The Accuracy of Predicting Compressibility Factor for Sour Natural Gases

8/10/2019 The Accuracy of Predicting Compressibility Factor for Sour Natural Gases

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THE ACCURACY OF PREDICTINGCOMPRESSIBILITY FACTOR FOR SOUR

NATURAL GASES

Adel M. Elsharkawy* and Ali Elkamel

College of Engineering and Petroleum Kuwait

University, P.O. Box 5969, Safat 13060, Kuwait

ABSTRACT

This paper presents the initial stage of an effort aimed at

developing a new correlation to estimate pseudo critical

properties for sour gas when the exact composition is not

known. Several mixing rules and gas gravity correlations

available in the literature are first evaluated and compared.

The evaluation is performed on a large database consisting of

more than 2106 samples of sour gas compositions collected

worldwide. Several evaluation criteria are used including the

average absolute deviation (AAD), the standard deviation

(SD), the coefficient of correlation, R, and cross plots and

error histograms. The mixing rules include: Kays mixing rule

combined with WichertAziz correlation for the presence of

non-hydrocarbons, SSBV mixing rule with Wichert and Aziz,

Corredor et al. mixing rule, and Piper et al. mixing rule. These

methods, in one form or another, use information on gas

*Corresponding author. Fax: (965) 484-9558; E-mail: [email protected].

edu.kw

PETROLEUM SCIENCE AND TECHNOLOGY, 19(5&6), 711731 (2001)

711

Copyright 2001 by Marcel Dekker, Inc. www.dekker.com


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pressure and temperature (Ppr,Tpr). Standing and Katz (1942) presented

a chart for determining gas compressibility factor based on the principle

of corresponding states. Standing and Katz will be referred to as (SK).

The SK chart was prepared for binary mixtures of low molecular weight

sweet gases. Several mathematical expressions fitting the SK chart, have

been proposed to calculate the gas compressibility factor (Papy, 1968;

Hall and Yarborough, 1973; Yarborough and Hall, 1974; Dranchuk and

Abou Kassem, 1975; Dranchk et al., 1974; Hankinson et al., 1969; Brill

and Beggs, 1974). Evaluation of these methods by Takacs (1976) and

Elsharkawy et al. (2000) concluded that DranchukAbou-Kassem (DK)

correlation is the most accurate representation of SK chart. When

dealing with gas mixtures, the mixture critical pressure (Ppc) and

temperature (Tpc) are required. Critical properties of natural gas arecalculated from either gas composition or gas gravity. Several mixing

rules have been proposed to calculate mixture critical properties of

natural gases. Among these methods, Kays (1936) mixing rule and

StewartBurkhardtVoo (1959) are the most widely used. Kays mixing

rule is simple and provides an accurate determination of gas

compressibility factor for sweet gases of low molecular weight. Satter

and Campbell (1963) evaluated several mixing rules for calculating

properties of natural gases. They concluded that StewartBurkhardtVoo

rule known as SBV provided the most satisfactory results, especially for

gases of high molecular weight. Sutton (1985) studied the performance of

several mixing rule for calculating compressibility factor for gas

condensates that contain a large amount of heptane plus fraction. He

modified SBV mixing rule to account for the presence of heptane plus in

the natural gases.

Standard laboratory analysis gives composition of natural gases

through hexane and lump components heavier than hexane in a heptane

plus fraction known as C7+. Critical properties of pure components are

well documents, Table 1. The critical properties of the C7+ fraction are,

however, calculated from correlations using molecular weight and specific

gravity of the heptane plus (Win, 1957; Keseler and Lee, 1976; Sim et al.,

1980; Lin and Chao, 1984; Watansiri et al., 1985; Pedersen et al., 1989).

Whitson (1983) and Elsharkawy et al. (2000) reviewed several methods

for calculating pseudo critical properties of the heptane plus fraction.

Whitson (1983) recommended that KeslerLee (1976) correlation to be

used to estimate critical properties of C7+. However, Elsharkawy et al.(2000) found that LinChoa (1984) and Kesler Lee (1976), respectively,

with SSBV mixing rule and DK correlation are the best combination to

determine gas compressibility factor for gas condensate reservoirs.

