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Paper published in The Journal of Pipeline Engineering: A practical Approach to Pipeline Corrosion Modelling: Part 2 - Short-term integrity forecasting
Citation preview
2nd Quarter, 2009 69
*Author’s contact details:
tel: +55 21 3211 7264
email: [email protected]
A practical approach to pipelinecorrosion modelling: Part 2 –Short-term integrity forecasting
by Dr Érika S M Nicoletti*, Ricardo Dias de Souza,and Dr Sérgio da Cunha Barros
Petrobras Transporte SA, Rio de Janeiro, RJ, Brazil
THE PIPELINE industry is continuously being required to meet the expectations of its many stakeholders,driven by the market’s rising energy demands, and the requirements for increased profitability,
operational safety, and environmentally-friendly procedures. Consequently, more-sophisticated fitness-for-purpose analyses are required in order to achieve maintenance cost reductions while keeping orimproving the system’s overall reliability. In such a complex context, limit-state approaches are best fittedto achieving successful outcomes for those wide-ranging but conflicting expectations. Indeed, cutting-edgepipeline defect-assessment codes have embraced this philosophy, but none have included clear and conciseguidance on the subjects of forecasting corrosion growth and estimating in-line inspection (ILI) toolmeasurement error. Current work has been undertaken aiming to provide a set of guidelines on modellingand analysis procedures for corrosion metal-loss growth on ageing pipelines, using as its input corrosion-monitoring and inspection data. In the preliminary stage, ILI results and electrical-resistance probe (ERP)readings from several oil pipelines were evaluated in order to define the typical variances in pipelinecorrosion. This investigative work gave rise to the development of a predictable relationship between thegrowth rate and its standard deviation, and a short-term forecasting model has been developed based onthe premise of a steady metal-loss rate coefficient of variation. In this paper, the mathematical frameworkfor this is detailed based on different configurations of the input data: single and multiple ILI, with or withoutthe addition of ERP results. Additionally, two case studies are given which illustrate the model’s applicationand results. The model is easily implemented using commercially-available mathematical spreadsheets, andthe entire procedure demands little skilled work. The results are highly reproducible, with their overallquality relying mostly on the consistency of the input data.
PIPELINE OPERATORS often make use of periodical
in-line inspection (ILI) to manage their systems’
corrosion. Another widely-used practice is in-service
monitoring, such as by using electrical-resistance probes
(ERP). While the latter captures corrosive conditions at
particular locations as they vary with time, the former maps
the accumulated damage due to corrosion, along the whole
pipeline length, at a single moment in time. Both techniques
can independently produce vast amounts of data; providing
altogether a valuable resource for estimating future corrosion
– at least when the past and future operating conditions are
expected to be similar.
However, there is no consistent guidance in the technical
literature concerning the use of those data for estimating
corrosion rates, particularly when a combination of ILI and
ERP is available. The current work has therefore been
developed with the aim of providing a systematic approach
for inferring corrosion growth rates from the available
collected inspection and monitoring data. The overall
objective was to determine the pipeline’s short-term
acceptability for continued service.
In the preliminary stage, ILI results and electrical-resistance
probe readings from several oil pipelines were evaluated in
an attempt to characterize typical metal-loss rate values.
The study provided evidence that the standard deviation of
the data is roughly proportional to the mean, making the
ratio (commonly known as the coefficient of variation) a
suitable parameter for representing the pipeline corrosion
processes.
The Journal of Pipeline Engineering70
Subsequent work included the development of a
mathematical model for forecasting metal loss due to
corrosion, based on the premise that each operating regime
for each pipeline could be characterized by a modelling
metal-loss process considering steady relative variability.
This could be determined by using either ERP or ILI data,
according to the operational history particulars of each
case.
Detailed formulae are presented for each of the possible
configurations of data sets. The procedures have been
validated and calibrated for short-term applications,
including the prediction of the locations of possible failure
sites, ascertaining rehabilitation needs, and establishing re-
inspection intervals as well as maximum operating pressure
profiles. In order to demonstrate the model’s application
and results, two case studies are briefly presented.
