Ideal kinetic model mathematical relations

Narrow channels of meaningful communication about densification (and the closely related process of deformation) appear to exist between those with scientific interests on the one hand and those concerned with practical engineering objectives on the other. Unfortunately, scientists usually find it necessary to simplify their kinetic models and to establish rather restrictive boundary conditions in order to make them mathematically tractable. Many of the terms employed in such models convey well-defined conceptual quantities, but are not amenable to direct experimental measurement. Consequently, it is not surprising that such models, though valid scientifically, are not always readily adaptable to practical densification problems. The practicing engineer is more likely to rely on personal judgment developed by cut-and-try methods with real materials than he is to accept predictions based on an obviously oversimplified model which is predicated upon an unrealistically idealized material or process. 

As will be shown in Chapter 6, process modeling is concerned with the construction of a mathematical description of a chemical process in terms appropriate to a specific purpose. To achieve this, it is necessary to obtain a reaction model which expresses the rate of reaction as a function of relevant variables. This requires, ideally, knowledge of the individual reaction steps, the rate at which they occur, and the mass transport rates for the species in the reaction. But often, detailed quantitative kinetic data are not available and not easy to determine. Semiempirical relations may have to be used. 

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