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RockMechanics,Aubert/n,Hassan/& M/tn (eds) 1996 Balkema,Rotterdam. SBN 90 54 I0 838 X

Usage ndapplicabilityf pseudo-3Dtressnalysisn borehole tabilityproblemsn petroleumrilling ndproductionperationsG.G. Ramos & B.S.WiltonARCOExploration& Production echnologyo.,Plano,Tex.,USAA. E PolilloPetroleo Brasileiro S.A., Rio de Janeiro, Brazil

ABSTRACT:n a drilling/productionperatingnvironment,ellborenstabilitiesrisen all hree tagesf awell'sifespan:rilling,timulationnd roductionhases.he iming nd everityf theoccurrencef suchboreholeroblemsictate hichmethodfstabilitynalysishouldeused. seudo-3Dodesreplane-strain,non-isotropicubsetsf full 3D numericalndanalyticalodes. heir peed, ortability,ndease f usehavepopularizedhem mongperationsngineers.here renumerousersionsfpseudo-3Dtressnalysis,romsimpleinear-elastico sophisticatedoro-elastic-plastic,achwith ts ownadvantagehatsuitsa particularwellboreroblem.impleinear lasticodesre e-emergingn popularityecausef ease f useand ield-calibration schemes.1 INTRODUCTIONRecent echnological dvances re pushing hereach of boreholes eyond25,000 ft in length.Highly nclined, xtended-reachellboresERD)must emainopen or prolongedime-periods,otonlyduringhedrilling rogramutalson the ifeof a reservoir. In a commercial operatingenvironment,he technical taffmustperformong-rangeplanningo avoidpotential rillingandproductionazards,ndstill be able o quicklysolve occurrences of unplanned wellboreinstabilities. his paper presents trategiesnanalyzingvarious wellbore stressproblemsencounteredn day-to-dayield activities.2 INSTABILITIES IN FIELD OPERATIONSThereare hree tagesn the ife of a well:1. dtilling,2. completionndstimulation,nd3. flow tests, roduction,nddepletion.Thesedifferentusesandstagesn the ife of a wellshoulddictatewhich methodof stabilityanalysis sappropriatendapplicable.heusual roblems tofind the feasible/acceptableimits of the wellborepressurewduring ll the hreephases.lthoughgooddrilling ndcompletionlansncludeockmechanicalanalysis, in any field operation,unforeseennstabilitiesmay still arise, and thetimingof such ventsmayalsodictatehemannerin which hestability nalysiss performed.

2.1 Drilling stageThisstagewarrantsn ntegratedtability nalysisbecauset is themost apital-intensive.reviewofrecentadvancesn drillingERD wells s givenbyPayne,Wilton and Ramos 1995). The mainconcerns to determinehe mud compositionnddensitywhichwill maintainhe integrity f thewell, without the loss of drilling fluids.Conventionally,hechoice f muddensity r wellpressurewsdictatedy hehighestormationorepressurer along he well path,Figure1. Otheroperationalndgeological actorsistedbelowmust be considered:Abnormallyressuredayers, epletedonesFractured ormations, ossof circulationzonesPenetrationate,mud clay compositionsDifferentialsticking, icks andblow-outsCoting ecovery,ementingfficiencyFormation amage,ogging,well tests

Commonly ncounterednstabilities nd theirpresumedechanismsf failure re istedn Table1, assuminghatmudchemistry asalready eenoptimized.nstability implymeanshatat somepoint,he ock hear trengthr ensiletrengthasbeen exceeded, and its severity ranges fromnegligibleo collapse.Rockmechanically,hemodes f failureareshearor tensile or a mixture of both. Major wellborecollapse roblemsreshear-failurenduced, ut ncase f lossof drilling irculation,hemechanismstensile failure.

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Table1. DrillingProblemsndSuspected odesofFailureObserved Problem Failure ModeBreakouts Shear &/or TensileDoglegs Shear&/or TensileStuckpipe ShearTight spots ShearLedges ShearCollapse ShearFrequenteaming Shear&/or TensileLargecuttings Shear&/or TensileLoss of mud volume TensileLossof mudpressure Tensile2.2 CompletionandstimulationCompletion and stimulation engineers have toensure that the reservoir can be connected to thewell via perforations,and if required, hydraulicfracture(s) an be propagated. his operation ouldfail if the rock adjacent o the cementedcasing snon-elastic. There are also cases where thebottomhole reatingpressures ustbe minimized norder to prevent chemical reservoir formationdamage.