PREDICTING COMPRESSIBILITY FACTOR 713
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Composition of natural gases, from which pseudo critical properties

are computed, is not always available. Therefore, correlations relating

pseudo critical pressure and temperature to gas gravity are used. Standing

(1981) presented correlation of pseudo critical properties to gas gravity

based on low molecular weight California natural gases. His correlation has

the following form:

Ppc 706 51:7 gg 11:1 g2

g 1

Tpc 187 330 gg 71:5 g2g 2

Standing indicated that his correlation works only when there is no

non-hydrocarbon gases present in the natural gas. Sutton (1985), working

with PVT reports of high molecular weight gases which are rich in heptane

plus, developed the following correlation:

Ppc 756:8 131:0 gg 3:6 g2g 3

Tpc 169:2 349:5 gg 74:0 g2g 4

The gases that were used to develop Suttons gas gravity correlationare mostly sweet gases. These gases have minor amount of carbon dioxide

and nitrogen, and no hydrogen sulfide. Using a large data bank of

retrograde gases, Elsharkawy et al. (2000) presented another correlation for

gas condensates. The latter correlation covers heavier gases than that used in

Table 1. Physical Properties of Defined Components

Critical Pressure Critical Temperature

Component Molecular Weight psi R

H2S 34.08 1300.00 672.45

CO2 44.01 1071.00 547.45

N2 28.01 493.00 227.27

C1 16.04 667.80 343.04

C2 30.07 707.80 549.76

C3 44.01 616.30 665.68

i-C4 58.12 529.10 734.65

n-C4 58.12 550.70 765.32

i-C5 72.15 490.40 828.77n-C5 72.15 488.60 845.37

C6 86.18 436.90 913.37

714 ELSHARKAWY AND ELKAMEL
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Suttons and have a minor amount of hydrogen sulfide. Elsharkawy et al.,

gas gravity correlation has the following form:

Ppc 787:06 147:34 gg 7:916g2g 5

Tpc 149:18358:14gg 66:976g2g 6

Thus there is a need for correlation relating gas gravity to pseudo

critical properties for sour gases.

This study has two objectives. The first objective is to evaluate the

previously published methods of calculating gas compressibility factor for

sour gases. The second objective is to develop a correlation to estimate

pseudo critical properties from gas gravity for sour gas when detailedcomposition is not available.

GAS DATA BANK

One of the main objectives of the current work is to evaluate the

previously published methods of calculating gas compressibility factors of

sour gases using either gas composition or gas gravity. The best test to

evaluate such methods is the accuracy with which these methods

approximate reliable experimental data. The data bank used in this

study comprises measurements of two thousand and one hundred and six-

gas compressibility factor for sour gases. Some of these data have been

collected from the literature (Whitson, 1985; Simon et al., 1964; Robinsonet al., 1965; Buxton and Campbell, 1967; McLeod, 1968; Wichert and

Aziz, 1970; Elsharkawy and Foda, 1988). These measurements cover a

pressure range from 90 psi to 12,000psi, a temperature range from 40 to

327F, and a wide range of molecular weights from 16.4 to 55 (gas gravity

from 0.566 to 1.895). A complete description of the data bank is reported

in Table 2.

Calculating Gas Compressibility Factor When Composition

Is Known

When gas composition is available, pseudo critical properties arecalculated using a given mixing rule. In order to calculate the pseudo-critical

properties of natural gas mixtures, critical properties of the heptane plus

fraction must be computed. In this study, KeslerLee (1976) method,

Eqs. (7) and (8), are used to calculate critical properties of the C7+.

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Pc exp 8:36340:0566=g 0:242442:2898=g0:11857=g2 103 Tb

1:46853:648=g0:47227=g2 107 T2b

0:420191:6977=g2 1010 T3b

7

Tc 341:7811:g 0:42440:1174:g Tb

0:46693:2623:g 105=Tb8

The KL method correlates critical properties as a function of boiling

point and specific gravity. However, laboratory reports normally provide

only the specific gravity and molecular weight of the heptane plus fraction.

