Abstract
The macroscopic mathematical model based on compartments with ideal mixing zones and tanks-in series was evaluated. Based on the experimental data obtained in a 300 dm3 pilot reactor and the dependence of mixing time on the volume of liquid phase, we have found mathematical relations between the ratio of vessel diameter to liquid level, adjustable parameters of model and the mixing time.
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Abbreviations
- V dm3 :
-
total volume of bioreactor
- V g dm3 :
-
total volume of liquid
- V 1 dm3 :
-
volume of ideally mixed zone in the vessel
- V 2 dm3 :
-
volume of macromixer in inner circulation flows
- V 3 dm3 :
-
volume of liquid phase in the pump
- V 4 dm3 :
-
volume of liquid phase in the pipe between the vessel and the pump
- V 5 dm3 :
-
volume of liquid phase in the pipe between the pump and air input system included falling jet
- V LT dm3 :
-
volume of liquid in the tank
- V LC dm3 :
-
volume of liquid in the circulation system
- F E dm3/s:
-
inner volumetric circulation flow rate across the macromixers
- F cir dm3/s:
-
external volumetric circulation flow rate, pumping capacity
- t A s:
-
time interval of the pulse application
- t AA s:
-
time point of the pulse application related to the free choosen starting point of the experiment
- t m s:
-
mixing time
- t c s:
-
circulation time
- t end s:
-
end time of simulation
- C *,* kg/m3 :
-
concentration of tracer in the indicated compartment
- C 0 kg/m3 :
-
concentration of the tracer before the injection
- C t kg/m3 :
-
concentration of the tracer at the indicated time
- C ∞ kg/m3 :
-
theoretical concentration of the full mixed tracer
- C sim kg/m3 :
-
calculated concentration of tracer during numerical integration method
- i :
-
index of an arbitrary tank
- D T m:
-
diameter of bioreactor
- D 1/s:
-
dilution rate
- H L m:
-
level of liquid in the unaerated vessel
- δ :
-
vector of inhomogenities
References
Lafferty, R. M.; Moser, A.; Steiner W.; Saria, A.; Weber, J.: Gas-Flüssigkeitsstrahl-Schlaufenreaktor. VDI-Berichte 315 (1978) 257–267
Steiner, W.; Moser, A.; Saria, A.; Lafferty, R. M.: Mixing problems in a deep jet aeration bioreactor. Paper 33, 4th FEMS Symposium, Vienna, (1977)
Horvat, P.; Mayr, B.; Jury, W.; Steiner, W.; Moser, A.: Mathematical model for mixing in deep jet bioreactors: Analysis. (In press, this journal)
Burden, R. L.; Faires, J. D.: Error control and the Runge-Kutta-Fehlberg method. In: Numerical Analysis, pp. 251–255 Boston: Pws-Kent Publ. 1989
Jury, W.: Mixing in Bioreactors. Ph. D. Thesis, Institute for Biotechnology, Graz University of Technology (1989).
Bajpai, R. K.; Reuss, M.: Coupling of mixing and microbial kinetics for evaluating the performance of bioreactors. Can. J. Chem. Eng. (1982) 384–392
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Moser, A., Mayr, B., Jury, W. et al. Mathematical models for mixing in deep-jet bioreactors: Calculation of parameters. Bioprocess Engineering 7, 177–182 (1991). https://doi.org/10.1007/BF00387414
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DOI: https://doi.org/10.1007/BF00387414