Transient growth of an isolated bubble in muddy, fine-grained sediments

Methane bubbles in fine-grained sediments have been shown to grow initially by elastic expansion and fracture. A previous growth model assumed quasi-steady state diffusion in which the methane porewater concentration quickly adjusted to changes in bubble geometry [Gardiner B. S, Boudreau B. P and Johnson B. D. (2003a) Growth of disk-shaped bubbles in sediments. Geochim. Cosmochim. Acta, 67 (8), 1485–1494]. Here, we present a finite-element model that solves the transient form of the reaction–diffusion equation, and the coupled linear elastic fracture mechanics (LEFM). In so doing we also employ a new theory for the post-fracture bubble sizes, based upon the full principles of LEFM.Our findings indicate that the quasi-steady state assumption is flawed due to violation of conservation of mass during fracture events. When the new model is applied to sediment conditions found at Cape Lookout Bight, NC, USA, it is found that bubbles grow somewhat faster than previously thought. A reference bubble of 0.5 cm3 will form in about 6 days, 2.5 days quicker than the old model predicted. Moreover, typical bubbles of 0.04 cm3 for this site can grow in as little as a day and a half. We examined the sensitively of the finite-element model to the various parameters in order to gain an understanding of how bubbles may behave under different sediment conditions. The influence of tides on bubble growth, through the process of rectified diffusion, was also examined and it was found that this had little influence upon growth.