sour natural gas eos

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Society of Petroleum Engineers

WE 26906Sour Natural Gas and Liquid Equation of StateMohsen Mohsen-Nia, U. of !Ilinois; Hamid Moddaress, Amlr-Kabir U.; and G.A. MansoorL*U. of IllinoisqSPE Member

%Yk@ 19S3,SOCWof PetroleumEngineers,Inc.Thhpe#arWOErepamlforpreeanlatlon81the 1S93 EasternRegionalC~~ference& Sxh!bltionheld in Pittsburgh,PA, U.S.A., 2-4 November1SS3.Th!dpepet waaaelectadfor pr%enlalionby an SPE ProgramCommltfeefollowingreviewof Informationcontainedinm abetracfeubmittedbythe author(s).Contenteofthe paper.asWeeentad.havenot been reviewedby the Sdety of PetroleumEngmeereand are subjectto cofrecflonby the author(s).The matermt,as presented.d~s notneceaaarilyraflectanypaaltkwrof the &clety of PetroleumEngineara,rfaofficer%ormember%Paperapreaenwdal SPEmeetlngaaresubjectto publicationreviewbyEditorialCommltfeeaofthe SoclatyofPefrofeumEr@were. Parmtaahntocopylareafrkfadtoan abafractofM owe than3W wo+de.lluefratlonsm~ynotbecqrled. Theabstractshouldwntaln conaplcuouaacknowledgmentotwtremand bywhomthe papnrla praaemed.Write Librarlen,SPE, P.O. Sox6338SS,Richardson,TX 75023-3636. U.S.A., Telex 1S3245SPEUT.

ABsTIwcrIlie major gaseous impurities in the subquality natural gassources are acidic components, such as hydrogen sulfideand carbon dioxide. Considering that H2S easilydissociates into hydrogen and elemental sulfur,thermodynamic properties and specially phase equilibriaof liquid and gaseous systems containing hydrogen,hydrogen sulfide, carbon dioxide, other acidiccomponents, and light hydrocarbons are of much interestto the natural gas and gas condensate productionindustries.In this paper we report the development of a simple andaccurate cubic equation of state for prediction ofthermodynamic properties and phase behavior of sournatural gas and liquid mixtures. This cubic equation ofstate, which is based on statistical mechanicaltheoretical grounds, is applied to pure fluids as well asmixtures with quite accurate results. All thethermodynamic property relations of sour gaseous andliquid mixtures are derived and reported in this report.Parameters of this equation of state are derived fordifferent components of sour natural gas systems. Theresulting equation of state is tested for phase behaviorand other thermodynamic properties of simulated andnaturai sour gm mixtures. It is shown that the presentequation of state, even though it is simple, predicts theproperties of interest with ease and accuracy.----------- -----_ _-,____ ______ ____ ._,References and Illustrations at enci of paper

INTRODUCTIONIn the past two decades, a number of subquality naturalgas / gas condensate fields have been discovered aroundthe worldl2. The major impurities of these subqualitynatural gas / gas condensate sources consist of N2, cm andH2S. since that H2S easily dissociates into hydrogen andelemental sulfur therefore, thermodynamic propertiesand specially phase equilibria of liquid and gaseoussystems containing hydrogen, hydrogen sulfide, carbondioxide, other acidic components, and light hydrocarbonsare of much interest to the natural gas and gas condensateproduction industries24.Transportation, and processing of sour and hydrogencontaining natural gas is of major concern to the industiesinvolved. Carbon dioxide and hydrogen sulfide areconsidered as being impurities in natural gas and oil andare responsible for corrosion of the flow-line andpnxessing equipment. Separation of these gases fromnatural gas and oil is usually the most expensive part ofnatural gas and oil treatment processes. The economicalimportance of treatment of sour gas has made it importantfor the gas and oil industry to have accurate equation ofstate to represent properties of sour gases and liquidmixtures3~. Presence of sour gases in crude oiI could alsocause deposition of heavy organics, such as asphalteneand wax, from oil which would plug the well, pipelineand refining equiprnen~.As of yet no satisfactory equation of state has been

