Introduction of Feed : the q-line

Consider the section of the distillation column ( see the Figure below) at the tray where the feed is introduced (known as the feed tray location), say tray f :

Feed tray location

The feed may consists of liquid, vapour or a mixture of both. The quantities of the liquid stream and vapour stream in the rectifying and stripping sections may change abruptly because of the addition of the feed stream.

 

Define:

q = The moles of liquid flow in the stripping section that results from the introduction of each mole of feed.

The value of q can be controlled by adjusting the amount of preheat the feed stream is subjected to before entering the column.

For different feed conditions, q has the following numerical limits :

· cold feed (below bubble point) q > 1
· feed at bubble point (saturated liquid) q = 1
· feed partially vapour 0 < q < 1
· feed at dew point (saturated vapour) q = 0
· feed superheated vapour q < 0

If the feed is a mixture of liquid and vapour, then q is the fraction of the feed that is liquid. For example, if a feed is 25% liquid and 75% vapour, then q = 0.25.


Recall our analysis of Flash Distillation: by changing the fraction of feed vapourised, we change the composition of the more volatile component in the vapour and liquid product streams.

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Effect of various feed conditions on vapour and liquid loading in column:

The following table summarizes the effect of different feed conditions on the vapour and liquid flowrates in the rectifying and stripping sections respectively.

q: Cold Feed

As an example, consider the Figure above whereby the feed is a cold liquid. In this case, all the liquid feed will go to the stripping section. In addition, because the feed is cold, it will also condense some of the rising vapour. As a result, the amount of liquid flow in the stripping section L' is much larger than the liquid flow in the rectifying section L. The vapour flow in the rectifying section V, is lower than the vapour flow in the stripping section V' because of the condensation into the liquid. Hence for case (a), we have L' > L and V' > V.

Similar evaluation can be carried out for the other feed conditions. See the left Figure below for saturated liquid,and the right Figure below for vapour-liquid mixture,

q: Saturated Liquid

The left Figure below is for saturated vapour and the right Figure below is for superheated vapour.

q: Saturated Vapour

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The feed section operating line (or simply the q-line) can be obtained by performing a material balance around the feed tray. Click here for more information.

Plotting of the q-line requires the q-value and the feed MVC mole fraction, xF. As shown above, q = 1.0 for saturated liquid and q = 0.0 for saturated vapour. For vapour-liquid mixture, q = fraction of feed that is liquid. For other conditions, we need to calculate the q-values. Click here for more information.

The feed tray location can be identified once the number of theoretical trays is determined. Click here for more information.

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