Partially miscible bubbles (e.g., CO2) trapped inside a porous medium and surrounded by a wetting phase (e.g., water) occur in a number of applications including underground hydrogen storage, geologic carbon sequestration, and the operation of electrochemcial devices such as fuel cells and electrolyzers. Such bubbles evolve due to a process called Ostwald ripening that is driven by differences in their interfacial curvature. For spherical bubbles, small bubbles shrink and vanish while feeding into larger ones, resulting in one large bubble at equilibrium. Within the confinement of a porous medium, however, bubbles can attain a distribution of sizes at equilibrium that have identical curvature. This work concerns itself with the formulation of a kinetic theory that predicts the statistical evolution of bubble states, defined as the sizes of the pores within which bubbles are trapped and the extent to which those pores are saturated with bubbles. The theory consists of a population balance equation and appropriate closure approximations. Systematic comparisons against a previously published pore network model (PNM) are conducted to validate the theory. Our theory generalizes existing variants in the literature limited to spherical bubbles trapped in homogeneous media to non-spherical (deformed) bubbles inside microstructures with arbitrary heterogeneity and spatial correlation in pore/throat sizes. We discuss the applicability, limitations, and implications of the theory towards future extensions.

中文翻译：

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Ostwald 在多孔介质中成熟的广义动力学理论


被困在多孔介质中并被润湿相（例如水）包围的部分混溶气泡（例如 CO2）存在于许多应用中，包括地下储氢、地质碳封存以及燃料电池和电解槽等电化学设备的运行。这种气泡是由于一个称为 Ostwald 成熟的过程而演变的，该过程是由它们的界面曲率差异驱动的。对于球形气泡，小气泡在进入较大的气泡时收缩和消失，从而产生一个处于平衡状态的大气泡。然而，在多孔介质的范围内，气泡可以达到具有相同曲率的平衡尺寸分布。这项工作涉及动力学理论的制定，该理论预测气泡状态的统计演变，气泡状态定义为气泡被困在其内的孔隙的大小以及这些孔隙被气泡饱和的程度。该理论由种群平衡方程和适当的闭合近似值组成。与先前发表的孔隙网络模型 （PNM） 进行系统比较以验证该理论。我们的理论将文献中仅限于被困在均质介质中的球形气泡推广到微观结构内具有任意异质性和孔/喉尺寸空间相关性的非球形（变形）气泡。我们讨论了该理论对未来扩展的适用性、局限性和影响。