Numerical assessment of the mechanical stability in vertical, directional and horizontal wellbores

ContentslistsavailableatScienceDirect

InternationalJournalofMiningScienceandTechnology

journalhomepage:www.elsevier.com/locate/ijmst

Numericalassessmentofthemechanicalstabilityinvertical,directional

andhorizontalwellbores

KamranGoshtasbia,,AyubElyasia,AliNaeimipourb

ab

DepartmentofMiningEngineering,TarbiatModaresUniversity,Tehran14115143,IranSchoolofEnergyandMineralEngineering,PennsylvaniaStateUniversity,PA16802,USA

articleinfoabstract

Inthisresearchthestabilityofwellboreisevaluatedinsevendifferentstressregimesanddiverseorien-tationsusingFLAC3Dsoftware.Thenormalizedyieldedzonearea(NYZA,i.e.,theratioofsurroundingyieldedcross-sectionalareatoinitialareaofwellbore)isdeterminedfordifferentmudpressuresaswellasdiverseorientationsofwellbore.BymeansofMATLABsoftwarethebestcurveisttedtotherecordedpointsandthentheoptimizedmudpressureiscalculatedusingtheseplots.Theoptimizedorientationisselectedconsideringthesedata.FinallythemudpressureresultedfromthismethodwascomparedwiththemudpressureobtainedfromtheMogi-Coulombcriterionandthenwiththeeldsdata.TheminimumallowablemudpressureobtainedfromtheNYZAcriterionisclosetoactualdataandthevalueobtainedfromtheMogi-Coulombcriterion.Hence,theNYZAisconsideredtobeanappropriatecriterionforwell-borestabilityanalysis.

2013PublishedbyElsevierB.V.onbehalfofChinaUniversityofMining&Technology.

Articlehistory:

Received4March2013

Receivedinrevisedform21April2013Accepted22May2013

Availableonline2December2013Keywords:NYZA

Mudpressure

OptimumorientationStressregime

1.Introduction

Wellborestabilityisoneofthecrucialissuesinoilandgasindustries.Theissuesrelatedtoinstabilityofwellbores,imposesignicantunwantedcostsondrillingoperation.Furthermore,ithasadeteriorateeffectonthetimescheduleoftheproject.Hence,inmanyoilcompanieswellborestabilityanalysisisoneofthema-joractivitiesinthewellboredesignstage[1].

Themostimportantconditionforstabilityofwellboreistokeepabalancebetweentheinducedin-situstressinthewellborewallandthesurroundingrockmassstrength.Ingeneral,theinstabilityinwellboreisthereactionofthesurroundingrockmassagainsttheinducedstressesasaresultofdrillingoperation.Ifthestrengthofrockmassismorethantheinducedstresses,thewellborewouldbestable,otherwisethesurroundingrockmasswouldyieldanden-hancetheprobabilityofoverbreakinthewellbore[2].

Oftenseveralfactorsareinvolvedintheinstabilityofwellbore.Thesefactorscouldbedividedintotwocategorieswhicharecon-trollableanduncontrollable(natural).Forinstancemudpressureandwellboreorientationareamongcontrollablefactors.Therefore,bycorrectdesigningofmudpressureforeachdesiredwellboredirection,thewellboreinstabilitywillbeminimized[3].

Optimizationofmudpressureisnecessaryforreductionoftheprobabilityofoverbreakinwellboreandotherpertinentissues

andalsotominimizethemudinvasionintothesurroundingfor-mation[4].Intheaggregate,drillingundermudpressurehigherthantheporepressurewillleadstolessinstabilityproblems.Thereasonisthatthedevelopmentofyieldedareainadjacentrockmassisreducedinthiscase[5].

Themostcommonandsimplestmodelforwellborestabilityanalysisisthelinearelasticmodel.Theimportantadvantageoflin-earelasticmodelemploymentisitslimitednumberofparameterstobedened[6].However,elastoplasticconstitutivemodelgivesmorerealisticresultsformechanicalstability.Itisbecausethismodelsimulatesthebehaviorofamediumafterreachingthecrit-icalstresslevel.Inotherwords,goingoverthecriticalstresslimitinthiscasedoesnotmeanthattherockmasshascompletelyfailed,separatedorcollapsed.Incontrast,itmeansthatthemed-iumiscapableofabsorbingmorestressesandacceptingmoredeformation[7].

