reseng flame ch6
DESCRIPTION
goodTRANSCRIPT
CONTENTS
1 COMPOSITIONBLACKOILMODELS
2 GASSOLUBILITY,Rs
3 OILFORMATIONVOLUMEFACTOR,Bo
4 TOTALFORMATIONVOLUMEFACTOR,BT
5 BELOWTHEBUBBLEPOINT
6 OILCOMPRESSIBILITY
7 BLACKOILCORRELATIONS
8 FLUIDDENSITY 8.1 SpecificGravityofaLiquid 8.2 DensityBasedonIdealSolutionPrinciples
9 FORMATIONVOLUMEFACTOROFGAS CONDENSATE,Bgc
10 VISCOSITYOFOIL
11 INTERFACIALTENSION
12 COMPARISONOFRESERVOIRFLUID MODELS
Properties of Reservoir Liquids
�
LEARNING OBJECTIVES
Having worked through this chapter the Student will be able to:
• Definegassolubility,Rsandplotvs.Pforareservoirfluid.
• Defineundersaturatedandsaturatedoil.
• Explainbrieflyflashanddifferentialliberation
• Define theoil formationvolumefactorBo, andplotBovs.P fora reservoirfluid.
• DefinetheTotalFormationVolumefactorBt,andplotBtvs.PalongsideaBovs.Pplot.
• PresentanequationtoexpressBtintermsofBo,RsandBg.
• Expressoilcompressibilityintermsofoilformationvolumefactor.
• Use black oil correlations and their graphical form to calculate fluidproperties.
• Calculatethedensityofareservoirfluidmixture,usingidealsolutionprinciples,atreservoirpressureandtemperature,usingdensitycorrectionchartforC1&C2andotherprerequisitedata.
• Definetheformationvolumefactorofagascondensate
• Calculatethereservesandproductionofgasandcondensateoperatingabovethedewpoint,givenprerequisitedata.
• Useviscosityequationsandcorrelationstocalculateviscosityoffluidatreservoirconditions.
• Calculatetheinterfacialtensionofequilibriumgas-oilsystemsgivenprerequisiteequationsanddata.
• Listthecomparisonsoftheblackoilandcompositionalmodelinpredictingliquidproperties
Institute of Petroleum Engineering, Heriot-Watt University �
1 COMPOSITION - BLACK OIL MODEL
As introduced in the chapter onComposition, petroleumengineers are requiringacompositionaldescriptiontooltouseasabasisforpredictingreservoirandwellfluidbehaviour.Thetwoapproachesthatarecommonlyusedarethemulticomponentcompositional modeldescribedintheearlierchapterandthetwocomponentblack oil model.Thelattersimplisticapproachhasbeenusedformanyyearstodescribethecompositionandbehaviourofreservoirfluids.Itiscalledthe“Black Oil Model”.
Theblackoilmodelconsidersthefluidbeingmadeupoftwocomponents-gasdissolvedinoilandstocktankoil.Thecompositionalchangesinthegaswhenchangingpressureandtemperatureareignored.Tothoseappreciatingthermodynamicsthissimplistictwocomponentmodelisdifficulttocopewith.TheBlackOilModel,illustratedinFigure1,isatthecoreofmanypetroleumengineeringcalculations,andassociatedproceduresandreports.
AssociatedwiththeblackoilmodelareBlackOilmodeldefinitionsinrelationtoGas Solubility and Formation Volume Factors.
Reservoir Fluid
Solution Gas
Stock Tank Oil
/ = Rs
/ = Bo
Bo = Oil Formation Volume Factor
Rs = Solution Gas to Oil Ratio
Figure 1 "BlackOilModel"
Properties of Reservoir Liquids
�
2 GAS SOLUBILITY
Althoughthegasassociatedwithoilandtheoilitselfaremulticomponentmixturesitisconvenienttorefertothesolubilityofgasincrudeoilasifweweredealingwithatwo-componentsystem.
Theamountofgas formingmolecules in the liquidphase is limitedonlyby thereservoirconditionsoftemperatureandpressureandthequantityoflightcomponentspresent.
Thesolubility is referred tosomebasisand it iscustomary touse thestock tankbarrel.
Solubility = f(pressure,temperature,compositionofgas compositionofcrudeoil)
Forafixedgasandcrude,atconstantT,thequantityofsolutiongasincreaseswithp,andatconstantp,thequantityofsolutiongasdecreaseswithTRatherthandeterminetheamountofgaswhichwilldissolveinacertainamountofoilitiscustomarytomeasuretheamountofgaswhichwillcomeoutofsolutionasthepressuredecreases.Figure2illustratesthebehaviourofanoiloperatingoutsidethePTphasediagraminitssinglephasestatewhenthereservoirpressureisaboveitsreservoirbubblepointat1.Fluidbehaviourinthereservoirissinglephaseandtheoilissaidtobeundersaturated.Inthiscaseaslightreductionofpressurecausesthefluidtoremainsinglephase.Iftheoilwasontheboundarybubblepointpressurelineat2thenafurtherreductioninpressurewouldcausetwophasestobeproduced,gasandliquid.Thissaturatedfluidisonethatuponaslightreductionofpressuresomegasisreleased.Theconceptofgasbeingproducedorcomingoutofsolutiongivesrisetothisgassolubilityperspective.Clearlywhenthefluidsareproducedtothesurfaceasshownbytheundersaturatedoilinfigure2thesurfaceconditionsliewithinthetwophaseareaandgasandoilareproduced.Thegasproducedistermedsolution gasandtheoilatsurfaceconditionsstock tank oil.Thesearethetwocom-ponentsmakingupthereservoirfluid,clearlyaverysimplisticconcept.
The gas solubility Rs is defined as the number of cubic feet (cubic metre) of gas measured at standard conditions, which will dissolve in one barrel (cubic metre) of stock tank oil when subjected to reservoir pressure and temperature.
Inmetricunitsthevolumesareexpressedascubicmetreofgasatstandardconditionswhichwilldissolveinonecubicmetreofstocktankoil.
Institute of Petroleum Engineering, Heriot-Watt University �
Solution Gas
Stock Oil Tank
Oil Reservoir
Oil and Dissolved Gas
Rsi scf/stb
1 st b. oil
Bo rb.oil
Pre
ssur
e
Temperature
Pi 1
2
P
+
Surface
Phase Diagram
Figure 2 Productionofreservoirhydrocarbonsabovebubblepoint
Figure3givesatypicalshapeofgassolubilityasafunctionofpressureforareser-voirfluidatreservoirtemperature.Whenthereservoirpressureisabovethebubblepointpressurethentheoilisundersaturated,i.e.capableofcontainingmoregas.Asthereservoirpressuredropsgasdoesnotcomeoutofsolutionuntilthebubblepointisreached,overthispressurerangethereforethe gas in solution is constant.Atthebubblepointpressure,correspondingtothereservoirtemperature,twophasesareproduced,gasandoil.Thegasremaininginsolutionthereforedecreases.
Thenatureoftheliberationofthegasisnotstraightforward.Withinthereservoirwhengasisreleasedthenitstransportandthatoftheliquidisinfluencedbytherelativepermeabilityoftherock(discussedinChapter10).Thegasdoesnotremainwithitsassociatedoili.e.thesystemchanges.Intheproductiontubingandintheseparatoritisconsideredthatthegasandassociatedliquidremaintogetheri.e.thesystemisconstant.Theamountofgasliberatedfromasampleofreservoiroildependsontheconditionsoftheliberation.Therearetwobasicliberationmechanisms:
Properties of Reservoir Liquids
�
1000 2000 3000
200
600
400
Pressure (psig)
Pb
Rsi
Rs
scf
/stb
Figure 3 SolutionGas-OilRatioasaFunctionofPressure.
Flashliberation - thegasisevolvedduringadefinitereductionin pressureandthegasiskeptincontactwiththeliquid untilequilibriumhasbeenestablished.
Differentialliberation - thegasbeingevolvedisbeingcontinuously removedfromcontactwiththeliquidandtheliquidisin equilibriumwiththegasbeingevolvedoverafinite pressurerange.
ThetwomethodsofliberationgivedifferentresultsforRs.ThistopiciscoveredinmoredetailinthePVTanalysischapter.
Productionofacrudeoilatreservoirpressuresbelowthebubblepointpressureoccursbyaprocesswhichisneitherflashordifferentialvaporisation.Onceenoughgasispresentforthegastomovetowardthewellborethegastendstomovefasterthantheoil.Thegasformedinaparticularporetendstoleavetheliquidfromwhichitwasformedthusapproximatingdifferentialvaporisation,however,thegasisincontactwithliquidthroughoutthepaththroughthereservoir.Thegaswillalsomigrateverticallyasaresultofitslowerdensitythantheoilandcouldformasecondarygascap.
