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Presented at the Pipeline Integrity & Safety Conference, Houston TX, September 2001

A SYSTEMATIC RISK AND RELIABILITY-BASED APPROACH TO INTEGRITY MANAGEMENT OF PIGGABLE AND NONPIGGABLE PIPELINES Andrew Francis, Mike Gardiner, Andrew Goodfellow, Marcus McCallum, Gary Senior, and Bob Greenwood, Advantica Technologies Ltd Loughborough UK ABSTRACT Pipeline designers and operators generally acknowledge that complex combinations of failure mitigating measures are needed to ensure safe operation of onshore high-pressure pipelines. Such measures include hydrostatic testing, in-line inspection, Close Interval Surveys (CIS), Direct Current Voltage Gradient (DCVG) measurements and Pearson Surveys. However, the relative contribution of each activity to the overall structural reliability is generally unknown. Basically, each activity is routinely undertaken in the belief that it is necessary and makes some contribution to the integrity but the actual worth of the activity is not known. This paper describes techniques based on structural reliability and analysis and probability theory for rigorously quantifying the effects of these activities and it is shown by analysis and simple case study how the approach can be used to optimize in-line inspection scheduling. More significantly a new methodology based on Bayesian updating is described for undertaking Direct Assessment studies. The approach is specifically used to evaluate the contributions of activities such as CIS and DCVG to structural reliability and is of particular relevance in situations where in-line inspections are not practicable. The approach is clearly illustrated by a simple case study and it is indicated how the approach may be validated for future use in the field. INTRODUCTION The structural integrity of a high-pressure pipeline is determined by a complex combination of failure mitigating measures. These include • Measures that are introduced at the design stage, such as the selection of wall thickness and material grade. • Measures that are introduced at the construction stage, such as weld inspections, coating inspections and hydrostatic pressure test. • Measures in continued operation such as Close Interval Surveys, Direct Current Voltage Gradient measurements and in-line inspections.

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Presented at the Pipeline Integrity & Safety Conference, Houston TX, September 2001

It is generally acknowledged by pipeline designers and operators that these and many other factors contribute to the overall integrity and hence safety of the pipeline. However, the relative contribution of each activity to the overall structural reliability is generally unknown. Basically, each activity is routinely undertaken in the belief that it is necessary and makes some contribution to the integrity but the actual worth of the activity is not known. Structural Reliability Analysis (SRA) is a technique developed over recent years that allows the relative contribution of each mitigating activity to be quantified. The technique is based on combining theoretical and empirical structural mechanics with uncertainty analysis, and is briefly described below. Recent applications of SRA to onshore pipelines are given in [1–6]. The approach is also well suited to risk/reliability-based inspection and can be used to optimize the scheduling of in-line inspections. Following a general description of SRA this paper describes how the approach is used for risk/reliability based inspection, with a particular focus on in-line inspection taking account of the reliability of the inspection tool. The method is illustrated using a practical example. The above application is valuable to operators who routinely examine their pipelines using in-line inspection or at least have the option to do so. A significant number of operators do not currently have such an option and the cost of system modifications in order to allow in-line inspections could be prohibitive. In-line inspection is, however, just one measure that is undertaken in order to demonstrate an adequate level of structural reliability/integrity. Thus, in situations where in-line inspection is not viable, it is necessary to understand and quantify the effects of other mitigating activities. In-line inspection is generally used in order to mitigate failures caused by defects due to corrosion and/or external interference. This type of damage becomes more severe as time increases and the purpose of in-line inspection is to detect the presence of the damage before it becomes a threat to integrity. However, it is important to note that depending on the pipeline design and operating parameters, and the severity of the impact, defects caused by external interference can fail instantaneously. If a particular pipeline (thin walled, for instance) is more prone to this, then more attention should be given to other mitigating measures such as depth of burial and surveillance. More recently the emergence of in-line inspection tools that are capable of detecting crack-like defects has allowed in-line inspection also to be used for the purpose of mitigating failures due to Stress Corrosion Cracking (SCC). However, no matter what the purpose of the in-line inspection, alternative measures must be invoked if in-line inspection is not possible.

