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Statistical characteristics of dent defect sizes in gas pipelines


STATISTICAL CHARACTERISTICS OF DENT DEFECT SIZES IN GAS PIPELINES

Zorin A.A.

Ural Federal University, Ekaterinburg andreyzorin1989[AT]gmail.com

Timashev S.A.

Ural Federal University, Ekaterinburg

Science and Engineering Center «Reliability and Safety of Large Systems and Machines» of the Ural Branch of the Russian Academy of Sciences, Ekaterinburg, timashevs[AT]gmail.com Ensuring reliability and uninterrupted gas supply to the consumer are priorities for Russian gas transportation system and currently are not fully solved. At the design stage the pipeline reliability is ensured by right choices of its geometric parameters, steel brand and comprehensive corrosion protection.

Due to the inevitable presence of defects during operation (originated during construction and installation, or formed during operation or repair, and identified by inspection of the pipeline) measures have to be taken to ensure and maintain the desired level of pipeline reliability. For these purposes it is generally necessary to carry out calculations of the static and dynamic strength of pipeline sections with defects, followed by reliability analysis. The vast majority of existing methods use deterministic approach for assessing gas pipelines strength and reliability. The main reason for this is lack of sufficient, representative volumes of initial data.

In this paper a statistical analysis of the size of dents (one of the most common defects in pipelines) revealed by in-line inspection (ILI) of gas pipelines 5720 km long is described. The pipelines diameters are from 219 mm to 1420 mm. The number of identified dents in pipes of various diameters is shown in Figure 1. According to the figure, the highest number of dents found in gas pipelines with diameters 530 mm and 1020 mm. This is due, presumably, to the fact that these diameters are used most frequently and, consequently, the volume of the ILI for the same diameters of the pipelines is maximal (Table 1).

2954
1
1
II
495
640
i7rt
n n
1
86

50 00 tLi 377

530 720

S20

1020 1220 1420 Pipe diameter, mm Figure 1. Number of detected dents in pipelines of different diameters

To determine the statistical characteristics of dents identified during the ILI on the same type of gas pipelines define the number of dents on each a combination "diameter-wall thickness" (Table 2). It shows that a number of combinations "diameter-wall thickness" con- tains very small number of dents. This is primarily due to the low frequency of usage of this type of pipes, mainly where the pipeline intersect with roads and railways. In these areas pipes with increased wall thickness are used to enhance their reliability. Because of this specificity combinations of "diameter - wall thickness", which revealed less than 10 dents, further were not considered.

Table 1

ILI volume and number of detected dents on pipelines of different diameters

Diameter, mm
Length of inspected pipelines, km
Number of dents, pcs
Specific number of dents per 1 km, pcs / km
1
219
31
227
7,32
3
325
88.6
499
5,63
4
377
61
260
4,26
5
500
1088.76
2954
2,71
6
700
428.6
370
0,86
7
820
140
640
4,57
8
1000
2209
2253
1,02
9
1200
812.5
1066
1,31
10
1400
811.5
86
0,11
Total
5670.96
8355

Table 2

Distribution of the number of detected dents on pipelines with different combination "diameter - wall thickness"

Wall thickness, mm
Pipe diameter, mm
Total number of dents
219
325
377
530
720
820
1020
1220
1420
1
5
227
3
-
-
-
-
-
-
-
230
2
6
-
328
119
-
25
-
-
-
-
472
3
7
-
2
-
1159
-
-
-
-
-
1161
4
7.5
-
-
-
732
4
-
-
-
-
736
5
8
-
133
5
978
304
-
-
-
-
1420
6
9
-
-
52
43
23
403
253
-
-
774
7
10
-
32
-
38
11
135
39
71
-
326
8
10.5
-
-
-
-
-
-
313
-
-
313
9
10.6
-
-
-
-
-
-
10
-
-
10
10
11
-
1
-
-
1
96
794
1
-
893
11
11.2
-
-
-
-
-
-
189
-
-
189
12
11.5
-
-
-
-
-
-
64
-
-
64
13
12
-
-
82
4
2
6
575
792
-
1461
14
12.9
-
-
-
-
-
-
4
-
-
4
15
13.5
-
-
-
-
-
-
5
-
-
5
16
14
-
-
2
-
-
-
7
-
-
9
17
14.5
-
-
-
-
-
-
-
49
-
49
18
15
-
-
-
-
-
-
-
151
-
151
19
15.4
-
-
-
-
-
-
-
2
-
2
20
16.5
-
-
-
-
-
-
-
-
80
80
21
18.7
-
-
-
-
-
-
-
-
5
5
22
19.5
-
-
-
-
-
-
-
-
1
1
Total
227
499
260
2954
370
640
2253
1066
86
8355

Histograms of the basic geometrical parameters of dents with a combination of "diameter - wall thickness" 530x7 mm are shown in Figures 2-4. Smoothing of the histogram by

36 the x --method shows that with a confidence level of 0.99, they obey the two-parameter Weibull law. It also turned out that the size of dents on all other gas pipelines from Table 2 also obey this law.

