In the previous lecture, we discussed
column
efficiencies
and how to use them:
The overall column efficiency, EO, is the ratio of
ideal trays
to
real trays
in the column.
The Murphree tray efficiency, EM, is the
effectiveness of a
single real tray
when compared to a
ideal tray.
The Murphree point efficiency, EP, is the
efficiency of a single point on a tray. This is only useful
when considering the flow on a tray in detail.
A constant Murphree tray efficiency is relatively easy
to use, forming an “effective”
VLE line
below the true
VLE line, which we called the
Murphree line.
But what is happening at the bottom of the stepping
when using the Murphree efficiency?
This is the first example of a case where we have
different efficiencies for different parts of the column.
The bottom stage is usually a
re-boiler stage,
and it is often assumed to have a Murphree efficiency of
EM=1.0
!
This is because the
re-boilers actually generate
vapour from the liquid.
On trays, you are
contacting
vapour and liquid
phases to try to get them to come into equilibrium.
Generating vapour will typically be more effective at
achieving equilibrium concentrations.
So the re-boiler stage shouldn't use the
Murphree line, but should instead
go to the
VLE line
!
But we must be careful where we start our stepping
using the
murphree line. We must use whole
numbers of stages as they correspond to
real
trays.
If we start stepping from the top, we may
significantly over-design our column.
Its important to remember that the start point of
stepping can effect the final result
if the Murphree
tray/stage efficiencies vary.
Here we've seen the difference that the re-boiler
efficiency can make when using the Murphree tray efficiency.
How does having a ideal reboiler stage effect overall
efficiency calculations?
Let's double check how the overall efficiency works
when considering the re-boiler as an ideal stage.
We start off by calculating how many ideal stages are
required for the design.
Here we need around 2.6 ideal stages to perform the
separation.
But one ideal stage is provided by a re-boiler, so we
only need 1.6 ideal trays!
Assuming we have an overall efficiency of EO=0.4,
this would give us
1.6/0.4=4
real stages and a reboiler
stage!
Contrast this to our previous design with a Murphree
tray efficiency of EM=0.5.
Let's consider the distillation trays in a real
distillation column.
The tray's in a column will actually vary in type,
from random/structured packing, to sieve/valve/chimney trays.
They will vary as the viscosity of the column mixture
changes with concentration (compare the heavy components of
crude to the light paraffin's).
This means the efficiency will vary significantly in
the column.
The efficiency will also change due to the difference
in vapour and liquid flow rates in the stripping and
enrichment sections due to the addition of feed.
The most complex case we will consider in this course
is that we have two Murphree efficiencies.
In the upper enrichment section, we might have a
higher efficiency due to the increased vapour flow-rates, and
lower liquid flow-rates resulting in longer liquid tray
residency times.
Let's do the previous Murphree example with two
different tray efficiencies…
In summary, for efficiencies:
Remember that the re-boiler is nearly ideal, so it
should always contact the
VLE line.
You can have varying tray efficiencies in the
column, and the simplest example of this is when the
enrichment and stripping efficiencies are different.
Always start stepping from the bottom when using the
Murphree tray efficiency, as this uses the ideal re-boiler
stage to its maximum, and gives the minimum real-tray design.
The last bit of ambiguity to clarify in distillation
design is
which tray is the feed tray?
The feed tray is defined as the tray below where the
feed enters the column.
The liquid falling down from the feed point will land
on this tray, and the feed vapour will join the rising vapour
from the tray.
Therefore,
the feed tray is the tray which
connects the two
operating lines.