A continuum theory of diffusive bubble depletion in porous media

We present a continuum theory for predicting the depletion of partially miscible bubbles (or droplets) in a non-wetting porous material by a concentration sink. Bubble dissolution is controlled by interfacial curvature, leading to mass exchange between bubbles via Ostwald ripening and their eventual diffusion into the sink. The result is the emergence of a depletion zone that grows diffusively away from the sink. Namely, l∼t1/2 holds, where l is the zone's width and t is time. Closure is achieved by linking the theory to pore-scale data readily measurable from lab experiments (e.g., pore-size distribution, X-ray μCT images). Such data can be transformed into a plot of macroscale capillary pressure versus bubble saturation that is then subjected to a simple graphical construction technique yielding the necessary inputs for the theory. Remarkably accurate predictions, compared against pore-network simulations, are possible without resorting to parameter fitting. The theory and its associated analytical solutions are extended from linear to curvilinear coordinates, where implications on potential leakage risks in underground H2/CO2 storage are discussed. The theory also applies to the drying of super-hydrophobic porous materials occurring in fuel cells and electrolyzers.

© This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/

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Work Title A continuum theory of diffusive bubble depletion in porous media
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Open Access
Creators
  1. Yashar Mehmani
  2. Ke Xu
Keyword
  1. Porous media
  2. Bubbles
  3. Ostwald ripening
  4. Pore scale
  5. Darcy theory
  6. CO2 sequestration
License CC BY-NC-ND 4.0 (Attribution-NonCommercial-NoDerivatives)
Work Type Article
Publisher
  1. Advances in Water Resources
Publication Date January 28, 2024
Publisher Identifier (DOI)
  1. https://doi.org/10.1016/j.advwatres.2024.104625
Deposited April 25, 2024

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Version 1
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  • Created
  • Added Mehmani___Xu__2024__-_bubble_depletion__pre-print_.pdf
  • Added Creator Yashar Mehmani
  • Added Creator Ke Xu
  • Published
  • Updated
  • Updated Keyword, Publication Date Show Changes
    Keyword
    • Porous media, Bubbles, Ostwald ripening, Pore scale, Darcy theory, CO2 sequestration
    Publication Date
    • 2024-03-01
    • 2024-01-28