1.

11.

%323

March19, 1981.

EMPIRICALFOMULA TO DETERMINEEQUILIBRIUMRATIOSFOR =ANES PLUSFROM EQUILIBRIUMRATIOS

FCR HEPTANE

INTRODUCTION UNSOLICITEDIn 1977(1)*I was askedto determinethe optimumseparatorconditionsfor a gas condensatereservoir.

Havingno specificbackgroundon the subject,I comenced ingatheringinfonuationon the methodsto tacklethisproblem.Thisled me to severalcorrelationsand experimental.work fromwhichthe equilibriumratios(K-values)for singlecomponentscouldbe derived. The K-valuesare requiredto predictrecoverylevels. SoonI realisedthat I had to becomea highlycompetentmathematiciansnd a skilledcomputerengineerif I wantedtomake uae of the many formulaepublishedin technicalmagazinesand books. SinceI couldnot sparew time to do this,Irejectedthis solution.The remainingchoicewas to use theK-chartspublishedby the I?GPA(ref.1), but stillaimingtocomeup with reliableseparatorresultsforhighlyvolatileoilsand gas condensates.

In 1957,NaturalGas ProcessorsA~sociation(NGpA)have co~iledall experimentieallyderiveddata for equilibriumratios(X)ofsinglecomponentsin convergencepressurecharts. It has beenfomd that at a giventemperature,the K-valuesof all componentsin the mixtureconvergeto unityat a certain@ressure. Thispressurehas been called(apparent)convergencepressure,pk.

The K-chartsare isothermallog K versuslog P curves. NGPAhaveregularlyrevisedand updatedthe graphsas more experimentaldabbecameavailable.Theyare presentedin section18 of the M-gineeringDataBook (ref.1).

AlthoughNGPA recognize that thereare indicationsthatcoruposi-tion effectsin hydrocarbonmixturesare not fullyrepresentedbyconvergencepressurealone9the convergencepressurecorrelationhas been retainedforthe following reasons:1) The chartsin use providea usefuland rapidgraphicalapproach

for engineers.

Note (1) : At that the employedwith Maraven,Lagunillas,Venezuela.

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2) The valuesare sufficientlyaccurateto satisfymanycalculations.

3) The graphsare tidel.yusedin the industry.

113.LIMITATIONSOF THE K-CHARTS

In thepastspredictions,usingthe K-valuesof the graphspublishedby NGPAhave semethes failed. Ofthenthe K-valueswere suspectedfor this failure. The main fieldsofuncer-tain~ are however:

1. K-valueformethane

2.

M the caseof meth=e, interpretationbetweenpk chartsisa must to obtainaccurateK-values. M.B. standingpointedoutin Ref. 2 that the K-valueformethaneinfluencesin a largemeasurethe liquidrecove~.

2. The equilibriumratioforheptanesplus

h the EhgiaeeringDaL.:?-nknO K-chartsare givenfortheheptsnesplus fraction. In factno suchgraphscan beconstmcted. The K-valuesforheptanesplushave alwaysto beestimated.

As a firstapproximationit was assumedthatthe K-valueforheptanespluswouldbe 15% of the K-valueof heptane. Thiseasysolutionwas basedon a papermadeby D. ~tz and .K. Hachmuch(ref.3) and on informationfromref.2. Appli-cationof the 0.15correlationforthe gas condensatereser-voir fluidsgaveresultswhichwere oftennot satisfactory.Thereforaa methodfor determiningK-valuesforheptanespluswas workedout. The finalformulahas yieldedgoodresultsand has been in closeagreementwith laborato~test data.

IV. DETERMnW?IONOF THE RATIOKc47+/~7: K-m

me idea of a relationshipbetweenthe equilibriumratiosforheptsnesplus and heptanes,set fowardby ~tz and Hachmuchwasmaintained.Aftermany experimentsit was foundthattheformula;!expressingthis relationshiphad to includethe follo-wingparameters:

./.

.

3.

a) The molecularweightof the heptanesplus,b) The specificgravityof the heptanesplus.c) The separatorand convergencepressure.

Discussion

1. Themledularwe~ghtof the heptanesplus givesthe first~dicatiOn Of howvolatilethis &action is. The higherthemolecularweightthemore longand littlevolatileh@rocarbonmoleculesare present. The ratio~ is proportionaltwiththe ratiomolecul~ weightof heptane/molecul~weightofheptanesplus.