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. *2 SOURNATUR4L GASAND LIQUIDEQUATIONOF STATE SPE26906available to predict the behavior of sour gases andliquids in reservoir, well, pipeline and compression /expansion facilities. Recently, experimental andmodeling studies on the phase behavior of high H2S-content natural gas mixtures were reported by Gu, et al.*.These workers used the Peng-Robinson (PR) equation ofstate for phase equilibria calculations, but because the PRequation was not accurate for PVT calculation, they used,instead, a 33-constant super equation of state. By usingthis equation of state, Li and GU09 studied thesupercompressibility and compressibility factors ofnatural gas mixtures. However, it is not convenient forengineering calculations to use such a lengthy equation.0 have performed some experimentalorris and Byerswork to obtain VLE data for binary and ternary systemscontaining CH4, C02, and H2S. Afterwards, they used thePR and Soave-Redlich-Kwong (SRK) equations of statefor VLE calculations of the same systems and comparedtheir experimental results with these calculations.Huron, et all. and Evelein and Moore* used the SRKequation of state to study the hydrocarbon systemscontaining hydrogen sulfide and carbon dioxide Theyreported phase equilibria calculations, bu otherthermodynamic property calculations were not reported intheir paper. On the same subject, some otherexperimental research -works have been reported, such asthe works of Morris and Byers13, Hunage et. al, Hall et15al , Robinson et alls, Mraw et al7, and Eakin andDevaney 18. By reviewing the above literature onequations of state of sour gases and liquids it is concludedthat there is no simple and accu?ate equation of stateavailable for predicting thermodynamic properties ofsour and hydrogen containing gases and liquids.In this paper we report the development of an accurateequation of state for sour and hydrogen containing naturalgas / gas condensate systems. This equation of state istested with success for variety of cases of interest in thenatural gas engineering for which experimental data areavailable for comparisons. The basic aim of the presentpaper is to produce a simple two-constant cubic equation ofstate which is capable of calculating thermodynamicproperties and phase behavior of sour natural gases andliquids. This equation of state is designed specially topredict thermodynamic properties and phase equilibriaof liquids and vapors which consist of hydrogen, methane,other light hydrocarbons and acidic componentsappearing in the natural gas and gas condensate streams.In the first part of this report we introduce a two-constantcubic equation of state. This cubic equation of state, whichis based on statistical mechanical theoretical grounds, isextended to mixtures. Then parameters of this equation ofstate are derived for different components of sour natural

gas systems. The resulting equation of state is tested forphase behavior and other thermodynamic properties ofsimulated and natural sour gas mixtures. It is shown thatthe present equation of state, even though it is simple,predicts the properties of interest with ease mid accuracy.

THE EQUATION OF STATEA new simple two-constant cubic equations of state forhydrocarbons, hydrocarbon mixtures, and other non-associating fluids was introduced earlier 9. This equationof state model is based on the statistical mechanicalinformation available for the repulsive thermodynamicfunctions and the phenomenological knowledge of theattractive potential tail contributions to thethermodynamic properties. This new two-constant-parameter cubic equation is in the following form:Z = (v + 1.3191b)/(v -b)- a / [ RT 3 2 ( v + b)] (1)Equation (1) is cubic in terms of volume and contains onlytwo adjustable parameters. By applying the critical pointconstraints on the above equation, parameters a & b aredetermined to be*9a = ().486989R2TC52PC and b=0.W2RTC/PC (2)The critical compressibility factor based on this equationof state is calculated to be,Zc=1/3, (3)the same as the Redlich-Kwong (RIO equation of state. Itis shown that this equation of state is more accurate thanthe Redlich-Kwong equation, which had been consideredto be the best two-constant-parar.leter cubic equation ofstate19. For multicomponent mixtures this equation ofstate assumes the following form9Zm= v + ~.3191bRm- arn/R~2 (4)v-b~ V +b~where we use the following mixing rule for am,bk and%.a~=~,~,xjlbh = (3/4)~ifi~x~ij + 1/4)~/%b.b ~ btiAm = ~

(5)(6)(7)

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..,WE 269(M M.MOHSEN-MA, H.MODDARESS AND G.A.MANSOORI 3Subscript (R) in bm stands for the repulsive mixing ruleand subscript (A) in b~~ stands for the attractive mixingrule of b. For reasons mentioned elsewhere19 the mixingrule for parameter b when appears in the repulsive(positive) term of the equation of state (bR~) will bedifferent from that of the attractive (negative) term@A~).For unlik~interaction parameters aij and bij we usethe following combining rules,bij= (bti113+b@/8aij = (1 - ki)(au a#2.

