Determination From Well Logs Porosity and Permeabilityin Heterogeneous Reservoir

7/28/2019 Determination From Well Logs Porosity and Permeabilityin Heterogeneous Reservoir

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SPE 28792Determination From Well Logs of Porosity and Permeability in aHeterogeneous ReservoirJing Long Lin, Daqing Petroleum lnst., and H.A. Salisch, * U. of New South Wales*SPE Member

Copyright1894, Soclely of Petroleum Engi.-a, lnc.Thla papar was preparad 1or p!'M811tallon atlhe SPE Asia Paclflc 011 & Gas Conference hald In Melbourne, AUIIrlllla, 7-10 November 1894.Thla waa oelecled for tatlon by an SPE Prograrn Comm- lollowlng revlew of lnformatlon conlalned In an - a c t eubmllled by !ha a u l ~ c,::anta of !ha=a =ted. have not b e e n ~ by the Soclely of ~ u ~ and are U,: o s ~ r n e : ' : = ~ : : ~ ~ : : . . ~ ~ C o r n m ~ S o c l e l yany poeltlon o1 !ha Soclely ol Petroleum Englnoere, 118 olllcara, or llfl8l8=-- Ulu8tr8tlone may 1101 be copled. The abelnlelllhouldcon1a1n conep1cuoua ICknowtedgmenl= = ~ E ~ = : : : = n : = ~ = - = ~ - : . ; : . r . o ~ ~ . R ~ e o n . TX 75083-3836, U.S.A. Telex 183245 SPEUT.ABSTRACTA tecbnique bas been develqm foc tbe petropbysical e v a l ~of we11 logs mm litbologically amplex sandstgical cbaracteristics.They are, fnm tq ) tobOOml:


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2 DETERMINATION FROM WELL LOGS OF POROSITY AND PERMEABILITY IN A.. SPE 028792q Bidmbatedsandymudstme. Bi~ muddysandstone. Bio@batedsandsttmeq Stllmgly~ted bedsQ slightly~ted beds

- LxqonenL chstexaudB)esdkximWm t RnalysiawereusedtixthedassificaticmandidentitkadmGfti~kmiclogswreutilisedt oeadmate~ pausitybecausetheyafe theadytype ofpmositykWa_ forotheruellsdrilledinthefidd. !kmicpmmitkw=tbm usedmtk~ty~m~tie@*of ~ ~~fhefive sdeuedlitbofadea aredifb=trn M* tkies.lkequadmsd exiwdforeachl ithdhckahave~itetocunputethere@edpetrophysical~**@F.Ihemethodology waslater appl.iedtGa _ well[mlllll,outside of [email protected] wtreequdbCc43siatentithaxe analysisdata.-ICTING LITHOFACmSipmaneeTheMennin@Ont)flithobde aisdfundmentalimpxtmcerntheevaluatkmoartxrvok, mcresowhen itis Meq@xnwLithe&ea andtheir architeUmearean@m CUItmlfiWkrrnfluidflowmdfluiddistribudon intbepmes~tia~.The lithologicalpammetm requiredfix log in@preWkm,sud3asthetmtuosity fktm[a],thewxalled cfanentadmexpcaent[mlandthe satumdm~t[n]mwk eadmatdasaecumtdyRapoasible.Thesepamm@=smdo@y*mtitypesoflith*.Cme&ima betwmamustic rntervdtmnait timeandpmsi?yand betwem pmosityandpermeaWty vmiedti Mtititolithokies in thisstudy.

tin-l nnn*r -w31vSCA Flnm=rmdwzk - I* ~Aa~ ~- J- - Jthedwaudahof theresuwim lhe misdvity, smic and_my@sbtiek* l& Band Guue firststandardhed tGminimke theeffeus ofscaks andunitsoflqlwiablesand thenrmnsfbned rntoanewselof~rntiarea Gf@nL5palcunpments. Theti tburecnnpenents wereseleued fachlsteranalyakmle~~ -ztitistudy.~-softidw analysis aresbwn m thedmdrogcamufFigure 1.Usingaaxrdation cod3kkntofabaIt 0.92aSabGUn*WueRx theckWkamm Gfdeuric Meaintheae reauvokfiwtypeaofdectricfilcka wuedetmkl. Cmparedtidle*

thefivedectrictaciea cmespmdtGfil'edistinct MMildesMhobgyandLoRespmesofthe Five TypesofLiihott&sn3emavairswregfouped int(-)fivet)pesoflithohd eabasedonVRllbganalysis.- rhegedqicd pmpcnksofthe fiwtypeaofMA - Iuka., ?ke..Ahm.lme tHlnw@SW- WV U-J M S-VW=.Facies1:BwturbatedSiwiy Mud@oneFacies2:BioturbatedMu@ SanaWmeFacies3:BwtudmtedSamir&neFacies4: StnmglyC@bonate-CemntedBea3Facies5:Slightly#rbonate-Canented BedsAdetaikddex@don [email protected] IMkrentlithotilckaaed istinui nthdrgeophydd pq=tiesuchaseleUrical amustic andnudeardamUerM ea.GeGpllywdllGgdRta eultainnmch Mxmatum al%nltgeophyaic!alpexdc#lith&xka. Table lshGwthelGsreqmses tixthefiw typeIithokies.