SOO 1000

Dent length, mm

Figure 2. Histogram of dents lengths in pipes whose "length - wall thickness" is 530x7 mm

600 SOO

Dent width, mm

Figure 3. Histogram of dents widths in pipes whose "length - wall thickness" is 530x7 mm 400r

40 30

Dent depth, mm

Figure 4. Histogram of dents depths in pipes whose "length - wall thickness" is 530x7 mm

According to the results of statistical analysis of dents sizes, revealed during ILI of pipelines with various diameters, their main parameters are described by the Weibull distribution. The analysis was performed using a software algorithm designed by the first author. The software algorithm selects out of the total data set information about found dents, separately for each combination of "diameter-wall thickness". It calculates basic statistical parameters of dents samples, determines whether the sample is well described by the Weibull distribution and stores the results in the analysis file (See Table 3).

This data is recommended for practical use when evaluating residual life, probability of failure, time of next diagnostics, time and the amount of preventive maintenance. Statistical characteristics of the basic geometrical parameters of dents for different combinations of gas pipelines "diameter - wall thickness"

General data
Results for the length of dents
Results for the width of the dents
Results for the depth of the dent
Diameter, mm
Wall
Thickness,
mm
Sample size, pcs
Type of distribution
me
distribution
nciramptpr V
The distribution parameter, X
Mathematical
expectation
Variance
Standard
deviation
Type of distribution
me
distribution
n'ltnmpfpr V
The distribution parameter, X
Mathematical
expectation
Variance
Standard
deviation
Type of distribution
me
distribution
n'ltnmpfpr V
The distribution parameter. X
Mathematical
expectation
Variance
Standard
deviation
219
5.0
227
W(k./.)
l.ii
168.69
162.39
21540
146.78
W(k./.)
1.93
112.56
99.84
2908
53.92
W(k./.)
1.45
3.40
3.08
4.65
2.16
325
6.0
328
W(k./.)
2.12
238.36
211.10
11010
104.93
W(k./.)
3.20
178.68
160.04
3008
54.84
W(k./.)
2.00
9.72
8.62
20.37
4.51
325
8.0
133
W(k./.)
1.69
233.43
208.40
16160
127.14
W(k./.)
4.92
182.32
167.23
1513
38.90
W(k./.)
2.38
8.14
7.21
10.38
3.22
325
10.0
32
-
3.40
278.78
250.47
6606
81.28
-
4.65
153.08
139.97
1172
34.24
-
2.77
9.48
8.44
10.87
3.30
377
6.0
119
W(k./.)
2.41
188.79
167.37
5478
74.02
W(k./.)
3.31
181.12
162.50
2919
54.03
W(k./.)
2.39
7.08
6.28
7.80
2.79
377
9.0
52
W(k./.)
2.30
275.95
244.46
12720
112.78
W(k./.)
4.37
180.65
164.58
1815
42.60
W(k./.)
1.98
12.41
11.00
33.65
5.80
377
12.0
82
W(k./.)
3.62
222.24
200.32
3783
61.50
W(k./.)
4.37
195.36
177.98
2123
46.08
W(k./.)
2.67
9.85
8.76
12.48
3.53
530
7.0
1159
W(k./.)
1.77
302.78
269.52
24820
157.55
W(k./.)
3.25
241.20
216.20
5349
73.14
W(k./.)
1.56
13.20
11.87
60.33
7.77
530
7.5
732
W(k./.)
1.99
217.13
192.44
10180
100.90
W(k./.)
2.73
201.31
179.08
5029
70.91
W(k./.)
1.77
