Graphical Methods for Analyzing Binary Distillation

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Graphical Methods for Analyzing Binary
Distillation
Last lecture We described a graphical method
for analyzing multistage separation systems which
involveddrawing operating lines and equilibrium
curves and stepping off stages. This approach is
equivalent to the algebraic method and group
methods. This approach is demonstrated
usingadsorption and stripping.
Todays lecture will focus on Extending these
types of analysis to multisection cascades. We
begin by describing a typical binary distillation
column. We then describe the process generally
and make important definitions. We perform mass
balances to get operating lines. We plot
equilibrium data to get an equilibrium curve.
We step of stages noting the cross-over between
sections.
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McCabe-Thiele Method for Trayed Towers
Absorption and stripping cascades are common
methods for separating vapor and liquid mixtures.
A more complete separation can be achieved by
combining these processes into a binary
distillation column.
Absorption
Stripping
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McCabe-Thiele Method for Trayed Towers

• The general countercurrent-flow, multistage,
  binary distillation column shown below consists
  of
• A column of N theoretical stages
• A total condenser to produce a reflux liquid to
  act as an absorbent and a liquid distillate
• A partial reboiler to produce boilup vapor to
  act as a stripping agent and a bottoms product
• An intermediate feed stage.
• This configuration allows one to achieve a sharp
  separation, except in cases where an azeotrope
  exists where one of the products will approach
  the azeotropic concentration.

The goal of distillation is to achieve a
distillate rich in the light key and a bottoms
rich in the heavy key.
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McCabe-Thiele Method for Trayed Towers
The feed contains a more volatile component (the
light key, LK) and a less volatile component (the
heavy key, HK). At the feed temperature and
pressure it may consist of a liquid, vapor or
mixture of vapor and liquid. The feed composition
is given by the light key mole fraction ZF. The
bottoms composition is given by the LK mole
fraction XB, whereas the distillate composition
is given by the LK mole fraction XD.
The difficulty in achieving the separation is
determined by the relative volatility, ?
between the LK1, and the HK2.
If the two components form an ideal solution then
Raoults Law applies and
The relative volatility is then just the ratio
of the vapor pressures
As T increases, ? decreases until at some point
it becomes equal to one and no separation is
possible.
Only a function of T
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McCabe-Thiele Method Equilibrium Curve
We can rewrite the relative volatility in terms
of the mole fractions of the light key in a
binary mixture as follows
For close boiling point components the
temperature, and thus ? will be nearly constant
in the column. Solving for the mole fraction of
the LK in the vapor gives
For components which do not have close boiling
points ? will vary depending on composition. The
equilibrium curve will appear similar to that of
fixed ?, but wont fit the equation above for
constant ?.
Increasing relative volatility
Equilibrium curve
y1
y1
45 line
45 line
x1
x1
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Specifications for the McCabe-Thiele Method
Specifications F Total Feed Rate zF mole
fraction composition of the feed P Column
operating pressure (assume uniform in
column) Phase condition of the feed
_at_P Vapor-liquid equilibrium curve for the
binary _at_P Type of overhead condenser (total or
partial) xD Mole fraction composition of the
distillate xB Mole fraction composition of the
bottoms R/Rmin Ratio of reflux to minimum
reflux Results D Distillate flow
rate B Bottoms flow rate Nmin Minimum number of
equilibrium stages Rmin Minimum reflux ratio,
Lmin/D R Reflux ratio, L/D VB Boilup ratio,
V/B N Number of equilibrium stages Optimal
feed- stage location Stage vapor and liquid
compositions
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McCabe-Thiele Method Column Mass Balance
A mass balance in the LK component around the
column gives
A total mass balance around the column gives
So we know that the mole fraction of the light
key of the feed is between that of the distillate
and bottoms
If D, F, are zF, specified, theneither xD or xB
can be specified.
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McCabe-Thiele Method Rectifying Section
The rectifying section extends from stage 1 to
the stage just above the feed stage. If we
perform a material balance in the light key
around the n stages of the rectifying section
including the condenser
Which we can rearrange to find
If L and V are constant in the column from stage
to stage, then this is a straight line.
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McCabe-Thiele Method Constant Molar Overflow

• If L and V are constant, then this is a straight
  line. This requires that
• The two components have equal and constant
  enthalpies of vaporization
• The heat capacity changes are negligible compared
  to the heat of vaporization
• The column is well insulated so heat loss is
  negligible
• The pressure in the column is uniform
• These conditions lead to the condition of
  constant molar overflow.

