Global Optimization for the Phase Stability Problem

The Gibbs tangent plane criterion has become an important tool in determining the quality of obtained solutions to the phase and chemical equilibrium problem. The ability to determine if a postulated solution is thermodynamically stable with respect to perturbations in any or all of the phases is very useful in the search for the true equilibrium solution. Previous approaches have concentrated on nding the stationary points of the tangent plane distance function. However, no guarantee of obtaining all stationary points can be provided. These diiculties arise due to the complex and nonlinear nature of the models used to predict equilibrium. In this work, simpler formulations for the stability problem are presented for the special class of problems where nonideal liquid phases can be adequately modeled using the NRTL and UNIQUAC activity coeecient equations. It is shown how the global minimum of the tangent plane distance function can be obtained for this class of problems. The advantage of a global optimization approach is that if a nonnegative solution is found, then it can be deenitively asserted that the postulated solution is the globally stable equilibrium one, unlike available local algorithms. is used to guarantee obtaining-global convergence to the global minimum. For the UNIQUAC equation, a branch and bound algorithm based on that of Falk and Soland (1969) is used to guarantee convergence to the global solution. The computational results demonstrate the eeciency of both global optimization algorithms in solving a variety of challenging problems.