Table l- AverageLog ValueafatheFiverypesafLMlokkY

1 1 2!3:4~5... ......... . .. . ........... .................. . ...... ........ ...... ..... ................ ..................... ...R i 2.228! 2154 ! 2514 i 4397 i 4LB6................ . ...... .................. .. .... ... .... . ............ .................. ..... .... . ...........Rum! 2A39 ~ 2103 : 2179 : 12.476 ~ 3.642+ .."-"" ...."+""_- ......u.+-- ......""".f"-"""..-_" ... . ........ . .. . .. ....*; 2359 ~2298:2207:2529i 2.304.................. ................ ........... ............. ....... . ... ........ .. ..................... ..................h ~ 116591 : 122673 ! 130.34 : sa.055 i 105.77... ............... ........... ..... ................ .. ...... .... . ........ .. . . .... . ..... ..... . . ..........GR ~ 103.245: 112531 j loa.275 ~ a6.34 ~ 91.512

Wherel?t-deepinveatigati mreaistivityn -: --11.. &.#Ml 4.*.4.,~ - Uuutmplnaluuuy UA.imKu lcalauvuypb-btdkdmsityA(-amustictmnsittimeGR-natumlgammaray

IhediOkmma inlc)gmspmse afathefive typesoflithdadeacanbeusedtGidutti@ thelithofadea.I&ntMWkmBays Wdminan tanalpiswsappliedi nordertoattenpt tG. . . teammgt hefive~e frocks ntempmsea fed

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SPE028792 J.i.,. LiN and I-M. SALRCH ~fim the (3amma-Ray,Hv@ md sdc W - M fmthispulposcOneofthekey stepsindkdndmmt anaUsiaistckosethesmndafd aampkswhicb eanrepresmt acezlain litM%cieatoestahbhthedbhninm tfunetkm withlnaeacemaey. msumdardsatnplcawaeseleued bast!donthereadt$ OfclustaanalysisandeaedataBays dkxbinm t fiutcdon Fix) is daiwd h BayEs

vFi(x) = iqgi j + G + ~CUzk

td

H, z ....0,wherezx. (XlXz,...,Xv\stqie fix fidiKZ@kIM~V.nukle$ofvariabkG numb ofcategaiea (G5)q- nJNN-tad numberof samplesnr td numberoftheith categorysamples6i*Qr~t-. . .DMnmmantfktcrsvmet hendmmmed. Iheyafeexpmsedinmatrixftxl nasfollows

Inthedkahnhn t - a -Pk x = (h h .... d h. . .kxmunant analysis isentaed into the above dkhnbntfuncdals toCaleldateunaien wllues.If F{x)= MAX{F~x))j=l, Z..., G.&t@2 X bekmgstotheitheategay.Iheearectdkxhnbm tradofa standardsampkaisuptoso%fakieslandfacies2 90%fabcies4and ltM%fahcies3andtiKiea5.T- identiikadm ofiitho@cksk2r-*@i-welisAIi atidcwas dcae using Bays dkiminm t aoalysis tdmique. fheeuIeudkiminm tmtioiscketo 84.3%fix WEUJ%81.5%fa wellB and 78.7%fa U@C.

Paoaity isanhnpatant paramem in the emhmticaofareserv& Theamount ofhydmcmbm[cil andkrgas]inareaavoh isesdnMt@ amcflgahathing$ ffompaeaityvalueaand fianthe thiclmessandarealextensim ofamsemoir. TotalPaosityisdeiiaed astheratioof thetotalvoidspxe intherocktoitslndk volutne. Eff@ive Paosity istheratio of theinterconnectedwuidspaceintherocktoitsbul kvohnne.IWeewdls ~Band Cwheze~, CNLand BHCSeaiilogshad bee$ltakenwerewlected askeywe'lls. saniebgsareusedhereto6tknatewfmaadon po@tyofthegiven. KXrvo&sbecausetheyarethe adylypeofpaoaity logsavaila bkinallthevdlsdrilledinthekld.

