在储层建模中利用多点地质统计学整合地质概念模型及其解释

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F培1Trainingimageexample8

a—Categorical(meanderingchannels);b_一(bntinuous(porositydistribution);c—Largescale(braidedchannels)

d—Smallscale(rock

poresize)

Fig.2ExampieofmuItiple-pointgeostatisticssimuIationbymergingaIIavailabIeinfomationa—Traininginlage.b—Wellfaciesdata;c一』乜imuthdata;卜MPSsimulation;eSandprobability;d—Scalingfactor

highstandandlowstandtractshavedifferentge—ometries.(3)Obiect书asedalgorithms(HaldorsenandDamsleth,1990;Dubrule,1993;Holdeneta1.,1998).Obiect—basedalgorithmshavetheca—pabilitytogeneraterealisticshapesforgeologicalbodiesandtheirspatialdistribution.Eventhoughtheyarehardtoconditiontodensewelllocations,object-basedalgorithmsareflexible萏矗dwellsuitedtocreatenon—condltlonalsimulationsthatcanbeusedastrainingimages.(4)Process—basedmodels(HarbaughandBonhanl_Carter,1970),aregener—atedbyforwardmodelingthege0109icalprocessesthroughthephysicallawsthatgovernthetrans—portationofsourcematerials,thedepositionandcompactionofrocks,theirerosion,redeposition,etc.

Similartoobject-basedmodels,

conditioning

30TuanfengZhang/地学前缘(EarthscienCeFrontiers)2008.15(1)

F醇3Anillustrationofphysicalregionconcept

essarilyhaVetocreateanewtrainingimageforeachnewreservoirintervaltobemodeled.(5)TheVerticalproportioncurVeistypicallyappliedtofa—ciesdata.ItdeterminesthevariationoffaciesDro—portionsalongthestratigraphicallyupdirection,a110wingthereproductionofchangesintrendoffa—ciesdistribution.Thisinformationisextractedfromwelllogsorothergeologicalinterpretations.(6)Faciesprobabilitymaps,alsocalledsoftcon—t10nS。

Figure2isanexamplethatillustrateshowmultiple—pointsimulationbuildsafluvialdeltasvs—temfromastationarychanneltrainingimageswiththeintegrationofdiversedata(Scarleteta1.,2005).Theprincipleofmultiple—pointsimulationwillbediscussedinsection4.

AnotherapproachtodealwithnonstationaryreserVoirsistheuseofphysicalregionconcept

straints,indicatethe1ikelihoodoffaciesoccur一(Wueta1.,2007).Itproceedsbysplittingtheen

renceswithinthedifferent

areasofthereservoir.

This

type

ofinformationtypicallyisusedtoreducetheuncertaintvoffaciesdistributionbetweenwells,especiaUyintheareasthatarefaraway

fromweH10cations.Faciesprobabilitymaps

are

mostoftenderivedfromseismicdata,but

canbeproducedfromwell—andmap-basedinterpreta—tlrenonstatlonaryregionintoseveralsmallstation—aryregIonsandtnensImulatlngeachreglon1nse—

quenceuslngdl士ierenttralnlnglmages.

Thenumbersoffacieswithdifferentregions

arenotnecessarilythesameprovidedthefaciesarecodedconsistentlyamonga11thesub—regions.The

keytothe

slmulatlonlstoensurethesmooth

tran—

TuanfengZhang/地学前缘(EarmScienceFrontiers)2008.15(1)

Fig.4Anonstationaryfaciesdistributioncreatedbyperfomingnonconditionalmultiple—

pointsimulationineachoff。urstatio眦rysub-regionsinsequence

a—simulatedregion1;b_一simulated

region2;c—Simulatedregion3;d—Simulatedregion4

sitionacrossdifferentsub—regionboundaries.Fig—ure3isa2I)syntheticalexample,showingthe

splittingofanonstationaryregionintofoursta—tionaryphysicalsub—regions;eachsub—regionhasacorrespondingtrainingimage.Notethatthesub—regionR2consistsoftwoseparatepieces,buttheysharethesame4faciestrainingimage.

Figure4i11ustrateshowthemultiple—pointsimulationproceedsfrom

onesub—regiontoanoth—er.

EVenthoughaspecifiedtrainingimageisuti—

lizedineachsub—region,thesimulationinthe

cur—rentsub—regionisconstrainedbythepreviously

simulatedvaluesinotherregions,henceensuring

asmoothtransitionacrosssub—regionboundaries.

