Dripping into subterranean cavities from unsaturated fractures under evaporative conditions

Abstract

Water dripping into subterranean cavities within fractured porous media is studied in order to improve estimates of dripping rates, drop sizes, and chemical composition of droplets that could affect long‐term integrity of waste disposal canisters placed in caverns. Steady state liquid flux in fracture surfaces supported by flow in partially liquid‐filled grooves and liquid films in adjacent planes was calculated as a function of the matric potential (vapor pressure) of the fracture. At an intersection of a vertical fracture with a wider cavity the liquid flux feeds a growing pendant drop that eventually detaches. Equilibrium state size and approximate shape of liquid drops suspended from the cavity ceiling were determined from lateral and vertical force balance considering capillarity, gravity, and hydrostatic pressure. A one‐dimensional, viscous extension model with appropriate gravitational and surface tension components was employed to determine dripping rate from specified fracture roughness geometry as a function of matric potential (flux). The effect of evaporation from drop surface during drop formation was incorporated; the resulting alterations in drop volume, dripping rate, and drop solute concentration were determined. To facilitate experimental testing of the proposed model, a decoupled solution that considers independently controlled flux and evaporation is presented. Under evaporative conditions, dripping in finite period is possible only when volumetric flux exceeds evaporative demand. Calculations indicate that dripping rate and solute concentration are extremely sensitive to ambient matric potential. The results of this work may be extended to study other phenomena including formation and growth of stalactites and rivulet flow in cave ceilings.