IADC_SPE_19941_MRMcLean and MAAddis_BP_Wellbore Stability Analysis_A Review of Current Methods ofAnalysis and Their Field Application

twohorizontalstresses,%x the maximumhorizontal stress, and ~~ the minimum horizontal stress, wh%hare generallyunequal.. The redistributed stresses are normally refereedto as the hoop str

.

lADC/SPE

lADC/SPE 19941

Wellbore Stability Analysis: A Review of Current Methods of

Analysis and Their Field Application

M,R McLean and M.A Addis,* British Petroleum

●SPE Member

Copyright 1990, IADWSPE Drilllng Conference.

This paper was prepared for presentation at the 1S90 IADCLSPE Drilling Conference held In Hou$lon, Texaa, February 27-March 2, 1SS0.

Tfria paper was selected for presentation by an lADC/SPE Program Committee following review of information containad in an abatracr submitted by tha author@ Contents of the fwef, ss PfeWntedt have not been reviewed by the Wfefy Of petroleum Engineers or the International wathn of Drilling Contr=tom and are 8Ublect to rxrrsdkm by the auffror(sl The material, as presented, does not rreceesarlly reflect any position of the IADC or SPE, ita Oftioera, or members Papers presented at lAfXKiPE meetings are subjeot to publication review by Editorial Grnmittees of the IAOC and SPE Permission to 00PY la restrloted to an abstract of not more than 300 words Illuatratlona may not be copied The abafracf should corrfaln oons@ououa@now&dgment of where and by w.iwrnthe paper is presented Write Publiitkms Manager, SPE, P.O S0s S23S3S,Ffiidaon, TX 7WSNfJXt Telex, 720WS SPEDAL.

reeultingfrom pore fluid migration(e.g Detournay& Hole pmblemeduring the drillingphase of operations Cheng[1])are not consideredeither

are often the consequence of mechanical wellbore

instability.Thieleadsto higherthannecessarydrilling A numberof publicationson the subjectof mechanical costs A numberof analyticalandnumericalmodelsare wellborestabilitycan be found in the Iitera-, how-available for the diagnosisand predictionof wellbore ever,only a fewactuallyattemptto predictthe stability instability thispaperreviewsthe meritsandpitfalleof of a field case Most workers concentrateon speci6c applyingthese modelsto fie~dsituations Attintion is aspectsof an analysis,e.g.in-situstressdetemnination, fixused on the peak-strengthcriterionand constitutive stressconcentrationsarounda borehole,rock mechan-behaviourmodel Anomaliesfkomthe incorporationof ical properties etc., This paper reviews some of the the intermediateprincipal stress into Peak-strea elementewhich go into the developmentof a wellbore criteriaare highlighted To illustratethe reliabilityof stabilitymodel,and appliesthe modelto a field case

a numberofmodels,theirpredictionsarecomparedwith

laboratoryresuk.e,andwitba casehistmyofahorizontal The two main elementsrequiredin a wellborestability well drilledin the CyrusField in the NorthSea model are the failure criterion and the constitutive

behaviourmodel A numberof previouslyused criteria andbehaviourmodeisarereviewed,andtheirsuitability

analysisof a horizontalwelldrilIedin1988 k the Cyrus

duringtheplanningstageof a fieldarisesfmmeconomic linear-elasticanalysis and a Finite Element Method considerations and the escalating use of deviated, (FEM) analysisusing a constitutivemodel considered extendedreach and horizontalwells Wellboreinsta- more representativeof the reservoir rock The well bility can result in lost circulation(Figure la) where responseduringdrillingindicatedthat the predictions tensile failure has occurred,and epallingand/or hole of the FEM were significantlymore accuratethan the closure(IYguraIb)in thecaseof compressivefailure In linear-elasticanalysis

severecases the hole instabilitycan lead to stuck pipe

and eventuallyloss of the openhole section The causes

of instabilityare often classifiedinto eitherchemicalor 2.0 BACKGROUND TO WELLBORE STAEILITY mechanicaleffects Often,fieldinstancesof instability MODELLING

are a result of a combination of both chemical and

mechanicalefkts However,only the mechanical Before a well is drilled, compressive stresses exist

withinthe rock formations(Figure2) The stressescan Referencesand illustrationsatend of paper beresolvedintoa verticalor overburdenstress,~, and

m4

ml

.

