A sequence-based method for dynamic reliability assessment of MPD systems

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Zhu, J., Chen, G., Khan, F., Yang, M., Li, X., Meng, X., & He, R. (2021). A sequence-based method for

dynamic reliability assessment of MPD systems. Process Safety and Environmental Protection, 146,

927-942. https://doi.org/10.1016/j.psep.2020.12.015

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Rui

He

a_{CentreforOffshoreEngineeringandSafetyTechnology,ChinaUniversityofPetroleum,Qingdao,Shandong266580,China} b_{CentreforRisk,IntegrityandSafetyEngineering(C-RISE),MemorialUniversity,StJohn’s,NL,A1B3X5,Canada}

c_{SafetyandSecurityScienceGroup,FacultyofTechnology,Policy,andManagement,DelftUniversityofTechnology,theNetherlands} d_{SchoolofResourcesEngineering,Xi’anUniversityofArchitectureandTechnology,No.13YantaRoad,Xi’an,710055,China} e_{NavigationCollege,DalianMaritimeUniversity,No.1,LinghaiRoad,Dalian,China}

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Received16July2020

Receivedinrevisedform2November2020 Accepted10December2020

Availableonline15December2020 Keywords:

Reliabilityassessment MPDsystem GO-FLOWmethod Dynamicbayesiannetwork Deepwaterdrilling

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ManagedPressureDrilling(MPD)systemiswidelyusedinthedeepwaterdrillingoperation.Reliability assessmentplaysacriticalroleintheMPDsysteminthemanagementofdrillingoperationriskand thepreventionofblowouts.However,thereliabilityassessmentoftheMPDsystemischallengeddueto itssequentialoperationsandmultipleprocesses.Consequently,thepresentworkproposesa sequence-baseddynamicreliabilityassessmentmethod,whichfocusesonthedynamicmodelingofsequential operationsfortheMPDsystembyintegratingGO-FLOWanddynamicBayesianNetwork(DBN).GO-FLOW modelsarefirstlyusedtodefinethetimeinteractionbetweenmultiplephasesforcomplexsystems.A sequence-basedmappingmethodisalsoproposedfortheDBNtoconstructthereliabilitymodelofthe MPDsystemthroughouttheentiredrillingcycle.Intheend,thecasestudyanalyzedbytheproposed frameworkindicatesthatthereliabilityoftheMPDsystemdecreaseswithincreasingdrillingdepth,and thereliabilityof“trippingin”ishighestamongfourdifferentphases,whilethe“drillingprocess”isthe lowest.Themethodprovidesanimportanttechniquethatcanbeimplementedwithonlinecondition monitoringtoolstoassessandmonitorthereliabilityoftheMPDoperationinreal-time.

©2020PublishedbyElsevierB.V.onbehalfofInstitutionofChemicalEngineers.

1. Introduction

Deepwaterdrillingoperationfacesnotonlytheharsh environ-ment buttheoperationalchallengesofcomplexoperationsand equipment (Abimbola et al.,2014; Pui et al., 2017; Sule et al., 2018).Unintendedinfluxes,kicks,andblowoutsmayoccurwhen complexgeologicalenvironmentsareencounteredduringdrilling operationswithanarrowdrillingwindow(Wuetal.,2019).The MPDsystemhasbeenwidelydevelopedtoovercomethechallenge ofwellcontrolduetoitsprecisecontroloverwellborepressures (Hannegan,2006).Meanwhile,additionalequipmentalsoincreases thecomplexityandhighriskoftheMPDoperationscomparedwith theconventionaldrillingoperation.Thereliabilityassessmentof theMPDsystemshouldbefurtherinvestigatedtopreventkicksor blowoutindeepwaterdrilling.

∗ Correspondingauthor.

E-mailaddress:offshore@126.com(G.Chen).

Inthepastdecades,various methodshavebeenexploredto assesssystemreliability,includingfaulttreeanalysis(FTA),failure modeandeffectsanalysis(FMEA),Markovapproach,MonteCarlo (MC),GOmethodologyandGO-FLOWmethod,etc.FTAandFMEA aretwooftheearliestwidelyusedreliabilityanalysismethods(Jia andLin,2015).However,bothofthemarenotcapableofthe reli-abilityanalysisofcomplexsystemswithdependentrelationships (Xuetal.,2002).TheMarkovapproachisappliedtoreliability eval-uationforredundantandnon-redundantsystemswithsubstantial flexibility(Kimetal.,2005).Nevertheless,thismethodmaysuffer state-explosionconsequenceswhenappliedtoalarge-scalesystem (VeeramanyandPandey,2011).TheGOmethodologyisa success-orientedanalysismethodofsystemreliability,whichwasinitially developedbyKamanSciencesCorporationtoassessthecomplex system(Shenetal.,2003;Liuetal.,2018).TheGO-FLOWmethod wasdevelopedbasedonGOmethodologytoactualizereliability analysisforcomplexsystemswithaphasedmissionproblem.By consideringcommoncausefailureanalysisand logic loop solu-tion,theGO-FLOWmethodwasimprovedandfurtherappliedto elevatorsystems,railwaysystems,andnuclearpowerplant

sys-https://doi.org/10.1016/j.psep.2020.12.015

tems(MatsuokaandKobayashi,1988,1989,1997;Hashimetal., 2013,2014;Yangetal.,2014;Liuetal.,2016).Basedonthe GO-FLOWtechnique,Hashimetal.conductedareliabilityevaluationfor AP1000ADSsystemtodeterminetheinfluencingfactors(Hashim et al.,2014).Toassessreliabilityinreal-time, ariskmonitoring systemwasdevelopedbasedontheGO-FLOWmethodwithonline receivedinformation(Yangetal.,2014).In addition,Yang etal. presentedanewframeworkofanimprovedriskmonitorsystem basedontheGO-FLOWtechnique,whichintegratedmultiple appli-cations oftheinvestigationofrisk factors,risk monitoring,and management(Yangetal.,2020).Themethodhasalsobeenapplied toanauxiliaryfeedwatersystem,aircraftelectro-hydrostatic actu-ator,chemicalandvolumecontrolsystem,etc.(Liuetal.,2016;Lan etal.,2017;Luetal.,2019).AlthoughtheGO-FLOWmethodhas beenappliedtothereliabilityassessmentofmanysystems,some limitationsstillexist.TherearemanyGO-FLOWoperators,which inducesthecalculationprocessintricate.Besides,GO-FLOWcannot constructintermittentoperationcharts,especiallyfortheentire drillingcycleofasophisticatedMPDsystem(Yangetal.,2014).

