A Thermal Effect Model for the Impact of Vertical Groundwater Migration on Temperature Distribution of Layered Rock Mass and Its Application

Abstract

On the basis of the one-dimensional heat conduction–convection equation, a thermal effect model for vertical groundwater migration in the stratified rock mass was established, the equations for temperature distribution in layered strata were deduced, and the impacts of the vertical seepage velocity of groundwater and the thermal conductivity of surrounding rocks on the temperature field distribution in layered strata were analyzed. The proposed model was employed to identify the thermal convection and conduction regions at two temperature-measuring boreholes in coal mines, and the vertical migration velocity of groundwater was obtained through reverse calculation. The results show that the vertical temperature distribution of the layered rock mass is subject to the migration of the geothermal water; the temperature curve of the layered formation is convex when the geothermal water travels upward, but concave when the water moves downward. The temperature distribution in the stratified rock mass is also subject to the thermal conductivity of the rock mass; greater thermal conductivity of the rock mass leads to a larger temperature difference among regions of the rock mass, while weaker thermal conductivity results in a smaller temperature difference. A greater velocity of the vertical migration of geothermal water within the surrounding rock leads to a larger curvature of the temperature curve. The model was applied to a study case, which showed that the model could appropriately describe the variation pattern of the ground temperature in the stratified rock mass, and a comparison between the modeling result and the measured ground temperature distribution revealed a high goodness of fit of the model with the actual situation.