Chapter 2
r o
2.1
r t i e s
o f
l
G
Introduction
Properties of natural gas include gas-specific gas-specific gravity, pseudocritical pseudocritical pre ssure and temperature, viscosity, compressibility factor, gas density, and gas compressibility. Knowledge of these property values is essential for designing and analyzing natural gas production and processing systems. Because natural gas is a complex mixture of light hydrocarbons with a minor amount of inorganic compounds, it is always desirable to find the composition of the gas through measurements. Once the gas composition is know n, gas properties properties can usually be estimated u sing established established c orrelations with confidence. This chapter focuses on determination of gas properties with correlations developed from various lab measurements. Example problems are presented and solved using computer programs provided with this this book
2.2 Specific Gravity Gas-specific gravity is defined defined as the ratio ratio of the apparent olecular weight of a natural gas to to that of air, air, its itsel elff a mixture of gases. The m olecular weight of air is usually taken as equal to 28.97 (approximately 79% nitrogen nitrogen and 2 % oxy gen). Therefore Therefore the gas gravity gravity is (2.1) wh ere the the apparent m olecular we ight of gas can be calculated calculated on the basis o f g a s c o m p o s i t i o n . G a s c o m p o s i t i o n i s u s u a l l y d e t er m i n e d i n a
laboratory laboratory and reported in mole fract fractions ions of comp onen ts in the the gas. Let be the ole fract fraction ion of comp onent i, the apparent molecular weight of the gas can can be formu formu lated lated using m ixing rule as
(2.2) where is the molecular weight of component i, and is the num ber of components. The molecular weights of compounds (MWi) can be found in textbooks on organic chemistry or petroleum fluids such as that by McCain (1973). A light gas reservoir is one that contains primarily methane 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 gravity equal to 0.75 0.75 or, in some rare ca ses, higher than 0.9.
2.3 Pseudocritical Properties Similar to gas apparent molecular weight, the critical properties of a gas can be determined on the basis of the critical properties of compounds in the gas using the mixing rule. The gas critical properties determined in such such a w ay are called called p seudocritical prop erties. Gas pseudocritical pseudocritical p ressure (p and pseudocritical temperature are, respectively, pc expressed as
(2.3)
(2.4)
where ci ci are critical pressure and critical temperature of component i, respectively.
2.
the gas composition given in the following text, determine apparent molecular weight, pseudocritical pressure, and pseudocritical temperature of the gas.
Component
Mole Fraction Fraction
O,
0.775 0.083 0.021
i-C
0.006
n-C
0.002
i-C
0.003
n-C
0.008 0.001 0.001
0.050 0.030 S
0.020
Solution
T h i s p r o b l e m is s o l v e d w i t h spreadsheet program MixingR ule.xls. ule.xls. R esult ar shown in T ab a b le le 2 If the gas composition is i s not known but gas-specific gravity is given, the t he pseudocritical pre pressure ssure and temperature can be determined from from various charts or correlations developed based on the charts. One set of simple correlations is (2.5) (2.6)
Click to View Calculation Example
Table Tab le 2-1
Results Results Given Given by
ixingR ixingR ule.xls YiTci R)
Pc (psia)
YiPci (psia)
Tci R)
12.43
67
521.58
34
266.60
30.07
2.50
70
58.85
55
45.65
0.021
44.10
0.93
61
12.98
66
13.99
i-
0.006
58.12
0.35
53
3.18
73
4.40
n-
0.002
58.12
0.12
55
1.10
76
1.53
i-
0.003
72.15
0.22
48
1.45
83
2.49
n-
0.008
72.15
0.58
48
3.88
84
6.78
0.001
86.18
0.09
43
0.43
91
0.92
0.001
114.23
0.11
36
0.36
1024
1.02
0.050
28.02
1.40
22
11.35
49
24.60
0.030
44.01
1.32
1073
32.19
54
16.44
0.020
34.08
0.68
67
13.45
1306
26.12
1.000
MW
20.71
Ppc =
g
0.71
Compound
7+
CO
Yi
MWj
0.775
16.04
0.083
66
'p
41
a. This spr spread eadshe sheet et calculates ates gas gas appa appare rent nt molecul ecular ar weight, specifi specific gravity, gravity, pseudocrititical cal pressure, pressure, and pseudocritical pseudocritical temperature. temperature. which are valid for H S < 3% ,
< 5%, and total content of inorganic
