,.

Predicting Phase Behavior of

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Condensate/Crude-Oil Systems Using MethaneInteraction CoefficientsD. L. Katz, SP&AIME, U. of MichiganA. Fuoozabadi, AbadanInstituteof Technology

IntroductionPrediction of phase behavior of complex hydrocarbonsystems has improved gradually. Recent papets usingequations of state for predicting phase fugacities of con-stituents have extended their usefulnessto higher boilingcompmenfs .1-5Using extended analysis with boilingpoints of higher boiling hydrocarbon groups and theirdensities and molecular weights provides a basis forimprovement when predicting phase behavior. At thehigh pressureof reservoir condkions, properties of theseCd+groupsare impor~t.

Using the Peng-Robutson5equation of state has theadvantageof improvingaccuracywhencalculatingliquiddensity. When used by Bergman et af.46with extendedgas analyses, the equation gave good prediction of dewpoints and liquid yield at pipelineconditions. Bergmanetal, used interaction coefficients but did not completelyexplore their usage since phase behavior of condensatesat pipeline conditions appeared rather insensitive to theCo+interactioncoefficients.

This paper reports the extension of the Peng-Robinson-AGA procedure for phase prediction of con-densates and natuml-gas/crude-oil systems at reservoirwnditions. New interaction coefficients were foundnecessary for methane and Ce+constituents (especiallythe highest boiling group, such as Cm+)so that experi-mental behavior could be matched by prediction. Stepsfor developing interaction parameters are presented.Then, agreementbetween measuredand predictedphase0148-21%/78/001 1-6721$0025@197880ciety o!Pemleum Enghews OfAME

behavior up to pressures of 64121 kpa (9,300 psia) isshown for several crude oil and condensate systems.

Calculations of Phase BehaviorThe equationof state, using the relationshipof fugacity topartial molal volumes, is used to compute the fugacityofeach component !n both liquid and gaseous phases. Atequilibrium the fugacity of each component in liquidequals its fugacity in the gaseous state.

Basic parameters for each constituent are the criticalproperties, normal boiling point or vapor pressure. Forhextme and heavier groups present in natural-gas andcrudeoil systems, average normal boiling point, liquiddensity, and molecular weight are used7instead of mea-suredproperties available for pure components.

For systemscontaining variousmolecularfamilies, theinteractioncoefficients between the primary constituentsmust be includedto accountfor the degreeof compatibil-ity. Here methane and higher boiling C6+groups are theprincipal components for which interaction coefficientsappear sigtilcant.

Sincepropertiesof Cd+groupsin crudeoil and ccmden-sates are neededhere, generalizedproperties are given inthe absenceof measured values.

Properties of Hexanes and Heavier GroupsAverage boiling @nts, liquid densities, and molecularweights were reported by Bergman et al, 8 from C6through C15,based on analysis of 26 condensates andnaturallyrecurring liquidhydrocarbons.This correlation

IThispaper extends the Peng-Robinson-AGA procedure forcomputingphase behavior to includegas-coruknsate and crude-oil systems at reservoir conditions. Irnwaction coeficientsfiomwethane to the C6+groups were correlated with liquid density. With these coefficients, thebehavior of gas condimsate systems maybe predicted reliably.

NOVEMBER, 1978 1649

. .

I t0.s ..-. J=-.

procedure. Accordingly, interaction coefficients formethane binaries were compiled based on bubble pointsalongwithdescriptivepropertiesthat mightallow a corre-lation related to knownpropertiesof the C8+groups. Theinteractioncoefficientsobtained are the values fhatgaveminimum error for the bubble point for the range oftemperatm and pressure indicated in Table 2, using datafrom Refs. 12through 20.

The use of liquid density at 15.5C (60F) for thebinary component in the methane binary gave a cor-relation of the interaction coefficients for these systems(Fig. 3).

