Projected area

2013-10-04T17:58:51Z

216.49.150.43: it wanted curlies that it didn't care for in the preview. Weird.

The '''Lee-Kesler method'''
<ref>Lee B.I., Kesler M.G., "A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States", AIChE J., 21(3), 510-527, 1975
</ref>
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 ==
<math> \ln P_r = f^{(0)} + \omega \cdot f^{(1)} </math>

<math> f^{(0)}=5.92714 - \frac{6.09648}{T_r} - 1.28862 \cdot \ln T_r + 0.169347 \cdot T_r^6 </math>

<math> f^{(1)}=15.2518 - \frac{15.6875}{T_r}-13.4721 \cdot \ln T_r + 0.43577 \cdot T_r^6 </math>

with

<math>P_r=\frac{P}{P_c}</math> ([[reduced pressure]]) und <math>T_r=\frac{T}{T_c}</math> ([[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%.
<ref>Reid R.C., Prausnitz J.M., Poling B.E., "The Properties of Gases & Liquids", 4. Auflage, McGraw-Hill, 1988
</ref>

== Example calculation ==
For [[benzene]] with
* Tc = 562.12 K<ref name="Brunner">Brunner E., Thies M.C., Schneider G.M., J.Supercrit.Fluids, 39(2), 160-173, 2006</ref>
* Pc = 4898 kPa<ref name="Brunner" />
* Tb = 353.15 K<ref>Silva L.M.C., Mattedi S., Gonzalez-Olmos R., Iglesias M., J.Chem.Thermodyn., 38(12), 1725-1736, 2006</ref>
* ω = 0.2120<ref>[[Dortmund Data Bank]]</ref>

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 ==
<references/>

{{DEFAULTSORT:Lee-Kesler Method}}
[[Category:Thermodynamic models]]

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Projected area