Biological processes and biochemical reactions Fig 27.1

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Biological processes and biochemical reactions
(Fig 27.1 )

• Chemical and environmental engineers are
  particularly concerned with the two types of
  fermentation indicated
• Enzyme fermentations
• Microbial fermentations

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Fig. 27.1
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Fermentation

• Definition from p.611

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Enzyme and microbial fermentations

• Eqn 1 and 2

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Enzyme Fermentation Michaelis-Menten Kinetics
studied previously

• Example 2.2 Mechanism for the enzyme-substrate
  reaction.
• Prob. 2.23 The steady state and equilibrium
  assumptions in deriving the Michaelis-Menten
  rate expression for enzyme catalyzed reactions.
• Problem 3.15 Integral method of analysis to find
  Michaelis-Menten kinetics constants.
• Reactions of changing order (Chapter 3)

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Previously

• Example 2.2
• Mechanism for the enzyme-substrate reaction.
• Prob. 2.23
• The steady state and equilibrium assumptions
• in deriving the Michaelis-Menten rate expression
• for enzyme catalyzed reactions.

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Fig. 27.2
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Fig. 27.3
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Michaelis-Menten kinetics in batch reactor
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Reactions of changing order

• Michaelis-Menten
• kinetics is an example
• of reactions that exhibit
• changing order
• For example,
• Chapter 3
• Demonstrates
• the case

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Fig. 3.16
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Reactions of changing order- differential analysis

• The differential method
• avoids the issues
• related to integration
• but still needs
• appropriate linearized
• forms to test the
• rA vs CA expression.
• The rA will come
• from the slope
• (graphically determinded)
• of the batch CA vs t data

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Fig. 3.19

• Testing the rate equation by differential analysis

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Michaelis-Menten kinetics from batch reactor
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Fig. 27.5
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Michaelis-Menten kinetics from MFR

• A batch reactor is usually preferred for
  obtaining rate data and kinetic parameters
  because it is more practical to use in the
  laboratory.
• However, if there is MFR data it can be used to
  obtain kinetic parameters as well by using the
  M-M rate expression in the MFR performance
  equation.

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Michaelis-Menten kinetics from MFR
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Fig. 27.6
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Conceptual models of inhibition

• If the presence of B slows down the reaction then
  it is an inhibitor (opposite of catalyst)
• Two models of inhibition (competitive and
  noncompetitive) are presented in Fig. 27.7
• Important in pharmacological applications (drugs
  for disease)

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Microbial fermentation

• In a typical natural system we have a wide
  variety of microorganisms living on a wide
  variety of food sources
• We grossly simplify this situation to one where a
  single type of microorganism (cells, bugs, C in
  the equation below) is eating away at one type of
  food (substrate, A in the equation below).
• R product, or waste material

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Microbial fermentation product poisoning

• In some cases the presence of R inhibits the
  action of cells
• The bugs responsible for making wine quit around
  12-13 alcohol

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Microbial fermentation, Monod kinetics

• Parameters k and CM
• Note the similarity with M-M kinetics, except
  that CE0 has been replaced by CC which is not
  constant
• Chapter 28 starts out by examining this reaction
  in three different systems
• Constant environment fermentor
• Batch fermentor
• Mixed flow fermentor

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Monod kinetics
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Fig. 28.1

• Growth in constant environment

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Microbial fermentation in batch reactor

• Time periods from the start
• Induction (time lag)
• Exponential growth
• Stationary (food getting scarce, possible
  inhibition by products)
• Death (food finished or environment becomes
  toxic to the bugs)

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Fig.28.2

• Two types of lag curve
• Depending on whether young or old cells adapt to
  a new environment more rapidly, the lag time may
  increase or decrease with the age of cells
  introduced into a fresh medium.

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Microbial fermentation - Substrate limiting and
poison limiting mechanism that bring the reaction
to an end
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Product Poisoning (Fig.28.4)
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Fig. 28.4
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Microbial fermentation in MFR

• Steady state MFR operates under constant CA, CC,
  and CR conditions.
• No adaption or lag time involved
• k k(temperature, composition, presence of trace
  components,
• light intensity etc.)

