Common Versions of The Fenske Equation
This is one of the many different but equivalent versions of the Fenske equation:
| where: | |
| = minimum number of theoretical plates required at total reflux (of which the reboiler is one) | |
| = mole fraction of more volatile component in the overhead distillate | |
| = mole fraction of more volatile component in the bottoms | |
| = average relative volatility of more volatile component to less volatile component |
For ease of expression, the more volatile and the less volatile components are commonly referred to as the light key (LK) and the heavy key (HK), respectively. Using that terminology, the above equation may be expressed as:
or also:
If the relative volatility of the light key to the heavy key is constant from the column top to the column bottom, then is simply . If the relative volatility is not constant from top to bottom of the column, then the following approximation may be used:
| where: | |
| = relative volatility of light key to heavy key at top of column | |
| = relative volatility of light key to heavy key at bottom of column |
The above forms of the Fenske equation can be modified for use in the total reflux distillation of multi-component feeds. It is also helpful in solving liquid-liquid extraction problems, because an extraction system can also be represented as a series of equilibrium stages and relative solubility can be substituted for relative volatility.
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