SPE 10067

Evaluating Constant Volume Depletion Data

SPESociety of Petroleum EngIneers ofAIME

by ~urtis Hays Whitson, Roga/and District College and Stein B0rre Torp NorwegianInstItute of Technology ,

Copyr!ght 1981, Society of Petroleum Engineers of AIME

This paper.was presented at the 56th Annual Fall Technical Conference and Exhibition of the Society of Petroleum Engineers of AIME, held InSan Antonio, Texas, October 57, 1981. The material Is subject to correction by the author. Permission to copy Is restricted to an abstract ofnot more than 300 words. Write: 6200 N. Central Expressway, Dallas, Texas 75206.

ABSTRACT

This paper presents results of analyzing constantvolume depletion data obtained from experimentalanalyses of gas condensates and volatile oils.Theoretical and practical developments are suppor.tedby analyses of experimental data from two North Seacondensate reservoirs.

The three maj or contributions of this work are:(1) presentation of material balance equations usedto calculate fluid (particularly liquid) propertiesfrom measured constant volume depletion data(2) a simple method for calculating "black oh"formation volume factors and solution gas-oil ratiosfor volatile systems using material balance resultsand a separator flash program, and (3) investigationof the Peng-Robinson equation of state as a tool formatching measured PVT data and studying vapor-liquidequilibria phenomena during constant volume depletion.

The main example presented is a rich gascondensate whose measured, calculated and simulatedphase behavior are fully documented in tables andfigures. Complete description of the heptanes-plusfraction is also included so that other engineers cancheck, modify and hopefully improve fluid character-ization using the Peng-Robinson (or: any other)equation of state.

INTRODUCTION

Constant volume depletion (CVD) experiments areperformed on gas condensate and volatile oil fluidsto simulate reservoir depletion performance and comp-ositional variation. Resulting data can be used ina variety of reservoir engineering calculations,among the most useful being material balance calcula-tions, generating "black oil" PVT properties and morerecently, the tuning of empirical equations of state.All of these applications are addressed in thepresent work.

References and illustrations at end of paper

Few engineers are aware of potentially-useful datawhich can be derived from CVD data, some of the mostimportant being liquid composition (and therefromK-values), density, molecular mass (and specificallyC7+ molecular mass); vapon density (using two indep-endent methods); and total ~y~tem molecular mass.No assumptions or empirical relations are used tocalculate these data - only experimental CVD dataand simple material balance equations.A procedure outlining these calculations was firstpresented by Reudelhuber and Hinds: Their descrip-tion, however, is somewhat difficult to follow andnot extensively known or used by the industry. Wetherefore decided to present the material balancesin equation-form using current SPE nomenclature.

Using the material balance-derived properties,a method is proposed for calculating "black oil"PVT properties - Le., formation volume factors andsolution gas-oil ratios used in two-phase flowequations and reservoir material balances. Themethod is not new in principle, as it was firstsuggested by Dodson, Goodwill and Mayer 2 in 1953 forsolution gas/crude oil systems. Their method,however, requires expensive and time-consuming liquidsample removals and experimental flash separations.The proposed method follows the same procedure butuses experimentally-determined vapor compositionsand material balance-derived liquid compositionstogether with a routine multi-stage separator flashprogram (using low pressure K-values independent ofsystem composition). PVT properties calculated usingthis method are compared with those calculated usingthe Peng-Robinson3 equation of state.

Though more complicated, empirical equations ofstate can also be used to evaluate CVD data. Severalinves tiga tors 5 ,16 have used the Peng-Robinson EOS tosimulate PVT studies of light gas condensates andcrude oils, needless to say avoiding systems operat-ing near the critical point. Results have rangedfrom excellent to poor, depending on which propertieswere compared. Conrad and Gravier 16 proposed amethod to improve liquid density estimations byadjusting properties of the heaviest plus fraction(boiling point and Cl interaction coefficient).

2 EVALUATING CONSTANT VOLUME DEPLETION DATA SPE 10067

Firoozabadi, Hekim and Katz 5 studied another leangas condensate and found that by only adjusting themethane-plus fraction interaction coefficient, thePeng-Robinson EOS overestimated liquid drop-out bynearly 100%. [As discussed later in this work,material balance calculations of CVD data for thissystem indicate that measured liquid volumes areapproximately 100% low -. i.e. calculated liquiddensities were much too high.]

Over 30 constant volume depletion studiesperformed by commercial and private laboratorieswere analyzed using the material balance approach.Three of these (North Sea fluids) were chosen tobe analyzed using the Peng-Robinson equation of state.Their choice was based on (1) internal consistencyof measured CVD data, as indicated by materialbalance calculations, and (2) availability ofextended compositional data for the heptanes-plusfraction. All three fluids have similar paraffin-naphthene-aromatic content, withWatson4 character-ization factors ranging from 11.95 to 12.05 for theC7+ fraction.

The first fluid (NS-l) is a rich gas condensateand was chosen to illustrate proposed techniques foranalyzing constant volume depletion data. Extensivedata for this sample and its heptanes-plus fractionhave been included in tabular form so that otherengineers can duplicate, modify and hopefully improveour analyses.

The second fluid (NS-2) is a lean gas condensatesimilar to the systems analyzed in References 5 and 16.Our discussion of NS-2 is limited to behavior orobservations which differ from those presented forthe rich gas condensate. The last fluid (NS-3) is avolatile oil operating near its critical point. Wehad not completed our analysis of NS-3 using thePeng-Robinson EOS when this paper was written;convergence problems were encountered when trying tosimulate the CVD process.. NS-3 is therefore .onlymentioned withregaud to material balance calculationsand K-value behavior. More information on any or allof these fluids can be obtained from the authorsf

DESCRIPTION OF THE CONSTANT VOLUME DEPLETION PROCESS

A constant volume depletion experiment isconducted at reservoir temperature and begins atsaturation pressure. Cell volume, Vcell, or thevolume contained by the fluid, is initially notedand used asa reference volume.

Mercury is then withdrawn from the bottom of thecell, thereby lowering the pressure as fluid expands ..During this process, a second phase develops -either retrograde liquid (for gas condensates) orsolution gas (for volatile oils). Mercury withdrawlis ceased when a predetermined pressure is reached.Some laboratories measure liquid volumes during thefirst pressure reduction, before any vapor has beenremoved; these volumes, reported relative to Vcell,represent constant composition depletion. Theyclosely approximate, however, volumes which wouldhave been measured if the process had been constantvolume depletion. [This was checked using the Peng-Robinson EOS simulator for lean and rich condensates.]

* Rogaland District College, Ullandhaug, 4000Stavanger, Norway

Mercury is reinJected into the cell at constantpressure while simultaneously withdrawing an equiv-alent volume of vapor. When initial cell volume isreached, mercury injection is ceased. Withdrawnvapor is analyzed using gas chromotography to deter-mine composition, Yj' Moles of vapor produced arecalculated using the real gas law and are reported asa cumulative percent of initial moles, np ' Compres-sibility factor, Z, is also calculated by notingproduced vapor surface volume and equivilant cellvolume (at pressure and tem~erature). From measuredvapor gravity and composition, heptanes-plusmolecular mass is back-calculated. Liquid volumeis measured visually and reported as a percent orfraction of cell volume, which in essence is a typeof hydrocarbon liquid saturation, SL.

