The governing nonlinear equations for the hydraulically induced propagation of a circular crack in a poroelastic medium are derived. A Lagrangian formulation is utilized with the crack maximum width and radius selected as generalized coordinates. Explicit time‐dependent solutions for the crack geometry and fluid pressure associated with Newtonian and non‐Newtonian fracturing fluids are derived. The classical expression relating fracture width in terms of fracture radius is deduced as a special case. In addition, parameter sensitivity responses and comparison of results are presented.
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Advani et al. (1987) studied this question.
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