A Reliable and Useful Method to Determine the Saturation State from Helmholtz Energy Equations of State

This paper discusses iterative calculation methods to determine the saturation state of pure fluids by using Helmholtz energy equations of state. The commonly used method is based on the successive substitution approach. This method is simple, but requires an aid of ancillary equations to estimate sufficiently accurate initial guesses for the saturation pressure and saturated liquid and vapor densities. In particular, in the vicinity of the critical point very accurate initial guesses are needed. This paper presents an alternative method based on the Newton-Raphson approach. The alternative method does not require accurate initial guesses. Therefore, the aid of ancillary equations is unnecessary. The iterative process is more stable than that in the commonly used method, even if rough initial guesses are given. The usability of the alternative method is demonstrated for several published equations of state.