.,

SPESPE 14265

Compressibility Factors for High-Molecular-WeightReservoir Gasesby R.P. Sutton, Marathon OilCo.

SPE Membar

Copyriiht 19S5, Society of Petroleum Engineers

This papar wasprepared for presentation at the 60th Annual Technical Conference and Exhibitionof the .S@ety of Petroleum Engineera held in LasVagaa, NV September 22-25, 1985.

This papa was selected for presentation by an SPE Program Committee following review of informationcontained in an abstract aubmiltad by theauthor(a). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correctionby theauthor(s).The material, as presented, doas not neceaaarily reflect any positionof the Society of Petroleum Engineers, its officers, or members. Paperspresentad at SPE meetings are subject to publicationreview by Editorial Commifteea of the Society of Petroleum Engineers. Permission to copy isrestrictedto an abatract of notmore than 300 words. Illustrationsmay notbe copied. The abatractshouldcontainconspicuousacknowledgmentofwhereand by whom the papar ia preaentad. Write Publication Manager, SPE, P.O. Box 633836, Richardson, TX 75063-3836. Telex, 730989 SPEDAL.

kBSTRACT resulting pressure drop from flow through pipe, staticpressure gradiente in gae wells, and reeervoir

This paper examines the effect of high performance. Ideally, gae PVT properties areconcentrations of the heptanes-plus fraction in determined from laboratory etudiee designed tonatural gases on the calculation of gas duplicate conditions of interest. However, quitecompreeaibility (Z) factors. Laboratory meaeured gae often experimental data ie unavailable, or PVTcompositions and Z factore are ueed to evaluate the properties muet be evaluated at conditions differentaccuracy of the Standing-Katz chart. It was from those examined by the laboratory etudies. Indetermined that the chart itself provides eatiefactory theee casea, PVT properties must be determined fromsccuracy; however, Kay’e molar average combination correlation. Probably the most widelyrulee or

acceptedcomparable gravity relationships for correlation for natural gas mixtures ie the

18 (SK) z factor chart.calculating pseudo-critical pressure and temperature Standing-Katzreeult in unsatisfactory Z factore for high molecular@e~Qht reeervoir gasee. The contribution of thie~..- The SK chart wae developed using data for binarypaper are two-fold. Firet, mixtures or met”nanewith pr~p=nz,pseudo-critical “

.new .Fhqa=....-. . . LWCZW, and

property - gae gravity relationehipe are developed, natural gaees having a wide range of composition.3

snd second, alternate methode for calculating None of the gas mixturee had molecular weights inpseudo-critical properties from composition are excese of 40. The SK chart is actually a modificationestablished. By utilizing either of theee methods to and exteneion of a generalized Z factor chart

Holcomb1$2 (BH) and is:alculate pseudo-critical preeaure and temperature, developed by Brown andthe overall accuracy of Z factors from the identical to the BH chart at reduced preesuree lessStanding-Katz chart is increased almost three-fold. than 4. Above thie value, the BH chart wae found to

be consistently inaccurate; therefore, Standing andKatz used data from 16 natural gaa mixtures, along

INTRODUCTION with methane Z factors ae a guide, to extend the chartto re~ueed ~i~8S.u?~S ef ~~- ~in~~ the SK chart

.1:-I.. ..-l.--.,l= w~+mhr hvdrnca~b~n gaSeS KIOrlIlall~n~gu ~v~=~...-r-%-=..-..._ -- appeared in the literature in 1941, equatione of stateencountered in the petroleum industry can be grouped have been developed which effectively reproduce afidinto two general categories. Natural gaees in the extend the chart aa ehown by the Dranchuk andEiret category contain relatively high concentration Abou-Kaseem method 5 in Fige. 1A and lB. Thie chartof ethane and propane typically ae the result of a low correlate Z factor ae a function of peeudo-reducedpressure flash with crude oil, while gasee in the preeaure and temperature:second category are gae-condeneatee and derive their~igh molecular weight from the quantity of z =f(Ppr, Tpr) . . . . . . . . . . . . . .(1)leptanes-plue present. This paper is concerned withlatter category of gaeee. where the peeudo-reduced pressure and temperature are

defined relative to pseudo-critical pressure andThe calculation of natural gas volume, density, temperature.

