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Mixing-models applied to industrial batch bioreactors

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Abstract

Mixing models for bioreactors on the basis of the tanks-in-series concept are presented and a suitable parameter-estimation method is introduced. The Monte-Carlo-optimization procedure with the inhomogeneity-curve included in the objective function is used. Results of the parameter optimization procedure are given for stirred-tank-bioreactors equipped with one and three Rushton turbines under aerated conditions. The model designed for the stirredtank with three Rushton turbines is capable to describe the mixing properties, while in case of the stirred-tank with one Rushton turbine the simulated radial circulation time does not correlate with the measured one.

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Abbreviations

a 00...a XY :

coefficients in Eq. (9)

d i m:

stirrer diameter

D m:

tank diameter

E :

relative error

F AX m3/s:

axial liquid flow rate

F G m3/s:

aeration flow rate

F RAD m3/s:

radial liquid flow rate

g m/s2 :

acceleration of gravity

h l m:

height of fluid in the tank

i s(t):

simulated inhomogeneity-curve

i m(t):

measured inhomogeneity-curve

k :

number of sensors

n 1/s:

stirrer revolutions

N :

number of tanks in the tanks-of-series-cascade

p :

number of measured time intervalls

t s:

time

t c.AX s:

axial circulation time

t c,RAD s:

radial circulation time

T i °C:

temperature of sensors

T ∞ °C:

temperature at the end of the experiment

T 0 °C:

temperature before pulse injection

V tot m3 :

total liquid volume

V C m3 :

liquid volume of circulation cascade, additional index specifications describe the cascade elements (Figs.1 and 2)

V M m3 :

liquid volume of well mixed stirrer compartment

w 0 m/s:

superficial gas velocity

X, Y :

exponents in eq. (9)

ρ kg/m3 :

density

η :

Pas dynamic viscosity

ν m2/s:

kinematic viscosity

τ s:

time constant (time for 63,2% of T ∞) of the signal

\(Fr_s = n\sqrt {d_i /g} \) :

stirrer Froude number

\(Fr_A = \frac{{w_0 }}{{\sqrt {g \cdot h_i } }} = \frac{{F_G }}{{V_{tot} }} \cdot \sqrt {\frac{{h_i }}{g}} \) :

aeration Froude number

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Authors and Affiliations

  1. Institute for Biotechnology, Petersgasse 12, 8010, Graz, Austria

    B. Mayr & A. Moser

  2. Faculty of Food Technology and Biotechnology, University of Zagreb, Pierottijeva 6, 41000, Zagreb, Croatia

    P. Horvat

  3. Research Institute for Technical Chemistry of Hungarian Academy of Sciences, P.O. Box 125, 8201, Veszprém, Hungary

    E. Nagy

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  2. P. Horvat
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  3. E. Nagy
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  4. A. Moser
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Mayr, B., Horvat, P., Nagy, E. et al. Mixing-models applied to industrial batch bioreactors. Bioprocess Engineering 9, 1–12 (1993). https://doi.org/10.1007/BF00389534

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