Whitson (1983) has presented an equation for estimating boiling point

(Tb) from molecular weight (M) and specific gravity (g) of the heptaneplus fraction.

Tb 4:5579M0:15178 g0:15427

39

Table 2. Properties of Sour Gas Data Used in the Study

Min. Ave. Max.

Pressure, psi 90 2900 12,000

Reservoir temperature, F 40 190 327

Composition mole %

Methane 17.27 74.14 97.40

Ethane 0 6.00 28.67

Propane 0 2.56 13.16

Iso-Butane 0 0.50 2.61

N-Butane 0 0.84 5.20

Iso-Pentane 0 0.35 2.85

n-Pentane 0 0.32 2.09Hexane 0 0.44 5.30

Heptane plus 0 1.64 17.20

Mw C7+ 98.0 127.0 253.0

g C7+ 0.72 0.77 0.85

Z-factor 0.402 0.900 1.775

Gas gravity (air 1) 0.566 0.811 1.895

Hydrogen sulfide 0 7.45 73.85

Carbon dioxide 0 4.04 67.16

Nitrogen 0 1.72 25.15

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In this study, Kays mixing rule, Stewart-Burkhardt-Voo (SBV)

mixing rule as modified by Sutton (SSBV) are considered.

Kays (1936) mixing rule, based on molar weighted average critical

properties, has the following form:

Ppc X

yiPci 10

Tpc X

yiTci 11

StewartBurkhardtVoo (1959) (SBV) proposed the following mixing

rule for high molecular weight gases.

J1

3X

yiTc=Pcih i

2

3X

yiTc=Pc0:5ih i2

12

KX

yiTc=P0:5c i

13

Tpc K2=J 14

Ppc Tpc=J 15

If the natural gas contains heptane plus fraction, Sutton (1985)

modification of SBV (SSBV) is used.

Fj1

3

yTc=Pc C7 2

3

yiTc=Pc0:5i

2

C716

Ej0:6081Fj 1:1325F2j 14:004FjyC7 64:434Fjy

2C7

17

Ek Tc=P0:5c C7 0:3129yC7 4:8156y

2C7

27:3751y3C7

h i 18

J0 J Ej 19

K0 K Ek 20

Tpc K02=J0 21

Ppc Tpc=J0 22

Eqs. (10) and (11) or (12) through (22) provide critical properties for

sweet natural gas systems. For sour gases, these equations must be corrected

for the presence of non-hydrocarbon components. The method proposed by

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Wichert and Aziz (1972) is used to correct the pseudo critical properties of

natural gases to the presence of these non-hydrocarbon components. The

correction factor is given below:

120A0:9 A1:6 1:5B0:5 B4 23

Where the coefficient A is the sum of the mole fraction of H2S and CO2and B is the mole fraction of H2S in the gas mixture. The corrected pseudo

critical properties P 0pc andT0pc are:

T0pc Tpc 24

P0pc PpcT0pc=Tpc B1B 25

Reduced pressure (Ppr) and reduced temperature (Tpr) are calculate

from pressure (P) and temperature (T) of interest and critical properties of

the natural gas (P0pc,T0pc) by the following relationship:

Ppr P=P0pc 26

Tpr T=T0pc 27

Recently, Corredor et al. (1992), and Piper et al. (1993) proposed a

mixing rule similar to SBV rule, Eqs. (12) and (13). However, they treated

the non-hydrocarbons and the C7+ plus fraction differently. Their mixing

rule has the following form:

J a0X

aiyiTc=Pci a4X

yjTc=Pcj a5X

yiTc=Pci

h i2

a6yC7MC7 a7yC7MC7 2

28

K b0X

biyi Tc=P0:5c

i b4

Xyj Tc=P

0:5c

j b5

Xyj Tc=P

0:5c

j

h i2

b6yC7MC7 b7yC7MC7 2 29

Where yi[ fyH2S;yCO2;yN2 g and yj [ fyC1;yC2;. . .; yC6 g and a and b

are constants. The difference between Corredor et al. method and Piper

et al., method is that each method has different values for a and b. To

calculate the pseudo critical properties of the gas condensate, Corredor et al.

and Piper et al., used the weight fraction of the C7+rather than the critical

properties. Thus, they eliminate the need to characterize the heptane plus

fraction. They also eliminated the corrections needed for presence of acid

gases, Eq. (23) through (25).