Dr viscosity at elevated pressuree and temperaturerequires

..values of Z factor. Tbeee quantities are ‘pr =P/Ppc . . . . . . . . . . . . . . . .(2)

necessary for the evaluation of gae reeerves, the

‘pr =T/Tpc . . . . . . . . . . . . . . . .(3):.,..-~---:--”references and IiLUWLLaLLU~L. at end cf paper. .

. .

2 COMPRESSIBILITY FACTORS FOR HIGH MOLECULAR WEIGHT RESERVOIR GASES SPE 14265

W.S b=gis for a generalized Z factor chart comes adjusting pseudo-critical properties. A total offrom van der Waals’ principle of corresponding states 1,085 Z factors from 9i gas mixttire~Were tltiiiZSd Ec

rhich says that two SaibStt3ikC~S at -n--nspfi~ing develo~ the adjustment parameters. The ranges of dataG“..-:onditions, referenced to some basic properties such used In the development of the method and theIs critical pressure and temperature, will have equations are detailed below:

similar physical properties. Therefore, if thexinciple could be applied without error, all gases Pressure, psia 154 to 7,026rould have the same Z factor at the same reduced Temperature, “F 40 to 300>ressure and temperature. However, the principle of Carbon Dioxide, mole Z O to 54.46

‘~rresp??ding ‘tates :s ‘ot ‘Xact aa ‘hem byHydrogen Sulfide, mole % O to 73.85

?lg. 2, but when applled to gasea having a similar:hemical structure, such as the paraffin hydrocarbons c s IZO.(AO.9 - A1.6) + 15.(B005 - B4) . . (6)

present in light natural gas mixtures, it providea acorrelating method with suitable accuracy for manyengineering calculations. T’ =TPC-E . . . . . . . . . . . . . . .(7)pc

The SK chart effectively provides a corresponding]tatea average Z factor correlation for natural gases. P;c = PPc”T;c/(Tpc +B”(l-B)E) . ...”(8)in independent confirmation of the chart’s accuracy:ss .-nnrt.d by Matthews et.-F---- al.14 The average Values from Eqs. 7 and 8 are then used to

~bsolute error for 231 data points from 29 different caiculate pseudo-rediiced ........_pa=..u.c =.m,~ temperaturegases was 1.2% with a maximum error of 6.7Z. The data for use with SK chart. The average absolutelsed in that study encompassed the following ranges of error in calculated Z factor from the Wichert and?alues: Aziz method was reported to be 0.97% with a

maximum error of 6.59%. This method waa used toPressure, psia 15 to 8,220 adjust the pseudo-critical properties of gasesTemperature, ‘F 20 to 280 containing carbon dioxide for

Gas Gravity, (air=l)

all further0.591 to 1.074 calculations performed for this paper.

Nitrogen, mole % o to 7.5Carbon Dioxide, mole % O to 1.8 To date, similar work for heavy hydrocarbon

gases has not appeared in the literature, althoughRoberts et al,15 showed that the chemical nature (i.e.The principle of corresponding states, as

?roposed by van der Waals, applies to single component paraffinic, naphthenic, or aromatic) of the heavy~ases, but subsequent work by Kay12 extended it to fraction in the gas affects the accuracy of the Zoixtures. For gas mixtures, pseudo-criticai pressiire fsctcr .s....-.I-,tIag~e~ by nc. mnre than 2.2%. Therefore,md temperature are used in place of critical pressure the effects of the quantity, and not necessarily theand temperature. The pseudo-critical valuea have no nature of the heavy fraction, must be ascertained.physical significance, but merely provide a means ofcorrelating mixture properties applicable tocorresponding states principles. Kay proposed that LABORATORY PVT DATA>seudo-critical pressure and temperature could be:alculated using simple mole average relationships. To determine the accuracy of Z factors calculated

by the traditional method (i.e. Ksy’s combinationP =xyi.P . . . . . . . . . . . . . . . . . (4)pc cl rules and the SK chart) and to arrive at a more

accurate method, a data bank of laboratory measuredT =Zyi.T , . . . . . . . . . . . . . . . . (5)pc cl natural gas compositions and PVT properties was

created. The data included 634 compositions from 275For low molecular weight, homologous gas individual PVT reports. A total of 1,761 single phase

mixtures, Kay suggested that the error in pseudo- 2 factors covering a wide range of pressures and:ritical properties determined from Eqs. 4 and 5 is on temperatures were provided by the reports. The:he order of 2% to 3X. However, for gas mixtures producing areas repreaented by the data and thevhose components differ greatly in molecular weight or distribution of the reports within each area is:hemical nature, the pseudo-critical pressure and provided below:temperature from these equations, when used with ageneralized compressibility factor chart, can lead to Location PVT Reports Total Compositionsinaccurate Z factors. These errors can become greater Gulf of Mexico 112 290:han tolerable for normal engineering calculation. Louisiana 85 131

