RECYCLE REACTOR SYSTEM

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RECYCLE REACTOR SYSTEM

• Figure 6.13 shows a PFR where part of the
  reactor output is recycled to the input. As the
  recycle ratio increases the reactor behaves more
  like a MFR!
• The reactor in the system is still governed by
  the performance equation for a PFR but we need to
  account for the fact that the feed to the PFR is
  not the feed to the system.
• We can obtain the properties of the feed to the
  PFR in terms of the properties of the feed to the
  system by writing mass balances around the mixing
  point.

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Recycle reactor system
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Recycle reactor Mass balances around mixing point
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• So we now have expressions relating the feed to
  the PFR and the feed to the system as a whole
• The PFR itself had been analyzed previously

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Performance equation for plug flow reactor
derived earlier

• In our system, we have v0(R1) entering the
  reactor instead of v0 and an entering conversion
  XA1 instead of 0.
• Thus we get, for the performance equation for the
  recycle reactor

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Performance equation for the recycle reactor
system

• This is shown graphically in Fig. 6.14
• The integral gives the area under the curve
  between XA1 and XAf . It represents the V/FA0
  for the PFR if there was no recycle.
• If we multiply the average 1/rA in this interval
  with (R1) we get the required volume of the
  reactor with recycle

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Fig6_14
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Recycle reactor system performance

• We can evaluate the performance of the recycle
  reactor system at any recycle ratio relative to a
  straight PFR (recycle ratio of zero) by looking
  at the space time ratio.
• This will need to be done for specific reaction
  rate expressions, rA
• Figure 6.16 looks at 1st order reaction, 6.17
  looks at 2nd order. (these are analogous to Fig.
  6.5 and 6.6 which looked at the effect of N for
  MFRs in series).

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1st order rxn PFR with recycle
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2nd order rxn PFR with recycle
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RECYCLE REACTOR

• We have seen that recycling makes a PFR behave
  more like a MFR.
• We have also seen that PFR is the more attractive
  solution in most cases because it achieves the
  same conversion with smaller volume.
• Why then, would we be interested in degrading the
  performance of a PFR by recycling some of its
  output to the inlet?
• An autocatalytic reaction proceeds faster with
  some product in the feed, or in extreme cases may
  not proceed at all if there is no product in the
  feed.

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AUTOCATALYTIC REACTIONS

• one of the products acts as a catalyst
•  A M M M
• Important examplethe treatment of biodegradable
  organic wastes by microorganisms, biodegradation
•  biodegradable material microorganisms O2
  (dissolved oxygen)
• ------? CO2 H20 more microorganisms
• The presence of microorganisms is required for
  the reaction to proceed. The product of the
  reaction is more microorganisms.
• The reaction rate shows some dependence on the
  initial presence of microorganisms (Fig. 6.18).
•  

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Fig6_18
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Autocatalytic reactions

• See Chp. 3 for test of
• reaction rate expression
• from batch reactor data
• for the special case

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Autocatalytic reactions

• What type of reactor is best for these reactions?
• PFR with pure A in the feed will not work! We
  need at least some product in the feed. But how
  much? If we have too much, that might affect the
  reaction rate as well. Where do we get the
  product? One possibility is to use recycle.
•  
• MFR with pure A feed will work if we get it going
  initially by having some product in the reactor.
•  
• We have also seen that a PFR in recycle mode
  behaves more and more like a MFR as recycle rate
  increases.
•  
• So the question is not simply PFR vs MFR, but a
  PFR with the optimum recycle ratio vs a MFR.

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Fig6_19
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Autocatalytic reactions MFR vs PFR

• Figure 6.19 shows that for an autocatalytic
  reaction MFR is more efficient than PFR at low
  conversions. At higher conversions they become
  equivalent, and at even higher conversions, PFR
  becomes better.
• What about a combination of MFR and PFR in series?

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Autocatalytic reactions MFR- PFR in series

• Since MFR is better than PFR at low XA it makes
  sense to use MFR at low XA and then switch to PFR
  for high XA , Fig. 6.21 (a)
• If the product can be separated from the
  remaining reactant we dont need the PFR, we can
  simply operate a MFR with a separator, Fig. 6.21
  (b)
• Note Fig. 6.21 has been drawn using CA instead
  of XA. You should be able to go from one to the
  other with ease.

