Numerical study of heat transfer across rough fracture surfaces

Maximizing heat exploitation in geothermal systems is crucial for the economic efficiency of many geothermal systems. As the hydraulic flow in most geothermal systems is primarily due to fracture flow, heat transfer processes along the fracture surfaces are essential. However, while flow and mass transport in a single fracture have been studied experimentally and theoretically to a great extent, heat transfer processes have been rarely investigated. Laboratory experiments show the influence of the fracture surface morphology on flow and heat transfer processes, though a physical interpretation has been missing so far. Further, in many geothermal systems but also in many natural hydrothermal systems, the solid and fluid phases are not in local thermal equilibrium. Parameterization of local thermal non-equilibrium models was originally developed for porous media and adoptions to fractures have been cumbersome. In this work, I present a numerical study on heat transfer processes across rough fracture surfaces. Using a three-dimensional steady-state flow model, heat transfer across the fracture surface is studied for both scenarios: assuming and neglecting a thermal equilibrium across phase boundaries. Also, separate fracture morphologies have been studied using natural sandstone probes as well as synthetically generated fractures. The numerical simulations results are compared to laboratory experiments using artificially generated and 3D-printed fracture surfaces of various fracture morphologies for code validation. The full three-dimensional simulations reveal the role of flow channeling effects on the heat transfer taking place along rough surfaces, which is not captured by simulations with reduced spatial dimensions. The simulations results suggest a re-examination of the effective heat transfer coefficient for fractured reservoirs under local thermal non-equilibrium conditions incorporating characteristics of fracture morphology. The simulations results can also be linked to thermal stress generation and possibly explaining the deformations of fracture surfaces observed in the laboratory. However, parameterization of surface roughness is neither distinct nor trivial. Various parameters exist, such as the joint roughness coefficient, Hurst exponent or statistical descriptions, but none has been successfully linked to flow, transport or transfer characteristics. Relating fracture morphology with results of numerical simulations and laboratory findings regarding transfer and transport processes indicate a shortfall of conventional roughness parameterizations to sufficiently describe the observed variation in heat transfer parameters.