(531a) Globally Optimal Microkinetic Modeling (MKM) for Rational Catalyst Design and Optimization of Reaction Systems

Microkinetic modeling (MKM) provides a detailed description of elementary steps of a particular reaction and plays a crucial role in elucidating reaction mechanisms in heterogeneous catalysis at the molecular level [1]. The integration of MKM with reactor models is important to capture the critical interplay between reaction kinetics and transport [2]. An inevitable first step of microkinetic analysis is the reliable estimation of physically meaningful kinetic parameters associated with each elementary reaction. These parameters include pre-exponential factors, activation energies, adsorption entropies, steric factors, and active site densities [1]. Traditional parameter estimation of MKM involves expert-driven selection of plausible reaction mechanisms, estimation of chemically realistic parameter ranges, and subsequent numerical optimization to align model predictions with experimental data. An optimization model is formulated for parameter estimation of MKM coupled with a steady state reactor model. We address two optimization problems: i) a nonconvex nonlinear programming problem for parameter estimation in MKM, and ii) a global optimization problem utilizing the established MKM to obtain optimal catalyst compositions for maximizing product yields and conversions. Nonetheless, such problems involve highly nonconvex signomials and are susceptible to trivial solutions. To calibrate the kinetic parameters to the experimental data, a combination of the Rosenbrock [3] or gradient-based Levenberg–Marquardt algorithm [4] is often employed. However, these techniques do not guarantee global solutions and often fail to obtain non-trivial solutions to nonlinear system of equations describing the microkinetic surface coverage and concentrations. Moreover, a large set of elementary rate expressions involving signomial functions induce severe nonconvexity in the model [5]. Even state-of-the-art solvers struggle to find non-trivial solutions to MKM related optimization lacking inadequate bounding techniques.

To address these challenges, we propose a global optimization-based technique for estimating MKM parameters and solving subsequent catalyst design problems. Global optimization with tighter bounding techniques can address such problems to find the solutions of nonlinear systems of equations [6]. In particular, we develop tight lower bounds on surface coverage and concentrations using our newly developed Separable Edge-Concave (SEC) underestimators [7] for the global optimization of MKM parameters. The SEC underestimator provides a linear relaxation technique to achieve tighter lower bounds for signomial functions within a branch-and-bound framework, thereby enhancing the convergence and computational efficiency. Our proposed framework is designed to consider user provided available data, obtained from an array of data sources including DFT simulations as well as actual laboratory experiments.

The efficacy of our framework is illustrated through a detailed case study in the area of in-tandem catalysis. Specifically, we consider CO₂ hydrogenation to hydrocarbons using tandem catalysts. It consists of two MKMs, the first describing the CO₂-to-methanol process over In₂O₃ [8] (involving 13 elementary steps and 52 kinetic parameters) and the second describing the methanol-to-hydrocarbon conversion over HZSM-5 (involving over 25 elementary reactions and 100 kinetic parameters). We apply the proposed technique to develop robust MKM parameter estimation and optimization platform and elucidate different trade-offs and interactions between the two catalyst systems when they are mixed together at different compositions. We further perform systematic optimization of catalyst composition and the overall reaction mechanism that leads to maximum conversion and product yield.

Keywords: Data-driven Modeling, Microkinetic Modeling, Signomials, Parameter Estimation, Global Optimization, Edge-Concave Underestimators.

References:

[1] Dumesic, J. A.; Rudd, D. F.; Aparicio, L. M.; Rekoske, J. E.; Treviño, A. A. (1993). The Microkinetics of Heterogeneous Catalysis; American Chemical Society: Washington DC.

[2] Klumpers, B., Luijten, T., Gerritse, S., Hensen, E., & Filot, I. (2023). Direct coupling of microkinetic and reactor models using neural networks. Chemical Engineering Journal, 475, 145538.

[3] Rosenbrock, H. (1960). An automatic method for finding the greatest or least value of a function. The computer journal, 3(3), 175-184.

[4] Marquardt, D. W. (1963). An algorithm for least-squares estimation of nonlinear parameters. Journal of the society for Industrial and Applied Mathematics, 11(2), 431-441.

[5] Ureel, Y., Tomme, L., Sabbe, M. K., & Van Geem, K. M. (2025). Genesys-Cat: automatic microkinetic model generation for heterogeneous catalysis with improved Bayesian optimization. Catalysis Science & Technology.

[6] Maranas, C. D., & Floudas, C. A. (1995). Finding all solutions of nonlinearly constrained systems of equations. Journal of Global Optimization, 7, 143-182.

[7] Nath Roy, B., Hasan, M. M. F. (2025). Separable Edge-Concave Underestimator for High-Dimensional Signomials in Nonnegative Orthant, Under Review.

[8] Mahnaz, F., Mangalindan, J. R., Dharmalingam, B. C., Vito, J., Lin, Y. T., Akbulut, M., ... & Shetty, M. (2024). Intermediate Transfer Rates and Solid-State Ion Exchange are Key Factors Determining the Bifunctionality of In2O3/HZSM-5 Tandem CO2 Hydrogenation Catalyst. ACS Sustainable Chemistry & Engineering, 12(13), 5197-5210.