Fenske equation

The Fenske equation is used to estimate the number of the minimum required theoretical plates in the rectification of a binary mixture of chemical compounds under the condition of the complete return flow. The column is operated without feed and without removal of the top and bottom product. The calculated number is therefore always lower than the number of the actually need soil, when separating columns in production.

Defining equation

In the Fenske equation, the compositions of the head and the bottom product are related. The proportionality factor is the repeated running (on the theoretical plates ) evaporation and condensation, which is described by the relative volatility. The difference in volatility of the components ensures that the low boiler in the steam and the high boiler enriched in the liquid. The number of trays is the exponent of the relative volatility:

With L = low boiler S = high boiler   = Amount of substance ( mole fraction )   = Relative volatility of the low boiler in relation to the high boiler in the composition of the feed   = Minimum number of floors

This equation can be switched so that directly the theoretical number soils can be determined:

However, the relative volatility is not over the entire separation column constant because it depends both on the composition of the mixture, as is also the temperature and pressure dependent; therefore is usually done by means of an approximate calculation of the geometric mean of the relative volatilities of the components in the top and bottom of the column:

Example calculation

With the arbitrarily fixed values

Follows

The number of theoretical plates calculated increases with lower relative volatility and with higher purity levels for the low-boiling components in the head and for the high boiler in the bottom of the column.

Credentials

• Distillation