Detailed Design.ppt
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Transcript of Detailed Design.ppt
McCabe-Thiele Method
1. Draw the q-line
2. Draw the TOL from your chosen value of R.
3. Now draw the BOL
4. Start to count the number of stages required
…so there are six stages required for this particular reflux ratio
xDxW
Detailed Design
Once distillation is identified as the most economically viable process we need to think about a more detailed design
Plate Design
Plate Efficiency
Column Dynamics (L/V) and Geometry
Packing vs Trays
Side-streams and Multiple Feeds
Batch vs Continuous
This will form the basis of the next couple of lectures, and will conclude the section on distillation
Plate Design
The most basic is the sieve tray, which is essentially a perforated plate:
The design is simple (and therefore relatively cheap), but what can you say about the efficiency of sieve trays?
Very short vapour pathway through the liquid – hence little time for mass transfer
Liquid ‘weeping’ through perforations
Low turn-down ratio, i.e. very sensitive to changes in L/V
Entrainment at high vapour flows
Entrainment and Flooding
The vapour can ‘entrain’ the liquid on the plate, carrying it vertically as droplets or as a foam.
Entrainment is where liquid droplets are carried in the vapour
Flooding occurs when the vapour forces the liquid up to the stage above
Look at the liquid on each sieve plate as we move up the column…
How can we prevent this happening?
Plate Design
The bubble cap tray is the most complicated in terms of its design:
Introduces a horizontal flow of vapour:
Prolongs vapour-liquid contact
Improves mixing
No weeping due to presence of cap
Expensive to manufacture
Relatively high pressure drop at high vapour flow rates
Tolerates higher vapour flows before entrainment occurs
Plate Design
The valve tray is often used as a compromise – better vapour-liquid contact but with a lower pressure drop and capital cost.
Instead of a fixed bubble-cap a moveable valve is used. This can open more at high vapour flows and can close to prevent weeping
Allows some degree of horizontal vapour flow – better vapour/liquid contact than with a sieve tray but not as good as a bubble-cap tray.
Plate Efficiency
How do you think the three plate designs are ranked in terms of their efficiency?
Remember, efficiency in this case relates to how close we come to complete vapour-liquid equilibrium
LOW HIGH INTERMEDIATE
Our choice of tray is not just a matter of efficiency…
Plate Selection
Efficiency Low High Intermediate
Cost HighLow Intermediate
Pressure Drop Low High Intermediate
Turn-down ratio
Low High Intermediate
…we should also consider using packing instead of trays
Packing
1
2
3
4
In a tray column the separation takes place over a discrete number of stages
In a packed column the separation takes place continually over the height of the packed sections
Why Packing?
Why use packing? Consider a liquid droplet falling in vapour and a bubble of vapour rising through liquid
The terminal settling velocity is governed by Stokes’ Law, one form of which is given by:
18
212
gd
vs
Equilibrium can be enhanced if we increase the contact time and provide a large surface area between liquid and vapour
Packing
Packing is used to slow down the flow of liquid, and to provide a large surface area for the liquid to wet.
This enhances the gas-liquid contact and gives a very high efficiency
Columns can be filled with ‘structured’ or ‘random’ packing
Metal ‘Raschig Rings’
Ceramic ‘Berl Saddles’
Plastic Random Packing
The Random packing shown above can also be called ‘dumped packing’
Packing
Structured packing is manufactured to give a more defined internal geometry than random packing
Metal ‘Maxpax’
Structured Packing can be engineered to give an open structure for high vapour flows
Both types rely on providing a large wetted surface area to improve vapour-liquid contact and hence improve mass-transfer.
Calculating Plate Efficiencies
Q: How does ‘plate efficiency’ relate to vapour liquid equilibrium?
There are two approaches we can use to convert the theoretical number of stages (calculated using the McCabe-Thiele approach) to the actual number of stages:
1. Overall Plate Efficiency, EO
This is equal to the number of ideal stages divided by the actual number of stages used, and is often expressed as a percentage.
60% - 70% are typical values of EO
If we use the McCabe-Thiele method to calculate that we need 7 theoretical stages, and we assume an overall plate efficiency of 65%, how many stages are required?
Number of Stages = 7
0.65= 10.77 11 stages required
Calculating Plate Efficiencies
2. Individual Plate Efficiency
We know that changing the plate geometry and design affects the plate efficiency
Q: Would the efficiencies change throughout the column if all the plates are the same?
