[PDF] SANDSTONE PORE ASPECT RATIO SPECTRA FROM - CORE

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SANDSTONEPOREASPECTRATIOSPECTRA

FROMDIRECTOBSERVATIONSANDVELOCITYINVERSION

by

D.R.Burns,C.H.ChengandR.H.Wilkens

EarthResourcesLaboratory

DepartmentofEarth,Atmospheric,andPlanetarySciences

MassachusettsInstituteofTechnology

Cambridge,MA02139

ABSTRACT

MeasurementsofporeshapesfromScanningElectronMicroscope(SEM)images forthreesandstonesamples(theNavajoSandstone,the

WeberSandstone,andthe

KayentaSandstone)arecomparedtotheaspectratiospectraobtainedfrom invertinglaboratoryvelocityversuspressuredatausingthemethodofChengand Toksiiz(1979).Theresultsindicatethattheinversionmethodisinverygood agreementwiththeobservationsathighaspectratios(ex>0.01).

Atlowaspect

'ratiostheagreementisverygoodforthecleanNavajoSandstonesample,butpoor fortheWeberandKayentasampleswhichcontainclay.TheNavajosampleis composed chieflyofquartzwithsignificantpressuredissolutionapp,arentalonggrain contactsresultinginsmooth,flatcracksbetweengrains.TheWeberandKayenta sampleshaveroughercracksurfaces aswellastaperedporeedges,indicatingthat asperities,andnon-ellipticalporeshapesmayresultinanoverestimationoflow aspectratiocracksbyvelocityinversion.Thepresenceofdegradedfeidsparsmay alsoplayarole.

INTRODUCTION

For thepastthirtyyearstheeffectofcracksandporestructureonvariousrock propertieshasbeenthesubjectof intensestudy.Thisefforthasbeenespecially fruitfulinexplainingthebehaviorofrocksasafunctionofpressuredueto'the closingofcracks(Walsh,1965).Recentstudieshavecontinuedthislineof investigationbyattemptingtodescribetheporestructureinsomequantitativeway.

Simmonsetal.(1974)introducedthethedifferentialstrainanalysis(DSA)techniquewhichrelateshighprecisionstaticstrainmeasurementstotheclosurepressuresof

pennyshapedcracksasdescribedbyWalsh(1965).FevesandSimmons(1976) appliedtheDSAmethodtotheWesterlyGranitetoestimatetheaspectratiosof stressinducedcracks.ChengandToksiiz(1979)estimatedporestructureby calculatingaspectrumofporeaspectratios(ex)fromtheinversionoflaboratory velocitymeasurementsatvariouspressures.Theirprocedurewasbasedon calculatedcrackclosurerates,andthevelocitymodellingoftwophasemedia developedbyKusterandToksiiz(1974).Morerecently,Simmonsetal.(1982,

1983)haveemployedScanningElectronMicroscope(SEM)imagesandpointcounting

techniquestoquantifyporespaceinanefforttoexplainrockbehaviorandtherole ofclays.PorestructureestimatesfromboththeSEMandinversionmethodshave beenusedsuccessfullytopredictrockproperties.Toksozetal.(1976)usedthe inversionspectratomodelthein-situvelocityofrockswithvaryingporefluids. 463
464

Burnsatal.

Brace(1977)usedthecrackspectrafrombothmethodstoestimatepermeability usingtheCarman-Kozenycapiilarymodel.Wilkensetal.(1984)usedSEMporosity studiestoderiveaneffectiveaspectratiospectrumofasuiteofsandstoneswhich successfullyexplainedthevelocitybehaviorofawiderangeofsamples.Allofthese studiesindicatethataknowledge.ofporestructureprovidesameansofpredicting manyrockproperties. Althoughthevelocityinversionspectrumhasbeensuccessfulinpredictingrock behaviorinseveralinstances,acomparisonofthisspectrumwiththeactualpore distributionfromSEMimageswouldprovideameasureofhowwelltheinversion techniquerepresentstheporestructure.ChengandToksoz(1979)comparedthe InversionspectrumforWesterlyGranitetothatobtainedbyHadley(1976)fromSEM images.Theagreementwasquitegooddowntoaspectratiosofabout0.001,but smallervalueswerebeyondtheresolutionoftheSEMimages.Kowallisetal.(1982) comparedcrackaspectratiospectrafromtheSEMandinversionmethodsfor Icelandicbasalt.Theyconcludedthatthetwospectraweresimilarinasmallregion ofoverlap,butthattheresolutionlimitsofthetwomethodsweresignificantiy different.Theinversionmethodcanonlybeexpectedtoresolvebetweenaspect ratiosthatclosewithinthepressurerangeofthelabmeasurements(1-2kbars). UsingthepennyshapedcrackexpressionsfromWalsh(1965),andassumingquartz moduli,apressureof1kbarwouldclosecrackswithanaspectratioofabout0.001. SEMimages,ontheotherhand,aremorereliableatthehighaspectratioend.

