SCM Truncated Gaussian Algorithm Petrel 2010

7/27/2019 SCM Truncated Gaussian Algorithm Petrel 2010

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Petrel is a mark of Schlumberger

4801 Woodway Drive, Suite 150W Houston, TX 77056 www.scminc.com [email protected]

2011 SCM E&P Solutions, Inc.

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Reefs

BuildingmodelsthatreplicatethisorderlyfaciestransitionhasbeendifficultinPetrel.Analgorithmcalled

TruncatedGaussiansimulationallowstheseorderedtransitionstobemodeledeasily.ThediscussionbelowdemonstratestheuseofthisalgorithmontheAfricantrainingdatasetandondatarepresentingapinnaclereef.

TheauthorshaveusedTruncatedGaussiansimulationonacoupleprojectsandfounditsimplertousethantheTruncatedGaussianwithtrendsalgorigthm(availableinpreviousreleasesandstillavailable)andthatitproducedbetterresultsthantheotherforthatdata.Becauseofthelimitednumberofprojectstheyhave

workedusing

this

tool,

the

authors

are

not

experts,

but

felt

atips

and

tricks

article

was

important

to

make

all

awareofthenewtool.

TruncatedGaussiansimulationTheAlgorithm

TruncatedGaussiansimulationisastochasticalgorithm.Thismeansthatitusesaseedand,iftheseedisallowedtovary,willproduceadifferentresultuponreexecution.

Primaryinputinclude:

Faciesdataasapropertymodelupscaledfromafacieslog Thefaciestobemodeled Theorderthefaciesaretooccur(adjacencyinthemodel) Onevariogram(usedforallfacies) Theglobalfractionofeachfacies(tendstobedominatedbyTrendsiftheyareused)

Optionalinputdatainclude:

VerticalfaciesproportionsfromtheDataAnalysisprocess. Trend(3D,2D,or1D)foreachfacies Smoothingandwhetherdataarehonoredduringsmoothing


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Figure:ParametersavailableontheTruncatedGaussiansimulationdialog.

Thealgorithmbasicallymodelstheprobabilityofthefaciesinnormalscorespaceandthenconvertsthat

modeledprobabilitybacktoafaciescode.Althoughtheauthorsdontunderstandexactlyhowthealgoirthm

works,wehavebeenabletopickupenoughfromthedocumentationtoeffectivelyusethetool.Our

interpretationofthemodelingprocessgoessomethinglikethis(seefiguresbelow).GivenWells1and2and

threestacksofcellsinbetweenthem,theprogram:

1. Checkstheprobabilityofeachfaciesandbuildsacumulativeprobabilityfunctionthattotals100%(010=green,10.01to40=red,and40.01to100=yellow).Actuallynormalscorevaluesof0to1are

usedbutpercentsareusedinthisexample.

2. Assignstoeachfaciesthepercentatthecenterofitsportionoftheprobabilityfunctionandthesearethe

values

that

are

used

to

model

that

facies

(5

for

green,

25

for

red,

and

70

for

yellow).

3. Buildsacontinuousmodelfromtheinputdata(probablyusingSGS).4. Convertsthemodeledprobabilityvaluesbacktofaciesspacebycomparingthevalueinthecellto

theprobabilityrangeandassigningtothatcellthefacieswhoseprobabilityrangeitlieswithin.


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Figure:Wellswithmidpointprobabilityvalues(displayedas%)thatarepassedtothemodelingprocess.Stacks

ofcells(,,andofwaybetweenwells)withcontinuousprobabilityvaluesmodeled(displayedas%).The

probabilityvaluesareconvertedtofacies(color)basedonwhichfaciesprobabilityrangeitsvaluefallsin.

Thisexampleisbasedononlyoneprobabilitynumberforeachfacies,thatis,notrendsorverticalproportions

wereused.Theprocessgetsmorecomplexastrendsetc.areaddedbutthegeneralapproachissimilar.

