Internal and external combustion studies consider that the combustion of gaseous fuels emits exhaust pollutants that are cleaner than the case of solid or liquid fuels. The researchers prefer that natural gas (which is mostly composed of methane) be mixed with additives that improve the reaction of the mixture to ensure greater effectiveness and reduce pollutants emitted from combustion, and as a result improving combustion efficiency and the performance of the equipment used. In this study the effect of hydrogen or nitrogen addition to methane on the flame formed in the cylindrical combustion chamber was investigated. The study adopted the combustion properties of the pre-mixed using CFD-FLUENT code. Characteristic parameters of the reactive flow (axial velocity, temperature, and mass fraction of carbon monoxide) were adopted. This study focused on addressing the phenomenon of methane enrichment with hydrogen or nitrogen, using mathematical models. The study results showed that the enrichment of methane flame with hydrogen or nitrogen directly affects the studied factors. A correlation appeared between carbon monoxide and temperature. Also, the methane enrichment with hydrogen caused a decrease in the flame temperature, and the exact opposite happened when methane was enriched with nitrogen, as the temperature increased with the increase in nitrogen in the mixture. The flame spreading speed of the hydrogen methane mixture was higher than that of methane and methane-nitrogen mixture. Carbon monoxide emissions are reduced by enrichment of methane with hydrogen.