[email protected] ofclay minemls inamsavoirisusuallyeadms@dfiun Giun3naRaytmd spontaneousPotentiallogs.Theseesdmatmdo na namally rqxesent the trueamountofdayminaals duetodiff&encea inthenatuce ofclayminaalsinthesands andinthe al@ent shaka.Ihe _toccumenceof2WioaaiveminemlssuchaspotasaiumWdspar,glauconiteandahaheavy minemls inthereamoim studiedhaedd to thediffiadty. lheshale distributicminthemsexwir rn its threemodtxstmetm& laminar anddkpmed. makea itditlkulttoeadmatepaosity aecumtdy with traditional*suc12 as theWyllietimeaverageequadonafk emec&onfa elaycontent.Topredictporosity intheseresemks fmlnlbdl logs themainprcMemsto besokdlK etheeffkmofcarbma@ and clayswhichfampartofthercck aswllastheefikc tsofthedifkrentIibfkiea.

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4 DETERMINATION FROM WELL LOOS OF POROSHY AND PERMEABILITY IN A.. SPE 028792Atechnique has beendevelqedh exetoe admate porosityand~ty m heterogeneousmsmmirsof dlisnatme.Fiveidmdfiable oflilhohcie swredetumid fiunwell logs.Distinctrelationshipsbetweenfennadcm@ty andS(XliC ha%dtimeexist tiXeach lithotkciealT@ure2].Ik fivematkmadcalmodels fmthedekzmhm mofpausity fian-tnmsittimmwremtabhshed bystatisdcaltedmiques.cIlM410tAnalyaiaFcrthestudy ofpcrosity, 306samples wereusedikxn thethreewlls~Band C.c-mecrositieand XOtlStiC transit times - aoss-@tted infigure2. Tldsfigureshowsthataud atapointsa rekXatedhtwodistinctareas.(lneofthe miscanpmedo fsandstcmeaudshaleeknent& the OthK Culsist mainly of ~tedcmprments. Figure 2 also indicatesthat distinu relationshipsexistbetwtxmpau6ityand acoustictransitdmetithefivetypeaOfIithofacks.Study ofa ModeJ

lleobjective ofthisstudy wmtotrytoind better sadctransfamswith thesmalleststandardumcfcrthed@mnhmdcmcfporosity. ThX@ewell known porosity Uanstlmnswtm. . .-. .. .cumukrd me wyme rimeawrage equab, me Raiga-@ZllUlfXZiU WkOUStiC-CXI=tfX equatkmandtheRaymer-Hunt-Gardnexquatkm.Basedmthethreeequaticxw threemodek linear,mcipmmlandlqarithmicwreused todekxminesadcpaositytransferms.A Iinearmodd fkxntheWyllieequationk

@ ,=a+b At ....................(2)

A re@mcal modelWed on theRayner-Hunt-GarduerequatkmCanheexpmsedw@,=a+-& ..................(3)

A logarithmicmodelduived tlem theAcrosticFczmatim=equatial k

log(l -$)= a+b.log(&)..........(4)

'lllethreemodels wemtalominmgressial fmt?ad3lithofa&s.C4mhtim andenuanalysis wreusedin thesmdy ofthe*. Cmdatlm analysisisamarhematicdmelbodf crtheSh3dyofcmdatml betweenvariabk Twomriablm ammaelhl=ly cmeMabk theclmez thevalue of thecmelaticmcoel&imtlJqis tolcx-1.Standarderrs [SE]is givenasfollows.

i=T,-Tc, YSE= = ~ ~ .......... (5)whereN - numlxxofsamplcsfG -- [cOKS]valueofthe ith sampleTi- logderivedvalueof the ith samplellueefmmsofpresentatial werecmsidmd fa tic trawl time!tircmekaca. and fcrerrm analysis.l%eresuksocmelatimanalysis anderrcr analysis aregiven in Tables 2and3,WP@~Y.

Table2ComeMkmCodE&nt farthethreeModels:I%icu \FaLicd :Frlciea :Facics ~Fadcsjl j2 !3 :4 IS"""." . . ... . ... .... . .. ... ...... .. ... .... . .. . ... . . ... . . . . ... . ..... . .......

