Abstract
The equilibrium configuration of a gas and brine in a porous medium, and the timescales to reach equilibrium, are investigated analytically. If the gas is continuous in the pore space, we have the traditional gravity-capillary transition zone: where is the capillary pressure (pressure difference between the gas and aqueous phases), is the aqueous phase (brine) saturation, is the density difference between the phases, is the gravitational acceleration, and is a vertical distance coordinate increasing upwards, where indicates the level where . However, if the gas is disconnected, as may occur during water influx in carbon dioxide and hydrogen storage, then the nature of equilibrium is different where diffusion through the aqueous phase (Ostwald ripening) maintains a capillary pressure gradient consistent with the thermodynamically-determined brine density as a function of depth: , where is the aqueous phase pressure at is the specific molar volume of the gas dissolved in the aqueous phase, is the molecular mass of the gas, is the universal gas constant, and is the absolute temperature. The capillary pressure decreases with depth. This means that a deep column of trapped gas cannot be sustained indefinitely. Instead a transition zone forms in equilibrium with connected gas near the top of the formation: its thickness is typically less than 1 m for carbon dioxide, hydrogen, methane or nitrogen in a permeable reservoir. The timescales to reach equilibrium are, however, estimated to be millions of years, and hence do not significantly affect long-term storage over millennia. At the scale of laboratory experiments, in contrast, Ostwald ripening leads to local capillary equilibrium in a few weeks to a year, dependent on the gas considered.
- Received 8 August 2022
- Accepted 22 September 2022
DOI:https://doi.org/10.1103/PhysRevE.106.045103
©2022 American Physical Society