A continuum theory of diffusive bubble depletion in porous media

We present a continuum theory for predicting the depletion of partially miscible bubbles (or droplets) in a non-wetting porous material by a concentration sink. Bubble dissolution is controlled by interfacial curvature, leading to mass exchange between bubbles via Ostwald ripening and their eventual diffusion into the sink. The result is the emergence of a depletion zone that grows diffusively away from the sink. Namely, l∼t^1/2 holds, where l is the zone's width and t is time. Closure is achieved by linking the theory to pore-scale data readily measurable from lab experiments (e.g., pore-size distribution, X-ray μCT images). Such data can be transformed into a plot of macroscale capillary pressure versus bubble saturation that is then subjected to a simple graphical construction technique yielding the necessary inputs for the theory. Remarkably accurate predictions, compared against pore-network simulations, are possible without resorting to parameter fitting. The theory and its associated analytical solutions are extended from linear to curvilinear coordinates, where implications on potential leakage risks in underground H₂/CO₂ storage are discussed. The theory also applies to the drying of super-hydrophobic porous materials occurring in fuel cells and electrolyzers.