Post on 10-Oct-2015
description
transcript
WWW.GeoNeurale.Com January2012 2012RobertEBallay,LLC
The essence of carbonate petrophysics is (often) pore system heterogeneity, as compared to clay conductivity issues for clastics
The foundation of the Lucia petrophysical classification is the concept that pore-size distribution controls permeability and saturation
The focus of this classification is on petrophysical properties and not genesis Petrophysical classifications focus on contemporary rock fabrics that include depositional and diagenetic textures
To determine the relationships between rock fabric and petrophysical parameters, one must define and classify pore space as it exists today in terms of petrophysical properties
Addition of vuggy pore space alters the manner in which the pore space is connected
Courtesy of Jerry Lucia
Figure 1
a : Rock Types 1 and 2 correspond to intergranular grainstone
Limestone and dolostoneb : Rock Type 3 is sucrosic dolostone with intercrystalline porosityc : Rock Types 4 and 5 correspond to moldic limestone and dolostoned : Rock Type 6 is mudstones and chalkse : Rock Type 7 is the combination of matrix and moldic / vuggy porosity, ie vuggy packstone / wackestone f : Rock Type 8 is fracture / fissure porosity
Cementation Exponents in ME Carbonate Reservoirs. J W Focke and D Munn, SPE Formation Evaluation, June 1987
Illustrative, generic thin sections
Porosity is black
Figure 2
ThemExponentinCarbonatePetrophysicsRE(Gene)Ballay,PhDwww.GeoNeurale.com
In1952ArchiestatedIndiscussingthepetrophysicsoflimestones,itisnecessarytofirstclassifytheminamannertoportrayasmuchaspossibletheessentialporecharacteristicsofareservoir.Theapplicationofpetrophysicalrelationshipsinlimestonescanbemuchmoredifficultthanforsandstonesbecauseoftheheterogeneity.Thisisduemainlytothevariationofporesizedistribution.
TheattributewithinArchiesequationwhichrepresentstheporesystemtortuosityisthemexponent.Complicationsincarbonateformationevaluationcanariseduetomixedmineralogys(whichaffectstheestimationoftotalporosity)andwettability(Sweeny&Jennings)/surfaceroughness(Diederix)whichdrivethenexponent,butfromoneperspectivethemexponentcanbesaidtooftenrepresenttheessenceofcarbonatepetrophysics.
Ascomparedtoclasticpetrophysics,whichistypicallycompromisedbyclayconductivityissues,carbonatepetrophysicsissueswillinmanycasesrevolvearoundpropercharacterizationoftheporesystem,whichreflectsbothdepositionalanddiageneticproperties.JerryLuciaadvisesustofocusonpetrophysicalproperties,notgenesis,andwethusrealizethatpetrophysicalzonesmaybegenuinelydifferentthangeologicalzones:Figure1.
Whilethereareseveralcarbonateclassificationsystemsinthepublicdomain(Lucia,Lny,etc),FockeandMunnsworkisparticularlycompleteinthatitillustrateseachofthefollowing:Figure2.
Poregeometryperthinsections.
Laboratorymmeasurementscorrelatedwiththinsectiondescriptions.
Wirelinemethodologyfordeterminingminthewellbore,across
WWW.GeoNeurale.Com January2012 2012RobertEBallay,LLC
Interparticle vs moldic porosity and Sw
J W Focke and D Munn: Cementation Exponents in Middle Eastern Carbonate Reservoirs, SPE Formation Evaluation 2 (1987) : 155-167See Also A M Borai: A New Correlation for the Cementation Factor in Low-Porosity Carbonates, SPE Formation Evaluation 2 (1987): 495-499Schlumberger Technical Review, Volume 36 Number 3
Saturation Variations
0.00
0.20
0.40
0.60
0.80
1.00
1.5 1.7 1.9 2.1 2.3 2.5
Saturation Exponent
Wat
er S
atur
atio
n
Boxing in the uncertainty for specific criteria
= 0.2, Rw@FT = 0.1 ohm-m, R = 50 ohm-m At each value of 'n', a range (1.5 - 4.0) of 'm' values are displayed in steps of 0.25
m = 3.50
m = 3.00
m = 2.50
m = 2.00
m = 1.75
Pore Geometry Effects on Sw
Figure 3
Dots, ambient pressureOpen circles, reservoir pressure
1.9 < n < 2.1
Middle East Carbonate Sw calculated with both constant and variable exponent
Variable (high m) exponent evaluation consistent with water test in lower zone
Schlumberger Technical ReviewSeeking the Saturation Solution M. Watfa: Middle East Well Evaluation Review No. 3 (1987)
Where m ~ 2.0 2.5, calculations and test agree
Across the water test m approaches 3.5
Failure to recognize this yields Sw(Actual) ~ Sw(m=2) / 0.25 orSw(Actual) ~ 4 * Sw(m=2)
Sw calculates good but Test is water!!
Figure 4
boththewaterlegandhydrocarboncolumn.
Comparisonofwirelinedeterminedmandlabdeterminedm.FockeandMunnfindthatthedifferencebetweenaninterparticleandvuggyporesystemcanbeaslargeasanmof~2versusanmof~4,correspondingtoanSwuncertaintyof~20%versus~75%:Figure3.
Theconsequencescanbedevastating:anintervalofhighresistivity(apparentlypay)maybenothingmorethanrelativelytortuous,waterfilledporesystem.
Oneapproachtothisuncertaintyistocombine
anonArchietool(suchasthedielectric)withaconventional(shallowreading,sincethedielectricisalsoshallow)resistivitymeasurement,andwiththismultiplicityofmeasurementsdeducewhatthefootbyfootmisinthewellbore:Figure4.
Anotheroptionmightbetopartitiontheporesystemwithmoderntools(Gomaaetal,Ramamoorthy,etal,etc)andtothenindependentlyestimatethecorrespondingfootbyfootmwithsomekindofelectricalcircuitmodel(Aguilera,Wang&Lucia,etc).