twohorizontalstresses,%x (the maximumhorizontal

stress), and ~~ (the minimum horizontal stress),

wh%hare generallyunequal When the well is drilled,

the rock stresses in the vicinity of the wellbore are

redistributedas the support originallyoffered by the

drilledout rockis replacedby the hydraulicpressureof

the mud The redistributed stresses are normally

refereedto as the hoop stress, OWwhich acts

circum-ferentiallyaroundthe wellborewall, the radial stress,

a,, and the axkd stress, q, which acts parallel to the

wellbore axis (see Figure 6 for stress state within a

hollowcylinder) In deviatedwellsan additionalshear

component,%*,is generated

If the redistributed stress state exceeds the rock

strength,either in tensionor compression,then

insta-bility may result (Figure 1) In order to evaluatethe

potentialfor wellbore stabilitya realistic constitutive

model must be used to compute the stresses and/or

strainsaroundthewellbore.Thecomputedstressesand

strainsmust then be comparedagainsta given failure

miterion

3.0 WHICH STRENGTH CRITERION?

In a purely elastic analysisthe stresses are compared

against a peak-strengthcriterionnormally definedin

terms of the principal stresses In an elasto-plastic

analysis,plastic strainsare developedonce the stress

state reaches a yield criterion,which in the case of

Perfbct-plasticitycoincideswith the

peak-strengthcri-terion

An elasto-plasticanalysisof wellborestabilityis more

realisticthana simpleelasticanalysis,sincerocksrarely

behaveina purelyelasticmannerupto ultimateftilure

However,specifyingthe allowableextentof the plastic

deformationbefore instability occurs, is difiicult and

somewhatarbitrary(e.g.Antheuniset al [21)

Incaseswherewelldefinedrockpropertiesareobtained

from laboratory testing of core, more sophisticated

numerical unalyses incorporating non-linear

aniso-tropicmaterielbehaviourmaybe performedto evaluate

wellborestability(e.g.Morita& Gray[3]) However,in

the majorityof cases,the poor definitionof

inputpara-meters (in-situ stressesand strengths)onlyjustifies a

simple elastic annlysis at best In these cases, rock

fdure is determinedusing a peak-strengthcriterion

The peek-strergthcriterioncanbe determineddirectly

ihmlaboratorytesting (ifcoreis available)orfkomback

analysis of hole conditionsrecorded from caliper and

dIWing logs (bearing in mind that this assumes a

knowledgeof the in-situ stresses,and the likely stress

concentmtiona-roundthe hole)

A numberof different strengthcriteria are commonly

used to predict the onset of rock fhilureand wellbore instability These criteria fall into one of the four categories(A,B,C& D) shownin Table 1

Examplesofpublicationswhichusethetiteriafkom the differentcategoriesarw

CategoryA- Woodland[71,Fuh et al [81 CategoryB - Mitihell et al [91,Hsaio [101,~~ &

Chenevert[11], Gnirk[121 CategoV C - Bradley[131,Hottmanet d [141,

Nakkenet al [151,Marsdenet d [161 CategoryD - Santarelli[171,Kwakwaet al [M]

3.1 Effect of the Intermediate Stress The question of whether the intermediate principal stressshouldor shouldnotbe incorporatedintoa failure criterionis an old one,andone whichis stillapparently unresolved,as witnessedby the continuinginvestiga-tionson the subject

Theintemnediateprincipal.stresswouldappearto have some effect on rock strength as seen in true triaxisl testing(e.g.Mogi[191andTakahashi&Koide[201).me variation of strengthwith the intermediateprincipal stressfoundby Takahashi& Koidewasinvestigatedfor

a numberof rock types In the case of the Yamaguchi marble,02had thegreatist influencewhereaa=20MPa and ~1>62= 803 Forthis stress shti the

pnncipalstressatfailurowasapproximatelyti%higher than the standardtriaxial test strengthfor the same valueof a~ Theinfluenceof aaon the strengthwasless markedfor theotherrockstested,whichincludedthree

sandstonesand a shale The resultsfrom Mogi’s tests

showeda2 had a similarinfluenceon strength From references[19) and [X)] it is reasonableto expectthat the compressivestrengthof a rock sampletested biax-ially(wherecq=craand c@) is unlikelyto be morethan twiceits uniaxialstrength(i.e al > ug=o#N

