Probabilistic Engineering Critical Assessment of Circumferential Girth Weld Flaws in Sour Service

Amir Bahrami1, David Baker2, Xiaofei Cui3, Fokion Oikonomidis3, Guiyi Wu3 ExxonMobil Production Company1, ExxonMobil Upstream Research Company2, TWI3

Spring TX, USA1, 2; Cambridge UK3

ABSTRACT

Engineering Critical Assessment (ECA) is a sophisticated deterministic

tool based on fracture mechanics, which is mainly used to assess

criticality of defects in metallic structures and particularly welds. Such

analyses are routinely undertaken in the development phases of Oil and

Gas pipeline projects to develop weld defect acceptance criteria. This

enables an efficient fabrication campaign, while ensuring the integrity

of the joint are not compromised at the time of fabrication, during

installation and for the intended service life. The ECA of pipeline girth

welds operating in inert environments is generally considered to be a

mature technology and codified through dedicated industry standards

which provide a robust framework for such analysis. Although the

same fracture mechanics principles can be used, the assessment of

defect criticality in a girth weld when in an aggressive environment

such as sour service requires additional considerations. This is due to

inherent uncertainties associated in defining some of the key input

parameters required for an ECA, in particular the material resistance to

crack extension (i.e. fracture toughness) in a hydrogen charging (e.g.

sour service) environment. As a result, the traditional deterministic

ECA, which is designed to define safe boundaries may be too

conservative or otherwise based on the values used for such inputs.

This is driven by the large scatter seen in toughness data which is

influenced by multitude of factors, consequently a probabilistic

approach to ECAs may offer potential advantages.

Probabilistic fracture mechanics assessment could provide an

alternative approach, which would not just define the conditions at

which a given defect is determined to be “safe” but provide a

quantitative measure of level of uncertainty associated with a defect

which is not deterministically safe. This would enable the probability

of failure to be estimated taking into account uncertainties and scatter

in input data. This approach involves a large number of iterations

where various combinations of input parameters are considered. The

choice of key variables in such assessments depends on which

parameters are likely to carry high levels of uncertainty and/or have a

significant effect on the results.

The paper presents the results of a study, which was aimed at

examining applicability of a probabilistic fracture mechanics method to

the assessment of circumferential girth weld defects in sour service.

The paper further discusses the approach and the challenges associated

with the determination of relevant input parameters.

KEY WORDS: Engineering critical assessment (ECA), sour service,

environmental cracking, probabilistic analysis, fracture mechanics

INTRODUCTION

Engineering Critical Assessment (ECA) methods are employed to

identify appropriate operational limits for the design and development

of pipelines and other integrity critical structures. ECA has been

successfully employed for decades and is considered a mature

technique for performing structural evaluations.

The vast majority of ECAs are conducted using a deterministic fracture

mechanics approach that involves conservative estimates of the input

parameters required for the fitness for purpose assessment. The usual

approach for conducting deterministic fracture assessments consists of

using lower bound values for tensile properties and fracture toughness;

and upper bound values for the flaw size and both primary and

secondary stresses. Although this practice is expected to yield

conservative assessments, the results can be overly conservative

predicting failure when it would not actually occur. Also, expert

engineering judgement is needed to evaluate associated safety margins,

particularly when definition of input parameters is, in some cases,

subject to considerable uncertainties.

Probabilistic fracture mechanics provides an alternative approach that

would not simply produce a ‘go/no-go’ result, but instead would enable

the likelihood of failure to be estimated taking into account

uncertainties and scatter in input data (Provan, 1987; Sandvik et al.,

2006; Mechab et al., 2014; Lee et al., 2015 and Agrell et al., 2016).

Of particular interest is the scatter that arises for fracture toughness in

sour environments. Other parameter may also be impacted by

environment. The assessment of flaws in sour environments is

considerably more complex given the substantial uncertainties affecting

definition of key input parameters, in particular, the material resistance

to crack extension by hydrogen embrittlement (i.e. the fracture

toughness of hydrogen-embrittled material). As a result, the resolution

of a deterministic ECAs are limited when flaws in sour environment

are being assessed and, consequently, probabilistic ECAs may offer

more granularity in defining failure probabilities.

A probabilistic approach typically involves a large number of

calculations where various combinations of input parameters are

considered. The choice of key variables in such assessments depends

on which parameters are likely to carry high levels of uncertainty

and/or have a significant effect on the result.