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Presented at the Pipeline Integrity & Safety Conference, Houston TX, September 2001

The focus of the latter part of this paper is on the use of methods other than inline inspection and hydrostatic testing to mitigate failures due to corrosion. Such methods include CIS measurements, Direct Current Voltage Gradient measurements and Bell-Hole excavations. These activities have recently been termed direct assessment (DA) techniques, since they are based on direct measurements of quantities external to the pipeline. The analysis described here shows how information can be systematically combined using probability theory and SRA in order to quantify the effect of DA techniques on structural reliability, and hence determine the required levels of one or more activities to achieve an acceptable level of safety. The scope of this paper is limited to the consideration of DA techniques for the purpose of addressing corrosion damage. However, it should be noted that the principles discussed here could be applied to other damage mechanisms.

STRUCTURAL RELIABILITY ANALYSIS Structural Reliability Analysis makes a contribution to methods used in both piggable and non-piggable situations and is briefly described in this section. The method comprises six elements. These are w w w w w w

Establishment of Limit States Identification of Failure Modes Formulation of Limit State Functions Uncertainty Analysis Evaluation of Failure Probability Assessment of Results

The relationship between these items is shown schematically in Figure 1 and a brief description of each of them and the role they play in the overall analysis is given below. A detailed description of the overall methodology is given in [4]. The primary focus of the present study is on the application of the methodology to external corrosion in situations where pigging is possible, and where pigging is not possible. APPLICATION TO THE EXTERNAL CORROSION FAILURE MODE Limit State and Failure Mode A limit state is defined as the state of a structure at which it no longer satisfies a particular design requirement. A failure mode is a mechanism that leads to a structure reaching a limit state. Copyright Š 2001 Advantica Technologies Ltd. All rights reserved. Page 3 of 22


Presented at the Pipeline Integrity & Safety Conference, Houston TX, September 2001

If left undetected, and unprotected, the corrosion failure mode will eventually lead to a breach of the pipeline wall resulting in the ultimate limit state being reached at which loss of containment occurs. Limit State Function A limit state function is the relationship that exists between relevant parameters characterizing the failure mode at the onset of failure. Such expressions are generally obtained through structural mechanics studies supported and validated by test data. The limit state function for corrosion defects relates the defect depth at failure to the defect length and hoop stress and is given by a = ac

(1)

where a is the actual depth of the defect, and ac is the depth of at failure which is related to the wall thickness, w, hoop stress, σ h , and ultimate tensile strength, σ u , through the expression [7]

σh    1− σ  u  a c = w  σ h −1  1 − σ Q  u  

(2)

where Q is a length correction factor given by the expression

  l   Q = 1 + 0.31 2 Rw   

2

  

1 2

(3)

in which l is the axial length of the corrosion defect.

Uncertainty Analysis The probability of failure will depend on the likelihood of any particular defect reaching a depth ac and on the number of defects that are likely to be present in the pipeline.

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Presented at the Pipeline Integrity & Safety Conference, Houston TX, September 2001

It is thus necessary to take account of the uncertainty in the number of defects present, the defect depth and the critical defect depth, which depends on the uncertainty in wall thickness, hoop stress, ultimate tensile strength and defect length. It is important to note that the time dependent nature of the uncertainties in the number of defects, defect depth and length must be taken into account. In the case of piggable lines these uncertainties may be quantified by analysis of previous in-line inspections. The computed failure probabilities based on these quantities can be used to determine future inspection frequencies. An outline of the procedure used for this purpose is given in the following section In the case of unpiggable lines it is necessary to quantify the uncertainties in these time dependent quantities using other information. In the present study the information provided by CIS, DCVG and bell-hole excavations is used. The methodical procedure for taking account of this information and for determining the number of required excavations is presented in a later section.