Anattractionofamathematicalrepresentationofthemexponentisthatwhatifcalculationscanbedone,toascertainthe
WWW.GeoNeurale.Com January2012 2012RobertEBallay,LLC
Comparison of Empirical Models for Calculating the Vuggy Porosity and Cementation Exponent of Carbonates from Log Responses. Fred P. Wang and F. Jerry Lucia
In the graphic at right, cementation exponents calculated by the Archie equation (thick black line - mres ) are compared with those from SPI/Nugent, Nurmi /Asquith, Lucia, modified Myers, and Dual Porosity.
Cementation Exponent Models vs Wireline mm(Dual Porosity) ~ m(Archie)
Figure 5
0.00
0.10
0.20
0.30
0.40
0.50
0 0.1 0.2 0.3 0.4
RelativeUncertainty
Porosity
RelativeContribution ToSwUncertainty
a
Rw
Phi
m
n
Rt
Below: Illustrative (Chen & Fang) Best Estimate of each parameter, with corresponding individual uncertainty, and associated relative uncertainty on Sw(Archie).
Right: Relative impact on Sw(Archie) uncertainty of m & n, across a range of porosity values, for a fixed Phi uncertainty.
Attribute Uncertainties Specified IndividuallyLight Green Cells require User SpecificationLight Blue Cells are calculated results
Individual Best Relative UncertaintyAttribute Uncertainty Estimate On Sw(Archie)a 0.0% 1.00 0.0000Rw 4.4% 0.02 0.0019Phi 15.0% 0.20 0.0900m 10.0% 2.00 0.1036n 5.0% 2.00 0.0480Rt 1.0% 40.00 0.0001Sw 11%Sw^n 1%Sw^n=0.367 is an inflection point
After C. Chen and J. H. Fang. Sensitivity Analysis of the Parameters in Archies Water Saturation Equation. The Log Analyst. Sept Oct 1986
Identifying the Biggest Bang for the Buck, in Improved Sw Estimation
Figure 6
rangeofestimatescorrespondingtoarangeofinputuncertainties(uncertaintyin,forexample,theporositypartition).
Regardlessofwhatapproachisusedtoestimatethewellborem,duediligencerequiresthatateveryopportunitytheresultbecomparedagainsttheinferredArchieestimateinthewaterleg[whereSw=1andm=log(Rw/Ro)/Log(Phi)]:Figure5.
Weshouldfurthermorenotlosesightofthefactthattheremaybeintervals,particularlyinthevicinityofthetransitionzone,acrosswhichtheArchiecalculationissimplynotvalid(Griffithsetal).
WheretoFocusAlthoughthemexponentmay(logically)bethefirstissuethatcomestomindincarbonateevaluation,itdoesnotalwaysdominatetheuncertaintyinSwestimates.Therearetwobasicwaysofidentifyingwherethefocusshouldbe:Figure6.
TakethevariouspartialderivativesofArchiesequation,andcomparemagnitudesforlocallyspecificvaluesanduncertainties.
MonteCarlosimulation.
Thetwooptionscomplementoneanotherinthatthederivativesareeasytocodeintoaspreadsheetor
WWW.GeoNeurale.Com January2012 2012RobertEBallay,LLC
0.00
0.10
0.20
0.30
0.40
0.50
0 0.1 0.2 0.3 0.4
RelativeUncertainty
Porosity
RelativeContribution ToSwUncertainty
a
Rw
Phi
m
n
Rt
At 20 pu, formation evaluation should focus on improved porosity and m estimates, with n of relatively less importance.
If porosity rises to 30 pu, however, improved porosity estimates become more important with m and n having similar, and less, impact.
As porosity drops to 10 pu, it is the pore connectivity (m) that begins to dominate the accuracy.
The Porosity Dependence
The relative importance of m and n depend not only upon their specific uncertainty, but also upon the porosity of the interval in question; there is a link
Figure 7
After C. Chen and J. H. Fang. Sensitivity Analysis of the Parameters in Archies Water Saturation Equation. The Log Analyst. Sept Oct 1986
0.00
0.10
0.20
0.30
0.40
0.50
0 0.1 0.2 0.3 0.4
RelativeUncertainty
Porosity
RelativeContribution ToSwUncertainty
a
Rw
Phi
m
n
Rt
Light Green Cells require User SpecificationLight Blue Cells are calculated results
Individual Best Relative UnAttribute Uncertainty Estimate On Sw(Archa 0.0% 1.00 0.0000Rw 4.4% 0.02 0.0019Phi 15.0% 0.20 0.0900m 10.0% 2.00 0.1036n 5.0% 2.00 0.0480Rt 1.0% 40.00 0.0001Sw 11%Sw^n 1%0.367 is a logarithmic inflection point
0.00
0.10
0.20
0.30
0.40
0.50
0 0.1 0.2 0.3 0.4
RelativeUncertainty
Porosity
RelativeContribution ToSwUncertainty
a
Rw
Phi
m
n
RtLight Green Cells require User SpecificationLight Blue Cells are calculated results
Individual Best Relative UnAttribute Uncertainty Estimate On Sw(Archa 0.0% 1.00 0.0000Rw 4.4% 0.20 0.0019Phi 15.0% 0.20 0.0900m 10.0% 2.00 0.1036n 5.0% 2.00 0.0108Rt 1.0% 40.00 0.0001Sw 35%Sw^n 13%0.367 is a logarithmic inflection point
If the water were fresher, say Rw = 0.2 instead of 0.02, n diminishes in importance as compared to both the amount of porosity, and its connectivity (m).
After C. Chen and J. H. Fang. Sensitivity Analysis of the Parameters in Archies Water Saturation Equation. The Log Analyst. Sept Oct 1986
The Rw Dependence
The Rw Dependence
Figure 8
petrophysicals/wpackage(forfootbyfootdisplay),whiletheMonteCarlogivesinsightintotheupanddownsides(with95%confidence,theuncertaintywillbelessthanhighlowcalculations).
UsingChenandFangsparameterstoillustratethedifferentialapproach(Figure6)wenotethatasporosityvaries,therelativeimportanceofmandnalsovaries.Thatis,theimportanceofasingleattribute,mforexample,islinkedtothemagnitudeofother
attributes.
Inthecaseathand,a20puformationevaluationshouldfocusonimprovedporosityandmestimates,withnofrelativelylessimportance.Asporositydropsto10pu,theporeconnectivity(m)beginstodominatetheaccuracy:Figure7.