Overview of assumptions
In Part 1 of this paper, the simplifying assumptions for the
long-term model were defined. For the short-term model,
the principal difference is that the growth of axial and
longitudinal flaws is disregarded.
Before introducing the specific aspects of the current work,
for the sake of general understanding, the remaining and
unmodified simplifying assumptions are summarized below,
together with the postulated ‘principle of local corrosion
activity’.
Unmodified assumptions
• the defect population for analysis should be defined
based on a dimensional threshold related to the ILI
tool’s accuracy;
• the corrosion process can be characterized by a
constant probability density function (pdf) based
on past process behaviour;
• the distribution of all data is assumed to follow a
Gaussian curve
• the internal and external corrosion processes should
be analysed separately;
• all defects were instantaneously formed at their first
environmental exposure;
• a coating degradation time is assumed for external
defects;
• cathodic protection remains in the steady-state
condition during the service life of the pipeline.
The principle of local corrosion activity
The principle postulates that incidences of metal loss
located close to each other and on the same side of the pipe
wall (either external or internal) will be subjected to similar
conditions of corrosion attack. Each defect is associated
with a local zone of influence of the corrosion process,
which is individually defined by its axial up- and downstream
extent and its range length, as specified in Equn 1. The zone
of influence will include a predetermined number of
adjacent metal-loss anomalies, empirically defined by the
vicinity parameter (n). In order to be as representative as
possible, the following ranges of the control parameters are
recommended: vicinity parameter greater than 25 (n > 25),
and segment length average larger than 1km (Li>1000).
L H Hi i n i n
= −+ − (1)
As typical corrosion-rate histograms generally present
tailored patterns, one of the major advantages of the
application of the local corrosion activity principle is its
normalizing effect on the population of corrosion rate
data, as demonstrated by the histograms in Fig.1.
Hot spot considerations
Given that the current model has the primary aim of
pipeline rehabilitation, safety measures have been
introduced in order to prevent underestimating the growth
of metal loss in the presence of highly-localized corrosion
conditions. The general logic for this is presented in Fig.2;
0
1000
2000
3000
4000
5000
6000
7000
0,05
6
0,06
4
0,07
2
0,08
0
0,08
8
0,09
6
0,10
4
0,11
2
0,12
0
0,12
8
mm/year
Local
Individual
Fig.1. The normalizingeffect of the application
of the local corrosionactivity principle.
2nd Quarter, 2009 71
the following additional considerations are also applicable:
• stray current influence zones: use characteristic
lengths (Li) not greater than 100m;
• microbiologically induced corrosion (MIC):
individual corrosion rates greater than their local
99 percentile must be individually determined,
taking into account specific evolution times. These
should be established based on expert judgment,
independently of the pipeline’s service life (!ts).
Note that both onshore approach areas subject to tidal
variations (the tide zones on offshore pipelines), and regions
around insulating joints (such as on piers and industrial
pipelines) could also require special consideration.
Relative variability of metal loss
The short-term forecasting project included a preliminary
study in which ILI and ERP metal-loss rate data from
several different pipelines were evaluated. Using the
Gaussian behaviour premise, these data were characterized
by their expected value (the mean) and their relative
variability or coefficient of variance, as represented by
Equn 2. The results that were obtained are presented in
Tables 1 and 2, for the ILI and ERP data evaluations,
respectively.
cvR
r=σ
(2)
A comparison of the values of average corrosion rates
shows that there are few strong similarities between the
results from the two techniques. In this regard, it is worth
noting that ILI represents the overall damage accumulated
during the pipeline’s entire service life, whilst ERP data are
usually restricted to a relatively short period. Thus, as ILI
data have consistently produced larger averages than ERP,
this could be interpreted as evidence of a thriving company
strategy for internal corrosion mitigation. Indeed, further
investigation, incorporating historical weight-loss coupon
data (out of the scope of this article), has given ample
confirmation of this.