4Theprincipleofmultiple—pointsimulation

Toperformmultiple_pointsimulation,the

se—quentialsimulationparadigmingeostatisticsisuti—lized.However,unlikethetraditional2一Dointorvariogranl_basedsimulationinwhichthespatialvariableisassumedtof01lowmulti_Gaussiandistri—butionsuchthatateachDixelthedeterminationofthemeanandvarianceoftheconditionaldistribu—tlOnamOuntstOsOlVmgasetO士kn91ngequatlOns,inmultiple—pointsimulationthelocalconditionaldistributionisbu订tbydirectlyscanningthetrain—ingimage.Supposethereisareservoifthathas

beendiscretizedbyagridwithN—N_。×N,pixels,andthereservoirattributeisdenoted

asarandomfunction{Z(z)lz∈reservoir).Thespatiallow,whichgovernsthereservoirZ—attributedistribu—tion,isthenfullydeterminedbyajointdistribu—tionofNvariables:

P(Zl≤z1,Z2≤z2,…,ZN≤zN)(2)

Usingsequentialdecomposition,thisN—dimension—aljointdistributioncanbedecomposedasaseriesof10calconditionaldistributions:

P(Z1≤z1,Z2≤22,…,ZN≤2N)一P(Zl≤z1)×

P(Z2≤z2Iz-≤z1)×…×JP(ZN≤zNZ1≤z1,

Zj≤≤z2,…,Z(N—1)≤≤z(N1))(3)Theabovedecompositionalsoholdsfordiscretevariablessuchasfaciesindicators.Theseauential

simulationalgorithmproceeds

asfollows(Goo—verts,1997,p380):

?DefinearandompathvisitingallNnodes

?Fbreachnodei一1,2,N,perform

a)modeltheconditionaldistribution

P(乙≤蕾lZ1≤z1,Z2≤z2,…,z(H)≤z(H))of乙,givenalli一1

previouslydrawnvalues

b)drawasimulatedvaluefromtheabovecon—ditionalmodel

ThisprocesscontinuesuntilallNpixelsareVisitedandonerealizationisgenerated.ByseedinganotherrandompathofvisitingNpixels,anew

realizationcanbedrawn.Forthe

purpose

of

gai—

32Tuanfeng历ang/地学前缘fEartbsdenceFrontj仑rs)20D8,15fj)

Fig.5111ustrationofsequentialmultiple—pointsimulation

Fig.6Afluvialtrainingirnagein(a)诵th4faciesandthreeconditionalSNESIM

realizations(c),(d)and(e)谢thallbeingconditionedto50welllocationsin(b)

ningcomputationalefficiency,onlythosepreVious一1ysimulatedvalueswithinaspecifiedneighborhoodareusedformodeling

theconditionaldistribution.Figure5givesanillustrationofthesequentialmultiple-pointsimulationandexplainshowthe10—calconditionaldistributioniscalculatedbyscan—

ningatrainingimage(courtesyofSebastienStre—belle,Chevron).Beforethesimulation,aneigh—borho。dtemplateisspecifiedf。rscanningthe

trainingimage.Supposethe10cationuatthe

simu—

Tuanfeng

Zhang/地学前缘(Earth

Scknce

Frontiers)2008.15(1)

1ationgridisthecurrentlysimulatedpixel.Withinthesearchtemplatecenteredat甜(redcircle),there

are

datavalues:

two

are

sandlocations

(blackpixel)andtwoforshalebackground(whitepixel).

Allfourdatavaluesalongwiththeirgeom—

etry

configurationtogether

are

caned

data

event;

thisdataevent

isthenusedto

scan

thechannel

trainingimageforinferringthesandprobabilityat10cation“.Supposethattherearefourreplicatesofthedataevenfoundinthetrainingimageinwhichthere

are

threesandand

one

shaleobservations

attemplate

center乱.

Hence,thesandprobability

at

pixel“is3/4—0.75anddrawingfromthisproba—bilitygivesa

simulatedvalue

at

pixel“.

Eithersand

or

shalecouldbedrawn。butthereismore

chanceto

drawsanddue

to

itshigherprobabnity

thanshale(O.75>O.25).

Supposesandhasbeen

drawn

as

intheillustrationexamDle.Thissimula—

tedvalueisthenadded

to

theconditioningdata

set

forconstrainingthesimulationatotherpixels.Next,thesimulationmovestoanotherDixelloca—

tion。

Thissequential

process

continuesuntilall

pixelsinthesimulationgrid

are

visited,resulting

in

one

multiple—pointsimulationofchannels.

Thesequentialmultiple-pointsimulationalgo—rithmdescribedabovehasbeengivenaname:

SNESIM(SingleNormalEquationSIMulation).Theo“ginalSNESIMalgorithmwasdevelopedby

GuadianoandSrivastavain1993anditwasCPUdemandingbecausethetrainingimagehastobescannedpersimulationnode.In2000,Strebelleproposed

tousea

dynamicdata

structure,

named

’’

?

