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Cost minimization in the predesign of an enzymatic CSTR: an overall approach

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Abstract

The balance equations pertaining to the modelling of a CSTR performing an enzyme-catalyzed reaction in the presence of enzyme deactivation are developed. Combination of heuristic correlations for the size-dependent cost of equipment and the purification-dependent cost of recovery of product with the mass balances was used as a basis for the development of expressions relating a (suitably defined) dimensionless economic parameter with the optimal outlet substrate concentration under the assumption that overall production costs per unit mass of product were to be minimized. The situation of Michaelis-Menten kinetics for the substrate depletion and first order kinetics for the deactivation of enzyme (considering that the free enzyme and the enzyme in the enzyme/substrate complex deactivate at different rates) was explored, and plots for several values of the parameters germane to the analysis are included.

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Abbreviations

C E mol m−3 :

concentration of active enzyme

C E,0 mol m−3 :

initial concentration of active enzyme

C p mol m−3 :

concentration of product of interest

C s mol m−3 :

concentration of substrate

C s,0 mol m−3 :

initial concentration of substrate

I $:

capital cost of equipment

k d s−1 :

deactivation constant of free enzyme

k ⋆ d s−1 :

deactivation constant of enzyme in enzyme/substrate complex

K m mol m−3 :

Michaelis-Menten constant

K ⋆ m :

dimensionless counterpart of K m

k r s−1 :

rate constant associated with conversion of enzyme/substrate complex into product

M w kg mol−1 :

molecular weight of product of interest

P $ kg−1 :

cost of recovery of product of interest in pure form

Q m3s−1 :

volumetric flow rate

V m3 :

volume of reactor

X $ kg−1 :

global manufacture cost of product of interest in pure form

X ⋆ :

dimensionless counterpart of X

α 1 $ m−1.8 :

constant

α 2 $ m−3 :

constant

Δt s:

useful life of CSTR

ɛ 0 :

ratio of initial concentrations of enzyme and substrate

η :

ratio of deactivation constant of free enzyme to rate constant of depletion of substrate

ζ :

ratio of deactivation constants

Φ :

univariate function expressing the dependence of the rate of enzyme deactivation on C S

Ψ :

univariate function expressing the dependence of the rate of substrate depletion on C S

Ω :

dimensionless economic parameter

References

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Authors and Affiliations

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

    F. X. Malcata

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  1. F. X. Malcata
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Malcata, F.X. Cost minimization in the predesign of an enzymatic CSTR: an overall approach. Bioprocess Engineering 13, 51–55 (1995). https://doi.org/10.1007/BF00368767

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  • DOI: https://doi.org/10.1007/BF00368767

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