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
4
datavalues:
two
are
sandlocations
(blackpixel)andtwoforshalebackground(whitepixel).
Allfourdatavaluesalongwiththeirgeom—
etry
configurationtogether
are
caned
a
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
’’
?
.
r
1?
searchtree,tostore
a儿tralnlngpatternstound
Ina
trainingimagewithina
searchtemplatebeforethe
simulation.ThisseminalideamadeSNESIM
a
morepracticalalgorithmbecausetheconditionaldistributionofeachdataeventinthesimulation
stage
can
bedirectlyread
fromthesearch
tree
wlthOutrescannlngthetralnlnglmage;hence1t
1s
severalordersofmagnitudefasterthantheoriginal
SNESIMalgorithm.
Figure6
is
a
2DsyntheticaleXamplethat
showsthreeconditionalSNESIMrealizationsof
a
fluvialdeDositionin(c),(d),and(e).Thetrain_
ing
image
in
(a)
contains4facies:
channel
(green),1evee(yellow),crevasse(red),andshalebackground(blue).There
are
50well10cationsin
(c).
Allthreerealizationshave
a
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
a
cOntlnuousVarlable
tralnlng1mage,torexanlple,
spatialdistributionsofporosityorpermeability,anothermultiple—pointsimulationapproachtermed
FILTERSIM
wasproposed.Unlike
SNESIMalgo—
rithmthatdirectlycallsforhigherorderstatistics
to
reproduce
patterns
from
a
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
a
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
a
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
释
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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