* ! a74n i 0.6635 ~ 0.7620 ! 0.s052 : 0.74s9.. ... . ... ... . . . . . . ... . . . . .. . ... . . . . ....... . . . . . . .. . .. .. . . . . . .. . . .... .... . ....- : 0.746s : 0.6614 : 0.7574 ! 0.8065 : 0.7603bar-ic!!ii;.7471 oti2a 0.7609 0.s053 0.7547

Tahle3-Stauiard Errarforthetbree Modelsj Facies ~Fa&s/i%i?d jl%ird jFuiEs:1 ~z :3 :4:5. . .. . . .. .....~. ... ........+ ............ ...p ........ ..... . ...... .... . ...."......I!.399 i 1.622 ~ 0.965 ! 1.S32 ~ 1.s64.-.-.."..-. --&-- ....--4 .-- ....--. &...-...-.-". !..-" _-A.._.""."._ I

- :1~ il@ i 0.969 ; 1.SW i 1s43.. ..... . . . . . ....... ... .......... . .... ............ . ........ ...... .. . .. . .... . . . .. . .....~ : 1.399 ! 1.623 j 0.%7 : 1.s11 ! 1.534. .. .. . . . . .. ... . . .... . .. . .. ..... . ... . ........ . ...... ...... .. . .. . . . . . . . . . . . ....IThereadtsoftheandysis mabks2and3] indicaethatrheliuearmodels t& fhciesl, bciea2andfkcies3 havethehigheatcmelath melkients andtheloweat srandardemm,=themc@mcal*@ethebeatmsuhsf m*4andhcies5.

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SPE028792 J.L. LIN and H.A. SALISCH 5Basedmthermults ofcareladcmandaror andysisthel inearmodels aodrecipmcal models wexesekedheretomtimatefamaticmpaosityfcr faciml, 2and3and for fiwks4md5,-~Y.l%eequatkmsfa axnputing paosityfansatic traveltimeserthe fivetypmoflithofkies byregressimanalysis=Equations-fwfwiesIOS= -0.49503+ 0.162939At

ofa model f~ the twosections.Basedcmthe results of careladm and arm analysisthe linearmodel wasseleued fcr Sectkmland thereciprocal model wassekaed fa Sectb 2Jnthe One Group' modeJalinear equationwasusedto@imatepaosities fkxnsadcl ogsafkresukshad beeaobtained inamanner similactotheTwo Groupmodel fa correlationandara analysis.TabIe5give8 thecamparison of the three modelsfcr the five

-fw$lcies2@S= -0.29080 + 0.193642At-fw@cil?s3OS= -9.91978+ 0.294179At-f-wjack 4@= 46.68793-2704.26 IAt-Jmfmus 5@S= 56.73825-3653.45 i Athe valoes fixthe arelatim codiieieatN and the standardara[SE] czdadatedbasedcmthe306sampksf rcmweJls~ Band C by using the above five equatims are 0.885088 and1.520843,respecdvely.@np@sonoftheModdsInthisprcje ctwveralmode lsw reusedtorelinerhecksitbdcm. The OneGroupmodelplaces the entireintervalinto cmecategay theTwo Grapmodel does sOiuto twocategaieaaud the`Pive Group' modeldividmthemsmmimhUofiveCategcrk?.llecmeladcm coefficiemsadstandadara ti3Msamplmlkxnthethmewells menticmedabovearegivenbyTable4.

IntheTwo Groupmodel themaavoir Wasdivided intotwoparts calledSeuimland Seuion2.1k fama~ds@ihciml, kies2and kiea3withsands aod [email protected]~ &ies4aud5witb ~ted ekueats.fhetbree *afacou8dc interval tmnait time: linear,~mdl~-~ .onmkedrnthe sektitm

Tabk S- CampwkmafStandaml Error [SE]

oncGmup / 3.8688~ 1.6492 ; 3.0133~ 2.0619 j 3.260smold:............... ........ . ................. .................... ..........TwoGraqI : 2.S6S6: 1.85% ; 2.1648 ~ 1.850S: 1.7503lldd~............................................ ........................................ ......................................FiveCuwkP~ 1.3991j 1.6219~ 0.%54 ; 1.8133 i 1.5642MYkl:

Applkationsl%el%eG .rmpmodelw asusedfm thedeknninationof~titi~rntie k@mUs&Bmd CmdtiafdmU,D.'Iheresults franthe `PiveGraup'madel werecanparedwiththoseb a modeiusedatpresmi tilWAfield. F@-. 3 and4givethetworeauksfcrwellBandwellD,m pectively.h the preamtlyusedmodelpaoaity is dekmninedby theWyllietimeavemge equatkmThe apparent sadc matrix valoes [AMand apparentsatic fluid values[Ad am obtainedby singlewellregreskms faeachofthe wdlsdrilledin the field. 1kyvaryllcm wellto well.he pafametas fa the fivewellsmentionedabove aregivenrn Table6.

