Enzyme kinetics and associated reactor design:

1
CP504 Lecture 6
Enzyme kinetics and associated reactor design
Enzyme Reactor Design
2
Batch Enzyme Reactor
Mass balance for the substrate
0 0 d(VCs)/dt (-rS)V
For a batch reactor with constant volume reacting
mixture, the above becomes
(27)
- dCs/dt -rS
V for volume of the reacting mixture at time t
CS for concentration of the substrate in V at
time t
(-rS) for substrate utilization rate in V at time
t
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Batch Enzyme Reactor
Substituting (-rS) for the simple enzyme reaction
in (27), we get
(28)
Rearranging (28), we get
(29)
Integrating (29) gives
(30)
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Batch Enzyme Reactor
Determination of M-M kinetic parameters
(30) in linear form becomes
(31)
- KM
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Plug-flow Enzyme Reactor at steady-state
F
F
F
F
CSf
CS0
CSdCS
CS
dV
Mass balance for the substrate over dV
FCS F(CS dCS) (-rS) dV
The above can be simplified to
- FdCS / dV -rS
F for the steady flow rate through the reactor
CS for concentration of the substrate
dV for small volume of the reacting mixture
(-rS) for substrate utilization rate in dV
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Plug-flow Enzyme Reactor at steady-state
F
F
F
F
CSf
CS0
CSdCS
CS
dV
Introducing space-time ? ( V/F), we get
- dCS / d? -rS
(32)
which is very similar to (27)
F for the steady flow rate through the reactor
CS for concentration of the substrate
dV for small volume of the reacting mixture
(-rS) for substrate utilization rate in dV
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Plug-flow Enzyme Reactor at steady-state
Substituting (-rS) for the simple enzyme reaction
in (32), we get
(33)
Rearranging (33), we get
(34)
Integrating (34) gives
(35)
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Plug-flow Enzyme Reactor at steady-state
(35) in linear form becomes
(36)
Determination of M-M kinetic parameters
- KM
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Continuous Stirred Tank Enzyme Reactor at
steady-state
F
CS0
V
CS
F
CS
F for the steady flow rate through the reactor
CS for concentration of the substrate in the
reactor and at the exit
V for the volume of the reacting mixture
(-rS) for substrate utilization rate in V
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Continuous Stirred Tank Enzyme Reactor at
steady-state
F
CS0
V
CS
F
CS
Mass balance for the substrate over V
FCS0 FCS (-rS) V
(37)
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Continuous Stirred Tank Enzyme Reactor at
steady-state
Introducing space-time ? ( V/F) in (37), we get
CS0 CS (-rS) ?
(38)
Substituting (-rS) for the simple enzyme reaction
in (38), we get
(39)
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Continuous Stirred Tank Enzyme Reactor at
steady-state
(39) in linear form becomes
(40)
CS
Determination of M-M kinetic parameters
- KM