From the above discussion,it is informativeto check various strengthcriteria against the two stress paths (i.e uniaxialand biaxial) For strengthcriteriawhich fdl into CategoriesB & D, Table 1, the uniaxiaIand biaxial stxt qth are the same For criteriawhich fd intoCategmtisA & C thedifferenceis oftenextreme,as shownin I?Sgure3, whichpresentsstrengthdata for a Gebdykesdolomitetested by Santarelii[17] The data

hasbeen convertedfkoma al - cr~strw.ssspaceto a ~-q~

stress space (as used in references[13] & [14), where

~ and a, are definedas

Boththeuniaxialandbiaxialstresspathsareplottedin

. .

t

envelope exists outside the range of the experimental

data However,ihm extrapolationthepkicted biaxial

strength is likely to be around 6 times the uniaxial

strength, which appears excessivein the light of the

previousdiscussion

Nakkenet al [16] and Marsdenet al [16] expresstheir

critefiain termsof theq-pstressspaceas usedin critical

statesoilmechanics.Thesestressinvariant aredefined

I as

For standardtriaxialtesting(whereaz=cr$)the general

form ofp can be expressedas

1

Figures4 and 6 show the strengthcriteriagivenin q-p

spaceforclaystonestestedby Nakkenetal andMarsden

et al (NotzxTheseplotsareactuallyin termsof themean

e~ctive pressure,p’, sincesomeof thetestswerecarried

out withnon-zero”porepressures).Forthis stressspace,

the predicted biaxial strengthsin Figures 4 & 5 are

approximately10 and 20 times the uniaxialstrengths,

respectively

The majorproblemwithmanyof the criteriawhichfdl

intoCategoriesA&C, Table 1,arethattheygivefar too

greata signMcanceto theinfluenceof 6Zonthestrength

of fictional materialsthanis indicatedby true triaxial

tasting Mogi [19] showedthat if 62was to be incorp

rated into a ftilure criterion for cornpetantrock, then

the ‘mean’ stress term, p, should be adapted to the

equationgivenbelow

1

where the factor n typicallytakes on values of around

0.1.GreenandBishop[211arrivedat similarconclusions

based on experimentsperformedon sands

Despila Mogi’s work and the irreconcilableMerences

between the predicteduniaxial and biaxial strengths,

researcherscontinueusing strengthcriteriadefied in

termsofq-p and t~-a~

It is our conclusionthat a strengthcriterionexpressed

in terms of U1and us is adequati for the purposesof

wellborestability, Althoughthe intermediateprincipal

stress may have some influence, the et%wtis small

relativetetheaccuracytowhichdown-holestrengthand

in-situstressbscan be determined

8.2 Linear or Non-Linear?

Restrictingour attentionto fiiilurecriteriagroupedin CategoriesB&D, Table 1,we nowconsiderthequestion

of whethera linear or non-linearstrengthcriterionis required A numberof researchersgo to somelengthto fit anon-linearcriterionto triaxialtestdata earnedout overa widerangeof con!iningpressures.Kwakwaet al [18] back-analysefield conditionsto produce a Hoek-Brown failure criterionwhich is plotted for minimum principal stressesup to 10,000 psi (70 MPa) This is warrantedwhen the minimumprincipalstress vanes considerablythroughouttheregionofinterest.Inelastic analysesofwellborestabilityweareconcernedoniywith the stateof stressat the wellborewall(in somespecific cases, e.g underbalance drilling, it may also be necessarytolookat pointsjust ineidethewellborewall)

