Semi-Analytical Solutions for the Effect of Well Shut-Down on Rock Stability
Authors: Han G. , Ioannidis M. , Dusseault M.B. 
Published: March 2010

Abstract
Poorly consolidated rock around the wellbore may become unstable after the process of well shut-down and restart. Possible reasons for instability include pressure recovery and water hammer effects. These are defined and analyzed by two different fluid mechanics models. The pressure recovery model results in a quasi-static solution defined in the context of Darcy theory. The water hammer model is based on inertial effects inside the wellbore, and seeks to specify the magnitude of short-term stress variation from the generation of a compressional shockwave due to sudden shut-down of a flowing well.
To quantify the effect of well shut-down on rock stability, a fully coupled geomechanics model accounting for the changes of fluid pressure is developed. The redistribution of fluid pressure in a reservoir are analytically solved and coupled with the stress model, while the water hammer equations provide a boundary condition for the bottom-hole pressure. This approach allows a direct solution for the relationships among fluid properties, rock properties, and production parameters, within the context of rock stability, and defined as an effective stress-dependent strength or yield threshold. Model calculations demonstrate that the fluctuations of effective stresses and shear stresses may reach several hundred kPa because of the pressure wave created by a water hammer inside the wellbore.
The model can be applied to evaluate the risks of triggering rock instability and select the wells that may start sanding if they are shut-down or started up abruptly. Furthermore, the paper provides a method to quantify the effect of pressure fluctuation on rock stability.

Introduction
Dynamic pressure fluctuations near a well in a reservoir can, in principle, lead to rock instability; however, there is little field documentation available. Santarelli et al. reported the injectivity decline of some water injectors in the Norwegian Sea after well shut-in(1). Dusseault et al. developed a new workover method to clean up wellbore damage based on a strong dynamic pressure pulse method, clearly demonstrating that dynamic pressure perturbation can re-initiate sand influx in heavy oil wells that use sand production as a means of recovery(2). Santos has indicated that during the well drilling process, pressure oscillation at bottom hole not only can destabilize sand but also shale(3). The lack of more extensive documentation of dynamic pressure pulse induced instability is, we believe, due to several reasons: first, monitoring rapid downhole pressure fluctuations has traditionally been difficult; second, the presence of gas in the oil dampens the effect of pressure oscillations; and third, the impact of dynamic effects on sand instability has not been widely understood. We note also that the solution to this problem is, in principle, relatively simple: smooth production rate or injection rate reductions can be easily implemented to avoid abrupt pressure changes.
However, it is valuable to evaluate rock stability before a production strategy is chosen, and a thorough understanding of mechanisms and quantitative analysis of their potential effects should be pursued.
When production (or injection) is adjusted at the wellhead, or when the drilling string is moved up or down during drilling, pressure fluctuations will appear within the wellbore.