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Gas viscosity
Just as the compressibility of natural gas is much greater than that of oil, water, or rock, the viscosity of natural gas is usually several orders of magnitude smaller than oil or water. This makes gas much more mobile in the reservoir than either oil or water.
Correlation charts
Reliable correlation charts are available to estimate gas viscosity. Carr et al.^{[1]} have developed charts (Figs. 1 through 4) that are the most widely used for estimating the viscosity of natural gas from the pseudoreduced critical temperature and pressure. Fig. 1 gives the viscosities for individual components. Fig. 2 gives the viscosities for gas at the desired temperature and atmospheric pressure based on the temperature and specific gravity or molecular weight.
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.
where:
- μ_{ga} = viscosity of the gas mixture at the desired temperature and atmospheric pressure
- y_{i} = mole fraction of the ith component
- μ_{i} = viscosity of the ith component of the gas mixture at the desired temperature and atmospheric pressure (obtained from Fig. 1)
- M_{gi} = 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.^{[1]}) are based on pseudocritical properties determined with Kay’s rules. It would not be correct, then, to use the methods of Sutton^{[2]} or Piper et al.^{[3]} 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 N_{2}, CO_{2}, and H_{2}S.
Lee et al.^{[4]} 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.^{[4]} are for specific units as noted below and are as follows:
where:
- Y = 2.4 - 0.2X
- μ_{g} = gas viscosity, cp
- ρ =gas density, g/cm^{3}
- p = pressure, psia
- T = temperature °R
- M_{g} = gas molecular weight = 28.967 γ_{g}
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 < CO_{2} (mol%) < 3.20 and 0.0 < N_{2} (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 N_{2}, CO_{2}, and H_{2}S using the method of Wichert and Aziz.^{[5]} The equations of Lee et al.^{[4]} 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^{[6]} rules. The charts of Carr et al.^{[1]} are based on pseudocritical properties determined with Kay’s rules; it would not be correct, then, to use the methods of Sutton^{[2]} or Piper et al.^{[3]} 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:
These parameters are then used to determine the viscosity at 1 atm. First, the viscosity for M_{g} = 20.079 at p = 1 atm and T = 150°F is read from Fig. 2. This gives μ_{ga} = 0.0114 cp, but a correction is needed for the nitrogen. The correction for 15.8% N_{2} is 0.0013 cp. Hence, this gives μ_{ga} = 0.0127 cp.
Next, the ratio of μ_{g}/μ_{ga} is read from Fig. 4 using the pseudoreduced properties calculated above, which gives μ_{g}/μ_{ga} = 1.32.
Hence, μ_{g} = (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,^{[7]} the z factor is required; this is most accurately determined with the Piper et al.^{[3]} method, the details of which are in Table 3.
The calculations are:
Look up the chart of Fig.2 from Real gases, which gives a value of z = 0.91; then,
This method gives a value that is 5.5% less than the experimentally determined value of 0.0172 cp.
Nomenclature
K_{1} | = | parameter in the Lee et al.^{[7]} viscosity, cp |
M_{g} | = | average molecular weight of gas mixture |
N | = | number of components in the gas mixture |
p | = | absolute pressure, Pa |
p_{pc} | = | pseudocritical pressure of a gas mixture, Pa |
R | = | gas law constant, J/(g mol-K) |
T | = | absolute temperature, K |
T_{pc} | = | corrected pseudocritical temperature, K |
X | = | parameter used to calculate Y |
y_{i} | = | mole fraction of component i in a gas mixture |
z | = | compressibility factor (gas deviation factor) |
ρ_{g} | = | density of gas, kg/m^{3} |
γ_{g} | = | specific gravity for gas |
μ | = | viscosity, Pa•s |
μ_{g} | = | viscosity of gas, Pa•s |
μ_{ga} | = | viscosity of gas mixture at desired temperature and atmospheric pressure, Pa•s |
References
- ↑ ^{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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