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HandbookofBoreholeAcousticsandRock PhysicsforReservoirCharacterization

HandbookofBoreholeAcoustics andRockPhysicsforReservoir

Characterization

VimalSaxena MichelKrief

LudmilaAdam

Elsevier

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ListofTables

Table1.1Interrelationofelasticconstants

Table4.1Coefficient P and Q definedforsimplerinclusions

Table4.2Parameters a and b inanalyticalDEMapproximationforporousrockwith dryinclusions; α istheaspectratioofinclusion

Table5.1Limitationsofthetime-averageconcept

Table5.2Polynomialregressioncoefficientforcleanlithology

Table5.3Propertiesforasetofsixcalcitesamples

Table5.4Typicalcriticalporosityvaluesfordifferentrocks

Table5.5CoefficientinGardner’spowerlawfordifferentlithology

Table5.6Coefficientsinpolynomialrelationfordifferentlithologies

Table8.1Thomsenparameterlimitsinfinelylayeredmedia

Table8.2Thomsenparametersindryclayminerals

Table8.3Elasticparameterstocalculateelasticboundsoforganicclays

Table9.1Parametersforgeneralizedrelationshipforunconfinedcompressivestrength310

Table11.1Monopole(Mn)anddipole(Dp)modeevaluationinopenholeandcasedhole406

ListofFigures

Fig.1.1Examplesof(A)isotropicandheterogeneous,(B)isotropicandhomogeneous, (C)anisotropicandheterogeneous,and(D)isotropicandhomogeneousrock.2

Fig.1.2(A)Verticaltransverseisotropy,(B)Horizontaltransverseisotropy,and (C)Tiltedtransverseisotropy. 3

Fig.1.3Componentsofstresstensor. 4

Fig.1.4Displacementandstrainunderstress. 5

Fig.1.5Stressparallelto Y-axisonsurfacesperpendicularto(A) y-axis,(B) z-axis,and (C) x-axis. 10

Fig.2.1Criticalfrequencyinwater-saturatedporousmediaforvaryingporosityand permeabilitywithrespecttovariousacousticmeasurements. 26

Fig.2.2Generalfrequencydependenceof P-wavevelocity(Vp)andtheassociated attenuation(1/Q)withbothlowandhighfluidmobility. 27

Fig.2.3Dispersioncharacteristicsof P-waveand S-wavevelocityandtheassociated attenuation(1/Q)forvaryingporosityandpermeability. 29

Fig.2.4ComparisonofBiot’sdispersionwithGeerstma-Smitapproximationforclean sandstonesamples. 31

Fig.2.5 P-and S-waveexcitationinsolidandwavepropagationinaborehole.

Fig.2.6Snell’slawforwavetravelintheborehole.(A)Generalrefraction.(B)Critical refractionandheadwaves.

Fig.2.7Wavetraininafastformation(Vs > Vmud).

Fig.2.8Wavetraininaslowformation(Vs < Vmud).

Fig.2.9Characteristicwavetraingeneratedintheboreholethroughvariouselasticwave modesanddetectedbyreceiversinacousticlogging.

Fig.2.10Boreholeschematicforwavetraintravelintheborehole.

Fig.2.11Leakymodesforreceiversatdifferentoffsets.

Fig.2.12Pseudo-Rayleigh(pR)wavesforreceiversatdifferentoffsets.

Fig.3.1(A)Singletransmitterdualreceivermonopolesonic.(B)Effectoftoolangle. (C)Effectofvaryingboreholediameter.

Fig.3.2(A)Boreholecompensated(BHC)measurementand(B)long-spacedsonic (LSS)measurement.

Fig.3.3(Left)Arraysonictoolconfigurationandrecordedwaveformsfromdifferent receivers(right)inafastformation.

Fig.3.4(Left)Monopolewavetraininfastformationand(right)timesnapshotof acousticwaveevaluationandspreadinginformation.

Fig.3.5(Left)Monopolewavetraininslowformationand(right)timesnapshotof acousticwaveevaluationandspreadinginformation.

Fig.3.6(A)Dipoletoolconfigurationand(B)wavetrainexcitationatboreholebydipole toolfrequency.

Fig.3.7(Left)Acousticwavetraininslowformationondipoleexcitationand(right)time snapshotofacousticwaveevaluationandspreadinginformation.

Fig.3.8Sonicscannertoolconfiguration.

Fig.3.9High-qualitycompressionalandshearwithradialprofilingbythesonicscanner tool.

Fig.3.10InfluenceofinterferencewithtoolflexuralwavesinwirelinedipoleandLWD dipoletools.

Fig.3.11Quadrupolesonicexcitation;(A)positiveandnegativepressurepulsein orthogonaldirectionand(B)screwwaves.

