Operating line ( Absorption)

Like distillation, operating lines can also be found in absorption. The basic principle to obtain the operating lines is the same. If we do the mass balance of the solute absorbed, we will end up with one equation, a linear equation.

Before we have a look at the mass balance, it is important to introduced a new term; loading. Loading is defined in the same way as molar fraction is. Normally a big capital X is used to represent loading, while a small one, x represents molar fraction.

Molar fraction, x = mole of solute / total mole available

Loading, X = mole of solute / (total mole available - mole of solute)

If molar fraction is given, it can simply be converted into loading via a very simple equation:

X = x/(1-x) or

x = X/(1+X)

Again X is for liquid phase and Y is for gas phase. There is however one important assumption to do the mass balance around the absorption column: Absorbent does not evaporate and carrier gas is not absorbed at the same time. This allows us to say that gas, G and liquid flow rate, L remain unchanged through out the column.

We know already G(in) = G(out) and it also valids L(in) = L(out)

Mass balance using loading:

G*Y(n+1) + L*Xo = G*Y1 + L*Xn

With some rearrangement we will get this final equation:

Y(n+1) = L/G *(Xn-Xo) + Y1

This is a straight line on a Y against X diagram.

Absorption

Absorption is one of many unit operations used in process industries. It is a separation process that involves a mass transfer from a gas to a liquid. The solute which is absorbed is called absorptive and the solvent which absorbs solute is referred as absorbent. The reversed process (mass transfer from a liquid to a gas) is desorption.

These are the applications of (physical) absorption:

1) Air purification
2) Odor control
3) Purification in refinery and petro-chemical industry

Meanwhile desorption is sometimes used in:

1) Regenerating of loaded absorbent
2) Removing of solved components from liquids

There are some similarities between distillation and absorption:

1) Both involve two phases, liquid and gas
2) Both phases are normally saturated

With that being said absorption differs from distillation in many ways:

1) Feed in distillation is mostly liquid, vapour is sometimes generated as a part of the liquid feed
2) The operating temperature for absorption is normally lower than that for distillation
3) Liquid to gas ratio in absorption is mostly lower than that in distillation

Physical absorption and chemical absorption:

a) Physical absorption: where absorbed solute does not react with the aqueous solution
b) Chemical absorption: solute is absorbed and then reacts with the aqueous solution

Physical absorption is normally preferred at high pressure while at low pressure chemical absorption works best. However the regeneration in case of chemical absorption is really challenging.

Dividing-wall column

A dividing-wall column or divided-wall column is a type of new column to be used in separating a multicomponent mixture. It is however not widely used in industry as people are still doing some researches on that topic.

It looks exactly similar to the normal distillation column. The only noticeable and probably main difference is that a vertical wall is installed or welded inside the column that separates the internal column into two regions.

Since distillation is responsible for the largest fraction of huge amount of energy consumed in process industries, it then becomes a major concern and primary target of energy saving effort in industrially developed countries. This separation process also is the most widely used in industry compared to other unit operations and needs most of the time a large expenditure of capital.

It is important to do many improvements in this area as the distillation applications will definitely increase from year to year. Therefore distillation systems that are sustainable and economically feasible must designed and if they are proven to be successful, they must be introduced. This is the reason why a dividing-wall column is introduced as it is said that this type of column is capable of reducing both capital and operating costs.

The welded wall separates the column into two sections namely a feed section and a side draw section. The former acts as a prefractionator and the latter allows the separation of high purity intermediate-boiling component in a ternary mixture, for example.

Example of a dividing-wall column:

So only one column is required to separate a mixture that contains A,B and C. Since we know that we need at least two columns to separate a ternary mixture via ordinary distillation, a dividing-wall column is obviously advantageous in terms of capital cost. The capital cost can be reduced by installing this type of column. In addition to that it has been proven that this type of column also consumes relatively less energy than the two-column system. The operating cost is said to be reduced up to 10%.
 le and economically feasible must be designed and introduced

Therefore distillation systems that are

sustaina

ble and economically feasible must be designed and introduced.

Number of theoretical stages

As mentioned several times this McCabe-Thiele diagram can be used to determine the number of theoretical stages too. Knowing the number of theoretical stages is crucial in order to get a rough estimation of the cost and other aspects of distillation.

First of all, mark all those given or known compositions in the diagram. Then draw a feed line from the feed composition that depends on the feed phase. In this example we again use a saturated-liquid feed. So the feed line will be a vertical line.

Secondly draw an operating line for the rectifying section, provided we know the reflux ratio that we want to operate at. Since it is known, we can simply calculate the slope and/or the y-intercept of the operating line. Draw the line until it intercepts with the feed line.

Next step is to connect the intersection point with the bottom composition, forming another straight line. This is the operating line for a stripping section of the column.

Last step is to draw steps in between those operating lines and the equilibrium curve. This is drawn in red. In total we need 10 stages, 9 stages and 1 reboiler as reboiler is counted as a stage as well.

Minimum reflux ratio ii

Sometimes the equilibrium curve does not look really curvy. The more curvy the equilibrium curve is, the better is the separation of the key components. Previously we already learned how to determine the minimum reflux ratio in case of an easily-separated mixture. This time we will discuss how to determine the same parameter when the equilibrium curve differs or gets less curvy.

Example:

Notice that the equilibrium curve gets closer to the bisecting line as X-value approaches one. This is a completely different mixture in comparison to the one that we used as an example in the previous entry.

First step is to mark all those given compositions such bottom-, feed- and distillate composition. In reality only the distillate composition is required. However there is no harm in marking all those points on the diagram.

Secondly from that distillate composition draw a tangent to the curve and extrapolate it until we have the value of y-intercept, a.

Since we know a is equal to xd/(v+1) , we can easily determine its minimum reflux ratio, provided xd is known before.

Minimum reflux ratio

With the help of McCabe-Thiele diagram we can also determine the minimum reflux ratio. It is again pretty simple and direct. One only has to know how to use the diagram.

First of all, we need to mark all those points that we know such as distillate-,bottom- and feed composition. This time feed composition and feed phase are important and cannot be neglected.

Secondly draw a feed line from the feed composition point marked in the diagram. In case of having a saturated-liquid feed, a vertical line is drawn until it touches the equilibrium curve.

Then draw an operating line from the distillate composition that passes through the intersection point between feed line and equilibrium curve.

After that extrapolate that operating line until it intersects with y-axis at point a.

Knowing the value of a, the minimum reflux ratio can be calculated. We have seen that the y-intercept of an operating line for a rectifying section is equal to xd/(v+1). Since xd is normally known or given, v or v(min) can easily be determined.

Minimum number of stages

In this entry we will learn how to determine the number of stages from a very popular diagram used in distillation field, McCabe-Thiele diagram. It is actually pretty easy and direct if one knows how to use it.

First of all we have to know what it means by minimum number of stages. It is actually another way of saying that we have an infinite amount of reflux ratio. We know that the slope of the operating line for a rectifying section is equal to v/v+1, this means the slope will be one in case of having a very high reflux ratio. The operating line will simply follow the y=x line in the diagram.

Secondly we need to mark all those important points such distillate composition, feed composition and bottom composition. Feed composition is however not needed in this case. Feed has no influence on the minimum number of stages if we have an infinite reflux ratio.

The next step is to draw stages in the diagram. It is worth mentioning that the order to start drawing the stage does not matter. We can either start stepping off from distillate or from bottom. The result remains the same and will not change at all.

Hence for this example we need minimum 3 stages without considering the tray efficiency. Normally we need more than 3 if we take the tray efficiency into account.