Kinetic Theory of Multicomponent Ostwald Ripening in Porous Media

Abstract: Partially miscible bubble populations trapped in porous media are ubiquitous in subsurface applications such as underground hydrogen storage (UHS), where cyclic injections fragment gas into numerous bubbles with distributions of sizes and compositions. These bubbles exchange mass through Ostwald ripening, driven by differences in composition and interfacial curvature. While kinetic theories have been developed for single-component ripening in porous media, accounting for bubble deformation and spatial correlations in pore size, no such theory exists for multicomponent systems. We present the first kinetic theory for multicomponent Ostwald ripening of bubbles in porous media. The formulation describes the bubble population with a number-density function $g(s; t)$ in a 3D statistical space of bubble states $s = (R_p, S^b, y)$, consisting of pore size, bubble saturation, and composition. Evolution is governed by a population balance equation with closure through mean-field approximations that account for spatial correlations in pore size and ensure mass conservation. The theory generalizes previous single-component formulations, removing key limitations such as the inability to capture interactions between distant bubbles. Systematic validation against pore-network simulations across homogeneous, heterogeneous, correlated, and uncorrelated networks demonstrates good agreement without adjustable parameters. Pending challenges and limitations are discussed. Since the theory imposes no constraints on bubble count or correlation length, it enables predictions beyond the pore scale.