Convective burning is commonly identified in the literature as the key step in deflagration-to-detonation transition (DDT) of granular explosives. The prevalent physical picture of convective burning is of rapid and deep penetration of hot gases which controls the propagation rate via convective heat transfer. This investigation includes a review of relevant literature, new transient measurements of permeability at high pressures, and analysis of the experimental results. Results presented here show that deep penetration (many particle diameters) of gas at high velocities is not physically plausible for the low porosity granular beds of interest. The measured permeabilities are consistent with measurements made at lower pressures in similar materials, but are significantly lower than predictions based on beds of spherical particles. The important time and space scales of this experiment are identified. The interface region between the reservoir and porous bed is analysed. The wave hierarchy of the permeation experiment is studied, and short- and long-time limits are investigated using simplified asymptotic analysis. The low-speed flow approximation is also considered for flow within the bed. It is shown that drag dissipation terms in the energy equation cannot be neglected under adiabatic conditions as is commonly done. These results indicate that compaction processes play a larger role than commonly thought, and motivate the consideration of an asymptotic large drag limit of two-phase, two-velocity models.