Calculating gas properties

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:

• γ_g = 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:

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

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

• First, the viscosity for M_g = (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 μ_ga = 0.0109 cp.
• Next, the ratio of μ_g/μ_ga is read from Fig. 4, which gives μ_g/μ_ga = 1.55.
• Hence, μ_g = (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 p_r = 3.200 and T_r = 1.500 to give c_rT_r = 0.5. Because T_r = 1.500 then c_r = 0.5/1.5 = 0.3333. Because c_r = c_g   p_pc,

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.

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

• 

  Table 1

Calculating actual density

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

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

Solution.

The density is calculated from

where

• p = 1,525 psia
• M_g = 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 z_g from the known composition in Table 2.

• 

  Table 2

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

T_pc =Σy_iT_i = 393.8°R,

T_pr = 534.67/393.8 = 1.3577,

p_pc =Σy_ip_ci = 662.88 psia,

p_pr = p/p_pc = 1,525/662.88 =2.301,

and from Fig. 1, z_g = 0.71.

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

This gives

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

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

The details of the calculations are found in Table 2.

Then,

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

Conclusion.

Even though the Sutton correlation and the Piper et al. correlation gave slightly different critical properties, the z factors from those two methods are the same. Kay’s 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

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.

• 

  Table 3

The experimental value is z = 0.998.

Solution.

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

The details of the calculation are in Table 4.

• 

  Table 4

Then,

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. equations, K•Pa–1
K	=	parameter in the Stewart et al. equations, K•Pa–1/2
M	=	molecular weight
Ma	=	molecular weight of air
	=	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. equations (Eqs. 5.9 and 5.10), K•Pa–1
K	=	parameter in the Stewart et al. equations (Eqs. 5.9 and 5.10), K•Pa–1/2
ρg>	=	density of gas, kg/m3

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