Bioreactor mathematical modeling

Keywords. Cellulase production. Solid-state fermentation. Operating conditions, Bioreactor, Mathematical model... 

A number of examples from biochemical engineering are presented in this chapter. The mathematical models are either algebraic or differential and they cover a wide area of topics. These models are often employed in biochemical engineering for the development of bioreactor models for the production of bio-pharmaceuticals or in the environmental engineering field. In this chapter we have also included an example dealing with the determination of the average specific production rate from batch and continuous runs. 

Other major early contributions of biochemical engineering have been in the development of the artificial kidney and physiologically based pharmacokinetic models. The artificial kidney has been literally a lifesaver. Pharmacokinetic models divide the body of an animal or human into various compartments that act as bioreactors. These mathematical models have been used very successfully in developing therapeutic strategies for the optimal delivery of chemotherapeutic drugs and in assessing risk from exposure to toxins. 

Rottenbacher, L., Schofiler, M. and Bauer, W., Mathematical modelling of alcoholic fermentation in a gas/solid bioreactor - combined effects of solids mixing and non-steady-state kinetics. Proceedings of the First IFAC Symposium on Modelling and Control of Biotechnological Processes, Noordwijkerhout, 1985b, 151-157. 

Due to the complexity of insect cell/baculovirus interactions and the possibility of using low MOTs, which, in turn, increase the complexity of the process since several different population types coexist simultaneously in the bioreactor vessel, the development of mathematical models as tools for describing the system dynamics is extremely useful. 

Figure 14.3 also shows the concentration-polarization layer that also forms during the filtration. Due to it, there is a backdiffusion of the retained compound that has higher concentration on the membrane surface. These phenomena can also decrease the efficiency ofthe filtration. This effect should also be taken into account during the mathematical modeling of the transport processes of the membrane bioreactor, as will be discussed later. 

Mathematical Modeling of Membrane Bioreactor 314 Modeling of Enzyme Membrane Layer/Biofilm Reactor 314... 

Several interesting parameter-control models or systems have been reported in recent years. These are a five-state mathematical model for temperature control by Bailey and Nicholson [106], a mathematical-model description of the phenomenon of light absorption of Coffea arabica suspension cell cultures in a photo-culture vessel by Kurata and Furusaki [107], and a bioreactor control system for controlling dissolved concentrations of both 02 and C02 simultaneously by Smith et al. [108]. 

Various adsorbents have been examined for their potential to increase in situ product separation in plant cell culture. Suspended solid adsorbents were popular, and the use of immobilized adsorbent has been investigated recently [17-20]. The advantages of immobilized adsorbent are that it is easy to use in a bioreactor operation and that it allows adsorbents to be easily separated from culture broth for the repeated use of cells and adsorbents [21, 22]. The design and optimization of in situ separation process for phytochemicals using immobilized adsorbent required a detailed mathematical model. It was difficult to achieve an optimal design based on purely empirical correlations, because the effects of various design parameters and process variables were coupled. 

Application of mathematical models as a tool for approaching the previously mentioned challenges. What can mathematical models tell us about the degradation of MTBE in bioreactors How can they be used to increase understanding of the factors which are most important for bioremediation of MTBE ... 

Enzyme thermal inactivation during bioreactor operation is of paramount importance and must be considered for proper bioreactor design, as shown in Fig. 3.1. To do so, a mathematical model must be developed based on experimentally calculated and validated parameters. Mechanistic models to describe enzyme inactivation were presented in sections 5.4.1 and 5.4.2. 

In these mathematical models most attention has been paid to the heat transfer problem. Similar approaches need to be developed for the water balance to ensure that substrate beds do not dry out to levels which will decrease bioreactor performance. 

Much more needs to be done. More attention needs to be given to the auxihary operations such as substrate preparation, sterihzation, aseptic transferal of substrate, preparation of inoculum, and downstream processing. With respect to the bioreactor step itself, mathematical models need to be improved in order to improve their usefulness as tools in the design process. 

Three main areas are associated with the flow of further work bioreactors, kinetics, and conversion. This pathway will also be followed in this book (Chapters 3-6). (Chapter 4 is a detailed look at the problems associated with the coupling of kinetic and transport phenomena in the formulation of an analysis of process kinetics.) The goal in each of the three main areas is the establishment of a mathematical model. In correspondence with the main objective of this book (see Sect. 1.2), the hallmark of this procedure lies in the careful formulation of the biokinetics. Basic research is primarily interested... 

Figure 2.20. Overview of the five levels of process research and mathematical modeling of bioprocessing and bioreactor operation.

Figure 3.41. Classification of mathematical models of bioreactors according to engineering criteria. (Adapted from A. Moser, 1977a)...

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