The experimental procedure is repeated severaltimes (6-7) until a low pressure is reached, say700 psig (4828 kPa). The remaining liquid is removed,s epara ted (i. e. dis ti lled) and analyzed us ing gaschromotography. Measured liquid composition shouldcheck with material balance-derived composition.[Some. majOlL taboJ1a:toJUell -6moo:th and "adjU6:t" me.a-6UJl.e.dvapoJL c.ompoJ.lWo n-6 untU :the ma:te.JUat batane-e. ehe.ek.6.T!UJ.> pJLoc.edUILe. 16 dMc.oUILage.d -in gene.JLaL 1:t 1.-6 goodpMc.:Uc.e. :to -inqu-LlLe whe.:the.JL a taboJ1a:toJL{1 JLe.powme.a-6 UlLed oJL "-6moo:thed" da..ta, and :to wha..t ex.:te.ntma:te.JUat batcmee-de.JUve.d da.:t.a Me. U-6e.d -in Mnat CVvJLe.poJd6 ]

MATERIAL BALANCE EQUATIONS

Liquid Composition and K-value Calculations

Perhaps the most useful application of constantvolume depletion data is for calculating liquid ,compositions which, together with measured vaporcompositions, yield high pressure K-values havingmany important reservoir and process engineeringapplications. To arrive at the final express:i:.on forliquid composition in terms of measured CVD data, we

'first state molal and component material balances,respec tively,

n.tk. = nLk. + nvk. (,1)

where nL = moles of liquid with composition Xj,nv = moles of vapor with composition Yj and nt =total moles in the system with composition Zj, eachquantity being determined at pressure stage k.Subscript j designates component numbers making upeach phase.

Eq. 1 s ta tes that total moles of the two phasesystem equals the sum of liquid and vapor moles, whileEq. 2 states that total moles of component j in thetwo phase system equals moles of j in the liquid plusmoles of j in the vapor. The only data measureddirectly and appearing in either of the equations isvapor composition. The remaining unknowns can bedetermined from reported CVD data and modified formsof the material balance relations.

SPE 10067 C. H. WHITSON AND S. B. TORP 3

First we note that total moles at stage k equalsinitial moles minus cumulative moles of vaporproduced. We assume a basis of one mole initialfluid, that is nt1 = 1, yielding

All unknowns in Eq. 1 have now been defined interms of measured CVD data except liquid composition,which when written in terms of the other variables,becomes

I

4 EVALUATING CONSTANT VOLUME DEPLETION DATA SPE 10067

m.:tk = MLk'VLCk + M0k 'VLvk (16J.

mLk = m.:tk - mvk (14J.

Liquid mass is calculated as the difference betweentotal mass and vapor mass,

We can al.so calculate molecular mass of theequilibrium liquid, and specifically its heptanes-plus fraction. Rewriting the mass balance as

"BLACK OIL" PVT PROPERTIES

Dodson, e;t.a~ suggested an experimentalprocedure for determining so-called black oil PVTproperties used in two-phase flow equations andsolution-gas drive material balance relations.Current laboratory procedures for estimating oilformation volume factor Bo and solution gas-oil ratioRso only approximate the Dodson, e.:t.a. method -without flashing the liquid phase at each stage ofthe differential vaporization process. For mediumto low volatile crudes this procedure appears validfor most engineering calculations. The "vapor"solution gas-oil ratio Rsg is also assumed equal toinfinity - i.e. liquid condensation is neglected.

Highly volatile oils and gas condensate fluidscannot, howeVer, be analyzed or described by the samedifferential process, The basic problem posed bythese more volatile fluids is that during two phaseflow there exist both two phases aVLd two components.That is, flowing oil contains solution gas which,when undergoing pressure reducti0n, evolves and mixeswith the existing vapor phase. Likewise, flowing gascontains retrograde liquid which also evolves andmixes with the existing liquid when pressure declines.This complex thermodynamic phenomenon is, for allpractical purposes, impossible to simulate in thelaboratory.

'" ..' '" < { 1.51Mvk'Pk

Zk RT

Having calculated masses and volumes of equilibriumliquid and vapor, respective densities can becalculated directly from the ratio of m to V. i.e.p ~ m/V (where volumes come from Eqs. 6 and 7).

An independent check of vapor density can beused to check the consistency of measured Z factors.The relation is derived directly from the real gaslaw and can be stated as

.......... (1S)

we can solve for liquid molecular mass MLk'

Using Kay's mixing rule, the heptanes-plus molecularmass can be back-calculated to yield

N-1

,[:/ Mj Xjl volume Jr.u,ulting oJr.om .:the 61Mh 06 x.R = j.60 .6.:toc.k .:tank oil volume Jr.U,ultiVLg Mom 61Mh 06 x.

j

B9

.:to.:ta gM volume Jr.U,ultiVLg oJr.om .:the 61Mh 06 y.- . j

.6.:toc.k .:tank oil volume Jr.U,ultiVLg 6Jr.om 6iMh 06 y.j

where x' are liquid compositions determined frommaterial balance equations. Yj are vapor compositionsmeasured experimentally,

SPE 10067 C. H. WHITSON AND S. B. TORP 5

First, liquid composition x' is flashed using aset of appropriate K-va1ues and ~asic vapor-liquidequilibria equations. [Glas and Whitson 9 havedocumented that Standing' s10 low pressure "black oil"K-values are quite accurate for flash calculations ofblack oils. We have since found that they are alsoaccurate for flash calculations of medium to highlyvolatile gas condensates - i.e. systems with gas-oilratios less than about 50 000 SCF/STB (9000 Sm3/Sm3).]The sum of surface gas volumes divided by stocktank oil volume is defined as the" liquid" gas-oilratio Rso .

APPLICATION OF THE PENG-ROBINSON EQUATION OF STATE

Measured CVD data and material balance-derivedproperties were controlled using a fluid propertiespackage based on the Peng-Robinson equation of stateand developed by Roga1and Research Institute. Acomplete description of the computer programs can beobtained from the authors. The PVT package not onlyincludes general vapor-liquid equilibrium options,but it also includes two options for characterizingthe heptanes-plus fraction - methods presented byWhitson ll or Robinson and Peng.~

Oil formation volume factor Bo is calculatedfrom the relation

At the same depletion stage k, vapor phase withcomposition Yj is separated through the flashsimulator using identical K-values. The resultingsurface gas volumes divided by stock tank oil volumedefines the "vapor" solution gas-oil ratio Rsg Gas formation volume factor, on the other hand, canbe accurately estimated from the CVD compressibilityfactor Z using the real gas law,

VSTO'PL

where VSTO is stock tank oil volume (e.g. 1 STB) andwhere mg and mSTO are masses of total surface gasesand stock tank oil, respectively. Liquid density, PL'can be determined from either material balancecalculations (ffiL from Eq. 14 and VL fromEq. 6), orfrom one of several compositional density correlationsavai1ab1e 67 using material balance-derived liquidcompositions. We caution the use of PL calculatedfrom material balance equations since only a slighterror in retrograde liquid volume can result in asubstantial error in liquid density - and thereforeBo ' The same error will ,not affect liquid compositionto the same degree.

Pure component properties (critical pressure,critical temperature, acentric factor and molecularmass) were used for non-hydrocarbons and hydrocarbonsfrom methane to n-pentane. Only n-hexane wasconsidered for the C6 fraction. Heptanes andheavier properties were estimated using the procedureand equations suggested by Whitson~1 with severalmodifications given in Appendix B.

To manipulate the retrograde liquid volume curve,the Watson charact13rization factor of the heaviestcomponent was adjusted, making sure that adjustedproperties were physically realistic.

