Time-dependent brittle creep as a mechanism for time-delayed wellbore failure

• Time-dependency of borehole breakout development is modeled based on brittle creep.
• Stress transfer from damaged elements reduces peak stresses.
• Breakout growth declines following an Omori-type power law.
• Damaged zone around breakout yields to a dog-ear shape of the breakouts.

By drilling a wellbore cavity, high stresses arise at the wellbore wall, leading to the formation of breakouts which enlarge the hole to an elongated shape oriented along the direction of the minimum principal stress. If formation of breakouts is delayed, rock debris falls on the drill bit which may lead to stuck pipe problems or even abandonment of the drill string. Reasons for such time-delayed failure of the wellbore may be due to chemical fluid–rock interaction, especially in swelling clays. However, such delayed instabilities have also been observed e.g. in gneiss formations at the KTB borehole (Germany) that are not known to exhibit a swelling behavior. We propose to explain observations of delayed wellbore failure by time-dependent brittle creep, which has been observed for many types of rocks. Following this approach, rock fails under loads less than their short-time strength but after a long enough time span. This time is in exponential relation to the load applied to the rock. We implement a model developed for the creation of shear bands on the basis of time-dependent brittle creep by Amitrano and Helmstetter (2006). Here, progressive damage of the formation is captured by a damage parameter D and the time-to-failure TTF. Young׳s modulus E is decreased by a factor every time TTF is expired, i.e. when failure is reached. Subsequently, stresses are redistributed according to the new distribution of E in the formation. Using this approach, we obtain closure of the well with primary and secondary creep phases. Wellbore breakouts are formed progressively with deepening and widening of the initially damaged zone. After a certain time the formation of breakouts comes to an end with an Omori-like decay of failure approaching a steady-state.