Global solution approaches in equilibrium and stability analysis using homotopy continuation in the complex domain

Recently, significant attention has been shown to physical and chemical equilibrium and stability analysis in the real and complex domains. In this work, a new procedure involving the continuation method in the complex domain using bifurcation theory is propounded. Based on this method, homotopy branches in real and complex space are connected to each other through bifurcation branches. Thus, by just one initial guess, multiple solution branches are found. When calculations are only made in the real domain, multiple solutions are not always found from an arbitrary initial guess. Examples are presented to show the application of the method to nonlinear sets of equations in phase equilibrium, chemical and phase equilibrium, and stability analysis. These types of problems are believed to contain significant nonlinearities in process simulations. The results can be applied to flowsheet calculations.