compounds less than than 7% Corrections for for imp urities urities in sour gases are always necessary. T he corrections tions can be m ade using either charts or correlations correlations such as the the W ichertAziz (1972) correction expressed as follows: (2.7) (2.8)
(2.9) pc
(2.10)
(corrected
(2.11)
(corrected
Correlations with impurity corrections for mixture pseudocriticals are also available (Ahmed 1989): (2.12)
Applications of the pseudocritical pressure and temperature are normally found in natural gas engineering through pseudoreduced pressure and temperature 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 ju in centipoises (cp) is usually used in the natural engineering:
Kinem atic ati c viscosit viscos ityy density
j is related relat ed to the dynam ic viscosit vi scosityy through
(2.16)
Kinem atic atic viscosity viscosity is not normally used in natural gas eng ineering. Direct measurements of gas viscosity are preferred for a new gas. If gas composition and viscosities of gas components are known, the mixing rule can be used for determ ining the viscosity viscosity of the gas m ixture:
(2.17)
Gas viscosity is very often estimated with charts or correlations developed based on the charts. The gas viscosity correlation of Carr, Kobayashi, and Burrows (1954) involves a two-step procedure: the ga s viscosity at temperature and atmospheric pressure is estimated first from gas-specific gravity and inorganic compound content. The atmospheric value is then adjusted to pressure conditions by means of a correction factor on the basis of reduced temperature and pressure state of the gas. The atmospheric pressure viscosity (/Z ) 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 ju is determined from the right-hand side of this equation, gas viscosity at elevated pressure can be readily calculated using the following following relation: relation:
(2.24) Other correlations for gas viscosity include Dean-Stiel (1958) and LeeGonzalez-Eakin Gonzalez-Eakin (1966).
Example Problem .2
A 0.65 specific gravity natural gas contains 10% nitrogen, 8% carbon carbon dioxide, and 2% hydrogen hydrogen sulfide. sulfide. Estimate Estimate viscosity of the gas at 10, 10,000 000 psia and 180 Solution This problem is solved with the spreadsheet Carr-KobayashiBurrows Burrows Viscosity.xls Viscosity.xls that s attached to this book. The result result is shown sh own in Tabl Tablee 2 -2
2.5 Compressibility Factor Gas compressibility factor is also called deviation factor, or z-factor. Its value reflects how much the real gas deviates from the ideal gas at given pressure and temperature. Definition of the compressibility factor is expressed expressed as:
(2.25) Introducing the z-factor to the gas law for ideal gas results in the gas law for real gas as: (2.26)
Click to View Calculation Example Tab le
-2
Resu lts lts Given by Carr-Kobayashi-Burrows Carr-Kobayashi-Burr ows
Input Data Pressure:
10,000 10, 000 psia
Temperature: Gas-specific Gas-specific gravity:
0.65 0.65 air =1
Mole fraction fraction of N
0.1
Mole Mol e fraction fraction of CO
0.08
Mole fraction fraction of H
0.02
Calculated Calculated Parameter Parameter Values Pseudocritical Pseudocritical pressure:
697.164 psia
Pseudocritical Pseudocritical tempe temperature: rature:
345.357
Uncorrected Uncorrected gas viscosity at 14. 14.7 7 psia:
0.012174 cp
correction correction for gas viscosity at a t 14. 14.77 psia:
a.
0.000800 cp
correction correction for gas viscosity viscosity at 14. 14.77 psia:
0.000363 cp
S correcti correction on for gas viscosity viscosity at 14. 14.7 7 psia:
0.000043 cp
Corrected Corrected gas viscosity viscosity at 14.7 psi psiaa (^ ):
0.013380 cp
Pseudoreduced Pseudoreduced pressure:
14.34
Pseudoreduced Pseudoreduced tem temperature: perature:
1.85
In (Mg/p-rTpr)
1.602274
Gas viscosity:
0.035843 cp
This spread spreadshe sheet et calc calculat ulates es gas viscosity viscosity with with correl correlati ation on of Carr, Kobayashi, and Burrows.
where volume
is the number of mo les of gas.
hen p ressure
is entered in psia,
in ft , and temperature in R, the gas constant
is equal to
The gas com pressibilit pressibilityy factor factor can be determined on the basis of measu rements in PVT laboratories. For a given amount of gas, if temperature is kept constant and volume is measured at 14.7 psia and an elevated pressure z-fact z-factor or can then be determined determined with the following following formula:
(2.27) where
and V a r e g a s v o l u m e s m e a s u r e d a t 1 4 . 7 p s i a a n d / ?
