20 gas properties and correlations

Chapter 20

Gas Properties and Correlations Robert S. Metcalfe, Amoco ProductIon Co.*

Molecular Weight Molecules of a particular chemical species are composed of groups of atoms that always combine according to a specific formula. The chemical formula and the international atomic weight table provide us with a scale for determining the weight ratios of all atoms combined in any molecule. The molecular weight, M, of a molecule is sim- ply the sum of all the atomic weights of its constituent atoms. It follows, then, that the number of molecules in a given mass of material is inversely proportional to its molecular weight. Therefore, when masses of different materials have the same ratio as their molecular weights, the number of molecules present is equal. For instance, 2 lbm hydrogen contains the same number of molecules as 16 lbm methane. For this reason, it is convenient to define the term “lbm mol” as a weight of the material in pounds equal to its molecular weight. (Similarly, a “g mol” is its weight in grams.) One lbm mol of any compound, therefore, represents a fixed number of molecules.

Ideal Gas The kinetic theory of gases postulates that a gas is com-

posed of a large number of very small discrete particles. These particles can be shown to be identified with molecules. For an ideal gas, the volume of these particles is assumed to be so small that it is negligible compared with the total volume occupied by the gas. It is assumed also that these particles or molecules have neither attractive nor repulsive forces between them. The average energy of the particles or molecules can be shown to be a function of temperature only. Thus, the kinetic energy, EL, is independent of molecule type or size. Since kinetic energy is related to mass and velocity by

Ek = 5/2mv’,

it follows that small molecules (less mass) must travel faster than large molecules (more mass) when both are

‘Author of the ormmal ChaDter on ths ~ODC in the 1962 edllion was Charles F Wemaua.

at the same temperature. Molecules are considered to be

moving about in all directions in a random manner as a result of frequent collisions with one another and with the walls of the containing vessel. The collisions with the walls create the pressure exerted by the gas. Thus, as the volume occupied by the gas is decreased, the collisions of the particles with the walls are more frequent, and an increase in pressure results. It is a statement of Boyle’s law that this increase in pressure is inversely proportional to the change in volume at constant temperature.

"I P2 -=-

“2 PI

where p is the absolute pressure and V is the volume. Further, if the temperature is increased, the velocity

of the molecules and, therefore, the energy with which they strike the walls of the containing vessel will be increased, resulting in a rise in pressure. To maintain the pressure constant while heating a gas, the volume must be increased in proportion to the change in absolute temperature. This is a statement of Charles’s law,

“I TI -=-

“2 T2

where T is the absolute temperature and p is constant. From a historical viewpoint, it is interesting to note that

the observations of Boyle and Charles in no small degree led to the establishment of the kinetic theory of gases, rather than vice versa.

It follows from this discussion that, at zero degrees absolute, the kinetic energy of an ideal gas, as well as its volume and pressure, would be zero. This agrees with the definition of absolute zero, which is the temperature at which all the molecules present have zero kinetic energy.

20-Z PETROLEUM ENGINEERING HANDBOOK

Fig. 20.1-Typical preponent.

TABLE 20.1-VALUES OF THE GAS CONSTANT, R, IN pV= RT FOR 1 MOLE OF IDEAL GAS

Temperature Pressure Units Units

K -

Volume Energy Units Units R/g mol - - -

cm3

: L L

calories absolute joules

international joules - - - - -

1.9872 8.3144 8.3130

82.057 0.082054

62.361 0.08314 0.08478

Rllbm mol

R R R R R R

Ft K K K

- -

atm atm

mm Hg bar

kg/cm 3

- - -

atm in. Hg

mm Hg lbmlsq in., abs. lbmlsq ft, abs.

atm mm Hg

- Btu (IT) 1.986 - hp-hr 0.0007805 - kw-hr 0.0005819

cu ft - 0.7302 cu ft - 21.85 cu ft - 555.0 cu ft - 10.73 cu ft ft-lbm 1545.0 cu ft - 1.314 cu ft - 998.9 - - 1.988

Because the kinetic energy of a molecule is dependent only on temperature, and not on size or type of molecule, equal molecular quantities of different gases at the same pressure and temperature would occupy equal volumes. The volume occupied by an ideal gas, therefore, depends on three things: temperature, pressure, and number of molecules (moles) present. It does not depend on the type of molecule present. The ideal-gas law, which is actually a combination of Boyle’s and Charles’s laws, is a statement of this fact:

PV=nRT, . . . . . . . . . . . . . . . . . (1)

t T1 < T2 <T3 <Tc XT,

ssure volume diagram for pure com-

where

P= v= n= R= T=

pressure, volume, number of moles, gas-law constant, and absolute temperature.

The gas-law constant, R, is a proportionality constant dependent only on the units of p, V, n, and T. Table 20.1 presents different values of R for the various units of these parameters.

Critical Temperature and Pressure Typical PVT relationships for a pure fluid are illustrated in Fig. 20.1. The curve segment B-C-D defines the limits of vapor/liquid coexistence, B-C being the bubblepoint curve of the liquid and C-D, the dewpoint curve of the vapor. Any combination of temperature, pressure, and volume above that line segment indicates that the fluid exists in a single phase. At low temperatures and pressures, the properties of equilibrium vapors and liquids are extremely different-e.g., the density of a gas is low while that of a liquid is relatively high. As the pressure and temperature are increased along the coexistence curves, liquid density, viscosity, etc. generally decrease while vapor density, viscosity, etc. generally increase. Thus, the difference in physical properties of the coexisting phases decreases. These changes continue as the temperature and pressure are raised until a point is reached where the properties of the equilibrium vapor and liquid become equal. The temperature, pressure, and volume at this point are called the “critical” values for that species. Location C on Fig. 20.1 is the critical point. The critical temperature and pressure are unique values for each species and are useful in correlating physical properties. Critical constants for some of the commonly occurring hydrocarbons and other components of natural gas can be found in Table 20.2.

