THE ACCURACYOF PVT-PARAYWEM CALCULATED

FROM COMPUTERFLASH SEPARATIONAT PRXSSURES

LESS THAN 1000 PSI

by

@.S.GLASO and C.H.WHXTSON ,SINTEFN-7034 Trondheim-NTH, NORWAY

.. —— .. . _—_. ._ ..-,.’ . . . . . .

,“. .

ABSTMCTa

An investigationwas madeto check the generalapplicabilityof equilibrium

constantspresentedb.yKatz and Hacbmuthat pres$uresand cempeeaturesen-

counteredat flashseparatorconditionsfor crudeoil-naturalgas systems..

Simplealgebraicequatioxzs”developedby Standinggeneratedthe Katz and Hach-

muth K valuesfor hydrocarbons’,as well as the non-hydrocarbonsC02, N2 and

H2S● These K valueerAuationswere incorporatedin a flashseparatorprogram. .

to yieldthe following‘calculatedwell effluentproperties:gas-oilratio,

surfacegas gravity,stocktankoil gravityand bubblepointformationvolume

factor. Comparison~of calculatedlaboratory-determinedfla’sh”propercieswere

made on 25 crudeoils from

chosento representa wide

tent.

The”calculatedK valuesin

severalregionsof the world; the sampleswere

rangeof paraffiaicitiesand non-hydrocarboncon-

the pressureand temperature range of flashsepa-

rationmay have the best applicabilitydescribingseparatorflashoptimiza-

tion,givenherewith an example.

.

0I

INTRODUCTION

Standinglderiveda set of equationswhich fit the equilibriumconstant

data of Katz and Hachmuth2at prassuresless than1000psia (70 atm) and

temperaturesbelow200°F (93°C). A standarddeviationof 3.5%between..calculatedend chart.ivaluesis reportedby Standing.

The applicationof theseequationsshouldbe of considerableinterestto

the petroleumindustry,particularlyin the areaof flashseparatoropti-

mization. Not reported,however,is the accuracyof the Katz and Eachmutb.

“Kvaluesappliedto reservoirfluidsof varyingparaffinicityand containing

significantamountsof non-hydrocarbons.Becausetke data of-lta~zand.

Hachmuthwas fox an OklahomaCity crudeoil containingno non-hydrocarbons,

it was necessaryto investigatetheirgeneralapplicability.

A separatorflashprogramwas developedwhich incorporatesthe Standing

‘ K value equations.The programwas use~ to analyze25 crudeoils from

variousregionsof the world,somecontaining~ubstantialamountsof non-

hy&ocarbons. Flashparameterswere calculatedand Qomparedwith the

experimental-Iues obtainedfroma PVT analysisof the fluidsamples.

Gas-oilratio,averagegas gravity,stocktankoil gravityand bubblepoint

formationvolumefactorwere”usedin the comparisons.

Resultsyieldedaveragedeviationsof -0.75,5.25and 1.,88percmt and stan-

dard deviationsof 6.84,6.86 and 5.25 percentfor gas-oilratio,averagegas

gravity and stock tank oil gravityrespectively.Bubblepoint formation

volumefactor,calculatedusingbubblepointoil densityand a correlation

by Glas@3,yieldedaveragedeviationsof -0.32and 0.02percentand standard

deviationsof 2.03and 3.72percent,respectively,for eachmethod.

Sinceflashoptimizationis usuallymost dependenton stocktankoil gravity

and formationvolumefactor,the statisticaldeviationsindicatechatKatz

and HachmuthlsK valuedata fic by Standingtsequationshas generalapplic-

ability. The effectof paraffinicityappearsrelativelyinsignificant.

Modifiedparametersfor calculatingKvalues of non-hydrocarbonswere

sufficientlyaccuratefor estimatingphasebehaviourof sampleswith signifi-

,2, N2 and H2S.cantquantitiesof CO

.

.

FLASHPROGRAMDESCRIPTION

Directapplicationof the Kvalue equationsby Standingis preseneedas a

computerprogram(listingin AppendixA). As written,the programcan be

easilyintegratedas a flashsubroutinein separatoroptimizationprograms.

The algorithmused for calculationsis describedby Standing4.

The flowdiagramin Fig.1describesinputdata,calculationprocedureand

finaloutputof the flashprogram. A n-stageflashcan

the program, but a maximum3-stageseparatorsimulation

work.

be performedby

was used in this

Vaporand liquidequilibriumcalculationsuse the Katz and HachmuthK values

fit by Standing. The basic equationfor fittingK valuedata was given

by Hoffman,Crumpand Hocotts,

1K.— ~O(a+cF)

Psep

(1)

wherecoefficientsa and c are functionsof separatorpressure.P “se~ ‘smmsured in psia~and F is a charactizationfactor.

Equationsfit by Standingfor the Katz

-4P +a=102+4*5X10sep

and Hachmuthdata

15 x 1{)-8pzsep

- 1.7 xlo-bep- 305 Xlo -8 P2C = 0.89 sep

are:

(3)

The characterizationfactbr,F, as definedby Hoffman,et.al.5,is

.f=b(l/TB- l/T )

sep(4)

whereseparatortemperature,Tseps is in ‘R and coefficientb is defined

for th@ pure componentsC3, i-C4, n-.C4, i-c5, n-c and C6 ~~5

,

where

(l/TB-I/Tc)

pc =

Tc =

TB =

criticalpressureof each component,

(5)

.

psia

criticaltemperatureof eachcomponent,‘R

averageboilingpointof eachcomponent,‘R

,

@

.

