Chapter 2
P r o p e r t i e s o f N a t u r a l G a s
2.1 Introduction
Properties of natural gas include gas-specific gravity, pseudocritical pres-sure and temperature, viscosity, compressibility factor, gas density, andgas compressibility. Knowledge of these property values is essential fordesigning and analyzing natural gas production and processing systems.Because natural gas is a complex mixture of light hydrocarbons with aminor amount of inorganic compounds, it is always desirable to find thecomposition of the gas through measurements. Once the gas compositionis known, gas properties can usually be estimated using established corre-lations with confidence. This chapter focuses on determination of gasproperties with correlations developed from various lab measurements.Example problems are presented and solved using computer programsprovided with this book.
2.2 Specific Gravity
Gas-specific gravity (yg) is defined as the ratio of the apparent molecularweight of a natural gas to that of air, itself a mixture of gases. The molec-ular weight of air is usually taken as equal to 28.97 (approximately 79%nitrogen and 21% oxygen). Therefore the gas gravity is
where the apparent molecular weight of gas can be calculated on the basisof gas composition. Gas composition is usually determined in a
(2.1)
laboratory and reported in mole fractions of components in the gas. Let yt
be the mole fraction of component i, the apparent molecular weight of thegas can be formulated using mixing rule as
(2.2)
where MWt is the molecular weight of component i, and Nc is the numberof components. The molecular weights of compounds (MWi) can befound in textbooks on organic chemistry or petroleum fluids such as thatby McCain (1973). A light gas reservoir is one that contains primarilymethane with some ethane. Pure methane would have a gravity equal to(16.04/28.97) = 0.55. A rich or heavy gas reservoir may have a gravityequal to 0.75 or, in some rare cases, higher than 0.9.
2.3 Pseudocritical Properties
Similar to gas apparent molecular weight, the critical properties of a gascan be determined on the basis of the critical properties of compounds inthe gas using the mixing rule. The gas critical properties determined insuch a way are called pseudocritical properties. Gas pseudocritical pres-sure (ppc) and pseudocritical temperature (Tpc) are, respectively,expressed as
(2.3)
(2.4)
and
where pci and Tci are critical pressure and critical temperature of compo-nent i, respectively.
Example Problem 2.1
For the gas composition given in the following text, determineapparent molecular weight, pseudocritical pressure, and pseud-ocritical temperature of the gas.
Component Mole Fraction
O, 0.775
C2 0.083
C3 0.021
i-C4 0.006
n-C4 0.002
i-C5 0.003
n-C5 0.008
C6 0.001
C7+ 0.001
N2 0.050
CO2 0.030
H2S 0.020
Solution
This problem is solved with the spreadsheet programMixingRule.xls. Results are shown in Table 2 -1 .
If the gas composition is not known but gas-specific gravity is given, thepseudocritical pressure and temperature can be determined from variouscharts or correlations developed based on the charts. One set of simplecorrelations is
(2.5)
(2.6)
(2.7)
(2.8)
Table 2-1 Results Given by MixingRule.xlsa
Compound
Ci
C2
C3
i-C4
n-C4
i-C5
n-C5
C6
C7+
N2
CO2
H2S
Yi
0.775
0.083
0.021
0.006
0.002
0.003
0.008
0.001
0.001
0.050
0.030
0.020
1.000
MWj
16.04
30.07
44.10
58.12
58.12
72.15
72.15
86.18
114.23
28.02
44.01
34.08
MW3 =
g =
Y1MW1
12.43
2.50
0.93
0.35
0.12
0.22
0.58
0.09
0.11
1.40
1.32
0.68
20.71
0.71
Pci(psia)
673
709
618
530
551
482
485
434
361
227
1073
672
Ppc =
YiPci(psia)
521.58
58.85
12.98
3.18
1.10
1.45
3.88
0.43
0.36
11.35
32.19
13.45
661
Tci(0R)
344
550
666
733
766
830
847
915
1024
492
548
1306
' pc =
YiTci(0R)
266.60
45.65
13.99
4.40
1.53
2.49
6.78
0.92
1.02
24.60
16.44
26.12
411
a. This spreadsheet calculates gas apparent molecular weight, specific gravity,pseudocritical pressure, and pseudocritical temperature.
which are valid for H2S < 3%, N2 < 5%, and total content of inorganiccompounds less than 7%.
