McCabe Thiele Part Two

1
McCabe Thiele Part Two
Today we will discuss 1) McCabe-Thiele graphical
construction 2) Determination of N and XB 3)
Minimum number of stages N 4) Minimum reflux 5)
Example 6) Subcooled Reflux 7) Multiple Feeds 8)
Side stream products 9) Open steam 10) Non-ideal
distillation Murphree efficiency
2
Construction Lines for McCabe-Thiele Method
y
Rectifying Section Operating line SlopeL/VR/(R
1)lt1
Equilibrium curve
q-line
yN
Stripping Section Operating line SlopeL/V(VB1
) /VB
yB
45 line
xD
xzF
xB
qgt1
q1
L
L
0ltqlt1
xy
LV
V
q0
V
qlt0
xzF
3
Construction for the McCabe-Thiele Method
1.
2.
equilibrium curve
equilibrium curve
Step 1 Plot equilibrium curve and 45 degree
line. Step 2 Plot given compositions (F, B, and
D) Step 3 Draw q-line from LF and VF Step 4
Determine Rmin from intersection of
the rectifying section OL and the equilibrium
curve. Step 5 Determine R from R/Rmin Step 6
Draw OL for Rectifying section Step 7 Draw OL
for Stripping section
45 line
y
y
45 line
xB
xD
xzF
x
7.
5. and 6.
4.
3.
equilibrium curve
equilibrium curve
equilibrium curve
equilibrium curve
y
y
y
y
xB
xD
xB
xD
xB
xD
xzF
xzF
xzF
xB
xD
xzF
R/(R1)
Rmin/(Rmin1)
4
Feed Location for the McCabe-Thiele Method
Equilibrium curve
Equilibrium curve
1
1
y
y
2
2
3
3
yN
yN
4
5
4
yB
yB
6
xB
xB
xzF
xD
xzF
xD
Feed stage located one tray too low.
Feed stage located one tray too high.
5
Optimum Feed Location for McCabe-Thiele
Equilibrium curve
1
y
2
yN
3
4
yB
xB
xD
xzF
Optimum feed stage location.
6
Determination of N and xB for McCabe-Thiele
Equilibrium curve
Construction Step 1 Plot equilibrium curve and
45 degree line. Step 2 Plot given compositions
(F, B, and D) Step 3 Draw q-line from LF and
VF Step 4 Determine Rmin from intersection of
the Rectifying section OL and the equilibrium
curve. Step 5 Determine R from R/Rmin Step 6
Draw OL for Rectifying section Step 7 Draw OL
for Stripping section
1
y
2
yN
3
Solution Step 1 From xD locate x1 and y1
drawing a horizontal line to the equilibrium
condition for stage 1. Step 2 Find y2 drawing a
vertical line to the rectifying OL locate the
mass balance condition between x1 and y2. Step 3
From y2 draw a horizontal line to the equilibrium
condition for stage 2 to locate x2. Step 4
Return to step 2 and cycle through steps 2 and 3
until xi ltzF. Draw subsequent vertical lines to
the stripping section OL. Step 5 End after
predetermined number of stages, or when xi is
less than xB.
4
yB
xB
xD
xzF
7
Minimum Number of Stages for McCabe-Thiele
Equilibrium curve
1
y
2
yN
3
4
yB
xB
xD
xzF
Although this is the minimum number of stages, no
product is produced (note the feed must thengo
to zero).
By returning all the exiting vapor as reflux and
all the exiting liquid as boilup the operating
lines have slope of one.
8
Minimum Reflux for McCabe-Thiele
Equilibrium curve
y
yN
yB
xB
xD
xzF
Although this is the minimum amount of reflux, it
takes infinite stages (note the pinch point
between the operating lines and equilibrium).
By returning no exiting vapor as reflux and no
exiting liquid as boilup the operating line
intersection is as far to the left as equilibrium
allows.
9
Minimum Reflux for Non-ideal McCabe-Thiele
Equilibrium curve
y
yN
yB
xB
xD
xzF
Although this is the minimum amount of reflux, it
takes infinite stages (note the pinch point
between the operating lines and equilibrium).