Thementalimagethatemergesisthatasporositydecreases,itsconnectivity(orefficiency)becomesincreasinglyimportant.
Weretheformationwaterresistivitytochange,itsquitepossiblethatthefocusshouldalsochange:Figure8.
Insummary,eachsituationshouldbeevaluatedwithitslocallyspecificparametersanduncertainties,andourfocus(andbudget)appliedaccordingly.
WWW.GeoNeurale.Com January2012 2012RobertEBallay,LLC
Generalized slope-intercept straight line equationy = m * x + b
Log(FF) = - m * Log( ) + bAt = 100 % , Log ( ) = Log(1) = 0
Leaving Log(FF) = Log(1) = 0 b = 0 to give Log(FF) = - m * Log( )
At = 10 % , FF = 100Log(100) = 2.0 = - m * Log (0.1) = m
to give m = 2.0
1
Schlumberger Technical Review, Volume 36 Number 3G E Archie: The Electrical Resistivity Log as an Aid in Determining Some Reservoir Characteristics. Petroleum Transactions of the AIME 146 (1942): 54-62.
The Key to working with the Log-Log displays is to think in terms of decades and take logarithms
when working with numerical values
Figure 9
mandCarbonatePoreSystemsArchiemeasuredtheporosity,permeabilityandresistivityofbrinesaturatedcarbonateandnonshalysandsamples,acrossarangeofbrinesalinities,toobservealinearrelationbetweenRo(brinesaturatedsampleresistivity)andRw(brineresistivity).
ThisresistivityratioisknownastheFormationFactor,where
FF=R(sample)/R(brine)=1/mArchiecommentedthatmwasabout1.3inunconsolidatedrockandincreasedasthecementationincreased.Atypicalformationstartingpointvalueformis2.0.
ItwasHubertGuyodwhogaveusthetermcementationexponent,andwhoincidentally,alsosuggestedtheoriginalnameoftheSPWLAJournal(TheLogAnalyst).
Themexponenttypicallyinvolvesaloglogdisplayofthebasicdata,andassuchislessintuitivethanasimplelineardisplay.Semilogandloglogdisplaysarecommoninmanypetrophysicalendeavors(phiperm,etc),however,anditsusefultobeabletodrawourownlinethroughthedataanddeducethecorrespondingexponent.TheKeytoworkingwiththe
LogLogdisplaysistothinkintermsofdecadesandtakelogarithmswhenworkingwithnumericalvalues.
SketchingourlinethroughArchies1942dataanddrawingupontheslopeinterceptformulationofalinearrelation,revealsthatm~2.0isindeedareasonablestartingpointwiththatdataset:Figure9.
WhileitwasMrGuyodwhogaveustheterminology
cementationexponent,itappearsthatwederivethemnomenclaturefromthemathematiciansslopeinterceptrepresentationofastraightline,whereintheslopeisdenotedbym:y=m*x+b.
Lookingaheadjustabit,totheResistivityIndex(incontrasttotheFormationFactor),itwouldfurtherseemthatournnomenclaturemayhavearisenalphabetically,sincenfollowsm.
Interestinglyfromahistoricalperspective,thiskindofrelationshiphadbeenpostulatedearlierbySundberg,butwithoutthesupportingdata.
WWW.GeoNeurale.Com January2012 2012RobertEBallay,LLC
Archies 1947 Data - Sandstone and Limestone
G E Archie: Electrical Resistivity as an Aid in Core Analysis Interpretation, AAPG Bulletin 31 (1947): 350-366Schlumberger Technical Review, Volume 36 Number 3
Suggested to Archie that permeability (molecular fluid flow) and resistivity (ionic movement) were different
Formation Factor (Rformation / Rbrine )
Figure 10 Conceptually,giventhatbothrepresentaflow,onemightexpectastrongerrelationshipbetweenresistivityandpermeability,ascomparedtoresistivityandporosity.Archieaddressedthisbyplottinghismeasurementsbothways:Figure10.
Perhapssurprisingly,thevariousFormationFactormeasurementsconvergemuchbetterwhendisplayedagainstporosity,thanagainst
permeability,promptingArchietosuggestthatmolecularfluidflow(permeability)andionicmotion(current)weredifferent.ThosewhohaveworkedbothIG/IXandchalksystemsarealreadyawareofthis,havingnoticedthatthemforthetwoverydifferentpermeabilitiescanbothbeabout2.
Verweretalhaveperformedadigitalimageanalysisofthinsectionsrepresentingcarbonateplugsuponwhichresistivitymeasurementsweremade.Threeattributeswererecognizedasplayinganimportantrole.
Perimeteroverarea:twodimensionalequivalenttotheporesurface/porevolumeratio.
Dominantporesize:theupperboundaryofporesizeswithwhich50%oftheporosityonthethinsectioniscomposed.
Microporosity:calculatedasthedifferencebetweentheobservedmacroporosityinDIAandthemeasuredporosityfromtheplugsample.
Theirmeasurements,nicelyillustratedwithaccompanyingthinsections,demonstratethatinadditiontoourintuitiveexpectations,
sampleswithhighresistivitycanhavehighpermeability, sampleswithlowpermeabilitycanhavea(relatively)lowmexponent.
AsArchiepointedoutin1952,carbonateporesystemsmaybequitevariable,causinganm=2calculationtobenonrepresentative.WyllieandGregoryboundedthemexponentforarangeofbeadpacksconsistingofunconsolidatedandcementedspheres,viachemicalflushes,andfoundtherelationbetweenformationfactorandporositycouldinvolveanadditionalparameter,C,whichdifferedfromunity.
