On the use of extensive variables in process dynamics and control

In this paper we propose a methodology to determine the structure of the pseudo-stoichiometric coefficient matrix kappa in a macroscopic mass balance based model. The first step consists in estimating the minimal number of reactions that must be taken into account to represent the main mass transfer within the bioreactor. This provides the dimension of kappa. Then we discuss the identifiability of the components of kappa and we propose a method to estimate their values. Finally we present a method to select among a set of possible macroscopic reaction networks those which are in agreement with the available measurements. These methods are illustrated with three examples: real data of the growth and biotransformation of the filamentous fungi Pycnoporus cinnabarinus, real data of an anaerobic digester involving a bacterial consortium degrading a mixture of organic substrates and a process of lipase production from olive oil by Candida rugosa. (C) 2004 Elsevier Inc. All rights reserved.

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On the estimation of the pseudo-stoichiometric matrix for macroscopic mass balance modelling of biotechnological processes

http://lup.lub.lu.se/search/ws/files/22426301/fjeld_74.pdf

Reaction invariants and their importance in the analysis of eigenvectors, state observability and controllability of the continuous stirred tank reactor

The dynamics of a chemostat in which two microbial populations grow and compete for a common substrate is examined. It is shown that the two populations cannot coexist in a spatially uniform environment which is subject to time invariant external influences unless the dilution rate takes on one of a discrete set of special values. The dynamics of the same system are next considered in the stochastic environment created by random fluctuations of the dilution rate about a value that allows coexistence. The information needed for the description of the random process of the state of the chemostat is obtained from the transition probability density function. By modeling the system as a Markov process continuous in time and space, the transition probability density is obtained as solution of the Fokker-Planck equation. Analytical and numerical solutions of this equation show that extinction of either one population or the other will ultimately take place. The time required for extinction, the evolution of the mean composition with time, the steady states of the latter and the dependence of all the above on the intensity of the random noise are also calculated using constants appropriate to the competition of E. coli and Spirillum sp. The question of making predictions as to which population is the more likely to become extinct is treated finally, and the probabilities of extinction are calculated as solutions of the steady state version of the backward Fokker-Planck (Kolmogorov) equation.

M. Field

Papers

Response modes of continuous stirred tank reactors