StructuralMechanicsandDesignofMetalPipes:A SystematicApproachforOnshoreandOffshore Pipelines1stEditionSpyrosA.A.Karamanos
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StructuralMechanicsand DesignofMetalPipes
ASystematicApproachforOnshore andOffshorePipelines
SpyrosA.Karamanos ProfessorofStructuralMechanics, UniversityofThessaly,Volos,Greece
Elsevier
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Dedication
Tomyfather, AnthonyS.Karamanos
Foreword
Sincethedevelopmentofthefirstindustrialfacilities,metalpipeshavebeenemployed asbasiccomponentstofacilitatetheoperationofmachinery,mainlyusedtocontain steamunderpressureandasmeansoftransportingwaterandotherliquidsdepending ontheapplication.Inmoremodernyears,metalpipesareusedfortransportationand storageoftraditionalenergyresources,mainlyintheOil&GasandNuclearsectors,as wellasforthetransportationofwaterandbasicchemicalandpetrochemicalproducts.
Aswearealreadygoingthroughtheeraof“EnergyTransition,”pipesremain keycomponentsfortransportingenergyresources.Furthertotraditionalonshoreand offshoreOil&Gasapplicationswherepipesaredominantelements,toachievethe “NetZero”targetsinthefollowingyears’pipeswillbeusedinevenmoredemandingapplications,forexample,inhigh-pressure/high-temperatureapplications,forthe transportationofhydrogenandammonia,andincarboncapture&storageapplications.
Thisbookisacompleteguidethatdescribesthebasicprinciplesusedfortheanalysis ofonshoreandoffshorepiperesponseunderbasicandmoreelaborateloadingconditions.Startingfromthefirstprinciples,thetheoreticalformulationofthemechanical problemandthebasicequationsforeachcasearepresentedindetail.Insightfuldiscussiononthestructuralresponseundervariousconditionsisalsoprovided,allowing forthereadertounderstandindepththekeyfeaturesofpiperesponseanddesign. Thetraditionalmethodsaswellasthe“state-of-the-art”intheanalysisanddesignof pipesandpipelinesarediscussedwhilethelimitationsandbenefitsthateachanalysis approachoffersareexplained.
ThebookisbuiltontheknowledgeandexperienceofProfessorKaramanosgained overmanyyearsofscientificandprofessionalwork,R&Dprojects,andnumerous publicationswhichresultedinsignificantcontributionstothisfield,acombinationthat ishardtofindinanyothertextbook.Itsstructurecanserveengineersofalllevels.It canbeausefulreferencedocumentoftheoreticalandappliedknowledgeforstudents inthefieldwhowouldliketogainagoodunderstandingofpipeanalysisanddesign. Itcanbealsousedasa“go-by”forearlyandmidcareerprofessionalswhowanta completeguidebookwithreferencetopipelinedesigncodesanddiscussionoftheir provisions.Finally,itcanalsoservematureengineeringprofessionalswhoarelooking foracompletesourceofinformationanddescriptionofthe“state-of-the-art.”Itisvery
fortunatethatProfessorKaramanoshasaccomplishedtodeliversuchacompletebook onthistopic.
Dr.GeorgeE.Varelis PrincipalSubseaSystemsEngineer InnovationandTechnologyLead Worley,UK
Preface
Theoriginsofthisbookgobackto1989whenIstartedmygraduatestudiesatThe UniversityofTexasatAustin(UTAustin)underthesupervisionofJohnTassoulas. ThefirstresearchprojectIworkedatUTAustinwasonthestructuralstabilityofdeepwaterpipelinesundercombinedloading,sponsoredbythenewlyestablishedOffshore TechnologyResearchCenter.Thesewereexcitingtimesfortheoffshoreindustry, extendingitsdeep-wateractivitiesintheGulfofMexicoandelsewhere,andplanning theconstructionofpipelinesinwaterdepthsthatexceeded7000feet(2000m).John’s supervisionandguidanceofmyresearchwereuniquetowarddevelopingstate-of-theartcomputationalmethodologiesandexploringthemechanicalbehaviorofoffshore pipelines.
Duringmypost-docyearatDelftUniversityofTechnology,in1996,Icontinued myresearchontubularsandtubularstructureswithJaapWardenier.Amongother projects,IstartedmycooperationwithNolGresnigtononshorepipelinemechanics. Nol’sexperienceinpipelinemechanicsandespeciallyinlarge-scalelaboratorytesting hasbeenexceptional.OurcooperationbecameveryclosewhenIstartedteachingat theUniversityofThessalyin1999,andsincethen,wehavecooperatedinnumerous projects.Allthoseyears,ourresearchteamhadastronginteractionwithNolthrough commonprojectsonissuesrelatedtopipelinemechanicsanddesign,andthishasbeen agreatassetforus.Nol’sfriendship,cooperation,andsupportcontinueuntiltoday,and Ireallyappreciatehisinstructiveadviceandcommentsonseveralpartsofthebook.
Thebookmaybeconsideredasapersonaljourneyinthe“worldofpipelines,” whicharethespearheadofmetaltubulars.Myinitialintentionwastoincludealso topicsrelatedtopipingcomponentsandsystems,verycommoninindustrialfacilities, powerplants,andterminals.However,thiswouldincreasethesizeofthebookby asignificantamount,andtherefore,thesetopicswillbepartofafuturepublication. Inthepresentbook,themechanicsanddesignofpipesaretackledfromastructural engineeringpoint-of-view.Emphasisisgivenonpipestress–strainanalysisconsidered asalongcylindricalshell,andonbucklingandstructuralinstabilityundercombined action,whereastopicsrelatedtomaterialbehavior,pipefracture,orassessmentofaged pipesaretreatedbrieflyandwillbethesubjectofafuturebook.
Thecontentsofthisbookaredividedintofourparts. PartI isintroductoryand offersanoverviewofpipelineengineeringintermsofpipemanufacturing,design, andconstruction(Chapters1and2).Thestructuralmechanicsofpipesistreated extensivelyin PartII;Chapters3and4refertoelasticpipes,whereasinChapters5and 6,themechanicsofmetallicpipesispresented. PartIII focusesonthestructuraldesign ofonshoreandoffshorepipelines(Chapters7and8),withreferencetomajorpipeline specifications.Italsocomprises“strain-baseddesign”againstgeohazards(Chapter9).
