Spontaneous Ignition in Porous Media at Long Times

If oxygen is in intimate contact with fuel Arrhenius law says that reaction will occur, even at low temperatures. Heat losses can become equal to the small reaction heat generated, so that the system remains trapped in a slow reaction mode. Such a mode is indistinguishable from extinction. On the other hand, if heat losses remain smaller than the heat generated by the reaction the temperature increases and spontaneous ignition occurs. Heat losses are strongly dependent on the geometry of the heat generating region. We therefore distinguish three idealized geometries, viz. linear, cylindrical and spherical infinite domains. We analyze the long time behavior of a basic heat diffusion problem that incorporates an Arrhenius heat generation term; the resulting model is temperature controlled. Only in spherical geometry the model recovers the results from the conventional heat transfer concept. Indeed, we come to the following results. As reactant depletion is ignored, spontaneous ignition always occurs, in linear and cylindrical coordinates, even if it takes very long time. For the spherical case, the occurrence of ignition or extinction depends on the process conditions.