Quantifying flow regime impacts on hydrodynamic heat transfer in rough-walled rock fractures

Hydrodynamic heat transfer in rock fractures is crucial for many geophysical processes and engineering activities, notably in harnessing geothermal energy. Despite extensive research, characterizing hydrodynamic heat transfer in rock fractures, complicated by their geometric heterogeneity, remains a formidable challenge. To address this challenge, we experimentally investigated the hydrodynamic heat transfer in rock fractures with diverse geometric features at steady-state elevated temperatures. We found that both heterogeneous fracture geometry and elevated temperatures promote the transition of fracture flow from a linear to nonlinear regime. This flow regime transition enhances the heterogeneity of heat transfer intensity within the fracture and exacerbates the increase in heat transfer efficiency with flow rate. At a fortyfold increase in flow rate, the heat transfer coefficient in the most heterogeneous fracture rises by approximately 72 times, compared to about 28 times in the least heterogeneous one. Leveraging experimental data, we developed parametric models linking heat transfer coefficients, outflow temperature, and heat recovery rate to flow rate and geometric features, yielding a theoretical formulation for the maximal heat recovery rate. By introducing the concept of an energy conversion rate, we quantitatively evaluated the effect of nonlinear flow resistance on heat extraction feasibility, revealing that energy conversion rates in highly heterogeneous fractures can be up to 452 times lower than in less heterogeneous ones. This highlights the pivotal role of flow resistance in heat extraction feasibility. Our findings are instrumental for understanding and predicting the hydrodynamic heat transfer within fractured geothermal reservoirs and analogous hydro-thermal systems.