Switching from Batch to Continuous Reactors Is a Trajectory Optimization Problem

Over the past two decades, the pharmaceutical and specialty chemical industries have led a considerable effort toward transitioning from existing batch to continuous flow processes. The transition promises many benefits, including improved automation, simpler scale-up, and higher throughput. The switch from batch reactor vessels to continuous flow reactors (CFRs) is among the most challenging problems that must be solved to succeed in making the batch to continuous process switch, and the best methodology by which the feasibility of the switch can be determined remains an open problem. In this work, we offer a novel, optimization-based framework for assessing the feasibility of the switch. Starting from first principles, we develop a general nondimensionalization algorithm for describing an arbitrary reactive system. We then define nondimensional performance metrics that allow us to assign "scores" for a given batch reactor or CFR. Finally, we construct two optimization problems that (1) minimize the difference in total performance between an existing batch reactor and a potential new CFR and (2) separately maximize the total performance of the two reactors. The design variables for each reactor are allowed to vary between realistic bounds for the particular reactor vessel type. Problem 1 provides insight into whether the switch is feasible, while problem 2 provides insight into whether the switch is desirable. Finally, we illustrate the utility of our framework using two case studies.