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 length scales: a diffusion length ä(a lengthscale representative of the distance of propagation of the pore pressure perturbation from the boundary) and a microstructural length ë (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 pressur- ization 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 experi- ments 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.