:

‘z

.. :<.,

AU etherfractionsexceptC,+, i.e.Cl, C2, C02, N2 and H2~have modified

valuesof b and TB given in Table1. The following’temperatureand pressure

dependentfunctionswere developedby Standingfrom the Katz and Hachmuth

data to handlethe C,+ fraction:

b = 1013+ 324N + 4.256N2C7+

‘B C,+” 301 + 59.85N-0.971N2

I (6)

(7)

where

N = 3,85 + 0.0075Tsep+ 0.0016Psep (8)

I

Eqs. 6-8 were not availableduringthis,study. Instead,the following

C7+ Kvalue equationwas used:

= 0.15KKC7+ . c, (9) .

,..,

, .

whereKC was calculatedfromEqs. 1-5 as a pure component. A checkwas “.

made to ‘seewhat, if any, errorresultedin usingEq.9 insteadof Eqs.6-8,

It was foundthat thereis no significantlossof accuracyin calculated

flashparametersunlessthe oil contains

0.70). It is recommended,however,that

As indicatedin Fig.1,the flashprogram

a lar~eC7+ fraction(greaterthan

Eqs.6-8be used for aU calculations.

assumesthatone mole of rese~oi% fluid

is flashedat 1st stageseparatorpressureand temperature.Liquidfrom

each subsequentstageof separationis flasheduntil the finalliquidfeed

is flashedat stocktank (nth stage)conditions,PSt and T At eachSt”stage,the compositionand molesof liquidand vaporare calculated,con-

vertingto a basisof one barrelstocktankoil. From thesedata, total

gas-oilratio,average gas gravity,stocktankoil gravityand bubblepoint

formationvolumefactorare calculated.

Two methodsare used :0 calculatebubblepointfbrmationvolumefactor.

The firstcombinesgas and stocktankoil weightswith bubblepointoil

densityas follows,

nZw. +wsto

j=l ‘JB=ob S.6146Pob

(lo)

where

BOb = bubblepointformationvolumefactor,Bbl/STB

= weightof gas at stagej per barrelstocktankoil, lb‘gj

wsto = weightof one barrelstocktankoil, lb

P~b = bubblepointoil density,lb/ft3

n = numberof stagesof separation

The bubblepointoil densityis eitherreportedfromPVT

fromtheAlaniand Kennedy6correlation(notincludedin

analysisor calculated

the flashprogram).

The secondmethodof determiningBob uses a North Sea corre~acionby

Glas@3,

log(Bob-l)= ‘6.58511+ 2.91329lo8(B~b)- 0.27683(log(B~b))2 (11)

where

7 0.526B~b = GOR (~) + 0.968T

8co

and

(12)

GOR = total gas-oil ratio, SCF/STB

T = averagegas gravit;y,(air= 1)

Y:to = stocktankoil gravity= 141.5/(131.5+ OAJ?ISto)

T = reservoirtemperature,‘F

This correlationwas c!evelo~~d‘o?Nor~hSea crudeoilsbut has been

provedequallyapplicableto L.‘sof varyingparaffinicity,

RESULTSAND DISCUSSION

Tables2 and 3 containexperimentaland

ratio,average gas gravity,stocktank

calculatedvaluesof totalgas-oil

oil gravityand formationvolume

factorfor the 25 samplescompared in thisstudy, Samples7-14were analyzed

at severalseparatorconditions,indicatf~dby associatedletters,e.g.,

,7a, 7b, etc. Separatorpressureand temperaturewere variedfpr separator

designsfromone to threestages.

Statisticalanalysisof che data gave

of comparisons,range,and averageof

averageand standarddeviation,number

calculateddata for each parameter.

Resultsare foundin Table4, Although25 samplesand a maximumof 51

comparisonsdo not constitutean exhaustiveanalysis,applicabilityof the

w’””’”

correlationsis supportedby thewide rangeof oil-typesstudied.

of non-hydrocarbons

calculatedand

Six of the 25 samplescontainedrelativelylargeamounts

C02, N2 and H S2’as shownin Table5. Comparisonof the

experimentaldata for thesesamplesdid not deviatesubstantiallyfrompure

hydrocarbonsamples,suggestingthe modifiedparametersfor non-hydrocarbon

K valuesare sufficientlyaccuratefor estimating theirphasebehaviour.

SEPARATORFMSH OPTIMIZATION

Becauseof economicand/ormechanicallimitationson

typeof separatordesignsavailable,i; is necessary

the size,numberand

to determinea range

of separatorconditions,withintheselimits,whichwill optimizeproduced

fluidproperties.To establishthis range, one separatorconditionis,,variedwhile all othersremainconstant.

0

An exampleof a simpleflashoptimizationis given in Fig.2. The first

fouranalysesof sample11 (labeledha, b, c, d) are for a two-stage

separation.Primaryseparatorpressure,P--- ,, is variedfxomO to 400 psig ‘&icp,A

whileprimaryseparatortemperature,Tsep,l’ is held constantat

Stocktankconditionsof O psig and 60°F are also held constant.