11.09
9.87
33.17
5.76
530
8.0
978
W(k./.)
1.82
295.69
262.82
22400
149.67
W(k./.)
2.76
220.50
196.24
5907
76.86
W(k./.)
1.41
11.84
10.77
59.73
7.73
530
9.0
43
-
3.89
223.38
202.14
3387
58.20
-
3.94
215.77
195.40
3093
55.61
-
2.34
10.31
9.14
17.19
4.15
530
10.0
38
-
5.73
224.24
207.50
1760
41.95
-
4.04
189.77
172.11
2291
47.87
-
2.81
9.66
8.61
10.98
3.31
720
6.0
25
W(k./.)
1.95
287.62
255.04
18620
136.47
W(k./.)
1.30
324.43
299.76
54280
232.98
W(k./.)
2.10
10.79
9.56
22.89
4.78
720
8.0
304
W(k./.)
2.07
309.74
274.36
19270
138.82
W(k./.)
2.39
269.54
238.92
11350
106.55
W(k./.)
1.80
10.56
9.39
29.01
5.39
720
9.0
23
W(k./.)
2.11
373.39
330.70
27150
164.78
W(k./.)
2.25
317.64
281.35
17490
132.24
W(k./.)
1.55
13.68
12.30
65.78
8.11
720
10.0
11
W(k./.)
1.68
409.63
365.73
49880
223.34
W(k./.)
3.05
320.35
286.27
10510
102.53
W(k./.)
1.13
16.51
15.82
198.33
14.08
820
9.0
403
W(k./.)
2.88
392.28
349.68
17410
131.94
W(k./.)
3.12
295.19
264.07
8582
92.64
W(k./.)
1.81
21.09
18.75
114.52
10.70
820
10.0
135
W(k./.)
3.15
468.87
419.62
21340
146.09
W(k./.)
3.18
312.31
279.62
9323
96.56
W(k./.)
1.83
18.50
16.44
86.34
9.29
820
11.0
96
W(k./.)
3.74
442.84
399.87
14220
119.27
W(k./.)
3.15
290.49
259.99
8174
90.41
W(k./.)
1.71
23.89
21.31
165.38
12.86
1020
9.0
253
W(k./.)
1.37
460.93
421.66
97150
311.69
W(k./.)
2.01
289.13
256.22
17840
133.56
W(k./.)
3.32
16.56
14.86
24.29
4.93
1020
10.0
39
W(k./.)
1.29
365.81
338.33
69790
264.18
W(k./.)
2.71
294.17
261.62
10880
104.30
W(k./.)
3.45
12.60
11.33
13.19
3.63
1020
10.5
313
W(k./.)
1.47
433.67
392.66
74220
272.43
W(k./.)
2.67
318.79
283.39
13060
114.27
W(k./.)
1.90
11.81
10.48
32.86
5.73
1020
11.0
794
W(k./.)
1.60
420.93
377.38
58270
241.39
W(k./.)
3.47
324.81
292.12
8668
93.10
W(k./.)
1.95
11.20
9.93
28.22
5.31
1020
11.2
189
W(k./.)
1.49
361.83
327.01
50120
223.87
W(k./.)
2.15
287.08
254.24
15550
124.71
W(k./.)
1.57
12.52
11.25
53.52
7.32
1020
11.5
64
W(k./.)
3.99
269.59
244.31
4727
68.75
W(k./.)
4.82
258.01
236.39
3137
56.01
W(k./.)
2.17
10.13
8.97
19.03
4.36
1020
12.0
575
W(k./.)
1.29
436.59
403.96
99840
315.97
W(k./.)
2.40
283.23
251.08
12390
111.32
W(k./.)
1.56
11.60
10.43
46.83
6.84
1220
10.0
71
W(k./.)
2.20
1334.00
1181.00
321900
567.34
W(k./.)
1.85
654.10
580.96
105900
325.47
W(k./.)
2.74
34.14
30.38
143.25
11.97
1220
12.0
792
W(k./.)
2.03
1200.00
1063.00
301900
549.45
W(k./.)
1.24
558.23
521.06
179100
423.23
W(k./.)
1.95
32.34
28.68
236.41
15.38
1220
14.5
49
W(k./.)
2.18
1269.00
1124.00
296700
544.66
W(k./.)
1.58
661.73
594.06
148200
384.95
W(k./.)
2.13
32.88
29.12
207.17
14.39
1220
15.0
151
W(k./.)
2.16
1018.00
901.16
192600
438.91
W(k./.)
4.45
511.15
466.18
14080
118.67
W(k./.)
1.97
19.10
16.93
80.27
8.96
1420
16.5
80
W(k./.)
1.42
486.39
442.24
99480
315.41
W(k./.)
1.94
414.10
367.25
39070
197.66
W(k./.)
1.26
11.59
10.79
74.79
8.65

W(k, X) - The Weibull distribution notation








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