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To what extent is a constant volume design worse than a minimum volume design for a series of CSTR's?

Abstract

The balance equations for substrate in a cascade of CSTR's undergoing an enzyme-catalyzed reaction following Michaelis-Menten kinetics are developed in dimensionless form. Analytical expressions relating the intermediate concentrations are independently obtained for the cases of minimum overall volume and constant volume. The fractional deviations between the overall volumes following these two design criteria are calculated and presented for several values of the relevant parameters. For situations of practical interest, the fractional deviation is below 10%. Increasing values of the Michaelis-Menten parameter, K m(or decreasing values of the number of reactors in the cascade, N) lead to lower values of the maximum deviation; this maximum deviation is attained at lower conversions of substrate when K mis increased or N decreased.

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Abbreviations

C S, imol.m−3 :

concentration of substrate at the outlet of the i-th reactor

C * S, i :

normalized concentration of substrate at the outlet of the i-th reactor

C * S, i, eq :

normalized concentration of substrate at the outlet of the i-th reactor using the design criterion of constant volume

C * S, i, opt :

normalized concentration of substrate at the outlet of the i-th reactor using the design criterion of minimum overall volume

C S, 0 mol.m−3 :

concentration of substrate at the inlet to the first reactor

Da i :

Damköhler number for the i-th reactor

Da eq :

constant Damköhler number for each reactor of the cascade

Da tot, eq :

overall Damköhler number for the cascade assuming equal-sized reactors

Da tot, min :

minimum overall Damköhler number for the cascade

Er :

fractional deviation between the overall volumes using the two different design criteria

K mmol. m−3 :

Michaelis-Menten constant

K * M :

dimensionless Michaelis-Menten constant

N :

number of reactors of the cascade

Q m3. s−1 :

volumetric flow rate

V im3 :

volume of the i-th reactor

v max mol. m−3. s−1 :

reaction rate under saturation conditions of the enzyme with substrate

V tot, opt m3 :

minimum overall volume of the cascade

V tot, eq m3 :

overall volume of the cascade assuming equal-sized reactors

References

  1. 1.

    Luyben, K.C.; Tramper, J.: Optimal design for continuous stirred tank reactors in series using Michaelis-Menten kinetics. Biotechnol. Bioeng. 24 (1982) 1217

  2. 2.

    Malcata, F.X.: Optimal design on an economic basis for continuous stirred tank reactors in series using Michaelis-Menten kinetics for ping-pong reactions. Can. J. Chem. Eng. 66 (1988) 168

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Malcata, F.X. To what extent is a constant volume design worse than a minimum volume design for a series of CSTR's?. Bioprocess Engineering 13, 105–107 (1995). https://doi.org/10.1007/BF00420436

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Keywords

  • Waste Water
  • Water Pollution
  • Balance Equation
  • Maximum Deviation
  • Constant Volume