Calculating gas viscosity
The viscosity of gas mixtures at one atmosphere and reservoir temperature can either be read from Fig. 2 or determined from the gas-mixture composition with Eq. 1.
Vol1 page 0236 eq 001.png....................(1)
μga = viscosity of the gas mixture at the desired temperature and atmospheric pressure
yi = mole fraction of the ith component
μi = viscosity of the ith component of the gas mixture at the desired temperature and atmospheric pressure (obtained from Fig. 1)
Mgi = molecular weight of the ith component of the gas mixture
N = number of components in the gas mixture.
This viscosity is then multiplied by the viscosity ratio (from Fig. 3 or Fig. 4) to obtain the viscosity at reservoir temperature and pressure.
Note that Figs. 3 and 4 (from Carr et al.) are based on pseudocritical properties determined with Kay’s rules. It would not be correct, then, to use the methods of Sutton or Piper et al. to calculate the pseudocritical properties for use with those charts. However, Kay’s rules require a full gas composition.
If only specific gravity is known, then the pseudocritical properties would have to be obtained from Fig. 5 (or Eqs. 10 and 11 in Real gases). The inserts of Fig. 2 are corrections to be added to the atmospheric viscosity when the gas contains N2, CO2, and H2S.
Fig. 5 – Pseudocritical properties of methane-based natural gases (from Sutton).
Lee et al. developed a useful analytical method that gives a good estimate of gas viscosity for most natural gases. This method lends itself for use in computer programs and spreadsheets. The method uses the gas temperature, pressure, z factor, and molecular weight, which have to be measured or calculated; the density can be measured or calculated as well. The equations of Lee et al. are for specific units as noted below and are as follows:
Vol1 page 0237 eq 001.png....................(3)
Vol1 page 0238 inline 001.png
Vol1 page 0238 inline 002.png
Vol1 page 0238 inline 003.png
Y = 2.4 - 0.2X
μg = gas viscosity, cp
ρ =gas density, g/cm3
p = pressure, psia
T = temperature °R
Mg = gas molecular weight = 28.967 γg
For the data from which the correlation was developed, the standard deviation in the calculated gas viscosity was 2.7%, and the maximum deviation was 9%. The ranges of variables used in the correlation were 100 psia < p < 8,000 psia, 100 < T (°F) < 340, and 0.90 < CO2 (mol%) < 3.20 and 0.0 < N2 (mol%) < 4.80. In using these equations, it is important either to measure the density or to ensure that the z -factor calculation has included the effect of N2, CO2, and H2S using the method of Wichert and Aziz. The equations of Lee et al. were originally written to give the viscosity in micropoise, but the modified form above gives the viscosity in the more commonly used centipoise. This viscosity unit (cp) is also easily converted to the SI unit of Pa•s by dividing by 1,000.
Example of calculating viscosity
Calculate the viscosity at 150°F (609.67°R) and 2,012 psia for the gas of the composition shown in Table 1.
Solution (by the Carr et al. method).
First, calculate the pseudocritical properties using Kay’s rules. The charts of Carr et al. are based on pseudocritical properties determined with Kay’s rules; it would not be correct, then, to use the methods of Sutton or Piper et al. to calculate the pseudocritical properties for use with the viscosity calculation. The details are in Table 2.
Calculating the pseudocritical properties using Kay’s rules yields:
Vol1 page 0249 eq 001.png
These parameters are then used to determine the viscosity at 1 atm. First, the viscosity for Mg = 20.079 at p = 1 atm and T = 150°F is read from Fig. 2. This gives μga = 0.0114 cp, but a correction is needed for the nitrogen. The correction for 15.8% N2 is 0.0013 cp. Hence, this gives μga = 0.0127 cp.
Next, the ratio of μg/μga is read from Fig. 4 using the pseudoreduced properties calculated above, which gives μg/μga = 1.32.
Hence, μg = (1.32) (0.0127) = 0.0168 cp. This represents a 2.5% error from the experimentally determined value of 0.0172 cp.
Solution (by the Lee et al. method).
In this method, the z factor is required; this is most accurately determined with the Piper et al. method, the details of which are in Table 3.
The calculations are:
Vol1 page 0250 eq 001.png
Look up the chart of Fig.2 from Real gases, which gives a value of z = 0.91; then,
Vol1 page 0251 eq 001.png
This method gives a value that is 5.5% less than the experimentally determined value of 0.0172 cp.
K1 = parameter in the Lee et al. viscosity, cp
Mg = average molecular weight of gas mixture
N = number of components in the gas mixture
p = absolute pressure, Pa
ppc = pseudocritical pressure of a gas mixture, Pa
R = gas law constant, J/(g mol-K)
T = absolute temperature, K
Tpc = corrected pseudocritical temperature, K
X = parameter used to calculate Y
yi = mole fraction of component i in a gas mixture
z = compressibility factor (gas deviation factor)
ρg = density of gas, kg/m3
γg = specific gravity for gas
μ = viscosity, Pa•s
μg = viscosity of gas, Pa•s
μga = viscosity of gas mixture at desired temperature and atmospheric pressure, Pa•s
↑ 1.0 1.1 1.2 1.3 1.4 1.5 1.6 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 Sutton, R.P. 1985. Compressibility Factors for High-Molecular-Weight Reservoir Gases. Presented at the SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, USA, 22-26 September. SPE-14265-MS. http://dx.doi.org/10.2118/14265-MS
↑ 3.0 3.1 3.2 Piper, L.D., McCain Jr., W.D., and Corredor, J.H. 1993. Compressibility Factors for Naturally Occurring Petroleum Gases (1993 version). Presented at the SPE Annual Technical Conference and Exhibition, Houston, 3–6 October. SPE-26668-MS. http://dx.doi.org/10.2118/26668-MS
↑ 4.0 4.1 4.2 Lee, A.L., Gonzalez, M.H., and Eakin, B.E. 1966. The Viscosity of Natural Gases. J Pet Technol 18 (8): 997–1000. SPE-1340-PA. http://dx.doi.org/10.2118/1340-PA
↑ Wichert, E. and Aziz, K. 1972. Calculate Z's for Sour Gases. Hydrocarbon Processing 51 (May): 119–122.
↑ Kay, W. 1936. Gases and Vapors At High Temperature and Pressure - Density of Hydrocarbon. Ind. Eng. Chem. 28 (9): 1014-1019. http://dx.doi.org/10.1021/ie50321a008
↑ 7.0 7.1 Lee, A.L., Gonzalez, M.H., and Eakin, B.E. 1966. The Viscosity of Natural Gases. J Pet Technol 18 (8): 997–1000. SPE-1340-PA. http://dx.doi.org/10.2118/1340-PA
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Calculating gas properties
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