OPTIMISATION OF IN-LINE INSPECTION SCHEDULING FOR PIGGABLE PIPELINES Corrosion Incident Rate In-line inspection results give an indication of the mean rate, dEN / dt , at which corrosion defects are introduced into a given length of pipeline. The quantity EN (t ) thus represents the expected number of defects at time t. It is assumed that the defects have a finite depth at the time of introduction and the uncertainty in the defect depth is described by the probability density function pI (a) . Corrosion Growth Once initiated each defect will begin to grow through the pipeline wall. It is assumed here that growth rate is proportional to the instantaneous depth and hence may be expressed as a power law in the form da = Ka n (4) dt where K and n are constants which may be determined by appropriate analysis of inspection data. Using the above expression it is possible to determine the distribution of the depth at time t of a defect that was introduced at time τ . In general this distribution, p(a, t − τ ) , is related to pI (a) through the following expressions of the form

p(a, t − τ ) = f (a, t − τ ) p I ( g (a, t − τ ))

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(5)


Presented at the Pipeline Integrity & Safety Conference, Houston TX, September 2001

where expressions for f and g are given in [2]. Probability of Failure In practice the calculation of the probability of failure will be a complex one which would take into account the uncertainties in the material and geometrical properties. However, in order to simplify the analysis, it is assumed here that all these quantities are known exactly. The probability of failure, p F , due to corrosion within time interval (0,t) is given by

p F = EN

∫ p(a, t )da

(6)

ac

giving an annual probability of failure, p FA ,of

p FA = EN

dp(a, t ) da dt ac

(7)

where EN is the expected number of defects and it has been assumed that all defects are introduced at the same time. It is a straightforward matter to modify these expressions to take account of a variable rate of introduction of defects as a function of time. The above, or appropriately modified, expressions for annual failure probability can be used to set inspection intervals. The annual failure probability will naturally increase with time if no mitigating action is taken. Conducting an in-line inspection will reveal the presence of corrosion defects and allow any necessary repairs to be undertaken. The annual failure probability following an in-line inspection will thus be reduced to a negligible level. The above expressions can thus be used to set the inspection frequency based directly on a prescribed acceptable failure probability. The value of an acceptable failure probability depends on a number of issues including the consequences of failure, societal attitudes and costs of failure mitigation. However, for the purpose of inspection interval scheduling the most appropriate approach is to use the value which leads to minimum expected cost. For an inspection interval, TI , the expected cost per year, EC , is given by EC =

1 1 C F p F (TI ) + C I TI TI

where C F is the cost of a failure and C I is the in-line inspection cost. Minimizing cost gives

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(8)


Presented at the Pipeline Integrity & Safety Conference, Houston TX, September 2001

TI p FA (TI ) − p F (TI ) =

CI CF

(9)

The above expression gives both the optimum inspection interval and the annual probability of failure at the end of the interval. The above model assumes that the repairs undertaken at time T I will reduce the annual failure probability at that time to a negligible level. A simple case study illustrating the above is given later.

DIRECT ASSESSMENT APPROACH FOR NON-PIGGABLE LINES The objective of direct assessment is to acquire an acceptable level of confidence in the structural integrity/reliability of the pipeline based on an appropriate consideration of the information obtained from direct measurements such as CIS, DCVG and defect measurements at bell-hole sites. This section describes a detailed methodology, based on probability theory and Structural Reliability Analysis, to progress from DA results to the likelihood that a given length of pipeline will contain a specified number of defects and the likelihood that these defects will lead to failure within a specified time.