WWW.GeoNeurale.Com January2012 2012RobertEBallay,LLC
Wyllie and Gregory constructed bead packs with varying degrees of cementation
The baseline represents a formation of unconsolidated spheres
This data prompted them to propose the relation
FF = C / mC was a formation dependent constant
m ~ 1 for unconsolidated spheres
m ~ 4 for cemented bead pack
M R Wyllie and A R Gregory: Formation Factors of Unconsolidated Porous Media: Influence of Particle Shape and Effect of Cementation, Petroleum Trans of the AIME (1953): 103-110. Schlumberger Technical Review, Volume 36 Number 3
Figure 11Archie commented that m was about 1.3 in unconsolidated sand and became higher as cementation increased
Cementation Exponents in Middle Eastern Carbonate Reservoir. J W Focke and D Munn, SPE Form Evaluation, June 1987
Geological descriptions of hundreds of samples reveal a systematic relation between Rock Type and Archies m exponent
Rock with a more tortuous and/or poorly interconnected porosity (moldic) display well-defined trends of increasing m with increasing porosity
The additional moldic porosity is less effective at electrical conduction
In some rock m is found to rise from 2 @ 5 pu, to 5.4 @ 35 pu
m variations, within a specific Rock Type, can be reduced by segregating the samples of a specific Rock Type into Permeability Classes
Figure 12
Rock Type 4, the moldic limestone grainstone, represents a diagenetic inversion whereby the original porosity (between the grains) was filled with cement, and the original grains were dissolved to form the current porosity
Symbols refer to different wells
FF=R(sample)/R(brine)=C/mCisformationdependent,andtherangeofmexponentswasfoundtobem~1for
unconsolidatedbeadsm~4forcementedbeads:Figure11.
FockeandMunnthenconductedadetailedstudyofmmeasurementsonactualcarbonatesamples,supportedwiththinsectiondescriptionstofindsystematicrelationsbetweentheporositytypeandm.
Whiletheintergranular/intercrystallineporesystemhadm~2(solongas>5pu),consistentwithArchies
earlierlabwork,vuggyporesystemscouldexhibitanmthatreached5:Figure12.
TheirRockType4,representingadiageneticinversioninwhichOriginalPorosityRockandOriginalRockPorosityisanexampleofwhereanincreaseinporositycorrespondstoanincreaseinvuggyporositycontent.Becausethevuggyporosityislessefficientatelectricalconduction,themexponent(counterintuitively)risesasporosityincreases:Figure13.
WWW.GeoNeurale.Com January2012 2012RobertEBallay,LLC
Rock Type 4, the moldic limestone grainstone, represents a diagenetic inversion whereby the original porosity (between the grains) was filled with cement, and the original grains were dissolved to form the current porosity
Perm Class 1: Perm < 0.1 md
Perm Class 2: 0.1 md < Perm < 1 md
Perm Class 3: 1.0 md < Perm < 100 md
Perm Class 4: 100 md < Perm
Moldic Rock
1
2
3
4
5
0 5 10 15 20 25 30 35Porosity
Cem
ent E
xpon
ent
RT4/PC1RT4/PC2RT4/PC3RT4/PC4
m vs PorosityRock Type 4: Classes 1, 2, 3, 4
Figure 13
Cementation Exponents in Middle Eastern Carbonate Reservoir. J W Focke and D Munn, SPE Form Evaluation, June 1987
Fracture porosity has an effect opposite to vuggy porosityProvides a conductive conduit => lowers m
m can be estimated with Charts
R Aguilera: Analysis of Naturally Fractured Reservoirs from Sonic and Resistivity Logs, SPE 4398, Journal of Petroleum Technology 26 (1974)R Aguilera: Analysis of Naturally Fractured Reservoirs from Conventional Well Logs, SPE 5342, Journal of Petroleum Technology 28 (1976)Schlumberger Technical Review, Volume 36 Number 3
Illustrative calculation
is the fraction of porosity that is fracture
Phi(Total) ~ 20 pu ~ 50 %m ~ 1.35
Figure 14
Althoughextreme,diageneticinversionisreportedinotherstudies,forexampleEberlietal,whoillustrateitwiththinsectionsanddescribetheprocessastheoriginalgrainsaredissolvedtoproduceporesastheoriginalporespaceisfilledwithcementtoformtherock
FockeandMunnnextnoticedthatthecorrelationbetweenmandporositycouldbe
improvedbybreakingthatRockTypeintopermeabilityclasses,eachofwhichcorrespondedtodiageneticallyinvertedrock,butwithdifferentpermeabilities.Weshallreturntothedifferentmvstrendsassociatedwiththedifferentpermeabilityclasses,withinthecontextofadigitalmexponentmodel,shortly.
Fractureporosityhasaneffectoppositetovuggyporosity,conceptuallyformingakindofshortcircuit,whichisrepresentedmathematicallybyadecreaseinvalue:Figure14.
WWW.GeoNeurale.Com January2012 2012RobertEBallay,LLC
The Dual Porosity Cementation Exponent model follows from a simple two component (intergranular and vuggy porosity) electrical model
1/R(equivalent) = 1/R1 + 1/R2 = C0 = C1 + C2
Each component satisfies Archies relation between resistivity and formation factor
Resistivity = Rw * FF Conductivity = Cw / FFFormation Factor is related to porosity as FF = a / m
The two component parallel circuit equation is then
C0 = Cw [1/FF1 + 1/FF2]
C0 = Cw [(1)m(1) / a(1) + (2)m(2) / a(2)]Now take a(1) as 1.0, m(2) as 1 and allow a(2) to vary from 1 to infinity [av(2) represents the tortuosity of the vuggy partition]
intergranular vuggy
Figure 15
Comparison of Empirical Models for Calculating the Vuggy Porosity and Cementation Exponent of Carbonates from Log Responses. Fred P. Wang and F. Jerry Lucia
Type I formula: Assuming that mv is 1 and that av varies from 1 to infinity, we can write the parallel circuit equation as below
The deduction of the net effective m from the conductivity equation follows from(relative to the simple Archie relation)
Ro = Rw / ( m) => Co = Cw * ( m) Take logarithm of Co - Cw equation
log(Co) = log(Cw) + m log()Following exhibit
Details following
exhibit
Figure 16
Comparison of Empirical Models for Calculating the Vuggy Porosity and Cementation Exponent of Carbonates from Log Responses. Fred P. Wang and F. Jerry Lucia
DigitalmExponentModelWithintheLuciasystem,vuggyporosityiseverythingthatisnotinterparticle,andincludesbothtouchingvugs(fractures,etc)andseparatevugs(moldic,intraparticle,etc).Whiletherearechartsavailabletoestimatem,asafunctionofvuggyporositycontent,forthevariousscenarios,itwouldbeadvantageoustohaveadigitalmodel.
