Analytical modelling of filtration combustion in inert porous media

A study is made of the self-sustaining combustion waves during the filtration of lean methane–air mixtures in inert porous media using the two-temperature approximation. Such processes are characterized by an intense thermal interaction between the gas and the porous material. Due to interfacial heat transfer, the solid phase is able to redistribute heat absorbed from reaction products to the unburned mixture. The analytical solution is built in three different regions: the pre-heating region, the reaction region and the region occupied by the combustion products. Analytic expressions predicting the temperature and methane mass fraction profiles in the wave, as well as the combustion wave velocity and the longitudinal extension of the reaction region are derived. The results are confirmed by numerical calculations using the finite difference method and a full set of basic equations.