Lee–Kesler method

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 {r}}=f^{(0)}+\omega \cdot f^{(1)}

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

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

with

P_{\rm {r}}={\frac {P}{P_{\rm {c}}}}

(reduced pressure) and

T_{\rm {r}}={\frac {T}{T_{\rm {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

T_c = 562.12 K^[3]
P_c = 4898 kPa^[3]
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.

References

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

[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

[Brunner-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

[1]

[2]

[3]

[4]

[5]

Equations

Typical errors

Example calculation

See also

References