Description: A one-dimensional gas-flow drives a wedge-shaped fracture into a linearly elastic, impermeable half-space which is in uniform compression, sigma/sub infinity/, at infinity. Under a constant driving pressure, p/sub 0/, 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 accommodate 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 = p/sub 0//sigma/sub infinity/ ..-->.. infinity) which exploits the disparity between the fracture-length and penetration-length of the flow. The considered prototypic problem has geologic applications: containment evaluation of underground nuclear tests, explosive stimulation of oil and gas wells, and explosive permeability-enhancement prior to in-situ combustion of coal or oil-shale.
Date: October 1, 1981
Creator: Nilson, R.H.
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