Evaluation of analytical models for heat transfer in mine tunnels

The heat contained in underground flooded mine workings is actively exploited, often via heat pump technology, at a number of locations in Europe and North America. Several different heat exchange configurations may be utilised in this context, but for those (“standing column” and “open loop” arrangements) were mine water reinjection is practised, the rate of heat transfer between mine walls and mine water is a critical process to quantify. The two most commonly-used analytical solutions to this problem have been applied to the same baseline scenario, exploring and comparing their sensitivity, strengths, weaknesses and areas of application. It is found that the Rodríguez- Díaz solution generally predicts heat transfer rates (typically of the order of several tens of W per m of tunnel) greater than the Lauwerier-Pruess-Bodvarsson approach, the difference being due to the fact that the former assumes a radial heat conductive flow geometry in the rock surrounding the mine void, while the latter assumes a less efficient parallel linear flow. The Rodríguez-Díaz solution is more appropriate for approximately cylindrical mine shafts and tunnels. The Lauwerier-Pruess-Bodvarsson approach is more likely to be applicable to tabular mined void geometries. Improvements to the Rodríguez and Díaz model are proposed to enhance its transparency and applicability.