In the case of a wellbore,the minimumeffbctivestress

is invariably the overbalancepressure (well pressure less formationpressure),and is generallyin the region

of 0-1,000psi (O-7MPa) In extremecasesthe overbal-ancepressuremaybe as high as 2,oOOpsi (14 MPa).As such, there is no requirementto adapt criteria to fit peak-strengthdataforconfiningpressuresgreaterthan 2,000 psi (14 MPa) Overthis smallrangeof cofining

pressures a linear failure criterion is more than

adequatafor all but the weakestformations

In conclusion,we considerthata linearfhilurecriterion which incorporatesonly the maximumand minimum principal stresses (i.e Mohr-Coulomb)is the most applicablein a wellborestabilityanalysis.Forveryweak formations(uniaxial strength less than 1,600 psi (10 MPa)) a non-linear criterion may be justified Any allowancefor the effbct of the intermediateprincipal stress can result in gross overpredictionaof strength (depen&ngon the stress path) and shouldbe checked thoroughly

4.0 WHICH CONSTITUTIVE MODEL?

There are many publishedconstitutivemodelsused to determinethe stress state arounda wellbore It is not reasonableto list them all, thus, only those considered the most indicativeare discussedhere Table 2 sum-marisesthesemodels Themodelsassumehomogeneity andisotropyunless stated

Givena strengthcriterionexpressedin termsof 61and

us, it is known ffom laboratory testing that small diameterboreholesin rock (usuallyaround1“ dia.) are far strongerthan predictedby a linear-elasticanalysis (e.g.SantareW[171,Guenot[271).Itisgenerallythought that wellbores are also stronger than predicted by linear-elasticity.Fewpublications,however,havemade thecomparisonbetweenthepredictedresponseofawell, based on laboratory determinedrock properties,and actualresponseduringdrilling Oneexample,although

inconclusive,is presentedby Kleinand McLean [26].

28

4 WELLBORESTABILI’IYANALYSIS A REVIE

In the caseof laboratoryscalewellbores,references[171

and [27] show that a variety of hollow cylinder rock

samples,tested under conditionsdetailedin Figure 6,

start to f~ at outir pressuresof between2 to 8 times

the failurepressurepredictedby linear-elasticityand a

CategoryB or D criterion(Table l) Wherethe failure

criterionis definsdin either a q-p or z=-crd space, the

predictedstrengthof thehollowcylinders oftengreater

than the true strength For examplethe stress path

followed at the internal wall of the hollow cylinder

depicted in Figure 6 is plotted in Figure 3 for the

Gebdykesdolomite.Itcanbe shownthattheintersection

point betweenthe feilure criterionand the stresspath

is predicted when the pressure applied to the hollow

cylinderis around130MPa(18,600psi) Actualhollow

cylindersof this rock testedby Santarelli[171suffered

int8rnalwall ftilure at an outer pressure of 52 MPa

(7,500 psi) In certaincases a z~-cr@criterionused in

associationwith a linear-elasticconstitutivemodelcan

give accuratepredictionsof hollowcylinderftilure, an

exampleofwhichis givenbyVeekenetal[2S]).However,

as inferred by the authors, this is likely to be pure

coincidence,ratherthan soundmodelling

Armed with the knowledgethat the use of

linear-elas-ticity underpredictshole stability(usingCategoryB &

D type criteria)the mainthrustin analysisis to utilise

modelswhichareless conservativein theirpredictions

To this end plasticityoffers an obvious,and commonly

used,behaviourforimprovingpredictions.Westergaard

[241 was one of the first to utilise an elasto-plastic

approachto the analysisof a wellbow, the post yield

behaviourbeingmodelledusingperf’plasticity More

recent models still use perf6c&plasticitydue to its

modellingsimplicity(e.g Mitchell& Goodman[9], and

Bratli& Risnes[29]) However,rocksare rarelyableto

sustain large amounts of permanent deformation

withouta changein strength,particularlyat the

rela-tively low values of minimum effiwtive stress, 69’,

encounteredat the wall of a wellbore Also, somelimit

to the amount of permanent deformation must be

assigned,whichis often arbitraryin nature In effect,

a borehole can have any strengththe analyst desires

dependingon the chosenaUowabZeplasticdeformation.

