Stable–unstable flow of geothermal fluids in fractured rock

Abstract

AbstractDensity‐driven geothermal flow in 3‐D fractured rock is investigated and compared with density‐driven haline flow. For typical matrix and fracture hydraulic conductivities, haline flow tends to be unstable (convecting) while geothermal flow is stable (non‐convecting). Thermal diffusivity is generally three orders of magnitude larger than haline diffusivity and, as a result, large heat conduction diminishes growth of geothermal instabilities while low mass diffusion enables formation of unstable haline ‘fingering’ within fractures. A series of thermal flow simulations is presented to identify stable and unstable conditions for a wide range of hydraulic conductivities for matrix and fractures. The classic Rayleigh stability criterion can be applied to classify these simulations when fracture aperture is very small. However, the Rayleigh criterion is not applicable when the porous matrix hydraulic conductivity is very small, because stabilizing fracture–matrix heat conduction is independent of matrix hydraulic conductivity. In that case, the numerically estimated critical fracture conductivity is nine orders of magnitude larger than the theoretically calculated critical fracture conductivity based on Rayleigh theory. The numerical stability analysis presented here may be used as a guideline to predict if a geothermal system in 3‐D fractured rock is stable or unstable.