Quantification and Application of Uncertainties in Transient Kinetic Experiments
Author(s)
Yonge, Adam C.
Advisor(s)
Editor(s)
Collections
Supplementary to:
Permanent Link
Abstract
Extracting mechanistic insights from kinetic experiments is a necessary step in the design of catalytic materials and the optimization of reactor performance. The flexibility of the mechanism and the ease at which these details can be extracted varies broadly with the computational and experimental approaches being used. To add to the challenge, sources of uncertainty present in the experiments or models can obscure our fundamental understanding and lead to inaccurate conclusions about a catalysts performance. Transient kinetic experiments can rapidly provide investigators with precise quantitative insights into individual kinetic processes, but sources of uncertainty present in these systems have been explored to a limited degree. In this thesis, we develop ways in which transient uncertainties can properly be accounted for and systematically reduced through model-based experimental design.
Of the transient kinetic methods available, we focus on the temporal analysis of products (TAP) reactor system. TAP has many beneficial features, including isothermal operating conditions, a gradual evolution in the catalytic materials structure or coverage, and a well-defined transport occurring primarily through Knudsen diffusion. Various categories of uncertainty are discussed with respect to TAP, including experimental, parametric, and structural uncertainties. Experimental sources of uncertainty primarily occur in the mass spectrometer signal from the outlet flux of gas species. This source is present in the objective function space and can be quantified using derivatives of the loss function with respect to fitted parameters. Parametric sources of uncertainty are also present in TAP experiments (specification of void packing, surface composition, pulse intensity, etc.), but can not be directly quantified through derivative evaluations. For this reason, we introduce two approaches for quantifying parametric uncertainties in TAP: sensitivity-based and ensemble-based. The sensitivity-based approach is rapid but is only accurate for linear transformations from the initial condition space to the kinetic parameter space. The ensemble-based approach is robust in estimating the uncertainty distribution around the kinetic parameter, but requires the utilization of more computational resources. Of the sources of uncertainty quantified on a platinum catalyzed carbon monoxide oxidation data set, all are an order of magnitude lower than the standard error in DFT ($\sim$0.2 eV). The experimental data and mechanism associated with carbon monoxide oxidation are relatively simple compared to other catalytic systems, so the relevance and quantitative impact of these uncertainties are likely to increase with the structural complexity of the mechanism or catalyst.
Beyond quantifying the impact of these sources of uncertainty, we would also like to limit their values, especially for more complex systems. For this reason, we apply the model-based design of experiments to TAP simulations to guide the selection of experiments to reduce uncertainties in a targeted manner. This approach entails the calculation of dynamic sensitivity matrices for each gas species in the system and the subsequent condensing of this information into Fisher information matrices and optimality criteria. For an oxidative propane dehydrogenation mechanism, we show that experiments selected by our approach reduce the uncertainty on kinetic parameters more effectively than arbitrarily selected experiments. It is also necessary to account for the possibility of multiple reaction mechanisms or active site structures describing the experimental data. We implement a similar approach to that of MBDoE for precision to evaluate the divergence between proposed mechanisms with structural differences in TAP experiments. A deterministic approach, as well as one incorporating prior covariance matrix, are used to perform this analysis on OPDH mechanisms. Although the prospect of maximizing divergence is shown, complications related to reoptimization make the utility of divergence optimization unknown for highly complex systems. All of these methods have been implemented in the open source python package TAPsolver, with the greater goal of making TAP analysis more accessible to a wider audience.
Sponsor
Date
2022-12-13
Extent
Resource Type
Text
Resource Subtype
Dissertation