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![Page 1: Application of SRA for Pipeline Design Operation & Maintenance Andrew Francis Advantica Technologies ASRANeT, 2 nd Annual Colloquium, 9 th July 2001.](https://reader037.fdocuments.net/reader037/viewer/2022102800/56649ee75503460f94bf825b/html5/thumbnails/1.jpg)
Application of SRA for Pipeline Design Operation & Maintenance
Andrew Francis
Advantica Technologies
ASRANeT, 2nd Annual Colloquium, 9th July 2001
![Page 2: Application of SRA for Pipeline Design Operation & Maintenance Andrew Francis Advantica Technologies ASRANeT, 2 nd Annual Colloquium, 9 th July 2001.](https://reader037.fdocuments.net/reader037/viewer/2022102800/56649ee75503460f94bf825b/html5/thumbnails/2.jpg)
INTRODUCTION
Uses of SRA Wall thickness determination Uprating Life extension Risk Based Inspection
Generally Determination of required level of failure mitigation
![Page 3: Application of SRA for Pipeline Design Operation & Maintenance Andrew Francis Advantica Technologies ASRANeT, 2 nd Annual Colloquium, 9 th July 2001.](https://reader037.fdocuments.net/reader037/viewer/2022102800/56649ee75503460f94bf825b/html5/thumbnails/3.jpg)
Present Study
Failure Mode
• Fatigue Crack Growth
Uncertainty
• Construction Defect Depth
Mitigation Measures
• Construction process
• Weld Inspection
• Hydrostatic Test
![Page 4: Application of SRA for Pipeline Design Operation & Maintenance Andrew Francis Advantica Technologies ASRANeT, 2 nd Annual Colloquium, 9 th July 2001.](https://reader037.fdocuments.net/reader037/viewer/2022102800/56649ee75503460f94bf825b/html5/thumbnails/4.jpg)
Mitigation effects using Bayes Theorem
Conditional probability
p( X | Y ) is the probability of event X occurring given prior knowledge that event Y has already occurred
p (XY) is the probability that both X and Y will occur before any prior knowledge has been obtained
p ( Y ) is the probability that Y will occur before any prior knowledge is obtained
)(
)()|(
Yp
YXpYXp
![Page 5: Application of SRA for Pipeline Design Operation & Maintenance Andrew Francis Advantica Technologies ASRANeT, 2 nd Annual Colloquium, 9 th July 2001.](https://reader037.fdocuments.net/reader037/viewer/2022102800/56649ee75503460f94bf825b/html5/thumbnails/5.jpg)
Construction Process
For a given weld constructed to an appropriate standard, the probability of having a defect of depth a is
p(D) is the probability that the weld contains a defect and p(a) is the probability that the defect has depth a
)()()( apDpaDp
![Page 6: Application of SRA for Pipeline Design Operation & Maintenance Andrew Francis Advantica Technologies ASRANeT, 2 nd Annual Colloquium, 9 th July 2001.](https://reader037.fdocuments.net/reader037/viewer/2022102800/56649ee75503460f94bf825b/html5/thumbnails/6.jpg)
Construction Process
The Likelihood of a Defect of Given Depth Being Present
0.0E+00
2.0E-03
4.0E-03
6.0E-03
8.0E-03
1.0E-02
0 2 4 6
a (mm)
p(D
a
)
![Page 7: Application of SRA for Pipeline Design Operation & Maintenance Andrew Francis Advantica Technologies ASRANeT, 2 nd Annual Colloquium, 9 th July 2001.](https://reader037.fdocuments.net/reader037/viewer/2022102800/56649ee75503460f94bf825b/html5/thumbnails/7.jpg)
Pre-Service Weld Inspection
Objective: To detect any defects, which are unacceptable according to the appropriate criteria
Issue: Inspection techniques often only 70% - 80% reliable, sometimes lower