Effect of Close Interval Survey. An indication of the number of corrosion defects can be found by prioritizing the CIS results into different types, for example: Type I: “On”, “Off” potentials shifted in a positive direction, with both potentials more positive than -850mV, indicating a probable defect. Type II: “On”, “Off” potentials shifted in a positive direction, with the “On” potential more negative than -850mV and the “Off” potential more positive than -850mV, indicating a possible defect. Type III: “On”, “Off” potentials shifted in a positive direction, with both potentials more negative than -850mV, indicating a possible defect. The different types can be seen in Figure 2. It is important to note that the CIS output is only an indicator that corrosion is actually taking place when the reading is taken, and no indication is given of the extent or depth of such a defect. The CIS reading does not indicate the presence of defects that were not corroding at the time of the survey but had been

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Presented at the Pipeline Integrity & Safety Conference, Houston TX, September 2001

corroding previously. There is thus a probability, p m , that a defect will be missed. It is customary to express this probability in the form p m = 1 − PoD where PoD is known as the probability of detection. Contrarily, it is possible that for each of the region types mentioned there is no corrosion defect. It thus follows that there is a probability per unit length, p f , of a false indication. It is readily apparent from the above that the number of corrosion defects, N CIS , indicated by CIS in a length L of pipeline will generally differ from the actual number of defects present, N AC , which is, of course, unknown. The uncertainty in the value of N AC can be determined using probability theory. The conditional probability, p( N AC | N CIS ) , of the pipeline containing N AC defects given that the CIS indicates that there are N CIS defects present can be obtained using Bayes Theorem, viz

p( N AC | N CIS ) =

p( N CIS | N AC ) p( N AC ) ∑ p( N CIS | N AC ) p( N AC )

(10)

N AC

In the above the probability, p( N AC ) , denotes ‘initial’ knowledge of the probability that the pipeline contains N AC defects prior to obtaining the CIS results. The conditional probability, p( N CIS | N AC ) appearing in the right hand side of the above expression can be deduced from a logical consideration of the combinations of missed defects, detected defects and false indications that can result in N CIS defects being reported when N AC defects are actually present. Such an analysis results in an expression having the functional dependence p ( N CIS | N AC ) = p ( N AC , N CIS , PoD, p f L)

(11)

Equation (11) can be used in conjunction with equation (10) in order to determine the change in the confidence in the number of corrosion defects based on the CIS data. The expected number of defects following the CIS is given by

EN =

∑N

N AC =1

AC

p( N AC | N CIS )

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(12)


Presented at the Pipeline Integrity & Safety Conference, Houston TX, September 2001

In order to perform the associated calculation it is necessary to determine the values of p f and PoD . The method used for this purpose is described below. Definition of Probability of Detection and Probability of False Indication The approach adopted here to determine the effectiveness of the CIS system was to compare the CIS readings on a particular piggable pipeline with results from an in-line inspection of the same pipeline. The analysis technique and results are described below. For each type of region, a probability of detection, PoD and a probability of false indication, Pf is calculated as follows: Number of defects in region PoD = Total number of defects (13)

Pf =

Number of defect free regions Number of regions

Effect of DCVG Once a CIS has been completed and the Type I, II and III regions have been calculated, a direct current voltage gradient (DCVG) survey, which is able to examine the size and the nature of the defect, can be carried out. This can either look at the whole pipeline or concentrate on the regions highlighted by the CIS results. An analogous procedure to that described above is used to determine the updated distribution of N AC , but in this case the prior distribution is taken as the posterior distribution following the CIS analysis. Thus, introducing the shorthand notation pCIS ( N AC ) = p( N AC | N CIS ) , it is appropriate to determine the quantity p( N AC | N DCVG ) using the expression

p( N AC | N DCVG ) =

p( N DCVG | ( N AC ) pCIS ( N AC ) ∑ p( N DCVG | ( N AC ) pCIS ( N AC )

(14)

N AC

The expected number of defects following the DCVG and using the information gathered from the CIS is given by

EN =

∑N

N AC =1

AC

p( N AC | N DCVG )

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(15)


Presented at the Pipeline Integrity & Safety Conference, Houston TX, September 2001

As is the case with the CIS, there will be a probability of detection and a probability of false indication. In order to perform the associated calculation it is necessary to determine the values of p f and PoD . The approach to this is described below. Determining Probability of Detection and Probability of False Indication The calculation of the PoD involves finding out how many ‘hits’ and ‘misses’ there are, where a ‘hit’ comes when a defect lies within ∆x metres either side of the DCVG indication. The calculation of Pf involves finding out how many times a DCVG indication is nowhere near a defect. A schematic of the definition of a ‘hit’, ‘miss’ and a false indication is given in Figure 3.

