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CP504 – ppt_Set 05. Enzyme kinetics and associated reactor design: Enzyme Reactor Design. Batch Enzyme Reactor. Mass balance for the substrate:. 0 = 0 + d(VC s )/dt + (-r S )V. For a batch reactor with constant volume reacting mixture, the above becomes. (29). - dC s /dt = -r S.

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## Enzyme kinetics and associated reactor design: Enzyme Reactor Design

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**CP504 – ppt_Set 05**Enzyme kinetics and associated reactor design: Enzyme Reactor Design**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 (29) - 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**(**) CS0 rmaxCS dCS - (CS0 – CS) rmax t KM ln + = = CS dt KM + CS CS t ) ( ∫ ∫ KM + CS dCS - rmax dt = CS CS0 0 Batch Enzyme Reactor Substituting (-rS) for the simple enzyme reaction in (29), we get (30) Rearranging (30), we get (31) Integrating (31) gives (32)**(CS0 – CS)**t rmax - KM + = ln(CS0/CS) ln(CS0/CS) (CS0 – CS) ln(CS0/CS) rmax t ln(CS0/CS) Batch Enzyme Reactor Determination of M-M kinetic parameters (32) in linear form becomes (33) - KM**Plug-flow Enzyme Reactor at steady-state**F F F F CSf CS0 CS CS+dCS 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**Plug-flow Enzyme Reactor at steady-state**F F F F CSf CS0 CS CS+dCS dV Introducing space-time θ ( = V/F), we get - dCS / dθ = -rS (34) which is very similar to (29) 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**(**) CS0 rmaxCS dCS (CS0 – CS) rmax θ KM ln - + = = CS dθ KM + CS CS θ ) ( ∫ ∫ KM + CS dCS - rmax dθ = CS CS0 0 Plug-flow Enzyme Reactor at steady-state Substituting (-rS) for the simple enzyme reaction in (34), we get (35) Rearranging (33), we get (36) Integrating (34) gives (37)**(CS0 – CS)**θ rmax - KM + = ln(CS0/CS) ln(CS0/CS) (CS0 – CS) ln(CS0/CS) rmax θ ln(CS0/CS) Plug-flow Enzyme Reactor at steady-state (37) in linear form becomes (38) Determination of M-M kinetic parameters - KM**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**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 (39)**rmaxCS**θ CS0 = CS + KM + CS Continuous Stirred Tank Enzyme Reactor at steady-state Introducing space-time θ ( = V/F) in (39), we get CS0 = CS + (-rS) θ (40) Substituting (-rS) for the simple enzyme reaction in (40), we get (41)**CSθ**CS - KM + rmax = (CS0 – CS) rmax CSθ (CS0-CS) Continuous Stirred Tank Enzyme Reactor at steady-state (41) in linear form becomes (42) CS Determination of M-M kinetic parameters - KM

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