Scaling behavior of microbubbles rising in water-saturated porous media

Abstract:

Gas transport in the form of discrete microbubbles in saturated porous media is of importance in a number of processes relevant to many geo-environmental and engineering systems such as bubbling of greenhouse gases in river and sea beds, hydrocarbon gas migration in coal cleats and rock fractures, and air sparging for remediation of soil contaminated with volatile organic compounds. Under the assumption of no or minor volume expansion during gravity-driven migration, the transport of a single microbubble can be well described using various drag force models. However, not enough attention has been paid to the collective behavior of microbubbles during their ascend as a plume through the saturated porous medium, involving dynamic interactions between individual bubbles, bubbles and the ambient fluid, as well as bubbles and the solid matrix. With our quasi-2D, lab-scale microbubble migration experiments, where bubbles are continuously released from a diffuser at the bottom of a porous bed of hydrated gel beads, we establish a scaling relationship between the gas (bubble) release rate and various characteristic parameters of the bubble plume, such as plume tip velocity, plume width, and breakthrough time of the plume front. We find that the characteristic width of the bubble plume varies as a power of both the gas release rate and the bed thickness, with exponents of 0.2 and 0.4, respectively. Moreover, the characteristic breakthrough time also scales with both the gas release rate and the bed thickness with power-law exponents of -0.4 and 1.2, respectively. The mean pore-water velocity of the circulating ambient water also follows a power-law relationship with the gas release rate being an exponent of 0.6 of the gas release rate. This can be quantitatively proven using a simplified momentum exchange model together with the above power-law exponents for the bubble plume. These analyses on the experimental results are carried out on the basis of non-dimensional parameters and variables in order to explore the bubble transport mechanism in a way that is independent of the actual scale of the physical model. Our findings thus have implications for engineering processes and for fundamental research on bubble transport phenomena in porous media in general.