2. The specifiegratityof the heptanesplusis alsolinkedtoa certaindegreewiththe K-value. SomearomaticshavingaZow bubblepoint end low molecularweightare in factheavycomponents.This distortiveeffectis takeninto accountby calculatingthe expectedmolecularweightbasedon thespecificgravityof the heptanesplus. For thisexclusivepurposethe averagerelationshipbetweenmolecularweightand specificgratityhas been definedby a straightlineona semi-logaritticscale,accordingto the formula:

~0/3M (c?+, C) = 5.8 X G (CT+) - 2.585Note : seenomenclatureat the end of thisnote.

Again,the ratioKr is proportionalwiththe ratiomolecularweightof Mptsne/calculatedmolecularweightof heptanesplus.

Whenthe separatorpressureis approachingthe convergencepressurethe rationKr comescloser to one. At the conver-gencepressureitselfK-valuesof all componentsare equalto one. This shouldalsobe the case forthe multi-componentC7+.

Fomu,laforKr&lcti-8tion

The followingempiricalformulawhichis reflectingthe abovementionedeffects,has been in~ose.agreementwith reel labo-ratoryteatg.:

,.

,.

4,

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1%7+/%7 = KJ

( @&/P~ep)M(C7) M(C7+,C)fi= xM@7+,m M(C7+,m))v. RESULTS

In tabulations1 and 2 the calculateddataand laboratorydataare given. The resemoir fluidis a gas-condensate.As can beseen fromthe tabulationsagreementat all pressurestepsisexcellent.

J.A.Follet.

I

i.:

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$

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K(C7)

K(C7+ )

%

M(C7)

M(C7+,=)

M(C7+,m)

Pk

%p

:

:

:

.

.

l.

:

:

:

l.

Specificgravityof the heptanesplusfraction,in g/cc and 60/600 F

(- repofiedinthe WT study).

Ik@libriumratioforheptane.

Equilibriumratioforheptanesplus

Ratio K(C7+)~(~).

Molecularweightof heptane.

Calculatedmolecularweightofheptanesplue(fr~the specificgratity)

Measuredmolecularweightof heptanesplus(as reportedin the PVT study).

Convergencepressuxe.

Separatorpressure.

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REFERENms

i

I 1. EngineeringDataBook,publishedby the NaturalGas ProcessorsSuppliersAssociation,Section18 : EquilibriumRatios(1976).1 2. Volumetricand phasebehaviorof oil fieldhydrocarbonsystems,i by M.P.. Standing(1952) l..i

J1I 3. Vaporizationequilibriumconstantsin a crudeoil-naturalgas\ system,by D. Katz and K. Hachmuch,Ind.Eng.Chem.29, 1072(1937)l!

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L6TCD COWOSJTIONS IMMOL PERCENT {NO* OF c~@!pl&NTti m 311.-.------..-- . . . . ..------..*.-.

1S? sTAGE 2ND STA6E 3RD STAGE QTM sTsSE .--------..0---- --------------- --------------- ---------------

HMC7XON OF LIOUID = 0.3834 O.aE$ls 0.2265fJl 3a3u

0.19760.65S8. 0.90a3 0.a63U

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,TOR CONL)I 7X(WW / CALCUL.A710NS------------------------------

;uREo IN PSIA / TCMPcRATUREQ IN FWR =RGENCE PRESSURE, IN PSIA =CAL PKSWTE?4P (PSI WFAHRJ OF c2+Q =

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1S00/$60 21s/ 100 75/ 100 15/ 100S2S0 6000 6500 7000

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Separator

Separator

Analyoea of Separator Gas~sFrom IL4uM -SQige Separation Teat

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Reasure, PSIG: 1500

Temperature, F. - 160

Component

Hydrogen SulfideCarbon DioxideNitrogenMethaneEthanePropane ,iso-13utanen-Butaneiso-Pentane

.

n-PentaneHexanesHeptanes plus

MolPercent .

Nil3.350.74

77.31, 10.24

4.080.751.100.370.350.5?1.14

100.00

GPM

2.5791.1200.2450.3460.1350.1260.2320.517

200

100 l

MolPercent GPM

Nil4.400.30

67.4716.837.121.141.530.400.320.230.26

4.2391.9540.3720.4820.1460.1150.093

0.1175.300 100.00

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Nil4.990.09

41.2527.5616.192.853.931.010.840.620.67

7.518 100.00

GPM

6.9424.4440.9301.2360.3690.3040.2530.304

14.782

100

MolPercent

o

100

MolPercent GPM

Nil2.140.038.00

23.5732.22

8.4413.054.123.372.872.19

5.9388.8432.7544.1031.5041.2181.1680.992

100.00 26.520