Fluidproducedfromreservoirtothesurfaceisconsideredtoundergoaflashprocesswherethesystemremainsconstant.
3 OIL FORMATION VOLUME FACTOR, B o
Thevolumeoccupiedbytheoilbetweensurfaceconditionsandreservoirorotheroperatingchangesisthatofthetotalsystem;the‘stocktankoil’plusitsassociatedordissolved‘solutiongas’.Theeffectofpressureonthecomplexstocktankliquidandthesolutiongasistoinducesolutionofthegasintheliquiduntilequilibriumisreached.Aunitvolumeofstocktankoilbroughttoequilibriumwithitsassociated
Institute of Petroleum Engineering, Heriot-Watt University �
gasatreservoirpressureandtemperaturewilloccupyavolumegreaterthanunity(unlesstheoilhasverylittledissolvedgasatveryhighpressure).
Therelationshipbetweenthevolumeof theoiland itsdissolvedgasat reservoirconditiontothevolumeatstocktankconditionsiscalledthe Oil Formation Volume Factor Bo.TheshapeoftheBovs.pressurecurveisshowninFigure4.Itshowsthatabovethebubblepointpressurethereductioninpressurefromtheinitialpres-surecausesthefluidtoexpandasaresultofitscompressibility.ThisrelatestothechapteronPhaseBehaviourwhereforanoilthePVdiagramshowsalargedeclineinpressureforasmallincreaseinvolume,beingagainanindicationofthecom-pressibilityoftheliquid.Belowthebubblepointpressurethisexpansionduetocompressibilityoftheliquidissmallcomparedtothe‘shrinkage’oftheoilasgasisreleasedfromsolution.
The oil formation volume factor, is the volume in barrels (cubic metres) occupied in the reservoir, at the prevailing pressure and temperature, by one stock tank barrel (one stock tank cubic metre) of oil plus its dissolved gas.
1000 2000 30001.0
1.2
1.1
Pressure (psig)
Pb
Bo
rb./s
tb
Units - rb (oil and dissolved gas)
Figure 4 Oilformationvolumefactor
Theseblackoilparameters,BoandRsareillustratedinFigure5a,b,&cfromCraftandHawkins1reservoirengineeringtext.,wheretheypresenttheRsandBocurvefortheBigSandyfieldintheUSA.Thevisualconceptofthechangesduringpressureandtemperaturedecreaseisalsopresented.
Properties of Reservoir Liquids
�
P01
P01 = 3500 PSIAT01 = 160º F
A
PB = 2500 PSIAT01 = 160º F
B
P = 1200 PSIAT01 = 160º F
C
PA = 14.7 PSIAT01 = 160º F
D
PA = 14.7 PSIAT01 = 60º F
E
PB
P
PA PA
Free Gas 676 Cu. Ft.Free Gas
2.990 Cu. Ft.
Free Gas 567 Cu. Ft.
1,000 BBL1,040 BBL1,210 BBL1,333 BBL1,310 BBL
567SCF/STB
AT 1200 PSIARS = 337
BU
BB
LE P
OIN
T P
RE
SS
UR
E
INIT
IAL
PR
ES
SU
RE
Sol
utio
n G
as, S
CF
/ST
B
600
500
400
300
200
100
00 500 1000 1500 2000
Pressure, PSIA
2500 3000 3500
(a)
(b)
Figure 5 GastooilratioandoilformationvolumefactorforBigSandyFieldreservoiroil1.
For
mat
ion
Vol
ume
Fac
tor,
BB
L/S
TB
0 500
1.40
1.30
1.20
1.10
1.001000 1500 2000
Pressure, PSIA2500 3000 3500
BU
BB
LE P
OIN
T P
RE
SS
UR
E
INIT
IAL
PR
ES
SU
RE1200 PSIA
BO = 1.210
14.7 PSIA & 160º FBO = 1.040
2500 PSIABOB = 1.333
3500 PSIABOI = 1.310
14.7 PSIA & 60º FBO = 1.000
(b)
Figure 5b
Institute of Petroleum Engineering, Heriot-Watt University �
Thereciprocaloftheoilformationvolumefactoriscalledthe‘shrinkagefactorbo
b
Boo
= 1
TheformationfactorBomaybemultipliedbythevolumeofstocktankoiltofindthe volumeof reservoir required to produce that volumeof stock tankoil. Theshrinkagefactorcanbemultipliedbythevolumeofreservoiroiltofindthestocktankvolume.
Itisimportanttonotethatthemethodofprocessingthefluidswillhaveaneffectontheamountofgasreleasedandthereforeboththevaluesofthesolutiongas-oilratioandtheformationvolumefactor.AreservoirfluiddoesnothavesingleBoorRsvalues.Bo&Rsaredependantonthesurfaceprocessingconditions.Thissimplisticreservoirmodel(Figure6)demonstratesthattheblackoilmodeldescriptionofthereservoirfluidsisanaftertheevent,processing,descriptionintermsoftheproducedfluids.Thissimplisticapproachtomodellingreservoirfluidsbecomesmoredifficulttoconsiderwhenoneisinvolvedinreservoirswhichbecomepartofatotalreservoirsystem(Figure7).
Rs
BO
Figure 6 Blackoildescriptionofreservoirfluid
Properties of Reservoir Liquids
10
Rs 3
Bo 3
Rs 2
Bo 2
Rs 4
Bo 4
Rs 1
Rs
Bo
Bo 1
?
Multi Reservoir System
Figure 7 Integratedsystemofreservoircommonpipelineandfinalcollectionsystem.
4 TOTAL FORMATION VOLUME FACTOR, Bt
Inreservoirengineeringitissometimesconvenienttoknowthevolumeoccupiedinthereservoirbyonestocktankbarrelofoilplusthefreegasthatwasoriginallydissolved in it. A factor is used called the total formation-volume factor Bt, orthetwo-phasevolume-factorandisdefined as the volume in barrels that 1.0 STB and its initial complement of dissolved gas occupies at reservoir temperature and pressure,i.e.itincludesthevolumeofthegaswhichhasevolvedfromtheliquidandisrepresentedby:
Bg(Rsb-Rs)
i.e. Bt=Bo+Bg(Rsb-Rs) (1)
Rsb=thesolutiongastooilratioatthebubblepoint
Institute of Petroleum Engineering, Heriot-Watt University 11
Oil
Oil
Gas
Hg
B0
Bt
B0bBg(Rsb-Rs)
Figure 8a Totalformationvolumefactorortwophasevolumefactor
ItsapplicationcomesfromtheMaterialBalanceequation(Chapter15)whereitissometimesusedtoexpressthevolumeofoilandassociatedgasasafunctionofpres-sure.ItisimportanttonotethatBtdoesnothavevolumesignificanceinreservoirtermssincetheassumptioninBtisthatthesystemremainsconstant.Asmentionedearlier if thepressuredropsbelow thebubblepoint in the reservoir then thegascomingoutofsolutionmovesawayfromitsassociatedoilbecauseofitsfavourablerelativepermeabilitycharacteristics.
Figure8bgivesacomparisonofthetotalformation-volumefactorwiththeoilfor-mation-volumefactor.ClearlyabovePbthetwovaluesareidenticalsincenofreegasisreleased.BelowPbthedifferencebetweenthevaluesrepresentsthevolumeoccupiedbyfreegas.
BoBt
Pressure Pb
Figure 8b Totalandoilformationvolumefactor
ThevalueofBTcanbeestimatedbycombiningestimatesofBOandcalculationofBgandknownsolubilityvaluesforthepressuresconcerned.
Properties of Reservoir Liquids
1�
5 BELOW THE BUBBLE POINT
Figure9depicts thebehaviourbelowthebubblepointwhenproducedgasat thesurfacecomesfromtwosources,thesolutiongasassociatedwiththeoilenteringthewellboreplusfreegaswhichhascomeoutofsolutioninthereservoirandmigratedtothewellbore.ThetotalproducinggastooilratioismadeupofthetwocomponentssolutiongasRsandthefreegaswhichisthedifference.Thediagramillustratesthevolumesoccupiedbythesetwointhereservoir,thesolutiongasbeingpartofBoandthefreegasvolumethroughBg.