respectively. Very often the z-factor is estimated with the chart developed by Standing and Katz (1942). This chart has been set up for computer solution by a num ber of individu individu als. Brill and Beggs (1974) yield z-fact z-factor or values accurate enough for many engineering calculations. Brill and Beggs' z-factor correlation correlation is expressed as follows: (2.28)
(2.29)
(2.30) (2.31) (2.32)
(2.33)
(2.34)
Exam ple Problem Problem 2.3
For the natural gas described in Example Problem 2.2, estimate z-factor at 5,000 psia and 180 Solution
This problem problem s solved with the spreadsheet program program Brill Brill-Beggs-Z.x -Beggs-Z.xls. ls. The resul resultt is is shown in Table -3 Click to View Calculation Example Ta ble 2- 3
Resu lts lts Given by Brill-Begg Brill-Begg s-Z.xls
Input Data Pressure:
5,000 psia
Temperature: Gas-specific Gas-specific gravity:
0.65 0.65 1 for for air
Mole fraction fraction of N
0.1
Mole Mol e fracti fraction on of CO
0.08
Mole fraction fraction of H
0.02
Calcul Ca lculated ated Paramete Parameterr Values V alues Pseudocritical Pseudocritical pressure:
697 psia
Pseudocritical Pseudocritical temperature: tem perature:
345
Pseudo-reduced Pseudo-reduced pressure:
7.17
Pseudo-reduced Pseudo-reduced tem temperature: perature:
1.85
A=
0.5746
B=
2.9057
C=
0.0463
D=
1.0689
Gas compressibi com pressibilility ty factor z: a.
0.9780
This spreads spreadsheet heet calc calculat ulates es gas compressibil compressibility ity factor based based on Brill Brill and and Beggs Beggs correlation.
Hall and Yarborough (1973) presented presented ore accurate correlat correlation ion to esti mate z-factor z-factor of natural gas. This correlation correlation is summ arized as follows:
(2.35)
(2.36)
(2.37)
(2.38) (2.39)
an
(2.40)
where
is the the reduced density to be solved from from
(2.41)
If Newton-Raphson's iteration method is used to solve Equation (2.41) for F, the following derivative is needed:
(2.42) Example Problem .4
For a natural gas wit w ithh a specifi specificc gravity gravity of 0.7 0 .7 , esti ate z-factor z-factor at 5,000 5,000 psia and 18
Solution
This problem is solved with the spreadsheet program HaIIYarborogh-z.xls. Yarborogh-z.xls. The resul resultt is shown n Table Table -4 Click to View Calculation Example Ta ble 2-4 Results Given by Hall-Yarborogh-z.xls Instructions: Instructions: 1) Input data; 2) Run Macro Soluti So lution; on; 3) View result resu lt Input Data T: p:
5,000 psia
SGFG:
0.71 0.71 a ir= 1
Calculate Critical and Reduced Temperature and Pressure c= 16 169. 9.00 + 314. 314.0* 0*SGFG: SGFG:
391.94
Ppc Ppc = 708.75 708.75 - 57.5*SGFG 57.5*SGFG
667.783 psia
Tpr = (T + 460.0)/Tpc: 460.0)/Tpc:
1.632902995
t
1/Tpr:
0.61240625
Ppr = p/Ppc:
7.487462244
Calculate Temperature-dependent Terms A = 0.06125*t 0 .06125*t*EXP(-1. *EXP(-1.2*(1 2*(1 .-t**2) .-t** 2)
0.031322282
B = t*(14. t*(14.76 76
6.430635935
9.76*t + 4.58*t*t): 4.58*t*t):
C = t*( t*(90. 90.7 7 - 242 2*t 2*t + 42 .4 t):
-25.55144909
D = 2.18 2.18 + 2.82*t: 2.82*t:
3.906985625
Calculate Reduced Density (use Macro Solution) Y = ASSUMED: ASSUMED:
0.239916681
F = -A*Pp r + (Y + Y*Y Y*Y + Y**3 Y**3 - Y**4)/ Y**4)/(1 (1 .-Y)* .-Y)**3 *3 - B*Y*Y C*Y**D:
-7.30123E-06
Calculate z-Factor z-Factor Z = A*Ppr/Y: A*Ppr/Y: a.
