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# 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:

• 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:

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.[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,

## 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, 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

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

This gives

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

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[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

## 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

The details of the calculation are in 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.[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 = 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. Kay, W.B.: "Density of Hydrocarbon Gases at High Temperature and Pressure," Ind. Eng. Chem. (September 1936) 28, 1014–1019.
3. 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. 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. 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.