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Fig6_21
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Autocatalytic reactions MFR vs PFR

• What is different about these reactions?
• i.e. what happened to our analysis resulting in
  Fig. 6.2 which showed PFR better than MFR?
• Compare Fig. 6.18 and 6.19 with Fig. 6.2. It is
  the minimum in the 1/rA curve ( maximum in rA )
  that gives rise to the observation in Fig.6.19

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Autocatalytic reactions recycle reactor
using a PFR

• In Figure 6.20 we can distinguish two systems
• 1) The actual PFR with feed at XAi and product at
  XAf
• 2) The recycle reactor with feed XA0 and
  product at XAf
• The PFRs performance equation says the area
  under the 1/rA curve from XAi to XAf is V/FAi
• We can define an average rate for the PFR by
  drawing a line that will give us the same area
  underneath, between XAi to XAf

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Autocatalytic reactions recycle reactor
using a PFR

• Now looking at the recycle reactor, the only
  reaction taking place is in the PFR. So the same
  reaction rate applies.
• The feed to the recycle reactor is at XA0 and
  its flow is FA0 .
• The rectangular area under (1/rA)average from
  XA0 to XAf is V/FA0
• This is the actual measure of performance for our
  system.
• If we had no recycle (just the PFR) V/FA0 would
  be the area under the 1/rA curve from XA0 to
  XAf
• If we had a MFR, V/FA0 would be the rectangular
  area under the 1/rA (evaluated at Xaf ) line
  from XA0 to XAf

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Autocatalytic reactions optimum recycle ratio
in PFR

• At high recycle rate (I.e. high XAi, see Fig.
  6.14) the recycle reactor resembles a MFR and
  is clearly inferior to the PFR.
• As we reduce the recycle rate, the recycle
  reactors performance improves (V/FA0 is
  reduced).
• At even lower recycle rates the performance
  deteriorates again.

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Autocatalytic reactions optimum recycle ratio
in PFR

• Recall the performance equation
• The optimal recycle rate is obtained
• by taking the derivative of V/FA0
• w.r.t. R in the performance equation
• And setting it equal to zero, giving
• The optimum recycle is one that introduces a feed
  which corresponds to the average reaction rate
  in the reactor.

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Recycle reactor - recap

• recycling of reactor output to the input may be
  done for different reasons
• Performance equation for a PFR with recycle
  follows from the equation for a PFR but
  incorporates a mass balance around the mixing
  point to relate fresh feed, recycle stream, and
  reactor feed
• Increasing the recycle rate makes PFR look more
  like a MFR

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Autocatalytic reactions - recap

• These require recycle if a PFR is to be used
• MFR superior to PFR at low XA (In contrast to
  reactions of general order ngt0)
• PFR superior at high XA
• There is an optimum recycle rate
• Good idea to use two reactors in series (MFR
  first, PFR next)

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Example 6.3 Best reactor setup for an
autocatalytic reaction

• Degradation of A in the presence of an enzyme
• Reaction rate data has been obtained in a MFR
  (Table E6.3)
• v00.1 m3/min with CA010 mmol/m3 to be treated
  to XA0.9
• Alternatives considered
• (a) PFR with recycle
• (b) 1 or 2 MFRs in series
• (c) MFR-PFR in series

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Example 6.3 (a) PFR with recycle

• Trial and error graphical solution find optimum
  recycle by adjusting feed to correspond to the
  average rate of reaction, Fig.E6.3a
• CAi6.6 mmol/m3
• R0.607
• V1.08 m3

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Example 6.3 (b) 1 or 2 MFRs

• For one MFR we can use the reaction rate data
  directly in the general form of the performance
  equation.
• Two MFRs in series. Possibilities
• Equal size
• Unequal size
• How do we determine the size(s)?
• For two equal sized MFRs we could use Fig.6.5 if
  the reaction was 1st order (or Fig.6.6 if the
  reaction was second order as in Example 6.2) But
  we do not even have a reaction rate expression,
  just numerical data.
• The graphical method of maximization of
  rectangles enables us to find the optimum sizes
  of two unequal MFRs in series (which turns out
  slightly better than two equal size MFRs) even
  when we only have reaction rate data but no
  reaction rate expression.

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Example 6.3 (b) 1 MFR

• One MFR,
• CA010 mmol/m3 CAf1 mmol/m3 (90 conversion)
• 1/rA 10 m3.min/mmol (from reaction rate data)

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Example 6.3 (b) 2 MFRs

• Two MFRs in series Fig.E6.3b

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Example 6.3 (c) MFR-PFR combo

• Fig.E6.3c
• MFR
• PFR

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Example 6.3 Summary
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MFRs in series equal or unequal size? Reality
check!

• Example 6.3(b) arrived at V10.59 m3, V21.6 m3
  as optimum for 2 MFRs of unequal size
• What would be the volumes if we used 2 equal
  sized MFRs?
• If this had been a 1st or 2nd order reaction we
  could have made use of Fig.6.5 or 6.6 to answer
  the question.
• We only have the rate data which we need to use
  graphically.
• Find that 2 MFRs of 1.25 m3 will do the job
  (exercise, see Fig 6.8)
• Vtotal2.2 m3 vs Vtotal2.5 m3
• The operational advantages of 2 identical
  reactors may outweigh the marginal total volume
  advantage of 2 unequal reactors.