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Greenhouse gas emissions from the combustion of fossil fuels pose a serious threat to global warming. Mitigation measures to counter the exponential growth and harmful impact of these gases on the environment require techniques for the reduction and capturing of carbon. Oxy-fuel combustion is one such effective method, which is used for the carbon capture. In the present work, a numerical study was carried out to analyze characteristics of oxy-fuel combustion inside a porous plate reactor. The advantage of incorporating porous plates is to control local oxy-fuel ratio and to avoid hot spots inside the reactor. A modified two-steps reaction kinetics model was incorporated in the simulation for modeling of methane air-combustion and oxy-fuel combustion. Simulations were performed for different oxidizer ratios, mass flow rates, and reactor heights. Results showed that that oxy-combustion with an oxidizer ratio (OR) of 0.243 could have the same adiabatic flame temperature as that of air-combustion. It was found that not only does OR need to be changed, but also flow field or reactor dimensions should be changed to achieve similar combustion characteristics as that of air-combustion. Fifty percent higher mass flow rates or 40% reduction in reactor height may achieve comparable outlet temperature to air-combustion. It was concluded that not only does the oxidizer ratio of oxy-combustion need to be changed, but the velocity field is also required to be matched with air-combustion to attain similar outlet temperature.