Results from a probabilistic assessment would enable a decision

process that is based upon acceptable levels of probability of failure

384

Proceedings of the Twenty-seventh (2017) International Ocean and Polar Engineering ConferenceSan Francisco, CA, USA, June 25-30, 2017Copyright © 2017 by the International Society of Offshore and Polar Engineers (ISOPE)ISBN 978-1-880653-97-5; ISSN 1098-6189

www.isope.org

and it is likely that a transition phase will be needed whilst meaningful

probabilities of failure are determined. It is expected, for example, that

a whole new design philosophy (e.g., loads expressed in a statistical

form) and testing regime will be needed.

This paper explores the applicability of probabilistic ECA for assessing

the significance of circumferential girth weld flaws in pipelines

carrying sour hydrocarbons. It presents a summary of a study

undertaken to investigate extending current ECA methods. The scope

of work was carried out in a staged approach for applying probabilistic

fracture mechanics methods for the assessment of circumferential girth

weld flaws in the sour environment.

1) Determination of inputs to perform a suite of sensitivity studies on

key input parameters used for the assessment of circumferential

flaws in sour environments and to adapt into probabilistic ECA

techniques;

2) To generate additional data on effects of hydrogen charging X65

pipeline steels;

3) Develop an approach for conducting probabilistic sour ECA and

perform realistic case studies of the probabilistic ECA approach.

This paper focusses on the parts 1 and 3, and will briefly discuss the

additional testing efforts.

DETERMINATION OF INPUTS

The objective of this activity is to assemble input data that are required

for assessing the significance of circumferentially oriented external and

internal surface flaws in girth welds in sour service. The task focusses

on the highly important fracture toughness parameter which was

determined through a literature review - a number of previous papers

(Ali and Pargeter, 2014) and in house data on fracture toughness in sour

service. The results from literature review have been examined in order

to determine the key ECA input parameters.

The papers and reports considered could be summarized as follows:

1) API 5L X65 linepipe parent material – various suppliers/heats

2) Sour environments of 10% H2S with balance of CO2

3) Solution pH of both 2.7 and 4.5 included

4) Fracture toughness data from SENB specimens

a. Specimen geometries varied slightly, however a/W of 0.5 was

consistent

b. Both side grooves and no side grooves were included

5) Samples were both coated and non-coated

6) Samples were pre-charged before toughness testing

7) Loading rates varied from roughly 0.005 to 0.042 MPam0.5s-1

8) Testing was performed at room temperature

In summary, in order to obtain a fracture toughness value to be used in

the deterministic engineering critical assessments, results from the

surveyed references were carefully analysed. The selected fracture

toughness results were parsed as provided in Table 1.

All entries in Table 1 were manufactured from parent material. All

specimens were pre-charged and tested in the sour environment, subject

to an initial K-rate between 0.005 and 0.009 MPam0.5s-1. It is also noted

that the average toughness values from tests of side grooved specimens

are lower than that of plane-sided specimens. The values obtained from

side-grooved specimens were selected. As a result, the toughness value

(Jmax) to be used in assessing key input parameters was determined to

be 67 Nmm-1. It should be emphasised that this value was selected for

use in specific work effort only it may or may not be appropriate for

use in other efforts.

At present, there is no well-established guidance on the selection of

fracture toughness values for assessing the significance of girth weld

flaws in sour service. This is still the subject of on-going research. It is

feasible that a fracture toughness value significantly lower than that

determined at maximum load (i.e. lower than Jmax) may be more

appropriate (for example the fracture toughness at initiation of crack

extension, J0.2). Therefore, a couple of additional parameter studies

utilized a lower initiation fracture toughness value.

Table 1 Shortlisted fracture toughness tests in sour environment for

deterministic ECA

Side-

grove

Pre-

charge

K-rate

(MPam0.5

s-1)

J0.2BL

(N/m

m)

Jm

(N/mm)

Average

(N/mm)

No Yes 0.009 NA 102.8

~92

No Yes 0.008 NA 94.1

No Yes 0.009 NA 81.4

Yes Yes 0.0077 NA 58.84

~67

Yes Yes 0.0075 NA 74.23

Yes Yes 0.005 NA 67.56

Yes Yes 0.005 NA 60

Yes Yes 0.005 NA 94.5

Yes Yes 0.005 NA 58.5

Yes Yes 0.005 NA 59.9

Yes Yes 0.005 NA 64.9

Yes Yes 0.008 26.56 75.19

Yes Yes 0.006 20.16 64.52

Yes Yes 0.007 21.39 65.81

Yes Yes 0.007 9.3 58.4

Yes Yes 0.007 16.89 61.6

Yes Yes 0.007 11.4 61.77

Yes Yes 0.008 8.53 49.4

Yes Yes 0.005 20.7 74.69

Yes Yes 0.009 38.95 89.12

Yes Yes 0.005 15.02 52.88

Yes Yes 0.007 19.7 86.96

Yes Yes 0.007 10.96 61.58

Yes Yes 0.008 5.43 78.59

Yes Yes 0.009 22.03 76.55

Yes Yes 0.008 NA 75.19

Yes Yes 0.006 NA 64.52

KEY PARAMETER ASSESSMENT

A series of deterministic engineering critical assessments (ECA) with

realistic ranges of key input parameters were carried out to establish the

relative influence of these parameters on the outcome of the ECA.