Corrections for impurities in sour gases are always necessary. The correc-tions can be made using either charts or correlations such as the Wichert-Aziz (1972) correction expressed as follows:
Click to View Calculation Example
Click to View Calculation Example
(2.9)
(2.10)
(2.11)
Correlations with impurity corrections for mixture pseudocriticals arealso available (Ahmed 1989):
(corrected Tpc)
(corrected ppc)
(2.12)
(2.13)
Applications of the pseudocritical pressure and temperature are normallyfound in natural gas engineering through pseudoreduced pressure andtemperature defined as:
(2.14)
(2.15)
2.4 Viscosity
Gas viscosity is a measure of the resistance to flow exerted by the gas.Dynamic viscosity (jug) in centipoises (cp) is usually used in the naturalengineering:
Kinematic viscosity ( v j is related to the dynamic viscosity throughdensity (pg)
(2.16)
Kinematic viscosity is not normally used in natural gas engineering.
Direct measurements of gas viscosity are preferred for a new gas. If gascomposition and viscosities of gas components are known, the mixingrule can be used for determining the viscosity of the gas mixture:
(2.17)
Gas viscosity is very often estimated with charts or correlations devel-oped based on the charts. The gas viscosity correlation of Carr, Koba-yashi, and Burrows (1954) involves a two-step procedure: the gasviscosity at temperature and atmospheric pressure is estimated first fromgas-specific gravity and inorganic compound content. The atmosphericvalue is then adjusted to pressure conditions by means of a correctionfactor on the basis of reduced temperature and pressure state of the gas.The atmospheric pressure viscosity (/Z1) can be expressed as:
(2.18)
where
(2.19)
(2.20)
(2.21)
(2.22)
Dempsey (1965) developed the following relation:
(2.23)
where
Thus, once the value of jur is determined from the right-hand side of this
equation, gas viscosity at elevated pressure can be readily calculatedusing the following relation:
(2.24)
Other correlations for gas viscosity include Dean-Stiel (1958) and Lee-Gonzalez-Eakin (1966).
Example Problem 2.2
A 0.65 specific gravity natural gas contains 10% nitrogen, 8%carbon dioxide, and 2% hydrogen sulfide. Estimate viscosity ofthe gas at 10,000 psia and 180 0F.
Solution
This problem is solved with the spreadsheet Carr-Kobayashi-Burrows Viscosity.xls that is attached to this book. The result isshown in Table 2-2.
2.5 Compressibility Factor
Gas compressibility factor is also called deviation factor, or z-factor. Itsvalue reflects how much the real gas deviates from the ideal gas at givenpressure and temperature. Definition of the compressibility factor isexpressed as:
(2.25)
Introducing the z-factor to the gas law for ideal gas results in the gas lawfor real gas as:
(2.26)
Table 2-2 Results Given by Carr-Kobayashi-BurrowsViscosity.xls3
Input Data
Pressure:
Temperature:
Gas-specific gravity:
Mole fraction of N2:
Mole fraction of CO2:
Mole fraction of H2S:
Calculated Parameter Values
Pseudocritical pressure:
Pseudocritical temperature:
Uncorrected gas viscosity at 14.7 psia:
N2 correction for gas viscosity at 14.7 psia:
CO2 correction for gas viscosity at 14.7 psia:
H2S correction for gas viscosity at 14.7 psia:
Corrected gas viscosity at 14.7 psia (^1):
Pseudoreduced pressure:
Pseudoreduced temperature:
In (Mg/p-rTpr):
Gas viscosity:
10,000 psia
1800F
0.65 air =1
0.1
0.08
0.02
697.164 psia
345.357 0R
0.012174 cp
0.000800 cp
0.000363 cp
0.000043 cp
0.013380 cp
14.34
1.85
1.602274
0.035843 cp
a. This spreadsheet calculates gas viscosity with correlation of Carr, Kobayashi, andBurrows.
