SPE 26906

Sour Natural Gas and Liquid Equation of State Mohsen Mohsen-Nia, U. of Illinois at Chicago; Hamid Moddaress, Amir-Kabir U. of Technology ; and G.Ali Mansoori, * U. of Illinois at Chicago

•spe Member

Copyright 1993, SOciety of Petroleum Engineers. Inc.

Thia paper was prepared for presentation at the 1993 Eastern Regional C"nterence & Exhibition held In Pittsburgh, PA. U.S.A., 2--4 November 1993.

Thia paper was Nlected for pr?Sentatlon by an SPE Program Committee following review of Information contained In an abstract submitted by the authorts). Contents of the paper.

&& l)rfl9nted, have not been reviewed by the SOclety of Petroleum Engineers and are subject to correctlOn by the author(&). The material, as presented. does not neceS$llrily reflect

any politlOn of the Society of Petroleum Engineers. its officers, or IT!Ambers. Papers presented al SPE meetings are subject to publlcauon review by Ed1torIaI Committees of the Society

of P,troleum Englneefl. PermlSaion to eopy Is restricted to an at>stract of not more than 300 words. lllustratlOns may not be copied. The abstract should contain conspicuous acknowledgment

OI whefe and by whom the pap,,r la presented. Write Librarian, SPE. P.O. Box 833836, Richardson, TX 75083-3836. U.S.A., Telex 163245 SPEUT.

ABSTRACT

The major gaseous impurities in the subquality natural gas sources are acidic components, such as hydrogen sulfide and carbon dioxide. Considering that H2S easily dissociates into hydrogen and elemental sulfur, thermodynamic properties and specially phase equilibria of liquid and gaseous systems containing hydrogen, hydrogen sulfide, carbon dioxide, other acidic components, and light hydrocarbons are of much interest to the natural gas and gas condensate production industries.

In this paper we report the development of a simple and accurate cubic equation of state for prediction of thermodynamic properties and phase behavior of sour natural gas and liquid mixtures. This cubic equation of state, which is based on statistical mechanical theoretical grounds, is applied to pure fluids as well as mixtures with quite accurate results. All the thermodynamic property relations of sour gaseous and liquid mixtures are derived and reported in this r�port. Parameters of this equation of state are derived for different components of sour natural gas systems. The resulting equation of state is tested for phase behavior and other thermodynamic properties of simulated and natural sour gas mixtures. It is shown that the present equation of state, even though it is simple, predicts the properties of interest with ease and accuracy.

(*). Corresponding author, email: mansoori@uic.edu

References and Illustrations at end of paper

INTRODUCTION

In the past two decades, a number of subquaHty natural gas / gas condensate fields have been discovered around

the world1'

2• The major impurities of these subquality

natural gas / gas condensate sources consist of N2, CO2 and H2S. �ince that H2S easily dissociates into hydrogen and elemental sulfur therefore, thermodynamic properties and specially phase equilibria of liquid and gaseous systems containing hydrogen, hydrogen sulfide, carbon dioxide, other acidic components, and light hydrocarbons are of much interest to the natural gas and gas condensate production industries

24.

Transportation, and processing of sour and hydrogen containing natural gas is of major concern to the industries involved. Carbon dioxide and hydrogen sulfide are considered as being impurities in natural gas and oil and are responsible for corrosion of the flow-line and precessing equipment. Separation of these gases from natural gas and oil is usually the most expensive pa1·t of n�tural gas and oil treatment processes. The economical importance of treatment of sour gas has made it important for the gas and oil industry to have accurate equation of state to represent properties of sour g'.lses and liquid mixtures3.S. Presence of sour gases in crude oil could also cause deposition of heavy organics, such as asphaltene and wax, from oil which would plug the well, pipeline and refining equipment6. As of yet no satisfactory equation of state has been

173

. .