Binary interaction coefficients were set equalto zero except 13 : Nz- Nz c -0.02, COz - hydrocarbonsc 0.15, Nz - hydrocarbons c 0.12, and Cl - Cn'n = 6,7, . , which were estimated using a linearfit of the Katz and Firoozabadi 13 data (their Table 2),

The numerical solution technique used includesa pre-iterative sucessive substitutions methodfollowed by Newton's method using analyticalderivatives. Convergence problems were encounteredfor the NS-l fluid at temperatures approaching thecritical point - i.e. below reservoir temperature.Several alternative numerical methods were tried(Powell's method and a newly-developed acceleratedsucessive substitution method~ ) without successSimilar problems were noted with the volatile oilsystem (NS-3) which, from all indications, lies verynear the critical point at reservoir temperature.The lean gas condensate (NS-2) was solved problem-free OVer a wide range of temperatures.

... . . . . . . . (20)

J.>tage1>L m + mSTO1=1 g-

6 EVALUATING CONSTANT VOLUME DEPLETION DATA SPE 10067

Heptanes-Plus Characterization

Y 6.01077.K~p1824 .MO.17947 (24)

Eq. 23 was then inverted and combined with NS-l SCNmolecular masses to yield SCN specific gravities andnormal boiling points, Tb, for the NS-l fluid,

Properties of the single carbon number (SCN)groups were estimated** by defining the Kuop factorsfrom NS-lb SCN molecular masses and specific gravitiesusing the relation ll

Based on these results, it was decided to lowerthe Peng-Robinson liquid volumes by adjusting thecharacterization factor of the Czs+ fraction.By lowering the factor from 12.42 to 11.80 resultedin a decrease of the liquid volumes - 8% for themaximum drop-out (from 32% to 26%). The adjustmenthad little or no effect on other estimated data. Tohave lowered the Kuop factor more would have createda physically unrealistic system. Adjusted physicalproperties for the C2S+ fraction are found inTable 3, as is the methane interaction coefficientused to adjust dew point pressure. Complete resultsof the CVD simulation are presented in Table 5.Peng-Robinson liquid densities are compared withAlani-Kennedy estimates in Table 4.

Over twenty other adjustments of the C7+ char-acterization procedure were attempted for improvingliquid volume predictions. None of these were part-icularly helpful, though some are worth mentioning:(1) extending the C7+ split to C40+ such that thelast component was very heavy, (2) increasing thenumber of MCN groups used to nine, C2S+ inclusive,(3) splitting the C7+ fraction into eight SCN groupsand a ClS+ fraction, (4) using TBP Kuop factors**instead of those estimated from Eq. 23, and(5) using the Lee-Kessler~property correlations.***

The CVD simulator was run using the MCNproperties, as given in Table 3. The overall matchwas good to excellent,except for liquid volumeswhich were much too high (32% simulated maximum vs22% measured maximum). To check if measured volumeswere low we compared material balance liquid densitieEwith Alani-Kennedy 7 densities (using material balancecompositions and molecular masses). Table 4 showsresults of the comparison, indicating that measuredvolumes are consistent except for perhaps smallerrors in the first two volume measurements.

MCN specific gravities and Eq. 22, as was the CI-C6coefficient. Using these data in the Peng-RobinsonEOS yielded a dew point pressure much lower thanmeasured. The CI-CZS+ interaction coefficient wasthen increased until dew point pressure matched.

........ (23)K ~ 4 5579.MO.15178 -0.84573uop' .y

where Tb ~ (Y'Kuop)3, per definition. SCN data forNS-l calculated using Eq. 24 are given in Table 3,together with critical properties estimated using theRiazi-DaubertlScorrelations (except for Tb > 850 OF,when modified correlations were used 11 )

Extended compositional data of the C7+ fractionwas not available for the NS-l fluid, only molecularmass and specific gravity. Complete true boilingpoint (TBP) data were, however, available from anoffsetting well, NS-lb. These data were adapted tothe NS-l fluid using the method presented in Ref. 11,slightly modified as discussed in Appendix B.

Molal distribution (mole fraction vs molecularmass) of the NS-lb fluid was fit using the gammadistribution parameter alpha and variable upperboundry molecular masses. The optimal alpha was 0.712for eta (minimum molecular mass in the C7+ fraction)of 92. Table 2 gives results of the match.

Molal distribution of the NS-l C7+ fraction wasthen calculated using a ~ 0.712, n ~ 92 and MC7+ ~184 (as compared to 177 for the NS-lb fluid). We alsochose to hold upper boundry molecular masses constant(equivalent to paraffin values), giving the resultspresented in Table 3.

Tuning the Peng-Robinson Equation of State

Single carbon number groups were combined intofive multiple carbon number (MCN) groups - C7-C9,CIO-CI3, CI4-C17, CIa-Cz4 and C2S+- as suggested inRef. 11. Group properties were calculated usingKay's pseudocritical mixing rule, except for specificgravities which used a volume-weighted mixing rule.Methane interaction coefficients were estimated using

* The TBP analysis was performed according to theprocedure outlined in Ref. 14 and discussed by Katz,et.al. 13 The laboratory only reported, however,single carbon number molecular masses, mole fractionsand specific gravities. Cumulative volume percentswere then calculated by noting that incrementalvolume (per mole) ~ mole fraction x molecular mass +specific gravity. Little curvature was exhibited bythe TBP curve and normal boiling points were, there-fore, merely averages of the boiling point range fora given SCN group.

** Actually Kuo is defined as TS/3 /Y and could,

therefore, have Eeen calculated dlrectly using normalboiling points determined from TBP analysis. UsingKuop estimated from Eq. 23 and measured molecularmasses and specific gravities, estimated normalboiling points were calculated from Tb ~ (Y'Kuop)3and are presented in Table 2. Some of these valueswere higher than upper boiling point boundries definecfor the specific SCN group. Two possible explanation!are provided: (1) due to distillation under vacuum itwas not possible to duplicate exact boiling pointboundries as defined in Ref. 14, or (2) measuredmolecular masses of the heavier fractions were inerror. It was found, however, that using estimatedKuop factors from Eq. 23 - when used for criticalproperty estimations in the Peng-Robinson EOS - gave abetter match of measured constant volume depletiondata; the difference was only minor.

*** Information on these or other simulation runs canbe obtained from the authors. We would also apprec-iate suggestions as to how one might improve theliquid volume prediction.

SPE 10067 C. H. WHITSON AND S. B. TORP 7

RESULTS AND DISCUSSION

Most results presented in this paper are takenfrom the three North Sea systems NS-1, NS-2 and NS-3.It has been our experience, however', that somefeatures of CVD analysis are common to all systems.We have tried to differentiate between observationswhich are specific to a given system, and those whichare more general in nature. We note in particularthat the K-va1ue correlation developed in Appendix Awas developed from our analysis of many fluids,ranging from volatile oils to light gas condensates.

Fig. 6 compares measured (or more correctly,"smoothed") vapor compositions with those simulatedusing the Peng-Robinson EOS. The match is excellent,showing only slight deviation for the C7+ and C6components. Deviation of the hexane component isprobably due to its incorrect characterization asn-hexane.

Fig. 7 presents heptanes-p1us molecular masses ofliquid and vapor phases and the total system.Simulated and material balance-derived values matchwell. Our experience has shown that a good match ofC7+ molecular mass using the Peng-Robinson EOS isusually difficult, and very dependent on propercharacterization of the plus fraction.