0.97752439
This spreadsheet spreadsheet comput computes es gas gas com compressibi pressibilility ty factor with the Hall-Yar Hall-Yarborough borough method.
Density
Because natural gas is compressible, its density depends upon pressure and temperature. Ga density can be calculated from gas law for real ga with good accuracy:
(2.43) where
is mass of gas and = 10.73
mole - °
is gas density. Taking ai molecular weight
Equation (2.43) is rearranged to yield:
(2.44) where the gas density is in lbm/ft . This equation is also coded in the spreadsheet program Hall-Yarborogh-z.xls.
2.7 Formation Vo lum e Factor and Expansion Factor Formation volume factor is defined as the ratio of gas volume condition to the gas volume standard cond ition, ition, that is,
reservoir
(2.45)
where th unit formation volume factor is ft /scf. If expressed in rb/scf, it takes th form
(2.46)
Gas formation formation v olum e factor factor is frequentl frequentlyy used in athem atical m odeling of gas well infl inflow ow performance relationsh relationsh ip (IPR ). Gas expansion factor is defined, in scf/ft , as:
(2.47)
(2.48)
in scf/rb. It is normally used for estimating gas reserves.
.8 Com pressibi pressibili lity ty of of Na ural ural Gas com pressibili pressibility ty is defined defined as:
(2.49)
Becau se the gas law law for real gas gives
(2.50)
Substituting Substituting Eq uation (2.50) into Equation (2.49) yields:
(2.51)
2.9 Re al
as Pseud opressure
Real gas pseudopressure m(p) is defined as
(2.52)
where is the base pressure (14.7 psia in most states in the U.S.). The pseudopressure is considered to be a "pseudoproperty" of gas because it depends on gas viscosity and compressibility factor, which are properties of the gas. The pseudopressure is widely used for mathematical modeling of IPR of gas wells. Determination of the pseudopressure at a given pressure requires knowledge of gas viscosity and z-factor as functions of pressure and and tem perature. As these functions functions are complicated and not exp licit, licit, a num erical integration integration techniqu e is frequentl frequentlyy used.
Example Problem .5
Natural Natural gas from from a gas reservoi reservoirr has a specific specific gravity gravity of 0.7 1. also contains contains the following com pounds: Mole Mol e fraction fraction of
:
0.10
Mole Mol e fraction fraction of CO :
0.08
Molee fracti Mol fraction on of
0.02
S:
Click to View Calculation Example Table 2-
Input Data and Calculated Parameters Given PseudoP.xls
Input Data Base pressure:
14.7 psia
Maximum Maxi mum pressure:
10,000 psia
Temperature: Gas-specific Gas-specific gravity:
0.6 1 for air
Mole fraction f N Mole fraction Mole fraction f H Calculated Parameter Values Pseudocritical Pseudocritical pressure: pressu re:
673 psi
Pseudocritical Pseudocritical temperature: tem perature:
357.57
Uncorrected
0.010504
viscosity at 14. psia:
correction for gasviscosity at 14.7 psia: correction for ga viscosity at 14.7 psia:
0.000000
S correction for gasviscosity at 14.7 psia:
0.000000
Corrected
viscosity at 14.7 psia
Pseudoreduced Pseudoreduced tem temperature: perature: a.
0.000000
0.010504 1.45
This spreadsh spreadsheet eet comput computes es real gas pseudopressures pseudopressures Calculated gas viscosities, z-factors, and pseudopressures at pressures between 9,950 psia and 10,000 psia ar presented in T a b l e 2 - 6 . P s e u d o p r e s s u r e v a l u e s in the w h o l e r a n g e of pressure ar plotted in F ig ig u e 2
For the convenience of engineering applications, pseudopressures of sweet natural gases at various pressures and temperatures have been generated with PseudoP.xls. The results are presented in Appendix A.