These cases are intended to simulate the circumferential girth welds of

offshore flowlines. All cases were assessed using CrackWISE® 5

automating the fracture and fatigue clauses of BS 7910:2013-A1 (BSI,

2013). Table 2 provides a summary of cases analysed with input data

used in each analysis. Pairs of analysis cases (i.e. Cases 1 and 2, Cases

3 and 4) were differentiated by their residual stress – whether to allow

relaxation or include PWHT. There were, in total, 50 cases analysed by

varying the input parameters as discussed below.

Flaw type and component geometry

In all assessments, a pipe/cylinder containing a circumferentially

oriented external surface flaw was considered (this geometry is suitable

for assessing both external and internal flaws). The maximum tolerable

flaw size was determined through sensitivity-criticality analysis. Final

385

assessment output was the limiting (or critical) flaw height (a) versus

flaw length (2c) curve. The following input data were assumed for the

pipe geometry:

Section thickness: 25.4mm (-10% to 12.5% of thickness

representing manufacturing tolerance that will be considered for

probabilistic efforts);

Outside radius, ro: 178mm.

Table 2. Deterministic ECA matrix

Case

No.

Yield

strength

(MPa)

UTS

(MPa)

Primary

stress

(MPa)

e

(mm)

L

(mm)

Fracture

toughness

(Nmm-1)

1 511 600 102.2 0.5 63.5 67

2 511 600 102.2 0.5 63.5 67

3 450 535 90 0.5 63.5 67

4 450 535 90 0.5 63.5 67

3a 450 535 90 0.5 63.5 15

4a 450 535 90 0.5 63.5 15

5 511 600 408.8 0.5 63.5 67

6 511 600 408.8 0.5 63.5 67

7 450 535 360 0.5 63.5 67

8 450 535 360 0.5 63.5 67

9 511 600 102.2 1.5 63.5 67

10 511 600 102.2 1.5 63.5 67

11 450 535 90 1.5 63.5 67

12 450 535 90 1.5 63.5 67

13 511 600 408.8 1.5 63.5 67

14 511 600 408.8 1.5 63.5 67

15 450 535 360 1.5 63.5 67

16 450 535 360 1.5 63.5 67

17 511 600 102.2 0.5 25.4 67

18 511 600 102.2 0.5 25.4 67

19 450 535 90 0.5 25.4 67

20 450 535 90 0.5 25.4 67

21 511 600 408.8 0.5 25.4 67

22 511 600 408.8 0.5 25.4 67

23 450 535 360 0.5 25.4 67

24 450 535 360 0.5 25.4 67

25 511 600 102.2 1.5 25.4 67

26 511 600 102.2 1.5 25.4 67

27 450 535 90 1.5 25.4 67

28 450 535 90 1.5 25.4 67

29 511 600 408.8 1.5 25.4 67

30 511 600 408.8 1.5 25.4 67

31 450 535 360 1.5 25.4 67

32 450 535 360 1.5 25.4 67

33 511 600 102.2 0.5 6.35 67

34 511 600 102.2 0.5 6.35 67

35 450 535 90 0.5 6.35 67

36 450 535 90 0.5 6.35 67

37 511 600 408.8 0.5 6.35 67

38 511 600 408.8 0.5 6.35 67

39 450 535 360 0.5 6.35 67

40 450 535 360 0.5 6.35 67

41 511 600 102.2 1.5 6.35 67

42 511 600 102.2 1.5 6.35 67

43 450 535 90 1.5 6.35 67

44 450 535 90 1.5 6.35 67

45 511 600 408.8 1.5 6.35 67

46 511 600 408.8 1.5 6.35 67

47 450 535 360 1.5 6.35 67

48 450 535 360 1.5 6.35 67

Material properties

Two sets of tensile properties were to be considered in the deterministic

ECA. The first set of tensile data is from actual test results reported in

surveyed literature while the second set is the minimum required tensile

strength by API 5L (API, 2007). Option 1 assessment route of

BS 7910:2013-A1 was adopted in all deterministic ECAs (BSI, 2013).

In summary, the tensile properties considered were:

Yield strength: 511MPa (actual), 450 MPa (API 5L);

UTS: 600MPa (actual), 535 MPa (API 5L);

Young’s modulus: 207GPa;

Poisson’s ratio: 0.3.

