6.1 The wellbore environment

Wellbore stability is critical for drilling. A stable open-hole requires the surrounding sediment and rock to bear the stresses that amplify around the wellbore cavity. The surrounding rock must hold stresses until casing is set or for undetermined time if left uncased.

Wellbore stability depends on two set of variables (Figure 6.1): one set which is out of our control and another set of variables that we can control.

• In-situ variables out of our control include far-field stresses $\uuline{S}{}_G$, pore presssure $P_p$, and rock properties.
• Controllable variables include mud pressure $P_W$ ($W$ for wellbore), mud composition, mud fluid chemistry, and wellbore orientation (direction azimuth and deviation).

Figure 6.1: Wellbore stability analysis includes inherent variables, such as in-situ stresses and rock properties, and controllable variables, such as wellbore orientation and mud pressure during drilling.

The pressure in the wellbore $P_W$ is one of the main variables to maintain wellbore stability. Mud (mass) density and vertical depth $z$ (TVD) determine the mud hydrostatic pressure (in the absence of additional pressure controls at the surface - such as in managed pressure drilling):

$$P_W = \rho_{mud} \: g \: z$$ (6.1)

The pressure gradient within the wellbore is proportional to mud density $dP_W/dz = \rho_{mud} g$ (Fig. 6.2). This quantity is usually measured and reported in p.p.g. (pounds-force per gallon). For example the pressure gradient for fresh water is 9,800 N/m$^3$ (= 9.8 MPa/km = 0.44 psi/ft), about 8.3 ppg. The lithostatic gradient of 1 psi/ft is equivalent to 1 (psi/ft) $\times$ (8.3 ppg/0.44 (psi/ft)) = 18.9 ppg. The “equivalent circulation density” is also reported in ppg and take into account pressure drops in the annulus.

Figure 6.2: Wellbore mud pressure and equivalent density. Mud pressure $P_W$ is usually reported in terms of gradient (depth-independent) rather than in absolute values.

Over-balanced drilling implies $P_W > P_p$. Over-balanced drilling favors the formation of a “mud-cake” or “filter-cake” on the wall of the wellbore which permits adding stress support on the wellbore wall approximately equal to $P_W - P_p$ (Fig. 6.3). The resulting effect is similar to an impermeable and elastic membrane applying a stress on the wellbore wall (similar to the membranes used in triaxial tests). Under-balanced drilling $P_W < P_p$ may be preferred in some specific instances.

Figure 6.3: Leak-off of mud filtrate favors clogging of mud particulates which help apply a normal stress on the wellbore wall. This layer of particulates is called mud-cake.