Despite the fact that ERP monitoring data are theoretically
better fitted to reflect the most recent operational
circumstances, they can only capture variations in the
severity of the corrosion process attack over time at their
specific location. Due this restriction, they have
conventionally been used as a qualitative indication to
characterize the trend of the process, and not as a quantitative
measurement of the continuity of the pipeline’s corrosion.
Therefore, in order to produce a consistent profile of the
corrosion rate along the pipeline’s length, ILI data should
be used. However, when significant changes in the system’s
operating conditions have taken place, the run-comparison
approach is preferred1.
Special considerations for ERP
ERP data usually contain large amounts of electronic noise,
and therefore a filtering procedure is strongly advised. In
the current study, a 3-hr sampling period was averaged for
Fig.2. Logic flowchart for metal-lossgrowth under general hot-spotconditions.
1 If this approach is not feasible, a proportionality study can be made
based on available data from ERP or coupons.
dINSP
d i>=perc 0.8dLi. dLi = di
Loop i >N
∑+=
−= +=
inj
nij
j
Lin
dd
12
cvd LiLi .=σ
Y
N
The Journal of Pipeline Engineering72
the daily value and the corrosion rate was obtained using a
five-point algorithm that minimizes the effect of the noise
on the numerical derivative. Figures 3a and 3b illustrate
this procedure: firstly in a standard situation, where the
slope of the trend line corresponds to the local EPR-
measured metal-loss growth; and secondly, where a change
in the operational regime is illustrated by a shift in the slope
of the trend line.
It is worth noting, for instance, that when the flow regime
is expected to present very low corrosivity conditions, the
use of ERP data should be avoided, given that – under such
conditions – it could became difficult to differentiate
between electronic noise and a real sensor response.
Furthermore, data-acquisition periods must be
representative of the pipeline’s future operational service
conditions2.
Framework for single runs
According to the principle of local corrosion activity, each
defect will have an associated population, defined as being
the (n) – the vicinity parameter – defects immediately up-
and downstream. The defect-analysis population will have
Table 1. EPR data evaluation results.
Table 2. ILI data evaluation results.
2 When seasonal operational changes are expected, greater acquisition
periods are recommended.
)raey/mm( VC
1RPE 4000.0 011.0
2RPE 6150.0 873.0
3RPE 6100.0 520.0
4RPE 3000.0 881.0
5RPE 6720.0 240.0
6RPE 4000.0 391.0
7RPE 3100.0 978.0
8RPE 3400.0 222.0
9RPE 6050.0 210.0
01RPE 9110.0 420.0
11RPE 3000.0 962.0
naem 410.0 312.0
etarlacoL vclacoL efilecivreS
1ILI 560.0 891.0 72
2ILI 780.0 082.0 91
3ILI 410.0 019.0 32
4ILI 080.0 031.0 33
5ILI 540.0 032.0 23
6ILI 940.0 340.0 24
8ILI 390.0 082.0 13
9ILI 870.0 091.0 13
naem 460.0 382.0
2nd Quarter, 2009 73
its local corrosion rates, defined as random variables, with
their average established by Equns 3aa and 3ab – respectively
- for the internal or external anomalies being considered.
The associated standard deviation values are defined by
Equn 3b. As previously discussed, the coefficient of variance
(cv) values should be determined based on ILI or ERP data,
depending on which is the most appropriate for representing
the future anticipated short-term corrosion process.
Rd
tLi
i
s
=∆ (3)
R
d
n tLi
jj i n
j n i
s
=+
= −
= +
∑( ).2 1 ∆
(3a-a)
R
d
n t tLi
jj i n
j n i
s c
=+ −
= −
= +
∑( ).2 1 ∆ ∆
(3a-b)
σLi
R cvLi
= . (3b)
Future defect depth
Once defect corrosion rates have been determined, the
future defect depth can then be defined as being the
original defect depth added to the metal loss which should
be expected within the time period under consideration
(Equn 4a). The associated dispersion of future defect
depths should take account of tool measurement error on
ILI-measured depths as well as the expected deviation on
the overall metal-loss rate over the period of time considered,
as shown in Equn 4b.
d d R tfi i Li f
= + .∆ (4a)
σ σfi f Li
ttE
c= ( ) +
∆
22
(4b)
Damage tolerance
Several metal-loss defect-assessment criteria can be used to
determine damage tolerance. In each case, the analyst
should choose an appropriate criterion in order to find out
the maximum allowable pressure in the defect region
according to its forecast depth, as represented by Equn 5.
