Lee–Kesler method

Method to estimate saturated vapor pressure

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

ln ⁡ P r = f ( 0 ) + ω ⋅ f ( 1 ) {\displaystyle \ln P_{\rm {r}}=f^{(0)}+\omega \cdot f^{(1)}}
f ( 0 ) = 5.92714 − 6.09648 T r − 1.28862 ⋅ ln ⁡ T r + 0.169347 ⋅ T r 6 {\displaystyle 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 − 15.6875 T r − 13.4721 ⋅ ln ⁡ T r + 0.43577 ⋅ T r 6 {\displaystyle 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 r = P P c {\displaystyle P_{\rm {r}}={\frac {P}{P_{\rm {c}}}}} (reduced pressure) and T r = T T c {\displaystyle 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

  • 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.

See also

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