When designing a distillation column from scratch, the
only design specifications we will have are the feed and
outlet concentrations.
We will need to decide upon a
column operating
pressure
and use this to calculate the
$q$
-value of the
feed stream (see the last lecture's slides).
We will also need to choose a
reflux ratio.
Selecting the
reflux ratio
and the
column
operating pressure
requires examining the economic
trade-off between
capital
and
operating costs.
The
column operating pressure
will require a
full optimisation study. However, we can make some educated
estimates when it comes to the
reflux ratio
…
To understand the values of the reflux ratio, we need
to understand its limits and what they physically correspond
to.
\begin{align*}
R&=\frac{L_{n}}{D}
\end{align*}
The first limit to consider is when we have the
maximum reflux ratio $R\to\infty$.
This condition is known as
total reflux, and
occurs when
no distillate is collected
(
$D=0$), but all
rising vapour is refluxed back down the column
(
$L_{N+1}=V_N$).
But what effect does this have on the column design?
The intercept of the enrichment
operating line
with the
$y$
-axis (
$x=0$)
goes to zero!
\begin{align*}
y(x=0)=\lim_{R\to\infty}\left(\frac{x_D}{R+1}\right)=0
\end{align*}
The last class example on the McCabe-Thiele method for a
Benzene-Toluene mixture. Here we have a typical value of $R=3$
for the operating reflux ratio.
At a reflux ratio of
$R\to\infty$, the enrichment
operating line coincides with the
$45^\circ$
line.
When performing distillation at total reflux, the number
of trays required to reach a certain separation is at a
minimum! (compare
$R=3$
and
$R=\infty$).
We cannot actually operate at a total reflux ratio.
Without producing any distillate, if any feed is added
it must leave in the bottoms product.
What goes in, must come out, so we achieve nothing in
this case.
However, we can use this to estimate the minimum
number of trays needed for a given separation!
Also, during the start-up of a column, it is operated
under total reflux until sufficient column vapour and liquid
flow-rates have been obtained.
Thus total reflux helps us understand what is
achievable, and is industrially relevant during
plant
startup.
Just as we had a maximum reflux ratio, we can also
have a
minimum reflux ratio.
The reflux ratio should not reach zero, as some
liquid must be returned to the column to allow a multi-stage
separation to take place. For
$R=0$, we will have only one
(partial reboiler) or zero (total reboiler) stages.
So what actually is the minimum (but non-zero) reflux
ratio to perform a distillation at?
Lets consider a distillation of an equimolar
($x_F=0.5$) Benzene-Toluene feed stream which, upon entering
the column, flashes to equal amounts of vapour and liquid
(
$q=0.5$).
If the top and bottoms product have concentrations of
90% ($x_D=0.9$) and 10% (
$x_W=0.1$) benzene respectively,
what is the minimum possible reflux ratio?
From the data given already, we can draw most of the
McCabe-Thiele constructs including the
$q$
-line. We're only missing the
operating lines.
The only restriction on the placement of the enrichment
operating line
is that it must intersect the
$q$
-line
somewhere below the
VLE
line.
The higher the interception of the enrichment
operating line
with the
$y$
-axis, the lower
the reflux ratio. So the minimum reflux ratio is where the
$q$
-line,
VLE
line, and the
operating line
coincide (
$R_{min}\approx1.31$)!
At
$R=R_{min}\approx1.31$, it is still theoretically
possible to achieve a separation. However, it will take
an
infinite number of plates to overcome the pinch.
The minimum reflux ratio corresponds to the first
(highest) $R$
where a
pinch
is formed.
We can then just read off the $y$
-intercept of the
enrichment
operating line
to find the
minimum reflux ratio.
\begin{align*}
R_{min}=\frac{x_D}{y(x=0)}-1
\end{align*}
The
optimum reflux ratio
(see C&R vol. 2,
pg. 575 for details) is generally around 1.1–1.5 times the
minimum reflux ratio.
This is where the running costs of the column (heating
steam for the boiler, cooling water for the condenser, pumps)
roughly balance with the capital costs of the column (number
of trays, cost of reboiler and condenser).
