Optimal Synthesis of Sequence of CSTR with Non-Linear Cost Objective Function

In this work, a method is presented that identifies the sequence of mixed flow reactors (CSTR's) which globally minimizes a linear (total residence time) or non-linear (capital cost) objective function, subject to a constraint specifying the terminal concentration of the sequence. Following a review of the relevant literature, the mathematical problem formulation is first presented, and proofs for the existence of the global optimum and for the applicability of the first-order necessary conditions of optimality are provided. The special structure of the resulting equations is then exploited in creating a solution method, which involves exhaustive search in a low dimensional space. For reaction schemes involving reaction rates that are linear in species concentrations, a proof is provided that the optimal sequence of CSTRs consists of identical reactors. Finally, the methodology is illustrated on a number of case studies and conclusions are drawn.