Targeting of Bell-Hole Excavations If the calculated probability of failure cannot be considered to be acceptable then further information must be acquired in addition to undertaking possible remedial work. Bell-hole excavations can be used for this purpose. This involves uncovering short sections of pipeline at the locations that are considered most likely to contain a defect based on the indications of the CIS and DCVG. If defects are discovered that are of a level of severity such that they could pose a threat to integrity within some future time interval then remedial action will be taken. The effect of bell-hole excavations is multi-functional. (i) The initial findings allow a further updating of the number of defects that are present to be performed. (ii) The measurements allow an updating of the distribution of defect depth to be performed. (iii) The repairs result in a reduction in the numbers of onerous defects. The effects of these functions are discussed below. Updating of probability of false indication The prior belief of the likelihood that a defect will be present in a type I location is simply equal to 1 − p f , where p f is the probability of a false indication in a type I area. This belief is naturally based on the assumption that the value of p f is a true attribute of the CIS/DCVG system. This is the only sensible belief that can be held without further information. However, once further information is obtained Copyright © 2001 Advantica Technologies Ltd. All rights reserved. Page 10 of 22


Presented at the Pipeline Integrity & Safety Conference, Houston TX, September 2001

from a number of excavations it is possible, and indeed necessary, to challenge this belief. It is thus appropriate to formulate the null hypothesis, H 0 , that p f is a true attribute of the CIS/DCVG system and the alternative hypothesis, H 1 that it is not. The initial strategy to adopt will be to undertake M excavations in type I locations. The expected number of defects will simply be M (1 − p f ) . If the actual number of defects found, m , is greater than this quantity then alternative hypothesis will be that p f is less than the prior value and, conversely, if fewer defects are found, that it is greater than the prior value. Using Bayes’ Theorem, to determine the probability, p( H 0 | m) that H 0 is true given m defects were found in M excavations, an updated value of the probability of false indication can be obtained using

p f = p f p( H 0 | m) + p f (1 − p( H 0 | m))

(16)

where p f is a suitable alternative value of the probability of false indication associated with H 1 . A similar approach may be applied to type II and type III regions.

Updating Probability of Detection In order to update the view held on the probability of detection it is necessary to perform some excavations in regions that do not have any indications from the CIS. Note that the information obtained from these locations can only update the combined PoD from type I, II and III. It cannot directly update the view on the individual PoDs. The prior belief of the likelihood that a defect will be present in a region with no indication of a defect is given by 1 − PoD , where PoD is the combined probability of detection by types I,II and III. This belief is naturally based on the assumption that the value of PoD is a true attribute of the CIS/DCVG system. This is the only sensible belief that can be held without further information. However, once further information is obtained from a number of excavations it is possible, and indeed necessary, to challenge this belief. It is thus appropriate to formulate the null hypothesis, H 0 , that PoD is a true attribute of the CIS/DCVG system and the alternative hypothesis, H 1 that it is not. The initial strategy to adopt will be to make M excavations in locations with no indication. The expected number of defects will simply be M (1 − PoD ) . If the Copyright © 2001 Advantica Technologies Ltd. All rights reserved. Page 11 of 22


Presented at the Pipeline Integrity & Safety Conference, Houston TX, September 2001

actual number of defects found, m , is greater than this quantity then the alternative hypothesis will be that PoD is less than the prior value and, conversely, if fewer defects are found, that it is greater than the prior value. Using Bayes’ Theorem to determine the probability, p( H 0 | m) , that H 0 is true given m defects were found in M excavations, an updated value of the probability of detection can be obtained using PoD = PoDp ( H 0 | m) + PoD p ( H 1 | m)

(17)

where PoD is a suitable alternative value of the probability of detection associated with H 1 . Updating the Defect Size Distribution The measurements of defect size made at the sites of bell-hole excavations will allow an updating of the distribution p (a, T ) to be undertaken where T is the time of the excavation relative to some reference time. This can be achieved using Bayesian updating techniques such as those used above. This issue will be addressed in a future note.

