Abstract
A one-dimensional gas-flow drives a wedge-shaped fracture into a linearly elastic, impermeable half space which is in uniform compression, σ∞, at infinity. Under a constant driving pressure, p0, the fracture/flow system accelerates through a sequence of three self-similar asymptotic regimes (laminar, turbulent, inviscid) in which the fracture grows like an elementary function of time (exponential, near-unity power, and linear, respectively). In each regime, the transport equations are reducible under a separation-of-variables transformation. The integro-differential equations which describe the viscous flows are solved by iterative shooting methods, using expansion techniques to accomodate a zero-pressure singularity at the leading edge of the flow. These numerical results are complemented by an asymptotic analysis for large pressure ratio (N = p0/σ∞ → ∞) which exploits the disparity between the fracture length and penetration length of the flow. Since the seepage losses to a surrounding porous medium are shown to be negligable in the late-time long-fracture limit, the results have application to geologic problems such as: containment evaluation of underground nuclear tests, stimulation of oil and gas wells, and permeability enhancement prior to in situ combustion processes.
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