BayesianNetworks(BNs)aredirectedacyclicgraphscomprised ofnodesandarcsthatrepresentasetofvariablesandtheir con-ditional dependencies(Pearl,1988).Theapplicationofdynamic BayesianNetwork(DBN)forconductingreliabilityevaluationand quantitativeriskanalysisisrelativelynewandhasbecomevery popularrecently(Khakzadetal.,2013a;Bhandarietal.,2015;Amin etal.,2018).Consideringthedynamicvariationsofthecomplex system,classicalBNhasbeenextendedtomodelsystemsinthe dynamicdomain,sotheDBNwasdeveloped(Murphy,2002).This methodpossessesthefeaturesofupdatingnewevidenceand pos-teriorreasoningandcanalsoovercomethelimitationofuncertain knowledge(Heetal.,2018).Asaneffectivemethodforthe relia-bilityorriskanalysis,itwaswidelyappliedtotheoffshoreoiland gasindustryandotherfieldsspecificincludingdeepwaterdrilling operations(Bhandarietal.,2015;Khakzadetal.,2013b;Changetal., 2019),leakagefailureofsubmarinepipelines(Lietal.,2016,2019), firealarmsystems(Aminetal.,2018),catastrophicshipping acci-dents(ZhangandThai,2016),andcollisionhazardsfortheHigh SpeedCraft(Truccoetal.,2008).FortheMPDsystemin deepwa-terdrilling,theriskofdeepwaterdrillingoperationswasevaluated byBNmethod(Abimbolaetal.,2015).Furthermore,the reliabil-ityassessmentsofkickscontroloperationoftheMPDsystemwere performedbyusingtheFTA andBNmethods(Suleetal.,2018). However,mostofthepreviousstudiesrarelytookaccountof dif-ferentdrillingphasesandthesequencebetweendifferentdrilling phasesintheMPDdrillingprocess.

ThedrillingoperationoftheMPDsystemisacomplicatedtask, whichfacesoperationalsequences,phasedmissionproblems,and multiple processes. For instance,the MPD systemincludes the phasedmissionsof drillingand makingconnection, anddrilling containsmultipleprocessesofrigpumpactionanddrillingstring open, which are all subjected toa specifictime sequence. The appointedtimesequenceiscriticalforthereliabilityassessmentof suchanintermittentsystem.TheGO-FLOWmethodisapplicable tosystemswithcomplexsequencesofsystemoperationor sys-temstatechangesovertime(MatsuokaandKobayashi,1988,1989). Ontheotherhand,DBNisapowerfulandflexibletooltomodel dynamicsystembehaviorandupdatereliabilitywithlifecycledata (ZhuandCollette,2015;Wuetal.,2019).Thedrillingoperationof theMPDsystemisatypicalphased-missionprocess,facingtime sequenceproblems(Zhangetal.,2018).Oneuniqueadvantageof DBNisthat itcanbeusedtodevelop timesequence modelsof phased-missionsystems sinceit containsa seriesoftime slices andtemporallinks.InanydrillingphasesoftheMPDsystem,its GO-FLOWmodelscanbedirectlyconvertedbasedonthefunction chartssystemstructure.Itrelaxestheexistinglimitationsofthe modelbuildingoftheDBNmethod.Inaddition,theDBNmodelsof

theentiredrillingcyclefortheMPDsystemscanalsobedeveloped duetotheabilitytocapturethedependencyrelationshipsamong differentphases.Therefore,GO-FLOWandDBNcanbeusedforthe reliabilityassessmentoftimesequencesofMPDsystems.Aiming torealizethedynamicsequencereliabilityoftheMPDsystem,a novelmethodfordynamicreliabilityassessmentofMPD opera-tionisdevelopedbyintegratingGO-FLOWwithDBN.Thepotential contributionscanbespecifiedas(1)Theprimarynoveltyof pro-posedmethodsistheideaofdynamicsequentialmodelingforthe reliabilityassessmentofMPDsystems.(2)GO-FLOWmodelsare firstlyusedtodefinetheinteractionbetweenmultipleprocesses. (3)Sincethereisnospecificsemantictoguidethemodel devel-opmentofDBN,asequence-basedmappingmethodisproposedto enrichthewaysofdevelopingDBN.

Therestofthispaperisorganizedasfollows.Abriefdiscussion ontheGO-FLOWmethodandDBNmethodisprovidedinSection

2.ThemethodforthereliabilityassessmentoftheMPDsystemis proposedinSection3.Applicationsofthemethodarepresentedby acasestudyinSection4.Section5providesthereliabilityanalysis andresultsoftheMPDsystemindeepwaterdrilling.The conclu-sionsofthispaperaredemonstratedinSection6.

2. Basicmethods

2.1. GO-FLOWmethod

GO-FLOW can evaluate an extensive system with complex operationalsequences(Hashimetal.,2013,2014).TheGO-FLOW methodologyisasuccess-orientedmethodologyforsystem relia-bilityanalysis.Itincludestwonecessarysteps:first,constructthe GO-FLOWchartfor thephysicalsystem,and thencalculatethe systemreliability. (Matsuokaand Kobayashi,1988,1989,1997). Thesystemfunctiondiagramcanbedirectlyconvertedintoa GO-FLOWmodelingbygraphicaldeduction.Andthen,theprobability ofoccurrenceofdifferentstatesinthesystemiscalculatedbyone computerrun.

TheclassicGO-FLOWmethodutilizes14basicoperatorsand signallinestomodelthesystemfunction(Hashimet al.,2013;

Fanetal.,2016).Themeaningsandsymbolsof14operatorsare showninFig.1.Accordingtotheirfunction,theseoperatorscan bedividedintofunctionoperators,logical operators,andsignal operators.Generally,thefunctionoperatorsareusedtomodelthe physicalcomponentandindicatethenormalorfailurecondition ofthecomponent;thelogicaloperatorssimulatetheconsistent relationshipbetweensystemcomponents,and thesignal opera-torsrepresenttheexternalinputsignalofthesystem(Yangetal., 2014,2020).

Thesignallinesareusedtoconnecttheinputsandoutputsto theoperators.Asignalrepresentssomephysicalquantityor infor-mation,suchasfluidflow,electriccurrents,requiredsignals,etc. Avariablecalled‘intensity’isassociatedwithasignalline. Usu-ally,theintensitycandescribethedigitalfeaturesandrepresent theprobabilityofsignalexistence.Ifasignalisusedasasub-input signaltothetype35,37,or38operators,theintensityrepresentsa timeintervalbetweenthesuccessivetimepoints(Liuetal.,2016). WhentheGO-FLOWchartisconstructed,alimitednumberof discrete-timepoints need tobedefined toindicate thesystem operationsequence.Thetimepointsdonotnecessarilyrepresent real-timebutreflectanorderingofthesystemoperation.The num-beroftimepointsisdefinedbytheanalysts,whichdependson theobjectiveoftheanalysisandthesequenceofthesystem run-ning.Finally,thesedataareinputtotheGO-FLOWmodel,andthe intensityofthefinalsignalatall-timepointsisobtained.

physi-Fig.1. OperatorsdefinedintheGO-FLOWmethod.

callayoutofthesystem;(2)RevisionsandupdatestotheGO-FLOW chartsarereadilycompleted;(3)TheGO-FLOWchartcontainsall possiblesystemoperationalstates.However,likeotherreliability assessmentmethods,GO-FLOWalsohasitsdefects.Theproblemof thecombinatorialexplosionbecomesverysignificantasthe num-berofcomponentsincreases.Besides,GO-FLOWcannotconstruct hierarchicalcharts.Furthermore,GO-FLOWisunabletobuild inter-mittentoperationchartsforsophisticatedsystems.

