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SchlumbergerPublicIntroductiontoInductionLoggingTomBarberSPC2InductionLoggingDec2006SchlumbergerPublicFormationResistivityArchie’sequationlinksformationresistivityandhydrocarbonsaturationYouhaveheardaboutgettingporositySoweneedtoknowtheresistivityofthepartoftheformationofinterest3InductionLoggingDec2006SchlumbergerPublicResistivityintheLab„Smallsample„Isolatedfromenvironment„Simple4-terminalresistivitymeasurement4InductionLoggingDec2006SchlumbergerPublicResistivityintheWell„Weneedtomeasuretheresistivityofthefluid-containingrocks„Typically,wellsaredrilledwithahigherpressureinthewellborethanintheformation„Producesinvasion–Invasioncanbedeep–Annulusprofilecommon–OBMinvasionbringsfurthercomplications–Invadingfluidcangravity-segregate5InductionLoggingDec2006SchlumbergerPublicResistivityintheWell„Andlastbutnotleast,high-diporwelldeviation6InductionLoggingDec2006SchlumbergerPublicTheInvasionProcesson2Fronts„Mudfiltrateinvades„Adsorbedwaterdoesnotmove„Movessaltions„Salinewaterbanksinfrontoffiltrate„Non-monotonicresistivityprofiledependingonRmfandRw7InductionLoggingDec2006SchlumbergerPublicAnnulusResistivityProfile„ResistivityprofiledependsonRmf/Rwratio„Figureillustrates9casesdependingonRmfandRw8InductionLoggingDec2006SchlumbergerPublicHowDeepIsInvasion?„Invasioncanbefrominchestofeet!„Largelyafunctionof$spentonmudsystemAsmuchas4-6ft!9InductionLoggingDec2006SchlumbergerPublicThisSetstheInvestigationVolumeoftheMeasurement„Theremustbesignificantresponsefrombeyondtheinvasionfront„Volumemustbeatleast25ftindiameter—asbigasthisroom10InductionLoggingDec2006SchlumbergerPublicWhatAreTypicalValuesofResistivity?„Dependsonrockporosity,hydrocarbonsaturation„Youngunconsolidatedwatersands—GulfofMexico–φ=40%,Sw=1–0.1ohm-m„Oil-filledcarbonatereservoirs—SaudiArabia–φ=20%,Sw.1–10,000ohm-m5decadesofdynamicrange!11InductionLoggingDec2006SchlumbergerPublicTheInductionTool„Designedtoinvestigatealargevolumeoftheformation„Let’sseehowitworks„Westartwithacoilofwirecarryinganalternatingcurrent–Ontheorderof1-2amps–20-25kHz12InductionLoggingDec2006SchlumbergerPublicInductionPrinciples„Transmitterinducescurrentdistributioninformation„Computationisfor–20kHz–1ohm-m„EMfieldoutintheformationis–Smallerthanitwouldbeinavacuum–Phaseshifted„Skineffect13InductionLoggingDec2006SchlumbergerPublic„Addareceivercoiltothetool„SpacingLwilldeterminevolumeofinvestigation„Formationcurrentinducesvoltageinreceiver„VinthereceiverisproportionaltoformationconductivityσInductionPrinciples14InductionLoggingDec2006SchlumbergerPublic2-coilArrayandPracticalArrayR1andR2woundsoV1+V2=0infreespaceCoilsareinseriesOnlyV1+V2ismeasuredEliminatesdirectcouplingVoltageV1includessignalfromformationanddirectmutualMutualcanbe1000timesformationsignal15InductionLoggingDec2006SchlumbergerPublicMeasurement„Measurevoltageonreceivercoils„Alsomeasuretransmittercurrent„Fundamentalmeasurementisimpedancefromtransmittertoreceiver—Z=V/I„Voltageiscomplex—requiresphasesensitivemeasurementofnanovolts„Conversiontoconductivityunitsσa=Z/K=σR+iσX„Realpart—R-signal„Imaginarypart—X-signal16InductionLoggingDec2006SchlumbergerPublicBornresponse„Realpart(R)comesfromnearthetool„Imaginarypart(X)comesfromdeeperintheformation()()()()kHzatiiikeikreikrrrLzrgRTikrRikrTRTB20)(112,,2333σωεωεσωμρσ−=−−=SpatialResponse—Wheredoesthesignalcomefrom?17InductionLoggingDec2006SchlumbergerPublicSpatialResponse3CoilarraygB()()RTikrRikrTRTBeikreikrrrLg−−=112333ρ18InductionLoggingDec2006SchlumbergerPublicSpatialResponseVerticalresponsegVz,σ()=gB0∞∫(r,z,σ)drGrr,σ()=0ρ∫gB−∞∞∫r,z,σ()dzdrRadialresponse19InductionLoggingDec2006SchlumbergerPublicIsolatingtheInterestingPartsoftheFormation„Theinductiontoolmeasuresalargevolume—„Howdowedeterminetheresistivityoftheuninvadedzoneinabed1mthick?20InductionLoggingDec2006SchlumbergerPublicIsolatingResponsetoaSingleBed„Inductionresponsecoversalotofvolume21InductionLoggingDec2006SchlumbergerPublicIsolatingResponsetoaSingleBed„Inductionresponsecoversalotofvolume„Tendsto“smear”logandaveragethebeds22InductionLoggingDec2006SchlumbergerPublicDeconvolution„Startwithlogmeasurements23InductionLoggingDec2006SchlumbergerPublicDeconvolution„Startwithlogmeasurements„Iftheresponsefunctionismathematicallywell-behaved,wecanformaninversefunction24InductionLoggingDec2006SchlumbergerPublicDeconvolution„Startwithlogmeasurements„Iftheresponsefunctionismathematicallywell-behaved,wecanformaninversefunction„Thatinverse,appliedtothelog,shouldreturntheformationprofile25InductionLoggingDec2006SchlumbergerPublicWhyThisIsNotEasy„Responseshapechangeswithconductivity26InductionLoggingDec2006SchlumbergerPublicWhyThisIsNotEasy„Filterdesignedatlowconductivitydoesnotworkathighconductivity27InductionLoggingDec2006SchlumbergerPublicSkinEffectSignal„Comparelog–withskineffectand–without28InductionLoggingDec2006SchlumbergerPublicSkinEffectSignal„Comparelog–withskineffectand–without„Thedifferenceissmoothandlazy„Morancalledthisdifferencetheskineffectsignal29InductionLoggingDec2006SchlumbergerPublicCanWeFittheSkin-effectSignal?„Theimaginarypar

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