2 SOUR NATURAL GAS AND LIQUID EQUATION OF Sf ATE SPE26906

available to predict the behavior of sour gases and liquids in reservoir, well, pipeline and compression / expansion facilities7

• Recently, experimental and modeling studies on the phase behavior of high H2S­content natural gas mixtures were reported by Gu, et al. 8

•

These workers used the Peng-Robinson (PR) equation of state for phase equilibria calculations, but because the PR equation was not accurate for PVT calculation, they used, instead, a 33-constant super equation of state. By using this equation of state, Li and Guo9 studied the supercompressibility and compressibility factors of natural gas mixtures. However, it is not convenient for engineering calculations to use such a lengthy equation. Morris and By�rs10 have performed some experimental work to obtain VLE data for binary and ternary systems containing CH4, CO2, and H2S. Afterwards, they used the PR and Soave-Redlich-Kwong (SRK) equations of state for VLE calculations of the same systems and compared their experimental results with these calculations. Huron, et al11• and Evelein and Moore12 used the SRK equation of state to study the hydrocarbon systems containing hydrogen sulfide and carbon dioxide They reported phase equilibria calculations, bu· other thermodynamic property calculations were not reported in their paper. On the same subject, some other experimental research works have been reported, such as the works of Morris and Byers13, Hunage et. al 14, Hall et

15

al , Robinson et al16, Mraw et al17

, and Eakin and Devaney 18

• By reviewing the above literature on equations of state of sour gases and liquids it is concluded that there is no simple and accurate equation of state available for predicting thermodynamic properties of sour and hydrogen containing gases and liquids.

In this paper we report the development of an accurate equation of state for sour and hydrogen containing natural gas / gas condensate systems. This equation of state is tested with success for variety of cases of interest in the natural gas engineering for which experimental data are available for comparisons. The basic aim of the present paper is to produce a simple two-constant cubic equation of state which is capable of calculating thermodynamic properties and phase behavior of sour natural gases and liquids. This equation of state is designed specially to predict thermodynamic properties and phase equilibria of liquids and vapors which consist of hydrogen, methane, other light hydrocarbons and acidic components appearing in the natural gas and gas condensate streams.

gas systems. The resulting equation of state is tested for phase behavior and other thermodynamic properties of simulated and natural sour gas mixtures. It is shown that the present equation of state, even though it is simple, predicts the properties of interest with ease ·md accuracy.

THE EQUATION OF STATE:

A new simple two-constant cubic equations of state for hydrocarbons, hydrocarbon mixtures, and other non­associating fluids was introduced earlier19

• This equation of state model is based on the statistical mechanical information available for the repulsive thermodynamic functions and the phenomenological knowledge of the attractive potential tail contributions to the thermodynamic properties. This new two-constant­parameter cubic equation is in the following form:

[ 3/2 ]Z = (v + 1.3191b)/(v-b)- a/ RT (v + b) (1)

Equation (1) is cubic in terms of volume and contains only two adjustable parameters. By applying the critical point constraints on the above equation, parameters a & b are determined to be19

a = 0 486989R2T 512 /P and b == 0.064662RT IP (2) ' C C C C

The critical compressibility factor based on this equation of state is calculated to be,

zc

== 1/3, (3)

the same as the Redlich-Kwong (RK) equation of state. It is shown that this equation of state is more accurate than the Redlich-Kwong equation, which had been considered to be the best two-coru;tant-parar,leter cubic equation of state19

• For multicomponent mixtures this equation of state assumes the following form19

z = v + 1.3191bRm _ am/RT112

m v - bRm v+bAm

where we use the following mixing rule for am, b Am and �m

(4)

(5)

In the first part of this report we introduce a two-constant bRm = (3/4>I,,.u,xplj + (1/4)Lj'\bucubic equation of state. This cubic equation of state, which (6)

is based on statistical mechanical theoretical grounds, is extended to mixtures. Then parameters of this equation of bAm = L�bil state are derived for different components of sour natural

174

(7)

SPE26906 M. MOHSEN-NIA, H. MODDARESS AND G.A. MANSOORI 3

Subscript (R) in bRm stands for the repulsive mixing rule and subscript(A) in bA m stands for the attractive mixing rule of b. For reasons mentioned elsewhere19 the mixing rule for parameter b when appears in the repulsive (positive) term of the equation of state (bRm) will be different from that of the attractive (negative) term (bAm>· For unlike-interaction parameters a

1i and b1i we use

the following combining rules,

(8)

(9)

Parameter �i is defined as the coupling parameter which can be determined using some mixture data. The theoretical foundations for the choice of the above mixing and combining rules are discussed elsewhere19• The above cubic equation of state was applied for calculation of thennodynamic properties of hydrocarbons and other non­associating fluids and fluid mixtures. It was shown that tlus two-constant cubic equation of state and its mixture version are far superior to the RK equation of state which is also a two-constant cubic equation. However, the better accuracies achieved by this simple cubic equation of state is not still sufficient enough to be used for engineering design calculations.