Free Gas& Solution Gas
Stock Oil Tank
Oil Reservoir
rb (oil and dissolved gas) /stb
1 st b. oil
Bo
Pre
ssur
e
Temperature
R= Rs + (R - Rs)
+
(R - Rs) Bg
Gas Oil
Reservoir
rb (free gas) /stb
SurfacePi
P
Figure 9 Productionofreservoirhydrocarbonsbelowbubblepoint
6 OIL COMPRESSIBILITY
Thevolumechangesofoilabovethebubblepointareverysignificantinthecontextofrecoveryofundersaturatedoil.Theoilformationvolumefactorvariationsabovethebubblepointreflectthesechangesbuttheyaremorefundamentallyembodiedinthecoefficientofcompressibilityoftheoil,oroilcompressibility.
Theequationforoilcompressibilityis
c
VVPo
T
= − ∂∂
1
intermsofformationvolumefactorsthisequationyields
Institute of Petroleum Engineering, Heriot-Watt University 1�
c
BBPo
o
o
T
= − ∂∂
1
Assumingthatthecompressibilitydoesnotchangewithpressuretheaboveequationcanbeintegratedtoyield;
c P P
VVo 2 1
2
1
−( ) = − ln
whereP1&P2,andV1&V2representthepressureandvolumeatconditions1&2.
7 BLACK OIL CORRELATIONS
Overtheyearstherehavebeenmanycorrelationsgeneratedbasedonthetwocom-ponentbasedblackoilmodelcharacterisationofoil. Thecorrelationsarebasedondatameasuredontheoilsofinterest.Theseempiricalcorrelationsrelateblackoilparameters,thevariablesofBoandRsto;reservoirtemperature,andoilandgassurfacedensity.Itisimportanttoappreciatethatthesecorrelationsareempiricalandareobtainedbytakingagroupofdataforaparticularsetofoilsandfindingabestfitcorrelation.Usingthecorrelationforfluidswhosepropertiesdonotfallwithinthoseforthecorrelationcanresultinsignificanterrors.Danesh2hasgivenanexcellentreviewofmanyofthesecorrelations
Anumberofempiricalcorrelations,basedonlargelyUScrudeoils,andotherloca-tionsacrosstheworldhavebeenpresentedtoestimateblackoilparametersofgassolubilityandoilformationvolumefactor.ThemostcommonlyusedisStanding’s3correlation.Othercorrelationsinclude,Lasater4,andrecentlyGlaso6
Pb=f(Rs,γg,po,T)
where Pb=bubblepointpressureatToF
Rs=solutiongas-oilratio(cuft/bbl) γg=gravityofdissolvedgas ρo=densityofstock-tankoil.(specificgravity)Standing’scorrelationforthecalculationofPb,bubblepointpressureis:
PR
T APIbs
g
=
− −
. ( . . ( )) .
.
18 2 0 00091 0 0125 1 4
0 83
10γ
(2)Hiscorrelationfortheoilformationvolumefactoris;
B R To s
g
o
= +
+
. . .. .
0 9759 0 000120 1 250 5 1 2
γρ
(3)
Properties of Reservoir Liquids
1�
Standing's correlations have been presented as nomographs enabling quick lookpredictionstobemade.Figures10&11givethenomogramformsofthesecorrelationsforgassolubilityandoilformationvolumefactor.Standing’scorrelationisbasedonasetof22Californiacrudes.
OthercorrelationshavebeenpresentedbyLasater4basedon137Canadian,USAandSouthAmericancrudes,VasquezandBeggs5using6000datapoints,Glaso6us-ing45NorthSeacrudesamples,andMahoun7whoused69MiddleEasterncrudes.Danesh2givesaveryusefultableshowingtherangescoveredbytherespectiveblackoilcorrelations
Institute of Petroleum Engineering, Heriot-Watt University 1�
20
30
40
50
6070
8090100
150
200
300
400
500
600700
8009001000
1500
2000
1.021.03
1.041.05
1.061.07
1.081.09
1.10
Formation volume of bubble-point liquid
Gas-o
il ra
tio, c
u ft p
er b
bl
bbl p
er b
bl o
f tan
k oi
l1.20
1.30
1.40
1.50
1.60
1.70
1.80
1.90
1.10
1.20
1.30
1.40
1.50
0.50 0.
60 0.70 0.
80 0.90 1.
00
Gas
gra
vity
Air
=1
Tank oil gravity, ºAPI50 30 10
Temperature, ºF
100
140160
180200
220240
260
120
Figure 10 Oil-formationvolumefactorasafunctionofgassolubility,temperature,gasgravityandoilgravity(Standing)
Properties of Reservoir Liquids
1�
600
500
400
300
200
20
30
40
50
6070
8090
100
150
200
300
400
500 60
0 700
700 80
0 900 10
00
1500
2000
3000
4000
5000
6000
800 90
0 1000
1500
2000
Tank
oil g
ravit
y, ºA
PI
Tempe
ratur
e, ºF
Gas g
ravit
y Air
= 1
60
1.50
1.40
1.30
1.20
8010
0
120
140
160
180
200
220
240 26
0
1.10
1.00
0.90
0.80 10 14
1618
2022
2426
2830
3234
3638
4012
4244
4648
5052
5456
58
Bubble-point Press
ure,
psia
Gas-o
il rat
io, cu
ft p
er b
bl
60
(STANDING)
0.70
0.60
0.50
Figure 11 Gassolubilityasafunctionofpressure.Temperature,gasgravityandoilgravity
Institute of Petroleum Engineering, Heriot-Watt University 1�
Correlation Standing Lasater Vasquez-Beggs Glaso MarhounRef 3 4 5 6 7Bubble - point pressure (psia) 130-7000 45-5780 15-6055 165-7142 130-3573Temperature, °F 100-258 82-272 162-180 80-280 74-240Bo 1.024-2.15 1.028-2.226 1.025-2.588 1.032-1.997Gas - oil ratio (scf/stb) 20-1425 3-2905 0-2199 90-2637 26-1602Oil Gravity, oAPI 16.5-63.8 17.9-51.1 15.3-59.5 22.3-48.1 19.4-44.6Gas Gravity 0.59-0.95 0.574-1.22 0.511-1.651 0.65-1.276 0.752-1.367Separator Pressure 265-465 15-605 60-565 415Searator Temperature °F 100 36-106 76-150 125
Table 1 Blackoilcorrelationandtheirrangesatapplication2
8 FLUID DENSITY
Liquidshaveamuchgreaterdensityandviscositythangases,andthedensityisaffectedmuchlessbychangesintemperatureandpressure.Forpetroleumengineersitisimportantthattheyareabletoestimatethedensityofareservoirliquidatreservoirconditions.
8.1 Specific Gravity of a Liquid
γ ρ
ρoo
w
= (4)
ThespecificgravityofaliquidistheratioofitsdensitytothatofwaterbothatthesameT&P.Itissometimesgivenas60˚/60˚,i.e.bothliquidandwateraremeasuredat60˚and1atmos.
Thepetroleumindustryusesanothertermcalled˚API gravity where
° = −API
o
141 5131 5
..
γ (5)
whereγoisspecificgravityat60˚/60˚.
Thereareseveralmethodsofestimatingthedensityofapetroleumliquidatreservoirconditions.Themethodsuseddependontheavailabilityandnatureofthedataofdata.Whenthereiscompositionalinformationonthereservoirfluidthenthedensitycanbedeterminedusingtheideal solution principle. Whentheinformationwehaveisthatoftheproducedoilandgasthenempiricalmethodscanbeusedtocalculatethedensityofthereservoirfluid.
8.2 Density based on Ideal Solution PrinciplesMixturesofliquidhydrocarbonsatatmosphericconditionsbehaveasidealsolutions.Anidealsolutionisahypotheticalliquidwherenochangeinthecharacteroftheliquidsiscausedbymixingandthepropertiesofthemixturearestrictlyadditive.
Properties of Reservoir Liquids
1�
Petroleumliquidmixturesaresuchthatideal-solutionprinciplescanbeappliedforthecalculationofdensitiesandthisenablesthevolumeofamixturefromthecomposi-tionandthedensityoftheindividualcomponents.Theprincipleisillustratedusingthefollowingexercise.Dataforthespecificcomponentsaregiveninthetablesattheendofthechapter
ExErcIsE 1.
calculate the density at 1�.�psia and �0 ºF of the hydrocarbon liquid mixture with the composition given below:
Component Mol. fract. 1b mol. nC4 0.25 nC5 0.32 nC6 0.43 1.00
solUtIon ExErcIsE 1
Solution Component Mol. Mol. Weight Liquid Liquid density
fract. weight 1b Density at volume 1b mol. 1b/1b at 60˚F and 14.7 cu ft mol. psia 1b/cu ft
nC4 0.25 58.1 14.525 36.45 0.3985 nC5 0.32 72.2 23.104 39.36 0.5870 nC6 0.43 86.2 37.066 41.43 0.8947 ____ _____ _____ 1 74.695 1.8801
Liquidsattheirbubblepointorsaturationpressurecontainlargequantitiesofdis-solvedgaswhichatsurfaceconditionsaregasesandthereforesomeconsiderationforthesemustbegivenintheadditivevolumetechnique.Thisphysicallimitationdoesnotimpairthemathematicaluseofa“pseudoliquiddensity“formethaneandethanesince it isonlyastep in itsapplicationtodetermineareservoirconditiondensity.Thisisachievedbyobtainingapparentliquiddensitiesforthesegasesanddeterminingapseudoliquiddensityforthemixtureatstandardconditionswhichcanthenbeadjustedtoreservoirconditions.
