Model building is considered here as an adaptive process (cf. Fig. 2.18): It involves stepwise fitting of the parameters, k, and discrimination of the function, j, itself. All of the models in this chapter should be considered as working hypotheses. The nature of formal kinetic descriptions means that other mathematical functions can always be found that serve the same descriptive function to within the precision of the measurements (see Esener et al., 1983). The lack of basic content in formal kinetic models in comparison with structured models (Harder and Roels, 1981;Roels and Kossen, 1978) can to some extent be compensated for by subsequent analysis (Esener et al., 1983;A. Moser, 1978bA. Moser, , 1984a.The basic kinetic scheme for a typical bioprocess is presented in Fig. 5.1 as the starting point for the analysis (A. Moser, 1980a). A chosen rate, somehow connected with the biological growth process, is plotted as a function of a chosen, relevant quantity-for example, a concentration, the pH, or the temperature. One observes a typical pattern offour regions: maintenance level endogenous metabolism, stimulation, inhibition, and toxicity. The typical biological optimum, with r max intermediate between two critical concentration values, is a consequence of opposing stimulatory and inhibitory factors. The influence of a transport limitation is schematically illustrated by the quantity representing an effective diffusion coefficient Deff in the liquid and/or solid phase. The goal of a formal kinetic analysis is description of the various factors influencing this course of events.To a large extent, the formal kinetic analysis techniques presented in this chapter relate to discontinuous batch operations. Even if the goal is a continuous operation, the batch process kinetic model serves as a start-up. The most significant element of a kinetic analysis is the time dependence of the macroscopic process variables mentioned in Chap. 2. Bacteria, molds, viruses, and yeasts all have different reproduction mechanisms, and formulating a structured kinetic model more closely related to the actual mechanism is a desirable goal. More structured models are desirable not only to deal with active cells but also to extend kinetic analysis to more complex situations involving inactive cells, mixed populations of cells, multiple substrates, and A. Moser, Bioprocess Technology