2.2. Dynamicbayesiannetworkmethod

BayesianNetwork(BN)isagraphicaltechnique,whichhasbeen appliedtoqualitativeandquantitativeriskanalysisduetoits for-wardanalysisandbackwardanalysis(Heetal.,2018).ABNconsists ofnodesandarcs,inwhichthenodesrepresentstatesofvariables, andarcsdepictcausalrelationshipsbetweenthelinkednodes.The qualitativeanalysiscanbeperformedbyanetworkstructure,while thequantitativecalculationisexpressedbyassigningconditional probabilitydistributionstothenodes.Consideringtheconditional dependenciesbetweenthevariables,thejointprobability distri-butionP(U)ofvariablesU={X1,X2...Xn}inthenetworkcanbe

writtenas(Bhandarietal.,2015):

P(U)=

n



i=1

P(Xi



WherePa(Xi)istheparentsetofanynodeXi.

BNtakesadvantageofBayestheoremtoupdatetheprior occur-rence(orfailure)probabilitywithnewobservationsofevidence E.TheupdatingposteriorsofP(U)couldbeobtainedfromEq.(2)

(Khakzadetal.,2013b).

P(U





U

P(U,E)

(2)

AdynamicBayesianNetwork(DBN)consistsofasequenceof time slicesand temporallinksdevelopedfromtheconventional staticBN(Heetal.,2018).Inotherwords,thetimeattributeisadded tothestaticBN,andthetrendofthevariablesandtheircausal rela-tionshipcanbepresentedinvarioustimeslicesatdifferenttime points.Fig.2showsasimpleDBNmodelwiththreenodes.(X1,X2)

aretheparentnodeofZininitialtimet1underphase1.

Accord-ingtothetimeseries,theDBNstructureexpandedtotn-1andtn

Fig.2.AsimpleDBNmodel.

underdifferentstages.Meanwhile,thedynamiccharacteristicsand reliabilityofthetargetsystemcanbecaptured(Aminetal.,2018). ComparedtostaticBN,thejointprobabilitydistribution func-tionofaDBNfortimet=1toNcanbeexpressedas(Lietal., 2016): P(Z1:N)= N





P(Zi,t



WhereZi,tistheithnodeattimet;Pa(Zi,t)istheparentsetofany

nodeZi,t;nisthenumberofnodes;Nisthenumberoftimepoints

inthenetwork.

Modeldevelopmentandparameterestimationaretwocritical partsforreliabilityassessmentbyusingtheDBNmethod.However, aweakpointofDBNisthatthereisnospecificsemantictoguide modeldevelopment.Toovercomethisproblem,manystudiestry totranslateclassicaldependabilitymodelssuchasFT,eventtree, andMarkovmodelintoBNmodels(Liuetal.,2018).Butthisway hasnoapplicationtosequentialoperationsystems,especiallyfor thecomplexoperationsoftheMPDsystem.

3. ProposedmethodforMPDsystem

3.1. DescriptionoftheMPDsystem

Fig.3. DynamicannularpressurecontroloftheMPDprocessflowdiagram.

Device (RCD) bearing assembly and the Choke Manifold with-out activatingsecondary safety barriers(Gabaldonet al., 2014;

Abimbolaetal.,2015).InternationalAssociationofDrilling Con-tractors (IADC)definedthatMPDisanadaptivedrillingprocess employedtocontroltheannularpressureprofilethroughoutthe wellbore(Hannegan,2006).Thepressuremarginsareusually nar-rowindeepwaterdrillingduetoitscomplexconditionsandexact requirements(Wangetal.,2011).MPDtechnologyisarelatively advancedmethodforpressurecontrolduringthedrillingoperation. Thistechnologyaimstoascertainthedownholepressure environ-ment limitsand manage theannular hydraulicpressure profile accordingly. TheequipmentlayoutoftheMPDsystemisshown inFig.3(Chustzetal.,2008).

3.2. ThecombinationofDBNandGO-FLOW

AccordingtotheGO-FLOWmodelofthetargetsystem,aDBN modelisestablishedbasedonmappingrules.First,theoperator shouldbeconvertedintoanodeoftheBayesiannetwork,andthe conditionalprobabilitytable(CPT)ofthemappingnodeneedsto be givenbased onthemapping algorithm ofeach operator. As showninFig.4,thefrequently-usedoperatorsandtheequivalent DBNnodesintheMPDsystemincludetype25ofthesignal oper-ator,type 22,23,30oflogical operators,and type21,26,35 of functionoperators.Besides,thedifferentcharactersinDBNnodes representdifferentmeanings.Hereinto,Srepresentstheinput sig-nal,Rrepresentstheoutputsignal,trepresentstimepoint,and t isthetime pointbeforetimet. TheType21operator usually describessometwo-statephysicalequipment.Theoutputsignal willbepresentedwhentheinputsignalisgivenandtheoperator isgood.Therefore,thereisacharacterCfortype21operatorinthe equivalentDBNmodelcomparedwiththeGO-FLOWmethod,andC representstheoperatoritself.Similarly,thecharacterCfortype26 operatoralsorepresentsthecomponentitself,butitisunnecessary forotheroperators.Duetospacelimitations,themappingrulesof type25,22,35operatorsareintroduceddetailedinthispaper,and theremainingoperatorscanbecomputedbasedonthefollowing methods.

