The instability of a vaporization front in hot porous rock

Abstract

IN many geothermal systems, water migrates into vapour-dominated porous rock either through natural recharge or through forced injection of water from a well^1–5. If the host rock is initially very hot, then a fraction of this injected water vaporizes^6,7; as the water injection rate increases, the fraction which vaporizes decreases⁷. For modelling purposes, it is generally assumed that liquid–vapour interfaces in hot porous rocks are planar and stable^6,7. But we show here, both theoretically and experimentally, that if a sufficient fraction of the liquid vaporizes, the interface can become unstable. The resulting 'fingering' instability can itself be stabilized: at short wavelengths by thermal diffusion, and at long wavelengths by the pressure increase caused by the excess vaporization at the tips of the fingers. These liquid fingers migrate through the porous rock much more rapidly than does a planar liquid front, and could therefore limit the time during which vapour may be extracted for geothermal power applications. We suggest that an optimal water injection rate for geothermal energy production may be that for which the interface is just stable, thereby maximizing the fraction of liquid which vaporizes, while suppressing the fingering instability.