Standing&Katz8 carriedoutexperimentsonmixturescontainingmethaneplusothercompoundsandethaneplusothercompoundsandfromthiswereabletodetermineapseudo-liquid(fictitious)densityformethaneandethane
Institute of Petroleum Engineering, Heriot-Watt University 1�
Correlationshavebeenobtainedbyexperimentgivingapparentliquiddensitiesofmethaneandethaneversusthepseudoliquiddensity(Figure12).
0.1
0.2
0.3
0.4
0.5 0.6 0.7 0.8 0.9
0.3
0.4
0.5
0.6
0.40.3
Density of system, 60ºF B atm. pressure
Ap
par
ren
t d
ensi
ty o
f M
eth
ane,
g/c
cA
pp
arre
nt
den
sity
of
of
Eth
ane,
g/c
c
Ethane - N - ButaneEthane - HeptaneEthane - Crystal oilMethane - Cyclo Hexane
Methane - Crude oilMethane - Crystal oilMethane - Propane
Methane - HexaneMethane - Pentane
Methane - Heptane
Methane - Benzene
Figure 12 Variationofapparentdensityofmethaneandethanewithdensityofthesystem8.
Tousethecorrelationsatrialanderrortechniqueisrequiredwherebythedensityofthesystemisassumedandtheapparentliquiddensitiescanbedetermined.Theseliquiddensitiesarethenusedtocomputethedensityofthemixturebyadditivevol-umesandthevaluecheckedagainsttheinitialassumption.Theprocedurecontinuesuntilthetwovaluesarethesame.
Whennonhydrocarbonsarepresent,theprocedureistoaddthemolefractionsofthenitrogentomethane,themolefractionofcarbondioxidetoethaneandthemolefractionofhydrogensulphidetopropane.
Properties of Reservoir Liquids
�0
ExErcIsE �: Calculate the “surface pseudo liquid density” of the following reservoircomposition.
Component Mole percent Methane 44.04 Ethane 4.32 Properties ofPropane 4.05 heptane + Butane 2.84 API gravities = 34.2Pentane 1.74 SG = 0.854Hexane 2.9 Mol wt = 164Heptane + 40.11
solUtIon ExErcIsE �
Estimate ρο 44.65 lb/cu ft. 0.716 gm/cc lb/cuft From fig 12 Density 0.326 20.3424 C1 Density 0.47 29.328 C2 Component Mole Mol Weight Liq Liquid fraction Weight Density Volume lb/lb lb at 60°F & mole 14.7 psia lb/cu.ft cu ft. z M zM ρo zM/ρo Methane 0.4404 16 7.0464 20.3424 0.34639 Ethane 0.0432 30.1 1.30032 29.328 0.04434 Propane 0.0405 44.1 1.78605 31.66 0.05641 Butane 0.0284 58.1 1.65004 35.78 0.04612 Pentane(n&i) 0.0174 72.2 1.25628 38.51 0.03262 Hexane(n&i) 0.029 86.2 2.4998 41.43 0.06034 Heptane+ 0.4011 164 65.7804 53.26 1.23508 Total 1 81.31929 1.8213 Density = 81.32 lb / 1.82 cu ft = 44.65 lb/cu.ft
This trialanderrormethod isvery tedioussoStandingandKatzdevisedachartwhichremovesthetrailanderrorrequiredinthecalculation.Thedensitieshavebeenconvertedintothedensityoftheheaviercomponents,C3+,andtheweightpercentofthetwolightcomponents,methaneandethaneintheC1+andC2+mixtures.Figure13.
Institute of Petroleum Engineering, Heriot-Watt University �1
70
60
50
40
30
10
20
30
40
50
60
70
Den
sity
of s
yste
m in
clud
ing
met
hane
and
eth
ane,
lb/c
u ft
Den
sity
of p
ropa
ne p
lus,
lb/c
u ft
Wt %
eth
ane
in e
than
e pl
us m
ater
ial
01020304050
Wt %
met
hane
in e
ntire
syste
m
0
10
20
30
Figure 13 Pseudo-liquiddensityofsystemscontainingmethaneandethane10.
Weshallexaminethroughexamplesvariouswaysofcalculatingdownholereservoirfluidsdensitiesdependantonthedataavailable.Thethreeconsideredare:
1.Thecompositionofthereservoirfluidisknown.
2.Thegassolubility,thegascompositionandthesurfaceoilgravityisknown
3.Thegassolubility,andgasandliquidgravitiesareknown.
1. The composition of the reservoir fluid is known.Theprocedureisillustratedusingthefollowingtwoexercises.
Properties of Reservoir Liquids
��
ExErcIsE �.
calculate the surface density of the mixture in exercise � using the chart of figure 1�
Thepseudodensityisconvertedtoreservoirconditionsfirstlybytakingtheeffectofpressureandsecondlyaccountingfortheeffectoftemperature.Thevariationofdensitywithrespect topressureandtemperaturehasbeeninvestigatedandithasbeendemonstratedthatthermalexpansionisnotaffectedbypressure.Standing&KatztookNationalPetroleumStandardsdataandwithsupplementarydataproducedcorrectionfactorsforpressureandtemperature toconvertatmosphericdensity toreservoirdensity.
ThecompressibilityandthermalexpansioneffectshavebeenexpressedgraphicallyinFigures14and15.
10
9
8
7
6
5
4
3
2
1
025 30 35 40 45 50 55 60 65
Density at 60ºF and 14.7 psia, lb/cu ft
Den
sity
of p
ress
ure
min
us d
ensi
ty a
t 60º
F β
14.
7 ps
ia lb
/cu
ft
Pressure, psia
15,000 10,000 8,000
5,000 6,000
4,000 3,000
2,000
1,000
Figure 14 Densitycorrectionforcompressibilityofliquids8.
Institute of Petroleum Engineering, Heriot-Watt University ��
10
9
8
7
6
5
4
3
2
1
025 30 35 40 5045 55 60 65
Density at 60ºF and pressure P, lb/cu ft
Den
sity
at 6
0ºF
min
us d
ensi
ty a
t tem
pera
ture
, lb/
cu ft
80
100
120
160
180
200
220
Temperature ºF
240
140
60
Figure 15 Densitycorrectionforthermalexpansionofliquids10.
ExErcIsE �.
calculate the density of the reservoir liquid of exercise � at a reservoir temperature of �,�00 psia and 1�0 oF
Fullcompositionaldatamaynotalwaysbeavailableandthecharacterisationoftheproducedfluidswillvaryfromfullcompositionalanalysistoadescriptionofthefluidsintermsofgasandoilgravity.Theprocedurejustdescribedisforthesitua-tionwherethecompositionofthereservoirfluidisknown.Theprocedureswhichfollowcoverthesituationwherealesscomprehensiveanalysisisavailable.Thesemethodsmakeuseofempiricalcorrelations.
Properties of Reservoir Liquids
��
2. Reservoir Density when the Gas Solubility , the gas composition and the surface oil gravity are known
Byconsideringsurfaceliquidasasinglecomponentandknowingthecompositionofthecollectedgasthetechniquespreviouslydiscussedcanbeusedtodeterminereservoirliquiddensity.Againwewillillustratetheprocedurewithanexample
ExErcIsE �.
A reservoir at a pressure of �,000 psia and a temperature of �00oF has a producing gas to oil ratio of �00 scf/stB. the oil produced has a gravity of �� oAPI. calculate the density of the reservoir liquid. the produced gas has the following composition
component Mole Fraction Methane 0.�1 Ethane 0.1� Propane 0.0� Butane 0.0� Pentane 0.0� Hextane 0.01
3. The Gas Solubility, and Gas and Liquid gravities are known.Katzhasproducedacorrelation(figure16)toenabledensitiestobedeterminedwhentheonlyinformationonthegasisitssolubilityanditsgravity.Thefiguregivesap-parentliquiddensitiesofgasesagainstgravityfordifferentAPIcrudes
0.615
20
25
30
35
40
45
0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4
Gas Gravity
App
aren
t Liq
uid
dens
ity o
f Dis
solv
ed G
as a
t60
F a
nd 1
4.7
psia
, lb/
cu. f
t.