Calculated equilibrium constants were correlatedusing the Hoffman, et.al. 8 method. Three main reasonsare given for this choice: (1) the log Kp vs F plotprovides a simple means of defining the approximatepressure- and temperature-dependence of K-va1ues,(2) material balance-derived K-va1ues can be evaluatedfor consistency by checking that log Kp vs F plots arelinear and converge, more or less, to a single pointand (3) an approximate estimate of convergencepressure can be determined by extrapolating the slope(of lag Kp vs F plots) vs pressure curve to zero,which can in turn be used to improve initial K-va1ueestimates for the Peng-Robinson (or any other)equation of state. See Appendix A.

Fig. 8 presents NS-1 K-va1ues calculated usingmaterial balance relations. The log Kp vs F plotsare linear and appear to approach a common point.As discussed in Appendix A, the convergence point cangive an estimate of the apparent convergence pressure.Actually, the most accurate value is obtained byextrapolating the slope vs pressure curve to zero,as done in Fig. 11. The resulting estimate of PK ~8000 psia (55170 kPa).

Fig. 9 presents NS-1 K-values calculated fromthe Peng-Robinson EOS. Once again linear plots oflog Kp vs F converge to a point. From the extrapola-tion of slope to zero in Fig. 11, PK ~ 7500 psia(51720 kPa). Experience with the Peng-Robinson EOSand material balance evaluation of CVD data has shownthat rich gas condensates and volatile oils exhibita more well-defined convergence point than leanersystems.

Another interesting feature shown in Fig. 9 isthat heavy components are better correlated using thelog Kp vs F method at higher pressures. This maifsuggest that methane interaction coefficients of theplus fractions have most influence on K-values atlow pressures.

Temperature effects on the log Kp vs F plots ofNS-l were investigated by running the Peng-RobinsonEOS simulator at 340 of (l71.l 0C), some 60 OF higherthan reservoir temperature. Fig. 10 presents theresults, indicating that temperature influence is(1) largest for heavy components at large pressures,(2) neglibible at low pressures (as was found inRef. 10), (3) relatively small compared to theinfluence of pressure, and (4) not significant inchanging the apparent convergence pressure of thesystem. 1hese observations are also illustrated inFig. 11.

For lighter systems such as NS-2, there does notalways appear such a unique convergence point forlog Kp vs F plots. We thought that this perhapsresulted from a change in the total composition ofthe system, or from alteration in the heptanes-plusproperties. We investigated these possibilities byrunning a constant composition simulation of NS-l(at 280 and 340 OF) and NS-2 (at 241 OF). ResultingK-values were compared with CVD K-va1ues and arepresented as log K vs log P plots in Figs. 12, 13 and14. All three systems clearly indicate that compsi-tional change during constant volume depletion is notsignificant enough to influence K-va1ues orconver-gence pressure, if in fact there exists a trueconvergence of K-va1ues to unity. As seen in Fig. 14,the lean gas condensate (NS-2) does not appear tohave a convergence pressure for components heavierthan hexane.

CONCLUSIONS

1. Measured constant volume depletion data for twogas condensates and a volatile oil were analyzed usinsimple material balances and the Peng-Robinsonequation of state (EOS).

2. A simple method is proposed for calculating"black oil" PV1 properties (formation volume factorsand solution gas-oil ratios) of gas condensates andvolatile oils.

3. Material balance-derived K-values can be correlatedto yield an estimate of the apparent convergencepressure which, when used in a newly-developed K-va1ucorrelation, helps calculate high pressure K-va1uesused as initial estimates in equations of state.

4. Simulated constant composition and constant volumedepletion studies of lean and rich gas condensatesusing the Peng-Robinson EOS indicate that K-va1uesare indep~nd~t of the depletion process.

5. Temperature effects on the Hoffman, et.al. 8 K-va1uecorrelating technique (lag Kp vs F) were studiedusing the Peng-Robinson EOS.

6. 1he Peng-Robinson equation of state usually over-estimated liquid drop-out for gas condensates duringconstant volume depletion. The problem was normallycorrected or improved by reducing the Watson4

characterization factor of the heaviest component.

8 EVALUATING CONSTANT VOLUME DEPLETION DATA SPE 10067

NOMENCLATURE

REFERENCES

ACKNOWLEDGMENTS

convergence

liquid phase

carbon number

= oilproduced

reduced

= saturated (bubble or dew point)= standard condition= stock tank oil

total (two phase)

= vapor phase

= incrementalinteraction coefficient

parameter in gamma distribution(minimum molecular mass)

density, 1bm/ft3 ; kg/m3 (gm/cc)

= acentric factor

= parameter in gamma distribution= parameter in gamma distribution= gamma function

specific gravity relative to air orwater (60/60)

t

v

n

p

o

s

STO

sc

K

L

w

P

R

f3ry

The authors wish to thank H. Norvik, H. Asheim,D. Murphy, V. Dalen and G. Nielsen for useful coriunentsconcerning this paper. We also acknowledge computertime and facilities donated by Roga1and DistrictCollege, Norwegian Institute of Technology (NTH) andContinental Shelf Institute (IKU). Phillips Petro-leum Norway and Statoi1 should be thanked for contri-buting well-needed fluid data to the petroleum liter-ature. Economical support from frying pan publica-tions, Inc. is, as usual, appreciated.

slope of .tog Kp vs F plotslope of the straight line connecting thecritical point and atmospheric boilingpoint on a .tog vapor pressure vs1/Tplot, cycle-OR ; cycle-K

formation volume factor, Bb1/STB ; m3 /Sm3

heptanes-plus component

constant volume depletion

eX ; e = 2.71828 ..equation of state

component characterization factor, cycle.

equilibrium constant (K-va1ue)

Watson characterization factor

natural logarithm to base e

logarithm to base 10

mass, lbm ; kg

mo1euc1ar mass, lbm/1b-mole ; kg/kg-mo1e

molecular mass of the total system

(1) moles, lbm-mo1e ; kg~mo1e

(2) exponent in K-va1ue correlation

North Sea sample

pressure, psia j kPa

probability density function

=. cumulative probability functionuniversal gas constant, 10.732 psia-ft 3 /mole-OR; 8.3143J/mo1e-K

"vapor" solution gas-oil ratio, SCF/STB.Sm 3 /Sm3

"liquid" solution gas-oil ratio (same)

saturation, fraction or percent

absolute temperature, oR ; K

volume, ft 3 ;m3

liquid composition, fraction or percent

vapor composition, fraction or percent.

intercept of .tog Kp vs F plottotal system composition

vapor compressibility factor

y

Y or Y(p)

RsoS

T

V

m

R

B

Rsg

z

A or A(p)

b

z

n

x

NS

p

p(x)

Pr

M

M

C7+

CVD

exp(x)

EOS

F or F(T)

K

Kuop.tv!.tog

Subscripts

a atmospheric

b bubble point (Pb) or boiling (Tb)

c critical

cell cell, pertaining to PVT cell volume

d dew point

g gas

i index for summation

1. Reude1huber, F.O. and Hinds, R.F.: "A Composition-al Material Balance Method for Prediction ofRecovery from Volatile Oil Depletion Drive Reser-voirs," T!l.an.o. ,AIME(1957) 21 0,19-26

2. Dodson, C.R., Goodwill, D. and Mayer, E.H.:"Application of Laboratory PVT Data to ReservoirEngineering Problems," TMn.o. ,AIME(1953) 79 g,287-298

3. Peng, D.-Y. and Robinson, D.B.: "A New Two-Constant Equation of State," IV!d. EYIfJ.Chem. FuV!d.(1976)15,No.l,59-64

j

k

component.identifier

depletion stage

SPE 10067 C. H. WHITSON AND S. B. TORP 9

4. Watson, K.M., Nelson, E.F. and Murphy, G.B.:"Characterization of Petroleum Fractions,t' Ind.Eng.Chem.(1935)27,1460-l464