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Pre-Service Weld Inspection
We want to know probability, p(D a | I)
Event I: Weld was inspected and no defect was found
Using Bayes Theorem
)(
)()()|()|(
Ip
daapDpaDIpdaIaDp
![Page 9: Application of SRA for Pipeline Design Operation & Maintenance Andrew Francis Advantica Technologies ASRANeT, 2 nd Annual Colloquium, 9 th July 2001.](https://reader037.fdocuments.net/reader037/viewer/2022102800/56649ee75503460f94bf825b/html5/thumbnails/9.jpg)
Pre-Service Weld Inspection
Probability, p ( I | D a) , that the weld was inspected and nothing was found given that the weld contains a defect of depth a is given by
PoD(a) is the probability of detection of a defect of depth a
)(1)|( aPoDaDIp
![Page 10: Application of SRA for Pipeline Design Operation & Maintenance Andrew Francis Advantica Technologies ASRANeT, 2 nd Annual Colloquium, 9 th July 2001.](https://reader037.fdocuments.net/reader037/viewer/2022102800/56649ee75503460f94bf825b/html5/thumbnails/10.jpg)
Pre-Service Weld Inspection
Probability of Detection
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 2 4 6 8 10 12a (mm)
Po
D(a
)
![Page 11: Application of SRA for Pipeline Design Operation & Maintenance Andrew Francis Advantica Technologies ASRANeT, 2 nd Annual Colloquium, 9 th July 2001.](https://reader037.fdocuments.net/reader037/viewer/2022102800/56649ee75503460f94bf825b/html5/thumbnails/11.jpg)
Pre-Service Weld Inspection
Probability of inspecting weld and finding nothing is given by
)(1)](1)[()()(0
DpdaaPoDapDpIp
![Page 12: Application of SRA for Pipeline Design Operation & Maintenance Andrew Francis Advantica Technologies ASRANeT, 2 nd Annual Colloquium, 9 th July 2001.](https://reader037.fdocuments.net/reader037/viewer/2022102800/56649ee75503460f94bf825b/html5/thumbnails/12.jpg)
Pre-Service Weld Inspection
Probability that the weld contains a defect of depth a, given that the weld was inspected and nothing was found is given by
)(1)()](1[)(
)()](1)[()|(
0
DpdaapaPoDDp
apaPoDDpIaDp
![Page 13: Application of SRA for Pipeline Design Operation & Maintenance Andrew Francis Advantica Technologies ASRANeT, 2 nd Annual Colloquium, 9 th July 2001.](https://reader037.fdocuments.net/reader037/viewer/2022102800/56649ee75503460f94bf825b/html5/thumbnails/13.jpg)
Pre-Service Weld Inspection
The likelihood of a defect of given depth being present following inspection
0.00E+00
2.00E-03
4.00E-03
6.00E-03
8.00E-03
1.00E-02
0 2 4 6
a (mm)
p(D
a
|I)
![Page 14: Application of SRA for Pipeline Design Operation & Maintenance Andrew Francis Advantica Technologies ASRANeT, 2 nd Annual Colloquium, 9 th July 2001.](https://reader037.fdocuments.net/reader037/viewer/2022102800/56649ee75503460f94bf825b/html5/thumbnails/14.jpg)
Pre-Service Hydrostatic Test
Objective: To give assurance integrity of the pipeline prior to gassing up
![Page 15: Application of SRA for Pipeline Design Operation & Maintenance Andrew Francis Advantica Technologies ASRANeT, 2 nd Annual Colloquium, 9 th July 2001.](https://reader037.fdocuments.net/reader037/viewer/2022102800/56649ee75503460f94bf825b/html5/thumbnails/15.jpg)
Pre-Service Hydrostatic Test
We want to know the probability, P(D a | H)
Event H: Survival of the Hydrostatic Test
Using Bayes Theorem
)(
)()()|()|(
Hp
daapDpaDHpdaHaDp
