Overview

In Chapter 1 we introduced the notion of a compartment, which is one of two mainstays of modeling at an elementary level, the other being what we referred to as the one-dimensional pipe. The principal feature of a compartment, or stirred tank as it is often called, is that its contents are assumed to be uniformly distributed so that their properties and the associated state variables vary at most with time, and not at all with spatial distance. In the most common application of this model, mass or energy enters and leaves the compartment, frequently accompanied by chemical reactions, phase changes, or by an exchange of mass and energy with the surroundings. Uniformity may be achieved by thoroughly mixing the contents of the compartment or, more frequently, by conceptually deducing from the physical situation that the state variable is uniformly distributed or very nearly uniformly distributed in space. For example, in the case of a thermocouple response to a change in ambient temperatures, which we considered in Example 1.5, no physical mixing of the contents took place. Instead it was deduced from the small dimensions of the device and its high thermal conductivity that the state variable, here the temperature, would be uniformly distributed in space. The thermocouple could consequently be regarded as a compartment and its response derived from a compartmental model.

Compartmental models are usually set up by performing integral mass and energy balances around the compartment. These can be instantaneous in time, in which case we...