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Calculating gas properties

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This page provides a number of examples that illustrate the mathematical calculations behind the different fundamental gas properties.

Calculating properties of natural gas

Find the density, formation volume factor (FVF), viscosity, and isothermal compressibility of a gas with the following properties and conditions:

  • γg = 0.7
  • H2S = 7%
  • CO2 = 10%
  • p = 2,010 psia
  • T = 75°F.

Solution

The density is calculated from Eq. 3 in Gas formation volume factor and density:

RTENOTITLE

The formation volume factor is calculated from Eq. 2 in Gas formation volume factor and density:

RTENOTITLE

The viscosity is determined using the charts of Carr et al.[1] in Figs. 1-4 in Gas viscosity.

  • First, the viscosity for Mg = (0.7)(28.967) = 20.3 at p = 1 atm and T = 75°F is read from Fig. 2.
  • This gives 0.0102 cp, but corrections are needed for the acid gases. The correction for 10% CO 2 is 0.0005 cp, and the correction for 7% H2S is 0.0002 cp. Hence, this gives μga = 0.0109 cp.
  • Next, the ratio of μg/μga is read from Fig. 4, which gives μg/μga = 1.55.
  • Hence, μg = (1.55) (0.0109 cp) = 0.0169 cp.

The compressibility is determined by first reading Figs. 1-2 in Isothermal compressibility of gases for the previously calculated values of pr = 3.200 and Tr = 1.500 to give crTr = 0.5. Because Tr = 1.500 then cr = 0.5/1.5 = 0.3333. Because cr = cgppc,

RTENOTITLE


Calculating the relative density (specific gravity)

Calculate the relative density (specific gravity) of natural gas with the following composition (all compositions are in mol%):

C1 = 83.19%
C2 = 8.48%
C3 = 4.37%
i-C4 = 0.76%
n-C4 = 1.68%
i-C5 = 0.57%
n-C5 = 0.32%
C6 = 0.63%
Total = 100%

Solution.

First, calculate the apparent mole weight from the information presented in Table 1.

RTENOTITLE

where the molecular weight of air, Ma, is 28.967.


Calculating actual density

Calculate the actual density of the same mixture at 1,525 psia and 75°F

  1. Using Kay’s[2] rules
  2. Sutton’s[3] correlation
  3. Piper et al.[4] correlation.

Solution.

The density is calculated from

RTENOTITLE

where

  • p = 1,525 psia
  • Mg = 20.424
  • R = 10.7316 (psia-ft3)/(lbm mol°R)
  • T = 75°F + 459.67 = 534.67°R
  • z must be obtained from Fig. 2 in Real gases

1. Calculate zg from the known composition in Table 2.

Using Kay’s[2] rules, we obtain from the known gas composition:

TpcyiTi = 393.8°R,

Tpr = 534.67/393.8 = 1.3577,

ppcyipci = 662.88 psia,

ppr = p/ppc = 1,525/662.88 =2.301,

and from Fig. 1, zg = 0.71.

2. From Sutton’s[3] gas gravity method, γg = 0.705; then, we obtain from Eq. 4-5 in Real gases that

RTENOTITLE

This gives

RTENOTITLE

From Fig. 2 in Real gases, we obtain zg = 0.745.

3. Using the Piper et al.[4] method, we first calculate J and K using

RTENOTITLE

The details of the calculations are found in Table 2.

Then,

RTENOTITLE

Finally, looking up the z-factor chart (Fig. 2 in Real gases) gives z = 0.745.

Conclusion.

Even though the Sutton[3] correlation and the Piper et al.[4] correlation gave slightly different critical properties, the z factors from those two methods are the same. Kay’s[2] rule gives a value that is 4.6% lower, but the result using Sutton’s correlation and the Piper et al. correlation has been shown to be more accurate. The density is then given by

RTENOTITLE


Calculating the z factor for a reservoir fluid

Calculate the z factor for the reservoir fluid in Table 3 at 307°F and 6,098 psia.

The experimental value is z = 0.998.

Solution.

Using the Piper et al.[4] method, we first calculate J and K using

RTENOTITLE

The details of the calculation are in Table 4.

Then,

RTENOTITLE

RTENOTITLE

Finally, looking up the z-factor chart (Fig. 2 in Real gases) gives z = 1.02. This represents a 2% error with the experimental value.

Nomenclature

J = parameter in the Stewart et al.[5] equations, K•Pa–1
K = parameter in the Stewart et al.[5] equations, K•Pa–1/2
M = molecular weight
Ma = molecular weight of air
RTENOTITLE = molecular weight of C7+ fraction
Mg = average molecular weight of gas mixture
n = number of moles
p = absolute pressure, Pa
pc = critical pressure, Pa
ppc = pseudocritical pressure of a gas mixture, Pa
pr = reduced pressure
R = gas-law constant, J/(g mol-K)
T = absolute temperature, K
Tc = critical temperature, K
Tci = critical temperature of component i in a gas mixture, K
Tpc = corrected pseudocritical temperature, K
Tr = reduced temperature
z = compressibility factor (gas-deviation factor)
ρpc = relative density of C7+ fraction
μg = viscosity of gas, Pa•s
Bg = gas formation volume factor (RB/scf or Rm3/Sm3)
μga = viscosity of gas mixture at desired temperature and atmospheric pressure, Pa•s
cg = coefficient of isothermal compressibility
cr = dimensionless pseudoreduced gas compressibility
J = parameter in the Stewart et al.[5] equations (Eqs. 5.9 and 5.10), K•Pa–1
K = parameter in the Stewart et al.[5] equations (Eqs. 5.9 and 5.10), K•Pa–1/2
ρg> = density of gas, kg/m3

References

  1. Carr, N.L., Kobayashi, R., and Burrows, D.B. 1954. Viscosity of Hydrocarbon Gases Under Pressure. J Pet Technol 6 (10): 47-55. SPE-297-G. http://dx.doi.org/10.2118/297-G
  2. 2.0 2.1 2.2 Kay, W.B.: "Density of Hydrocarbon Gases at High Temperature and Pressure," Ind. Eng. Chem. (September 1936) 28, 1014–1019.
  3. 3.0 3.1 3.2 Sutton, R.P.: "Compressibility Factors for High-Molecular-Weight Reservoir Gases," paper SPE 14265 presented at the 1985 SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, 22–25 September.
  4. 4.0 4.1 4.2 4.3 Piper, L.D., McCain, W.D. Jr., and Corredor, J.H.: "Compressibility Factors for Naturally Occurring Petroleum Gases," paper SPE 26668 presented at the 1993 SPE Annual Technical Conference and Exhibition, Houston, 3–6 October. Cite error: Invalid <ref> tag; name "r4" defined multiple times with different content
  5. 5.0 5.1 5.2 5.3 Stewart, W.F., Burkhardt, S.F., and Voo, D.: "Prediction of Pseudocritical parameters for Mixtures," presented at the 1959 AIChE meeting, Kansas City, Missouri, 18 May. [edit]

Noteworthy papers in OnePetro

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External links

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See also

Gas properties

Real gases

Gas formation volume factor and density

Gas viscosity

PEH:Gas_Properties