Finally,specialtopicsarepresentedin PartIV:large-diametersteelwatertransmission pipelines(Chapter10),upheavalandlateralbuckling(Chapter11),andmechanicallylinedpipes(Chapter12).
Thebookisaddressedtobothresearchersandpracticingengineersthatwishto deepentheirknowledgeandunderstandingofpipemechanics.Itmaybeusedasa referencebookforresearchersandgraduatestudentsworkinginthefieldofpipes andtubularstructures.Itmaybealsousefultopracticingengineersinthisfield, asacompleteguidebookforpipelinemechanicaldesign,whichoffersextensive backgroundtopipelinedesignstandards,anddiscussestheirrelevantprovisions.
Thereareseveralwaystoreadandmakeuseofthisbook.Belowaresomehints:
PartII(Chapters3–6)containsthebasicsofpipemechanicsandthenecessarybackground forunderstandingcurrentdesignstandardsandspecifications.Apartfromtheirusefulnessto practicingengineers,partsofthosechapterscanbeincorporatedinanelectiveorgraduate courseonstructuralmechanicsoradvancedmechanicsofmaterials.
Chapters1,2,7,and/or8constituteasetofchapterssuitableforanintroductorycourseon pipelinemechanicaldesign(onshoreand/oroffshore)addressedtopracticingengineers.This setofchaptersmayalsobeaddressedtoresearchersinthisfieldforanoverviewofpipeline engineering.
Chapter9onpipelinedesignagainstgeohazardsisastandalonechapterthatintroducesstrainbaseddesigntoresearchersandengineeringprofessionals.Itmaycomplementtheabove introductorycourseonpipelinemechanicaldesign.Itmayalsobepartofagraduatecourse ongeohazard(orseismic)designofcriticalinfrastructuresystems.
Chapter10isanotherstandalonechapter,offeringanoverviewoflarge-diametersteelpipes forwatertransmission.
Chapters3and4explaininsimpleterms,thedevelopmentofstressandstrainindeforming elasticpipes,presentingelegantanalyticalsolutions,andnumericalsimulations.Theycan beusedaspartofastructuralmechanicscourse,orasanintroductiontothemechanicsof elastictubesfromsoft/biologicalmaterials.
Duringmycareer,Ihadthechancetocooperateandinteractwithnumerous individualsandgroupsthatinfluencedmyresearchonpipesandpipelines.Whilea graduatestudentatUTAustin,ImetSteliosKyriakides,aworldwideexpertinthe field.Stelios’workandinparticularhishigh-qualityexperimentshavebeeninspiring formeandformystudents,andhislegacyisapparentinChapters5and6ofthis book.InThessaly,IhadtheopportunitytocooperatewithPhilipPerdikarisandCharis Papatheocharisinperformingnumerouslaboratoryexperiments,whichgaveadded valuetothenumericalmodelsofourresearchteamandimprovedourunderstanding onthestructuralbehaviorofpipeandtubularcomponents.Inaddition,mylongtime cooperationwithPanosDakoulaswasessentialfordevelopingastrongandunique expertisein“pipelinesandgeohazards”.Iwouldalsoliketothankallourpartners atCentroSviluppoMateriali,and,particularly,GiuseppeDemofontiandElisabetta Mecozzi,fortheircooperationinnumerousEuropeanresearchprojects,manyof whichrefertosteelpipesandtubularstructures.ManysincerethankstoBrentKeil andRichMielke,NorthwestPipeCompany,andBobCard,LAN,forourlongtime cooperationinsteelwaterpipelines,whichisreflectedinChapter10ofthepresent book.IamgratefultoCorinthPipeworks,andparticularlytoThanasisTazedakis,
ChrisPalagkas,TimDourdounis,andJohnVoudouris,forourlongtimecollaboration inmanyissuesrelatedtopipemanufacturing.Inallthosecollaborationswithresearch andindustrialpartners,thesystematicandcontinuousadministrativesupportofIoanna Charalambous-Moisidouhasbeentremendousandindispensable.Finally,Iwouldlike tothankmycolleaguesinThessalyandinEdinburghforprovidingafertileacademic environment,necessaryforwritingthisbook.
Asaprofessor,Ihadthehonortosupervisetop-qualityPhDstudents.Iwouldlike tothankallmyPhDstudents;theirexcellentresearchhasformedthefoundationof thepresentbook.Iamproudthatmostofthemarealreadywell-establishedinthe fieldofpipelinesandenergyinfrastructure,inGreeceorabroad.Specialthanksgo toGeorgeE.VarelisforwritingtheForewordofthebookandforhisconstructive inputinupheavalandlateralbuckling(Chapter11).ManythanksalsogotoArisG. StamouandApostolosNasikasfortheirgreathelpinthesectionsofcollapseandlocal buckling(Chapters3,5,and6);IliasGavriilidisforhisinputinlinedpipemechanics (Chapter12);DanielVasilikisforprovidinginformationonconfinedcylinderbuckling (Chapters3and5);PolynikisVazourasandGregorySarvanisfortheirstronginputin the“strain-demand”section(Chapter9);AglaiaPournaraforherworkonbuckled pipes(Chapter9);PatriciaPappaforherassistanceinissuesrelatedtopipeline construction(Chapter1);GiannoulaChatzopoulouandKostisChatziioannoufortheir inputincyclicplasticity(AppendixD).
IamindebtedtoAVAXS.A.,GeorgeTasakosandFoteiniMarnariforproviding severalphotosononshorepipelineconstruction,includingtheleftphotoofthecover page.ManythanksgotoDuaneDeGeer,Intecsea,andChrisTimms,C-FERTechnologies,fortheirvaluableinputandsupport.IamalsogratefultoSaipemS.p.A.andto RiccardoCastellaniandLuiginoVitali,forprovidingphotosfromoffshorepipeline installation,includingtherightphotoonthecoverpage.
Itwouldbeimpossibletoaccomplishwritingthisbookwithouttheprecious,continuous,andmeticuloussupportofKellyGeorgiadi-Stefanidi.Throughoutthewriting process,Kellyhasbeenmydirectandclosestassistantandhasdevotedtremendous effortsinmanagingandreviewingthemanuscript,inorganizingthefiguresandthe referencesandinscrutinizingtheproofs.ManythanksalsogotoDennisMcGonangle, KameshRamajogiandAeraGariguez,whocoordinatedthisprojectonbehalfof Elsevier.