Fig.3.12Quadrupolewavedispersioneffectforfastandslowformations.

Fig.3.13Quadrupoledispersioncurvesandeffectofmudslownessandcollarthickness.58

Fig.3.14FieldcomparisonbetweenLWDandwirelinesonicdata.

Fig.3.15Seismicwhiledrilling(SWD)configuration.

Fig.3.16(Left)Firstmotiondetection(FMD);(A)Correctfirst-motiondetection, (B)Noiseeffect:Earlydetectionandreducedtraveltime,and(C)Cycleskipping: Delayeddetectionandincreasetraveltimeand(right)frequencyfiltrationfrom waveform.

Fig.3.17Slowness-time-coherence(STC)semblanceprocessingconcept.

Fig.3.18Flexuralwavefrequencydispersionandestimatedshearinthedipoletool.67

Fig.3.19Slownesstimecoherence(STC)processingresultforP,S,andStwaves.68

Fig.3.20Dispersioncorrectionofdipolesheardata.

Fig.3.21Boreholesizeeffectonflexuralwavedispersion.

Fig.3.22(A)Theprocesseddispersiveflexuralwaveformarray,(B)slowness-timeplane throughnondispersiveSTCprocessing,and(C)slowness-timeplanethrough dispersiveprocessing.

Fig.3.23Waveformandslownessdispersionatrepresentativedepthandslownessfrequencyprojection.

Fig.3.24Cramer-Raoboundsasafunctionofsignal-to-noiseratio(centraldashed), slownessstandarddeviation(solid),and SDofcalculatedbound.

Fig.3.25Configurationofvariousoverlappingsubarrayswithaperturesrangingfrom0.5 to3.5ft.(A)0.5ftresolution;28waveform,(B)1ftresolution;54waveform, (C)1.5ftresolution;80waveform,(D)2ftresolution;100waveform,(E)2.5ft resolution;108waveform,(F)3ftresolution;98waveform,and(G)3.5ft resolution;64waveform.

Fig.3.26Enhancementofverticalresolutionwithdecreasingsub-arrayaperturesranging from3to0.5ft.

Fig.3.27Raytracingforformationandmudarrivalsinaborehole(A)withoutaltered zoneand(B)withalteredzone.

Fig.3.28Effectondeeper(P 3)arrivalsin(A)waveformsfromdifferentsourcetypesand (B)waveformswithvaryinginvasioninthequadrupoletool.

Fig.3.29Sixleast-timepathsforacousticsignalfromtransmittertoreceiverunder influenceofalteredzone.

Fig.4.1Conceptualmodelforcompositewithtwo-phaseporousmedia.

Fig.4.2(A)Bulkmodulus,(B)shearmodulusforafluidsaturatedsandstone:VoigtReussboundsandVRHapproximation.

Fig.4.3(A)Bulkmodulus(B)shearmodulusforafluidsaturatedsandstone:HSbounds andcomparisontoVoigt-Reussbounds. 95

Fig.4.4BulkandshearmodulusforadryframeporoussandstonerockfromHSupper boundandVoigtupperbound. 96

Fig.4.5CompositespheremodelofHashin(1962). 97

Fig.4.6ComparisonofBMMandMSboundswithHSboundsforasand-water composite.

Fig.4.7BulkmodulusderivedfromtheKTmodelforporoussandwithvaryingaspect ratioofellipsoidalinclusionsunder(A)dryand(B)water-saturatedinclusion scheme.HS+andHS-representHashin-Shtrikmanboundsforthebulk modulusofthecomposite.

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Fig.4.8WetshearmodulusderivedfromtheKTmodelforporoussandwithvarying aspectratioofwetellipsoidalinclusions.Thebrackets()denotetherespective aspectratiowhileHS+representstheupperHSboundsforthecomposite.103

Fig.4.9(A)Normalizedbulkmodulusand(B)Normalizedshearmodulusfora compositewithwetellipsoidalinclusionasestimatedfromDEM.Resultsare comparedwithHSlowerandupperbounds. α ¼ 1denotessphericalinclusion. Shearlowerbound(notindicated)iszero.

Fig.4.10Computationofparameters a and b fordrysphericalporeinclusions.

Fig.4.11Normalizedbulkmodulusforcompositewithwater-wetsphericalinclusion fromM-DEMforvariouscriticalporosities.ResultscomparewithDEM estimation,HSupperbound,andReussbound.

Fig.4.12Hertz-contactconceptualmodel.

Fig.4.13CoordinationnumbersfromMurphy(1982)andDuttaetal.(2010)

Fig.4.14ModifiedlowerHashin-Shtrikman(LHS)boundusingHertz-Mindlincontact theory.

