Tarek Ahmed. Reservoir engineering handbook

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where p = system pressure, psia

= pseudo-reduced pressure, dimensionless

T = system temperature, °R

= pseudo-reduced temperature, dimensionless

, T

= pseudo-critical pressure and temperature, respectively, and

defined by the following relationships:

It should be pointed out that these pseudo-critical properties, i.e., p

and T

, do not represent the actual critical properties of the gas mixture.

These pseudo properties are used as correlating parameters in generating

gas properties.

Based on the concept of pseudo-reduced properties, Standing and Katz

(1942) presented a generalized gas compressibility factor chart as shown

in Figure 2-1. The chart represents compressibility factors of sweet natur-

al gas as a function of p

and T

. This chart is generally reliable for nat-

ural gas with minor amount of nonhydrocarbons. It is one of the most

widely accepted correlations in the oil and gas industry.

Example 2-5

A gas reservoir has the following gas composition: the initial reservoir

pressure and temperature are 3000 psia and 180°F, respectively.

Component y

0.02

0.01

0.85

0.04

0.03

i - C

0.03

n - C

0.02

Calculate the gas compressibility factor under initial reservoir condi-

tions.

TyT

pc i ci

(2 -15)

pyp

pc i ci

(2 -14)

38 Reservoir Engineering Handbook

Reservoir Eng Hndbk Ch 02a 2001-10-24 09:23 Page 38

Reservoir-Fluid Properties 39

Figure 2-1. Standing and Katz compressibility factors chart. (Courtesy of GPSA

and GPA Engineering Data Book, EO Edition, 1987.)

Reservoir Eng Hndbk Ch 02a 2001-10-24 09:23 Page 39

Solution

Component y

,°R y

0.02 547.91 10.96 1071 21.42

0.01 227.49 2.27 493.1 4.93

0.85 343.33 291.83 666.4 566.44

0.04 549.92 22.00 706.5 28.26

0.03 666.06 19.98 616.4 18.48

i - C

0.03 734.46 22.03 527.9 15.84

n - C

0.02 765.62 15.31 550.6 11.01

= 383.38 p

= 666.38

Step 1. Determine the pseudo-critical pressure from Equation 2-14:

= 666.18

Step 2. Calculate the pseudo-critical temperature from Equation 2-15:

= 383.38

Step 3. Calculate the pseudo-reduced pressure and temperature by apply-

ing Equations 2-12 and 2-13, respectively:

Step 4. Determine the z-factor from Figure 2-1, to give:

z = 0.85

Equation 2-11 can be written in terms of the apparent molecular

weight M

and the weight of the gas m:

Solving the above relationship for the gas specific volume and density,

give:

pV z

3000

666 38

450

640

383 38

167

40 Reservoir Engineering Handbook

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where v = specific volume, ft

/lb

= density, lb/ft

Example 2-6

Using the data in Example 2-5 and assuming real gas behavior, calcu-

late the density of the gas phase under initial reservoir conditions. Com-

pare the results with that of ideal gas behavior.

Solution

Component y

• M

,°R y

0.02 44.01 0.88 547.91 10.96 1071 21.42

0.01 28.01 0.28 227.49 2.27 493.1 4.93

0.85 16.04 13.63 343.33 291.83 666.4 566.44

0.04 30.1 1.20 549.92 22.00 706.5 28.26

0.03 44.1 1.32 666.06 19.98 616.40 18.48

i - C

0.03 58.1 1.74 734.46 22.03 527.9 15.84

n - C

0.02 58.1 1.16 765.62 15.31 550.6 11.01

= 20.23 T

= 383.38 P

= 666.38

Step 1. Calculate the apparent molecular weight from Equation 2-5:

= 20.23

Step 2. Determine the pseudo-critical pressure from Equation 2-14:

= 666.18

Step 3. Calculate the pseudo-critical temperature from Equation 2-15:

= 383.38

Step 4. Calculate the pseudo-reduced pressure and temperature by apply-

ing Equations 2-12 and 2-13, respectively:

zRT

(2 -17)

zRT

== (2 -16)

Reservoir-Fluid Properties 41

Reservoir Eng Hndbk Ch 02a 2001-10-24 09:23 Page 41

Step 5. Determine the z-factor from Figure 2-1:

z = 0.85

Step 6. Calculate the density from Equation 2-17:

Step 7. Calculate the density of the gas assuming an ideal gas behavior

from Equation 2-7:

The results of the above example show that the ideal gas equation esti-

mated the gas density with an absolute error of 15% when compared with

the density value as predicted with the real gas equation.