Thereareseveraldigitalmodelsavailable,andhereweuseWang&Luciaforillustrativepurposes,because:
Itisbaseduponasimplecircuitmodelthatiseasytofollowforthosenotparticularlycomfortablewithelectricalcircuittheory,
Itallowsforbothtouchingandseparatevugs,andeverythinginbetween, WangandLuciaincludedindependentQCchecksontheviabilityoftheirmodel,
WangandLuciarepresentvuggyrockasatwocomponent,parallelcircuit:Figure15.
Eachcomponent(independently)satisfiesArchiesequation,andtheythensimplifytheresultingnetconductivityexpressionbysettingthemofthevuggyfractiontobe1andrepresentingthetortuosityofthevugs(betheytouching,separateorsomethinginbetween)withaparameterav:Figure16.
WWW.GeoNeurale.Com January2012 2012RobertEBallay,LLC
Type I formula: Assuming that mv is 1 and that av varies from 1 to infinity, we can write the parallel circuit equation as below (details in exhibits following)
The deduction of m from the conductivity equation follows from (relative to the simple Archie relation)
Ro = Rw / ( m) => Co = Cw * ( m) log(Co) = log(Cw) + m log()
m log() = log(Co) - log(Cw) = log(Co / Cw) = log [ ]
m = log(Co / Cw) / log() = log [ ] / log()
Figure 17
Comparison of Empirical Models for Calculating the Vuggy Porosity and Cementation Exponent of Carbonates from Log Responses. Fred P. Wang and F. Jerry Lucia
This indicates that equation 30 can be used to model reservoirs with separate vugs, touching vugs, and fractures using appropriate values of av.
av represents the connectivity, or lack thereof, of the vuggy portion of the pore system
Figure 18
Thisleavesthemwithanexpressionforthenetcementationexponentasafunctionofthetotalporosity,theporositypartition,theexponentoftheinterparticlefraction(mip)andtheconnectivityofthevuggyfraction(av):Figure17.
Withthisdigitalmodelinhand,duediligencerequiresthatitbetested,withonesuchtestbeingacomparisonofthecalculatedmtothatinferredfrom
Archiesequationinthewaterleg,Figure5,wheretheyfindthatanappropriatechoiceofavresultsinamatch.
Whilethereisatendencytothinkofnonfracturevugsasseparate,withoutcontributiontopermeability,aliteraturesearchwillrevealinstancesofthepermeabilityactuallyincreasing,withthepresenceofvuggycontent.Thisbehaviorbringsforwardtheimportanceofparameterav,whichisavailabletorepresentsuchasituation.
WangandLuciaalsotestedtheirmodelinsuchasituation,drawinguponMeyersdata,wheretheyagainfoundthatalocallyappropriatechoiceofavbroughtmeasurementsandestimatesintoagreement:Figure18.
Theattractionofadigitalmodelisthatitallowswhatifcalculations.Suppose,forexample,avisualexaminationofcoreindicatesthatabout1puofvuggyporosityispresent,dispersedamongstthematrixporosity.Ifthatvuggyporosityisnotwellconnected(ieav>>1)andthetotalporosityis~5puor
WWW.GeoNeurale.Com January2012 2012RobertEBallay,LLC
So long as ~ 5 pu and greater, only at av ~ 1 does a small (v ~ 1 pu) cause the Cementation Exponent to differ from mip = 2.0
Dual-porosity Model / What If Characterizations
0
1
2
3
4
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
Cem
ent E
xpon
ent
Total Porosity [ Phi(v)=0.01 ]
Dual Porosity / Type 1
av=1
av=10
av=100
av=1000
ip + v = 2 pu
0
1
2
3
4
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
Cem
ent E
xpon
ent
Total Porosity [ Phi(v)=0.05 ]
Dual Porosity / Type 1
av=1
av=10
av=100
av=1000
ip + v = 6 puSo long as ~ 10 pu (or more) and the vugs are not present as fractures (or connected vugs), an m of ~ 2.5 would be a reasonable starting point.
Figure 19
Monte Carlo Dual-porosity Model What If Characterizations
The Monte Carlo method relies on repeated random sampling to model results
Advantages of Monte Carlo include
any type of distribution can be used to characterize the uncertainty distribution of any parameter
normal, log normal, etc
insight is gained into the upside and downside
0
100
200
300
400
500
600
1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60 2.80 3.00
Frequency
DualPorosity"m"
MonteCarloDistribution
"m"DualPhi
0
1
2
3
4
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
Cement Exponent
Total Porosity [ Phi(v)=0.05 ]
Dual Porosity / Type 1
av=1
av=10
av=100
av=1000
Figure 20
more,thedualporositymodelwouldindicatethataneffectivemofabout2isareasonablestartingpoint:Figure19.
If,however,that1puispresentintheformofwellconnectedvugs(fractures),thenav~1andtheeffectivembecomesmuchmoresensitivetotheporositypartitionandconnectivity.
Nextconsideranintervalwithabout5puofvuggyporosity(Figure19,again),withamatrixcementationexponentof2.Solongasthetotalporosityis10puorgreater,areasonableinitial
valueoftheeffectivemwouldbeabout2.5,solongasthevuggyportionisnotwellconnected.
Buildinguponthisconcept,werealizethatifitispossibletopartitionporosity,footbyfootinthewellbore,thenonemayalsocalculatemfootbyfootandusethatexponentvaluetothenestimateSw.Insuchasituation,itwouldbeadvisabletoseekoutawaterintervalatthefirstopportunityandcomparetheresultingSw(whichishopefullycloseto100%)withthatdeducedfromaninversionofArchie(asWang&Luciadid,inFigure5),forvalidationpurposes.
IfthecalculateddualporosityexponentisafairrepresentationoftheinvertedArchiem,thentheevaluationofvuggyintervalshingesupontheaccuracyoftheporositypartition,whichmayinfactbeahurdle.Limitationsthatwillariseare,
theimagelogwillbecompromisedifthevugsizeislessthanthebuttonresolution,about35mm,
incarbonatestheNMRT2willlosetheporesizerelationatporebodysizesofabout50100um.