5. Firoozabadi, A., Hekim, Y. and Katz, D.L.:"Reservoir Depletion Calculations for Gas Conden-sates Using Extended Analyses in the Peng-Robinson Equation of State," Can.J.Chem.Eng.(Oct.,1978)56,610-6l5

6. Standing, M.B. and Katz, D.L.: "Vapor-LiquidEquilibria of Natural Gas-Crude Oil Systems,"Tnano.,AIME(1944)155,232

20. Standing, M.B.: Votumwue and Phcu,e Behav-tOlt On'Oil F-tud HyMoeMbon Sy.6teJnJ.>, 8th Printing,Society of Petroleum Engineers of AlME, Dallas(1977)

21. Robinson, D.B. and Peng, D.-Y.: "The Characteri-zation of the Heptanes and Heavier Fractions,"Research Report 28, GPA Tulsa, Oklahoma (1978)

22. Kessler, M.G. and Lee, B.1.: "Improve Predictionof Entha1apy of Fractions," HydM. PMe. (March,1978)153-158

7.

8.

9.

10.

A1ani, G.H. and Kennedy, H.T.: "Volumes of LiquidHydrocarbons at High Temperatures and Pressures,"Tnano."AIME(1960)219,288-292

Hoffman, A.E., Crump, J.S. and Hocott, C.R.:"Equilibrium Constants for a Gas-CondensateSystem," Tltano., AIME( 1953) 198,1-10

Glas, C/J. and Whitson, C. H.: "The Accuracy of PVT-Parameters Calculated from Computer Flash Separa-tion at Pressures Less Than 1000 ps ia," SPE Paper8033 (1979)

Standing, M.B.: "A Set of Equations for ComputingEquilibrium Ratios of a Crude Oil/Natural GasSystem at Pressures Below 1,000 psia," J.Pd.Teeh. (Sept. ,1979)1193-1195

APPENDIX A

IMPROVED K-VALUE ESTIMATION AT HIGH PRESSURES

Solution of the Peng-Robinson (or any other)cubic equation of state requires initial estimatesof K-values. At higher pressures (> 500 psia) andparticularly near phase boundries or the criticalpoint, these estimates are very important for deter-mining the "correct" solution to the equation.Accurate K-va1ue estimates can also reduce numericaldivergence when searching for the solution.

Wi1son w proposed the following thermodynamicrelation for estimating K-values which should, inpractice, only be used at low pressures,

11. Whitson, C.H.: "Characterizing Hydrocarbon PlusFractions," EUR Paper 183 Presented at the EUROPECMeeting held in London, England, Oct. 21-24, 1980

K.j

12. Risnes, R., Dalen, V. and Jensen, J.1.: "PhaseEquilibrium Calculations in the Near-CriticalRegion," Paper Presented at the 1981 EuropeanSymposium on Enhanced Oil Recovery, Sept. 21-23,1981

1+ W,j

19. Brinkman, F.H. and Sickling, J.N.: "EquilibriumRatios for Reservoir Studies," Tnano.,AlME(1960)219,313-319

18. Wilson, G.M.: "A Modified Redlich-Kwong Equationof State, Application to General Physical DataCalcua1ations," paper presented at the 65thNational AIChE Meeting, Cleveland, 1969

13.

14.

15.

16.

17.

Katz, D.L. and Firoozabadi, A.: "Predicting PhaseBehavior of Condensate/Crude-Oil Systems UsingMethane Interaction Coefficients," TMno.,AlME(1978)265,1649-1655

"Selected Values of Properties of Hydrocarbons andRelated Compounds," API Project 44, Texas A&MUniv., College Station (1969)

Riazi, M.R. and Daubert, T.E.: "Simplify PropertyPredictions," Hydno. PMe. (March, 1980)115-116

Conrad, P.G. and Gravier, J.F.: "Peng-RobinsonEquation of State Checks Validity of PVT Exper-iments," OilWcu, J.(April 21,1980)77-86

Yarborough, L.: "Application of a GeneralizedEquation of State to Petroleum Reservoir Fluids,"from Equationo 06 State by Chao and Robinson

where

TIT,ej

plPej

i Tb/Tej7 1 - Tb/Tej

5.37 = '?"tn(70)3

'T and p define the system's temperature and pressure,Tb is the atmospheric boiling point at Pa' and Tc andPc are critical temperature and pressure, respectively.Actually, Eq. A-l appeared in the petroleum literaturesome 10 years before Wilson proposed his relation.Hoffman, d.at. 8 presented Eq. A-1 graphically (theirFig. 4) and suggested the following generalization(albeit graphically),

A(p)' Fj(T) + YIp) (A-2l

where

11Tb , - liTJ tog (Pe/Pal ....... (A-3l11Tb, - 1IT ,

j ej

10 EVALUATING CONSTANT VOLUME DEPLETION DATA SPE 10067

A(p)

Y(p)

pJr.eJ.,!.>U!te-depertdent !.>,tope

~e!.>!.>U!te-depertdent lnteJr.eeptand that exponent n = 0.6 for all systems.

It is easily shown that Eqs. A-l & A-2 are identicalfor A(P=Pa) = 1 and Y(P=Pa) = ,tog Pa - i.e. atatmospheric pressure.

We can now reformulate Eq. 1 (the Wilson-typeequation) to give K-values at all pressures andtemperatures,

Engineers familiar with Eq. A-l are aware thatits accuracy is usually limited to low pressures.An investigation of the pressure-dependent slope inEq. A-2 showed, however, that Eq. A-l could bereformulated to yield equally-accurate results athigher pressures.

The quasi-thermodynamical model used to extendEq. A-l is based on the suggestion by Brinkman andSicklingl~ that plots of ,tog Kp vs F(T) at severalpressures intersect at a common point defining theapparent convergence pressure of the system. Theirrelation, after dropping pressure- and temperature-dependent notation, is

K,j

.. ..... (A-7)

Note that A=l for pcp , reducing E.q. A-7 to Eq. A-I.For P=PK' K.=l, thus ~aking Eq. A-7 consistent atboth pressute boundries. Using Eqs. A-5 (n~0.6),A-6 and A-7, K-values can be estimated directly frominput data used by equations of state .

I. (A-3)K,j

where PK = convergence pressure and FK = the F-va1uecorresponding to PK at the common point of intersec-tion. Eq. A-3 is easily derived by noting that Kj=lat convergence pressure PK' We can also show fromEq. A-l that FK = ,tog(PK/Pa), or in terms of theintercept in Eq. A-2,

APPENDIX B

MODIFIED C7+ SPLITTING METHOD

Methods presented in Ref. 11 were used todetermine the molal distribution of the C7+ fractionwith the following modifications:

y

The pressure-dependence of slope A was investi-gated and found to have the following two properties:(1) it ranged from 0 ~ A ~ 1 forPK < p < Pa and(2) its form varied from sligt1y concave up tolinear (see Fig. 11). From these observations, ageneral equation-form was found to fit A(p),

(1) Minimum molecular mass (eta) was set equal to 92

(2) The. error function used to determine the optimalalpha (~) was

and was minimized using the half-interval method.

In some cases, Eq. 2 was used twice in order toincrease the accuracy of the estimated mole fraction.

