natural gas engineering hand book (2005) ch.2

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


/knovel2/view_hotlink.jsp?hotlink_id=417357050

(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



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:








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.



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.



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:








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.



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



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,

natural gas engineering hand book (2005) ch.2

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