An analysis about analytical calculation of volume roots from cubic equations of state

The calculation of volume roots from cubic equation of state, for given temperature and pressure, is still an important operation both in industry and academic field. It is proposed the use of Ferrari's formula to calculate the pressure range containing three real positive roots (for pressure and temperature below the critical). In addition, a modification in the Cardano-Tartaglia's formula is proposed to provide the roots in the ascending order. For low values of reduced temperatures, it is proposed a simple and efficient approximation method to avoid the round-off errors presented by Cardano-Tartaglia's formula. It is also proposed a method for calculating the saturation pressure from cubic equations of state. Examples of the methods proposed are presented for the Van der Waals, Soave-Redlich-Kwong e Peng-Robinson equations of state in order to show the quality and reliability of the methods proposed.

Automated summary

This paper proposes methods for calculating volume roots using Ferrari's formula and modifying Cardano-Tartaglia's formula to ensure roots are in ascending order, as well as providing approximate methods for different temperatures and pressures, and a method for calculating saturation pressure.