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Stochastic Techniques of Seismic Inversion and Reservoir Properties Prediction

By Kimberly Hamilton,2014-02-18 23:25
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Stochastic Techniques of Seismic Inversion and Reservoir Properties Predictionof,and

    Stochastic Techniques of Seismic Inversion

    and Reservoir Properties Prediction 20107月岩性油气藏

    LITH0L0GICRESERVOIRSCEG会议专刊

    ?

    地震解释?

    StochasticTechniquesofSeismicInversionandReservoirPropertiesPrediction DenisKashcheev,DmitryKirnos

    (CentralGeophysicalExpedition,Russia)

    Abstract:Inthisarticle,stochastictechniquesofseismicinversionandreservoirpropertiespredictionareintroduced.

    It'smoreaccurateandreliablethandeterministicseismicinversionanddeterministicsimulation.Stochasticseismic

    inversiontechnique,whichisabletoovercometheband-limitednatureofseismicfield,usesgeologicalandgeostatistical

    prioridatamorethoroughlyandgetsmorepreciseresultsthandeterministicinversion,Thestochasticreservoir

    propertiespredictiontechniqueintegratesallavailableseismic,petrophysical,geostatistiealandgeologicalinformation

    intothevolumetricdistributionofreservoirpropertiesandporefluidsandcombineswellloganalysis,rockphysics

    results,velocityanalysisresult,seismic(pre-andpost

    stack)inversions,seismicattributes,BayesianandKohonen

    classifications,neuralnetworkpredictionandotherstechniquesforimprovingaccuracyofdigitalreservoirmodels.

    Keywords:seismicinversion;seismicattributes;simulation;stochastictechniques 中图分类号:P631.4文献标识码:A

Introduction

    Nowadaystheexploitationofseismicinversionbecame thecolnlTlOntechniqueofintegratingseismicdataintointer- wellreservoirpropertiesprediction.Upto-dateseismic

    inversionalgorithmspermittoinvertseismicdatatovolu

    mesofcompressionalwavesvelocity(Vp),shearwaves velocity(V.)anddensity(Den).Moderninversionalgo

    rithmsextensivelyusenonseismicaprioriinformation

    andobtainresultswhicharefreeofseismicinterferenee andrefinedfromtheseismicnoise.Furthermoreelastic parametersandtheircombinations,suchasV/VP,,/4o, etc.,aredirectlyinfluencedbyreservoirpropertiesspatial variations(variationsofporosity,lithofaeiesandfluid saturation).Thesevariationsarethedependablebasisfor reservoirpropertiesprediction.

    Therearedeterministicandstochasticseismicinver- siontechniques.Theobjectiveofdeterministicalgorithms istofinduniquesolutionwhichwillbeoptimalestimate ofunknownelasticproperties.Sinceseismicdatahave bandlimitedspectrum,deterministicinversiontechniques cannotgenerateoptimalresultswithfrequencycontent higherthantheinputseismicdata.Presenceofseismic noiseconsiderablycomplicatessolutionofinversionprob- lem.Thereforeuniqueoptimalsolutionoftheconventional deterministicinversionisarelativelysmoothestimateof therealelasticproperties.Asarule,verticalresolutionof thissmoothingsolutionisnotsufficientforpurposesof detailgeologicalmodelbuilding.

    Useofup??to-?datemulti-?tracedeterministicinversion algorithms,utilizationofallavailablepriorinformation

    greatlyreducesinfluenceofseismicnoiseontheinversion results,permitstoobtaingeologicallyconsistentsolution withimprovedverticalresolution.

    Stochasticinversionalgorithmistechniqueofcondi- tionalstochasticsimulationofmuhiplerealizationsofelas- ticpropertieswhichareconsistentwithnotonlyratio

    gramandstochasticrelationshipbetweenVp,Vand density,butseismicdatatoo.Incontrasttodeterministic techniques,stochasticinversionalgorithmsallowtoobtain detailequiprobableelasticpropertiesvolumeswhichrepro- ducedetailedgeologicalfeatures.