mlbie6-sdcMairixlmlimki vaiuI%hseii eiijhimeWdt~A!B~ C~D............................ . ............. . .......................................Ab@c!ua)~ n i 61 ! n i 73...........................~~&@Mcda) ~ 302 : 310: 2s5; 306

l%e Iithofacks fathetbee keyvdswaeidmtified by theIlqK!s didlnbl tfimeticms which h@ been @abMhed andwereshown earlier inthepapa. lk paositieawaethezlmldated Ikxnkweltolevel byusingthe appropriateequationsfbrthe diikxentlithokies.Figum3givesthetwormults fawdl B.l'kfigureindicates that


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6 DETERMINATION FROM WELL LOGS OF POROSITY AND PERMEABILITY IN A.. SPE 028792the pcmity values derived tkxn rhe We Group model areti@~mdcl~m tie-ti, _yktieti_ti85t093me&es and from 103tol10me&ea. Onlythelastdigitsof thedepth figureshavebeendisplayed.llgure 4 showsthereds forwellD.The figureindieateathatthevaluesof porosityekmated tiwn the We Groupmodel areagainhigberandclosa totheccmda@ eape&llyin therntervalsfkom102metres to107metres andtianl14 metrestol18metres. only the lastdigitsof rhedepthfiguresare shown.Thecmelation inefficientnd standarderrer valuesof the fourwellshowthat rheresultsffomthe FNeGroupmodelaremereaccuratethanthosepreaentlyused.Detailsmgiveain Table7.

WeU ; A! ii: c: ~..................... ............................................. ..................... .R~ ! 0.704 : 0.768 ! 0.557 ! 0.831..................... .......................... ...............................................R [5] : 0.715 : 0.823 ~ 0.654 ~ 0.854..................... .................................................. ...............................................sE~ ! 3.247 ! 2.905 ~ 3.015 i 2.114..................... .................................................. ...............................................SE[51 ; 2521 ; 2.170 ; 2.529 ! 1.953

[p] - PfWdy U8ed IUOdd[5] - FiveGroupmodel

Permeabilityofarock ismeof the most important flowpammetm asdated with suktrface produaion and injectkmopemtims. TheimpaTance of theparameter isrdteetdbythenumbez of sources -well logs mea rmd well testing ameng** t@l & employed to ~ ~ ty.well logevaluation has the special advantage of ecmany and tbecxminuityof measurementinthe esdmate ofthiiparameler.Permeabilityofafcrmarim @intluX averycanplex timaionWhiehisaffectedbyxrumyfactmssuchas porosityandptre$pa&&mWeristic&~ amamt and diatributkmof Ay !nimm@rockmatrix canpositicn andsizeofmaaix grains. lhecmmdlingfaetmcxtheva lueofpemneabilityin arewmoiraredependenten its geologicaland sedimentarypmpades. Manyempirical cmelatims have beelldevdoped toeadmatepenneabiIityw,atleasLapameaMity indextiwdllogs.lheinterval studiedisdmaamsd by its mnplex Iithdogicdcunpositicmand largeamamt ofclayminti byIigh pmosityand lowpermeaWty. Based (m these heterogexmousgeologicalchameMMcs atedmique has been devdopedhtxeferaealdnuals eadmateofpermeaWty * welllogs.

Thememoirs showfivetypesof tithotkciesidenti6ableMm welllogs. There is a distina relatkmship between pmosity andpermeabilityfcceach lithofaciea.Ihe empiricalcometadcnsfcrthetypesoflithofaeiesweremtabikhedbyregreaskm.Cro6s-Plot AnalysisThepermeabilityof themervohs wasstudied using306sampleafranwells AjBand C.Cm pcrositynd are ~ty wae cross-pklttedin I@ore5. Itindicatea thatthe datapoints are spread over two areas.Thosem oneareaareeunpoaedof sandskmeand shaleeIeanent&theothers emsistsmairdyof mbMXXmmted Cunponalts.Furthmmq figure 5 showsthattherearedistinadatknships!x%w&l!pc=oskyandpeneabdityforeaeb Ofthefive typesoflithofhcies.l%ismeans that pemeaMity is not only dated toPmOsityhtalsotothe intrinsicchmetaMca Ofeachlithofacies

he 6rst famula relating measurable rock properties withpmneabilitywas proposedin 1927by J. KozmyandmodifiedbyP.c. Carmam

a+=ss;(l-d ................. (6)

wherek-~tyO-p(xoaitySt-grain _areaperunit8did volumeIf thelithdogy ofafamatim deea not vary, the total grainsurfaee [SJinthe fcmmdamabecnnsidued to be constant.ll~pmeabdity vdllbea fimaiat of porositytbradistinaI.ithobcies.The nextmajx S@ was taken byTimur who extendedWyllieand Rmeseqiri&mbasedoMomtory studies of 155sandstonearea. lle Timurequatkmis describedas follows:

k=O.W$ ........................(7)

k - ptmrteability[red]@- p(xosity[%]L-imedueiblesammtnm [%]Inedueible water satumticm iaaiimaicm a- the rockCkma+aeri. E theMhok)gydoes not Vagy, tbe .irbk