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Fig.4.15Generalizedcasesofcemented-contactscheme.(A)Cementwithgraincontact. (B)Cementdistributionwithgraincontact.(C)Cementwithno-graincontact.128

Fig.4.16Constant-cementmodelfordryandwetsandincomparisonwithmodified lowerHSbound.

Fig.4.17Biot’sconstantfromtheKriefandMurphy-Schwartzschemes.

Fig.4.18Biot-Gassmann-Kriefmodeltopredict(A)Normalizedbulkmodulus, (B)Normalizedshearmoduluswatersaturatedforcleansandstone. # MichelKrief.

Fig.4.19Dryframecompressionalandshearmoduliinconsolidatedandunconsolidated porositydomains.

Fig.5.1Slowness-porosityplotforRaymer-Hunt-GardnerandTime-averageequations. BackgroundlinesareplottedwithdifferentBiot-KriefexponentsintheBiotGassmann-Kriefmodel. # MichelKrief.

Fig.5.2(A) Vp–Vs cleansandandshalelineand(B) Vp/Vs–Vs profilefordifferent lithologiesfromCastagna’s(1993)equation.

Fig.5.3Biot’sconstantandporosityofcarbonatesampleswithvariableKriefexponents. # MichelKrief.

Fig.5.4(Left)Biot’sconstant-porosityand(right)Gassmanncoefficient-porosityin Gulfcarbonate. # MichelKrief.

Fig.5.5Velocityinwater-saturatedshalysandwith15%clayfromdifferentequations (A) Vp (B) Vs.

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Fig.5.6Pickett’sslownessplotforvaryinglithologies.

Fig.5.7 Vp/Vs versuscompressionalslownesstrend:fromcompactedtoundercompactedshalysands.

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Fig.5.8 Vp/Vs plotsforsandstoneusingBGKmodelwithvariableBiot-Kriefexponent. # MichelKrief. 155

Fig.5.9ModifiedVoigtmodelincleansandstonewiththeoreticalReussaverageand BGKmodel. # MichelKrief. 157

Fig.5.10 Vp-porosityincarbonatesandtheirdependenceondifferentdominantpore types.

Fig.5.11(A)Velocity-porosityplot;effectsofporestructureoncarbonatevelocityby (B)PoA,(C)DOMsize,and(D)roundness.

Fig.5.12Stressdependenceof Vp and Vs in(A)consolidatedGulfCoastsandand (B)unconsolidatedOttawasandstone.

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Fig.5.13Dependenceofvelocityand Vp/Vs ratioondifferentialstress:empiricalmodel.162

Fig.5.14Dependenceof Vp/Vs ratioondifferentialstressforunconsolidatedsandstone.163

Fig.5.15 Vp and Vs fordryandwater-saturatedBedfordlimestonesampleatvariable effectivepressuresandfittingrelations.

Fig.5.16Compressionalslowness—densityplotforsandstonewithvaryingBiot-Krief exponents,withdataforunder-compactedsandstone. # MichelKrief.

Fig.5.17Compressionalslowness—densityplotforcarbonatewithvaryingBiot-Krief exponents,withcarbonatedata. # MichelKrief.

Fig.5.18 Vp and Vs versusporosityforwater-saturatedcleansandstonewithvarying aspectratios.

Fig.5.19Drycompressionalvelocitieswithdifferentaspectratiosandlabmeasurements incleansandstone.

Fig.5.20Dualporositywithmicroandmacroporesforvelocitymodeling.

Fig.6.1GenerationandpropagationofStoneleywaves.

Fig.6.2Stoneleywaveformincarbonateandshale.

Fig.6.3Stoneleywaveenergyandpermeability.

Fig.6.4Permeability,Stoneleyslowness,andStoneleyamplituderatiobetweentwo receivers.

Fig.6.5ComparisonofdifferencebetweenmeasuredStoneleyslownessandpredicted nonpermeableelasticslowness(ΔΔT),andcoremeasuredpermeabilityfor limestone.

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Fig.6.6Stoneleyvelocityandattenuationdispersionundervaryingpermeability.179

Fig.6.7ComparisonofBiot’slow-frequencyresultswithWhite’smodelforcoresamples ofvaryingporosityandpermeability;dashedcurvesareresultsfromWhite’s model,solidcurvesareBiot’slow-frequencysolution.