    Figure1showscomparisonofVpvelocitysections

    obtainedbydeterministicandstochasticinversions. Detailedreservoirstructureisbetterobservedinthe stochasticinversionresuh.Butthisstochasticinversion resultisoneofequiprobablepossiblesolutionsofinverse problem.

    Analysisofthemultiplestochasticinversionrealiza. Abouttheauthor:DenisKasheheev,JSCCentralGeophysicalExpedition,Moscow,Russia.

    E-mail:manukov@cge.ru

    岩性油气藏2010

    l

    一一Fig.1Comparisonofdeterministicpre-stackinversion result-',pvelocitysection(topleft)andonerealizationof stochasticAVAinversion.',pvelocitysectionstopright;

    ',svelocitysectionbottomleft,Den~ffsectionbottom

    right.Bothsyntheticfieldsareagreedwithseismicdata tionsallowsmoreaccurateestimationofvolume,connec- tivityanduncertaintythanispossiblewithadetermini' sticinversion.

    Reservoirpropertiespredictionisnotvalidwithout predictionaccuracyestimation.Toestimateprediction accuracyforsuchreservoirproperties,asporosity,per. meability.etc.,confidenceintervalscanbeobtainedfor thereservoirpropertiesforeachpointofthevolume. Dealingwiththecategoricalvariables(suchaslithology, fluidunits,etc.),probabilitydistributionforcategorical variablehastobecalculatedateachpointofthevolume. Toquantifythepredictionaccuracy,allexistingsources 0funcertaintieshavetobetakenintoaccount.Inaddition toinaccuracyofthemathematicalmodelrelatingacoustic parametersandreservoirproperties,uncertaintiescaused bynon-uniquenessandinaccuracyofinversionresults areamongtheprimarysourcesofpredictionuncertainty. Inthiswork,wedescribestochastictechniqueof solvinginversionproblemfordeterministicapproaches anddiscussstochasticinversionalgorithms.Variousreser- voirpropertiespredictiontechniquesapplyingtoseismic inversionandattributeanalysisresultsareconsidered. Mode133pre-stackand

    inversiontechnologies

    poststackseismic

    Weapplymulti-tracedeterministicandstochasticseis micinversionswhichconvert(2D,3Dor2D+3D)stack seismicdata(acousticinversiontoP-Impedanceand P-Velocity)orangularoffsetstacks(Simultaneous AVAinversiontoP-Velocity,S-VelocityandDensity volumes).

    Deterministicseismicinversionsarebasedon

stochasticglobaloptimizationandgeostatistics.Themulti

    traceapproachandextensiveuseofapriorigeological knowledgegreatlyreduceinfluenceofseismicnoiseonthe inversionresults,enabletoimproveverticalresolution. Simult,~neousAVAstochasticinversion.Wehave createdanefficientAVAstochasticinversionalgorithm whichperformsjointinversionofequalangleoffsetvolumes tovolumesofVp,Vanddensity.ExactsolutionofZoep

    pritzequationsisusediflordertodeterminereflection c0emcients.Thusthereisnolimitationonthemaximum angularoffsetsthatcanbeused.Individualwaveletsare usedfordifferentangularoffsetsandcanbevariedoverthe area.Thealgorithmperformsinversiononstratigraphicgrid andprovidesconsistencybetweensyntheticandseismic dataforallangularoffsetssimultaneously.

    UsingMarkovChainsMonteCadomethod(combina- tionofSimulatedAnnealingandMetropolisHasting

    sampler),wegenerateasetofequiprobablehighresolu-

    tionvolumesofelasticpropertieswhichareconsistent withseismicdata,wellmeasurementsandreproduce detailedgeologicalfeatures.

    Attheinitialphase,alowfrequencyaprioriacoustic

    modelisbuilt.Interpolationofinitialacousticproperties isguidedbythemainstructuralsurfacesandfaults(resu

    ltsofstructuralseismicinterpretation)andincorporates depositionalmodelusingdetailedstratigra-phicgrid.Velo- cityanalysisresultsarealsotakenintoaccountforproper defininglowfrequencyvariationsofelasticproperties. Next.theinitialmode1isrefinediteratively.

