Simultaneous calculation of chemical and phase equilibria using convexity analysis

Chemical and phase equilibria were considered for closed multicomponent reactive systems at: (a) constant pressure and temperature; (b) constant pressure and enthalpy. Equilibrium at constant P and T was found by minimization of G, while equilibrium at constant P and H was found by maximization of S or minimization of −S, all with respect to the number of moles of each component in each phase. Both cases could be handled as optimization problems, satisfying the restrictions imposed by mole or atom balances, and non-negativity of number of moles. Convexity analyses were carried out, and the conditions were found in order to guarantee global minimum, for one liquid phase, one gas phase, and a number of solid phases. The minimum point was then found either by analytical methods or by direct minimization methods. These strategies were tested for a number of cases, with good results.