An interactive introduction in distillation and separation processes

I studied process engineering and distillation were a big topic when I went to university (German Hochschule). The content is a combination of chemistry and physics. The definitions are a little bit confusing at the beginning but it's not hard to deal with when you spend some time with it.

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Many people don't know about this topic at all. It's not really famous and people prefer to talk about black holes and rocket science. I can't really blame them, it's not that interesting. I even didn't understand most of it when I passed the exam, other topics in studies were more interesting. But I gave it a second chance and here we are.

Many things can be visualised for better understanding. I use JavaScript for doing that. So please allow it for this site, you won't be dissapointed (If you see the plots than it's activated).

So, what is it about? All the topic builts up on the equilibrium of a mixture. This mixture can be water and ethanol, both liquid. If you heat it up, a gas mixture will arise, which is also a mixture of water and ethanol. Depending on the different boiling points, ethanol will occur in a bigger fractional part in the gas phase. This is how we seperate this chemicals from each other. It's called distillation.

The picture below shows a big distillation tower (or column) which contains many distillations behind each other. And it's an ongoing process with a constand feed going into it. This setup makes almost pure outputs possible. It's one part to create fuel out of raw oil.

Links to much better websites about this topic

Content

  1. Definitions
  2. Phase diagram
  3. Equilibrium Curve
  4. Relative Volatility
  5. Flash distillation
  6. Continuous distillation
  7. Summary

Definitions

A     = MVC = more volatile component in mol
B     = LVC = less volatile component in mol

A[L]  = MVC in liquid phase in mol
B[L]  = LVC in liquid phase in mol
A[V]  = MVC in vapour phase in mol
B[V]  = LVC in vapour phase in mol

x[A]  = A[L] / ( A[L] + B[L] )
x[B]  = B[L] / ( A[L] + B[L] )

y[A]  = A[V] / ( A[V] + B[V] )
y[B]  = B[V] / ( A[V] + B[V] )

x[A]  = 1 - x[B]
x[B]  = 1 - x[A]

We are not really interested in B. For our calculations, we need only x[A] and y[A]. So we just say x[A] = x and y[A] = y.

Phase diagram

Collected data of the equilibrium state of H2O and ethylene glycol from this YouTube video: Binary Phase. It's also a really good introduction how to read these diagrams.

Mole fraction MVC in Liquid (x) and Vapour (y).

T (°C)   x         y
69.5     1         1
76.1     0.77      0.998
78.9     0.69      0.997
83.1     0.6       0.99
89.6     0.46      0.98
103.1    0.27      0.94
118.4    0.15      0.87
128      0.1       0.78
134.7    0.07      0.7
145      0.03      0.53
160.7    0         0

Water is A, the more volatile component. Imagine a mixture of x=0.4 water mole fraction in liquid phase. At T=95 the liquid starts to boil and a small amount of vapour is arising with a mole fraction of water y=0.967.

If you keep heating up, you move on the x-line from right to left. The amount of vapour is increasing, but the y amount is decreasing (the vapour mix gets more ethylene glycol).

Equilibrium Curve (constant pressure)

We can create a x,y plot out of it if we use the temperature to find x and y and plot only these:

x      y
0      0
0.03   0.53
0.07   0.7
0.1    0.78
0.15   0.87
0.27   0.94
0.46   0.98
0.6    0.99
0.69   0.997
0.77   0.998
1      1

Example: A liquid mixture of x1 = 0.2 is distillated two times.

Start values: x[0] = 0.2

First distillation (red): We heat the liquid till the x value reaches a concentration of x = 0.1. The vapour phase reaches a concentration of y=0.78.

Second distillation (blue): We cool down the vapour phase and repeating the process again. So x[1] will get y. x[1] = 0.78. It gets heated until x = 0.6. We get a new concentration of y = 0.99. Cooling down leads to x[2] = 0.99.

Reapeting this process gets less and less vapour phase, especially if you want a high purity.

You can use the diagonal to make the transission from y = 0.78 to x = 0.78 without searching for the value on the x - axis.

