Nicoletti Jpe Part1

1st Quarter, 2009 19

Nomenclature

Dt1: pipeline service life under original operatingconditions [years]

Dt2: pipeline service life under posterior operatingconditions [years]

Dtc: coating degradation lag [years]

Dtf: forecasting lag [years]

Dts: pipeline service life [years]

sdi: forecast dimension standard deviation [mm]

sRi

: local depth corrosion rate standard deviation [mm]

d: maximum metal-loss depth [mm]D

f: maximum metal-loss forecast dimension [mm]

Dj: pig-reported dimension (depth, width and length)

[mm]d

j: pig-reported defect depth [mm]

Epig

: tool measurement error [mm] (at 80% confidencelevel)

Fh: service conditions linearization factor

H: defect odometer [m]l: maximum defect length [mm]lf: defect forecast length [mm]

LSEGi

: local segment length [m]N: total number of active corrosion sitesn: vicinity parameterR

i: individual defect dimension corrosion rate [mm/

year]R

Di: local defect dimension corrosion rate [mm/year]

RDij

: individual corrosion rate at a nearby defect [mm/year]

s: scoring factor for service condition changesw: maximum defect width [mm]w

f: defect forecast width [mm]

FOR OVER ONE hundred years pipelines have beenused to transport hydrocarbons from their distant

location to refineries and onwards to consumers. Manymajor world markets nowadays depend upon thisincreasingly-ageing pipeline infrastructure to supply mostof their energy demands. It is unfortunate that ageingadversely affects a pipeline’s integrity, and it can suffer from

A practical approach in pipelinecorrosion modelling: Part 1 –Long-term integrity forecasting

by Dr Érika S M Nicoletti* and Ricardo Dias de SouzaPetrobras Transporte SA, Rio de Janeiro, RJ, Brazil

NOWADAYS, MANY MAJOR MARKETS worldwide depend upon an increasingly-ageing pipelineinfrastructure to supply most energy demands. As corrosion damage accumulation is usually

expected under typical pipeline service conditions, forecast metal-loss growth over time is a key elementin their integrity management; but there is little industrial guidance on this issue. The current work has beenundertaken aiming to provide a corrosion rate model by means of straightforward stochastic treatmentof metal-loss ILI data. This first part will present a model framework regarding long-term scenarios andremaining-life predictions, based on a cost-effective pecuniary threshold for the system’s future remedialactions. The concept of local activity breaks new ground by merging two traditional approaches: theindividual defect and the pipeline segment corrosion growth rates. The model’s underlying assumptions aredetailed, together with its mathematical framework; an empirical balance has been established betweenover- and under-conservative premises, and the accuracy of the results has been considered suitable forforecasting intervals of up to 30 years. The technique provides powerful information with no need to carryout any further expensive and/or laborious analyses: the whole algorithm could be easily put into practiceusing commercial mathematical packages. In order to illustrate the model’s applicability, four case studieswill be presented.

*Author’s contact details:tel: +55 21 3211 7264email: [email protected]

The Journal of Pipeline Engineering20

many types of damage under typical service conditions.

Corrosion has historically been the greatest time-dependentthreat to pipeline integrity. The process itself reduces thelocal metal cross-section, affecting the remaining strengthand, consequently, reducing the pipeline’s containmentcapacity in the area of the damage.

Operators can quantify corrosion in their systems throughperiodic metal-loss in-line inspections (ILI). Subsequently,the system’s fitness-for-purpose can be assessed at eachpoint by carrying out damage tolerance analysis using, asinput, ILI data and required service conditions [1, 2].

However, given that pig inspections show only the state ofstatic damage at the time of the inspection, integrityforecasting must take into account corrosion growthestimates. Furthermore, although the phenomenon ofcorrosion is widely known, a plethora of factors impact theprocess kinetics along a pipeline’s length, and the inherentrandomness generally associated with real field conditions,makes its mechanistic modelling a complex task. Thisrequires highly-skilled work, the difficulties of which areoften compounded by an inconvenient lack of historicaldata concerning many of the process control parameters.Thus, it has become common practice to adopt an empiricalapproach, mostly based on worst-case scenarios(recommended practices and/or historical data) [3, 4].However, such procedures usually give rise to highly-inaccurate forecasts, particularly when dealing with long-term scenarios.

