Fracture initiation refers to the moment when a hydraulic fracture first forms in the rock due to fluid injection. As fluid is pumped into the wellbore, the pressure increases until it exceeds the near-wellbore compressive stresses and surpasses the tensile strength of the surrounding rock. At this point, the rock fails and a fracture begins to form. The pressure required to initiate this fracture is known as the breakdown pressure.
Fracture Initiation Near the Wellbore
Fracture from a vertical wellbore is aided by the stress concentration effect of a circular hole. If a block has a distributed compressive stress, σ, acting on it in the vertical direction (Figure 3.5.1), the rock at the sides of the circular hole experiences an amplified compression of 3σ acting parallel to the wellbore wall (stress parallel to the wellbore wall is called circumferential or hoop stress). At the top and the bottom of the circular hole, the hoop stress caused by the external vertical compression is a horizontal tension of −σ. These stress concentrations magnitudes are drawn in Figure 3.5.1a. The expected deformation of the wellbore is in Figure 3.5.1b. If the induced tension at the top and bottom of the hole exceeds the tensile strength of the rock, an opening crack will form at those locations as a vertical plane. At the sides of the hole, if the compressive strength of the rock is exceeded due to the three times compression, the rock will crumble locally and fall into the hole, creating what is called a wellbore breakout.
Figure 3.5.1: Uniaxial loading in the vertical direction of a block with a circular hole, showing a) the stress concentrations caused by the external compressive loading of σ around the circumference of the circular hole, and b) the failure that would result if rock strength were exceeded by these stress concentrations in either tension (opening crack at top and bottom of hole) or compression (breakouts at sides of hole).
In the subsurface, loading is not from only one direction, but there is compression in all directions, represented by the principal stresses summarized in the previous topic – Svert, SHmax and Shmin. Rotating Figure 3.5.1 to be a view of a horizontal plane looking down from above on a vertical wellbore, the stresses in the two horizontal directions are SHmax and Shmin (Figure 3.5.2a). These two horizontal stresses will induce stress concentrations around the vertical wellbore comparable to those shown in Figure 3.5.1, but at locations 90 degrees away from each other given there are two different stresses applied in orthogonal directions (SHmax in the y-direction and Shmin in the x-direction).
- Location A (Figure 3.5.2a) – The circumferential stress on the wellbore wall due to the in situ stresses is equal to (3SHmax − Shmin) and is the most compressive.
- Location B (Figure 3.5.2a) – The circumferential stress is equal to (3Shmin − SHmax) and is the least compressive.
- Everywhere (Figure 3.5.2b) – For the hydraulic fracturing scenario, the wellbore is pressurized to a magnitude of Pw which causes a circumferential tension of −Pw everywhere around the wellbore (the sign convention is compression is positive).
Figure 3.5.2: Stress concentration around a vertical wellbore due to a) the remotely applied in situ horizontal stresses, Shmin and SHmax, and b) the internally applied wellbore pressure, Pw. Combining the effects of the remote stress and the wellbore pressure results in the breakdown equation, which predicts the initiation of hydraulic fracture.
Combining all this information, and specifying that a hydraulic fracture will initiate when the hoop stress at the wellbore wall exceeds the tensile stress of the rock, T, we can write a failure equation for location B (the location of the least compressive stress). This equation is known as the breakdown equation, where the wellbore pressure at failure, Pb, assuming no pore pressure, is given as
\[ P_b = 3S_{hmin} - S_{Hmax} + T \tag{3.3} \]
If we account for pore pressure, Pp, we need to take into account effective stress effects, and the resulting equation is modified to
\[ P_b = 3S_{hmin} - S_{Hmax} - P_p + T \tag{3.4} \]
A similar equation can be written to predict the initiation of breakout failure at location A.