In order to improve the accuracy of the present equation of state to the level that it could be used for engineering design calculations it is necessary to make parameters a & b temperature-dep�ndent similar to the many modifications of the van der Waals and RK equations o:

state4.5,15•20• For this purpose we replace parameters a & b with the following temperature-dependent expressions

and

Where

2...5/2a, = 0.486989R T, /Pct

(10)

(11)

The dimensionless temperature-dependent parameters a(T

1) & B<T,) while are different from each other reduce

to unity at the critical point:

a(T =1) = B(T =1) = 1 r r

(12)

There have been a variety of empirical functional forms for a & 8 reported in the literature. However, in line with the variational and perturbation molecular theories

of fluids21 we may use the following polynomial expression for 8(Tr)

S(t/13 =b+ 8itTr+ �/1/+ .. ]/(t+ 8i+ 8i+ .. ] (13)

Then for simplicity, and as a first approximation, we use the following form for 8(Tr)

(14)

where 81

is a constant. Eq. (14) satisfies the basic theoretical conditions for 8(Tr) at the critical point, i.e.: 8(Tr)-+ 1 at Tr-+ 1. This fn�-:tional form will remain finite and positive for all possible temperature ranges. For symmetry and simplicity we also use the same functional form for parameter a(Tr), i.e.

(15)

Where a1

is a constant. Eq. (15) also satisfies the basic theoretical conditions for c:x(Tr) at the critical point, i.e.: a(T r> -+ 1 at Tr -+ 1. It can also be inferred from the form of the equation of state, that as the temperature tends to infinity, the attractive term of the equation of state, -a/ (RT312(v+b) ], must tend_ to zero. The form of a (T 1)

considered in this work is conducive to this requirement.

The constants a1

and 81

have been determined for the components of the sour natural gas and gas-condensate mixtures as reported in Table 1. These constants were found by minimization of vapor pressures and saturation liquid densities.

For ease of calculations, we have correlated parameters cx1 and 8

1 of the major components of natural gas (see Table

1) to their acentric factor in the following forms:

cx1 = -0.036139 + 0.14167 (I); 0.22 S (I) S 0.18

8 1 = 0.0634 - 0.18769 (I) 0.22 � (I) s; 0.18

(16)

(17)

These correlations are for (I) in the range of -0.22S(l)S0.18 and they do not hold very well for parameters of the components of natural gas which are in minute quantities (C4 till C, .>. However, because of the very small concentrations of these components in natural gas streams application of correlations (15) for these components will not cause any appreciable error in the computation of the

175

4 SOUR NATURAL GAS AND LIQUID EQUATION OF STAT&: SPE26906

natural gas thermodynamic properties. Formulation of equation of state of hydrocarbon mixtures containing appreciable amounts of heavier hydrocarbons requires the application of the continuous thermodynamics and C7•

fraction characterization techniques which is out of thescope of the present report4,20,22,23.

Table 1: Equation of state constants

Substances

Major Components of Sour Natural Gas

-0.07099-0.02474-O.D2281-0.00580-0.02351-0.03662-0.02898-0.02133-0.00841-O.Ol457

0.12307 0.06393 0.06066 0.01456 0.04207 0.05957 0.03865 0.04504 0.04624 0.03657

Components of Natural Gas in Minute Quantities

n-C4H10i-C4H10n-CsH12n�H14n-C7H16

-0.00663-0.01373-0.00878-0.007610.00425

0.03613 0.02852 0.02251 0.01258 0.01342

One of the requireme:tts of equations of state for industrial applications is their analytic representation of thermod}rnamic functions. Such properties of fluids (like entropy, enthalpy, and fugacity) are of direct interest in energy balance and phase behavior calculations in industrial practice. The analytic expressions of these functions are as the following:

Hm· Hm1g = (Zm -1)- 2.3191T b�/(v-biu)

