A level set approach to Ostwald ripening of trapped gas bubbles in porous media

Abstract

Ostwald ripening of gas bubbles is a thermodynamic process for mass transfer, which is important for both foam enhanced oil recovery and geological CO2 storage. We present a methodology for simulating Ostwald ripening of gas ganglia surrounded by liquid in arbitrary pore geometries. The method couples a conservative level set model for capillary-controlled displacement and a ghost-bubble technique that calculates mass transfer based on difference in chemical potentials. The methodology is implemented in a software framework for parallel computations. As a validation of the model, we show that simulations of bubble ripening in a pore throat connecting two pore bodies are consistent with previously reported trends in similar geometries. Then we investigate the impact of gas type, compressibility factor, and local capillary pressure on gas-bubble ripening in various water-wet pore geometries. The results confirm that gas solubility and compressibility factor are proportional to the rate of mass transfer. Our simulations suggest that Ostwald ripening has largest impact in heterogeneous or fractured porous structures where differences in gas-bubble potentials are high. However, 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 stabilise smaller bubbles. Finally, we simulated Ostwald ripening on a 3-D pore-space image of sandstone containing a residual gas/water configuration after imbibition. Characterization of gas-bubble morphology during the coarsening shows that large ganglia get more ramified at the expense of small spherical ganglia that cease to exist.

Effective Approach for Fabricating Highly Precise High-Curvature Structural Patterns via Air-Bubble Induction

“…When the volume of each air pocket expanded and the air pockets came into contact with each other, the air pocket grown in the ring diffused into that (relatively large in volume) grown in the hole; this process is attributed to the Ostwald ripening effect. 34 Consequently, the volume of the air pocket grown in the hole increased and the PDMS filled the groove of the ring pattern from which the air escaped. When curing occurred in this state, the PDMS mold exhibited a structure that included both a hollow spherical concave pattern and a ring-shaped 2D convex pattern (Figure 4a).…”

“…First, if the IAL process is applied using a Si master containing a hole-centered ring-shaped pattern, the volume of air pockets trapped between the hole and ring groove expands and grows into a spherical shape. When the volume of each air pocket expanded and the air pockets came into contact with each other, the air pocket grown in the ring diffused into that (relatively large in volume) grown in the hole; this process is attributed to the Ostwald ripening effect . Consequently, the volume of the air pocket grown in the hole increased and the PDMS filled the groove of the ring pattern from which the air escaped.…”

Ripening of Capillary-Trapped CO2 Ganglia Surrounded by Oil and Water at the Pore Scale: Impact of Reservoir Pressure and Wettability

“…9−11 Research studies assessing the impact of Ostwald ripening on subsurface stored gas in two-phase systems suggest a slow process that can lead to significant mass distribution within the porous medium at both pore scale and field scale. 9−11,35−38 However, the pace of ripening depends strongly on the gas type and the gas solubility in the liquid, 11,38,39 and the most significant bubble alterations typically occur early and long before thermodynamic equilibrium is reached (that is, before all bubbles have attained the same pressure). 11,33,39 Numerical models for Ostwald ripening of gas bubbles on the pore scale in porous media must describe both the diffusive mass transfers and the resulting displacement of the fluid/fluid interfaces.…”

“…9 Calculation of gas bubble pressures based on updating the interface positions can be incorporated either through a precalculated pressure−volume relation on idealized pore geometries, as is the case for pore-network models, 9,33,34 or by using a direct simulation model for capillarycontrolled displacement that can handle arbitrary bubble arrangements on imaged pore geometries. 11 In the latter case, interface tracking methods, like phase field methods 40,41 or levelset methods, 42 can be used to determine bubble pressures at different instances. The key to a successful implementation will be computational efficiency in determining capillary equilibrium.…”

Pore‐Scale Observations of Hydrogen Trapping and Migration in Porous Rock: Demonstrating the Effect of Ostwald Ripening

“…In a bulk fluid, the equilibrium state is the aggregation of all the gas in a single bubble; in porous media, multiple equilibrium states are possible with a distribution of ganglia of equal capillary pressure. This process has been explored in the context of carbon dioxide storage, experimentally, numerically and theoretically, and has also been observed for trapped air and natural gas (de Chalendar et al, 2018;Gao et al, 2022;Garing et al, 2017;Singh et al, 2022;Xu et al, 2017). However, hitherto no direct studies of Ostwald ripening (Ostwald, 1897) have been made for hydrogen, despite the likely rearrangement of gas over day-long time scales at the mm-scale thanks to hydrogen's high diffusion coefficient in water (Blunt, 2022).…”