Continuous versus Discrete Models

In a continuous model, a variable has a value at any given instant of time. In a discrete model, a variable has only values at diserete instances in time, for example, every second. Variables can also have continuous or discrete values with respect to a spatial coordinate, this type of behavior will not be considered here. 

Discrete time models describe the state of the system at given time intervals and are therefore useful for efficient computation. When using computers for calculation of the model output, continuous models need to be discretized, since numerical solution methods require discrete models. 

Discretization of model equations refers to the approximation of (usually) the first and higher order derivatives in the model. There are several difference approximations that can be made, a forward difference approximation, a backward and a central difference approximation. A backward approximation can be written as  

The input-output relationship between an input and the output yk can be written as a pulse transfer function. This is a function in the shift-operator z  

For prediction of a process variable, any type of model can be used. It is good practice to start with a Unear model. Only if the prediction is poor and adding more model eomplexity does not improve the prediction, would one consider developing a non-linear model. 

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Continuous versus Discrete Models The preceding discussion has focused on systems where variables change continuously with... 

Kwapinska, M., Saage, G., Tsotsas, E., 2008. Continuous versus discrete modelling of heat transfer to agitated beds. Powder Technd. 181 331-342. 

Groppi, G. andTronconi, E. (1996). Continuous versus Discrete Models of Nonadiabahc Monolith Catalysts, AIChEJ.,4,1, pp. 2382-2387. 

Figure 2.2. Continuous versus discrete modeling of a packed column absorber.

In fact, the flow patterns are even more complex than appear in the figure. Russell and co-workers identified no less than 26 regions of flow behavior, including both horizontal and vertical configurations [P.T Cichy, J.B. Ultman, and T.W.F. Russell, Ind. Eng. Chem., 61, 6 (1968)]. The most basic divisions, as far as reactor modeling is concerned, are those systems in which both gas and liquid phases are continuous versus those in which the two phases are discrete. Those are treated accordingly below. 

Structure of kinetic models 12,1 Discrete versus continuous... 

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