RT - a ' ln(v /(v+b )]/Rb T1'2m Am Am

+ [ bAm'/RT1/2J {(am/bAm2)1n[v/(v+bAm)]

+am/lbAai(v+bAiJU + (15am/bAaiRT312) In[ v/(v+bAm)) (17)

S -Sm1g m R

= lnZm + 2.3191n((v-bRid/v) - 23191 T b�/(v-biw)

-[am'/(bAmT112)] ln[v/(v+bAm)] + [�bAm'/1'1'21{ (1/b Am 2) ln[v /(v+b Am)]+ 1/(bAm v+bA m 2)}+ [c\n/(2bAm'i812)] ln[v/(v+bAm)] (18)

lnf1 = - 2.31915 ln{l-bRm/v) + 2.3191[d(nbiw)/dJ\]/(v-bRid + [d(nbAm)/dJ\Ua/(bAm v+b,�/)+ (a/b111

/ln(1+1'An

/v)] /(R1'312) - lnZ111

- [d(n2aAm

)/c:h\) ln[(l+bAm/v)] /R'I612iibAm (19)

In the above eqllations Hm • Hm1g and 5m - Sm1g are theRT R

mixture enthalpy departure function and mixture entropy departure function, respectively, and f

1 is the fugacity of

<.'Omponent i in a multicomponent mixture, am, bRm and b Am are defh1ed by eq's (5), (6) and (7) and parameters a' and b' refer to (da/dT) and (db/dT), respectively. Expressions for the other thermodynamic functions can be easily derived from the above equations.

RESULTS AA'l> DISCUSSION

In order to test the accuracy and applicability of the present equation of state it is first used for density, enthalpy and entropy calculations of the major pure components of the sour natural gas at different temperatures and pressures. Table 2 shows results of these calculations using the present equation of state along with the SRK and PR equations. According to this table even though predictions by the SRI< and PR equations are some times better than the present equation, over all the presen! equation of state is more accurate than the SRI< and PR equations.

We have used the present equation of stite for calculation of compressibility factors of binary mixtures of methane­hydrogen sulfide at T= 377.65 K and at two different pressures. Fig. l shows the results of this calculation by using the present equation of state along with the PR equation (all with k

1tO>. According to this figure the

results of calculations by the present equation oi state are generally doser to the experimental data than the PR equation.

Another compressibility factor calculation was performed for a methane-carbon dioxide mixture (xc

02 = 0.4761) at

250 K and at different pressures. Fig. 2 shows results of this calculation based on the present equation of state along with those obtained form the PR and SRI< equations (all with �tO). According to this figure also the present

176

M. MOHSEN-NIA, H MODDARESS AND G.A. MANSOORI 5

equation of state is more accurate than the other equations NOTATIONS reported.

A third set of compressibility factor calculations were performed for the nitrogen-carbon dioxide <xc02 = 0.447) mixture at cor.stant volume (isochore) and at different temperatures and pressures. Table 3 shows the results of this calculation as compared with the results of the PR and SRK equations of state (all with k

1t0). According to this table also the compressibility factors calculated by the present equation are closer to the experimental data than the other equations.

A fourth set of compressibility factor calculations were performed for three different sour natural gas mixtures. Table 4 shows the compositions of these sour natural gas mixtures. The results of these calculations are reported in Table 5. According to this table the compressibilities calculated using the present equation of state are much closer to the experimental data than the PR equation, while the calculations by the SRK equation are equally accurate as the present equation of state.

The present equation of state is used for the vapor-liquid equilibria (VLE) �alculations of seven different binary sour and hydrogen containing fluid mixtures for which experimental data are available. Table 6 compares results of the VLE calculations using the present equation of state, PR equation and SRK equation assuming k

1i's=O

for all the equations. According to this table the present equation of state is overall superior to the other equations for the mixtures tested.

On Figures 3 through 7 the results of the VLE calculations along with the experimental data for five different binary mixtures comprising the major components of sour natural gas systems are reported. According to these figures the present equation of state can predict thermodynamic properties of sour and hydrogen containing vapor and liquid mixtures with good accuracy.