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SPE028792 J.L. LIN and H.A. SALISCH 7-Watef Satm-ath SkM remem?Qm!tm -has W@pumeability wi.llbatidmof@tY fcradisdnctlithokka.'IEereareatherequationsimilartothat@W=bY ThnWsuCJImtheMinis andBiggsequation.Theseequatkmsam beqressedwitha generalfernmhx

k=c~ WI............................ (8)Areaemir withvariationsin lithology,withdiffemneeaeitherinthe canpositicm,stmciumw Oth=~ m dqlent3ybecksitied intoseveraldiserea Iithoiheiea.l%epmneability fcragivenlithofacies maybedeaaibed~ yasafuncticmof theptxaaity. lle gceatezthenumbercf Iithotkiea iutowhichamervoir istroken up, themmeaccmate will be the distinctrelationshipsbetweenpermeabilityandparosity .Ontheothezside thegreaterthenumberof lithofiteieshat aredemmimd feragiveninterval theharder willbe their identificatkmby. . .dmmmmantanalysisfian welllogs.he merwirswexegroupedintofivetypesoflithofaciesbasedonboth their lithdogical properties and rhe pmsikd.ityof theiridentificationffan well10gS.Twomodelswvremnsideredin the studyofpemneability

log(k) = a+ b.log(0).m$...o......(9)

log(k) =a+ ho ............. (10)Thetwomodels wereentefed intoregmasicmfmeashlhltofSciea.fheccrrdatic manderrc ranalysiswereused toselectthetinalmodelfff theesdmateof pumeahilityfhxnwelllogs.l%eresultsOfcmelaam anderrcr analysisare givvnin Tablea8and9,WAY.Thecameladm me&iemsinTable8 and standarderrcxsinTabie 9 wre calculatedfm the i-t of ~ma.-- flQg&J] and logarithm of ~ riea 6xlm logs@og(&)].lld.smeans thatthe wIhKarnbUhTw 8and9reQecttherelaticmshipsbMveenlog&)andlog&).?We S - ~Qweiat!t! Qdfide@ fmtheTwoModels

jl=ui?a ~Fades ~Fu5ca /F&ied ~F&iea~1~ 2~3 ;4 !5........................... . ............ . ............. ........ ......... .........II@)= * : 0.7166 ~ 0.8937 : 0.72s6 ! o.75m i 0.9114................ ........ ...................... .................... ..................................... .. ............... ...w)= ~ 0.7209 ~ 0.8983 : 0.7302 ~ 0.7438 ~ 0.9046**) i i

TatAe9-Standard Error forthehvoModels

The results of the analysisin Tables 8 and 9 indicatethat thesemi- logarithmicmodelsfix tkcies4 and f%eies5 have higheremdatkm coeliiaent valuesand lower standarderrs, and thatthesame appliestoheduallo garithmicmodels fmikcieal,fkeiea2andtkies3.Equationsa~;ti~e@ W _ to obtain a mgreasicn. l%eesdmateofpexmeabilit yfcanwel llogsfcxthefivetJQesoflitl@cies afe:-farjhcies Ilog(k)= -11.W + 7.732442log(cD)-forjileies 2log(k)= -16.5817+ 12.25489log(~)-fotfmies 3log(k)= -11.6038+8.88765log(Q)-faPJacias4log(k)= -2.68508+0.142257(0)-fwjheies 5log(k)= -2.07977+0.141827(@)Themmelaticmeoeilicient~] and staudardmar [SE]ealadatedftxthe306samplea fkotnwells~Band C byusingtheabovefiw tt@tkXIS are 0.9530 and 0.2130 [b Iq ~) and 1~~] ~d 0.9292and2.69f31[h lcmrend&], mapectivdy. .onma&onof the Ma@a

Inthis~several models wae used toohtaina~,.elambtm TheOne GroupmodeLtheTwo GroupmodeLandtheFiw Gmupmoddt&whieh theinterval was dividedintoone twoandfive&k& ~~y.IntheTwo Groupmodel thereaer@r was divided into twopartscalledSaimland Sectia12. llefimneris eunposedoft%iesl, tt@es2and fkies3with sands and shale$thelattexccm@seahcks4nd5witb arbonab eunentedekznents.Tvmmode& semi-logarirbmieand dual logarithmi~ wue studiedwithin theTwo Gnmpmodelfman eadmate ofpmneabilityffcmsonicpcrositiea.Basedonthereaultsofemela&m and~analysis the dual logarithmic model showed the highest

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cmelath me!Ticientnd lmw?sttandarderrcr in Secdon1; thesameappliedto the semi-logarithmicmodelin Sectioo2.h theOneGroupmodel a semi-logarithmicequath wasusedtoesdmate pmmbility ~sadcpmosities acuxdiog to theresultsofthecmelatioo andarw analysis.Table10givestheresultsobtainedfran the threemodelsfcr thefiveIithofa&s.

