Micro-macromixer model

Figure 3.3 Micro-macromixer model [22] - a schematic representation of the discrete simulation procedure.

Assuming that oxygen supply is sufficient to avoid local oxygen limitations, the kinetic model required for the simulation includes only the material balance equation for the substrate. As suggested in earfier simulations based on recirculation models (micro-macromixer) by Bajpai and Reuss [60], the uptake kinetics are only considered in the vicinity of the so-called critical sugar concentration. Thus, a rather simple unstructured empirical model is chosen for the purpose of this study. It involves a Monod type of kinetics for substrate uptake... 

Several macroscale models with varying levels of complexity and covering macroscale phenomena such as the reactor residence time effects and micro- and macromixing behavior have been developed for olefin polymerization but is not discussed here in detail for the sake of brevity [149-157],... 

The same model of inhomogeneity has also been used to model conversion in various combinations of reactors (Tsai et al., 1969,1971 Wen and Fan, 1975 see Chap. 6). Finally, a systematic picture of the various types of bioreactors on the basis of the criteria discussed is shown in Fig. 3.3. Of course, in practice a strict classification is not possible since the intermediate states (especially with regard to micro and macromixing) are often dominant. 

Similar to RTD-based models (Section 12.6), multi-zone models do not explicitly account for the effects of micro-mixing. The latter may affect macromixing, that is, the transport rates between zones. Micro-mixing may also affect the averaged reaction rates at the scale of the zones or the macro-scale, as a result of non-uniformities within the individual zones. Micro-mixing effects can eventually be accounted for by the methods discussed in Sections 12.5 and 12.4. 

A special kind of compartment model is the two-environment model, which divides the tank into micro- and macromixers, the numbers of which depend on the number of impellers. The flow behavior in the macromixer is characterized by the circulation-time distribution (Figure 3.3). Bajpai and Reuss [22] used a Monte Carlo simulation method in which the physical system of the macromixer was divided into a number of discrete elements. In each of these elements, the reaction process was simulated for a short period, at the end of which the system-specific interactions were simulated. The approach has been successfully applied to simulate the growth and metabolic overflow to ethanol at glucose concentrations beyond a threshold value for the yeast S. cerevisiae. 

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