At approximately2[10psig primaryseparatorpressure,each curve

100°F.

reaches

itsminimum(forBob) or maximum(forAPI gravity),indicatingthe optimal

firststagepressurefor a two stagedesign. Independentof the unusually

high deviationof calculatedvaluesfor sample11,both experimentaland

calculatedcurvessharean almostidenticalform. The usefulnessof flash

optimizationusinggeneralizedK valuesis, therefore,indicatedby how

closelythe formof calculatedand experimentalcurvesmatchas separator

conditionsare varied; usefulnessismot determinedsoleyby minimum

averageand standarddeviationsof calculatedflashparameters.

CONCLUSIONS

1. The Katz and Hachmueh2K valuedata are applicableEO most blackoils,

independentof paraffinicity,at pressuresbelow 1000psia (70atm) arid

temperaturesbelow200°1?(93°C).

2. The usefulnessof Katz and Hachmuth’swork is

developedby Standingl,which fit the Kvalue

Modifiedparametersare presentedto Senerate

extendedby equations,

data of Katz and Hachmuth.

Kvalues for the pseudo-

Iightcomponents(Cl,C2, C02,.N2and H2S),with a specialcorrelation

givenfor the C7+ fraction.

3. An efficientand user-orientedflashseparatorprogramis presented

whichuses Standingtsequationsfor calculatingK values. Flashpara-

meters: gas-oil ratio,averagedsurfacegas gravity,stocktankoil

gravityand bubblepointformationvolumefactor‘arecalcula~adfrom

givenequations. By varyin&separatorconditions,one can optimize“

producedfluidpropertiesfor the rangeof separatordesignsavailable.

,1i

REFERENCES “7

1.

2.

3.

4.

5.

6.

PersonalcommunicationfromDr. M.B.Standing,Steanford

University,(Nov.17,1978)

Katz,D.L. and

Constantsin a

Hachmuth,D.H.: “VaporizationEquilibrium

CrudeOil - NaturalGas System”,~. ~. Chem.

(Sept.1937)~, 1072-1077

Glas@,0.: “GeneralizedPressure-Volume-TemperatureCorrelations”,

SPE paper8016 (1979).

Standing,M.B.:VolumetricPhaseBehaviourof Oil Field

HydrocarbonSystems,SixthPrinting,Chemon ResearchCompany

(Sept.1970),43-56

Hoffman,A.E.,Crump,J.S.,and Hocott,C.R.:“Equilibrium

Constantsfor a Gas-CondensateSystem”,Trans.,AIME (1953)198,—.1-1o

Alani,G,H.,and Kennedy,T.H.: “Volues of LiquidHydrocarbonsat

High Temperaturesand Pressures$“Trans.,AIME,(1960)

NOMENCLATURE

a

b

BobB~b

c

C7+F

GOR

i

j

K

L

log

M

n

N

N

P:

P sep. . T

‘BT=

Tsep’

‘~w-Stov

v

Xi

Yi

%to,

Pob.

variable

variable

inK value equation

in characterizationfaczorequation

bubblepointfo~eion volumefactor,Bbl/STB

correlatingnumberfar Bob

variablein K value equntion

heptanesplus fraction

characterizationfactor

gas-oilratio,SCF/STB

subscriptdesignating components(e.g.~Cl, C2S etc.)

subscriptdesignatingstagenumberswhere j = 1,2$..0.

equilibriumconstant(-Y/x)

moles of materialin liquidstate

logarithmto base 10

molecularwei~ht

numberof stagesof separation

pseudocarbon numberfor C,+ fraction

molesof gas phaseper barrelof stocktankoil

criticalpressure,psia

separatorpressure,psia

msemoir temperature,‘F

averageboilingpoint temperature,‘R

criticaltemperaturezoR

separatortemperature,‘R

weightof gas (basis:one barrelstocktankoil), lbs

weightof one barrelstocktankoil, lbs

specificvolume,cc/gin

amlesof materialin vaporstate

liquidmole fractieaof componenti

vapormole fractionof componenti

surfacegas gravity,(air= 1)

averagedsurfacegas gravity,(air= 1)

stocktankoil gravity,gin/cc

bubblepointoil density,lb/ft3

.

Table1 MODIFIEDVALUESOF b ~ TB

FOR USE IN EQo5 (FROMST~ING1)

b

(cycle‘R)TB (OR)

Corlponent

300 94c1

1,145 303C2C02 652 194

470 109‘2H2S 1,136 331

EQ. 6 EQ. 7C7+

. .. ..

../”‘

\;

i .

Table2 COMPARISONOF EXPERIMENTALAND CALCUUTED FLUIDPROPERTIESFROM— SEPARATORFLASH @/

ExperimentalFlashData ComputerFlashData:, Total Averaged Stocktank, Total Averaged Stocktanki $as-oilratio gas gravity oilogzavity gas-oilratio gas gravity oil 8ravity

Sample (SCF/STB) (air-l) ( API) (SCF/STB) (air-l) (“API)

::12

:567a7b8a8b9a9b9C10a10b10CllallbIlcUdUeIU?12a12b12C13a13b14a14b14C15161718.1920a20b20C21a;,21b21C22a22b22C23a23b23c24a24b24c25a

32578614811168--104110564486.2302292336296266307887257107266786763263163172632644954934972928401525134414524974974971252125212522036203620365055055051052105210521689

1!1 891 89

0.7060.7550.7930.804”--0● 8810.9200.8890.7130,935.’0.9310.9570.8900.889..0.896.0.850

-0.671.0.682!.0.863.0.8490.911:----.-.-0.6601.248

0.850.8270.;260.936‘0.9360.8200.8200.8200.7600.7600.7600.7850.7850.7850.7460.7460.7460.738

“:.;;:=●

23.3136.742.540.4-.-27.026.834.936.726.026.025.938.038.238.133.734.735*134.936.836.937.238.237.922.9222.9135.7235.8035● 6823.6127.944.548,147.736.8536.8536.8536.0036.0036.0036.1536.1536.1534.3234.3234.3233.8033.8033.8036.1236.1236.12

32075714681116136694010610159446521822022060760261081970867668265965829629229426026357658361430586014941299135849449449412441244124420492049204951151151110561056105616571657- ==1657 .

