Electrons to Reactors Multiscale Modeling: Catalytic CO Oxidation over RuO2

Active Probing of a RuO2/CZ Catalyst Surface as a Tool for Bridging the Gap Between CO Oxidation Catalytic Tests in a Model and Realistic Exhaust Gas Stream

Herein, we present a paper that attempts to bridge the gap between CO oxidation catalytic tests performed in a model stream and a more realistic exhaust gas stream by incorporating characterization methods that allow for active probing of the catalyst surface. The results have shown that it is not just the abundance of a given type of species on the surface that impacts the activity of a system but also the ease of extraction of ions from their surface (time-of-flight secondary ion mass spectrometry) and the response of the support to change in the feed composition (dynamic in situ X-ray diffraction (XRD) with variable atmosphere). The study utilizes the method of doping a catalyst (RuO2/CZ) with a small amount of alkali-metal (K+ or Na+) carbonates in order to slightly modify its surface to gain insight into parameters that may cause discrepancies between model stream activity and complex stream activity. The most pronounced difference is that in the model stream, which contains only CO and O2 in helium, both alkali ions improve the activity of the system at temperatures around 175 °C, whereas in the complex stream, which mimics the exhaust stream from a diesel engine under oxygen lean conditions, the K+-doped catalyst is slightly worse than RuO2 /CZ and RuO2 + Na+/CZ and much worse in propane combustion. The total hydrogen consumption values (temperature-programmed reduction) and the Oads/Olatt ratios (X-ray photoelectron spectroscopy) both place the RuO2 + K+/CZ system between the other two and hence provided no reason for the unusual behavior of the K+-doped catalyst. In contrast, both in situ XRD measurement tests and ToF SIMS results show a pronounced difference between the RuO2 + K+/CZ catalyst and the other two systems, which indicates that the interaction of the surfaces with the reagents might be the cause of the discrepancy. The CO2-TPD results show that this system retains more CO2, i.e., the product, at adsorption sites, which might reduce the adsorption of other reagents, i.e., oxygen ions, CO, and propane, hence lowering the overall activity of the system.

Speeding up the Detection of Adsorbate Lateral Interactions in Graph-Theoretical Kinetic Monte Carlo Simulations

Kinetic Monte Carlo (KMC) has become an indispensable tool in heterogeneous catalyst discovery, but realistic simulations remain computationally demanding on account of the need to capture complex and long-range lateral interactions between adsorbates. The Zacros software package (https://zacros.org) adopts a graph-theoretical cluster expansion (CE) framework that allows such interactions to be computed with a high degree of generality and fidelity. This involves solving a series of subgraph isomorphism problems in order to identify relevant interaction patterns in the lattice. In an effort to reduce the computational burden, we have adapted two well-known subgraph isomorphism algorithms, namely, VF2 and RI, for use in KMC simulations and implemented them in Zacros. To benchmark their performance, we simulate a previously established model of catalytic NO oxidation, treating the O* lateral interactions with a series of progressively larger CEs. For CEs with long-range interactions, VF2 and RI are found to provide impressive speedups relative to simpler algorithms. RI performs best, giving speedups reaching more than 150× when combined with OpenMP parallelization. We also simulate a recently developed methane cracking model, showing that RI offers significant improvements in performance at high surface coverages.

Nonlinear Reactor Design Optimization With Embedded Microkinetic Model Information

Despite the success of multiscale modeling in science and engineering, embedding molecular-level information into nonlinear reactor design and control optimization problems remains challenging. In this work, we propose a computationally tractable scale-bridging approach that incorporates information from multi-product microkinetic (MK) models with thousands of rates and chemical species into nonlinear reactor design optimization problems. We demonstrate reduced-order kinetic (ROK) modeling approaches for catalytic oligomerization in shale gas processing. We assemble a library of six candidate ROK models based on literature and MK model structure. We find that three metrics—quality of fit (e.g., mean squared logarithmic error), thermodynamic consistency (e.g., low conversion of exothermic reactions at high temperatures), and model identifiability—are all necessary to train and select ROK models. The ROK models that closely mimic the structure of the MK model offer the best compromise to emulate the product distribution. Using the four best ROK models, we optimize the temperature profiles in staged reactors to maximize conversions to heavier oligomerization products. The optimal temperature starts at 630–900K and monotonically decreases to approximately 560 K in the final stage, depending on the choice of ROK model. For all models, staging increases heavier olefin production by 2.5% and there is minimal benefit to more than four stages. The choice of ROK model, i.e., model-form uncertainty, results in a 22% difference in the objective function, which is twice the impact of parametric uncertainty; we demonstrate sequential eigendecomposition of the Fisher information matrix to identify and fix sloppy model parameters, which allows for more reliable estimation of the covariance of the identifiable calibrated model parameters. First-order uncertainty propagation determines this parametric uncertainty induces less than a 10% variability in the reactor optimization objective function. This result highlights the importance of quantifying model-form uncertainty, in addition to parametric uncertainty, in multi-scale reactor and process design and optimization. Moreover, the fast dynamic optimization solution times suggest the ROK strategy is suitable for incorporating molecular information in sequential modular or equation-oriented process simulation and optimization frameworks.