Stochasticrealizationsgeneratingprocessiscon

    s~ainedtoreproduceseismicdata,welldata,low-frequency elastictrends.3Dvariogramsforelasticparameters,esti- matesofprobabilitydistributionsof(V.,V,Den),esti

    matesofverticalalterationofelasticproperties,etc.The multi.traceapproachandextensiveuseofapriorigeolo? gicalknowledgegreatlyreduceinfluenceofseismicnoise 0ntheinversionresultsforeachobtainedsolutions. Aswenoteaboveduringinversionprocessweuse

    c0mbinationofSimulatedAnnealingandMetropolis- Hastingsampler.ThisiterativeMarkovchainsMonteCarlo techniquepermitstoobtainsamplesfromtargetmulti

    variateprobabilitydistribution(PD)'rr.Targetprobability distributioncanbedefinednotonlyanalyticallybut

    CEG会议专刊

    DenisKashcheev,etal:StochasticTechniquesofSeismicInversionandReservoirProperties

    !

    implicitlytoo.Inourapproachweconsiderimplicitde. finitionusingasetofknowncharacteristicsthatdefine (withgreaterorlesseraccuracy)thetargetprobability distribution.

    herativesimulationisperformedintwophases.First, inrandomlyselectedpointjinthevolume,wegenerate newvaluesofVp(),v(),Den(j)usingproposaldistil- butionR.JumpingdistributionR(,)=P()isthe

    probabilityofgeneratinganewset

    =

    ((1),V.(1),Den(1),,(),(),

    Den(j),,V.(?),V(?),Den(N))

    fromthe

=

    ((1),(1),Den(1),,V(),(),

    Den(j),,Vp(?),V.(?),Den(N))

    whereNisthetotalnumberofpointsinmevolume. Atthesecondphase,thenewsetisacceptedwith acceptanceprobability

    P

    accept=min{,×exp)}

    (1)

    whereEistheobjectivefunctionfortheentirevolume. ObjectivefunctionEisthesumofseveralcompo- nents.Oneofeachismeasureofdeviationofsyntheticand seismictraces,theothersaremeansofcontroloverver- ticalvariogram,oversmoothnessofsolution,overinterval velocities.Thetermswhicharemeansofcontroloverpro- babilitydistributionofelasticparametersvector(V.,V, HCbeafngandBrinereservoirsdiscrimination Den,andmulti-pointstatisticsareincludedin.

    Comparingequation(1)withstandardacceptancepro- babilityofMetropolisHastingalgorithm,weconcludethat theexpression~xexp(二与上)canbeinterpretedasa

    setofconditionsthatdefinethetargetPD1T. StartingthesimulationwithasufficientlyhighTvalue andallowingastateofMarkovchainclosetoanequili- briumtobereached,whilekeepingtheTvaluefixed,and bygraduallydecreasingtheTtoasmallvalue,weobtain asetofequiprobablevolumesofelasticparameterswhich satisfvbothseismicdataandaprioriin_formation.Thisis howwe''algorithmically"willdefinethetargetPD. Theseismicinversionalgorithmhasbeenefficiently

    parallelized.Itusesasharedmemorycomputerandinverts simultaneouslydifferent1Dmodelso13differentprocessors preservingspatialcorrelationofelasticproperties. Fig.1demonstratesoneof20detailedstochastic

    inversionresuhs.Stratigraphicdresolutionis1msec, averagevelocityisabout5000m/see.Thereareonly2 wellswithinseismicsurvey.

    Reservoirpropertiesprediction

    Two-stagetechniqueisused(Fig.2).Firstonthebasis ofrockphysics,seismicinversionresultsandseismicattri- butes,thegeologicalvolumeisdifferentiatedintodifferent lithofacies(crossploting,Bayesianclassification,Kohonen h

    

    

    Fig.2ReservoirpropertiespredictionwithuseofsimultaneousAVA-inversionresults.Predi

    ctionisprovedbysubsequentdrilling

    96岩性油气藏2010

    network).Next,quantitativeprediction(neuralnetwork, multiplyregression)ofreservoirpropertiesrunsforpoten- tialreservoirs.Crossvalidationmethodsareapplied.

