Building a McCabe-Thiele Diagram.

This chapter describes how to build a McCabe-Thiele diagram showing how many stages are required to achieve our separation defined by:

• feed is 0.8009 mol fraction benzene
• top product must be 0.9997 mol fraction benzene
• process 170 kg mol/hr of feed

and in addition:

• produce a bottom product that is 5 mol per cent benzene
• utilize a feed stream that is a saturated liquid
• operates at a reflux ratio that is 20% higher than the minimum
• operates at a pressure close to atmospheric

We will set up a new data file for just benzene and toluene. The following execution of start403a does this:

Give the name to be used for your
 data file.  No more than 16 characters.
bt1
The output file is called:bt1
Give the number of compounds:
2
 
 
If you want to see names, formulae or headings used in
the 301 data base, execute the FORTRAN program:
       shownoh.
Give the name for compound #  1 
benzene
Give the name for compound #  2
toluene
Give the number of reactions to set or 0 to skip.
0
 
If you want to set plug flow reactor parms, reply:y
 

Next we create the outline of our McCabe-Thiele diagram:

>>start403b
 
Copyright 1996 Rice University
All rights reserved
 
If you have not run the FORTRAN program start403a to
produce a data file, do so now.
   <-- Specifying bt1 as the file
 
How many streams will there be?3
 
Here are your compounds' names:
 benzene
 toluene
 

Choosing 110 kPa as our operating pressure, we find:

>>help mcbt
 
  mcbt - McCabe-Thiele Diagram for compounds in data file
  function mcbt(p,n)
  p is the total pressure in kPa
  n is one minus the number of points on the curve.
  Example:
     start301a and start301b
     specify two compounds as toluene and benzene
     mcbt(200,25)
 
>>mcbt(110,25)
 

Next we find the minimum reflux ratio:

>>help rmin
 
  Rmin - minimum reflux ratio calculation
  function R=rmin(p,q,xf,xd)
  Binary system min R=L/D
  p is the pressure in kPa
  q is the quality of the feed: 0 for sat liq., 1 for sat 
vap.
  xf is the feed mol frac of the 1st comp.
  xd if the mol fraction of the 1st comp. in the distillate.
>>Rmn=rmin(110,0,0.8009,0.9997)
 
Rmn =
    0.8207
 

Then we find the points on the operating lines for a reflux ratio 20% higher than the minimum:

>>help oplines
 
  Oplines - Calculate vectors for plotting operating lines.
  function 
[LoV,DxDoV,LpoVp,BxboVp,xo,yo]=oplines(R,q,xf,xd,xb)
  Binary Ideal Distillation
  R is the reflux ratio: L/D
  q is the fraction vapor in the feed
  xf, xd, xb are the mol fractions of the 1st compound
      in the feed, distillate & bottoms.
  LoV = L/V
  DxDoV = D*xd/V
  Top op line: y=LoV*x+DxDoV
  LpoVp = Lp/Vp
  BxboVp = B*xb/Vp
  Bottom op line = y=LpoVp*x-BxboVp
  xo and yo vectors to plot for operating lines.
>>[LoV,DxDoV,LpoVp,BxboVp,xo,yo]=oplines(1.2*Rmn,0,0.8009,0.9997,0.05);
 

We add the operating lines to our McCabe-Thiele plot:

>>hold
 
Current plot held
>>plot(xo,yo)
 

It is obvious that we will need a lot of stages in the top part of our column since the operating line and the equilibrium line almost coincide. Let's see how many stages will be required to achieve the separation.

>>[np,xs,ys]=ptop(1.2*Rmn,110,0,0.8009,0.9997,0.05,100);
>>np
np =
   34.5226
 

We can add the steps to our plot by:

>>plot(xs,ys)
 

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