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Dr Saad Al-ShahraniChE 334: Separation Processes
Limiting condition
D
LRD
McCabe Thiele Graphical Equilibrium-Stage
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
a) Minimum number of plates:
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no products are withdrawn (D=0, B=0), but the vapor is boil up and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.
Dr Saad Al-ShahraniChE 334: Separation Processes
Distillation of Binary Mixture
Since the liquid flow rate in the column is same as the vapor flow
rate, and 0.1V
L
V
L
The operating line
nD
nn xDL
Dxx
DL
Ly
1 m
Bmm x
BL
Bxx
BL
Ly
1,
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.
Dr Saad Al-ShahraniChE 334: Separation Processes
Binary Multistage Distillation
The minimum number of ideal plates can be done by:
a) Graphically as shown in the figure
y
XDXFXB
XB
x
y1
y2
y3
y4
X1
X2
X3
Operating lines as total reflux
Composition of liquid
in reflux drum
Composition of liquid
in re-boiler
y1 = xD
y2 = x1
y3 = x2
y4 = x3
xB = xB
Minimum number of plates = 3+reboiler
Dr Saad Al-ShahraniChE 334: Separation Processes
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
product bottomin ration mole
product in top ratio mole
/
/
/
/
BA
BA
BB
AA
B
AAB xx
yy
xy
xy
K
K (1)
Dr Saad Al-ShahraniChE 334: Separation Processes
An ideal mixture follows Raoult’s law and = vapor product ratio
Binary Multistage Distillation
P
xP
P
PxPP A
satAA
AsatAA Ay
P
xP
P
PxPP B
satBB
BsatBB By
satB
satA
BBsatB
AAsatA
BB
AA
B
AAB P
P
PxxP
PxxP
xy
xy
K
K
/
/
/
/
satB
satA PP / does not change much over the range of temperature
encountered,AB constant
1
, 1 A
A
B
A
A
A
B
A
x
x
x
x
y
y
y
y
(2)
Dr Saad Al-ShahraniChE 334: Separation Processes
Binary Multistage Distillation
Substitute (2) in (1)
1
1
1
1
1
1
n
nAB
n
n
x
x
y
y
ABA
A
A
A
A
AAB x
x
y
y
y
y
11 ,
1
DL
Dxx
DL
Ly D
nn
1
For plate n+1
Since D = 0 (total reflux), L / V= 1.0 ,
Then yn+1 = xn and 1
1
1
1
n
nAB
n
n
x
x
x
x
zero
Dr Saad Al-ShahraniChE 334: Separation Processes
Binary Multistage Distillation
At the top of the column, if a total condenser is used y1 = xD , n = 0
Substitute in (2)
1
1
1
1 x
x
x
xAB
D
D
= y 1
For plate (1) xD
y1 water
Re-boiler
Vb
yb
Lb, xb
steam
x1
x2
x3
xn
xn-1
x0
y2
y3
y4
yn-1
yn
yrB
BAB
n
n
x
x
x
x
1
1
= y r
For plate (n)
. . . .
. . . .
. . . .
n
nAB
n
n
x
x
x
x
1
1 1
1 = y n
For re-boiler plate
Dr Saad Al-ShahraniChE 334: Separation Processes
Binary Multistage Distillation
If all equations are multiplied together and all the intermediate terms canceled,
B
BnAB
D
D
x
x
x
x
1) (
1
B
BNAB
D
D
x
x
x
x
1) (
11min
AB
BBDD xxxxN
ln
)]1//()1/ln[(1min
AB
BBADBA
AB
BD xxxxN
ln
)//()/ln(
ln
])ration mole/()ration moleln[(1or min
)1
/()1
() (B
B
D
DnAB x
x
x
x
Dr Saad Al-ShahraniChE 334: Separation Processes
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
solutionxB = 0.05 , xD = 0.9
61.419163.0
14.5 ,
5.2ln
)]05.01/05.0/()9.01/9.0ln[(1 minmin
NN
AB
BBDD xxxxN
ln
)]1//()1/ln[(1min
Dr Saad Al-ShahraniChE 334: Separation Processes
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 0.0474, of m-cresol 0.0.0006. 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 100=D + B
For phenol 100*0.35=D*0.952+B*xB,p
= zero
D= 36.8 Kmol, B = 63.2 Kmol
For o – cresol
100*0.15=0.0474*36.8+xB,o*63.2 xB,o=0.21
Dr Saad Al-ShahraniChE 334: Separation Processes
McCabe Thiele Graphical Equilibrium-Stage
o-m= 1/0.7=1.43 43.1ln
)]474.0/21.0/()0006.0/0474.0ln[(1min N 5.13min N
component Feed top Bottms
phenol 0.35 0.952 0 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 0.316
For m – cresol
100*0.3=0.0006*36.8+xB,m*63.2 xB,m=0.474 xB,X=0.316
Dr Saad Al-ShahraniChE 334: Separation Processes
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.
Dr Saad Al-ShahraniChE 334: Separation Processes
To obtain the RDmin
McCabe Thiele Graphical Equilibrium-Stage
111
D
Dn
D
Dn R
xx
R
Ry
xx
yx
R
R
D
D
D
D
1min
min
xy
yxR DD
min
or1
intercept abmin
D
D
R
x
y`
1min D
D
R
x
x
a
bx`
(xD,xD)
y
xD
xD
Dr Saad Al-ShahraniChE 334: Separation Processes
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
xy
yxR DD
min
x`
1min D
D
R
x
a
b
y`
Feed lineNon-ideal Line VLE
cy`
Dr Saad Al-ShahraniChE 334: Separation Processes
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. 18-16. 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?
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x
y
.
Feed line
21
3
4
5
6
7
8
9
10R
xD=0.974xB=0.0235
1D
D
R
x
xF=0.44