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The gas compressibility factor (Z) is computed from DK correlation

using reduced pressure (Pr) and reduced temperature (Tr) as follows:

Z 1 A1 A2=Tr A3=Tr3 A4=Tr

4 A5=Tr5

rr

A6 A7=Tr Ag=Tr2

r2r A9 A7=Tr Ag=Tr

2

r5r

A10 1 A11r2r

r2r =Tr

3

exp A11r2r

30

Where

rr 0:27 Pr=ZTr 31

The constants A1 through A11 in Eq. (30) are as follows:

Because the gas compressibility factor appears on both sides of DKs

correlation, Eq. (30), an iteration solution is necessary. NewtonRaphson

method is used which has the following iteration formula:

Zn1 Zn fz=f0

z 32

WhereZn+1and Znare the new and old values of gas compressibilityfactors, fz is the function described in Eq. (30), and f

0z is its derivative.

Calculating Gas Compressibility Factor When Composition

Is Unknown

When gas composition is not available, the compressibility factor is

computed via estimating the critical properties from gravity correlations. In

this section, the accuracy with which gas gravity correlations, Eq. (1) through

(6), reproduced the pseudo critical properties is evaluated. Although

Standings gas gravity correlations, Eqs. (1) and (2) were prepared to

estimate critical properties of sweet low molecular gases, it is important to

know the magnitude of the error that results from using that correlation. The

accuracy of the gas gravity correlations developed by Sutton, Eqs. (3) and

(4), and Elsharkawy et al. given in Eqs. (5) and (6) is also studied in this

section.

A1 0.3265 A2 1.0700 A3 0.5339 A4 0.01569

A5 0.05165 A6 0.5475 A7 0.7361 A8 0.1844

A9 0.1056 A10 0.6134 A11 0.7210

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RESULTS AND DISCUSSION

The accuracy of four different methods for the calculation of gas

compressibility factor for sour gases is discussed in this section. The first

method is Kays mixing rule with WichertAziz correction for the presence

of non-hydrocarbons. The second is SSBV-Wichert and Aziz. The third is

Corredor et al. method. The last method is Piper et al. Table 3 shows the

accuracy of these methods. Piper et al. and Corridor et al. have the best

accuracy. Both of these methods account for 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% and coefficient of

correlation (R) of 99.10%. SSBV-Whichert and Aziz shows the highest

errors and the lowest correlation coefficient.Figure 1 through 4 show the error distribution for the four methods

considered in this study. KayWichert and Aziz method, Figure 1,

Table 3. Accuracy of Calculating Z-factor for Sour Gases Using Compositional

Data

Method ARE AAD SD R

Kay-Wichert and Aziz 0.69 1.38 2.13 98.57

SSVB-Wichert and Aziz 0.65 2.14 2.85 97.65

Corredor et al. 0.25 1.36 2.51 98.8

Piper et al. 0.31 1.21 1.92 99.10

Figure 1. Histogram of Er% with normal curve (Kay-WA).

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Corredor et al. method, Figure 2, and Piper et al. methods, Figure 4 have

comparable error distribution. However, Piper et al. method has the

smallest error range and the highest frequency of zero error. SSBV-Wichert

and Aziz method, Figure 2 has a wider error range and smaller frequency of

error distribution around zero error line comparing to the other methods.

The accuracy of calculating gas compressibility factor for sour gases

using gas gravity when gas composition is unknown is shown in Table 4.

Standing gas gravity correlation, Eqs. (1) and (2) has an average absolute

deviation (AAD) of 3.50% and standard deviation (SD) of 6.78%. Sutton

gas gravity correlation, Eqs. (3) and (4), has AAD of 3.47% and SD of

7.14. Elsharkawy et al. gas gravity correlation, Eqs. (5) and (6) shows AAD

Figure 2. Histogram of Er% with normal curve (SBV-KA).

Figure 3. Histogram of Er% with normal curve (Piper).

