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Copyright 2000, Society of Petroleum Engineers, Inc.

This paper was prepared for presentation at the 2000 SPE Asia Pacific Oil & GasConference and Exhibition held in Brisbane, Australia, 16-18, October 2000.

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AbstractThis paper presents the initial stage of an effort aimed atdeveloping a new correlation to estimate pseudo criticalproperties for sour gas when the exact composition is notknown. Several mixing rules and gas gravity correlationsavailable in the literature are first evaluated and compared.The evaluation is performed on a large database consistingof more than 2000 samples of sour gas compositionscollected worldwide. Several evaluation criteria are usedincluding the average absolute deviation (AAD), thestandard deviation (SD), the coefficient of correlation, R,and cross plots and error histograms. The mixing rulesinclude: Kay’s mixing rule combined with Wichert-Azizcorrelation for the presence of non-hydrocarbons, SSBVmixing rule with Wichert and Aziz, Corredor et al. mixingrule, and Piper et al. mixing rule. These methods, in oneform or another, use information on gas composition. Threedifferent other methods that are based on gas gravity alonewere also analyzed. These are: Standing, Sutton, andElsharkawy et al. gas gravity correlations. While themethods based on knowledge of composition showedreasonable accuracy, those based on gas gravity aloneshowed weak accuracy with low correlation coefficients. Anew gas gravity correlation that is based on the fraction ofnon-hydrocarbons present in the sour gas was proposed.Preliminary results indicate that a good improvement overpast gravity correlations was achieved. The compositionalcorrelations, still show, however, better accuracy. Researchis still going on to come up with more accurate correlationsthat are based on only readily available descriptors.

IntroductionGas compressibility factor is involved in calculating gasproperties such as formation volume factor, density,compressibility, and viscosity. All these properties arenecessary in the oil and gas industry for evaluating newlydiscovered gas reservoirs, calculating initial and gasreserves, predicting future gas production, and designingproduction tubing and pipelines.The industry standard is to measure gas properties, Pressure-Volume-Temperature (PVT), in laboratory using reservoirsamples1. The draw back is that these isothermally measuredPVT data is applicable at measured pressured and reservoirtemperature. Calculation methods such as correlations andequations of state are used to predict properties at otherpressures and temperatures. Also, laboratory analyses forPVT behavior are sometimes expensive and timeconsuming. Correlations, which are used to predict gascompressibility factor, are much easier and faster thanequations of state. Sometimes these correlations havecomparable accuracy to equations of state. Predictingcompressibility factor for sour gases is much more difficultthan that of sweet gases. Therefore, several attempts havebeen made to predict compressibility factor for sweet gases2-

4. Wichert and Aziz5 presented corrections for the presenceof hydrogen sulfide and carbon dioxide for determiningcompressibility factor of sour gases.Because there is no exact method for predicting the PVTbehavior of natural gases several approximations have beenproposed. The most common method is to use one of theforms of the principle of corresponding states6,7. In thisform, gas compressibility factor is expressed as a function ofpseudo reduced pressure and temperature (Ppr,Tpr). Standingand Katz8 (SK) presented a chart for determining gascompressibility factor based on the principle ofcorresponding states. The SK chart was prepared for binarymixtures of low molecular weight sweet gases. Severalmathematical expressions fitting the SK chart, have beenproposed to calculate the gas compressibility factor9-15.Evaluation of these methods by Takacs16 and Elsharkawy etal.17 concluded that Dranchuk-Abou-Kassem12 (DK)correlation is the most accurate representation of SK chart.When dealing with gas mixtures, the mixture criticalpressure (Ppc) and temperature (Tpc) are required. Criticalproperties of natural gas are calculated from either gascomposition or gas gravity. Several mixing rules have beenproposed to calculate mixture critical properties of natural

SPE 64284

Compressibility Factor for Sour Gas ReservoirsAdel M. Elsharkawy and Ali ElkamelCollege of Engineering and PetroleumKuwait University, P.O. Box 5969, Safat 13060, Kuwait

