Batch Distillation

1
Batch Distillation
In differential distillation a feed mixture (an
initial charge) of a given composition is placed
in a single stage separator (a still pot, retort
or flask) and heated to boiling. The vapor is
collected and condensed to a distillate. The
composition of the remaining liquid and the
distillate are functions of time. There may be
several reasons for running a batch process such
as this 1) Small capacity doesnt warrant
continuous operation 2) Separation is to be done
only occasionally 3) Separation is preparative to
produce a new product 4) Upstream operations are
batchwise or feedstocks vary with time or from
batch to batch 5) Feed materials are not
appropriate for a continuous flow system.
The Differential Distillation operation requires
a much simpler apparatus, but is complicated
because the process is now a function of time.
2
Batch Distillation
To analyze this process we must perform component
balances in the form of rates The rate of
depletion of the liquid is equal to the rate of
distillate output
The instantaneous rate of depletion of a
component in the liquid is given by
Change in the total amount of the liquid
Change in composition in the liquid
Change in total amount of that component in the
liquid
The instantaneous rate of the component leaving
in the distillate is
Conservation of species requires that these two
rates be equal to each other
3
Batch Distillation
Rate of depletion equals the component flow rate
in Distillate
Multiplying the above equation by dt gives
But we know that the rate of total liquid
depletion is equal to the flow rate of
distillate
Which then gives
Rearranging to use separation of variables gives
The distillate composition and liquid composition
are related through an equilibrium equation
(ykx). We can then integrate both sides
4
Batch Distillation
If the mixture is a binary and the relative
volatility constant we can substitute the
relationship
Into
and then integrate both sides to obtain
The average composition of the liquid and vapor
during the process is just
The average composition of the distillate is the
amount of light key vaporized dividedby the
amount of material vaporized.
5
Batch Distillation
Procedure Given an amount and composition of a
feed stock, the equilibrium data for the
liquid-vapor equilibrium, Rate D, and
pressure 1) Determine W using the W(x)
relationship derived above for x from x0 to xf
in increments. 2) Relate y to time by using
x as a function of time and 3) Relate W (and
thus x) to time using the rate D
t(W0-W)/D 4) Determine T as a function of t,
x and W by using the equilibrium data (which
relates T to y and x)
6
Batch Distillation
Example A batch still is loaded with 100 kmol
50 benzene in toluene with a relative volatility
2.41. The boilup rate is constant at 10
kmol/hr.
1) Determine W using the W(x) relationship
derived above for x from x0 to xf in
increments. 2) Relate y to time by using x
as a function of time and 3) Relate W (and
thus x) to time using the rate D
t(W0-W)/D 4) Determine T as a function of t,
x and W by using the equilibrium data (which
relates T to y and x)
7
Batch Rectification with Constant Reflux
In Batch Rectification a feed mixture (an initial
charge) of a given composition is placed in a
multistage separator (a rectifier column) and
heated. The vapor is collected and condensed to a
distillate some of which is returned as reflux.
The composition of the remaining liquid and the
distillate are functions of time.
Total condenser
Batch Distillation
1
Reflux
Distillate
2
QB
N
Composition xi(t) Distillate composition
y(t) Distillate flow D(t)
No boilup No reboiler No feed stream
Batch Rectification with constant reflux
operation requires a simpler apparatus than a
distillation column, but is complicated because
the process is now a function of time.
8
Batch Rectification with Constant Reflux
Total condenser
For Batch Distillation we integrated the equation
Batch Rectification
Reflux drum
1
Reflux
because the relationship between y and x was
simple. In this case y and x depends on the
equilibrium relationship, the number of trays,
and the ratio V/L and so the above equation
cannot be integrated analytically. It can be
analyzed graphically using a McCabe-Thiele
procedure.
Distillate
2
N
QB
y
xD0
Operating line at time 0 SlopeL/VR/(R1)lt1
Equilibrium curve
xD1
yN
Operating line at time 1 SlopeL/VR/(R1)lt1
yB
45 line
9
Batch Rectification with Constant Reflux
Total condenser
Batch Distillation of a two-stage column with R1
Batch Rectification
Reflux drum
y
xD0
1
Reflux
Operating line at time 0 SlopeL/VR/(R1)lt1
Distillate
2
Equilibrium curve
xD1
yN
QB
N
Operating line at time 1 SlopeL/VR/(R1)lt1
yB
45 line
x0
xD0
xW
xD
10
Batch Rectification with Constant Reflux
Example Batch Distillation with 3 stages, R1
is initially Charged with 100 kmol of 20mol
n-hexane in n-octane. How many moles of charge
must be distilled to produce an average
distillate of 70mol n-hexane? The boilup rate is
10kmol/hr.
1) We start by drawing a series of operating
lines. 2) We step off 3 stages on one of the
operating lines. This gives us a Xw. 3) We
determine From the the graph. 4) We
construct a table of Xw and 1/(Y-X)
andnumerically integrate 5) We set the
integral to ln (W0/W) and solve for W. 6) We use
To determine the average composition. This
compositionwill typically be higher or lower
than our target and we repeat the above steps for
a different XW
y
xD0
Equilibrium curve
xD1
yN
yB
45 line
x0
xD0
xW
xD