GAS PROPERTIES AND CORRELATIONS 20-3

TABLE 20.2-SOME PHYSICAL CONSTANTS OF HYDROCARBONS

Number Compound

1

2

3 4

z

7

a

9

10 11

12

13

14

15

16 17

la

19 20 21

22

23

24

25 26 27

28

29

30 31

:z 34

35

36

37

38

39

40 41

42

43

44

45

46 47

48

49

50 51

52

53

54 55

56

57

58

59

60 61

62

63

64

methane

ethane

propane n-butane

rsobutane n-pentane

rsopentane

neopentane n-hexane

2-methylpentane

3-methylpentane neohexane

2,3-dimethylbutane

n-heptane 2-methvlhexane

3-methylhexane 3-ethylpentane

2,2-dimethylpentane

2,4-dimethylpentane

33.dimethylpentane triptane

n-octane

dirsobutyl

isooctane

n-nonane n-decane

cyclopentane

meihylcyclopentane

cyclohexane

methylcyclohexane ethylene

propene

I-butene

cis-2.butene

trans-Pbutene

isobutene

1-pentene

1.2.butadiene

1,3-butadiene

isoprene acetylene

benzene

toluene

ethylbenzene

o-xylene m-xylene

p-xylene

styrene

Isopropylbenzene

methyl alcohol ethyl alcohol

carbon monoxide carbon dioxide

hydrogen sulfide sulfur dioxrde

ammonra

air

hydrogen

oxygen

nrtrogen chlonne

water

hehum

hydrogen chlonde

Formula

Molecular

Weight

16043

30.070

44097 58124

56124 72151

72151

72.151

86 178

86 178 86.178 86178

86.178

100.205 100205

100.205

100.205

100205

100.205 100205

100205

114232 114232

114.232

120259 142286

70 135 84 162

84.162

98.189 28054

42.081

56.108 56.108

56.108

56.108 70.135

54.092 54.092

68.119

26.038 78.114

92.141

106.168 106.168

106168 106168

104152

120.195

32.042 46.069

28010 44010

34076 64059

17031 28.964

2.016

31.999

28.013 70.906

la.015

4.003 36.461

Vapor Pressure

(lOOoF, psia)

(5000)

(800) 188.0 51.54

72.39 15.575 20.4444

36.66 4.960

6.767 6.103

9.859

7.406

1.620 2.2719

2.131

2.013

3.494

3293 2.774

3.375

0.537 1.1017

1.709

0.1796 0.0609

9.914

4503

3.266

16093

227.6

62.10

45.95

49.94

63.64 19.117

36 5

59.4

16.68

3.225

1.033

0.376

0.263

0.325 0.3424

0.238

0.188

4.63 2.125

387 I 8546

211.9

-

154.9

0.9495

906.3

Critical Constants

Pressure

bsial

667.8

707.6

616.3 550.7

529.1

488.6

490.4

464.0

436.9

436.6 453.1 4469

453.5

396.8 396.5

408.1 419.3

402.2

397.0 427.1

428.4

360.6

360.6

372.5

331 8 3044

6530 549 0

590.9

503.6 731 1

6672

583.5 612 1

587 1

580 0

591.8

(653.0) 628.0

(55a 4)

a904 7104

595 5 5234

541 6

5129

5092

580.0

465.4 1.174.4

9253

5075 1,071 0

1,306 0 1,145 0

1,636 0 5469

188 I

7369

493 0 1.1184

3,207 9 32.99

205.1

Temperature

(OF)

- 116.68

90.1

206.01 305.62

274.96

385.6

369.03

321.08

453.6

43574 448.2 420.04

4400

512.7

494.89

503.67 513.36

477.12

475.84

505.74

496.33

564.10 530.31

519.33 610.54 651.6

461.6

499.24

536.6

570.15 48.56

197.06

295.48 324.37

311.86 292 55

376.93

(340.0)

305.0

(412.0)

95.32 552.22

605.57

651.29 674.92

651.02 649.54

706.0

676.3

463.08

465.39

-220.4 87.67

212.6

315.6

270.4 -221.4

- 399.9 -181.2

-232.7 291.0

705.5

-450.308 124.8

Volume

(cu ftllbm)

0.0988

0.0788

0.0737 0.0703

0.0724 0.0674

0.0679

0.0673

0.06887

0.0682 0.0682

0.0668

0.0665

0.0690

0.0673 0.0646 0.0665

0.0665

0.0668

0.0682 0.0636

0.0690 0.0676

0.0657 0.0684

0.0679

0.0594 0.0607

0.0589

0.0601 0.0748

0.0689

0.0686

0.0668

0.0679 0.0682

0.0676

(0.0649) 0.0655

(0.0850) 0.0695

0.0525

0.0549 00565

0.0557

0.0567 0.0570

0.0541

0.0572

0.0589

0.0580 0.0532

0.0342

0.046 0.0306

0.0681

0.0517

0.5164 0.0367

0.0516 0.0280

0.0509

0 230

0.0356

Gas Densrty (60°F. 14.696 psia)

Calculated as Ideal Gas’

(cu 11 gas/gal liquid)

59.1. 37.48"

36.49' t 31.80"

30.65" 27.67

27.38

26.16"

24.38

24.16

24.56 24.02

24.47

21.73

21.56

21.64 22.19

21.41

21.39

22.03 21.93

19.58 19.33

19.26 17.81

16.32

33.85

28.33

29.45

24.92

39.25”

33.91" 35.36"

34.40"

33.86" 29.13"

38.4"

36.69' *

31.67

35.82

29.94

25.97

26.36

25.88 25.80

27.68

22.80

78.61 54.36

-

59.78' *

73.07 69.01

114.71 -

- 63.53

175.6

74.88

20-4 PETROLEUM ENGINEERING HANDBOOK

Specific Gravity (Relative Density) The specific gravity of a gas, y, is the ratio of the density of the gas at a given pressure and temperature to the density of air at the same pressure and temperature. The ideal- gas laws can bc used to show that the specific gravity (ratio of densities)* is also equal to the ratio of the molecular weights, When the ideal-gas assumptions are not valid (high pressures or most real gases), this will not always be true. By convention, specific gravities of all gases at all pressures are defined as the ratio of the molecular weight of the gas to that of air (28.966).

Mole Fraction and Apparent Molecular Weight of Gas Mixtures The analysis of a gas mixture can be expressed in terms of a mole fraction, y;, of each component, which is the ratio of the number of moles of a given component to the total number of moles present. Analyses also can be expressed in terms of the volume, weight, or pressure fraction of each component present. Under limited sets of conditions, where gaseous mixtures conform reasonably well with the ideal-gas laws, the mole fraction can be shown to be equal to the volume fraction but not to the weight fraction. The apparent molecular weight of a gas mixture is equal to the sum of the mole fraction times the molecular weight of each component.

Specific Gravity of Gas Mixtures The specific gravity (yR) of a gas mixture is the ratio of the density of the gas mixture to that of air. It is measured easily at the wellhead in the field and, therefore, is used as an indication of the composition of the gas. As mentioned earlier, the specific gravity of gas is proportional to its molecular weight (M,) if it is measured at low pressures where gas behavior approaches ideality. Once again, by convention, the specific gravity is defined as the mole weight of the gas mixture divided by 28.966. Specific gravity also has been used to correlate other physical properties of natural gases. To do this, it is necessary to assume that the analyses of gases vary regularly with their gravities. Since this assumption is only an approximation and is known to do poorly for gases with an appreciable nonhydrocarbon content, it should be used only in the absence of a complete analysis or of correlations based on a complete analysis of the gas.

Dalton’s Law The partial pressure of a gas in a mixture of gases is defined as the pressure that the gas would exert if it alone were present at the same temperature and volume as the mixture. Dalton’s law states that the sum of the partial pressures of the gases in a mixture is equal to the total pressure of the mixture. This law can be shown to be true if the ideal-gas laws apply.