(3) The upper molecular mass boundry was allowed tovary between 14i - 12 and l4i + 12, except for C7which had a range of 93 to l4i + 12. Measured molefraction was matched by varying the upper botindry.Only two iterations are required since the relationbetween boundry molecular masses and mole fractions~s nearly linear. That is ,. if upper b.oundry Ml yieldsZl, and M2 yields 22 , and Z = measured mole fraction,then the optimal tipper molecular mass boundry is verynearly

......... (B-2)M2 ~.MlA . A2 2 - 2 1

M' .opt

A A(p)

where exponent n varied from 0.5 to 0.8 for variouscondensate and volatile oil systems. We found,however, that n = 0.6 gave reasonable K-va1ueestimates for all fluid systems at most pressures andtemperatures. In practice, exponent nand PK for aparticular system can be determined exactly byplotting ,tog(l-A) vs ,tog(P-Pa) where n is the slopeand the intercept equals n.,tog(PK-Pa)' Slope A isusually determined by drawing a best straight line orusing linear regression through data for componentsethane through hexane, where our experience has shownthat methane and carbon dioxide also lie on the line.

For more general use of Eq. A-5 (for example,initial K-value estimates for an equation of state),we have found that a good estimate of apparentconvergence pressure can be obtained from theheptanes-plus molecular mass~

SPE 10067 C. H. WHITSON AND S. B. TORI' 11

(4) In the original method presented in Ref. 11,sin~le carbon number molecular masses correspondingto z with molecular mass boundries Mi and Ml+l wasmereh the arithmetic average. Dale Embry (PhillipsPetroleum Company, Bartlesville) noted in apersonal comnunication that this approximation wasnot necessary and that the exact analytical expres-sion is given by

M',.{,

where

P~(M~;+I,a+l,~,n) - P~(M

TABLE 1 - MEASURED CONSTAID VOLUME DEPLETION DATA FOR THE NS-1 FLUID AT 280 of

Compositions

F:quilibriuni EquilibriumVapo,r. Liquid

Pressure - psia Exp. Calc.

Cor~ponent 6764.7 5514.7 4314.7 3114.7 2114.7' 1214.7 714.7 714.7 714.7

Carbon Dioxide 2.37 2.40 2.45 2.50 2.53 2.57 2.60 0.59 0.535Nitrogen 0.31 0.32 0.33 0.34 0.34 0.34 0.33 0.02 0.017Methane 73.19 75.56 77 .89 79.33 79.62 78.90 77 .80 12.42 10.704Ethane 7.80 7.83 7.87 7.92 ':8.04 8.40 8.70 3.36 3.220Propane 3.55 3.47 3.40 3.41 3.53 3.74 3.91 2.92 2.896iso-Butane 0.71 0.67 0.65 0.64 0.66 0.72 0.78 0.91 0.916normal-Butane 1.45 1. 37 1.31 1.30 1.33 1.44 1.56 2.09 2.103iso-Pentane 0.64 0.59 0.55 0.53 0.54 0.59 0.64 1.40 1.417normal-Pentane 0.68 0.62 0.58 0.56 0.57 0 . 61 0.66 1.60 1.624Hexanes 1. 09 0.97 0.88 0.83 0.82 0.85 0.90 3.68 3.755Heptanes-plus 8.21 6.20 4.09 2.64 2.02 1.84 2.12 71.01 72 .815

Totals 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.000,

MC7 +184.0 160.0 142.0 127.0 119.0 115.0 114.0 213.0 207.9

YC7+ 0.816 0.799 0.783 0.770 0.762 0.758 0.757 0.833 0.843

Z 1. 238 1.089 0.972 0.913 0.914 0.937 0.960

n -. % 0.000 9.024 21. 744 38.674 55.686 72.146 81. 301pSL - % 0.0 14.1 19.7 21.6 21.3 20.2 19.3

TABLE 2 - COMPOSITIONAL AND PROPERTIES DATA OF FLUID Ns-IB SAMPLED FROMA WELL OFFSETTING NS-1 COMPARED WITH CALCULATED DATAGENERATED USING THE METl10DPRESENTED IN REF. 11

Measured Calculatedi'

SingleCarbonNumber

789

10111213141516171819202122232425+

MolePercent

0.940.840.740.600.410.340.310.260.220.190.170.150.130.110.080.070.060.060.51

MolalMass

95104118132144154167180197212226234250262277292308329471

SpecificGravity

0.71580.73650.77570.76390.77230.78140.79390.80530.80960.81520.82550.83030.83410.84000.84770.85310.85770.86660.8826

KuopFactor

12.0511. 9311.9011.9912.0412.0412.0312.0212.1312.3012.1912.2012.2612.2812.2912.3212.3612.3812.87

BoilingPoint(Pa)

641. 7678.3727.3768.4804.0832.7871.2907.0947.1

1008.11019.01039.41069.41097.61130.81161.01191.41234 .91465.6

MolePercent

0.9350.8380.7390.6000.4100.3400.3100.2600.2200.1900.1700.1500.1300.1100.0800.0700.0600.0700.508

MolalMass

95.1105.4118.9134.2148.7161. 7175.0188.7202.1215.4228.9242.8256.8270.6283.0294.1304.8316.7439.1

UpperMolalMass

99.6111.9126.8142.4155.5i68.4182.2195.7209.1222./,236.1250.12M .1277 .8289.0299.9310.3324.0

6.19 177 0.8061 12.25(12.02)*

6.190 177.0

* The higher average Kuop value was calculated using a weight-averagemixing rule, whereas the lower value was estimated using the Whitsoncorrelation.

i" The gamma distribution (Ref. 11) was used where an optimal alpha of0.712 was fou.nd for eta (minimum molecular mass in the C7+ fraction)of 92. Upper molecular masses were found by fitting the measuredcompositions.

TABLE 3. - PHYSICAL PROPERTIES OF THE C7+ SINGLE AND MULTIPLE CARBON NUMBERGROUPS USED IN THE PENG-ROBINSON EQUATIllN OF STATE TO DESCRIBERESERVOIR FLUID BEHAVIOR OF THE NS-1 FLUID

Single Boiling Critical MethaneCarbon Mole Molal Specific Point Temp. Press. Acentric InteractionNumber Percent Mass Gravity (OR) (OR) (psia) Factor Coefficient

7 1. 2136 95.3 0.7177 646.8 971.6 457.5 0.27428 1.1730 106.5 0.7409 690.6 1021.4 423.4 0.30569 0.8600 120.7 0.7599 739.4 1073.2 383.2 0.3454

10 0.6872 134.7 0.7682 781.4 1112.9 345.9 0.386111 0.5681 148.7 0.7781 822.2 1152.1 316.8 0.425112 0.4783 162.7 0.7908 863.1 1192.3 294.0 0.462213 0.4074 176.7 0.8034 902.8 1231. 2 274.9 0.498414 0.3498 190.7 0.8153 941.2 1268.3 258.4 0.534215 0.3021 204.7 0.8168 972.6 1294.2 240.4 0.574016 0.2621 218.7 0.8210 1029.8 1321.5 225.7 0.612717 0.2282 232.7 0.8310 1039.5 1354.0 214.6 0.648618 0.1992 246.6 0.8389 1072 .0 1383.6 204.3 0.685519 0,1744 260.6 0.8432 1104.7 1408.7 194.0 0.724620 0.1529 274.6 0.8486 1131.6 1434.4 185.1 0.763421 0.1343 288.6 0.8554 1161.9 1461.0 177 .4 0.801622 0.1182 302.6 0.8602 1190.2 1484.9 170.0 0.841623 0.1041 316.5 0.8639 1217.4 1507.0 162.9 0.883024 0.0918 330.5 0.8690 1245.1 1530.2 156.8 0.924125+ 0.7054 462.3 0.9192 1488.0 1734.6 91.4 1.0590

8.2100 184.0 0.8160

MULTIPLE CARBON NUMBER PROPERTIES USED IN THE FINAL CVD SIMULATION

7- 9 3.2466 106.1 0.7385 688.3 1016.5 425.5 0.3044 0.03659***10-13 2,1410 152.7 0.7837 835.0 1163.6 313.1 0.4348 0.04292***14-17 1.1421 209.2 0.8205 984.4 1304.5 237.4 0.5856 0.04807***18-24 0.9749 281.5 0.8524 1146.9 1446.0 182.7 0.7832 0.05254***

25+ 0.7054 462.3 0.9192 1276.1* 1584.2* 168.8* 0.8819* 0.18400**

8.2100 184.0 0.8160

* Adjusted values representing a Kuop factor of 11.80. The original valuescorrespond to a Kuop factor of 12.42 and are given above (e.g. 1488.0).

