Tensile fractures analysis for deviated wellbores

The procedure to find tensile failure is equivalent to the one used for shear failure, but using a tensile strength failure criterion. For example, consider a place subjected to normal faulting stress regime with $S_{Hmax}$ oriented at an azimuth of 070$^{\circ }$ and known values of principal stresses (Fig. 6.24). The maximum stress anisotropy lies in a plane that contains $S_1 = S_{v}$ and $S_3 = S_{hmin}$, perpendicular to a horizontal wellbore drilled in the direction of $S_{Hmax}$. For a given rock tensile strength, we can calculate the maximum mud pressure that the wellbore can bear without failing in tension. Fig. 6.24 shows an example of this calculation. The maximum possible $P_W$ corresponds to the wellbore direction with minimum stress anisotropy (blue region), and the minimum possible $P_W$ corresponds to the wellbore direction with maximum stress anisotropy (red region). For example, tensile fractures would tend to occur in the top and bottom of a horizontal wellbore drilled in the direction of $S_{Hmax}$.

Figure 6.24: Calculation of required $T_S$ as a function of wellbore orientation in order to prevent open-mode fractures with $P_W = 35$ MPa. Stresses and pore pressure: $S_v =$ 70 MPa, $S_{Hmax} =$ 55 MPa, $S_{hmin} =$ 45 MPa, and $P_p =$ 32 MPa, Notice that the stress regimes dictates the orientation of the least and most convenient drilling direction.

PROBLEM 6.7: Consider a place with principal stresses $S_v = 70$ MPa, $S_{Hmax} = 105$ MPa (at 070$^{\circ }$), $S_{hmin} = 55$ MPa, and $P_p = 32$ MPa. Calculate the maximum wellbore pressure $P_W$ at the limit of tensile strength with $T_s = 0$ MPa) for all possible wellbore orientations. Plot results in a stereonet projection.

SOLUTION
TBD

PROBLEM 6.8: Consider a place with principal stresses $S_v = 70$ MPa, $S_{Hmax} = 105$ MPa (at 070$^{\circ }$), $S_{hmin} = 85$ MPa, and $P_p = 32$ MPa. Calculate the maximum wellbore pressure $P_W$ at the limit of tensile strength with $T_s = 0$ MPa) for all possible wellbore orientations. Plot results in a stereonet projection.

SOLUTION
TBD