A Mathematical Model For Mine Fires

Mine fires have always been of great concern to mining engineers and their behavior has been studied for a long time. Although an abundance of observations exist, no satisfactory mathematical model for their interpretation and extrapolation has become known. The paper presented here tries to close this gap, making use of the laws of chemical kinetics, energy and momentum conservation. To overcome the mathematical difficulties, the fire zone is axially divided into segments and radially into sections, each one with an extension of only a few inches. Conditions in segments and sections are updated in time intervals of one second or less. To solve the large number of resulting equations, a numerical solution is performed. The model has so far been tried on timber fires. It confirms experimental observations on the ignition phases and equilibria of these fires.