![Page 16: Application of SRA for Pipeline Design Operation & Maintenance Andrew Francis Advantica Technologies ASRANeT, 2 nd Annual Colloquium, 9 th July 2001.](https://reader037.fdocuments.net/reader037/viewer/2022102800/56649ee75503460f94bf825b/html5/thumbnails/16.jpg)
Pre-Service Hydrostatic Test
Now the probability p(H | D a) , that the weld survived the hydrostatic test given that the weld contains a defect of depth a is given by
H is the Heaviside step function defined by
aH is the depth of defect that would just fail under the hydrostatic test pressure
)()|( aaHaDHp H
0,0)( xxH
0,1)( xxH
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Pre-Service Hydrostatic Test
The value of aH depends on geometrical and material parameters and can be evaluated using fracture mechanics procedures such as BS7910
Since geometrical and material parameters are subject to uncertainty, aH is also subject to uncertainty. This is not considered here for simplicity
![Page 18: Application of SRA for Pipeline Design Operation & Maintenance Andrew Francis Advantica Technologies ASRANeT, 2 nd Annual Colloquium, 9 th July 2001.](https://reader037.fdocuments.net/reader037/viewer/2022102800/56649ee75503460f94bf825b/html5/thumbnails/18.jpg)
Pre-Service Hydrostatic Test
Probability of surviving the hydrostatic test is given by
)(1)()()(0
DpdaapDpHpHa
![Page 19: Application of SRA for Pipeline Design Operation & Maintenance Andrew Francis Advantica Technologies ASRANeT, 2 nd Annual Colloquium, 9 th July 2001.](https://reader037.fdocuments.net/reader037/viewer/2022102800/56649ee75503460f94bf825b/html5/thumbnails/19.jpg)
Pre-Service Hydrostatic Test
Probability that the weld contains a defect of depth given that the hydrostatic test was survived is given by
)(1)()(
)()()()|(
0
DpdaapDp
aaHapDpHaDp
HaH
![Page 20: Application of SRA for Pipeline Design Operation & Maintenance Andrew Francis Advantica Technologies ASRANeT, 2 nd Annual Colloquium, 9 th July 2001.](https://reader037.fdocuments.net/reader037/viewer/2022102800/56649ee75503460f94bf825b/html5/thumbnails/20.jpg)
Pre-Service Hydrostatic Test
Combining with effects of inspection leads to
)(1)](1)[()(
)()](1)[()()|(
0
0
0
DpdaaPoDapDp
aaHaPoDapDpIHaDp
HaH
![Page 21: Application of SRA for Pipeline Design Operation & Maintenance Andrew Francis Advantica Technologies ASRANeT, 2 nd Annual Colloquium, 9 th July 2001.](https://reader037.fdocuments.net/reader037/viewer/2022102800/56649ee75503460f94bf825b/html5/thumbnails/21.jpg)
Pre-Service Hydrostatic Test
The Effect of a Hydrotest
0.0E+00
2.0E-03
4.0E-03
6.0E-03
8.0E-03
1.0E-02
0 2 4 6
a (mm)
p(D
a
|IH
)
![Page 22: Application of SRA for Pipeline Design Operation & Maintenance Andrew Francis Advantica Technologies ASRANeT, 2 nd Annual Colloquium, 9 th July 2001.](https://reader037.fdocuments.net/reader037/viewer/2022102800/56649ee75503460f94bf825b/html5/thumbnails/22.jpg)
Fatigue Crack Growth
Fatigue crack growth rate is dependent on the instantaneous defect depth, a, giving
Function f depends on stress intensity factor which is dependent on depth and the magnitude of the cyclic loading
nKaafdt
da )(
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Fatigue Crack Growth
Underlying assumption: the following continuity equation is satisfied:
This equation states that all defects which lie within the interval [a(t), a(t) +da(t)] at time t will lie within the interval [a(t+dt), a(t+dt) + da(t+dt)] at time t+dt
)(]),([)(]),([ dttdadttdttaptdattap