0.76400.75790.79710.76610.72170.64160.93730.94391.1091-0.91740.92880.97320.88170.87530.888s0.97860.77320.72020.72830.69940.69770.98350.97200.98090.62160.62180.76860.78230.82620.66071.19790.90790.92130.95251.03271.03271.03270.88720.88720.88720.78200.78200.78200.86470.86470.86470.78210.78210.78210.77220.77220.7722

23.4836.6544.0042.5438.3134.2127.4527.5435.09 .37.5626.4326.3826.4139.0939● 2239● 0534.6536.4337.1336.9637.6037.6437● 7137.8237.7523.1123.01 “36.0835●8835● 0523.9127.25

.. 45.7150.4050.0037.0237.0237.0235.7635.7635.7635● 1435*1435● 1434● 4434● 4434s4436.0836.0836.0836.56-36.5636.56

Table3 COMPARISONOF EXPERIMENTALAND CALCULATEDBUBBLEPOINTFORMATION ;VOLUMEFACTORUSINGTWO METHODS

Reservoir BubblePointFormationVolumeFactorcalculatedfromBubblepoint —Sample Temperature oil density Correlation3- Density Experimental

(°F) (lb/ft3) (Bbl/STB) (Bbl/STB) ,(Bbl/STB)

1234567a7b8a8b9a9b9C10a10b10CllallbllClldllellf12a12b12C13a13b14a14b14C151617181920a20b20C21a21b21C22a22b22C23a23b23c24a24b24c25a25b25c

170196255275202233102102185185 -838383929292242242242242242242253253253170170175175175170240246248249150215280150215280150215280150215280150215280150215280

52.1042.8434.8835.4338.4144.3153.6853.6845● 0245.0253.4553.4553*4544.9444.9444.9442.1942.1942.1942.1942.1942.1945.0845.o#45.0851.7751.77*45● 00*45.00*45.0052.1%44.5035.3<36.5836.1?46.0!?44● 3(f42.4P41.81*40.14*38.4?38.1$35.8f34● 9946.61*44.9@43.27442.59*41.03*39●3fY39.68*38.09*36.47*

1.15991.40691.86901.6622“..72831.48021.04781.04621.3814 .1.23901●08601.08751.09031.29911.29521.30221.52701.40931.37921.38441.36551.36441.21781.21461.21651.12101.12191● 30001.30671.33201.14301.59801,94301.84201.91101.29021.32611.36101.72341.75981.79612.09962.13542.17011.27011.30571.34181.55551.59281.63011.8850‘1.92161.9582

1.15631.40601.89641.75871.70141.38641005991.05751.37501.26131.09581.09721.09961.31261.30931.31491.51651.42151.39681.40121.38481.38381.2441,1.24121.24311● 14451.14561.30321.30881.32991.14201.57551.93011.77061.84251.28731.33801..39531.62041.68781.76331.95962.0831 I2,13791.26941.31601.36741.49951.55651.6251?..76121.83471.9162

1.1561,4351.8791.753.-1.48281,0611.0641.3521.2761,10901.10861.11171.32571.32411.32581,4981●4451#4331.4421● 4001,3981.31311.27401.28531.1451● 1451.3381,3371.3381.1431.593--1.851.9011,2531,3081.3631.6311.7081.7621.9152.0112,1101.268i.31t31.3691.4471.5121,5831,7161,8071.913

.

m1-

4

i!%&

H

-1, = s●

ua841

0f-.

ml-i1-

u

.

LWAQ

I

.

*

Table5 NON-HYDROCARBONCONTENTOF CRUDE

OIL SAMPLES

Sample

7

12

16

17

18’

19

Mole*percent

co.

9.0

24,0

21,3

Mole*percentN.

16.5

7.0

6.0

4.0

4.0

L

5.0

57*O

6.o

2.0

Mole*percentHms

*Mole percentin separatorgases

.

1

i

.,.

,..

r

VAK)R

I. Ompoaition

2. lmze@T2

* 3. gruviQ/

4. gaa-dz lutio

S. ueight

LIWD

I 1. moles* )Plwpl

T 2* Canpoeitio?lsepl

1

AmFvoirFluid

..,.,.

VA~R

1. 0ci7Qmition

& mzem’m

3. grcrvity

4. ga8-oiz rutio

& ueight

Lravxo

1. moLe8bP8ep2

T 2. Cmpodtim8epz

t STOCKTANX...—~ S-e Sth

Stape

p-stage flash ...

output

STOCKTANK——VARM

1. Compom”tfon

2. moZee/STE

r3. fpvity

4. gae%liz Iutio

6. ueipht

.

c1STOCKTANK7ziiIr-

1.PSt

T 2.8*

3.