    Probabilityvolumesforlogderivedlithologyunitsand

    porefluidsaregeneratedusingBayesianapproachand areusedforcascadedstochasticsimulation,uncertainty analysis.

    RockPhysicsAnalysisisperformedtodeterminethe sensitivityofelasticpropertiesandseismicattributesto variationsofporefluid,reservoirproperties,lithologyand isafoundationofreservoirpropertiespredictiononthe baseofSeismicdata(seismicinversion,AVOanalysis,

attributes'analysis).

    Unknownelasticconstants(compressionandshear modulus)forrocksareestimatedonthebasisoflogdata. Gassmann'sequationappliestodeterminefluidsubstitu tioneffect,influenceofporosityandlithologychangeson .,V,Density.

    Syntheticseismogramsarecalculated(reflectivities arecomputedviaZoeppritzequations)andestablishthe linkbetweenreservoirparametersandseismicattributes. RockPhysicsAnalysisresultsarealsoappliedto reconstructmissinglogcurvesandcorrectlogcurveswhich areaffectedbydrilling(deepinvasionofthedrillingflu- ids,etc.).

    SimultaneousAVAinversionresultsareusedfor cascadedstochasticsimulationoflithologyandfluidun- its.forsimulationofreservoirproperties,uncertaintyanaly

    sis.Duringcascadedstochasticsimulationweusecondi- tionalprobabilitieswhicharecalculatedusingBayesian rule.BasedonBayesianapproachwecantakeintoaccount existinguncertainties,inparticular,uncertaintiescaused bvinaccuracyofthemathematicalmode1thatrelatesela- sticparametersandreservoirproperties,uncertaintiescau. sedbyinaccuracyofseismicinversionresults.Bayesian approachpermitsproperlytotakeintoaccountuncertain' tiesofhydrocarbontrap'slocationtoo.

    Asexample,considerprobabilityofhydrocarbon presenceatpointjonthevolume.Desiredprobabilityof hydrocarbonreservoirpresencecanbewrittenas P(r0c(),s()lSeism(j))=P(res(j)ISeism(j))P(hydroc(j)fres(j),Seism(j))

    whereP(res(J)ISeism(j))isaposterioriprobabilityof

    reservoirpresence,giventheseismicinversionresultsin pointjSeismie(j).ProbabilityP(hydroc()Ires(), Seismic(J))isequal:

    JP(c(J.)Ires(),Seismic(j))~P(hydroc(j)Ires(j))P(Seismic(Ihydroc(),res(j))

    ThefirstprobabilityP(hydroc(J)Ires(J))canbe estimatedusingprobabilisticmapsofhydrocarbontrap's location(thesemapsareobtainedusingstochasticmodel- ingofstructuralsurfaces,hydrocarbon-watercontact,ere.). Conditionalprobability

    P(Seismic(J))l(hydroc(),res(J))

    iscalculatedoffthebaseoffluidsubstitutionmodeling resultsforreservoir.

    Conclusion

    Theprincipaldifficultyofseismicinversionalgori. thms.bothstochasticanddeterministic,isthebandli

    mitednatureoftheseismicfield.Theonlywaytoover- comethisdifficultyistousethegeologicalandgeostatis

    ticalaprioridata.Thestochasticinversiontechnology usesaprioridatamuchmorethoroughlythanthedeter- ministicone,andthestochasticinversionresults,in general,aremoreprecisethanthoseafterthedetermi. nisticinversion.

    Weproposetheoriginaldeterministicandstochastic pre.stackinversiontechniqueswithpossibilityofutiliza- tionofallavailableaprioriinformation.Stochasticap

    proachallowsonetogetnotonlytheelasticproperties buttheuncertaintiesestimationsaswel1.Analysisofthe multiplestochasticinversionrealizationsallowsmoreaccu

    rateestimationofvolume,connectivityanduncertaintythan ispossiblewithadeterministicinversion.

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