Amagat’s Law The partial volume of a gas in a mixture of gases is defined as that volume which the gas would occupy if it alone were present at the same temperature and pressure as the

mixture of the gases. If the ideal-gas laws hold, then Amagat’s law, that the sum of the partial volumes is equal to the total volume, also must be true.

Real Gases At low pressures and relatively high temperatures, the volume of most gases is so large that the volume of the molecules themselves may be neglected. Also, the distance between molecules is so great that the presence of even fairly strong attractive or repulsive forces is not sufti- cient to affect the behavior in the gas state. However, as the pressure is increased, the total volume occupied by the gas becomes small enough that the volume of the molecules themselves is appreciable and must be considered. Also, under these conditions, the distance between the molecules is decreased to the point where the attractive or repulsive forces between the molecules become important. This behavior negates the assumptions required for ideal-gas behavior, and serious errors are observed when comparing experimental volumes to those calculated using the ideal-gas law. Consequently, a real-gas law was formulated (in terms of a correction to the ideal-gas law) by use of a proportionality term called the compressibility factor, z. The real-gas law is thus

pV=znRT. . . . . (2)

Tables of compressibility factors are available for most pure gases as functions of temperature and pressure. Com- pressibility factors for mixtures (or unknown pure compounds) are measured easily in a Burnett’ apparatus or a variable-volume PVT equilibrium cell. Excellent correlations are also available for the calculation of compressibility factors as discussed in the section on equations of state (EOS’s). For this reason, compressibility factors are no longer routinely measured on dry gas mixtures or most of the leaner wet gases. Rich gas condensate systems require other equilibrium studies, and compressibility factors can be obtained routinely from these data. A knowledge of the compressibility factor means that the density, p, is also known from the relationship

PM P=-,

ZRT

because V=(IIM)/P. where M is the molecular weight. Many times it is more convenient to report compressi-

bilities than densities because the range in z is usually small-e.g., between 0.3 and 2.0.

Principle of Corresponding States The principle of corresponding states has been useful in correlating the properties of gases. This principle was dc- veloped because observers noticed that the behavior of pure gases was qualitatively similar when compared (on p-V plots, for instance) even though the quantitative values of p and V were very dissimilar. The idea was advanced that the properties of substances could be correlated if they were all compared at “corresponding” values of T and p, which could be referenced easily. In the application


of the principle of corresponding states to a single- component gas, the critical state of the gas is used as the reference point. The following terms are used.

P~=~, 7.,=$, and V,=I, PC c V,

where p,. = reduced pressure, T, = reduced temperature, V, = reduced volume, PC = critical pressure, T,. = critical temperature, and V, = critical volume.

Compressibility factors of many pure compounds are available as functions of pressure in most handbooks deal- ing with gas properties (e.g., Katz et al. *). While the principle of corresponding states is not entirely rigorous, its application has been used widely in the determination of gas volumes for engineering purposes. It also has application in the estimation of gas viscosities.

In application of the principle of corresponding states to a mixture of gases, the true critical temperature and pressure for the gases cannot be used because the paraffn- ic hydrocarbon series does not strictly follow the principle as stated above. “Pseudocritical” temperature and pressure are defined for use in place of the true critical temperature and pressure to determine the compressibility factor for a mixture. The pseudocritical temperature and pseudocritical pressure normally are defined as the molal average critical temperature and pressure of the mixture components, Thus

Ppc =CYiPci

and

Tpc = Cyi Tci 3

where

PPC = pseudocritical pressure of the gas mixture, T PC = pseudocritical temperature of the gas

mixture, pci = critical pressure of Component i in the gas

mixture, Tci = critical temperature of Component i in the

gas mixture, and yi = mole fraction of Component i in the gas

mixture.

These relations are known as “Kay’s rule” after W.B. Kay, who first suggested their use.

The pseudocritical pressure and temperature are then used to determine the pseudoreduced conditions:

P p/W=----,

PPC

where pPr is the pseudoreduced pressure, and

T

T,,,=k. P’

PSEUDOREDUCEDPRESSURE


Fig. 20.2~Compressibility factor for natural gases (from Ref.

3).

where Tpr is the pseudoreduced temperature. These reduced conditions are used to determine the compressibility factor, z, from Fig. 20.2, which was developed by Standing and Katz3 from data collected on methane and natural gases. The data used to develop Fig. 20.2 ranged up to 8,200 psia and 250°F. Compressibility factors of high-pressure natural gases (10,000 to 20,000 psia) may be obtained from Fig. 20.2A, which was developed by Katz ef al. * Figs. 20.2B and 20.2C may be used for low- pressure applications after Brown et al. 4

Fig. 20.3 presents a correlation developed by Brown et al. 4 between the pseudocritical temperatures and pseudocritical pressures of naturally occurring systems with their specific gravities. Values from this chart then can be used to determine the compressibility factor of a gas whose complete analysis is not known but should be used with caution since many different compositions can result in similar gravities. It should be used only when small amounts of nonhydrocarbons are present.

Figs. 20.2A through 20.2C do not consider the presence of large quantities of nonhydrocarbons such as nitrogen, carbon dioxide, and hydrogen sulfide. However, it has been shown that nitrogen does not pose a problem for the calculation of compressibilities, and Wichert and Aziz5 have proposed corrections for the pseudocritical constants for natural gases with significant concentrations of carbon dioxide and hydrogen sulfide. Their procedure involves calculation of corrected pseudocritical constants for mixtures. The corrections are defined as follows.

7;;< =TP’.-t _. _. _. (3)


PSE”cQRED”CEo PRESSURE

Flg. 20.2A-Compressibility factor for natural gases at pressures of 10,000 to 20,000 psia (from Ref. 2).

0.90 I I I I 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

PSEUDOREDUCED PRESSURE

Fig. 20.2B-Compressibility factors for natural gases near atmospheric pressures.

and

Pbc = PpC GC

Tpc+Y~~s(l-YH,Sk '

where


+lS(~H~s’.~-yH~s~.‘), . . . . . . . . . . . . . .(4)

Tbc = corrected pseudocritical temperature,

P;, = corrected pseudocritical pressure,

Yco, = mole fraction of CO2 in mixture, and yH,s = mole fraction of Hz S in mixture.

The correction factor, E, has been plotted against hydrogen sulfide and carbon dioxide concentrations in Fig. 20.4 for convenience. This correction is reported to reproduce compressibility factors with less than 1% error.

Equations of State An EOS seeks to describe specific PVT relationships of fluids mathematically. There are hundreds of these equations ranging from those for a specific pure compound to generalized forms that claim to relate the properties of multicomponent mixtures. Naturally, there is a large range of complexity from the simple ideal-gas law to

z-

1111111111”““’

hi i

0.6

I I I I I I’ I\1 ‘\, \ \-

Fig. 20.2C-Compressibility factors for natural gases at low reduced pressures.


