Stresses and dimensions are given in the corresponding sections for the 12 inch line. IGSCC crack initiation and growth are the dominant degradation mechanisms. Table F.24 summarizes the results for this weld.

Table F.24 Cumulative PRAISE Results for the Weld
in the 28 inch Recirculation Line

odw=2.0 ksi

ote=1.75 ksi P = 1,125 psi Type 304 full residual stress 3 HU-CD/yr

F.3.7 Feedwater Elbow

The feedwater elbow is one of the base case systems. This system is subject to flow accelerated corrosion (FAC), which can be a serious degradation mechanism if left unchecked. PRAISE can not model FAC, but some analyses are provided for fatigue crack initiation and growth.

F.3.7.1 Dimensions and Welds — The layout of the feedwater system is given in the piping isometrics made available to the panel members. There are some 123 welds in the two loops of the feedwater systems, all but 6 of them in 12 and 20 inch piping. The 12 inch lines are schedule 100 (17.4 mm [0.687 inches] thick) and the 20 inch lines are schedule 80 (32.5 mm [1.281 inches] thick). The material is A — 333 Grade 6 (which is a carbon steel).

F.3.7.2 Stresses and Cycles — The feedwater line elbow is considered in Reference F.5, so this is evidently the high stress point in the system. Note that there are at least 6 such elbows in a feedwater system. (There are many more elbows, but they are likely to not be so highly stressed). The degradation mechanism is fatigue and flow accelerated corrosion (FAC). Stresses do not contribute to FAC, so are not needed for this mechanism. For fatigue, there are a considerable number of cycles of high stress amplitude. They are available from Reference F.5. Table F.25, which (except for the column of temperatures) is page A.25 of Reference F.5, summarizes the stresses. These stresses are “decomposed” according to the procedure discussed above for the surge line. The analysis reported in Reference F.5
used a temperature of 590°F (310°C), as indicated in the text at the top of Table F.25. However, Table 5­123 of Reference F.18 provides the temperatures for these transients, and it is suggested that these temperatures be used, because their use is more realistic and less conservative. They are included as the right-hand column of Table F.25. The temperature influences the strain-life curve, and has a noticeable effect on the computed failure probabilities because of its influence on the initiation probabilities.

The values of the deadweight and restraint of thermal expansion under normal operation that Reference F.5 uses for this location are

Cdw = 0

Cte = 115 MPa (16.68 ksi).

The stress history in Table F.25 most likely contains seismic events. It is not possible to eliminate them from the list using information currently available, but their influence on the calculated failure probabilities is expected to be minimal.

Table F.25 Summary of Stress Cycles for Feedwater Line Elbow
(from Page A.25 of NUREG/CR-6674 [F.5])

NAME OF PLANT	=	GE-NEW
NAME OF COMPONENT	=	FEEDWATER	LINE ELBOW
NUM OF LOAD PAIRS	=	28
MATERIAL	=	LAS
WALL THICK (INCH)	=	1.000
INNER DIAMETER	=	12.000
AIR/WATER	=	WATER
TEMPERATURE(F)	=	590.000
SULFUR(WHT%)	=	. 015
DISOL O2 (PPM)	=	.100
STR RATE (%/SEC)	=	0.00100
USEAGE(DETERM.)	=	3.68800
P-INITIATION@40	=	1.59E-01
P-INITIATION@60	=	3.65E-01
P-TWC @40	=	1.01E-03
p-twc @60	=	1.46E-02
LOAD PAIR	AMP(KSI)	NUM/4 0 YR	EDOT(%/S)	USEAGE	TEMP, °C
HIGH 18/LOW 21	106.040	5.0	.117000	.025000	200
HIGH 18/LOW 21	103.960	5.0	.114000	. 024000	200
HIGH 18/LOW 21	102.610	5.0	.113000	. 024000	200
HIGH 14/LOW 17	91.590	8.0	.001000	.123000	200
HIGH 8/LOW 17	89.400	10.0	.095000	. 037000	200
HIGH 3/LOW 16	88.270	5.0	.094000	.018000	200
HIGH 8/HIGH 7	83.760	126.0	. 041000	.519000	200
HIGH 7/HIGH 7	81.430	10.0	.086000	. 033000	215
HIGH 7/LOW 13	67.930	97.0	.001000	.740000	200
HIGH 7/LOW 13	66.710	14.0	.001000	.101000	200
HIGH 7/LOW 15	61.290	6.0	.001000	.035000	200
HIGH 7/LOW 15	61.160	64.0	.001000	.451000	212
HIGH 8/LOW 12	55.500	92.0	.001000	.391000	200
HIGH 3/LOW 12	46.630	88.0	.001000	.254000	215
HIGH 7/LOW 22	42.880	15.0	.001000	. 029000	212
HIGH 3/HIGH 7	39.440	212.0	.001000	.315000	215
HIGH 3/HIGH 7	38.130	69.0	.001000	.104000	224
HIGH 3/LOW 20	36.800	11.0	.001000	. 014000	224
HIGH 4/LOW 20	34.320	60.0	.001000	. 053000	215
LOW 11/LOW 20	32.950	203.0	.001000	.122000	200
HIGH 7/LOW 11	32.530	360.0	.001000	.203000	200
HIGH 6/LOW 11	29.770	222.0	. 025000	. 035000	200
HIGH 2/HIGH 19	26.090	30.0	. 028000	.003000	212
HIGH 5/HIGH 19	26.040	81.0	. 028000	.007000	200
HIGH 5/HIGH 9	21.640	96.0	.001000	.012000	212
HIGH 1/HIGH 11	20.560	40.0	.001000	.003000	200
LOW 10/LOW 11	14.180	30.0	.001000	.001000	200
HIGH 5/LOW 11	11.220	11515.0	.001000	.008000	200

