Robust optimization of a multiscale heterogeneous catalytic reactor system with spatially-varying uncertainty descriptions using polynomial chaos expansions

This paper explores the effects of spatially-varying parametric uncertainty on the performance of a heterogeneous catalytic flow reactor system. The catalytic reactor behaviour is simulated using a spatially-dependent multiscale model that combines kinetic Monte Carlo (kMC) with continuum transport equations to capture the relevant phenomena on the scales in which they occur. Polynomial chaos expansions (PCEs) are implemented to effectively propagate parametric uncertainty through the reactor model. These expansions are used to perform uncertainty analysis on the catalytic reactor system in order to accurately and effectively evaluate and compare the effects of spatially-constant and spatially-varying uncertainty distributions. The uncertainty comparison is further extended through application to robust optimization. To reduce the computational cost of the optimization, statistical data-driven models (DDMs) are identified to approximate the key statistical parameters (mean, variance, and probabilistic bounds) of the reactor output variability for each uncertainty description. The DDMs are incorporated into robust optimization formulations that maximize the reactor productivity and minimize the output variability subject to parametric uncertainty. The results demonstrate the impact of spatially-varying parametric uncertainty on the catalytic reactor performance and highlight the importance of its inclusion to adequately account for phenomena such as catalyst fouling in robust optimization and process improvement studies.