10
Example Determination of N and xB for
McCabe-Thiele
Given 100 Kmol/hr of a feed of 60 benzene and
40 heptane is to be separated by distillation.
The distillate is to be 90 benzene and The
bottoms 10 benzene. The feed enters the column
as 30mol vapor. Use R 1.5 times the minimum.
Assume a constant relative Volatility of ? of 4
and that the pressure is constant throughout the
column at 1atm.
Construction Step 1 Plot equilibrium curve and
45 degree line. The equilibrium curve is found
using
Step 2 Plot given compositions (F, B, and
D) Step 3 Draw q-line from LF and VF. Use
y
to find q. Then plot the q-line using
Step 4 Determine Rmin from intersection of
the rectifying section OL and the equilibrium
curve. This happens at a slope of about .25
x
11
Example Determination of N and xB for
McCabe-Thiele
Given 100 Kmol/hr of a feed of 60 benzene and
40 heptane is to be separated by distillation.
The distillate is to be 90 benzene and The
bottoms 10 benzene. The feed enters the column
as 30mol vapor. Use R 3 times the minimum.
Assume a constant relative Volatility of ? of 4
and that the pressure is constant throughout the
column at 1atm.
Construction Step 5 From Rmin0.333 and R3Rmin
we have R1 And the slope of rectifying section
OL is 0.5 Step 6 Draw the line with slope 0.5
which is the rectifying section OL. Step 7. Draw
the stripping section operating line from the
Bottoms composition to the intersection of the
rectifying section OL and the q-line.
Solution Step 1 From xD locate x1 and y1
drawing a horizontal line to the equilibrium
condition for stage 1. Step 2 Find y2 drawing a
vertical line to the rectifying OL locate the
mass balance condition between x1 and y2. Step 3
From y2 draw a horizontal line to the equilibrium
condition for stage 2 to locate x2. Step 4
Return to step 2 and cycle through steps 2 and 3
until xi ltzF.
y
Results Feed at stage between 2 and 3. 5 stages
(minimum stages 3.2) xB0.05 benzene
x
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Example Determination of N and xB for
McCabe-Thiele
Given 100 Kmol/hr of a feed of 60 benzene and
40 heptane is to be separated by distillation.
The distillate is to be 90 benzene and The
bottoms 10 benzene. The feed enters the column
as 30mol vapor. Use R 3 times the minimum.
Assume a constant relative Volatility of ? of 4
and that the pressure is constant throughout the
column at 1atm.
Minimum number of stages is determined by
stepping off between the equilibrium curve and
the 45 degree line.The result is 3.2 stages.
y
x
13
McCabe-Thiele Method Subcooled Reflux
Distillation Column (subcooled reflux)
Total condenser
Overhead vapor
Reflux drum
Distillate
Reflux
Feed
Boilup
Partial reboiler
Bottoms
If the liquid reflux is colder than the
bubble-point temperature, then it will condense
some vapor in the top stage. This changes the
refluxratio to the internal reflux ratio.
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McCabe-Thiele Method Subcooled Reflux
The amount of extra reflux that is produced
depends onthe heat capacity of the liquid, and
the heat of vaporizationof the vapor.
Total condenser
Overhead vapor
Reflux drum
Distillate
Reflux
The total amount of reflux, called the internal
reflux isthe sum of the reflux ratio and the
vapor condensed bythe subcooled reflux
Feed
Boilup
Partial reboiler
Bottoms
H
P1
T
V
P2
Bubble point line
Pcr
V
L
L
T
Tm
Tb
XD(L)
X1(V)
0
XB
1
15
McCabe-Thiele Method Partial Condenser
Distillation Column (partial condenser)
Partial condenser
VaporDistillate
Overhead vapor
Reflux
Feed
Boilup
Partial reboiler
Bottoms
If the liquid reflux is obtained from a partial
condenser, then the reflux is produced as the
liquid in equilibrium with the vapor distillate
in the condenser.