Indeed, the US’ Office of Pipeline Safety estimated that theability to accurately forecast corrosion rates could saveAmerican pipeline companies more than US$ 100 millionper year through reduced maintenance costs and accidentavoidance [5].

Fortunately, ILI metal-loss mapping reflects either unknownservice condition variances and/or local electrochemicalmechanism abnormalities, providing a good background,insofar as processing past behaviour is concerned, forcorrosion-rate inferences.

The current work aims to develop a simplified methodologyto allow reasonably-accurate pipeline-integrity forecasts,chiefly by using ILI data. Two basic algorithms have beenconstructed: the first, which is presented in this paper, hasbeen directed to long-term scenarios. The second part ofthe methodology has targets short-term predictions, andwill be published in the second art of the paper [in the June,2009, issue of the Journal of Pipeline Engineering].

The main differences between the algorithms result fromtheir diverse application expectations. Short-term scenariosare usually applied in order to define reinspection intervalsand rehabilitation scopes. As operational pipeline safetyand reliability often depends on the result, conservativeapproaches have always been preferable. On the other

hand, long-term scenario predictions are typically associatedwith the system’s economic viability forecasting (andestimating its remaining life); such analyses are usuallybetter served with accurate modelling.

Despite both algorithms being developed with the aim ofincorporating them into a company’s proprietary defect-assessment software [6], they can also be easily implementedusing any common commercial mathematical package.Accordingly, both are presented in only their most simplisticinterpretations. The underlying assumptions of the models,and the descriptive formulations, will be described anddiscussed. Real cases studies will then be presented toillustrate the methodology anticipated results and overallperformance, before final conclusions are given.

Theoretical backgroundThe corrosion process is irreversible: once it takes place,metal-loss damage at a particular site can only either grow,or remain the same over time, the latter being a sign of siteinactivity (and possible repassivation).

As time goes by, it is expected that new active sites will arise,while some of the existing ones will cease growing.Additionally, time-dependent defect enlargements usuallyslow down over time although, as a general rule,deterministic approaches treat those processes as linear [7,8]. Valor et al. [9] suggest the following should be taken intoaccount:

• the slowing down effect: 0-10% of reduction in pastcorrosion rates

• the cessation of growth effect: 0-20% of the numberof sites nucleated per year

• new defect nucleation: 0-65% of the number of sitesnucleated per year

Conversely, probabilistic models often use the followingdistributions in order to represent:

• nucleation time – exponential and Weibull [9, 10]• number of sites nucleated over time: Poisson [9]• growth rate: gamma, log-normal, or extreme-value

distributions [6, 10, 11]

The Bayesian approach and the Markovian process havealso been widely used in probabilistic framework modelling[12-15].

Given that metal-loss measurements reflect operationalcondition variations and the overall randomness of thecorrosion process itself, the proper treatment of ILI datacan lead to reasonable estimates of past behaviour [16-18].

In order to determine the corrosion rate, damage must bequantified at two different points in time. However, inorder to avoid the usual laborious defect-matching


procedures [5, 19], the current model has been adapted touse a single ILI data set. Also, the model has been constructedunder the premise of a linear relationship existing with theprocess’s past behaviour. Its breakthrough came with theassumption that only adjacent metal loss represents thecorrosion activity at each point, which will be describedfurther below.

The local corrosion activity principle

The authors consider it a rational assumption that allmetal-loss located in close vicinity and on the same side ofthe pipe wall (external/internal) is under similar conditionsof corrosion attack. If, regarding the variations in corrosionactivity along a pipeline’s length, it is expected that futureservice conditions remain similar, then future corrosiongrowth can be predicted based on the metal-loss anomalypopulation located in the defect neighbourhood.

To define the range of each defect’s environment, a vicinityparameter must be empirically determined, using therelationship expressed in Equn 1. Each defect will also haveits associated characteristic length, as defined by Equn 21.

2n+1 > = 7 (1)

L H HSi i n i n= −+ − (2)

Figure 1 illustrates the principle in a pipe section from casestudy 4. All the anomalies displayed are internal metal-loss,and channelling can be clearly noted. Two anomalies havebeen arbitrarily chosen to exemplify the neighbourhood’sdelimitation mechanism: for the purpose of illustration,the lower recommended value for the vicinity parameterhas been used in the figure (n = 3). Note that only axialproximity is taken into account: n anomalies immediatelyup- or downstream are considered as belonging to eachdefect’s local population.

