Mathematical Modeling of Spontaneous Heating of a Coalbed – RI 9296

To have the capability to predict the development of localized spontaneous heating within a porous coalbed that is subjected to forced air ventilation or in an otherwise quiescent environment in which buoyancy develops, the Bureau of Mines developed three time-dependent mathematical models, which were used to calculate the temperature increase associated with chemisorption of oxygen by the coal. In each model, spontaneous heating is driven by an Arrhenius first-order reaction between the oxygen and coal. Two models are two-dimensional, and one is one-dimensional. In the first two-dimensional model, a constant-velocity forced convection airflow is specified; and in the other, buoyant flow is allowed to develop in the absence of forced convection. The third model evaluates the airflow from Darcy's law and a specification of the pressure at the surface of a one-dimensional porous coalbed. Numerical computations demonstrated how each model could be used to predict the onset of spontaneous heating when the porous coalbed was subjected to constraints of an imposed internal heat source or a high- temperature airflow. The effects of particle size and coalbed compaction upon spontaneous heating were examined with the third model.