Use of Nonsmooth Models and Generalized Derivatives to Improve the Robustness of Process Simulations

Many important operations and phenomena present in chemical processes, including pressure-driven flow, heat transfer, and phase change are best described using nondifferentiable functions. Despite this, nonsmooth models have been largely overlooked by the chemical engineering community due to a lack of robust methods for handling them effectively in simulation and optimization problems. While it is well known that the use of derivative information in process simulation and optimization algorithms is beneficial for achieving rapid convergence and high accuracy, the aforementioned physical phenomena are often handled either with smooth approximations, resulting in the loss of accuracy and desirable convergence properties, or by using discrete-continuous frameworks (e.g. mixed-integer models).

This presentation illustrates how computationally-relevant generalized derivatives (along with automatic methods for their evaluation)[1] allow for robust simulation of discrete-continuous behavior, such as in the operation of heat exchangers, refrigeration cycles with phase change, and pressure-relief systems. The automatic calculation of exact sensitivity information about the participating nonsmooth functions in the simulation models allow such problems to be solved as readily as their smooth counterparts.

[1]Barton PI, Khan KA, Stechlinski P, Watson HAJ. 2018. Computationally relevant generalized derivatives: theory, evaluation and applications. Optimization Methods and Software . 33(4-6):1030-1072.