Error reduction, uncertainty quantification, and sensitivity analysis methods for microkinetic modeling: application and insights into the catalytic conversion of ethanol on late transition metals

Abstract

Microkinetic modeling is a powerful computational technique for investigating chemical mechanisms under more realistic conditions than are possible with electronic structure calculations. Microkinetic models for species with more than two C atoms (e.g., the polyols and sugars arising in biomass processing) can require hundreds or thousands of parameters. Since it is not feasible to obtain all of the required parameters solely from high level electronic structure calculations (e.g., density functional theory, DFT) or by regression from experimental data, first principles-based semi-empirical methods (FPSEM) have been developed (typically by regression from DFT estimates) to enable the rapid estimation of the required kinetic parameters (species free energies and reaction activation energies), albeit with reduced accuracy compared to more rigorous methods. Despite the popularity of these methods, the level of accuracy that can be expected from them and the impact that this has on microkinetic model results has yet to be quantified. Errors in FPSEM estimates arising from the regression process were quantified by comparison to the corresponding DFT values. Theoretical and numerical techniques were also employed to demonstrate how errors propagate when multiple types of FPSEM are used sequentially. It was found that linear Brønsted-Evans-Polanyi (BEP) correlations for estimating activation energies have the largest uncertainty of the methods currently in use. Furthermore, when used in conjunction with FPSEM-estimated species free energies, the BEP error dominates the error contributed by the species energies. DFT calculations related to ethanol activation on close-packed facets of a variety of pure transition metals were carried out. The DFT results showed that the identities of the key steps for initial activation and selectivity to possible products can only be identified using microkinetic models. A fully DFT-parameterized model of ethanol steam reforming on Pt/Al 2 O 3 identified the rate determining step as the initial α C H activation with the selectivity to C-C cracking controlled by the C-C barrier in CHCO. The DFT results on all metals were used to develop FPSEM correlations for parameterizing a qualitative high throughput microkinetic model of ethanol hydrodeoxygenation. The high throughput model successfully predicted the qualitative behavior of the pure metals; oxophilic metals exhibited more C-O scission, whereas less oxophilic metals exhibited more C-C scission. A purely FPSEM-parameterized model of ethanol steam reforming was demonstrated to be in good qualitative agreement with the full DFT-parameterized model. After hierarchical refinement, the FPSEM-parameterized model was shown to be in quantitative agreement with the DFT-parameterized model. Finally, Bayesian and frequentist methods were utilized to estimate the inherent variability in DFT results. The resulting uncertainty distributions were used as inputs in a global uncertainty quantification and derivative-based sensitivity analysis algorithm to determine the impact of DFT-based uncertainty on the results of the full DFT-parameterized model of ethanol steam reforming. The qualitative predictions were shown to be quite robust to parametric uncertainty, and the globally sensitive parameters were identified to be the enthalpies of key species and the initial α C-H abstraction.