P f d l wif f i i
= ( , , ) (5)
0,0322
0,0323
0,0324
0,0325
0,0326
0,0327
0,0328
0 500 1000 1500 2000 2500 3000 3500
h
mm
0,0373
0,0374
0,0375
0,0376
0,0377
0,0378
0,0379
0 500 1000 1500 2000 2500 3000 3500
h
mm
Fig.3. Examples of ERP-acquireddata: (a – top) standard case understeady corrosive attack (trend line inred); (b – bottom) after a change inthe pipeline operating conditions.
3 The maximum allowable pressure profile can be determined based on
hydraulic simulation of worst-case operational scenarios. Otherwise, it
can be assumed to be constant.
The Journal of Pipeline Engineering74
Defect relativity acceptance
The failure pressure associated with a defect’s future depth
(Pif) should not be exceeded by the maximum operating
pressure expected at the defect’s location (MAOPi)3. This
failure pressure is represented by the limit-state function
shown in Equn 6, where Pif is characterized by a normal
distribution, while the MAOPi is a deterministic value; in
other words, the probability of the pipeline exceeding the
limit-state condition at each defect (POEi) can be determined
as the area on the left-hand side of the maximum allowable
operating pressure under the Pif probability density function
(pdf), as shown in Fig.4.
MAOP Pi if
− < 0 (6)
The widely-known Pipeline Operator’s Forum concept of
‘estimated repair factor’ (ERF) has been adapted to the
current approach. Using this, each defect has its operational
acceptability determined by Equn 7, where APF is allowable
probability of failure at each defect location, which should
be previously determined based on ROW reliability studies.
ERFPOE
APFi
i
i
= (7)
The single run procedure:a case study
A 100-km long trunk line with a constant 22in diameter
and 6.35mm wall thickness (referred to in Part 1 as Pipeline
3) was chosen to demonstrate the single-run model. The
pipeline has recently been rehabilitated to meet a flow-
capacity expansion, and hydraulic simulation was used to
define its new maximum operating pressure profile. Pipeline
degradation had principally been caused by internal
corrosion, and the accumulated channelling damage is
extensive. ERP data were available.
The pipeline’s future integrity condition was ascertained
considering a five-year metal-loss growth of the anomalies
reported by internal inspection. The single-run modelling
procedure was used to forecast the acceptability of each
defective region, considering both ILI and ERP cvs.
Additionally, in order to provide a reference, ERF was also
determined using a traditional deterministic approach.
Figure 5 presents the results obtained for the 200 worst
pipeline anomalies: blue and red dots representing single-
run model results for ILI and ERP cv, respectively, and the
green indicating ERFs settled on deterministically. In the
figure, the results of the first two procedures present a
remarkable match, demonstrating the model’s overall
robustness. They also provide a clear distinction of defect
impact on pipeline reliability, easily permitting their
categorization by risk. The deterministic approach results,
on the other hand, show only a very slight variation among
the defects that are considered, concealing their true
operational risk.
Framework for run comparisons
When two sets of ILI data are available, and an estimate of
the corrosion rates based on the operational period between
the inspections is required, data resulting from both runs
can be compared4. In such a case, the quality of the results
would depend on a number of factors, including:
• Tool technologies: must be the same or similar,
otherwise comparison of the raw signals is necessary.
• Tool accuracy: both inspections should have been
performed using tools of a similar accuracy.
• Run performance: both runs must have been
successfully completed.
• Data alignment: independent of the segmentation
strategy adopted, the quality of the data alignment
could have a considerable impact on the results.
Fig.4. Plot of the future probabilisticfailure pressure of a defect versus its
deterministic MAOP.