20 API Crude
30
40
50 60
Figure 16 Apparentliquiddensitiesofnaturalgases
Institute of Petroleum Engineering, Heriot-Watt University ��
ExErcIsE �.
Use the correlation of Katz to calculate the reservoir fluid density of a field with a Gor of �00scf/stB with a gas gravity of 0.� and a ��oAPI oil for reservoir
conditions of �,000psia and a temperature of 1�0oF.Katz method
9 FORMATION VOLUME FACTOR OF GAS CONDENSATE
Thesituationforawetgasorgascondensateisdifferentforaconventionaloilwhenoneisconsideringthevolumechangestakingplaceuponreleasetosurfacecondi-tions.Forawetgasorcondensatesystemliquidatsurfaceisgasintheformation.Thecomparisonthereforewithrespecttoconditionsinthereservoirtothoseatthesurfaceisdistinctlydifferentfromanoilsystem,whereanoilinthereservoirproducesgasandliquidsatthesurface.Forawetgasorcondensate,agasinthereservoirproducesgasandliquidsatthesurface.
The formation-volume factor therefore for a condensate, Bgc is defined as the volume of gas in the reservoir required to produce 1.0 STB of condensate at the surface.Theunitsaregenerallybarrelsofgasatres.conditionsperbarrelofstocktankoil.ThereareanumberofmethodsofestimatingBgc.
Tocalculatethepropertiesofthereservoirfluidfromtheinformationontheproducedfluidsrequiresacombinationofthe quantitiesandcharacteristicsofthesefluids.Themethodsuseddependsonthelevelofdetailofthecharacteristicsoftheproducedfluids.Anumberofmethodsarepresentedusingexampleswhichvaryaccordingtothelevelofdetail.
ExErcIsE �.
A gas condensate produces gas and liquids with the compositions detailed below, with a producing Gor of �0,000 scF/stB. Determine the composition of the
reservoir gas.
Component Composition Gas LiquidMethane 0.84 Ethane 0.08 Propane 0.04 0.15Butane 0.03 0.36Pentane 0.01 0.28Hexane 0.12Heptane + 0.09 1.00 1.00
Properties of Reservoir Liquids
��
ExErcIsE �.
the gas condensate reservoir above is contained in reservoir sands with an average pay thickness of 100ft, with a porosity of 0.1� and a connate water
saturation of 0.1�. the aerial extent of the field is � sq. miles. the initial reservoir pressure is �,000 psia and the reservoir temperature is 1�0 oF. Determine the initial
reserves of the field in terms of condensate and gas.
ExErcIsE �.
calculate the gas condensate formation factor for the example in exercise �.
10 VISCOSITY OF OIL
Theviscosityofoilatreservoirtemperatureandpressureislessthantheviscosityofthedeadoilbecauseofthedissolvedgasesandthehighertemperature.Correla-tionsareavailablewhichenablethedissolvedgasandpressureeffectonthedeadoilviscositytobedetermined.Danesh2hasgivenagoodreviewofmanyoftheempiricalapproaches.ThefavouredcorrelationsarethoseofBeggsandRobinson11
,EgbogahandNg12,VazquezandBeggs13,andLabedi14.Figure17givesplots,
presentedbyMcCain17,ofthecorrelationofdeadoilviscosityfromEgbogahandNg12,andfigure18stheimpactofdissolvedgasfromtheBeggsandRobinson11
correlation.
ReservoirTemperature, ºF
100º
150º
200º
250º300º
1000800
600700
500400300
200
10080
6070
504030
20
10
10 20 30
Stock - Tank Oil Gravity, ºAPI 40 50
8
67
543
2
10.8
0.60.7
0.50.40.3
0.2
0.1
Vis
cosi
ty o
f Gas
-Fre
e O
il, µ
oD, c
p
Figure 17 Deadoilviscosities17.
Institute of Petroleum Engineering, Heriot-Watt University ��
0
100
200
500
1000
1500
2000
200
100806070
504030
20
10
0.4 2 3 4 5 6 78 10 20 30 200 300 40 60 801000.6 0.8 1
Viscosity of Gas-Free Oil, µoD, cp
8
67
543
2
10.80.60.7
0.50.40.3
0.2
0.1
Vis
cosi
ty o
f Gas
-Sat
urat
ed O
il, µ
oD, c
p
Solutio
n Gas
-Oil R
atio
Figure 18 Viscositiesofsaturatedblackoils11.
BeggsandRobinson11examined600oilsamplesoverawiderangeofpressureandtemperatureandcameupwiththefollowingcorrelation.
µod=10A-1 (6)
where,logA=3.0324-0.0202oAPI-1.163logT µodisthedeadoilviscosityincpandTisin
oF.
EgbogahandNg12,hadadifferentexpressionforA logA=1.8653-0.025086oAPI-0.56441logT
Examinationofthesecorrelationshasshownthattheyarenotveryreliablewitherrorsoftheorderof25%(DeGetto15)
BeggsandRobinson11gaveacorrelationtogivetheimpactofdissolvedgas.
µob=CµodB (7)
where C =10.715(Rs+100)-0.515
and B =5.44(Rs+150)-0.338
µobisthesaturatedoilviscosity
VazquezandBeggs13presentedanequationtotakeintoaccountpressureonviscosityabovethesaturationpressure.
Properties of Reservoir Liquids
��
µo=µob(P/Pb)D (8)
where D =2.6P1.187e-11.513-8.98x10-5P
Thisispresentedinfigure19fromMcCain17.
Pressure 6000 psia
50004000
3000
2000
1000500
100
60
40
20
10
6
4
2
1
0.6
0.4
0.2
0.1
0.1
0.2
2
3
45678910
20
30
405060708090
100
200
0.3
0.40.50.60.70.80.91.0
10,0009,0008,0007,000
6,000
5,000
4,000
3,000
2.000
1.000900800700600
500
400
300
200
Bub
ble
Poi
nt p
ress
ure,
Pb,
psi
a
Vis
cosi
ty o
f Oil
Abo
ve B
ubbl
e P
oint
, µo,
cp
Viscosity of Oil At Bubble Point, cp
Figure 19 Viscositiesofundersaturatedblackoils17.
Labedi(ref14)alsoproducedanempiricalcorrelationtodetermineviscosityatpres-suresabovethebubblepoint
µo=µob+(P/Pb-1)(10-2.488µob
0.9036Pb0.6151/100.0197oAPI) (9)
Danesh2inhistextcomparedthevariouscorrelationsfromapublishedexperimentalviscosityvalueinawellknownPVTreport,usingthefollowingexercise.
Institute of Petroleum Engineering, Heriot-Watt University ��
ExErcIsE. 10
calculate the viscosity of oil in the PVt report of chapter 1� at a pressure of �,000psig and ��0°F. the °API of the oil is �0.1 and the Gor, r
s is ��� scf/st
Beggs and robinson
µod
= 10A -1log A = �.0��� - 0.0�0�°API - 1.1�� log tx µ
od = dead oil viscosity cp.
(Beggs �.0��� 0.0�0� 1.1��)(Egbogah 1.���� 0.0��0�� 0.����1) Beggs EgbolgahAPI = �0.1t = ��0r
s = ���
P = �,000 psigP
b = �,��� psig
log A = -0.�0�1 -0.��A = 0.�1�0 0.��Viscositydead oil = 1.0� cp 1.�1 cpMeasured value = 1.�� cp
Viscosity at bubble pointBeggsµ
ob = cµ
obB
µob
= oil viscosity at bubble point pressurec = 10.�1� (r
s + 100) -0.�1�
B = �.�� (rs + 1�0) -0.���
c = 0.����B = 0.����µ
ob = 0.���� cp
Measured value = 0.��� cp
Viscosity at pressure of �01� psigVazquez - Beggsµ
o = µ
ob (P/P
b)D
D = �.�p 1.1�� e -11.�1� - �.��x 10-�p
e function = -11.����D = 0.���� cplabed, correlationµ
o= µ
ob + (P/P
b-1)(10 -�.���µ
ob0.�0�� P
b0.�1�1 /10 0.01��oAPI )
µo = 0.��0� cp
Measured value = 0.�� cp
Properties of Reservoir Liquids
�0
11 INTERFACIAL TENSION
Inrecentyearsinterfacialtensionhasbecometoberealisedasanimportantphysicalpropertyinthecontextoftherecoveryofreservoirheldhydrocarbons,inparticularfor gas condensates. Interfacial tension, arises from the imbalance ofmolecularforcesattheinterfacebetweentwophases.Formanyyearsithasbeenneglectedbutmorerecentlyithasbeenrealisedthatingasinjectionandcondensationprocessesthemagnitudeofthevariousforces;surface,gravitationalandviscousforcescanhaveasignificantimpactonthemobilityofthevariousphases.Amajoradvanceinknowledgehasbeenthatinthecontextofgascondensateswhereitwasconsideredthatinthetraditionofrelativepermeabilityknowledgeliquidformationbyretrogradecondensationwouldbeimmobile.Recentresearchhasshownthatsuchfluidsaremobilebecauseoftheassociatedlowinterfacialtension16.Danesh2inhistextcoversthetopicofinterfacialtensionextensively.MentionedbrieflybelowaresomeofthetechniqueswhicharecurrentlyusedinpredictingITforreservoirfluids.
