Modelling spontaneous combustion in wet lignite

A model of self-heating of wet coal is presented. This involves coupled heat and mass transport within a coal pile, together with an exothermic reaction and phase changes of water. There are four state variables: temperature, oxygen, water vapour and liquid water concentrations. Heat and mass are conducted or diffused through the pile, while simultaneously undergoing chemical reaction. As demonstrated by experiment, the heat release rate depends in a quadratic fashion on the liquid water content and this feature is a distinctive aspect of the model. After development of the model, an illustrative spatially uniform model of just three state variables (temperature, oxygen and liquid water concentrations) is analysed for its bifurcational structure of steady states, periodic solutions and their stability. By this means, thresholds for the onset of ignition can be determined as a function of the physical and chemical parameters.