MultiStage Counter Current Operation Numerical

Mass Transfer Assignment

1. Single Stage and Multistage
Adsorption

2. Problem

3. The equilibrium data, when plotted on logarithmic coordinates, provide a
straight line, so that the Freundlich equation applies. The slope of the line
1/n is 1.66. Since at X=663, Y* = 4.3 at above table,
The Freundlich equation can be stated as
The equilibrium data can also be plotted on arithmetic coordinates.

4. y = 1.6886x -4.1325
R² = 0.9992
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
2 2.2 2.4 2.6 2.8 3 3.2 3.4
log Y
log X
X Ylog Xlog Y
223 0.72.348305-0.1549
395 1.72.5965970.230449
663 4.32.8215140.633468
825 6.32.9164540.799341
1000 8.6 30.934498
According to the book, slope = 1/n = 1.66.

5. Equilibrium Data

6. Single Stage Case
L
s= Total amount of liquid (solvent)
Y
0 =Initial amount of solute /kg of liquid solvent
Y
1 = Final amount of solute/ kg of liquid solvent
S
s= Total amount of solid adsorbent
X
1 = Amount of solute /kg of adsorbent
X
0= Initial Amount of solute /kg of adsorbent

7. Single Stage Operation
Alternatively, using Freundlich Equation, Y=K X
1/n
It follows that, X= (Y/K)
n

X
1=(Y
1/K)
n
, and so on. Here,
Since slope (1/n) = 1.66, n = 1/1.66

8. Two Stage Crosscurrent Operation

9. Chart
Y2/Y0 = 0.10, Slope 1/n = 1.66 gives Y1/Y0 =0.344 fraction of 1. ).
1/n

10. 1/n =1.66, n= 1/1.66
Two Stage Crosscurrent Operation
Since slope (1/n) = 1.66, n = 1/1.66

11. Theory
L
s= Total amount of liquid (solvent)
Y
0 =Initial amount of solute /kg of liquid solvent
Y
1 = Amount of solute/ kg of liquid solvent after 1
st
stage
Y
2 = Amount of solute/ kg of liquid solvent after 2
nd
stage
S
s1= Amount of solid adsorbent after first stage
S
s2= Amount of solid adsorbent after second stage
X
0 = initial amount of solute /kg of adsorbent initially
X
1 = Amount of solute /kg of adsorbent after first stage
X
2 = Amount of solute /kg of adsorbent after second stage

12. Two Stage Countercurrent Operation
Here, X
Np+1= X
0
Since slope (1/n) = 1.66, n = 1/1.66
See the chart in next slide.

13. Chart
1/n
Y
2/Y
0= 0.1
Slope, 1/n = 1.66
Y
2/Y
1=0.217

14. Theory
L
s= Total amount of liquid (solvent)
Y
0 =Initial amount of solute /kg of liquid solvent
Y
1 = Amount of solute/ kg of liquid solvent after 1
st
stage
Y
2 = Amount of solute/ kg of liquid solvent after 2
nd
stage
S
s= Amount of solid adsorbent
X
0 = Initial amount of solute /kg of adsorbent
X
1 = Amount of solute /kg of adsorbent after 1
st
stage
X
2 = Amount of solute /kg of adsorbent after 2
nd
stage

15. Multistage Countercurrent

16. Counting the stages of operations