AfricanModel

TheAfricandataset,commonlyusedfortraining,showshowthealgorithmworks.Themodelisfirstbuiltusing

SequentialIndicatorsimulationandthenusingtheTruncatedGaussiansimulation.Figure:ThesamedatamodeledwithSequentialIndicatorsimulation(left)andTruncatedGaussiansimulation(right).Thevariogramsweremadeasalikeaspossible(sphericalleftandgaussianright).

Notethehaloofyellowfaciesaroundtheredfacies.TheorderthefacieswereinputtotheTruncatedGaussiansimulationalgorithmwasGrey,Yellow,andRedandthisistheorderthefacieshadtostayinwhenmodeledbecauseofhowthealgorithmworks.Becauseitisastochasticalgorithm,youwillstillgetanumberoffacies

bodiesthatareunsupportedbydatabutthedatawillbehonoredinallcases.


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Figure:parametersusedtobuildtheAfricanmodelwithTruncatedGaussiansimulation.


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Thelargerthenuggetthemorefuzzyistheboundarybetweenthefacies.

Figure:Modelbuiltwithnugget=.001(left)andnugget=.1(right).

PinnacleReef

InthepastithasoftenbeensaidthatPetrelisnotfriendlytomodelerstryingtobuildcarbonatemodels.Forthis

reason,wehavebuiltaPinnaclereefmodelsimilarinstyletopinnaclesseenintheMichiganBasin.Sincewe

didnthavedataforPinnaclereefswestudiedtheliteratureandmanufacturedourown.

StructuralFrameworkandtheMentalGeologicModel

Thehorizonsmodeledfromtopdownaresummarizedinthetablebelow.Belowarecrosssectionand3Dviews

showingthehorizongeometry,pinnacleform,andlayeringusedinthemodel.Normallythereis40%to60%

compactioninthecarbonates(littleornoneintheevaporates)whichcreatesadrapingeffectoverthe

pinnacles.Wedidnottakethetimetobuildthiscompactionformintothemodelasitwasnotthegoalofthis

study,althoughthedrapewouldhavecreatedamoreelegantandaccuratefaciesmodelatboundariesbetween

reefand

evaporite.

Layering

was

made

proportional

in

the

A

2Carbonate

and

Lower

Niagara

and

made

to

followthetopintheotherzones.

Theshapeofthehorizons,thelayering,andtheapproachusedtomodelfacieswerealldictatedbyourmental

imageofhowthereefshouldlookandthedistributionoftherocksinthatmentalimage.Thementalmodel

usedtoguidethisworkwasderivedfromworkdonebyK.J.Mesolella,K.D.Robinson,L.M.McCormick,andA.R.

Ormiston,1974,CyclicdepositionofSiluriancarbonatesandevaporatesinMichiganbasin:AAPGBulletin,v.58,

P.3462.Modelnumber3fromthispublicationwasused(twoperiodsofgrowthseparatedbyevaporate

deposition.


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Figure:Section(left)throughthehorizonsmodeledforthePinnaclereefstudy.ReefisfoundintheNiagaraand

A1Carbonatezones.A3DviewofthetopNiagarawiththecrosssectioncuttingitisshownintherightview.

Figure:Sectionshowingthelayeringusedtoguidethecorrelationsineachzone.


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Table:Listofhorizonsmodeledanddescriptionofrocklyingbeloweachhorizon.

Horizon Zonerockdescription

A2Carbonate Coarsegrained,densecarbonate,unfossiliferous.

A2Evaporite Halitewithoccasionalthindolomitebedscappedby

fewfeetofdenseanhydrite

A1Carbonate Densefinegrained,unfossiliferous,argillaceous,

thinbeddedcarbonates.

A1Evaporite

Clear,

coarsely

crystalline

halite

thinly

interbedded

withanhydriteanddolomite,commonlycapped

withafootortwoofanhydrite.