Interfacialtensiondecreasesastemperatureandpressureincreasesasshownfortheeffectoftemperatureforpurecomponentsinfigure20fromMcCain’stext17adaptedfromKatz19data.
Mol wt.240
-200 -200 00
5
10
15
20
25
30
35
100 200 300 400 500 600
220200180160
140
n - Octane
n - Heptane
n - Hexane
n - Pentane
l - Butane
n - Butane
PropaneEthaneMethane
Temperature, ºF
Sur
face
Ten
sion
, dyn
es p
er c
m
Figure 20Interfacialtensionsofhydrocarbons.(AdaptedfromKatz,etal.,J.Pet.Tech.,Sept.1943.)
Institute of Petroleum Engineering, Heriot-Watt University �1
ThereareseveralmethodsforpredictingIFT,andtheyrequireexperimentallydeterminedparameters.WorkonpurecompoundshaveshownthatIFTcanberelatedtodensity,compressibilityandlatentheatofvaporisation.ThemulticomponentperspectiveofreservoirfluidpropertieshasmadeuseoftheIFT/densityrelationships.
TheParachormethodofMcLeod18hasgainedacceptancewheretheIFTbetweenvapourandliquidisrelatedtothedensitydifferenceoftherespectivephases.
σρ ρ
σ=−
PM
L g4
(10)
whereρLandρgarethedensityoftheliquidandgasphases,andMisthemolecularweight.σistheIFT.Pσiscalledtheparachor.
Katz19hasprovidedtheparachorsforpurecomponentsasshowninthetablebelowandtheyarealsopresentedinthefigure21preparedbyMaCainusingKatz’s19data.
Parachors, Ps, for IFT
Component ParachorMethane 77Ethane 108Propane 150.3i-Butane 181.5n-Butane 189.9i-Pentane 225n-Pentane 231.5n-Hexane 271n-Heptane 312.5n-Octane 351.5Hydrogen 34Nitrogen 41Carbon dioxide 78
Parachorshavebeenshowntohavealinearrelationshipwithmolecularweightac-cordingtotherelationship;
Pσ=21.99+2.892M (11)
andalsotothecriticalproperties
Properties of Reservoir Liquids
��
600
500
400
300
200
100
0 50 100 150 200
i - C5
i - C4
Molecular Weight
Par
acho
r, P
Figure 21 Parachorsforcomputinginterfacialtensionofnormalparaffinhydrocarbons19.
Pσ=0.324Tc1/4vc
7/8
whereTcisinKandthecriticalvolumevcisincm3/gmol.
ToapplytheparachorapproachtomixturesthemolaraveragingapproachofWeinaugandKatz20canbeused.
σ ρ ρσ= −
∑P xM
yjMj
L
L
g
gj
4
(12)
xjandyjarethemolefractionsofthecomponentsintheliquidandgasphases.
Firoozabadi21hasprovidedparachorstoenablecalculationstobemadeforheavycomponentsusingthefollowingequation.
Ps=-11.4+3.23M-0.0022M2 (13)
whereMisthemolecularweightoftheheavycomponent.Figure22.
Institute of Petroleum Engineering, Heriot-Watt University ��
Molecular weight
Par
acho
r. P
1400
1200
1000
800
600
400
200
0 100 200 300 400 500
Figure 22 Parachorsofheavyfractionsforcomputinginterfacialtensionofreservoirliquids.McCain17
ThismethodisillustratedusinganexamplefromMcCain17.
ExErcIsE 11.
calculate the IFt of the following volatile oil mixture at ��1� psia and 1�0°F for the oil with the following composition.
12 COMPARISON OF RESERVOIR FLUID MODELS
It isuseful to summarise thedifferencesbetween theBlackOilModelapproachcomparedtotheCompositionalModelinpredictedfluidproperties.
Thesuitabilityofthetwoapproachesislargelyrelatedtothenatureofthefluid.ForheavieroilswheretherearelowGOR’sascomparedtovolatileoilswithhighGOR’s,blackoilmodelsarelikelytobesuitable.Forthemorevolatilesystemswheretherearemoresignificantcompositionalvariationsinareservoiraspressureisdepleted,compositionalmodelsareconsideredmorecapableofpredictingfluidbehaviour.
Thecomputationalrequirementsofcompositionalmodelsusedtobearestrictionwhencarryingoutlargereservoirsimulation.Thecontinueddevelopmentofcomputingandassociatedequationsofstatemodellingreducestheseformerrestrictions.
Properties of Reservoir Liquids
��
Companiesarenowfocusingtheirattentiononbeingcapableofmodellingthetotalprocessfromfluidextractionfromthereservoir,throughwellproductionandfacil-itytreatment.Atpresentseparatemodellingoccurs,andmanyofthesemodelsarenotcompatible.Theblackoilapproachiscertainlyconsideredbymanytobefromaformerera.
Thelistbelowgivesasummarycomparisonofthetwoapproaches.
Black Oil Models• 2components-solutiongasandstocktankoil• Bo,Rg,etc.• Empiricalcorrelations• Aftertheeventdescriptionoffluidproperties
Compositional Models• Ncomponentsbasedonparaffinseries• Equationofstatebasedcalculations• Feedforwardcalculationoffluidproperties
Inasubsequentchapteronvapourliquidequilibriawewilldescribehowthevolumesandcompositionsofvapourandliquidequilibriummixturescanbecalculatedwhenamixtureisprocessedataparticularpressureandtemperature.Thesecalculationsalthoughcalculationintensivecanbeconsideredfeedforwardcalculationsanden-abletheeffectsoftemperatureandpressurechangestobedeterminedonaparticularfeedmixture.
Theblackoilapproachwhichhasbeenamajorthemeofthischapterusesthechar-acteristicsoftheproducedfluidstodeterminethecompositionandpropertiesofthefeedreservoirmixture,i.e.abackcalculation.AswillbeseeninthesectiononPVTreports,thequantitiesandcharacteristicsoftheproducedfluidsaredependantonthepressureandtemperatureconditionsusedtoseparatethefluid.
Atthebackofthischapteraretablesofphysicalpropertieswhichareusefulinmanyoftheproceduresdescribed.
Institute of Petroleum Engineering, Heriot-Watt University ��
Properties of Reservoir Liquids
��
Institute of Petroleum Engineering, Heriot-Watt University ��
Properties of Reservoir Liquids
��
Institute of Petroleum Engineering, Heriot-Watt University ��
Solutions to Exercises
ExErcISE 1.
Calculatethedensityat14.7psiaand60ºFofthehydrocarbonliquidmixturewiththecompositiongivenbelow:
Component Mol. fract. 1b mol.
nC4 0.25 nC5 0.32 nC6 0.43
1.00
SoLutIon ExErcISE 1
Solution Component Mol. Mol. Weight Liquid Liquid density
fract. weight 1b Density at volume 1b mol. 1b/1b at 60˚F and 14.7 cu ft mol. psia 1b/cu ft
nC4 0.25 58.1 14.525 36.45 0.3985 nC5 0.32 72.2 23.104 39.36 0.5870 nC6 0.43 86.2 37.066 41.43 0.8947 ____ _____ _____ 1 74.695 1.8801
ExErcISE 2: Calculate the “surface pseudo liquid density” of the following reservoircomposition.