F.3.7.3 Results — PRAISE runs for this component were made using the version that can treat fatigue crack initiation with details of the circumferential variation of the stresses. The feedwater system is

relatively more likely to experience water hammer, so the influence of an overload event with a stress of 0.42cflo = 128 MPa (18.5 ksi) above that normally present was considered. This stress is denoted as cDL, and results were generated for one cycle of this stress at 24, 39, or 59 years. The results are summarized in Table F.26, which includes the effects of cDL (columns D & F).

Table F.26 Cumulative PRAISE Results for Feedwater Line Elbow

	A	B	C	D	E	F	G
Stresses	Ref. F.5	Table F.25	Table F.25	Table F.25	Table F.25	Table F.25	80% of Table F.25
Failure Criterion	^flow	^flow	^flow	^flow	^flow & J-T	^flow & J-T	^flow
Odl	no	no	no	ODL@(t-1)	no	ODL@(t-1)	no
о A	25	—	—	<10-8	2.5×10-8	1.0×10-7	3.10×10-6	<10-7
40	0.001	2×10-6	5.69×10-6	7.19×10-6	1.54×10-5	1.43×10-4	<10-7
60	0.0146	1.8×10-4	2.57×10-4	2.59×10-4	~5×10-4	2.9×10-3	4.6×10-7
		Ref F.6 Table 4-8	108 trials				GEN6TWA4
>100	25	—	—	<10-8	1.5×10-6 *	<10-7	1.70×10-6*
40	—	—	<10-8	1.5×10-6 *	<10-7	1.70×10-6*
60	—	—	<10-8	1.50×10-6*	—	2.1×10-6 *
			GENC6TW4
>1500	25	—	—					<10-7
40	—	—					<10-7
60	—	—					<10-7
			axi- symmetric actual T					reduced stresses

* also a break

Case A is directly from Reference F.5, and Case B is directly from Table 4-8 of Reference F.6. Case C is Case B rerun with 108 trials. Cases D-G are variations of C with different failure criteria, overloads and reduction of stresses. The results for various failure criteria (critical net section stress only or critical net section stress and tearing instability) show that consideration of tearing instability noticeably increases the computed failure probability (compare, for instance, cases C&E). Consideration of an overload event also has a noticeable effect (E&F). The use of lower stresses markedly reduces the computed failure probabilities (G & C). In the case of an overload event, the probability of a 100 gpm failure is the same as a complete pipe break.

F.3.7.4 Alternate Procedure — The results of Table F.26 show that the probability of a large leak was obtainable from the Monte Carlo procedure only when a large overload occurred. When this did not occur, there were no leaks of even 380 lpm (100 gpm) in 107 or 108 trials. In order to obtain estimates for the larger leak probabilities, the alternate procedure discussed for the surge line was also applied to Case C of Table F.26 for the feedwater elbow.

