Detailed experimental information on the performance of CSSFBs is not available. With this lack, simulation is a useful tool in understanding the potential of the various bioreactors. Note that almost no attention has been given to the modeling of the continuous operation of SSF bioreactors in the literature. The intention of the present section is to present simple models, while recognizing that many improvements in these models will be necessary in order for them to describe continuous performance reliably. For example, the models presented here for the mixed bioreactors do not take into account the fact that each particle is a batch mi-cro-bioreactor and therefore will be most appropriate for very small particle sizes.
The different systems described above will be simulated using different flow models. The kinetic information has been taken from Ramos-Sánchez (2000), in which the logistic model is used to describe the growth kinetics of the yeast Candida utilis for the enrichment of sugarcane byproducts. The logistic model is frequently used to describe the growth kinetics in SSF (see Sect. 14.4) hence it is interesting to simulate the behavior of these systems using this kinetic model. The parameters of this model are the initial biomass content (Xo), the maximum possible biomass content (Xmax), and the specific growth rate constant (^). In these simulations Xo is set at 2.5 g kg-dry-matter1, Xmax is set at 263 g kg-dry-matter1, and ^is set at 0.3 h-1.
Constant temperature is assumed; heat and mass transfer phenomena are not modeled. The performance of each system is evaluated on the basis of the productivity of single-cell biomass (g-biomass kg-dry-matter-1 h-1).
11.4.1 Continuous Tubular Flow Bioreactors (CTFBs) with Recycling
The operation of tubular flow SSF bioreactors with recycling, such as those shown in Figs. 11.3 and 11.5, can be simulated using a plug-flow bioreactor with a recycle stream (Fig. 11.6). The operating variables are the dilution rate (kg-solids kg-solids-1 h-1), defined as in Sect. 188.8.131.52, and the ratio of recycled solid-flow to entrance mass-flow (/=fR/F), the so-called "recycle ratio" (dimensionless).
The results of the simulation are presented in Fig. 11.7 from which it is possible to conclude that:
• There is an optimal dilution rate above which the productivity falls rapidly with increasing dilution rate, as is characteristic of continuous SLF processes.
• Since the feed is inoculated with biomass, there is always biomass in the exit stream, regardless of dilution rate. Note that the graph therefore appears different from the graphs for "classical" continuous SSF processes in which there is no biomass in the feed and therefore above a critical dilution rate the steady state biomass concentration is zero. Of course, if a continuous SLF process were to have a certain level of inoculum in the inlet stream, then at dilution rates greater than the critical rate, the outlet stream would have a concentration of biomass equal to the inlet concentration, in the same manner as occurs for the situation in the CSSFB shown in Fig. 11.7 at high dilution rates.
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