Wellbore breakouts are zones of enlargement that develop due to failure of the rock at the wellbore wall. These failures occur at orientations where the greatest stress concentrated

Figure 1. The upper diagram in this figure shows schematic stress-strain plots of an elastic-perfectly plastic rock in which no decrease in strength occurs, compared to one with lower residual strength after failure. A simple way to describe this behavior is to use a linear Mohr-Coulomb model with “cohesion weakening,” shown schematically in the lower diagram. (Graphics courtesy of GeoMechanics International)
around the well by drilling exceeds the strength of the rock to support the load. Breakout analyses performed to determine the optimal mud weight that will maintain wellbore stability typically define hole quality in terms of the width of failed zones but do not provide quantitative information about the breakout depth.

Although laboratory experiments have been run and theoretical models have been developed to predict enlargement depth as a function of breakout width, relationships derived from these studies have never been validated using field data. However, theoretical analyses and laboratory data indicate that it is possible to quantify stress magnitudes using measurements of breakout shape (principally breakout width).

Once these stresses are known, it is then possible to predict the minimum mud weights required to drill wells in which instabilities are minimized, thus allowing drilling to continue and the installation of casing to be accomplished.

Unfortunately, it is not sufficient simply to reach a target depth and install casing. Modern completion methods (including installations that require expandable screens or effective zonal isolation using swell packers or other soft elements) require that hole quality standards be maintained for maximum hole size also.

Recently, an evaluation of logging data (both wellbore images and caliper data) was conducted to determine if it is possible to predict the depths of breakouts if their widths are known. Breakouts were deeper in some rock types (strong sands) than in others (weak sands and shales).

Breakout theory
In order to provide some insights into why some breakouts are deeper than others (rather
Figure 2. At the top is a series of plots of axial stress vs. axial strain for rocks tested in the laboratory, revealing a decrease in the ability to support load after yielding. Data showing variations in the tangent of the angle of internal friction (on the bottom) reveal a systematic decrease as a function of the specific surface area of clay-bearing rocks, which supports the observation that higher clay contents are known to be associated with lower angles of internal friction.
than simply ascribing these differences to time-dependent phenomena that are inherently difficult to quantify), a simple rheological model is used that relates the stable depth of a breakout to the residual rock strength. A linear Mohr-Coulomb strength envelope (see the lower sketch in Figure 1) defines the shear stress that can be supported by the intact rock as a function of normal stress. When the rock is unconfined, it can support a finite amount of shear stress, which increases linearly as the normal stress increases. The slope of the line is controlled by the angle of internal friction; the intercept is the cohesion.

The rock around the well is modeled as an elasto-plastic material, in which the stress increases linearly with strain until a yield limit is reached, after which the stress state lies on the strength envelope. The extent of wellbore breakouts is roughly defined by the zone within which this strength envelope has been reached. For rock with a known strength envelope, the shape of the breakout can be computed from the far-field stresses, the pore pressure and the mud pressure acting on the wellbore wall.

The upper sketch of Figure 1 shows schematic plots of stress vs. strain for an elastic-perfectly plastic rock which, after yielding, can support the same load as it did before the stress state reached the strength envelope, and for a rock in which the strength after yielding (the residual strength) decreases. In general, real rocks have lower residual than intact strength. This can be modeled using “cohesion weakening,” for which the slope of the strength envelope is the same for the rock after yielding but the intercept (the cohesion) decreases (lower sketch in Figure 1).

Figure 2 shows actual stress-strain curves of rocks tested in the laboratory that exhibit this behavior. In these rocks, failure leads to a decrease in the rock’s ability to support a load (strain weakening) that the simple model (shown schematically in Figure 1) attempts to capture.

Under low confining pressure, as is likely to exist in the near-wellbore, brittle rocks (e.g., well-cemented sands) have almost no residual strength. Less brittle rocks (i.e., poorly cemented sands or rocks containing significant amounts of structural clay) have much larger ratios of residual-to-intact strength. Furthermore, as confining pressure increases, the residual strength also increases in many rocks. This suggests that although cohesion can decrease dramatically, internal friction may be relatively unaffected, which is consistent with the model discussed here.

It has previously been demonstrated that the shapes of the initial zones of predicted failure are a function of cohesion and internal friction. In a balanced well, the width of the zone is nearly independent of internal friction since confining pressure at the hole wall is zero. The confining stress is much larger at the back of the zone; hence, the depth of the initial failure zone is strongly influenced by internal friction. The lowermost plot in Figure 2 reveals that internal friction is a strong function of specific surface area in clay-bearing rocks. Consequently, other things being equal, one would expect the initial zone of failure in a clay-rich rock to be much deeper than in a rock with little clay. However, this does not take into account the impact of cohesion weakening.

Cohesion weakening
Using the simple rheological model described above, it is possible to investigate the influence of both the intact and residual properties of the rock on breakout shape. This was done in
Figure 3. Shown are models for the shape of the yielded zone around a wellbore for different conditions of internal friction and residual strength. The intact cohesion is the same in all three cases.
three cases (Figure 3). The first case (A) concerned a brittle rock. In this case, cohesion inside the failed zone is one-fourth its value outside the zone. The result is the creation of a deep breakout with a finite width. In case B, the same rock is assumed to have no reduction in strength (i.e., it is perfectly plastic). The breakout is much shallower in this case. In case C, the rock has nearly the same cohesion as in A and B and the same residual strength as in B, but the angle of internal friction is lower (the lower the angle of internal friction, the less of an increase in strength occurs due to confinement). The breakout is somewhat deeper than in case B but not as deep as in case A, which has a low residual strength.

Modeling thus reveals that in brittle rocks with low residual strengths, the zones of failure that lead to breakouts are much deeper than in rocks with similar cohesion that do not lose strength after failure. This offsets the increased depth of the initial zone of failure in rocks with low internal friction.


Summary
The simple rheological model discussed above provides one possible explanation for the relationships between breakout width and depth. The explanation is that rocks with higher clay contents have larger residual strengths and therefore tend to have breakouts that do not deepen as much with time as those in rocks with smaller residual strengths.

Combined with the observation that “brittle” rocks (hard sandstones, basement crystalline rock) have almost zero residual strength when unconfined, and finite values of residual strength even under elevated confining pressures, it can be surmised that the relationship between breakout width and depth is lithologically controlled by a few simple parameters. It also suggests that petrophysical methods may be used to predict those parameters and to predict breakout depth as well as breakout width. It might also be possible to invert such measurements to compute stress magnitudes.

At the present time we do not have enough data to predict breakout widths and depths. However, by collecting additional data and comparing petrophysical properties to breakout observations, it may be possible to establish lithologically based relationships that will allow predictions of both breakout width and depth. This, in turn, will allow quantitative predictions to be made of cuttings volumes for hole-cleaning optimization and of requirements for installation of completions such as expandable screens for which maintaining hole size within a specific range is an absolute requirement.

Acknowledgment
This information comes from D. Moos, S. Willson and C.A. Barton, Impact of rock properties on the relationship between wellbore breakout width and depth, in: Eberhardt, Stead & Morrison, Rock Mechanics: Meeting Society’s Challenges and Demands. Proceedings of the 1st Canada-US Rock Mechanics Symposium, Vancouver, Canada, 27-31 May 2007, pp. 1677-1683. © 2007 Taylor & Francis Group. Used with permission.