We have studied standard distillation columns where the feed
tray is located within the middle of the column.
The feed tray may instead be located at the very top or
bottom of the column to create either an
enrichment/rectification
column or a
stripping
column.
These configurations can be extremely useful if the
feed-conditions or operating-modes are favourable.
A typical multistage distillation column.
Enrichment columns
have the feed tray located at the bottom of the column.
This allows a low-concentration volatile component to be
extracted at high purity from the feed stream.
This design is also key to the understanding of
multi-stage batch distillation, as the large
reboiler/still volume allows it to be approximated as an
enrichment column with a slowly-varying bottoms
concentration.
A enrichment distillation column with reboiler.
Enrichment columns
may also be designed without a reboiler if the feed stream
partially/fully vapourises on entry to the column.
This is an efficient (but rare) configuration if the feed
stream is to be condensed anyway as part of the overall
plant design.
However, the reflux ratio is no-longer an adjustable
parameter but is set by the ratio of the two product
flow-rates, $R=W/D.$
The design of enrichment columns is relatively
straightforward, requiring only the enrichment
operating line equation.
\begin{align*} y_n &= x_{n+1}\frac{R}{R+1} +
\frac{x_D}{R+1} \end{align*}
A enrichment distillation column without re-boiler.
The design of an enrichment column with no reboiler (vapour
feed at $y_F$ entering at the bottom).
Stripping columns
are handled similarly to enrichment column design and may be
designed without a condenser if the feed stream is liquid.
This condenser-less design is useful when separating
highly-volatile compounds which would otherwise require a
cryogenic condenser (e.g., separation of air or natural gas
as propane boils at -42${}^\circ$ C, ethane at -89
${}^\circ$ C).
Its design only requires the use of the stripping section
equation, which we can rewrite: \begin{align*} y_{m} &=
x_{m+1}\frac{L_m}{V_m} - x_{W}\frac{W}{V_m} \\
&=x_{m+1}\frac{F}{F-W} - x_{W}\frac{W}{F-W} \end{align*}
A stripping distillation column without condenser.
The design of a stripping column without a condenser (liquid
feed $x_F$ entering at the top).
One important example of this design is in the
SAGE gas terminal.
High-pressure gas passes through an expansion turbine
(turbo-expander), which causes it to cool and condense (
Joule-Thomson effect).
This liquid is fed to a
stripping column
which is used to separate off a variable fraction of NGLs,
allowing the plant to control its gas composition (and
recover NGLs which are sold on).
The product vapour/gas is then re-compressed using a
compressor which is partially powered by the expansion
turbine (turbo-expander) for efficiency.
At no point is a condenser required to liquefy the light
fractions of the gas (methane, ethane, propane, …).
A stripping distillation column without condenser.
Batch distillation
is a technique to carry out small scale or controlled
separations on a fixed volume.
The design of
single-stage
batch distillation systems follows Rayleigh's equation:
\begin{align*} \ln\left(\frac{L_{final}}{L_{initial}}\right)
= \int_{x_{initial}}^{x_{final}} \frac{{\rm d}x}{y-x}
\end{align*}
This single-stage approach is limited to either low recovery
or highly volatile systems.
Multi-stage
batch distillation, such as the column on the right, enables
high purities to collected while still running in batch
operation.
Most batch stills are in-fact multi-stage systems…
A multi-stage batch distillation column.
The copper stills used in the whisky industry contain more
than one stage of distillation.
No insulation is deliberately used to allow condensation to
form inside the still causing a small reflux stream to form.
This counter-current flow of liquid and vapour results in
more than one stage of distillation overall.
But how can we design multi-stage distillation columns like
this one?
A multi-stage batch distillation column.
The first step is to realise that Rayleigh's equation still
holds for this system: \begin{align*}
\ln\left(\frac{L_{final}}{L_{initial}}\right) =
\int_{x_{initial}}^{x_{final}} \frac{{\rm d}x}{y-x}
\end{align*}
$y$ is the “produced” concentration given a liquid
concentration of $x$ in the still.
If we can calculate the top product concentration $x_D$
which will be produced from a multi-stage still given the
still concentration $x$, we can write \begin{align*}
\ln\left(\frac{L_{final}}{L_{initial}}\right) =
\int_{x_{initial}}^{x_{final}} \frac{{\rm d}x}{x_D-x}
\end{align*}
All we need is some relationship between $x_D$ and $x$ for
the column, then we can integrate it.
A simplified diagram of a pot still.
If we can
assume that we have a fixed reflux ratio, then
multi-stage batch distillation columns can be assumed to be
an enrichment distillation column with a slowly varying
bottoms product concentration.
The bottoms product varies slowly as there is a large volume
of liquid in the reboiler, acting as “feed” to the column.
We can then find the relationship $x_D-x$ by performing
repeated distillation column designs for the range
$x\in\left[x_{initial},x_{final}\right]$ …
A multi-stage batch distillation column.
As the bottoms product concentration drops over time, so does
the top product concentration. The slope of the operating line
remains constant as the reflux ratio doesn't change.
Plotting these differences, we can perform the integration
using the trapezium rule (note that this integral is negative
as we're integrating backwards). The area of a trapezium is
$(Y_1+Y_2) * (X_2-X_1)/2$.
An alternative batch distillation operating mode to fixed
reflux-ratio is
fixed top-product concentration.
This assumes that the reflux ratio of the batch column is varied
to keep the top-product concentration fixed.
This piece of process control can be done by altering the reflux
ratio depending on the temperature at the top of the column
(temperature is concentration at fixed pressure).
As the distillation continues, the reflux ratio must increase
exponentially to maintain the top product concentration.
In this case, $x_D$ is constant and we have \begin{align*}
\ln\left(\frac{L_{final}}{L_{initial}}\right) &=
\int_{x_{initial}}^{x_{final}} \frac{{\rm d}x}{x_D-x}
=\left[-\ln(x_D-x)\right]_{x_{initial}}^{x_{final}} \\
x_D(L_{initial}-L_{final})&=x_{initial} L_{initial}-x_{final} L_{final}
\end{align*}
This can be obtained directly from a mass balance.
Fixed reflux ratio and fixed top-product concentration methods
can both achieve identical separations; however, fixed reflux
ratio is the simplest to perform operationally.
