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Abstract

This paper examines the dependence of the drilling specific energy E (the amount of energy required to drill a unit volume of rock) on the virgin pore pressure p0 in low-permeability fluid-saturated rocks, through a two-dimensional analysis of the cutting process. For this analysis, we consider a single cutter advancing at steady speed v and removing material over a constant depth of cut d from a fluid-saturated half-plane subjected to a surface pressure pm and a far-field pore pressure p0. On the basis of a simple failure mechanism involving a moving single shear plane (shear shock), we first establish that the specific energy E (here equal to the ratio of the cutting force parallel to the cutter velocity over the depth of cut) depends linearly on the difference between the surface pressure pm and the average pore pressure pb on the shear plane. Next, we address the dependence of pb on the virgin pore pressure p0 and the conditions for which there is cavitation on the shear plane (pb=0). The relationship between pb and p0 is determined by considering fluid mass balance across the shear plane. Different pore pressure regimes are identified that are controlled by a dimensionless number λ: low-speed, transient, and high-speed regime. In the high-speed regime, the rock in the shear zone is undrained and pressure drop induced by shear-induced dilatancy leads to cavitation. It is shown that the drilling conditions in low-permeability shear-dilatant rocks, such as shales, are in the high-speed regime, leading therefore to the conclusion that the specific energy E does not depend on the virgin pore pressure p0 in these rocks.