Finally,IwouldliketoexpressmysinceregratitudetotheKaramanosfamily:my wifePeny,mykidsIoannaandTony,andmyparentsAnthonyandLily,fortheir continuoussupportandlove.TheendlesshoursIspentinthepreparationofthisbook wouldhaveotherwisebeenspentwiththem.
4.4Anoteonpost-bucklingbehaviorofaxially-compressed elasticcylinders 109
4.5Bucklingofelasticcylindricalshellsunderuniform externalpressure 110
4.6Uniformbendingofanelastictube 112
4.7Uniformbendingofanelastictubeinthepresenceofpressure122
4.8Bucklingofanelastictubeunderbending 124
5Mechanicalbehaviorofmetalpipesunderinternalandexternal pressure
5.1Abriefnoteonpiperesponseunderinternalpressure
5.2Externalpressurecollapseandpost-bucklingresponse 135
5.3Factorsinfluencingpipecollapse 152
5.4Bucklepropagationandarrestinlongmetalcylinders 159
5.5Effectoftensiononcollapseandbucklingpropagation 173
5.6Externally-pressurizedcylindersunderlateralconfinement177 References 184
6Metalpipesandtubesunderstructuralloading 187
6.1Metalpipesubjectedtotransverseloading 187
6.2Uniformaxialcompressionofametalpipe 200
6.3Anoteonconstitutivemodelingforbucklingcalculations210
6.4Bendingoflongmetalpipes 211
6.5Effectofinternalpressureonbendingresponse 214
6.6Bendingofexternallypressurizedpipes 219 References 228
7Basiconshorepipelinemechanicaldesign
7.1Briefintroductiontopipelinestandards,pipesizesand pressuredesign 233
7.2ASMEB31.8Gastransmission&distributionpipingsystems236
7.3ASMEB31.4Pipelinetransportationsystemsforliquids andslurries 245
7.4EN1594Gassupplysystems–Pipelinesformaximum operatingpressureover16bar–Functionalrequirements 248 References 250
8Offshorepipelinemechanicaldesign
8.1Offshorepipelinemechanicaldesignframework 251
8.2MechanicaldesignofoffshorepipelinesaccordingtoAPI1111253
8.3DNV-ST-F101provisionsforthemechanicaldesignof offshorepipelines
8.4Ashortnoteonbucklepropagationandarrestordesign
8.5DiscussionofAPIandDNVcollapseformulae
8.6Otherformulaeforpredictingthecollapsepressureofpipes andtubes
8.7Discussionofcollapseformulaeandtheslendernessapproach277
8.8Effectofpipemanufacturingonthecollapsepressure
PartI IntroductiontoPipelines
1.Introductiontopipelineengineering 3
2.Linepipemanufacturing 43
Introductiontopipeline engineering
1.1Historicalnote
Thehistoryofhydrocarbonpipelinesstartsinearly19th centuryinLondon,UK,where theWestminstergaslightcompanyconstructedgaspipesbelowpublicstreets1 , 2 .The gaswasburnttolightthestreetsofLondonusinglampposts(MiesnerandLeffler, 2006).ThisconceptwassoonadoptedbygaslightcompaniesinmajorUScities,using pipesmadeofleadorhollowedwoodenlogs.Inmid-nineteenthcentury,hollowed logswerealsousedfortransportingoilorgasfromtheproductionwelltothenearest refinery,inacontinuousmanner.Thetransitionfromhollowedwoodenlogsandlead pipestocastironpipesprovidedmoreopportunitiestotheoilandgasindustry.At thesametime,thefirststeeltubesemerged,manufacturedfromsteelsheets,rolled toacircularshapeandlaporbuttwelded.Inlate19th century,theinventionofthe rollpiercingprocessbytheMannesmannbrothershasbeenamilestoneinsteelpipe fabricationanditsindustrialproduction.Inmid-twentiethcentury,theadvancementof weldingtechnologyenabledthefabricationofweldedpipes,openingnewopportunities tothepipelineandpipingindustrialsector.
Thedemandsandrequirementsimposedbytheoffshoreindustrialsectorhave motivatedsignificantdevelopmentsinpipelineengineering.Thediscoveryoflarge offshorefieldsinthe70’s,bothintheGulfofMexicoandintheNorthSea,signaledthe beginningofanewerainpipelinetechnology(VeldmanandLagers,1997).Theneedto transportgasfromtheenormousgasreserveslocatedinNorthAfricatoEuropeanmarkets,motivatedtheconstructionofseveraloffshorepipelinesacrosstheMediterranean Seaindeepwater.Furthermore,theexploitationofnewoffshorehydrocarbonreserves locatedintheNorthSea,theGulfofMexico,thePersianGulf,Brazil,WestAfrica, South-EastAsia,WestAustralia,andrecentlyinEastMediterranean,inincreasingly deeperwaters,combinedwiththestricterenvironmentalrequirements,haveimposed newchallengesforpipelinedesignandconstruction.
Finally,theexploitationofhugeoilandgasreservesintheCaspianSeaandthe needtotransporttheminEuropeanmarkets,leadtothedesignandconstructionof large-diameterpipelinesthatcrosstheCaucasusmountains,AnatoliaandSouth-East Europe,andaresubjectedtoseveregeohazardthreats,imposingsignificantchallenges fortheirstructuralintegrity.
1 Thepresentchapterreferstohydrocarbonpipelines,whichhavebeendevelopedratherindependentlyof watertransmissionpipelines.SteelwaterpipelineswillbepresentedinChapter10ofthisbook.
2 ItisalsosaidthatChinese,severalthousandyearsago,usedbamboosealedwithmudtotransportnatural gas.However,thereexistsverylimited,ifany,informationonthisissue.
1.2Hydrocarbonpipelineprojects
MajorhydrocarbonpipelineprojectsrequireaninvestmentofbillionsofEuros(or dollars)andlong-termplanninguntiltheirconstructionstarts.Usually,thesemajor pipelinesarequitelong,crossingdifferentcountriesandcontinentalborders.Therefore,inadditiontofinancialaspects,geopoliticalissuesarisingfromtensionand conflictsbetweenneighboringcountries,maybedecisiveforthedesignandcompletion ofamajorpipelineproject.Furthermore,environmentalandsafetyissuesmayaffect theplanningandthefinaldecisionforsuchaproject.Thefollowingexamplesdescribe somemajorpipelineprojectspresentingtheirkeytechnicalfeatures,aswellassome importantnon-technicalinformation.Theyrefertoonshorepipelineprojectsingeohazardareasandtooffshorepipelineprojects,becausetheyconstitutetwotopicsassociatedwithuniquedesignaspects,whicharediscussedextensivelyinthepresentbook.
