Growth of disk-shaped bubbles in sediments

Disc-shaped methane bubbles, often observed in marine sediments, result from growth in a medium that elastically resists expansion of the bubbles and yields by fracture. We have modeled this process to obtain estimates of growth times by using a reaction-diffusion model coupled to a linear elastic fracture mechanics (LEFM). For comparison, we also modeled the growth of a constant eccentricity bubble in a nonresistant medium. Discoidal bubbles that grow in sediments that obey LEFM grow much faster than spherical bubbles (two- to fourfold faster for the times and conditions tested here) and become more eccentric with time (aspect ratios falling from 0.3 to 0.03 over 8 d of growth). In addition, their growth is not continuous but punctuated by fracture events. Furthermore, under some conditions, LEFM predicts that bubble growth can become arrested, which is not possible for a bubble in a nonresistant medium, even for nonspherical bubbles. Cessation of growth occurs when the dissolved gas concentration gradient near the bubble surface disappears as a result of the increase in bubble gas pressure needed to overcome sediment elasticity.