A number of additional simplistic assumptions have beenmade, and a general outline of them will be given in thefollowing paragraphs.

• Process characterization: irreversible, evolving at aconstant rate, and at discrete time intervals.

• Defect population: ILI reported metal-loss anomaliestrimmed, based on the empirical criterion definedin Equn 3:

DE

jt≥ 2

1 28.(3)

where Et represents tool the measurement error and

– eventually – measurement bias, with a confidencelevel of 80%. The mathematical framework to bepresented is independently applied to the anomalypopulations located on the external and internalsurfaces. New defect generation, as well as the rateof cessation of defect growth, are considered to benegligible.

• Nucleation time: defect populations are assumed tobe instantaneously nucleated at the first exposure tocorrosive conditions.

• Defect growth: determined based on the pastbehaviour of local corrosion activity. The details ofthis premise regarding external and internal surfacecorrosion are described below.

• Coating protection effectiveness: the coatingcondition is considered to be perfect at the time ofpipeline commissioning. All pipeline coatingholidays are considered to be instantaneouslygenerated after a specific coating degradation lag.The protection effectiveness is assumed to be 0% atall active sites of external corrosion, and 100% inholiday-free regions. Water and air permeationtime dependency is not taken into consideration.

• Coating degradation lag: must be empirically definedbased on coating data history and engineering bestjudgment.

• Cathodic protection: is assumed to remain in asteady-state condition throughout the entire servicelife of the pipeline.

• Probability density functions (PDFs): defect depthdimensions and corrosion rates are described byGaussian PDFs. It is worth noting that, given thateach defect’s corrosion rate is represented in termsof a local average, there is a normalizing effect on theoverall depth corrosion rate data set2.

Mathematical framework

Corrosion rates PDFs

The probability density functions should be individuallydefined, taking account of the damage accumulated in eachdefect neighbourhood, according to the previously-outlinedprinciple of local corrosion activity3. If a significant changein the system’s operating conditions takes place after any

1. The parameter n should be adjusted in order to obtain an averagesegment length not exceeding 1-2 km.

2. Pipeline geometry, material features, and the axial and circumferentialcorrosion rates, have only been considered deterministically, as will bethe allowable damage as a consequence.

3. Clustering criteria should preferably be applied after a futuremorphology forecast, not before.


particular event, then a factor Fh is defined accordingly,

using Equn 4; otherwise, Fh is assumed as 14.

Ft s t

ths

= +Δ ΔΔ

1 2(4)

Internal defects

Individual defect growths (radial, axial, and circumferential)are determined by means of Equn 5a. The subsequentapplication of the local corrosion activity principle leads tothe determination of the corrosion rate average for thedefect population located in the adjoined region by usingEqun 5b, while the dispersion is obtained from Equn 5c.Furthermore, the characteristic length associated with eachdefect neighbourhood (L

seg) can also be defined, as previously

discussed.

Hence, each flaw on a pipe’s inside surface will have onesingle PDF representing its depth corrosion growth rate,while axial and circumferential rates, as well as itsneighbourhood characteristic length, are deterministicallydefined.

RD

tii

s

=Δ (5a)

R F

R

nLi h

jj i n

j i n

=+

= −

= +

∑( )2 1

(5b)

σLi

Li jj i n

j i n

R R

n=

−( )= −

= +

∑ 2

2(5c)

External defects

It is proposed that pipeline coating holidays are consideredstationary. Thus, circumferential and axial growth rates areassumed as zero at all active sites located on the pipeline’sexternal surface. Equation 5d represents the depth growthrate, considering the lag in coating degradation.

Rd

t tdij

s c

=−Δ Δ (5d)

Equations 5b and 5c must therefore also be applied inorder to characterize the defect’s depth corrosion rate PDF,

while Equn 2 should be used to define its neighbourhoodcharacteristic length.

Future defect morphology

The average dimensions of future defects can be calculatedfrom Equn 6a, and Equn 6b is used to determine theassociated dispersion.

