Steady-state temperature field of multilayer overlying strata under an equivalent fixed-wall-temperature heat source: similarity experiments and 3D simulation

In view of the problem that the thermal response of overlying multilayer strata under the background of hidden coal fires is significantly affected by lithological differences and stratigraphic sequence, this paper equivalently treats the coal-fire heat source as a fixed-wall-temperature boundary and studies the quasi-steady/steady-state heat conduction process of the multilayer overlying strata system under given thermal boundary conditions. This paper does not simulate the complete evolution process of hidden coal fires, and does not explicitly consider the multi-field coupling effects such as combustion reaction, oxygen supply, gas migration, moisture migration, thermal radiation, and thermal damage. By constructing a 10:1 multilayer similarity experimental platform, five lithologies, namely fine sandstone, siltstone, sandy mudstone, mudstone, and carbonaceous mudstone, were selected, and quasi-steady temperature measurement data were obtained under two fixed-wall-temperature conditions of 500 °C and 700 °C. Meanwhile, a three-dimensional steady-state heat conduction model considering temperature-dependent thermal conductivity was established, and eight experimental measurement points were used for point-by-point comparison with the numerical results to verify the applicability of the model within the measurement-point coverage range. The results show that, under the action of the equivalent fixed-wall-temperature heat source, the multilayer temperature field presents obvious stratified attenuation characteristics; the vertical propagation of heat is jointly controlled by lithological differences and layer-thickness combinations, and the carbonaceous mudstone layer shows a strong thermal resistance effect. Under the 500 °C and 700 °C conditions, the experimental-numerical root mean square errors within the measurement-point coverage range are 4.17 K and 5.78 K, respectively, and the mean signed errors are + 3.13 K and + 4.13 K, respectively, indicating that the model can well characterize the quasi-steady spatial temperature distribution in the monitored region, but the temperature magnitude has a slight overall positive deviation. The research results can provide a reference for the analysis of the heat conduction mechanism of overlying multilayer strata in coal-fire areas under fixed thermal boundary conditions.