Derivation of McCabe - Thiele Method

[Dario56]

TL;DR

Derivation of McCabe - Thiele method from general energy and mass balance around a tray at stationary state column operation

McCabe - Thiele method is used to find minimum number of separation stages or theoretical plates for a given efficiency of separation in distillation for two - component mixture if components have similar enthalpy of vaporization.

If components have similar enthalpy of vaporization ,than on every stage of the column for one mole of vapor that condenses there is one mole of liquid which is vaporized and this ensures constant molar overflow condition which is essence of McCabe - Thiele method.

However, I can't find derivation of this method from general energy and mass balances written around a tray with condition that column operates stationary. If someone can provide it, it would be nice.

 

[Chestermiller]

Summary:: Derivation of McCabe - Thiele method from general energy and mass balance around a tray at stationary state column operation

McCabe - Thiele method is used to find minimum number of separation stages or theoretical plates for a given efficiency of separation in distillation for two - component mixture if components have similar enthalpy of vaporization.

If components have similar enthalpy of vaporization ,than on every stage of the column for one mole of vapor that condenses there is one mole of liquid which is vaporized and this ensures constant molar overflow condition which is essence of McCabe - Thiele method.

However, I can't find derivation of this method from general energy and mass balances written around a tray with condition that column operates stationary. If someone can provide it, it would be nice.

See Mass Transfer Operations by Treybel or Chemical Engineers' Handbook by Perry et al