(i)Signaloperator-type25

IntheGO-FLOWmethod,thetype25operatorisdedicatedto simulatingasingle-signalgeneratorwithoutinputsignalsbutwith oneoutputsignal.Thisoperatorcangenerateoneorsomesignals atonespecificorsomeconsecutivetimepoints.Thesignalgivenby thisoperatoriscommonlyusedtostartthecomponent.Theoutput signalofthetype25operatorhastwostates:successandfailure. Thesuccessstatemeansthesignalcanbesentoutsuccessfully. Takingtheconditionalstatementoftimepointt1 asanexample,

theintensityR(t1)representstheprobabilityofthesignalbeing

emittedattimepointt1.Instead,thefailurestatemeansthereare

nosignaloutputs,andthefailureprobabilityalsocanbecalculated by1-R(t1).Therefore,theBNmodeloftype25operatorisshownin

Fig.4(d),anditsCPTscanbedefinedinTable1,wheretirepresents

conditionalstatementatdifferenttimepoints. (ii)Logicaloperator-type22

There are three logical operators in the GO-FLOW method, includingtypes22,23,and30operators,whichcorrespondtothe “OR”gate,“NOT”gate,and“AND”gate.Forsimplicity,thissection takesthe“OR”gateasanexampletodescribethemappingrules oflogicaloperators.Thetype22operatorhasmorethanoneinput signal(Sj)butonlyoneoutputsignalR(t).Accordingtothe defini-tionofthe“OR”gate,theoutputsignalRisinthefailurestatewhen alltheinputsignalsbreakdown.Assumingthat therearethree inputsignals,theoutputintensitycanbeobtainedbyEq.(4).The equivalentDBNmodelofthe“OR”gateoperatorwiththreeinput components(S1,S2,S3)isshowninFig.4(b).Basedonthelogical

relationshipsofthreeinputsignals,theCPTsoftype22operatorcan bedefinedinTable2.Justasthegeneralinputsignal,eachinput signaloftype22operatoralsohastwostates:successandfailure. TakingtheinputsignalS1asanexample,thesuccessstatemeans

thattheinputsignalS1exists,whileitistheoppositeofthe

fail-urestate.ThecorrespondingCPTsareshowninTable3.Herein, P(ti)representsthefailureprobabilityofinputsignalS1atthetime

pointti.

R(t)=1−[(1−S1(t))·(1−S2(t))·(1−S3(t))] (4)

(iii)Functionoperator-type35

Type35operatoris usedtoemulatea component(e.g.,arig pump)withincreasingfailureprobabilitiesastheincreasing work-ingtimeintheMPDsystem.IthastheprimaryinputsignalS(t), severalsub-inputsignalsP(t),andoneoutputsignalR(t).The pri-maryinputsignalS(t)canbeobtainedfromthepreviousoperator. Theintensityofthesub-inputsignaldenotes atime interval in whichthefailureprobabilityofthecomponentgraduallyincreases duetothefailurerate.Generally,assumingthatisaconstantand thefailureprobabilityofthiscomponentfollowsanexponential distribution,whichcanbecalculatedfromEq.(5).ForMPD sys-tems,therigpumporsomephysicalequipmenthastwostates: successandfailure.Therefore,theP(t)canbeusedtoindicatesthe probabilityofthefailurestateofacomponent.Theinputsignalalso hastwostates:successandfailure(existenceandnon-existence). TheoutputsignalRisinthesuccessstatewhentheinputsignalS andsub-inputsignalParebothinsuccess.TheDBNmodeloftype 35operatorisshowninFig.4(g),andtheCPTsofthisoperatorcan bedefinedinTable4.SimilartoinputsignalS1,theCPTsofPandS

canalsobedeterminedinTable5.

P(t)=



e−tdt (5)

3.3. Integratedframework

Fig.4.OperatorsinGO-FLOWmodelandthecorrespondingDBNmodel. Table1

CPTsoftype25operator.

Time t1 ti _... tn

State success failure success failure success failure

Value R(t1) 1-R(t1) R(ti) 1-R(ti) R(tn) 1-R(tn)

Table2

CPTsoftype22operator.

S1 success failure

S2 success failure success failure

S3 success failure success failure success failure success failure

R success 1 1 1 1 1 1 1 0

failure 0 0 0 0 0 0 0 1

Table3

CPTsofinputsignalS1.

Time t1 ti _... tn

State success failure success failure success failure

Value 1-P(t1) P(t1) 1-P(ti) P(ti) 1-P(tn) P(tn)

Table4

CPTsoftype35operator.

P success failure

S success failure success failure

R success 1 0 0 0

failure 0 1 1 1

Step1:Definethesystemandcollectthenecessary

informa-tion.ThescopeoftheMPDsystemisdefinedfirstlyandstudied

adequately. Meanwhile, therequiredinformation, includingthe

systemfunction,structuralcomposition,operationprinciple,

fail-uredataofequipment,wellstructure,operationschedule,etc.need

tobecollectedinthewholedrillingoperation.Thesemayhelpto

understandthelayoutoftheMPDsystem,processtechniques,and

equipmentfunctions.

Step2:ConstructGO-FLOWmodelsfordifferentdrillingphases.

TheMPDdrillingoperationisdividedintofourphasesbasedon

Section2.2.Successcriteriaaredeterminedconsideringtheir

func-tionsandobjectivesfordifferentdrillingphases,andflowchartsare

Table5 CPTsofPandS.

Time t1 ti _... tn

State success failure success failure success failure

P 1-P(t1) P(t1) 1-P(ti) P(ti) 1-P(tn) P(tn)

Fig.5. TheframeworkofreliabilityassessmentfortheMPDsystem.

developedcorrespondingly.Hereinto,thesuccesscriteriareferto

thepurposesofdifferentphases.Forthedrillingprocess,itmeans

that thestep of ¨separate mud¨isachievedwithouta kickevent.

Different flowchartscanbeconvertedintoGO-FLOWmodelsby

usingsignallinesandoperators.TheGO-FLOWmodelsrepresent

differentfunctionsofthesystemduringthedrillingoperation.

Step3:EstablishtheDBNmodelfortheMPDoperation.Four

differentDBNmoselscanbetransformedfromGO-FLOW

mod-elsbasedonthemappingrulesinSection3.3.2.TheDBNmodel

isestablishedbasedontheselectedwellstructureandoperation

schedule.The failureprobabilities ofequipmentand operations

areobtainedfromOREDAdatabase(OREDA,2002),published

lit-erature, expert knowledge, or historical statistic under specific industries(Khakzadetal.,2013a).Moreover,thedrillingoperation oftheMPDsystemiscontinuous.TheDBNmodelsoftheentire drillingcycleshouldbeconstructedaccordingtothewelldepths.

Step4:AssessthereliabilityoftheMPDsystem.Inthisstep, systemreliabilitycanbecalculatedbyDBNmodelingduringthe drillingcycle.Reliabilityanalysisincludestwoparts,i.e.,sensitive analysisandinformationupdating.Sensitivityanalysisiscarried outtoidentifythecriticalcomponentsandranktheimportance ofsystemcomponents.Informationupdatingaimstoupdatethe real-timereliabilityoncesomenewevidenceiscollected.

Step5:Safetymeasures.Identifyingcritical componentsand unitsfortheoperatingsystemscanbeperformedwith sensitiv-ityanalysisandinformationupdating.Toimprovethereliability oftheMPDsystem,safetymeasuresandanefficientmaintenance plancanbeproposedbasedontheassessmentresults.