1.2.1Onshorepipelineprojects
Alargenumberofonshorepipelinesareinoperationandtheirdesignprocesshasbeen wellestablished.However,theconstructionoflarge-diameterhydrocarbonpipelines inearthquake-proneorgeohazardareas,hasimposedanumberofchallengesfor theirstructuralintegrity.Twolandmarkpipelineprojectsarepresentedbelow.The firstistheBaku-Tbilisi-Ceyhan(BTC)crudeoilpipeline,andthesecondisthe “SouthernGasCorridor”connectingBaku,Azerbaijan,withLecce,Italy,whichis composedbythreeconsecutivepipelines:(a)theSouthCaucasusPipelineexpansion (SCPX);(b)theTrans-AnatolianPipeline(TANAP);(c)theTrans-AdriaticPipeline (TAP).Herein,TANAPandTAPpipelinesaredescribedinmoredetail(seealso Table1.1).Finally,ashortmentiontotheInterconnectorGreece-Bulgaria(IGB) pipelineasbranchoftheTAPpipelineismade.
1.2.1.1Baku-Tbilisi-Ceyhan(BTC)pipeline
TheBaku-Tbilisi-Ceyhan(BTC)pipelinetransportscrudeoilfromtheCaspianSea (Baku,Azerbaijan)totheMediterraneanSea(Ceyhan,Turkey).Ithasbeenproposed asanalternativetocrudeoiltransportationwithtankersthroughtheBlackSeaandthe straitofBosporus.ThehighlycongestedBosporusstraitandtheensuingenvironmental issueshaveimposedamajordrawbackinthetankertransportationsolution,andthis wasadecisivefactorforthefinaldecisionforconstructingtheBTCpipeline(Güney andGudmestad,1999).Thepipelinewascommissionedinlate2005andisdesignedto deliveruptoonemillionbarrelsofcrudeoilperdayfromtheSangachalterminalnear Baku,Azerbaijan,toCeyhan,Turkey,intheMediterraneanthroughTbilisi,Georgia. Thetotalpipelinelengthis1,760km,ofwhich442kmareinAzerbaijan,248kmin Georgiaand1060kminTurkey.
ThefirstpartoftheBTCpipelineinAzerbaijanhasadiameterof42inches (1,070mm).Thediametersizeincreasesto46inches(1,170mm)initssecondpartin theCaucasusmountainsandinGeorgia.Then,itrevertsto1,070mminTurkey,and reducesto34inches(865mm)nearitsfinaldestinationinCeyhan.Thelinepipeis
Table1.1 Threeimportantonshorepipelineprojects(BTC,TANAP,TAP)andasummaryfor theirtechnicalandoperationaldetails.
Baku-TbilisiCeyhan(BTC) Trans-Anatolian Pipeline(TANAP) Trans-Adriatic Pipeline(TAP) Typeofcontent
(offshore)
Pipesize 42in,46in,34in56in,48inand 2 × 36in(offshore) 48in,36in(offshore)
part) n/a 70m(MarmaraSea)810m(AdriaticSea)
Specialissues Seismic,Landslides Seismic,Anatolia faultcrossing Seismic,Landslides
API5LsteelgradeX65,withthicknessupto25.8mmdependingonthediametersize andthelocationalongitsalignment.
ThemaintechnicalchallengesoftheBTCpipelineprojectarethehighlyseismic andgeohazardareascrossed,andhavemotivatedasignificantamountofresearch. ThereexistnumerousactiveseismicfaultsalongthealignmentinAzerbaijan,Georgia andTurkey(Hengeshetal.,2004).Furthermore,inseveralmountainousareasthereis ahighriskoflandslideactionduetoslopeinstability.ThedesignofBTCpipelinein thoseareasrequiredthedesignandimplementationofinnovativetechnicalsolutions formitigatingthosethreatsandhasbeenamilestoneinpipelinedesignpracticeagainst geohazards(Shilstonetal.,2004).
1.2.1.2SouthernGasCorridor
TheSouthernGasCorridorisaEuropeaninitiativefordevelopinganaturalgassupply routefromtheCaspianSeaandtheMiddleEasttoEurope,inanattempttoestablish diversesourcesofenergysupply.TheroutefromAzerbaijantoEuropestartsfrom theShahDeniz2GasFieldandconsistsoftheSouthCaucasusPipeline(SCPX),the Trans-AnatolianPipeline(TANAP),andtheTrans-AdriaticPipeline(TAP),reaching itsfinaldestinationinSanFoca,nearLecce,Italy.Inthefollowing,theTANAPand TAPpipelinesarebrieflydescribed.
1.2.1.2.1TANAPpipeline
TheTrans-AnatolianNaturalGasPipeline(TANAP)ProjectisthesecondsegmentoftheSouthernGasCorridor.ItstartsfromtheTurkish-Georgianborderat Türkgözü/Posof/ArdahanwhereitconnectstoSCPXandendsattheGreek-Turkish borderin ˙ Ipsala/Edirne,whereitconnectstoTAPpipeline.Itincludesashortoffshore
StructuralMechanicsandDesignofMetalPipes partthatcrossestheSeaofMarmara.Therearetwooff-takestationsatEski¸sehirand atEastThrace,whichconnectthepipelinewiththelocalTurkishgasdistribution system.Itsmaximumdischargeis16 × 109 m3 (570 × 109 ft3 )ofgasperyearand wascommissionedin2018.
TheTANAPpipelinehastotallength1,841kmandnominalcapacity31 × 109 m3 peryear,inhigh-flowconditions.Itsdiametersizeis56inchesuptotheEski¸sehir CompressorStationand48inchesfromEski¸sehirCompressorStationtotheGreekTurkishborder.Theonshorelengthis1,832km,madeofAPI5LX70linepipe,with designpressureequalto95.5bar.The56-inch-diameterpartofTANAPhasthree differentwallthicknessesof19.45mm,23.34mmand28.01mm,dependingonthe location,whereasthepartwiththe48-inch-diameterhasthreethicknessesof16.67mm, 20.01mmand24.01mm.
The18-km-longoffshoresectionofTANAPcrossestheCanakkaleStrait (Dardanelles)intheSeaofMarmara.Itconsistsoftwo36-inch-diameterpipelines, madeofAPI5LX65linepipe,with22.9mmwallthickness,installedatamaximum waterdepthofapproximately70m.