4 The proposed run-comparison procedure should preferentially use
non-clustered data.
2nd Quarter, 2009 75
Segmentation strategy
A common procedure when dealing with run comparisons
is to divide the pipeline into a number of sections;
traditionally, this is on the basis of constant length (e.g. 1
or 10km), or zones of similar characteristics. The latter
could be based on distinctive features affecting the corrosion
process that takes place along the pipeline, such as stray
current influence zones, changes of flow regime, etc.
Alternatively, instead of pipeline sections, a population
segmentation process can also be adopted in which the
global population is separated into sub-groups which contain
defects with similar characteristics. In this case, the division
criteria should be determined based on statistical analysis
and expert judgment. Some examples of such a procedure
are:
• Cathodic protection effectiveness: within a specific
distance from the pipeline rectifiers or anode beds.
• ROW topography (water accumulation at low
points).
• Coating effectiveness (field/plant applied coatings)
Mathematical formulae
After having been defined, inspection data sub-populations
must be paired with those from the preceding inspection,
and both should then have their average depths determined.
The metal-loss growth rate between these inspections can
be inferred based on the average depth differences. In the
current work, the corrosion rate was assumed to be
represented by a Gaussian distribution, and can be
determined based on Equns 8a and 8b, in which the cv
value is based on the most recent inspection or ERP data.
Rd d
trc
i
=−2 1
∆ (8a)
σrc
R cvrc
= . (8b)
A broad outline of the run-comparison logic is shown in the
flowchart in Fig.6. Future defect geometry and acceptability
can be determined, as has been discussed above5.
The run comparison procedure:a case study
A 2.5-km long subsea oil pipeline section of constant 34in
diameter, with wall thicknesses ranging from 0.375 to
0.5in, and with a service life of 35 years, was chosen to
demonstrate the run-comparison model. No ERP data
were available. The two last ILIs were performed using MFL
tools, with an interval of seven years. Several internal
corrosion-mitigation actions have been implemented over
the last decade. Only the internal metal-loss anomaly
population has been assessed.
Figure 7 depicts local depth histograms of the internal
metal-loss anomalies, considering the population reported
by the two most-recent ILI inspections; by comparing them,
one can clearly note the growth in overall metal loss. The
corrosion rate has been generically defined for the whole
segment, according to the formulae presented in the previous
section and also, individually, as stated by the proposed
0
1
2
3
4
5
0 20 40 60 80 100 120 140 160 180 200
worst anomalies
ER
F
a
b
c
Fig.5. Five-year ERF of the worst internal metal anomalies determined by:(a) the single-run probabilistic approach based on ILI data;
(b) the single-run probabilistic approach based on ILI and ERP data;(c) the traditional deterministic approach.
5 Application of the current procedure is not recommended when the
relative variability of the metal-loss rate is greater than unity.
The Journal of Pipeline Engineering76
single-run methodology for both inspections. The results
from these procedures demonstrate that the mitigation
strategy has reduced the metal-loss rate by almost 50%.
The pipeline’s future integrity was assessed taking into
account a time-interval of five years and defect geometries
as forecast by the run-comparison and single-run procedures
(using as input to the latter the data from the most-recent
inspection). The resulting acceptability condition for the
200 worst anomalies is displayed, as ERFs, in Fig.8. The use
of the run-comparison procedure has reduced the
rehabilitation scope by more than 70%.
Conclusions
In recent years growing quantities of pipeline metal-loss
data derived from ILI and ERP monitoring are becoming
available worldwide. Both represent a considerable body of
Fig.6. Flowchart for determining the corrosion rate by run comparison on a pipeline by splitting its defect population intotwo sub-groups.
Fig.7. Histogram oflocal metal-lossaverage depths
from the run-comparison case
study inspections 1and 2.
