Capillary equilibration of trapped ganglia in porous media: A pore-network modeling approach

Ganglia, or bubbles, trapped by capillary forces inside porous materials occur in a wide range of subsurface and manufacturing applications. In geologic CO₂ storage, ganglia are desired as they render the injected CO₂ hydrodynamically immobile. But they may evolve by dissolution or mass exchange across the brine, called ripening. In fuel cells and electrolyzers, water/oxygen ganglia must be removed to ensure optimal performance of the device. In both applications, the porous microstructure plays a key role in how the geometry/topology of ganglia evolve as they grow/shrink in size. This dependence is poorly understood but important for controlling ganglion dynamics. Pore-scale models are useful tools for probing the physics, but existing ones are either computationally expensive (e.g., CFD) or incapable of accurately simulating ganglia spanning multiple pores (e.g., pore networks). Our main contribution is a new pore-network model (PNM) that removes this barrier. The PNM can simulate the evolution of multi-pore occupying ganglia due to diffusive mass transfer by ripening or an external concentration field. We validate the PNM against published microfluidic experiments, 2D direct numerical simulations, and an analytical solution previously derived by the authors for a 2D homogeneous domain. We then use the PNM to study quasi-static growth-shrinkage cycles of trapped ganglia inside heterogeneous porous media. The findings constitute our second contribution, generalizing previous theoretical results by the authors from 2D homogeneous to 3D-planar heterogeneous microstructures. They include: (1) the interfacial area of a ganglion depends approximately linearly on its volume; (2) if the throat-to-pore aspect ratio is large, growth is percolation-like; but (3) if it is small, a hitherto unreported intermittent growth regime precedes percolation, in which ganglia repeatedly fragment and reconnect. These outcomes have implications for selecting optimal storage sites for CO₂ and designing fuel cells and electrolyzers with finetuned porous microstructures.