Tensile fractures and wellbore breakdown

Wellbore tensile (or open mode) fractures occur when the minimum principal stress $\sigma _3$ on the wellbore wall goes below the limit for tensile stress: the tensile strength. Unconsolidated sands have no tensile strength. Hence, an open-mode fracture occurs as soon as effective stress goes to zero. The minimum hoop stress is located on the wall of the wellbore $(r=a)$ and at $\theta = 0$ and $\pi$ (Fig. 6.14):

$$\sigma_{\theta \theta} = -(P_W - P_p) -\sigma_{Hmax} + 3 \sigma_{hmin} + \sigma^{\Delta T}$$ (6.16)

Notice that we have added a temperature term $\sigma^{\Delta T}$ that takes into account wellbore cooling, an important phenomenon that contributes to tensile fractures in wellbores.

Figure 6.14: Occurrence of tensile fractures around a vertical wellbore.

Matching the lowest value of hoop stress $\sigma _{\theta \theta }$ with tensile strength $T_s$ permits finding the mud pressure $P_W = P_{b}$ that would produce a tensile (or open mode) fracture:

$$-T_s = -(P_b - P_p) -\sigma_{Hmax} + 3 \sigma_{hmin} + \sigma^{\Delta T}$$ (6.17)

and therefore

$$P_b = P_p - \sigma_{Hmax} + 3 \sigma_{hmin} + T_s + \sigma^{\Delta T}$$ (6.18)

The subscript $b$ of $P_b$ corresponds to “breakdown” pressure because in some cases when $P_b > S_3$, a mud pressure $P_W>P_b$ can create a hydraulic fracture that propagates far from the wellbore and causes lost circulation. When $P_b < S_3$ and $P_W>P_b$, the mud pressure will produce short tensile fractures around the wellbore that do not propagate far from the wellbore.

In the equations above we have added the contribution of thermal stresses $\sigma^{\Delta T} = [\alpha_T E/(1-\nu)] \Delta T$ where $\alpha_T$ is the linear thermal expansion coefficient and $\Delta T$ is the change in temperature ( $\sigma^{\Delta T}<0$ for $\Delta T < 0$). Wellbores are usually drilled and logged with drilling mud cooler than the formation $T_{mud} < T_{rock}$. Hence, ignoring thermal stresses is conservative for preventing breakouts but it is not for tensile fractures.

Fig. 6.15 shows an example of calculation of the local minimum principal stress $S_3$ around a wellbore. The locations with the lowest stress align with the direction of the far-field maximum horizontal stress in the plane perpendicular to wellbore axis.

Figure 6.15: Example of calculation of tensile strength required for wellbore stability. The figure shows that a tensile strength of $\sim 3$ MPa is required to avert tensile fractures in this example.

PROBLEM 6.3: Calculate the maximum mud weight (ppg) in a vertical wellbore for avoiding drilling-induced tensile fractures in a site onshore at 7000 ft of depth where $S_{hmin} =$ 4300 psi and $S_{Hmax} =$ 6300 psi and with hydrostatic pore pressure. The rock mechanical properties are $UCS =$ 3500 psi, $\mu_i=$ 0.6, and $T_s$ = 800 psi.

SOLUTION
The problem variables are the same of problem 6.1. The breakdown pressure $P_b$ in the absence of thermal effects is

$$P_b = 3080$$    psi$$- 3220$$    psi$$+ 3 \times 1220$$    psi$$+ 800$$    psi$$= 4320$$    psi

This pressure can be achieved with an equivalent circulation density of

$$\frac{4320 \text{ psi}} {7000 \text{ ft}} \times \frac{8.33 \text{ ppg}} {0.44 \text{ psi/ft}} = 11.68 \text{ ppg} \: \: \blacksquare$$