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Pollard 1976
Pollard, D.D. (1976). On the form and stability of open hydraulic fractures in the earth’s crust. Geophysical Research Letters 3: doi: 10.1029/GL003i009p00513. issn: 0094-8276.

The cross-sectional form and stability of large hydraulic fractures are found to be very sensitive to symmetric gradients in fluid pressure and regional stress. Horizontal sections through vertical fractures may be subjected to symmetric pressure gradients by locating inflow and outflow wells near the fracture center and tips. A dumbbell form, resulting from flow from the tips toward the center, has a limital length beyond which the fracture closes at the center and propagates unstably at the tips. A diamond form, resulting from the opposite sense of flow, has no limital length and a stable propagation. These features of fracture form and stability may play an important role in the design of hydraulic fractures for geothermal energy production.

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Geophysical Research Letters
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