Optimal Synthesis of Quaternary Zeotropic Distillation Sequences Using an Array Formulation

The optimal synthesis of distillation sequences has been a popular research topic in the field of chemical process system engineering for many years. In most works, the optimization procedure first generates a set of information about the presence or absence of stream states or equipment through some specific rules, usually represented by explicit binary variables, and then corresponds to a specific process structure, i.e., “encoding → structure”. The purpose of encoding information is to “draw” the corresponding process structures and evaluate their performance. Typically, only the fully stacked structures with exactly N – 1 columns are considered for N-component separation. The current work developed an array formulation to completely consider the complete search space of the state-equipment-network distillation sequence superstructure. The presence or absence of stream states or equipment is determined by the calculation results of the previous devices, which then corresponds to a specific encoding form, i.e., “structure → encoding”. The purpose of encoding information on the “already drawn” nonstacked process structures is to evaluate the performance of their corresponding various stacked structures. As an alternative, the features of this inverse procedure are that the binary variables representing the on/off state of equipment, and the logical constraints between different process alternatives are implicitly included in the “Selector” module of the process simulator. A close-boiling industrial organosilicon case, which was abstracted as a quaternary zeotropic system, was surveyed using the proposed method. The optimal configuration along with corresponding operating parameters was found from 63 flowsheet equivalents in 4.2 CPU hours. Furthermore, five high-quality solutions including both stacked and nonstacked configurations were compared and analyzed to demonstrate the optimality of the final solution.