CASE STUDY — PIGGABLE LINES A very simple case study is presented here in order to illustrate the approach to optimization of inspection intervals. It is assumed for a particular pipeline that the expected number of defects per kilometer is 2 and the probability of failure within time interval TI is given by p f = exp(−100 / TI )

A plot describing the above expression is given in Figure 4 and the associated annual failure probability, p fa is given in Figure 5. (Whilst the above is simplified expression for the purpose of illustration it has been obtained by approximating SRA results from an actual pipeline study.) It is further assumed that the cost of a repair to minor leak from a failed corrosion defect , C F , is $30k and that the cost of in-line inspection, C I , is $1k per kilometer.

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Presented at the Pipeline Integrity & Safety Conference, Houston TX, September 2001

Using the above information in equation (13) it is found that this equation is satisfied when TI = 17.7 years. The minimum cost thus occurs with approximately an 18-year inspection interval, as shown in Figure 6. CASE STUDY — NON PIGGABLE LINES This case study, involving the application of the DA procedure to a 100km pipeline, begins by assuming that p f and PoD values have been established by correlating CIS and DCVG data with in-line inspection results from a ‘similar’ piggable pipeline. It is assumed that this correlation has resulted in p f = 0.1 and PoD = 0.75 for the CIS system, and p f = 0.05 , PoD = 0.75 for the DCVG system. Based on considerations of the age of the pipeline and previous CIS, DCVG and Bell-Hole excavations it is considered that the prior distribution of the number of defects in the entire length of the, p( N AC ) line is given by

p( N AC ) = Weibull( N AC ,α = 11, β = 102) and this is shown as the solid curve in Figure 7. The expected value of N AC is 98. The CIS has indicated that there are 75 Type I, 105 Type II and 200 Type III indications. For simplicity only the Type I indications are addressed here. Using the above methodology the updated distribution p( N AC | N CIS ) is shown by the short dotted line in Figure 7. The expected number of defects is 91. It is assumed that the DCVG is also applied to the entire length of the pipe and that this gives 60 indications. The updated distribution p( N AC | N DCVG ) is shown as the longer dotted line in Figure 7. The expected number of defects once the CIS and DCVG are taken into account is 74. Bell-Hole Excavations In order to illustrate the effect of bell-hole excavations suppose that 20 excavations are undertaken in Type I locations and suppose that the confidence held in the null hypothesis regarding the probability of false indication is 90%. The expected number of defects that will be excavated in this case is 18, based on p f = 0.1. The variation in p f and p f with m is shown in Figure 8. It is seen Copyright © 2001 Advantica Technologies Ltd. All rights reserved. Page 13 of 22


Presented at the Pipeline Integrity & Safety Conference, Houston TX, September 2001

from this Figure that the value of p f does not differ significantly from p f for values of m close to the expected value, i.e. values in the range (16–19). However, as m decreases below 16 the value of p f begins to increase and approaches the estimated value p f as m falls below 12; that is, for values of m below 12 the null hypothesis becomes insignificant and the updated belief is dominated by the observations. Suppose also that six excavations are made in locations for which there are no indications and again that there is 90% confidence in the null hypothesis that PoD=0.9. In this case the expected number of defects is 0.6 and the variation in

