Mathematical models and the design of biochemical reactors



The application of so-called macroscopic methods, that is a widely accepted tool in chemical as well as in biochemical engineering, rests on the possibility to construct a balance equation for the rate of change of the amount of an extensive quantity present in the system. In such a balance equation two types of contribution appear, one due to exchange of matter or energy with the environment and the other due to conversion in the system. A special class of quantities, i.e. the amounts of the chemical elements and energy, are not subject to net conversion in the system. These are termed conserved quantities. This observation leads to useful approaches towards the analysis of the stoicheiometry of aerobic and anaerobic growth and the calculation of heat production. For the kinetic description of the behaviour of systems a reduction of the complexity inherent to reality is a necessary prerequisite to obtain a workable model. The comparison of the relaxation times of the internal mechanisms of the system and those of changes in its environment is shown to be a powerful tool in the reduction of model complexity. An unstructured model, based on a very simplified picture of the complexity of the biomass present in a culture, is treated and its range of validity is analysed. Finally some aspects of the description of transport phenomena inside fermentation equipment and their interaction with microbial metabolism are discussed.