WWW.GeoNeurale.Com January2012 2012RobertEBallay,LLC
Matrix has a relatively uniform amount of interparticle porosity (the background), with variable amounts of vuggy porosity, with different degrees of connectivity
mip = 2.0, ip & av constant across range of v
Moldic Rock
1
2
3
4
5
0 5 10 15 20 25 30 35Porosity
Cem
ent E
xpon
ent
RT4/PC1RT4/PC2RT4/PC3RT4/PC4
Focke & Munns DataRock Type 4, Perm Classes 1 => 4, a moldic limestone grainstone: representing a diagenetic inversion whereby the original porosity (between the grains) was filled with cement, and the original grains were dissolved to form the current porosity
Dual Porosity / Type 1
1
2
3
4
5
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
Total Porosity [ Phi(ip)=0.01 ]
Cem
ent E
xpon
ent
av=1
av=10
av=100
av=1000
ip + v = 2 pu
The Dual Porosity Model has captured the essential trends of the independent Focke & Munn data.
The Dual Porosity Model vs Lab Data
Figure 21 Thereisyetanotheradvantageofexpressingthevuggyporesystemexponentinmathematicalform:itbecomespossibletoperformaMonteCarlosimulation:Figure20.
Nowweareabletoaccountforuncertaintyinthevariousinputs(theporositypartition,asanexample),andcharacterizetheBestEstimateintermsofprobabilities.Thatis,ratherthangowithahigh/lowestimate,onecanidentify(for
example)95%oftheMCdistribution.Inmanycaseswewillfindthat,ifwecanaccepttwostandarddeviationsofuncertainty(95%),thelikelyhigh/lowvaluesarenotsoextremeasthepossiblehigh/low.Thisisbecause,ingeneral,itisunlikelythatallthehigh(orlow)inputvalueswilloccursimultaneously.
Theprecedingillustrationsrepresentafixedvuggyportioninthepresenceofmoreorlessmatrixporosity.Itisalsopossiblethatmostoftheporosityisintheformofvugs,withsomesmallamountof(background)matrixporosity:Figure21.
Thatis,insteadofaconstant1pu(or5pu)ofvuggyporosity,asthetotalporositygoesupanddown(Figure19),onemighthaveasmallamountofinterparticleporosity,withmoreorlessvugspresent.Thedualporositymodelexponenttrendsarenowverydifferent,becausethebulkoftheporosityisnotefficient.
Solongasthevugsarenotconnected,Figure21revealsatrendofincreasingm,withincreasingporosity.Asavvariesfromslightlyconnected(av~10)toseparate(av~1000),thedifferenttrendsseparate,andexhibitapatternverysimilartowhatFockeandMunnfoundexperimentally.
FockeandMunnsRockType4(diageneticallyinverted),withdifferentpermeabilityclasses,canberepresentedwiththedualporositymodel.Atasimplelevel,theavvaluescorrespondtothechokingoffoftheporethroats,whichbothreducespermeabilityandincreasesm.
Itisimportanttorealizethat,conceptually,someporesystemsmaynotsatisfytheparallelcircuitassumptionandthatadditionallyinsomereservoirstheporesystemisatripleporositysystem,notdual.Insuchasituation,thisparallelcircuitdualporositymodelisnotgoingtobesufficient.
WWW.GeoNeurale.Com January2012 2012RobertEBallay,LLC
Cementation Exponents in Middle Eastern Carbonate ReservoirsJ W Focke and D Munn, SPE Formation Evaluation, June 1987
m(EPT) & m(core), foot by foot, with the two m estimates compared in crossplot in later graphic
Immobile oil in black, movable oil shaded, both as a fraction of porosity, calculated with Schlumbergers Global package
MoldicIG / IX
Upper Interval
m from logs, foot-by-foot,
compared to core
Figure 22
mfromnonArchieTechniquesIftheporesystemcanbepartitioned,amathematicalmodelofthemexponentwillallowonetothenevaluatethehydrocarboncolumnwithvariablem.Analternativeapproachistoincludeanadditionaltoolinthesuite,whichwhencombinedwitharesistivitymeasurement,allowsonetodeducethelocalm,andtothenusethatmintheinterpretationofthedeepresistivity.
FockeandMunncombinedthedielectriclogwithanRxomeasurementinjustthisway,to
calculatemfootbyfootinthehydrocarboncolumn, comparethewellboremestimateswithlabm.
Althoughtheconceptisstraightforward,FockeandMunnwerecarefultopointoutkeyissuesthatmustbekeptinmind.
TheevaluationrequiresthatthedielectricbepairedwithroutineporosityandRxotools,whichhaveagreaterdepthofinvestigationandlessverticalresolution.Theyarethenreflectinga
largervolumeofreservoirthanisthedielectric.
Rxomayalsobereflectingamixofmudfiltrateandformationbrine.Ifso,aneffectivevalueRmfeshouldbeused.
Archiessaturationexponentisassumedtobe2.0andcarbonatescanassumenonwaterwetvalueswithn>2.0.
Intheirillustrativewell,twoporesystemsarerecognized,moldicandIG/IX:Figure22.
Asexpected,themoldicporosityexhibitsanincreasedm,andreaches~3.5inplaces,asseenwithbothlabdataandthedielectricbasedestimate.
WWW.GeoNeurale.Com January2012 2012RobertEBallay,LLC
Wireline m(EPT) vs Laboratory m(core) are in general agreement
m and from corem from logs vs from logsCementation Exponents in Middle Eastern Carbonate Reservoirs J W Focke & D Munn, SPE Form Evaluation, June 1987
Figure 23
Similar Trends
Labandwirelinecanalsobecomparedviacrossplot.Recognizingthedifferentvolumesofinvestigation,andattemptingtocompensate,FockeandMunncrossplotmversusporosityforcore,andforlog:Figure23.
Inthemoldicintervals,thetworesultsdisplayanalmostidenticaltrendofincreasingmas(moldic)porosityincreases.
RasmusandKenyonprovideyetanother
illustrationofthecontributionthatadielectriclogcanmakeinthepresenceofoomoldicporosity.