More realistic attempta to model plastic behaviour

aroundboreholesby incorporatingboth

strain-harden-ing and strain-softenstrain-harden-ingare made by a number of

researched, notablyMorita & Gray [3] and Veeken et

al [2S] Morita and Gray only presentadan analysis,

whileVeekenet d wentone stepfbrtherand compared

theirpredictionsagainsthollowcylindertestsfor which

they found good agreement However, they used a

Drucker-Prager criterion (scribed within the

Mohr-Coulombequivalent)and theplasticdetbrmation

at which f~ure ia deemedta occuris somewhatarbib

rary The use of strain-softeningbehaviouris alsoopen

to criticism,einceitis normallyaseociatedwithlocalised

deformationofuniaxial andtriaxialsamples,whereasa

.

homogeneousdeformationis assumedin the develop ment of the constitutivemodel Despitethis, strength

degradation undoubtedly occurs with continued

permanent deformation and the modelling of strain-softeningshould not be ruled out altogether Perhapsthe biggest problemassociatedwith an elas-to-plasticmodel incorporatingstrain-softening,is the robustnessof thealgorithm.Numericalinstabilitiescan

be generated within the computations,which lead to non-uniquenessof theresulte,ornon-convergencein the algorithm

A rigid-plasticconstitutivemodelhasbeenincorporated extensivelyin a bifiwcationanalysisof boreholefdure (e.g.[261,[301& [311).Themodelassumesthatallshear strainis permanent,whichis acceptableprovidingthe materialdoes not attemptto unload elastically This constitutivemodelcoupledwithbifurcationanalysishas been used in the abovereferencesto provideextremely accurate predictions of hollow cylinder fdure The model,althoughsomewhatcomplex,has the advantage

of only requiring uniaxial test data for defining the constitutivebehaviour(seeFigure7) However,itwould

be instructive to compare its predictions of triaxial responseagainsttest data to assesswhetherthe model

is truelyrepresentativeof rockbehaviourovertherange

of rehvant stress states Providingtriaxialdata sup-portsthe constitutivemodelthenit wouldappearto be the most powe#ul predictivemodelpublishedto date

4.1 Recent Developments Santarelli[17], amongstothers,noted that the elastic modulus for rocks determinedfkom uniaxialhriaxial testingincreasedwithconhingpressure (e.g.Figure8) The rate of increase is particularly marked at low confiningpressure He incorporate the variation of elastic moduluswith confiningpressureinto a consti-tutive behaviour model assuming a power law

rela-tionship between the secant modulus, E,, and the

minimumprincipalstress,Og,givenby

where E is the uniaxial modulus and A and b are

The minimumprincipaleffectivestress,cJ8’,is assumed when non-zero pore pressures are presenk where effbctivestressis definedbytotalstressminusporefluid pressure

ha additionto the elasticmodulusvariatim Santardli

incorporated pre-peek yielding into the constitutive modelto predictthestressstatedevelopedwithinhollow cylinders and obtained an improved predictionof the

.

fdure pressurefor threerock types (seeTable 3) The the effect of scale To comctly judge the quantitative

analysisassumed that failure occurredwhen a stress predictionsof consititutivemodels and failure criteria

point at the wall of the hollow cylinder reached its we need to have a better understandingof any scaie

models which appear to improvepredictionsof hollow

$ant mlli’tamodelprovidesbetterpredictionsof f~ure cylinderfailure relativeto a linear-elasticanalysisare

comparedto linear-elasticityand simpleelasto-plastic those presented by Suiem and Vardoulakis[261 and

analyses,althoughit still underestimatesthe pressure Santarelli [17] In the field applicationgiven in the

at whichftilure is initiatedwithinthehollowcylinders followingsection, the model proposedby $antarelli is

It is easy to assign the difference between the actual used A brief descriptionof how the model is

incorpo-failure and true fdure to the iniluence of the integ- rated into an FEM analysisis given by Duncan-Fama

mediateprincipalstress.However,anotherfactorwhich and Brown[33] A full descriptionis foundin [341

hasreceivedattentionrecently,andmayaccountfor the

‘abnormal’strengthof hollow cylindersis the effect of

Laboratorytesting showingthe effects of scale on the 6.1 Backgr(sund

failure around a circular opening are presented by

Antheunis et al [2] and Haimson and Hernck [32] The Cyrus Field in the UK ContinentalShelf (UKC$),