Seismically-inducedgeohazardsexistalongtheentirealignmentofTANAP pipeline,giventhefactthatTurkeyrepresentsoneofthemostactiveseismiccountries intheplanet.Seismicthreatsconsistofstronggroundshakingaction,activetectonic faults,soilliquefactionandlateralspreading,andlandslides,constitutingseverethreats forthestructuralintegrityofthepipeline(Robletal.,2020).Inparticular,TANAP crossesnineactivefaultsincludingtheNorthAnatolianFaultZone(NAFZ)whichis crossedtwice.Thisisanotoriousseismicfault:itssurfaceruptureisassociatedwitha maximumhorizontaldisplacementofmorethan7m.
1.2.1.2.2TAPpipeline
TheTrans-AdriaticPipeline(TAP)startsattheGreek-TurkishborderatKipoi,Evros, whereitconnectswithTANAPgaspipeline.ItpassesthroughGreeceandAlbania,and aftercrossingtheAdriaticSea,itcomesashoreinSouthItaly,atSanFoca,nearLecce. ThetotallengthofTAPpipelineis878km,ofwhich550kmareinGreece,215kmin Albania,105kmareoffshoreintheAdriaticSea,andthefinal8kmarelocatedinItaly. AtitshighestpointtheTAPpipelinerisesupto1,800mintheAlbanianmountains, andtheoffshorepartisinstalledatamaximumwaterdepthof810m.Thepipelinewas commissionedin2020.
ThecurrentcapacityofTAPpipelineis10 × 109 m3 (350 × 109 ft3 )ofnatural gasperyear,ofwhich8 × 109 m3 (280 × 109 ft3 )aredeliveredtoItaly,1 × 109 m3 (35 × 109 ft3 )toGreece,and1 × 109 m3 (35 × 109 ft3 )toBulgaria,throughtheIGB (GasInterconnectorGreece-Bulgaria)pipeline.ItismadeofAPI5LX7048-inchdiameterlinepipes,designedforinternalpressureof95barintheonshoresectionand API5LX6536-inch-diameterlinepipes,designedforinternalpressureof145baron theoffshoresection.
GeohazardsexistalongtheTAPpipelineroute,includingseveraltectonicfault crossingsandnumeroussoilliquefactionareas,associatedwithlateralspreadingand buoyancy(Slejkoetal.,2021).Inaddition,especiallyintheAlbaniansectionofthe
Table1.2 Alistoflandmarkoffshorepipelineprojects.
pipeline,thereexistseveralareasofpotentiallandslideaction,whichconstitutesevere threatsforTAPpipelineintegrity(Marinosetal.,2019).
1.2.1.3InterconnectorGreece-Bulgaria(IGB)pipeline
TheIGBpipelineisabranchofTAPpipelineinterconnectingKomotini,Greece,with StaraZagora,Bulgaria.Itisa32-inch-diameter,182-kmlongpipeline(ofwhich31km areinGreece),operatingat55barinternalpressure.TheIGBpipelineisdesignedfor 3 × 109 m3 (105 × 109 ft3 )annualcapacity,whichmaybeexpandedupto5 × 109 m3 peryear.Itactsasastrategicgasinfrastructureprovidingdiversificationofgassupply toBulgariaandtoSoutheastEuropegasmarket.Becauseofitsreverseflowcapability, italsoimprovesGreece’senergysecurity.
1.2.2Offshorepipelineprojects
Theconstructionofoffshorepipelinesisafascinatingengineeringprocess.Offshore technologyhasallowedtheconstructionofdeep-waterpipelinesinwaterdepthsthat exceed2,000meters.Becauseofsuchlargedepths,thedesignofthosepipelinesis requiredtoconfrontseveralchallenges. Table1.2 listsafewlandmarkoffshorepipeline projectssortedbythecorrespondingwaterdepth.Fourofthosepipelineprojectsare describedinmoredetailbelow,togetherwiththefamousOman-IndiaPipeline,and theirtechnicalcharacteristicsaresummarizedin Table1.3.AshortnoteontheEastMedpipelineprojectisalsomade.
1.2.2.1BlueStreampipeline
BlueStreamisagaspipelinethattransmitsnaturalgasfromRussiatoTurkeycrossing theBlackSea,bypassingseveralcountries.Itwascommissionedin2005,andat
Table1.3 Landmarkoffshoregaspipelineprojects.
fullcapacityitiscapableofconveying16 × 109 m3 ofnaturalgasfromRussiato Turkey.TheoffshorepartofBlueStreampipelineconnectsDzhubga,Russiawith Samsun,Turkey.Itis396-kmlong,consistingofapairof24-inchoutsidediametersteel pipelines.Atthetimeofitsconstruction,BlueStreamwasthedeepestoffshorepipeline projectintheworld,anditisstillconsideredalandmarksubmarinepipelineproject (maximumwaterdepthof2,150m).ThetwopipelinesaremadeofAPI5LgradeX65 linepipes,withmaximumwallthicknessof31.8mm,installedindeepwatersusing theJ-laymethod,andextensivetestingwasperformedtoqualifythecollapsecapacity ofthelinepipes(DeGeer,2005).Furthermore,bucklearrestorswithoutsidediameter equalto652mmandthicknessequalto52.7mmareemployed.
1.2.2.2Medgazpipeline
TheMedgazpipelineisa210kmsubseapipelinebetweenBeniSaf,Algeriaand Almería,Spain,andwascommissionedin2010atamaximumdepthof2,160m.It isa24-inch-diameterpipelinelaidacrosstheMediterraneanSeawiththecapacityto carry8billioncubicmetersperyearofnaturalgas,butthiscapacitywasextendedto 10.5billioncubicmetersperyear.Thiscapacityisexpectedtodoubleinasubsequent plannedupgrade.ThepipelineismadeofAPI5LgradeX70linepipe,withouter diameter624mmandthickness29.9mm.Initsdeepestpart,thepipelinewasinstalled withtheJ-laymethod.Eachbucklearrestoris4mlongwithouterdiameterequal to675mmandwallthickness55.6mm.Anextensiveexperimentalprogramwas conductedfordeterminingthecollapsestrengthoflinepipes,includingaseriesof full-scalecollapsetests(DeGeeretal.,2007).
