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

Martin J. Blunt
Phys. Rev. E 106, 045103 – Published 10 October 2022

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: Pc(Sw)=Δρgz where Pc is the capillary pressure (pressure difference between the gas and aqueous phases), Sw is the aqueous phase (brine) saturation, Δρ=ρwρg 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 Pc=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: Pc=P*[e(Vgρwmg)gz/RT1]+ρwgz, where P* is the aqueous phase pressure at z=0, Vg is the specific molar volume of the gas dissolved in the aqueous phase, mg 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.

  • Figure
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  • Received 8 August 2022
  • Accepted 22 September 2022

DOI:https://doi.org/10.1103/PhysRevE.106.045103

©2022 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsFluid Dynamics

Authors & Affiliations

Martin J. Blunt*

  • Department of Earth Science and Engineering, Imperial College London, London SW7 2BP, United Kingdom

  • *Corresponding author: m.blunt@imperial.ac.uk

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Issue

Vol. 106, Iss. 4 — October 2022

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