This paper presents a comprehensive computational analysis of a real gas turbine, considering the first and second laws of thermodynamics and employing an iterative trial-and-error approach. An equilibrium constant-based combustion model capable of calculating mole fractions of 10 species and applicable to various hydrocarbon fuels has been developed. The model can predict the mole fractions and production rates of pollutants such as NOx, CO, and CO2. In addition, steam injection has been employed in this model to reduce the formation of NOx and other combustion-generated pollutants. This technique lowers the flame temperature and alters the mechanisms of pollutant formation. A comprehensive simulation model was employed in this paper to investigate the impact of steam injection and other key parameters on the performance and emissions of a combined gas cycle. Energy, exergy, economic, and environmental analyses were conducted to provide a comprehensive evaluation of the system. Finally, a modified genetic algorithm is employed to optimize a multi-objective function considering total cost rate, CO2 index, and second law efficiency. The results of the developed combustion model have been validated against CEA and GASEQ software, demonstrating a maximum average error of only 0.5027% for 10 species. As a result of the multi-objective optimization, a three-dimensional Pareto front is obtained, indicating a maximum achievable exergy efficiency of 40.58%, a minimum total cost rate of $1471.2 per hour, and a CO2 index of 0.5075 kg/kWh. The distribution of the primary decision variables reveals the optimal range for these variables where Pareto optimal points are obtained. Based on the scatter analysis, the optimal steam injection mass flow rate was determined to be 26.9 kg/s (corresponding to 10.63% of the total air mass flow rate). This optimal value simultaneously optimizes the system's performance, economic, and environmental indicators.

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