probabilistic engineering critical assessment of...
TRANSCRIPT
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
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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
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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;
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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
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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.
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