for the BWR CRDs and other penetrations are not based on analysis, but instead, were based on engineering judgment, i. e., BWR CRDs and other penetrations LOCA frequencies were simply assumed to be a factor of 10 less than the PWR CRDM LOCA frequencies, which were based on analysis.
The first contributor is the BWR shell region, the failure probabilities for which are dominated by the irradiated reactor vessel beltline region. The upper section of Table I.4 summarizes the results of this analysis from Table I.2, in terms of the probability of leaks of various sizes due to degradation or failure of the RPV beltline region. (Note that these were modified slightly relative to those in Table I.2 to eliminate the negative time factor for Category 5 and 6 LOCAs in the 25 — 40 year period.)
The second section of Table I.4 addresses large nozzle contributions to LOCA probability, which in BWRs are assumed to correspond to the 12 inch diameter Feedwater Nozzles that experienced thermal fatigue cracking in the 1980s [I.5]. LOCA probabilities due to this contributor are given for break Categories 1 through 4, taken from Table I.3 as this nozzle size could not lead to larger break sizes. For the Category 2 through 4 LOCAs for 0-25 year time frame, an assumption was made as to the size factor that each successive LOCA size greater than Category 1 was 5 times less likely to occur than the previous size LOCA. Then, for the 25-40 and 40-60 year time frames, the same time factor as determined for the Category 0 LOCAs in Table I.3 was assumed for the larger size LOCAs. Breaks of the other, larger diameter nozzles, such as recirculation outlet nozzles, are considered to be adequately encompassed by the vessel beltline case.
Finally, the third section of Table I.4 lists LOCA probabilities due to failures of CRDs and other small penetrations in the BWR vessel. These were estimated from the detailed analysis of PWR CRDM penetrations described above (Table I.1) but they assume that the BWR penetrations have about an order of magnitude lower LOCA probability than similar penetrations in a PWR. The order of magnitude reduction is deemed appropriate, because problems in small vessel penetrations in BWRs have occurred at a much lower frequency than the recent PWSCC experience in PWRs, upon which Table 1.1 is based. The problems in BWR penetrations have also been attributed to a fairly well-understood phenomenon (IGSCC) and in most cases the nozzles of concern have been mitigated by design and materials changes.
Table I.5 provides a similar summary for PWR RPVs. In this case, LOCA probabilities are reported for only two categories of LOCA contributors, the shell region (RPV beltline) and small penetrations. Again, as was the case for BWRs, Table 4.5 in Section 4 only includes the results for PWR CRDMs. It does not include the results for the PWR beltline region as reported in Table I.5 of this appendix. As was the case for BWR CRDs and other penetrations, the PWR beltline results in Table I.5 are not based on analysis. Again, they are based on engineering judgment, i. e., the PWR beltline LOCA frequencies in Table I.5 of this appendix were simply assumed to be a factor of ten greater than the BWR beltline LOCA frequencies from Table I.4. It was judged that the large nozzles in a PWR RPV do not pose a significant LOCA risk because they are not subject to significant thermal cycles such as the BWR Feedwater nozzles, and except for the safe-ends (which are covered in the piping elicitation), they have not experienced any degradation mechanisms to date. The contributions for the two PWR RPV LOCA contributors are summed in the bottom section of Table I.5.
For the PWR beltline region, results from a prior analysis of a PWR vessel using a third version of the VIPER software (VIPER-PWR) were reviewed. Based on this review, it was estimated that the PWR RPV beltline region presents about an order of magnitude increase in large rupture probability relative to that of a BWR, because PWR beltlines are more highly irradiation embrittled, and because they are potentially subject to PTS transients. Thus, the BWR RPV beltline region LOCA frequency entries in Table I.4 were multiplied by a factor of ten and entered in the upper section of Table I.5.
PWR CRDM penetrations results were entered directly from the above PFM analysis results in Table I.1.