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The most important point to understand regarding the control of tray temperatures is that it is not the tray temperature that you really want to control. The tray temperature is just a consequence of the composition on the tray, and it is the composition that you are really trying to control. A liquid with a higher ABV boils at a lower temperature than a liquid with a lower ABV, so the temperature is just an indication of the composition (i.e. ABV).
People will say "Of course I can control the temperature - if I put more steam into the boiler the tray temperatures all increase". That is true, but it helps if you understand why the tray temperatures increase. The boiler is the part of the column where you will find the lowest ABV. If you put more steam into the boiler you force this low ABV material up the column and dilute the ABV on all of the trays. And spirit with a lower ABV boils at a higher temperature and so the higher temperatures observed only mean that the ABV on each of the trays has decreased.
The opposite effect is when you increase the reflux. Now you are taking the highest ABV material in the column (i.e. the top product) and pouring it down the column increasing the ABV on each plate. Increased ABV means it boils at a lower temperature and we see the tray temperatures decrease when we increase reflux. It's tempting to think that the tray temperatures have decreased because we have added cold reflux, but that is not the true cause. It is the higher ABV resulting in lower boiling points on each of the trays.
It is difficult to measure ABV in real time so we use the tray temperature as a proxy for the ABV. Because we are measuring temperatures all the time we come to think of the temperature as the variable that we are controlling, but remember it is actually the ABV that you are controlling and the temperature is just an alias for ABV.
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