Inthisresearchthecriteriaforassessingthewellboreinstabil-ity,isbasedonthedevelopmentofyielded(plastic)area.Thecri-terionwhichisoftenusedforindicationofwellboreinstabilityriskisthenormalizedyieldedzonearea(NYZA),whichisdividingthecross-sectionalareaofplasticzonetotheoriginalareaofthewellbore.Fromtheexperiencegained,theinstabilityoftenoccurswhentheamountofNYZAismorethanone[5].

Finally,ascasestudiesandverication,thewellborestabilityanalysiswascarriedoutintwowellboresintwoIranianoilelds.TheNYZAanalysisisthencomparedwiththeMogi-Coulombcrite-rionresultsandwiththeactualeldsdataaccordingly[8].

Correspondingauthor.Tel.:+982182883377.

E-mailaddress:goshtasb@modares.ac.ir(K.Goshtasbi).

2095-2686/$-seefrontmatter2013PublishedbyElsevierB.V.onbehalfofChinaUniversityofMining&Technology.http://dx.doi.org/10.1016/j.ijmst.2013.11.010

938K.Goshtasbietal./InternationalJournalofMiningScienceandTechnology23(2013)937–942

2.In-situstressesandgeomechanicalparametersoftherock

mass

ThegeomechanicalparametersusedtomodeltherockmassadjacenttothewellboreareshowninTable1.Moreover,thesevenin-situstressesusedinthisresearcharegiveninTable2[8,9].3.Stabilityanalysisusingnumericalmodeling3.1.Numericalmodels

Inthisresearchstudy,theFLAC3Dnumericalcodewhichisbasedonthenitedifferencemethodisutilizedinordertoanalyzethestabilityofwellbores.Thedimensionsofthegeneratedmodelsare400cm 400cm 800cm(Fig.1).Themodeledwellboresare32cmindiameter.

ThefailurecriteriaassumedintheseanalysesisMohr-Coulombandthein-situstressregimesconsideredarehydrostatic,normalfaulting(NF),strike-slipfaulting(SS),normal-strikeslipfaulting(NF-SS),reversefaulting(RF)andreverse-strikeslipfaulting(RF-SS).Furthermore,themodeledwellboreshavegotanangleof0,15,30,45,60,75and90degreerelativetohorizontalline(i)andthedirectionof0,30,60and90degreerelativetothemaximumhorizontalstress(a).Infact,threefactorsofinclination,directionofwellboreandin-situstressregimearesimultaneouslyconsid-eredingeneratedmodels.Altogether,1050numericalmodelsaregeneratedforthisresearchstudyconsideringthevariouswellboredirectionsandconsideringunderdifferentstressregimesandmudpressures.

3.2.Plasticzonearoundwellbore

Assumingthatthewellboreisdrilledinthedirectionofaprin-cipalin-situstress,twocasesareanticipatedforthewaythattheplasticzoneisdevelopedaroundthewellboreperiphery:(a)Symmetricaldevelopmentofplasticzone

Intheconditionwherethetwootherprincipalstresses,whichareperpendiculartothewellboreaxis,areequal,theplasticzonearoundthewellboreissymmetrical.Inotherwords,inthiscasethedisplacementsandtheradiioftheplasticzoneinthedirectionofthetwoequalin-situstressesareidentical.InFig.2thiscondi-tionisshownforNFstressregimewithisotropichorizontalstresses.

(b)Asymmetricaldevelopmentofplasticzone

Inthecasewheretheprincipalin-situstresses,perpendiculartothewellboreaxis,arenotequal,theshapeofplasticzonearoundthewellboreiselliptical.InFig.3thegeneratedplasticzonearoundthewellboreperipheryisshownforstrike-slipfaultingstressregimeandwellboredirectionalongthemeanin-situprin-cipalstress.Inthissituationthedisplacementsandradiiofplastic

Table1

Rockmassgeomechanicalparameters.Parameter

QuantityTensilestrength(T,MPa)1.5

Cohesion(C,MPa)

1.3Internalfrictionangle(u,°

)30Bulkmodulus(K,GPa)11.0Shearmodulus(G,GPa)8.7Young’smodulus(E,GPa)20.6Poisson’sratio(t)

0.1

zonearemoreinthedirectionofminimumin-situstressandtheinstabilityofwellborewouldcommenceinthisdirection.Hence,atthetimeofwellborecasingoperation,specialmeasuresshouldbetakenforthisdirection.Themoredifferencebetweenthetwoin-situstressesperpendiculartothewellboreaxisexists,themorediversityisobservedbetweentheamountsofdisplacementsandradiiofplasticzoneinthesetwostressdirections.