Table 10- Resultshorn Standard Error [SE]Analyaisk)rtbetbreeModelsi nthefiveLitMkks

~ Fadcsl ~ l%de.s2 ! Fuies3 ~ l%dcd4 ~ -5.......................... .................... ........................................ .............. ..... .................Olb?Grulp ~ 0.3433 ~ 0.2260 j 0.1937 ~ 0.3733 / 15797-;.........................+................... ....... ...........+_.._-_ ~

: 0.1740Twokup ! 0.3018 ~ 0.2202 . : 0.37230~ 0.3222IuxM.......................... .................... ........................................ ....................me GTcup ; 0.1987 ~ 0.2165 ~ 0.1515 : 0.3083 \ 0.1755

IIKddj

TheFheGroupmodelshowst obethemestaccumte model.Table11makesacunparison ofthetbreemodelsfw 306samplesfium weUsABand C.

Table ll-Resuits ofCarreiation and Error Anaiysisfromtbethree Modelsbased ondatafrom306san@esI : CM3rcW1WM:Tw@wPIIXIIM ! FivcGKNPdell

R; 0.7960 0.9413 : 0.9530...................................................... .............................. . ........................SE; 0.42s5 ; 0.2373 ~ 02130

Inthestudypsenteda firstlyithc4icies$wxeidmti&dfathefourwellsbytheBaysdisdmhmt functkms.Pmsitieswethenadahtedusing theapprqmmequationaeachufthelithohcies.ThepemeaMitywasedmatedIkantheFiveGroupmodel.R~6@mtiew~Kti@B. ~efi~rnti~tithepermeabilityvaluesderivedIkemthe FNeGroupmodelaremaeaecmate Thisismostappareat intheintemalsti 102to107m. and fixxnl14to l18m. Onlythelastdigits ofthedepthfigureshave&emdisplayed.Figure7makestheampaism oftbetworesultstlr well D.Alsohem theresults ticmtheFheGrmp model afemmeaccumte. Again, cmlytbe lastdigits af the depth figmes areShown.

Table 12- Correlation Coeffklent end StandardError for the three Wells

A: B~C~D.................. ............................ . ............ . .......... .......................R~/ 0.576 ~ 0.663 j 0.597 ~ 0.623.............................................. . . .................... .............R [5] j 0.611 ~ 0.713 : 0.694 j 0.716............................................. ........................................................SE~ ~ 0.993 ~ 0.891 0.872 ~ 1.049.................. ........................... ................ ..................................................................SE [5] ; 0.776 ~ 0.619 ~ 0.685 \ 0.842

[P] - Presentlyusedmodel[5] - five GroupmodelHE isoittshmva he fiew Wmii-i giivmnuaeamr-zipelmeawtyvzdues.CONCLUSIOhQ

Applicdonsllel%e(kmp model wasusedfaan esdmateofpmabilityinthethree pilotwellsA, Band Caodrnawell Doutsideoftbepilot area Theresults fkxntheFive Group model werecanpmedwththowt kcsnthemetbod prmently inuse in thisfield

h the melbod used at present a semi-logarithmicequarh isappliedtodelemme theptmneabilitiesduivedfcr weUa~BandC.Theeqwkmfat hemefhalusedpesentlyix

log(k)= -5.4524 +0.23810

1. The Iithofacieaof the memoirs Subjeaof thisstudycanbeidentifiedffan well logs.2. llediff&ent lith@wies of these mervuim have disthmrdationsbipsbetween@ty andX!U3StiCntervaltraosittime.3. ThedilWent litboikks of thesememoirs have distinctreladonsldpsetweenpaosityandpexmeaMty.4. The techniquepesemedintbispsptx -heecalledl%eGroupmodel- ismtxe~than thepresmtly usedmodeltirheevaluaticmoftberesmdrs fiomw?lllogs5. Thenewmodel isrdiable andaccumre rntheevaluatkmofheterogeneousresmmim ftxthegiwm amditicasand rntheamastudied6. Itwuddbe ofgeneral interest toapply tbemodeltoctberrmavahsand testtheextmtof itsvalidity.