The calculations and comparisons reported here indicate that the present equation of state is quite suitable for property prediction of sour and hydrogen containing natural gas and liquid systems of interest in the oil and gas industries. One major c:dvantage of this equation of state is its sound theoretical basis in the choice of its mixing and combining rules and the functional forms of a(Tr) and S(Tr) as reported by eq's (14) and (15). Thesetheoretically correct choices make the present equation of state more suitable for extrapolation purposes than the empirical equations, beyond the ranges of the available experimental data on which equation of state parameters are based upon.

a b f H klj n p PR R RK s

SRK T T

r

V

z

parameter in equation of state parameter in the equation of state fugacity enthalpy coupling parameter total number of moles pressure Peng-Robinson equation of state Universal gas constant Redlich-Kwong equation of state entropy Soave-Redlich-I< wong equation of state absolute temperature =T/T

c

molar volume =Pv /RT, compressibility factor

Greek letters

a parameter in equation of state a1

constant in equation of state 8 parameter in equation of state 81

constant in equation of state

p densi� 1t 3.1415927 <0 acentric factor

Subaa;ipts A attractive c critical i,j component indices ij property of i-j interaction ig ideal gas m mixture r reduced R repulsive

ACKNOt /1.EGMENTS

This resea1ch is supported in part by the Gas Research rnstitute contract :\Jo. 5090-260-2085, and in part by Rotoflow Corporation, Inc.

REFERENCES

1. International Petoleum Encyclopedia, PennWellPublishing Co., Tulsa, OK, 1993.

2. Campbell, J.M.: Gas Conditioning and Processing,Campbell Petrol. Series, Norman, OK 1976.

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6 SOUR NATURAL GAS AND LIQUID EQUATION OF STA TE SPE 26906

3. Katz, D.L. and Lee, L.L.: Natural Gas Engineering,McGraw-Hitt 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.

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7. Wichert, E. and Aziz, K.: "Calculation of Z's 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 I-125-Content Natural Gas Mixtures,"Fluid Phase Equilibria, 1993, Vol. 82, 173-182.

..

9. Li, Q. and Guo, T.M.: "A Study on theSupercompressibitity 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.

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12. Evelein, K.A. and Moore, G.R.: "Prediction of PhaseEquilibria in Sour Natural Gas Systems Using the Soave­R�lich-Kwong Equation of State," Ind. Eng. Chem.Process Des. Dev., 1979, vol. 18, No. 4, 618-624.

13. Morris, J.S. and Byers, C.H.: "Critical Region Vapor­Liquid Equilibria of the CH4-CO2-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, 49()..498.

178

15. Hall, K.R. et al: "PhaseEquilibria Calculated for theSystems: N2+CO2, CH4+CO2, CH4+H2S," J. Fluid PhaseEquilibria, 1983, vol 15, 11-32.

16. Robinson, D.B., Katra, H. and Rempis, H.: "TheEquilibrium Phase Properties of a Synthetic Sour GasMixture and a Simulated Natural Gas Mixture," ResearchReport, 1978, RR-31, Gas Processor Association.

17. Mraw, S.C. and Hwang, S.C., Kobayashi, R.: "TheVapor-Liquid Equilibria of the CH4-CO2 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 Compounds," SPE Paper #26667, Proceedings of the ,1993 Annual Thechnical Conference and Exhibition of theSocitey of Petroleum Engineers, Houston, TX.

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Characterization Advances in Thermodynamics, Vol. I,Taylor & Francis Pub. Co., New York, N.Y., 1988 .

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22. Du, P.C. and Mansoori, G.A.: "A Continuous MixtureComputational Algorithm for Reservoir Fluids PhaseBehavior," 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 Rc�ervoir Fluid PhaseBehavior Applicable for Compositional ReservoirSimulation," SPE Paper# 15953, Proceedings of the 1986Eastern Regional Meeting of SPE and Proceed' "gs of the9th SPE Symposium on Reservoir Simulation, Society ofPetroleum 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.R.,Eubank, P.T., Marsh, K.M. and Rogers, W.J.: "Properties ofCO2 Mixtures with N2 and with CH4," Research Report

SPE26906 M. MOHSEN-NIA, H. MODDARESS AND G.A. MANSOORI

RR-122, Gas Processors Association and the Gas Research Institute, July 1989.