2.3 Flow tests,production nd depletionPrior to full production,downhole tests that areperformed include open-hole logging, fluidsampling, build-up, drawdown, injection, anddeliverability tests. It is not unusual to inducefailure and/orcollapseduring a well testingphase.An aim of the stability analysis should be tomaximize hydrocarbon roductionand minimizeground/sandcontrol measuresStability analysisshould nclude fluid flow and geometrical actorswhich are functions of the completion method:open-hole or bare-foot completion, perforatedbehind cementedcasing, packed with liners orscreens, and hydraulically fractured. As thehydrocarbonsare depleted, the drainage regioncompacts nd may fail, compoundinghe problemof solidsproduction.

2.4 Timing, urgency ndschedulingIn an operatingenvironment, he need for resultsfrom a stability analysis may also be describedaccordingo expediency:1. short-term,mmediate, ndurgent2. pre-drilling ield study.3. post-mortemailure analysis.A short-termanalysis s usually n responseo animmediate need to cope with an unexpected,existing or impending nstability, such as stuckpipe, ostcirculafion, r fightreamingn a well inprogress. n urgent ase equiresastreslonsend

IN-SlTU Stresses

Shale, ,C, ndlpha

Reservoir, ,C, ndlphaFigure 1. Generalized wellbore trajectory

recommendationso be relayed within hours or afew days. The analysthas to decidewhich logs,cores, eismic ata,offset-weB, nddrilling ecordsare relevant, f they exist at all, and then gleanoutfrom the available nformation he necessarynputsuch as elastic modulus, failure strength.parameters,nd nsitu tresses.he ackof qualityxnput data and the need for quick answersmayjustify the use of speedy, conventional inearly-elastic methods.On the other hand, n a rigorous ield pre-drillingstudy,as in multi-well development lanningof a100-million+ barrel oil field, the analysthas thebenefitof weeksof lead-time,goodcoredata,pilothole 'engineering' well data, and a staff of

technologists nd consultants.An example of anintegrated ield study s in the development f theCusiana ield (Columbia), an active thrust-faultingenvironmentLast and McLean 1995). Similarly, na post-mortemailure analysis, pplicableoolsvaryfrom the simple to sophisticated 3D. Back-calibration of a basic linear-elastic method isusually he first step.3 STABILITY ANALYSIS METHODSConfronted with various types and severity ofinstabilities,productionobjectives, xpediency, ndschedulingconstraints,an operations echnologisthas a choice of analytical tools. Recentreviews ofmodeling technology, wellbore stability, anddrilling advances re given by McLean and Addis(1990), Charlez (1994), and Payneet al (1995). Thesignificant advances are in rock masscharacterization, computation, modeling,monitoring, and logging tool developments. heavailabilityof desktopand ap-topcomputersPCs)with programs or wellbore stress-strainnalysishave contributed o wider field applicationsandacceptance f rock mechanicalmodels.Numericalcodes such as finite elements, disllacement

