Feed composition

A feed is necessary in order to perform the distillation. The phase state of the feed must not necessarily be liquid. It can be vapour as well.

Depending on the feed temperature or pressure, a liquid-feed can either be a sub-cooled liquid or saturated liquid. A saturated liquid simply means that it is available at its boiling point and about to vaporise.

In addition to that, a feed can also be a vapour. Again, depending on temperature or pressure, that feed can also contain two phases in a certain ratio, it can be a saturated vapour and a superheated vapour. These different types of feed are important if we want to use McCabe-Thiele diagram in order to determine parameters such reflux ratio and number of stages, just to name a few.

With the help of total mass balance and the mass balance for each component, a feed line can be obtained. It is a again a straight line. To be able to extract necessary information from the McCabe-Thiele diagram, both operating line and feed line are crucial.

Depending on the feed phase, the feed line can either have a positive slope or a negative slope(zero and infinite also possible). In order to see the influence of the feed on the feed line in the McCabe-Thiele diagram, a diagram would be helpful:

There are 5 different feed lines, a,b,c,d,e in the diagram above.

a) sub-cooled liquid feed
b) saturated liquid feed
c) two phases feed
d) saturated vapour feed.
e) superheated vapour feed

A/C-Path Modification

Since this type of column sequence needs 6 heat exchangers, other alternative sequences must be found so that the energy requirement can be lowered. Plus this A/C-Path also uses 3 columns which means not only operating cost is higher than other sequences, its capital cost is relatively higher as well. There are two alternatives available:

A/C-path: 6 heat exchangers and 3 columns

First modification: 4 heat exchangers and 2 columns (simply coupling two columns). This arrangement is superior to A/C-path.

Second modification: 3 heat exchangers and 2 columns (with side rectifying and side stripping). This sequence is superior to the first modification.

Column's arrangement

If we have a three-component mixture and we want to separate them into their pure products respectively, we need at least two columns. It is however possible to use only one column for this kind of mixture. The only disadvantage is that the purity of the intermediate-boiling component will always be low!

One simple equation is available to be used in order to know how many columns are needed:

Number of columns needed = Number of components - 1

So in case of having three different components, as mentioned we need 2 columns (3-1 = 2).

There are however many ways to rearrange these two columns. The number of rearrangement also can be easily calculated using one simple equation:

Number of sequence = (2(p-1)!)/p!(p-1)!

with p = number of component

Hence for a ternary mixture, we have 5 different ways to arrange the two columns needed. In this entry 3 of them will be shown. There are also known as:

1) A-path
2) C-path
3) A/C-path

A-path: where the separation is done in a descending order of relative volatility

 C-path: where the separation is done in an ascending order of relative volatility

A/C-path: Separation of the B  from A and C is done first.

This type of sequence consumes a lot of energy as it has 6 heat exchangers compared to only 4 in A-path and C-path respectively.

Operating region

In the last three posts we talked about reflux ratio or reboiler ratio (depending on column's section). We know that this parameter has a big influence on cost and quality of the product. There are however several factors or parameters that are just as important as reflux ratio for distillation fields. They tell us whether the column will run smoothly or not. In other words they affect the efficiency of the column.

Those factors are :

1) Liquid load, L

2) Gas load, G

If we plot G/A against L/A in a diagram, we will obtain this kind of diagram:

If gas load is too low, it will lead to weeping. Weeping means liquid starts to fall through the perforations as gas flow is not sufficient to hold it up.

If gas load is too high, then we will have a situation called flooding. It is the opposite of weeping. Instead of leaking through, liquid gets carried upwards together with the vapour/gas.

If liquid load is too low, there will be no homogeneous distribution of liquid on each tray or plate. Hence the mass transfer quality becomes poor.

If liquid load is too high, we will have a similar situation with weeping.

The shaded area is the region where distillation should be operated or run. This guarantees a good separation efficiency.

Operating line ii

In the previous entry we have discussed how to obtain the equation for the operating line of the rectifying section. Now we will derive the second operating line but for the bottom part of the column. This column's part is also known as stripping section.

Here is again a picture to ease the derivation:

For the stripping section, we have a new parameter called reboiler ratio. It is actually quite comparable to reflux ratio. In fact the definition is also similar.

Reboiler ratio w = gas goes back to the column / liquid which is taken out at the bottom column

or

w = G/B

Total mass (flow) balance:

What comes in = what goes out

hence:

G + B = L

Mass balance for one component (the more volatile one):

G*y + B*xb = L*x

Combining these three equations and with some re-arrangements we will obtain our goal which looks like below:

y = (w+1)/w *x - xb/w

This is again an equation for a straigh line with the slope w+1/w and has a y-intercept -1/w.

Operating line

Basically an operating line is a tool which can be used for example in a Mc-Cabe Thiele diagram to determine parameters such as reflux ratio, reboiler ratio and so forth.

Therefore knowing how to derive and then draw it on that diagram is necessary. Otherwise you cannot gain much from that Mc-Cabe Thiele diagram. It is a very useful diagram although it is only valid in a certain case. One important assumption that enables us to work with it is that the evaporation enthalpy of each species is all equal where this is of course not the case in reality.

Let us look at this diagram once again and derive the equation we need:

Total mass (flow) balance:

What goes in = what comes out

hence:

G = L + D

Mass balance for one component ( the more volatile one):

G*y = L*x + D*xd

and then we know that reflux ratio is defined:

v = L/D

Combining all these three equations and do some re-arrangement, you will get this equation looking like this:

y = (v/v+1)x + xd/(v+1)

This is a linear equation and a straight line with the slope v/v+1 and the y-intercept xd/v+1 is to be expected. This is however valid for a rectifying section ( column's part above the feed).

Reflux ratio

In distillation there are lots of important which might affect process's efficiency, operating cost and capital cost. One of them is reflux ratio. This ratio is already defined in a certain way.

Below is the picture of the upper part of the column ( column section above the feed ):

Reflux ratio is defined like this:

v = liquid which is going back to the column, R / liquid which is taken out, D

Normally the reflux ratio is 1.5 to 2 times bigger than the minimum reflux ratio.
It is worth mentioning  that if reflux ratio is too low, it is bad and if it is too high, it is also problematic. Below is the graph that can explain why the right range of reflux ratio's value is crucial:

Theoretically high reflux ratio is good to obtain a pure top product. However high reflux ratio also means high operating cost. More liquid remains in the column therefore more energy is needed to reboil it.

If it is too low, capital cost increases significantly. This is because more stages are needed to obtain the same product's quality. Minimum reflux ratio means the number of stages that we need is infinite. In practice we want to avoid a situation with high number of stages and high energy consumption.