Kinetic Monte Carlo simulations for heterogeneous catalysis: Fundamentals, current status, and challenges

Kinetic Monte Carlo (KMC) simulations in combination with first-principles (1p)-based calculations are rapidly becoming the gold-standard computational framework for bridging the gap between the wide range of length scales and time scales over which heterogeneous catalysis unfolds. 1p-KMC simulations provide accurate insights into reactions over surfaces, a vital step toward the rational design of novel catalysts. In this Perspective, we briefly outline basic principles, computational challenges, successful applications, as well as future directions and opportunities of this promising and ever more popular kinetic modeling approach.

How a Quantum Computer Could Quantify Uncertainty in Microkinetic Models

A method of uncertainty quantification on a quantum circuit using three samples for the Rh(111)-catalyzed CO oxidation reaction is demonstrated. Three parametrized samples of a reduced, linearized microkinetic model populate a single block diagonal matrix for a quantum circuit. This approach leverages the logarithmic scaling of the number of qubits with respect to matrix size. The Harrow, Hassidim, and Lloyd (HHL) algorithm for solving linear systems is employed, and the results are compared with the classical results. This application area of uncertainty quantification in chemical kinetics can experience a quantum advantage using the method reported here, although issues related to larger systems are discussed.

How a Quantum Computer Could Solve a Microkinetic Model

A CO oxidation microkinetic model is set up for a quantum circuit. The CO oxidation microkinetic model, and microkinetic models in general, exhibit an advantage of not requiring an encoding step because of being a subclass of systems of equations. The microkinetic model is cast as a nonlinear set of equations at first. Then, a linearizing approximation is made, and the resulting linear set of equations may be iterated to converge to the solution to the nonlinear set of equations. In this CO oxidation, the linearized set of equations is realized to chemical accuracy with one iteration. Current limitations in executing the quantum circuit to obtain the solution are discussed.

Vacancy assisted diffusion on single-atom surface alloys

Bimetallic surfaces can exhibit an improved catalytic activity through tailoring the concentration and/or the arrangement of the two metallic components. However, in order to be catalytically active, the active bimetallic surface structure has to be stable under operating conditions. Typically, structural changes in metals occur via vacancy diffusion. Based on the first-principles determination of formation energies and diffusion barriers we have performed kinetic Monte-Carlo (kMC) simulations to analyse the (meta-)stability of PtRu/Ru(0001), AgPd/Pd(111), PtAu/Au(111) and InCu/Cu(100) surface alloys. In a first step, here we consider single-atom alloys together with one vacancy per simulation cell. We will present results of the time evolution of these structures and analyse them in terms of the interaction between the constituents of the bimetallic surface.

A Critical Look at Direct Catalytic Hydrogenation of Carbon Dioxide to Olefins

One of the main initiatives for fighting climate change is to use carbon dioxide as a resource instead of waste. In this respect, thermocatalytic carbon dioxide hydrogenation to high-added-value chemicals is a promising process. Among the products of this reaction (alcohols, alkanes, olefins, or aromatics), light olefins are interesting because they are building blocks for making polymers, as well as other important chemicals. Olefins are mainly produced from fossil fuel sources, but the increasing demand of plastics boosts the need to develop more sustainable synthetic routes. This review gives a critical overview of the most recent achievements in direct carbon dioxide hydrogenation to light olefins, which can take place through two competitive routes: the modified Fischer-Tropsch synthesis and methanol-mediated synthesis. Both routes are compared in terms of catalyst development, reaction performance, and reaction mechanisms. Furthermore, practical aspects of the commercialization of this reaction, such as renewable hydrogen production and carbon dioxide capture, compression, and transport, are discussed. It is concluded that, to date, the catalysts used in the carbon dioxide hydrogenation reaction give a wide product distribution, which reduces the specific selectivity to lower olefins. More efforts are needed to reach better control of the C/H surface ratio and interactions within the functionalities of the catalyst, as well as understanding the reaction mechanism and avoiding deactivation. Renewable H₂ production and carbon dioxide capture and transport technologies are being developed, although they are currently still too expensive for industrial application.