Interactioncoefficientsfornonhydrocarbom usedhereare0.12 for nitrogenhydrocarbons,2021and0.1SforC02hydrocarbons.8 Ethane and propane intel actioncoefficient were considered with other hydrocmbons.Because of the variation found with temperatun! andpressure, and the relativelysmall influenceon thepredic-tions, the value of 0,01 used in the Peng-Robinson-AGAprocedure was continued. The interaction coefficientsbetween nitihane and ethane through n-pentane werezero. Later, the significance of the interaction coeffl-cients for methane and the last composite group, such asCm+,will be discussed.

Natural-Gas Condensate SystemsThe natural-gascondensatesystem used whencomparingexperimentaldata withcalculatedvaluesis listed in Table3. The measured dew-point pressure at stated tempera-tures, the liquid yieldwhen flashed at given temperaturesand pressures, and the corresponding equilibrium ratiosare used to give three methods for comparison. For eachsystem, the extended analysis was available. The predic-tions for the condensates were based on the interactioncoefficientsof Fig. 3, which is correlated on liquid den-sity of the hydrocarbon groups as developed here. Fornatural-gas condensates, none of the experimental databeing compared were used to generate the calculationprocedure. Each comparisonwill be discussed in turn.

I 1 I 1 I I I 1 I005

10.60 070 a90

OENSITY AT 15.5~ghnfLo

fl . 3lnteractbn coefficient from methaneto otherr?hy rocarbonsas a functbn of the densityof the iwavler

hydrocarbon,

Hoffman et al. 8Lean-Gas CondensateHoffman et al.s data on the gas-cap material at thereservoir temperature of 93,9C (201F) are the mostcomplete because true boiling-point distillations withdensities and molecularweights were determinedon cutecorresponding to n-paraffins up to C22. The analysisgiven and the densities and molecular weights for eachcut wereused to predict(1) dew-pointpressure,(2) liquidyield as a function of pressure down to 3551 kFa (515psia), and (3) vapor-liquid equilibrium ratios all at93,90C, Table 4 compares experimental data, predictedvalues in this study, and, published predictions byStarling.i Fig. 4 compares equilibrium ratios. The dew-point pressure and liquid-yiekiprpdictions are excellent,end predicted equilibrium ratibs for methane have anaverageabsolute error of 0.76% with experimentaldata.

Starlingl Rkh-Gas Condensate (Fluid B)Starling reported the analysis on a rich-gas condensate

TABLE 2INTERACTIONCOEFFICIENTSFOR BINARY METHANE/HYDROCAftBON SYSTEMSBoning D&y Pressure Temperature

Heavier Intereotbn Point Moiecuiar Range RangeComwnent Coeffwnt (c) 1S,6C) Weight (kPa) (=c) Ref.

nC4 0.02 -0.50 0.584 58.12 4100to12400 71.1,87.8,104.4,121.1 12nC8 0.02 38.07 0.6312 72.15 4100to16100 71.1,104,4,137.8 12nCa 0.025 68,74 0.6F40 86.18 4050to 16200 75,100,150 13G 0.025 88.43 0.5882 100.20 4100t020800 71.1,104.4,137.8 14nc, 0.036 126.86 0.7068 114.23 4050to 7080 75,100,150 15rlc* 0.035 150.80 0.7217 128.26 4050 to 30400 75,100,160 16nClo 0.035 174.12 0.7341 142.28 4100to 32750 71.1,104.4,137.8 12a 0.054 343,8 0.795 282.57 500to 8050 40 17

E??nzene 0.08 80.03 0.6s44 78.11 9970to 24200 37.8,71.1,104.4 18,19Cycbhexerw 0.03 80.72 0.7834 84.16 4100t024 100 71,1,104.4,137.8 20

TABW=~wwNm~/CRUM~LSwTUSUwDIN COMPARlSt3NSOFEXPERlMENTALWl~PREDfCTEDBEHAVtOR

TemperatureRange PressureRangeAuthors System ~c) ~F) (kPa x 10+) (paia)

Hoffman,etal.s Condensate,crudeStarting!