InthetimesinceFockeandRasmus,significantadvanceshavebeenmadeindielectricmeasurements,andtheynowoffermoresophisticatedoptions(ZappingRocks.RomuloCarmona,etal.OilfieldReview.Spring2011.).
SummaryIn1952Archiepointedoutthecomplicationsthatarisewithcarbonateporesystems,whichcanresultintortuouswaterfilledporesystemshavingaresistivitysimilartoaninterparticleporesystemthatishydrocarboncharged.Inonesensethen,andrecognizingthatothercomplicationscanbepresent,thecementationexponent(whichrepresentstheporesystemtortuosity)representstheessenceofcarbonatepetrophysics.
WyllieandGregoryboundedthemwithlaboratorybeadpackstudies,findingthatinapackofunconsolidatedbeadsm~1,whilem~4inachemicallycementedpack.FockeandMunninterpretedhundredsofcarbonateformationfactormeasurements,withinthecontextofthinsectiondescriptions,tofindasystematicrelationbetweenRockTypeandm.
Inthecaseofmoldicporosity,FockeandMunnfoundthatmsystematicallyincreasesastotalporosityincreases:theadditionalporosityissimplynoteffectiveintheelectricalconductionsense.
WWW.GeoNeurale.Com January2012 2012RobertEBallay,LLC
Petrophysical Characterization of Permian Shallow-Water Dolostone. M H Holtz, R. P. Major. SPE 75214, 2002http://www.beg.utexas.edu/mainweb/presentations/2002_presentations/holtz_spe0402ab.pdf
Pore geometries control the interrelationship of petrophysical properties. The three most important pore-geometry characteristics are
amount and types of pores or shapeinterconnectedness of pores (tortuosity)size of interconnecting pore throats
Various m exponents as a function of vuggy porosity ratioNote the Myers trend is relatively flat: the vugs in this data set exhibit touching behavior.
As the separate vug fraction increases, so too
does the Archie m
Figure 23
Ingeneral,thepresenceofvuggyporositycorrespondstoanincreaseinm,withthemagnitudeofthatincreasedifferingfromonedatasettothenext:Figure23.
Therearebothchartsandmathematicalmodelsthatallowonetoestimatemforvariousporositypartitions.Theadvantageofthemathematicalmodelisthattheyeasilyallowbothfootbyfoot
estimatesandMonteCarlosimulation.
Chartsandmodelsshouldalwaysbetested,atthefirstopportunity,bycomparingthemestimatetothatdeducedbyinvertingArchiesequationinthewaterlegofarepresentativewell.InthecaseoftheDualPorositymodelusedforillustrationsherein,thatcomparisonisreasonable.TheDualPorositymmodelisalsofoundtomatchtheindependentlabmeasurementsofMeyers,andtocapturethepatternsreportedbyFockeandMunn.
AwellborealternativetommodelsistoaddanonArchietooltothetoolsuite,whichallowsaneffectivemtobededuced.Thatmisthenusedtointerpretthedeepresistivitymeasurement.
Regardlessoftheapproachused,weshouldbearinmindthatparticularlyinthevicinityofthetransitionzone,thereservoirmayfailtosatisfythebasicArchiecriteria.
AcknowledgementMohamedWatfasArchiesLaw:ElectricalConductioninClean,WaterbearingRockisanimportantsinglepointhistoricaloverviewsource.FockeandMunnsCementationExponentsinMiddleEastCarbonateReservoirsliterallysetthestandardforasystematicinvestigationoftheissue,backin1987.TothesemustreadarticlesIhaveaddedmorerecentmaterial,andmypersonalthoughts/techniques.
ThisoneisformyMother,whoisalwaysthere,throughthickandthin.
ReferencesAguilera,R.AnalysisofNaturallyFracturedReservoirsfromSonicandResistivityLogs,SPE4398,JournalofPetroleumTechnology26(1974):12331238
Aguilera,R.AnalysisofNaturallyFracturedReservoirsfromConventionalWellLogs,SPE5342,JournalofPetroleumTechnology28(1976):764772
WWW.GeoNeurale.Com January2012 2012RobertEBallay,LLC
AlGhamdi,AliandBoChen,HamidBehmanesh,FarhadQanbari&RobertoAguilera.AnImprovedTriplePorosityModelforEvaluationofNaturallyFracturedReservoirs.TrinidadandTobagoEnergyResourcesConference.June2010.
Archie,G.E.TheElectricalResistivityLogasanAidinDeterminingSomeReservoirCharacteristics.PetroleumTransactionsoftheAIME146(1942):5462.
Archie,G.E.ElectricalResistivityasanAidinCoreAnalysisInterpretation,AAPGBulletin31(1947):350366
Archie,G.E.ClassificationofCarbonateReservoirRocksandPetrophysicalConsiderations.AAPG,Vol36,No2,1952.
Ballay,GeneandRoyCox.FormationEvaluation:CarbonatevsSandstones.2005.www.GeoNeurale.Com.
Ballay,Gene.RiskyBusiness.March2009.www.GeoNeurale.com
Ballay,Gene.RollingtheDice.July2009.www.GeoNeurale.com
Ballay,Gene.CoffeeOrTea.October2009.www.GeoNeurale.com.
Ballay,Gene.SplitPersonality.December2009.www.GeoNeurale.com.
Ballay,Gene.StatisticsArePliable.February2010.www.GeoNeurale.com.
Ballay,Gene.TheBiggestBangfortheBuck.April2011.www.GeoNeurale.com
Carmona,Romuloetal.ZappingRocks.OilfieldReview.Spring2011
Chen,CandJ.H.Fang.SensitivityAnalysisoftheParametersinArchiesWaterSaturationEquation.TheLogAnalyst.SeptOct1986
Diederix,K.M.AnomalousRelationshipsBetweenResistivityIndexandWaterSaturationsintheRotliegendSandstone(TheNetherlands),TransactionsoftheSPWLA23rdAnnualLoggingSymposium,CorpusChristi,Texas,July69,1982,PaperX
Eberli,GregorP.andGregorTBaechle,FlavioSAnselmetti&MichalLIncze.Factorscontrollingelasticpropertiesincarbonatesedimentsandrocks.THELEADINGEDGEJULY2003
Focke,J.W.andDMunn.CementationExponentsinMECarbonateReservoirs.SPEFormationEvaluation,June1987
Gomaa,N.andA.AlAlyak,D.Ouzzane,O.Saif,M.Okuyiga,D.Allen,D.Rose,R.Ramamoorthy&E.Bize.CasestudyofPermeability,VugQuantificationandRockTypinginaComplexCarbonate.2006SPEAnnualTechnicalConferenceandExhibition.SanAntonio,Texas,U.S.A.,2427September2006.