Inallstressregimesandorientationsofwellbore,byincreasingthemudpressurethedisplacementsanddevelopmentofplasticzonearereduced.Forinstance,inFig.4theplasticzonessurround-ingtheverticalwellboreindifferentmudpressuresareshownforNFstressregime.Asitcanbeobserved,byincreasingmudpressureinthiscase,theradiusofplasticzoneisdecreased.

Theoptimummudpressure(theminimummudpressureneededforwellborestability)isthepressureinwhichtheNYZAisequaltoone.Therefore,ineachmodelthevariationofNYZAindifferentmudpressuresarecalculatedandthenthebestcurveisttedtotheresultedpointsemployingMATLABsoftware.Asare-sult,theoptimummudpressureisaccuratelydeterminedusingthecurveformula.Forexample,inFig.5thevariationofNYZAver-susoverbalancemudpressure(mudpressure-porepressure)isillustratedforaparticularorientationandstressregime.

Asmentioned,withtheincreaseinmudpressure,theNYZAre-ducesandthereforethewellboregetsmorestable.Atthebegin-ning,theNYZAdecreaseswithahighratebutgraduallylowerrateofreductionisseen.Fig.5showsthevariationofNYZAversusoverbalancepressureforawellboredrilledwitha30degreeincli-nationanddirectionof60degreerelativetomaximumhorizontalstressinSSstressregime.

Havingtheoptimumpressureineachcase,itbecomespossibletoplotthegraphswhichshowtheminimumoverbalancepressureindifferentwellboreorientationsandforaspecicstressregime(Figs.6–12).Thentheoptimumtrajectoryofwellbore,theorienta-tionwiththelowestoverbalancepressure,isdeterminedbymeansoftheseplots.InFig.8,forinstance,awellborewithinclinationof15degreeandadirectionalongtheminimumhorizontalstresshastheoptimumorientationinNFstressregime.Itshouldbenotedthattheoptimumpressureistheminimumpressuretostabilizethewellboreandtheamountslowerthanthispressuremakesinstabilityinthewellboreverylikely.

3.3.Wellborestabilityanalysisinvariedstressregimes

Inthefollowingsections,theoptimummudpressureindiffer-entorientationsofwellboreanddiversein-situstressregimesisdetermined.Inallguresshowninthisresearch,themeaningofminimumoverbalancepressureistheoptimummudpressureminustheporepressure.

3.3.1.Hydrostaticstressregime

Ingeneral,inhydrostaticstressregimetheamountofoptimummudpressuresforvariedinclinationsanddirectionsofwellborearenotsignicantlydifferent.However,themaximumoptimummudpressureisobservedinwellboreswithinclinationof45de-gree.Moreover,theoptimummudpressuresineachspecicincli-nationforwellboresdrilledinthedirectionofrHandrh,whicharebothequal,arethesame.Thisfactisalsotrueaboutthewellboreswith30and60degreedirectionsfromthehorizontalstresses.Gen-

erally,inequalinclinationsthewellboresdrilledinthe30and60degreedirectionsfromrHhavegotrelativelylessoptimummudpressurethanthewellboresinthedirectionofhorizontalstresses(Fig.6).

3.3.2.NFstressregimewithisotropichorizontalstresses

InNFstressregimewithisotropichorizontalstresses,byincreasingthewellboreinclinationthewellboregetsmorestable.

K.Goshtasbietal./InternationalJournalofMiningScienceandTechnology23(2013)937–942

Table2

Sevenin-situstressregimesusedinmodeling(MPa).Stressregime

VerticalstressrvMaximumhorizontalstressrHMinimumhorizontalstressrh939

PorepressureHydrostatic54.054.0NF

69.055.2NFwithisotropichorizontalstresses58.844.1SS41.450.5NF-SS44.4.6RF49.160.7SS-RF

49.1

60.7

800cm400cm

mc004

Fig.1.Generalschemeofgeneratedmodels.

None

Shear-nshear-p

Shear-nshear-ptension-pShear-p

Shear-ptension-p

Fig.2.PlasticzonearoundtheverticalwellboreinNFstressregimewithisotropichorizontalstresses.

None

Shear-nshear-p

Shear-nshear-ptension-pShear-p

Shear-ptension-p

Fig.3.PlasticzonearoundtheverticalwellboreinSSstressregime.

