Nonreacting Multistage Isothermal Systems

Show that the steady- state and dynamic models for a double-pipe, counter-current heat exchanger can have the same form as the model of a packed bed absorber. Discuss the assumptions inherent in both the heat exchanger and the absorber models which might lead to significant differences in the kinds of model equations used to describe each system. 

2 Nonreacting Multistage Isothermal Systems and High Dimensional Linear and Nonlinear Systems 

Many chemical and biological processes are multistage. Multistage processes include absorption towers, distillation columns, and batteries of continuous stirred tank reactors (CSTRs). These processes may be either cocurrent or countercurrent. The steady state of a multistage process is usually described by a set of linear equations that can be treated via matrices. On the other hand, the unsteady-state dynamic behavior of a multistage process is usually described by a set of ordinary differential equations that gives rise to a matrix differential equation. 

We start with isothermal processes with fixed temperatures in all stages, so that the model simply consists of the mass-balance design equations. 

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