Page 33 - Petroleum Production Engineering, A Computer-Assisted Approach

Guo, Boyun / Computer Assited Petroleum Production Engg 0750682701_chap02 Final Proof page 22 22.12.2006 7:08pm

2/22 PETROLEUM PRODUCTION ENGINEERING FUNDAMENTALS
compressibility factor, gas density, gas formation volume where p ci and T ci are critical pressure and critical tempera-
factor, and gas compressibility. The first two are com- ture of component i, respectively.
position dependent.The latter four are pressure dependent.
Example Problem 2.2 For the gas composition given in
the following text, determine apparent molecular weight,
2.3.1 Specific Gravity of Gas specific gravity, pseudo-critical pressure, and pseudo-
‘‘Specific gravity gas’’ is defined as the ratio of the appar- critical temperature of the gas.
ent molecular weight of the gas to that of air. The molecu-
lar weight of air is usually taken as equal to 28.97 ( 79%
nitrogen and 21% oxygen). Therefore, the gas-specific Component Mole Fraction
gravity is
C 1 0.775
MW a C 2 0.083
g g ¼ , (2:18)
28:97 C 3 0.021
i-C 4 0.006
where MW a is the apparent molecular weight of gas, which
n-C 4 0.002
can be calculated on the basis of gas composition. Gas
i-C 5 0.003
composition is usually determined in a laboratory and
n-C 5 0.008
reported in mole fractions of components in the gas. Let
C 6 0.001
y i be the mole fraction of component i, and the apparent
C 7þ 0.001
molecular weight of the gas can be formulated using a
N 2 0.050
mixing rule such as
CO 2 0.030
Nc
X H 2 S 0.020
MW a ¼ y i MW i , (2:19)
i¼1
Solution Example Problem 2.2 is solved with the
where MW i is the molecular weight of component i, and
spreadsheet program MixingRule.xls. Results are shown
N c is number of components. The molecular weights of
in Table 2.2.
compounds (MW i ) can be found in textbooks on organic
chemistry or petroleum fluids such as that by Ahmed If the gas composition is not known but gas-specific
(1989). Gas-specific gravity varies between 0.55 and 0.9. gravity is given, the pseudo-critical pressure and tempera-
ture can be determined from various charts or correlations
2.3.2 Gas Pseudo-Critical Pressure and Temperature developed based on the charts. One set of simple cor-
Similar to gas apparent molecular weight, the critical relations is
properties of a gas can be determined on the basis of the
p pc ¼ 709:604 58:718g g (2:22)
critical properties of compounds in the gas using the mix-
ing rule. The gas critical properties determined in such a T pc ¼ 170:491 þ 307:344g g , (2:23)
way are called ‘‘pseudo-critical properties.’’ Gas pseudo-
critical pressure ( p pc ) and pseudo-critical temperature which are valid for H 2 S < 3%, N 2 < 5%, and total content
(T pc ) are, respectively, expressed as of inorganic compounds less than 7%.
Corrections for impurities in sour gases are always
X
N c
p pc ¼ y i p ci (2:20) necessary. The corrections can be made using either charts
i¼1 or correlations such as the Wichert and Aziz (1972)
correction expressed as follows:
and
(2:24)
A ¼ y H 2 S þ y CO 2
X
N c
T pc ¼ y i T ci , (2:21)
B ¼ y H 2 S (2:25)
i¼1
Table 2.2 Results Given by the Spreadsheet Program MixingRule.xls
MixingRule.xls
Description: This spreadsheet calculates gas apparent molecular weight, specific gravity, pseudo-critical pressure,
and pseudo-critical temperature.
Instruction: (1) Update gas composition data (y i ); (2) read result.
Compound y i MW i y i MW i p ci (psia) y i p ci (psia) T ci ,(8R) y i T ci (8R)
C 1 0.775 16.04 12.43 673 521.58 344 266.60
C 2 0.083 30.07 2.50 709 58.85 550 45.65
C 3 0.021 44.10 0.93 618 12.98 666 13.99
i-C 4 0.006 58.12 0.35 530 3.18 733 4.40
0.002 58.12 0.12 551 1.10 766 1.53
n-C 4
0.003 72.15 0.22 482 1.45 830 2.49
i-C 5
0.008 72.15 0.58 485 3.88 847 6.78
n-C 5
0.001 86.18 0.09 434 0.43 915 0.92
C 6
C 7þ 0.001 114.23 0.11 361 0.36 1024 1.02
0.050 28.02 1.40 227 11.35 492 24.60
N 2
CO 2 0.030 44.01 1.32 1,073 32.19 548 16.44
H 2 S 0.020 34.08 0.68 672 13.45 1306 26.12
1.000 MW a ¼ 20.71 p pc ¼ 661 T pc ¼ 411
g g ¼ 0.71