The notebook computes the number of equilibrium stages for a binary ideal mixture with relative volatility equal to 2.45 . The feed is a two phase mixture with a feed quality is equal to 0.85 . The distillate, feed and bottom mole fractions are 0.9, 0.5 and 0.1, respectively . The minimum reflux ratio and pinch point position are calculated . The reflux ratio is taken to be 1.5 times greater than the minimum reflux ratio . We draw the McCabe and Thiele Diagram and get the number of theoretical plates equal to 9. If we take the Murphree liquid efficiency equal to 0.5, 19 stages are need to meet the distillation column specifications .
Equilibrium curve for a constant relative volatility equal to 2.45
In[]:=
equilb=Function[With[{a=2.45},(a#/(1+(a-1)#))]]
Out[]=
With{a=2.45},
a#1
1+(a-1)#1
&
In[]:=
plt0=Plot[equilb[x],{x,0,1},PlotStyleRGBColor[1,0,0],​​Epilog{RGBColor[0,1,0],Line[{{0,0},{1,1}}]}]
Out[]=
0.2
0.4
0.6
0.8
1.0
0.2
0.4
0.6
0.8
1.0
Distillate, Bottom and Feed Compositions
In[]:=
xd=0.9;
In[]:=
xb=0.1;
In[]:=
zf=0.5;
Drawing Feed Line, determining of the pinch point and obtaining the Minimum Reflux Ratio. The feed is a two phase mixture with a feed quality is q=0.85.
In[]:=
feed=Function[With[{q=0.85},(q#/(q-1)-zf/(q-1))]]
Out[]=
With{q=0.85},
q#1
q-1
-
zf
q-1
&
In[]:=
pinch=FindRoot[feed[x]equilb[x],{x,0.5}]
Out[]=
{x0.467734}
In[]:=
xpinch=pinch[[1,2]]
Out[]=
0.467734
In[]:=
ypinch=feed[xpinch]
Out[]=
0.682838
In[]:=
plt1=Plot[feed[x],{x,xpinch,zf},PlotStyleRGBColor[0,0,1],PlotRange{{0,1},{0,1}}​​]
Out[]=
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
In[]:=
opertRect=Function[ypinch+(#-xpinch)/(xd-xpinch)(xd-ypinch)]
Out[]=
ypinch+
(#1-xpinch)(xd-ypinch)
xd-xpinch
&
In[]:=
opertRect[xd]
Out[]=
0.9
In[]:=
opertRect[xpinch]
Out[]=
0.682838
In[]:=
opertStrp=Function[ypinch+(#-xpinch)/(xb-xpinch)(xb-ypinch)]
Out[]=
ypinch+
(#1-xpinch)(xb-ypinch)
xb-xpinch
&
In[]:=
opertStrp[xpinch]
Out[]=
0.682838
In[]:=
opertStrp[xb]
Out[]=
0.1
In[]:=
plt2=Plot[opertRect[x],{x,xpinch,xd},PlotStyleRGBColor[0,1,1]]
Out[]=
0.5
0.6
0.7
0.8
0.9
0.70
0.75
0.80
0.85
0.90
In[]:=
plt3=Plot[opertStrp[x],{x,xb,xpinch},PlotStyleRGBColor[1,0,1]]
Out[]=
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.2
0.3
0.4
0.5
0.6
0.7
In[]:=
Show[plt0,plt1,plt2,plt3]
Out[]=
0.2
0.4
0.6
0.8
1.0
0.2
0.4
0.6
0.8
1.0
In[]:=
Rmin=(xd-ypinch)/(xd-xpinch)/(1-(xd-ypinch)/(xd-xpinch))//Simplify
Out[]=
1.00957
Real Relux Ration is 1.5 times larger than the minimum reflux ration
In[]:=
R=1.5Rmin
Out[]=
1.51435
Operating line of the rectifying section
In[]:=
OpRect=Function[R/(R+1)#+xd/(R+1)]
Out[]=
R#1
R+1
+
xd
R+1
&
Intersection Between Feed Line and Rectifying Operating Line
In[]:=
inters=FindRoot[feed[x]OpRect[x],{x,0.5}]
Out[]=
{x0.474623}
In[]:=
xinters=inters[[1,2]]
Out[]=
0.474623
In[]:=
yinters=OpRect[xinters]
Out[]=
0.643803
Drawing operating lines for rectfying and stripping sections
In[]:=
plt4=Plot[OpRect[x],{x,xinters,xd},PlotStyleRGBColor[0,1,1]]
Computing the number of equilibrium stages and Drawing the McCabe and Thiele Diagram. 9 stages are need for this distillation problem. Optimum feed stage location is fifth stage.
Taking into account the Murphree liquid efficiency=0.5.Computing the number of equilibrium stages and Drawing the McCabe and Thiele Diagram. Less than 19 stages are need for this distillation problem. Optimum feed stage location is stage number 9.

CITE THIS NOTEBOOK

McCabe-Thiele method for an ideal binary mixture​
by Housam Binous and Ahmed Bellagi
Wolfram Community, STAFF PICKS, April 13 2023
​https://community.wolfram.com/groups/-/m/t/2897388