Hadley

(1976)andKowallisetal.(1982)bothhadSEMresolutionlimitsofabout

0.03fJ-mforcrackwidthmeasurementsduetotheconductivecoatingonthe

samples.Thislimit,togetherwiththefactthatmostcracklengthswereontheorder oftheaveragecrystalsize(roughly10fJ-m),restrictedtheaspectratio measurementstovaluesgreaterthanabout0.003. Todatetherehavebeennocomparisonsbetweenthetwotechniquesforclastic rocks.Sandstonespresentseveralproblemssincetheporosity(inmostcases)is primarilycontainedinlarge,irregular,hi9haspectratiopores.Suchporesaredifficult tocharacterizeandmeasureonSEMimagesandalsofallintheregionofpoorest resolutionforthevelocityinversionmethod.ThisstudywillcompareSEMand velocityinversionspectraforthreesandstonesofvaryingporosity:Weber(9.5%),

Navajo(11.8%),andKayenta(22.2%).

PROBLEMFORMULATION

SEM SEMimagesusingthebackscatteredelectronmodewereacquiredforall3 samplesfrom cracksectionsasdescribedinSimmonsandRichter(1976)andusedin

Simmons

etal.(1982,1983).Aconductivecarboncoatingwasappliedtoall samples toavoidsurfacechargebuildup.Magnificationrangesfrom20to7700x wereusedwhichallowedmeasurementofcrackwidthsdownto0.2fJ-m.Pore measurements wereperformedonimagesat112xwhichprovidedadequate resolutionandafairlyrepresentativearea(about1mm 2 ).Crackwidthswere measuredathighermagnificationsandappliedtocracksvisibleonthe112ximages. There wereveryfewcracksobservableathighmagnificationwhichcouldnotbe identifiedontheprimaryimage(112x)andthesewereignoredduetotheextremely smallporevolumerepresented.BecauseporeshapesInsandstonescanbelargeand

Irregular,a

setofcriteriawasdevelopedtoallowconsistentmeasurementstobe 15-2 ( (

SandstonePoreSpectra

obtained.Poreswerecategorizedintofourgroupsfollowingtheterminologyusedby Simmonsetal.(1982,1983):intergranular,intergranularjtabular,connective,and micro (clayfilling).Thesegroupingswerebasedonthefollowingsetofcriteria: intergranu1.ar: highaspectratioporessituatedbetween

