Separation Processes 1

Varying Stage Efficiencies and Feed Location

In the previous lecture, we discussed column efficiencies and how to use them:
- The overall column efficiency, $E_O$ , is the ratio of ideal trays to real trays in the column.
- The Murphree tray efficiency, $E_M$ , is the effectiveness of a single real tray when compared to a ideal tray.
- The Murphree point efficiency, $E_P$ , is the efficiency of a single point on a tray. This is only useful when considering the flow on a tray in detail.
A constant Murphree tray efficiency is relatively easy to use, forming an “effective” VLE line below the true VLE line, which we called the Murphree line.

But what is happening at the bottom of the stepping when using the Murphree efficiency?
This is the first example of a case where we have different efficiencies for different parts of the column.
The bottom stage is usually a re-boiler stage, and it is often assumed to have a Murphree efficiency of $E_M=1.0$ !
This is because the re-boilers actually generate vapour from the liquid.
On trays, you are contacting vapour and liquid phases to try to get them to come into equilibrium.
Generating vapour will typically be more effective at achieving equilibrium concentrations.

Let's double check how the overall efficiency works when considering the re-boiler as an ideal stage.
We start off by calculating how many ideal stages are required for the design.
Here we need around 2.6 ideal stages to perform the separation.
But one ideal stage is provided by a re-boiler, so we only need 1.6 ideal trays!
Assuming we have an overall efficiency of $E_O=0.4$ , this would give us $1.6/0.4=4$ real stages and a reboiler stage!
Contrast this to our previous design with a Murphree tray efficiency of $E_M=0.5$ .