Percolation phenomena in filtration combustion

Using a pore-network model, we study the effect of randomness in the solid fuel distribution on the propagation of Filtration combustion fronts in porous media. Both a complex pore-network model for full filtration combustion and a more simplified gasless combustion model are used. We find that the minimum threshold (akin to a "percolation threshold") for the fuel distribution is a function of the kinetic and heat-transfer parameters and can vary over a wide range. The balance between heat transfer and reaction kinetics endows the system with a behavior more complex than simple percolation, which was earlier suggested as a model for such systems. The long-range effect of heat conduction acts to move the behavior away from true percolation behavior. Conversely, the effect of heat losses is sufficient to lead to extinction (thus, to "nonpercolation") even for systems with fully occupied fuel sites. In either case, the availability of the fuel and its distribution in space are important parameters in the process.