“F.

modern equations with 15 or more universal constants plus adjustable parameters. Historically, use of these equations has been limited to applications by researchers having large computing facilities. Recently, however, operating engineers have been provided with the same computing tools previously reserved only for researchers and special projects. The use of EOS’s, therefore, has become relatively common. Some applications, such as calculation of compressibility factors, are possible on hand-held programmable calculators. The modern engineer should not forget the use of EOS’s when the need arises for calculation or estimation of fluid properties.

Van der Waals’ Equation Van der Waals6 added terms to the ideal-gas law in an attempt to take into account forces between molecules as well as volume of the molecules themselves. His equation becomes

. ._ ____.

where VM is the molar volume and a and b are constants characteristic of the gas.

The term b is a constant to correct for the volume occupied by the molecules themselves. The term a/Vi is a correction factor to account for the attraction between molecules as a function of the average distance between them (which is related to the molar volume). When an EOS such as the van der Waals equation is applied to mixtures, either special constants for a and b must be developed for each mixture or constants for each gas in the mixture must be included in the equation along with ad- justments for the interaction between unlike gases. The latter is the more common approach.

t i i i i i i i I

MS QMV1l-Y (AIR I 1)

Fig. 20.3-Pseudocritical properties of natural gases.

PERCENT H,S

Van der Waals’ law extends the range of pressures and temperatures for describing gas behavior beyond that of the ideal-gas law. However, it has two disadvantages in actual application. The correction factors are inadequate at very high pressures and it is not always easy to obtain the mixture coefficients and interaction constants. In addition, this two-parameter formulation does not really treat the attractive and repulsive forces correctly. Despite these criticisms, modifications of the van der Waals equation have been used successfully in industry for many years.

Redlich and Kwong7 developed the first major extension of the two-parameter EOS when they proposed their own form and showed how they related the a and b terms toR,p,, and T,. Other researchers since have modified the original Redlich and Kwong equation to improve its accuracy and generality further. Most notable of the modifications are those of Soave,’ Zudkevitch and Joffe, 9 and Peng and Robinson. lo Some companies have their own versions, such as the one published by Yar- borough. ’ ’

The most common equations of state in use today and the computer programs available are the following.

1. The Starling-Hon I2 extension of the Benedict- Webb-Rubin I3 EOS:

p=RTpM+ B,RTM,-Cf5-5 T= T3 1-4

+ (bRT-a-++a(a+dj$

2

+ 2E (1 +y&) exp(-yp$), . . . . . ( > T*

PSEUDOCRITICAL TEMPERATURE ADJUSTbENT FACTOA, E. “F

Fig. 20.4-Pseudocritical temperature adjustment factor, 5,

20-a PETROLEUM ENGINEERING HANDBOOK

0.024 I

# / .\ I

i 0.018

B

E O.OlS} , U'] I/ I

0.008

0.006

0.004 [ I I I I I I r;n inn im 3nn 3m m vin Ann

TEMPERATURE, "F

Fig. ZOS-Viscosity of pure compounds at 14.7 psia.

where A ,, , B,,, C, D,,, E,, a. b, c, d, 01, and y are empirical constants, and pM equals n/V,++ (subscript M refers to molar values). This equation usu ,lly is called the “BWRS” and is available from Exxon C ,rp.

2. The Peng-Robinson lo EOS (Equipha eTM):

RT a(T) -- ‘= I’,-b VM(V,,,+b)+b(VM-b)’ ““”

. (7)

where a and b are constants characteristic of the fluid, a(T) is a functional relationship, and V, is the molar volume. It is available from the Gas Processors Suppli- ers Assn. (GPSA).

3. The Soave’ modification of the Redlich-Kwong’ EOS:

RT a(T) -- p= V~.lb vM(V~+b), . . (8)

where a(T) is a functional relationship. It, too, is available from the GPA.

The first equation, BWRS, is an empirical form using 11 constants. The values of these constants have been determined fiti properties measured on many different fluids. It is ext :mely accurate in the prediction of most thermodynamic properties. Eqs. 7 and 8 are variations of the original equation proposed by van der Waals ?.?d as such are not as accurate as the BWRC for calculation of pure component properties or properties of mixtures of light hydrocarbons. Both the Peng-Robinson and the

Soave RK EOS’s are more reliable for phase equilibrium calculations or for calculation of properties of gas condensate systems. One cannot assess their accuracy directly because it is dependent on how well the constants represent the specific components.

The Redlich-Kwong EOS and its extension are cubic in compressibility factor. J.J. Martin14 proposed a generalized cubic equation that, through suitable adjustment of parameters, can be used to obtain any other cubic including those that have been proposed after his work was published. All cubic equations have limitations in their ability to represent behavior at near-critical conditions. They are incorrect in the prediction of the critical compressibility factor and/or the shape of the critical isotherm. They can be manipulated by additional terms to circum- vent this problem but errors then appear in some other region of pressure-temperature-composition space. In general, however, EOS’s can be used routinely to calculate gas properties for both hydrocarbon and nonhydrocarbon systems and their mixtures.

One particularly useful application of EOS’s in gas property estimations is the direct calculation of the compressibility factor, z. As noted previously, the principle of corresponding states can be used to obtain compressibilities with reasonable accuracy. However, one can solve an EOS directly for z quite readily. The most reliable methods for typical natural gases are those of Robinson and Jacoby I5 and Hall and Yarborough. I6 Robinson and Jacoby proposed the following equations.

RT a -_ P= vM-b fiv,(v,+b) ? . . (9)

ai=cr,+PjT, . . . . . . . . . . . . . . . . . . . . . . . . . . ..(lO)

and

bi=yi+hiT, . . . . . . (II)

where 01, 0, y, and 6 are constants for Substance i, and for mixtures

a~; %[Kjjai+(l-Kij)aj],

a f7t =CiC;YjYiay,

and

b,,, =C,y,bi,

where KY is a constant for each binary pair when used for mixtures.

Their equations are another modification of the Redlich- Kwong equation designed specifically for the region of temperatures from 70 to 250°F and pressures below 1,500 psia. It is untested t’Jr gas mixtures containing large amounts of Cd+ material. Within these stated limits, it should be expected to calculate 8~. mpressibility factors with less than 2% error.

The Hall-Yarborough equation is

(1 +x+x2 -X”)-,4X+&c z= (1 + ) . . (12)


MOLEWLAR WEIQHT

Fig. 20.6-Viscosity of gases at 14.7 psia.

where L = compressibility factor,

A = (14.76t-9.76t2 +4.5&‘), B = (90.7t-242.2t2 +42.4t3), C = 1.18+2.82t,

xi = bpM14,

b = 0.245(RT,/p,) exp[-1.2(1-t)*], and t = TJT.

