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


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


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’


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


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


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


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.


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)

Detailed Design.ppt

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