Interval Analysis: Application to Phase Equilibrium Problems

Abstract

ilibrium the total Gibbs energy of the system is minimized. Phase stability analysis may be interpreted as a global optimality test that determines whether the phase being tested corresponds to a global optimum in the total Gibbs energy of the system. If it is determined that a phase will split, then a phase split problem is solved, which can be interpreted as finding a local minimum in the total Gibbs energy of the system. This local minimum can then be tested for global optimality using phase stability analysis. If necessary the phase split calculation must then be repeated, perhaps changing the number of phases assumed to be present, until a solution is found that meets the global optimality test. Clearly the correct solution of the phase stability problem, itself a global optimization problem, is the key in this two-stage global optimization procedure for phase equilibrium. As emphasized in [10], while it is possible to apply rigorous global optimization technique