Effect of compressibility on the rise velocity of an air bubble in porous media

The objective of this study is to develop a theoretical model to analyze the effect of air compressibility on air bubble migration in porous media. The model is obtained by combining the Newton's second law of motion and the ideal gas law assuming that the air phase in the bubble behaves as an ideal gas. Numerical and analytical solutions are presented for various cases of interest. The model results compare favorably with both experimental data and analytical solutions reported in the literature obtained for an incompressible air bubble migration. The results show that travel velocity of a compressible air bubble in porous media strongly depends on the depth of air phase injection. A bubble released from greater depths travels with a slower velocity than a bubble with an equal volume injected at shallower depths. As an air bubble rises up, it expands with decreasing bubble pressure with depth. The volume of a bubble injected at a 1‐m depth increases 10% as the bubble reaches the water table. However, bubble volume increases almost twofold when it reaches to the surface from a depth of 10 m. The vertical rise velocity of a compressible bubble approaches that of an incompressible one regardless of the injection depth and volume as it reaches the water table. The compressible bubble velocity does not exceed 18.8 cm/s regardless of the injection depth and bubble volume. The results demonstrate that the effect of air compressibility on the motion of a bubble cannot be neglected except when the air is injected at very shallow depths.