(psia) Plot of pseu pseudo dopr pres essu su es calculated y PseudoP.xls PseudoP.xls Pressure
Figur Figure e
2.10 Re al
1
a s N o r m a l iz iz e d P r e s s u r e
Real gas normalized gas pressure n(p) is defined as
(2.53)
where is the pseudoreduced pressure. For the convenience of engineering applications, the normalized gas pressures of sweet natural gases at various pressures and temperatures have been generated with the spreadsheet spreadsheet program orm P.xls. The results results are are presented in App endix B
Click to View Calculation Example Table 2-6
P (Psia) (Psia)
l Ou Outp tput ut Gi Give ven n by Pseudo Pse udoP.x P.xls ls M- ( C P )
2p%z)
m(p)
9,950
0.045325
1.462318
300,244
2,981,316,921
9,952
0.045329
1.462525
300,235
2,981,916,517
9,954
0.045333
1.462732
300,226
2,982,516,096
9,956
0.045337
1.462939
300,218
2,983,115,657
9,958
0.045341
1.463146
300,209
2,983,715,201
9,960
0.045345
1.463353
300,200
2,984,314,727
9,962
0.045349
1.463560
300,191
2,984,914,236
9,964
0.045353
1.463767
300,182
2,985,513,727
9,966
0.045357
1.463974
300,174
2,986,113,200
9,968
0.045361
1.464182
300,165
2,986,712,656
9,970
0.045365
1.464389
300,156
2,987,312,094
9,972
0.045369
1.464596
300,147
2,987,911,515
9,974
0.045373
1.464803
300,138
2,988,510,918
9,976
0.045377
1.465010
300,130
2,989,110,304
9,978
0.045381
1.465217
300,121
2,989,709,672
9,980
0.045385
1.465424
300,112
2,990,309,022
9,982
0.045389
1.465631
300,103
2,990,908,355
9,984
0.045393
1.465838
300,094
2,991,507,670
9,986
0.045397
1.466045
300,086
2,992,106,968
9,988
0.045401
1.466252
300,077
2,992,706,248
9,990
0.045405
1.466459
300,068
2,993,305,510
9,992
0.045409
1.466666
300,059
2,993,904,755
9,994
0.045413
1.466873
300,050
2,994,503,982
9,996
0.045417
1.467080
300,041
2,995,103,191
9,998
0.045421
1.467287
300,033
2,995,702,383
10,000
0.045425
1.467494
300,024
2,996,301,557
2.11
References
Ahmed, T. Hydrocarbon Phase Behavior. Houston: Gulf Publishing Company, 1989. Brill, J. P., and H. D. Beggs. "Two-Phase Flow in Pipes." INTERCOM P Course, The Hague, 1974. 1974. Carr, Carr, N.L., R. K obayashi, and and D . B. Burrows. "Viscosity "Viscosity of H ydrocarbon G ases ases under Pressure." Trans. AI (1954) (1954):: 26 4-72 Dempsey, J. R. "Computer Routine Treats Gas Viscosity as a Variable." Oil & G as Journal (Aug. 16, 1965): 141. Dean , D. E. and L. I. I. Stiel. Stiel. "Th e Viscosity Viscosity of No n-polar G as M ixtures at oderate oderate and High P ressures." AIChE Journal 4 (1958): (1958): 43 0-6 Hall, K. R. and L. Yarborough. "A New Equation of State for ZFactor Calculations." Oil & G as Journal (June 18, 1973): 82. Lee, A. L., . H. Gonzalez, and B . E. Eakin. "T he V iscosity iscosity of N atuPetroleum um Technology (Aug. 1966): ral Gases." Journal of Petrole 1966): 997 -100 0.
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. AIME 146: (1954) 140-9. Standing, Standing, M. B .: Volumetric Volumetric and Pha se Behavior o f Oil Field Field Hydrocarbon Systems. Society of Petroleum Engineers of AIME, Dallas, 1977. Wichert, E. and K. Aziz. "Calculate Zs for Sour Gases." Hydrocarbon Processing Processing 51 (May 1972): 119.
2.12 Problems 2-1
Estim ate gas visco sities of a 0.70 specific specific gravity gas at 200 and 100 psia, 1,000 psia, 5,000 psia, and 10,000 psia.
2-2
Ca lculate gas com pressibility factors of a 0.65 specific specific gravity gas at 150 F and 50 psia, 500 psia, and 5,000 psia with Ha ll-
Yarborough method. Compare the results with that given by the Brill and Beggs' correlation. What is your conclusion? 2-3
For a 0.65 specific specific gravity gas at 250 , calculate and p lot pseudo pressures in a pressure range range from 14.7 14.7 psia and 8,000 psia. Under wh at condition condition is the the pseudop ressure linearly linearly proportional to pressure?
2-4
Prove that the com pressibilit pressibilityy of an ideal gas is equal to inverse of p ressure, that is,