16
McCabe-Thiele Method Partial Condenser
VaporDistillate
Partial condenser
The vapor distillate composition then
determinesthe yD and stages are stepped off from
the intersectionof yD and the equilibrium curve.
Overhead vapor
Reflux
Feed
Boilup
yD
Partial reboiler
Bottoms
Equilibrium curve
q-line
yN
45 line
yB
xzF
xB
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McCabe-Thiele Method Multiple Feeds
Distillation Column (multiple feeds)
Total condenser
Overhead vapor
Reflux drum
Distillate
Reflux
Feed 1
Feed 2
Boilup
Partial reboiler
Bottoms
The McCabe-Thiele method for cascades can be
applied to systems with more thantwo sections.
Here, we show a cascade with 2 feeds A 3 section
cascade.
How do you make the McCabe-Thiele graphical
construction for such a cascade?
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McCabe-Thiele Method Multiple Feeds
First, note that each feed stream changes the
slope of the operating line from section to
section.
The feed stream changes the flow rates in the
stages above and below it. Consequently, it
changes the mass balances and the slopes of the
operating lines.
Distillate
Distillate
Reflux
Reflux
Feed 1
Feed 1
Feed 2
Feed 2
Boilup
Boilup
Bottoms
Bottoms
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McCabe-Thiele Method Multiple Feeds
Total condenser
The flow rates above Feed 1 are constant due to
constant molar overflow (CMO). The feed changes
the slope depending on the feed condition. Flow
rates in the intermediate section are
constant, but change when Feed 2 is introduced.
Overhead vapor
Reflux drum
Distillate
Reflux
Feed 1
Feed 2
Boilup
Partial reboiler
y
Bottoms
Rectifying Section Operating Line Constant
Slope (CMO)
Equilibrium curve
Feed 1 introduced
yN
Intermediate section Operating Line Constant
Slope (CMO)
Feed 2 introduced
yB
Stripping Section Operating Line Constant Slope
(CMO)
xB
xD
20
McCabe-Thiele Method Multiple Feeds
qgt1
Example Feed 1 a saturated vapor of composition
zF1, and Feed 2 a saturated liquid of composition
zF2
q1
L
L
0ltqlt1
xy
LV
V
q0
V
qlt0
xzF
y
Saturated vapor
Rectifying Section Operating line SlopeL/VR/(R
1)lt1
Equilibrium curve
yN
Intermediate section Operating line SlopeL/V
yB
Saturated liquid
Stripping Section Operating line SlopeL/V(VB1
) /VB
xB
xzF2
xzF1
xD
21
McCabe-Thiele Method Side Stream
Occasionally a cascade is configured such that
anintermediate side stream of intermediate
compositionis removed from the column.
Distillate
Reflux
How do we analyze this configuration?
Ls
Use the multiple mass balance envelopes
andassume a constant molar overflow condition.
Feed
Boilup
If we perform a material balance in the light key
around the stages above the side
stream including the condenser
Bottoms
Distillate
Which we can rearrange to find
Reflux
Ls
Feed
For L and V constant from stage to stage, then
Boilup
Bottoms
Operating line above side stream
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McCabe-Thiele Method Side Stream
If we perform a material balance in the light key
around the stages above the side
stream including the side stream and condenser
Distillate
Reflux
Ls
Which we can rearrange to find
Feed
Boilup
Bottoms
For L and V constant from stage to stage, then
Operating line below side stream
The two operating lines intersect at
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McCabe-Thiele Method Side Stream
Side Stream Liquid withdrawn
y
Rectifying Section Operating line SlopeL/VR/(R
1)lt1
Equilibrium curve
yN
Intermediate section Operating line SlopeL/V
Saturated liquid feed
yB
Stripping Section Operating line SlopeL/V(VB1
) /VB
Total condenser
Distillation
xB
xxs
xD
xzF
Overhead vapor
Reflux drum
1
Distillate
Reflux
Rectifying section stages
2
Side Stream xs
Feed
Boilup
N
Stripping section stages
Partial reboiler
Bottoms
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McCabe-Thiele Method Open Steam
Total condenser
Consider the cascade shown on the left In this
example, the reboiler is replaced by asource of
hot steam or an inert gas. In this case,the
vapor entering the bottom stage of the columnhas
no light key and so yB is zero, although xB is
non-zero.
