Lee–Kesler method explained

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 P_c, the critical temperature T_c, and the acentric factor ω are known.

Equations

ln P _{\rm} = f ^{(0)} + \omega ⋅ f ^{(1)} f ^{(0)} =5 . 92714 - (6 . 09648)/(T _{\rm}) - 1 . 28862 ⋅ ln T _{\rm} + 0 . 169347 ⋅ T ^{6} _{\rm r} f ^{(1)} =15 . 2518 - (15 . 6875)/(T _{\rm}) -13 . 4721 ⋅ ln T _{\rm} + 0 . 43577 ⋅ T ^{6} _{\rm r}

with

P _{\rm} = (P)/(P _{\rm}) (reduced pressure) and T _{\rm} = (T)/(T _{\rm}) (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

• T_c = 562.12 K^[3]
• P_c = 4898 kPa
• T_b = 353.15 K^[4]
• ω = 0.2120^[5]

the following calculation for T = T_b results:

• T_r = 353.15 / 562.12 = 0.628247
• f⁽⁰⁾ = −3.167428
• f⁽¹⁾ = −3.429560
• P_r = exp(f⁽⁰⁾ + ω f⁽¹⁾) = 0.020354
• P = P_r · P_c = 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 T_c as well as for P and P_c. The unit system used (K or R for T) is irrelevant because of the usage of the reduced values T_r and P_r.

See also

• Vapour pressure of water
• Antoine equation
• Tetens equation
• Arden Buck equation
• Goff–Gratch equation

Notes and 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. 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]