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SPE269 06

, Table 2 • Comparison of the present, PR and SRK equations of state for density (p), enthalpy (H) and entropy (S) predictions of the major pure components of sour natural gas ,

SRK PR Present --- ---- ---- ------ --- ----- ------ ---· ----

No.of Substance T (K) P (bar) data p% H% S% p% H% S% p% Ho/o S%

Methane 110·500 10-500 90 2.4 1.3 0.5 5.3 1.0 0.9 1.8 1.2 0.6 Ethane 200-500 1.5-350 80 3.1 1.0 0.5 5.1 0.6 1.3 2.2 1.0 0.5 Ethylene 150-450 10-400 70 3.7 2.6 0.6 4.7 0.8 1.1 1.7 1.1 1.2 Propane 150-560 0.5-500 80 4.5 0.6 0.5 4.6 2.5 0.4 2.5 3.1 0.5 Propylene 100-600 10-400 75 4.0 2.6 2.5 5.0 1.6 2.3 1.6 1.9 2.1 Hydrogen 20-500 0.1-400 70 1.3 0.5 2.4 6.0 2.1 1.7 2.3 0.8 1.2 Nitrogen 74-700 0.75-500 60 2.9 0.6 0.7 4.7 0.8 0.5 2.2 0.8 0.4

co 80·600 5.0-500 85 1.4 0.5 0.7 5.3 0.6 0.3 1.4 0.5 0.6 CO2 250·1000 2.0-500 90 8.0 0.5 1.7 1.8 0.4 0.5 2.1 0.4 0.5 H� 255-480 1.0·210 80 2.6 2.4 0.2 ,u 3.1 0.4 1.5 1.7 0.1

MO% 3.4 1.3 1.1 4.7 1.4 0.9 1.9 1.2 0.8

Table 3-Comparison between the experlmenta125 and calculated compressibility factors for (Nitrogen + Carbon dlo,dde) system at xN2

-0.553 using the present, PR Table 4 • Compositions (In mole fractions) of three different and SRK equations of state Ocijs • 0) samples of sour natural gas used in the calculations

reported in Table 5

T (K) P(bar) Zexp.

300.10 318.29 0.8870

320.06 372.49 0.9736

268.79 287.52 0.8326

273.19 245.07 0.7500

260.02 209.51 0.8736

250.06 183.18 0.6123

242.95 185.10 0.5680

241.99 162.69 0.!5820

241.03 180.45 0.5564

240.00 157.98 0.5502

239.82 157.57 0.5492

Overall '.\ deviations

SRK PR present

0.9311 0.8629 0.9146

1.0169 0.9439 0.9997

0.8763 0.8113 0.8803

0.7923 0.7322 0.7789

0.7127 0.6574 0.6978

0.6487 0.G955 0.8321

0.5987 0.5484 0.5821

0.5897 0.5418 0.5751

0.5828 0.5353 0.5682

0.5753 0.5282 0.5607

0.5740 0.5270 0.5594

5.1 3.2 2.7

Components Sample Sample Sample A B C

N2 0.0000 0.0052 0.0081

CH4 0.7130 0.7458 0.8303

� o.ocoo 0.2018 0.0744

C2Hs 0.0900 0.0474 0.0130

H2S 0.1 970 0.0000 0.0735

C3H8 0.0000 0.0000 0.0007

Tables- Comparison b.:tween the experimentaJ3,26,21 ili\d calculated rompressiblllty facto.r.; for the three sour natural gas samples of Table 4 using the

present, PR and SRK equations of state all with k,{s "' o.

Compreasibility Factor (Z)

Sample T (K) P(bar) Exp. $fl( PR present

A 311.93 70.72 0.830 0.820 0.790 0.830

A 327.87 70.72 0.856 0.855 0.825 0.857

A 311.93 139.65 0.714 0.709 0.865 0.711

A 327.87 139.65 0.762 0.765 0.721 0.767

B 310.93 70.72 0.865 0.861 0.831 0.864

B 310.93 139.65 0.778 0.782 0.738 0.785

B 310.93 208.58 0.11a 0.791 0.737 0.791

C 310.93 112.0 0.821 0.823 0.783 0.826

180

SPE 26906SOUR NATURAL GAS AND LIQUID EQUATION OF STA TE

iPi26906Table6=Thepercentagedeviations of pressures and vapor compositionsfrom the

axparfmcntsl data~7*1 for seven different bfnary mixtures by using the present, PRandSRKequationsofstateallAh ki;s=o.

