ENVE3002 Systems Modelling

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ENVE3002 Systems Modelling

• The principles of chemical and biochemical
  transformations in natural and engineered systems

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Basic principles

• Conservation of mass
• Thermodynamics
• Kinetics
• Fluid behaviour

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Fluid behaviour

• Types of fluid behaviour in systems
• Completely mixed flow
• Plug flow
• Partially (intermediate) mixed flow
• What is the significance of this behaviour
• When system inputs change?
• When there is a reaction going on?

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Ideal behaviour

• Ideal mixed flow
• Concentration and temperature the same throughout
  system
• Mean residence time for molecules space time
• Ideal plug flow
• Concentration and temperature only a function of
  distance from inlet (i.e. uniform in a plane ? to
  flow)
• residence time for all molecules space time
• Thin plugs behave like independent batch reactors
  as they go from inlet to outlet

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Non-ideal behaviour

• Fig. 11.1 demonstrates flow patterns encountered
  in various process equipment that will violate
  the ideal assumptions.
• Note despite the various idiosynchrasies in Fig.
  11.1, our analysis will assume the fluid enters
  and leaves the vessel only once, i.e. no
  backmixing at inlet and exit the closed vessel
  boundary condition.

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Non-ideal behaviour

• Deviation from the ideal residence time is the
  most tangible and quantifiable aspect of
  non-ideal behavior. Residence time distribution
  (RTD) is also the easiest aspect of non-ideality
  to observe by tracer stimulus-response
  experiments.
• Other aspects are
• State of aggregation of the flowing stream
• Earlines of mixing

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Road map for studying non-ideal behaviour in
reactors

• Chapter 11 Quantitative analysis of
  non-ideality
• Chp 12 Compartment models to explain gross
  malfunctions
• Chapter 13 The dispersed plug flow model
• Chapter 14 The tanks-in-series model

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The age (or residence time) distribution (RTD) of
fluid in the reactor, E

• E is the fraction of exit stream of age between t
  and tdt. Thus
• Fig 11.6 shows this graphically

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How do we determine RTD?

• Stimulus-response introduce a change at the
  inlet, observe response at the outlet.
• Types of stimulus
• Pulse
• Step
• Periodic
• Random
• Fig. 11.7

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The pulse experiment

• Instantaneous introduction of M units (e.g. kg)
  of tracer at the reactor inlet.
• Monitor concentration at outlet, Cpulse, vs t
• Fig. 11.8 PFR example
• Area under curve has units of kg.s/m3 and is
  equal to M/v, (kg)/(m3/s)
• Cm/V dmCdV dV vdt (m mass)

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E, from pulse experiment
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The mean residence time, tmean
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E? , using non-dimensional time

• Fig. 11.10. tmean, ?1 by definition

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The step input experiment

• At t0 start introducing tracer at a
  concentration of Cmax (e.g. kg/m3) at the
  reactor inlet.
• Monitor concentration at outlet, Cstep, vs t,
  Fig. 11.11

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F, from step experiment

• Normalize the Cstep curve
• (Fig.11.12)
• Relation between E and F curves
• Fig. 11.13

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Corrections to Box 6, Chp 11
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Fig.11.14 E and F curves PFR, MFR and
arbitrary system

• Note the EC notation on the y axis.
• In the step experiment we used Cmax to normalize
  Cstep
• In the pulse experiment we used M/v to normalize
  Cpulse
• The C above is the normalized concentration
• Box 9 summarizes the relation between v, C, M, m,
  t, ?

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Box 9 Chp 11 Levenspiel

• Note the correction for E(v/M)Cpulse

M
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Example 11.1 RTD from Cpulse
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Conversion in a non-ideal reactor, early or late
mixing

• The early or late mixing depicted in Figures 11.4
  and 11.5 can be thought of as different types of
  reactors in series as in Fig. 11.17
• Recall the principles for optimal arrangement of
  reactors of different types
• If 0ltnlt1 keep reactant concentrations as low as
  possible MFR first, PFR next, i.e. early mixing
• If ngt1 keep concentrations as high as possible,
  PFR first, MFR next, i.e. late mixing

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Conversion in a non-ideal reactor, macrofluid
behaviour

• Elements (clumps) of fluid act independently as
  they go through reactor different residence
  time, different concentrations, hence different
  reaction rate.
• The mean concentration at the exit will be found
  by

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Conversion in a non-ideal reactor, macrofluid
behaviour

• Box (Eqn. 13) formulates the situation using
  nomenclature we have developed.
• The CA/CA0 or XA terms will come from the batch
  performance equations applied individually to
  each element of fluid, e.g.

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Equation 13, Chp 11 Levenspiel
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Example 11.4 First order reaction in non-ideal PFR

• Cpulse vs time data from Example 11.1
• -rA(0.307 min-1)CA
• Ideal PFR gives CA/CA0 0.01, i.e. XA0.99
• The reactor with E from Example 11.1 gives
• CA/CA0 0.0469, i.e. XA0.9531

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