83.8B 201 26.43 to 3.55 3,842to 616C&%eate 10JIJ glJ 214,250

Rohrl&J26.16 to 3.55

crude on3,705to 515

.,. 120,200 7.22 to 64.63 1,047to 9,374stalKwJf and

crude Ofl 48.88,121.11 120,250 6.26 to 38.13 1,010to 6,530Katzend

l+aohmut~ Crude oil 03.33 200 0.813to 16.54 118to2,333Evarmand Harriet Crudeo!i 87.78 1s0 7.65 to 41.37 l,l10t06,000

NOVEMBER, 1978 16S1

TABLE4-COMPARISON OF PREDICTEt)WtTH EXPERIMENTAL DATA FOR GAS-OAPCDMP~lllm OFHOFFMAN ot8L@AT 36.9%

Ltquki Ylsld*Pressure Expsrtmental This work

(kP@Starlingl

(pals) (rrrVmxlOe) (bbVMMsof) (rnVmaxlOo) (trbl/MMsef) (n$/mxlO$) (bbl/MMaef)

20098 2,915 51,02 9.07 64.6017340 2,516

Q.6069.97

63.66 11.312.44 70.26 12.49 77.62 13.8

13633 2,016 67,52 15.56 84.40 15.02 90.66 160119446 1,515 95.51 16,08 92.878998

16,511,015 95.29

96.4416,94

17.6

355104,50

515 84.8216.60

15.0897.31 17.3

88.00 15.25 83.81 14.0Experimentaldew-poht pressureis36430 kPa(3,642psia),Predicteddew pokrtforthis studyis26682 kPa (3,670pale),Starllngt>35267 kPa (6,116psia).Averageabsolutedeviationbetweenexperimentalandpradictsdylsldsforthisstudy 1s2.6%,and8,2%forStarling.Llquldbulunwal raprtad pmawe andtempaa!urw oaa standardcrx@kmafor nwtrk unkaare 15Cand 101.326 kPa.

with extended analysis to Cm, but did not include liquiddensities and molecular weights for the groups. Hisanalysis with generalized liquid densities and moleeularweights of Table 1were used with the interactioncoeftl-cienta in Fig. 3. Dew-point measurements at temperat-ures of 101.1*C am 121.1C (214F and 25(PF) arewmpaiwd with predictions along with liquid yields atthese temperatures in Table 5. The method in this studyshowed no improvement when predicting dew-pointpressure, but a modest improvement when predictingliquid yieId, Note that the Starling method involved re-

PRESSLJRE, Psio

0-kJ5L=--(R& ~to)c \ IPrsdktsd:1.0 C3l[j

-c{a

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,01 %==+++Em-. ; /:

..,L-Ju&JJ1ooo 40,000

PRESSURE;kpoFig. 4Comparisonof prediotedwith experimentalK valuesof

Hoffmanetal,condensateat 93.WC(201F),1652

gression analysis on measured equilibrium ratios to de-termine parameters for the common Bendict-Webb-Rubm equation of state and then predictions were madeon the same systems.

Crude-OiUNatural-GasSystemsDataavailableforcrude-oil/natum!-gassystemsare listedin Table 3. Before making phase calculations, extendedanalyseshad to be preparedfor some systemsby convert-ing distillations to individual hydrocarbon groups us-ing the generalized properties in Table 1. Density andmolecular weight of the last fraction were adjustedto provide an over-all match of reported density andmolecularweight of the ~+ fmction.

Pteliminaq trials when predicting the behavior ofcrude-oilhatural-gas systems indicated that the interac-tion coefficient relationship with density did not givesatisfactoryresults whenextendedto the last fraction. Weknew that asphrdticand high-boiling constituents occur-ring in the last fntction, such as C20+,were not likelyto have a continuous volatility behavior when measuredin terms of liquid density. In the work of RokmdzqandStanding and Katz?$the downward curvature of thevapor-liquid equilibrium ratios with increased pressurewas unexpected. At that time, the explanation was thatconcentrationof the high-boiling and asphaltic fractionsin the liquid state by retrograde vaporizationof the inter-mediate constituents was responsible for the behavioqequilibriumcell contents were approachingdew points atincreasedpressure. One might, therefore, expeet to havea discontinuity in the interaction-coefficient/densityfunction as the last constituent is reached. Accordingly,tineinteraction coefficient for the last group was deter-mined from even a single reliable point (a bubble point,for example)because its use for predicting equilibria forother conditions is shown to be reliable.