3ormoregrains

intergranu1.ar/tabular: tabularporesconnectingintergranularpores; situatedbetween2grains ccmneetive; cracksoflowaspectratio,comprisedofgrain contactsandintragraincracks micro: theporescontainedinclayfillingmaterial exceptions: (i)nointergranularjtabularporecanhaveitsmajoraxis perpendiculartoagrainface. (ij)noporeissubdividediftheporewidthchangesbyless .than50%overthelengthofthepore. (iii)poreswithmajoraxisdirectionchangesofmorethan30degrees aresubdividedintomultiplepores. TheeffectofclaysontheelasticpropertiesofporousrocksisthesUbjectof muchdiscussion.Wilkensetal.(1984),basedonastudy20sandstonesamples withvaryingclaycontent,contendthattheclayfillingisnon-supportiveand, therefore,theshapeoftheporecontainingtheclaywillaffecttheelasticproperties oftherock,buttheeffectoftheclayIslimitedtoreducingtheporosityofthe sample.If,ontheotherhand,theclayiscoupledtothesandstoneframework,then theshapeoftheindividualporeswithintheclayzoneswouldaffecttheelastic propertiesoftherock.Inordertosimplifythecharacterizationoftheporevolume containedintheclayzones,thetotalareacontainingclayontheSEMimagewas measured.Then, basedontheresultsofSimmonsetal.(1982,1983)andWilkenset al.(1984),theclayfilledzoneswereassumedtohaveaporosityof50%andthe poreswereassumedtohaveanaspectratioof0.2.Sincetheresultsofthisstudy areonlyconcernedwiththetotalporevolumecontainedinporesofgivenaspect ratios,theentireporevolumeoftheseclayzoneswasrepresentedbyasingle 'equivalentpore'ofaspectratio0.2. Foreachsampletheporesweretracedonmylarandcharacterizedbythe criteriajustgiven.EachporewasmeasuredInthefollowingway.Porelengthwas takenasthelongeststraightlinewhichcouldbedrawntotallywithinthepore.Pore widthwasmeasuredperpendiculartothelengthchordandtakenasthemeanwidth ofthepore.Cracklengthsweremeasuredfromthesamemicrographbutcrack 15-3 465
466

Bumseta1•.

widthswerebasedonhighermagnificationimages.

Porevolume

wascalculatedbyusingtheareaaverageapproximation(Hadley,

1976).Thisschemecomparedfavorablywiththeconventionalpointcounting

techniqueforoneofthesamples(NavajoSandstone,seenextsection).Itis assumedthroughoutthispaperthatthesamplesareisotropic,thatthepore distributioniscompletelyrandom,andthatthemeasurementofporeshapesintwo dimensionsissomehowrepresentativeoftheactualthreedimensionalstructure. Noneoftheseassumptionsisstrictlytrueforanyrock;howevertheresultsappear tobesufficientlyconsistenttoJustifytheapproachtaken.Inaddition,the complicatednatureofthesandstoneporestructurenecessitatedtheuseofa somewhatsubjectivesetofcriteriaforanaiysis.However,becausethegreat majorityofporevolumeiscontainedinhighaspectratiopores(>0.01),thecriteria arenottoocriticaiformeasuringaspectratios.Thestudyofporewidthsandlengths wouldbemuchmoresensitivetothesecriteria.

VelocityInversion

Velocitydataforthe3sampleswaspreviouslycollectedbyCoyner(19<34). TheinversionprocedureofChengandToksoz(1979)wasusedtogeneratethe aspectratiospectrumwhichprovidedthebestfittothevelocityversuspressure data,withtheaddedconstraintthatthecrackclosingrateiscontrolledbythestatic ratherthanthedynamiccompressibility.

RESULTS

In thissectiontheporeaspectratiospectrumof.eachsamplebasedonSEM imageanalysisandvelocityinversionispresented.

NavajoSandstone

TheNavajoSandstoneisafinegrainedandwellsortedquartzrichsandstone whichcontainsessentiallynoclayfilling.Thesamplehasameasuredporosityof

11.8%(Coyner,1984).AlowmagnificationSEMimage(Figure1)showsthatthe

porosityisnothomogeneouslydistributedonthissmallscale.Inordertoobtaina representativearea,twomicrographswereusedintheanaiysisofthissample representingthehighandlowporosit¥zonesseeninFigure1(Figures2and3).The areaofeachimagewas0.9375mm.ThecharacterizedporesareshowninFigures

4through7.The

calculatedporosityfromtheareaaveragemethodwas7.2%forthe lowporosityimage(Figure2)and13.8%forthehighporosityimage(Figure3).The overallcalculatedporosityforbothimageswas10.6%.Thisvaluewascheckedby pointcounting(1518points)overbothimageswhichyielded10.9%porosity.Atotal of486poresweremeasuredfromthetwoimageswitharangeofaspectratiosof