D D R tf i Li f= . .Δ (6a)

σ σDf f Litt

E= ( ) + ⎛⎝⎜

⎞⎠⎟

Δ 22

1 28.(6b)

Damage tolerance

There are a number of metal-loss assessment criteria thatcan be used to determine damage tolerance. The mostsimplistic and widely known is ASME B31.G, which onlytakes into account axially-oriented corrosion defectssubmitted to internal pressure loading. Depending on theparticular system’s damage characteristics (which can includecircumferential- or even helically-oriented defects), or theexistence of axial loads (such as those geotechnically orthermally induced), an appropriate criterion should bechosen to deterministically find out the maximum allowabledefect depth as a function of its forecast width and length,according to Equn 7.

d f l wa f f= ( , ) (7)

Probability of exceedance

The future defect depth (df) shall not exceed its allowable

depth (da) [22, 23], as represented by the limit-state function

in Equn8:

d df a− < 0 (8)

In the current approach, df is characterized by a normal

distribution, while da is deterministic. This means that the

probability of a pipeline exceeding the limit-state conditionat each defect can be determined as the area on the right-hand side of the allowable depth under the d

f PDF (see

Fig.2)5.

Economic remediation rate

The economic remediation rate which provides cost-effectiveoperation must be ascertained by a pipeline’s own operator,considering each case individually. It is outside the scope of

4. The scoring factor for changes in service conditions (s) should bedetermined based on historical data (coupons/probes, comparison ofmultiple ILI data or computation simulations) and engineering bestjudgment [20]. 5. Most commercial packages have standard functions to perform this.


this work to accomplish a full perspective into problem, butsome of the factors that must be taken into account in suchan analysis include:

• technical and economic viability of alternativepipeline systems, or other modes of transportation

• the ratio between the cost of a new pipeline and theestimated maintenance costs of the existing one

• the impact of a possible delivery shortage on thelocal economy

• current, and possible future, economic scenarios

Restriction on the model’s applicability

As the whole model is based on averaging the behaviour ofthe local corrosion process, its application is notrecommended to systems where hot-spot mechanisms (suchas stray current, under-coat corrosion, etc.) are significantfeatures.

Case studiesIn order to illustrate the model’s application, four casestudies have been chosen, the input data for which issummarized in Table 1. A brief introduction is given foreach, before the model results and overall performance arediscussed.

• Pipeline 1: an onshore pipeline carrying dry gassince its operation began. Accumulated corrosiondamage was slight on both the external and internalpipeline surfaces.

• Pipeline 2: an onshore gas pipeline that has beenused to transport both wet and sour products.Accumulated internal corrosion is severe although,on the other hand, almost no external metal-lossindications have been reported as a result of thedryness of the of region crossed by this pipeline, inthe NE of Brazil.

• Pipeline 3: a trunk line responsible for transportingall of one refinery’s crude oil supply. During itsoperational life, it endured production waterpumped through recurrently, together with somehigh-BSW content product. Long shut-down periodswere also a regular occurrence. Internal corrosiondamage is quite severe and channelling damage isgeneral. In order to meet an increase in demand, anincrease in flow capacity was required. The resultantnew service conditions were simulated by the worst-case hydraulic scenarios, and the maximumoperational pressure profile was defined accordingly.

• Pipeline 4: an onshore line which has been used totransport naphtha and crude oil, the latter usually

1enilepiP 2enilepiP 3enilepiP 4enilepiP

)ni(retemaiD 61 41 22 61

muminiM)mm(ssenkciht 7.8 2.8 3.6 9.7

lairetamepiP 06X 56X 64/04X 53X

)mk(htgneL 481 822 89 89

)ry(efilecivreS 62 63 23 14

)mcqs/gk(POAM 001 79 *65-12 *14-13

.egnardetalumisciluardyhoiranecsesactsrow*Table 1. Constructionand operational data.

Fig.1. Local corrosion activity.


with a high BSW content. Again, production watertransportation was a frequent occurrence togetherwith extensive shutdown periods. The whole pipelinehas bad channelling damage, as shown in Fig.1.

Results and discussion

The model’s output data from the four case studies aresummarized in Table 2, while Fig.3 shows the overallnormalized local corrosion activity. Figures 4 and 5 presentthe expected probability of exceedance for safe operations(at the required levels) without repair to the 200 mostcritical metal-loss areas in each case study, for the next 20and 30 years, respectively. Pipeline 2 was not analysed forexternal corrosion, due the lack of significant indicationson its external surface. In view of a desirable operational

POE threshold range of 10-4-10-5, and the economicremediation rate specified for each case, it can be concludedthat pipeline 3 could be safely operated for almost 30 years,while pipeline 4 would be cost-effectively operational forapproximately 20 years at most.