where n is the number of moles of gas. When pressure p is entered in psia,
volume V in ft3, and temperature in 0R, the gas constant R is equal to
Click to View Calculation Example
and
(2.28)
(2.29)
(2.30)
(2.31)
(2.32)
(2.33)
(2.34)
The gas compressibility factor can be determined on the basis of measure-ments in PVT laboratories. For a given amount of gas, if temperature iskept constant and volume is measured at 14.7 psia and an elevated pres-sure P1, z-factor can then be determined with the following formula:
(2.27)
where VQ and V1 are gas volumes measured at 14.7 psia and/? l 9
respectively.
Very often the z-factor is estimated with the chart developed by Standingand Katz (1942). This chart has been set up for computer solution by anumber of individuals. Brill and Beggs (1974) yield z-factor values accu-rate enough for many engineering calculations. Brill and Beggs' z-factorcorrelation is expressed as follows:
Example Problem 2.3
For the natural gas described in Example Problem 2.2, estimatez-factor at 5,000 psia and 180 0F.
Solution
This problem is solved with the spreadsheet program Brill-Beggs-Z.xls.The result is shown in Table 2-3.
Table 2-3 Results Given by Brill-Beggs-Z.xlsa
Input Data
Pressure:
Temperature:
Gas-specific gravity:
Mole fraction of N2:
Mole fraction of CO2:
Mole fraction of H2S:
Calculated Parameter Values
Pseudocritical pressure:
Pseudocritical temperature:
Pseudo-reduced pressure:
Pseudo-reduced temperature:
A =
B =
C =
D =
Gas compressibility factor z:
5,000 psia
1800F
0.65 1 for air
0.1
0.08
0.02
697 psia
345 0R
7.17
1.85
0.5746
2.9057
0.0463
1.0689
0.9780
a. This spreadsheet calculates gas compressibility factor based on Brill and Beggscorrelation.
Click to View Calculation Example
Hall and Yarborough (1973) presented more accurate correlation to esti-mate z-factor of natural gas. This correlation is summarized as follows:
(2.35)
(2.36)
(2.37)
(2.38)
(2.39)
(2.40)
(2.41)
(2.42)
Example Problem 2.4
For a natural gas with a specific gravity of 0.71, estimate z-factorat 5,000 psia and 180 0F.
If Newton-Raphson's iteration method is used to solve Equation (2.41)for F, the following derivative is needed:
where Y is the reduced density to be solved from
and
Solution
This problem is solved with the spreadsheet program HaII-Yarborogh-z.xls. The result is shown in Table 2-4.
Table 2-4 Results Given by Hall-Yarborogh-z.xlsa
Instructions: 1) Input data; 2) Run Macro Solution; 3) View result.
Input Data
T:
p:
SGFG:
Calculate Critical and Reduced Temperature and Pressure
Tpc= 169.0 + 314.0*SGFG:
Ppc = 708.75 - 57.5*SGFG:
Tpr = (T + 460.0)/Tpc:
t = 1/Tpr:
Ppr = p/Ppc:
Calculate Temperature-dependent Terms
A = 0.06125*t*EXP(-1.2*(1 .-t**2):
B = t*(14.76 - 9.76*t + 4.58*t*t):
C = t*(90.7 - 242.2*t + 42.4Tt):
D = 2.18 + 2.82*t:
Calculate Reduced Density (use Macro Solution)
Y = ASSUMED:
F = -A*Ppr + (Y + Y*Y + Y**3 - Y**4)/(1 .-Y)**3 - B*Y*Y +C*Y**D:
Calculate z-Factor
Z = A*Ppr/Y:
1800F
5,000 psia
0.71 air= 1
391.94 0R
667.783 psia
1.632902995
0.61240625
7.487462244
0.031322282
6.430635935
-25.55144909
3.906985625
0.239916681
-7.30123E-06
0.97752439
a. This spreadsheet computes gas compressibility factor with the Hall-Yarboroughmethod.
