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

Abstract

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.

Multilevel Monte Carlo applied to chemical engineering systems subject to uncertainty

“…More efficient selection of uncertain parameter realizations can be achieved using Latin hypercube sampling 5,6 and response surface methodology. [7][8][9] Alternatively, low-order closed-form expressions that relate the uncertain parameters to the observables via sensitivities (Taylor Series/ Power Series expansions [PSE] 7,[10][11][12][13][14] or an orthogonal polynomial basis (Polynomial Chaos expansions [PCE] 2,[15][16][17][18][19][20][21] ) can be developed using a small number of time-consuming evaluations of the full model. Once developed, the low-order expressions can be employed to rapidly construct probability density functions of the observables using a sufficiently large number of realizations of uncertain parameters.…”

Bayesian Objective Functions for Estimating Parameters in Nonlinear Stochastic Differential Equation Models with Limited Data

“…It is recommended that the proposed algorithms should be tested on larger-scale SDE parameter estimation problems and that the performance of these algorithm should be compared with particle filter-based methods and PC-based methods. These types of simulations can determine whether the B-spline and other approximations used to develop the proposed methods result in any significant degradation in the quality of parameter estimates when compared with particle filter methods.The computation time for the proposed ABEM and LAB methods is expected to be significantly lower than for particle filter techniques. ,, In future, it will be desirable to test the proposed methodologies using larger-scale models with a larger number of states and parameters …”

A Perspective on the Impact of Process Systems Engineering on Reaction Engineering

“…Monte Carlo sampling of uncertain parameters are then used to compute the distribution for the rate vector and its confidence intervals. In the context of application to uncertain reacting systems, PCE has been found to be more computationally efficient and accurate than power series expansion. − …”