Interval methods for reliable computations of phase equilibrium from equation of state models

Calculation of phase equilibrium is an essential and recurrent element in the simulation of chemical processes. This includes two subproblems: the prediction of phase stability and the phase split calculations. The success of the latter depends on the the correctness of the phase stability analysis. Reliably solving the phase stability, however, is a challenging computational problem.; In this work, we have developed an alternative approach to solve phase stability problem using interval analysis, in particular the use of an interval Newton/generalized bisection (IN/GB) algorithm. This interval method provides absolute rigor for locating global minima. To improve the efficiency of this global algorithm, various techniques have been investigated. Amongst them, the use of certain enhanced interval extensions has been proven to be very effective. Also, a number of local search methods have been successfully developed to quickly detect phase instability. This interval algorithm for phase stability analysis was implemented in the package INTSTAB. The parallel features of the IN/GB algorithm have also been studied. Two coarse grained parallel algorithms were implemented on a Cray/SGI Origin 2000 supercomputer. Encouraging speedup results were obtained. INTSTAB has been applied to solve phase stability problem for a generalized cubic equation of state model. Our results demonstrate that the IN/GB algorithm can solve phase stability problems efficiently and with complete reliability. It provides significant improvements over the conventional methods in that it can guarantee with mathematical certainty that the correct solutions are found and it is initialization independent. The method is also model independent and can be applied in connection with other equations of state.; We have addressed the phase split problem with the Gibbs energy minimization approach. INTSTAB is first used to obtain all the stationary points. They provide extremely good initial estimates for the equilibrium phase compositions. An enhanced Han-Powell method for successive quadratic programming (SQP) is then used to perform a local minimization of Gibbs free energy to locate prospective global minima. INTSTAB is again used to verify if a global minimum has been reached. By combining the speed of this local SQP solver with the reliability of INTSTAB, we have developed an efficient and completely reliable approach for computing multi-phase equilibria. This method was implemented in the package INTFLASH.