For this condition the amount of vapor
transferred to the liquid stream in each stage is
equal to the amount of liquid transferred to the
vapor stream. Thus the liquid and vapor stream
flow rates are constant in the entire section.
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McCabe-Thiele Method Rectifying Section
Operating Line
In the case of constant molar overflow we can
then drop the stage subscripts
We define this equation as the operating line of
the rectifying section.
The liquid entering stage one is the reflux L and
its ratio to the distillate L/D is the reflux
ratio R. If we have constant molar overflow, then
R is a constant and
and
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McCabe-Thiele Method Operating Line
We can then rewrite
as
If R and XD are specified then we can graph the
line shown in the following plot.
y1
y2
Rectifying Section Operating line SlopeL/VR/(R1
)lt1
Equilibrium curve
y
45 line
x1
x0xD
x
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McCabe-Thiele Method Stripping Section
The stripping section extends from the stage just
below the feed stage to the bottom stage N. If
we perform a material balance in the light key
around the bottom stages of the rectifying
section including the condenser we have
Which we can rearrange and use the constant molar
overflow assumption to find
We define this equation as the operating line of
the stripping section.
Since
VB is called the boilup ratio.
Then
This is also the operating line of the
stripping section .
and
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McCabe-Thiele Method Stripping Section
L xm
V ym1
m1
Boilup
V, yB
If VB and XB are specified then we can graph this
as the line shown in the following plot.
N
Bottoms
L, xN
B, xB
Ym1
Equilibrium curve
y
yN
Stripping Section Operating Line SlopeL/V(VB1)/
VB
yB
45 line
xm
xN
xB
x
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Feed Stage Considerations
In determining the operating lines for the
rectifying and stripping sections we needed the
bottoms and distillate compositions and reflux
and reboil ratios. The compositions can be
independently specified, but R and VB are
related to the vapor to liquid ratio in the feed.
Partially Vaporized
Bubble Point Liquid
Subcooled Liquid
L
L
L
F
F
F
Dew Point Vapor
Superheated Vapor
L
L
F
F
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Feed Conditions
Consider the cases where the feed is not a
supercooled liquid or a superheated vapor
Mass balance around the reboiler
Mass balance around the condenser
Mass balance around the column
Vapor entering the rectifying section
Liquid entering the stripping section
Substitute this into the column balance
In other words, the vapor entering the rectifying
sectionis the vapor entering the condenser minus
the feed vapor flow rate.
Substitute in the reboiler balance
So except in the cases where the feed is a
supercooled liquid or superheated vapor the
boilup is related to the reflux by the material
balance
Dividing by B gives the boilup ratio
Distillation operations can be specified by the
reflux ratio or boilup ratio although the
reflux ratio (or R/Rmin) is most often specified.
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The q-line
First, we define the parameter q by
Subtracting the two operating lines
minus
Gives
Using a material balance in the LK
Using a material balance around the feed stage to
elminate vapor flow rates
Simplifying and using the definition of q results
in the q-line
The q-line has slope q/(q-1)and intercepts the
45 degreeline at yzF
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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
45 line
yB
xzF
xD
xB
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Feed Stage Location Using McCabe-Thiele
Equilibrium curve
Equilibrium curve
1
1
y
y
2
2
3
3
yN
yN
4
5
4
yB
yB
xB
xB
xD
xzF
xzF
xD
Feed stage located one tray too low.
Feed stage located one tray too high.
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Construction Lines for McCabe-Thiele Method
Equilibrium curve
1
y
2
yN
3
4
yB
xD
xB
xzF
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Summary
This lecture We extended the analsis used for
adsorption and stripping to binary distillation.
We described a typical binary distillation
configuration. We made definitions such as
reflux ratio, constant molar overflow, etc. We
described operating lines. We plotted the
equilibrium curve. We stepped through stages to
show the change in composition as you go
throughthe column.
Next lecture well continue our discussion of
binary distillation and the McCabe Thiele
method.