1.0to0.0011.Thespectraobtainedfromeachofthetwoimagesseparatelyare

showninFigure8a.Althoughthelowporosityimagecontainedfewerveryhigh aspectratiopores(>0.1)andmoreloweraspectratiopores"0.1),ingeneralthe agreementbetweenthetwospectraisverygood.Thiscomparisonsupportsthe assumptionofhomogeneityoftheporedistributionsinceaverysimilarspectrumcan beobtainedeveninzonesdifferingbyafactorof2inporosity.Thepore characterizationsfrombothimageswerecombinedtogiveanoverallSEMaspect ratiospectrumwhichisshown,togetherwiththevelocityinversionspectruminFigure 8b. 15-4

SandstonePoreSpectra

TheagreementbetweentheSEMporeaspectratiospectrumandthespectrum obtainedfromvelocityinversionisverygoodovertheentirerangeofaspectratios. SincetheSEMdatarepresentsacontinuumofaspectratios,theporevolume containedinarangeofaspectratiosissummedtogivethehistogramshowninFigure

8b(inthisandsubsequentfigureseachbarofthehistogramcontainsallaspect

ratioslessthanorequaltotheleftedgevalueandgreaterthantherightedge value).Initially,thespectrumobtainedfromtheSEMimagesforeachsamplewillbe presentedwiththesameaspectratiogroupingsforeasycomparison.Aslightly differentgroupingoftheSEMdataforthissample(dashedlineinFigure8b)reflects thefactthattheinversionmethodhaslumpedallporevolumeforaspectratios between0.1and0.005intothesinglevalueat0.1.

WeberSandstone

TheWeberSandstoneisaveryfinegrainedarkosicsandstonecontaininga moderateamountofclayandsomecalcite.Figure9showsthesampleatlow magnification. ArepresentativeareanearthecenterofFigure9waschosenfor anaiysis(Figure10).Figures11and12showtheporecharacterization.Atotalof

386poresweremeasured.Thecalculatedporosity(areaaverage)was9.4%versus

ameasuredporosityof9.5%(Coyner,1984).Therangeofaspectratiosmeasured was1.0through0.0018.PoreaspectratiospectrafromtheSEManalysisand velocityinversionareshowninFigure13.Theagreementbetweenthetwospectrais verygoodatthehighaspectratioend(a>0.005)butpoorattheiowaspectratio end.Theinversionmethodpredictsthat26%oftheporevolumeiscontainedin poreswithanaspectratioof0.1.Thisvalueismuchhigherthanthatpredictedfor theNavajoSandstone(5-12%dependingonthegrouping,Figure8b)andisinclose agreementwiththeobservedspectrum.Mostoftheobserveddifferencebetween theWeberSandstoneandNavajoSandstoneforabetween0.2and0.02canbe attributedtotheclaypresentintheWebersample.TheclaycontentoftheWeber Sandstoneis2.1%oftheareaexamined(Figure12)containing1.05%porosityor

11%ofthetotalporositywhichisincludedintheaspectratioof0.2.Inaddition,

thereisagreaterdensityofgraintograincontactsandintragraincrackspresentin theWebersample(Figure12).

KayentaSandstone

TheKayentaSandstoneisafinetomediumgrainedpoorlyconsolidatedarkose whichisclayrich(Figure14).Asinglemicrographwasusedforanalysisandis showninFigure15.Thecalculatedporosityofthissamplebasedonthearea averagemethodwas17.9%versusameasuredporosityof22.2%.Atotalof246 poresweremeasured(Figures16and17)encompassinganaspectratiorangeof1.0 -0.00167.ThespectraobtainedfromthetwomethodsaregiveninFigure18(the SEMdataisgivenbythesolidlineandtheinversiondataisgivenbythestars).The agreementbetweenthetwomethodsispooratallaspectratios.Theimageanalyzed forthissample(Figure15)hadaclaycontentof3%(1.5%porosityorabout8%of thetotalporosity).Acloserexaminationofthelowmagnificationimage(Figure14) indicatesthattheclaycontentoftheoverallsampleisprobablycloseto10%.It seems,then,thattheanalysiscarriedoutforthissampleunder-representedtheclay fillingmaterialbyaboutafactor3.Inordertoseeifthisunder-samplingwas responsibleforthepooragreementbetweenthetwospectra,theclaycontentofthe SEMdatawasincreasedbyafactorof3(allotherporedatawereleftunchanged). Thecalculatedporosityforthiscaseincreasedtoabout21%,veryclosetothe measuredvalueforthesample,andtheagreementbetweenthetwospectraismuch 15-5 467

468Burnsetal.

improved atthehighaspectratios(dashedlineinFigure18),althoughtheagreement isstillrelativelypooratthelowaspectratioend.