Texas 53 98Natural gaaes often contain nitrogen, carbon Mississippi 6 6

,,llOXidE &il.d/Oi hy~~s~el? sulfide which can affect the Wyoming 1 6~ccuracy of calculated Z factors. Additionally, Other 18 i03~uantities of high molecular weight hydrocarbons, Total m m?hich are usually lumped together and reported asIeptanes-plus, can be present in the gas which can None of the gases contained hydrogen sulfide, but thesignificantly affect the accuracy of calculated Z samplea did contain varied amounts of carbon dioxideFactors. and nitrogen. Eighty-six compositions (14% of the

total) contained concentrationsWiehert and Aziz24

of carbon dioxidehave examined the effects of greater than 5%. ‘“””The ranges of data covered by the

:arbon dioxide and hydrogen sulfide on the calculation reports is aa follows:>f gas Z factor and have proposed methods Eor suitably

.-

SPE 14265 R. P. SUTTON 3

pressure, psia 200 to

Temperature, “F 100 to

Compressibility Factor 0.748 to

Gas Gravity, (air=l) 0.571 toCarbon Dioxide, mole % 0.01 to

Nitrogen, mole % o to

Heptanes-plus, mole % 0.02 to

12,5003602.1471.67911.862.8614.27

;oUPONENT CRITICAL PROPERTIES

The critical pressure and temperature for themre components norm lly present in natural gases aremovided in Table 1.

?‘he critical pr’’pertig::o:~$

~eptanes-plus fraction must be estimated.Las reviewed various methoas for eaLCU~~....=-----~-..+:+:..-.V-l.soaof

.ee-Kess~ej!sure >

:ritical pr and temperature and recommended thecorrelations (Eqs. 9 and 10). From the

:urrent study, Table 2 provides a comparison of theradiations in accuracy of the calculated Z factor

4,13,14,19ming different methods to characterize theLeptanes-plus fraction. The Lee-Kessler equations}how a slight improvement in calculated Z factor:ompared with the results obtained using the othercorrelations. Based these findings and Whitson’srecommendation, the Lee-Kessler equations were used?or further calculations.

PC n I)ww!l-f -= exp!t?.mk - v.”av”, , (0,24244 + 2.2898/Y +

0.11857/Y2)0

0.47227/Y2)-

10-10.Tb3]

0-3.Tb +

o-7.Tb2 -

. . . . .

1.4685 + 3.648/Y +

(0.42019 + 1.6977/Y2)”

. . . . . . . . . (9)

Tc = 341.7 + 811oY + (0.4244 + 0.1174.y).Tb +

(0.4669 - 3.2623”Y)”105/Tb . . . . . . (10)

The Lee-Kessler equations correlate criticalc..-.*:--of hoiIio.gp~int and specific>roperties &s a .“&L&.&W..

~ravity; however, laboratory reports normally providemly the specific gravity and moiecuiar weight of the

nitson22 has provided ani~~titF.~S-pl’U8 f~=~~~on,

~quation suitable for estimating the boiling point:rom specific gravity and molecular weight.

Tb = (4.5579°M0”15178@”15427)3 . . . . . . (11)

CALCULATION METHOD AND RESULTS

Numerical representation of the SK chart for:omputer calculations is ffered by many investigatorsis reviewed by Takacs. 2f T e most recent methods~tilize equations of state5~6~8,9 that offer increased~ccuracy while significantly extending the range ofthe SK chart. Each of these equations of state offer:omparable accuracy over its range of applicability.3ased on results presented by Takacs, the Dranchuk andibou-Kassem correlation was selected for thewaluation presented in this paper. This correlationis an 11 constant, generalized Starling equation of~tate as given by Eq. 12.