It is designed specifically to fit the Standing-Katz charts and provides excellent results for multicomponent systems. Hall and Yarborough also include the correction factors proposed by Wichert and Aziz for systems with high concentrations of nonhydrocarbons. The method has been programmed for hand calculators by Ajitsaria. I7 Note that the equations contain both z and PM, making the solution trial and error and not well suited for use

without a computer or calculator algorithm.

Viscosity Viscosity is an important property in determining resistance to flow during production and marketing of gas. Generally, the viscosity of a gas increases with increasing pressure, except at very low pressures where it becomes more or less independent of the pressure. At low pressures, the viscosity of a gas, unlike that for liquids, increases as the temperature is raised. This is caused by the increasing activity of the molecules as temperature increases. Viscosity of a fluid is obtained by determining the force per unit area necessary to shear two parallel planes with a standard spacing and velocity difference. The standard unit of viscosity is the poise, which is defined as 1 dyne-s/cm2 [6.9 lbf-seclsq in.]. However, the common unit is the centipoise (0.01 poise). Carr et al. ‘* used the data of many researchers to produce Fig. 20.5, which presents viscosities as a function of temperature at atmospheric pressure for a number of pure compounds.

Viscosity Correlations Viscosities can be estimated both by the principle of corresponding states and by a residual viscosity function based on reduced density. Carr et al., I8 using the the-

I I 1 I 1 i : ! ! : ; ’ 1 “ao.S 1.0 12 1.4 1.6 1.8 2.0 2.2 2.4 26 2.3 3.0 3.2

I

PSEUDOREDUCED TEMPERATURE

Fig. 20.7-Viscosity ratio vs. pseudoreduced temperature.

ories of transport processes, correlated viscosities of pure gases and gas mixtures against molecular weight and temperature. Fig. 20.6 presents their correlation for viscosities at atmospheric pressure. Fig. 20.7 permits estimation of a pressure correction for gas viscosities by corresponding-states techniques. The ratio of the viscosity at some elevated pressure to the viscosity from Fig. 20.6 is plotted against pseudoreduced temperature and pressure. Viscosi- ties calculated from this correlation should be expected to have less than 2% error.

The residual viscosity function (P--C(*) also has been used to correlate gas viscosities with even better success

than the corresponding-states technique described previously. (I* is a correlating parameter obtained from Fig. 20.8.) Thodos et al. 19,*o have shown that the residual viscosity function can be well correlated against density, thereby making it a useful tool for both gas and liquid viscosities. The Thodos method requires two steps, as does the technique of Carr et al. First p* must be estimated, then the effect of pressure can be calculated from another correlation. The correlation for CL* is shown in Fig. 20.8, and the effects of pressure can be estimated

PSEUDO REOUCEO TEMPERATURE

Fig. 20.6-Thodos viscosity correlation

PETROLEUM ENGINEERING HANDBOOK

Fig. 20.9-Thodos viscosity correlation-pressure correction.

from Fig. 20.9. Viscosities calculated using the correlations of Thodos et al. can be expected to have an accuracy on the order of 3%.

To use Figs. 20.8 and 20.9, one mug first calculate the average mole weight of the mixture, M, =CyiMi, and the pseudocritical temperature, pressure, and volume by Kay’s rules (T, in units of Kelvin and V, in cm3/g mol) or Fig. 20.3 if the CT+ concentration is small. Alterna- tively, the correlation of Matthews et al. *’ (Fig. 20.10) may be used to get T,. andp, for C7+ fractions. The following may be used for V, of the C7+ fraction.

(WC,+ = 1.561(Mc,+ IpR) ‘.15,

where MC,+ is the molecular weight of the CT+ fraction, and ~a is the relative density of the CT+ fraction.

Calculation of the pseudocritical density, ppcr and the viscosity parameter, t, are as follows.

ppc =M,/V,, . . . . . . . . . . . . . . (13)

(Mg),~(Ppc)% ) . . I.. . . . . . (14)

where Tpc is the pseudocritical temperature, K, and ppc is the pseudocritical pressure, atm. Caution: This is a correlation and the terms should not be converted to a con- sistent set of units.

Fig. 20.10-Pseudocritical properties of C,+ fractions

For very quick estimations, Katz’ provides graphs of viscosity vs. temperature (“F) and pressure (psia) for gas gravities ranging from 0.6 to 1 .O. Errors can be expected to be on the order of 4 to 5 % .

If gas density is not known it can be obtained from the compressibility factor through pR =M,pl (z,RT). Com- pressibility factors can be obtained by using the methods discussed above. Reduced conditions then can be calculated making sure ,o and pPc are in the same units. It is possible to use Fig. 20.8 to obtain p* and then obtain t from p*=(p*l) 14. The final step is to obtain (p-p*)[ from Fig. 20.9 and solve for p with P=/~*+[(P-P*)[]/[.

Within the limitations of each correlation, that of Carr et al. may have a slight advantage. That of Thodos et al. is a more general relationship and can be used for both gases and liquids, making it the preferred method for phase equilibrium calculations or for the near-critical region.

Natural Gasoline Content of Gas In the handling and evaluating of gas, determination of natural gasoline or liquefiable content is important. This can be accomplished because the liquid volumes of the heavier components in natural gasoline are essentially additive. The required number of cubic feet of gas to form, by condensation, 1 gal of various materials is shown in Table 20.2 under the heading “cu ft gas/gal liquid.” Mole fraction, or cubic feet of any component per cubic foot of mixture, divided by the cubic feet of gas per gallon of liquid gives the total gallons of liquid that each component could contribute to the natural gasoline per cubic

GAS PROPERTIES AND CORRELATIONS 20-l 1

foot of gas mixture. If only a part of the component under consideration is to be recovered as liquid, a suitable correction must be made. Using the principle of additive volumes, the sum of contributions of each component can be assumed to give the recoverable gasoline content per cubic foot. Use of this procedure can lead to errors of about 10% if relatively large amounts of aromatic and/or naphthenic compounds are present.

Formation Volume Factor The gas FVF, B,, is defined as barrels of reservoir gas contained in 1 scf. It is sometimes erroneously reported as the reciprocal of this definition. In either case, it is a way of relating reservoir PV to produced surface volumes. The definition of B, assumes that no liquids will con- dense as the reservoir gas is brought to standard conditions (60°F and 1 atm [288 K and 100 kPa]). This may be an invalid assumption for gas condensates but is probably acceptable for most wet gases.

The real-gas law, pV=:nRT, can be used to convert measurements at standard conditions to reservoir conditions. If the above assumption holds, then

where the subscript rc refers to reservoir conditions and SC to standard conditions. Since, by definition,

VU B = 5.61458

s v.>,. .

it follows that

TI.J r<, B,s =0.005035- . (16)

P,-c~z\c~

when T is in “R and p in psia, or

T,.,.z j.<. B, =0.34722-

P/G.W

when T is in K and p in kPa. Many times it is assumed that z,,, = 1 .O, but this is not

necessarily true. If greater precision is desired, Fig. 20.2B or 20.2C can be used to determine z for the gas at standard conditions. For rough engineering calculations, this extra precision may not be required.

