Mathematical model and methods for solving heat-transfer problem during underground coal gasification

Purpose. A mathematical model development for heat transfer during underground coal gasification based on the transcendental equation solution by the Newton-Raphson method. Methods. The heat-transfer model development is based on the research into a temperature field with a variable size of the gasification zone when passing through the phase transformation boundary, which changes abruptly. The research on the coal seam T(x, t) temperature field and the displacement length of the phase transition boundary S(t) is based on the integration of the differential heat-transfer equation with the fulfillment of one-phase Stefan problem conditions. The proportionality factor (β), characterizing the ratio of the displacement length of the “generator gas – coal” phase transition boundary to the time of coal seam gasification, is determined by substituting the Boltzmann equation and using the Newton-Raphson method based on solving the obtained transcendental equation. Findings. The main problems related to laboratory research on the coal gasification process have been identified. A mathematical model of heat transfer during underground coal gasification for a closed georeactor system has been developed, taking into account the effective change in its active zones. Originality. A mathematical model of heat transfer during underground coal gasification at the phase transition boundary has been developed, under which the one-phase Stefan problem conditions are fulfilled. Dependences of the change in the underground gas generator temperature, taking into account the change in the active zones of chemical reactions along the length of the combustion face and the gasification column, have been revealed. In addition, the dependences of the change in the phase transition boundary of a “generator gas – coal” heterogeneous system have been determined, which characterize the displacement length of the phase transition boundary on time and reveal the relationship between the thermal conductivity coefficient, specific heat capacity, as well as bulk density of coal and its calorific value. Practical implications. A method has been developed to determine the displacement length of the phase transition boundary of a “generator gas – coal” heterogeneous system and its relationship between the time and temperature of gasification process. This makes it possible to predict in the future the change in the active zones of the underground gas generator along the length of the gasification column.