Mathematical Model of Thermal Condition of Industrial Mining Waste

Rock wastes are technogenic wastes of the mining industry. Storing rock waste in a dump can cause its spontaneous combustion. Dust and toxic gases generated as a result of rock waste combustion cause serious atmospheric air contamination in the mining industry agglomerations. The mining industry contributes to climate change as well due to greenhouse gas emissions. A mathematical model of the thermal condition of rock wastes based on the method of thermodynamics of irreversible processes has been developed for the analysis of the thermal condition of the mining industry wastes in addition to the existing contact and remote methods. During rock waste combustion, the differential equation of heat transfer in a rock is complicated by overlaying the processes of changing the specific mass content due to the reaction of dehydration, combustion of the organic part of the material, as well as decarbonization and desulfurization reactions. Calculation formulas to determine the effective coefficient of thermal diffusivity and efficient heat capacity have been obtained. During carbon combustion in the waste, powerful sources of heat are generated, hence, experimentally determined thermal properties are combined and include endo- and exothermal effects. A differential equation of thermal conductivity with internal heat sources containing effective thermophysical properties including physical and chemical phase transformations in the rock has been developed. Based on the available experimental data and using the known solution of the thermal conductivity equation, it is possible to determine the effective thermal properties of mining industry waste material and its heating rate. Using the developed differential equation of thermal conductivity with internal heat sources, it is possible to determine the heat condition of rock waste and calculate its temperature field.