The above tensile properties were obtained from tests carried out in air.

As discussed above, the fracture toughness value (Jm) to be used was

chosen as 67 Nmm-1. A lower value of 15 Nmm-1 will be applied to

represent the J0.2BL.

Misalignment The presence of misalignment, either axial, angular or both, at a welded

joint may cause an increase in stresses acting on this joint when it is

loaded, due to the introduction of local bending stresses. The bending

stresses arising from misalignment affect both the stress intensity factor

and reference stress. Further details regarding misalignment are given

in Annex D of BS 7910:2013-A1 (BSI, 2013).

For this study, an upper and lower bound for girth weld misalignment

of 1.5mm and 0.5mm respectively was used.

Loading conditions For primary stresses, 20% and 80% of the yield strength was assumed

to represent the lower band and upper band of the possible axial stress

during operation. In terms of residual stresses, both as-welded

condition and post weld heat treatment (PWHT) were considered. The

PWHT condition was selected purely as an approximate and pragmatic

way for considering cases where the magnitude of girth weld residual

stress is significantly lower than the default yield-magnitude value. The

latter is normally assumed to ensure conservative assessments but it can

lead to pessimistic results if the girth weld flaw is in a region of low

residual stresses. During the assessment of the girth weld in as-welded

condition, relaxation of residual stresses due to the application of

mechanical loads was allowed. According to BS 7910:2013-A1 (BSI,

2013), the residual stress for the weld after PWHT is 20% of its yield

strength.

Environmental tensile properties The effect of environment on the tensile properties was examined.

Due to the limited amount of testing no results are provided here.

Rather a qualitative discussion of the activity is provided below.

The tensile testing was carried out on X65 grade steel (API 5L: 2015)

in air, hydrogen and sour environments. Round tensile specimens were

machined from the parent material of the specified pipe in the

longitudinal orientation. Tensile testing was carried out at room

temperature at a strain rate of 10-6 sec-1 in the following environments:

Air;

Gaseous Hydrogen at 250bar, 99.9% pure;

Sour environment, modified NACE A solution (standard

TM0177:2005), purged with a mixture of 10% H2S balance CO2.

386

The 10mm gauge diameter specimens were tested in air and in the sour

environment. The 5mm gauge diameter specimens were tested in the

gaseous hydrogen environment; the specimen size was dictated by the

limitations of the hydrogen vessel dimensions. All environmental tests

were exposed to their relevant test environment prior to testing.

Hydrogen concentration measurements were performed on the tested

tensile specimen and compared to reference specimens that

accompanied the tests specimens for environment exposure but were

not strained.

It was observed that the yield and tensile strengths were roughly 10%

lower for the tests performed in hydrogen gas than the corresponding

in-air tests, whereas the sour environment yield and tensile strengths

were roughly equivalent to the in-air results. More variability was

realized for the sour environment test results than the other two

environments.

As soon as the tensile tests were completed, the broken halves of the

specimens, and the exposed coupons, were subjected to hydrogen

measurement. The diffusible hydrogen was measured at 400oC using

the Nitrogen gas carrier method. Hydrogen content was measured by

thermal conductivity in accordance with standard BS EN ISO

3690:2012.

The hydrogen absorption in the sour environment was generally higher

than that in the gaseous high pressure hydrogen environment. In both

cases, the strained material absorbed more hydrogen than the

unstrained material. Particularly for the hydrogen content in unstrained

material, the measured values were almost zero. This suggests there is

little need to pre-charge tensile specimens without load prior to testing

in hydrogen gas, as the main effect of the hydrogen is experienced once

the specimen is under load.

The observed reduction in area for the tensile coupons was in line with

the measured hydrogen contents. The effect of hydrogen on yield or

tensile strength is more complicated and nuanced. Due to the limited

test data and other considerations, the difference on yield or tensile

strength should not be broadly interpreted as a real difference.

Nevertheless, it is possible to address a reliable conclusion after a lot

more data being generated. Due to the lack of sufficient tensile data, the

tensile properties obtained from this effort were not considered as

distribution parameters adopted in the probabilistic ECA effort. Instead,

the tensile properties were adopted as deterministic values.