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of 3.48% and SD of 7.30%. All of these gas gravity correlations have similar

correlation coefficients. The reason for the low accuracy of these

correlations is that Standings gas gravity correlation was prepared for

sweet gases. Sutton gas gravity correlation was prepared for heavy gases rich

in C7+with minor amounts of hydrocarbons. The latter gas gravity

correlation is applicable for gases that have no hydrogen sulfide and with

a nitrogen content less than 12% and a CO2content less than 3% (Lee andWattenberger, 1996). Elsharkawy et al. gas gravity correlation was prepared

from data on gas condensate that has a significant portion of hydrogen

sulfide and carbon dioxide, however, the concentration of the acid gases is

not comparable with the sour gases used in this paper.

Figure 4. Histogram of error with normal curve (corredore).

Table 4. Accuracy of Calculating Z-Factor for Sour Gases Using Gas Gravity

Equation

Method ARE AAD SD R

Standing 0.81 3.50 6.79 92.08

Sutton 1.72 3.47 7.14 91.43

Elsharkawy et al. 2.25 3.48 7.30 91.23

Current study 0.26 1.69 3.12 97.66

ARE: Average relative error %.AAD: Average absolute deviation %.

SD: Standard deviation %.

R: Coefficient of correlation.

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New Gas Gravity Correlation

One of the objectives of this study is to start the development of a new

correlation to estimate pseudo critical properties from gas gravity for sour

gas when composition is not available. Using large data bank of sour gas

system, inferred pseudo critical pressures and temperatures are calculated

from experimentally measured gas compressibility factors using DK

equations. The first attempt was to correlate these inferred pseudo critical

values to gas gravity for sour gases. Figure 5 shows that pseudo-critical

pressures of sour gases are not strongly correlated to total gas gravity.

In order to improve the correlations it was attempt to study the effect of

non-hydrocarbon component on pseudo-critical properties. Figure 6 shows

that pseudo-critical pressures are highly correlated to the percentage ofnon-hydrocarbon gases. The percentage of non-hydrocarbon component is

expressed as molecular weight of non-hydrocarbon components divided

by the total molecular weight of the gas. This percentage can also be

related to non-hydrocarbon gas gravity (g2) divided by total gas gravity

(gg). Pseudo critical temperature, however, is strongly dependent on total

gas gravity, Figure 7. Therefore, it was found that best correlation

of pseudo-critical properties to gas gravity can be achieved by considering

both the hydrocarbon and non-hydrocarbon portions of gas gravity

as follows:

Pc 193:941131:347 gg 217:144 g1=gg 1060:349 g2=gg

344:573 g1=gg2 60:591 g2=gg

2 33

Figure 5. Pseudo-critical pressure as a function of total gas gravity for sour gases.

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Tc 195:958 206:121 gg25:855g1=gg 6:421 g2=gg 9:022 g1=gg2

163:247 g2=gg2 34

The new gas gravity correlation presented in this study has smallererror range than the other correlations. Correlating critical properties to the

amount of hydrocarbon and non-hydrocarbon gases, Eqs. (33) and (34),

improves the accuracy of the proposed correlation. Among the gas gravity

correlations considered in this study, the new correlation shows the smallest

Figure 6. Pseudo-critical pressure as a function of non-hydrocarbon to total gas

gravity for sour gases.

Figure 7. Pseudo-critical temperature as a function of total sour gas gravity.

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AAD (1.69%), the least SD (3.22%), and the highest correlation coefficient

(97.66%). However, the standard deviation is still high.

Figures 810 show the absolute error percentage in estimating gas

compressibility factor from gas gravity correlations is highly dependent on

the amount of CO2 and H2S present in the sour gas. An error as high as

50% in gas compressibility factor occurs if these gas gravity correlations are

used to estimate the gas compressibility for sour gases. Figure 11 shows first

smaller error level in calculating gas compressibility factor using the new gas

gravity correlation than the other correlations. Second, the error is not

dependent on the amount of CO2and H2S present in the sour gas. Figure 12

shows a crossplot of measured and calculated gas compressibility factor

Figure 8. Error % inz-factor using Standing gas gravity equation.

