# Lee–Kesler method

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The Lee–Kesler method [1] allows the estimation of the saturated vapor pressure at a given temperature for all components for which the critical pressure Pc, the critical temperature Tc, and the acentric factor ω are known.

## Equations

${\displaystyle \ln P_{r}=f^{(0)}+\omega \cdot f^{(1)}}$

${\displaystyle f^{(0)}=5.92714-{\frac {6.09648}{T_{r}}}-1.28862\cdot \ln T_{r}+0.169347\cdot T_{r}^{6}}$

${\displaystyle f^{(1)}=15.2518-{\frac {15.6875}{T_{r}}}-13.4721\cdot \ln T_{r}+0.43577\cdot T_{r}^{6}}$

with

${\displaystyle P_{r}={\frac {P}{P_{c}}}}$ (reduced pressure) and ${\displaystyle T_{r}={\frac {T}{T_{c}}}}$ (reduced temperature).

## Typical errors

The prediction error can be up to 10% for polar components and small pressures and the calculated pressure is typically too low. For pressures above 1 bar, that means, above the normal boiling point, the typical errors are below 2%. [2]

## Example calculation

For benzene with

• Tc = 562.12 K[3]
• Pc = 4898 kPa[3]
• Tb = 353.15 K[4]
• ω = 0.2120[5]

the following calculation for T=Tb results:

• Tr = 353.15 / 562.12 = 0.628247
• f(0) = -3.167428
• f(1) = -3.429560
• Pr = exp( f(0) + ω f(1) ) = 0.020354
• P = Pr * Pc = 99.69 kPa

The correct result would be P = 101.325 kPa, the normal (atmospheric) pressure. The deviation is -1.63 kPa or -1.61 %.

It is important to use the same absolute units for T and Tc as well as for P and Pc. The unit system used (K or R for T) is irrelevant because of the usage of the reduced values Tr and Pr.

## References

1. ^ Lee B.I., Kesler M.G., "A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States", AIChE J., 21(3), 510-527, 1975
2. ^ Reid R.C., Prausnitz J.M., Poling B.E., "The Properties of Gases & Liquids", 4. Auflage, McGraw-Hill, 1988
3. ^ a b Brunner E., Thies M.C., Schneider G.M., J.Supercrit.Fluids, 39(2), 160-173, 2006
4. ^ Silva L.M.C., Mattedi S., Gonzalez-Olmos R., Iglesias M., J.Chem.Thermodyn., 38(12), 1725-1736, 2006
5. ^ Dortmund Data Bank