Antheunisshowedsome scaleeffbct,but the limitation Block 16/!28,willbe developedusingthe SingleWellOil

of the testingequipmentmadethe resultsinconclusive ProductionSystem(SWOPS).Developmentwiilbe tlom

However,Hainwonand Herrick’steste on a Alabama two horizontalwells drilledfivm a singlelocation The

limestoneshoweda very consistenttrendover a range first well was drilledin 1986,and the secondin i989

ofholesizes(Figure9b) Thesetesteindicatethatbeyond

a certain hole size (in this case around 6 cm) a Prior to drilling the first horizontalwell a study was

linear-elasticanalysis coupled with a simple ftilure carriedoutto assessthestabilityofthe8 I./2”,600mlong

critsrionis perfectlyadequatefor predictingthe onset honzontai section through the resemir Figure 10

failureof the boreholewall Belowthis hole sise, scale shows the Iithology,planned well profile and casing

effbctsmay enhance the strengthof the opening con- programme

siderably.Therefore,it shouldbe considereddangerous

to make quantitativepredictionsof the stabilityof fill Previousexplorationand

appraisalwellsweresuccees-scalewellboresbaeed on laboratorysimulations,which fidly drilled through the reservoir with a 1,16 S.(3

are often carried out on holes of 1“ diameter or lese, densitymud.Inordertolimitthepotentiaiforformation

unlessthe eff’ of scalecan be quantified damageit was considerednecessaryto restrictthe mud

weightswhile chillingthe reservoir section of the

hori-DeepitetheevidencepresentibyHaimeon andHerrick zontalwells to a similarmud density The rock

mech-suggeoting that in the case of fbli scale wellbores, anics studywas performedto determinewhethermud

linear-elasticitygives an adequate descriptionof the weights of around 1.15 S.G would be sut%cientto

stressstate,their test resultsdo not contradictthe we preventspallingof the wellborewall

of $smtarelli’smodelwhichutilisesa coniiningpressure

dependentmodulus ‘IMs is due to the stress path

adoptedwithin their testsamples ‘he circularholes 5.2 Approach

were formed within blocks which were loaded in one

directiononly (see ESgure9a) Under these conditions The use of numericelhmalyticdmodels to predict the

the minimumprincipal stress is either zero or tensile mechanicalbehaviourof a wellborerequiresa number

throughout the sample In this case, assuming a ofinputparameterstobe definedor assesmd.Theinput

modulusvariationgiven by equations(7) and (8), E is parameter requiredto fblly utilisethe modelsused in

constant throughout the eample and equivalent b this studyare the in=rntuSIZINSStS* (e~d~ ~

linear-elasticityareequivalentforthisloadingpath (It to the in-situ stresses,the formationpressureand the

may be arguedthatE, isbee than E@for teneilevalues mechanicalpropertiesof the formation(elasti%plastic

of ~ However, the rate of change of modulus must and strength).

quicklyreducein the tensileregion,otherwiseE, would

becomezero or negative.)

59sIn=situ Straea state

Inconclusion,it is ditllcult to assess the quality of a

conetitutivemodelinite applicationtowellborestability Knowledge of the in-situ stress state in the Cyrw

analysis dw to a nundm of uncertainties,in particular Field is limited It wae thereforenecesewy to

per-forma stabiiity analysisueing a q of assumedbut

I

m

. .