Coefficient of Isothermal Compressibility Reservoir engineering equations that deal with system compressibility require a gas compressibility term. This is not the gas compressibility factor, z, but the coefficient of isothermal compressibility, c~, It is defined as the rate of change of volume with respect to pressure at constant

temperature divided by the actual volume. It can be writ- ten in differential form as

i av CR=-- - .

( > v ap T

If a gas is ideal it can easily be shown that cg = l/p. As we have already discussed, however, reservoir gases and most surface gases do not follow the ideal-gas law. Consequently, this result should only be considered as an order-of-magnitude approximation.

When the real-gas law, pV=znRT, is differentiated to calculate c,, the result is

1 i a7. CR=---

( > - . . . . . . . . . . . . . .

P z aP r (17)

If z’s are known as function of pressure, it can be evalu- ated over a small range as

However, Trube** has correlated a term called pseudoreduced compressibility against pseudoreduced pressure to eliminate the need for these evaluations. His definition of pseudoreduced compressibility is

cpr=cK Xp,,‘., . . . . . (18)

and is nondimensional. The correlating work of Trube is presented in Figs. 20.11 and 20.12. A knowledge of pseudoreduced temperature and pseudoreduced pressure is required to obtain the pseudoreduced compressibility. The coefficient of isothermal compressibility then can be calculated directly from this relationship. Trube does not give any estimates of the accuracy of his correlation, but a method based on pseudoreduced properties should be at least as accurate as the z-factor correlations on which it is based because the coefficient of compressibility is a slope rather than an absolute number.

Vapor Pressure At a given temperature, the vapor pressure of a pure compound is the pressure at which vapor and liquid coexist at equilibrium. The term “vapor pressure” should be used only in conjunction with pure compounds and is usually considered as a liquid (rather than gas) property. For a pure compound, there is only one vapor pressure at any temperature. A plot of these pressures for various temperatures is shown in Fig. 20.13 for n-butane. The temperature at which the vapor pressure is equal to 1 atm (14.696 psia or 101.32 kPa) is known as the normal boiling point.

The Clapeyron equation gives a rigorous quantitative relationship between vapor pressure and temperature:

dp, Lt. dT =TAv, . . . . ..I................... (19)


2 3 4 5 6 7 6 9 10

PSEUDOREOUCEDPRESS”RE

Fig. 20.1 l-Reduced compressibility coefficients for low pseudoreduced pressures and fixed pseudoreduced temperatures

0.07

0.06


Fig. 20.12~Reduced compressibility coefficients for moderate pseudoreduced pressures and fixed pseudoreduced temperatures.

500

400

300

200

100

0 100 200 300

TEMPERATURE ‘F

Fig. 20.13-Vapor pressure of n-butane

where pv = vapor pressure,

T = absolute temperature, AV = increase in volume while vaporizing 1

mole, and L, = molal latent heat of vaporization.

Assuming ideal-gas behavior of the vapor and neglect- ing the liquid volume, the Clapeyron equation can be sim- plified over a small temperature range to give the approximation

d In pv L, -=-

dT RT2’

which is known as the Clausius-Clapeyron equation. This equation suggests that a plot of logarithm of vapor

pressure against the reciprocal of the absolute temperature would approximate a straight line. Such a plot is useful in interpolating and extrapolating data over short ranges. However, the shape of this relationship for real substances is not a straight line but rather S-shaped. There- fore, the use of the Clausius-Clapeyron equation is not recommended when other methods are available.

Cox Chart COXES further improved the method of estimating vapor pressure by plotting the logarithm of vapor pressure against an arbitrary temperature scale. The vapor- pressure/temperature plot forms a straight line, at least for the reference compound, and usually for most of the materials related to the reference compound. This is es- pecially true for petroleum hydrocarbons. A Cox chart using water as a reference material is shown in Fig. 20.14. In addition to forming nearly straight lines, compounds of the same family appear to converge on a single point.

GAS PROPERTIES AND CORRELATIONS 20-l 3

VAPOR PRESSURE, PSIA

Fig. 20.14-Cox chart for normal paraffin hydrocarbons.

Thus, it is necessary to know only vapor pressure at one temperature to estimate the position of the vapor-pressure line. This approach is very handy and can be much better than the previous method. Its accuracy is dependent to a large degree on the readability of the chart.

Calingeart and Davis Equation The Cox chart was fit with a three-parameter function by Calingeart and Davis. x Their equation is

B lnp,,=A-- T-c’ . . . .

where A and E are empirical constants, and, for compounds boiling between 32 and 212”F, C is a constant with a value of 43 when T is in K, and C is a constant with a value of 77.4 when T is in “R.

This equation generally is known as the Antoine25 equation because he proposed one of very similar nature that used 13 K for the constant C. Knowledge of the vapor pressure at two temperatures will fix A and B and permit approximations of vapor pressures at other temperatures. Generally, the Antoine approach can be expected to have less than 2% error and is the preferred approach if the vapor pressure is expected to be less than 1,500 mm Hg [200 kPa] and if the constants are available.

Lee-Kesler Vapor pressures also can be calculated by corresponding- states principles. The most common expansions of the Clapeyron equation lead to a two-parameter expression. Pitzer extended the expansion to contain three parameters:

In pvr=fo( T,)+wf’( T,), . . .(21)

where pvr is the reduced vapor pressure (vapor pressure/critical pressure), f” andf’ are functions of reduced temperature, and w is the acentric factor.

Lee and Kesler26 have expressed f’ and f’ in analyt- ical forms:

f” =5.92714-(6.09648/T,)

- 1.28862 In T, +O. 169347( T,-)6 . .(22)

and

f’ =15.2518-(15.6875/T,)- 13.4721 In T,

+0.43577(T,)6, . . . . . . . . . . . . . . . . . . . . . . . ..(23)

which can be solved easily by high-speed computer or a hand-held calculator. Lee-Kesler is the preferred method of calculation but should be used only for nonpolar liquids.

The advent of computers and calculators makes use of approximations and charts much less advantageous than they were in the 1960’s. Values of acentric factors can be found in Ref. 27, which also presents many other available vapor-pressure correlations and calculation techniques with comments about their advantages and limitations.

Example Problems Example Problem 1. Calculate relative density (specific gravity) of the following natural gas. All compositions are in mole percent.

Cl 83.19 C2 8.48

c3 4.37 iC4 0.76

nC4 1.68 iC5 0.57

nC5 0.32

c6 0.63

Total 100.00


TABLE 20.3-DATA FOR EXAMPLE PROBLEM 1

I Y,

-0.8319 3

2 0.0848 0.0437

iC, 0.0076

nC4 0.0168 iC, 0.0057

nC5 0.0032 C6 0.0063

Total 1 .oooo

‘From Table 20 2

M,’ Y,M, 16.04 13.344 30.07 2.550 44.10 1.927 58.12 0.442 58.12 0.976 72.15 0.411 72.15 0.231 86.18 0.543

20.424

Solutioion. First calculate the apparent mole weight from

information in Table 20.3.

ti, =Cy;M; ~20.424.