** Adjusted value used to match the measured dew point pressure.*** Calculated using the Katz and Firoozabadi correlation, curve-fit to yieldthe following relation 6C -G == O.14Yn - 0.0668. Though not shown in thistable, the metane-hexane 1 n interaction coefficient was also calculated usingthis relation.

TABLE 4 - CALCULATED LIQUID DENSITIES AS A FUNCTION OF PRESSURE FOR NS-1

Calculated Liquid Densities (gm/cc)

Measured CVD Data Simulated CVD Data

Alani-Kennedy Alani-KennedyMaterial Density Peng- Density

Pressure Balance (M.B. Liquid Robinson (P~R Liquid( psia) Density Properties) * Density** Properties) *

5514.7 0.670 (l.608 0.541 0.570

4314.7 0.680 0.649 0.554 0.596

3114.7 0.688 0.670 0.580 0.632

2114.7 0.700 0.682 0.608 0.664

1214.7 0.711 0.700 0.636 0.692

714.7 0.722 0.711 0.653 0.707

* The Alani-Kennedy density correlation requires liquid compositions,total liquid molecular mass, heptanes-plus molecular mass and specificgravity (as well as pressure and temperature). These data were availablefrom either material balance calculations or P-R simulation results.

** The Peng-Robinson simulation used properties given in Table 3 with anadjusted Kuop = 11.8 for the C2S+ fraction. Using the original Kuo ]? factorof 12.42 gave even lower liquid densities than those given above, wlth alarger deviation from the Alani-Kenedy values.

TABLE 5 - SllIDLATED CONSTANT VOLUME DEPLETION DATA FOR THE NS-1 FLUID AT 280 of USING THE PENG-ROBINSONEQUATION OF STATE

Compositions

Equilibrium EquilibriumVapor Liquid

Pressure - psia Exp. Calc.Component 6764.7 5514.7 4314.7 3114.7 2114.7 1214.7 714.7 714.7 714.7

Carbon Dioxide 2.370 2.403 2.447 2.497 2.541 2.576 2.583 0.590 0.595Nitrogen 0.310 0.323 0.336 0.344 0.343 0.334 0.321 0.020 0.029Methane 73.190 75.549 77.644 79.135 79.712 79.242 77.772 12.420 11. 939Ethane 7.800 7.779 7.793 7.880 8.057 8.372 8.711 3.360 3.623Propane 3.550 3.474 3.405 3.383 3.444 3.660 3.989 2.920 3.133iso-Butane. 0.710 0.686 0.660 0.644 0.647 0.691 0.778 0.910 0 .. 967normal-Butane 1.450 1.390 1.326 1.281 1.282 1.375 1.567 2.090 2.314iso-Pentane 0.640 0.604 0.564 0.530 0.516 0.548 0.638 1.400 1.509normal-Pentane 0.680 0.639 0.592 0.550 0.532 0.563 0.659 1.600 1.770Hexanes 1.090 0.996 0.889 0.789 0.727 0.744 0.877 3.680 4.223Heptanes-P1us 8.210 6.157 4.343 2.969 2.198 1.895 2.105 71.010 69.897

----Totals 100.000 100.000 100.000 100.000 100.000 100.000 100.000 100.600 100.000

M 184.0 161.0 142.7 129.1 121.2 116.4 114.5 213.0 209.1C7+

C7+ 0.816 0.799 0.783 0.770 0.7620.758 0.757 0.833 0.843

Z 1.203 1.037 0.937 0.890 0.886 0.911 0.936

n - % 0.000 9.637 22.581 39.492 56.196 72 .413 81. 535pSL - % 0.00 19.55 26.11 26.65 25.11 23.00 21.58

IDENTICAL MULTI-STAGE SEPARATION

VgR "-M VSTO

P ZTB "_~_c._9 hc.p VAPOR

Yj

PVT CELL

Fig. 1 - Schematic description of the procedure for calculating "black011" PVT properties.

u.. 0.030u NS-1(/)

2800 F......."'.j..J

'I-

" 0.025---0---- PENG-ROBINSON Z-FACTORS

OJ ---6- MEASURED Z-FACTORScoc:::0I-ue( 0.020u..uJ::E::J...J0>z 0.0150Hl-e(::Ec:::0 0.010u..(/)e(I.!)

0.005

o.000 1-.L...L......L....l.-I-.L...J-1.....l.-L....l-..I-l..-'---'-l-.l-I.....L......L-l-.l-L....L......L-L-J.....J-..I-l.......L-J-l-.l-Jo 1000 2000 3000 4000 5000 6000 7000

PRESSURE, psia

Fig. 2 - Gas formation volume factor vs pressure for NS1 at 280 'F.

*STANDING LOW PRESSURE"BLACK OIL" K-VALUECORRELATION USED

-0- PENG-ROBINSON RESULTS-6- MATERIAL BALANCE RESULTS

USING MEASURED DATA

1558060

CONDITIONS *TEMPERATURE

(0 F)

1014.7264.714.7

PRESSURE(psia)

SEPARATOR

20000

30000

In 50000 ,........-,-,-,--.--r-r--r-r-,-,........-,-,-,--.--r-r--r-r-,-,r-r-...,..--r-r-T""""T-'-1'"""""T'"-,-,---r--tl-(/).......I.L.U(/)

a:::o~ 10000?

..~ 40000

a:::..

oHl-e:(a:::...JHoI

(/)e:((,.!)

zoHI-::>...Jo(/)

5000 6000 7000PRESSURE, psia

Fig. 3 - "Vapor" solution gas-oil ratio vs pressure for NS1 at 280 'F.

*STANDING LOW PRESSURE,"BLACK OIL" K-VALUECORRELATION USED

1558060

CONDITIONS*TEMPERATURE

(0 F)

1014.7264.714.7

PRESSURE(psia)

~PENG-ROBINSON RESULTS-6-MATERIAL BALANCE RESULTS-o-MATERIAL BALANCE RESULTS

USING P-R LIQUID VOLUMES (SL)

SEPARATOR

...JHo

1.2

~ 1.6::>...Jo>ZoH

~ 1.4::;;:a:::oI.L.

..o

In 1.8..a:::oI-Uc:(I.L.

In 2 0 ,........-,-,r-r-..,-,r-r-..,-,-,..,-,-,.,--,..-,..,..-,..,--r-,..,.,-o--T--r-T1""-o--T..."l-(/).......-J

..cOJ

1000 2000 3000 4000 5000 6000 7000PRESSURE, psia

Fig. 4-011 formation volume factor vs pressure for NS-1 at 280 of.