Generally,inthisstressregimeandinsimilarwellboreinclinations,theresultedamountsofoptimummudpressuresarenotvariedfordifferentwellboredirections.IneachinclinationtheoptimummudpressureisidenticalforwellboreswithdirectionofrHandrh.Thisfactisalsotrueaboutthewellboreswith30and60degreedirec-tionsfromthehorizontalstresses.Forinclinationsapproximatelylessthan45degree,thewellboreswithdirectionsof30and60de-greefromrHhavelessoptimummudpressurecomparedtowellb-oreswiththesamedirectionsashorizontalstresses.Theoptimummudpressureisthesameforalldirectionsofwellboreswith

54.024.848.331.744.126.536.018.636.323.754.024.849.6

24.8

inclinationmorethan45degree.Inthisstressregimetheleastoptimummudpressureisforverticalwellboreandthehighest

optimummudpressureisforhorizontalwellboresalongthehori-zontalstresses(Fig.7).

3.3.3.NFstressregime

Byincreaseofwellboredeviationfrommaximumhorizontal

stressinNFstressregime,theoptimummudpressuredecreases.Hence,inthesameinclinationsofwellbore,thedirectionofmini-mumhorizontalstressisthemoststableandthedirectionofmax-imumhorizontalstressisthemostunstabledirection.Indirectionsotherthanthedirectionofrh,byincreaseofangleofwellboreinclination,thewellboregetsmorestableandtheoptimummudpressurereduces.Therefore,themaximumoptimummudpressureisneededforthewellboredrilledhorizontallyalongrH(Fig.8).Whenthewellboreisindirectionofrh,atthebeginningtheoptimummudpressuredecreasesbyincreaseofwellboreinclina-tionbutthenstartstoincreaseandthusthehorizontaldrillingis

nottheoptimumdrillingtrajectoryinthisstresscondition.Inthiscase,theleastoptimummudpressureisrelatedtoawellborewithaninclinationof15degreeandparallelto

rh

(Fig.8).

3.3.4.SSstressregime

ConsideringSSstressregime,byincreasingthewellboreincli-nationitgetsmoreunstableandthusmoremudpressureisneeded.Insimilarinclinations,thewellboredrilledparalleltorHdirectionhastheminimumoptimummudpressure.Deviationofwellborefromthisdirectionleadstolessstabilityandmorere-quiredmudpressure.Inthisstressregime,theleastoptimummudpressureisneededforthehorizontalwellborealongrH.Hence,thisisthemostfavorabletrajectoryforwellboredrilling(Fig.9).

Forwellboresdrilledalong

rh,the

mudpressurevariationrate

islessthanotherdirections(Fig.9).

3.3.5.NF-SSstressregime

Inthisstresscondition,theverticalandmaximumhorizontalstressesareequal.ThedifferencebetweenthisstressregimeandNFregimeisthatinthiscase,themeanprinciplestressisequaltothemaximumprinciplestress.Ingeneral,inalldirections,thehorizontalwellboresarethemoststable(Fig.10).WellboresdrilledinthedirectionofrhshowthehigheststabilityandtheothersboredalongrHaretheleaststable.Hence,byconsideringequaldirections,wellboresalongrhdirectionrequiretheminimumopti-mummudpressure.Optimummudpressuresinwellboresparalleltorhandalsodeviated30degreefromthisdirection,showmoresensitivetothevariationofwellboreinclination.Incontrast,lessimpactionisobservedaboutwellboresdeviating60and90degreefromtheminimumprinciplestress.Inthisstresscondition,theoptimumtrajectoryisalongrhinhorizontalplane(Fig.10).3.3.6.RFstressregime

InRFstressregime,byincreaseofwellboreinclination,moremudpressureisneededforwellboresindirectionsotherthanrh.

940K.Goshtasbietal./InternationalJournalofMiningScienceandTechnology23(2013)937–942

(a)Overbalancepressure=0(b)Overbalancepressure=2MPa(c)Overbalancepressure=4MPa

None

Shear-nshear-pShear-p

(d)Overbalancepressure=6MPa

(e)Overbalancepressure=8MPa

Fig.4.PlasticzonesurroundingaverticalwellboreinvarietyofmudpressureinNFstressregime.

54A3ZYN210

1

34678Overbalancepressure(MPa)

10

)

a8.97PM

(8.28eru7.59sser6.90pecn6.21ala

b5.52rev

O4.83

α=0°α=30°α=60°α=90°

015

30456075

Boreholeinclination(°)

90

Fig.5.VariationofNYZAforawellborewiththeinclinationof30degreeand

directionof60degreetothemaximumhorizontalstressversusthemudpressureinSSstressregime.