SPE members

2 ADEL M. ELSHARKAWY AND ALI ELKAMEL SPE 64284

gases. Among these methods, Kay’s2 mixing rule andStewart-Burkhardt-Voo3 (SBV) are the most widely used.Kay’s mixing rule is simple and provides an accuratedetermination of gas compressibility factor for sweet gasesof low molecular weight. Satter and Campbell18 evaluatedseveral mixing rules for calculating properties of naturalgases. They concluded that Stewart-Burkhardt-Voo ruleknown as SBV provided the most satisfactory results,especially for gases of high molecular weight. Sutton4

studied the performance of several mixing rule forcalculating compressibility factor for gas condensates thatcontain a large amount of heptane plus fraction. Hemodified SBV mixing rule to account for the presence ofheptane plus in the natural gases.Standard laboratory analysis gives composition of naturalgases through hexane and lump components heavier thanhexane in a heptane plus fraction known as C7+. Criticalproperties of pure components are well documents, Table(1). The critical properties of the C7+ fraction are, however,calculated from correlations using molecular weight andspecific gravity of the heptane plus19-26. Whitson27 andElsharkawy et al.17 reviewed several methods for calculatingpseudo critical properties of the heptane plus fraction.Whitson27 recommended that Kesler-Lee20 (KL) correlationto be used to estimate critical properties of C7+. However,Elsharkawy et al. 17 found that Lin-Choa24 (LC) and KeslerLee20, respectively, with SSBV mixing rule and DKcorrelation are the best combination to determine gascompressibility factor for gas condensate reservoirs.Composition of natural gases, from which pseudo criticalproperties are computed, is not always available. Therefore,correlations relating pseudo critical pressure andtemperature to gas gravity are used. Standing1 presentedcorrelation of pseudo critical properties to gas gravity basedon low molecular weight California natural gases. Hiscorrelation has the following form:

Ppc = 706 - 51.7 γg - 11.1 γg2 (1)

Tpc = 187 + 330 γg - 71.5 γg2 (2)

Standing indicated that his correlation works only whenthere is no non-hydrocarbon gases present in the natural gas.Sutton4, working with PVT reports of high molecular weightgases which are rich in heptane plus, developed thefollowing correlation:

Ppc = 756.8 - 131.0 γg - 3.6 γg2 (3)

Tpc = 169.2 + 349.5 γg - 74.0 γg2 (4)

The gases that were used to develop Sutton’s gas gravitycorrelation are mostly sweet gases. These gases have minoramount of carbon dioxide and nitrogen, and no hydrogensulfide. Using a large data bank of retrograde gases,Elsharkawy et al.17 presented another correlation for gascondensates. The latter correlation covers heavier gases thanthat used in Sutton’s and have a minor amount of hydrogensulfide. Elsharkawy et al. gas gravity correlation has thefollowing form:

Ppc = 787.06 - 147.34 γg - 7.916 γg2 (5)

Tpc = 149.18 + 358.14 γg - 66.976 γg2 (6)

Thus there is a need for correlation relating gas gravity topseudo critical properties for sour gases.This study has two objectives. The first objective is toevaluate the previously published methods of calculating gascompressibility factor for sour gases. The second objectiveis to develop a correlation to estimate pseudo criticalproperties from gas gravity for sour gas when composition isnot available.

Gas data bankOne of the main objectives of the current work is to evaluatethe previously published methods of calculating gascompressibility factors of sour gases using either gascomposition or gas gravity. The best test to evaluate suchmethods is the accuracy with which these methodsapproximate reliable experimental data. The data bank usedin this study comprises measurements of two thousand andone hundred and six gas compressibility factor for sourgases. Some of these data have been collected from theliterature28-33. These measurements cover a pressure rangefrom 90 psi to 12,000 psi, a temperature range from 40 οF to327 οF, and a wide range of molecular weights from 16.4 to55 (gas gravities from 0.566 to 1.895). A completedescription of the data bank is reported in Table (2).

Calculating gas compressibility factor whencomposition is knownWhen gas composition is available, pseudo criticalproperties are calculated using a given mixing rule. In orderto calculate the pseudo-critical properties of natural gasmixtures, critical properties of the heptane plus fractionmust be computed. In this study, Kesler-Lee20 (KL) method,equations (7) and (8), are used to calculate critical propertiesof the C7+.