Hoffman et aLs Crude-Oil SystemData are composed of composition of the equilibriumliquid and gas phases at93.!PC(201F)and26455 kPa(3,837 psia)at reservoirconditions. The interactioncoef-ficient of the last group, Cm+, is computed using thebubblepoint pressure of the liquid of 0.17. Using this -value, the gas-condensatecomposition calculatedas partof the bubblqxint computation is compared with themeasuredcomposition of the gas-cap fluid in Table 6.

Roland23Natural-GatdCrude-OilSystemBased on the distillation curve, density and molecular

JOURNALOFPETROLEUMT2CHNOU)OY

,TABLE 5-COMPARISON OF PREDtCTED WtTH EXPERIMENTAL DATA FOR STARLING CONDENSATE ATTEMPERATURES OF 101.1and 121.lC (214mMf28(FC)

LiquidYieldPressure Temperature Experimental Thiework Starling

(kPa) (peia) (%) (rn/m3xl&) (bbl/MMsof) (m/mxl&) (bbi/MMeof) (m/m$x109 (bbl/MMsof)G 2,015 101.1 880.2 166.5 823.60 148.4 1058.9 187.910445 1,515 101.1 677.5 156.0 780.7 136.8 390.0 178.06928 1,015 101.1 822.9 145.3 706.5 125.8 872.4 165.13661 515 101.1 848.8 115,3 576.0 102.4 872.4 119.713893 2,016 121.1 672.2 119.5 6S0.2 122.7 830.8 147.78722 1,265 121.1 711.0 126,4 633.9 112.7 755.4 134.3

Oew-PointTemperature Measured(kPa) This Study(kPa) Starling(kPa)101,1C (214F) 26156 (3,795psla) 26641 24 235to25614121.lC (250F) 24235 (3,515 P$ia) 25788 23 548to24235

Lk@dKIkmraal rermrtedmeawre andterrrpwature,andgassrandardcmritbmsfw metricunts are 15C ard 101.326 kPa. Avers@ absolutedetia!bn kmthh studyla9.4/.wit 12.1/0forStarting.

weight of the C7+residue, and the generalizedpropertiesin Table 1, an extendedanalysis up to the ~u+ group wasconducted for the crude oil of constant composite com-position of Roland.m

The interaction coefficient for methane through C=+was computed by adjusting methane K values for the24587-kPa (3,566 psia) and 38480-kPa (5,581 psia)runs at 1200F.Tne equilibrium ratios of all other runs ofconstant composition then were computed. FYedictedequilibrium ratios at 93.3C (2WF) are compared withexperimentaldata in Flg. 5. The averageabsolute devia-tion of 14runs at 93.3C(200F)for methaneK values is2.30%. However, if the K value of the runat54917 kPa

PRESSURE, psio200 500 1000 3000 10,000

10.0 i

F111111 t 1I1

-i bc1 Ii

.D Experimen?ol- Colculoted

I .0 1______.;; -7 -,~.

o JC4

x

f

I ~:g C5a ,1:01, .7,

1.

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(7,965 psia), which seems to be in some e~or~ is ex-cluded, the absolute deviation will improve to 1.68%.Furthermore, for 13 runs of 48.9C (120F)and 93.3C(2WF) and below 46471 kPa (6,740 psia). absolutedeviation for methane equilibrium ratios is only 0.83%.MethaneK values and componentsthroughCc+(Table7)indicate excellent agreement between predicted andmeasuredvalues.

