Nonsmooth differential-algebraic equations in chemical engineering. (9th June 2018) - Stechlinski, Peter; Patrascu, Michael; Barton, Paul I.
Highlights: Advocates nonsmooth modeling paradigm for simulation and optimization of process operations. Highlights challenges faced by prevalent modeling frameworks in process systems engineering. Several examples of process operations modeled as nonsmooth DAEs are illustrated. Presents the relevant mathematical theory for nonsmooth DAEs. Abstract: 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.