PoD and PoD is shown in Figure 9. It can be seen that PoD is not significantly different from PoD for values of m less than or equal to 2 but begins to decrease as m increases above 2 and approaches the estimated value at m=5; that is, the null hypothesis becomes insignificant and the updated belief is dominated by observations. Figure 10 illustrates the effect on a prior distribution of the updating that results from bell-hole excavations. It has been assumed that 20 excavations were made, with an expectation of finding 18 defects, but that only 10 were found. The probability of a false indication is thus, by reference to Figure 8, modified to a value of 0.495. Likewise, it was assumed that 6 excavations were made at locations that were not expected to contain any defects and that 4 defects were found. From Figure 9, the probability of detection is thus modified to 0.528. In Figure 10, we see how these excavations modify our view of the distribution of defects. The prior distribution is shown by a solid line, with an expected value of 98 defects. The result of digging at locations where defects were indicated, taken in isolation, is to increase p f and reduce the expectation to 54 defects in 100km. Similarly, it can be seen that the digs at locations where no defects were indicated reduced PoD and, taken in isolation, increased the expectation to 107 defects. Applying the modified p f and PoD together can be seen to broaden the posterior distribution of actual defect number and alter the expectation to 78 defects.

DISCUSSION The preceding text has described the development of a new methodology for performing direct assessment analyses of pipelines that are subject to the problem of external corrosion and has illustrated the application of the approach using a simple case study. In particular it has been shown how the approach is used to systematically change the confidence in the expected number of corrosion defects based on information gathered from CIS, DCVG and Bell-hole Copyright Š 2001 Advantica Technologies Ltd. All rights reserved. Page 14 of 22


Presented at the Pipeline Integrity & Safety Conference, Houston TX, September 2001

excavations. A methodology has also been given to the determine the structural reliability based on the new confidence in the number of defects and on the likelihood of any given defect failing within a specified time period taking account of corrosion growth. The simple case study presented illustrates that this new method has significant potential for the purpose of integrating key data from a number sources in order to demonstrate an adequate level of structural reliability without recourse to inline inspection and/or re-hydrostatic testing. The basic principles and mechanics of the method are now regarded as complete. However, it is anticipated that further development and validation will be necessary in order to take account of other data (e.g. Pearson Survey results) that are often available to enhance confidence in structural reliability. During the next stage of the development program it is proposed to ascertain the likely range of p m and p f values that occur in practice. In order to do this a number of data sets containing CIS, DCVG and in-line inspection results will be analyzed. Similar models that take account of other data (e.g. Pearson Survey results) will be developed and combined with the above models in order to produce a technique that leads to further confidence in structural reliability.

CONCLUSIONS A structural reliability based methodology for optimizing in-line inspection intervals has been presented and illustrated by a simple case study. The potential cost savings to operators who are able to use in-line inspection tools has been made apparent. A rigorous methodology for performing direct assessment analyses based on structural reliability and Bayesian statistics has been presented. The methodology takes account the CIS, DCVG and Bell-hole excavation results in addition to corrosion growth effects. A simple case study has been given to illustrate the strong potential of this technique for operators who are unable to use in-line inspection tools.

ACKNOWLEDGEMENT The authors would like to give their thanks to a number of their colleagues for useful contributions to this work and to Advantica Technologies Inc. for permission to publish this paper.

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Presented at the Pipeline Integrity & Safety Conference, Houston TX, September 2001