Efficient Implementation of Cluster Expansion Models in Surface Kinetic Monte Carlo Simulations with Lateral Interactions: Subtraction Schemes, Supersites, and the Supercluster Contraction

While lateral interaction models for reactions at surfaces have steadily gained popularity and grown in terms of complexity, their use in chemical kinetics has been impeded by the low performance of current kinetic Monte Carlo (KMC) algorithms. The origins of the additional computational cost in KMC simulations with lateral interactions are traced back to the more elaborate cluster expansion Hamiltonian, the more extensive rate updating, and to the impracticality of rate-catalog-based algorithms for interacting adsorbate systems. Favoring instead site-based algorithms, we propose three ways to reduce the cost of KMC simulations: (1) representing the lattice energy by a smaller Supercluster Hamiltonian without loss of accuracy, (2) employing the subtraction schemes for updating key quantities in the simulation that undergo only small, local changes during a reaction event, and (3) applying efficient search algorithms from a set of established methods (supersite approach). The cost of the resulting algorithm is fixed with respect to the number of lattice sites for practical lattice sizes and scales with the square of the range of lateral interactions. The overall added cost of including a complex lateral interaction model amounts to less than a factor 3. Practical issues in implementation due to finite numerical accuracy are discussed in detail, and further suggestions for treating long-range lateral interactions are made. We conclude that, while KMC simulations with complex lateral interaction models are challenging, these challenges can be overcome by modifying the established variable step-size method by employing the supercluster, subtraction, and supersite algorithms (SSS-VSSM). © 2019 Wiley Periodicals, Inc.

Systematic Enumeration of Elementary Reaction Steps in Surface Catalysis

The direct synthesis of complex chemicals from simple precursors (such as syngas) is one of the main objectives of current research in heterogeneous catalysis. To rationally design catalytic materials for this purpose, it is essential to identify the critical elementary reaction steps that ultimately determine a catalyst's activity and selectivity with respect to a desired product. Unfortunately, the number of potentially relevant elementary steps is in the thousands, even for relatively simple target species like ethanol. The challenge of identifying the critical steps is thus akin to finding the proverbial needle in a haystack. Recently, a model-reduction scheme has been proposed, which tackles this problem by prescreening the barriers of all potential reactions with computationally inexpensive approximations. Although this route appears highly promising, it raises the question of how the starting point of the model-reduction process can be determined. In this contribution, we present a systematic method for enumerating all intermediates and elementary reactions relevant to a chemical process of interest. Using this approach, we construct reaction networks for C,H,O-containing systems consisting of up to four non-hydrogen atoms (more than 1 million reactions). Importantly, the scheme goes beyond simple bond-breaking reactions and allows considering rearrangement and transfer reactions as well. The presented reaction networks thus cover the chemistry of syngas-based processes (and beyond) to an unprecedented scale.

SQERT-T: alleviating kinetic Monte Carlo (KMC)-stiffness in transient KMC simulations

Lattice based kinetic Monte Carlo (KMC) is often used for simulating the dynamics of systems at a supramolecular scale, based on molecular scale transitions. A common challenge in KMC simulations is rapid 'back-and-forth' reactions, which dominate the events executed during simulations and inhibit the ability for simulations to reach longer time scales. Such processes are fast frivolous processes (FFPs) and are one manifestation of a phenomenon referred to as KMC-stiffness. Here, an algorithm for staggered quasi-equilibrium rank-based throttling geared towards transient kinetics (SQERT-T) is presented. Within the SQERT-T methodology, a pace-restrictor reaction and an FFP floor are utilized along with throttling of the process transition rate constants to accelerate the KMC simulations while still retaining sufficient time resolution for sampling of the data. KMC simulations were performed for CO oxidation over RuO₂(1 1 0) and over RuO₂(1 1 1), and the results were compared to experimental data obtained using RuO₂ powders. The experiments and simulations were for transient conditions: the system was subjected to a temperature program which included temperatures in the range of 363 to 453 K. The timescales that were achieved during the KMC simulations in this study would not have been accessible without KMC acceleration, and were enabled by the use of SQERT-T.