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Fatigue Crack Growth
P(a,t) P(a,t)
a(t) a+da(t)a(t+dt)
a(t+dt)+da(t+dt)
a(t+dt)
Growth
a(t)
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Fatigue Crack Growth
Distribution at time t based on distribution at time of commissioning following inspection and hydrostatic test
0,)1()1(1),( 1
1111 nnn
nn KtnapKtantap
![Page 26: Application of SRA for Pipeline Design Operation & Maintenance Andrew Francis Advantica Technologies ASRANeT, 2 nd Annual Colloquium, 9 th July 2001.](https://reader037.fdocuments.net/reader037/viewer/2022102800/56649ee75503460f94bf825b/html5/thumbnails/26.jpg)
Fatigue Crack Growth
Effect of Fatigue Crack Growth
0.00E+00
2.00E-03
4.00E-03
6.00E-03
8.00E-03
1.00E-02
0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00
a
p(a
)
![Page 27: Application of SRA for Pipeline Design Operation & Maintenance Andrew Francis Advantica Technologies ASRANeT, 2 nd Annual Colloquium, 9 th July 2001.](https://reader037.fdocuments.net/reader037/viewer/2022102800/56649ee75503460f94bf825b/html5/thumbnails/27.jpg)
Probability of Failure
Probability of failure in time interval[0, T]
aop is the defect size that would fail at the specified operating conditions
H
op
a
a
f daTapTp ),()(
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Probability of Failure
Probability of Failure @105% SMYS
1.00E-09
1.00E-08
1.00E-07
1.00E-06
1.00E-05
1.00E-04
1.00E-03
1.00E-02
0 10 20 30 40 50
Time
Pf
Nothing
Just Hydrotest
Just Inspection (Rad)
Just Inspection (TOF)
Both
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Probability of Failure
Probability of Failure @100% SMYS
1.00E-09
1.00E-08
1.00E-07
1.00E-06
1.00E-05
1.00E-04
1.00E-03
1.00E-02
0 10 20 30 40 50
Time
Pf
Nothing
Just Hydro
Just Insp - Rad
Just Insp - ToF
Both
![Page 30: Application of SRA for Pipeline Design Operation & Maintenance Andrew Francis Advantica Technologies ASRANeT, 2 nd Annual Colloquium, 9 th July 2001.](https://reader037.fdocuments.net/reader037/viewer/2022102800/56649ee75503460f94bf825b/html5/thumbnails/30.jpg)
Probability of Failure
Probability of Failure @90% SMYS
1.00E-05
1.00E-04
1.00E-03
1.00E-02
0 10 20 30 40 50
Time
Pf
Nothing
Just Hydrotest
Just Inspection (Rad)
Just Inspection (TOF)
Both
![Page 31: Application of SRA for Pipeline Design Operation & Maintenance Andrew Francis Advantica Technologies ASRANeT, 2 nd Annual Colloquium, 9 th July 2001.](https://reader037.fdocuments.net/reader037/viewer/2022102800/56649ee75503460f94bf825b/html5/thumbnails/31.jpg)
Conclusions
SRA & Bayes theorem used to systematically quantify effect of hydro test on construction defects taking account of inspection
An acceptable fatigue life may be achieved without any pre-service inspection if a hydrostatic test pressure of 105%SMYS is used.
![Page 32: Application of SRA for Pipeline Design Operation & Maintenance Andrew Francis Advantica Technologies ASRANeT, 2 nd Annual Colloquium, 9 th July 2001.](https://reader037.fdocuments.net/reader037/viewer/2022102800/56649ee75503460f94bf825b/html5/thumbnails/32.jpg)
Conclusions
If test pressure of 90%SMYS then pre-service inspection using a technique such as radiography or better is likely to be required.
If sophisticated TOF is used then may be possible to achieve an acceptable fatigue life without the need for a hydrostatic test.
Results are preliminary and further validation work required