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Fig.6.8ComparisonofBiot’slow-frequencyapproximationwithBiot’sfullsolutionfor coresamplesofvaryingporosityandpermeability,dashedcurvesarefull solutions,solidcurvesareresultsfromthelow-frequencyapproximation.182

Fig.6.9ComparisonbetweenlaboratoryresultswiththeoreticalmodelingforBerea sandstone. 183

Fig.6.10Comparisonbetweenlaboratoryresultswiththeoreticalmodelingforsynthetic glassbeadsamples. 183

Fig.6.11FieldcomputationofStoneleypermeabilityindolomiticlimestone. 185

Fig.6.12MatchbetweenStoneley-derivedfieldpermeabilityandmeasuredwholecore permeability. 186

Fig.6.13MatchbetweenStoneleyandNMR-derivedpermeability. 187

Fig.6.14NormalizationofStoneleypermeabilityindexwithcoredpermeability. 188

Fig.6.15ComparisonofStoneleypermeabilityindicesfromStoneleyattenuationand slownessincarbonate(SchlumbergerOilfieldReview,January1995). 189

Fig.6.16Computationofmembraneimpedancewithmulti-frequencyanalysis. 193

Fig.6.17Effectofmud-cakeimpedanceonStoneleyslownessdifferencebetween permeableandnon-permeableformations. 194

Fig.6.18SensitivityanalysisofStoneleypermeabilitywithStoneleyslowness. 196

Fig.6.19SensitivityanalysisofStoneleypermeabilitywith(A)shearslownessand (B)formationdensity. 196

Fig.6.20Dynamicpermeabilityfor(A)10%porosityand(B)20%porosityformations.198

Fig.7.1Fluideffectonvelocityforshalysand.(A)CombineddatafromHanetal. (1986)andYin(1992)and(B)KhazanehdariandMcCann’s(2005)data.206

Fig.7.2VelocitiesfromGassmann’smodelinfluid-saturatedcleansandstones.208

Fig.7.3ComparativeinfluenceofsquirtandBiot’smechanismonacousticdispersion.212

Fig.7.4Comparisonofmeasured Ksat withestimated Ksat fromGassmann’soriginaland modifiedequations. 216

Fig.7.5(A)Porosity-shaleinlaminatedshalysandand(B)Fluidsubstitutionin laminatedshalysand. 217

Fig.7.6Water-gaseffectivefluidmodulusthroughdifferentmixinglaws(using Kw 2.4GPa, Kg 0.05GPa, Kf inlogarithmicscale)

Fig.7.7Shearweakeningatseismicfrequenciesandshearstrengtheningatultrasonic frequencies.

Fig.7.8 Vp prediction(40MPa,20%porositysand)frompatchysaturationand comparisonwithdifferentmixinglaws.

Fig.7.9 Vp prediction(20MPa,34.6%porositysand)frompatchysaturationand comparisonwithdifferentmixinglaws.

Fig.7.10Differentialcompressibilityinshalysand(with Vcl ¼ 0%,20%,40%)with differentsaturants.

Fig.7.11Correlationbetweenshearcompressibilityandestimateddryframebulk compressibility.

Fig.7.12Hydrocarbonsaturationfrommodulusdecompositioninshalysand.

Fig.7.13Shearcompressibilitydependenceonporosityincarbonate.

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Fig.7.14Hydrocarbonsaturationfrommodulusdecompositionindolomiticlimestone.235

Fig.8.1Homogeneity-inhomogeneityandisotropy-anisotropy.

Fig.8.2(A) Vp and(B) Vs velocityanisotropyinshaleforselectpropagationdirectionas afunctionofpressure.

Fig.8.3 Vp and Vs velocitiesparallelandperpendiculartolayer,andRHGaveragefordry clayminerals.

Fig.8.4ImpactofbrinesaturationonThomsenanisotropyparametersin(A)Bazhenov shaleand(B)Montereyshale.

Fig.8.5Relationshipbetweenkerogenvolumeandclayvolume.

Fig.8.6(A) Vp measurementversusmodifiedBackusaveragepredictiononlow-porosity shale,(B)anisotropydependenceonkerogenvolume.

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ListofFigures

Fig.8.7Rockphysicsmodelthroughelasticboundsinorganicclays.

Fig.8.8Characteristicanisotropyincontextwithborehole.

Fig.8.9Planeofpolarizationparallel(X–Z)andperpendicular(Y–Z)tofracturefor shearwavetravelingin Z-directioninafracturedformation.

Fig.8.10Cross-dipoleanisotropymeasurement.

Fig.8.11Fieldexampleoffour-componentcross-dipolewaveformdata.

Fig.8.12Anisotropyanalysisresultfromcross-dipoleanisotropymeasurement.

Fig.8.13Fieldexampleofshearsplittingduetostress-inducedanisotropy(left) monopoletool,(right)dipoletool.

Fig.8.14Flexuralwavedispersionforanisotropicrockinunstressedandstressed conditions.

Fig.8.15Flexuralwavedispersionforananisotropicrockunder(A)unstressedand (B)stressedconditions.

Fig.8.16AnisotropyevaluationusingStoneleywaves.

Fig.8.17Anisotropyevaluationusingcross-dipoleandStoneleywaves.

Fig.8.18Impactofwelldeviationonsoniclog.