(8)(9)

Parameter ~j is defined as the coupling parameter whichcan be determined using some mixture data. Thetheoretical foundations for the choice of the above mixingand combining rules are discussed elsewhere9. The abovecubic equation of state was applied for calculation ofthermodynamic properties of hydrocarbons and other non-associating fluids and fluid mixtures. It was shown thatthis two-constant cubic equation of state and its mixtureversion are far superior to the RK equation of state whichis also a two-constant cubic equation. However, the betteraccuracies achieved by this simple cubic equation of stateis not still sufficient enough to be used for engineeringdesign calculations.In order to improve the accuracy of the present equation ofstate to the level that it could be used for engineeringdesign calculations it is necessary to make parameters a &b temperature-dependent similar to the manymodifications of the van der Waals and RK equations o:state4$~1s~20.or this purpose we replace parameters a & bwith the following temperature-dependent expressionsa = aCa(Tr) and b= bCf3(Tr) (10)WhereaC= 0.486989R%C52/Pe bC= 0.064662RTC/PC (11)The dimensionless tem~rature-dependent parametersa(Tr) & il(Tr) while are different from each other reduceto unity at the critical Poinfia(Tr=l) = NT,.1 ) = 1 (12)There have beerI a variety of empirical functional formsfor a & R reported in the literature. However, in linewith the variational and perturbation molecular theories

of fluids21 we may use the following polynomialexpression for fl(Tr)8(TJ1/3 =[1+ ~/Tr+ $/T:+ .]/[l+ $+ $+- ] (13)Then for simplicity, and as a first approximation, we usethe following form for f?(Tr)

(14)t?(Tr)= (1+ fll/Tr)3/(1 +i$)3where f$ is a constant. Eq. (14) satisfies the basictheoretical conditions for fi(Tr) at the critical point, i.e.:f.l(Tr)+l at Tr+l. This fuwtional form will remain finiteand positive for all possible temperature ranges. Forsymmetry and simplicity we also use the same functionalform for parameter a(Tr), i.e.

(15)a(Tr)= (1 + al /TJ3/(1 + al)3Where a, is a constant. Eq. (15) also satisfies the basictheoretical conditions for oc(Tr) at the critical point, i.e.:a(Tr) +1 at Tr +1. It can also beinferred from the form ofthe equation of state, that as the temperature tends toinfinity, the attractive term of the equation of state,-a/ [Rp2(v-tb) 1,must tend. to zero. The form of a (Tr)considered in this work is conducive to this requirement.The constants al and i$ have been determined for thecomponents of the sour natural gas and gas-condensatemixtures as reported in Table 1. These constants werefound by minimization of vapor pressures and saturationliquid densities.For ease of calculations, we have correlated parametersal and g, of the major components of natural gas (see Table1) to their acentric factor in the following form%al = -0.036139+ 0.14167 co; 0.22 s o s 0.18 (16)$ = 0.0634-0.18769 co ().~< u ~ (),l& (17)These correlations are for a) in the range of -0.22


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4 SOURNATURALGASAND LIQUIDEQUATIONOF STAI5 SPE269(%natural gas thermodynamic properties. Formulation ofequation of state of hydrocarbon mixtures containingappreciable amounts of heavier hydrocarbons requires theapplication of the continuous thermodynamics and C,+fraction characterization techniques which is out of theXOpe of the present repOr@J201~M.

Table 1:Equafwn o~sfafeconstantsSubstances al %

Major Components ofSour NaturaI GasH2 -0.07099 0.12307N2 4.02474 0.06393co -0.02281 0.06066co~ -0.00580 0.01456H2S -0.02351 0.04207CH4 -0.03662 0.05957C2H4 -0.02898 0.03865C2H6 -0.02133 0.04504C3H6 -0.00841 0.04624c3Hg -0.01457 0.03657Components of Natural Gas in Minute Quantitiesn-C4H10 -0.00663 0.03613i-C4Hlo -o.olw3 0.02852~-%w2 -(MNW78 0.02251n-C6H14 -fMW761 0.01258n-C7H~6 0.00425 0.01342