Fig.8.MinimumoverbalancepressureasafunctionofboreholetrajectoryinNFstressregime.

)

a4.97PM

(4.93eru

s4.90serpe4.86cnalab4.83rev

O4.79

0

15

α=0°α=30°α=60°α=90°

30456075Boreholeinclination(°)

90

)a5.52

PM(5.17eru4.83sser4.48pecn4.14ala

b3.79rev

O3.45

α=0°α=30°α=60°α=90°

0

15

30

45

60

75

90

Fig.6.Minimumoverbalancepressureasafunctionofboreholetrajectoryin

hydrostaticstressregime.

Boreholeinclination(°)

Fig.9.MinimumoverbalancepressureasafunctionofboreholetrajectoryinSS

stressregime.

4.90)a

P4.76M

(4.62eru4.48sser

p4.34e

c4.21nala4.07bre

v3.93O

3.79

α=0°α=30°α=60°α=90°

015

30456075Boreholeinclination(°)

90

)

a3.45PM(er3.10usser

p2.76ecnal2.41abrev

O2.07

0

α=0°α=30°α=60°α=90°

15

30456075

Boreholeinclination(°)

90

Fig.7.MinimumoverbalancepressureasafunctionofboreholetrajectoryinNF

stressregimewithisotropichorizontalstress.

Fig.10.MinimumoverbalancepressureasafunctionofboreholetrajectoryinNF-SSstressregime.

K.Goshtasbietal./InternationalJournalofMiningScienceandTechnology23(2013)937–942941

)a5.86

PM(5.52erusse5.17rp

e4.83cnala4.48brev

O4.14

Table4ComparisonofactualdrillingandcalculatedmudpressuresfromNYZAandtheMogi-Coulombcriteriaforwells32and54(MPa).Well

Actual25.0

6.8

Mogi-Coulomb22.97.0

NYZA21.36.5

α=0°α=30°α=60°α=90°

0

15

30

45

60

75

90

32

54

AccordingtoFigs.6–12,theoptimumdrillingtrajectory(thestableorientationofwellborewiththeleastoptimummudpres-sure)withregardtothestressregimes,asmentionedinTable2,issummarizedinTable3.4.Casestudiesandverication

Boreholeinclination(°)

Fig.11.MinimumoverbalancepressureasafunctionofboreholetrajectoryinRF

stressregime.

)5.52aPM(5.17eruss4.83erpec4.48nala4.14brev

O3.79

Ascasestudies,thewellborestabilityanalysiswascarriedoutintwowellbores(well54fromeld1andwell32fromeld2).Thedominantrocksinbothwellboresconsistoflimestonehaving

α=0°α=30°α=60°α=90°

0

15

30456075Boreholeinclination(°)

90

differentproperties.Theconcerneddepthswherethecollapseis

probableinwellbores32and54are28and3485m,respec-tively.Moreover,intheabovementioneddepthstheporepres-suresare11and30MPa,respectively,forwellbores32and54.

Rockmasspropertiesandin-situstressesinelds1and2arepresentedinTable3.

Theactualdrillingmudpressureandthecalculatedmudpres-suresusingtheMogi-CoulombandNYZAcriteriaarepresentedinTable4.TheresultsshowthatthemudpressurecalculatedfromNYZAmethodisveryclosetotheactualdrillingandtheMogi-Cou-lombmudpressures.ItisknownthattheMogi-Coulombcanaccu-ratelyestimatethefailureofvariedrockmasses[10].Hence,itcanbeconcludedthattheNYZAcriterioncanprovideagoodestimateofmudpressureneededforwellboredrilling.5.Conclusions

Accordingtotheobtainedresults,itcanbeconcludedthat:TheNYZAcriterioncanprovideagoodestimateofmudpres-sureneededforwellboredrilling.

Incaseswherethewellboreisdrilledinthedirectionofaprin-ciplestress,ifthetwootherprinciplestressesareequal,thentheplasticzoneanddistributionofdisplacementaresymmetricalaroundthewellbore.Otherwise,theamountofdisplacementsandinstabilitiesaremoresignicantinthedirectionofthemini-mumprincipalstress.

Inidenticalhorizontalstressessituation,thevariationofwell-boredirectiondoesnotaffectthewellborestabilityconsiderably.

