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1.11 Compartmental Models

In compartmental models, a set of macroscopic models are interconnected to form a system model for a complicated process. For example, the transport of pollutants in the environment is modeled in this manner. Here it is common to use four compartments as shown in Figure 1.14 to simplify an otherwise complex situation. An application of this model in environmental engineering is described in Chapter 13.

Figure 1.14

Figure 1.14 Illustration of a compartmental model for pollutant distribution in the environment. Species can be transferred across compartments, as indicated by the arrows. The transfer rate model uses an inter-compartmental exchange parameter.

Compartmental models are also widely used in biomedical systems modeling. A simple two-compartment model to represent the body is shown in Figure 1.15. A simulation example based on this model is provided in Chapter 13.

Figure 1.15

Figure 1.15 Schematic sketch of a simple two-compartment model to study drug uptake and metabolism.

Examples and solutions to compartmental models are taken up in Sections 13.7 and 13.8. It is common practice to simplify each compartment to be a well-mixed system with a constant composition. In addition, an exchange parameter needs to be assigned to model the transfer between the various parameters. In turn, the compartmental models typically use many simplifying (perhaps crude) assumptions. Despite this background, they have proven to have value in environmental and biomedical engineering.

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