A poroelastic model for laboratory hydraulic fracturing of weak permeable rock

Water injection laboratory experiments in weak, poorly consolidated sandstones show evidence that the peak injection pressure is much larger than the one predicted by the Haimson-Fairhurst breakdown criterion. A model based on poroelasticity, fracture mechanics, and lubrication theory is constructed to simulate the laboratory experiments. It aims at computing the propagation of a bi-wing hydraulic fracture from a borehole with increasing injection rate, until the crack reaches the boundary of the sample. The model is applicable to situations for which the pore pressure field reaches a steady state quasi-instantaneously when changing the injection rate, on account of the large permeability of these rocks. Taking advantage of the linearity of the poroelasticity equations, the model is formulated in terms of singular integral equations. Combined with the nonlinear lubrication equation, the convolution integrals, resulting from the application of the boundary conditions, are approximated by discretizing the unknown distribution of singularities. Finally, the injection rate corresponding to a given crack length is obtained by solving a nonlinear system of equations involving only unknowns along the crack. Two asymptotic regimes of solution are found: (i) a rock-flow regime where the induced fracture is hydraulically invisible, and (ii) a fracture-flow regime where the fluid penetrates the rock via the crack. In the rock-flow regime, fracture propagation is stable, i.e., the borehole pressure increases with the injection rate; while in the fracture-flow regime, the reverse is true. It is concluded that the peak injection pressure reflects a transition between two flow regimes, rather than breakdown. A parametric analysis also indicates that poroelasticity significantly affects the magnitude of the injection pressure.