Rigorous NLP distillation models for simultaneous optimization to reduce utility and capital costs

Abstract

Two non-linear programming (NLP) models with rigorous stage-by-stage MESH calculations are proposed based on the concept of bypass efficiency. The models can be used to simultaneously optimize the number of stages, feed stage location and operating parameters such as the reflux ratio and column pressure. They can also be used for simultaneous flowsheet optimization with distillation columns and heat integration, as demonstrated in a case study. The first model removes an over-specification where the enthalpy of the outlet stream is calculated using an equation-of-state. A degrees of freedom (DOF) analysis shows that the calculation is not required since the enthalpy of the outlet stream is computed from the inlet stream and equilibrium stream and the outlet temperature does not need to be known for subsequent stage calculations. The second model reduces the number of free variables by grouping the bypass efficiencies in a systematic manner. This modification reduces the model size and solution time without sacrificing accuracy or the number of unique solutions. Other than that, the pressure drop equations were improved. The improvement proved to be significant as the original equations caused all stages to be active in a case study, while the same problem was not observed with the new set of pressure drop constraints. Both proposed models had shorter solution times, smaller model size and they yielded minimized objective values 1.5–5.4% lower compared to the original bypass efficiency model. • A modified bypass efficiency model with the removal of enthalpy equations is proposed in this work. • An NLP distillation model with grouped bypass efficiencies to reduce the free variables is presented in this paper. • A new set of pressure drop equations was developed to improve the original set of pressure drop constraints. • The proposed models performed better in terms of convergence, objective values and solution speed in the case studies.