Stage-to-stage calculations of distillation columns by fixed-point iteration and application of the Banach fixed-point theorem

Abstract

This work presents a novel approach for stage-to-stage calculations of distillation columns based on the MESH equations. No simplifying assumptions such as constant molar overflow are used. The transition from one stage to the next is formulated as a fixed-point problem, which can be solved by fixed-point iteration. Applying the Banach fixed-point theorem, bounds on the minimum energy requirement are derived. Within these bounds a solution to the fixed-point problem is proven to exist and convergence of the fixed-point iteration is guaranteed. Additionally, energy bounds are derived below which it can be guaranteed that no fixed-point exists. The stage-to-stage calculations are combined with an outer optimization loop in order to conduct process simulation and optimization. The approach is illustrated by examples.