Relative Volatility

The x,y relationship can be described with one variable: α, the relative volatility. It's possible because we assume the liquid mixture is an ideal solution and the gas mixture has an ideal gas behaviour.

a = MVC
b = LVC


    (ya / xa)
α = --------
    (yb / xb)


x = xa
y = ya

      1                x
β = -----     y = ----------
      α           (1-β)*x+β

Separation is possible if α > 1. Separation gets easier when α is increasing. β is useful when we are searching for a function which fits to the points.

With a curve fitting algorithm and the x,y points from the table above I get β = 0.029 and α = 34.5.

The points and the calculated function fit well together. This table shows a section of a bigger table with values from separationprocesses.com:

The α = 34.5 which I calculated above is different to the α = 80 in the table. Because it happened at different pressures.

Here an interactive plot where you can see the relationship between the relative volatility α and the Equilibrium Curve.

α:

You can imagine, the seperation is much better if α ist larger. Separation gets more and more difficult if the Equilibrium Curve gets closer to the diagonal.

Flash distillation

A flash distillation is like a simple distillation but with a continuous feed flowing into the vaporizer.

                y[d]  V (mol)
F (mol) /----\  ---->
---->   |    |  
x[f]    \----/  ----> L (mol)
                x[b]

Material balance:

F * x[f] = V * y[d] + L * x[b]

with L = F-V

F * x[f] = V * y[d] + F * x[b] - V * x[b]
F * x[f] = V * ( y[d] - x[b] ) + F * x[b]

divided by F

x[f] = V/F * ( y[d] - x[b] ) + x[b]

with V/F = f

x[f] = f * y[d] - f * x[b] + x[b]
f * y[d] = x[f] + f * x[b] - x[b]

y[d] = x[f]  +  x[b] * (f-1)
       ----     ------------
         f           f

Equation of a Straight Line:

y[d] =    -(1-f) * x[b]  +  x[f]
           -----            ----
             f               f

y =    -(1-f) * x  +  x[f]
        -----         ----
          f            f

This formula is called operating line equation. These are just two functions and we are searching for the intersection point depending on given parameters.

For drawing the straight line:

P1( x[f] / (1-f), 0      )
P2( 0           , x[f]/f )
P3( x[f] / x[f] )

InputOutput
x[f]x[d]
f (V/F)x[b]

black line = Equilibrium Curve
red line = Operation line

If the MVC increases in the Feed, the vapur phase will be purer.
If f increases, the vapour phase will be less pure.

Continuous distillation (Distillation Column)

I'm showing here only how to use the given equations to find the solutions. Click on the links to get the derivation of each formula.

Head:

    Vaporizer
   /----------\
   |          |
/-----\  L    |
|     |  x[d] |
|     |<------->  D, x[d]
\-----/

R = L/D = Reflux Ratio

Rectifying Section Operating Line (ROL)

      R           1
y = ----- * x + -----  * x[D]
    (R+1)       (R+1)



Feed:

F * q     = liquid flow
F * (1-q) = vapour flow

Feed Section Operating Line (q-line)

      q           1
y = ----- * x + ----- * x[F]
    (q-1)       (1-q)



Bottom:

/----\   V'
|    |<---\
|    |    |
\----/    |
   |  L'  |
   \--------------> B, x[b]
        Heater

Stripping Section Operating Line (SOL)

       L'           B
y =  ------ * x + ------ * x[B]
     (L'-B)       (B-L')  

α Interception
Head R (L/D) Columns
x[D] Feed location
Feed q
x[F]
Bottom x[B]

I don't know if it would make sense to explain here what's exactly happening. ROL, Feed and SOL-line have to intercept in one point. Then you start to draw triangles down the lines until you reach x[B].

With the given values in the table you can count now how many columns the distillation tower needs and in which stage the feed has to enter.

The condenser and the heater are stages by themselves, so we don't have to count these triangles. Feed location happens at the transition point.

The solution is normally not perfect. The heater triangle has to hit the x[B] point exactly. Same with the feed input. But the concentration is often between two stages.

But it's a very first step to get a clue what is needed.

Summary

I know, it's not a good introduction. Books are so much better. And this topic relates on many rules in physics which you have to know before. I left out a lot of things.

If you found mistakes, have suggestions or questions just write me an E-Mail (look it up on my GitHub profile).

You can use the interactive programs and the content for free. It's under the MIT licence.

GitHub link to the files: github.com/ben165/distillation. Thanks for reading :)