Ostwald ripening and gravitational equilibrium: Implications for long-term subsurface gas storage

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: P_{c}(S_{w})=Δρgz where P_{c} is the capillary pressure (pressure difference between the gas and aqueous phases), S_{w} is the aqueous phase (brine) saturation, Δρ=ρ_{w}-ρ_{g} is the density difference between the phases, g is the gravitational acceleration, and z is a vertical distance coordinate increasing upwards, where z=0 indicates the level where P_{c}=0. 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: P_{c}=P^{*}[e^{(V_{g}ρ_{w}-m_{g})gz/RT}-1]+ρ_{w}gz, where P^{*} is the aqueous phase pressure at z=0, V_{g} is the specific molar volume of the gas dissolved in the aqueous phase, m_{g} is the molecular mass of the gas, R is the universal gas constant, and T 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.