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© 2018 Elsevier B.V. We investigate theoretical optimal campaigns in a continuous process of pharmaceuticals production. The simulated process, inspired by a pilot plant previously tested at MIT, includes several reaction and separation steps to produce final tablets. This paper, demonstrates the use of nonsmooth differential-algebraic equations (DAEs) framework for such optimal campaigns design. We embed the model developed in the first part of this series in a dynamic optimization problem formulated as a hybrid discrete/continuous and nonsmooth problem. We enforce the quality constraints only on an interior epoch (on-spec) and optimize its duration. We then use a gradient-based optimization tool (IPOPT) to solve the problem. We consider the on-specification productivity over the entire campaign. Various control valves are chosen as decision variables, as well as the timings of the control switchings. The yield and the productivity of the process are considered as objectives under a constant (short) time horizon. Pareto curves of optimal yield and productivity for various campaign durations are calculated. 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.

© 2018 Elsevier B.V. We investigate theoretical optimal campaigns in a continuous process of pharmaceuticals production. The simulated process, inspired by a pilot plant previously tested at MIT, includes several reaction and separation steps to produce final tablets. This paper, demonstrates the use of nonsmooth differential-algebraic equations (DAEs) framework for such optimal campaigns design. We embed the model developed in the first part of this series in a dynamic optimization problem formulated as a hybrid discrete/continuous and nonsmooth problem. We enforce the quality constraints only on an interior epoch (on-spec) and optimize its duration. We then use a gradient-based optimization tool (IPOPT) to solve the problem. We consider the on-specification productivity over the entire campaign. Various control valves are chosen as decision variables, as well as the timings of the control switchings. The yield and the productivity of the process are considered as objectives under a constant (short) time horizon. Pareto curves of optimal yield and productivity for various campaign durations are calculated. 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.

This article advocates a nonsmooth differential-algebraic equations (DAEs) modeling paradigm for dynamic simulation and optimization of process operations. A variety of systems encountered in chemical engineering are traditionally viewed as exhibiting hybrid continuous and discrete behavior. In many cases such discrete behavior is nonsmooth (i.e. continuous but nondifferentiable) rather than discontinuous, and is appropriately modeled by nonsmooth DAEs. A computationally relevant theory of nonsmooth DAEs (i.e. well-posedness and sensitivity analysis) has recently been established (Stechlinski and Barton, 2016a, 2017) which is suitable for numerical implementations that scale efficiently for large-scale dynamic optimization problems. Challenges posed by competing hybrid modeling approaches for process operations (e.g. hybrid automata) are highlighted as motivation for the nonsmooth DAEs approach. Several examples of process operations modeled as nonsmooth DAEs are given to illustrate their wide applicability before presenting the appropriate mathematical theory., Natural Sciences and Engineering Research Council of Canada