Results and discussion

The results of the deterministic ECA cases tabulated in Table 2 are

presented in Figure 1. In general, the maximum tolerable flaw height

decreases with the increase of flaw length. However, there are some

exceptions such as Case 8 (shown in Figure 2) where the maximum

tolerable flaw height increases with the increase of flaw length but

decreases when the flaw length is greater than 8mm. The reason for this

is that the maximum value of stress intensity around the crack tip was

selected for the assessment and the location of maximum stress

intensity factor may change as the crack grows. When the flaw height is

less than 8mm, the maximum stress intensity factor was found at the

surface point of the crack. It was observed that the stress intensity

factor decreased at the surface point when the flaw length increased to

about 130mm. When the flaw length is greater than 130mm, the

maximum stress intensity factor was found at the deepest point of the

flaw. Figure 2 shows the critical flaw size when only the deepest point

of the flaw is concerned. For this case, the critical flaw height

decreased with the increase of flaw length. For the results shown in

Figure 1 and the discussion below, the maximum stress intensity factor

found at the crack tip was used for the deterministic studies.

Figure 1. 2c versus a curves for all cases in deterministic assessment

Figure 2. Critical flaw sizes for Case 8 by defining the stress intensity

factor taken from the maximum value around the crack tip and from the

deepest point of the crack.

In Figure 3, the effect of secondary stresses on the maximum tolerable

flaw sizes can be seen. From Table 2, it can be seen that the difference

between cases 1 and 2 (or cases 3 and 4, 5 and 6, 7 and 8) is the level of

residual stress. For cases 1 and 2, the applied stress equals to 20% of

yield strength. However, the residual stress for case 1 is assumed to be

equal to yield strength. The residual stress for case 2 is equal to 20% of

yield stress as a result of PWHT. Since residual stresses contribute to

the crack driving force and a larger value of residual stress was

considered for case 1, smaller critical flaw heights were obtained at the

same flaw length compared to case 2. This is also supported by results

of cases 3 and 4. However, when the primary stress increases to 80% of

yield strength, the difference between the critical flaw heights reduces

dramatically. This can be concluded from the results of cases 5 and 6 in

Figure 3. The reason is that the residual stresses relaxed considering the

interaction with large primary stresses. The residual stress level in the

presence of primary stress with a value of 80% of yield strength is

about 50% to 60% of yield strength for cases 5 and case 7 while the

residual stress considered for case 6 and 8 was 20% of yield strength.

The difference between residual stresses decreases. Hence, primary

stresses contributed more to the final crack driving force.

Consequently, a smaller difference of critical flaw height between cases

5 and 6 or between cases 7 and 8 was observed compared to cases 1

and 2 or cases 3 and 4. It is also indicated that if the primary stress is

large, the critical flaw sizes are not very sensitive to the residual stress.

In other words, the influence of residual stress on critical flaw sizes is

small when the primary stress is large.

387

Figure 3. Critical flaw sizes for cases 1, 2, 5 and 6

In Figure 4, the influence of misalignment on the critical flaw sizes is

exhibited. It can be seen that when the misalignment increases from

0.5mm to 1.5mm, the maximum tolerable flaw height decreases for a

low primary stress (20% of yield strength). This can be found by

comparing the results of cases 1 and 9, cases 2 and 10, cases 3 and 11

or cases 4 and 12. However, when the primary stress increases from

20% of yield strength to 80% of yield strength, the effect of

misalignment becomes smaller and can be ignored (see cases 5 and 13).

This may arise as the bending stress due to misalignment has small

contribution to the crack driving force and limit load. It is also found

that for small primary stress if the residual stress is high, a large portion

of contribution to the crack driving force may be from residual stress

and the bending stress due to misalignment is very small. Therefore,

the critical flaw size may be not sensitive to misalignment if the

primary stress is high or if the primary stress is low but the secondary

stress is high.

Figure 4. Critical flaw sizes for cases 1, 2, 5, 9, 10 and 13

In Figure 5, the influence of Mk factor on the critical flaw sizes is

illustrated by changing the weld cap width. The weld cap width

assumed for cases 1 and 2 is 63.5mm, 25.4mm for cases 17 and 18 and

12.7mm for cases 33 and 34. It can be seen that for cases 2, 18 and 34,

the maximum tolerable flaw height decreases as the weld cap width

increases. Considering that the maximum value of stress intensity

factor was observed at the surface point of this flaw, the contribution of

Mk factor to stress intensity is more evident. However, the maximum

value of stress intensity factor is observed at the deepest point in case

17 when the flaw size is about 40mmX10mm. The stress concentration

affects the crack driving force for a shallow flaw but the effect

decreases gradually for deeper flaws. Therefore, it was found that the

same critical flaw sizes in cases 17 and 33 when the flaw length is

greater than 40mm.

Figure 5 Critical flaw sizes for cases 1, 2, 17, 18, 33 and 34.

