Summary
An off-line parameter estimation method has been developed to predict the dynamic behaviour of a continuous lactose fermentation system. The model used is an unstructured model taking into account cell growth, substrate consumption, and metabolite production (lactic acid). This method, based on the Hooke-Jeeves non-linear-programming technique, results in a good estimation of the biological parameters of the model, and so gives a better understanding of the different phenomena involved in lactose fermentation.
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Abbreviations
- Cp, Cs, Cz, Dp, Ds, Dz :
-
coefficients in system (A)
- Fe :
-
bioreactor influent flow rate (1/h)
- I :
-
current in the ED unit (A)
- J :
-
lactate flux in the ED unit (g/h)
- Kd :
-
mortality constant (h-1)
- Kp :
-
product inhibition constant (g/l)
- Ks :
-
strbstrate saturation constant (g/l)
- P 0 :
-
product concentration in the bioreactor (g/l)
- P 1 :
-
product concentration in the D tank (g/l)
- P 0r :
-
estimation of P 0 (g/l)
- Q 0 :
-
retentate flow rate (UF influent) (1/h)
- Q 1 :
-
permeate flow rate (1/h)
- Q 22 :
-
cell bleed flow rate (1/h)
- Q 3 :
-
recycling flow rate in the ED (influent) (1/h)
- Se :
-
substrate concentration in the influent (g/l)
- S 0 :
-
supstrate concentration in the bioreactor (g/l)
- S 1 :
-
substrate concentration in tank D (g/l)
- S 0r :
-
estimation of S 0 (g/l)
- t :
-
time (h)
- V 0 :
-
fermentation broth volume (1)
- V 1 :
-
tank D volume (1)
- X 0 :
-
biomass concentration in the bioreactor (g/l)
- Y P/S :
-
(=1/Y S/P) lactic acid yield coefficient (g lactic acid/g lactose consumed)
- Y X/S :
-
(=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)
- Y x, Y m :
-
input mathematical parameters of the linear system (M 2)
- Ze :
-
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)
- Z 0r :
-
estimation of Z 0 (g/l)
- α, β:
-
constants of the Luedeking and Piret's model
- μ:
-
specific growth rate (h-1)
- μmax :
-
maximum specific growth rate (h-1)
References
Aborhey S, Williamson D (1978) State and parameter estimation of microbial growth processes. Automatica 14:493–498
Accolas JP, Bloquel R, Didienne R, Regnier J (1977) Propriétés acidifiantes des bactéries thermophiles en relation avec la fabrication de yoghourt. Lait 57:1–23
Bastin G, Dochain D (1985) Adaptative estimation of microbial growth rates. In: Dillings SA (ed) Proc. 7th IFAC/IFORS Symposium on Identification and System Parameter estimation, Pergamon, Oxford, England, pp 1161–1166
Cardenas R, Boyaval P, Corre C (1987) Mieux conduire les procédés de fermentation. Mesures, March 23rd:91–96
Dochain D, Bastin G (1984) Adaptative identification and control algorithms for nonlinear bacterial growth systems. Automatica 20:621–634
Holmberg A, Ranta J (1982) Procedures for parameter and state estimation of microbiol growth process models. Automatica 18:181–193
Hooke R, Jeeves JA (1961) Direct search solution of numerical and statistical problems. J Assoc Comput Machinery 8:212–229
Nihtila M, Harmo P, Perttula M (1984) Real-time growth estimation in batch fermentation. In: Gertler J, Keviczky L (eds) Proc. 9th IFAC triennal world congress: Bridge between control science and technology, Pergamon, Oxford, England, pp 225–230
Raucourt A de (1987) Modélisation et conduite d'un procédé de valorisation du lactose par fermentation continue. PhD thesis, ESE, Rennes, France
Stephanopulos G, San K-Y (1983) On-line estimation of time-varying parameters: A application to biochemical reactors. In: Halme A (ed) Modelling and control of biotechnical processes, Pergamon Press, Oxford, pp 195–199
Vialas C (1984) Modélisation et contribution à la conception d'un procédé biotechnologique. PhD thesis, INPG, Grenoble, France
Vialas C, Cheruy A (1985) Modelling and simulation of light-dependent biotechnological processes. In: Johnson A (ed) Proc. 1st IFAC Symposium on modelling and control of biotechnological process, Pergamon, Oxford, England, pp 155–159
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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: model identification. Appl Microbiol Biotechnol 30, 528–534 (1989). https://doi.org/10.1007/BF00263860
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DOI: https://doi.org/10.1007/BF00263860