Decomposition and smart enumeration for the globally optimal design of distillation columns with associated equipment

Several articles on the optimal design of distillation columns have focused on minimizing cost, addressing only the determination of the optimal number of trays and the feed tray location, while making several assumptions about condenser and reboiler costs and, in most cases, ignoring tray geometry design. However, no prior work determines the detailed geometry design of a distillation column and its associated equipment simultaneously. In this work, we present this method for the first time, and we guarantee global optimality. Aside from considering exchangers, drum and plate geometry, we propose a Bilevel Optimization Approach aided by Set Trimming and Smart/Segmental Enumeration. Set Trimming is used to rule out infeasible separations from the candidate solutions. Smart Enumeration searches the set of candidates organized in ascending order of the objective function lower bound until a stopping criterion is met. Results for columns with two diameters further demonstrate the versatility and efficiency of the proposed method.