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discontinuitylements r boundary lements, hichused o reside n mainframecomputers, an now beexecuted n PC's. For any borehole of arbitrarytrajectory, radley 1979), Roegiers ndDetournay(1988), Aadnoy and Chenevert 1987), Last andMcLean (1995) among others, have givenexpressionsor thestressesnddisplacementst theborehole wall, assuming linear elasticity andisotropy,and theseare not presented ere for thesakeof brevity.Figure 1 illustrateshe general aseof an ERD and the major input requirementsn astabilityanalysiswhich include nsitustressesSv,Shm,Shmin)'Pt)' wellborepressurePw),cohesivestrengthC), and ntergranularrictional ngleAlthough a well traverses multiple layers ofvaryingpropertiesndporepressuresFig. 1), a fullthree-dimensional odel of the boreholealong tsentire length s not always necessary ecause nlythe problematic ormationneed be analyzed.Andeven if a full 3D numerical model can be created,input data requirementswould be very intensive.Someof thesewellbore stress-strainnalysis odesare pseudo-3D rograms a smallersubset f fullthreedimensional lasto-plastic ellboremodels.Apseudohree-dimensionalP3D or pseudo-3D)ypeof analysis s a plane-strainmethodof estimatingstresses n the vicinity of the wellbore in ananisotropicmedium.Thus, he P3D models ocusonly on a given cross-sectionormal o the boreaxis, and assume that there are no strains(displacements)long hisborehole xis.With P3D(or plane-strain codes), the borehole stabilityproblem s one of computing he inducednear-wellbore stresseswhich exceedrock strength.Thesolution to this problem could be performedanalytically or numerically, n mainframes e.g.UNIX) or desktops e.g. PC), dependingon theadditionalassumptionsboutrock behaviorunderstress.Rock responseo strainor stress alls into afew categories uchas purely linearly)elastic L-E), poroelasticP-E), non-linear lasticandelasto-plastic E-P).Rock strengthproperties re commonlygiven interms of the Mohr-Coulomb failure parameterscohesive trengthC and ntergranularrictionangle(alpha). When stresses xceedrock strength, herock is described s non-elastic or plastic). f porefluid pressure gradient is included in thecalculationsof effective stresses,hen the method iscalledporoelastic. able 2 compareshesevarioussolutionschemes, umerical Numl.) or Analytical(Anal.), and he computing latform Unix or PC).The linearlyelasticmethods thebase asebecauseit assumeshat failure s equal o the elastic imit,thus acquiring the label as 'conservative' orpessimistic Charlez 1994). An elasto-plasticmethod implies that even after straining theboreholebeyond ts elastic limit, the non-elasticregion remains ntact and load-bearing,and notnecessarilyn a collapsed tate,and thus abeled'less conservative'.

Table 2. CommonlyUsedComputation ethodsType Comp. Method OutputFull 3D Unix Numl. RealisticLinear PC Anal. Conservative

elasticPoroelastic PC Anal. ConservativeElastoplasticPerfectly PC Anal. Lessplastic conservativeStrain Unix Numl. Leastsoftening conservativeChemical Unix Anal. Prototypeseffects onlyStress PC Numl. Lessdependent conservative

Not shown n the table are specialcasessuch asthermo-elastic or viscoelastic codes.

3.1 Applicability and Resurgence f Linear-ElasticModelsLinear elastic-limit methods assume that the onsetof instabilityand collapse s at the elastic imit, themost conservative ption.The applicabilityof thisapproachseems arguably limited to hard, brittleformations, may be justified in the followingcircumstances:

1. High confiningstressesn deepboreholesenhance linear elastic behavior.2. Scarcityof laboratory ataon non-linear tress-strain elationshipsor shales, et alone n-situordownhole data.3. Scarcityof datarelating aboratory-measuredplasticstrains o observed hear ailuremodes.4. Simplified nputand outputwhichpromotesfastercomputation, arametric nalysis, ackcalculation, nd nterpretation.5. Urgentneeds or results.For example, n an unexpected, rgentproblemofimminentcollapseof a deviatedboreholewhere heinput in-situ stress and strength properties areuncertain, quick but apparently conservativeanswers obtained from a linear elastic model wouldsuffice.An engineer acedwith inputdata rom ogs

only, may opt for a less data intensive code.Usually, ield logs, pore and mud pressuresre theonly known variables, but with simpler elasticcodes, t is fast and effortless o iterativelyback-calculate the unknown variables (like insitu stressgradient and strength).The use of elastic-plasticmodels n a data-poor ield case would give lessconservative estimates but it also reduces theengineer'smarginof safety.Furthermore,he speedand flexibility of linearly-elastic L-E) brittle rockmodelshave enabledoperators o back-calibrate rperformpost-mortemsor data-poor ield cases,anexample of which is given by Zoback and Peska(1995).1069

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A novel approach considers mud and shaleinteractions in terms of chemical activitycoefficientsWanget al 1994), reduceshe strengthof the shale with time, and still retains the elastic-limit constraints. his is applicablewhen dealingwith reactiveshales.Non-linearelasticity in termsof confining-stress ependentYoung's modulus(Santarelli, Brown, and Maury, 1986) also givesmore conservative nswers nd relies on laboratorytriaxial data.

