## What Can the Models Be Used to Do

Chapters 22 to 25 present case studies intended to give insights into how mathematical models can be useful tools in the design of SSF bioreactors and the optimization of their performance. Several of the models are available in the form of programs (see Appendix for details). Note that details of how to run the programs and interpret the output files are also given in the appendix. You will obtain a better understanding of these chapters if you:

• use the supplied programs to simulate performance of each bioreactor under design and operating conditions that are different from those presented in the various case studies;

• use a spreadsheeting or graphing program to plot the results;

• inspect and interpret the results;

• return to the model and further explore the predicted performance, changing the design and operating variables on the basis of the analysis of the results generated in the previous simulations.

In fact, you can use the models in two different manners:

• You can use them directly as tools in bioreactor design without trying to understand why a certain combination of design and operating variables is optimal. For example, you might want to build a certain type of bioreactor with a bed volume of 1 m3. You can explore how various design variables (bioreactor length and height) and operating variables (e.g., aeration rate) affect the performance of such a bioreactor, seeking to find the combination that gives the most growth in the least time (i.e., the highest productivity). You can change the variables by trial-and-error or be more systematic, using a strategy in which you vary the variables one-by-one in order to search for the optimum combination. It is also possible to use more sophisticated means to search for the optimum combination, namely by incorporating the bioreactor model as part of the objective function within an optimization program. This program will find the optimum combination of design and operating variables using powerful search algorithms;

• You can use them as tools to increase your understanding of how certain types of bioreactors might be expected to operate under a range of different design and operating conditions and sizes, and to explore the question as to why they would be expected to operate in that manner. For instance, various of the models presented in the case studies give detailed predictions about temperature gradients within subsystems and about temperatures and moisture contents of different subsystems. These can be plotted and analyzed, in an effort to understand how the various phenomena are interacting with each other. For example, in a system in which the model describes spatial gradients and recognizes the substrate particles and inter-particle air in the bed as separate systems, you can plot both the air and solids temperatures as functions of height. This will give an idea of how close the bed is to equilibrium: The solids and air might not be in thermal equilibrium near the air inlet, but soon after the air inlet they may have almost the same temperature, this being maintained until the top of the bed. Further, knowing these temperatures as a function of height may help you to understand why one part of the bed dries out more quickly than another.

Obviously, there are no limits on the range of simulations that can be done. Chapters 22 to 25 do not aim to give in-depth demonstrations of all of the possibilities. Rather, they present relatively brief studies into the question of design and operation of large-scale bioreactors. If you wish more detail about how the models can be used, you should consult the original papers that are cited, in which the model predictions are explored in greater depth. However, you should not restrict yourself simply to what has already been done. You are encouraged to use the models to explore the various bioreactors further.