Buoyancy-driven propagation of an isolated fluid-filled crack in rock: implication for fluid transport in metamorphism

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Abstract
A new model for upward transport of buoyant fluid released during metamorphism is proposed. The model is fluid transport by buoyancy-driven propagation of isolated fluid-filled cracks. The mechanical behavior of a two-dimensional, isolated, vertical, and fluid-filled crack in impermeable rock is investigated using linear fractire mechanics and fluid dynamics. The results show that steady-state crack propagation which causes long-distance transport of the fluid occurs when the vertical cross-sectional area of the crack exceeds a critical value. Propagation velocity and average thickness of the crack under the steady-state propagation regime are expressed explicitly by the following seven parameters: vertical crack length; rigidity, Poisson's ratio, and fracture toughness of the rock; fluid viscosity; density difference between the rock and the fluid; gravitational acceleration. An isolated H2O-filled crack of vertical length 100 m, for example, propagates upwards in the crust at ∼0.3 m/s with the average thickness ∼0.2 mm when the following likely values are assumed: 0.1 mPa s for the H2O viscosity; 3 MPa m1/2 for the fracture toughness of the crustal rock. The application of the obtained results to the transport of H2O released during metamorphism suggests that the number density of isolated cracks propagating in the crust is very low. Since the propagation velocity is high, our model is suitable particularly for fluid transport through hot quartz-rich rock where fluid-filled cracks have geologically short lifetimes.