3.2 Porepressure nd luid flowPoroelasticityncludes he fluid or pore pressuredistribution ear he borehole n calculating trainsand effectivestressesCui et al 1995, Detournay,Roegiers,and Cheng 1987, Mody and Hale 1993,among others). This implies that stability is afunction of time. Most of these formulations are stillunderdevelopment nd requireextensive ield andlaboratoryvalidation.During well-completion,t isdesirable o perforate nto an elastic ock, or a zonewith minimalplasticstrain. f hydraulic racturingsplanned, formation breakdown and fracturepropagation re the primary concern,and thereforethe appropriate nalysis s a poroelasticormulation(e.g. Weng 1993, Wang and Dusseault,1991). In aproduction mode, maximum flow rates can beobtained when the borehole or perforation isallowed to exceed the elastic-limit (i.e. plastic).Thus, hesedesign tages all for elasto-plasticndporoelastic odes.

3.3 AnisotropyLike plasticity, ransverse nisotropy r othotropicanisotropys an attractive eaturebut not a popularone, owing to lack of field data on coefficientsofanisotropy and the relative insensitivity of thecomputedoutput o the coefficients f anisotropy.There are information on elastic toodull,particularly n the seismicand dynamicdomains,and still less published data regarding staticmechanicalproperties.n spite of the lack of fielddata, formulationsusing anisotropyare easier toimplement n P3D than n FEM.Anisotropy n cohesiveand frictional strengthsmoredifficult to implement.One usefulapplicationof non-isotropicstrength ncludes the effects ofbedding and joints or any plane of weakness.Aformulationby Liao and Mear (1991), considerstensionless Mohr-Coulomb joint, in addition totransverse nisotropy. his simulates weak planewhich could ntersect he boreholeat any arbitraryangle.This is a convenient ndpowerful eature nanalyzing he formationof doglegs, edgesand ossof circulationalong pre-existing rictional surfaces.Example applications re in evaluating he impactof clay partings, eddingoints,or fault-crossings.

3.4 Elastic-plastic ptionsThe most common shear failure criterion is theMohr-Coulomb,and other esspopularcriteria areVon-Mises, Tresca and Drucker-Prager.McLeanandAddis 1990) andCharlez 1994) comparehesecriteria with example applications. The classicMohr-Coulombcriterion,hasemerged s the mostpopular because of the availability of data oncohesive nd frictionalstrength roperties f rocks,and its proven applicability n mine/tunneldesign.The other criteria are more sensitive to themagnitude of the intermediate in-situ stress andmorepopular n numericalmethods. novelelasto-plastic or EP (Drucker-Prager) pproachncludesthe effect of water contenton shalestrength ModyandHale, 1993) andwouldbe an appropriatemodelfor reactiveshales.An exampleDrucker-Prager -Papplication, erformedn a PC spread-sheets givenby Lal andGuild (1995).Elastic-plastic models extend the stress-strainanalysisbeyond he elastic imit. A mathematicallyconvenient formulation is to assume that no stressesexceed he elastic imit, i.e., perfectplasticity, hemostcommon eatureamongelasto-plasfic odels.Analytical and numericalsolutions an estimate heregion around he well that is non-elastic,which isloosely eferred o as plasticized, ilated,disturbed,damaged, r dis-aggregated.arious nterpretationsof such zones could be the reaction fronts betweendrilling mud and shale,spallingskin,breakouts,hedamaged region around a perforation, and theablated ing aroundopen-hole ompletions,o namea few.Again, the acceptability and significance of aplasticzone depends n the stageof life of the well.During drilling of an ERD, a plasticzone may notbe an acceptable isk since t is 'unsupported'orperiodsof weeks. n this stage, he engineer suallyopts for the conservative high-mud wtrecommendationsrom a L-E model, ust to ensurethe well remains open. However, if the same wellhas another formation uphole which wouldbreakdown i.e. fracture) with suchmud pressure,then a less conservativeelasto-plasticmethodshould be used. In the stimulation phase, theengineermay look at the plasticzoneas a zone oflow stress, and it serves to lower the fractureinitiation pressure.And in the acid-stimulation ndproduction tages, he dilatedor non-elastic one sa region of enhanced permeability, and thedevelopmentof a plastic zone is tolerable, if nothighly desirable,up to point of massivesanding.For example,our North Seaoil-fieldexperience asdemonstratedhat a horizontalwell canbe designedfor maximizing production,as an elastic-plasticopen-hole,especially f the input to the model arelaboratory and log data (Ramos et al, 1994).McLellan and Wang (1994) gives an exampleof aporo-elastic-plastic application in an acidifiedsandstone.

