LAUSR

In this study, a fully coupled analytical model is developed for thermal energy transfer in a single fracture-rock matrix system where the coupling implies that the governing equations of thermal transfer in the fracture and rock matrix are supplemented with the continuity conditions of temperature and thermal flux at the interfaces of the fracture-rock matrix. The proposed model accounts for thermal convection, longitudinal thermal conduction and thermal dispersion in the fracture, and transverse thermal conduction in the rock matrix. The fully coupled two-dimensional model is established to investigate the thermal energy transfer processes, assess the spatiotemporal temperature distribution in the fracture and rock matrix system and investigate the role of the rock matrix. The solutions are verified with the existing studies and proven to be accurate and robust. The present study demonstrates that: 1) thermal dispersion in the fracture plays an important role in the temperature distribution in the fracture and rock matrix domains, and longitudinal thermal conduction in the fracture has minor effects on the temperature distribution in the system; 2) transverse thermal conduction in the rock matrix is a critical parameter that determines the spatiotemporal temperature distribution in both the fracture and the rock matrix domains. Ignoring thermal conduction in the rock matrix will lead to a significant overestimation of temperature in the short and long terms; 3) the sensitivity analysis implies that thermal energy transfer in the system is sensitive to the fluid velocity in the fracture, thermal dispersivity in the fracture and thermal conductivity in the rock matrix, and less sensitive to thermal conductivity in the fracture.