An analytical solution for the stress distribution around the cased borehole in the orthotropic formation

To calculate the stress distribution more efficiently and accurately than the finite element method, we derived an analytical approach based on a pure elastic cased borehole model, in which isotropic casing and cement are both embedded in the orthotropic formation. The borehole model takes into consideration the welded boundaries and the generalized plain strain. The derivation could be subjected to arbitrary far field stresses. The accuracy of the derived approach is validated by comparing its stress curves with those by the classic borehole solution and from a finite element method for isotropic and anisotropic cased holes. Then based on the analytical approach, we developed numerical examples to analyze the effect of the mechanical properties' change, such as anisotropy and thickness, on the stress distribution of the cased borehole model. The effect range of the cased borehole on formation is about twice of formation's radius with respect to the borehole axis.

Automated summary

A more efficient and accurate analytical approach based on a pure elastic cased borehole model was proposed to calculate stress distribution, which was validated and used to analyze the impact of mechanical properties changes on the cased borehole model. The derived approach showed a larger effect range of the cased borehole on formation compared to the borehole axis.