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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:
- γ_{g} = 0.7
- H_{2}S = 7%
- CO_{2} = 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 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% H_{2}S 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_{r}T_{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%):
C_{1} | = | 83.19% |
C_{2} | = | 8.48% |
C_{3} | = | 4.37% |
i-C_{4} | = | 0.76% |
n-C_{4} | = | 1.68% |
i-C_{5} | = | 0.57% |
n-C_{5} | = | 0.32% |
C_{6} | = | 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.
Calculating actual density
Calculate the actual density of the same mixture at 1,525 psia and 75°F
- Using Kay’s^{[2]} rules
- Sutton’s^{[3]} correlation
- Piper et al.^{[4]} correlation.
Solution.
The density is calculated from
where
- p = 1,525 psia
- M_{g} = 20.424
- R = 10.7316 (psia-ft^{3})/(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.
Using Kay’s^{[2]} rules, we obtain from the known gas composition:
T_{pc} =Σy_{i}T_{i} = 393.8°R,
T_{pr} = 534.67/393.8 = 1.3577,
p_{pc} =Σy_{i}p_{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^{[3]} 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.^{[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
References
- ↑ 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
- ↑ ^{2.0} ^{2.1} ^{2.2} Kay, W.B.: "Density of Hydrocarbon Gases at High Temperature and Pressure," Ind. Eng. Chem. (September 1936) 28, 1014–1019.
- ↑ ^{3.0} ^{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.
- ↑ ^{4.0} ^{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 - ↑ ^{5.0} ^{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]
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