4. Casestudy

4.1. DifferentMPDdrillingphasesandcorrespondingflowcharts MPDtechnologyincludesfourdifferentphases:drillingprocess, makingaconnection,tripping out,andtrippingin,asshown in

Fig.6.Itisnecessarytostarttherigpumpforthedrillingprocess whencarryingoutoneparticularholesectionoperation.Andthen, thewellheadpressureshouldbeincreasedtomakeaconnection afterstoppingtherigpump.Drillingtoacertaindepth,afterthe drillingprocessandmakingaconnectioncyclingalternately,the drilltoolsneedtobereplacedbythetrippingoutoperation.The drillingtoolsshouldbecombinedandtrippedinforthenextsection ofdrilling.Thecorrespondingoperatingprocedureswillbeinitiated tocontroltheBHPduringthedrillingoperation.

Inthissection,acasestudyoftheMPDsystemintheSouthChina Seaisconductedtoverifytheeffectivenessoftheproposedmethod. Generally,thedrillingprocessoftheMPDsystemincludesfourwell sections,whichare26”,17_−1/2¨,12−1/4¨and8−1/2 ¨wellsections.As mentionedinSection2.2,therearefourdifferentdrillingphases ineach wellsection,and thephases ofthedrillingprocess and makingaconnectionarealternatedduringeachwellsection.The drilltoolsneedtobereplacedinthe‘trippingout’phaseattheend ofthepriorwellsection.Andthen,thedrillingtoolswillbe com-binedagainandtrippedinthenextwellsection.Thephasesofthe drillingprocessandmakingaconnectionarealternateduntilthe wellcompletion,asshowninFig.6.ThedrillingphasesoftheMPD systemareintroduceddetailedlyandcorrespondingflowchartsare constructedthoroughly,asshowninFig.7.

(i)Drillingprocess.Muddensityshouldbedeterminedbasedon formationparametersbeforethedrillingfluidispumpedinto thebottomholeviadrillingstrings.TraversingRCD,drilling fluidwillreturnfromthewellboretochokemanifolds,andthe wellheadbackpressurecanbecontrolledbyadjustingchoke valves.There arethree flow linesfor choke manifolds.The flowlines1installedthechokevalveAC-2,whichismainline forreturneddrillingfluid.Ifflowline1fails,theflowline2 installedthechokevalveAC-3beginstotakeeffect.The back-flowline3andthepressurereliefvalvewillworktoconvey thefluidsandchokemanifoldsagainstoverpressurehazards

Fig.7.FlowchartsoftheMPDsystemduringtheentiredrillingcycle.

whenbothflowline1andflowline2fail.Flowmeasurement iscarriedoutwheneffusivefluidpassesthroughtheCoriolis flowmeter.Finally,theBHPcanbemonitoredallthetime dur-ingthedrillingprocess.IfthereisnoabnormalityinBHP,the fluidwillflowintothemudpoolviatheshaleshaker.Returned fluidscanbeseparatedintogas,oil,andcontamination-free drillingfluidbyaseparatorifthisprocesssucceeds.Theflow chartofthedrillingprocessisconstructed,asillustratedin

Fig.7(a).

Fig.8.GO-FLOWmodelofdrillingprocessfortheMPDsystem.

(iii)Trippingout.The drillingstrings areliftedtotheprojected depthbyinjectingtheheavymudcap,andthetrippingspeed needstobecontrolledstrictlyinthisphase.Thereisan exces-sivepressuredropinthebottomholeduetotheswabbing effectsandstoppingdownholecirculation.Hence,thespeedof thebackpressurepumpandthechokevalveopeningof man-ifoldsshouldberegulatedintime.Therestofthedrillstrings areliftedtothederrickfloorintheusualway.Similarly,the correspondingflowchartoftrippingoutisshowninFig.7(c). (iv)Trippingin.Beforetheoperationoftrippingin,bottomhole

assemblymaybeloweredtothecasingshoeanddrilling circu-latingalsobestartedbyrigpumps.ChokemanifoldsandDAPC systemscanbeusedtoavoidlostcirculation.Meanwhile,the trippingspeedshouldbekeptinreasonablebounds,andthen theheavymudcapwillbedisplaced.Thedrillingbitsarerun intothebottomtoprepareforthenextholesection.Andthe flowchartoftrippinginisconstructedinFig.7(d).

4.2. ConvertflowchartsintoGO-FLOWmodel

Asshownin Fig.8,theGO-FLOWmodel oftheMPDdrilling processisconvertedfromitsflowchartbasedonthefunctionand structureofthesystem.Basedontheoperationsequenceandthe

flowchart,thedrillingprocesscanbedividedintofivetimepoints. Timepoint1isaninitialtime.Attimepoint2,therigpumpbegins tooperate.Attimepoint3,whichisnexttotimepoint2,drilling stringsNRVandRCDarestarted.Attimepoint4,chokevalve2 and3begintooperate.Timepoint5is0.1haftertimepoint3and thedrillingoperationofonethribbleiscompleted.Similarly,other GO-FLOWmodelsoftheMPDdrillingphasesalsocanbeestablished accordingtotheirflowcharts,asshowninAppendixA.

AsacriticalelementoftheGO-FOLWmodel,different opera-torsshouldbeselectedappropriatelytorepresenttheiroperations andcomponents.Intotal,27operatorsareusedinthisGO-FLOW model,fromtheinitialdrillingsignalofoperator101tothe com-pletesignaloffinaloperator127.Herein,type25operatorsareused togenerateinputsignalsatfivetimepoints.Therigpump,drilling stringsNRV,andRCDaredenotedbytype26operators.Thereare twocriticalparametersinwhichPprepresentsthefailure

proba-bilityofstart-up,andPgrepresentsthefailureprobabilityofthe

usualstart.Giventherigpumpmayfailastheincreasingservice time,therigpumpcanbepresentedbytype35operatorsandthe failurerate␭isaconstantorvariable.Flowlines,valves, flowme-ter,andseparatoronlyhavetwostatuses,whichcanbedenotedby type21operators.Thelogicalrelationshipcanbepresentedbytype 22,23,and30operators.Theoperatorparametersofthedrilling processfortheMPDsystemaregiveninTable6,whichare inves-tigatedfrompublishedliterature,expertknowledge,orhistorical datastatistics(Abimbolaetal.,2014;Suleetal.,2018;Abimbola etal.,2015;Rathnayakaetal.,2013).

4.3. DBNgraphicalstructureofdifferentMPDdrillingoperation Toovercomethelimitationsofconventionalreliability assess-mentmethods(e.g.FTAorFMEAetc.),theequivalentDBNmodel (Fig.9)isdevelopedfromtheconstructedGO-FLOWmodelofthe drillingprocessfortheMPDsystem.TheCPTscanbedetermined accordingtothecollectedoperatorparameters.Adistinct advan-tageofDBNisthatthecomputationalprocessismoreconvenient anduser-friendlythanGO-FLOW.AnotheradvantageofDBNisthat thedynamicsystemreliabilitycanbeobtainedthrough observa-tionalevidenceupdating.InAppendixA,otherDBNmodelsofthe MPDdrillingphasesalsocanbeestablishedaccordingtotheirflow chartsinthesameway.

