Application of machine-learning techniques to reproduce a microkinetic model for the methanol synthesis

Introduction
The conversion of sustainable COx (e.g. from biomass or captured CO2) and green H2 to methanol is a key reaction to integrate renewable energy with the chemical industry and the mobility sector, as methanol is a building block for the production of several valuable fuels (e.g. gasoline, diesel, jet fuel) and chemicals (e.g. formaldehyde, dimethyl ether) [1].
In order to better understand the methanol synthesis and allow possibilities for optimization, we previously developed a microkinetic model (MM) with extensive experimental validation [2], based on ab initio density functional theory calculations [3-4]. This type of model is useful to gain insights into the chemistry behind the process, and can simulate complex reaction networks that are not be fully described by a formal kinetic model. However, the complexity and high computational effort requirements of a MM may hinder its use in real applications, such as reactor and plant optimization, especially if the kinetic model is incorporated into detailed reactor models (i.e., computational fluid dynamics) [5].
Machine learning techniques could extract the information of the MM and pass on to the reactor model, drastically reducing the required computational effort [5]. ... mehrWhile this is a promising solution, it has not been explored in literature yet, to the best of our knowledge. Therefore, the objective of this work is the development of an artificial neural network (ANN) that provides both simulation quality of the methanol synthesis similarly to the MM and flexible adaption to the desired process configuration.

Materials and Methods
With the MM, a total of 120,000 data points of reaction rate were generated, covering a wide range of industrially relevant operating conditions. Each data point consists in six inputs (the fugacity of H2, CO, CO2, CH3OH, and H2O, and temperature) and three outputs (the reaction rates of the main reactions: CO hydrogenation, CO2 hydrogenation and the reverse water-gas shift reaction).
Since the thermodynamic equilibrium is described by known equations, this a priori information is used in a data treatment of the generated points. The advantage of this procedure is that the ANN focuses on learning the kinetics of the methanol synthesis, whereas correct thermodynamics is ensured by known equations. The treated data points were randomly divided into three groups (training, test, and validation), and used for training and validation of the ANN.

Results and Discussion
The developed ANN accurately reproduces the simulations of the MM, with the courses of the curves in the diagram being almost the same. The ANN also adequately simulated the experimental data, with most points being inside the ± 20% lines.

Significance
In this work, the information of a MM for the methanol synthesis was successfully transferred to the ANN, which is a model requiring significantly less computational effort. The same methodology can be applied to other reacting systems that are described by microkinetic modeling.

References
1. Bozzano and Manetti. Prog. Energy Combust. 56, 71-105 (2016).
2. Lacerda de Oliveira Campos, B., Herrera Delgado, K., Wild, S., Studt, F., Pitter, S., and Sauer, J. Reac. Chem. Eng. 6: 868-887 (2021).
3. Studt, F., Behrens, M., Kunken, E. L., Thomas, N., Zander, S., Tarasov, A., Schumann, J., Frei, E., Varley, J. B., Abild-Petersen, F., Nørskov, J. K., Schlögl, R. ChemCatChem 7, 1105-1111 (2015).
4. Studt, F., Behrens, M., Abild-Petersen, F. Catalysis Letters 144, 1973-1977 (2014).
5. Park, J., Kim, H. S., Lee, W. B., Park. M.-J. Catalysts 10, 655 (2020).
6. Seidel, C., Jörke, A., Vollbrecht, B., Seidel-Morgenstein, A., Kienle, A. Chem. Eng. Sci. 175, 130-138 (2018).