Process Description

Process Description

Systematically analyzing the Van der Waals equation and other equations of state can allow a better understanding of the interconnection between various macroscopically measurable properties of a system, including pressure, temperature, and volume. The Van der Waals equation and the Peng Robinson equation, both derived from the Ideal Gas equation, contain similarities and differences, although the parameters of each equation are significantly different. The first parameter, a, is dependent upon the attractive forces between molecules while the second parameter, b, is dependent upon repulsive forces. In both equations a and b are highly dependent on the structure of the compound; Peng-Robinson works best for hydrocarbons and inorganic gases, while Van der Waals is inaccurate near the gas-liquid interface.

Equation 1 Van der Waals

Equation 2 Peng-Robinson

Also, a(t) in the Peng-Robinson equation is a function of temperature and since boiling pressure is a function of temperature, pressure should naturally be more dependent on temperature in the Peng-Robinson equation. The parameters in the Peng-Robinson equation are expressible in terms of the critical properties and the acentric factor, w, which is constant for each gas and can be calculated using the following formula:

We used excel to generate an algorithm for the Peng-Robinson equation and made PT, PV, and VT diagrams. For each of the diagrams we used the following equations to calculate the parameters and to plot Pr (P/Pc), Tr (T/Tc), and Vr (V/Vc) against one another appropriately:

For example, on the PV diagram, the user inputs a reasonable temperature, and the algorithm calculates the corresponding parameters, pressure and volume in the Peng-Robinson equation. Similarly the user inputs pressure and volume respectively for the other two diagrams, VT and PT. The program will also calculate and graph the corresponding Van der Waals diagram with the Peng-Robinson diagram for comparison.