Hunter and Nash Graphical Equilibrium Stage Method
​Authors: Housam Binous and Ahmed Bellagi

We compute the number of equilibrium stages using the Hunter and Nash graphical method and the McCabe and Thiele diagram of a liquid liquid extraction problem. One feed of acetic acid (35 wt %) in water which flow rate = 1000 kg/hr is extracted using a solvent consisting of pure isopropyl ether which flow rate = 1475 kg/h . The exiting raffinate stream specification is 10 wt % acetic acid .
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Reference:
H. Binous, Equilibrium Staged Separations using Matlab® and Mathematica®, Chemical Engineering Education, 42(2), pp. 69-73, 2008.
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Liquid Liquid Equilibrium of ternary system Isopropyl ether-water-Acetic Acid.
Component 1 = water
Component 2= Acetic Acid
Component 3=Isopropyl ether
In[]:=
tbl1={{98.1,0.69},{97.1,1.41},{95.5,2.89},{91.7,6.42},{84.4,13.30},{71.1,25.50},{58.9,36.70},{45.1,44.30},{37.1,46.40}};
In[]:=
tbl2={{0.5,0.18},{0.7,0.37},{0.8,0.79},{1.0,1.93},{1.9,4.82},{3.9,11.40},{6.9,21.60},{10.8,31.10},{15.1,36.20}};
In[]:=
plt1=ListPlot[tbl1,JoinedTrue,PlotStyleRGBColor[1,0,0],AspectRatio->1]
Out[]=
40
50
60
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10
20
30
40
In[]:=
plt2=ListPlot[tbl2,JoinedTrue,PlotStyleRGBColor[0,0,1],AspectRatio->1]
Out[]=
2
4
6
8
10
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14
5
10
15
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30
35
In[]:=
Show[plt1,plt2,PlotRange{{0,100},{0,100}},EpilogLine[{{100,0},{0,100}}],AxesOrigin->{0,0}]
Out[]=
20
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60
80
100
20
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100
In[]:=
rafnt=Evaluate[Interpolation[tbl1,InterpolationOrder1]]
Out[]=
InterpolatingFunction
Domain: {{37.1,98.1}}
Output: scalar

In[]:=
rafnt[90]
Out[]=
8.02219
In[]:=
Extrc=Evaluate[Interpolation[tbl2,InterpolationOrder1]]
Out[]=
InterpolatingFunction
Domain: {{0.5,15.1}}
Output: scalar

In[]:=
plt3=Plot[rafnt[x],{x,37.1,98.1},PlotRange{0,100},PlotStyleRGBColor[1,0,0],AspectRatio->1]
Out[]=
40
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100
In[]:=
plt4=Plot[Extrc[x],{x,0.5,15.1},PlotRange{0,100},PlotStyleRGBColor[0,0,1],AspectRatio->1]
Out[]=
0
2
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100
In[]:=
Show[plt3,plt4,PlotRange{{0,100},{0,100}},EpilogLine[{{100,0},{0,100}}],AspectRatio->1,AxesOrigin->{0,0}]
Out[]=
0
20
40
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100
20
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100
Using interpolation to get tie lines
In[]:=
tbl3={{0.5,98.1},{0.7,97.1},{0.8,95.5},{1.0,91.7},{1.9,84.4},{3.9,71.1},{6.9,58.9},{10.8,45.1},{15.1,37.1}};
Feed and Solvent
Mixing Point
Raffinate Product is such that acetic acid wt % is 10
Extract Product
Operating Point
Plotting Feed, Solvent, Extract, Raffinate and Operating Point
Stepping off Stages
Plotting the Hunter and Nash Diagram. 5.35 equilibrium stages are needed to achieve the raffinate product requirement of 10 wt % acetic acid composition.
Checking our results
Relationship between McCabe-Thiele and Triangular Diagrams
Equilibrium Curve
Curved Operating Line
From the McCabe and Thiele Diagram, we conclude that 5.35 equilibrium stages are needed.