Z = 1 + (Al + A2/Tr + A3/Tr3 + A41Tr4 +

A5/Tr5)Pr + (A6 + A7/Tr + A8/Tr2)Pr2 -

2)Pr5 + Alo(l + A11Pr2)o~(A7/Tr + A81Tr

(pr2/Tr3)exp(-A11Pr2) . . . . . . . . . . (12)

where

Pr = 0.27[Pr/(Z*Tr)] . . . . . . . . . . . . (13)

The constants, Al - All, in Eq. 12 are as follows:

‘1.. = 0,3265 A, = -0.7361

A2 = -1.0700 A8 = 0.1844A3 = -0.5339 % = 0.1056A4 = 0.01569 Alo = 0.6134A5 = -0.05165 Al1 = 0.7210

n </,7<‘6 = ‘“2-’2

These constants were determined by fitting theequation, using nonlinear regression methods, to 1,500data points from the SK chart. The resulting equationwas reported to duplicate Z factors from the SK chartwith an average absolute error of 0.585% and isapplicable over the range:

o.25PDr <30

1.0 < Tpr~3.0

< 1.0;‘pr 0.7 <Tpr~ 1.0

Nonlinear regression methods16 can also be usedwith the Dranchuk and Abou-Kassem equations todetermine the pseudo-critical pressure and temperatureof a natural gas mixture. This provides pseudo-critical properties, hereafter referred to asIIinferredllvalues, for a gas mixture which are “tuned”

to the equation and thus the SK chart, therebyproviding more accurate Z factors. The results ofthese calculations for 264 compositions are shown inFigs. 3A and 3B. The scatter of the data in theseplots can be from compositional differences over anarrow range of gas gravities, deviation Erom the

Prifieipie ‘s CC~reSpC??ldiEg states, or errors inlaboratory &ta. The trends in Figs. 3A and 3B can berepresented by the Eqs. i4 and i5 as shown irIFig. ~.

19 which are basedFor reference, curves from Standing,on Kay’s combination rules for California naturalgases, are also presented.

= 756.8 - 131.O.Y -Ppc g3.6.Yg2 . . . . . (14)

Tpc = 169.2 + 349.5.Yg - 74.0*Yg2 . . . . . (15)

As shown by Fig. 4, Standing’s curves do notadequately represent the current data set. Plots ofthe “inferred” pseudo-critical properties versus thosefrom Kay’s rules (Figs. 5 and 6) further show this tobe the case. Using the “inferred” pseudo-criticalconstants aa a standard, Kay’s method predictedpseudo-critical pressure and temperature with anaverage absolute error of 3.86% and 2.23%,respectively. As a result, Z factors areunderpredicted with errora ranging as high as 15%(Figs. 7 and 8). The average absolute error for Fig.8 amounts to 2.78%. Alternatively, increased accuracy

4 COMPRESSIBILITY FACTORS FOR HIGH MOLECULAR WEIGHT RESERVOIR GASES SPE 14265

~ calculated Z factor iS obtalP.-‘ -d by utilizing Eqs.

~ and 15 to determine pseudo-critical pressure and!mperature. This is evident in Figs. 9 and 10 wherererage absolute error in calculated Z factor is!duced to 1.20%.

In 1959, Stewart, Burkhardt and Voo20 (SBV)lveloped and compared 21 different sets of mixingties for determining pseudo-critical pressure andxnperature. Overall, they found the best method forIlculating pseudo-critical constants is given by the)iiowlng equations:

J = l/3Zyi”(Tc/Pc)i +

(2/3).[Eyi”(Tc/Pc)~”5]2 _ . . . . . . (16)

K=~yi.(Tc/Pc0”5)i . . . . . . . . . . . (17)

Tpc =K2/J . . . . . . . . . . . . . . .(18)

Ppc =Tpc/J . . . . . . . . . . . . . . .(19)

These equations are essentially -qu~.:=~ep.~~Q ~’e

>mbination rules proposed by Joffe 16.In 1949 but are

~:;;}?nally ‘impler.” ln 1963’ ‘atter andevaluated 8 different combination rules andIncluded that the SBV rules provide more satisfactory?Sults over more complicated rules utilizingiditional correlating parameters. Both Stewart et1. and Satter and Campbell noted a decrease in the>thod’S accuracy when carbon dioxide or hydrogenllfide are present in the gas.

Figs. 11 and 12 show the increased accuracy in~lculated Z factors as a result of using the SBVlles as opposed to the results obtained from usingmy’s combination rules (Figs. 7 and 8). The average>solute error amounts to 1.31%. However, the errorsre still larger than those obtained from the>eudo-critical property - gas gravity relationships.~oking at Figs. 13 and 14, it can be seen that theres an increasing deviation at the end pointsxresponding to gases with high heptanes-plusmcentrations. Therefore, substantial improvement in~lcuiated z factcrs C.s?lbe cbtained by minimizinglese deviations. This is best accomplished utilizingmpirically derived adjustment factors applied to theW “J” and “K” terms.

