Currently, the process of creating industrial installations is associated with digital technologies and must involve the stage of developing digital models. It is also necessary to combine installations with different properties, functions, and operational principles into a single system. Some tasks require the use of predictive modeling and the creation of “digital twins”. The main processes during the fuel cell modeling involve electrochemical transformations as well as the movement of heat and mass flows, including monitoring and control processes. Numerical methods are utilized in addressing various challenges related to fuel cells, such as electrochemical modeling, collector design, performance evaluation, electrode microstructure impact, thermal stress analysis, and the innovation of structural components and materials. A digital model of the membrane-electrode unit for a solid oxide fuel cell (SOFC) is presented in the article, incorporating factors like fluid dynamics, mass transfer, and electrochemical and thermal effects within the cell structure. The mathematical model encompasses equations for momentum, mass, mode, heat and charge transfer, and electrochemical and reforming reactions. Experimental data validates the model, with a computational mesh of 55 million cells ensuring numerical stability and simulation capability. Detailed insights on chemical flow distribution, temperature, current density, and more are unveiled. Through a numerical model, the influence of various fuel types on SOFC efficiency was explored, highlighting the promising performance of petrochemical production waste as a high-efficiency, low-reagent consumption fuel with a superior fuel utilization factor. The recommended voltage range is 0.6–0.7 V, with operating temperatures of 900–1300 K to reduce temperature stresses on the cell when using synthesis gas from petrochemical waste. The molar ratio of supplied air to fuel is 6.74 when operating on synthesis gas. With these parameters, the utilization rate of methane is 0.36, carbon monoxide CO is 0.4, and hydrogen is 0.43, respectively. The molar ratio of water to synthesis gas is 2.0. These results provide an opportunity to achieve electrical efficiency of the fuel cell of 49.8% and a thermal power of 54.6 W when using synthesis gas as fuel. It was demonstrated that a high-temperature fuel cell can provide consumers with heat and electricity using fuel from waste from petrochemical production.