## Theory Modeling of Ideal Suspended Growth Reactors

The primary function of a mathematical model is to reduce a complex system to the minimum terms essential for its description so that those terms may be manipulated, thereby helping us to understand how the system will respond under a variety of conditions. Generally, mathematical models do not describe a system completely, but if the terms are chosen with care, the model response will be qualitatively similar to the real system. In Part I we considered in detail the major events occurring in biochemical operations. Now the mathematical descriptions of those events will be incorporated into mass balance equations for the major reacting components in order to develop mathematical models describing a number of reactor configurations representing suspended growth systems. Chapter 4 presents the techniques for describing both ideal and nonideal reactors in mathematical terms. Chapter 5 establishes several fundamental principles governing the performance of suspended growth biochemical operations by considering the situation of heterotrophic microbial growth on a soluble substrate in a single ideal reactor. Chapter 6 extends the concepts of Chapter 5 by adding additional reactions, such as autotrophic growth of nitrifying bacteria, in a single ideal reactof. In Chapter 7, other reactor configurations are included to demonstrate how the engineer can control system performance through selection of the appropriate reaction environment. Finally, Chapter 8 describes techniques whereby the kinetic and stoichiometric parameters used in the models may be evaluated. In investigating reactor performance through modeling, it will be assumed that the reactors are ideal, with respect to both fluid flow and the response of the microbial culture. In other words, we will investigate how the reactors would respond if the mathematical models were absolutely correct. In Part III, any significant deviations from ideality are discussed and incorporated into the application of the models to design.

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