Niagara Denseargillaceous,micriticcarbonate,rangingfrom

massivetandolomitetograymicriticcrinoidal

limestonetolightgraynodularlimestone.

TopLowerNiagara SameastheNiagarabutwithouthavinganyreef

development(zoneaddedtoseparatethelower

nonreefNiagarafromtheupperreefbearing

Niagara.

BaseLowerNiagara

(topClinton)

Baseofmodelsonorocksmodeledbeneath.

FaciesModeling

Thefaciesmodeledarelistedinthefigurebelow.Notallfacieswerefoundineachzone.Infactitwasnecessary

tomodeleachzoneseparatelysothatfaciesfromonezonewouldnotblurintoazonetheydidnotbelongin.

OneofthemostimportantaspectsofusingtheTruncatedGaussiansimulationalgorithmistousehorizonsorsomeothermeanstorestrictthemodelingareastohavejustthosefaciesthatmatchthestyle(adjacencyorder)

ofthealgorithm.TheWellsectionbelowshowsthefaciesdistributionineachwellandzone.Basedonthe

distributionandrelationshipofthefacies,thefollowingalgorithmswereusedtomodeleachzone:

A2Carbonate TruncatedGaussiansimulation(limestoneanddolomite)

A2Evaporite SequentialIndicatorsimulation(saltandanhydrite)

A1Carbonate TruncatedGaussiansimulation(reefandcarbonate)

A1Evaporite

Sequential

Indicator

simulation

(salt

and

anhydrite)

Niagara TruncatedGaussiansimulation(reefandcarbonate)

LowerNiagara Assignvalue(Interreefmud)

TheA2CarbonatecouldhavebeenmodeledwitheitherSequentialIndicatororTruncatedGaussianequallywellastherewereonlytwofaciesinthezone.


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usedwhichdramaticallyimpactthepercentofeachfacies.Needlesstosay,themodelwasworkeduntilits

geologicfeatures(faciesdistributions)lookedacceptable,andmatchedthementalimageofthegeology.

Figure:DataAnalysisdialogforthetworeefzones(remember,layeringissettofollowtop).

Figure:Trends

used

to

model

the

A

1Carbonate

(top

row):

Reef

Rock,

Reef

Talus,

Dolomite,

Limestone

and

Niagara(bottomrow):ReefRock,ReefTalus,andInterreefMud.


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Figure:FaciesmodelingparametersusedtomodeltheA1Carbonate.

Figure:Jindexsectionwitha1:1verticalexaggerationshowingthefinalfaciesmodel.

Figure:Iindexsection(topleft,5:1),Jindexsection(topright,5:1),Kindex(bottomleft,throughA1

Carbonate),and3Dviewofreefrockandtalus(bottomright5:1),allshowingthefinishedmodel.


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Experiments

Someexperimentsweremadetoseewhattheeffectwouldbeiftrendswerenotused,iftheSequentialIndicatorsimulationalgorithmwasusedwiththesametrends,andifthereefsandtheintermediateevaporatewereallmodeledasonezone.Thefiguresbelowshowthesescenarioscomparedtothebestcasemodel.It

wasfoundthatforthisdata,SISandTGScouldbothbeusedtoproduceacceptableresultsbutthatthetrends

weremore

rigorously

followed

with

TGS.

Figure:ModelsbuiltwithTruncatedGaussiansimulation:withouttrends(left)andwithtrends(right).

Figure:Modelsbuiltwithtrends:SequentialIndicatorsimulation(left)andTruncatedGaussiansimulation(right).TrendstendtobehonoredmorerigorouslywithTruncatedGaussiansimulationbutbothproduceacceptableformswiththisdata.


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Figure:ModelsbuiltwithSequentialIndicatorsimulation:onezonefromtopA1CarbonatedowntoBaseNiagara(left)andseparatezones(right).

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SCM Truncated Gaussian Algorithm Petrel 2010