Abstract
A numerical method suitable for computer simulation of complex continuous cultivation of microorganisms is described in detail. The method makes possible an iterative solution of a set of nonlinear algebraic equations that represent the steady state mass balances of a chemostat. The continuation algorithm makes it possible to map the dependence of state variables for the whole range of dilution rates. Easy implementation of the method is possible when the computer code written in BASIC language is used. Two examples, first for oxygen limited cultivation, second for anacrobic acetone — ethanol — butanol fermentation, demonstrate the feasibility of the method.
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Abbreviations
- AA:
-
acetic acid concentration, g/L
- ABE:
-
the 2nd test system — acetone — butanol — ethanol continuous cultivation
- a :
-
experimentally adjustable parameter
- B:
-
butanol concentration, g/L
- β :
-
vector of coefficients in Eq. 7
- BA:
-
butyric acid concentration, g/L
- c*:
-
equilibrium dissolved oxygen concentration, mg/L
- D :
-
dilution rate, 1/h
- Ei :
-
ethanol concentration, g/L
- EPS:
-
prescribed computation accuracy
- F:
-
vector of right hand sides
- |F|:
-
Euclidean norm of functional F
- J:
-
Jacobi matrix of partial derivatives
- k La:
-
acration capacity, 1/h
- K 1–K 11 :
-
parameters of the model (see Table II)
- K s,K o :
-
saturation constants, g/L
- K i,K iba :
-
inhibition constants, g/L
- μ :
-
specific growth rate; 1/h
- μ max :
-
maximum specific growth rate, 1/h
- n,N :
-
number of dependent variables in the model
- O:
-
dissolved oxygen concentration, mg/L
- OLCC:
-
the 1st test system — oxygen limited continuous cultivation
- PI:
-
print interval
- S:
-
substrate concentration, g/L
- s:
-
vector of Newton’s improvements
- S0 :
-
inlet substrate concentration, g/L
- t :
-
current time, h
- X :
-
biomass concentration, g/L
- X(I):
-
dependent variable,
- y :
-
relative RNA concentration, RNA/RNAmin
- y :
-
vector of state variables
- Y s/x,Y o/x :
-
yield coefficients
- z:
-
the length of the are of the solution
- i, j :
-
indices
References
Holodniok M., Klíč A., Kubíček M., Marek M.:The Methods of the Analysis of Nonlinear Dynamic Models. (In Czech) Academia, Prague 1986.
Kubíček M.: Dependence of solution of nonlinear systems on a parameter.ACM Trans.Math.Software 2, 98 (1976).
Perlmutter D.D.:Stability of Chemical Reactor. Prentice Hall, Englewood Cliffs, New Jersey 1972.
Schwippel J., Votruba J.: Identification of mathematical models of complex cultures in continuous cultivations of microorganisms — numerical approach.Folia Microbiol. 37, 427–432 (1992).
Shrivastava A.F.: Search for marker of physiological state ofClostridium acetobutylicum. McGill University, Montreal 1990.
Volesky B., Votruba J.:Modeling and Optimization of Fermentations Processes. Elsevier, Amsterdam 1992.
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Schwippel, J., Votruba, J. Method for computer simulation of complex continuous cultivation of microorganisms. Folia Microbiol 38, 311–319 (1993). https://doi.org/10.1007/BF02898600
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DOI: https://doi.org/10.1007/BF02898600