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3.5 Data availabilityandsensitivityAvailability of, or lack of data can sometimesdictate the course of the stability analysis. Thesensitivityof the resultsdependsmainly on twoboundary-conditionnput parameters:nsitu stressand rock strength.n mostcases, he required nputdataare available.However, as a logicalalternative,the method of back-calculating 'unknown'boundaryconditions s becomingpopular,madefeasibleby fasterPC's. For example, t takesonly afew secondso iterativelychange in the PC) inputvalues or in-situstresses,o comeup with a criticalmud wt whichconformso the known ield collapsefailure conditions. The same back-calculationscheme is done to derive unknown strengthparameters,ince he majorgeometrical onstraints,azimuth, deviation,are alreadyknown. This back-calculation option is commonly performed ininterpretingeak-off tests n deviatedwells, lossofcirculation roblems, reakouts, ashouts, ndevenlaboratory ollow-cylinderestdata.

4 EXAMPLE COMPARISONTo illustrate the differencesamong some of theseoptions,we comparea numerical inite elementmethod (FEM) to an analytical wellbore model.Horizontalborehole tability n shales ndreservoirrocks was analyzed with a numerical 2D FEM(Polillo and Crafton, 1991) under plane-strainelastic-plasticndporo-elasfic onditions. he FEMresults summarized in Table 3 will serve as a basisof comparison. he numericalmodel requires hatthe well is alignedwith one of the principal nsitustresses,.g. the azimuth rom Shmax s either0 or90 degrees. he criticaldifferential ressure DP isthe differenceP, - P.), which s referred o asoverbalance if positive, or underbalance ordrawdownwhen negative.The two valuesof CDPare for shear failure and tensile failure.The 2D FEM analysis resentedbovemplieshatthe horizontal ell maynot easiblef parallel oShmax ecauseensileracturingnitiatest420psioverbalance, while shear failure starts atoverbalance ressures elow 710 psi. With theporoelastic, enetratingluid case, he breakdownTable 3. Horizontal Well Linear Elastic and Elastic-Plastic Critical Differential Pressures CDPs(Polillo andCrafton 1991, Table 4)Azim Shear Tensile Fluid Modeldeg. CDP CDP flow typepsi psi

0 >710 415 none L-E90 >710 4300 none L-E0 >710 320 Darcy E-P90 >710 3324 Darcy E-P

