1. McCabe Thiele Graphical Equilibrium-Stage
Limiting condition
a) Minimum number of plates:
If the reflux ratio ( ) is increased to very large value, the operating lines become the 45o line. The infinite reflux ratio occurs in real life when the column is operated under what are called (total reflux) condition
Under these conditions, no feed is added to the column (F=0) and no products are withdrawn (D=0, B=0), but the vapor is boil up and condensed to the column. So the column is just circulating vapor and liquid up and down. Most columns are started up under total reflux conditions.
ChE 334: Separation Processes
Dr Saad Al-Shahrani

2. Distillation of Binary Mixture
Since the liquid flow rate in the column is same as the vapor flow rate, and
The operating line ,
The composition in the base of the column under total reflux = xB, and the composition of the liquid in the reflux drum = xD
In this case the number of ideal plates is minimum.
ChE 334: Separation Processes
Dr Saad Al-Shahrani

3. Operating lines as total reflux
Binary Multistage Distillation
The minimum number of ideal plates can be done by:
a) Graphically as shown in the figure
Composition of liquid
in reflux drum y1
Minimum number of plates = 3+reboiler y2
y1 = xD
y2 = x1
y3 = x2
y4 = x3
xB = xB y X1
Operating lines as total reflux y3 X2 y4 XB X3
Composition of liquid
in re-boiler XD XB XF x
ChE 334: Separation Processes
Dr Saad Al-Shahrani

4. Binary Multistage Distillation
b) Analytically (using Fenske Equation)
This equation gives the number of plates required under total reflux at constant .
It is applicable to multi-component system as well as binary system (= constant, total reflux, ideal system).
It is very useful for getting quick estimates of the size of a column.
Derivation of Fenske Equation
Consider two component (A,B) forming ideal solution
(1)
ChE 334: Separation Processes
Dr Saad Al-Shahrani

5. Binary Multistage Distillation
An ideal mixture follows Raoult’s law and  = vapor product ratio
does not change much over the range of temperature encountered,AB  constant
(2)
ChE 334: Separation Processes
Dr Saad Al-Shahrani

6. Binary Multistage Distillation
Substitute (2) in (1)
For plate n+1
zero
Since D = 0 (total reflux), L / V= 1.0 ,
Then yn+1 = xn and
ChE 334: Separation Processes
Dr Saad Al-Shahrani

7. Binary Multistage Distillation
At the top of the column, if a total condenser is used y1 = xD , n = 0 y1
water
Substitute in (2) x0
= y1 xD x1 y2
For plate (1) x2 y3 y4 x3
= yn
yn-1
For plate (n) yn
xn-1
= yr
steam Vb yb yr
For re-boiler plate xn
Re-boiler
Lb, xb
ChE 334: Separation Processes
Dr Saad Al-Shahrani

8. Binary Multistage Distillation
If all equations are multiplied together and all the intermediate terms canceled,
ChE 334: Separation Processes
Dr Saad Al-Shahrani

9. McCabe Thiele Graphical Equilibrium-Stage
Example:
Calculate the minimum number of trays required to achieved a separate from 5 mole % bottoms to 90 moles % distillate in a binary column with =2.5
solution
xB = , xD = 0.9
ChE 334: Separation Processes
Dr Saad Al-Shahrani

10. McCabe Thiele Graphical Equilibrium-Stage
Example: in a mixture to be fed to a continuous distillation column, the mole fraction of phenol is 0.35, of o-cresol 0.15, of m-cresol 0.3 and of xylenes 0.2. it is hoped to obtain a product with a mole fraction of phenol 0.952, of o-cresol , of m-cresol if p-o= 1.26, m-o=0.7, estimate how many theoretical plates would be required at total reflux.
Solution:
A  light component (o-cresol)
B  heavy component (m-cresol)
Total balance =D + B
= zero
For phenol *0.35=D*0.952+B*xB,p
D= 36.8 Kmol, B = 63.2 Kmol
For o – cresol *0.15=0.0474*36.8+xB,o*63.2
xB,o=0.21
ChE 334: Separation Processes
Dr Saad Al-Shahrani

11. McCabe Thiele Graphical Equilibrium-Stage
For m – cresol *0.3=0.0006*36.8+xB,m*63.2
xB,X=0.316
xB,m=0.474
component
Feed
top
Bottms 
phenol
0.35
0.952
p-o= 1.26
o-cresol
0.15
0.0474
0.21
oo-o= 1.0
m-cresol
0.3
0.0006
0.474
m-o=0.7
xylenes
0.2
0.316
o-m= 1/0.7=1.43
ChE 334: Separation Processes
Dr Saad Al-Shahrani

12. McCabe Thiele Graphical Equilibrium-Stage
b) Minimum Reflux Ratio
The next figure shows how changing the reflux ratio affects the operating lines: the lower the reflux ratio, the closer the operating line moves toward the equilibrium curve, and the larger the number of plates.
If the reflux ratio finally reduced to the point where either operating line intersects or becomes tangent to the VLE curve, an infinite number of plates will be required and the reflux ratio is minimum.
ChE 334: Separation Processes
Dr Saad Al-Shahrani

13. McCabe Thiele Graphical Equilibrium-Stage
To obtain the RDmin xD
(xD,xD) y y` a or b x` xD x
ChE 334: Separation Processes
Dr Saad Al-Shahrani

14. McCabe Thiele Graphical Equilibrium-Stage
If the equilibrium curve has a cavity upward, e.g., the curve for water-ethanol shown in the figure in this case the minimum reflux ratio must be computed from the slope of the operating line (ac) that is tangent to the equilibrium a b y`
Feed line
Non-ideal
Line VLE c x`
ChE 334: Separation Processes
Dr Saad Al-Shahrani

15. McCabe Thiele Graphical Equilibrium-Stage
Examole. A continuous fractionating column is to be design to separate 30.W Ib/h of a mixture of 40 percent benzene and 60 percent toluene into an overhead product containing 97 percent benzene and a bottom product containing 98 percent toluene. These percentages are by weight. A reflux ratio of 3.5 mol to 1 mol of product is to be used. The molal latent heats of benzene and toluene are 7,360 and 7,960 cal/ gmol, respectively. Benzene and toluene form an id91 system with a relative volatility of about 2.5; the equilibrium curve is shown in Fig The feed has a boiling point of 95 oC at a pressure of 1 atm. (a) Calculate the moles of overhead product and bottom product per hour. (b) Determine the number of deal plate and the position of the feed plate (i) if the feed is liquid and at its boiling point. ii)if the feed is liquid and at 20 oC (specific heat 0.44 cal/ g-oC) (iii) if the feed is a mixture of two-thirds and one-third liquid. (c) If steam at 20 Ib,/in2(1.36 atm) gauge is used for heating, how much steam is required per hour for each of the above three cases, neglecting heat losses and assuming the reflux is a saturated liquid? (d) If cooling water enters the condenser at 25°C and leaves at 40°C, how much cooling water a required, in gallons per minute?
ChE 334: Separation Processes
Dr Saad Al-Shahrani

16. 1 2 3 4
Feed line 5 6 7 8 . 9 10 R
xF=0.44
xB=0.0235
xD=0.974