J’=J-EJ . . . . . . . . . . . . . . . .(20)

K’=K-cK . . . . . . . . . . . . . . . .(21)

The terms, CJ and CK, were derived using multiplezgression analyses resulting in Eqs. 23 and 24.sptanes-plus concentrations of up tn 14.27% were usedn the development of these equations so theijustment parameters should be suitable for allsses.

FJ = (i/3)”iy”(Tci’Pc)]C7++

(2/3)-[Y-(Tc/Pc)0”5]:7+ . . . . . . . . (22)

‘J = 0.6081.FJ + 1.1325.FJ2 -

14.004.FJyC7+ + 64.434.FJy~7+ . . . . . (23)

EK . (Tc/Pc0”5)~7+”[0.3129”yC7+ - 4.8156*y$7+ +

27.3751”y~7+] . . . . . . . . . . . . (24)

The pseudo-critical pressure and temperature are:alculated from Eqs. 18 and 19 using the adjustedValues, J’ and K’. The adjusted pseudo-criticalconstants are plotted againat the “inferred”pseudo-critical values in Figa. 15 and 16. Thesverage absolute error of these adjusted pseudo-:ritical pressures and temperatures amounted to 1.24%

.-and i.72z, respectively. Mere importantly} subsequentcalculations of z factors evidence the increasedsccuracy of the modified SBV method as shown in Figs.17 and 18 where the average absolute error in:alculated Z factor is reduced to 0.95%.

Table 3 provides a summary of the accuracy of thecalculated Z factors for the different combinationrules over several ranges of gas gravity. Thenodified SBV method consistently yields more accurateresults for the higher specific gravity reservoirgases.

CONCLUSIONS

As a result of the work performed for this paper,the following has been concluded:

1. Significant improvements in the accuracy ofcalculated Z factors from the Standing-Katz chart canbe obtained, particularly for high molecular weightreservoir gases. The improvement is the result ofnewly defined methods for calculating pseudo-criticalpressure and temperature.

2. Pseudo-critical property - gas gravityrelationships are established which are suitable forall reservoir gases and provide more accurate resultsthan those offered from relationships derived withKay’s rules.

3. The Stewart, Burkhardt, and Voo (SBV) combinationrules, together with empirical adjustment factorsrelated to the presence of heptanes-plus,significantly improve the acd~racy ef calculated Zfactor. Overall, this method provides results almostthree times more accurate than those obtained usingKay’s combination rules. For high molecular weightreservoir gases (i.e.yg > 1.25), the modified SBVrules give Z factors over eight times more accurate.

4. Kay’s combination rules should not be used todetermine the pseudo-critical pressure and temperaturefor reservoir gases with specific gravities greaterthan about 0.75. This method consistently results inunderpredicted Z factors with errors ranging as highas 15%.

5. The Lee-Kessler equations should be used tocalculate the critical pressure and temperature forthe heptanes-plus fraction.

6. The Wichert and Aziz method should be used toadjust pseudo-critical pze$s’urs and temperature forthe presence of carbon dioxide in the gas mixture.

SPE 14265 R. P. SUTTON 5

NOMENCLATURE

A.

B=

J=

K=

M=

P=

Pc =

PCC7+ =

Ppc =

‘pr =

T=

Tb =

Tc =

~cc7+ =

Tpc =

‘pr =

Yi =

YL.7+=

z=

E=

Y=

Yg =

P= =

Ei =

E=

lE/=

u=

mole fraction (C02 + H2S)

mole fraction H2S

SBV parameter, Tpc/Ppc, “R/psia

SBV parameter, Tpc/Ppc0”,5,0R/psia0”5

molecular weight, lb-mole

pressure, psia

critical pressure, psia

critical pressure of heptanes-plus fraction,psia

pseudo-critical pressure, psia

pseudo-reduced pressure

temperature, “R (“F + 459.47)

normal boiling point temperature, “R

critical temperature, “R

critical temperature of heptanes-plusfraction, “R

pseudo-critical temperature, ‘R

pseudo-reduced temperature

mole fraction of component “it!

mole fraction of the heptanes-plus component

compressibility factor

adjustment factor

specific gravity, (water=l)

gas specific gravity, (air=l)

reduced density

calculated - measuredmeasured

x 100, percent error

ns average percent error

+, average absolute percent error

[=%0”5n = number of observations

standard deviation(absolute standarddeviation determinedusing absolute error andaverage absolute error)

aCKNOWLEDGEMENTS

The author would like to thank the management of4arathon Oil Company for permission to publish this>aper. John Neal with Weatheriy ‘~b~rat~iie~, Ific.should be recognized for contributing a significant?ortion of the laboratory data. Finally, the author

.. ... -- _,?OUld LLK6? ~0 CkItiIIK ~Oiig k@~.~G~L ad Ecb P~rsQns for

:heir technical support and help during theundertaking of this project.