NS-1280 of

5000 6000 7000PRESSURE, psia

4000300020001000

* STANDING LOW PRESSURE"BLACK OIL" K-VALUECORRELATION USED

--0- PENG-ROBINSON RESULTS-6- MATERIAL BALANCE RESULTS-0- MATERIAL BALANCE RESULTS

USING P-R LIQUID VOLUMES (SL)

SEPARATOR CONDITIONS*

PRESSURE TEMPERATURE(psi a) ( oF)

1014.7 155264.7 8014.7 60

"a(f)

~

" 1500oHl-e:(~

--lHoI

(/)

~ 1000zoHI-::::>--lo(/)

~ 2000rr-'--~--,-~-'--r-r-'--~-'--rr-,--,r-r--nr-r---,-;-r--,-;--r-,-,--r-r-r-,-,(/).......u..U(/)

e 500::::>C!JH--l

Fig. 5 - "Liquid" solution gas-oil ratio vs pressure for NS1 at 280 0 F.

-0- PENG-ROBINSON MATCH-t:.- MATERIAL BALANCE RESULTS

USING MEASURED DATA

120

(/) 240 r--r--,....-T""""""T---r-..,--,---.--.---r-r-r-~--,-~--,-r-r-,....--r-r---,-...-T--r,...,,-,-..---,-,-,......,UJ(/)(/)e:(::E

~ 220--l::::>uUJ--l

~ 200(/)

::::>--le..~ 180UJze:(l-e..UJ

:c 160

140

* MEASURED (-6-)NS-12800 F

7000psia

Fig. 6 - Caloulated and measured vapor oomposltiQns vs pressure for NS1 at 280 0 F.

o......o ...--_)----....0--__--< >----------_0

o

...(/)

zoI-!l-I-!(/)

o0-:EoU

...J------0>- 0

NS-1280F

10-1 L...J..-l-J...,....!.-I-.J......J.-l.....J.......J--'-...J......JL......l..-l-.l-l......l-J....J..-l-J...,....!.-I.-.J......J.-l.....J.......J--'--'--L......l.......L.....Jo 1000 2000 3000 4000 5000 6000 7000

PRESSURE, psia

Fig. 7 - Calculated heptanesplus molecular masses vs pressure for NS1 at 280 of.

INSERT

EXTRAPOLATION OF SLOPESTO ZERO YIELDSAPPARENT CONVERGENCEPRESSURE'" 7500 psia

10'L-c-~~--'-'--'-~--'---'~~---"----'----'-~L....L~~-L-J2.0 2.5 3.0 3.5 4.0

*ADJUSTED C7+ F VALUES10-3 I....-.l....-.l....-.l....-.l....-.l....-.l....-.i--.i--.i--.i--.i--.i--.i--.i--.l....-.i--.i--.i--.i--.i--........................"'--'

-4 -2 0 2 4 6COMPONENT CHARACTERIZATION FACTOR, F=b(1/Tb - 1/T)

...I-U

25 10 3o~

0-

W~ 10 2=>VlVlW~

0- 10I

I-Z

H~

COI-!...JH=>OJW

C\l 10 5 ~r-..-..-,---,---.-..,--r--r-r--.- r-r-"-'-'---'-'-7r-r--rr-r-r-r--;'r-VlQ.

...~ 10 4

Fig. 8- NS1 Kvalues at 280 of calculated using the material balance approach.

ro 10 5 r-r--r-r--,-..,-.-r-,-r--,--'--.-r-,-,--,--,--,....,-,-,--,--,--,....,-,-,--,-.,..--,'r-

6

V)

UJa..o....JV)

oIC3

Iii -C 4n-C4

Iii -C 5n-C5

PRESSURE 0 MATERIAL BALANCE RESULTS(psia) USING MEASURED DATA

1- 5514.7 _ LEAST SQUARES LINEAR2-4314.7 REGRESSION3-3114.7 (N 2 AND C7+ DATA EXCLUDED)4-2114.75-1214.76- 714.7

I1 C7+10 L......J.---l..--'-:..L...-l-.J.---l..--'--'--l-.J.---l..--'-...L-l-.J.---l..--'-...L-l-.J.---l..--'--'--l-.J.---l..--'--l-l-1 0 1 2 3 4 5

COMPONENT CHARACTERIZATION FAtTOR, F=b(1fTb - 1fT)

(fj

Q.

~ 102

t-l0::COt-l....Jt-l:::JC!JUJ

,I-u

25 104o0::a..UJ0:::::JV)V)

UJ0::0... 103

I-Zc:(l-V)

Zou

Fig. 9 - NS1 Kvalues at 280 'F oaloulated using the Peng-Robinson EOS.

NS-1280 of

__~":

wuzw'"'"w>zou

6000 8000PRESSURE, ps~a

r EXTRAPOLATED

NS-1280 of 1340 of

0.00 2000

1.0

u..

ClZ

{f 2.0

Fig. 11 - Slopes and Intercepts of log Kp vs F plots vs pressure for NS-1.

w w'":::> uU) zU) uJw '"'" '"0. W>c- z;'; 80 c-o.

Z3 uJW '"Q 0.

0.

NS-1280 of

2114.7

1214.7

- COSTANT CO POSITION----CONSTANT VOLUME DEPLETION

N2C

C01

C~

;-0, ~=~~;;~~~~;;.~~~~.~~.itn-C6~ ro

C7 -C 9 I .~

ClO

-C13

I .[ ~5514.7"'; ~

:1; ~~ ~II g:

10-5 C25+

PRESSURE I(ps i a) 714.7

10-6 '----:---'--'--'-.L.....J...-'--__---'__'---L......L.....L....l-.l-L..J3x10

2103 104

PRESSURE, psi a

Fig. 12 - Peng-Roblnson K-values for NS1 at 280 of representing twodepletion processes.

..t-Z

C!JUJ

'"'"D.

UJ

'":::>U)U)UJ

'"0-UJUZUJOJ

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+

UJ

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'"~I2114.7

CONSTANT VOLUME DEPLETIONCONSTANT COMPOSITION

N2C1

CO2C2

. C3,-C 4

. n-C4

oo

C10-C131 .[ ~

C25+~~~""""~1PRESSURE I 1214.7

(psia)714.710 -5 L---L-l-....l...-.!-l.....l-I.-::-__..l.-_..l.---L.---l..-l-...l--I.....J...J

3X 10 2 103 104PRESSURE, psia

10...I-Zex:l-(/)

Zou

:E:::JH~IJ)H-lH:::Jr:JJllJ

Fig. 13- Peng-Robinson K-values for NS-1 at 340 'F representing twodepletion processes.

1\

ro(f)

Q.

llJUZllJl!:l~

llJ>Zou

oooo

NS-Z241F

CONSTANT COMPOSITIONCONSTANT VOLUME DEPLETION

C2C3

i -C4--------- -==n- C4 =:::::::::::::: :::::::==----:::::;; llJ

~

:::J(/)(/)

llJ~

l:l..

ClOC11C12C13C14

:E:::JH~IJ)H-lH:::J

~ 10-1

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Zou

>< 10 2 ~---,----r--,---.-TT..,----~--r----,----r--,---,--rT""'I--..>..II~

10 -4 L--'---'----.l..--L-LLL-__--'--_--'--_.L.-...L.-.L.....l---.l..-.L.3x10 2 103 104

PRESSURE, psiaFig. 14-Peng-Roblnson K-values for NS-2 at 241 'F representing twodepletion processes.

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