Reliable determination of convective heat transfer coefficients as fluid flows through rock fractures

Abstract

During heat-mining of earth's stored thermal energy, low-temperature fluids are injected into hot dry rock, forcing convective heat transfer between the fluid and the rock fracture. The convective heat transfer coefficient (HTC) is a crucial parameter characterizing the intensity of convective heat transfer, which affects heat influx into the fluid. Generally, HTC is obtained experimentally or determined by analytical methods dependent on measured outlet fluid temperatures, both of which are difficult to apply in practical geothermal engineering. Based on the boundary layer theory, an innovative analytical method for determining the HTC is proposed. It assumes that heat exchange near the fracture surface occurs mainly via heat conduction in the viscous sublayer. The HTC is independent of rock block properties, but depends on fracture aperture, fluid velocity, fluid thermal conductivity, fluid kinematic viscosity, and surface roughness. This method allows the HTC to be obtained dynamically, thus improving the precision of the calculated convective heat transfer process, and it can also be easily utilized in prospective geothermal simulations. The reliability of this method was well verified by comparing its numerical results with 78 experimental results. The proposed method also performed well when applied in numerical simulations of heat transfer within rock masses containing intersecting fractures. The simulations indicated that the HTC is influenced by both fracture aperture and fluid velocity, resulting in the changes in temperature distributions after intersections of fractures. Therefore, the HTC should be determined dynamically in heat transfer simulations using the local thermal non-equilibrium model, otherwise, large errors in the temperature distributions of fractured rock masses may occur.