Plate efficiency is related to the closeness to equilibrium at each stage – which is related to L/V
We would expect a marked difference in individual plate efficiency between the stripping and rectifying sections
Individual Plate Efficiency
Individual plate efficiencies are often known as ‘Murphree Efficiencies’, EmV or EmL
xn-1
ynxn
yn+1
1*
1
nn
nnmV yy
yyE
*1
1
nn
nnmL xx
xxE
(6.1)
They are expressed as the actual difference in mole fraction across the tray, divided by the difference which would occur if equilibrium had been achieved
yn*
yn* is the vapour that would be
in equilibrium with liquid composition xn
Individual Plate Efficiency
Example – consider a single distillation plate operating at total reflux
If x and y are measured as 0.5 and 0.68, calculate the Stage efficiency.
x
y
yn*
yn+1
643.050.078.0
50.068.0
mvE
1*
1
nn
nnmV yy
yyE
Using the Murphree Efficiency
x
y
We can incorporate EmV with the McCabe-Thiele method
Starting from the top, we know that y1 is equal to xD
If equilibrium were achieved on stage 1, the liquid leaving will be in equilibrium with y1
xD
y1
x1*
If we assume a stage efficiency of 50% for the top plate then the liquid will contain a greater fraction of the MVC
x1
y1*
…and the vapour composition that would be in equilibrium with x1 can be found
Using the Murphree Efficiency
x
y
xD
y1
x1* x1
y1*
y2
The vapour entering from below, y2 is known from our TOL.
…note, the TOL is derived from a mass balance, and does not assume equilibrium is reached
A
B
C
If we define points A, B & C
1*
1
nn
nnmV yy
yyE 5.0
AC
BC
So x1 and y1 are related at point B – B becomes a point on the ‘effective equilibrium curve’
Using the Murphree Efficiency
x
y
xD
y1
x1* x1
y1*
y2
So x1 and y1 are related at point B – B becomes a point on the ‘effective equilibrium curve’
BWe can then continue this process for the next stage down and so on
In practice, we are likely to assume that the Murphree Efficiencies are equal where L/V is constant
Individual Plate Efficiency
How are Overall efficiency and plate efficiencies related?
• They could be constant if L/V is constant in the column (i.e. in some types of batch distillation)
• In continuous distillation, L/V changes either side of the feed point
• EmV and EmL are related to L/V
• We would expect different values for plate efficiency in the rectifying and stripping sections of the column
• Plate efficiencies can also vary within the rectifying and stripping sections
Individual Plate Efficiency
We can also define a point efficiency, Ep
Large trays will often result in complicated liquid flow regimes, meaning that different areas on the plate will vary in efficiency, and xn will not be constant on the plate.
If the liquid composition at any point is xn then we can define the point efficiency:
1*
1
n
nnp yy
yyE
n
Which is analogous to EmV
xn-1
ynxn
yn+1
Empirical Correlations
So how do we get the actual values of EO, Ep or EmV?
Usually use Empirical Correlations, e.g.
Drickamer & Bradford – Overall efficiency for petroleum mixtures:
W
LfO xE
10log616.017.0
Chu – Includes a liquid ‘submergence’ factor
LLO hV
LE 3.0log25.0log3.067.1log 101010
You should always be very careful to explore the assumptions and limitations of any correlations that you use!
Concluding Efficiency
To recap:
We use the term ‘efficiency’ to account for the fact that equilibrium is not attained in plate columns
Overall Efficiency or Overall Plate Efficiency is the simplest quantity, and is used to correct calculations which are based on 100% efficiency (e.g. McCabe-Thiele)
Individual Plate Efficiency or ‘Murphree Efficiency’ is used to quantify the closeness to equilibrium on each individual plate
Plate efficiency directly related to vapour-liquid contact time, and is hence affected by plate design and geometry, liquid and vapour flowrate, liquid and vapour viscosity and surface tension, and many other quantities
Relation between efficiencies
If the Murphree and Overall Efficiencies were both 50%:
xDxF
Firstly, let us calculate the number of stages in the rectifying section using the overall efficiency:
3.3 theoretical stages so we need 6.6 actual stages.
Let us fix the reflux ratio and feed condition
xF
Relation between efficiencies
If the Murphree and Overall Efficiencies were both 50%:
xD
Now let us calculate the number of stages using the Murphree Efficiency:
y1
x1*x1
y1*
y2
x2*
x2
...So we would need 7.7 stages here, compared with 6.6 using the overall efficiency.
Relation between efficiencies
For an equivalent number of stages in the rectifying section, EmV > EO
In the stripping section, EmV < EO for the example used here
The Murphree and Overall Efficiencies can be related by considering the relative gradients of the operating line and equilibrium line at a given point.
If we define: = Gradient of Equilibrium Line
Gradient of Operating Line
Then the following equation derived by Lewis can be used:
ln
11ln mV
O
EE (6.6)