Purpose of this study is to numerically investigate combustion within a porous channel, which has three layers with different pore densities. Non-premixed combustion inside the porous channel is modelled with thermal non-equilibrium energy equations. Flow and chemistry are decoupled with tabulated chemistry using flamelets, thereby reducing the computational cost. GRI 3.0 mechanism is used to account for methane/air combustion. Simulations are performed for different pore densities at the third layer in 8-30 PPI range. Also, the effects of thermal power and excess-air-ratio (EAR) are investigated for the porous burner. Temperatures and species mass fraction distributions are obtained. Maximum temperature in the burner found to be similar for all cases since combustion occurs in stoichiometric conditions at the flame front as a result of the non-premixed combustion model. NOx and CO emissions values of all simulations are compared against international gas emission standards. This comparison showed that while CO emissions are always below all international standards, NOx emissions are below these limits only for high values of excess air ratio and thermal power. Besides, as the pore density of the third layer is decreased, the values of emissions decrease strongly.