Pore-network modeling of Ostwald ripening in porous media: How do trapped bubbles equilibrate?

Ostwald ripening of trapped bubbles in porous media is relevant to several subsurface (e.g., CO₂ storage) and manufacturing (e.g., fuel cells) applications. A fundamental question common to both is: how does an initially heterogeneous distribution of bubble sizes, PDF_o, evolves towards a stable equilibrium distribution, PDF_e? And what is PDF_e? We develop a pore-network model (PNM) that simulates the temporal evolution of a partially miscible population of bubbles from PDF_o to PDF_e. The PNM is validated against published micromodel experiments. We subsequently propose a theory that can predict PDF_e directly. The predictions are compared against PNM simulations and found to be in close agreement. Using the PNM, we also show that bubble equilibration in heterogeneous porous media is a lot slower than homogeneous media. Limitations and potential extensions of both the PNM and the theory are discussed.