reasonablevaluesfor thein-situstresses.Thefollowing

assumptionsweremade

1 Principal stresses are vertical and horizontally

oriented This is a reasonableassumptionin relatively

simplesedimentarybasinsawayffornsaltdomes,faults

andfolds

2 The overburdenor vertical stress gradient can be

approximatedto the weight of overlyingrock A value

of 1 psilft (0.023 MPa/m)is reasonablein sedimentsuy

basinsbelow depthaof around2,000m

3 No InstantaneousShut in Pressures(ISIP’S)from

hydraulicfracturingwere availableRom nearbywells

However, ISIP’S camied out in other reservoirs

throughoutthe UKCS, show that the

minimumhor-izontalstressgradientin normallypressuredreservoirs

invariably resides between 0.6-0.9 pstift (0.014-O.021

Ml%/m)

themaximurnhorizontalstress However,ifit is greater

than the vertical stress, then a horizontalwell will be

morestablethana verticalwell(assumingisotropicrock

properties) Thus, the maximumhorizontal stress is

takentobe no greaterthan 1 psilft(0.023MPa/m),since

valuesin excessof this do not constitutea problem

6. The directionof the maximumand

minimumhori-zontalpzincipalstressesaredeterminedroutinelyusing

breakout analysis (e.g Klein and Barr [3S1) In the

CyrusFieldno consistentelongationtrendswerefound

in the explorationand apmaisal wells, indicatingthat

the two horizontalstressesare similarin magnitude

6 From Drill StringTeste (DSI”S)the formationhad

been establishedto be normallypressured;equivalent

to 0.45 pai/ft(0.10 MPa/m)

From the above considerations,the wellbore stability

analysis was carzied out assuming a vertical in-situ

stressgradientof 1.0 psih (0.023MPa/m),and a range

of isotropichorizontalstressgradienteequalto 0.6,0,7

and 1.0 pdft (0.014, 0.016 and 0.023 h!lpalm~ a

horizontal stress gradient of 0.7 pai/ft (0.016 MPa/m)

beingconsideredthe most probable

&4 Itock Material Propartiea

Aserieeofinetrumentadtriaxialanduniaxialtaetawere

carriedout on plugstaken from reservoircore fkoman

oihet well to determine the mechanical pmpertiee of the

rock anticipatedin the horizontaleectionof the CynM

productionweile The rock testingwaa carriedout in

accdance with ISRMrecommendation [361 Prior to

testingthe samplesweresaturatedundervacuumwith water However,no pore fluid pressureswere applied duringtesting

The strengths of the plugs tested as a fimction of confiningpressuresare plottedin Figure11 To these results a Mohr-Coulombcriterion is fitted, giving a ftilure envelopedeilnedby

cr~= 4000+5.5x~: (psi)

The valuesof the tangentmodulusat SO%strength,Eat

are plotted againstconfiningpressurein Figure 12 A linear relationshipbetween the elastic modulus and minimumprincipaleffectivestresswasassumedfor the FEM analysis,givenby

E==1.3X106+490X63’ (psi)

There was no apparentrelationshipbetweenPoisson’s

ratioandconfiningpressure;a constantvalueof 0.2 was assumedfor the analysis

6.6 Re6ult8 Figure13 showsthe computedmaximumeffbctivehoop stress, CO’,at the wellbore wail as a fimction of mud density using both linear-elasticity and the FEM analysis Also shown is the maximumallowablehoop stress as determined by the Mohr-Coulombf~ure criterion

Usinglinear-elasticity,a minimummuddeneityof 1.24 S.G is predictedfor preventionof compressivefailure assurningthemostfavorable horizontalstrewgradient

(1.0Psi/R).ThiscontparesWithaminim-muddtity

of 1.07 S.G predictedby the FEM ass- the same horizontalin-situ stress state If we assumethe least favorable horizontal stress gradient (0.6 psi/1’t), the minimum mud density requirementpredictedby the FEM is 1.18 S.G (Notw The mud weigh~ P~cted neglectthe effbcteof swaband surgspressuIws)

On the basis of the FEM, it was consideredthat a 1.18

S.G mud would be sufficientto supportthe welllme, providedswabandsurgepressureswereminimieedand good fluid 10s8characteristicswem maintahad to

p-vide an ef&tive mud cake JNthou@, -b P~

*&~ti_wmud~tNml.18S.G.ti was not considereda problemas the mmmmemhtim were heed on thehat fburable etreee etate d

plaeticityefthctshadnotbeenallowedforhti ti*D which would mean the meulte are of a mneervative nature

