Unequal size MFRs in series

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Unequal size MFRs in series

• The case for equal size MFRs in series was
  summarized for 1st and 2nd order reactions in
  Fig. 6.5 and 6.6
• Example 6.2 demonstrates the use of these Fig 6.6
• As the number of reactors increased, the required
  total volume decreased.
• N MFRs in series approach PFR behaviour as N??
• What about unequal size MFRs in series?

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Unequal size MFRs in series

• Two types of questions
• (1) What is the performance of a given setup?
• (2) What is the best setup to achieve desired
  performance?
• (1) Fig 6.8 shows graphical method for this
  question.
• Given reaction rate data (r vs C), C0 , and
  ?V/?
• Draw line with slope 1/?1 starting at C0,
• Find C1 from the MFR performance equation.
• Repeat for successive reactors

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Fig6_8
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Unequal size MFRs in series

• What is the best setup for 2 reactors?
• Fig 6.9 shows V1 and V2 as X1 is changed for the
  same final X2
• We want to minimize the total volume this is
  the same as maximizing area KLMN
• Maximizing the area of the rectangle
• Fig.6.10 shows graphical procedure for
  maximizing Axy, subject to an arbitrary yf(x)
• dAydxxdy0 (at maximum)
• -dy/dxy/x
• i.e. the slope of the curve at M is equal to the
  slope of the diagonal.
• Point M needs to be determined by graphical trial
  and error.

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Reactors of different type in series

• Fig. 6.12 shows 2 MFRs and 1 PFR in series.
• What is the best arrangement for multiple, mixed
  type reactors?
• General principles
• For ngt0, connect reactors in series (instead of
  parallel)
• If 0ltnlt1 arrange the reactors to keep reactant
  concentration as low as possible
• If ngt1 arrange the reactors to keep
  concentrations as high as possible (e.g. in Fig
  6.12, PFR, small MFR, big MFR)
• For autocatalytic type reactions (with a maximum
  in the rate curve) special considerations apply.
• NOTE This does not say how to find optimum
  volumes etc.

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Fig6_12
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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
• 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)
• 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.