One of the requirements of equations of state tor industrialapplications is their analytic representation ofthermodynamic functions. Such properties of fluids (likeentropy, enthdpy, and fugacity) are of direct interest inenergy balance and phase behavior calculations inindustrial practice. The analytic expressions of thesefunctions a;e as the following - -

Hm-H * = (Z~ - 1) -2.3191Tbw/(v-b~RT. amInlv/(v+bA #/~~ ~T12+ [bAm/ RFq {(am/bh~2)Jn[v/(v+bA J]+aJ1bJV+b~Jl +0.5aJbJ@~ ~[ V/(V+bJl (17)

k%!?k = InZm + 2319ln((v-b~/v) -23191T bh/(v-b~s [a~/(b.~Ti2)] )n[v/(v+bA# + [~bA;~iq{(1/b~~2) InIv/(v+bAJl + l/(bA#+bA~2)}

2)] ln[v/(v+b~ J][aJ(2bA ~ 1 (18)lnfi = -2.31915 In(l-bM/v) + 2.3191[d(nb#&,]/(v-b~

+ [&*A#~][a/(b#+b~2)+(a~~2 ln(l+bb /v)] /(R@2) - lnz~- [d(nza~)/d@ ln[(l+b~/v)l /RT%b% (19

In the above equations Hm- Hmig ~d Sm - %t g are themixture enthalpy departur~~nction and r%xture entropydeparture function, respectively, and fi is the fugacity ommpcment i in a mukicomponent titure. am,b~and bbare defkd by eqs (5), (6) and (7) and parameters a andb refer to (da/dT) and (db/dT), respectively. Expressionsfor the other thermodynamic functions can be easilyderived t%omthe above equations.RESULTS AND DXSCUSSIONIn order to test the accuracy and applicability of thpresent equation of state it is first used for densityenthalpy and entropy calculations of the major purecomponents of the sour natural gas at differenttemperatures and pressures. Table 2 shows results of thescalculations using the present equation of state along witthe SRK and PR equations. According to this table evethough predictions by the SRK and PR equations are somtimes better than the present equation, over all thpresent equation of state is more accurate than the SRand PR equations.We have used the present equation of state for calculationof compressibility factors of binary mixtures of methanehydrogen sulfide at T= 377.65 K and at two differenpressures. Fig. 1 shows the results of this calculation busing the present equation of state along with the Pequation (all with kij=O). According to this figure thresults of calculations by the present equation of state argenerally closer to the experimental data than the Pequation.Another compressibility factor calculation was performedfor a methane-carbon dioxide mixture (xcoz = 0.4761)250 K and at different pressures. Fig. 2 shows resultsthis calculation based on the present equation of statalong with those obtained form the PR and SRK equation(all with \j=O). According to this figure also the presen

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..SPE269W M.MOHSEN-NIA, H.MOI)DARESS AND G.A.MANSOORI 5equation of state is more accurate than the other equationsreported.A third set of compressibility factor calculations wereperformed for the nitrogen-carbon dioxide (xcoz = 0.447)mixture at constant volume (isochore) and at differenttemperatures and pressures. Table 3 shows the results ofthis calculation as compared with the results of the PRand SRK equations of state (all with kij=O).According tothis table also the compressibility factors calculated bythe present equation are closer to the experimental datathan the other equations.A fourth set of compressibility factor calculations wereperformed for three different sour natural gas mixtures.Table 4 shows the compositions of these sour natural gasmixtures. The results of these calculations are reported inTable 5. According to this table the compressibilitiescalculated using the present equation of state are muchcloser to the experimental data than the PR equation,while the calculations by the SRK equation are equallyaccurate as the present equation of state.The present equation of state is used for the vapor-liquidequilibria (VLE) calculations of seven different binarysour and hydrogen containing fluid mixtures for whichexperimental data are available. Table 6 comparesresults of the VLE calculations using the present equationof state, PR equation and SRK equation assuming ki~s=Ofor all the equations. According to this table the presentquation of state is overall superior to the other equationsfor the mixtures tested.On I@res 3 through 7 the results of the VLE calculationsalong with the experimental data for five differentbinary mixtures comprising the major components of sournatural gas systems are reported. According to thesefigures the present equation of state can predictthermodynamic properties of sour and hydrogencontaining vapor and liquid mixtures with good accuracy.The calculations and comparisons reported hwe indicatethat the present equation of state is quite suitable forproperty prediction of sour and hydrogen containingnatural gas and liquid systems of interest in the oil andgas industries. One major advantage of this equation ofstate is its sound theoretical basis in the choice of itsmixing and combhing rules and the functional forms ofa(Tr) and f3(Tr)as reported by eqs (14) and 05). Thesetheoretically correct choices make the present equation ofstate more suitable for extrapolation purposes than theempirical equations, b eyond the ra ng es of the availableexpimental data on which equation of state parametersare basal upon.