Click to View Calculation Example
2.6 Gas Density
Because natural gas is compressible, its density depends upon pressureand temperature. Gas density can be calculated from gas law for real gaswith good accuracy:
(2.43)
where m is mass of gas and p is gas density. Taking air molecular weight
29 and R = 10.73 , Equation (2.43) is rearranged to yield:mole - ° R
(2.44)
where the gas density is in lbm/ft3. This equation is also coded in thespreadsheet program Hall-Yarborogh-z.xls.
2.7 Formation Volume Factor and Expansion Factor
Formation volume factor is defined as the ratio of gas volume at reservoircondition to the gas volume at standard condition, that is,
where the unit of formation volume factor is ft3/scf. If expressed in rb/scf,it takes the form of
(2.46)
(2.45)
Gas formation volume factor is frequently used in mathematical modelingof gas well inflow performance relationship (IPR).
Gas expansion factor is defined, in scf/ft3, as:
(2.47)
(2.48)
(2.49)
(2.50)
(2.51)
or
in scf/rb. It is normally used for estimating gas reserves.
2.8 Compressibility of Natural Gas
Gas compressibility is defined as:
Substituting Equation (2.50) into Equation (2.49) yields:
Because the gas law for real gas gives
2.9 Real Gas Pseudopressure
Real gas pseudopressure m(p) is defined as
(2.52)
where pb is the base pressure (14.7 psia in most states in the U.S.). Thepseudopressure is considered to be a "pseudoproperty" of gas because itdepends on gas viscosity and compressibility factor, which are propertiesof the gas. The pseudopressure is widely used for mathematical modelingof IPR of gas wells. Determination of the pseudopressure at a given pres-sure requires knowledge of gas viscosity and z-factor as functions of pres-sure and temperature. As these functions are complicated and not explicit,a numerical integration technique is frequently used.
Example Problem 2.5
Natural gas from a gas reservoir has a specific gravity of 0.71. Italso contains the following compounds:
Mole fraction of N2: 0.10
Mole fraction of CO2: 0.08
Mole fraction of H2S: 0.02
Table 2-5 Input Data and Calculated Parameters Given byPseudoP.xls3
Input Data
Base pressure:
Maximum pressure:
Temperature:
Gas-specific gravity:
Mole fraction of N2:
Mole fraction of CO2:
Mole fraction of H2S:
Calculated Parameter Values
Pseudocritical pressure:
Pseudocritical temperature:
Uncorrected gas viscosity at 14.7 psia:
N2 correction for gas viscosity at 14.7 psia:
CO2 correction for gas viscosity at 14.7 psia:
H2S correction for gas viscosity at 14.7 psia:
Corrected gas viscosity at 14.7 psia ((X1):
Pseudoreduced temperature:
14.7 psia
10,000 psia
600F
0.6 1 for air
0
0
0
673 psia
357.57 0R
0.010504 cp
0.000000 cp
0.000000 cp
0.000000 cp
0.010504 cp
1.45
a. This spreadsheet computes real gas pseudopressures.
Calculated gas viscosities, z-factors, and pseudopressures atpressures between 9,950 psia and 10,000 psia are presented inTable 2-6. Pseudopressure values in the whole range ofpressure are plotted in Figure 2 -1 .
For the convenience of engineering applications, pseudopressures ofsweet natural gases at various pressures and temperatures have been gen-erated with PseudoP.xls. The results are presented in Appendix A.
Click to View Calculation Example
Pseu
dopre
ssure
(psia
2/cp)
Pressure (psia)Figure 2-1 Plot of pseudopressures calculated by PseudoP.xls.
2.10 Real Gas Normalized Pressure
Real gas normalized gas pressure n(p) is defined as
(2.53)
where pr is the pseudoreduced pressure. For the convenience of engi-neering applications, the normalized gas pressures of sweet natural gasesat various pressures and temperatures have been generated with thespreadsheet program NormP.xls. The results are presented in Appendix B.