REFERENCES 1. Francis, A., Edwards, A.M., Espiner, R.J., & Senior, G., “Applying Structural Reliability Methods to Ageing Pipelines”, Paper C571/011/99, IMechE Conference on Ageing Pipelines, Newcastle, UK, October 1999 2. Francis, A, Edwards, A.M. & Espiner, R.J., “A Fundamental Consideration of the Deterioration Processes Affecting Offshore Pipelines using Structural Reliability Analysis”, Paper OMAE00-5042, ETCE/OMAE 2000 Joint Conference, New Orleans, USA, February 2000 3. Edwards, A.M., “The application of Structural Reliability Analysis Towards Developing Pipeline Integrity Management Programs”, AGA Operations Conference, May 7-9, 2000, Denver Colorado 4. Francis, A., Edwards, A.M., Espiner, R.J., & Senior, G., “An Assessment Procedure to Justify Operation of Gas Transmission Pipelines at Design Factors up to 0.8”, Paper PIPE90, Pipeline Technology Conference, Brugge, Belgium, May 2000. 5. Francis, A., Espiner, R.J., Edwards, A.M. & Hay, R.J., ‘A Consideration of Data Requirements for Structural Reliability Based Assessments of Onshore Pipelines’ 5th International Conference on Engineering Structural Integrity Assessment, Churchill College, Cambridge, UK September 2000 6. Francis, A., McCallum, M., Gardiner, M. & Michie, R., ‘A Fundamental Investigation of the Effects of The Hydrostatic Pressure Test on the Structural Integrity of Pipelines using Structural Reliability Analysis’, 20th International Conference on Offshore Mechanics and Artic Engineering, Rio de Janeiro, Brazil, June 2001. 7. Batte, A.D., Fu, B., Kirkwood, M.G. & Vu, D., "New Methods for Determining the Remaining Strength of Corroded Pipelines", 16th International Conference on Offshore Mechanics and Arctic Engineering, Yokohama, Japan, April 1997.

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Presented at the Pipeline Integrity & Safety Conference, Houston TX, September 2001

Establish limit states

Identify failure modes

Identify limit state functions

Quantify variation in pipeline geometry

Quantify variation in material properties

Quantify variation in defect size and growth

Calculate probability of failure, pf

Is pf acceptable?

No

Introduce further mitigating measures

Yes

Report results

Figure 1 The SRA Methodology

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Quantify variation in loads


Presented at the Pipeline Integrity & Safety Conference, Houston TX, September 2001

1000 Type III

Potential

950 900

Type I

850 Type II

800 Off Potential On Potential

750

850 mV

700 0

50

100

150

200

Distance

Figure 2 : Illustration of Different Types of Regions

100

90 Hit

DCVG

80

DCVG

90

Defect

80

70

70

60

60

50

50

40

40

False Indication

30

Miss

30

20

20

10

10

0 0

50

100

150

Defect

100

0 200

Distance Figure 3 : Illustration of Hits, Misses and False Indications

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Presented at the Pipeline Integrity & Safety Conference, Houston TX, September 2001

0.18 0.16 0.14 0.12 0.1 Pf 0.08 0.06 0.04 0.02 0 0

10

20

30

40

50

40

50

TI (years)

Figure 4 : Probability of Failure

0.012 0.01 0.008 Pfa 0.006 0.004 0.002 0 0

10

20

30 TI (years)

Figure 5 : Annual Probability of Failure

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Presented at the Pipeline Integrity & Safety Conference, Houston TX, September 2001

0.2

0.15

EC ($k) 0.1

0.05

0 5

15

25

35

45

TI (years)

Figure 6 : Expected Cost Per Kilometre 0.12

0.1

Probability

0.08 P(Nac) P(Nac|CIS)

0.06

P(Nac|DCVG+CIS) 0.04

0.02

0 0

50

100

150

Nac

Figure 7 : Effect of CIS and DCVG on Prior Distribution

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Presented at the Pipeline Integrity & Safety Conference, Houston TX, September 2001

1.2 1 0.8 Pf 0.6

Pf

0.4

Pf

0.2 0 0

5

10

15

20

25

m

Figure 8 : Effect of Excavation on Probability of False Indication

1.2 1

PoD

0.8 0.6

PoD

0.4

PoD

0.2 0 0

1

2

3

4

5

6

m

Figure 9 : Effect of Excavation on Probability of Detection

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7


Presented at the Pipeline Integrity & Safety Conference, Houston TX, September 2001

0.08 0.07

Probability

0.06 0.05

P(Nac) Modified Pf

0.04

Modified PoD Modified Pf & PoD

0.03 0.02 0.01 0 0

50

100

150

Nac

Figure 10 : Effect of Excavation on Prior Distribution

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A systematic Approach