Wilkens

etal.(1984)Intheirdiscussionoftheeffectofclaysonthevelocityof porousrocksindicatedthattheclaycontentreducestheporosityoftherock,but doesn'treducetheframeworkporespace.Ineffect,theyarguethattheclayis decoupledfromthegrainframeworkoftherockandthatthevelocityoftherockis stillcontrolledbytheframeworkporespace.Inordertotestthishypothesis,the KayentaSandstonevelocitydatawasinvertedasecondtimewiththesameaspect ratiodistributionbutwitha5%increaseinporosity(representingtheapproximate non-voidvolumeoftheclayfilling).Theresults(trianglesinFigure18)showbetter agreementatthehighaspectratioswiththeactualSEMobservations(solidlinein

Figure

18).Althoughtheagreementatlowaspectratiosisslightlybetter,thematch

isstillfairlypoor.ThisoneexamplelendssomesupporttotheWilkensetal.(1984) claymodel,althoughmuchadditionalworkisneededtofUllyevaluatethehypothesis.

DISCUSSIONANDCONCLUSIONS

Thereisgoodagreementathighaspectratiosbetweenthespectraobtained fromtheanaiysisofSEMimagesandvelocityinversionfortheNavajoandWeber Sandstones.TheKayentaSandstoneshowedpooragreement,butthiscanbe attributedinparttothenon-representativeareausedfortheanalysiswhich severelyundersampledtheclaycontent.Theagreementatlowaspectratioswas goodfortheNavajoSandstone,butquitepoorfortheWeberandKayenta Sandstones,bothofwhichhadafairamountofclay.Thereisundoubtedlysomeerror involvedinSEMmeasurementsforfinecrackswithlowaspectratios,butthisdoes notexplainthediscrepenciesbetweentheapparentagreementforthecleansampie and thelackofagreementforthetwosampleswithclay.Acloseexaminationofthe SEMimagesforthe3samplesindicatesthatthegraintograincontactsare somewhatdifferentfortheNavajosamplewhencomparedtotheWeberandKayenta samples.TheNavajoSandstoneispredominantlycomposedofquartzwithsome feldspar.Thefeldsparisveryfreshwithalmostnodegradationvisible.Thegrain contactsbetweenthequartzgrainshavealmostallbeencementedbythe reprecipitationofquartzthroughpressuredissolution.Theresultisthatthegrain contactsappearasfinecrackswithfewasperities.TheWeberandKayenta samples,ontheotherhand,havelessquartzdissolutionalonggrainboundariesand thefeldsparsaredegraded,especiallyintheKayentaSandstone.Asaresult,the NavajoSandstonegraincontactsappearasflatcrackswhiletheWeberandKayenta samplesappeartohavefairlyroughcracksurfaces.Inaddition,theWeberand KayentasampleshavemoretaperingalongtheporeedgesthantheNavajosample. All oftheseobservedfeaturescouldaffecttheelasticbehavioroftherocks. Asperitiesalongcracksurfacesmayalterthecrackstiffnesses,whiletaperedpore edgeswouldresultinnon-ellipticalporeshapes(MavkoandNur,1978)whichwould havesomewhatlessstiffnessthananellipticalcrackofthesameaspectratio( a non-ellipticalpore,then,wouldbehavelikeathinnerellipticalpore,orsome combination ofthinnerellipticalpores).Degradedfeldspargrainscouldalsoalterthe elasticbehaviorofthesample.Ingeneral,then,thelackofagreementatlowaspect ratiosfortheWeberandKayentasamplesmaybeduetothepresenceofdegraded feldsparsorthefactthattherehasbeenlessquartzdissolutionalonggrain boundaries tosmoothoutandflattenthegraincontacts,resultinginan overestimationofthelowaspectratiocracksfromthevelocityinversion.Forthe NavajoSandstonesample,thevelocityinversionmethoddoesnotappeartobe 15-6 ( (

