The key message of this book is that mathematical modeling is a powerful tool that can help in the design of SSF bioreactors and in the optimization of their performance. It is not necessary for all workers in the area of SSF to know how to construct and solve models, because modeling can be done in collaboration with colleagues with the appropriate expertise. However, even if you have no intention of undertaking the modeling work yourself, it is useful to know what models are and what they can do, because this facilitates interactions with these colleagues. The aim of Chaps. 12 to 20 is to give you an understanding of how models of SSF bioreactors are developed. These chapters do not attempt to provide the necessary background in all the mathematical and computing skills required. Rather they attempt to convey the "modeling way of thinking". This will provide the basis for understanding the uses and limitations of the various models presented in the modeling case study chapters (Chaps. 22 to 25).What is a mathematical model? The type of mathematical model that we are talking about in this book is a set of differential and algebraic equations that summarizes our knowledge of how a process operates. In other words, a model is a set of equations that describes how the various phenomena that occur within the system combine to control its overall performance, which, in the case of SSF bioreactors, will be evaluated in terms of growth and product formation. A model is a simplification of reality, and the equations therefore only describe the phenomena that are thought to be the most important in influencing the performance of the system. It is the modeler who, on the basis of experience with the system being modeled, decides which phenomena will be included and which will not be. As a simple example of this, amongst other factors, growth within an SSF bioreactor depends on both the O 2 concentration and the temperature experienced by the microorganism. However, in many models of SSF bioreactors the problem of controlling temperature is considered to be more difficult than the problem of supplying O 2 , and therefore frequently equations describing energy generation and water transfer are written in order to predict temperatures, but equations to describe O 2 supply and consumption are not included within the model.
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