Design of Distillation Column |ChemFam #15|

Greetings to everyone! In my previous post, we have learnt about the basic purpose and mechanism of distillation process. After learning about distillation and its construction, now let us go to understand some of the basics of the analysis of the design of the distillation column. Today, we will be discussing about the design of a distillation column for the separation purpose.

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WHAT WE SHALL LEARN?

We shall learn about the stages, the equilibrium stage and the estimation of number of ideal stage. The basis of design of these columns are that we determine the number of stages, the location of the feed to the column and the reflux ratio. Now let us first see what a stage is.

STAGE

Stage is a single device or a group of devices that brings separation of a mixture. Now let us see what happens in a stage. First the liquid and vapor are brought into intimate contact and then they are mechanically separated. They are mechanically separated because unless we separate them out we can not get a better product from the initial feed and this can be brought about as we learnt earlier by some tray or plate column or by a portion of packing. It should be noted here, that staged are effective in bringing amount about separation, but they do not represent any kind of physical entity. That is why they are named as stage, a plate is not a stage!

EQUILIBRIUM STAGE

An equilibrium stage is also called ideal or theoretical stage, and the name suggests that it gives maximum separation between the liquid and the vapor because the liquid and vapor are so intimately contacted for long enough time. So, that these two phases come to equilibrium and that will give the maximum possible separation under the given condition in the column which are pressure and temperature.

Here we find that the column is taken to be comprising of various stages. Earlier we found that the total column was given in terms of the trays or packing, but now we are putting the column in terms of stages. So, here we find the feed is going and the stages may be numbered from 1,2, …. Like that upto n and the condenser is there right above the first stage. To it, the reflux drum is connected from which reflux is coming and if the liquid is going, it is getting vaporised in the partial reboiler and the liquid is taken out as a product and the vapor is going back to the column. This is how, a distillation column has been reduced in terms of stages.

BINARY DISTILLATION COLUMN DESIGN

Now, we shall be concentrating on the binary distillation column design. There are various other methods for the multi component but we will limit our study to some binary column and this can still be used for multi component with some modifications. In designing this, also we have 2 types which are very common - McCabe-Thiele method and Ponchon-Savarit method. We shall be looking into the McCabe-Thiele method which is easier of the two. After doing this design, we shall get some approximate number of the equilibrium stages and the reflux required for the separation.

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Design of a distillation column in terms of stages
©️Hive account@splash-of-angs63 (Image drawn by me)

McCabe-Thiele method

The McCabe-Thiele method is based on the equilibrium composition diagram i.e., xy diagram for a vapor-liquid equilibrium. Now, there are some assumptions in this McCabe-Thiele method.

Assumptions of McCabe-Thiele Method-

The pressure in the column is taken to be constant
The molar latent heat of vaporization of the liquid and the vapor are taken to be constant. This is possible if all the components can be assumed to have the same and constant enthalphy of vaporization.
A constant liquid and vapor flow rates throughout each section (constant molar overflow).
We assume that there is not a significant sensible heat transfer
The total operation is adiabatic in nature i.e., there is no heat in leak or out leak from between the system and the surroundings.

RECTIFICATION SECTION

In the rectification section or enriching section, we number the stages from top to bottom as 1,2 upto n and this particular section comprises of the stage just above the feed stage. First we choose a particular control volume, which is where the condenser is included and some n^th number of stages. We put x₁, x₂ as mole fractions of liquid and y₁, y₂ as mole fractions of the vapor. In this case the subscript corresponds to the stage number from which the particular stream comes out.

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Rectification section
©️Hive account@splash-of-angs63 (Image drawn by me)

The liquid which is going into the column as reflux, it is taken to be coming out from a stage, which is zeroth. Zeroth does not exist physically, but as per nomenclature any stage that is above this first stage is take to be zero. So, we are giving x₀ as the mole fraction of the reflux liquid and we put x_d as the distillate composition. D is the flow rate of the distillate and V is the flow rate of the vapor.

CONCEPT OF REFLUX RATIO

Now from the overall mass balance i.e., the overall material balance, we have-

V = L + D

(Please note that all these balances are made at steady state.)

Then we put the component material balance with respect to the lighter component as,

Vy_n+1 = Lx_n + Dx_d

Then we define a reflux ratio R which is the ratio of the liquid reflux to the amount of distillate taken. So this is taken as, R = L/D
Now, this particular equation is correlating the composition of the two crossing stream. So the two stream y_n+1 and x_n compositions are being related by a particular operating line. We can see that V is going inside the condenser and it is being split into 2 streams L and D.
Now, doing some rearrangements we get,

L/V = L/L+D = R/R+1 and D/V = D/L+D = 1/R+1

So, the equation of operating line is given as,

y_n+1 = (R/R+1)x_n + (1/R+1)x_d

Thus we find that the operating line of a rectification section is a straight line and it passes through (x_D, x_D). Since, for a given operation R is constant, so the slope is also constant. Hence, we can say it is a straight line and it will intersect at 45° line which means where x=y; so (x_D,x_D) will be there on a 45° line and has a slope of R/(R+1) and the y intercept is x_d/(R+1) which is obtain by putting x_n=0.

B I B LI O GR A PH Y

Distillation column designing by ACS

The theory of the distillation column

Design of distillation column control system

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