From the previous lectures and tutorials, we have discovered
that
flash drums
and
batch distillation stills
did not achieve a high degree of separation for Benzene-Tolulene
mixtures.
This is because the relative volatility of these components
($\alpha\approx2.5$) is not high enough to make
single-stage
distillation particulary effective.
Economical use of flash drums is usually limited to systems
where a very high relative volatility is possible (e.g., flash
separation of seawater).
We need to use
multi-stage distillation
to increase the degree of separation achieved, and to obtain
higher flow-rates of the purified products.
But how do we actually carry out
multi-stage
distillation?
We could try and implement something along the lines of
multi-stage evaporation, where we chain multiple flash stages to
create more vapour.
But, exactly like batch distillation, the average vapour
concentration will drop as more and more vapour is generated (we
gain nothing over batch distillation in terms of separation).
We need to condense and partly re-boil the vapour produced from
each stage to increase the purity of the vapour phase, while
recycling the liquid phase to increase the recovery.
Can we take a hint from the multi-stage absorption/stripping
approach?
In a multi-stage
stripper
(see right), a vapour phase becomes richer in a component as
it is stripped from the liquid phase.
The partly stripped liquid is then recycled by passing down
the column while the vapour continues to rise.
But consider if the liquid and vapour phases are not inert
gas, inert liquid, and absorbent, but two phases of a
binary mixture at its boiling point.
At each stage, the
rising vapour condenses
and mixes with the falling liquid phase.
The heat released from condensing the rising vapour causes
more vapour in equilibrium with the mixture to boil from the
stage.
This vapour will rise to the next stage and the mixed liquid
will overflow to the lower stage.
The result is that we have multiple stages of distillation
allowing a high degree of separation.
We know this scheme will work (at least in the limit of low
concentration) as multi-stage stripping/absorption works.
But binary distillation has a major difference to gas
stripping/absorption:
We have only
one feed stream
(which may be liquid, vapour, or multiphase) with one
overall concentration.
We cannot
directly
create counter-flowing liquid and gas phases with differing
concentrations from the feed stream.
But if we can
generate contacting counter-current vapour and liquid
streams from the one inlet stream, we can create multiple stages of distillation.
To create these counter-flowing phases, we use
condensers
and
re-boilers.
The
re-boiler
at the bottom of the column generates a vapour phase, which
then flows up through the column.
At the top of the column, a condenser converts the vapour
phase back into a liquid phase which is returned to the
column (known as the
reflux).
Together, these units generate a continually circulating
flow of vapour and liquid.
The feed stream will enter the column at a tray which
matches its concentration, and this may be the condenser or
the re-boiler.
The liquid products are then collected from the condensate (
top product) and the re-boiler (
bottom product).
Distillation column, displaying the equipment attached to
the column.
We have described a
distillation column
along with its auxiliary equipment (condenser, pumps,
re-boiler).
This separation process is known as
Fractionation,
Rectification
or
Stage-Distillation with Reflux.
This process is used to separate a wide range of liquid
products, but is most well known for its use in the
fractional distillation unit of oil refineries.
We will now examine how to design distillation columns for
binary fluids.
Distillation column, displaying the equipment attached to
the column.
This similarity with absorption towers is convenient as it
implies similarity between the design methods.
We need to generate
operating line
equations, linking the concentrations of the phases between
the stages in the column.
When combined with the
VLE data
we can estimate the number of trays to achieve a given
separation.
But we have some additional complexities to the absorbtion
tower.
We must account for the location of the
feed tray
(where the feed is added to the system) and its effect
on the flow within the column.
We also need to optimise how much of the condensed
vapour is returned to the column versus how much is
removed
(the
reflux ratio).
Distillation column, displaying the trays/stages and the
counter-current flows of vapour and liquid.
To generate our
operating line
equations we need to perform a mass balance over the stages
within a column.
In distillation this is complicated as, conceptually at
least, the vapour entering a phase supplies the energy for
new vapour to boil.
We will then need to perform an energy balance, to take into
account boiling point rise, heats of solution, and sensible
heat changes to solve for the change in vapour and liquid
flow-rates through the column.
However, if the two components are alike, we can neglect
heats of solution.
We can also neglect sensible heat change provided the change
in boiling temperature between stages is not too large.
If we then also assume that the latent heat of vapourisation
is roughly constant as a function of concentration and
temperature, we arrive at the
constant molar overflow
assumption.
This assumes that for every mole of vapour condensed on a
stage, another mole of vapour is produced. \begin{align*}
V_{n-1}=V_n \end{align*}
This also means that the liquid flow-rates in the column are
constant! \begin{align*} L_{n+1}=L_n \end{align*}