U!FERENCES

1. Brown, G.G.: “The Compressibility ofI- Pure Gases,” Pet. Eng. (Jan.,

2. Brown, G.G. and Holcomb, D.E.: “The

Gases, Part940) 21-24.

Compressibility of Gases, Part 11 - GaseousMixtures,” Pet. Eng. (Feb., 1940) 23-26.

? Rv.wll-. “.” . . . . G.G,, Katz, D.L., Oberfell, G.G., and

Alden,’R,C. : Natural Gasoline and TheVolatile Hydrocarbons, Natural Gas. ASSOC. ofAmerica, Tulsa, OK (1948) Chapts. 2 and 4.

4. Cavett, R.H.: “Physical Data for DistillationCalculations - Vapor- Liquid Equilibria,”Proc. 27th Mid-Year Meeting, API, SanFransico, CA (1962) 351-366.

5. Dranchuk, P.M., Purvis, R.A. and Robinson, D.B.:“Computer Calculation of Natural GasCompressibility Factors Using the Standingand Katz Correlations,” Institute of PetroleumTechnical Series, No. IP74-008 (1974) 1-13.

6. Dranchuk, P.M. and Abou-Kassem, J.H.:“Calculation of Z Factors For Natural GasesUsing Equations of State,” J. Cdn. Pet. Tech.(July-Sept., 1975) 34-36.

7. Engineering Da$tiEmit, 9th EditiC!t,GESProcessors Suppliers Assn., Tulsa, OK (1972)Sec. 16.

8. Hall, K.R. and Yarborough, L.: “A New Equationof State for Z-Factor Calculations,” Oil andGas J. (June 18, 1973) 82-85, 90, 92.

9. Hall, K.R. and Yarborough, L.: “How to SolveEquation of State for Z-Factors,” Oil and GasJ. (Feb. 18, 1974) 86-88.—

10. Joffe. J.: “Commessibilities of Gas Mixtures.”Ind. Eng. Chern.(July, 1947) 837-838. -

11. Katz, D.L., Cornell, D., Kobayashi, R.,Poettmann, F.H., Vary, J.A., Elenbaas, J.R.,and Weinaug, C.F. : Handbook of Natural GasEngineering, McGraw-Hill Book Co., NY (1959).

12. Kay, W.B.: “Density of Hydrocarbon Gases andVapors at High Temperature and Pressure,” Ind.Eng. Chem. (Sept., 1936) 1014-1019. —

13. Kessler, M.G. and Lee, B.I.: “Improve Predictionof Enthalpy of Fractions,” Hyd. Proc. (March,1976) 153-158.

A COMPRESSIBILITY FACTORS FOR HIGH MOLECULAR WEIGHT RESERVOIR GASES SPE 14265

. .

.

). Matthews, T.A., Roland, C.H., and Katz~ D.L.:“High Pressure Gas Measurement,” Petrol.

Refiner (June, 1942) 58-70.

j. Roberts, D.S., Clark, C.R.~ and swift) ‘“: “PVTBehavior for Mixtures of Methane, Propane, and0. u“dr~~grbQns3VSSot. Pet. En- (Sept.,;$6?) 338-342.

~. SAS User’s Guide: statistics, SAS ~n~~i~~teInc., Cary, North Carolina (1982) 15-35.

7. Satter, A. and Campbell, J.M.: “Non-Ideal

Behavior of Gases and Their Mixtures,” SM.Pet. Eng. J. (Dec.j 1963) 333-347.

1. Standing, M.B. and Katz, D.L.: “Density of

Natural Gases,” Trans. AIME (1942) Vol. 146,140-149, Phase Behavior SPE Reprint Series No.15 (1980) 119-128.

3. Standing, M.B.: Volumetric and Phase Behavior ofOil Field Hydrocarbon Systems, 9th printing,Society of Petroleum Engineers of AIME,Dallas, TX (1981).