As before, the crack length for a given leak rate, b( q), was obtained from a pcPRAISE run, along with the half-crack length of any cracks that become through-wall. Figure F.11 provides a plot of the leak rate as a function of b for the feedwater elbow.

12000 half crack length, b, inches

Figure F.11 Leak Rate as a Function of Half Crack Length for Feedwater Elbow Base Case C

The results in Table F.27 are obtained from this figure and the corresponding pcPRAISE results. This table also includes the portion of the circumference that is cracked and the proportion of the crack opening area to the flow area of the pipe. It is seen that the opening area of the crack is nearly equal to the flow area of the pipe when the leak rate is 19,000 lpm (5,000 gpm). The value of b for a complete pipe break, as obtained from Equation E.7 is also included. Table F.29 defines b( q).

Table F.27 Half Crack Lengths and Areas for a Given Leak Rate
(Feedwater Elbow Base Case C)

q, gpm	b, inches	b nRI	A, in2	A Apipe
100	5.737	0.32	1.837	0.02
1500	9.743	0.55	27.554	0.27
5000	11.095	0.62	90.877	0.91
DEGB	15.925	0.89	—	—

As before, the next step is to estimate the probability of having a through-wall crack exceeding a given length as a function of time. The modified version of pcPRAISE was used to generate a table of values of b and the time at which the leak first occurred. A run was made with 107 trials, with 2,607 cracks becoming through-wall within 60 years. This corresponds to a leak probability of 2.607×10-4 at 60 years, which agrees closely with the leak probability obtained earlier. Of these 2,607 cracks, none appeared before 25 years, and 64 occurred between 25 and 40 years. The statistical distribution of these 64 cracks at 40 years provides the probability of having a through-wall crack greater than a given length within 40 years. Extrapolation is required to obtain results for the crack lengths included in Table F.27. Figure F.12 shows the complementary cumulative distribution of b at 40 years, along with the curve fit of Equation F.10.

P(> b) = e“534(b-1) (40 years) [F.10]

Note that the plot starts at a half-crack length of 25 mm (1 inch), and that the data are closely approximated by a straight line on log-linear scales.

Figure F.12 Complementary Cumulative Distribution of Half-Crack Length of Through-Wall
Cracks in Feedwater Elbow within 40 Years, Along with Fit

Figure F.13 provides a similar plot for the 2,607 through-wall cracks that occurred within 60 years. Equation F.11 is the fit of the distribution at 60 years within the range of interest.

P(> b) = 0.0274e“2’25(b_1) (60 years) [F.11]

Note that in this case the data appear bilinear and are not well approximated by a straight line on log — linear scales. To represent the data at the longer crack lengths of interest, a straight line was assumed beyond a crack length of 50 mm (2 inches). This corresponds to a probability below about 0.003.

rO

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ь

яз

Ы>

Й

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яЗ

Л

<4-1

0

1

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Figure F.13 Complementary Cumulative Distribution of Half-Crack Length of Through-Wall
Cracks in Feedwater Elbow within 60 Years, Along with Fit

The probability of a leak exceeding a given size within 40 and 60 years is then obtained by taking using the value of b for a given leak rate from Table F.27 in conjunction with Equations F.10 and F.11, respectively. Table F.28 summarizes the results.

Table F.28 Cumulative Results for Feedwater Elbow Case C

	time years	P(> q)
	25	Л p ос
	40	5.69×10-6
О A	60	2.57×10-4
	25	—
О О Л	40	1.03×10-11
60	6.44×10-7 *
	25	—
О О LO Л	40	5.29×10-21
60	7.84×10-11
	25	—
LO л	40	3.88×10-24
60	3.74×10-12
со	25	—
CL Ш	40	2.44×10-35
О	60	7.14×10-17

* direct Monte Carlo gave <10’8

The leak (>0) results in Table F.28 came directly from the Monte Carlo simulation. With 108 trials, no leaks exceeding 380 lpm (100 gpm) were obtained. Hence, the Monte Carlo simulation predicts <10-8 probability of a leak exceeding 380 lpm (100 gpm) within 60 years. The alternative procedure gave a corresponding value of 6.44×10-7. This suggests that the alternative procedure overestimates the probability of a given leak, as was also the case for the surge line elbow.