Ostwald ripening of multi-component bubbles in porous media: A theory and a pore-scale model of how bubble populations equilibrate

Bubbles trapped inside porous materials occur in many applications ranging from geologic CO2 sequestration, underground hydrogen storage (UHS), groundwater remediation, to fuel cells and electrolyzers. If partially miscible in their surrounding wetting phase, bubbles can evolve through a process called Ostwald ripening, in which those with a high interfacial curvature dissolve fastest and feed into bubbles with a low curvature. For single-component bubbles, the physics are relatively well-understood. This work focuses on the ripening of bubbles comprised of multiple components, which remains unexplored. We first present a pore-network model (PNM) to simulate the temporal evolution of a population of partially miscible, multi-component bubbles inside a heterogeneous porous microstructure. We then use the model to identify the different ripening regimes between two adjacent bubbles, some rather counterintuitive. We also show that, under conditions prevalent in the subsurface, multi-component ripening proceeds in two stages separated in timescale: partitioning and coevolution. Based on this insight, we propose a theory to predict the probability density function (PDF) of bubble sizes at the ends of partitioning and coevolution (i.e., equilibrium) from their initial state and the pore-size distribution. The theory is systematically compared against the PNM and very good agreement is found. Limitations of both the PNM and theory are discussed and implications for UHS are outlined.