Conversely, with the exception of pipeline 1, Figs 6 and 7show that internal corrosion developing over 30 yearswould be a direct threat. Pipeline 4 is not expected tomaintain its present use for long, while the operationalreliability of pipelines 2 and 3 will not be cost-effective formore than 20 and 10 years, respectively.

As a result of applying these forecasts, the company’s boardof directors has undertaken the following:

Fig.2. The probabilistic limit-statefunction.

1enilepiP 2enilepiP 3enilepiP 4enilepiP

EXTERNAL

deretlif-noitalupoP 312 - 768 222

)n(retemarapytiniciV 5 - 5 5

naissuaGsetarnoisorroclacoLsretemarapnoitubirtsid

]raey/mm[600.0-80.0 - 400.0-350.0 600.0-08.0

etarnoitaidemeryrainucePsriapergnitaocevitceffe-tsoC

rebmun05 - 001 001

rednudetcepxEefilgniniameR]sraey[snoitidnoccirotsih 03> - 03 02

INTERNAL

deretlif-noitalupoP 733 073,01 523,05 04232

)n(retemarapytiniciV 5 01 02 51

naissuaGsetarnoisorroclacoLsretemarapnoitubirtsid 800.0-560.0 600.0-080.0 300.0-540.0 700.0-180.0

etarnoitaidemeryrainucePsriapergnitaocevitceffe-tsoC

rebmun04 08 08 05

rednudesaBefilgniniameR]sraey[snoitidnoccirotsih 03 02-51 01 5

Table 2. Modellingparameters and output.


�

��

��

��

��

��

��

mm/yearLocal IndividualFig.3. Internal corrosion rate

histogram for pipeline 3.

Fig.4. 20-year POE forecast of theworst external metal-loss anomalies.

Fig.5. 30-year POE forecast ofthe worst external metal-lossanomalies.


• pipeline 4 was converted to specified dieseltransportation;

• a major rehabilitation project is being carried outon pipeline 3, together with several mitigating actions(including a new strategy regarding productionwater);

• a brand new pipeline is under construction toreplace pipeline 2 (mainly in order to supply thelocal market’s forecast rising demand) while analternative use for pipeline 2 is being studied.

ConclusionsNowadays, new onshore pipeline systems must be plannedwell in advance. Sometimes almost a decade can pass

between the conceptual design and commissioning stages,mostly as consequence of the complexities concerning thelegal agreements with landowners through whose land thepipeline will be routed, together with the tougher regulationsregarding environmental and operational issues.

Pipeline operators therefore need to forecast their systems’remaining lives with reasonable long-term accuracy. Despitecorrosion being the major time-dependent threat to ageingpipeline systems, there is little available guidance concerningcorrosion modelling for real pipeline service conditions,and the subject remains controversial.

The current work has been developed to support theoperator’s long-term strategic planning, by providing astraightforward stochastic model to forecast the remaining

Fig.6. 10-year POE forecast of theworst internal metal-loss anomalies.

Fig.7. 20-year POE forecast of theworst internal metal-loss anomalies.


life of corroded pipelines. As input data, the newly-developedmodel requires pipeline geometry and material properties,the worst-case scenario for operational pressure, a good-quality set of metal-loss ILI data, and also the economicthreshold for the system’s future remediation. Thepioneering concept of local corrosion activity wasintroduced, and the underlying simplistic assumptions aredetailed together with the entire mathematical framework.The definitions and roles of the empirical parameters havealso been described.

A balance has been established between over- and under-conservative assumptions, and the model had beenconsidered suitable for forecasting periods of up to 30years. Its algorithm is set out in detail and it can easily beimplemented using standard commercial mathematicalpackages.

The technique provides powerful information with noneed for further expensive or laborious analyses. The use ofthe model has already proved to be particularly relevant toforecasting critical problems long before they present anyreal threat. The model has also been used to give rise toactive mitigation planning, such as a review of inhibitorstrategy and definition of the scope of coating rehabilitationprojects.

Additionally, if more-sophisticated mathematical packagesare available, the model could be easily adapted toincorporate further refinements, incuding:

• non-Gaussian behaviour (for which an automaticbest-fitting-distribution tool is required)

• full limit-state approach: pipeline geometry andmaterial properties could also be consideredprobabilistically (if convolution integrals can beeasily solved) [2, 10, 24]

• any specifics of a system’s history could be takeninto consideration by making the necessaryadjustments to the model’s premises andassumptions.

