Reliable Asymmetric Phase Stabilty Computations using Interval Analysis

The calculation of phase equilibrium is a fundamental and reoccurring problem in modeling of chemical engineering phenomena. A key step in the computation of multiphase equilibrium is phase stability analysis. A reliable technique for phase stability analysis will assure both that the correct number of phases is found, and that the phase split computed corresponds to a global minimum in the total Gibbs energy. That is, phase stability analysis serves as a global optimality test in solving the global optimization problem that determines phase equilibrium at constant temperature and pressure. However, phase stability analysis is itself a global optimization problem that can be very difficult to solve reliably. Stochastic global optimization methods (e.g., simulated annealing, genetic algorithms, etc.) have been frequently proposed in this context. However, none of these techniques is actually guaranteed to produce the correct results. Thus, there has been significant interest in the development of deterministic techniques that guarantee the correct solution of the phase stability problem. These efforts have been focused primarily on the case of symmetric models (same thermodynamic model used for all phases). Work on deterministic stability analysis for the asymmetric case (different models used for different phases) has been limited to cases involving either an ideal gas vapor phase or a pure solid phase. In this thesis, a deterministic method for the more general asymmetric case will be presented, focusing on the common situation in modeling vapor-liquid equilibrium in which nonidealities are represented in the vapor phase by an equation of state and in the liquid phase by an excess Gibbs energy model. In comparison to the symmetric model case, the use of multiple thermodynamic models in the asymmetric case adds an additional layer of complexity to the phase stability problem. To deal with this additional complexity the phase stability problem is formulated in terms of a new type of tangent plane distance function, which uses a binary variable to account for the presence of different liquid- and vapor-phase models. To then solve the problem deterministically, an interval-Newton approach is used. The new methodology is tested using several examples with NRTL as the liquid-phase model and a cubic equation of state as the vapor-phase model. In three cases, published phase equilibrium computations were found to be incorrect (not stable). Procedures for deterministic phase stability analysis, such as described here, can be used in connection with any algorithm or software package for computing phase equilibrium, to validate the computed results and to provide corrective feedback if needed.