SchlumbergerPublicIntroductiontoInductionLoggingTomBarberSPC2InductionLoggingDec2006SchlumbergerPublicFormationResistivityArchie’sequationlinksformationresistivityandhydrocarbonsaturationYouhaveheardaboutgettingporositySoweneedtoknowtheresistivityofthepartoftheformationofinterest3InductionLoggingDec2006SchlumbergerPublicResistivityintheLabSmallsampleIsolatedfromenvironmentSimple4-terminalresistivitymeasurement4InductionLoggingDec2006SchlumbergerPublicResistivityintheWellWeneedtomeasuretheresistivityofthefluid-containingrocksTypically,wellsaredrilledwithahigherpressureinthewellborethanintheformationProducesinvasion–Invasioncanbedeep–Annulusprofilecommon–OBMinvasionbringsfurthercomplications–Invadingfluidcangravity-segregate5InductionLoggingDec2006SchlumbergerPublicResistivityintheWellAndlastbutnotleast,high-diporwelldeviation6InductionLoggingDec2006SchlumbergerPublicTheInvasionProcesson2FrontsMudfiltrateinvadesAdsorbedwaterdoesnotmoveMovessaltionsSalinewaterbanksinfrontoffiltrateNon-monotonicresistivityprofiledependingonRmfandRw7InductionLoggingDec2006SchlumbergerPublicAnnulusResistivityProfileResistivityprofiledependsonRmf/RwratioFigureillustrates9casesdependingonRmfandRw8InductionLoggingDec2006SchlumbergerPublicHowDeepIsInvasion?Invasioncanbefrominchestofeet!Largelyafunctionof$spentonmudsystemAsmuchas4-6ft!9InductionLoggingDec2006SchlumbergerPublicThisSetstheInvestigationVolumeoftheMeasurementTheremustbesignificantresponsefrombeyondtheinvasionfrontVolumemustbeatleast25ftindiameter—asbigasthisroom10InductionLoggingDec2006SchlumbergerPublicWhatAreTypicalValuesofResistivity?Dependsonrockporosity,hydrocarbonsaturationYoungunconsolidatedwatersands—GulfofMexico–φ=40%,Sw=1–0.1ohm-mOil-filledcarbonatereservoirs—SaudiArabia–φ=20%,Sw.1–10,000ohm-m5decadesofdynamicrange!11InductionLoggingDec2006SchlumbergerPublicTheInductionToolDesignedtoinvestigatealargevolumeoftheformationLet’sseehowitworksWestartwithacoilofwirecarryinganalternatingcurrent–Ontheorderof1-2amps–20-25kHz12InductionLoggingDec2006SchlumbergerPublicInductionPrinciplesTransmitterinducescurrentdistributioninformationComputationisfor–20kHz–1ohm-mEMfieldoutintheformationis–Smallerthanitwouldbeinavacuum–PhaseshiftedSkineffect13InductionLoggingDec2006SchlumbergerPublicAddareceivercoiltothetoolSpacingLwilldeterminevolumeofinvestigationFormationcurrentinducesvoltageinreceiverVinthereceiverisproportionaltoformationconductivityσInductionPrinciples14InductionLoggingDec2006SchlumbergerPublic2-coilArrayandPracticalArrayR1andR2woundsoV1+V2=0infreespaceCoilsareinseriesOnlyV1+V2ismeasuredEliminatesdirectcouplingVoltageV1includessignalfromformationanddirectmutualMutualcanbe1000timesformationsignal15InductionLoggingDec2006SchlumbergerPublicMeasurementMeasurevoltageonreceivercoilsAlsomeasuretransmittercurrentFundamentalmeasurementisimpedancefromtransmittertoreceiver—Z=V/IVoltageiscomplex—requiresphasesensitivemeasurementofnanovoltsConversiontoconductivityunitsσa=Z/K=σR+iσXRealpart—R-signalImaginarypart—X-signal16InductionLoggingDec2006SchlumbergerPublicBornresponseRealpart(R)comesfromnearthetoolImaginarypart(X)comesfromdeeperintheformation()()()()kHzatiiikeikreikrrrLzrgRTikrRikrTRTB20)(112,,2333σωεωεσωμρσ−=−−=SpatialResponse—Wheredoesthesignalcomefrom?17InductionLoggingDec2006SchlumbergerPublicSpatialResponse3CoilarraygB()()RTikrRikrTRTBeikreikrrrLg−−=112333ρ18InductionLoggingDec2006SchlumbergerPublicSpatialResponseVerticalresponsegVz,σ()=gB0∞∫(r,z,σ)drGrr,σ()=0ρ∫gB−∞∞∫r,z,σ()dzdrRadialresponse19InductionLoggingDec2006SchlumbergerPublicIsolatingtheInterestingPartsoftheFormationTheinductiontoolmeasuresalargevolume—Howdowedeterminetheresistivityoftheuninvadedzoneinabed1mthick?20InductionLoggingDec2006SchlumbergerPublicIsolatingResponsetoaSingleBedInductionresponsecoversalotofvolume21InductionLoggingDec2006SchlumbergerPublicIsolatingResponsetoaSingleBedInductionresponsecoversalotofvolumeTendsto“smear”logandaveragethebeds22InductionLoggingDec2006SchlumbergerPublicDeconvolutionStartwithlogmeasurements23InductionLoggingDec2006SchlumbergerPublicDeconvolutionStartwithlogmeasurementsIftheresponsefunctionismathematicallywell-behaved,wecanformaninversefunction24InductionLoggingDec2006SchlumbergerPublicDeconvolutionStartwithlogmeasurementsIftheresponsefunctionismathematicallywell-behaved,wecanformaninversefunctionThatinverse,appliedtothelog,shouldreturntheformationprofile25InductionLoggingDec2006SchlumbergerPublicWhyThisIsNotEasyResponseshapechangeswithconductivity26InductionLoggingDec2006SchlumbergerPublicWhyThisIsNotEasyFilterdesignedatlowconductivitydoesnotworkathighconductivity27InductionLoggingDec2006SchlumbergerPublicSkinEffectSignalComparelog–withskineffectand–without28InductionLoggingDec2006SchlumbergerPublicSkinEffectSignalComparelog–withskineffectand–withoutThedifferenceissmoothandlazyMorancalledthisdifferencetheskineffectsignal29InductionLoggingDec2006SchlumbergerPublicCanWeFittheSkin-effectSignal?Theimaginarypar