Then

YI: = M,/M,=CviMi128.966

= 20.424128.966

= 0.705,

where M, is the molecular weight of air=28.966

Example Problem 2. Calculate actual density of the same mixture at 1,525 psia and 75°F.

Solution.

PM, PK = -

z,RT’

p = 1,525 psia,

M, = 20.424,

R = 10.73 psiaxcu ft

“R Xlbm mol (from Table 20. l),

T = 75”F+460=535”R, and

zK must be obtained from Fig. 20.2.

Calculate zg from known composition or gas gravity in Table 20.4. From the known gas composition we obtain

T,,,. =Ey;Tci =393.8”R,

535 T/Jr= -=11.36,

393.8

~~~.=~y;p~i=662.6 psia,

1,525 = - =2.30, and

Ppr 662.6

zR =0.712.

From gas gravity we obtain

iis =CyjMj =20.424


Methane Ethane Propane i-butane n-butane i-pentane n-pentane Hexanes

Mole Fraction (O:‘) ~ ~ 0.8319 343 0.0848 550 0.0437 666 0.0076 735 0.0168 766 0.0057 829 0.0032 846 0.0063 914

(p%*) M;

xii-- 16.04 708 30.07 616 44.09 529 58.12 551 58.12 490 72.15 489 72.15 437 86.17

1 .oooo

‘From Table 20 2

and

M* 20.424 - =0.705

‘“=z= 28.966

From Fig. 20.3 we obtain

TPc =392”R.

535 Tp,=---1.36,

392

pPc. =663 psia,

1,525 ~ =2.30, pv= (-63

and

zR =0.712.

Conclusion. Composition and gas gravity methods yield identical results for this hydrocarbon gas at surface processing conditions. Then,

1,525 x 20.424

Psi = 0.712 x 10.73~535

=7.62 lbm/cu ft=O.122 g/cm3.

Example Problem 3. Calculate the z factor for the reservoir fluid in Table 20.5 at 307°F and 6,098 psia. For the C 7 + fraction:

y = 0.825(40”API),

Mh’ = 119, and

the experimental zR = 0.998.

Solution. From the known gas composition we obtain (Fig. 20.2)

Tp, = C>‘iT,.i=487”R,

767 T/w = ==1.58,

ppc = CJ’;p,i=822 psia,

6,098 PP = -=7.42. and

824

ZR = 0.962 (-4% error).



Mole Fraction &J (:!a) & ~~

Nitrogen 0.1186 226 493 28.02 Methane 0.3636 343 660 16.04 Carbon Dioxide 0.0849 546 1071 44.01 Ethane 0.0629 550 708 30.07 Hydrogen sulfide 0.2419 673 1306 34.08 Propane 0.0261 666 616 44.09 I-butane 0.0123 735 529 58.12 n-butane 0.0154 766 551 50.12 kpentane 0.0051 I329 490 72.15 n-pentane 0.0052 846 489 72.15 Hexanes 0.0067 914 437 66.17 Heptanes plus 0.0373 1,116* 453’ 119.00

Total 1 .oooo

‘Otdamed from Ffg 20 10

From gas gravity we obtain

M,? = EyiMi=31.87, and

31.87 YK = MS/M, = ~=l.loo.

28.966

T I’( = 524”R,

767 T,j, = 524 = 1.464,

P[K = 652 psia,

6,098 Ppr = __ =9.3.5, and

652

zx = 1.087 (9% error).

By including corrections to calculated criticals with Wichert and Aziz’s chart we obtain

c = 31.2 (Fig. 20.4),

T;,. = 487-31=456”R,

Pi, = (822)(456)/[487+(0.2419)(1-0.2419)(31.2)],

= 762 psia.

767 T,,, = 456 = I .68,

6,098 P/Jr = ~ =8.00, and

762

zfi = 1.010 (1% error).

Example Problem 4. Calculate the viscosity at 150°F and 2,012 psia for the gas of the composition shown in Table 20.6.


Mole Fraction

Nitrogen 0.156 Methane 0.739 Ethane 0.061 Propane 0.034 i-butane 0.002 n-butane 0.006

Total 1.000

M, Molecular T,

Weight (OR) (p?a)

---5&z---- 22a 492 16.04 343 666 30.07 550 706 44.09 666 616 58.12 735 529 56.12 765 551

Solution by the Carr-Kobayashi-Burrows Method.

Tpc = CyiT,.i =350”R,

460+ 150 Tpr = =1.74,

350

ppc = Cyip,i=639 psia.

2,012 PPr = -=3.15,

639

M, = CyiMi=l9.98, and

19.98 “fh’ = -=0.690.

28.966

Viscosity at 150”F, 1 atm (Fig. 20.6) = 0.0116 cp Correction for N2 (Fig. 20.6) = +0.0013 cp

Viscosity, r.i r = 0.0129 cp

Viscosity ratio, h/h, (Fig. 20.7) = 1.32 Viscosity, ~=(1.32)(0.0129) = 0.0170 cp

Solution by the Thodos Method.

Vllc =CyiV,.i=lO4.5 cm3/g mol.

Viscosity parameter,

(350/1.8)x

= (19.98)“(639/14.7)” =0.0435.

Pseudocritical density,

~-0.1912 g/cm”.

Viscosity factor, p*l (Fig. 20.8)=55x 10m5,

/~*=55xlO-s/0.0435=0.0126 cp.


Density,

zg = 0.876 (Fig. 20.2),

MgP (19.98)(2,012) pg=-= =7.017 lbm/cu ft

z,RT (0.876)(10.73)(610)

=O. 112 g/cm3, and

p,,=O.l12/0.1912=0.58.

Viscosity factor, (p--*)4= 18.9~ lo-’ (from Fig. 20.9).

Viscosity, ~=~*+(~--~*)[I{

=O.Ol26+l8.9x1O-5/O.O435

=0.0169 cp

Results. Carr et al. =0.0170 cp, Thodos et al. =00.0169 cp, and experimental=0.0172 cp.

Conclusion. Excellent results are obtained from either correlation for viscosity of a natural gas.

Example Problem 5. A new discovery in the Lower Tus- caloosa formation produces a gas consisting of 96 % C t and 4% C?. There is no liquid production at the surface. Reservoir conditions are 6,000 psia and 245°F. Calcu- late the gas formation volume factor and the coefficient of isothermal compressibility.

Solution. The pseudocritical pressure and temperature of the mixture are

T,,,.=O.96~343=329.3 +0,04x550= 22.0

=351.3”R.

and

p,,.=O.96~668=641.3 +0.04x708= 28.3

=669.6 psia.

The reduced quantities at reservoir (subscript TC) and surface (subscript SC) conditions are

245 +459.6 VP,),,. =

704.6

351.3 =~=2.00,

352.24

60+459.6 (T,,).,,. = 351 .3 = 1.48,

6,000 (p,r),.=669.6=8.96,

and

14.7 ~Pp,L,.=~=0.022.

From Fig. 20.2, zrc = 1.095, zSr =0.998 (probably could have assumed 1 .O), and

Td, 0.005035 x704.6x 1.095 B, =0.005035- =

Pd& 6,000x0.998

=0.00065 RB/scf.

From Fig. 20.11, by using Tp, =2.00 and ppr =8.96, we obtain:

Cpr =0.074,

CPr =cp XPpc,

and

Cpr 0.074 CR=-= - =0.0001105

ppr 669.6

=llO.5XlO-6 psi-‘.

By using a computer to calculate the numerical deriva- tive of z with respect to pressure. we get cg = 107.4X lop6 psi-t, which indicates Trube’s correlation to be in error by about 3%.

