Acoustic waves in saturated porous media with gas bubbles.

The present framework employs various interface characteristics of gas bubbles into a continuum description of acoustics in porous media. It first extends the bubble compressibility in classic models by surface tension and higher-order curvature effects. This modelling extension is significantly relevant to estimate the impact of interface effects, e.g. on emerging nano-scale bubbles or pickering emulsions. The gas bubble dynamics is then homogenized to derive a manageable set of continuum equations. Respective assumptions and limitations are summarized in this process to provide a quick reference when choosing the compromise between a model's complexity and applicability. The acoustic response of a water-saturated sandstone with gas bubbles is finally evaluated with respect to the practical importance at ambient and reservoir conditions. The shape of the bubble-size distribution is represented in the evolution of the inverse quality factor but less distinct in the dispersion of the phase velocity. The presented, rigorous framework thus allows to predict what frequencies and acoustic properties relate to specific gas bubble sizes and whether respective signals may be detected with current apparatus. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'.