Figure 9. Error % in z-factor using Sutton gas gravity equation.

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using the new gas gravity correlation for the sour gases used in this study.

The figure illustrates that most of the data fall on the 45 parity line.

Therefore, calculating the gas compressibility factor for sour gases from

pseudo-critical pressure and temperature estimated from total gas gravity

correlations has some limitations. The major limitation is in the process of

correlating gas gravity to pseudo critical properties. For any gas, there could

be an infinite number of hydrocarbon and other non-hydrocarboncombination. Each hydrocarbon and non-hydrocarbon component has a

unique pseudo critical property. However, different mixtures can have

different pseudo-critical properties and the same gas gravity. This is the

reason why calculating gas compressibility factor using gas gravity is not as

Figure 10. Error % inz-factor using Elsharkawy et al. gas gravity equation.

Figure 11. Error % inz-factor using new gas gravity equation.

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much accurate as calculating gas compressibility factor from composition.

Correlating pseudo critical properties to hydrocarbon portion of gas gravity

and non-hydrocarbon portion have resulted in little improvement of gas

compressibility calculations.

CONCLUSIONS

In this paper, several methods of calculating sour gas compressibility

factors were compared. Two classes of methods were considered: methods

that are based on composition and those that are based on gas gravity alone.

From the methods based on composition, Piper et al. (1992) and Corridor

et al. (1993) showed the best accuracy and correlation coefficient. These

methods account for the presence of heptane plus and non-hydrocarbons.

Of the methods based on gas gravity Sutton and Elsharkawy et al., methods

were the most accurate. The accuracy of these methods was, however,

poorer than those methods based on composition. It was decided therefore

to study the effect of the presence of non-hydrocarbons on accuracy. A plot

of pseudo-critical pressure with both gas gravity and non-hydrocarbon gas

gravity was evaluated. It was found that while the correlation with gasgravity is weak, that with the non-hydrocarbon gas gravity is strong with a

correlation coefficient more that 0.84. The correlation of pseudo-critical

temperature was rather indifferent to the presence of non-hydrocarbons.

A new correlation was then proposed to account for the presence of

Figure 12. Crossplot of measured and calculated z-factor using new gas gravity

equation.

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non-hydrocarbons without knowing the compositional details. This

correlation is based on two descriptors: gravity of the gas and gravity of

the non-hydrocarbon portion in the gas. The new correlation provided a

good improvement over past gas gravity methods. Research is still going on

to develop more improvement strategies.

NOMENCLATURE

rr Reduced density

Wichert and Aziz pseudo-critical

gg gas specific gravity, (air 1)

g1 Hydrocarbon gas specific gravity, (air 1)

g2 Non-hydrocarbon gas specific gravity, (air 1)A mole fraction (CO2 + H2S)

B mole fraction H2S

AAPD Average absolute error

EJ Sutton SBV parameter, R/psia

EK Sutton SBV parameter, R/psia0.5

ARE Average relative error

FJ Sutton adjustment parameter temperature

adjustment parameter, R

J SBV parameter, R/psia

J0 Sutton parameter, R/psia

Jinf Inferred value of J parameter, R/psia

K SBV parameter, R/psia0.5

K0 Sutton parameter, R/psia0.5

Kinf Inferred value of K parameter, R/psia0.5

M Molecular weight, lb-mole

MC7 molar mass of heptane plus fraction, lb-mole

P pressure, psia

pc critical pressure, psia

Ppc pseudo-critical pressure, psia

Ppr pseudo-reduced pressure

R correlation coefficient

SD standard deviation

T temperature, R

Tb normal boiling point temperature, R

Tc critical temperature,

RTpc pseudo-critical temperature, R

Tpr pseudo-reduced temperature

yC7 mole fraction of heptane plus fraction

yi mole fraction of component, i

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yi mole fraction of theith component

Z gas compressibility factor

ACKNOWLEDGMENT

The first author thanks the Kuwait Foundation for the Advancement

of Science (KFAS) for providing financial support for this study, research

grant No. 99-9-09.

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The Accuracy of Predicting Compressibility Factor for Sour Natural Gases

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