Uncertainty Analysis and Robust Optimization of a Single Pore in a Heterogeneous Catalytic Flow Reactor System

Abstract

Catalytic systems are crucial to a wide number of chemical production processes, and as a result there is significant demand to develop novel catalyst materials and to optimize existing catalytic reactor systems. These optimization and design studies are most readily implemented using model-based approaches, which require less time and fewer resources than the alternative experimental-based approaches. The behaviour of a catalytic reactor system can be captured using multiscale modeling approaches that combine continuum transport equations with kinetic modeling approaches such as kinetic Monte Carlo (kMC) or the mean-field (MF) approximation in order to model the relevant reactor phenomena on the length and time scales on which they occur. These multiscale modeling approaches are able to accurately capture the reactor behaviour and can be readily implemented to perform robust optimization and process improvement studies on catalytic reaction systems. The problem with multiscale-based optimization of catalytic reactor systems, however, is that this is still an emerging field and there still remain a number of challenges that hinder these methods. One such challenge involves the computational cost. Multiscale modeling approaches can be computationally-intensive, which limit their application to model-based optimization processes. These computational burdens typically stem from the use of fine-scale models that lack closed-form expressions, such as kMC. A second common challenge involves model-plant mismatch, which can hinder the accuracy of the model. This mismatch stems from uncertainty in the reaction pathways and from difficulties in obtaining the values of the system parameters from experimental results. In addition, the uncertainty in catalytic flow reactor systems can vary in space due to kinetic events not taken into consideration by the multiscale model, such as non-uniform catalyst deactivation due to poisoning and fouling mechanisms. Failure to adequately account for model-plant mismatch can result in substantial deviations from the predicted catalytic reactor performance and significant losses in reactor efficiency. Furthermore, uncertainty propagation techniques can be computationally intensive and can further increase the computational demands of the multiscale models.

Based on the above challenges, the objective of this research is to develop and implement efficient strategies that study the effects of parametric uncertainty in key parameters on the performance of a multiscale single-pore catalytic reactor system and subsequently to implement them to perform robust and dynamic optimization on the reactor system subject to uncertainty. To this end, low-order series expansions such as Polynomial Chaos Expansion (PCE) and Power Series Expansion (PSE) were implemented in order to efficiently propagate parametric uncertainty through the multiscale reactor model. These uncertainty propagation techniques were used to perform extensive uncertainty analyses on the catalytic reactor system in order to observe the impact of parametric uncertainty in various key system parameters on the catalyst reactor performance. Subsequently, these tools were implemented into robust optimization formulations that sought to maximize the reactor productivity and minimize the variability in the reactor performance due to uncertainty. The results highlight the significant effect of parametric uncertainty on the reactor performance and illustrate how they can be accommodated for when performing robust optimization.

In order to assess the impact of spatially-varying uncertainty due to catalyst deactivation on the catalytic reactor system, the uncertainty propagation techniques were applied to evaluate and compare the effects of spatially-constant and spatially-varying uncertainty distributions. To accommodate for the spatially-varying uncertainty, unique uncertainty descriptions were applied to each uncertain parameter at discretized points across the reactor length. The uncertainty comparison was furthermore extended through application to robust optimization. To reduce the computational cost, statistical data-driven models (DDMs) were identified to approximate the key statistical parameters (mean, variance, and probabilistic bounds) of the reactor output variability for each uncertainty distribution. The DDMs were incorporated into robust optimization formulations that aimed to maximize the reactor productivity subject to uncertainty and minimize the uncertainty-induced output variability. The results demonstrate the impact of spatially-varying parametric uncertainty on the catalytic reactor performance. They also highlight the importance of its inclusion to adequately account for phenomena such as catalyst fouling in robust optimization and process improvement studies.

The dynamic behaviour of the catalytic reactor system was similarly assessed within this work to evaluate the effects of uncertainty on the reactor performance as it evolves in time and space. For this study, uncertainty analysis was performed on a transient multiscale catalytic reactor model subject to changes in the system temperature. These results were used to formulate robust dynamic optimization studies to maximize the transient catalytic reactor behaviour. These studies aimed to determine the optimal temperature trajectories that maximize the reactor’s performance under uncertainty. Dynamic optimization was also implemented to identify the optimal design and operating policies that allow the reactor, under spatially-varying uncertainty, to meet targeted performance specifications within a level of confidence. These studies illustrate the benefits of performing dynamic optimization to improve performance for multiscale process systems under uncertainty.