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Fractionating Columns

How Many Ideal Stages?

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DefinitionA fractionating column consists of a series of equilibrium plates or stages arranged in a stack in which a facility for downflow of refluxing liquid forms an integral part of the system.

Feed is introduced at some plate near the centre of the stack.

The section of column above this feed plate is termed

the rectifying sectionrectifying section 

and that below the feed plate is termed

the stripping sectionstripping section

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Energy Management

Energy is supplied from a reboiler at (or connected with) the base of the column.

Energy is removed using a condenser placed at the top of the rectifying section and below which there is a reflux divider.

It is usual to thermally insulate the column so that energy is neither lost from it nor gained by it.

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Reflux Divider

This is a device that diverts a proportion of the condensate back into the rectifying sectionrectifying section of the column.

It is usually electromagnetic with a timing device that diverts condensate for short, but frequent, intervals of a few seconds such that it is assumed to provide a continuous reflux.

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Definition Diagram

Plate n + 1

Plate n

Feed Plate: F, xf

Plate m + 1

Plate m

D, xd

W, xw

V, yt

condenser

Refluxdivider

liquidvapour

liquid

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Internal Flows

Plate n + 1

Plate n

Feed Plate: F, xf

Plate m + 1

Plate m

Ln +1

Ln

F + Ln I

Lm + 1

Vn

Vm

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A Typical Plate

Flow of Vapour and Liquid

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Plate n

Plate (n+1)

Plate (n −1)

Vn+1

Vn

Vn-1

Ln+1

Ln

Ln-1

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Features

EachEach plate receives:-

a flow of vapour from the plate below.

a flow of liquid from the plate above.

The vapour and liquid arriving at the plate are not in equilibrium.  

The purpose of the plate is to facilitate this equilibrium.

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Assumptions

• No heat losses

Hvap of the MVC = Hvap of the LVC

• No heat of mixing.

• Steady state operation.

• Feed enters at its bubble point

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Assumptions

Hvap of the MVC = Hvap of the LVC

These enthalpies of vaporization are measured in mole units. So that as one molecule of volatile component evaporates, one molecule of less volatile component condenses.

The technical term is Equimolecular Counter DiffusionEquimolecular Counter Diffusion

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Material Balances

The analysis of the process proceeds with mass balances taken around………

1) the top of the column and underneath the top plate (n+1)

2) and around the column base and above the bottom plate (m)

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Top of the Column Balance

1) the top of the column and underneath the top plate (n+1)

D

Ln + 1Vn

Vn = Ln+1 + D

And for the MVC

Vnyn = Ln+1xn+1 + Dxd

(n+1)

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The Top Operating Line

dividing

As a result of assumption (2) Ln+1 = Ln = Ln1= Ln2 and so on (down to

the feed plate).

This relates the composition of vapour leaving plate n to the liquid composition on the plate above (n + 1) in the RECTIFYING SECTION

MVC: Vnyn = Ln+1xn+1 + Dxd by Vn gives

(i.e. Constant molar overflow)

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Bottom of the Column Balance

Lm = Vm + W

And for the MVC

xm+1Lm = ymVm + Wxw

2) and around the column base and above the bottom plate (m)

W

Lm + 1Vm

(m)

(Assuming Lm = Lm+1)

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The Bottom Operating Line

dividing by Vm gives:-

This relates the composition of vapour leaving plate m to the liquid composition on the plate above (m + 1) etc. in the STRIPPING SECTION

xm+1Lm = ymVm + Wxw

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Equilibrium Data

VLE data are required to find the compositions of liquid and vapour that exist at, and flow away from, a given plate.

It may be necessary to find experimental data or use Raoult’s law if the system approaches ideality.

The relation y = f(x) is required.

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Number of plates?

The estimation of the number of plates then proceeds from plate to plate using the operating lines and the VLE data in sequence.

Calculation: Sorel-Lewis method (can be automated)

Graph: McCabe –Thiele method

In both cases it is necessary to evaluate an overall mass balance to define all streams compositions and flows associated with the column.

Useful Information

Note that all vapour leaving the top of the column is condensed so that no change in composition occurs.

Liquid of this composition (xd) is used as reflux (which falls on

to plate n + 1).

