A unified presentation of phase stability analysis including all major specifications

Abstract

The major specifications for phase equilibrium are: pressure and temperature (PT), volume, temperature and moles (VTN), pressure, enthalpy and moles (PHN), pressure, entropy and moles (PSN), internal energy, volume and moles (UVN) and entropy, volume and moles (SVN). For some of these specifications, stability testing is not well documented in the literature. It appears that derivations of stability criteria for PHN, PSN and SVN stability are presented here for the first time, as well as the possibility to solve the stability problem in their hyperspaces. Two general stability criteria are derived, which include all state functions and specifications. The general tangent plane distance (TPD) function degenerates to the TPD function corresponding to any desired specifications. The formalism is not model dependent. It is shown that stability testing for any specifications naturally reduces to either PT stability (when pressure is a specification, as in PHN and PSN stability) or VTN stability (when volume is a specification, as in UVN and SVN stability), by solving the appropriate nonlinear equation in temperature. In other words, there is no need (moreover, it is shown that there it is not even recommended) to minimize a specific TPD function in its hyperspace (defined by natural variables of the state function). This paper presents the first unified treatment of phase stability testing including all major specifications; beyond its theoretical importance, an important practical consequence is a unified calculation framework for phase stability testing, allowing a versatile numerical treatment and using existing highly robust and efficient procedures for PT, volume-based PT or VTN stability, whatever the specifications.