Hot–spot thermal ignition in a porous medium under conditions of natural gas filtration

The development of a hot spot in a porous reactive medium with chemical reactions occurring at the inner surface of the pores between a solid skeleton and a gaseous oxidizer is studied by asymptotic methods at large values of the Peclet number, the Frank–Kamenetskii parameter, and the temperature head. It is shown that upon natural gas filtration, the process develops in two stages. In the first stage, the pressure, density, and temperature of the gas are equalized over the entire porous medium, and a hot spot develops on the skeleton in the second stage. The limit of hot–spot ignition and the ignition time for a hot spot are determined. An example of calculation of the critical parameters of the system is given.