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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. | 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== | == Correlation charts == | ||
Reliable correlation charts are available to estimate gas viscosity. Carr ''et al.''<ref name="r1" /> 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. | |||
Reliable correlation charts are available to estimate gas viscosity. Carr ''et al.''<ref name="r1">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</ref> 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. | |||
<gallery widths="300px" heights="200px"> | <gallery widths="300px" heights="200px"> | ||
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</gallery> | </gallery> | ||
==Calculating gas viscosity== | == 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'''. | 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'''. | ||
[[File:Vol1 page 0236 eq 001.png]]....................(1) | [[File:Vol1 page 0236 eq 001.png|RTENOTITLE]]....................(1) | ||
where: | where: | ||
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*''μ''<sub>''i''</sub> = viscosity of the ''i''th component of the gas mixture at the desired temperature and atmospheric pressure (obtained from '''Fig. 1''') | *''μ''<sub>''i''</sub> = viscosity of the ''i''th component of the gas mixture at the desired temperature and atmospheric pressure (obtained from '''Fig. 1''') | ||
*''M''<sub>''gi''</sub> = molecular weight of the ''i''th component of the gas mixture | *''M''<sub>''gi''</sub> = molecular weight of the ''i''th component of the gas mixture | ||
*''N'' = number of components in 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. | 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.''<ref name="r1" />) are based on pseudocritical properties determined with Kay’s rules. It would not be correct, then, to use the methods of Sutton<ref name="r2" /> or Piper ''et al.''<ref name="r3" /> to calculate the pseudocritical properties for use with those charts. However, Kay’s rules require a full gas composition. | Note that '''Figs. 3''' and '''4''' (from Carr ''et al.''<ref name="r1">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</ref>) are based on pseudocritical properties determined with Kay’s rules. It would not be correct, then, to use the methods of Sutton<ref name="r2">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</ref> or Piper ''et al.''<ref name="r3">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</ref> 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<sub>2</sub>, CO<sub>2</sub>, and H<sub>2</sub>S. | 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|Real gases]]). The inserts of '''Fig. 2''' are corrections to be added to the atmospheric viscosity when the gas contains N<sub>2</sub>, CO<sub>2</sub>, and H<sub>2</sub>S. | ||
<gallery widths="300px" heights="200px"> | <gallery widths="300px" heights="200px"> | ||
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</gallery> | </gallery> | ||
Lee ''et al.''<ref name="r4" /> 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.''<ref name="r4" /> are for specific units as noted below and are as follows: | Lee ''et al.''<ref name="r4">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</ref> 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.''<ref name="r4">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</ref> are for specific units as noted below and are as follows: | ||
[[File:Vol1 page 0237 eq 001.png]]....................(3) | [[File:Vol1 page 0237 eq 001.png|RTENOTITLE]]....................(3) | ||
where: | where: | ||
*[[File:Vol1 page 0238 inline | *[[File:Vol1 page 0238 inline 001.png|RTENOTITLE]] | ||
*[[File:Vol1 page 0238 inline | *[[File:Vol1 page 0238 inline 002.png|RTENOTITLE]] | ||
*''Y'' = 2.4 - 0.2''X'' | *[[File:Vol1 page 0238 inline 003.png|RTENOTITLE]] | ||
*''Y'' = 2.4 - 0.2''X'' | |||
*''μ''<sub>''g''</sub> = gas viscosity, cp | *''μ''<sub>''g''</sub> = gas viscosity, cp | ||
*''ρ'' =gas density, g/cm<sup>3</sup> | *''ρ'' =gas density, g/cm<sup>3</sup> | ||
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*''M''<sub>''g''</sub> = gas molecular weight = 28.967 ''γ''<sub>''g''</sub> | *''M''<sub>''g''</sub> = gas molecular weight = 28.967 ''γ''<sub>''g''</sub> | ||