Table 2-6 Partial Output Given by PseudoP.xls
P (Psia)
9,950
9,952
9,954
9,956
9,958
9,960
9,962
9,964
9,966
9,968
9,970
9,972
9,974
9,976
9,978
9,980
9,982
9,984
9,986
9,988
9,990
9,992
9,994
9,996
9,998
10,000
M- (CP)
0.045325
0.045329
0.045333
0.045337
0.045341
0.045345
0.045349
0.045353
0.045357
0.045361
0.045365
0.045369
0.045373
0.045377
0.045381
0.045385
0.045389
0.045393
0.045397
0.045401
0.045405
0.045409
0.045413
0.045417
0.045421
0.045425
Z
1.462318
1.462525
1.462732
1.462939
1.463146
1.463353
1.463560
1.463767
1.463974
1.464182
1.464389
1.464596
1.464803
1.465010
1.465217
1.465424
1.465631
1.465838
1.466045
1.466252
1.466459
1.466666
1.466873
1.467080
1.467287
1.467494
2p%z)
300,244
300,235
300,226
300,218
300,209
300,200
300,191
300,182
300,174
300,165
300,156
300,147
300,138
300,130
300,121
300,112
300,103
300,094
300,086
300,077
300,068
300,059
300,050
300,041
300,033
300,024
m(p)
2,981,316,921
2,981,916,517
2,982,516,096
2,983,115,657
2,983,715,201
2,984,314,727
2,984,914,236
2,985,513,727
2,986,113,200
2,986,712,656
2,987,312,094
2,987,911,515
2,988,510,918
2,989,110,304
2,989,709,672
2,990,309,022
2,990,908,355
2,991,507,670
2,992,106,968
2,992,706,248
2,993,305,510
2,993,904,755
2,994,503,982
2,995,103,191
2,995,702,383
2,996,301,557
Click to View Calculation Example
2.11 References
Ahmed, T. Hydrocarbon Phase Behavior. Houston: Gulf PublishingCompany, 1989.
Brill, J. P., and H. D. Beggs. "Two-Phase Flow in Pipes." INTER-COMP Course, The Hague, 1974.
Carr, N.L., R. Kobayashi, and D. B. Burrows. "Viscosity of Hydrocar-bon Gases under Pressure." Trans. AIME 201 (1954): 264-72.
Dempsey, J. R. "Computer Routine Treats Gas Viscosity as aVariable." Oil & Gas Journal (Aug. 16, 1965): 141.
Dean, D. E. and L. I. Stiel. "The Viscosity of Non-polar Gas Mixturesat Moderate and High Pressures." AIChE Journal 4 (1958): 430-6.
Hall, K. R. and L. Yarborough. "A New Equation of State for Z-Factor Calculations." Oil & Gas Journal (June 18, 1973): 82.
Lee, A. L., M. H. Gonzalez, and B. E. Eakin. "The Viscosity of Natu-ral Gases." Journal of Petroleum Technology (Aug. 1966): 997-1000.
McCain, W. D., Jr. The Properties of Petroleum Fluids, Tulsa:PennWell Books, 1973.
Standing, M. B. and D. L. Katz. "Density of Natural Gases." Trans.AIME146: (1954) 140-9.
Standing, M. B.: Volumetric and Phase Behavior of Oil Field Hydro-carbon Systems. Society of Petroleum Engineers of AIME, Dallas,1977.
Wichert, E. and K. Aziz. "Calculate Zs for Sour Gases." Hydrocar-bon Processing 51 (May 1972): 119.
2.12 Problems
2-1 Estimate gas viscosities of a 0.70 specific gravity gas at 200 0Fand 100 psia, 1,000 psia, 5,000 psia, and 10,000 psia.
2-2 Calculate gas compressibility factors of a 0.65 specific gravitygas at 150 0F and 50 psia, 500 psia, and 5,000 psia with Hall-
Yarborough method. Compare the results with that given bythe Brill and Beggs' correlation. What is your conclusion?
2-3 For a 0.65 specific gravity gas at 250 0F, calculate and plotpseudopressures in a pressure range from 14.7 psia and 8,000psia. Under what condition is the pseudopressure linearlyproportional to pressure?
2-4 Prove that the compressibility of an ideal gas is equal to
inverse of pressure, that is,