# Example 2.1: Refrigeration system

Propane is used to cool a process, as shown in the diagram of figure 1. The fluid that to be cooled in exchanger E103 should have an outlet temperature of -30 °C. What pressure will the exchanger work at?

## Analysis:

• Pressure and temperature are the basic properties of the system.
• Only propane appears in the process. It is a well-known light hydrocarbon.
• Propane will evaporate to cool the process. It is a vapor-liquid equilibrium of a pure component.

## Model requirement:

A vapour pressure curve is enough to solve the question asked. As long as the temperature remains within the limits provided by the database, the Antoine’s equation is sufficient (see chapter 3):

For propane, the values are:

Table 1: Constants for example 1
Parameter Tc (K) Pc (bar) A B C
Value 369.82 42.4 5.75442079 -5.48259492 -0.04723775

## Solution:

### See complete results in file (xls):

Some help on nomenclature and tips to use this file can be found here.

The refrigeration system uses the heat of vaporization of propane to cool the process fluid. The propane, a pure component (), is at liquid-vapor equilibrium, i.e. a two-phase equilibrium (φ=2). The Gibbs' phase rule indicates that . If temperature is imposed (lower than -30 °C: say -35 °C), then pressure must be as well.

We therefore find that, at -35 °C, the pressure is 1.4 bar. With this information, the thermodynamic state is defined, indicating that temperature was a sufficient piece of information.