2,7
3,2
0,00
0,05
0,10
0,15
0,20
0,25
2,00 2,25 2,50 2,75 3,00 3,25 3,50 3,75 4,00 4,25
d [mm]
f(x)
INSP1
INSP2
Segmetation
Criterion
INSP1A
Y Y
d1A
INSP2A
d2A
RrcA = (d2A – d1A)∆ti
σrcA = RA.cv INSP1B
d1B
RrcB = (d2B – d1B)∆ti
σrcB = RB.cv
d2B
INSP2B
Segmetation
Criterion
N
INSP2
N
Loop j
<N1 >N1
Loop j
<N2
>N2
INSP1
2nd Quarter, 2009 77
evidence regarding past behaviour of the corrosion process,
but there is a lack of industrial guidelines regarding their
use in corrosion-rate estimation.
This paper introduces a simple approach for accomplishing
short-term metal-loss forecasting through the use of ILI
data, where necessary juxtaposed with available ERP data.
The project also considers long-term forecast modelling,
which was presented in the first part of this work. As the
latter was aimed at remaining-life estimation, the current
work has been mainly directed towards the prediction of
rehabilitation needs and the definition of re-inspection
intervals.
The project was undertaken based on two innovative
principles: local corrosion activity, and the steady relative
variability in metal-loss growth under typical pipeline
operational conditions. The work included the development
of an independent mathematical framework suitable for
different input data sets, which include data from a single
ILI run, and comparison of data between two ILI runs.
Available ERP data can be incorporated into both when it
is necessary to reflect the most recent operational
circumstances.
The single ILI modelling procedure can incorporate special
considerations to avoid underestimation of the metal-loss
growth rate at hot-spot sites. Also, the proposed strategy for
dividing the pipeline defect population into sub-groups for
run-comparison purposes could considerably enhance the
result’s significance.
Implementation of the model is straightforward and does
not require special skills. Its application is simple, only
requiring expert judgment in order to define its validity in
non-standard cases and for interpretation of general results.
It is worth noting that the entire study was carried out, and
consequently consistently calibrated, using downstream
pipeline system data. Thus, it is strongly recommended that
a validation analysis of the proposed values of the model’s
empirical parameters is established for upstream
applications.
Acknowledgments
The authors would like to thank Petrobras Transporte S.A.
for permission to publish this paper, and their colleagues
Carlos Alexandre Martins and João Hipólito de Lima
Oliver for many contributions and enlightening discussions.
Nomenclature
"r: standard deviation on a population of
corrosion rate values [mm]
"fi: forecast defect depth standard deviation
[mm]
"Li: local corrosion rate standard deviation
[mm/year]
"rc: standard deviation of corrosion growth rate
produced by run comparison [mm/year]
!ti: re-inspection interval [years]
!tc: coating degradation lag [years]
0
1
2
3
4
0 25 50 75 100 125 150 175 200
worst anomalies
ER
F
single run procedure
run comparison procedure
Fig.8. Five-year ERF of the 200 worst internal metal anomalies determined by single run and run comparison procedures.
The Journal of Pipeline Engineering78
!tf: forecasting lag [years]
!ts: pipeline service life [years]
APFi: allowable probability of failure
c: confidence level Gaussian adjustment
parameter
cv: coefficient of variance of corrosion rate
population
d1: previous inspection (INSP1) metal-loss depth
average [mm]
d1A/B
: metal-loss depth average of a INSP1 sub-
population [mm]
d2: newest inspection (INSP2) metal-loss depth
average [mm]
d2A/B
: metal-loss depth average of a INSP1 sub-
population [mm]
dfi: defect future depth [mm]
di: individual metal-loss depth [mm]
dj: individual metal-loss depth [mm]
dINSP
: defect depth population reported by ILI
[mm]
dLi: the local average for a defect metal-loss depth
[mm]
ERFi: estimated repair factor for defect future
geometry
Et: tool measurement error [mm]
Hi: defect odometer [m]
INSP1: defect depth population reported by the first
ILI
INSP1A/B:
INSP1 sub-population
INSP2: defect depth population reported by the
second ILI
INSP2A/B:
INSP2 sub population
li: defect length [mm]
Li: local segment length [m]
N: analysis defect population
n: vicinity parameter
Pif: defect forecast failure pressure [kg/cm2]
POEi: defect probability of exceedance in the limit-
state condition
RLi: local defect depth corrosion rate [mm/year]
Rrc: corrosion growth rate determined by run
comparison, in a defect population sub-
group [mm/year]
wi: defect width [mm]
Bibliography
1. S.A.Timashev and A.V.Bushinskaya, 2009. Diligent statistical
analysis of ILI data: implications, inferences and lessons
learned. The Pipeline Pigging and Integrity Management
Conference, Houston.
