Generalized short-cut distillation column modeling for superstructure-based process synthesis

We introduce a generalized Underwood method to calculate the minimum vapor flowrate for distillation in superstructure-based process synthesis. Our method addresses two important limitations of current methods, namely, separation tasks where (1) the flow rates of some components may be zero, and (2) the key components may be unknown prior to optimization. This is achieved through the introduction of binary variables and mixed-integer constraints to implicitly determine the active roots and the root loci. In addition, we develop strategies tailored to improve the numerical stability and computational performance when using the proposed method.