Simulation of borehole shrinkage in shale based on the triaxial fractional constitutive equation

Shale drilling has become more common because of the prosperous development of shale gas. The time-dependent behaviors of shale can lead to severe borehole shrinkage. We need a faster and more accurate method to describe the time-dependent behaviors. In this study, we propose a borehole shrinkage simulation method based on the triaxial fractional constitutive equation, two-parameter correspondence principle, and Stehfest inverse Laplace transform. Real axial and lateral creep data are used to calculate radial displacements during borehole creep under constant, rising, and fluctuating inner pressure. The simulation results indicate that the short- and long-term scales of the borehole shrinkage curve are different and should be analyzed separately. The lateral constitutive parameters critically impact the borehole creep along the low load direction. When the time is large enough, the fluctuation of the borehole creep curve with the periodic change of inner pressure disappears and it converges to a curve with a constant average inner pressure. This is because that the elastic deformation is offset by creep recovery. Article highlights We develop a new model for shale borehole shrinkage simulation based on triaxial fractional constitutive equation. The borehole shrinkage curves of short-term creep and long-term creep should be analyzed separately. When the inner pressure fluctuates periodically, the fluctuation of the borehole creep curve disappears and converges on the curve calculated by the average pressure.