Enhanced Automatic Initialization Method for Solving Large Nonlinear Algebraic Systems

New aspects of an interval-arithmetic (IA) based automatic initialization scheme for root-finding algorithms to efficiently solve nonlinear algebraic equation systems (NLEs) are presented. Using the model of a partial condenser, it is demonstrated how additional constraints may eliminate non-physical solutions by the help of interval arithmetic for initialization. Finally, the number of stages of a multicomponent distillation column is varied to investigate the required time of the approach to obtain initial values and solutions by root-finding as a function of the system size. The overall method finds a physically feasible solution for the distillation column with 20 stages without any initial values required.