Toevaluatethesystemreliabilitythroughouttheentiredrilling cycle,reliabilityassessmentshouldbeimplemented,which com-binesthedrillingprocess,makingaconnection,trippingout,and trippinginphases.Thespecificparametersofwellprofileandwork schedulearepresentedinAppendixB,whichwereobtainedfrom acertainwellinSouth ChinaSea.Given thatthe36”conductor isjettedintoshallowsubsea soil,fourremainingsectionsneed

Table6

TheoperatorparametersofthedrillingprocessfortheMPDsystem.

Operator

Meaning Parameter Operator Meaning Parameter

No Type No Type

101 25 Initialtime R(1)=0,R(t)=1(t=/ 1) 115 23 Notgate /

102 21 Startsignalofdrilling P=1.0×10−4 _{116 21 Chokeflowline2 P=3.6×10}−4

103 25 Startsignalofrigpump R(2)=1,R(t)=0(t=/ 2) 117 25 Startsignalofchokevalve3 R(t)=0,t=/(4,5)R(t)=1,t=(4,5) 104 26 Rigpump Pp=4.3×10−5Pg=4.3×10−4 118 26 Chokevalve3 Pp=2.5×10−4Pg=2.5×10−3

105 25 Timeinterval t=3.75h 119 23 Notgate /

106 35 Failurerateofrigpump ␭=2.52×10−6h−1 120 21 PRV P=2.2×10−5 107 25 StartsignalofDS-NRV R(3)=1,R(t)=0(t=/ 3) 121 21 Backupflowline3 P=3.6×10−4 108 26 DS-NRV Pp=1.3×10−6Pg=1.3×10−5 122 22 ORgate /

109 25 StartsignalofRCD R(3)=1,R(t)=0(t=/ 3) 123 25 Startsignalofmeasurement R(t)=0,t=/(4,5)R(t)=1,t=(4,5) 110 26 RCD PP=6.7×10−6Pg=6.7×10−5 124 21 PWDtools P=1.1×10−5

111 21 Adjustwellheadbackpressure P=1.0×10−4 125 30 ANDgate /

Fig.9.DBNmodelofthedrillingprocessfortheMPDsystem.

Fig.10.DBNmodeloftheentiredrillingcyclefortheMPDsystem.

tobedrilledusingtheMPDsystem,whichincludes26”section,

17−1/2¨section,12−1/4¨section,and 8−1/2¨section. Theresults of

endnodesfordifferentphasesrepresentthereliabilityoftheMPD

operationindifferentdrillingdepthsortime.TheDBNmodelofthe

entiredrillingcycleisestablishedinFig.10.

5. Resultsanddiscussion

5.1. Dynamicreliabilityassessment

The outputintensitiesof componentsinthe drillingprocess fortheMPDsystemareexpressedinFig.11.Sixcomponentsare selectedtopresentavarietyofintensitiesatdifferenttimepoints. Alloutputintensitiesofcomponentsequal0attimepoint1because thesystemhasnotbeenstartedintheinitialtime.Astheenabled operator,theintensityofS101equalto1aftertimepoint2.The sequentialoperationofoperatorS106issimilartooperatorS101. However,outputintensitiesbegintodecreasewithtraversinga seriesofcomponents.AlthoughtheoperatorS111andS112start attimepoint 3simultaneously,theoutputintensityofoperator

Fig.12.ReliabilityofthedrillingprocessfortheMPDsystem.

S112islowerthanoperatorS112duetothedependencyamong the causation factors. Outputintensities of operator S125and S127aresimilar.AstheendpointofthedrillingprocessfortheMPD system,theoutputintensityofoperatorS127canalsorepresent thereliabilityofthedrillingprocess.Usingthismethod,the reliabil-ityoffourdifferentphases(drillingprocess,makingaconnection, trippingout,andtrippingin)arepresentedinFig.12.The reliabil-ityof“trippingin”and“makingaconnectionoperation”ishigher comparedtothatofthedrillingprocessandtrippingout,whilethe “drillingprocess”isthelowest.Theresultsindicatethatthe crit-icalcausesshouldbeemphasizedinthedrillingprocessandthe trippingoutphases.Forinstance,thestandbyNRVcanbeinstalled orthespeedoftrippingoutshouldbecontrolledtoimprovethe reliabilityoftheMPDsystem.

ThechangeofdynamicreliabilitywithdepthisanalyzedbyDBN, asshowninFig.13.ItisclearthatthereliabilityoftheMPD sys-temdecreaseswithincreasingdrillingdepth.Thatisbecausethe MPDsystemcomponentswillsuffersomewearandtearwiththe drillingoperation.Thereliabilityofthedescendingslopeisstablein

fourrespectivedrillingsections.Thereliabilitiesgointoadramatic declineindifferentjunctionsbetweendifferentsections.Itisdueto ajobconversion,whichdecreasessystemreliability.Thereliability oftheMPDsystemdecreasesto0.9348whenthe8−1/2sectionis completed.Asexpected,whentheMPDsystemworksalongcycle inthedeepwaterdrilling,thesystemreliabilitydecreased signifi-cantly.Therefore,itisnecessarytoimplementsomemaintenance toimprovethesystemreliabilitybythedecision-maker.

5.2. Sensitivityanalysisandupdating

Itisevidentthatsomecomponentsinasystemaremore impor-tantthananyother.Thesensitivityanalysisisaneffectivemethod toidentifythemostcriticalcomponentbychangingtheparameters ofdifferentcomponents.Inthisstudy,thesensitivityofselected componentswascarriedoutatacertainphaseinsteadoftheentire drillingcycle.Forexample,thefailureprobabilityofthenormal start(Pg)forrigpump(RP)ischangedtocalculatethesystem

reli-abilityofthedrillingprocess.Similarly,fivedifferentcomponents areselectedindifferentphasesforthesensitivityanalysis,andthe resultsareshowninFig.14.

Thesteepnessofthesloperepresentsthesensitivityof com-ponents. The higher the steepness is, the more sensitive the componentis.Thesensitivityalsoillustratestheimportanceand criticality of different components in the system. Asshown in

Fig.14(a),thesensitivityoftherigpump(RP)ishigherthanany othercomponent,whichindicatesthattherigpumpisthemost crucialfactorinthedrillingphase.Thedrillingprocesswouldbe forcedtoshutdownoncetherigpumpfails.FromFig.14,some con-clusionscanbededucedthatrigpump(RP),checkvalve1,RCD,and RParethemostsensitivecomponentsamongselectedcomponents fordifferentphases.Andthesensitivityofthesamecomponentin differentphasesisunequal.Forinstance,RCDisthemost sensi-tivecomponentintrippingout,whileinotherphases,itistheleast responsiveelement.Explanationsforitisthatthesame compo-nentplaysdifferentrolesindifferentphasesduetotheprinciples ofoperationandstructuralpositions.

