Analysis of a Mixing Process

This chapter will analyze the mixing process in more detail. The process was already introduced in chapter 4, but some special properties of the Laplace transform and some special cases of the mixing process will be reviewed. In subsequent chapters other types of processes will be analyzed for their dynamic behavior. The purpose of the Laplace transform is to analyze how the process output of interest changes if the process input is changed. This will result in knowledge about the behavioral properties of the system, such as order, stability, integrating or non-minimum phase response behavior. 

The process was already introduced in chapter 4, it is shown again in Fig. 11.1. 

The mixer with two components, can be described by two basic balances, the mass balance and the component balance, in which the density is a function of the composition. Because the density p and the height h are defined as measurable output variables, the system is transformed into a combination of the volume and density balance. The volume balance (compare with Eqn. (4.26)) can be written as  

We are interested in developing an understanding on how the density p and the level h vary as a function of changes in Ae manipulated variable F.  

Linearization of the density balance can be achieved by substituting in the left hand-side of the balance  

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