.iABLE 1

20. Stewart, W.F., Burkhardt, S.F., and VO08 ‘“:“Prediction of Pseudocritical Parameters for!4ixtures,”paper presented at the AIChEMeeting, Kansas City, MO (May 18, 1959).

21. Takacs, G.: “Comparisons Made for ComputerZ-Factor Calculations,” Oil and Gas J. (Dec.20, ‘--e’ “ ‘LlY/OJ U4-UU.

22. Whitson, C.H. and Torp, S.B.: “EvaluatingCofistan~Vc~uw Depletion Data~” J. _Pet.

~ (March, 1983) 610-620.

~~. Whitmni C,H.: “Effect of Physical PropertiesEstimation on Equation-of-State Predictions,t;paper SPE 11200 presented at the 57th AnnualFall Technical Conference and Exhibition, NewOrleans, LA (Sept. 26-29, 1982).

24. Wichert, E. and Aziz, K.:Sour Gases,” Hyd. PrOc.~~g-~~~e

S1 Metric Conversion Factors

‘tCalculateZ’s for(May, 1972)

degree F (°F-32)/l.8 = “Cpsi x 6.894 757 E+OO = kPa

Component

Carbon DioxideNitrogenMethaneEthanePropaneIsobutanen-ButaneIsopentanen-PentaneHexaneAir

PHYSICAL PROPERTIES OF DEFINED COMPONENTS

CriticalMolecular Weight Pressure, psia Temperature, “R

44.01028.01316.04330.07044.09758.12458.12472.15172.15186.17828.964

1,071.0493.0667.8707.8616.3529.1550.7490.4488.6436.9---

TABLE 2

EFFECT OF HEPTANES-PLUS CHARACTERIZATIONSTATISTICAL ACCURACY OF COMPRESSIBILITY FACTOR

Average % ErrorStandard DeviationAverage Absolute %Standard Deviation

547.57227.27343.04549.76665.68734.65765.32828.77845.37913.37---

ON THECALCULATIONS

Critical Property CorrelationMatthews,

Roland & Katz-2.40

Cavett-2.31

Lee-Kessler-2.29

3.77 3.58 3.58

Error 2.90 2.80 2.78

3.41 3.21 3.21

SPE 14265

STATISTICAL ACCURACY OF

Gas Gravity Range

0.56 < Yz~0.75 -

Average % ErrorStandard DeviationAverage Absolute %Standard Deviation

0.75 <Yz~ 1.00 -

Average % ErrorStandard DeviationAverage Absolute %Standard Deviation

1.00 <YE~l .25 -

Average % ErrorStandard Deviation

.k--1,.*sAverage fiuvu~U.=ZStandard Deviation

TABLE 3COMPRESSIBILITY FACTOR CALCULATIONS

SBV Eqs. 14 & 15

242 compositions, 626 data points

0.16 -0.191.09 1.25

Error 0.77 0.830.79 0.95

273 compositions, 548 data points

-1.03 -0.891.84 1.82

Error 1.52 1.371.46 1.50

75 compositions, 291 data points

-3.76 -1.422.48 1.78

v..,..u..”. 3.83 1.752.37 1.45

1.25 <Y ~ - 44 compositions, 296 data points

Average % Error -8.34 -0.15Standard Deviation 2.66 2.43Average Absolute % Error 8.34 1.76Standard Deviation 2.66 1.68

. .Total - 634 compositions, 1,761 data pointsAverage % Error -2.29 -0.56Standard Deviation 3.58 1.84Average Absolute % Error 2.78 1.31Standard Deviation 3.21 1.41

0.121.12

0.780.81

-0.171.591.051.20

-0.051.441.110.91

0.441.151.000.7’2

0.051.360.960.96

0.171.010.690.76

-0.031.801.251.29

-0.711.951.65

1.26

-1.491.531.761.21

-0.311.661.201.19

lSBV combination rules without heptanes-plus correction

2SBV combination rules with heptanes-plus correction

SPE w265

PSEUDO-REOUCEO PRESSURE

H!+ lA-~IMOCI gas mmprnglbll~ factorchart(after Oranchuk●td.c).

*.OsPE 1

1 1 1 1

: Q6\ x \ ,

j#\

1+

= Qs

.-:

!

\

~ ~,,

j CM.