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<sub>2</sub> (mol%) < 3.20 and 0.0 < N<sub>2</sub> (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<sub>2</sub>, CO<sub>2</sub>, and H<sub>2</sub>S using the method of Wichert and Aziz.<ref name="r5" /> The equations of Lee ''et al.''<ref name="r4" /> 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. | 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<sub>2</sub> (mol%) < 3.20 and 0.0 < N<sub>2</sub> (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<sub>2</sub>, CO<sub>2</sub>, and H<sub>2</sub>S using the method of Wichert and Aziz.<ref name="r5">Wichert, E. and Aziz, K. 1972. Calculate Z's for Sour Gases. Hydrocarbon Processing 51 (May): 119–122.</ref> The equations of Lee ''et al.''<ref name="r4">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</ref> 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'''. | Calculate the viscosity at 150°F (609.67°R) and 2,012 psia for the gas of the composition shown in '''Table 1'''. | ||
<gallery widths=300px heights=200px> | <gallery widths="300px" heights="200px"> | ||
File:Vol1 Page 249 Image 0001.png|'''Table 1''' | File:Vol1 Page 249 Image 0001.png|'''Table 1''' | ||
</gallery> | </gallery> | ||
Line 67: | Line 70: | ||
''Solution'' (by the Carr ''et al''. method). | ''Solution'' (by the Carr ''et al''. method). | ||
First, calculate the pseudocritical properties using Kay’s<ref name="r6" /> rules. The charts of Carr ''et al.''<ref name="r1" /> are based on pseudocritical properties determined with Kay’s rules; it would not be correct, then, to use the methods of Sutton<ref name="r2" /> or Piper ''et al.''<ref name="r3" /> to calculate the pseudocritical properties for use with the viscosity calculation. The details are in '''Table 2'''. | First, calculate the pseudocritical properties using Kay’s<ref name="r6">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</ref> rules. The charts of Carr ''et al.''<ref name="r1">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</ref> are based on pseudocritical properties determined with Kay’s rules; it would not be correct, then, to use the methods of Sutton<ref name="r2">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</ref> or Piper ''et al.''<ref name="r3">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</ref> to calculate the pseudocritical properties for use with the viscosity calculation. The details are in '''Table 2'''. | ||
<gallery widths=300px heights=200px> | <gallery widths="300px" heights="200px"> | ||
File:Vol1 Page 250 Image 0001.png|'''Table 2''' | File:Vol1 Page 250 Image 0001.png|'''Table 2''' | ||
</gallery> | </gallery> | ||
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Calculating the pseudocritical properties using Kay’s rules yields: | Calculating the pseudocritical properties using Kay’s rules yields: | ||
[[File:Vol1 page 0249 eq 001.png]] | [[File:Vol1 page 0249 eq 001.png|RTENOTITLE]] | ||
These parameters are then used to determine the viscosity at 1 atm. First, the viscosity for ''M''<sub>''g''</sub> = 20.079 at p = 1 atm and ''T'' = 150°F is read from '''Fig. 2'''. This gives ''μ''<sub>''ga''</sub> = 0.0114 cp, but a correction is needed for the nitrogen. The correction for 15.8% N<sub>2</sub> is 0.0013 cp. Hence, this gives ''μ''<sub>''ga''</sub> = 0.0127 cp. | These parameters are then used to determine the viscosity at 1 atm. First, the viscosity for ''M''<sub>''g''</sub> = 20.079 at p = 1 atm and ''T'' = 150°F is read from '''Fig. 2'''. This gives ''μ''<sub>''ga''</sub> = 0.0114 cp, but a correction is needed for the nitrogen. The correction for 15.8% N<sub>2</sub> is 0.0013 cp. Hence, this gives ''μ''<sub>''ga''</sub> = 0.0127 cp. | ||
Next, the ratio of ''μ''<sub>''g''</sub>/''μ''<sub>''ga''</sub> is read from '''Fig. 4''' using the pseudoreduced properties calculated above, which gives ''μ''<sub>''g''</sub>/''μ''<sub>''ga''</sub> = 1.32. | Next, the ratio of ''μ''<sub>''g''</sub>/''μ''<sub>''ga''</sub> is read from '''Fig. 4''' using the pseudoreduced properties calculated above, which gives ''μ''<sub>''g''</sub>/''μ''<sub>''ga''</sub> = 1.32. | ||
Hence, ''μ''<sub>''g''</sub> = (1.32) (0.0127) = 0.0168 cp. This represents a 2.5% error from the experimentally determined value of 0.0172 cp. | Hence, ''μ''<sub>''g''</sub> = (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). | ''Solution'' (by the Lee ''et al''. method). | ||
In this method,<ref name="r7" /> the ''z'' factor is required; this is most accurately determined with the Piper ''et al.''<ref name="r3" /> method, the details of which are in '''Table 3'''. | In this method,<ref name="r7">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</ref> the ''z'' factor is required; this is most accurately determined with the Piper ''et al.''<ref name="r3">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</ref> method, the details of which are in '''Table 3'''. | ||
<gallery widths=300px heights=200px> | <gallery widths="300px" heights="200px"> | ||
File:Vol1 Page 251 Image 0001.png|'''Table 3''' | File:Vol1 Page 251 Image 0001.png|'''Table 3''' | ||
</gallery> | </gallery> | ||
Line 94: | Line 96: | ||
The calculations are: | The calculations are: | ||