Distillation
Overhead vapor
1
Distillate
Reflux
Rectifying section stages
2
Feed Stage
Feed
N
Stripping section stages
Steam or inert hot gas (y0)
Bottoms
Does the slope of the rectifying section
operating line increase or decrease?
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McCabe-Thiele Method Open Steam
y
Rectifying Section Operating line SlopeL/VR/(R
1)lt1
Equilibrium curve
yN
Saturated liquid feed
Stripping Section Operating line SlopeL/V
yB
Total condenser
Distillation
Overhead vapor
Reflux drum
xB
xD
xzF
1
Distillate
Reflux
Rectifying section stages
2
Feed
Feed Stage
N
Stripping section stages
Steam or inert hot gas (y0)
Bottoms
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Non-equilibrium McCabe-Thiele Murphree Efficiency
Equilibrium curve
Actual separation attained
The Murphree Plate Efficiency gives the ratio of
the actual composition difference between two
sequential plates, and that predicted by
equilibrium.
E
A
B
y
For the vapor efficiency
2
yN
3
E
For the liquid efficiency
4
yB
A
B
xB
xD
xzF
Component distribution obtained less than
theoretical limit described by equilibrium
27
McCabe-Thiele Algebraic Method
We have already developed the McCabe-Thiele
Graphical Method for cascades. The same
equations we used for the operating lines,
q-line, and equilibrium curve can be used to
solvefor the compositions in each stage
algebraically.
Equilibrium curve
y
yN
Rectifying Section Operating line SlopeL/VR/(R
1)lt1
Stripping Section Operating line SlopeL/V(VB1
) /VB
yB
45 line
q-line
xzF
xB
xD
28
McCabe-Thiele Minimum Reflux
To carry out the algebraic method we need to
determine the slopes of the operating
linesalgebraically. This can be done finding the
intersections between the q-line and
equilibrium curve, and the q-line and the
rectifying section operating line.
yD
y
yB
45 line
xzF
xB
xD
29
McCabe-Thiele Rectifying Section Operating Line
The slope of the operating line for the
rectifying section with minimum reflux can be
determinedfrom the rise over run. We can then
also find the minimum reflux from this slope.
y
yD
yq
45 line
From the minimum reflux, and R/Rmin we can
determine the reflux R.
yB
We determine the slope of the rectifying
sectionoperating line from
xzF
xB
xq
xD
30
McCabe-Thiele Rectifying Section Operating Line
We can find the intersection of the operating
line and the q-line to determine the
strippingsection operating line
y
yD
yQR
45 line
From the minimum reflux, and R/Rmin we can
determine the reflux R.
We determine the slope of the stripping
sectionoperating line from
yB
xzF
xB
xD
xQR
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McCabe-Thiele Algebraic Method
Equilibrium curve
1. In total condenser y1x0
2. x1 is determined from the equilibrium curve
1
y
2
3. y2 is determined from operating line forthe
rectifying section
yN
3
4. Repeat steps 2 and 3 until xn is less thanxQR
(you are on a point of the equilibriumcurve to
the left of the intersection of the OLand the
q-line).
4
yB
5. y3 is determined from operating line forthe
stripping section
xD
xB
xQR
xzF
6. x3 is determined from the equilibrium curve
7. Repeat steps 5 and 6 until xn is less than xB
32
McCabe-Thiele Algebraic Method Examples
Equilibrium curve
xD0.9, xB0.1, zF0.5, q0.8
1. Alpha 4, RRmin 2. Alpha4 R2Rmin 3.
Alpha4 R4Rmin 4. Alpha4 R20Rmin 5. Alpha1.1
R3Rmin
1
y
2
yN
3
4
yB
xD
xB
xQR
xzF