D

(n+1)

yn+1 i.e. yt

xd

xd L

Calculation Procedure

The composition of liquid xn+1 on plate n + 1 (in equilibrium with

vapour yt, (= xd = yn+1) is read from the (curve on the) VLE

diagram (or calculated from a curve fit).

y = x

VLE diagram

y

x

Since all vapour yt is condensed yt = xd

(y = x)

y – mol fraction MVC in vapour

x – mol fraction MVC in liquid

yt

xd0 1

1

Continued on next slide…

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Calculation Procedure

The composition of liquid xn+1 on plate n + 1 (in equilibrium with

vapour yt, (= xd = yn+1) is read from the (curve on the) VLE

diagram (or calculated from a curve fit as VLE y = f(x) )

VLE diagramSince all vapour yt is condensed yt = xd

y – mol fraction MVC in vapour

x – mol fraction MVC in liquid

yn+1

xdxn+1

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Calculation Procedure

The composition of the vapour rising to this plate from that below (yn) is obtained by substituting xn+1 in an operating line equation.

If xn+1 > xf then the the top operating line is used else the bottom

line is used.

The liquid composition (xn) in equilibrium with vapour yn is read

from the VLE diagram (or calculated…..).

If xn+1< xw then stop.

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Evaluation

Each cycle of calculation/use of VLE diagram/data constitutes the calculation over a complete stage.

The reboiler and condenser constitute one complete stage of separation, the number of plates/stages in the actual column = the number of calculation cycles 1.

NB: If the VLE curve is accurately represented by a polynomial or other function in the range 0 to 1 mf, then the stagewise calculation may be performed entirely automatically. It is most convenient when the function is expressed in the form x = f(y) for the order of procedure given above.

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Graphical Procedure - Data

The operating lines are plotted on a VLE diagram together with the diagonal line y = x.

y = xy =

f(x)

Graphical Procedure - TOLIf xn+1 = 0, the TOL is seen to pass through point (0, Dxd/Vn)

y = xy =

f(x)

Dxd/Vn

So when xn+1 = 0

0 1

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Graphical Procedure - TOL

By substituting xn+1 = xd in the TOL it is seen that it passes

through the point (xd, xd)

y = xy =

f(x)

yn = xd

xd

Dxd/Vn

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Graphical Procedure - BOL

By substituting xm+1 = xw in the BOL it is seen that it passes

through point (xw, xw) and has a slope of Lm/Vm.

y = xy =

f(x)

ym=xw

xw

y = mx + c

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Graphical Procedure – Feed

The simultaneous solution of the TOL and BOL is at xf * – the intersection of the vertical x = xf may be used to plot the BOL

y = xy =

f(x)

xd

xd

xw

xw xf

* Only if the feed is at its bubble point.

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Graphical Procedure – Feed

The simultaneous solution of the TOL and BOL is at xf * – the intersection of the vertical x = xf may be used to plot the BOL

y = xy =

f(x)

xd

xd

xw

xw xf

* Only if the feed is at its bubble point.

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Graphical Procedure – Plate Count

It is usual to start from xd when the quality of the distillate is prescribed.

y = xy =

f(x)

xdxw xf

5 stages,

4 plates in the column.

y

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A Stage or Plate

Each full step (horizontal + vertical segments) represents a stage of enrichment (i.e. no. of plates in the column = No. of steps - 1).

Each vertical line represents enrichment (vapour and liquid in equilibrium)

Each horizontal line represents conversion of vapour to liquid of the same composition.

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Limits to The Operation

The quantity Ln/D is usually termed the reflux ratio (R). The

TOL may be expressed in terms of R as follows:-

the intercept of the TOL is (0, xd/(R+1)) and the slope R/(R+1).

Limits to The Operation

As reflux increases, the slope tends to 1 and y = x

y = xy =

f(x)As reflux decreases, the

slope tends to 0 (y = xd)

xd

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Increasing Reflux

As R increases the same enrichment (xd) is obtained with a

falling number of theoretical (but not necessarily actual) stages.

y = x

y = f(

x)

R =

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Limits to The Operation

As R decreases the number of plates increases. At some value (Rmin) the TOL intersects the VLE curve at xf.

y = x

y = f(

x)Below this value of R enrichment to xd is not

possible.

See C & R vol 2, 5th Ed.

p571 578

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Additional Information

The feed is best input to the plate bearing liquid closest to the composition xf.

As the reflux ratio is increased so increasing amounts of condensed vapour are recycled as reflux liquid. This liquid needs to be re-evaporated in the reboiler.

As the reflux ratio is decreased so an increasing number of plates are required. This reduces the demand for heat from the reboiler, but the capital cost of the column increases.

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Ease of Separation

y = xy =

f(x)

As the difference in volatilities of components increases separation becomes easier.