1?

searchtree,tostore

a儿tralnlngpatternstound

Ina

trainingimagewithina

searchtemplatebeforethe

simulation.ThisseminalideamadeSNESIM

morepracticalalgorithmbecausetheconditionaldistributionofeachdataeventinthesimulation

stage

can

bedirectlyread

fromthesearch

tree

wlthOutrescannlngthetralnlnglmage;hence1t

1s

severalordersofmagnitudefasterthantheoriginal

SNESIMalgorithm.

Figure6

is

2DsyntheticaleXamplethat

showsthreeconditionalSNESIMrealizationsof

fluvialdeDositionin(c),(d),and(e).Thetrain_

ing

image

in

(a)

contains4facies:

channel

(green),1evee(yellow),crevasse(red),andshalebackground(blue).There

are

50well10cationsin

(c).

Allthreerealizationshave

goodreproduc—

tionof

thefaciesgeometryandtheirassociations

wh订econditionedto50welldata.InthisexamDle,thenumberofpixelsinthesimulationgridandthenumberofthetrainingimagearethesame;both

are

150×150pixels.However,thisisnotrequired

formulti—pointsimulation,i.e.,

thendmberof

33

pixels/voxels

inthesimulationgridcouldbediffer—

ent

fromthatinthetrainingimageprovidedbothgridshavethesamepixel/voxelresolution.Thesimulatedtarget

faciesproportions

are

setto

bethe

same

as

those

1n

the

tralnlnglmage(agaln,not

re—quired

formultiple-point

simuIation);they

are

0.45,0.25,0.25,andO.15respectively.

SNESIMalgorithmonlydealswithcategorical

variabletrainingimagessuchasfacies.Forpurpo—sesofmodelingcontinuousfeaturescapturedfrom

cOntlnuousVarlable

tralnlng1mage,torexanlple,

spatialdistributionsofporosityorpermeability,anothermultiple—pointsimulationapproachtermed

FILTERSIM

wasproposed.Unlike

SNESIMalgo—

rithmthatdirectlycallsforhigherorderstatistics

to

reproduce

patterns

from

trainingimage,FIL—

TERSIM

starts

withtrainingimagepatternclassi—

ficationbasedonfiltersandthenperformspattern

reconstruction.

Adeta订eddiscussion

on

thisalgo一

“thmanditsapplicationscan

befoundinthe

paper

writtenbyZhang

et

a1.

(2006aand2006b).

Atheoreticlinkbetweenmultiple—pointand2一pointgeostatistics

Thissectionaimsat

answeringthequestion:

why

doesmultiple—point

geostatisticsreproduce

highlynon—linearstructuresmuchbetterthanthetraditional2一pointvariogran卜basedmethod?Inor—dertoanswerthisauestion,weneedtotakeaclos—

er

100k

at

theconnectionbetweenmultiple—point

and2一pointgeostatistics.

Let’stake

simple

ex—

ample:estimatethesandprobabilityP(jo一1)at10cationHogiventhethreeknowndataJ1,工2,andLwitheachbeingeithersand(一1)orshale(一0)observations(seeFig.7).

F嘻7

0nedataeventconfiguration谢ththree

knowndata

to

infom

one

unknoWn

Inthe2一pointframework,thiscan

beformu—

lized

as

estimatingtheconditionalexpectationby

Hnearcombinationofthethreeknownindicators:

P(jo一1

11,j2,j3)=E{I。1

11,j2,13),

在储层建模中利用多点地质统计学整合地质概念模型及其解

作者:张团峰, Tuanfeng Zhang

作者单位:斯伦贝谢道尔研究中心

刊名:

地学前缘

英文刊名:EARTH SCIENCE FRONTIERS

年,卷(期):2008,15(1)

被引用次数:4次

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引证文献(4条)

1.张挺.卢德唐.李道伦.杜奕基于软硬数据的多点地质统计法在图像统计信息重构中的应用研究[期刊论文]-计算机研究与发展 2010(1)

2.周金应.桂碧雯.林闻多点地质统计学在滨海相储层建模中的应用[期刊论文]-西南石油大学学报(自然科学版) 2010(6)

3.张挺.卢德唐.李道伦基于二维图像和多点统计方法的多孔介质三维重构研究[期刊论文]-中国科学技术大学学报 2010(3)

4.唐海发.贾爱林.彭仕宓.罗娜.刘伟洪积扇相储层沉积微相-岩石相随机模拟[期刊论文]-中国石油大学学报(自然科学版) 2010(3)

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