The effect of fracture toughness on critical flaw sizes is presented in

Figure 6. For cases 3 and 4, the J-integral fracture toughness assumed

was 67kJ/mm2 while this value was 15kJ/mm2 for cases 3a and 4a. By

comparing the results from cases 3 and 3a or cases 4 and 4a, it can be

seen that the maximum critical flaw sizes decrease with the decrease of

fracture toughness.

Figure 6 Critical flaw sizes for cases 3, 4, 3a and 4a.

PROBABILISTIC ENGINEERING CRITICAL

ASSESSMENT

The purpose of performing a probabilistic ECA analysis is to assess the

component taking into account uncertainties in the understanding of

loading conditions, flaw dimension and material properties, which will

help to mitigate the conservatism of the deterministic ECA. It is also

required for a risk-based inspection (RBI) assessment to provide

guidance for operators to schedule the inspection plan economically

and effectively. An inspection should be scheduled when the predicted

probability of failure (PoF), i.e. the probability that a flaw is not

acceptable, exceeds the target PoF.

Considering the nature of the assessment procedure and the equations

given for the stress intensity factor and reference stress in

388

BS 7910:2013-A1 (BSI, 2013), Monte Carlo Simulation (MCS)

technique (performing a large number of iterations with different

combinations of input data) was found to be more suitable compared to

various other techniques including FORM (First Order Reliability

Method) or SORM (Second Order Reliability Method) for probabilistic

ECA. Alternatively, a sampling method can also be applied in order to

accelerate the Monte Carlo Simulation.

To support the probabilistic ECA analysis, a development version of

CrackWISE®5 was built. This builds upon the interfaces already

present in the software and incorporates a probabilistic interface option.

In this CrackWISE®5 probabilistic version, MCS and Latin Hypercube

Sampling (LHS) techniques were automated.

In summary, to execute a probabilistic fracture assessment, it is

required to set up a normal deterministic fracture assessment case,

select appropriate parameters (geometry, material, loading)

representing the distributions. The distributions that can be chosen are

normal, log-normal and Weibull distributions. If normal distribution is

selected, the distribution parameters are mean value and standard

deviation. If log-normal distribution is selected, the distribution

parameters are location and scale. If Weibull distribution is selected,

the distribution parameters are shape and scale. After setting up the

parameters, the probability of failure can be calculated in the results

interface that allows the user to plot the failure assessment diagram.

CrackWISE®5 probabilistic version allows majority of input

parameters of ECA to be defined as distributions. For the case studies,

parameters related to component/flaw dimensions and fracture

toughness were considered as distributions. In Table 3, the assessment

matrix of the three case studies is presented with the parameters

assumed to be normal, log-normal or Weibull distributions.

Table 3 Assessment matrix of probabilistic ECA case studies

Case

Study

Distributed

parameter

Distribution

type Distribution parameters

1 Toughness

Weibull Scale: 73.01 Shape: 5.95

Log-normal

Log-mean: 4.2, Log-std:

0.165

2

Thickness Normal Mean:25.4, std: 1.296

Toughness Weibull Scale: 73.01 Shape: 5.95

3

Flaw length Normal Mean:50.56, std: 1.29

Flaw height Normal Mean: 6.078, std: 0.155

Thickness Normal Mean:25.4, std: 1.296

Toughness Weibull Scale: 73.01 Shape: 5.95

Case study 1 The base case of this initial case study is Case 8. The example flaw

dimensions are: 2c is equal to 15mm and a is 3mm. This flaw size is

recommended by BS 7910 as the minimum flaw dimensions can be

detected by Non-destructive Test (NDT) (e.g. manual Ultra-sonic).

Under the given conditions, the assessment point of this analysis lies

under the Failure Assessment Line (FAL) on the FAD, which will be

considered as acceptable in a deterministic assessment.

In this case study, it was assumed that fracture toughness can be

expressed as Weibull or log-normal distributions. The fracture

toughness data in Table 1 was processed using statistical software for

fitting a distribution using maximum-likelihood estimation (mle)

approach.

Generally, Weibull distribution and log-normal distribution are

believed to be the most appropriate distribution types that can be

applied for fracture toughness values (Tuma et al, 2006). Both of them

were tried on the available fracture toughness data generated in the sour

environment to fit the test results sample shortlisted in Table 1. It was

found that the Kolmogorov-Smirnov (K-S) value for this sample was

0.144 (log-normal distribution) and 0.174 (Weibull distribution). K-S

test is one of the most useful and general nonparametric methods for

comparing a sample with a reference probability distribution to

determine the most suitable distribution type for this sample. Figure 7

and Figure 8 show the R plot for each distribution. Regarding the K-S

test, the lower the K-S value the better the fitting is observed. The exact

critical value for a K-S test is a function of sample size and the

preferred significance level. In general, if the K-S value of a fit is over

0.05 (which is a conservative value giving the significance level of 0.05

for the sample size over 600), the fitting needs to be reviewed. In this

project, the high K-S value is most probably due to the small size of the

sample considered.