abfHkijnPPRRRK~RKTT,;

parameter in equation of stateparameter in the equation of statefugacityenthalpycoupling parametertotal number of molespressurePeng-Robinson equation of stateUniversal gas constantRedlich-Kwong equation of stateentropySoave-Redlich-Kwong equation of stateabsolute temperature=T/TC -molar volume=Pv/RT, compressibility factor

a parameter in equation of state% constant in equation of statefl parameter in equation of state@l constant in equation of stateP densityz 3.14159270) acentric factor=ttractivec criticalitj mmponent indimsij property of i-j interactionig ideaI gasm mixturer reducedR repuIsive

ACKNO} J?.EGMI?NTSThis research is supported in part by the Gas ResearchInstitute contract No. 5090-260-2085, and in part byRotoflow Corporation, Inc.REFERENCES1. International Petoleum Encyclopedia, PennWellPublishing Co., Tulsa, Oi(, 1993.2. Campbell, J.M.: Gas Conditioning and Processing,CampbellPetrol. Series, Norman, OK 1976.


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6 SOURNATURALGASAND LIQUIDEQUATIONOFSTATE SPE269063. Katz, D.L. and Lee, L.L.: Natural Gas Engineering,McGraw-Hill Book Co., New York, NY 1990.4. Mansoori, G.A. and Savidge, J.L.: PredictingRetrograde Phenomena and Miscibility using Equations ofState; SPE Paper No. 19809, Proceedings of the 1989Annual SPE Meeting, Society of Petroleum Engineers,Richardson, TX.5. Edmister, W.C. and Lee, B.i: Applied HydrocarbonThermodynamics, Gulf Pub. Co., Houston, TX 1986.6. Mansoon, G.A. and Jian& T.S.: Asphaltene Depositionand its Role in Enhanced Oil Recovery Miscible GasFioodin& Proceedings of the 3rd European Conference onEnhanced Oil Recovery, Rome, Italy, April 1985.7. Wichert, E. and Aziz, K.: Calculation of Zs for SourGases, Hydrocarbon Processing, 1972, VOL 51, No.5,pp.119-12.8. Gu, M.X., Li, Q., Zhou, S.Y., Chen, W.D. and Guo, T.M.:Experimental and Modeling Studies on the PhaseBehavior of High H2S-Content Natural Gas Mixtures:Fluid Phase Equilibria, 1993, VOL82,173-182.9. Li, Q. and Guo, T.M.: A Study on ~he%qxrcompressibility and Compressibility Factors ofNatural Gas Mixtures: Journal of Petroleum Science andEngineering 1991,6,235-247.10. Morris, J.S. and Byers, C.H.: Near-Critical-RegionEquilibria of the Methane-Carbon Dioxide and HydrogenSulfide System: Fluid Phase Equilibria, 1991, 66, 291-308.11. Huron, M.J. and Dufour, G.N., and Vidal, J.: Vapor-Liquid Equilibria and Critical Locus Curve Calculationswith the Soave Equation for Hydrocarbon Systems withCarbon Dioxide and Hydrogen Sulfide, Fluid PhaseEquilibria, 1978,1,247-252.12. Evelein, K.A. and Moore, G.R.: *Prediction of PhaseEquilibria in Sour Natural Gas Systems Using the Soave-Re#lich-Kwong Equation of State, Ind. Eng. Chem.Process Des. Dev., 1979, vol. 18, No. 4,618-624.13. Morns, ],S. and Byers, C.H.: Critical Region Vapor-Liquid Equilibria of the CH4-C02-H2S System, 1990,ORNL/TM-10806, Oak Ridge, TN.14. Huang, F.H., Li, M.H., Lee, L.L., and Starling, K.E.: An Accurate Equation of State for Carbon Dioxide,, J.Chem. Eng. of Japan, 1985,18,490-498.