AcknowledgmentsThe authors thank Petrobras Transporte SA for permissionto publish this paper, and their colleagues Dr SérgioCunha, Carlos Alexandre Martins, and João Hipólito deLima Oliver for many enlightening discussions andcontributions.

References1. B.Gu, R.Kania, and M.Gao, 2004. Probabilistic based

corrosion assessment for pipeline integrity. Corrosion 2004,NACE International, New Orleans.

2. R.Bea et al., 2003. Reliability based fitness-for-serviceassessment of corrosion defects using different burst pressurepredictors and different inspection techniques. 22ndInternational Conference on Onshore Mechanics and ArcticEngineering, June 8-13, Cancun.

3. NACE RP-0775. Preparation, installation, analysis andinterpretation of corrosion coupons in oilfield operations.

4. NACE SP0502, 2008. Pipeline external corrosion directassessment methodology.

5. 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.

6. S.B.Cunha, A.P.F.Souza, E.S.M.Nicoletti, and L.D.Aguiar,2006. A risk-based inspection methodology to optimize in-line inspection programs. The Journal of Pipeline Integrity,pp133-144.

7. M.Ahammed, 1998. Probabilistic estimation of remaininglife of a pipeline in the presence of active corrosion defects.International Journal of Pressure Vessels and Piping, 75, pp321-329

8. S.L.Fenyvesi, H.Lu, and T.R.Jack, 2004. Prediction ofcorrosion defect growth on operating pipeline. Proc.International Pipeline Conference, October 4 - 8, Calgary,Canada.

9. A.Valor, F.Caleyo, L.Alfonso, D.Rivas, and J.M.Hallen, 2007.Stochastic modeling of pitting corrosion: a new model forinitiation and growth of multiple corrosion pits. CorrosionScience, 49, pp559–579.

10. A.Ainouche, 2006. Future integrity management strategy ofa gas pipeline using Bayesian risk analysis. 23rd World GasConference, Amsterdam.

11. P.J.Laycock and P.A.Scarf. Exceedances, extremes,extrapolation and order statistics for pits, pitting and otherlocalized corrosion phenomena. Corrosion Science, 35. no 1-4,pp135-145, 193.

12. J.L.Alamilla and E.Sosa, 2008. Stochastic modelling ofcorrosion damage propagation in active sites from fieldinspection data. Corrosion Science, 50, pp1811–1819.

13. J.L.Alamilla, D.De Leon, and O.Flores, 2005. Reliabilitybased integrity assessment of steel pipelines under corrosion.Corrosion Engineering, Science and Technology, 40, 1.

14. S.A.Timashev, 2003. Updating pipeline remaining lifethrough in-line inspection. International Pipeline PiggingConference, Houston.

15. S.A.Timashev et al., 2008. Markov description of corrosiondefect growth and its application to reliability based inspectionand maintenance of pipelines. Proc. 7th International PipelineConference, Calgary.

16. G.Desjardins, 2002. Optimized pipeline repair and inspectionplanning using in-line inspection data. Pipeline Pigging,Integrity Assessment, and Repair Conference, Houston.

17. B.Gu, R.Kania, S.Sharma, and M.Gao, 2002. Approach toassessment of corrosion growth in pipelines. 4th InternationalPipeline Conference, Calgary.

18. G.Desjardins, 2001. Predicting corrosion rates and futurecorrosion severity from in-line inspection data. MaterialsPerformance, August, 40,8.

19. J.M.Race et al., 2007. Development of a predictive model forpipeline external corrosion rates. Journal of Pipeline Engineering,6, pp15-29.

20. R.B.Eckert and B.Cookingham, 2002. Advanced proceduresfor analysis of coupons used for evaluating and monitoringinternal corrosion. CC Technolgies, Doublin, OH, USA.

21. ASME B 31G. Manual for determining the remaining strengthof corroded pipelines.


22. H.Plummer and J.M.Race, 2003. Determining pipelinecorrosion growth rates. Corrosion Management, April.

23. F.Caleyo et al., 2002. A study on the reliability assessmentmethodology for pipelines with active corrosion defects.International Journal of Pressure Vessels and Piping, 79, pp77-86.

24. G.Pognonec, 2008. Predictive assessment of externalcorrosion on transmission pipelines. 7th InternationalPipeline Conference, Calgary.

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