reseng flame ch6

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

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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"


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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.


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:


�

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


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.


�

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


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


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.


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)


1�

Standing's correlations have been presented as nomographs enabling quick lookpredictionstobemade.Figures10&11givethenomogramformsofthesecorrelationsforgassolubilityandoilformationvolumefactor.Standing’scorrelationisbasedonasetof22Californiacrudes.

OthercorrelationshavebeenpresentedbyLasater4basedon137Canadian,USAandSouthAmericancrudes,VasquezandBeggs5using6000datapoints,Glaso6us-ing45NorthSeacrudesamples,andMahoun7whoused69MiddleEasterncrudes.Danesh2givesaveryusefultableshowingtherangescoveredbytherespectiveblackoilcorrelations


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)


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


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.


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


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.


�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.


��

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.


��

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


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


��

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.


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.


��

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.


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


�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.)


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


��

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.


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.


��

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.

��


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


�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


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


��

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


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


��

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.


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.


��

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


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


��

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.

reseng flame ch6

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