Why have reflux? Why is it important? After all, we've shown that repeated distillations will produce increasing concentrations of volatile compounds, and you can achieve this in a simple pot still by distilling the product several times. Eventually, you'll end up with a product containing a very high concentration of all the most volatile components of our original brew.
The crux of the issue is that little word "all". You will end up with all the ethanol, all the propanol, all the butanol, etc, etc. This may be desirable if making whiskey or brandy, and judicious selection of the "heads" and the "tails" of the distillate will ensure that just enough of these compounds are included in the final product. However, raw whiskey tastes awful and has to go through many stages of maturation over a very long time before it's palatable.
Refluxing means feeding a condensed product back to the still for re-distillation, so repeated pot distilling is a form of "manual" refluxing. However, it is very inefficient process and the losses as you discard enough heads and tails to isolate pure ethanol mean that you end up with very, very little product after a great deal of time and effort.
We've already seen that a reflux column can do this for us, and that a compound column with imposed reflux can separate efficiently enough to allow collection of individual compounds. But what amount of reflux should be imposed, and why? Once again, theory and calculation can provide the answer.
Let's start by looking at a single stage of distillation, one "plate". Figure 8-08 shows a plate with the one above it and the one below it.
This plate, which we'll call "plate N", is at temperature TN It's holding liquid that's boiling and giving off a quantity of vapor VN, and the mol fraction of its most volatile component is YN
Having boiled at Tn, the excess liquid drips down to the lower plate, "plate N-1". The quantity of this liquid is Ln and the mol fraction of that volatile component is Xn
At the same time, plate N is receiving a quantity Vn-1 of vapor from the lower plate N-1 with mol fraction YN-1. This vapor is at TN-1 so it condenses on the cooler plate N because TN is lower than TN-1
To complete the picture, plate N is also receiving liquid from the upper plate N+1. The quantity is LN+1 and its mol fraction is XN+1. This liquid, at temperature TN+1, starts to boil when it hits plate N because TN+1 is lower than TN
Since a quantity of liquid L with mol fraction X of a component contains LX mols of that component, the balance equation at plate N for the volatile component we're considering is:
Total mols received = Total mols lost
This equation will apply at every point in the column if it's in balance (ie. in equilibrium). You just have to change the suffixes to match the plate number.
The condenser on top of the compound column is considered the top plate, and the boiler is the bottom plate. The liquid returned to the column from the top condenser is a special case of 'imposed' reflux, unlike the 'natural' reflux generated inside the column. We've therefore set it apart by identifying the final mol fraction of the liquid coming from the condenser as XD . So, if XD is the final mol fraction of the liquid condensed at the top of the column, and LN+1 is the reflux, then
The balance equation for plate N may be written:
You can consider the whole column and as one block unit. Material entering this block = V0Y0 +LN+1XN+1
Material leaving the block is = VNYN + L1X1
Which means that
But VNYN = LN+1 + DXD (consider what enters and leaves the condenser). So V0Y0 = L1X1 + DXd
This describes the balance of the column as a whole.
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