Forced periodic operation of methanol synthesis

Methanol is an important feed material in the chemical industry. Traditionally it is produced from synthesis gas using a heterogeneous Cu/ZnO/Al2O3 catalyst under steady state conditions. In this project, the potential of alternative forced periodic operation modes is studied and rigorously evaluated. This is a joint project with the PCF group and the Petkovska group from the University of Belgrade. It combines mathematical modeling (PSD and PCF groups), with nonlinear frequency response analysis (Petkovska group), rigorous numerical optimization (PSD group) and experimental validation (PCF group). The focus during the current first period of the project was on a gradientless isothermal reactor.

In general, forced periodic operation is beneficial if the time averaged reactor performance under forced periodic operation is better than the corresponding steady state values, which is only possible for nonlinear systems. The idea is not new and has been discussed since the 60’s (see, e.g., [R1] for a recent review). However, new methods and tools are developed in this project for the optimization of forced periodic operation with single and multiple periodic inputs and the comparison with optimal steady state operation to exploit and evaluate the full potential of this concept for a challenging and highly relevant chemical reaction.

The starting point was the lumped kinetic Langmuir Hinshelwood model for methanol synthesis presented in [1,2,3]. it is based on a comprehensive set of steady state and dynamic data obtained previously by the PCF group [R3], accounts for three different active centers for the three reactions shown in Fig. 1 and dynamic changes of the catalyst morphology, which can play an important role under transient conditions. The model shows good agreement with steady state and transient data obtained by the PCF group over a wide range of operating conditions. Using the approximate NFR analysis, it was shown, that no improvement is possible for single periodic input [4] and that significant improvements can be expected for periodic variation of the total feed flow rate and the CO concentration in the feed [5].

Fig. 1: Pareto fronts for methanol synthesis: cross - optimal steady-state operation, square -
optimal forced periodic operation.

Rigorous numerical optimization of the full-blown nonlinear model was undertaken to validate the results of the approximate NFR analysis. [6]. Further, additional constraints arising in practice and additional degrees of freedom can be easily addressed with the numerical optimization approach. For a rigorous evaluation of the potential of forced periodic operation, a comparison with optimal steady states is essential. For this purpose, frameworks for steady state and dynamic optimization of forced periodic operation were developed using a sequential approach. For the efficient calculation of periodic states, dynamic simulation was used in combination with a periodicity condition in the constraint set of the optimization problem. For the evaluation of the reactor performance a multi-objective optimization problem was solved using the ε-constraint method (e.g. [R2]), which calculates optimal values of a first objective function with respect to given or restricted values of a second objective function in the constraint set of the optimization problem. Time-averaged methanol flow rate and methanol yield based on total carbon feed to the reactor were used as objective functions. The front of Pareto optimal steady state solutions and Pareto optimal forced periodic solutions with harmonic forcing of the CO feed to the reactor and the total feed flow rate are shown in Fig. 1 on the right. In this figure, the mean value of the input variables for forced periodic operation is not necessarily equal to the corresponding steady state value but is also optimized.

The results in Fig. 1 show that, for the given conditions, forced periodic operation of the total feed flow rate and the CO fraction in the feed is superior compared to steady state operation. Improvements in terms of methanol flow rate or methanol yield relative to the total amount of carbon in the feed can be substantial as indicated by the arrows in Fig. 1. Even greater improvements were found, when the shape of the forcing function is also optimized using a discretization approach of the input functions or a simple square wave forcing. Results will be validated experimentally and extended in the second project period to nonisothermal fixed bed reactors frequently used in practice. Further we also aim to conduct a more detailed economic evaluation using suitable economic cost functions.

Cooperation partners

  • Prof. Seidel-Morgenstern, PCF group
  • Prof. Menka Petkovska, University Belgrade
  • Prof. Sager, OVGU

Publications

[1] C. Seidel, A. Jörke, B. Vollbrecht, A. Seidel-Morgenstern, and A. Kienle. Kinetic modelling of methanol synthesis from renewable resources. Chem. Eng. Sci., 175:130–138, 2018.
[2] C. Seidel, A. Jörke, B. Vollbrecht, A. Seidel-Morgenstern, and A. Kienle. Corrigendum to ’Kinetic modeling of methanol synthesis from renewable resources’ (Chem. Eng. Sci. 175 (2018) 130-138). Chem. Eng. Sci., 223:115724, 2020.
[3] C. Seidel and A. Kienle. Methanol kinetics from optimal dynamic experiments. In Computer Aided Chem. Eng., 48:7-12, 2020.
[4] D. Nikolić, C. Seidel, M. Felischak, T. Milicić, A. Kienle, A. Seidel-Morgenstern, and M. Petkovska. Forced periodic operations of a chemical reactor for methanol synthesis - The search for the best scenario based on the nonlinear frequency response method. Part I Single input modulations. Chem. Eng. Sci., 248A:117134, 2022
[5] D. Nikolić, C. Seidel, M. Felischak, T. Milicić, A. Kienle, A. Seidel-Morgenstern, and M. Petkovska. Forced periodic operations of a chemical reactor for methanol synthesis - The search for the best scenario based on the nonlinear frequency response method. Part II Simultaneous modulation of two inputs. Chem. Eng. Sci., 248A:117133, 2022
[6] C. Seidel, D. Nikolić, M. Felischak, M. Petkovska, A. Seidel-Morgenstern, and A. Kienle. Optimization of methanol synthesis under forced periodic operation. Processes, 9(5):872, 2021.

[R1] P. L. Silveston, and R. R. Hudgins. Periodic Operation of Reactors. Elsevier, Amsterdam, 2013.
[R2] M. Ehrgott. Multicriteria optimization: Second edition. Springer Science & Media, 2005.

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