1.2.2.3NordStreampipeline
TheNordStreamGasPipeline(NSGP)projectsuppliesEuropewithnaturalgasfrom RussiathroughtheBalticSeaandGermany,andconsistsofatwin-pipelinesystem withacombinedcapacityof55billioncubicmetersperyear.Thefirstpipelinewas commissionedin2011andthesecondin2012.TheoffshorepartofNordStream is1,224-km-longandconnectsVyborg,nearLeningrad,RussiatoLubmin,near Greifswald,Germany.Thediameterofthepipeis1,220mm(48in),madeofSAWL 485gradecarbonsteellinepipe(equivalenttoAPI5LX70),withwallthickness rangingfrom26.8mmto41mm.Thepipelineisinstalledinmaximumwaterdepthof 213mandtheworkingpressureis220bar.Bucklearrestorsarerequiredatthedeepest sectionsofthepipelinetoavoidpropagationbuckling.Thebucklearrestorsare12.2 mlongpipesegmentswith41mmthickness.Duetounevenseabed,theformationof freespansisassociatedwithsignificantlocalpipelinebendingmomentsinthepipeline (Bruschi,2012; Pettinellietal.,2012),whichhavebeenmitigatedbymeansofspecialpurposeseabedinterventionworks(e.g.,rockdumping).
1.2.2.4SouthStream(TurkStream)pipeline
TheSouthStreamprojectwasaimedatconstructingalong,deep-seapipeline,to transportnaturalgasfromtheBlackSeatoBulgariaandthroughSerbia,Hungary, SloveniaandfurthertoAustria.However,theprojectwascancelledin2014,seven
yearsafteritsstart.TheTurkStreampipelineprojectwasannouncedinlate2014, replacingSouthStreampipelineproject.TurkStreamstartsfromtheRusskaya,near Anapa,Russia,crossestheBlackSea,andterminatesatKıyıköy,intheEuropeanpart ofTurkey.Inmostofitspart,theTurkStreampipelinefollowstheSouthStream alignmentbutdeviatesfromitinthewestpartoftheBlackSea,goingsouthwestto TurkeyinsteadofcontinuingwesttowardsBulgaria.
TheoffshoresectionofTurkStreamisa910-km-longnaturalgaspipeline,which crossestheBlackSeaatdepthsof2,200m.Itconsistsoftwoparallelpipelinesrunning acrosstheBlackSea,eachhavingadiameterof32inches.Thepipelineoperatesat 300barinternalpressure,anditismadeofSAWL450steelgradelinepipewith39mm wallthicknesstowithstandthehighexternalpressureatthosedepths.Asubstantial amountofcollapsetestinghasbeenperformedinsupportofTurkStreampipeline construction(Timmsetal.,2018).Itisthefirstlarge-diameteroffshorepipeline(with diameterlargerthan30inches)installedinwaterdepththatexceeds2,000meters.
1.2.2.5Oman-Indiapipeline
ThefamousOman-IndiaPipelineproject(OIP)hasbeenalandmarkinoffshore pipelineengineering.Itsdesignwasconductedintheearly90’sandreferstoa 1140-km-longpipeline,withdiametersizesof20to26inches,designedfor 3,500metersofwaterdepth.Thisextremewaterdepthimposedanumberofsignificant technicalchallenges,includingcollapseresistanceinultra-deep-waterconditions.This projectisstillconsideredasthestate-of-the-artofoffshorepipelinedesign.TheOIP designhadtoconfrontnumeroustechnicalmatters,suchasthedevelopmentofaqualifieddeep-waterpipelinerepairsystem,pipemillupgradesnecessarytomanufacture thethick-walledlinepipe,theupgradeoflayvesselswithadequatetensioncapacity toenabletheinstallationofpipesin3,500mwaterdepth,andthemitigationofdeep offshoregeohazards,suchasmudflows,seismicfaultsandslopefailures(McKeehan, 1995).TheOIPpipelinewasnotconstructed,forgeopoliticalreasons,butitisstill consideredasamilestoneinoffshorepipelineengineering,withimmensecontributions tothe“state-of-the-art”ofdeep-waterpipelinedesign.
1.2.2.6EastMedpipeline
ThelastoffshorepipelineprojectmentionedinthisbriefintroductionistheEastMed pipelineproject.Itreferstoa1,900-kilometersubseapipelineaimedatdelivering naturalgasfromtherecentlydiscoveredgasfieldsofEastMediterraneanSeato Europeanmarkets.Thepre-FEEDstageoftheEastMedprojecthasbeencompleted in2018,andtheprojectiscurrentlyattheFEEDstage.Theproposedalignment crossestheEastMediterraneanSeafromeasttowest.ThefirstpartofEastMed pipelineconnectsthegasfieldsinEastMediterranean,southofCyprus,withthe islandofCrete,Greece.SubsequentlyitcrossesthesouthpartoftheAegeanSea,it becomesonshoreinGreeceandthen,crossingtheAdriaticSea,itconnectstoItaly. Itsconstructionhasnotstartedyet,anditisexpectedtobecommissionedby2025. Uponitsconstruction,itwillbethelongestanddeepestunderwaterpipelineinthe
world,tobeinstalledinwaterdepthsthatreachorevenexceed3,000meters.Apart fromitsdesignagainstcollapseinthosewaterdepths,theconstructionofEastMedis associatedwithnumeroustechnicalchallengesfromdeep-watergeohazards,including seismicactions,underwaterlandslidesandmudflows.Thepipeline,initsfirststageof operation,isexpectedtodeliver10 × 109 m3 ofnaturalgasperyear.
1.3Introductiontohydrocarbonpipelinedesignand
construction
1.3.1Initialstepsofapipelineproject
Tostartahydrocarbonpipelineprojecttheneedforsuchapipelinehastobeestablished.Atthatstage,thefollowingpartiesarenecessarytoagreeonthisproject: (a)thehydrocarbonproducer,(b)thehydrocarbonconsumer(client)and(c)the investoroftheproject.Uponagreement,theinterestedpartiesformthe“pipeline consortium”,whichistheownerofthepipeline,andappointthecontractorandthe projectmanager.
Attheinitialstage,severalalternativesforhydrocarbontransportationareconsidered,e.g.,roadtransportation,railway,ortankers.Inthisprocess,thefollowing featureshavetobetakenintoaccount,andmakethepipelineanattractivesolutionfor hydrocarbontransportation:
Thepipelineconstitutesthesafestwayfortransportingenergyresources,andexhibitsthe lowestrateofincidents,casualtiesetc.comparedwithothertransportationmeans. Itrequiresanimportantinitialinvestment,butitisacost-effectiveinvestment,withhighest returnoftheinvestedcapital.
