Time-dependent pore-network modeling of Ostwald ripening in porous media

We present a time-dependent pore-network model that couples transient mass transfer in the aqueous phase, capillary pressure heterogeneity, and realistic pore-throat geometries to capture the dynamic evolution of gas clusters during Ostwald ripening in porous media. The model is applied to Bentheimer sandstone to study Ostwald ripening after imbibition to residual gas saturation. Both imbibition (shrinkage) and drainage (growth) events occur as the local capillary pressure in trapped gas clusters approaches equilibrium. The model tracks event statistics, capillary pressure equilibration, cluster volume distributions, and spatial saturation profiles over 48 h. While the volume-weighted average capillary pressure is constant, there is a rapid initial decline in average number-weighted cluster pressure and a shift in cluster size distributions toward fewer, larger ganglia, consistent with pore-scale imaging studies. Pore and throat occupancy analysis reveal persistent gas trapping in larger pore spaces. Since growth is by drainage, the pore-scale configuration of fluid is different from that predicted by an equilibrium percolation-without-trapping model that only allows imbibition events. The model reproduces the displacement and ganglion rearrangement observed during laboratory experiments. Presented as a preliminary framework study assuming constant fluid properties and a nonreactive system, the model could be extended to incorporate detailed thermophysical equations of state to provide a foundational framework for analyzing time-dependent ripening in porous media, establishing the physics necessary to inform future upscaled constitutive relationships for hydrogen, natural gas and carbon dioxide storage in the subsurface.