So we can now calculate a rough reflux ratio, given
just the outlet conditions and the $q$
value! We can design
binary distillation columns…
Pinches
don't just appear at the intersection of
the
$q$
-line,
VLE
line, and
the
operating line.
If the fluid is a non-ideal mixture, the pinch can
occur at some other point along the
enrichment
operating line
and the
VLE
line.
A pinch can also occur somewhere along the
stripping
operating line
and the
VLE
line.
Lets take a look at two examples…
This graph illustrates a pinch occurring on the
enrichment
operating line
for a fictitious non-ideal
mixture's VLE curve.
This graph illustrates a pinch occurring on the
stripping
operating line
for a fictitious non-ideal
mixture's VLE curve.
There is a particular form of pinch which cannot be
overcome by changing the reflux ratio.
This type of pinch was introduced to you in EG3029
Chemical Thermodynamics, and is called an
azeotrope.
The most famous azeotrope exists in Ethanol-Water
mixtures, and prevents the distillation of more than 95.6% at
atmospheric pressure.
We cannot place the top and bottoms product
concentrations on different sides of the
azeotrope, and
enrichment beyond the
azeotrope
concentration in a
single column is impossible.
This graph illustrates the limitations placed on
distillation by the occurrence of an azeotrope. The top product
concentration cannot be moved above the azeotrope
concentration.
One way of overcoming this azeotrope is to utilise
pressure swing distillation. At different pressures the
position of the azeotrope shifts (dotted blue line).
If we first distill using the high pressure, we can use
this top product as the feed into a low-pressure distillation
column. Then we can concentrate up to arbitrary strength.
The next subject on distillation design is
plate
efficiencies.
So far we've only concerned ourselves with an
overall plate efficiency,
$E_O$.
We can convert from theoretical stages ($N$) to real
stages (
$N_{real}$) by just dividing by the efficiency.
\begin{align*}
N_{real} = N / E_O
\end{align*}
There are expressions for the overall efficiency
available in the literature for certain types of distillations
(See C&R Vol. 2, Eq. 11.126).
However, in general an overall efficiency is a very
crude approximation and can only be used for rough
calculations.
But there are better definitions of the efficiency
available…
The
Murphree
Tray
Efficiency
is a
parameter that appears to fit reality a little better.
The expression for the Murphree tray efficiency is
\begin{align*}
E_M = \frac{y_n-y_{n-1}}{y_{n}^{*}-y_{n-1}}
\end{align*}
where
$y_n$
is the real concentration of vapour coming off a
stage, and
$y_{n}^{*}$
is the equilibrium vapour
concentration.
If the tray efficiency is one, these two values are
the same. At efficiencies less than one, the outlet vapour
will not reach equilibrium with the average tray
concentration.
The easiest way to use such an efficiency is to apply it as
you step. Here we'll draw the
curved
Murphree line
on
the almost complete McCabe-Thiele chart, just for illustration.
To plot the
Murphree line, we
just put points at a fraction of the distance between the
operating line
and the
VLE
line
equal to the Murphree tray efficiency. The example above
is calculated at
$E_M=0.5$.
To determine the number of real trays, we just perform
the stepping as usual, but use the
Murphree line
in place of the
VLE line.
We can also calculate the Murphree line as we step, which
is more accurate, so its highly recommended. This distillation requires
at least 5 real trays and an ideal reboiler stage.
We can extend the Murphree tray efficiency to the
Murphree point efficiency.
The expression for the Murphree point efficiency is
\begin{align*}
E_P = \frac{y'_p-y'_{n-1}}{y_{n}^{*}-y'_{n-1}}
\end{align*}
where the primes denote the concentration at a certain point
on the plate.
This is used to take into account that the
concentration varies along the plate as the tray fluid is not
well mixed.
Use of this efficiency requires us to consider the
hydrodynamics within a plate, and this is too detailed for
this course.
But, as always, you need to be aware of the
approximations of your solutions.