InNFstressregimewithisotropichorizontalstresses,theleastcollapseprobabilityisfortheverticalwellbore.However,incon-ventionalconditions,thehorizontalstressesareanisotropicandhencetheoptimumwellboretrajectoryisalongrhwith15degreeinclination.

InNFstressregimewithisotropichorizontalstressesinallwell-boredirections,inNFstressregime(withanisotropichorizontalstresses)inwellboredirectionsof0,30and60degreefromrHandinRFstressregimeinwellboresalongboreinclinationtheinstabilitydecreases.

Fig.12.MinimumoverbalancepressureasafunctionofboreholetrajectoryinSS-RFstressregime.

Forwellboresinthedirectionofrh,theincreaseofwellboreincli-nationleadstolessoptimummudpressure.Therefore,inthisstressconditionwithanisotropichorizontalstresses,theoptimumdrillinginclinationchangesbetweenhorizontalandverticalandiscontingentonthedirectionofthewellbore.Indirectionparallelto

rh,verticalneartorH,

wellboreisthemoststableconditionandfordirectionshorizontaldirectionistheoptimumtrajectory.Consid-

eringthesameinclinations,thewellboredinrHdirectionhastheleastmudpressure.Bydeviatingfromthisdirection,thestabilityofwellboredecreasesandthusmoremudpressureisneeded.Inthisstressregime,theminimummudpressureisrequiredforhorizon-talwellboredalong(Fig.11).

r

H

andthereforeitistheoptimumtrajectory

Theleastvariationofoptimummudpressureversuswellboreinclinationisforthewellboresinthedirectionofrh(Fig.11).

3.3.7.SS-RFstressregime

Inwellboresdrilledindirectionof0,30and60degreefromrH,theincreaseofwellboreinclination,increasestheneededmudpressure.However,inthecaseofthewellboredinthedirectionofrh,byincreaseofinclination,theoptimummudpressurede-creasesatthebeginningandthenincreasesagain.Italsoshouldbehighlightedthatthevariationofmudpressureisnotsignicantinthiscase(Fig.12).

Forthesameinclinations,drillinginthedirectionofrHisthemostfavorablecondition.Gradually,thedeviationofwellboredirectionfromthispositionmakesthewellboreunstable.Inthisstresscondition,theoptimumtrajectoryisforahorizontalwell-borewithadirectionalong

rh,by

increaseofwell-

InNFandNF-SSstressregimes,thewellboredrilledinthedirectionofrhandinSS,RFandSS-RFstressregimes,thewellboredinthedirectionof

rH(Fig.

12).

r

H,havethemoststablecondition.

Table3Rockmasspropertiesandin-situstressesinwells32and54.Well3254

rc(MPa)

1816

t

0.330.25

E(GPa)10.58.5

C(MPa)3.74.0

u(°)

41.535.0

rv(MPa)

7284

rH(MPa)

4882

rh(MPa)

4378

942K.Goshtasbietal./InternationalJournalofMiningScienceandTechnology23(2013)937–942

InSS,RFandSS-RFstressregimes,variationofwellboredirec-tionintheplaneperpendiculartothemaximumin-situstress

(i.e.,r2,r3),hasatrivialimpactonthewellborestability.

ThemoststablewellboretrajectoryinNFstressregimeisobli-queandhasa15degreeinclination.However,inNFstressregimewithisotropichorizontalstresses,theoptimumorientationisver-ticalandinotherstressregimesexcepthydrostatic,thisinclinationishorizontal.Inhydrostaticstressregime,thevariationofinclina-tiondoesnotaffectthestabilityconsiderably.

TheincreaseofrH/rhcausesthewellboreoptimumorientationtoapproachrHdirection.Incaseofdrillingthewellboreinrhdirection,theoptimuminclinationchangesgraduallyfromverticaltohorizontalbydecreasingthemeanprinciplestresstowardtheminimumprinciplestress.However,inothercases,wellborewithdirectionsotherthanrh,byincreaseofstressfromthemeanprin-ciplestresstowardthemaximumprinciplestress,theoptimumwellboreinclinationchangesgraduallyfromverticaltohorizontal.Ingeneral,inallin-situstressregimes,theorientationexactlyornearlyparalleltothemaximumin-situstress,isthefavorabletrajectory.

Byincreasingofinclination,theimpactofdirectionislessenedandthedifferencebetweenminimumandmaximumoptimummudpressureinvarieddirectionsisdecreased.Inotherwords,allcurvesineachstressregimeconvergetojustoneparticularpressureinverticalcondition.

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