Fig.8.19Slownessdependenceof(A) qSVandSHwaves,(B) qP waves,onanglebetween boreholeaxisandTIsymmetryaxis.

Fig.9.1(A)Uniaxialcompression,(B)perpendicularandparallelstress,(C)Mohr’s circle.

Fig.9.2Mohr’scirclewithequalandnonzerolateralstress(σ 2 ¼ σ 3 ¼ 0).283

Fig.9.3Generalstress-strainbehavior:(A)linearandnonlinearelasticelastic, (B)hysteretic.

Fig.9.4Deformationprocessstages:(I)poreclosure,(II)stablefracturegrowth, (III)unstablefracturegrowth,(IV)postfailure.(A)Stress-strainprofile.(B)Pore deformation.

Fig.9.5Relativestiffness,strength,andbrittlenessfromstress-strainprofiles.

Fig.9.6StaticYoung’smodulusfromauniaxialstress-strainprofile.

Fig.9.7TypicalstaticversusdynamicYoung’smoduliforsandstone.

Fig.9.8EffectofconfiningpressureonratioofstatictodynamicYoung’smodulusfor limestone.

Fig.9.9Typicalstaticversusdynamicbulkmoduliforacarbonate.

Fig.9.10CoulombfailuremodelandMohr’scirclediagram.

Fig.9.11Mohr-CoulombfailuremodelandMohr’scirclediagram.

Fig.9.12Griffith’sfailuremodel:(A) σ 1–σ 3 parabolaand(B)failureenvelopeinMohr’s circle.

Fig.9.13Empiricalfailuremodeltodefineafunction(A) f1 forfractureand(B) f2 foryield indifferentrocks.

Fig.9.14GraphicalrepresentationofthemodifiedLadefailuremodel.

Fig.9.15ComparisonbetweenMohr-CoulombandHoek-Brownfailurecriteriain σ 1 – σ 2 space.

Fig.9.16(A)ComparisonbetweenmodifiedLadeandWiebols-Cookfailurecriteriaand (B)inscribedandcircumscribedDrucker-Pagerfailurecriteria(Colmenaresand Zoback,2002.Int.J.RockMech.Min.Sci.39).

Fig.9.17Scatterofpredictedvs.measuredUCSinshale.

Fig.9.18Normalandabnormalporepressuredefinition.

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Fig.9.19Uniaxialcoremeasurementforporevolumecompressibility.

Fig.9.20Log-derivedporevolumecompressibilityusingaspectratioinversion.

Fig.9.21Comparinglog-derivedporevolumecompressibilityincarbonatewithlab measurements.

Fig.10.1Conceptualmodelfortheintegrationofexperimentalandtheoreticalrock physicsintotheinterpretationofgeophysicalwelllogsandseismic.In parenthesesareexamplesofrockproperties.

Fig.10.2Conceptualmodelofspatial(A)andfrequency(B)scalingofelasticdataset. Therelaxedandunrelaxedregimesrefertofluidflowandpressuresinthepore spaceofanundrainedsample(C).

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Fig.10.3Wave-inducedfluidflow(arrows)sketchshowingtheperturbationoffluidsin theporespaceduetoelasticwavedeformation(compressionanddilatation). Theimageat t ¼ 0representsarelaxedstate.Thefluidreturnstoitsoriginal equilibriumstatewithinonewaveperiod(T).Thedifferentbackgroundpatterns refertoelasticallysoft (darkgray) andstiff (lightgray) rockinhomogeneity.331

Fig.10.4Ultrasonic P-(A)and S-wave(B)velocityforbasaltsandclasticsamples.Basalt sampleshavelowporosityandpresentmicro-fractures.Clasticsampleshave variableporosityandclaycontent.

Fig.10.5Ultrasonic P-(A)and S-wave(B)velocitiesforasyntheticcarbonatesamplewith porespacesofadifferentaspectratio(α).

Fig.10.6Ultrasonic P-(A)and S-wave(B)velocitiesasafunctionofdifferentialpressure. GranitedatafromNurandSimmons(1969).BereasandstonefromToksoz etal.(1979).Solidsymboliswater-saturated,opensymbolisdry.

Fig.10.7Conceptual P-(A)and S-wave(B)attenuationintermsofqualityfactor(Q)asa functionofdifferentialpressureforsandstones.W:fully-watersaturated, pW:partialwatersaturation,D:dry.

Fig.10.8Velocity(A)andbulkmodulus(B)asafunctionofwatersaturation.Carbonate dataarefromforcedoscillationandultrasonicdatafromAdametal.(2009). SandstonedataareacquiredwiththeresonancebarbyWinklerandMurphy (1995).

Fig.10.9Bulkmoduliofasaturatedanddrycarbonatesampleasafunctionoffrequency. Dataatfrequenciesbetween3and3000Hzareacquiredwithaseismic frequencysystem,whileMHzdataisfrompulsetransmission.Dashedlinesare hand-drawntoshowthedispersiontrend.

