Analysis of up⁃scaling method for the development of fire zone in coal mines: From the coal⁃particle scale to gob scale

Mesoscale characteristics are the intrinsic features of the development of fire zones in coal mines.To investi⁃ gate the effect of mesoscale on the connections between the microcosmic mechanism of heat transfer and the macro⁃ scopic phenomenon of energy variation during the development of fire zones is of great significance for the studies on coal spontaneous combustion and coal mine thermodynamic disaster.Firstly，the Discrete Element Method (DEM) was employed to simulate the falling，packing and compacting of coal particles，which generated the packing structure of coal particles.Based on the mesoscale II between the coal⁃particle scale and the gob scale，the mathematic model was built for the fluid flow and heat transfer in coal particles packing.The high⁃accuracy of the model was validated with the mean error of 1.77%.Secondly，on the basis of the generated packing and corresponding simulations，an up⁃ scaling method，i.e.the inverse operation method of effective heat conductivity，was developed specializing in the devel⁃ opment of fire zones.The proposed method utilized the numerical temperature solutions and nonlinear least⁃square fit⁃ ting method to calculate the effective heat conductivity that could bridge the gap between two boundary scales and pre⁃ dict the heat transfer process in the gob accurately. Thirdly， the effective heat conductivities were calculated according to the Rep ranging from 3 to 6 000.The results showed that the effective heat conductivity and Rep presented a linear relation.Finally，an empirical equation for up⁃scaling was developed.For 3