Multiscale Fracture Roughness Effects on Coupled Nonlinear Seepage and Heat Transfer in an EGS Fracture

The seepage characteristics and heat transfer efficiency in rough fractures are indispensable for assessing the lifetime and production performance of geothermal reservoirs. In this study, a two-dimensional rough rock fracture model with different secondary roughness is developed using the wavelet analysis method to simulate the coupled flow and heat transfer process under multiscale roughness based on two theories: local thermal equilibrium (LTE) and local thermal nonequilibrium (LTNE). The simulation results show that the primary roughness controls the flow behavior in the main flow zone in the fracture, which determines the overall temperature distribution and large-scale heat transfer trend. Meanwhile, the nonlinear flow behaviors induced by the secondary roughness significantly influence heat transfer performance: the secondary roughness usually leads to the formation of more small-scale eddies near the fracture walls, increasing flow instability, and these changes profoundly affect the local water temperature distribution and heat transfer coefficient in the fracture–matrix system. The eddy aperture and eddy area fraction are proposed for analyzing the effect of nonlinear flow behavior on heat transfer. The eddy area fraction significantly and positively correlates with the overall heat transfer coefficient. Meanwhile, the overall heat transfer coefficient increases by about 3% to 10% for eddy area fractions of 0.3% to 3%. As the eddy aperture increases, fluid mixing is enhanced, leading to a rise in the magnitude of the local heat transfer coefficient. Finally, the roughness characterization was decomposed into primary roughness root mean square and secondary roughness standard deviation, and for the first time, an empirical correlation was established between multiscale roughness, flow velocity, and the overall heat transfer coefficient.