Fig.10.10Young’smodulusasafunctionofapparentfrequencyacquiredwithanSFS system.Thefluidsarewater (diamond) andglycerin (square); circle symbolsarefor adrysample.Trianglesareultrasonicdata.

Fig.10.11MeasuredandGassmann-modeledbulkmodulusat100Hzand0.8MHzfor brine-saturatedcarbonatesatlow-3.5MPa(A)andhigh-31MPa(B)confining pressure.

Fig.10.12 P-(circles)and S-wave(squares)velocitiesasafunctionoftemperaturefor awater-saturatedgranite( 1MHz)andBereasandstone(resonancebar, 1.7–34kHz).Opensymbolsareforwhenthefluidpressureisbeingheld constant.Solidsymbolsareforaclosedsystem,wherethefluidpressure increasesasaresultofincreasingtemperature.

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ListofFigures

Fig.10.13Temperatureeffectonultrasonic P-wavevelocitiesasaresultofsaturatingfluid transformations.(A)FontainebleausandstonesaturatedwithCO2 fordifferent porefluidpressures—symbols.LinesareGassmann-modeledvelocitiesbasedon theexperimentalCO2 conditions.(B)and(C)arethedensityandbulkmodulus, respectively,ofpureCO2 estimatedwiththeNISTonlinecalculator(2015).344

Fig.10.14ColdLakesandstonedry(opentriangles)andsaturated(closedtriangles)with heavyoil,andheavyoil-saturatedBereasandstone(stars)anditscorresponding Gassmannmodeling(solidline).

Fig.10.15Sketchofa P-wavewavefrontinahorizontallylayeredmediumwiththelayering normaltothe z-direction.

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Fig.10.16Modeledelasticwaveformsforananisotropicsample(A).(B)Modeled waveformandlocationofpiezocrystals(transducers).(C)Modeledultrasonic waveformsasafunctionofoffset(zoomof(B))andtransducerwidth.347

Fig.10.17Laserultrasonictransmissionscans(bottom)andmicrophotographs(top)of twoorganicmudstones.(A)Induratedandpreservedorganicmudstonewith visiblelaminations(black arrows).(B)Organicmudstonewithmicrofractures (arrows)measuredat1MPaconfiningpressure.

Fig.10.18Ultrasonictransducerexperimental P-(A)and S-velocities(B)forthree mudstonesasafunctionofdifferentialpressure.Ongetal.(2016)measureda dryDuvernaymudstone(Canada),VernikandLiu(1997)awater-saturated Bakkenmudstone(UnitedStates),andDewhustandSiggins(2006)apreserved andpore-fluidpressure-controlledMuderongmudstone(Australia).

Fig.10.19Thomsen’selasticanisotropyparametersforthedatainFig.10.17.Solidand opensymbolsarethe ε (P-waveanisotropy)and γ (S-waveanisotropy) parameters,respectively.

Fig.10.20Shearmodulusofadry(humidified)samplecomparedtoafullybrine-saturated carbonatesamplemeasuredwiththeSFSsystem(100Hz)andultrasonic transducers(0.8MHz).Frameweakeningisobservedatlowfrequencies,while modulidispersiondominatestheultrasonicdomain.

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Fig.10.21SEMimagesofthemicrostructureofabasaltsamplebefore(A)andafter(B) reactionswithcarbonicacid.Beforethereactions,thefreshbasalthasglass, plagioclase(plg),andolivineasframe-formingminerals.Afterthereactions, carbonates(carb)precipitatepluggingmicrofracturesandporespaces.352

Fig.10.22Ultrasonictransduceracquisitiongeometries:(A)transmissionsetup, (B)pulsedecho-setup,and(C)passiverecording.Piezocrystalsinside transducersactassourcesorreceivers.Arrowsrepresentwavepaths.In(C)the grayfracture(rockfracturing)isthesourceofultrasonicwaves.

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Fig.10.23Spectralratiomethodologyonsyntheticwaveforms.(A)Waveformsonan aluminumandarocksamplewitha Qr of50.(B)Normalizedamplitudespectra ofthewaveformsin(A).(C)Naturallogarithmoftheratioofthespectrain(B), with Qr ¼ 53fromthislinearfit.357

Fig.10.24Pulse-echosetupwithonetransducershowingthereflectioninterphasesfortwo events(A).Exampleofarecorded S-wavepulse-echotrainpropagatingina sedimentarycoresample(B).359

Fig.10.25(A)Resonancebarsystemsketch.[a]or[b]aretwopossiblelocationsofthe rigidsupportsforthesample.(B)Resonanceultrasoundsystem.The transducerscouldalsobeplacedflatonthesampleends.

