Compartment Models to analyze nonideal behaviour

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Compartment Modelsto analyze non-ideal behaviour

• Consider non-ideal reactors to consist of
• Mixed flow regions
• Plug flow regions
• Dead, stagnant regions
• Also consider flows as
• Active flow
• Bypass flow
• Recycle flow

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• Ideal PFR
• We expect a pulse at V/v

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PFR malfunctions

• If we get an immediate peak (typically small)
  this indicates by-pass. The main peak will then
  come at tV/va
• vvavb
• va active flow,
• vb bypass flow

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PFR Malfunctions

• If Cpulse is observed at a time tltV/v then the
  actual V must be less than calculated from vessel
  dimensions there is some dead volume

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PFR malfunctions

• If we get two Cpulse peaks, one on either side of
  overall tmean this might mean parallel paths. The
  extreme version is the by-pass situation.

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2 PFRs in parallel

• V Vp1 Vp2 v v1 v2
• E 2 peaks at t Vp1 / v1 and t Vp2 / v2
• 1-F 1 until t Vp1 / v1
• 1-F v2 /v between t Vp1 / v1 and t Vp2 / v2
  
• Recall that area under 1-F must be V/v
• Looking at figure

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PFR malfunctions

• Multiple peaks with decaying intensity means
  internal recirculation.

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Tracer balance in MFR for pulse experiment

• input output accumulation (no reaction
  term for tracer)
• Assuming instantaneous addition of tracer pulse,
  no more input after time 0.

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Tracer balance in MFR for step experiment

• input output accumulation (no reaction
  term for tracer)

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Properties of exponential decay curves
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The C on the time coordinate is not the same as
the C on the vertical axis.
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MFR malfunctions

• If we get exponential decay, but starting at a
  higher value than v/V, then the actual V must be
  less than calculated from vessel dimensions
  there is some dead volume

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• Ideal MFR
• We expect an exponential decay starting at Ev/V

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MFR malfunctions

• If we get an immediate sharp peak followed by
  exponential decay, this indicates by-pass.
• The first peak area vb/v
• Remaining exponential area va/v
• Total area 1

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2 MFRs in parallel

• V V1 V2 v v1 v2
• E the sum of 2 exponentials, weighted by the
  fraction of the flow

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• Exponential decay with changing slope parallel
  MFRs

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Compartment models with MFR-PFR combinations

• Fig. 12.1 shows several combinations
• PFR-MFR in series
• PFR-MFR in series with dead volume
• PFR-MFR in series with bypass and dead volume
• PFR-MFR in series with recycle and dead volume

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PFR and MFR malfunctions - summary

• Figs. 12.3 and 12.4 summarize the most important
  malfunctions and their symptoms
• Bypass, channeling, parallel flow
• Dead volume
• Internal recirculation

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Example 11.2 Non-ideal behaviour

• Gas-liquid reactor
• V860 L, v(liquid) 5 L/s,
• Pulse experiment with M150 g
• Fig. E11.2a
• Is this a properly done experiment?
• If so, find the liquid fraction in the vessel
• Determine the E curve for the liquid
• Qualitatively what do you think is
• happening in the vessel?

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Is this a properly done experiment?(Can we
account for all the tracer?)

• Area under the curve
• So, we are able to account for all the tracer.

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(b) find the liquid fraction in the vessel

• V860 L Vliquid Vgas
• Vgas is equivalent to Vdead from the liquid
  phase perspective
• We expect dead volume to be indicated by a tmean
  lt V / v
• i.e. 860/3002.87 min

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(c) Determine the E curve for the liquid

• Note erroneous values in text E1.5C, E9/8
• In Fig E11.2b, Area A1 should be 0.375/0.50.75
• Then

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(d) What is happening?

• Multiple decaying peaks is sign of internal
  recirculation, probably due to action of rising
  bubbles

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• Example 11.2 demonstrated how we can have some
  unexpected behaviour from a reactor due to
• Dead volume (in the gas phase)
• Recirculation (due to rising bubbles)