Figure 7. R plot of Log-normal distribution Fitting parameters of

fracture toughness. (Jm).

Figure 8. R plot of Weibull distribution Fitting parameters of fracture

toughness. (Jm).

The scale parameter of Weibull distribution is 73.01, and shape

parameter is 5.95. For log-normal distribution, the log-mean is 4.2 and

log-standard deviation is 0.165. These two different distribution types

have been adopted in Case study 1 and the results are as follows.

Weibull distribution: CrackWISE®5 probabilistic version calculated

that the probability of failure for this case is 0.0243, based on

Monte Carlo with 106 iterations, and 0.025 using LHS method;

389

Log-normal distribution: CrackWISE®5 probabilistic version

calculated that the probability of failure (PoF) for this case is

0.00066, based on Monte Carlo with 106 iterations, and 0.001 using

LHS method.

As discussed above and shown in Figure 6, the critical flaw size will

decrease by reducing material fracture toughness. Therefore, a

distribution considering J0.2BL value as a lower band of the material

fracture toughness was also fitted and the same assessment was

repeated to study the effect of lower toughness in probabilistic ECA.

The J0.2BL values corresponding with the data in Table 1 testing were

fitted with statistical software.

Figure 9 and Figure 10 show the R plot for each distribution. The scale

parameter of Weibull distribution is 20.91, and shape parameter is 2.21

with K-S value of 0.138. For log-normal distribution, the Log-mean is

2.79 and log-standard deviation is 0.508 with K-S value of 0.143.

Adopting these two distribution types in this case study resulting in:

Weibull distribution: CrackWISE®5 probabilistic version calculated

that the probability of failure for this case is 0.9821, based on

Monte Carlo with 106 iterations, and 0.982 using LHS method;

Log-normal distribution: CrackWISE®5 probabilistic version

calculated that the probability of failure (PoF) for this case is

0.9585, based on Monte Carlo with 106 iterations, and 0.958 using

LHS method.

Figure 9. R plot of Log-normal distribution Fitting parameters of

fracture toughness (J0.2BL).

Comparison between different distribution types showed in this

particular case that the Weibull distribution seems more conservative.

Moreover, by reducing fracture toughness, the probability of failure

will increase, which is in line with the discussion in Section 4.5. The

benefit of probabilistic assessment in this case is that it can represent

the influence of toughness between its lower and upper band, rather

than just deterministically show two points on the FAD for the worst

and best cases.

Besides, it is important to emphasise that the sample size for either Jm

or J0.2BL was too small to generate an accurate distribution model.

Figure 10. R plot of Weibull distribution Fitting parameters of fracture

toughness. (J0.2BL).

Case study 2 The base case of Case study 2 is Case 8 as well. The example flaw

dimensions are: 2c is equal to 15mm, and a is 3mm. This case is

designed to investigate the effect of pipe manufacturing tolerance (i.e.

wall thickness) on PoF considering that fracture toughness is

represented as a Weibull distribution as was the case in Case Study 1.

The K-S values for both Log-normal distribution and Weibull

distribution are more than 0.05, which means it is hard to decide which

distribution type is more suitable. Considering that Weibull distribution

has been more commonly used (Vadholm, 2014) and for Jm values, the

Weibull distribution seems more conservative as shown in Case study

1, it will be used in Case studies 2 and 3, to represent the fracture

toughness for Weibull distributed Jm:

Scale: 73.01;

Shape: 5.95.

As suggested by ExxonMobil, the thickness of the pipe can also be a

distribution due to the manufacturing tolerance. The thickness was

assumed to be normally distributed and the mean value is 25.4mm with

a standard deviation of 1.423mm which allows a -10% and +12.5% of

manufacturing tolerance with 95% confidence interval.

CrackWISE®5 probabilistic version calculated that the probability of

failure for this case is 0.0248, based on Monte Carlo Simulation with

106 iterations, and 0.024 using LHS method.

Comparison with the assessment results between Case study 1 and 2,

the influence of manufacturing tolerance to the total PoF is not very

significant in this case.

Case study 3 The base case of this case study is Case 8. Case study 3 is designed to

investigate the contribution of inspection error to PoF considering that

fracture toughness and thickness are expressed as distributions.

The assumptions made on the thickness and fracture toughness in the

previous case studies are valid for this case as well. It is also assumed

that the flaw size is normally distributed as a result of inspection error.

