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A continuum-scale representation of Ostwald ripening in heterogeneous porous media

Published online by Cambridge University Press:  21 February 2020

Yaxin Li Open the ORCID record for Yaxin Li [Opens in a new window] ,
Charlotte Garing  and
Sally M. Benson
Yaxin Li*
Affiliation:
Department of Energy Resources Engineering, Stanford University, Stanford, CA 94305, USA
Charlotte Garing
Affiliation:
Department of Geology, University of Georgia, Athens, GA 30602, USA
Sally M. Benson
Affiliation:
Department of Energy Resources Engineering, Stanford University, Stanford, CA 94305, USA
*
†Email address for correspondence: yaxinl@stanford.edu
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Abstract

Ostwald ripening is a pore-scale phenomenon that coarsens a dispersed phase until thermodynamic equilibrium. Based on our previous finding that multi-bubble equilibrium is possible and likely in complex porous media, we develop a new continuum-scale model for Ostwald ripening in heterogeneous porous media. In this model, porous media with two different capillary pressure curves are put into contact, allowing only diffusive flow through the aqueous phase to redistribute a trapped gas phase. Results show that Ostwald ripening can increase the gas saturation in one medium while decreasing the gas saturation in the other, even when the gas phase is trapped in pore spaces by capillary forces. We develop an analogous retardation factor to show that the characteristic time for Ostwald ripening is about $10^{5}$ times slower than a single-phase diffusion problem due to the fact that separate-phase gas requires a much larger amount of mass transfer before equilibrium is established. An approximate solution has been developed to predict the saturation redistribution between the two media. The model has been validated by numerical simulation over a wide range of physical parameters. Millimetre to centimetre-scale systems come to equilibrium in years, ranging up to 10 000 years and longer for metre-scale systems. These findings are particularly relevant for geological $\text{CO}_{2}$ storage, where residual trapping is an important mechanism for immobilizing $\text{CO}_{2}$. Our work demonstrates that Ostwald ripening due to heterogeneity in porous media is slow and on a similar time scale compared to other processes that redistribute trapped $\text{CO}_{2}$ such as convective mixing.

JFM classification

Drops and Bubbles: Bubble dynamics Multiphase and Particle-laden Flows: Multiphase flow Low-Reynolds-number flows: Porous media
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 889 , 25 April 2020 , A14
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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