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Lee–Kesler method

{{Short description|Method to estimate saturated vapor pressure}}

The Lee–Kesler method

Lee B.I., Kesler M.G., "A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States", AIChE J., 21(3), 510–527, 1975

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

: \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%.

Reid R.C., Prausnitz J.M., Poling B.E., "The Properties of Gases & Liquids", 4. Auflage, McGraw-Hill, 1988

Example calculation

For benzene with

  • Tc = 562.12 KBrunner E., Thies M.C., Schneider G.M., J.Supercrit. Fluids, 39(2), 160–173, 2006
  • Pc = 4898 kPa
  • Tb = 353.15 KSilva L.M.C., Mattedi S., Gonzalez-Olmos R., Iglesias M., J. Chem. Thermodyn., 38(12), 1725–1736, 2006
  • ω = 0.2120Dortmund Data Bank

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.

See also

References

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{{DEFAULTSORT:Lee-Kesler Method}}

Category:Thermodynamic models