Distillation 3

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Distillation 3
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1
2
3
4
5
B
xD
xB
xF
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The intersection of the operating lines

• The position of the intersection is related t the
  introduction of the feed.
• It is not the point on the rectifying operating
  line where
• x xF
• The state of the feed and its flowrate have an
  effect on the flows in the column and hence on
  the two mass balances.

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The feed will be in one of 5 states
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The Feed State Parameter, q

• q is defined as the number of moles of liquid in
  the stripping section resulting from the addition
  of one mole of feed.

So for a sub-cooled liquid we first have to raise
the temperature of the feed to the boiling point
and then evaporate it, so the heat required is
This gives
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For a superheated vapour the feed actually causes
a decrease in the number of moles of liquid in
the stripping section, so q will be negative. In
this case
This represents the number of moles of liquid
evaporated by the vapours superheat. Since TF is
greater than TB,, q is indeed negative.
For a mixture of liquid and vapour q is equal to
the mole fraction of liquid in the mixture.
Where the feed is saturated liquid q 1 and for
saturated vapour q 0.
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We can use q to relate the flows in the stripping
and rectifying sections
and for the vapour
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At the intersection of the two operating lines
D
rectifying operating line
we can use a mass balance around the rectifying
section to substitute for L D
so the operating line becomes
or
B
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Similarly for the stripping section
the mass balance gives
giving the operating line as
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Now we have 2 equations in x and y
subtracting one equation from the other
remembering that
and
gives
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a mass balance over the whole column gives
substituting this into (1) gives
rearranging for y
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This is a straight line, gradient
This line is the locus of all the points at which
the two operating lines can intersect for a feed
with this value of q. This is known as the
q-line. We can draw the q-line if we know one
point on it and its gradient. A convenient point
is its intersection with the diagonal, y
x. Putting y x into the above equation gives
So the q-line intersects the diagonal at x xF