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The article presents a comparison of mathematical models of steam methane reforming. The analysis is divided into two parts. The first concerns the reforming process using separate steam reformers. The second part of the article compares models of steam methane reforming processes directly inside fuel cells. Due to the fact that the steam reforming process takes place at very high temperatures, internal steam reforming can only be carried out in high temperature fuel cells. Therefore, the second part of the article deals with molten carbonate fuel cells and solid oxide fuel cells powered by methane. In the case of both of fuel cells, the methane steam reforming may take place directly on the anodes of these electrochemical devices. The mathematical models (for both external and internal reforming) were compared based on available experimental data. In this analysis of mathematical models, particular attention was paid to the causes of discrepancies between the mathematical models and the experimental data. The steam reforming process is influenced by a number of different parameters such as: temperature, ratio of the amount of water vapor to carbon contained in the fuel (steam to carbon ratio), reaction time, presence of a catalyst, type of catalyst and many others. The models presented in this article were also compared in terms of taking into account various parameters that may affect the process of steam reforming. An attempt was also made to assess the accuracy of mathematical models. Unfortunately, for most of the equations considered in this article, numerical values for inaccuracies are not given or described as acceptable or minor. • Review of mathematical models of SMR. • The kinetics models of the steam methane reforming reaction. • Description of mathematical models for the molten carbonate fuel cell (MCFC). [ABSTRACT FROM AUTHOR]

In order to improve the energy efficiency of the Sabatier reactor-based power-to-gas process, molten carbonate fuel cells and solid oxide electrolyzers were installed instead of a conventional amine CO 2 capture system and a classical alkaline electrolyzer. The plant is a multi-module prototype with a nominal capacity of 50 kW consisting of two SOE-MCFC units. The system was commissioned in 2022. The article describes the theoretical basis. The initial assumptions that were formulated at the stage of preparing for the research investment, as well as the deviations from them that became the result of detailed design were presented. The developed startup and shutdown procedures, as well as the first results of pioneering research were shown. The trial operation of the system was intended to provide information on integrated SOE-MCFC module and its performance and efficiency. The basic barriers for market implementation and recommendations for future research were discussed. The optimal operating point for hydrogen production needed 35.8 kWh/kgH 2. Thus, electrical energy conversion to chemical energy efficiency is 93.9%. Flow preheating and electrical auxiliary heater power are not included. An MCFC at its ideal functioning point (around 4 kW el) outputs 5.4 kg/h of CO 2 separated. • Operational experience of upgraded novel P2G installation is reported. • A start-up procedure of MCFC-SOE tandem in proposed and experimentally verified. • Energy required for synthesis of a kilogram of hydrogen was 35.8 kWh/kgH 2. [ABSTRACT FROM AUTHOR]