Unconstrained optimisation for the design of distillation columns

Abstract

In the traditional constrained formulation the separation objectives are posed as inequality constraints. The optimisation variables are the number of stages on each section of the column, the reflux ratio and the product flow rates. The main objective of this work is to reformulate the original constrained problem into an unconstrained problem. The reflux ratio and product flow rate are calculated to satisfy the two active constraints at each stage of the optimisation problem, adding two equations to the modelling system of the distillation column. The design problem of a distillation column is formulated as an unconstrained optimisation problem where the number of stages in each section of the column is treated as continuous optimisation variable. Therefore an unconstrained non-linear programming problem is solved. The objective function used corresponds to the minimisation of the total cost, thus leading to a convex problem. A numerical example corresponding to a real column is included. The total cost versus the number of stages in each section of the column is graphically shown.