Various quantitative approaches have been proposed for scale-up of SSF bioreactors, including the use of mathematical models and of various "simplified approaches" that have some similarity with the "rule-of-thumb" approaches to scal-ing-up SLF bioreactors. Given the complexity of SSF systems, models will be more powerful tools, and should be preferred where possible, especially since various fast-solving models are available in the literature, and can be adapted to new systems without requiring an onerous amount of work. Some of these mathematical models are presented in Chaps. 22 to 25, where their potential uses are demonstrated and discussed.
It is worthwhile remembering, as noted in Chap. 2, that the inter-particle phenomena themselves are independent of scale, since we will typically be using the same sized substrate particles at small scale and large scale. Significant intra-
particle mass transfer limitations, of O2 and nutrients, may occur even in particles of only 1 to 5 mm diameter. These limitations are intrinsic to SSF. The best that can be done in the manner in which the bioreactor is operated is to control the inter-particle conditions, for example, to maintain the O2 concentration in the gas phase in contact with the particle surface at as high a concentration as possible.
The knowledge framework concerning scale up of SSF processes can be characterized as follows:
• in relation to current large-scale bioreactors: there is no evidence in the literature that anything other than "best-guess" or "trial-and-error" approaches have been used for the development of almost all current large-scale SSF biore-actors. It is likely that some engineering calculations have been done, even if they were not reported. This is most likely in the soy sauce industry, but the knowledge about scale-up, if it has been generated, has not been made widely available because it is important proprietary information;
• in relation to the strategies themselves: Since the work of Saucedo-Castaneda et al. (1990), mathematical modeling work has been done with the aim of developing rational scale-up strategies for SSF bioreactors. However, although such models are potentially very useful tools for guiding the selection and design of large-scale bioreactors, there are no reports describing a scale-up study in which this has actually been done. To date the investigations have been limited to the use of models to demonstrate, using simulations, how models might be used to guide scale up.
Finally, it is important to point out that although mathematical models of biore-actor behavior can be used to predict how a bioreactor will perform before it is built, this modeling work does not replace the need to do experimental work, rather, it is a tool for guiding the experimental program. As will be shown later, mathematical modeling can help to raise questions about bioreactor operation that can be answered through experimentation, it can also help to eliminate ideas which appear reasonable but are actually unfruitful, without wasting time and money to test the ideas experimentally.
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