Ithasalifespanofatleast40yearsandrequiresrelativelylowmaintenancecost. Itismuchlessaggressivetotheenvironmentthanothertransportationmeans(road,rail, tanker).
Overall,thepipelineprojectshouldbeeconomicallyfeasible,andthefinaldecision forsuchaprojectshouldbebasedontheexpectedrateofreturnoftheinvestedcapital.
1.3.2Introductiontopipelinemechanicaldesign
Themechanicaldesignofapipeline,alsocalledstructuraldesign,constitutesamajor partofthepipelineengineeringproject,whichaimsatdeterminingthepipediameter andwallthickness,thesteelgrade,themethodofpipemanufacturing,andthemethod ofinstallation(mainlyforoffshorepipelines).
Themagnitudeofhydrocarbonsupplyisthemajorparameterfordeterminingthe sizeofthepipeline.Inaddition,fluidcontainmentproperties(foreitherliquidorgas) determinetheoperatingpressureandtemperatureandshouldbeconsideredasthe initialinputtomechanicaldesign.
Pipelinedesignisperformedinaccordancewiththecodesandstandardsandother specificationsimposedbytheowner.Inmajoronshorehydrocarbonpipelineprojects,
ASMEstandardsareusuallyfollowedinmanypartsoftheworld,unlessacompleteset ofnationalstandardsisavailable.Inoffshorepipelines,theDNVstandardsaremostly used,butAPIandASMEstandardsarealsoemployed,especiallyinNorthAmerica.
Theoptimumpipelinealignmentshouldbechosenintermsoftopography,easy access,andgeologicalissues(includingseismicandothergeohazards).Inonshore pipelines,asurveyoftheinstallationsiteisusuallycommissioned,andthepipeline alignmentisselected.Themainloadingconditionisinternalpressure,whichis associatedprimarilywiththedevelopmentofhoopstressesinthepipewall.However, additionalsourcesofpipewallstressesexist,suchastemperature,soilsettlements, geohazardandseismicactions,andpipelinecrossingswithrailwaysandhighways.
Thedesignofoffshorepipelinesismorechallenginganddependsonthewater depth.Selectingthepipelinealignmentisacriticaltask,whichrequiresthorough underwaterinvestigationanddepends,amongotherissues,onthereliefandthe geologicalparametersoftheseafloor.Thoseparametersinfluencetheselectionofthe basicpipelineparameters,aswellastheinstallationmethodtobeused.Itisimportant tounderlinethat,inanoffshorepipeline,themostsevereloadingconditionsoccur duringtheinstallationphase,ratherthaninitsoperation.
1.3.3Pipefabrication
Onceallthebasicparametersofthepipearespecified,theyaresubmittedtothepipe millfortheproductionofthelinepipes.“Linepipe”isthepipesegmentproducedinthe pipemillandconstitutesthebasiccomponentforpipelineconstruction.Thepipemill receivestherawmaterialfromthesteelproducer(steelmill)intheformofsteelplates, coilsorbillets,dependingonthetypeoflinepipetobefabricated(seeChapter2).Line pipefabricationisaverysystematicprocess,whichfollowsstrictspecifications.Those include:
dimensionaltolerances(e.g.,cross-sectionalovality,walleccentricity,out-of-straightness); minimumspecifiedyieldstressandmaximumyield-to-tensile(Y/T)stressratioforductility; toughnessandrelatedmechanicalcharacteristicsofthepipematerial,suchasthenon-ductile transitiontemperature; weldcharacteristics(forseam-weldedpipes); specialcorrosionresistancerequirements.
Duringthelinepipemanufacturingprocess,continuouscommunicationbetween thedesigner,thecontractorandthefabricatorisessential.Directcommunicationwith thesteelmillproducerthatsuppliestherawmaterialtothepipemill(plates,coils,or billets)isalsonecessary.Thisallowsforefficientcontrolofthefabricationprocess, reducesthecost,resolvesanyproblemsthatmayariseandresultsincostoptimization ofthepipelineproject.
1.3.4Pipelineconstruction
Uponmanufacturing,thelinepipesareshippedtotheconstructionsiteforbuildingthe pipeline.Inoffshoreprojects,theyareshippedtoayardclosetotheoffshoreproject andtransferredinsmallerquantitiestothelaybargeformarineinstallation.Theoverall
Figure1.1 Loweringofastraightpipelinesectioninthetrench(photobyS.A.Karamanos).
installationisadministeredbyaconstructionprojectengineer,whoshouldbeinclose communicationwiththepipelinedesignengineerandthepipemill.Adescription ofpipelineconstructionprocessforonshoreandoffshorepipelinesisofferedin Sections1.5 and 1.6 respectively.
1.4Pipelinedesignconsiderations
Similartoanyotherengineeringdesignproject,thedesignofapipelineconsistsof asystematicsetoftasks.Ontheotherhand,itmaynotbeconsideredasasimple sequenceoftasksbutrequiresseveral“iterations”becauseofnumerousinteractions amongdifferentfactors.
Thepipelinehasthesimplestgeometryinstructuralengineering:anelongated cylinder(Fig.1.1).Therefore,onemayunderestimatetheimportanceanddifficulty ofpipelinedesign.Pipelinedesignisatopicinvolvingimportanttechnologicalimplicationsandverystrictrequirementsthatrequirehigh-leveldesignexperiencein ordertoconvergetoanoptimaldesign.Italsoinvolvesaseriesofdesigncalculations. Inmostcases,thosecalculationsarenotverycomplicated,andnowadaystheycan beperformedbytheuseofcomputermethodsusingspecial-purposesoftwareinan efficientandeconomicalmanner.Thisallowsthepipelinedesignertoconcentrateon thenon-quantitativeaspectsofthedesignprocessandoptimizethepipelinedesign.
