Ostwald ripening of trapped gas bubbles in porous media : A pore-scale perspective

Abstract

Ostwald ripening of gas bubbles is a thermodynamic process for mass transfer, which is significant for both foam-enhanced oil recovery and underground gas storage. During recovery, it can impact the macroscopic efficiency. Meanwhile, during temporary or permanent subsurface gas storage, it can impact the life and volume of capillary trapped gas. Previous work in this research area typically deals with simplified pore geometry and single pore bubbles in a two-phase gas-liquid environment. This work presents a methodology for simulating the Ostwald ripening of gas ganglia surrounded by one or two liquids in arbitrary pore geometries. The method couples a local volume conserving level-set model for capillary-controlled displacement and a chemical-potential difference based mass transfer model. The methodology is implemented in a software framework that enables parallel computations. The computational performance of the previously published level set model is improved while incorporating adaptive mesh refinement capabilities into it. Three-phase capillary and thermodynamic equilibrium states predicted by the model are validated against analytical solutions. The model is used to investigate factors affecting ripening in two-phase (gas-oil or gas-brine) and three-phase (gas-oil-brine) environments. The results confirm that gas solubility and gas compressibility factors are proportional to the rate of mass transfer. If the liquid separating the gas bubbles is also a disconnected phase, which can happen in intermediate-wet porous media, the resulting local capillary pressure can limit the coarsening and stabilize smaller bubbles. The results show that gas bubble coarsening occurs at different rates depending on the spatial scale of chemical-potential difference in the bubble distribution. So, a gas volume stored with spatial disparity at large scales will have a slower ripening rate. The results underscore that improved interface resolution from mesh refinement can reveal additional evolution details. For bubbles having interfaces in pore throats, the throat that provides a larger change in capillary pressure per unit volume change provides a faster ripening rate. Ripening in three-phase scenarios in porous media stabilizes gas bubbles to sizes that depend on their surrounding liquids. Bubbles in oil decrease in size, while bubbles in water increase in size with increasing oil/water capillary pressure. A potential implication for field-scale gas storage is that the trapped gas fractions in oil and water vary with depth in the oil/water transition zone. Depending on reservoir conditions and gas type, bubbles surrounded by one of the liquids typically reach local equilibrium before the three-phase system stabilizes globally. In addition, reservoir pressure and wettability impact the final number, size, and location of post-ripening residual bubbles. CO2 bubbles trapped in near-miscible conditions take longer time to reach equilibrium than those trapped in immiscible conditions. Bubbles trapped in wetting conditions that promote very small gas-liquid interface curvatures take a longer ripening time. In cases where gas is the intermediate wetting phase, gas bubbles tend to equilibrate near the inflection points in the pore geometry where the center of gas-liquid curvature shifts from the liquid phase to the gas phase. If the liquid phase is also isolated, then the equilibrium size of trapped bubbles also depends on which liquid phase is trapped. The work demonstrates that ripening does not necessarily proceed only by dissolution and growth but can also proceed through the merging and splitting of bubbles to reach equilibrium, and volumetrically similar distributions can have different rates and ripening paths depending on the initial fluid phase location. The results underscore the importance of using reservoir conditions and realistic pore geometries in analyzing Ostwald ripening at the pore scale in porous media.