Generally speaking, the inspection results may incorporate 5% error

which means that the flaw size determined through the inspection will

390

be normally distributed with a ±5% error and 95% confidence interval,

i.e. for 2c, the mean is 15mm with 0.383 standard deviation while for a,

the mean is 3mm with standard deviation of 0.077. This error can be

mitigated if inspection can be repeated or if the inspection technique

can be improved.

CrackWISE®5 probabilistic version calculated that the probability of

failure for this case is 0.0254, based on Monte Carlo with 106

iterations, and 0.026 using LHS method.

Comparison among the above three case studies, the influence of

distribution of fracture toughness to PoF is the most significant in this

project. However, it should be noted that due to the small size of the

sample, the fitting of this distribution has a relatively wider scatter

band. This will also result in a relatively more scattered plot when

applying simulation approach for estimating probability.

CONCLUSIONS

This paper summarizes a work effort to investigate the development of

probabilistic ECA approach, with particular emphasis on utility in sour

environments. Key parameters were identified and then utilized in both

deterministic and probabilistic assessments. The findings are presented

below.

1. From literature review, for the specific material(X65)

/environment combination, an appropriate initial K-rate for SENB

fracture toughness tests was found to be approximately

0.008MPam0.5s-1. For this specific combination, the value of

67Nmm-1 is close to the average value of Jm results considered and

a value of 15Nmm-1 is close to the average value of J0.2 results

considered.

2. The deterministic ECA analyses carried out in this report for the

pipes containing circumferentially oriented surface flaws reveal

that:

For the same loading ratio (i.e. same applied stress/yield

stress), the influence of yield strength and ultimate tensile

strength on critical flaw size is small;

The critical flaw size may be insensitive to misalignment if

the primary stress is high or if the primary stress is low but

the secondary stress is high;

If the other conditions are the same and stress relaxation is

allowed, the residual stress has relatively smaller influence

on critical flaw sizes when the primary stress is large;

The weld cap width affects the crack driving force for a

shallow flaw but the effect decreases gradually as the flaw

becomes deeper.

3. The effect of hydrogen on yield or tensile strength is more

complicated and a number of factors need to be taken into

account. The difference in the tensile properties observed in air

and environment (sour/hydrogen gas) was certainly significant

and further investigation is warranted.

4. The probabilistic studies indicated that the distribution of fracture

toughness played the most significant role on the determination

of PoF in this project compared with inspection error and

manufacturing tolerance.

5. It should be noted that due to the small size of the samples, the

distribution of toughness fitted had a relatively wider scatter

band. A good fitting of the samples in terms of both size and

scatter should result in a K-S value of up to 0.05 in general.

ACKNOWLEDGEMENTS

The authors wish to acknowledge the management of ExxonMobil

Production Company, ExxonMobil Upstream Research Company and

TWI for their support of this publication. The authors also thank

Richard Pargeter (TWI) and Andreea Crintea (TWI) for the work effort.

REFERENCES

Ali M and Pargeter R (2014): ‘Techniques for determining the effect of

a sour environment on fracture toughness of steel’, Steely Hydrogen.

2nd International Conference on Metals and Hydrogen. 5-7 May 2014,

Gent, Belgium.

Agrell C, Ostby E, Levold E, Hauge M and Bjerke S (2016): ‘The use

of probabilistic fracture assessment procedures in design of pipelines

subjected to large strains’, The 26th International Ocean and Polar

Engineering Conference, 26 June – 2 July, Rhodes, Greece.

API, 2007: API Specification 5L Specification for Line Pipe.

BSI, 2013: BS 7910-A1 ‘Guide to methods for assessing the

acceptability of flaws in metallic structures’ British Standards

Institution, London.

Lee J, Kim K, Cho W, Shim S and Huh N (2015): ‘On probabilistic

fracture assessment of defective pipeline based on target failure

probabilities’, ASME 2015 34th International Conference on Ocean,

Offshore and Arctic Engineering, Vol. 5B, Canada, May 31- June 5,

2015.

Mechab B, Serier B, Kaddouri K and Bouiadjra B (2014):

‘Probabilistic elastic-plastic analysis of cracked pipes subjected

to internal pressure load’, Nuclear Engineering and Design,

Vol. 275, pp. 281-286.

Provan J (1987): ‘Probabilistic fracture mechanics and reliability’,

Springer Science and Business Media Dordrecht.

Sandvik A, Ostby E and Thaulow C (2006): ‘Probabilistic fracture

assessment of surface cracked pipes using strain-based approach’,

Engineering Fracture Mechanics, Vol. 73, pp. 1491-1509.

Vadholm T (2014): ‘Investigation of low temperature toughness and

crack initiation in welded structural steels’, Materials Science and

Engineering, Norwegian University of Science and Technology.

391