ITfO&8* Ild6?8/22’2

Cxmpodtti

gravity

2. reservoip f%dd cmpoaitioa

2. 17/OkUh we~ht cad dendty of C7+

3. Opti’o?luz: bubbze po$nt oil deti~

wd/oP re8e2uo$p temperature

1. total gasdz ratio,00R

2. aveqed gae titu, ~g

3. etouk’d oiZ gravit~, ‘API

4. optionaZ: babbZe point fomation

vozme fato~, Bob

(m methodd

.J ,

Fig. 1 Schematic diagram of separator flash program:

...

,,

( ?.. ,

‘,)

1,55

1150

,1“,45

1s40

1 Z7

lilo zoo

,,

COMPUTER FIASH

EXPERIMENTAL

EXPERIMENTAL

CCWWTER FLASH

COMPUTER FLASH

(EQ, 10)

(EQ, ID ll~i~ll, ;::

300

PRIMARY SEPARATOR pRESSu,RE~ PseP,l* psIG

4(XI

~7,0

5b,o

35,0

34,0

33.6

FIG~ 2 EFFECTOF PRIMARY SEPARATOR PRESSURE ON FORMATION VOLUME FACTOR AND STOCK TANK OIL GRAVITy.

1*

::

;:O*

?*

::

10s11*t2*13816915*10*17816*19X20*21822*2392b*25*

, 2092?*23*29w30931*32*33*3.9

If ’mlc!COMRONI

REAL 66“oxfwNsfOWSLEoouaLE

1 toRFMTc2 foR~Arc3 FORMAT(b FORMAT(S FOR!’!AT(

ftox*@**6 fORr4AT(7 FORMAT(8 FO~{4A?(9 FORMAT(10 FORMAT(fl Foi?f4AT(

Iloxb*do12 FORMAT(

“ !3 fO!MAT(16 fOR14A7(15 PORHATC16 fQRMAT(17 fORNAT(IS PO:MAT(19 fORMATC?S FORMAT(

l&OXelAP200 fORwhTc2ot FORMAT(

l12x*~no22x~laua

&& CORMA7C

.lLK1/ Sao~t*tR@~a~80acOP&s.eoasINZt12)ZXlC121CX2(12>OX3(?21#vl:121#Y2[1zJ#v3{12)oA(61IREC14[ON Kl(12)#K2c12)#K3Cl 2)IRECISXON RLleRL2eHL3#Mtl#flf2*Nf3#MVl #RV2#f4VS‘2$6.6)!f6.?),7))A4)‘0XC~6AsPROpERT1ESCt40X.~OIL PROPERTIEst/l**0**9*****l#&fJx# C**w**D********k) ,‘/20X#~aAsIs fOR CALC-1 B8L S~Oflll)10xt$~ANK GAS$.60X.~STO~)!xt*kast *t+x0;io02cboxttto.2)!X#$MOLES: tt2XCP10.SSAUX#F10C5)!%4:scFt ~*6x#flo*21~/lQx,100am##f~oms,2x, IRgs 8aLjsT0 aaL Ar aU8BLE POIMT~/mtCfto.202x8tscf/aaL STO~l!x’+$LRsj ~#6x0flo@3# sx*flu.s#30x#flo*s)!X#~MOLESt;*2xzFt0.3~ 5XOF10~SeSOX#F10.310x#tTAN14 GASICtOXOIH.P. GAsI#30x01sToI)OX#~TANK GAS~CIOX*tSECOSEPO 6AS~#fOX#t14.P. GAS~zZOXtISTO~)

!x#lscF\ t@&x*flo93# sxs#lo@3#sox#fle.3)!X#*L6S 10,2X,F1O.34 sx*flo.3*lox*fto.3#20x#flom3)!X~~mOLESl tP2X,f10030 sbf o.3~lox@flo.3@20xOfto.3)!x#tscFl#6x#Flo.3# sx#flu.3#lox0#lo.3# 2ox#rlo0s),ox,tspEctplc GRAVITY of ocL8!,p6.~1

GRAVITY 0? OtL= lcfs.2)

‘/?//2Xt~S&cXFtC GRAVt?Y 0; c7*tc#F10c5)ECULAR WE[t3HT Of C7+t$tf10,3/ILE POINT 06NSITY Of OIL :l#f10.3#2X$kES/CUalc ft.]‘H+l

30* 71 fORMATt)l10/l~ATQTAL SUZ.E.A&LGAS GRAVITY=$.f10.5)

73 fORHhT(//lOXt~CORRELATXON CALC a08 s$~FIO,Sc~RES BBLIS78*)aEAo(s,?o) ~RREAO(S,3)NANTDo 6oJ8?et4ANTRgAo(s#200)s#a#R~gAB(s,~)AREAO(S/l)ZREAo(s#3)NRRgAo~5,2)y,pN81CALL KV(T#P.Kl)CALC XVCK1.Z#Xl#Yl .Vl,SLf~SZl#SXl #SYl)CALL GCCY1.6G~l#O)CALL LIST(N#Kl*z.XlbYt#P#t#SLl oVl*GGR1.SZl~SXl#SYl#A)SPCt4R_l)21,20~21

20 CONT!NUEQR!Tic6;A6}CALL OENS (X1.Vl*SLl#SA~NLl#UOl*VGl ●uGltnvl#GGRl#R$l)WRITE(6~5}HRk14URbRUR

%APnRURGG

IG1}1.5/S60:131;S:602S1 SGO#APl~(wtl) 80a#GORt Gcal

?Q. aooS=ALoGIO(CCGGRT/sGO)**o,s26) ●GOR*?.986WTR)

72u aoac.qo.ow0(04,s8sl*2,97350aoes-o.27b8.ceons**2.ol ) ● 1.0

I,,

..