In cases where the composition of a natural gas is not available, the

pseudo-critical properties, i.e., p

and T

, can be predicted solely from

the specific gravity of the gas. Brown et al. (1948) presented a graphical

method for a convenient approximation of the pseudo-critical pressure

and pseudo-critical temperature of gases when only the specific gravity

of the gas is available. The correlation is presented in Figure 2-2. Stand-

ing (1977) expressed this graphical correlation in the following mathe-

matical forms:

Case 1: Natural Gas Systems

= 168 + 325 g

- 12.5 g

(2-18)

= 677 + 15.0 g

- 37.5 g

(2-19)

Case 2: Gas-Condensate Systems

= 187 + 330 g

- 71.5 g

(2-20)

lb ft==

()(.)

(.)( )

3000 20 23

10 73 640

884

lb ft==

()(.)

(. )( . )( )

3000 20 23

085 1073 640

10 4

3000

666 38

450

640

383 38

167

42 Reservoir Engineering Handbook

Reservoir Eng Hndbk Ch 02a 2001-10-24 09:23 Page 42

= 706 - 51.7 g

- 11.1 g

(2-21)

where T

= pseudo-critical temperature, °R

= pseudo-critical pressure, psia

= specific gravity of the gas mixture

Example 2-7

Rework Example 2-5 by calculating the pseudo-critical properties

from Equations 2-18 and 2-19.

Reservoir-Fluid Properties 43

300

0.5

350

400

450

500

550

600

650

700

0.6 0.7 0.8 0.9

Specific Gravity of the Gas

Pseudo-critical Properties of Natural Gases

Pseudo-Critical Temperature,°R Pseudo-Critical Pressure, psia

1.0 1.1 1.2

Miscellaneous gases

Condensate well fluids

Limitations:

Max. 5% N

2% CO2

2% H

Figure 2-2. Pseudo-critical properties of natural gases. (Courtesy of GPSA and

GPA Engineering Data Book, 10th Edition, 1987.)

Reservoir Eng Hndbk Ch 02a 2001-10-24 09:23 Page 43

Solution

Step 1. Calculate the specific gravity of the gas:

Step 2. Solve for the pseudo-critical properties by applying Equations

2-18 and 2-19:

= 168 + 325 (0.699) - 12.5 (0.699)

= 389.1°R

= 677 + 15 (0.699) - 37.5 (0.699)

= 669.2 psia

Step 3. Calculate p

and T

Step 4. Determine the gas compressibility factor from Figure 2-1:

z = 0.824

Step 5. Calculate the density from Equation 2-17:

EFFECT OF NONHYDROCARBON COMPONENTS

ON THE Z-FACTOR

Natural gases frequently contain materials other than hydrocarbon

components, such as nitrogen, carbon dioxide, and hydrogen sulfide.

Hydrocarbon gases are classified as sweet or sour depending on the

hydrogen sulfide content. Both sweet and sour gases may contain nitro-

gen, carbon dioxide, or both. A hydrocarbon gas is termed a sour gas if it

contains one grain of H

S per 100 cubic feet.

The common occurrence of small percentages of nitrogen and carbon

dioxide is, in part, considered in the correlations previously cited. Con-

lb ft==

()(.)

(. )( . )( )

3000 20 23

0 845 10 73 640

10 46

3000

669 2

448

640

389 1

164

===

28 96

20 23

28 96

0 699

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centrations of up to 5 percent of these nonhydrocarbon components will

not seriously affect accuracy. Errors in compressibility factor calculations

as large as 10 percent may occur in higher concentrations of nonhydro-

carbon components in gas mixtures.

