We extend classical models of tensile failure around a pressurized borehole to include size effects. We use a mixed criterion with a mean stress approximation, including also the effect of pore pressure for poroelastic media. The mixed criterion gives the fracture initiation pressure and the corresponding length of the initial fracture. The initiation pressure with size effects is greater than, or equal to, the one without them. We quantify size effects for a range of laboratory and field conditions. Using typical borehole sizes and tensile strength over fracture toughness ratios for a variety of rocks, size effects for laboratory conditions are shown to be small or large, and small or negligible for field conditions. We show that the lower the initiation pressure, due to low confinement and/or high stress anisotropy, the larger the size effects. Using conditions of four representative reservoirs, the reservoir with shallowest depths and highest stress anisotropy is the only one that shows significant increase in initiation pressures, on average 13% or 565 i, which may be non-negligible for some applications. For the other fields, the average increase in initiation pressures was negligible. For laboratory conditions, size effects can be very significant.

1 Introduction
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