This paper studies the transient pressurization of a pre-existing, fingerlike crack in a poroelastic, permeable rock due to a fluid injection, the problem previously considered in the nonporoelastic reservoir context in the companion paper (Sarvaramini and Garagash, 2015, “Breakdown of a Pressurized Fingerlike Crack in a Permeable Solid,” J. Appl. Mech., 82(6), p. 061006). Large-scale fluid leak-off from the crack and the associated pore-fluid diffusion within the permeable rock formation lead to dilation of the pore volume, which acts to additionally confine/close the crack. The influence of this so-called “poroelastic backstress” on the evolution of the fluid pressure in the crack and the onset of the fracture propagation are investigated. We first revisit the existing solution to an auxiliary problem of a poroelastic crack subjected to a step pressure increase and generalize it to account for the full-space fluid leak-off diffusion. This solution is then used to formulate the solution to the transient pressurization of the crack due to a constant rate of fluid injection via the Green's function approach. Comparison to the reference solution for a fingerlike crack in a nonporoelastic reservoir shows that the poroelasticity has a minor effect on the fluid pressure evolution in the crack. However, the evolution of the fracture volume and the onset of the fracture propagation are shown to be significantly hindered by the poroelastic backstress at large enough injection time when fluid diffusion becomes fully two- or three-dimensional.

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