SandstonePoreSpectra

overestimatingtheporevolumeintheselowaspectratiopores,probablyduetothe freshgrainsandsmooth,flatgraincontacts. Ingeneral,theresultsindicatethatthevelocityinversionmethodofChengand

Toks6z

(1979)isrepresentativeoftheporestructureofsandstonesathighaspect ratiosasquantifiedby2dimensionalSEMimages.Anempiricalresuitofthisstudyis thatthegreatmajorityofsandstoneporevolumeiscontainedinhighaspectratio pores(>0.01)andthattheclayzoneporosityisanimportantsourceofporevoiume in the0.2aspectratiorange. TheauthorswouldliketothankTomWisslerfortheuseofhiscracksections andhishelpinobtainingtheSEMimagesusedinthisstudy.D.R.Burnswaspartially supportedbyaPhillipsPetroleumFellowship.

REFERENCES

Brace,1977,Permeabilityfromresistivityandporeshape:J.Geophys.Res., v.82,p.3343-3349. Cheng,C.H.andToksQz,M.N.,1979,Inversionofseismicvelocitiesforthepore aspectratiospectrumofarock:J.Geophys.Res.;v.84,p.7533-7543. Coyner,K.B.,1984,Effectsofstress,porepressure,andporefluidsonbuikstrain, velocity,andpermeabilityinrocks:Ph.D.thesis,MIT,Cambridge,MA.

Feves,

M.andSimmons,G.,1976,Effectsofstressoncracksinwesterlygranite:

BSSA,v.66,p.1755-1765.

Hadley,K.,1976,Comparisonofcalculatedandobservedcrackdensitiesandseismic velocitiesinwesterlygranite:J.Geophys.Res.,v.81,p.3484-3494. Kowallis,B.J.,Roeloffs,E.A.,andWang,H.F.,1982,MicrocrackstudiesoftheIceland researchdrillingproject:J.Geophys.Res.,v.87,p.6650-6656. Kuster,G.T.andToksQz,M.N.,1974,Velocityandattenuationofseismicwavesintwo phasemedia,partI-theoreticalformulations:Geophysics,v.39,p.587-606. Mavko,G.andNur,A.,1978,TheeffectofnonellipticaJcracksonthecompressibility ofrocks:J.Geophys.Res.,v.83,p.4459-4468. Simmons,G.andRichter,D.,1976,Microcracksinrocks,inThephysicsandchemistry ofmineralsandrocks,editedbyR.J.G.Sterns:Interscience,NewYork,p.105 137.
Simmons,G.,Siegfried,R.W.,andFeves,M.,1974,Differentialstrainanaiysis:anew methodforexaminingcracksinrocks:J.Geophys.Res.,v.79,p.4383-4385. Simmons,G.,Wilkens,R.,Caruso,L.,Wissler,T.,andMiller,F.,1982,Physical propertiesandmicrostructuresofasetofsandstones:annualreporttothe 15-7 469
470

Burnsetal.

Schiumberger-DollResearch

Center.

Simmons,G.,Wilkens,R.,Caruso,L,Wissler,T.,andMiller,F.,1983,Physical propertiesandmicrostructuresofasetofsandstones:annualreporttothe

Schiumberger-DollResearchCenter.

Toksoz,M.N.,Cheng,C.H.,andTimur,A.,1976,Velocitiesofseismicwavesinporous rocks:Geophysics,v.41,p.621-645. Walsh,J.B.,1965,Theeffectofcracksonthecompressibilityofrock:J.Geophys. Res., v.70,p.381-389. Wilkens,R.H.,Simmons,G.,Wissler,T.,andCaruso,L,1984,Thephysicaiproperties ofasetofsandstones,III:theeffectsoffinegrainedporefillingon compressional wavevelocity:submittedtoGeophysics. 15-8 (

SandstonePoreSpectra

Figure1:Lowmagnification(21.9x).8EMimageofNavajoSandstone 15-9 471
472

Burnsetal.