15. Hall, K.R. et al: PhaseEquilibria Calculated for theSystems N2+C02, CH4+C02, CH4+H2S~ J. Fluid PhaseEquilibria, 1983, VOI15,11-32.16. Robinson, D. B., Kalra, H. and Rempis, H.: TheEquilibrium Phase Properties of a Synthetic Sour GasMixture and a Simulated Natural Gas Mixturet ResearchReport, 1978,RR-31,Gas Processor Association.17. Mraw, S.C. and Hwang, S.C., Kobayashi, R.: TheVapor-Liquid Equilibria of the CH4-C02 System at LowTemperatures; J. of Chemical Engineering Data, 1978,Vol. 23, No. 2,135-139.18. Eakin, B.E. and Devaney, W. E.: Enthalpies ofHydrogen Sulfied-Methane-Ethane Systems, 1975,Research Report, RR-9, Gas Processor Association.19. Mohsen-Nia, M., Moddaress, H. and Mansoori, G.A:A Simple Cubic Equation of State for Hydrocarbons andOther Compound% SPE Paper #26667, Proceedings of the,1993Annual Technical Conference and Exhibition of theSocitey of Petroleum Engineers, Houston, TX.20.Chore, L.G. and G.A. Mansoori (Editors): C7+ FractionCharacterization Advances in Thermodynamics, Vol. 1Taylor & Francis Pub. Co., New York, N.Y., 1988.21. Mansoori, G.A. and Canfield, F.B.: Perturbation andVariational Approaches to the EquilibriumThermodynamic Properties of Liquids and PhaseTransitions, Industrial and Engineering Chemistry(monthly), 1970, Vol. 62, No. 8,12-29.22. Du, P.C. and Mansoori, G.A.: A Continuous MixtureComputational Algorithm for Reservoir Fluids PhaseBehavioral SPE Paper # 15082, Proceedings of the 1986California Regional Meeting of SPE, Society of PetroleumEngineers, Richardson, TX, 1986.23. Du, P.C. and Mansoori, G.A.: Continuous MixtureComputational Algorithm of Reservoir Fluid PhaseBehavior Applicable for Compositional ReservoirSimulation; SPE Paper # 15953, Proceedings of the 1986Eastern Regional Meeting of SPE and Proceed~qgs of the9th SPE Synqmsium on Reservoir Simulation, Society oPetroleum Engineers, Richardson, TX, 1986.24. Sage, B. H. and Lacey, W. N.: Some Properties of theLighter Hydrocarbons, Hydrogen Sulfide and CarbonDioxide;, 1955, pp., 44..57, Am. Petroleum Inst., NewYork.25. Bailey, D.M., Esper, G.J., Holste, J.C., Hall, K.REubank, P.T., Marsh, K.M. and Rogers, W.J.: Properties oC02 Mixtures with N2 and with CH4; Research Repor

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SPE26% M.MOHSEN-NIA, H.MODDARESS AND G.A,MANSOORI 7RR-122, Gas Processors Association and the Gas ResearchInstitute, July 1989.26. Buxton, T.S. and Campbell, J.M.: ComperessibilityFactors for Lean Natural Gas-Carbon Dioxide Mixtures atHigh pressures; Trans. AIME, 1967, Vol. 240,80-8627. Satter, A. and Campbell, J.M.: Non-Ideal Behaviorof Gases and thier Mixtures: Trans. AIME, 1963, Vol. 228,333-347.28. Wichterle, L and Kobayashi, R.: Vapor-LiquidEquilibrium of Methane-Ethane System at LowTemperatures and High Presures, J. C.hem. Eng. Data,1972, vol. 17,1,9-14.29. Reamer, H.H., Sage, B.H. and Lacey, W.N.: PhaseEquilibria in Hydrocarbon Systems,* Ind. Eng.Chem.,1951, 43,976-981.30. Sobocinski, D.P. and Kurata, F.: HeterogeneousPhase Equilibria of the Hydrogen Sulfide-CarbonDioxide System; AIChE J., 1959,5,4,545-551.31. Sagara, H., Arai, Y. and Saito, S.: Vapor-LiquidEquilibria of Einary and Ternary Systems ContainingHydrogen and Light Hydrocarbons;, J. Chem. Eng. ofJapan, 1972, vol. 5, No. 4.,339-348.