AnotheradvantageofreliabilityassessmentusingDBNisthe capacitytoupdate reliabilityin real-time.For instance,when a

Fig.14.ComponentsimportantanalysisoftheMPDsystemfordifferentphases.

Fig.16.TraditionalmodelsofMPDsystemfailure.

newevidenceEisgiven,theupdatedreliabilityofsystemZcan becalculatedthroughR(Z|E).Thecommonlyusedevidencein probabilityupdatingistheinformationaboutthespecific conse-quence orevent.In thispaper,theMPDsystemtypicallyworks untildrillingto12_−1/4”section,buttheRCDneedstobereplaced duetoweariness.Otherwise,itmayshutdownasaresultofsealing failure.Therefore,thenewevidenceisthatanewRCDischanged whendrillingto1780m. AsshowninFig.15,thedynamic reli-ability oftheMPDsystemcanbeupdatedand predictedinthe remainingdrillingoperationbasedonthisevent.Thereliability oftheMPDsystemreturnsto1afterreplacingtheRCD. Further-more,theupdatedreliabilitydecreasesto0.9589whenthedrilling operationiscompleted.Itcanalsocapturesomenewobservations simultaneously,andthedynamicreliabilityoftheMPDsystemwill beupdatedatdifferenttimepoints.

5.3. Validationofthemodel

Validation is anecessary and essential aspectofa proposed methodasitwillprovideareasonableamountofconfidencetothe resultsofthemodelandproducetherequiredresultsinasound anddefensiblemanner(Jonesetal.,2010).Thevalidationofthe developedmodelrequiresthemonitoringrecordsofitsparameters. However,fortheMPDsystemthatweanalyzedinthispaper,these monitoringrecordsarenotavailable.Therefore,thevalidationin thisparticularstudyisconductedbyathree-axioms-based sensi-tivityanalysismethod(Caietal.,2013).Thefollowingthreeaxioms mustbesatisfied:Axiom1.Aslightincrease/decreaseintheprior subjectiveprobabilitiesofeachparentnodeshouldcertainlyresult intheeffectofarelativeincrease/decreaseoftheposterior proba-bilitiesofthechildnode;Axiom2.Giventhevariationofsubjective probabilitydistributionsofeachparentnode,itsinfluence magni-tudetothechildnodevaluesshouldkeepconsistency;Axiom3.

Thetotalinfluencemagnitudesofthecombinationofthe proba-bilityvariationsfromxattributes(evidence)onthevaluesshould alwaysbegreaterthantheonefromthesetofx-y(y∈x)attributes (sub-evidence).

Thevalidationofthedevelopedmodelaimstodemonstratethe constructedmodelwithrationalanalysis.Themodelshouldatleast satisfythethreeaxiomsdescribedinSection3.3.Takingthe par-entnodesof“S127”forexample,thesuccessfulprobabilityofa drillingprocessdecreasesfrom99.87%to79.89%whenthefailure probabilityof“S126”(Flowmeasurement)issetto80%.However, thesuccessfulprobabilitydecreasesfrom79.89%to49.93%when thefailureprobabilityof“S126”issetto50%.Whenthe“C127” (MudSeparator)offailureprobabilityissetto50%,itresultsin arevisedsuccessprobabilityof49.94%from99.87%.Theresult

indicatesthattheestablishedmodelaccordswithAxiom1and2. Furthermore,whenbothchangesandthefailureprobabilitiesof thetwonodesaresetto50%,thesuccessfulprobabilitydecreases to24.97%from99.87%.Theexerciseofincreasingfailure probabil-ityofeachinfluencingnodesatisfiesthethreeaxioms,thusgivinga partialvalidationoftheDBNmodelatitshighesthierarchicallevel. 5.4. Methodcomparison

Anearlystudywascarriedouttoevaluatethesafetyandrisk analysisofmanagedpressuredrillingoperations.Inthisstudy,a bow-tiemodelwasdevelopedtoidentifytherootcausesofkicksin anoffshoredrillingoperation.Inthebow-tiemodel,thekickevent isthecentralevent,culminatinginablowoutandotherescalated consequences.Asacriticalbarriertopreventingthekickevent,the faulttree(FT)modeloftheMPDsystemfailurewasdeveloped,as showninFig.16(a)(Abimbolaetal.,2015).Theobtainedfailure probabilityoftheMPDsystembasedontheFTmodelis1.0×10−4. However,theanalyticalresultscannotbeeasilyupdatedbytheFT techniquewhennewevidenceorobservationsaregiven.TheFT modelfortheMPDsystemismappedintotheBNmodel,asshown inFig.16(b).TheposteriorprobabilityoftheMPDsystemisupdated to1.23×10-3_{byassumingakickoccurrence.}

ComparedwithstaticBN,theproposedmethodisanintegrated framework. The dynamic reliability of theMPD systemcan be obtained,consideringthechangeoftheenvironmentaland opera-tionalconditionsofthesystem.ThereliabilityoftheMPDsystem wouldbedecreasedfrom99.98%to93.48%,whichmeansthatthe failureprobabilityoftheMPDsystemis2.0×10−4.Itisofthesame orderofmagnitudeasthatofAbimbolaetal.,1.0×10−4,which canalsovalidatetheproposedmethod(Abimbolaetal.,2015).The obtaineddynamic anddecreasingreliability oftheMPDsystem matchestheinherentpropertyofthesystem.Furthermore,the pro-posedmethodproducesamorerationalresultsincethesequence operations,phasedmissionproblems,andmultipleprocessesofthe MPDsystemareallconsidered.

6. Conclusions

reli-therearenouniformstandardsforthereliabilityleveloftheMPD system atpresent. The determination ofthe evaluation criteria mayprovideadirectivefunctionforthedecision-makerstomake therequireddecisions,sothiswillbepartofourfuturework.On theotherhand,thedetailedmaintenancestrategiesor decision-making should beconstructed based onthe reliability analysis results,whichcanimprovethereliabilityoftheMPDsystem.

DeclarationofCompetingInterest

Theauthorsdeclarethattheyhavenoknowncompeting finan-cialinterestsorpersonalrelationshipsthatcouldhaveappearedto influencetheworkreportedinthispaper.

Acknowledgment

The authors gratefully acknowledge the financial sup-port provided by National Key R&D Program of China (No: 2017YFC0804501),NationalNaturalScienceFoundationofChina (No.52004142)andPostgraduateInnovationEngineeringProject ofChinaUniversityofPetroleum(EastChina)(No:YCX2020057). AuthorFaisalKhanthankfullyacknowledgesthefinancialsupport providedbyNaturalScienceandEngineeringResearchCouncilof Canada (NSERC)and CanadaResearch ChairProgram(Tier I) of OffshoreSafetyandRiskEngineeringtostrengthentheresearch collaboration.

AppendixA

SeeFig.A1TablesA1–A3.

AppendixB

SeeTableB1.

TableA1

TheoperatorparametersofmakingaconnectionforMPDsystem.