[[File:Vol1 page 0250 eq 001.png]] | [[File:Vol1 page 0250 eq 001.png|RTENOTITLE]] | ||
Look up the chart of Fig.2 from [[Real_gases|Real gases]], which gives a value of ''z'' = 0.91; then, | |||
[[File:Vol1 page 0251 eq 001.png|RTENOTITLE]] | |||
This method gives a value that is 5.5% less than the experimentally determined value of 0.0172 cp. | |||
== Nomenclature == | |||
{| | {| | ||
|- | |- | ||
|''M''<sub>''g''</sub> | | ''K''<sub>1</sub> | ||
|= | | = | ||
|average molecular weight of gas mixture | | parameter in the Lee ''et al.''<ref name="r7">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</ref> viscosity, cp | ||
|- | |||
| ''M''<sub>''g''</sub> | |||
| = | |||
| average molecular weight of gas mixture | |||
|- | |- | ||
|''N'' | | ''N'' | ||
|= | | = | ||
|number of components in the gas mixture | | number of components in the gas mixture | ||
|- | |- | ||
|''p'' | | ''p'' | ||
|= | | = | ||
|absolute pressure, Pa | | absolute pressure, Pa | ||
|- | |- | ||
|''p''<sub>''pc''</sub> | | ''p''<sub>''pc''</sub> | ||
|= | | = | ||
|pseudocritical pressure of a gas mixture, Pa | | pseudocritical pressure of a gas mixture, Pa | ||
|- | |- | ||
|''R'' | | ''R'' | ||
|= | | = | ||
|gas law constant, J/(g mol-K) | | gas law constant, J/(g mol-K) | ||
|- | |- | ||
|''T'' | | ''T'' | ||
|= | | = | ||
|absolute temperature, K | | absolute temperature, K | ||
|- | |- | ||
|''T''<sub>''pc''</sub> | | ''T''<sub>''pc''</sub> | ||
|= | | = | ||
|corrected pseudocritical temperature, K | | corrected pseudocritical temperature, K | ||
|- | |- | ||
|''X'' | | ''X'' | ||
|= | | = | ||
|parameter used to calculate ''Y'' | | parameter used to calculate ''Y'' | ||
|- | |- | ||
|''y''<sub>''i''</sub> | | ''y''<sub>''i''</sub> | ||
|= | | = | ||
|mole fraction of component ''i'' in a gas mixture | | mole fraction of component ''i'' in a gas mixture | ||
|- | |- | ||
|''z'' | | ''z'' | ||
|= | | = | ||
|compressibility factor (gas deviation factor) | | compressibility factor (gas deviation factor) | ||
|- | |- | ||
|''ρ''<sub>''g''</sub> | | ''ρ''<sub>''g''</sub> | ||
|= | | = | ||
|density of gas, kg/m<sup>3</sup> | | density of gas, kg/m<sup>3</sup> | ||
|- | |- | ||
|''γ''<sub>''g''</sub> | | ''γ''<sub>''g''</sub> | ||
|= | | = | ||
|specific gravity for gas | | specific gravity for gas | ||
|- | |- | ||
|''μ'' | | ''μ'' | ||
|= | | = | ||
|viscosity, Pa•s | | viscosity, Pa•s | ||
|- | |- | ||
|''μ''<sub>''g''</sub> | | ''μ''<sub>''g''</sub> | ||
|= | | = | ||
|viscosity of gas, Pa•s | | viscosity of gas, Pa•s | ||
|- | |- | ||
|''μ''<sub>''ga''</sub> | | ''μ''<sub>''ga''</sub> | ||
|= | | = | ||
|viscosity of gas mixture at desired temperature and atmospheric pressure, Pa•s | | viscosity of gas mixture at desired temperature and atmospheric pressure, Pa•s | ||
|} | |} | ||
==References== | == References == | ||
<references | |||
<references /> | |||
== Noteworthy papers in OnePetro == | |||
Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read | Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read | ||
==External links== | == External links == | ||
Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro | Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro | ||
==See also== | == See also == | ||
[[Real gases]] | |||
[[Real_gases|Real gases]] | |||
[[Gas_properties|Gas properties]] | |||
[[ | [[Calculating_gas_properties|Calculating gas properties]] | ||
[[ | [[Gas_formation_volume_factor_and_density|Gas formation volume factor and density]] | ||
[[ | [[Vapor_pressure|Vapor pressure]] | ||
[[ | [[PEH:Gas_Properties]] | ||
[[ | [[Category:5.2 Fluid characterization]] |
Latest revision as of 16:06, 3 June 2015
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.
Fig. 1 – Viscosity of pure hydrocarbons at 1 atm (from Carr et al.[1]).
Fig. 2 – Viscosity of natural gases at 1 atm (from Carr et al.[1]).
Fig. 3 – Effect of temperature and pressure on viscosity of natural gases (from Carr et al.[1]).
Fig. 4 – Effect of temperature and pressure on viscosity of natural gases (from Carr et al.[1]).
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:
- 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.[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 N2, CO2, and H2S.
Fig. 5 – Pseudocritical properties of methane-based natural gases (from Sutton[2]).
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
- 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.[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 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,[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
K1 | = | parameter in the Lee et al.[7] 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 |
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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