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sPE26w16, Table2- Comparfeonofthepresent,PRandSRKWpU@W ofstatefOrdensity(p),enthdpy (H)and entropy (S)predtcttonaofthe majorpure componentsofsournatu ralgas . t5RK PR. .- Present

Substarm T (K) I P (bar) ----p%m3.13.74.54 . 01 . 32 . 91 . 48 . 02 . 6x i

----H%T1.02 . 60 . 82 . 60 . 50 . 80 . 50 . 52 . 4n - -

,---- ------s% p%

.0.5 5 . 30 . 5 5 . 10 . 8 4 . 70 . 5 4 . 62 . 5 5 . 02 . 4 6 . 00 . 7 4 . 70 . 7 5 . 31 . 7 1 . 80 . 2 4 . 4n - 4 . 7

---H%iT0 . 60 . 82 . 51 . 62 . 10 . 60 . 60 . 43 . 1G

----We

631,31.10.42.31.70.50.30.50.4r

-----p 701.82.21.72.51.62.32.21.42.11.5

1.9

,----Hkw1.01.13.11.90.60.80.50.41.77-I-

----s%0.60.51.20.52.11.20.40.80.50.1-0.6

No. of&ta.9 08 07 08 07 57 06 08 59 00 0[-tthane 110.500 10.500Ethnr 200.500 1.5-350Ethylenr 150.450 10.400Propane 150.560 0.5-500Propylene 100.600 10.400Hydrogen 20-500 0.1-400Nitrogen 74-700 0.75.500co 80-600 5.0.500cm 250.1000 2.0.500H#i 255.480 1.0.210

w% -1 L. -L

Table3- ComwsriaonLmtweenhe exwirnentd= andcakufetedcomwessibilt~ Table4- Compositions (inmole fractions)ofUueedtfferentsamples ofsour naturet gasusedtn thecakulationereported inTable5-------------------------------- .------- --Components Sample Sample SampleA B c

factors for (Ni&ogen+Carbondiordd;) sprn at Xm=0.SS3using thi present,%and SRKequatfoneof state~is = O)

T (K) P(bar) Zexp. SRK PR present300.10 318.29 0.8870 0.9311 0.8629320.08

0.9148372.49 0.9738 1.0169 0.9439288.79

0.9997287.52 0.8326 0.8763 0.8113 0.8803273.19 245.07 0.7500 0.7923260.020.7322 0.7789209.51 0.8736 0.7127 0.6574 0.6976

250.06 163.16 0.6123 0.6467 0.5955 0.6321242.95 165.10 0.5680 0.5967 0.5464 0.5621241.99 162.69 0.5620 0.5897 0.5418241.030.5751180.45 0.5564 0.5828 0.5353 0.5682240.00 157,98 0.5502 0.5753 0.5282

239.620.5607

157.57 0.5492 0.5740 0.5270 0.5594Oweretf% devfatiorrs 5.1 3.2 2.7

0.0000 0.0052 0.0081L 0.9130 0.7458 0.83030.0000 0.2016 0.0744C2H6 0.0900 o.oA74 0.0130H2S r).1970 0.0000 0.0735C3H8 0.0000 0.0000 0,0007

Table 5- Comparison buIweenthe experimenta13,M,varrdcalculatedmmpressibfljty fartorsor the three sour natural gassamplesofTable4 using thepresen~ Pil end SRKequationsofstateSUwith~;s. O.

Compreasibiiity Factor (Z)presentample T (K) P(bar)

AAAABBBc

311.93327.87311,93327.87310.93310.93310.93310.93

70.7270.72139.65139.6570.72139.65208.58112.0

0.6300.8560.7140.7620.6650.7780.7780.821J-.820 0.7900.855 0.6250.709 0.6650.765 0.7210.661 0.6310.762 0.7380.791 0.7370.823 0.763 0.8300.8570.7110.7670.8640.7650.7910.626-160


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iPi26906Table6=Th epercentagedeviationsof pressures and vapor compositionsfrom theaxparfmcntsldata~7*1 forsevendifferentbfnarymixturesby using thepresent,PRandSRKequ ationsfstateallAh ki;s=o.

