On the shape and velocity of fluid-filled fractures in the Earth

In this paper I present a model to estimate the shape and velocity of slowl y ascending buoyancy-driven fluid-filled fractures. The model considers ela stic deformation, linear fracture mechanics and fluid flow. An attempt is m ade to incorporate the effect ofthe 2-D fluid pattern on the viscous pressu re drop. Most other models assume that the viscous pressure drop can be app roximated by flow through a channel with constant width, although the form of the fracture is known to deviate from such a simple shape. The 2-D flow in my model has an important consequence for the mechanism of buoyancy-driv en fracture propagation-it predicts a large pressure gradient at the tail o f the propagating fracture, indicating that the tail of the fracture is mos t important in hindering the fracture propagation. A singularity at the tai l of the fracture can be avoided when a small amount of fluid trails in the channel left behind the propagating fracture. The trailing and decoupling of fluids at the tail seems to be accompanied by small flow and shape insta bilities, which is indicated by the jerky movement of the tail observed in propagating air-filled fractures in solidified gelatine, and by numerical b oundary element solutions of the coupled flow-deformation-fracturing proble m. By comparing the predictions for propagation velocities with laboratory observations of buoyancy-driven fracture propagation in gelatine, I derive a non-dimensional effective thickness at the tail of the fracture for which trailing of fluids may occur. The model is applied to Earth-relevant probl ems such as oil- and water-filled fractures in pressurized sediments or mag ma-filled dykes in the lithosphere, which are discussed in the paper.