Operator

Meaning Parameter Operator Meaning Parameter

No Type No Type

201 25 Initialtime R(1)=0R(t)=1(t=/ 1) 216 21 Chokeflowline1 P=3.6×10−4

202 21 Stoptopdrive P=3.0×10−4 _{217 25 Startsignalofchokevalve2 R(t)=0,t}=/(4,5)R(t)=1,t=(4,5) 203 21 Lifting P=1.0×10−4 _{218 26 Chokevalve2 Pp=2.5×10}−4_Pg=2.5×10−3 204 21 Adjustwellheadbackpressure P=1.0×10−4 _{219 22 ORgate /}

205 25 StartsignalofRCD R(2)=1R(t)=0(t=/ 2) 220 23 NOTgate /

206 26 RCD PP=6.7×10−6Pg=6.7×10−5 221 21 Chokeflowline2 P=3.6×10−4

207 25 Startsignalofrigpump R(3)=1R(t)=0(t=/ 2) 222 25 Startsignalofchokevalve3 R(t)=0,t=/(4,5)R(t)=1,t=(4,5) 208 26 Rigpump Pp=4.3×10−5Pg=4.3×10−4 223 26 Chokevalve3 Pp=2.5×10−4Pg=2.5×10−3

209 25 Timeinterval t=0.1h 224 23 NOTgate /

210 35 Failurerateofrigpump ␭=2.52×10−6_h−1 _{225 21 Pressurereliefvalve P=2.2×10}−5 211 25 Startsignalofbackpressurepump R(3)=1R(t)=0(t =/ 3) 226 21 Backupflowline3 P=3.6×10−4

212 26 Backpressurepump Pp=4.3×10−5Pg=4.3×10−4 227 25 Startsignalofchokevalve1 R(t)=0,t=/(4,5)R(t)=1,t=(4,5) 213 25 Timeinterval t=0.1h 228 26 Chokevalve1 Pp=2.5×10−4Pg=2.5×10−3 214 35 Failurerateofbackpressurepump ␭=2.52×10−6h−1 229 30 ANDgate /

215 21 Checkvalve1 P=3.12×10−3 _{230 21 Connect P=1.5×10}−4

TableA2

TheoperatorparametersoftrippingoutforMPDsystem. Operator

Meaning Parameter Operator Meaning Parameter

No Type No Type

301 25 Initialtime R(1)=0R(t)=1(t=/ 1) 318 22 ORgate / 302 21 Startsignaloftrippingoutsystem P=1.0×10−4 _{319 23 NOTgate /}

303 21 Adjustwellheadbackpressure P=1.0×10−4 _{320 21 Chokeflowline2 P=3.6×10}−4

304 25 StartsignalofRCD R(2)=1,R(t)=0(t =/ 2) 321 25 Startsignalofchokevalve3 R(t)=0,t=/(4,5)R(t)=1,t=(4,5) 305 26 RCD PP=6.7×10−6Pg=6.7×10−5 322 26 Chokevalve3 Pp=2.5×10−4Pg=2.5×10−3 306 25 Startsignalofrigpump R(3)=1R(t)=0(t=/ 3) 323 23 NOTgate /

307 26 Rigpump Pp=4.3×10−5Pg=4.3×10−4 324 21 Pressurereliefvalve P=2.2×10−5 308 25 Timeinterval t=8h 325 21 Backupflowline3 P=3.6×10−4

309 35 Failurerateofrigpump ␭=2.52×10−6_h−1 _{326 25 Startsignalofchokevalve1 R(t)=0,t}=/(4,5)R(t)=1,t=(4,5) 310 25 Startsignalofbackpressurepump R(3)=1R(t)=0(t =/ 3) 327 26 Chokevalve1 Pp=2.5×10−4Pg=2.5×10−3 311 26 Backpressurepump Pp=4.3×10−5Pg=4.3×10−4 328 30 ANDgate /

312 25 Timeinterval t=8h 329 21 Pulloutstringstocertaindepth P=3.5×10−4 313 35 Failurerateofbackpressurepump ␭=2.52×10−6h−1 330 21 Pumpintoweightedmud P=1.0×10−4 314 21 Checkvalve1 P=3.12×10−3 _{331 21 Continuetoliftthedrillingstrings P=3.0×10}−4 315 21 Chokeflowline1 P=3.6×10−4 _{332 21 Closeblindram P=2.6×10}−4 316 25 Startsignalofchokevalve2 R(t)=0,t=/(4,5)R(t)=1,t=(4,5) 333 21 Drillingtoolschange P=1.0×10−4 317 26 Chokevalve2 Pp=2.5×10−4Pg=2.5×10−3

TableA3

TheoperatorparametersoftrippinginforMPDsystem. Operator

Meaning Parameter Operator Meaning Parameter

No Type No Type

401 25 Initialtime R(1)=0R(t)=1(t=/ 1) 417 21 Checkvalve1 P=3.12×10−3 402 21 Startsignaloftrippinginsystem P=1.0×10−4 _{418 21 Chokeflowline1 P=3.6×10}−4

403 21 Openblindram P=2.6×10−4 419 25 Startsignalofchokevalve2 R(t)=0,t=/(4,5)R(t)=1,t=(4,5) 404 21 Runningstringstocertaindepth P=1.2×10−4 420 26 Chokevalve2 Pp=2.5×10−4Pg=2.5×10−3

405 21 Replaceweightedmud P=1.0×10−4 _{421 22 ORgate /}

406 21 Adjustwellheadbackpressure P=1.0×10−4 _{422 23 NOTgate /}

407 25 StartsignalofRCD R(2)=1,R(t)=0(t =/ 2) 423 21 Chokeflowline2 P=3.6×10−4

408 26 RCD PP=6.7×10−6Pg=6.7×10−5 424 25 Startsignalofchokevalve3 R(t)=0,t=/(4,5)R(t)=1,t=(4,5) 409 25 Startsignalofrigpump R(3)=1,R(t)=0(t =/ 3) 425 26 Chokevalve3 Pp=2.5×10−4Pg=2.5×10−3 410 26 Rigpump Pp=4.3×10−5Pg=4.3×10−4 426 23 NOTgate /

411 25 Timeinterval t=8h 427 21 Pressurereliefvalve P=2.2×10−5 412 35 Failurerateofrigpump ␭=2.52×10−6_h−1 _{428 21 Backupflowline3 P=3.6×10}−4

413 25 Startsignalofbackpressurepump R(3)=1,R(t)=0(t =/ 3) 429 25 Startsignalofchokevalve1 R(t)=0,t=/(4,5)R(t)=1,t=(4,5) 414 26 Backpressurepump Pp=4.3×10−5Pg=4.3×10−4 430 26 Chokevalve1 Pp=2.5×10−4Pg=2.5×10−3

415 25 Timeinterval t=8h 431 30 ANDgate /

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