I P %Deviation I y, v. Deviation Systems

IT Range No.of(1) + (2) () dataICH4+C2H8) ; :; -:: ;(cFf4+H2s) -(w&&c&) 183-230103.143(H2+C2H4) 173.198(H2+C2H6) 173.223(C02+H2S) 233-316Overall % deviations SF?T6 3.320 20.025 19.212 24.416 22.11$.8:: 1?.0---t=

1.07J

0.9a1 Oyg o.7-== 0.6-i!g o.5-Z 0.4-

1-377.65 K

Thlawommq P=126afrn

v o P=os.latrno.30~. 1X(CI14]. Figure 1 - Comparison of the calculatedcompresaibiMyactor of the m.fxfureof (methane+

hydrogen sulfide)with the experimentaldata24ascalculatedby thepresentandPR equationsof state@js = O)at differentmole fractionaat 3T7.65K andtwo different praamresof1%and66.1atrrt.

m

21.320.316.23829.217.124.13rasent sw m2.5 0.5 0.220.4 14.8 16.717.7 9.9 10.319.4 4.2 54.9 2.2 37.6 1.5 3.517.1 22.6 23.214.9 9.3 lri Present0.115.39.620.21.4228.4

a 1=ExP. \ \ q~ 0.6 THISWORK %* , *E \ %*----0 0.6Q mFigure 2 - Com parison of th e calcu latedCcsmpressibtityactorof the mixtureof (methane+carbon dioxide) wi th the experimentaldata= ascalculatedby the present,SRKand PReq uationaofstate ~jS = O)at differentpressuresand at 250Kand ~z =0 .4761.

so Tfv3wosk O EXP.(T = 189 .65 K) I40 J -.-. ma work b E XP , ( T . 156.15) A

10o .....x...-- K..4.w*..*-..."""m."-"""."...."".".-".#0.0 0.2 0.4 0.6 0:8 1;0

X{l),v(l)Figu re 3 - comparison of th e calcu lated eq uilib riumpress ur e-composi ti on d iagr am of (metha se + e ti ,a ne )VSt em by the p rs aent equat iono f s ta te (%,= O)w it h t he-, --e-xp erim en tal d ata~s at tw o d ifferen t t emperatu r~ of139.65an d 156.lSK.

181


10/10

8 0 ---...---. Thiswork

ExP. ...09QQo~60 - ..4YOa q Q@. ..6x )40-n / * * : * , * eq&20 ,a. . - ..~ l f - - T-230K

-0:0 0:2 C.4 0.6 0. 8x(1), Y(1)Figure 4 - Com parison of th e calcu latedequilibrium pressure-composition diagram of(m eth an e + carb on d ioxid e) system b y th ep re sent equat ion o f s ta te (t qi= 0.07) w ith theexperimentaldatal~ at 23oK.

0.0 0.2 0.4 0.6 0.8 1*(1), Y(1)Hgure 6 - Comparison of th e ca lcu lat edequtlibrtumtemperature-compositiondiagramof (carbondioxide+ hydrogensulfide)system bythe presentequationofstate (kjj=0.08)w iththe

exper imental dats?o at two differentpressuresof 6.895and 34.473bar.

SPE26?; i

150-1---1--)-o- This Wodt .*,.,.... .. --------.,.. q %,q. o0 ExP. q .a&..*&G*oq EXP. . .P 4

1?79J

qs!~.........-

9-a

\.t,.44,.....*4*-..,.,.e..e..-a~

T m277.6 Koo~.x(1), Y(t)

Figure 5 - Compar ison o f t he ca lcu la ted equ il ib rip ressure-compos it ion d iagram of (methane + hydrogsulf ide)system by the presentequation of state (lqj = 0.0with the experimentaldatazg at 277.6K.

120 This Wolk q EXP.(T=143.05 K)

oo~x(1), Y(i)

Figu re 7 - Comparison of th e calcu lated eq uilib rpressure-composition diagram of (hydrogen + methasystem by thepresmt equationofstate*{= 0.144)withexperimental datasl at two differenttem~eraturesof 143and 173.65K.

sour natural gas eos

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