03

Uc, H,*

0.1

00 0.2 0.4 Q6 0.3 LO 1.2 1.8 20 2.2 2A 2.6 2.8 an

d: mu, R

Fig. 2-DWiallOn lrom prindpla of cormpondlng smtas (aft- K8k d al.11).

1>0

725-

700

.+

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650+ ++

1615 - . . + “+’*++ ‘+ ~+

s

2

boo:, +:

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g,

3

t+

500

475 -

450

0506070 8091011 ‘2’ 314’ 5’6’7’8,920

GAS GRAV1 TY

Fig. 9A-VUlatiOn of p@oudMx12icd pmnum with P gmvlty (PP fromrcgr.nion wuiy9i9 of Eqs. 12 ●nd 19).

600

575- .

550

525-+ +

500-+ .++ ,+ t

w *75-:+ ,+ +

:m

. .

450:

2

~

$ 400

;

375 -g

y

350

325 -

0506070 8091011 ‘213141 516’7’8 ‘920

4L65

SPE 14265

700.

_ 50(

77----

‘“+-

E675 =- . . . . . . . . . .

650

625

600

575

550

5J---475

!

450

425

E

400

375

:/

300

0’5

II=

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1011121 314153 6’7181

GAS GRAVITY

mg. ~ d pscutbcdtkd pmpony mkt10n8hlfm.

++ /’

+

++

+++ .,.

++++ , .++

++

c

0 550 600 650

PsEuDO-CRITICAL PRESSURE (lMFERREO)

Fig. 5-ACCUNCY ofUay’s pnudodbl pmlwmmlatiOmhlP.

600’

S50

500

4s0

.-

0

/

+

+‘++

● *

400

3s0- ++

300 350 400 450 SOD

+.+

.

PSEIJD-l TICAL TEwllRATURf ( INFERRED)

Fig. o-AccumEy ofK@* p-u dodlkd tolnpmtum rdmiOrmhlp.

Soo

,.

..o~/- [00 0.5 ,0 15 20 2.5 3.0

UIASURED Z FACTOR

++++++ ‘1

, ,+&.+ *..+ +

$ ++!+++”.+

0.5 06 0.7 00 0.9 1.0 11 12 13 14 “5 “1.7 2 8 1.9

t0

GAS GRAvITY

F@.8-Emor In cdculat.d Z factor using PD.udo-dtlcd wnmmts lrom Kay’s comblnmtlonIUIC8.

2.5

I20 /+

.

*

0.0 05 10 ,5 20 25 30

hbsAsuRfO Z FACTCR

Fig. 9-CakuiMd vs. -rod Z bctom using new Pwudodttil propenY/ga8 gmvlty correk-tlons (*. 14 and 15).

15 ,

I

GAS GRAVITY

Fig. 10—EwOf in Cdoulakd z IDctOfUslrlgnow p9Nld0dticd propwtylgn WaVHY-I* (la*. 14 d W.

bBSOLUTE PERCENT ERROR

9?

—.

-++ ●

‘++-Ld%++ * ‘‘ +. +-.+++,+: ●

k*+-R + + + <.+x+0+

, * +“*+ *+~@*++

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++ +7++ *’+++

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++,++

a+** +++*

.—

++

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++

+++

‘+

++

+

++

+

+

+

.* I

CMCMATED Z FACWM

WE 14265

700 ‘

+ /

/

++ ++

+++

/

+’++

+

++ +

;/ ,

+ +500 650

1

5s0600

SooPSC”W&CRITICti PRESSURE ( lwcmRCo)

Fb. lS-*my d SSV ~*1 prossum ml@On*lp.

‘“”r550

I

500

450

.+● ☞

.++

. ++ +# .

++-+++++++ ‘.

%+ *$’

+++

1400 ++>s0 .+v

,,.y*5O 500 s50

300 350 400

PSEIIC,CI-CR,TICU TEWERhTURC ( lNrE*REO)

F@. 14-mw ~ -v~1 tmw-~ ~p”

,

. .

..

SpE 14265

/

+++++++

,

y ,1

500 6 SO700

500 550600

PSCUOO.CRJ 11 CAL PRESSURE ( lN=Rm~O)

Fig. IS--ACCUMCV of modifhd SBV PWU_i=l pm Ml~~*ip”

o

F@. m-Aewmw ~ ~ SBV~ tompmtumrolstlon*lp.

-.

‘“~ ‘K14’65

)5

10 -

05 -

00 05 10 15 20 25 30

U! ASUREOz FAC1OR