Component Mole percent Methane 44.04 Ethane 4.32 Properties ofPropane 4.05 heptane + Butane 2.84 API gravities = 34.2Pentane 1.74 SG = 0.854Hexane 2.9 Mol wt = 164Heptane + 40.11
Properties of Reservoir Liquids
�0
SoLutIon ExErcISE 2
Estimate ρο 44.65 lb/cu ft. 0.716 gm/cc lb/cuft From fig 12 Density 0.326 20.3424 C1 Density 0.47 29.328 C2 Component Mole Mol Weight Liq Liquid fraction Weight Density Volume lb/lb lb at 60°F & mole 14.7 psia lb/cu.ft cu ft. z M zM ρo zM/ρo Methane 0.4404 16 7.0464 20.3424 0.34639 Ethane 0.0432 30.1 1.30032 29.328 0.04434 Propane 0.0405 44.1 1.78605 31.66 0.05641 Butane 0.0284 58.1 1.65004 35.78 0.04612 Pentane(n&i) 0.0174 72.2 1.25628 38.51 0.03262 Hexane(n&i) 0.029 86.2 2.4998 41.43 0.06034 Heptane+ 0.4011 164 65.7804 53.26 1.23508 Total 1 81.31929 1.8213 Density = 81.32 lb / 1.82 cu ft = 44.65 lb/cu.ft
ExErcISE 3.
Calculatethesurfacedensityofthemixtureinexercise2usingthechartoffigure13
SoLutIon ExErcISE 3
Component Mole Mol Weight Liq Liquid fraction Weight Density Volume lb/lb lb at 60°F & mole 14.7 psia lb/cu.ft cu ft. z M zM ρo zM/ρo Methane 0.4404 16 7.0464 Ethane 0.0432 30.1 1.30032 Propane 0.0405 44.1 1.78605 31.66 0.05641 Butane 0.0284 58.1 1.65004 35.78 0.04612 Pentane(n&i) 0.0174 72.2 1.25628 38.51 0.03262 Hexane(n&i) 0.029 86.2 2.4998 41.43 0.06034 Heptane+ 0.4011 164 65.7804 53.26 1.23508 1 Weight of propane + 72.97 lbs. = Volume = 1.43 Density of propane + = 51.01 lb cu ft Weight per cent ethane in ethane + 1.75 Weight per cent methane in 8.67 methane + From figure 13 pseudo liquid density = 45 lb/cu ft
Institute of Petroleum Engineering, Heriot-Watt University �1
ExErcISE 4.
Calculatethedensityofthereservoirliquidofexercise3atareservoirtemperatureof5,500psiaand180oF
SoLutIon ExErcISE 4Densityoffollowingreservoirliquidat6,000psiaand180˚F.
Step 1 Pseudoliquiddensityatstandardconditions fromexercise3ρo=45lb/cuft
Step 2 Adjustto60˚Fand5,500psia i.e.correction=+1.9lb/cuft (Figure14) i.e.ρo=45+1.9=46.9lb/cuftat60˚F6,000psi
Step 3Adjustto180˚F. (Figure15)i.e.thermalcorrection=-3.18lb/cuftρo=46.9-3.18=42.32lb/cuftat180˚and6,000psiaρo=42.32lb/cuft@180˚Fand6,000psia
ExErcISE 5.
Areservoiratapressureof4,000psiaandatemperatureof200oFhasaproducinggastooilratioof600scf/STB.Theoilproducedhasagravityof42oAPI.Calculatethedensityofthereservoirliquid.Theproducedgashasthefollowingcomposition
Component MoleFraction Methane 0.71 Ethane 0.13 Propane 0.08 Butane 0.05 Pentane 0.02 Hextane 0.01
Properties of Reservoir Liquids
��
Calculation of pseudo density of gas. From PV=znRT, Solubility of gas, Rs = 600 scf/STB 1 lb mole = 379 scf Oil = 42 API Density of crude = 50.87 lb/cuft 285.62 lb/STBDensity of water = 62.37 lb./cuft Component Mole Solubility Mol Weight Liq Density Liquid Volume fraction Weight volume scf lb/lb mole lb/STB at 60°F fraction gas/STB & 14.7 psia lb/cu.ft cu ft/STB. z zRs M zRsM/379 ρo zm/ρo Methane 0.71 426 16 17.98 Ethane 0.13 78 30.1 6.19 Propane 0.08 48 44.1 5.59 31.66 0.176 Butane 0.05 30 58.1 4.60 35.78 0.129 Pentane(n&i) 0.02 12 72.2 2.29 38.51 0.059 Hexane(n&i) 0.01 6 86.2 1.36 41.43 0.033 Oil 42 API 285.62 5.615 Totals 600 323.63 lb 6.01 cu ft Density of propane + = 323/6.01/lb cuft = 49.81 lb/ cu ft Weight % C2+ = 2.315 Weight% C1+ = 5.557 From Figure 13 Pseudoliquid density of reservoir fluid at 60°F & 14.7 psia = 46.5 lb / cu ft Correction for pressure Fig 14 = 1.23 + = 47.73 Correction for temperature Fig 15 3.55 - = 44.18 Density of Reservoir Fluid = 44.18 lb/cu ft
ExErcISE 6.
UsethecorrelationofKatztocalculatethereservoirfluiddensityofafieldwithaGORof500scf/STBwithagasgravityof0.8anda35oAPIoilforreservoircondi-tionsof4,000psiaandatemperatureof180oF.Katzmethod
SoLutIon ExErcISE 6.
MassofgasperSTB.Molecularweightofgas=molecularweightairx0.8=29.2x0.8=23.2
Mas og gas STBscfstb
xlb mole
scfx
lblb mole
lb STB / .
.
. /= =500379
23 230 61
Institute of Petroleum Engineering, Heriot-Watt University ��
Component Weight Liq Density Liquid Volume lb/STB at 60ºF cu ft/STB. & 14.7 psia lb/cu.ft Gas 30.61 26.3 1.164 Oil 297.62 from chart 5.615 328.23 6.779
Pseudodensity of reservoir fluid= 328.23 / 6.779 = 48.42
Correction for pressure at Fig 14 +1.13 = 49.55 Correction for pressure at Fig 15 -2.9 = 46.65 Reservoir density= 46.65 lb/cu ft
ExErcISE 7.
Agascondensateproducesgasandliquidswiththecompositionsdetailedbelow,with a producingGORof 30,000 SCF/STB. Determine the composition of thereservoirgas.
Component Composition Gas LiquidMethane 0.84 Ethane 0.08 Propane 0.04 0.15Butane 0.03 0.36Pentane 0.01 0.28Hexane 0.12Heptane + 0.09 1.00 1.00
Properties of Reservoir Liquids
��
SoLutIon ExErcISE 7
Liquid Component Mol. Fractn Mol.Wgt. Wgt. Liquid Liquid lb mole lb/lb mol lb/lb mole density volume lb/cu ft cu ftC3 0.15 44.1 6.615 31.66 0.223C4 0.36 58.1 20.916 35.78 0.585C5 0.28 72.2 20.216 38.51 0.506C6 0.12 86.2 10.344 41.3 0.25C7+* 0.09 114.2 10.278 43.68 0.235* C8 used for C7+ 68.369 1.799 Mol.Wgt. 68.369 liq. Density of liquid= 38.00 lb/cu ft GOR= 30000 scf/STB 213.39 lb/STB = 79.16 lb mole gas/STB 3.12 lb mole /STB Note: 1 lb mole = 379 SCF GOR = 25.36 lb mole gas/lb mole liquid 2. Recombination according to the above GOR of 25.36 lb mole gas / lb moleliquid Component Composition lb mole gas/ lb moles Composition Gas Liquid lb mole oil Res fluid Res Fluid lb mole lb mole 25.36 y x 25.36y 25.36y + x Methane 0.84 21.30 21.30 0.808Ethane 0.08 2.03 2.03 0.077Propane 0.04 0.15 1.01 1.16 0.044Butane 0.03 0.36 0.76 1.12 0.043Pentane 0.01 0.28 0.25 0.53 0.020Hexane 0.12 0.12 0.005Heptane + 0.09 0.09 0.003 1 1 25.36 26.36 1.000
ExErcISE 8.
Thegascondensatereservoiraboveiscontainedinreservoirsandswithanaveragepaythicknessof100ft,withaporosityof0.18andaconnatewatersaturationof0.16.Theaerialextentofthefieldis5sq.miles.Theinitialreservoirpressureis5,000psiaandthereservoirtemperatureis180oF.Determinetheinitialreservesofthefieldintermsofcondensateandgas.
