Capillary equilibrium of bubbles in porous media

Abstract

In geologic, biologic, and engineering porous media, bubbles (or droplets, ganglia) emerge in the aftermath of flow, phase change, or chemical reactions, where capillary equilibrium of bubbles significantly impacts the hydraulic, transport, and reactive processes. There has previously been great progress in general understanding of capillarity in porous media, but specific investigation into bubbles is lacking. Here, we propose a conceptual model of a bubble’s capillary equilibrium associated with free energy inside a porous medium. We quantify the multistability and hysteretic behaviors of a bubble induced by multiple state variables and study the impacts of pore geometry and wettability. Surprisingly, our model provides a compact explanation of counterintuitive observations that bubble populations within porous media can be thermodynamically stable despite their large specific area by analyzing the relationship between free energy and bubble volume. This work provides a perspective for understanding dispersed fluids in porous media that is relevant to CO2 sequestration, petroleum recovery, and fuel cells, among other applications.

The Effect of Pore-Scale Two-Phase Flow on Mineral Reaction Rates

“…A variety of complex hydrodynamics can arise from the migration of fluid-fluid interfaces depending on the velocity (e.g., capillary numbers) and pore morphology (e.g., Berg et al, 2013;Spurin et al, 2019;Li et al, 2021;Wang et al, 2021).…”

Pore-network modeling of Ostwald ripening in porous media: How do trapped bubbles equilibrate?

“…And (2) can we develop a theory that predicts PDFe directly? Ostwald ripening in porous media is fundamentally different from that in bulk fluids 13,[17][18][19][20] , for which most classical theories [21][22][23] have been developed. In a bulk fluid, bubbles are spherical and so Pc is inversely proportional to bubble volume, Vb.…”

“…Each mechanism leads to an initial distribution (PDFo) of bubble sizes, ranging from those that occupy a single pore to those that span multiple pores [9][10][11][12] . The capillary pressure, or Pc, across each bubble's interface depends, aside from its volume, on the bubble's shape and morphology as dictated by the confining solid [13][14][15] . Now, if bubbles are partially miscible within the surrounding wetting phase, a thermodynamic competition is set in motion.…”

“…Ripening, therefore, transports mass from small to large bubbles. In a porous medium, the relationship between Pc and Vb is non-monotonic 17 and, when bubbles span more than one pore, discontinuous 13 . It is shown both experimentally 17,24 and computationally 18,20 that under such conditions an initially heterogeneous distribution of bubbles has a stable equilibrium distribution.…”

“…At any rate, the existence of an equilibrium distribution of bubble sizes in porous materials is in stark contrast to what happens in bulk fluids, where all bubbles merge into one. This is because any initial distribution of bubble sizes is unstable in a bulk fluid 13,28 . Applications, other than CO2 storage, where the equilibrium state and equilibration rate of bubbles are important include oxygen supply to groundwater [29][30][31] , water management in PEM fuel cells 32,33 , and hydrocarbon recovery by solution gas drive 34,35 .…”