Stsnding and Katz24Natural-Gas/Crude-OilSystemSix runs were selected fmm Standing and Katz data.These runs belong to 49,9API crude oil with a GOR of650 mVm3 (3,660 scf/bbl) at 48 .9C (120F) and121.1C(250F). Standing28gives extended analysis forcrude oil with cut intervals of 37.8C (100F), and alsodata for molecular weight and density of high-boilingconstituents vs boiling point.

The interaction coefficient between methane and thelast group, with boiling points starting at 371. lC(7000F),was obtained by using the methaneK values fortwo runs at 121.1C (250F) w~thpressures of 21960kPa (3,185 psia) and 29715 kPa (4,310 psia). Fig. 6comparespredicted with experimentalK values for threeruns at 48.9C (120F).The proposedpweedure is capa-ble of predicting downward curvature of ethane throughheptane plus K values at high pressures, Deviationof theK values is given in Table 7.

Katz and Hachmuth25Crude-Oil/Natural-Gas System

~ 0.1 ~

-.)--C61

,TABLE 7AVERAGE ASSOLUTE PERCENTAGE DEVIATtON FOR METHANE TNROUGHC,+ K VALUES FOR C13UDE-OILSYSTEMS

Component Roland= Standingand Katz Katzand HachmuthZO Evansand Harrk$c, 2.4* 2.2c, 3.0 4.8G 3.4 8.1c, &oc, 4.3 1::cc 8.7 13.6c,+ 1Q.8 18.9

Equilibriacompared 20 8

lAverageabaolutadetiatbns aapefoemtofexpadnmntalva!uva

crude-oil/natural-gas system, the smoothness of themeasuredK values indicates that the compositecomposi-tion change is negligible. Based on this assumption, onecan compute the composite composition in the cell.Vapor- and liquid-phase compositions of the run at12024 kPa (1,744 psia) and 93.3C (20(YF)were se-lectedto compute thecompositecomposition. Liquidandvapor phasesof this run were combined as 2 mol gas and1mol liquid, Extended analysis was conducted the sameway as for Roland crude oil. The interaction coefficientfor methaneand the last fxaction(i.e., ~s+) wasobtainedby matching predicted vaporizatitxr to equal 66,67%,With this value of interaction coefficient;,K values werepredicted for other rur at 93.3C (200F).Table7indi-cates that predicted values agree well with experimentalmeasurements.

PRESSURE,psia10.0t 1,000 t

c,

\Lo c, -b

:7

1,,x

y

c30g 15a C4~~ 01m tCCJ -~3g i:

ce

0.01-H-c~

KJo

1 I o u Experiment! Predicted 1o.cq,&_wJL J

I Io.000 [00.000PRESSURE,kf%

Fig. 6CamparLsonof redictedwith expermentelK valuesforE650-ma/m(3,680scf/b 1)gaa-to~il ratioof Standingand Katzz

crude oil at48,9W(120F).

2.32.33.6

F310.133.5,

7

289.66.8

10,313.113.937.2

10

Evans and HarrisgCrude-Oil/Natural-Gas SystemExtended analysis for the crude oil was conducted for upto CM+;the intemctioncoefficientbetween this last fmc-tion and methane was obtained by adjusting methane Kvalues for runs of Mixture B. Fig. 7 compares predictedwith experimental K values for constituents of MixtureA, and Table 7 shows percentagedeviations,

General ComparisonTable 8 assembles the interaction coefficient betweenmethane and the last group for crude oils, accompaniedby properties of the last fraction. All extended analysis,except for Hoffman et af, crude oil, did not have trueboiling-point distillaticm analyses. Extended analyseswere improvised using judgment and generalized ex-

PRESSURE,psio10.0. 1,000 2,000 10,0001

IIo 0 Experimentoi

.p

Predic1

,.0 c%di

0.1

~y--~6/ I..._ 0 T.___+I Cy ~

\d

1

I

i

1

1

--

--.

o.(),~100,000

PRESSURE,kPoR . 7Ccmparlsonof radictedwith experimentalK vaiueafor

$lixtureAcrudeoilo~EvansandHarrisO at87.6C(1900F).JOURNALOF PETROLEUMTECHNOLOGY1654