Institute of Petroleum Engineering, Heriot-Watt University ��
SoLutIon ExErcISE 8
Component Mol. Fract. Critical Temperature Critical Pressure
R R psia psia
lb mole yj Tcj yjTcj Pcj yjPcj
C1 0.808 344 278.00 667 539.026
C2 0.077 551 42.41 708 54.491
C3 0.044 666 29.42 616 27.210
C4 0.043 750 31.89 540 22.960
C5 0.020 838 16.96 489 9.899
C6 0.005 914 4.16 437 1.989
C7+ 0.003 1025 3.50 360 1.229
Totals 1 406.34 656.80
Tpc= 406.34 Ppc = 656.80
Reservoir pressure = 5000 psia
Reservoir temperature = 180 F = 640 R
Pseudo reduced pressure = 7.61
Pseudo reduced temperature = 1.58
Compressibility factor from Standing & Katz chart figure 2 Gas properties chapter
z= 0.98
R= 10.73 cu ft. psi/lb.mol R
Volume of the reservoir = 5 square miles x 100 feet (1 mole = 5280 ft)Volume of the reservoir = 2.1076 x 109 cu ft
PV=znRT V/n=zRT/P
Specific volume at reservoir conditions = 1.3460 cu ft/lb.mol
No of lb moles in reservoir= 1.5658 x 109 lb moles
No. of standard cubic feet of gas in reservoir = 5.9345 x 1011 SCF (1 lb mole 379 scf)
Reserves in reservoir in terms of produced fluids
From previous exercise GOR of = 30,000 SCF/STB
= 25.36 lb mole gas/lb mole condensate
For each 26.36 lb mole of reservoir fluid 25.36 lb mol is produced gas
and 1 lb mole is condensate
Reserves in terms of produced fluids
Gas 1.506428 x 109 lb moles = 5.70936 x 1011 SCF
Condensate 1.9643E+09 lb moles = 6.2935E+08 STB
ExErcISE 9.
Calculatethegascondensateformationfactorfortheexampleinexercise8.
SoLutIon ExErcISE 9. Bgc=bblsofgasinreservoir/STBcondensateVolumeofgasinreservoir=6.9696x1010cuft=1.2412x1010bblsCondensate=6.2935x106STBBgc=1972.2 bblsresgas/STBcondensate Insomecasesfullcompositionalinformationmaynotbeavailablebutonlyblackoildescriptionsoftheoilandgasgravityforthegas.Inthiscasecorrelationscanbeusedtoprovidethenecessarydatatocalculatethesamedataasforexercise8&9.
Properties of Reservoir Liquids
��
ExErcISE 10
CalculatetheviscosityofoilinthePVTreportofchapter12atapressureof5,000psigand220°F.The°APIoftheoilis40.1andtheGOR,Rs
is795scf/ST
Beggs and robinson
µod=10A-1
LogA=3.0324-0.0202°API-1.163logTxµod=deadoilviscositycp.(Beggs3.03240.02021.163)(Egbogah1.86530.0250860.56441) Beggs EgbolgahAPI=40.1T=220Rs= 795P= 5,000psigPb= 2,635psiglogA=-0.5031-0.46A= 0.3140 0.34Viscositydeadoil= 1.06cp1.21cpMeasuredvalue=1.29cp
ViscosityatbubblepointBeggsµob=Cmob
B
µob=oilviscosityatbubblepointpressureC=10.715(Rs+100)
-0.515
B=5.44(Rs+150)-0.338
C=0.3234B=0.5369µob=0.3584cpMeasuredvalue=0.355cp
Viscosity at pressure of �01� psigVazquez - Beggsµ
o = µ
ob (P/P
b)D
D = �.�p 1.1�� e -11.�1� - �.��x 10-�p
e function = -11.����D = 0.���� cplabed, correlationµ
o= µ
ob + (P/P
b-1)(10 -�.���µ
ob0.�0�� P
b0.�1�1 /10 0.01��oAPI )
µo = 0.��0� cp
Measuredvalue=0.45cp
Institute of Petroleum Engineering, Heriot-Watt University ��
ExErcISE 11
CalculatetheIFTofthefollowingvolatileoilmixtureat2315psiaand190°Ffortheoilwiththefollowingcomposition.
SoLutIon ExErcISE 11
Component Liquid Composition Gas Composition Mole fraction Mole fractionCarbon dioxide 0.0159 0.0259Nitrogen 0.0000 0.0022Methane 0.3428 0.8050Ethane 0.0752 0.0910Propane 0.0564 0.0402i - Butane 0.0097 0.0059n - Butane 0.0249 0.0126i - Pentane 0.0110 0.0039n - Pentane 0.0140 0.0044Hexane 0.0197 0.0040Heptanes plus 0.4303 0.0049
PropertiesofheptanesplusofliquidSpecificgravity=0.868Molecularweight=217lb/lbmoleDensityofliquidsandgasfrompreviousmethodsPL=0.719g/ccPg=0.137g/cc
Molecularweight ML=110.1g/smole Mg=21.1g/gmole
Component xj yi Pσ Equation 12Co2 0.0159 0.0259 78.0 -0.0050N2 0.0000 0.0022 41.0 -0.0006C1 0.3428 0.8050 77.0 -0.2301C2 0.0752 0.0910 108.0 -0.0108C3 0.0564 0.0402 150.3 0.0161i-C4 0.0097 0.0059 181.5 0.0046n-C4 0.0249 0.0126 189.9 0.0154i-C5 0.0110 0.0039 225.0 0.0105i-C5 0.0141 0.0044 231.5 0.0147C6 0.0197 0.0040 271.0 0.0278C7+* 0.4303 0.0049 *586.6 1.6297 1.000 1.000 1.4723
fromfigure23
Properties of Reservoir Liquids
��
REFERENCES
1.Craft,BC&Hawkins,MF.AppliedReservoirEngineering”1959PrenticeHall,NY
2.Danesh,A,PVT and Phase Behaviour of PetroleumReservoir Fluids. 1998Elsevier.pp66-77
3.StandingMB“Apressure-Volume-TemperatureCorrelation forMixtures ofCalifornianOilsandGases”,Drill&Prod,Proc.275-287(1947)
4.Lasater,J.A.“BubblePointCorrelation“,TransAIME,213,379-381(1958).5.Vasquez,MandBeggs,HD“CorrelationsforFluidPhysicalPropertyPrediction
“JPT,968-970,(June1980)6.Glaso,O“GeneralisedPressureVolumeTemperatureCorrelations” JPT,785
795(May1980)7.Marhoun,MA,“PVTCorrelationsforMiddleEastCrudeOils”JPT,650-665
(May1988)8.Standing,M.B.andKatz,D.L.“DensityofCrudeOilsSaturatedwithNatural
Gas”TransAIME146,159(1942)9.Kessler,MGandLee,BI,:“ImprovedPredictionofEnthalpyofFractions,”Hyd
Proc.(Mar.1976)55,153-158.10.Standing,M“VolumetricandPhaseBehaviourofOilFieldHydrocarbonSystems”
SPEDallas195111.Beggs,HD.andRobinson,JR:EstimatingtheViscosityofCrudeOilSystems”
JPT,27,1140-1141(1975)12.Egboghah,EOandNg,JT:‘AnimprovedTemperatureViscosityCorrelations
forCrudeOilSystems”,J.PetSciandEng.,5,197-200(1990)13.Vasquez,M.andBeggs,HD:”CorrelationsforFluidPhysicalPropertyPredictions”.
JPT,968(June1980)14.Labedi,R:“UseofProductionDatatoEstimateVolumeFactor,Densityand
CompressibilityofReservoirFluids”,J.ofPet.SciandEng.4.375-90,(1990)15.DeGhetto,G.,Paone,F.andVilla,M.:“ReliabilityAnalysisofPVTCorrelations
“,SPE28904,ProcofEuro.PetConf.Lndn,375-393(Oct.,1994)16.Danesh,A.,Krinis,D.,HendersonG.D.,andPeden,J>M>“VisualInvestigation
ofRetrogradePhenomenaandGasCondensateFlow inPorousMedia”5thEuropeanSymposiumonImprovedOilRecovery,Budapest(1988)
17.McCain,WD.,“ThePropertiesofPetroleumFluids”PennwellBooks,Tulsa,Ok1990.ISBN0-87814-335-1
18.Macleod,DB.,“OnaRelationBetweenSurfaceTensionandDensity,”Trans.,FaradaySoc.(1923)19,38-42.
19.Katz,DL.,”HandbookofNaturalGas Engineering”,McGrawHillBookCoInc.,NewYk,(1959)
20.Weinaug,KGandKatz,DL,:“SurfaceTensionofMethane-PropaneMixtures”.I&EC,239-246(1943)
21.Firoozabadi,A,Katz,D.L.,Soroosh,H.MandSajjadian,V.A.:“SurfaceTensionofReservoirCrude-Oil/GasSystemsRecognising theAsphalt in theHeavyFraction,”SPEResEng.(Feb)1988,3,No1,265-272.