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, Stechlinski and Barton, 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.

本文提倡一种非光滑的微分-代数方程（DAE）建模范例，以进行过程操作的动态仿真和优化。传统上，化学工程中遇到的各种系统都表现出混合的连续和离散行为。在许多情况下，此类离散行为是非平滑的（即连续但不可微分）而不是不连续的，并且可以通过非平滑的DAE进行适当建模。最近建立了与计算相关的非光滑DAE理论（即，适定性和敏感性分析）（Stechlinski和Barton，2016a； Stechlinski和Barton，2017），适用于可大规模缩放以解决大规模动态优化问题的数值实现。竞争性混合建模方法对过程操作的挑战（例如 混合自动机）被强调为非平滑DAE方法的动机。在介绍适当的数学理论之前，给出了几个以非光滑DAE为模型的过程操作示例，以说明它们的广泛适用性。