Derivation of McCabe - Thiele Method

In summary: McCabe - Thiele method from general energy and mass balance around a tray at stationary state column operation. This method is based on the concept that for two-component mixtures with similar enthalpy of vaporization, there is a constant molar overflow condition on every stage of the column, meaning that for every mole of vapor that condenses, one mole of liquid is vaporized. This ensures efficient separation with a minimum number of stages or theoretical plates.
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Dario56
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TL;DR 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.
 
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  • #2
Dario56 said:
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
 

1. What is the McCabe-Thiele method?

The McCabe-Thiele method is a graphical technique used in chemical engineering to determine the number of theoretical stages required for the separation of two components in a binary distillation process.

2. How does the McCabe-Thiele method work?

The method involves constructing a graph known as the McCabe-Thiele diagram, which plots the composition of the liquid and vapor phases at each stage of the distillation process. By analyzing this graph, the number of theoretical stages can be determined.

3. What are the assumptions made in the McCabe-Thiele method?

The method assumes that the mixture being distilled is ideal, the vapor and liquid phases are in equilibrium at each stage, and there is no change in temperature or pressure throughout the process.

4. What information is needed to use the McCabe-Thiele method?

To use the method, you will need to know the composition of the feed mixture, the desired composition of the distillate and bottoms products, and the vapor-liquid equilibrium data for the components being separated.

5. What are the limitations of the McCabe-Thiele method?

The method is only applicable to binary distillation processes and assumes ideal behavior, which may not always be the case in real-world systems. It also does not account for non-idealities such as vapor-liquid non-equilibrium or pressure changes in the system.

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