Pc = exp [8.3634 - 0.0566/γ - ( 0.24244 + 2.2898/γ + 0.11857/γ2).10-3.Tb + (1.4685 + 3.648/γ + 0.47227/γ2) .10-7.Tb

2 - (0.42019 + 1.6977/γ2 ).10-10.Tb3 ] (7)

Tc = 341.7 +811. γ + (0.4244 + 0.1174. γ). Tb + (0.4669 - 3.2623. γ) .105 / Tb (8)

The KL method correlates critical properties as a function ofboiling point and specific gravity. However, laboratoryreports normally provide only the specific gravity andmolecular weight of the heptane plus fraction. Whitson28

has presented an equation for estimating boiling point (Tb)from molecular weight (M) and specific gravity (γ) of theheptane plus fraction.

Tb = (4.5579. M0.15178 γ0.15427 )3 (9)

In this study, Kay’s mixing rule, Stewart-Burkhardt-Voo(SBV) mixing rule as modified by Sutton (SSBV) areconsidered.

Kay’s2 mixing rule, based on molar weighted averagecritical properties, has the following form:

Ppc = ∑ yi Pci (10)

SPE 64284 COMPRESSIBILITY FACTOR FOR SOUR GAS RESERVOIRS 3

Tpc = ∑ yi Tci (11)

Stewart-Burkhardt-Voo3 (SBV) proposed the followingmixing rule for high molecular weight gases.

J = (1/3) [ ∑ yi (Tc/Pc)i ] + (2/3) [ ∑ yi (Tc/Pc)i

0.5 ]2 (12)

K = ∑ [yi (Tc / Pc 0.5)i] (13)

Tpc = K2/J (14)Ppc = Tpc /J (15)

If the natural gas contains heptane plus fraction, Sutton4

modification of SBV (SSBV) is used.

Fj = (1/3)[ y (Tc/Pc) ]c7+ + (2/3)[ yi (Tc/Pc)i

0.5 ]2c7+

(16)Εj = 0.6081 Fj + 1.1325 Fj

2 - 14.004 Fj yc7+

+ 64.434 Fj yc7+2

(17)

Ek = (Tc/Pc0.5)c7+ [ 0.3129 yc7+ - 4.8156 yc7+

2

+ 27.3751 yc7+3 ] (18)

J′ = J - Ej (19)

K′ = K - Ek (20)

Tpc = K′2/J′ (21)Ppc = Tpc /J′ (22)

Equations (10) and (11) or (12) through (22) provide criticalproperties for sweet natural gas systems. For sour gases,these equations must be corrected for the presence of non-hydrocarbon components. The method proposed by Wichertand Aziz5 is used to correct the pseudo critical properties ofnatural gases to the presence of these non-hydrocarboncomponents. The correction factor is given below :

∈ = 120. (A0.9 - A1.6 ) + 1.5 (B0.5 - B4) (23)

Where the coefficient A is the sum of the mole fraction ofH2S and CO2 and B is the mole fraction of H2S in the gasmixture. The corrected pseudo critical properties Ppc′ andTpc′ are:

Tpc′ = Tpc - ∈ (24)Ppc ′ = Ppc Tpc′ / [Tpc + B (1-B) ∈ ] (25)

Reduced pressure (Ppr) and reduced temperature (Tpr) arecalculate from pressure (P) and temperature (T) of interestand critical properties of the natural gas (Ppc ′, Tpc′) by thefollowing relationship:

Ppr = P/ Ppc ′ (26)Tpr = T/ Tpc′ (27)

Recently, Corredor et al.34 , and Piper et al.35 proposed amixing rule similar to SBV rule, equations (12) and (13).However, they treated the non-hydrocarbons and the C7+

plus fraction differently. Their mixing rule has the followingform:

J = α0 + ∑αi yi (Tc/Pc)i + α4∑yj (Tc/Pc)j + α5[∑ yi (Tc/Pc)i ]2

+ α6 (yc7+ Mc7+) + α7 (yc7+ Mc7+)2 (28)

K = β0 +∑βi yi (Tc/Pc0.5)i+ β4 ∑yj (Tc /Pc

0.5)j

+ β5 [∑ yj (Tc/Pc 0.5)j]

