A Modified Model of Cement Sheath Stress Distribution with a Fixed Far-Field Displacement Boundary Condition

The existing stress distribution model of casing-cement-formation mostly does not fix the far-field displacement boundary in model building, and the disturbance of formation displacement at infinity caused by the well construction process can not be eliminated, which is not completely in line with reality. Taking the strata stress as the stress boundary and initial stress field condition, and fixing the farfield displacement boundary of the formation, a modified model of casing-cement-formation combination for directional well is derived with the undetermined coefficients method. On the basis, the sensitivity analysis of the mechanical failure law of the wellbore integrity was carried out, and the calculation results showed that, as the elastic modulus of the formation and sheath decreases, the radial and circumferential compressive stresses on the casing and the cement sheath increase. The Poisson’s ratio of the cement sheath has little effect on the stress state of the casing and the cement sheath. The radial and circumferential compressive stresses on the casing and the cement sheath increase as the Poisson’s ratio of the cement sheath increases. When the pressure inside the casing is high, as the elastic modulus of the cement sheath increases, the tendency of the tensile circumferential stress at the cement sheath increases, and the compressive stress on the casing decreases. The traditional model overestimates the stress distribution of combination and the shear failure risk of the cement, but underestimates the tensile failure risk of the cement. For a vertical well on site in Bohai Bay, the mechanical property of the cement sheath at the 9-5/8” casing were evaluated, and the on-site cement slurry is reasonably used to meet the mechanical requirements of wellbore integrity. This paper can provide a theoretical basis for reasonably choosing cementing slurry formula.