Rate of growth of isolated bubbles in sediments with a diagenetic source of methane

Abstract

Observation of bubbles in estuarine and coastal sediments indicates that bubbles at or below 10 cm depth grow on seasonal time scales (May-October). In order to determine the controls on this growth rate, we have constructed a diffusion-reaction model that accounts for the dynamics of methane formation, its diffusion through pore waters, its incorporation into a bubble, and the consequent growth of the bubble. The model produces an explicit equation for the radius of a growing bubble, R(t), with time using mean parameter values and under the assumption that the mechanics of the sediment response to growth can be neglected: R(t) = [phi D/2c (sub g) {SR (super 2) (sub 1) /3D + (c (sub 1) -c (sub 0) )}t + R (super 2) (sub 0) ] (super 1/2) where phi is the porosity, D is the tortuosity-corrected diffusivity, C (sub g) is the concentration of gas in the bubble, S is the rate of methanogenesis near the bubble, R (sub 1) is the half-separation distance between bubbles (R (sub 1) >>R), c (sub 1) is the ambient CH (sub 4) concentration, c (sub 0) is the pore-water CH (sub 4) concentration at R, t is time, and R (sub 0) is the initial bubble radius, if not zero. The effects of the source S and supersaturation (c (sub 1) -c (sub 0) ), thus, appear as separate contributing terms, and this formula can then be applied even in those cases where apparently c (sub 1) nearly equal c (sub 0) . The model is applied to three sediments where bubbles have been previously studied, i.e., Cape Lookout Bight (USA), White Oak River (USA) and Eckernforde Bay (Germany). In all three cases, using the site-specific time-averaged parameter values, the model predicts seasonal growth rates, consistent with the observations. Furthermore, the source term dominates the rate of growth at the first of these two sites, whereas diffusion from the ambient supersaturation dominates at the German location. Real bubbles may follow a more complicated growth history than predicted by the above equation because of the mechanical properties of sediments; nevertheless, the overall growth times are concordant with ultimate diffusion control. The effects of rectified diffusion, that is, the pumping of gas into a bubble by pressure oscillations, e.g., from waves and tides, were also examined. Existing models for that process suggest that it is negligible, due to the low frequency of these types of oscillations.