2 + β6 (yc7+ Mc7+)

+ β7 (yc7+ Mc7+)2 (29)

Where yi ∈{yH2S,yCO2 , yN2} and yj ∈{yC1,yC2 , ... ,yC6} and αand β are constants. The difference between Corredor et al.method and Piper et al. method is that each method hasdifferent values for α and β. To calculate the pseudo criticalproperties of the gas condensate, Corredor et al. and Piper etal. used the weight fraction of the C7+ rather than the criticalproperties. Thus, they eliminate the need to characterize theheptane plus fraction. They also eliminated the correctionsneeded for presence of acid gases, equations (23) through(25).

The gas compressibility factor (Z) is computed from DKcorrelation using reduced pressure (Pr) and reducedtemperature (Tr) as follows:

Z = 1 + (A1 + A2/Tr + A3/Tr 3 + A4/Tr 4 + A5/Tr 5 ) ρr + (A6

+ A7/Tr + A8/Tr 2 ) ρr2 - A9 (A7/Tr + A8/Tr 2 ) ρr

5 + A10 (1 +

A11 ρr2 ) .( ρr

2/Tr 3 ) exp (-A11 ρr2 ) (30)

Where ρr = 0.27 [Pr / ZTr ] (31)

The constants A1 through A11 in equation (30) are asfollows:

A1 = 0.3265 A2 = -1.0700 A3 = -0.5339A4 = 0.01569 A5 = -0.05165 A6 = 0.5475A7 = -0.7361 A8 = 0.1844 A9 = 0.1056A10 = 0.6134 A11 = 0.7210

Because the gas compressibility factor appears on both sidesof DK’s correlation, equation (30), an iteration solution isnecessary. Newton-Raphson method is used which has thefollowing iteration formula:

Zn+1 = Zn - ( fz/ f′z ) (32)

Where Zn+1 and Zn are the new and old values of gascompressibility factors, fz is the function described inequation (30), and f′z is its derivative.

Calculating gas compressibility factor whencomposition is unknownWhen gas composition is not available, the compressibilityfactor is computed via estimating the critical properties fromgravity correlations. In this section, the accuracy withwhich gas gravity correlations, equations (1) through (6),reproduced the experimentally measured gas compressibilityfactor is evaluated. Although Standing gas gravitycorrelations, equations (1) and (2) were prepared to estimatecritical properties of sweet low molecular gases, it isimportant to know the magnitude of the error that resultsfrom using that correlation. The accuracy of the gas gravitycorrelations developed by Sutton, equations (3) and (4), andElsharkawy et al. given in equations (5) and (6) are alsostudied in this section.


Results and DiscussionThe accuracy of four different methods for the calculation ofgas compressibility factor for sour gases is discussed in thissection. The first method is Kay’s mixing rule with Wichert-Aziz correction for the presence of non-hydrocarbons. Thesecond is SSBV-Wichert and Aziz. The third is Corredor etal. method. The last method is Piper et al. Table (3) showsthe accuracy of these methods. Piper et al. and Corridor etal. have the best accuracy. Both of these methods accountfor the presence of heptane plus and non-hydrocarbons.Piper et al. methods has average absolute deviation (AAD)of 1.21% and standard deviation (SD) of 1.92% andcoefficient of correlation (R) of 99.10%. SSBV-Whichertand Aziz shows the highest errors and the lowest correlationcoefficient.Figures (1) through (4) show the error distribution for thefour methods considered in this study. Kay-Wichert andAziz method, Figure (1), Coredor et al. method, Figure (2),and Piper et al. methods, Figure (4) have comparable errordistribution. However, Piper et al. method has the smallesterror range and the highest frequency of zero error. SSBV-Wichert and Aziz method, Figure (2) has a wider error rangeand smaller frequency of error distribution around zero errorline comparing to the other methods.The accuracy of calculating gas compressibility factor forsour gases using gas gravity when gas composition isunknown is shown in Table (4). Standing gas gravitycorrelation, equations (1) and (2) has an average absolutedeviation (AAD) of 3.50% and standard deviation (SD) of6.78%. Sutton gas gravity correlation, equations (3) and (4),has AAD of 3.47% and SD of 7.14. Elsharkawy et al. gasgravity correlation, equations (5) and (6), shows AAD of3.48% and SD of 7.30%. All of these gas gravitycorrelations have similar correlation coefficients. The reasonfor the low accuracy of these correlations is that Standinggas gravity correlation was prepared for sweet gases. Suttongas gravity correlation was prepared for heavy gases rich inC7+ with minor amounts of hydrocarbons. The latter gasgravity correlation is applicable for gases that have nohydrogen sulfide and with a nitrogen content less than 12%and a CO2 content less than 3%36. Elsharkawy et al. gasgravity correlation was prepared from data on gascondensate that has a significant portion of hydrogen sulfideand carbon dioxide, however, the concentration of the acidgases is not comparable with the sour gases used in thispaper.

