Stress concentrations and failure modes in horizontal wells accounting for elastic anisotropy of shale formations

This study presents a systematic analysis of stress changes near the horizontal well sections drilled in shale and clay formations using a new approach. Most of the prior analyses of stress concentrations and wellbore stability in anisotropic shale formations use the traditional Lekhnitskii-Amadei solutions. We present a faster set of analytical stress functions, based on largely overlooked solutions by Green and Taylor. First the full theoretical range of possible compliances for transverse isotropic materials is evaluated, using data for 5 shale/clay samples and 12 additional test materials. Contour plots show the principal stress trajectory patterns and variation in the spatial stress concentration due to deviation from isotropic elasticity. Next, we show how uni-axial far-field stress solutions can be mutually superposed and combined with stress function solutions for local stress concentration due to internal pressure on the wellbore. The reappraised set of Green and Taylor equations is then applied to horizontal wells in three Andersonian stress states for compressional, strike-slip and extensional basins. The stress concentrations in the horizontal wellbore are evaluated for well depths between 0 and 10,000 ft, using the elastic stiffnesses from five shale and clay samples to show the stress deviations from the isotropic reference case. Finally, a full wellbore stability evaluation model combines the stress concentrations around the wellbore with failure criteria, to determine the safe drilling window at each well depth (for each Andersonian stress state). Practical graphs and supporting equations are provided to assess wellbore stability in transverse isotropic shale.