pressuresre owerby 20%. On the otherhand, hewell perpendicular to Shmax is more stable,breaking down at CDP=4300 psi and failing inshear with CDP of 710 psi. (The model is notsuitable or investigating therwellboreazimuths.)The model also calculated the annular volumewhich s plasticized, sually rom radialdistances f0.05r to 1.Sr. The benefits of this kind of analysisare the calculatedmagnitudes f the following:the extentof non-elastic failed' regioneffectof permeability& pore-pressureradientmaterialanisotropy, v:Kheffectof residual trength f the plastic oneeffect of non-linear material behaviorIts disadvantagesre the requirementsor:a meshor grid of cellsor elementsmaterialpropertiesor eachelementor cellthe borehole lignedwith a principalstressmainframe-typeomputing owervoluminous esults ndprintoutspre- andpost-dataprocessorWith the numericalapproach bove, t was notpossibleo nvestigaterbitrarily riented orizontalwells. In actual field cases, the orientation of ahorizontalor ERD well is the foremostproductiondesign riterion. f the 0-deg.azimuth s not stable,the alternative 90-degree azimuth may not beacceptableo the reservoirand facilitiesengineers.Thus, we use a P3D code (one by Liao and Meat,1991, amongothers) o determineotherhorizontalazimuthal options.From Figure 2, the analyticalsolution shows that for horizontal wellboreazimuthswithin 40 degreesof Sh ... either shearfailure or breakdowndevelops,suggestingmajordifficultiesof drilling wells within +40 degreesofSh. Thus, o reach he desiredarget, he operatorhas the option of other more favorable welltrajectories,.e. +50 degreesrom Shmin.n seriouscases nvolving loss of well due to collapse, theeffectsof Sv, Sh ... and Shminre easilyanalyzedwith the analyticalP3D The polar (stereographic)plot of Figure3 illustrateshe effectson trajectoryof an ERD well (Payneet al, 1995) of two typesofinsitu stress egimes.The top quadrant Fig. 3) isfor a normal gravity-stressegime, similar to theprevious xample Table 3), showing he minimumP, or shear tability,ncreasing ith deviation ndazimuthal roximity o Sh. The lowerquadrantsfor a tectonic egionwhereSh > Sv> Sh..and mplies hat he verticalwell is the eaststable,the 30-degree eviation equires13.5 ppg while the85-degreedeviation equires12.5 ppg.The examplesabove give azimuths elative toSh, whoseorientation nd magnitude re notusually nown. n an actual ield case, o quantifythe boundsof insitu stresses nd strengths,helogical ecourses to study hepilot-hole'saliperand leak-off data. With this minimal amount ofinformation, a sensitivity analysis or back-calculation cheme an be performedn order o

create field-validated odelor nput-data et.1 o71

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5.004.504.003.503.002.502.001.50.000.500.00

Shearailureensile Failure0 20 40 60 80

Well Azimuth rom Shmax,degreesFigure 2. Critical Pressures or Horizontal

Well

lOO

Max, Hor,

60

. 30

60

90

Stress

0, Normalgravitati

Max. horzl tectonic stressgreater than vertical

Figure3. Polarstereographiclotshowingmud densityin ppg,asa functionof trajectorywhereazimuth sfrom Shmax, radius = sineof deviation rom vertical.Top quadrant= Normalstress egimeBot. quadrant = Thrust fault stress egime

Table4. Operating roblems, trategy ndTypeof AnalysisTypeof Problem Stress-handlingtrategyGeologicalhazardsAbnormallyressured Prevent irculationossn adjacentormallyformations pressured ectionsDepleted Fracturedormationsrevent irculationossn zoneReactive lays Optimizemudwt belowcollapse ressure

Operational actorsRisk of differential tickingKicks and risk of blow-outsFormationdamagePoor Coring recoverySlow Penetration rateMud / clay nteractionDifficulties while drillingDoglegs, edges, argecuttingsStuckpipe,Tight spots,BreakoutsCollapseBit-bailing,Frequent eamingDifferential sticksLoss of mud circulationWell control & kicksLeakoff est nterpretationCompletion ndProductionStimulation difficulties

Reducemudwt w/o collapsingdjacent eakersectionsOptimizemudwt belowcollapse ressureReducemud wt to the minimumpossibleOptimizemudwt belowcollapse ressureReducemudwt to the minimumpossibleOptimizemudwt belowcollapse ressureOptimizemudwtIncrease mud wtIncrease mud wtOptimizemudwtReducemudwt w/o collapsingdjacent eakersectionsReducemudwt w/o collapsingdjacent eakerformationsIncreasemudwt, plankill wellBack-calculate unknown variables

Optimize reating ressureWell flow tests anding,ollapse ecrease rawdown ressureSanding uring roduction, Decrease rawdown ressurecollapse

Preferred ModelPoroelasticElasto-plastic,oroelasticElasto-plastic,hemicalcouplingLinear elasticPoroelasticPoroelasticPoroelasticPoroelasticPoroelastic,ChemicalcouplingLinearelastic,AnisotropicLinear elasticElasto-plasticElasto-plastic,hemicalcouplingElasto-plasticElasto-plastic,oroelasticElasto-plastic,oroelasticLinear elastic, PoroelasticElasto-plastic,oroelasticElasto-plastic, oroelasticElasto-plastic,oroelastic

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