New gas gravity correlationOne of the objectives of the this study is to start thedevelopment of a new correlation to estimate pseudo criticalproperties from gas gravity for sour gas when composition isnot available. Using large data bank of sour gas system,inferred pseudo critical pressures and temperatures arecalculated from experimentally measured gascompressibility factors using DK equations. The firstattempt was to correlate these inferred pseudo critical valuesto gas gravity for sour gases. Figure (5) shows that pseudo-critical pressures of sour gases are not strongly correlated tototal gas gravity. In order to improve the correlations it wasattempt to study the effect of non-hydrocarbon componenton pseudo-critical properties. Figure (6) shows that pseudo-

critical pressures are highly correlated to the percentage ofnon-hydrocarbon gases. The percentage of non-hydrocarboncomponent is expressed as molecular weight of non-hydrocarbon components divided by the total molecularweight of the gas. This percentage can also be related tonon-hydrocarbon gas gravity (γ2) divided by total gas gravity(γg). Pseudo critical temperature, however, is stronglydependent on total gas gravity, Figure (7). Therefore, it wasfound that best correlation of pseudo-critical properties togas gravity can be achieved by considering both thehydrocarbon and non-hydrocarbon portions of gas gravityas follows:

Pc = 193.941 -131.347 γg + 217.144 γ1/γg + 1060.349 γ2/γg

+344.573 (γ1/γg)2 -60.591 (γ2/γg)

2 (33)

Tc = 195.958 206.121γg + 25.855 γ1/γg - 6.421 γ2/γg

+ 9.022 (γ1/γg)2 + 163.247 (γ2/γ g)

2 (34)

The new gas gravity correlation presented in this study hassmaller error range than the other correlations. Correlatingcritical properties to the amount of hydrocarbon and non-hydrocarbon gases, equation (33) and (34), improves theaccuracy of the proposed correlation. Among the gas gravitycorrelations considered in this study, the new correlationshows the smallest AAD (1.69%), the least SD (3.22%), andthe highest correlation coefficient (97.66%). However, Thestandard deviation is still high.

Figures (8), (9), and (10) show the absolute error percentagein estimating gas compressibility factor from gas gravitycorrelations is highly dependent on the amount of CO2 andH2S present in the sour gas. An error as high as 50% in gascompressibility factor occurs if these gas gravitycorrelations are used to estimate the gas compressibility forsour gases. Figure (11) shows first smaller error level incalculating gas compressibility factor using the new gasgravity correlation than the other correlations. Second, theerror is not dependent on the amount of CO2 and H2Spresent in the sour gas. Figure (12) shows a crossplot ofmeasured and calculated gas compressibility factor using thenew gas gravity correlation for the sour gases used in thisstudy. The figure illustrates that most of the data fall on the45o parity line. Therefore, calculating the gascompressibility factor for sour gases from pseudo-criticalpressure and temperature estimated from total gas gravitycorrelations has some limitations. The major limitation is inthe process of correlating gas gravity to pseudo criticalproperties. For any gas, there could be an infinite number ofhydrocarbon and other non-hydrocarbon combination. Eachhydrocarbon and non-hydrocarbon component has a uniquepseudo critical property. However, different mixtures canhave different pseudo-critical properties and the same gasgravity. This is the reason why calculating gascompressibility factor using gas gravity is not as muchaccurate as calculating gas compressibility factor fromcomposition. Correlating pseudo critical properties tohydrocarbon portion of gas gravity and non-hydrocarbonportion have resulted in little improvement of gascompressibility calculations.

