Microkinetic models entail a detailed reaction mechanism of all relevant reactions of a catalytic system. Such models become increasing important for understanding the important pathways and eventually for reactor and catalyst design. A hierarchy of models at different scales, with density functional theory (DFT) at the quantum scale, molecular dynamics (MD) and kinetic Monte Carlo (KMC) models at the atomic scale, and computational fluid dynamics (CFD) models at the macroscale, are glued together to describe catalytic systems with high fidelity [1,2]. Success in predicting catalyst performance purely from first-principles depends on the ability to connect these models at different scales.

Using a purely first-principles approach at each scale, the computational effort is tremendous. Our introduction of the hierarchical, multiscale, modeling framework renders first-principles modeling feasible by focusing computational resources on scales and phenomena that are important [3]. Yet, the uncertainty of kinetic parameters can be large and in fact, the elementary steps themselves may be incomplete in complex systems. As a result, model validation and/or refinement using experimental data injected into the multiscale framework is a necessity [4]. This motivates the development of rational methods to design experiments for obtaining the maximum parametric information about the system, i.e., to maximize the number of identifiable and/or important parameters and thus the information (in our case, kinetic) content.

In this contribution, we formulate an optimization problem in the entire experimental operating region to maximize information content. We describe methods involving sensitivity analysis and the Fisher information matrix (FIM) for design of experiments of catalytic systems. We use a global Monte Carlo search to randomly search the operating space and generate candidate optimal operating conditions for conducting experiments. We augment the sensitivity analysis with a novelty sampling (min/max) method and clustering analysis to indicate potentially important regions of the operating space. Our analysis illustrates that classical experimental design methods (A, D or E optimal designs) may not always generate conditions that are optimal for delineating chemistry, and we provide guidelines for experimental design that are generic with specific focus on catalytic systems. We further extend the scope of the experimental design through the use of transient experiments. In transient operation, the reaction system may potentially excite different modes (combinations of reactions) at different points in time. We introduce a method (based on identification of low dimensional manifolds) to identify the subset of important reactions at any time. This approach enables us to choose and control (to some extent) the modes that are excited at different transient conditions. Finally, we describe the use of steady state and transient data to discriminate between candidate microkinetic models using a probabilistic (maximum likelihood) framework. We illustrate our methods with the decomposition of ammonia to hydrogen on ruthenium for portable power generation.

References:

1. S. Raimondeau and D. G. Vlachos, "Recent developments on multiscale, hierarchical modeling of chemical reactors", Chem. Eng. J. 90, 3-23 (2002).

2. D. G. Vlachos, "A review of multiscale analysis: Examples from systems biology, materials engineering, and other fluid-surface interacting systems", Adv. Chem. Eng. 30, 1-61, invited (2005).

3. A. B. Mhadeshwar and D. G. Vlachos, "Hierarchical multiscale mechanism development for methane partial oxidation and reforming, and for thermal decomposition of oxygenates on Rh", J. Phys. Chem. B 109, 16819-16835 (2005).

4. D. G. Vlachos, A. B. Mhadeshwar, and N. Kaisare, "Hierarchical multiscale model-based design of experiments, catalysts, and reactors for fuel processing", Comput. Chem. Eng. 30, 1712-1724 (2006).