2. R.G.Mora et al., 2009. Dealing with uncertainty in pipeline
integrity and rehabilitation. The Pipeline Pigging and Integrity
Management Conference, Houston.
3. R.Bea et al., 2003. Reliability based fitness-for-service
assessment of corrosion defects using different burst pressure
predictors and different inspection techniques. 22nd
International Conference on Onshore Mechanics and Arctic
Engineering, June 8-13, Cancun.
4. J.M.Race, S.J.Dawson, L.Stanley, and S.Kariyawasam, 2006.
Predicting corrosion rates for onshore oil and gas pipelines.
International Pipeline Conference, Calgary.
5. Ahammed, 1998. Probabilistic estimation of remaining life
of a pipeline in the presence of active corrosion defects.
Int.J.Pressure Vessels and Piping, 75, pp 321-329.
6. A.Valor a, F.Caleyo, L.Alfonso, D.Rivas, and J.M.Hallen,
2007. Stochastic modeling of pitting corrosion: a new model
for initiation and growth of multiple corrosion pits. Corrosion
Science, 49, pp 559–579.
7. A.Ainouche, 2006. Future integrity management strategy of
a gas pipeline using Bayesian risk analysis. 23rd World Gas
Conference, Amsterdam.
8. P.J.Laycock and P.A.Scarf, 1989. Exceedances, extremes,
extrapolation and order statistics for pits, pitting and other
localized corrosion phenomena. Corrosion Science, 35, 1-4, pp
135-145, 193.
9. J.L.Alamilla and E.Sosa, 2008. Stochastic modelling of
corrosion damage propagation in active sites from field
inspection data. Corrosion Science, 50, pp 1811–1819.
10. J.L.Alamilla, D.De Leon, and O.Flores, 2005. Reliability
based integrity assessment of steel pipelines under corrosion.
Corrosion Engineering, Science and Technology, 40, 1.
11. S.A.Timashev, 2003. Updating pipeline remaining life
through in-line inspection. International Pipeline Pigging
Conference, Houston.
12. S.A.Timashev et al., 2008. Markov description of corrosion
defect growth and its application to reliability based inspection
and maintenance of pipelines. 7th International Pipeline
Conference, Calgary.
13. G.Desjardins, 2002. Optimized pipeline repair and inspection
planning using in-line inspection data. Pipeline Pigging,
Integrity Assessment & Repair Conference, Houston.
14. B.Gu, R.Kania, S.Sharma, and M.Gao, 2002. Approach to
assessment of corrosion growth in pipelines. 4th International
Pipeline Conference, Calgary.
15. G.Desjardins, 2001. Predicting corrosion rates and future
corrosion severity from in-line inspection data. Materials
Performance, August, 40, 8.
16. J.Race et al., 2007. Development of a predictive model for
pipeline external corrosion rates. Journal of Pipeline Engineering,
1st Quarter, pp15-29.
17. ASME B 31G: Manual for determining the remaining strength
of corroded pipelines.
18. H.Plummer and J.Race, 2003. Determining pipeline corrosion
growth rates. Corrosion Management, April.
19. F.Caleyo et al., 2002. A study on the reliability assessment
methodology for pipelines with active corrosion defects.
Int.J.of Pressure Vessels and Piping, 79, pp77-86.
20. G.Pognonec, 2008. Predictive assessment of external
corrosion on transmission pipelines. IPC.
21. R.L.Burden and J.D.Faires, 1993. Numerical Analysis, 5th
Ed., PWS Publishers.