(651g) A New Global Optimization Tool for Phase Stability and Equilibrium Problems

Wasylkiewicz, S. K. - Presenter, Computer Modelling Group Ltd.
Wasylkiewicz, M. J., University of Alberta

Finding an arbitrary local minimum is relatively straightforward by using classical local minimization methods. Finding the global minimum of a function that has multiple local minima and maxima is far more difficult. Numerical solution strategies used for global optimization can be grouped into the following three categories: deterministic methods, stochastic methods and heuristic strategies.
While most current deterministic global optimization methods theoretically guarantee convergence to the global solution, they are often too expensive in terms of computational effort even for moderate size problems. Also, for some methods, problem reformulation is needed depending on the thermodynamic model being used.
The stochastic and heuristic global optimization methods are easy to implement, are independent of a model and can handle large number of decision variables. They can locate good solutions quite quickly but do not guarantee the global optimality. If calculations of a single point of an objective function is very time consuming (e.g. in shale gas reservoir modeling and optimization), these methods may offer the best compromise between quality of solution and efficiency for multivariable optimization.
On the other hand, if the objective function calculation is quick and partial derivates can be easily calculated analytically or numerically, the more reliable deterministic methods should be used. For some modeling problems of physical systems (e.g. in liquid phase stability analysis) we have to find all stationary points of a tangent plane to the Gibbs free energy surface to be sure whether the examined liquid is stable or not. Failure to find the globally optimal solutions in phase stability calculations can have serious consequences in subsequent process calculations. Using an erroneous VLE solution instead of a correct VLLE one, or switching between them during distillation column simulation, can cause convergence failures in the column or give erroneous conclusions about simulated plant performance.
In the paper, we present a new global optimization algorithm that has been developed for finding all singular points of a mathematical model by exploring the natural connectedness that exists between singular points of an objective function. The idea of following ridges and valleys using information gathered along the way has been significantly enhanced by applying the arc length continuation method. The algorithm has been applied to the Gibbs tangent plane stability test for multiphase liquid mixtures. The algorithm gives an efficient and robust scheme for locating all stationary points of the tangent plane distance function predicted by any thermodynamic model. The algorithm is self-starting and significantly improves reliability and robustness of multiphase equilibrium calculations. The developed technique was tested on several mixtures, containing also ionic liquids. For each optimization problem we also do check for global consistency of the solution.