Monotonic reformulation and bound tightening for global optimization of ideal multi-component distillation columns

This paper addresses the problem of determining cost-minimal process designs for ideal multi-component distillation columns. The special case of binary distillation was considered in the former work (Ballerstein et al. in Optim Eng 16(2):409–440, 2015. https://doi.org/10.1007/s11081-014-9267-5). Therein, a problem-specific bound-tightening strategy based on monotonic mole fraction profiles of single components was developed to solve the corresponding mixed-integer nonlinear problems globally. In the multi-component setting, the mole fraction profiles of single components may not be monotonic. Therefore the bound-tightening strategy from the binary case cannot be applied directly. In this follow-up paper, a model reformulation for ideal multi-component distillation columns is presented. The reformulation is achieved by suitable aggregations of the involved components. Proofs are given showing that mole fraction profiles of aggregated components are monotonic. This property is then used to adapt the bound-tightening strategy from the binary case to the proposed model reformulation. Computational results are provided that indicate the usefulness of both the model reformulation and the adapted bound tightening technique for deterministic global optimization of ideal multi-component distillation column designs.