Summary
Dynamic modelling of a continuous lactose fermentation system for control and optimisation of operation has been carried out. The bioreactor used was coupled with an ultrafiltration module and an electrodialysis unit. A unstructured model taking into account cell growth, substrate consumption, and metabolite (lactic acid) production, has been analysed. The metabolite production model was represented by the Luedeking-Piret equation, modified in order to improve the description of lactic acid production at low dilution rate.
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Abbreviations
- Fe :
-
bioreactor influent flow rate (1/h)
- J :
-
lactate flux in the ED unit (g/h)
- Kd :
-
mortality constant (h-1)
- Kp :
-
product inhibition constant (g/l)
- Ks :
-
substrate saturation constant (g/l)
- P 0 :
-
product concentration in the bioreactor (g/l)
- P 1 :
-
product concentration in tank D (g/l)
- P 3 :
-
product concentration in the effluent of the ED unit (g/l)
- Q 0 :
-
retentate flow rate (UF influent) (1/h)
- Q 1 :
-
permeate flow rate (1/h)
- Q 2 :
-
retentate flow rate (UF effluent) (1/h)
- Q 21 :
-
cell recycling flow rate (1/h)
- Q 22 :
-
cell bleed flow rate (1/h)
- Q 3 :
-
recycling flow rate in the ED unit (influent) (1/h)
- Q 41 :
-
recycling flow rate in the ED unit (effluent) (1/h)
- Q 42 :
-
tank D overflow (1/h)
- Q 43 :
-
recycling flow rate to the ED unit to the bioreactor (1/h)
- q p :
-
specific rate of product formation (h-1)
- q S :
-
substrate consumption specific rate (h-1)
- q Z :
-
nitrogen consumption specific rate (h-1)
- S e :
-
substrate concentration in the influent (g/l)
- S 0 :
-
substrate concentration in the bioreactor (g/l)
- S 1 :
-
substrate concentration in tank D (g/l)
- S 3 :
-
substrate concentration in the effluent of the unit (g/l)
- t :
-
time (h)
- t 1 :
-
time when μ=Kd (h)
- V 0 :
-
fermentation broth volume (1)
- V 1 :
-
tank D volume (1)
- X 0 :
-
bromass concentration in the bioreactor (g/l)
- X 2 :
-
biomass concentration in the retentate UF flow rate (g/l)
- Y P/S :
-
(=1/Y S/P) lactic acid yield coefficient (g lactic acid/g substrate consumed)
- Y X/Z :
-
(=1/Y S/X) cell yield coefficient (g cells produced/g lactose consumed)
- Y X/Z :
-
(=1/Y Z/X) second cell yield coefficient (g cells produced/g nitrogen consumed)
- Z e :
-
nitrogen concentration in the influent (g/l)
- Z 0 :
-
nitrogen concentration in the bioreactor (g/l)
- Z 1 :
-
nitrogen concentration in tank D (g/l)
- α, β:
-
constants of the Luedeking and Piret model
- μ0, β0 :
-
coefficients in Eq. (23)
- μ:
-
specific growth rate (h-1)
- μmax :
-
maximum specific growth rate (h-1)
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de Raucourt, A., Girard, D., Prigent, Y. et al. Lactose continuous fermentation with cells recycled by ultrafiltration and lactate separation by electrodialysis: modelling and simulation. Appl Microbiol Biotechnol 30, 521–527 (1989). https://doi.org/10.1007/BF00263859
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DOI: https://doi.org/10.1007/BF00263859