Figure2:OneoftwoprimarySEMimagesusedinporecharacterizationfor NavajoSandstone(112x).Thisimageisrepresentiveofthehighporosityzones ofthesample. Figure3:Thesecondprimaryimageusedincharacterizingtheporesofthe NavajoSandstone(112x).Thisimageisrepresentiveofthelowporosityzones ofthesample. 15-10

SandstonePoreSpectra

_...;UDU2+85 473
Figure4:Intergranular(open)andintergranularjtabular(shaded)poresfrom thehighpO:9sityimage(fig.2)forth:.1'!

Burnsetal.

-"?" /-, 7\- : -(" .- ;-r( (\-

112XlQaU

- Figure6:Connectiveporesfromthehighporosityimage(fig.2)fortheNavajo

Sandstone.

Figure7:Connectiveporesfromthelowporosityimage(fig.3)fortheNavajo

Sandstone.

15-12 ( as - o - 1

SandstonePoreSpectra

..., I I I

I1..._

SIW highporoalWImaga lowporoaltyImaga 475
e- - e- C' o ...l 2 I I I L_ -3 -, I I I I I I

I I'!=-::.

II'--'

!.J -- '-- ....)-----_=1-3 o-1-. LOGa F"I.gureBa:AspectratiospectrafortheNavajoSandstonefromtheSEMmeas urementsonthehighandlowporosityimages. 15-13 ( ( 476

Burnsetal.

- ---SEM •

INVERSION

I errorbar. ----------------, • I I II I I 1 I I I I I I I I f ,... 3 "1.'(-; + - '-- , 4 -1 -2-3 '1 - Cll ... o ... & --2 & C' o ...I LOGa Figure8b:AspectratiospectrafromSEMmeasurements(histogram)andvelo cityinversion(stars)fortheNavajoSandstone.TheSEMspectraisgrouped suchthatallporevolumewithaspectratiolessthanorequaltotheleftedge valueandgreaterthantherightedgevalueisincludedineachbar. 15-14 (

SandstonePoreSpectra

Figure9:Lowmagnificationimage(22.1x)oftheWeberSandstone. 477
Figure10:PrimaryimageusedinporecharacterizationoftheWeberSandstone (114x). 15-15

473Burnsatal.

Figure11:Intergranular(open)andintergranularjtabular(shaded)poresfor theWeberSandstone. 1cau2 - Figure12:Connective(lines)andmicro(shaded)poresfortheWeberSand stone.

SandstonePoreSpectra

479
. 3 LOGa • 1 -- SEW ,.

INVERSION

• ••• •• J - - J I I - -4 o -3 • 1 o as -o - -& - -& C' o -J Figure13:AspectratiospectrafromtheSEM(histogram)andthevelocity inversion(stars)methodsfortheWeberSandstone. 15-17 480

Burnsetal.

Figure14:Lowmagnificationimage(22x)oftheKayentaSandstone. Figure15:PrimaryimageusedinporecharacterizationoftheKayentaSand stone(112x). 15-18 481
_......1/jU1U2519

SandstonePoreSpectra

'::""':":'':':':'::-'-=::--rf> 112X
Figure16:Intergranular(open)andintergranularjtabular(shaded)poresfor theSandstone. " - '-/1'I I - / , , Act ...(l...t -- ) -. "'\. .... ....U'-"", C. \- ~~0 .t 9 ~/- 1-

112)1.

2519
Figure17:Connective(lines)andmicro(shaded)poresfortheKayentaSand stone. 15-19 482

BumsetaI.

3-2 LOGa -1 o SEM /-------- ---SEM(incclay) • •

INVERSION

...--------, , ""

INVERSION

I (Incporosity)

1_______

• , •• • "'""" "" "" 3 .-- f- - - f-. ........ - -4 o -1 lIS -o - & - &-2 o -I Figure18:AspectratiospectrafromtheSEM(histogram)andthevelocity inversion(symbols)methodsfortheKayentaSandstone.Thesolidline representsthemeasuredSEMspectrum,whilethedashedlinerepresentsthe measuredspectrumwithapostulatedclaycontent3xthatmeasured.Thestars representthevelocityinversionresultsfortheKayentaSandstoneusingthe measuredporosityof22.2%,whilethetrianglesrepresenttheinversionresults using27.2%porositytoaccountforthenon-voidclayvolume. 15-20

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