Fig.10.26Elasticmodulidependenceonstrainamplitude.Murphy(1982)shearmodulus data(squares)areacquiredwitharesonancesystemona1mMassillon sandstoneat66–78Hzandis92%watersaturated.Young’smodulusdata (circles)combineaseismicfrequencysystemandanaxialcyclingloading (0.001–0.05Hz)acquiredonabrine-saturatedtightsandstone.

Fig.10.27SeismicfrequencysystemsetupafterSpencer(1981)andBatzleetal.(2006) (A).Sketchofthestraingaugesignalsforaparticularfrequency(B).Dataof calculatedstrainswithfrequencyappliedonacarbonatesample(C).

Fig.10.28Seismicfrequencysystemdatameasuredonabrine-saturatedcarbonatesample withasystemshowninFig.10.27.(A) P-wavevelocityasafunctionof frequency.(B)Inverseofthe P-wavequalityfactorestimatedfromthestrainstressphaselagsforthesamesample.

Fig.10.29Multi-transducer(A)andmultipathtransducer(B)pulse-transmissionsystems. (A)Designfrom(Saroutetal.,2014),where P-wavetransducerscanbe substituted/combinedwith S-wavemodes.(B)Multipathtransducersetup redrawnafterLokajı´cˇekandSvitek(2015).Therocksampleissphericalandis rotatedalongthe θ and λ angles,providing3-D P-andtwoorthogonally polarized S-wavepathwaysonthesample.

Fig.10.30Examplesetupsforascanninglaser-ultrasonicsystem.(A)Transmissionsetup wherethesampleisrotatedaroundthecylinder’sverticalaxis.(B)Transmission setupwherethesampleistranslatedalongthecylinder’sverticalaxis. (C)Reflectionsetupwiththereceiverlaseronthetranslationalstage.

Fig.10.31Noncontactinglaserultrasonicrotationalscansonanisotropic(A)and anisotropic(B)cylinder.Thewaveformsrecordedonanaluminumsampleare plottedevery10degreestoillustratesomeofthewavemodesrecordedandthe repeatabilityofthesystemonanisotropicmaterial.Theanisotropic ultramylonitesamplehasfoliationparalleltothecylinderaxis.Theacquisition setupforbothsamplesisthatofFig.10.30A.

Fig.10.32Scanningacousticmicroscopysetup.

Fig.11.1Cementbondlog-variabledensitylog(CBL-VDL)sonictool.

Fig.11.2WavetrainandcorrespondingVDL.

Fig.11.3CBLin(A)badcementationand(B)well-bondedcementzone.

Fig.11.4Compensatedcementbondtool.

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Fig.11.5Ultrasonictool(A)deviceconfiguration,(B)reflections,(C)evaluationconcept.386

Fig.11.6Cementchannelevaluationbyultrasonictool.

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Fig.11.7Cementevaluationbyultrasonicimagingtool. 391

Fig.11.8Casingevaluationbyultrasonicimagingtool.

Fig.11.9Toolsetupforflexuralwave,third-interfacewave,andnormalultrasonicecho pulse.

Fig.11.10Interpretingflexuralattenuation(A)withacousticimpedanceand(B)withSLG mappingforclassGcement.

Fig.11.11Cementevaluationbyflexuralattenuation,ultrasonicmeasurement,andSLG map.

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Fig.11.12AdvancedcementevaluationbycombiningTIEwithflexuralattenuation.400

Fig.11.13Characteristicsyntheticseismogramofan(A)openholeand(B)casedhole.401

Fig.11.14Syntheticwaveformof(A)bondedcasingand(B)un-bondedcasing.

Fig.11.15Casedholedipolebefore(left)andafter(right)toolcentralization,lowfrequencyfiring,andoptimizedT-Rspacing.

Fig.11.16Casedholehydrocarbonevaluationinshaly-sandpotentialreservoir.

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Fig.11.17Bypasshydrocarbonevaluationthroughcasedholesonicinshalysand.408

Fig.12.1HSandVoigt-Reussboundsinaquartz-calcite-claycomposite:(A)matrixbulk modulus,(B)matrixshearmodulus,(C)HSandVRHaveragesformatrix modulusinaquartz-claycomposite.

Fig.12.2Brie’sfluidmodulusforawater-gasmixturewithvariable e.

Fig.12.3WatersaturatedvelocitypredictionfromHan,Eberhart-Han-Zoback(EHZ), Castagna-Batzle-Eastwood(CBE)relationships,(A)VP prediction(B)VS prediction.

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Fig.12.4Water-saturated Vp-Vs profilefromCastagnaandHan’srelations. 417

Fig.12.5Drybulkandshearmodulifromvariousmodels.