105*

1J7*

la9*110=111*IT2*113*116*115*ltb*Tf?*11s=119*123*121=122*123*12**12s=129*l~?m12a*129*13ii*131=1s2-133*13.913S*1s0=JJ7W138*139*1629161*

21

22

riR17E(6c73) EOSCGO?O 50CONTINUEREAo(5,2)T,pivai?CALL KVC7#PJK2)CALL XY(K2*X1.x2*Y2#V2*5L2#S22# 5X2@5~2~SL28SL2*SL1v~8v20SLlCALL GG(Y2aGGR2#O)CALL &S S?(N#K2~Xl.X2*Y2#P#t.SL2eV2dG6R2#sZ2#Sx2#SY2#A)tP(NR-2)22# e22CALL ogNS tX2#V2.SL2~S.QdML2#U02#VG2#uG2#RV2#GGh2#HF21tivVGUCU8URSR

;:URURBOGoAPURURGGUR

iMr2*vlmHVlmS79.bmMvl*GGRl*2t!.977E(at4+)

Tgt4#s):TE(6#6):TEC6~16)‘TE(6412) dG2#HGl#Ho2:TEC6C13) MV2#nVlfillL2,TCt6#16) VG2#VGlls(u02*wGz+uGl)/(R*S.61658S)18vGfwG2

=141.5/SG0:131.S7E(6.2S) SGO#API

TEf6.tl) B08cGORIT 8 (GGRf*vGl+GGR2.vG2)/GoR:TE{68?1) GGRt

BOBS=ALOG~O(C(GGRT/SGO) ●*Q.S2e)*GOR+o.98b*TR)

BOOC*lO,O=*(-0eS8sl*2.91 3S*80ES-O.276$*(BOBS**2.0) ) + 1.0

ldR17g(6~73) S08CGOTO SOCONTINUEREAo(SC2)T#P!@CALL KV(T,P,K3)CALL xY(K3#x2#X3.Y3#v3.SL3#sZ3e5xS#SY3)SLs8SL3*SL2v3mv3.5L2CALL GG(Y3#GGR3#Q)uRlTE(6#4&)CALL LlSt(t4,K3,X2,X3,YS#P~T,SL3,V3.G6R3#sZ3eSX3#SVs.A)CALL BEN’S (x3.V3.SL3,S.Q,ML3#U03#VG3#bG3#MV3,GGR$.?tF3)MvzsMF3*v2VG2SIIW2*379.L~G2sMV2WGGR2*28,92Mv18(fl$3svl)vG18mvl*379.&IJGI=uv1wGGR1*28.92aRITE(ot6L)

*R1TE(6#5)4RxTE(6#o)MRlT&c6#15)bR!TE(6~17) MGS#UG2#UGl#U03uR1TE(6#lS) MV3CMV2#HVlZML3tialTE(6#19) VG3CVG2CVG180B=(NOS*uG3*UG2+uG7)/(R*S .616505)Ga~8vGl+vG2*vGsAPlat41.s/sGoi131;sHRlTE(6~2s) SGO#AP!UR!TE(6#ll) BOB#GORGGRT o (GGRt*vG1.GGR2*vG2+GGa3 ●’:G3)/60RdRtTE(6z71) GGRT

SO~S=ALQGt,QCftGGRt/SGU) ●*0.s20)*GOR+0,986~?R)

&!08C~10.0**(~e,3851*2.91 3s*e09S-O.2?~8*(Bo8S**2mO) ) ● 1s0

URITE(O~73) aosc50 CONTINUE

dRlTE(6zZOl)$C40R60 CONT:NUE

ENO

.. -.0

I &*

Q.

?00102

103

106

36

t0s

200

210

250

260

.

. .

SUBRWTXNE XYCK#ZtX*YtU#SL#SZ*SX#SY)~HPL1cIT RgALo8(A-rl#o-z)

00U8LE PRIZCISION K(12)oXfIIENs:ON z(12)#X(12)#Yf12)SZ9QOQSx=o.oSY=O.OVSZ(1)+ZC2)+ZC3)00 100 1=1412sz8sz*z{~)cONTINUgcONTINUEslml~o.oSUI’4280,000 10s 1sl#12sun?~sufllo cz(ll*(Kcx)-1.o))/(v*(K( I)-1,O)*1OO}SUH28SLM2+ tc(K([)-1.o)9*2*o)92cI)) /(cc~(!)-loo2*w*l*Q~9*2*oJRatloSSU?Itl$UN2IF~ABSCRATIO)OLE.O.oOOOUOOl ) GOTO 106V s V + RAT;O:co?iTs1(oNT*tlFCICONT.GE,SO) GOTO 1056070 102

CJ27’

