In this article series, Optimal Campaigns in End-to-End Continuous Pharmaceuticals Manufacturing, the authors investigate the optimal dynamic operation of a continuous process that includes several reaction and separation steps to produce an active pharmaceutical ingredient at final dosage from advanced intermediates, inspired by a pilot plant previously tested at MIT.

Part 1: Nonsmooth Dynamic Modeling (click here for 50 days of free access) illustrates the use of nonsmooth differential-algebraic equations (DAEs) as a new paradigm for modeling dynamic process systems in an equation-oriented approach. Such a formulation has been recently shown to admit a unique solution and computationally tractable sensitivity analysis, facilitating its embedding in optimization schemes to find optimal operational procedures. The nonsmooth dynamics of several units are demonstrated from start-up. The nominal overall campaign performance is characterized in terms of on-specification productivity and yield, showing significant room for improvement.

In Part 2: Dynamic optimization (click here for free access this month), the new model is embedded in a dynamic optimization problem formulated as a hybrid discrete/continuous and nonsmooth problem. The authors enforce the quality constraints only on an interior epoch (on-spec), optimize its duration and then use a gradient-based optimization tool (IPOPT) to solve the problem. The results show a significant improvement over a “nominal” operating procedure that only considers steady-state operation. This methodology can be used to guide decision makers, in both the design stage of new plants and the operation of existing configurations.