SPE 64284 COMPRESSIBILITY FACTOR FOR SOUR GAS RESERVOIRS 5

ConclusionsIn this paper, several methods of calculating sour gascompressibility factors were compared. Two classes ofmethods were considered: methods that are based oncomposition and those that are based on gas gravity alone.From the methods based on composition, Piper et al. andCorridor et al. Showed the best accuracy and correlationcoefficient. These methods account for the presence ofheptane plus and non-hydrocarbons. Of the methods basedon gas gravity Sutton and Elsharkawy et al. Methods werethe most accurate. The accuracy of these methods were,however, poorer than those methods based on composition.It was decided therefore to study the effect of the presenceof non-hydrocarbons on accuracy. A plot of pseudo-criticalpressure with both gas gravity and non-hydrocarbon gasgravity was evaluated. It was found that while thecorrelation with gas gravity is weak, that with the non-hydrocarbon gas gravity is strong with a correlationcoefficient more that 0.84. The correlation of pseudo criticaltemperature was rather indifferent to the presence of non-hydrocarbons. A new correlation was then proposed toaccount for the presence of non-hydrocarbons withoutknowing the compositional details. This correlation is basedon two descriptors: gravity of the gas and gravity of the non-hydrocarbon portion in the gas. The new correlationprovided a good improvement over past gas gravitymethods. Research is still going on to develop moreimprovement strategies.

AcknowledgmentThe first author thanks the Kuwait Foundation for theAdvancement of Science (KFAS) for providing financialsupport for this study, research grant No. 99-9-09.

Nomenclatureρr = Reduced density

∈= Wichert and Aziz pseudo-criticalγg = gas specific gravity, (air =1)γ1 = Hydrocarbon gas specific gravity, (air =1)γ2 = Non-hydrocarbon gas specific gravity, (air =1)A = mole fraction (CO2 + H2S)B = mole fraction H2SAAPD = Average absolute errorEJ = Sutton SBV parameter, oR/psiaEK = Sutton SBV parameter, oR/psia0.5

ARE = Average relative errorFJ = Sutton adjustment parameter temperature adjustment parameter, oRJ = SBV parameter, oR/psia

J′ = Sutton parameter, oR/psiaJinf = Inferred value of J parameter, oR/psiaK = SBV parameter, oR/psia0.5

K′ = Sutton parameter, oR/psia0.5

Kinf = Inferred value of K parameter, oR/psia0.5

M = Molecular weight, lb-moleMC7+ = molar mass of heptane plus fraction, lb-moleP = pressure, psiapc = critical pressure, psiaPpc = pseudo-critical pressure, psia

Ppr = pseudo-reduced pressureR = correlation coefficientSD = standard deviationT = temperature, oRTb = normal boiling point temperature, oRTc = critical temperature, oRTpc = pseudo-critical temperature, oRTpr = pseudo-reduced temperatureyC7+ = mole fraction of heptane plus fraction yi = mole fraction of component, “i”yi = mole fraction of the i-th componentZ = gas compressibility factor

References1- Standing, M. B.: Volumetric and Phase Behavior of OilField Hydrocarbon Systems, 9th printing, Society ofPetroleum Engineers of AIME, Dallas, TX (1981).

2- Kay, W.B.: Density of Hydrocarbon Gases and Vapor atHigh Temperature and Pressure, Ind., Eng. Chem. (Sept,,1936) 1014-1019.

3- Stewart, W.F., Burkhard, S.F., and Voo, D., Prediction ofPseudo Critical Parameters for Mixtures, Paper presented atthe AIChE Meeting, Kansas City, MO (1959).

4- Sutton, R. P.: Compressibility Factors for High MolecularWeight Reservoir Gases, Paper SPE 14265 presented at theSPE Annual Technical Meeting and Exhibition, Las Vegas,Sent. 22-25, 1985.