CON?XNUgX’f(v ●GT. I*O ●We v ,LT.d.o~ Go To ~fJQ00 Sk 1=1012X(f)d(I)/(1-V+V*K(~))Y(;)SXCX)9KCI)Sxs$x+xfl]sy8sy+y(:JSLDI,O-Vm:~:uE

lffV .67. 1.0] GO TO 250v = 0,0sL m 1.0Sx = 1*Q00 2fo 2=1412x(:) ● z(:)Y(t) D O.(jcoNfINuEREfugN

v = 1.0SL m 0.0Sv ● 1.0bo 260 I 8 f*12Y(x) 8 Zcl)X(I) ● Oeo:;;;::UE

gNo “

Subroutine KVCTtP:KJXHpLICXT RllAL*6(AoM#O&z)Oou8LE PREC;SION KCIZ)A81.2*{*.SEW4)*P*(1S.E-81 :POPC~o.dS96:(l .?E-6)*P-C3.$G-8~*P*PK(l)810.o**(&*c*t300.oJ96.00300.o/T) )/Ps(z)810.0**(A+C*(lf6S.0f303.O-l T45*OIT))IPK(S)*70.O.*<A+C*(1799.O/b16,0-t799,01?) )iPK;~)=10.0*9;A*C*C2037,0t4?l .O-2037.OIT)jlP&[5)*10.0**(A+C*(2153.O/491 ,0-21S3.OtT))tPK(6)s10.0**(A+C*(2368,U/5&2.O-2368.OIT) )IPK(?)s10.0**(A*C*C268Q.O/$S?*O-2680,0/T) )/PK(a)m10.0..(AOCW(i?aOPO/616.0-2?80.0/T) )/PK(9)810.o*9(A+c*(3068.o/669.o-3ooa.ofT) )*o*t5/PKCIQ)*10.0*.(A+<:i652,01?9&.o-6s2.olT) )/PlCc?f)=lo.o**(A*c*(471j.Qflo9.09470,01t) jfPK(:2}810.0s*CA*C*:?136.0133t .O-11S6,01T))IPENO

.=

,---... ,

SU9HOUTINE &lST(Nf&oZ{X#V.P#rdSL#V#GGR#SZOSX#SV #&lIMPLICZT RgAL*6(A-N#o-Z).D;MENstON A(lD)# 2(12)0x(!2)#Y(12)$OU!3LE pRECtSIoN ‘[(12)PORMAT(aA4)FORMAf(ltit)#oWl&t(l/)PORMAT(12X~21HfLASH CALCULATIONS - ●4h6)FO~#lAt(/#5X#7HsT&GE ,Il#sXe4H~ s cf601~Sn PSIA#hX~MT ● ●fS.l*6H

loEfJ f)o f(L%FIATC/#18XAIL m *F7.5*8XAHV ● #F705#6X#6H13GR ● sf7c4)? foRRAT(//#39x#kHFEEo*llx*6HLiQutB*9x*snvAPoR)8 foRMAT(SX.9HCOflPONENT#loX#lHK# 12X#9HnOL fRACT#6X*9HR0L FRACT#6X.9H

31

foRmhTFORMATFORHATFOffMATFORMATfoRHATFORMATFORMATFORMATFoRMATFoRfjATT8T-&a

lrfoL FRACT)9 tORRAt(/*9X.4H Cl ,8xcF7.3*tOX4C7.5#aX~f7.S#&XoF?.5>

10 FORHAT(9K,4H C2 ,8x~F7.3~10xo$7.S#UX#f7.S.8XOF7.S)11 FORMAT{9X,6H g3 ,ax#F?.3010x.F7,5#8x#f7.5~axcF7.S)1213lb151617f6

;:2122

:9x.4tiIc6 ;8x~f7.3#10xeF7.5~Sx~F7.S.8X#f7.S):9x#bHNc4 ●ax#f7.S#10x*F7.508X#F7.5~8Xe f7.S):9xc4H1c5 .8xcf7,3c10x#f7.5c8x~f7.St8XCr7.S )‘9x#4HNC5 .8x#r7.3#10x#F7.S.6X~F705#8X0F7.S ):9XC6H C6 csx#F7.3c10x#F7,SZ8X~F70SC8X#F7. 5):9X*6H c7+.8x#F7.3~10x*F?.S.8X#F7.S.8X#$7mS):9xc6HC02 CUx/F7.3S10x,f7,5C8X*F7.SOSxCf?.S ):9%,6H N2 ,7X#f8.3.10X#F7,5,8Kef7.5#dX#F7.5):9X.4HH2S .~gX#F7,3*10~f~7TS#8X~f7,S08~*r7.S):38x#?H-------.#8x#7H-------#8x#7H---w---):38x~F7.S#8x.f7.S#8X#~7.s)I.a

IF (N-t) e3f032uR:TE(6a2)‘dR1TE(6#4)AGo To 33WR1TE(643)uR!7Etoos)N#p#TuRITE(606)sL#w4GGRuff1TE(6#?)HRi?E(688)uRtTE(6#9)Ktl)#z(l )?x (l)sYtl)HR1TE{6*10JK(2) szc2)cx(2) ●Y(2)MRtTEt6*l~)UC3).ZC3)*Xt3) tY(3)HR1TE(6t12JK(4) #Zf6)#X(6) #?(k)IdRXTE(6C13)K(S)#Z(S)#XCs) ●VC5)URlTEC6,1b)g(d) tZ(6)tx(o) ●Y(6)diIXTE(6#lS)K(7)#Z(7)#XC7) ,Y(7)URlTEC6#16)KCa) #2C8)#X(a)#Vt8)uR1TE(6~17JK(9)~ZC9)~X(9) ●Y(9)llJR1T8(6#18)K(lol#z(lo)#x(lo) 4Y{1O)nRtTEC6#19)K(ll I#Z(tf )~Xfll}Cy(tl)uRXTE(6,20)KC12)#Z(12}#XC12) #Y{12)

suflQOuTIN& GG(C.GGR#9)lhpLtCIT REAL*8(A:H#O:Z)OIMENS:ON C(12)GG~=(f6,0&@CCl)*30.07*C (2)*6A.09*C(3)*S8,12*CC6) ●S8,12*C(S)*72.f5*

