Influence of pressurization rate on the magnitude of the breakdown pressure

A mathematical model is proposed to account for rate and size effects on the magnitude of the breakdown pressure during a hydraulic fracturing experiment. This model recognizes the existence of two lengthscales: A diffusion length 6 (a lengthscale representative of the distance of propagation of the pore pressure perturbation from the boundary) and a microstructural length A (which underpins the failure process). In this context, rate effects are seen as a consequence of the interaction of these two lengthscales. An expression for the breakdown pressure pt, which depends explicitly on the pressurization rate, is derived. It is demonstrated that the Haimson-Fairhurst (H-F) and the Hubbert-Willis (H-W) expression for the breakdown pressure correspond respectively to the asymptotically slow and fast pressurisation regimes. However, the H-F limit is shown to be the appropriate expression for "permeable" rocks, as hydraulic fracturing experiments in these rocks are practically always in the slow regime. It is also shown that in low permeability/low porosity rocks, rate effects are potentially significant and that both the H-F and the H-W expressions are acceptable limits, depending on the pressurization rate.