A COUPLING ANALYSIS FOR HEAT TRANSFER AND WATER FLOW IN A FRACTAL ROUGH FRACTURE OF GEOTHERMAL RESERVOIRS

Abstract

The coupling of heat transfer and water flow in rock fractures is a key issue to geothermal energy extraction. However, this coupling in a rough fracture has not been well studied so far. This paper will study this coupling in a rock fracture with different roughness. First, multi-scale and self-affine rough fracture are constructed through the Weierstrass–Mandelbrot function and embedded into a rock block. Its single scale trend line is also derived. Second, a roughness factor is proposed based on the standard deviation of each segment from the trend line and introduced into the governing equation of fracture flow. After coupling with heat transfer and matrix deformation, a thermal-hydro-mechanical (THM) coupling model is formulated for a rough fracture flow. Third, an analytical solution is derived through the Laplace transform and Stehfest method and used for the validation of this THM coupling model. Finally, the effects of fracture roughness and matrix deformation on heat transfer and fracture flow are numerically investigated. The simulation results indicate that the rock fracture with lower fractal dimension has higher heat transfer efficiency. The effect of fracture roughness on heat transfer is much greater than that of aperture variation induced by the shrinkage of rock matrix.