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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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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.