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Stoichiometry for biochemical reactions

• Microorganisms (cells, bugs) and biodegradable
  organics (food, substrate) are all complex
  chemicals. Not practical to quantify with moles.
  Instead use mass units,
• i.e. Concentration mass /volume (mg/L)
• Reaction rate mass/volume.time (mg/L.hr)
• When we had A2B C
• we could write rB2rA
• Now we need to relate
• the reaction rates
• by mass ratios.
• Levenspiel uses C/A in a circle instead of C/A.
  Most wastewater literature uses other notation
  which will be introduced below.

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Notation for stoichiometry

• These ratios may depend on the composition of the
  reaction mixture for batch and plug flow reactors
  but we can assume they are constant for
• the exponential growth phase of batch reactors
• mixed flow reactors (where composition does not
  change at steady state)

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Substrate Limiting Microbial Fermentation in
batch or plug reactor

• Poison-free Monod kinetics

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Monod kinetics Batch reactor performance
equation

• Substituting the Monod expression for rA in the
  batch reactor performance equation and
  integrating, we can get
• The constants in the reaction rate expressions (k
  and CM) can then be determined by comparing a
  linearized form of this equations with batch
  reactor data (Fig. 29.2)

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Monod kinetics in Batch reactor- linear form to
obtain parameters
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Monod constants from batch data integral method
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Monod constants from batch data differential
method Fig.29.3
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Monod kinetics maximum reaction rate in batch
reactor

• CA starts high and decreases
• CC starts low and increases
• The product must go through a maximum. The CA at
  the maximum rate corresponds to drC/dt0
• Figures 29.1 and 29.6 demonstrates this behaviour
  (recall the discussion on autocatalytic
  reactions)

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Figure 29.1
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1/rA vs CA for Monod kinetics

• Figure 29.6
• We start with CA0 and CC0, as CA decreases, CC
  increases.
• There is a maximum rate (minimum 1/rA)
• This is the autocatalytic reaction type we have
  seen earlier.
• MFR better than PFR to the right of the minimum

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Fig. 29.6
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Monod kinetics mixed reactor performance
equation

• Recall MFR performance equation
• Substitute the Monod expressions for rA
• Box 7 gives the result in terms of A, C, or R,
  when there are no microorganisms in the feed,
  CC00
• Typically we use only one of these

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Monod constants from MFR data Fig.29.4

• Monod constants from mixed reactor data
• Equation 29.7 (for CA) re-arranged
• Plot as in Fig 29.4 to get k and CM

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Washout

• C balance on MFR
• Input generation output accumulation
• Or
• Accumulation input generation output
• Normally, we operate at steady state by ensuring
  that input generation output
• However, if there is no input, and
  outputgtgeneration then there is the possibility
  of microorganisms being washed out of the MFR and
  all reaction coming to a stop.

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Washout In mathematical terms
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• Washout In mathematical terms
• Note that in Box 7
• all the solutions given
• Are for
• Since there is washout
• At lower ?m

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Optimum operating conditions for MFR

• Our general aim has been to minimize V (?) for a
  desired conversion.
• We saw the possibility of washout when ? is too
  low with Monod kinetics and CC00
• What would be the optimal operating condition?
• Maximum rate of cell production
• or,
• maximum rate of substrate utilization
• Figure 29.5 shows this graphically

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Optimum operating conditions for MFR

• Let
• (not to be confused with N, the number of MFRs in
  the tanks in series model)
• Optimal conditions and washout depend on CA0 and
  CM via the above parameter, as shown in Fig.29.5
  and equations 29.10 and 29.11

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Fig.29.5
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Optimal conditions in MFR for Monod kinetics with
CC00
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2
3
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MFR with Monod kinetics when CC0?0
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Notation from Wastewater treatment literature
(e.g. Metcalf Eddy)
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Notation from Wastewater treatment literature
(e.g. Metcalf Eddy)
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Notation from Wastewater treatment literature
(e.g. Metcalf Eddy)

• Thus