5- Wichert, E., and Aziz, K., Calculation of Z’s for SourGases, Hydrocarbon Processing, Vol. 51, No. 5, 1972, pp.119-122.

6- MacCain, William D., Jr.: The Properties of PetroleumFluids, 2nd ed., PennWell Books, Tulsa,1990.

7- Ahmed,T., Hydrocarbon Phase Behavior, Gulf publishingCo, 1989.

8- Standing, M. B. and Katz, D. L., Density of NaturalGases, Tran. AIME, Vol. 146, 1942, pp. 140-149.

9- Papay, J., ATermelestechnologiai Parameterek Valtozasaa Gazlelepk Muvelese Soran, OGIL MUSZ, Tud, Kuzl.,Budapest, 1968, pp. 267-273.

10- Hall, K. R. and Yaborough, L.: A New Equation of Statefor Z-Factor Calculations, Oil and Gas J. (June 18,1973)82-85, 90, 92.

11- Yarborough, L. and Hall, K.R., How to Solve Equation-of-State for Z-Factors, Oil and Gas Journal, February 18,1974, pp. 86-88.

12- Dranchk, P.M. and Abou-Kasem, J.H.: Calculation of ZFactors for Natural Gases Using Equations of State, J. Cdn.Pet. Tech. (July-Sept., 1975) 34-36.

13- Dranchk, P.M., Purvis, R.A. and Robinson, D.B.:


Computer Calculation of Natural Gas compressibilityFactors Using the Standing and Katz correlations, Instituteof Petroleum Technical Series, No. IP74-008 (1974) 1-13.

14- Hankinson, R.W., Thomas, L.K., and Philips, K.A.,Predict Natural Gas Properties, Hydrocarbon Processing,April, 1969, pp.106-108.

15- Brill, J. P. and Beggs , H. D.: Two-phase flow in pipes,INTERCOMP Course, The Huge, 1974.

16- Takacs, G. Comparison Made for Computer Z-FactorCalculation, Oil and Gas Journal, Dec., 20, 1976, pp. 64-66.

17- Elsharkawy, A. M., Hashem Y. Kh., and Alikhan, A. A.,Compressibility factor for gas condensate reservoirs, PaperSPE 59702 presented at the SPE 2000 Permian Basin Oiland Gas Recover Conference held in Midland, TX., 21-23March, 2000.

18-Sattar, A., and Campbell, J. M., Non-ideal behavior ofgases and their mixtures, SPEJ, December, 1963, 333-347.

19- Win, F. W., Simplified monograph presentation,characterization of petroleum fraction, Petroleum Refiner,Vol. 36, No. 2, 1957, 157.

20- Keseler, M.G. and Lee, B. I. : Improve Prediction ofEnthalpy of Fraction, Hyd. Proc. (March, 1976) 153-158.

21- Rowe, A. M., Internally Consistent Correlation forPredicting phase Composition of Heptane and HeavierFractions, Research Report 28, GPA, Tulsa, 1978.

22- Sim, W.J. and Duabert, T. E., Prediction of Vapor-Liquid Equilibria of Undefined Mixtures, Ind. Eng. Chem.Process Des. Dev., Vol. 19, No. 3, 1980, pp. 380-393.

23- Riazi, M. R. and Daubert, T. E., Simplify PropertyPrediction, Hydrocarbon Processing, March 1980, pp. 115-116.

24- Lin, H. M. and Chao, K. C., Correlation of criticalProperties and Acentric Factor of HydrocarbonDerivatives, AIChE Journal, Vol. 30, No. 6, Nov. 1984, PP.153-158..

25- Watansiri, S. , Owens, V. H., and Starling, K. E.,Correlations for Estimating Critical Constants , Accentric

Factor, and Dipole Moment for Undefined Fractions, Ind.Eng. Chem. Process Des. Dev., 1985, Vol. 24, pp. 294-296.

26- Pedersen, K. S., Fredensland, Aa. And Thomassen, P.Advances in Thermodynamics 1, 1989, 137.

27- Whitson, C. H. Evaluating constant-volume depletiondata, JPT, March 83, 610.-620.