Itisalsoimportanttounderlinethatpipelinedesignfollowsadifferentphilosophy thantraditionalstructuraldesign.Inmanystructuralsystems,e.g.,steelbuildings, optimizationofstructuraldesignrefersmainlytosimplifyingtheconstructionandthe correspondingstructuraldetails,ratherthansavingquantitiesofsteel.Ontheother hand,optimizingpipelinedesignintermsofsavingsteelmaterial,mainlybyreducing pipewallthickness,mayleadtosubstantialsavings.Thosesavingsareduetomaterial costreduction,butalsototransportationandinstallationcost,aswellastoweldingcost. Asanexample,theuseofamoreelaboratedesignapproachfora48-inch-diameter onshorepipelinethatreducesitswallthicknessfrom22mmto19mm,resultsin significantmaterialcostsavings,andfurthermore,transportingandhandlinglighter linepipesbecomeeasierandmoreeconomical.
1.4.1Routeselection
Theselectionofpipelineroute(alignment)isacriticalpartofthedesignprocess.A poorlychosenalignmentmayresultinverycostlysurprisesanddelaysatalaterstage oftheproject,withseriousconsequencesfortheprogressofpipelineconstruction. Problemsmayariseifthealignmenthasconflictswithpublicauthoritiesandother operators,orviolatesenvironmentalrequirements.Inaddition,goodunderstandingof geomorphologicalfactorsshouldbeacquiredattheinitialstageofdesign,especially inareaswithseveregeohazards(seismicorlandslides).Incaseswheregeohazardsare expectedtooccur,appointinganexperiencedteamofgeologiststovisitthesite,to inspecttheproposedpipelinealignmentandreportanyalignmentconflictsorpotential geohazardscanbeofsignificantbenefitforthepipelineprojectanditstimelyexecution.
1.4.2Pipematerials
Materialsneedtobespecifiedatanearlystageofpipelinedesign.Inhydrocarbon pipelines,steelmaterialdominatesthemarket.Currently,steelgradesX60,X65and X70accordingtoAPI5L (AmericanPetroleumInstitute,2018) aremainlyusedin pipelineapplications.GradeX70steelisquitecommoninonshorepipelineprojects. Inoffshorepipelines,X70islessfrequent,butitsuseissteadilyincreasing.Inspecial projects,especiallyoffshore,besidescarbonsteel,variouskindsofstainlesssteelcan beused,mainlyintheformofcladorlinedbi-materialpipes(seealsoChapter12). Inoffshorepipelineprojects,thedesignermayneedtoconsidermaterialsforanticorrosioncoatings,concretecoatings,ormaterialsforthermalinsulation,depending ontherequirementsoftheproject.
1.4.3Pipelinedesignforoptimumthickness
Anonshorepipeneedstobestrongenoughnottoburst.Itshouldbealsocapableof resistingactionsfromhydraulicsandfromground-inducedactions,ifany.Anoffshore pipeneedstobestrongenoughnottoburst,andnottodeformexcessivelyunder externalpressure(buckling),especiallyduringitsinstallationphase,whenthepipeline isemptywithnointernalpressure.Furthermore,anoffshorepipelineshouldbeheavy enoughtobehydrodynamicallystableontheseabed,andsafeagainstupheavalbucklingandvortex-inducedvibrations(VIV)inspansontheseabed.Ontheotherhand, aheavypipeisalwaysmoreexpensive.Apartfromtheamountofmaterial,aheavy pipeismoredifficulttotransport,bend,weldandinstall.Therefore,itisthedesigner’s responsibilitytodetermineanoptimumthicknessforthepipelinetobeconstructed, consideringallrelevantparametersthroughoutthepipelineconstructionproject.
1.4.4Pipelineconstructability
Thedesignedpipelinemustbeconstructable.Morespecifically,theprimarytaskof thedesigneristoensurethatthepipelinecanbeconstructedeasilyandeconomically, withouttechnicaldifficulties.Towardsthispurpose,thedesignermustensurethatthe pipelinecanbeconstructedbyalargenumberofcontractorsaspossible,sothatthe ownerisinastrongnegotiatingpositionfortheawardoftheconstructioncontract.This
Figure1.2 Fracturedsteelpipeafterburstduetoexcessiveinternalpressure(photobyS.A. Karamanos).
ispossibleinonshorepipelineprojects.Ontheotherhand,thechoiceofcontractors inoffshorepipelinesismorelimited,becauseoffshoreconstructionrequiresmore specializedequipmentandpersonnel.Thechoiceofcontractorbecomesquitelimited inthecaseofdeepoffshorepipelineprojects,wherefewcontractorshavethenecessary equipmentandexpertiseforperformingtheinstallationtask.
1.4.5Pipelineprotection
Thepipelinemustbesecuredagainstinternalandexternalcorrosion,andthisrequires coatingofthepipeline,aswellascathodicprotectiononsite.Protectingthepipeline againstinternalcorrosionmayalsorequiretheuseofspecialchemicalsinjectedinto thepipelinetocontrolthecorrosion(corrosioninhibitors),ortheuseofpipeslined withathin-walledpipemadeofaCorrosionResistanceAlloy(seealsoChapter12).
Thepipelinemustalsobeprotectedfromvarioussourcesofexternaldamagesuchas droppedobjects,excessivesettlement,geohazardsandseismicactions.Forthecaseof offshorepipelines,trawlgearandshipanchorsmayimposesignificantthreats.Finally, changesofseabedlevelshouldbeaccountedfor.
1.4.6Principalstructuralfailuremodesofpipelines
Underexcessiveinternalpressure,pipelinesburst.Thishappensbecausethepipeline wallmaynotbeabletoresisttensilestresseshigherthanacertainlimit,andthiscauses pipewallrupturewithcatastrophicconsequences(Fig.1.2).Burstisaccompaniedwith explosion,whichisaseriousthreatforhumanlives,especiallyinonshoregaspipelines. Furthermore,itmaydestroynearbyproperties,facilities,orinfrastructure.Burstin offshoreoilpipelineisalsodangerous,itmayalsobeaccompaniedwithexplosion, andconstitutesaseriousenvironmentalthreatduetooilspill.Burstandtheassociated spillcanbeaveryseriousmatterinoffshorepipelinesorflowlinesconveyingliquid hydrocarbons,especiallyindeepwater,wherelimitedaccesstothedamagedareaexists andthespreadofoilintothemarineenvironmentissometimesverydifficulttostop.
Inoffshorepipelines,apartfromburst,structuralinstabilityduetoexternalpressure isalsoveryimportant,primarilyduringtheirinstallationprocess.Inmostcases, pipelinesareinstalledempty,andaresubjectedtoexternalpressure,whichmaycause bucklingandcollapse(Fig.1.3).Collapseleadstoflatteningofthecross-sectionand,
