Model reduction and selection

Even though the model in Table 3.1 results from several assumptions (detailed in Section 3.2.1), it can be considered as quite comprehensive. In fact, what is commonly found in the fitera-ture is a simplified version of this model The well-known classification of fixed-bed reactor models by Froment [51] and Froment and Bischoff [62] clearly exemplifies how a more general model unfolds into a hierarchy of several others with decreasing complexity. The dimensionafity of the model (usually one- or two-dimensional) and the presence of interphase and intraparticular resistances to mass/heat transfer are the main basis for distinguishing between different categories. 

For particular cases, it maybe required to add more complex phenomena with additional effects or more evolved descriptions of the same mechanisms. In general, however, reduced models are appropriate and desirable. Historically, this stemmed from the shorter computational effort and time required for the numerical solution of such models. Today this is also an advantage for optimization, control, and real-time simulation applications, and reliable simplified models are still used for almost all purposes due to the lower number of dimensionless parameters requiring estimation and to the success found in the description of experimental results. On the other hand, complex detailed models fulfill the most generic purpose of reactor simulation, which is related to the prediction of the actual behavior from fundamental, independently measured parameters. Therefore, it is important to understand the equivalence and agreement between both detailed and reduced models, so as to take advantage of their predictive power without unnecessary effort. 

In the following sections, we revisit and systematize models presented in the literature with different degrees of complexity, using scaling and perturbation analysis. Assuming the dominance of certain mechanisms, it is possible to estimate the error in using simplified models and to find equivalent formulations. 

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