I P %DeviationI

y, v. Deviation —

Systems

I

T Range No.of(1) + (2) (’) data

I(CH4+C2H8) ;:;-::;(cFf4+H2s) -(w&&c&) 183-230

103.143(H2+C2H4) 173.198(H2+C2H6) 173.223(C02+H2S) 233-316

Overall % deviations

SF?’

T26 3.320 20.025 19.212 24.416 22.1

1$.8:: 1?.0

---t=

1.07J

0.9“a1 O“yg o.7-== 0.6-

i!g o.5-

Z 0.4-

1’-377.65 K

—Thlawom

—m● P=126afrn

v o P=os.latrn

o.30~. 1

“X(CI14]. “Figure 1 - Comparison of the calculatedcompresaibiMyfactor of the m.fxfureof (methane+hydrogen sulfide) with the experimentaldata24ascalculatedby thepresentand PR equationsof state@j’s = O)at differentmole fractionaat 3T7.65K and

two different praamresof1%and66.1atrrt.

m

21.320.316.23829.217.1

24.13Prasent sw m

2.5 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 23.2

14.9 9.3 lri

Present

0.115.39.620.21.422

8.4

a

1=● ExP.

\\

●

~ 0.6 — THISWORK ‘%*, *

E \%*----

0 0.6Q —m

Figure 2 - Comparison of the calculatedCcsmpressibtityfactorof themixtureof (methane+carbon dioxide) with the experimentaldata= ascalculatedby thepresent,SRKand PRequationaofstate ~jS = O)at differentpressuresand at 250Kand ~z = 0.4761. I

so— Tfv3wosk O EXP.(T = 189.65 K) I

40 J ““-.-.” ma work b EXP,(T. 156.15’) A

10“

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

X{l),v(l)Figure 3 - comparison of the calculated equilibriumpressure-composition diagram of (methase + eti,ane)VStem by the prsaent equation of state (%,= O)with the

-, --e-xperimental data~s at two different temperatur~ of139.65and 156.lSK.

181

SPE 26906 M. MOHSEN-NIA, H. MODDARESS AND G.A. MANSOORI

80-‘--...-”-”-”.’ Thiswork

ExP....09QQ

o~60 - ..4Y””’Oa

● Q@. ..6”””x )~40-n

/“”*

*:*,*’e

●

&20 ,a..-..~lf””--’”

T-230K

-0:0 0:2 C.4 0.6 0.8x(1), Y(1)

Figure 4 - Comparison of the calculatedequilibrium pressure-composition diagram of(methane + carbon dioxide) system by thepresent equation of state (tqi = 0.07) with theexperimentaldatal~ at 23oK. “

0.0 0.2 0.4 0.6 0.8 1

*x(1), Y(1)

Hgure 6 - Comparison of the calculatedequtlibrtumtemperature-compositiondiagramof (carbondioxide+ hydrogensulfide)system bythe presentequationof state (kjj= 0.08) withtheexperimental dats?o at two differentpressuresof 6.895 and34.473bar.

SPE26?; i “

150-1 1

-“--1‘--)-o- This Wodt .*,.,.. .. .. --------

.,.. ● %,●.. o

0 ExP. ● .“a&..*&G*o

● EXP. . .P ‘4

1?479’””

J“●

s!~..........-

9

-a

\

.t

,.4”4,.....*”4*-..,.,.e..e....-’a””~

T m277.6 K

oo~. 0.8

x(1), Y(t)

Figure 5 - Comparison of the calculated equilibriumpressure-composition diagram of (methane + hydrogensulfide)system by the presentequation of state (lqj = 0.055)

with the experimentaldatazg at 277.6K.

120— This Wolk ● EXP.(T=143.05 K)

oo~

x(1), Y(i) “Figure 7 - Comparison of the calculated equilibriumpressure-composition diagram of (hydrogen + methane)system by the presmt equationof state*{= 0.144)withtheexperimental datasl at two differenttem~eraturesof 143.05and 173.65K.

SPE 26906SOUR NATURAL GAS AND LIQUID EQUATION OF STA TE