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This work was supported by the research fund of Hanyang University (HY-201700000002411). The data presented in this study are available at http://jwjang1977.wixsite.com/mysite/data.

To provide insight into the mechanism of bubble migration in in situ air sparging in a coarse porous medium, the rise of air bubbles through a granular porous medium is studied through video photography enhanced with image analysis. The porous medium is simulated by a fully saturated cylindrical glass column filled with 4-mm glass beads in random packing order. The experimental procedure for introducing and visualizing a single air bubble is discussed, and the average rise velocity as a function of the emerging bubble radius is directly measured. Compressed air is injected into the base of the column through the use of an electronically controlled solenoid valve. The resulting bubble motion is recorded by camcorder, and still frames are captured and enhanced from the videotape with an image analyzer. The vertical rise of a bubble through the porous medium displays a linear dependence on time. This is the first study to quantify the terminal velocity of an air bubble rising in a stationary porous medium. Comparison is made to experimental data on air bubbles in water and Soltrol obtained using the same video photography and image analysis techniques. Although a porous medium is sometimes represented as a bundle of capillary tubes, an air bubble rising in a granular porous medium is shown to exhibit significantly different behavior from a bubble rising in either a capillary tube or a tube with a diameter comparable to the equivalent diameter of the bubble. The effect of a bubble chain, a series of single bubbles separated vertically from each other by a few centimeters, on air bubble migration in a granular porous medium is also discussed.

[1] 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.