28-Simon, R., and Briggs, J. E., Application of Benedict-webb-Rubin equation of state to hydrogen sulfide mixtures,AIChE J., Vol. 10, No. 4, July, 1964, 548-550.

29-Robinson , R. L., Jr., and Jacoby, R. H., Bettercompressibility factors, Hydrocarbon Processing, Vol. 44,No. 4, April, 1965, 141-145.

30-Buxton, T. S., and Campbell , J. M., Compressibilityfactors for lean natural gas-carbon dioxide mixtures at highpressures, SPEJ, March, 1967, 80-86.

31-McLeod, W. R., Application of Molecular refraction tothe principle of corresponding states, Ph. D. Thesis,University of Oklahoma, 1968.

32-Wichert, E., Compressibility of sour natural gases, Ms.Thesis, University of Calgary, Alberta, 1970.

33- Elsharkawy, A. M., and Foda, S. G.: EOS simulationand GRNN modeling of the constant volume depletionbehavior of gas condensate reservoirs, Energy & Fuels,1988, 12, 353-364.

34- Corredor, J.H., Piper. L.D., and McCain, W. D., Jr.:Compressibility Factors for Naturally Occurring PetroleumGases, Paper SPE 24864 presented at the SPE AnnualTechnical Meeting and Exhibition, Washington, D.C., Oct.4-7, 1992.

35- Piper, L.D., McCain, Jr., Corredor, J. H.,Compressibility Factors for Naturally Occurring PetroleumGases, SPE 26668, Houston, TX, Oct. 3-6,1993.

36-Lee, J. and Wattenberger, R. A. : Gas ReservoirEngineering, SPE Text Book Series Vol. 5, 1996,

SPE 64284 DETERMINATION AND PREDICTION OF WAX DEPOSITION FROM KUWAIT CRUDE OILS 7

Table (1) Physical properties of defined components

Component Molecularweight

Criticalpressure

Criticaltemperature

psia Deg RH2S 34.08 1300.00 672.45CO2 44.01 1071.00 547.45N2 28.01 493.00 227.27C1 16.04 667.80 343.04C2 30.07 707.80 549.76C3 44.01 616.30 665.68

i-C4 58.12 529.10 734.65n-C4 58.12 550.70 765.32i-C5 72.15 490.40 828.77n-C5 72.15 488.60 845.37C6 86.18 436.90 913.37

Table 2-Properties of sour gas data used in the study

Min. Ave. Max.

Pressure, psi 90 2900 12,000Reservoir temperature, F 40 190 327

Composition mole %Methane 17.27 74.14 97.40Ethane 0 6.00 28.67Propane 0 2.56 13.16iso-Butane 0 0.50 2.61n-Butane 0 0.84 5.20iso-Pentane 0 0.35 2.85n-Pentane 0 0.32 2.09Hexane 0 0.44 5.30Heptane plus 0 1.64 17.20Mw C7+ 98.0 127.0 253.0γ C7+ 0.72 0.77 0.85Z-factor 0.402 0.900 1.775Gas gravity (air=1) 0.566 0.811 1.895Hydrogen sulfide 0 7.45 73.85Carbon dioxide 0 4.04 67.16Nitrogen 0 1.72 25.15

8 ADEL M. ELSHARKAWY, TAHER AL-SHAHAF, MOHAMED A. FAHIM AND WAFAA AL-ZABBAI SPE 64284

Table-3 Accuracy of calculating Z-factor for sour gases using compositional data

Method ARE AAD SD RKay- Wichert & Aziz 0.69 1.38 2.13 98.57SSVB- Wichert & Aziz 0.65 2.14 2.85 97.65Corredor et. al 0.25 1.36 2.51 98.8Piper et. al 0.31 1.21 1.92 99.10

Table-4 Accuracy of calculating Z-factor for sour gases using gas gravity equation

Method ARE AAD SD RStanding -0.81 3.50 6.79 92.08Sutton -1.72 3.47 7.14 91.43Elsharkawy et al. -2.25 3.48 7.30 91.23Current study -0.26 1.69 3.12 97.66

ARE : Average relative error % AAD : Average absolute deviation % SD : Standard deviation % R : Coefficient of correlation


Figure 4–Histogram of error with normal curve (Corredor)

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