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SPE028792 J.L. LIN and H.A. SALISCHACKNOWLEDGMENIfl

lheauthm wish toacknowledge tbeassistac eoftbecilcan@eswhichsuppliedth edatathatmaethisst udypossible.Theytuealso gmtefulfcr rbecmpuatimreceivedattheCmtreh PetroleumEngineeringof theUniwxsityofNewSouthWalesthrougheutthecourseofthiswak

1.-JohnC. RasmuxA Summaryof theEffectsofVariousPoreGeanetries and Their WettaMity cm Masured and In-situValues of Cmnenraticmand Samahon ExpaIems. he LogAMIYSLVol 28,NO.2 1987.2.- 3). Maricm, A. Nur, aod F. Alaberc Modding theR4atimships Belweensonic velocity, Pmosity, ~vvand Sbdiness m SaucLSl@g aud Shaky Sand, SPWLATltirtielbAnnualLoggingsympdllm!1989.3.- A. E.Bussian:Eleurical Cenductamzm a PromsMedium,@@@c& VoL48,No.9,1983.4.- U. Ahme&S. F. Crary, and G. RCoates :~vEstimadcxuthe Various Sourcesand Iheir IIItemlationship,SF%19604,1989.5.- M.R WyUieand G. H Gardner :TheGmerahM Kozeay-- Equatien,Wcxld(XLMarch-1958.6.- J. Kumar:NewClint OffersFast PmrneabilityEsdmat&,WorldGil , Fe&wry, 1971.7.- GeorgeRCoatesand J. L. Dumanoic ANew AppmachtoImproved Log-derived RlmeaMi&, 3chhllnbexgtX well!ltzvim - Texas.8.-RichardH.Benneq KathleenM.Fischtx,Da- W-Rand RichardRezak Pwcmelryand Fahic of MarineClayand&bonate sedimmts Deets d RmneaMi~, MarineGeology,P. 127-15? 1989.

9

9.- Lev Vemik and AtnasNuc Pe&cpbysicalClassMcarkmofSiIiciclasticsh Lithdogy and PmosityPredicdm b SeismicVelocities,AAPGBulletin,V.7Q No. 9,p,1295-1309, 1992.

503


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10 DETERMINATION FROM WELL LOGS OF POROSITY AND PERMEABILITY IN A.. SPE 028792FfGURE1 ELECTRIC FACIES FROM WELL LOGS

I Rlld I I RIM I I Rud 1

1.

FiGURE 2EEiEEil

Wells A, B and Cz 35.8 30-25E 20 A facies 4g 15 IQ 10* 70 80 90 100 110 120 130 140

ACOUSTICINTERVALTJUUJSITTIMEpO&Rwedftl

504


11/12

SPE 028792 J.L. LIN and H.A. SALISCH 11

WELL B - COMPARISON OF RESULTS BETWEEN THE FIVE GROUP MODELFIGURE3 AND THE PRESENTLY USED MODEL3530~ 25

z 20g 15g 10

50F?=O76S SE=2.905for presenuy umnn-R+l QO1 CC-9 17nf?w12hmrmm model80.00 85.00 90.00 95.00 loo.(x) 105.00 110.00 115.00 120.00

DEPTH [mares] - Oldylast digits of depth figures are ShOW31

WELL D - COMPARISON OF RESUL~ BETWEEN THE FIVE GROUPFIGLJRE4 MODEL AND TEE PRESMWZY USEDMODEL40

E 30E 208M 102

0100 105 110 115 120 125 130 135 140

DEPTH [mares] - only last digits of depth figuresare shown


12/12

12 DETERMINATION FROM WELL LOGS OF POROSITY AND PERMEABILITY IN A.. SPE 028792

FIGURE5 STUDY OF PERMEABILITY Wells A, B and C- 1001!g lo-&,G/~ 01 ns 4~ 0.01 , # ,

0 5 10 15 20 25 30 35POROSITY[CoRS,%]

FIGURE6

1000100101

0.10.010.0010.00010.00001

WELL B - COMPARISONOFRESULTSBETWEENTHE FIVEGROUP MODELANDTHEPRESENTLYUSEDMODEL

80.00 85.00 90.00 9s.00 .-.. --lW.W i05.00 liMO ii~.g) ~mnna2u.ul.lDEPIT-I[mares] - only lastdigits of depth figures are shown

WELLD - COMPARISONOFRESULTSBETWEENTHEFIVE GROUPMODELANDFtGURE THEPRESENTLYUSEDMODEL

DEPITI [met!es]- only last digitsof depth figures are shown

Documents

Determination From Well Logs Porosity and Permeabilityin Heterogeneous Reservoir