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Gas bubbles driven in radial oscillations are subject to an instability of the spherical shape that is opposed by surface tension and viscosity. An exact linear formulation for the study of the phenomenon has been available for many years, but its complexity has discouraged a detailed investigation. With the recent theory of sonoluminescence of Lohse and co-workers [Hilgenfeldt et al., Phys. Fluids, 8, 2808 (1996)], there has been a renewed interest in the problem and new data have become available. This paper presents a numerical method for the solution of the pertinent equations and compares the theory with these new data. The coupling of the strong nonlinearity of the bubble radial oscillations with the parametric mechanism of the surface instability results in a very complex structure for the stability boundary. Nevertheless, a good agreement between theory and data is found. A comparison with earlier approximate models is also made.

BackgroundCarbon storage in deep saline reservoirs has the potential to lower the amount of CO2 emitted to the atmosphere and to mitigate global warming. Leakage back to the atmosphere through abandoned wells and along faults would reduce the efficiency of carbon storage, possibly leading to health and ecological hazards at the ground surface, and possibly impacting water quality of near-surface dilute aquifers. We use static equilibrium and reactive transport simulations to test the hypothesis that perturbations in water chemistry associated with a CO2 gas leak into dilute groundwater are important measures for the potential release of CO2 to the atmosphere. Simulation parameters are constrained by groundwater chemistry, flow, and lithology from the High Plains aquifer. The High Plains aquifer is used to represent a typical sedimentary aquifer overlying a deep CO2 storage reservoir. Specifically, we address the relationships between CO2 flux, groundwater flow, detection time and distance. The CO2 flux ranges from 103 to 2 × 106 t/yr (0.63 to 1250 t/m2/yr) to assess chemical perturbations resulting from relatively small leaks that may compromise long-term storage, water quality, and surface ecology, and larger leaks characteristic of short-term well failure.ResultsFor the scenarios we studied, our simulations show pH and carbonate chemistry are good indicators for leakage of stored CO2 into an overlying aquifer because elevated CO2 yields a more acid pH than the ambient groundwater. CO2 leakage into a dilute groundwater creates a slightly acid plume that can be detected at some distance from the leak source due to groundwater flow and CO2 buoyancy. pH breakthrough curves demonstrate that CO2 leaks can be easily detected for CO2 flux ≥ 104 t/yr within a 15-month time period at a monitoring well screened within a permeable layer 500 m downstream from the vertical gas trace. At lower flux rates, the CO2 dissolves in the aqueous phase in the lower most permeable unit and does not reach the monitoring well. Sustained pumping in a developed aquifer mixes the CO2-affected water with the ambient water and enhances pH signal for small leaks (103 t/yr) and reduces pH signal for larger leaks (≥ 104t/yr).ConclusionThe ability to detect CO2 leakage from a storage reservoir to overlying dilute groundwater is dependent on CO2 solubility, leak flux, CO2 buoyancy, and groundwater flow. Our simulations show that the most likely places to detect CO2 are at the base of the confining layer near the water table where CO2 gas accumulates and is transported laterally in all directions, and downstream of the vertical gas trace where groundwater flow is great enough to transport dissolved CO2 laterally. Our simulations show that CO2 may not rise high enough in the aquifer to be detected because aqueous solubility and lateral groundwater transport within the lower aquifer unit exceeds gas pressure build-up and buoyancy needed to drive the CO2 gas upwards.