The reservoirsectionof the first Cyrushorizontalwell

was actually drilled with a 1.17 S.G mud It is not

possible to state whether the hole stiered any

com-pressivefdure, sinceno caliperswererunin the 8 l/2°

hole However,duringdrillingof this sectionthe hole

appeared to be in perfect condition No excessive

overpullswhile trippingout nor drag whiletrippingin

were encounteredand

drillingproceededwithoutinci-dent Inaddition,goodagreementbetweenfiepticted

andactualtorquewhiledrilling(CMldandCocl@g[371)

suggestsan in-gaugehole This responsesuggeststhat

the linear-elasticanalysis carried out was extremely

conservative However,it is not possibleto determine

the accuracyof theFEManalysis,sinceevenlowermud

weightsmay haveprovedsuccessfid

1 Carefulconsiderationshouldbe givento the type of

strengthcriterionused Those

criteriawhichincorpor-ate the intermedicriteriawhichincorpor-ate principal stress may lead to

unacceptable overpredictions of formation strength

resulting in optimistic predictions of hole stability

Criteria which do not consider the influence of the

intermediateprincipalstress are likely to be

conserva-tive in nature, particularitywhere used in association

withlinear-elasticity

2 Fitting of peak-strengthcriteriashouldbe directed

towards the appropriate conilning pressure range,

whichinmost downholeinstancesis unlikelyto include

confiningpressuresgreaterthan 2000 psi (14 MPa)

3 Incorporationof a stressdependentelasticmodulus

determinedfrom triaxialand uniaxialtestingappears

to improvethe predictionsof elasticand e}ast.o-plastic

models However,the main basis for this assumption

arehollowcylindertestresults,whichmaybe subjectto

scale effects relative to Ml scale wellbores The

importance(or othemise) of the scale effect shouldbe

quantified before any degree of confidence can be

assignedtomodelsvalidatedagainsthollow@ndertest

resulte

4. Application of a FEM incorporating a stress

dependent modulushas been applied to a horizontal

well drilledin the NorthSea The actualwellresponse

implies tit theFEM analysis gives much improved

predictionsof hole stabilityrelativeto a linear-elastic

approach

5 The problemsand costs of wellboreinstabili y

con-tinuetabs amajorcost ftirinchillhgwells Toreduce

these costs continuedIUkDeffort needs to be directed

towards a better understanding of * behaviour

aroundcircularops~ inboththelaboratoryandfield

in orderto improvethe predictionsof wellborestability models

NOMENCLATURE (Compressionassumedpositivethroughout)

Elasticmodulus(secantmodulusassumed) Elasticmodulusfor uniaxialloading Secantmodulus

Maximumdeviatorstress Meanpressure

Meaneffectivepressure(meanpressure minuspore pressure)

Vertical/Overburdenstress Maximumhorizontalin-situstress Minimumhorizontalin-situstress Radial,circumferenthdand axial stresses Maximum,intermediateand minimum principalstresses

Effectivestress(totalstressminuspore pressure)

Octahedralshearstress Octahedralnormal

ACKNOWLEDGEMENTS The authors wish to thank

stress

the British Petroleum Companyfor permissionand encouragementto publish this paper Further we wish to thank Bob Klein and Marc Greenway for assistancewith the analysis and testing

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and monitoring ISRM S~ested Methods

Pe~ mon, Ofiord.

simulator improves drilling pefiorrnance Oil & Gas

TABLE1 Categorizationof Peak.StrengthCriterion

I Function of 6, & a, only

LinearCriterion

Non-LinearCriterion

e.e Rrisesu r51 e.iz.Hock-Brown t61

TABLE2 Seleetionof PublishedWellboreStabilityModels

-—

Source Basic Model Behaviour Additional Features

attiso-tropy

softening bchaviour

smda-harden-ing

SPE 1994~ ‘

TABLE3 PredictedandActualFailure~essure of HollowCylindem (after

Santarelli [171)

A

Lincar-Ehstic Santarclli[171 TestResults

Sandstone

stone

Dolomite

Figure 1 Types of Stress Induced

Wellbore InstabiH&

ul

Figure 2 In.Situ Stress FielcL

m