In the chapters that follow, the order of presentation will not follow the order of classification in Groups I to IV presented in Chap. 3.3. Rather, the "mathematically simpler" models will be presented first. The first two case study chapters deal with bioreactors within which each of the subsystems is assumed to be well mixed, namely the continuously-mixed, forcefully-aerated bioreactor from Group IVa (Chap. 22) and the rotating-drum bioreactor from Group III (Chap. 23). The models of these bioreactors involve ordinary differential equations. The other two chapters deal with models in which there are gradients within the substrate bed, namely, packed-bed bioreactors from Group II (Chap. 24) and intermittently-mixed, forcefully-aerated bioreactors from Group IVb (Chap. 25). The models of these bioreactors involve partial differential equations. A case study is not presented for tray bioreactors (Group I).
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