Distillation columns are prevalent process units used to purify chemicals. However, they consume significant amounts of energy for heating and cooling. A rigorous non-linear programming (NLP) distillation model where mass, equilibrium, summation and heat (MESH) equations are applied to each stage is proposed to be used in conjunction with existing Heat Integration models for simultaneous process optimisation to reduce energy consumption. In the NLP model, a continuous variable is used for each stage to determine whether a stage is active or inactive. This variable controls whether there are any changes in stream properties as a stream passes through a stage. It also enforces the equilibrium constraint for streams exiting active stages. The continuous variable mimics a binary variable as it only takes on values of 0 or 1 in an optimal solution.
The distillation model and a Heat Integration model for a multi-stream heat exchanger (MHEX) were implemented in GAMS with a case study on the separation of air consisting of N2, O2 and Ar. Analysis of the model performance showed that it achieved convergence in a short time (6 min for a model with 2,161 variables and 25,260 equations) even with crude initialisation methods. Results of the case study showed that the energy requirement per unit mass of oxygen product is not minimized at 100 % oxygen recovery. The average oxygen recovery was around 96 %. Optimisation of the case study on an air separation unit (ASU) reduced energy requirement by 5.4 % for some cases.