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On the optimum distribution of enzyme feed in a cascade of CSTR's performing an enzyme-catalyzed reaction with deactivation

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Abstract

A search for the optimum fractional distribution of an enzyme-rich stream to the various reactors of a cascade of CSTR's was implemented. A theoretical analysis, laid out in dimensionless form and based on the assumptions that the system is operated under steady state conditions, the enzyme undergoes first order deactivation, and the reaction catalyzed by the enzyme follows Michaelis-Menten kinetics, is reported. The objective function utilised is the minimisation of the overall volume of the cascade, and analytical expressions are obtained for the concentration of active enzyme and substrate in the outlet stream from each reactor. It is found that the best option is to add the whole enzyme-rich stream to the first reactor in the cascade irrespective of the operating and kinetic parameters of the system.

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Abbreviations

C E, i -mol·m−3 :

concentration of active enzyme in thei-th reactor

C S, i -mol·m−3 :

concentration of substrate in thei-th reactor

C *S, i :

normalized concentration of substrate in thei-th reactor

Da i :

Damköhler number associated with thei-th reactor using as reference the volumetric flow rate of substrate to the first unit

\(\hat Da_i \) :

Damköhler number associated with thei-th reactor using as reference the whole volumetric flow rate if all enzyme stream were added to the first unit

i :

dummy integer variable

j :

dummy integer variable

k -s−1 :

deactivation constant

K m -mol·m−3 :

Michaelis-Menten constant

K *m :

dimensionless Michaelis-Menten parameter

I :

dummy integer variable

m :

dummy integer variable

n :

dummy integer variable

N :

number of CSTRs in the cascade

p :

dummy integer variable

q :

dummy integer variable

Q -m3·s−1 :

volumetric flow rate of substrate-rich stream

r :

dummy integer variable

s :

dummy integer variable

t :

dummy integer variable

u :

dummy integer variable

v :

dummy integer variable

v max, i -mol·m−3·s−1 :

maximum rate of reaction at thei-th reactor

V i -m3 :

holdup volume of thei-th reactor

α i :

fraction of overall enzyme added to thei-th reactor

β :

ratio of overall volumetric flow rate of enzyme-rich stream to volumetric flow rate of substrate-rich stream to the first reactor

Θ i :

auxiliary function associated with thei-th reactor

τ i -s:

space time of thei-th reactor

Ξ :

ratio of time constants associated with enzyme-catalyzed reaction and deactivation reaction

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Authors and Affiliations

  1. Escola Superior de Biotecnologia, Universidade Católica Portuguesa, Rua Dr. António Bernardino de Almeida, 4200, Porto, Portugal

    N. E. Moreira & F. X. Malcata

Authors
  1. N. E. Moreira
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  2. F. X. Malcata
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Moreira, N.E., Malcata, F.X. On the optimum distribution of enzyme feed in a cascade of CSTR's performing an enzyme-catalyzed reaction with deactivation. Bioprocess Engineering 15, 301–306 (1996). https://doi.org/10.1007/BF02426438

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  • DOI: https://doi.org/10.1007/BF02426438

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