Example Problem 6. The vapor pressure of pure hexane as a function of temperature is 54.04 kPa at 50°C and 188.76 kPa at 90°C. Estimate the vapor pressure of hexane at lOO”C, using all the methods outlined in the text.

Solution. Clausius-Clapeyron, The Clausius-Clapeyron equation can be solved graphically by plotting log of vapor pressure vs. reciprocal absolute temperature and extrapolating. It also can be solved by slopes.

T, = 50°C [581.67”R],

l/T, = 0.001719,

T2 = 90°C [617.67”R], l/T1 = 0.001619,

p,, at TI = 54.04 kPa=7.8374 psia, logp,, = 0.89417,

p,. at T2 = 105.37 kPa= 15.2826 psia, log p,, = 1.18420,

A log p,, = -0.29003, l/T1 - l/T2 = 0.0001, and

slope =

=

Alogp,. 4

i-’ = >

-0.29003

TI T2 0.0001

-2900.3.

Solving log p v = -2900.3(l/T)+b for h yields

b = 5.87977,

T3 = 100”C=671.67”R, and l/T, = 0.001489.


Pc =

Solving for pr at 100°C:

log Pl, = -2900.3(0.001489)+5.87977

= 1.56122, and

p,, = 36.4102 psia r251.04 kPa].

However, if you know that the vapor pressure at 70°C is 105.37 kPa, you can use the 70 to 90°C temperature differential to calculate the slopes and ultimately will calculate p,,=35.81 psia=246.7 kPa.

Cox Chart. 2g From Fig. 20.14, the vapor pressure at 100°C can be approximated between 35 and 36 psia. A larger chart is required for more precise readings.

The Calingeart and Davis or Antoine Equation. This can be used by obtaining the Antoine constants from Reid et al. ?’ For n-hexane, with temperature in K, these constants are A= 15.8366, B=2697.55, and C= -48.78. Then,

B lnp,. = A--

T-tC

2697.55 = 15.8366- =3.60223, and

373 -48.78

pY = 36.68 psia [252.73 kPa].

Lee-Kesler. The use of the Lee-Kesler equation requires pr, T,., and w for n-hexane. These can be obtained from Table 20.2.

pc, = 436.9 psia [29.7 atm] T,. = 453.7”F or 913.3”R or 507.4 K, and w = 0.3007.

For lOO”C,

T,. = 0.7351, (T,)6 = 0.15782, In T, = -0.30775,

f’=5.92714-(6.0964810.7351)+1.28862(0.30775)

+O. 169347(0.15782),

and

f’=l5.2518-(15.687510.7351)+13.4721(0.30775)

+0.43577(0.15782).

Therefore,

f o =5.92714-8.29340+0.39657+0.02673

= - 1.94296,

f’ =15.2518-21.34063+4.14604+0.06877

z-1.87402,

In pvr= -1.94296+0.3007(-1.87402)

= -2.50648,

P VI =p”=O.O816, PL

and

p,=O.O816~29.7=2.4235 atm=35.62 psia

=245.59 kPa.

Experimental Value. 35.69 psia=245.90 kPa. Conclusions. Lee-Kesler gives the best answer, but the

Clausius-Clapeyron method can be even more accurate if the extrapolation is short.

Nomenclature a=

a; = aij = a, =

a(T) = A=

4, = b=

bi = b, =

B=

B, =

Bo = c=

constant characteristic of the fluid constant for Substance i mixture parameter Parameter a characteristic functional relationship empirical constant empirical constant constant characteristic of the fluid constant characteristic for Substance i Parameter b for mixture empirical constant gas FVF

cg =

empirical constant

empirical constant coefficient of isothermal

c= compressibility

constant with value of 43 when temperature is in K, and a value of 77.4 when temperature is in “R

d= empirical constant

Do = empirical constant Ek = kinetic energy

E,, = empirical constant

fO,f' = functions of reduced temperature K, = constant for each binary pair when

L,. =

m= M=

M, =

MC,+ =

M, =

P’

used for mixtures molar latent heat of vaporization mass molecular weight molecular weight of air molecular weight of CT+ fraction

average mole weight of gas mixture absolute pressure critical pressure

20-l 8

(

PETROLEUM ENGINEERING HANDBOOK

PC, = critical pressure of Component i in gas mixture

Ppc = pseudocritical pressure of gas mixture

P’pc = corrected pseudocritical pressure

Pr = reduced pressure

Pm = pressure at reservoir conditions

Pw = pressure at standard conditions

PI, = vapor pressure

Pw = reduced vapor pressure (vapor

R= t=

pressure/critical pressure) absolute temperature ratio of critical to absolute

temperature T,. =

T,.i = critical temperature critical temperature of Component i in

gas mixture T,,<. =

T, = T,,. =

7-w. = v= v=

v,. =

Vc)c. = v, =

v, = v,,. =

v.,, = AV =

corrected pseudocritical temperature reduced temperature temperature at reservoir conditions temperature at standard conditions velocity volume critical volume critical volume of CT+ fraction molar volume reduced volume volume at reservoir conditions

volume at standard conditions increase in volume while vaporizing

1 mole x; = mole fraction of Component i in

liquid

YCO! = mole fraction of CO* in mixture

L’H,S = mole fraction of H 2 S in mixture ?‘; = mole fraction of Component i in gas

mixture compressibility factor

compressibility factor at reservoir conditions

z.\, = compressibility factor at standard conditions

a; =

Pi =

Yg =

Yi =

6j =

E=

CL=

lJ *=

c;=

PM =

P/X =

PR =

CO=

empirical constant for Substance i empirical constant for Substance i specific gravity for gas empirical constant for Substance i empirical constant for Substance i correction factor viscosity correlating parameter viscosity parameter molar density pseudocritical density relative density of CT+ fraction acentric factor

References

8

9

10

II

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13

14

15

16.

17.

18.

19.

20.

21.

22.

23.

24.

25. 26.

21.

28.

29.

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20 gas properties and correlations

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