Nonhydrocarbon Adjustment Methods

There are two methods that were developed to adjust the pseudo-criti-

cal properties of the gases to account for the presence of the nonhydro-

carbon components. These two methods are the:

• Wichert-Aziz correction method

• Carr-Kobayashi-Burrows correction method

The Wichert-Aziz Correction Method

Natural gases that contain H

S and or CO

frequently exhibit different

compressibility-factors behavior than do sweet gases. Wichert and Aziz

(1972) developed a simple, easy-to-use calculation procedure to account

for these differences. This method permits the use of the Standing-Katz

chart, i.e., Figure 2-1, by using a pseudo-critical temperature adjustment

factor, which is a function of the concentration of CO

and H

S in the

sour gas. This correction factor is then used to adjust the pseudo-critical

temperature and pressure according to the following expressions:

T¢

= T

-e (2 - 22)

where T

= pseudo-critical temperature, °R

= pseudo-critical pressure, psia

T¢

= corrected pseudo-critical temperature, °R

p¢

= corrected pseudo-critical pressure, psia

B = mole fraction of H

S in the gas mixture

e=pseudo-critical temperature adjustment factor and is defined

mathematically by the following expression

e=120 [A

0.9

- A

1.6

] + 15 (B

0.5

- B

4.0

) (2 - 24)

where the coefficient A is the sum of the mole fraction H

S and CO

the gas mixture, or:

TBB

pc pc

()1 e

(2 - 23)

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Reservoir Eng Hndbk Ch 02a 2001-10-24 09:23 Page 45

A = y

+ y

The computational steps of incorporating the adjustment factor e into

the z-factor calculations are summarized below:

Step 1. Calculate the pseudo-critical properties of the whole gas mixture

by applying Equations 2-18 and 2-19 or Equations 2-20 and 2-21.

Step 2. Calculate the adjustment factor e from Equation 2-24.

Step 3. Adjust the calculated p

and T

(as computed in Step 1) by

applying Equations 2-22 and 2-23.

Step 4. Calculate the pseudo-reduced properties, i.e., p

and T

, from

Equations 2-11 and 2-12.

Step 5. Read the compressibility factor from Figure 2-1.

Example 2-8

A sour natural gas has a specific gravity of 0.7. The compositional

analysis of the gas shows that it contains 5 percent CO

and 10 percent

S. Calculate the density of the gas at 3500 psia and 160°F.

Solution

Step 1. Calculate the uncorrected pseudo-critical properties of the gas

from Equations 2-18 and 2-19:

= 168 + 325 (0.7) - 12.5 (0.7)

= 389.38°R

= 677 + 15 (0.7) - 37.5 (0.7)

= 669.1 psia

Step 2. Calculate the pseudo-critical temperature adjustment factor from

Equation 2-24:

e=120 (0.15

0.9

- 0.15

1.6

) + 15 (0.1

0.5

- 0.1

) = 20.735

Step 3. Calculate the corrected pseudo-critical temperature by applying

Equation 2-22:

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T¢

= 389.38 - 20.735 = 368.64

Step 4. Adjust the pseudo-critical pressure p

by applying Equation 2-23:

Step 5. Calculate p

and T

Step 6. Determine the z-factor from Figure 2-1:

z = 0.89

Step 7. Calculate the apparent molecular weight of the gas from Equa-

tion 2-10:

= (28.96) (0.7) = 20.27

Step 8. Solve for gas density:

The Carr-Kobayashi-Burrows Correction Method

Carr, Kobayashi, and Burrows (1954) proposed a simplified procedure

to adjust the pseudo-critical properties of natural gases when nonhydro-

carbon components are present. The method can be used when the com-

position of the natural gas is not available. The proposed procedure is

summarized in the following steps:

Step 1. Knowing the specific gravity of the natural gas, calculate the

pseudo-critical temperature and pressure by applying Equations

2-18 and 2-19.

lb ft==

()(.)

(. )( . )( )

3500 20 27

089 1073 620

11 98

3500

630 44

555

160 460

368 64

168

(.)(.)

..(.)(.)

669 1 368 64

389 38 0 1 1 0 1 20 635

Reservoir-Fluid Properties 47

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