1. Application of SRA for Pipeline Design Operation & Maintenance Andrew Francis Advantica Technologies ASRANeT, 2 nd Annual Colloquium, 9 th July 2001

2. INTRODUCTION l Uses of SRA l Wall thickness determination l Uprating l Life extension l Risk Based Inspection l Generally l Determination of required level of failure mitigation

3. Present Study l Failure Mode Fatigue Crack Growth l Uncertainty Construction Defect Depth l Mitigation Measures Construction process Weld Inspection Hydrostatic Test

4. Mitigation effects using Bayes Theorem l Conditional probability l p( X | Y ) is the probability of event X occurring given prior knowledge that event Y has already occurred p (X  Y) 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

5. Construction Process l 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

6. Construction Process

7. Pre-Service Weld Inspection l Objective: To detect any defects, which are unacceptable according to the appropriate criteria l Issue: Inspection techniques often only 70% - 80% reliable, sometimes lower

8. Pre-Service Weld Inspection l We want to know probability, p(D  a | I) l Event I: Weld was inspected and no defect was found l Using Bayes Theorem

9. Pre-Service Weld Inspection l 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 l PoD(a) is the probability of detection of a defect of depth a

10. Pre-Service Weld Inspection

11. l Probability of inspecting weld and finding nothing is given by

12. 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

13. Pre-Service Weld Inspection

14. Pre-Service Hydrostatic Test l Objective: To give assurance integrity of the pipeline prior to gassing up

15. Pre-Service Hydrostatic Test l We want to know the probability, P(D  a | H) l Event H: Survival of the Hydrostatic Test l Using Bayes Theorem

16. Pre-Service Hydrostatic Test l 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 l H is the Heaviside step function defined by l a H is the depth of defect that would just fail under the hydrostatic test pressure

17. Pre-Service Hydrostatic Test l The value of a H depends on geometrical and material parameters and can be evaluated using fracture mechanics procedures such as BS7910 l Since geometrical and material parameters are subject to uncertainty, a H is also subject to uncertainty. This is not considered here for simplicity

18. Pre-Service Hydrostatic Test l Probability of surviving the hydrostatic test is given by

19. Pre-Service Hydrostatic Test l Probability that the weld contains a defect of depth a given that the hydrostatic test was survived is given by

20. Pre-Service Hydrostatic Test l Combining with effects of inspection leads to

21. Pre-Service Hydrostatic Test

22. Fatigue Crack Growth l Fatigue crack growth rate is dependent on the instantaneous defect depth, a, giving l Function f depends on stress intensity factor which is dependent on depth and the magnitude of the cyclic loading

23. Fatigue Crack Growth l Underlying assumption: the following continuity equation is satisfied: l 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

24. Fatigue Crack Growth

25. l Distribution at time t based on distribution at time of commissioning following inspection and hydrostatic test

26. Fatigue Crack Growth

27. Probability of Failure l Probability of failure in time interval[0, T] l a op is the defect size that would fail at the specified operating conditions

28. Probability of Failure

31. Conclusions l SRA & Bayes theorem used to systematically quantify effect of hydro test on construction defects taking account of inspection l An acceptable fatigue life may be achieved without any pre-service inspection if a hydrostatic test pressure of 105%SMYS is used.

32. Conclusions l If test pressure of 90%SMYS then pre-service inspection using a technique such as radiography or better is likely to be required. l If sophisticated TOF is used then may be possible to achieve an acceptable fatigue life without the need for a hydrostatic test. l Results are preliminary and further validation work required