.TABLE O-INTERACTION COEFFtOtENTSBETWEENMETHANEAND MSTFRACTIONOPCRUDE=OILSYSIEM8

Last FraotlonInteractbn Density,at 15J5C

Fr~@&rMolsoular

CrudeOil Coefficient (g/ml) mHoflmanetal.s G+ 0.17 0.202 361Rolan& Go+ 0.17 0.028 , 492standngandKatz* Css+ 0.25 1.008KatzandHaohmutffs ox!+ 0.20 0.930 %EvansandHarrbs %8+ 0.25 0.914 342

tendedhexaneplus its propetiies. Therefore, any correla-tion of methane with the last groups interaction coeffi-cient should wait for more data with systems, includingtrue boiling-point analyses.

RecommendationWhen obtaining composition data for crude-oil reser-voirs, bubble-point presswe customarily is obtained atthe reservoir temperature on a bottom-hole or recom-bined sample. The composition with extended analysesto GO+or more, using a tme boiiing distillation alongwith bubble point, Peng-Robinson-AGAprocedure, andour proposed technique (including properties of thegroups, if necessary)can be used to assess the interactioncoefficientfor methaneand the last fiaction.The interac-tion coefficient then will give the information requiredfor predicting phase behavior at other conditions.

ConclusionsProper estimation of methaneK values in both crude-oiland condensate systems is essenthd for an accurate esti-mate of bubble point, dew point, and flashhtg of thesesystems. UsirtSour proposedprocedure, predictedmeth-ane K values agree well with measured Vah-es.

Forgas-condensate systems, the Peng-R.,. i m-AGAprocedurewith extended an~ysis and interact!..2 coeffi-cients for methane and C6+constituents correlated withdensity seems to give reliable results. For crudeoil/natural-gas systems, the interaction coefficient for me-thane and the last fraction shottld be determined witha bubble @rtt, or selected from Table 8. Gatheringdata with true boiling-point analyses of crude oils shouldhelp correlate the interaction coefficients for the lastfraction containing the high boiling-point material andmphalt.

References1. Starling, K. E.: *ANew Approachfor L%tmminingEquation-of-

StateParametersUsingPhaseEquilibriaDcta, Sac. Pet. Eng.J.(Dw. 1966)363-371;Trans., AIME, 237.

2. Soave, G.: *EquilibriumConstants From a Modified Redlich-Kwong Equation of State, Citenr. Eng. Sci. (1972) 27,1197-1203.

3, West, E. H. and Erbar, J. H.: *AnEvaluationof Four MethodsofPredictingthe Thermodyrramicproperties of Light HydmcasbonSystem, Proc., NGPA 52nd AnnurdConvention]:,Dallas (1973)56-61.

4. Bcrgrnan,D. F.: P,tilcting the PhaseBchaviorof NaturalGsrsinpipelines, PhDdissertation,U. of Michigan,Ann Arbor (1976).

S. Pcrtg,D. Y. and Robinson, D. B.: ANew Two-ConstantEqu-tion of State,*Ind. Eng. Chem. Fund. (1976)15, No. 1,59-64.

6. Bergman; D. F., Tek, M. R., and Katz, D. L.: Retrograde Con-densationin Natural Gas Pipeiines, MonographSeries, AmericanG= Association, New YorkCity (1%5).

7. Cavett, R. H.: Physicsl Data for DhNillauon Calculations Vapor-LiquidE@Ubna, Prac., API 27th Mid-YearMeeting(1%2)52,351-366.

.

8. Hoftinarm,A. E., Crump, J. S., and HocQtt,C. R.: EquilibriumConstants for a Gas-CondensateSystem, Trans., AIME (1953)198.1-10.--.---

9. Evans, R. B. and Harris, D.: 2quiJibrium VaporizationRatios-Hydmcsubon Mixture Containing TWOConcentrationsof Hep-tanes and Heavier Fkacrions, Ind. Eng. Chem. (19S6) 1, No. 1,45-50.

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ls