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Fig.12.6Shearvelocityfrom Vp incarbonatefromGreenberg-Castagna’srelation.420

Fig.12.7FlowchartfordryframeeffectivemediummodulifromWu’sself-consistent theory.

Fig.12.8FlowchartforeffectivemediummodulifromDEMtheory.

Fig.12.9FlowchartforGassmann’sfluidsubstitutionusinglogdata.

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Fig.12.10FlowchartforvelocitypredictionandfluidsubstitutionfromXu-Whitemodel.428

Fig.B.1Hydrocarbongaspropertiesasafunctionoftemperature,pressure,and compositionforlightgas(G ¼ 0.6)andheavygas(G ¼ 1.2):(A)gasdensityand (B)gasbulkmodulus.

Preface

Seismictechnologyhasbeenanintegralpartofhydrocarbonexplorationsincethefirst seismicexplorationpatentin1917andthefirstfieldtestinOklahomain1921.Borehole acousticswasfirstpatentedin1935andsuccessfullydevelopedlaterasacontinuous velocityloggingtool,providingamuchfinerverticalsubsurfaceperspectivethanseismic acoustics.Rockphysicsisthecrucialdisciplinethatinterfacesacousticwaveamplitudeand velocities,fromseismicorboreholesonicmeasurements,withpetrophysicalcharacterization. Thefoundationfortheoreticalrockphysicscanbetracedbacktoseminalworksbetween the1940sandthe1960sbyMauriceA.BiotandFritzGassmann.Atthesametime, experimentaldevelopmentswerebeingledbyM.R.J.Wylie,A.R.Gregory,L.W.Gardner, G.Simmons,A.Nur,andG.R.Pickett,providingthebasisforexperimentalvalidationof theoreticalmodeling.Sincethen,thefieldofboreholeacousticsandrockphysicshas rapidlyprogressed,developingnewpetrophysicaloutlookstoextractquantitativerock propertiesfromgeophysicalobservations.

Poroelasticity,asubdisciplineofrockphysics,aimstocharacterizerockphysicalproperties basedonelasticwavepropagation.Throughtheoryandempiricalrelationships,itconnects theacousticdatatotheintrinsicrockpropertiessuchaslithology,porevolumeandshape, fluidtypeandpressure,geomechanicalbehavior,tectonicstresses,andtheoverallrock architecturesuchaslaminationsandfractures.Seismic,boreholesonic,andexperimentalelastic corestudiesaimatcharacterizingtheserockelements;however,theyrepresentthephysical propertiesatdifferentfrequencyandscaledomains.Rockphysicsbringsthesestudiestogether todevelopquantitativelythepetrophysicalcharacterizationofreservoirs.

Whileboreholeacousticandrockphysicsjointlyservetoprovidebroadreservoircharacterization, thesedisciplinesrarelyfindacomplementingplatforminasinglebook.The Handbookof BoreholeAcousticsandRockPhysicsforReservoirCharacterization aimstobringbothbranches togethertounderstandbetterthetheoreticalbackgroundandapplicationpotentialforfundamental andadvancedconceptsinboreholeacousticsandrockphysicsforreservoircharacterization. Thebookprovidesbackgroundmodelingconceptsandkeyresults,balancingthemathematics withitsapplications.Therefore,thebookaimstoserveasatechnicalreferenceforoilandgas professionals,scientists,andstudentsinmultidisciplinaryareasofreservoircharacterization.

Thebookcombinesfundamentalconceptsofrockphysics,acousticlogging,waveformprocessing, experimentalcoreacoustics,andelasticitymodeling.Eachchapterdemonstratesconceptsand applicationsthroughgraphicalexamplesderivedfromfielddata.Resultsfromcorestudiesand adetailedexplanationofexperimentalsetupsandmethodologiesareincludedtovalidatesome ofthetheoreticalconceptsandmodels.Thebookdiscusseslimitationsonacousticsonicand experimentaldata,modelingtechniquesandpresentingpracticalwaystoovercomethese limitations.Thebookaimstoprovidethebasictheoryandpetro-acousticapplicationsbehind thetransitionfromconventionaltomodernboreholeacousticsandtheroadahead.

Thehandbookattemptstoencapsulateawiderangeoftopicsonelasticwavepropagation,borehole sonictooltechnology,andporoelasticmodeling,andtheirapplicationtowardslithology,porosity, fluidsaturation,Stoneleypermeability,anisotropy,coreacoustics,rockmechanics,andcasedhole acoustics.Thebookalsoprovidessomekeyworkflowssupportedbyexamplesforeasy implementationandunderstanding.Eachchaptercombineshistoricalresearchfrompeerreviewedliteraturewithtechnicalup-to-datematerialonthetechnology.Wehopethatthe handbookwillbeofinteresttogeoscienceprofessionals,students,andacademics.