IC(6)*?2.IS*C(7)*SQ.!7*C (?)* a*cc9)+6&,01*c{10)*28.02*c (11}*3~0028+CC12))?28.97

EMB

SUOQOUTINE OENS (x#v#SL#S~Q*HL#Uo*VG~UG~RV*GGRoNFjIMOLI(:T qEAL.a(~&##oOz)COHPONIBLU?I sGO

a--

OOIJ8LE PQECISION MLKVOsML,MF#MVOIMENS:ON X(12)MLKvOS16.(16*X(1)+30*IY7*X (2)+46.09*Xes)@S.l 2*x(6}*58.12*xfS)*72, 1$

1.X(6)+72.ls*X(7)+86.17.X Ca)*Q*X(9)*&k.ol*XClo) ●2a.02*X(ll)*36.02J2*X(1,2)

SGOW’lLKVOttt6,0L*X(f>/O.3~S0.07*X (2)/O.38+66,09+x(3)/O.S072l~58,12*xck) 10.S62S*s8, 12*x(S)/O.Sa36*72.?S*x(6) /0.62blb72.lS*X(7)2/.63OS*86.l7*x(8)/.6637+Q*x(Q) 1s)

uo8qGoosso.R~S~ojuL~~(j‘!f8M~/sLPIVSWS*VvG911v.37QC&

“w*Mv*GGR*28.97ENO

-4

—.-— ....— ..—~---------- . . .. . . - — ----------- . .. --—-- .-. — .—..-. .. . . . ---- i. .. .’

FINAL OUTPUT (SAMPLE ha)

LBS :

MOLES :

SCF:

GAS PROPERTIES● ***********9*

BASIS FOR CALC - 1 B8L STO

TANK GAS H.P. GAS

.000 61.163

.000 2.158

.000 818. s60

OIL PROPERTIES

***mm****e***m

STO298.067

1.520

SPECIFICGRAVITYOF OIL = .8516

API GRAVITY OF OIL = 34.65

.SOB = 1.51651RES 8BL/STOBBL’AT BU8BLE PoINTWR .818.560 scF/BSLsTo

TOTLL, SURFACEGAS GRAVITY = 0.7986

CORRELATIONCALC BOB = 1.S207aL/STB

●

#

.-. ..* >,’7-,

APPENDIXB

Equilibrium.calculationsmake use of Kvalues (asdiscussedpreviously),

fluid compositionand an initialassumptionof 1 mole reservoirfluid.

The followingequationsare used to determinevaporand liquidproperties

at each sta’geof separation:

Lj+Vj=L. J-1

e

(B.1)

& . .

f L. +lV,K, = 1.0000J JA

(B.2)

where

zL

v

ji

K

mole fractionof

mole fractionof

mole fractionof

any componentin the system

liquidat equilibrium

vapor at equilibrium

stageof separationwhere j = 1, 2* •...~n

component

equilibriumconstantfor component= Yx

STOCKTANK OIL GRAVITY

x (Xi)sto ● NJ!i●

Y=Sto ; (Xi)gtoo g~

ii

where

(B.3)

x = mole fractionof any componentin the liquid

M = molecularweight

V = specificvolume,ccfgm

sto = stocktankoil (nth)stage

MOMS .OF VAPORPER.STOCKTANK BARREL

i

iI

i

At each stageof separation,the numberof molesof vapor,N ●

.sj’ascalculatedon a basisof one barrelstocktankoil. At stagej,

i.350 “ Y8to

N .“ ,l-A%)= (L.-8J k-l x (xi)8to. M.

i z

(B.4)

GAs GRAVITY

me gas gravityat stagej, y8j, (air=l)iS givenby

~y.. .M.i lJ 1

——— .‘sj = ~

air

where

y = mole fractionof any componentin thevaporphase. .

GAS OIL RATZO

At each stage j of

SCF/STBis

separation,the gas-oilratio, GORj,~iven in

WRj = 379.4 Nd “

(B.5)

.

(B.6)

The totalgas-oil ratio,GOR, is just the sum of all stagesj=l, 2 . . . . n

.

AVERAGEDGAS ~VITY

The gravityof all gases,Yg, recombinedfromeach stage,is a volumetri-

callyweightedaverage

~ GORj 0 yj=1 gj

Yg =GOR

,...

WEIGHTOF VAPORAND LIQUID

(B.8)

At each stagej, the weightof vapor (gas)Wgj$ in Ibs is calculated

on a basisof one barrelstocktankoil:

350 ●Ys to

z (x.Jsto g Mi.w. = 28.96 “gl L (Lj-l-Lj)*y

Sto gj(B.9)

and theweightof the one barrelstocktankoil, W8to,in lbs is

wStd = 350 “ ySto (B.’LO)