R.Griffiths,A.Carnegie,A.Gyllensten,M.T.Ribeiro,A.Prasodjo,andY.Sallam.EstimatingSwwithavolumemeasurement.WorldOil,October2006
Guyod,H.FundamentalDatafortheInterpretationofElectricLogs,TheOilWeekly115,No38(October30,1944):2127
WWW.GeoNeurale.Com January2012 2012RobertEBallay,LLC
Hartmann,DanandEdwardBeaumont.PredictingReservoirSystemQualityandPerformance.www.searchanddiscovery.net/documents/beaumont/index.htm
Herrick,D.C.andW.D.Kennedy.SPWLA34thAnnualLoggingSymposium,1993.ELECTRICALEFFICIENCY:APOREGEOMETRICMODELFORTHEELECTRICALPROPERTIESOFROCKS.
Lny,Arve.MakingSenseofCarbonatePoreSystems.AAPGBulletin,v.90,no.9(September2006),pp.13811405
Lucia,Jerry.TheOilfieldReview.Winter2000
Lucia,Jerry.RockFabric/PetrophysicalClassificationofCarbonatePoreSpaceforReservoirCharacterization.AAPGBulletin79,no.9(September1995):12751300.
Lucia,Jerry.Petrophysicalparametersestimatedfromvisualdescriptionofcarbonaterocks:afieldclassificationofcarbonateporespace.JournalofPetroleumTechnology.March,v.35,p.626637.1983.
Lucia,Jerry.www.beg.utexas.edu
Mazzullo,S.J.OverviewofPorosityEvolutioninCarbonateReservoirs
www.searchanddiscovery.net/documents/2004/mazzullo/images/mazzullo.pdf
Myers,M.T.,1991,Porecombinationmodeling:atechniqueformodelingthepermeabilityandresistivitypropertiesofcomplexporesystems:SocietyofPetroleumEngineers,AnnualTechnicalConferenceandExhibition,SPEpaperno.22662.
Morgan,W.B.andS.J.Pirson.TheEffectofFractionalWettabilityontheArchieSaturationExponent
Ramamoorthy,RaghuandAustinBoyd,ThomasJ.Neville,NikitaSeleznev,HaitaoSun,CharlesFlaum&JuntaoMa.ANewWorkflowforPetrophysicalandTexturalEvaluationofCarbonateReservoirs.Petrophysics,Vol51,No1,February2010.
Rasmus,J.C.andWEKenyon.AnImprovedPetrophysicalEvaluationofOomoldicLansingKansasCityFormationsUtilizingConductivityandDielectricLogMeasurements,TransactionsoftheSPWLA26thAnnualLoggingSymposium,Dallas,June1720,1985,PaperV
Sundberg,K.EffectofImpregnatingWatersonElectricalConductivityofSoilsandRocks,PetroleumTransactionsoftheAIME97(1932):367391.
Sweeney,S.A.andHYJenningsJr:TheElectricalResistivityofPreferentiallyWaterWetandPreferentiallyOilWetCarbonateRock,ProducersMonthly24,No7(May1960):2932
Toumelin,E.andC.TorresVerdn.INFLUENCEOFOILSATURATIONANDWETTABILITYONROCKRESISTIVITYMEASUREMENTS:AUNIFORMPORESCALEAPPROACH.SPWLA46thAnnualLoggingSym.NewOrleans,LA.June,2005.
Verwer,KlaasandGregorP.Eberli&RalfJ.Weger.Effectofporestructureonelectricalresistivityincarbonates.AAPGBulletin,v.95,no.2.Feb2011
Wang,FredP.andF.JerryLucia.ComparisonofEmpiricalModelsforCalculatingtheVuggyPorosityandCementationExponentofCarbonatesfromLogResponses.
WWW.GeoNeurale.Com January2012 2012RobertEBallay,LLC
Chattanooga shale
Mississippian limestoneR. E. (Gene) Ballays 35 years in petrophysics include research and operations assignments in Houston (Shell Research), Texas; Anchorage (ARCO), Alaska; Dallas (Arco Research), Texas; Jakarta (Huffco), Indonesia; Bakersfield (ARCO), California; and Dhahran, Saudi Arabia. His carbonate experience ranges from individual Niagaran reefs in Michigan to the Lisburne in Alaska to Ghawar, Saudi Arabia (the largest oilfield in the world).
He holds a PhD in Theoretical Physics with double minors in Electrical Engineering & Mathematics, has taught physics in two universities, mentored Nationals in Indonesia and Saudi Arabia, published numerous technical articles and been designated co-inventor on both American and European patents. At retirement from the Saudi Arabian Oil Company he was the senior technical petrophysicist in the Reservoir Description Division and had represented petrophysics in three multi-discipline teams bringing on-line three (one clastic, two carbonate) multi-billion barrel increments. Subsequent to retirement from Saudi Aramco he established Robert E Ballay LLC, which provides physics - petrophysics training & consulting.He served in the U.S. Army as a Microwave Repairman and in the U.S. Navy as an Electronics Technician; he is a USPA Parachutist, a PADI Nitrox certified Dive Master and a Life Member of Disabled American Veterans.
Watfa,M.etal.ArchiesLaw:ElectricalConductioninClean,WaterbearingRock.TechnicalReview,Volume36Number3
Watfa,M.SeekingtheSaturationSolution.MiddleEastWellEvaluationReviewNo.3(1987)
Wyllie,M.R.andARGregory:FormationFactorsofUnconsolidatedPorousMedia:InfluenceofParticleShapeandEffectofCementation,PetroleumTransoftheAIME(1953):103110.
Biography