(171f) Robust Process Flowsheeting through Nonsmooth Models and Generalized Derivatives

The use of analytical derivatives in process simulation and optimization routines is well known to be beneficial for achieving rapid convergence and high accuracy (e.g. [1]). These advantages can be directly extended to flowsheets containing nondifferentiable process models through the use of generalized derivatives and implicit function sensitivity results for nonsmooth functions [2, 3]. Importantly, this allows process simulation and optimization formulations to be augmented with nonsmooth algorithms for non-ideal vapor-liquid equilibrium (“flash”) calculations for greater reliability when the phase regimes at the results of these calculations are not known or fixed a priori [4]. This significantly improves the robustness of flash subroutines underlying many key process units, e.g. flash drums, throttle valves, compressors and turbines, without increasing the size or complexity of the problem compared to the case of using classical flash formulations. Furthermore, process models for inherently nonsmooth unit operations such as multistream heat exchangers may be seamlessly integrated into process flowsheets, so long as sensitivities of these models' outputs in the form of generalized derivatives with respect to their inputs are computed correctly and communicated to the simulation or optimization algorithm. These techniques may be used in sequential-modular formulations, as well as hybrid methods in which only the most difficult to converge submodels are treated in a modular manner, while the remaining flowsheet equations are handled simultaneously as in an equation-oriented framework. This new nonsmooth flowsheeting strategy is capable of solving process simulation and optimization problems more reliably and efficiently than the algorithms implemented in existing software, and, in some cases, even allows for the solution of problems that are beyond the capabilities of classical approaches. As examples of the latter, it will be shown that the nonsmooth approach is particularly well-suited for highly accurate simulation and optimization of cryogenic liquefaction processes, in which many or all of the aforementioned nonsmooth modeling elements are present simultaneously in combination with non-ideal thermodynamic behavior and complex heat transfer considerations.

[1] D. Wolbert, X. Joulia, B. Koehret, L. T. Biegler, 1994. Flowsheet optimization and optimal sensitivity analysis using analytical derivatives. Computers & Chemical Engineering, 18(11/12): 1083–1095.

[2] K. A. Khan, P. I. Barton, 2015. A vector forward mode of automatic differentiation for generalized derivative evaluation. Optimization Methods and Software. 30(6):1185-1212.

[3] K. A. Khan, P. I. Barton, In Press. Generalized Derivatives for Hybrid Systems. IEEE Transactions on Automatic Control.

[4] H. A. J. Watson, M. Vikse, T. Gundersen, P. I. Barton, 2017. Reliable Flash Calculations: Part 1. Nonsmooth Inside-Out Algorithms. Industrial & Engineering Chemistry Research, 56(4): 960-973.