Rising energy costs and growing environmental awareness motivate a critical revision of the design of distillation units. Systematic design techniques

such as the rectification body

column profile map

and temperature collocation methods

require exact knowledge of all pinch points in a particular system

because these stationary points delineate the possible composition trajectories realizable in separation columns. This paper demonstrates novel methods for rigorously determining all pinch points for the constant relative volatility

ideal and non-ideal systems. Constant relative volatility and ideal solution systems are transformed into one-dimensional polynomial and nonlinear functions

regardless of the number of the components. A deflation method is proposed to locate all zeros in ideal and non-ideal zeotropic problems. For more challenging non-ideal problems

a novel hybrid sequential niche algorithm is used to solve hard azeotropic problems successfully. Finally

the design implications of these pinch point locations are investigated to show how new separation configurations can be devised. Methodically the paper points out the use of rigorous pinch point computations in conjunction with continuous composition profiles for robust distillation design.