[Dzoni]

The McCabe-Thiele method uses the following assumptions, or so Wikipedia claims:

"The McCabe-Thiele method is based on the assumption of constant molar overflow which requires that:

    * the molal heats of vaporization of the feed components are equal
    * for every mole of liquid vaporized, a mole of vapour is condensed
    * heat effects such as heats of solution and heat transfer to and from the distillation column are negligible."

All of these, I believe are correct... However, what does one do in cases where these assumptions do not hold?

I've found plenty of places where it states that the McCabe-Thiele method only works when the assumptions are made, but nowhere does it seem to explain WHY... Any ideas? (And I'm sure someone does know.)

[eugenedakin]

Hello Dzoni,

This is a very good question. 

These assumptions are used to assist in simplifying the McCabe-Thiele derivation.   I'll go through each on one of the possible assumptions to explain a version of the reasonings:

1)

* the molal heats of vaporization of the feed components are equal

If the heats of vaporization are not equal, then the formula would need to compensate for this change.  Assuming this equal HOV (heat of vapourization) eliminates some compicated steps:  Take all of the components (if you know them in a mixture such as crude oil), and then determine their molarity concentration, then perform some statistical analysis to determine the mean HOV.  Since most feedstocks change, this calculation would also need to be completed on a continuous basic and the McCabe-Thiele diagram would be in a constant state of flux.

2)

* for every mole of liquid vaporized, a mole of vapour is condensed

When this is NOT true, this means that a chemical reaction is occuring due to activation energy being supplied (either thermally or some other energy means). Each possible cracking or chemical reaction would need to be calulated and added into the equation for the McCabe-Thiele method.  Since, the composition of crude oils are largely changing, this reaction (and possible products) are continuously changing, even within the distillation tower.  This would also need to be continuously calculated.  Even if we had the ability to know every chemical reaction, we would need to know every single ingredient in the crude feedstock.

3)

* heat effects such as heats of solution and heat transfer to and from the distillation column are negligible.

If heats of solution and transfer are considered, then all of these calculations would need to be incorporated into the McCabe-Thiele method.  Since we only have a limited number of charts for heats of solution (I would guess at about 1000 or so), this pales in comparison to the over 12000 organic compounds documented in the CRC Handbook (82nd Edition).  All of these charts would need to be built, and a model created to simulate all of the possible complicated reactions.

I have made a honest attempt to answer 1 possible scenario of the 3 basis of the McCabe-Thiele method.  There are definately more possible scenarios available.

I hope this provides a brief glimpse as to reasons for knowing the assumptions, and reasons why these assumptions have not been expanded.

Take care, and I wish you the best,

Eugene